LMFDB - Embedded newform 462.2.j.f.295.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			295.2
Root			$-1.34500 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	462.295
Dual form			462.2.j.f.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.640271 + 1.97055i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.640271 + 1.97055i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.07196 q^{10} +(1.47776 - 2.96921i) q^{11} -1.00000 q^{12} +(1.31751 - 4.05488i) q^{13} +(0.809017 - 0.587785i) q^{14} +(1.67625 + 1.21787i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.16251 + 3.57783i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(1.59420 - 1.15825i) q^{19} +(0.640271 - 1.97055i) q^{20} +1.00000 q^{21} +(-2.36723 - 2.32297i) q^{22} +7.63304 q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.571960 - 0.415553i) q^{25} +(-3.44929 - 2.50605i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-2.41696 - 1.75602i) q^{29} +(1.67625 - 1.21787i) q^{30} +(-2.51899 + 7.75266i) q^{31} +1.00000 q^{32} +(-0.549723 - 3.27075i) q^{33} +3.76195 q^{34} +(-0.640271 + 1.97055i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-6.91232 - 5.02209i) q^{37} +(-0.608929 - 1.87409i) q^{38} +(-1.31751 - 4.05488i) q^{39} +(-1.67625 - 1.21787i) q^{40} +(-5.54250 + 4.02686i) q^{41} +(0.309017 - 0.951057i) q^{42} -8.20463 q^{43} +(-2.94079 + 1.53354i) q^{44} +2.07196 q^{45} +(2.35874 - 7.25946i) q^{46} +(0.317511 - 0.230685i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.218469 - 0.672379i) q^{50} +(3.04348 + 2.21122i) q^{51} +(-3.44929 + 2.50605i) q^{52} +(-2.87573 + 8.85058i) q^{53} -1.00000 q^{54} +(6.79715 + 1.01091i) q^{55} -1.00000 q^{56} +(0.608929 - 1.87409i) q^{57} +(-2.41696 + 1.75602i) q^{58} +(3.50910 + 2.54951i) q^{59} +(-0.640271 - 1.97055i) q^{60} +(-0.359118 - 1.10525i) q^{61} +(6.59481 + 4.79141i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} +8.83391 q^{65} +(-3.28054 - 0.487899i) q^{66} -14.0700 q^{67} +(1.16251 - 3.57783i) q^{68} +(6.17526 - 4.48659i) q^{69} +(1.67625 + 1.21787i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-5.69750 - 4.13948i) q^{73} +(-6.91232 + 5.02209i) q^{74} +(0.218469 - 0.672379i) q^{75} -1.97054 q^{76} +(2.94079 - 1.53354i) q^{77} -4.26355 q^{78} +(3.27768 - 10.0876i) q^{79} +(-1.67625 + 1.21787i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.11705 + 6.51559i) q^{82} +(2.96590 + 9.12809i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(-6.30598 + 4.58156i) q^{85} +(-2.53537 + 7.80306i) q^{86} -2.98752 q^{87} +(0.549723 + 3.27075i) q^{88} -2.94305 q^{89} +(0.640271 - 1.97055i) q^{90} +(3.44929 - 2.50605i) q^{91} +(-6.17526 - 4.48659i) q^{92} +(2.51899 + 7.75266i) q^{93} +(-0.121278 - 0.373256i) q^{94} +(3.30311 + 2.39985i) q^{95} +(0.809017 - 0.587785i) q^{96} +(2.22372 - 6.84390i) q^{97} +1.00000 q^{98} +(-2.36723 - 2.32297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.640271	+	1.97055i	0.286338	+	0.881257i	0.985994	+	0.166778i	$0.0533363\pi$
$5$	0.640271	+	1.97055i	0.286338	+	0.881257i	−0.699657	+	0.714479i	$0.746664\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.07196			0.655211
$11$	1.47776	−	2.96921i	0.445562	−	0.895251i
$11$	1.47776	−	2.96921i	0.445562	−	0.895251i
$12$	−1.00000			−0.288675
$13$	1.31751	−	4.05488i	0.365412	−	1.12462i	−0.584311	−	0.811530i	$-0.698635\pi$
$13$	1.31751	−	4.05488i	0.365412	−	1.12462i	0.949723	−	0.313092i	$-0.101365\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	1.67625	+	1.21787i	0.432806	+	0.314452i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.16251	+	3.57783i	0.281950	+	0.867751i	0.987296	+	0.158889i	$0.0507912\pi$
$17$	1.16251	+	3.57783i	0.281950	+	0.867751i	−0.705347	+	0.708862i	$0.749209\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	1.59420	−	1.15825i	0.365734	−	0.265721i	−0.389706	−	0.920939i	$-0.627423\pi$
$19$	1.59420	−	1.15825i	0.365734	−	0.265721i	0.755440	+	0.655218i	$0.227423\pi$
$20$	0.640271	−	1.97055i	0.143169	−	0.440629i
$21$	1.00000			0.218218
$22$	−2.36723	−	2.32297i	−0.504696	−	0.495260i
$23$	7.63304			1.59160			0.795800	−	0.605560i	$-0.207051\pi$
$23$	7.63304			1.59160			0.795800	+	0.605560i	$0.207051\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	0.571960	−	0.415553i	0.114392	−	0.0831107i
$26$	−3.44929	−	2.50605i	−0.676461	−	0.491478i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−2.41696	−	1.75602i	−0.448818	−	0.326085i	0.340311	−	0.940313i	$-0.389468\pi$
$29$	−2.41696	−	1.75602i	−0.448818	−	0.326085i	−0.789129	+	0.614228i	$0.789468\pi$
$30$	1.67625	−	1.21787i	0.306040	−	0.222351i
$31$	−2.51899	+	7.75266i	−0.452424	+	1.39242i	0.421708	+	0.906732i	$0.361431\pi$
$31$	−2.51899	+	7.75266i	−0.452424	+	1.39242i	−0.874132	+	0.485688i	$0.838569\pi$
$32$	1.00000			0.176777
$33$	−0.549723	−	3.27075i	−0.0956945	−	0.569364i
$34$	3.76195			0.645170
$35$	−0.640271	+	1.97055i	−0.108226	+	0.333084i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−6.91232	−	5.02209i	−1.13638	−	0.825627i	−0.149768	−	0.988721i	$-0.547853\pi$
$37$	−6.91232	−	5.02209i	−1.13638	−	0.825627i	−0.986611	+	0.163094i	$0.947853\pi$
$38$	−0.608929	−	1.87409i	−0.0987813	−	0.304018i
$39$	−1.31751	−	4.05488i	−0.210971	−	0.649301i
$40$	−1.67625	−	1.21787i	−0.265039	−	0.192562i
$41$	−5.54250	+	4.02686i	−0.865592	+	0.628890i	−0.929401	−	0.369072i	$-0.879675\pi$
$41$	−5.54250	+	4.02686i	−0.865592	+	0.628890i	0.0638082	+	0.997962i	$0.479675\pi$
$42$	0.309017	−	0.951057i	0.0476824	−	0.146751i
$43$	−8.20463			−1.25119			−0.625597	−	0.780147i	$-0.715144\pi$
$43$	−8.20463			−1.25119			−0.625597	+	0.780147i	$0.715144\pi$
$44$	−2.94079	+	1.53354i	−0.443341	+	0.231189i
$45$	2.07196			0.308870
$46$	2.35874	−	7.25946i	0.347777	−	1.07035i
$47$	0.317511	−	0.230685i	0.0463137	−	0.0336489i	−0.564388	−	0.825510i	$-0.690888\pi$
$47$	0.317511	−	0.230685i	0.0463137	−	0.0336489i	0.610701	+	0.791861i	$0.290888\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.218469	−	0.672379i	−0.0308962	−	0.0950888i
$51$	3.04348	+	2.21122i	0.426173	+	0.309633i
$52$	−3.44929	+	2.50605i	−0.478330	+	0.347527i
$53$	−2.87573	+	8.85058i	−0.395012	+	1.21572i	0.533941	+	0.845522i	$0.320710\pi$
$53$	−2.87573	+	8.85058i	−0.395012	+	1.21572i	−0.928953	+	0.370199i	$0.879290\pi$
$54$	−1.00000			−0.136083
$55$	6.79715	+	1.01091i	0.916528	+	0.136311i
$56$	−1.00000			−0.133631
$57$	0.608929	−	1.87409i	0.0806546	−	0.248229i
$58$	−2.41696	+	1.75602i	−0.317362	+	0.230577i
$59$	3.50910	+	2.54951i	0.456847	+	0.331918i	0.792293	−	0.610141i	$-0.208887\pi$
$59$	3.50910	+	2.54951i	0.456847	+	0.331918i	−0.335446	+	0.942059i	$0.608887\pi$
$60$	−0.640271	−	1.97055i	−0.0826586	−	0.254397i
$61$	−0.359118	−	1.10525i	−0.0459803	−	0.141513i	0.925431	−	0.378917i	$-0.123703\pi$
$61$	−0.359118	−	1.10525i	−0.0459803	−	0.141513i	−0.971411	+	0.237404i	$0.923703\pi$
$62$	6.59481	+	4.79141i	0.837541	+	0.608509i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	8.83391			1.09571
$66$	−3.28054	−	0.487899i	−0.403807	−	0.0600563i
$67$	−14.0700			−1.71892			−0.859461	−	0.511201i	$-0.829201\pi$
$67$	−14.0700			−1.71892			−0.859461	+	0.511201i	$0.829201\pi$
$68$	1.16251	−	3.57783i	0.140975	−	0.433876i
$69$	6.17526	−	4.48659i	0.743414	−	0.540122i
$70$	1.67625	+	1.21787i	0.200350	+	0.145563i
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	0.868297	+	0.496045i	$0.165215\pi$
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	−0.410899	+	0.911681i	$0.634785\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−5.69750	−	4.13948i	−0.666842	−	0.484489i	0.202125	−	0.979360i	$-0.435215\pi$
$73$	−5.69750	−	4.13948i	−0.666842	−	0.484489i	−0.868967	+	0.494871i	$0.835215\pi$
$74$	−6.91232	+	5.02209i	−0.803541	+	0.583807i
$75$	0.218469	−	0.672379i	0.0252267	−	0.0776397i
$76$	−1.97054			−0.226036
$77$	2.94079	−	1.53354i	0.335135	−	0.174763i
$78$	−4.26355			−0.482752
$79$	3.27768	−	10.0876i	0.368767	−	1.13495i	−0.578821	−	0.815455i	$-0.696487\pi$
$79$	3.27768	−	10.0876i	0.368767	−	1.13495i	0.947588	−	0.319494i	$-0.103513\pi$
$80$	−1.67625	+	1.21787i	−0.187411	+	0.136162i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.11705	+	6.51559i	0.233789	+	0.719527i
$83$	2.96590	+	9.12809i	0.325550	+	1.00194i	0.971192	+	0.238299i	$0.0765897\pi$
$83$	2.96590	+	9.12809i	0.325550	+	1.00194i	−0.645642	+	0.763640i	$0.723410\pi$
$84$	−0.809017	−	0.587785i	−0.0882710	−	0.0641326i
$85$	−6.30598	+	4.58156i	−0.683979	+	0.496940i
$86$	−2.53537	+	7.80306i	−0.273396	+	0.841426i
$87$	−2.98752			−0.320296
$88$	0.549723	+	3.27075i	0.0586007	+	0.348663i
$89$	−2.94305			−0.311963			−0.155981	−	0.987760i	$-0.549854\pi$
$89$	−2.94305			−0.311963			−0.155981	+	0.987760i	$0.549854\pi$
$90$	0.640271	−	1.97055i	0.0674905	−	0.207714i
$91$	3.44929	−	2.50605i	0.361584	−	0.262706i
$92$	−6.17526	−	4.48659i	−0.643816	−	0.467759i
$93$	2.51899	+	7.75266i	0.261207	+	0.803914i
$94$	−0.121278	−	0.373256i	−0.0125089	−	0.0384984i
$95$	3.30311	+	2.39985i	0.338892	+	0.246220i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	2.22372	−	6.84390i	0.225784	−	0.694893i	−0.772427	−	0.635104i	$-0.780957\pi$
$97$	2.22372	−	6.84390i	0.225784	−	0.694893i	0.998211	−	0.0597890i	$-0.0190428\pi$
$98$	1.00000			0.101015
$99$	−2.36723	−	2.32297i	−0.237916	−	0.233468i
$100$	−0.706982			−0.0706982
$101$	1.34923	−	4.15250i	0.134253	−	0.413190i	−0.861220	−	0.508233i	$-0.830299\pi$
$101$	1.34923	−	4.15250i	0.134253	−	0.413190i	0.995473	+	0.0950432i	$0.0302989\pi$
$102$	3.04348	−	2.21122i	0.301350	−	0.218944i
$103$	8.48329	+	6.16347i	0.835883	+	0.607305i	0.921218	−	0.389048i	$-0.127196\pi$
$103$	8.48329	+	6.16347i	0.835883	+	0.607305i	−0.0853343	+	0.996352i	$0.527196\pi$
$104$	1.31751	+	4.05488i	0.129193	+	0.397614i
$105$	0.640271	+	1.97055i	0.0624840	+	0.192306i
$106$	7.52875	+	5.46996i	0.731257	+	0.531289i
$107$	4.83026	−	3.50939i	0.466959	−	0.339266i	−0.329296	−	0.944227i	$-0.606811\pi$
$107$	4.83026	−	3.50939i	0.466959	−	0.339266i	0.796255	+	0.604961i	$0.206811\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	6.30483			0.603893			0.301946	−	0.953325i	$-0.402364\pi$
$109$	6.30483			0.603893			0.301946	+	0.953325i	$0.402364\pi$
$110$	3.06187	−	6.15209i	0.291937	−	0.586579i
$111$	−8.54410			−0.810970
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−16.6634	+	12.1067i	−1.56756	+	1.13890i	−0.638114	+	0.769942i	$0.720285\pi$
$113$	−16.6634	+	12.1067i	−1.56756	+	1.13890i	−0.929446	+	0.368958i	$0.879715\pi$
$114$	−1.59420	−	1.15825i	−0.149310	−	0.108480i
$115$	4.88722	+	15.0413i	0.455735	+	1.40261i
$116$	0.923195	+	2.84130i	0.0857165	+	0.263808i
$117$	−3.44929	−	2.50605i	−0.318887	−	0.231685i
$118$	3.50910	−	2.54951i	0.323039	−	0.234702i
$119$	−1.16251	+	3.57783i	−0.106567	+	0.327979i
$120$	−2.07196			−0.189143
$121$	−6.63243	−	8.77558i	−0.602948	−	0.797780i
$122$	−1.16213			−0.105214
$123$	−2.11705	+	6.51559i	−0.190888	+	0.587491i
$124$	6.59481	−	4.79141i	0.592231	−	0.430281i
$125$	9.56633	+	6.95035i	0.855639	+	0.621658i
$126$	−0.309017	−	0.951057i	−0.0275294	−	0.0847268i
$127$	1.39069	+	4.28011i	0.123404	+	0.379799i	0.993607	−	0.112895i	$-0.0360123\pi$
$127$	1.39069	+	4.28011i	0.123404	+	0.379799i	−0.870203	+	0.492694i	$0.836012\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−6.63768	+	4.82256i	−0.584415	+	0.424603i
$130$	2.72983	−	8.40155i	0.239422	−	0.736865i
$131$	7.00893			0.612373			0.306187	−	0.951971i	$-0.400947\pi$
$131$	7.00893			0.612373			0.306187	+	0.951971i	$0.400947\pi$
$132$	−1.47776	+	2.96921i	−0.128623	+	0.258437i
$133$	1.97054			0.170867
$134$	−4.34786	+	13.3813i	−0.375598	+	1.15597i
$135$	1.67625	−	1.21787i	0.144269	−	0.104817i
$136$	−3.04348	−	2.21122i	−0.260977	−	0.189611i
$137$	−2.13055	−	6.55717i	−0.182026	−	0.560217i	0.817859	−	0.575419i	$-0.195161\pi$
$137$	−2.13055	−	6.55717i	−0.182026	−	0.560217i	−0.999884	+	0.0152017i	$0.995161\pi$
$138$	−2.35874	−	7.25946i	−0.200789	−	0.617966i
$139$	−9.68437	−	7.03610i	−0.821417	−	0.596795i	0.0957008	−	0.995410i	$-0.469491\pi$
$139$	−9.68437	−	7.03610i	−0.821417	−	0.596795i	−0.917118	+	0.398616i	$0.869491\pi$
$140$	1.67625	−	1.21787i	0.141669	−	0.102929i
$141$	0.121278	−	0.373256i	0.0102135	−	0.0314338i
$142$	12.4721			1.04664
$143$	−10.0928	−	9.90412i	−0.844005	−	0.828224i
$144$	1.00000			0.0833333
$145$	1.91282	−	5.88707i	0.158851	−	0.488894i
$146$	−5.69750	+	4.13948i	−0.471528	+	0.342585i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	2.64027	+	8.12592i	0.217029	+	0.667946i
$149$	−7.32502	−	22.5441i	−0.600089	−	1.84688i	−0.527562	−	0.849516i	$-0.676894\pi$
$149$	−7.32502	−	22.5441i	−0.600089	−	1.84688i	−0.0725266	−	0.997366i	$-0.523106\pi$
$150$	−0.571960	−	0.415553i	−0.0467003	−	0.0339298i
$151$	−12.7553	+	9.26730i	−1.03801	+	0.754162i	−0.969897	−	0.243515i	$-0.921699\pi$
$151$	−12.7553	+	9.26730i	−1.03801	+	0.754162i	−0.0681177	+	0.997677i	$0.521699\pi$
$152$	−0.608929	+	1.87409i	−0.0493907	+	0.152009i
$153$	3.76195			0.304136
$154$	−0.549723	−	3.27075i	−0.0442980	−	0.263565i
$155$	−16.8899			−1.35663
$156$	−1.31751	+	4.05488i	−0.105485	+	0.324650i
$157$	6.46894	−	4.69996i	0.516277	−	0.375097i	−0.298922	−	0.954277i	$-0.596627\pi$
$157$	6.46894	−	4.69996i	0.516277	−	0.375097i	0.815200	+	0.579180i	$0.196627\pi$
$158$	−8.58107	−	6.23451i	−0.682673	−	0.495991i
$159$	2.87573	+	8.85058i	0.228060	+	0.701897i
$160$	0.640271	+	1.97055i	0.0506179	+	0.155786i
$161$	6.17526	+	4.48659i	0.486679	+	0.353593i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	0.646830	+	0.762634i	$0.276094\pi$
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	−0.971562	+	0.236787i	$0.923906\pi$
$164$	6.85090			0.534966
$165$	6.09321	−	3.17742i	0.474356	−	0.247362i
$166$	9.59785			0.744937
$167$	1.35086	−	4.15751i	0.104533	−	0.321718i	−0.885088	−	0.465424i	$-0.845902\pi$
$167$	1.35086	−	4.15751i	0.104533	−	0.321718i	0.989620	+	0.143706i	$0.0459019\pi$
$168$	−0.809017	+	0.587785i	−0.0624170	+	0.0453486i
$169$	−4.18901	−	3.04349i	−0.322231	−	0.234115i
$170$	2.40867	+	7.41312i	0.184737	+	0.568561i
$171$	−0.608929	−	1.87409i	−0.0465660	−	0.143315i
$172$	6.63768	+	4.82256i	0.506118	+	0.367717i
$173$	5.95884	−	4.32935i	0.453042	−	0.329155i	−0.337753	−	0.941235i	$-0.609667\pi$
$173$	5.95884	−	4.32935i	0.453042	−	0.329155i	0.790796	+	0.612080i	$0.209667\pi$
$174$	−0.923195	+	2.84130i	−0.0699873	+	0.215399i
$175$	0.706982			0.0534428
$176$	3.28054	+	0.487899i	0.247280	+	0.0367768i
$177$	4.33749			0.326026
$178$	−0.909452	+	2.79901i	−0.0681663	+	0.209794i
$179$	−21.1712	+	15.3818i	−1.58241	+	1.14969i	−0.668549	+	0.743668i	$0.733084\pi$
$179$	−21.1712	+	15.3818i	−1.58241	+	1.14969i	−0.913863	+	0.406022i	$0.866916\pi$
$180$	−1.67625	−	1.21787i	−0.124940	−	0.0907745i
$181$	4.72696	+	14.5481i	0.351352	+	1.08135i	0.958094	+	0.286453i	$0.0924761\pi$
$181$	4.72696	+	14.5481i	0.351352	+	1.08135i	−0.606742	+	0.794899i	$0.707524\pi$
$182$	−1.31751	−	4.05488i	−0.0976604	−	0.300568i
$183$	−0.940183	−	0.683083i	−0.0695003	−	0.0504949i
$184$	−6.17526	+	4.48659i	−0.455246	+	0.330756i
$185$	5.47054	−	16.8366i	0.402202	−	1.23785i
$186$	8.15163			0.597707
$187$	12.3412	+	1.83546i	0.902481	+	0.134222i
$188$	−0.392465			−0.0286234
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	3.30311	−	2.39985i	0.239633	−	0.174104i
$191$	−3.17035	−	2.30339i	−0.229398	−	0.166668i	0.467149	−	0.884179i	$-0.345281\pi$
$191$	−3.17035	−	2.30339i	−0.229398	−	0.166668i	−0.696547	+	0.717511i	$0.745281\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	−1.68289	−	5.17942i	−0.121137	−	0.372823i	0.872040	−	0.489434i	$-0.162797\pi$
$193$	−1.68289	−	5.17942i	−0.121137	−	0.372823i	−0.993178	+	0.116612i	$0.962797\pi$
$194$	−5.82177	−	4.22976i	−0.417979	−	0.303679i
$195$	7.14679	−	5.19244i	0.511792	−	0.371839i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	0.395753			0.0281962			0.0140981	−	0.999901i	$-0.495512\pi$
$197$	0.395753			0.0281962			0.0140981	+	0.999901i	$0.495512\pi$
$198$	−2.94079	+	1.53354i	−0.208993	+	0.108984i
$199$	−5.89086			−0.417592			−0.208796	−	0.977959i	$-0.566955\pi$
$199$	−5.89086			−0.417592			−0.208796	+	0.977959i	$0.566955\pi$
$200$	−0.218469	+	0.672379i	−0.0154481	+	0.0475444i
$201$	−11.3829	+	8.27013i	−0.802885	+	0.583330i
$202$	−3.53233	−	2.56639i	−0.248534	−	0.180570i
$203$	−0.923195	−	2.84130i	−0.0647956	−	0.199420i
$204$	−1.16251	−	3.57783i	−0.0813918	−	0.250498i
$205$	−11.4838	−	8.34349i	−0.802065	−	0.582735i
$206$	8.48329	−	6.16347i	0.591059	−	0.429429i
$207$	2.35874	−	7.25946i	0.163944	−	0.504567i
$208$	4.26355			0.295624
$209$	−1.08325	−	6.44513i	−0.0749299	−	0.445819i
$210$	2.07196			0.142979
$211$	1.46628	−	4.51273i	0.100943	−	0.310669i	−0.887814	−	0.460202i	$-0.847777\pi$
$211$	1.46628	−	4.51273i	0.100943	−	0.310669i	0.988757	+	0.149533i	$0.0477770\pi$
$212$	7.52875	−	5.46996i	0.517077	−	0.375678i
$213$	10.0902	+	7.33094i	0.691367	+	0.502308i
$214$	−1.84500	−	5.67832i	−0.126121	−	0.388162i
$215$	−5.25318	−	16.1676i	−0.358264	−	1.10262i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−6.59481	+	4.79141i	−0.447685	+	0.325262i
$218$	1.94830	−	5.99625i	0.131955	−	0.406117i
$219$	−7.04250			−0.475888
$220$	−4.90481	−	4.81311i	−0.330682	−	0.324500i
$221$	16.0393			1.07892
$222$	−2.64027	+	8.12592i	−0.177203	+	0.545376i
$223$	18.6951	−	13.5828i	1.25191	−	0.909569i	0.253583	−	0.967314i	$-0.418391\pi$
$223$	18.6951	−	13.5828i	1.25191	−	0.909569i	0.998331	+	0.0577444i	$0.0183908\pi$
$224$	0.809017	+	0.587785i	0.0540547	+	0.0392731i
$225$	−0.218469	−	0.672379i	−0.0145646	−	0.0448253i
$226$	6.36485	+	19.5890i	0.423384	+	1.30304i
$227$	13.5788	+	9.86554i	0.901254	+	0.654799i	0.938788	−	0.344496i	$-0.111950\pi$
$227$	13.5788	+	9.86554i	0.901254	+	0.654799i	−0.0375341	+	0.999295i	$0.511950\pi$
$228$	−1.59420	+	1.15825i	−0.105578	+	0.0767071i
$229$	4.39234	−	13.5182i	0.290254	−	0.893309i	−0.694521	−	0.719473i	$-0.744384\pi$
$229$	4.39234	−	13.5182i	0.290254	−	0.893309i	0.984774	−	0.173837i	$-0.0556165\pi$
$230$	15.8154			1.04283
$231$	1.47776	−	2.96921i	0.0972297	−	0.195360i
$232$	2.98752			0.196141
$233$	6.10429	−	18.7871i	0.399905	−	1.23078i	−0.525170	−	0.850998i	$-0.675998\pi$
$233$	6.10429	−	18.7871i	0.399905	−	1.23078i	0.925075	−	0.379785i	$-0.124002\pi$
$234$	−3.44929	+	2.50605i	−0.225487	+	0.163826i
$235$	0.657870	+	0.477970i	0.0429147	+	0.0311793i
$236$	−1.34036	−	4.12520i	−0.0872499	−	0.268528i
$237$	−3.27768	−	10.0876i	−0.212908	−	0.655263i
$238$	3.04348	+	2.21122i	0.197280	+	0.143332i
$239$	−9.64938	+	7.01068i	−0.624166	+	0.453483i	−0.854374	−	0.519658i	$-0.826059\pi$
$239$	−9.64938	+	7.01068i	−0.624166	+	0.453483i	0.230208	+	0.973141i	$0.426059\pi$
$240$	−0.640271	+	1.97055i	−0.0413293	+	0.127199i
$241$	−28.6611			−1.84622			−0.923111	−	0.384533i	$-0.874363\pi$
$241$	−28.6611			−1.84622			−0.923111	+	0.384533i	$0.874363\pi$
$242$	−10.3956	+	3.59601i	−0.668255	+	0.231161i
$243$	−1.00000			−0.0641500
$244$	−0.359118	+	1.10525i	−0.0229902	+	0.0707565i
$245$	−1.67625	+	1.21787i	−0.107092	+	0.0778067i
$246$	5.54250	+	4.02686i	0.353377	+	0.256743i
$247$	−2.59620	−	7.99029i	−0.165192	−	0.508410i
$248$	−2.51899	−	7.75266i	−0.159956	−	0.492295i
$249$	7.76482	+	5.64147i	0.492076	+	0.357514i
$250$	9.56633	−	6.95035i	0.605028	−	0.439579i
$251$	4.10408	−	12.6311i	0.259048	−	0.797266i	−0.733958	−	0.679195i	$-0.762329\pi$
$251$	4.10408	−	12.6311i	0.259048	−	0.797266i	0.993005	−	0.118071i	$-0.0376711\pi$
$252$	−1.00000			−0.0629941
$253$	11.2798	−	22.6641i	0.709157	−	1.42488i
$254$	4.50038			0.282379
$255$	−2.40867	+	7.41312i	−0.150837	+	0.464228i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.99901	+	5.08508i	0.436586	+	0.317199i	0.784277	−	0.620411i	$-0.213034\pi$
$257$	6.99901	+	5.08508i	0.436586	+	0.317199i	−0.347691	+	0.937609i	$0.613034\pi$
$258$	2.53537	+	7.80306i	0.157845	+	0.485797i
$259$	−2.64027	−	8.12592i	−0.164058	−	0.504920i
$260$	−7.14679	−	5.19244i	−0.443225	−	0.322022i
$261$	−2.41696	+	1.75602i	−0.149606	+	0.108695i
$262$	2.16588	−	6.66589i	0.133808	−	0.411820i
$263$	11.8383			0.729983			0.364992	−	0.931011i	$-0.381072\pi$
$263$	11.8383			0.729983			0.364992	+	0.931011i	$0.381072\pi$
$264$	2.36723	+	2.32297i	0.145693	+	0.142969i
$265$	−19.2818			−1.18447
$266$	0.608929	−	1.87409i	0.0373358	−	0.114908i
$267$	−2.38098	+	1.72988i	−0.145713	+	0.105867i
$268$	11.3829	+	8.27013i	0.695319	+	0.505178i
$269$	−4.07318	−	12.5360i	−0.248346	−	0.764331i	−0.995068	−	0.0991948i	$-0.968373\pi$
$269$	−4.07318	−	12.5360i	−0.248346	−	0.764331i	0.746722	−	0.665137i	$-0.231627\pi$
$270$	−0.640271	−	1.97055i	−0.0389656	−	0.119924i
$271$	17.4489	+	12.6774i	1.05995	+	0.770096i	0.974078	−	0.226211i	$-0.0726338\pi$
$271$	17.4489	+	12.6774i	1.05995	+	0.770096i	0.0858674	+	0.996307i	$0.472634\pi$
$272$	−3.04348	+	2.21122i	−0.184538	+	0.134075i
$273$	1.31751	−	4.05488i	0.0797394	−	0.245413i
$274$	−6.89462			−0.416519
$275$	−0.388644	−	2.31236i	−0.0234361	−	0.139441i
$276$	−7.63304			−0.459455
$277$	5.07643	−	15.6236i	0.305013	−	0.938733i	−0.674659	−	0.738129i	$-0.735710\pi$
$277$	5.07643	−	15.6236i	0.305013	−	0.938733i	0.979672	−	0.200604i	$-0.0642905\pi$
$278$	−9.68437	+	7.03610i	−0.580830	+	0.421997i
$279$	6.59481	+	4.79141i	0.394821	+	0.286854i
$280$	−0.640271	−	1.97055i	−0.0382635	−	0.117763i
$281$	−1.17523	−	3.61700i	−0.0701086	−	0.215772i	0.909863	−	0.414908i	$-0.136186\pi$
$281$	−1.17523	−	3.61700i	−0.0701086	−	0.215772i	−0.979972	+	0.199136i	$0.936186\pi$
$282$	−0.317511	−	0.230685i	−0.0189075	−	0.0137371i
$283$	−18.7691	+	13.6365i	−1.11571	+	0.810608i	−0.983553	−	0.180621i	$-0.942189\pi$
$283$	−18.7691	+	13.6365i	−1.11571	+	0.810608i	−0.132153	+	0.991229i	$0.542189\pi$
$284$	3.85410	−	11.8617i	0.228699	−	0.703863i
$285$	4.08287			0.241848
$286$	−12.5382	+	6.53831i	−0.741401	+	0.386618i
$287$	−6.85090			−0.404396
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	2.30384	−	1.67384i	0.135520	−	0.0984610i
$290$	−5.00784	−	3.63841i	−0.294070	−	0.213655i
$291$	−2.22372	−	6.84390i	−0.130357	−	0.401197i
$292$	2.17625	+	6.69781i	0.127355	+	0.391960i
$293$	−9.72195	−	7.06341i	−0.567962	−	0.412649i	0.266402	−	0.963862i	$-0.414165\pi$
$293$	−9.72195	−	7.06341i	−0.567962	−	0.412649i	−0.834364	+	0.551213i	$0.814165\pi$
$294$	0.809017	−	0.587785i	0.0471828	−	0.0342803i
$295$	−2.77717	+	8.54725i	−0.161693	+	0.497640i
$296$	8.54410			0.496615
$297$	−3.28054	−	0.487899i	−0.190356	−	0.0283108i
$298$	−23.7042			−1.37315
$299$	10.0566	−	30.9511i	0.581589	−	1.78995i
$300$	−0.571960	+	0.415553i	−0.0330221	+	0.0239920i
$301$	−6.63768	−	4.82256i	−0.382590	−	0.277968i
$302$	4.87211	+	14.9948i	0.280358	+	0.862854i
$303$	−1.34923	−	4.15250i	−0.0775113	−	0.238555i
$304$	1.59420	+	1.15825i	0.0914335	+	0.0664303i
$305$	1.94802	−	1.41532i	0.111543	−	0.0810410i
$306$	1.16251	−	3.57783i	0.0664561	−	0.204531i
$307$	27.3074			1.55851			0.779257	−	0.626705i	$-0.215597\pi$
$307$	27.3074			1.55851			0.779257	+	0.626705i	$0.215597\pi$
$308$	−3.28054	−	0.487899i	−0.186926	−	0.0278007i
$309$	10.4859			0.596523
$310$	−5.21925	+	16.0632i	−0.296434	+	0.912329i
$311$	−11.2239	+	8.15466i	−0.636450	+	0.462408i	−0.858629	−	0.512598i	$-0.828683\pi$
$311$	−11.2239	+	8.15466i	−0.636450	+	0.462408i	0.222178	+	0.975006i	$0.428683\pi$
$312$	3.44929	+	2.50605i	0.195277	+	0.141877i
$313$	8.68924	+	26.7427i	0.491145	+	1.51159i	0.822880	+	0.568216i	$0.192366\pi$
$313$	8.68924	+	26.7427i	0.491145	+	1.51159i	−0.331735	+	0.943373i	$0.607634\pi$
$314$	−2.47091	−	7.60469i	−0.139442	−	0.429157i
$315$	1.67625	+	1.21787i	0.0944460	+	0.0686191i
$316$	−8.58107	+	6.23451i	−0.482723	+	0.350719i
$317$	−2.16104	+	6.65098i	−0.121376	+	0.373556i	−0.993223	−	0.116221i	$-0.962922\pi$
$317$	−2.16104	+	6.65098i	−0.121376	+	0.373556i	0.871848	+	0.489777i	$0.162922\pi$
$318$	9.30605			0.521857
$319$	−8.78569	+	4.58147i	−0.491904	+	0.256513i
$320$	2.07196			0.115826
$321$	1.84500	−	5.67832i	0.102978	−	0.316933i
$322$	6.17526	−	4.48659i	0.344134	−	0.250028i
$323$	5.99730	+	4.35729i	0.333698	+	0.242446i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−0.931456	−	2.86673i	−0.0516679	−	0.159017i
$326$	10.8541	+	7.88597i	0.601153	+	0.436763i
$327$	5.10071	−	3.70588i	0.282070	−	0.204936i
$328$	2.11705	−	6.51559i	0.116894	−	0.359764i
$329$	0.392465			0.0216373
$330$	−1.13900	−	6.77686i	−0.0627001	−	0.373054i
$331$	4.30925			0.236858			0.118429	−	0.992963i	$-0.462214\pi$
$331$	4.30925			0.236858			0.118429	+	0.992963i	$0.462214\pi$
$332$	2.96590	−	9.12809i	0.162775	−	0.500969i
$333$	−6.91232	+	5.02209i	−0.378793	+	0.275209i
$334$	−3.53659	−	2.56948i	−0.193514	−	0.140596i
$335$	−9.00860	−	27.7256i	−0.492192	−	1.51481i
$336$	0.309017	+	0.951057i	0.0168583	+	0.0518844i
$337$	−13.7786	−	10.0107i	−0.750566	−	0.545318i	0.145436	−	0.989368i	$-0.453541\pi$
$337$	−13.7786	−	10.0107i	−0.750566	−	0.545318i	−0.896002	+	0.444049i	$0.853541\pi$
$338$	−4.18901	+	3.04349i	−0.227852	+	0.165544i
$339$	−6.36485	+	19.5890i	−0.345691	+	1.06393i
$340$	7.79462			0.422723
$341$	19.2968	+	18.9360i	1.04498	+	1.02544i
$342$	−1.97054			−0.106554
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	6.63768	−	4.82256i	0.357880	−	0.260015i
$345$	12.7949	+	9.29604i	0.688854	+	0.500482i
$346$	−2.27608	−	7.00504i	−0.122363	−	0.376593i
$347$	6.33204	+	19.4880i	0.339922	+	1.04617i	0.964247	+	0.265006i	$0.0853740\pi$
$347$	6.33204	+	19.4880i	0.339922	+	1.04617i	−0.624325	+	0.781165i	$0.714626\pi$
$348$	2.41696	+	1.75602i	0.129562	+	0.0941327i
$349$	5.56088	−	4.04021i	0.297667	−	0.216268i	−0.428920	−	0.903343i	$-0.641106\pi$
$349$	5.56088	−	4.04021i	0.297667	−	0.216268i	0.726587	+	0.687075i	$0.241106\pi$
$350$	0.218469	−	0.672379i	0.0116777	−	0.0359402i
$351$	−4.26355			−0.227572
$352$	1.47776	−	2.96921i	0.0787650	−	0.158259i
$353$	−0.825305			−0.0439266			−0.0219633	−	0.999759i	$-0.506992\pi$
$353$	−0.825305			−0.0439266			−0.0219633	+	0.999759i	$0.506992\pi$
$354$	1.34036	−	4.12520i	0.0712393	−	0.219252i
$355$	−20.9064	+	15.1894i	−1.10960	+	0.806170i
$356$	2.38098	+	1.72988i	0.126192	+	0.0916835i
$357$	1.16251	+	3.57783i	0.0615264	+	0.189359i
$358$	8.08669	+	24.8883i	0.427395	+	1.31539i
$359$	4.68376	+	3.40295i	0.247199	+	0.179601i	0.704485	−	0.709719i	$-0.251178\pi$
$359$	4.68376	+	3.40295i	0.247199	+	0.179601i	−0.457285	+	0.889320i	$0.651178\pi$
$360$	−1.67625	+	1.21787i	−0.0883462	+	0.0641873i
$361$	−4.67141	+	14.3771i	−0.245863	+	0.756690i
$362$	15.2968			0.803981
$363$	−10.5239	−	3.20115i	−0.552362	−	0.168017i
$364$	−4.26355			−0.223471
$365$	4.50910	−	13.8776i	0.236017	−	0.726387i
$366$	−0.940183	+	0.683083i	−0.0491441	+	0.0357053i
$367$	26.6110	+	19.3341i	1.38908	+	1.00923i	0.995965	+	0.0897421i	$0.0286043\pi$
$367$	26.6110	+	19.3341i	1.38908	+	1.00923i	0.393120	+	0.919487i	$0.371396\pi$
$368$	2.35874	+	7.25946i	0.122958	+	0.378425i
$369$	2.11705	+	6.51559i	0.110209	+	0.339188i
$370$	−14.3220	−	10.4056i	−0.744568	−	0.540960i
$371$	−7.52875	+	5.46996i	−0.390873	+	0.283986i
$372$	2.51899	−	7.75266i	0.130604	−	0.401957i
$373$	7.12769			0.369058			0.184529	−	0.982827i	$-0.440924\pi$
$373$	7.12769			0.369058			0.184529	+	0.982827i	$0.440924\pi$
$374$	5.55928	−	11.1700i	0.287463	−	0.577589i
$375$	11.8246			0.610622
$376$	−0.121278	+	0.373256i	−0.00625445	+	0.0192492i
$377$	−10.3048	+	7.48690i	−0.530726	+	0.385595i
$378$	−0.809017	−	0.587785i	−0.0416113	−	0.0302324i
$379$	−4.37433	−	13.4628i	−0.224694	−	0.691538i	−0.998322	−	0.0578984i	$-0.981560\pi$
$379$	−4.37433	−	13.4628i	−0.224694	−	0.691538i	0.773628	−	0.633640i	$-0.218440\pi$
$380$	−1.26168	−	3.88304i	−0.0647226	−	0.199196i
$381$	3.64088	+	2.64526i	0.186528	+	0.135521i
$382$	−3.17035	+	2.30339i	−0.162209	+	0.117852i
$383$	−7.26233	+	22.3512i	−0.371088	+	1.14209i	0.574992	+	0.818159i	$0.305005\pi$
$383$	−7.26233	+	22.3512i	−0.371088	+	1.14209i	−0.946080	+	0.323932i	$0.894995\pi$
$384$	−1.00000			−0.0510310
$385$	4.90481	+	4.81311i	0.249972	+	0.245299i
$386$	−5.44596			−0.277192
$387$	−2.53537	+	7.80306i	−0.128880	+	0.396652i
$388$	−5.82177	+	4.22976i	−0.295556	+	0.214734i
$389$	−2.49178	−	1.81039i	−0.126338	−	0.0917903i	0.522822	−	0.852442i	$-0.324879\pi$
$389$	−2.49178	−	1.81039i	−0.126338	−	0.0917903i	−0.649160	+	0.760652i	$0.724879\pi$
$390$	−2.72983	−	8.40155i	−0.138230	−	0.425429i
$391$	8.87347	+	27.3097i	0.448751	+	1.38111i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	5.67035	−	4.11975i	0.286031	−	0.207814i
$394$	0.122294	−	0.376384i	0.00616111	−	0.0189619i
$395$	21.9768			1.10577
$396$	0.549723	+	3.27075i	0.0276246	+	0.164361i
$397$	−27.9861			−1.40458			−0.702291	−	0.711890i	$-0.747839\pi$
$397$	−27.9861			−1.40458			−0.702291	+	0.711890i	$0.747839\pi$
$398$	−1.82038	+	5.60255i	−0.0912473	+	0.280830i
$399$	1.59420	−	1.15825i	0.0798097	−	0.0579851i
$400$	0.571960	+	0.415553i	0.0285980	+	0.0207777i
$401$	0.667146	+	2.05326i	0.0333157	+	0.102535i	0.966332	−	0.257300i	$-0.0828329\pi$
$401$	0.667146	+	2.05326i	0.0333157	+	0.102535i	−0.933016	+	0.359835i	$0.882833\pi$
$402$	4.34786	+	13.3813i	0.216852	+	0.667401i
$403$	28.1173	+	20.4284i	1.40062	+	1.01761i
$404$	−3.53233	+	2.56639i	−0.175740	+	0.127683i
$405$	0.640271	−	1.97055i	0.0318153	−	0.0979175i
$406$	−2.98752			−0.148268
$407$	−25.1264	+	13.1027i	−1.24547	+	0.649475i
$408$	−3.76195			−0.186244
$409$	−3.09666	+	9.53054i	−0.153120	+	0.471255i	−0.997966	−	0.0637555i	$-0.979692\pi$
$409$	−3.09666	+	9.53054i	−0.153120	+	0.471255i	0.844846	+	0.535010i	$0.179692\pi$
$410$	−11.4838	+	8.34349i	−0.567146	+	0.412056i
$411$	−5.57786	−	4.05256i	−0.275136	−	0.199898i
$412$	−3.24033	−	9.97271i	−0.159640	−	0.491320i
$413$	1.34036	+	4.12520i	0.0659547	+	0.202988i
$414$	−6.17526	−	4.48659i	−0.303498	−	0.220504i
$415$	−16.0884	+	11.6889i	−0.789748	+	0.573786i
$416$	1.31751	−	4.05488i	0.0645963	−	0.198807i
$417$	−11.9705			−0.586200
$418$	−6.46442	−	0.961423i	−0.316185	−	0.0470248i
$419$	−24.0854			−1.17665			−0.588324	−	0.808625i	$-0.700212\pi$
$419$	−24.0854			−1.17665			−0.588324	+	0.808625i	$0.700212\pi$
$420$	0.640271	−	1.97055i	0.0312420	−	0.0961530i
$421$	10.7135	−	7.78381i	0.522144	−	0.379360i	−0.295267	−	0.955415i	$-0.595409\pi$
$421$	10.7135	−	7.78381i	0.522144	−	0.379360i	0.817411	+	0.576055i	$0.195409\pi$
$422$	−3.83876	−	2.78902i	−0.186868	−	0.135767i
$423$	−0.121278	−	0.373256i	−0.00589675	−	0.0181483i
$424$	−2.87573	−	8.85058i	−0.139658	−	0.429822i
$425$	2.15169	+	1.56329i	0.104372	+	0.0758308i
$426$	10.0902	−	7.33094i	0.488870	−	0.355185i
$427$	0.359118	−	1.10525i	0.0173789	−	0.0534869i
$428$	−5.97054			−0.288597
$429$	−13.9868	−	2.08019i	−0.675288	−	0.100432i
$430$	−16.9997			−0.819796
$431$	4.76277	−	14.6583i	0.229415	−	0.706066i	−0.768399	−	0.639971i	$-0.778946\pi$
$431$	4.76277	−	14.6583i	0.229415	−	0.706066i	0.997813	−	0.0660943i	$-0.0210538\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	18.4380	+	13.3960i	0.886075	+	0.643771i	0.934852	−	0.355038i	$-0.115532\pi$
$433$	18.4380	+	13.3960i	0.886075	+	0.643771i	−0.0487764	+	0.998810i	$0.515532\pi$
$434$	2.51899	+	7.75266i	0.120916	+	0.372140i
$435$	−1.91282	−	5.88707i	−0.0917129	−	0.282263i
$436$	−5.10071	−	3.70588i	−0.244280	−	0.177480i
$437$	12.1686	−	8.84099i	0.582102	−	0.422922i
$438$	−2.17625	+	6.69781i	−0.103985	+	0.320034i
$439$	5.40625			0.258026			0.129013	−	0.991643i	$-0.458819\pi$
$439$	5.40625			0.258026			0.129013	+	0.991643i	$0.458819\pi$
$440$	−6.09321	+	3.17742i	−0.290482	+	0.151478i
$441$	1.00000			0.0476190
$442$	4.95641	−	15.2543i	0.235753	−	0.725572i
$443$	26.8595	−	19.5146i	1.27613	−	0.927166i	0.276706	−	0.960955i	$-0.410757\pi$
$443$	26.8595	−	19.5146i	1.27613	−	0.927166i	0.999429	+	0.0337886i	$0.0107573\pi$
$444$	6.91232	+	5.02209i	0.328044	+	0.238338i
$445$	−1.88435	−	5.79943i	−0.0893267	−	0.274919i
$446$	−7.14088	−	21.9774i	−0.338131	−	1.04066i
$447$	−19.1771	−	13.9330i	−0.907048	−	0.659009i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	5.10805	−	15.7209i	0.241064	−	0.741917i	−0.755195	−	0.655500i	$-0.772458\pi$
$449$	5.10805	−	15.7209i	0.241064	−	0.741917i	0.996259	−	0.0864177i	$-0.0275420\pi$
$450$	−0.706982			−0.0333274
$451$	3.76610	+	22.4076i	0.177339	+	1.05513i
$452$	20.5971			0.968806
$453$	−4.87211	+	14.9948i	−0.228911	+	0.704517i
$454$	13.5788	−	9.86554i	0.637282	−	0.463013i
$455$	7.14679	+	5.19244i	0.335047	+	0.243426i
$456$	0.608929	+	1.87409i	0.0285157	+	0.0877623i
$457$	6.46565	+	19.8992i	0.302450	+	0.930846i	0.980616	+	0.195937i	$0.0627750\pi$
$457$	6.46565	+	19.8992i	0.302450	+	0.930846i	−0.678166	+	0.734909i	$0.737225\pi$
$458$	−11.4993	−	8.35472i	−0.537326	−	0.390391i
$459$	3.04348	−	2.21122i	0.142058	−	0.103211i
$460$	4.88722	−	15.0413i	0.227868	−	0.701304i
$461$	−41.9122			−1.95204			−0.976022	−	0.217672i	$-0.930154\pi$
$461$	−41.9122			−1.95204			−0.976022	+	0.217672i	$0.930154\pi$
$462$	−2.36723	−	2.32297i	−0.110134	−	0.108074i
$463$	13.0050			0.604393			0.302196	−	0.953246i	$-0.402280\pi$
$463$	13.0050			0.604393			0.302196	+	0.953246i	$0.402280\pi$
$464$	0.923195	−	2.84130i	0.0428583	−	0.131904i
$465$	−13.6642	+	9.92761i	−0.633661	+	0.460382i
$466$	−15.9812	−	11.6111i	−0.740317	−	0.537872i
$467$	0.414846	+	1.27676i	0.0191968	+	0.0590816i	0.960196	−	0.279327i	$-0.0901114\pi$
$467$	0.414846	+	1.27676i	0.0191968	+	0.0590816i	−0.940999	+	0.338409i	$0.890111\pi$
$468$	1.31751	+	4.05488i	0.0609020	+	0.187437i
$469$	−11.3829	−	8.27013i	−0.525611	−	0.381879i
$470$	0.657870	−	0.477970i	0.0303453	−	0.0220471i
$471$	2.47091	−	7.60469i	0.113854	−	0.350406i
$472$	−4.33749			−0.199649
$473$	−12.1245	+	24.3613i	−0.557485	+	1.12013i
$474$	−10.6068			−0.487186
$475$	0.430502	−	1.32495i	0.0197528	−	0.0607928i
$476$	3.04348	−	2.21122i	0.139498	−	0.101351i
$477$	7.52875	+	5.46996i	0.344718	+	0.250452i
$478$	3.68573	+	11.3435i	0.168582	+	0.518841i
$479$	−12.6218	−	38.8459i	−0.576704	−	1.77491i	−0.630301	−	0.776351i	$-0.717069\pi$
$479$	−12.6218	−	38.8459i	−0.576704	−	1.77491i	0.0535971	−	0.998563i	$-0.482931\pi$
$480$	1.67625	+	1.21787i	0.0765100	+	0.0555878i
$481$	−29.4710	+	21.4120i	−1.34376	+	0.976302i
$482$	−8.85676	+	27.2583i	−0.403414	+	1.24158i
$483$	7.63304			0.347316
$484$	0.207593	+	10.9980i	0.00943603	+	0.499911i
$485$	14.9100			0.677030
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	11.7850	−	8.56231i	0.534030	−	0.387995i	−0.287833	−	0.957681i	$-0.592935\pi$
$487$	11.7850	−	8.56231i	0.534030	−	0.387995i	0.821863	+	0.569685i	$0.192935\pi$
$488$	0.940183	+	0.683083i	0.0425601	+	0.0309217i
$489$	4.14590	+	12.7598i	0.187484	+	0.577016i
$490$	0.640271	+	1.97055i	0.0289245	+	0.0890204i
$491$	−3.00816	−	2.18556i	−0.135756	−	0.0986328i	0.517835	−	0.855481i	$-0.326738\pi$
$491$	−3.00816	−	2.18556i	−0.135756	−	0.0986328i	−0.653591	+	0.756848i	$0.726738\pi$
$492$	5.54250	−	4.02686i	0.249875	−	0.181545i
$493$	3.47302	−	10.6889i	0.156417	−	0.481402i
$494$	−8.40149			−0.378001
$495$	3.06187	−	6.15209i	0.137621	−	0.276516i
$496$	−8.15163			−0.366019
$497$	−3.85410	+	11.8617i	−0.172880	+	0.532070i
$498$	7.76482	−	5.64147i	0.347950	−	0.252800i
$499$	−25.6369	−	18.6263i	−1.14767	−	0.833828i	−0.159498	−	0.987198i	$-0.550987\pi$
$499$	−25.6369	−	18.6263i	−1.14767	−	0.833828i	−0.988169	+	0.153370i	$0.950987\pi$
$500$	−3.65401	−	11.2459i	−0.163412	−	0.502932i
$501$	−1.35086	−	4.15751i	−0.0603519	−	0.185744i
$502$	−10.7446	−	7.80643i	−0.479556	−	0.348418i
$503$	13.3797	−	9.72089i	0.596569	−	0.433433i	−0.248090	−	0.968737i	$-0.579803\pi$
$503$	13.3797	−	9.72089i	0.596569	−	0.433433i	0.844659	+	0.535304i	$0.179803\pi$
$504$	−0.309017	+	0.951057i	−0.0137647	+	0.0423634i
$505$	9.04659			0.402568
$506$	−18.0692	−	17.7314i	−0.803274	−	0.788255i
$507$	−5.17790			−0.229958
$508$	1.39069	−	4.28011i	0.0617020	−	0.189899i
$509$	−22.3275	+	16.2219i	−0.989649	+	0.719022i	−0.959844	−	0.280533i	$-0.909489\pi$
$509$	−22.3275	+	16.2219i	−0.989649	+	0.719022i	−0.0298050	+	0.999556i	$0.509489\pi$
$510$	6.30598	+	4.58156i	0.279233	+	0.202875i
$511$	−2.17625	−	6.69781i	−0.0962717	−	0.296294i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.59420	−	1.15825i	−0.0703855	−	0.0511381i
$514$	6.99901	−	5.08508i	0.308713	−	0.224293i
$515$	−6.71383	+	20.6630i	−0.295847	+	0.910523i
$516$	8.20463			0.361189
$517$	−0.215747	−	1.28365i	−0.00948854	−	0.0564551i
$518$	−8.54410			−0.375406
$519$	2.27608	−	7.00504i	0.0999086	−	0.307487i
$520$	−7.14679	+	5.19244i	−0.313407	+	0.227704i
$521$	18.6084	+	13.5198i	0.815248	+	0.592312i	0.915347	−	0.402665i	$-0.131916\pi$
$521$	18.6084	+	13.5198i	0.815248	+	0.592312i	−0.100099	+	0.994977i	$0.531916\pi$
$522$	0.923195	+	2.84130i	0.0404072	+	0.124360i
$523$	1.32839	+	4.08836i	0.0580863	+	0.178771i	0.975890	−	0.218263i	$-0.0700392\pi$
$523$	1.32839	+	4.08836i	0.0580863	+	0.178771i	−0.917804	+	0.397035i	$0.870039\pi$
$524$	−5.67035	−	4.11975i	−0.247710	−	0.179972i
$525$	0.571960	−	0.415553i	0.0249624	−	0.0181362i
$526$	3.65825	−	11.2589i	0.159507	−	0.490913i
$527$	−30.6661			−1.33583
$528$	2.94079	−	1.53354i	0.127982	−	0.0667385i
$529$	35.2634			1.53319
$530$	−5.95839	+	18.3380i	−0.258816	+	0.796554i
$531$	3.50910	−	2.54951i	0.152282	−	0.110639i
$532$	−1.59420	−	1.15825i	−0.0691172	−	0.0502166i
$533$	9.02614	+	27.7796i	0.390965	+	1.20327i
$534$	0.909452	+	2.79901i	0.0393559	+	0.121125i
$535$	10.0081	+	7.27132i	0.432689	+	0.314367i
$536$	11.3829	−	8.27013i	0.491664	−	0.357215i
$537$	−8.08669	+	24.8883i	−0.348967	+	1.07401i
$538$	−13.1811			−0.568277
$539$	3.28054	+	0.487899i	0.141303	+	0.0210153i
$540$	−2.07196			−0.0891630
$541$	10.4297	−	32.0994i	0.448408	−	1.38006i	−0.430294	−	0.902689i	$-0.641590\pi$
$541$	10.4297	−	32.0994i	0.448408	−	1.38006i	0.878702	−	0.477370i	$-0.158410\pi$
$542$	17.4489	−	12.6774i	0.749495	−	0.544540i
$543$	12.3753	+	8.99122i	0.531077	+	0.385850i
$544$	1.16251	+	3.57783i	0.0498421	+	0.153398i
$545$	4.03680	+	12.4240i	0.172917	+	0.532185i
$546$	−3.44929	−	2.50605i	−0.147616	−	0.107249i
$547$	14.3977	−	10.4605i	0.615599	−	0.447259i	−0.235782	−	0.971806i	$-0.575765\pi$
$547$	14.3977	−	10.4605i	0.615599	−	0.447259i	0.851382	+	0.524547i	$0.175765\pi$
$548$	−2.13055	+	6.55717i	−0.0910128	+	0.280109i
$549$	−1.16213			−0.0495985
$550$	−2.31928	−	0.344936i	−0.0988945	−	0.0147081i
$551$	−5.88702			−0.250796
$552$	−2.35874	+	7.25946i	−0.100395	+	0.308983i
$553$	8.58107	−	6.23451i	0.364904	−	0.265118i
$554$	−13.2903	−	9.65594i	−0.564649	−	0.410241i
$555$	−5.47054	−	16.8366i	−0.232211	−	0.714673i
$556$	3.69910	+	11.3847i	0.156877	+	0.482817i
$557$	13.7677	+	10.0028i	0.583356	+	0.423833i	0.839932	−	0.542691i	$-0.182595\pi$
$557$	13.7677	+	10.0028i	0.583356	+	0.423833i	−0.256577	+	0.966524i	$0.582595\pi$
$558$	6.59481	−	4.79141i	0.279180	−	0.202836i
$559$	−10.8097	+	33.2688i	−0.457201	+	1.40712i
$560$	−2.07196			−0.0875563
$561$	11.0631	−	5.76909i	0.467086	−	0.243571i
$562$	−3.80314			−0.160426
$563$	−8.50788	+	26.1846i	−0.358564	+	1.10355i	0.595349	+	0.803467i	$0.297014\pi$
$563$	−8.50788	+	26.1846i	−0.358564	+	1.10355i	−0.953914	+	0.300081i	$0.902986\pi$
$564$	−0.317511	+	0.230685i	−0.0133696	+	0.00971359i
$565$	−34.5259	−	25.0845i	−1.45252	−	1.05531i
$566$	7.16915	+	22.0644i	0.301342	+	0.927435i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	−10.0902	−	7.33094i	−0.423374	−	0.307599i
$569$	−7.01767	+	5.09864i	−0.294196	+	0.213746i	−0.725086	−	0.688659i	$-0.758200\pi$
$569$	−7.01767	+	5.09864i	−0.294196	+	0.213746i	0.430890	+	0.902405i	$0.358200\pi$
$570$	1.26168	−	3.88304i	0.0528458	−	0.162643i
$571$	15.7382			0.658624			0.329312	−	0.944221i	$-0.393183\pi$
$571$	15.7382			0.658624			0.329312	+	0.944221i	$0.393183\pi$
$572$	2.34377	+	13.9450i	0.0979981	+	0.583071i
$573$	−3.91876			−0.163709
$574$	−2.11705	+	6.51559i	−0.0883638	+	0.271956i
$575$	4.36580	−	3.17194i	0.182066	−	0.132279i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−0.275904	−	0.849144i	−0.0114860	−	0.0353503i	0.945149	−	0.326639i	$-0.105916\pi$
$577$	−0.275904	−	0.849144i	−0.0114860	−	0.0353503i	−0.956635	+	0.291288i	$0.905916\pi$
$578$	−0.879988	−	2.70832i	−0.0366027	−	0.112651i
$579$	−4.40587	−	3.20105i	−0.183102	−	0.133031i
$580$	−5.00784	+	3.63841i	−0.207939	+	0.151077i
$581$	−2.96590	+	9.12809i	−0.123046	+	0.378697i
$582$	−7.19610			−0.298288
$583$	22.0296	+	21.6177i	0.912373	+	0.895314i
$584$	7.04250			0.291421
$585$	2.72983	−	8.40155i	0.112865	−	0.347361i
$586$	−9.72195	+	7.06341i	−0.401610	+	0.291787i
$587$	23.2673	+	16.9047i	0.960345	+	0.697731i	0.953231	−	0.302243i	$-0.0977356\pi$
$587$	23.2673	+	16.9047i	0.960345	+	0.697731i	0.00711388	+	0.999975i	$0.497736\pi$
$588$	−0.309017	−	0.951057i	−0.0127436	−	0.0392209i
$589$	4.96376	+	15.2769i	0.204528	+	0.629474i
$590$	7.27073	+	5.28249i	0.299331	+	0.217477i
$591$	0.320171	−	0.232618i	0.0131701	−	0.00956862i
$592$	2.64027	−	8.12592i	0.108514	−	0.333973i
$593$	−20.1905			−0.829125			−0.414563	−	0.910021i	$-0.636065\pi$
$593$	−20.1905			−0.829125			−0.414563	+	0.910021i	$0.636065\pi$
$594$	−1.47776	+	2.96921i	−0.0606334	+	0.121828i
$595$	−7.79462			−0.319548
$596$	−7.32502	+	22.5441i	−0.300044	+	0.923441i
$597$	−4.76581	+	3.46256i	−0.195052	+	0.141713i
$598$	−26.3286	−	19.1288i	−1.07666	−	0.782236i
$599$	−8.33201	−	25.6433i	−0.340437	−	1.04776i	−0.963982	−	0.265969i	$-0.914308\pi$
$599$	−8.33201	−	25.6433i	−0.340437	−	1.04776i	0.623545	−	0.781787i	$-0.285692\pi$
$600$	0.218469	+	0.672379i	0.00891897	+	0.0274498i
$601$	8.51661	+	6.18768i	0.347400	+	0.252401i	0.747777	−	0.663950i	$-0.231121\pi$
$601$	8.51661	+	6.18768i	0.347400	+	0.252401i	−0.400378	+	0.916350i	$0.631121\pi$
$602$	−6.63768	+	4.82256i	−0.270532	+	0.196553i
$603$	−4.34786	+	13.3813i	−0.177059	+	0.544931i
$604$	15.7665			0.641528
$605$	13.0462	−	18.6883i	0.530403	−	0.759787i
$606$	−4.36620			−0.177365
$607$	12.4409	−	38.2893i	0.504962	−	1.55411i	−0.295872	−	0.955228i	$-0.595610\pi$
$607$	12.4409	−	38.2893i	0.504962	−	1.55411i	0.800834	−	0.598887i	$-0.204390\pi$
$608$	1.59420	−	1.15825i	0.0646532	−	0.0469733i
$609$	−2.41696	−	1.75602i	−0.0979400	−	0.0711576i
$610$	−0.744078	−	2.29004i	−0.0301268	−	0.0927209i
$611$	−0.517077	−	1.59140i	−0.0209187	−	0.0643811i
$612$	−3.04348	−	2.21122i	−0.123026	−	0.0893833i
$613$	−9.04901	+	6.57449i	−0.365486	+	0.265541i	−0.755337	−	0.655337i	$-0.772527\pi$
$613$	−9.04901	+	6.57449i	−0.365486	+	0.265541i	0.389851	+	0.920878i	$0.372527\pi$
$614$	8.43844	−	25.9708i	0.340548	−	1.04810i
$615$	−14.1948			−0.572389
$616$	−1.47776	+	2.96921i	−0.0595408	+	0.119633i
$617$	44.9893			1.81120			0.905601	−	0.424132i	$-0.139421\pi$
$617$	44.9893			1.81120			0.905601	+	0.424132i	$0.139421\pi$
$618$	3.24033	−	9.97271i	0.130345	−	0.401161i
$619$	23.7278	−	17.2393i	0.953701	−	0.692904i	0.00202178	−	0.999998i	$-0.499356\pi$
$619$	23.7278	−	17.2393i	0.953701	−	0.692904i	0.951679	+	0.307094i	$0.0993564\pi$
$620$	13.6642	+	9.92761i	0.548767	+	0.398702i
$621$	−2.35874	−	7.25946i	−0.0946530	−	0.291312i
$622$	4.28716	+	13.1945i	0.171899	+	0.529052i
$623$	−2.38098	−	1.72988i	−0.0953918	−	0.0693062i
$624$	3.44929	−	2.50605i	0.138082	−	0.100322i
$625$	−6.47862	+	19.9392i	−0.259145	+	0.797566i
$626$	28.1190			1.12386
$627$	−4.66472	−	4.57750i	−0.186291	−	0.182808i
$628$	−7.99604			−0.319077
$629$	9.93258	−	30.5693i	0.396038	−	1.21888i
$630$	1.67625	−	1.21787i	0.0667834	−	0.0485210i
$631$	13.1521	+	9.55557i	0.523577	+	0.380401i	0.817950	−	0.575290i	$-0.195111\pi$
$631$	13.1521	+	9.55557i	0.523577	+	0.380401i	−0.294373	+	0.955691i	$0.595111\pi$
$632$	3.27768	+	10.0876i	0.130379	+	0.401265i
$633$	−1.46628	−	4.51273i	−0.0582792	−	0.179365i
$634$	5.65766	+	4.11053i	0.224695	+	0.163250i
$635$	−7.54376	+	5.48086i	−0.299365	+	0.217501i
$636$	2.87573	−	8.85058i	0.114030	−	0.350948i
$637$	4.26355			0.168928
$638$	1.64231	+	9.77144i	0.0650197	+	0.386855i
$639$	12.4721			0.493390
$640$	0.640271	−	1.97055i	0.0253089	−	0.0778929i
$641$	−17.9218	+	13.0209i	−0.707867	+	0.514295i	−0.882485	−	0.470341i	$-0.844131\pi$
$641$	−17.9218	+	13.0209i	−0.707867	+	0.514295i	0.174618	+	0.984636i	$0.444131\pi$
$642$	−4.83026	−	3.50939i	−0.190635	−	0.138505i
$643$	−12.0083	−	36.9579i	−0.473563	−	1.45748i	−0.847886	−	0.530179i	$-0.822125\pi$
$643$	−12.0083	−	36.9579i	−0.473563	−	1.45748i	0.374323	−	0.927298i	$-0.377875\pi$
$644$	−2.35874	−	7.25946i	−0.0929474	−	0.286063i
$645$	−13.7530	−	9.99215i	−0.541524	−	0.393440i
$646$	5.99730	−	4.35729i	0.235960	−	0.171435i
$647$	11.9467	−	36.7681i	0.469672	−	1.44550i	−0.383338	−	0.923608i	$-0.625226\pi$
$647$	11.9467	−	36.7681i	0.469672	−	1.44550i	0.853010	−	0.521894i	$-0.174774\pi$
$648$	1.00000			0.0392837
$649$	12.7557	−	6.65170i	0.500704	−	0.261102i
$650$	−3.01425			−0.118229
$651$	−2.51899	+	7.75266i	−0.0987271	+	0.303851i
$652$	10.8541	−	7.88597i	0.425079	−	0.308838i
$653$	8.28518	+	6.01954i	0.324224	+	0.235563i	0.737976	−	0.674827i	$-0.235782\pi$
$653$	8.28518	+	6.01954i	0.324224	+	0.235563i	−0.413752	+	0.910390i	$0.635782\pi$
$654$	−1.94830	−	5.99625i	−0.0761845	−	0.234472i
$655$	4.48762	+	13.8115i	0.175346	+	0.539658i
$656$	−5.54250	−	4.02686i	−0.216398	−	0.157222i
$657$	−5.69750	+	4.13948i	−0.222281	+	0.161496i
$658$	0.121278	−	0.373256i	0.00472792	−	0.0145510i
$659$	17.5886			0.685156			0.342578	−	0.939489i	$-0.388700\pi$
$659$	17.5886			0.685156			0.342578	+	0.939489i	$0.388700\pi$
$660$	−6.79715	−	1.01091i	−0.264579	−	0.0393495i
$661$	−38.4532			−1.49565			−0.747827	−	0.663893i	$-0.768903\pi$
$661$	−38.4532			−1.49565			−0.747827	+	0.663893i	$0.768903\pi$
$662$	1.33163	−	4.09834i	0.0517553	−	0.159287i
$663$	12.9761	−	9.42766i	0.503949	−	0.366140i
$664$	−7.76482	−	5.64147i	−0.301333	−	0.218932i
$665$	1.26168	+	3.88304i	0.0489257	+	0.150578i
$666$	2.64027	+	8.12592i	0.102308	+	0.314873i
$667$	−18.4487	−	13.4038i	−0.714338	−	0.518997i
$668$	−3.53659	+	2.56948i	−0.136835	+	0.0994163i
$669$	7.14088	−	21.9774i	0.276082	−	0.849694i
$670$	−29.1524			−1.12626
$671$	−3.81242	−	0.567003i	−0.147177	−	0.0218889i
$672$	1.00000			0.0385758
$673$	2.73118	−	8.40571i	0.105279	−	0.324016i	−0.884517	−	0.466509i	$-0.845512\pi$
$673$	2.73118	−	8.40571i	0.105279	−	0.324016i	0.989796	+	0.142492i	$0.0455117\pi$
$674$	−13.7786	+	10.0107i	−0.530730	+	0.385598i
$675$	−0.571960	−	0.415553i	−0.0220148	−	0.0159947i
$676$	1.60006	+	4.92447i	0.0615407	+	0.189403i
$677$	−1.75070	−	5.38810i	−0.0672849	−	0.207082i	0.911761	−	0.410721i	$-0.134723\pi$
$677$	−1.75070	−	5.38810i	−0.0672849	−	0.207082i	−0.979046	+	0.203639i	$0.934723\pi$
$678$	16.6634	+	12.1067i	0.639954	+	0.464954i
$679$	5.82177	−	4.22976i	0.223419	−	0.162323i
$680$	2.40867	−	7.41312i	0.0923683	−	0.284280i
$681$	16.7843			0.643174
$682$	23.9723	−	12.5008i	0.917946	−	0.478681i
$683$	−47.5727			−1.82032			−0.910159	−	0.414259i	$-0.864041\pi$
$683$	−47.5727			−1.82032			−0.910159	+	0.414259i	$0.864041\pi$
$684$	−0.608929	+	1.87409i	−0.0232830	+	0.0716577i
$685$	11.5571	−	8.39673i	0.441575	−	0.320823i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	−4.39234	−	13.5182i	−0.167578	−	0.515752i
$688$	−2.53537	−	7.80306i	−0.0966600	−	0.297489i
$689$	32.0992	+	23.3215i	1.22288	+	0.888477i
$690$	12.7949	−	9.29604i	0.487093	−	0.353894i
$691$	14.5395	−	44.7480i	0.553109	−	1.70229i	−0.147778	−	0.989021i	$-0.547212\pi$
$691$	14.5395	−	44.7480i	0.553109	−	1.70229i	0.700886	−	0.713273i	$-0.252788\pi$
$692$	−7.36553			−0.279996
$693$	−0.549723	−	3.27075i	−0.0208823	−	0.124246i
$694$	20.4909			0.777824
$695$	7.66439	−	23.5886i	0.290727	−	0.894765i
$696$	2.41696	−	1.75602i	0.0916145	−	0.0665618i
$697$	−20.8506	−	15.1489i	−0.789773	−	0.573804i
$698$	−2.12407	−	6.53720i	−0.0803971	−	0.247437i
$699$	−6.10429	−	18.7871i	−0.230885	−	0.710592i
$700$	−0.571960	−	0.415553i	−0.0216181	−	0.0157064i
$701$	25.4161	−	18.4659i	0.959952	−	0.697446i	0.00681230	−	0.999977i	$-0.497832\pi$
$701$	25.4161	−	18.4659i	0.959952	−	0.697446i	0.953140	+	0.302531i	$0.0978316\pi$
$702$	−1.31751	+	4.05488i	−0.0497262	+	0.153042i
$703$	−16.8364			−0.634999
$704$	−2.36723	−	2.32297i	−0.0892185	−	0.0875503i
$705$	0.813171			0.0306258
$706$	−0.255033	+	0.784912i	−0.00959831	+	0.0295406i
$707$	3.53233	−	2.56639i	0.132847	−	0.0965190i
$708$	−3.50910	−	2.54951i	−0.131880	−	0.0958166i
$709$	1.76269	+	5.42501i	0.0661993	+	0.203741i	0.978685	−	0.205369i	$-0.0658394\pi$
$709$	1.76269	+	5.42501i	0.0661993	+	0.203741i	−0.912485	+	0.409109i	$0.865839\pi$
$710$	7.98555	+	24.5770i	0.299692	+	0.922358i
$711$	−8.58107	−	6.23451i	−0.321815	−	0.233812i
$712$	2.38098	−	1.72988i	0.0892309	−	0.0648300i
$713$	−19.2276	+	59.1764i	−0.720079	+	2.21617i
$714$	3.76195			0.140788
$715$	13.0544	−	26.2298i	0.488208	−	0.980937i
$716$	26.1691			0.977985
$717$	−3.68573	+	11.3435i	−0.137646	+	0.423632i
$718$	4.68376	−	3.40295i	0.174796	−	0.126997i
$719$	1.66947	+	1.21294i	0.0622608	+	0.0452351i	0.618480	−	0.785800i	$-0.287749\pi$
$719$	1.66947	+	1.21294i	0.0622608	+	0.0452351i	−0.556220	+	0.831035i	$0.687749\pi$
$720$	0.640271	+	1.97055i	0.0238615	+	0.0734381i
$721$	3.24033	+	9.97271i	0.120676	+	0.371403i
$722$	12.2299	+	8.88554i	0.455150	+	0.330686i
$723$	−23.1873	+	16.8466i	−0.862345	+	0.626530i
$724$	4.72696	−	14.5481i	0.175676	−	0.540676i
$725$	−2.11212			−0.0784423
$726$	−6.29654	+	9.01962i	−0.233687	+	0.334750i
$727$	10.1902			0.377933			0.188966	−	0.981984i	$-0.439486\pi$
$727$	10.1902			0.377933			0.188966	+	0.981984i	$0.439486\pi$
$728$	−1.31751	+	4.05488i	−0.0488302	+	0.150284i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−11.8050	−	8.57683i	−0.436922	−	0.317443i
$731$	−9.53794	−	29.3548i	−0.352773	−	1.08573i
$732$	0.359118	+	1.10525i	0.0132734	+	0.0408513i
$733$	17.7452	+	12.8926i	0.655433	+	0.476200i	0.865118	−	0.501569i	$-0.167244\pi$
$733$	17.7452	+	12.8926i	0.655433	+	0.476200i	−0.209685	+	0.977769i	$0.567244\pi$
$734$	26.6110	−	19.3341i	0.982231	−	0.713633i
$735$	−0.640271	+	1.97055i	−0.0236167	+	0.0726849i
$736$	7.63304			0.281358
$737$	−20.7921	+	41.7768i	−0.765887	+	1.53887i
$738$	6.85090			0.252185
$739$	9.67827	−	29.7867i	0.356021	−	1.09572i	−0.599394	−	0.800454i	$-0.704592\pi$
$739$	9.67827	−	29.7867i	0.356021	−	1.09572i	0.955415	−	0.295266i	$-0.0954083\pi$
$740$	−14.3220	+	10.4056i	−0.526489	+	0.382517i
$741$	−6.79695	−	4.93827i	−0.249692	−	0.181412i
$742$	2.87573	+	8.85058i	0.105571	+	0.324915i
$743$	10.2317	+	31.4900i	0.375365	+	1.15525i	0.943232	+	0.332134i	$0.107769\pi$
$743$	10.2317	+	31.4900i	0.375365	+	1.15525i	−0.567867	+	0.823120i	$0.692231\pi$
$744$	−6.59481	−	4.79141i	−0.241777	−	0.175662i
$745$	39.7343	−	28.8686i	1.45575	−	1.05766i
$746$	2.20258	−	6.77883i	0.0806421	−	0.248191i
$747$	9.59785			0.351167
$748$	−8.90543	−	8.73892i	−0.325615	−	0.319526i
$749$	5.97054			0.218159
$750$	3.65401	−	11.2459i	0.133426	−	0.410642i
$751$	8.49696	−	6.17340i	0.310059	−	0.225271i	−0.421863	−	0.906660i	$-0.638624\pi$
$751$	8.49696	−	6.17340i	0.310059	−	0.225271i	0.731922	+	0.681389i	$0.238624\pi$
$752$	0.317511	+	0.230685i	0.0115784	+	0.00841222i
$753$	−4.10408	−	12.6311i	−0.149561	−	0.460302i
$754$	3.93609	+	12.1141i	0.143344	+	0.441168i
$755$	−26.4286	−	19.2015i	−0.961833	−	0.698813i
$756$	−0.809017	+	0.587785i	−0.0294237	+	0.0213775i
$757$	12.1120	−	37.2768i	0.440217	−	1.35485i	−0.447428	−	0.894320i	$-0.647660\pi$
$757$	12.1120	−	37.2768i	0.440217	−	1.35485i	0.887645	−	0.460528i	$-0.152340\pi$
$758$	−14.1556			−0.514156
$759$	−4.19606	−	24.9658i	−0.152307	−	0.906200i
$760$	−4.08287			−0.148101
$761$	−7.02074	+	21.6076i	−0.254502	+	0.783276i	0.739426	+	0.673238i	$0.235097\pi$
$761$	−7.02074	+	21.6076i	−0.254502	+	0.783276i	−0.993927	+	0.110038i	$0.964903\pi$
$762$	3.64088	−	2.64526i	0.131895	−	0.0958275i
$763$	5.10071	+	3.70588i	0.184658	+	0.134162i
$764$	1.21096	+	3.72697i	0.0438112	+	0.134837i
$765$	2.40867	+	7.41312i	0.0870856	+	0.268022i
$766$	19.0130	+	13.8138i	0.686969	+	0.499112i
$767$	14.9613	−	10.8700i	0.540220	−	0.392493i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	−36.6139			−1.32033			−0.660165	−	0.751121i	$-0.729514\pi$
$769$	−36.6139			−1.32033			−0.660165	+	0.751121i	$0.729514\pi$
$770$	6.09321	−	3.17742i	0.219584	−	0.114506i
$771$	8.65125			0.311567
$772$	−1.68289	+	5.17942i	−0.0605687	+	0.186411i
$773$	37.7004	−	27.3909i	1.35599	−	0.985183i	0.357300	−	0.933990i	$-0.383697\pi$
$773$	37.7004	−	27.3909i	1.35599	−	0.985183i	0.998689	−	0.0511935i	$-0.0163025\pi$
$774$	6.63768	+	4.82256i	0.238587	+	0.173343i
$775$	1.78088	+	5.48099i	0.0639711	+	0.196883i
$776$	2.22372	+	6.84390i	0.0798268	+	0.245682i
$777$	−6.91232	−	5.02209i	−0.247978	−	0.180167i
$778$	−2.49178	+	1.81039i	−0.0893348	+	0.0649055i
$779$	−4.17171	+	12.8392i	−0.149467	+	0.460013i
$780$	−8.83391			−0.316305
$781$	40.9154	+	6.08515i	1.46407	+	0.217744i
$782$	28.7152			1.02685
$783$	−0.923195	+	2.84130i	−0.0329923	+	0.101540i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	13.4034	+	9.73812i	0.478387	+	0.347569i
$786$	−2.16588	−	6.66589i	−0.0772544	−	0.237764i
$787$	2.84013	+	8.74101i	0.101240	+	0.311583i	0.988829	−	0.149051i	$-0.0476219\pi$
$787$	2.84013	+	8.74101i	0.101240	+	0.311583i	−0.887590	+	0.460634i	$0.847622\pi$
$788$	−0.320171	−	0.232618i	−0.0114056	−	0.00828667i
$789$	9.57742	−	6.95840i	0.340965	−	0.247726i
$790$	6.79121	−	20.9012i	0.241620	−	0.743631i
$791$	−20.5971			−0.732348
$792$	3.28054	+	0.487899i	0.116569	+	0.0173368i
$793$	−4.95480			−0.175950
$794$	−8.64818	+	26.6164i	−0.306912	+	0.944579i
$795$	−15.5993	+	11.3335i	−0.553249	+	0.401959i
$796$	4.76581	+	3.46256i	0.168920	+	0.122727i
$797$	3.52835	+	10.8591i	0.124980	+	0.384650i	0.993898	−	0.110307i	$-0.0351835\pi$
$797$	3.52835	+	10.8591i	0.124980	+	0.384650i	−0.868917	+	0.494958i	$0.835184\pi$
$798$	−0.608929	−	1.87409i	−0.0215559	−	0.0663421i
$799$	1.19446	+	0.867827i	0.0422570	+	0.0307015i
$800$	0.571960	−	0.415553i	0.0202218	−	0.0146920i
$801$	−0.909452	+	2.79901i	−0.0321339	+	0.0988980i
$802$	2.15893			0.0762345
$803$	−20.7105	+	10.7999i	−0.730859	+	0.381121i
$804$	14.0700			0.496210
$805$	−4.88722	+	15.0413i	−0.172252	+	0.530136i
$806$	28.1173	−	20.4284i	0.990390	−	0.719561i
$807$	−10.6637	−	7.74765i	−0.375381	−	0.272730i
$808$	1.34923	+	4.15250i	0.0474658	+	0.146085i
$809$	−6.37016	−	19.6053i	−0.223963	−	0.689287i	−0.998395	−	0.0566303i	$-0.981964\pi$
$809$	−6.37016	−	19.6053i	−0.223963	−	0.689287i	0.774432	−	0.632657i	$-0.218036\pi$
$810$	−1.67625	−	1.21787i	−0.0588975	−	0.0427915i
$811$	−1.13662	+	0.825804i	−0.0399122	+	0.0289979i	−0.607562	−	0.794272i	$-0.707853\pi$
$811$	−1.13662	+	0.825804i	−0.0399122	+	0.0289979i	0.567650	+	0.823270i	$0.307853\pi$
$812$	−0.923195	+	2.84130i	−0.0323978	+	0.0997102i
$813$	21.5680			0.756424
$814$	4.69689	+	27.9456i	0.164626	+	0.979493i
$815$	−27.7983			−0.973731
$816$	−1.16251	+	3.57783i	−0.0406959	+	0.125249i
$817$	−13.0798	+	9.50302i	−0.457604	+	0.332469i
$818$	8.10716	+	5.89019i	0.283460	+	0.205946i
$819$	−1.31751	−	4.05488i	−0.0460376	−	0.141689i
$820$	4.38643	+	13.5001i	0.153181	+	0.471442i
$821$	12.0269	+	8.73808i	0.419743	+	0.304961i	0.777534	−	0.628840i	$-0.216470\pi$
$821$	12.0269	+	8.73808i	0.419743	+	0.304961i	−0.357791	+	0.933802i	$0.616470\pi$
$822$	−5.57786	+	4.05256i	−0.194550	+	0.141349i
$823$	7.11669	−	21.9029i	0.248072	−	0.763488i	−0.747044	−	0.664775i	$-0.768527\pi$
$823$	7.11669	−	21.9029i	0.248072	−	0.763488i	0.995116	−	0.0987132i	$-0.0314726\pi$
$824$	−10.4859			−0.365294
$825$	−1.67359	−	1.64230i	−0.0582669	−	0.0571775i
$826$	4.33749			0.150921
$827$	−14.9982	+	46.1597i	−0.521538	+	1.60513i	0.249523	+	0.968369i	$0.419726\pi$
$827$	−14.9982	+	46.1597i	−0.521538	+	1.60513i	−0.771061	+	0.636761i	$0.780274\pi$
$828$	−6.17526	+	4.48659i	−0.214605	+	0.155920i
$829$	25.8864	+	18.8076i	0.899073	+	0.653215i	0.938228	−	0.346018i	$-0.112466\pi$
$829$	25.8864	+	18.8076i	0.899073	+	0.653215i	−0.0391544	+	0.999233i	$0.512466\pi$
$830$	6.14522	+	18.9130i	0.213304	+	0.656481i
$831$	−5.07643	−	15.6236i	−0.176099	−	0.541978i
$832$	−3.44929	−	2.50605i	−0.119583	−	0.0868818i
$833$	−3.04348	+	2.21122i	−0.105450	+	0.0766143i
$834$	−3.69910	+	11.3847i	−0.128089	+	0.394218i
$835$	9.05751			0.313448
$836$	−2.91199	+	5.85094i	−0.100713	+	0.202359i
$837$	8.15163			0.281762
$838$	−7.44280	+	22.9066i	−0.257107	+	0.791295i
$839$	−5.77177	+	4.19344i	−0.199264	+	0.144774i	−0.682943	−	0.730472i	$-0.739300\pi$
$839$	−5.77177	+	4.19344i	−0.199264	+	0.144774i	0.483679	+	0.875245i	$0.339300\pi$
$840$	−1.67625	−	1.21787i	−0.0578362	−	0.0420204i
$841$	−6.20342	−	19.0922i	−0.213911	−	0.658351i
$842$	−4.09219	−	12.5945i	−0.141026	−	0.434034i
$843$	−3.07680	−	2.23543i	−0.105971	−	0.0769923i
$844$	−3.83876	+	2.78902i	−0.132136	+	0.0960021i
$845$	3.31526	−	10.2033i	0.114048	−	0.351004i
$846$	−0.392465			−0.0134932
$847$	−0.207593	−	10.9980i	−0.00713297	−	0.377897i
$848$	−9.30605			−0.319571
$849$	−7.16915	+	22.0644i	−0.246045	+	0.757247i
$850$	2.15169	−	1.56329i	0.0738023	−	0.0536205i
$851$	−52.7620	−	38.3339i	−1.80866	−	1.31407i
$852$	−3.85410	−	11.8617i	−0.132039	−	0.406375i
$853$	15.4075	+	47.4193i	0.527542	+	1.62361i	0.759234	+	0.650818i	$0.225574\pi$
$853$	15.4075	+	47.4193i	0.527542	+	1.62361i	−0.231692	+	0.972789i	$0.574426\pi$
$854$	−0.940183	−	0.683083i	−0.0321724	−	0.0233746i
$855$	3.30311	−	2.39985i	0.112964	−	0.0820732i
$856$	−1.84500	+	5.67832i	−0.0630607	+	0.194081i
$857$	−29.9071			−1.02161			−0.510803	−	0.859698i	$-0.670652\pi$
$857$	−29.9071			−1.02161			−0.510803	+	0.859698i	$0.670652\pi$
$858$	−6.30052	+	12.6594i	−0.215096	+	0.432185i
$859$	19.1028			0.651779			0.325889	−	0.945408i	$-0.394336\pi$
$859$	19.1028			0.651779			0.325889	+	0.945408i	$0.394336\pi$
$860$	−5.25318	+	16.1676i	−0.179132	+	0.551312i
$861$	−5.54250	+	4.02686i	−0.188888	+	0.137235i
$862$	−12.4691	−	9.05933i	−0.424699	−	0.308562i
$863$	−5.38409	−	16.5705i	−0.183277	−	0.564068i	0.816638	−	0.577151i	$-0.195835\pi$
$863$	−5.38409	−	16.5705i	−0.183277	−	0.564068i	−0.999914	+	0.0130830i	$0.995835\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	12.3465	+	8.97024i	0.419793	+	0.304997i
$866$	18.4380	−	13.3960i	0.626550	−	0.455215i
$867$	0.879988	−	2.70832i	0.0298860	−	0.0919795i
$868$	8.15163			0.276684
$869$	−25.1087	−	24.6393i	−0.851755	−	0.835830i
$870$	−6.19003			−0.209862
$871$	−18.5374	+	57.0521i	−0.628114	+	1.93314i
$872$	−5.10071	+	3.70588i	−0.172732	+	0.125497i
$873$	−5.82177	−	4.22976i	−0.197037	−	0.143156i
$874$	−4.64798	−	14.3050i	−0.157220	−	0.483874i
$875$	3.65401	+	11.2459i	0.123528	+	0.380181i
$876$	5.69750	+	4.13948i	0.192501	+	0.139860i
$877$	4.98432	−	3.62132i	0.168309	−	0.122283i	−0.500442	−	0.865770i	$-0.666829\pi$
$877$	4.98432	−	3.62132i	0.168309	−	0.122283i	0.668751	+	0.743487i	$0.266829\pi$
$878$	1.67062	−	5.14165i	0.0563808	−	0.173522i
$879$	−12.0170			−0.405323
$880$	1.13900	+	6.77686i	0.0383958	+	0.228448i
$881$	−26.8987			−0.906241			−0.453120	−	0.891449i	$-0.649689\pi$
$881$	−26.8987			−0.906241			−0.453120	+	0.891449i	$0.649689\pi$
$882$	0.309017	−	0.951057i	0.0104051	−	0.0320237i
$883$	−6.86304	+	4.98629i	−0.230960	+	0.167802i	−0.697246	−	0.716832i	$-0.745592\pi$
$883$	−6.86304	+	4.98629i	−0.230960	+	0.167802i	0.466286	+	0.884634i	$0.345592\pi$
$884$	−12.9761	−	9.42766i	−0.436432	−	0.317087i
$885$	2.77717	+	8.54725i	0.0933535	+	0.287313i
$886$	−10.2594	−	31.5753i	−0.344672	−	1.06079i
$887$	21.6111	+	15.7014i	0.725629	+	0.527200i	0.888178	−	0.459500i	$-0.151971\pi$
$887$	21.6111	+	15.7014i	0.725629	+	0.527200i	−0.162549	+	0.986701i	$0.551971\pi$
$888$	6.91232	−	5.02209i	0.231962	−	0.168530i
$889$	−1.39069	+	4.28011i	−0.0466424	+	0.143550i
$890$	−6.09788			−0.204401
$891$	−2.94079	+	1.53354i	−0.0985203	+	0.0513754i
$892$	−23.1084			−0.773726
$893$	0.238983	−	0.735515i	0.00799727	−	0.0246131i
$894$	−19.1771	+	13.9330i	−0.641379	+	0.465989i
$895$	−43.8660	−	31.8705i	−1.46628	−	1.06531i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	−10.0566	−	30.9511i	−0.335781	−	1.03343i
$898$	−13.3730	−	9.71608i	−0.446264	−	0.324230i
$899$	19.7021	−	14.3144i	0.657103	−	0.477413i
$900$	−0.218469	+	0.672379i	−0.00728231	+	0.0224126i
$901$	−35.0089			−1.16632
$902$	22.4747	+	3.34255i	0.748325	+	0.111295i
$903$	−8.20463			−0.273033
$904$	6.36485	−	19.5890i	0.211692	−	0.651520i
$905$	−25.6412	+	18.6294i	−0.852343	+	0.619264i
$906$	12.7553	+	9.26730i	0.423768	+	0.307885i
$907$	−6.67950	−	20.5574i	−0.221789	−	0.682596i	−0.998602	−	0.0528646i	$-0.983165\pi$
$907$	−6.67950	−	20.5574i	−0.221789	−	0.682596i	0.776813	−	0.629732i	$-0.216835\pi$
$908$	−5.18662	−	15.9628i	−0.172124	−	0.529744i
$909$	−3.53233	−	2.56639i	−0.117160	−	0.0851217i
$910$	7.14679	−	5.19244i	0.236914	−	0.172128i
$911$	−8.79436	+	27.0663i	−0.291370	+	0.896745i	0.693046	+	0.720893i	$0.256268\pi$
$911$	−8.79436	+	27.0663i	−0.291370	+	0.896745i	−0.984417	+	0.175852i	$0.943732\pi$
$912$	1.97054			0.0652510
$913$	31.4861	+	4.68278i	1.04204	+	0.154978i
$914$	20.9233			0.692080
$915$	0.744078	−	2.29004i	0.0245985	−	0.0757063i
$916$	−11.4993	+	8.35472i	−0.379947	+	0.276048i
$917$	5.67035	+	4.11975i	0.187251	+	0.136046i
$918$	−1.16251	−	3.57783i	−0.0383685	−	0.118086i
$919$	−11.9222	−	36.6929i	−0.393278	−	1.21039i	−0.930294	−	0.366814i	$-0.880449\pi$
$919$	−11.9222	−	36.6929i	−0.393278	−	1.21039i	0.537016	−	0.843572i	$-0.319551\pi$
$920$	−12.7949	−	9.29604i	−0.421835	−	0.306481i
$921$	22.0921	−	16.0509i	0.727960	−	0.528894i
$922$	−12.9516	+	39.8608i	−0.426537	+	1.31275i
$923$	53.1756			1.75030
$924$	−2.94079	+	1.53354i	−0.0967450	+	0.0504496i
$925$	−6.04052			−0.198611
$926$	4.01876	−	12.3685i	0.132065	−	0.406453i
$927$	8.48329	−	6.16347i	0.278628	−	0.202435i
$928$	−2.41696	−	1.75602i	−0.0793405	−	0.0576442i
$929$	−5.72435	−	17.6177i	−0.187810	−	0.578019i	0.812176	−	0.583413i	$-0.198283\pi$
$929$	−5.72435	−	17.6177i	−0.187810	−	0.578019i	−0.999985	+	0.00539398i	$0.998283\pi$
$930$	5.21925	+	16.0632i	0.171146	+	0.526733i
$931$	1.59420	+	1.15825i	0.0522477	+	0.0379602i
$932$	−15.9812	+	11.6111i	−0.523483	+	0.380333i
$933$	−4.28716	+	13.1945i	−0.140355	+	0.431969i
$934$	1.34247			0.0439270
$935$	4.28488	+	25.4942i	0.140131	+	0.833751i
$936$	4.26355			0.139359
$937$	−11.5070	+	35.4149i	−0.375917	+	1.15695i	0.566940	+	0.823759i	$0.308127\pi$
$937$	−11.5070	+	35.4149i	−0.375917	+	1.15695i	−0.942858	+	0.333196i	$0.891873\pi$
$938$	−11.3829	+	8.27013i	−0.371663	+	0.270029i
$939$	22.7487	+	16.5279i	0.742376	+	0.539368i
$940$	−0.251284	−	0.773372i	−0.00819597	−	0.0252246i
$941$	12.4014	+	38.1677i	0.404275	+	1.24423i	0.921499	+	0.388381i	$0.126966\pi$
$941$	12.4014	+	38.1677i	0.404275	+	1.24423i	−0.517223	+	0.855851i	$0.673034\pi$
$942$	−6.46894	−	4.69996i	−0.210769	−	0.153133i
$943$	−42.3061	+	30.7372i	−1.37768	+	1.00094i
$944$	−1.34036	+	4.12520i	−0.0436250	+	0.134264i
$945$	2.07196			0.0674009
$946$	19.4223	+	19.0591i	0.631472	+	0.619666i
$947$	25.2952			0.821984			0.410992	−	0.911639i	$-0.365182\pi$
$947$	25.2952			0.821984			0.410992	+	0.911639i	$0.365182\pi$
$948$	−3.27768	+	10.0876i	−0.106454	+	0.327632i
$949$	−24.2916	+	17.6489i	−0.788539	+	0.572907i
$950$	−1.12707	−	0.818863i	−0.0365669	−	0.0265674i
$951$	2.16104	+	6.65098i	0.0700764	+	0.215673i
$952$	−1.16251	−	3.57783i	−0.0376771	−	0.115958i
$953$	−2.70786	−	1.96737i	−0.0877160	−	0.0637294i	0.543063	−	0.839692i	$-0.317265\pi$
$953$	−2.70786	−	1.96737i	−0.0877160	−	0.0637294i	−0.630779	+	0.775963i	$0.717265\pi$
$954$	7.52875	−	5.46996i	0.243752	−	0.177096i
$955$	2.50907	−	7.72212i	0.0811916	−	0.249882i
$956$	11.9273			0.385756
$957$	−4.41485	+	8.87059i	−0.142712	+	0.286745i
$958$	−40.8450			−1.31964
$959$	2.13055	−	6.55717i	0.0687992	−	0.211742i
$960$	1.67625	−	1.21787i	0.0541008	−	0.0393065i
$961$	−28.6789	−	20.8365i	−0.925126	−	0.672144i
$962$	11.2569	+	34.6453i	0.362938	+	1.11701i
$963$	−1.84500	−	5.67832i	−0.0594542	−	0.182981i
$964$	23.1873	+	16.8466i	0.746813	+	0.542591i
$965$	9.12880	−	6.63246i	0.293866	−	0.213506i
$966$	2.35874	−	7.25946i	0.0758912	−	0.233569i
$967$	−42.6839			−1.37262			−0.686310	−	0.727309i	$-0.740771\pi$
$967$	−42.6839			−1.37262			−0.686310	+	0.727309i	$0.740771\pi$
$968$	10.5239	+	3.20115i	0.338251	+	0.102889i
$969$	7.41307			0.238142
$970$	4.60746	−	14.1803i	0.147937	−	0.455302i
$971$	39.4168	−	28.6379i	1.26494	−	0.919036i	0.265955	−	0.963986i	$-0.414313\pi$
$971$	39.4168	−	28.6379i	1.26494	−	0.919036i	0.998989	+	0.0449500i	$0.0143128\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−3.69910	−	11.3847i	−0.118588	−	0.364975i
$974$	−4.50147	−	13.8541i	−0.144236	−	0.443914i
$975$	−2.43858	−	1.77173i	−0.0780972	−	0.0567409i
$976$	0.940183	−	0.683083i	0.0300945	−	0.0218650i
$977$	0.00286657	−	0.00882239i	9.17097e−5	−	0.000282253i	−0.951011	−	0.309158i	$-0.899953\pi$
$977$	0.00286657	−	0.00882239i	9.17097e−5	−	0.000282253i	0.951102	+	0.308876i	$0.0999528\pi$
$978$	13.4164			0.429009
$979$	−4.34913	+	8.73854i	−0.138999	+	0.279285i
$980$	2.07196			0.0661863
$981$	1.94830	−	5.99625i	0.0622044	−	0.191445i
$982$	−3.00816	+	2.18556i	−0.0959942	+	0.0697439i
$983$	−11.1366	−	8.09123i	−0.355203	−	0.258070i	0.395845	−	0.918317i	$-0.370452\pi$
$983$	−11.1366	−	8.09123i	−0.355203	−	0.258070i	−0.751049	+	0.660247i	$0.770452\pi$
$984$	−2.11705	−	6.51559i	−0.0674889	−	0.207710i
$985$	0.253389	+	0.779852i	0.00807365	+	0.0248481i
$986$	−9.09248	−	6.60607i	−0.289564	−	0.210380i
$987$	0.317511	−	0.230685i	0.0101065	−	0.00734279i
$988$	−2.59620	+	7.99029i	−0.0825962	+	0.254205i
$989$	−62.6263			−1.99140
$990$	−4.90481	−	4.81311i	−0.155885	−	0.152971i
$991$	8.60390			0.273312			0.136656	−	0.990619i	$-0.456365\pi$
$991$	8.60390			0.273312			0.136656	+	0.990619i	$0.456365\pi$
$992$	−2.51899	+	7.75266i	−0.0799781	+	0.246147i
$993$	3.48626	−	2.53291i	0.110633	−	0.0803796i
$994$	10.0902	+	7.33094i	0.320041	+	0.232523i
$995$	−3.77175	−	11.6082i	−0.119572	−	0.368006i
$996$	−2.96590	−	9.12809i	−0.0939781	−	0.289235i
$997$	−32.4364	−	23.5664i	−1.02727	−	0.746356i	−0.0595102	−	0.998228i	$-0.518954\pi$
$997$	−32.4364	−	23.5664i	−1.02727	−	0.746356i	−0.967761	+	0.251872i	$0.918954\pi$
$998$	−25.6369	+	18.6263i	−0.811523	+	0.589606i
$999$	−2.64027	+	8.12592i	−0.0835345	+	0.257093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.f.295.2	✓	8
11.4	even	5		5082.2.a.cc.1.3		4
11.5	even	5	inner	462.2.j.f.379.2	yes	8
11.7	odd	10		5082.2.a.bx.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.f.295.2	✓	8	1.1	even	1	trivial
462.2.j.f.379.2	yes	8	11.5	even	5	inner
5082.2.a.bx.1.3		4	11.7	odd	10
5082.2.a.cc.1.3		4	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.640271 + 1.97055i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.640271 + 1.97055i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.07196 q^{10} +(1.47776 - 2.96921i) q^{11} -1.00000 q^{12} +(1.31751 - 4.05488i) q^{13} +(0.809017 - 0.587785i) q^{14} +(1.67625 + 1.21787i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.16251 + 3.57783i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(1.59420 - 1.15825i) q^{19} +(0.640271 - 1.97055i) q^{20} +1.00000 q^{21} +(-2.36723 - 2.32297i) q^{22} +7.63304 q^{23} +(-0.309017 + 0.951057i) q^{24} +(0.571960 - 0.415553i) q^{25} +(-3.44929 - 2.50605i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-2.41696 - 1.75602i) q^{29} +(1.67625 - 1.21787i) q^{30} +(-2.51899 + 7.75266i) q^{31} +1.00000 q^{32} +(-0.549723 - 3.27075i) q^{33} +3.76195 q^{34} +(-0.640271 + 1.97055i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-6.91232 - 5.02209i) q^{37} +(-0.608929 - 1.87409i) q^{38} +(-1.31751 - 4.05488i) q^{39} +(-1.67625 - 1.21787i) q^{40} +(-5.54250 + 4.02686i) q^{41} +(0.309017 - 0.951057i) q^{42} -8.20463 q^{43} +(-2.94079 + 1.53354i) q^{44} +2.07196 q^{45} +(2.35874 - 7.25946i) q^{46} +(0.317511 - 0.230685i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.218469 - 0.672379i) q^{50} +(3.04348 + 2.21122i) q^{51} +(-3.44929 + 2.50605i) q^{52} +(-2.87573 + 8.85058i) q^{53} -1.00000 q^{54} +(6.79715 + 1.01091i) q^{55} -1.00000 q^{56} +(0.608929 - 1.87409i) q^{57} +(-2.41696 + 1.75602i) q^{58} +(3.50910 + 2.54951i) q^{59} +(-0.640271 - 1.97055i) q^{60} +(-0.359118 - 1.10525i) q^{61} +(6.59481 + 4.79141i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} +8.83391 q^{65} +(-3.28054 - 0.487899i) q^{66} -14.0700 q^{67} +(1.16251 - 3.57783i) q^{68} +(6.17526 - 4.48659i) q^{69} +(1.67625 + 1.21787i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-5.69750 - 4.13948i) q^{73} +(-6.91232 + 5.02209i) q^{74} +(0.218469 - 0.672379i) q^{75} -1.97054 q^{76} +(2.94079 - 1.53354i) q^{77} -4.26355 q^{78} +(3.27768 - 10.0876i) q^{79} +(-1.67625 + 1.21787i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.11705 + 6.51559i) q^{82} +(2.96590 + 9.12809i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(-6.30598 + 4.58156i) q^{85} +(-2.53537 + 7.80306i) q^{86} -2.98752 q^{87} +(0.549723 + 3.27075i) q^{88} -2.94305 q^{89} +(0.640271 - 1.97055i) q^{90} +(3.44929 - 2.50605i) q^{91} +(-6.17526 - 4.48659i) q^{92} +(2.51899 + 7.75266i) q^{93} +(-0.121278 - 0.373256i) q^{94} +(3.30311 + 2.39985i) q^{95} +(0.809017 - 0.587785i) q^{96} +(2.22372 - 6.84390i) q^{97} +1.00000 q^{98} +(-2.36723 - 2.32297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

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