LMFDB - Embedded newform 462.2.j.d.295.1

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			295.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	462.295
Dual form			462.2.j.d.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.190983 - 0.587785i) 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} +0.618034 q^{10} +(0.309017 - 3.30220i) q^{11} -1.00000 q^{12} +(0.618034 - 1.90211i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.118034 + 0.363271i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.92705 - 2.85317i) q^{19} +(-0.190983 + 0.587785i) q^{20} -1.00000 q^{21} +(3.04508 + 1.31433i) q^{22} -4.85410 q^{23} +(0.309017 - 0.951057i) q^{24} +(3.73607 - 2.71441i) q^{25} +(1.61803 + 1.17557i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.309017 + 0.951057i) q^{28} +(2.00000 + 1.45309i) q^{29} +(0.500000 - 0.363271i) q^{30} +(1.42705 - 4.39201i) q^{31} -1.00000 q^{32} +(-1.69098 - 2.85317i) q^{33} -0.381966 q^{34} +(-0.190983 + 0.587785i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.11803 - 2.26538i) q^{37} +(1.50000 + 4.61653i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(-0.500000 - 0.363271i) q^{40} +(-2.11803 + 1.53884i) q^{41} +(0.309017 - 0.951057i) q^{42} +10.0000 q^{43} +(-2.19098 + 2.48990i) q^{44} -0.618034 q^{45} +(1.50000 - 4.61653i) q^{46} +(-5.23607 + 3.80423i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.42705 + 4.39201i) q^{50} +(0.309017 + 0.224514i) q^{51} +(-1.61803 + 1.17557i) q^{52} +(0.145898 - 0.449028i) q^{53} +1.00000 q^{54} +(-2.00000 + 0.449028i) q^{55} -1.00000 q^{56} +(1.50000 - 4.61653i) q^{57} +(-2.00000 + 1.45309i) q^{58} +(4.23607 + 3.07768i) q^{59} +(0.190983 + 0.587785i) q^{60} +(3.76393 + 11.5842i) q^{61} +(3.73607 + 2.71441i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.23607 q^{65} +(3.23607 - 0.726543i) q^{66} -12.1803 q^{67} +(0.118034 - 0.363271i) q^{68} +(-3.92705 + 2.85317i) q^{69} +(-0.500000 - 0.363271i) q^{70} +(2.00000 + 6.15537i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(8.23607 + 5.98385i) q^{73} +(3.11803 - 2.26538i) q^{74} +(1.42705 - 4.39201i) q^{75} -4.85410 q^{76} +(-2.19098 + 2.48990i) q^{77} +2.00000 q^{78} +(4.47214 - 13.7638i) q^{79} +(0.500000 - 0.363271i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.809017 - 2.48990i) q^{82} +(0.854102 + 2.62866i) q^{83} +(0.809017 + 0.587785i) q^{84} +(0.190983 - 0.138757i) q^{85} +(-3.09017 + 9.51057i) q^{86} +2.47214 q^{87} +(-1.69098 - 2.85317i) q^{88} -15.7984 q^{89} +(0.190983 - 0.587785i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(3.92705 + 2.85317i) q^{92} +(-1.42705 - 4.39201i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(-2.42705 - 1.76336i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-3.14590 + 9.68208i) q^{97} -1.00000 q^{98} +(-3.04508 - 1.31433i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	0.899226	−	0.437485i	$-0.144131\pi$
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	−0.984636	+	0.174619i	$0.944131\pi$
$6$	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
$10$	0.618034			0.195440
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−1.00000			−0.288675
$13$	0.618034	−	1.90211i	0.171412	−	0.527551i	−0.828040	−	0.560670i	$-0.810544\pi$
$13$	0.618034	−	1.90211i	0.171412	−	0.527551i	0.999451	+	0.0331183i	$0.0105438\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	−0.500000	−	0.363271i	−0.129099	−	0.0937962i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.118034	+	0.363271i	0.0286274	+	0.0881062i	0.964349	−	0.264632i	$-0.0852506\pi$
$17$	0.118034	+	0.363271i	0.0286274	+	0.0881062i	−0.935722	+	0.352738i	$0.885251\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	3.92705	−	2.85317i	0.900927	−	0.654562i	−0.0377767	−	0.999286i	$-0.512028\pi$
$19$	3.92705	−	2.85317i	0.900927	−	0.654562i	0.938704	+	0.344724i	$0.112028\pi$
$20$	−0.190983	+	0.587785i	−0.0427051	+	0.131433i
$21$	−1.00000			−0.218218
$22$	3.04508	+	1.31433i	0.649214	+	0.280216i
$23$	−4.85410			−1.01215			−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410			−1.01215			−0.506075	+	0.862489i	$0.668904\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	3.73607	−	2.71441i	0.747214	−	0.542882i
$26$	1.61803	+	1.17557i	0.317323	+	0.230548i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.309017	+	0.951057i	0.0583987	+	0.179733i
$29$	2.00000	+	1.45309i	0.371391	+	0.269831i	0.757787	−	0.652502i	$-0.226280\pi$
$29$	2.00000	+	1.45309i	0.371391	+	0.269831i	−0.386397	+	0.922333i	$0.626280\pi$
$30$	0.500000	−	0.363271i	0.0912871	−	0.0663240i
$31$	1.42705	−	4.39201i	0.256306	−	0.788829i	−0.737264	−	0.675605i	$-0.763882\pi$
$31$	1.42705	−	4.39201i	0.256306	−	0.788829i	0.993570	−	0.113223i	$-0.0361176\pi$
$32$	−1.00000			−0.176777
$33$	−1.69098	−	2.85317i	−0.294362	−	0.496673i
$34$	−0.381966			−0.0655066
$35$	−0.190983	+	0.587785i	−0.0322820	+	0.0993538i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−3.11803	−	2.26538i	−0.512602	−	0.372427i	0.301208	−	0.953558i	$-0.402610\pi$
$37$	−3.11803	−	2.26538i	−0.512602	−	0.372427i	−0.813810	+	0.581132i	$0.802610\pi$
$38$	1.50000	+	4.61653i	0.243332	+	0.748899i
$39$	−0.618034	−	1.90211i	−0.0989646	−	0.304582i
$40$	−0.500000	−	0.363271i	−0.0790569	−	0.0574382i
$41$	−2.11803	+	1.53884i	−0.330781	+	0.240327i	−0.740762	−	0.671767i	$-0.765535\pi$
$41$	−2.11803	+	1.53884i	−0.330781	+	0.240327i	0.409981	+	0.912094i	$0.365535\pi$
$42$	0.309017	−	0.951057i	0.0476824	−	0.146751i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−2.19098	+	2.48990i	−0.330303	+	0.375366i
$45$	−0.618034			−0.0921311
$46$	1.50000	−	4.61653i	0.221163	−	0.680670i
$47$	−5.23607	+	3.80423i	−0.763759	+	0.554903i	−0.900061	−	0.435764i	$-0.856478\pi$
$47$	−5.23607	+	3.80423i	−0.763759	+	0.554903i	0.136302	+	0.990667i	$0.456478\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.42705	+	4.39201i	0.201815	+	0.621124i
$51$	0.309017	+	0.224514i	0.0432710	+	0.0314382i
$52$	−1.61803	+	1.17557i	−0.224381	+	0.163022i
$53$	0.145898	−	0.449028i	0.0200406	−	0.0616787i	−0.940536	−	0.339694i	$-0.889677\pi$
$53$	0.145898	−	0.449028i	0.0200406	−	0.0616787i	0.960577	+	0.278015i	$0.0896765\pi$
$54$	1.00000			0.136083
$55$	−2.00000	+	0.449028i	−0.269680	+	0.0605469i
$56$	−1.00000			−0.133631
$57$	1.50000	−	4.61653i	0.198680	−	0.611474i
$58$	−2.00000	+	1.45309i	−0.262613	+	0.190799i
$59$	4.23607	+	3.07768i	0.551489	+	0.400680i	0.828334	−	0.560234i	$-0.189289\pi$
$59$	4.23607	+	3.07768i	0.551489	+	0.400680i	−0.276845	+	0.960915i	$0.589289\pi$
$60$	0.190983	+	0.587785i	0.0246558	+	0.0758827i
$61$	3.76393	+	11.5842i	0.481922	+	1.48320i	0.836390	+	0.548135i	$0.184662\pi$
$61$	3.76393	+	11.5842i	0.481922	+	1.48320i	−0.354467	+	0.935068i	$0.615338\pi$
$62$	3.73607	+	2.71441i	0.474481	+	0.344731i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.23607			−0.153315
$66$	3.23607	−	0.726543i	0.398332	−	0.0894312i
$67$	−12.1803			−1.48807			−0.744033	−	0.668143i	$-0.767089\pi$
$67$	−12.1803			−1.48807			−0.744033	+	0.668143i	$0.767089\pi$
$68$	0.118034	−	0.363271i	0.0143137	−	0.0440531i
$69$	−3.92705	+	2.85317i	−0.472761	+	0.343481i
$70$	−0.500000	−	0.363271i	−0.0597614	−	0.0434192i
$71$	2.00000	+	6.15537i	0.237356	+	0.730508i	0.996800	+	0.0799347i	$0.0254712\pi$
$71$	2.00000	+	6.15537i	0.237356	+	0.730508i	−0.759444	+	0.650573i	$0.774529\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	8.23607	+	5.98385i	0.963959	+	0.700357i	0.954067	−	0.299594i	$-0.0968512\pi$
$73$	8.23607	+	5.98385i	0.963959	+	0.700357i	0.00989205	+	0.999951i	$0.496851\pi$
$74$	3.11803	−	2.26538i	0.362464	−	0.263346i
$75$	1.42705	−	4.39201i	0.164782	−	0.507146i
$76$	−4.85410			−0.556804
$77$	−2.19098	+	2.48990i	−0.249686	+	0.283750i
$78$	2.00000			0.226455
$79$	4.47214	−	13.7638i	0.503155	−	1.54855i	−0.300696	−	0.953720i	$-0.597219\pi$
$79$	4.47214	−	13.7638i	0.503155	−	1.54855i	0.803851	−	0.594831i	$-0.202781\pi$
$80$	0.500000	−	0.363271i	0.0559017	−	0.0406150i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.809017	−	2.48990i	−0.0893410	−	0.274963i
$83$	0.854102	+	2.62866i	0.0937499	+	0.288532i	0.986926	−	0.161175i	$-0.0515283\pi$
$83$	0.854102	+	2.62866i	0.0937499	+	0.288532i	−0.893176	+	0.449707i	$0.851528\pi$
$84$	0.809017	+	0.587785i	0.0882710	+	0.0641326i
$85$	0.190983	−	0.138757i	0.0207150	−	0.0150503i
$86$	−3.09017	+	9.51057i	−0.333222	+	1.02555i
$87$	2.47214			0.265041
$88$	−1.69098	−	2.85317i	−0.180259	−	0.304149i
$89$	−15.7984			−1.67462			−0.837312	−	0.546725i	$-0.815874\pi$
$89$	−15.7984			−1.67462			−0.837312	+	0.546725i	$0.815874\pi$
$90$	0.190983	−	0.587785i	0.0201314	−	0.0619580i
$91$	−1.61803	+	1.17557i	−0.169616	+	0.123233i
$92$	3.92705	+	2.85317i	0.409423	+	0.297463i
$93$	−1.42705	−	4.39201i	−0.147978	−	0.455430i
$94$	−2.00000	−	6.15537i	−0.206284	−	0.634878i
$95$	−2.42705	−	1.76336i	−0.249010	−	0.180916i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−3.14590	+	9.68208i	−0.319418	+	0.983066i	0.654480	+	0.756079i	$0.272887\pi$
$97$	−3.14590	+	9.68208i	−0.319418	+	0.983066i	−0.973898	+	0.226987i	$0.927113\pi$
$98$	−1.00000			−0.101015
$99$	−3.04508	−	1.31433i	−0.306043	−	0.132095i
$100$	−4.61803			−0.461803
$101$	−3.51722	+	10.8249i	−0.349977	+	1.07712i	0.608889	+	0.793256i	$0.291616\pi$
$101$	−3.51722	+	10.8249i	−0.349977	+	1.07712i	−0.958865	+	0.283861i	$0.908384\pi$
$102$	−0.309017	+	0.224514i	−0.0305972	+	0.0222302i
$103$	−6.92705	−	5.03280i	−0.682543	−	0.495896i	0.191658	−	0.981462i	$-0.438614\pi$
$103$	−6.92705	−	5.03280i	−0.682543	−	0.495896i	−0.874200	+	0.485566i	$0.838614\pi$
$104$	−0.618034	−	1.90211i	−0.0606032	−	0.186518i
$105$	0.190983	+	0.587785i	0.0186380	+	0.0573620i
$106$	0.381966	+	0.277515i	0.0370998	+	0.0269546i
$107$	−0.927051	+	0.673542i	−0.0896214	+	0.0651138i	−0.631694	−	0.775218i	$-0.717640\pi$
$107$	−0.927051	+	0.673542i	−0.0896214	+	0.0651138i	0.542072	+	0.840332i	$0.317640\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	4.14590			0.397105			0.198553	−	0.980090i	$-0.436376\pi$
$109$	4.14590			0.397105			0.198553	+	0.980090i	$0.436376\pi$
$110$	0.190983	−	2.04087i	0.0182095	−	0.194589i
$111$	−3.85410			−0.365815
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	9.32624	−	6.77591i	0.877339	−	0.637424i	−0.0552074	−	0.998475i	$-0.517582\pi$
$113$	9.32624	−	6.77591i	0.877339	−	0.637424i	0.932546	+	0.361051i	$0.117582\pi$
$114$	3.92705	+	2.85317i	0.367802	+	0.267224i
$115$	0.927051	+	2.85317i	0.0864479	+	0.266059i
$116$	−0.763932	−	2.35114i	−0.0709293	−	0.218298i
$117$	−1.61803	−	1.17557i	−0.149587	−	0.108682i
$118$	−4.23607	+	3.07768i	−0.389962	+	0.283324i
$119$	0.118034	−	0.363271i	0.0108202	−	0.0333010i
$120$	−0.618034			−0.0564185
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−12.1803			−1.10276
$123$	−0.809017	+	2.48990i	−0.0729466	+	0.224507i
$124$	−3.73607	+	2.71441i	−0.335509	+	0.243761i
$125$	−4.80902	−	3.49396i	−0.430132	−	0.312509i
$126$	−0.309017	−	0.951057i	−0.0275294	−	0.0847268i
$127$	1.52786	+	4.70228i	0.135576	+	0.417260i	0.995679	−	0.0928601i	$-0.0296009\pi$
$127$	1.52786	+	4.70228i	0.135576	+	0.417260i	−0.860103	+	0.510120i	$0.829601\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	8.09017	−	5.87785i	0.712300	−	0.517516i
$130$	0.381966	−	1.17557i	0.0335006	−	0.103104i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−0.309017	+	3.30220i	−0.0268965	+	0.287419i
$133$	−4.85410			−0.420904
$134$	3.76393	−	11.5842i	0.325154	−	1.00072i
$135$	−0.500000	+	0.363271i	−0.0430331	+	0.0312654i
$136$	0.309017	+	0.224514i	0.0264980	+	0.0192519i
$137$	1.61803	+	4.97980i	0.138238	+	0.425453i	0.996080	−	0.0884614i	$-0.0281950\pi$
$137$	1.61803	+	4.97980i	0.138238	+	0.425453i	−0.857842	+	0.513914i	$0.828195\pi$
$138$	−1.50000	−	4.61653i	−0.127688	−	0.392985i
$139$	1.30902	+	0.951057i	0.111029	+	0.0806676i	0.641914	−	0.766776i	$-0.278140\pi$
$139$	1.30902	+	0.951057i	0.111029	+	0.0806676i	−0.530885	+	0.847444i	$0.678140\pi$
$140$	0.500000	−	0.363271i	0.0422577	−	0.0307020i
$141$	−2.00000	+	6.15537i	−0.168430	+	0.518375i
$142$	−6.47214			−0.543130
$143$	−6.09017	−	2.62866i	−0.509286	−	0.219819i
$144$	1.00000			0.0833333
$145$	0.472136	−	1.45309i	0.0392088	−	0.120672i
$146$	−8.23607	+	5.98385i	−0.681622	+	0.495227i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	1.19098	+	3.66547i	0.0978982	+	0.301300i
$149$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$149$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$150$	3.73607	+	2.71441i	0.305049	+	0.221631i
$151$	−5.85410	+	4.25325i	−0.476400	+	0.346125i	−0.799930	−	0.600093i	$-0.795130\pi$
$151$	−5.85410	+	4.25325i	−0.476400	+	0.346125i	0.323530	+	0.946218i	$0.395130\pi$
$152$	1.50000	−	4.61653i	0.121666	−	0.374450i
$153$	0.381966			0.0308801
$154$	−1.69098	−	2.85317i	−0.136263	−	0.229915i
$155$	−2.85410			−0.229247
$156$	−0.618034	+	1.90211i	−0.0494823	+	0.152291i
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	−0.701028	−	0.713134i	$-0.747275\pi$
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	0.461601	+	0.887087i	$0.347275\pi$
$158$	11.7082	+	8.50651i	0.931455	+	0.676741i
$159$	−0.145898	−	0.449028i	−0.0115705	−	0.0356102i
$160$	0.190983	+	0.587785i	0.0150985	+	0.0464685i
$161$	3.92705	+	2.85317i	0.309495	+	0.224861i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	3.09017	−	9.51057i	0.242041	−	0.744925i	−0.754068	−	0.656796i	$-0.771911\pi$
$163$	3.09017	−	9.51057i	0.242041	−	0.744925i	0.996109	−	0.0881289i	$-0.0280887\pi$
$164$	2.61803			0.204434
$165$	−1.35410	+	1.53884i	−0.105417	+	0.119799i
$166$	−2.76393			−0.214523
$167$	3.94427	−	12.1392i	0.305217	−	0.939361i	−0.674379	−	0.738385i	$-0.735589\pi$
$167$	3.94427	−	12.1392i	0.305217	−	0.939361i	0.979596	−	0.200976i	$-0.0644113\pi$
$168$	−0.809017	+	0.587785i	−0.0624170	+	0.0453486i
$169$	7.28115	+	5.29007i	0.560089	+	0.406928i
$170$	0.0729490	+	0.224514i	0.00559493	+	0.0172194i
$171$	−1.50000	−	4.61653i	−0.114708	−	0.353035i
$172$	−8.09017	−	5.87785i	−0.616870	−	0.448182i
$173$	−15.1631	+	11.0167i	−1.15283	+	0.837580i	−0.988855	−	0.148884i	$-0.952432\pi$
$173$	−15.1631	+	11.0167i	−1.15283	+	0.837580i	−0.163976	+	0.986464i	$0.552432\pi$
$174$	−0.763932	+	2.35114i	−0.0579135	+	0.178240i
$175$	−4.61803			−0.349091
$176$	3.23607	−	0.726543i	0.243928	−	0.0547652i
$177$	5.23607			0.393567
$178$	4.88197	−	15.0251i	0.365919	−	1.12618i
$179$	12.9721	−	9.42481i	0.969583	−	0.704443i	0.0142265	−	0.999899i	$-0.495471\pi$
$179$	12.9721	−	9.42481i	0.969583	−	0.704443i	0.955356	+	0.295456i	$0.0954714\pi$
$180$	0.500000	+	0.363271i	0.0372678	+	0.0270766i
$181$	5.47214	+	16.8415i	0.406741	+	1.25182i	0.919433	+	0.393247i	$0.128648\pi$
$181$	5.47214	+	16.8415i	0.406741	+	1.25182i	−0.512692	+	0.858572i	$0.671352\pi$
$182$	−0.618034	−	1.90211i	−0.0458117	−	0.140994i
$183$	9.85410	+	7.15942i	0.728436	+	0.529240i
$184$	−3.92705	+	2.85317i	−0.289506	+	0.210338i
$185$	−0.736068	+	2.26538i	−0.0541168	+	0.166554i
$186$	4.61803			0.338611
$187$	1.23607	−	0.277515i	0.0903902	−	0.0202939i
$188$	6.47214			0.472029
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	2.42705	−	1.76336i	0.176077	−	0.127927i
$191$	11.8262	+	8.59226i	0.855717	+	0.621714i	0.926716	−	0.375762i	$-0.122619\pi$
$191$	11.8262	+	8.59226i	0.855717	+	0.621714i	−0.0709997	+	0.997476i	$0.522619\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	5.60739	+	17.2578i	0.403629	+	1.24224i	0.922035	+	0.387107i	$0.126526\pi$
$193$	5.60739	+	17.2578i	0.403629	+	1.24224i	−0.518406	+	0.855135i	$0.673474\pi$
$194$	−8.23607	−	5.98385i	−0.591315	−	0.429616i
$195$	−1.00000	+	0.726543i	−0.0716115	+	0.0520288i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	20.1803			1.43779			0.718895	−	0.695119i	$-0.244648\pi$
$197$	20.1803			1.43779			0.718895	+	0.695119i	$0.244648\pi$
$198$	2.19098	−	2.48990i	0.155706	−	0.176949i
$199$	4.38197			0.310629			0.155315	−	0.987865i	$-0.450361\pi$
$199$	4.38197			0.310629			0.155315	+	0.987865i	$0.450361\pi$
$200$	1.42705	−	4.39201i	0.100908	−	0.310562i
$201$	−9.85410	+	7.15942i	−0.695055	+	0.504987i
$202$	−9.20820	−	6.69015i	−0.647887	−	0.470717i
$203$	−0.763932	−	2.35114i	−0.0536175	−	0.165018i
$204$	−0.118034	−	0.363271i	−0.00826403	−	0.0254341i
$205$	1.30902	+	0.951057i	0.0914257	+	0.0664247i
$206$	6.92705	−	5.03280i	0.482631	−	0.350652i
$207$	−1.50000	+	4.61653i	−0.104257	+	0.320871i
$208$	2.00000			0.138675
$209$	−8.20820	−	13.8496i	−0.567773	−	0.957995i
$210$	−0.618034			−0.0426484
$211$	6.38197	−	19.6417i	0.439353	−	1.35219i	−0.449207	−	0.893428i	$-0.648293\pi$
$211$	6.38197	−	19.6417i	0.439353	−	1.35219i	0.888560	−	0.458761i	$-0.151707\pi$
$212$	−0.381966	+	0.277515i	−0.0262335	+	0.0190598i
$213$	5.23607	+	3.80423i	0.358769	+	0.260661i
$214$	−0.354102	−	1.08981i	−0.0242059	−	0.0744981i
$215$	−1.90983	−	5.87785i	−0.130249	−	0.400866i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−3.73607	+	2.71441i	−0.253621	+	0.184266i
$218$	−1.28115	+	3.94298i	−0.0867706	+	0.267053i
$219$	10.1803			0.687924
$220$	1.88197	+	0.812299i	0.126882	+	0.0547652i
$221$	0.763932			0.0513876
$222$	1.19098	−	3.66547i	0.0799335	−	0.246010i
$223$	3.69098	−	2.68166i	0.247167	−	0.179577i	−0.457304	−	0.889311i	$-0.651185\pi$
$223$	3.69098	−	2.68166i	0.247167	−	0.179577i	0.704470	+	0.709734i	$0.251185\pi$
$224$	0.809017	+	0.587785i	0.0540547	+	0.0392731i
$225$	−1.42705	−	4.39201i	−0.0951367	−	0.292801i
$226$	3.56231	+	10.9637i	0.236961	+	0.729291i
$227$	5.85410	+	4.25325i	0.388550	+	0.282298i	0.764861	−	0.644195i	$-0.222808\pi$
$227$	5.85410	+	4.25325i	0.388550	+	0.282298i	−0.376311	+	0.926493i	$0.622808\pi$
$228$	−3.92705	+	2.85317i	−0.260075	+	0.188956i
$229$	−1.23607	+	3.80423i	−0.0816817	+	0.251390i	−0.983555	−	0.180611i	$-0.942192\pi$
$229$	−1.23607	+	3.80423i	−0.0816817	+	0.251390i	0.901873	+	0.432001i	$0.142192\pi$
$230$	−3.00000			−0.197814
$231$	−0.309017	+	3.30220i	−0.0203318	+	0.217269i
$232$	2.47214			0.162304
$233$	0.236068	−	0.726543i	0.0154653	−	0.0475974i	−0.943026	−	0.332719i	$-0.892034\pi$
$233$	0.236068	−	0.726543i	0.0154653	−	0.0475974i	0.958491	+	0.285122i	$0.0920340\pi$
$234$	1.61803	−	1.17557i	0.105774	−	0.0768494i
$235$	3.23607	+	2.35114i	0.211098	+	0.153372i
$236$	−1.61803	−	4.97980i	−0.105325	−	0.324157i
$237$	−4.47214	−	13.7638i	−0.290496	−	0.894056i
$238$	0.309017	+	0.224514i	0.0200306	+	0.0145531i
$239$	20.8713	−	15.1639i	1.35005	−	0.980871i	0.351045	−	0.936359i	$-0.385826\pi$
$239$	20.8713	−	15.1639i	1.35005	−	0.980871i	0.999009	−	0.0445127i	$-0.0141735\pi$
$240$	0.190983	−	0.587785i	0.0123279	−	0.0379414i
$241$	29.1246			1.87608			0.938041	−	0.346525i	$-0.112639\pi$
$241$	29.1246			1.87608			0.938041	+	0.346525i	$0.112639\pi$
$242$	5.28115	−	9.64932i	0.339485	−	0.620282i
$243$	−1.00000			−0.0641500
$244$	3.76393	−	11.5842i	0.240961	−	0.741602i
$245$	0.500000	−	0.363271i	0.0319438	−	0.0232085i
$246$	−2.11803	−	1.53884i	−0.135041	−	0.0981130i
$247$	−3.00000	−	9.23305i	−0.190885	−	0.587485i
$248$	−1.42705	−	4.39201i	−0.0906178	−	0.278893i
$249$	2.23607	+	1.62460i	0.141705	+	0.102955i
$250$	4.80902	−	3.49396i	0.304149	−	0.220977i
$251$	7.56231	−	23.2744i	0.477329	−	1.46907i	−0.365463	−	0.930826i	$-0.619089\pi$
$251$	7.56231	−	23.2744i	0.477329	−	1.46907i	0.842791	−	0.538240i	$-0.180911\pi$
$252$	1.00000			0.0629941
$253$	−1.50000	+	16.0292i	−0.0943042	+	1.00775i
$254$	−4.94427			−0.310231
$255$	0.0729490	−	0.224514i	0.00456824	−	0.0140596i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.2533	+	8.17599i	0.701961	+	0.510004i	0.880570	−	0.473916i	$-0.157160\pi$
$257$	11.2533	+	8.17599i	0.701961	+	0.510004i	−0.178609	+	0.983920i	$0.557160\pi$
$258$	3.09017	+	9.51057i	0.192386	+	0.592102i
$259$	1.19098	+	3.66547i	0.0740041	+	0.227761i
$260$	1.00000	+	0.726543i	0.0620174	+	0.0450583i
$261$	2.00000	−	1.45309i	0.123797	−	0.0899437i
$262$		0			0
$263$	17.0344			1.05039			0.525194	−	0.850982i	$-0.323993\pi$
$263$	17.0344			1.05039			0.525194	+	0.850982i	$0.323993\pi$
$264$	−3.04508	−	1.31433i	−0.187412	−	0.0808913i
$265$	−0.291796			−0.0179249
$266$	1.50000	−	4.61653i	0.0919709	−	0.283057i
$267$	−12.7812	+	9.28605i	−0.782194	+	0.568297i
$268$	9.85410	+	7.15942i	0.601935	+	0.437331i
$269$	2.43769	+	7.50245i	0.148629	+	0.457433i	0.997460	−	0.0712319i	$-0.0226930\pi$
$269$	2.43769	+	7.50245i	0.148629	+	0.457433i	−0.848831	+	0.528664i	$0.822693\pi$
$270$	−0.190983	−	0.587785i	−0.0116229	−	0.0357715i
$271$	7.50000	+	5.44907i	0.455593	+	0.331007i	0.791800	−	0.610781i	$-0.209144\pi$
$271$	7.50000	+	5.44907i	0.455593	+	0.331007i	−0.336207	+	0.941788i	$0.609144\pi$
$272$	−0.309017	+	0.224514i	−0.0187369	+	0.0136132i
$273$	−0.618034	+	1.90211i	−0.0374051	+	0.115121i
$274$	−5.23607			−0.316322
$275$	−7.80902	−	13.1760i	−0.470901	−	0.794545i
$276$	4.85410			0.292183
$277$	−5.11803	+	15.7517i	−0.307513	+	0.946427i	0.671215	+	0.741263i	$0.265773\pi$
$277$	−5.11803	+	15.7517i	−0.307513	+	0.946427i	−0.978728	+	0.205164i	$0.934227\pi$
$278$	−1.30902	+	0.951057i	−0.0785096	+	0.0570406i
$279$	−3.73607	−	2.71441i	−0.223673	−	0.162508i
$280$	0.190983	+	0.587785i	0.0114134	+	0.0351269i
$281$	−7.14590	−	21.9928i	−0.426289	−	1.31198i	−0.901755	−	0.432247i	$-0.857721\pi$
$281$	−7.14590	−	21.9928i	−0.426289	−	1.31198i	0.475467	−	0.879734i	$-0.342279\pi$
$282$	−5.23607	−	3.80423i	−0.311803	−	0.226538i
$283$	−10.1180	+	7.35118i	−0.601455	+	0.436982i	−0.846395	−	0.532556i	$-0.821232\pi$
$283$	−10.1180	+	7.35118i	−0.601455	+	0.436982i	0.244940	+	0.969538i	$0.421232\pi$
$284$	2.00000	−	6.15537i	0.118678	−	0.365254i
$285$	−3.00000			−0.177705
$286$	4.38197	−	4.97980i	0.259111	−	0.294462i
$287$	2.61803			0.154538
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	13.6353	−	9.90659i	0.802074	−	0.582741i
$290$	1.23607	+	0.898056i	0.0725844	+	0.0527357i
$291$	3.14590	+	9.68208i	0.184416	+	0.567573i
$292$	−3.14590	−	9.68208i	−0.184100	−	0.566601i
$293$	−15.4443	−	11.2209i	−0.902264	−	0.655533i	0.0367825	−	0.999323i	$-0.488289\pi$
$293$	−15.4443	−	11.2209i	−0.902264	−	0.655533i	−0.939047	+	0.343790i	$0.888289\pi$
$294$	−0.809017	+	0.587785i	−0.0471828	+	0.0342803i
$295$	1.00000	−	3.07768i	0.0582223	−	0.179190i
$296$	−3.85410			−0.224015
$297$	−3.23607	+	0.726543i	−0.187776	+	0.0421583i
$298$		0			0
$299$	−3.00000	+	9.23305i	−0.173494	+	0.533961i
$300$	−3.73607	+	2.71441i	−0.215702	+	0.156717i
$301$	−8.09017	−	5.87785i	−0.466310	−	0.338794i
$302$	−2.23607	−	6.88191i	−0.128671	−	0.396009i
$303$	3.51722	+	10.8249i	0.202059	+	0.621874i
$304$	3.92705	+	2.85317i	0.225232	+	0.163640i
$305$	6.09017	−	4.42477i	0.348722	−	0.253361i
$306$	−0.118034	+	0.363271i	−0.00674755	+	0.0207668i
$307$	0.437694			0.0249805			0.0124903	−	0.999922i	$-0.496024\pi$
$307$	0.437694			0.0249805			0.0124903	+	0.999922i	$0.496024\pi$
$308$	3.23607	−	0.726543i	0.184392	−	0.0413986i
$309$	−8.56231			−0.487093
$310$	0.881966	−	2.71441i	0.0500923	−	0.154168i
$311$	−26.2705	+	19.0866i	−1.48966	+	1.08230i	−0.515385	+	0.856959i	$0.672351\pi$
$311$	−26.2705	+	19.0866i	−1.48966	+	1.08230i	−0.974279	+	0.225345i	$0.927649\pi$
$312$	−1.61803	−	1.17557i	−0.0916031	−	0.0665536i
$313$	5.47214	+	16.8415i	0.309303	+	0.951938i	0.978036	+	0.208435i	$0.0668370\pi$
$313$	5.47214	+	16.8415i	0.309303	+	0.951938i	−0.668733	+	0.743503i	$0.733163\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$	0.500000	+	0.363271i	0.0281718	+	0.0204680i
$316$	−11.7082	+	8.50651i	−0.658638	+	0.478528i
$317$	−4.14590	+	12.7598i	−0.232857	+	0.716660i	0.764542	+	0.644574i	$0.222965\pi$
$317$	−4.14590	+	12.7598i	−0.232857	+	0.716660i	−0.997398	+	0.0720853i	$0.977035\pi$
$318$	0.472136			0.0264761
$319$	5.41641	−	6.15537i	0.303261	−	0.344634i
$320$	−0.618034			−0.0345492
$321$	−0.354102	+	1.08981i	−0.0197640	+	0.0608275i
$322$	−3.92705	+	2.85317i	−0.218846	+	0.159001i
$323$	1.50000	+	1.08981i	0.0834622	+	0.0606389i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−2.85410	−	8.78402i	−0.158317	−	0.487250i
$326$	8.09017	+	5.87785i	0.448073	+	0.325544i
$327$	3.35410	−	2.43690i	0.185482	−	0.134761i
$328$	−0.809017	+	2.48990i	−0.0446705	+	0.137482i
$329$	6.47214			0.356820
$330$	−1.04508	−	1.76336i	−0.0575300	−	0.0970695i
$331$	2.76393			0.151919			0.0759597	−	0.997111i	$-0.475798\pi$
$331$	2.76393			0.151919			0.0759597	+	0.997111i	$0.475798\pi$
$332$	0.854102	−	2.62866i	0.0468749	−	0.144266i
$333$	−3.11803	+	2.26538i	−0.170867	+	0.124142i
$334$	10.3262	+	7.50245i	0.565027	+	0.410516i
$335$	2.32624	+	7.15942i	0.127096	+	0.391161i
$336$	−0.309017	−	0.951057i	−0.0168583	−	0.0518844i
$337$	−12.6803	−	9.21281i	−0.690742	−	0.501854i	0.186162	−	0.982519i	$-0.440395\pi$
$337$	−12.6803	−	9.21281i	−0.690742	−	0.501854i	−0.876904	+	0.480666i	$0.840395\pi$
$338$	−7.28115	+	5.29007i	−0.396043	+	0.287742i
$339$	3.56231	−	10.9637i	0.193478	−	0.595464i
$340$	−0.236068			−0.0128026
$341$	−14.0623	−	6.06961i	−0.761517	−	0.328688i
$342$	4.85410			0.262480
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	8.09017	−	5.87785i	0.436193	−	0.316913i
$345$	2.42705	+	1.76336i	0.130668	+	0.0949359i
$346$	−5.79180	−	17.8253i	−0.311369	−	0.958295i
$347$	0.843459	+	2.59590i	0.0452792	+	0.139355i	0.971140	−	0.238509i	$-0.0766586\pi$
$347$	0.843459	+	2.59590i	0.0452792	+	0.139355i	−0.925861	+	0.377864i	$0.876659\pi$
$348$	−2.00000	−	1.45309i	−0.107211	−	0.0778935i
$349$	−17.1803	+	12.4822i	−0.919643	+	0.668159i	−0.943435	−	0.331558i	$-0.892426\pi$
$349$	−17.1803	+	12.4822i	−0.919643	+	0.668159i	0.0237925	+	0.999717i	$0.492426\pi$
$350$	1.42705	−	4.39201i	0.0762791	−	0.234763i
$351$	−2.00000			−0.106752
$352$	−0.309017	+	3.30220i	−0.0164707	+	0.176008i
$353$	−11.8885			−0.632763			−0.316382	−	0.948632i	$-0.602468\pi$
$353$	−11.8885			−0.632763			−0.316382	+	0.948632i	$0.602468\pi$
$354$	−1.61803	+	4.97980i	−0.0859975	+	0.264673i
$355$	3.23607	−	2.35114i	0.171753	−	0.124786i
$356$	12.7812	+	9.28605i	0.677400	+	0.492160i
$357$	−0.118034	−	0.363271i	−0.00624702	−	0.0192264i
$358$	4.95492	+	15.2497i	0.261875	+	0.805970i
$359$	−28.0623	−	20.3885i	−1.48107	−	1.07606i	−0.977209	−	0.212278i	$-0.931912\pi$
$359$	−28.0623	−	20.3885i	−1.48107	−	1.07606i	−0.503863	−	0.863784i	$-0.668088\pi$
$360$	−0.500000	+	0.363271i	−0.0263523	+	0.0191461i
$361$	1.40983	−	4.33901i	0.0742016	−	0.228369i
$362$	−17.7082			−0.930723
$363$	−9.94427	+	4.70228i	−0.521939	+	0.246806i
$364$	2.00000			0.104828
$365$	1.94427	−	5.98385i	0.101768	−	0.313209i
$366$	−9.85410	+	7.15942i	−0.515082	+	0.374229i
$367$	−14.4443	−	10.4944i	−0.753985	−	0.547802i	0.143075	−	0.989712i	$-0.454301\pi$
$367$	−14.4443	−	10.4944i	−0.753985	−	0.547802i	−0.897059	+	0.441910i	$0.854301\pi$
$368$	−1.50000	−	4.61653i	−0.0781929	−	0.240653i
$369$	0.809017	+	2.48990i	0.0421157	+	0.129619i
$370$	−1.92705	−	1.40008i	−0.100183	−	0.0727869i
$371$	−0.381966	+	0.277515i	−0.0198307	+	0.0144078i
$372$	−1.42705	+	4.39201i	−0.0739891	+	0.227715i
$373$	−3.27051			−0.169341			−0.0846703	−	0.996409i	$-0.526984\pi$
$373$	−3.27051			−0.169341			−0.0846703	+	0.996409i	$0.526984\pi$
$374$	−0.118034	+	1.26133i	−0.00610339	+	0.0652217i
$375$	−5.94427			−0.306961
$376$	−2.00000	+	6.15537i	−0.103142	+	0.317439i
$377$	4.00000	−	2.90617i	0.206010	−	0.149675i
$378$	−0.809017	−	0.587785i	−0.0416113	−	0.0302324i
$379$	2.90983	+	8.95554i	0.149468	+	0.460015i	0.997558	−	0.0698364i	$-0.0222477\pi$
$379$	2.90983	+	8.95554i	0.149468	+	0.460015i	−0.848091	+	0.529851i	$0.822248\pi$
$380$	0.927051	+	2.85317i	0.0475567	+	0.146365i
$381$	4.00000	+	2.90617i	0.204926	+	0.148888i
$382$	−11.8262	+	8.59226i	−0.605083	+	0.439619i
$383$	7.38197	−	22.7194i	0.377201	−	1.16090i	−0.564781	−	0.825241i	$-0.691039\pi$
$383$	7.38197	−	22.7194i	0.377201	−	1.16090i	0.941982	−	0.335664i	$-0.108961\pi$
$384$	1.00000			0.0510310
$385$	1.88197	+	0.812299i	0.0959139	+	0.0413986i
$386$	−18.1459			−0.923602
$387$	3.09017	−	9.51057i	0.157082	−	0.483449i
$388$	8.23607	−	5.98385i	0.418123	−	0.303784i
$389$	−1.14590	−	0.832544i	−0.0580993	−	0.0422116i	0.558357	−	0.829601i	$-0.311432\pi$
$389$	−1.14590	−	0.832544i	−0.0580993	−	0.0422116i	−0.616456	+	0.787389i	$0.711432\pi$
$390$	−0.381966	−	1.17557i	−0.0193416	−	0.0595273i
$391$	−0.572949	−	1.76336i	−0.0289753	−	0.0891767i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$		0			0
$394$	−6.23607	+	19.1926i	−0.314169	+	0.966911i
$395$	−8.94427			−0.450035
$396$	1.69098	+	2.85317i	0.0849751	+	0.143377i
$397$	−25.4164			−1.27561			−0.637806	−	0.770197i	$-0.720158\pi$
$397$	−25.4164			−1.27561			−0.637806	+	0.770197i	$0.720158\pi$
$398$	−1.35410	+	4.16750i	−0.0678750	+	0.208898i
$399$	−3.92705	+	2.85317i	−0.196598	+	0.142837i
$400$	3.73607	+	2.71441i	0.186803	+	0.135721i
$401$	4.81966	+	14.8334i	0.240682	+	0.740744i	0.996317	+	0.0857504i	$0.0273287\pi$
$401$	4.81966	+	14.8334i	0.240682	+	0.740744i	−0.755634	+	0.654994i	$0.772671\pi$
$402$	−3.76393	−	11.5842i	−0.187728	−	0.577767i
$403$	−7.47214	−	5.42882i	−0.372214	−	0.270429i
$404$	9.20820	−	6.69015i	0.458125	−	0.332847i
$405$	−0.190983	+	0.587785i	−0.00949002	+	0.0292073i
$406$	2.47214			0.122690
$407$	−8.44427	+	9.59632i	−0.418567	+	0.475672i
$408$	0.381966			0.0189101
$409$	3.32624	−	10.2371i	0.164472	−	0.506192i	−0.834525	−	0.550970i	$-0.814258\pi$
$409$	3.32624	−	10.2371i	0.164472	−	0.506192i	0.998997	+	0.0447775i	$0.0142579\pi$
$410$	−1.30902	+	0.951057i	−0.0646477	+	0.0469693i
$411$	4.23607	+	3.07768i	0.208950	+	0.151811i
$412$	2.64590	+	8.14324i	0.130354	+	0.401188i
$413$	−1.61803	−	4.97980i	−0.0796182	−	0.245040i
$414$	−3.92705	−	2.85317i	−0.193004	−	0.140226i
$415$	1.38197	−	1.00406i	0.0678380	−	0.0492872i
$416$	−0.618034	+	1.90211i	−0.0303016	+	0.0932588i
$417$	1.61803			0.0792355
$418$	15.7082	−	3.52671i	0.768313	−	0.172497i
$419$	36.9443			1.80485			0.902423	−	0.430851i	$-0.141787\pi$
$419$	36.9443			1.80485			0.902423	+	0.430851i	$0.141787\pi$
$420$	0.190983	−	0.587785i	0.00931902	−	0.0286810i
$421$	6.92705	−	5.03280i	0.337604	−	0.245284i	−0.406046	−	0.913852i	$-0.633093\pi$
$421$	6.92705	−	5.03280i	0.337604	−	0.245284i	0.743650	+	0.668569i	$0.233093\pi$
$422$	16.7082	+	12.1392i	0.813343	+	0.590928i
$423$	2.00000	+	6.15537i	0.0972433	+	0.299284i
$424$	−0.145898	−	0.449028i	−0.00708543	−	0.0218067i
$425$	1.42705	+	1.03681i	0.0692221	+	0.0502928i
$426$	−5.23607	+	3.80423i	−0.253688	+	0.184315i
$427$	3.76393	−	11.5842i	0.182149	−	0.560598i
$428$	1.14590			0.0553891
$429$	−6.47214	+	1.45309i	−0.312478	+	0.0701556i
$430$	6.18034			0.298042
$431$	−11.8435	+	36.4504i	−0.570479	+	1.75575i	0.0806014	+	0.996746i	$0.474316\pi$
$431$	−11.8435	+	36.4504i	−0.570479	+	1.75575i	−0.651081	+	0.759008i	$0.725684\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−18.5623	−	13.4863i	−0.892047	−	0.648110i	0.0443636	−	0.999015i	$-0.485874\pi$
$433$	−18.5623	−	13.4863i	−0.892047	−	0.648110i	−0.936411	+	0.350905i	$0.885874\pi$
$434$	−1.42705	−	4.39201i	−0.0685006	−	0.210823i
$435$	−0.472136	−	1.45309i	−0.0226372	−	0.0696701i
$436$	−3.35410	−	2.43690i	−0.160632	−	0.116706i
$437$	−19.0623	+	13.8496i	−0.911874	+	0.662515i
$438$	−3.14590	+	9.68208i	−0.150317	+	0.462628i
$439$	24.6180			1.17495			0.587477	−	0.809241i	$-0.300121\pi$
$439$	24.6180			1.17495			0.587477	+	0.809241i	$0.300121\pi$
$440$	−1.35410	+	1.53884i	−0.0645543	+	0.0733614i
$441$	1.00000			0.0476190
$442$	−0.236068	+	0.726543i	−0.0112286	+	0.0345581i
$443$	−0.927051	+	0.673542i	−0.0440455	+	0.0320009i	−0.609590	−	0.792717i	$-0.708666\pi$
$443$	−0.927051	+	0.673542i	−0.0440455	+	0.0320009i	0.565545	+	0.824718i	$0.308666\pi$
$444$	3.11803	+	2.26538i	0.147975	+	0.107510i
$445$	3.01722	+	9.28605i	0.143030	+	0.440201i
$446$	1.40983	+	4.33901i	0.0667574	+	0.205458i
$447$		0			0
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	7.27051	−	22.3763i	0.343117	−	1.05600i	−0.619468	−	0.785022i	$-0.712652\pi$
$449$	7.27051	−	22.3763i	0.343117	−	1.05600i	0.962584	−	0.270982i	$-0.0873484\pi$
$450$	4.61803			0.217696
$451$	4.42705	+	7.46969i	0.208462	+	0.351734i
$452$	−11.5279			−0.542225
$453$	−2.23607	+	6.88191i	−0.105060	+	0.323340i
$454$	−5.85410	+	4.25325i	−0.274747	+	0.199615i
$455$	1.00000	+	0.726543i	0.0468807	+	0.0340608i
$456$	−1.50000	−	4.61653i	−0.0702439	−	0.216189i
$457$	5.67376	+	17.4620i	0.265407	+	0.816840i	0.991599	+	0.129348i	$0.0412884\pi$
$457$	5.67376	+	17.4620i	0.265407	+	0.816840i	−0.726192	+	0.687492i	$0.758712\pi$
$458$	−3.23607	−	2.35114i	−0.151212	−	0.109862i
$459$	0.309017	−	0.224514i	0.0144237	−	0.0104794i
$460$	0.927051	−	2.85317i	0.0432240	−	0.133030i
$461$	21.0557			0.980663			0.490332	−	0.871536i	$-0.336876\pi$
$461$	21.0557			0.980663			0.490332	+	0.871536i	$0.336876\pi$
$462$	−3.04508	−	1.31433i	−0.141670	−	0.0611481i
$463$	−38.5410			−1.79115			−0.895577	−	0.444907i	$-0.853237\pi$
$463$	−38.5410			−1.79115			−0.895577	+	0.444907i	$0.853237\pi$
$464$	−0.763932	+	2.35114i	−0.0354647	+	0.109149i
$465$	−2.30902	+	1.67760i	−0.107078	+	0.0777968i
$466$	0.618034	+	0.449028i	0.0286299	+	0.0208008i
$467$	8.61803	+	26.5236i	0.398795	+	1.22736i	0.925966	+	0.377606i	$0.123253\pi$
$467$	8.61803	+	26.5236i	0.398795	+	1.22736i	−0.527171	+	0.849759i	$0.676747\pi$
$468$	0.618034	+	1.90211i	0.0285686	+	0.0879252i
$469$	9.85410	+	7.15942i	0.455020	+	0.330591i
$470$	−3.23607	+	2.35114i	−0.149269	+	0.108450i
$471$	−1.14590	+	3.52671i	−0.0528002	+	0.162502i
$472$	5.23607			0.241010
$473$	3.09017	−	33.0220i	0.142086	−	1.51835i
$474$	14.4721			0.664727
$475$	6.92705	−	21.3193i	0.317835	−	0.978195i
$476$	−0.309017	+	0.224514i	−0.0141638	+	0.0102906i
$477$	−0.381966	−	0.277515i	−0.0174890	−	0.0127065i
$478$	7.97214	+	24.5357i	0.364637	+	1.12224i
$479$	−5.70820	−	17.5680i	−0.260814	−	0.802704i	−0.992628	−	0.121200i	$-0.961326\pi$
$479$	−5.70820	−	17.5680i	−0.260814	−	0.802704i	0.731814	−	0.681505i	$-0.238674\pi$
$480$	0.500000	+	0.363271i	0.0228218	+	0.0165810i
$481$	−6.23607	+	4.53077i	−0.284340	+	0.206585i
$482$	−9.00000	+	27.6992i	−0.409939	+	1.26166i
$483$	4.85410			0.220869
$484$	7.54508	+	8.00448i	0.342958	+	0.363840i
$485$	6.29180			0.285696
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	1.90983	−	1.38757i	0.0865427	−	0.0628769i	−0.543673	−	0.839297i	$-0.682967\pi$
$487$	1.90983	−	1.38757i	0.0865427	−	0.0628769i	0.630215	+	0.776420i	$0.282967\pi$
$488$	9.85410	+	7.15942i	0.446074	+	0.324092i
$489$	−3.09017	−	9.51057i	−0.139742	−	0.430083i
$490$	0.190983	+	0.587785i	0.00862773	+	0.0265534i
$491$	−5.07295	−	3.68571i	−0.228939	−	0.166334i	0.467402	−	0.884045i	$-0.345190\pi$
$491$	−5.07295	−	3.68571i	−0.228939	−	0.166334i	−0.696341	+	0.717711i	$0.745190\pi$
$492$	2.11803	−	1.53884i	0.0954883	−	0.0693763i
$493$	−0.291796	+	0.898056i	−0.0131418	+	0.0404464i
$494$	9.70820			0.436793
$495$	−0.190983	+	2.04087i	−0.00858405	+	0.0917303i
$496$	4.61803			0.207356
$497$	2.00000	−	6.15537i	0.0897123	−	0.276106i
$498$	−2.23607	+	1.62460i	−0.100201	+	0.0728000i
$499$	−22.2705	−	16.1805i	−0.996965	−	0.724337i	−0.0355296	−	0.999369i	$-0.511312\pi$
$499$	−22.2705	−	16.1805i	−0.996965	−	0.724337i	−0.961435	+	0.275031i	$0.911312\pi$
$500$	1.83688	+	5.65334i	0.0821478	+	0.252825i
$501$	−3.94427	−	12.1392i	−0.176217	−	0.542340i
$502$	19.7984	+	14.3844i	0.883645	+	0.642005i
$503$	−16.3262	+	11.8617i	−0.727951	+	0.528887i	−0.888915	−	0.458073i	$-0.848540\pi$
$503$	−16.3262	+	11.8617i	−0.727951	+	0.528887i	0.160964	+	0.986960i	$0.448540\pi$
$504$	−0.309017	+	0.951057i	−0.0137647	+	0.0423634i
$505$	7.03444			0.313029
$506$	−14.7812	−	6.37988i	−0.657102	−	0.283620i
$507$	9.00000			0.399704
$508$	1.52786	−	4.70228i	0.0677880	−	0.208630i
$509$	11.7361	−	8.52675i	0.520192	−	0.377942i	−0.296484	−	0.955038i	$-0.595814\pi$
$509$	11.7361	−	8.52675i	0.520192	−	0.377942i	0.816676	+	0.577096i	$0.195814\pi$
$510$	0.190983	+	0.138757i	0.00845687	+	0.00614428i
$511$	−3.14590	−	9.68208i	−0.139166	−	0.428310i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−3.92705	−	2.85317i	−0.173384	−	0.125971i
$514$	−11.2533	+	8.17599i	−0.496361	+	0.360628i
$515$	−1.63525	+	5.03280i	−0.0720579	+	0.221772i
$516$	−10.0000			−0.440225
$517$	10.9443	+	18.4661i	0.481329	+	0.812138i
$518$	−3.85410			−0.169340
$519$	−5.79180	+	17.8253i	−0.254232	+	0.782445i
$520$	−1.00000	+	0.726543i	−0.0438529	+	0.0318610i
$521$	−16.0623	−	11.6699i	−0.703702	−	0.511270i	0.177434	−	0.984133i	$-0.443221\pi$
$521$	−16.0623	−	11.6699i	−0.703702	−	0.511270i	−0.881136	+	0.472863i	$0.843221\pi$
$522$	0.763932	+	2.35114i	0.0334364	+	0.102907i
$523$	4.91641	+	15.1311i	0.214980	+	0.661639i	0.999155	+	0.0410998i	$0.0130862\pi$
$523$	4.91641	+	15.1311i	0.214980	+	0.661639i	−0.784176	+	0.620539i	$0.786914\pi$
$524$		0			0
$525$	−3.73607	+	2.71441i	−0.163055	+	0.118467i
$526$	−5.26393	+	16.2007i	−0.229518	+	0.706385i
$527$	1.76393			0.0768381
$528$	2.19098	−	2.48990i	0.0953503	−	0.108359i
$529$	0.562306			0.0244481
$530$	0.0901699	−	0.277515i	0.00391673	−	0.0120545i
$531$	4.23607	−	3.07768i	0.183830	−	0.133560i
$532$	3.92705	+	2.85317i	0.170259	+	0.123701i
$533$	1.61803	+	4.97980i	0.0700848	+	0.215699i
$534$	−4.88197	−	15.0251i	−0.211263	−	0.650202i
$535$	0.572949	+	0.416272i	0.0247707	+	0.0179970i
$536$	−9.85410	+	7.15942i	−0.425632	+	0.309240i
$537$	4.95492	−	15.2497i	0.213820	−	0.658071i
$538$	−7.88854			−0.340099
$539$	3.23607	−	0.726543i	0.139387	−	0.0312944i
$540$	0.618034			0.0265959
$541$	2.13525	−	6.57164i	0.0918018	−	0.282537i	−0.894605	−	0.446857i	$-0.852543\pi$
$541$	2.13525	−	6.57164i	0.0918018	−	0.282537i	0.986407	+	0.164321i	$0.0525431\pi$
$542$	−7.50000	+	5.44907i	−0.322153	+	0.234058i
$543$	14.3262	+	10.4086i	0.614798	+	0.446677i
$544$	−0.118034	−	0.363271i	−0.00506067	−	0.0155751i
$545$	−0.791796	−	2.43690i	−0.0339168	−	0.104385i
$546$	−1.61803	−	1.17557i	−0.0692455	−	0.0503098i
$547$	−11.5623	+	8.40051i	−0.494369	+	0.359180i	−0.806862	−	0.590740i	$-0.798836\pi$
$547$	−11.5623	+	8.40051i	−0.494369	+	0.359180i	0.312493	+	0.949920i	$0.398836\pi$
$548$	1.61803	−	4.97980i	0.0691190	−	0.212726i
$549$	12.1803			0.519844
$550$	14.9443	−	3.35520i	0.637226	−	0.143066i
$551$	12.0000			0.511217
$552$	−1.50000	+	4.61653i	−0.0638442	+	0.196492i
$553$	−11.7082	+	8.50651i	−0.497883	+	0.361734i
$554$	−13.3992	−	9.73508i	−0.569277	−	0.413604i
$555$	0.736068	+	2.26538i	0.0312443	+	0.0961602i
$556$	−0.500000	−	1.53884i	−0.0212047	−	0.0652614i
$557$	−9.61803	−	6.98791i	−0.407529	−	0.296087i	0.365072	−	0.930979i	$-0.381045\pi$
$557$	−9.61803	−	6.98791i	−0.407529	−	0.296087i	−0.772601	+	0.634892i	$0.781045\pi$
$558$	3.73607	−	2.71441i	0.158160	−	0.114910i
$559$	6.18034	−	19.0211i	0.261401	−	0.804508i
$560$	−0.618034			−0.0261167
$561$	0.836881	−	0.951057i	0.0353331	−	0.0401536i
$562$	23.1246			0.975453
$563$	−11.9787	+	36.8667i	−0.504843	+	1.55375i	0.296192	+	0.955128i	$0.404283\pi$
$563$	−11.9787	+	36.8667i	−0.504843	+	1.55375i	−0.801035	+	0.598617i	$0.795717\pi$
$564$	5.23607	−	3.80423i	0.220478	−	0.160187i
$565$	−5.76393	−	4.18774i	−0.242490	−	0.176180i
$566$	−3.86475	−	11.8945i	−0.162447	−	0.499962i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	5.23607	+	3.80423i	0.219701	+	0.159622i
$569$	26.2705	−	19.0866i	1.10132	−	0.800154i	0.120043	−	0.992769i	$-0.461697\pi$
$569$	26.2705	−	19.0866i	1.10132	−	0.800154i	0.981274	+	0.192615i	$0.0616969\pi$
$570$	0.927051	−	2.85317i	0.0388299	−	0.119506i
$571$	−43.1246			−1.80471			−0.902354	−	0.430995i	$-0.858163\pi$
$571$	−43.1246			−1.80471			−0.902354	+	0.430995i	$0.858163\pi$
$572$	3.38197	+	5.70634i	0.141407	+	0.238594i
$573$	14.6180			0.610677
$574$	−0.809017	+	2.48990i	−0.0337677	+	0.103926i
$575$	−18.1353	+	13.1760i	−0.756292	+	0.549479i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−8.43769	−	25.9686i	−0.351266	−	1.08108i	−0.958143	−	0.286289i	$-0.907578\pi$
$577$	−8.43769	−	25.9686i	−0.351266	−	1.08108i	0.606877	−	0.794795i	$-0.292422\pi$
$578$	5.20820	+	16.0292i	0.216633	+	0.666727i
$579$	14.6803	+	10.6659i	0.610094	+	0.443259i
$580$	−1.23607	+	0.898056i	−0.0513249	+	0.0372897i
$581$	0.854102	−	2.62866i	0.0354341	−	0.109055i
$582$	−10.1803			−0.421989
$583$	−1.43769	−	0.620541i	−0.0595432	−	0.0257002i
$584$	10.1803			0.421265
$585$	−0.381966	+	1.17557i	−0.0157924	+	0.0486039i
$586$	15.4443	−	11.2209i	0.637997	−	0.463532i
$587$	−15.7984	−	11.4782i	−0.652069	−	0.473756i	0.211907	−	0.977290i	$-0.432033\pi$
$587$	−15.7984	−	11.4782i	−0.652069	−	0.473756i	−0.863975	+	0.503534i	$0.832033\pi$
$588$	−0.309017	−	0.951057i	−0.0127436	−	0.0392209i
$589$	−6.92705	−	21.3193i	−0.285424	−	0.878445i
$590$	2.61803	+	1.90211i	0.107783	+	0.0783088i
$591$	16.3262	−	11.8617i	0.671572	−	0.487925i
$592$	1.19098	−	3.66547i	0.0489491	−	0.150650i
$593$	−8.50658			−0.349323			−0.174662	−	0.984629i	$-0.555883\pi$
$593$	−8.50658			−0.349323			−0.174662	+	0.984629i	$0.555883\pi$
$594$	0.309017	−	3.30220i	0.0126791	−	0.135491i
$595$	−0.236068			−0.00967784
$596$		0			0
$597$	3.54508	−	2.57565i	0.145091	−	0.105415i
$598$	−7.85410	−	5.70634i	−0.321178	−	0.233350i
$599$	1.26393	+	3.88998i	0.0516429	+	0.158940i	0.973552	−	0.228466i	$-0.0733710\pi$
$599$	1.26393	+	3.88998i	0.0516429	+	0.158940i	−0.921909	+	0.387406i	$0.873371\pi$
$600$	−1.42705	−	4.39201i	−0.0582591	−	0.179303i
$601$	26.5623	+	19.2986i	1.08350	+	0.787208i	0.978290	−	0.207242i	$-0.0664487\pi$
$601$	26.5623	+	19.2986i	1.08350	+	0.787208i	0.105209	+	0.994450i	$0.466449\pi$
$602$	8.09017	−	5.87785i	0.329731	−	0.239563i
$603$	−3.76393	+	11.5842i	−0.153279	+	0.471745i
$604$	7.23607			0.294431
$605$	0.864745	+	6.74315i	0.0351569	+	0.274148i
$606$	−11.3820			−0.462361
$607$	7.40983	−	22.8051i	0.300756	−	0.925631i	−0.680471	−	0.732775i	$-0.738225\pi$
$607$	7.40983	−	22.8051i	0.300756	−	0.925631i	0.981227	−	0.192856i	$-0.0617751\pi$
$608$	−3.92705	+	2.85317i	−0.159263	+	0.115711i
$609$	−2.00000	−	1.45309i	−0.0810441	−	0.0588820i
$610$	2.32624	+	7.15942i	0.0941866	+	0.289877i
$611$	4.00000	+	12.3107i	0.161823	+	0.498039i
$612$	−0.309017	−	0.224514i	−0.0124913	−	0.00907544i
$613$	−14.7812	+	10.7391i	−0.597005	+	0.433750i	−0.844815	−	0.535059i	$-0.820289\pi$
$613$	−14.7812	+	10.7391i	−0.597005	+	0.433750i	0.247809	+	0.968809i	$0.420289\pi$
$614$	−0.135255	+	0.416272i	−0.00545844	+	0.0167994i
$615$	1.61803			0.0652454
$616$	−0.309017	+	3.30220i	−0.0124506	+	0.133049i
$617$	44.7214			1.80041			0.900207	−	0.435462i	$-0.143415\pi$
$617$	44.7214			1.80041			0.900207	+	0.435462i	$0.143415\pi$
$618$	2.64590	−	8.14324i	0.106434	−	0.327569i
$619$	−6.59017	+	4.78804i	−0.264881	+	0.192448i	−0.712296	−	0.701879i	$-0.752345\pi$
$619$	−6.59017	+	4.78804i	−0.264881	+	0.192448i	0.447415	+	0.894326i	$0.352345\pi$
$620$	2.30902	+	1.67760i	0.0927324	+	0.0673740i
$621$	1.50000	+	4.61653i	0.0601929	+	0.185255i
$622$	−10.0344	−	30.8828i	−0.402344	−	1.23829i
$623$	12.7812	+	9.28605i	0.512066	+	0.372038i
$624$	1.61803	−	1.17557i	0.0647732	−	0.0470605i
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$	−17.7082			−0.707762
$627$	−14.7812	−	6.37988i	−0.590302	−	0.254788i
$628$	3.70820			0.147973
$629$	0.454915	−	1.40008i	0.0181387	−	0.0558250i
$630$	−0.500000	+	0.363271i	−0.0199205	+	0.0144731i
$631$	−39.2705	−	28.5317i	−1.56333	−	1.13583i	−0.933208	−	0.359336i	$-0.883003\pi$
$631$	−39.2705	−	28.5317i	−1.56333	−	1.13583i	−0.630126	−	0.776493i	$-0.716997\pi$
$632$	−4.47214	−	13.7638i	−0.177892	−	0.547495i
$633$	−6.38197	−	19.6417i	−0.253660	−	0.780686i
$634$	−10.8541	−	7.88597i	−0.431071	−	0.313192i
$635$	2.47214	−	1.79611i	0.0981037	−	0.0712765i
$636$	−0.145898	+	0.449028i	−0.00578523	+	0.0178051i
$637$	2.00000			0.0792429
$638$	4.18034	+	7.05342i	0.165501	+	0.279248i
$639$	6.47214			0.256034
$640$	0.190983	−	0.587785i	0.00754927	−	0.0232343i
$641$	28.4164	−	20.6457i	1.12238	−	0.815457i	0.137812	−	0.990458i	$-0.455993\pi$
$641$	28.4164	−	20.6457i	1.12238	−	0.815457i	0.984568	+	0.175001i	$0.0559929\pi$
$642$	−0.927051	−	0.673542i	−0.0365878	−	0.0265826i
$643$	10.8607	+	33.4257i	0.428303	+	1.31818i	0.899795	+	0.436312i	$0.143716\pi$
$643$	10.8607	+	33.4257i	0.428303	+	1.31818i	−0.471492	+	0.881870i	$0.656284\pi$
$644$	−1.50000	−	4.61653i	−0.0591083	−	0.181917i
$645$	−5.00000	−	3.63271i	−0.196875	−	0.143038i
$646$	−1.50000	+	1.08981i	−0.0590167	+	0.0428782i
$647$	−11.0557	+	34.0260i	−0.434646	+	1.33770i	0.458804	+	0.888538i	$0.348278\pi$
$647$	−11.0557	+	34.0260i	−0.434646	+	1.33770i	−0.893449	+	0.449164i	$0.851722\pi$
$648$	−1.00000			−0.0392837
$649$	11.4721	−	13.0373i	0.450321	−	0.511758i
$650$	9.23607			0.362268
$651$	−1.42705	+	4.39201i	−0.0559305	+	0.172136i
$652$	−8.09017	+	5.87785i	−0.316836	+	0.230194i
$653$	−17.1803	−	12.4822i	−0.672319	−	0.488468i	0.198482	−	0.980105i	$-0.436399\pi$
$653$	−17.1803	−	12.4822i	−0.672319	−	0.488468i	−0.870801	+	0.491636i	$0.836399\pi$
$654$	1.28115	+	3.94298i	0.0500970	+	0.154183i
$655$		0			0
$656$	−2.11803	−	1.53884i	−0.0826953	−	0.0600817i
$657$	8.23607	−	5.98385i	0.321320	−	0.233452i
$658$	−2.00000	+	6.15537i	−0.0779681	+	0.239961i
$659$	−23.0902			−0.899465			−0.449733	−	0.893163i	$-0.648481\pi$
$659$	−23.0902			−0.899465			−0.449733	+	0.893163i	$0.648481\pi$
$660$	2.00000	−	0.449028i	0.0778499	−	0.0174784i
$661$	0.360680			0.0140288			0.00701441	−	0.999975i	$-0.497767\pi$
$661$	0.360680			0.0140288			0.00701441	+	0.999975i	$0.497767\pi$
$662$	−0.854102	+	2.62866i	−0.0331956	+	0.102166i
$663$	0.618034	−	0.449028i	0.0240025	−	0.0174388i
$664$	2.23607	+	1.62460i	0.0867763	+	0.0630466i
$665$	0.927051	+	2.85317i	0.0359495	+	0.110641i
$666$	−1.19098	−	3.66547i	−0.0461497	−	0.142034i
$667$	−9.70820	−	7.05342i	−0.375903	−	0.273110i
$668$	−10.3262	+	7.50245i	−0.399534	+	0.290279i
$669$	1.40983	−	4.33901i	0.0545072	−	0.167756i
$670$	−7.52786			−0.290827
$671$	39.4164	−	8.84953i	1.52165	−	0.341633i
$672$	1.00000			0.0385758
$673$	0.798374	−	2.45714i	0.0307751	−	0.0947159i	−0.934489	−	0.355992i	$-0.884143\pi$
$673$	0.798374	−	2.45714i	0.0307751	−	0.0947159i	0.965264	+	0.261276i	$0.0841432\pi$
$674$	12.6803	−	9.21281i	0.488428	−	0.354864i
$675$	−3.73607	−	2.71441i	−0.143801	−	0.104478i
$676$	−2.78115	−	8.55951i	−0.106967	−	0.329212i
$677$	4.90983	+	15.1109i	0.188700	+	0.580759i	0.999992	−	0.00388147i	$-0.00123551\pi$
$677$	4.90983	+	15.1109i	0.188700	+	0.580759i	−0.811292	+	0.584641i	$0.801236\pi$
$678$	9.32624	+	6.77591i	0.358172	+	0.260227i
$679$	8.23607	−	5.98385i	0.316071	−	0.229639i
$680$	0.0729490	−	0.224514i	0.00279747	−	0.00860972i
$681$	7.23607			0.277287
$682$	10.1180	−	11.4984i	0.387440	−	0.440298i
$683$	−19.3820			−0.741630			−0.370815	−	0.928707i	$-0.620922\pi$
$683$	−19.3820			−0.741630			−0.370815	+	0.928707i	$0.620922\pi$
$684$	−1.50000	+	4.61653i	−0.0573539	+	0.176517i
$685$	2.61803	−	1.90211i	0.100030	−	0.0726760i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	1.23607	+	3.80423i	0.0471589	+	0.145140i
$688$	3.09017	+	9.51057i	0.117812	+	0.362587i
$689$	−0.763932	−	0.555029i	−0.0291035	−	0.0211449i
$690$	−2.42705	+	1.76336i	−0.0923963	+	0.0671298i
$691$	5.08359	−	15.6457i	0.193389	−	0.595190i	−0.806603	−	0.591094i	$-0.798696\pi$
$691$	5.08359	−	15.6457i	0.193389	−	0.595190i	0.999992	−	0.00409598i	$-0.00130379\pi$
$692$	18.7426			0.712488
$693$	1.69098	+	2.85317i	0.0642351	+	0.108383i
$694$	−2.72949			−0.103610
$695$	0.309017	−	0.951057i	0.0117217	−	0.0360756i
$696$	2.00000	−	1.45309i	0.0758098	−	0.0550790i
$697$	−0.809017	−	0.587785i	−0.0306437	−	0.0222640i
$698$	−6.56231	−	20.1967i	−0.248387	−	0.764456i
$699$	−0.236068	−	0.726543i	−0.00892891	−	0.0274804i
$700$	3.73607	+	2.71441i	0.141210	+	0.102595i
$701$	−8.00000	+	5.81234i	−0.302156	+	0.219529i	−0.728523	−	0.685021i	$-0.759793\pi$
$701$	−8.00000	+	5.81234i	−0.302156	+	0.219529i	0.426368	+	0.904550i	$0.359793\pi$
$702$	0.618034	−	1.90211i	0.0233262	−	0.0717906i
$703$	−18.7082			−0.705593
$704$	−3.04508	−	1.31433i	−0.114766	−	0.0495356i
$705$	4.00000			0.150649
$706$	3.67376	−	11.3067i	0.138264	−	0.425532i
$707$	9.20820	−	6.69015i	0.346310	−	0.251609i
$708$	−4.23607	−	3.07768i	−0.159201	−	0.115666i
$709$	−12.1353	−	37.3485i	−0.455749	−	1.40265i	−0.870254	−	0.492604i	$-0.836045\pi$
$709$	−12.1353	−	37.3485i	−0.455749	−	1.40265i	0.414504	−	0.910047i	$-0.363955\pi$
$710$	1.23607	+	3.80423i	0.0463888	+	0.142770i
$711$	−11.7082	−	8.50651i	−0.439092	−	0.319019i
$712$	−12.7812	+	9.28605i	−0.478994	+	0.348009i
$713$	−6.92705	+	21.3193i	−0.259420	+	0.798413i
$714$	0.381966			0.0142947
$715$	−0.381966	+	4.08174i	−0.0142847	+	0.152648i
$716$	−16.0344			−0.599235
$717$	7.97214	−	24.5357i	0.297725	−	0.916303i
$718$	28.0623	−	20.3885i	1.04728	−	0.760891i
$719$	37.4164	+	27.1846i	1.39540	+	1.01381i	0.995249	+	0.0973643i	$0.0310412\pi$
$719$	37.4164	+	27.1846i	1.39540	+	1.01381i	0.400148	+	0.916451i	$0.368959\pi$
$720$	−0.190983	−	0.587785i	−0.00711752	−	0.0219055i
$721$	2.64590	+	8.14324i	0.0985384	+	0.303270i
$722$	3.69098	+	2.68166i	0.137364	+	0.0998009i
$723$	23.5623	−	17.1190i	0.876292	−	0.636663i
$724$	5.47214	−	16.8415i	0.203370	−	0.625910i
$725$	11.4164			0.423995
$726$	−1.39919	−	10.9106i	−0.0519287	−	0.404932i
$727$	25.6869			0.952675			0.476338	−	0.879263i	$-0.341964\pi$
$727$	25.6869			0.952675			0.476338	+	0.879263i	$0.341964\pi$
$728$	−0.618034	+	1.90211i	−0.0229059	+	0.0704970i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	5.09017	+	3.69822i	0.188396	+	0.136877i
$731$	1.18034	+	3.63271i	0.0436564	+	0.134361i
$732$	−3.76393	−	11.5842i	−0.139119	−	0.428164i
$733$	−26.1246	−	18.9806i	−0.964935	−	0.701066i	−0.0106430	−	0.999943i	$-0.503388\pi$
$733$	−26.1246	−	18.9806i	−0.964935	−	0.701066i	−0.954292	+	0.298877i	$0.903388\pi$
$734$	14.4443	−	10.4944i	0.533148	−	0.387355i
$735$	0.190983	−	0.587785i	0.00704451	−	0.0216808i
$736$	4.85410			0.178925
$737$	−3.76393	+	40.2219i	−0.138646	+	1.48159i
$738$	−2.61803			−0.0963712
$739$	−10.2361	+	31.5034i	−0.376540	+	1.15887i	0.565894	+	0.824478i	$0.308531\pi$
$739$	−10.2361	+	31.5034i	−0.376540	+	1.15887i	−0.942434	+	0.334393i	$0.891469\pi$
$740$	1.92705	−	1.40008i	0.0708398	−	0.0514681i
$741$	−7.85410	−	5.70634i	−0.288528	−	0.209628i
$742$	−0.145898	−	0.449028i	−0.00535609	−	0.0164843i
$743$	1.28115	+	3.94298i	0.0470009	+	0.144654i	0.971803	−	0.235795i	$-0.0757694\pi$
$743$	1.28115	+	3.94298i	0.0470009	+	0.144654i	−0.924802	+	0.380449i	$0.875769\pi$
$744$	−3.73607	−	2.71441i	−0.136971	−	0.0995152i
$745$		0			0
$746$	1.01064	−	3.11044i	0.0370023	−	0.113881i
$747$	2.76393			0.101127
$748$	−1.16312	−	0.502029i	−0.0425278	−	0.0183560i
$749$	1.14590			0.0418702
$750$	1.83688	−	5.65334i	0.0670734	−	0.206431i
$751$	31.6525	−	22.9969i	1.15502	−	0.839168i	0.165876	−	0.986147i	$-0.446955\pi$
$751$	31.6525	−	22.9969i	1.15502	−	0.839168i	0.989140	+	0.146979i	$0.0469550\pi$
$752$	−5.23607	−	3.80423i	−0.190940	−	0.138726i
$753$	−7.56231	−	23.2744i	−0.275586	−	0.848166i
$754$	1.52786	+	4.70228i	0.0556415	+	0.171247i
$755$	3.61803	+	2.62866i	0.131674	+	0.0956666i
$756$	0.809017	−	0.587785i	0.0294237	−	0.0213775i
$757$	−6.40983	+	19.7274i	−0.232969	+	0.717006i	0.764415	+	0.644724i	$0.223028\pi$
$757$	−6.40983	+	19.7274i	−0.232969	+	0.717006i	−0.997384	+	0.0722811i	$0.976972\pi$
$758$	−9.41641			−0.342019
$759$	8.20820	+	13.8496i	0.297939	+	0.502708i
$760$	−3.00000			−0.108821
$761$	−14.3262	+	44.0916i	−0.519326	+	1.59832i	0.255945	+	0.966691i	$0.417613\pi$
$761$	−14.3262	+	44.0916i	−0.519326	+	1.59832i	−0.775271	+	0.631629i	$0.782387\pi$
$762$	−4.00000	+	2.90617i	−0.144905	+	0.105279i
$763$	−3.35410	−	2.43690i	−0.121427	−	0.0882216i
$764$	−4.51722	−	13.9026i	−0.163427	−	0.502978i
$765$	−0.0729490	−	0.224514i	−0.00263748	−	0.00811732i
$766$	19.3262	+	14.0413i	0.698285	+	0.507334i
$767$	8.47214	−	6.15537i	0.305911	−	0.222257i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	−1.34752			−0.0485930			−0.0242965	−	0.999705i	$-0.507735\pi$
$769$	−1.34752			−0.0485930			−0.0242965	+	0.999705i	$0.507735\pi$
$770$	−1.35410	+	1.53884i	−0.0487984	+	0.0554560i
$771$	13.9098			0.500950
$772$	5.60739	−	17.2578i	0.201814	−	0.621121i
$773$	−18.5623	+	13.4863i	−0.667640	+	0.485069i	−0.869234	−	0.494400i	$-0.835388\pi$
$773$	−18.5623	+	13.4863i	−0.667640	+	0.485069i	0.201595	+	0.979469i	$0.435388\pi$
$774$	8.09017	+	5.87785i	0.290795	+	0.211275i
$775$	−6.59017	−	20.2825i	−0.236726	−	0.728567i
$776$	3.14590	+	9.68208i	0.112931	+	0.347566i
$777$	3.11803	+	2.26538i	0.111859	+	0.0812702i
$778$	1.14590	−	0.832544i	0.0410824	−	0.0298481i
$779$	−3.92705	+	12.0862i	−0.140701	+	0.433034i
$780$	1.23607			0.0442583
$781$	20.9443	−	4.70228i	0.749445	−	0.168261i
$782$	1.85410			0.0663026
$783$	0.763932	−	2.35114i	0.0273007	−	0.0840229i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	1.85410	+	1.34708i	0.0661757	+	0.0480795i
$786$		0			0
$787$	7.10081	+	21.8541i	0.253117	+	0.779013i	0.994195	+	0.107594i	$0.0343147\pi$
$787$	7.10081	+	21.8541i	0.253117	+	0.779013i	−0.741078	+	0.671419i	$0.765685\pi$
$788$	−16.3262	−	11.8617i	−0.581598	−	0.422556i
$789$	13.7812	−	10.0126i	0.490622	−	0.356458i
$790$	2.76393	−	8.50651i	0.0983363	−	0.302648i
$791$	−11.5279			−0.409884
$792$	−3.23607	+	0.726543i	−0.114989	+	0.0258166i
$793$	24.3607			0.865073
$794$	7.85410	−	24.1724i	0.278732	−	0.857848i
$795$	−0.236068	+	0.171513i	−0.00837247	+	0.00608295i
$796$	−3.54508	−	2.57565i	−0.125652	−	0.0912917i
$797$	−1.92047	−	5.91061i	−0.0680267	−	0.209365i	0.911264	−	0.411822i	$-0.135107\pi$
$797$	−1.92047	−	5.91061i	−0.0680267	−	0.209365i	−0.979291	+	0.202457i	$0.935107\pi$
$798$	−1.50000	−	4.61653i	−0.0530994	−	0.163423i
$799$	−2.00000	−	1.45309i	−0.0707549	−	0.0514065i
$800$	−3.73607	+	2.71441i	−0.132090	+	0.0959690i
$801$	−4.88197	+	15.0251i	−0.172496	+	0.530887i
$802$	−15.5967			−0.550740
$803$	22.3050	−	25.3480i	0.787125	−	0.894512i
$804$	12.1803			0.429567
$805$	0.927051	−	2.85317i	0.0326743	−	0.100561i
$806$	7.47214	−	5.42882i	0.263195	−	0.191222i
$807$	6.38197	+	4.63677i	0.224656	+	0.163222i
$808$	3.51722	+	10.8249i	0.123735	+	0.380818i
$809$	−13.0902	−	40.2874i	−0.460226	−	1.41643i	−0.864889	−	0.501964i	$-0.832611\pi$
$809$	−13.0902	−	40.2874i	−0.460226	−	1.41643i	0.404663	−	0.914466i	$-0.367389\pi$
$810$	−0.500000	−	0.363271i	−0.0175682	−	0.0127641i
$811$	10.4721	−	7.60845i	0.367726	−	0.267169i	−0.388541	−	0.921431i	$-0.627021\pi$
$811$	10.4721	−	7.60845i	0.367726	−	0.267169i	0.756268	+	0.654263i	$0.227021\pi$
$812$	−0.763932	+	2.35114i	−0.0268088	+	0.0825089i
$813$	9.27051			0.325131
$814$	−6.51722	−	10.9964i	−0.228428	−	0.385424i
$815$	−6.18034			−0.216488
$816$	−0.118034	+	0.363271i	−0.00413202	+	0.0127170i
$817$	39.2705	−	28.5317i	1.37390	−	0.998198i
$818$	8.70820	+	6.32688i	0.304475	+	0.221214i
$819$	0.618034	+	1.90211i	0.0215959	+	0.0664652i
$820$	−0.500000	−	1.53884i	−0.0174608	−	0.0537387i
$821$	5.23607	+	3.80423i	0.182740	+	0.132768i	0.675395	−	0.737457i	$-0.263973\pi$
$821$	5.23607	+	3.80423i	0.182740	+	0.132768i	−0.492655	+	0.870225i	$0.663973\pi$
$822$	−4.23607	+	3.07768i	−0.147750	+	0.107347i
$823$	15.2918	−	47.0633i	0.533039	−	1.64052i	−0.214811	−	0.976656i	$-0.568914\pi$
$823$	15.2918	−	47.0633i	0.533039	−	1.64052i	0.747850	−	0.663868i	$-0.231086\pi$
$824$	−8.56231			−0.298282
$825$	−14.0623	−	6.06961i	−0.489587	−	0.211317i
$826$	5.23607			0.182186
$827$	−6.06231	+	18.6579i	−0.210807	+	0.648797i	0.788618	+	0.614884i	$0.210797\pi$
$827$	−6.06231	+	18.6579i	−0.210807	+	0.648797i	−0.999425	+	0.0339136i	$0.989203\pi$
$828$	3.92705	−	2.85317i	0.136474	−	0.0991545i
$829$	−3.14590	−	2.28563i	−0.109262	−	0.0793832i	0.531813	−	0.846862i	$-0.321511\pi$
$829$	−3.14590	−	2.28563i	−0.109262	−	0.0793832i	−0.641074	+	0.767479i	$0.721511\pi$
$830$	0.527864	+	1.62460i	0.0183224	+	0.0563906i
$831$	5.11803	+	15.7517i	0.177543	+	0.546420i
$832$	−1.61803	−	1.17557i	−0.0560952	−	0.0407556i
$833$	−0.309017	+	0.224514i	−0.0107068	+	0.00777895i
$834$	−0.500000	+	1.53884i	−0.0173136	+	0.0532857i
$835$	−7.88854			−0.272994
$836$	−1.50000	+	16.0292i	−0.0518786	+	0.554382i
$837$	−4.61803			−0.159623
$838$	−11.4164	+	35.1361i	−0.394373	+	1.21376i
$839$	−35.2705	+	25.6255i	−1.21767	+	0.884691i	−0.995905	−	0.0904080i	$-0.971183\pi$
$839$	−35.2705	+	25.6255i	−1.21767	+	0.884691i	−0.221768	+	0.975099i	$0.571183\pi$
$840$	0.500000	+	0.363271i	0.0172516	+	0.0125340i
$841$	−7.07295	−	21.7683i	−0.243895	−	0.750631i
$842$	2.64590	+	8.14324i	0.0911837	+	0.280634i
$843$	−18.7082	−	13.5923i	−0.644345	−	0.468144i
$844$	−16.7082	+	12.1392i	−0.575120	+	0.417849i
$845$	1.71885	−	5.29007i	0.0591301	−	0.181984i
$846$	−6.47214			−0.222517
$847$	7.54508	+	8.00448i	0.259252	+	0.275037i
$848$	0.472136			0.0162132
$849$	−3.86475	+	11.8945i	−0.132638	+	0.408217i
$850$	−1.42705	+	1.03681i	−0.0489474	+	0.0355624i
$851$	15.1353	+	10.9964i	0.518830	+	0.376952i
$852$	−2.00000	−	6.15537i	−0.0685189	−	0.210879i
$853$	13.5836	+	41.8060i	0.465093	+	1.43141i	0.858865	+	0.512202i	$0.171170\pi$
$853$	13.5836	+	41.8060i	0.465093	+	1.43141i	−0.393772	+	0.919208i	$0.628830\pi$
$854$	9.85410	+	7.15942i	0.337200	+	0.244990i
$855$	−2.42705	+	1.76336i	−0.0830034	+	0.0603055i
$856$	−0.354102	+	1.08981i	−0.0121030	+	0.0372491i
$857$	28.2492			0.964975			0.482488	−	0.875903i	$-0.339733\pi$
$857$	28.2492			0.964975			0.482488	+	0.875903i	$0.339733\pi$
$858$	0.618034	−	6.60440i	0.0210993	−	0.225470i
$859$	−43.4164			−1.48135			−0.740674	−	0.671864i	$-0.765494\pi$
$859$	−43.4164			−1.48135			−0.740674	+	0.671864i	$0.765494\pi$
$860$	−1.90983	+	5.87785i	−0.0651247	+	0.200433i
$861$	2.11803	−	1.53884i	0.0721824	−	0.0524436i
$862$	−31.0066	−	22.5276i	−1.05609	−	0.767293i
$863$	13.5729	+	41.7732i	0.462029	+	1.42198i	0.862681	+	0.505748i	$0.168783\pi$
$863$	13.5729	+	41.7732i	0.462029	+	1.42198i	−0.400653	+	0.916230i	$0.631217\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	9.37132	+	6.80866i	0.318635	+	0.231502i
$866$	18.5623	−	13.4863i	0.630773	−	0.458283i
$867$	5.20820	−	16.0292i	0.176880	−	0.544380i
$868$	4.61803			0.156746
$869$	−44.0689	−	19.0211i	−1.49493	−	0.645248i
$870$	1.52786			0.0517994
$871$	−7.52786	+	23.1684i	−0.255072	+	0.785031i
$872$	3.35410	−	2.43690i	0.113584	−	0.0825238i
$873$	8.23607	+	5.98385i	0.278749	+	0.202523i
$874$	−7.28115	−	22.4091i	−0.246289	−	0.757999i
$875$	1.83688	+	5.65334i	0.0620979	+	0.191118i
$876$	−8.23607	−	5.98385i	−0.278271	−	0.202176i
$877$	−9.32624	+	6.77591i	−0.314925	+	0.228806i	−0.734007	−	0.679142i	$-0.762352\pi$
$877$	−9.32624	+	6.77591i	−0.314925	+	0.228806i	0.419082	+	0.907948i	$0.362352\pi$
$878$	−7.60739	+	23.4131i	−0.256737	+	0.790155i
$879$	−19.0902			−0.643895
$880$	−1.04508	−	1.76336i	−0.0352298	−	0.0594427i
$881$	34.8541			1.17426			0.587132	−	0.809491i	$-0.300257\pi$
$881$	34.8541			1.17426			0.587132	+	0.809491i	$0.300257\pi$
$882$	−0.309017	+	0.951057i	−0.0104051	+	0.0320237i
$883$	−44.3607	+	32.2299i	−1.49286	+	1.08462i	−0.519735	+	0.854328i	$0.673969\pi$
$883$	−44.3607	+	32.2299i	−1.49286	+	1.08462i	−0.973121	+	0.230296i	$0.926031\pi$
$884$	−0.618034	−	0.449028i	−0.0207867	−	0.0151024i
$885$	−1.00000	−	3.07768i	−0.0336146	−	0.103455i
$886$	−0.354102	−	1.08981i	−0.0118963	−	0.0366130i
$887$	1.00000	+	0.726543i	0.0335767	+	0.0243949i	0.604447	−	0.796645i	$-0.293394\pi$
$887$	1.00000	+	0.726543i	0.0335767	+	0.0243949i	−0.570870	+	0.821040i	$0.693394\pi$
$888$	−3.11803	+	2.26538i	−0.104634	+	0.0760213i
$889$	1.52786	−	4.70228i	0.0512429	−	0.157709i
$890$	−9.76393			−0.327288
$891$	−2.19098	+	2.48990i	−0.0734007	+	0.0834147i
$892$	−4.56231			−0.152757
$893$	−9.70820	+	29.8788i	−0.324873	+	0.999855i
$894$		0			0
$895$	−8.01722	−	5.82485i	−0.267986	−	0.194703i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	3.00000	+	9.23305i	0.100167	+	0.308283i
$898$	19.0344	+	13.8293i	0.635188	+	0.461491i
$899$	9.23607	−	6.71040i	0.308040	−	0.223804i
$900$	−1.42705	+	4.39201i	−0.0475684	+	0.146400i
$901$	0.180340			0.00600799
$902$	−8.47214	+	1.90211i	−0.282091	+	0.0633334i
$903$	−10.0000			−0.332779
$904$	3.56231	−	10.9637i	0.118481	−	0.364646i
$905$	8.85410	−	6.43288i	0.294320	−	0.213836i
$906$	−5.85410	−	4.25325i	−0.194490	−	0.141305i
$907$	9.61803	+	29.6013i	0.319362	+	0.982894i	0.973922	+	0.226884i	$0.0728538\pi$
$907$	9.61803	+	29.6013i	0.319362	+	0.982894i	−0.654560	+	0.756010i	$0.727146\pi$
$908$	−2.23607	−	6.88191i	−0.0742065	−	0.228384i
$909$	9.20820	+	6.69015i	0.305417	+	0.221898i
$910$	−1.00000	+	0.726543i	−0.0331497	+	0.0240847i
$911$	−15.2361	+	46.8918i	−0.504793	+	1.55359i	0.296324	+	0.955087i	$0.404239\pi$
$911$	−15.2361	+	46.8918i	−0.504793	+	1.55359i	−0.801118	+	0.598507i	$0.795761\pi$
$912$	4.85410			0.160735
$913$	8.94427	−	2.00811i	0.296012	−	0.0664589i
$914$	−18.3607			−0.607317
$915$	2.32624	−	7.15942i	0.0769031	−	0.236683i
$916$	3.23607	−	2.35114i	0.106923	−	0.0776839i
$917$		0			0
$918$	0.118034	+	0.363271i	0.00389570	+	0.0119897i
$919$	17.9443	+	55.2268i	0.591927	+	1.82176i	0.569464	+	0.822016i	$0.307151\pi$
$919$	17.9443	+	55.2268i	0.591927	+	1.82176i	0.0224626	+	0.999748i	$0.492849\pi$
$920$	2.42705	+	1.76336i	0.0800175	+	0.0581361i
$921$	0.354102	−	0.257270i	0.0116681	−	0.00847734i
$922$	−6.50658	+	20.0252i	−0.214283	+	0.659494i
$923$	12.9443			0.426066
$924$	2.19098	−	2.48990i	0.0720780	−	0.0819116i
$925$	−17.7984			−0.585207
$926$	11.9098	−	36.6547i	0.391381	−	1.20455i
$927$	−6.92705	+	5.03280i	−0.227514	+	0.165299i
$928$	−2.00000	−	1.45309i	−0.0656532	−	0.0476999i
$929$	−3.35410	−	10.3229i	−0.110045	−	0.338682i	0.880837	−	0.473420i	$-0.156981\pi$
$929$	−3.35410	−	10.3229i	−0.110045	−	0.338682i	−0.990881	+	0.134738i	$0.956981\pi$
$930$	−0.881966	−	2.71441i	−0.0289208	−	0.0890091i
$931$	3.92705	+	2.85317i	0.128704	+	0.0935089i
$932$	−0.618034	+	0.449028i	−0.0202444	+	0.0147084i
$933$	−10.0344	+	30.8828i	−0.328513	+	1.01106i
$934$	−27.8885			−0.912541
$935$	−0.399187	−	0.673542i	−0.0130548	−	0.0220272i
$936$	−2.00000			−0.0653720
$937$	1.43769	−	4.42477i	0.0469674	−	0.144551i	−0.924823	−	0.380399i	$-0.875787\pi$
$937$	1.43769	−	4.42477i	0.0469674	−	0.144551i	0.971790	+	0.235848i	$0.0757867\pi$
$938$	−9.85410	+	7.15942i	−0.321748	+	0.233763i
$939$	14.3262	+	10.4086i	0.467519	+	0.339673i
$940$	−1.23607	−	3.80423i	−0.0403161	−	0.124080i
$941$	−6.15248	−	18.9354i	−0.200565	−	0.617276i	−0.999866	−	0.0163452i	$-0.994797\pi$
$941$	−6.15248	−	18.9354i	−0.200565	−	0.617276i	0.799301	−	0.600930i	$-0.205203\pi$
$942$	−3.00000	−	2.17963i	−0.0977453	−	0.0710161i
$943$	10.2812	−	7.46969i	0.334800	−	0.243247i
$944$	−1.61803	+	4.97980i	−0.0526625	+	0.162079i
$945$	0.618034			0.0201046
$946$	30.4508	+	13.1433i	0.990043	+	0.427325i
$947$	33.9230			1.10235			0.551174	−	0.834390i	$-0.314180\pi$
$947$	33.9230			1.10235			0.551174	+	0.834390i	$0.314180\pi$
$948$	−4.47214	+	13.7638i	−0.145248	+	0.447028i
$949$	16.4721	−	11.9677i	0.534708	−	0.388488i
$950$	18.1353	+	13.1760i	0.588385	+	0.427487i
$951$	4.14590	+	12.7598i	0.134440	+	0.413764i
$952$	−0.118034	−	0.363271i	−0.00382550	−	0.0117737i
$953$	9.70820	+	7.05342i	0.314480	+	0.228483i	0.733816	−	0.679348i	$-0.237737\pi$
$953$	9.70820	+	7.05342i	0.314480	+	0.228483i	−0.419337	+	0.907831i	$0.637737\pi$
$954$	0.381966	−	0.277515i	0.0123666	−	0.00898487i
$955$	2.79180	−	8.59226i	0.0903404	−	0.278039i
$956$	−25.7984			−0.834379
$957$	0.763932	−	8.16348i	0.0246944	−	0.263888i
$958$	18.4721			0.596808
$959$	1.61803	−	4.97980i	0.0522490	−	0.160806i
$960$	−0.500000	+	0.363271i	−0.0161374	+	0.0117245i
$961$	7.82624	+	5.68609i	0.252459	+	0.183422i
$962$	−2.38197	−	7.33094i	−0.0767977	−	0.236359i
$963$	0.354102	+	1.08981i	0.0114108	+	0.0351188i
$964$	−23.5623	−	17.1190i	−0.758891	−	0.551366i
$965$	9.07295	−	6.59188i	0.292069	−	0.212200i
$966$	−1.50000	+	4.61653i	−0.0482617	+	0.148534i
$967$	−30.0000			−0.964735			−0.482367	−	0.875969i	$-0.660223\pi$
$967$	−30.0000			−0.964735			−0.482367	+	0.875969i	$0.660223\pi$
$968$	−9.94427	+	4.70228i	−0.319621	+	0.151137i
$969$	1.85410			0.0595623
$970$	−1.94427	+	5.98385i	−0.0624268	+	0.192130i
$971$	−14.0344	+	10.1966i	−0.450387	+	0.327225i	−0.789748	−	0.613431i	$-0.789789\pi$
$971$	−14.0344	+	10.1966i	−0.450387	+	0.327225i	0.339362	+	0.940656i	$0.389789\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−0.500000	−	1.53884i	−0.0160293	−	0.0493330i
$974$	0.729490	+	2.24514i	0.0233744	+	0.0719389i
$975$	−7.47214	−	5.42882i	−0.239300	−	0.173862i
$976$	−9.85410	+	7.15942i	−0.315422	+	0.229168i
$977$	−3.70820	+	11.4127i	−0.118636	+	0.365124i	−0.992688	−	0.120708i	$-0.961483\pi$
$977$	−3.70820	+	11.4127i	−0.118636	+	0.365124i	0.874052	+	0.485832i	$0.161483\pi$
$978$	10.0000			0.319765
$979$	−4.88197	+	52.1694i	−0.156028	+	1.66734i
$980$	−0.618034			−0.0197424
$981$	1.28115	−	3.94298i	0.0409041	−	0.125890i
$982$	5.07295	−	3.68571i	0.161884	−	0.117616i
$983$	−40.7426	−	29.6013i	−1.29949	−	0.944134i	−0.299538	−	0.954084i	$-0.596833\pi$
$983$	−40.7426	−	29.6013i	−1.29949	−	0.944134i	−0.999950	+	0.00995062i	$0.996833\pi$
$984$	0.809017	+	2.48990i	0.0257905	+	0.0793751i
$985$	−3.85410	−	11.8617i	−0.122802	−	0.377945i
$986$	−0.763932	−	0.555029i	−0.0243286	−	0.0176757i
$987$	5.23607	−	3.80423i	0.166666	−	0.121090i
$988$	−3.00000	+	9.23305i	−0.0954427	+	0.293742i
$989$	−48.5410			−1.54351
$990$	−1.88197	−	0.812299i	−0.0598128	−	0.0258166i
$991$	−1.59675			−0.0507224			−0.0253612	−	0.999678i	$-0.508074\pi$
$991$	−1.59675			−0.0507224			−0.0253612	+	0.999678i	$0.508074\pi$
$992$	−1.42705	+	4.39201i	−0.0453089	+	0.139446i
$993$	2.23607	−	1.62460i	0.0709595	−	0.0515551i
$994$	5.23607	+	3.80423i	0.166078	+	0.120663i
$995$	−0.836881	−	2.57565i	−0.0265309	−	0.0816538i
$996$	−0.854102	−	2.62866i	−0.0270633	−	0.0832921i
$997$	46.9787	+	34.1320i	1.48783	+	1.08097i	0.974927	+	0.222526i	$0.0714304\pi$
$997$	46.9787	+	34.1320i	1.48783	+	1.08097i	0.512904	+	0.858446i	$0.328570\pi$
$998$	22.2705	−	16.1805i	0.704961	−	0.512184i
$999$	−1.19098	+	3.66547i	−0.0376810	+	0.115970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.d.295.1	✓	4
11.4	even	5		5082.2.a.bf.1.1		2
11.5	even	5	inner	462.2.j.d.379.1	yes	4
11.7	odd	10		5082.2.a.bp.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.d.295.1	✓	4	1.1	even	1	trivial
462.2.j.d.379.1	yes	4	11.5	even	5	inner
5082.2.a.bf.1.1		2	11.4	even	5
5082.2.a.bp.1.1		2	11.7	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.190983 - 0.587785i) 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} +0.618034 q^{10} +(0.309017 - 3.30220i) q^{11} -1.00000 q^{12} +(0.618034 - 1.90211i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.118034 + 0.363271i) q^{17} +(0.809017 + 0.587785i) q^{18} +(3.92705 - 2.85317i) q^{19} +(-0.190983 + 0.587785i) q^{20} -1.00000 q^{21} +(3.04508 + 1.31433i) q^{22} -4.85410 q^{23} +(0.309017 - 0.951057i) q^{24} +(3.73607 - 2.71441i) q^{25} +(1.61803 + 1.17557i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.309017 + 0.951057i) q^{28} +(2.00000 + 1.45309i) q^{29} +(0.500000 - 0.363271i) q^{30} +(1.42705 - 4.39201i) q^{31} -1.00000 q^{32} +(-1.69098 - 2.85317i) q^{33} -0.381966 q^{34} +(-0.190983 + 0.587785i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.11803 - 2.26538i) q^{37} +(1.50000 + 4.61653i) q^{38} +(-0.618034 - 1.90211i) q^{39} +(-0.500000 - 0.363271i) q^{40} +(-2.11803 + 1.53884i) q^{41} +(0.309017 - 0.951057i) q^{42} +10.0000 q^{43} +(-2.19098 + 2.48990i) q^{44} -0.618034 q^{45} +(1.50000 - 4.61653i) q^{46} +(-5.23607 + 3.80423i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.42705 + 4.39201i) q^{50} +(0.309017 + 0.224514i) q^{51} +(-1.61803 + 1.17557i) q^{52} +(0.145898 - 0.449028i) q^{53} +1.00000 q^{54} +(-2.00000 + 0.449028i) q^{55} -1.00000 q^{56} +(1.50000 - 4.61653i) q^{57} +(-2.00000 + 1.45309i) q^{58} +(4.23607 + 3.07768i) q^{59} +(0.190983 + 0.587785i) q^{60} +(3.76393 + 11.5842i) q^{61} +(3.73607 + 2.71441i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.23607 q^{65} +(3.23607 - 0.726543i) q^{66} -12.1803 q^{67} +(0.118034 - 0.363271i) q^{68} +(-3.92705 + 2.85317i) q^{69} +(-0.500000 - 0.363271i) q^{70} +(2.00000 + 6.15537i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(8.23607 + 5.98385i) q^{73} +(3.11803 - 2.26538i) q^{74} +(1.42705 - 4.39201i) q^{75} -4.85410 q^{76} +(-2.19098 + 2.48990i) q^{77} +2.00000 q^{78} +(4.47214 - 13.7638i) q^{79} +(0.500000 - 0.363271i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.809017 - 2.48990i) q^{82} +(0.854102 + 2.62866i) q^{83} +(0.809017 + 0.587785i) q^{84} +(0.190983 - 0.138757i) q^{85} +(-3.09017 + 9.51057i) q^{86} +2.47214 q^{87} +(-1.69098 - 2.85317i) q^{88} -15.7984 q^{89} +(0.190983 - 0.587785i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(3.92705 + 2.85317i) q^{92} +(-1.42705 - 4.39201i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(-2.42705 - 1.76336i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-3.14590 + 9.68208i) q^{97} -1.00000 q^{98} +(-3.04508 - 1.31433i) 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

Introduction

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