LMFDB - Embedded newform 546.2.i.h.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.h.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(-0.207107 - 0.358719i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.62132 + 2.09077i) q^{14} -1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.62132 - 4.54026i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.50000 + 2.59808i) q^{19} -1.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} +0.414214 q^{22} +(4.53553 - 7.85578i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.50000 + 2.59808i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 2.44949i) q^{28} +5.00000 q^{29} +(0.707107 - 1.22474i) q^{30} +(-3.41421 - 5.91359i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.207107 + 0.358719i) q^{33} +5.24264 q^{34} +(2.29289 - 2.95680i) q^{35} +1.00000 q^{36} +(2.53553 - 4.39167i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(0.707107 - 1.22474i) q^{40} +4.58579 q^{41} +(2.62132 + 0.358719i) q^{42} +4.82843 q^{43} +(-0.207107 + 0.358719i) q^{44} +(0.707107 + 1.22474i) q^{45} +(4.53553 + 7.85578i) q^{46} +(-4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(6.74264 + 1.88064i) q^{49} -3.00000 q^{50} +(-2.62132 + 4.54026i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-6.15685 - 10.6640i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.585786 q^{55} +(2.62132 + 0.358719i) q^{56} +3.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(-3.79289 - 6.56948i) q^{59} +(0.707107 + 1.22474i) q^{60} +(2.62132 - 4.54026i) q^{61} +6.82843 q^{62} +(-1.62132 + 2.09077i) q^{63} +1.00000 q^{64} +(0.707107 - 1.22474i) q^{65} +(-0.207107 - 0.358719i) q^{66} +(7.32843 + 12.6932i) q^{67} +(-2.62132 + 4.54026i) q^{68} -9.07107 q^{69} +(1.41421 + 3.46410i) q^{70} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.535534 + 0.927572i) q^{73} +(2.53553 + 4.39167i) q^{74} +(1.50000 - 2.59808i) q^{75} +3.00000 q^{76} +(-0.414214 - 1.01461i) q^{77} +1.00000 q^{78} +(-6.65685 + 11.5300i) q^{79} +(0.707107 + 1.22474i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.29289 + 3.97141i) q^{82} -7.65685 q^{83} +(-1.62132 + 2.09077i) q^{84} -7.41421 q^{85} +(-2.41421 + 4.18154i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(-0.207107 - 0.358719i) q^{88} +(3.12132 - 5.40629i) q^{89} -1.41421 q^{90} +(2.62132 + 0.358719i) q^{91} -9.07107 q^{92} +(-3.41421 + 5.91359i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(2.12132 + 3.67423i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.89949 q^{97} +(-5.00000 + 4.89898i) q^{98} +0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 8 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} + 12 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{38} - 2 q^{39} + 24 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 4 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} - 12 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 2 q^{61} + 16 q^{62} + 2 q^{63} + 4 q^{64} + 2 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 4 q^{77} + 4 q^{78} - 4 q^{79} - 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 24 q^{85} - 4 q^{86} - 10 q^{87} + 2 q^{88} + 4 q^{89} + 2 q^{91} - 8 q^{92} - 8 q^{93} - 18 q^{94} - 2 q^{96} - 8 q^{97} - 20 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 8 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^38 - 2 * q^39 + 24 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 4 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 - 12 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 2 * q^61 + 16 * q^62 + 2 * q^63 + 4 * q^64 + 2 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 4 * q^77 + 4 * q^78 - 4 * q^79 - 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 24 * q^85 - 4 * q^86 - 10 * q^87 + 2 * q^88 + 4 * q^89 + 2 * q^91 - 8 * q^92 - 8 * q^93 - 18 * q^94 - 2 * q^96 - 8 * q^97 - 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	−0.663470	−	0.748203i	$-0.730917\pi$
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	0.979698	+	0.200480i	$0.0642503\pi$
$6$	1.00000			0.408248
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.707107	+	1.22474i	0.223607	+	0.387298i
$11$	−0.207107	−	0.358719i	−0.0624450	−	0.108158i	0.833113	−	0.553103i	$-0.186556\pi$
$11$	−0.207107	−	0.358719i	−0.0624450	−	0.108158i	−0.895558	+	0.444945i	$0.853223\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−1.62132	+	2.09077i	−0.433316	+	0.558782i
$15$	−1.41421			−0.365148
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.62132	−	4.54026i	−0.635764	−	1.10117i	−0.986353	−	0.164645i	$-0.947352\pi$
$17$	−2.62132	−	4.54026i	−0.635764	−	1.10117i	0.350589	−	0.936529i	$-0.385981\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$	−1.41421			−0.316228
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$	0.414214			0.0883106
$23$	4.53553	−	7.85578i	0.945724	−	1.63804i	0.191429	−	0.981506i	$-0.438688\pi$
$23$	4.53553	−	7.85578i	0.945724	−	1.63804i	0.754295	−	0.656536i	$-0.227979\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.50000	+	2.59808i	0.300000	+	0.519615i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	−1.00000	−	2.44949i	−0.188982	−	0.462910i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	0.707107	−	1.22474i	0.129099	−	0.223607i
$31$	−3.41421	−	5.91359i	−0.613211	−	1.06211i	−0.990696	−	0.136097i	$-0.956544\pi$
$31$	−3.41421	−	5.91359i	−0.613211	−	1.06211i	0.377485	−	0.926016i	$-0.376789\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.207107	+	0.358719i	−0.0360527	+	0.0624450i
$34$	5.24264			0.899105
$35$	2.29289	−	2.95680i	0.387570	−	0.499790i
$36$	1.00000			0.166667
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	−0.578780	−	0.815483i	$-0.696471\pi$
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	0.995620	+	0.0934968i	$0.0298045\pi$
$38$	−1.50000	−	2.59808i	−0.243332	−	0.421464i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	0.707107	−	1.22474i	0.111803	−	0.193649i
$41$	4.58579			0.716180			0.358090	−	0.933687i	$-0.383428\pi$
$41$	4.58579			0.716180			0.358090	+	0.933687i	$0.383428\pi$
$42$	2.62132	+	0.358719i	0.404479	+	0.0553516i
$43$	4.82843			0.736328			0.368164	−	0.929761i	$-0.379986\pi$
$43$	4.82843			0.736328			0.368164	+	0.929761i	$0.379986\pi$
$44$	−0.207107	+	0.358719i	−0.0312225	+	0.0540790i
$45$	0.707107	+	1.22474i	0.105409	+	0.182574i
$46$	4.53553	+	7.85578i	0.668728	+	1.15827i
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$	1.00000			0.144338
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	−3.00000			−0.424264
$51$	−2.62132	+	4.54026i	−0.367058	+	0.635764i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−6.15685	−	10.6640i	−0.845709	−	1.46481i	−0.885004	−	0.465583i	$-0.845845\pi$
$53$	−6.15685	−	10.6640i	−0.845709	−	1.46481i	0.0392951	−	0.999228i	$-0.487489\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.585786			−0.0789874
$56$	2.62132	+	0.358719i	0.350289	+	0.0479359i
$57$	3.00000			0.397360
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	−3.79289	−	6.56948i	−0.493793	−	0.855274i	0.506182	−	0.862427i	$-0.331056\pi$
$59$	−3.79289	−	6.56948i	−0.493793	−	0.855274i	−0.999974	+	0.00715287i	$0.997723\pi$
$60$	0.707107	+	1.22474i	0.0912871	+	0.158114i
$61$	2.62132	−	4.54026i	0.335626	−	0.581321i	−0.647979	−	0.761658i	$-0.724386\pi$
$61$	2.62132	−	4.54026i	0.335626	−	0.581321i	0.983605	+	0.180337i	$0.0577189\pi$
$62$	6.82843			0.867211
$63$	−1.62132	+	2.09077i	−0.204267	+	0.263412i
$64$	1.00000			0.125000
$65$	0.707107	−	1.22474i	0.0877058	−	0.151911i
$66$	−0.207107	−	0.358719i	−0.0254931	−	0.0441553i
$67$	7.32843	+	12.6932i	0.895310	+	1.55072i	0.833421	+	0.552639i	$0.186379\pi$
$67$	7.32843	+	12.6932i	0.895310	+	1.55072i	0.0618892	+	0.998083i	$0.480287\pi$
$68$	−2.62132	+	4.54026i	−0.317882	+	0.550587i
$69$	−9.07107			−1.09203
$70$	1.41421	+	3.46410i	0.169031	+	0.414039i
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	0.535534	+	0.927572i	0.0626795	+	0.108564i	0.895662	−	0.444735i	$-0.146702\pi$
$73$	0.535534	+	0.927572i	0.0626795	+	0.108564i	−0.832983	+	0.553299i	$0.813369\pi$
$74$	2.53553	+	4.39167i	0.294750	+	0.510522i
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$	3.00000			0.344124
$77$	−0.414214	−	1.01461i	−0.0472040	−	0.115626i
$78$	1.00000			0.113228
$79$	−6.65685	+	11.5300i	−0.748955	+	1.29723i	0.199370	+	0.979924i	$0.436111\pi$
$79$	−6.65685	+	11.5300i	−0.748955	+	1.29723i	−0.948324	+	0.317303i	$0.897223\pi$
$80$	0.707107	+	1.22474i	0.0790569	+	0.136931i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.29289	+	3.97141i	−0.253208	+	0.438569i
$83$	−7.65685			−0.840449			−0.420224	−	0.907420i	$-0.638049\pi$
$83$	−7.65685			−0.840449			−0.420224	+	0.907420i	$0.638049\pi$
$84$	−1.62132	+	2.09077i	−0.176901	+	0.228122i
$85$	−7.41421			−0.804184
$86$	−2.41421	+	4.18154i	−0.260331	+	0.450907i
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$	−0.207107	−	0.358719i	−0.0220777	−	0.0382396i
$89$	3.12132	−	5.40629i	0.330859	−	0.573065i	−0.651821	−	0.758373i	$-0.725995\pi$
$89$	3.12132	−	5.40629i	0.330859	−	0.573065i	0.982681	+	0.185307i	$0.0593281\pi$
$90$	−1.41421			−0.149071
$91$	2.62132	+	0.358719i	0.274789	+	0.0376040i
$92$	−9.07107			−0.945724
$93$	−3.41421	+	5.91359i	−0.354037	+	0.613211i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$	2.12132	+	3.67423i	0.217643	+	0.376969i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	7.89949			0.802072			0.401036	−	0.916062i	$-0.368650\pi$
$97$	7.89949			0.802072			0.401036	+	0.916062i	$0.368650\pi$
$98$	−5.00000	+	4.89898i	−0.505076	+	0.494872i
$99$	0.414214			0.0416300
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	0.585786	+	1.01461i	0.0582879	+	0.100958i	0.893697	−	0.448671i	$-0.148103\pi$
$101$	0.585786	+	1.01461i	0.0582879	+	0.100958i	−0.835409	+	0.549629i	$0.814769\pi$
$102$	−2.62132	−	4.54026i	−0.259549	−	0.449553i
$103$	−3.24264	+	5.61642i	−0.319507	+	0.553402i	−0.980385	−	0.197091i	$-0.936851\pi$
$103$	−3.24264	+	5.61642i	−0.319507	+	0.553402i	0.660878	+	0.750493i	$0.270184\pi$
$104$	1.00000			0.0980581
$105$	−3.70711	−	0.507306i	−0.361777	−	0.0495080i
$106$	12.3137			1.19601
$107$	−6.82843	+	11.8272i	−0.660129	+	1.14338i	0.320452	+	0.947265i	$0.396165\pi$
$107$	−6.82843	+	11.8272i	−0.660129	+	1.14338i	−0.980581	+	0.196112i	$0.937168\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	0.823620	−	0.567142i	$-0.191951\pi$
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	−0.902969	+	0.429705i	$0.858617\pi$
$110$	0.292893	−	0.507306i	0.0279263	−	0.0483697i
$111$	−5.07107			−0.481324
$112$	−1.62132	+	2.09077i	−0.153200	+	0.197559i
$113$	−6.07107			−0.571118			−0.285559	−	0.958361i	$-0.592179\pi$
$113$	−6.07107			−0.571118			−0.285559	+	0.958361i	$0.592179\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$	−6.41421	−	11.1097i	−0.598128	−	1.03599i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	7.58579			0.698328
$119$	−5.24264	−	12.8418i	−0.480592	−	1.17721i
$120$	−1.41421			−0.129099
$121$	5.41421	−	9.37769i	0.492201	−	0.852518i
$122$	2.62132	+	4.54026i	0.237323	+	0.411056i
$123$	−2.29289	−	3.97141i	−0.206743	−	0.358090i
$124$	−3.41421	+	5.91359i	−0.306605	+	0.531056i
$125$	11.3137			1.01193
$126$	−1.00000	−	2.44949i	−0.0890871	−	0.218218i
$127$	9.89949			0.878438			0.439219	−	0.898380i	$-0.355255\pi$
$127$	9.89949			0.878438			0.439219	+	0.898380i	$0.355255\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.41421	−	4.18154i	−0.212560	−	0.368164i
$130$	0.707107	+	1.22474i	0.0620174	+	0.107417i
$131$	−4.94975	+	8.57321i	−0.432461	+	0.749045i	−0.997085	−	0.0763036i	$-0.975688\pi$
$131$	−4.94975	+	8.57321i	−0.432461	+	0.749045i	0.564623	+	0.825349i	$0.309022\pi$
$132$	0.414214			0.0360527
$133$	−4.86396	+	6.27231i	−0.421759	+	0.543878i
$134$	−14.6569			−1.26616
$135$	0.707107	−	1.22474i	0.0608581	−	0.105409i
$136$	−2.62132	−	4.54026i	−0.224776	−	0.389324i
$137$	6.53553	+	11.3199i	0.558368	+	0.967122i	0.997633	+	0.0687646i	$0.0219057\pi$
$137$	6.53553	+	11.3199i	0.558368	+	0.967122i	−0.439265	+	0.898358i	$0.644761\pi$
$138$	4.53553	−	7.85578i	0.386090	−	0.668728i
$139$	−21.2132			−1.79928			−0.899640	−	0.436632i	$-0.856171\pi$
$139$	−21.2132			−1.79928			−0.899640	+	0.436632i	$0.856171\pi$
$140$	−3.70711	−	0.507306i	−0.313308	−	0.0428752i
$141$	9.00000			0.757937
$142$	0.500000	−	0.866025i	0.0419591	−	0.0726752i
$143$	−0.207107	−	0.358719i	−0.0173191	−	0.0299976i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.53553	−	6.12372i	0.293610	−	0.508548i
$146$	−1.07107			−0.0886422
$147$	−1.74264	−	6.77962i	−0.143731	−	0.559173i
$148$	−5.07107			−0.416839
$149$	−7.94975	+	13.7694i	−0.651269	+	1.12803i	0.331547	+	0.943439i	$0.392430\pi$
$149$	−7.94975	+	13.7694i	−0.651269	+	1.12803i	−0.982815	+	0.184592i	$0.940904\pi$
$150$	1.50000	+	2.59808i	0.122474	+	0.212132i
$151$	3.79289	+	6.56948i	0.308661	+	0.534617i	0.978070	−	0.208278i	$-0.0667857\pi$
$151$	3.79289	+	6.56948i	0.308661	+	0.534617i	−0.669408	+	0.742895i	$0.733452\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	5.24264			0.423842
$154$	1.08579	+	0.148586i	0.0874952	+	0.0119734i
$155$	−9.65685			−0.775657
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−3.96447	−	6.86666i	−0.316399	−	0.548019i	0.663335	−	0.748323i	$-0.269140\pi$
$157$	−3.96447	−	6.86666i	−0.316399	−	0.548019i	−0.979734	+	0.200304i	$0.935807\pi$
$158$	−6.65685	−	11.5300i	−0.529591	−	0.917278i
$159$	−6.15685	+	10.6640i	−0.488270	+	0.845709i
$160$	−1.41421			−0.111803
$161$	14.7071	−	18.9655i	1.15908	−	1.49469i
$162$	1.00000			0.0785674
$163$	−8.57107	+	14.8455i	−0.671338	+	1.16279i	0.306187	+	0.951971i	$0.400947\pi$
$163$	−8.57107	+	14.8455i	−0.671338	+	1.16279i	−0.977525	+	0.210820i	$0.932387\pi$
$164$	−2.29289	−	3.97141i	−0.179045	−	0.310115i
$165$	0.292893	+	0.507306i	0.0228017	+	0.0394937i
$166$	3.82843	−	6.63103i	0.297144	−	0.514668i
$167$	12.3137			0.952863			0.476432	−	0.879211i	$-0.341930\pi$
$167$	12.3137			0.952863			0.476432	+	0.879211i	$0.341930\pi$
$168$	−1.00000	−	2.44949i	−0.0771517	−	0.188982i
$169$	1.00000			0.0769231
$170$	3.70711	−	6.42090i	0.284322	−	0.492460i
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	−2.41421	−	4.18154i	−0.184082	−	0.318839i
$173$	−10.1569	+	17.5922i	−0.772211	+	1.33751i	0.164137	+	0.986438i	$0.447516\pi$
$173$	−10.1569	+	17.5922i	−0.772211	+	1.33751i	−0.936349	+	0.351072i	$0.885817\pi$
$174$	5.00000			0.379049
$175$	3.00000	+	7.34847i	0.226779	+	0.555492i
$176$	0.414214			0.0312225
$177$	−3.79289	+	6.56948i	−0.285091	+	0.493793i
$178$	3.12132	+	5.40629i	0.233953	+	0.405218i
$179$	6.17157	+	10.6895i	0.461285	+	0.798969i	0.999025	−	0.0441415i	$-0.0140552\pi$
$179$	6.17157	+	10.6895i	0.461285	+	0.798969i	−0.537740	+	0.843111i	$0.680722\pi$
$180$	0.707107	−	1.22474i	0.0527046	−	0.0912871i
$181$	−11.5858			−0.861165			−0.430582	−	0.902551i	$-0.641692\pi$
$181$	−11.5858			−0.861165			−0.430582	+	0.902551i	$0.641692\pi$
$182$	−1.62132	+	2.09077i	−0.120180	+	0.154978i
$183$	−5.24264			−0.387547
$184$	4.53553	−	7.85578i	0.334364	−	0.579135i
$185$	−3.58579	−	6.21076i	−0.263632	−	0.456624i
$186$	−3.41421	−	5.91359i	−0.250342	−	0.433606i
$187$	−1.08579	+	1.88064i	−0.0794006	+	0.137526i
$188$	9.00000			0.656392
$189$	2.62132	+	0.358719i	0.190673	+	0.0260930i
$190$	−4.24264			−0.307794
$191$	−1.17157	+	2.02922i	−0.0847720	+	0.146829i	−0.905294	−	0.424785i	$-0.860350\pi$
$191$	−1.17157	+	2.02922i	−0.0847720	+	0.146829i	0.820522	+	0.571615i	$0.193683\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	7.87868	+	13.6463i	0.567120	+	0.982280i	0.996849	+	0.0793225i	$0.0252757\pi$
$193$	7.87868	+	13.6463i	0.567120	+	0.982280i	−0.429729	+	0.902958i	$0.641391\pi$
$194$	−3.94975	+	6.84116i	−0.283575	+	0.491167i
$195$	−1.41421			−0.101274
$196$	−1.74264	−	6.77962i	−0.124474	−	0.484258i
$197$	9.55635			0.680862			0.340431	−	0.940270i	$-0.389427\pi$
$197$	9.55635			0.680862			0.340431	+	0.940270i	$0.389427\pi$
$198$	−0.207107	+	0.358719i	−0.0147184	+	0.0254931i
$199$	−5.29289	−	9.16756i	−0.375203	−	0.649871i	0.615154	−	0.788407i	$-0.289094\pi$
$199$	−5.29289	−	9.16756i	−0.375203	−	0.649871i	−0.990357	+	0.138536i	$0.955760\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$	7.32843	−	12.6932i	0.516907	−	0.895310i
$202$	−1.17157			−0.0824316
$203$	13.1066	+	1.79360i	0.919903	+	0.125886i
$204$	5.24264			0.367058
$205$	3.24264	−	5.61642i	0.226476	−	0.392268i
$206$	−3.24264	−	5.61642i	−0.225925	−	0.391314i
$207$	4.53553	+	7.85578i	0.315241	+	0.546014i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	1.24264			0.0859553
$210$	2.29289	−	2.95680i	0.158225	−	0.204038i
$211$	−28.3848			−1.95409			−0.977044	−	0.213036i	$-0.931665\pi$
$211$	−28.3848			−1.95409			−0.977044	+	0.213036i	$0.931665\pi$
$212$	−6.15685	+	10.6640i	−0.422854	+	0.732405i
$213$	0.500000	+	0.866025i	0.0342594	+	0.0593391i
$214$	−6.82843	−	11.8272i	−0.466782	−	0.808490i
$215$	3.41421	−	5.91359i	0.232847	−	0.403304i
$216$	1.00000			0.0680414
$217$	−6.82843	−	16.7262i	−0.463544	−	1.13545i
$218$	1.65685			0.112216
$219$	0.535534	−	0.927572i	0.0361880	−	0.0626795i
$220$	0.292893	+	0.507306i	0.0197469	+	0.0342026i
$221$	−2.62132	−	4.54026i	−0.176329	−	0.305411i
$222$	2.53553	−	4.39167i	0.170174	−	0.294750i
$223$	21.3848			1.43203			0.716015	−	0.698085i	$-0.245964\pi$
$223$	21.3848			1.43203			0.716015	+	0.698085i	$0.245964\pi$
$224$	−1.00000	−	2.44949i	−0.0668153	−	0.163663i
$225$	−3.00000			−0.200000
$226$	3.03553	−	5.25770i	0.201921	−	0.349737i
$227$	13.0711	+	22.6398i	0.867557	+	1.50265i	0.864485	+	0.502658i	$0.167644\pi$
$227$	13.0711	+	22.6398i	0.867557	+	1.50265i	0.00307185	+	0.999995i	$0.499022\pi$
$228$	−1.50000	−	2.59808i	−0.0993399	−	0.172062i
$229$	3.58579	−	6.21076i	0.236955	−	0.410419i	−0.722884	−	0.690970i	$-0.757184\pi$
$229$	3.58579	−	6.21076i	0.236955	−	0.410419i	0.959839	+	0.280551i	$0.0905171\pi$
$230$	12.8284			0.845881
$231$	−0.671573	+	0.866025i	−0.0441863	+	0.0569803i
$232$	5.00000			0.328266
$233$	1.86396	−	3.22848i	0.122112	−	0.211504i	−0.798488	−	0.602010i	$-0.794367\pi$
$233$	1.86396	−	3.22848i	0.122112	−	0.211504i	0.920600	+	0.390506i	$0.127700\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	6.36396	+	11.0227i	0.415139	+	0.719042i
$236$	−3.79289	+	6.56948i	−0.246896	+	0.427637i
$237$	13.3137			0.864818
$238$	13.7426	+	1.88064i	0.890803	+	0.121904i
$239$	−2.51472			−0.162664			−0.0813318	−	0.996687i	$-0.525917\pi$
$239$	−2.51472			−0.162664			−0.0813318	+	0.996687i	$0.525917\pi$
$240$	0.707107	−	1.22474i	0.0456435	−	0.0790569i
$241$	8.24264	+	14.2767i	0.530955	+	0.919641i	0.999347	+	0.0361207i	$0.0115001\pi$
$241$	8.24264	+	14.2767i	0.530955	+	0.919641i	−0.468392	+	0.883521i	$0.655167\pi$
$242$	5.41421	+	9.37769i	0.348039	+	0.602821i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.24264			−0.335626
$245$	7.07107	−	6.92820i	0.451754	−	0.442627i
$246$	4.58579			0.292379
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$	−3.41421	−	5.91359i	−0.216803	−	0.375513i
$249$	3.82843	+	6.63103i	0.242617	+	0.420224i
$250$	−5.65685	+	9.79796i	−0.357771	+	0.619677i
$251$	12.8284			0.809723			0.404862	−	0.914378i	$-0.367320\pi$
$251$	12.8284			0.809723			0.404862	+	0.914378i	$0.367320\pi$
$252$	2.62132	+	0.358719i	0.165128	+	0.0225972i
$253$	−3.75736			−0.236223
$254$	−4.94975	+	8.57321i	−0.310575	+	0.537931i
$255$	3.70711	+	6.42090i	0.232148	+	0.402092i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.8995	−	18.8785i	0.679892	−	1.17761i	−0.295121	−	0.955460i	$-0.595360\pi$
$257$	10.8995	−	18.8785i	0.679892	−	1.17761i	0.975013	−	0.222147i	$-0.0713066\pi$
$258$	4.82843			0.300605
$259$	8.22183	−	10.6024i	0.510879	−	0.658803i
$260$	−1.41421			−0.0877058
$261$	−2.50000	+	4.33013i	−0.154746	+	0.268028i
$262$	−4.94975	−	8.57321i	−0.305796	−	0.529655i
$263$	3.77817	+	6.54399i	0.232972	+	0.403520i	0.958681	−	0.284482i	$-0.0918215\pi$
$263$	3.77817	+	6.54399i	0.232972	+	0.403520i	−0.725709	+	0.688002i	$0.758488\pi$
$264$	−0.207107	+	0.358719i	−0.0127465	+	0.0220777i
$265$	−17.4142			−1.06975
$266$	−3.00000	−	7.34847i	−0.183942	−	0.450564i
$267$	−6.24264			−0.382043
$268$	7.32843	−	12.6932i	0.447655	−	0.775361i
$269$	1.84315	+	3.19242i	0.112379	+	0.194645i	0.916729	−	0.399510i	$-0.130820\pi$
$269$	1.84315	+	3.19242i	0.112379	+	0.194645i	−0.804350	+	0.594155i	$0.797486\pi$
$270$	0.707107	+	1.22474i	0.0430331	+	0.0745356i
$271$	7.69239	−	13.3236i	0.467279	−	0.809351i	−0.532022	−	0.846731i	$-0.678568\pi$
$271$	7.69239	−	13.3236i	0.467279	−	0.809351i	0.999301	+	0.0373791i	$0.0119009\pi$
$272$	5.24264			0.317882
$273$	−1.00000	−	2.44949i	−0.0605228	−	0.148250i
$274$	−13.0711			−0.789652
$275$	0.621320	−	1.07616i	0.0374670	−	0.0648948i
$276$	4.53553	+	7.85578i	0.273007	+	0.472862i
$277$	8.20711	+	14.2151i	0.493117	+	0.854104i	0.999969	−	0.00792936i	$-0.00252402\pi$
$277$	8.20711	+	14.2151i	0.493117	+	0.854104i	−0.506851	+	0.862033i	$0.669191\pi$
$278$	10.6066	−	18.3712i	0.636142	−	1.10183i
$279$	6.82843			0.408807
$280$	2.29289	−	2.95680i	0.137027	−	0.176702i
$281$	7.31371			0.436299			0.218150	−	0.975915i	$-0.429998\pi$
$281$	7.31371			0.436299			0.218150	+	0.975915i	$0.429998\pi$
$282$	−4.50000	+	7.79423i	−0.267971	+	0.464140i
$283$	−8.53553	−	14.7840i	−0.507385	−	0.878816i	−0.999963	−	0.00854836i	$-0.997279\pi$
$283$	−8.53553	−	14.7840i	−0.507385	−	0.878816i	0.492579	−	0.870268i	$-0.336054\pi$
$284$	0.500000	+	0.866025i	0.0296695	+	0.0513892i
$285$	2.12132	−	3.67423i	0.125656	−	0.217643i
$286$	0.414214			0.0244930
$287$	12.0208	+	1.64501i	0.709566	+	0.0971019i
$288$	1.00000			0.0589256
$289$	−5.24264	+	9.08052i	−0.308391	+	0.534148i
$290$	3.53553	+	6.12372i	0.207614	+	0.359597i
$291$	−3.94975	−	6.84116i	−0.231538	−	0.401036i
$292$	0.535534	−	0.927572i	0.0313398	−	0.0542820i
$293$	−18.7279			−1.09410			−0.547048	−	0.837101i	$-0.684249\pi$
$293$	−18.7279			−1.09410			−0.547048	+	0.837101i	$0.684249\pi$
$294$	6.74264	+	1.88064i	0.393239	+	0.109681i
$295$	−10.7279			−0.624604
$296$	2.53553	−	4.39167i	0.147375	−	0.255261i
$297$	−0.207107	−	0.358719i	−0.0120176	−	0.0208150i
$298$	−7.94975	−	13.7694i	−0.460517	−	0.797638i
$299$	4.53553	−	7.85578i	0.262297	−	0.454311i
$300$	−3.00000			−0.173205
$301$	12.6569	+	1.73205i	0.729529	+	0.0998337i
$302$	−7.58579			−0.436513
$303$	0.585786	−	1.01461i	0.0336526	−	0.0582879i
$304$	−1.50000	−	2.59808i	−0.0860309	−	0.149010i
$305$	−3.70711	−	6.42090i	−0.212268	−	0.367660i
$306$	−2.62132	+	4.54026i	−0.149851	+	0.259549i
$307$	−19.6274			−1.12020			−0.560098	−	0.828426i	$-0.689237\pi$
$307$	−19.6274			−1.12020			−0.560098	+	0.828426i	$0.689237\pi$
$308$	−0.671573	+	0.866025i	−0.0382664	+	0.0493464i
$309$	6.48528			0.368935
$310$	4.82843	−	8.36308i	0.274236	−	0.474991i
$311$	3.29289	+	5.70346i	0.186723	+	0.323413i	0.944156	−	0.329500i	$-0.106880\pi$
$311$	3.29289	+	5.70346i	0.186723	+	0.323413i	−0.757433	+	0.652913i	$0.773547\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	−9.07107	+	15.7116i	−0.512727	+	0.888069i	0.487164	+	0.873310i	$0.338031\pi$
$313$	−9.07107	+	15.7116i	−0.512727	+	0.888069i	−0.999891	+	0.0147588i	$0.995302\pi$
$314$	7.92893			0.447456
$315$	1.41421	+	3.46410i	0.0796819	+	0.195180i
$316$	13.3137			0.748955
$317$	−0.414214	+	0.717439i	−0.0232646	+	0.0402954i	−0.877423	−	0.479717i	$-0.840739\pi$
$317$	−0.414214	+	0.717439i	−0.0232646	+	0.0402954i	0.854159	+	0.520012i	$0.174073\pi$
$318$	−6.15685	−	10.6640i	−0.345259	−	0.598007i
$319$	−1.03553	−	1.79360i	−0.0579788	−	0.100422i
$320$	0.707107	−	1.22474i	0.0395285	−	0.0684653i
$321$	13.6569			0.762251
$322$	9.07107	+	22.2195i	0.505511	+	1.23824i
$323$	15.7279			0.875125
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$	−8.57107	−	14.8455i	−0.474708	−	0.822218i
$327$	−0.828427	+	1.43488i	−0.0458121	+	0.0793489i
$328$	4.58579			0.253208
$329$	−14.5919	+	18.8169i	−0.804477	+	1.03741i
$330$	−0.585786			−0.0322465
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	−0.371908	−	0.928270i	$-0.621296\pi$
$331$	11.2426	−	19.4728i	0.617951	−	1.07032i	0.989859	−	0.142053i	$-0.0453705\pi$
$332$	3.82843	+	6.63103i	0.210112	+	0.363925i
$333$	2.53553	+	4.39167i	0.138946	+	0.240662i
$334$	−6.15685	+	10.6640i	−0.336888	+	0.583507i
$335$	20.7279			1.13249
$336$	2.62132	+	0.358719i	0.143005	+	0.0195698i
$337$	28.6569			1.56104			0.780519	−	0.625132i	$-0.214955\pi$
$337$	28.6569			1.56104			0.780519	+	0.625132i	$0.214955\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	3.03553	+	5.25770i	0.164868	+	0.285559i
$340$	3.70711	+	6.42090i	0.201046	+	0.348222i
$341$	−1.41421	+	2.44949i	−0.0765840	+	0.132647i
$342$	3.00000			0.162221
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	4.82843			0.260331
$345$	−6.41421	+	11.1097i	−0.345330	+	0.598128i
$346$	−10.1569	−	17.5922i	−0.546036	−	0.945762i
$347$	−2.87868	−	4.98602i	−0.154536	−	0.267664i	0.778354	−	0.627825i	$-0.216055\pi$
$347$	−2.87868	−	4.98602i	−0.154536	−	0.267664i	−0.932890	+	0.360162i	$0.882721\pi$
$348$	−2.50000	+	4.33013i	−0.134014	+	0.232119i
$349$	5.41421			0.289816			0.144908	−	0.989445i	$-0.453711\pi$
$349$	5.41421			0.289816			0.144908	+	0.989445i	$0.453711\pi$
$350$	−7.86396	−	1.07616i	−0.420346	−	0.0575231i
$351$	1.00000			0.0533761
$352$	−0.207107	+	0.358719i	−0.0110388	+	0.0191198i
$353$	−6.31371	−	10.9357i	−0.336045	−	0.582047i	0.647640	−	0.761946i	$-0.275756\pi$
$353$	−6.31371	−	10.9357i	−0.336045	−	0.582047i	−0.983685	+	0.179900i	$0.942423\pi$
$354$	−3.79289	−	6.56948i	−0.201590	−	0.349164i
$355$	−0.707107	+	1.22474i	−0.0375293	+	0.0650027i
$356$	−6.24264			−0.330859
$357$	−8.50000	+	10.9612i	−0.449868	+	0.580126i
$358$	−12.3431			−0.652356
$359$	7.72792	−	13.3852i	0.407864	−	0.706441i	−0.586786	−	0.809742i	$-0.699607\pi$
$359$	7.72792	−	13.3852i	0.407864	−	0.706441i	0.994650	+	0.103301i	$0.0329404\pi$
$360$	0.707107	+	1.22474i	0.0372678	+	0.0645497i
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	5.79289	−	10.0336i	0.304468	−	0.527354i
$363$	−10.8284			−0.568345
$364$	−1.00000	−	2.44949i	−0.0524142	−	0.128388i
$365$	1.51472			0.0792840
$366$	2.62132	−	4.54026i	0.137019	−	0.237323i
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	0.623443	−	0.781869i	$-0.285733\pi$
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	−0.988840	+	0.148983i	$0.952400\pi$
$368$	4.53553	+	7.85578i	0.236431	+	0.409511i
$369$	−2.29289	+	3.97141i	−0.119363	+	0.206743i
$370$	7.17157			0.372832
$371$	−12.3137	−	30.1623i	−0.639296	−	1.56595i
$372$	6.82843			0.354037
$373$	5.55025	−	9.61332i	0.287381	−	0.497759i	−0.685803	−	0.727788i	$-0.740549\pi$
$373$	5.55025	−	9.61332i	0.287381	−	0.497759i	0.973184	+	0.230029i	$0.0738820\pi$
$374$	−1.08579	−	1.88064i	−0.0561447	−	0.0972454i
$375$	−5.65685	−	9.79796i	−0.292119	−	0.505964i
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$	5.00000			0.257513
$378$	−1.62132	+	2.09077i	−0.0833917	+	0.107538i
$379$	−33.6569			−1.72884			−0.864418	−	0.502773i	$-0.832313\pi$
$379$	−33.6569			−1.72884			−0.864418	+	0.502773i	$0.832313\pi$
$380$	2.12132	−	3.67423i	0.108821	−	0.188484i
$381$	−4.94975	−	8.57321i	−0.253583	−	0.439219i
$382$	−1.17157	−	2.02922i	−0.0599429	−	0.103824i
$383$	−3.24264	+	5.61642i	−0.165691	+	0.286986i	−0.936901	−	0.349596i	$-0.886319\pi$
$383$	−3.24264	+	5.61642i	−0.165691	+	0.286986i	0.771209	+	0.636582i	$0.219652\pi$
$384$	1.00000			0.0510310
$385$	−1.53553	−	0.210133i	−0.0782581	−	0.0107094i
$386$	−15.7574			−0.802028
$387$	−2.41421	+	4.18154i	−0.122721	+	0.212560i
$388$	−3.94975	−	6.84116i	−0.200518	−	0.347307i
$389$	−11.5000	−	19.9186i	−0.583073	−	1.00991i	−0.995113	−	0.0987463i	$-0.968517\pi$
$389$	−11.5000	−	19.9186i	−0.583073	−	1.00991i	0.412039	−	0.911166i	$-0.364817\pi$
$390$	0.707107	−	1.22474i	0.0358057	−	0.0620174i
$391$	−47.5563			−2.40503
$392$	6.74264	+	1.88064i	0.340555	+	0.0949865i
$393$	9.89949			0.499363
$394$	−4.77817	+	8.27604i	−0.240721	+	0.416941i
$395$	9.41421	+	16.3059i	0.473680	+	0.820439i
$396$	−0.207107	−	0.358719i	−0.0104075	−	0.0180263i
$397$	9.87868	−	17.1104i	0.495797	−	0.858745i	−0.504192	−	0.863592i	$-0.668209\pi$
$397$	9.87868	−	17.1104i	0.495797	−	0.858745i	0.999988	+	0.00484675i	$0.00154277\pi$
$398$	10.5858			0.530618
$399$	7.86396	+	1.07616i	0.393690	+	0.0538753i
$400$	−3.00000			−0.150000
$401$	−9.53553	+	16.5160i	−0.476182	+	0.824771i	−0.999628	−	0.0272878i	$-0.991313\pi$
$401$	−9.53553	+	16.5160i	−0.476182	+	0.824771i	0.523446	+	0.852059i	$0.324646\pi$
$402$	7.32843	+	12.6932i	0.365509	+	0.633080i
$403$	−3.41421	−	5.91359i	−0.170074	−	0.294577i
$404$	0.585786	−	1.01461i	0.0291440	−	0.0504788i
$405$	−1.41421			−0.0702728
$406$	−8.10660	+	10.4539i	−0.402324	+	0.518816i
$407$	−2.10051			−0.104118
$408$	−2.62132	+	4.54026i	−0.129775	+	0.224776i
$409$	1.29289	+	2.23936i	0.0639295	+	0.110729i	0.896219	−	0.443613i	$-0.146303\pi$
$409$	1.29289	+	2.23936i	0.0639295	+	0.110729i	−0.832289	+	0.554342i	$0.812970\pi$
$410$	3.24264	+	5.61642i	0.160143	+	0.277375i
$411$	6.53553	−	11.3199i	0.322374	−	0.558368i
$412$	6.48528			0.319507
$413$	−7.58579	−	18.5813i	−0.373272	−	0.914326i
$414$	−9.07107			−0.445819
$415$	−5.41421	+	9.37769i	−0.265773	+	0.460333i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	10.6066	+	18.3712i	0.519408	+	0.899640i
$418$	−0.621320	+	1.07616i	−0.0303898	+	0.0526366i
$419$	−27.4558			−1.34131			−0.670653	−	0.741771i	$-0.733986\pi$
$419$	−27.4558			−1.34131			−0.670653	+	0.741771i	$0.733986\pi$
$420$	1.41421	+	3.46410i	0.0690066	+	0.169031i
$421$	10.5858			0.515920			0.257960	−	0.966156i	$-0.416950\pi$
$421$	10.5858			0.515920			0.257960	+	0.966156i	$0.416950\pi$
$422$	14.1924	−	24.5819i	0.690875	−	1.19663i
$423$	−4.50000	−	7.79423i	−0.218797	−	0.378968i
$424$	−6.15685	−	10.6640i	−0.299003	−	0.517889i
$425$	7.86396	−	13.6208i	0.381458	−	0.660705i
$426$	−1.00000			−0.0484502
$427$	8.50000	−	10.9612i	0.411344	−	0.530448i
$428$	13.6569			0.660129
$429$	−0.207107	+	0.358719i	−0.00999921	+	0.0173191i
$430$	3.41421	+	5.91359i	0.164648	+	0.285179i
$431$	−7.24264	−	12.5446i	−0.348866	−	0.604253i	0.637183	−	0.770713i	$-0.280100\pi$
$431$	−7.24264	−	12.5446i	−0.348866	−	0.604253i	−0.986048	+	0.166460i	$0.946766\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	17.8995	+	2.44949i	0.859203	+	0.117579i
$435$	−7.07107			−0.339032
$436$	−0.828427	+	1.43488i	−0.0396745	+	0.0687182i
$437$	13.6066	+	23.5673i	0.650892	+	1.12738i
$438$	0.535534	+	0.927572i	0.0255888	+	0.0443211i
$439$	5.29289	−	9.16756i	0.252616	−	0.437544i	−0.711629	−	0.702555i	$-0.752042\pi$
$439$	5.29289	−	9.16756i	0.252616	−	0.437544i	0.964245	+	0.265011i	$0.0853757\pi$
$440$	−0.585786			−0.0279263
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$	5.24264			0.249367
$443$	−11.3640	+	19.6830i	−0.539918	+	0.935166i	0.458990	+	0.888442i	$0.348211\pi$
$443$	−11.3640	+	19.6830i	−0.539918	+	0.935166i	−0.998908	+	0.0467240i	$0.985122\pi$
$444$	2.53553	+	4.39167i	0.120331	+	0.208420i
$445$	−4.41421	−	7.64564i	−0.209254	−	0.362438i
$446$	−10.6924	+	18.5198i	−0.506299	+	0.876936i
$447$	15.8995			0.752020
$448$	2.62132	+	0.358719i	0.123846	+	0.0169479i
$449$	−33.9411			−1.60178			−0.800890	−	0.598811i	$-0.795640\pi$
$449$	−33.9411			−1.60178			−0.800890	+	0.598811i	$0.795640\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	−0.949747	−	1.64501i	−0.0447219	−	0.0774605i
$452$	3.03553	+	5.25770i	0.142780	+	0.247301i
$453$	3.79289	−	6.56948i	0.178206	−	0.308661i
$454$	−26.1421			−1.22691
$455$	2.29289	−	2.95680i	0.107492	−	0.138617i
$456$	3.00000			0.140488
$457$	7.60660	−	13.1750i	0.355822	−	0.616301i	−0.631436	−	0.775428i	$-0.717534\pi$
$457$	7.60660	−	13.1750i	0.355822	−	0.616301i	0.987258	+	0.159126i	$0.0508677\pi$
$458$	3.58579	+	6.21076i	0.167553	+	0.290210i
$459$	−2.62132	−	4.54026i	−0.122353	−	0.211921i
$460$	−6.41421	+	11.1097i	−0.299064	+	0.517994i
$461$	−33.4558			−1.55819			−0.779097	−	0.626903i	$-0.784322\pi$
$461$	−33.4558			−1.55819			−0.779097	+	0.626903i	$0.784322\pi$
$462$	−0.414214	−	1.01461i	−0.0192710	−	0.0472040i
$463$	−37.9411			−1.76327			−0.881637	−	0.471929i	$-0.843558\pi$
$463$	−37.9411			−1.76327			−0.881637	+	0.471929i	$0.843558\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$	4.82843	+	8.36308i	0.223913	+	0.387829i
$466$	1.86396	+	3.22848i	0.0863463	+	0.149556i
$467$	0.121320	−	0.210133i	0.00561404	−	0.00972380i	−0.863205	−	0.504854i	$-0.831546\pi$
$467$	0.121320	−	0.210133i	0.00561404	−	0.00972380i	0.868819	+	0.495130i	$0.164880\pi$
$468$	1.00000			0.0462250
$469$	14.6569	+	35.9018i	0.676791	+	1.65779i
$470$	−12.7279			−0.587095
$471$	−3.96447	+	6.86666i	−0.182673	+	0.316399i
$472$	−3.79289	−	6.56948i	−0.174582	−	0.302385i
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$	−6.65685	+	11.5300i	−0.305759	+	0.529591i
$475$	−9.00000			−0.412948
$476$	−8.50000	+	10.9612i	−0.389597	+	0.502404i
$477$	12.3137			0.563806
$478$	1.25736	−	2.17781i	0.0575103	−	0.0996107i
$479$	15.5711	+	26.9699i	0.711460	+	1.23229i	0.964309	+	0.264779i	$0.0852992\pi$
$479$	15.5711	+	26.9699i	0.711460	+	1.23229i	−0.252849	+	0.967506i	$0.581368\pi$
$480$	0.707107	+	1.22474i	0.0322749	+	0.0559017i
$481$	2.53553	−	4.39167i	0.115610	−	0.200243i
$482$	−16.4853			−0.750884
$483$	−23.7782	−	3.25397i	−1.08194	−	0.148061i
$484$	−10.8284			−0.492201
$485$	5.58579	−	9.67487i	0.253637	−	0.439313i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	11.8640	+	20.5490i	0.537607	+	0.931163i	0.999032	+	0.0439840i	$0.0140051\pi$
$487$	11.8640	+	20.5490i	0.537607	+	0.931163i	−0.461425	+	0.887179i	$0.652662\pi$
$488$	2.62132	−	4.54026i	0.118662	−	0.205528i
$489$	17.1421			0.775194
$490$	2.46447	+	9.58783i	0.111333	+	0.433134i
$491$	−26.2843			−1.18619			−0.593096	−	0.805132i	$-0.702095\pi$
$491$	−26.2843			−1.18619			−0.593096	+	0.805132i	$0.702095\pi$
$492$	−2.29289	+	3.97141i	−0.103372	+	0.179045i
$493$	−13.1066	−	22.7013i	−0.590292	−	1.02242i
$494$	−1.50000	−	2.59808i	−0.0674882	−	0.116893i
$495$	0.292893	−	0.507306i	0.0131646	−	0.0228017i
$496$	6.82843			0.306605
$497$	−2.62132	−	0.358719i	−0.117582	−	0.0160908i
$498$	−7.65685			−0.343112
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	−0.305989	−	0.952035i	$-0.598987\pi$
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	0.977481	−	0.211024i	$-0.0676797\pi$
$500$	−5.65685	−	9.79796i	−0.252982	−	0.438178i
$501$	−6.15685	−	10.6640i	−0.275068	−	0.476432i
$502$	−6.41421	+	11.1097i	−0.286280	+	0.495852i
$503$	35.7990			1.59620			0.798099	−	0.602526i	$-0.205839\pi$
$503$	35.7990			1.59620			0.798099	+	0.602526i	$0.205839\pi$
$504$	−1.62132	+	2.09077i	−0.0722193	+	0.0931303i
$505$	1.65685			0.0737290
$506$	1.87868	−	3.25397i	0.0835175	−	0.144657i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	−4.94975	−	8.57321i	−0.219610	−	0.380375i
$509$	−6.48528	+	11.2328i	−0.287455	+	0.497887i	−0.973202	−	0.229954i	$-0.926143\pi$
$509$	−6.48528	+	11.2328i	−0.287455	+	0.497887i	0.685747	+	0.727840i	$0.259476\pi$
$510$	−7.41421			−0.328307
$511$	1.07107	+	2.62357i	0.0473813	+	0.116060i
$512$	1.00000			0.0441942
$513$	−1.50000	+	2.59808i	−0.0662266	+	0.114708i
$514$	10.8995	+	18.8785i	0.480756	+	0.832694i
$515$	4.58579	+	7.94282i	0.202074	+	0.350002i
$516$	−2.41421	+	4.18154i	−0.106280	+	0.184082i
$517$	3.72792			0.163954
$518$	5.07107	+	12.4215i	0.222810	+	0.545771i
$519$	20.3137			0.891673
$520$	0.707107	−	1.22474i	0.0310087	−	0.0537086i
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	0.977633	−	0.210318i	$-0.0674500\pi$
$521$	7.00000	+	12.1244i	0.306676	+	0.531178i	−0.670957	+	0.741496i	$0.734117\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	1.92893	−	3.34101i	0.0843463	−	0.146092i	−0.820766	−	0.571264i	$-0.806453\pi$
$523$	1.92893	−	3.34101i	0.0843463	−	0.146092i	0.905112	+	0.425172i	$0.139786\pi$
$524$	9.89949			0.432461
$525$	4.86396	−	6.27231i	0.212281	−	0.273746i
$526$	−7.55635			−0.329472
$527$	−17.8995	+	31.0028i	−0.779714	+	1.35050i
$528$	−0.207107	−	0.358719i	−0.00901317	−	0.0156113i
$529$	−29.6421	−	51.3417i	−1.28879	−	2.23225i
$530$	8.70711	−	15.0812i	0.378213	−	0.655083i
$531$	7.58579			0.329195
$532$	7.86396	+	1.07616i	0.340946	+	0.0466574i
$533$	4.58579			0.198632
$534$	3.12132	−	5.40629i	0.135073	−	0.233953i
$535$	9.65685	+	16.7262i	0.417502	+	0.723135i
$536$	7.32843	+	12.6932i	0.316540	+	0.548263i
$537$	6.17157	−	10.6895i	0.266323	−	0.461285i
$538$	−3.68629			−0.158927
$539$	−0.721825	−	2.80821i	−0.0310912	−	0.120958i
$540$	−1.41421			−0.0608581
$541$	−6.43503	+	11.1458i	−0.276663	+	0.479195i	−0.970553	−	0.240886i	$-0.922562\pi$
$541$	−6.43503	+	11.1458i	−0.276663	+	0.479195i	0.693890	+	0.720081i	$0.255895\pi$
$542$	7.69239	+	13.3236i	0.330416	+	0.572298i
$543$	5.79289	+	10.0336i	0.248597	+	0.430582i
$544$	−2.62132	+	4.54026i	−0.112388	+	0.194662i
$545$	−2.34315			−0.100369
$546$	2.62132	+	0.358719i	0.112182	+	0.0153518i
$547$	−5.75736			−0.246167			−0.123083	−	0.992396i	$-0.539278\pi$
$547$	−5.75736			−0.246167			−0.123083	+	0.992396i	$0.539278\pi$
$548$	6.53553	−	11.3199i	0.279184	−	0.483561i
$549$	2.62132	+	4.54026i	0.111875	+	0.193774i
$550$	0.621320	+	1.07616i	0.0264932	+	0.0458875i
$551$	−7.50000	+	12.9904i	−0.319511	+	0.553409i
$552$	−9.07107			−0.386090
$553$	−21.5858	+	27.8359i	−0.917921	+	1.18370i
$554$	−16.4142			−0.697373
$555$	−3.58579	+	6.21076i	−0.152208	+	0.263632i
$556$	10.6066	+	18.3712i	0.449820	+	0.779111i
$557$	5.48528	+	9.50079i	0.232419	+	0.402561i	0.958519	−	0.285027i	$-0.0920027\pi$
$557$	5.48528	+	9.50079i	0.232419	+	0.402561i	−0.726101	+	0.687589i	$0.758669\pi$
$558$	−3.41421	+	5.91359i	−0.144535	+	0.250342i
$559$	4.82843			0.204221
$560$	1.41421	+	3.46410i	0.0597614	+	0.146385i
$561$	2.17157			0.0916839
$562$	−3.65685	+	6.33386i	−0.154255	+	0.267178i
$563$	0.242641	+	0.420266i	0.0102261	+	0.0177121i	0.871093	−	0.491118i	$-0.163412\pi$
$563$	0.242641	+	0.420266i	0.0102261	+	0.0177121i	−0.860867	+	0.508830i	$0.830078\pi$
$564$	−4.50000	−	7.79423i	−0.189484	−	0.328196i
$565$	−4.29289	+	7.43551i	−0.180603	+	0.312814i
$566$	17.0711			0.717551
$567$	−1.00000	−	2.44949i	−0.0419961	−	0.102869i
$568$	−1.00000			−0.0419591
$569$	12.7929	−	22.1579i	0.536306	−	0.928909i	−0.462793	−	0.886466i	$-0.653153\pi$
$569$	12.7929	−	22.1579i	0.536306	−	0.928909i	0.999099	−	0.0424428i	$-0.0135140\pi$
$570$	2.12132	+	3.67423i	0.0888523	+	0.153897i
$571$	0.828427	+	1.43488i	0.0346686	+	0.0600478i	0.882839	−	0.469676i	$-0.155629\pi$
$571$	0.828427	+	1.43488i	0.0346686	+	0.0600478i	−0.848171	+	0.529723i	$0.822296\pi$
$572$	−0.207107	+	0.358719i	−0.00865957	+	0.0149988i
$573$	2.34315			0.0978863
$574$	−7.43503	+	9.58783i	−0.310332	+	0.400188i
$575$	27.2132			1.13487
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	0.990278	−	0.139100i	$-0.0444210\pi$
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	−0.615603	+	0.788056i	$0.711088\pi$
$578$	−5.24264	−	9.08052i	−0.218065	−	0.377700i
$579$	7.87868	−	13.6463i	0.327427	−	0.567120i
$580$	−7.07107			−0.293610
$581$	−20.0711	−	2.74666i	−0.832688	−	0.113951i
$582$	7.89949			0.327445
$583$	−2.55025	+	4.41717i	−0.105621	+	0.182940i
$584$	0.535534	+	0.927572i	0.0221606	+	0.0383832i
$585$	0.707107	+	1.22474i	0.0292353	+	0.0506370i
$586$	9.36396	−	16.2189i	0.386822	−	0.669995i
$587$	11.2426			0.464033			0.232017	−	0.972712i	$-0.425468\pi$
$587$	11.2426			0.464033			0.232017	+	0.972712i	$0.425468\pi$
$588$	−5.00000	+	4.89898i	−0.206197	+	0.202031i
$589$	20.4853			0.844081
$590$	5.36396	−	9.29065i	0.220831	−	0.382490i
$591$	−4.77817	−	8.27604i	−0.196548	−	0.340431i
$592$	2.53553	+	4.39167i	0.104210	+	0.180497i
$593$	14.2929	−	24.7560i	0.586939	−	1.01661i	−0.407692	−	0.913120i	$-0.633666\pi$
$593$	14.2929	−	24.7560i	0.586939	−	1.01661i	0.994631	−	0.103488i	$-0.0330004\pi$
$594$	0.414214			0.0169954
$595$	−19.4350	−	2.65962i	−0.796759	−	0.109034i
$596$	15.8995			0.651269
$597$	−5.29289	+	9.16756i	−0.216624	+	0.375203i
$598$	4.53553	+	7.85578i	0.185472	+	0.321247i
$599$	7.43503	+	12.8778i	0.303787	+	0.526175i	0.976991	−	0.213283i	$-0.0684155\pi$
$599$	7.43503	+	12.8778i	0.303787	+	0.526175i	−0.673203	+	0.739457i	$0.735082\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	−17.8284			−0.727237			−0.363618	−	0.931548i	$-0.618459\pi$
$601$	−17.8284			−0.727237			−0.363618	+	0.931548i	$0.618459\pi$
$602$	−7.82843	+	10.0951i	−0.319063	+	0.411447i
$603$	−14.6569			−0.596873
$604$	3.79289	−	6.56948i	0.154331	−	0.267309i
$605$	−7.65685	−	13.2621i	−0.311295	−	0.539179i
$606$	0.585786	+	1.01461i	0.0237959	+	0.0412158i
$607$	−13.5355	+	23.4442i	−0.549390	+	0.951572i	0.448926	+	0.893569i	$0.351807\pi$
$607$	−13.5355	+	23.4442i	−0.549390	+	0.951572i	−0.998316	+	0.0580031i	$0.981527\pi$
$608$	3.00000			0.121666
$609$	−5.00000	−	12.2474i	−0.202610	−	0.496292i
$610$	7.41421			0.300193
$611$	−4.50000	+	7.79423i	−0.182051	+	0.315321i
$612$	−2.62132	−	4.54026i	−0.105961	−	0.183529i
$613$	17.8995	+	31.0028i	0.722954	+	1.25219i	0.959811	+	0.280648i	$0.0905494\pi$
$613$	17.8995	+	31.0028i	0.722954	+	1.25219i	−0.236857	+	0.971545i	$0.576117\pi$
$614$	9.81371	−	16.9978i	0.396049	−	0.685977i
$615$	−6.48528			−0.261512
$616$	−0.414214	−	1.01461i	−0.0166891	−	0.0408799i
$617$	−6.48528			−0.261088			−0.130544	−	0.991443i	$-0.541672\pi$
$617$	−6.48528			−0.261088			−0.130544	+	0.991443i	$0.541672\pi$
$618$	−3.24264	+	5.61642i	−0.130438	+	0.225925i
$619$	−21.7279	−	37.6339i	−0.873319	−	1.51263i	−0.858543	−	0.512742i	$-0.828630\pi$
$619$	−21.7279	−	37.6339i	−0.873319	−	1.51263i	−0.0147761	−	0.999891i	$-0.504704\pi$
$620$	4.82843	+	8.36308i	0.193914	+	0.335869i
$621$	4.53553	−	7.85578i	0.182005	−	0.315241i
$622$	−6.58579			−0.264066
$623$	10.1213	−	13.0519i	0.405502	−	0.522914i
$624$	1.00000			0.0400320
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−9.07107	−	15.7116i	−0.362553	−	0.627960i
$627$	−0.621320	−	1.07616i	−0.0248131	−	0.0429776i
$628$	−3.96447	+	6.86666i	−0.158199	+	0.274009i
$629$	−26.5858			−1.06004
$630$	−3.70711	−	0.507306i	−0.147695	−	0.0202116i
$631$	36.6274			1.45811			0.729057	−	0.684453i	$-0.239959\pi$
$631$	36.6274			1.45811			0.729057	+	0.684453i	$0.239959\pi$
$632$	−6.65685	+	11.5300i	−0.264795	+	0.458639i
$633$	14.1924	+	24.5819i	0.564097	+	0.977044i
$634$	−0.414214	−	0.717439i	−0.0164505	−	0.0284931i
$635$	7.00000	−	12.1244i	0.277787	−	0.481140i
$636$	12.3137			0.488270
$637$	6.74264	+	1.88064i	0.267153	+	0.0745136i
$638$	2.07107			0.0819944
$639$	0.500000	−	0.866025i	0.0197797	−	0.0342594i
$640$	0.707107	+	1.22474i	0.0279508	+	0.0484123i
$641$	−16.5858	−	28.7274i	−0.655099	−	1.13467i	−0.981869	−	0.189561i	$-0.939293\pi$
$641$	−16.5858	−	28.7274i	−0.655099	−	1.13467i	0.326770	−	0.945104i	$-0.394040\pi$
$642$	−6.82843	+	11.8272i	−0.269497	+	0.466782i
$643$	36.3137			1.43207			0.716036	−	0.698063i	$-0.245954\pi$
$643$	36.3137			1.43207			0.716036	+	0.698063i	$0.245954\pi$
$644$	−23.7782	−	3.25397i	−0.936991	−	0.128224i
$645$	−6.82843			−0.268869
$646$	−7.86396	+	13.6208i	−0.309403	+	0.535902i
$647$	−14.3137	−	24.7921i	−0.562730	−	0.974677i	−0.997257	−	0.0740180i	$-0.976418\pi$
$647$	−14.3137	−	24.7921i	−0.562730	−	0.974677i	0.434527	−	0.900659i	$-0.356916\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.57107	+	2.72117i	−0.0616698	+	0.106815i
$650$	−3.00000			−0.117670
$651$	−11.0711	+	14.2767i	−0.433909	+	0.559547i
$652$	17.1421			0.671338
$653$	−7.55635	+	13.0880i	−0.295703	+	0.512172i	−0.975148	−	0.221554i	$-0.928887\pi$
$653$	−7.55635	+	13.0880i	−0.295703	+	0.512172i	0.679445	+	0.733726i	$0.262220\pi$
$654$	−0.828427	−	1.43488i	−0.0323941	−	0.0561082i
$655$	7.00000	+	12.1244i	0.273513	+	0.473738i
$656$	−2.29289	+	3.97141i	−0.0895224	+	0.155057i
$657$	−1.07107			−0.0417863
$658$	−9.00000	−	22.0454i	−0.350857	−	0.859419i
$659$	30.7279			1.19699			0.598495	−	0.801127i	$-0.295766\pi$
$659$	30.7279			1.19699			0.598495	+	0.801127i	$0.295766\pi$
$660$	0.292893	−	0.507306i	0.0114009	−	0.0197469i
$661$	6.77817	+	11.7401i	0.263640	+	0.456639i	0.967207	−	0.253991i	$-0.0817434\pi$
$661$	6.77817	+	11.7401i	0.263640	+	0.456639i	−0.703566	+	0.710630i	$0.748410\pi$
$662$	11.2426	+	19.4728i	0.436958	+	0.756833i
$663$	−2.62132	+	4.54026i	−0.101804	+	0.176329i
$664$	−7.65685			−0.297144
$665$	4.24264	+	10.3923i	0.164523	+	0.402996i
$666$	−5.07107			−0.196500
$667$	22.6777	−	39.2789i	0.878083	−	1.52088i
$668$	−6.15685	−	10.6640i	−0.238216	−	0.412602i
$669$	−10.6924	−	18.5198i	−0.413392	−	0.716015i
$670$	−10.3640	+	17.9509i	−0.400395	+	0.693504i
$671$	−2.17157			−0.0838326
$672$	−1.62132	+	2.09077i	−0.0625438	+	0.0806532i
$673$	−1.17157			−0.0451608			−0.0225804	−	0.999745i	$-0.507188\pi$
$673$	−1.17157			−0.0451608			−0.0225804	+	0.999745i	$0.507188\pi$
$674$	−14.3284	+	24.8176i	−0.551910	+	0.955937i
$675$	1.50000	+	2.59808i	0.0577350	+	0.100000i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−14.0858	+	24.3973i	−0.541361	+	0.937664i	0.457465	+	0.889227i	$0.348757\pi$
$677$	−14.0858	+	24.3973i	−0.541361	+	0.937664i	−0.998826	+	0.0484369i	$0.984576\pi$
$678$	−6.07107			−0.233158
$679$	20.7071	+	2.83370i	0.794666	+	0.108748i
$680$	−7.41421			−0.284322
$681$	13.0711	−	22.6398i	0.500884	−	0.867557i
$682$	−1.41421	−	2.44949i	−0.0541530	−	0.0937958i
$683$	−2.72792	−	4.72490i	−0.104381	−	0.180793i	0.809104	−	0.587665i	$-0.199953\pi$
$683$	−2.72792	−	4.72490i	−0.104381	−	0.180793i	−0.913485	+	0.406872i	$0.866619\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	18.4853			0.706286
$686$	−14.8640	+	11.0482i	−0.567509	+	0.421822i
$687$	−7.17157			−0.273613
$688$	−2.41421	+	4.18154i	−0.0920410	+	0.159420i
$689$	−6.15685	−	10.6640i	−0.234557	−	0.406265i
$690$	−6.41421	−	11.1097i	−0.244185	−	0.422941i
$691$	−5.57107	+	9.64937i	−0.211933	+	0.367079i	−0.952320	−	0.305102i	$-0.901309\pi$
$691$	−5.57107	+	9.64937i	−0.211933	+	0.367079i	0.740386	+	0.672182i	$0.234643\pi$
$692$	20.3137			0.772211
$693$	1.08579	+	0.148586i	0.0412456	+	0.00564433i
$694$	5.75736			0.218546
$695$	−15.0000	+	25.9808i	−0.568982	+	0.985506i
$696$	−2.50000	−	4.33013i	−0.0947623	−	0.164133i
$697$	−12.0208	−	20.8207i	−0.455321	−	0.788639i
$698$	−2.70711	+	4.68885i	−0.102466	+	0.177475i
$699$	−3.72792			−0.141003
$700$	4.86396	−	6.27231i	0.183840	−	0.237071i
$701$	48.4853			1.83126			0.915632	−	0.402018i	$-0.131691\pi$
$701$	48.4853			1.83126			0.915632	+	0.402018i	$0.131691\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$	7.60660	+	13.1750i	0.286888	+	0.496905i
$704$	−0.207107	−	0.358719i	−0.00780563	−	0.0135197i
$705$	6.36396	−	11.0227i	0.239681	−	0.415139i
$706$	12.6274			0.475239
$707$	1.17157	+	2.86976i	0.0440615	+	0.107928i
$708$	7.58579			0.285091
$709$	16.0208	−	27.7489i	0.601674	−	1.04213i	−0.390893	−	0.920436i	$-0.627834\pi$
$709$	16.0208	−	27.7489i	0.601674	−	1.04213i	0.992568	−	0.121695i	$-0.0388328\pi$
$710$	−0.707107	−	1.22474i	−0.0265372	−	0.0459639i
$711$	−6.65685	−	11.5300i	−0.249652	−	0.432409i
$712$	3.12132	−	5.40629i	0.116976	−	0.202609i
$713$	−61.9411			−2.31971
$714$	−5.24264	−	12.8418i	−0.196201	−	0.480592i
$715$	−0.585786			−0.0219072
$716$	6.17157	−	10.6895i	0.230643	−	0.399485i
$717$	1.25736	+	2.17781i	0.0469569	+	0.0813318i
$718$	7.72792	+	13.3852i	0.288403	+	0.499529i
$719$	11.1421	−	19.2987i	0.415532	−	0.719722i	−0.579953	−	0.814650i	$-0.696929\pi$
$719$	11.1421	−	19.2987i	0.415532	−	0.719722i	0.995484	+	0.0949285i	$0.0302623\pi$
$720$	−1.41421			−0.0527046
$721$	−10.5147	+	13.5592i	−0.391589	+	0.504972i
$722$	−10.0000			−0.372161
$723$	8.24264	−	14.2767i	0.306547	−	0.530955i
$724$	5.79289	+	10.0336i	0.215291	+	0.372895i
$725$	7.50000	+	12.9904i	0.278543	+	0.482451i
$726$	5.41421	−	9.37769i	0.200940	−	0.348039i
$727$	−38.8284			−1.44007			−0.720033	−	0.693939i	$-0.755874\pi$
$727$	−38.8284			−1.44007			−0.720033	+	0.693939i	$0.755874\pi$
$728$	2.62132	+	0.358719i	0.0971526	+	0.0132950i
$729$	1.00000			0.0370370
$730$	−0.757359	+	1.31178i	−0.0280311	+	0.0485513i
$731$	−12.6569	−	21.9223i	−0.468131	−	0.810826i
$732$	2.62132	+	4.54026i	0.0968868	+	0.167813i
$733$	14.5061	−	25.1253i	0.535795	−	0.928024i	−0.463330	−	0.886186i	$-0.653345\pi$
$733$	14.5061	−	25.1253i	0.535795	−	0.928024i	0.999124	−	0.0418379i	$-0.0133213\pi$
$734$	14.0000			0.516749
$735$	−9.53553	−	2.65962i	−0.351723	−	0.0981017i
$736$	−9.07107			−0.334364
$737$	3.03553	−	5.25770i	0.111815	−	0.193670i
$738$	−2.29289	−	3.97141i	−0.0844026	−	0.146190i
$739$	−3.48528	−	6.03668i	−0.128208	−	0.222063i	0.794774	−	0.606905i	$-0.207589\pi$
$739$	−3.48528	−	6.03668i	−0.128208	−	0.222063i	−0.922982	+	0.384842i	$0.874256\pi$
$740$	−3.58579	+	6.21076i	−0.131816	+	0.228312i
$741$	3.00000			0.110208
$742$	32.2782	+	4.41717i	1.18497	+	0.162159i
$743$	11.4853			0.421354			0.210677	−	0.977556i	$-0.432433\pi$
$743$	11.4853			0.421354			0.210677	+	0.977556i	$0.432433\pi$
$744$	−3.41421	+	5.91359i	−0.125171	+	0.216803i
$745$	11.2426	+	19.4728i	0.411898	+	0.713429i
$746$	5.55025	+	9.61332i	0.203209	+	0.351969i
$747$	3.82843	−	6.63103i	0.140075	−	0.242617i
$748$	2.17157			0.0794006
$749$	−22.1421	+	28.5533i	−0.809056	+	1.04332i
$750$	11.3137			0.413118
$751$	17.1716	−	29.7420i	0.626600	−	1.08530i	−0.361630	−	0.932322i	$-0.617780\pi$
$751$	17.1716	−	29.7420i	0.626600	−	1.08530i	0.988229	−	0.152980i	$-0.0488872\pi$
$752$	−4.50000	−	7.79423i	−0.164098	−	0.284226i
$753$	−6.41421	−	11.1097i	−0.233747	−	0.404862i
$754$	−2.50000	+	4.33013i	−0.0910446	+	0.157694i
$755$	10.7279			0.390429
$756$	−1.00000	−	2.44949i	−0.0363696	−	0.0890871i
$757$	23.4437			0.852074			0.426037	−	0.904706i	$-0.359909\pi$
$757$	23.4437			0.852074			0.426037	+	0.904706i	$0.359909\pi$
$758$	16.8284	−	29.1477i	0.611236	−	1.05869i
$759$	1.87868	+	3.25397i	0.0681918	+	0.118112i
$760$	2.12132	+	3.67423i	0.0769484	+	0.133278i
$761$	8.92893	−	15.4654i	0.323674	−	0.560619i	−0.657569	−	0.753394i	$-0.728415\pi$
$761$	8.92893	−	15.4654i	0.323674	−	0.560619i	0.981243	+	0.192775i	$0.0617487\pi$
$762$	9.89949			0.358621
$763$	−1.65685	−	4.05845i	−0.0599822	−	0.146926i
$764$	2.34315			0.0847720
$765$	3.70711	−	6.42090i	0.134031	−	0.232148i
$766$	−3.24264	−	5.61642i	−0.117161	−	0.202929i
$767$	−3.79289	−	6.56948i	−0.136953	−	0.237210i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−6.92893			−0.249864			−0.124932	−	0.992165i	$-0.539871\pi$
$769$	−6.92893			−0.249864			−0.124932	+	0.992165i	$0.539871\pi$
$770$	0.949747	−	1.22474i	0.0342265	−	0.0441367i
$771$	−21.7990			−0.785071
$772$	7.87868	−	13.6463i	0.283560	−	0.491140i
$773$	14.7990	+	25.6326i	0.532283	+	0.921941i	0.999290	+	0.0376870i	$0.0119990\pi$
$773$	14.7990	+	25.6326i	0.532283	+	0.921941i	−0.467007	+	0.884254i	$0.654668\pi$
$774$	−2.41421	−	4.18154i	−0.0867771	−	0.150302i
$775$	10.2426	−	17.7408i	0.367927	−	0.637267i
$776$	7.89949			0.283575
$777$	−13.2929	−	1.81909i	−0.476880	−	0.0652595i
$778$	23.0000			0.824590
$779$	−6.87868	+	11.9142i	−0.246454	+	0.426871i
$780$	0.707107	+	1.22474i	0.0253185	+	0.0438529i
$781$	0.207107	+	0.358719i	0.00741086	+	0.0128360i
$782$	23.7782	−	41.1850i	0.850306	−	1.47277i
$783$	5.00000			0.178685
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$	−11.2132			−0.400216
$786$	−4.94975	+	8.57321i	−0.176552	+	0.305796i
$787$	4.08579	+	7.07679i	0.145643	+	0.252260i	0.929612	−	0.368538i	$-0.120142\pi$
$787$	4.08579	+	7.07679i	0.145643	+	0.252260i	−0.783970	+	0.620799i	$0.786808\pi$
$788$	−4.77817	−	8.27604i	−0.170215	−	0.294822i
$789$	3.77817	−	6.54399i	0.134507	−	0.232972i
$790$	−18.8284			−0.669885
$791$	−15.9142	−	2.17781i	−0.565844	−	0.0774340i
$792$	0.414214			0.0147184
$793$	2.62132	−	4.54026i	0.0930858	−	0.161229i
$794$	9.87868	+	17.1104i	0.350581	+	0.607224i
$795$	8.70711	+	15.0812i	0.308809	+	0.534873i
$796$	−5.29289	+	9.16756i	−0.187602	+	0.324936i
$797$	−36.9706			−1.30956			−0.654782	−	0.755818i	$-0.727240\pi$
$797$	−36.9706			−1.30956			−0.654782	+	0.755818i	$0.727240\pi$
$798$	−4.86396	+	6.27231i	−0.172182	+	0.222037i
$799$	47.1838			1.66924
$800$	1.50000	−	2.59808i	0.0530330	−	0.0918559i
$801$	3.12132	+	5.40629i	0.110286	+	0.191022i
$802$	−9.53553	−	16.5160i	−0.336711	−	0.583201i
$803$	0.221825	−	0.384213i	0.00782805	−	0.0135586i
$804$	−14.6569			−0.516907
$805$	−12.8284	−	31.4231i	−0.452143	−	1.10752i
$806$	6.82843			0.240521
$807$	1.84315	−	3.19242i	0.0648818	−	0.112379i
$808$	0.585786	+	1.01461i	0.0206079	+	0.0356939i
$809$	−17.5208	−	30.3469i	−0.615999	−	1.06694i	−0.990208	−	0.139597i	$-0.955419\pi$
$809$	−17.5208	−	30.3469i	−0.615999	−	1.06694i	0.374209	−	0.927344i	$-0.377914\pi$
$810$	0.707107	−	1.22474i	0.0248452	−	0.0430331i
$811$	26.7696			0.940006			0.470003	−	0.882665i	$-0.344253\pi$
$811$	26.7696			0.940006			0.470003	+	0.882665i	$0.344253\pi$
$812$	−5.00000	−	12.2474i	−0.175466	−	0.429801i
$813$	−15.3848			−0.539568
$814$	1.05025	−	1.81909i	0.0368113	−	0.0637591i
$815$	12.1213	+	20.9947i	0.424591	+	0.735414i
$816$	−2.62132	−	4.54026i	−0.0917646	−	0.158941i
$817$	−7.24264	+	12.5446i	−0.253388	+	0.438881i
$818$	−2.58579			−0.0904099
$819$	−1.62132	+	2.09077i	−0.0566535	+	0.0730574i
$820$	−6.48528			−0.226476
$821$	4.80761	−	8.32703i	0.167787	−	0.290615i	−0.769855	−	0.638219i	$-0.779671\pi$
$821$	4.80761	−	8.32703i	0.167787	−	0.290615i	0.937641	+	0.347604i	$0.113005\pi$
$822$	6.53553	+	11.3199i	0.227953	+	0.394826i
$823$	4.05025	+	7.01524i	0.141183	+	0.244536i	0.927942	−	0.372724i	$-0.121576\pi$
$823$	4.05025	+	7.01524i	0.141183	+	0.244536i	−0.786759	+	0.617260i	$0.788243\pi$
$824$	−3.24264	+	5.61642i	−0.112963	+	0.195657i
$825$	−1.24264			−0.0432632
$826$	19.8848	+	2.72117i	0.691880	+	0.0946816i
$827$	13.5269			0.470377			0.235188	−	0.971950i	$-0.424429\pi$
$827$	13.5269			0.470377			0.235188	+	0.971950i	$0.424429\pi$
$828$	4.53553	−	7.85578i	0.157621	−	0.273007i
$829$	−9.34924	−	16.1934i	−0.324713	−	0.562419i	0.656742	−	0.754116i	$-0.271934\pi$
$829$	−9.34924	−	16.1934i	−0.324713	−	0.562419i	−0.981454	+	0.191697i	$0.938601\pi$
$830$	−5.41421	−	9.37769i	−0.187930	−	0.325504i
$831$	8.20711	−	14.2151i	0.284701	−	0.493117i
$832$	1.00000			0.0346688
$833$	−9.13604	−	35.5431i	−0.316545	−	1.23150i
$834$	−21.2132			−0.734553
$835$	8.70711	−	15.0812i	0.301322	−	0.521905i
$836$	−0.621320	−	1.07616i	−0.0214888	−	0.0372197i
$837$	−3.41421	−	5.91359i	−0.118012	−	0.204404i
$838$	13.7279	−	23.7775i	0.474223	−	0.821379i
$839$	2.51472			0.0868177			0.0434089	−	0.999057i	$-0.486178\pi$
$839$	2.51472			0.0868177			0.0434089	+	0.999057i	$0.486178\pi$
$840$	−3.70711	−	0.507306i	−0.127907	−	0.0175037i
$841$	−4.00000			−0.137931
$842$	−5.29289	+	9.16756i	−0.182405	+	0.315935i
$843$	−3.65685	−	6.33386i	−0.125949	−	0.218150i
$844$	14.1924	+	24.5819i	0.488522	+	0.846145i
$845$	0.707107	−	1.22474i	0.0243252	−	0.0421325i
$846$	9.00000			0.309426
$847$	17.5563	−	22.6398i	0.603243	−	0.777911i
$848$	12.3137			0.422854
$849$	−8.53553	+	14.7840i	−0.292939	+	0.507385i
$850$	7.86396	+	13.6208i	0.269732	+	0.467189i
$851$	−23.0000	−	39.8372i	−0.788430	−	1.36560i
$852$	0.500000	−	0.866025i	0.0171297	−	0.0296695i
$853$	−17.6985			−0.605985			−0.302992	−	0.952993i	$-0.597986\pi$
$853$	−17.6985			−0.605985			−0.302992	+	0.952993i	$0.597986\pi$
$854$	5.24264	+	12.8418i	0.179399	+	0.439437i
$855$	−4.24264			−0.145095
$856$	−6.82843	+	11.8272i	−0.233391	+	0.404245i
$857$	25.6924	+	44.5005i	0.877635	+	1.52011i	0.853929	+	0.520390i	$0.174213\pi$
$857$	25.6924	+	44.5005i	0.877635	+	1.52011i	0.0237065	+	0.999719i	$0.492453\pi$
$858$	−0.207107	−	0.358719i	−0.00707051	−	0.0122465i
$859$	−0.100505	+	0.174080i	−0.00342919	+	0.00593953i	−0.867735	−	0.497027i	$-0.834425\pi$
$859$	−0.100505	+	0.174080i	−0.00342919	+	0.00593953i	0.864306	+	0.502967i	$0.167758\pi$
$860$	−6.82843			−0.232847
$861$	−4.58579	−	11.2328i	−0.156283	−	0.382814i
$862$	14.4853			0.493371
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	−0.898056	−	0.439880i	$-0.855021\pi$
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	0.829976	+	0.557800i	$0.188354\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	14.3640	+	24.8791i	0.488389	+	0.845915i
$866$	9.50000	−	16.4545i	0.322823	−	0.559146i
$867$	10.4853			0.356099
$868$	−11.0711	+	14.2767i	−0.375777	+	0.484582i
$869$	5.51472			0.187074
$870$	3.53553	−	6.12372i	0.119866	−	0.207614i
$871$	7.32843	+	12.6932i	0.248314	+	0.430093i
$872$	−0.828427	−	1.43488i	−0.0280541	−	0.0485911i
$873$	−3.94975	+	6.84116i	−0.133679	+	0.231538i
$874$	−27.2132			−0.920500
$875$	29.6569	+	4.05845i	1.00258	+	0.137201i
$876$	−1.07107			−0.0361880
$877$	−11.7071	+	20.2773i	−0.395321	+	0.684716i	−0.993142	−	0.116914i	$-0.962700\pi$
$877$	−11.7071	+	20.2773i	−0.395321	+	0.684716i	0.597821	+	0.801629i	$0.296033\pi$
$878$	5.29289	+	9.16756i	0.178626	+	0.309390i
$879$	9.36396	+	16.2189i	0.315839	+	0.547048i
$880$	0.292893	−	0.507306i	0.00987343	−	0.0171013i
$881$	−41.1127			−1.38512			−0.692561	−	0.721359i	$-0.743518\pi$
$881$	−41.1127			−1.38512			−0.692561	+	0.721359i	$0.743518\pi$
$882$	−1.74264	−	6.77962i	−0.0586778	−	0.228282i
$883$	−0.928932			−0.0312611			−0.0156305	−	0.999878i	$-0.504976\pi$
$883$	−0.928932			−0.0312611			−0.0156305	+	0.999878i	$0.504976\pi$
$884$	−2.62132	+	4.54026i	−0.0881645	+	0.152705i
$885$	5.36396	+	9.29065i	0.180308	+	0.312302i
$886$	−11.3640	−	19.6830i	−0.381780	−	0.661262i
$887$	−20.6569	+	35.7787i	−0.693589	+	1.20133i	0.277065	+	0.960851i	$0.410638\pi$
$887$	−20.6569	+	35.7787i	−0.693589	+	1.20133i	−0.970654	+	0.240481i	$0.922695\pi$
$888$	−5.07107			−0.170174
$889$	25.9497	+	3.55114i	0.870327	+	0.119101i
$890$	8.82843			0.295930
$891$	−0.207107	+	0.358719i	−0.00693834	+	0.0120176i
$892$	−10.6924	−	18.5198i	−0.358008	−	0.620087i
$893$	−13.5000	−	23.3827i	−0.451760	−	0.782472i
$894$	−7.94975	+	13.7694i	−0.265879	+	0.460517i
$895$	17.4558			0.583485
$896$	−1.62132	+	2.09077i	−0.0541645	+	0.0698477i
$897$	−9.07107			−0.302874
$898$	16.9706	−	29.3939i	0.566315	−	0.980886i
$899$	−17.0711	−	29.5680i	−0.569352	−	0.986147i
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	−32.2782	+	55.9074i	−1.07534	+	1.86255i
$902$	1.89949			0.0632463
$903$	−4.82843	−	11.8272i	−0.160680	−	0.393584i
$904$	−6.07107			−0.201921
$905$	−8.19239	+	14.1896i	−0.272324	+	0.471679i
$906$	3.79289	+	6.56948i	0.126010	+	0.218256i
$907$	16.0503	+	27.7999i	0.532940	+	0.923079i	0.999260	+	0.0384629i	$0.0122462\pi$
$907$	16.0503	+	27.7999i	0.532940	+	0.923079i	−0.466320	+	0.884616i	$0.654421\pi$
$908$	13.0711	−	22.6398i	0.433779	−	0.751327i
$909$	−1.17157			−0.0388586
$910$	1.41421	+	3.46410i	0.0468807	+	0.114834i
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	−1.50000	+	2.59808i	−0.0496700	+	0.0860309i
$913$	1.58579	+	2.74666i	0.0524819	+	0.0909013i
$914$	7.60660	+	13.1750i	0.251604	+	0.435791i
$915$	−3.70711	+	6.42090i	−0.122553	+	0.212268i
$916$	−7.17157			−0.236955
$917$	−16.0503	+	20.6976i	−0.530026	+	0.683494i
$918$	5.24264			0.173033
$919$	12.8995	−	22.3426i	0.425515	−	0.737014i	−0.570953	−	0.820983i	$-0.693426\pi$
$919$	12.8995	−	22.3426i	0.425515	−	0.737014i	0.996468	+	0.0839688i	$0.0267596\pi$
$920$	−6.41421	−	11.1097i	−0.211470	−	0.366277i
$921$	9.81371	+	16.9978i	0.323373	+	0.560098i
$922$	16.7279	−	28.9736i	0.550905	−	0.954195i
$923$	−1.00000			−0.0329154
$924$	1.08579	+	0.148586i	0.0357198	+	0.00488814i
$925$	15.2132			0.500207
$926$	18.9706	−	32.8580i	0.623411	−	1.07978i
$927$	−3.24264	−	5.61642i	−0.106502	−	0.184467i
$928$	−2.50000	−	4.33013i	−0.0820665	−	0.142143i
$929$	−9.14214	+	15.8346i	−0.299944	+	0.519518i	−0.976123	−	0.217220i	$-0.930301\pi$
$929$	−9.14214	+	15.8346i	−0.299944	+	0.519518i	0.676179	+	0.736737i	$0.263635\pi$
$930$	−9.65685			−0.316661
$931$	−15.0000	+	14.6969i	−0.491605	+	0.481673i
$932$	−3.72792			−0.122112
$933$	3.29289	−	5.70346i	0.107804	−	0.186723i
$934$	0.121320	+	0.210133i	0.00396972	+	0.00687576i
$935$	1.53553	+	2.65962i	0.0502173	+	0.0869790i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	40.5980			1.32628			0.663139	−	0.748496i	$-0.269224\pi$
$937$	40.5980			1.32628			0.663139	+	0.748496i	$0.269224\pi$
$938$	−38.4203	−	5.25770i	−1.25447	−	0.171670i
$939$	18.1421			0.592046
$940$	6.36396	−	11.0227i	0.207570	−	0.359521i
$941$	10.4853	+	18.1610i	0.341810	+	0.592033i	0.984769	−	0.173868i	$-0.0556266\pi$
$941$	10.4853	+	18.1610i	0.341810	+	0.592033i	−0.642959	+	0.765901i	$0.722293\pi$
$942$	−3.96447	−	6.86666i	−0.129169	−	0.223728i
$943$	20.7990	−	36.0249i	0.677308	−	1.17313i
$944$	7.58579			0.246896
$945$	2.29289	−	2.95680i	0.0745878	−	0.0961846i
$946$	2.00000			0.0650256
$947$	−8.62132	+	14.9326i	−0.280155	+	0.485243i	−0.971423	−	0.237356i	$-0.923719\pi$
$947$	−8.62132	+	14.9326i	−0.280155	+	0.485243i	0.691268	+	0.722599i	$0.257053\pi$
$948$	−6.65685	−	11.5300i	−0.216205	−	0.374477i
$949$	0.535534	+	0.927572i	0.0173842	+	0.0301103i
$950$	4.50000	−	7.79423i	0.145999	−	0.252878i
$951$	0.828427			0.0268636
$952$	−5.24264	−	12.8418i	−0.169915	−	0.416205i
$953$	−10.2132			−0.330838			−0.165419	−	0.986223i	$-0.552898\pi$
$953$	−10.2132			−0.330838			−0.165419	+	0.986223i	$0.552898\pi$
$954$	−6.15685	+	10.6640i	−0.199336	+	0.345259i
$955$	1.65685	+	2.86976i	0.0536145	+	0.0928631i
$956$	1.25736	+	2.17781i	0.0406659	+	0.0704354i
$957$	−1.03553	+	1.79360i	−0.0334741	+	0.0579788i
$958$	−31.1421			−1.00616
$959$	13.0711	+	32.0174i	0.422087	+	1.03390i
$960$	−1.41421			−0.0456435
$961$	−7.81371	+	13.5337i	−0.252055	+	0.436572i
$962$	2.53553	+	4.39167i	0.0817489	+	0.141593i
$963$	−6.82843	−	11.8272i	−0.220043	−	0.381126i
$964$	8.24264	−	14.2767i	0.265478	−	0.459821i
$965$	22.2843			0.717356
$966$	14.7071	−	18.9655i	0.473193	−	0.610206i
$967$	9.38478			0.301794			0.150897	−	0.988549i	$-0.451784\pi$
$967$	9.38478			0.301794			0.150897	+	0.988549i	$0.451784\pi$
$968$	5.41421	−	9.37769i	0.174019	−	0.301410i
$969$	−7.86396	−	13.6208i	−0.252627	−	0.437562i
$970$	5.58579	+	9.67487i	0.179349	+	0.310641i
$971$	−28.7782	+	49.8453i	−0.923536	+	1.59961i	−0.129636	+	0.991562i	$0.541381\pi$
$971$	−28.7782	+	49.8453i	−0.923536	+	1.59961i	−0.793900	+	0.608049i	$0.791952\pi$
$972$	1.00000			0.0320750
$973$	−55.6066	−	7.60959i	−1.78267	−	0.243952i
$974$	−23.7279			−0.760292
$975$	1.50000	−	2.59808i	0.0480384	−	0.0832050i
$976$	2.62132	+	4.54026i	0.0839064	+	0.145330i
$977$	−1.24264	−	2.15232i	−0.0397556	−	0.0688587i	0.845463	−	0.534034i	$-0.179325\pi$
$977$	−1.24264	−	2.15232i	−0.0397556	−	0.0688587i	−0.885219	+	0.465175i	$0.845991\pi$
$978$	−8.57107	+	14.8455i	−0.274073	+	0.474708i
$979$	−2.58579			−0.0826421
$980$	−9.53553	−	2.65962i	−0.304601	−	0.0849585i
$981$	1.65685			0.0528993
$982$	13.1421	−	22.7628i	0.419382	−	0.726392i
$983$	11.0858	+	19.2011i	0.353582	+	0.612421i	0.986874	−	0.161491i	$-0.0516303\pi$
$983$	11.0858	+	19.2011i	0.353582	+	0.612421i	−0.633292	+	0.773913i	$0.718297\pi$
$984$	−2.29289	−	3.97141i	−0.0730948	−	0.126604i
$985$	6.75736	−	11.7041i	0.215307	−	0.372923i
$986$	26.2132			0.834798
$987$	23.5919	+	3.22848i	0.750938	+	0.102763i
$988$	3.00000			0.0954427
$989$	21.8995	−	37.9310i	0.696363	−	1.20614i
$990$	0.292893	+	0.507306i	0.00930876	+	0.0161232i
$991$	3.65685	+	6.33386i	0.116164	+	0.201202i	0.918244	−	0.396014i	$-0.129607\pi$
$991$	3.65685	+	6.33386i	0.116164	+	0.201202i	−0.802081	+	0.597216i	$0.796274\pi$
$992$	−3.41421	+	5.91359i	−0.108401	+	0.187757i
$993$	−22.4853			−0.713549
$994$	1.62132	−	2.09077i	0.0514252	−	0.0663152i
$995$	−14.9706			−0.474599
$996$	3.82843	−	6.63103i	0.121308	−	0.210112i
$997$	−3.34924	−	5.80106i	−0.106072	−	0.183721i	0.808104	−	0.589040i	$-0.200494\pi$
$997$	−3.34924	−	5.80106i	−0.106072	−	0.183721i	−0.914176	+	0.405319i	$0.867161\pi$
$998$	15.0000	+	25.9808i	0.474817	+	0.822407i
$999$	2.53553	−	4.39167i	0.0802207	−	0.138946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.h.79.2	✓	4
3.2	odd	2		1638.2.j.n.1171.1		4
7.2	even	3		3822.2.a.bs.1.1		2
7.4	even	3	inner	546.2.i.h.235.2	yes	4
7.5	odd	6		3822.2.a.bp.1.2		2
21.11	odd	6		1638.2.j.n.235.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.h.79.2	✓	4	1.1	even	1	trivial
546.2.i.h.235.2	yes	4	7.4	even	3	inner
1638.2.j.n.235.1		4	21.11	odd	6
1638.2.j.n.1171.1		4	3.2	odd	2
3822.2.a.bp.1.2		2	7.5	odd	6
3822.2.a.bs.1.1		2	7.2	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(-0.207107 - 0.358719i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.62132 + 2.09077i) q^{14} -1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.62132 - 4.54026i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.50000 + 2.59808i) q^{19} -1.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} +0.414214 q^{22} +(4.53553 - 7.85578i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.50000 + 2.59808i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 2.44949i) q^{28} +5.00000 q^{29} +(0.707107 - 1.22474i) q^{30} +(-3.41421 - 5.91359i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.207107 + 0.358719i) q^{33} +5.24264 q^{34} +(2.29289 - 2.95680i) q^{35} +1.00000 q^{36} +(2.53553 - 4.39167i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(0.707107 - 1.22474i) q^{40} +4.58579 q^{41} +(2.62132 + 0.358719i) q^{42} +4.82843 q^{43} +(-0.207107 + 0.358719i) q^{44} +(0.707107 + 1.22474i) q^{45} +(4.53553 + 7.85578i) q^{46} +(-4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(6.74264 + 1.88064i) q^{49} -3.00000 q^{50} +(-2.62132 + 4.54026i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-6.15685 - 10.6640i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.585786 q^{55} +(2.62132 + 0.358719i) q^{56} +3.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(-3.79289 - 6.56948i) q^{59} +(0.707107 + 1.22474i) q^{60} +(2.62132 - 4.54026i) q^{61} +6.82843 q^{62} +(-1.62132 + 2.09077i) q^{63} +1.00000 q^{64} +(0.707107 - 1.22474i) q^{65} +(-0.207107 - 0.358719i) q^{66} +(7.32843 + 12.6932i) q^{67} +(-2.62132 + 4.54026i) q^{68} -9.07107 q^{69} +(1.41421 + 3.46410i) q^{70} -1.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.535534 + 0.927572i) q^{73} +(2.53553 + 4.39167i) q^{74} +(1.50000 - 2.59808i) q^{75} +3.00000 q^{76} +(-0.414214 - 1.01461i) q^{77} +1.00000 q^{78} +(-6.65685 + 11.5300i) q^{79} +(0.707107 + 1.22474i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.29289 + 3.97141i) q^{82} -7.65685 q^{83} +(-1.62132 + 2.09077i) q^{84} -7.41421 q^{85} +(-2.41421 + 4.18154i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(-0.207107 - 0.358719i) q^{88} +(3.12132 - 5.40629i) q^{89} -1.41421 q^{90} +(2.62132 + 0.358719i) q^{91} -9.07107 q^{92} +(-3.41421 + 5.91359i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(2.12132 + 3.67423i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.89949 q^{97} +(-5.00000 + 4.89898i) q^{98} +0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 8 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} + 12 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{38} - 2 q^{39} + 24 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 4 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} - 12 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 2 q^{61} + 16 q^{62} + 2 q^{63} + 4 q^{64} + 2 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 4 q^{77} + 4 q^{78} - 4 q^{79} - 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 24 q^{85} - 4 q^{86} - 10 q^{87} + 2 q^{88} + 4 q^{89} + 2 q^{91} - 8 q^{92} - 8 q^{93} - 18 q^{94} - 2 q^{96} - 8 q^{97} - 20 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 8 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^38 - 2 * q^39 + 24 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 4 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 - 12 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 2 * q^61 + 16 * q^62 + 2 * q^63 + 4 * q^64 + 2 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 4 * q^77 + 4 * q^78 - 4 * q^79 - 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 24 * q^85 - 4 * q^86 - 10 * q^87 + 2 * q^88 + 4 * q^89 + 2 * q^91 - 8 * q^92 - 8 * q^93 - 18 * q^94 - 2 * q^96 - 8 * q^97 - 20 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more