LMFDB - Embedded newform 930.2.s.b.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			769.1
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	930.769
Dual form			930.2.s.b.439.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23205 + 0.133975i) q^{10} +(0.322876 - 0.559237i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-4.58258 - 2.64575i) q^{13} +(1.32288 + 2.29129i) q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +(-5.19615 + 3.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-2.64575 - 4.58258i) q^{19} +(0.133975 - 2.23205i) q^{20} +(-1.32288 + 2.29129i) q^{21} +(-0.559237 - 0.322876i) q^{22} -9.29150i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(-2.64575 + 4.58258i) q^{26} -1.00000i q^{27} +(2.29129 - 1.32288i) q^{28} -2.64575 q^{29} +(2.00000 - 1.00000i) q^{30} +(1.14575 + 5.44860i) q^{31} -1.00000i q^{32} -0.645751i q^{33} +(3.00000 + 5.19615i) q^{34} +(-2.64575 - 5.29150i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.46410 - 2.00000i) q^{37} +(-4.58258 + 2.64575i) q^{38} -5.29150 q^{39} +(-2.23205 - 0.133975i) q^{40} +(-1.64575 + 2.85052i) q^{41} +(2.29129 + 1.32288i) q^{42} +(-9.77873 + 5.64575i) q^{43} +(-0.322876 + 0.559237i) q^{44} +(1.86603 + 1.23205i) q^{45} -9.29150 q^{46} -9.29150i q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.598076 + 4.96410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.58258 + 2.64575i) q^{52} +(-1.98450 - 1.14575i) q^{53} -1.00000 q^{54} +(1.20499 + 0.795598i) q^{55} +(-1.32288 - 2.29129i) q^{56} +(-4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(-0.322876 - 0.559237i) q^{59} +(-1.00000 - 2.00000i) q^{60} +10.0000 q^{61} +(5.44860 - 1.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(6.51940 - 9.87408i) q^{65} -0.645751 q^{66} +(9.77873 + 5.64575i) q^{67} +(5.19615 - 3.00000i) q^{68} +(-4.64575 - 8.04668i) q^{69} +(-5.29150 + 2.64575i) q^{70} +(-3.29150 + 5.70105i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-5.70105 - 3.29150i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.59808 + 1.96410i) q^{75} +(2.64575 + 4.58258i) q^{76} +1.70850i q^{77} +5.29150i q^{78} +(7.29150 + 12.6293i) q^{79} +(-0.133975 + 2.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.85052 + 1.64575i) q^{82} +(8.29913 + 4.79150i) q^{83} +(1.32288 - 2.29129i) q^{84} +(-6.00000 - 12.0000i) q^{85} +(5.64575 + 9.77873i) q^{86} +(-2.29129 + 1.32288i) q^{87} +(0.559237 + 0.322876i) q^{88} +3.29150 q^{89} +(1.23205 - 1.86603i) q^{90} +14.0000 q^{91} +9.29150i q^{92} +(3.71655 + 4.14575i) q^{93} -9.29150 q^{94} +(10.5830 - 5.29150i) q^{95} +(-0.500000 - 0.866025i) q^{96} +11.2288i q^{97} +(-0.322876 - 0.559237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.23205	+	0.133975i	0.705836	+	0.0423665i
$11$	0.322876	−	0.559237i	0.0973507	−	0.168616i	−0.813237	−	0.581933i	$-0.802296\pi$
$11$	0.322876	−	0.559237i	0.0973507	−	0.168616i	0.910587	+	0.413317i	$0.135630\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−4.58258	−	2.64575i	−1.27098	−	0.733799i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	−4.58258	−	2.64575i	−1.27098	−	0.733799i	−0.975172	+	0.221449i	$0.928921\pi$
$14$	1.32288	+	2.29129i	0.353553	+	0.612372i
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−2.64575	−	4.58258i	−0.606977	−	1.05131i	−0.991736	−	0.128298i	$-0.959049\pi$
$19$	−2.64575	−	4.58258i	−0.606977	−	1.05131i	0.384759	−	0.923017i	$-0.374285\pi$
$20$	0.133975	−	2.23205i	0.0299576	−	0.499102i
$21$	−1.32288	+	2.29129i	−0.288675	+	0.500000i
$22$	−0.559237	−	0.322876i	−0.119230	−	0.0688373i
$23$		−	9.29150i		−	1.93741i	−0.248211	−	0.968706i	$-0.579842\pi$
$23$		−	9.29150i		−	1.93741i	0.248211	−	0.968706i	$-0.420158\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	−2.64575	+	4.58258i	−0.518875	+	0.898717i
$27$		−	1.00000i		−	0.192450i
$28$	2.29129	−	1.32288i	0.433013	−	0.250000i
$29$	−2.64575			−0.491304			−0.245652	−	0.969358i	$-0.579002\pi$
$29$	−2.64575			−0.491304			−0.245652	+	0.969358i	$0.579002\pi$
$30$	2.00000	−	1.00000i	0.365148	−	0.182574i
$31$	1.14575	+	5.44860i	0.205783	+	0.978598i
$31$	1.14575	+	5.44860i	0.205783	+	0.978598i
$32$		−	1.00000i		−	0.176777i
$33$		−	0.645751i		−	0.112411i
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	−2.64575	−	5.29150i	−0.447214	−	0.894427i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	−0.187453	−	0.982274i	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$	−4.58258	+	2.64575i	−0.743392	+	0.429198i
$39$	−5.29150			−0.847319
$40$	−2.23205	−	0.133975i	−0.352918	−	0.0211832i
$41$	−1.64575	+	2.85052i	−0.257023	+	0.445177i	−0.965443	−	0.260614i	$-0.916075\pi$
$41$	−1.64575	+	2.85052i	−0.257023	+	0.445177i	0.708420	+	0.705791i	$0.249408\pi$
$42$	2.29129	+	1.32288i	0.353553	+	0.204124i
$43$	−9.77873	+	5.64575i	−1.49124	+	0.860969i	−0.999950	−	0.0100257i	$-0.996809\pi$
$43$	−9.77873	+	5.64575i	−1.49124	+	0.860969i	−0.491292	+	0.870995i	$0.663475\pi$
$44$	−0.322876	+	0.559237i	−0.0486753	+	0.0843082i
$45$	1.86603	+	1.23205i	0.278171	+	0.183663i
$46$	−9.29150			−1.36996
$47$		−	9.29150i		−	1.35530i	−0.735382	−	0.677652i	$-0.762997\pi$
$47$		−	9.29150i		−	1.35530i	0.735382	−	0.677652i	$-0.237003\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$		0			0
$50$	−0.598076	+	4.96410i	−0.0845807	+	0.702030i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	4.58258	+	2.64575i	0.635489	+	0.366900i
$53$	−1.98450	−	1.14575i	−0.272592	−	0.157381i	0.357473	−	0.933923i	$-0.383638\pi$
$53$	−1.98450	−	1.14575i	−0.272592	−	0.157381i	−0.630065	+	0.776542i	$0.716972\pi$
$54$	−1.00000			−0.136083
$55$	1.20499	+	0.795598i	0.162481	+	0.107278i
$56$	−1.32288	−	2.29129i	−0.176777	−	0.306186i
$57$	−4.58258	−	2.64575i	−0.606977	−	0.350438i
$58$			2.64575i			0.347404i
$59$	−0.322876	−	0.559237i	−0.0420348	−	0.0728065i	0.844243	−	0.535961i	$-0.180051\pi$
$59$	−0.322876	−	0.559237i	−0.0420348	−	0.0728065i	−0.886277	+	0.463155i	$0.846717\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	5.44860	−	1.14575i	0.691973	−	0.145511i
$63$			2.64575i			0.333333i
$64$	−1.00000			−0.125000
$65$	6.51940	−	9.87408i	0.808632	−	1.22473i
$66$	−0.645751			−0.0794865
$67$	9.77873	+	5.64575i	1.19466	+	0.689738i	0.959360	−	0.282184i	$-0.0910589\pi$
$67$	9.77873	+	5.64575i	1.19466	+	0.689738i	0.235302	+	0.971922i	$0.424392\pi$
$68$	5.19615	−	3.00000i	0.630126	−	0.363803i
$69$	−4.64575	−	8.04668i	−0.559283	−	0.968706i
$70$	−5.29150	+	2.64575i	−0.632456	+	0.316228i
$71$	−3.29150	+	5.70105i	−0.390629	+	0.676590i	−0.992533	−	0.121979i	$-0.961076\pi$
$71$	−3.29150	+	5.70105i	−0.390629	+	0.676590i	0.601903	+	0.798569i	$0.294409\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−5.70105	−	3.29150i	−0.667257	−	0.385241i	0.127779	−	0.991803i	$-0.459215\pi$
$73$	−5.70105	−	3.29150i	−0.667257	−	0.385241i	−0.795037	+	0.606561i	$0.792548\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	−4.59808	+	1.96410i	−0.530940	+	0.226795i
$76$	2.64575	+	4.58258i	0.303488	+	0.525657i
$77$			1.70850i			0.194701i
$78$			5.29150i			0.599145i
$79$	7.29150	+	12.6293i	0.820358	+	1.42090i	0.905416	+	0.424526i	$0.139559\pi$
$79$	7.29150	+	12.6293i	0.820358	+	1.42090i	−0.0850576	+	0.996376i	$0.527107\pi$
$80$	−0.133975	+	2.23205i	−0.0149788	+	0.249551i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.85052	+	1.64575i	0.314788	+	0.181743i
$83$	8.29913	+	4.79150i	0.910947	+	0.525936i	0.880736	−	0.473608i	$-0.157049\pi$
$83$	8.29913	+	4.79150i	0.910947	+	0.525936i	0.0302116	+	0.999544i	$0.490382\pi$
$84$	1.32288	−	2.29129i	0.144338	−	0.250000i
$85$	−6.00000	−	12.0000i	−0.650791	−	1.30158i
$86$	5.64575	+	9.77873i	0.608797	+	1.05447i
$87$	−2.29129	+	1.32288i	−0.245652	+	0.141827i
$88$	0.559237	+	0.322876i	0.0596149	+	0.0344187i
$89$	3.29150			0.348899			0.174449	−	0.984666i	$-0.444185\pi$
$89$	3.29150			0.348899			0.174449	+	0.984666i	$0.444185\pi$
$90$	1.23205	−	1.86603i	0.129870	−	0.196696i
$91$	14.0000			1.46760
$92$			9.29150i			0.968706i
$93$	3.71655	+	4.14575i	0.385388	+	0.429894i
$94$	−9.29150			−0.958345
$95$	10.5830	−	5.29150i	1.08579	−	0.542897i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			11.2288i			1.14011i	0.821607	+	0.570054i	$0.193078\pi$
$97$			11.2288i			1.14011i	−0.821607	+	0.570054i	$0.806922\pi$
$98$		0			0
$99$	−0.322876	−	0.559237i	−0.0324502	−	0.0562054i
$100$	4.96410	+	0.598076i	0.496410	+	0.0598076i
$101$	6.64575			0.661277			0.330638	−	0.943757i	$-0.392736\pi$
$101$	6.64575			0.661277			0.330638	+	0.943757i	$0.392736\pi$
$102$	5.19615	+	3.00000i	0.514496	+	0.297044i
$103$	−5.75539	−	3.32288i	−0.567095	−	0.327413i	0.188893	−	0.981998i	$-0.439510\pi$
$103$	−5.75539	−	3.32288i	−0.567095	−	0.327413i	−0.755988	+	0.654585i	$0.772843\pi$
$104$	2.64575	−	4.58258i	0.259437	−	0.449359i
$105$	−4.93704	−	3.25970i	−0.481806	−	0.318114i
$106$	−1.14575	+	1.98450i	−0.111285	+	0.192752i
$107$	−4.33013	+	2.50000i	−0.418609	+	0.241684i	−0.694482	−	0.719510i	$-0.744366\pi$
$107$	−4.33013	+	2.50000i	−0.418609	+	0.241684i	0.275873	+	0.961194i	$0.411033\pi$
$108$			1.00000i			0.0962250i
$109$	−6.70850			−0.642558			−0.321279	−	0.946985i	$-0.604113\pi$
$109$	−6.70850			−0.642558			−0.321279	+	0.946985i	$0.604113\pi$
$110$	0.795598	−	1.20499i	0.0758573	−	0.114891i
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	−2.29129	+	1.32288i	−0.216506	+	0.125000i
$113$	−11.5108	−	6.64575i	−1.08284	−	0.625180i	−0.151181	−	0.988506i	$-0.548308\pi$
$113$	−11.5108	−	6.64575i	−1.08284	−	0.625180i	−0.931662	+	0.363326i	$0.881641\pi$
$114$	−2.64575	+	4.58258i	−0.247797	+	0.429198i
$115$	20.7391	+	1.24483i	1.93393	+	0.116081i
$116$	2.64575			0.245652
$117$	−4.58258	+	2.64575i	−0.423659	+	0.244600i
$118$	−0.559237	+	0.322876i	−0.0514819	+	0.0297231i
$119$	7.93725	−	13.7477i	0.727607	−	1.26025i
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	5.29150	+	9.16515i	0.481046	+	0.833196i
$122$		−	10.0000i		−	0.905357i
$123$			3.29150i			0.296785i
$124$	−1.14575	−	5.44860i	−0.102892	−	0.489299i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	2.64575			0.235702
$127$	−11.4564	+	6.61438i	−1.01659	+	0.586931i	−0.913116	−	0.407700i	$-0.866331\pi$
$127$	−11.4564	+	6.61438i	−1.01659	+	0.586931i	−0.103479	+	0.994632i	$0.532997\pi$
$128$			1.00000i			0.0883883i
$129$	−5.64575	+	9.77873i	−0.497081	+	0.860969i
$130$	−9.87408	−	6.51940i	−0.866014	−	0.571789i
$131$	−1.35425	−	2.34563i	−0.118321	−	0.204938i	0.800781	−	0.598957i	$-0.204418\pi$
$131$	−1.35425	−	2.34563i	−0.118321	−	0.204938i	−0.919103	+	0.394018i	$0.871085\pi$
$132$			0.645751i			0.0562054i
$133$	12.1244	+	7.00000i	1.05131	+	0.606977i
$134$	5.64575	−	9.77873i	0.487719	−	0.844753i
$135$	2.23205	+	0.133975i	0.192104	+	0.0115307i
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−9.16515	−	5.29150i	−0.783032	−	0.452084i	0.0544719	−	0.998515i	$-0.482652\pi$
$137$	−9.16515	−	5.29150i	−0.783032	−	0.452084i	−0.837504	+	0.546432i	$0.815986\pi$
$138$	−8.04668	+	4.64575i	−0.684979	+	0.395473i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.64575	+	5.29150i	0.223607	+	0.447214i
$141$	−4.64575	−	8.04668i	−0.391243	−	0.677652i
$142$	5.70105	+	3.29150i	0.478421	+	0.276217i
$143$	−2.95920	+	1.70850i	−0.247461	+	0.142872i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	0.354463	−	5.90545i	0.0294366	−	0.490421i
$146$	−3.29150	+	5.70105i	−0.272407	+	0.471822i
$147$		0			0
$148$	−3.46410	+	2.00000i	−0.284747	+	0.164399i
$149$	−9.32288	−	16.1477i	−0.763760	−	1.32287i	−0.940900	−	0.338685i	$-0.890018\pi$
$149$	−9.32288	−	16.1477i	−0.763760	−	1.32287i	0.177140	−	0.984186i	$-0.443315\pi$
$150$	1.96410	+	4.59808i	0.160368	+	0.375431i
$151$	−11.7085			−0.952824			−0.476412	−	0.879222i	$-0.658063\pi$
$151$	−11.7085			−0.952824			−0.476412	+	0.879222i	$0.658063\pi$
$152$	4.58258	−	2.64575i	0.371696	−	0.214599i
$153$			6.00000i			0.485071i
$154$	1.70850			0.137675
$155$	−12.3151	+	1.82740i	−0.989169	+	0.146780i
$156$	5.29150			0.423659
$157$		−	1.29150i		−	0.103073i	−0.998671	−	0.0515366i	$-0.983588\pi$
$157$		−	1.29150i		−	0.103073i	0.998671	−	0.0515366i	$-0.0164119\pi$
$158$	12.6293	−	7.29150i	1.00473	−	0.580081i
$159$	−2.29150			−0.181728
$160$	2.23205	+	0.133975i	0.176459	+	0.0105916i
$161$	12.2915	+	21.2895i	0.968706	+	1.67785i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	1.64575	−	2.85052i	0.128512	−	0.222589i
$165$	1.44135	+	0.0865143i	0.112209	+	0.00673513i
$166$	4.79150	−	8.29913i	0.371893	−	0.644137i
$167$	18.9439	−	10.9373i	1.46592	−	0.846350i	0.466647	−	0.884444i	$-0.345462\pi$
$167$	18.9439	−	10.9373i	1.46592	−	0.846350i	0.999274	+	0.0380934i	$0.0121284\pi$
$168$	−2.29129	−	1.32288i	−0.176777	−	0.102062i
$169$	7.50000	+	12.9904i	0.576923	+	0.999260i
$170$	−12.0000	+	6.00000i	−0.920358	+	0.460179i
$171$	−5.29150			−0.404651
$172$	9.77873	−	5.64575i	0.745621	−	0.430485i
$173$	−5.44860	−	3.14575i	−0.414249	−	0.239167i	0.278364	−	0.960476i	$-0.410208\pi$
$173$	−5.44860	−	3.14575i	−0.414249	−	0.239167i	−0.692614	+	0.721308i	$0.743541\pi$
$174$	1.32288	+	2.29129i	0.100287	+	0.173702i
$175$	12.1654	−	5.19652i	0.919615	−	0.392820i
$176$	0.322876	−	0.559237i	0.0243377	−	0.0421541i
$177$	−0.559237	−	0.322876i	−0.0420348	−	0.0242688i
$178$		−	3.29150i		−	0.246709i
$179$	−1.61438	−	2.79619i	−0.120664	−	0.208997i	0.799366	−	0.600845i	$-0.205169\pi$
$179$	−1.61438	−	2.79619i	−0.120664	−	0.208997i	−0.920030	+	0.391848i	$0.871836\pi$
$180$	−1.86603	−	1.23205i	−0.139085	−	0.0918316i
$181$	0.354249	−	0.613577i	0.0263311	−	0.0456068i	−0.852560	−	0.522630i	$-0.824951\pi$
$181$	0.354249	−	0.613577i	0.0263311	−	0.0456068i	0.878891	+	0.477023i	$0.158284\pi$
$182$		−	14.0000i		−	1.03775i
$183$	8.66025	−	5.00000i	0.640184	−	0.369611i
$184$	9.29150			0.684979
$185$	4.00000	+	8.00000i	0.294086	+	0.588172i
$186$	4.14575	−	3.71655i	0.303981	−	0.272511i
$187$			3.87451i			0.283332i
$188$			9.29150i			0.677652i
$189$	1.32288	+	2.29129i	0.0962250	+	0.166667i
$190$	−5.29150	−	10.5830i	−0.383886	−	0.767772i
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−17.8797	+	10.3229i	−1.28701	+	0.743057i	−0.978120	−	0.208040i	$-0.933291\pi$
$193$	−17.8797	+	10.3229i	−1.28701	+	0.743057i	−0.308892	+	0.951097i	$0.599958\pi$
$194$	11.2288			0.806178
$195$	0.708927	−	11.8109i	0.0507673	−	0.845796i
$196$		0			0
$197$	−20.0624	−	11.5830i	−1.42938	−	0.825255i	−0.432312	−	0.901724i	$-0.642302\pi$
$197$	−20.0624	−	11.5830i	−1.42938	−	0.825255i	−0.997072	+	0.0764693i	$0.975635\pi$
$198$	−0.559237	+	0.322876i	−0.0397432	+	0.0229458i
$199$	8.14575	−	14.1089i	0.577437	−	1.00015i	−0.418335	−	0.908293i	$-0.637386\pi$
$199$	8.14575	−	14.1089i	0.577437	−	1.00015i	0.995772	−	0.0918575i	$-0.0292804\pi$
$200$	0.598076	−	4.96410i	0.0422904	−	0.351015i
$201$	11.2915			0.796441
$202$		−	6.64575i		−	0.467593i
$203$	6.06218	−	3.50000i	0.425481	−	0.245652i
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	−6.14203	−	4.05530i	−0.428978	−	0.283234i
$206$	−3.32288	+	5.75539i	−0.231516	+	0.400997i
$207$	−8.04668	−	4.64575i	−0.559283	−	0.322902i
$208$	−4.58258	−	2.64575i	−0.317744	−	0.183450i
$209$	−3.41699			−0.236358
$210$	−3.25970	+	4.93704i	−0.224941	+	0.340688i
$211$	8.29150	+	14.3613i	0.570811	+	0.988673i	0.996483	+	0.0837956i	$0.0267043\pi$
$211$	8.29150	+	14.3613i	0.570811	+	0.988673i	−0.425672	+	0.904877i	$0.639962\pi$
$212$	1.98450	+	1.14575i	0.136296	+	0.0786905i
$213$			6.58301i			0.451060i
$214$	2.50000	+	4.33013i	0.170896	+	0.296001i
$215$	−11.2915	−	22.5830i	−0.770074	−	1.54015i
$216$	1.00000			0.0680414
$217$	−9.83307	−	10.9686i	−0.667512	−	0.744599i
$218$			6.70850i			0.454357i
$219$	−6.58301			−0.444838
$220$	−1.20499	−	0.795598i	−0.0812403	−	0.0536392i
$221$	31.7490			2.13567
$222$	−3.46410	−	2.00000i	−0.232495	−	0.134231i
$223$	23.0759	−	13.3229i	1.54528	−	0.892166i	0.546784	−	0.837274i	$-0.315852\pi$
$223$	23.0759	−	13.3229i	1.54528	−	0.892166i	0.998492	−	0.0548921i	$-0.0174815\pi$
$224$	1.32288	+	2.29129i	0.0883883	+	0.153093i
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	−6.64575	+	11.5108i	−0.442069	+	0.765686i
$227$	12.9904	+	7.50000i	0.862202	+	0.497792i	0.864749	−	0.502204i	$-0.167477\pi$
$227$	12.9904	+	7.50000i	0.862202	+	0.497792i	−0.00254715	+	0.999997i	$0.500811\pi$
$228$	4.58258	+	2.64575i	0.303488	+	0.175219i
$229$	−8.58301	−	14.8662i	−0.567181	−	0.982386i	−0.996843	−	0.0793965i	$-0.974701\pi$
$229$	−8.58301	−	14.8662i	−0.567181	−	0.982386i	0.429662	−	0.902990i	$-0.358633\pi$
$230$	1.24483	−	20.7391i	0.0820814	−	1.36750i
$231$	0.854249	+	1.47960i	0.0562054	+	0.0973507i
$232$		−	2.64575i		−	0.173702i
$233$		−	7.29150i		−	0.477682i	−0.971059	−	0.238841i	$-0.923232\pi$
$233$		−	7.29150i		−	0.477682i	0.971059	−	0.238841i	$-0.0767675\pi$
$234$	2.64575	+	4.58258i	0.172958	+	0.299572i
$235$	20.7391	+	1.24483i	1.35287	+	0.0812034i
$236$	0.322876	+	0.559237i	0.0210174	+	0.0364032i
$237$	12.6293	+	7.29150i	0.820358	+	0.473634i
$238$	−13.7477	−	7.93725i	−0.891133	−	0.514496i
$239$	12.2915	−	21.2895i	0.795071	−	1.37710i	−0.127723	−	0.991810i	$-0.540767\pi$
$239$	12.2915	−	21.2895i	0.795071	−	1.37710i	0.922794	−	0.385294i	$-0.125900\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	−0.976068	−	0.217465i	$-0.930221\pi$
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	0.299704	−	0.954032i	$-0.403112\pi$
$242$	9.16515	−	5.29150i	0.589158	−	0.340151i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	3.29150			0.209859
$247$			28.0000i			1.78160i
$248$	−5.44860	+	1.14575i	−0.345987	+	0.0727553i
$249$	9.58301			0.607298
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−5.35425	−	9.27383i	−0.337957	−	0.585359i	0.646091	−	0.763260i	$-0.276403\pi$
$251$	−5.35425	−	9.27383i	−0.337957	−	0.585359i	−0.984048	+	0.177901i	$0.943069\pi$
$252$		−	2.64575i		−	0.166667i
$253$	−5.19615	−	3.00000i	−0.326679	−	0.188608i
$254$	6.61438	+	11.4564i	0.415023	+	0.718841i
$255$	−11.1962	−	7.39230i	−0.701130	−	0.462924i
$256$	1.00000			0.0625000
$257$	4.58258	+	2.64575i	0.285853	+	0.165037i	0.636070	−	0.771631i	$-0.280559\pi$
$257$	4.58258	+	2.64575i	0.285853	+	0.165037i	−0.350217	+	0.936669i	$0.613892\pi$
$258$	9.77873	+	5.64575i	0.608797	+	0.351489i
$259$	−5.29150	+	9.16515i	−0.328798	+	0.569495i
$260$	−6.51940	+	9.87408i	−0.404316	+	0.612364i
$261$	−1.32288	+	2.29129i	−0.0818839	+	0.141827i
$262$	−2.34563	+	1.35425i	−0.144913	+	0.0836658i
$263$			23.1660i			1.42848i	0.699902	+	0.714239i	$0.253227\pi$
$263$			23.1660i			1.42848i	−0.699902	+	0.714239i	$0.746773\pi$
$264$	0.645751			0.0397432
$265$	2.82325	−	4.27600i	0.173431	−	0.262673i
$266$	7.00000	−	12.1244i	0.429198	−	0.743392i
$267$	2.85052	−	1.64575i	0.174449	−	0.100718i
$268$	−9.77873	−	5.64575i	−0.597331	−	0.344869i
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	−0.717933	−	0.696112i	$-0.754912\pi$
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	0.961817	+	0.273692i	$0.0882449\pi$
$270$	0.133975	−	2.23205i	0.00815343	−	0.135838i
$271$	−22.2915			−1.35411			−0.677056	−	0.735931i	$-0.736745\pi$
$271$	−22.2915			−1.35411			−0.677056	+	0.735931i	$0.736745\pi$
$272$	−5.19615	+	3.00000i	−0.315063	+	0.181902i
$273$	12.1244	−	7.00000i	0.733799	−	0.423659i
$274$	−5.29150	+	9.16515i	−0.319671	+	0.553687i
$275$	−1.93725	+	2.58301i	−0.116821	+	0.155761i
$276$	4.64575	+	8.04668i	0.279641	+	0.484353i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			4.00000i			0.239904i
$279$	5.29150	+	1.73205i	0.316794	+	0.103695i
$280$	5.29150	−	2.64575i	0.316228	−	0.158114i
$281$	18.5830			1.10857			0.554285	−	0.832327i	$-0.312992\pi$
$281$	18.5830			1.10857			0.554285	+	0.832327i	$0.312992\pi$
$282$	−8.04668	+	4.64575i	−0.479173	+	0.276650i
$283$		−	18.7085i		−	1.11210i	−0.831147	−	0.556052i	$-0.812315\pi$
$283$		−	18.7085i		−	1.11210i	0.831147	−	0.556052i	$-0.187685\pi$
$284$	3.29150	−	5.70105i	0.195315	−	0.338295i
$285$	6.51940	−	9.87408i	0.386176	−	0.584890i
$286$	1.70850	+	2.95920i	0.101026	+	0.174981i
$287$		−	8.70850i		−	0.514046i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$	−5.90545	−	0.354463i	−0.346780	−	0.0208148i
$291$	5.61438	+	9.72439i	0.329121	+	0.570054i
$292$	5.70105	+	3.29150i	0.333629	+	0.192621i
$293$	−11.8719	+	6.85425i	−0.693564	+	0.400429i	−0.804946	−	0.593348i	$-0.797806\pi$
$293$	−11.8719	+	6.85425i	−0.693564	+	0.400429i	0.111382	+	0.993778i	$0.464472\pi$
$294$		0			0
$295$	1.29150	−	0.645751i	0.0751942	−	0.0375971i
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−0.559237	−	0.322876i	−0.0324502	−	0.0187351i
$298$	−16.1477	+	9.32288i	−0.935411	+	0.540060i
$299$	−24.5830	+	42.5790i	−1.42167	+	2.46241i
$300$	4.59808	−	1.96410i	0.265470	−	0.113397i
$301$	14.9373	−	25.8721i	0.860969	−	1.49124i
$302$			11.7085i			0.673748i
$303$	5.75539	−	3.32288i	0.330638	−	0.190894i
$304$	−2.64575	−	4.58258i	−0.151744	−	0.262829i
$305$	−1.33975	+	22.3205i	−0.0767136	+	1.27807i
$306$	6.00000			0.342997
$307$	−12.0157	+	6.93725i	−0.685771	+	0.395930i	−0.802026	−	0.597289i	$-0.796244\pi$
$307$	−12.0157	+	6.93725i	−0.685771	+	0.395930i	0.116255	+	0.993219i	$0.462911\pi$
$308$		−	1.70850i		−	0.0973507i
$309$	−6.64575			−0.378064
$310$	1.82740	+	12.3151i	0.103789	+	0.699448i
$311$	−11.8745			−0.673342			−0.336671	−	0.941622i	$-0.609301\pi$
$311$	−11.8745			−0.673342			−0.336671	+	0.941622i	$0.609301\pi$
$312$		−	5.29150i		−	0.299572i
$313$	−12.0700	+	6.96863i	−0.682238	+	0.393890i	−0.800698	−	0.599069i	$-0.795538\pi$
$313$	−12.0700	+	6.96863i	−0.682238	+	0.393890i	0.118460	+	0.992959i	$0.462204\pi$
$314$	−1.29150			−0.0728837
$315$	−5.90545	−	0.354463i	−0.332734	−	0.0199718i
$316$	−7.29150	−	12.6293i	−0.410179	−	0.710451i
$317$	−14.1089	+	8.14575i	−0.792432	+	0.457511i	−0.840818	−	0.541318i	$-0.817926\pi$
$317$	−14.1089	+	8.14575i	−0.792432	+	0.457511i	0.0483859	+	0.998829i	$0.484592\pi$
$318$			2.29150i			0.128501i
$319$	−0.854249	+	1.47960i	−0.0478287	+	0.0828418i
$320$	0.133975	−	2.23205i	0.00748941	−	0.124775i
$321$	−2.50000	+	4.33013i	−0.139536	+	0.241684i
$322$	21.2895	−	12.2915i	1.18642	−	0.684979i
$323$	27.4955	+	15.8745i	1.52989	+	0.883281i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	21.1660	+	15.8745i	1.17408	+	0.880559i
$326$	10.0000			0.553849
$327$	−5.80973	+	3.35425i	−0.321279	+	0.185490i
$328$	−2.85052	−	1.64575i	−0.157394	−	0.0908714i
$329$	12.2915	+	21.2895i	0.677652	+	1.17373i
$330$	0.0865143	−	1.44135i	0.00476245	−	0.0793437i
$331$	−9.58301	+	16.5983i	−0.526730	+	0.912322i	0.472785	+	0.881178i	$0.343249\pi$
$331$	−9.58301	+	16.5983i	−0.526730	+	0.912322i	−0.999515	+	0.0311448i	$0.990085\pi$
$332$	−8.29913	−	4.79150i	−0.455474	−	0.262968i
$333$		−	4.00000i		−	0.219199i
$334$	−10.9373	−	18.9439i	−0.598460	−	1.03656i
$335$	−13.9117	+	21.0702i	−0.760078	+	1.15119i
$336$	−1.32288	+	2.29129i	−0.0721688	+	0.125000i
$337$		−	35.1033i		−	1.91220i	−0.293046	−	0.956098i	$-0.594669\pi$
$337$		−	35.1033i		−	1.91220i	0.293046	−	0.956098i	$-0.405331\pi$
$338$	12.9904	−	7.50000i	0.706584	−	0.407946i
$339$	−13.2915			−0.721895
$340$	6.00000	+	12.0000i	0.325396	+	0.650791i
$341$	3.41699	+	1.11847i	0.185041	+	0.0605688i
$342$			5.29150i			0.286132i
$343$		−	18.5203i		−	1.00000i
$344$	−5.64575	−	9.77873i	−0.304399	−	0.527234i
$345$	18.5830	−	9.29150i	1.00048	−	0.500238i
$346$	−3.14575	+	5.44860i	−0.169117	+	0.292919i
$347$	−3.10297	+	1.79150i	−0.166576	+	0.0961729i	−0.580970	−	0.813925i	$-0.697327\pi$
$347$	−3.10297	+	1.79150i	−0.166576	+	0.0961729i	0.414394	+	0.910098i	$0.363994\pi$
$348$	2.29129	−	1.32288i	0.122826	−	0.0709136i
$349$	5.29150			0.283248			0.141624	−	0.989921i	$-0.454768\pi$
$349$	5.29150			0.283248			0.141624	+	0.989921i	$0.454768\pi$
$350$	−5.19652	−	12.1654i	−0.277766	−	0.650266i
$351$	−2.64575	+	4.58258i	−0.141220	+	0.244600i
$352$	−0.559237	−	0.322876i	−0.0298074	−	0.0172093i
$353$	19.6661	−	11.3542i	1.04672	−	0.604326i	0.124993	−	0.992158i	$-0.460109\pi$
$353$	19.6661	−	11.3542i	1.04672	−	0.604326i	0.921730	+	0.387832i	$0.126776\pi$
$354$	−0.322876	+	0.559237i	−0.0171606	+	0.0297231i
$355$	−12.2841	−	8.11060i	−0.651970	−	0.430466i
$356$	−3.29150			−0.174449
$357$		−	15.8745i		−	0.840168i
$358$	−2.79619	+	1.61438i	−0.147783	+	0.0853225i
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$	−1.23205	+	1.86603i	−0.0649348	+	0.0983482i
$361$	−4.50000	+	7.79423i	−0.236842	+	0.410223i
$362$	−0.613577	−	0.354249i	−0.0322489	−	0.0186189i
$363$	9.16515	+	5.29150i	0.481046	+	0.277732i
$364$	−14.0000			−0.733799
$365$	8.11060	−	12.2841i	0.424528	−	0.642977i
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	29.8411	+	17.2288i	1.55769	+	0.899334i	0.997477	+	0.0709862i	$0.0226146\pi$
$367$	29.8411	+	17.2288i	1.55769	+	0.899334i	0.560214	+	0.828348i	$0.310719\pi$
$368$		−	9.29150i		−	0.484353i
$369$	1.64575	+	2.85052i	0.0856744	+	0.148392i
$370$	8.00000	−	4.00000i	0.415900	−	0.207950i
$371$	6.06275			0.314762
$372$	−3.71655	−	4.14575i	−0.192694	−	0.214947i
$373$		−	15.1660i		−	0.785266i	−0.919695	−	0.392633i	$-0.871564\pi$
$373$		−	15.1660i		−	0.785266i	0.919695	−	0.392633i	$-0.128436\pi$
$374$	3.87451			0.200346
$375$	−3.76795	−	10.5263i	−0.194576	−	0.543575i
$376$	9.29150			0.479173
$377$	12.1244	+	7.00000i	0.624436	+	0.360518i
$378$	2.29129	−	1.32288i	0.117851	−	0.0680414i
$379$	−2.35425	−	4.07768i	−0.120930	−	0.209456i	0.799205	−	0.601059i	$-0.205254\pi$
$379$	−2.35425	−	4.07768i	−0.120930	−	0.209456i	−0.920135	+	0.391602i	$0.871921\pi$
$380$	−10.5830	+	5.29150i	−0.542897	+	0.271448i
$381$	−6.61438	+	11.4564i	−0.338865	+	0.586931i
$382$	6.92820	+	4.00000i	0.354478	+	0.204658i
$383$	14.2526	+	8.22876i	0.728275	+	0.420470i	0.817791	−	0.575516i	$-0.195199\pi$
$383$	14.2526	+	8.22876i	0.728275	+	0.420470i	−0.0895157	+	0.995985i	$0.528532\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−3.81345	−	0.228895i	−0.194352	−	0.0116656i
$386$	10.3229	+	17.8797i	0.525421	+	0.910055i
$387$			11.2915i			0.573979i
$388$		−	11.2288i		−	0.570054i
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	0.588777	−	0.808296i	$-0.299610\pi$
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	−0.994393	+	0.105748i	$0.966276\pi$
$390$	−11.8109	−	0.708927i	−0.598068	−	0.0358979i
$391$	27.8745	+	48.2801i	1.40967	+	2.44163i
$392$		0			0
$393$	−2.34563	−	1.35425i	−0.118321	−	0.0683128i
$394$	−11.5830	+	20.0624i	−0.583543	+	1.01073i
$395$	−29.1660	+	14.5830i	−1.46750	+	0.733751i
$396$	0.322876	+	0.559237i	0.0162251	+	0.0281027i
$397$	32.1867	−	18.5830i	1.61540	−	0.932654i	0.627317	−	0.778764i	$-0.284153\pi$
$397$	32.1867	−	18.5830i	1.61540	−	0.932654i	0.988088	−	0.153890i	$-0.0491801\pi$
$398$	−14.1089	−	8.14575i	−0.707213	−	0.408310i
$399$	14.0000			0.700877
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$		−	11.2915i		−	0.563169i
$403$	9.16515	−	28.0000i	0.456549	−	1.39478i
$404$	−6.64575			−0.330638
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	−3.50000	−	6.06218i	−0.173702	−	0.300861i
$407$		−	2.58301i		−	0.128035i
$408$	−5.19615	−	3.00000i	−0.257248	−	0.148522i
$409$	5.20850	+	9.02138i	0.257544	+	0.446079i	0.965583	−	0.260094i	$-0.0837536\pi$
$409$	5.20850	+	9.02138i	0.257544	+	0.446079i	−0.708040	+	0.706173i	$0.750420\pi$
$410$	−4.05530	+	6.14203i	−0.200277	+	0.303333i
$411$	−10.5830			−0.522021
$412$	5.75539	+	3.32288i	0.283548	+	0.163706i
$413$	1.47960	+	0.854249i	0.0728065	+	0.0420348i
$414$	−4.64575	+	8.04668i	−0.228326	+	0.395473i
$415$	−11.8067	+	17.8821i	−0.579571	+	0.877799i
$416$	−2.64575	+	4.58258i	−0.129719	+	0.224679i
$417$	−3.46410	+	2.00000i	−0.169638	+	0.0979404i
$418$			3.41699i			0.167131i
$419$	13.9373			0.680879			0.340440	−	0.940266i	$-0.389424\pi$
$419$	13.9373			0.680879			0.340440	+	0.940266i	$0.389424\pi$
$420$	4.93704	+	3.25970i	0.240903	+	0.159057i
$421$	−15.9373	+	27.6041i	−0.776734	+	1.34534i	0.157080	+	0.987586i	$0.449792\pi$
$421$	−15.9373	+	27.6041i	−0.776734	+	1.34534i	−0.933815	+	0.357757i	$0.883542\pi$
$422$	14.3613	−	8.29150i	0.699097	−	0.403624i
$423$	−8.04668	−	4.64575i	−0.391243	−	0.225884i
$424$	1.14575	−	1.98450i	0.0556426	−	0.0963758i
$425$	27.5885	−	11.7846i	1.33824	−	0.571638i
$426$	6.58301			0.318948
$427$	−22.9129	+	13.2288i	−1.10883	+	0.640184i
$428$	4.33013	−	2.50000i	0.209305	−	0.120842i
$429$	−1.70850	+	2.95920i	−0.0824870	+	0.142872i
$430$	−22.5830	+	11.2915i	−1.08905	+	0.544525i
$431$	−19.5203	−	33.8101i	−0.940258	−	1.62857i	−0.764979	−	0.644055i	$-0.777251\pi$
$431$	−19.5203	−	33.8101i	−0.940258	−	1.62857i	−0.175279	−	0.984519i	$-0.556083\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	9.16601i		−	0.440490i	−0.975445	−	0.220245i	$-0.929314\pi$
$433$		−	9.16601i		−	0.440490i	0.975445	−	0.220245i	$-0.0706857\pi$
$434$	−10.9686	+	9.83307i	−0.526511	+	0.472002i
$435$	−2.64575	−	5.29150i	−0.126854	−	0.253708i
$436$	6.70850			0.321279
$437$	−42.5790	+	24.5830i	−2.03683	+	1.17596i
$438$			6.58301i			0.314548i
$439$	−2.43725	+	4.22145i	−0.116324	+	0.201479i	−0.918308	−	0.395866i	$-0.870444\pi$
$439$	−2.43725	+	4.22145i	−0.116324	+	0.201479i	0.801984	+	0.597345i	$0.203778\pi$
$440$	−0.795598	+	1.20499i	−0.0379287	+	0.0574456i
$441$		0			0
$442$		−	31.7490i		−	1.51015i
$443$	6.92820	+	4.00000i	0.329169	+	0.190046i	0.655472	−	0.755219i	$-0.272470\pi$
$443$	6.92820	+	4.00000i	0.329169	+	0.190046i	−0.326303	+	0.945265i	$0.605803\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	−0.440978	+	7.34680i	−0.0209043	+	0.348272i
$446$	−13.3229	−	23.0759i	−0.630856	−	1.09268i
$447$	−16.1477	−	9.32288i	−0.763760	−	0.440957i
$448$	2.29129	−	1.32288i	0.108253	−	0.0625000i
$449$	−13.1660			−0.621342			−0.310671	−	0.950517i	$-0.600554\pi$
$449$	−13.1660			−0.621342			−0.310671	+	0.950517i	$0.600554\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$	1.06275	+	1.84073i	0.0500428	+	0.0866766i
$452$	11.5108	+	6.64575i	0.541421	+	0.312590i
$453$	−10.1399	+	5.85425i	−0.476412	+	0.275057i
$454$	7.50000	−	12.9904i	0.351992	−	0.609669i
$455$	−1.87564	+	31.2487i	−0.0879316	+	1.46496i
$456$	2.64575	−	4.58258i	0.123899	−	0.214599i
$457$			17.1660i			0.802992i	0.915861	+	0.401496i	$0.131510\pi$
$457$			17.1660i			0.802992i	−0.915861	+	0.401496i	$0.868490\pi$
$458$	−14.8662	+	8.58301i	−0.694652	+	0.401057i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$	−20.7391	−	1.24483i	−0.966966	−	0.0580403i
$461$	−17.2288			−0.802423			−0.401212	−	0.915985i	$-0.631411\pi$
$461$	−17.2288			−0.802423			−0.401212	+	0.915985i	$0.631411\pi$
$462$	1.47960	−	0.854249i	0.0688373	−	0.0397432i
$463$			13.3542i			0.620625i	0.950635	+	0.310312i	$0.100434\pi$
$463$			13.3542i			0.620625i	−0.950635	+	0.310312i	$0.899566\pi$
$464$	−2.64575			−0.122826
$465$	−9.75145	+	7.74010i	−0.452213	+	0.358939i
$466$	−7.29150			−0.337772
$467$			26.7490i			1.23780i	0.785471	+	0.618898i	$0.212421\pi$
$467$			26.7490i			1.23780i	−0.785471	+	0.618898i	$0.787579\pi$
$468$	4.58258	−	2.64575i	0.211830	−	0.122300i
$469$	−29.8745			−1.37948
$470$	1.24483	−	20.7391i	0.0574195	−	0.956624i
$471$	−0.645751	−	1.11847i	−0.0297546	−	0.0515366i
$472$	0.559237	−	0.322876i	0.0257410	−	0.0148616i
$473$			7.29150i			0.335264i
$474$	7.29150	−	12.6293i	0.334910	−	0.580081i
$475$	10.3930	+	24.3307i	0.476866	+	1.11637i
$476$	−7.93725	+	13.7477i	−0.363803	+	0.630126i
$477$	−1.98450	+	1.14575i	−0.0908640	+	0.0524603i
$478$	−21.2895	−	12.2915i	−0.973759	−	0.562200i
$479$	5.70850	+	9.88741i	0.260828	+	0.451767i	0.966462	−	0.256809i	$-0.0826712\pi$
$479$	5.70850	+	9.88741i	0.260828	+	0.451767i	−0.705634	+	0.708576i	$0.749338\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$	−21.1660			−0.965087
$482$	−18.1865	+	10.5000i	−0.828374	+	0.478262i
$483$	21.2895	+	12.2915i	0.968706	+	0.559283i
$484$	−5.29150	−	9.16515i	−0.240523	−	0.416598i
$485$	−25.0632	−	1.50437i	−1.13806	−	0.0683098i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−14.9205	−	8.61438i	−0.676114	−	0.390355i	0.122275	−	0.992496i	$-0.460981\pi$
$487$	−14.9205	−	8.61438i	−0.676114	−	0.390355i	−0.798389	+	0.602142i	$0.794314\pi$
$488$			10.0000i			0.452679i
$489$	5.00000	+	8.66025i	0.226108	+	0.391630i
$490$		0			0
$491$	−14.9059	+	25.8177i	−0.672693	+	1.16514i	0.304445	+	0.952530i	$0.401529\pi$
$491$	−14.9059	+	25.8177i	−0.672693	+	1.16514i	−0.977137	+	0.212608i	$0.931804\pi$
$492$		−	3.29150i		−	0.148392i
$493$	13.7477	−	7.93725i	0.619166	−	0.357476i
$494$	28.0000			1.25978
$495$	1.29150	−	0.645751i	0.0580487	−	0.0290244i
$496$	1.14575	+	5.44860i	0.0514458	+	0.244649i
$497$		−	17.4170i		−	0.781259i
$498$		−	9.58301i		−	0.429425i
$499$	8.22876	+	14.2526i	0.368370	+	0.638035i	0.989311	−	0.145822i	$-0.0465827\pi$
$499$	8.22876	+	14.2526i	0.368370	+	0.638035i	−0.620941	+	0.783857i	$0.713249\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	10.9373	−	18.9439i	0.488640	−	0.846350i
$502$	−9.27383	+	5.35425i	−0.413911	+	0.238972i
$503$	−6.92820	+	4.00000i	−0.308913	+	0.178351i	−0.646440	−	0.762965i	$-0.723743\pi$
$503$	−6.92820	+	4.00000i	−0.308913	+	0.178351i	0.337527	+	0.941316i	$0.390410\pi$
$504$	−2.64575			−0.117851
$505$	−0.890362	+	14.8337i	−0.0396206	+	0.660089i
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$	12.9904	+	7.50000i	0.576923	+	0.333087i
$508$	11.4564	−	6.61438i	0.508297	−	0.293466i
$509$	1.32288	−	2.29129i	0.0586354	−	0.101560i	−0.835218	−	0.549920i	$-0.814658\pi$
$509$	1.32288	−	2.29129i	0.0586354	−	0.101560i	0.893853	+	0.448360i	$0.147992\pi$
$510$	−7.39230	+	11.1962i	−0.327337	+	0.495774i
$511$	17.4170			0.770482
$512$		−	1.00000i		−	0.0441942i
$513$	−4.58258	+	2.64575i	−0.202326	+	0.116813i
$514$	2.64575	−	4.58258i	0.116699	−	0.202129i
$515$	8.18790	−	12.4011i	0.360802	−	0.546460i
$516$	5.64575	−	9.77873i	0.248540	−	0.430485i
$517$	−5.19615	−	3.00000i	−0.228527	−	0.131940i
$518$	9.16515	+	5.29150i	0.402694	+	0.232495i
$519$	−6.29150			−0.276166
$520$	9.87408	+	6.51940i	0.433007	+	0.285895i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	2.29129	+	1.32288i	0.100287	+	0.0579007i
$523$			29.8745i			1.30632i	0.757219	+	0.653161i	$0.226557\pi$
$523$			29.8745i			1.30632i	−0.757219	+	0.653161i	$0.773443\pi$
$524$	1.35425	+	2.34563i	0.0591606	+	0.102469i
$525$	7.93725	−	10.5830i	0.346410	−	0.461880i
$526$	23.1660			1.01009
$527$	−22.2993	−	24.8745i	−0.971373	−	1.08355i
$528$		−	0.645751i		−	0.0281027i
$529$	−63.3320			−2.75357
$530$	−4.27600	−	2.82325i	−0.185738	−	0.122634i
$531$	−0.645751			−0.0280232
$532$	−12.1244	−	7.00000i	−0.525657	−	0.303488i
$533$	15.0836	−	8.70850i	0.653342	−	0.377207i
$534$	−1.64575	−	2.85052i	−0.0712186	−	0.123354i
$535$	−5.00000	−	10.0000i	−0.216169	−	0.432338i
$536$	−5.64575	+	9.77873i	−0.243859	+	0.422377i
$537$	−2.79619	−	1.61438i	−0.120664	−	0.0696656i
$538$	−6.92820	−	4.00000i	−0.298696	−	0.172452i
$539$		0			0
$540$	−2.23205	−	0.133975i	−0.0960522	−	0.00576535i
$541$	13.9373	+	24.1400i	0.599209	+	1.03786i	0.992938	+	0.118634i	$0.0378516\pi$
$541$	13.9373	+	24.1400i	0.599209	+	1.03786i	−0.393729	+	0.919227i	$0.628815\pi$
$542$			22.2915i			0.957502i
$543$		−	0.708497i		−	0.0304045i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	0.898768	−	14.9737i	0.0384990	−	0.641403i
$546$	−7.00000	−	12.1244i	−0.299572	−	0.518875i
$547$	−20.1710	−	11.6458i	−0.862451	−	0.497936i	0.00238124	−	0.999997i	$-0.499242\pi$
$547$	−20.1710	−	11.6458i	−0.862451	−	0.497936i	−0.864832	+	0.502061i	$0.832575\pi$
$548$	9.16515	+	5.29150i	0.391516	+	0.226042i
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$	2.58301	+	1.93725i	0.110140	+	0.0826048i
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$	8.04668	−	4.64575i	0.342489	−	0.197736i
$553$	−33.4139	−	19.2915i	−1.42090	−	0.820358i
$554$	2.00000			0.0849719
$555$	7.46410	+	4.92820i	0.316833	+	0.209191i
$556$	4.00000			0.169638
$557$		−	4.29150i		−	0.181837i	−0.995858	−	0.0909184i	$-0.971020\pi$
$557$		−	4.29150i		−	0.181837i	0.995858	−	0.0909184i	$-0.0289802\pi$
$558$	1.73205	−	5.29150i	0.0733236	−	0.224007i
$559$	59.7490			2.52711
$560$	−2.64575	−	5.29150i	−0.111803	−	0.223607i
$561$	1.93725	+	3.35542i	0.0817909	+	0.141666i
$562$		−	18.5830i		−	0.783877i
$563$	25.6196	+	14.7915i	1.07974	+	0.623388i	0.930826	−	0.365463i	$-0.119089\pi$
$563$	25.6196	+	14.7915i	1.07974	+	0.623388i	0.148913	+	0.988850i	$0.452423\pi$
$564$	4.64575	+	8.04668i	0.195621	+	0.338826i
$565$	16.3758	−	24.8023i	0.688935	−	1.04344i
$566$	−18.7085			−0.786377
$567$	2.29129	+	1.32288i	0.0962250	+	0.0555556i
$568$	−5.70105	−	3.29150i	−0.239211	−	0.138108i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−9.87408	−	6.51940i	−0.413580	−	0.273068i
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	−0.0554391	−	0.998462i	$-0.517656\pi$
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	0.892413	−	0.451219i	$-0.149011\pi$
$572$	2.95920	−	1.70850i	0.123731	−	0.0714359i
$573$			8.00000i			0.334205i
$574$	−8.70850			−0.363486
$575$	−5.55703	+	46.1240i	−0.231744	+	1.92350i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−30.9596	+	17.8745i	−1.28886	+	0.744125i	−0.978452	−	0.206477i	$-0.933800\pi$
$577$	−30.9596	+	17.8745i	−1.28886	+	0.744125i	−0.310412	+	0.950602i	$0.600467\pi$
$578$	−16.4545	−	9.50000i	−0.684416	−	0.395148i
$579$	−10.3229	+	17.8797i	−0.429004	+	0.743057i
$580$	−0.354463	+	5.90545i	−0.0147183	+	0.245211i
$581$	−25.3542			−1.05187
$582$	9.72439	−	5.61438i	0.403089	−	0.232723i
$583$	−1.28149	+	0.739870i	−0.0530740	+	0.0306423i
$584$	3.29150	−	5.70105i	0.136203	−	0.235911i
$585$	−5.29150	−	10.5830i	−0.218777	−	0.437553i
$586$	6.85425	+	11.8719i	0.283146	+	0.490424i
$587$		−	3.00000i		−	0.123823i	−0.998082	−	0.0619116i	$-0.980280\pi$
$587$		−	3.00000i		−	0.123823i	0.998082	−	0.0619116i	$-0.0197197\pi$
$588$		0			0
$589$	21.9373	−	19.6661i	0.903909	−	0.810329i
$590$	−0.645751	−	1.29150i	−0.0265852	−	0.0531703i
$591$	−23.1660			−0.952922
$592$	3.46410	−	2.00000i	0.142374	−	0.0821995i
$593$			24.4575i			1.00435i	0.864766	+	0.502175i	$0.167467\pi$
$593$			24.4575i			1.00435i	−0.864766	+	0.502175i	$0.832533\pi$
$594$	−0.322876	+	0.559237i	−0.0132477	+	0.0229458i
$595$	29.6222	+	19.5582i	1.21439	+	0.801808i
$596$	9.32288	+	16.1477i	0.381880	+	0.661435i
$597$		−	16.2915i		−	0.666767i
$598$	42.5790	+	24.5830i	1.74119	+	1.00527i
$599$	−1.64575	+	2.85052i	−0.0672436	+	0.116469i	−0.897687	−	0.440634i	$-0.854754\pi$
$599$	−1.64575	+	2.85052i	−0.0672436	+	0.116469i	0.830443	+	0.557103i	$0.188087\pi$
$600$	−1.96410	−	4.59808i	−0.0801841	−	0.187716i
$601$	3.58301	+	6.20595i	0.146154	+	0.253146i	0.929803	−	0.368058i	$-0.119977\pi$
$601$	3.58301	+	6.20595i	0.146154	+	0.253146i	−0.783649	+	0.621204i	$0.786644\pi$
$602$	−25.8721	−	14.9373i	−1.05447	−	0.608797i
$603$	9.77873	−	5.64575i	0.398221	−	0.229913i
$604$	11.7085			0.476412
$605$	−21.1660	+	10.5830i	−0.860521	+	0.430260i
$606$	−3.32288	−	5.75539i	−0.134983	−	0.233797i
$607$	32.2954	+	18.6458i	1.31083	+	0.756808i	0.982233	−	0.187663i	$-0.0600913\pi$
$607$	32.2954	+	18.6458i	1.31083	+	0.756808i	0.328596	+	0.944471i	$0.393425\pi$
$608$	−4.58258	+	2.64575i	−0.185848	+	0.107299i
$609$	3.50000	−	6.06218i	0.141827	−	0.245652i
$610$	22.3205	+	1.33975i	0.903731	+	0.0542447i
$611$	−24.5830	+	42.5790i	−0.994522	+	1.72256i
$612$		−	6.00000i		−	0.242536i
$613$	−14.4700	+	8.35425i	−0.584437	+	0.337425i	−0.762895	−	0.646523i	$-0.776223\pi$
$613$	−14.4700	+	8.35425i	−0.584437	+	0.337425i	0.178458	+	0.983948i	$0.442889\pi$
$614$	6.93725	+	12.0157i	0.279965	+	0.484913i
$615$	−7.34680	−	0.440978i	−0.296252	−	0.0177819i
$616$	−1.70850			−0.0688373
$617$	−21.2895	+	12.2915i	−0.857083	+	0.494837i	−0.863034	−	0.505145i	$-0.831439\pi$
$617$	−21.2895	+	12.2915i	−0.857083	+	0.494837i	0.00595119	+	0.999982i	$0.498106\pi$
$618$			6.64575i			0.267331i
$619$	14.5830			0.586140			0.293070	−	0.956091i	$-0.405323\pi$
$619$	14.5830			0.586140			0.293070	+	0.956091i	$0.405323\pi$
$620$	12.3151	−	1.82740i	0.494585	−	0.0733902i
$621$	−9.29150			−0.372855
$622$			11.8745i			0.476124i
$623$	−7.54178	+	4.35425i	−0.302155	+	0.174449i
$624$	−5.29150			−0.211830
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	6.96863	+	12.0700i	0.278522	+	0.482415i
$627$	−2.95920	+	1.70850i	−0.118179	+	0.0682308i
$628$			1.29150i			0.0515366i
$629$	−12.0000	+	20.7846i	−0.478471	+	0.828737i
$630$	−0.354463	+	5.90545i	−0.0141222	+	0.235279i
$631$	13.4373	−	23.2740i	0.534929	−	0.926524i	−0.464238	−	0.885710i	$-0.653672\pi$
$631$	13.4373	−	23.2740i	0.534929	−	0.926524i	0.999167	−	0.0408132i	$-0.0129948\pi$
$632$	−12.6293	+	7.29150i	−0.502365	+	0.290040i
$633$	14.3613	+	8.29150i	0.570811	+	0.329558i
$634$	8.14575	+	14.1089i	0.323509	+	0.560334i
$635$	−13.2288	−	26.4575i	−0.524967	−	1.04993i
$636$	2.29150			0.0908640
$637$		0			0
$638$	1.47960	+	0.854249i	0.0585780	+	0.0338200i
$639$	3.29150	+	5.70105i	0.130210	+	0.225530i
$640$	−2.23205	−	0.133975i	−0.0882296	−	0.00529581i
$641$	24.5203	−	42.4703i	0.968492	−	1.67748i	0.268567	−	0.963261i	$-0.413450\pi$
$641$	24.5203	−	42.4703i	0.968492	−	1.67748i	0.699925	−	0.714216i	$-0.253217\pi$
$642$	4.33013	+	2.50000i	0.170896	+	0.0986671i
$643$		−	23.8745i		−	0.941519i	−0.882262	−	0.470759i	$-0.843980\pi$
$643$		−	23.8745i		−	0.941519i	0.882262	−	0.470759i	$-0.156020\pi$
$644$	−12.2915	−	21.2895i	−0.484353	−	0.838924i
$645$	−21.0702	−	13.9117i	−0.829640	−	0.547773i
$646$	15.8745	−	27.4955i	0.624574	−	1.08179i
$647$		−	2.00000i		−	0.0786281i	−0.999227	−	0.0393141i	$-0.987483\pi$
$647$		−	2.00000i		−	0.0786281i	0.999227	−	0.0393141i	$-0.0125173\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−0.416995			−0.0163685
$650$	15.8745	−	21.1660i	0.622649	−	0.830199i
$651$	−14.0000	−	4.58258i	−0.548703	−	0.179605i
$652$		−	10.0000i		−	0.391630i
$653$			0.874508i			0.0342221i	0.999854	+	0.0171111i	$0.00544689\pi$
$653$			0.874508i			0.0342221i	−0.999854	+	0.0171111i	$0.994553\pi$
$654$	3.35425	+	5.80973i	0.131162	+	0.227178i
$655$	5.41699	−	2.70850i	0.211659	−	0.105830i
$656$	−1.64575	+	2.85052i	−0.0642558	+	0.111294i
$657$	−5.70105	+	3.29150i	−0.222419	+	0.128414i
$658$	21.2895	−	12.2915i	0.829951	−	0.479173i
$659$	−34.0627			−1.32690			−0.663448	−	0.748222i	$-0.730908\pi$
$659$	−34.0627			−1.32690			−0.663448	+	0.748222i	$0.730908\pi$
$660$	−1.44135	−	0.0865143i	−0.0561045	−	0.00336756i
$661$	3.22876	−	5.59237i	0.125584	−	0.217518i	−0.796377	−	0.604800i	$-0.793253\pi$
$661$	3.22876	−	5.59237i	0.125584	−	0.217518i	0.921961	+	0.387282i	$0.126586\pi$
$662$	16.5983	+	9.58301i	0.645109	+	0.372454i
$663$	27.4955	−	15.8745i	1.06783	−	0.616515i
$664$	−4.79150	+	8.29913i	−0.185946	+	0.322069i
$665$	−17.2487	+	26.1244i	−0.668876	+	1.01306i
$666$	−4.00000			−0.154997
$667$			24.5830i			0.951858i
$668$	−18.9439	+	10.9373i	−0.732961	+	0.423175i
$669$	13.3229	−	23.0759i	0.515092	−	0.892166i
$670$	21.0702	+	13.9117i	0.814014	+	0.537456i
$671$	3.22876	−	5.59237i	0.124645	−	0.215891i
$672$	2.29129	+	1.32288i	0.0883883	+	0.0510310i
$673$	6.47765	+	3.73987i	0.249695	+	0.144161i	0.619625	−	0.784898i	$-0.287285\pi$
$673$	6.47765	+	3.73987i	0.249695	+	0.144161i	−0.369930	+	0.929060i	$0.620618\pi$
$674$	−35.1033			−1.35213
$675$	−0.598076	+	4.96410i	−0.0230200	+	0.191068i
$676$	−7.50000	−	12.9904i	−0.288462	−	0.499630i
$677$	26.2332	+	15.1458i	1.00822	+	0.582099i	0.910671	−	0.413132i	$-0.135565\pi$
$677$	26.2332	+	15.1458i	1.00822	+	0.582099i	0.0975530	+	0.995230i	$0.468898\pi$
$678$			13.2915i			0.510457i
$679$	−14.8542	−	25.7283i	−0.570054	−	0.987362i
$680$	12.0000	−	6.00000i	0.460179	−	0.230089i
$681$	15.0000			0.574801
$682$	1.11847	−	3.41699i	0.0428286	−	0.130843i
$683$		−	22.1660i		−	0.848159i	−0.905625	−	0.424079i	$-0.860598\pi$
$683$		−	22.1660i		−	0.848159i	0.905625	−	0.424079i	$-0.139402\pi$
$684$	5.29150			0.202326
$685$	13.0388	−	19.7482i	0.498187	−	0.754538i
$686$	−18.5203			−0.707107
$687$	−14.8662	−	8.58301i	−0.567181	−	0.327462i
$688$	−9.77873	+	5.64575i	−0.372811	+	0.215242i
$689$	6.06275	+	10.5010i	0.230972	+	0.400056i
$690$	−9.29150	−	18.5830i	−0.353721	−	0.707443i
$691$	0.583005	−	1.00979i	0.0221786	−	0.0384144i	−0.854723	−	0.519084i	$-0.826273\pi$
$691$	0.583005	−	1.00979i	0.0221786	−	0.0384144i	0.876902	+	0.480670i	$0.159606\pi$
$692$	5.44860	+	3.14575i	0.207125	+	0.119584i
$693$	1.47960	+	0.854249i	0.0562054	+	0.0324502i
$694$	1.79150	+	3.10297i	0.0680045	+	0.117787i
$695$	0.535898	−	8.92820i	0.0203278	−	0.338666i
$696$	−1.32288	−	2.29129i	−0.0501435	−	0.0868510i
$697$		−	19.7490i		−	0.748047i
$698$		−	5.29150i		−	0.200286i
$699$	−3.64575	−	6.31463i	−0.137895	−	0.238841i
$700$	−12.1654	+	5.19652i	−0.459808	+	0.196410i
$701$	11.3856	+	19.7205i	0.430029	+	0.744832i	0.996875	−	0.0789915i	$-0.0251700\pi$
$701$	11.3856	+	19.7205i	0.430029	+	0.744832i	−0.566846	+	0.823824i	$0.691837\pi$
$702$	4.58258	+	2.64575i	0.172958	+	0.0998574i
$703$	−18.3303	−	10.5830i	−0.691340	−	0.399146i
$704$	−0.322876	+	0.559237i	−0.0121688	+	0.0210770i
$705$	18.5830	−	9.29150i	0.699876	−	0.349938i
$706$	−11.3542	−	19.6661i	−0.427323	−	0.740145i
$707$	−15.2273	+	8.79150i	−0.572683	+	0.330638i
$708$	0.559237	+	0.322876i	0.0210174	+	0.0121344i
$709$	−12.7085			−0.477278			−0.238639	−	0.971108i	$-0.576701\pi$
$709$	−12.7085			−0.477278			−0.238639	+	0.971108i	$0.576701\pi$
$710$	−8.11060	+	12.2841i	−0.304385	+	0.461012i
$711$	14.5830			0.546905
$712$			3.29150i			0.123354i
$713$	50.6257	−	10.6458i	1.89595	−	0.398687i
$714$	−15.8745			−0.594089
$715$	−3.41699	−	6.83399i	−0.127788	−	0.255577i
$716$	1.61438	+	2.79619i	0.0603321	+	0.104498i
$717$		−	24.5830i		−	0.918069i
$718$	−15.5885	−	9.00000i	−0.581756	−	0.335877i
$719$	3.29150	+	5.70105i	0.122752	+	0.212613i	0.920852	−	0.389912i	$-0.127495\pi$
$719$	3.29150	+	5.70105i	0.122752	+	0.212613i	−0.798100	+	0.602525i	$0.794161\pi$
$720$	1.86603	+	1.23205i	0.0695427	+	0.0459158i
$721$	17.5830			0.654825
$722$	7.79423	+	4.50000i	0.290071	+	0.167473i
$723$	−18.1865	−	10.5000i	−0.676364	−	0.390499i
$724$	−0.354249	+	0.613577i	−0.0131655	+	0.0228034i
$725$	13.1338	+	1.58236i	0.487776	+	0.0587674i
$726$	5.29150	−	9.16515i	0.196386	−	0.340151i
$727$	1.06413	−	0.614378i	0.0394666	−	0.0227860i	−0.480137	−	0.877194i	$-0.659413\pi$
$727$	1.06413	−	0.614378i	0.0394666	−	0.0227860i	0.519603	+	0.854408i	$0.326080\pi$
$728$			14.0000i			0.518875i
$729$	−1.00000			−0.0370370
$730$	−12.2841	−	8.11060i	−0.454653	−	0.300187i
$731$	33.8745	−	58.6724i	1.25289	−	2.17008i
$732$	−8.66025	+	5.00000i	−0.320092	+	0.184805i
$733$	−37.9964	−	21.9373i	−1.40343	−	0.810271i	−0.408688	−	0.912674i	$-0.634013\pi$
$733$	−37.9964	−	21.9373i	−1.40343	−	0.810271i	−0.994743	+	0.102403i	$0.967347\pi$
$734$	17.2288	−	29.8411i	0.635925	−	1.10145i
$735$		0			0
$736$	−9.29150			−0.342489
$737$	6.31463	−	3.64575i	0.232602	−	0.134293i
$738$	2.85052	−	1.64575i	0.104929	−	0.0605809i
$739$	−14.3542	+	24.8623i	−0.528030	+	0.914574i	0.471436	+	0.881900i	$0.343736\pi$
$739$	−14.3542	+	24.8623i	−0.528030	+	0.914574i	−0.999466	+	0.0326740i	$0.989598\pi$
$740$	−4.00000	−	8.00000i	−0.147043	−	0.294086i
$741$	14.0000	+	24.2487i	0.514303	+	0.890799i
$742$		−	6.06275i		−	0.222570i
$743$			2.58301i			0.0947613i	0.998877	+	0.0473806i	$0.0150874\pi$
$743$			2.58301i			0.0947613i	−0.998877	+	0.0473806i	$0.984913\pi$
$744$	−4.14575	+	3.71655i	−0.151991	+	0.136255i
$745$	37.2915	−	18.6458i	1.36625	−	0.683127i
$746$	−15.1660			−0.555267
$747$	8.29913	−	4.79150i	0.303649	−	0.175312i
$748$		−	3.87451i		−	0.141666i
$749$	6.61438	−	11.4564i	0.241684	−	0.418609i
$750$	−10.5263	+	3.76795i	−0.384365	+	0.137586i
$751$	−17.8542	−	30.9245i	−0.651511	−	1.12845i	−0.982756	−	0.184905i	$-0.940802\pi$
$751$	−17.8542	−	30.9245i	−0.651511	−	1.12845i	0.331246	−	0.943545i	$-0.392531\pi$
$752$		−	9.29150i		−	0.338826i
$753$	−9.27383	−	5.35425i	−0.337957	−	0.195120i
$754$	7.00000	−	12.1244i	0.254925	−	0.441543i
$755$	1.56864	−	26.1340i	0.0570887	−	0.951112i
$756$	−1.32288	−	2.29129i	−0.0481125	−	0.0833333i
$757$	5.30483	+	3.06275i	0.192807	+	0.111317i	0.593296	−	0.804984i	$-0.297826\pi$
$757$	5.30483	+	3.06275i	0.192807	+	0.111317i	−0.400489	+	0.916302i	$0.631160\pi$
$758$	−4.07768	+	2.35425i	−0.148108	+	0.0855102i
$759$	−6.00000			−0.217786
$760$	5.29150	+	10.5830i	0.191943	+	0.383886i
$761$	−12.0000	−	20.7846i	−0.435000	−	0.753442i	0.562296	−	0.826936i	$-0.309918\pi$
$761$	−12.0000	−	20.7846i	−0.435000	−	0.753442i	−0.997296	+	0.0734946i	$0.976585\pi$
$762$	11.4564	+	6.61438i	0.415023	+	0.239614i
$763$	15.3711	−	8.87451i	0.556471	−	0.321279i
$764$	4.00000	−	6.92820i	0.144715	−	0.250654i
$765$	−13.3923	−	0.803848i	−0.484200	−	0.0290632i
$766$	8.22876	−	14.2526i	0.297317	−	0.514968i
$767$			3.41699i			0.123381i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	3.20850	+	5.55728i	0.115701	+	0.200401i	0.918060	−	0.396442i	$-0.129755\pi$
$769$	3.20850	+	5.55728i	0.115701	+	0.200401i	−0.802359	+	0.596842i	$0.796422\pi$
$770$	−0.228895	+	3.81345i	−0.00824881	+	0.137427i
$771$	5.29150			0.190569
$772$	17.8797	−	10.3229i	0.643506	−	0.371528i
$773$		−	4.83399i		−	0.173867i	−0.996214	−	0.0869333i	$-0.972293\pi$
$773$		−	4.83399i		−	0.173867i	0.996214	−	0.0869333i	$-0.0277067\pi$
$774$	11.2915			0.405865
$775$	−2.42895	−	27.7327i	−0.0872504	−	0.996186i
$776$	−11.2288			−0.403089
$777$			10.5830i			0.379663i
$778$	−13.8564	+	8.00000i	−0.496776	+	0.286814i
$779$	17.4170			0.624029
$780$	−0.708927	+	11.8109i	−0.0253837	+	0.422898i
$781$	2.12549	+	3.68146i	0.0760561	+	0.131733i
$782$	48.2801	−	27.8745i	1.72649	−	0.996790i
$783$			2.64575i			0.0945514i
$784$		0			0
$785$	2.88270	+	0.173029i	0.102888	+	0.00617565i
$786$	−1.35425	+	2.34563i	−0.0483045	+	0.0836658i
$787$	−21.9031	+	12.6458i	−0.780761	+	0.450772i	−0.836700	−	0.547662i	$-0.815518\pi$
$787$	−21.9031	+	12.6458i	−0.780761	+	0.450772i	0.0559392	+	0.998434i	$0.482185\pi$
$788$	20.0624	+	11.5830i	0.714692	+	0.412627i
$789$	11.5830	+	20.0624i	0.412366	+	0.714239i
$790$	14.5830	+	29.1660i	0.518840	+	1.03768i
$791$	35.1660			1.25036
$792$	0.559237	−	0.322876i	0.0198716	−	0.0114729i
$793$	−45.8258	−	26.4575i	−1.62732	−	0.939534i
$794$	−18.5830	−	32.1867i	−0.659486	−	1.14226i
$795$	0.307003	−	5.11475i	0.0108883	−	0.181401i
$796$	−8.14575	+	14.1089i	−0.288719	+	0.500075i
$797$	45.7907	+	26.4373i	1.62199	+	0.936456i	0.986387	+	0.164438i	$0.0525811\pi$
$797$	45.7907	+	26.4373i	1.62199	+	0.936456i	0.635601	+	0.772018i	$0.280752\pi$
$798$		−	14.0000i		−	0.495595i
$799$	27.8745	+	48.2801i	0.986129	+	1.70803i
$800$	−0.598076	+	4.96410i	−0.0211452	+	0.175507i
$801$	1.64575	−	2.85052i	0.0581498	−	0.100718i
$802$			22.0000i			0.776847i
$803$	−3.68146	+	2.12549i	−0.129916	+	0.0750070i
$804$	−11.2915			−0.398221
$805$	−49.1660	+	24.5830i	−1.73287	+	0.866437i
$806$	−28.0000	−	9.16515i	−0.986258	−	0.322829i
$807$		−	8.00000i		−	0.281613i
$808$			6.64575i			0.233797i
$809$	−22.2915	−	38.6100i	−0.783727	−	1.35746i	−0.929756	−	0.368176i	$-0.879983\pi$
$809$	−22.2915	−	38.6100i	−0.783727	−	1.35746i	0.146029	−	0.989280i	$-0.453351\pi$
$810$	−1.00000	−	2.00000i	−0.0351364	−	0.0702728i
$811$	2.64575	−	4.58258i	0.0929049	−	0.160916i	−0.815827	−	0.578295i	$-0.803718\pi$
$811$	2.64575	−	4.58258i	0.0929049	−	0.160916i	0.908732	+	0.417379i	$0.137051\pi$
$812$	−6.06218	+	3.50000i	−0.212741	+	0.122826i
$813$	−19.3050	+	11.1458i	−0.677056	+	0.390899i
$814$	−2.58301			−0.0905343
$815$	−22.3205	−	1.33975i	−0.781853	−	0.0469293i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	51.7442	+	29.8745i	1.81030	+	1.04518i
$818$	9.02138	−	5.20850i	0.315425	−	0.182111i
$819$	7.00000	−	12.1244i	0.244600	−	0.423659i
$820$	6.14203	+	4.05530i	0.214489	+	0.141617i
$821$	49.1033			1.71372			0.856858	−	0.515553i	$-0.172413\pi$
$821$	49.1033			1.71372			0.856858	+	0.515553i	$0.172413\pi$
$822$			10.5830i			0.369125i
$823$	15.0292	−	8.67712i	0.523886	−	0.302466i	−0.214637	−	0.976694i	$-0.568857\pi$
$823$	15.0292	−	8.67712i	0.523886	−	0.302466i	0.738523	+	0.674228i	$0.235524\pi$
$824$	3.32288	−	5.75539i	0.115758	−	0.200498i
$825$	−0.386208	+	3.20558i	−0.0134461	+	0.111604i
$826$	0.854249	−	1.47960i	0.0297231	−	0.0514819i
$827$	11.6195	+	6.70850i	0.404048	+	0.233277i	0.688229	−	0.725493i	$-0.258388\pi$
$827$	11.6195	+	6.70850i	0.404048	+	0.233277i	−0.284181	+	0.958771i	$0.591722\pi$
$828$	8.04668	+	4.64575i	0.279641	+	0.161451i
$829$	17.7490			0.616449			0.308224	−	0.951314i	$-0.400265\pi$
$829$	17.7490			0.616449			0.308224	+	0.951314i	$0.400265\pi$
$830$	17.8821	+	11.8067i	0.620698	+	0.409818i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$	4.58258	+	2.64575i	0.158872	+	0.0917249i
$833$		0			0
$834$	2.00000	+	3.46410i	0.0692543	+	0.119952i
$835$	21.8745	+	43.7490i	0.756999	+	1.51400i
$836$	3.41699			0.118179
$837$	5.44860	−	1.14575i	0.188331	−	0.0396030i
$838$		−	13.9373i		−	0.481454i
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$	3.25970	−	4.93704i	0.112470	−	0.170344i
$841$	−22.0000			−0.758621
$842$	27.6041	+	15.9373i	0.951301	+	0.549234i
$843$	16.0934	−	9.29150i	0.554285	−	0.320016i
$844$	−8.29150	−	14.3613i	−0.285405	−	0.494336i
$845$	−30.0000	+	15.0000i	−1.03203	+	0.516016i
$846$	−4.64575	+	8.04668i	−0.159724	+	0.276650i
$847$	−24.2487	−	14.0000i	−0.833196	−	0.481046i
$848$	−1.98450	−	1.14575i	−0.0681480	−	0.0393453i
$849$	−9.35425	−	16.2020i	−0.321037	−	0.556052i
$850$	−11.7846	−	27.5885i	−0.404209	−	0.946276i
$851$	−18.5830	−	32.1867i	−0.637017	−	1.10335i
$852$		−	6.58301i		−	0.225530i
$853$			40.4575i			1.38524i	0.721303	+	0.692619i	$0.243543\pi$
$853$			40.4575i			1.38524i	−0.721303	+	0.692619i	$0.756457\pi$
$854$	13.2288	+	22.9129i	0.452679	+	0.784063i
$855$	0.708927	−	11.8109i	0.0242448	−	0.403924i
$856$	−2.50000	−	4.33013i	−0.0854482	−	0.148001i
$857$	−19.1612	−	11.0627i	−0.654535	−	0.377896i	0.135656	−	0.990756i	$-0.456686\pi$
$857$	−19.1612	−	11.0627i	−0.654535	−	0.377896i	−0.790192	+	0.612860i	$0.790019\pi$
$858$	2.95920	+	1.70850i	0.101026	+	0.0583271i
$859$	4.35425	−	7.54178i	0.148565	−	0.257322i	−0.782132	−	0.623112i	$-0.785868\pi$
$859$	4.35425	−	7.54178i	0.148565	−	0.257322i	0.930697	+	0.365790i	$0.119201\pi$
$860$	11.2915	+	22.5830i	0.385037	+	0.770074i
$861$	−4.35425	−	7.54178i	−0.148392	−	0.257023i
$862$	−33.8101	+	19.5203i	−1.15158	+	0.664863i
$863$	−24.0314	−	13.8745i	−0.818037	−	0.472294i	0.0317022	−	0.999497i	$-0.489907\pi$
$863$	−24.0314	−	13.8745i	−0.818037	−	0.472294i	−0.849739	+	0.527204i	$0.823241\pi$
$864$	−1.00000			−0.0340207
$865$	7.75145	−	11.7401i	0.263557	−	0.399176i
$866$	−9.16601			−0.311474
$867$		−	19.0000i		−	0.645274i
$868$	9.83307	+	10.9686i	0.333756	+	0.372299i
$869$	9.41699			0.319450
$870$	−5.29150	+	2.64575i	−0.179399	+	0.0896994i
$871$	−29.8745	−	51.7442i	−1.01226	−	1.75328i
$872$		−	6.70850i		−	0.227178i
$873$	9.72439	+	5.61438i	0.329121	+	0.190018i
$874$	24.5830	+	42.5790i	0.831533	+	1.44026i
$875$	9.96906	+	27.8499i	0.337016	+	0.941499i
$876$	6.58301			0.222419
$877$	−13.7477	−	7.93725i	−0.464228	−	0.268022i	0.249593	−	0.968351i	$-0.419703\pi$
$877$	−13.7477	−	7.93725i	−0.464228	−	0.268022i	−0.713820	+	0.700329i	$0.753037\pi$
$878$	4.22145	+	2.43725i	0.142467	+	0.0822533i
$879$	−6.85425	+	11.8719i	−0.231188	+	0.400429i
$880$	1.20499	+	0.795598i	0.0406201	+	0.0268196i
$881$	12.0000	−	20.7846i	0.404290	−	0.700251i	−0.589948	−	0.807441i	$-0.700852\pi$
$881$	12.0000	−	20.7846i	0.404290	−	0.700251i	0.994239	+	0.107190i	$0.0341852\pi$
$882$		0			0
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	−31.7490			−1.06783
$885$	0.795598	−	1.20499i	0.0267437	−	0.0405052i
$886$	4.00000	−	6.92820i	0.134383	−	0.232758i
$887$	−29.7324	+	17.1660i	−0.998316	+	0.576378i	−0.907750	−	0.419512i	$-0.862201\pi$
$887$	−29.7324	+	17.1660i	−0.998316	+	0.576378i	−0.0905667	+	0.995890i	$0.528868\pi$
$888$	3.46410	+	2.00000i	0.116248	+	0.0671156i
$889$	17.5000	−	30.3109i	0.586931	−	1.01659i
$890$	7.34680	+	0.440978i	0.246265	+	0.0147816i
$891$	−0.645751			−0.0216335
$892$	−23.0759	+	13.3229i	−0.772638	+	0.446083i
$893$	−42.5790	+	24.5830i	−1.42485	+	0.822639i
$894$	−9.32288	+	16.1477i	−0.311804	+	0.540060i
$895$	6.45751	−	3.22876i	0.215851	−	0.107925i
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$			49.1660i			1.64161i
$898$			13.1660i			0.439355i
$899$	−3.03137	−	14.4156i	−0.101102	−	0.480789i
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	13.7490			0.458046
$902$	1.84073	−	1.06275i	0.0612896	−	0.0353856i
$903$		−	29.8745i		−	0.994161i
$904$	6.64575	−	11.5108i	0.221034	−	0.382843i
$905$	1.32207	+	0.872905i	0.0439472	+	0.0290163i
$906$	5.85425	+	10.1399i	0.194494	+	0.336874i
$907$		−	15.4170i		−	0.511913i	−0.966688	−	0.255956i	$-0.917610\pi$
$907$		−	15.4170i		−	0.511913i	0.966688	−	0.255956i	$-0.0823904\pi$
$908$	−12.9904	−	7.50000i	−0.431101	−	0.248896i
$909$	3.32288	−	5.75539i	0.110213	−	0.190894i
$910$	31.2487	+	1.87564i	1.03588	+	0.0621770i
$911$	−19.6458	−	34.0274i	−0.650893	−	1.12738i	−0.982907	−	0.184105i	$-0.941061\pi$
$911$	−19.6458	−	34.0274i	−0.650893	−	1.12738i	0.332014	−	0.943275i	$-0.392272\pi$
$912$	−4.58258	−	2.64575i	−0.151744	−	0.0876096i
$913$	5.35917	−	3.09412i	0.177363	−	0.102400i
$914$	17.1660			0.567801
$915$	10.0000	+	20.0000i	0.330590	+	0.661180i
$916$	8.58301	+	14.8662i	0.283590	+	0.491193i
$917$	6.20595	+	3.58301i	0.204938	+	0.118321i
$918$	5.19615	−	3.00000i	0.171499	−	0.0990148i
$919$	8.72876	−	15.1186i	0.287935	−	0.498718i	−0.685382	−	0.728184i	$-0.740365\pi$
$919$	8.72876	−	15.1186i	0.287935	−	0.498718i	0.973317	+	0.229466i	$0.0736979\pi$
$920$	−1.24483	+	20.7391i	−0.0410407	+	0.683748i
$921$	−6.93725	+	12.0157i	−0.228590	+	0.395930i
$922$			17.2288i			0.567399i
$923$	30.1671	−	17.4170i	0.992963	−	0.573287i
$924$	−0.854249	−	1.47960i	−0.0281027	−	0.0486753i
$925$	−18.3923	+	7.85641i	−0.604735	+	0.258317i
$926$	13.3542			0.438848
$927$	−5.75539	+	3.32288i	−0.189032	+	0.109138i
$928$			2.64575i			0.0868510i
$929$	17.2915			0.567316			0.283658	−	0.958926i	$-0.408452\pi$
$929$	17.2915			0.567316			0.283658	+	0.958926i	$0.408452\pi$
$930$	7.74010	+	9.75145i	0.253808	+	0.319763i
$931$		0			0
$932$			7.29150i			0.238841i
$933$	−10.2836	+	5.93725i	−0.336671	+	0.194377i
$934$	26.7490			0.875255
$935$	−8.64810	−	0.519086i	−0.282823	−	0.0169759i
$936$	−2.64575	−	4.58258i	−0.0864791	−	0.149786i
$937$	5.70105	−	3.29150i	0.186245	−	0.107529i	−0.403978	−	0.914769i	$-0.632373\pi$
$937$	5.70105	−	3.29150i	0.186245	−	0.107529i	0.590224	+	0.807240i	$0.299040\pi$
$938$			29.8745i			0.975437i
$939$	−6.96863	+	12.0700i	−0.227413	+	0.393890i
$940$	−20.7391	−	1.24483i	−0.676435	−	0.0406017i
$941$	16.5516	−	28.6683i	0.539568	−	0.934559i	−0.459359	−	0.888250i	$-0.651921\pi$
$941$	16.5516	−	28.6683i	0.539568	−	0.934559i	0.998927	−	0.0463083i	$-0.0147457\pi$
$942$	−1.11847	+	0.645751i	−0.0364419	+	0.0210397i
$943$	26.4857	+	15.2915i	0.862492	+	0.497960i
$944$	−0.322876	−	0.559237i	−0.0105087	−	0.0182016i
$945$	−5.29150	+	2.64575i	−0.172133	+	0.0860663i
$946$	7.29150			0.237067
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	−0.442659	−	0.896690i	$-0.645965\pi$
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	0.555227	+	0.831699i	$0.312631\pi$
$948$	−12.6293	−	7.29150i	−0.410179	−	0.236817i
$949$	17.4170	+	30.1671i	0.565380	+	0.979266i
$950$	24.3307	−	10.3930i	0.789393	−	0.337195i
$951$	−8.14575	+	14.1089i	−0.264144	+	0.457511i
$952$	13.7477	+	7.93725i	0.445566	+	0.257248i
$953$			7.41699i			0.240260i	0.992758	+	0.120130i	$0.0383311\pi$
$953$			7.41699i			0.240260i	−0.992758	+	0.120130i	$0.961669\pi$
$954$	1.14575	+	1.98450i	0.0370951	+	0.0642505i
$955$	−14.9282	−	9.85641i	−0.483065	−	0.318946i
$956$	−12.2915	+	21.2895i	−0.397536	+	0.688552i
$957$			1.70850i			0.0552279i
$958$	9.88741	−	5.70850i	0.319448	−	0.184433i
$959$	28.0000			0.904167
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	−28.3745	+	12.4855i	−0.915307	+	0.402758i
$962$			21.1660i			0.682420i
$963$			5.00000i			0.161123i
$964$	10.5000	+	18.1865i	0.338182	+	0.585749i
$965$	−20.6458	−	41.2915i	−0.664610	−	1.32922i
$966$	12.2915	−	21.2895i	0.395473	−	0.684979i
$967$	−22.9129	+	13.2288i	−0.736828	+	0.425408i	−0.820915	−	0.571050i	$-0.806536\pi$
$967$	−22.9129	+	13.2288i	−0.736828	+	0.425408i	0.0840866	+	0.996458i	$0.473203\pi$
$968$	−9.16515	+	5.29150i	−0.294579	+	0.170075i
$969$	31.7490			1.01993
$970$	−1.50437	+	25.0632i	−0.0483023	+	0.804729i
$971$	3.55163	−	6.15161i	0.113977	−	0.197414i	−0.803393	−	0.595449i	$-0.796974\pi$
$971$	3.55163	−	6.15161i	0.113977	−	0.197414i	0.917370	+	0.398034i	$0.130308\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	9.16515	−	5.29150i	0.293821	−	0.169638i
$974$	−8.61438	+	14.9205i	−0.276022	+	0.478085i
$975$	26.2676	+	3.16472i	0.841235	+	0.101352i
$976$	10.0000			0.320092
$977$		−	9.41699i		−	0.301276i	−0.988589	−	0.150638i	$-0.951867\pi$
$977$		−	9.41699i		−	0.301276i	0.988589	−	0.150638i	$-0.0481328\pi$
$978$	8.66025	−	5.00000i	0.276924	−	0.159882i
$979$	1.06275	−	1.84073i	0.0339655	−	0.0588300i
$980$		0			0
$981$	−3.35425	+	5.80973i	−0.107093	+	0.185490i
$982$	25.8177	+	14.9059i	0.823877	+	0.475666i
$983$	16.7069	+	9.64575i	0.532868	+	0.307652i	0.742184	−	0.670197i	$-0.233790\pi$
$983$	16.7069	+	9.64575i	0.532868	+	0.307652i	−0.209315	+	0.977848i	$0.567124\pi$
$984$	−3.29150			−0.104929
$985$	28.5417	−	43.2284i	0.909414	−	1.37737i
$986$	−7.93725	−	13.7477i	−0.252774	−	0.437817i
$987$	21.2895	+	12.2915i	0.677652	+	0.391243i
$988$		−	28.0000i		−	0.890799i
$989$	52.4575	+	90.8591i	1.66805	+	2.88915i
$990$	−0.645751	−	1.29150i	−0.0205233	−	0.0410466i
$991$	18.5830			0.590309			0.295154	−	0.955450i	$-0.404629\pi$
$991$	18.5830			0.590309			0.295154	+	0.955450i	$0.404629\pi$
$992$	5.44860	−	1.14575i	0.172993	−	0.0363776i
$993$			19.1660i			0.608215i
$994$	−17.4170			−0.552434
$995$	30.4004	+	20.0720i	0.963756	+	0.636324i
$996$	−9.58301			−0.303649
$997$	29.3362	+	16.9373i	0.929086	+	0.536408i	0.886522	−	0.462686i	$-0.153114\pi$
$997$	29.3362	+	16.9373i	0.929086	+	0.536408i	0.0425638	+	0.999094i	$0.486447\pi$
$998$	14.2526	−	8.22876i	0.451159	−	0.260477i
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.b.769.1	yes	8
5.4	even	2	inner	930.2.s.b.769.4	yes	8
31.5	even	3	inner	930.2.s.b.439.2	✓	8
155.129	even	6	inner	930.2.s.b.439.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.b.439.2	✓	8	31.5	even	3	inner
930.2.s.b.439.3	yes	8	155.129	even	6	inner
930.2.s.b.769.1	yes	8	1.1	even	1	trivial
930.2.s.b.769.4	yes	8	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-0.133975 + 2.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.23205 + 0.133975i) q^{10} +(0.322876 - 0.559237i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-4.58258 - 2.64575i) q^{13} +(1.32288 + 2.29129i) q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +(-5.19615 + 3.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-2.64575 - 4.58258i) q^{19} +(0.133975 - 2.23205i) q^{20} +(-1.32288 + 2.29129i) q^{21} +(-0.559237 - 0.322876i) q^{22} -9.29150i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(-2.64575 + 4.58258i) q^{26} -1.00000i q^{27} +(2.29129 - 1.32288i) q^{28} -2.64575 q^{29} +(2.00000 - 1.00000i) q^{30} +(1.14575 + 5.44860i) q^{31} -1.00000i q^{32} -0.645751i q^{33} +(3.00000 + 5.19615i) q^{34} +(-2.64575 - 5.29150i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.46410 - 2.00000i) q^{37} +(-4.58258 + 2.64575i) q^{38} -5.29150 q^{39} +(-2.23205 - 0.133975i) q^{40} +(-1.64575 + 2.85052i) q^{41} +(2.29129 + 1.32288i) q^{42} +(-9.77873 + 5.64575i) q^{43} +(-0.322876 + 0.559237i) q^{44} +(1.86603 + 1.23205i) q^{45} -9.29150 q^{46} -9.29150i q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.598076 + 4.96410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.58258 + 2.64575i) q^{52} +(-1.98450 - 1.14575i) q^{53} -1.00000 q^{54} +(1.20499 + 0.795598i) q^{55} +(-1.32288 - 2.29129i) q^{56} +(-4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(-0.322876 - 0.559237i) q^{59} +(-1.00000 - 2.00000i) q^{60} +10.0000 q^{61} +(5.44860 - 1.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(6.51940 - 9.87408i) q^{65} -0.645751 q^{66} +(9.77873 + 5.64575i) q^{67} +(5.19615 - 3.00000i) q^{68} +(-4.64575 - 8.04668i) q^{69} +(-5.29150 + 2.64575i) q^{70} +(-3.29150 + 5.70105i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-5.70105 - 3.29150i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.59808 + 1.96410i) q^{75} +(2.64575 + 4.58258i) q^{76} +1.70850i q^{77} +5.29150i q^{78} +(7.29150 + 12.6293i) q^{79} +(-0.133975 + 2.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.85052 + 1.64575i) q^{82} +(8.29913 + 4.79150i) q^{83} +(1.32288 - 2.29129i) q^{84} +(-6.00000 - 12.0000i) q^{85} +(5.64575 + 9.77873i) q^{86} +(-2.29129 + 1.32288i) q^{87} +(0.559237 + 0.322876i) q^{88} +3.29150 q^{89} +(1.23205 - 1.86603i) q^{90} +14.0000 q^{91} +9.29150i q^{92} +(3.71655 + 4.14575i) q^{93} -9.29150 q^{94} +(10.5830 - 5.29150i) q^{95} +(-0.500000 - 0.866025i) q^{96} +11.2288i q^{97} +(-0.322876 - 0.559237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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