LMFDB - Embedded newform 784.2.x.k.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$-1.40526 + 0.158880i$ of defining polynomial
Character	$\chi$	$=$	784.557
Dual form			784.2.x.k.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27404 - 0.613848i) q^{2} +(2.68432 - 0.719263i) q^{3} +(1.24638 + 1.56414i) q^{4} +(0.857592 + 0.229791i) q^{5} +(-3.86147 - 0.731395i) q^{6} +(-0.627801 - 2.75787i) q^{8} +(4.09018 - 2.36147i) q^{9} +O(q^{10})$	\(q+(-1.27404 - 0.613848i) q^{2} +(2.68432 - 0.719263i) q^{3} +(1.24638 + 1.56414i) q^{4} +(0.857592 + 0.229791i) q^{5} +(-3.86147 - 0.731395i) q^{6} +(-0.627801 - 2.75787i) q^{8} +(4.09018 - 2.36147i) q^{9} +(-0.951553 - 0.819195i) q^{10} +(1.36269 + 5.08562i) q^{11} +(4.47072 + 3.30218i) q^{12} +(2.22066 + 2.22066i) q^{13} +2.46733 q^{15} +(-0.893069 + 3.89903i) q^{16} +(-1.62780 + 2.81943i) q^{17} +(-6.66066 + 0.497865i) q^{18} +(-0.671653 + 2.50664i) q^{19} +(0.709460 + 1.62780i) q^{20} +(1.38567 - 7.31580i) q^{22} +(6.62774 - 3.82653i) q^{23} +(-3.66886 - 6.95147i) q^{24} +(-3.64747 - 2.10587i) q^{25} +(-1.46607 - 4.19237i) q^{26} +(3.38567 - 3.38567i) q^{27} +(-1.53721 - 1.53721i) q^{29} +(-3.14349 - 1.51457i) q^{30} +(1.22066 - 2.11425i) q^{31} +(3.53122 - 4.41933i) q^{32} +(7.31580 + 12.6713i) q^{33} +(3.80460 - 2.59286i) q^{34} +(8.79159 + 3.45433i) q^{36} +(1.72139 + 0.461245i) q^{37} +(2.39441 - 2.78128i) q^{38} +(7.55822 + 4.36374i) q^{39} +(0.0953379 - 2.50939i) q^{40} -7.77589i q^{41} +(-7.51575 + 7.51575i) q^{43} +(-6.25620 + 8.47006i) q^{44} +(4.05035 - 1.08529i) q^{45} +(-10.7930 + 0.806742i) q^{46} +(-5.55792 - 9.62661i) q^{47} +(0.407138 + 11.1086i) q^{48} +(3.35436 + 4.92196i) q^{50} +(-2.34163 + 8.73909i) q^{51} +(-0.705636 + 6.24122i) q^{52} +(1.07250 + 4.00262i) q^{53} +(-6.39179 + 2.23521i) q^{54} +4.67452i q^{55} +7.21173i q^{57} +(1.01486 + 2.90209i) q^{58} +(-2.50344 - 9.34298i) q^{59} +(3.07524 + 3.85926i) q^{60} +(1.23431 - 4.60651i) q^{61} +(-2.85301 + 1.94435i) q^{62} +(-7.21173 + 3.46279i) q^{64} +(1.39413 + 2.41471i) q^{65} +(-1.54238 - 20.6346i) q^{66} +(-1.26436 + 0.338785i) q^{67} +(-6.43885 + 0.967979i) q^{68} +(15.0387 - 15.0387i) q^{69} -12.1113i q^{71} +(-9.08045 - 9.79767i) q^{72} +(5.55501 + 3.20719i) q^{73} +(-1.91000 - 1.64432i) q^{74} +(-11.3057 - 3.02934i) q^{75} +(-4.75787 + 2.07367i) q^{76} +(-6.95084 - 10.1992i) q^{78} +(3.64128 + 6.30687i) q^{79} +(-1.66185 + 3.13856i) q^{80} +(-0.431344 + 0.747110i) q^{81} +(-4.77322 + 9.90684i) q^{82} +(-1.96506 - 1.96506i) q^{83} +(-2.04387 + 2.04387i) q^{85} +(14.1889 - 4.96187i) q^{86} +(-5.23203 - 3.02071i) q^{87} +(13.1700 - 6.95088i) q^{88} +(0.576282 - 0.332717i) q^{89} +(-5.82653 - 1.10359i) q^{90} +(14.2459 + 5.59741i) q^{92} +(1.75595 - 6.55331i) q^{93} +(1.17177 + 15.6765i) q^{94} +(-1.15201 + 1.99533i) q^{95} +(6.30029 - 14.4028i) q^{96} -8.34450 q^{97} +(17.5832 + 17.5832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8	$ 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30} - 16 q^{31} + 28 q^{32} + 24 q^{33} - 24 q^{34} + 48 q^{36} - 16 q^{37} + 16 q^{38} - 28 q^{40} - 64 q^{43} + 32 q^{44} + 8 q^{45} - 20 q^{46} - 24 q^{47} + 40 q^{48} - 28 q^{50} - 8 q^{51} - 32 q^{52} + 8 q^{53} + 16 q^{54} - 12 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} + 40 q^{62} - 64 q^{64} + 48 q^{65} + 16 q^{66} - 28 q^{68} + 88 q^{69} - 44 q^{72} + 4 q^{74} - 28 q^{75} - 48 q^{76} + 24 q^{78} + 24 q^{79} + 12 q^{80} - 40 q^{81} - 4 q^{82} - 80 q^{85} + 40 q^{88} - 32 q^{90} + 72 q^{92} - 16 q^{93} - 28 q^{94} - 16 q^{95} - 8 q^{96} - 64 q^{97} + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.27404	−	0.613848i	−0.900886	−	0.434056i
$2$	−1.27404	−	0.613848i	−0.900886	−	0.434056i
$3$	2.68432	−	0.719263i	1.54980	−	0.415266i	0.620380	−	0.784301i	$-0.286978\pi$
$3$	2.68432	−	0.719263i	1.54980	−	0.415266i	0.929415	+	0.369035i	$0.120312\pi$
$4$	1.24638	+	1.56414i	0.623190	+	0.782070i
$5$	0.857592	+	0.229791i	0.383527	+	0.102766i	0.445431	−	0.895316i	$-0.353051\pi$
$5$	0.857592	+	0.229791i	0.383527	+	0.102766i	−0.0619040	+	0.998082i	$0.519717\pi$
$6$	−3.86147	−	0.731395i	−1.57644	−	0.298591i
$7$		0			0
$7$		0			0
$8$	−0.627801	−	2.75787i	−0.221961	−	0.975056i
$9$	4.09018	−	2.36147i	1.36339	−	0.787156i
$10$	−0.951553	−	0.819195i	−0.300908	−	0.259052i
$11$	1.36269	+	5.08562i	0.410866	+	1.53337i	0.792974	+	0.609256i	$0.208532\pi$
$11$	1.36269	+	5.08562i	0.410866	+	1.53337i	−0.382108	+	0.924118i	$0.624802\pi$
$12$	4.47072	+	3.30218i	1.29059	+	0.953259i
$13$	2.22066	+	2.22066i	0.615901	+	0.615901i	0.944477	−	0.328576i	$-0.106569\pi$
$13$	2.22066	+	2.22066i	0.615901	+	0.615901i	−0.328576	+	0.944477i	$0.606569\pi$
$14$		0			0
$15$	2.46733			0.637063
$16$	−0.893069	+	3.89903i	−0.223267	+	0.974757i
$17$	−1.62780	+	2.81943i	−0.394800	+	0.683813i	−0.993076	−	0.117477i	$-0.962519\pi$
$17$	−1.62780	+	2.81943i	−0.394800	+	0.683813i	0.598276	+	0.801290i	$0.295853\pi$
$18$	−6.66066	+	0.497865i	−1.56993	+	0.117348i
$19$	−0.671653	+	2.50664i	−0.154088	+	0.575063i	0.845094	+	0.534618i	$0.179544\pi$
$19$	−0.671653	+	2.50664i	−0.154088	+	0.575063i	−0.999182	+	0.0404454i	$0.987122\pi$
$20$	0.709460	+	1.62780i	0.158640	+	0.363987i
$21$		0			0
$22$	1.38567	−	7.31580i	0.295427	−	1.55973i
$23$	6.62774	−	3.82653i	1.38198	−	0.797887i	0.389586	−	0.920990i	$-0.372618\pi$
$23$	6.62774	−	3.82653i	1.38198	−	0.797887i	0.992394	+	0.123103i	$0.0392847\pi$
$24$	−3.66886	−	6.95147i	−0.748902	−	1.41896i
$25$	−3.64747	−	2.10587i	−0.729494	−	0.421173i
$26$	−1.46607	−	4.19237i	−0.287521	−	0.822192i
$27$	3.38567	−	3.38567i	0.651573	−	0.651573i
$28$		0			0
$29$	−1.53721	−	1.53721i	−0.285453	−	0.285453i	0.549826	−	0.835279i	$-0.314694\pi$
$29$	−1.53721	−	1.53721i	−0.285453	−	0.285453i	−0.835279	+	0.549826i	$0.814694\pi$
$30$	−3.14349	−	1.51457i	−0.573921	−	0.276521i
$31$	1.22066	−	2.11425i	0.219238	−	0.379731i	−0.735338	−	0.677701i	$-0.762976\pi$
$31$	1.22066	−	2.11425i	0.219238	−	0.379731i	0.954575	+	0.297970i	$0.0963097\pi$
$32$	3.53122	−	4.41933i	0.624238	−	0.781234i
$33$	7.31580	+	12.6713i	1.27352	+	2.20580i
$34$	3.80460	−	2.59286i	0.652483	−	0.444672i
$35$		0			0
$36$	8.79159	+	3.45433i	1.46527	+	0.575722i
$37$	1.72139	+	0.461245i	0.282995	+	0.0758283i	0.397524	−	0.917592i	$-0.369869\pi$
$37$	1.72139	+	0.461245i	0.282995	+	0.0758283i	−0.114530	+	0.993420i	$0.536536\pi$
$38$	2.39441	−	2.78128i	0.388425	−	0.451183i
$39$	7.55822	+	4.36374i	1.21028	+	0.698758i
$40$	0.0953379	−	2.50939i	0.0150742	−	0.396770i
$41$		−	7.77589i		−	1.21439i	−0.794553	−	0.607195i	$-0.792295\pi$
$41$		−	7.77589i		−	1.21439i	0.794553	−	0.607195i	$-0.207705\pi$
$42$		0			0
$43$	−7.51575	+	7.51575i	−1.14614	+	1.14614i	−0.158836	+	0.987305i	$0.550774\pi$
$43$	−7.51575	+	7.51575i	−1.14614	+	1.14614i	−0.987305	+	0.158836i	$0.949226\pi$
$44$	−6.25620	+	8.47006i	−0.943158	+	1.27691i
$45$	4.05035	−	1.08529i	0.603790	−	0.161785i
$46$	−10.7930	+	0.806742i	−1.59133	+	0.118948i
$47$	−5.55792	−	9.62661i	−0.810707	−	1.40418i	−0.912370	−	0.409366i	$-0.865750\pi$
$47$	−5.55792	−	9.62661i	−0.810707	−	1.40418i	0.101664	−	0.994819i	$-0.467583\pi$
$48$	0.407138	+	11.1086i	0.0587653	+	1.60339i
$49$		0			0
$50$	3.35436	+	4.92196i	0.474377	+	0.696070i
$51$	−2.34163	+	8.73909i	−0.327894	+	1.22372i
$52$	−0.705636	+	6.24122i	−0.0978542	+	0.865502i
$53$	1.07250	+	4.00262i	0.147319	+	0.549803i	0.999641	+	0.0267853i	$0.00852703\pi$
$53$	1.07250	+	4.00262i	0.147319	+	0.549803i	−0.852322	+	0.523017i	$0.824806\pi$
$54$	−6.39179	+	2.23521i	−0.869813	+	0.304174i
$55$			4.67452i			0.630312i
$56$		0			0
$57$			7.21173i			0.955217i
$58$	1.01486	+	2.90209i	0.133258	+	0.381063i
$59$	−2.50344	−	9.34298i	−0.325921	−	1.21635i	−0.913383	−	0.407101i	$-0.866540\pi$
$59$	−2.50344	−	9.34298i	−0.325921	−	1.21635i	0.587463	−	0.809251i	$-0.300127\pi$
$60$	3.07524	+	3.85926i	0.397012	+	0.498228i
$61$	1.23431	−	4.60651i	0.158037	−	0.589803i	−0.840789	−	0.541363i	$-0.817908\pi$
$61$	1.23431	−	4.60651i	0.158037	−	0.589803i	0.998826	−	0.0484399i	$-0.0154249\pi$
$62$	−2.85301	+	1.94435i	−0.362332	+	0.246932i
$63$		0			0
$64$	−7.21173	+	3.46279i	−0.901467	+	0.432849i
$65$	1.39413	+	2.41471i	0.172921	+	0.299508i
$66$	−1.54238	−	20.6346i	−0.189854	−	2.53995i
$67$	−1.26436	+	0.338785i	−0.154467	+	0.0413892i	−0.335224	−	0.942139i	$-0.608812\pi$
$67$	−1.26436	+	0.338785i	−0.154467	+	0.0413892i	0.180757	+	0.983528i	$0.442145\pi$
$68$	−6.43885	+	0.967979i	−0.780825	+	0.117385i
$69$	15.0387	−	15.0387i	1.81045	−	1.81045i
$70$		0			0
$71$		−	12.1113i		−	1.43735i	−0.695348	−	0.718674i	$-0.744750\pi$
$71$		−	12.1113i		−	1.43735i	0.695348	−	0.718674i	$-0.255250\pi$
$72$	−9.08045	−	9.79767i	−1.07014	−	1.15467i
$73$	5.55501	+	3.20719i	0.650165	+	0.375373i	0.788519	−	0.615010i	$-0.210848\pi$
$73$	5.55501	+	3.20719i	0.650165	+	0.375373i	−0.138354	+	0.990383i	$0.544181\pi$
$74$	−1.91000	−	1.64432i	−0.222032	−	0.191148i
$75$	−11.3057	−	3.02934i	−1.30546	−	0.349798i
$76$	−4.75787	+	2.07367i	−0.545766	+	0.237866i
$77$		0			0
$78$	−6.95084	−	10.1992i	−0.787027	−	1.15483i
$79$	3.64128	+	6.30687i	0.409675	+	0.709579i	0.994853	−	0.101326i	$-0.0323086\pi$
$79$	3.64128	+	6.30687i	0.409675	+	0.709579i	−0.585178	+	0.810905i	$0.698975\pi$
$80$	−1.66185	+	3.13856i	−0.185801	+	0.350901i
$81$	−0.431344	+	0.747110i	−0.0479271	+	0.0830122i
$82$	−4.77322	+	9.90684i	−0.527114	+	1.09403i
$83$	−1.96506	−	1.96506i	−0.215694	−	0.215694i	0.590987	−	0.806681i	$-0.298738\pi$
$83$	−1.96506	−	1.96506i	−0.215694	−	0.215694i	−0.806681	+	0.590987i	$0.798738\pi$
$84$		0			0
$85$	−2.04387	+	2.04387i	−0.221689	+	0.221689i
$86$	14.1889	−	4.96187i	1.53003	−	0.535052i
$87$	−5.23203	−	3.02071i	−0.560932	−	0.323854i
$88$	13.1700	−	6.95088i	1.40393	−	0.740966i
$89$	0.576282	−	0.332717i	0.0610858	−	0.0352679i	−0.469146	−	0.883121i	$-0.655438\pi$
$89$	0.576282	−	0.332717i	0.0610858	−	0.0352679i	0.530232	+	0.847853i	$0.322105\pi$
$90$	−5.82653	−	1.10359i	−0.614170	−	0.116329i
$91$		0			0
$92$	14.2459	+	5.59741i	1.48524	+	0.583570i
$93$	1.75595	−	6.55331i	0.182084	−	0.679547i
$94$	1.17177	+	15.6765i	0.120859	+	1.61690i
$95$	−1.15201	+	1.99533i	−0.118193	+	0.204717i
$96$	6.30029	−	14.4028i	0.643020	−	1.46998i
$97$	−8.34450			−0.847256			−0.423628	−	0.905836i	$-0.639244\pi$
$97$	−8.34450			−0.847256			−0.423628	+	0.905836i	$0.639244\pi$
$98$		0			0
$99$	17.5832	+	17.5832i	1.76718	+	1.76718i
$100$	−1.25226	−	8.32986i	−0.125226	−	0.832986i
$101$	−1.23696	−	4.61640i	−0.123082	−	0.459349i	0.876682	−	0.481070i	$-0.159752\pi$
$101$	−1.23696	−	4.61640i	−0.123082	−	0.459349i	−0.999764	+	0.0217217i	$0.993085\pi$
$102$	8.34782	−	9.69659i	0.826557	−	0.960105i
$103$	16.6465	−	9.61088i	1.64023	−	0.946988i	0.659482	−	0.751720i	$-0.270776\pi$
$103$	16.6465	−	9.61088i	1.64023	−	0.946988i	0.980750	−	0.195268i	$-0.0625576\pi$
$104$	4.73017	−	7.51844i	0.463832	−	0.737244i
$105$		0			0
$106$	1.09059	−	5.75787i	0.105927	−	0.559254i
$107$	−3.37044	−	0.903107i	−0.325833	−	0.0873066i	0.0921947	−	0.995741i	$-0.470612\pi$
$107$	−3.37044	−	0.903107i	−0.325833	−	0.0873066i	−0.418028	+	0.908434i	$0.637278\pi$
$108$	9.51551	+	1.07583i	0.915630	+	0.103522i
$109$	−3.34112	+	0.895251i	−0.320021	+	0.0857495i	−0.415254	−	0.909706i	$-0.636307\pi$
$109$	−3.34112	+	0.895251i	−0.320021	+	0.0857495i	0.0952324	+	0.995455i	$0.469641\pi$
$110$	2.86945	−	5.95555i	0.273591	−	0.567840i
$111$	4.95253			0.470073
$112$		0			0
$113$	3.35149			0.315281			0.157641	−	0.987497i	$-0.449611\pi$
$113$	3.35149			0.315281			0.157641	+	0.987497i	$0.449611\pi$
$114$	4.42691	−	9.18807i	0.414618	−	0.860542i
$115$	6.56320	−	1.75860i	0.612021	−	0.163991i
$116$	0.488463	−	4.32036i	0.0453527	−	0.401136i
$117$	14.3269	+	3.83889i	1.32453	+	0.354906i
$118$	−2.54567	+	13.4401i	−0.234348	+	1.23726i
$119$		0			0
$120$	−1.54899	−	6.80460i	−0.141403	−	0.621172i
$121$	−14.4804	+	8.36025i	−1.31640	+	0.760022i
$122$	−4.40026	+	5.11122i	−0.398381	+	0.462748i
$123$	−5.59291	−	20.8730i	−0.504296	−	1.88206i
$124$	4.82840	−	0.725873i	0.433603	−	0.0651853i
$125$	−5.78313	−	5.78313i	−0.517259	−	0.517259i
$126$		0			0
$127$	−5.55623			−0.493036			−0.246518	−	0.969138i	$-0.579286\pi$
$127$	−5.55623			−0.493036			−0.246518	+	0.969138i	$0.579286\pi$
$128$	11.3137	+	0.0151595i	0.999999	+	0.00133992i
$129$	−14.7689	+	25.5805i	−1.30033	+	2.25224i
$130$	−0.293923	−	3.93224i	−0.0257788	−	0.344880i
$131$	3.53986	−	13.2109i	0.309279	−	1.15425i	−0.619920	−	0.784665i	$-0.712835\pi$
$131$	3.53986	−	13.2109i	0.309279	−	1.15425i	0.929199	−	0.369580i	$-0.120498\pi$
$132$	−10.7015	+	27.2362i	−0.931444	+	2.37061i
$133$		0			0
$134$	1.81882	+	0.344500i	0.157122	+	0.0297603i
$135$	3.68152	−	2.12553i	0.316855	−	0.182936i
$136$	8.79757	+	2.71923i	0.754386	+	0.233172i
$137$	4.26568	+	2.46279i	0.364441	+	0.210410i	0.671027	−	0.741433i	$-0.265853\pi$
$137$	4.26568	+	2.46279i	0.364441	+	0.210410i	−0.306586	+	0.951843i	$0.599187\pi$
$138$	−28.3915	+	9.92852i	−2.41685	+	0.845172i
$139$	7.58393	−	7.58393i	0.643261	−	0.643261i	−0.308095	−	0.951356i	$-0.599691\pi$
$139$	7.58393	−	7.58393i	0.643261	−	0.643261i	0.951356	+	0.308095i	$0.0996914\pi$
$140$		0			0
$141$	−21.8433	−	21.8433i	−1.83954	−	1.83954i
$142$	−7.43450	+	15.4303i	−0.623889	+	1.29489i
$143$	−8.26738	+	14.3195i	−0.691353	+	1.19746i
$144$	5.55461	+	18.0567i	0.462885	+	1.50472i
$145$	−0.965062	−	1.67154i	−0.0801440	−	0.138814i
$146$	−5.10861	−	7.49604i	−0.422792	−	0.620376i
$147$		0			0
$148$	1.42406	+	3.26738i	0.117057	+	0.268577i
$149$	3.68278	+	0.986799i	0.301705	+	0.0808417i	0.406496	−	0.913653i	$-0.366751\pi$
$149$	3.68278	+	0.986799i	0.301705	+	0.0808417i	−0.104790	+	0.994494i	$0.533417\pi$
$150$	12.5444	+	10.7995i	1.02424	+	0.881773i
$151$	1.87431	+	1.08213i	0.152529	+	0.0880625i	0.574322	−	0.818630i	$-0.305266\pi$
$151$	1.87431	+	1.08213i	0.152529	+	0.0880625i	−0.421793	+	0.906692i	$0.638599\pi$
$152$	7.33466	+	0.278662i	0.594920	+	0.0226024i
$153$			15.3760i			1.24308i
$154$		0			0
$155$	1.53267	−	1.53267i	0.123107	−	0.123107i
$156$	2.59492	+	17.2610i	0.207760	+	1.38199i
$157$	−5.38577	+	1.44311i	−0.429831	+	0.115173i	−0.467247	−	0.884127i	$-0.654754\pi$
$157$	−5.38577	+	1.44311i	−0.429831	+	0.115173i	0.0374157	+	0.999300i	$0.488087\pi$
$158$	−0.767685	−	10.2704i	−0.0610738	−	0.817072i
$159$	5.75787	+	9.97293i	0.456629	+	0.790905i
$160$	4.04387	−	2.97854i	0.319696	−	0.235474i
$161$		0			0
$162$	1.00816	−	0.687072i	0.0792088	−	0.0539815i
$163$	−3.01390	+	11.2480i	−0.236067	+	0.881015i	0.741598	+	0.670845i	$0.234068\pi$
$163$	−3.01390	+	11.2480i	−0.236067	+	0.881015i	−0.977665	+	0.210170i	$0.932598\pi$
$164$	12.1626	−	9.69172i	0.949738	−	0.756797i
$165$	3.36221	+	12.5479i	0.261748	+	0.976855i
$166$	1.29733	+	3.70983i	0.100692	+	0.287938i
$167$		−	12.4649i		−	0.964562i	−0.876016	−	0.482281i	$-0.839808\pi$
$167$		−	12.4649i		−	0.964562i	0.876016	−	0.482281i	$-0.160192\pi$
$168$		0			0
$169$		−	3.13731i		−	0.241332i
$170$	3.85861	−	1.34936i	0.295942	−	0.103491i
$171$	3.17217	+	11.8387i	0.242582	+	0.905328i
$172$	−21.1232	−	2.38820i	−1.61063	−	0.182098i
$173$	−5.09752	+	19.0242i	−0.387557	+	1.44638i	0.446539	+	0.894764i	$0.352656\pi$
$173$	−5.09752	+	19.0242i	−0.387557	+	1.44638i	−0.834096	+	0.551619i	$0.814010\pi$
$174$	4.81158	+	7.06020i	0.364765	+	0.535232i
$175$		0			0
$176$	−21.0460	+	0.771348i	−1.58640	+	0.0581426i
$177$	−13.4401	−	23.2789i	−1.01022	−	1.74975i
$178$	−0.938447	+	0.0701462i	−0.0703396	+	0.00525768i
$179$	−1.33542	+	0.357825i	−0.0998139	+	0.0267451i	−0.308380	−	0.951263i	$-0.599787\pi$
$179$	−1.33542	+	0.357825i	−0.0998139	+	0.0267451i	0.208566	+	0.978008i	$0.433120\pi$
$180$	6.74582	+	4.98263i	0.502804	+	0.371384i
$181$	−16.0038	+	16.0038i	−1.18955	+	1.18955i	−0.212362	+	0.977191i	$0.568115\pi$
$181$	−16.0038	+	16.0038i	−1.18955	+	1.18955i	−0.977191	+	0.212362i	$0.931885\pi$
$182$		0			0
$183$		−	13.2532i		−	0.979702i
$184$	−14.7140	−	15.8762i	−1.08473	−	1.17041i
$185$	1.37026	+	0.791120i	0.100744	+	0.0581643i
$186$	−6.25990	+	7.27132i	−0.458998	+	0.533159i
$187$	−16.5568	−	4.43637i	−1.21075	−	0.324420i
$188$	8.13007	−	20.6918i	0.592947	−	1.50910i
$189$		0			0
$190$	2.69254	−	1.83499i	0.195337	−	0.133124i
$191$	−1.25560	−	2.17477i	−0.0908521	−	0.157360i	0.817018	−	0.576612i	$-0.195626\pi$
$191$	−1.25560	−	2.17477i	−0.0908521	−	0.157360i	−0.907870	+	0.419252i	$0.862292\pi$
$192$	−16.8680	+	14.4824i	−1.21734	+	1.04518i
$193$	−5.04719	+	8.74199i	−0.363305	+	0.629262i	−0.988503	−	0.151204i	$-0.951685\pi$
$193$	−5.04719	+	8.74199i	−0.363305	+	0.629262i	0.625198	+	0.780466i	$0.285018\pi$
$194$	10.6313	+	5.12226i	0.763281	+	0.367757i
$195$	5.47912	+	5.47912i	0.392368	+	0.392368i
$196$		0			0
$197$	−13.5617	+	13.5617i	−0.966232	+	0.966232i	−0.999448	−	0.0332158i	$-0.989425\pi$
$197$	−13.5617	+	13.5617i	−0.966232	+	0.966232i	0.0332158	+	0.999448i	$0.489425\pi$
$198$	−11.6084	−	33.1952i	−0.824970	−	2.35908i
$199$	4.86063	+	2.80629i	0.344561	+	0.198932i	0.662287	−	0.749250i	$-0.269586\pi$
$199$	4.86063	+	2.80629i	0.344561	+	0.198932i	−0.317726	+	0.948183i	$0.602919\pi$
$200$	−3.51783	+	11.3813i	−0.248748	+	0.804781i
$201$	−3.15029	+	1.81882i	−0.222204	+	0.128290i
$202$	−1.25782	+	6.64080i	−0.0885002	+	0.467245i
$203$		0			0
$204$	−16.5877	+	7.22959i	−1.16137	+	0.506173i
$205$	1.78683	−	6.66854i	0.124798	−	0.465751i
$206$	−27.1081	+	2.02625i	−1.88871	+	0.141176i
$207$	18.0725	−	31.3024i	1.25612	−	2.17567i
$208$	−10.6416	+	6.67522i	−0.737865	+	0.462843i
$209$	−13.6631			−0.945096
$210$		0			0
$211$	3.86025	+	3.86025i	0.265750	+	0.265750i	0.827385	−	0.561635i	$-0.189827\pi$
$211$	3.86025	+	3.86025i	0.265750	+	0.265750i	−0.561635	+	0.827385i	$0.689827\pi$
$212$	−4.92392	+	6.66633i	−0.338176	+	0.457846i
$213$	−8.71121	−	32.5107i	−0.596882	−	2.22759i
$214$	3.73972	+	3.21954i	0.255642	+	0.220083i
$215$	−8.17249	+	4.71839i	−0.557359	+	0.321792i
$216$	−11.4628	−	7.21173i	−0.779944	−	0.490696i
$217$		0			0
$218$	4.80629	+	0.910351i	0.325523	+	0.0616568i
$219$	17.2183	+	4.61362i	1.16350	+	0.311760i
$220$	−7.31161	+	5.82624i	−0.492949	+	0.392805i
$221$	−9.87581	+	2.64621i	−0.664319	+	0.178004i
$222$	−6.30974	−	3.04010i	−0.423482	−	0.204038i
$223$	−12.5348			−0.839390			−0.419695	−	0.907665i	$-0.637863\pi$
$223$	−12.5348			−0.839390			−0.419695	+	0.907665i	$0.637863\pi$
$224$		0			0
$225$	−19.8917			−1.32612
$226$	−4.26994	−	2.05730i	−0.284032	−	0.136850i
$227$	21.4525	−	5.74818i	1.42385	−	0.381520i	0.537004	−	0.843580i	$-0.319556\pi$
$227$	21.4525	−	5.74818i	1.42385	−	0.381520i	0.886849	+	0.462059i	$0.152889\pi$
$228$	−11.2802	+	8.98857i	−0.747047	+	0.595282i
$229$	−9.96527	−	2.67019i	−0.658524	−	0.176451i	−0.0859440	−	0.996300i	$-0.527391\pi$
$229$	−9.96527	−	2.67019i	−0.658524	−	0.176451i	−0.572580	+	0.819849i	$0.694057\pi$
$230$	−9.44133	−	1.78827i	−0.622543	−	0.117915i
$231$		0			0
$232$	−3.27437	+	5.20449i	−0.214973	+	0.341692i
$233$	−0.158206	+	0.0913400i	−0.0103644	+	0.00598388i	−0.505173	−	0.863018i	$-0.668571\pi$
$233$	−0.158206	+	0.0913400i	−0.0103644	+	0.00598388i	0.494809	+	0.869002i	$0.335238\pi$
$234$	−15.8967	−	13.6855i	−1.03920	−	0.894648i
$235$	−2.55432	−	9.53286i	−0.166626	−	0.621855i
$236$	11.4935	−	15.5606i	0.748162	−	1.01291i
$237$	14.3107	+	14.3107i	0.929577	+	0.929577i
$238$		0			0
$239$	0.261087			0.0168883			0.00844417	−	0.999964i	$-0.497312\pi$
$239$	0.261087			0.0168883			0.00844417	+	0.999964i	$0.497312\pi$
$240$	−2.20350	+	9.62021i	−0.142235	+	0.620982i
$241$	−3.76511	+	6.52137i	−0.242532	+	0.420078i	−0.961435	−	0.275033i	$-0.911311\pi$
$241$	−3.76511	+	6.52137i	−0.242532	+	0.420078i	0.718903	+	0.695111i	$0.244645\pi$
$242$	23.5806	−	1.76258i	1.51582	−	0.113303i
$243$	−4.33823	+	16.1905i	−0.278297	+	1.03862i
$244$	8.74365	−	3.81083i	0.559755	−	0.243963i
$245$		0			0
$246$	−5.68725	+	30.0264i	−0.362606	+	1.91441i
$247$	−7.05792	+	4.07489i	−0.449085	+	0.259279i
$248$	−6.59717	−	2.03911i	−0.418921	−	0.129483i
$249$	−6.68826	−	3.86147i	−0.423851	−	0.244711i
$250$	3.81800	+	10.9179i	0.241472	+	0.690511i
$251$	−2.22521	+	2.22521i	−0.140454	+	0.140454i	−0.773838	−	0.633384i	$-0.781665\pi$
$251$	−2.22521	+	2.22521i	−0.140454	+	0.140454i	0.633384	+	0.773838i	$0.281665\pi$
$252$		0			0
$253$	28.4918	+	28.4918i	1.79127	+	1.79127i
$254$	7.07889	+	3.41068i	0.444169	+	0.214005i
$255$	−4.01633	+	6.95648i	−0.251512	+	0.435632i
$256$	−14.4049	−	6.96421i	−0.900303	−	0.435263i
$257$	1.40714	+	2.43723i	0.0877748	+	0.152030i	0.906570	−	0.422055i	$-0.138691\pi$
$257$	1.40714	+	2.43723i	0.0877748	+	0.152030i	−0.818795	+	0.574085i	$0.805358\pi$
$258$	34.5188	−	23.5248i	2.14905	−	1.46459i
$259$		0			0
$260$	−2.03932	+	5.19027i	−0.126474	+	0.321887i
$261$	−9.91754	−	2.65740i	−0.613881	−	0.164489i
$262$	−12.6195	+	14.6584i	−0.779632	+	0.905598i
$263$	7.38346	+	4.26284i	0.455283	+	0.262858i	0.710059	−	0.704142i	$-0.248668\pi$
$263$	7.38346	+	4.26284i	0.455283	+	0.262858i	−0.254776	+	0.967000i	$0.582002\pi$
$264$	30.3531	−	28.1311i	1.86810	−	1.73135i
$265$			3.67907i			0.226003i
$266$		0			0
$267$	1.30762	−	1.30762i	0.0800249	−	0.0800249i
$268$	−2.10579	−	1.55539i	−0.128631	−	0.0950104i
$269$	15.7335	−	4.21577i	0.959286	−	0.257040i	0.254988	−	0.966944i	$-0.417929\pi$
$269$	15.7335	−	4.21577i	0.959286	−	0.257040i	0.704298	+	0.709904i	$0.251262\pi$
$270$	−5.99518	+	0.448122i	−0.364855	+	0.0272719i
$271$	−13.3688	−	23.1554i	−0.812094	−	1.40659i	−0.911396	−	0.411531i	$-0.864994\pi$
$271$	−13.3688	−	23.1554i	−0.812094	−	1.40659i	0.0993018	−	0.995057i	$-0.468339\pi$
$272$	−9.53931	−	8.86479i	−0.578406	−	0.537507i
$273$		0			0
$274$	−3.92288	−	5.75618i	−0.236990	−	0.347744i
$275$	5.73928	−	21.4193i	0.346092	−	1.29163i
$276$	42.2667	+	4.77870i	2.54415	+	0.287644i
$277$	3.31891	+	12.3863i	0.199414	+	0.744223i	0.991080	+	0.133269i	$0.0425475\pi$
$277$	3.31891	+	12.3863i	0.199414	+	0.744223i	−0.791666	+	0.610954i	$0.790786\pi$
$278$	−14.3177	+	5.00689i	−0.858716	+	0.300293i
$279$		−	11.5302i		−	0.690296i
$280$		0			0
$281$			28.4095i			1.69477i	0.530980	+	0.847384i	$0.321824\pi$
$281$			28.4095i			1.69477i	−0.530980	+	0.847384i	$0.678176\pi$
$282$	14.4209	+	41.2379i	0.858752	+	2.45568i
$283$	1.95496	+	7.29602i	0.116210	+	0.433703i	0.999375	−	0.0353608i	$-0.0112580\pi$
$283$	1.95496	+	7.29602i	0.116210	+	0.433703i	−0.883164	+	0.469064i	$0.844591\pi$
$284$	18.9438	−	15.0953i	1.12411	−	0.895741i
$285$	−1.65719	+	6.18472i	−0.0981635	+	0.366351i
$286$	19.3230	−	13.1688i	1.14260	−	0.778688i
$287$		0			0
$288$	4.00724	−	26.4147i	0.236129	−	1.55650i
$289$	3.20053	+	5.54348i	0.188266	+	0.326087i
$290$	0.203463	+	2.72201i	0.0119477	+	0.159842i
$291$	−22.3993	+	6.00189i	−1.31307	+	0.351837i
$292$	1.90717	+	12.6862i	0.111609	+	0.742404i
$293$	−8.64751	+	8.64751i	−0.505193	+	0.505193i	−0.913047	−	0.407854i	$-0.866277\pi$
$293$	−8.64751	+	8.64751i	−0.505193	+	0.505193i	0.407854	+	0.913047i	$0.366277\pi$
$294$		0			0
$295$		−	8.58773i		−	0.499997i
$296$	0.191366	−	5.03695i	0.0111229	−	0.292767i
$297$	21.8319	+	12.6046i	1.26681	+	0.731396i
$298$	−4.08629	−	3.51790i	−0.236712	−	0.203786i
$299$	23.2154	+	6.22055i	1.34258	+	0.359744i
$300$	−9.35284	−	21.4593i	−0.539986	−	1.23896i
$301$		0			0
$302$	−1.72369	−	2.52922i	−0.0991869	−	0.145540i
$303$	−6.64080	−	11.5022i	−0.381504	−	0.660785i
$304$	−9.17364	−	4.85740i	−0.526144	−	0.278591i
$305$	2.11707	−	3.66687i	0.121223	−	0.209964i
$306$	9.43853	−	19.5897i	0.539565	−	1.11987i
$307$	22.9681	+	22.9681i	1.31086	+	1.31086i	0.920782	+	0.390077i	$0.127552\pi$
$307$	22.9681	+	22.9681i	1.31086	+	1.31086i	0.390077	+	0.920782i	$0.372448\pi$
$308$		0			0
$309$	37.7720	−	37.7720i	2.14877	−	2.14877i
$310$	−2.89351	+	1.01186i	−0.164340	+	0.0574699i
$311$	−22.9893	−	13.2729i	−1.30360	−	0.752635i	−0.322583	−	0.946541i	$-0.604551\pi$
$311$	−22.9893	−	13.2729i	−1.30360	−	0.752635i	−0.981020	+	0.193906i	$0.937884\pi$
$312$	7.28959	−	23.5842i	0.412692	−	1.33519i
$313$	−17.4811	+	10.0927i	−0.988088	+	0.570473i	−0.904702	−	0.426045i	$-0.859907\pi$
$313$	−17.4811	+	10.0927i	−0.988088	+	0.570473i	−0.0833856	+	0.996517i	$0.526573\pi$
$314$	7.74756	+	1.46745i	0.437220	+	0.0828132i
$315$		0			0
$316$	−5.32642	+	13.5562i	−0.299634	+	0.762598i
$317$	−0.340449	+	1.27057i	−0.0191215	+	0.0713624i	−0.974827	−	0.222961i	$-0.928428\pi$
$317$	−0.340449	+	1.27057i	−0.0191215	+	0.0713624i	0.955706	+	0.294324i	$0.0950944\pi$
$318$	−1.21393	−	16.2404i	−0.0680735	−	0.910718i
$319$	5.72294	−	9.91241i	0.320423	−	0.554989i
$320$	−6.98044	+	1.31247i	−0.390218	+	0.0733692i
$321$	−9.69693			−0.541230
$322$		0			0
$323$	−5.97399	−	5.97399i	−0.332402	−	0.332402i
$324$	−1.70620	+	0.256501i	−0.0947891	+	0.0142500i
$325$	−3.42338	−	12.7762i	−0.189895	−	0.708697i
$326$	10.7444	−	12.4804i	0.595079	−	0.691227i
$327$	−8.32473	+	4.80629i	−0.460359	+	0.265788i
$328$	−21.4449	+	4.88171i	−1.18410	+	0.269547i
$329$		0			0
$330$	3.41892	−	18.0505i	0.188205	−	0.993648i
$331$	−14.2631	−	3.82179i	−0.783972	−	0.210065i	−0.155437	−	0.987846i	$-0.549678\pi$
$331$	−14.2631	−	3.82179i	−0.783972	−	0.210065i	−0.628535	+	0.777781i	$0.716345\pi$
$332$	0.624417	−	5.52285i	0.0342693	−	0.303106i
$333$	8.13002	−	2.17843i	0.445522	−	0.119377i
$334$	−7.65155	+	15.8808i	−0.418674	+	0.868961i
$335$	−1.16216			−0.0634955
$336$		0			0
$337$	−27.6212			−1.50462			−0.752312	−	0.658807i	$-0.771061\pi$
$337$	−27.6212			−1.50462			−0.752312	+	0.658807i	$0.771061\pi$
$338$	−1.92583	+	3.99708i	−0.104752	+	0.217412i
$339$	8.99647	−	2.41060i	0.488621	−	0.130926i
$340$	−5.74434	−	0.649458i	−0.311530	−	0.0352218i
$341$	12.4157	+	3.32677i	0.672346	+	0.180155i
$342$	3.22568	−	17.0303i	0.174425	−	0.920892i
$343$		0			0
$344$	25.4459	+	16.0091i	1.37195	+	0.863152i
$345$	16.3529	−	9.44133i	0.880408	−	0.508304i
$346$	18.1724	−	21.1086i	0.976956	−	1.13480i
$347$	3.05763	+	11.4112i	0.164142	+	0.612586i	0.998148	+	0.0608309i	$0.0193750\pi$
$347$	3.05763	+	11.4112i	0.164142	+	0.612586i	−0.834006	+	0.551755i	$0.813958\pi$
$348$	−1.79628	−	11.9486i	−0.0962908	−	0.640512i
$349$	−7.97685	−	7.97685i	−0.426991	−	0.426991i	0.460611	−	0.887602i	$-0.347630\pi$
$349$	−7.97685	−	7.97685i	−0.426991	−	0.426991i	−0.887602	+	0.460611i	$0.847630\pi$
$350$		0			0
$351$	15.0369			0.802609
$352$	27.2870	+	11.9363i	1.45440	+	0.636207i
$353$	5.38113	−	9.32039i	0.286409	−	0.496074i	−0.686541	−	0.727091i	$-0.740872\pi$
$353$	5.38113	−	9.32039i	0.286409	−	0.496074i	0.972950	+	0.231017i	$0.0742052\pi$
$354$	2.83356	+	37.9086i	0.150602	+	2.01482i
$355$	2.78307	−	10.3866i	0.147710	−	0.551261i
$356$	1.23868	+	0.486694i	0.0656500	+	0.0257947i
$357$		0			0
$358$	1.92103	+	0.363860i	0.101530	+	0.0192306i
$359$	15.5646	−	8.98625i	0.821470	−	0.474276i	−0.0294531	−	0.999566i	$-0.509377\pi$
$359$	15.5646	−	8.98625i	0.821470	−	0.474276i	0.850923	+	0.525290i	$0.176043\pi$
$360$	−5.53590	−	10.4890i	−0.291767	−	0.552819i
$361$	10.6223	+	6.13282i	0.559071	+	0.322780i
$362$	30.2135	−	10.5657i	1.58798	−	0.555318i
$363$	−32.8568	+	32.8568i	−1.72453	+	1.72453i
$364$		0			0
$365$	4.02695	+	4.02695i	0.210780	+	0.210780i
$366$	−8.13543	+	16.8851i	−0.425246	+	0.882599i
$367$	8.35453	−	14.4705i	0.436103	−	0.755352i	−0.561282	−	0.827625i	$-0.689692\pi$
$367$	8.35453	−	14.4705i	0.436103	−	0.755352i	0.997385	+	0.0722722i	$0.0230250\pi$
$368$	9.00071	+	29.2591i	0.469195	+	1.52524i
$369$	−18.3625	−	31.8048i	−0.955915	−	1.65569i
$370$	−1.26015	−	1.84905i	−0.0655119	−	0.0961278i
$371$		0			0
$372$	12.4389	−	5.42136i	0.644926	−	0.281085i
$373$	21.2808	+	5.70218i	1.10188	+	0.295248i	0.763529	−	0.645773i	$-0.223465\pi$
$373$	21.2808	+	5.70218i	1.10188	+	0.295248i	0.338349	+	0.941021i	$0.390131\pi$
$374$	18.3708	+	15.8155i	0.949932	+	0.817799i
$375$	−19.6834	−	11.3642i	−1.01645	−	0.586845i
$376$	−23.0597	+	21.3716i	−1.18921	+	1.10216i
$377$		−	6.82725i		−	0.351621i
$378$		0			0
$379$	23.6361	−	23.6361i	1.21411	−	1.21411i	0.244443	−	0.969664i	$-0.421395\pi$
$379$	23.6361	−	23.6361i	1.21411	−	1.21411i	0.969664	−	0.244443i	$-0.0786052\pi$
$380$	−4.55682	+	0.685047i	−0.233760	+	0.0351421i
$381$	−14.9147	+	3.99639i	−0.764105	+	0.204741i
$382$	0.264717	+	3.54150i	0.0135441	+	0.181199i
$383$	−4.91665	−	8.51589i	−0.251229	−	0.435141i	0.712635	−	0.701535i	$-0.247501\pi$
$383$	−4.91665	−	8.51589i	−0.251229	−	0.435141i	−0.963864	+	0.266393i	$0.914168\pi$
$384$	30.3805	−	8.09683i	1.55035	−	0.413189i
$385$		0			0
$386$	11.7966	−	8.03948i	0.600431	−	0.409199i
$387$	−12.9926	+	48.4890i	−0.660450	+	2.46483i
$388$	−10.4004	−	13.0520i	−0.528002	−	0.662613i
$389$	3.78801	+	14.1371i	0.192060	+	0.716777i	0.993008	+	0.118044i	$0.0376624\pi$
$389$	3.78801	+	14.1371i	0.192060	+	0.716777i	−0.800948	+	0.598733i	$0.795671\pi$
$390$	−3.61730	−	10.3440i	−0.183169	−	0.523788i
$391$			24.9153i			1.26002i
$392$		0			0
$393$		−	38.0085i		−	1.91728i
$394$	25.6031	−	8.95340i	1.28986	−	0.451066i
$395$	1.67346	+	6.24545i	0.0842011	+	0.314243i
$396$	−5.58722	+	49.4179i	−0.280768	+	2.48334i
$397$	6.60834	−	24.6626i	0.331663	−	1.23778i	−0.575779	−	0.817605i	$-0.695301\pi$
$397$	6.60834	−	24.6626i	0.331663	−	1.23778i	0.907442	−	0.420177i	$-0.138032\pi$
$398$	−4.47003	−	6.55902i	−0.224062	−	0.328774i
$399$		0			0
$400$	11.4683	−	12.3409i	0.573414	−	0.617045i
$401$	−9.40322	−	16.2869i	−0.469575	−	0.813327i	0.529820	−	0.848110i	$-0.322259\pi$
$401$	−9.40322	−	16.2869i	−0.469575	−	0.813327i	−0.999395	+	0.0347829i	$0.988926\pi$
$402$	5.13009	−	0.383459i	0.255866	−	0.0191252i
$403$	7.40572	−	1.98436i	0.368905	−	0.0988478i
$404$	5.67897	−	7.68857i	0.282539	−	0.382521i
$405$	−0.541596	+	0.541596i	−0.0269121	+	0.0269121i
$406$		0			0
$407$			9.38288i			0.465092i
$408$	25.5714	+	0.971519i	1.26597	+	0.0480974i
$409$	−25.6410	−	14.8038i	−1.26787	−	0.732003i	−0.293283	−	0.956026i	$-0.594748\pi$
$409$	−25.6410	−	14.8038i	−1.26787	−	0.732003i	−0.974584	+	0.224023i	$0.928081\pi$
$410$	−6.36997	+	7.39918i	−0.314591	+	0.365419i
$411$	13.2219	+	3.54278i	0.652186	+	0.174753i
$412$	35.7807	+	14.0587i	1.76279	+	0.692622i
$413$		0			0
$414$	−42.2400	+	28.7869i	−2.07598	+	1.41480i
$415$	−1.23367	−	2.13677i	−0.0605583	−	0.104890i
$416$	17.6555	−	1.97219i	0.865632	−	0.0966944i
$417$	14.9029	−	25.8126i	0.729798	−	1.26405i
$418$	17.4074	+	8.38706i	0.851423	+	0.410225i
$419$	1.15229	+	1.15229i	0.0562929	+	0.0562929i	0.734693	−	0.678400i	$-0.237326\pi$
$419$	1.15229	+	1.15229i	0.0562929	+	0.0562929i	−0.678400	+	0.734693i	$0.737326\pi$
$420$		0			0
$421$	19.7275	−	19.7275i	0.961459	−	0.961459i	−0.0378258	−	0.999284i	$-0.512043\pi$
$421$	19.7275	−	19.7275i	0.961459	−	0.961459i	0.999284	+	0.0378258i	$0.0120432\pi$
$422$	−2.54852	−	7.28773i	−0.124060	−	0.354761i
$423$	−45.4658	−	26.2497i	−2.21062	−	1.27630i
$424$	10.3654	−	5.47067i	0.503389	−	0.265679i
$425$	11.8747	−	6.85586i	0.576008	−	0.332558i
$426$	−8.85814	+	46.7674i	−0.429178	+	2.26589i
$427$		0			0
$428$	−2.78827	−	6.39746i	−0.134776	−	0.309233i
$429$	−11.8928	+	44.3847i	−0.574192	+	2.14291i
$430$	13.3085	−	0.994772i	0.641793	−	0.0479722i
$431$	−10.1980	+	17.6634i	−0.491219	+	0.850817i	−0.999949	−	0.0101095i	$-0.996782\pi$
$431$	−10.1980	+	17.6634i	−0.491219	+	0.850817i	0.508730	+	0.860926i	$0.330115\pi$
$432$	10.1772	+	16.2245i	0.489651	+	0.780601i
$433$	28.3107			1.36052			0.680262	−	0.732969i	$-0.261866\pi$
$433$	28.3107			1.36052			0.680262	+	0.732969i	$0.261866\pi$
$434$		0			0
$435$	−3.79281	−	3.79281i	−0.181851	−	0.181851i
$436$	−5.56461	−	4.11016i	−0.266496	−	0.196841i
$437$	5.14020	+	19.1835i	0.245889	+	0.917670i
$438$	−19.1048	−	16.4474i	−0.912862	−	0.785885i
$439$	−3.95973	+	2.28615i	−0.188988	+	0.109112i	−0.591509	−	0.806299i	$-0.701467\pi$
$439$	−3.95973	+	2.28615i	−0.188988	+	0.109112i	0.402521	+	0.915411i	$0.368134\pi$
$440$	12.8917	−	2.93467i	0.614590	−	0.139905i
$441$		0			0
$442$	14.2066	+	2.69085i	0.675739	+	0.127991i
$443$	−9.74483	−	2.61112i	−0.462991	−	0.124058i	0.0197808	−	0.999804i	$-0.493703\pi$
$443$	−9.74483	−	2.61112i	−0.462991	−	0.124058i	−0.482772	+	0.875746i	$0.660370\pi$
$444$	6.17274	+	7.74645i	0.292945	+	0.367630i
$445$	0.570670	−	0.152911i	0.0270523	−	0.00724865i
$446$	15.9699	+	7.69444i	0.756195	+	0.364343i
$447$	10.5956			0.501153
$448$		0			0
$449$	13.0695			0.616790			0.308395	−	0.951258i	$-0.400208\pi$
$449$	13.0695			0.616790			0.308395	+	0.951258i	$0.400208\pi$
$450$	25.3430	+	12.2105i	1.19468	+	0.575609i
$451$	39.5453	−	10.5961i	1.86211	−	0.498952i
$452$	4.17723	+	5.24219i	0.196480	+	0.246572i
$453$	5.80958	+	1.55667i	0.272958	+	0.0731388i
$454$	−30.8600	−	5.84514i	−1.44833	−	0.274326i
$455$		0			0
$456$	19.8890	−	4.52753i	0.931390	−	0.212021i
$457$	−27.6363	+	15.9559i	−1.29277	+	0.746383i	−0.979145	−	0.203162i	$-0.934878\pi$
$457$	−27.6363	+	15.9559i	−1.29277	+	0.746383i	−0.313629	+	0.949546i	$0.601545\pi$
$458$	11.0571	+	9.51910i	0.516665	+	0.444798i
$459$	4.03448	+	15.0569i	0.188313	+	0.702795i
$460$	10.9309	+	8.07387i	0.509658	+	0.376446i
$461$	−11.2878	−	11.2878i	−0.525727	−	0.525727i	0.393568	−	0.919295i	$-0.371241\pi$
$461$	−11.2878	−	11.2878i	−0.525727	−	0.525727i	−0.919295	+	0.393568i	$0.871241\pi$
$462$		0			0
$463$	−21.0406			−0.977839			−0.488919	−	0.872329i	$-0.662609\pi$
$463$	−21.0406			−0.977839			−0.488919	+	0.872329i	$0.662609\pi$
$464$	7.36646	−	4.62079i	0.341980	−	0.214515i
$465$	3.01178	−	5.21656i	0.139668	−	0.241912i
$466$	0.257630	−	0.0192571i	0.0119345	−	0.000892068i
$467$	−2.47257	+	9.22775i	−0.114417	+	0.427009i	−0.999243	−	0.0389127i	$-0.987611\pi$
$467$	−2.47257	+	9.22775i	−0.114417	+	0.427009i	0.884826	+	0.465922i	$0.154277\pi$
$468$	11.8523	+	27.1941i	0.547871	+	1.25705i
$469$		0			0
$470$	−2.59741	+	13.7133i	−0.119809	+	0.632545i
$471$	−13.4192	+	7.74756i	−0.618323	+	0.356989i
$472$	−24.1951	+	12.7697i	−1.11367	+	0.587773i
$473$	−48.4639	−	27.9806i	−2.22837	−	1.28655i
$474$	−9.44785	−	27.0170i	−0.433954	−	1.24093i
$475$	7.72848	−	7.72848i	0.354607	−	0.354607i
$476$		0			0
$477$	13.8388	+	13.8388i	0.633634	+	0.633634i
$478$	−0.332637	−	0.160268i	−0.0152145	−	0.00733049i
$479$	5.26638	−	9.12164i	0.240627	−	0.416778i	−0.720266	−	0.693698i	$-0.755980\pi$
$479$	5.26638	−	9.12164i	0.240627	−	0.416778i	0.960893	+	0.276920i	$0.0893136\pi$
$480$	8.71270	−	10.9040i	0.397679	−	0.497695i
$481$	2.79836	+	4.84690i	0.127594	+	0.221000i
$482$	8.80005	−	5.99731i	0.400831	−	0.273170i
$483$		0			0
$484$	−31.1247	−	12.2293i	−1.41476	−	0.555876i
$485$	−7.15617	−	1.91749i	−0.324945	−	0.0870688i
$486$	15.4656	−	17.9644i	0.701534	−	0.814881i
$487$	−2.99593	−	1.72970i	−0.135759	−	0.0783803i	0.430582	−	0.902551i	$-0.358308\pi$
$487$	−2.99593	−	1.72970i	−0.135759	−	0.0783803i	−0.566341	+	0.824171i	$0.691642\pi$
$488$	−13.4791	−	0.512103i	−0.610169	−	0.0231818i
$489$			32.3612i			1.46342i
$490$		0			0
$491$	0.356972	−	0.356972i	0.0161099	−	0.0161099i	−0.699006	−	0.715116i	$-0.746374\pi$
$491$	0.356972	−	0.356972i	0.0161099	−	0.0161099i	0.715116	+	0.699006i	$0.246374\pi$
$492$	25.6774	−	34.7638i	1.15763	−	1.56727i
$493$	6.83633	−	1.83179i	0.307893	−	0.0824997i
$494$	11.4935	−	0.859104i	0.517116	−	0.0386529i
$495$	11.0387	+	19.1196i	0.496154	+	0.859364i
$496$	7.15339	+	6.64757i	0.321197	+	0.298485i
$497$		0			0
$498$	6.15079	+	9.02526i	0.275623	+	0.404431i
$499$	5.96768	−	22.2717i	0.267150	−	0.997018i	−0.693771	−	0.720196i	$-0.744052\pi$
$499$	5.96768	−	22.2717i	0.267150	−	0.997018i	0.960921	−	0.276822i	$-0.0892814\pi$
$500$	1.83764	−	16.2536i	0.0821819	−	0.726884i
$501$	−8.96553	−	33.4598i	−0.400550	−	1.49487i
$502$	4.20095	−	1.46907i	0.187498	−	0.0655680i
$503$		−	27.6867i		−	1.23449i	−0.786772	−	0.617243i	$-0.788249\pi$
$503$		−	27.6867i		−	1.23449i	0.786772	−	0.617243i	$-0.211751\pi$
$504$		0			0
$505$		−	4.24323i		−	0.188821i
$506$	−18.8102	−	53.7896i	−0.836216	−	2.39124i
$507$	−2.25655	−	8.42156i	−0.100217	−	0.374015i
$508$	−6.92518	−	8.69073i	−0.307255	−	0.385589i
$509$	−8.79130	+	32.8096i	−0.389667	+	1.45426i	0.441009	+	0.897503i	$0.354621\pi$
$509$	−8.79130	+	32.8096i	−0.389667	+	1.45426i	−0.830676	+	0.556756i	$0.812046\pi$
$510$	9.38721	−	6.39746i	0.415673	−	0.283284i
$511$		0			0
$512$	14.0775	+	17.7151i	0.622142	+	0.782904i
$513$	6.21267	+	10.7607i	0.274296	+	0.475095i
$514$	−0.296665	−	3.96891i	−0.0130853	−	0.175061i
$515$	16.4844	−	4.41699i	0.726390	−	0.194636i
$516$	−58.4192	+	8.78240i	−2.57176	+	0.386624i
$517$	41.3836	−	41.3836i	1.82005	−	1.82005i
$518$		0			0
$519$			54.7336i			2.40254i
$520$	5.78423	−	5.36080i	0.253655	−	0.235087i
$521$	16.9294	+	9.77420i	0.741691	+	0.428216i	0.822684	−	0.568499i	$-0.192476\pi$
$521$	16.9294	+	9.77420i	0.741691	+	0.428216i	−0.0809928	+	0.996715i	$0.525809\pi$
$522$	11.0042	+	9.47351i	0.481639	+	0.414644i
$523$	9.83797	+	2.63608i	0.430184	+	0.115268i	0.467413	−	0.884039i	$-0.345186\pi$
$523$	9.83797	+	2.63608i	0.430184	+	0.115268i	−0.0372283	+	0.999307i	$0.511853\pi$
$524$	25.0758	−	10.9290i	1.09544	−	0.477437i
$525$		0			0
$526$	−6.79012	−	9.96337i	−0.296063	−	0.434424i
$527$	3.97399	+	6.88316i	0.173110	+	0.299835i
$528$	−55.9394	+	17.2081i	−2.43445	+	0.748888i
$529$	17.7847	−	30.8039i	0.773246	−	1.33930i
$530$	2.25839	−	4.68730i	0.0980981	−	0.203603i
$531$	−32.3027	−	32.3027i	−1.40182	−	1.40182i
$532$		0			0
$533$	17.2676	−	17.2676i	0.747944	−	0.747944i
$534$	−2.46864	+	0.863285i	−0.106829	+	0.0373580i
$535$	−2.68294	−	1.54899i	−0.115993	−	0.0669688i
$536$	1.72810	+	3.27427i	0.0746424	+	0.141427i
$537$	−3.32733	+	1.92103i	−0.143585	+	0.0828988i
$538$	−22.6330	−	4.28688i	−0.975777	−	0.184820i
$539$		0			0
$540$	7.91320	+	3.10920i	0.340530	+	0.133799i
$541$	−0.575849	+	2.14910i	−0.0247577	+	0.0923970i	−0.977199	−	0.212324i	$-0.931897\pi$
$541$	−0.575849	+	2.14910i	−0.0247577	+	0.0923970i	0.952442	+	0.304721i	$0.0985633\pi$
$542$	2.81852	+	37.7074i	0.121066	+	1.61967i
$543$	−31.4484	+	54.4703i	−1.34958	+	2.33754i
$544$	6.71188	+	17.1498i	0.287769	+	0.735293i
$545$	−3.07104			−0.131549
$546$		0			0
$547$	−6.76891	−	6.76891i	−0.289418	−	0.289418i	0.547432	−	0.836850i	$-0.315605\pi$
$547$	−6.76891	−	6.76891i	−0.289418	−	0.289418i	−0.836850	+	0.547432i	$0.815605\pi$
$548$	1.46451	+	9.74169i	0.0625607	+	0.416144i
$549$	−5.82957	−	21.7562i	−0.248800	−	0.928534i
$550$	−20.4603	+	23.7661i	−0.872430	+	1.01339i
$551$	4.88571	−	2.82076i	0.208138	−	0.120169i
$552$	−50.9162	−	32.0336i	−2.16714	−	1.36344i
$553$		0			0
$554$	3.37489	−	17.8181i	0.143385	−	0.757017i
$555$	4.24725	+	1.13805i	0.180286	+	0.0483074i
$556$	21.3148	+	2.40987i	0.903949	+	0.102201i
$557$	−4.53648	+	1.21555i	−0.192217	+	0.0515043i	−0.353643	−	0.935380i	$-0.615057\pi$
$557$	−4.53648	+	1.21555i	−0.192217	+	0.0515043i	0.161426	+	0.986885i	$0.448391\pi$
$558$	−7.07781	+	14.6900i	−0.299627	+	0.621878i
$559$	−33.3799			−1.41182
$560$		0			0
$561$	−47.6346			−2.01114
$562$	17.4391	−	36.1950i	0.735625	−	1.52679i
$563$	−25.6398	+	6.87017i	−1.08059	+	0.289543i	−0.754837	−	0.655912i	$-0.772284\pi$
$563$	−25.6398	+	6.87017i	−1.08059	+	0.289543i	−0.325752	+	0.945455i	$0.605618\pi$
$564$	6.94092	−	61.3911i	0.292266	−	2.58503i
$565$	2.87421	+	0.770141i	0.120919	+	0.0324001i
$566$	1.98794	−	10.4955i	0.0835592	−	0.441159i
$567$		0			0
$568$	−33.4014	+	7.60348i	−1.40149	+	0.319035i
$569$	−20.3493	+	11.7487i	−0.853086	+	0.492530i	−0.861691	−	0.507433i	$-0.830594\pi$
$569$	−20.3493	+	11.7487i	−0.853086	+	0.492530i	0.00860467	+	0.999963i	$0.497261\pi$
$570$	5.90782	−	6.86235i	0.247451	−	0.287432i
$571$	9.13856	+	34.1056i	0.382437	+	1.42727i	0.842168	+	0.539215i	$0.181279\pi$
$571$	9.13856	+	34.1056i	0.382437	+	1.42727i	−0.459731	+	0.888058i	$0.652054\pi$
$572$	−32.7021	+	4.91624i	−1.36734	+	0.205558i
$573$	−4.93467	−	4.93467i	−0.206149	−	0.206149i
$574$		0			0
$575$	−32.2326			−1.34419
$576$	−21.3200	+	31.1937i	−0.888335	+	1.29974i
$577$	7.20904	−	12.4864i	0.300116	−	0.519817i	−0.676046	−	0.736860i	$-0.736308\pi$
$577$	7.20904	−	12.4864i	0.300116	−	0.519817i	0.976162	+	0.217043i	$0.0696412\pi$
$578$	−0.674764	−	9.02728i	−0.0280665	−	0.375485i
$579$	−7.26051	+	27.0966i	−0.301737	+	1.12610i
$580$	1.41168	−	3.59286i	0.0586169	−	0.149185i
$581$		0			0
$582$	32.2220	+	6.10312i	1.33565	+	0.252983i
$583$	−18.8944	+	10.9087i	−0.782524	+	0.451791i
$584$	5.35758	−	17.3335i	0.221698	−	0.717265i
$585$	11.4045	+	6.58440i	0.471519	+	0.272232i
$586$	16.3256	−	5.70906i	0.674403	−	0.235839i
$587$	−13.2110	+	13.2110i	−0.545276	+	0.545276i	−0.925071	−	0.379795i	$-0.875995\pi$
$587$	−13.2110	+	13.2110i	−0.545276	+	0.545276i	0.379795	+	0.925071i	$0.375995\pi$
$588$		0			0
$589$	4.47981	+	4.47981i	0.184587	+	0.184587i
$590$	−5.27156	+	10.9411i	−0.217027	+	0.450440i
$591$	−26.6496	+	46.1585i	−1.09622	+	1.89871i
$592$	−3.33573	+	6.29983i	−0.137098	+	0.258921i
$593$	−8.19296	−	14.1906i	−0.336445	−	0.582739i	0.647317	−	0.762221i	$-0.275891\pi$
$593$	−8.19296	−	14.1906i	−0.336445	−	0.582739i	−0.983761	+	0.179482i	$0.942558\pi$
$594$	−20.0775	−	29.4603i	−0.823788	−	1.20877i
$595$		0			0
$596$	3.04666	+	6.99032i	0.124796	+	0.286335i
$597$	15.0660	+	4.03691i	0.616609	+	0.165220i
$598$	−25.7590	−	22.1760i	−1.05336	−	0.906844i
$599$	29.4485	+	17.0021i	1.20323	+	0.694687i	0.961273	−	0.275599i	$-0.0888762\pi$
$599$	29.4485	+	17.0021i	1.20323	+	0.694687i	0.241961	+	0.970286i	$0.422210\pi$
$600$	−1.25684	+	33.0814i	−0.0513104	+	1.35054i
$601$		−	3.33457i		−	0.136020i	−0.997685	−	0.0680099i	$-0.978335\pi$
$601$		−	3.33457i		−	0.136020i	0.997685	−	0.0680099i	$-0.0216649\pi$
$602$		0			0
$603$	−4.37145	+	4.37145i	−0.178019	+	0.178019i
$604$	0.643494	+	4.28042i	0.0261834	+	0.174168i
$605$	−14.3394	+	3.84222i	−0.582978	+	0.156208i
$606$	1.40007	+	18.7308i	0.0568741	+	0.760886i
$607$	5.23683	+	9.07046i	0.212556	+	0.368159i	0.952514	−	0.304495i	$-0.0984877\pi$
$607$	5.23683	+	9.07046i	0.212556	+	0.368159i	−0.739957	+	0.672654i	$0.765154\pi$
$608$	8.70592	+	11.8198i	0.353072	+	0.479355i
$609$		0			0
$610$	−4.94814	+	3.37220i	−0.200344	+	0.136536i
$611$	9.03517	−	33.7197i	0.365524	−	1.36415i
$612$	−24.0502	+	19.1643i	−0.972172	+	0.774673i
$613$	−3.29334	−	12.2909i	−0.133017	−	0.496425i	0.866982	−	0.498340i	$-0.166057\pi$
$613$	−3.29334	−	12.2909i	−0.133017	−	0.496425i	−0.999998	+	0.00191560i	$0.999390\pi$
$614$	−15.1635	−	43.3613i	−0.611948	−	1.74992i
$615$		−	19.1857i		−	0.773643i
$616$		0			0
$617$			2.93899i			0.118319i	0.998249	+	0.0591597i	$0.0188421\pi$
$617$			2.93899i			0.118319i	−0.998249	+	0.0591597i	$0.981158\pi$
$618$	−71.3094	+	24.9369i	−2.86848	+	1.00311i
$619$	2.65281	+	9.90042i	0.106625	+	0.397932i	0.998525	−	0.0543029i	$-0.0172937\pi$
$619$	2.65281	+	9.90042i	0.106625	+	0.397932i	−0.891899	+	0.452235i	$0.850627\pi$
$620$	4.30759	+	0.487019i	0.172997	+	0.0195592i
$621$	9.48400	−	35.3948i	0.380580	−	1.42034i
$622$	21.1419	+	31.0222i	0.847711	+	1.24388i
$623$		0			0
$624$	−23.7644	+	25.5726i	−0.951336	+	1.02372i
$625$	6.89868	+	11.9489i	0.275947	+	0.477954i
$626$	28.4670	−	2.12783i	1.13777	−	0.0850452i
$627$	−36.6762	+	9.82735i	−1.46470	+	0.392466i
$628$	−8.96995	−	6.62543i	−0.357940	−	0.264383i
$629$	−4.10253	+	4.10253i	−0.163579	+	0.163579i
$630$		0			0
$631$			9.59471i			0.381959i	0.981594	+	0.190980i	$0.0611665\pi$
$631$			9.59471i			0.381959i	−0.981594	+	0.190980i	$0.938834\pi$
$632$	15.1076	−	14.0016i	0.600947	−	0.556955i
$633$	13.1387	+	7.58562i	0.522216	+	0.301501i
$634$	1.21369	−	1.40978i	0.0482016	−	0.0559896i
$635$	−4.76498	−	1.27677i	−0.189092	−	0.0506672i
$636$	−8.42256	+	21.4362i	−0.333976	+	0.850000i
$637$		0			0
$638$	−13.3760	+	9.11585i	−0.529561	+	0.360900i
$639$	−28.6005	−	49.5374i	−1.13142	−	1.95967i
$640$	9.69905	+	2.61279i	0.383389	+	0.103279i
$641$	7.91443	−	13.7082i	0.312601	−	0.541441i	−0.666324	−	0.745663i	$-0.732133\pi$
$641$	7.91443	−	13.7082i	0.312601	−	0.541441i	0.978925	+	0.204222i	$0.0654664\pi$
$642$	12.3543	+	5.95244i	0.487586	+	0.234924i
$643$	10.3033	+	10.3033i	0.406321	+	0.406321i	0.880454	−	0.474132i	$-0.157238\pi$
$643$	10.3033	+	10.3033i	0.406321	+	0.406321i	−0.474132	+	0.880454i	$0.657238\pi$
$644$		0			0
$645$	−18.5439	+	18.5439i	−0.730164	+	0.730164i
$646$	3.94401	+	11.2783i	0.155175	+	0.443737i
$647$	−9.11681	−	5.26359i	−0.358419	−	0.206933i	0.309968	−	0.950747i	$-0.399682\pi$
$647$	−9.11681	−	5.26359i	−0.358419	−	0.206933i	−0.668387	+	0.743814i	$0.733015\pi$
$648$	2.33123	+	0.720557i	0.0915795	+	0.0283061i
$649$	44.1035	−	25.4631i	1.73121	−	0.999516i
$650$	−3.48112	+	18.3789i	−0.136541	+	0.720880i
$651$		0			0
$652$	−21.3500	+	9.30518i	−0.836130	+	0.364419i
$653$	8.64357	−	32.2582i	0.338249	−	1.26236i	−0.562054	−	0.827100i	$-0.689989\pi$
$653$	8.64357	−	32.2582i	0.338249	−	1.26236i	0.900304	−	0.435263i	$-0.143344\pi$
$654$	13.5564	−	1.01330i	0.530098	−	0.0396233i
$655$	6.07151	−	10.5162i	0.237233	−	0.410900i
$656$	30.3184	+	6.94441i	1.18374	+	0.271134i
$657$	30.2947			1.18191
$658$		0			0
$659$	−14.9087	−	14.9087i	−0.580759	−	0.580759i	0.354353	−	0.935112i	$-0.384701\pi$
$659$	−14.9087	−	14.9087i	−0.580759	−	0.580759i	−0.935112	+	0.354353i	$0.884701\pi$
$660$	−15.4361	+	20.8985i	−0.600851	+	0.813472i
$661$	8.12957	+	30.3400i	0.316204	+	1.18009i	0.922864	+	0.385126i	$0.125842\pi$
$661$	8.12957	+	30.3400i	0.316204	+	1.18009i	−0.606660	+	0.794961i	$0.707491\pi$
$662$	15.8259	+	13.6245i	0.615089	+	0.529532i
$663$	−24.6065	+	14.2066i	−0.955639	+	0.551739i
$664$	−4.18572	+	6.65306i	−0.162438	+	0.258189i
$665$		0			0
$666$	−11.6952	−	2.21518i	−0.453181	−	0.0858364i
$667$	−16.0704	−	4.30606i	−0.622249	−	0.166731i
$668$	19.4968	−	15.5360i	0.754355	−	0.601106i
$669$	−33.6474	+	9.01579i	−1.30088	+	0.348571i
$670$	1.48064	+	0.713389i	0.0572022	+	0.0275606i
$671$	25.1090			0.969321
$672$		0			0
$673$	45.9274			1.77037			0.885186	−	0.465237i	$-0.154031\pi$
$673$	45.9274			1.77037			0.885186	+	0.465237i	$0.154031\pi$
$674$	35.1907	+	16.9552i	1.35549	+	0.653091i
$675$	−19.4789	+	5.21936i	−0.749744	+	0.200893i
$676$	4.90720	−	3.91029i	0.188738	−	0.150396i
$677$	−42.3069	−	11.3361i	−1.62599	−	0.435682i	−0.673234	−	0.739430i	$-0.735095\pi$
$677$	−42.3069	−	11.3361i	−1.62599	−	0.435682i	−0.952752	+	0.303748i	$0.901762\pi$
$678$	−12.9417	−	2.45126i	−0.497021	−	0.0941400i
$679$		0			0
$680$	6.91987	+	4.35359i	0.265365	+	0.166953i
$681$	53.4510	−	30.8600i	2.04825	−	1.18256i
$682$	−13.7760	−	11.8598i	−0.527510	−	0.454135i
$683$	−4.61649	−	17.2290i	−0.176645	−	0.659248i	−0.996266	−	0.0863413i	$-0.972482\pi$
$683$	−4.61649	−	17.2290i	−0.176645	−	0.659248i	0.819621	−	0.572907i	$-0.194184\pi$
$684$	−14.5637	+	19.7173i	−0.556855	+	0.753908i
$685$	3.09228	+	3.09228i	0.118150	+	0.118150i
$686$		0			0
$687$	−28.6706			−1.09385
$688$	−22.5920	−	36.0162i	−0.861313	−	1.37310i
$689$	−6.50682	+	11.2701i	−0.247890	+	0.429358i
$690$	−26.6298	+	1.99050i	−1.01378	+	0.0757771i
$691$	8.45153	−	31.5415i	0.321511	−	1.19990i	−0.596262	−	0.802790i	$-0.703348\pi$
$691$	8.45153	−	31.5415i	0.321511	−	1.19990i	0.917773	−	0.397106i	$-0.129985\pi$
$692$	−36.1100	+	15.7382i	−1.37269	+	0.598275i
$693$		0			0
$694$	3.10920	−	16.4153i	0.118024	−	0.623117i
$695$	8.24664	−	4.76120i	0.312813	−	0.180603i
$696$	−5.04607	+	16.3257i	−0.191271	+	0.618823i
$697$	21.9236	+	12.6576i	0.830416	+	0.479441i
$698$	5.26629	+	15.0594i	0.199332	+	0.570008i
$699$	−0.358977	+	0.358977i	−0.0135778	+	0.0135778i
$700$		0			0
$701$	23.1180	+	23.1180i	0.873153	+	0.873153i	0.992815	−	0.119662i	$-0.0381810\pi$
$701$	23.1180	+	23.1180i	0.873153	+	0.873153i	−0.119662	+	0.992815i	$0.538181\pi$
$702$	−19.1577	−	9.23036i	−0.723059	−	0.348378i
$703$	−2.31235	+	4.00511i	−0.0872121	+	0.151056i
$704$	−27.4378	−	31.9575i	−1.03410	−	1.20444i
$705$	−13.7133	−	23.7521i	−0.516471	−	0.894554i
$706$	−12.5771	+	8.57140i	−0.473346	+	0.322589i
$707$		0			0
$708$	19.6600	−	50.0366i	0.738870	−	1.88049i
$709$	40.4313	+	10.8335i	1.51843	+	0.406862i	0.919224	−	0.393734i	$-0.128817\pi$
$709$	40.4313	+	10.8335i	1.51843	+	0.406862i	0.599205	+	0.800596i	$0.295484\pi$
$710$	−9.92152	+	11.5246i	−0.372348	+	0.432509i
$711$	29.7870	+	17.1975i	1.11710	+	0.644957i
$712$	−1.27938	−	1.38043i	−0.0479468	−	0.0517339i
$713$		−	18.6836i		−	0.699707i
$714$		0			0
$715$	−10.3805	+	10.3805i	−0.388210	+	0.388210i
$716$	−2.22413	−	1.64280i	−0.0831196	−	0.0613942i
$717$	0.700843	−	0.187790i	0.0261735	−	0.00701316i
$718$	−25.3462	+	1.89456i	−0.945913	+	0.0707043i
$719$	23.9987	+	41.5669i	0.894999	+	1.55018i	0.833806	+	0.552058i	$0.186157\pi$
$719$	23.9987	+	41.5669i	0.894999	+	1.55018i	0.0611931	+	0.998126i	$0.480509\pi$
$720$	0.614326	+	16.7617i	0.0228946	+	0.624670i
$721$		0			0
$722$	−9.76873	−	14.3340i	−0.363555	−	0.533456i
$723$	−5.41621	+	20.2136i	−0.201431	+	0.751751i
$724$	−44.9790	−	5.08536i	−1.67163	−	0.188996i
$725$	2.36977	+	8.84409i	0.0880109	+	0.328461i
$726$	62.0301	−	21.6920i	2.30215	−	0.805064i
$727$			35.3027i			1.30931i	0.755930	+	0.654653i	$0.227185\pi$
$727$			35.3027i			1.30931i	−0.755930	+	0.654653i	$0.772815\pi$
$728$		0			0
$729$			43.9928i			1.62936i
$730$	−2.65858	−	7.60245i	−0.0983984	−	0.281379i
$731$	−8.95601	−	33.4243i	−0.331250	−	1.23624i
$732$	20.7298	−	16.5185i	0.766195	−	0.610541i
$733$	−2.32031	+	8.65952i	−0.0857026	+	0.319847i	−0.995446	−	0.0953238i	$-0.969611\pi$
$733$	−2.32031	+	8.65952i	−0.0857026	+	0.319847i	0.909744	+	0.415170i	$0.136278\pi$
$734$	−19.5267	+	13.3076i	−0.720744	+	0.491193i
$735$		0			0
$736$	6.49334	−	42.8025i	0.239348	−	1.57772i
$737$	−3.44587	−	5.96842i	−0.126930	−	0.219850i
$738$	3.87135	+	51.7926i	0.142506	+	1.90651i
$739$	−1.14785	+	0.307565i	−0.0422243	+	0.0113140i	−0.279869	−	0.960038i	$-0.590291\pi$
$739$	−1.14785	+	0.307565i	−0.0422243	+	0.0113140i	0.237645	+	0.971352i	$0.423624\pi$
$740$	0.470443	+	3.12932i	0.0172938	+	0.115036i
$741$	−16.0148	+	16.0148i	−0.588319	+	0.588319i
$742$		0			0
$743$		−	46.9253i		−	1.72152i	−0.509008	−	0.860762i	$-0.669988\pi$
$743$		−	46.9253i		−	1.72152i	0.509008	−	0.860762i	$-0.330012\pi$
$744$	−19.1756	−	0.728527i	−0.703011	−	0.0267091i
$745$	2.93157	+	1.69254i	0.107404	+	0.0620099i
$746$	−23.6124	−	20.3280i	−0.864513	−	0.744262i
$747$	−12.6779	−	3.39703i	−0.463860	−	0.124291i
$748$	−13.6969	−	31.4265i	−0.500809	−	1.14907i
$749$		0			0
$750$	18.1016	+	26.5611i	0.660978	+	0.969875i
$751$	5.75909	+	9.97504i	0.210152	+	0.363995i	0.951762	−	0.306837i	$-0.0992707\pi$
$751$	5.75909	+	9.97504i	0.210152	+	0.363995i	−0.741610	+	0.670832i	$0.765937\pi$
$752$	42.4980	−	13.0733i	1.54974	−	0.476733i
$753$	−4.37267	+	7.57369i	−0.159349	+	0.276000i
$754$	−4.19090	+	8.69823i	−0.152623	+	0.316771i
$755$	1.35872	+	1.35872i	0.0494491	+	0.0494491i
$756$		0			0
$757$	−14.6371	+	14.6371i	−0.531994	+	0.531994i	−0.921165	−	0.389172i	$-0.872761\pi$
$757$	−14.6371	+	14.6371i	−0.531994	+	0.531994i	0.389172	+	0.921165i	$0.372761\pi$
$758$	−44.6225	+	15.6045i	−1.62076	+	0.566781i
$759$	96.9745	+	55.9882i	3.51995	+	2.03224i
$760$	6.22611	+	1.92442i	0.225845	+	0.0698060i
$761$	−5.84549	+	3.37489i	−0.211899	+	0.122340i	−0.602194	−	0.798350i	$-0.705706\pi$
$761$	−5.84549	+	3.37489i	−0.211899	+	0.122340i	0.390295	+	0.920690i	$0.372373\pi$
$762$	21.4552	+	4.06380i	0.777240	+	0.147216i
$763$		0			0
$764$	1.83668	−	4.67452i	0.0664488	−	0.169118i
$765$	−3.53326	+	13.1863i	−0.127745	+	0.476753i
$766$	1.03657	+	13.8677i	0.0374528	+	0.501060i
$767$	15.1883	−	26.3069i	0.548418	−	0.949887i
$768$	−43.6764	−	8.33332i	−1.57604	−	0.300703i
$769$	−2.23508			−0.0805990			−0.0402995	−	0.999188i	$-0.512831\pi$
$769$	−2.23508			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$770$		0			0
$771$	5.53022	+	5.53022i	0.199166	+	0.199166i
$772$	−19.9644	+	3.00134i	−0.718535	+	0.108020i
$773$	6.08368	+	22.7046i	0.218815	+	0.816627i	0.984789	+	0.173756i	$0.0555904\pi$
$773$	6.08368	+	22.7046i	0.218815	+	0.816627i	−0.765974	+	0.642871i	$0.777743\pi$
$774$	46.3180	−	53.8016i	1.66487	−	1.93386i
$775$	−8.90466	+	5.14111i	−0.319865	+	0.184674i
$776$	5.23868	+	23.0131i	0.188058	+	0.826121i
$777$		0			0
$778$	3.85191	−	20.3365i	0.138098	−	0.729099i
$779$	19.4914	+	5.22270i	0.698351	+	0.187123i
$780$	−1.74104	+	15.3992i	−0.0623393	+	0.551379i
$781$	61.5935	−	16.5039i	2.20399	−	0.590557i
$782$	15.2942	−	31.7432i	0.546920	−	1.13514i
$783$	−10.4090			−0.371987
$784$		0			0
$785$	−4.95040			−0.176688
$786$	−23.3315	+	48.4246i	−0.832206	+	1.72725i
$787$	−5.48157	+	1.46878i	−0.195397	+	0.0523564i	−0.355190	−	0.934794i	$-0.615584\pi$
$787$	−5.48157	+	1.46878i	−0.195397	+	0.0523564i	0.159793	+	0.987150i	$0.448917\pi$
$788$	−38.1155	−	4.30936i	−1.35781	−	0.153515i
$789$	22.8857	+	6.13220i	0.814752	+	0.218312i
$790$	1.70169	−	8.98424i	0.0605435	−	0.319645i
$791$		0			0
$792$	37.4535	−	59.5309i	1.33085	−	2.11534i
$793$	12.9705	−	7.48852i	0.460596	−	0.265925i
$794$	−23.5584	+	27.3648i	−0.836058	+	0.971141i
$795$	2.64621	+	9.87581i	0.0938516	+	0.350259i
$796$	1.66877	+	11.1004i	0.0591480	+	0.393444i
$797$	26.5404	+	26.5404i	0.940110	+	0.940110i	0.998305	−	0.0581955i	$-0.0185347\pi$
$797$	26.5404	+	26.5404i	0.940110	+	0.940110i	−0.0581955	+	0.998305i	$0.518535\pi$
$798$		0			0
$799$	36.1888			1.28027
$800$	−22.1865	+	8.68308i	−0.784412	+	0.306993i
$801$	1.57140	−	2.72174i	0.0555226	−	0.0961681i
$802$	1.98247	+	26.5223i	0.0700034	+	0.936536i
$803$	−8.74080	+	32.6211i	−0.308456	+	1.15117i
$804$	−6.77135	−	2.66055i	−0.238807	−	0.0938304i
$805$		0			0
$806$	−10.6533	−	2.01783i	−0.375247	−	0.0710749i
$807$	39.2015	−	22.6330i	1.37996	−	0.796718i
$808$	−11.9549	+	6.30956i	−0.420571	+	0.221969i
$809$	−5.44560	−	3.14402i	−0.191457	−	0.110538i	0.401207	−	0.915987i	$-0.368591\pi$
$809$	−5.44560	−	3.14402i	−0.191457	−	0.110538i	−0.592665	+	0.805449i	$0.701924\pi$
$810$	1.02248	−	0.357560i	0.0359261	−	0.0125634i
$811$	28.2328	−	28.2328i	0.991388	−	0.991388i	−0.00857565	−	0.999963i	$-0.502730\pi$
$811$	28.2328	−	28.2328i	0.991388	−	0.991388i	0.999963	+	0.00857565i	$0.00272975\pi$
$812$		0			0
$813$	−52.5409	−	52.5409i	−1.84269	−	1.84269i
$814$	5.75967	−	11.9542i	0.201876	−	0.418995i
$815$	−5.16940	+	8.95366i	−0.181076	+	0.313633i
$816$	−31.9827	−	16.9347i	−1.11962	−	0.592833i
$817$	−13.7913	−	23.8873i	−0.482497	−	0.835709i
$818$	23.5805	+	34.6005i	0.824472	+	1.20978i
$819$		0			0
$820$	12.6576	−	5.51669i	0.442023	−	0.192651i
$821$	16.3630	+	4.38445i	0.571072	+	0.153018i	0.532788	−	0.846249i	$-0.321144\pi$
$821$	16.3630	+	4.38445i	0.571072	+	0.153018i	0.0382839	+	0.999267i	$0.487811\pi$
$822$	−14.6705	−	12.6299i	−0.511692	−	0.440517i
$823$	−32.3363	−	18.6694i	−1.12717	−	0.650774i	−0.183951	−	0.982935i	$-0.558889\pi$
$823$	−32.3363	−	18.6694i	−1.12717	−	0.650774i	−0.943223	+	0.332162i	$0.892222\pi$
$824$	−36.9563	−	39.8753i	−1.28743	−	1.38912i
$825$		−	61.6244i		−	2.14549i
$826$		0			0
$827$	−5.32642	+	5.32642i	−0.185218	+	0.185218i	−0.793625	−	0.608407i	$-0.791809\pi$
$827$	−5.32642	+	5.32642i	−0.185218	+	0.185218i	0.608407	+	0.793625i	$0.291809\pi$
$828$	71.4865	−	10.7469i	2.48433	−	0.373480i
$829$	7.89725	−	2.11606i	0.274283	−	0.0734939i	−0.119056	−	0.992888i	$-0.537987\pi$
$829$	7.89725	−	2.11606i	0.274283	−	0.0734939i	0.393339	+	0.919394i	$0.371320\pi$
$830$	0.260092	+	3.47963i	0.00902794	+	0.120780i
$831$	17.8181	+	30.8618i	0.618102	+	1.07058i
$832$	−23.7045	−	8.32514i	−0.821806	−	0.288622i
$833$		0			0
$834$	−34.8320	+	23.7383i	−1.20613	+	0.821989i
$835$	2.86432	−	10.6898i	0.0991239	−	0.369935i
$836$	−17.0294	−	21.3710i	−0.588975	−	0.739131i
$837$	−3.02540	−	11.2909i	−0.104573	−	0.390272i
$838$	−0.760736	−	2.17539i	−0.0262792	−	0.0751477i
$839$		−	7.20540i		−	0.248758i	−0.992235	−	0.124379i	$-0.960306\pi$
$839$		−	7.20540i		−	0.248758i	0.992235	−	0.124379i	$-0.0396939\pi$
$840$		0			0
$841$		−	24.2740i		−	0.837033i
$842$	−37.2434	+	13.0240i	−1.28349	+	0.448837i
$843$	20.4339	+	76.2603i	0.703780	+	2.62654i
$844$	−1.22663	+	10.8493i	−0.0422223	+	0.373448i
$845$	0.720926	−	2.69053i	0.0248006	−	0.0925571i
$846$	41.8122	+	61.3524i	1.43753	+	2.10934i
$847$		0			0
$848$	−16.5642	+	0.607087i	−0.568816	+	0.0208475i
$849$	10.4955	+	18.1787i	0.360205	+	0.623893i
$850$	−19.3374	+	1.44541i	−0.663266	+	0.0495772i
$851$	13.1739	−	3.52994i	0.451596	−	0.121005i
$852$	39.9938	−	54.1462i	1.37016	−	1.85502i
$853$	−13.0316	+	13.0316i	−0.446192	+	0.446192i	−0.894086	−	0.447894i	$-0.852174\pi$
$853$	−13.0316	+	13.0316i	−0.446192	+	0.446192i	0.447894	+	0.894086i	$0.352174\pi$
$854$		0			0
$855$			10.8817i			0.372147i
$856$	−0.374690	+	9.86222i	−0.0128066	+	0.337084i
$857$	11.8030	+	6.81447i	0.403183	+	0.232778i	0.687856	−	0.725847i	$-0.258552\pi$
$857$	11.8030	+	6.81447i	0.403183	+	0.232778i	−0.284674	+	0.958625i	$0.591885\pi$
$858$	42.3975	−	49.2477i	1.44743	−	1.68129i
$859$	43.5800	+	11.6772i	1.48693	+	0.398422i	0.908699	−	0.417451i	$-0.137077\pi$
$859$	43.5800	+	11.6772i	1.48693	+	0.398422i	0.578231	+	0.815873i	$0.303743\pi$
$860$	−17.5663	−	6.90201i	−0.599005	−	0.235357i
$861$		0			0
$862$	23.8353	−	16.2440i	0.811835	−	0.553272i
$863$	25.5923	+	44.3271i	0.871171	+	1.50891i	0.860786	+	0.508966i	$0.169972\pi$
$863$	25.5923	+	44.3271i	0.871171	+	1.50891i	0.0103847	+	0.999946i	$0.496694\pi$
$864$	−3.00684	−	26.9180i	−0.102295	−	0.915768i
$865$	−8.74318	+	15.1436i	−0.297277	+	0.514899i
$866$	−36.0691	−	17.3784i	−1.22568	−	0.590544i
$867$	12.5785	+	12.5785i	0.427188	+	0.427188i
$868$		0			0
$869$	−27.1125	+	27.1125i	−0.919727	+	0.919727i
$870$	2.50400	+	7.16042i	0.0848936	+	0.242761i
$871$	−3.56006	−	2.05540i	−0.120628	−	0.0696445i
$872$	4.56655	+	8.65235i	0.154643	+	0.293006i
$873$	−34.1305	+	19.7053i	−1.15514	+	0.666922i
$874$	5.22690	−	27.5959i	0.176802	−	0.933445i
$875$		0			0
$876$	14.2442	+	32.6821i	0.481266	+	1.10423i
$877$	7.83642	−	29.2459i	0.264617	−	0.987564i	−0.697867	−	0.716227i	$-0.745867\pi$
$877$	7.83642	−	29.2459i	0.264617	−	0.987564i	0.962484	−	0.271337i	$-0.0874659\pi$
$878$	6.44823	−	0.481987i	0.217617	−	0.0162663i
$879$	−16.9929	+	29.4326i	−0.573156	+	0.992735i
$880$	−18.2261	−	4.17467i	−0.614402	−	0.140728i
$881$	29.7369			1.00186			0.500930	−	0.865488i	$-0.332991\pi$
$881$	29.7369			1.00186			0.500930	+	0.865488i	$0.332991\pi$
$882$		0			0
$883$	14.3040	+	14.3040i	0.481368	+	0.481368i	0.905568	−	0.424200i	$-0.139445\pi$
$883$	14.3040	+	14.3040i	0.481368	+	0.481368i	−0.424200	+	0.905568i	$0.639445\pi$
$884$	−16.4481	−	12.1490i	−0.553208	−	0.408614i
$885$	−6.17683	−	23.0522i	−0.207632	−	0.774893i
$886$	10.8125	+	9.30853i	0.363254	+	0.312726i
$887$	49.1086	−	28.3528i	1.64890	−	0.951995i	0.671395	−	0.741099i	$-0.265695\pi$
$887$	49.1086	−	28.3528i	1.64890	−	0.951995i	0.977509	−	0.210896i	$-0.0676381\pi$
$888$	−3.10920	−	13.6584i	−0.104338	−	0.458347i
$889$		0			0
$890$	−0.820923	−	0.155490i	−0.0275174	−	0.00521203i
$891$	−4.38731	−	1.17558i	−0.146980	−	0.0393833i
$892$	−15.6231	−	19.6061i	−0.523100	−	0.656462i
$893$	27.8634	−	7.46599i	0.932415	−	0.249840i
$894$	−13.4992	−	6.50406i	−0.451481	−	0.217528i
$895$	−1.22747			−0.0410298
$896$		0			0
$897$	66.7919			2.23012
$898$	−16.6512	−	8.02271i	−0.555657	−	0.267721i
$899$	−5.12646	+	1.37363i	−0.170977	+	0.0458132i
$900$	−24.7927	−	31.1135i	−0.826423	−	1.03712i
$901$	−13.0309	−	3.49163i	−0.434124	−	0.116323i
$902$	−56.8869	−	10.7749i	−1.89413	−	0.358763i
$903$		0			0
$904$	−2.10406	−	9.24297i	−0.0699802	−	0.307417i
$905$	−17.4022	+	10.0472i	−0.578470	+	0.333980i
$906$	−6.44610	−	5.54947i	−0.214157	−	0.184369i
$907$	−5.58142	−	20.8301i	−0.185328	−	0.691653i	−0.994560	−	0.104164i	$-0.966783\pi$
$907$	−5.58142	−	20.8301i	−0.185328	−	0.691653i	0.809232	−	0.587489i	$-0.199883\pi$
$908$	35.7290	+	26.3903i	1.18571	+	0.875793i
$909$	−15.9609	−	15.9609i	−0.529389	−	0.529389i
$910$		0			0
$911$	−7.88055			−0.261094			−0.130547	−	0.991442i	$-0.541673\pi$
$911$	−7.88055			−0.261094			−0.130547	+	0.991442i	$0.541673\pi$
$912$	−28.1188	−	6.44058i	−0.931105	−	0.213269i
$913$	7.31580	−	12.6713i	0.242118	−	0.419360i
$914$	45.0044	−	3.36395i	1.48861	−	0.111270i
$915$	3.04546	−	11.3658i	0.100680	−	0.375742i
$916$	−8.24398	−	18.9151i	−0.272389	−	0.624974i
$917$		0			0
$918$	4.10253	−	21.6597i	0.135404	−	0.714877i
$919$	−1.83468	+	1.05925i	−0.0605206	+	0.0349416i	−0.529955	−	0.848026i	$-0.677791\pi$
$919$	−1.83468	+	1.05925i	−0.0605206	+	0.0349416i	0.469434	+	0.882967i	$0.344458\pi$
$920$	−8.97039	−	16.9964i	−0.295745	−	0.560355i
$921$	78.1739	+	45.1337i	2.57592	+	1.48721i
$922$	7.45220	+	21.3102i	0.245425	+	0.701816i
$923$	26.8951	−	26.8951i	0.885264	−	0.885264i
$924$		0			0
$925$	−5.30740	−	5.30740i	−0.174506	−	0.174506i
$926$	26.8066	+	12.9157i	0.880921	+	0.424437i
$927$	45.3916	−	78.6205i	1.49085	−	2.58224i
$928$	−12.2217	+	1.36521i	−0.401196	+	0.0448151i
$929$	16.1033	+	27.8918i	0.528333	+	0.915099i	0.999454	+	0.0330307i	$0.0105159\pi$
$929$	16.1033	+	27.8918i	0.528333	+	0.915099i	−0.471122	+	0.882068i	$0.656151\pi$
$930$	−7.03932	+	4.79736i	−0.230829	+	0.157312i
$931$		0			0
$932$	−0.340053	−	0.133611i	−0.0111388	−	0.00437658i
$933$	−71.2574	−	19.0934i	−2.33286	−	0.625088i
$934$	8.81460	−	10.2388i	0.288422	−	0.335023i
$935$	−13.1795	−	7.60919i	−0.431016	−	0.248847i
$936$	1.59272	−	41.9219i	0.0520596	−	1.37026i
$937$			17.8409i			0.582836i	0.956596	+	0.291418i	$0.0941271\pi$
$937$			17.8409i			0.582836i	−0.956596	+	0.291418i	$0.905873\pi$
$938$		0			0
$939$	−39.6655	+	39.6655i	−1.29444	+	1.29444i
$940$	11.7271	−	15.8769i	0.382495	−	0.517847i
$941$	27.3429	−	7.32652i	0.891354	−	0.238838i	0.216055	−	0.976381i	$-0.430681\pi$
$941$	27.3429	−	7.32652i	0.891354	−	0.238838i	0.675300	+	0.737544i	$0.264014\pi$
$942$	21.8525	−	1.63341i	0.711992	−	0.0532193i
$943$	−29.7547	−	51.5366i	−0.968946	−	1.67826i
$944$	38.6643	−	1.41707i	1.25842	−	0.0461217i
$945$		0			0
$946$	44.5693	+	65.3981i	1.44907	+	2.12627i
$947$	6.15356	−	22.9654i	0.199964	−	0.746275i	−0.790962	−	0.611865i	$-0.790419\pi$
$947$	6.15356	−	22.9654i	0.199964	−	0.746275i	0.990926	−	0.134410i	$-0.0429138\pi$
$948$	−4.54735	+	40.2204i	−0.147691	+	1.30630i
$949$	5.21373	+	19.4579i	0.169245	+	0.631630i
$950$	−14.5905	+	5.10232i	−0.473380	+	0.165541i
$951$			3.65550i			0.118538i
$952$		0			0
$953$			30.3038i			0.981636i	0.871262	+	0.490818i	$0.163302\pi$
$953$			30.3038i			0.981636i	−0.871262	+	0.490818i	$0.836698\pi$
$954$	−9.13632	−	26.1261i	−0.295799	−	0.845865i
$955$	−0.577052	−	2.15359i	−0.0186730	−	0.0696884i
$956$	0.325414	+	0.408377i	0.0105247	+	0.0132079i
$957$	8.23259	−	30.7244i	0.266122	−	0.993180i
$958$	−12.3089	+	8.38862i	−0.397683	+	0.271024i
$959$		0			0
$960$	−17.7938	+	8.54386i	−0.574291	+	0.275752i
$961$	12.5200	+	21.6852i	0.403870	+	0.699523i
$962$	−0.589974	−	7.89294i	−0.0190215	−	0.254478i
$963$	−15.9184	+	4.26532i	−0.512962	+	0.137448i
$964$	−14.8931	+	2.23894i	−0.479674	+	0.0721115i
$965$	−6.33726	+	6.33726i	−0.204004	+	0.204004i
$966$		0			0
$967$		−	13.3675i		−	0.429869i	−0.976629	−	0.214934i	$-0.931046\pi$
$967$		−	13.3675i		−	0.429869i	0.976629	−	0.214934i	$-0.0689537\pi$
$968$	32.1473	+	34.6865i	1.03325	+	1.11487i
$969$	−20.3330	−	11.7393i	−0.653190	−	0.377119i
$970$	7.94024	+	6.83577i	0.254946	+	0.219483i
$971$	−12.7754	−	3.42316i	−0.409982	−	0.109854i	0.0479326	−	0.998851i	$-0.484737\pi$
$971$	−12.7754	−	3.42316i	−0.409982	−	0.109854i	−0.457914	+	0.888996i	$0.651403\pi$
$972$	−30.7313	+	13.3939i	−0.985706	+	0.429610i
$973$		0			0
$974$	2.75518	+	4.04277i	0.0882816	+	0.129539i
$975$	−18.3789	−	31.8332i	−0.588596	−	1.01948i
$976$	16.8586	+	8.92655i	0.539630	+	0.285732i
$977$	−26.6156	+	46.0996i	−0.851509	+	1.47486i	0.0283371	+	0.999598i	$0.490979\pi$
$977$	−26.6156	+	46.0996i	−0.851509	+	1.47486i	−0.879846	+	0.475259i	$0.842355\pi$
$978$	19.8648	−	41.2296i	0.635208	−	1.31838i
$979$	2.47736	+	2.47736i	0.0791769	+	0.0791769i
$980$		0			0
$981$	−11.5517	+	11.5517i	−0.368817	+	0.368817i
$982$	−0.673925	+	0.235672i	−0.0215058	+	0.00752059i
$983$	0.255896	+	0.147742i	0.00816182	+	0.00471223i	0.504075	−	0.863660i	$-0.331833\pi$
$983$	0.255896	+	0.147742i	0.00816182	+	0.00471223i	−0.495914	+	0.868372i	$0.665167\pi$
$984$	−54.0539	+	28.5286i	−1.72318	+	0.909459i
$985$	−14.7468	+	8.51406i	−0.469871	+	0.271280i
$986$	−9.83424	−	1.86269i	−0.313186	−	0.0593201i
$987$		0			0
$988$	−15.1706	−	5.96071i	−0.482640	−	0.189635i
$989$	−21.0532	+	78.5717i	−0.669453	+	2.49843i
$990$	−2.32728	−	31.1354i	−0.0739659	−	0.989548i
$991$	21.0182	−	36.4046i	0.667665	−	1.15643i	−0.310890	−	0.950446i	$-0.600627\pi$
$991$	21.0182	−	36.4046i	0.667665	−	1.15643i	0.978555	−	0.205985i	$-0.0660397\pi$
$992$	−5.03314	−	12.8604i	−0.159802	−	0.408318i
$993$	−41.0357			−1.30223
$994$		0			0
$995$	3.52358	+	3.52358i	0.111705	+	0.111705i
$996$	−2.29624	−	15.2742i	−0.0727592	−	0.483983i
$997$	−11.9231	−	44.4977i	−0.377609	−	1.40926i	−0.849495	−	0.527597i	$-0.823093\pi$
$997$	−11.9231	−	44.4977i	−0.377609	−	1.40926i	0.471885	−	0.881660i	$-0.343574\pi$
$998$	−21.2745	+	24.7119i	−0.673434	+	0.782241i
$999$	7.38970	−	4.26644i	0.233800	−	0.134984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.k.557.1		16
7.2	even	3	inner	784.2.x.k.765.3		16
7.3	odd	6		784.2.m.g.589.3		8
7.4	even	3		112.2.m.c.29.3	✓	8
7.5	odd	6		784.2.x.j.765.3		16
7.6	odd	2		784.2.x.j.557.1		16
16.5	even	4	inner	784.2.x.k.165.3		16
28.11	odd	6		448.2.m.c.337.4		8
56.11	odd	6		896.2.m.f.673.1		8
56.53	even	6		896.2.m.e.673.4		8
112.5	odd	12		784.2.x.j.373.1		16
112.11	odd	12		448.2.m.c.113.4		8
112.37	even	12	inner	784.2.x.k.373.1		16
112.53	even	12		112.2.m.c.85.3	yes	8
112.67	odd	12		896.2.m.f.225.1		8
112.69	odd	4		784.2.x.j.165.3		16
112.101	odd	12		784.2.m.g.197.3		8
112.109	even	12		896.2.m.e.225.4		8
224.11	odd	24		7168.2.a.bd.1.8		8
224.53	even	24		7168.2.a.bc.1.1		8
224.123	odd	24		7168.2.a.bd.1.1		8
224.165	even	24		7168.2.a.bc.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.3	✓	8	7.4	even	3
112.2.m.c.85.3	yes	8	112.53	even	12
448.2.m.c.113.4		8	112.11	odd	12
448.2.m.c.337.4		8	28.11	odd	6
784.2.m.g.197.3		8	112.101	odd	12
784.2.m.g.589.3		8	7.3	odd	6
784.2.x.j.165.3		16	112.69	odd	4
784.2.x.j.373.1		16	112.5	odd	12
784.2.x.j.557.1		16	7.6	odd	2
784.2.x.j.765.3		16	7.5	odd	6
784.2.x.k.165.3		16	16.5	even	4	inner
784.2.x.k.373.1		16	112.37	even	12	inner
784.2.x.k.557.1		16	1.1	even	1	trivial
784.2.x.k.765.3		16	7.2	even	3	inner
896.2.m.e.225.4		8	112.109	even	12
896.2.m.e.673.4		8	56.53	even	6
896.2.m.f.225.1		8	112.67	odd	12
896.2.m.f.673.1		8	56.11	odd	6
7168.2.a.bc.1.1		8	224.53	even	24
7168.2.a.bc.1.8		8	224.165	even	24
7168.2.a.bd.1.1		8	224.123	odd	24
7168.2.a.bd.1.8		8	224.11	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27404 - 0.613848i) q^{2} +(2.68432 - 0.719263i) q^{3} +(1.24638 + 1.56414i) q^{4} +(0.857592 + 0.229791i) q^{5} +(-3.86147 - 0.731395i) q^{6} +(-0.627801 - 2.75787i) q^{8} +(4.09018 - 2.36147i) q^{9} +O(q^{10})\)	\(q+(-1.27404 - 0.613848i) q^{2} +(2.68432 - 0.719263i) q^{3} +(1.24638 + 1.56414i) q^{4} +(0.857592 + 0.229791i) q^{5} +(-3.86147 - 0.731395i) q^{6} +(-0.627801 - 2.75787i) q^{8} +(4.09018 - 2.36147i) q^{9} +(-0.951553 - 0.819195i) q^{10} +(1.36269 + 5.08562i) q^{11} +(4.47072 + 3.30218i) q^{12} +(2.22066 + 2.22066i) q^{13} +2.46733 q^{15} +(-0.893069 + 3.89903i) q^{16} +(-1.62780 + 2.81943i) q^{17} +(-6.66066 + 0.497865i) q^{18} +(-0.671653 + 2.50664i) q^{19} +(0.709460 + 1.62780i) q^{20} +(1.38567 - 7.31580i) q^{22} +(6.62774 - 3.82653i) q^{23} +(-3.66886 - 6.95147i) q^{24} +(-3.64747 - 2.10587i) q^{25} +(-1.46607 - 4.19237i) q^{26} +(3.38567 - 3.38567i) q^{27} +(-1.53721 - 1.53721i) q^{29} +(-3.14349 - 1.51457i) q^{30} +(1.22066 - 2.11425i) q^{31} +(3.53122 - 4.41933i) q^{32} +(7.31580 + 12.6713i) q^{33} +(3.80460 - 2.59286i) q^{34} +(8.79159 + 3.45433i) q^{36} +(1.72139 + 0.461245i) q^{37} +(2.39441 - 2.78128i) q^{38} +(7.55822 + 4.36374i) q^{39} +(0.0953379 - 2.50939i) q^{40} -7.77589i q^{41} +(-7.51575 + 7.51575i) q^{43} +(-6.25620 + 8.47006i) q^{44} +(4.05035 - 1.08529i) q^{45} +(-10.7930 + 0.806742i) q^{46} +(-5.55792 - 9.62661i) q^{47} +(0.407138 + 11.1086i) q^{48} +(3.35436 + 4.92196i) q^{50} +(-2.34163 + 8.73909i) q^{51} +(-0.705636 + 6.24122i) q^{52} +(1.07250 + 4.00262i) q^{53} +(-6.39179 + 2.23521i) q^{54} +4.67452i q^{55} +7.21173i q^{57} +(1.01486 + 2.90209i) q^{58} +(-2.50344 - 9.34298i) q^{59} +(3.07524 + 3.85926i) q^{60} +(1.23431 - 4.60651i) q^{61} +(-2.85301 + 1.94435i) q^{62} +(-7.21173 + 3.46279i) q^{64} +(1.39413 + 2.41471i) q^{65} +(-1.54238 - 20.6346i) q^{66} +(-1.26436 + 0.338785i) q^{67} +(-6.43885 + 0.967979i) q^{68} +(15.0387 - 15.0387i) q^{69} -12.1113i q^{71} +(-9.08045 - 9.79767i) q^{72} +(5.55501 + 3.20719i) q^{73} +(-1.91000 - 1.64432i) q^{74} +(-11.3057 - 3.02934i) q^{75} +(-4.75787 + 2.07367i) q^{76} +(-6.95084 - 10.1992i) q^{78} +(3.64128 + 6.30687i) q^{79} +(-1.66185 + 3.13856i) q^{80} +(-0.431344 + 0.747110i) q^{81} +(-4.77322 + 9.90684i) q^{82} +(-1.96506 - 1.96506i) q^{83} +(-2.04387 + 2.04387i) q^{85} +(14.1889 - 4.96187i) q^{86} +(-5.23203 - 3.02071i) q^{87} +(13.1700 - 6.95088i) q^{88} +(0.576282 - 0.332717i) q^{89} +(-5.82653 - 1.10359i) q^{90} +(14.2459 + 5.59741i) q^{92} +(1.75595 - 6.55331i) q^{93} +(1.17177 + 15.6765i) q^{94} +(-1.15201 + 1.99533i) q^{95} +(6.30029 - 14.4028i) q^{96} -8.34450 q^{97} +(17.5832 + 17.5832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8	\( 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30} - 16 q^{31} + 28 q^{32} + 24 q^{33} - 24 q^{34} + 48 q^{36} - 16 q^{37} + 16 q^{38} - 28 q^{40} - 64 q^{43} + 32 q^{44} + 8 q^{45} - 20 q^{46} - 24 q^{47} + 40 q^{48} - 28 q^{50} - 8 q^{51} - 32 q^{52} + 8 q^{53} + 16 q^{54} - 12 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} + 40 q^{62} - 64 q^{64} + 48 q^{65} + 16 q^{66} - 28 q^{68} + 88 q^{69} - 44 q^{72} + 4 q^{74} - 28 q^{75} - 48 q^{76} + 24 q^{78} + 24 q^{79} + 12 q^{80} - 40 q^{81} - 4 q^{82} - 80 q^{85} + 40 q^{88} - 32 q^{90} + 72 q^{92} - 16 q^{93} - 28 q^{94} - 16 q^{95} - 8 q^{96} - 64 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

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