LMFDB - Embedded newform 784.2.x.j.373.1

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			373.1
Root			$-1.40526 - 0.158880i$ of defining polynomial
Character	$\chi$	$=$	784.373
Dual form			784.2.x.j.557.1

$q$-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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.27404	+	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	$-0.713022\pi$
$3$	−2.68432	−	0.719263i	−1.54980	−	0.415266i	−0.929415	+	0.369035i	$0.879688\pi$
$4$	1.24638	−	1.56414i	0.623190	−	0.782070i
$5$	−0.857592	+	0.229791i	−0.383527	+	0.102766i	−0.445431	−	0.895316i	$-0.646949\pi$
$5$	−0.857592	+	0.229791i	−0.383527	+	0.102766i	0.0619040	+	0.998082i	$0.480283\pi$
$6$	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	−0.382108	−	0.924118i	$-0.624802\pi$
$11$	1.36269	−	5.08562i	0.410866	−	1.53337i	0.792974	−	0.609256i	$-0.208532\pi$
$12$	−4.47072	+	3.30218i	−1.29059	+	0.953259i
$13$	−2.22066	+	2.22066i	−0.615901	+	0.615901i	−0.944477	−	0.328576i	$-0.893431\pi$
$13$	−2.22066	+	2.22066i	−0.615901	+	0.615901i	0.328576	+	0.944477i	$0.393431\pi$
$14$		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	$-0.0374807\pi$
$17$	1.62780	+	2.81943i	0.394800	+	0.683813i	−0.598276	+	0.801290i	$0.704147\pi$
$18$	−6.66066	−	0.497865i	−1.56993	−	0.117348i
$19$	0.671653	+	2.50664i	0.154088	+	0.575063i	0.999182	+	0.0404454i	$0.0128777\pi$
$19$	0.671653	+	2.50664i	0.154088	+	0.575063i	−0.845094	+	0.534618i	$0.820456\pi$
$20$	−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	0.992394	−	0.123103i	$-0.0392847\pi$
$23$	6.62774	+	3.82653i	1.38198	+	0.797887i	0.389586	+	0.920990i	$0.372618\pi$
$24$	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	−0.835279	−	0.549826i	$-0.814694\pi$
$29$	−1.53721	+	1.53721i	−0.285453	+	0.285453i	0.549826	+	0.835279i	$0.314694\pi$
$30$	−3.14349	+	1.51457i	−0.573921	+	0.276521i
$31$	−1.22066	−	2.11425i	−0.219238	−	0.379731i	0.735338	−	0.677701i	$-0.237024\pi$
$31$	−1.22066	−	2.11425i	−0.219238	−	0.379731i	−0.954575	+	0.297970i	$0.903690\pi$
$32$	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	−0.114530	−	0.993420i	$-0.536536\pi$
$37$	1.72139	−	0.461245i	0.282995	−	0.0758283i	0.397524	+	0.917592i	$0.369869\pi$
$38$	−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	−0.987305	−	0.158836i	$-0.949226\pi$
$43$	−7.51575	−	7.51575i	−1.14614	−	1.14614i	−0.158836	−	0.987305i	$-0.550774\pi$
$44$	−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	−0.101664	−	0.994819i	$-0.532417\pi$
$47$	5.55792	−	9.62661i	0.810707	−	1.40418i	0.912370	−	0.409366i	$-0.134250\pi$
$48$	−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	−0.852322	−	0.523017i	$-0.824806\pi$
$53$	1.07250	−	4.00262i	0.147319	−	0.549803i	0.999641	−	0.0267853i	$-0.00852703\pi$
$54$	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	−0.587463	−	0.809251i	$-0.699873\pi$
$59$	2.50344	−	9.34298i	0.325921	−	1.21635i	0.913383	−	0.407101i	$-0.133460\pi$
$60$	3.07524	−	3.85926i	0.397012	−	0.498228i
$61$	−1.23431	−	4.60651i	−0.158037	−	0.589803i	−0.998826	−	0.0484399i	$-0.984575\pi$
$61$	−1.23431	−	4.60651i	−0.158037	−	0.589803i	0.840789	−	0.541363i	$-0.182092\pi$
$62$	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	0.180757	−	0.983528i	$-0.442145\pi$
$67$	−1.26436	−	0.338785i	−0.154467	−	0.0413892i	−0.335224	+	0.942139i	$0.608812\pi$
$68$	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	$0.255250\pi$
$71$			12.1113i			1.43735i	−0.695348	+	0.718674i	$0.744750\pi$
$72$	−9.08045	+	9.79767i	−1.07014	+	1.15467i
$73$	−5.55501	+	3.20719i	−0.650165	+	0.375373i	−0.788519	−	0.615010i	$-0.789152\pi$
$73$	−5.55501	+	3.20719i	−0.650165	+	0.375373i	0.138354	+	0.990383i	$0.455819\pi$
$74$	−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	−0.585178	−	0.810905i	$-0.698975\pi$
$79$	3.64128	−	6.30687i	0.409675	−	0.709579i	0.994853	+	0.101326i	$0.0323086\pi$
$80$	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	$-0.701262\pi$
$83$	1.96506	−	1.96506i	0.215694	−	0.215694i	0.806681	+	0.590987i	$0.201262\pi$
$84$		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	$-0.344562\pi$
$89$	−0.576282	−	0.332717i	−0.0610858	−	0.0352679i	−0.530232	+	0.847853i	$0.677895\pi$
$90$	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	$-0.360756\pi$
$97$	8.34450			0.847256			0.423628	+	0.905836i	$0.360756\pi$
$98$		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	$-0.840248\pi$
$101$	1.23696	−	4.61640i	0.123082	−	0.459349i	0.999764	+	0.0217217i	$0.00691477\pi$
$102$	8.34782	+	9.69659i	0.826557	+	0.960105i
$103$	−16.6465	−	9.61088i	−1.64023	−	0.946988i	−0.980750	−	0.195268i	$-0.937442\pi$
$103$	−16.6465	−	9.61088i	−1.64023	−	0.946988i	−0.659482	−	0.751720i	$-0.729224\pi$
$104$	−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	−0.418028	−	0.908434i	$-0.637278\pi$
$107$	−3.37044	+	0.903107i	−0.325833	+	0.0873066i	0.0921947	+	0.995741i	$0.470612\pi$
$108$	−9.51551	+	1.07583i	−0.915630	+	0.103522i
$109$	−3.34112	−	0.895251i	−0.320021	−	0.0857495i	0.0952324	−	0.995455i	$-0.469641\pi$
$109$	−3.34112	−	0.895251i	−0.320021	−	0.0857495i	−0.415254	+	0.909706i	$0.636307\pi$
$110$	−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	−0.929199	−	0.369580i	$-0.879502\pi$
$131$	−3.53986	−	13.2109i	−0.309279	−	1.15425i	0.619920	−	0.784665i	$-0.287165\pi$
$132$	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	−0.306586	−	0.951843i	$-0.599187\pi$
$137$	4.26568	−	2.46279i	0.364441	−	0.210410i	0.671027	+	0.741433i	$0.265853\pi$
$138$	28.3915	+	9.92852i	2.41685	+	0.845172i
$139$	−7.58393	−	7.58393i	−0.643261	−	0.643261i	0.308095	−	0.951356i	$-0.400309\pi$
$139$	−7.58393	−	7.58393i	−0.643261	−	0.643261i	−0.951356	+	0.308095i	$0.900309\pi$
$140$		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	−0.104790	−	0.994494i	$-0.533417\pi$
$149$	3.68278	−	0.986799i	0.301705	−	0.0808417i	0.406496	+	0.913653i	$0.366751\pi$
$150$	−12.5444	+	10.7995i	−1.02424	+	0.881773i
$151$	1.87431	−	1.08213i	0.152529	−	0.0880625i	−0.421793	−	0.906692i	$-0.638599\pi$
$151$	1.87431	−	1.08213i	0.152529	−	0.0880625i	0.574322	+	0.818630i	$0.305266\pi$
$152$	−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	$-0.345246\pi$
$157$	5.38577	+	1.44311i	0.429831	+	0.115173i	−0.0374157	+	0.999300i	$0.511913\pi$
$158$	−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	−0.977665	−	0.210170i	$-0.932598\pi$
$163$	−3.01390	−	11.2480i	−0.236067	−	0.881015i	0.741598	−	0.670845i	$-0.234068\pi$
$164$	−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	0.834096	+	0.551619i	$0.185990\pi$
$173$	5.09752	+	19.0242i	0.387557	+	1.44638i	−0.446539	+	0.894764i	$0.647344\pi$
$174$	−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	0.208566	−	0.978008i	$-0.433120\pi$
$179$	−1.33542	−	0.357825i	−0.0998139	−	0.0267451i	−0.308380	+	0.951263i	$0.599787\pi$
$180$	−6.74582	+	4.98263i	−0.502804	+	0.371384i
$181$	16.0038	+	16.0038i	1.18955	+	1.18955i	0.977191	+	0.212362i	$0.0681154\pi$
$181$	16.0038	+	16.0038i	1.18955	+	1.18955i	0.212362	+	0.977191i	$0.431885\pi$
$182$		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	−0.907870	−	0.419252i	$-0.862292\pi$
$191$	−1.25560	+	2.17477i	−0.0908521	+	0.157360i	0.817018	+	0.576612i	$0.195626\pi$
$192$	16.8680	+	14.4824i	1.21734	+	1.04518i
$193$	−5.04719	−	8.74199i	−0.363305	−	0.629262i	0.625198	−	0.780466i	$-0.285018\pi$
$193$	−5.04719	−	8.74199i	−0.363305	−	0.629262i	−0.988503	+	0.151204i	$0.951685\pi$
$194$	−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	0.0332158	−	0.999448i	$-0.489425\pi$
$197$	−13.5617	−	13.5617i	−0.966232	−	0.966232i	−0.999448	+	0.0332158i	$0.989425\pi$
$198$	−11.6084	+	33.1952i	−0.824970	+	2.35908i
$199$	−4.86063	+	2.80629i	−0.344561	+	0.198932i	−0.662287	−	0.749250i	$-0.730414\pi$
$199$	−4.86063	+	2.80629i	−0.344561	+	0.198932i	0.317726	+	0.948183i	$0.397081\pi$
$200$	−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	−0.561635	−	0.827385i	$-0.689827\pi$
$211$	3.86025	−	3.86025i	0.265750	−	0.265750i	0.827385	+	0.561635i	$0.189827\pi$
$212$	−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	$-0.362137\pi$
$223$	12.5348			0.839390			0.419695	+	0.907665i	$0.362137\pi$
$224$		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	$-0.680444\pi$
$227$	−21.4525	−	5.74818i	−1.42385	−	0.381520i	−0.886849	+	0.462059i	$0.847111\pi$
$228$	−11.2802	−	8.98857i	−0.747047	−	0.595282i
$229$	9.96527	−	2.67019i	0.658524	−	0.176451i	0.0859440	−	0.996300i	$-0.472609\pi$
$229$	9.96527	−	2.67019i	0.658524	−	0.176451i	0.572580	+	0.819849i	$0.305943\pi$
$230$	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	0.494809	−	0.869002i	$-0.335238\pi$
$233$	−0.158206	−	0.0913400i	−0.0103644	−	0.00598388i	−0.505173	+	0.863018i	$0.668571\pi$
$234$	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	$-0.0886887\pi$
$241$	3.76511	+	6.52137i	0.242532	+	0.420078i	−0.718903	+	0.695111i	$0.755355\pi$
$242$	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	$-0.218335\pi$
$251$	2.22521	+	2.22521i	0.140454	+	0.140454i	−0.633384	+	0.773838i	$0.718335\pi$
$252$		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	$-0.861309\pi$
$257$	−1.40714	+	2.43723i	−0.0877748	+	0.152030i	0.818795	+	0.574085i	$0.194642\pi$
$258$	−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	−0.254776	−	0.967000i	$-0.582002\pi$
$263$	7.38346	−	4.26284i	0.455283	−	0.262858i	0.710059	+	0.704142i	$0.248668\pi$
$264$	−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	$-0.582071\pi$
$269$	−15.7335	−	4.21577i	−0.959286	−	0.257040i	−0.704298	+	0.709904i	$0.748738\pi$
$270$	−5.99518	−	0.448122i	−0.364855	−	0.0272719i
$271$	13.3688	−	23.1554i	0.812094	−	1.40659i	−0.0993018	−	0.995057i	$-0.531661\pi$
$271$	13.3688	−	23.1554i	0.812094	−	1.40659i	0.911396	−	0.411531i	$-0.135006\pi$
$272$	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	−0.791666	−	0.610954i	$-0.790786\pi$
$277$	3.31891	−	12.3863i	0.199414	−	0.744223i	0.991080	−	0.133269i	$-0.0425475\pi$
$278$	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	$-0.678176\pi$
$281$		−	28.4095i		−	1.69477i	0.530980	−	0.847384i	$-0.321824\pi$
$282$	14.4209	−	41.2379i	0.858752	−	2.45568i
$283$	−1.95496	+	7.29602i	−0.116210	+	0.433703i	−0.999375	−	0.0353608i	$-0.988742\pi$
$283$	−1.95496	+	7.29602i	−0.116210	+	0.433703i	0.883164	+	0.469064i	$0.155409\pi$
$284$	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	$-0.133723\pi$
$293$	8.64751	+	8.64751i	0.505193	+	0.505193i	−0.407854	+	0.913047i	$0.633723\pi$
$294$		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	−0.390077	+	0.920782i	$0.627552\pi$
$307$	−22.9681	+	22.9681i	−1.31086	+	1.31086i	−0.920782	+	0.390077i	$0.872448\pi$
$308$		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	$-0.395449\pi$
$311$	22.9893	−	13.2729i	1.30360	−	0.752635i	0.981020	+	0.193906i	$0.0621156\pi$
$312$	7.28959	+	23.5842i	0.412692	+	1.33519i
$313$	17.4811	+	10.0927i	0.988088	+	0.570473i	0.904702	−	0.426045i	$-0.140093\pi$
$313$	17.4811	+	10.0927i	0.988088	+	0.570473i	0.0833856	+	0.996517i	$0.473427\pi$
$314$	−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	0.955706	−	0.294324i	$-0.0950944\pi$
$317$	−0.340449	−	1.27057i	−0.0191215	−	0.0713624i	−0.974827	+	0.222961i	$0.928428\pi$
$318$	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	−0.628535	−	0.777781i	$-0.716345\pi$
$331$	−14.2631	+	3.82179i	−0.783972	+	0.210065i	−0.155437	+	0.987846i	$0.549678\pi$
$332$	−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	−0.834006	−	0.551755i	$-0.813958\pi$
$347$	3.05763	−	11.4112i	0.164142	−	0.612586i	0.998148	−	0.0608309i	$-0.0193750\pi$
$348$	1.79628	−	11.9486i	0.0962908	−	0.640512i
$349$	7.97685	−	7.97685i	0.426991	−	0.426991i	−0.460611	−	0.887602i	$-0.652370\pi$
$349$	7.97685	−	7.97685i	0.426991	−	0.426991i	0.887602	+	0.460611i	$0.152370\pi$
$350$		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	$-0.259128\pi$
$353$	−5.38113	−	9.32039i	−0.286409	−	0.496074i	−0.972950	+	0.231017i	$0.925795\pi$
$354$	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	0.850923	−	0.525290i	$-0.176043\pi$
$359$	15.5646	+	8.98625i	0.821470	+	0.474276i	−0.0294531	+	0.999566i	$0.509377\pi$
$360$	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	$-0.310308\pi$
$367$	−8.35453	−	14.4705i	−0.436103	−	0.755352i	−0.997385	+	0.0722722i	$0.976975\pi$
$368$	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	0.338349	−	0.941021i	$-0.390131\pi$
$373$	21.2808	−	5.70218i	1.10188	−	0.295248i	0.763529	+	0.645773i	$0.223465\pi$
$374$	−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	0.969664	+	0.244443i	$0.0786052\pi$
$379$	23.6361	+	23.6361i	1.21411	+	1.21411i	0.244443	+	0.969664i	$0.421395\pi$
$380$	−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	$-0.752499\pi$
$383$	4.91665	−	8.51589i	0.251229	−	0.435141i	0.963864	+	0.266393i	$0.0858319\pi$
$384$	−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	−0.800948	−	0.598733i	$-0.795671\pi$
$389$	3.78801	−	14.1371i	0.192060	−	0.716777i	0.993008	−	0.118044i	$-0.0376624\pi$
$390$	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	−0.907442	−	0.420177i	$-0.861968\pi$
$397$	−6.60834	−	24.6626i	−0.331663	−	1.23778i	0.575779	−	0.817605i	$-0.304699\pi$
$398$	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	−0.999395	−	0.0347829i	$-0.988926\pi$
$401$	−9.40322	+	16.2869i	−0.469575	+	0.813327i	0.529820	+	0.848110i	$0.322259\pi$
$402$	−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	$-0.405252\pi$
$409$	25.6410	−	14.8038i	1.26787	−	0.732003i	0.974584	+	0.224023i	$0.0719190\pi$
$410$	−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	$-0.762674\pi$
$419$	−1.15229	+	1.15229i	−0.0562929	+	0.0562929i	0.678400	+	0.734693i	$0.262674\pi$
$420$		0			0
$421$	19.7275	+	19.7275i	0.961459	+	0.961459i	0.999284	−	0.0378258i	$-0.0120432\pi$
$421$	19.7275	+	19.7275i	0.961459	+	0.961459i	−0.0378258	+	0.999284i	$0.512043\pi$
$422$	−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	0.508730	−	0.860926i	$-0.330115\pi$
$431$	−10.1980	−	17.6634i	−0.491219	−	0.850817i	−0.999949	+	0.0101095i	$0.996782\pi$
$432$	−10.1772	+	16.2245i	−0.489651	+	0.780601i
$433$	−28.3107			−1.36052			−0.680262	−	0.732969i	$-0.738134\pi$
$433$	−28.3107			−1.36052			−0.680262	+	0.732969i	$0.738134\pi$
$434$		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	$-0.298533\pi$
$439$	3.95973	+	2.28615i	0.188988	+	0.109112i	−0.402521	+	0.915411i	$0.631866\pi$
$440$	−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	−0.482772	−	0.875746i	$-0.660370\pi$
$443$	−9.74483	+	2.61112i	−0.462991	+	0.124058i	0.0197808	+	0.999804i	$0.493703\pi$
$444$	−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	−0.313629	−	0.949546i	$-0.601545\pi$
$457$	−27.6363	−	15.9559i	−1.29277	−	0.746383i	−0.979145	+	0.203162i	$0.934878\pi$
$458$	−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	$-0.628759\pi$
$461$	11.2878	−	11.2878i	0.525727	−	0.525727i	0.919295	+	0.393568i	$0.128759\pi$
$462$		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	$-0.0123894\pi$
$467$	2.47257	+	9.22775i	0.114417	+	0.427009i	−0.884826	+	0.465922i	$0.845723\pi$
$468$	−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	$-0.244020\pi$
$479$	−5.26638	−	9.12164i	−0.240627	−	0.416778i	−0.960893	+	0.276920i	$0.910686\pi$
$480$	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	−0.566341	−	0.824171i	$-0.691642\pi$
$487$	−2.99593	+	1.72970i	−0.135759	+	0.0783803i	0.430582	+	0.902551i	$0.358308\pi$
$488$	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	0.715116	−	0.699006i	$-0.246374\pi$
$491$	0.356972	+	0.356972i	0.0161099	+	0.0161099i	−0.699006	+	0.715116i	$0.746374\pi$
$492$	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	0.960921	+	0.276822i	$0.0892814\pi$
$499$	5.96768	+	22.2717i	0.267150	+	0.997018i	−0.693771	+	0.720196i	$0.744052\pi$
$500$	−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	0.830676	+	0.556756i	$0.187954\pi$
$509$	8.79130	+	32.8096i	0.389667	+	1.45426i	−0.441009	+	0.897503i	$0.645379\pi$
$510$	−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	$-0.807524\pi$
$521$	−16.9294	+	9.77420i	−0.741691	+	0.428216i	0.0809928	+	0.996715i	$0.474191\pi$
$522$	11.0042	−	9.47351i	0.481639	−	0.414644i
$523$	−9.83797	+	2.63608i	−0.430184	+	0.115268i	−0.467413	−	0.884039i	$-0.654814\pi$
$523$	−9.83797	+	2.63608i	−0.430184	+	0.115268i	0.0372283	+	0.999307i	$0.488147\pi$
$524$	−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	0.952442	−	0.304721i	$-0.0985633\pi$
$541$	−0.575849	−	2.14910i	−0.0247577	−	0.0923970i	−0.977199	+	0.212324i	$0.931897\pi$
$542$	−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	−0.836850	−	0.547432i	$-0.815605\pi$
$547$	−6.76891	+	6.76891i	−0.289418	+	0.289418i	0.547432	+	0.836850i	$0.315605\pi$
$548$	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	0.161426	−	0.986885i	$-0.448391\pi$
$557$	−4.53648	−	1.21555i	−0.192217	−	0.0515043i	−0.353643	+	0.935380i	$0.615057\pi$
$558$	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	$-0.227716\pi$
$563$	25.6398	+	6.87017i	1.08059	+	0.289543i	0.325752	+	0.945455i	$0.394382\pi$
$564$	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	0.00860467	−	0.999963i	$-0.497261\pi$
$569$	−20.3493	−	11.7487i	−0.853086	−	0.492530i	−0.861691	+	0.507433i	$0.830594\pi$
$570$	−5.90782	−	6.86235i	−0.247451	−	0.287432i
$571$	9.13856	−	34.1056i	0.382437	−	1.42727i	−0.459731	−	0.888058i	$-0.652054\pi$
$571$	9.13856	−	34.1056i	0.382437	−	1.42727i	0.842168	−	0.539215i	$-0.181279\pi$
$572$	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	$-0.263692\pi$
$577$	−7.20904	−	12.4864i	−0.300116	−	0.519817i	−0.976162	+	0.217043i	$0.930359\pi$
$578$	−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	$-0.124005\pi$
$587$	13.2110	+	13.2110i	0.545276	+	0.545276i	−0.379795	+	0.925071i	$0.624005\pi$
$588$		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	$-0.724109\pi$
$593$	8.19296	−	14.1906i	0.336445	−	0.582739i	0.983761	+	0.179482i	$0.0574422\pi$
$594$	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	0.241961	−	0.970286i	$-0.422210\pi$
$599$	29.4485	−	17.0021i	1.20323	−	0.694687i	0.961273	+	0.275599i	$0.0888762\pi$
$600$	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	$-0.901512\pi$
$607$	−5.23683	+	9.07046i	−0.212556	+	0.368159i	0.739957	+	0.672654i	$0.234846\pi$
$608$	−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	−0.999998	−	0.00191560i	$-0.999390\pi$
$613$	−3.29334	+	12.2909i	−0.133017	+	0.496425i	0.866982	+	0.498340i	$0.166057\pi$
$614$	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	$-0.981158\pi$
$617$		−	2.93899i		−	0.118319i	0.998249	−	0.0591597i	$-0.0188421\pi$
$618$	−71.3094	−	24.9369i	−2.86848	−	1.00311i
$619$	−2.65281	+	9.90042i	−0.106625	+	0.397932i	−0.998525	−	0.0543029i	$-0.982706\pi$
$619$	−2.65281	+	9.90042i	−0.106625	+	0.397932i	0.891899	+	0.452235i	$0.149373\pi$
$620$	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	$-0.938834\pi$
$631$		−	9.59471i		−	0.381959i	0.981594	−	0.190980i	$-0.0611665\pi$
$632$	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	0.978925	−	0.204222i	$-0.0654664\pi$
$641$	7.91443	+	13.7082i	0.312601	+	0.541441i	−0.666324	+	0.745663i	$0.732133\pi$
$642$	−12.3543	+	5.95244i	−0.487586	+	0.234924i
$643$	−10.3033	+	10.3033i	−0.406321	+	0.406321i	−0.880454	−	0.474132i	$-0.842762\pi$
$643$	−10.3033	+	10.3033i	−0.406321	+	0.406321i	0.474132	+	0.880454i	$0.342762\pi$
$644$		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	$-0.600318\pi$
$647$	9.11681	−	5.26359i	0.358419	−	0.206933i	0.668387	+	0.743814i	$0.266985\pi$
$648$	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	0.900304	+	0.435263i	$0.143344\pi$
$653$	8.64357	+	32.2582i	0.338249	+	1.26236i	−0.562054	+	0.827100i	$0.689989\pi$
$654$	−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	−0.935112	−	0.354353i	$-0.884701\pi$
$659$	−14.9087	+	14.9087i	−0.580759	+	0.580759i	0.354353	+	0.935112i	$0.384701\pi$
$660$	−15.4361	−	20.8985i	−0.600851	−	0.813472i
$661$	−8.12957	+	30.3400i	−0.316204	+	1.18009i	0.606660	+	0.794961i	$0.292509\pi$
$661$	−8.12957	+	30.3400i	−0.316204	+	1.18009i	−0.922864	+	0.385126i	$0.874158\pi$
$662$	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	$-0.264905\pi$
$677$	42.3069	−	11.3361i	1.62599	−	0.435682i	0.952752	+	0.303748i	$0.0982381\pi$
$678$	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	0.819621	+	0.572907i	$0.194184\pi$
$683$	−4.61649	+	17.2290i	−0.176645	+	0.659248i	−0.996266	+	0.0863413i	$0.972482\pi$
$684$	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	−0.917773	−	0.397106i	$-0.870015\pi$
$691$	−8.45153	−	31.5415i	−0.321511	−	1.19990i	0.596262	−	0.802790i	$-0.296652\pi$
$692$	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	−0.119662	−	0.992815i	$-0.538181\pi$
$701$	23.1180	−	23.1180i	0.873153	−	0.873153i	0.992815	+	0.119662i	$0.0381810\pi$
$702$	−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	0.599205	−	0.800596i	$-0.295484\pi$
$709$	40.4313	−	10.8335i	1.51843	−	0.406862i	0.919224	+	0.393734i	$0.128817\pi$
$710$	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	−0.0611931	+	0.998126i	$0.519491\pi$
$719$	−23.9987	+	41.5669i	−0.894999	+	1.55018i	−0.833806	+	0.552058i	$0.813843\pi$
$720$	−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	$-0.0303887\pi$
$733$	2.32031	+	8.65952i	0.0857026	+	0.319847i	−0.909744	+	0.415170i	$0.863722\pi$
$734$	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	0.237645	−	0.971352i	$-0.423624\pi$
$739$	−1.14785	−	0.307565i	−0.0422243	−	0.0113140i	−0.279869	+	0.960038i	$0.590291\pi$
$740$	−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	$0.330012\pi$
$743$			46.9253i			1.72152i	−0.509008	+	0.860762i	$0.669988\pi$
$744$	−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	−0.741610	−	0.670832i	$-0.765937\pi$
$751$	5.75909	−	9.97504i	0.210152	−	0.363995i	0.951762	+	0.306837i	$0.0992707\pi$
$752$	−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	0.389172	−	0.921165i	$-0.372761\pi$
$757$	−14.6371	−	14.6371i	−0.531994	−	0.531994i	−0.921165	+	0.389172i	$0.872761\pi$
$758$	−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	$-0.294294\pi$
$761$	5.84549	+	3.37489i	0.211899	+	0.122340i	−0.390295	+	0.920690i	$0.627627\pi$
$762$	−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	$-0.487169\pi$
$769$	2.23508			0.0805990			0.0402995	+	0.999188i	$0.487169\pi$
$770$		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	0.765974	+	0.642871i	$0.222257\pi$
$773$	−6.08368	+	22.7046i	−0.218815	+	0.816627i	−0.984789	+	0.173756i	$0.944410\pi$
$774$	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	$-0.384416\pi$
$787$	5.48157	+	1.46878i	0.195397	+	0.0523564i	−0.159793	+	0.987150i	$0.551083\pi$
$788$	−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	$-0.981465\pi$
$797$	−26.5404	+	26.5404i	−0.940110	+	0.940110i	0.0581955	+	0.998305i	$0.481465\pi$
$798$		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	−0.592665	−	0.805449i	$-0.701924\pi$
$809$	−5.44560	+	3.14402i	−0.191457	+	0.110538i	0.401207	+	0.915987i	$0.368591\pi$
$810$	−1.02248	−	0.357560i	−0.0359261	−	0.0125634i
$811$	−28.2328	−	28.2328i	−0.991388	−	0.991388i	0.00857565	−	0.999963i	$-0.497270\pi$
$811$	−28.2328	−	28.2328i	−0.991388	−	0.991388i	−0.999963	+	0.00857565i	$0.997270\pi$
$812$		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	0.0382839	−	0.999267i	$-0.487811\pi$
$821$	16.3630	−	4.38445i	0.571072	−	0.153018i	0.532788	+	0.846249i	$0.321144\pi$
$822$	14.6705	−	12.6299i	0.511692	−	0.440517i
$823$	−32.3363	+	18.6694i	−1.12717	+	0.650774i	−0.943223	−	0.332162i	$-0.892222\pi$
$823$	−32.3363	+	18.6694i	−1.12717	+	0.650774i	−0.183951	+	0.982935i	$0.558889\pi$
$824$	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	0.608407	−	0.793625i	$-0.291809\pi$
$827$	−5.32642	−	5.32642i	−0.185218	−	0.185218i	−0.793625	+	0.608407i	$0.791809\pi$
$828$	71.4865	+	10.7469i	2.48433	+	0.373480i
$829$	−7.89725	−	2.11606i	−0.274283	−	0.0734939i	0.119056	−	0.992888i	$-0.462013\pi$
$829$	−7.89725	−	2.11606i	−0.274283	−	0.0734939i	−0.393339	+	0.919394i	$0.628680\pi$
$830$	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	$-0.147826\pi$
$853$	13.0316	+	13.0316i	0.446192	+	0.446192i	−0.447894	+	0.894086i	$0.647826\pi$
$854$		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	$-0.741448\pi$
$857$	−11.8030	+	6.81447i	−0.403183	+	0.232778i	0.284674	+	0.958625i	$0.408115\pi$
$858$	42.3975	+	49.2477i	1.44743	+	1.68129i
$859$	−43.5800	+	11.6772i	−1.48693	+	0.398422i	−0.908699	−	0.417451i	$-0.862923\pi$
$859$	−43.5800	+	11.6772i	−1.48693	+	0.398422i	−0.578231	+	0.815873i	$0.696257\pi$
$860$	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	0.0103847	−	0.999946i	$-0.496694\pi$
$863$	25.5923	−	44.3271i	0.871171	−	1.50891i	0.860786	−	0.508966i	$-0.169972\pi$
$864$	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	0.962484	+	0.271337i	$0.0874659\pi$
$877$	7.83642	+	29.2459i	0.264617	+	0.987564i	−0.697867	+	0.716227i	$0.745867\pi$
$878$	−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	$-0.667009\pi$
$881$	−29.7369			−1.00186			−0.500930	+	0.865488i	$0.667009\pi$
$882$		0			0
$883$	14.3040	−	14.3040i	0.481368	−	0.481368i	−0.424200	−	0.905568i	$-0.639445\pi$
$883$	14.3040	−	14.3040i	0.481368	−	0.481368i	0.905568	+	0.424200i	$0.139445\pi$
$884$	−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	−0.977509	−	0.210896i	$-0.932362\pi$
$887$	−49.1086	−	28.3528i	−1.64890	−	0.951995i	−0.671395	−	0.741099i	$-0.734305\pi$
$888$	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	0.809232	+	0.587489i	$0.199883\pi$
$907$	−5.58142	+	20.8301i	−0.185328	+	0.691653i	−0.994560	+	0.104164i	$0.966783\pi$
$908$	−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	0.469434	−	0.882967i	$-0.344458\pi$
$919$	−1.83468	−	1.05925i	−0.0605206	−	0.0349416i	−0.529955	+	0.848026i	$0.677791\pi$
$920$	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	0.471122	+	0.882068i	$0.343849\pi$
$929$	−16.1033	+	27.8918i	−0.528333	+	0.915099i	−0.999454	+	0.0330307i	$0.989484\pi$
$930$	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	$-0.569319\pi$
$941$	−27.3429	−	7.32652i	−0.891354	−	0.238838i	−0.675300	+	0.737544i	$0.735986\pi$
$942$	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	0.990926	+	0.134410i	$0.0429138\pi$
$947$	6.15356	+	22.9654i	0.199964	+	0.746275i	−0.790962	+	0.611865i	$0.790419\pi$
$948$	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	$-0.836698\pi$
$953$		−	30.3038i		−	0.981636i	0.871262	−	0.490818i	$-0.163302\pi$
$954$	−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	$0.0689537\pi$
$967$			13.3675i			0.429869i	−0.976629	+	0.214934i	$0.931046\pi$
$968$	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	$-0.515263\pi$
$971$	12.7754	−	3.42316i	0.409982	−	0.109854i	0.457914	+	0.888996i	$0.348597\pi$
$972$	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	−0.879846	−	0.475259i	$-0.842355\pi$
$977$	−26.6156	−	46.0996i	−0.851509	−	1.47486i	0.0283371	−	0.999598i	$-0.490979\pi$
$978$	−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	$-0.668167\pi$
$983$	−0.255896	+	0.147742i	−0.00816182	+	0.00471223i	0.495914	+	0.868372i	$0.334833\pi$
$984$	−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	0.978555	+	0.205985i	$0.0660397\pi$
$991$	21.0182	+	36.4046i	0.667665	+	1.15643i	−0.310890	+	0.950446i	$0.600627\pi$
$992$	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	−0.471885	−	0.881660i	$-0.656426\pi$
$997$	11.9231	−	44.4977i	0.377609	−	1.40926i	0.849495	−	0.527597i	$-0.176907\pi$
$998$	−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.j.373.1		16
7.2	even	3		784.2.m.g.197.3		8
7.3	odd	6		784.2.x.k.165.3		16
7.4	even	3	inner	784.2.x.j.165.3		16
7.5	odd	6		112.2.m.c.85.3	yes	8
7.6	odd	2		784.2.x.k.373.1		16
16.13	even	4	inner	784.2.x.j.765.3		16
28.19	even	6		448.2.m.c.113.4		8
56.5	odd	6		896.2.m.e.225.4		8
56.19	even	6		896.2.m.f.225.1		8
112.5	odd	12		896.2.m.e.673.4		8
112.13	odd	4		784.2.x.k.765.3		16
112.19	even	12		448.2.m.c.337.4		8
112.45	odd	12		784.2.x.k.557.1		16
112.61	odd	12		112.2.m.c.29.3	✓	8
112.75	even	12		896.2.m.f.673.1		8
112.93	even	12		784.2.m.g.589.3		8
112.109	even	12	inner	784.2.x.j.557.1		16
224.19	even	24		7168.2.a.bd.1.1		8
224.61	odd	24		7168.2.a.bc.1.1		8
224.131	even	24		7168.2.a.bd.1.8		8
224.173	odd	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	112.61	odd	12
112.2.m.c.85.3	yes	8	7.5	odd	6
448.2.m.c.113.4		8	28.19	even	6
448.2.m.c.337.4		8	112.19	even	12
784.2.m.g.197.3		8	7.2	even	3
784.2.m.g.589.3		8	112.93	even	12
784.2.x.j.165.3		16	7.4	even	3	inner
784.2.x.j.373.1		16	1.1	even	1	trivial
784.2.x.j.557.1		16	112.109	even	12	inner
784.2.x.j.765.3		16	16.13	even	4	inner
784.2.x.k.165.3		16	7.3	odd	6
784.2.x.k.373.1		16	7.6	odd	2
784.2.x.k.557.1		16	112.45	odd	12
784.2.x.k.765.3		16	112.13	odd	4
896.2.m.e.225.4		8	56.5	odd	6
896.2.m.e.673.4		8	112.5	odd	12
896.2.m.f.225.1		8	56.19	even	6
896.2.m.f.673.1		8	112.75	even	12
7168.2.a.bc.1.1		8	224.61	odd	24
7168.2.a.bc.1.8		8	224.173	odd	24
7168.2.a.bd.1.1		8	224.19	even	24
7168.2.a.bd.1.8		8	224.131	even	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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