LMFDB - Embedded newform 784.2.x.j.165.3

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			165.3
Root			$0.840224 - 1.13755i$ of defining polynomial
Character	$\chi$	$=$	784.165
Dual form			784.2.x.j.765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.105414 - 1.41028i) q^{2} +(0.719263 + 2.68432i) q^{3} +(-1.97778 - 0.297327i) q^{4} +(0.229791 - 0.857592i) q^{5} +(3.86147 - 0.731395i) q^{6} +(-0.627801 + 2.75787i) q^{8} +(-4.09018 + 2.36147i) q^{9} +(-1.18522 - 0.414472i) q^{10} +(-5.08562 + 1.36269i) q^{11} +(-0.624417 - 5.52285i) q^{12} +(-2.22066 + 2.22066i) q^{13} +2.46733 q^{15} +(3.82319 + 1.17609i) q^{16} +(1.62780 - 2.81943i) q^{17} +(2.89917 + 6.01723i) q^{18} +(-2.50664 - 0.671653i) q^{19} +(-0.709460 + 1.62780i) q^{20} +(1.38567 + 7.31580i) q^{22} +(-6.62774 + 3.82653i) q^{23} +(-7.85458 + 0.298415i) q^{24} +(3.64747 + 2.10587i) q^{25} +(2.89767 + 3.36584i) q^{26} +(-3.38567 - 3.38567i) q^{27} +(-1.53721 + 1.53721i) q^{29} +(0.260092 - 3.47963i) q^{30} +(-1.22066 + 2.11425i) q^{31} +(2.06164 - 5.26779i) q^{32} +(-7.31580 - 12.6713i) q^{33} +(-3.80460 - 2.59286i) q^{34} +(8.79159 - 3.45433i) q^{36} +(-0.461245 + 1.72139i) q^{37} +(-1.21145 + 3.46426i) q^{38} +(-7.55822 - 4.36374i) q^{39} +(2.22087 + 1.17213i) q^{40} -7.77589i q^{41} +(-7.51575 - 7.51575i) q^{43} +(10.4634 - 1.18300i) q^{44} +(1.08529 + 4.05035i) q^{45} +(4.69782 + 9.75034i) q^{46} +(5.55792 + 9.62661i) q^{47} +(-0.407138 + 11.1086i) q^{48} +(3.35436 - 4.92196i) q^{50} +(8.73909 + 2.34163i) q^{51} +(5.05224 - 3.73171i) q^{52} +(-4.00262 + 1.07250i) q^{53} +(-5.13164 + 4.41785i) q^{54} +4.67452i q^{55} -7.21173i q^{57} +(2.00585 + 2.32994i) q^{58} +(-9.34298 + 2.50344i) q^{59} +(-4.87983 - 0.733606i) q^{60} +(4.60651 + 1.23431i) q^{61} +(2.85301 + 1.94435i) q^{62} +(-7.21173 - 3.46279i) q^{64} +(1.39413 + 2.41471i) q^{65} +(-18.6413 + 8.98158i) q^{66} +(0.338785 + 1.26436i) q^{67} +(-4.05772 + 5.09222i) q^{68} +(-15.0387 - 15.0387i) q^{69} +12.1113i q^{71} +(-3.94481 - 12.7627i) q^{72} +(5.55501 + 3.20719i) q^{73} +(2.37902 + 0.831944i) q^{74} +(-3.02934 + 11.3057i) q^{75} +(4.75787 + 2.07367i) q^{76} +(-6.95084 + 10.1992i) q^{78} +(3.64128 + 6.30687i) q^{79} +(1.88714 - 3.00848i) q^{80} +(-0.431344 + 0.747110i) q^{81} +(-10.9662 - 0.819691i) q^{82} +(1.96506 - 1.96506i) q^{83} +(-2.04387 - 2.04387i) q^{85} +(-11.3916 + 9.80704i) q^{86} +(-5.23203 - 3.02071i) q^{87} +(-0.565366 - 14.8810i) q^{88} +(0.576282 - 0.332717i) q^{89} +(5.82653 - 1.10359i) q^{90} +(14.2459 - 5.59741i) q^{92} +(-6.55331 - 1.75595i) q^{93} +(14.1621 - 6.82344i) q^{94} +(-1.15201 + 1.99533i) q^{95} +(15.6233 + 1.74518i) 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} + 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}+ \cdots + 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

Character values

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

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

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 $

$2$	0.105414	−	1.41028i	0.0745392	−	0.997218i
$2$	0.105414	−	1.41028i	0.0745392	−	0.997218i
$3$	0.719263	+	2.68432i	0.415266	+	1.54980i	0.784301	+	0.620380i	$0.213022\pi$
$3$	0.719263	+	2.68432i	0.415266	+	1.54980i	−0.369035	+	0.929415i	$0.620312\pi$
$4$	−1.97778	−	0.297327i	−0.988888	−	0.148664i
$5$	0.229791	−	0.857592i	0.102766	−	0.383527i	−0.895316	−	0.445431i	$-0.853051\pi$
$5$	0.229791	−	0.857592i	0.102766	−	0.383527i	0.998082	+	0.0619040i	$0.0197173\pi$
$6$	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
$10$	−1.18522	−	0.414472i	−0.374800	−	0.131068i
$11$	−5.08562	+	1.36269i	−1.53337	+	0.410866i	−0.924118	−	0.382108i	$-0.875198\pi$
$11$	−5.08562	+	1.36269i	−1.53337	+	0.410866i	−0.609256	+	0.792974i	$0.708532\pi$
$12$	−0.624417	−	5.52285i	−0.180254	−	1.59431i
$13$	−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
$16$	3.82319	+	1.17609i	0.955798	+	0.294023i
$17$	1.62780	−	2.81943i	0.394800	−	0.683813i	−0.598276	−	0.801290i	$-0.704147\pi$
$17$	1.62780	−	2.81943i	0.394800	−	0.683813i	0.993076	+	0.117477i	$0.0374807\pi$
$18$	2.89917	+	6.01723i	0.683340	+	1.41828i
$19$	−2.50664	−	0.671653i	−0.575063	−	0.154088i	−0.0404454	−	0.999182i	$-0.512878\pi$
$19$	−2.50664	−	0.671653i	−0.575063	−	0.154088i	−0.534618	+	0.845094i	$0.679544\pi$
$20$	−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	$-0.960715\pi$
$23$	−6.62774	+	3.82653i	−1.38198	+	0.797887i	−0.389586	+	0.920990i	$0.627382\pi$
$24$	−7.85458	+	0.298415i	−1.60331	+	0.0609136i
$25$	3.64747	+	2.10587i	0.729494	+	0.421173i
$26$	2.89767	+	3.36584i	0.568279	+	0.660096i
$27$	−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	$0.314694\pi$
$30$	0.260092	−	3.47963i	0.0474862	−	0.635291i
$31$	−1.22066	+	2.11425i	−0.219238	+	0.379731i	−0.954575	−	0.297970i	$-0.903690\pi$
$31$	−1.22066	+	2.11425i	−0.219238	+	0.379731i	0.735338	+	0.677701i	$0.237024\pi$
$32$	2.06164	−	5.26779i	0.364450	−	0.931223i
$33$	−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
$37$	−0.461245	+	1.72139i	−0.0758283	+	0.282995i	−0.993420	−	0.114530i	$-0.963464\pi$
$37$	−0.461245	+	1.72139i	−0.0758283	+	0.282995i	0.917592	+	0.397524i	$0.130131\pi$
$38$	−1.21145	+	3.46426i	−0.196524	+	0.561978i
$39$	−7.55822	−	4.36374i	−1.21028	−	0.698758i
$40$	2.22087	+	1.17213i	0.351150	+	0.185330i
$41$		−	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	$-0.550774\pi$
$44$	10.4634	−	1.18300i	1.57742	−	0.178344i
$45$	1.08529	+	4.05035i	0.161785	+	0.603790i
$46$	4.69782	+	9.75034i	0.692655	+	1.43761i
$47$	5.55792	+	9.62661i	0.810707	+	1.40418i	0.912370	+	0.409366i	$0.134250\pi$
$47$	5.55792	+	9.62661i	0.810707	+	1.40418i	−0.101664	+	0.994819i	$0.532417\pi$
$48$	−0.407138	+	11.1086i	−0.0587653	+	1.60339i
$49$		0			0
$50$	3.35436	−	4.92196i	0.474377	−	0.696070i
$51$	8.73909	+	2.34163i	1.22372	+	0.327894i
$52$	5.05224	−	3.73171i	0.700619	−	0.517495i
$53$	−4.00262	+	1.07250i	−0.549803	+	0.147319i	−0.523017	−	0.852322i	$-0.675194\pi$
$53$	−4.00262	+	1.07250i	−0.549803	+	0.147319i	−0.0267853	+	0.999641i	$0.508527\pi$
$54$	−5.13164	+	4.41785i	−0.698328	+	0.601193i
$55$			4.67452i			0.630312i
$56$		0			0
$57$		−	7.21173i		−	0.955217i
$58$	2.00585	+	2.32994i	0.263381	+	0.305936i
$59$	−9.34298	+	2.50344i	−1.21635	+	0.325921i	−0.809251	−	0.587463i	$-0.800127\pi$
$59$	−9.34298	+	2.50344i	−1.21635	+	0.325921i	−0.407101	+	0.913383i	$0.633460\pi$
$60$	−4.87983	−	0.733606i	−0.629984	−	0.0947081i
$61$	4.60651	+	1.23431i	0.589803	+	0.158037i	0.541363	−	0.840789i	$-0.317908\pi$
$61$	4.60651	+	1.23431i	0.589803	+	0.158037i	0.0484399	+	0.998826i	$0.484575\pi$
$62$	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
$66$	−18.6413	+	8.98158i	−2.29459	+	1.10556i
$67$	0.338785	+	1.26436i	0.0413892	+	0.154467i	0.983528	−	0.180757i	$-0.0578548\pi$
$67$	0.338785	+	1.26436i	0.0413892	+	0.154467i	−0.942139	+	0.335224i	$0.891188\pi$
$68$	−4.05772	+	5.09222i	−0.492071	+	0.617522i
$69$	−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	$0.744750\pi$
$72$	−3.94481	−	12.7627i	−0.464900	−	1.50410i
$73$	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	$0.544181\pi$
$74$	2.37902	+	0.831944i	0.276556	+	0.0967115i
$75$	−3.02934	+	11.3057i	−0.349798	+	1.30546i
$76$	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	$0.698975\pi$
$80$	1.88714	−	3.00848i	0.210989	−	0.336359i
$81$	−0.431344	+	0.747110i	−0.0479271	+	0.0830122i
$82$	−10.9662	−	0.819691i	−1.21101	−	0.0905197i
$83$	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
$86$	−11.3916	+	9.80704i	−1.22838	+	1.05752i
$87$	−5.23203	−	3.02071i	−0.560932	−	0.323854i
$88$	−0.565366	−	14.8810i	−0.0602682	−	1.58632i
$89$	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
$93$	−6.55331	−	1.75595i	−0.679547	−	0.182084i
$94$	14.1621	−	6.82344i	1.46071	−	0.703784i
$95$	−1.15201	+	1.99533i	−0.118193	+	0.204717i
$96$	15.6233	+	1.74518i	1.59455	+	0.178117i
$97$	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
$100$	−6.58774	−	5.24942i	−0.658774	−	0.524942i
$101$	−4.61640	+	1.23696i	−0.459349	+	0.123082i	−0.481070	−	0.876682i	$-0.659752\pi$
$101$	−4.61640	+	1.23696i	−0.459349	+	0.123082i	0.0217217	+	0.999764i	$0.493085\pi$
$102$	4.22358	−	12.0777i	0.418197	−	1.19587i
$103$	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
$107$	0.903107	−	3.37044i	0.0873066	−	0.325833i	−0.908434	−	0.418028i	$-0.862722\pi$
$107$	0.903107	−	3.37044i	0.0873066	−	0.325833i	0.995741	+	0.0921947i	$0.0293882\pi$
$108$	5.68945	+	7.70276i	0.547468	+	0.741198i
$109$	0.895251	+	3.34112i	0.0857495	+	0.320021i	0.995455	−	0.0952324i	$-0.0303594\pi$
$109$	0.895251	+	3.34112i	0.0857495	+	0.320021i	−0.909706	+	0.415254i	$0.863693\pi$
$110$	6.59238	+	0.492762i	0.628559	+	0.0469830i
$111$	−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	$0.449611\pi$
$114$	−10.1706	−	0.760220i	−0.952560	−	0.0712011i
$115$	1.75860	+	6.56320i	0.163991	+	0.612021i
$116$	3.49731	−	2.58320i	0.324717	−	0.239844i
$117$	3.83889	−	14.3269i	0.354906	−	1.32453i
$118$	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
$122$	2.22632	−	6.36635i	0.201561	−	0.576382i
$123$	20.8730	−	5.59291i	1.88206	−	0.504296i
$124$	3.04282	−	3.81858i	0.273253	−	0.342918i
$125$	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	$0.579286\pi$
$128$	−5.64372	+	9.80553i	−0.498839	+	0.866695i
$129$	14.7689	−	25.5805i	1.30033	−	2.25224i
$130$	3.55238	−	1.71157i	0.311564	−	0.150115i
$131$	13.2109	+	3.53986i	1.15425	+	0.309279i	0.784665	−	0.619920i	$-0.212835\pi$
$131$	13.2109	+	3.53986i	1.15425	+	0.309279i	0.369580	+	0.929199i	$0.379502\pi$
$132$	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
$136$	6.75371	+	6.25931i	0.579126	+	0.536731i
$137$	−4.26568	−	2.46279i	−0.364441	−	0.210410i	0.306586	−	0.951843i	$-0.400813\pi$
$137$	−4.26568	−	2.46279i	−0.364441	−	0.210410i	−0.671027	+	0.741433i	$0.734147\pi$
$138$	−22.7941	+	19.6235i	−1.94036	+	1.67046i
$139$	−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
$142$	17.0803	+	1.27671i	1.43335	+	0.107139i
$143$	8.26738	−	14.3195i	0.691353	−	1.19746i
$144$	−18.4149	+	4.21791i	−1.53457	+	0.351492i
$145$	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
$149$	−0.986799	+	3.68278i	−0.0808417	+	0.301705i	−0.994494	−	0.104790i	$-0.966583\pi$
$149$	−0.986799	+	3.68278i	−0.0808417	+	0.301705i	0.913653	+	0.406496i	$0.133249\pi$
$150$	15.6248	+	5.46400i	1.27576	+	0.446133i
$151$	−1.87431	−	1.08213i	−0.152529	−	0.0880625i	0.421793	−	0.906692i	$-0.361401\pi$
$151$	−1.87431	−	1.08213i	−0.152529	−	0.0880625i	−0.574322	+	0.818630i	$0.694734\pi$
$152$	3.42600	−	6.49134i	0.277886	−	0.526517i
$153$			15.3760i			1.24308i
$154$		0			0
$155$	1.53267	+	1.53267i	0.123107	+	0.123107i
$156$	13.6510	+	10.8778i	1.09295	+	0.870918i
$157$	−1.44311	−	5.38577i	−0.115173	−	0.429831i	0.884127	−	0.467247i	$-0.154754\pi$
$157$	−1.44311	−	5.38577i	−0.115173	−	0.429831i	−0.999300	+	0.0374157i	$0.988087\pi$
$158$	9.27830	−	4.47038i	0.738142	−	0.355644i
$159$	−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
$163$	11.2480	+	3.01390i	0.881015	+	0.236067i	0.670845	−	0.741598i	$-0.265932\pi$
$163$	11.2480	+	3.01390i	0.881015	+	0.236067i	0.210170	+	0.977665i	$0.432598\pi$
$164$	−2.31199	+	15.3790i	−0.180536	+	1.20090i
$165$	−12.5479	+	3.36221i	−0.976855	+	0.261748i
$166$	−2.56414	−	2.97843i	−0.199016	−	0.231171i
$167$		−	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
$170$	−3.09788	+	2.66697i	−0.237596	+	0.204547i
$171$	11.8387	−	3.17217i	0.905328	−	0.242582i
$172$	12.6298	+	17.0991i	0.963015	+	1.30379i
$173$	−19.0242	−	5.09752i	−1.44638	−	0.387557i	−0.551619	−	0.834096i	$-0.685990\pi$
$173$	−19.0242	−	5.09752i	−1.44638	−	0.387557i	−0.894764	+	0.446539i	$0.852656\pi$
$174$	−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
$178$	−0.408475	−	0.847792i	−0.0306165	−	0.0635447i
$179$	0.357825	+	1.33542i	0.0267451	+	0.0998139i	0.978008	−	0.208566i	$-0.0668797\pi$
$179$	0.357825	+	1.33542i	0.0267451	+	0.0998139i	−0.951263	+	0.308380i	$0.900213\pi$
$180$	−0.942176	−	8.33337i	−0.0702257	−	0.621133i
$181$	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
$184$	−6.39218	−	20.6808i	−0.471238	−	1.52461i
$185$	1.37026	+	0.791120i	0.100744	+	0.0581643i
$186$	−3.16720	+	9.05690i	−0.232230	+	0.664084i
$187$	−4.43637	+	16.5568i	−0.324420	+	1.21075i
$188$	−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	$0.862292\pi$
$192$	4.10812	−	21.8493i	0.296478	−	1.57684i
$193$	−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	$0.285018\pi$
$194$	0.879630	−	11.7681i	0.0631538	−	0.844899i
$195$	−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	$0.989425\pi$
$198$	−22.9437	−	26.6507i	−1.63054	−	1.89398i
$199$	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	$0.602919\pi$
$200$	−8.09760	+	8.73719i	−0.572586	+	0.617813i
$201$	−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
$205$	−6.66854	−	1.78683i	−0.465751	−	0.124798i
$206$	−11.7992	−	24.4894i	−0.822092	−	1.70626i
$207$	18.0725	−	31.3024i	1.25612	−	2.17567i
$208$	−11.1017	+	5.87832i	−0.769767	+	0.407588i
$209$	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	$0.189827\pi$
$212$	8.23517	−	0.931074i	0.565594	−	0.0639464i
$213$	−32.5107	+	8.71121i	−2.22759	+	0.596882i
$214$	−4.65806	−	1.62893i	−0.318419	−	0.111351i
$215$	−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
$219$	−4.61362	+	17.2183i	−0.311760	+	1.16350i
$220$	1.38986	−	9.24516i	0.0937046	−	0.623308i
$221$	2.64621	+	9.87581i	0.178004	+	0.664319i
$222$	−0.522068	+	6.98445i	−0.0350389	+	0.468766i
$223$	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
$226$	0.353295	−	4.72653i	0.0235008	−	0.314404i
$227$	5.74818	+	21.4525i	0.381520	+	1.42385i	0.843580	+	0.537004i	$0.180444\pi$
$227$	5.74818	+	21.4525i	0.381520	+	1.42385i	−0.462059	+	0.886849i	$0.652889\pi$
$228$	−2.14425	+	14.2632i	−0.142006	+	0.944603i
$229$	−2.67019	+	9.96527i	−0.176451	+	0.658524i	0.819849	+	0.572580i	$0.194057\pi$
$229$	−2.67019	+	9.96527i	−0.176451	+	0.658524i	−0.996300	+	0.0859440i	$0.972609\pi$
$230$	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	$-0.664762\pi$
$233$	0.158206	−	0.0913400i	0.0103644	−	0.00598388i	0.505173	+	0.863018i	$0.331429\pi$
$234$	−19.8003	−	6.92418i	−1.29439	−	0.452647i
$235$	9.53286	−	2.55432i	0.621855	−	0.166626i
$236$	19.2227	−	2.17333i	1.25129	−	0.141471i
$237$	−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	$0.497312\pi$
$240$	9.43309	+	2.90182i	0.608904	+	0.187311i
$241$	3.76511	−	6.52137i	0.242532	−	0.420078i	−0.718903	−	0.695111i	$-0.755355\pi$
$241$	3.76511	−	6.52137i	0.242532	−	0.420078i	0.961435	+	0.275033i	$0.0886887\pi$
$242$	−10.2638	−	21.3027i	−0.659785	−	1.36939i
$243$	−16.1905	−	4.33823i	−1.03862	−	0.278297i
$244$	−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
$248$	−5.06450	−	4.69376i	−0.321596	−	0.298054i
$249$	6.68826	+	3.86147i	0.423851	+	0.244711i
$250$	−7.54621	−	8.76546i	−0.477264	−	0.554376i
$251$	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
$254$	−0.585707	+	7.83584i	−0.0367505	+	0.491664i
$255$	4.01633	−	6.95648i	0.251512	−	0.435632i
$256$	13.2336	+	8.99287i	0.827100	+	0.562054i
$257$	−1.40714	−	2.43723i	−0.0877748	−	0.152030i	0.818795	−	0.574085i	$-0.194642\pi$
$257$	−1.40714	−	2.43723i	−0.0877748	−	0.152030i	−0.906570	+	0.422055i	$0.861309\pi$
$258$	−34.5188	−	23.5248i	−2.14905	−	1.46459i
$259$		0			0
$260$	−2.03932	−	5.19027i	−0.126474	−	0.321887i
$261$	2.65740	−	9.91754i	0.164489	−	0.613881i
$262$	6.38481	−	18.2580i	0.394455	−	1.12798i
$263$	−7.38346	−	4.26284i	−0.455283	−	0.262858i	0.254776	−	0.967000i	$-0.417998\pi$
$263$	−7.38346	−	4.26284i	−0.455283	−	0.262858i	−0.710059	+	0.704142i	$0.751332\pi$
$264$	39.5388	−	12.2210i	2.43344	−	0.752149i
$265$			3.67907i			0.226003i
$266$		0			0
$267$	1.30762	+	1.30762i	0.0800249	+	0.0800249i
$268$	−0.294111	−	2.60136i	−0.0179657	−	0.158903i
$269$	4.21577	+	15.7335i	0.257040	+	0.959286i	0.966944	+	0.254988i	$0.0820715\pi$
$269$	4.21577	+	15.7335i	0.257040	+	0.959286i	−0.709904	+	0.704298i	$0.751262\pi$
$270$	2.60950	+	5.41604i	0.158809	+	0.329610i
$271$	13.3688	+	23.1554i	0.812094	+	1.40659i	0.911396	+	0.411531i	$0.135006\pi$
$271$	13.3688	+	23.1554i	0.812094	+	1.40659i	−0.0993018	+	0.995057i	$0.531661\pi$
$272$	9.53931	−	8.86479i	0.578406	−	0.537507i
$273$		0			0
$274$	−3.92288	+	5.75618i	−0.236990	+	0.347744i
$275$	−21.4193	−	5.73928i	−1.29163	−	0.346092i
$276$	25.2718	+	34.2147i	1.52118	+	2.05948i
$277$	−12.3863	+	3.31891i	−0.744223	+	0.199414i	−0.610954	−	0.791666i	$-0.709214\pi$
$277$	−12.3863	+	3.31891i	−0.744223	+	0.199414i	−0.133269	+	0.991080i	$0.542547\pi$
$278$	−11.4949	+	9.89601i	−0.689419	+	0.593523i
$279$		−	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	$-0.321824\pi$
$282$	28.5026	+	33.1078i	1.69730	+	1.97154i
$283$	7.29602	−	1.95496i	0.433703	−	0.116210i	−0.0353608	−	0.999375i	$-0.511258\pi$
$283$	7.29602	−	1.95496i	0.433703	−	0.116210i	0.469064	+	0.883164i	$0.344591\pi$
$284$	3.60102	−	23.9534i	0.213681	−	1.42138i
$285$	−6.18472	−	1.65719i	−0.366351	−	0.0981635i
$286$	−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
$290$	2.45906	−	1.18480i	0.144401	−	0.0695740i
$291$	6.00189	+	22.3993i	0.351837	+	1.31307i
$292$	−10.0330	−	7.99476i	−0.587136	−	0.467858i
$293$	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
$296$	−4.45781	−	2.35275i	−0.259105	−	0.136751i
$297$	21.8319	+	12.6046i	1.26681	+	0.731396i
$298$	5.08973	+	1.77988i	0.294840	+	0.103106i
$299$	6.22055	−	23.2154i	0.359744	−	1.34258i
$300$	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
$304$	−8.79345	−	5.51590i	−0.504339	−	0.316359i
$305$	2.11707	−	3.66687i	0.121223	−	0.209964i
$306$	21.6844	+	1.62085i	1.23962	+	0.0926579i
$307$	−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
$310$	2.32305	−	1.99992i	0.131940	−	0.113588i
$311$	−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	$0.937884\pi$
$312$	16.7797	−	18.1051i	0.949963	−	1.02500i
$313$	−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
$317$	1.27057	+	0.340449i	0.0713624	+	0.0191215i	0.294324	−	0.955706i	$-0.404906\pi$
$317$	1.27057	+	0.340449i	0.0713624	+	0.0191215i	−0.222961	+	0.974827i	$0.571572\pi$
$318$	−14.6716	+	7.06892i	−0.822741	+	0.396405i
$319$	5.72294	−	9.91241i	0.320423	−	0.554989i
$320$	−4.62685	+	5.38900i	−0.258649	+	0.301254i
$321$	9.69693			0.541230
$322$		0			0
$323$	−5.97399	+	5.97399i	−0.332402	+	0.332402i
$324$	1.07524	−	1.34937i	0.0597355	−	0.0749648i
$325$	−12.7762	+	3.42338i	−0.708697	+	0.189895i
$326$	5.43615	−	15.5452i	0.301081	−	0.860967i
$327$	−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
$331$	3.82179	−	14.2631i	0.210065	−	0.783972i	−0.777781	−	0.628535i	$-0.783655\pi$
$331$	3.82179	−	14.2631i	0.210065	−	0.783972i	0.987846	−	0.155437i	$-0.0496785\pi$
$332$	−4.47072	+	3.30218i	−0.245363	+	0.181231i
$333$	−2.17843	−	8.13002i	−0.119377	−	0.445522i
$334$	−17.5790	−	1.31398i	−0.961879	−	0.0718977i
$335$	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	$0.771061\pi$
$338$	4.42449	+	0.330718i	0.240660	+	0.0179887i
$339$	2.41060	+	8.99647i	0.130926	+	0.488621i
$340$	3.43462	+	4.65001i	0.186268	+	0.252182i
$341$	3.32677	−	12.4157i	0.180155	−	0.672346i
$342$	−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
$346$	−9.19435	+	26.2921i	−0.494291	+	1.41347i
$347$	−11.4112	+	3.05763i	−0.612586	+	0.164142i	−0.551755	−	0.834006i	$-0.686042\pi$
$347$	−11.4112	+	3.05763i	−0.612586	+	0.164142i	−0.0608309	+	0.998148i	$0.519375\pi$
$348$	9.44964	+	7.52992i	0.506554	+	0.403646i
$349$	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
$352$	−3.30636	+	29.5994i	−0.176230	+	1.57765i
$353$	−5.38113	+	9.32039i	−0.286409	+	0.496074i	−0.972950	−	0.231017i	$-0.925795\pi$
$353$	−5.38113	+	9.32039i	−0.286409	+	0.496074i	0.686541	+	0.727091i	$0.259128\pi$
$354$	−34.2466	+	16.5004i	−1.82019	+	0.876985i
$355$	10.3866	+	2.78307i	0.551261	+	0.147710i
$356$	−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	$-0.823957\pi$
$359$	−15.5646	+	8.98625i	−0.821470	+	0.474276i	0.0294531	+	0.999566i	$0.490623\pi$
$360$	−11.8517	+	0.450275i	−0.624639	+	0.0237316i
$361$	−10.6223	−	6.13282i	−0.559071	−	0.322780i
$362$	24.2569	−	20.8828i	1.27491	−	1.09758i
$363$	32.8568	+	32.8568i	1.72453	+	1.72453i
$364$		0			0
$365$	4.02695	−	4.02695i	0.210780	−	0.210780i
$366$	18.6907	+	1.39707i	0.976976	+	0.0730262i
$367$	−8.35453	+	14.4705i	−0.436103	+	0.755352i	−0.997385	−	0.0722722i	$-0.976975\pi$
$367$	−8.35453	+	14.4705i	−0.436103	+	0.755352i	0.561282	+	0.827625i	$0.310308\pi$
$368$	−29.8395	+	6.83471i	−1.55549	+	0.356284i
$369$	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
$373$	−5.70218	+	21.2808i	−0.295248	+	1.10188i	0.645773	+	0.763529i	$0.276535\pi$
$373$	−5.70218	+	21.2808i	−0.295248	+	1.10188i	−0.941021	+	0.338349i	$0.890131\pi$
$374$	22.8820	+	8.00184i	1.18320	+	0.413766i
$375$	19.6834	+	11.3642i	1.01645	+	0.586845i
$376$	−30.0382	+	9.28446i	−1.54910	+	0.478810i
$377$		−	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	$0.421395\pi$
$380$	2.87168	−	3.60380i	0.147314	−	0.184871i
$381$	−3.99639	−	14.9147i	−0.204741	−	0.764105i
$382$	−3.19938	+	1.54150i	−0.163695	+	0.0788698i
$383$	4.91665	+	8.51589i	0.251229	+	0.435141i	0.963864	−	0.266393i	$-0.0858319\pi$
$383$	4.91665	+	8.51589i	0.251229	+	0.435141i	−0.712635	+	0.701535i	$0.752499\pi$
$384$	−30.3805	−	8.09683i	−1.55035	−	0.413189i
$385$		0			0
$386$	11.7966	+	8.03948i	0.600431	+	0.409199i
$387$	48.4890	+	12.9926i	2.46483	+	0.660450i
$388$	−16.5035	−	2.48105i	−0.837841	−	0.125956i
$389$	−14.1371	+	3.78801i	−0.716777	+	0.192060i	−0.598733	−	0.800948i	$-0.704329\pi$
$389$	−14.1371	+	3.78801i	−0.716777	+	0.192060i	−0.118044	+	0.993008i	$0.537662\pi$
$390$	7.14951	+	8.30466i	0.362029	+	0.420523i
$391$			24.9153i			1.26002i
$392$		0			0
$393$			38.0085i			1.91728i
$394$	−20.5554	+	17.6962i	−1.03557	+	0.891522i
$395$	6.24545	−	1.67346i	0.314243	−	0.0842011i
$396$	−40.0036	+	29.5476i	−2.01025	+	1.48482i
$397$	24.6626	+	6.60834i	1.23778	+	0.331663i	0.817605	−	0.575779i	$-0.195301\pi$
$397$	24.6626	+	6.60834i	1.23778	+	0.331663i	0.420177	+	0.907442i	$0.361968\pi$
$398$	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	$0.988926\pi$
$402$	2.23296	+	4.63452i	0.111370	+	0.231149i
$403$	−1.98436	−	7.40572i	−0.0988478	−	0.368905i
$404$	9.49798	−	1.07385i	0.472542	−	0.0534259i
$405$	0.541596	+	0.541596i	0.0269121	+	0.0269121i
$406$		0			0
$407$		−	9.38288i		−	0.465092i
$408$	−11.9443	+	22.6312i	−0.591332	+	1.12041i
$409$	−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	$0.928081\pi$
$410$	−3.22289	+	9.21615i	−0.159167	+	0.455153i
$411$	3.54278	−	13.2219i	0.174753	−	0.652186i
$412$	−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
$416$	7.11978	+	16.2762i	0.349076	+	0.798006i
$417$	14.9029	−	25.8126i	0.729798	−	1.26405i
$418$	1.44029	−	19.2688i	0.0704467	−	0.942466i
$419$	−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	$0.512043\pi$
$422$	−5.03710	−	5.85095i	−0.245202	−	0.284820i
$423$	−45.4658	−	26.2497i	−2.21062	−	1.27630i
$424$	−0.444969	−	11.7120i	−0.0216096	−	0.568787i
$425$	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
$429$	44.3847	+	11.8928i	2.14291	+	0.574192i
$430$	5.79275	+	12.0229i	0.279351	+	0.579795i
$431$	−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	$0.330115\pi$
$432$	−8.96222	−	16.9260i	−0.431195	−	0.814350i
$433$	−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
$436$	−0.777198	−	6.87417i	−0.0372210	−	0.329213i
$437$	19.1835	−	5.14020i	0.917670	−	0.245889i
$438$	23.7962	+	8.32155i	1.13703	+	0.397619i
$439$	−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
$443$	2.61112	−	9.74483i	0.124058	−	0.462991i	−0.875746	−	0.482772i	$-0.839630\pi$
$443$	2.61112	−	9.74483i	0.124058	−	0.462991i	0.999804	+	0.0197808i	$0.00629683\pi$
$444$	9.79499	+	1.47252i	0.464850	+	0.0698828i
$445$	−0.152911	−	0.570670i	−0.00724865	−	0.0270523i
$446$	1.32134	−	17.6775i	0.0625675	−	0.837055i
$447$	−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	$0.400208\pi$
$450$	−2.09688	+	28.0529i	−0.0988476	+	1.32243i
$451$	10.5961	+	39.5453i	0.498952	+	1.86211i
$452$	−6.62849	−	0.996489i	−0.311778	−	0.0468709i
$453$	1.55667	−	5.80958i	0.0731388	−	0.272958i
$454$	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	$-0.398455\pi$
$457$	27.6363	−	15.9559i	1.29277	−	0.746383i	0.979145	+	0.203162i	$0.0651219\pi$
$458$	13.7723	+	4.81619i	0.643539	+	0.225046i
$459$	−15.0569	+	4.03448i	−0.702795	+	0.188313i
$460$	−1.52671	−	13.5034i	−0.0711830	−	0.629600i
$461$	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	$0.662609\pi$
$464$	−7.68496	+	4.06915i	−0.356765	+	0.188905i
$465$	−3.01178	+	5.21656i	−0.139668	+	0.241912i
$466$	−0.112138	−	0.232743i	−0.00519468	−	0.0107816i
$467$	−9.22775	−	2.47257i	−0.427009	−	0.114417i	0.0389127	−	0.999243i	$-0.487611\pi$
$467$	−9.22775	−	2.47257i	−0.427009	−	0.114417i	−0.465922	+	0.884826i	$0.654277\pi$
$468$	−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
$472$	−1.03865	−	27.3384i	−0.0478079	−	1.25835i
$473$	48.4639	+	27.9806i	2.22837	+	1.28655i
$474$	18.6735	+	21.6906i	0.857701	+	0.996281i
$475$	−7.72848	−	7.72848i	−0.354607	−	0.354607i
$476$		0			0
$477$	13.8388	−	13.8388i	0.633634	−	0.633634i
$478$	0.0275224	−	0.368206i	0.00125884	−	0.0168414i
$479$	−5.26638	+	9.12164i	−0.240627	+	0.416778i	−0.960893	−	0.276920i	$-0.910686\pi$
$479$	−5.26638	+	9.12164i	−0.240627	+	0.416778i	0.720266	+	0.693698i	$0.244020\pi$
$480$	5.08675	−	12.9974i	0.232178	−	0.593248i
$481$	−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
$485$	1.91749	−	7.15617i	0.0870688	−	0.324945i
$486$	−7.82482	+	22.3758i	−0.354941	+	1.01499i
$487$	2.99593	+	1.72970i	0.135759	+	0.0783803i	0.566341	−	0.824171i	$-0.308358\pi$
$487$	2.99593	+	1.72970i	0.135759	+	0.0783803i	−0.430582	+	0.902551i	$0.641692\pi$
$488$	−6.29604	+	11.9293i	−0.285008	+	0.540013i
$489$			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	$0.746374\pi$
$492$	−42.9451	+	4.85540i	−1.93611	+	0.218898i
$493$	1.83179	+	6.83633i	0.0824997	+	0.307893i
$494$	−5.00273	−	10.3832i	−0.225083	−	0.467162i
$495$	−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
$499$	−22.2717	−	5.96768i	−0.997018	−	0.267150i	−0.276822	−	0.960921i	$-0.589281\pi$
$499$	−22.2717	−	5.96768i	−0.997018	−	0.267150i	−0.720196	+	0.693771i	$0.755948\pi$
$500$	−13.1572	+	9.71825i	−0.588409	+	0.434614i
$501$	33.4598	−	8.96553i	1.49487	−	0.400550i
$502$	3.37273	−	2.90360i	0.150532	−	0.129594i
$503$		−	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
$506$	−37.1780	−	43.1849i	−1.65276	−	1.91980i
$507$	−8.42156	+	2.25655i	−0.374015	+	0.100217i
$508$	10.9890	+	1.65202i	0.487557	+	0.0732965i
$509$	−32.8096	−	8.79130i	−1.45426	−	0.389667i	−0.556756	−	0.830676i	$-0.687954\pi$
$509$	−32.8096	−	8.79130i	−1.45426	−	0.389667i	−0.897503	+	0.441009i	$0.854621\pi$
$510$	−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
$514$	−3.58551	+	1.72754i	−0.158150	+	0.0761984i
$515$	−4.41699	−	16.4844i	−0.194636	−	0.726390i
$516$	−36.8154	+	46.2013i	−1.62071	+	2.03390i
$517$	−41.3836	−	41.3836i	−1.82005	−	1.82005i
$518$		0			0
$519$		−	54.7336i		−	2.40254i
$520$	−7.53470	+	2.32889i	−0.330419	+	0.102128i
$521$	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	$0.525809\pi$
$522$	−13.7064	−	4.79312i	−0.599912	−	0.209789i
$523$	2.63608	−	9.83797i	0.115268	−	0.430184i	−0.884039	−	0.467413i	$-0.845186\pi$
$523$	2.63608	−	9.83797i	0.115268	−	0.430184i	0.999307	+	0.0372283i	$0.0118529\pi$
$524$	−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
$528$	−13.0670	−	57.0490i	−0.568669	−	2.48274i
$529$	17.7847	−	30.8039i	0.773246	−	1.33930i
$530$	5.18851	+	0.387826i	0.225375	+	0.0168461i
$531$	32.3027	−	32.3027i	1.40182	−	1.40182i
$532$		0			0
$533$	17.2676	+	17.2676i	0.747944	+	0.747944i
$534$	1.98195	−	1.70626i	0.0857672	−	0.0738373i
$535$	−2.68294	−	1.54899i	−0.115993	−	0.0669688i
$536$	−3.69965	+	0.140559i	−0.159800	+	0.00607121i
$537$	−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
$541$	2.14910	+	0.575849i	0.0923970	+	0.0247577i	0.304721	−	0.952442i	$-0.401437\pi$
$541$	2.14910	+	0.575849i	0.0923970	+	0.0247577i	−0.212324	+	0.977199i	$0.568103\pi$
$542$	34.0648	−	16.4128i	1.46321	−	0.704989i
$543$	−31.4484	+	54.4703i	−1.34958	+	2.33754i
$544$	−11.4963	−	14.3876i	−0.492898	−	0.616862i
$545$	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	$0.315605\pi$
$548$	7.70430	+	6.13915i	0.329111	+	0.262251i
$549$	−21.7562	+	5.82957i	−0.928534	+	0.248800i
$550$	−10.3519	+	29.6022i	−0.441406	+	1.26224i
$551$	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
$555$	−1.13805	+	4.24725i	−0.0483074	+	0.180286i
$556$	12.7444	+	17.2542i	0.540483	+	0.731742i
$557$	1.21555	+	4.53648i	0.0515043	+	0.192217i	0.986885	−	0.161426i	$-0.0516094\pi$
$557$	1.21555	+	4.53648i	0.0515043	+	0.192217i	−0.935380	+	0.353643i	$0.884943\pi$
$558$	−16.2608	−	1.21545i	−0.688376	−	0.0514542i
$559$	33.3799			1.41182
$560$		0			0
$561$	−47.6346			−2.01114
$562$	−40.0653	−	2.99477i	−1.69005	−	0.126327i
$563$	−6.87017	−	25.6398i	−0.289543	−	1.08059i	−0.945455	−	0.325752i	$-0.894382\pi$
$563$	−6.87017	−	25.6398i	−0.289543	−	1.08059i	0.655912	−	0.754837i	$-0.272284\pi$
$564$	49.6958	−	36.7066i	2.09257	−	1.54563i
$565$	0.770141	−	2.87421i	0.0324001	−	0.120919i
$566$	−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	$-0.502739\pi$
$569$	20.3493	−	11.7487i	0.853086	−	0.492530i	0.861691	+	0.507433i	$0.169406\pi$
$570$	−2.98906	+	8.54749i	−0.125198	+	0.358015i
$571$	−34.1056	+	9.13856i	−1.42727	+	0.382437i	−0.888058	−	0.459731i	$-0.847946\pi$
$571$	−34.1056	+	9.13856i	−1.42727	+	0.382437i	−0.539215	+	0.842168i	$0.681279\pi$
$572$	−20.6086	+	25.8627i	−0.861690	+	1.08137i
$573$	4.93467	−	4.93467i	0.206149	−	0.206149i
$574$		0			0
$575$	−32.2326			−1.34419
$576$	37.6746	−	2.86683i	1.56977	−	0.119451i
$577$	−7.20904	+	12.4864i	−0.300116	+	0.519817i	−0.976162	−	0.217043i	$-0.930359\pi$
$577$	−7.20904	+	12.4864i	−0.300116	+	0.519817i	0.676046	+	0.736860i	$0.263692\pi$
$578$	8.15524	−	3.92928i	0.339213	−	0.163436i
$579$	−27.0966	−	7.26051i	−1.12610	−	0.301737i
$580$	−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
$584$	−12.3325	+	13.3065i	−0.510321	+	0.550629i
$585$	−11.4045	−	6.58440i	−0.471519	−	0.272232i
$586$	13.1070	−	11.2838i	0.541444	−	0.466131i
$587$	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
$590$	12.1111	+	0.905270i	0.498606	+	0.0372694i
$591$	26.6496	−	46.1585i	1.09622	−	1.89871i
$592$	−3.78795	+	6.03874i	−0.155684	+	0.248191i
$593$	8.19296	+	14.1906i	0.336445	+	0.582739i	0.983761	−	0.179482i	$-0.0574422\pi$
$593$	8.19296	+	14.1906i	0.336445	+	0.582739i	−0.647317	+	0.762221i	$0.724109\pi$
$594$	20.0775	−	29.4603i	0.823788	−	1.20877i
$595$		0			0
$596$	3.04666	−	6.99032i	0.124796	−	0.286335i
$597$	−4.03691	+	15.0660i	−0.165220	+	0.616609i
$598$	−32.0845	−	11.2200i	−1.31203	−	0.458818i
$599$	−29.4485	−	17.0021i	−1.20323	−	0.694687i	−0.241961	−	0.970286i	$-0.577790\pi$
$599$	−29.4485	−	17.0021i	−1.20323	−	0.694687i	−0.961273	+	0.275599i	$0.911124\pi$
$600$	−29.2777	−	15.4522i	−1.19526	−	0.630835i
$601$		−	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
$604$	3.38521	+	2.69749i	0.137742	+	0.109759i
$605$	−3.84222	−	14.3394i	−0.156208	−	0.582978i
$606$	−16.9214	+	8.15289i	−0.687384	+	0.331189i
$607$	−5.23683	−	9.07046i	−0.212556	−	0.368159i	0.739957	−	0.672654i	$-0.234846\pi$
$607$	−5.23683	−	9.07046i	−0.212556	−	0.368159i	−0.952514	+	0.304495i	$0.901512\pi$
$608$	−8.70592	+	11.8198i	−0.353072	+	0.479355i
$609$		0			0
$610$	−4.94814	−	3.37220i	−0.200344	−	0.136536i
$611$	−33.7197	−	9.03517i	−1.36415	−	0.365524i
$612$	4.57170	−	30.4103i	0.184800	−	1.22926i
$613$	12.2909	−	3.29334i	0.496425	−	0.133017i	−0.00191560	−	0.999998i	$-0.500610\pi$
$613$	12.2909	−	3.29334i	0.496425	−	0.133017i	0.498340	+	0.866982i	$0.333943\pi$
$614$	29.9703	+	34.8126i	1.20950	+	1.40492i
$615$		−	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	$-0.0188421\pi$
$618$	57.2507	−	49.2873i	2.30296	−	1.98263i
$619$	9.90042	−	2.65281i	0.397932	−	0.106625i	−0.0543029	−	0.998525i	$-0.517294\pi$
$619$	9.90042	−	2.65281i	0.397932	−	0.106625i	0.452235	+	0.891899i	$0.350627\pi$
$620$	−2.57557	−	3.48697i	−0.103437	−	0.140040i
$621$	35.3948	+	9.48400i	1.42034	+	0.380580i
$622$	−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
$626$	12.3908	+	25.7171i	0.495234	+	1.02786i
$627$	9.82735	+	36.6762i	0.392466	+	1.46470i
$628$	1.25282	+	11.0809i	0.0499928	+	0.442177i
$629$	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	$-0.0611665\pi$
$632$	−19.6796	+	6.08272i	−0.782811	+	0.241958i
$633$	13.1387	+	7.58562i	0.522216	+	0.301501i
$634$	0.614065	−	1.75597i	0.0243876	−	0.0697386i
$635$	−1.27677	+	4.76498i	−0.0506672	+	0.189092i
$636$	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
$640$	7.11226	+	7.09323i	0.281137	+	0.280385i
$641$	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	$0.0654664\pi$
$642$	1.02220	−	13.6754i	0.0403428	−	0.539724i
$643$	−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
$646$	7.79525	+	9.05474i	0.306700	+	0.356254i
$647$	−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	$0.733015\pi$
$648$	−1.78964	−	1.65863i	−0.0703036	−	0.0651571i
$649$	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
$653$	−32.2582	−	8.64357i	−1.26236	−	0.338249i	−0.435263	−	0.900304i	$-0.643344\pi$
$653$	−32.2582	−	8.64357i	−1.26236	−	0.338249i	−0.827100	+	0.562054i	$0.810011\pi$
$654$	5.90066	+	12.2468i	0.230734	+	0.478890i
$655$	6.07151	−	10.5162i	0.237233	−	0.410900i
$656$	9.14518	−	29.7287i	0.357059	−	1.16071i
$657$	−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	$0.384701\pi$
$660$	25.8167	−	2.91885i	1.00491	−	0.113616i
$661$	30.3400	−	8.12957i	1.18009	−	0.316204i	0.385126	−	0.922864i	$-0.374158\pi$
$661$	30.3400	−	8.12957i	1.18009	−	0.316204i	0.794961	+	0.606660i	$0.207491\pi$
$662$	−19.7121	−	6.89333i	−0.766133	−	0.267917i
$663$	−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
$667$	4.30606	−	16.0704i	0.166731	−	0.622249i
$668$	−3.70615	+	24.6528i	−0.143395	+	0.953844i
$669$	9.01579	+	33.6474i	0.348571	+	1.30088i
$670$	0.122508	−	1.63897i	0.00473290	−	0.0633188i
$671$	−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	$0.154031\pi$
$674$	−2.91167	+	38.9536i	−0.112153	+	1.50044i
$675$	−5.21936	−	19.4789i	−0.200893	−	0.749744i
$676$	0.932809	−	6.20490i	0.0358773	−	0.238650i
$677$	−11.3361	+	42.3069i	−0.435682	+	1.62599i	0.303748	+	0.952752i	$0.401762\pi$
$677$	−11.3361	+	42.3069i	−0.435682	+	1.62599i	−0.739430	+	0.673234i	$0.764905\pi$
$678$	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
$682$	−17.1589	−	6.00046i	−0.657047	−	0.229770i
$683$	17.2290	−	4.61649i	0.659248	−	0.176645i	0.0863413	−	0.996266i	$-0.472482\pi$
$683$	17.2290	−	4.61649i	0.659248	−	0.176645i	0.572907	+	0.819621i	$0.305816\pi$
$684$	−24.3575	+	2.75387i	−0.931331	+	0.105297i
$685$	−3.09228	+	3.09228i	−0.118150	+	0.118150i
$686$		0			0
$687$	−28.6706			−1.09385
$688$	−19.8949	−	37.5734i	−0.758487	−	1.43247i
$689$	6.50682	−	11.2701i	0.247890	−	0.429358i
$690$	11.5911	+	24.0573i	0.441265	+	0.915848i
$691$	31.5415	+	8.45153i	1.19990	+	0.321511i	0.802790	−	0.596262i	$-0.203348\pi$
$691$	31.5415	+	8.45153i	1.19990	+	0.321511i	0.397106	+	0.917773i	$0.370015\pi$
$692$	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
$696$	11.6154	−	12.5329i	0.440281	−	0.475057i
$697$	−21.9236	−	12.6576i	−0.830416	−	0.479441i
$698$	−10.4087	−	12.0905i	−0.393975	−	0.457630i
$699$	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	$0.0381810\pi$
$702$	1.58510	−	21.2062i	0.0598259	−	0.800377i
$703$	2.31235	−	4.00511i	0.0872121	−	0.151056i
$704$	41.3949	+	7.78310i	1.56013	+	0.293337i
$705$	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
$709$	−10.8335	+	40.4313i	−0.406862	+	1.51843i	0.393734	+	0.919224i	$0.371183\pi$
$709$	−10.8335	+	40.4313i	−0.406862	+	1.51843i	−0.800596	+	0.599205i	$0.795484\pi$
$710$	5.01980	−	14.3546i	0.188390	−	0.538717i
$711$	−29.7870	−	17.1975i	−1.11710	−	0.644957i
$712$	0.555800	+	1.79819i	0.0208295	+	0.0673901i
$713$		−	18.6836i		−	0.699707i
$714$		0			0
$715$	−10.3805	−	10.3805i	−0.388210	−	0.388210i
$716$	−0.310640	−	2.74755i	−0.0116092	−	0.102681i
$717$	0.187790	+	0.700843i	0.00701316	+	0.0261735i
$718$	11.0324	+	22.8978i	0.411725	+	0.854537i
$719$	−23.9987	−	41.5669i	−0.894999	−	1.55018i	−0.833806	−	0.552058i	$-0.813843\pi$
$719$	−23.9987	−	41.5669i	−0.894999	−	1.55018i	−0.0611931	−	0.998126i	$-0.519491\pi$
$720$	−0.614326	+	16.7617i	−0.0228946	+	0.624670i
$721$		0			0
$722$	−9.76873	+	14.3340i	−0.363555	+	0.533456i
$723$	20.2136	+	5.41621i	0.751751	+	0.201431i
$724$	−26.8935	−	36.4103i	−0.999491	−	1.35318i
$725$	−8.84409	+	2.36977i	−0.328461	+	0.0880109i
$726$	49.8008	−	42.8737i	1.84828	−	1.59119i
$727$			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
$730$	−5.25463	−	6.10362i	−0.194482	−	0.225905i
$731$	−33.4243	+	8.95601i	−1.23624	+	0.331250i
$732$	3.94053	−	26.2118i	0.145646	−	0.968815i
$733$	−8.65952	−	2.32031i	−0.319847	−	0.0857026i	0.0953238	−	0.995446i	$-0.469611\pi$
$733$	−8.65952	−	2.32031i	−0.319847	−	0.0857026i	−0.415170	+	0.909744i	$0.636278\pi$
$734$	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
$738$	46.7893	−	22.5436i	1.72234	−	0.829841i
$739$	0.307565	+	1.14785i	0.0113140	+	0.0422243i	0.971352	−	0.237645i	$-0.0763755\pi$
$739$	0.307565	+	1.14785i	0.0113140	+	0.0422243i	−0.960038	+	0.279869i	$0.909709\pi$
$740$	−2.47485	−	1.97207i	−0.0909772	−	0.0724949i
$741$	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	$0.669988\pi$
$744$	8.95687	−	16.9708i	0.328375	−	0.622180i
$745$	2.93157	+	1.69254i	0.107404	+	0.0620099i
$746$	29.4108	+	10.2850i	1.07681	+	0.376559i
$747$	−3.39703	+	12.6779i	−0.124291	+	0.463860i
$748$	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	$0.765937\pi$
$752$	9.92722	+	43.3410i	0.362009	+	1.58048i
$753$	−4.37267	+	7.57369i	−0.159349	+	0.276000i
$754$	−9.62833	−	0.719691i	−0.350643	−	0.0262096i
$755$	−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	$0.872761\pi$
$758$	35.8251	−	30.8420i	1.30123	−	1.12023i
$759$	96.9745	+	55.9882i	3.51995	+	2.03224i
$760$	−4.77965	−	4.42976i	−0.173376	−	0.160684i
$761$	−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
$765$	13.1863	+	3.53326i	0.476753	+	0.127745i
$766$	12.5281	−	6.03615i	0.452657	−	0.218095i
$767$	15.1883	−	26.3069i	0.548418	−	0.949887i
$768$	−14.6213	+	41.9915i	−0.527602	+	1.51524i
$769$	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
$772$	12.5814	−	15.7890i	0.452816	−	0.568260i
$773$	22.7046	−	6.08368i	0.816627	−	0.218815i	0.173756	−	0.984789i	$-0.444410\pi$
$773$	22.7046	−	6.08368i	0.816627	−	0.218815i	0.642871	+	0.765974i	$0.277743\pi$
$774$	23.4346	−	67.0134i	0.842339	−	2.40875i
$775$	−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
$779$	−5.22270	+	19.4914i	−0.187123	+	0.698351i
$780$	12.4656	−	9.20737i	0.446339	−	0.329677i
$781$	−16.5039	−	61.5935i	−0.590557	−	2.20399i
$782$	35.1375	+	2.62643i	1.25652	+	0.0939210i
$783$	10.4090			0.371987
$784$		0			0
$785$	−4.95040			−0.176688
$786$	53.6026	+	4.00665i	1.91194	+	0.142912i
$787$	−1.46878	−	5.48157i	−0.0523564	−	0.195397i	0.934794	−	0.355190i	$-0.115584\pi$
$787$	−1.46878	−	5.48157i	−0.0523564	−	0.195397i	−0.987150	+	0.159793i	$0.948917\pi$
$788$	22.7898	+	30.8543i	0.811852	+	1.09914i
$789$	6.13220	−	22.8857i	0.218312	−	0.814752i
$790$	−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
$794$	11.9194	−	34.0846i	0.423004	−	1.20962i
$795$	−9.87581	+	2.64621i	−0.350259	+	0.0938516i
$796$	−8.77885	−	6.99540i	−0.311158	−	0.247946i
$797$	−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
$800$	18.6130	−	14.8726i	0.658070	−	0.525825i
$801$	−1.57140	+	2.72174i	−0.0555226	+	0.0961681i
$802$	−23.9603	+	11.5443i	−0.846066	+	0.407643i
$803$	−32.6211	−	8.74080i	−1.15117	−	0.308456i
$804$	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
$808$	−0.513202	−	13.5080i	−0.0180544	−	0.475210i
$809$	5.44560	+	3.14402i	0.191457	+	0.110538i	0.592665	−	0.805449i	$-0.298076\pi$
$809$	5.44560	+	3.14402i	0.191457	+	0.110538i	−0.401207	+	0.915987i	$0.631409\pi$
$810$	0.820894	−	0.706710i	0.0288433	−	0.0248313i
$811$	−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
$814$	−13.2325	−	0.989091i	−0.463798	−	0.0346676i
$815$	5.16940	−	8.95366i	0.181076	−	0.313633i
$816$	30.6572	+	19.2305i	1.07322	+	0.673202i
$817$	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
$821$	−4.38445	+	16.3630i	−0.153018	+	0.571072i	0.846249	+	0.532788i	$0.178856\pi$
$821$	−4.38445	+	16.3630i	−0.153018	+	0.571072i	−0.999267	+	0.0382839i	$0.987811\pi$
$822$	−18.2730	−	6.39009i	−0.637346	−	0.222880i
$823$	32.3363	+	18.6694i	1.12717	+	0.650774i	0.943223	−	0.332162i	$-0.107778\pi$
$823$	32.3363	+	18.6694i	1.12717	+	0.650774i	0.183951	+	0.982935i	$0.441111\pi$
$824$	16.0549	+	51.9428i	0.559299	+	1.80951i
$825$		−	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	$0.791809\pi$
$828$	−45.0503	+	56.5357i	−1.56561	+	1.96475i
$829$	2.11606	+	7.89725i	0.0734939	+	0.274283i	0.992888	−	0.119056i	$-0.0379867\pi$
$829$	2.11606	+	7.89725i	0.0734939	+	0.274283i	−0.919394	+	0.393339i	$0.871320\pi$
$830$	−3.14349	+	1.51457i	−0.109112	+	0.0525714i
$831$	−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
$835$	−10.6898	−	2.86432i	−0.369935	−	0.0991239i
$836$	−27.0225	−	4.06241i	−0.934594	−	0.140501i
$837$	11.2909	−	3.02540i	0.390272	−	0.104573i
$838$	1.50358	+	1.74651i	0.0519402	+	0.0603323i
$839$		−	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
$842$	29.9008	−	25.7417i	1.03045	−	0.887117i
$843$	76.2603	−	20.4339i	2.62654	−	0.703780i
$844$	−8.78246	+	6.48695i	−0.302305	+	0.223290i
$845$	2.69053	+	0.720926i	0.0925571	+	0.0248006i
$846$	−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
$850$	−8.41692	−	17.4694i	−0.288698	−	0.599194i
$851$	−3.52994	−	13.1739i	−0.121005	−	0.451596i
$852$	66.8889	−	7.56250i	2.29158	−	0.259087i
$853$	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
$856$	8.72828	+	4.60662i	0.298326	+	0.157451i
$857$	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	$0.591885\pi$
$858$	21.4510	−	61.3411i	0.732325	−	2.09415i
$859$	11.6772	−	43.5800i	0.398422	−	1.48693i	−0.417451	−	0.908699i	$-0.637077\pi$
$859$	11.6772	−	43.5800i	0.398422	−	1.48693i	0.815873	−	0.578231i	$-0.196257\pi$
$860$	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	$0.496694\pi$
$864$	−24.8151	+	10.8550i	−0.844226	+	0.369294i
$865$	−8.74318	+	15.1436i	−0.297277	+	0.514899i
$866$	−2.98435	+	39.9259i	−0.101412	+	1.35674i
$867$	−12.5785	+	12.5785i	−0.427188	+	0.427188i
$868$		0			0
$869$	−27.1125	−	27.1125i	−0.919727	−	0.919727i
$870$	4.94911	+	5.74874i	0.167790	+	0.194901i
$871$	−3.56006	−	2.05540i	−0.120628	−	0.0696445i
$872$	−9.77643	+	0.371430i	−0.331072	+	0.0125782i
$873$	−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
$877$	−29.2459	−	7.83642i	−0.987564	−	0.264617i	−0.271337	−	0.962484i	$-0.587466\pi$
$877$	−29.2459	−	7.83642i	−0.987564	−	0.264617i	−0.716227	+	0.697867i	$0.754133\pi$
$878$	2.80670	+	5.82533i	0.0947216	+	0.196595i
$879$	−16.9929	+	29.4326i	−0.573156	+	0.992735i
$880$	−5.49768	+	17.8716i	−0.185327	+	0.602452i
$881$	−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	$0.139445\pi$
$884$	−2.29727	−	20.3189i	−0.0772656	−	0.683399i
$885$	−23.0522	+	6.17683i	−0.774893	+	0.207632i
$886$	−13.4677	−	4.70965i	−0.452456	−	0.158224i
$887$	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
$891$	1.17558	−	4.38731i	0.0393833	−	0.146980i
$892$	−24.7910	−	3.72693i	−0.830063	−	0.124787i
$893$	−7.46599	−	27.8634i	−0.249840	−	0.932415i
$894$	−1.11692	+	14.9427i	−0.0373555	+	0.499758i
$895$	1.22747			0.0410298
$896$		0			0
$897$	66.7919			2.23012
$898$	1.37772	−	18.4317i	0.0459750	−	0.615074i
$899$	−1.37363	−	5.12646i	−0.0458132	−	0.170977i
$900$	39.3414	+	5.91436i	1.31138	+	0.197145i
$901$	−3.49163	+	13.0309i	−0.116323	+	0.434124i
$902$	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
$906$	−8.02903	−	2.80776i	−0.266747	−	0.0932814i
$907$	20.8301	−	5.58142i	0.691653	−	0.185328i	0.104164	−	0.994560i	$-0.466783\pi$
$907$	20.8301	−	5.58142i	0.691653	−	0.185328i	0.587489	+	0.809232i	$0.300117\pi$
$908$	−4.99020	−	44.1373i	−0.165605	−	1.46475i
$909$	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	$0.541673\pi$
$912$	8.48167	−	27.5718i	0.280856	−	0.912995i
$913$	−7.31580	+	12.6713i	−0.242118	+	0.419360i
$914$	−19.5889	−	40.6569i	−0.647945	−	1.34481i
$915$	11.3658	+	3.04546i	0.375742	+	0.100680i
$916$	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	$-0.655542\pi$
$919$	1.83468	−	1.05925i	0.0605206	−	0.0349416i	0.529955	+	0.848026i	$0.322209\pi$
$920$	−19.2045	+	0.729627i	−0.633154	+	0.0240551i
$921$	−78.1739	−	45.1337i	−2.57592	−	1.48721i
$922$	−14.7291	−	17.1089i	−0.485078	−	0.563452i
$923$	−26.8951	−	26.8951i	−0.885264	−	0.885264i
$924$		0			0
$925$	−5.30740	+	5.30740i	−0.174506	+	0.174506i
$926$	−2.21798	+	29.6731i	−0.0728873	+	0.975119i
$927$	−45.3916	+	78.6205i	−1.49085	+	2.58224i
$928$	4.92853	+	11.2669i	0.161787	+	0.369853i
$929$	−16.1033	−	27.8918i	−0.528333	−	0.915099i	−0.999454	−	0.0330307i	$-0.989484\pi$
$929$	−16.1033	−	27.8918i	−0.528333	−	0.915099i	0.471122	−	0.882068i	$-0.343849\pi$
$930$	7.03932	+	4.79736i	0.230829	+	0.157312i
$931$		0			0
$932$	−0.340053	+	0.133611i	−0.0111388	+	0.00437658i
$933$	19.0934	−	71.2574i	0.625088	−	2.33286i
$934$	−4.45975	+	12.7531i	−0.145927	+	0.417293i
$935$	13.1795	+	7.60919i	0.431016	+	0.248847i
$936$	37.1018	+	19.5816i	1.21271	+	0.640046i
$937$			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
$940$	−19.6133	+	2.21750i	−0.639716	+	0.0723267i
$941$	7.32652	+	27.3429i	0.238838	+	0.891354i	0.976381	+	0.216055i	$0.0693190\pi$
$941$	7.32652	+	27.3429i	0.238838	+	0.891354i	−0.737544	+	0.675300i	$0.764014\pi$
$942$	−9.51166	−	19.7415i	−0.309906	−	0.643212i
$943$	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
$947$	−22.9654	−	6.15356i	−0.746275	−	0.199964i	−0.134410	−	0.990926i	$-0.542914\pi$
$947$	−22.9654	−	6.15356i	−0.746275	−	0.199964i	−0.611865	+	0.790962i	$0.709581\pi$
$948$	32.5582	−	24.0483i	1.05744	−	0.781053i
$949$	−19.4579	+	5.21373i	−0.631630	+	0.169245i
$950$	−11.7140	+	10.0846i	−0.380053	+	0.327188i
$951$			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	$-0.163302\pi$
$954$	−18.0577	−	20.9754i	−0.584641	−	0.679102i
$955$	−2.15359	+	0.577052i	−0.0696884	+	0.0186730i
$956$	−0.516372	−	0.0776284i	−0.0167007	−	0.00251068i
$957$	30.7244	+	8.23259i	0.993180	+	0.266122i
$958$	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
$962$	−7.13047	+	3.43554i	−0.229896	+	0.110766i
$963$	4.26532	+	15.9184i	0.137448	+	0.512962i
$964$	−9.38553	+	11.7783i	−0.302288	+	0.379354i
$965$	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	$0.931046\pi$
$968$	13.9657	+	45.1836i	0.448875	+	1.45226i
$969$	−20.3330	−	11.7393i	−0.653190	−	0.377119i
$970$	−9.89007	−	3.45856i	−0.317551	−	0.111048i
$971$	−3.42316	+	12.7754i	−0.109854	+	0.409982i	−0.998851	−	0.0479326i	$-0.984737\pi$
$971$	−3.42316	+	12.7754i	−0.109854	+	0.409982i	0.888996	+	0.457914i	$0.151403\pi$
$972$	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
$976$	16.1599	+	10.1367i	0.517266	+	0.324468i
$977$	−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	$0.842355\pi$
$978$	45.6383	+	3.41133i	1.45935	+	0.109082i
$979$	−2.47736	+	2.47736i	−0.0791769	+	0.0791769i
$980$		0			0
$981$	−11.5517	−	11.5517i	−0.368817	−	0.368817i
$982$	0.541060	−	0.465800i	0.0172659	−	0.0148643i
$983$	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	$0.665167\pi$
$984$	2.32044	+	61.0764i	0.0739729	+	1.94704i
$985$	−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
$989$	78.5717	+	21.0532i	2.49843	+	0.669453i
$990$	−28.1277	+	13.5522i	−0.893956	+	0.430718i
$991$	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	$-0.0660397\pi$
$992$	8.62086	+	10.7890i	0.273713	+	0.342552i
$993$	41.0357			1.30223
$994$		0			0
$995$	3.52358	−	3.52358i	0.111705	−	0.111705i
$996$	−12.0798	−	9.62572i	−0.382762	−	0.305003i
$997$	−44.4977	+	11.9231i	−1.40926	+	0.377609i	−0.881660	−	0.471885i	$-0.843574\pi$
$997$	−44.4977	+	11.9231i	−1.40926	+	0.377609i	−0.527597	+	0.849495i	$0.676907\pi$
$998$	−10.7639	+	30.7802i	−0.340724	+	0.974331i
$999$	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.165.3		16
7.2	even	3	inner	784.2.x.j.373.1		16
7.3	odd	6		112.2.m.c.85.3	yes	8
7.4	even	3		784.2.m.g.197.3		8
7.5	odd	6		784.2.x.k.373.1		16
7.6	odd	2		784.2.x.k.165.3		16
16.13	even	4	inner	784.2.x.j.557.1		16
28.3	even	6		448.2.m.c.113.4		8
56.3	even	6		896.2.m.f.225.1		8
56.45	odd	6		896.2.m.e.225.4		8
112.3	even	12		448.2.m.c.337.4		8
112.13	odd	4		784.2.x.k.557.1		16
112.45	odd	12		112.2.m.c.29.3	✓	8
112.59	even	12		896.2.m.f.673.1		8
112.61	odd	12		784.2.x.k.765.3		16
112.93	even	12	inner	784.2.x.j.765.3		16
112.101	odd	12		896.2.m.e.673.4		8
112.109	even	12		784.2.m.g.589.3		8
224.3	even	24		7168.2.a.bd.1.8		8
224.45	odd	24		7168.2.a.bc.1.8		8
224.115	even	24		7168.2.a.bd.1.1		8
224.157	odd	24		7168.2.a.bc.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.3	✓	8	112.45	odd	12
112.2.m.c.85.3	yes	8	7.3	odd	6
448.2.m.c.113.4		8	28.3	even	6
448.2.m.c.337.4		8	112.3	even	12
784.2.m.g.197.3		8	7.4	even	3
784.2.m.g.589.3		8	112.109	even	12
784.2.x.j.165.3		16	1.1	even	1	trivial
784.2.x.j.373.1		16	7.2	even	3	inner
784.2.x.j.557.1		16	16.13	even	4	inner
784.2.x.j.765.3		16	112.93	even	12	inner
784.2.x.k.165.3		16	7.6	odd	2
784.2.x.k.373.1		16	7.5	odd	6
784.2.x.k.557.1		16	112.13	odd	4
784.2.x.k.765.3		16	112.61	odd	12
896.2.m.e.225.4		8	56.45	odd	6
896.2.m.e.673.4		8	112.101	odd	12
896.2.m.f.225.1		8	56.3	even	6
896.2.m.f.673.1		8	112.59	even	12
7168.2.a.bc.1.1		8	224.157	odd	24
7168.2.a.bc.1.8		8	224.45	odd	24
7168.2.a.bd.1.1		8	224.115	even	24
7168.2.a.bd.1.8		8	224.3	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+(0.105414 - 1.41028i) q^{2} +(0.719263 + 2.68432i) q^{3} +(-1.97778 - 0.297327i) q^{4} +(0.229791 - 0.857592i) q^{5} +(3.86147 - 0.731395i) q^{6} +(-0.627801 + 2.75787i) q^{8} +(-4.09018 + 2.36147i) q^{9} +(-1.18522 - 0.414472i) q^{10} +(-5.08562 + 1.36269i) q^{11} +(-0.624417 - 5.52285i) q^{12} +(-2.22066 + 2.22066i) q^{13} +2.46733 q^{15} +(3.82319 + 1.17609i) q^{16} +(1.62780 - 2.81943i) q^{17} +(2.89917 + 6.01723i) q^{18} +(-2.50664 - 0.671653i) q^{19} +(-0.709460 + 1.62780i) q^{20} +(1.38567 + 7.31580i) q^{22} +(-6.62774 + 3.82653i) q^{23} +(-7.85458 + 0.298415i) q^{24} +(3.64747 + 2.10587i) q^{25} +(2.89767 + 3.36584i) q^{26} +(-3.38567 - 3.38567i) q^{27} +(-1.53721 + 1.53721i) q^{29} +(0.260092 - 3.47963i) q^{30} +(-1.22066 + 2.11425i) q^{31} +(2.06164 - 5.26779i) q^{32} +(-7.31580 - 12.6713i) q^{33} +(-3.80460 - 2.59286i) q^{34} +(8.79159 - 3.45433i) q^{36} +(-0.461245 + 1.72139i) q^{37} +(-1.21145 + 3.46426i) q^{38} +(-7.55822 - 4.36374i) q^{39} +(2.22087 + 1.17213i) q^{40} -7.77589i q^{41} +(-7.51575 - 7.51575i) q^{43} +(10.4634 - 1.18300i) q^{44} +(1.08529 + 4.05035i) q^{45} +(4.69782 + 9.75034i) q^{46} +(5.55792 + 9.62661i) q^{47} +(-0.407138 + 11.1086i) q^{48} +(3.35436 - 4.92196i) q^{50} +(8.73909 + 2.34163i) q^{51} +(5.05224 - 3.73171i) q^{52} +(-4.00262 + 1.07250i) q^{53} +(-5.13164 + 4.41785i) q^{54} +4.67452i q^{55} -7.21173i q^{57} +(2.00585 + 2.32994i) q^{58} +(-9.34298 + 2.50344i) q^{59} +(-4.87983 - 0.733606i) q^{60} +(4.60651 + 1.23431i) q^{61} +(2.85301 + 1.94435i) q^{62} +(-7.21173 - 3.46279i) q^{64} +(1.39413 + 2.41471i) q^{65} +(-18.6413 + 8.98158i) q^{66} +(0.338785 + 1.26436i) q^{67} +(-4.05772 + 5.09222i) q^{68} +(-15.0387 - 15.0387i) q^{69} +12.1113i q^{71} +(-3.94481 - 12.7627i) q^{72} +(5.55501 + 3.20719i) q^{73} +(2.37902 + 0.831944i) q^{74} +(-3.02934 + 11.3057i) q^{75} +(4.75787 + 2.07367i) q^{76} +(-6.95084 + 10.1992i) q^{78} +(3.64128 + 6.30687i) q^{79} +(1.88714 - 3.00848i) q^{80} +(-0.431344 + 0.747110i) q^{81} +(-10.9662 - 0.819691i) q^{82} +(1.96506 - 1.96506i) q^{83} +(-2.04387 - 2.04387i) q^{85} +(-11.3916 + 9.80704i) q^{86} +(-5.23203 - 3.02071i) q^{87} +(-0.565366 - 14.8810i) q^{88} +(0.576282 - 0.332717i) q^{89} +(5.82653 - 1.10359i) q^{90} +(14.2459 - 5.59741i) q^{92} +(-6.55331 - 1.75595i) q^{93} +(14.1621 - 6.82344i) q^{94} +(-1.15201 + 1.99533i) q^{95} +(15.6233 + 1.74518i) q^{96} +8.34450 q^{97} +(17.5832 - 17.5832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) \) 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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