LMFDB - Embedded newform 784.2.x.k.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.k.765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.105414 - 1.41028i) q^{2} +(-0.719263 - 2.68432i) q^{3} +(-1.97778 - 0.297327i) q^{4} +(-0.229791 + 0.857592i) q^{5} +(-3.86147 + 0.731395i) q^{6} +(-0.627801 + 2.75787i) q^{8} +(-4.09018 + 2.36147i) q^{9} +O(q^{10})$	\(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}+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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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	$-0.786978\pi$
$3$	−0.719263	−	2.68432i	−0.415266	−	1.54980i	0.369035	−	0.929415i	$-0.379688\pi$
$4$	−1.97778	−	0.297327i	−0.988888	−	0.148664i
$5$	−0.229791	+	0.857592i	−0.102766	+	0.383527i	−0.998082	−	0.0619040i	$-0.980283\pi$
$5$	−0.229791	+	0.857592i	−0.102766	+	0.383527i	0.895316	+	0.445431i	$0.146949\pi$
$6$	−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	−0.328576	−	0.944477i	$-0.606569\pi$
$13$	2.22066	−	2.22066i	0.615901	−	0.615901i	0.944477	+	0.328576i	$0.106569\pi$
$14$		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	−0.993076	−	0.117477i	$-0.962519\pi$
$17$	−1.62780	+	2.81943i	−0.394800	+	0.683813i	0.598276	+	0.801290i	$0.295853\pi$
$18$	2.89917	+	6.01723i	0.683340	+	1.41828i
$19$	2.50664	+	0.671653i	0.575063	+	0.154088i	0.534618	−	0.845094i	$-0.320456\pi$
$19$	2.50664	+	0.671653i	0.575063	+	0.154088i	0.0404454	+	0.999182i	$0.487122\pi$
$20$	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	−0.735338	−	0.677701i	$-0.762976\pi$
$31$	1.22066	−	2.11425i	0.219238	−	0.379731i	0.954575	+	0.297970i	$0.0963097\pi$
$32$	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	$0.207705\pi$
$41$			7.77589i			1.21439i	−0.794553	+	0.607195i	$0.792295\pi$
$42$		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	$-0.865750\pi$
$47$	−5.55792	−	9.62661i	−0.810707	−	1.40418i	0.101664	−	0.994819i	$-0.467583\pi$
$48$	0.407138	−	11.1086i	0.0587653	−	1.60339i
$49$		0			0
$50$	3.35436	−	4.92196i	0.474377	−	0.696070i
$51$	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	0.407101	−	0.913383i	$-0.366540\pi$
$59$	9.34298	−	2.50344i	1.21635	−	0.325921i	0.809251	+	0.587463i	$0.199873\pi$
$60$	−4.87983	−	0.733606i	−0.629984	−	0.0947081i
$61$	−4.60651	−	1.23431i	−0.589803	−	0.158037i	−0.0484399	−	0.998826i	$-0.515425\pi$
$61$	−4.60651	−	1.23431i	−0.589803	−	0.158037i	−0.541363	+	0.840789i	$0.682092\pi$
$62$	−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	0.138354	−	0.990383i	$-0.455819\pi$
$73$	−5.55501	−	3.20719i	−0.650165	−	0.375373i	−0.788519	+	0.615010i	$0.789152\pi$
$74$	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	−0.806681	−	0.590987i	$-0.798738\pi$
$83$	−1.96506	+	1.96506i	−0.215694	+	0.215694i	0.590987	+	0.806681i	$0.298738\pi$
$84$		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	−0.530232	−	0.847853i	$-0.677895\pi$
$89$	−0.576282	+	0.332717i	−0.0610858	+	0.0352679i	0.469146	+	0.883121i	$0.344562\pi$
$90$	−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	$-0.639244\pi$
$97$	−8.34450			−0.847256			−0.423628	+	0.905836i	$0.639244\pi$
$98$		0			0
$99$	17.5832	−	17.5832i	1.76718	−	1.76718i
$100$	−6.58774	−	5.24942i	−0.658774	−	0.524942i
$101$	4.61640	−	1.23696i	0.459349	−	0.123082i	−0.0217217	−	0.999764i	$-0.506915\pi$
$101$	4.61640	−	1.23696i	0.459349	−	0.123082i	0.481070	+	0.876682i	$0.340248\pi$
$102$	4.22358	−	12.0777i	0.418197	−	1.19587i
$103$	−16.6465	+	9.61088i	−1.64023	+	0.946988i	−0.659482	+	0.751720i	$0.729224\pi$
$103$	−16.6465	+	9.61088i	−1.64023	+	0.946988i	−0.980750	+	0.195268i	$0.937442\pi$
$104$	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	−0.369580	−	0.929199i	$-0.620498\pi$
$131$	−13.2109	−	3.53986i	−1.15425	−	0.309279i	−0.784665	+	0.619920i	$0.787165\pi$
$132$	−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	0.951356	−	0.308095i	$-0.0996914\pi$
$139$	7.58393	+	7.58393i	0.643261	+	0.643261i	−0.308095	+	0.951356i	$0.599691\pi$
$140$		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	0.999300	−	0.0374157i	$-0.0119126\pi$
$157$	1.44311	+	5.38577i	0.115173	+	0.429831i	−0.884127	+	0.467247i	$0.845246\pi$
$158$	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	$0.160192\pi$
$167$			12.4649i			0.964562i	−0.876016	+	0.482281i	$0.839808\pi$
$168$		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	0.894764	−	0.446539i	$-0.147344\pi$
$173$	19.0242	+	5.09752i	1.44638	+	0.387557i	0.551619	+	0.834096i	$0.314010\pi$
$174$	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	$-0.931885\pi$
$181$	−16.0038	−	16.0038i	−1.18955	−	1.18955i	−0.212362	−	0.977191i	$-0.568115\pi$
$182$		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	0.317726	−	0.948183i	$-0.397081\pi$
$199$	−4.86063	−	2.80629i	−0.344561	−	0.198932i	−0.662287	+	0.749250i	$0.730414\pi$
$200$	−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	$-0.637863\pi$
$223$	−12.5348			−0.839390			−0.419695	+	0.907665i	$0.637863\pi$
$224$		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	$-0.819556\pi$
$227$	−5.74818	−	21.4525i	−0.381520	−	1.42385i	0.462059	−	0.886849i	$-0.347111\pi$
$228$	−2.14425	+	14.2632i	−0.142006	+	0.944603i
$229$	2.67019	−	9.96527i	0.176451	−	0.658524i	−0.819849	−	0.572580i	$-0.805943\pi$
$229$	2.67019	−	9.96527i	0.176451	−	0.658524i	0.996300	−	0.0859440i	$-0.0273906\pi$
$230$	−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	−0.961435	−	0.275033i	$-0.911311\pi$
$241$	−3.76511	+	6.52137i	−0.242532	+	0.420078i	0.718903	+	0.695111i	$0.244645\pi$
$242$	−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	0.633384	−	0.773838i	$-0.281665\pi$
$251$	−2.22521	−	2.22521i	−0.140454	−	0.140454i	−0.773838	+	0.633384i	$0.781665\pi$
$252$		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	0.906570	−	0.422055i	$-0.138691\pi$
$257$	1.40714	+	2.43723i	0.0877748	+	0.152030i	−0.818795	+	0.574085i	$0.805358\pi$
$258$	34.5188	+	23.5248i	2.14905	+	1.46459i
$259$		0			0
$260$	−2.03932	−	5.19027i	−0.126474	−	0.321887i
$261$	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	$-0.917929\pi$
$269$	−4.21577	−	15.7335i	−0.257040	−	0.959286i	0.709904	−	0.704298i	$-0.248738\pi$
$270$	2.60950	+	5.41604i	0.158809	+	0.329610i
$271$	−13.3688	−	23.1554i	−0.812094	−	1.40659i	−0.911396	−	0.411531i	$-0.864994\pi$
$271$	−13.3688	−	23.1554i	−0.812094	−	1.40659i	0.0993018	−	0.995057i	$-0.468339\pi$
$272$	−9.53931	+	8.86479i	−0.578406	+	0.537507i
$273$		0			0
$274$	−3.92288	+	5.75618i	−0.236990	+	0.347744i
$275$	−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	−0.469064	−	0.883164i	$-0.655409\pi$
$283$	−7.29602	+	1.95496i	−0.433703	+	0.116210i	0.0353608	+	0.999375i	$0.488742\pi$
$284$	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	0.407854	−	0.913047i	$-0.366277\pi$
$293$	−8.64751	−	8.64751i	−0.505193	−	0.505193i	−0.913047	+	0.407854i	$0.866277\pi$
$294$		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	$-0.372448\pi$
$307$	22.9681	−	22.9681i	1.31086	−	1.31086i	0.920782	−	0.390077i	$-0.127552\pi$
$308$		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	0.981020	−	0.193906i	$-0.0621156\pi$
$311$	22.9893	+	13.2729i	1.30360	+	0.752635i	0.322583	+	0.946541i	$0.395449\pi$
$312$	16.7797	−	18.1051i	0.949963	−	1.02500i
$313$	17.4811	−	10.0927i	0.988088	−	0.570473i	0.0833856	−	0.996517i	$-0.473427\pi$
$313$	17.4811	−	10.0927i	0.988088	−	0.570473i	0.904702	+	0.426045i	$0.140093\pi$
$314$	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	−0.887602	−	0.460611i	$-0.847630\pi$
$349$	−7.97685	+	7.97685i	−0.426991	+	0.426991i	0.460611	+	0.887602i	$0.347630\pi$
$350$		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	−0.686541	−	0.727091i	$-0.740872\pi$
$353$	5.38113	−	9.32039i	0.286409	−	0.496074i	0.972950	+	0.231017i	$0.0742052\pi$
$354$	−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	−0.561282	−	0.827625i	$-0.689692\pi$
$367$	8.35453	−	14.4705i	0.436103	−	0.755352i	0.997385	+	0.0722722i	$0.0230250\pi$
$368$	−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	0.712635	−	0.701535i	$-0.247501\pi$
$383$	−4.91665	−	8.51589i	−0.251229	−	0.435141i	−0.963864	+	0.266393i	$0.914168\pi$
$384$	30.3805	+	8.09683i	1.55035	+	0.413189i
$385$		0			0
$386$	11.7966	+	8.03948i	0.600431	+	0.409199i
$387$	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	−0.420177	−	0.907442i	$-0.638032\pi$
$397$	−24.6626	−	6.60834i	−1.23778	−	0.331663i	−0.817605	+	0.575779i	$0.804699\pi$
$398$	−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	0.974584	−	0.224023i	$-0.0719190\pi$
$409$	25.6410	+	14.8038i	1.26787	+	0.732003i	0.293283	+	0.956026i	$0.405252\pi$
$410$	−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	−0.678400	−	0.734693i	$-0.737326\pi$
$419$	1.15229	−	1.15229i	0.0562929	−	0.0562929i	0.734693	+	0.678400i	$0.237326\pi$
$420$		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	$-0.261866\pi$
$433$	28.3107			1.36052			0.680262	+	0.732969i	$0.261866\pi$
$434$		0			0
$435$	−3.79281	+	3.79281i	−0.181851	+	0.181851i
$436$	−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	−0.402521	−	0.915411i	$-0.631866\pi$
$439$	3.95973	−	2.28615i	0.188988	−	0.109112i	0.591509	+	0.806299i	$0.298533\pi$
$440$	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	−0.919295	−	0.393568i	$-0.871241\pi$
$461$	−11.2878	+	11.2878i	−0.525727	+	0.525727i	0.393568	+	0.919295i	$0.371241\pi$
$462$		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	0.465922	−	0.884826i	$-0.345723\pi$
$467$	9.22775	+	2.47257i	0.427009	+	0.114417i	−0.0389127	+	0.999243i	$0.512389\pi$
$468$	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	−0.720266	−	0.693698i	$-0.755980\pi$
$479$	5.26638	−	9.12164i	0.240627	−	0.416778i	0.960893	+	0.276920i	$0.0893136\pi$
$480$	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	$0.211751\pi$
$503$			27.6867i			1.23449i	−0.786772	+	0.617243i	$0.788249\pi$
$504$		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	0.897503	−	0.441009i	$-0.145379\pi$
$509$	32.8096	+	8.79130i	1.45426	+	0.389667i	0.556756	+	0.830676i	$0.312046\pi$
$510$	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	0.0809928	−	0.996715i	$-0.474191\pi$
$521$	−16.9294	−	9.77420i	−0.741691	−	0.428216i	−0.822684	+	0.568499i	$0.807524\pi$
$522$	−13.7064	−	4.79312i	−0.599912	−	0.209789i
$523$	−2.63608	+	9.83797i	−0.115268	+	0.430184i	−0.999307	−	0.0372283i	$-0.988147\pi$
$523$	−2.63608	+	9.83797i	−0.115268	+	0.430184i	0.884039	+	0.467413i	$0.154814\pi$
$524$	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	$0.105618\pi$
$563$	6.87017	+	25.6398i	0.289543	+	1.08059i	−0.655912	+	0.754837i	$0.727716\pi$
$564$	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	−0.676046	−	0.736860i	$-0.736308\pi$
$577$	7.20904	−	12.4864i	0.300116	−	0.519817i	0.976162	+	0.217043i	$0.0696412\pi$
$578$	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	0.379795	−	0.925071i	$-0.375995\pi$
$587$	−13.2110	−	13.2110i	−0.545276	−	0.545276i	−0.925071	+	0.379795i	$0.875995\pi$
$588$		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	0.647317	−	0.762221i	$-0.275891\pi$
$593$	−8.19296	−	14.1906i	−0.336445	−	0.582739i	−0.983761	+	0.179482i	$0.942558\pi$
$594$	−20.0775	+	29.4603i	−0.823788	+	1.20877i
$595$		0			0
$596$	3.04666	−	6.99032i	0.124796	−	0.286335i
$597$	−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	$0.0216649\pi$
$601$			3.33457i			0.136020i	−0.997685	+	0.0680099i	$0.978335\pi$
$602$		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	0.952514	−	0.304495i	$-0.0984877\pi$
$607$	5.23683	+	9.07046i	0.212556	+	0.368159i	−0.739957	+	0.672654i	$0.765154\pi$
$608$	8.70592	−	11.8198i	0.353072	−	0.479355i
$609$		0			0
$610$	−4.94814	−	3.37220i	−0.200344	−	0.136536i
$611$	−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	−0.452235	−	0.891899i	$-0.649373\pi$
$619$	−9.90042	+	2.65281i	−0.397932	+	0.106625i	0.0543029	+	0.998525i	$0.482706\pi$
$620$	−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	−0.474132	−	0.880454i	$-0.657238\pi$
$643$	10.3033	−	10.3033i	0.406321	−	0.406321i	0.880454	+	0.474132i	$0.157238\pi$
$644$		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	0.668387	−	0.743814i	$-0.266985\pi$
$647$	9.11681	+	5.26359i	0.358419	+	0.206933i	−0.309968	+	0.950747i	$0.600318\pi$
$648$	−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	−0.794961	−	0.606660i	$-0.792509\pi$
$661$	−30.3400	+	8.12957i	−1.18009	+	0.316204i	−0.385126	+	0.922864i	$0.625842\pi$
$662$	−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	$-0.598238\pi$
$677$	11.3361	−	42.3069i	0.435682	−	1.62599i	0.739430	−	0.673234i	$-0.235095\pi$
$678$	−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	−0.397106	−	0.917773i	$-0.629985\pi$
$691$	−31.5415	−	8.45153i	−1.19990	−	0.321511i	−0.802790	+	0.596262i	$0.796652\pi$
$692$	−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	$0.186157\pi$
$719$	23.9987	+	41.5669i	0.894999	+	1.55018i	0.0611931	+	0.998126i	$0.480509\pi$
$720$	0.614326	−	16.7617i	0.0228946	−	0.624670i
$721$		0			0
$722$	−9.76873	+	14.3340i	−0.363555	+	0.533456i
$723$	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	$-0.772815\pi$
$727$		−	35.3027i		−	1.30931i	0.755930	−	0.654653i	$-0.227185\pi$
$728$		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	0.415170	−	0.909744i	$-0.363722\pi$
$733$	8.65952	+	2.32031i	0.319847	+	0.0857026i	−0.0953238	+	0.995446i	$0.530389\pi$
$734$	−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	−0.390295	−	0.920690i	$-0.627627\pi$
$761$	5.84549	−	3.37489i	0.211899	−	0.122340i	0.602194	+	0.798350i	$0.294294\pi$
$762$	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	$-0.512831\pi$
$769$	−2.23508			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$770$		0			0
$771$	5.53022	−	5.53022i	0.199166	−	0.199166i
$772$	12.5814	−	15.7890i	0.452816	−	0.568260i
$773$	−22.7046	+	6.08368i	−0.816627	+	0.218815i	−0.642871	−	0.765974i	$-0.722257\pi$
$773$	−22.7046	+	6.08368i	−0.816627	+	0.218815i	−0.173756	+	0.984789i	$0.555590\pi$
$774$	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	0.987150	−	0.159793i	$-0.0510828\pi$
$787$	1.46878	+	5.48157i	0.0523564	+	0.195397i	−0.934794	+	0.355190i	$0.884416\pi$
$788$	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	−0.0581955	−	0.998305i	$-0.518535\pi$
$797$	26.5404	−	26.5404i	0.940110	−	0.940110i	0.998305	+	0.0581955i	$0.0185347\pi$
$798$		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	0.999963	−	0.00857565i	$-0.00272975\pi$
$811$	28.2328	+	28.2328i	0.991388	+	0.991388i	−0.00857565	+	0.999963i	$0.502730\pi$
$812$		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	0.919394	−	0.393339i	$-0.128680\pi$
$829$	−2.11606	−	7.89725i	−0.0734939	−	0.274283i	−0.992888	+	0.119056i	$0.962013\pi$
$830$	−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	$0.0396939\pi$
$839$			7.20540i			0.248758i	−0.992235	+	0.124379i	$0.960306\pi$
$840$		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	0.447894	−	0.894086i	$-0.352174\pi$
$853$	−13.0316	−	13.0316i	−0.446192	−	0.446192i	−0.894086	+	0.447894i	$0.852174\pi$
$854$		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	0.284674	−	0.958625i	$-0.408115\pi$
$857$	−11.8030	−	6.81447i	−0.403183	−	0.232778i	−0.687856	+	0.725847i	$0.741448\pi$
$858$	21.4510	−	61.3411i	0.732325	−	2.09415i
$859$	−11.6772	+	43.5800i	−0.398422	+	1.48693i	0.417451	+	0.908699i	$0.362923\pi$
$859$	−11.6772	+	43.5800i	−0.398422	+	1.48693i	−0.815873	+	0.578231i	$0.803743\pi$
$860$	−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	$-0.332991\pi$
$881$	29.7369			1.00186			0.500930	+	0.865488i	$0.332991\pi$
$882$		0			0
$883$	14.3040	−	14.3040i	0.481368	−	0.481368i	−0.424200	−	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	$0.734305\pi$
$887$	−49.1086	+	28.3528i	−1.64890	+	0.951995i	−0.977509	+	0.210896i	$0.932362\pi$
$888$	−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	$0.0105159\pi$
$929$	16.1033	+	27.8918i	0.528333	+	0.915099i	−0.471122	+	0.882068i	$0.656151\pi$
$930$	−7.03932	−	4.79736i	−0.230829	−	0.157312i
$931$		0			0
$932$	−0.340053	+	0.133611i	−0.0111388	+	0.00437658i
$933$	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	$-0.905873\pi$
$937$		−	17.8409i		−	0.582836i	0.956596	−	0.291418i	$-0.0941271\pi$
$938$		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	$-0.930681\pi$
$941$	−7.32652	−	27.3429i	−0.238838	−	0.891354i	0.737544	−	0.675300i	$-0.235986\pi$
$942$	−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	−0.888996	−	0.457914i	$-0.848597\pi$
$971$	3.42316	−	12.7754i	0.109854	−	0.409982i	0.998851	+	0.0479326i	$0.0152633\pi$
$972$	−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	0.495914	−	0.868372i	$-0.334833\pi$
$983$	−0.255896	−	0.147742i	−0.00816182	−	0.00471223i	−0.504075	+	0.863660i	$0.668167\pi$
$984$	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	0.527597	−	0.849495i	$-0.323093\pi$
$997$	44.4977	−	11.9231i	1.40926	−	0.377609i	0.881660	+	0.471885i	$0.156426\pi$
$998$	−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.k.165.3		16
7.2	even	3	inner	784.2.x.k.373.1		16
7.3	odd	6		784.2.m.g.197.3		8
7.4	even	3		112.2.m.c.85.3	yes	8
7.5	odd	6		784.2.x.j.373.1		16
7.6	odd	2		784.2.x.j.165.3		16
16.13	even	4	inner	784.2.x.k.557.1		16
28.11	odd	6		448.2.m.c.113.4		8
56.11	odd	6		896.2.m.f.225.1		8
56.53	even	6		896.2.m.e.225.4		8
112.11	odd	12		896.2.m.f.673.1		8
112.13	odd	4		784.2.x.j.557.1		16
112.45	odd	12		784.2.m.g.589.3		8
112.53	even	12		896.2.m.e.673.4		8
112.61	odd	12		784.2.x.j.765.3		16
112.67	odd	12		448.2.m.c.337.4		8
112.93	even	12	inner	784.2.x.k.765.3		16
112.109	even	12		112.2.m.c.29.3	✓	8
224.67	odd	24		7168.2.a.bd.1.8		8
224.109	even	24		7168.2.a.bc.1.8		8
224.179	odd	24		7168.2.a.bd.1.1		8
224.221	even	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	112.109	even	12
112.2.m.c.85.3	yes	8	7.4	even	3
448.2.m.c.113.4		8	28.11	odd	6
448.2.m.c.337.4		8	112.67	odd	12
784.2.m.g.197.3		8	7.3	odd	6
784.2.m.g.589.3		8	112.45	odd	12
784.2.x.j.165.3		16	7.6	odd	2
784.2.x.j.373.1		16	7.5	odd	6
784.2.x.j.557.1		16	112.13	odd	4
784.2.x.j.765.3		16	112.61	odd	12
784.2.x.k.165.3		16	1.1	even	1	trivial
784.2.x.k.373.1		16	7.2	even	3	inner
784.2.x.k.557.1		16	16.13	even	4	inner
784.2.x.k.765.3		16	112.93	even	12	inner
896.2.m.e.225.4		8	56.53	even	6
896.2.m.e.673.4		8	112.53	even	12
896.2.m.f.225.1		8	56.11	odd	6
896.2.m.f.673.1		8	112.11	odd	12
7168.2.a.bc.1.1		8	224.221	even	24
7168.2.a.bc.1.8		8	224.109	even	24
7168.2.a.bd.1.1		8	224.179	odd	24
7168.2.a.bd.1.8		8	224.67	odd	24

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.105414 - 1.41028i) q^{2} +(-0.719263 - 2.68432i) q^{3} +(-1.97778 - 0.297327i) q^{4} +(-0.229791 + 0.857592i) q^{5} +(-3.86147 + 0.731395i) q^{6} +(-0.627801 + 2.75787i) q^{8} +(-4.09018 + 2.36147i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8}+O(q^{10}) \) 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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