LMFDB - Embedded newform 504.2.cs.b.85.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.9
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.972690 + 1.02658i) q^{2} +(0.821098 + 1.52506i) q^{3} +(-0.107748 - 1.99710i) q^{4} +(2.72052 + 1.57069i) q^{5} +(-2.36427 - 0.640483i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 + 2.50444i) q^{9} +O(q^{10})$	\(q+(-0.972690 + 1.02658i) q^{2} +(0.821098 + 1.52506i) q^{3} +(-0.107748 - 1.99710i) q^{4} +(2.72052 + 1.57069i) q^{5} +(-2.36427 - 0.640483i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 + 2.50444i) q^{9} +(-4.25867 + 1.26504i) q^{10} +(2.21426 - 1.27840i) q^{11} +(2.95721 - 1.80413i) q^{12} +(0.964474 + 0.556840i) q^{13} +(1.37539 + 0.329083i) q^{14} +(-0.161584 + 5.43864i) q^{15} +(-3.97678 + 0.430365i) q^{16} +1.14970 q^{17} +(-0.964525 - 4.13155i) q^{18} +4.46665i q^{19} +(2.84370 - 5.60238i) q^{20} +(0.910189 - 1.47362i) q^{21} +(-0.841401 + 3.51662i) q^{22} +(-0.842409 + 1.45909i) q^{23} +(-1.02436 + 4.79069i) q^{24} +(2.43416 + 4.21608i) q^{25} +(-1.50978 + 0.448481i) q^{26} +(-5.17554 - 0.462390i) q^{27} +(-1.67566 + 1.09186i) q^{28} +(4.17557 - 2.41077i) q^{29} +(-5.42605 - 5.45599i) q^{30} +(3.39388 - 5.87838i) q^{31} +(3.42637 - 4.50111i) q^{32} +(3.76776 + 2.32718i) q^{33} +(-1.11831 + 1.18027i) q^{34} -3.14139i q^{35} +(5.17956 + 3.02855i) q^{36} +3.26969i q^{37} +(-4.58539 - 4.34466i) q^{38} +(-0.0572845 + 1.92810i) q^{39} +(2.98528 + 8.36867i) q^{40} +(-1.46544 + 2.53822i) q^{41} +(0.627462 + 2.36776i) q^{42} +(-9.14833 + 5.28179i) q^{43} +(-2.79168 - 4.28435i) q^{44} +(-8.42692 + 4.21923i) q^{45} +(-0.678480 - 2.28405i) q^{46} +(-5.80079 - 10.0473i) q^{47} +(-3.92166 - 5.71145i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.69584 - 1.60208i) q^{50} +(0.944020 + 1.75337i) q^{51} +(1.00814 - 1.98615i) q^{52} +9.23136i q^{53} +(5.50888 - 4.86336i) q^{54} +8.03193 q^{55} +(0.509014 - 2.78225i) q^{56} +(-6.81189 + 3.66755i) q^{57} +(-1.58668 + 6.63150i) q^{58} +(-11.4997 - 6.63933i) q^{59} +(10.8789 - 0.263302i) q^{60} +(2.64571 - 1.52750i) q^{61} +(2.73345 + 9.20195i) q^{62} +(2.99471 + 0.178105i) q^{63} +(1.28797 + 7.89564i) q^{64} +(1.74925 + 3.02979i) q^{65} +(-6.05391 + 1.60430i) q^{66} +(-9.47390 - 5.46976i) q^{67} +(-0.123878 - 2.29607i) q^{68} +(-2.91690 - 0.0866623i) q^{69} +(3.22490 + 3.05560i) q^{70} +13.2125 q^{71} +(-8.14717 + 2.37141i) q^{72} -7.16456 q^{73} +(-3.35661 - 3.18040i) q^{74} +(-4.43109 + 7.17404i) q^{75} +(8.92032 - 0.481271i) q^{76} +(-2.21426 - 1.27840i) q^{77} +(-1.92363 - 1.93425i) q^{78} +(-2.48070 - 4.29670i) q^{79} +(-11.4949 - 5.07549i) q^{80} +(-3.54445 - 8.27266i) q^{81} +(-1.18027 - 3.97330i) q^{82} +(10.8973 - 6.29154i) q^{83} +(-3.04103 - 1.65896i) q^{84} +(3.12780 + 1.80583i) q^{85} +(3.47629 - 14.5291i) q^{86} +(7.10511 + 4.38851i) q^{87} +(7.11368 + 1.30145i) q^{88} +6.04820 q^{89} +(3.86539 - 12.7549i) q^{90} -1.11368i q^{91} +(3.00472 + 1.52516i) q^{92} +(11.7516 + 0.349144i) q^{93} +(15.9567 + 3.81788i) q^{94} +(-7.01573 + 12.1516i) q^{95} +(9.67783 + 1.52956i) q^{96} +(5.01036 + 8.67820i) q^{97} +(-0.402702 - 1.35567i) q^{98} +(-0.455381 + 7.65690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.972690	+	1.02658i	−0.687796	+	0.725904i
$2$	−0.972690	+	1.02658i	−0.687796	+	0.725904i
$3$	0.821098	+	1.52506i	0.474061	+	0.880492i
$3$	0.821098	+	1.52506i	0.474061	+	0.880492i
$4$	−0.107748	−	1.99710i	−0.0538738	−	0.998548i
$5$	2.72052	+	1.57069i	1.21665	+	0.702436i	0.964201	−	0.265174i	$-0.0854293\pi$
$5$	2.72052	+	1.57069i	1.21665	+	0.702436i	0.252453	+	0.967609i	$0.418763\pi$
$6$	−2.36427	−	0.640483i	−0.965210	−	0.261476i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.15499	+	1.83194i	0.761904	+	0.647690i
$9$	−1.65160	+	2.50444i	−0.550533	+	0.834814i
$10$	−4.25867	+	1.26504i	−1.34671	+	0.400042i
$11$	2.21426	−	1.27840i	0.667625	−	0.385453i	−0.127551	−	0.991832i	$-0.540712\pi$
$11$	2.21426	−	1.27840i	0.667625	−	0.385453i	0.795176	+	0.606379i	$0.207378\pi$
$12$	2.95721	−	1.80413i	0.853674	−	0.520808i
$13$	0.964474	+	0.556840i	0.267497	+	0.154439i	0.627750	−	0.778415i	$-0.283976\pi$
$13$	0.964474	+	0.556840i	0.267497	+	0.154439i	−0.360253	+	0.932855i	$0.617309\pi$
$14$	1.37539	+	0.329083i	0.367589	+	0.0879510i
$15$	−0.161584	+	5.43864i	−0.0417208	+	1.40425i
$16$	−3.97678	+	0.430365i	−0.994195	+	0.107591i
$17$	1.14970			0.278844			0.139422	−	0.990233i	$-0.455475\pi$
$17$	1.14970			0.278844			0.139422	+	0.990233i	$0.455475\pi$
$18$	−0.964525	−	4.13155i	−0.227341	−	0.973815i
$19$			4.46665i			1.02472i	0.858771	+	0.512359i	$0.171228\pi$
$19$			4.46665i			1.02472i	−0.858771	+	0.512359i	$0.828772\pi$
$20$	2.84370	−	5.60238i	0.635870	−	1.25273i
$21$	0.910189	−	1.47362i	0.198620	−	0.321570i
$22$	−0.841401	+	3.51662i	−0.179387	+	0.749745i
$23$	−0.842409	+	1.45909i	−0.175654	+	0.304242i	−0.940388	−	0.340105i	$-0.889537\pi$
$23$	−0.842409	+	1.45909i	−0.175654	+	0.304242i	0.764733	+	0.644347i	$0.222871\pi$
$24$	−1.02436	+	4.79069i	−0.209097	+	0.977895i
$25$	2.43416	+	4.21608i	0.486831	+	0.843216i
$26$	−1.50978	+	0.448481i	−0.296092	+	0.0879544i
$27$	−5.17554	−	0.462390i	−0.996033	−	0.0889871i
$28$	−1.67566	+	1.09186i	−0.316670	+	0.206342i
$29$	4.17557	−	2.41077i	0.775384	−	0.447668i	−0.0594077	−	0.998234i	$-0.518921\pi$
$29$	4.17557	−	2.41077i	0.775384	−	0.447668i	0.834792	+	0.550565i	$0.185588\pi$
$30$	−5.42605	−	5.45599i	−0.990657	−	0.996124i
$31$	3.39388	−	5.87838i	0.609560	−	1.05579i	−0.381753	−	0.924264i	$-0.624680\pi$
$31$	3.39388	−	5.87838i	0.609560	−	1.05579i	0.991313	−	0.131524i	$-0.0419870\pi$
$32$	3.42637	−	4.50111i	0.605702	−	0.795691i
$33$	3.76776	+	2.32718i	0.655884	+	0.405110i
$34$	−1.11831	+	1.18027i	−0.191788	+	0.202414i
$35$		−	3.14139i		−	0.530991i
$36$	5.17956	+	3.02855i	0.863261	+	0.504758i
$37$			3.26969i			0.537534i	0.963205	+	0.268767i	$0.0866162\pi$
$37$			3.26969i			0.537534i	−0.963205	+	0.268767i	$0.913384\pi$
$38$	−4.58539	−	4.34466i	−0.743848	−	0.704797i
$39$	−0.0572845	+	1.92810i	−0.00917287	+	0.308743i
$40$	2.98528	+	8.36867i	0.472014	+	1.32320i
$41$	−1.46544	+	2.53822i	−0.228864	+	0.396403i	−0.957472	−	0.288527i	$-0.906834\pi$
$41$	−1.46544	+	2.53822i	−0.228864	+	0.396403i	0.728608	+	0.684931i	$0.240168\pi$
$42$	0.627462	+	2.36776i	0.0968194	+	0.365353i
$43$	−9.14833	+	5.28179i	−1.39511	+	0.805466i	−0.993875	−	0.110510i	$-0.964752\pi$
$43$	−9.14833	+	5.28179i	−1.39511	+	0.805466i	−0.401233	+	0.915976i	$0.631418\pi$
$44$	−2.79168	−	4.28435i	−0.420861	−	0.645889i
$45$	−8.42692	+	4.21923i	−1.25621	+	0.628966i
$46$	−0.678480	−	2.28405i	−0.100036	−	0.336765i
$47$	−5.80079	−	10.0473i	−0.846132	−	1.46554i	−0.884634	−	0.466285i	$-0.845592\pi$
$47$	−5.80079	−	10.0473i	−0.846132	−	1.46554i	0.0385022	−	0.999259i	$-0.487741\pi$
$48$	−3.92166	−	5.71145i	−0.566042	−	0.824376i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−6.69584	−	1.60208i	−0.946935	−	0.226568i
$51$	0.944020	+	1.75337i	0.132189	+	0.245520i
$52$	1.00814	−	1.98615i	0.139804	−	0.275429i
$53$			9.23136i			1.26802i	0.773323	+	0.634012i	$0.218593\pi$
$53$			9.23136i			1.26802i	−0.773323	+	0.634012i	$0.781407\pi$
$54$	5.50888	−	4.86336i	0.749663	−	0.661819i
$55$	8.03193			1.08302
$56$	0.509014	−	2.78225i	0.0680199	−	0.371794i
$57$	−6.81189	+	3.66755i	−0.902257	+	0.485779i
$58$	−1.58668	+	6.63150i	−0.208342	+	0.870759i
$59$	−11.4997	−	6.63933i	−1.49713	−	0.864367i	−0.497134	−	0.867674i	$-0.665614\pi$
$59$	−11.4997	−	6.63933i	−1.49713	−	0.864367i	−0.999995	+	0.00330678i	$0.998947\pi$
$60$	10.8789	−	0.263302i	1.40446	−	0.0339921i
$61$	2.64571	−	1.52750i	0.338749	−	0.195577i	−0.320970	−	0.947089i	$-0.604009\pi$
$61$	2.64571	−	1.52750i	0.338749	−	0.195577i	0.659719	+	0.751513i	$0.270675\pi$
$62$	2.73345	+	9.20195i	0.347149	+	1.16865i
$63$	2.99471	+	0.178105i	0.377298	+	0.0224391i
$64$	1.28797	+	7.89564i	0.160996	+	0.986955i
$65$	1.74925	+	3.02979i	0.216968	+	0.375799i
$66$	−6.05391	+	1.60430i	−0.745185	+	0.197476i
$67$	−9.47390	−	5.46976i	−1.15742	−	0.668238i	−0.206737	−	0.978397i	$-0.566284\pi$
$67$	−9.47390	−	5.46976i	−1.15742	−	0.668238i	−0.950685	+	0.310159i	$0.899618\pi$
$68$	−0.123878	−	2.29607i	−0.0150224	−	0.278439i
$69$	−2.91690	−	0.0866623i	−0.351154	−	0.0104329i
$70$	3.22490	+	3.05560i	0.385449	+	0.365214i
$71$	13.2125			1.56803			0.784015	−	0.620742i	$-0.213168\pi$
$71$	13.2125			1.56803			0.784015	+	0.620742i	$0.213168\pi$
$72$	−8.14717	+	2.37141i	−0.960153	+	0.279474i
$73$	−7.16456			−0.838548			−0.419274	−	0.907860i	$-0.637715\pi$
$73$	−7.16456			−0.838548			−0.419274	+	0.907860i	$0.637715\pi$
$74$	−3.35661	−	3.18040i	−0.390199	−	0.369714i
$75$	−4.43109	+	7.17404i	−0.511658	+	0.828387i
$76$	8.92032	−	0.481271i	1.02323	−	0.0552055i
$77$	−2.21426	−	1.27840i	−0.252338	−	0.145688i
$78$	−1.92363	−	1.93425i	−0.217809	−	0.219011i
$79$	−2.48070	−	4.29670i	−0.279101	−	0.483417i	0.692061	−	0.721839i	$-0.256703\pi$
$79$	−2.48070	−	4.29670i	−0.279101	−	0.483417i	−0.971162	+	0.238422i	$0.923370\pi$
$80$	−11.4949	−	5.07549i	−1.28517	−	0.567457i
$81$	−3.54445	−	8.27266i	−0.393828	−	0.919184i
$82$	−1.18027	−	3.97330i	−0.130339	−	0.438778i
$83$	10.8973	−	6.29154i	1.19613	−	0.690586i	0.236440	−	0.971646i	$-0.424019\pi$
$83$	10.8973	−	6.29154i	1.19613	−	0.690586i	0.959690	+	0.281060i	$0.0906860\pi$
$84$	−3.04103	−	1.65896i	−0.331804	−	0.181007i
$85$	3.12780	+	1.80583i	0.339257	+	0.195870i
$86$	3.47629	−	14.5291i	0.374858	−	1.56671i
$87$	7.10511	+	4.38851i	0.761748	+	0.470498i
$88$	7.11368	+	1.30145i	0.758320	+	0.138735i
$89$	6.04820			0.641108			0.320554	−	0.947230i	$-0.396131\pi$
$89$	6.04820			0.641108			0.320554	+	0.947230i	$0.396131\pi$
$90$	3.86539	−	12.7549i	0.407447	−	1.34449i
$91$		−	1.11368i		−	0.116745i
$92$	3.00472	+	1.52516i	0.313264	+	0.159009i
$93$	11.7516	+	0.349144i	1.21858	+	0.0362045i
$94$	15.9567	+	3.81788i	1.64581	+	0.393784i
$95$	−7.01573	+	12.1516i	−0.719799	+	1.24673i
$96$	9.67783	+	1.52956i	0.987740	+	0.156110i
$97$	5.01036	+	8.67820i	0.508725	+	0.881138i	0.999949	+	0.0101046i	$0.00321645\pi$
$97$	5.01036	+	8.67820i	0.508725	+	0.881138i	−0.491224	+	0.871033i	$0.663450\pi$
$98$	−0.402702	−	1.35567i	−0.0406791	−	0.136943i
$99$	−0.455381	+	7.65690i	−0.0457675	+	0.769547i
$100$	8.15764	−	5.31552i	0.815764	−	0.531552i
$101$	10.3557	−	5.97887i	1.03043	−	0.594920i	0.113323	−	0.993558i	$-0.463851\pi$
$101$	10.3557	−	5.97887i	1.03043	−	0.594920i	0.917108	+	0.398638i	$0.130517\pi$
$102$	−2.71822	−	0.736366i	−0.269143	−	0.0729111i
$103$	3.87345	−	6.70902i	0.381663	−	0.661059i	−0.609637	−	0.792680i	$-0.708685\pi$
$103$	3.87345	−	6.70902i	0.381663	−	0.661059i	0.991300	+	0.131621i	$0.0420183\pi$
$104$	1.05833	+	2.96685i	0.103778	+	0.290923i
$105$	4.79079	−	2.57939i	0.467534	−	0.251722i
$106$	−9.47676	−	8.97925i	−0.920464	−	0.872142i
$107$			5.46939i			0.528746i	0.964421	+	0.264373i	$0.0851650\pi$
$107$			5.46939i			0.528746i	−0.964421	+	0.264373i	$0.914835\pi$
$108$	−0.365786	+	10.3859i	−0.0351977	+	0.999380i
$109$		−	10.1589i		−	0.973049i	−0.873667	−	0.486524i	$-0.838264\pi$
$109$		−	10.1589i		−	0.973049i	0.873667	−	0.486524i	$-0.161736\pi$
$110$	−7.81258	+	8.24544i	−0.744900	+	0.786172i
$111$	−4.98647	+	2.68474i	−0.473295	+	0.254824i
$112$	2.36110	+	3.22881i	0.223103	+	0.305094i
$113$	7.92723	−	13.7304i	0.745731	−	1.29164i	−0.204121	−	0.978946i	$-0.565434\pi$
$113$	7.92723	−	13.7304i	0.745731	−	1.29164i	0.949852	−	0.312699i	$-0.101233\pi$
$114$	2.86081	−	10.5604i	0.267939	−	0.989069i
$115$	−4.58358	+	2.64633i	−0.427421	+	0.246772i
$116$	−5.26444	−	8.07926i	−0.488791	−	0.750141i
$117$	−2.98750	+	1.49579i	−0.276194	+	0.138286i
$118$	18.0014	−	5.34735i	1.65717	−	0.492263i
$119$	−0.574852	−	0.995674i	−0.0526966	−	0.0912733i
$120$	−10.3115	+	11.4242i	−0.941306	+	1.04288i
$121$	−2.23136	+	3.86484i	−0.202851	+	0.351349i
$122$	−1.00535	+	4.20183i	−0.0910201	+	0.380416i
$123$	−5.07420	−	0.150757i	−0.457525	−	0.0135933i
$124$	−12.1054	−	6.14453i	−1.08709	−	0.551795i
$125$		−	0.413681i		−	0.0370007i
$126$	−3.09576	+	2.90108i	−0.275793	+	0.258449i
$127$	16.1006			1.42869			0.714347	−	0.699791i	$-0.246724\pi$
$127$	16.1006			1.42869			0.714347	+	0.699791i	$0.246724\pi$
$128$	−9.35833	−	6.35780i	−0.827167	−	0.561956i
$129$	−15.5667	−	9.61486i	−1.37057	−	0.846542i
$130$	−4.81181	−	1.15129i	−0.422023	−	0.100975i
$131$	5.63758	+	3.25486i	0.492557	+	0.284378i	0.725635	−	0.688080i	$-0.241546\pi$
$131$	5.63758	+	3.25486i	0.492557	+	0.284378i	−0.233077	+	0.972458i	$0.574880\pi$
$132$	4.24163	−	7.77533i	0.369187	−	0.676756i
$133$	3.86823	−	2.23332i	0.335418	−	0.193654i
$134$	14.8303	−	4.40537i	1.28115	−	0.380566i
$135$	−13.3539	−	9.38713i	−1.14932	−	0.807915i
$136$	2.47760	+	2.10619i	0.212453	+	0.180605i
$137$	8.94475	+	15.4928i	0.764202	+	1.32364i	0.940668	+	0.339330i	$0.110200\pi$
$137$	8.94475	+	15.4928i	0.764202	+	1.32364i	−0.176466	+	0.984307i	$0.556466\pi$
$138$	2.92621	−	2.91015i	0.249095	−	0.247728i
$139$	−8.01173	−	4.62558i	−0.679546	−	0.392336i	0.120138	−	0.992757i	$-0.461666\pi$
$139$	−8.01173	−	4.62558i	−0.679546	−	0.392336i	−0.799684	+	0.600421i	$0.795000\pi$
$140$	−6.27365	+	0.338477i	−0.530220	+	0.0286065i
$141$	10.5596	−	17.0963i	0.889282	−	1.43977i
$142$	−12.8516	+	13.5637i	−1.07848	+	1.13824i
$143$	2.84746			0.238117
$144$	5.49022	−	10.6704i	0.457518	−	0.889200i
$145$	15.1463			1.25783
$146$	6.96889	−	7.35502i	0.576750	−	0.608705i
$147$	−1.73129	−	0.0514372i	−0.142794	−	0.00424247i
$148$	6.52989	−	0.352302i	0.536754	−	0.0289590i
$149$	18.0266	+	10.4077i	1.47680	+	0.852629i	0.999657	−	0.0261974i	$-0.00833985\pi$
$149$	18.0266	+	10.4077i	1.47680	+	0.852629i	0.477141	+	0.878827i	$0.341673\pi$
$150$	−3.05468	−	11.5270i	−0.249414	−	0.941176i
$151$	−3.29469	−	5.70657i	−0.268118	−	0.464394i	0.700258	−	0.713890i	$-0.253068\pi$
$151$	−3.29469	−	5.70657i	−0.268118	−	0.464394i	−0.968376	+	0.249496i	$0.919735\pi$
$152$	−8.18264	+	9.62558i	−0.663700	+	0.780738i
$153$	−1.89885	+	2.87937i	−0.153513	+	0.232783i
$154$	3.46618	−	1.02963i	0.279313	−	0.0829702i
$155$	18.4663	−	10.6615i	1.48325	−	0.856353i
$156$	3.85677	−	0.0933453i	0.308789	−	0.00747361i
$157$	−14.8869	−	8.59497i	−1.18811	−	0.685954i	−0.230231	−	0.973136i	$-0.573948\pi$
$157$	−14.8869	−	8.59497i	−1.18811	−	0.685954i	−0.957876	+	0.287183i	$0.907281\pi$
$158$	6.82388	+	1.63271i	0.542879	+	0.129892i
$159$	−14.0783	+	7.57984i	−1.11649	+	0.601121i
$160$	16.3914	−	6.86358i	1.29585	−	0.542614i
$161$	1.68482			0.132782
$162$	11.9402	+	4.40806i	0.938113	+	0.346330i
$163$		−	9.53517i		−	0.746852i	−0.927660	−	0.373426i	$-0.878183\pi$
$163$		−	9.53517i		−	0.746852i	0.927660	−	0.373426i	$-0.121817\pi$
$164$	5.22697	+	2.65314i	0.408158	+	0.207176i
$165$	6.59499	+	12.2491i	0.513420	+	0.953595i
$166$	−4.14087	+	17.3067i	−0.321394	+	1.34326i
$167$	−7.95846	+	13.7845i	−0.615844	+	1.06667i	0.374392	+	0.927271i	$0.377852\pi$
$167$	−7.95846	+	13.7845i	−0.615844	+	1.06667i	−0.990236	+	0.139403i	$0.955482\pi$
$168$	4.66104	−	1.50822i	0.359607	−	0.116362i
$169$	−5.87986	−	10.1842i	−0.452297	−	0.783401i
$170$	−4.89622	+	1.45443i	−0.375523	+	0.111549i
$171$	−11.1865	−	7.37710i	−0.855449	−	0.564141i
$172$	11.5340	+	17.7010i	0.879456	+	1.34969i
$173$	4.25768	−	2.45817i	0.323705	−	0.186891i	−0.329338	−	0.944212i	$-0.606825\pi$
$173$	4.25768	−	2.45817i	0.323705	−	0.186891i	0.653043	+	0.757321i	$0.273492\pi$
$174$	−11.4162	+	3.02533i	−0.865463	+	0.229350i
$175$	2.43416	−	4.21608i	0.184005	−	0.318706i
$176$	−8.25545	+	6.03687i	−0.622278	+	0.455046i
$177$	0.683017	−	22.9892i	0.0513387	−	1.72797i
$178$	−5.88303	+	6.20899i	−0.440952	+	0.465383i
$179$		−	7.84907i		−	0.586667i	−0.956010	−	0.293334i	$-0.905235\pi$
$179$		−	7.84907i		−	0.586667i	0.956010	−	0.293334i	$-0.0947647\pi$
$180$	9.33419	+	16.3747i	0.695729	+	1.22050i
$181$			1.16256i			0.0864122i	0.999066	+	0.0432061i	$0.0137572\pi$
$181$			1.16256i			0.0864122i	−0.999066	+	0.0432061i	$0.986243\pi$
$182$	1.14328	+	1.08326i	0.0847459	+	0.0802969i
$183$	4.50192	+	2.78063i	0.332791	+	0.205550i
$184$	−4.48836	+	1.60109i	−0.330886	+	0.118034i
$185$	−5.13569	+	8.89527i	−0.377583	+	0.653993i
$186$	−11.7891	+	11.7244i	−0.864416	+	0.859672i
$187$	2.54575	−	1.46979i	0.186163	−	0.107482i
$188$	−19.4403	+	12.6673i	−1.41783	+	0.923858i
$189$	2.18733	+	4.71334i	0.159105	+	0.342845i
$190$	−5.65050	−	19.0220i	−0.409931	−	1.38000i
$191$	−10.9574	−	18.9788i	−0.792852	−	1.37326i	−0.924194	−	0.381923i	$-0.875262\pi$
$191$	−10.9574	−	18.9788i	−0.792852	−	1.37326i	0.131342	−	0.991337i	$-0.458071\pi$
$192$	−10.9838	+	8.44732i	−0.792684	+	0.609632i
$193$	−0.00294224	+	0.00509610i	−0.000211787	+	0.000366826i	−0.866131	−	0.499817i	$-0.833401\pi$
$193$	−0.00294224	+	0.00509610i	−0.000211787	+	0.000366826i	0.865919	+	0.500183i	$0.166734\pi$
$194$	−13.7824	−	3.29765i	−0.989521	−	0.236757i
$195$	−3.18429	+	5.15545i	−0.228032	+	0.369190i
$196$	1.78341	+	0.905236i	0.127386	+	0.0646597i
$197$		−	6.08721i		−	0.433696i	−0.976205	−	0.216848i	$-0.930422\pi$
$197$		−	6.08721i		−	0.433696i	0.976205	−	0.216848i	$-0.0695776\pi$
$198$	−7.41750	−	7.91527i	−0.527139	−	0.562514i
$199$	−12.7449			−0.903459			−0.451729	−	0.892155i	$-0.649193\pi$
$199$	−12.7449			−0.903459			−0.451729	+	0.892155i	$0.649193\pi$
$200$	−2.47804	+	13.5449i	−0.175224	+	0.957766i
$201$	0.562698	−	18.9395i	0.0396897	−	1.33589i
$202$	−3.93508	+	16.4466i	−0.276872	+	1.15718i
$203$	−4.17557	−	2.41077i	−0.293068	−	0.169203i
$204$	3.39992	−	2.07422i	0.238042	−	0.145224i
$205$	−7.97353	+	4.60352i	−0.556896	+	0.321524i
$206$	3.11970	+	10.5022i	0.217360	+	0.731724i
$207$	−2.26290	−	4.51960i	−0.157282	−	0.314134i
$208$	−4.07515	−	1.79935i	−0.282561	−	0.124763i
$209$	5.71018	+	9.89032i	0.394981	+	0.684128i
$210$	−2.01200	+	7.42709i	−0.138841	+	0.512518i
$211$	14.1689	+	8.18044i	0.975430	+	0.563165i	0.900887	−	0.434053i	$-0.142917\pi$
$211$	14.1689	+	8.18044i	0.975430	+	0.563165i	0.0745426	+	0.997218i	$0.476250\pi$
$212$	18.4359	−	0.994657i	1.26618	−	0.0683133i
$213$	10.8487	+	20.1497i	0.743342	+	1.38064i
$214$	−5.61478	−	5.32002i	−0.383819	−	0.363669i
$215$	−33.1843			−2.26315
$216$	−10.3062	−	10.4777i	−0.701246	−	0.712920i
$217$	−6.78777			−0.460784
$218$	10.4290	+	9.88149i	0.706340	+	0.669259i
$219$	−5.88280	−	10.9264i	−0.397523	−	0.738335i
$220$	−0.865421	−	16.0405i	−0.0583467	−	1.08145i
$221$	1.10886	+	0.640201i	0.0745901	+	0.0430646i
$222$	2.09418	−	7.73045i	0.140552	−	0.518834i
$223$	7.54800	+	13.0735i	0.505451	+	0.875467i	0.999980	+	0.00630607i	$0.00200730\pi$
$223$	7.54800	+	13.0735i	0.505451	+	0.875467i	−0.494529	+	0.869161i	$0.664659\pi$
$224$	−5.61126	−	0.716769i	−0.374918	−	0.0478911i
$225$	−14.5792	−	0.867071i	−0.971945	−	0.0578047i
$226$	6.38463	+	21.4934i	0.424699	+	1.42972i
$227$	−22.9345	+	13.2412i	−1.52222	+	0.878852i	−0.522561	+	0.852602i	$0.675023\pi$
$227$	−22.9345	+	13.2412i	−1.52222	+	0.878852i	−0.999655	+	0.0262499i	$0.991643\pi$
$228$	8.05842	+	13.2088i	0.533682	+	0.874776i
$229$	−17.9709	−	10.3755i	−1.18755	−	0.685632i	−0.229801	−	0.973238i	$-0.573808\pi$
$229$	−17.9709	−	10.3755i	−1.18755	−	0.685632i	−0.957749	+	0.287605i	$0.907141\pi$
$230$	1.74172	−	7.27949i	0.114846	−	0.479995i
$231$	0.131515	−	4.42657i	0.00865306	−	0.291247i
$232$	13.4147	+	2.45423i	0.880719	+	0.161128i
$233$	13.1760			0.863191			0.431596	−	0.902067i	$-0.357951\pi$
$233$	13.1760			0.863191			0.431596	+	0.902067i	$0.357951\pi$
$234$	1.37035	−	4.52186i	0.0895826	−	0.295603i
$235$		−	36.4451i		−	2.37741i
$236$	−12.0203	+	23.6813i	−0.782456	+	1.54152i
$237$	4.51582	−	7.31123i	0.293334	−	0.474915i
$238$	1.58130	+	0.378348i	0.102500	+	0.0245247i
$239$	−3.75351	+	6.50127i	−0.242794	+	0.420532i	−0.961509	−	0.274773i	$-0.911397\pi$
$239$	−3.75351	+	6.50127i	−0.242794	+	0.420532i	0.718715	+	0.695305i	$0.244731\pi$
$240$	−1.69801	−	21.6978i	−0.109606	−	1.40059i
$241$	−10.4970	−	18.1813i	−0.676171	−	1.17116i	−0.976125	−	0.217209i	$-0.930305\pi$
$241$	−10.4970	−	18.1813i	−0.676171	−	1.17116i	0.299954	−	0.953954i	$-0.403029\pi$
$242$	−1.79715	−	6.04997i	−0.115525	−	0.388907i
$243$	9.70594	−	12.1981i	0.622636	−	0.782512i
$244$	−3.33564	−	5.11916i	−0.213542	−	0.327720i
$245$	−2.72052	+	1.57069i	−0.173808	+	0.100348i
$246$	5.09039	−	5.06245i	0.324551	−	0.322770i
$247$	−2.48720	+	4.30797i	−0.158257	+	0.274109i
$248$	18.0826	−	6.45045i	1.14825	−	0.409604i
$249$	18.5427	+	11.4530i	1.17509	+	0.725803i
$250$	0.424678	+	0.402383i	0.0268590	+	0.0254490i
$251$			15.9379i			1.00599i	0.864289	+	0.502996i	$0.167769\pi$
$251$			15.9379i			1.00599i	−0.864289	+	0.502996i	$0.832231\pi$
$252$	0.0330201	−	5.99991i	0.00208007	−	0.377959i
$253$			4.30776i			0.270826i
$254$	−15.6609	+	16.5286i	−0.982650	+	1.03710i
$255$	−0.185774	+	6.25283i	−0.0116336	+	0.391568i
$256$	15.6296	−	3.42293i	0.976848	−	0.213933i
$257$	−1.09021	+	1.88830i	−0.0680054	+	0.117789i	−0.898023	−	0.439948i	$-0.854997\pi$
$257$	−1.09021	+	1.88830i	−0.0680054	+	0.117789i	0.830018	+	0.557737i	$0.188330\pi$
$258$	25.0120	−	6.62825i	1.55718	−	0.412657i
$259$	2.83164	−	1.63485i	0.175949	−	0.101584i
$260$	5.86230	−	3.81987i	0.363564	−	0.236898i
$261$	−0.858740	+	14.4391i	−0.0531547	+	0.893757i
$262$	−8.82500	+	2.62148i	−0.545210	+	0.161955i
$263$	5.79496	+	10.0372i	0.357332	+	0.618918i	0.987514	−	0.157530i	$-0.0503530\pi$
$263$	5.79496	+	10.0372i	0.357332	+	0.618918i	−0.630182	+	0.776448i	$0.717020\pi$
$264$	3.85623	+	11.9174i	0.237335	+	0.733464i
$265$	−14.4996	+	25.1141i	−0.890705	+	1.54275i
$266$	−1.46990	+	6.14339i	−0.0901251	+	0.376675i
$267$	4.96616	+	9.22385i	0.303924	+	0.564491i
$268$	−9.90285	+	19.5096i	−0.604913	+	1.19174i
$269$		−	2.15568i		−	0.131434i	−0.997838	−	0.0657171i	$-0.979067\pi$
$269$		−	2.15568i		−	0.131434i	0.997838	−	0.0657171i	$-0.0209335\pi$
$270$	22.6259	−	4.57811i	1.37697	−	0.278615i
$271$	14.7673			0.897051			0.448526	−	0.893770i	$-0.351949\pi$
$271$	14.7673			0.897051			0.448526	+	0.893770i	$0.351949\pi$
$272$	−4.57212	+	0.494792i	−0.277226	+	0.0300012i
$273$	1.69842	−	0.914439i	0.102793	−	0.0553444i
$274$	−24.6051	−	5.88713i	−1.48645	−	0.355654i
$275$	10.7797	+	6.22367i	0.650041	+	0.375302i
$276$	0.141217	+	5.83467i	0.00850023	+	0.351206i
$277$	7.34491	−	4.24059i	0.441313	−	0.254792i	−0.262841	−	0.964839i	$-0.584660\pi$
$277$	7.34491	−	4.24059i	0.441313	−	0.254792i	0.704154	+	0.710047i	$0.251326\pi$
$278$	12.5415	−	3.72546i	0.752188	−	0.223438i
$279$	9.11672	+	18.2085i	0.545804	+	1.09011i
$280$	5.75484	−	6.76966i	0.343918	−	0.404565i
$281$	−7.88091	−	13.6501i	−0.470136	−	0.814299i	0.529281	−	0.848446i	$-0.322462\pi$
$281$	−7.88091	−	13.6501i	−0.470136	−	0.814299i	−0.999417	+	0.0341477i	$0.989128\pi$
$282$	7.27955	+	27.4698i	0.433491	+	1.63580i
$283$	28.0432	+	16.1907i	1.66699	+	0.962439i	0.969246	+	0.246095i	$0.0791476\pi$
$283$	28.0432	+	16.1907i	1.66699	+	0.962439i	0.697748	+	0.716344i	$0.254186\pi$
$284$	−1.42361	−	26.3865i	−0.0844758	−	1.56575i
$285$	−24.2925	−	0.721739i	−1.43896	−	0.0427521i
$286$	−2.76970	+	2.92316i	−0.163776	+	0.172850i
$287$	2.93088			0.173005
$288$	5.61378	+	16.0152i	0.330795	+	0.943703i
$289$	−15.6782			−0.922246
$290$	−14.7327	+	15.5490i	−0.865132	+	0.913066i
$291$	−9.12076	+	14.7667i	−0.534668	+	0.865642i
$292$	0.771964	+	14.3083i	0.0451758	+	0.837330i
$293$	−20.4389	−	11.8004i	−1.19406	−	0.689388i	−0.234832	−	0.972036i	$-0.575454\pi$
$293$	−20.4389	−	11.8004i	−1.19406	−	0.689388i	−0.959224	+	0.282647i	$0.908787\pi$
$294$	1.73681	−	1.72728i	0.101293	−	0.100737i
$295$	−20.8567	−	36.1249i	−1.21432	−	2.10327i
$296$	−5.98989	+	7.04616i	−0.348156	+	0.409550i
$297$	−12.0511	+	5.59258i	−0.699277	+	0.324514i
$298$	−28.2186	+	8.38239i	−1.63466	+	0.485579i
$299$	−1.62496	+	0.938173i	−0.0939740	+	0.0542559i
$300$	14.8047	+	8.07632i	0.854749	+	0.466286i
$301$	9.14833	+	5.28179i	0.527301	+	0.304437i
$302$	9.06298	+	2.16845i	0.521516	+	0.124780i
$303$	17.6212	+	10.8838i	1.01231	+	0.625258i
$304$	−1.92229	−	17.7629i	−0.110251	−	1.01877i
$305$	9.59696			0.549520
$306$	−1.10892	−	4.75006i	−0.0633927	−	0.271543i
$307$			22.9528i			1.30998i	0.755636	+	0.654991i	$0.227328\pi$
$307$			22.9528i			1.30998i	−0.755636	+	0.654991i	$0.772672\pi$
$308$	−2.31451	+	4.55984i	−0.131882	+	0.259821i
$309$	13.4121	+	0.398479i	0.762989	+	0.0226687i
$310$	−7.01703	+	29.3275i	−0.398541	+	1.66569i
$311$	−3.06168	+	5.30299i	−0.173612	+	0.300705i	−0.939680	−	0.342055i	$-0.888877\pi$
$311$	−3.06168	+	5.30299i	−0.173612	+	0.300705i	0.766068	+	0.642759i	$0.222211\pi$
$312$	−3.65561	+	4.05009i	−0.206958	+	0.229291i
$313$	0.163360	+	0.282948i	0.00923366	+	0.0159932i	0.870605	−	0.491982i	$-0.163727\pi$
$313$	0.163360	+	0.282948i	0.00923366	+	0.0159932i	−0.861372	+	0.507975i	$0.830394\pi$
$314$	23.3038	−	6.92243i	1.31511	−	0.390655i
$315$	7.86742	+	5.18831i	0.443279	+	0.292328i
$316$	−8.31364	+	5.41716i	−0.467679	+	0.304739i
$317$	−0.988446	+	0.570680i	−0.0555167	+	0.0320526i	−0.527501	−	0.849554i	$-0.676871\pi$
$317$	−0.988446	+	0.570680i	−0.0555167	+	0.0320526i	0.471985	+	0.881607i	$0.343538\pi$
$318$	5.91252	−	21.8254i	0.331558	−	1.22391i
$319$	6.16387	−	10.6761i	0.345111	−	0.597749i
$320$	−8.89769	+	23.5033i	−0.497396	+	1.31387i
$321$	−8.34113	+	4.49090i	−0.465556	+	0.250658i
$322$	−1.63881	+	1.72961i	−0.0913271	+	0.0963872i
$323$			5.13532i			0.285737i
$324$	−16.1394	+	7.96996i	−0.896632	+	0.442776i
$325$			5.42174i			0.300744i
$326$	9.78865	+	9.27476i	0.542143	+	0.513682i
$327$	15.4929	−	8.34147i	0.856762	−	0.461284i
$328$	−7.80789	+	2.78523i	−0.431119	+	0.153789i
$329$	−5.80079	+	10.0473i	−0.319808	+	0.553924i
$330$	−18.9897	−	5.14431i	−1.04535	−	0.283185i
$331$	−0.734494	+	0.424060i	−0.0403715	+	0.0233085i	−0.520050	−	0.854136i	$-0.674087\pi$
$331$	−0.734494	+	0.424060i	−0.0403715	+	0.0233085i	0.479678	+	0.877444i	$0.340753\pi$
$332$	−13.7390	−	21.0850i	−0.754023	−	1.15719i
$333$	−8.18876	−	5.40022i	−0.448741	−	0.295930i
$334$	−6.40978	−	21.5780i	−0.350728	−	1.18070i
$335$	−17.1826	−	29.7612i	−0.938788	−	1.62603i
$336$	−2.98543	+	6.25198i	−0.162869	+	0.341073i
$337$	−4.90148	+	8.48961i	−0.267001	+	0.462459i	−0.968086	−	0.250619i	$-0.919366\pi$
$337$	−4.90148	+	8.48961i	−0.267001	+	0.462459i	0.701085	+	0.713077i	$0.252699\pi$
$338$	16.1742	+	3.86992i	0.879762	+	0.210496i
$339$	27.4486	+	0.815509i	1.49080	+	0.0442924i
$340$	3.26941	−	6.44108i	0.177309	−	0.349317i
$341$		−	17.3550i		−	0.939827i
$342$	18.4542	−	4.30819i	0.997887	−	0.232960i
$343$	1.00000			0.0539949
$344$	−29.3905	−	5.37701i	−1.58463	−	0.289909i
$345$	−7.79937	−	4.81733i	−0.419904	−	0.259356i
$346$	−1.61788	+	6.76190i	−0.0869780	+	0.363522i
$347$	−0.898387	−	0.518684i	−0.0482279	−	0.0278444i	0.475692	−	0.879612i	$-0.342198\pi$
$347$	−0.898387	−	0.518684i	−0.0482279	−	0.0278444i	−0.523920	+	0.851767i	$0.675531\pi$
$348$	7.99872	−	14.6624i	0.428776	−	0.785989i
$349$	−10.5858	+	6.11171i	−0.566644	+	0.327152i	−0.755808	−	0.654793i	$-0.772756\pi$
$349$	−10.5858	+	6.11171i	−0.566644	+	0.327152i	0.189164	+	0.981946i	$0.439422\pi$
$350$	1.96048	+	6.59981i	0.104792	+	0.352775i
$351$	−4.73420	−	3.32791i	−0.252693	−	0.177631i
$352$	1.83264	−	14.3469i	0.0976801	−	0.764693i
$353$	−1.22662	−	2.12456i	−0.0652863	−	0.113079i	0.831535	−	0.555473i	$-0.187463\pi$
$353$	−1.22662	−	2.12456i	−0.0652863	−	0.113079i	−0.896821	+	0.442394i	$0.854129\pi$
$354$	22.9359	+	23.0625i	1.21903	+	1.22576i
$355$	35.9448	+	20.7527i	1.90775	+	1.10144i
$356$	−0.651680	−	12.0788i	−0.0345390	−	0.640177i
$357$	1.04645	−	1.69423i	0.0553840	−	0.0896681i
$358$	8.05773	+	7.63472i	0.425864	+	0.403507i
$359$	4.44789			0.234750			0.117375	−	0.993088i	$-0.462552\pi$
$359$	4.44789			0.234750			0.117375	+	0.993088i	$0.462552\pi$
$360$	−25.8893	−	6.34523i	−1.36449	−	0.334423i
$361$	−0.950925			−0.0500487
$362$	−1.19346	−	1.13081i	−0.0627270	−	0.0594339i
$363$	−7.72626	−	0.229550i	−0.405524	−	0.0120483i
$364$	−2.22412	+	0.119996i	−0.116576	+	0.00628951i
$365$	−19.4913	−	11.2533i	−1.02022	−	0.589026i
$366$	−7.23352	+	1.91690i	−0.378102	+	0.100198i
$367$	−8.48896	−	14.7033i	−0.443120	−	0.767507i	0.554799	−	0.831985i	$-0.312795\pi$
$367$	−8.48896	−	14.7033i	−0.443120	−	0.767507i	−0.997919	+	0.0644776i	$0.979462\pi$
$368$	2.72213	−	6.16504i	0.141901	−	0.321375i
$369$	−3.93650	−	7.86223i	−0.204926	−	0.409292i
$370$	−4.13631	−	13.9246i	−0.215036	−	0.723903i
$371$	7.99459	−	4.61568i	0.415058	−	0.239634i
$372$	−0.568931	−	23.5066i	−0.0294977	−	1.21876i
$373$	−21.8343	−	12.6060i	−1.13054	−	0.652716i	−0.186468	−	0.982461i	$-0.559704\pi$
$373$	−21.8343	−	12.6060i	−1.13054	−	0.652716i	−0.944070	+	0.329745i	$0.893037\pi$
$374$	−0.967363	+	4.04307i	−0.0500212	+	0.209062i
$375$	0.630887	−	0.339672i	0.0325789	−	0.0175406i
$376$	5.90537	−	32.2785i	0.304546	−	1.66464i
$377$	5.36964			0.276551
$378$	−6.96623	−	2.33915i	−0.358304	−	0.120313i
$379$		−	34.4947i		−	1.77187i	−0.463806	−	0.885937i	$-0.653516\pi$
$379$		−	34.4947i		−	1.77187i	0.463806	−	0.885937i	$-0.346484\pi$
$380$	25.0238	+	12.7018i	1.28370	+	0.651588i
$381$	13.2201	+	24.5543i	0.677288	+	1.25795i
$382$	30.1415	+	7.21180i	1.54218	+	0.368988i
$383$	3.23187	−	5.59776i	0.165141	−	0.286032i	−0.771565	−	0.636151i	$-0.780525\pi$
$383$	3.23187	−	5.59776i	0.165141	−	0.286032i	0.936705	+	0.350119i	$0.113859\pi$
$384$	2.01191	−	19.4924i	0.102670	−	0.994715i
$385$	−4.01596	−	6.95585i	−0.204672	−	0.354503i
$386$	−0.00236969	−	0.00797738i	−0.000120614	−	0.000406038i
$387$	1.88143	−	31.6349i	0.0956384	−	1.60809i
$388$	16.7913	−	10.9412i	0.852451	−	0.555457i
$389$	−11.5957	+	6.69480i	−0.587927	+	0.339440i	−0.764277	−	0.644888i	$-0.776904\pi$
$389$	−11.5957	+	6.69480i	−0.587927	+	0.339440i	0.176350	+	0.984327i	$0.443571\pi$
$390$	−2.19517	−	8.28360i	−0.111157	−	0.419457i
$391$	−0.968521	+	1.67753i	−0.0489802	+	0.0848363i
$392$	−2.66400	+	0.950305i	−0.134553	+	0.0479976i
$393$	−0.334841	+	11.2702i	−0.0168905	+	0.568505i
$394$	6.24903	+	5.92097i	0.314822	+	0.298294i
$395$		−	15.5857i		−	0.784201i
$396$	15.3406	+	0.0844260i	0.770895	+	0.00424257i
$397$		−	31.1981i		−	1.56579i	−0.622155	−	0.782894i	$-0.713742\pi$
$397$		−	31.1981i		−	1.56579i	0.622155	−	0.782894i	$-0.286258\pi$
$398$	12.3968	−	13.0837i	0.621395	−	0.655824i
$399$	6.58214	+	4.06549i	0.329519	+	0.203529i
$400$	−11.4946	−	15.7189i	−0.574728	−	0.785943i
$401$	8.43370	−	14.6076i	0.421159	−	0.729469i	−0.574894	−	0.818228i	$-0.694957\pi$
$401$	8.43370	−	14.6076i	0.421159	−	0.729469i	0.996053	+	0.0887591i	$0.0282901\pi$
$402$	18.8956	+	18.9999i	0.942427	+	0.947628i
$403$	6.54663	−	3.77970i	0.326111	−	0.188280i
$404$	−13.0562	−	20.0371i	−0.649569	−	0.996884i
$405$	3.35106	−	28.0732i	0.166516	−	1.39497i
$406$	6.53639	−	1.94164i	0.324396	−	0.0963622i
$407$	4.17999	+	7.23996i	0.207194	+	0.358871i
$408$	−1.17771	+	5.50788i	−0.0583054	+	0.272681i
$409$	−1.08388	+	1.87733i	−0.0535944	+	0.0928282i	−0.891578	−	0.452867i	$-0.850401\pi$
$409$	−1.08388	+	1.87733i	−0.0535944	+	0.0928282i	0.837984	+	0.545695i	$0.183734\pi$
$410$	3.02988	−	12.6633i	0.149635	−	0.625396i
$411$	−16.2828	+	26.3623i	−0.803173	+	1.30036i
$412$	−13.8159	−	7.01277i	−0.680661	−	0.345495i
$413$			13.2787i			0.653400i
$414$	6.84084	+	2.07312i	0.336209	+	0.101888i
$415$	39.5283			1.94037
$416$	5.81104	−	2.43327i	0.284910	−	0.119301i
$417$	0.475853	−	16.0164i	0.0233026	−	0.784326i
$418$	−15.7075	−	3.75824i	−0.768278	−	0.183822i
$419$	−19.8122	−	11.4386i	−0.967890	−	0.558812i	−0.0692976	−	0.997596i	$-0.522076\pi$
$419$	−19.8122	−	11.4386i	−0.967890	−	0.558812i	−0.898592	+	0.438785i	$0.855409\pi$
$420$	−5.66748	−	9.28975i	−0.276544	−	0.453293i
$421$	−21.0770	+	12.1688i	−1.02723	+	0.593070i	−0.916189	−	0.400746i	$-0.868751\pi$
$421$	−21.0770	+	12.1688i	−1.02723	+	0.593070i	−0.111039	+	0.993816i	$0.535418\pi$
$422$	−22.1799	+	6.58857i	−1.07970	+	0.320726i
$423$	34.7433	+	2.06630i	1.68928	+	0.100467i
$424$	−16.9113	+	19.8935i	−0.821286	+	0.966113i
$425$	2.79856	+	4.84725i	0.135750	+	0.235126i
$426$	−31.2378	−	8.46235i	−1.51348	−	0.410002i
$427$	−2.64571	−	1.52750i	−0.128035	−	0.0739210i
$428$	10.9229	−	0.589314i	0.527978	−	0.0284856i
$429$	2.33805	+	4.34255i	0.112882	+	0.209660i
$430$	32.2781	−	34.0665i	1.55659	−	1.64283i
$431$	−11.5368			−0.555710			−0.277855	−	0.960623i	$-0.589623\pi$
$431$	−11.5368			−0.555710			−0.277855	+	0.960623i	$0.589623\pi$
$432$	20.7810	−	0.388544i	0.999825	−	0.0186938i
$433$	−36.9204			−1.77428			−0.887141	−	0.461498i	$-0.847312\pi$
$433$	−36.9204			−1.77428			−0.887141	+	0.461498i	$0.847312\pi$
$434$	6.60240	−	6.96821i	0.316925	−	0.334485i
$435$	12.4366	+	23.0990i	0.596289	+	1.10751i
$436$	−20.2883	+	1.09460i	−0.971636	+	0.0524219i
$437$	−6.51726	−	3.76274i	−0.311763	−	0.179996i
$438$	16.9390	+	4.58878i	0.809375	+	0.219260i
$439$	−1.37686	−	2.38479i	−0.0657138	−	0.113820i	0.831297	−	0.555829i	$-0.187599\pi$
$439$	−1.37686	−	2.38479i	−0.0657138	−	0.113820i	−0.897010	+	0.442009i	$0.854266\pi$
$440$	17.3087	+	14.7140i	0.825161	+	0.701464i
$441$	−1.34311	−	2.68255i	−0.0639577	−	0.127740i
$442$	−1.73580	+	0.515621i	−0.0825635	+	0.0245256i
$443$	2.23105	−	1.28810i	0.106000	−	0.0611993i	−0.446063	−	0.895002i	$-0.647174\pi$
$443$	2.23105	−	1.28810i	0.106000	−	0.0611993i	0.552063	+	0.833802i	$0.313841\pi$
$444$	5.89896	+	9.66918i	0.279952	+	0.458879i
$445$	16.4543	+	9.49987i	0.780007	+	0.450337i
$446$	−20.7629	−	4.96783i	−0.983153	−	0.235234i
$447$	−1.07068	+	36.0373i	−0.0506415	+	1.70451i
$448$	6.19384	−	5.06323i	0.292631	−	0.239215i
$449$	29.7950			1.40611			0.703057	−	0.711133i	$-0.251818\pi$
$449$	29.7950			1.40611			0.703057	+	0.711133i	$0.251818\pi$
$450$	15.0711	−	14.1234i	0.710461	−	0.665781i
$451$			7.49371i			0.352865i
$452$	−28.2750	−	14.3520i	−1.32994	−	0.675062i
$453$	5.99758	−	9.71023i	0.281791	−	0.456226i
$454$	8.71492	−	36.4238i	0.409012	−	1.70945i
$455$	1.74925	−	3.02979i	0.0820060	−	0.142039i
$456$	−21.3983	−	4.57546i	−1.00207	−	0.214265i
$457$	14.6563	+	25.3855i	0.685593	+	1.18748i	0.973250	+	0.229748i	$0.0737902\pi$
$457$	14.6563	+	25.3855i	0.685593	+	1.18748i	−0.287657	+	0.957733i	$0.592876\pi$
$458$	28.1314	−	8.35648i	1.31450	−	0.390473i
$459$	−5.95034	−	0.531613i	−0.277738	−	0.0248135i
$460$	5.77885	+	8.86871i	0.269440	+	0.413506i
$461$	−20.1446	+	11.6305i	−0.938226	+	0.541685i	−0.889404	−	0.457122i	$-0.848880\pi$
$461$	−20.1446	+	11.6305i	−0.938226	+	0.541685i	−0.0488222	+	0.998807i	$0.515547\pi$
$462$	4.41632	+	4.44069i	0.205466	+	0.206600i
$463$	−5.91766	+	10.2497i	−0.275017	+	0.476344i	−0.970139	−	0.242548i	$-0.922017\pi$
$463$	−5.91766	+	10.2497i	−0.275017	+	0.476344i	0.695122	+	0.718892i	$0.255350\pi$
$464$	−15.5678	+	11.3841i	−0.722718	+	0.528494i
$465$	31.4220	+	19.4080i	1.45716	+	0.900023i
$466$	−12.8162	+	13.5263i	−0.593699	+	0.626594i
$467$			11.1239i			0.514752i	0.966311	+	0.257376i	$0.0828579\pi$
$467$			11.1239i			0.514752i	−0.966311	+	0.257376i	$0.917142\pi$
$468$	3.30914	+	5.80515i	0.152965	+	0.268343i
$469$			10.9395i			0.505140i
$470$	37.4139	+	35.4497i	1.72577	+	1.63517i
$471$	0.884203	−	29.7607i	0.0407419	−	1.37130i
$472$	−12.6188	−	35.3744i	−0.580826	−	1.62824i
$473$	−13.5045	+	23.3905i	−0.620939	+	1.07550i
$474$	3.11309	+	11.7474i	0.142989	+	0.539577i
$475$	−18.8317	+	10.8725i	−0.864060	+	0.498865i
$476$	−1.92652	+	1.25532i	−0.0883017	+	0.0575373i
$477$	−23.1194	−	15.2465i	−1.05856	−	0.698089i
$478$	−3.02309	−	10.1770i	−0.138273	−	0.465485i
$479$	7.09183	+	12.2834i	0.324034	+	0.561243i	0.981316	−	0.192401i	$-0.0616275\pi$
$479$	7.09183	+	12.2834i	0.324034	+	0.561243i	−0.657282	+	0.753644i	$0.728294\pi$
$480$	23.9263	+	19.3621i	1.09208	+	0.883755i
$481$	−1.82070	+	3.15354i	−0.0830166	+	0.143789i
$482$	28.8750	+	6.90876i	1.31522	+	0.314685i
$483$	1.38340	+	2.56944i	0.0629469	+	0.116914i
$484$	7.95887	+	4.03982i	0.361767	+	0.183628i
$485$			31.4790i			1.42939i
$486$	3.08155	+	21.8290i	0.139782	+	0.990182i
$487$	−1.07391			−0.0486634			−0.0243317	−	0.999704i	$-0.507746\pi$
$487$	−1.07391			−0.0486634			−0.0243317	+	0.999704i	$0.507746\pi$
$488$	8.49978	+	1.55504i	0.384767	+	0.0703934i
$489$	14.5417	−	7.82930i	0.657597	−	0.354053i
$490$	1.03378	−	4.32064i	0.0467012	−	0.195187i
$491$	11.1376	+	6.43031i	0.502634	+	0.290196i	0.729801	−	0.683660i	$-0.239613\pi$
$491$	11.1376	+	6.43031i	0.502634	+	0.290196i	−0.227167	+	0.973856i	$0.572946\pi$
$492$	0.245658	+	10.1499i	0.0110751	+	0.457593i
$493$	4.80068	−	2.77167i	0.216212	−	0.124830i
$494$	−2.00321	−	6.74364i	−0.0901285	−	0.303411i
$495$	−13.2655	+	20.1155i	−0.596240	+	0.904124i
$496$	−10.9669	+	24.8376i	−0.492428	+	1.11524i
$497$	−6.60623	−	11.4423i	−0.296330	−	0.513258i
$498$	−29.7937	+	7.89540i	−1.33509	+	0.353801i
$499$	9.13839	+	5.27605i	0.409090	+	0.236188i	0.690399	−	0.723429i	$-0.257435\pi$
$499$	9.13839	+	5.27605i	0.409090	+	0.236188i	−0.281308	+	0.959617i	$0.590768\pi$
$500$	−0.826160	+	0.0445731i	−0.0369470	+	0.00199337i
$501$	−27.5568	−	0.818722i	−1.23114	−	0.0365778i
$502$	−16.3616	−	15.5027i	−0.730254	−	0.691917i
$503$	40.4074			1.80168			0.900838	−	0.434155i	$-0.142953\pi$
$503$	40.4074			1.80168			0.900838	+	0.434155i	$0.142953\pi$
$504$	6.12729	+	5.86995i	0.272931	+	0.261468i
$505$	37.5639			1.67157
$506$	−4.42227	−	4.19011i	−0.196594	−	0.186273i
$507$	10.7036	−	17.3294i	0.475362	−	0.769624i
$508$	−1.73480	−	32.1544i	−0.0769692	−	1.42662i
$509$	−6.56409	−	3.78978i	−0.290948	−	0.167979i	0.347421	−	0.937709i	$-0.387057\pi$
$509$	−6.56409	−	3.78978i	−0.290948	−	0.167979i	−0.638369	+	0.769730i	$0.720391\pi$
$510$	−6.23836	−	6.27278i	−0.276239	−	0.277763i
$511$	3.58228	+	6.20469i	0.158471	+	0.274479i
$512$	−11.6888	+	19.3745i	−0.516577	+	0.856241i
$513$	2.06533	−	23.1173i	0.0911867	−	1.02065i
$514$	−0.878060	−	2.95592i	−0.0387296	−	0.130380i
$515$	21.0756	−	12.1680i	0.928703	−	0.536187i
$516$	−17.5245	+	32.1242i	−0.771474	+	1.41419i
$517$	−25.6889	−	14.8315i	−1.12980	−	0.652289i
$518$	−1.07600	+	4.49711i	−0.0472767	+	0.197592i
$519$	7.24482	+	4.47480i	0.318012	+	0.196422i
$520$	−1.78078	+	9.73369i	−0.0780926	+	0.426850i
$521$	26.4340			1.15809			0.579047	−	0.815294i	$-0.303425\pi$
$521$	26.4340			1.15809			0.579047	+	0.815294i	$0.303425\pi$
$522$	−13.9876	−	14.9263i	−0.612223	−	0.653308i
$523$			6.40721i			0.280168i	0.990140	+	0.140084i	$0.0447372\pi$
$523$			6.40721i			0.280168i	−0.990140	+	0.140084i	$0.955263\pi$
$524$	5.89282	−	11.6095i	0.257429	−	0.507162i
$525$	8.42845	+	0.250412i	0.367848	+	0.0109289i
$526$	−15.9407	−	3.81404i	−0.695047	−	0.166300i
$527$	3.90197	−	6.75840i	0.169972	−	0.294401i
$528$	−15.9851	−	7.63317i	−0.695663	−	0.332191i
$529$	10.0807	+	17.4603i	0.438291	+	0.759142i
$530$	−11.6781	−	39.3133i	−0.507263	−	1.70766i
$531$	35.6206	−	17.8347i	1.54580	−	0.773961i
$532$	−4.87695	−	7.48459i	−0.211443	−	0.324498i
$533$	−2.82676	+	1.63203i	−0.122441	+	0.0706912i
$534$	−14.2996	−	3.87377i	−0.618804	−	0.167634i
$535$	−8.59073	+	14.8796i	−0.371410	+	0.643301i
$536$	−10.3959	−	29.1429i	−0.449034	−	1.25878i
$537$	11.9703	−	6.44486i	0.516556	−	0.278116i
$538$	2.21299	+	2.09681i	0.0954086	+	0.0903999i
$539$			2.55681i			0.110130i
$540$	−17.3081	+	27.6804i	−0.744824	+	1.19118i
$541$			6.31237i			0.271390i	0.990751	+	0.135695i	$0.0433267\pi$
$541$			6.31237i			0.271390i	−0.990751	+	0.135695i	$0.956673\pi$
$542$	−14.3640	+	15.1599i	−0.616988	+	0.651173i
$543$	−1.77297	+	0.954573i	−0.0760852	+	0.0409646i
$544$	3.93931	−	5.17495i	0.168897	−	0.221874i
$545$	15.9566	−	27.6376i	0.683504	−	1.18386i
$546$	−0.713292	+	2.63304i	−0.0305261	+	0.112684i
$547$	−31.9762	+	18.4615i	−1.36720	+	0.789356i	−0.990570	−	0.137007i	$-0.956252\pi$
$547$	−31.9762	+	18.4615i	−1.36720	+	0.789356i	−0.376634	+	0.926362i	$0.622918\pi$
$548$	29.9768	−	19.5328i	1.28054	−	0.834401i
$549$	−0.544112	+	9.14885i	−0.0232221	+	0.390463i
$550$	−16.8744	+	5.01257i	−0.719529	+	0.213737i
$551$	10.7680	+	18.6508i	0.458734	+	0.794551i
$552$	−6.12714	−	5.53036i	−0.260788	−	0.235388i
$553$	−2.48070	+	4.29670i	−0.105490	+	0.182714i
$554$	−2.79101	+	11.6649i	−0.118579	+	0.495596i
$555$	−17.7827	−	0.528331i	−0.754834	−	0.0224264i
$556$	−8.37447	+	16.4986i	−0.355157	+	0.699696i
$557$			29.4941i			1.24970i	0.780743	+	0.624852i	$0.214841\pi$
$557$			29.4941i			1.24970i	−0.780743	+	0.624852i	$0.785159\pi$
$558$	−27.5603	−	8.35215i	−1.16672	−	0.353575i
$559$	−11.7644			−0.497583
$560$	1.35194	+	12.4926i	0.0571300	+	0.527909i
$561$	4.33182	+	2.67557i	0.182889	+	0.112963i
$562$	21.6787	+	5.18694i	0.914460	+	0.218798i
$563$	−27.1145	−	15.6546i	−1.14274	−	0.659761i	−0.195632	−	0.980677i	$-0.562676\pi$
$563$	−27.1145	−	15.6546i	−1.14274	−	0.659761i	−0.947108	+	0.320916i	$0.896009\pi$
$564$	−35.2808	−	19.2465i	−1.48559	−	0.810424i
$565$	43.1324	−	24.9025i	1.81459	−	1.04766i
$566$	−43.8984	+	13.0401i	−1.84519	+	0.548116i
$567$	−5.39211	+	7.20591i	−0.226447	+	0.302620i
$568$	28.4727	+	24.2045i	1.19469	+	1.01560i
$569$	3.81743	+	6.61199i	0.160035	+	0.277189i	0.934881	−	0.354961i	$-0.115506\pi$
$569$	3.81743	+	6.61199i	0.160035	+	0.277189i	−0.774846	+	0.632150i	$0.782173\pi$
$570$	24.3700	−	24.2362i	1.02075	−	1.01514i
$571$	0.877928	+	0.506872i	0.0367402	+	0.0212119i	0.518258	−	0.855225i	$-0.326581\pi$
$571$	0.877928	+	0.506872i	0.0367402	+	0.0212119i	−0.481517	+	0.876437i	$0.659914\pi$
$572$	−0.306808	−	5.68666i	−0.0128283	−	0.237771i
$573$	19.9467	−	32.2942i	0.833284	−	1.34911i
$574$	−2.85084	+	3.00880i	−0.118992	+	0.125585i
$575$	−8.20222			−0.342056
$576$	−21.9014	−	9.81478i	−0.912557	−	0.408949i
$577$	4.43655			0.184696			0.0923481	−	0.995727i	$-0.470563\pi$
$577$	4.43655			0.184696			0.0923481	+	0.995727i	$0.470563\pi$
$578$	15.2500	−	16.0950i	0.634317	−	0.669462i
$579$	−0.0101877		0.000302681i	−0.000423387		1.25790e-5i
$580$	−1.63198	−	30.2486i	−0.0677642	−	1.25601i
$581$	−10.8973	−	6.29154i	−0.452095	−	0.261017i
$582$	−6.28762	−	23.7267i	−0.260630	−	0.983503i
$583$	11.8014	+	20.4406i	0.488764	+	0.846565i
$584$	−15.4396	−	13.1251i	−0.638893	−	0.543119i
$585$	−10.4770	−	0.623100i	−0.433170	−	0.0257620i
$586$	31.9949	−	9.50412i	1.32170	−	0.392612i
$587$	−2.66824	+	1.54051i	−0.110130	+	0.0635837i	−0.554053	−	0.832481i	$-0.686920\pi$
$587$	−2.66824	+	1.54051i	−0.110130	+	0.0635837i	0.443923	+	0.896065i	$0.353586\pi$
$588$	0.0838171	+	3.46309i	0.00345656	+	0.142815i
$589$	26.2566	+	15.1593i	1.08189	+	0.624627i
$590$	57.3723	+	13.7272i	2.36198	+	0.565138i
$591$	9.28335	−	4.99820i	0.381866	−	0.205598i
$592$	−1.40716	−	13.0029i	−0.0578340	−	0.534414i
$593$	−7.07396			−0.290493			−0.145246	−	0.989396i	$-0.546398\pi$
$593$	−7.07396			−0.290493			−0.145246	+	0.989396i	$0.546398\pi$
$594$	5.98075	−	17.8113i	0.245393	−	0.730807i
$595$		−	3.61167i		−	0.148064i
$596$	18.8428	−	37.1223i	0.771831	−	1.52059i
$597$	−10.4648	−	19.4366i	−0.428294	−	0.795488i
$598$	0.617473	−	2.58071i	0.0252503	−	0.105533i
$599$	−15.1086	+	26.1689i	−0.617323	+	1.06923i	0.372650	+	0.927972i	$0.378449\pi$
$599$	−15.1086	+	26.1689i	−0.617323	+	1.06923i	−0.989972	+	0.141262i	$0.954884\pi$
$600$	−22.6914	+	7.34249i	−0.926372	+	0.299756i
$601$	1.20922	+	2.09443i	0.0493250	+	0.0854334i	0.889634	−	0.456675i	$-0.150960\pi$
$601$	1.20922	+	2.09443i	0.0493250	+	0.0854334i	−0.840309	+	0.542108i	$0.817626\pi$
$602$	−14.3207	+	4.25398i	−0.583668	+	0.173379i
$603$	29.3458	−	14.6930i	1.19505	−	0.598345i
$604$	−11.0416	+	7.19467i	−0.449275	+	0.292747i
$605$	−12.1409	+	7.00958i	−0.493600	+	0.284980i
$606$	−28.3131	+	7.50302i	−1.15014	+	0.304789i
$607$	−11.5566	+	20.0165i	−0.469066	+	0.812446i	−0.999375	−	0.0353585i	$-0.988743\pi$
$607$	−11.5566	+	20.0165i	−0.469066	+	0.812446i	0.530309	+	0.847805i	$0.322076\pi$
$608$	20.1049	+	15.3044i	0.815360	+	0.620675i
$609$	0.248006	−	8.34746i	0.0100497	−	0.338256i
$610$	−9.33486	+	9.85208i	−0.377958	+	0.398899i
$611$		−	12.9204i		−	0.522705i
$612$	5.95497	+	3.48194i	0.240715	+	0.140749i
$613$			43.2417i			1.74651i	0.487260	+	0.873257i	$0.337997\pi$
$613$			43.2417i			1.74651i	−0.487260	+	0.873257i	$0.662003\pi$
$614$	−23.5629	−	22.3259i	−0.950922	−	0.901001i
$615$	−13.5677	−	8.38015i	−0.547102	−	0.337920i
$616$	−2.42975	−	6.81135i	−0.0978973	−	0.274437i
$617$	2.24846	−	3.89445i	0.0905198	−	0.156785i	−0.817210	−	0.576340i	$-0.804481\pi$
$617$	2.24846	−	3.89445i	0.0905198	−	0.156785i	0.907730	+	0.419555i	$0.137814\pi$
$618$	−13.4549	+	13.3811i	−0.541236	+	0.538265i
$619$	5.80594	−	3.35206i	0.233361	−	0.134731i	−0.378761	−	0.925495i	$-0.623650\pi$
$619$	5.80594	−	3.35206i	0.233361	−	0.134731i	0.612121	+	0.790764i	$0.290316\pi$
$620$	−23.2817	−	35.7301i	−0.935017	−	1.43496i
$621$	5.03459	−	7.16208i	0.202031	−	0.287404i
$622$	−2.46589	−	8.30124i	−0.0988733	−	0.332849i
$623$	−3.02410	−	5.23790i	−0.121158	−	0.209852i
$624$	−0.601977	−	7.69228i	−0.0240984	−	0.307937i
$625$	12.8205	−	22.2058i	0.512822	−	0.888234i
$626$	−0.449369	−	0.107518i	−0.0179604	−	0.00429728i
$627$	−10.3947	+	16.8293i	−0.415124	+	0.672096i
$628$	−15.5610	+	30.6567i	−0.620950	+	1.22334i
$629$			3.75918i			0.149888i
$630$	−12.9788	+	3.02995i	−0.517087	+	0.120716i
$631$	−44.2673			−1.76225			−0.881126	−	0.472881i	$-0.843214\pi$
$631$	−44.2673			−1.76225			−0.881126	+	0.472881i	$0.843214\pi$
$632$	2.52543	−	13.8039i	0.100456	−	0.549088i
$633$	−0.841558	+	28.3254i	−0.0334489	+	1.12583i
$634$	0.375601	−	1.56982i	0.0149170	−	0.0623454i
$635$	43.8019	+	25.2891i	1.73823	+	1.00357i
$636$	16.6546	+	27.2991i	0.660397	+	1.08248i
$637$	−0.964474	+	0.556840i	−0.0382139	+	0.0220628i
$638$	4.96441	+	16.7123i	0.196543	+	0.661647i
$639$	−21.8217	+	33.0898i	−0.863252	+	1.30901i
$640$	−15.4734	−	31.9956i	−0.611639	−	1.26474i
$641$	−24.1643	−	41.8538i	−0.954433	−	1.65313i	−0.735661	−	0.677350i	$-0.763128\pi$
$641$	−24.1643	−	41.8538i	−0.954433	−	1.65313i	−0.218772	−	0.975776i	$-0.570205\pi$
$642$	3.50305	−	12.9311i	0.138254	−	0.510351i
$643$	−7.88176	−	4.55054i	−0.310826	−	0.179456i	0.336470	−	0.941694i	$-0.390767\pi$
$643$	−7.88176	−	4.55054i	−0.310826	−	0.179456i	−0.647296	+	0.762239i	$0.724100\pi$
$644$	−0.181535	−	3.36474i	−0.00715349	−	0.132589i
$645$	−27.2476	−	50.6080i	−1.07287	−	1.99269i
$646$	−5.27184	−	4.99508i	−0.207418	−	0.196529i
$647$	−19.5917			−0.770229			−0.385115	−	0.922869i	$-0.625838\pi$
$647$	−19.5917			−0.770229			−0.385115	+	0.922869i	$0.625838\pi$
$648$	7.51678	−	24.3207i	0.295287	−	0.955409i
$649$	−33.9510			−1.33269
$650$	−5.56587	−	5.27367i	−0.218311	−	0.206850i
$651$	−5.57342	−	10.3517i	−0.218440	−	0.405716i
$652$	−19.0426	+	1.02739i	−0.745767	+	0.0402358i
$653$	20.1514	+	11.6344i	0.788585	+	0.455290i	0.839464	−	0.543415i	$-0.182869\pi$
$653$	20.1514	+	11.6344i	0.788585	+	0.455290i	−0.0508794	+	0.998705i	$0.516202\pi$
$654$	−6.50662	+	24.0185i	−0.254429	+	0.939196i
$655$	10.2248	+	17.7098i	0.399514	+	0.691979i
$656$	4.73538	−	10.7246i	0.184886	−	0.418726i
$657$	11.8330	−	17.9432i	0.461648	−	0.700031i
$658$	−4.67198	−	15.7279i	−0.182133	−	0.613136i
$659$	−28.0008	+	16.1663i	−1.09076	+	0.629748i	−0.933778	−	0.357854i	$-0.883509\pi$
$659$	−28.0008	+	16.1663i	−1.09076	+	0.629748i	−0.156979	+	0.987602i	$0.550175\pi$
$660$	23.7521	−	14.4906i	0.924550	−	0.564048i
$661$	−4.82385	−	2.78505i	−0.187626	−	0.108326i	0.403245	−	0.915092i	$-0.367882\pi$
$661$	−4.82385	−	2.78505i	−0.187626	−	0.108326i	−0.590871	+	0.806766i	$0.701216\pi$
$662$	0.279102	−	1.16650i	0.0108476	−	0.0453373i
$663$	−0.0658603	+	2.21674i	−0.00255780	+	0.0860912i
$664$	35.0092	+	6.40496i	1.35862	+	0.248561i
$665$	14.0315			0.544117
$666$	13.5089	−	3.15370i	0.523459	−	0.122203i
$667$			8.12341i			0.314540i
$668$	28.3864	+	14.4086i	1.09830	+	0.557484i
$669$	−13.7402	+	22.2458i	−0.531227	+	0.860071i
$670$	47.2657	+	11.3090i	1.82604	+	0.436905i
$671$	3.90553	−	6.76458i	0.150771	−	0.261144i
$672$	−3.51428	−	9.14603i	−0.135566	−	0.352816i
$673$	9.75438	+	16.8951i	0.376004	+	0.651258i	0.990477	−	0.137680i	$-0.0439647\pi$
$673$	9.75438	+	16.8951i	0.376004	+	0.651258i	−0.614473	+	0.788938i	$0.710631\pi$
$674$	−3.94767	−	13.2895i	−0.152059	−	0.511894i
$675$	−10.6486	−	22.9460i	−0.409865	−	0.883193i
$676$	−19.7053	+	12.8400i	−0.757897	+	0.493845i
$677$	−21.1081	+	12.1868i	−0.811249	+	0.468375i	−0.847390	−	0.530972i	$-0.821827\pi$
$677$	−21.1081	+	12.1868i	−0.811249	+	0.468375i	0.0361403	+	0.999347i	$0.488494\pi$
$678$	−27.5362	+	27.3851i	−1.05752	+	1.05172i
$679$	5.01036	−	8.67820i	0.192280	−	0.333039i
$680$	3.43219	+	9.62150i	0.131618	+	0.368968i
$681$	−39.0251	−	24.1041i	−1.49545	−	0.923670i
$682$	17.8164	+	16.8811i	0.682225	+	0.646409i
$683$			9.84739i			0.376800i	0.982092	+	0.188400i	$0.0603301\pi$
$683$			9.84739i			0.376800i	−0.982092	+	0.188400i	$0.939670\pi$
$684$	−13.5275	+	23.1353i	−0.517236	+	0.884599i
$685$			56.1979i			2.14721i
$686$	−0.972690	+	1.02658i	−0.0371375	+	0.0391951i
$687$	1.06737	−	35.9259i	0.0407228	−	1.37066i
$688$	34.1078	−	24.9417i	1.30035	−	0.950892i
$689$	−5.14038	+	8.90341i	−0.195833	+	0.339193i
$690$	12.5318	−	3.32094i	0.477076	−	0.126426i
$691$	8.36113	−	4.82730i	0.318072	−	0.183639i	−0.332461	−	0.943117i	$-0.607879\pi$
$691$	8.36113	−	4.82730i	0.318072	−	0.183639i	0.650533	+	0.759478i	$0.274546\pi$
$692$	−5.36796	−	8.23813i	−0.204059	−	0.313167i
$693$	6.85876	−	3.43408i	0.260543	−	0.130450i
$694$	1.40632	−	0.417751i	0.0533834	−	0.0158576i
$695$	−14.5307	−	25.1680i	−0.551182	−	0.954675i
$696$	7.27194	+	22.4734i	0.275642	+	0.851850i
$697$	−1.68483	+	2.91820i	−0.0638174	+	0.110535i
$698$	4.02251	−	16.8120i	0.152254	−	0.636343i
$699$	10.8188	+	20.0942i	0.409205	+	0.760033i
$700$	−8.68219	−	4.40697i	−0.328156	−	0.166568i
$701$			28.5557i			1.07853i	0.842135	+	0.539266i	$0.181298\pi$
$701$			28.5557i			1.07853i	−0.842135	+	0.539266i	$0.818702\pi$
$702$	8.02128	−	1.62303i	0.302744	−	0.0612571i
$703$	−14.6046			−0.550822
$704$	12.9457	+	15.8365i	0.487910	+	0.596859i
$705$	55.5808	−	29.9249i	2.09329	−	1.12704i
$706$	3.37416	+	0.807317i	0.126988	+	0.0303838i
$707$	−10.3557	−	5.97887i	−0.389466	−	0.224859i
$708$	−45.9852	+	1.11298i	−1.72823	+	0.0418283i
$709$	31.9698	−	18.4578i	1.20065	−	0.693197i	0.239952	−	0.970785i	$-0.422868\pi$
$709$	31.9698	−	18.4578i	1.20065	−	0.693197i	0.960700	+	0.277588i	$0.0895350\pi$
$710$	−56.2675	+	16.7143i	−2.11168	+	0.627278i
$711$	14.8580	+	0.883652i	0.557217	+	0.0331395i
$712$	13.0338	+	11.0800i	0.488463	+	0.415239i
$713$	5.71808	+	9.90400i	0.214144	+	0.370908i
$714$	0.721396	+	2.72223i	0.0269976	+	0.101877i
$715$	7.74659	+	4.47249i	0.289706	+	0.167262i
$716$	−15.6754	+	0.845719i	−0.585815	+	0.0316060i
$717$	−12.9968	−	0.386140i	−0.485374	−	0.0144207i
$718$	−4.32641	+	4.56613i	−0.161460	+	0.170406i
$719$	−28.5055			−1.06308			−0.531539	−	0.847034i	$-0.678386\pi$
$719$	−28.5055			−1.06308			−0.531539	+	0.847034i	$0.678386\pi$
$720$	31.6962	−	20.4056i	1.18125	−	0.760472i
$721$	−7.74691			−0.288510
$722$	0.924955	−	0.976204i	0.0344233	−	0.0363305i
$723$	19.1085	−	30.9372i	0.710653	−	1.15057i
$724$	2.32174	−	0.125263i	0.0862867	−	0.00465535i
$725$	20.3280	+	11.7364i	0.754963	+	0.435878i
$726$	7.75091	−	7.70837i	0.287663	−	0.286085i
$727$	15.3515	+	26.5896i	0.569356	+	0.986153i	0.996630	+	0.0820310i	$0.0261406\pi$
$727$	15.3515	+	26.5896i	0.569356	+	0.986153i	−0.427274	+	0.904122i	$0.640526\pi$
$728$	2.04020	−	2.39997i	0.0756147	−	0.0889487i
$729$	26.5724	+	4.78624i	0.984163	+	0.177268i
$730$	30.5115	−	9.06348i	1.12928	−	0.335454i
$731$	−10.5179	+	6.07250i	−0.389018	+	0.224600i
$732$	5.06812	−	9.29037i	0.187323	−	0.343382i
$733$	−19.2294	−	11.1021i	−0.710253	−	0.410065i	0.100902	−	0.994896i	$-0.467827\pi$
$733$	−19.2294	−	11.1021i	−0.710253	−	0.410065i	−0.811155	+	0.584832i	$0.801161\pi$
$734$	23.3513	+	5.58714i	0.861913	+	0.206225i
$735$	−4.62921	−	2.85926i	−0.170751	−	0.105465i
$736$	3.68114	+	8.79117i	0.135689	+	0.324047i
$737$	−27.9703			−1.03030
$738$	11.9002	+	3.60637i	0.438054	+	0.132752i
$739$		−	7.42933i		−	0.273292i	−0.990620	−	0.136646i	$-0.956368\pi$
$739$		−	7.42933i		−	0.273292i	0.990620	−	0.136646i	$-0.0436323\pi$
$740$	18.3181	+	9.29801i	0.673386	+	0.341802i
$741$	−8.61213	−	0.255870i	−0.316375	−	0.00939961i
$742$	−3.03788	+	12.6967i	−0.111524	+	0.466112i
$743$	−0.0239107	+	0.0414146i	−0.000877200	+	0.00151935i	−0.866464	−	0.499240i	$-0.833613\pi$
$743$	−0.0239107	+	0.0414146i	−0.000877200	+	0.00151935i	0.865586	+	0.500759i	$0.166946\pi$
$744$	24.6849	+	22.2806i	0.904993	+	0.816847i
$745$	32.6945	+	56.6286i	1.19783	+	2.07471i
$746$	34.1792	−	10.1530i	1.25139	−	0.371727i
$747$	−2.24111	+	37.6827i	−0.0819979	+	1.37874i
$748$	−3.20960	−	4.92573i	−0.117355	−	0.180103i
$749$	4.73663	−	2.73469i	0.173073	−	0.0999236i
$750$	−0.264955	+	0.978054i	−0.00967480	+	0.0357135i
$751$	7.44702	−	12.8986i	0.271746	−	0.470677i	−0.697563	−	0.716523i	$-0.745732\pi$
$751$	7.44702	−	12.8986i	0.271746	−	0.470677i	0.969309	+	0.245846i	$0.0790657\pi$
$752$	27.3925	+	37.4593i	0.998900	+	1.36600i
$753$	−24.3062	+	13.0866i	−0.885769	+	0.476902i
$754$	−5.22300	+	5.51239i	−0.190210	+	0.200749i
$755$		−	20.6998i		−	0.753342i
$756$	9.17732	−	4.87615i	0.333776	−	0.177344i
$757$		−	15.4496i		−	0.561525i	−0.959777	−	0.280762i	$-0.909413\pi$
$757$		−	15.4496i		−	0.561525i	0.959777	−	0.280762i	$-0.0905873\pi$
$758$	35.4117	+	33.5527i	1.28621	+	1.21869i
$759$	−6.56957	+	3.53709i	−0.238460	+	0.128388i
$760$	−37.3799	+	13.3342i	−1.35591	+	0.483681i
$761$	−19.3223	+	33.4672i	−0.700433	+	1.21318i	0.267882	+	0.963452i	$0.413676\pi$
$761$	−19.3223	+	33.4672i	−0.700433	+	1.21318i	−0.968315	+	0.249733i	$0.919657\pi$
$762$	−38.0661	−	10.3121i	−1.37899	−	0.373569i
$763$	−8.79789	+	5.07946i	−0.318505	+	0.183889i
$764$	−36.7219	+	23.9280i	−1.32855	+	0.865683i
$765$	−9.68847	+	4.85087i	−0.350287	+	0.175384i
$766$	2.60296	+	8.76267i	0.0940488	+	0.316608i
$767$	−7.39408	−	12.8069i	−0.266985	−	0.462431i
$768$	18.0536	+	21.0254i	0.651452	+	0.758690i
$769$	21.7548	−	37.6804i	0.784499	−	1.35879i	−0.144800	−	0.989461i	$-0.546254\pi$
$769$	21.7548	−	37.6804i	0.784499	−	1.35879i	0.929298	−	0.369330i	$-0.120413\pi$
$770$	11.0471	+	2.64317i	0.398108	+	0.0952531i
$771$	−3.77493	−	0.112155i	−0.135951	−	0.00403915i
$772$	0.0104944	+	0.00532684i	0.000377703	+	0.000191717i
$773$		−	30.5921i		−	1.10032i	−0.835059	−	0.550161i	$-0.814566\pi$
$773$		−	30.5921i		−	1.10032i	0.835059	−	0.550161i	$-0.185434\pi$
$774$	30.6458	+	32.7024i	1.10154	+	1.17546i
$775$	33.0450			1.18701
$776$	−5.10069	+	27.8801i	−0.183104	+	1.00084i
$777$	4.81829	+	2.97604i	0.172855	+	0.106765i
$778$	4.40628	−	18.4160i	0.157973	−	0.660244i
$779$	−11.3373	−	6.54561i	−0.406202	−	0.234521i
$780$	10.6390	+	5.80385i	0.380939	+	0.207811i
$781$	29.2558	−	16.8909i	1.04686	−	0.604403i
$782$	−0.780052	−	2.62598i	−0.0278946	−	0.0939050i
$783$	−22.7255	+	10.5463i	−0.812145	+	0.376893i
$784$	1.61568	−	3.65918i	0.0577030	−	0.130685i
$785$	−27.0001	−	46.7656i	−0.963676	−	1.66914i
$786$	−11.2441	−	11.3061i	−0.401063	−	0.403276i
$787$	25.2543	+	14.5806i	0.900220	+	0.519742i	0.877271	−	0.479995i	$-0.159361\pi$
$787$	25.2543	+	14.5806i	0.900220	+	0.519742i	0.0229483	+	0.999737i	$0.492695\pi$
$788$	−12.1567	+	0.655883i	−0.433066	+	0.0233649i
$789$	−10.5490	+	17.0791i	−0.375555	+	0.608033i
$790$	16.0000	+	15.1601i	0.569255	+	0.539371i
$791$	−15.8545			−0.563720
$792$	−15.0083	+	15.6663i	−0.533298	+	0.556678i
$793$	3.40230			0.120819
$794$	32.0275	+	30.3461i	1.13661	+	1.07694i
$795$	−50.2060	−	1.49164i	−1.78062	−	0.0529030i
$796$	1.37323	+	25.4527i	0.0486728	+	0.902147i
$797$	−7.46331	−	4.30894i	−0.264364	−	0.152631i	0.361960	−	0.932194i	$-0.382108\pi$
$797$	−7.46331	−	4.30894i	−0.264364	−	0.152631i	−0.626324	+	0.779563i	$0.715441\pi$
$798$	−10.5759	+	2.80265i	−0.374385	+	0.0992127i
$799$	−6.66920	−	11.5514i	−0.235939	−	0.408659i
$800$	27.3174	+	3.48946i	0.965815	+	0.123371i
$801$	−9.98920	+	15.1474i	−0.352951	+	0.535206i
$802$	6.79254	+	22.8666i	0.239853	+	0.807446i
$803$	−15.8642	+	9.15920i	−0.559836	+	0.323221i
$804$	−37.8845	+	0.916919i	−1.33608	+	0.0323372i
$805$	4.58358	+	2.64633i	0.161550	+	0.0932709i
$806$	−2.48767	+	10.3971i	−0.0876243	+	0.366224i
$807$	3.28754	−	1.77002i	0.115727	−	0.0623078i
$808$	33.2694	+	6.08666i	1.17041	+	0.214128i
$809$	−30.6847			−1.07882			−0.539409	−	0.842044i	$-0.681352\pi$
$809$	−30.6847			−1.07882			−0.539409	+	0.842044i	$0.681352\pi$
$810$	25.5599	+	30.7467i	0.898084	+	1.08033i
$811$			22.8266i			0.801549i	0.916177	+	0.400774i	$0.131259\pi$
$811$			22.8266i			0.801549i	−0.916177	+	0.400774i	$0.868741\pi$
$812$	−4.36463	+	8.59877i	−0.153168	+	0.301758i
$813$	12.1254	+	22.5210i	0.425257	+	0.789846i
$814$	−11.4983	−	2.75113i	−0.403014	−	0.0964269i
$815$	14.9768	−	25.9406i	0.524615	−	0.908660i
$816$	−4.50875	−	6.56648i	−0.157838	−	0.229873i
$817$	−23.5919	−	40.8624i	−0.825376	−	1.42959i
$818$	−0.872961	−	2.93876i	−0.0305224	−	0.102751i
$819$	2.78914	+	1.83935i	0.0974606	+	0.0642721i
$820$	10.0528	+	15.4279i	0.351059	+	0.538765i
$821$	35.7103	−	20.6174i	1.24630	−	0.719551i	0.275930	−	0.961178i	$-0.411014\pi$
$821$	35.7103	−	20.6174i	1.24630	−	0.719551i	0.970369	+	0.241627i	$0.0776809\pi$
$822$	−11.2250	−	42.3581i	−0.391516	−	1.47741i
$823$	6.17838	−	10.7013i	0.215365	−	0.373023i	−0.738021	−	0.674778i	$-0.764239\pi$
$823$	6.17838	−	10.7013i	0.215365	−	0.373023i	0.953385	+	0.301755i	$0.0975726\pi$
$824$	20.6378	−	7.36192i	0.718952	−	0.256465i
$825$	−0.640256	+	21.5499i	−0.0222909	+	0.750272i
$826$	−13.6317	−	12.9160i	−0.474306	−	0.449406i
$827$			7.53865i			0.262145i	0.991373	+	0.131072i	$0.0418420\pi$
$827$			7.53865i			0.262145i	−0.991373	+	0.131072i	$0.958158\pi$
$828$	−8.78225	+	5.00620i	−0.305204	+	0.173977i
$829$			42.2972i			1.46904i	0.678585	+	0.734522i	$0.262593\pi$
$829$			42.2972i			1.46904i	−0.678585	+	0.734522i	$0.737407\pi$
$830$	−38.4488	+	40.5791i	−1.33458	+	1.40852i
$831$	12.4980	+	7.71948i	0.433552	+	0.267786i
$832$	−3.15439	+	8.33233i	−0.109359	+	0.288872i
$833$	−0.574852	+	0.995674i	−0.0199175	+	0.0344980i
$834$	15.9793	+	16.0675i	0.553318	+	0.556372i
$835$	−43.3023	+	25.0006i	−1.49854	+	0.865181i
$836$	19.1367	−	12.4694i	0.661855	−	0.431264i
$837$	−20.2833	+	28.8545i	−0.701093	+	0.997357i
$838$	31.0138	−	9.21269i	1.07135	−	0.318247i
$839$	−4.34598	−	7.52746i	−0.150040	−	0.259877i	0.781202	−	0.624278i	$-0.214607\pi$
$839$	−4.34598	−	7.52746i	−0.150040	−	0.259877i	−0.931242	+	0.364402i	$0.881274\pi$
$840$	15.0494	+	3.21791i	0.519254	+	0.111029i
$841$	−2.87640	+	4.98207i	−0.0991861	+	0.171795i
$842$	8.00907	−	33.4737i	0.276011	−	1.15358i
$843$	14.3462	−	23.2269i	0.494111	−	0.799978i
$844$	14.8105	−	29.1781i	0.509797	−	1.00435i
$845$		−	36.9418i		−	1.27084i
$846$	−35.9157	+	33.6571i	−1.23481	+	1.15715i
$847$	4.46273			0.153341
$848$	−3.97285	−	36.7111i	−0.136428	−	1.26066i
$849$	−1.66561	+	56.0616i	−0.0571636	+	1.92403i
$850$	−7.69824	−	1.84192i	−0.264047	−	0.0631772i
$851$	−4.77079	−	2.75442i	−0.163541	−	0.0944203i
$852$	39.0720	−	23.8370i	1.33859	−	0.816642i
$853$	42.8080	−	24.7152i	1.46572	−	0.846232i	0.466451	−	0.884547i	$-0.345532\pi$
$853$	42.8080	−	24.7152i	1.46572	−	0.846232i	0.999266	+	0.0383147i	$0.0121989\pi$
$854$	4.14157	−	1.23026i	0.141722	−	0.0420986i
$855$	−18.8458	−	37.6400i	−0.644513	−	1.28726i
$856$	−10.0196	+	11.7865i	−0.342463	+	0.402854i
$857$	−18.9793	−	32.8732i	−0.648321	−	1.12293i	−0.983524	−	0.180779i	$-0.942138\pi$
$857$	−18.9793	−	32.8732i	−0.648321	−	1.12293i	0.335202	−	0.942146i	$-0.391195\pi$
$858$	−6.73218	−	1.82375i	−0.229833	−	0.0622619i
$859$	10.2126	+	5.89622i	0.348448	+	0.201176i	0.664001	−	0.747731i	$-0.268857\pi$
$859$	10.2126	+	5.89622i	0.348448	+	0.201176i	−0.315554	+	0.948908i	$0.602190\pi$
$860$	3.57553	+	66.2722i	0.121925	+	2.25986i
$861$	2.40654	+	4.46977i	0.0820147	+	0.152329i
$862$	11.2218	−	11.8435i	0.382215	−	0.403392i
$863$	53.5701			1.82355			0.911774	−	0.410693i	$-0.134713\pi$
$863$	53.5701			1.82355			0.911774	+	0.410693i	$0.134713\pi$
$864$	−19.8146	+	21.7113i	−0.674106	+	0.738635i
$865$	15.4441			0.525117
$866$	35.9121	−	37.9019i	1.22034	−	1.28796i
$867$	−12.8733	−	23.9101i	−0.437201	−	0.812030i
$868$	0.731366	+	13.5558i	0.0248242	+	0.460115i
$869$	−10.9858	−	6.34268i	−0.372669	−	0.215161i
$870$	−35.8100	−	9.70095i	−1.21407	−	0.328893i
$871$	−6.09156	−	10.5509i	−0.206405	−	0.357503i
$872$	18.6106	−	21.8924i	0.630234	−	0.741370i
$873$	−30.0092	−	1.78474i	−1.01566	−	0.0604044i
$874$	10.2020	−	3.03053i	0.345089	−	0.102509i
$875$	−0.358258	+	0.206840i	−0.0121113	+	0.00699248i
$876$	−21.1871	+	12.9258i	−0.715847	+	0.436722i
$877$	1.42863	+	0.824823i	0.0482416	+	0.0278523i	0.523927	−	0.851763i	$-0.324467\pi$
$877$	1.42863	+	0.824823i	0.0482416	+	0.0278523i	−0.475685	+	0.879616i	$0.657800\pi$
$878$	3.78744	+	0.906199i	0.127820	+	0.0305827i
$879$	1.21396	−	40.8599i	0.0409459	−	1.37817i
$880$	−31.9412	+	3.45666i	−1.07674	+	0.116524i
$881$	−9.02450			−0.304043			−0.152022	−	0.988377i	$-0.548578\pi$
$881$	−9.02450			−0.304043			−0.152022	+	0.988377i	$0.548578\pi$
$882$	4.06029	+	1.23047i	0.136717	+	0.0414321i
$883$			54.0475i			1.81884i	0.415875	+	0.909422i	$0.363475\pi$
$883$			54.0475i			1.81884i	−0.415875	+	0.909422i	$0.636525\pi$
$884$	1.15907	−	2.28348i	0.0389836	−	0.0768018i
$885$	37.9671	−	61.4697i	1.27625	−	2.06628i
$886$	−0.847780	+	3.54328i	−0.0284817	+	0.119039i
$887$	18.4551	−	31.9652i	0.619661	−	1.07328i	−0.369886	−	0.929077i	$-0.620603\pi$
$887$	18.4551	−	31.9652i	0.619661	−	1.07328i	0.989547	−	0.144208i	$-0.0460634\pi$
$888$	−15.6641	−	3.34935i	−0.525652	−	0.112397i
$889$	−8.05028	−	13.9435i	−0.269998	−	0.467650i
$890$	−25.7573	+	7.65124i	−0.863387	+	0.256470i
$891$	−18.4241	−	13.7866i	−0.617232	−	0.461868i
$892$	25.2958	−	16.4827i	0.846965	−	0.551882i
$893$	44.8776	−	25.9101i	1.50177	−	0.867048i
$894$	−35.9539	−	36.1523i	−1.20248	−	1.20911i
$895$	12.3285	−	21.3536i	0.412096	−	0.713771i
$896$	−0.826856	+	11.2835i	−0.0276233	+	0.376954i
$897$	−2.76502	−	1.70783i	−0.0923213	−	0.0570228i
$898$	−28.9813	+	30.5871i	−0.967120	+	1.02070i
$899$		−	32.7275i		−	1.09152i
$900$	−0.160752	+	29.2094i	−0.00535840	+	0.973648i
$901$			10.6133i			0.353581i
$902$	−7.69292	−	7.28906i	−0.256146	−	0.242699i
$903$	−0.543361	+	18.2886i	−0.0180819	+	0.608606i
$904$	42.2364	−	15.0666i	1.40476	−	0.501107i
$905$	−1.82602	+	3.16276i	−0.0606990	+	0.105134i
$906$	4.13458	+	15.6021i	0.137362	+	0.518344i
$907$	26.7112	−	15.4217i	0.886931	−	0.512070i	0.0139934	−	0.999902i	$-0.495546\pi$
$907$	26.7112	−	15.4217i	0.886931	−	0.512070i	0.872937	+	0.487832i	$0.162212\pi$
$908$	28.9152	+	44.3757i	0.959583	+	1.47266i
$909$	−2.12973	+	35.8099i	−0.0706388	+	1.18774i
$910$	1.40885	+	4.74279i	0.0467030	+	0.157222i
$911$	6.79661	+	11.7721i	0.225182	+	0.390026i	0.956374	−	0.292145i	$-0.0943691\pi$
$911$	6.79661	+	11.7721i	0.225182	+	0.390026i	−0.731192	+	0.682172i	$0.761036\pi$
$912$	25.5110	−	17.5166i	0.844754	−	0.580034i
$913$	16.0863	−	27.8622i	0.532378	−	0.922105i
$914$	−40.3163	−	9.64627i	−1.33355	−	0.319070i
$915$	7.88004	+	14.6359i	0.260506	+	0.483848i
$916$	−18.7845	+	37.0075i	−0.620659	+	1.22276i
$917$		−	6.50971i		−	0.214970i
$918$	6.33358	−	5.59143i	0.209039	−	0.184545i
$919$	−11.6627			−0.384715			−0.192358	−	0.981325i	$-0.561613\pi$
$919$	−11.6627			−0.384715			−0.192358	+	0.981325i	$0.561613\pi$
$920$	−14.7255	−	2.69404i	−0.485485	−	0.0888199i
$921$	−35.0043	+	18.8465i	−1.15343	+	0.621012i
$922$	7.65477	−	31.9929i	0.252096	−	1.05363i
$923$	12.7431	+	7.35722i	0.419443	+	0.242166i
$924$	−8.85445	+	0.214304i	−0.291290	+	0.00705009i
$925$	−13.7853	+	7.95895i	−0.453258	+	0.261689i
$926$	−4.76612	−	16.0448i	−0.156624	−	0.527263i
$927$	10.4050	+	20.7814i	0.341743	+	0.682552i
$928$	3.45593	−	27.0549i	0.113446	−	0.888120i
$929$	20.0169	+	34.6702i	0.656732	+	1.13749i	0.981456	+	0.191685i	$0.0613952\pi$
$929$	20.0169	+	34.6702i	0.656732	+	1.13749i	−0.324724	+	0.945809i	$0.605271\pi$
$930$	−50.4878	+	13.3794i	−1.65556	+	0.438727i
$931$	−3.86823	−	2.23332i	−0.126776	−	0.0731942i
$932$	−1.41969	−	26.3138i	−0.0465034	−	0.861937i
$933$	−10.6013	−	0.314969i	−0.347071	−	0.0103116i
$934$	−11.4196	−	10.8201i	−0.373661	−	0.354044i
$935$	9.23434			0.301995
$936$	−9.17823	−	2.24950i	−0.300000	−	0.0735272i
$937$	−46.9538			−1.53391			−0.766956	−	0.641699i	$-0.778230\pi$
$937$	−46.9538			−1.53391			−0.766956	+	0.641699i	$0.778230\pi$
$938$	−11.2303	−	10.6408i	−0.366683	−	0.347433i
$939$	−0.297377	+	0.481462i	−0.00970454	+	0.0157119i
$940$	−72.7843	+	3.92687i	−2.37396	+	0.128080i
$941$	26.0233	+	15.0246i	0.848336	+	0.489787i	0.860089	−	0.510144i	$-0.170408\pi$
$941$	26.0233	+	15.0246i	0.848336	+	0.489787i	−0.0117532	+	0.999931i	$0.503741\pi$
$942$	29.6918	+	29.8557i	0.967412	+	0.972751i
$943$	−2.46900	−	4.27644i	−0.0804018	−	0.139260i
$944$	48.5890	+	21.4541i	1.58144	+	0.698272i
$945$	−1.45255	+	16.2584i	−0.0472514	+	0.528885i
$946$	−10.8766	−	36.6153i	−0.353629	−	1.19047i
$947$	20.5354	−	11.8561i	0.667311	−	0.385272i	−0.127746	−	0.991807i	$-0.540774\pi$
$947$	20.5354	−	11.8561i	0.667311	−	0.385272i	0.795057	+	0.606535i	$0.207441\pi$
$948$	−15.0878	−	8.23075i	−0.490028	−	0.267322i
$949$	−6.91003	−	3.98951i	−0.224309	−	0.129505i
$950$	7.15591	−	29.9080i	0.232168	−	0.970342i
$951$	−1.68193	−	1.03885i	−0.0545403	−	0.0336871i
$952$	0.585216	−	3.19876i	0.0189670	−	0.103673i
$953$	−49.9460			−1.61791			−0.808955	−	0.587871i	$-0.799966\pi$
$953$	−49.9460			−1.61791			−0.808955	+	0.587871i	$0.799966\pi$
$954$	38.1398	−	8.90387i	1.23482	−	0.288274i
$955$		−	68.8431i		−	2.22771i
$956$	13.3881	+	6.79562i	0.433001	+	0.219786i
$957$	21.3429	+	0.634105i	0.689917	+	0.0204977i
$958$	−19.5081	−	4.66759i	−0.630278	−	0.150803i
$959$	8.94475	−	15.4928i	0.288841	−	0.500287i
$960$	−43.1497	+	5.72899i	−1.39265	+	0.184902i
$961$	−7.53690	−	13.0543i	−0.243126	−	0.421106i
$962$	−1.46640	−	4.93651i	−0.0472785	−	0.159159i
$963$	−13.6978	−	9.03323i	−0.441404	−	0.291092i
$964$	−35.1788	+	22.9225i	−1.13303	+	0.738284i
$965$	−0.0160088	+	0.00924271i	−0.000515343	+	0.000297533i
$966$	−3.98337	−	1.07910i	−0.128163	−	0.0347194i
$967$	−23.1224	+	40.0491i	−0.743566	+	1.28789i	0.207296	+	0.978278i	$0.433534\pi$
$967$	−23.1224	+	40.0491i	−0.743566	+	1.28789i	−0.950862	+	0.309615i	$0.899800\pi$
$968$	−11.8887	+	4.24095i	−0.382118	+	0.136309i
$969$	−7.83166	+	4.21660i	−0.251589	+	0.135457i
$970$	−32.3158	−	30.6193i	−1.03760	−	0.983126i
$971$			29.1228i			0.934596i	0.884100	+	0.467298i	$0.154773\pi$
$971$			29.1228i			0.934596i	−0.884100	+	0.467298i	$0.845227\pi$
$972$	−25.4067	−	18.0694i	−0.814919	−	0.579575i
$973$			9.25115i			0.296578i
$974$	1.04458	−	1.10246i	0.0334705	−	0.0353250i
$975$	−8.26846	+	4.45178i	−0.264803	+	0.142571i
$976$	−9.86404	+	7.21317i	−0.315740	+	0.230888i
$977$	−22.6511	+	39.2328i	−0.724672	+	1.25517i	0.234437	+	0.972131i	$0.424675\pi$
$977$	−22.6511	+	39.2328i	−0.724672	+	1.25517i	−0.959109	+	0.283038i	$0.908658\pi$
$978$	−6.10711	+	22.5437i	−0.195284	+	0.720869i
$979$	13.3923	−	7.73205i	0.428020	−	0.247117i
$980$	3.42995	+	5.26390i	0.109566	+	0.168149i
$981$	25.4424	+	16.7785i	0.812314	+	0.535695i
$982$	−17.4347	+	5.17901i	−0.556364	+	0.165269i
$983$	−0.389552	−	0.674724i	−0.0124248	−	0.0215204i	0.859746	−	0.510722i	$-0.170622\pi$
$983$	−0.389552	−	0.674724i	−0.0124248	−	0.0215204i	−0.872171	+	0.489201i	$0.837288\pi$
$984$	−10.6587	−	9.62053i	−0.339786	−	0.306691i
$985$	9.56115	−	16.5604i	0.304643	−	0.527658i
$986$	−1.82422	+	7.62427i	−0.0580949	+	0.242806i
$987$	−20.0857	−	0.596753i	−0.639334	−	0.0189948i
$988$	8.87141	+	4.50301i	0.282237	+	0.143260i
$989$		−	17.7977i		−	0.565934i
$990$	−7.74699	−	33.1843i	−0.246216	−	1.05467i
$991$	41.5739			1.32064			0.660320	−	0.750985i	$-0.270421\pi$
$991$	41.5739			1.32064			0.660320	+	0.750985i	$0.270421\pi$
$992$	−14.8305	−	35.4178i	−0.470870	−	1.12451i
$993$	−1.24981	−	0.771951i	−0.0396614	−	0.0244971i
$994$	18.1723	+	4.34799i	0.576391	+	0.137910i
$995$	−34.6726	−	20.0183i	−1.09920	−	0.634621i
$996$	20.8748	−	38.2655i	0.661442	−	1.21249i
$997$	5.90652	−	3.41013i	0.187061	−	0.108000i	−0.403545	−	0.914960i	$-0.632222\pi$
$997$	5.90652	−	3.41013i	0.187061	−	0.108000i	0.590606	+	0.806960i	$0.298889\pi$
$998$	−14.3051	+	4.24936i	−0.452821	+	0.134511i
$999$	1.51188	−	16.9224i	0.0478336	−	0.535402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.9	✓	72
8.5	even	2	inner	504.2.cs.b.85.33	yes	72
9.7	even	3	inner	504.2.cs.b.421.33	yes	72
72.61	even	6	inner	504.2.cs.b.421.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.9	✓	72	1.1	even	1	trivial
504.2.cs.b.85.33	yes	72	8.5	even	2	inner
504.2.cs.b.421.9	yes	72	72.61	even	6	inner
504.2.cs.b.421.33	yes	72	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.972690 + 1.02658i) q^{2} +(0.821098 + 1.52506i) q^{3} +(-0.107748 - 1.99710i) q^{4} +(2.72052 + 1.57069i) q^{5} +(-2.36427 - 0.640483i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 + 2.50444i) q^{9} +O(q^{10})\)	\(q+(-0.972690 + 1.02658i) q^{2} +(0.821098 + 1.52506i) q^{3} +(-0.107748 - 1.99710i) q^{4} +(2.72052 + 1.57069i) q^{5} +(-2.36427 - 0.640483i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 + 2.50444i) q^{9} +(-4.25867 + 1.26504i) q^{10} +(2.21426 - 1.27840i) q^{11} +(2.95721 - 1.80413i) q^{12} +(0.964474 + 0.556840i) q^{13} +(1.37539 + 0.329083i) q^{14} +(-0.161584 + 5.43864i) q^{15} +(-3.97678 + 0.430365i) q^{16} +1.14970 q^{17} +(-0.964525 - 4.13155i) q^{18} +4.46665i q^{19} +(2.84370 - 5.60238i) q^{20} +(0.910189 - 1.47362i) q^{21} +(-0.841401 + 3.51662i) q^{22} +(-0.842409 + 1.45909i) q^{23} +(-1.02436 + 4.79069i) q^{24} +(2.43416 + 4.21608i) q^{25} +(-1.50978 + 0.448481i) q^{26} +(-5.17554 - 0.462390i) q^{27} +(-1.67566 + 1.09186i) q^{28} +(4.17557 - 2.41077i) q^{29} +(-5.42605 - 5.45599i) q^{30} +(3.39388 - 5.87838i) q^{31} +(3.42637 - 4.50111i) q^{32} +(3.76776 + 2.32718i) q^{33} +(-1.11831 + 1.18027i) q^{34} -3.14139i q^{35} +(5.17956 + 3.02855i) q^{36} +3.26969i q^{37} +(-4.58539 - 4.34466i) q^{38} +(-0.0572845 + 1.92810i) q^{39} +(2.98528 + 8.36867i) q^{40} +(-1.46544 + 2.53822i) q^{41} +(0.627462 + 2.36776i) q^{42} +(-9.14833 + 5.28179i) q^{43} +(-2.79168 - 4.28435i) q^{44} +(-8.42692 + 4.21923i) q^{45} +(-0.678480 - 2.28405i) q^{46} +(-5.80079 - 10.0473i) q^{47} +(-3.92166 - 5.71145i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.69584 - 1.60208i) q^{50} +(0.944020 + 1.75337i) q^{51} +(1.00814 - 1.98615i) q^{52} +9.23136i q^{53} +(5.50888 - 4.86336i) q^{54} +8.03193 q^{55} +(0.509014 - 2.78225i) q^{56} +(-6.81189 + 3.66755i) q^{57} +(-1.58668 + 6.63150i) q^{58} +(-11.4997 - 6.63933i) q^{59} +(10.8789 - 0.263302i) q^{60} +(2.64571 - 1.52750i) q^{61} +(2.73345 + 9.20195i) q^{62} +(2.99471 + 0.178105i) q^{63} +(1.28797 + 7.89564i) q^{64} +(1.74925 + 3.02979i) q^{65} +(-6.05391 + 1.60430i) q^{66} +(-9.47390 - 5.46976i) q^{67} +(-0.123878 - 2.29607i) q^{68} +(-2.91690 - 0.0866623i) q^{69} +(3.22490 + 3.05560i) q^{70} +13.2125 q^{71} +(-8.14717 + 2.37141i) q^{72} -7.16456 q^{73} +(-3.35661 - 3.18040i) q^{74} +(-4.43109 + 7.17404i) q^{75} +(8.92032 - 0.481271i) q^{76} +(-2.21426 - 1.27840i) q^{77} +(-1.92363 - 1.93425i) q^{78} +(-2.48070 - 4.29670i) q^{79} +(-11.4949 - 5.07549i) q^{80} +(-3.54445 - 8.27266i) q^{81} +(-1.18027 - 3.97330i) q^{82} +(10.8973 - 6.29154i) q^{83} +(-3.04103 - 1.65896i) q^{84} +(3.12780 + 1.80583i) q^{85} +(3.47629 - 14.5291i) q^{86} +(7.10511 + 4.38851i) q^{87} +(7.11368 + 1.30145i) q^{88} +6.04820 q^{89} +(3.86539 - 12.7549i) q^{90} -1.11368i q^{91} +(3.00472 + 1.52516i) q^{92} +(11.7516 + 0.349144i) q^{93} +(15.9567 + 3.81788i) q^{94} +(-7.01573 + 12.1516i) q^{95} +(9.67783 + 1.52956i) q^{96} +(5.01036 + 8.67820i) q^{97} +(-0.402702 - 1.35567i) q^{98} +(-0.455381 + 7.65690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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