LMFDB - Embedded newform 504.2.cs.a.85.20

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			85.20
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.109593 + 1.40996i) q^{2} +(0.416131 - 1.68132i) q^{3} +(-1.97598 + 0.309044i) q^{4} +(-0.226907 - 0.131005i) q^{5} +(2.41620 + 0.402467i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.652293 - 2.75218i) q^{8} +(-2.65367 - 1.39930i) q^{9} +O(q^{10})$	\(q+(0.109593 + 1.40996i) q^{2} +(0.416131 - 1.68132i) q^{3} +(-1.97598 + 0.309044i) q^{4} +(-0.226907 - 0.131005i) q^{5} +(2.41620 + 0.402467i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.652293 - 2.75218i) q^{8} +(-2.65367 - 1.39930i) q^{9} +(0.159844 - 0.334288i) q^{10} +(2.18749 - 1.26295i) q^{11} +(-0.302665 + 3.45085i) q^{12} +(2.11981 + 1.22387i) q^{13} +(-1.16627 + 0.799891i) q^{14} +(-0.314684 + 0.326988i) q^{15} +(3.80898 - 1.22133i) q^{16} +7.94098 q^{17} +(1.68213 - 3.89492i) q^{18} -5.81397i q^{19} +(0.488850 + 0.188739i) q^{20} +(1.66413 - 0.480280i) q^{21} +(2.02044 + 2.94587i) q^{22} +(0.783213 - 1.35657i) q^{23} +(-4.89874 - 0.0485563i) q^{24} +(-2.46568 - 4.27068i) q^{25} +(-1.49330 + 3.12298i) q^{26} +(-3.45694 + 3.87938i) q^{27} +(-1.25563 - 1.55673i) q^{28} +(-1.60072 + 0.924174i) q^{29} +(-0.495528 - 0.407857i) q^{30} +(3.39752 - 5.88468i) q^{31} +(2.13946 + 5.23667i) q^{32} +(-1.21314 - 4.20343i) q^{33} +(0.870276 + 11.1965i) q^{34} -0.262010i q^{35} +(5.67604 + 1.94488i) q^{36} -5.05596i q^{37} +(8.19747 - 0.637170i) q^{38} +(2.93984 - 3.05479i) q^{39} +(-0.212540 + 0.709944i) q^{40} +(-3.20862 + 5.55748i) q^{41} +(0.859553 + 2.29372i) q^{42} +(4.16396 - 2.40406i) q^{43} +(-3.93214 + 3.17159i) q^{44} +(0.418822 + 0.665155i) q^{45} +(1.99854 + 0.955630i) q^{46} +(5.42014 + 9.38796i) q^{47} +(-0.468405 - 6.91235i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(5.75126 - 3.94454i) q^{50} +(3.30449 - 13.3513i) q^{51} +(-4.56693 - 1.76323i) q^{52} +11.9617i q^{53} +(-5.84862 - 4.44900i) q^{54} -0.661811 q^{55} +(2.05731 - 1.94099i) q^{56} +(-9.77514 - 2.41937i) q^{57} +(-1.47848 - 2.15566i) q^{58} +(-10.0882 - 5.82442i) q^{59} +(0.520756 - 0.743373i) q^{60} +(-12.6142 + 7.28281i) q^{61} +(8.66951 + 4.14545i) q^{62} +(-0.115007 - 2.99779i) q^{63} +(-7.14903 + 3.59046i) q^{64} +(-0.320667 - 0.555412i) q^{65} +(5.79372 - 2.17114i) q^{66} +(4.47954 + 2.58627i) q^{67} +(-15.6912 + 2.45411i) q^{68} +(-1.95490 - 1.88134i) q^{69} +(0.369424 - 0.0287145i) q^{70} +13.1679 q^{71} +(-2.12016 + 8.21614i) q^{72} -9.64768 q^{73} +(7.12871 - 0.554098i) q^{74} +(-8.20641 + 2.36843i) q^{75} +(1.79677 + 11.4883i) q^{76} +(2.18749 + 1.26295i) q^{77} +(4.62932 + 3.81028i) q^{78} +(1.84252 + 3.19133i) q^{79} +(-1.02429 - 0.221868i) q^{80} +(5.08393 + 7.42655i) q^{81} +(-8.18748 - 3.91496i) q^{82} +(-7.77411 + 4.48838i) q^{83} +(-3.13986 + 1.46331i) q^{84} +(-1.80187 - 1.04031i) q^{85} +(3.84597 + 5.60755i) q^{86} +(0.887724 + 3.07589i) q^{87} +(-4.90276 - 5.19657i) q^{88} -0.168315 q^{89} +(-0.891943 + 0.663419i) q^{90} +2.44775i q^{91} +(-1.12838 + 2.92259i) q^{92} +(-8.48021 - 8.16112i) q^{93} +(-12.6426 + 8.67104i) q^{94} +(-0.761659 + 1.31923i) q^{95} +(9.69481 - 1.41798i) q^{96} +(-1.37383 - 2.37955i) q^{97} +(-1.27586 - 0.610070i) q^{98} +(-7.57213 + 0.290497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * 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 $

$2$	0.109593	+	1.40996i	0.0774939	+	0.996993i
$2$	0.109593	+	1.40996i	0.0774939	+	0.996993i
$3$	0.416131	−	1.68132i	0.240253	−	0.970710i
$3$	0.416131	−	1.68132i	0.240253	−	0.970710i
$4$	−1.97598	+	0.309044i	−0.987989	+	0.154522i
$5$	−0.226907	−	0.131005i	−0.101476	−	0.0585872i	0.448403	−	0.893831i	$-0.351993\pi$
$5$	−0.226907	−	0.131005i	−0.101476	−	0.0585872i	−0.549879	+	0.835244i	$0.685326\pi$
$6$	2.41620	+	0.402467i	0.986409	+	0.164307i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−0.652293	−	2.75218i	−0.230620	−	0.973044i
$9$	−2.65367	−	1.39930i	−0.884557	−	0.466433i
$10$	0.159844	−	0.334288i	0.0505473	−	0.105711i
$11$	2.18749	−	1.26295i	0.659554	−	0.380794i	−0.132553	−	0.991176i	$-0.542317\pi$
$11$	2.18749	−	1.26295i	0.659554	−	0.380794i	0.792107	+	0.610382i	$0.208984\pi$
$12$	−0.302665	+	3.45085i	−0.0873718	+	0.996176i
$13$	2.11981	+	1.22387i	0.587930	+	0.339441i	0.764278	−	0.644886i	$-0.223095\pi$
$13$	2.11981	+	1.22387i	0.587930	+	0.339441i	−0.176349	+	0.984328i	$0.556429\pi$
$14$	−1.16627	+	0.799891i	−0.311698	+	0.213780i
$15$	−0.314684	+	0.326988i	−0.0812512	+	0.0844281i
$16$	3.80898	−	1.22133i	0.952246	−	0.305332i
$17$	7.94098			1.92597			0.962986	−	0.269553i	$-0.0868758\pi$
$17$	7.94098			1.92597			0.962986	+	0.269553i	$0.0868758\pi$
$18$	1.68213	−	3.89492i	0.396482	−	0.918042i
$19$		−	5.81397i		−	1.33382i	−0.745140	−	0.666908i	$-0.767617\pi$
$19$		−	5.81397i		−	1.33382i	0.745140	−	0.666908i	$-0.232383\pi$
$20$	0.488850	+	0.188739i	0.109310	+	0.0422033i
$21$	1.66413	−	0.480280i	0.363143	−	0.104806i
$22$	2.02044	+	2.94587i	0.430760	+	0.628062i
$23$	0.783213	−	1.35657i	0.163311	−	0.282863i	−0.772743	−	0.634719i	$-0.781116\pi$
$23$	0.783213	−	1.35657i	0.163311	−	0.282863i	0.936054	+	0.351856i	$0.114449\pi$
$24$	−4.89874	−	0.0485563i	−0.999951	−	0.00991152i
$25$	−2.46568	−	4.27068i	−0.493135	−	0.854135i
$26$	−1.49330	+	3.12298i	−0.292860	+	0.612466i
$27$	−3.45694	+	3.87938i	−0.665289	+	0.746586i
$28$	−1.25563	−	1.55673i	−0.237292	−	0.294194i
$29$	−1.60072	+	0.924174i	−0.297246	+	0.171615i	−0.641205	−	0.767370i	$-0.721565\pi$
$29$	−1.60072	+	0.924174i	−0.297246	+	0.171615i	0.343959	+	0.938985i	$0.388232\pi$
$30$	−0.495528	−	0.407857i	−0.0904706	−	0.0744642i
$31$	3.39752	−	5.88468i	0.610213	−	1.05692i	−0.380991	−	0.924579i	$-0.624417\pi$
$31$	3.39752	−	5.88468i	0.610213	−	1.05692i	0.991204	−	0.132341i	$-0.0422494\pi$
$32$	2.13946	+	5.23667i	0.378207	+	0.925721i
$33$	−1.21314	−	4.20343i	−0.211180	−	0.731723i
$34$	0.870276	+	11.1965i	0.149251	+	1.92018i
$35$		−	0.262010i		−	0.0442878i
$36$	5.67604	+	1.94488i	0.946007	+	0.324147i
$37$		−	5.05596i		−	0.831195i	−0.909549	−	0.415598i	$-0.863572\pi$
$37$		−	5.05596i		−	0.831195i	0.909549	−	0.415598i	$-0.136428\pi$
$38$	8.19747	−	0.637170i	1.32981	−	0.103363i
$39$	2.93984	−	3.05479i	0.470751	−	0.489157i
$40$	−0.212540	+	0.709944i	−0.0336055	+	0.112252i
$41$	−3.20862	+	5.55748i	−0.501101	+	0.867933i	0.498898	+	0.866661i	$0.333738\pi$
$41$	−3.20862	+	5.55748i	−0.501101	+	0.867933i	−0.999999	+	0.00127236i	$0.999595\pi$
$42$	0.859553	+	2.29372i	0.132632	+	0.353929i
$43$	4.16396	−	2.40406i	0.634998	−	0.366616i	−0.147687	−	0.989034i	$-0.547183\pi$
$43$	4.16396	−	2.40406i	0.634998	−	0.366616i	0.782685	+	0.622418i	$0.213850\pi$
$44$	−3.93214	+	3.17159i	−0.592792	+	0.478136i
$45$	0.418822	+	0.665155i	0.0624343	+	0.0991555i
$46$	1.99854	+	0.955630i	0.294668	+	0.140900i
$47$	5.42014	+	9.38796i	0.790609	+	1.36937i	0.925590	+	0.378526i	$0.123569\pi$
$47$	5.42014	+	9.38796i	0.790609	+	1.36937i	−0.134982	+	0.990848i	$0.543098\pi$
$48$	−0.468405	−	6.91235i	−0.0676084	−	0.997712i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	5.75126	−	3.94454i	0.813351	−	0.557842i
$51$	3.30449	−	13.3513i	0.462721	−	1.86956i
$52$	−4.56693	−	1.76323i	−0.633319	−	0.244517i
$53$			11.9617i			1.64307i	0.570158	+	0.821535i	$0.306882\pi$
$53$			11.9617i			1.64307i	−0.570158	+	0.821535i	$0.693118\pi$
$54$	−5.84862	−	4.44900i	−0.795897	−	0.605432i
$55$	−0.661811			−0.0892386
$56$	2.05731	−	1.94099i	0.274920	−	0.259376i
$57$	−9.77514	−	2.41937i	−1.29475	−	0.320454i
$58$	−1.47848	−	2.15566i	−0.194133	−	0.283053i
$59$	−10.0882	−	5.82442i	−1.31337	−	0.758274i	−0.330717	−	0.943730i	$-0.607291\pi$
$59$	−10.0882	−	5.82442i	−1.31337	−	0.758274i	−0.982653	+	0.185455i	$0.940624\pi$
$60$	0.520756	−	0.743373i	0.0672293	−	0.0959691i
$61$	−12.6142	+	7.28281i	−1.61508	+	0.932469i	−0.626916	+	0.779087i	$0.715683\pi$
$61$	−12.6142	+	7.28281i	−1.61508	+	0.932469i	−0.988167	+	0.153382i	$0.950983\pi$
$62$	8.66951	+	4.14545i	1.10103	+	0.526473i
$63$	−0.115007	−	2.99779i	−0.0144896	−	0.377687i
$64$	−7.14903	+	3.59046i	−0.893629	+	0.448807i
$65$	−0.320667	−	0.555412i	−0.0397738	−	0.0688903i
$66$	5.79372	−	2.17114i	0.713158	−	0.267249i
$67$	4.47954	+	2.58627i	0.547263	+	0.315963i	0.748017	−	0.663679i	$-0.231006\pi$
$67$	4.47954	+	2.58627i	0.547263	+	0.315963i	−0.200754	+	0.979642i	$0.564339\pi$
$68$	−15.6912	+	2.45411i	−1.90284	+	0.297605i
$69$	−1.95490	−	1.88134i	−0.235342	−	0.226487i
$70$	0.369424	−	0.0287145i	0.0441546	−	0.00343203i
$71$	13.1679			1.56274			0.781372	−	0.624066i	$-0.214520\pi$
$71$	13.1679			1.56274			0.781372	+	0.624066i	$0.214520\pi$
$72$	−2.12016	+	8.21614i	−0.249863	+	0.968281i
$73$	−9.64768			−1.12918			−0.564588	−	0.825373i	$-0.690965\pi$
$73$	−9.64768			−1.12918			−0.564588	+	0.825373i	$0.690965\pi$
$74$	7.12871	−	0.554098i	0.828696	−	0.0644126i
$75$	−8.20641	+	2.36843i	−0.947595	+	0.273483i
$76$	1.79677	+	11.4883i	0.206104	+	1.31780i
$77$	2.18749	+	1.26295i	0.249288	+	0.143927i
$78$	4.62932	+	3.81028i	0.524167	+	0.431429i
$79$	1.84252	+	3.19133i	0.207299	+	0.359053i	0.950863	−	0.309612i	$-0.100199\pi$
$79$	1.84252	+	3.19133i	0.207299	+	0.359053i	−0.743564	+	0.668665i	$0.766866\pi$
$80$	−1.02429	−	0.221868i	−0.114519	−	0.0248056i
$81$	5.08393	+	7.42655i	0.564881	+	0.825172i
$82$	−8.18748	−	3.91496i	−0.904156	−	0.432335i
$83$	−7.77411	+	4.48838i	−0.853319	+	0.492664i	−0.861769	−	0.507300i	$-0.830644\pi$
$83$	−7.77411	+	4.48838i	−0.853319	+	0.492664i	0.00845021	+	0.999964i	$0.497310\pi$
$84$	−3.13986	+	1.46331i	−0.342587	+	0.159660i
$85$	−1.80187	−	1.04031i	−0.195440	−	0.112837i
$86$	3.84597	+	5.60755i	0.414722	+	0.604677i
$87$	0.887724	+	3.07589i	0.0951740	+	0.329770i
$88$	−4.90276	−	5.19657i	−0.522636	−	0.553957i
$89$	−0.168315			−0.0178413			−0.00892066	−	0.999960i	$-0.502840\pi$
$89$	−0.168315			−0.0178413			−0.00892066	+	0.999960i	$0.502840\pi$
$90$	−0.891943	+	0.663419i	−0.0940190	+	0.0699305i
$91$			2.44775i			0.256594i
$92$	−1.12838	+	2.92259i	−0.117641	+	0.304701i
$93$	−8.48021	−	8.16112i	−0.879357	−	0.846268i
$94$	−12.6426	+	8.67104i	−1.30399	+	0.894350i
$95$	−0.761659	+	1.31923i	−0.0781446	+	0.135350i
$96$	9.69481	−	1.41798i	0.989472	−	0.144722i
$97$	−1.37383	−	2.37955i	−0.139491	−	0.241606i	0.787813	−	0.615915i	$-0.211213\pi$
$97$	−1.37383	−	2.37955i	−0.139491	−	0.241606i	−0.927304	+	0.374308i	$0.877880\pi$
$98$	−1.27586	−	0.610070i	−0.128881	−	0.0616264i
$99$	−7.57213	+	0.290497i	−0.761028	+	0.0291961i
$100$	6.19195	+	7.67676i	0.619195	+	0.767676i
$101$	−2.44634	+	1.41240i	−0.243420	+	0.140539i	−0.616748	−	0.787161i	$-0.711550\pi$
$101$	−2.44634	+	1.41240i	−0.243420	+	0.140539i	0.373328	+	0.927700i	$0.378217\pi$
$102$	19.1870	+	3.19599i	1.89980	+	0.316450i
$103$	1.58261	−	2.74116i	0.155939	−	0.270095i	−0.777461	−	0.628931i	$-0.783493\pi$
$103$	1.58261	−	2.74116i	0.155939	−	0.270095i	0.933401	+	0.358836i	$0.116826\pi$
$104$	1.98559	−	6.63243i	0.194703	−	0.650363i
$105$	−0.440523	−	0.109030i	−0.0429906	−	0.0106403i
$106$	−16.8656	+	1.31092i	−1.63813	+	0.127328i
$107$		−	6.73799i		−	0.651387i	−0.945475	−	0.325693i	$-0.894402\pi$
$107$		−	6.73799i		−	0.651387i	0.945475	−	0.325693i	$-0.105598\pi$
$108$	5.63195	−	8.73391i	0.541934	−	0.840421i
$109$		−	4.28640i		−	0.410563i	−0.978703	−	0.205282i	$-0.934189\pi$
$109$		−	4.28640i		−	0.410563i	0.978703	−	0.205282i	$-0.0658110\pi$
$110$	−0.0725299	−	0.933128i	−0.00691545	−	0.0889703i
$111$	−8.50069	−	2.10394i	−0.806850	−	0.199697i
$112$	2.96219	+	2.68801i	0.279901	+	0.253993i
$113$	6.08446	−	10.5386i	0.572378	−	0.991388i	−0.423943	−	0.905689i	$-0.639354\pi$
$113$	6.08446	−	10.5386i	0.572378	−	0.991388i	0.996321	−	0.0856990i	$-0.0273123\pi$
$114$	2.33993	−	14.0477i	0.219155	−	1.31569i
$115$	−0.355434	+	0.205210i	−0.0331444	+	0.0191359i
$116$	2.87737	−	2.32084i	0.267157	−	0.215485i
$117$	−3.91271	−	6.21400i	−0.361731	−	0.574485i
$118$	7.10660	−	14.8623i	0.654216	−	1.36818i
$119$	3.97049	+	6.87709i	0.363974	+	0.630422i
$120$	1.10520	+	0.652777i	0.100890	+	0.0595901i
$121$	−2.30991	+	4.00089i	−0.209992	+	0.363717i
$122$	−11.6509	−	16.9874i	−1.05482	−	1.53797i
$123$	8.00870	+	7.70735i	0.722120	+	0.694948i
$124$	−4.89481	+	12.6780i	−0.439567	+	1.13852i
$125$			2.60211i			0.232740i
$126$	4.21417	−	0.490693i	0.375428	−	0.0437144i
$127$	−3.33572			−0.295997			−0.147998	−	0.988988i	$-0.547283\pi$
$127$	−3.33572			−0.295997			−0.147998	+	0.988988i	$0.547283\pi$
$128$	−5.84589	−	9.68636i	−0.516708	−	0.856161i
$129$	−2.30924	−	8.00135i	−0.203318	−	0.704479i
$130$	0.747966	−	0.512997i	0.0656009	−	0.0449928i
$131$	6.91558	+	3.99271i	0.604217	+	0.348845i	0.770699	−	0.637200i	$-0.219907\pi$
$131$	6.91558	+	3.99271i	0.604217	+	0.348845i	−0.166482	+	0.986045i	$0.553241\pi$
$132$	3.69618	+	7.93097i	0.321711	+	0.690303i
$133$	5.03505	−	2.90699i	0.436594	−	0.252068i
$134$	−3.15561	+	6.59942i	−0.272603	+	0.570103i
$135$	1.29262	−	0.427382i	0.111251	−	0.0367832i
$136$	−5.17985	−	21.8550i	−0.444168	−	1.87405i
$137$	2.16307	+	3.74655i	0.184804	+	0.320090i	0.943510	−	0.331343i	$-0.107502\pi$
$137$	2.16307	+	3.74655i	0.184804	+	0.320090i	−0.758707	+	0.651432i	$0.774168\pi$
$138$	2.43837	−	2.96251i	0.207568	−	0.252186i
$139$	10.8826	+	6.28310i	0.923054	+	0.532926i	0.884608	−	0.466335i	$-0.154426\pi$
$139$	10.8826	+	6.28310i	0.923054	+	0.532926i	0.0384460	+	0.999261i	$0.487759\pi$
$140$	0.0809725	+	0.517726i	0.00684343	+	0.0437559i
$141$	18.0396	−	5.20637i	1.51921	−	0.438455i
$142$	1.44311	+	18.5662i	0.121103	+	1.55804i
$143$	6.18276			0.517029
$144$	−11.8168	−	2.08890i	−0.984732	−	0.174075i
$145$	0.484286			0.0402177
$146$	−1.05732	−	13.6029i	−0.0875043	−	1.12578i
$147$	1.24800	+	1.20104i	0.102933	+	0.0990601i
$148$	1.56251	+	9.99048i	0.128438	+	0.821212i
$149$	5.12874	+	2.96108i	0.420163	+	0.242581i	0.695147	−	0.718868i	$-0.255339\pi$
$149$	5.12874	+	2.96108i	0.420163	+	0.242581i	−0.274984	+	0.961449i	$0.588673\pi$
$150$	−4.23876	−	11.3112i	−0.346093	−	0.923552i
$151$	−10.2678	−	17.7843i	−0.835581	−	1.44727i	−0.893556	−	0.448951i	$-0.851798\pi$
$151$	−10.2678	−	17.7843i	−0.835581	−	1.44727i	0.0579747	−	0.998318i	$-0.481536\pi$
$152$	−16.0011	+	3.79241i	−1.29786	+	0.307605i
$153$	−21.0728	−	11.1118i	−1.70363	−	0.898336i
$154$	−1.54098	+	3.22269i	−0.124175	+	0.259692i
$155$	−1.54185	+	0.890185i	−0.123844	+	0.0715013i
$156$	−4.86500	+	6.94473i	−0.389512	+	0.556024i
$157$	0.295777	+	0.170767i	0.0236056	+	0.0136287i	0.511756	−	0.859131i	$-0.328995\pi$
$157$	0.295777	+	0.170767i	0.0236056	+	0.0136287i	−0.488151	+	0.872759i	$0.662328\pi$
$158$	−4.29772	+	2.94762i	−0.341909	+	0.234500i
$159$	20.1115	+	4.97765i	1.59495	+	0.394753i
$160$	0.200570	−	1.46852i	0.0158565	−	0.116097i
$161$	1.56643			0.123452
$162$	−9.91398	+	7.98204i	−0.778916	+	0.627128i
$163$		−	6.52858i		−	0.511358i	−0.966762	−	0.255679i	$-0.917701\pi$
$163$		−	6.52858i		−	0.511358i	0.966762	−	0.255679i	$-0.0822990\pi$
$164$	4.62265	−	11.9731i	0.360968	−	0.934940i
$165$	−0.275400	+	1.11272i	−0.0214399	+	0.0866248i
$166$	−7.18043	−	10.4693i	−0.557310	−	0.812575i
$167$	−2.18296	+	3.78101i	−0.168923	+	0.292583i	−0.938041	−	0.346523i	$-0.887362\pi$
$167$	−2.18296	+	3.78101i	−0.168923	+	0.292583i	0.769119	+	0.639106i	$0.220696\pi$
$168$	−2.40732	−	4.26671i	−0.185729	−	0.329184i
$169$	−3.50427	−	6.06957i	−0.269559	−	0.466890i
$170$	1.26932	−	2.65457i	0.0973526	−	0.203596i
$171$	−8.13548	+	15.4284i	−0.622136	+	1.17984i
$172$	−7.48493	+	6.03722i	−0.570721	+	0.460334i
$173$	−9.46237	+	5.46310i	−0.719411	+	0.415352i	−0.814536	−	0.580113i	$-0.803008\pi$
$173$	−9.46237	+	5.46310i	−0.719411	+	0.415352i	0.0951249	+	0.995465i	$0.469675\pi$
$174$	−4.23960	+	1.58875i	−0.321403	+	0.120443i
$175$	2.46568	−	4.27068i	0.186388	−	0.322833i
$176$	6.78966	−	7.48220i	0.511790	−	0.563992i
$177$	−13.9907	+	14.5377i	−1.05161	+	1.09272i
$178$	−0.0184461	−	0.237317i	−0.00138259	−	0.0177877i
$179$		−	4.74701i		−	0.354808i	−0.984138	−	0.177404i	$-0.943230\pi$
$179$		−	4.74701i		−	0.354808i	0.984138	−	0.177404i	$-0.0567700\pi$
$180$	−1.03315	−	1.18490i	−0.0770061	−	0.0883171i
$181$			12.9536i			0.962836i	0.876491	+	0.481418i	$0.159878\pi$
$181$			12.9536i			0.962836i	−0.876491	+	0.481418i	$0.840122\pi$
$182$	−3.45123	+	0.268256i	−0.255822	+	0.0198844i
$183$	6.99558	+	24.2391i	0.517128	+	1.79181i
$184$	−4.24440	−	1.27067i	−0.312901	−	0.0936750i
$185$	−0.662357	+	1.14724i	−0.0486974	+	0.0843464i
$186$	10.5775	−	12.8512i	0.775579	−	0.942293i
$187$	17.3709	−	10.0291i	1.27028	−	0.733398i
$188$	−13.6114	−	16.8753i	−0.992711	−	1.23076i
$189$	−5.08811	−	1.05411i	−0.370105	−	0.0766753i
$190$	−1.94354	−	0.929331i	−0.140999	−	0.0674208i
$191$	−7.34619	−	12.7240i	−0.531551	−	0.920674i	−0.999322	−	0.0368239i	$-0.988276\pi$
$191$	−7.34619	−	12.7240i	−0.531551	−	0.920674i	0.467770	−	0.883850i	$-0.345057\pi$
$192$	3.06178	+	13.5139i	0.220965	+	0.975282i
$193$	−10.6516	+	18.4492i	−0.766722	+	1.32800i	0.172610	+	0.984990i	$0.444780\pi$
$193$	−10.6516	+	18.4492i	−0.766722	+	1.32800i	−0.939331	+	0.343011i	$0.888553\pi$
$194$	3.20450	−	2.19783i	0.230070	−	0.157795i
$195$	−1.06726	+	0.308020i	−0.0764283	+	0.0220578i
$196$	0.720350	−	1.86577i	0.0514536	−	0.133269i
$197$			7.82459i			0.557479i	0.960367	+	0.278739i	$0.0899166\pi$
$197$			7.82459i			0.557479i	−0.960367	+	0.278739i	$0.910083\pi$
$198$	−1.23944	−	10.6446i	−0.0880833	−	0.756477i
$199$	1.05144			0.0745347			0.0372674	−	0.999305i	$-0.488135\pi$
$199$	1.05144			0.0745347			0.0372674	+	0.999305i	$0.488135\pi$
$200$	−10.1453	+	9.57172i	−0.717384	+	0.676823i
$201$	6.21242	−	6.45532i	0.438190	−	0.455323i
$202$	−2.25952	−	3.29446i	−0.158980	−	0.231797i
$203$	−1.60072	−	0.924174i	−0.112348	−	0.0648643i
$204$	−2.40346	+	27.4032i	−0.168276	+	1.91861i
$205$	1.45612	−	0.840689i	0.101700	−	0.0587163i
$206$	4.03838	+	1.93101i	0.281367	+	0.134540i
$207$	−3.97663	+	2.50393i	−0.276395	+	0.174035i
$208$	9.56907	+	2.07273i	0.663496	+	0.143718i
$209$	−7.34276	−	12.7180i	−0.507909	−	0.879724i
$210$	0.105451	−	0.633068i	0.00727678	−	0.0436859i
$211$	16.4146	+	9.47697i	1.13003	+	0.652421i	0.943942	−	0.330112i	$-0.107087\pi$
$211$	16.4146	+	9.47697i	1.13003	+	0.652421i	0.186085	+	0.982534i	$0.440420\pi$
$212$	−3.69670	−	23.6361i	−0.253890	−	1.62334i
$213$	5.47957	−	22.1395i	0.375454	−	1.51697i
$214$	9.50031	−	0.738437i	0.649428	−	0.0504785i
$215$	−1.25978			−0.0859160
$216$	12.9317	+	6.98365i	0.879890	+	0.475177i
$217$	6.79504			0.461278
$218$	6.04366	−	0.469760i	0.409328	−	0.0318161i
$219$	−4.01470	+	16.2208i	−0.271288	+	1.09610i
$220$	1.30773	−	0.204529i	0.0881668	−	0.0137893i
$221$	16.8334	+	9.71876i	1.13234	+	0.653754i
$222$	2.03486	−	12.2162i	0.136571	−	0.819899i
$223$	6.71018	+	11.6224i	0.449347	+	0.778291i	0.998344	−	0.0575332i	$-0.0183235\pi$
$223$	6.71018	+	11.6224i	0.449347	+	0.778291i	−0.548997	+	0.835824i	$0.684990\pi$
$224$	−3.46536	+	4.47116i	−0.231539	+	0.298742i
$225$	0.567142	+	14.7832i	0.0378095	+	0.985545i
$226$	15.5258	+	7.42390i	1.03276	+	0.493830i
$227$	−7.91950	+	4.57233i	−0.525636	+	0.303476i	−0.739237	−	0.673445i	$-0.764814\pi$
$227$	−7.91950	+	4.57233i	−0.525636	+	0.303476i	0.213602	+	0.976921i	$0.431481\pi$
$228$	20.0632	+	1.75968i	1.32872	+	0.116538i
$229$	9.54541	+	5.51104i	0.630778	+	0.364180i	0.781053	−	0.624464i	$-0.214683\pi$
$229$	9.54541	+	5.51104i	0.630778	+	0.364180i	−0.150275	+	0.988644i	$0.548016\pi$
$230$	−0.328291	−	0.478658i	−0.0216468	−	0.0315618i
$231$	3.03371	−	3.15232i	0.199603	−	0.207408i
$232$	3.58763	+	3.80263i	0.235540	+	0.249655i
$233$	10.6785			0.699571			0.349785	−	0.936830i	$-0.386255\pi$
$233$	10.6785			0.699571			0.349785	+	0.936830i	$0.386255\pi$
$234$	8.33269	−	6.19778i	0.544725	−	0.405162i
$235$		−	2.84026i		−	0.185278i
$236$	21.7340	+	8.39123i	1.41477	+	0.546223i
$237$	6.13237	−	1.76985i	0.398340	−	0.114964i
$238$	−9.26129	+	6.35192i	−0.600321	+	0.411734i
$239$	−5.95867	+	10.3207i	−0.385435	+	0.667592i	−0.991829	−	0.127571i	$-0.959282\pi$
$239$	−5.95867	+	10.3207i	−0.385435	+	0.667592i	0.606395	+	0.795164i	$0.292615\pi$
$240$	−0.799268	+	1.62983i	−0.0515925	+	0.105205i
$241$	−1.84275	−	3.19173i	−0.118702	−	0.205597i	0.800552	−	0.599264i	$-0.204540\pi$
$241$	−1.84275	−	3.19173i	−0.118702	−	0.205597i	−0.919253	+	0.393666i	$0.871207\pi$
$242$	−5.89424	−	2.81842i	−0.378896	−	0.181175i
$243$	14.6020	−	5.45729i	0.936718	−	0.350086i
$244$	22.6747	−	18.2890i	1.45160	−	1.17083i
$245$	0.226907	−	0.131005i	0.0144966	−	0.00836960i
$246$	−9.98936	+	12.1366i	−0.636898	+	0.773803i
$247$	7.11556	−	12.3245i	0.452752	−	0.784190i
$248$	−18.4119	−	5.51207i	−1.16916	−	0.350017i
$249$	4.31136	+	14.9385i	0.273221	+	0.946690i
$250$	−3.66888	+	0.285173i	−0.232040	+	0.0180359i
$251$			13.8749i			0.875777i	0.899029	+	0.437888i	$0.144273\pi$
$251$			13.8749i			0.875777i	−0.899029	+	0.437888i	$0.855727\pi$
$252$	1.15370	+	5.88804i	0.0726764	+	0.370911i
$253$		−	3.95664i		−	0.248752i
$254$	−0.365571	−	4.70323i	−0.0229380	−	0.295107i
$255$	−2.49890	+	2.59661i	−0.156487	+	0.162606i
$256$	13.0167	−	9.30403i	0.813545	−	0.581502i
$257$	−0.671102	+	1.16238i	−0.0418622	+	0.0725075i	−0.886197	−	0.463308i	$-0.846662\pi$
$257$	−0.671102	+	1.16238i	−0.0418622	+	0.0725075i	0.844335	+	0.535815i	$0.179996\pi$
$258$	11.0285	−	4.13284i	0.686605	−	0.257299i
$259$	4.37859	−	2.52798i	0.272073	−	0.157081i
$260$	0.805278	+	0.998381i	0.0499412	+	0.0619170i
$261$	5.54097	−	0.212574i	0.342977	−	0.0131580i
$262$	−4.87167	+	10.1883i	−0.300973	+	0.629433i
$263$	−10.8194	−	18.7397i	−0.667150	−	1.15554i	−0.978697	−	0.205308i	$-0.934181\pi$
$263$	−10.8194	−	18.7397i	−0.667150	−	1.15554i	0.311547	−	0.950231i	$-0.399153\pi$
$264$	−10.7773	+	6.08065i	−0.663296	+	0.374238i
$265$	1.56705	−	2.71421i	0.0962629	−	0.166732i
$266$	4.65054	+	6.78063i	0.285143	+	0.415747i
$267$	−0.0700410	+	0.282991i	−0.00428644	+	0.0173188i
$268$	−9.65075	−	3.72603i	−0.589513	−	0.227604i
$269$			9.46531i			0.577110i	0.957463	+	0.288555i	$0.0931748\pi$
$269$			9.46531i			0.577110i	−0.957463	+	0.288555i	$0.906825\pi$
$270$	0.744255	+	1.77571i	0.0452939	+	0.108066i
$271$	−8.20964			−0.498700			−0.249350	−	0.968413i	$-0.580217\pi$
$271$	−8.20964			−0.498700			−0.249350	+	0.968413i	$0.580217\pi$
$272$	30.2471	−	9.69854i	1.83400	−	0.588060i
$273$	4.11544	+	1.01858i	0.249078	+	0.0616474i
$274$	−5.04543	+	3.46044i	−0.304806	+	0.209053i
$275$	−10.7873	−	6.22805i	−0.650499	−	0.375566i
$276$	4.44426	+	3.11334i	0.267513	+	0.187401i
$277$	−24.8125	+	14.3255i	−1.49084	+	0.860737i	−0.999945	−	0.0104824i	$-0.996663\pi$
$277$	−24.8125	+	14.3255i	−1.49084	+	0.860737i	−0.490895	+	0.871219i	$0.663330\pi$
$278$	−7.66626	+	16.0327i	−0.459792	+	0.961577i
$279$	−17.2503	+	10.8619i	−1.03275	+	0.650282i
$280$	−0.721100	+	0.170907i	−0.0430939	+	0.0102137i
$281$	3.13872	+	5.43642i	0.187240	+	0.324310i	0.944329	−	0.329002i	$-0.106712\pi$
$281$	3.13872	+	5.43642i	0.187240	+	0.324310i	−0.757089	+	0.653312i	$0.773379\pi$
$282$	9.31779	+	24.8646i	0.554866	+	1.48067i
$283$	6.83108	+	3.94392i	0.406065	+	0.234442i	0.689098	−	0.724668i	$-0.258007\pi$
$283$	6.83108	+	3.94392i	0.406065	+	0.234442i	−0.283032	+	0.959110i	$0.591340\pi$
$284$	−26.0195	+	4.06946i	−1.54397	+	0.241478i
$285$	1.90110	+	1.82957i	0.112612	+	0.108374i
$286$	0.677588	+	8.71746i	0.0400666	+	0.515474i
$287$	−6.41723			−0.378797
$288$	1.65024	−	16.8901i	0.0972412	−	0.995261i
$289$	46.0592			2.70937
$290$	0.0530743	+	0.682824i	0.00311663	+	0.0400968i
$291$	−4.57247	+	1.31965i	−0.268043	+	0.0773591i
$292$	19.0636	−	2.98155i	1.11561	−	0.174482i
$293$	22.7271	+	13.1215i	1.32773	+	0.766565i	0.984948	−	0.172850i	$-0.0552975\pi$
$293$	22.7271	+	13.1215i	1.32773	+	0.766565i	0.342782	+	0.939415i	$0.388631\pi$
$294$	−1.55665	+	1.89126i	−0.0907855	+	0.110300i
$295$	1.52606	+	2.64321i	0.0888504	+	0.153893i
$296$	−13.9149	+	3.29797i	−0.808790	+	0.191691i
$297$	−2.66258	+	12.8521i	−0.154499	+	0.745752i
$298$	−3.61293	+	7.55583i	−0.209291	+	0.437698i
$299$	3.32053	−	1.91711i	0.192031	−	0.110869i
$300$	15.4837	−	7.21610i	0.893955	−	0.416622i
$301$	4.16396	+	2.40406i	0.240007	+	0.138568i
$302$	23.9500	−	16.4262i	1.37816	−	0.945223i
$303$	1.35669	+	4.70082i	0.0779398	+	0.270055i
$304$	−7.10076	−	22.1453i	−0.407256	−	1.27012i
$305$	3.81634			0.218523
$306$	13.3578	−	30.9295i	0.763613	−	1.76812i
$307$			3.46867i			0.197967i	0.995089	+	0.0989837i	$0.0315592\pi$
$307$			3.46867i			0.197967i	−0.995089	+	0.0989837i	$0.968441\pi$
$308$	−4.71275	−	1.81953i	−0.268534	−	0.103677i
$309$	−3.95020	−	3.80156i	−0.224719	−	0.216263i
$310$	−1.42410	−	2.07638i	−0.0808835	−	0.117931i
$311$	−12.1749	+	21.0875i	−0.690375	+	1.19576i	0.281340	+	0.959608i	$0.409221\pi$
$311$	−12.1749	+	21.0875i	−0.690375	+	1.19576i	−0.971715	+	0.236157i	$0.924112\pi$
$312$	−10.3250	−	6.09837i	−0.584536	−	0.345252i
$313$	−5.85619	−	10.1432i	−0.331011	−	0.573329i	0.651699	−	0.758478i	$-0.274057\pi$
$313$	−5.85619	−	10.1432i	−0.331011	−	0.573329i	−0.982710	+	0.185149i	$0.940723\pi$
$314$	−0.208360	+	0.435750i	−0.0117584	+	0.0245908i
$315$	−0.366630	+	0.695288i	−0.0206573	+	0.0391750i
$316$	−4.62703	−	5.73658i	−0.260291	−	0.322708i
$317$	20.0639	−	11.5839i	1.12690	−	0.650615i	0.183746	−	0.982974i	$-0.441178\pi$
$317$	20.0639	−	11.5839i	1.12690	−	0.650615i	0.943153	+	0.332358i	$0.107844\pi$
$318$	−4.81421	+	28.9019i	−0.269967	+	1.62074i
$319$	−2.33437	+	4.04325i	−0.130700	+	0.226379i
$320$	2.09253	+	0.121857i	0.116976	+	0.00681202i
$321$	−11.3287	−	2.80389i	−0.632308	−	0.156498i
$322$	0.171669	+	2.20860i	0.00956676	+	0.123080i
$323$		−	46.1686i		−	2.56889i
$324$	−12.3409	−	13.1036i	−0.685604	−	0.727975i
$325$		−	12.0707i		−	0.669562i
$326$	9.20504	−	0.715486i	0.509820	−	0.0396271i
$327$	−7.20681	−	1.78371i	−0.398538	−	0.0986391i
$328$	17.3882	+	5.20559i	0.960101	+	0.287431i
$329$	−5.42014	+	9.38796i	−0.298822	+	0.517575i
$330$	−1.59907	−	0.266358i	−0.0880258	−	0.0146625i
$331$	5.19948	−	3.00192i	0.285790	−	0.165001i	−0.350252	−	0.936656i	$-0.613904\pi$
$331$	5.19948	−	3.00192i	0.285790	−	0.165001i	0.636041	+	0.771655i	$0.280571\pi$
$332$	13.9744	−	11.2715i	0.766943	−	0.618603i
$333$	−7.07480	+	13.4169i	−0.387697	+	0.735240i
$334$	−5.57031	−	2.66352i	−0.304794	−	0.145742i
$335$	−0.677627	−	1.17369i	−0.0370227	−	0.0641253i
$336$	5.75207	−	3.86183i	0.313801	−	0.210680i
$337$	−1.42196	+	2.46291i	−0.0774591	+	0.134163i	−0.902153	−	0.431416i	$-0.858014\pi$
$337$	−1.42196	+	2.46291i	−0.0774591	+	0.134163i	0.824694	+	0.565579i	$0.191347\pi$
$338$	8.17381	−	5.60606i	0.444597	−	0.304930i
$339$	−15.1868	−	14.6154i	−0.824835	−	0.793797i
$340$	3.88195	+	1.49877i	0.210528	+	0.0812823i
$341$		−	17.1636i		−	0.929461i
$342$	−22.6450	−	9.77986i	−1.22450	−	0.528835i
$343$	−1.00000			−0.0539949
$344$	−9.33254	−	9.89182i	−0.503177	−	0.533331i
$345$	0.197116	+	0.682992i	0.0106124	+	0.0367710i
$346$	−8.73977	−	12.7429i	−0.469853	−	0.685060i
$347$	10.9112	+	6.29959i	0.585744	+	0.338180i	0.763413	−	0.645911i	$-0.223522\pi$
$347$	10.9112	+	6.29959i	0.585744	+	0.338180i	−0.177669	+	0.984090i	$0.556856\pi$
$348$	−2.70471	−	5.80355i	−0.144988	−	0.311103i
$349$	−13.7717	+	7.95110i	−0.737183	+	0.425613i	−0.821044	−	0.570865i	$-0.806608\pi$
$349$	−13.7717	+	7.95110i	−0.737183	+	0.425613i	0.0838611	+	0.996477i	$0.473275\pi$
$350$	6.29170	+	3.00847i	0.336306	+	0.160809i
$351$	−12.0759	+	3.99268i	−0.644565	+	0.213114i
$352$	11.2937	+	8.75315i	0.601957	+	0.466545i
$353$	11.8334	+	20.4961i	0.629831	+	1.09090i	0.987585	+	0.157083i	$0.0502091\pi$
$353$	11.8334	+	20.4961i	0.629831	+	1.09090i	−0.357755	+	0.933816i	$0.616458\pi$
$354$	−22.0309	−	18.1331i	−1.17093	−	0.963764i
$355$	−2.98789	−	1.72506i	−0.158581	−	0.0915568i
$356$	0.332586	−	0.0520166i	0.0176270	−	0.00275687i
$357$	13.2148	−	3.81389i	0.699403	−	0.201853i
$358$	6.69310	−	0.520239i	0.353741	−	0.0274955i
$359$	−10.0214			−0.528907			−0.264453	−	0.964398i	$-0.585192\pi$
$359$	−10.0214			−0.528907			−0.264453	+	0.964398i	$0.585192\pi$
$360$	1.55743	−	1.58655i	0.0820840	−	0.0836186i
$361$	−14.8023			−0.779066
$362$	−18.2641	+	1.41963i	−0.959940	+	0.0746139i
$363$	5.76554	+	5.54859i	0.302612	+	0.291226i
$364$	−0.756460	−	4.83669i	−0.0396493	−	0.253512i
$365$	2.18913	+	1.26389i	0.114584	+	0.0661553i
$366$	−33.4095	+	12.5199i	−1.74634	+	0.654427i
$367$	−14.3990	−	24.9398i	−0.751621	−	1.30185i	−0.947037	−	0.321125i	$-0.895939\pi$
$367$	−14.3990	−	24.9398i	−0.751621	−	1.30185i	0.195416	−	0.980720i	$-0.437394\pi$
$368$	1.32644	−	6.12369i	0.0691453	−	0.319220i
$369$	16.2912	−	10.2579i	0.848085	−	0.534006i
$370$	−1.69015	−	0.808168i	−0.0878665	−	0.0420147i
$371$	−10.3592	+	5.98087i	−0.537821	+	0.310511i
$372$	19.2789	+	13.5054i	0.999562	+	0.700224i
$373$	−21.4729	−	12.3974i	−1.11182	−	0.641912i	−0.172522	−	0.985006i	$-0.555192\pi$
$373$	−21.4729	−	12.3974i	−1.11182	−	0.641912i	−0.939301	+	0.343094i	$0.888525\pi$
$374$	16.0443	+	23.3931i	0.829632	+	1.20963i
$375$	4.37498	+	1.08282i	0.225923	+	0.0559166i
$376$	22.3019	−	21.0409i	1.15013	−	1.08510i
$377$	−4.52429			−0.233013
$378$	0.928634	−	7.28956i	0.0477638	−	0.374934i
$379$			19.8307i			1.01863i	0.860579	+	0.509317i	$0.170102\pi$
$379$			19.8307i			1.01863i	−0.860579	+	0.509317i	$0.829898\pi$
$380$	1.09732	−	2.84216i	0.0562914	−	0.145800i
$381$	−1.38809	+	5.60840i	−0.0711142	+	0.287327i
$382$	17.1352	−	11.7523i	0.876713	−	0.601300i
$383$	−13.3996	+	23.2088i	−0.684687	+	1.18591i	0.288848	+	0.957375i	$0.406728\pi$
$383$	−13.3996	+	23.2088i	−0.684687	+	1.18591i	−0.973535	+	0.228538i	$0.926606\pi$
$384$	−18.7185	+	5.79801i	−0.955226	+	0.295879i
$385$	−0.330906	−	0.573145i	−0.0168645	−	0.0292102i
$386$	−27.1800	−	12.9965i	−1.38342	−	0.661504i
$387$	−14.4138	+	0.552970i	−0.732693	+	0.0281090i
$388$	3.45005	+	4.27736i	0.175150	+	0.217150i
$389$	−13.6680	+	7.89121i	−0.692994	+	0.400100i	−0.804733	−	0.593637i	$-0.797691\pi$
$389$	−13.6680	+	7.89121i	−0.692994	+	0.400100i	0.111739	+	0.993738i	$0.464358\pi$
$390$	−0.551260	−	1.47104i	−0.0279142	−	0.0744892i
$391$	6.21948	−	10.7725i	0.314533	−	0.544787i
$392$	2.70961	+	0.811190i	0.136856	+	0.0409713i
$393$	9.59081	−	9.96580i	0.483792	−	0.502708i
$394$	−11.0324	+	0.857520i	−0.555802	+	0.0432012i
$395$		−	0.965515i		−	0.0485803i
$396$	14.8726	−	2.91414i	0.747376	−	0.146441i
$397$		−	34.5232i		−	1.73267i	−0.499464	−	0.866334i	$-0.666470\pi$
$397$		−	34.5232i		−	1.73267i	0.499464	−	0.866334i	$-0.333530\pi$
$398$	0.115231	+	1.48249i	0.00577599	+	0.0743106i
$399$	−2.79233	−	9.67521i	−0.139791	−	0.484366i
$400$	−14.6076	−	13.2555i	−0.730380	−	0.662777i
$401$	1.64927	−	2.85662i	0.0823607	−	0.142653i	−0.821903	−	0.569628i	$-0.807087\pi$
$401$	1.64927	−	2.85662i	0.0823607	−	0.142653i	0.904264	+	0.426975i	$0.140421\pi$
$402$	9.78258	+	8.05180i	0.487911	+	0.401588i
$403$	14.4042	−	8.31627i	0.717525	−	0.414263i
$404$	4.39743	−	3.54689i	0.218780	−	0.176464i
$405$	−0.180666	−	2.35116i	−0.00897735	−	0.116830i
$406$	1.12762	−	2.35823i	0.0559629	−	0.117037i
$407$	−6.38543	−	11.0599i	−0.316514	−	0.548219i
$408$	−38.9008	−	0.385585i	−1.92588	−	0.0190893i
$409$	2.93228	−	5.07886i	0.144992	−	0.251134i	−0.784378	−	0.620283i	$-0.787018\pi$
$409$	2.93228	−	5.07886i	0.144992	−	0.251134i	0.929370	+	0.369150i	$0.120351\pi$
$410$	1.34492	+	1.96093i	0.0664208	+	0.0968436i
$411$	7.19927	−	2.07776i	0.355114	−	0.102488i
$412$	−2.28007	+	5.90558i	−0.112331	+	0.290947i
$413$		−	11.6488i		−	0.573202i
$414$	−3.96625	−	5.33248i	−0.194931	−	0.262077i
$415$	2.35200			0.115455
$416$	−1.87377	+	13.7192i	−0.0918690	+	0.672638i
$417$	15.0925	−	15.6826i	0.739083	−	0.767981i
$418$	17.1272	−	11.7468i	0.837719	−	0.574555i
$419$	−13.3650	−	7.71627i	−0.652922	−	0.376965i	0.136653	−	0.990619i	$-0.456365\pi$
$419$	−13.3650	−	7.71627i	−0.652922	−	0.376965i	−0.789575	+	0.613654i	$0.789699\pi$
$420$	0.904158	+	0.0793012i	0.0441184	+	0.00386950i
$421$	−2.72804	+	1.57503i	−0.132956	+	0.0767625i	−0.565003	−	0.825089i	$-0.691125\pi$
$421$	−2.72804	+	1.57503i	−0.132956	+	0.0767625i	0.432046	+	0.901851i	$0.357792\pi$
$422$	−11.5632	+	24.1825i	−0.562889	+	1.17719i
$423$	−1.24671	−	32.4969i	−0.0606172	−	1.58006i
$424$	32.9209	−	7.80255i	1.59878	−	0.378925i
$425$	−19.5799	−	33.9134i	−0.949764	−	1.64504i
$426$	31.8163	+	5.29965i	1.54150	+	0.256769i
$427$	−12.6142	−	7.28281i	−0.610444	−	0.352440i
$428$	2.08233	+	13.3141i	0.100653	+	0.643563i
$429$	2.57284	−	10.3952i	0.124218	−	0.501885i
$430$	−0.138063	−	1.77624i	−0.00665797	−	0.0856577i
$431$	−11.7240			−0.564723			−0.282362	−	0.959308i	$-0.591118\pi$
$431$	−11.7240			−0.564723			−0.282362	+	0.959308i	$0.591118\pi$
$432$	−8.42945	+	18.9985i	−0.405562	+	0.914068i
$433$	32.7624			1.57446			0.787229	−	0.616661i	$-0.211515\pi$
$433$	32.7624			1.57446			0.787229	+	0.616661i	$0.211515\pi$
$434$	0.744689	+	9.58074i	0.0357462	+	0.459890i
$435$	0.201526	−	0.814239i	0.00966244	−	0.0390398i
$436$	1.32469	+	8.46984i	0.0634409	+	0.405632i
$437$	−7.88703	−	4.55358i	−0.377288	−	0.217827i
$438$	−23.3107	−	3.88288i	−1.11383	−	0.185531i
$439$	15.7037	+	27.1996i	0.749497	+	1.29817i	0.948064	+	0.318080i	$0.103038\pi$
$439$	15.7037	+	27.1996i	0.749497	+	1.29817i	−0.198567	+	0.980087i	$0.563629\pi$
$440$	0.431695	+	1.82143i	0.0205802	+	0.0868331i
$441$	2.53866	−	1.59850i	0.120889	−	0.0761189i
$442$	−11.8582	+	24.7995i	−0.564039	+	1.17959i
$443$	2.92976	−	1.69150i	0.139197	−	0.0803654i	−0.428784	−	0.903407i	$-0.641058\pi$
$443$	2.92976	−	1.69150i	0.139197	−	0.0803654i	0.567981	+	0.823042i	$0.307725\pi$
$444$	17.4474	+	1.53026i	0.828017	+	0.0726231i
$445$	0.0381918	+	0.0220501i	0.00181047	+	0.00104527i
$446$	−15.6517	+	10.7348i	−0.741129	+	0.508308i
$447$	7.11274	−	7.39085i	0.336421	−	0.349575i
$448$	−6.68394	−	4.39601i	−0.315787	−	0.207692i
$449$	27.5964			1.30236			0.651178	−	0.758925i	$-0.274275\pi$
$449$	27.5964			1.30236			0.651178	+	0.758925i	$0.274275\pi$
$450$	−20.7815	+	2.41978i	−0.979651	+	0.114070i
$451$			16.2093i			0.763266i
$452$	−8.76588	+	22.7044i	−0.412312	+	1.06793i
$453$	−34.1739	+	9.86283i	−1.60563	+	0.463396i
$454$	−7.31472	−	10.6651i	−0.343297	−	0.500538i
$455$	0.320667	−	0.555412i	0.0150331	−	0.0260381i
$456$	−0.282305	+	28.4811i	−0.0132201	+	1.33375i
$457$	19.2079	+	33.2691i	0.898509	+	1.55626i	0.829400	+	0.558654i	$0.188682\pi$
$457$	19.2079	+	33.2691i	0.898509	+	1.55626i	0.0691087	+	0.997609i	$0.477984\pi$
$458$	−6.72424	+	14.0626i	−0.314203	+	0.657103i
$459$	−27.4515	+	30.8061i	−1.28133	+	1.43790i
$460$	0.638911	−	0.515335i	0.0297894	−	0.0240276i
$461$	−29.1756	+	16.8445i	−1.35884	+	0.784528i	−0.989468	−	0.144753i	$-0.953761\pi$
$461$	−29.1756	+	16.8445i	−1.35884	+	0.784528i	−0.369374	+	0.929281i	$0.620428\pi$
$462$	4.77713	+	3.93194i	0.222252	+	0.182930i
$463$	19.3607	−	33.5337i	0.899768	−	1.55844i	0.0719778	−	0.997406i	$-0.477069\pi$
$463$	19.3607	−	33.5337i	0.899768	−	1.55844i	0.827790	−	0.561038i	$-0.189598\pi$
$464$	−4.96838	+	5.47516i	−0.230651	+	0.254178i
$465$	0.855075	+	2.96277i	0.0396532	+	0.137395i
$466$	1.17029	+	15.0562i	0.0542125	+	0.697467i
$467$		−	27.4459i		−	1.27004i	−0.772494	−	0.635021i	$-0.780991\pi$
$467$		−	27.4459i		−	1.27004i	0.772494	−	0.635021i	$-0.219009\pi$
$468$	9.65184	+	11.0695i	0.446156	+	0.511690i
$469$			5.17253i			0.238845i
$470$	4.00466	−	0.311273i	0.184721	−	0.0143579i
$471$	0.410196	−	0.426235i	0.0189009	−	0.0196399i
$472$	−9.44941	+	31.5638i	−0.434945	+	1.45284i
$473$	6.07242	−	10.5177i	0.279210	−	0.483606i
$474$	3.16748	+	8.45244i	0.145487	+	0.388234i
$475$	−24.8296	+	14.3354i	−1.13926	+	0.657752i
$476$	−9.97093	−	12.3619i	−0.457017	−	0.566608i
$477$	16.7380	−	31.7425i	0.766382	−	1.45339i
$478$	−15.2048	−	7.27042i	−0.695454	−	0.332541i
$479$	−2.32492	−	4.02688i	−0.106228	−	0.183993i	0.808011	−	0.589167i	$-0.200544\pi$
$479$	−2.32492	−	4.02688i	−0.106228	−	0.183993i	−0.914239	+	0.405174i	$0.867211\pi$
$480$	−2.38559	−	0.948319i	−0.108887	−	0.0432846i
$481$	6.18786	−	10.7177i	0.282142	−	0.488684i
$482$	4.29826	−	2.94799i	0.195780	−	0.134277i
$483$	0.651839	−	2.63366i	0.0296597	−	0.119836i
$484$	3.32789	−	8.61953i	0.151268	−	0.391797i
$485$			0.719915i			0.0326897i
$486$	9.29484	+	19.9901i	0.421623	+	0.906771i
$487$	−40.1944			−1.82138			−0.910692	−	0.413087i	$-0.864451\pi$
$487$	−40.1944			−1.82138			−0.910692	+	0.413087i	$0.864451\pi$
$488$	28.2718	+	29.9661i	1.27980	+	1.35650i
$489$	−10.9766	−	2.71674i	−0.496380	−	0.122855i
$490$	0.209579	+	0.305573i	0.00946783	+	0.0138044i
$491$	20.6126	+	11.9007i	0.930234	+	0.537071i	0.886886	−	0.461989i	$-0.152864\pi$
$491$	20.6126	+	11.9007i	0.930234	+	0.537071i	0.0433485	+	0.999060i	$0.486197\pi$
$492$	−18.2069	−	12.7545i	−0.820832	−	0.575018i
$493$	−12.7113	+	7.33885i	−0.572486	+	0.330525i
$494$	18.1569	+	8.68198i	0.816918	+	0.390621i
$495$	1.75623	+	0.926071i	0.0789366	+	0.0416238i
$496$	5.75399	−	26.5641i	0.258362	−	1.19276i
$497$	6.58395	+	11.4037i	0.295331	+	0.511528i
$498$	−20.5902	+	7.71600i	−0.922670	+	0.345762i
$499$	−4.39642	−	2.53828i	−0.196811	−	0.113629i	0.398356	−	0.917231i	$-0.369581\pi$
$499$	−4.39642	−	2.53828i	−0.196811	−	0.113629i	−0.595167	+	0.803602i	$0.702914\pi$
$500$	−0.804166	−	5.14172i	−0.0359634	−	0.229945i
$501$	5.44868	+	5.24365i	0.243429	+	0.234269i
$502$	−19.5631	+	1.52059i	−0.873143	+	0.0678674i
$503$	−17.2129			−0.767486			−0.383743	−	0.923440i	$-0.625365\pi$
$503$	−17.2129			−0.767486			−0.383743	+	0.923440i	$0.625365\pi$
$504$	−8.17546	+	2.27196i	−0.364164	+	0.101201i
$505$	0.740123			0.0329351
$506$	5.57870	−	0.433620i	0.248004	−	0.0192767i
$507$	−11.6631	+	3.36606i	−0.517978	+	0.149492i
$508$	6.59130	−	1.03088i	0.292442	−	0.0457380i
$509$	25.4326	+	14.6835i	1.12728	+	0.650834i	0.943249	−	0.332087i	$-0.107753\pi$
$509$	25.4326	+	14.6835i	1.12728	+	0.650834i	0.184029	+	0.982921i	$0.441086\pi$
$510$	−3.93498	−	3.23879i	−0.174244	−	0.143416i
$511$	−4.82384	−	8.35514i	−0.213394	−	0.369610i
$512$	14.5449	+	17.3334i	0.642798	+	0.766036i
$513$	22.5546	+	20.0986i	0.995809	+	0.887373i
$514$	−1.71246	−	0.818839i	−0.0755335	−	0.0361174i
$515$	−0.718213	+	0.414660i	−0.0316482	+	0.0182721i
$516$	7.03578	+	15.0968i	0.309733	+	0.664601i
$517$	23.7131	+	13.6907i	1.04290	+	0.602118i
$518$	4.04422	+	5.89660i	0.177693	+	0.259082i
$519$	5.24764	+	18.1826i	0.230346	+	0.798129i
$520$	−1.31943	+	1.24483i	−0.0578606	+	0.0545892i
$521$	−20.2603			−0.887620			−0.443810	−	0.896121i	$-0.646374\pi$
$521$	−20.2603			−0.887620			−0.443810	+	0.896121i	$0.646374\pi$
$522$	0.906972	+	7.78925i	0.0396971	+	0.340926i
$523$		−	15.7899i		−	0.690446i	−0.938521	−	0.345223i	$-0.887803\pi$
$523$		−	15.7899i		−	0.690446i	0.938521	−	0.345223i	$-0.112197\pi$
$524$	−14.8990	−	5.75230i	−0.650864	−	0.251290i
$525$	−6.15433	−	5.92275i	−0.268597	−	0.258490i
$526$	25.2365	−	17.3086i	1.10036	−	0.754691i
$527$	26.9797	−	46.7301i	1.17525	−	2.03560i
$528$	−9.75459	−	14.5292i	−0.424514	−	0.632300i
$529$	10.2732	+	17.7936i	0.446659	+	0.773636i
$530$	3.99866	+	1.91202i	0.173691	+	0.0830527i
$531$	18.6206	+	29.5725i	0.808066	+	1.28334i
$532$	−9.05076	+	7.30019i	−0.392400	+	0.316503i
$533$	−13.6033	+	7.85388i	−0.589225	+	0.340189i
$534$	−0.406682	−	0.0677412i	−0.0175988	−	0.00293145i
$535$	−0.882711	+	1.52890i	−0.0381629	+	0.0661001i
$536$	4.19590	−	14.0155i	0.181235	−	0.605379i
$537$	−7.98124	−	1.97538i	−0.344416	−	0.0852439i
$538$	−13.3457	+	1.03733i	−0.575375	+	0.0447225i
$539$			2.52590i			0.108798i
$540$	−2.42212	+	1.24397i	−0.104231	+	0.0535322i
$541$			36.4356i			1.56649i	0.621713	+	0.783245i	$0.286437\pi$
$541$			36.4356i			1.56649i	−0.621713	+	0.783245i	$0.713563\pi$
$542$	−0.899719	−	11.5753i	−0.0386462	−	0.497201i
$543$	21.7792	+	5.39041i	0.934634	+	0.231324i
$544$	16.9894	+	41.5843i	0.728416	+	1.78291i
$545$	−0.561540	+	0.972617i	−0.0240537	+	0.0416623i
$546$	−0.985138	+	5.91424i	−0.0421600	+	0.253106i
$547$	2.04005	−	1.17782i	0.0872261	−	0.0503600i	−0.455753	−	0.890107i	$-0.650630\pi$
$547$	2.04005	−	1.17782i	0.0872261	−	0.0503600i	0.542979	+	0.839747i	$0.317296\pi$
$548$	−5.43203	−	6.73462i	−0.232045	−	0.287689i
$549$	43.6648	−	1.67516i	1.86357	−	0.0714939i
$550$	7.59910	−	15.8922i	0.324027	−	0.677647i
$551$	5.37312	+	9.30652i	0.228903	+	0.396471i
$552$	−3.90263	+	6.60743i	−0.166107	+	0.281231i
$553$	−1.84252	+	3.19133i	−0.0783517	+	0.135709i
$554$	−22.9177	−	33.4147i	−0.973679	−	1.41965i
$555$	1.65324	+	1.59103i	0.0701762	+	0.0675356i
$556$	−23.4456	−	9.05206i	−0.994316	−	0.383893i
$557$		−	43.0571i		−	1.82439i	−0.409759	−	0.912194i	$-0.634387\pi$
$557$		−	43.0571i		−	1.82439i	0.409759	−	0.912194i	$-0.365613\pi$
$558$	−17.2053	−	23.1319i	−0.728359	−	0.979251i
$559$	11.7691			0.497779
$560$	−0.320000	−	0.997992i	−0.0135225	−	0.0421729i
$561$	−9.63352	−	33.3794i	−0.406727	−	1.40928i
$562$	−7.32116	+	5.02127i	−0.308825	+	0.211809i
$563$	−10.6713	−	6.16109i	−0.449743	−	0.259659i	0.257979	−	0.966151i	$-0.416944\pi$
$563$	−10.6713	−	6.16109i	−0.449743	−	0.259659i	−0.707722	+	0.706491i	$0.750277\pi$
$564$	−34.0370	+	15.8627i	−1.43321	+	0.667941i
$565$	−2.76122	+	1.59419i	−0.116165	+	0.0670681i
$566$	−4.81214	+	10.0638i	−0.202269	+	0.423012i
$567$	−3.88962	+	8.11609i	−0.163349	+	0.340844i
$568$	−8.58933	−	36.2405i	−0.360400	−	1.52062i
$569$	−17.2836	−	29.9361i	−0.724567	−	1.25499i	−0.959152	−	0.282891i	$-0.908706\pi$
$569$	−17.2836	−	29.9361i	−0.724567	−	1.25499i	0.234585	−	0.972096i	$-0.424627\pi$
$570$	−2.37127	+	2.88099i	−0.0993215	+	0.120671i
$571$	−36.7501	−	21.2177i	−1.53795	−	0.887933i	−0.998959	−	0.0456184i	$-0.985474\pi$
$571$	−36.7501	−	21.2177i	−1.53795	−	0.887933i	−0.538986	−	0.842315i	$-0.681192\pi$
$572$	−12.2170	+	1.91074i	−0.510819	+	0.0798922i
$573$	−24.4500	+	7.05645i	−1.02141	+	0.294787i
$574$	−0.703283	−	9.04804i	−0.0293545	−	0.377658i
$575$	−7.72460			−0.322138
$576$	23.9953	+	0.475729i	0.999804	+	0.0198221i
$577$	8.93965			0.372162			0.186081	−	0.982534i	$-0.440421\pi$
$577$	8.93965			0.372162			0.186081	+	0.982534i	$0.440421\pi$
$578$	5.04777	+	64.9417i	0.209959	+	2.70122i
$579$	26.5865	+	25.5861i	1.10490	+	1.06332i
$580$	−0.956938	+	0.149665i	−0.0397347	+	0.00621452i
$581$	−7.77411	−	4.48838i	−0.322524	−	0.186210i
$582$	−2.36176	−	6.30238i	−0.0978982	−	0.261242i
$583$	15.1071	+	26.1662i	0.625671	+	1.08369i
$584$	6.29311	+	26.5522i	0.260411	+	1.09874i
$585$	0.0737582	+	1.92259i	0.00304952	+	0.0794892i
$586$	−16.0101	+	33.4823i	−0.661369	+	1.38314i
$587$	−8.64317	+	4.99014i	−0.356742	+	0.205965i	−0.667651	−	0.744475i	$-0.732700\pi$
$587$	−8.64317	+	4.99014i	−0.356742	+	0.205965i	0.310909	+	0.950440i	$0.399367\pi$
$588$	−2.83719	−	1.98754i	−0.117004	−	0.0819649i
$589$	−34.2134	−	19.7531i	−1.40974	−	0.813912i
$590$	−3.55957	+	2.44136i	−0.146545	+	0.100509i
$591$	13.1556	+	3.25605i	0.541150	+	0.133936i
$592$	−6.17499	−	19.2581i	−0.253790	−	0.791503i
$593$	19.2451			0.790303			0.395152	−	0.918616i	$-0.370692\pi$
$593$	19.2451			0.790303			0.395152	+	0.918616i	$0.370692\pi$
$594$	−18.4127	−	2.34564i	−0.755482	−	0.0962427i
$595$		−	2.08062i		−	0.0852970i
$596$	−11.0494	−	4.26602i	−0.452600	−	0.174743i
$597$	0.437538	−	1.76781i	0.0179072	−	0.0723516i
$598$	3.06695	+	4.47171i	0.125417	+	0.182862i
$599$	17.7148	−	30.6829i	0.723806	−	1.25367i	−0.235657	−	0.971836i	$-0.575724\pi$
$599$	17.7148	−	30.6829i	0.723806	−	1.25367i	0.959463	−	0.281833i	$-0.0909425\pi$
$600$	11.8713	+	21.0406i	0.484645	+	0.858981i
$601$	−9.20477	−	15.9431i	−0.375470	−	0.650334i	0.614927	−	0.788584i	$-0.289185\pi$
$601$	−9.20477	−	15.9431i	−0.375470	−	0.650334i	−0.990397	+	0.138250i	$0.955852\pi$
$602$	−2.93329	+	6.13448i	−0.119552	+	0.250023i
$603$	−8.26827	−	13.1313i	−0.336710	−	0.534748i
$604$	25.7851	+	31.9683i	1.04918	+	1.30077i
$605$	1.04827	−	0.605220i	0.0426183	−	0.0246057i
$606$	−6.47929	+	2.42806i	−0.263203	+	0.0986331i
$607$	−21.6066	+	37.4237i	−0.876985	+	1.51898i	−0.0223522	+	0.999750i	$0.507116\pi$
$607$	−21.6066	+	37.4237i	−0.876985	+	1.51898i	−0.854633	+	0.519233i	$0.826218\pi$
$608$	30.4458	−	12.4388i	1.23474	−	0.504459i
$609$	−2.21994	+	2.30674i	−0.0899565	+	0.0934738i
$610$	0.418244	+	5.38089i	0.0169342	+	0.217866i
$611$			26.5343i			1.07346i
$612$	45.0733	+	15.4443i	1.82198	+	0.624298i
$613$		−	41.3206i		−	1.66892i	−0.551065	−	0.834462i	$-0.685778\pi$
$613$		−	41.3206i		−	1.66892i	0.551065	−	0.834462i	$-0.314222\pi$
$614$	−4.89069	+	0.380142i	−0.197372	+	0.0153413i
$615$	−0.807532	−	2.79803i	−0.0325628	−	0.112828i
$616$	2.04898	−	6.84420i	0.0825560	−	0.275761i
$617$	5.22793	−	9.05504i	0.210469	−	0.364542i	−0.741393	−	0.671071i	$-0.765834\pi$
$617$	5.22793	−	9.05504i	0.210469	−	0.364542i	0.951861	+	0.306529i	$0.0991677\pi$
$618$	4.92714	−	5.98625i	0.198199	−	0.240802i
$619$	−3.74664	+	2.16312i	−0.150590	+	0.0869432i	−0.573402	−	0.819274i	$-0.694377\pi$
$619$	−3.74664	+	2.16312i	−0.150590	+	0.0869432i	0.422812	+	0.906218i	$0.361043\pi$
$620$	2.77155	−	2.23548i	0.111308	−	0.0897792i
$621$	2.55510	+	7.72794i	0.102533	+	0.310112i
$622$	−31.0669	−	14.8551i	−1.24567	−	0.595634i
$623$	−0.0841574	−	0.145765i	−0.00337169	−	0.00583994i
$624$	7.46691	−	15.2261i	0.298916	−	0.609534i
$625$	−11.9875	+	20.7629i	−0.479499	+	0.830517i
$626$	13.6597	−	9.36862i	0.545953	−	0.374446i
$627$	−24.4386	+	7.05316i	−0.975984	+	0.281676i
$628$	−0.637225	−	0.246024i	−0.0254280	−	0.00981744i
$629$		−	40.1493i		−	1.60086i
$630$	−1.02051	−	0.440735i	−0.0406581	−	0.0175593i
$631$	16.8833			0.672112			0.336056	−	0.941842i	$-0.390907\pi$
$631$	16.8833			0.672112			0.336056	+	0.941842i	$0.390907\pi$
$632$	7.58127	−	7.15262i	0.301567	−	0.284516i
$633$	22.7644	−	23.6545i	0.904805	−	0.940182i
$634$	18.5317	+	27.0197i	0.735987	+	1.07309i
$635$	0.756898	+	0.436995i	0.0300366	+	0.0173416i
$636$	−41.2782	−	3.62040i	−1.63679	−	0.143558i
$637$	−2.11981	+	1.22387i	−0.0839900	+	0.0484916i
$638$	−5.95666	−	2.84826i	−0.235826	−	0.112764i
$639$	−34.9433	−	18.4258i	−1.38233	−	0.728914i
$640$	0.0575132	+	2.96375i	0.00227341	+	0.117152i
$641$	1.30346	+	2.25766i	0.0514835	+	0.0891721i	0.890619	−	0.454751i	$-0.150272\pi$
$641$	1.30346	+	2.25766i	0.0514835	+	0.0891721i	−0.839135	+	0.543923i	$0.816938\pi$
$642$	2.71182	−	16.2803i	0.107027	−	0.642534i
$643$	11.8684	+	6.85224i	0.468045	+	0.270226i	0.715421	−	0.698694i	$-0.246235\pi$
$643$	11.8684	+	6.85224i	0.468045	+	0.270226i	−0.247376	+	0.968920i	$0.579568\pi$
$644$	−3.09523	+	0.484094i	−0.121969	+	0.0190760i
$645$	−0.524232	+	2.11809i	−0.0206416	+	0.0833996i
$646$	65.0960	−	5.05976i	2.56117	−	0.199074i
$647$	−13.9543			−0.548601			−0.274301	−	0.961644i	$-0.588446\pi$
$647$	−13.9543			−0.548601			−0.274301	+	0.961644i	$0.588446\pi$
$648$	17.1230	−	18.8362i	0.672656	−	0.739956i
$649$	−29.4238			−1.15499
$650$	17.0192	−	1.32286i	0.667548	−	0.0518870i
$651$	2.82763	−	11.4246i	0.110823	−	0.447767i
$652$	2.01761	+	12.9003i	0.0790159	+	0.505216i
$653$	−10.2203	−	5.90067i	−0.399950	−	0.230911i	0.286513	−	0.958076i	$-0.407504\pi$
$653$	−10.2203	−	5.90067i	−0.399950	−	0.230911i	−0.686462	+	0.727165i	$0.740837\pi$
$654$	1.72514	−	10.3568i	0.0674583	−	0.404983i
$655$	−1.04613	−	1.81195i	−0.0408757	−	0.0707988i
$656$	−5.43406	+	25.0871i	−0.212164	+	0.979488i
$657$	25.6018	+	13.5000i	0.998820	+	0.526685i
$658$	−13.8307	−	6.61333i	−0.539175	−	0.257815i
$659$	−16.0381	+	9.25963i	−0.624757	+	0.360704i	−0.778719	−	0.627373i	$-0.784130\pi$
$659$	−16.0381	+	9.25963i	−0.624757	+	0.360704i	0.153962	+	0.988077i	$0.450797\pi$
$660$	0.200307	−	2.28381i	0.00779694	−	0.0888974i
$661$	0.944132	+	0.545095i	0.0367225	+	0.0212017i	0.518249	−	0.855230i	$-0.326584\pi$
$661$	0.944132	+	0.545095i	0.0367225	+	0.0212017i	−0.481526	+	0.876432i	$0.659917\pi$
$662$	4.80242	+	7.00208i	0.186651	+	0.272144i
$663$	23.3452	−	24.2580i	0.906653	−	0.942103i
$664$	17.4238	+	18.4680i	0.676176	+	0.716699i
$665$	−1.52332			−0.0590718
$666$	−19.6926	−	8.50480i	−0.763073	−	0.329554i
$667$			2.89530i			0.112107i
$668$	3.14500	−	8.14582i	0.121684	−	0.315171i
$669$	22.3332	−	6.44552i	0.863452	−	0.249198i
$670$	1.58059	−	1.08406i	0.0610634	−	0.0418807i
$671$	−18.3957	+	31.8622i	−0.710157	+	1.23003i
$672$	6.07541	+	7.68696i	0.234364	+	0.296531i
$673$	−5.69153	−	9.85802i	−0.219392	−	0.379999i	0.735230	−	0.677818i	$-0.237074\pi$
$673$	−5.69153	−	9.85802i	−0.219392	−	0.379999i	−0.954622	+	0.297819i	$0.903741\pi$
$674$	−3.62844	−	1.73499i	−0.139762	−	0.0668293i
$675$	25.0912	+	5.19819i	0.965763	+	0.200078i
$676$	8.80012	+	10.9104i	0.338466	+	0.419630i
$677$	22.6414	−	13.0720i	0.870179	−	0.502398i	0.00277102	−	0.999996i	$-0.499118\pi$
$677$	22.6414	−	13.0720i	0.870179	−	0.502398i	0.867408	+	0.497598i	$0.165785\pi$
$678$	18.9427	−	23.0146i	0.727491	−	0.883869i
$679$	1.37383	−	2.37955i	0.0527228	−	0.0913186i
$680$	−1.68778	+	5.63766i	−0.0647232	+	0.216194i
$681$	4.39199	+	15.2179i	0.168302	+	0.583151i
$682$	24.2000	−	1.88101i	0.926666	−	0.0720276i
$683$		−	16.2899i		−	0.623316i	−0.950194	−	0.311658i	$-0.899116\pi$
$683$		−	16.2899i		−	0.623316i	0.950194	−	0.311658i	$-0.100884\pi$
$684$	11.3075	−	33.0003i	0.432353	−	1.26180i
$685$		−	1.13349i		−	0.0433086i
$686$	−0.109593	−	1.40996i	−0.00418428	−	0.0538326i
$687$	13.2380	−	13.7556i	0.505060	−	0.524807i
$688$	12.9243	−	14.2426i	0.492734	−	0.542994i
$689$	−14.6396	+	25.3566i	−0.557726	+	0.966010i
$690$	−0.941389	+	0.352777i	−0.0358381	+	0.0134300i
$691$	−2.71935	+	1.57002i	−0.103449	+	0.0597263i	−0.550832	−	0.834616i	$-0.685689\pi$
$691$	−2.71935	+	1.57002i	−0.103449	+	0.0597263i	0.447383	+	0.894343i	$0.352356\pi$
$692$	17.0091	−	13.7193i	0.646589	−	0.521528i
$693$	−4.03764	−	6.41241i	−0.153377	−	0.243587i
$694$	−7.68638	+	16.0748i	−0.291771	+	0.610190i
$695$	−1.64624	−	2.85136i	−0.0624453	−	0.108158i
$696$	7.88637	−	4.44956i	0.298932	−	0.168660i
$697$	−25.4796	+	44.1319i	−0.965107	+	1.67161i
$698$	−12.7200	−	18.5462i	−0.481460	−	0.701984i
$699$	4.44365	−	17.9539i	0.168074	−	0.679080i
$700$	−3.55230	+	9.20076i	−0.134264	+	0.347756i
$701$			12.5736i			0.474899i	0.971400	+	0.237449i	$0.0763114\pi$
$701$			12.5736i			0.474899i	−0.971400	+	0.237449i	$0.923689\pi$
$702$	−6.95296	−	16.5890i	−0.262423	−	0.626112i
$703$	−29.3952			−1.10866
$704$	−11.1039	+	16.8830i	−0.418494	+	0.636301i
$705$	−4.77539	−	1.18192i	−0.179852	−	0.0445137i
$706$	−27.6019	+	18.9309i	−1.03881	+	0.712475i
$707$	−2.44634	−	1.41240i	−0.0920041	−	0.0531186i
$708$	23.1526	−	33.0500i	0.870126	−	1.24210i
$709$	16.5781	−	9.57137i	0.622604	−	0.359460i	−0.155278	−	0.987871i	$-0.549627\pi$
$709$	16.5781	−	9.57137i	0.622604	−	0.359460i	0.777882	+	0.628410i	$0.216294\pi$
$710$	2.10482	−	4.40187i	0.0789924	−	0.165199i
$711$	−0.423806	−	11.0470i	−0.0158940	−	0.414294i
$712$	0.109790	+	0.463233i	0.00411457	+	0.0173604i
$713$	−5.32197	−	9.21792i	−0.199309	−	0.345214i
$714$	6.82569	+	18.2144i	0.255445	+	0.681658i
$715$	−1.40291	−	0.809973i	−0.0524660	−	0.0302913i
$716$	1.46703	+	9.37999i	0.0548256	+	0.350547i
$717$	14.8729	+	14.3132i	0.555437	+	0.534537i
$718$	−1.09827	−	14.1297i	−0.0409871	−	0.527316i
$719$	29.8775			1.11424			0.557121	−	0.830431i	$-0.311906\pi$
$719$	29.8775			1.11424			0.557121	+	0.830431i	$0.311906\pi$
$720$	2.40766	+	2.02205i	0.0897281	+	0.0753572i
$721$	3.16522			0.117879
$722$	−1.62222	−	20.8706i	−0.0603729	−	0.776723i
$723$	−6.13314	+	1.77007i	−0.228094	+	0.0658295i
$724$	−4.00324	−	25.5961i	−0.148779	−	0.951271i
$725$	7.89369	+	4.55743i	0.293164	+	0.169259i
$726$	−7.19143	+	8.73727i	−0.266899	+	0.324271i
$727$	−4.98386	−	8.63229i	−0.184841	−	0.320154i	0.758682	−	0.651461i	$-0.225844\pi$
$727$	−4.98386	−	8.63229i	−0.184841	−	0.320154i	−0.943523	+	0.331307i	$0.892510\pi$
$728$	6.73665	−	1.59665i	0.249677	−	0.0591757i
$729$	−3.09912	−	26.8215i	−0.114782	−	0.993391i
$730$	−1.54213	+	3.22510i	−0.0570768	+	0.119366i
$731$	33.0659	−	19.0906i	1.22299	−	0.706092i
$732$	−21.3141	−	45.7340i	−0.787790	−	1.69038i
$733$	−26.0739	−	15.0538i	−0.963062	−	0.556024i	−0.0659479	−	0.997823i	$-0.521007\pi$
$733$	−26.0739	−	15.0538i	−0.963062	−	0.556024i	−0.897114	+	0.441799i	$0.854340\pi$
$734$	33.5861	−	23.0352i	1.23968	−	0.850246i
$735$	−0.125838	−	0.436019i	−0.00464161	−	0.0160828i
$736$	8.77954	+	1.19911i	0.323618	+	0.0441998i
$737$	13.0653			0.481267
$738$	16.2487	+	21.8457i	0.598122	+	0.804153i
$739$			22.4457i			0.825678i	0.910804	+	0.412839i	$0.135463\pi$
$739$			22.4457i			0.825678i	−0.910804	+	0.412839i	$0.864537\pi$
$740$	0.954257	−	2.47161i	0.0350792	−	0.0908582i
$741$	−17.7604	−	17.0921i	−0.652446	−	0.627896i
$742$	−9.56808	−	13.9506i	−0.351255	−	0.512141i
$743$	−8.33676	+	14.4397i	−0.305846	+	0.529741i	−0.977449	−	0.211170i	$-0.932273\pi$
$743$	−8.33676	+	14.4397i	−0.305846	+	0.529741i	0.671603	+	0.740911i	$0.265606\pi$
$744$	−16.9293	+	28.6625i	−0.620659	+	1.05082i
$745$	−0.775832	−	1.34378i	−0.0284243	−	0.0492323i
$746$	15.1265	−	31.6346i	0.553822	−	1.15822i
$747$	26.9105	−	1.03239i	0.984604	−	0.0377733i
$748$	−31.2250	+	25.1856i	−1.14170	+	0.920876i
$749$	5.83527	−	3.36900i	0.213216	−	0.123100i
$750$	−1.04727	+	6.28722i	−0.0382407	+	0.229577i
$751$	−9.12047	+	15.7971i	−0.332811	+	0.576445i	−0.983062	−	0.183274i	$-0.941330\pi$
$751$	−9.12047	+	15.7971i	−0.332811	+	0.576445i	0.650251	+	0.759719i	$0.274664\pi$
$752$	32.1110	+	29.1388i	1.17097	+	1.06258i
$753$	23.3282	+	5.77378i	0.850125	+	0.210408i
$754$	−0.495830	−	6.37907i	−0.0180571	−	0.232312i
$755$			5.38053i			0.195818i
$756$	10.3798	+	0.510454i	0.377508	+	0.0185650i
$757$		−	28.5453i		−	1.03750i	−0.854927	−	0.518748i	$-0.826398\pi$
$757$		−	28.5453i		−	1.03750i	0.854927	−	0.518748i	$-0.173602\pi$
$758$	−27.9605	+	2.17330i	−1.01557	+	0.0789380i
$759$	−6.65237	−	1.64648i	−0.241466	−	0.0597634i
$760$	4.12759	+	1.23570i	0.149724	+	0.0448236i
$761$	−1.92443	+	3.33322i	−0.0697607	+	0.120829i	−0.898796	−	0.438367i	$-0.855557\pi$
$761$	−1.92443	+	3.33322i	−0.0697607	+	0.120829i	0.829035	+	0.559196i	$0.188890\pi$
$762$	−8.05975	−	1.34252i	−0.291974	−	0.0486343i
$763$	3.71214	−	2.14320i	0.134388	−	0.0775891i
$764$	18.4482	+	22.8720i	0.667431	+	0.827480i
$765$	3.32586	+	5.28199i	0.120247	+	0.190971i
$766$	−34.1920	−	16.3494i	−1.23541	−	0.590727i
$767$	−14.2567	−	24.6933i	−0.514779	−	0.891624i
$768$	−10.2264	−	25.7570i	−0.369013	−	0.929424i
$769$	−6.22953	+	10.7899i	−0.224642	+	0.389092i	−0.956212	−	0.292675i	$-0.905455\pi$
$769$	−6.22953	+	10.7899i	−0.224642	+	0.389092i	0.731570	+	0.681767i	$0.238788\pi$
$770$	0.771848	−	0.529377i	0.0278155	−	0.0190774i
$771$	1.67507	+	1.61204i	0.0603262	+	0.0580563i
$772$	15.3458	−	39.7470i	0.552308	−	1.43053i
$773$			37.3529i			1.34349i	0.740783	+	0.671745i	$0.234455\pi$
$773$			37.3529i			1.34349i	−0.740783	+	0.671745i	$0.765545\pi$
$774$	−2.35931	−	20.2622i	−0.0848038	−	0.728311i
$775$	−33.5087			−1.20367
$776$	−5.65281	+	5.33320i	−0.202924	+	0.191451i
$777$	−2.42828	−	8.41379i	−0.0871140	−	0.301843i
$778$	−12.6242	−	18.4065i	−0.452600	−	0.659905i
$779$	32.3111	+	18.6548i	1.15766	+	0.668377i
$780$	2.01370	−	0.938471i	0.0721020	−	0.0336027i
$781$	28.8047	−	16.6304i	1.03071	−	0.595083i
$782$	15.8704	+	7.58864i	0.567523	+	0.271369i
$783$	1.94836	−	9.40460i	0.0696288	−	0.336093i
$784$	−0.846792	+	3.90934i	−0.0302426	+	0.139619i
$785$	−0.0447427	−	0.0774967i	−0.00159694	−	0.00276597i
$786$	15.1025	+	12.4305i	0.538688	+	0.443381i
$787$	38.9082	+	22.4637i	1.38693	+	0.800744i	0.992968	−	0.118384i	$-0.0377713\pi$
$787$	38.9082	+	22.4637i	1.38693	+	0.800744i	0.393961	+	0.919127i	$0.371105\pi$
$788$	−2.41814	−	15.4612i	−0.0861426	−	0.550783i
$789$	−36.0097	+	10.3926i	−1.28198	+	0.369988i
$790$	1.36134	−	0.105814i	0.0484342	−	0.00376468i
$791$	12.1689			0.432677
$792$	5.73875	+	20.6504i	0.203918	+	0.733780i
$793$	−35.6530			−1.26607
$794$	48.6763	−	3.78350i	1.72746	−	0.134271i
$795$	−3.91135	−	3.76417i	−0.138721	−	0.133501i
$796$	−2.07763	+	0.324941i	−0.0736395	+	0.0115172i
$797$	−13.6194	−	7.86317i	−0.482424	−	0.278528i	0.239002	−	0.971019i	$-0.423180\pi$
$797$	−13.6194	−	7.86317i	−0.482424	−	0.278528i	−0.721426	+	0.692491i	$0.756513\pi$
$798$	13.3356	−	4.99741i	0.472077	−	0.176907i
$799$	43.0412	+	74.5496i	1.52269	+	2.63738i
$800$	17.0889	−	22.0489i	0.604184	−	0.779545i
$801$	0.446652	+	0.235522i	0.0157817	+	0.00832178i
$802$	4.20847	+	2.01234i	0.148606	+	0.0710583i
$803$	−21.1043	+	12.1845i	−0.744753	+	0.429983i
$804$	−10.2806	+	14.6755i	−0.362570	+	0.517564i
$805$	−0.355434	−	0.205210i	−0.0125274	−	0.00723269i
$806$	13.3042	+	19.3980i	0.468621	+	0.683264i
$807$	15.9142	+	3.93881i	0.560207	+	0.138653i
$808$	5.48290	+	5.81148i	0.192888	+	0.204447i
$809$	−16.9889			−0.597298			−0.298649	−	0.954363i	$-0.596536\pi$
$809$	−16.9889			−0.597298			−0.298649	+	0.954363i	$0.596536\pi$
$810$	3.29524	−	0.512402i	0.115783	−	0.0180040i
$811$		−	38.0773i		−	1.33707i	−0.743679	−	0.668537i	$-0.766921\pi$
$811$		−	38.0773i		−	1.33707i	0.743679	−	0.668537i	$-0.233079\pi$
$812$	3.44859	+	1.33146i	0.121022	+	0.0467250i
$813$	−3.41629	+	13.8030i	−0.119814	+	0.484093i
$814$	14.8942	−	10.2153i	0.522042	−	0.358046i
$815$	−0.855276	+	1.48138i	−0.0299590	+	0.0518905i
$816$	−3.71960	−	54.8909i	−0.130212	−	1.92156i
$817$	−13.9771	−	24.2091i	−0.488998	−	0.846970i
$818$	7.48235	+	3.57780i	0.261614	+	0.125095i
$819$	3.42513	−	6.49551i	0.119684	−	0.226972i
$820$	−2.61745	+	2.11119i	−0.0914052	+	0.0737259i
$821$	22.3177	−	12.8851i	0.778892	−	0.449694i	−0.0571452	−	0.998366i	$-0.518200\pi$
$821$	22.3177	−	12.8851i	0.778892	−	0.449694i	0.836038	+	0.548672i	$0.184866\pi$
$822$	3.71855	+	9.92298i	0.129699	+	0.346104i
$823$	−3.08031	+	5.33525i	−0.107373	+	0.185975i	−0.914705	−	0.404122i	$-0.867577\pi$
$823$	−3.08031	+	5.33525i	−0.107373	+	0.185975i	0.807332	+	0.590097i	$0.200911\pi$
$824$	−8.57652	−	2.56760i	−0.298777	−	0.0894465i
$825$	−14.9603	+	15.5452i	−0.520850	+	0.541215i
$826$	16.4244	−	1.27663i	0.571478	−	0.0444196i
$827$		−	47.7039i		−	1.65883i	−0.558635	−	0.829414i	$-0.688675\pi$
$827$		−	47.7039i		−	1.65883i	0.558635	−	0.829414i	$-0.311325\pi$
$828$	7.08391	−	6.17666i	0.246183	−	0.214654i
$829$			22.9097i			0.795686i	0.917453	+	0.397843i	$0.130241\pi$
$829$			22.9097i			0.795686i	−0.917453	+	0.397843i	$0.869759\pi$
$830$	0.257763	+	3.31623i	0.00894708	+	0.115108i
$831$	13.7605	+	47.6791i	0.477347	+	1.65397i
$832$	−19.5489	−	1.13841i	−0.677734	−	0.0394674i
$833$	−3.97049	+	6.87709i	−0.137569	+	0.238277i
$834$	23.7659	+	19.5611i	0.822946	+	0.677347i
$835$	0.990661	−	0.571959i	0.0342833	−	0.0197934i
$836$	18.4396	+	22.8613i	0.637745	+	0.790675i
$837$	11.0839	+	33.5233i	0.383114	+	1.15873i
$838$	9.41493	−	19.6897i	0.325233	−	0.680171i
$839$	11.9910	+	20.7690i	0.413974	+	0.717024i	0.995320	−	0.0966323i	$-0.0308071\pi$
$839$	11.9910	+	20.7690i	0.413974	+	0.717024i	−0.581346	+	0.813656i	$0.697474\pi$
$840$	−0.0127222	+	1.28352i	−0.000438959	+	0.0442856i
$841$	−12.7918	+	22.1561i	−0.441097	+	0.764002i
$842$	−2.51971	−	3.67382i	−0.0868349	−	0.126608i
$843$	10.4465	−	3.01493i	0.359796	−	0.103840i
$844$	−35.3637	−	13.6535i	−1.21727	−	0.469971i
$845$			1.83631i			0.0631709i
$846$	45.6828	−	5.31925i	1.57061	−	0.182880i
$847$	−4.61982			−0.158739
$848$	14.6092	+	45.5621i	0.501682	+	1.56461i
$849$	9.47362	−	9.84403i	0.325134	−	0.337846i
$850$	45.6707	−	31.3235i	1.56649	−	1.07439i
$851$	−6.85875	−	3.95990i	−0.235115	−	0.135744i
$852$	−3.98546	+	45.4405i	−0.136540	+	1.55677i
$853$	−23.7043	+	13.6857i	−0.811621	+	0.468589i	−0.847518	−	0.530766i	$-0.821904\pi$
$853$	−23.7043	+	13.6857i	−0.811621	+	0.468589i	0.0358977	+	0.999355i	$0.488571\pi$
$854$	8.88605	−	18.5837i	0.304075	−	0.635920i
$855$	3.86719	−	2.43502i	0.132255	−	0.0832759i
$856$	−18.5442	+	4.39514i	−0.633828	+	0.150223i
$857$	24.5992	+	42.6070i	0.840291	+	1.45543i	0.889648	+	0.456646i	$0.150949\pi$
$857$	24.5992	+	42.6070i	0.840291	+	1.45543i	−0.0493571	+	0.998781i	$0.515717\pi$
$858$	14.9388	+	2.48836i	0.510002	+	0.0849513i
$859$	−40.9962	−	23.6692i	−1.39877	−	0.807582i	−0.404510	−	0.914534i	$-0.632558\pi$
$859$	−40.9962	−	23.6692i	−1.39877	−	0.807582i	−0.994264	+	0.106951i	$0.965891\pi$
$860$	2.48929	−	0.389326i	0.0848841	−	0.0132759i
$861$	−2.67041	+	10.7894i	−0.0910073	+	0.367702i
$862$	−1.28486	−	16.5303i	−0.0437626	−	0.563025i
$863$	7.84887			0.267179			0.133589	−	0.991037i	$-0.457350\pi$
$863$	7.84887			0.267179			0.133589	+	0.991037i	$0.457350\pi$
$864$	−27.7110	−	9.80308i	−0.942747	−	0.333508i
$865$	2.86278			0.0973373
$866$	3.59052	+	46.1936i	0.122011	+	1.56972i
$867$	19.1667	−	77.4403i	0.650934	−	2.63001i
$868$	−13.4269	+	2.09996i	−0.455737	+	0.0712774i
$869$	8.06098	+	4.65401i	0.273450	+	0.157877i
$870$	1.17013	+	0.194909i	0.0396712	+	0.00660804i
$871$	6.33052	+	10.9648i	0.214502	+	0.371528i
$872$	−11.7970	+	2.79599i	−0.399496	+	0.0946842i
$873$	0.316002	+	8.23693i	0.0106950	+	0.278778i
$874$	5.55600	−	11.6194i	0.187935	−	0.393034i
$875$	−2.25350	+	1.30106i	−0.0761821	+	0.0439837i
$876$	2.92002	−	33.2928i	0.0986582	−	1.12486i
$877$	43.8304	+	25.3055i	1.48005	+	0.854506i	0.999745	−	0.0225971i	$-0.00719348\pi$
$877$	43.8304	+	25.3055i	1.48005	+	0.854506i	0.480303	+	0.877103i	$0.340527\pi$
$878$	−36.6294	+	25.1225i	−1.23618	+	0.847843i
$879$	31.5188	−	32.7512i	1.06310	−	1.10467i
$880$	−2.52083	+	0.808288i	−0.0849771	+	0.0272474i
$881$	−12.6339			−0.425648			−0.212824	−	0.977091i	$-0.568266\pi$
$881$	−12.6339			−0.425648			−0.212824	+	0.977091i	$0.568266\pi$
$882$	2.53204	+	3.40423i	0.0852581	+	0.114626i
$883$			34.9981i			1.17778i	0.808213	+	0.588890i	$0.200435\pi$
$883$			34.9981i			1.17778i	−0.808213	+	0.588890i	$0.799565\pi$
$884$	−36.2659	−	14.0018i	−1.21975	−	0.470932i
$885$	5.07911	−	1.46587i	0.170732	−	0.0492746i
$886$	2.70602	+	3.94547i	0.0909106	+	0.132551i
$887$	−0.701213	+	1.21454i	−0.0235444	+	0.0407802i	−0.877558	−	0.479471i	$-0.840828\pi$
$887$	−0.701213	+	1.21454i	−0.0235444	+	0.0407802i	0.854013	+	0.520251i	$0.174162\pi$
$888$	−0.245499	+	24.7679i	−0.00823841	+	0.831155i
$889$	−1.66786	−	2.88881i	−0.0559382	−	0.0968877i
$890$	−0.0269042	+	0.0562655i	−0.000901830	+	0.00188602i
$891$	20.5004	+	9.82479i	0.686790	+	0.329143i
$892$	−16.8510	−	20.8918i	−0.564213	−	0.699510i
$893$	54.5813	−	31.5125i	1.82649	−	1.05453i
$894$	11.2003	+	9.21870i	0.374595	+	0.308320i
$895$	−0.621882	+	1.07713i	−0.0207872	+	0.0360045i
$896$	5.46569	−	9.90587i	0.182596	−	0.330932i
$897$	−1.84150	−	6.38064i	−0.0614858	−	0.213043i
$898$	3.02437	+	38.9099i	0.100925	+	1.29844i
$899$			12.5596i			0.418886i
$900$	−5.68931	−	29.0360i	−0.189644	−	0.967866i
$901$			94.9879i			3.16451i
$902$	−22.8545	+	1.77642i	−0.760970	+	0.0591484i
$903$	5.77475	−	6.00054i	0.192172	−	0.199685i
$904$	−32.9730	−	9.87131i	−1.09667	−	0.328315i
$905$	1.69699	−	2.93927i	0.0564099	−	0.0977047i
$906$	−17.6514	−	47.1030i	−0.586429	−	1.56489i
$907$	−9.64868	+	5.57067i	−0.320379	+	0.184971i	−0.651562	−	0.758596i	$-0.725886\pi$
$907$	−9.64868	+	5.57067i	−0.320379	+	0.184971i	0.331182	+	0.943567i	$0.392552\pi$
$908$	14.2357	−	11.4823i	0.472429	−	0.381053i
$909$	8.46814	−	0.324872i	0.280871	−	0.0107753i
$910$	0.818251	+	0.391259i	0.0271248	+	0.0129701i
$911$	4.70367	+	8.14700i	0.155840	+	0.269922i	0.933364	−	0.358930i	$-0.116858\pi$
$911$	4.70367	+	8.14700i	0.155840	+	0.269922i	−0.777525	+	0.628852i	$0.783525\pi$
$912$	−40.1882	+	2.72329i	−1.33076	+	0.0901772i
$913$	−11.3372	+	19.6366i	−0.375207	+	0.649877i
$914$	−44.8031	+	30.7285i	−1.48195	+	1.01641i
$915$	1.58810	−	6.41649i	0.0525009	−	0.212123i
$916$	−20.5647	−	7.93976i	−0.679476	−	0.262337i
$917$			7.98542i			0.263702i
$918$	−46.4438	−	35.3294i	−1.53287	−	1.16604i
$919$	12.9049			0.425694			0.212847	−	0.977086i	$-0.431726\pi$
$919$	12.9049			0.425694			0.212847	+	0.977086i	$0.431726\pi$
$920$	0.796622	+	0.844362i	0.0262638	+	0.0278378i
$921$	5.83194	+	1.44342i	0.192169	+	0.0475623i
$922$	−26.9475	−	39.2904i	−0.887470	−	1.29396i
$923$	27.9135	+	16.1158i	0.918783	+	0.530460i
$924$	−5.02034	+	7.16647i	−0.165157	+	0.235760i
$925$	−21.5924	+	12.4664i	−0.709953	+	0.409892i
$926$	49.4030	+	23.6228i	1.62348	+	0.776292i
$927$	−8.03544	+	5.05960i	−0.263918	+	0.166179i
$928$	−8.26426	−	6.40519i	−0.271288	−	0.210261i
$929$	−23.2352	−	40.2445i	−0.762321	−	1.32038i	−0.941651	−	0.336590i	$-0.890726\pi$
$929$	−23.2352	−	40.2445i	−0.762321	−	1.32038i	0.179330	−	0.983789i	$-0.442607\pi$
$930$	−4.08368	+	1.53032i	−0.133909	+	0.0501812i
$931$	5.03505	+	2.90699i	0.165017	+	0.0952726i
$932$	−21.1005	+	3.30012i	−0.691168	+	0.108099i
$933$	30.3885	+	29.2451i	0.994876	+	0.957441i
$934$	38.6976	−	3.00787i	1.26622	−	0.0984206i
$935$	−5.25543			−0.171871
$936$	−14.5498	+	14.8219i	−0.475576	+	0.484468i
$937$	32.0966			1.04855			0.524275	−	0.851549i	$-0.324336\pi$
$937$	32.0966			1.04855			0.524275	+	0.851549i	$0.324336\pi$
$938$	−7.29307	+	0.566873i	−0.238127	+	0.0185091i
$939$	−19.4909	+	5.62522i	−0.636063	+	0.183572i
$940$	0.877765	+	5.61230i	0.0286295	+	0.183053i
$941$	−19.4567	−	11.2333i	−0.634269	−	0.366196i	0.148134	−	0.988967i	$-0.452673\pi$
$941$	−19.4567	−	11.2333i	−0.634269	−	0.366196i	−0.782404	+	0.622772i	$0.786007\pi$
$942$	0.645929	+	0.531648i	0.0210455	+	0.0173220i
$943$	5.02606	+	8.70539i	0.163671	+	0.283487i
$944$	−45.5393	−	9.86414i	−1.48218	−	0.321050i
$945$	1.01644	+	0.905753i	0.0330646	+	0.0294642i
$946$	15.4951	+	7.40921i	0.503789	+	0.240894i
$947$	2.33511	−	1.34818i	0.0758810	−	0.0438099i	−0.461579	−	0.887099i	$-0.652717\pi$
$947$	2.33511	−	1.34818i	0.0758810	−	0.0438099i	0.537460	+	0.843289i	$0.319384\pi$
$948$	−11.5705	+	5.39235i	−0.375792	+	0.175135i
$949$	−20.4513	−	11.8075i	−0.663876	−	0.383289i
$950$	−22.9334	−	33.4377i	−0.744059	−	1.08486i
$951$	−11.1270	−	38.5542i	−0.360818	−	1.25020i
$952$	16.3371	−	15.4134i	0.529488	−	0.499551i
$953$	−52.2359			−1.69209			−0.846043	−	0.533115i	$-0.821021\pi$
$953$	−52.2359			−1.69209			−0.846043	+	0.533115i	$0.821021\pi$
$954$	46.5901	+	20.1212i	1.50841	+	0.651448i
$955$			3.84955i			0.124568i
$956$	8.58466	−	22.2350i	0.277648	−	0.719132i
$957$	5.82659	+	5.60735i	0.188347	+	0.181260i
$958$	5.42295	−	3.71936i	0.175207	−	0.120167i
$959$	−2.16307	+	3.74655i	−0.0698493	+	0.120982i
$960$	1.07565	−	3.46751i	0.0347164	−	0.111913i
$961$	−7.58631	−	13.1399i	−0.244720	−	0.423867i
$962$	15.7897	+	7.55006i	0.509079	+	0.243424i
$963$	−9.42846	+	17.8804i	−0.303828	+	0.576188i
$964$	4.62761	+	5.73730i	0.149045	+	0.184786i
$965$	4.83387	−	2.79084i	0.155608	−	0.0898402i
$966$	3.78480	+	0.630436i	0.121774	+	0.0202839i
$967$	8.01178	−	13.8768i	0.257641	−	0.446248i	−0.707968	−	0.706244i	$-0.750388\pi$
$967$	8.01178	−	13.8768i	0.257641	−	0.446248i	0.965610	+	0.259996i	$0.0837214\pi$
$968$	12.5179	+	3.74755i	0.402341	+	0.120451i
$969$	−77.6242	−	19.2122i	−2.49365	−	0.617185i
$970$	−1.01505	+	0.0788977i	−0.0325914	+	0.00253325i
$971$			47.7738i			1.53313i	0.642165	+	0.766566i	$0.278036\pi$
$971$			47.7738i			1.53313i	−0.642165	+	0.766566i	$0.721964\pi$
$972$	−27.1667	+	15.2961i	−0.871371	+	0.490624i
$973$			12.5662i			0.402854i
$974$	−4.40503	−	56.6726i	−0.141146	−	1.81591i
$975$	−20.2947	−	5.02299i	−0.649950	−	0.160864i
$976$	−39.1526	+	43.1462i	−1.25324	+	1.38108i
$977$	7.55418	−	13.0842i	0.241680	−	0.418601i	−0.719513	−	0.694479i	$-0.755635\pi$
$977$	7.55418	−	13.0842i	0.241680	−	0.418601i	0.961193	+	0.275877i	$0.0889684\pi$
$978$	2.62754	−	15.7743i	0.0840195	−	0.504408i
$979$	−0.368188	+	0.212573i	−0.0117673	+	0.00679387i
$980$	−0.407878	+	0.328987i	−0.0130292	+	0.0105091i
$981$	−5.99796	+	11.3747i	−0.191500	+	0.363166i
$982$	−14.5205	+	30.3672i	−0.463368	+	0.969056i
$983$	1.56101	+	2.70374i	0.0497884	+	0.0862360i	0.889846	−	0.456262i	$-0.150812\pi$
$983$	1.56101	+	2.70374i	0.0497884	+	0.0862360i	−0.840057	+	0.542498i	$0.817479\pi$
$984$	15.9880	−	27.0689i	0.509679	−	0.862924i
$985$	1.02506	−	1.77546i	0.0326611	−	0.0565707i
$986$	−11.7406	−	17.1181i	−0.373896	−	0.545151i
$987$	13.5287	+	13.0196i	0.430622	+	0.414419i
$988$	−10.2514	+	26.5520i	−0.326140	+	0.844732i
$989$		−	7.53157i		−	0.239490i
$990$	−1.11325	+	2.57770i	−0.0353815	+	0.0819248i
$991$	−27.2570			−0.865846			−0.432923	−	0.901431i	$-0.642518\pi$
$991$	−27.2570			−0.865846			−0.432923	+	0.901431i	$0.642518\pi$
$992$	38.0850	+	5.20165i	1.20920	+	0.165153i
$993$	−2.88353	−	9.99119i	−0.0915059	−	0.317061i
$994$	−15.3573	+	10.5329i	−0.487103	+	0.334083i
$995$	−0.238580	−	0.137744i	−0.00756349	−	0.00436678i
$996$	−13.1358	−	28.1858i	−0.416224	−	0.893101i
$997$	26.4172	−	15.2520i	0.836642	−	0.483036i	−0.0194793	−	0.999810i	$-0.506201\pi$
$997$	26.4172	−	15.2520i	0.836642	−	0.483036i	0.856121	+	0.516775i	$0.172868\pi$
$998$	3.09705	−	6.47696i	0.0980355	−	0.205025i
$999$	19.6140	+	17.4782i	0.620559	+	0.552985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.20	✓	72
8.5	even	2	inner	504.2.cs.a.85.29	yes	72
9.7	even	3	inner	504.2.cs.a.421.29	yes	72
72.61	even	6	inner	504.2.cs.a.421.20	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.20	✓	72	1.1	even	1	trivial
504.2.cs.a.85.29	yes	72	8.5	even	2	inner
504.2.cs.a.421.20	yes	72	72.61	even	6	inner
504.2.cs.a.421.29	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)

\(f(q)\)	\(=\)	\(q+(0.109593 + 1.40996i) q^{2} +(0.416131 - 1.68132i) q^{3} +(-1.97598 + 0.309044i) q^{4} +(-0.226907 - 0.131005i) q^{5} +(2.41620 + 0.402467i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.652293 - 2.75218i) q^{8} +(-2.65367 - 1.39930i) q^{9} +O(q^{10})\)	\(q+(0.109593 + 1.40996i) q^{2} +(0.416131 - 1.68132i) q^{3} +(-1.97598 + 0.309044i) q^{4} +(-0.226907 - 0.131005i) q^{5} +(2.41620 + 0.402467i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.652293 - 2.75218i) q^{8} +(-2.65367 - 1.39930i) q^{9} +(0.159844 - 0.334288i) q^{10} +(2.18749 - 1.26295i) q^{11} +(-0.302665 + 3.45085i) q^{12} +(2.11981 + 1.22387i) q^{13} +(-1.16627 + 0.799891i) q^{14} +(-0.314684 + 0.326988i) q^{15} +(3.80898 - 1.22133i) q^{16} +7.94098 q^{17} +(1.68213 - 3.89492i) q^{18} -5.81397i q^{19} +(0.488850 + 0.188739i) q^{20} +(1.66413 - 0.480280i) q^{21} +(2.02044 + 2.94587i) q^{22} +(0.783213 - 1.35657i) q^{23} +(-4.89874 - 0.0485563i) q^{24} +(-2.46568 - 4.27068i) q^{25} +(-1.49330 + 3.12298i) q^{26} +(-3.45694 + 3.87938i) q^{27} +(-1.25563 - 1.55673i) q^{28} +(-1.60072 + 0.924174i) q^{29} +(-0.495528 - 0.407857i) q^{30} +(3.39752 - 5.88468i) q^{31} +(2.13946 + 5.23667i) q^{32} +(-1.21314 - 4.20343i) q^{33} +(0.870276 + 11.1965i) q^{34} -0.262010i q^{35} +(5.67604 + 1.94488i) q^{36} -5.05596i q^{37} +(8.19747 - 0.637170i) q^{38} +(2.93984 - 3.05479i) q^{39} +(-0.212540 + 0.709944i) q^{40} +(-3.20862 + 5.55748i) q^{41} +(0.859553 + 2.29372i) q^{42} +(4.16396 - 2.40406i) q^{43} +(-3.93214 + 3.17159i) q^{44} +(0.418822 + 0.665155i) q^{45} +(1.99854 + 0.955630i) q^{46} +(5.42014 + 9.38796i) q^{47} +(-0.468405 - 6.91235i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(5.75126 - 3.94454i) q^{50} +(3.30449 - 13.3513i) q^{51} +(-4.56693 - 1.76323i) q^{52} +11.9617i q^{53} +(-5.84862 - 4.44900i) q^{54} -0.661811 q^{55} +(2.05731 - 1.94099i) q^{56} +(-9.77514 - 2.41937i) q^{57} +(-1.47848 - 2.15566i) q^{58} +(-10.0882 - 5.82442i) q^{59} +(0.520756 - 0.743373i) q^{60} +(-12.6142 + 7.28281i) q^{61} +(8.66951 + 4.14545i) q^{62} +(-0.115007 - 2.99779i) q^{63} +(-7.14903 + 3.59046i) q^{64} +(-0.320667 - 0.555412i) q^{65} +(5.79372 - 2.17114i) q^{66} +(4.47954 + 2.58627i) q^{67} +(-15.6912 + 2.45411i) q^{68} +(-1.95490 - 1.88134i) q^{69} +(0.369424 - 0.0287145i) q^{70} +13.1679 q^{71} +(-2.12016 + 8.21614i) q^{72} -9.64768 q^{73} +(7.12871 - 0.554098i) q^{74} +(-8.20641 + 2.36843i) q^{75} +(1.79677 + 11.4883i) q^{76} +(2.18749 + 1.26295i) q^{77} +(4.62932 + 3.81028i) q^{78} +(1.84252 + 3.19133i) q^{79} +(-1.02429 - 0.221868i) q^{80} +(5.08393 + 7.42655i) q^{81} +(-8.18748 - 3.91496i) q^{82} +(-7.77411 + 4.48838i) q^{83} +(-3.13986 + 1.46331i) q^{84} +(-1.80187 - 1.04031i) q^{85} +(3.84597 + 5.60755i) q^{86} +(0.887724 + 3.07589i) q^{87} +(-4.90276 - 5.19657i) q^{88} -0.168315 q^{89} +(-0.891943 + 0.663419i) q^{90} +2.44775i q^{91} +(-1.12838 + 2.92259i) q^{92} +(-8.48021 - 8.16112i) q^{93} +(-12.6426 + 8.67104i) q^{94} +(-0.761659 + 1.31923i) q^{95} +(9.69481 - 1.41798i) q^{96} +(-1.37383 - 2.37955i) q^{97} +(-1.27586 - 0.610070i) q^{98} +(-7.57213 + 0.290497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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