LMFDB - Embedded newform 441.2.o.d.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.1
Root			$0.827154 + 1.43267i$ of defining polynomial
Character	$\chi$	$=$	441.293
Dual form			441.2.o.d.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81474 + 1.04774i) q^{2} +(0.958787 - 1.44247i) q^{3} +(1.19552 - 2.07070i) q^{4} +(-1.04492 + 1.80985i) q^{5} +(-0.228612 + 3.62227i) q^{6} +0.819421i q^{8} +(-1.16146 - 2.76605i) q^{9} +O(q^{10})$	\(q+(-1.81474 + 1.04774i) q^{2} +(0.958787 - 1.44247i) q^{3} +(1.19552 - 2.07070i) q^{4} +(-1.04492 + 1.80985i) q^{5} +(-0.228612 + 3.62227i) q^{6} +0.819421i q^{8} +(-1.16146 - 2.76605i) q^{9} -4.37920i q^{10} +(-2.79620 + 1.61439i) q^{11} +(-1.84068 - 3.70987i) q^{12} +(-2.68740 - 1.55157i) q^{13} +(1.60880 + 3.24252i) q^{15} +(1.53250 + 2.65437i) q^{16} -1.63261 q^{17} +(5.00584 + 3.80275i) q^{18} -5.53210i q^{19} +(2.49844 + 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(1.00527 + 0.580391i) q^{23} +(1.18199 + 0.785650i) q^{24} +(0.316304 + 0.547854i) q^{25} +6.50257 q^{26} +(-5.10354 - 0.976682i) q^{27} +(-7.05749 + 4.07464i) q^{29} +(-6.31688 - 4.19872i) q^{30} +(-5.16886 - 2.98424i) q^{31} +(-6.98146 - 4.03075i) q^{32} +(-0.352251 + 5.58130i) q^{33} +(2.96276 - 1.71055i) q^{34} +(-7.11621 - 0.901839i) q^{36} -5.65313 q^{37} +(5.79620 + 10.0393i) q^{38} +(-4.81474 + 2.38887i) q^{39} +(-1.48303 - 0.856225i) q^{40} +(1.35369 - 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +7.72014i q^{44} +(6.21974 + 0.788230i) q^{45} -2.43240 q^{46} +(-4.06759 - 7.04527i) q^{47} +(5.29820 + 0.334384i) q^{48} +(-1.14802 - 0.662809i) q^{50} +(-1.56532 + 2.35499i) q^{51} +(-6.42568 + 3.70987i) q^{52} -6.09412i q^{53} +(10.2849 - 3.57476i) q^{54} -6.74759i q^{55} +(-7.97990 - 5.30410i) q^{57} +(8.53834 - 14.7888i) q^{58} +(1.98103 - 3.43124i) q^{59} +(8.63765 + 0.545146i) q^{60} +(-4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(5.61621 - 3.24252i) q^{65} +(-5.20851 - 10.4977i) q^{66} +(0.336981 - 0.583668i) q^{67} +(-1.95182 + 3.38065i) q^{68} +(1.80103 - 0.893598i) q^{69} +7.01535i q^{71} +(2.26656 - 0.951721i) q^{72} -3.42110i q^{73} +(10.2590 - 5.92301i) q^{74} +(1.09353 + 0.0690158i) q^{75} +(-11.4553 - 6.61374i) q^{76} +(6.23458 - 9.37978i) q^{78} +(7.07973 + 12.2625i) q^{79} -6.40534 q^{80} +(-6.30204 + 6.42528i) q^{81} +5.67325i q^{82} +(-1.54535 - 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(3.53839 + 2.04289i) q^{86} +(-0.889066 + 14.0870i) q^{87} +(-1.32286 - 2.29127i) q^{88} -4.91531 q^{89} +(-12.1131 + 5.08625i) q^{90} +(2.40363 - 1.38774i) q^{92} +(-9.26052 + 4.59469i) q^{93} +(14.7632 + 8.52356i) q^{94} +(10.0122 + 5.78057i) q^{95} +(-12.5080 + 6.20594i) q^{96} +(-2.07939 + 1.20054i) q^{97} +(7.71314 + 5.85939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9	$ 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9} + 12 q^{11} + 12 q^{12} - 6 q^{13} - 3 q^{15} - 6 q^{16} - 24 q^{17} - 6 q^{18} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 27 q^{24} + 7 q^{25} + 6 q^{26} - 27 q^{27} - 15 q^{29} - 6 q^{30} - 9 q^{31} - 48 q^{32} - 9 q^{33} - 3 q^{34} - 18 q^{36} - 12 q^{37} + 18 q^{38} - 30 q^{39} - 15 q^{40} + 9 q^{41} + 3 q^{43} - 15 q^{45} + 26 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} + 3 q^{51} + 12 q^{52} + 18 q^{54} - 36 q^{57} + 8 q^{58} + 18 q^{59} + 51 q^{60} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} + 6 q^{66} - 10 q^{67} - 27 q^{68} + 3 q^{69} + 12 q^{72} + 30 q^{74} - 27 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} - 60 q^{80} + 33 q^{81} + 15 q^{83} + 18 q^{85} - 54 q^{86} + 24 q^{87} - 8 q^{88} + 48 q^{89} - 24 q^{90} + 39 q^{92} - 42 q^{93} - 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9 + 12 * q^11 + 12 * q^12 - 6 * q^13 - 3 * q^15 - 6 * q^16 - 24 * q^17 - 6 * q^18 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 27 * q^24 + 7 * q^25 + 6 * q^26 - 27 * q^27 - 15 * q^29 - 6 * q^30 - 9 * q^31 - 48 * q^32 - 9 * q^33 - 3 * q^34 - 18 * q^36 - 12 * q^37 + 18 * q^38 - 30 * q^39 - 15 * q^40 + 9 * q^41 + 3 * q^43 - 15 * q^45 + 26 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 + 3 * q^51 + 12 * q^52 + 18 * q^54 - 36 * q^57 + 8 * q^58 + 18 * q^59 + 51 * q^60 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 10 * q^67 - 27 * q^68 + 3 * q^69 + 12 * q^72 + 30 * q^74 - 27 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 - 60 * q^80 + 33 * q^81 + 15 * q^83 + 18 * q^85 - 54 * q^86 + 24 * q^87 - 8 * q^88 + 48 * q^89 - 24 * q^90 + 39 * q^92 - 42 * q^93 - 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.81474	+	1.04774i	−1.28321	+	0.740865i	−0.977435	−	0.211238i	$-0.932251\pi$
$2$	−1.81474	+	1.04774i	−1.28321	+	0.740865i	−0.305780	+	0.952102i	$0.598917\pi$
$3$	0.958787	−	1.44247i	0.553556	−	0.832812i
$3$	0.958787	−	1.44247i	0.553556	−	0.832812i
$4$	1.19552	−	2.07070i	0.597760	−	1.03535i
$5$	−1.04492	+	1.80985i	−0.467300	+	0.809388i	−0.999302	−	0.0373553i	$-0.988107\pi$
$5$	−1.04492	+	1.80985i	−0.467300	+	0.809388i	0.532002	+	0.846743i	$0.321440\pi$
$6$	−0.228612	+	3.62227i	−0.0933303	+	1.47879i
$7$		0			0
$7$		0			0
$8$			0.819421i			0.289709i
$9$	−1.16146	−	2.76605i	−0.387152	−	0.922016i
$10$		−	4.37920i		−	1.38482i
$11$	−2.79620	+	1.61439i	−0.843086	+	0.486756i	−0.858312	−	0.513128i	$-0.828487\pi$
$11$	−2.79620	+	1.61439i	−0.843086	+	0.486756i	0.0152257	+	0.999884i	$0.495153\pi$
$12$	−1.84068	−	3.70987i	−0.531359	−	1.07095i
$13$	−2.68740	−	1.55157i	−0.745350	−	0.430328i	0.0786612	−	0.996901i	$-0.474935\pi$
$13$	−2.68740	−	1.55157i	−0.745350	−	0.430328i	−0.824011	+	0.566573i	$0.808269\pi$
$14$		0			0
$15$	1.60880	+	3.24252i	0.415391	+	0.837215i
$16$	1.53250	+	2.65437i	0.383125	+	0.663593i
$17$	−1.63261			−0.395966			−0.197983	−	0.980206i	$-0.563439\pi$
$17$	−1.63261			−0.395966			−0.197983	+	0.980206i	$0.563439\pi$
$18$	5.00584	+	3.80275i	1.17989	+	0.896318i
$19$		−	5.53210i		−	1.26915i	−0.772861	−	0.634575i	$-0.781175\pi$
$19$		−	5.53210i		−	1.26915i	0.772861	−	0.634575i	$-0.218825\pi$
$20$	2.49844	+	4.32742i	0.558667	+	0.967640i
$21$		0			0
$22$	3.38292	−	5.85939i	0.721241	−	1.24923i
$23$	1.00527	+	0.580391i	0.209612	+	0.121020i	0.601131	−	0.799150i	$-0.294717\pi$
$23$	1.00527	+	0.580391i	0.209612	+	0.121020i	−0.391519	+	0.920170i	$0.628050\pi$
$24$	1.18199	+	0.785650i	0.241273	+	0.160370i
$25$	0.316304	+	0.547854i	0.0632608	+	0.109571i
$26$	6.50257			1.27526
$27$	−5.10354	−	0.976682i	−0.982176	−	0.187963i
$28$		0			0
$29$	−7.05749	+	4.07464i	−1.31054	+	0.756643i	−0.982186	−	0.187911i	$-0.939828\pi$
$29$	−7.05749	+	4.07464i	−1.31054	+	0.756643i	−0.328357	+	0.944554i	$0.606495\pi$
$30$	−6.31688	−	4.19872i	−1.15330	−	0.766578i
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.0420638	−	0.999115i	$-0.513393\pi$
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.886291	+	0.463129i	$0.846727\pi$
$32$	−6.98146	−	4.03075i	−1.23416	−	0.712542i
$33$	−0.352251	+	5.58130i	−0.0613190	+	0.971579i
$34$	2.96276	−	1.71055i	0.508109	−	0.293357i
$35$		0			0
$36$	−7.11621	−	0.901839i	−1.18603	−	0.150306i
$37$	−5.65313			−0.929369			−0.464684	−	0.885476i	$-0.653832\pi$
$37$	−5.65313			−0.929369			−0.464684	+	0.885476i	$0.653832\pi$
$38$	5.79620	+	10.0393i	0.940268	+	1.62859i
$39$	−4.81474	+	2.38887i	−0.770975	+	0.382526i
$40$	−1.48303	−	0.856225i	−0.234487	−	0.135381i
$41$	1.35369	−	2.34465i	0.211410	−	0.366173i	−0.740746	−	0.671785i	$-0.765528\pi$
$41$	1.35369	−	2.34465i	0.211410	−	0.366173i	0.952156	+	0.305612i	$0.0988611\pi$
$42$		0			0
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	0.782065	−	0.623196i	$-0.214166\pi$
$43$	−0.974903	−	1.68858i	−0.148671	−	0.257506i	−0.930737	+	0.365690i	$0.880833\pi$
$44$			7.72014i			1.16385i
$45$	6.21974	+	0.788230i	0.927185	+	0.117502i
$46$	−2.43240			−0.358637
$47$	−4.06759	−	7.04527i	−0.593319	−	1.02766i	−0.993782	−	0.111346i	$-0.964484\pi$
$47$	−4.06759	−	7.04527i	−0.593319	−	1.02766i	0.400463	−	0.916313i	$-0.368849\pi$
$48$	5.29820	+	0.334384i	0.764729	+	0.0482641i
$49$		0			0
$50$	−1.14802	−	0.662809i	−0.162354	−	0.0937353i
$51$	−1.56532	+	2.35499i	−0.219189	+	0.329765i
$52$	−6.42568	+	3.70987i	−0.891082	+	0.514466i
$53$		−	6.09412i		−	0.837092i	−0.908196	−	0.418546i	$-0.862540\pi$
$53$		−	6.09412i		−	0.837092i	0.908196	−	0.418546i	$-0.137460\pi$
$54$	10.2849	−	3.57476i	1.39960	−	0.486463i
$55$		−	6.74759i		−	0.909845i
$56$		0			0
$57$	−7.97990	−	5.30410i	−1.05696	−	0.702545i
$58$	8.53834	−	14.7888i	1.12114	−	1.94187i
$59$	1.98103	−	3.43124i	0.257908	−	0.446709i	−0.707773	−	0.706439i	$-0.750300\pi$
$59$	1.98103	−	3.43124i	0.257908	−	0.446709i	0.965681	+	0.259730i	$0.0836336\pi$
$60$	8.63765	+	0.545146i	1.11512	+	0.0703780i
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	−0.741575	−	0.670869i	$-0.765921\pi$
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	0.210202	+	0.977658i	$0.432588\pi$
$62$	12.5068			1.58837
$63$		0			0
$64$	10.7627			1.34534
$65$	5.61621	−	3.24252i	0.696605	−	0.402185i
$66$	−5.20851	−	10.4977i	−0.641123	−	1.29217i
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	−0.844707	−	0.535229i	$-0.820225\pi$
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	0.885876	+	0.463923i	$0.153559\pi$
$68$	−1.95182	+	3.38065i	−0.236693	+	0.409963i
$69$	1.80103	−	0.893598i	0.216819	−	0.107577i
$70$		0			0
$71$			7.01535i			0.832568i	0.909235	+	0.416284i	$0.136668\pi$
$71$			7.01535i			0.832568i	−0.909235	+	0.416284i	$0.863332\pi$
$72$	2.26656	−	0.951721i	0.267116	−	0.112161i
$73$		−	3.42110i		−	0.400409i	−0.979754	−	0.200205i	$-0.935839\pi$
$73$		−	3.42110i		−	0.400409i	0.979754	−	0.200205i	$-0.0641607\pi$
$74$	10.2590	−	5.92301i	1.19258	−	0.688536i
$75$	1.09353	+	0.0690158i	0.126270	+	0.00796926i
$76$	−11.4553	−	6.61374i	−1.31402	−	0.758648i
$77$		0			0
$78$	6.23458	−	9.37978i	0.705927	−	1.06205i
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	0.921862	+	0.387519i	$0.126668\pi$
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	−0.125330	+	0.992115i	$0.539999\pi$
$80$	−6.40534			−0.716138
$81$	−6.30204	+	6.42528i	−0.700227	+	0.713920i
$82$			5.67325i			0.626505i
$83$	−1.54535	−	2.67662i	−0.169624	−	0.293798i	0.768664	−	0.639653i	$-0.220922\pi$
$83$	−1.54535	−	2.67662i	−0.169624	−	0.293798i	−0.938288	+	0.345856i	$0.887589\pi$
$84$		0			0
$85$	1.70594	−	2.95477i	0.185035	−	0.320490i
$86$	3.53839	+	2.04289i	0.381554	+	0.220291i
$87$	−0.889066	+	14.0870i	−0.0953179	+	1.51028i
$88$	−1.32286	−	2.29127i	−0.141018	−	0.244250i
$89$	−4.91531			−0.521022			−0.260511	−	0.965471i	$-0.583891\pi$
$89$	−4.91531			−0.521022			−0.260511	+	0.965471i	$0.583891\pi$
$90$	−12.1131	+	5.08625i	−1.27683	+	0.536138i
$91$		0			0
$92$	2.40363	−	1.38774i	0.250596	−	0.144682i
$93$	−9.26052	+	4.59469i	−0.960272	+	0.476447i
$94$	14.7632	+	8.52356i	1.52271	+	0.879138i
$95$	10.0122	+	5.78057i	1.02723	+	0.593074i
$96$	−12.5080	+	6.20594i	−1.27659	+	0.633391i
$97$	−2.07939	+	1.20054i	−0.211130	+	0.121896i	−0.601837	−	0.798619i	$-0.705564\pi$
$97$	−2.07939	+	1.20054i	−0.211130	+	0.121896i	0.390706	+	0.920515i	$0.372231\pi$
$98$		0			0
$99$	7.71314	+	5.85939i	0.775199	+	0.588891i
$100$	1.51259			0.151259
$101$	−1.76025	−	3.04885i	−0.175152	−	0.303372i	0.765062	−	0.643957i	$-0.222708\pi$
$101$	−1.76025	−	3.04885i	−0.175152	−	0.303372i	−0.940214	+	0.340585i	$0.889375\pi$
$102$	0.373233	−	5.91375i	0.0369556	−	0.585549i
$103$	13.5832	+	7.84228i	1.33840	+	0.772723i	0.986569	−	0.163342i	$-0.0522275\pi$
$103$	13.5832	+	7.84228i	1.33840	+	0.772723i	0.351826	+	0.936065i	$0.385561\pi$
$104$	1.27139	−	2.20211i	0.124670	−	0.215935i
$105$		0			0
$106$	6.38506	+	11.0592i	0.620172	+	1.07417i
$107$		−	1.63949i		−	0.158496i	−0.996855	−	0.0792478i	$-0.974748\pi$
$107$		−	1.63949i		−	0.158496i	0.996855	−	0.0792478i	$-0.0252518\pi$
$108$	−8.12380	+	9.40026i	−0.781713	+	0.904541i
$109$	−5.81345			−0.556827			−0.278414	−	0.960461i	$-0.589809\pi$
$109$	−5.81345			−0.556827			−0.278414	+	0.960461i	$0.589809\pi$
$110$	7.06973	+	12.2451i	0.674072	+	1.16753i
$111$	−5.42015	+	8.15449i	−0.514458	+	0.773989i
$112$		0			0
$113$	13.9931	+	8.07894i	1.31636	+	0.760003i	0.983142	−	0.182845i	$-0.0585307\pi$
$113$	13.9931	+	8.07894i	1.31636	+	0.760003i	0.333222	+	0.942848i	$0.391864\pi$
$114$	20.0388	+	1.26470i	1.87680	+	0.118450i
$115$	−2.10084	+	1.21292i	−0.195904	+	0.113105i
$116$			19.4853i			1.80916i
$117$	−1.17042	+	9.23555i	−0.108206	+	0.853827i
$118$			8.30241i			0.764299i
$119$		0			0
$120$	−2.65699	+	1.31829i	−0.242549	+	0.120343i
$121$	−0.287505	+	0.497972i	−0.0261368	+	0.0452702i
$122$	5.02097	−	8.69658i	0.454577	−	0.787351i
$123$	−2.08420	−	4.20068i	−0.187926	−	0.378762i
$124$	−12.3590	+	7.13545i	−1.10987	+	0.640782i
$125$	−11.7712			−1.05285
$126$		0			0
$127$	−9.59240			−0.851188			−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59240			−0.851188			−0.425594	+	0.904914i	$0.639935\pi$
$128$	−5.56860	+	3.21503i	−0.492199	+	0.284171i
$129$	−3.37046	−	0.212719i	−0.296752	−	0.0187288i
$130$	−6.79464	+	11.7687i	−0.595929	+	1.03218i
$131$	1.23061	−	2.13148i	0.107519	−	0.186228i	−0.807246	−	0.590216i	$-0.799043\pi$
$131$	1.23061	−	2.13148i	0.107519	−	0.186228i	0.914765	+	0.403987i	$0.132376\pi$
$132$	11.1361	+	7.40197i	0.969272	+	0.644258i
$133$		0			0
$134$			1.41227i			0.122002i
$135$	7.10041	−	8.21607i	0.611106	−	0.707127i
$136$		−	1.33779i		−	0.114715i
$137$	15.0571	−	8.69322i	1.28641	−	0.742712i	0.308401	−	0.951256i	$-0.400206\pi$
$137$	15.0571	−	8.69322i	1.28641	−	0.742712i	0.978013	+	0.208545i	$0.0668727\pi$
$138$	−2.33215	+	3.50866i	−0.198526	+	0.298677i
$139$	8.61174	+	4.97199i	0.730438	+	0.421719i	0.818582	−	0.574389i	$-0.194760\pi$
$139$	8.61174	+	4.97199i	0.730438	+	0.421719i	−0.0881443	+	0.996108i	$0.528094\pi$
$140$		0			0
$141$	−14.0626	−	0.887527i	−1.18428	−	0.0747432i
$142$	−7.35026	−	12.7310i	−0.616820	−	1.06836i
$143$	10.0193			0.837860
$144$	5.56218	−	7.32191i	0.463515	−	0.610159i
$145$		−	17.0306i		−	1.41432i
$146$	3.58442	+	6.20840i	0.296649	+	0.513811i
$147$		0			0
$148$	−6.75843	+	11.7060i	−0.555540	+	0.962223i
$149$	−8.01695	−	4.62859i	−0.656774	−	0.379189i	0.134273	−	0.990944i	$-0.457130\pi$
$149$	−8.01695	−	4.62859i	−0.656774	−	0.379189i	−0.791047	+	0.611756i	$0.790464\pi$
$150$	−2.05679	+	1.02049i	−0.167936	+	0.0833229i
$151$	5.98489	+	10.3661i	0.487044	+	0.843584i	0.999889	−	0.0148966i	$-0.00474192\pi$
$151$	5.98489	+	10.3661i	0.487044	+	0.843584i	−0.512845	+	0.858481i	$0.671409\pi$
$152$	4.53311			0.367684
$153$	1.89620	+	4.51587i	0.153299	+	0.365087i
$154$		0			0
$155$	10.8020	−	6.23656i	0.867641	−	0.500933i
$156$	−0.809474	+	12.8258i	−0.0648098	+	1.02689i
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.967825	−	0.251626i	$-0.0809651\pi$
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.265998	+	0.963974i	$0.414298\pi$
$158$	−25.6957	−	14.8354i	−2.04424	−	1.18024i
$159$	−8.79060	−	5.84296i	−0.697140	−	0.463377i
$160$	14.5901	−	8.42358i	1.15345	−	0.665943i
$161$		0			0
$162$	4.70454	−	18.2631i	0.369623	−	1.43489i
$163$	17.8354			1.39697			0.698486	−	0.715623i	$-0.253857\pi$
$163$	17.8354			1.39697			0.698486	+	0.715623i	$0.253857\pi$
$164$	−3.23672	−	5.60616i	−0.252745	−	0.437768i
$165$	−9.73322	−	6.46950i	−0.757730	−	0.503650i
$166$	5.60881	+	3.23825i	0.435328	+	0.251337i
$167$	6.16899	−	10.6850i	0.477371	−	0.826830i	−0.522293	−	0.852766i	$-0.674923\pi$
$167$	6.16899	−	10.6850i	0.477371	−	0.826830i	0.999664	+	0.0259359i	$0.00825657\pi$
$168$		0			0
$169$	−1.68526	−	2.91896i	−0.129635	−	0.224535i
$170$			7.14952i			0.548343i
$171$	−15.3020	+	6.42528i	−1.17018	+	0.491354i
$172$	−4.66207			−0.355479
$173$	−4.53368	−	7.85256i	−0.344689	−	0.597019i	0.640608	−	0.767868i	$-0.278682\pi$
$173$	−4.53368	−	7.85256i	−0.344689	−	0.597019i	−0.985297	+	0.170849i	$0.945349\pi$
$174$	−13.1461	−	26.4957i	−0.996600	−	2.00863i
$175$		0			0
$176$	−8.57037	−	4.94810i	−0.646016	−	0.372977i
$177$	−3.05009	−	6.14741i	−0.229259	−	0.462067i
$178$	8.92002	−	5.14997i	0.668584	−	0.386007i
$179$			15.0210i			1.12272i	0.827571	+	0.561362i	$0.189722\pi$
$179$			15.0210i			1.12272i	−0.827571	+	0.561362i	$0.810278\pi$
$180$	9.06802	−	11.9369i	0.675891	−	0.889724i
$181$		−	2.34159i		−	0.174049i	−0.996206	−	0.0870246i	$-0.972264\pi$
$181$		−	2.34159i		−	0.174049i	0.996206	−	0.0870246i	$-0.0277359\pi$
$182$		0			0
$183$	−0.522815	+	8.28383i	−0.0386476	+	0.612358i
$184$	−0.475584	+	0.823736i	−0.0350605	+	0.0607266i
$185$	5.90704	−	10.2313i	0.434294	−	0.752220i
$186$	11.9914	−	18.0408i	0.879252	−	1.32281i
$187$	4.56510	−	2.63566i	0.333833	−	0.192739i
$188$	−19.4516			−1.41865
$189$		0			0
$190$	−24.2262			−1.75755
$191$	−7.82585	+	4.51825i	−0.566258	+	0.326929i	−0.755654	−	0.654972i	$-0.772681\pi$
$191$	−7.82585	+	4.51825i	−0.566258	+	0.326929i	0.189395	+	0.981901i	$0.439347\pi$
$192$	10.3191	−	15.5249i	0.744720	−	1.12041i
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	−0.750334	−	0.661058i	$-0.770108\pi$
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	0.947661	+	0.319279i	$0.103441\pi$
$194$	2.51570	−	4.35733i	0.180617	−	0.312838i
$195$	0.707501	−	11.2101i	0.0506652	−	0.802773i
$196$		0			0
$197$		−	2.88946i		−	0.205865i	−0.994688	−	0.102933i	$-0.967177\pi$
$197$		−	2.88946i		−	0.205865i	0.994688	−	0.102933i	$-0.0328226\pi$
$198$	−20.1365	−	2.55190i	−1.43104	−	0.181356i
$199$			5.14325i			0.364596i	0.983243	+	0.182298i	$0.0583535\pi$
$199$			5.14325i			0.364596i	−0.983243	+	0.182298i	$0.941646\pi$
$200$	−0.448923	+	0.259186i	−0.0317437	+	0.0183272i
$201$	−0.518832	−	1.04570i	−0.0365956	−	0.0737579i
$202$	6.38881	+	3.68858i	0.449515	+	0.259528i
$203$		0			0
$204$	3.00511	+	6.05676i	0.210400	+	0.424058i
$205$	2.82897	+	4.89993i	0.197584	+	0.342226i
$206$	−32.8667			−2.28993
$207$	0.437816	−	3.45471i	0.0304303	−	0.240119i
$208$		−	9.51113i		−	0.659479i
$209$	8.93095	+	15.4689i	0.617767	+	1.07000i
$210$		0			0
$211$	7.93224	−	13.7390i	0.546078	−	0.945835i	−0.452460	−	0.891785i	$-0.649454\pi$
$211$	7.93224	−	13.7390i	0.546078	−	0.945835i	0.998538	−	0.0540502i	$-0.0172131\pi$
$212$	−12.6191	−	7.28565i	−0.866684	−	0.500380i
$213$	10.1194	+	6.72622i	0.693373	+	0.460873i
$214$	1.71776	+	2.97525i	0.117424	+	0.203384i
$215$	4.07476			0.277897
$216$	0.800314	−	4.18194i	0.0544544	−	0.284545i
$217$		0			0
$218$	10.5499	−	6.09099i	0.714529	−	0.412534i
$219$	−4.93484	−	3.28010i	−0.333466	−	0.221649i
$220$	−13.9723	−	8.06689i	−0.942010	−	0.543870i
$221$	4.38747	+	2.53311i	0.295133	+	0.170395i
$222$	1.29237	−	20.4772i	0.0867382	−	1.37434i
$223$	−13.5288	+	7.81085i	−0.905955	+	0.523053i	−0.879127	−	0.476587i	$-0.841874\pi$
$223$	−13.5288	+	7.81085i	−0.905955	+	0.523053i	−0.0268275	+	0.999640i	$0.508540\pi$
$224$		0			0
$225$	1.14802	−	1.51122i	0.0765346	−	0.100748i
$226$	−33.8586			−2.25224
$227$	1.04045	+	1.80211i	0.0690569	+	0.119610i	0.898486	−	0.439001i	$-0.144668\pi$
$227$	1.04045	+	1.80211i	0.0690569	+	0.119610i	−0.829430	+	0.558611i	$0.811334\pi$
$228$	−20.5234	+	10.1828i	−1.35919	+	0.674375i
$229$	−5.57233	−	3.21719i	−0.368230	−	0.212598i	0.304455	−	0.952527i	$-0.401526\pi$
$229$	−5.57233	−	3.21719i	−0.368230	−	0.212598i	−0.672685	+	0.739929i	$0.734859\pi$
$230$	2.54165	−	4.40226i	0.167591	−	0.290277i
$231$		0			0
$232$	−3.33885	−	5.78305i	−0.219206	−	0.379676i
$233$		−	15.6141i		−	1.02291i	−0.859310	−	0.511456i	$-0.829106\pi$
$233$		−	15.6141i		−	1.02291i	0.859310	−	0.511456i	$-0.170894\pi$
$234$	−7.55245	−	17.9864i	−0.493719	−	1.17581i
$235$	17.0011			1.10903
$236$	−4.73672	−	8.20424i	−0.308334	−	0.534050i
$237$	24.4762	+	1.54476i	1.58990	+	0.100343i
$238$		0			0
$239$	−14.8777	−	8.58964i	−0.962358	−	0.555618i	−0.0654600	−	0.997855i	$-0.520851\pi$
$239$	−14.8777	−	8.58964i	−0.962358	−	0.555618i	−0.896898	+	0.442238i	$0.854185\pi$
$240$	−6.14135	+	9.23952i	−0.396423	+	0.596409i
$241$	−9.71544	+	5.60921i	−0.625827	+	0.361321i	−0.779134	−	0.626857i	$-0.784341\pi$
$241$	−9.71544	+	5.60921i	−0.625827	+	0.361321i	0.153307	+	0.988179i	$0.451008\pi$
$242$		−	1.20492i		−	0.0774552i
$243$	3.22598	+	15.2510i	0.206947	+	0.978352i
$244$			11.4583i			0.733544i
$245$		0			0
$246$	8.18350	+	5.43943i	0.521761	+	0.346806i
$247$	−8.58343	+	14.8669i	−0.546151	+	0.945961i
$248$	2.44535	−	4.23547i	0.155280	−	0.268953i
$249$	−5.34262	−	0.337187i	−0.338575	−	0.0213684i
$250$	21.3617	−	12.3332i	1.35103	−	0.780018i
$251$	−11.3837			−0.718535			−0.359267	−	0.933235i	$-0.616973\pi$
$251$	−11.3837			−0.718535			−0.359267	+	0.933235i	$0.616973\pi$
$252$		0			0
$253$	−3.74790			−0.235629
$254$	17.4077	−	10.0504i	1.09226	−	0.630615i
$255$	−2.62654	−	5.29376i	−0.164481	−	0.331508i
$256$	−4.02567	+	6.97267i	−0.251604	+	0.435792i
$257$	4.69024	−	8.12373i	0.292569	−	0.506745i	−0.681847	−	0.731494i	$-0.738823\pi$
$257$	4.69024	−	8.12373i	0.292569	−	0.506745i	0.974416	+	0.224750i	$0.0721565\pi$
$258$	6.33938	−	3.14534i	0.394672	−	0.195820i
$259$		0			0
$260$		−	15.5060i		−	0.961641i
$261$	19.4676	+	14.7888i	1.20502	+	0.915406i
$262$			5.15744i			0.318628i
$263$	7.62367	−	4.40153i	0.470096	−	0.271410i	−0.246184	−	0.969223i	$-0.579177\pi$
$263$	7.62367	−	4.40153i	0.470096	−	0.271410i	0.716280	+	0.697813i	$0.245843\pi$
$264$	−4.57343	−	0.288642i	−0.281475	−	0.0177647i
$265$	11.0294	+	6.36784i	0.677532	+	0.391173i
$266$		0			0
$267$	−4.71274	+	7.09021i	−0.288415	+	0.433914i
$268$	−0.805735	−	1.39557i	−0.0492181	−	0.0852482i
$269$	16.3295			0.995625			0.497812	−	0.867285i	$-0.334137\pi$
$269$	16.3295			0.995625			0.497812	+	0.867285i	$0.334137\pi$
$270$	−4.27709	+	22.3494i	−0.260295	+	1.36014i
$271$			14.5708i			0.885111i	0.896741	+	0.442555i	$0.145928\pi$
$271$			14.5708i			0.885111i	−0.896741	+	0.442555i	$0.854072\pi$
$272$	−2.50197	−	4.33355i	−0.151704	−	0.262760i
$273$		0			0
$274$	−18.2165	+	31.5519i	−1.10050	+	1.90612i
$275$	−1.76890	−	1.02127i	−0.106669	−	0.0615851i
$276$	0.302797	−	4.79772i	0.0182262	−	0.288789i
$277$	−14.3568	−	24.8668i	−0.862618	−	1.49410i	−0.869393	−	0.494122i	$-0.835490\pi$
$277$	−14.3568	−	24.8668i	−0.862618	−	1.49410i	0.00677410	−	0.999977i	$-0.497844\pi$
$278$	−20.8374			−1.24975
$279$	−2.25116	+	17.7634i	−0.134773	+	1.06347i
$280$		0			0
$281$	−4.76893	+	2.75334i	−0.284490	+	0.164251i	−0.635455	−	0.772138i	$-0.719187\pi$
$281$	−4.76893	+	2.75334i	−0.284490	+	0.164251i	0.350964	+	0.936389i	$0.385854\pi$
$282$	26.4498	−	13.1233i	1.57506	−	0.781481i
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.997357	−	0.0726567i	$-0.976852\pi$
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.561601	−	0.827408i	$-0.689814\pi$
$284$	14.5267	+	8.38699i	0.862001	+	0.497676i
$285$	17.9379	−	8.90005i	1.06255	−	0.527194i
$286$	−18.1825	+	10.4977i	−1.07515	+	0.620740i
$287$		0			0
$288$	−3.04059	+	23.9926i	−0.179168	+	1.41378i
$289$	−14.3346			−0.843211
$290$	17.8437	+	30.9062i	1.04782	+	1.81487i
$291$	−0.261951	+	4.15053i	−0.0153558	+	0.243308i
$292$	−7.08408	−	4.08999i	−0.414564	−	0.239349i
$293$	3.54362	−	6.13773i	0.207021	−	0.358570i	−0.743754	−	0.668453i	$-0.766957\pi$
$293$	3.54362	−	6.13773i	0.207021	−	0.358570i	0.950775	+	0.309883i	$0.100290\pi$
$294$		0			0
$295$	4.14001	+	7.17071i	0.241041	+	0.417495i
$296$		−	4.63229i		−	0.269246i
$297$	15.8473	−	5.50809i	0.919551	−	0.319612i
$298$	19.3982			1.12371
$299$	−1.80103	−	3.11948i	−0.104156	−	0.180404i
$300$	1.45025	−	2.18187i	0.0837304	−	0.125970i
$301$		0			0
$302$	−21.7220	−	12.5412i	−1.24996	−	0.721667i
$303$	−6.08559	−	0.384078i	−0.349608	−	0.0220647i
$304$	14.6842	−	8.47795i	0.842198	−	0.486244i
$305$		−	10.0149i		−	0.573449i
$306$	−8.17257	−	6.20840i	−0.467195	−	0.354911i
$307$			3.11346i			0.177695i	0.996045	+	0.0888473i	$0.0283183\pi$
$307$			3.11346i			0.177695i	−0.996045	+	0.0888473i	$0.971682\pi$
$308$		0			0
$309$	24.3357	−	12.0744i	1.38441	−	0.686887i
$310$	−13.0686	+	22.6355i	−0.742247	+	1.28561i
$311$	−9.72605	+	16.8460i	−0.551514	+	0.955249i	0.446652	+	0.894708i	$0.352616\pi$
$311$	−9.72605	+	16.8460i	−0.551514	+	0.955249i	−0.998166	+	0.0605417i	$0.980717\pi$
$312$	−1.95749	−	3.94530i	−0.110821	−	0.223358i
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.971195	−	0.238285i	$-0.923415\pi$
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.279237	+	0.960222i	$0.590081\pi$
$314$	−37.4073			−2.11101
$315$		0			0
$316$	33.8559			1.90454
$317$	14.0534	−	8.11372i	0.789316	−	0.455712i	−0.0504056	−	0.998729i	$-0.516051\pi$
$317$	14.0534	−	8.11372i	0.789316	−	0.455712i	0.839722	+	0.543017i	$0.182718\pi$
$318$	22.0746	+	1.39319i	1.23788	+	0.0781260i
$319$	13.1561	−	22.7871i	0.736601	−	1.27583i
$320$	−11.2461	+	19.4789i	−0.628677	+	1.08890i
$321$	−2.36492	−	1.57192i	−0.131997	−	0.0877362i
$322$		0			0
$323$			9.03174i			0.502540i
$324$	5.77063	+	20.7312i	0.320591	+	1.15173i
$325$		−	1.96307i		−	0.108892i
$326$	−32.3665	+	18.6868i	−1.79262	+	1.03497i
$327$	−5.57386	+	8.38574i	−0.308235	+	0.463732i
$328$	1.92126	+	1.10924i	0.106084	+	0.0612474i
$329$		0			0
$330$	24.4416	+	1.54258i	1.34547	+	0.0849161i
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	−0.985285	−	0.170919i	$-0.945326\pi$
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	0.344623	−	0.938741i	$-0.388007\pi$
$332$	−7.38999			−0.405578
$333$	6.56586	+	15.6368i	0.359807	+	0.856893i
$334$			25.8540i			1.41467i
$335$	0.704232	+	1.21977i	0.0384763	+	0.0666430i
$336$		0			0
$337$	5.93515	−	10.2800i	0.323308	−	0.559986i	−0.657860	−	0.753140i	$-0.728538\pi$
$337$	5.93515	−	10.2800i	0.323308	−	0.559986i	0.981168	+	0.193154i	$0.0618717\pi$
$338$	6.11662	+	3.53143i	0.332700	+	0.192085i
$339$	25.0701	−	12.4387i	1.36162	−	0.675580i
$340$	−4.07897	−	7.06498i	−0.221213	−	0.383152i
$341$	19.2709			1.04358
$342$	21.0372	−	27.6928i	1.13756	−	1.49745i
$343$		0			0
$344$	1.38366	−	0.798855i	0.0746019	−	0.0430714i
$345$	−0.264652	+	4.19333i	−0.0142484	+	0.225761i
$346$	16.4549	+	9.50024i	0.884621	+	0.510736i
$347$	−18.7979	−	10.8530i	−1.00913	−	0.582619i	−0.0981903	−	0.995168i	$-0.531305\pi$
$347$	−18.7979	−	10.8530i	−1.00913	−	0.582619i	−0.910936	+	0.412549i	$0.864639\pi$
$348$	28.1070	+	18.6822i	1.50669	+	1.00147i
$349$	−2.20868	+	1.27518i	−0.118228	+	0.0682588i	−0.557948	−	0.829876i	$-0.688411\pi$
$349$	−2.20868	+	1.27518i	−0.118228	+	0.0682588i	0.439720	+	0.898135i	$0.355078\pi$
$350$		0			0
$351$	12.1998	+	10.5432i	0.651180	+	0.562756i
$352$	26.0288			1.38734
$353$	−12.6873	−	21.9751i	−0.675279	−	1.16962i	−0.976387	−	0.216027i	$-0.930690\pi$
$353$	−12.6873	−	21.9751i	−0.675279	−	1.16962i	0.301109	−	0.953590i	$-0.402643\pi$
$354$	11.9760	+	7.96024i	0.636517	+	0.423082i
$355$	−12.6967	−	7.33044i	−0.673871	−	0.389059i
$356$	−5.87636	+	10.1782i	−0.311446	+	0.539441i
$357$		0			0
$358$	−15.7381	−	27.2592i	−0.831786	−	1.44070i
$359$		−	11.2437i		−	0.593421i	−0.954967	−	0.296711i	$-0.904110\pi$
$359$		−	11.2437i		−	0.593421i	0.954967	−	0.296711i	$-0.0958897\pi$
$360$	−0.645892	+	5.09659i	−0.0340415	+	0.268614i
$361$	−11.6041			−0.610741
$362$	2.45338	+	4.24938i	0.128947	+	0.223342i
$363$	0.442656	+	0.892167i	0.0232334	+	0.0468266i
$364$		0			0
$365$	6.19166	+	3.57476i	0.324086	+	0.187111i
$366$	−7.73053	−	15.5808i	−0.404081	−	0.814420i
$367$	−2.86810	+	1.65590i	−0.149714	+	0.0864372i	−0.572985	−	0.819566i	$-0.694215\pi$
$367$	−2.86810	+	1.65590i	−0.149714	+	0.0864372i	0.423272	+	0.906003i	$0.360882\pi$
$368$			3.55780i			0.185463i
$369$	−8.05767	−	1.02115i	−0.419465	−	0.0531590i
$370$			24.7562i			1.28701i
$371$		0			0
$372$	−1.55692	+	24.6688i	−0.0807224	+	1.27902i
$373$	3.32271	−	5.75510i	0.172043	−	0.297988i	−0.767091	−	0.641539i	$-0.778296\pi$
$373$	3.32271	−	5.75510i	0.172043	−	0.297988i	0.939134	+	0.343551i	$0.111630\pi$
$374$	−5.52298	+	9.56608i	−0.285586	+	0.494650i
$375$	−11.2861	+	16.9796i	−0.582810	+	0.876824i
$376$	5.77304	−	3.33307i	0.297722	−	0.171890i
$377$	25.2884			1.30242
$378$		0			0
$379$	−3.84940			−0.197730			−0.0988652	−	0.995101i	$-0.531521\pi$
$379$	−3.84940			−0.197730			−0.0988652	+	0.995101i	$0.531521\pi$
$380$	23.9397	−	13.8216i	1.22808	−	0.709033i
$381$	−9.19707	+	13.8368i	−0.471180	+	0.708880i
$382$	9.46792	−	16.3989i	0.484421	−	0.839041i
$383$	−17.1112	+	29.6374i	−0.874339	+	1.51440i	−0.0168739	+	0.999858i	$0.505371\pi$
$383$	−17.1112	+	29.6374i	−0.874339	+	1.51440i	−0.857465	+	0.514542i	$0.827962\pi$
$384$	−0.701503	+	11.1151i	−0.0357984	+	0.567214i
$385$		0			0
$386$			11.4889i			0.584768i
$387$	−3.53839	+	4.65784i	−0.179867	+	0.236771i
$388$			5.74107i			0.291459i
$389$	−11.6737	+	6.73982i	−0.591881	+	0.341723i	−0.765841	−	0.643030i	$-0.777677\pi$
$389$	−11.6737	+	6.73982i	−0.591881	+	0.341723i	0.173960	+	0.984753i	$0.444344\pi$
$390$	10.4614	+	21.0847i	0.529732	+	1.06767i
$391$	−1.64121	−	0.947550i	−0.0829993	−	0.0479197i
$392$		0			0
$393$	−1.89471	−	3.81875i	−0.0955753	−	0.192631i
$394$	3.02740	+	5.24361i	0.152518	+	0.264169i
$395$	−29.5909			−1.48888
$396$	21.3543	−	8.96660i	1.07309	−	0.450588i
$397$			29.5027i			1.48070i	0.672223	+	0.740349i	$0.265340\pi$
$397$			29.5027i			1.48070i	−0.672223	+	0.740349i	$0.734660\pi$
$398$	−5.38880	−	9.33367i	−0.270116	−	0.467855i
$399$		0			0
$400$	−0.969472	+	1.67918i	−0.0484736	+	0.0839588i
$401$	25.1534	+	14.5223i	1.25610	+	0.725209i	0.972314	−	0.233678i	$-0.0750763\pi$
$401$	25.1534	+	14.5223i	1.25610	+	0.725209i	0.283786	+	0.958888i	$0.408410\pi$
$402$	2.03717	+	1.35407i	0.101605	+	0.0675348i
$403$	9.26052	+	16.0397i	0.461300	+	0.798994i
$404$	−8.41768			−0.418795
$405$	−5.04368	−	18.1196i	−0.250622	−	0.900370i
$406$		0			0
$407$	15.8073	−	9.12634i	0.783538	−	0.452376i
$408$	−1.92973	−	1.28266i	−0.0955358	−	0.0635010i
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.316671	−	0.948536i	$-0.602565\pi$
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.979791	+	0.200023i	$0.935898\pi$
$410$	−10.2677	−	5.92806i	−0.507086	−	0.292766i
$411$	1.89681	−	30.0544i	0.0935630	−	1.48247i
$412$	32.4781	−	18.7512i	1.60008	−	0.923806i
$413$		0			0
$414$	2.82512	+	6.72812i	0.138847	+	0.330669i
$415$	6.45904			0.317062
$416$	12.5080	+	21.6645i	0.613254	+	1.06219i
$417$	15.4288	−	7.65512i	0.755551	−	0.374873i
$418$	−32.4147	−	18.7146i	−1.58545	−	0.915363i
$419$	−18.2902	+	31.6795i	−0.893534	+	1.54765i	−0.0579246	+	0.998321i	$0.518448\pi$
$419$	−18.2902	+	31.6795i	−0.893534	+	1.54765i	−0.835609	+	0.549325i	$0.814885\pi$
$420$		0			0
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	0.944625	−	0.328152i	$-0.106426\pi$
$421$	3.85999	+	6.68570i	0.188124	+	0.325841i	−0.756501	+	0.653993i	$0.773093\pi$
$422$			33.2437i			1.61828i
$423$	−14.7632	+	19.4339i	−0.717813	+	0.944910i
$424$	4.99365			0.242513
$425$	−0.516400	−	0.894431i	−0.0250491	−	0.0433863i
$426$	−25.4115	−	1.60379i	−1.23119	−	0.0777038i
$427$		0			0
$428$	−3.39490	−	1.96005i	−0.164099	−	0.0947424i
$429$	9.60641	−	14.4526i	0.463802	−	0.697780i
$430$	−7.39464	+	4.26930i	−0.356601	+	0.205884i
$431$			23.1299i			1.11413i	0.830469	+	0.557065i	$0.188073\pi$
$431$			23.1299i			1.11413i	−0.830469	+	0.557065i	$0.811927\pi$
$432$	−5.22870	−	15.0434i	−0.251566	−	0.723778i
$433$		−	34.9265i		−	1.67846i	−0.543776	−	0.839230i	$-0.683006\pi$
$433$		−	34.9265i		−	1.67846i	0.543776	−	0.839230i	$-0.316994\pi$
$434$		0			0
$435$	−24.5662	−	16.3288i	−1.17786	−	0.782904i
$436$	−6.95010	+	12.0379i	−0.332849	+	0.576512i
$437$	3.21078	−	5.56123i	0.153592	−	0.266030i
$438$	12.3922	+	0.782103i	0.592120	+	0.0373703i
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.617770	−	0.786359i	$-0.288036\pi$
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.989892	−	0.141824i	$-0.0452969\pi$
$440$	5.52912			0.263590
$441$		0			0
$442$	−10.6161			−0.504959
$443$	−32.3277	+	18.6644i	−1.53594	+	0.886774i	−0.536867	+	0.843667i	$0.680392\pi$
$443$	−32.3277	+	18.6644i	−1.53594	+	0.886774i	−0.999070	+	0.0431065i	$0.986275\pi$
$444$	10.4056	+	20.9724i	0.493829	+	0.995305i
$445$	5.13609	−	8.89596i	0.243474	−	0.421709i
$446$	16.3675	−	28.3493i	0.775023	−	1.34238i
$447$	−14.3632	+	7.12640i	−0.679354	+	0.337067i
$448$		0			0
$449$		−	23.9224i		−	1.12897i	−0.825445	−	0.564483i	$-0.809076\pi$
$449$		−	23.9224i		−	1.12897i	0.825445	−	0.564483i	$-0.190924\pi$
$450$	−0.499988	+	3.94530i	−0.0235697	+	0.185983i
$451$			8.74150i			0.411621i
$452$	33.4582	−	19.3171i	1.57374	−	0.908600i
$453$	20.6911	+	1.30587i	0.972153	+	0.0613552i
$454$	−3.77628	−	2.18024i	−0.177230	−	0.102324i
$455$		0			0
$456$	4.34629	−	6.53889i	0.203534	−	0.306212i
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	0.725380	−	0.688348i	$-0.241664\pi$
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	−0.958817	+	0.284024i	$0.908331\pi$
$458$	13.4831			0.630024
$459$	8.33207	+	1.59454i	0.388908	+	0.0744267i
$460$			5.80028i			0.270439i
$461$	−16.7279	−	28.9735i	−0.779094	−	1.34943i	−0.932465	−	0.361261i	$-0.882346\pi$
$461$	−16.7279	−	28.9735i	−0.779094	−	1.34943i	0.153371	−	0.988169i	$-0.450987\pi$
$462$		0			0
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	−0.463018	−	0.886349i	$-0.653233\pi$
$463$	11.5353	−	19.9798i	0.536092	−	0.928538i	0.999110	−	0.0421893i	$-0.0134333\pi$
$464$	−21.6312	−	12.4888i	−1.00420	−	0.579778i
$465$	1.36079	−	21.5612i	0.0631049	−	0.999876i
$466$	16.3595	+	28.3355i	0.757839	+	1.31262i
$467$	40.2791			1.86389			0.931946	−	0.362597i	$-0.118110\pi$
$467$	40.2791			1.86389			0.931946	+	0.362597i	$0.118110\pi$
$468$	17.7248	+	13.4649i	0.819330	+	0.622415i
$469$		0			0
$470$	−30.8527	+	17.8128i	−1.42313	+	0.821643i
$471$	27.6977	−	13.7424i	1.27624	−	0.633218i
$472$	2.81163	+	1.62329i	0.129416	+	0.0747182i
$473$	5.45205	+	3.14774i	0.250686	+	0.144733i
$474$	−46.0365	+	22.8414i	−2.11453	+	1.04914i
$475$	3.03078	−	1.74982i	0.139062	−	0.0802874i
$476$		0			0
$477$	−16.8566	+	7.07805i	−0.771812	+	0.324082i
$478$	35.9989			1.64655
$479$	−0.0777513	−	0.134669i	−0.00355255	−	0.00615319i	0.864244	−	0.503073i	$-0.167797\pi$
$479$	−0.0777513	−	0.134669i	−0.00355255	−	0.00615319i	−0.867796	+	0.496920i	$0.834464\pi$
$480$	1.83798	−	29.1222i	0.0838920	−	1.32924i
$481$	15.1922	+	8.77123i	0.692705	+	0.399934i
$482$	11.7540	−	20.3585i	0.535380	−	0.927305i
$483$		0			0
$484$	0.687435	+	1.19067i	0.0312471	+	0.0541215i
$485$		−	5.01784i		−	0.227848i
$486$	−21.8334	−	24.2966i	−0.990384	−	1.10212i
$487$	−16.5022			−0.747787			−0.373893	−	0.927472i	$-0.621977\pi$
$487$	−16.5022			−0.747787			−0.373893	+	0.927472i	$0.621977\pi$
$488$	−1.96341	−	3.40072i	−0.0888793	−	0.153944i
$489$	17.1003	−	25.7270i	0.773302	−	1.16342i
$490$		0			0
$491$	8.10003	+	4.67655i	0.365549	+	0.211050i	0.671512	−	0.740993i	$-0.265645\pi$
$491$	8.10003	+	4.67655i	0.365549	+	0.211050i	−0.305963	+	0.952043i	$0.598978\pi$
$492$	−11.1901	−	0.706235i	−0.504487	−	0.0318395i
$493$	11.5221	−	6.65230i	0.518930	−	0.299604i
$494$		−	35.9729i		−	1.61850i
$495$	−18.6642	+	7.83703i	−0.838892	+	0.352248i
$496$		−	18.2934i		−	0.821399i
$497$		0			0
$498$	10.0487	−	4.98577i	0.450295	−	0.223418i
$499$	−0.998116	+	1.72879i	−0.0446818	+	0.0773912i	−0.887501	−	0.460805i	$-0.847561\pi$
$499$	−0.998116	+	1.72879i	−0.0446818	+	0.0773912i	0.842820	+	0.538196i	$0.180894\pi$
$500$	−14.0727	+	24.3746i	−0.629351	+	1.09007i
$501$	−9.49808	−	19.1432i	−0.424343	−	0.855257i
$502$	20.6585	−	11.9272i	0.922035	−	0.532337i
$503$	15.7008			0.700063			0.350032	−	0.936738i	$-0.386171\pi$
$503$	15.7008			0.700063			0.350032	+	0.936738i	$0.386171\pi$
$504$		0			0
$505$	7.35727			0.327394
$506$	6.80147	−	3.92683i	0.302362	−	0.174569i
$507$	−5.82632	−	0.367715i	−0.258756	−	0.0163308i
$508$	−11.4679	+	19.8630i	−0.508807	+	0.881279i
$509$	−7.59893	+	13.1617i	−0.336817	+	0.583383i	−0.983832	−	0.179093i	$-0.942684\pi$
$509$	−7.59893	+	13.1617i	−0.336817	+	0.583383i	0.647016	+	0.762477i	$0.276017\pi$
$510$	10.3130	+	6.85486i	0.456667	+	0.303538i
$511$		0			0
$512$		−	29.7316i		−	1.31396i
$513$	−5.40310	+	28.2333i	−0.238553	+	1.24653i
$514$			19.6566i			0.867016i
$515$	−28.3867	+	16.3890i	−1.25087	+	0.722187i
$516$	−4.46993	+	6.72490i	−0.196778	+	0.296047i
$517$	22.7476	+	13.1333i	1.00044	+	0.577603i
$518$		0			0
$519$	−15.6739	−	0.989225i	−0.688010	−	0.0434222i
$520$	2.65699	+	4.60204i	0.116517	+	0.201813i
$521$	41.2320			1.80641			0.903204	−	0.429211i	$-0.141208\pi$
$521$	41.2320			1.80641			0.903204	+	0.429211i	$0.141208\pi$
$522$	−50.8236	−	6.44088i	−2.22449	−	0.281910i
$523$		−	42.7598i		−	1.86976i	−0.354970	−	0.934878i	$-0.615509\pi$
$523$		−	42.7598i		−	1.86976i	0.354970	−	0.934878i	$-0.384491\pi$
$524$	−2.94244	−	5.09645i	−0.128541	−	0.222640i
$525$		0			0
$526$	−9.22332	+	15.9753i	−0.402156	+	0.696554i
$527$	8.43872	+	4.87210i	0.367596	+	0.212232i
$528$	−15.3547	+	7.61834i	−0.668226	+	0.331546i
$529$	−10.8263	−	18.7517i	−0.470708	−	0.815291i
$530$	−26.6874			−1.15923
$531$	−11.7919	−	1.49438i	−0.511723	−	0.0648507i
$532$		0			0
$533$	−7.27579	+	4.20068i	−0.315149	+	0.181952i
$534$	1.12370	−	17.8046i	0.0486271	−	0.770481i
$535$	2.96723	+	1.71313i	0.128284	+	0.0740650i
$536$	0.478269	+	0.276129i	0.0206581	+	0.0119270i
$537$	21.6674	+	14.4020i	0.935018	+	0.621490i
$538$	−29.6337	+	17.1090i	−1.27760	+	0.737623i
$539$		0			0
$540$	−8.52435	−	24.5253i	−0.366830	−	1.05540i
$541$	−16.0862			−0.691599			−0.345800	−	0.938308i	$-0.612392\pi$
$541$	−16.0862			−0.691599			−0.345800	+	0.938308i	$0.612392\pi$
$542$	−15.2664	−	26.4421i	−0.655747	−	1.13579i
$543$	−3.37768	−	2.24509i	−0.144950	−	0.0963459i
$544$	11.3980	+	6.58063i	0.488685	+	0.282142i
$545$	6.07456	−	10.5214i	0.260206	−	0.450689i
$546$		0			0
$547$	−5.94015	−	10.2886i	−0.253982	−	0.439910i	0.710636	−	0.703560i	$-0.248407\pi$
$547$	−5.94015	−	10.2886i	−0.253982	−	0.439910i	−0.964619	+	0.263649i	$0.915074\pi$
$548$		−	41.5717i		−	1.77585i
$549$	11.4479	+	8.69658i	0.488586	+	0.371161i
$550$	4.28012			0.182505
$551$	22.5413	+	39.0427i	0.960293	+	1.66328i
$552$	0.732233	+	1.47580i	0.0311659	+	0.0628144i
$553$		0			0
$554$	52.1078	+	30.0845i	2.21385	+	1.27817i
$555$	−9.09477	−	18.3304i	−0.386052	−	0.778081i
$556$	20.5910	−	11.8882i	0.873254	−	0.504173i
$557$			30.4848i			1.29168i	0.763472	+	0.645841i	$0.223493\pi$
$557$			30.4848i			1.29168i	−0.763472	+	0.645841i	$0.776507\pi$
$558$	−14.5261	−	34.5945i	−0.614941	−	1.46450i
$559$			6.05052i			0.255910i
$560$		0			0
$561$	0.575088	−	9.11207i	0.0242802	−	0.384712i
$562$	5.76958	−	9.99320i	0.243375	−	0.421538i
$563$	11.2686	−	19.5177i	0.474914	−	0.822575i	−0.524673	−	0.851304i	$-0.675813\pi$
$563$	11.2686	−	19.5177i	0.474914	−	0.822575i	0.999587	+	0.0287288i	$0.00914592\pi$
$564$	−18.6499	+	28.0583i	−0.785302	+	1.18147i
$565$	−29.2433	+	16.8836i	−1.23027	+	0.710300i
$566$	63.4572			2.66730
$567$		0			0
$568$	−5.74852			−0.241202
$569$	−38.5935	+	22.2819i	−1.61792	+	0.934108i	−0.630465	+	0.776218i	$0.717136\pi$
$569$	−38.5935	+	22.2819i	−1.61792	+	0.934108i	−0.987457	+	0.157890i	$0.949531\pi$
$570$	−23.2277	+	34.9456i	−0.972902	+	1.46371i
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	0.214998	+	0.976614i	$0.431025\pi$
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	−0.953272	+	0.302113i	$0.902308\pi$
$572$	11.9783	−	20.7471i	0.500839	−	0.867479i
$573$	−0.985859	+	15.6206i	−0.0411849	+	0.652561i
$574$		0			0
$575$			0.734319i			0.0306232i
$576$	−12.5004	−	29.7702i	−0.520850	−	1.24042i
$577$			3.75461i			0.156306i	0.996941	+	0.0781531i	$0.0249023\pi$
$577$			3.75461i			0.156306i	−0.996941	+	0.0781531i	$0.975098\pi$
$578$	26.0136	−	15.0189i	1.08202	−	0.624705i
$579$	−4.22071	−	8.50677i	−0.175407	−	0.353529i
$580$	−35.2654	−	20.3605i	−1.46432	−	0.845423i
$581$		0			0
$582$	−3.87330	−	7.80658i	−0.160554	−	0.323593i
$583$	9.83827	+	17.0404i	0.407460	+	0.705741i
$584$	2.80332			0.116002
$585$	−15.4919	−	11.7687i	−0.640513	−	0.486574i
$586$			14.8512i			0.613497i
$587$	15.8021	+	27.3700i	0.652222	+	1.12968i	0.982583	+	0.185826i	$0.0594961\pi$
$587$	15.8021	+	27.3700i	0.652222	+	1.12968i	−0.330361	+	0.943855i	$0.607171\pi$
$588$		0			0
$589$	−16.5091	+	28.5946i	−0.680246	+	1.17822i
$590$	−15.0261	−	8.67532i	−0.618614	−	0.357157i
$591$	−4.16796	−	2.77037i	−0.171447	−	0.113958i
$592$	−8.66343	−	15.0055i	−0.356065	−	0.616722i
$593$	−37.1177			−1.52424			−0.762120	−	0.647436i	$-0.775841\pi$
$593$	−37.1177			−1.52424			−0.762120	+	0.647436i	$0.775841\pi$
$594$	−22.9876	+	26.5996i	−0.943193	+	1.09139i
$595$		0			0
$596$	−19.1689	+	11.0671i	−0.785187	+	0.453328i
$597$	7.41900	+	4.93128i	0.303640	+	0.201824i
$598$	6.53682	+	3.77403i	0.267310	+	0.154332i
$599$	24.5188	+	14.1559i	1.00181	+	0.578396i	0.908784	−	0.417267i	$-0.137012\pi$
$599$	24.5188	+	14.1559i	1.00181	+	0.578396i	0.0930277	+	0.995664i	$0.470345\pi$
$600$	−0.0565530	+	0.896063i	−0.00230877	+	0.0365816i
$601$	−20.8341	+	12.0286i	−0.849840	+	0.490655i	−0.860597	−	0.509287i	$-0.829909\pi$
$601$	−20.8341	+	12.0286i	−0.849840	+	0.490655i	0.0107568	+	0.999942i	$0.496576\pi$
$602$		0			0
$603$	−2.00584	−	0.254201i	−0.0816841	−	0.0103519i
$604$	28.6203			1.16454
$605$	−0.600836	−	1.04068i	−0.0244274	−	0.0423096i
$606$	11.4462	−	5.67912i	0.464969	−	0.230698i
$607$	−8.24496	−	4.76023i	−0.334653	−	0.193212i	0.323252	−	0.946313i	$-0.395224\pi$
$607$	−8.24496	−	4.76023i	−0.334653	−	0.193212i	−0.657905	+	0.753101i	$0.728557\pi$
$608$	−22.2985	+	38.6221i	−0.904323	+	1.56633i
$609$		0			0
$610$	10.4930	+	18.1744i	0.424848	+	0.735859i
$611$			25.2446i			1.02129i
$612$	11.6180	+	1.47235i	0.469629	+	0.0595162i
$613$	−2.46216			−0.0994459			−0.0497230	−	0.998763i	$-0.515834\pi$
$613$	−2.46216			−0.0994459			−0.0497230	+	0.998763i	$0.515834\pi$
$614$	−3.26210	−	5.65012i	−0.131648	−	0.228020i
$615$	9.78040	+	0.617267i	0.394384	+	0.0248906i
$616$		0			0
$617$	18.7738	+	10.8390i	0.755804	+	0.436364i	0.827787	−	0.561042i	$-0.189599\pi$
$617$	18.7738	+	10.8390i	0.755804	+	0.436364i	−0.0719831	+	0.997406i	$0.522933\pi$
$618$	−31.5122	+	47.4093i	−1.26761	+	1.90708i
$619$	20.8767	−	12.0532i	0.839105	−	0.484457i	−0.0178550	−	0.999841i	$-0.505684\pi$
$619$	20.8767	−	12.0532i	0.839105	−	0.484457i	0.856960	+	0.515383i	$0.172350\pi$
$620$		−	29.8238i		−	1.19775i
$621$	−4.56356	−	3.94387i	−0.183129	−	0.158262i
$622$		−	40.7615i		−	1.63439i
$623$		0			0
$624$	−13.7196	−	9.11915i	−0.549222	−	0.365058i
$625$	10.7184	−	18.5648i	0.428735	−	0.742591i
$626$	26.7643	−	46.3571i	1.06972	−	1.85280i
$627$	30.8763	+	1.94869i	1.23308	+	0.0778230i
$628$	36.9649	−	21.3417i	1.47506	−	0.851627i
$629$	9.22934			0.367998
$630$		0			0
$631$	3.37520			0.134365			0.0671824	−	0.997741i	$-0.478599\pi$
$631$	3.37520			0.134365			0.0671824	+	0.997741i	$0.478599\pi$
$632$	−10.0481	+	5.80128i	−0.399692	+	0.230762i
$633$	−12.2129	−	24.6149i	−0.485418	−	0.978353i
$634$	−17.0021	+	29.4486i	−0.675242	+	1.16955i
$635$	10.0232	−	17.3608i	0.397761	−	0.688941i
$636$	−22.6084	+	11.2173i	−0.896481	+	0.444797i
$637$		0			0
$638$			55.1368i			2.18289i
$639$	19.4048	−	8.14801i	0.767641	−	0.322330i
$640$		−	13.4377i		−	0.531174i
$641$	30.9152	−	17.8489i	1.22108	−	0.704989i	0.255930	−	0.966695i	$-0.417618\pi$
$641$	30.9152	−	17.8489i	1.22108	−	0.704989i	0.965148	+	0.261706i	$0.0842850\pi$
$642$	5.93868	+	0.374807i	0.234381	+	0.0147924i
$643$	−3.03956	−	1.75489i	−0.119868	−	0.0692060i	0.438867	−	0.898552i	$-0.355380\pi$
$643$	−3.03956	−	1.75489i	−0.119868	−	0.0692060i	−0.558735	+	0.829346i	$0.688713\pi$
$644$		0			0
$645$	3.90683	−	5.87774i	0.153831	−	0.231436i
$646$	−9.46292	−	16.3903i	−0.372314	−	0.644866i
$647$	−14.0599			−0.552752			−0.276376	−	0.961050i	$-0.589134\pi$
$647$	−14.0599			−0.552752			−0.276376	+	0.961050i	$0.589134\pi$
$648$	−5.26501	−	5.16402i	−0.206829	−	0.202862i
$649$			12.7926i			0.502153i
$650$	2.05679	+	3.56246i	0.0806739	+	0.139731i
$651$		0			0
$652$	21.3225	−	36.9317i	0.835055	−	1.44636i
$653$	10.2675	+	5.92792i	0.401797	+	0.231978i	0.687259	−	0.726412i	$-0.258814\pi$
$653$	10.2675	+	5.92792i	0.401797	+	0.231978i	−0.285462	+	0.958390i	$0.592147\pi$
$654$	1.32902	−	21.0579i	0.0519688	−	0.823429i
$655$	2.57177	+	4.45443i	0.100487	+	0.174049i
$656$	8.29810			0.323986
$657$	−9.46292	+	3.97345i	−0.369184	+	0.155019i
$658$		0			0
$659$	5.03144	−	2.90491i	0.195997	−	0.113159i	−0.398790	−	0.917042i	$-0.630570\pi$
$659$	5.03144	−	2.90491i	0.195997	−	0.113159i	0.594787	+	0.803883i	$0.297236\pi$
$660$	−25.0327	+	12.4202i	−0.974396	+	0.483455i
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	0.654660	−	0.755923i	$-0.272812\pi$
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	−0.327319	+	0.944914i	$0.606145\pi$
$662$	42.3046	+	24.4246i	1.64422	+	0.949288i
$663$	7.86058	−	3.90009i	0.305280	−	0.151467i
$664$	2.19328	−	1.26629i	0.0851158	−	0.0491416i
$665$		0			0
$666$	−28.2987	−	21.4975i	−1.09655	−	0.833010i
$667$	−9.45954			−0.366275
$668$	−14.7503	−	25.5483i	−0.570707	−	0.988493i
$669$	−1.70429	+	27.0039i	−0.0658915	+	1.04403i
$670$	−2.55600	−	1.47571i	−0.0987468	−	0.0570115i
$671$	7.73645	−	13.3999i	0.298662	−	0.517298i
$672$		0			0
$673$	13.4646	+	23.3214i	0.519023	+	0.898975i	0.999756	+	0.0221072i	$0.00703750\pi$
$673$	13.4646	+	23.3214i	0.519023	+	0.898975i	−0.480732	+	0.876867i	$0.659629\pi$
$674$			24.8740i			0.958110i
$675$	−1.07919	−	3.10492i	−0.0415380	−	0.119509i
$676$	−8.05905			−0.309964
$677$	−22.7056	−	39.3273i	−0.872648	−	1.51147i	−0.859247	−	0.511560i	$-0.829068\pi$
$677$	−22.7056	−	39.3273i	−0.872648	−	1.51147i	−0.0134007	−	0.999910i	$-0.504266\pi$
$678$	−32.4631	+	48.8400i	−1.24674	+	1.87569i
$679$		0			0
$680$	2.42120	+	1.39788i	0.0928487	+	0.0536062i
$681$	3.59706	+	0.227020i	0.137839	+	0.00869942i
$682$	−34.9717	+	20.1909i	−1.33913	+	0.773150i
$683$		−	43.4795i		−	1.66370i	−0.555003	−	0.831848i	$-0.687283\pi$
$683$		−	43.4795i		−	1.66370i	0.555003	−	0.831848i	$-0.312717\pi$
$684$	−4.98906	+	39.3675i	−0.190761	+	1.50526i
$685$			36.3347i			1.38828i
$686$		0			0
$687$	−9.98338	+	4.95334i	−0.380890	+	0.188982i
$688$	2.98808	−	5.17551i	0.113919	−	0.197314i
$689$	−9.45546	+	16.3773i	−0.360224	+	0.623927i
$690$	−3.91325	−	7.88709i	−0.148975	−	0.300256i
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.877705	−	0.479201i	$-0.840926\pi$
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.0238522	+	0.999715i	$0.507593\pi$
$692$	−21.6804			−0.824166
$693$		0			0
$694$	45.4845			1.72657
$695$	−17.9971	+	10.3906i	−0.682668	+	0.394139i
$696$	−11.5431	−	0.728519i	−0.437542	−	0.0276144i
$697$	−2.21004	+	3.82790i	−0.0837112	+	0.144992i
$698$	2.67212	−	4.62824i	0.101141	−	0.175182i
$699$	−22.5229	−	14.9706i	−0.851893	−	0.566239i
$700$		0			0
$701$		−	8.26437i		−	0.312141i	−0.987746	−	0.156070i	$-0.950117\pi$
$701$		−	8.26437i		−	0.312141i	0.987746	−	0.156070i	$-0.0498827\pi$
$702$	−33.1861	−	6.35095i	−1.25253	−	0.239701i
$703$			31.2737i			1.17951i
$704$	−30.0947	+	17.3752i	−1.13424	+	0.654852i
$705$	16.3005	−	24.5237i	0.613912	−	0.923616i
$706$	46.0484	+	26.5861i	1.73306	+	1.00058i
$707$		0			0
$708$	−16.3759	−	1.03353i	−0.615444	−	0.0388423i
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	−0.916954	−	0.398994i	$-0.869360\pi$
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	0.112938	−	0.993602i	$-0.463974\pi$
$710$	30.7216			1.15296
$711$	25.6957	−	33.8252i	0.963666	−	1.26854i
$712$		−	4.02771i		−	0.150945i
$713$	−3.46405	−	5.99992i	−0.129730	−	0.224699i
$714$		0			0
$715$	−10.4694	+	18.1335i	−0.391532	+	0.678153i
$716$	31.1041	+	17.9579i	1.16241	+	0.671120i
$717$	−26.6549	+	13.2250i	−0.995444	+	0.493898i
$718$	11.7805	+	20.4044i	0.439645	+	0.761487i
$719$	23.1451			0.863165			0.431583	−	0.902073i	$-0.357955\pi$
$719$	23.1451			0.863165			0.431583	+	0.902073i	$0.357955\pi$
$720$	7.43951	+	17.7175i	0.277254	+	0.660291i
$721$		0			0
$722$	21.0584	−	12.1581i	0.783712	−	0.452477i
$723$	−1.22390	+	19.3923i	−0.0455174	+	0.721207i
$724$	−4.84874	−	2.79942i	−0.180202	−	0.104040i
$725$	−4.46462	−	2.57765i	−0.165812	−	0.0957316i
$726$	−1.73807	−	1.15526i	−0.0645057	−	0.0428758i
$727$	−4.76878	+	2.75326i	−0.176864	+	0.102113i	−0.585819	−	0.810442i	$-0.699227\pi$
$727$	−4.76878	+	2.75326i	−0.176864	+	0.102113i	0.408954	+	0.912555i	$0.365894\pi$
$728$		0			0
$729$	25.0922	+	9.96907i	0.929340	+	0.369225i
$730$	−14.9817			−0.554497
$731$	1.59163	+	2.75679i	0.0588687	+	0.101964i
$732$	16.5283	+	10.9861i	0.610904	+	0.406058i
$733$	3.45543	+	1.99499i	0.127629	+	0.0736867i	0.562455	−	0.826828i	$-0.309857\pi$
$733$	3.45543	+	1.99499i	0.127629	+	0.0736867i	−0.434826	+	0.900514i	$0.643190\pi$
$734$	3.46991	−	6.01005i	0.128077	−	0.221835i
$735$		0			0
$736$	−4.67882	−	8.10395i	−0.172463	−	0.298716i
$737$			2.17607i			0.0801566i
$738$	15.6925	−	6.58922i	0.577648	−	0.242553i
$739$	−1.74331			−0.0641289			−0.0320644	−	0.999486i	$-0.510208\pi$
$739$	−1.74331			−0.0641289			−0.0320644	+	0.999486i	$0.510208\pi$
$740$	−14.1240	−	24.4635i	−0.519208	−	0.899295i
$741$	13.2155	+	26.6356i	0.485483	+	0.978483i
$742$		0			0
$743$	8.70204	+	5.02413i	0.319247	+	0.184317i	0.651057	−	0.759029i	$-0.274326\pi$
$743$	8.70204	+	5.02413i	0.319247	+	0.184317i	−0.331810	+	0.943346i	$0.607659\pi$
$744$	−3.76498	−	7.58826i	−0.138031	−	0.278199i
$745$	16.7541	−	9.67296i	0.613821	−	0.354390i
$746$			13.9253i			0.509843i
$747$	−5.60881	+	7.38329i	−0.205216	+	0.270140i
$748$		−	12.6040i		−	0.460846i
$749$		0			0
$750$	2.69103	−	42.6385i	0.0982626	−	1.55694i
$751$	11.6725	−	20.2174i	0.425936	−	0.737743i	−0.570571	−	0.821248i	$-0.693278\pi$
$751$	11.6725	−	20.2174i	0.425936	−	0.737743i	0.996507	+	0.0835052i	$0.0266115\pi$
$752$	12.4672	−	21.5938i	0.454631	−	0.787444i
$753$	−10.9146	+	16.4207i	−0.397749	+	0.598405i
$754$	−45.8919	+	26.4957i	−1.67128	+	0.964916i
$755$	−25.0148			−0.910383
$756$		0			0
$757$	−14.3334			−0.520957			−0.260479	−	0.965480i	$-0.583880\pi$
$757$	−14.3334			−0.520957			−0.260479	+	0.965480i	$0.583880\pi$
$758$	6.98566	−	4.03317i	0.253730	−	0.146491i
$759$	−3.59344	+	5.40625i	−0.130434	+	0.196234i
$760$	−4.73672	+	8.20424i	−0.171819	+	0.297599i
$761$	11.3178	−	19.6029i	0.410268	−	0.710606i	−0.584650	−	0.811285i	$-0.698768\pi$
$761$	11.3178	−	19.6029i	0.410268	−	0.710606i	0.994919	+	0.100680i	$0.0321017\pi$
$762$	2.19293	−	34.7463i	0.0794416	−	1.25873i
$763$		0			0
$764$			21.6067i			0.781702i
$765$	−10.1544	−	1.28687i	−0.367133	−	0.0465269i
$766$		−	71.7122i		−	2.59107i
$767$	−10.6476	+	6.14741i	−0.384463	+	0.221970i
$768$	6.19812	+	12.4922i	0.223655	+	0.450774i
$769$	−42.6873	−	24.6455i	−1.53934	−	0.888741i	−0.998877	−	0.0473762i	$-0.984914\pi$
$769$	−42.6873	−	24.6455i	−1.53934	−	0.888741i	−0.540468	−	0.841365i	$-0.681753\pi$
$770$		0			0
$771$	−7.22133	−	14.5545i	−0.260070	−	0.524167i
$772$	−6.55467	−	11.3530i	−0.235908	−	0.408604i
$773$	−22.0167			−0.791886			−0.395943	−	0.918275i	$-0.629582\pi$
$773$	−22.0167			−0.791886			−0.395943	+	0.918275i	$0.629582\pi$
$774$	1.54105	−	12.1601i	0.0553919	−	0.437085i
$775$		−	3.77571i		−	0.135627i
$776$	−0.983745	−	1.70390i	−0.0353144	−	0.0611663i
$777$		0			0
$778$	14.1232	−	24.4621i	0.506340	−	0.877007i
$779$	−12.9708	−	7.48872i	−0.464729	−	0.268311i
$780$	−22.3670	−	14.8669i	−0.800866	−	0.532322i
$781$	−11.3255	−	19.6163i	−0.405258	−	0.701927i
$782$	3.97115			0.142008
$783$	39.9978	−	13.9022i	1.42941	−	0.496823i
$784$		0			0
$785$	−32.3083	+	18.6532i	−1.15313	+	0.665761i
$786$	7.43946	+	4.94488i	0.265357	+	0.176378i
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	0.658108	−	0.752923i	$-0.271357\pi$
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	−0.322996	+	0.946400i	$0.604690\pi$
$788$	−5.98320	−	3.45440i	−0.213143	−	0.123058i
$789$	0.960390	−	15.2171i	0.0341908	−	0.541742i
$790$	53.6998	−	31.0036i	1.91055	−	1.10306i
$791$		0			0
$792$	−4.80130	+	6.32030i	−0.170607	+	0.224582i
$793$	14.8708			0.528079
$794$	−30.9112	−	53.5397i	−1.09700	−	1.90005i
$795$	19.7603	−	9.80424i	0.700826	−	0.347721i
$796$	10.6502	+	6.14887i	0.377485	+	0.217941i
$797$	−1.98299	+	3.43465i	−0.0702412	+	0.121661i	−0.899007	−	0.437934i	$-0.855710\pi$
$797$	−1.98299	+	3.43465i	−0.0702412	+	0.121661i	0.828766	+	0.559596i	$0.189044\pi$
$798$		0			0
$799$	6.64078	+	11.5022i	0.234934	+	0.406917i
$800$		−	5.09977i		−	0.180304i
$801$	5.70892	+	13.5960i	0.201715	+	0.480391i
$802$	−60.8624			−2.14913
$803$	5.52298	+	9.56608i	0.194902	+	0.337580i
$804$	−2.78560	−	0.175807i	−0.0982407	−	0.00620024i
$805$		0			0
$806$	−33.6109	−	19.4053i	−1.18389	−	0.683521i
$807$	15.6565	−	23.5548i	0.551134	−	0.829168i
$808$	2.49829	−	1.44239i	0.0878896	−	0.0507431i
$809$		−	41.5922i		−	1.46230i	−0.682215	−	0.731152i	$-0.738983\pi$
$809$		−	41.5922i		−	1.46230i	0.682215	−	0.731152i	$-0.261017\pi$
$810$	28.1376	+	27.5979i	0.988655	+	0.969692i
$811$		−	13.3293i		−	0.468056i	−0.972230	−	0.234028i	$-0.924809\pi$
$811$		−	13.3293i		−	0.468056i	0.972230	−	0.234028i	$-0.0751907\pi$
$812$		0			0
$813$	21.0179	+	13.9703i	0.737131	+	0.489958i
$814$	−19.1241	+	33.1239i	−0.670299	+	1.16099i
$815$	−18.6364	+	32.2792i	−0.652806	+	1.13069i
$816$	−8.64988	−	0.545918i	−0.302806	−	0.0191109i
$817$	−9.34139	+	5.39326i	−0.326814	+	0.188686i
$818$	63.4417			2.21819
$819$		0			0
$820$	13.5284			0.472432
$821$	33.4332	−	19.3027i	1.16683	−	0.673668i	0.213897	−	0.976856i	$-0.431384\pi$
$821$	33.4332	−	19.3027i	1.16683	−	0.673668i	0.952931	+	0.303188i	$0.0980510\pi$
$822$	28.0470	+	56.5283i	0.978251	+	1.97165i
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	−0.757616	−	0.652701i	$-0.773636\pi$
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	0.944063	+	0.329764i	$0.106969\pi$
$824$	−6.42613	+	11.1304i	−0.223865	+	0.387745i
$825$	−3.16916	+	1.57240i	−0.110336	+	0.0547441i
$826$		0			0
$827$			11.7079i			0.407125i	0.979062	+	0.203562i	$0.0652520\pi$
$827$			11.7079i			0.407125i	−0.979062	+	0.203562i	$0.934748\pi$
$828$	−6.63026	−	5.03677i	−0.230418	−	0.175040i
$829$		−	17.4300i		−	0.605367i	−0.953091	−	0.302684i	$-0.902117\pi$
$829$		−	17.4300i		−	0.605367i	0.953091	−	0.302684i	$-0.0978826\pi$
$830$	−11.7215	+	6.76740i	−0.406858	+	0.234900i
$831$	−49.6348	−	3.13259i	−1.72181	−	0.108668i
$832$	−28.9237	−	16.6991i	−1.00275	−	0.578937i
$833$		0			0
$834$	−19.9786	+	30.0574i	−0.691804	+	1.04080i
$835$	12.8921	+	22.3298i	0.446151	+	0.772756i
$836$	42.7085			1.47711
$837$	23.4648	+	20.2785i	0.811063	+	0.700928i
$838$		−	76.6534i		−	2.64795i
$839$	−0.704502	−	1.22023i	−0.0243221	−	0.0421271i	0.853608	−	0.520916i	$-0.174409\pi$
$839$	−0.704502	−	1.22023i	−0.0243221	−	0.0421271i	−0.877930	+	0.478789i	$0.841076\pi$
$840$		0			0
$841$	18.7055	−	32.3988i	0.645016	−	1.11720i
$842$	−14.0097	−	8.08853i	−0.482808	−	0.278749i
$843$	−0.600765	+	9.51892i	−0.0206914	+	0.327849i
$844$	−18.9663	−	32.8506i	−0.652848	−	1.13077i
$845$	7.04382			0.242315
$846$	6.42973	−	50.7356i	0.221059	−	1.74432i
$847$		0			0
$848$	16.1761	−	9.33925i	0.555488	−	0.320711i
$849$	−46.9860	+	23.3125i	−1.61256	+	0.800083i
$850$	1.87426	+	1.08211i	0.0642867	+	0.0371160i
$851$	−5.68290	−	3.28102i	−0.194807	−	0.112472i
$852$	26.0260	−	12.9130i	0.891637	−	0.442393i
$853$	28.0716	−	16.2071i	0.961153	−	0.554922i	0.0646255	−	0.997910i	$-0.479415\pi$
$853$	28.0716	−	16.2071i	0.961153	−	0.554922i	0.896528	+	0.442987i	$0.146081\pi$
$854$		0			0
$855$	4.36056	−	34.4082i	0.149128	−	1.17674i
$856$	1.34343			0.0459176
$857$	22.2270	+	38.4982i	0.759258	+	1.31507i	0.943229	+	0.332142i	$0.107771\pi$
$857$	22.2270	+	38.4982i	0.759258	+	1.31507i	−0.183971	+	0.982932i	$0.558895\pi$
$858$	−2.29054	+	36.2928i	−0.0781977	+	1.23902i
$859$	−13.5528	−	7.82472i	−0.462416	−	0.266976i	0.250644	−	0.968079i	$-0.419358\pi$
$859$	−13.5528	−	7.82472i	−0.462416	−	0.266976i	−0.713060	+	0.701103i	$0.752691\pi$
$860$	4.87147	−	8.43763i	0.166116	−	0.287721i
$861$		0			0
$862$	−24.2342	−	41.9748i	−0.825420	−	1.42967i
$863$		−	18.1185i		−	0.616762i	−0.951263	−	0.308381i	$-0.900213\pi$
$863$		−	18.1185i		−	0.616762i	0.951263	−	0.308381i	$-0.0997872\pi$
$864$	31.6934	+	27.3897i	1.07823	+	0.931818i
$865$	18.9492			0.644294
$866$	36.5939	+	63.3825i	1.24351	+	2.15383i
$867$	−13.7438	+	20.6773i	−0.466765	+	0.702237i
$868$		0			0
$869$	−39.5927	−	22.8589i	−1.34309	−	0.775434i
$870$	61.6896	+	3.89340i	2.09147	+	0.131999i
$871$	−1.81120	+	1.04570i	−0.0613703	+	0.0354321i
$872$		−	4.76366i		−	0.161318i
$873$	5.73587	+	4.35733i	0.194130	+	0.147473i
$874$			13.4562i			0.455164i
$875$		0			0
$876$	−12.6918	+	6.29716i	−0.428817	+	0.212761i
$877$	1.38926	−	2.40628i	0.0469121	−	0.0812542i	−0.841616	−	0.540077i	$-0.818395\pi$
$877$	1.38926	−	2.40628i	0.0469121	−	0.0812542i	0.888528	+	0.458822i	$0.151729\pi$
$878$	−40.7521	+	70.5847i	−1.37532	+	2.38212i
$879$	−5.45593	−	10.9964i	−0.184024	−	0.370898i
$880$	17.9106	−	10.3407i	0.603767	−	0.348585i
$881$	1.96106			0.0660696			0.0330348	−	0.999454i	$-0.489483\pi$
$881$	1.96106			0.0660696			0.0330348	+	0.999454i	$0.489483\pi$
$882$		0			0
$883$	−36.9657			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$883$	−36.9657			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$884$	10.4906	−	6.05676i	0.352838	−	0.203711i
$885$	14.3129	+	0.903329i	0.481124	+	0.0303651i
$886$	39.1110	−	67.7422i	1.31396	−	2.27584i
$887$	−11.2584	+	19.5001i	−0.378020	+	0.654750i	−0.990774	−	0.135524i	$-0.956728\pi$
$887$	−11.2584	+	19.5001i	−0.378020	+	0.654750i	0.612754	+	0.790274i	$0.290062\pi$
$888$	−6.68195	−	4.44138i	−0.224232	−	0.149043i
$889$		0			0
$890$			21.5251i			0.721525i
$891$	7.24888	−	28.1403i	0.242847	−	0.942736i
$892$			37.3521i			1.25064i
$893$	−38.9751	+	22.5023i	−1.30425	+	0.753011i
$894$	18.5988	−	27.9814i	0.622036	−	0.935839i
$895$	−27.1857	−	15.6957i	−0.908719	−	0.524649i
$896$		0			0
$897$	−6.22657	−	0.392976i	−0.207899	−	0.0131211i
$898$	25.0644	+	43.4129i	0.836411	+	1.44871i
$899$	48.6389			1.62220
$900$	−1.75681	−	4.18390i	−0.0585603	−	0.139463i
$901$			9.94931i			0.331459i
$902$	−9.15882	−	15.8635i	−0.304955	−	0.528198i
$903$		0			0
$904$	−6.62005	+	11.4663i	−0.220180	+	0.381362i
$905$	4.23792	+	2.44676i	0.140873	+	0.0813332i
$906$	−38.9172	+	19.3091i	−1.29294	+	0.641502i
$907$	9.55982	+	16.5581i	0.317428	+	0.549802i	0.979951	−	0.199240i	$-0.0638473\pi$
$907$	9.55982	+	16.5581i	0.317428	+	0.549802i	−0.662522	+	0.749042i	$0.730514\pi$
$908$	4.97550			0.165118
$909$	−6.38881	+	8.41005i	−0.211903	+	0.278944i
$910$		0			0
$911$	4.92610	−	2.84408i	0.163209	−	0.0942287i	−0.416171	−	0.909286i	$-0.636628\pi$
$911$	4.92610	−	2.84408i	0.163209	−	0.0942287i	0.579380	+	0.815058i	$0.303295\pi$
$912$	1.84984	−	29.3101i	0.0612544	−	0.970556i
$913$	8.64222	+	4.98959i	0.286016	+	0.165131i
$914$	18.1122	+	10.4571i	0.599100	+	0.345890i
$915$	−14.4462	−	9.60212i	−0.477576	−	0.317436i
$916$	−13.3237	+	7.69242i	−0.440226	+	0.254165i
$917$		0			0
$918$	−16.7912	+	5.83618i	−0.554193	+	0.192623i
$919$	21.8510			0.720798			0.360399	−	0.932798i	$-0.382640\pi$
$919$	21.8510			0.720798			0.360399	+	0.932798i	$0.382640\pi$
$920$	−0.993890	−	1.72147i	−0.0327676	−	0.0567551i
$921$	4.49108	+	2.98515i	0.147986	+	0.0983639i
$922$	60.7134	+	35.0529i	1.99949	+	1.15441i
$923$	10.8848	−	18.8530i	0.358278	−	0.620555i
$924$		0			0
$925$	−1.78811	−	3.09709i	−0.0587926	−	0.101832i
$926$			48.3441i			1.58869i
$927$	5.91581	−	46.6803i	0.194301	−	1.53318i
$928$	65.6955			2.15656
$929$	−8.08806	−	14.0089i	−0.265361	−	0.459618i	0.702297	−	0.711884i	$-0.252158\pi$
$929$	−8.08806	−	14.0089i	−0.265361	−	0.459618i	−0.967658	+	0.252266i	$0.918824\pi$
$930$	20.1211	+	40.5537i	0.659796	+	1.32981i
$931$		0			0
$932$	−32.3321	−	18.6669i	−1.05907	−	0.611456i
$933$	14.9747	+	30.1813i	0.490250	+	0.988091i
$934$	−73.0960	+	42.2020i	−2.39177	+	1.38089i
$935$			11.0162i			0.360267i
$936$	−7.56780	−	0.959069i	−0.247361	−	0.0313482i
$937$			14.0440i			0.458799i	0.973332	+	0.229400i	$0.0736762\pi$
$937$			14.0440i			0.458799i	−0.973332	+	0.229400i	$0.926324\pi$
$938$		0			0
$939$	−2.78686	+	44.1569i	−0.0909459	+	1.44101i
$940$	20.3252	−	35.2043i	0.662936	−	1.14824i
$941$	−21.5934	+	37.4009i	−0.703924	+	1.21923i	0.263154	+	0.964754i	$0.415237\pi$
$941$	−21.5934	+	37.4009i	−0.703924	+	1.21923i	−0.967078	+	0.254479i	$0.918096\pi$
$942$	−35.8656	+	53.9589i	−1.16856	+	1.75808i
$943$	2.72163	−	1.57133i	0.0886284	−	0.0511696i
$944$	12.1437			0.395244
$945$		0			0
$946$	−13.1921			−0.428911
$947$	−16.6235	+	9.59758i	−0.540191	+	0.311879i	−0.745156	−	0.666890i	$-0.767625\pi$
$947$	−16.6235	+	9.59758i	−0.540191	+	0.311879i	0.204965	+	0.978769i	$0.434292\pi$
$948$	32.4606	−	48.8362i	1.05427	−	1.58613i
$949$	−5.30807	+	9.19386i	−0.172307	+	0.298445i
$950$	−3.66672	+	6.35095i	−0.118964	+	0.206052i
$951$	1.77037	−	28.0509i	0.0574082	−	0.909614i
$952$		0			0
$953$		−	5.62718i		−	0.182282i	−0.995838	−	0.0911411i	$-0.970949\pi$
$953$		−	5.62718i		−	0.182282i	0.995838	−	0.0911411i	$-0.0290514\pi$
$954$	23.1744	−	30.5062i	0.750300	−	0.987675i
$955$		−	18.8848i		−	0.611097i
$956$	−35.5732	+	20.5382i	−1.15052	+	0.664252i
$957$	−20.2558	−	40.8253i	−0.654777	−	1.31969i
$958$	0.282197	+	0.162926i	0.00911736	+	0.00526391i
$959$		0			0
$960$	17.3151	+	34.8983i	0.558842	+	1.12634i
$961$	2.31141	+	4.00348i	0.0745616	+	0.129144i
$962$	−36.7599			−1.18519
$963$	−4.53491	+	1.90420i	−0.146135	+	0.0613619i
$964$			26.8237i			0.863934i
$965$	5.72894	+	9.92282i	0.184421	+	0.319427i
$966$		0			0
$967$	−7.62091	+	13.1998i	−0.245072	+	0.424477i	−0.962152	−	0.272514i	$-0.912145\pi$
$967$	−7.62091	+	13.1998i	−0.245072	+	0.424477i	0.717080	+	0.696991i	$0.245478\pi$
$968$	−0.408049	−	0.235587i	−0.0131152	−	0.00757206i
$969$	13.0280	+	8.65952i	0.418521	+	0.278184i
$970$	5.25740	+	9.10608i	0.168805	+	0.292379i
$971$	−40.8958			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$971$	−40.8958			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$972$	35.4370	+	11.5528i	1.13664	+	0.370558i
$973$		0			0
$974$	29.9472	−	17.2900i	0.959571	−	0.554009i
$975$	−2.83168	−	1.88217i	−0.0906862	−	0.0602776i
$976$	−12.7202	−	7.34404i	−0.407165	−	0.235077i
$977$	−8.98296	−	5.18631i	−0.287390	−	0.165925i	0.349374	−	0.936983i	$-0.386394\pi$
$977$	−8.98296	−	5.18631i	−0.287390	−	0.165925i	−0.636764	+	0.771058i	$0.719728\pi$
$978$	−4.07737	+	64.6045i	−0.130380	+	2.06582i
$979$	13.7442	−	7.93522i	0.439267	−	0.253611i
$980$		0			0
$981$	6.75206	+	16.0803i	0.215577	+	0.513404i
$982$	−19.5993			−0.625438
$983$	1.05850	+	1.83338i	0.0337609	+	0.0584756i	0.882412	−	0.470477i	$-0.155918\pi$
$983$	1.05850	+	1.83338i	0.0337609	+	0.0584756i	−0.848651	+	0.528953i	$0.822585\pi$
$984$	3.44212	−	1.70784i	0.109731	−	0.0544439i
$985$	5.22947	+	3.01924i	0.166625	+	0.0962009i
$986$	−13.9398	+	24.1444i	−0.443932	+	0.768914i
$987$		0			0
$988$	20.5234	+	35.5475i	0.652935	+	1.13092i
$989$		−	2.26330i		−	0.0719687i
$990$	25.6594	−	33.7774i	0.815510	−	1.07352i
$991$	34.1163			1.08374			0.541870	−	0.840462i	$-0.317717\pi$
$991$	34.1163			1.08374			0.541870	+	0.840462i	$0.317717\pi$
$992$	24.0575	+	41.6688i	0.763825	+	1.32298i
$993$	−40.2968	−	2.54324i	−1.27878	−	0.0807073i
$994$		0			0
$995$	−9.30850	−	5.37427i	−0.295099	−	0.170376i
$996$	−7.08543	+	10.6599i	−0.224510	+	0.337771i
$997$	−39.6843	+	22.9118i	−1.25682	+	0.725623i	−0.972454	−	0.233094i	$-0.925115\pi$
$997$	−39.6843	+	22.9118i	−1.25682	+	0.725623i	−0.284361	+	0.958717i	$0.591782\pi$
$998$		−	4.18307i		−	0.132413i
$999$	28.8510	+	5.52131i	0.912804	+	0.174687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.d.293.1		10
3.2	odd	2		1323.2.o.c.881.5		10
7.2	even	3		441.2.s.b.374.5		10
7.3	odd	6		441.2.i.b.68.1		10
7.4	even	3		63.2.i.b.5.1	✓	10
7.5	odd	6		63.2.s.b.59.5	yes	10
7.6	odd	2		441.2.o.c.293.1		10
9.2	odd	6		441.2.o.c.146.1		10
9.7	even	3		1323.2.o.d.440.5		10
21.2	odd	6		1323.2.s.b.962.1		10
21.5	even	6		189.2.s.b.17.1		10
21.11	odd	6		189.2.i.b.152.5		10
21.17	even	6		1323.2.i.b.1097.5		10
21.20	even	2		1323.2.o.d.881.5		10
28.11	odd	6		1008.2.ca.b.257.5		10
28.19	even	6		1008.2.df.b.689.3		10
63.2	odd	6		441.2.i.b.227.5		10
63.4	even	3		567.2.p.d.404.5		10
63.5	even	6		567.2.p.d.80.5		10
63.11	odd	6		63.2.s.b.47.5	yes	10
63.16	even	3		1323.2.i.b.521.1		10
63.20	even	6	inner	441.2.o.d.146.1		10
63.25	even	3		189.2.s.b.89.1		10
63.32	odd	6		567.2.p.c.404.1		10
63.34	odd	6		1323.2.o.c.440.5		10
63.38	even	6		441.2.s.b.362.5		10
63.40	odd	6		567.2.p.c.80.1		10
63.47	even	6		63.2.i.b.38.5	yes	10
63.52	odd	6		1323.2.s.b.656.1		10
63.61	odd	6		189.2.i.b.143.1		10
84.11	even	6		3024.2.ca.b.2609.5		10
84.47	odd	6		3024.2.df.b.17.5		10
252.11	even	6		1008.2.df.b.929.3		10
252.47	odd	6		1008.2.ca.b.353.5		10
252.151	odd	6		3024.2.df.b.1601.5		10
252.187	even	6		3024.2.ca.b.2033.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	7.4	even	3
63.2.i.b.38.5	yes	10	63.47	even	6
63.2.s.b.47.5	yes	10	63.11	odd	6
63.2.s.b.59.5	yes	10	7.5	odd	6
189.2.i.b.143.1		10	63.61	odd	6
189.2.i.b.152.5		10	21.11	odd	6
189.2.s.b.17.1		10	21.5	even	6
189.2.s.b.89.1		10	63.25	even	3
441.2.i.b.68.1		10	7.3	odd	6
441.2.i.b.227.5		10	63.2	odd	6
441.2.o.c.146.1		10	9.2	odd	6
441.2.o.c.293.1		10	7.6	odd	2
441.2.o.d.146.1		10	63.20	even	6	inner
441.2.o.d.293.1		10	1.1	even	1	trivial
441.2.s.b.362.5		10	63.38	even	6
441.2.s.b.374.5		10	7.2	even	3
567.2.p.c.80.1		10	63.40	odd	6
567.2.p.c.404.1		10	63.32	odd	6
567.2.p.d.80.5		10	63.5	even	6
567.2.p.d.404.5		10	63.4	even	3
1008.2.ca.b.257.5		10	28.11	odd	6
1008.2.ca.b.353.5		10	252.47	odd	6
1008.2.df.b.689.3		10	28.19	even	6
1008.2.df.b.929.3		10	252.11	even	6
1323.2.i.b.521.1		10	63.16	even	3
1323.2.i.b.1097.5		10	21.17	even	6
1323.2.o.c.440.5		10	63.34	odd	6
1323.2.o.c.881.5		10	3.2	odd	2
1323.2.o.d.440.5		10	9.7	even	3
1323.2.o.d.881.5		10	21.20	even	2
1323.2.s.b.656.1		10	63.52	odd	6
1323.2.s.b.962.1		10	21.2	odd	6
3024.2.ca.b.2033.5		10	252.187	even	6
3024.2.ca.b.2609.5		10	84.11	even	6
3024.2.df.b.17.5		10	84.47	odd	6
3024.2.df.b.1601.5		10	252.151	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81474 + 1.04774i) q^{2} +(0.958787 - 1.44247i) q^{3} +(1.19552 - 2.07070i) q^{4} +(-1.04492 + 1.80985i) q^{5} +(-0.228612 + 3.62227i) q^{6} +0.819421i q^{8} +(-1.16146 - 2.76605i) q^{9} +O(q^{10})\)	\(q+(-1.81474 + 1.04774i) q^{2} +(0.958787 - 1.44247i) q^{3} +(1.19552 - 2.07070i) q^{4} +(-1.04492 + 1.80985i) q^{5} +(-0.228612 + 3.62227i) q^{6} +0.819421i q^{8} +(-1.16146 - 2.76605i) q^{9} -4.37920i q^{10} +(-2.79620 + 1.61439i) q^{11} +(-1.84068 - 3.70987i) q^{12} +(-2.68740 - 1.55157i) q^{13} +(1.60880 + 3.24252i) q^{15} +(1.53250 + 2.65437i) q^{16} -1.63261 q^{17} +(5.00584 + 3.80275i) q^{18} -5.53210i q^{19} +(2.49844 + 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +(1.00527 + 0.580391i) q^{23} +(1.18199 + 0.785650i) q^{24} +(0.316304 + 0.547854i) q^{25} +6.50257 q^{26} +(-5.10354 - 0.976682i) q^{27} +(-7.05749 + 4.07464i) q^{29} +(-6.31688 - 4.19872i) q^{30} +(-5.16886 - 2.98424i) q^{31} +(-6.98146 - 4.03075i) q^{32} +(-0.352251 + 5.58130i) q^{33} +(2.96276 - 1.71055i) q^{34} +(-7.11621 - 0.901839i) q^{36} -5.65313 q^{37} +(5.79620 + 10.0393i) q^{38} +(-4.81474 + 2.38887i) q^{39} +(-1.48303 - 0.856225i) q^{40} +(1.35369 - 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +7.72014i q^{44} +(6.21974 + 0.788230i) q^{45} -2.43240 q^{46} +(-4.06759 - 7.04527i) q^{47} +(5.29820 + 0.334384i) q^{48} +(-1.14802 - 0.662809i) q^{50} +(-1.56532 + 2.35499i) q^{51} +(-6.42568 + 3.70987i) q^{52} -6.09412i q^{53} +(10.2849 - 3.57476i) q^{54} -6.74759i q^{55} +(-7.97990 - 5.30410i) q^{57} +(8.53834 - 14.7888i) q^{58} +(1.98103 - 3.43124i) q^{59} +(8.63765 + 0.545146i) q^{60} +(-4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(5.61621 - 3.24252i) q^{65} +(-5.20851 - 10.4977i) q^{66} +(0.336981 - 0.583668i) q^{67} +(-1.95182 + 3.38065i) q^{68} +(1.80103 - 0.893598i) q^{69} +7.01535i q^{71} +(2.26656 - 0.951721i) q^{72} -3.42110i q^{73} +(10.2590 - 5.92301i) q^{74} +(1.09353 + 0.0690158i) q^{75} +(-11.4553 - 6.61374i) q^{76} +(6.23458 - 9.37978i) q^{78} +(7.07973 + 12.2625i) q^{79} -6.40534 q^{80} +(-6.30204 + 6.42528i) q^{81} +5.67325i q^{82} +(-1.54535 - 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +(3.53839 + 2.04289i) q^{86} +(-0.889066 + 14.0870i) q^{87} +(-1.32286 - 2.29127i) q^{88} -4.91531 q^{89} +(-12.1131 + 5.08625i) q^{90} +(2.40363 - 1.38774i) q^{92} +(-9.26052 + 4.59469i) q^{93} +(14.7632 + 8.52356i) q^{94} +(10.0122 + 5.78057i) q^{95} +(-12.5080 + 6.20594i) q^{96} +(-2.07939 + 1.20054i) q^{97} +(7.71314 + 5.85939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9	\( 10 q + 3 q^{3} + 4 q^{4} + 12 q^{6} - 3 q^{9} + 12 q^{11} + 12 q^{12} - 6 q^{13} - 3 q^{15} - 6 q^{16} - 24 q^{17} - 6 q^{18} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 27 q^{24} + 7 q^{25} + 6 q^{26} - 27 q^{27} - 15 q^{29} - 6 q^{30} - 9 q^{31} - 48 q^{32} - 9 q^{33} - 3 q^{34} - 18 q^{36} - 12 q^{37} + 18 q^{38} - 30 q^{39} - 15 q^{40} + 9 q^{41} + 3 q^{43} - 15 q^{45} + 26 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} + 3 q^{51} + 12 q^{52} + 18 q^{54} - 36 q^{57} + 8 q^{58} + 18 q^{59} + 51 q^{60} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} + 6 q^{66} - 10 q^{67} - 27 q^{68} + 3 q^{69} + 12 q^{72} + 30 q^{74} - 27 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} - 60 q^{80} + 33 q^{81} + 15 q^{83} + 18 q^{85} - 54 q^{86} + 24 q^{87} - 8 q^{88} + 48 q^{89} - 24 q^{90} + 39 q^{92} - 42 q^{93} - 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 + 4 * q^4 + 12 * q^6 - 3 * q^9 + 12 * q^11 + 12 * q^12 - 6 * q^13 - 3 * q^15 - 6 * q^16 - 24 * q^17 - 6 * q^18 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 27 * q^24 + 7 * q^25 + 6 * q^26 - 27 * q^27 - 15 * q^29 - 6 * q^30 - 9 * q^31 - 48 * q^32 - 9 * q^33 - 3 * q^34 - 18 * q^36 - 12 * q^37 + 18 * q^38 - 30 * q^39 - 15 * q^40 + 9 * q^41 + 3 * q^43 - 15 * q^45 + 26 * q^46 - 15 * q^47 + 15 * q^48 + 3 * q^50 + 3 * q^51 + 12 * q^52 + 18 * q^54 - 36 * q^57 + 8 * q^58 + 18 * q^59 + 51 * q^60 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 10 * q^67 - 27 * q^68 + 3 * q^69 + 12 * q^72 + 30 * q^74 - 27 * q^75 - 9 * q^76 + 24 * q^78 + 20 * q^79 - 60 * q^80 + 33 * q^81 + 15 * q^83 + 18 * q^85 - 54 * q^86 + 24 * q^87 - 8 * q^88 + 48 * q^89 - 24 * q^90 + 39 * q^92 - 42 * q^93 - 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more