LMFDB - Embedded newform 231.2.n.a.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(89,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("231.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.n (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81398 - 1.04730i) q^{2} +(-1.71944 - 0.208619i) q^{3} +(1.19369 + 2.06753i) q^{4} +(1.09285 - 1.89288i) q^{5} +(2.90055 + 2.17921i) q^{6} +(2.41465 - 1.08141i) q^{7} -0.811414i q^{8} +(2.91296 + 0.717415i) q^{9} +O(q^{10})$	\(q+(-1.81398 - 1.04730i) q^{2} +(-1.71944 - 0.208619i) q^{3} +(1.19369 + 2.06753i) q^{4} +(1.09285 - 1.89288i) q^{5} +(2.90055 + 2.17921i) q^{6} +(2.41465 - 1.08141i) q^{7} -0.811414i q^{8} +(2.91296 + 0.717415i) q^{9} +(-3.96484 + 2.28910i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-1.62116 - 3.80403i) q^{12} -0.770665i q^{13} +(-5.51271 - 0.567219i) q^{14} +(-2.27399 + 3.02670i) q^{15} +(1.53759 - 2.66318i) q^{16} +(-2.28247 - 3.95336i) q^{17} +(-4.53270 - 4.35213i) q^{18} +(-2.70250 - 1.56029i) q^{19} +5.21812 q^{20} +(-4.37746 + 1.35568i) q^{21} -2.09461 q^{22} +(-4.59562 - 2.65328i) q^{23} +(-0.169276 + 1.39518i) q^{24} +(0.111340 + 0.192847i) q^{25} +(-0.807121 + 1.39797i) q^{26} +(-4.85899 - 1.84125i) q^{27} +(5.11820 + 3.70151i) q^{28} +5.27560i q^{29} +(7.29486 - 3.10883i) q^{30} +(2.53713 - 1.46481i) q^{31} +(-6.98372 + 4.03205i) q^{32} +(-1.59339 + 0.679052i) q^{33} +9.56177i q^{34} +(0.591888 - 5.75247i) q^{35} +(1.99389 + 6.87901i) q^{36} +(4.66539 - 8.08070i) q^{37} +(3.26820 + 5.66069i) q^{38} +(-0.160775 + 1.32511i) q^{39} +(-1.53591 - 0.886757i) q^{40} +6.60845 q^{41} +(9.36044 + 2.12535i) q^{42} -12.0059 q^{43} +(2.06753 + 1.19369i) q^{44} +(4.54142 - 4.72984i) q^{45} +(5.55759 + 9.62602i) q^{46} +(0.614816 - 1.06489i) q^{47} +(-3.19938 + 4.25841i) q^{48} +(4.66111 - 5.22246i) q^{49} -0.466428i q^{50} +(3.09983 + 7.27373i) q^{51} +(1.59338 - 0.919936i) q^{52} +(7.40366 - 4.27451i) q^{53} +(6.88578 + 8.42884i) q^{54} -2.18571i q^{55} +(-0.877470 - 1.95928i) q^{56} +(4.32129 + 3.24662i) q^{57} +(5.52516 - 9.56986i) q^{58} +(-0.195826 - 0.339180i) q^{59} +(-8.97225 - 1.08860i) q^{60} +(-10.1988 - 5.88830i) q^{61} -6.13642 q^{62} +(7.80960 - 1.41779i) q^{63} +10.7408 q^{64} +(-1.45878 - 0.842225i) q^{65} +(3.60156 + 0.436974i) q^{66} +(3.94968 + 6.84105i) q^{67} +(5.44913 - 9.43818i) q^{68} +(7.34837 + 5.52089i) q^{69} +(-7.09826 + 9.81500i) q^{70} +3.22448i q^{71} +(0.582121 - 2.36361i) q^{72} +(3.03459 - 1.75202i) q^{73} +(-16.9259 + 9.77217i) q^{74} +(-0.151212 - 0.354817i) q^{75} -7.45003i q^{76} +(1.55045 - 2.14385i) q^{77} +(1.67944 - 2.23535i) q^{78} +(-6.99520 + 12.1160i) q^{79} +(-3.36071 - 5.82092i) q^{80} +(7.97063 + 4.17960i) q^{81} +(-11.9876 - 6.92105i) q^{82} -2.44186 q^{83} +(-8.02824 - 7.43228i) q^{84} -9.97763 q^{85} +(21.7784 + 12.5738i) q^{86} +(1.10059 - 9.07109i) q^{87} +(-0.405707 - 0.702705i) q^{88} +(1.13159 - 1.95996i) q^{89} +(-13.1916 + 3.82362i) q^{90} +(-0.833404 - 1.86089i) q^{91} -12.6688i q^{92} +(-4.66803 + 1.98937i) q^{93} +(-2.23053 + 1.28780i) q^{94} +(-5.90689 + 3.41034i) q^{95} +(12.8493 - 5.47594i) q^{96} -11.6070i q^{97} +(-13.9247 + 4.59185i) q^{98} +(2.88140 - 0.835179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.81398	−	1.04730i	−1.28268	−	0.740556i	−0.305343	−	0.952243i	$-0.598771\pi$
$2$	−1.81398	−	1.04730i	−1.28268	−	0.740556i	−0.977338	+	0.211687i	$0.932104\pi$
$3$	−1.71944	−	0.208619i	−0.992720	−	0.120446i
$3$	−1.71944	−	0.208619i	−0.992720	−	0.120446i
$4$	1.19369	+	2.06753i	0.596846	+	1.03377i
$5$	1.09285	−	1.89288i	0.488739	−	0.846521i	−0.511177	−	0.859476i	$-0.670790\pi$
$5$	1.09285	−	1.89288i	0.488739	−	0.846521i	0.999916	+	0.0129544i	$0.00412364\pi$
$6$	2.90055	+	2.17921i	1.18415	+	0.889658i
$7$	2.41465	−	1.08141i	0.912653	−	0.408734i
$7$	2.41465	−	1.08141i	0.912653	−	0.408734i
$8$		−	0.811414i		−	0.286878i
$9$	2.91296	+	0.717415i	0.970986	+	0.239138i
$10$	−3.96484	+	2.28910i	−1.25379	+	0.723877i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−1.62116	−	3.80403i	−0.467987	−	1.09813i
$13$		−	0.770665i		−	0.213744i	−0.994273	−	0.106872i	$-0.965916\pi$
$13$		−	0.770665i		−	0.213744i	0.994273	−	0.106872i	$-0.0340835\pi$
$14$	−5.51271	−	0.567219i	−1.47333	−	0.151596i
$15$	−2.27399	+	3.02670i	−0.587141	+	0.781492i
$16$	1.53759	−	2.66318i	0.384396	−	0.665794i
$17$	−2.28247	−	3.95336i	−0.553581	−	0.958830i	−0.998012	−	0.0630172i	$-0.979928\pi$
$17$	−2.28247	−	3.95336i	−0.553581	−	0.958830i	0.444432	−	0.895813i	$-0.353406\pi$
$18$	−4.53270	−	4.35213i	−1.06837	−	1.02581i
$19$	−2.70250	−	1.56029i	−0.619997	−	0.357955i	0.156871	−	0.987619i	$-0.449859\pi$
$19$	−2.70250	−	1.56029i	−0.619997	−	0.357955i	−0.776868	+	0.629664i	$0.783193\pi$
$20$	5.21812			1.16681
$21$	−4.37746	+	1.35568i	−0.955240	+	0.295833i
$22$	−2.09461			−0.446572
$23$	−4.59562	−	2.65328i	−0.958253	−	0.553248i	−0.0626180	−	0.998038i	$-0.519945\pi$
$23$	−4.59562	−	2.65328i	−0.958253	−	0.553248i	−0.895635	+	0.444790i	$0.853278\pi$
$24$	−0.169276	+	1.39518i	−0.0345533	+	0.284790i
$25$	0.111340	+	0.192847i	0.0222681	+	0.0385694i
$26$	−0.807121	+	1.39797i	−0.158289	+	0.274165i
$27$	−4.85899	−	1.84125i	−0.935113	−	0.354349i
$28$	5.11820	+	3.70151i	0.967249	+	0.699520i
$29$			5.27560i			0.979655i	0.871819	+	0.489828i	$0.162940\pi$
$29$			5.27560i			0.979655i	−0.871819	+	0.489828i	$0.837060\pi$
$30$	7.29486	−	3.10883i	1.33185	−	0.567593i
$31$	2.53713	−	1.46481i	0.455682	−	0.263088i	−0.254545	−	0.967061i	$-0.581926\pi$
$31$	2.53713	−	1.46481i	0.455682	−	0.263088i	0.710227	+	0.703973i	$0.248592\pi$
$32$	−6.98372	+	4.03205i	−1.23456	+	0.712773i
$33$	−1.59339	+	0.679052i	−0.277373	+	0.118208i
$34$			9.56177i			1.63983i
$35$	0.591888	−	5.75247i	0.100047	−	0.972345i
$36$	1.99389	+	6.87901i	0.332315	+	1.14650i
$37$	4.66539	−	8.08070i	0.766986	−	1.32846i	−0.172204	−	0.985061i	$-0.555089\pi$
$37$	4.66539	−	8.08070i	0.766986	−	1.32846i	0.939190	−	0.343397i	$-0.111578\pi$
$38$	3.26820	+	5.66069i	0.530172	+	0.918285i
$39$	−0.160775	+	1.32511i	−0.0257446	+	0.212188i
$40$	−1.53591	−	0.886757i	−0.242848	−	0.140209i
$41$	6.60845			1.03207			0.516033	−	0.856569i	$-0.327408\pi$
$41$	6.60845			1.03207			0.516033	+	0.856569i	$0.327408\pi$
$42$	9.36044	+	2.12535i	1.44435	+	0.327949i
$43$	−12.0059			−1.83088			−0.915438	−	0.402460i	$-0.868155\pi$
$43$	−12.0059			−1.83088			−0.915438	+	0.402460i	$0.868155\pi$
$44$	2.06753	+	1.19369i	0.311692	+	0.179956i
$45$	4.54142	−	4.72984i	0.676994	−	0.705083i
$46$	5.55759	+	9.62602i	0.819421	+	1.41928i
$47$	0.614816	−	1.06489i	0.0896801	−	0.155331i	−0.817696	−	0.575651i	$-0.804749\pi$
$47$	0.614816	−	1.06489i	0.0896801	−	0.155331i	0.907376	+	0.420320i	$0.138082\pi$
$48$	−3.19938	+	4.25841i	−0.461790	+	0.614648i
$49$	4.66111	−	5.22246i	0.665873	−	0.746065i
$50$		−	0.466428i		−	0.0659629i
$51$	3.09983	+	7.27373i	0.434063	+	1.01853i
$52$	1.59338	−	0.919936i	0.220962	−	0.127572i
$53$	7.40366	−	4.27451i	1.01697	−	0.587149i	0.103746	−	0.994604i	$-0.466917\pi$
$53$	7.40366	−	4.27451i	1.01697	−	0.587149i	0.913225	+	0.407455i	$0.133584\pi$
$54$	6.88578	+	8.42884i	0.937036	+	1.14702i
$55$		−	2.18571i		−	0.294721i
$56$	−0.877470	−	1.95928i	−0.117257	−	0.261820i
$57$	4.32129	+	3.24662i	0.572369	+	0.430026i
$58$	5.52516	−	9.56986i	0.725489	−	1.25658i
$59$	−0.195826	−	0.339180i	−0.0254943	−	0.0441575i	0.852997	−	0.521916i	$-0.174783\pi$
$59$	−0.195826	−	0.339180i	−0.0254943	−	0.0441575i	−0.878491	+	0.477759i	$0.841449\pi$
$60$	−8.97225	−	1.08860i	−1.15831	−	0.140537i
$61$	−10.1988	−	5.88830i	−1.30583	−	0.753919i	−0.324430	−	0.945910i	$-0.605172\pi$
$61$	−10.1988	−	5.88830i	−1.30583	−	0.753919i	−0.981397	+	0.191990i	$0.938506\pi$
$62$	−6.13642			−0.779326
$63$	7.80960	−	1.41779i	0.983917	−	0.178625i
$64$	10.7408			1.34260
$65$	−1.45878	−	0.842225i	−0.180939	−	0.104465i
$66$	3.60156	+	0.436974i	0.443321	+	0.0537878i
$67$	3.94968	+	6.84105i	0.482531	+	0.835768i	0.999799	−	0.0200557i	$-0.00638436\pi$
$67$	3.94968	+	6.84105i	0.482531	+	0.835768i	−0.517268	+	0.855823i	$0.673051\pi$
$68$	5.44913	−	9.43818i	0.660804	−	1.14455i
$69$	7.34837	+	5.52089i	0.884640	+	0.664638i
$70$	−7.09826	+	9.81500i	−0.848404	+	1.17312i
$71$			3.22448i			0.382676i	0.981524	+	0.191338i	$0.0612826\pi$
$71$			3.22448i			0.382676i	−0.981524	+	0.191338i	$0.938717\pi$
$72$	0.582121	−	2.36361i	0.0686036	−	0.278555i
$73$	3.03459	−	1.75202i	0.355172	−	0.205059i	−0.311789	−	0.950151i	$-0.600928\pi$
$73$	3.03459	−	1.75202i	0.355172	−	0.205059i	0.666961	+	0.745093i	$0.267595\pi$
$74$	−16.9259	+	9.77217i	−1.96760	+	1.13599i
$75$	−0.151212	−	0.354817i	−0.0174604	−	0.0409707i
$76$		−	7.45003i		−	0.854577i
$77$	1.55045	−	2.14385i	0.176690	−	0.244315i
$78$	1.67944	−	2.23535i	0.190159	−	0.253104i
$79$	−6.99520	+	12.1160i	−0.787022	+	1.36316i	0.140762	+	0.990043i	$0.455045\pi$
$79$	−6.99520	+	12.1160i	−0.787022	+	1.36316i	−0.927784	+	0.373118i	$0.878289\pi$
$80$	−3.36071	−	5.82092i	−0.375739	−	0.650799i
$81$	7.97063	+	4.17960i	0.885626	+	0.464400i
$82$	−11.9876	−	6.92105i	−1.32381	−	0.764302i
$83$	−2.44186			−0.268029			−0.134015	−	0.990979i	$-0.542787\pi$
$83$	−2.44186			−0.268029			−0.134015	+	0.990979i	$0.542787\pi$
$84$	−8.02824	−	7.43228i	−0.875953	−	0.810928i
$85$	−9.97763			−1.08223
$86$	21.7784	+	12.5738i	2.34843	+	1.35587i
$87$	1.10059	−	9.07109i	0.117996	−	0.972523i
$88$	−0.405707	−	0.702705i	−0.0432485	−	0.0749086i
$89$	1.13159	−	1.95996i	0.119948	−	0.207756i	−0.799799	−	0.600268i	$-0.795061\pi$
$89$	1.13159	−	1.95996i	0.119948	−	0.207756i	0.919747	+	0.392512i	$0.128394\pi$
$90$	−13.1916	+	3.82362i	−1.39052	+	0.403045i
$91$	−0.833404	−	1.86089i	−0.0873645	−	0.195074i
$92$		−	12.6688i		−	1.32081i
$93$	−4.66803	+	1.98937i	−0.484052	+	0.206288i
$94$	−2.23053	+	1.28780i	−0.230062	+	0.132826i
$95$	−5.90689	+	3.41034i	−0.606034	+	0.349894i
$96$	12.8493	−	5.47594i	1.31142	−	0.558886i
$97$		−	11.6070i		−	1.17851i	−0.807946	−	0.589256i	$-0.799421\pi$
$97$		−	11.6070i		−	1.17851i	0.807946	−	0.589256i	$-0.200579\pi$
$98$	−13.9247	+	4.59185i	−1.40660	+	0.463847i
$99$	2.88140	−	0.835179i	0.289592	−	0.0839386i
$100$	−0.265812	+	0.460399i	−0.0265812	+	0.0460399i
$101$	7.21257	+	12.4925i	0.717678	+	1.24305i	0.961918	+	0.273339i	$0.0881282\pi$
$101$	7.21257	+	12.4925i	0.717678	+	1.24305i	−0.244240	+	0.969715i	$0.578538\pi$
$102$	1.99476	−	16.4409i	0.197511	−	1.62789i
$103$	2.68907	+	1.55254i	0.264962	+	0.152976i	0.626596	−	0.779344i	$-0.284448\pi$
$103$	2.68907	+	1.55254i	0.264962	+	0.152976i	−0.361634	+	0.932320i	$0.617781\pi$
$104$	−0.625329			−0.0613185
$105$	−2.21779	+	9.76755i	−0.216434	+	0.953216i
$106$	−17.9068			−1.73926
$107$	−4.66496	−	2.69332i	−0.450979	−	0.260373i	0.257265	−	0.966341i	$-0.417179\pi$
$107$	−4.66496	−	2.69332i	−0.450979	−	0.260373i	−0.708244	+	0.705968i	$0.750512\pi$
$108$	−1.99329	−	12.2440i	−0.191804	−	1.17818i
$109$	0.514035	+	0.890335i	0.0492356	+	0.0852786i	0.889593	−	0.456754i	$-0.150988\pi$
$109$	0.514035	+	0.890335i	0.0492356	+	0.0852786i	−0.840357	+	0.542033i	$0.817655\pi$
$110$	−2.28910	+	3.96484i	−0.218257	+	0.378033i
$111$	−9.70765	+	12.9210i	−0.921410	+	1.22641i
$112$	0.832754	−	8.09341i	0.0786879	−	0.764755i
$113$			9.18265i			0.863831i	0.901914	+	0.431916i	$0.142162\pi$
$113$			9.18265i			0.863831i	−0.901914	+	0.431916i	$0.857838\pi$
$114$	−4.43855	−	10.4150i	−0.415708	−	0.975457i
$115$	−10.0447	+	5.79930i	−0.936671	+	0.540788i
$116$	−10.9075	+	6.29744i	−1.01274	+	0.584703i
$117$	0.552887	−	2.24491i	0.0511144	−	0.207542i
$118$			0.820356i			0.0755199i
$119$	−9.78658	−	7.07770i	−0.897134	−	0.648812i
$120$	2.45591	+	1.84515i	0.224193	+	0.168438i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	12.3337	+	21.3626i	1.11664	+	1.93407i
$123$	−11.3628	−	1.37865i	−1.02455	−	0.124308i
$124$	6.05710	+	3.49707i	0.543943	+	0.314046i
$125$	11.4153			1.02101
$126$	−15.6513	−	5.60718i	−1.39433	−	0.499527i
$127$	16.0040			1.42013			0.710064	−	0.704137i	$-0.248666\pi$
$127$	16.0040			1.42013			0.710064	+	0.704137i	$0.248666\pi$
$128$	−5.51619	−	3.18477i	−0.487567	−	0.281497i
$129$	20.6434	+	2.50464i	1.81755	+	0.220522i
$130$	1.76413	+	3.05556i	0.154724	+	0.267991i
$131$	10.1674	−	17.6105i	0.888334	−	1.53864i	0.0464895	−	0.998919i	$-0.485197\pi$
$131$	10.1674	−	17.6105i	0.888334	−	1.53864i	0.841844	−	0.539720i	$-0.181470\pi$
$132$	−3.30598	−	2.48381i	−0.287748	−	0.216188i
$133$	−8.21293	−	0.845052i	−0.712151	−	0.0732753i
$134$		−	16.5461i		−	1.42936i
$135$	−8.79543	+	7.18526i	−0.756990	+	0.618409i
$136$	−3.20781	+	1.85203i	−0.275067	+	0.158810i
$137$	9.87546	−	5.70160i	0.843717	−	0.487120i	−0.0148088	−	0.999890i	$-0.504714\pi$
$137$	9.87546	−	5.70160i	0.843717	−	0.487120i	0.858526	+	0.512770i	$0.171381\pi$
$138$	−7.54777	−	17.7108i	−0.642509	−	1.50764i
$139$		−	12.4268i		−	1.05403i	−0.849856	−	0.527015i	$-0.823311\pi$
$139$		−	12.4268i		−	1.05403i	0.849856	−	0.527015i	$-0.176689\pi$
$140$	12.6000	−	5.64292i	1.06489	−	0.476914i
$141$	−1.27930	+	1.70276i	−0.107736	+	0.143398i
$142$	3.37701	−	5.84916i	0.283393	−	0.490850i
$143$	−0.385333	−	0.667416i	−0.0322231	−	0.0558121i
$144$	6.38952	−	6.65463i	0.532460	−	0.554552i
$145$	9.98608	+	5.76547i	0.829299	+	0.478796i
$146$	−7.33959			−0.607429
$147$	−9.10401	+	8.00731i	−0.750886	+	0.660432i
$148$	22.2762			1.83109
$149$	−6.74547	−	3.89450i	−0.552611	−	0.319050i	0.197564	−	0.980290i	$-0.436697\pi$
$149$	−6.74547	−	3.89450i	−0.552611	−	0.319050i	−0.750174	+	0.661240i	$0.770030\pi$
$150$	−0.0973056	+	0.801996i	−0.00794497	+	0.0654827i
$151$	10.0762	+	17.4525i	0.819990	+	1.42027i	0.905688	+	0.423944i	$0.139355\pi$
$151$	10.0762	+	17.4525i	0.819990	+	1.42027i	−0.0856981	+	0.996321i	$0.527312\pi$
$152$	−1.26604	+	2.19285i	−0.102690	+	0.177864i
$153$	−3.81254	−	13.1534i	−0.308226	−	1.06339i
$154$	−5.05775	+	2.26513i	−0.407565	+	0.182529i
$155$		−	6.40330i		−	0.514326i
$156$	−2.93163	+	1.24937i	−0.234718	+	0.100030i
$157$	−9.91749	+	5.72587i	−0.791502	+	0.456974i	−0.840491	−	0.541825i	$-0.817733\pi$
$157$	−9.91749	+	5.72587i	−0.791502	+	0.456974i	0.0489890	+	0.998799i	$0.484400\pi$
$158$	25.3784	−	14.6522i	2.01899	−	1.16567i
$159$	−13.6219	+	5.80522i	−1.08029	+	0.460384i
$160$			17.6258i			1.39344i
$161$	−13.9661	−	1.43701i	−1.10068	−	0.113253i
$162$	−10.0813	−	15.9294i	−0.792061	−	1.25153i
$163$	−9.67464	+	16.7570i	−0.757776	+	1.31251i	0.186206	+	0.982511i	$0.440381\pi$
$163$	−9.67464	+	16.7570i	−0.757776	+	1.31251i	−0.943982	+	0.329996i	$0.892953\pi$
$164$	7.88845	+	13.6632i	0.615984	+	1.06692i
$165$	−0.455979	+	3.75820i	−0.0354979	+	0.292575i
$166$	4.42950	+	2.55737i	0.343796	+	0.198491i
$167$	13.7490			1.06393			0.531964	−	0.846767i	$-0.321454\pi$
$167$	13.7490			1.06393			0.531964	+	0.846767i	$0.321454\pi$
$168$	1.10002	+	3.55193i	0.0848681	+	0.274037i
$169$	12.4061			0.954313
$170$	18.0993	+	10.4496i	1.38815	+	0.801449i
$171$	−6.75290	−	6.48388i	−0.516407	−	0.495835i
$172$	−14.3313	−	24.8225i	−1.09275	−	1.89270i
$173$	−8.43045	+	14.6020i	−0.640955	+	1.11017i	0.344265	+	0.938873i	$0.388128\pi$
$173$	−8.43045	+	14.6020i	−0.640955	+	1.11017i	−0.985220	+	0.171294i	$0.945205\pi$
$174$	−11.4966	+	15.3022i	−0.871558	+	1.16005i
$175$	0.477395	+	0.345254i	0.0360876	+	0.0260988i
$176$		−	3.07517i		−	0.231800i
$177$	0.265952	+	0.624053i	0.0199901	+	0.0469067i
$178$	−4.10536	+	2.37023i	−0.307709	+	0.177656i
$179$	2.05060	−	1.18392i	0.153269	−	0.0884900i	−0.421404	−	0.906873i	$-0.638463\pi$
$179$	2.05060	−	1.18392i	0.153269	−	0.0884900i	0.574673	+	0.818383i	$0.305129\pi$
$180$	15.2002	+	3.74356i	1.13295	+	0.279028i
$181$			5.46731i			0.406382i	0.979139	+	0.203191i	$0.0651312\pi$
$181$			5.46731i			0.406382i	−0.979139	+	0.203191i	$0.934869\pi$
$182$	−0.437136	+	4.24845i	−0.0324026	+	0.314916i
$183$	16.3079	+	12.2523i	1.20551	+	0.905712i
$184$	−2.15291	+	3.72895i	−0.158715	+	0.274902i
$185$	−10.1972	−	17.6620i	−0.749712	−	1.29854i
$186$	10.5512	+	1.28017i	0.773652	+	0.0938667i
$187$	−3.95336	−	2.28247i	−0.289098	−	0.166911i
$188$	2.93560			0.214101
$189$	−13.7239	+	0.808576i	−0.998269	+	0.0588152i
$190$	14.2867			1.03646
$191$	9.81154	+	5.66469i	0.709938	+	0.409883i	0.811038	−	0.584993i	$-0.198903\pi$
$191$	9.81154	+	5.66469i	0.709938	+	0.409883i	−0.101100	+	0.994876i	$0.532236\pi$
$192$	−18.4682	−	2.24073i	−1.33283	−	0.161711i
$193$	2.78157	+	4.81783i	0.200222	+	0.346795i	0.948600	−	0.316478i	$-0.102500\pi$
$193$	2.78157	+	4.81783i	0.200222	+	0.346795i	−0.748378	+	0.663273i	$0.769167\pi$
$194$	−12.1561	+	21.0549i	−0.872754	+	1.51165i
$195$	2.33258	+	1.75248i	0.167039	+	0.125498i
$196$	16.3615	+	3.40300i	1.16868	+	0.243071i
$197$			3.58361i			0.255321i	0.991818	+	0.127661i	$0.0407469\pi$
$197$			3.58361i			0.255321i	−0.991818	+	0.127661i	$0.959253\pi$
$198$	−6.10150	−	1.50270i	−0.433615	−	0.106792i
$199$	12.3386	−	7.12368i	0.874659	−	0.504985i	0.00576535	−	0.999983i	$-0.498165\pi$
$199$	12.3386	−	7.12368i	0.874659	−	0.504985i	0.868894	+	0.494999i	$0.164831\pi$
$200$	0.156479	−	0.0903430i	0.0110647	−	0.00638822i
$201$	−5.36408	−	12.5868i	−0.378353	−	0.887802i
$202$		−	30.2150i		−	2.12592i
$203$	5.70509	+	12.7388i	0.400419	+	0.894086i
$204$	−11.3384	+	15.0916i	−0.793850	+	1.05662i
$205$	7.22207	−	12.5090i	0.504411	−	0.873666i
$206$	−3.25196	−	5.63256i	−0.226575	−	0.392439i
$207$	−11.4833	−	11.0259i	−0.798147	−	0.766350i
$208$	−2.05242	−	1.18496i	−0.142310	−	0.0821624i
$209$	−3.12058			−0.215855
$210$	14.2526	−	15.3955i	0.983525	−	1.06239i
$211$	9.51884			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$211$	9.51884			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$212$	17.6754	+	10.2049i	1.21395	+	0.700874i
$213$	0.672687	−	5.54431i	0.0460918	−	0.379890i
$214$	5.64144	+	9.77127i	0.385641	+	0.667950i
$215$	−13.1206	+	22.7256i	−0.894821	+	1.54987i
$216$	−1.49402	+	3.94265i	−0.101655	+	0.268264i
$217$	4.54223	−	6.28069i	0.308347	−	0.426361i
$218$		−	2.15340i		−	0.145847i
$219$	−5.58330	+	2.37943i	−0.377285	+	0.160787i
$220$	4.51902	−	2.60906i	0.304673	−	0.175903i
$221$	−3.04672	+	1.75902i	−0.204944	+	0.118325i
$222$	31.1417	−	13.2716i	2.09010	−	0.890732i
$223$			17.6719i			1.18339i	0.806160	+	0.591697i	$0.201542\pi$
$223$			17.6719i			1.18339i	−0.806160	+	0.591697i	$0.798458\pi$
$224$	−12.5030	+	17.2883i	−0.835390	+	1.15512i
$225$	0.185978	+	0.641632i	0.0123985	+	0.0427755i
$226$	9.61703	−	16.6572i	0.639715	−	1.10802i
$227$	3.72926	+	6.45926i	0.247519	+	0.428716i	0.962837	−	0.270083i	$-0.0870512\pi$
$227$	3.72926	+	6.45926i	0.247519	+	0.428716i	−0.715317	+	0.698800i	$0.753718\pi$
$228$	−1.55421	+	12.8099i	−0.102930	+	0.848355i
$229$	19.8866	+	11.4815i	1.31414	+	0.758720i	0.982779	−	0.184784i	$-0.0591585\pi$
$229$	19.8866	+	11.4815i	1.31414	+	0.758720i	0.331362	+	0.943504i	$0.392492\pi$
$230$	24.2945			1.60193
$231$	−3.11315	+	3.36278i	−0.204830	+	0.221255i
$232$	4.28070			0.281042
$233$	21.0573	+	12.1575i	1.37951	+	0.796461i	0.992100	−	0.125446i	$-0.0400362\pi$
$233$	21.0573	+	12.1575i	1.37951	+	0.796461i	0.387411	+	0.921907i	$0.373370\pi$
$234$	−3.35404	+	3.49320i	−0.219260	+	0.228357i
$235$	−1.34381	−	2.32754i	−0.0876604	−	0.151832i
$236$	0.467511	−	0.809753i	0.0304324	−	0.0527104i
$237$	14.5555	−	19.3735i	0.945480	−	1.25844i
$238$	10.3402	+	23.0884i	0.670254	+	1.49660i
$239$		−	18.3745i		−	1.18855i	−0.804264	−	0.594273i	$-0.797440\pi$
$239$		−	18.3745i		−	1.18855i	0.804264	−	0.594273i	$-0.202560\pi$
$240$	4.56419	+	10.7098i	0.294617	+	0.691318i
$241$	−12.5815	+	7.26395i	−0.810448	+	0.467912i	−0.847111	−	0.531415i	$-0.821660\pi$
$241$	−12.5815	+	7.26395i	−0.810448	+	0.467912i	0.0366635	+	0.999328i	$0.488327\pi$
$242$	−1.81398	+	1.04730i	−0.116607	+	0.0673232i
$243$	−12.8331	−	8.84939i	−0.823243	−	0.567689i
$244$		−	28.1152i		−	1.79989i
$245$	−4.79157	−	14.5303i	−0.306122	−	0.928307i
$246$	19.1681	+	14.4012i	1.22212	+	0.918186i
$247$	−1.20246	+	2.08273i	−0.0765109	+	0.132521i
$248$	−1.18857	−	2.05866i	−0.0754742	−	0.130725i
$249$	4.19864	+	0.509418i	0.266078	+	0.0322831i
$250$	−20.7071	−	11.9552i	−1.30963	−	0.756116i
$251$	−22.9173			−1.44653			−0.723263	−	0.690573i	$-0.757358\pi$
$251$	−22.9173			−1.44653			−0.723263	+	0.690573i	$0.757358\pi$
$252$	12.2536	+	14.4542i	0.771903	+	0.910530i
$253$	−5.30656			−0.333621
$254$	−29.0311	−	16.7611i	−1.82157	−	1.05168i
$255$	17.1560	+	2.08152i	1.07435	+	0.130350i
$256$	−4.06994	−	7.04935i	−0.254371	−	0.440584i
$257$	−11.1714	+	19.3494i	−0.696853	+	1.20699i	0.272699	+	0.962099i	$0.412084\pi$
$257$	−11.1714	+	19.3494i	−0.696853	+	1.20699i	−0.969552	+	0.244886i	$0.921250\pi$
$258$	−34.8236	−	26.1633i	−2.16802	−	1.62885i
$259$	2.52677	−	24.5573i	0.157006	−	1.52592i
$260$		−	4.02142i		−	0.249398i
$261$	−3.78480	+	15.3676i	−0.234273	+	0.951231i
$262$	−36.8872	+	21.2968i	−2.27890	+	1.31572i
$263$	−4.86451	+	2.80853i	−0.299958	+	0.173181i	−0.642424	−	0.766349i	$-0.722071\pi$
$263$	−4.86451	+	2.80853i	−0.299958	+	0.173181i	0.342466	+	0.939530i	$0.388738\pi$
$264$	0.550992	+	1.29290i	0.0339112	+	0.0795724i
$265$		−	18.6856i		−	1.14785i
$266$	14.0131	+	10.1343i	0.859198	+	0.621376i
$267$	−2.35458	+	3.13397i	−0.144098	+	0.191796i
$268$	−9.42941	+	16.3322i	−0.575993	+	0.997648i
$269$	−12.0533	−	20.8768i	−0.734900	−	1.27288i	−0.954767	−	0.297354i	$-0.903896\pi$
$269$	−12.0533	−	20.8768i	−0.734900	−	1.27288i	0.219868	−	0.975530i	$-0.429437\pi$
$270$	23.4799	−	3.82246i	1.42894	−	0.232628i
$271$	1.51075	+	0.872231i	0.0917714	+	0.0529842i	0.545183	−	0.838317i	$-0.316460\pi$
$271$	1.51075	+	0.872231i	0.0917714	+	0.0529842i	−0.453412	+	0.891301i	$0.649793\pi$
$272$	−14.0380			−0.851178
$273$	1.04477	+	3.37355i	0.0632326	+	0.204177i
$274$	−23.8852			−1.44296
$275$	0.192847	+	0.111340i	0.0116291	+	0.00671407i
$276$	−2.64295	+	21.7833i	−0.159087	+	1.31120i
$277$	−4.29795	−	7.44427i	−0.258239	−	0.447283i	0.707531	−	0.706682i	$-0.249809\pi$
$277$	−4.29795	−	7.44427i	−0.258239	−	0.447283i	−0.965770	+	0.259399i	$0.916475\pi$
$278$	−13.0147	+	22.5421i	−0.780568	+	1.35198i
$279$	8.44143	−	2.44676i	0.505375	−	0.146484i
$280$	−4.66763	−	0.480267i	−0.278944	−	0.0287014i
$281$		−	0.174685i		−	0.0104208i	−0.999986	−	0.00521042i	$-0.998341\pi$
$281$		−	0.174685i		−	0.0104208i	0.999986	−	0.00521042i	$-0.00165853\pi$
$282$	4.10393	−	1.74896i	0.244385	−	0.104149i
$283$	10.5858	−	6.11173i	0.629262	−	0.363305i	−0.151204	−	0.988503i	$-0.548315\pi$
$283$	10.5858	−	6.11173i	0.629262	−	0.363305i	0.780466	+	0.625198i	$0.214982\pi$
$284$	−6.66673	+	3.84904i	−0.395597	+	0.228398i
$285$	10.8680	−	4.63160i	0.643765	−	0.274352i
$286$			1.61424i			0.0954521i
$287$	15.9571	−	7.14643i	0.941919	−	0.421841i
$288$	−23.2359	+	6.73497i	−1.36919	+	0.396862i
$289$	−1.91936	+	3.32442i	−0.112903	+	0.195554i
$290$	−12.0764	−	20.9169i	−0.709150	−	1.22828i
$291$	−2.42144	+	19.9576i	−0.141947	+	1.16993i
$292$	7.24473	+	4.18274i	0.423965	+	0.244777i
$293$	2.43433			0.142215			0.0711074	−	0.997469i	$-0.477347\pi$
$293$	2.43433			0.142215			0.0711074	+	0.997469i	$0.477347\pi$
$294$	24.9006	−	4.99048i	1.45223	−	0.291051i
$295$	−0.856036			−0.0498403
$296$	−6.55679	−	3.78557i	−0.381106	−	0.220032i
$297$	−5.12864	+	0.834927i	−0.297594	+	0.0484474i
$298$	8.15745	+	14.1291i	0.472548	+	0.818478i
$299$	−2.04479	+	3.54168i	−0.118253	+	0.204821i
$300$	0.553096	−	0.736177i	0.0319330	−	0.0425032i
$301$	−28.9900	+	12.9832i	−1.67095	+	0.748341i
$302$		−	42.2114i		−	2.42899i
$303$	−9.79542	−	22.9849i	−0.562732	−	1.32045i
$304$	−8.31066	+	4.79816i	−0.476649	+	0.275194i
$305$	−22.2917	+	12.8701i	−1.27642	+	0.736940i
$306$	−6.85975	+	27.8530i	−0.392146	+	1.59225i
$307$		−	7.14048i		−	0.407529i	−0.979020	−	0.203764i	$-0.934682\pi$
$307$		−	7.14048i		−	0.407529i	0.979020	−	0.203764i	$-0.0653177\pi$
$308$	6.28325	+	0.646502i	0.358021	+	0.0368379i
$309$	−4.29982	−	3.23049i	−0.244608	−	0.183776i
$310$	−6.70621	+	11.6155i	−0.380887	+	0.659715i
$311$	−12.6879	−	21.9761i	−0.719464	−	1.24615i	−0.961212	−	0.275809i	$-0.911054\pi$
$311$	−12.6879	−	21.9761i	−0.719464	−	1.24615i	0.241748	−	0.970339i	$-0.422279\pi$
$312$	1.07522	+	0.130455i	0.0608721	+	0.00738557i
$313$	15.3159	+	8.84261i	0.865703	+	0.499814i	0.865918	−	0.500186i	$-0.166735\pi$
$313$	15.3159	+	8.84261i	0.865703	+	0.499814i	−0.000214775		1.00000i	$0.500068\pi$
$314$	23.9869			1.35366
$315$	5.85105	−	16.3321i	0.329669	−	0.920208i
$316$	−33.4004			−1.87892
$317$	−19.5049	−	11.2611i	−1.09550	−	0.632488i	−0.160466	−	0.987041i	$-0.551300\pi$
$317$	−19.5049	−	11.2611i	−1.09550	−	0.632488i	−0.935036	+	0.354553i	$0.884633\pi$
$318$	30.7897	+	3.73570i	1.72660	+	0.209488i
$319$	2.63780	+	4.56881i	0.147689	+	0.255804i
$320$	11.7381	−	20.3310i	0.656181	−	1.13654i
$321$	7.45925	+	5.60420i	0.416335	+	0.312796i
$322$	23.8293	+	17.2335i	1.32796	+	0.960385i
$323$			14.2453i			0.792629i
$324$	0.873015	+	21.4687i	0.0485008	+	1.19271i
$325$	0.148620	−	0.0858061i	0.00824398	−	0.00475966i
$326$	35.0993	−	20.2646i	1.94397	−	1.12235i
$327$	−0.698113	−	1.63812i	−0.0386057	−	0.0905880i
$328$		−	5.36219i		−	0.296077i
$329$	0.332984	−	3.23621i	0.0183580	−	0.178418i
$330$	4.76311	−	6.33976i	0.262201	−	0.348992i
$331$	0.965864	−	1.67292i	0.0530887	−	0.0919523i	−0.838260	−	0.545271i	$-0.816427\pi$
$331$	0.965864	−	1.67292i	0.0530887	−	0.0919523i	0.891348	+	0.453319i	$0.149760\pi$
$332$	−2.91483	−	5.04863i	−0.159972	−	0.277080i
$333$	19.3873	−	20.1917i	1.06242	−	1.10650i
$334$	−24.9404	−	14.3993i	−1.36468	−	0.787897i
$335$	17.2657			0.943327
$336$	−3.12031	+	13.7424i	−0.170227	+	0.749710i
$337$	−14.1895			−0.772951			−0.386476	−	0.922300i	$-0.626308\pi$
$337$	−14.1895			−0.772951			−0.386476	+	0.922300i	$0.626308\pi$
$338$	−22.5044	−	12.9929i	−1.22408	−	0.706722i
$339$	1.91567	−	15.7890i	0.104045	−	0.857542i
$340$	−11.9102	−	20.6291i	−0.645922	−	1.11877i
$341$	1.46481	−	2.53713i	0.0793240	−	0.137393i
$342$	5.45906	+	18.8340i	0.295192	+	1.01843i
$343$	5.60735	−	17.6510i	0.302769	−	0.953064i
$344$			9.74172i			0.525238i
$345$	18.4811	−	7.87605i	0.994988	−	0.424032i
$346$	30.5854	−	17.6585i	1.64428	−	0.949326i
$347$	19.1991	−	11.0846i	1.03066	−	0.595052i	0.113487	−	0.993539i	$-0.463798\pi$
$347$	19.1991	−	11.0846i	1.03066	−	0.595052i	0.917174	+	0.398487i	$0.130465\pi$
$348$	20.0686	−	8.55258i	1.07579	−	0.458466i
$349$			22.3869i			1.19834i	0.800621	+	0.599171i	$0.204503\pi$
$349$			22.3869i			1.19834i	−0.800621	+	0.599171i	$0.795497\pi$
$350$	−0.504400	−	1.12626i	−0.0269613	−	0.0602013i
$351$	−1.41899	+	3.74466i	−0.0757399	+	0.199875i
$352$	−4.03205	+	6.98372i	−0.214909	+	0.372233i
$353$	13.9412	+	24.1468i	0.742014	+	1.28521i	0.951577	+	0.307411i	$0.0994626\pi$
$353$	13.9412	+	24.1468i	0.742014	+	1.28521i	−0.209563	+	0.977795i	$0.567204\pi$
$354$	0.171142	−	1.41055i	0.00909608	−	0.0749701i
$355$	6.10355	+	3.52389i	0.323943	+	0.187029i
$356$	5.40306			0.286361
$357$	15.3509	+	14.2114i	0.812456	+	0.752145i
$358$	−4.95968			−0.262127
$359$	−4.14489	−	2.39306i	−0.218759	−	0.126301i	0.386616	−	0.922241i	$-0.373644\pi$
$359$	−4.14489	−	2.39306i	−0.218759	−	0.126301i	−0.605376	+	0.795940i	$0.706977\pi$
$360$	−3.83786	−	3.68497i	−0.202273	−	0.194215i
$361$	−4.63098	−	8.02109i	−0.243736	−	0.422163i
$362$	5.72593	−	9.91761i	0.300948	−	0.521258i
$363$	−1.04039	+	1.38477i	−0.0546063	+	0.0726816i
$364$	2.85263	−	3.94442i	0.149518	−	0.206744i
$365$		−	7.65881i		−	0.400881i
$366$	−16.7504	−	39.3047i	−0.875558	−	2.05449i
$367$	−19.3210	+	11.1550i	−1.00855	+	0.582284i	−0.910766	−	0.412924i	$-0.864508\pi$
$367$	−19.3210	+	11.1550i	−1.00855	+	0.582284i	−0.0977805	+	0.995208i	$0.531174\pi$
$368$	−14.1323	+	8.15929i	−0.736698	+	0.425333i
$369$	19.2501	+	4.74100i	1.00212	+	0.246807i
$370$			42.7182i			2.22081i
$371$	13.2548	−	18.3278i	0.688155	−	0.951534i
$372$	−9.68527	−	7.27663i	−0.502158	−	0.377275i
$373$	0.479949	−	0.831295i	0.0248508	−	0.0430428i	−0.853333	−	0.521367i	$-0.825422\pi$
$373$	0.479949	−	0.831295i	0.0248508	−	0.0430428i	0.878183	+	0.478324i	$0.158756\pi$
$374$	4.78088	+	8.28073i	0.247214	+	0.428187i
$375$	−19.6279	−	2.38143i	−1.01358	−	0.122977i
$376$	−0.864068	−	0.498870i	−0.0445609	−	0.0257273i
$377$	4.06573			0.209396
$378$	25.7418	+	12.9064i	1.32402	+	0.663833i
$379$	9.79817			0.503298			0.251649	−	0.967819i	$-0.419027\pi$
$379$	9.79817			0.503298			0.251649	+	0.967819i	$0.419027\pi$
$380$	−14.1020	−	8.14179i	−0.723417	−	0.417665i
$381$	−27.5180	−	3.33874i	−1.40979	−	0.171049i
$382$	−11.8653	−	20.5513i	−0.607082	−	1.05150i
$383$	2.06361	−	3.57427i	0.105445	−	0.182637i	−0.808475	−	0.588531i	$-0.799707\pi$
$383$	2.06361	−	3.57427i	0.105445	−	0.182637i	0.913920	+	0.405894i	$0.133040\pi$
$384$	8.82036	+	6.62681i	0.450112	+	0.338173i
$385$	−2.36364	−	5.27773i	−0.120462	−	0.268978i
$386$		−	11.6526i		−	0.593103i
$387$	−34.9725	−	8.61318i	−1.77775	−	0.437832i
$388$	23.9979	−	13.8552i	1.21831	−	0.703390i
$389$	16.4018	−	9.46957i	0.831603	−	0.480126i	−0.0227979	−	0.999740i	$-0.507257\pi$
$389$	16.4018	−	9.46957i	0.831603	−	0.480126i	0.854401	+	0.519614i	$0.173924\pi$
$390$	−2.39587	−	5.62189i	−0.121320	−	0.284676i
$391$			24.2242i			1.22507i
$392$	−4.23758	−	3.78209i	−0.214030	−	0.191024i
$393$	−21.1562	+	28.1592i	−1.06719	+	1.42044i
$394$	3.75313	−	6.50060i	0.189080	−	0.327496i
$395$	15.2895	+	26.4821i	0.769297	+	1.33246i
$396$	5.16626	+	4.96045i	0.259615	+	0.249272i
$397$	26.9202	+	15.5424i	1.35109	+	0.780050i	0.988402	−	0.151862i	$-0.0485269\pi$
$397$	26.9202	+	15.5424i	1.35109	+	0.780050i	0.362685	+	0.931912i	$0.381860\pi$
$398$	−29.8427			−1.49588
$399$	13.9454	+	3.16639i	0.698141	+	0.158518i
$400$	0.684781			0.0342390
$401$	−12.3328	−	7.12033i	−0.615869	−	0.355572i	0.159390	−	0.987216i	$-0.449047\pi$
$401$	−12.3328	−	7.12033i	−0.615869	−	0.355572i	−0.775259	+	0.631644i	$0.782381\pi$
$402$	−3.45182	+	28.4500i	−0.172161	+	1.41896i
$403$	−1.12888	−	1.95528i	−0.0562335	−	0.0973993i
$404$	−17.2192	+	29.8245i	−0.856685	+	1.48382i
$405$	16.6222	−	10.5197i	0.825964	−	0.522731i
$406$	2.99242	−	29.0829i	0.148511	−	1.44336i
$407$		−	9.33079i		−	0.462510i
$408$	5.90201	−	2.51525i	0.292193	−	0.124523i
$409$	−2.74962	+	1.58749i	−0.135960	+	0.0784965i	−0.566437	−	0.824105i	$-0.691679\pi$
$409$	−2.74962	+	1.58749i	−0.135960	+	0.0784965i	0.430477	+	0.902601i	$0.358345\pi$
$410$	−26.2014	+	15.1274i	−1.29400	+	0.747089i
$411$	−18.1697	+	7.74336i	−0.896247	+	0.381952i
$412$			7.41300i			0.365212i
$413$	−0.839644	−	0.607235i	−0.0413162	−	0.0298801i
$414$	9.28315	+	32.0273i	0.456242	+	1.57405i
$415$	−2.66860	+	4.62215i	−0.130996	+	0.226892i
$416$	3.10736	+	5.38211i	0.152351	+	0.263880i
$417$	−2.59247	+	21.3672i	−0.126954	+	1.04636i
$418$	5.66069	+	3.26820i	0.276873	+	0.159853i
$419$	15.7774			0.770774			0.385387	−	0.922755i	$-0.374068\pi$
$419$	15.7774			0.770774			0.385387	+	0.922755i	$0.374068\pi$
$420$	−22.8421	+	7.07409i	−1.11458	+	0.345180i
$421$	−25.8469			−1.25970			−0.629851	−	0.776716i	$-0.716884\pi$
$421$	−25.8469			−1.25970			−0.629851	+	0.776716i	$0.716884\pi$
$422$	−17.2670	−	9.96912i	−0.840546	−	0.485289i
$423$	2.55490	−	2.66091i	0.124224	−	0.129378i
$424$	−3.46839	−	6.00743i	−0.168440	−	0.291747i
$425$	0.508262	−	0.880336i	0.0246543	−	0.0427026i
$426$	−7.02682	+	9.35278i	−0.340450	+	0.453143i
$427$	−30.9943	−	3.18910i	−1.49992	−	0.154331i
$428$		−	12.8600i		−	0.621609i
$429$	0.523322	+	1.22797i	0.0252662	+	0.0592869i
$430$	47.6013	−	27.4826i	2.29554	−	1.32533i
$431$	−4.73146	+	2.73171i	−0.227906	+	0.131582i	−0.609606	−	0.792705i	$-0.708672\pi$
$431$	−4.73146	+	2.73171i	−0.227906	+	0.131582i	0.381700	+	0.924286i	$0.375339\pi$
$432$	−12.3747	+	10.1093i	−0.595377	+	0.486382i
$433$			32.4957i			1.56164i	0.624754	+	0.780822i	$0.285199\pi$
$433$			32.4957i			1.56164i	−0.624754	+	0.780822i	$0.714801\pi$
$434$	−14.8173	+	6.63597i	−0.711254	+	0.318537i
$435$	−15.9677	−	11.9967i	−0.765592	−	0.575196i
$436$	−1.22720	+	2.12557i	−0.0587722	+	0.101796i
$437$	8.27979	+	14.3410i	0.396076	+	0.686024i
$438$	12.6200	+	1.53118i	0.603007	+	0.0731624i
$439$	−13.2271	−	7.63665i	−0.631293	−	0.364477i	0.149959	−	0.988692i	$-0.452086\pi$
$439$	−13.2271	−	7.63665i	−0.631293	−	0.364477i	−0.781253	+	0.624215i	$0.785419\pi$
$440$	−1.77351			−0.0845490
$441$	17.3243	−	11.8688i	0.824966	−	0.565183i
$442$	7.36892			0.350504
$443$	13.7966	+	7.96546i	0.655495	+	0.378450i	0.790558	−	0.612387i	$-0.209790\pi$
$443$	13.7966	+	7.96546i	0.655495	+	0.378450i	−0.135063	+	0.990837i	$0.543124\pi$
$444$	−38.3025	−	4.64722i	−1.81776	−	0.220547i
$445$	−2.47332	−	4.28391i	−0.117246	−	0.203077i
$446$	18.5078	−	32.0564i	0.876370	−	1.51792i
$447$	10.7860	+	8.10360i	0.510159	+	0.383287i
$448$	25.9353	−	11.6152i	1.22533	−	0.548766i
$449$			14.8699i			0.701753i	0.936422	+	0.350877i	$0.114116\pi$
$449$			14.8699i			0.701753i	−0.936422	+	0.350877i	$0.885884\pi$
$450$	0.334623	−	1.35869i	0.0157743	−	0.0640491i
$451$	5.72308	−	3.30422i	0.269489	−	0.155590i
$452$	−18.9854	+	10.9612i	−0.893000	+	0.515574i
$453$	−13.6845	−	32.1106i	−0.642956	−	1.50869i
$454$		−	15.6227i		−	0.733208i
$455$	−4.43323	−	0.456148i	−0.207833	−	0.0213845i
$456$	2.63436	−	3.50636i	0.123365	−	0.164200i
$457$	9.59314	−	16.6158i	0.448748	−	0.777255i	−0.549557	−	0.835457i	$-0.685203\pi$
$457$	9.59314	−	16.6158i	0.448748	−	0.777255i	0.998305	+	0.0582017i	$0.0185366\pi$
$458$	−24.0493	−	41.6546i	−1.12375	−	1.94639i
$459$	3.81139	+	23.4119i	0.177901	+	1.09278i
$460$	−23.9805	−	13.8451i	−1.11810	−	0.645533i
$461$	−8.96675			−0.417623			−0.208811	−	0.977956i	$-0.566960\pi$
$461$	−8.96675			−0.417623			−0.208811	+	0.977956i	$0.566960\pi$
$462$	9.16906	−	2.83961i	0.426583	−	0.132111i
$463$	−35.0764			−1.63014			−0.815070	−	0.579362i	$-0.803302\pi$
$463$	−35.0764			−1.63014			−0.815070	+	0.579362i	$0.803302\pi$
$464$	14.0499	+	8.11169i	0.652248	+	0.376576i
$465$	−1.33585	+	11.0101i	−0.0619485	+	0.510581i
$466$	−25.4651	−	44.1068i	−1.17965	−	2.04321i
$467$	−2.76437	+	4.78803i	−0.127920	+	0.221563i	−0.922870	−	0.385111i	$-0.874163\pi$
$467$	−2.76437	+	4.78803i	−0.127920	+	0.221563i	0.794951	+	0.606674i	$0.207497\pi$
$468$	5.30141	−	1.53662i	0.245058	−	0.0710304i
$469$	16.9351	+	12.2476i	0.781990	+	0.565539i
$470$			5.62950i			0.259670i
$471$	18.2471	−	7.77632i	0.840780	−	0.358314i
$472$	−0.275216	+	0.158896i	−0.0126678	+	0.00731377i
$473$	−10.3974	+	6.00293i	−0.478072	+	0.276015i
$474$	−46.6933	+	19.8992i	−2.14470	+	0.914001i
$475$		−	0.694893i		−	0.0318839i
$476$	2.95124	−	28.6827i	0.135270	−	1.31467i
$477$	24.6331	−	7.13995i	1.12787	−	0.326916i
$478$	−19.2436	+	33.3310i	−0.880184	+	1.52452i
$479$	7.42163	+	12.8546i	0.339103	+	0.587343i	0.984264	−	0.176703i	$-0.0565432\pi$
$479$	7.42163	+	12.8546i	0.339103	+	0.587343i	−0.645161	+	0.764046i	$0.723210\pi$
$480$	3.67707	−	30.3065i	0.167834	−	1.38330i
$481$	−6.22751	−	3.59546i	−0.283950	−	0.163939i
$482$	30.4303			1.38606
$483$	23.7141	+	5.38445i	1.07903	+	0.245001i
$484$	2.38738			0.108517
$485$	−21.9707	−	12.6848i	−0.997636	−	0.575985i
$486$	14.0110	+	29.4928i	0.635552	+	1.33782i
$487$	−5.82168	−	10.0835i	−0.263806	−	0.456925i	0.703444	−	0.710750i	$-0.251644\pi$
$487$	−5.82168	−	10.0835i	−0.263806	−	0.456925i	−0.967250	+	0.253826i	$0.918311\pi$
$488$	−4.77785	+	8.27548i	−0.216283	+	0.374613i
$489$	20.1308	−	26.7943i	0.910346	−	1.21168i
$490$	−6.52581	+	31.3759i	−0.294806	+	1.41742i
$491$			26.5335i			1.19744i	0.800958	+	0.598720i	$0.204324\pi$
$491$			26.5335i			1.19744i	−0.800958	+	0.598720i	$0.795676\pi$
$492$	−10.7133	−	25.1387i	−0.482994	−	1.13334i
$493$	20.8563	−	12.0414i	0.939323	−	0.542318i
$494$	4.36250	−	2.51869i	0.196278	−	0.113321i
$495$	1.56806	−	6.36687i	0.0704790	−	0.286170i
$496$		−	9.00910i		−	0.404520i
$497$	3.48698	+	7.78601i	0.156413	+	0.349250i
$498$	−7.08275	−	5.32133i	−0.317386	−	0.238454i
$499$	1.90045	−	3.29168i	0.0850759	−	0.147356i	−0.820348	−	0.571865i	$-0.806220\pi$
$499$	1.90045	−	3.29168i	0.0850759	−	0.147356i	0.905424	+	0.424509i	$0.139553\pi$
$500$	13.6263	+	23.6014i	0.609386	+	1.05549i
$501$	−23.6405	−	2.86829i	−1.05618	−	0.128146i
$502$	41.5716	+	24.0013i	1.85543	+	1.07123i
$503$	5.47285			0.244022			0.122011	−	0.992529i	$-0.461066\pi$
$503$	5.47285			0.244022			0.122011	+	0.992529i	$0.461066\pi$
$504$	−1.15041	−	6.33682i	−0.0512435	−	0.282264i
$505$	31.5291			1.40303
$506$	9.62602	+	5.55759i	0.427929	+	0.247065i
$507$	−21.3315	−	2.58814i	−0.947366	−	0.114943i
$508$	19.1039	+	33.0889i	0.847597	+	1.46808i
$509$	−6.73743	+	11.6696i	−0.298631	+	0.517244i	−0.975823	−	0.218562i	$-0.929863\pi$
$509$	−6.73743	+	11.6696i	−0.298631	+	0.517244i	0.677192	+	0.735807i	$0.263197\pi$
$510$	−28.9406	−	21.7433i	−1.28151	−	0.962811i
$511$	5.43283	−	7.51216i	0.240334	−	0.332318i
$512$			29.7890i			1.31650i
$513$	10.2586	+	12.5574i	0.452926	+	0.554424i
$514$	40.5295	−	23.3997i	1.78768	−	1.03212i
$515$	5.87753	−	3.39339i	0.258995	−	0.149531i
$516$	19.4634	+	45.6706i	0.856827	+	2.01054i
$517$		−	1.22963i		−	0.0540791i
$518$	−30.3025	+	41.9002i	−1.33141	+	1.84099i
$519$	17.5419	−	23.3485i	0.770004	−	1.02488i
$520$	−0.683393	+	1.18367i	−0.0299688	+	0.0519074i
$521$	−7.84066	−	13.5804i	−0.343506	−	0.594969i	0.641575	−	0.767060i	$-0.278281\pi$
$521$	−7.84066	−	13.5804i	−0.343506	−	0.594969i	−0.985081	+	0.172091i	$0.944948\pi$
$522$	22.9601	−	23.9128i	1.00494	−	1.04663i
$523$	13.4275	+	7.75240i	0.587146	+	0.338989i	0.763968	−	0.645254i	$-0.223249\pi$
$523$	13.4275	+	7.75240i	0.587146	+	0.338989i	−0.176822	+	0.984243i	$0.556582\pi$
$524$	48.5472			2.12079
$525$	−0.748826	−	0.693238i	−0.0326814	−	0.0302554i
$526$	11.7655			0.513001
$527$	−11.5819	−	6.68679i	−0.504513	−	0.291281i
$528$	−0.641538	+	5.28757i	−0.0279193	+	0.230112i
$529$	2.57981	+	4.46836i	0.112166	+	0.194277i
$530$	−19.5695	+	33.8955i	−0.850047	+	1.47232i
$531$	−0.327099	−	1.12851i	−0.0141949	−	0.0489730i
$532$	−8.05652	−	17.9892i	−0.349295	−	0.779932i
$533$		−	5.09290i		−	0.220598i
$534$	7.55339	−	3.21902i	0.326867	−	0.139300i
$535$	−10.1962	+	5.88680i	−0.440822	+	0.254509i
$536$	5.55093	−	3.20483i	0.239763	−	0.138428i
$537$	−3.77288	+	1.60788i	−0.162812	+	0.0693851i
$538$			50.4937i			2.17694i
$539$	1.42541	−	6.85334i	0.0613968	−	0.295194i
$540$	−25.3548	−	9.60786i	−1.09110	−	0.413457i
$541$	6.36323	−	11.0214i	0.273577	−	0.473848i	−0.696198	−	0.717849i	$-0.745127\pi$
$541$	6.36323	−	11.0214i	0.273577	−	0.473848i	0.969775	+	0.244001i	$0.0784600\pi$
$542$	−1.82698	−	3.16442i	−0.0784756	−	0.135924i
$543$	1.14058	−	9.40071i	0.0489471	−	0.403423i
$544$	31.8803	+	18.4061i	1.36686	+	0.789155i
$545$	2.24706			0.0962536
$546$	1.63794	−	7.21377i	0.0700972	−	0.308721i
$547$	21.9445			0.938278			0.469139	−	0.883124i	$-0.344564\pi$
$547$	21.9445			0.938278			0.469139	+	0.883124i	$0.344564\pi$
$548$	23.5765	+	13.6119i	1.00714	+	0.581471i
$549$	−25.4844	−	24.4692i	−1.08765	−	1.04432i
$550$	−0.233214	−	0.403939i	−0.00994429	−	0.0172240i
$551$	8.23148	−	14.2573i	0.350673	−	0.607383i
$552$	4.47973	−	5.96257i	0.190670	−	0.253784i
$553$	−3.78859	+	36.8207i	−0.161107	+	1.56578i
$554$			18.0050i			0.764961i
$555$	13.8488	+	32.4962i	0.587850	+	1.37939i
$556$	25.6929	−	14.8338i	1.08962	−	0.629094i
$557$	7.72810	−	4.46182i	0.327450	−	0.189053i	−0.327258	−	0.944935i	$-0.606125\pi$
$557$	7.72810	−	4.46182i	0.327450	−	0.189053i	0.654709	+	0.755881i	$0.272791\pi$
$558$	−17.8751	−	4.40236i	−0.756714	−	0.186367i
$559$			9.25249i			0.391339i
$560$	−14.4098	−	10.4212i	−0.608923	−	0.440377i
$561$	6.32140	+	4.74932i	0.266890	+	0.200516i
$562$	−0.182948	+	0.316876i	−0.00771721	+	0.0133666i
$563$	1.79149	+	3.10295i	0.0755023	+	0.130774i	0.901305	−	0.433186i	$-0.142611\pi$
$563$	1.79149	+	3.10295i	0.0755023	+	0.130774i	−0.825802	+	0.563960i	$0.809277\pi$
$564$	−5.04759	−	0.612421i	−0.212542	−	0.0257876i
$565$	17.3816	+	10.0353i	0.731251	+	0.422188i
$566$	−25.6034			−1.07619
$567$	23.7662	+	1.47277i	0.998085	+	0.0618504i
$568$	2.61639			0.109781
$569$	12.8245	+	7.40425i	0.537633	+	0.310402i	0.744119	−	0.668047i	$-0.232870\pi$
$569$	12.8245	+	7.40425i	0.537633	+	0.310402i	−0.206486	+	0.978449i	$0.566203\pi$
$570$	−24.5651	−	2.98046i	−1.02892	−	0.124838i
$571$	4.10989	+	7.11853i	0.171993	+	0.297901i	0.939117	−	0.343598i	$-0.111646\pi$
$571$	4.10989	+	7.11853i	0.171993	+	0.297901i	−0.767123	+	0.641500i	$0.778313\pi$
$572$	0.919936	−	1.59338i	0.0384645	−	0.0666224i
$573$	−15.6886	−	11.7870i	−0.655401	−	0.492408i
$574$	−36.4304	−	3.74843i	−1.52058	−	0.156457i
$575$		−	1.18167i		−	0.0492790i
$576$	31.2875	+	7.70561i	1.30364	+	0.321067i
$577$	−18.8119	+	10.8611i	−0.783151	+	0.452152i	−0.837546	−	0.546367i	$-0.816010\pi$
$577$	−18.8119	+	10.8611i	−0.783151	+	0.452152i	0.0543948	+	0.998520i	$0.482677\pi$
$578$	6.96336	−	4.02030i	0.289638	−	0.167222i
$579$	−3.77767	−	8.86426i	−0.156994	−	0.368386i
$580$			27.5287i			1.14307i
$581$	−5.89625	+	2.64065i	−0.244618	+	0.109553i
$582$	25.2941	−	33.6667i	1.04847	−	1.39553i
$583$	4.27451	−	7.40366i	0.177032	−	0.306628i
$584$	−1.42161	−	2.46231i	−0.0588268	−	0.101891i
$585$	−3.64513	−	3.49991i	−0.150707	−	0.144704i
$586$	−4.41583	−	2.54948i	−0.182416	−	0.105318i
$587$	−33.7987			−1.39502			−0.697510	−	0.716575i	$-0.745709\pi$
$587$	−33.7987			−1.39502			−0.697510	+	0.716575i	$0.745709\pi$
$588$	−27.4228	−	9.26458i	−1.13090	−	0.382065i
$589$	−9.14214			−0.376695
$590$	1.55284	+	0.896530i	0.0639292	+	0.0369096i
$591$	0.747607	−	6.16180i	0.0307524	−	0.253463i
$592$	−14.3469	−	24.8495i	−0.589653	−	1.02131i
$593$	13.6937	−	23.7182i	0.562334	−	0.973990i	−0.434959	−	0.900450i	$-0.643237\pi$
$593$	13.6937	−	23.7182i	0.562334	−	0.973990i	0.997292	−	0.0735399i	$-0.0234296\pi$
$594$	10.1777	+	3.85670i	0.417595	+	0.158242i
$595$	−24.0925	+	10.7899i	−0.987698	+	0.442343i
$596$		−	18.5953i		−	0.761694i
$597$	−22.7016	+	9.67470i	−0.929115	+	0.395959i
$598$	7.41844	−	4.28304i	0.303363	−	0.175146i
$599$	26.4914	−	15.2948i	1.08241	−	0.624930i	0.150865	−	0.988554i	$-0.451794\pi$
$599$	26.4914	−	15.2948i	1.08241	−	0.624930i	0.931546	+	0.363625i	$0.118461\pi$
$600$	−0.287903	+	0.122695i	−0.0117536	+	0.00500901i
$601$		−	39.0534i		−	1.59302i	−0.604625	−	0.796511i	$-0.706677\pi$
$601$		−	39.0534i		−	1.59302i	0.604625	−	0.796511i	$-0.293323\pi$
$602$	66.1847	+	6.80994i	2.69749	+	0.277553i
$603$	6.59738	+	22.7613i	0.268666	+	0.926910i
$604$	−24.0558	+	41.6658i	−0.978815	+	1.69536i
$605$	−1.09285	−	1.89288i	−0.0444308	−	0.0769565i
$606$	−6.30341	+	51.9529i	−0.256059	+	2.11044i
$607$	4.55094	+	2.62749i	0.184717	+	0.106646i	0.589507	−	0.807763i	$-0.299322\pi$
$607$	4.55094	+	2.62749i	0.184717	+	0.106646i	−0.404790	+	0.914410i	$0.632655\pi$
$608$	25.1647			1.02056
$609$	−7.15202	−	23.0937i	−0.289814	−	0.935805i
$610$	53.9156			2.18298
$611$	−0.820676	−	0.473817i	−0.0332010	−	0.0191686i
$612$	22.6442	−	23.5837i	0.915337	−	0.953315i
$613$	−11.0868	−	19.2028i	−0.447790	−	0.775595i	0.550452	−	0.834867i	$-0.314455\pi$
$613$	−11.0868	−	19.2028i	−0.447790	−	0.775595i	−0.998242	+	0.0592721i	$0.981122\pi$
$614$	−7.47825	+	12.9527i	−0.301798	+	0.522729i
$615$	−15.0275	+	20.0018i	−0.605969	+	0.806551i
$616$	−1.73955	−	1.25805i	−0.0700886	−	0.0506885i
$617$			26.1103i			1.05116i	0.850743	+	0.525581i	$0.176152\pi$
$617$			26.1103i			1.05116i	−0.850743	+	0.525581i	$0.823848\pi$
$618$	4.41649	+	10.3633i	0.177657	+	0.416872i
$619$	−6.18157	+	3.56893i	−0.248458	+	0.143447i	−0.619058	−	0.785345i	$-0.712485\pi$
$619$	−6.18157	+	3.56893i	−0.248458	+	0.143447i	0.370600	+	0.928793i	$0.379152\pi$
$620$	13.2390	−	7.64357i	0.531693	−	0.306973i
$621$	17.4447	+	21.3540i	0.700033	+	0.856905i
$622$			53.1523i			2.13121i
$623$	0.612866	−	5.95634i	0.0245539	−	0.238636i
$624$	3.28181	+	2.46565i	0.131377	+	0.0987049i
$625$	11.9185	−	20.6435i	0.476740	−	0.825738i
$626$	−18.5218	−	32.0807i	−0.740280	−	1.28220i
$627$	5.36566	+	0.651012i	0.214284	+	0.0259989i
$628$	−23.6768	−	13.6698i	−0.944809	−	0.545486i
$629$	−42.5945			−1.69835
$630$	−27.7183	+	23.4983i	−1.10433	+	0.936193i
$631$	24.1040			0.959566			0.479783	−	0.877387i	$-0.340715\pi$
$631$	24.1040			0.959566			0.479783	+	0.877387i	$0.340715\pi$
$632$	9.83113	+	5.67601i	0.391061	+	0.225779i
$633$	−16.3671	−	1.98581i	−0.650534	−	0.0789288i
$634$	23.5877	+	40.8550i	0.936786	+	1.62256i
$635$	17.4901	−	30.2937i	0.694072	−	1.20217i
$636$	−28.2628	−	21.2341i	−1.12069	−	0.841987i
$637$	−4.02477	−	3.59216i	−0.159467	−	0.142326i
$638$		−	11.0503i		−	0.437486i
$639$	−2.31329	+	9.39278i	−0.0915124	+	0.371572i
$640$	−12.0568	+	6.96099i	−0.476586	+	0.275157i
$641$	10.0529	−	5.80403i	0.397064	−	0.229245i	−0.288152	−	0.957585i	$-0.593041\pi$
$641$	10.0529	−	5.80403i	0.397064	−	0.229245i	0.685217	+	0.728339i	$0.259708\pi$
$642$	−7.66166	−	17.9780i	−0.302382	−	0.709536i
$643$		−	44.1251i		−	1.74012i	−0.492942	−	0.870062i	$-0.664079\pi$
$643$		−	44.1251i		−	1.74012i	0.492942	−	0.870062i	$-0.335921\pi$
$644$	−13.7002	−	30.5908i	−0.539862	−	1.20544i
$645$	27.3012	−	36.3382i	1.07498	−	1.43081i
$646$	14.9191	−	25.8407i	0.586986	−	1.01669i
$647$	12.3432	+	21.3791i	0.485263	+	0.840501i	0.999857	−	0.0169338i	$-0.00539046\pi$
$647$	12.3432	+	21.3791i	0.485263	+	0.840501i	−0.514593	+	0.857434i	$0.672057\pi$
$648$	3.39138	−	6.46748i	0.133226	−	0.254067i
$649$	−0.339180	−	0.195826i	−0.0133140	−	0.00768683i
$650$	−0.359460			−0.0140992
$651$	−9.12036	+	9.85168i	−0.357455	+	0.386118i
$652$	−46.1941			−1.80910
$653$	17.7222	+	10.2319i	0.693523	+	0.400406i	0.804931	−	0.593369i	$-0.202203\pi$
$653$	17.7222	+	10.2319i	0.693523	+	0.400406i	−0.111407	+	0.993775i	$0.535536\pi$
$654$	−0.449240	+	3.70265i	−0.0175667	+	0.144785i
$655$	−22.2231	−	38.4915i	−0.868327	−	1.50399i
$656$	10.1611	−	17.5995i	0.396722	−	0.687143i
$657$	10.0966	−	2.92650i	0.393904	−	0.114174i
$658$	−3.99333	+	5.52170i	−0.155676	+	0.215258i
$659$			34.5197i			1.34470i	0.740235	+	0.672349i	$0.234714\pi$
$659$			34.5197i			1.34470i	−0.740235	+	0.672349i	$0.765286\pi$
$660$	−8.31450	+	3.54337i	−0.323641	+	0.137926i
$661$	3.94464	−	2.27744i	0.153429	−	0.0885820i	−0.421320	−	0.906912i	$-0.638433\pi$
$661$	3.94464	−	2.27744i	0.153429	−	0.0885820i	0.574749	+	0.818330i	$0.305100\pi$
$662$	−3.50412	+	2.02311i	−0.136192	+	0.0786302i
$663$	5.60561	−	2.38893i	0.217704	−	0.0927785i
$664$			1.98136i			0.0768917i
$665$	−10.5751	+	14.6226i	−0.410085	+	0.567038i
$666$	−56.3151	+	16.3230i	−2.18217	+	0.632504i
$667$	13.9977	−	24.2447i	0.541992	−	0.938757i
$668$	16.4120	+	28.4265i	0.635000	+	1.09985i
$669$	3.68668	−	30.3857i	0.142535	−	1.17478i
$670$	−31.3197	−	18.0824i	−1.20999	−	0.698586i
$671$	−11.7766			−0.454631
$672$	25.1048	−	27.1178i	0.968438	−	1.04609i
$673$	−0.323016			−0.0124514			−0.00622568	−	0.999981i	$-0.501982\pi$
$673$	−0.323016			−0.0124514			−0.00622568	+	0.999981i	$0.501982\pi$
$674$	25.7395	+	14.8607i	0.991449	+	0.572414i
$675$	−0.185922	−	1.14205i	−0.00715614	−	0.0439574i
$676$	14.8090	+	25.6500i	0.569578	+	0.986538i
$677$	−16.4267	+	28.4519i	−0.631330	+	1.09350i	0.355950	+	0.934505i	$0.384157\pi$
$677$	−16.4267	+	28.4519i	−0.631330	+	1.09350i	−0.987280	+	0.158991i	$0.949176\pi$
$678$	−20.0109	+	26.6347i	−0.768514	+	1.02290i
$679$	−12.5519	−	28.0269i	−0.481698	−	1.07557i
$680$			8.09599i			0.310467i
$681$	−5.06472	−	11.8843i	−0.194080	−	0.455408i
$682$	−5.31429	+	3.06821i	−0.203495	+	0.117488i
$683$	−9.67455	+	5.58560i	−0.370186	+	0.213727i	−0.673540	−	0.739151i	$-0.735227\pi$
$683$	−9.67455	+	5.58560i	−0.370186	+	0.213727i	0.303354	+	0.952878i	$0.401894\pi$
$684$	5.34476	−	21.7016i	0.204362	−	0.829781i
$685$		−	24.9241i		−	0.952299i
$686$	−28.6576	+	26.1460i	−1.09415	+	0.998259i
$687$	−31.7985	−	23.8905i	−1.21319	−	0.911479i
$688$	−18.4600	+	31.9737i	−0.703782	+	1.21899i
$689$	−3.29421	−	5.70575i	−0.125500	−	0.217372i
$690$	−41.7730	−	5.06829i	−1.59027	−	0.192946i
$691$	−37.6500	−	21.7372i	−1.43227	−	0.826923i	−0.434978	−	0.900441i	$-0.643244\pi$
$691$	−37.6500	−	21.7372i	−1.43227	−	0.826923i	−0.997294	+	0.0735184i	$0.976577\pi$
$692$	−40.2534			−1.53020
$693$	6.05442	−	5.13264i	0.229988	−	0.194973i
$694$	−46.4358			−1.76268
$695$	−23.5225	−	13.5807i	−0.892259	−	0.515146i
$696$	−7.36041	−	0.893034i	−0.278996	−	0.0338504i
$697$	−15.0836	−	26.1256i	−0.571332	−	0.989576i
$698$	23.4459	−	40.6094i	0.887439	−	1.53709i
$699$	−33.6706	−	25.2970i	−1.27354	−	0.956819i
$700$	−0.143963	+	1.39916i	−0.00544130	+	0.0528832i
$701$		−	38.4056i		−	1.45056i	−0.688454	−	0.725280i	$-0.741711\pi$
$701$		−	38.4056i		−	1.45056i	0.688454	−	0.725280i	$-0.258289\pi$
$702$	6.49581	−	5.30663i	0.245169	−	0.200286i
$703$	−25.2165	+	14.5587i	−0.951058	+	0.549094i
$704$	9.30180	−	5.37040i	0.350575	−	0.202404i
$705$	1.82503	+	4.28242i	0.0687346	+	0.161285i
$706$		−	58.4026i		−	2.19801i
$707$	30.9254	+	22.3654i	1.16307	+	0.841138i
$708$	−0.972787	+	1.29479i	−0.0365596	+	0.0486612i
$709$	−6.43267	+	11.1417i	−0.241584	+	0.418436i	−0.961166	−	0.275972i	$-0.911000\pi$
$709$	−6.43267	+	11.1417i	−0.241584	+	0.418436i	0.719582	+	0.694408i	$0.244334\pi$
$710$	−7.38116	−	12.7846i	−0.277010	−	0.479796i
$711$	−29.0690	+	30.2751i	−1.09017	+	1.13540i
$712$	−1.59034	−	0.918185i	−0.0596006	−	0.0344104i
$713$	−15.5462			−0.582211
$714$	−12.9627	−	41.8562i	−0.485116	−	1.56643i
$715$	−1.68445			−0.0629948
$716$	4.89557	+	2.82646i	0.182956	+	0.105630i
$717$	−3.83325	+	31.5938i	−0.143156	+	1.17989i
$718$	5.01251	+	8.68193i	0.187065	+	0.324007i
$719$	11.5606	−	20.0235i	0.431136	−	0.746749i	−0.565835	−	0.824518i	$-0.691446\pi$
$719$	11.5606	−	20.0235i	0.431136	−	0.746749i	0.996971	+	0.0777688i	$0.0247796\pi$
$720$	−5.61359	−	19.3671i	−0.209206	−	0.721770i
$721$	8.17211	+	0.840853i	0.304345	+	0.0313150i
$722$			19.4002i			0.722000i
$723$	23.1486	−	9.86520i	0.860906	−	0.366891i
$724$	−11.3038	+	6.52628i	−0.420104	+	0.242547i
$725$	−1.01738	+	0.587387i	−0.0377847	+	0.0218150i
$726$	3.33753	−	1.42235i	0.123867	−	0.0527882i
$727$			7.47052i			0.277066i	0.990358	+	0.138533i	$0.0442387\pi$
$727$			7.47052i			0.277066i	−0.990358	+	0.138533i	$0.955761\pi$
$728$	−1.50995	+	0.676236i	−0.0559626	+	0.0250630i
$729$	20.2196	+	17.8932i	0.748874	+	0.662712i
$730$	−8.02110	+	13.8930i	−0.296874	+	0.514202i
$731$	27.4030	+	47.4634i	1.01354	+	1.75550i
$732$	−5.86536	+	48.3425i	−0.216790	+	1.78679i
$733$	−22.2472	−	12.8444i	−0.821719	−	0.474420i	0.0292899	−	0.999571i	$-0.490675\pi$
$733$	−22.2472	−	12.8444i	−0.821719	−	0.474420i	−0.851009	+	0.525151i	$0.824009\pi$
$734$	46.7306			1.72486
$735$	5.20753	+	25.9836i	0.192083	+	0.958420i
$736$	42.7927			1.57736
$737$	6.84105	+	3.94968i	0.251993	+	0.145488i
$738$	−29.9541	−	28.7608i	−1.10263	−	1.05870i
$739$	6.83627	+	11.8408i	0.251476	+	0.435570i	0.963933	−	0.266147i	$-0.0857506\pi$
$739$	6.83627	+	11.8408i	0.251476	+	0.435570i	−0.712456	+	0.701717i	$0.752417\pi$
$740$	24.3446	−	42.1661i	0.894925	−	1.55006i
$741$	2.50206	−	3.33027i	0.0919154	−	0.122341i
$742$	−43.2388	+	19.3646i	−1.58735	+	0.710897i
$743$		−	24.9322i		−	0.914672i	−0.889294	−	0.457336i	$-0.848804\pi$
$743$		−	24.9322i		−	0.914672i	0.889294	−	0.457336i	$-0.151196\pi$
$744$	1.61420	+	3.78771i	0.0591794	+	0.138864i
$745$	−14.7436	+	8.51224i	−0.540165	+	0.311864i
$746$	−1.74124	+	1.00530i	−0.0637512	+	0.0368068i
$747$	−7.11304	−	1.75183i	−0.260253	−	0.0640961i
$748$		−	10.8983i		−	0.398480i
$749$	−14.1768	−	1.45870i	−0.518011	−	0.0532996i
$750$	33.1105	+	24.8762i	1.20903	+	0.908351i
$751$	14.4900	−	25.0973i	0.528746	−	0.915815i	−0.470692	−	0.882297i	$-0.655996\pi$
$751$	14.4900	−	25.0973i	0.528746	−	0.915815i	0.999438	−	0.0335172i	$-0.0106708\pi$
$752$	−1.89066	−	3.27473i	−0.0689454	−	0.119417i
$753$	39.4049	+	4.78097i	1.43599	+	0.174228i
$754$	−7.37516	−	4.25805i	−0.268587	−	0.155069i
$755$	44.0473			1.60305
$756$	−18.0539	−	27.4095i	−0.656614	−	0.996874i
$757$	12.0638			0.438465			0.219233	−	0.975673i	$-0.429645\pi$
$757$	12.0638			0.438465			0.219233	+	0.975673i	$0.429645\pi$
$758$	−17.7737	−	10.2617i	−0.645570	−	0.372720i
$759$	9.12433	+	1.10705i	0.331192	+	0.0401833i
$760$	2.76720	+	4.79293i	0.100377	+	0.173858i
$761$	−24.7143	+	42.8064i	−0.895893	+	1.55173i	−0.0631976	+	0.998001i	$0.520130\pi$
$761$	−24.7143	+	42.8064i	−0.895893	+	1.55173i	−0.832695	+	0.553731i	$0.813203\pi$
$762$	46.4205	+	34.8761i	1.68164	+	1.26343i
$763$	2.20403	+	1.59397i	0.0797914	+	0.0577056i
$764$			27.0476i			0.978547i
$765$	−29.0644	−	7.15810i	−1.05083	−	0.258802i
$766$	−7.48669	+	4.32244i	−0.270505	+	0.156176i
$767$	−0.261394	+	0.150916i	−0.00943841	+	0.00544927i
$768$	5.52740	+	12.9700i	0.199453	+	0.468015i
$769$			4.10396i			0.147993i	0.997259	+	0.0739963i	$0.0235753\pi$
$769$			4.10396i			0.147993i	−0.997259	+	0.0739963i	$0.976425\pi$
$770$	−1.23977	+	12.0492i	−0.0446784	+	0.434222i
$771$	23.2452	−	30.9397i	0.837156	−	1.11426i
$772$	−6.64068	+	11.5020i	−0.239003	+	0.413966i
$773$	−10.6435	−	18.4350i	−0.382819	−	0.663062i	0.608645	−	0.793443i	$-0.291713\pi$
$773$	−10.6435	−	18.4350i	−0.382819	−	0.663062i	−0.991464	+	0.130381i	$0.958380\pi$
$774$	54.4190	+	52.2510i	1.95605	+	1.87812i
$775$	0.564969	+	0.326185i	0.0202943	+	0.0117169i
$776$	−9.41809			−0.338090
$777$	−9.46774	+	41.6977i	−0.339653	+	1.49590i
$778$	−39.6701			−1.42224
$779$	−17.8594	−	10.3111i	−0.639878	−	0.369434i
$780$	−0.838944	+	6.91460i	−0.0300390	+	0.247583i
$781$	1.61224	+	2.79248i	0.0576905	+	0.0999229i
$782$	25.3701	−	43.9422i	0.907232	−	1.57137i
$783$	9.71371	−	25.6341i	0.347140	−	0.916089i
$784$	−6.74147	−	20.4433i	−0.240767	−	0.730119i
$785$			25.0301i			0.893364i
$786$	67.8682	−	28.9233i	2.42078	−	1.03166i
$787$	14.3797	−	8.30212i	0.512581	−	0.295939i	−0.221313	−	0.975203i	$-0.571034\pi$
$787$	14.3797	−	8.30212i	0.512581	−	0.295939i	0.733894	+	0.679264i	$0.237701\pi$
$788$	−7.40923	+	4.27772i	−0.263943	+	0.152387i
$789$	8.95015	−	3.81427i	0.318634	−	0.135792i
$790$		−	64.0509i		−	2.27883i
$791$	9.93020	+	22.1729i	0.353077	+	0.788378i
$792$	−0.677676	−	2.33801i	−0.0240802	−	0.0830776i
$793$	−4.53791	+	7.85989i	−0.161146	+	0.279113i
$794$	−32.5552	−	56.3873i	−1.15534	−	2.00111i
$795$	−3.89817	+	32.1289i	−0.138254	+	1.13949i
$796$	29.4569	+	17.0070i	1.04407	+	0.602796i
$797$	−47.8296			−1.69421			−0.847106	−	0.531424i	$-0.821657\pi$
$797$	−47.8296			−1.69421			−0.847106	+	0.531424i	$0.821657\pi$
$798$	−21.9805	−	20.3488i	−0.778100	−	0.720340i
$799$	−5.61320			−0.198581
$800$	−1.55514	−	0.897859i	−0.0549824	−	0.0317441i
$801$	4.70237	−	4.89747i	0.166150	−	0.173044i
$802$	14.9143	+	25.8323i	0.526642	+	0.912171i
$803$	1.75202	−	3.03459i	0.0618275	−	0.107088i
$804$	19.6205	−	26.1151i	0.691962	−	0.921009i
$805$	−17.9830	+	24.8657i	−0.633818	+	0.876401i
$806$			4.72912i			0.166576i
$807$	16.3696	+	38.4110i	0.576236	+	1.35213i
$808$	10.1366	−	5.85238i	0.356605	−	0.205886i
$809$	−20.0614	+	11.5824i	−0.705320	+	0.407217i	−0.809326	−	0.587360i	$-0.800167\pi$
$809$	−20.0614	+	11.5824i	−0.705320	+	0.407217i	0.104006	+	0.994577i	$0.466834\pi$
$810$	−41.1698	+	1.67415i	−1.44656	+	0.0588237i
$811$			44.9695i			1.57909i	0.613691	+	0.789546i	$0.289684\pi$
$811$			44.9695i			1.57909i	−0.613691	+	0.789546i	$0.710316\pi$
$812$	−19.5277	+	27.0016i	−0.685288	+	0.947571i
$813$	−2.41568	−	1.81492i	−0.0847215	−	0.0636520i
$814$	−9.77217	+	16.9259i	−0.342514	+	0.593252i
$815$	21.1459	+	36.6258i	0.740710	+	1.28295i
$816$	24.1375	+	2.92858i	0.844981	+	0.102521i
$817$	32.4459	+	18.7326i	1.13514	+	0.655372i
$818$	6.65035			0.232524
$819$	−1.09264	−	6.01859i	−0.0381799	−	0.210307i
$820$	34.4837			1.20422
$821$	−18.5484	−	10.7089i	−0.647344	−	0.373744i	0.140094	−	0.990138i	$-0.455260\pi$
$821$	−18.5484	−	10.7089i	−0.647344	−	0.373744i	−0.787438	+	0.616394i	$0.788593\pi$
$822$	41.0692	+	4.98290i	1.43245	+	0.173799i
$823$	18.8081	+	32.5766i	0.655610	+	1.13555i	0.981741	+	0.190225i	$0.0609217\pi$
$823$	18.8081	+	32.5766i	0.655610	+	1.13555i	−0.326131	+	0.945325i	$0.605745\pi$
$824$	1.25975	−	2.18195i	0.0438855	−	0.0760119i
$825$	−0.308361	−	0.231675i	−0.0107358	−	0.00806587i
$826$	0.887141	+	1.98088i	0.0308676	+	0.0689235i
$827$		−	47.4230i		−	1.64906i	−0.565819	−	0.824530i	$-0.691440\pi$
$827$		−	47.4230i		−	1.64906i	0.565819	−	0.824530i	$-0.308560\pi$
$828$	9.08878	−	36.9037i	0.315857	−	1.28249i
$829$	−24.4742	+	14.1302i	−0.850023	+	0.490761i	−0.860659	−	0.509182i	$-0.829948\pi$
$829$	−24.4742	+	14.1302i	−0.850023	+	0.490761i	0.0106356	+	0.999943i	$0.496615\pi$
$830$	9.68159	−	5.58967i	0.336053	−	0.194020i
$831$	5.83706	+	13.6966i	0.202485	+	0.475130i
$832$		−	8.27756i		−	0.286973i
$833$	−31.2851	−	6.50692i	−1.08396	−	0.225451i
$834$	27.0807	−	36.0447i	0.937727	−	1.24813i
$835$	15.0256	−	26.0251i	0.519983	−	0.900637i
$836$	−3.72501	−	6.45191i	−0.128832	−	0.223144i
$837$	−15.0250	+	2.44602i	−0.519339	+	0.0845469i
$838$	−28.6199	−	16.5237i	−0.988657	−	0.570801i
$839$	−7.18511			−0.248057			−0.124029	−	0.992279i	$-0.539581\pi$
$839$	−7.18511			−0.248057			−0.124029	+	0.992279i	$0.539581\pi$
$840$	7.92553	+	1.79955i	0.273457	+	0.0620902i
$841$	1.16800			0.0402757
$842$	46.8859	+	27.0696i	1.61579	+	0.932879i
$843$	−0.0364425	+	0.300361i	−0.00125515	+	0.0103450i
$844$	11.3626	+	19.6805i	0.391115	+	0.677432i
$845$	13.5580	−	23.4832i	0.466410	−	0.807846i
$846$	−7.42133	+	2.15108i	−0.255150	+	0.0739558i
$847$	0.270799	−	2.63186i	0.00930478	−	0.0904317i
$848$		−	26.2897i		−	0.902791i
$849$	−19.4767	+	8.30036i	−0.668440	+	0.284868i
$850$	−1.84396	+	1.06461i	−0.0632472	+	0.0365158i
$851$	−42.8807	+	24.7572i	−1.46993	+	0.848666i
$852$	12.2660	−	5.22739i	0.420227	−	0.179087i
$853$		−	13.1861i		−	0.451483i	−0.974187	−	0.225741i	$-0.927520\pi$
$853$		−	13.1861i		−	0.451483i	0.974187	−	0.225741i	$-0.0724805\pi$
$854$	52.8832	+	38.2454i	1.80963	+	1.30873i
$855$	−19.6531	+	5.69649i	−0.672123	+	0.194816i
$856$	−2.18539	+	3.78522i	−0.0746953	+	0.129376i
$857$	24.5160	+	42.4630i	0.837451	+	1.45051i	0.892019	+	0.451997i	$0.149288\pi$
$857$	24.5160	+	42.4630i	0.837451	+	1.45051i	−0.0545688	+	0.998510i	$0.517378\pi$
$858$	0.336761	−	2.77559i	0.0114968	−	0.0947572i
$859$	47.0289	+	27.1522i	1.60461	+	0.926420i	0.990549	+	0.137157i	$0.0437966\pi$
$859$	47.0289	+	27.1522i	1.60461	+	0.926420i	0.614057	+	0.789262i	$0.289537\pi$
$860$	−62.6480			−2.13628
$861$	−28.9282	+	8.95892i	−0.985870	+	0.305319i
$862$	11.4437			0.389774
$863$	−23.5464	−	13.5945i	−0.801528	−	0.462762i	0.0424775	−	0.999097i	$-0.486475\pi$
$863$	−23.5464	−	13.5945i	−0.801528	−	0.462762i	−0.844005	+	0.536335i	$0.819808\pi$
$864$	41.3578	−	6.73294i	1.40702	−	0.229059i
$865$	18.4265	+	31.9156i	0.626520	+	1.08516i
$866$	34.0329	−	58.9467i	1.15648	−	2.00309i
$867$	3.99376	−	5.31573i	0.135635	−	0.180532i
$868$	18.4076	+	1.89401i	0.624793	+	0.0642868i
$869$			13.9904i			0.474592i
$870$	16.4010	+	38.4848i	0.556045	+	1.30476i
$871$	5.27216	−	3.04388i	0.178640	−	0.103138i
$872$	0.722430	−	0.417095i	0.0244646	−	0.0141246i
$873$	8.32704	−	33.8107i	0.281828	−	1.14432i
$874$		−	34.6858i		−	1.17327i
$875$	27.5639	−	12.3446i	0.931830	−	0.417322i
$876$	−11.5843	−	8.70337i	−0.391397	−	0.294060i
$877$	−1.55600	+	2.69508i	−0.0525425	+	0.0910063i	−0.891100	−	0.453806i	$-0.850066\pi$
$877$	−1.55600	+	2.69508i	−0.0525425	+	0.0910063i	0.838558	+	0.544812i	$0.183399\pi$
$878$	15.9958	+	27.7055i	0.539832	+	0.935016i
$879$	−4.18568	−	0.507846i	−0.141180	−	0.0171292i
$880$	−5.82092	−	3.36071i	−0.196223	−	0.113290i
$881$	4.57707			0.154205			0.0771027	−	0.997023i	$-0.475433\pi$
$881$	4.57707			0.154205			0.0771027	+	0.997023i	$0.475433\pi$
$882$	−43.8562	+	3.38610i	−1.47672	+	0.114016i
$883$	50.8231			1.71034			0.855168	−	0.518352i	$-0.173454\pi$
$883$	50.8231			1.71034			0.855168	+	0.518352i	$0.173454\pi$
$884$	−7.27367	−	4.19946i	−0.244640	−	0.141243i
$885$	1.47190	+	0.178585i	0.0494775	+	0.00600307i
$886$	−16.6845	−	28.8984i	−0.560527	−	0.970861i
$887$	−5.92193	+	10.2571i	−0.198839	+	0.344399i	−0.948152	−	0.317816i	$-0.897050\pi$
$887$	−5.92193	+	10.2571i	−0.198839	+	0.344399i	0.749313	+	0.662216i	$0.230384\pi$
$888$	10.4843	+	7.87693i	0.351829	+	0.264332i
$889$	38.6442	−	17.3069i	1.29608	−	0.580455i
$890$			10.3613i			0.347310i
$891$	8.99257	−	0.365679i	0.301262	−	0.0122507i
$892$	−36.5371	+	21.0947i	−1.22335	+	0.706304i
$893$	−3.32309	+	1.91858i	−0.111203	+	0.0642030i
$894$	−11.0787	−	25.9960i	−0.370526	−	0.869436i
$895$		−	5.17539i		−	0.172994i
$896$	−16.7637	−	1.72487i	−0.560037	−	0.0576238i
$897$	4.25476	−	5.66314i	0.142062	−	0.189087i
$898$	15.5733	−	26.9737i	0.519687	−	0.900125i
$899$	7.72777	+	13.3849i	0.257736	+	0.446411i
$900$	−1.10460	+	1.15043i	−0.0368199	+	0.0383475i
$901$	−33.7973	−	19.5129i	−1.12595	−	0.650068i
$902$	−13.8421			−0.460892
$903$	52.5551	−	16.2761i	1.74892	−	0.541634i
$904$	7.45093			0.247814
$905$	10.3489	+	5.97497i	0.344011	+	0.198615i
$906$	−8.80609	+	72.5801i	−0.292563	+	2.41131i
$907$	11.1854	+	19.3736i	0.371404	+	0.643291i	0.989782	−	0.142590i	$-0.0455430\pi$
$907$	11.1854	+	19.3736i	0.371404	+	0.643291i	−0.618377	+	0.785881i	$0.712210\pi$
$908$	−8.90316	+	15.4207i	−0.295462	+	0.511755i
$909$	12.0476	+	41.5646i	0.399593	+	1.37861i
$910$	7.56408	+	5.47038i	0.250747	+	0.181341i
$911$			33.5149i			1.11040i	0.831717	+	0.555200i	$0.187358\pi$
$911$			33.5149i			1.11040i	−0.831717	+	0.555200i	$0.812642\pi$
$912$	15.2907	−	6.51640i	0.506325	−	0.215780i
$913$	−2.11471	+	1.22093i	−0.0699869	+	0.0404069i
$914$	−34.8036	+	20.0939i	−1.15120	+	0.664646i
$915$	41.0142	−	17.4789i	1.35589	−	0.577836i
$916$			54.8215i			1.81135i
$917$	5.50668	−	53.5185i	0.181846	−	1.76734i
$918$	17.6056	−	46.4605i	0.581071	−	1.53343i
$919$	−4.99223	+	8.64680i	−0.164679	+	0.285232i	−0.936541	−	0.350558i	$-0.885992\pi$
$919$	−4.99223	+	8.64680i	−0.164679	+	0.285232i	0.771863	+	0.635789i	$0.219325\pi$
$920$	4.70563	+	8.15040i	0.155140	+	0.268711i
$921$	−1.48964	+	12.2776i	−0.0490852	+	0.404562i
$922$	16.2655	+	9.39091i	0.535677	+	0.309273i
$923$	2.48500			0.0817947
$924$	−10.6688	−	2.42242i	−0.350978	−	0.0796919i
$925$	2.07778			0.0683171
$926$	63.6281	+	36.7357i	2.09095	+	1.20721i
$927$	6.71934	+	6.45166i	0.220692	+	0.211900i
$928$	−21.2715	−	36.8433i	−0.698272	−	1.20944i
$929$	−8.37008	+	14.4974i	−0.274613	+	0.475644i	−0.970038	−	0.242955i	$-0.921883\pi$
$929$	−8.37008	+	14.4974i	−0.274613	+	0.475644i	0.695424	+	0.718600i	$0.255217\pi$
$930$	13.9541	−	18.5731i	0.457574	−	0.609036i
$931$	−20.7452	+	6.84102i	−0.679897	+	0.224206i
$932$			58.0490i			1.90146i
$933$	17.2315	+	40.4335i	0.564133	+	1.32373i
$934$	10.0290	−	5.79027i	0.328160	−	0.189463i
$935$	−8.64088	+	4.98882i	−0.282587	+	0.163152i
$936$	−1.82156	−	0.448620i	−0.0595394	−	0.0146636i
$937$			27.4695i			0.897389i	0.893685	+	0.448695i	$0.148111\pi$
$937$			27.4695i			0.897389i	−0.893685	+	0.448695i	$0.851889\pi$
$938$	−17.8931	−	39.9531i	−0.584230	−	1.30451i
$939$	−24.4900	−	18.3995i	−0.799200	−	0.600446i
$940$	3.20818	−	5.55674i	0.104639	−	0.181241i
$941$	−28.9541	−	50.1499i	−0.943876	−	1.63484i	−0.757987	−	0.652270i	$-0.773817\pi$
$941$	−28.9541	−	50.1499i	−0.943876	−	1.63484i	−0.185889	−	0.982571i	$-0.559516\pi$
$942$	−41.2441	−	5.00411i	−1.34380	−	0.163043i
$943$	−30.3699	−	17.5341i	−0.988980	−	0.570988i
$944$	−1.20440			−0.0391997
$945$	−13.4677	+	26.8614i	−0.438105	+	0.873801i
$946$	25.1476			0.817618
$947$	15.1380	+	8.73993i	0.491919	+	0.284010i	0.725370	−	0.688359i	$-0.241669\pi$
$947$	15.1380	+	8.73993i	0.491919	+	0.284010i	−0.233451	+	0.972369i	$0.575002\pi$
$948$	57.4301	+	6.96795i	1.86524	+	0.226309i
$949$	−1.35022	−	2.33865i	−0.0438301	−	0.0759159i
$950$	−0.727764	+	1.26052i	−0.0236118	+	0.0408968i
$951$	31.1882	+	23.4319i	1.01135	+	0.759833i
$952$	−5.74295	+	7.94096i	−0.186130	+	0.257368i
$953$		−	49.9562i		−	1.61824i	−0.587642	−	0.809121i	$-0.699944\pi$
$953$		−	49.9562i		−	1.61824i	0.587642	−	0.809121i	$-0.300056\pi$
$954$	−52.1618	−	12.8466i	−1.68880	−	0.415925i
$955$	21.4452	−	12.3814i	0.693949	−	0.400652i
$956$	37.9898	−	21.9334i	1.22868	−	0.709378i
$957$	−3.58241	−	8.40609i	−0.115803	−	0.271730i
$958$		−	31.0908i		−	1.00450i
$959$	17.6801	−	24.4468i	0.570919	−	0.789428i
$960$	−24.4244	+	32.5092i	−0.788295	+	1.04923i
$961$	−11.2086	+	19.4139i	−0.361569	+	0.626256i
$962$	7.53107	+	13.0442i	0.242811	+	0.420562i
$963$	−11.6566	−	11.1922i	−0.375629	−	0.360664i
$964$	−30.0369	−	17.3418i	−0.967424	−	0.558543i
$965$	12.1594			0.391426
$966$	−37.3779	−	34.6032i	−1.20261	−	1.11334i
$967$	16.0560			0.516327			0.258163	−	0.966101i	$-0.416883\pi$
$967$	16.0560			0.516327			0.258163	+	0.966101i	$0.416883\pi$
$968$	−0.702705	−	0.405707i	−0.0225858	−	0.0130399i
$969$	2.97183	−	24.4939i	0.0954690	−	0.786859i
$970$	26.5696	+	46.0199i	0.853098	+	1.47761i
$971$	−0.117046	+	0.202730i	−0.00375619	+	0.00650590i	−0.867897	−	0.496744i	$-0.834529\pi$
$971$	−0.117046	+	0.202730i	−0.00375619	+	0.00650590i	0.864141	+	0.503249i	$0.167862\pi$
$972$	2.97767	−	37.0963i	0.0955089	−	1.18986i
$973$	−13.4385	−	30.0065i	−0.430818	−	0.961965i
$974$			24.3883i			0.781451i
$975$	−0.273445	+	0.116534i	−0.00875725	+	0.00373206i
$976$	−31.3631	+	18.1075i	−1.00391	+	0.579608i
$977$	8.99046	−	5.19064i	0.287630	−	0.166063i	−0.349242	−	0.937032i	$-0.613561\pi$
$977$	8.99046	−	5.19064i	0.287630	−	0.166063i	0.636873	+	0.770969i	$0.280228\pi$
$978$	−64.5787	+	27.5214i	−2.06500	+	0.880037i
$979$		−	2.26317i		−	0.0723313i
$980$	24.3222	−	27.2514i	0.776945	−	0.870514i
$981$	0.858623	+	2.96228i	0.0274137	+	0.0945785i
$982$	27.7886	−	48.1313i	0.886771	−	1.53593i
$983$	15.1150	+	26.1800i	0.482095	+	0.835012i	0.999789	−	0.0205535i	$-0.00654283\pi$
$983$	15.1150	+	26.1800i	0.482095	+	0.835012i	−0.517694	+	0.855566i	$0.673209\pi$
$984$	−1.11865	+	9.21997i	−0.0356613	+	0.293922i
$985$	6.78333	+	3.91636i	0.216135	+	0.124786i
$986$	−50.4441			−1.60647
$987$	−1.24768	+	5.49501i	−0.0397141	+	0.174908i
$988$	−5.74148			−0.182661
$989$	55.1743	+	31.8549i	1.75444	+	1.01293i
$990$	−9.51249	+	9.90717i	−0.302327	+	0.314870i
$991$	−10.7298	−	18.5845i	−0.340843	−	0.590357i	0.643747	−	0.765239i	$-0.277379\pi$
$991$	−10.7298	−	18.5845i	−0.340843	−	0.590357i	−0.984589	+	0.174882i	$0.944046\pi$
$992$	−11.8124	+	20.4597i	−0.375044	+	0.649595i
$993$	−2.00975	+	2.67500i	−0.0637775	+	0.0848885i
$994$	1.82899	−	17.7756i	0.0580119	−	0.563809i
$995$		−	31.1406i		−	0.987223i
$996$	3.95864	+	9.28892i	0.125434	+	0.294331i
$997$	2.62355	−	1.51471i	0.0830886	−	0.0479713i	−0.457880	−	0.889014i	$-0.651391\pi$
$997$	2.62355	−	1.51471i	0.0830886	−	0.0479713i	0.540969	+	0.841043i	$0.318058\pi$
$998$	−6.89477	+	3.98070i	−0.218250	+	0.126007i
$999$	−37.5477	+	30.6739i	−1.18796	+	0.970479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.5	✓	52
3.2	odd	2	inner	231.2.n.a.89.22	yes	52
7.3	odd	6	inner	231.2.n.a.122.22	yes	52
21.17	even	6	inner	231.2.n.a.122.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.5	✓	52	1.1	even	1	trivial
231.2.n.a.89.22	yes	52	3.2	odd	2	inner
231.2.n.a.122.5	yes	52	21.17	even	6	inner
231.2.n.a.122.22	yes	52	7.3	odd	6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81398 - 1.04730i) q^{2} +(-1.71944 - 0.208619i) q^{3} +(1.19369 + 2.06753i) q^{4} +(1.09285 - 1.89288i) q^{5} +(2.90055 + 2.17921i) q^{6} +(2.41465 - 1.08141i) q^{7} -0.811414i q^{8} +(2.91296 + 0.717415i) q^{9} +O(q^{10})\)	\(q+(-1.81398 - 1.04730i) q^{2} +(-1.71944 - 0.208619i) q^{3} +(1.19369 + 2.06753i) q^{4} +(1.09285 - 1.89288i) q^{5} +(2.90055 + 2.17921i) q^{6} +(2.41465 - 1.08141i) q^{7} -0.811414i q^{8} +(2.91296 + 0.717415i) q^{9} +(-3.96484 + 2.28910i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-1.62116 - 3.80403i) q^{12} -0.770665i q^{13} +(-5.51271 - 0.567219i) q^{14} +(-2.27399 + 3.02670i) q^{15} +(1.53759 - 2.66318i) q^{16} +(-2.28247 - 3.95336i) q^{17} +(-4.53270 - 4.35213i) q^{18} +(-2.70250 - 1.56029i) q^{19} +5.21812 q^{20} +(-4.37746 + 1.35568i) q^{21} -2.09461 q^{22} +(-4.59562 - 2.65328i) q^{23} +(-0.169276 + 1.39518i) q^{24} +(0.111340 + 0.192847i) q^{25} +(-0.807121 + 1.39797i) q^{26} +(-4.85899 - 1.84125i) q^{27} +(5.11820 + 3.70151i) q^{28} +5.27560i q^{29} +(7.29486 - 3.10883i) q^{30} +(2.53713 - 1.46481i) q^{31} +(-6.98372 + 4.03205i) q^{32} +(-1.59339 + 0.679052i) q^{33} +9.56177i q^{34} +(0.591888 - 5.75247i) q^{35} +(1.99389 + 6.87901i) q^{36} +(4.66539 - 8.08070i) q^{37} +(3.26820 + 5.66069i) q^{38} +(-0.160775 + 1.32511i) q^{39} +(-1.53591 - 0.886757i) q^{40} +6.60845 q^{41} +(9.36044 + 2.12535i) q^{42} -12.0059 q^{43} +(2.06753 + 1.19369i) q^{44} +(4.54142 - 4.72984i) q^{45} +(5.55759 + 9.62602i) q^{46} +(0.614816 - 1.06489i) q^{47} +(-3.19938 + 4.25841i) q^{48} +(4.66111 - 5.22246i) q^{49} -0.466428i q^{50} +(3.09983 + 7.27373i) q^{51} +(1.59338 - 0.919936i) q^{52} +(7.40366 - 4.27451i) q^{53} +(6.88578 + 8.42884i) q^{54} -2.18571i q^{55} +(-0.877470 - 1.95928i) q^{56} +(4.32129 + 3.24662i) q^{57} +(5.52516 - 9.56986i) q^{58} +(-0.195826 - 0.339180i) q^{59} +(-8.97225 - 1.08860i) q^{60} +(-10.1988 - 5.88830i) q^{61} -6.13642 q^{62} +(7.80960 - 1.41779i) q^{63} +10.7408 q^{64} +(-1.45878 - 0.842225i) q^{65} +(3.60156 + 0.436974i) q^{66} +(3.94968 + 6.84105i) q^{67} +(5.44913 - 9.43818i) q^{68} +(7.34837 + 5.52089i) q^{69} +(-7.09826 + 9.81500i) q^{70} +3.22448i q^{71} +(0.582121 - 2.36361i) q^{72} +(3.03459 - 1.75202i) q^{73} +(-16.9259 + 9.77217i) q^{74} +(-0.151212 - 0.354817i) q^{75} -7.45003i q^{76} +(1.55045 - 2.14385i) q^{77} +(1.67944 - 2.23535i) q^{78} +(-6.99520 + 12.1160i) q^{79} +(-3.36071 - 5.82092i) q^{80} +(7.97063 + 4.17960i) q^{81} +(-11.9876 - 6.92105i) q^{82} -2.44186 q^{83} +(-8.02824 - 7.43228i) q^{84} -9.97763 q^{85} +(21.7784 + 12.5738i) q^{86} +(1.10059 - 9.07109i) q^{87} +(-0.405707 - 0.702705i) q^{88} +(1.13159 - 1.95996i) q^{89} +(-13.1916 + 3.82362i) q^{90} +(-0.833404 - 1.86089i) q^{91} -12.6688i q^{92} +(-4.66803 + 1.98937i) q^{93} +(-2.23053 + 1.28780i) q^{94} +(-5.90689 + 3.41034i) q^{95} +(12.8493 - 5.47594i) q^{96} -11.6070i q^{97} +(-13.9247 + 4.59185i) q^{98} +(2.88140 - 0.835179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

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