LMFDB - Embedded newform 63.2.g.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(4,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("63.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.g (of order $3$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	63.16
Dual form			63.2.g.b.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.335166 - 0.580525i) q^{2} +(-0.377302 + 1.69046i) q^{3} +(0.775327 - 1.34291i) q^{4} +1.42494 q^{5} +(1.10781 - 0.347551i) q^{6} +(2.21529 + 1.44655i) q^{7} -2.38012 q^{8} +(-2.71529 - 1.27563i) q^{9} +(-0.477591 - 0.827212i) q^{10} -4.93077 q^{11} +(1.97759 + 1.81734i) q^{12} +(-1.37730 - 2.38556i) q^{13} +(0.0972697 - 1.77086i) q^{14} +(-0.537632 + 2.40879i) q^{15} +(-0.752918 - 1.30409i) q^{16} +(0.559839 + 0.969670i) q^{17} +(0.169539 + 2.00384i) q^{18} +(-2.00752 + 3.47713i) q^{19} +(1.10479 - 1.91356i) q^{20} +(-3.28116 + 3.19906i) q^{21} +(1.65263 + 2.86244i) q^{22} +5.43661 q^{23} +(0.898025 - 4.02349i) q^{24} -2.96955 q^{25} +(-0.923251 + 1.59912i) q^{26} +(3.18087 - 4.10878i) q^{27} +(3.66015 - 1.85337i) q^{28} +(3.40555 - 5.89858i) q^{29} +(1.57856 - 0.495238i) q^{30} +(-1.25292 + 2.17012i) q^{31} +(-2.88483 + 4.99666i) q^{32} +(1.86039 - 8.33526i) q^{33} +(0.375279 - 0.650002i) q^{34} +(3.15664 + 2.06124i) q^{35} +(-3.81828 + 2.65735i) q^{36} +(0.709787 - 1.22939i) q^{37} +2.69142 q^{38} +(4.55234 - 1.42819i) q^{39} -3.39152 q^{40} +(0.124384 + 0.215440i) q^{41} +(2.95687 + 0.832581i) q^{42} +(-0.498313 + 0.863104i) q^{43} +(-3.82296 + 6.62156i) q^{44} +(-3.86911 - 1.81769i) q^{45} +(-1.82217 - 3.15609i) q^{46} +(4.73790 + 8.20628i) q^{47} +(2.48859 - 0.780738i) q^{48} +(2.81498 + 6.40905i) q^{49} +(0.995294 + 1.72390i) q^{50} +(-1.85041 + 0.580525i) q^{51} -4.27144 q^{52} +(-0.410229 - 0.710537i) q^{53} +(-3.45137 - 0.469454i) q^{54} -7.02604 q^{55} +(-5.27265 - 3.44296i) q^{56} +(-5.12050 - 4.70556i) q^{57} -4.56570 q^{58} +(3.29204 - 5.70197i) q^{59} +(2.81794 + 2.58959i) q^{60} +(-0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +(-4.16988 - 6.75368i) q^{63} +0.855913 q^{64} +(-1.96257 - 3.39927i) q^{65} +(-5.46237 + 1.71369i) q^{66} +(6.29385 - 10.9013i) q^{67} +1.73623 q^{68} +(-2.05125 + 9.19035i) q^{69} +(0.138603 - 2.52337i) q^{70} +0.0804951 q^{71} +(6.46270 + 3.03614i) q^{72} +(5.34551 + 9.25869i) q^{73} -0.951587 q^{74} +(1.12042 - 5.01990i) q^{75} +(3.11297 + 5.39183i) q^{76} +(-10.9231 - 7.13261i) q^{77} +(-2.35489 - 2.16407i) q^{78} +(0.922457 + 1.59774i) q^{79} +(-1.07286 - 1.85825i) q^{80} +(5.74555 + 6.92738i) q^{81} +(0.0833788 - 0.144416i) q^{82} +(-7.23583 + 12.5328i) q^{83} +(1.75206 + 6.88661i) q^{84} +(0.797736 + 1.38172i) q^{85} +0.668072 q^{86} +(8.68637 + 7.98248i) q^{87} +11.7358 q^{88} +(6.76292 - 11.7137i) q^{89} +(0.241583 + 2.85534i) q^{90} +(0.399711 - 7.27703i) q^{91} +(4.21515 - 7.30085i) q^{92} +(-3.19576 - 2.93679i) q^{93} +(3.17597 - 5.50094i) q^{94} +(-2.86059 + 4.95469i) q^{95} +(-7.35819 - 6.76192i) q^{96} +(2.70160 - 4.67930i) q^{97} +(2.77712 - 3.78226i) q^{98} +(13.3885 + 6.28982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 - 2 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 7 * q^10 - 8 * q^11 + 22 * q^12 - 8 * q^13 + 16 * q^14 - 19 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + q^19 + 5 * q^20 - 2 * q^21 - q^22 - 6 * q^23 + 3 * q^24 + 2 * q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 - 26 * q^30 - 3 * q^31 - 2 * q^32 - q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 - 40 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 + 32 * q^42 - 7 * q^43 - 10 * q^44 - q^45 + 3 * q^46 + 27 * q^47 - 5 * q^48 + 25 * q^49 + 19 * q^50 + 24 * q^51 + 20 * q^52 - 21 * q^53 - 53 * q^54 + 4 * q^55 - 45 * q^56 - 4 * q^57 + 20 * q^58 + 30 * q^59 - 41 * q^60 - 14 * q^61 - 12 * q^62 - 35 * q^63 - 50 * q^64 - 11 * q^65 - 41 * q^66 - 2 * q^67 - 54 * q^68 + 15 * q^69 - 29 * q^70 - 6 * q^71 + 48 * q^72 + 15 * q^73 + 72 * q^74 + 31 * q^75 + 5 * q^76 - 31 * q^77 - 20 * q^78 - 4 * q^79 + 20 * q^80 + 8 * q^81 - 5 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 + 16 * q^86 + 32 * q^87 + 36 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 12 * q^93 - 3 * q^94 - 14 * q^95 - q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.335166	−	0.580525i	−0.236998	−	0.410493i	0.722853	−	0.691002i	$-0.242830\pi$
$2$	−0.335166	−	0.580525i	−0.236998	−	0.410493i	−0.959852	+	0.280508i	$0.909497\pi$
$3$	−0.377302	+	1.69046i	−0.217836	+	0.975985i
$3$	−0.377302	+	1.69046i	−0.217836	+	0.975985i
$4$	0.775327	−	1.34291i	0.387664	−	0.671453i
$5$	1.42494			0.637251			0.318626	−	0.947881i	$-0.396779\pi$
$5$	1.42494			0.637251			0.318626	+	0.947881i	$0.396779\pi$
$6$	1.10781	−	0.347551i	0.452262	−	0.141887i
$7$	2.21529	+	1.44655i	0.837299	+	0.546745i
$7$	2.21529	+	1.44655i	0.837299	+	0.546745i
$8$	−2.38012			−0.841499
$9$	−2.71529	−	1.27563i	−0.905095	−	0.425209i
$10$	−0.477591	−	0.827212i	−0.151028	−	0.261587i
$11$	−4.93077			−1.48668			−0.743342	−	0.668911i	$-0.766761\pi$
$11$	−4.93077			−1.48668			−0.743342	+	0.668911i	$0.766761\pi$
$12$	1.97759	+	1.81734i	0.570881	+	0.524620i
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	0.609352	−	0.792900i	$-0.291429\pi$
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	−0.991347	+	0.131265i	$0.958096\pi$
$14$	0.0972697	−	1.77086i	0.0259964	−	0.473283i
$15$	−0.537632	+	2.40879i	−0.138816	+	0.621948i
$16$	−0.752918	−	1.30409i	−0.188230	−	0.326023i
$17$	0.559839	+	0.969670i	0.135781	+	0.235180i	0.925896	−	0.377780i	$-0.123312\pi$
$17$	0.559839	+	0.969670i	0.135781	+	0.235180i	−0.790115	+	0.612959i	$0.789979\pi$
$18$	0.169539	+	2.00384i	0.0399608	+	0.472309i
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	−0.998989	−	0.0449606i	$-0.985684\pi$
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	0.538431	+	0.842669i	$0.319017\pi$
$20$	1.10479	−	1.91356i	0.247039	−	0.427884i
$21$	−3.28116	+	3.19906i	−0.716009	+	0.698092i
$22$	1.65263	+	2.86244i	0.352342	+	0.610274i
$23$	5.43661			1.13361			0.566806	−	0.823851i	$-0.308179\pi$
$23$	5.43661			1.13361			0.566806	+	0.823851i	$0.308179\pi$
$24$	0.898025	−	4.02349i	0.183309	−	0.821291i
$25$	−2.96955			−0.593911
$26$	−0.923251	+	1.59912i	−0.181064	+	0.313613i
$27$	3.18087	−	4.10878i	0.612160	−	0.790734i
$28$	3.66015	−	1.85337i	0.691704	−	0.350254i
$29$	3.40555	−	5.89858i	0.632394	−	1.09534i	−0.354667	−	0.934993i	$-0.615406\pi$
$29$	3.40555	−	5.89858i	0.632394	−	1.09534i	0.987061	−	0.160346i	$-0.0512611\pi$
$30$	1.57856	−	0.495238i	0.288205	−	0.0904176i
$31$	−1.25292	+	2.17012i	−0.225031	+	0.389765i	−0.956329	−	0.292294i	$-0.905582\pi$
$31$	−1.25292	+	2.17012i	−0.225031	+	0.389765i	0.731298	+	0.682058i	$0.238915\pi$
$32$	−2.88483	+	4.99666i	−0.509970	+	0.883294i
$33$	1.86039	−	8.33526i	0.323853	−	1.45098i
$34$	0.375279	−	0.650002i	0.0643597	−	0.111474i
$35$	3.15664	+	2.06124i	0.533570	+	0.348414i
$36$	−3.81828	+	2.65735i	−0.636380	+	0.442891i
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	−0.801765	−	0.597639i	$-0.796106\pi$
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	0.918453	+	0.395529i	$0.129439\pi$
$38$	2.69142			0.436605
$39$	4.55234	−	1.42819i	0.728958	−	0.228694i
$40$	−3.39152			−0.536247
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	0.875575	−	0.483083i	$-0.160483\pi$
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	−0.856149	+	0.516729i	$0.827150\pi$
$42$	2.95687	+	0.832581i	0.456255	+	0.128470i
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	−0.901517	−	0.432743i	$-0.857546\pi$
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	0.825525	+	0.564365i	$0.190879\pi$
$44$	−3.82296	+	6.62156i	−0.576333	+	0.998238i
$45$	−3.86911	−	1.81769i	−0.576773	−	0.270965i
$46$	−1.82217	−	3.15609i	−0.268664	−	0.465340i
$47$	4.73790	+	8.20628i	0.691093	+	1.19701i	0.971480	+	0.237122i	$0.0762040\pi$
$47$	4.73790	+	8.20628i	0.691093	+	1.19701i	−0.280387	+	0.959887i	$0.590463\pi$
$48$	2.48859	−	0.780738i	0.359197	−	0.112690i
$49$	2.81498	+	6.40905i	0.402140	+	0.915578i
$50$	0.995294	+	1.72390i	0.140756	+	0.243796i
$51$	−1.85041	+	0.580525i	−0.259110	+	0.0812898i
$52$	−4.27144			−0.592342
$53$	−0.410229	−	0.710537i	−0.0563493	−	0.0975998i	0.836475	−	0.548005i	$-0.184613\pi$
$53$	−0.410229	−	0.710537i	−0.0563493	−	0.0975998i	−0.892824	+	0.450406i	$0.851279\pi$
$54$	−3.45137	−	0.469454i	−0.469672	−	0.0638846i
$55$	−7.02604			−0.947392
$56$	−5.27265	−	3.44296i	−0.704587	−	0.460085i
$57$	−5.12050	−	4.70556i	−0.678226	−	0.623267i
$58$	−4.56570			−0.599506
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	−0.568161	−	0.822917i	$-0.692345\pi$
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	0.996748	+	0.0805836i	$0.0256784\pi$
$60$	2.81794	+	2.58959i	0.363795	+	0.334315i
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	0.863606	−	0.504167i	$-0.168200\pi$
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	−0.868425	+	0.495821i	$0.834867\pi$
$62$	1.67974			0.213328
$63$	−4.16988	−	6.75368i	−0.525355	−	0.850883i
$64$	0.855913			0.106989
$65$	−1.96257	−	3.39927i	−0.243427	−	0.421628i
$66$	−5.46237	+	1.71369i	−0.672371	+	0.210941i
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	−0.169235	−	0.985576i	$-0.554130\pi$
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	0.938151	−	0.346226i	$-0.112537\pi$
$68$	1.73623			0.210549
$69$	−2.05125	+	9.19035i	−0.246941	+	1.10639i
$70$	0.138603	−	2.52337i	0.0165663	−	0.301600i
$71$	0.0804951			0.00955301			0.00477651	−	0.999989i	$-0.498480\pi$
$71$	0.0804951			0.00955301			0.00477651	+	0.999989i	$0.498480\pi$
$72$	6.46270	+	3.03614i	0.761637	+	0.357813i
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	0.988416	+	0.151769i	$0.0484971\pi$
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	−0.362772	+	0.931878i	$0.618170\pi$
$74$	−0.951587			−0.110620
$75$	1.12042	−	5.01990i	0.129375	−	0.579648i
$76$	3.11297	+	5.39183i	0.357083	+	0.618485i
$77$	−10.9231	−	7.13261i	−1.24480	−	0.812837i
$78$	−2.35489	−	2.16407i	−0.266639	−	0.245032i
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	0.913241	−	0.407420i	$-0.133571\pi$
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	−0.809456	+	0.587180i	$0.800238\pi$
$80$	−1.07286	−	1.85825i	−0.119950	−	0.207759i
$81$	5.74555	+	6.92738i	0.638395	+	0.769709i
$82$	0.0833788	−	0.144416i	0.00920765	−	0.0159481i
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	0.129088	+	0.991633i	$0.458795\pi$
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	−0.923323	+	0.384023i	$0.874538\pi$
$84$	1.75206	+	6.88661i	0.191165	+	0.751391i
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$	0.668072			0.0720400
$87$	8.68637	+	7.98248i	0.931277	+	0.855811i
$88$	11.7358			1.25104
$89$	6.76292	−	11.7137i	0.716868	−	1.24165i	−0.245366	−	0.969430i	$-0.578908\pi$
$89$	6.76292	−	11.7137i	0.716868	−	1.24165i	0.962235	−	0.272222i	$-0.0877584\pi$
$90$	0.241583	+	2.85534i	0.0254651	+	0.300980i
$91$	0.399711	−	7.27703i	0.0419011	−	0.762840i
$92$	4.21515	−	7.30085i	0.439460	−	0.761167i
$93$	−3.19576	−	2.93679i	−0.331385	−	0.304531i
$94$	3.17597	−	5.50094i	0.327576	−	0.567378i
$95$	−2.86059	+	4.95469i	−0.293491	+	0.508341i
$96$	−7.35819	−	6.76192i	−0.750992	−	0.690136i
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$98$	2.77712	−	3.78226i	0.280532	−	0.382066i
$99$	13.3885	+	6.28982i	1.34559	+	0.632151i
$100$	−2.30238	+	3.98783i	−0.230238	+	0.398783i
$101$	−5.13540			−0.510991			−0.255496	−	0.966810i	$-0.582239\pi$
$101$	−5.13540			−0.510991			−0.255496	+	0.966810i	$0.582239\pi$
$102$	0.957206	+	0.879639i	0.0947775	+	0.0870973i
$103$	−14.2112			−1.40027			−0.700137	−	0.714009i	$-0.746878\pi$
$103$	−14.2112			−1.40027			−0.700137	+	0.714009i	$0.746878\pi$
$104$	3.27814	+	5.67791i	0.321448	+	0.556765i
$105$	−4.67545	+	4.55846i	−0.456277	+	0.444860i
$106$	−0.274990	+	0.476296i	−0.0267094	+	0.0462620i
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	−0.619333	−	0.785128i	$-0.712597\pi$
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	0.989608	+	0.143794i	$0.0459303\pi$
$108$	−3.05148	−	7.45726i	−0.293629	−	0.717575i
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	0.822476	−	0.568800i	$-0.192592\pi$
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	−0.903833	+	0.427885i	$0.859259\pi$
$110$	2.35489	+	4.07880i	0.224530	+	0.388898i
$111$	1.81042	+	1.66371i	0.171838	+	0.157913i
$112$	0.218507	−	3.97807i	0.0206469	−	0.375892i
$113$	−0.300351	−	0.520224i	−0.0282547	−	0.0489385i	0.851552	−	0.524270i	$-0.175662\pi$
$113$	−0.300351	−	0.520224i	−0.0282547	−	0.0489385i	−0.879807	+	0.475331i	$0.842328\pi$
$114$	−1.01548	+	4.54972i	−0.0951082	+	0.426121i
$115$	7.74683			0.722395
$116$	−5.28083	−	9.14666i	−0.490312	−	0.849246i
$117$	0.696689	+	8.23439i	0.0644090	+	0.761270i
$118$	−4.41352			−0.406297
$119$	−0.162473	+	2.95793i	−0.0148939	+	0.271153i
$120$	1.27963	−	5.73322i	0.116814	−	0.523369i
$121$	13.3125			1.21023
$122$	−0.0252261	+	0.0436929i	−0.00228386	+	0.00395577i
$123$	−0.411122	+	0.128980i	−0.0370696	+	0.0116298i
$124$	1.94284	+	3.36510i	0.174472	+	0.302195i
$125$	−11.3561			−1.01572
$126$	−2.52308	+	4.68432i	−0.224773	+	0.417313i
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	5.48278	+	9.49645i	0.484614	+	0.839375i
$129$	−1.27103	−	1.16803i	−0.111908	−	0.102839i
$130$	−1.31557	+	2.27864i	−0.115384	+	0.199850i
$131$	−20.4530			−1.78698			−0.893492	−	0.449079i	$-0.851752\pi$
$131$	−20.4530			−1.78698			−0.893492	+	0.449079i	$0.851752\pi$
$132$	−9.75105	−	8.96088i	−0.848720	−	0.779945i
$133$	−9.47708	+	4.79886i	−0.821767	+	0.416114i
$134$	−8.43794			−0.728927
$135$	4.53255	−	5.85475i	0.390100	−	0.503896i
$136$	−1.33248	−	2.30793i	−0.114260	−	0.197903i
$137$	12.2116			1.04331			0.521655	−	0.853157i	$-0.325315\pi$
$137$	12.2116			1.04331			0.521655	+	0.853157i	$0.325315\pi$
$138$	6.02274	−	1.88950i	0.512690	−	0.160845i
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	0.808588	−	0.588375i	$-0.200232\pi$
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	−0.913842	+	0.406071i	$0.866899\pi$
$140$	5.21549	−	2.64094i	0.440789	−	0.223200i
$141$	−15.6600	+	4.91296i	−1.31881	+	0.413746i
$142$	−0.0269793	−	0.0467294i	−0.00226405	−	0.00392145i
$143$	6.79117	+	11.7626i	0.567906	+	0.983642i
$144$	0.380853	+	4.50143i	0.0317378	+	0.375119i
$145$	4.85269	−	8.40511i	0.402994	−	0.698006i
$146$	3.58327	−	6.20640i	0.296553	−	0.513645i
$147$	−11.8963	+	2.34046i	−0.981191	+	0.193038i
$148$	−1.10063	−	1.90635i	−0.0904715	−	0.156701i
$149$	−8.55593			−0.700929			−0.350465	−	0.936576i	$-0.613976\pi$
$149$	−8.55593			−0.700929			−0.350465	+	0.936576i	$0.613976\pi$
$150$	−3.28971	+	1.03207i	−0.268603	+	0.0842682i
$151$	−17.6592			−1.43709			−0.718544	−	0.695482i	$-0.755191\pi$
$151$	−17.6592			−1.43709			−0.718544	+	0.695482i	$0.755191\pi$
$152$	4.77814	−	8.27599i	0.387559	−	0.671271i
$153$	−0.283187	−	3.34708i	−0.0228943	−	0.270595i
$154$	−0.479615	+	8.73173i	−0.0386485	+	0.703623i
$155$	−1.78533	+	3.09228i	−0.143401	+	0.248378i
$156$	1.61162	−	7.22068i	0.129033	−	0.578117i
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	−0.964146	−	0.265371i	$-0.914505\pi$
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	0.711891	+	0.702289i	$0.247839\pi$
$158$	0.618353	−	1.07102i	0.0491936	−	0.0852057i
$159$	1.35591	−	0.425387i	0.107531	−	0.0337354i
$160$	−4.11070	+	7.11993i	−0.324979	+	0.562880i
$161$	12.0436	+	7.86433i	0.949172	+	0.619796i
$162$	2.09580	−	5.65726i	0.164662	−	0.444477i
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	−0.979265	−	0.202581i	$-0.935067\pi$
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	0.665073	+	0.746778i	$0.268400\pi$
$164$	0.385754			0.0301223
$165$	2.65094	−	11.8772i	0.206376	−	0.924640i
$166$	9.70083			0.752930
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	0.904132	−	0.427253i	$-0.140518\pi$
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	−0.822078	+	0.569375i	$0.807185\pi$
$168$	7.80956	−	7.61414i	0.602521	−	0.587444i
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$	0.534749	−	0.926212i	0.0410133	−	0.0710372i
$171$	9.88652	−	6.88056i	0.756041	−	0.526169i
$172$	0.772712	+	1.33838i	0.0589187	+	0.102050i
$173$	9.14404	+	15.8379i	0.695208	+	1.20414i	0.970110	+	0.242664i	$0.0780212\pi$
$173$	9.14404	+	15.8379i	0.695208	+	1.20414i	−0.274902	+	0.961472i	$0.588646\pi$
$174$	1.72265	−	7.71812i	0.130594	−	0.585109i
$175$	−6.57841	−	4.29561i	−0.497281	−	0.324718i
$176$	3.71247	+	6.43018i	0.279838	+	0.484693i
$177$	8.39684	+	7.71641i	0.631145	+	0.580001i
$178$	−9.06681			−0.679586
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	0.972604	−	0.232468i	$-0.0746801\pi$
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	−0.687625	+	0.726066i	$0.741347\pi$
$180$	−5.44081	+	3.78655i	−0.405534	+	0.282233i
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$	−4.35847	+	2.20697i	−0.323071	+	0.163592i
$183$	0.124384	−	0.0390227i	0.00919475	−	0.00288464i
$184$	−12.9398			−0.953933
$185$	1.01140	−	1.75180i	0.0743597	−	0.128795i
$186$	−0.633771	+	2.83953i	−0.0464704	+	0.208205i
$187$	−2.76044	−	4.78122i	−0.201863	−	0.349638i
$188$	14.6937			1.07165
$189$	12.9901	−	4.50082i	0.944891	−	0.327386i
$190$	3.83510			0.278227
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	−0.999083	−	0.0428150i	$-0.986367\pi$
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	0.462463	−	0.886639i	$-0.346966\pi$
$192$	−0.322938	+	1.44688i	−0.0233060	+	0.104420i
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	0.397078	+	0.917785i	$0.370024\pi$
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	−0.993364	+	0.115013i	$0.963309\pi$
$194$	−3.62194			−0.260040
$195$	6.48680	−	2.03509i	0.464529	−	0.145736i
$196$	10.7893	+	1.18885i	0.770663	+	0.0849178i
$197$	−4.03740			−0.287653			−0.143826	−	0.989603i	$-0.545941\pi$
$197$	−4.03740			−0.287653			−0.143826	+	0.989603i	$0.545941\pi$
$198$	−0.835960	−	9.88048i	−0.0594091	−	0.702175i
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.832468	−	0.554074i	$-0.813073\pi$
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.0636081	−	0.997975i	$-0.520261\pi$
$200$	7.06789			0.499775
$201$	16.0534	+	14.7525i	1.13232	+	1.04056i
$202$	1.72121	+	2.98123i	0.121104	+	0.209758i
$203$	16.0769	−	8.14075i	1.12837	−	0.571368i
$204$	−0.655085	+	2.93503i	−0.0458651	+	0.205493i
$205$	0.177240	+	0.306988i	0.0123790	+	0.0214410i
$206$	4.76312	+	8.24997i	0.331862	+	0.574803i
$207$	−14.7619	−	6.93508i	−1.02603	−	0.482022i
$208$	−2.07399	+	3.59226i	−0.143805	+	0.249078i
$209$	9.89864	−	17.1449i	0.684703	−	1.18594i
$210$	4.21335	+	1.18638i	0.290749	+	0.0818677i
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	0.706961	−	0.707253i	$-0.250066\pi$
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916732\pi$
$212$	−1.27225			−0.0873782
$213$	−0.0303710	+	0.136073i	−0.00208099	+	0.00932360i
$214$	−5.13495			−0.351018
$215$	−0.710065	+	1.22987i	−0.0484261	+	0.0838764i
$216$	−7.57086	+	9.77938i	−0.515132	+	0.665402i
$217$	−5.91476	+	2.99502i	−0.401520	+	0.203315i
$218$	−0.569377	+	0.986190i	−0.0385631	+	0.0667932i
$219$	−17.6683	+	5.54302i	−1.19391	+	0.374563i
$220$	−5.44748	+	9.43531i	−0.367269	+	0.636129i
$221$	1.54214	−	2.67106i	0.103735	−	0.179675i
$222$	0.359036	−	1.60862i	0.0240969	−	0.107963i
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	−0.562519	−	0.826784i	$-0.690168\pi$
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	0.997276	+	0.0737638i	$0.0235011\pi$
$224$	−13.6186	+	6.89599i	−0.909934	+	0.460758i
$225$	8.06319	+	3.78804i	0.537546	+	0.252536i
$226$	−0.201335	+	0.348723i	−0.0133926	+	0.0231967i
$227$	−28.9665			−1.92257			−0.961286	−	0.275551i	$-0.911140\pi$
$227$	−28.9665			−1.92257			−0.961286	+	0.275551i	$0.911140\pi$
$228$	−10.2892	+	3.22800i	−0.681418	+	0.213779i
$229$	15.4358			1.02003			0.510013	−	0.860167i	$-0.329640\pi$
$229$	15.4358			1.02003			0.510013	+	0.860167i	$0.329640\pi$
$230$	−2.59648	−	4.49723i	−0.171207	−	0.296538i
$231$	16.1787	−	15.7738i	1.06448	−	1.03784i
$232$	−8.10561	+	14.0393i	−0.532159	+	0.921727i
$233$	−2.47324	+	4.28378i	−0.162027	+	0.280640i	−0.935596	−	0.353073i	$-0.885137\pi$
$233$	−2.47324	+	4.28378i	−0.162027	+	0.280640i	0.773568	+	0.633713i	$0.218470\pi$
$234$	4.54677	−	3.16434i	0.297231	−	0.206859i
$235$	6.75121	+	11.6934i	0.440400	+	0.762795i
$236$	−5.10481	−	8.84179i	−0.332295	−	0.575551i
$237$	−3.04896	+	0.956542i	−0.198051	+	0.0621341i
$238$	1.77161	−	0.897080i	0.114836	−	0.0581491i
$239$	6.51732	+	11.2883i	0.421571	+	0.730182i	0.996093	−	0.0883069i	$-0.0281456\pi$
$239$	6.51732	+	11.2883i	0.421571	+	0.730182i	−0.574523	+	0.818489i	$0.694812\pi$
$240$	3.54608	−	1.11250i	0.228899	−	0.0718118i
$241$	14.5825			0.939339			0.469670	−	0.882842i	$-0.344373\pi$
$241$	14.5825			0.939339			0.469670	+	0.882842i	$0.344373\pi$
$242$	−4.46191	−	7.72826i	−0.286823	−	0.496791i
$243$	−13.8782	+	7.09889i	−0.890290	+	0.455394i
$244$	−0.116709			−0.00747154
$245$	4.01117	+	9.13249i	0.256265	+	0.583453i
$246$	0.212671	+	0.195437i	0.0135594	+	0.0124606i
$247$	11.0599			0.703722
$248$	2.98209	−	5.16514i	0.189363	−	0.327987i
$249$	−18.4561	−	16.9605i	−1.16961	−	1.07483i
$250$	3.80619	+	6.59251i	0.240724	+	0.416947i
$251$	−14.0715			−0.888187			−0.444094	−	0.895980i	$-0.646474\pi$
$251$	−14.0715			−0.888187			−0.444094	+	0.895980i	$0.646474\pi$
$252$	−12.3026	+	0.363444i	−0.774989	+	0.0228948i
$253$	−26.8067			−1.68532
$254$	−2.43323	−	4.21448i	−0.152674	−	0.264440i
$255$	−2.63672	+	0.827212i	−0.165118	+	0.0518020i
$256$	4.53120	−	7.84826i	0.283200	−	0.490517i
$257$	−8.36215			−0.521617			−0.260808	−	0.965391i	$-0.583989\pi$
$257$	−8.36215			−0.521617			−0.260808	+	0.965391i	$0.583989\pi$
$258$	−0.252065	+	1.12935i	−0.0156929	+	0.0703100i
$259$	3.35075	−	1.69670i	0.208206	−	0.105428i
$260$	−6.08653			−0.377471
$261$	−16.7714	+	11.6721i	−1.03812	+	0.722487i
$262$	6.85515	+	11.8735i	0.423512	+	0.733545i
$263$	3.27066			0.201678			0.100839	−	0.994903i	$-0.467847\pi$
$263$	3.27066			0.201678			0.100839	+	0.994903i	$0.467847\pi$
$264$	−4.42796	+	19.8389i	−0.272522	+	1.22100i
$265$	−0.584551	−	1.01247i	−0.0359087	−	0.0621956i
$266$	5.96226	+	3.89327i	0.365569	+	0.238712i
$267$	17.2499	+	15.8520i	1.05568	+	0.970129i
$268$	−9.75958	−	16.9041i	−0.596161	−	1.03258i
$269$	−7.69349	−	13.3255i	−0.469081	−	0.812471i	0.530295	−	0.847813i	$-0.322081\pi$
$269$	−7.69349	−	13.3255i	−0.469081	−	0.812471i	−0.999375	+	0.0353420i	$0.988748\pi$
$270$	−4.91799	−	0.668943i	−0.299299	−	0.0407106i
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	−0.715825	−	0.698279i	$-0.753949\pi$
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	0.962640	+	0.270783i	$0.0872827\pi$
$272$	0.843026	−	1.46016i	0.0511160	−	0.0885355i
$273$	12.1507	+	3.42133i	0.735393	+	0.207069i
$274$	−4.09293	−	7.08915i	−0.247263	−	0.428271i
$275$	14.6422			0.882958
$276$	10.7514	+	9.88016i	0.647158	+	0.594716i
$277$	12.8457			0.771826			0.385913	−	0.922535i	$-0.373887\pi$
$277$	12.8457			0.771826			0.385913	+	0.922535i	$0.373887\pi$
$278$	−0.831826	+	1.44077i	−0.0498896	+	0.0864114i
$279$	6.17029	−	4.29423i	0.369406	−	0.257089i
$280$	−7.51319	−	4.90601i	−0.448999	−	0.293190i
$281$	−0.724081	+	1.25415i	−0.0431951	+	0.0748161i	−0.886815	−	0.462125i	$-0.847087\pi$
$281$	−0.724081	+	1.25415i	−0.0431951	+	0.0748161i	0.843620	+	0.536941i	$0.180420\pi$
$282$	8.10079	+	7.44435i	0.482395	+	0.443305i
$283$	8.71926	−	15.1022i	0.518306	−	0.897732i	−0.481468	−	0.876464i	$-0.659896\pi$
$283$	8.71926	−	15.1022i	0.518306	−	0.897732i	0.999774	−	0.0212686i	$-0.00677053\pi$
$284$	0.0624100	−	0.108097i	0.00370335	−	0.00641440i
$285$	−7.29639	−	6.70513i	−0.432201	−	0.397178i
$286$	4.55234	−	7.88489i	0.269186	−	0.466243i
$287$	−0.0360979	+	0.657189i	−0.00213079	+	0.0387926i
$288$	14.2070	−	9.88741i	0.837156	−	0.582621i
$289$	7.87316	−	13.6367i	0.463127	−	0.802160i
$290$	−6.50584			−0.382036
$291$	6.89084	+	6.33244i	0.403948	+	0.371214i
$292$	16.5781			0.970158
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	0.838537	−	0.544845i	$-0.183412\pi$
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	−0.891118	+	0.453772i	$0.850078\pi$
$294$	5.34594	+	6.12167i	0.311781	+	0.357023i
$295$	4.69094	−	8.12495i	0.273117	−	0.473053i
$296$	−1.68938	+	2.92609i	−0.0981931	+	0.170075i
$297$	−15.6842	+	20.2594i	−0.910088	+	1.17557i
$298$	2.86766	+	4.96693i	0.166119	+	0.287727i
$299$	−7.48786	−	12.9693i	−0.433034	−	0.750037i
$300$	−5.87256	−	5.39668i	−0.339053	−	0.311578i
$301$	−2.35243	+	1.19119i	−0.135592	+	0.0686589i
$302$	5.91878	+	10.2516i	0.340588	+	0.589915i
$303$	1.93760	−	8.68117i	0.111312	−	0.498720i
$304$	6.04600			0.346762
$305$	−0.0536236	−	0.0928787i	−0.00307048	−	0.00531822i
$306$	−1.84815	+	1.28622i	−0.105652	+	0.0735286i
$307$	1.06478			0.0607699			0.0303850	−	0.999538i	$-0.490327\pi$
$307$	1.06478			0.0607699			0.0303850	+	0.999538i	$0.490327\pi$
$308$	−18.0474	+	9.13855i	−1.02835	+	0.520717i
$309$	5.36193	−	24.0234i	0.305029	−	1.36665i
$310$	2.39353			0.135943
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	−0.519751	−	0.854318i	$-0.673975\pi$
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	0.999736	+	0.0229591i	$0.00730874\pi$
$312$	−10.8351	+	3.39927i	−0.613418	+	0.192446i
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	0.958972	−	0.283502i	$-0.0914963\pi$
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	−0.725006	+	0.688743i	$0.758163\pi$
$314$	4.23750			0.239136
$315$	−5.94181	−	9.62356i	−0.334783	−	0.542226i
$316$	2.86082			0.160934
$317$	−3.27371	−	5.67023i	−0.183870	−	0.318472i	0.759325	−	0.650711i	$-0.225529\pi$
$317$	−3.27371	−	5.67023i	−0.183870	−	0.318472i	−0.943195	+	0.332239i	$0.892196\pi$
$318$	−0.701404	−	0.644566i	−0.0393328	−	0.0361455i
$319$	−16.7920	+	29.0846i	−0.940171	+	1.62842i
$320$	1.21962			0.0681790
$321$	9.76938	+	8.97773i	0.545274	+	0.501088i
$322$	0.528817	−	9.62750i	0.0294698	−	0.536519i
$323$	−4.49556			−0.250140
$324$	13.7575	−	2.34475i	0.764306	−	0.130264i
$325$	4.08997	+	7.08404i	0.226871	+	0.392952i
$326$	5.37786			0.297852
$327$	2.80747	−	0.880779i	0.155253	−	0.0487072i
$328$	−0.296049	−	0.512773i	−0.0163466	−	0.0283131i
$329$	−1.37500	+	25.0329i	−0.0758062	+	1.38011i
$330$	−7.78353	+	2.44191i	−0.428469	+	0.134422i
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	0.954946	+	0.296781i	$0.0959131\pi$
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	−0.220453	+	0.975398i	$0.570754\pi$
$332$	11.2203	+	19.4341i	0.615792	+	1.06658i
$333$	−3.49551	+	2.43271i	−0.191553	+	0.133312i
$334$	0.710806	−	1.23115i	0.0388936	−	0.0673657i
$335$	8.96834	−	15.5336i	0.489993	−	0.848692i
$336$	6.64231	+	1.87031i	0.362368	+	0.102034i
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$	−3.62794			−0.197334
$339$	0.992739	−	0.311449i	0.0539182	−	0.0169156i
$340$	2.47403			0.134173
$341$	6.17786	−	10.7004i	0.334550	−	0.579457i
$342$	−7.30796	−	3.43324i	−0.395169	−	0.185648i
$343$	−3.03502	+	18.2699i	−0.163876	+	0.986481i
$344$	1.18605	−	2.05429i	0.0639473	−	0.110760i
$345$	−2.92290	+	13.0957i	−0.157363	+	0.705048i
$346$	6.12955	−	10.6167i	0.329526	−	0.570757i
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	−0.497979	−	0.867189i	$-0.665924\pi$
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	0.999997	−	0.00233189i	$-0.000742265\pi$
$348$	17.4545	−	5.47595i	0.935659	−	0.293542i
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	0.109893	+	0.993943i	$0.464949\pi$
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	−0.915727	+	0.401801i	$0.868384\pi$
$350$	−0.288848	+	5.25868i	−0.0154396	+	0.281088i
$351$	−14.1827	−	1.92913i	−0.757019	−	0.102970i
$352$	14.2244	−	24.6374i	0.758164	−	1.31318i
$353$	6.25933			0.333150			0.166575	−	0.986029i	$-0.446729\pi$
$353$	6.25933			0.333150			0.166575	+	0.986029i	$0.446729\pi$
$354$	1.66523	−	7.46086i	0.0885060	−	0.396540i
$355$	0.114700			0.00608767
$356$	−10.4870	−	18.1639i	−0.555807	−	0.962686i
$357$	−4.93895	−	1.39069i	−0.261397	−	0.0736030i
$358$	2.55582	−	4.42680i	0.135079	−	0.233964i
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	−0.968614	−	0.248571i	$-0.920039\pi$
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	0.699575	+	0.714559i	$0.253372\pi$
$360$	9.20895	+	4.32631i	0.485354	+	0.228017i
$361$	1.43970	+	2.49364i	0.0757739	+	0.131244i
$362$	−5.20532	−	9.01587i	−0.273585	−	0.473864i
$363$	−5.02285	+	22.5042i	−0.263631	+	1.18117i
$364$	−9.46246	−	6.17885i	−0.495968	−	0.323860i
$365$	7.61701	+	13.1931i	0.398693	+	0.690556i
$366$	−0.0643431	−	0.0591291i	−0.00336327	−	0.00309073i
$367$	−28.6557			−1.49581			−0.747906	−	0.663804i	$-0.768941\pi$
$367$	−28.6557			−1.49581			−0.747906	+	0.663804i	$0.768941\pi$
$368$	−4.09332	−	7.08984i	−0.213379	−	0.369584i
$369$	−0.0629181	−	0.743649i	−0.00327538	−	0.0387128i
$370$	−1.35595			−0.0704926
$371$	0.119054	−	2.16746i	0.00618097	−	0.112529i
$372$	−6.42160	+	2.01463i	−0.332944	+	0.104454i
$373$	−16.0734			−0.832249			−0.416124	−	0.909308i	$-0.636612\pi$
$373$	−16.0734			−0.832249			−0.416124	+	0.909308i	$0.636612\pi$
$374$	−1.85041	+	3.20501i	−0.0956826	+	0.165727i
$375$	4.28469	−	19.1970i	0.221260	−	0.991330i
$376$	−11.2768	−	19.5319i	−0.581555	−	1.00728i
$377$	−18.7619			−0.966286
$378$	−6.96668	−	6.03256i	−0.358327	−	0.310281i
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	4.43579	+	7.68302i	0.227551	+	0.394130i
$381$	−2.73913	+	12.2723i	−0.140330	+	0.628730i
$382$	−4.97135	+	8.61063i	−0.254356	+	0.440558i
$383$	−11.5865			−0.592044			−0.296022	−	0.955181i	$-0.595660\pi$
$383$	−11.5865			−0.592044			−0.296022	+	0.955181i	$0.595660\pi$
$384$	−18.1220	+	5.68536i	−0.924784	+	0.290130i
$385$	−15.5647	−	10.1635i	−0.793250	−	0.517981i
$386$	11.1059			0.565275
$387$	2.45406	−	1.70791i	0.124747	−	0.0868181i
$388$	−4.18924	−	7.25598i	−0.212677	−	0.368367i
$389$	17.8135			0.903181			0.451590	−	0.892225i	$-0.350857\pi$
$389$	17.8135			0.903181			0.451590	+	0.892225i	$0.350857\pi$
$390$	−3.35558	−	3.08366i	−0.169916	−	0.156147i
$391$	3.04363	+	5.27172i	0.153923	+	0.266602i
$392$	−6.70000	−	15.2543i	−0.338401	−	0.770458i
$393$	7.71695	−	34.5749i	0.389269	−	1.74407i
$394$	1.35320	+	2.34381i	0.0681732	+	0.118079i
$395$	1.31444	+	2.27668i	0.0661369	+	0.114552i
$396$	18.8271	−	13.1028i	0.946096	−	0.658439i
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	−0.982184	−	0.187921i	$-0.939825\pi$
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	0.653836	+	0.756636i	$0.273159\pi$
$398$	−8.47348	+	14.6765i	−0.424737	+	0.735666i
$399$	−4.53653	−	17.8312i	−0.227111	−	0.892677i
$400$	2.23583	+	3.87257i	0.111792	+	0.193629i
$401$	14.1033			0.704285			0.352143	−	0.935946i	$-0.385453\pi$
$401$	14.1033			0.704285			0.352143	+	0.935946i	$0.385453\pi$
$402$	3.18366	−	14.2640i	0.158786	−	0.711423i
$403$	6.90259			0.343842
$404$	−3.98161	+	6.89636i	−0.198093	+	0.343107i
$405$	8.18706	+	9.87108i	0.406818	+	0.490498i
$406$	−10.1143	−	6.60452i	−0.501966	−	0.327777i
$407$	−3.49980	+	6.06183i	−0.173479	+	0.300474i
$408$	4.40421	−	1.38172i	0.218041	−	0.0684053i
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	−0.831461	−	0.555583i	$-0.812495\pi$
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	0.896879	+	0.442275i	$0.145829\pi$
$410$	0.118810	−	0.205784i	0.00586759	−	0.0101630i
$411$	−4.60747	+	20.6432i	−0.227270	+	1.01825i
$412$	−11.0183	+	19.0843i	−0.542835	+	0.940217i
$413$	15.5410	−	7.86940i	0.764722	−	0.387228i
$414$	0.921719	+	10.8941i	0.0453000	+	0.535415i
$415$	−10.3106	+	17.8585i	−0.506128	+	0.876639i
$416$	15.8931			0.779224
$417$	4.10155	−	1.28677i	0.200854	−	0.0630133i
$418$	−13.2708			−0.649094
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	0.906700	+	0.421776i	$0.138593\pi$
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	−0.0880816	+	0.996113i	$0.528074\pi$
$420$	2.49657	+	9.81299i	0.121820	+	0.478825i
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$	−2.52210	+	4.36841i	−0.122774	+	0.212651i
$423$	−2.39660	−	28.3262i	−0.116527	−	1.37727i
$424$	0.976394	+	1.69116i	0.0474179	+	0.0821302i
$425$	−1.66247	−	2.87949i	−0.0806418	−	0.139676i
$426$	0.0891734	−	0.0279761i	0.00432047	−	0.00135545i
$427$	0.0109214	−	0.198831i	0.000528522	−	0.00962212i
$428$	−5.93923	−	10.2871i	−0.287084	−	0.497244i
$429$	−22.4466	+	7.04210i	−1.08373	+	0.339996i
$430$	0.951960			0.0459076
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	0.880435	+	0.474166i	$0.157251\pi$
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	−0.0295774	+	0.999562i	$0.509416\pi$
$432$	−7.75316	−	1.05458i	−0.373024	−	0.0507386i
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$	3.72111	+	2.42983i	0.178619	+	0.116636i
$435$	12.3775	+	11.3745i	0.593458	+	0.545367i
$436$	−2.63423			−0.126157
$437$	−10.9141	+	18.9038i	−0.522093	+	0.904292i
$438$	9.13968	+	8.39905i	0.436711	+	0.401322i
$439$	−3.19906	−	5.54093i	−0.152683	−	0.264454i	0.779530	−	0.626365i	$-0.215458\pi$
$439$	−3.19906	−	5.54093i	−0.152683	−	0.264454i	−0.932213	+	0.361911i	$0.882125\pi$
$440$	16.7228			0.797229
$441$	0.532064	−	20.9933i	0.0253364	−	0.999679i
$442$	−2.06749			−0.0983404
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	0.931861	−	0.362815i	$-0.118184\pi$
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	−0.780138	+	0.625608i	$0.784851\pi$
$444$	3.63788	−	1.14130i	0.172646	−	0.0541638i
$445$	9.63674	−	16.6913i	0.456825	−	0.791245i
$446$	−8.70400			−0.412146
$447$	3.22817	−	14.4634i	0.152687	−	0.684097i
$448$	1.89609	+	1.23812i	0.0895819	+	0.0584957i
$449$	−11.7460			−0.554327			−0.277163	−	0.960823i	$-0.589394\pi$
$449$	−11.7460			−0.554327			−0.277163	+	0.960823i	$0.589394\pi$
$450$	−0.503456	−	5.95051i	−0.0237331	−	0.280510i
$451$	−0.613311	−	1.06229i	−0.0288797	−	0.0500210i
$452$	−0.931482			−0.0438132
$453$	6.66287	−	29.8522i	0.313049	−	1.40258i
$454$	9.70859	+	16.8158i	0.455647	+	0.789203i
$455$	0.569564	−	10.3693i	0.0267016	−	0.486121i
$456$	12.1874	+	11.1998i	0.570727	+	0.524478i
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	0.716334	−	0.697757i	$-0.245819\pi$
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	−0.962443	+	0.271485i	$0.912485\pi$
$458$	−5.17356	−	8.96087i	−0.241745	−	0.418714i
$459$	5.76494	+	0.784145i	0.269084	+	0.0366007i
$460$	6.00633	−	10.4033i	0.280046	−	0.485055i
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	−0.936657	−	0.350249i	$-0.886097\pi$
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	0.771653	+	0.636044i	$0.219430\pi$
$462$	−14.5797	−	4.10527i	−0.678307	−	0.190994i
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108654\pi$
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	−0.181246	+	0.983438i	$0.558013\pi$
$464$	−10.2564			−0.476141
$465$	−4.55376	−	4.18475i	−0.211176	−	0.194063i
$466$	3.31579			0.153601
$467$	1.96216	−	3.39856i	0.0907978	−	0.157266i	−0.817049	−	0.576568i	$-0.804392\pi$
$467$	1.96216	−	3.39856i	0.0907978	−	0.157266i	0.907847	+	0.419301i	$0.137725\pi$
$468$	11.5982	+	5.44876i	0.536126	+	0.251869i
$469$	29.7119	−	15.0450i	1.37197	−	0.694716i
$470$	4.52555	−	7.83849i	0.208748	−	0.361563i
$471$	−8.06196	−	7.40867i	−0.371476	−	0.341373i
$472$	−7.83544	+	13.5714i	−0.360655	+	0.624673i
$473$	2.45707	−	4.25577i	0.112976	−	0.195681i
$474$	1.57721	+	1.44940i	0.0724434	+	0.0665730i
$475$	5.96145	−	10.3255i	0.273530	−	0.473768i
$476$	3.84626	+	2.51155i	0.176293	+	0.115117i
$477$	0.207509	+	2.45261i	0.00950117	+	0.112297i
$478$	4.36878	−	7.56694i	0.199823	−	0.346104i
$479$	16.0865			0.735010			0.367505	−	0.930022i	$-0.380212\pi$
$479$	16.0865			0.735010			0.367505	+	0.930022i	$0.380212\pi$
$480$	−10.4850	−	9.63532i	−0.478571	−	0.439790i
$481$	−3.91036			−0.178297
$482$	−4.88755	−	8.46549i	−0.222622	−	0.385592i
$483$	−17.8384	+	17.3920i	−0.811675	+	0.791365i
$484$	10.3216	−	17.8775i	0.469162	−	0.812612i
$485$	3.84961	−	6.66771i	0.174802	−	0.302765i
$486$	8.77261	+	5.67736i	0.397934	+	0.257530i
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	0.823604	−	0.567166i	$-0.191960\pi$
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	−0.902982	+	0.429679i	$0.858627\pi$
$488$	0.0895692	+	0.155138i	0.00405461	+	0.00702279i
$489$	−10.2315	−	9.40242i	−0.462686	−	0.425192i
$490$	3.95723	−	5.38949i	0.178769	−	0.243472i
$491$	−20.5546	−	35.6017i	−0.927618	−	1.60668i	−0.787296	−	0.616575i	$-0.788520\pi$
$491$	−20.5546	−	35.6017i	−0.927618	−	1.60668i	−0.140321	−	0.990106i	$-0.544814\pi$
$492$	−0.145546	+	0.652100i	−0.00656171	+	0.0293989i
$493$	7.62624			0.343468
$494$	−3.70689	−	6.42053i	−0.166781	−	0.288873i
$495$	19.0777	+	8.96261i	0.857480	+	0.402839i
$496$	3.77338			0.169430
$497$	0.178320	+	0.116440i	0.00799873	+	0.00522306i
$498$	−3.66015	+	16.3988i	−0.164015	+	0.734849i
$499$	11.8297			0.529571			0.264785	−	0.964307i	$-0.414699\pi$
$499$	11.8297			0.529571			0.264785	+	0.964307i	$0.414699\pi$
$500$	−8.80470	+	15.2502i	−0.393758	+	0.682009i
$501$	−3.50482	+	1.09956i	−0.156584	+	0.0491247i
$502$	4.71631	+	8.16888i	0.210499	+	0.364595i
$503$	21.8595			0.974665			0.487332	−	0.873217i	$-0.337970\pi$
$503$	21.8595			0.974665			0.487332	+	0.873217i	$0.337970\pi$
$504$	9.92480	+	16.0746i	0.442086	+	0.716018i
$505$	−7.31762			−0.325630
$506$	8.98470	+	15.5620i	0.399419	+	0.691813i
$507$	6.90226	+	6.34294i	0.306540	+	0.281700i
$508$	5.62869	−	9.74918i	0.249733	−	0.432550i
$509$	16.8966			0.748930			0.374465	−	0.927241i	$-0.377826\pi$
$509$	16.8966			0.748930			0.374465	+	0.927241i	$0.377826\pi$
$510$	1.36396	+	1.25343i	0.0603971	+	0.0555029i
$511$	−1.55134	+	28.2432i	−0.0686271	+	1.24941i
$512$	15.8563			0.700756
$513$	7.90108	+	19.3088i	0.348841	+	0.852503i
$514$	2.80271	+	4.85444i	0.123622	+	0.214120i
$515$	−20.2501			−0.892326
$516$	−2.55401	+	0.801263i	−0.112434	+	0.0352736i
$517$	−23.3615	−	40.4633i	−1.02744	−	1.77957i
$518$	−2.10804	−	1.37652i	−0.0926218	−	0.0604807i
$519$	−30.2234	+	9.48190i	−1.32666	+	0.416209i
$520$	4.67115	+	8.09067i	0.204843	+	0.354799i
$521$	−17.2466	−	29.8720i	−0.755587	−	1.30872i	−0.945082	−	0.326834i	$-0.894018\pi$
$521$	−17.2466	−	29.8720i	−0.755587	−	1.30872i	0.189495	−	0.981882i	$-0.439315\pi$
$522$	12.3972	+	5.82413i	0.542610	+	0.254915i
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	−0.843437	−	0.537229i	$-0.819471\pi$
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	0.886972	+	0.461823i	$0.152805\pi$
$524$	−15.8577	+	27.4664i	−0.692749	+	1.19988i
$525$	9.74359	−	9.49977i	0.425245	−	0.414604i
$526$	−1.09622	−	1.89870i	−0.0477972	−	0.0827873i
$527$	−2.80573			−0.122220
$528$	−12.2707	+	3.84964i	−0.534012	+	0.167534i
$529$	6.55673			0.285075
$530$	−0.391843	+	0.678693i	−0.0170206	+	0.0294805i
$531$	−16.2124	+	11.2831i	−0.703558	+	0.489644i
$532$	−0.903426	+	16.4475i	−0.0391685	+	0.713090i
$533$	0.342629	−	0.593452i	0.0148409	−	0.0257052i
$534$	3.42093	−	15.3271i	0.148038	−	0.663266i
$535$	5.45772	−	9.45305i	0.235958	−	0.408691i
$536$	−14.9801	+	25.9463i	−0.647042	+	1.12071i
$537$	−12.6021	+	3.95364i	−0.543823	+	0.170612i
$538$	−5.15720	+	8.93253i	−0.222343	+	0.385109i
$539$	−13.8800	−	31.6016i	−0.597856	−	1.36118i
$540$	−4.34817	−	10.6261i	−0.187115	−	0.457276i
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	0.335810	+	0.941930i	$0.390990\pi$
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	−0.983640	+	0.180145i	$0.942343\pi$
$542$	−5.44724			−0.233979
$543$	−5.85971	+	26.2537i	−0.251464	+	1.12665i
$544$	−6.46015			−0.276977
$545$	−1.21033	−	2.09636i	−0.0518450	−	0.0897982i
$546$	−2.08633	−	8.20050i	−0.0892867	−	0.350949i
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	−0.653792	−	0.756674i	$-0.726823\pi$
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	0.982195	+	0.187864i	$0.0601563\pi$
$548$	9.46800	−	16.3991i	0.404453	−	0.700533i
$549$	0.0190357	+	0.224990i	0.000812426	+	0.00960232i
$550$	−4.90757	−	8.50016i	−0.209260	−	0.362448i
$551$	13.6734	+	23.6831i	0.582508	+	1.00893i
$552$	4.88221	−	21.8741i	0.207801	−	0.931025i
$553$	−0.267709	+	4.87384i	−0.0113842	+	0.207257i
$554$	−4.30546	−	7.45728i	−0.182921	−	0.316829i
$555$	2.57974	+	2.37069i	0.109504	+	0.100630i
$556$	−3.84846			−0.163211
$557$	−11.6412	−	20.1631i	−0.493252	−	0.854338i	0.506718	−	0.862112i	$-0.330859\pi$
$557$	−11.6412	−	20.1631i	−0.493252	−	0.854338i	−0.999970	+	0.00777438i	$0.997525\pi$
$558$	−4.56099	−	2.14273i	−0.193082	−	0.0907088i
$559$	2.74531			0.116114
$560$	0.311358	−	5.66850i	0.0131573	−	0.239538i
$561$	9.12397	−	2.86244i	0.385214	−	0.120852i
$562$	0.970751			0.0409487
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	−0.910053	−	0.414492i	$-0.863959\pi$
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	0.813987	+	0.580883i	$0.197293\pi$
$564$	−5.54396	+	24.8390i	−0.233443	+	1.04591i
$565$	−0.427982	−	0.741286i	−0.0180053	−	0.0311861i
$566$	−11.6896			−0.491351
$567$	2.70724	+	23.6574i	0.113693	+	0.993516i
$568$	−0.191588			−0.00803885
$569$	−9.09976	−	15.7612i	−0.381482	−	0.660746i	0.609793	−	0.792561i	$-0.291253\pi$
$569$	−9.09976	−	15.7612i	−0.381482	−	0.660746i	−0.991274	+	0.131815i	$0.957919\pi$
$570$	−1.44699	+	6.48307i	−0.0606078	+	0.271546i
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	−0.630736	−	0.775998i	$-0.717247\pi$
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	0.987402	+	0.158234i	$0.0505801\pi$
$572$	21.0615			0.880625
$573$	24.5126	−	7.69027i	1.02403	−	0.321266i
$574$	0.393614	−	0.199312i	0.0164291	−	0.00831912i
$575$	−16.1443			−0.673264
$576$	−2.32405	−	1.09182i	−0.0968353	−	0.0454927i
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	0.722503	−	0.691368i	$-0.242992\pi$
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	−0.959994	+	0.280022i	$0.909658\pi$
$578$	−10.5553			−0.439041
$579$	−21.1293	−	19.4171i	−0.878103	−	0.806947i
$580$	−7.52485	−	13.0334i	−0.312452	−	0.541183i
$581$	−34.1588	+	17.2968i	−1.41715	+	0.717592i
$582$	1.36657	−	6.12273i	0.0566460	−	0.253795i
$583$	2.02275	+	3.50350i	0.0837736	+	0.145100i
$584$	−12.7229	−	22.0368i	−0.526479	−	0.911889i
$585$	0.992739	+	11.7335i	0.0410447	+	0.485120i
$586$	−0.603332	+	1.04500i	−0.0249234	+	0.0431686i
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	−0.809190	−	0.587548i	$-0.800094\pi$
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	0.913426	+	0.407005i	$0.133427\pi$
$588$	−6.08052	+	17.7902i	−0.250756	+	0.733657i
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$	−6.28899			−0.258913
$591$	1.52332	−	6.82504i	0.0626610	−	0.280745i
$592$	−2.13765			−0.0878567
$593$	−9.98892	+	17.3013i	−0.410196	+	0.710480i	−0.994911	−	0.100759i	$-0.967873\pi$
$593$	−9.98892	+	17.3013i	−0.410196	+	0.710480i	0.584715	+	0.811239i	$0.301206\pi$
$594$	17.0179	+	2.31477i	0.698254	+	0.0949763i
$595$	−0.231513	+	4.21487i	−0.00949113	+	0.172793i
$596$	−6.63365	+	11.4898i	−0.271725	+	0.470641i
$597$	41.7808	−	13.1078i	1.70997	−	0.536465i
$598$	−5.01935	+	8.69378i	−0.205257	+	0.355515i
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	−0.907406	−	0.420256i	$-0.861940\pi$
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	0.817655	+	0.575709i	$0.195274\pi$
$600$	−2.66673	+	11.9480i	−0.108869	+	0.487774i
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	−0.503250	−	0.864141i	$-0.667862\pi$
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	0.999993	+	0.00375637i	$0.00119569\pi$
$602$	1.47997	+	0.966399i	0.0603191	+	0.0393875i
$603$	−30.9955	+	21.5715i	−1.26224	+	0.878457i
$604$	−13.6917	+	23.7147i	−0.557107	+	0.964937i
$605$	18.9695			0.771221
$606$	−5.68905	+	1.78481i	−0.231102	+	0.0725030i
$607$	13.1256			0.532752			0.266376	−	0.963869i	$-0.414174\pi$
$607$	13.1256			0.532752			0.266376	+	0.963869i	$0.414174\pi$
$608$	−11.5827	−	20.0618i	−0.469741	−	0.813615i
$609$	7.69574	+	30.2487i	0.311847	+	1.22574i
$610$	−0.0359456	+	0.0622597i	−0.00145540	+	0.00252082i
$611$	13.0510	−	22.6051i	0.527988	−	0.914502i
$612$	−4.71437	−	2.21479i	−0.190567	−	0.0895274i
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.767960	−	0.640497i	$-0.778728\pi$
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.170707	−	0.985322i	$-0.554605\pi$
$614$	−0.356877	−	0.618129i	−0.0144024	−	0.0249456i
$615$	−0.585823	+	0.183789i	−0.0236227	+	0.00741108i
$616$	25.9982	+	16.9765i	1.04750	+	0.684002i
$617$	14.1948	+	24.5862i	0.571463	+	0.989803i	0.996416	+	0.0845873i	$0.0269572\pi$
$617$	14.1948	+	24.5862i	0.571463	+	0.989803i	−0.424953	+	0.905215i	$0.639709\pi$
$618$	−15.7434	+	4.93912i	−0.633291	+	0.198680i
$619$	31.9212			1.28302			0.641511	−	0.767114i	$-0.278308\pi$
$619$	31.9212			1.28302			0.641511	+	0.767114i	$0.278308\pi$
$620$	2.76843	+	4.79506i	0.111183	+	0.192574i
$621$	17.2932	−	22.3378i	0.693951	−	0.896385i
$622$	−11.3482			−0.455023
$623$	31.9263	−	16.1663i	1.27910	−	0.647691i
$624$	−5.29004	−	4.86136i	−0.211771	−	0.194610i
$625$	−1.33399			−0.0533594
$626$	2.77469	−	4.80591i	0.110899	−	0.192083i
$627$	25.2480	+	23.2020i	1.00831	+	0.926601i
$628$	4.90122	+	8.48916i	0.195580	+	0.338754i
$629$	1.58947			0.0633762
$630$	−3.59523	+	6.67487i	−0.143237	+	0.265933i
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	−2.19556	−	3.80282i	−0.0873346	−	0.151268i
$633$	12.4359	−	3.90149i	0.494283	−	0.155070i
$634$	−2.19447	+	3.80094i	−0.0871537	+	0.150955i
$635$	10.3447			0.410517
$636$	0.480022	−	2.15068i	0.0190341	−	0.0852799i
$637$	11.4121	−	15.5425i	0.452163	−	0.615816i
$638$	22.5124			0.891276
$639$	−0.218567	−	0.102682i	−0.00864639	−	0.00406202i
$640$	7.81261	+	13.5318i	0.308821	+	0.534893i
$641$	−40.4001			−1.59571			−0.797854	−	0.602851i	$-0.794032\pi$
$641$	−40.4001			−1.59571			−0.797854	+	0.602851i	$0.794032\pi$
$642$	1.93743	−	8.68040i	0.0764642	−	0.342588i
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	0.962805	−	0.270198i	$-0.0870890\pi$
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	−0.715400	+	0.698715i	$0.753756\pi$
$644$	19.8988	−	10.0761i	0.784123	−	0.397052i
$645$	−1.81113	−	1.66437i	−0.0713132	−	0.0655344i
$646$	1.50676	+	2.60979i	0.0592827	+	0.102681i
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	0.975209	+	0.221287i	$0.0710258\pi$
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	−0.295964	+	0.955199i	$0.595641\pi$
$648$	−13.6751	−	16.4880i	−0.537209	−	0.647710i
$649$	−16.2323	+	28.1151i	−0.637173	+	1.10362i
$650$	2.74164	−	4.74866i	0.107536	−	0.186258i
$651$	−2.83130	−	11.1287i	−0.110967	−	0.436167i
$652$	6.22019	+	10.7737i	0.243602	+	0.421930i
$653$	−22.2944			−0.872446			−0.436223	−	0.899839i	$-0.643684\pi$
$653$	−22.2944			−0.872446			−0.436223	+	0.899839i	$0.643684\pi$
$654$	−1.45228	−	1.33460i	−0.0567888	−	0.0521869i
$655$	−29.1442			−1.13876
$656$	0.187302	−	0.324417i	0.00731293	−	0.0126664i
$657$	−2.70395	−	31.9589i	−0.105491	−	1.24683i
$658$	14.9931	−	7.59195i	0.584490	−	0.295965i
$659$	3.57493	−	6.19196i	0.139259	−	0.241204i	−0.787957	−	0.615730i	$-0.788861\pi$
$659$	3.57493	−	6.19196i	0.139259	−	0.241204i	0.927217	+	0.374526i	$0.122194\pi$
$660$	−13.8946	−	12.7687i	−0.540848	−	0.497021i
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	0.0600736	+	0.998194i	$0.480866\pi$
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	−0.894498	+	0.447072i	$0.852467\pi$
$662$	8.95760	−	15.5150i	0.348147	−	0.603008i
$663$	3.93346	+	3.61471i	0.152763	+	0.140384i
$664$	17.2221	−	29.8296i	0.668349	−	1.15761i
$665$	−13.5043	+	6.83807i	−0.523672	+	0.265169i
$666$	2.58383	+	1.21387i	0.100121	+	0.0470365i
$667$	18.5146	−	32.0683i	0.716889	−	1.24169i
$668$	3.28856			0.127238
$669$	16.5596	+	15.2177i	0.640232	+	0.588351i
$670$	−12.0235			−0.464510
$671$	0.185556	+	0.321392i	0.00716331	+	0.0124072i
$672$	−6.51903	−	25.6236i	−0.251477	−	0.988451i
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$	−3.19188	+	5.52850i	−0.122947	+	0.212950i
$675$	−9.44578	+	12.2012i	−0.363568	+	0.469626i
$676$	−4.19619	−	7.26801i	−0.161392	−	0.279539i
$677$	13.1808	+	22.8298i	0.506580	+	0.877422i	0.999971	+	0.00761453i	$0.00242380\pi$
$677$	13.1808	+	22.8298i	0.506580	+	0.877422i	−0.493391	+	0.869808i	$0.664243\pi$
$678$	−0.513537	−	0.471923i	−0.0197223	−	0.0181241i
$679$	12.7537	−	6.45800i	0.489440	−	0.247835i
$680$	−1.89871	−	3.28866i	−0.0728121	−	0.126114i
$681$	10.9291	−	48.9666i	0.418805	−	1.87640i
$682$	−8.28244			−0.317151
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	0.901183	−	0.433439i	$-0.142700\pi$
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	−0.825961	+	0.563728i	$0.809367\pi$
$684$	−1.57465	−	18.6113i	−0.0602084	−	0.711623i
$685$	17.4008			0.664850
$686$	11.6234	−	4.36155i	0.443782	−	0.166525i
$687$	−5.82396	+	26.0936i	−0.222198	+	0.995531i
$688$	1.50076			0.0572158
$689$	−1.13002	+	1.95725i	−0.0430503	+	0.0745653i
$690$	8.58203	−	2.69241i	0.326712	−	0.102498i
$691$	−9.95052	−	17.2348i	−0.378536	−	0.655643i	0.612314	−	0.790615i	$-0.290239\pi$
$691$	−9.95052	−	17.2348i	−0.378536	−	0.655643i	−0.990849	+	0.134972i	$0.956906\pi$
$692$	28.3585			1.07803
$693$	20.5607	+	33.3008i	0.781037	+	1.26499i
$694$	−12.5373			−0.475910
$695$	−1.76823	−	3.06266i	−0.0670727	−	0.116173i
$696$	−20.6746	−	18.9993i	−0.783669	−	0.720165i
$697$	−0.139270	+	0.241223i	−0.00527524	+	0.00913699i
$698$	20.1827			0.763925
$699$	−6.30838	−	5.79718i	−0.238605	−	0.219270i
$700$	−10.8690	+	5.50368i	−0.410810	+	0.208020i
$701$	43.7908			1.65396			0.826979	−	0.562234i	$-0.190058\pi$
$701$	43.7908			1.65396			0.826979	+	0.562234i	$0.190058\pi$
$702$	3.63367	+	8.88002i	0.137144	+	0.335155i
$703$	2.84983	+	4.93604i	0.107483	+	0.186166i
$704$	−4.22031			−0.159059
$705$	−22.3145	+	7.00066i	−0.840412	+	0.263660i
$706$	−2.09792	−	3.63370i	−0.0789561	−	0.136756i
$707$	−11.3764	−	7.42861i	−0.427853	−	0.279382i
$708$	16.8727	−	5.29343i	0.634115	−	0.198939i
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	−0.891449	−	0.453121i	$-0.850310\pi$
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	0.0533097	−	0.998578i	$-0.483023\pi$
$710$	−0.0384437	−	0.0665865i	−0.00144277	−	0.00249895i
$711$	−0.466612	−	5.51504i	−0.0174993	−	0.206830i
$712$	−16.0966	+	27.8801i	−0.603244	+	1.04485i
$713$	−6.81163	+	11.7981i	−0.255097	+	0.441842i
$714$	0.848042	+	3.33330i	0.0317372	+	0.124746i
$715$	9.67699	+	16.7610i	0.361899	+	0.626827i
$716$	11.8245			0.441904
$717$	−21.5414	+	6.75814i	−0.804480	+	0.252387i
$718$	6.83411			0.255047
$719$	−19.5096	+	33.7917i	−0.727586	+	1.26022i	0.230315	+	0.973116i	$0.426024\pi$
$719$	−19.5096	+	33.7917i	−0.727586	+	1.26022i	−0.957901	+	0.287100i	$0.907309\pi$
$720$	0.542692	+	6.41425i	0.0202249	+	0.239045i
$721$	−31.4819	−	20.5572i	−1.17245	−	0.765592i
$722$	0.965081	−	1.67157i	0.0359166	−	0.0622094i
$723$	−5.50200	+	24.6510i	−0.204622	+	0.916781i
$724$	12.0413	−	20.8561i	0.447510	−	0.775109i
$725$	−10.1130	+	17.5162i	−0.375586	+	0.650534i
$726$	14.7478	−	4.62678i	0.547341	−	0.171716i
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	−0.995681	−	0.0928402i	$-0.970405\pi$
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	0.578242	+	0.815865i	$0.303739\pi$
$728$	−0.951361	+	17.3202i	−0.0352598	+	0.641929i
$729$	−6.76407	−	26.1390i	−0.250521	−	0.968111i
$730$	5.10593	−	8.84373i	0.188979	−	0.327321i
$731$	−1.11590			−0.0412731
$732$	0.0440346	−	0.197292i	0.00162757	−	0.00729211i
$733$	−0.897039			−0.0331329			−0.0165664	−	0.999863i	$-0.505274\pi$
$733$	−0.897039			−0.0331329			−0.0165664	+	0.999863i	$0.505274\pi$
$734$	9.60441	+	16.6353i	0.354505	+	0.614021i
$735$	−16.9515	+	3.33501i	−0.625266	+	0.123014i
$736$	−15.6837	+	27.1649i	−0.578108	+	1.00131i
$737$	−31.0335	+	53.7517i	−1.14314	+	1.97997i
$738$	−0.410619	+	0.285771i	−0.0151151	+	0.0105194i
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	0.897074	−	0.441880i	$-0.145688\pi$
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	−0.831216	+	0.555949i	$0.812355\pi$
$740$	−1.56833	−	2.71643i	−0.0576531	−	0.0998581i
$741$	−4.17291	+	18.6962i	−0.153296	+	0.686823i
$742$	−1.29817	+	0.657346i	−0.0476572	+	0.0241319i
$743$	−24.7964	−	42.9486i	−0.909691	−	1.57563i	−0.814493	−	0.580173i	$-0.802985\pi$
$743$	−24.7964	−	42.9486i	−0.909691	−	1.57563i	−0.0951977	−	0.995458i	$-0.530348\pi$
$744$	7.60629	+	6.98992i	0.278860	+	0.256263i
$745$	−12.1917			−0.446668
$746$	5.38726	+	9.33101i	0.197242	+	0.341633i
$747$	35.6346	−	24.8000i	1.30380	−	0.907384i
$748$	−8.56098			−0.313020
$749$	18.0813	−	9.15573i	0.660676	−	0.334543i
$750$	−12.5804	+	3.94682i	−0.459373	+	0.144118i
$751$	−42.9030			−1.56555			−0.782776	−	0.622304i	$-0.786197\pi$
$751$	−42.9030			−1.56555			−0.782776	+	0.622304i	$0.786197\pi$
$752$	7.13450	−	12.3573i	0.260168	−	0.450625i
$753$	5.30922	−	23.7873i	0.193479	−	0.866858i
$754$	6.28835	+	10.8917i	0.229008	+	0.396654i
$755$	−25.1633			−0.915786
$756$	4.02740	−	20.9341i	0.146475	−	0.761365i
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	0.341510	+	0.591513i	0.0124042	+	0.0214847i
$759$	10.1142	−	45.3155i	0.367123	−	1.64485i
$760$	6.80856	−	11.7928i	0.246972	−	0.427769i
$761$	40.7197			1.47609			0.738044	−	0.674752i	$-0.235749\pi$
$761$	40.7197			1.47609			0.738044	+	0.674752i	$0.235749\pi$
$762$	8.04245	−	2.52314i	0.291347	−	0.0914036i
$763$	0.246505	−	4.48781i	0.00892410	−	0.162470i
$764$	−23.0001			−0.832113
$765$	−0.403524	−	4.76938i	−0.0145894	−	0.172437i
$766$	3.88342	+	6.72627i	0.140313	+	0.243030i
$767$	−18.1365			−0.654871
$768$	11.5575	+	10.6210i	0.417046	+	0.383251i
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	0.948850	−	0.315728i	$-0.102249\pi$
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	−0.747853	+	0.663864i	$0.768915\pi$
$770$	−0.683421	+	12.4422i	−0.0246288	+	0.448385i
$771$	3.15506	−	14.1359i	0.113627	−	0.509090i
$772$	12.8454	+	22.2489i	0.462317	+	0.800756i
$773$	−0.462831	−	0.801647i	−0.0166469	−	0.0288332i	0.857582	−	0.514347i	$-0.171966\pi$
$773$	−0.462831	−	0.801647i	−0.0166469	−	0.0288332i	−0.874229	+	0.485514i	$0.838632\pi$
$774$	−1.81401	−	0.852210i	−0.0652031	−	0.0306320i
$775$	3.72061	−	6.44428i	0.133648	−	0.231485i
$776$	−6.43012	+	11.1373i	−0.230828	+	0.399806i
$777$	1.60395	+	6.30447i	0.0575415	+	0.226172i
$778$	−5.97049	−	10.3412i	−0.214052	−	0.370750i
$779$	−0.998817			−0.0357863
$780$	2.29646	−	10.2890i	0.0822266	−	0.368406i
$781$	−0.396903			−0.0142023
$782$	2.04024	−	3.53381i	0.0729590	−	0.126369i
$783$	−13.4033	−	32.7553i	−0.478996	−	1.17058i
$784$	6.23854	−	8.49648i	0.222805	−	0.303446i
$785$	−4.50386	+	7.80092i	−0.160750	+	0.278427i
$786$	−22.6580	+	7.10844i	−0.808185	+	0.253550i
$787$	−11.5120	+	19.9393i	−0.410358	+	0.710761i	−0.994929	−	0.100582i	$-0.967930\pi$
$787$	−11.5120	+	19.9393i	−0.410358	+	0.710761i	0.584571	+	0.811343i	$0.301263\pi$
$788$	−3.13030	+	5.42184i	−0.111512	+	0.193145i
$789$	−1.23403	+	5.52891i	−0.0439325	+	0.196834i
$790$	0.881115	−	1.52614i	0.0313487	−	0.0542975i
$791$	0.0871659	−	1.58692i	0.00309926	−	0.0564243i
$792$	−31.8661	−	14.9705i	−1.13231	−	0.531955i
$793$	−0.103662	+	0.179548i	−0.00368114	+	0.00637593i
$794$	8.77102			0.311272
$795$	1.93209	−	0.606149i	0.0685242	−	0.0214979i
$796$	−39.2027			−1.38950
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	0.994151	−	0.108000i	$-0.0344447\pi$
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	−0.590606	+	0.806960i	$0.701111\pi$
$798$	−8.83098	+	8.61000i	−0.312613	+	0.304791i
$799$	−5.30492	+	9.18839i	−0.187675	+	0.325062i
$800$	8.56664	−	14.8379i	0.302877	−	0.524598i
$801$	−33.3056	+	23.1791i	−1.17680	+	0.818995i
$802$	−4.72695	−	8.18732i	−0.166914	−	0.289104i
$803$	−26.3575	−	45.6525i	−0.930135	−	1.61104i
$804$	32.2579	−	10.1202i	1.13765	−	0.356912i
$805$	17.1614	+	11.2062i	0.604861	+	0.394966i
$806$	−2.31352	−	4.00713i	−0.0814901	−	0.141145i
$807$	25.4290	−	7.97776i	0.895143	−	0.280831i
$808$	12.2229			0.429999
$809$	6.73753	+	11.6697i	0.236879	+	0.410286i	0.959817	−	0.280627i	$-0.0905422\pi$
$809$	6.73753	+	11.6697i	0.236879	+	0.410286i	−0.722938	+	0.690913i	$0.757209\pi$
$810$	2.98639	−	8.06125i	0.104931	−	0.283243i
$811$	−30.7348			−1.07924			−0.539622	−	0.841907i	$-0.681433\pi$
$811$	−30.7348			−1.07924			−0.539622	+	0.841907i	$0.681433\pi$
$812$	1.53257	−	27.9014i	0.0537825	−	0.979149i
$813$	10.3635	+	9.52372i	0.363465	+	0.334011i
$814$	4.69206			0.164457
$815$	−5.71590	+	9.90023i	−0.200219	+	0.346790i
$816$	2.15027	+	1.97602i	0.0752745	+	0.0691746i
$817$	−2.00075	−	3.46540i	−0.0699974	−	0.121239i
$818$	−1.77369			−0.0620158
$819$	−10.3681	+	19.2493i	−0.362291	+	0.672626i
$820$	0.549675			0.0191955
$821$	8.49319	+	14.7106i	0.296414	+	0.513405i	0.975313	−	0.220827i	$-0.0708757\pi$
$821$	8.49319	+	14.7106i	0.296414	+	0.513405i	−0.678899	+	0.734232i	$0.737542\pi$
$822$	13.5282	−	4.24416i	0.471849	−	0.148032i
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	−0.657402	−	0.753540i	$-0.728345\pi$
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	0.981286	+	0.192557i	$0.0616780\pi$
$824$	33.8244			1.17833
$825$	−5.52453	+	24.7520i	−0.192340	+	0.861754i
$826$	−9.77720	−	6.38438i	−0.340192	−	0.222141i
$827$	14.5419			0.505670			0.252835	−	0.967509i	$-0.418637\pi$
$827$	14.5419			0.505670			0.252835	+	0.967509i	$0.418637\pi$
$828$	−20.7585	+	14.4470i	−0.721408	+	0.502066i
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	0.937104	−	0.349051i	$-0.113496\pi$
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	−0.770839	+	0.637030i	$0.780163\pi$
$830$	13.8231			0.479806
$831$	−4.84673	+	21.7152i	−0.168131	+	0.753291i
$832$	−1.17885	−	2.04183i	−0.0408693	−	0.0707877i
$833$	−4.63872	+	6.31764i	−0.160722	+	0.218893i
$834$	−2.12170	−	1.94977i	−0.0734685	−	0.0675150i
$835$	1.51097	+	2.61708i	0.0522894	+	0.0905678i
$836$	−15.3494	−	26.5859i	−0.530869	−	0.919492i
$837$	4.93115	+	12.0508i	0.170446	+	0.416538i
$838$	11.2326	−	19.4554i	0.388023	−	0.672075i
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	−0.222664	−	0.974895i	$-0.571475\pi$
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	0.955616	−	0.294615i	$-0.0951913\pi$
$840$	11.1281	−	10.8497i	0.383957	−	0.374349i
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$	3.24375			0.111787
$843$	−1.84688	−	1.69722i	−0.0636100	−	0.0584554i
$844$	−11.6686			−0.401648
$845$	3.85599	−	6.67877i	0.132650	−	0.229757i
$846$	−15.6408	+	10.8853i	−0.537742	+	0.374243i
$847$	29.4911	+	19.2572i	1.01332	+	0.661687i
$848$	−0.617738	+	1.06995i	−0.0212132	+	0.0367423i
$849$	22.2398	+	20.4376i	0.763268	+	0.701417i
$850$	−1.11441	+	1.93021i	−0.0382239	+	0.0662058i
$851$	3.85883	−	6.68370i	0.132279	−	0.229114i
$852$	0.159186	+	0.146287i	0.00545364	+	0.00501170i
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	−0.717504	−	0.696555i	$-0.754715\pi$
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	0.961986	+	0.273099i	$0.0880486\pi$
$854$	−0.119087	+	0.0603014i	−0.00407507	+	0.00206347i
$855$	14.0877	−	9.80436i	0.481788	−	0.335302i
$856$	−9.11621	+	15.7897i	−0.311586	+	0.539682i
$857$	34.7790			1.18803			0.594013	−	0.804455i	$-0.297543\pi$
$857$	34.7790			1.18803			0.594013	+	0.804455i	$0.297543\pi$
$858$	11.6114	+	10.6705i	0.396408	+	0.364286i
$859$	−12.6486			−0.431564			−0.215782	−	0.976442i	$-0.569230\pi$
$859$	−12.6486			−0.431564			−0.215782	+	0.976442i	$0.569230\pi$
$860$	1.10107	+	1.90710i	0.0375460	+	0.0650316i
$861$	−1.09733	−	0.308981i	−0.0373969	−	0.0105300i
$862$	11.8409	−	20.5091i	0.403304	−	0.698543i
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	−0.547739	−	0.836649i	$-0.684511\pi$
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	0.998429	+	0.0560318i	$0.0178448\pi$
$864$	11.3539	+	27.7469i	0.386268	+	0.943967i
$865$	13.0297	+	22.5681i	0.443022	+	0.767337i
$866$	−1.83471	−	3.17782i	−0.0623461	−	0.107987i
$867$	20.0817	+	18.4544i	0.682011	+	0.626744i
$868$	−0.563839	+	10.2651i	−0.0191379	+	0.348420i
$869$	−4.54843	−	7.87811i	−0.154295	−	0.267247i
$870$	2.45467	−	10.9978i	0.0832210	−	0.372861i
$871$	−34.6741			−1.17489
$872$	2.02166	+	3.50162i	0.0684621	+	0.118580i
$873$	−13.3047	+	9.25942i	−0.450294	+	0.313384i
$874$	14.6322			0.494941
$875$	−25.1570	−	16.4272i	−0.850463	−	0.555341i
$876$	−6.25494	+	28.0245i	−0.211335	+	0.946860i
$877$	28.4534			0.960805			0.480402	−	0.877048i	$-0.340491\pi$
$877$	28.4534			0.960805			0.480402	+	0.877048i	$0.340491\pi$
$878$	−2.14443	+	3.71427i	−0.0723711	+	0.125350i
$879$	2.97489	−	0.933305i	0.100341	−	0.0314796i
$880$	5.29004	+	9.16261i	0.178327	+	0.308872i
$881$	−20.3637			−0.686071			−0.343036	−	0.939322i	$-0.611455\pi$
$881$	−20.3637			−0.686071			−0.343036	+	0.939322i	$0.611455\pi$
$882$	−12.3654	+	6.72736i	−0.416366	+	0.226522i
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	−2.39132	−	4.14189i	−0.0804288	−	0.139307i
$885$	11.9650	+	10.9954i	0.402198	+	0.369606i
$886$	2.14065	−	3.70771i	0.0719164	−	0.124563i
$887$	−4.21692			−0.141590			−0.0707952	−	0.997491i	$-0.522554\pi$
$887$	−4.21692			−0.141590			−0.0707952	+	0.997491i	$0.522554\pi$
$888$	−4.30902	−	3.95984i	−0.144601	−	0.132883i
$889$	16.0825	+	10.5016i	0.539388	+	0.352213i
$890$	−12.9196			−0.433067
$891$	−28.3300	−	34.1573i	−0.949092	−	1.14431i
$892$	−10.0673	−	17.4371i	−0.337078	−	0.583837i
$893$	−38.0457			−1.27315
$894$	−9.47836	+	2.97362i	−0.317004	+	0.0994527i
$895$	5.43294	+	9.41013i	0.181603	+	0.314546i
$896$	−1.59117	+	28.9685i	−0.0531574	+	0.967768i
$897$	24.7493	−	7.76453i	0.826355	−	0.259250i
$898$	3.93685	+	6.81883i	0.131375	+	0.227547i
$899$	8.53374	+	14.7809i	0.284616	+	0.492970i
$900$	11.3386	−	7.89113i	0.377953	−	0.263038i
$901$	0.459325	−	0.795574i	0.0153023	−	0.0265044i
$902$	−0.411122	+	0.712084i	−0.0136889	+	0.0237098i
$903$	−1.12607	−	4.42612i	−0.0374733	−	0.147292i
$904$	0.714872	+	1.23819i	0.0237763	+	0.0411817i
$905$	22.1301			0.735628
$906$	−19.5631	+	6.13748i	−0.649940	+	0.203904i
$907$	47.9851			1.59332			0.796659	−	0.604429i	$-0.206599\pi$
$907$	47.9851			1.59332			0.796659	+	0.604429i	$0.206599\pi$
$908$	−22.4585	+	38.8993i	−0.745311	+	1.29092i
$909$	13.9441	+	6.55085i	0.462496	+	0.217278i
$910$	−6.21054	+	3.14480i	−0.205878	+	0.104249i
$911$	−12.8667	+	22.2858i	−0.426294	+	0.738362i	−0.996540	−	0.0831113i	$-0.973514\pi$
$911$	−12.8667	+	22.2858i	−0.426294	+	0.738362i	0.570247	+	0.821474i	$0.306848\pi$
$912$	−2.28117	+	10.2205i	−0.0755371	+	0.338435i
$913$	35.6782	−	61.7965i	1.18078	−	2.04517i
$914$	−3.52675	+	6.10852i	−0.116655	+	0.202052i
$915$	0.177240	−	0.0556049i	0.00585937	−	0.00183824i
$916$	11.9678	−	20.7288i	0.395427	−	0.684900i
$917$	−45.3092	−	29.5863i	−1.49624	−	0.977024i
$918$	−1.47700	−	3.60951i	−0.0487482	−	0.119132i
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	−0.846702	−	0.532068i	$-0.821415\pi$
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	0.884135	+	0.467232i	$0.154749\pi$
$920$	−18.4384			−0.607895
$921$	−0.401742	+	1.79996i	−0.0132379	+	0.0593106i
$922$	4.74968			0.156422
$923$	−0.110866	−	0.192026i	−0.00364920	−	0.00632060i
$924$	−8.63900	−	33.9563i	−0.284202	−	1.11708i
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$	10.9774	−	19.0134i	0.360740	−	0.624819i
$927$	38.5875	+	18.1282i	1.26738	+	0.595408i
$928$	19.6488	+	34.0328i	0.645004	+	1.11718i
$929$	−22.9248	−	39.7069i	−0.752138	−	1.30274i	−0.946785	−	0.321868i	$-0.895689\pi$
$929$	−22.9248	−	39.7069i	−0.752138	−	1.30274i	0.194647	−	0.980873i	$-0.437644\pi$
$930$	−0.903084	+	4.04616i	−0.0296133	+	0.132679i
$931$	−27.9362	−	3.07824i	−0.915573	−	0.100885i
$932$	3.83514	+	6.64266i	0.125624	+	0.217587i
$933$	21.5903	+	19.8408i	0.706836	+	0.649558i
$934$	−2.63060			−0.0860757
$935$	−3.93346	−	6.81294i	−0.128638	−	0.222807i
$936$	−1.65820	−	19.5988i	−0.0542001	−	0.640608i
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$	−18.6925	−	12.2059i	−0.610330	−	0.398537i
$939$	−13.6814	+	4.29222i	−0.446475	+	0.140071i
$940$	20.9376			0.682908
$941$	17.6402	−	30.5536i	0.575053	−	0.996020i	−0.420983	−	0.907068i	$-0.638315\pi$
$941$	17.6402	−	30.5536i	0.575053	−	0.996020i	0.996036	−	0.0889519i	$-0.0283517\pi$
$942$	−1.59882	+	7.16331i	−0.0520923	+	0.233393i
$943$	0.676229	+	1.17126i	0.0220210	+	0.0381415i
$944$	−9.91453			−0.322691
$945$	18.5101	−	6.41338i	0.602133	−	0.208627i
$946$	−3.29411			−0.107101
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	0.902699	+	0.430272i	$0.141582\pi$
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	−0.0787236	+	0.996896i	$0.525084\pi$
$948$	−1.07940	+	4.83610i	−0.0350571	+	0.157069i
$949$	14.7248	−	25.5040i	0.477986	−	0.827896i
$950$	−7.99230			−0.259305
$951$	10.8204	−	3.39467i	0.350877	−	0.110080i
$952$	0.386705	−	7.04023i	0.0125332	−	0.228175i
$953$	25.9988			0.842184			0.421092	−	0.907018i	$-0.361647\pi$
$953$	25.9988			0.842184			0.421092	+	0.907018i	$0.361647\pi$
$954$	1.35425	−	0.942497i	0.0438455	−	0.0305145i
$955$	−10.5677	−	18.3038i	−0.341962	−	0.592296i
$956$	20.2122			0.653710
$957$	−42.8305	−	39.3598i	−1.38451	−	1.27232i
$958$	−5.39165	−	9.33861i	−0.174196	−	0.301717i
$959$	27.0522	+	17.6647i	0.873562	+	0.570424i
$960$	−0.460166	+	2.06172i	−0.0148518	+	0.0665417i
$961$	12.3604	+	21.4088i	0.398722	+	0.690607i
$962$	1.31062	+	2.27006i	0.0422562	+	0.0731898i
$963$	−18.8625	+	13.1274i	−0.607834	+	0.423024i
$964$	11.3062	−	19.5829i	0.364148	−	0.630722i
$965$	−11.8040	+	20.4451i	−0.379984	+	0.658152i
$966$	16.0753	+	4.52642i	0.517216	+	0.145635i
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	0.578239	−	0.815867i	$-0.303740\pi$
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	−0.995681	+	0.0928360i	$0.970407\pi$
$968$	−31.6854			−1.01841
$969$	1.69619	−	7.59955i	0.0544893	−	0.244133i
$970$	−5.16103			−0.165711
$971$	−3.97206	+	6.87981i	−0.127469	+	0.220783i	−0.922696	−	0.385530i	$-0.874019\pi$
$971$	−3.97206	+	6.87981i	−0.127469	+	0.220783i	0.795226	+	0.606313i	$0.207352\pi$
$972$	−1.22703	+	24.1411i	−0.0393572	+	0.774327i
$973$	0.360130	−	6.55643i	0.0115452	−	0.210189i
$974$	−1.17424	+	2.03384i	−0.0376249	+	0.0651683i
$975$	−13.5184	+	4.24110i	−0.432936	+	0.135824i
$976$	−0.0566680	+	0.0981518i	−0.00181390	+	0.00314176i
$977$	26.1274	−	45.2540i	0.835889	−	1.44780i	−0.0574149	−	0.998350i	$-0.518286\pi$
$977$	26.1274	−	45.2540i	0.835889	−	1.44780i	0.893304	−	0.449452i	$-0.148381\pi$
$978$	−2.02908	+	9.09104i	−0.0648828	+	0.290699i
$979$	−33.3464	+	57.7577i	−1.06576	+	1.84594i
$980$	15.3740	+	1.69404i	0.491106	+	0.0541140i
$981$	0.429654	+	5.07822i	0.0137178	+	0.162135i
$982$	−13.7784	+	23.8650i	−0.439688	+	0.761562i
$983$	−38.8379			−1.23874			−0.619369	−	0.785100i	$-0.712611\pi$
$983$	−38.8379			−1.23874			−0.619369	+	0.785100i	$0.712611\pi$
$984$	0.978520	−	0.306988i	0.0311941	−	0.00978643i
$985$	−5.75304			−0.183307
$986$	−2.55606	−	4.42722i	−0.0814015	−	0.140991i
$987$	−41.7982	−	11.7693i	−1.33045	−	0.374622i
$988$	8.57501	−	14.8524i	0.272807	−	0.472516i
$989$	−2.70914	+	4.69236i	−0.0861455	+	0.149208i
$990$	−1.19119	−	14.0791i	−0.0378585	−	0.447462i
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	0.508565	−	0.861023i	$-0.330176\pi$
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	−0.999951	+	0.00991892i	$0.996843\pi$
$992$	−7.22890	−	12.5208i	−0.229518	−	0.397536i
$993$	−44.1679	+	13.8567i	−1.40163	+	0.439728i
$994$	0.00782973	−	0.142546i	0.000248344	−	0.00452128i
$995$	−18.0122	−	31.1981i	−0.571025	−	0.989045i
$996$	−37.0859	+	11.6349i	−1.17511	+	0.368664i
$997$	47.0670			1.49063			0.745313	−	0.666714i	$-0.232300\pi$
$997$	47.0670			1.49063			0.745313	+	0.666714i	$0.232300\pi$
$998$	−3.96492	−	6.86745i	−0.125507	−	0.217385i
$999$	−2.79353	−	6.82688i	−0.0883834	−	0.215993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.g.b.16.2	yes	10
3.2	odd	2		189.2.g.b.100.4		10
4.3	odd	2		1008.2.t.i.961.4		10
7.2	even	3		441.2.f.e.295.2		10
7.3	odd	6		441.2.h.f.214.4		10
7.4	even	3		63.2.h.b.25.4	yes	10
7.5	odd	6		441.2.f.f.295.2		10
7.6	odd	2		441.2.g.f.79.2		10
9.2	odd	6		567.2.e.e.163.4		10
9.4	even	3		63.2.h.b.58.4	yes	10
9.5	odd	6		189.2.h.b.37.2		10
9.7	even	3		567.2.e.f.163.2		10
12.11	even	2		3024.2.t.i.289.1		10
21.2	odd	6		1323.2.f.e.883.4		10
21.5	even	6		1323.2.f.f.883.4		10
21.11	odd	6		189.2.h.b.46.2		10
21.17	even	6		1323.2.h.f.802.2		10
21.20	even	2		1323.2.g.f.667.4		10
28.11	odd	6		1008.2.q.i.529.1		10
36.23	even	6		3024.2.q.i.2305.5		10
36.31	odd	6		1008.2.q.i.625.1		10
63.2	odd	6		3969.2.a.bc.1.2		5
63.4	even	3	inner	63.2.g.b.4.2	✓	10
63.5	even	6		1323.2.f.f.442.4		10
63.11	odd	6		567.2.e.e.487.4		10
63.13	odd	6		441.2.h.f.373.4		10
63.16	even	3		3969.2.a.z.1.4		5
63.23	odd	6		1323.2.f.e.442.4		10
63.25	even	3		567.2.e.f.487.2		10
63.31	odd	6		441.2.g.f.67.2		10
63.32	odd	6		189.2.g.b.172.4		10
63.40	odd	6		441.2.f.f.148.2		10
63.41	even	6		1323.2.h.f.226.2		10
63.47	even	6		3969.2.a.bb.1.2		5
63.58	even	3		441.2.f.e.148.2		10
63.59	even	6		1323.2.g.f.361.4		10
63.61	odd	6		3969.2.a.ba.1.4		5
84.11	even	6		3024.2.q.i.2881.5		10
252.67	odd	6		1008.2.t.i.193.4		10
252.95	even	6		3024.2.t.i.1873.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.4	even	3	inner
63.2.g.b.16.2	yes	10	1.1	even	1	trivial
63.2.h.b.25.4	yes	10	7.4	even	3
63.2.h.b.58.4	yes	10	9.4	even	3
189.2.g.b.100.4		10	3.2	odd	2
189.2.g.b.172.4		10	63.32	odd	6
189.2.h.b.37.2		10	9.5	odd	6
189.2.h.b.46.2		10	21.11	odd	6
441.2.f.e.148.2		10	63.58	even	3
441.2.f.e.295.2		10	7.2	even	3
441.2.f.f.148.2		10	63.40	odd	6
441.2.f.f.295.2		10	7.5	odd	6
441.2.g.f.67.2		10	63.31	odd	6
441.2.g.f.79.2		10	7.6	odd	2
441.2.h.f.214.4		10	7.3	odd	6
441.2.h.f.373.4		10	63.13	odd	6
567.2.e.e.163.4		10	9.2	odd	6
567.2.e.e.487.4		10	63.11	odd	6
567.2.e.f.163.2		10	9.7	even	3
567.2.e.f.487.2		10	63.25	even	3
1008.2.q.i.529.1		10	28.11	odd	6
1008.2.q.i.625.1		10	36.31	odd	6
1008.2.t.i.193.4		10	252.67	odd	6
1008.2.t.i.961.4		10	4.3	odd	2
1323.2.f.e.442.4		10	63.23	odd	6
1323.2.f.e.883.4		10	21.2	odd	6
1323.2.f.f.442.4		10	63.5	even	6
1323.2.f.f.883.4		10	21.5	even	6
1323.2.g.f.361.4		10	63.59	even	6
1323.2.g.f.667.4		10	21.20	even	2
1323.2.h.f.226.2		10	63.41	even	6
1323.2.h.f.802.2		10	21.17	even	6
3024.2.q.i.2305.5		10	36.23	even	6
3024.2.q.i.2881.5		10	84.11	even	6
3024.2.t.i.289.1		10	12.11	even	2
3024.2.t.i.1873.1		10	252.95	even	6
3969.2.a.z.1.4		5	63.16	even	3
3969.2.a.ba.1.4		5	63.61	odd	6
3969.2.a.bb.1.2		5	63.47	even	6
3969.2.a.bc.1.2		5	63.2	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.335166 - 0.580525i) q^{2} +(-0.377302 + 1.69046i) q^{3} +(0.775327 - 1.34291i) q^{4} +1.42494 q^{5} +(1.10781 - 0.347551i) q^{6} +(2.21529 + 1.44655i) q^{7} -2.38012 q^{8} +(-2.71529 - 1.27563i) q^{9} +(-0.477591 - 0.827212i) q^{10} -4.93077 q^{11} +(1.97759 + 1.81734i) q^{12} +(-1.37730 - 2.38556i) q^{13} +(0.0972697 - 1.77086i) q^{14} +(-0.537632 + 2.40879i) q^{15} +(-0.752918 - 1.30409i) q^{16} +(0.559839 + 0.969670i) q^{17} +(0.169539 + 2.00384i) q^{18} +(-2.00752 + 3.47713i) q^{19} +(1.10479 - 1.91356i) q^{20} +(-3.28116 + 3.19906i) q^{21} +(1.65263 + 2.86244i) q^{22} +5.43661 q^{23} +(0.898025 - 4.02349i) q^{24} -2.96955 q^{25} +(-0.923251 + 1.59912i) q^{26} +(3.18087 - 4.10878i) q^{27} +(3.66015 - 1.85337i) q^{28} +(3.40555 - 5.89858i) q^{29} +(1.57856 - 0.495238i) q^{30} +(-1.25292 + 2.17012i) q^{31} +(-2.88483 + 4.99666i) q^{32} +(1.86039 - 8.33526i) q^{33} +(0.375279 - 0.650002i) q^{34} +(3.15664 + 2.06124i) q^{35} +(-3.81828 + 2.65735i) q^{36} +(0.709787 - 1.22939i) q^{37} +2.69142 q^{38} +(4.55234 - 1.42819i) q^{39} -3.39152 q^{40} +(0.124384 + 0.215440i) q^{41} +(2.95687 + 0.832581i) q^{42} +(-0.498313 + 0.863104i) q^{43} +(-3.82296 + 6.62156i) q^{44} +(-3.86911 - 1.81769i) q^{45} +(-1.82217 - 3.15609i) q^{46} +(4.73790 + 8.20628i) q^{47} +(2.48859 - 0.780738i) q^{48} +(2.81498 + 6.40905i) q^{49} +(0.995294 + 1.72390i) q^{50} +(-1.85041 + 0.580525i) q^{51} -4.27144 q^{52} +(-0.410229 - 0.710537i) q^{53} +(-3.45137 - 0.469454i) q^{54} -7.02604 q^{55} +(-5.27265 - 3.44296i) q^{56} +(-5.12050 - 4.70556i) q^{57} -4.56570 q^{58} +(3.29204 - 5.70197i) q^{59} +(2.81794 + 2.58959i) q^{60} +(-0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +(-4.16988 - 6.75368i) q^{63} +0.855913 q^{64} +(-1.96257 - 3.39927i) q^{65} +(-5.46237 + 1.71369i) q^{66} +(6.29385 - 10.9013i) q^{67} +1.73623 q^{68} +(-2.05125 + 9.19035i) q^{69} +(0.138603 - 2.52337i) q^{70} +0.0804951 q^{71} +(6.46270 + 3.03614i) q^{72} +(5.34551 + 9.25869i) q^{73} -0.951587 q^{74} +(1.12042 - 5.01990i) q^{75} +(3.11297 + 5.39183i) q^{76} +(-10.9231 - 7.13261i) q^{77} +(-2.35489 - 2.16407i) q^{78} +(0.922457 + 1.59774i) q^{79} +(-1.07286 - 1.85825i) q^{80} +(5.74555 + 6.92738i) q^{81} +(0.0833788 - 0.144416i) q^{82} +(-7.23583 + 12.5328i) q^{83} +(1.75206 + 6.88661i) q^{84} +(0.797736 + 1.38172i) q^{85} +0.668072 q^{86} +(8.68637 + 7.98248i) q^{87} +11.7358 q^{88} +(6.76292 - 11.7137i) q^{89} +(0.241583 + 2.85534i) q^{90} +(0.399711 - 7.27703i) q^{91} +(4.21515 - 7.30085i) q^{92} +(-3.19576 - 2.93679i) q^{93} +(3.17597 - 5.50094i) q^{94} +(-2.86059 + 4.95469i) q^{95} +(-7.35819 - 6.76192i) q^{96} +(2.70160 - 4.67930i) q^{97} +(2.77712 - 3.78226i) q^{98} +(13.3885 + 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 - 2 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 7 * q^10 - 8 * q^11 + 22 * q^12 - 8 * q^13 + 16 * q^14 - 19 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + q^19 + 5 * q^20 - 2 * q^21 - q^22 - 6 * q^23 + 3 * q^24 + 2 * q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 - 26 * q^30 - 3 * q^31 - 2 * q^32 - q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 - 40 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 + 32 * q^42 - 7 * q^43 - 10 * q^44 - q^45 + 3 * q^46 + 27 * q^47 - 5 * q^48 + 25 * q^49 + 19 * q^50 + 24 * q^51 + 20 * q^52 - 21 * q^53 - 53 * q^54 + 4 * q^55 - 45 * q^56 - 4 * q^57 + 20 * q^58 + 30 * q^59 - 41 * q^60 - 14 * q^61 - 12 * q^62 - 35 * q^63 - 50 * q^64 - 11 * q^65 - 41 * q^66 - 2 * q^67 - 54 * q^68 + 15 * q^69 - 29 * q^70 - 6 * q^71 + 48 * q^72 + 15 * q^73 + 72 * q^74 + 31 * q^75 + 5 * q^76 - 31 * q^77 - 20 * q^78 - 4 * q^79 + 20 * q^80 + 8 * q^81 - 5 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 + 16 * q^86 + 32 * q^87 + 36 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 12 * q^93 - 3 * q^94 - 14 * q^95 - q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more