LMFDB - Embedded newform 585.2.i.f.391.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.6
Root			$0.715744 + 1.23970i$ of defining polynomial
Character	$\chi$	$=$	585.391
Dual form			585.2.i.f.196.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.715744 + 1.23970i) q^{2} +(-1.70726 + 0.291973i) q^{3} +(-0.0245786 + 0.0425715i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.58392 - 1.90753i) q^{6} +(0.625355 + 1.08315i) q^{7} +2.79261 q^{8} +(2.82950 - 0.996950i) q^{9} +O(q^{10})$	\(q+(0.715744 + 1.23970i) q^{2} +(-1.70726 + 0.291973i) q^{3} +(-0.0245786 + 0.0425715i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.58392 - 1.90753i) q^{6} +(0.625355 + 1.08315i) q^{7} +2.79261 q^{8} +(2.82950 - 0.996950i) q^{9} -1.43149 q^{10} +(0.736973 + 1.27648i) q^{11} +(0.0295325 - 0.0798570i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.895188 + 1.55051i) q^{14} +(0.600776 - 1.62452i) q^{15} +(2.04795 + 3.54715i) q^{16} -3.53506 q^{17} +(3.26112 + 2.79419i) q^{18} +4.76114 q^{19} +(-0.0245786 - 0.0425715i) q^{20} +(-1.38390 - 1.66663i) q^{21} +(-1.05497 + 1.82726i) q^{22} +(-3.47223 + 6.01407i) q^{23} +(-4.76772 + 0.815366i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.43149 q^{26} +(-4.53963 + 2.52820i) q^{27} -0.0614815 q^{28} +(4.80583 + 8.32394i) q^{29} +(2.44393 - 0.417956i) q^{30} +(0.0516606 - 0.0894788i) q^{31} +(-0.139007 + 0.240766i) q^{32} +(-1.63090 - 1.96410i) q^{33} +(-2.53020 - 4.38243i) q^{34} -1.25071 q^{35} +(-0.0271037 + 0.144960i) q^{36} -9.80005 q^{37} +(3.40775 + 5.90240i) q^{38} +(0.600776 - 1.62452i) q^{39} +(-1.39630 + 2.41847i) q^{40} +(-3.07544 + 5.32682i) q^{41} +(1.07561 - 2.90850i) q^{42} +(2.83590 + 4.91192i) q^{43} -0.0724552 q^{44} +(-0.551367 + 2.94890i) q^{45} -9.94090 q^{46} +(-1.05732 - 1.83133i) q^{47} +(-4.53206 - 5.45798i) q^{48} +(2.71786 - 4.70748i) q^{49} +(0.715744 - 1.23970i) q^{50} +(6.03528 - 1.03214i) q^{51} +(-0.0245786 - 0.0425715i) q^{52} +8.82702 q^{53} +(-6.38343 - 3.81826i) q^{54} -1.47395 q^{55} +(1.74637 + 3.02480i) q^{56} +(-8.12852 + 1.39012i) q^{57} +(-6.87948 + 11.9156i) q^{58} +(2.04187 - 3.53661i) q^{59} +(0.0543920 + 0.0655044i) q^{60} +(-6.72419 - 11.6466i) q^{61} +0.147903 q^{62} +(2.84929 + 2.44132i) q^{63} +7.79382 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.26760 - 3.42764i) q^{66} +(5.57487 - 9.65596i) q^{67} +(0.0868870 - 0.150493i) q^{68} +(4.17206 - 11.2814i) q^{69} +(-0.895188 - 1.55051i) q^{70} +9.50636 q^{71} +(7.90169 - 2.78409i) q^{72} +8.24967 q^{73} +(-7.01432 - 12.1492i) q^{74} +(1.10649 + 1.33255i) q^{75} +(-0.117022 + 0.202688i) q^{76} +(-0.921739 + 1.59650i) q^{77} +(2.44393 - 0.417956i) q^{78} +(0.807978 + 1.39946i) q^{79} -4.09590 q^{80} +(7.01218 - 5.64175i) q^{81} -8.80490 q^{82} +(2.04065 + 3.53451i) q^{83} +(0.104965 - 0.0179509i) q^{84} +(1.76753 - 3.06145i) q^{85} +(-4.05955 + 7.03135i) q^{86} +(-10.6352 - 12.8080i) q^{87} +(2.05808 + 3.56469i) q^{88} -13.7502 q^{89} +(-4.05040 + 1.42712i) q^{90} -1.25071 q^{91} +(-0.170685 - 0.295635i) q^{92} +(-0.0620729 + 0.167847i) q^{93} +(1.51354 - 2.62153i) q^{94} +(-2.38057 + 4.12327i) q^{95} +(0.167024 - 0.451638i) q^{96} +(5.64510 + 9.77759i) q^{97} +7.78118 q^{98} +(3.35785 + 2.87706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.715744	+	1.23970i	0.506107	+	0.876604i	0.999975	+	0.00706659i	$0.00224938\pi$
$2$	0.715744	+	1.23970i	0.506107	+	0.876604i	−0.493868	+	0.869537i	$0.664417\pi$
$3$	−1.70726	+	0.291973i	−0.985690	+	0.168571i
$3$	−1.70726	+	0.291973i	−0.985690	+	0.168571i
$4$	−0.0245786	+	0.0425715i	−0.0122893	+	0.0212857i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.58392	−	1.90753i	−0.646634	−	0.778744i
$7$	0.625355	+	1.08315i	0.236362	+	0.409391i	0.959668	−	0.281137i	$-0.0907116\pi$
$7$	0.625355	+	1.08315i	0.236362	+	0.409391i	−0.723306	+	0.690528i	$0.757378\pi$
$8$	2.79261			0.987336
$9$	2.82950	−	0.996950i	0.943168	−	0.332317i
$10$	−1.43149			−0.452676
$11$	0.736973	+	1.27648i	0.222206	+	0.384872i	0.955477	−	0.295064i	$-0.0953410\pi$
$11$	0.736973	+	1.27648i	0.222206	+	0.384872i	−0.733272	+	0.679936i	$0.762008\pi$
$12$	0.0295325	−	0.0798570i	0.00852530	−	0.0230527i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.895188	+	1.55051i	−0.239249	+	0.414391i
$15$	0.600776	−	1.62452i	0.155120	−	0.419449i
$16$	2.04795	+	3.54715i	0.511987	+	0.886788i
$17$	−3.53506			−0.857378			−0.428689	−	0.903452i	$-0.641024\pi$
$17$	−3.53506			−0.857378			−0.428689	+	0.903452i	$0.641024\pi$
$18$	3.26112	+	2.79419i	0.768654	+	0.658596i
$19$	4.76114			1.09228			0.546140	−	0.837694i	$-0.316097\pi$
$19$	4.76114			1.09228			0.546140	+	0.837694i	$0.316097\pi$
$20$	−0.0245786	−	0.0425715i	−0.00549595	−	0.00951927i
$21$	−1.38390	−	1.66663i	−0.301991	−	0.363689i
$22$	−1.05497	+	1.82726i	−0.224920	+	0.389573i
$23$	−3.47223	+	6.01407i	−0.724009	+	1.25402i	0.235371	+	0.971906i	$0.424369\pi$
$23$	−3.47223	+	6.01407i	−0.724009	+	1.25402i	−0.959381	+	0.282115i	$0.908964\pi$
$24$	−4.76772	+	0.815366i	−0.973207	+	0.166436i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.43149			−0.280738
$27$	−4.53963	+	2.52820i	−0.873652	+	0.486552i
$28$	−0.0614815			−0.0116189
$29$	4.80583	+	8.32394i	0.892420	+	1.54572i	0.836966	+	0.547255i	$0.184327\pi$
$29$	4.80583	+	8.32394i	0.892420	+	1.54572i	0.0554542	+	0.998461i	$0.482339\pi$
$30$	2.44393	−	0.417956i	0.446198	−	0.0763080i
$31$	0.0516606	−	0.0894788i	0.00927851	−	0.0160709i	−0.861349	−	0.508014i	$-0.830380\pi$
$31$	0.0516606	−	0.0894788i	0.00927851	−	0.0160709i	0.870627	+	0.491943i	$0.163713\pi$
$32$	−0.139007	+	0.240766i	−0.0245731	+	0.0425619i
$33$	−1.63090	−	1.96410i	−0.283904	−	0.341907i
$34$	−2.53020	−	4.38243i	−0.433925	−	0.751581i
$35$	−1.25071			−0.211408
$36$	−0.0271037	+	0.144960i	−0.00451729	+	0.0241600i
$37$	−9.80005			−1.61112			−0.805559	−	0.592516i	$-0.798135\pi$
$37$	−9.80005			−1.61112			−0.805559	+	0.592516i	$0.798135\pi$
$38$	3.40775	+	5.90240i	0.552811	+	0.957496i
$39$	0.600776	−	1.62452i	0.0962012	−	0.260132i
$40$	−1.39630	+	2.41847i	−0.220775	+	0.382394i
$41$	−3.07544	+	5.32682i	−0.480303	+	0.831909i	−0.999745	−	0.0225970i	$-0.992807\pi$
$41$	−3.07544	+	5.32682i	−0.480303	+	0.831909i	0.519442	+	0.854506i	$0.326140\pi$
$42$	1.07561	−	2.90850i	0.165971	−	0.448792i
$43$	2.83590	+	4.91192i	0.432470	+	0.749060i	0.997085	−	0.0762941i	$-0.0243088\pi$
$43$	2.83590	+	4.91192i	0.432470	+	0.749060i	−0.564615	+	0.825354i	$0.690975\pi$
$44$	−0.0724552			−0.0109230
$45$	−0.551367	+	2.94890i	−0.0821930	+	0.439596i
$46$	−9.94090			−1.46571
$47$	−1.05732	−	1.83133i	−0.154226	−	0.267127i	0.778551	−	0.627581i	$-0.215955\pi$
$47$	−1.05732	−	1.83133i	−0.154226	−	0.267127i	−0.932777	+	0.360454i	$0.882622\pi$
$48$	−4.53206	−	5.45798i	−0.654147	−	0.787792i
$49$	2.71786	−	4.70748i	0.388266	−	0.672497i
$50$	0.715744	−	1.23970i	0.101221	−	0.175321i
$51$	6.03528	−	1.03214i	0.845109	−	0.144529i
$52$	−0.0245786	−	0.0425715i	−0.00340844	−	0.00590360i
$53$	8.82702			1.21249			0.606243	−	0.795280i	$-0.292676\pi$
$53$	8.82702			1.21249			0.606243	+	0.795280i	$0.292676\pi$
$54$	−6.38343	−	3.81826i	−0.868675	−	0.519599i
$55$	−1.47395			−0.198747
$56$	1.74637	+	3.02480i	0.233369	+	0.404206i
$57$	−8.12852	+	1.39012i	−1.07665	+	0.184126i
$58$	−6.87948	+	11.9156i	−0.903321	+	1.56460i
$59$	2.04187	−	3.53661i	0.265828	−	0.460428i	−0.701952	−	0.712224i	$-0.747688\pi$
$59$	2.04187	−	3.53661i	0.265828	−	0.460428i	0.967780	+	0.251796i	$0.0810213\pi$
$60$	0.0543920	+	0.0655044i	0.00702197	+	0.00845658i
$61$	−6.72419	−	11.6466i	−0.860944	−	1.49120i	−0.871019	−	0.491250i	$-0.836540\pi$
$61$	−6.72419	−	11.6466i	−0.860944	−	1.49120i	0.0100748	−	0.999949i	$-0.496793\pi$
$62$	0.147903			0.0187837
$63$	2.84929	+	2.44132i	0.358976	+	0.307577i
$64$	7.79382			0.974228
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	1.26760	−	3.42764i	0.156031	−	0.421913i
$67$	5.57487	−	9.65596i	0.681079	−	1.17966i	−0.293573	−	0.955937i	$-0.594844\pi$
$67$	5.57487	−	9.65596i	0.681079	−	1.17966i	0.974652	−	0.223726i	$-0.0718222\pi$
$68$	0.0868870	−	0.150493i	0.0105366	−	0.0182499i
$69$	4.17206	−	11.2814i	0.502257	−	1.35812i
$70$	−0.895188	−	1.55051i	−0.106995	−	0.185321i
$71$	9.50636			1.12820			0.564098	−	0.825708i	$-0.309224\pi$
$71$	9.50636			1.12820			0.564098	+	0.825708i	$0.309224\pi$
$72$	7.90169	−	2.78409i	0.931223	−	0.328108i
$73$	8.24967			0.965550			0.482775	−	0.875744i	$-0.339629\pi$
$73$	8.24967			0.965550			0.482775	+	0.875744i	$0.339629\pi$
$74$	−7.01432	−	12.1492i	−0.815399	−	1.41231i
$75$	1.10649	+	1.33255i	0.127766	+	0.153869i
$76$	−0.117022	+	0.202688i	−0.0134234	+	0.0232500i
$77$	−0.921739	+	1.59650i	−0.105042	+	0.181938i
$78$	2.44393	−	0.417956i	0.276720	−	0.0473242i
$79$	0.807978	+	1.39946i	0.0909046	+	0.157451i	0.907892	−	0.419204i	$-0.137691\pi$
$79$	0.807978	+	1.39946i	0.0909046	+	0.157451i	−0.816987	+	0.576655i	$0.804357\pi$
$80$	−4.09590			−0.457935
$81$	7.01218	−	5.64175i	0.779131	−	0.626861i
$82$	−8.80490			−0.972339
$83$	2.04065	+	3.53451i	0.223990	+	0.387963i	0.956016	−	0.293314i	$-0.0947583\pi$
$83$	2.04065	+	3.53451i	0.223990	+	0.387963i	−0.732026	+	0.681277i	$0.761425\pi$
$84$	0.104965	−	0.0179509i	0.0114526	−	0.00195861i
$85$	1.76753	−	3.06145i	0.191716	−	0.332061i
$86$	−4.05955	+	7.03135i	−0.437753	+	0.758210i
$87$	−10.6352	−	12.8080i	−1.14021	−	1.37316i
$88$	2.05808	+	3.56469i	0.219392	+	0.379998i
$89$	−13.7502			−1.45752			−0.728761	−	0.684768i	$-0.759903\pi$
$89$	−13.7502			−1.45752			−0.728761	+	0.684768i	$0.759903\pi$
$90$	−4.05040	+	1.42712i	−0.426950	+	0.150432i
$91$	−1.25071			−0.131110
$92$	−0.170685	−	0.295635i	−0.0177952	−	0.0308221i
$93$	−0.0620729	+	0.167847i	−0.00643666	+	0.0174050i
$94$	1.51354	−	2.62153i	0.156110	−	0.270390i
$95$	−2.38057	+	4.12327i	−0.244241	+	0.423038i
$96$	0.167024	−	0.451638i	0.0170468	−	0.0460951i
$97$	5.64510	+	9.77759i	0.573173	+	0.992764i	0.996238	+	0.0866648i	$0.0276209\pi$
$97$	5.64510	+	9.77759i	0.573173	+	0.992764i	−0.423065	+	0.906099i	$0.639046\pi$
$98$	7.78118			0.786017
$99$	3.35785	+	2.87706i	0.337477	+	0.289156i
$100$	0.0491573			0.00491573
$101$	−1.85697	−	3.21636i	−0.184775	−	0.320040i	0.758726	−	0.651410i	$-0.225822\pi$
$101$	−1.85697	−	3.21636i	−0.184775	−	0.320040i	−0.943501	+	0.331370i	$0.892489\pi$
$102$	5.59927	+	6.74322i	0.554410	+	0.667678i
$103$	4.23185	−	7.32979i	0.416977	−	0.722225i	−0.578657	−	0.815571i	$-0.696423\pi$
$103$	4.23185	−	7.32979i	0.416977	−	0.722225i	0.995634	+	0.0933459i	$0.0297562\pi$
$104$	−1.39630	+	2.41847i	−0.136919	+	0.237150i
$105$	2.13529	−	0.365173i	0.208383	−	0.0356373i
$106$	6.31789	+	10.9429i	0.613648	+	1.06287i
$107$	16.8261			1.62664			0.813321	−	0.581816i	$-0.197658\pi$
$107$	16.8261			1.62664			0.813321	+	0.581816i	$0.197658\pi$
$108$	0.00394887	−	0.255398i	0.000379980	−	0.0245757i
$109$	−17.4145			−1.66801			−0.834003	−	0.551760i	$-0.813957\pi$
$109$	−17.4145			−1.66801			−0.834003	+	0.551760i	$0.813957\pi$
$110$	−1.05497	−	1.82726i	−0.100587	−	0.174222i
$111$	16.7313	−	2.86135i	1.58806	−	0.271587i
$112$	−2.56139	+	4.43646i	−0.242029	+	0.419206i
$113$	−2.69915	+	4.67506i	−0.253914	+	0.439793i	−0.964600	−	0.263717i	$-0.915051\pi$
$113$	−2.69915	+	4.67506i	−0.253914	+	0.439793i	0.710686	+	0.703510i	$0.248385\pi$
$114$	−7.54128	−	9.08199i	−0.706306	−	0.850606i
$115$	−3.47223	−	6.01407i	−0.323787	−	0.560815i
$116$	−0.472483			−0.0438689
$117$	−0.551367	+	2.94890i	−0.0509739	+	0.272626i
$118$	5.84581			0.538150
$119$	−2.21067	−	3.82899i	−0.202652	−	0.351003i
$120$	1.67773	−	4.53665i	0.153155	−	0.414138i
$121$	4.41374	−	7.64482i	0.401249	−	0.694984i
$122$	9.62559	−	16.6720i	0.871460	−	1.50941i
$123$	3.69530	−	9.99223i	0.333194	−	0.900969i
$124$	0.00253949	+	0.00439853i	0.000228053	+	0.000395000i
$125$	1.00000			0.0894427
$126$	−0.987154	+	5.27963i	−0.0879427	+	0.470347i
$127$	−16.9895			−1.50757			−0.753786	−	0.657119i	$-0.771775\pi$
$127$	−16.9895			−1.50757			−0.753786	+	0.657119i	$0.771775\pi$
$128$	5.85639	+	10.1436i	0.517637	+	0.896574i
$129$	−6.27577	−	7.55793i	−0.552551	−	0.665439i
$130$	0.715744	−	1.23970i	0.0627749	−	0.108729i
$131$	−0.186875	+	0.323677i	−0.0163273	+	0.0282798i	−0.874074	−	0.485793i	$-0.838531\pi$
$131$	−0.186875	+	0.323677i	−0.0163273	+	0.0282798i	0.857746	+	0.514073i	$0.171864\pi$
$132$	0.123700	−	0.0211550i	0.0107667	−	0.00184130i
$133$	2.97740	+	5.15701i	0.258173	+	0.447169i
$134$	15.9607			1.37880
$135$	0.0803313	−	5.19553i	0.00691382	−	0.447160i
$136$	−9.87204			−0.846520
$137$	−7.83700	−	13.5741i	−0.669560	−	1.15971i	−0.978027	−	0.208477i	$-0.933149\pi$
$137$	−7.83700	−	13.5741i	−0.669560	−	1.15971i	0.308467	−	0.951235i	$-0.400184\pi$
$138$	16.9717	−	2.90247i	1.44473	−	0.247075i
$139$	6.01656	−	10.4210i	0.510318	−	0.883897i	−0.489611	−	0.871941i	$-0.662861\pi$
$139$	6.01656	−	10.4210i	0.510318	−	0.883897i	0.999929	−	0.0119555i	$-0.00380564\pi$
$140$	0.0307407	−	0.0532445i	0.00259807	−	0.00449998i
$141$	2.33982	+	2.81786i	0.197049	+	0.237307i
$142$	6.80412	+	11.7851i	0.570989	+	0.988982i
$143$	−1.47395			−0.123258
$144$	9.33101	+	7.99497i	0.777584	+	0.666248i
$145$	−9.61166			−0.798205
$146$	5.90465	+	10.2272i	0.488672	+	0.846405i
$147$	−3.26565	+	8.83045i	−0.269347	+	0.728323i
$148$	0.240872	−	0.417202i	0.0197995	−	0.0342938i
$149$	2.30691	−	3.99569i	0.188990	−	0.327339i	−0.755924	−	0.654659i	$-0.772812\pi$
$149$	2.30691	−	3.99569i	0.188990	−	0.327339i	0.944914	+	0.327320i	$0.106145\pi$
$150$	−0.860004	+	2.32548i	−0.0702190	+	0.189875i
$151$	−2.04596	−	3.54370i	−0.166498	−	0.288382i	0.770688	−	0.637212i	$-0.219912\pi$
$151$	−2.04596	−	3.54370i	−0.166498	−	0.288382i	−0.937186	+	0.348830i	$0.886579\pi$
$152$	13.2960			1.07845
$153$	−10.0025	+	3.52428i	−0.808652	+	0.284921i
$154$	−2.63892			−0.212650
$155$	0.0516606	+	0.0894788i	0.00414948	+	0.00718711i
$156$	0.0543920	+	0.0655044i	0.00435484	+	0.00524455i
$157$	−5.07740	+	8.79432i	−0.405221	+	0.701863i	−0.994347	−	0.106178i	$-0.966139\pi$
$157$	−5.07740	+	8.79432i	−0.405221	+	0.701863i	0.589126	+	0.808041i	$0.299472\pi$
$158$	−1.15661	+	2.00331i	−0.0920150	+	0.159375i
$159$	−15.0701	+	2.57725i	−1.19513	+	0.204389i
$160$	−0.139007	−	0.240766i	−0.0109894	−	0.0190343i
$161$	−8.68549			−0.684513
$162$	12.0130	+	4.65498i	0.943833	+	0.365730i
$163$	8.09508			0.634056			0.317028	−	0.948416i	$-0.397315\pi$
$163$	8.09508			0.634056			0.317028	+	0.948416i	$0.397315\pi$
$164$	−0.151180	−	0.261852i	−0.0118052	−	0.0204472i
$165$	2.51642	−	0.430353i	0.195903	−	0.0335029i
$166$	−2.92116	+	5.05960i	−0.226726	+	0.392701i
$167$	4.26053	−	7.37946i	0.329690	−	0.571039i	−0.652760	−	0.757564i	$-0.726389\pi$
$167$	4.26053	−	7.37946i	0.329690	−	0.571039i	0.982450	+	0.186525i	$0.0597225\pi$
$168$	−3.86468	−	4.65424i	−0.298166	−	0.359083i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	5.06040			0.388115
$171$	13.4717	−	4.74662i	1.03020	−	0.362983i
$172$	−0.278810			−0.0212591
$173$	−8.81686	−	15.2713i	−0.670334	−	1.16105i	−0.977809	−	0.209496i	$-0.932818\pi$
$173$	−8.81686	−	15.2713i	−0.670334	−	1.16105i	0.307476	−	0.951556i	$-0.400516\pi$
$174$	8.26606	−	22.3517i	0.626648	−	1.69448i
$175$	0.625355	−	1.08315i	0.0472724	−	0.0818782i
$176$	−3.01857	+	5.22831i	−0.227533	+	0.394099i
$177$	−2.45341	+	6.63410i	−0.184409	+	0.498650i
$178$	−9.84164	−	17.0462i	−0.737662	−	1.27767i
$179$	18.1466			1.35634			0.678171	−	0.734904i	$-0.262773\pi$
$179$	18.1466			1.35634			0.678171	+	0.734904i	$0.262773\pi$
$180$	−0.111987	−	0.0959524i	−0.00834702	−	0.00715187i
$181$	0.832634			0.0618892			0.0309446	−	0.999521i	$-0.490148\pi$
$181$	0.832634			0.0618892			0.0309446	+	0.999521i	$0.490148\pi$
$182$	−0.895188	−	1.55051i	−0.0663557	−	0.114931i
$183$	14.8805	+	17.9206i	1.10000	+	1.32473i
$184$	−9.69657	+	16.7949i	−0.714840	+	1.23814i
$185$	4.90002	−	8.48709i	0.360257	−	0.623983i
$186$	−0.252509	+	0.0431837i	−0.0185149	+	0.00316638i
$187$	−2.60525	−	4.51242i	−0.190514	−	0.329981i
$188$	0.103950			0.00758133
$189$	−5.57728	−	3.33606i	−0.405688	−	0.242663i
$190$	−6.81551			−0.494449
$191$	8.64515	+	14.9738i	0.625541	+	1.08347i	0.988436	+	0.151639i	$0.0484551\pi$
$191$	8.64515	+	14.9738i	0.625541	+	1.08347i	−0.362895	+	0.931830i	$0.618212\pi$
$192$	−13.3061	+	2.27559i	−0.960286	+	0.164226i
$193$	−3.92312	+	6.79504i	−0.282392	+	0.489118i	−0.971973	−	0.235091i	$-0.924461\pi$
$193$	−3.92312	+	6.79504i	−0.282392	+	0.489118i	0.689581	+	0.724208i	$0.257795\pi$
$194$	−8.08089	+	13.9965i	−0.580174	+	1.00489i
$195$	1.10649	+	1.33255i	0.0792373	+	0.0954257i
$196$	0.133603	+	0.231407i	0.00954305	+	0.0165291i
$197$	−3.70100			−0.263685			−0.131843	−	0.991271i	$-0.542089\pi$
$197$	−3.70100			−0.263685			−0.131843	+	0.991271i	$0.542089\pi$
$198$	−1.16335	+	6.22199i	−0.0826757	+	0.442177i
$199$	5.29240			0.375168			0.187584	−	0.982249i	$-0.439934\pi$
$199$	5.29240			0.375168			0.187584	+	0.982249i	$0.439934\pi$
$200$	−1.39630	−	2.41847i	−0.0987336	−	0.171012i
$201$	−6.69850	+	18.1130i	−0.472476	+	1.27759i
$202$	2.65823	−	4.60418i	0.187032	−	0.323949i
$203$	−6.01070	+	10.4108i	−0.421868	+	0.730697i
$204$	−0.104399	+	0.282300i	−0.00730941	+	0.0197649i
$205$	−3.07544	−	5.32682i	−0.214798	−	0.372041i
$206$	12.1157			0.844140
$207$	−3.82894	+	20.4785i	−0.266130	+	1.42335i
$208$	−4.09590			−0.283999
$209$	3.50883	+	6.07747i	0.242711	+	0.420388i
$210$	1.98103	+	2.38576i	0.136704	+	0.164633i
$211$	9.96330	−	17.2569i	0.685902	−	1.18802i	−0.287251	−	0.957855i	$-0.592741\pi$
$211$	9.96330	−	17.2569i	0.685902	−	1.18802i	0.973152	−	0.230162i	$-0.0739254\pi$
$212$	−0.216956	+	0.375779i	−0.0149006	+	0.0258086i
$213$	−16.2299	+	2.77560i	−1.11205	+	0.190181i
$214$	12.0432	+	20.8594i	0.823255	+	1.42592i
$215$	−5.67179			−0.386813
$216$	−12.6774	+	7.06026i	−0.862588	+	0.480390i
$217$	0.129225			0.00877235
$218$	−12.4643	−	21.5888i	−0.844190	−	1.46218i
$219$	−14.0844	+	2.40868i	−0.951733	+	0.162764i
$220$	0.0362276	−	0.0627480i	0.00244246	−	0.00423047i
$221$	1.76753	−	3.06145i	0.118897	−	0.205936i
$222$	15.5225	+	18.6938i	1.04180	+	1.25465i
$223$	−4.73228	−	8.19655i	−0.316897	−	0.548882i	0.662942	−	0.748671i	$-0.269308\pi$
$223$	−4.73228	−	8.19655i	−0.316897	−	0.548882i	−0.979839	+	0.199789i	$0.935974\pi$
$224$	−0.347714			−0.0232326
$225$	−2.27814	−	1.95195i	−0.151876	−	0.130130i
$226$	−7.72759			−0.514032
$227$	−5.96989	−	10.3401i	−0.396235	−	0.686299i	0.597023	−	0.802224i	$-0.296350\pi$
$227$	−5.96989	−	10.3401i	−0.396235	−	0.686299i	−0.993258	+	0.115925i	$0.963017\pi$
$228$	0.140608	−	0.380210i	0.00931202	−	0.0251800i
$229$	9.53852	−	16.5212i	0.630323	−	1.09175i	−0.357163	−	0.934042i	$-0.616256\pi$
$229$	9.53852	−	16.5212i	0.630323	−	1.09175i	0.987486	−	0.157709i	$-0.0504108\pi$
$230$	4.97045	−	8.60907i	0.327742	−	0.567665i
$231$	1.10752	−	2.99477i	0.0728693	−	0.197041i
$232$	13.4208	+	23.2455i	0.881118	+	1.52614i
$233$	−17.7574			−1.16333			−0.581664	−	0.813429i	$-0.697598\pi$
$233$	−17.7574			−1.16333			−0.581664	+	0.813429i	$0.697598\pi$
$234$	−4.05040	+	1.42712i	−0.264783	+	0.0932939i
$235$	2.11464			0.137944
$236$	0.100373	+	0.173850i	0.00653370	+	0.0113167i
$237$	−1.78804	−	2.15334i	−0.116145	−	0.139874i
$238$	3.16454	−	5.48115i	0.205127	−	0.355290i
$239$	−6.11052	+	10.5837i	−0.395256	+	0.684604i	−0.993134	−	0.116983i	$-0.962678\pi$
$239$	−6.11052	+	10.5837i	−0.395256	+	0.684604i	0.597878	+	0.801587i	$0.296011\pi$
$240$	6.99278	−	1.19589i	0.451382	−	0.0771945i
$241$	−0.692437	−	1.19934i	−0.0446038	−	0.0772561i	0.842862	−	0.538130i	$-0.180869\pi$
$241$	−0.692437	−	1.19934i	−0.0446038	−	0.0772561i	−0.887465	+	0.460874i	$0.847536\pi$
$242$	12.6364			0.812301
$243$	−10.3244	+	11.6793i	−0.662311	+	0.749229i
$244$	0.661086			0.0423217
$245$	2.71786	+	4.70748i	0.173638	+	0.300750i
$246$	15.0323	−	2.57079i	0.958424	−	0.163908i
$247$	−2.38057	+	4.12327i	−0.151472	+	0.262357i
$248$	0.144268	−	0.249879i	0.00916101	−	0.0158673i
$249$	−4.51591	−	5.43852i	−0.286184	−	0.344652i
$250$	0.715744	+	1.23970i	0.0452676	+	0.0784058i
$251$	−22.7662			−1.43699			−0.718496	−	0.695531i	$-0.755169\pi$
$251$	−22.7662			−1.43699			−0.718496	+	0.695531i	$0.755169\pi$
$252$	−0.173962	+	0.0612940i	−0.0109586	+	0.00386116i
$253$	−10.2358			−0.643516
$254$	−12.1601	−	21.0619i	−0.762994	−	1.32154i
$255$	−2.12378	+	5.74278i	−0.132996	+	0.359627i
$256$	−0.589534	+	1.02110i	−0.0368459	+	0.0638189i
$257$	2.58356	−	4.47486i	0.161158	−	0.279134i	−0.774126	−	0.633031i	$-0.781810\pi$
$257$	2.58356	−	4.47486i	0.161158	−	0.279134i	0.935284	+	0.353897i	$0.115144\pi$
$258$	4.87776	−	13.1896i	0.303676	−	0.821152i
$259$	−6.12851	−	10.6149i	−0.380807	−	0.659577i
$260$	0.0491573			0.00304861
$261$	21.8967	+	18.7614i	1.35537	+	1.16130i
$262$	−0.535018			−0.0330535
$263$	−0.193384	−	0.334951i	−0.0119246	−	0.0206540i	0.860002	−	0.510291i	$-0.170462\pi$
$263$	−0.193384	−	0.334951i	−0.0119246	−	0.0206540i	−0.871926	+	0.489637i	$0.837129\pi$
$264$	−4.55448	−	5.48497i	−0.280309	−	0.337577i
$265$	−4.41351	+	7.64443i	−0.271120	+	0.469593i
$266$	−4.26211	+	7.38219i	−0.261327	+	0.452631i
$267$	23.4753	−	4.01470i	1.43666	−	0.245695i
$268$	0.274045	+	0.474661i	0.0167400	+	0.0289945i
$269$	−1.52427			−0.0929363			−0.0464682	−	0.998920i	$-0.514797\pi$
$269$	−1.52427			−0.0929363			−0.0464682	+	0.998920i	$0.514797\pi$
$270$	6.49842	−	3.61908i	0.395481	−	0.220250i
$271$	−1.98110			−0.120343			−0.0601717	−	0.998188i	$-0.519165\pi$
$271$	−1.98110			−0.120343			−0.0601717	+	0.998188i	$0.519165\pi$
$272$	−7.23963	−	12.5394i	−0.438967	−	0.760313i
$273$	2.13529	−	0.365173i	0.129234	−	0.0221013i
$274$	11.2186	−	19.4311i	0.677739	−	1.17388i
$275$	0.736973	−	1.27648i	0.0444412	−	0.0769743i
$276$	0.377722	+	0.454892i	0.0227362	+	0.0273813i
$277$	−2.94241	−	5.09641i	−0.176793	−	0.306214i	0.763988	−	0.645231i	$-0.223239\pi$
$277$	−2.94241	−	5.09641i	−0.176793	−	0.306214i	−0.940780	+	0.339017i	$0.889905\pi$
$278$	17.2253			1.03310
$279$	0.0569679	−	0.304683i	0.00341058	−	0.0182409i
$280$	−3.49274			−0.208731
$281$	7.14684	+	12.3787i	0.426345	+	0.738451i	0.996545	−	0.0830549i	$-0.0264677\pi$
$281$	7.14684	+	12.3787i	0.426345	+	0.738451i	−0.570200	+	0.821506i	$0.693134\pi$
$282$	−1.81860	+	4.91756i	−0.108296	+	0.292836i
$283$	6.90065	−	11.9523i	0.410201	−	0.710489i	−0.584710	−	0.811242i	$-0.698792\pi$
$283$	6.90065	−	11.9523i	0.410201	−	0.710489i	0.994911	+	0.100753i	$0.0321252\pi$
$284$	−0.233653	+	0.404699i	−0.0138648	+	0.0240145i
$285$	2.86038	−	7.73457i	0.169434	−	0.458156i
$286$	−1.05497	−	1.82726i	−0.0623816	−	0.108048i
$287$	−7.69296			−0.454101
$288$	−0.153287	+	0.819832i	−0.00903254	+	0.0483091i
$289$	−4.50334			−0.264902
$290$	−6.87948	−	11.9156i	−0.403977	−	0.699709i
$291$	−12.4925	−	15.0447i	−0.732321	−	0.881937i
$292$	−0.202766	+	0.351200i	−0.0118660	+	0.0205524i
$293$	8.58733	−	14.8737i	0.501677	−	0.868930i	−0.498321	−	0.866993i	$-0.666050\pi$
$293$	8.58733	−	14.8737i	0.501677	−	0.868930i	0.999998	−	0.00193771i	$-0.000616794\pi$
$294$	−13.2845	+	2.27189i	−0.774769	+	0.132500i
$295$	2.04187	+	3.53661i	0.118882	+	0.205910i
$296$	−27.3677			−1.59071
$297$	−6.57276	−	3.93151i	−0.381390	−	0.228129i
$298$	6.60463			0.382596
$299$	−3.47223	−	6.01407i	−0.200804	−	0.347803i
$300$	−0.0839245	+	0.0143526i	−0.00484538	+	0.000828648i
$301$	−3.54688	+	6.14338i	−0.204439	+	0.354099i
$302$	2.92876	−	5.07277i	0.168531	−	0.291905i
$303$	4.10943	+	4.94900i	0.236080	+	0.284312i
$304$	9.75056	+	16.8885i	0.559233	+	0.968620i
$305$	13.4484			0.770052
$306$	−11.5283	−	9.87763i	−0.659028	−	0.564666i
$307$	−0.748107			−0.0426967			−0.0213484	−	0.999772i	$-0.506796\pi$
$307$	−0.748107			−0.0426967			−0.0213484	+	0.999772i	$0.506796\pi$
$308$	−0.0453102	−	0.0784796i	−0.00258179	−	0.00447179i
$309$	−5.08479	+	13.7495i	−0.289264	+	0.782180i
$310$	−0.0739515	+	0.128088i	−0.00420016	+	0.00727489i
$311$	−0.706690	+	1.22402i	−0.0400727	+	0.0694080i	−0.885366	−	0.464894i	$-0.846092\pi$
$311$	−0.706690	+	1.22402i	−0.0400727	+	0.0694080i	0.845293	+	0.534302i	$0.179426\pi$
$312$	1.67773	−	4.53665i	0.0949829	−	0.256837i
$313$	4.65284	+	8.05895i	0.262994	+	0.455519i	0.967036	−	0.254639i	$-0.0819567\pi$
$313$	4.65284	+	8.05895i	0.262994	+	0.455519i	−0.704042	+	0.710158i	$0.748623\pi$
$314$	−14.5365			−0.820341
$315$	−3.53889	+	1.24690i	−0.199394	+	0.0702546i
$316$	−0.0794360			−0.00446862
$317$	−13.1445	−	22.7670i	−0.738271	−	1.27872i	−0.953273	−	0.302109i	$-0.902309\pi$
$317$	−13.1445	−	22.7670i	−0.738271	−	1.27872i	0.215002	−	0.976614i	$-0.431024\pi$
$318$	−13.9813	−	16.8378i	−0.784035	−	0.944216i
$319$	−7.08353	+	12.2690i	−0.396602	+	0.686934i
$320$	−3.89691	+	6.74965i	−0.217844	+	0.377317i
$321$	−28.7266	+	4.91277i	−1.60336	+	0.274204i
$322$	−6.21659	−	10.7674i	−0.346437	−	0.600046i
$323$	−16.8309			−0.936497
$324$	0.0678276	+	0.437185i	0.00376820	+	0.0242881i
$325$	1.00000			0.0554700
$326$	5.79401	+	10.0355i	0.320900	+	0.555816i
$327$	29.7312	−	5.08456i	1.64414	−	0.281177i
$328$	−8.58849	+	14.8757i	−0.474220	+	0.821373i
$329$	1.32240	−	2.29046i	0.0729063	−	0.126277i
$330$	2.33462	+	2.81159i	0.128517	+	0.154773i
$331$	6.48299	+	11.2289i	0.356338	+	0.617195i	0.987346	−	0.158581i	$-0.0506920\pi$
$331$	6.48299	+	11.2289i	0.356338	+	0.617195i	−0.631008	+	0.775776i	$0.717359\pi$
$332$	−0.200625			−0.0110108
$333$	−27.7293	+	9.77016i	−1.51955	+	0.535402i
$334$	12.1978			0.667434
$335$	5.57487	+	9.65596i	0.304588	+	0.527561i
$336$	3.07764	−	8.32206i	0.167899	−	0.454006i
$337$	−0.946489	+	1.63937i	−0.0515586	+	0.0893021i	−0.890653	−	0.454684i	$-0.849752\pi$
$337$	−0.946489	+	1.63937i	−0.0515586	+	0.0893021i	0.839094	+	0.543986i	$0.183086\pi$
$338$	0.715744	−	1.23970i	0.0389313	−	0.0674311i
$339$	3.24317	−	8.76964i	0.176145	−	0.476301i
$340$	0.0868870	+	0.150493i	0.00471211	+	0.00816161i
$341$	0.152290			0.00824696
$342$	15.5267	+	13.3035i	0.839585	+	0.719371i
$343$	15.5535			0.839809
$344$	7.91954	+	13.7171i	0.426993	+	0.739574i
$345$	7.68396	+	9.25381i	0.413690	+	0.498209i
$346$	12.6212	−	21.8606i	0.678522	−	1.17523i
$347$	14.5026	−	25.1193i	0.778541	−	1.34847i	−0.154242	−	0.988033i	$-0.549293\pi$
$347$	14.5026	−	25.1193i	0.778541	−	1.34847i	0.932783	−	0.360439i	$-0.117373\pi$
$348$	0.806653	−	0.137952i	0.0432412	−	0.00739502i
$349$	1.47320	+	2.55166i	0.0788585	+	0.136587i	0.902758	−	0.430149i	$-0.141539\pi$
$349$	1.47320	+	2.55166i	0.0788585	+	0.136587i	−0.823899	+	0.566736i	$0.808206\pi$
$350$	1.79038			0.0956996
$351$	0.0803313	−	5.19553i	0.00428777	−	0.277317i
$352$	−0.409776			−0.0218412
$353$	14.7303	+	25.5136i	0.784015	+	1.35795i	0.929586	+	0.368606i	$0.120165\pi$
$353$	14.7303	+	25.5136i	0.784015	+	1.35795i	−0.145571	+	0.989348i	$0.546502\pi$
$354$	−9.98034	+	1.70682i	−0.530449	+	0.0907164i
$355$	−4.75318	+	8.23275i	−0.252272	+	0.436949i
$356$	0.337962	−	0.585367i	0.0179119	−	0.0310244i
$357$	4.89216	+	5.89164i	0.258920	+	0.311819i
$358$	12.9883	+	22.4964i	0.686454	+	1.18897i
$359$	−24.7647			−1.30703			−0.653515	−	0.756913i	$-0.726707\pi$
$359$	−24.7647			−1.30703			−0.653515	+	0.756913i	$0.726707\pi$
$360$	−1.53975	+	8.23511i	−0.0811521	+	0.434029i
$361$	3.66842			0.193075
$362$	0.595953	+	1.03222i	0.0313226	+	0.0542523i
$363$	−5.30334	+	14.3404i	−0.278353	+	0.752677i
$364$	0.0307407	−	0.0532445i	0.00161125	−	0.00279077i
$365$	−4.12483	+	7.14442i	−0.215904	+	0.373956i
$366$	−11.5657	+	31.2740i	−0.604546	+	1.63472i
$367$	4.98557	+	8.63526i	0.260245	+	0.450757i	0.966307	−	0.257393i	$-0.0828634\pi$
$367$	4.98557	+	8.63526i	0.260245	+	0.450757i	−0.706062	+	0.708150i	$0.749530\pi$
$368$	−28.4438			−1.48273
$369$	−3.39139	+	18.1383i	−0.176549	+	0.944242i
$370$	14.0286			0.729315
$371$	5.52002	+	9.56096i	0.286585	+	0.496380i
$372$	−0.00561984	−	0.00676799i	−0.000291375	−	0.000350904i
$373$	9.54564	−	16.5335i	0.494255	−	0.856074i	−0.505723	−	0.862696i	$-0.668774\pi$
$373$	9.54564	−	16.5335i	0.494255	−	0.856074i	0.999978	+	0.00662155i	$0.00210772\pi$
$374$	3.72938	−	6.45947i	0.192842	−	0.334011i
$375$	−1.70726	+	0.291973i	−0.0881628	+	0.0150774i
$376$	−2.95268	−	5.11419i	−0.152273	−	0.263744i
$377$	−9.61166			−0.495025
$378$	0.143823	−	9.30195i	0.00739746	−	0.478441i
$379$	20.7186			1.06424			0.532122	−	0.846668i	$-0.321395\pi$
$379$	20.7186			1.06424			0.532122	+	0.846668i	$0.321395\pi$
$380$	−0.117022	−	0.202688i	−0.00600312	−	0.0103977i
$381$	29.0055	−	4.96047i	1.48600	−	0.254133i
$382$	−12.3754	+	21.4349i	−0.633182	+	1.09670i
$383$	−16.7123	+	28.9466i	−0.853961	+	1.47910i	0.0236451	+	0.999720i	$0.492473\pi$
$383$	−16.7123	+	28.9466i	−0.853961	+	1.47910i	−0.877606	+	0.479383i	$0.840861\pi$
$384$	−12.9601	−	15.6079i	−0.661366	−	0.796485i
$385$	−0.921739	−	1.59650i	−0.0469762	−	0.0813651i
$386$	−11.2318			−0.571683
$387$	12.9211	+	11.0710i	0.656817	+	0.562772i
$388$	−0.554995			−0.0281756
$389$	3.71618	+	6.43662i	0.188418	+	0.326350i	0.944723	−	0.327870i	$-0.106331\pi$
$389$	3.71618	+	6.43662i	0.188418	+	0.326350i	−0.756305	+	0.654219i	$0.772997\pi$
$390$	−0.860004	+	2.32548i	−0.0435480	+	0.117755i
$391$	12.2745	−	21.2601i	0.620750	−	1.07517i
$392$	7.58992	−	13.1461i	0.383349	−	0.663980i
$393$	0.224540	−	0.607164i	0.0113265	−	0.0306274i
$394$	−2.64897	−	4.58815i	−0.133453	−	0.231148i
$395$	−1.61596			−0.0813075
$396$	−0.205012	+	0.0722342i	−0.0103023	+	0.00362991i
$397$	−1.80255			−0.0904674			−0.0452337	−	0.998976i	$-0.514403\pi$
$397$	−1.80255			−0.0904674			−0.0452337	+	0.998976i	$0.514403\pi$
$398$	3.78800	+	6.56102i	0.189876	+	0.328874i
$399$	−6.58891	−	7.93505i	−0.329858	−	0.397250i
$400$	2.04795	−	3.54715i	0.102397	−	0.177358i
$401$	12.8071	−	22.1825i	0.639554	−	1.10774i	−0.345976	−	0.938243i	$-0.612452\pi$
$401$	12.8071	−	22.1825i	0.639554	−	1.10774i	0.985531	−	0.169497i	$-0.0542144\pi$
$402$	−27.2492	+	4.66010i	−1.35906	+	0.232425i
$403$	0.0516606	+	0.0894788i	0.00257340	+	0.00445725i
$404$	0.182567			0.00908305
$405$	1.37981	+	8.89360i	0.0685632	+	0.441927i
$406$	−17.2085			−0.854042
$407$	−7.22237	−	12.5095i	−0.358000	−	0.620074i
$408$	16.8542	−	2.88237i	0.834406	−	0.142699i
$409$	−6.27038	+	10.8606i	−0.310050	+	0.537023i	−0.978373	−	0.206849i	$-0.933679\pi$
$409$	−6.27038	+	10.8606i	−0.310050	+	0.537023i	0.668323	+	0.743871i	$0.267013\pi$
$410$	4.40245	−	7.62527i	0.217422	−	0.376585i
$411$	17.3431	+	20.8864i	0.855472	+	1.03025i
$412$	0.208026	+	0.360312i	0.0102487	+	0.0177513i
$413$	5.10756			0.251327
$414$	−28.1278	+	9.91058i	−1.38241	+	0.487079i
$415$	−4.08130			−0.200343
$416$	−0.139007	−	0.240766i	−0.00681536	−	0.0118045i
$417$	−7.22921	+	19.5481i	−0.354016	+	0.957272i
$418$	−5.02285	+	8.69983i	−0.245675	+	0.425522i
$419$	−11.0535	+	19.1452i	−0.540000	+	0.935307i	0.458904	+	0.888486i	$0.348242\pi$
$419$	−11.0535	+	19.1452i	−0.540000	+	0.935307i	−0.998903	+	0.0468206i	$0.985091\pi$
$420$	−0.0369366	+	0.0998779i	−0.00180232	+	0.00487354i
$421$	17.0859	+	29.5937i	0.832717	+	1.44231i	0.895876	+	0.444304i	$0.146549\pi$
$421$	17.0859	+	29.5937i	0.832717	+	1.44231i	−0.0631590	+	0.998003i	$0.520118\pi$
$422$	28.5247			1.38856
$423$	−4.81744	−	4.12766i	−0.234232	−	0.200694i
$424$	24.6504			1.19713
$425$	1.76753	+	3.06145i	0.0857378	+	0.148502i
$426$	−15.0573	−	18.1336i	−0.729531	−	0.878577i
$427$	8.41001	−	14.5666i	0.406989	−	0.704925i
$428$	−0.413563	+	0.716312i	−0.0199903	+	0.0346242i
$429$	2.51642	−	0.430353i	0.121494	−	0.0207776i
$430$	−4.05955	−	7.03135i	−0.195769	−	0.339082i
$431$	−8.75050			−0.421497			−0.210748	−	0.977540i	$-0.567590\pi$
$431$	−8.75050			−0.421497			−0.210748	+	0.977540i	$0.567590\pi$
$432$	−18.2648	−	10.9251i	−0.878767	−	0.525636i
$433$	10.0228			0.481667			0.240834	−	0.970566i	$-0.422579\pi$
$433$	10.0228			0.481667			0.240834	+	0.970566i	$0.422579\pi$
$434$	0.0924918	+	0.160201i	0.00443975	+	0.00768987i
$435$	16.4096	−	2.80634i	0.786782	−	0.134554i
$436$	0.428025	−	0.741360i	0.0204987	−	0.0355047i
$437$	−16.5317	+	28.6338i	−0.790821	+	1.36974i
$438$	−13.0668	−	15.7365i	−0.624358	−	0.751917i
$439$	17.0191	+	29.4780i	0.812279	+	1.40691i	0.911266	+	0.411819i	$0.135106\pi$
$439$	17.0191	+	29.4780i	0.812279	+	1.40691i	−0.0989870	+	0.995089i	$0.531560\pi$
$440$	−4.11615			−0.196230
$441$	2.99708	−	16.0294i	0.142718	−	0.763305i
$442$	5.06040			0.240699
$443$	13.5229	+	23.4223i	0.642492	+	1.11283i	0.984875	+	0.173268i	$0.0554328\pi$
$443$	13.5229	+	23.4223i	0.642492	+	1.11283i	−0.342382	+	0.939561i	$0.611234\pi$
$444$	−0.289420	+	0.782603i	−0.0137353	+	0.0371407i
$445$	6.87511	−	11.9080i	0.325912	−	0.564496i
$446$	6.77420	−	11.7333i	0.320768	−	0.555586i
$447$	−2.77187	+	7.49525i	−0.131105	+	0.354513i
$448$	4.87390	+	8.44185i	0.230270	+	0.398840i
$449$	−24.6140			−1.16161			−0.580804	−	0.814043i	$-0.697262\pi$
$449$	−24.6140			−1.16161			−0.580804	+	0.814043i	$0.697262\pi$
$450$	0.789276	−	4.22131i	0.0372068	−	0.198994i
$451$	−9.06606			−0.426904
$452$	−0.132683	−	0.229813i	−0.00624087	−	0.0108095i
$453$	4.52766	+	5.45267i	0.212728	+	0.256189i
$454$	8.54582	−	14.8018i	0.401075	−	0.694682i
$455$	0.625355	−	1.08315i	0.0293171	−	0.0507787i
$456$	−22.6998	+	3.88207i	−1.06301	+	0.181795i
$457$	8.72394	+	15.1103i	0.408089	+	0.706831i	0.994676	−	0.103056i	$-0.0328620\pi$
$457$	8.72394	+	15.1103i	0.408089	+	0.706831i	−0.586587	+	0.809886i	$0.699529\pi$
$458$	27.3085			1.27604
$459$	16.0479	−	8.93733i	0.749050	−	0.417159i
$460$	0.341370			0.0159165
$461$	−13.1113	−	22.7094i	−0.610653	−	1.05768i	−0.991130	−	0.132892i	$-0.957574\pi$
$461$	−13.1113	−	22.7094i	−0.610653	−	1.05768i	0.380477	−	0.924790i	$-0.375760\pi$
$462$	4.50533	−	0.770493i	0.209607	−	0.0358466i
$463$	13.7238	−	23.7704i	0.637801	−	1.10470i	−0.348114	−	0.937452i	$-0.613178\pi$
$463$	13.7238	−	23.7704i	0.637801	−	1.10470i	0.985914	−	0.167251i	$-0.0534890\pi$
$464$	−19.6842	+	34.0940i	−0.913815	+	1.58277i
$465$	−0.114324	−	0.137680i	−0.00530163	−	0.00638478i
$466$	−12.7098	−	22.0140i	−0.588768	−	1.01978i
$467$	20.6056			0.953512			0.476756	−	0.879036i	$-0.341812\pi$
$467$	20.6056			0.953512			0.476756	+	0.879036i	$0.341812\pi$
$468$	−0.111987	−	0.0959524i	−0.00517660	−	0.00443540i
$469$	13.9451			0.643924
$470$	1.51354	+	2.62153i	0.0698144	+	0.120922i
$471$	6.10076	−	16.4967i	0.281108	−	0.760128i
$472$	5.70213	−	9.87637i	0.262462	−	0.454597i
$473$	−4.17996	+	7.23990i	−0.192195	+	0.332891i
$474$	1.38973	−	3.75788i	0.0638323	−	0.172605i
$475$	−2.38057	−	4.12327i	−0.109228	−	0.189188i
$476$	0.217341			0.00996180
$477$	24.9761	−	8.80011i	1.14358	−	0.402929i
$478$	−17.4943			−0.800169
$479$	8.45081	+	14.6372i	0.386127	+	0.668792i	0.991925	−	0.126827i	$-0.0404792\pi$
$479$	8.45081	+	14.6372i	0.386127	+	0.668792i	−0.605798	+	0.795619i	$0.707146\pi$
$480$	0.307618	+	0.370466i	0.0140408	+	0.0169094i
$481$	4.90002	−	8.48709i	0.223422	−	0.386978i
$482$	0.991216	−	1.71684i	0.0451486	−	0.0781997i
$483$	14.8284	−	2.53593i	0.674717	−	0.115389i
$484$	0.216968	+	0.375799i	0.00986216	+	0.0170818i
$485$	−11.2902			−0.512661
$486$	−21.8685	−	4.43981i	−0.991977	−	0.201394i
$487$	3.72906			0.168980			0.0844899	−	0.996424i	$-0.473074\pi$
$487$	3.72906			0.168980			0.0844899	+	0.996424i	$0.473074\pi$
$488$	−18.7780	−	32.5245i	−0.850041	−	1.47231i
$489$	−13.8204	+	2.36355i	−0.624982	+	0.106883i
$490$	−3.89059	+	6.73870i	−0.175759	+	0.304423i
$491$	10.4812	−	18.1540i	0.473010	−	0.819276i	−0.526513	−	0.850167i	$-0.676501\pi$
$491$	10.4812	−	18.1540i	0.473010	−	0.819276i	0.999523	+	0.0308904i	$0.00983429\pi$
$492$	0.334558	+	0.402910i	0.0150830	+	0.0181646i
$493$	−16.9889	−	29.4256i	−0.765142	−	1.32526i
$494$	−6.81551			−0.306644
$495$	−4.17054	+	1.46945i	−0.187452	+	0.0660469i
$496$	0.423193			0.0190019
$497$	5.94484	+	10.2968i	0.266663	+	0.461873i
$498$	3.50993	−	9.49098i	0.157284	−	0.425301i
$499$	5.16177	−	8.94044i	0.231072	−	0.400229i	−0.727052	−	0.686583i	$-0.759110\pi$
$499$	5.16177	−	8.94044i	0.231072	−	0.400229i	0.958124	+	0.286354i	$0.0924433\pi$
$500$	−0.0245786	+	0.0425715i	−0.00109919	+	0.00190385i
$501$	−5.11925	+	13.8426i	−0.228711	+	0.618444i
$502$	−16.2948	−	28.2234i	−0.727272	−	1.25967i
$503$	−15.9668			−0.711923			−0.355962	−	0.934501i	$-0.615847\pi$
$503$	−15.9668			−0.711923			−0.355962	+	0.934501i	$0.615847\pi$
$504$	7.95694	+	6.81764i	0.354430	+	0.303682i
$505$	3.71394			0.165268
$506$	−7.32618	−	12.6893i	−0.325688	−	0.564109i
$507$	1.10649	+	1.33255i	0.0491409	+	0.0591805i
$508$	0.417578	−	0.723267i	0.0185270	−	0.0320898i
$509$	9.69320	−	16.7891i	0.429644	−	0.744165i	−0.567198	−	0.823582i	$-0.691973\pi$
$509$	9.69320	−	16.7891i	0.429644	−	0.744165i	0.996841	+	0.0794169i	$0.0253058\pi$
$510$	−8.63944	+	1.47750i	−0.382561	+	0.0654248i
$511$	5.15897	+	8.93559i	0.228219	+	0.395287i
$512$	21.7378			0.960682
$513$	−21.6138	+	12.0371i	−0.954272	+	0.531450i
$514$	7.39668			0.326253
$515$	4.23185	+	7.32979i	0.186478	+	0.322989i
$516$	0.476002	−	0.0814050i	0.0209548	−	0.00358365i
$517$	1.55843	−	2.69929i	0.0685398	−	0.118714i
$518$	8.77288	−	15.1951i	0.385458	−	0.667633i
$519$	19.5115	+	23.4978i	0.856460	+	1.03144i
$520$	−1.39630	−	2.41847i	−0.0612320	−	0.106057i
$521$	−43.0972			−1.88812			−0.944060	−	0.329773i	$-0.893028\pi$
$521$	−43.0972			−1.88812			−0.944060	+	0.329773i	$0.893028\pi$
$522$	−7.58625	+	40.5738i	−0.332041	+	1.77587i
$523$	30.2809			1.32409			0.662045	−	0.749464i	$-0.269689\pi$
$523$	30.2809			1.32409			0.662045	+	0.749464i	$0.269689\pi$
$524$	−0.00918626	−	0.0159111i	−0.000401303	−	0.000695078i
$525$	−0.751396	+	2.03180i	−0.0327936	+	0.0886752i
$526$	0.276827	−	0.479478i	0.0120702	−	0.0209062i
$527$	−0.182623	+	0.316313i	−0.00795520	+	0.0137788i
$528$	3.62697	−	9.80745i	0.157843	−	0.426815i
$529$	−12.6127	−	21.8459i	−0.548379	−	0.949820i
$530$	−12.6358			−0.548863
$531$	2.25164	−	12.0425i	0.0977126	−	0.522600i
$532$	−0.292722			−0.0126911
$533$	−3.07544	−	5.32682i	−0.133212	−	0.230730i
$534$	21.7793	+	26.2289i	0.942484	+	1.13504i
$535$	−8.41305	+	14.5718i	−0.363728	+	0.629995i
$536$	15.5684	−	26.9653i	0.672453	−	1.16472i
$537$	−30.9811	+	5.29832i	−1.33693	+	0.228639i
$538$	−1.09099	−	1.88964i	−0.0470358	−	0.0814683i
$539$	8.01197			0.345100
$540$	0.219207	+	0.131119i	0.00943316	+	0.00564246i
$541$	18.2422			0.784292			0.392146	−	0.919903i	$-0.371733\pi$
$541$	18.2422			0.784292			0.392146	+	0.919903i	$0.371733\pi$
$542$	−1.41796	−	2.45598i	−0.0609066	−	0.105493i
$543$	−1.42153	+	0.243107i	−0.0610035	+	0.0104327i
$544$	0.491397	−	0.851124i	0.0210685	−	0.0364916i
$545$	8.70725	−	15.0814i	0.372978	−	0.646016i
$546$	1.98103	+	2.38576i	0.0847802	+	0.102101i
$547$	3.61677	+	6.26443i	0.154642	+	0.267848i	0.932929	−	0.360062i	$-0.117244\pi$
$547$	3.61677	+	6.26443i	0.154642	+	0.267848i	−0.778287	+	0.627909i	$0.783911\pi$
$548$	0.770491			0.0329138
$549$	−30.6372	−	26.2505i	−1.30757	−	1.12034i
$550$	2.10994			0.0899680
$551$	22.8812	+	39.6314i	0.974772	+	1.68835i
$552$	11.6509	−	31.5045i	0.495896	−	1.34092i
$553$	−1.01055	+	1.75032i	−0.0429728	+	0.0744310i
$554$	4.21203	−	7.29545i	0.178952	−	0.309954i
$555$	−5.88763	+	15.9204i	−0.249916	+	0.675782i
$556$	0.295758	+	0.512267i	0.0125429	+	0.0217250i
$557$	−0.960304			−0.0406894			−0.0203447	−	0.999793i	$-0.506476\pi$
$557$	−0.960304			−0.0406894			−0.0203447	+	0.999793i	$0.506476\pi$
$558$	0.418492	−	0.147452i	0.0177162	−	0.00624214i
$559$	−5.67179			−0.239891
$560$	−2.56139	−	4.43646i	−0.108238	−	0.187475i
$561$	5.76535	+	6.94323i	0.243413	+	0.293143i
$562$	−10.2306	+	17.7199i	−0.431553	+	0.747471i
$563$	4.44187	−	7.69354i	0.187202	−	0.324244i	−0.757114	−	0.653283i	$-0.773391\pi$
$563$	4.44187	−	7.69354i	0.187202	−	0.324244i	0.944316	+	0.329039i	$0.106725\pi$
$564$	−0.177470	+	0.0303506i	−0.00747284	+	0.00127799i
$565$	−2.69915	−	4.67506i	−0.113554	−	0.196681i
$566$	19.7564			0.830423
$567$	10.4959	+	4.06712i	0.440788	+	0.170803i
$568$	26.5475			1.11391
$569$	5.91857	+	10.2513i	0.248119	+	0.429755i	0.963004	−	0.269487i	$-0.0868542\pi$
$569$	5.91857	+	10.2513i	0.248119	+	0.429755i	−0.714885	+	0.699242i	$0.753521\pi$
$570$	11.6359	−	1.98994i	0.487373	−	0.0833496i
$571$	17.4935	−	30.2997i	0.732082	−	1.26800i	−0.223910	−	0.974610i	$-0.571882\pi$
$571$	17.4935	−	30.2997i	0.732082	−	1.26800i	0.955992	−	0.293394i	$-0.0947846\pi$
$572$	0.0362276	−	0.0627480i	0.00151475	−	0.00262363i
$573$	−19.1315	−	23.0402i	−0.799230	−	0.962516i
$574$	−5.50619	−	9.53700i	−0.229824	−	0.398067i
$575$	6.94445			0.289604
$576$	22.0527	−	7.77006i	0.918860	−	0.323752i
$577$	−11.2588			−0.468709			−0.234355	−	0.972151i	$-0.575298\pi$
$577$	−11.2588			−0.468709			−0.234355	+	0.972151i	$0.575298\pi$
$578$	−3.22324	−	5.58281i	−0.134069	−	0.232214i
$579$	4.71383	−	12.7464i	0.195900	−	0.529721i
$580$	0.236241	−	0.409182i	0.00980939	−	0.0169904i
$581$	−2.55226	+	4.42064i	−0.105886	+	0.183399i
$582$	9.70961	−	26.2551i	0.402476	−	1.08831i
$583$	6.50528	+	11.2675i	0.269421	+	0.466651i
$584$	23.0381			0.953323
$585$	−2.27814	−	1.95195i	−0.0941893	−	0.0807031i
$586$	24.5853			1.01561
$587$	−7.61101	−	13.1827i	−0.314140	−	0.544107i	0.665114	−	0.746742i	$-0.268383\pi$
$587$	−7.61101	−	13.1827i	−0.314140	−	0.544107i	−0.979254	+	0.202635i	$0.935049\pi$
$588$	−0.295660	−	0.356064i	−0.0121928	−	0.0146838i
$589$	0.245963	−	0.426021i	0.0101347	−	0.0175539i
$590$	−2.92290	+	5.06262i	−0.120334	+	0.208425i
$591$	6.31859	−	1.08059i	0.259912	−	0.0444496i
$592$	−20.0700	−	34.7623i	−0.824872	−	1.42872i
$593$	12.6917			0.521184			0.260592	−	0.965449i	$-0.416082\pi$
$593$	12.6917			0.521184			0.260592	+	0.965449i	$0.416082\pi$
$594$	0.169494	−	10.9622i	0.00695442	−	0.449786i
$595$	4.42133			0.181257
$596$	0.113401	+	0.196417i	0.00464511	+	0.00804556i
$597$	−9.03553	+	1.54524i	−0.369800	+	0.0632424i
$598$	4.97045	−	8.60907i	0.203257	−	0.352051i
$599$	−11.2419	+	19.4715i	−0.459331	+	0.795584i	−0.998926	−	0.0463405i	$-0.985244\pi$
$599$	−11.2419	+	19.4715i	−0.459331	+	0.795584i	0.539595	+	0.841925i	$0.318577\pi$
$600$	3.08999	+	3.72128i	0.126148	+	0.151921i
$601$	11.7541	+	20.3588i	0.479462	+	0.830452i	0.999723	−	0.0235555i	$-0.00749863\pi$
$601$	11.7541	+	20.3588i	0.479462	+	0.830452i	−0.520261	+	0.854007i	$0.674165\pi$
$602$	−10.1546			−0.413872
$603$	6.14760	−	32.8794i	0.250350	−	1.33895i
$604$	0.201147			0.00818457
$605$	4.41374	+	7.64482i	0.179444	+	0.310806i
$606$	−3.19400	+	8.63669i	−0.129747	+	0.350842i
$607$	18.9667	−	32.8513i	0.769836	−	1.33339i	−0.167816	−	0.985818i	$-0.553671\pi$
$607$	18.9667	−	32.8513i	0.769836	−	1.33339i	0.937652	−	0.347576i	$-0.112995\pi$
$608$	−0.661829	+	1.14632i	−0.0268407	+	0.0464895i
$609$	7.22216	−	19.5290i	0.292657	−	0.791355i
$610$	9.62559	+	16.6720i	0.389729	+	0.675030i
$611$	2.11464			0.0855492
$612$	0.0958133	−	0.512442i	0.00387302	−	0.0207142i
$613$	24.5881			0.993103			0.496551	−	0.868007i	$-0.334599\pi$
$613$	24.5881			0.993103			0.496551	+	0.868007i	$0.334599\pi$
$614$	−0.535453	−	0.927431i	−0.0216091	−	0.0374281i
$615$	6.80587	+	8.19634i	0.274439	+	0.330508i
$616$	−2.57406	+	4.45840i	−0.103712	+	0.179634i
$617$	4.52549	−	7.83838i	0.182189	−	0.315561i	−0.760436	−	0.649412i	$-0.775015\pi$
$617$	4.52549	−	7.83838i	0.182189	−	0.315561i	0.942626	+	0.333851i	$0.108348\pi$
$618$	−20.6847	+	3.53746i	−0.832060	+	0.142297i
$619$	6.07181	+	10.5167i	0.244047	+	0.422701i	0.961863	−	0.273531i	$-0.0881917\pi$
$619$	6.07181	+	10.5167i	0.244047	+	0.422701i	−0.717817	+	0.696232i	$0.754858\pi$
$620$	−0.00507899			−0.000203977
$621$	0.557857	−	36.0801i	0.0223860	−	1.44785i
$622$	−2.02324			−0.0811244
$623$	−8.59877	−	14.8935i	−0.344502	−	0.596696i
$624$	6.99278	−	1.19589i	0.279935	−	0.0478740i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.66048	+	11.5363i	−0.266206	+	0.461083i
$627$	−7.76496	−	9.35137i	−0.310103	−	0.373458i
$628$	−0.249591	−	0.432305i	−0.00995978	−	0.0172508i
$629$	34.6438			1.38134
$630$	−4.07872	−	3.49472i	−0.162500	−	0.139233i
$631$	−39.4322			−1.56977			−0.784885	−	0.619641i	$-0.787278\pi$
$631$	−39.4322			−1.56977			−0.784885	+	0.619641i	$0.787278\pi$
$632$	2.25636	+	3.90814i	0.0897534	+	0.155457i
$633$	−11.9714	+	32.3712i	−0.475821	+	1.28664i
$634$	18.8162	−	32.5907i	0.747289	−	1.29434i
$635$	8.49474	−	14.7133i	0.337104	−	0.583880i
$636$	0.260684	−	0.704900i	0.0103368	−	0.0279511i
$637$	2.71786	+	4.70748i	0.107686	+	0.186517i
$638$	−20.2800			−0.802892
$639$	26.8983	−	9.47737i	1.06408	−	0.374919i
$640$	−11.7128			−0.462989
$641$	−19.1148	−	33.1079i	−0.754990	−	1.30768i	−0.945379	−	0.325973i	$-0.894308\pi$
$641$	−19.1148	−	33.1079i	−0.754990	−	1.30768i	0.190389	−	0.981709i	$-0.439025\pi$
$642$	−26.6513	−	32.0962i	−1.05184	−	1.26674i
$643$	−15.7062	+	27.2040i	−0.619393	+	1.07282i	0.370204	+	0.928951i	$0.379288\pi$
$643$	−15.7062	+	27.2040i	−0.619393	+	1.07282i	−0.989597	+	0.143870i	$0.954045\pi$
$644$	0.213478	−	0.369754i	0.00841220	−	0.0145704i
$645$	9.68325	−	1.65601i	0.381278	−	0.0652053i
$646$	−12.0466	−	20.8654i	−0.473968	−	0.820937i
$647$	−45.8883			−1.80406			−0.902028	−	0.431677i	$-0.857922\pi$
$647$	−45.8883			−1.80406			−0.902028	+	0.431677i	$0.857922\pi$
$648$	19.5823	−	15.7552i	0.769264	−	0.618922i
$649$	6.01920			0.236274
$650$	0.715744	+	1.23970i	0.0280738	+	0.0486252i
$651$	−0.220621	+	0.0377301i	−0.00864681	+	0.00147876i
$652$	−0.198966	+	0.344619i	−0.00779211	+	0.0134963i
$653$	15.4584	−	26.7748i	0.604935	−	1.04778i	−0.387127	−	0.922027i	$-0.626532\pi$
$653$	15.4584	−	26.7748i	0.604935	−	1.04778i	0.992062	−	0.125752i	$-0.0401343\pi$
$654$	27.5833	+	33.2186i	1.07859	+	1.29895i
$655$	−0.186875	−	0.323677i	−0.00730180	−	0.0126471i
$656$	−25.1934			−0.983636
$657$	23.3425	−	8.22451i	0.910676	−	0.320869i
$658$	3.78600			0.147594
$659$	14.6909	+	25.4455i	0.572278	+	0.991215i	0.996332	+	0.0855776i	$0.0272736\pi$
$659$	14.6909	+	25.4455i	0.572278	+	0.991215i	−0.424053	+	0.905637i	$0.639393\pi$
$660$	−0.0435294	+	0.117705i	−0.00169438	+	0.00458166i
$661$	−6.41611	+	11.1130i	−0.249558	+	0.432247i	−0.963403	−	0.268057i	$-0.913619\pi$
$661$	−6.41611	+	11.1130i	−0.249558	+	0.432247i	0.713845	+	0.700303i	$0.246952\pi$
$662$	−9.28033	+	16.0740i	−0.360690	+	0.624734i
$663$	−2.12378	+	5.74278i	−0.0824808	+	0.223031i
$664$	5.69873	+	9.87049i	0.221154	+	0.383049i
$665$	−5.95480			−0.230917
$666$	−31.9592	−	27.3832i	−1.23839	−	1.06108i
$667$	−66.7477			−2.58448
$668$	0.209436	+	0.362754i	0.00810333	+	0.0140354i
$669$	10.4724	+	12.6120i	0.404887	+	0.487607i
$670$	−7.98036	+	13.8224i	−0.308308	+	0.534005i
$671$	9.91109	−	17.1665i	0.382613	−	0.662706i
$672$	0.593639	−	0.101523i	0.0229001	−	0.00391633i
$673$	−11.4517	−	19.8349i	−0.441431	−	0.764581i	0.556365	−	0.830938i	$-0.312196\pi$
$673$	−11.4517	−	19.8349i	−0.441431	−	0.764581i	−0.997796	+	0.0663573i	$0.978862\pi$
$674$	−2.70978			−0.104377
$675$	4.45930	+	2.66733i	0.171638	+	0.102666i
$676$	0.0491573			0.00189066
$677$	−14.3767	−	24.9013i	−0.552543	−	0.957033i	−0.998090	−	0.0617743i	$-0.980324\pi$
$677$	−14.3767	−	24.9013i	−0.552543	−	0.957033i	0.445547	−	0.895259i	$-0.353009\pi$
$678$	13.1930	−	2.25625i	0.506676	−	0.0866507i
$679$	−7.06038	+	12.2289i	−0.270952	+	0.469303i
$680$	4.93602	−	8.54944i	0.189288	−	0.327856i
$681$	13.2112	+	15.9103i	0.506255	+	0.609685i
$682$	0.109001	+	0.188794i	0.00417385	+	0.00722931i
$683$	−20.8274			−0.796938			−0.398469	−	0.917182i	$-0.630458\pi$
$683$	−20.8274			−0.796938			−0.398469	+	0.917182i	$0.630458\pi$
$684$	−0.129044	+	0.690173i	−0.00493414	+	0.0263894i
$685$	15.6740			0.598873
$686$	11.1323	+	19.2817i	0.425034	+	0.736180i
$687$	−11.4610	+	30.9910i	−0.437265	+	1.18238i
$688$	−11.6155	+	20.1187i	−0.442838	+	0.767019i
$689$	−4.41351	+	7.64443i	−0.168141	+	0.291229i
$690$	−5.97225	+	16.1492i	−0.227360	+	0.614789i
$691$	18.9207	+	32.7717i	0.719779	+	1.24669i	0.961087	+	0.276245i	$0.0890902\pi$
$691$	18.9207	+	32.7717i	0.719779	+	1.24669i	−0.241308	+	0.970449i	$0.577576\pi$
$692$	0.866826			0.0329518
$693$	−1.01643	+	5.43623i	−0.0386111	+	0.206505i
$694$	41.5206			1.57610
$695$	6.01656	+	10.4210i	0.228221	+	0.395291i
$696$	−29.6999	−	35.7677i	−1.12577	−	1.35577i
$697$	10.8719	−	18.8306i	0.411801	−	0.713261i
$698$	−2.10887	+	3.65266i	−0.0798218	+	0.138255i
$699$	30.3166	−	5.18469i	1.14668	−	0.196103i
$700$	0.0307407	+	0.0532445i	0.00116189	+	0.00201245i
$701$	8.41612			0.317872			0.158936	−	0.987289i	$-0.449194\pi$
$701$	8.41612			0.317872			0.158936	+	0.987289i	$0.449194\pi$
$702$	6.49842	−	3.61908i	0.245267	−	0.136593i
$703$	−46.6594			−1.75979
$704$	5.74384	+	9.94862i	0.216479	+	0.374953i
$705$	−3.61025	+	0.617418i	−0.135970	+	0.0232533i
$706$	−21.0863	+	36.5225i	−0.793592	+	1.37454i
$707$	2.32253	−	4.02274i	0.0873476	−	0.151291i
$708$	−0.222122	−	0.267502i	−0.00834786	−	0.0100534i
$709$	10.3699	+	17.9612i	0.389450	+	0.674547i	0.992376	−	0.123250i	$-0.0393318\pi$
$709$	10.3699	+	17.9612i	0.389450	+	0.674547i	−0.602926	+	0.797797i	$0.705998\pi$
$710$	−13.6082			−0.510708
$711$	3.68137	+	3.15426i	0.138062	+	0.118294i
$712$	−38.3990			−1.43906
$713$	0.358754	+	0.621381i	0.0134355	+	0.0232709i
$714$	−3.80236	+	10.2817i	−0.142300	+	0.384784i
$715$	0.736973	−	1.27648i	0.0275612	−	0.0477375i
$716$	−0.446019	+	0.772528i	−0.0166685	+	0.0288707i
$717$	7.34210	−	19.8533i	0.274196	−	0.741436i
$718$	−17.7252	−	30.7009i	−0.661498	−	1.14575i
$719$	−20.7856			−0.775173			−0.387587	−	0.921833i	$-0.626691\pi$
$719$	−20.7856			−0.775173			−0.387587	+	0.921833i	$0.626691\pi$
$720$	−11.5894	+	4.08341i	−0.431910	+	0.152180i
$721$	10.5856			0.394230
$722$	2.62565	+	4.54776i	0.0977165	+	0.169250i
$723$	1.53235	+	1.84541i	0.0569886	+	0.0686316i
$724$	−0.0204650	+	0.0354464i	−0.000760576	+	0.00131736i
$725$	4.80583	−	8.32394i	0.178484	−	0.309143i
$726$	−21.5737	+	3.68950i	−0.800676	+	0.136930i
$727$	−10.9963	−	19.0462i	−0.407831	−	0.706384i	0.586816	−	0.809721i	$-0.300381\pi$
$727$	−10.9963	−	19.0462i	−0.407831	−	0.706384i	−0.994646	+	0.103337i	$0.967048\pi$
$728$	−3.49274			−0.129450
$729$	14.2164	−	22.9541i	0.526535	−	0.850154i
$730$	−11.8093			−0.437082
$731$	−10.0251	−	17.3639i	−0.370790	−	0.642228i
$732$	−1.12865	+	0.193019i	−0.0417160	+	0.00713419i
$733$	−18.2052	+	31.5324i	−0.672425	+	1.16467i	0.304790	+	0.952420i	$0.401414\pi$
$733$	−18.2052	+	31.5324i	−0.672425	+	1.16467i	−0.977214	+	0.212254i	$0.931919\pi$
$734$	−7.13679	+	12.3613i	−0.263424	+	0.456263i
$735$	−6.01457	−	7.24336i	−0.221851	−	0.267176i
$736$	−0.965324	−	1.67199i	−0.0355823	−	0.0616304i
$737$	16.4341			0.605359
$738$	−24.9135	+	8.77805i	−0.917079	+	0.323125i
$739$	−51.0462			−1.87776			−0.938881	−	0.344241i	$-0.888136\pi$
$739$	−51.0462			−1.87776			−0.938881	+	0.344241i	$0.888136\pi$
$740$	0.240872	+	0.417202i	0.00885462	+	0.0153367i
$741$	2.86038	−	7.73457i	0.105079	−	0.284136i
$742$	−7.90184	+	13.6864i	−0.290086	+	0.502443i
$743$	23.4639	−	40.6407i	0.860808	−	1.49096i	−0.0103426	−	0.999947i	$-0.503292\pi$
$743$	23.4639	−	40.6407i	0.860808	−	1.49096i	0.871150	−	0.491016i	$-0.163374\pi$
$744$	−0.173345	+	0.468732i	−0.00635514	+	0.0171845i
$745$	2.30691	+	3.99569i	0.0845187	+	0.146391i
$746$	27.3289			1.00058
$747$	9.29775	+	7.96647i	0.340187	+	0.291478i
$748$	0.256134			0.00936517
$749$	10.5223	+	18.2251i	0.384476	+	0.665932i
$750$	−1.58392	−	1.90753i	−0.0578367	−	0.0696530i
$751$	11.3786	−	19.7083i	0.415210	−	0.719165i	−0.580240	−	0.814445i	$-0.697041\pi$
$751$	11.3786	−	19.7083i	0.415210	−	0.719165i	0.995451	+	0.0952800i	$0.0303746\pi$
$752$	4.33068	−	7.50095i	0.157923	−	0.273531i
$753$	38.8680	−	6.64713i	1.41643	−	0.242235i
$754$	−6.87948	−	11.9156i	−0.250536	−	0.433941i
$755$	4.09191			0.148920
$756$	0.279103	−	0.155437i	0.0101509	−	0.00565320i
$757$	−51.9029			−1.88644			−0.943222	−	0.332162i	$-0.892222\pi$
$757$	−51.9029			−1.88644			−0.943222	+	0.332162i	$0.892222\pi$
$758$	14.8292	+	25.6850i	0.538622	+	0.932920i
$759$	17.4751	−	2.98856i	0.634307	−	0.108478i
$760$	−6.64799	+	11.5147i	−0.241148	+	0.417681i
$761$	−10.0682	+	17.4386i	−0.364972	+	0.632149i	−0.988772	−	0.149435i	$-0.952255\pi$
$761$	−10.0682	+	17.4386i	−0.364972	+	0.632149i	0.623800	+	0.781584i	$0.285588\pi$
$762$	26.9101	+	32.4079i	0.974849	+	1.17401i
$763$	−10.8902	−	18.8624i	−0.394253	−	0.682866i
$764$	−0.849944			−0.0307499
$765$	1.94912	−	10.4245i	0.0704705	−	0.376900i
$766$	−47.8470			−1.72878
$767$	2.04187	+	3.53661i	0.0737275	+	0.127700i
$768$	0.708356	−	1.91542i	0.0255606	−	0.0691168i
$769$	−9.12677	+	15.8080i	−0.329120	+	0.570052i	−0.982337	−	0.187118i	$-0.940085\pi$
$769$	−9.12677	+	15.8080i	−0.329120	+	0.570052i	0.653218	+	0.757170i	$0.273419\pi$
$770$	1.31946	−	2.28537i	0.0475500	−	0.0823590i
$771$	−3.10428	+	8.39410i	−0.111798	+	0.302306i
$772$	−0.192850	−	0.334026i	−0.00694082	−	0.0120218i
$773$	24.9928			0.898929			0.449465	−	0.893298i	$-0.351615\pi$
$773$	24.9928			0.898929			0.449465	+	0.893298i	$0.351615\pi$
$774$	−4.47661	+	23.9424i	−0.160908	+	0.860592i
$775$	−0.103321			−0.00371141
$776$	15.7645	+	27.3050i	0.565914	+	0.980192i
$777$	13.5622	+	16.3331i	0.486543	+	0.585945i
$778$	−5.31967	+	9.21394i	−0.190719	+	0.330336i
$779$	−14.6426	+	25.3617i	−0.524625	+	0.908677i
$780$	−0.0839245	+	0.0143526i	−0.00300498	+	0.000513906i
$781$	7.00593	+	12.1346i	0.250692	+	0.434211i
$782$	35.1417			1.25666
$783$	−42.8612	−	25.6375i	−1.53174	−	0.916210i
$784$	22.2642			0.795149
$785$	−5.07740	−	8.79432i	−0.181220	−	0.313883i
$786$	0.913417	−	0.156211i	0.0325805	−	0.00557186i
$787$	−27.4424	+	47.5316i	−0.978216	+	1.69432i	−0.309329	+	0.950955i	$0.600104\pi$
$787$	−27.4424	+	47.5316i	−0.978216	+	1.69432i	−0.668887	+	0.743364i	$0.733229\pi$
$788$	0.0909655	−	0.157557i	0.00324051	−	0.00561273i
$789$	0.427954	+	0.515387i	0.0152356	+	0.0183483i
$790$	−1.15661	−	2.00331i	−0.0411503	−	0.0712745i
$791$	−6.75170			−0.240063
$792$	9.37716	+	8.03451i	0.333203	+	0.285494i
$793$	13.4484			0.477566
$794$	−1.29016	−	2.23463i	−0.0457862	−	0.0793041i
$795$	5.30307	−	14.3397i	0.188080	−	0.508576i
$796$	−0.130080	+	0.225305i	−0.00461056	+	0.00798573i
$797$	−4.76410	+	8.25167i	−0.168753	+	0.292289i	−0.937982	−	0.346685i	$-0.887307\pi$
$797$	−4.76410	+	8.25167i	−0.168753	+	0.292289i	0.769229	+	0.638974i	$0.220641\pi$
$798$	5.12115	−	13.8478i	0.181287	−	0.490206i
$799$	3.73769	+	6.47387i	0.132230	+	0.229029i
$800$	0.278013			0.00982925
$801$	−38.9063	+	13.7083i	−1.37469	+	0.484359i
$802$	36.6663			1.29473
$803$	6.07978	+	10.5305i	0.214551	+	0.371613i
$804$	−0.606456	−	0.730357i	−0.0213881	−	0.0257577i
$805$	4.34275	−	7.52186i	0.153062	−	0.265111i
$806$	−0.0739515	+	0.128088i	−0.00260483	+	0.00451170i
$807$	2.60233	−	0.445045i	0.0916064	−	0.0156663i
$808$	−5.18578	−	8.98204i	−0.182435	−	0.315987i
$809$	35.3596			1.24318			0.621589	−	0.783344i	$-0.286488\pi$
$809$	35.3596			1.24318			0.621589	+	0.783344i	$0.286488\pi$
$810$	−10.0378	+	8.07610i	−0.352694	+	0.283765i
$811$	−0.112318			−0.00394404			−0.00197202	−	0.999998i	$-0.500628\pi$
$811$	−0.112318			−0.00394404			−0.00197202	+	0.999998i	$0.500628\pi$
$812$	−0.295469	−	0.511768i	−0.0103689	−	0.0179595i
$813$	3.38226	−	0.578428i	0.118621	−	0.0202864i
$814$	10.3387	−	17.9072i	0.362373	−	0.627648i
$815$	−4.04754	+	7.01055i	−0.141779	+	0.245569i
$816$	16.0211	+	19.2943i	0.560851	+	0.675435i
$817$	13.5021	+	23.3863i	0.472378	+	0.818183i
$818$	−17.9519			−0.627675
$819$	−3.53889	+	1.24690i	−0.123659	+	0.0435701i
$820$	0.302360			0.0105589
$821$	−21.5970	−	37.4072i	−0.753742	−	1.30552i	−0.945997	−	0.324174i	$-0.894914\pi$
$821$	−21.5970	−	37.4072i	−0.753742	−	1.30552i	0.192256	−	0.981345i	$-0.438420\pi$
$822$	−13.4797	+	36.4496i	−0.470159	+	1.27133i
$823$	14.2883	−	24.7481i	0.498060	−	0.862664i	−0.501938	−	0.864904i	$-0.667379\pi$
$823$	14.2883	−	24.7481i	0.498060	−	0.862664i	0.999997	+	0.00223923i	$0.000712770\pi$
$824$	11.8179	−	20.4692i	0.411696	−	0.713079i
$825$	−0.885512	+	2.39446i	−0.0308296	+	0.0833643i
$826$	3.65570	+	6.33187i	0.127198	+	0.220314i
$827$	−6.91464			−0.240445			−0.120223	−	0.992747i	$-0.538361\pi$
$827$	−6.91464			−0.240445			−0.120223	+	0.992747i	$0.538361\pi$
$828$	−0.777688	−	0.666337i	−0.0270265	−	0.0231568i
$829$	44.7141			1.55299			0.776493	−	0.630126i	$-0.216997\pi$
$829$	44.7141			1.55299			0.776493	+	0.630126i	$0.216997\pi$
$830$	−2.92116	−	5.05960i	−0.101395	−	0.175621i
$831$	6.51149	+	7.84182i	0.225881	+	0.272030i
$832$	−3.89691	+	6.74965i	−0.135101	+	0.234002i
$833$	−9.60781	+	16.6412i	−0.332891	+	0.576584i
$834$	−29.4081	+	5.02931i	−1.01832	+	0.174151i
$835$	4.26053	+	7.37946i	0.147442	+	0.255377i
$836$	−0.344969			−0.0119310
$837$	−0.00829992	+	0.536808i	−0.000286887	+	0.0185548i
$838$	−31.6459			−1.09319
$839$	11.6590	+	20.1939i	0.402513	+	0.697172i	0.994028	−	0.109121i	$-0.0348036\pi$
$839$	11.6590	+	20.1939i	0.402513	+	0.697172i	−0.591516	+	0.806293i	$0.701470\pi$
$840$	5.96303	−	1.01979i	0.205744	−	0.0351860i
$841$	−31.6920	+	54.8921i	−1.09283	+	1.89283i
$842$	−24.4583	+	42.3630i	−0.842888	+	1.45993i
$843$	−15.8158	−	19.0470i	−0.544725	−	0.656014i
$844$	0.489769	+	0.848304i	0.0168585	+	0.0291998i
$845$	1.00000			0.0344010
$846$	1.66903	−	8.92655i	0.0573826	−	0.306901i
$847$	11.0406			0.379360
$848$	18.0773	+	31.3108i	0.620777	+	1.07522i
$849$	−8.29149	+	22.4205i	−0.284563	+	0.769469i
$850$	−2.53020	+	4.38243i	−0.0867851	+	0.150316i
$851$	34.0280	−	58.9382i	1.16646	−	2.02038i
$852$	0.280747	−	0.759149i	0.00961822	−	0.0260080i
$853$	4.00953	+	6.94471i	0.137284	+	0.237782i	0.926468	−	0.376375i	$-0.122829\pi$
$853$	4.00953	+	6.94471i	0.137284	+	0.237782i	−0.789184	+	0.614157i	$0.789496\pi$
$854$	24.0776			0.823920
$855$	−2.62514	+	14.0401i	−0.0897777	+	0.480161i
$856$	46.9887			1.60604
$857$	−3.28883	−	5.69642i	−0.112344	−	0.194586i	0.804371	−	0.594128i	$-0.202503\pi$
$857$	−3.28883	−	5.69642i	−0.112344	−	0.194586i	−0.916715	+	0.399542i	$0.869169\pi$
$858$	2.33462	+	2.81159i	0.0797026	+	0.0959861i
$859$	−2.88776	+	5.00175i	−0.0985292	+	0.170658i	−0.911076	−	0.412238i	$-0.864747\pi$
$859$	−2.88776	+	5.00175i	−0.0985292	+	0.170658i	0.812547	+	0.582896i	$0.198080\pi$
$860$	0.139405	−	0.241456i	0.00475367	−	0.00823360i
$861$	13.1339	−	2.24614i	0.447603	−	0.0765481i
$862$	−6.26312	−	10.8480i	−0.213323	−	0.369486i
$863$	14.4279			0.491131			0.245565	−	0.969380i	$-0.421026\pi$
$863$	14.4279			0.491131			0.245565	+	0.969380i	$0.421026\pi$
$864$	0.0223331	−	1.44443i	0.000759789	−	0.0491404i
$865$	17.6337			0.599565
$866$	7.17379	+	12.4254i	0.243775	+	0.422231i
$867$	7.68839	−	1.31485i	0.261111	−	0.0446548i
$868$	−0.00317617	+	0.00550129i	−0.000107806	+	0.000186726i
$869$	−1.19092	+	2.06273i	−0.0403991	+	0.0699732i
$870$	15.2241	+	18.3345i	0.516147	+	0.621597i
$871$	5.57487	+	9.65596i	0.188897	+	0.327180i
$872$	−48.6319			−1.64688
$873$	25.7206	+	22.0379i	0.870510	+	0.745868i
$874$	−47.3300			−1.60096
$875$	0.625355	+	1.08315i	0.0211408	+	0.0366170i
$876$	0.243633	−	0.658794i	0.00823161	−	0.0222586i
$877$	−26.8130	+	46.4414i	−0.905410	+	1.56822i	−0.0850435	+	0.996377i	$0.527103\pi$
$877$	−26.8130	+	46.4414i	−0.905410	+	1.56822i	−0.820366	+	0.571838i	$0.806230\pi$
$878$	−24.3627	+	42.1974i	−0.822200	+	1.42409i
$879$	−10.3181	+	27.9006i	−0.348022	+	0.941064i
$880$	−3.01857	−	5.22831i	−0.101756	−	0.176246i
$881$	54.2756			1.82859			0.914297	−	0.405046i	$-0.132744\pi$
$881$	54.2756			1.82859			0.914297	+	0.405046i	$0.132744\pi$
$882$	22.0169	−	7.75745i	0.741346	−	0.261207i
$883$	−8.60336			−0.289526			−0.144763	−	0.989466i	$-0.546242\pi$
$883$	−8.60336			−0.289526			−0.144763	+	0.989466i	$0.546242\pi$
$884$	0.0868870	+	0.150493i	0.00292233	+	0.00506162i
$885$	−4.51860	−	5.44177i	−0.151891	−	0.182923i
$886$	−19.3579	+	33.5288i	−0.650340	+	1.12642i
$887$	−7.28070	+	12.6106i	−0.244462	+	0.423421i	−0.961980	−	0.273119i	$-0.911945\pi$
$887$	−7.28070	+	12.6106i	−0.244462	+	0.423421i	0.717518	+	0.696540i	$0.245278\pi$
$888$	46.7239	−	7.99063i	1.56795	−	0.268148i
$889$	−10.6245	−	18.4021i	−0.356333	−	0.617186i
$890$	19.6833			0.659785
$891$	12.3693	+	4.79305i	0.414389	+	0.160573i
$892$	0.465252			0.0155778
$893$	−5.03404	−	8.71922i	−0.168458	−	0.291778i
$894$	−11.2758	+	1.92837i	−0.377121	+	0.0644945i
$895$	−9.07331	+	15.7154i	−0.303287	+	0.525309i
$896$	−7.32465	+	12.6867i	−0.244699	+	0.423832i
$897$	7.68396	+	9.25381i	0.256560	+	0.308976i
$898$	−17.6173	−	30.5141i	−0.587899	−	1.01827i
$899$	0.993088			0.0331213
$900$	0.139091	−	0.0490074i	0.00463636	−	0.00163358i
$901$	−31.2041			−1.03956
$902$	−6.48898	−	11.2392i	−0.216059	−	0.374226i
$903$	4.26176	−	11.5240i	0.141823	−	0.383494i
$904$	−7.53766	+	13.0556i	−0.250699	+	0.434223i
$905$	−0.416317	+	0.721082i	−0.0138388	+	0.0239696i
$906$	−3.51906	+	9.51567i	−0.116913	+	0.316137i
$907$	−14.5017	−	25.1176i	−0.481520	−	0.834017i	0.518255	−	0.855226i	$-0.326582\pi$
$907$	−14.5017	−	25.1176i	−0.481520	−	0.834017i	−0.999775	+	0.0212090i	$0.993248\pi$
$908$	0.586927			0.0194778
$909$	−8.46085	−	7.24941i	−0.280629	−	0.240448i
$910$	1.79038			0.0593504
$911$	2.15640	+	3.73500i	0.0714448	+	0.123746i	0.899535	−	0.436849i	$-0.143906\pi$
$911$	2.15640	+	3.73500i	0.0714448	+	0.123746i	−0.828090	+	0.560595i	$0.810572\pi$
$912$	−21.5778	−	25.9862i	−0.714511	−	0.860489i
$913$	−3.00781	+	5.20967i	−0.0995439	+	0.172415i
$914$	−12.4882	+	21.6302i	−0.413074	+	0.715464i
$915$	−22.9599	+	3.92656i	−0.759032	+	0.129808i
$916$	0.468887	+	0.812137i	0.0154925	+	0.0268338i
$917$	−0.467452			−0.0154366
$918$	22.5658	+	13.4978i	0.744783	+	0.445493i
$919$	−58.1294			−1.91751			−0.958757	−	0.284228i	$-0.908263\pi$
$919$	−58.1294			−1.91751			−0.958757	+	0.284228i	$0.908263\pi$
$920$	−9.69657	−	16.7949i	−0.319686	−	0.553713i
$921$	1.27722	−	0.218427i	0.0420857	−	0.00719741i
$922$	18.7686	−	32.5082i	0.618112	−	1.07060i
$923$	−4.75318	+	8.23275i	−0.156453	+	0.270984i
$924$	0.100270	+	0.120756i	0.00329865	+	0.00397258i
$925$	4.90002	+	8.48709i	0.161112	+	0.279054i
$926$	39.2910			1.29118
$927$	4.66661	−	24.9586i	0.153272	−	0.819748i
$928$	−2.67217			−0.0877182
$929$	−2.36408	−	4.09471i	−0.0775630	−	0.134343i	0.824635	−	0.565665i	$-0.191381\pi$
$929$	−2.36408	−	4.09471i	−0.0775630	−	0.134343i	−0.902198	+	0.431322i	$0.858047\pi$
$930$	0.0888566	−	0.240271i	0.00291372	−	0.00787881i
$931$	12.9401	−	22.4129i	0.424095	−	0.734554i
$932$	0.436453	−	0.755959i	0.0142965	−	0.0247623i
$933$	0.849125	−	2.29607i	0.0277991	−	0.0751698i
$934$	14.7483	+	25.5448i	0.482580	+	0.835853i
$935$	5.21049			0.170401
$936$	−1.53975	+	8.23511i	−0.0503284	+	0.269173i
$937$	18.4570			0.602965			0.301482	−	0.953472i	$-0.402519\pi$
$937$	18.4570			0.602965			0.301482	+	0.953472i	$0.402519\pi$
$938$	9.98111	+	17.2878i	0.325895	+	0.564466i
$939$	−10.2966	−	12.4003i	−0.336018	−	0.404667i
$940$	−0.0519750	+	0.0900233i	−0.00169524	+	0.00293624i
$941$	−0.0981277	+	0.169962i	−0.00319887	+	0.00554061i	−0.867620	−	0.497227i	$-0.834352\pi$
$941$	−0.0981277	+	0.169962i	−0.00319887	+	0.00554061i	0.864422	+	0.502768i	$0.167685\pi$
$942$	24.8176	−	4.24426i	0.808602	−	0.138285i
$943$	−21.3572	−	36.9918i	−0.695487	−	1.20462i
$944$	16.7265			0.544403
$945$	5.67776	−	3.16204i	0.184697	−	0.102861i
$946$	−11.9671			−0.389085
$947$	7.66451	+	13.2753i	0.249063	+	0.431390i	0.963266	−	0.268549i	$-0.0865440\pi$
$947$	7.66451	+	13.2753i	0.249063	+	0.431390i	−0.714203	+	0.699939i	$0.753211\pi$
$948$	0.135618	−	0.0231932i	0.00440467	−	0.000753279i
$949$	−4.12483	+	7.14442i	−0.133898	+	0.231918i
$950$	3.40775	−	5.90240i	0.110562	−	0.191499i
$951$	29.0886	+	35.0315i	0.943261	+	1.13597i
$952$	−6.17353	−	10.6929i	−0.200085	−	0.346558i
$953$	−3.12675			−0.101285			−0.0506427	−	0.998717i	$-0.516127\pi$
$953$	−3.12675			−0.101285			−0.0506427	+	0.998717i	$0.516127\pi$
$954$	28.7860	+	24.6644i	0.931982	+	0.798538i
$955$	−17.2903			−0.559501
$956$	−0.300376	−	0.520267i	−0.00971486	−	0.0168266i
$957$	8.51124	−	23.0147i	0.275129	−	0.743959i
$958$	−12.0972	+	20.9530i	−0.390844	+	0.676961i
$959$	9.80181	−	16.9772i	0.316517	−	0.548224i
$960$	4.68234	−	12.6612i	0.151122	−	0.408639i
$961$	15.4947	+	26.8375i	0.499828	+	0.865727i
$962$	14.0286			0.452302
$963$	47.6095	−	16.7748i	1.53420	−	0.540560i
$964$	0.0680767			0.00219260
$965$	−3.92312	−	6.79504i	−0.126290	−	0.218740i
$966$	13.7572	+	16.5678i	0.442630	+	0.533060i
$967$	−16.9686	+	29.3905i	−0.545675	+	0.945136i	0.452890	+	0.891567i	$0.350393\pi$
$967$	−16.9686	+	29.3905i	−0.545675	+	0.945136i	−0.998564	+	0.0535694i	$0.982940\pi$
$968$	12.3258	−	21.3490i	0.396168	−	0.686183i
$969$	28.7348	−	4.91417i	0.923095	−	0.157866i
$970$	−8.08089	−	13.9965i	−0.259462	−	0.449401i
$971$	−28.0546			−0.900314			−0.450157	−	0.892949i	$-0.648632\pi$
$971$	−28.0546			−0.900314			−0.450157	+	0.892949i	$0.648632\pi$
$972$	−0.243446	−	0.726587i	−0.00780853	−	0.0233053i
$973$	15.0499			0.482479
$974$	2.66905	+	4.62293i	0.0855220	+	0.148128i
$975$	−1.70726	+	0.291973i	−0.0546762	+	0.00935062i
$976$	27.5416	−	47.7034i	0.881585	−	1.52695i
$977$	−18.2048	+	31.5316i	−0.582422	+	1.00878i	0.412769	+	0.910836i	$0.364562\pi$
$977$	−18.2048	+	31.5316i	−0.582422	+	1.00878i	−0.995191	+	0.0979492i	$0.968772\pi$
$978$	−12.8220	−	15.4416i	−0.410002	−	0.493767i
$979$	−10.1336	−	17.5518i	−0.323870	−	0.560959i
$980$	−0.267205			−0.00853557
$981$	−49.2744	+	17.3614i	−1.57321	+	0.554307i
$982$	30.0074			0.957574
$983$	−3.71256	−	6.43033i	−0.118412	−	0.205096i	0.800726	−	0.599030i	$-0.204447\pi$
$983$	−3.71256	−	6.43033i	−0.118412	−	0.205096i	−0.919139	+	0.393934i	$0.871114\pi$
$984$	10.3195	−	27.9044i	0.328974	−	0.889559i
$985$	1.85050	−	3.20516i	0.0589618	−	0.102125i
$986$	24.3194	−	42.1224i	0.774488	−	1.34145i
$987$	−1.58893	+	4.29653i	−0.0505763	+	0.136760i
$988$	−0.117022	−	0.202688i	−0.00372297	−	0.00644838i
$989$	−39.3875			−1.25245
$990$	−4.80672	−	4.11848i	−0.152768	−	0.130894i
$991$	15.5263			0.493209			0.246605	−	0.969116i	$-0.420685\pi$
$991$	15.5263			0.493209			0.246605	+	0.969116i	$0.420685\pi$
$992$	0.0143623	+	0.0248763i	0.000456004	+	0.000789822i
$993$	−14.3467	−	17.2778i	−0.455279	−	0.548294i
$994$	−8.50997	+	14.7397i	−0.269920	+	0.467515i
$995$	−2.64620	+	4.58335i	−0.0838902	+	0.145302i
$996$	0.342521	−	0.0585772i	0.0108532	−	0.00185609i
$997$	−10.2376	−	17.7321i	−0.324229	−	0.561582i	0.657127	−	0.753780i	$-0.271772\pi$
$997$	−10.2376	−	17.7321i	−0.324229	−	0.561582i	−0.981356	+	0.192198i	$0.938438\pi$
$998$	14.7780			0.467790
$999$	44.4886	−	24.7764i	1.40756	−	0.783892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.f.391.6	yes	16
3.2	odd	2		1755.2.i.e.1171.3		16
9.2	odd	6		1755.2.i.e.586.3		16
9.4	even	3		5265.2.a.bb.1.3		8
9.5	odd	6		5265.2.a.be.1.6		8
9.7	even	3	inner	585.2.i.f.196.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.6	✓	16	9.7	even	3	inner
585.2.i.f.391.6	yes	16	1.1	even	1	trivial
1755.2.i.e.586.3		16	9.2	odd	6
1755.2.i.e.1171.3		16	3.2	odd	2
5265.2.a.bb.1.3		8	9.4	even	3
5265.2.a.be.1.6		8	9.5	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.715744 + 1.23970i) q^{2} +(-1.70726 + 0.291973i) q^{3} +(-0.0245786 + 0.0425715i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.58392 - 1.90753i) q^{6} +(0.625355 + 1.08315i) q^{7} +2.79261 q^{8} +(2.82950 - 0.996950i) q^{9} +O(q^{10})\)	\(q+(0.715744 + 1.23970i) q^{2} +(-1.70726 + 0.291973i) q^{3} +(-0.0245786 + 0.0425715i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.58392 - 1.90753i) q^{6} +(0.625355 + 1.08315i) q^{7} +2.79261 q^{8} +(2.82950 - 0.996950i) q^{9} -1.43149 q^{10} +(0.736973 + 1.27648i) q^{11} +(0.0295325 - 0.0798570i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.895188 + 1.55051i) q^{14} +(0.600776 - 1.62452i) q^{15} +(2.04795 + 3.54715i) q^{16} -3.53506 q^{17} +(3.26112 + 2.79419i) q^{18} +4.76114 q^{19} +(-0.0245786 - 0.0425715i) q^{20} +(-1.38390 - 1.66663i) q^{21} +(-1.05497 + 1.82726i) q^{22} +(-3.47223 + 6.01407i) q^{23} +(-4.76772 + 0.815366i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.43149 q^{26} +(-4.53963 + 2.52820i) q^{27} -0.0614815 q^{28} +(4.80583 + 8.32394i) q^{29} +(2.44393 - 0.417956i) q^{30} +(0.0516606 - 0.0894788i) q^{31} +(-0.139007 + 0.240766i) q^{32} +(-1.63090 - 1.96410i) q^{33} +(-2.53020 - 4.38243i) q^{34} -1.25071 q^{35} +(-0.0271037 + 0.144960i) q^{36} -9.80005 q^{37} +(3.40775 + 5.90240i) q^{38} +(0.600776 - 1.62452i) q^{39} +(-1.39630 + 2.41847i) q^{40} +(-3.07544 + 5.32682i) q^{41} +(1.07561 - 2.90850i) q^{42} +(2.83590 + 4.91192i) q^{43} -0.0724552 q^{44} +(-0.551367 + 2.94890i) q^{45} -9.94090 q^{46} +(-1.05732 - 1.83133i) q^{47} +(-4.53206 - 5.45798i) q^{48} +(2.71786 - 4.70748i) q^{49} +(0.715744 - 1.23970i) q^{50} +(6.03528 - 1.03214i) q^{51} +(-0.0245786 - 0.0425715i) q^{52} +8.82702 q^{53} +(-6.38343 - 3.81826i) q^{54} -1.47395 q^{55} +(1.74637 + 3.02480i) q^{56} +(-8.12852 + 1.39012i) q^{57} +(-6.87948 + 11.9156i) q^{58} +(2.04187 - 3.53661i) q^{59} +(0.0543920 + 0.0655044i) q^{60} +(-6.72419 - 11.6466i) q^{61} +0.147903 q^{62} +(2.84929 + 2.44132i) q^{63} +7.79382 q^{64} +(-0.500000 - 0.866025i) q^{65} +(1.26760 - 3.42764i) q^{66} +(5.57487 - 9.65596i) q^{67} +(0.0868870 - 0.150493i) q^{68} +(4.17206 - 11.2814i) q^{69} +(-0.895188 - 1.55051i) q^{70} +9.50636 q^{71} +(7.90169 - 2.78409i) q^{72} +8.24967 q^{73} +(-7.01432 - 12.1492i) q^{74} +(1.10649 + 1.33255i) q^{75} +(-0.117022 + 0.202688i) q^{76} +(-0.921739 + 1.59650i) q^{77} +(2.44393 - 0.417956i) q^{78} +(0.807978 + 1.39946i) q^{79} -4.09590 q^{80} +(7.01218 - 5.64175i) q^{81} -8.80490 q^{82} +(2.04065 + 3.53451i) q^{83} +(0.104965 - 0.0179509i) q^{84} +(1.76753 - 3.06145i) q^{85} +(-4.05955 + 7.03135i) q^{86} +(-10.6352 - 12.8080i) q^{87} +(2.05808 + 3.56469i) q^{88} -13.7502 q^{89} +(-4.05040 + 1.42712i) q^{90} -1.25071 q^{91} +(-0.170685 - 0.295635i) q^{92} +(-0.0620729 + 0.167847i) q^{93} +(1.51354 - 2.62153i) q^{94} +(-2.38057 + 4.12327i) q^{95} +(0.167024 - 0.451638i) q^{96} +(5.64510 + 9.77759i) q^{97} +7.78118 q^{98} +(3.35785 + 2.87706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

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