LMFDB - Embedded newform 966.2.l.c.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.43165 + 0.974877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.723421 + 1.25300i) q^{5} +(1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} -1.00000i q^{8} +(1.09923 - 2.79136i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.43165 + 0.974877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.723421 + 1.25300i) q^{5} +(1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} -1.00000i q^{8} +(1.09923 - 2.79136i) q^{9} +(1.25300 - 0.723421i) q^{10} +(2.11952 - 1.22371i) q^{11} +(-1.56009 - 0.752405i) q^{12} +3.42072i q^{13} +(0.747214 + 2.53804i) q^{14} +(-0.185839 - 2.49910i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.94087 - 3.36168i) q^{17} +(-2.34764 + 1.86777i) q^{18} +(6.23947 + 3.60236i) q^{19} -1.44684 q^{20} +(4.52179 + 0.743914i) q^{21} -2.44742 q^{22} +(0.866025 + 0.500000i) q^{23} +(0.974877 + 1.43165i) q^{24} +(1.45333 + 2.51723i) q^{25} +(1.71036 - 2.96243i) q^{26} +(1.14752 + 5.06786i) q^{27} +(0.621916 - 2.57162i) q^{28} -6.88037i q^{29} +(-1.08861 + 2.25721i) q^{30} +(2.91493 - 1.68294i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.84145 + 3.81819i) q^{33} +3.88173i q^{34} +(3.67215 - 1.08110i) q^{35} +(2.96700 - 0.443719i) q^{36} +(-3.58636 + 6.21176i) q^{37} +(-3.60236 - 6.23947i) q^{38} +(-3.33478 - 4.89727i) q^{39} +(1.25300 + 0.723421i) q^{40} -9.80512 q^{41} +(-3.54403 - 2.90514i) q^{42} -8.24338 q^{43} +(2.11952 + 1.22371i) q^{44} +(2.70237 + 3.39666i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-5.75052 + 9.96019i) q^{47} +(-0.128444 - 1.72728i) q^{48} +(0.343100 + 6.99159i) q^{49} -2.90665i q^{50} +(6.05586 + 2.92063i) q^{51} +(-2.96243 + 1.71036i) q^{52} +(-3.27867 + 1.89294i) q^{53} +(1.54015 - 4.96266i) q^{54} +3.54102i q^{55} +(-1.82440 + 1.91613i) q^{56} +(-12.4446 + 0.925404i) q^{57} +(-3.44018 + 5.95857i) q^{58} +(5.49526 + 9.51808i) q^{59} +(2.07137 - 1.41049i) q^{60} +(1.89515 + 1.09417i) q^{61} -3.36587 q^{62} +(-7.19884 + 3.34317i) q^{63} -1.00000 q^{64} +(-4.28617 - 2.47462i) q^{65} +(3.50384 - 2.38593i) q^{66} +(1.28247 + 2.22130i) q^{67} +(1.94087 - 3.36168i) q^{68} +(-1.72728 + 0.128444i) q^{69} +(-3.72072 - 0.899813i) q^{70} -12.4084i q^{71} +(-2.79136 - 1.09923i) q^{72} +(-2.08792 + 1.20546i) q^{73} +(6.21176 - 3.58636i) q^{74} +(-4.53464 - 2.18698i) q^{75} +7.20471i q^{76} +(-6.29382 - 1.52209i) q^{77} +(0.439373 + 5.90855i) q^{78} +(-5.93001 + 10.2711i) q^{79} +(-0.723421 - 1.25300i) q^{80} +(-6.58339 - 6.13669i) q^{81} +(8.49149 + 4.90256i) q^{82} +13.5344 q^{83} +(1.61665 + 4.28794i) q^{84} +5.61625 q^{85} +(7.13898 + 4.12169i) q^{86} +(6.70751 + 9.85026i) q^{87} +(-1.22371 - 2.11952i) q^{88} +(-4.34273 + 7.52183i) q^{89} +(-0.641991 - 4.29278i) q^{90} +(6.24078 - 6.55455i) q^{91} +1.00000i q^{92} +(-2.53250 + 5.25107i) q^{93} +(9.96019 - 5.75052i) q^{94} +(-9.02752 + 5.21204i) q^{95} +(-0.752405 + 1.56009i) q^{96} +3.37559i q^{97} +(3.19866 - 6.22644i) q^{98} +(-1.08596 - 7.26149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.43165	+	0.974877i	−0.826562	+	0.562845i
$3$	−1.43165	+	0.974877i	−0.826562	+	0.562845i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.723421	+	1.25300i	−0.323524	+	0.560359i	−0.981212	−	0.192930i	$-0.938201\pi$
$5$	−0.723421	+	1.25300i	−0.323524	+	0.560359i	0.657689	+	0.753290i	$0.271534\pi$
$6$	1.72728	−	0.128444i	0.705160	−	0.0524372i
$7$	−1.91613	−	1.82440i	−0.724229	−	0.689560i
$7$	−1.91613	−	1.82440i	−0.724229	−	0.689560i
$8$		−	1.00000i		−	0.353553i
$9$	1.09923	−	2.79136i	0.366410	−	0.930453i
$10$	1.25300	−	0.723421i	0.396234	−	0.228766i
$11$	2.11952	−	1.22371i	0.639061	−	0.368962i	−0.145192	−	0.989403i	$-0.546380\pi$
$11$	2.11952	−	1.22371i	0.639061	−	0.368962i	0.784253	+	0.620442i	$0.213047\pi$
$12$	−1.56009	−	0.752405i	−0.450360	−	0.217201i
$13$			3.42072i			0.948738i	0.880326	+	0.474369i	$0.157324\pi$
$13$			3.42072i			0.948738i	−0.880326	+	0.474369i	$0.842676\pi$
$14$	0.747214	+	2.53804i	0.199701	+	0.678321i
$15$	−0.185839	−	2.49910i	−0.0479833	−	0.645265i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.94087	−	3.36168i	−0.470729	−	0.815327i	0.528710	−	0.848802i	$-0.322676\pi$
$17$	−1.94087	−	3.36168i	−0.470729	−	0.815327i	−0.999440	+	0.0334756i	$0.989342\pi$
$18$	−2.34764	+	1.86777i	−0.553344	+	0.440239i
$19$	6.23947	+	3.60236i	1.43143	+	0.826437i	0.997230	−	0.0743785i	$-0.0236973\pi$
$19$	6.23947	+	3.60236i	1.43143	+	0.826437i	0.434201	+	0.900816i	$0.357031\pi$
$20$	−1.44684			−0.323524
$21$	4.52179	+	0.743914i	0.986736	+	0.162335i
$22$	−2.44742			−0.521791
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	0.974877	+	1.43165i	0.198996	+	0.292234i
$25$	1.45333	+	2.51723i	0.290665	+	0.503447i
$26$	1.71036	−	2.96243i	0.335430	−	0.580981i
$27$	1.14752	+	5.06786i	0.220841	+	0.975310i
$28$	0.621916	−	2.57162i	0.117531	−	0.485990i
$29$		−	6.88037i		−	1.27765i	−0.769351	−	0.638826i	$-0.779420\pi$
$29$		−	6.88037i		−	1.27765i	0.769351	−	0.638826i	$-0.220580\pi$
$30$	−1.08861	+	2.25721i	−0.198752	+	0.412107i
$31$	2.91493	−	1.68294i	0.523537	−	0.302264i	−0.214843	−	0.976649i	$-0.568924\pi$
$31$	2.91493	−	1.68294i	0.523537	−	0.302264i	0.738381	+	0.674384i	$0.235591\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.84145	+	3.81819i	−0.320555	+	0.664662i
$34$			3.88173i			0.665711i
$35$	3.67215	−	1.08110i	0.620706	−	0.182739i
$36$	2.96700	−	0.443719i	0.494501	−	0.0739532i
$37$	−3.58636	+	6.21176i	−0.589594	+	1.02121i	0.404691	+	0.914453i	$0.367379\pi$
$37$	−3.58636	+	6.21176i	−0.589594	+	1.02121i	−0.994285	+	0.106754i	$0.965954\pi$
$38$	−3.60236	−	6.23947i	−0.584379	−	1.01217i
$39$	−3.33478	−	4.89727i	−0.533993	−	0.784191i
$40$	1.25300	+	0.723421i	0.198117	+	0.114383i
$41$	−9.80512			−1.53130			−0.765652	−	0.643255i	$-0.777583\pi$
$41$	−9.80512			−1.53130			−0.765652	+	0.643255i	$0.777583\pi$
$42$	−3.54403	−	2.90514i	−0.546856	−	0.448273i
$43$	−8.24338			−1.25710			−0.628552	−	0.777768i	$-0.716352\pi$
$43$	−8.24338			−1.25710			−0.628552	+	0.777768i	$0.716352\pi$
$44$	2.11952	+	1.22371i	0.319530	+	0.184481i
$45$	2.70237	+	3.39666i	0.402846	+	0.506345i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−5.75052	+	9.96019i	−0.838799	+	1.45284i	0.0521006	+	0.998642i	$0.483408\pi$
$47$	−5.75052	+	9.96019i	−0.838799	+	1.45284i	−0.890900	+	0.454200i	$0.849925\pi$
$48$	−0.128444	−	1.72728i	−0.0185393	−	0.249312i
$49$	0.343100	+	6.99159i	0.0490143	+	0.998798i
$50$		−	2.90665i		−	0.411062i
$51$	6.05586	+	2.92063i	0.847990	+	0.408970i
$52$	−2.96243	+	1.71036i	−0.410816	+	0.237185i
$53$	−3.27867	+	1.89294i	−0.450360	+	0.260015i	−0.707982	−	0.706230i	$-0.750394\pi$
$53$	−3.27867	+	1.89294i	−0.450360	+	0.260015i	0.257622	+	0.966246i	$0.417061\pi$
$54$	1.54015	−	4.96266i	0.209587	−	0.675332i
$55$			3.54102i			0.477471i
$56$	−1.82440	+	1.91613i	−0.243796	+	0.256053i
$57$	−12.4446	+	0.925404i	−1.64832	+	0.122573i
$58$	−3.44018	+	5.95857i	−0.451718	+	0.782399i
$59$	5.49526	+	9.51808i	0.715422	+	1.23915i	0.962796	+	0.270228i	$0.0870990\pi$
$59$	5.49526	+	9.51808i	0.715422	+	1.23915i	−0.247374	+	0.968920i	$0.579568\pi$
$60$	2.07137	−	1.41049i	0.267412	−	0.182094i
$61$	1.89515	+	1.09417i	0.242649	+	0.140093i	0.616394	−	0.787438i	$-0.288593\pi$
$61$	1.89515	+	1.09417i	0.242649	+	0.140093i	−0.373745	+	0.927532i	$0.621926\pi$
$62$	−3.36587			−0.427467
$63$	−7.19884	+	3.34317i	−0.906968	+	0.421199i
$64$	−1.00000			−0.125000
$65$	−4.28617	−	2.47462i	−0.531634	−	0.306939i
$66$	3.50384	−	2.38593i	0.431293	−	0.293688i
$67$	1.28247	+	2.22130i	0.156679	+	0.271375i	0.933669	−	0.358137i	$-0.116588\pi$
$67$	1.28247	+	2.22130i	0.156679	+	0.271375i	−0.776990	+	0.629512i	$0.783255\pi$
$68$	1.94087	−	3.36168i	0.235365	−	0.407663i
$69$	−1.72728	+	0.128444i	−0.207940	+	0.0154629i
$70$	−3.72072	−	0.899813i	−0.444712	−	0.107548i
$71$		−	12.4084i		−	1.47260i	−0.676654	−	0.736301i	$-0.736571\pi$
$71$		−	12.4084i		−	1.47260i	0.676654	−	0.736301i	$-0.263429\pi$
$72$	−2.79136	−	1.09923i	−0.328965	−	0.129546i
$73$	−2.08792	+	1.20546i	−0.244372	+	0.141088i	−0.617185	−	0.786818i	$-0.711727\pi$
$73$	−2.08792	+	1.20546i	−0.244372	+	0.141088i	0.372812	+	0.927907i	$0.378393\pi$
$74$	6.21176	−	3.58636i	0.722102	−	0.416906i
$75$	−4.53464	−	2.18698i	−0.523615	−	0.252530i
$76$			7.20471i			0.826437i
$77$	−6.29382	−	1.52209i	−0.717247	−	0.173458i
$78$	0.439373	+	5.90855i	0.0497491	+	0.669012i
$79$	−5.93001	+	10.2711i	−0.667179	+	1.15559i	0.311511	+	0.950242i	$0.399165\pi$
$79$	−5.93001	+	10.2711i	−0.667179	+	1.15559i	−0.978690	+	0.205345i	$0.934168\pi$
$80$	−0.723421	−	1.25300i	−0.0808809	−	0.140090i
$81$	−6.58339	−	6.13669i	−0.731487	−	0.681855i
$82$	8.49149	+	4.90256i	0.937728	+	0.541397i
$83$	13.5344			1.48560			0.742798	−	0.669516i	$-0.233498\pi$
$83$	13.5344			1.48560			0.742798	+	0.669516i	$0.233498\pi$
$84$	1.61665	+	4.28794i	0.176391	+	0.467853i
$85$	5.61625			0.609168
$86$	7.13898	+	4.12169i	0.769816	+	0.444453i
$87$	6.70751	+	9.85026i	0.719120	+	1.05606i
$88$	−1.22371	−	2.11952i	−0.130448	−	0.225942i
$89$	−4.34273	+	7.52183i	−0.460329	+	0.797313i	−0.998977	−	0.0452180i	$-0.985602\pi$
$89$	−4.34273	+	7.52183i	−0.460329	+	0.797313i	0.538648	+	0.842531i	$0.318935\pi$
$90$	−0.641991	−	4.29278i	−0.0676718	−	0.452499i
$91$	6.24078	−	6.55455i	0.654212	−	0.687103i
$92$			1.00000i			0.104257i
$93$	−2.53250	+	5.25107i	−0.262608	+	0.544511i
$94$	9.96019	−	5.75052i	1.02731	−	0.593120i
$95$	−9.02752	+	5.21204i	−0.926204	+	0.534744i
$96$	−0.752405	+	1.56009i	−0.0767920	+	0.159226i
$97$			3.37559i			0.342739i	0.985207	+	0.171370i	$0.0548193\pi$
$97$			3.37559i			0.342739i	−0.985207	+	0.171370i	$0.945181\pi$
$98$	3.19866	−	6.22644i	0.323113	−	0.628966i
$99$	−1.08596	−	7.26149i	−0.109144	−	0.729807i
$100$	−1.45333	+	2.51723i	−0.145333	+	0.251723i
$101$	−2.74710	−	4.75812i	−0.273347	−	0.473451i	0.696370	−	0.717683i	$-0.254797\pi$
$101$	−2.74710	−	4.75812i	−0.273347	−	0.473451i	−0.969717	+	0.244232i	$0.921464\pi$
$102$	−3.78421	−	5.55727i	−0.374693	−	0.550252i
$103$	6.75677	+	3.90102i	0.665765	+	0.384379i	0.794470	−	0.607304i	$-0.207749\pi$
$103$	6.75677	+	3.90102i	0.665765	+	0.384379i	−0.128705	+	0.991683i	$0.541082\pi$
$104$	3.42072			0.335430
$105$	−4.20328	+	5.12765i	−0.410198	+	0.500407i
$106$	3.78588			0.367717
$107$	5.72784	+	3.30697i	0.553731	+	0.319697i	0.750625	−	0.660728i	$-0.229752\pi$
$107$	5.72784	+	3.30697i	0.553731	+	0.319697i	−0.196895	+	0.980425i	$0.563086\pi$
$108$	−3.81513	+	3.52771i	−0.367111	+	0.339454i
$109$	−1.46428	−	2.53621i	−0.140253	−	0.242925i	0.787339	−	0.616520i	$-0.211458\pi$
$109$	−1.46428	−	2.53621i	−0.140253	−	0.242925i	−0.927592	+	0.373595i	$0.878125\pi$
$110$	1.77051	−	3.06661i	0.168812	−	0.292390i
$111$	−0.921295	−	12.3893i	−0.0874455	−	1.17594i
$112$	2.53804	−	0.747214i	0.239823	−	0.0706051i
$113$			17.2501i			1.62275i	0.584527	+	0.811374i	$0.301280\pi$
$113$			17.2501i			1.62275i	−0.584527	+	0.811374i	$0.698720\pi$
$114$	11.2400	+	5.42086i	1.05272	+	0.507710i
$115$	−1.25300	+	0.723421i	−0.116843	+	0.0674593i
$116$	5.95857	−	3.44018i	0.553239	−	0.319413i
$117$	9.54847	+	3.76016i	0.882757	+	0.347627i
$118$		−	10.9905i		−	1.01176i
$119$	−2.41411	+	9.98233i	−0.221301	+	0.915079i
$120$	−2.49910	+	0.185839i	−0.228136	+	0.0169647i
$121$	−2.50508	+	4.33892i	−0.227734	+	0.394448i
$122$	−1.09417	−	1.89515i	−0.0990611	−	0.171579i
$123$	14.0375	−	9.55879i	1.26572	−	0.861887i
$124$	2.91493	+	1.68294i	0.261769	+	0.151132i
$125$	−11.4397			−1.02320
$126$	7.90596	+	0.704151i	0.704319	+	0.0627307i
$127$	15.6980			1.39297			0.696484	−	0.717572i	$-0.254747\pi$
$127$	15.6980			1.39297			0.696484	+	0.717572i	$0.254747\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	11.8016	−	8.03628i	1.03907	−	0.707555i
$130$	2.47462	+	4.28617i	0.217039	+	0.375922i
$131$	−6.69869	+	11.6025i	−0.585267	+	1.01371i	0.409575	+	0.912276i	$0.365677\pi$
$131$	−6.69869	+	11.6025i	−0.585267	+	1.01371i	−0.994842	+	0.101436i	$0.967656\pi$
$132$	−4.22738	+	0.314357i	−0.367946	+	0.0273612i
$133$	−5.38347	−	18.2859i	−0.466806	−	1.58559i
$134$		−	2.56494i		−	0.221577i
$135$	−7.18017	−	2.22835i	−0.617971	−	0.191786i
$136$	−3.36168	+	1.94087i	−0.288261	+	0.166428i
$137$	−2.73228	+	1.57748i	−0.233434	+	0.134773i	−0.612155	−	0.790737i	$-0.709697\pi$
$137$	−2.73228	+	1.57748i	−0.233434	+	0.134773i	0.378721	+	0.925511i	$0.376364\pi$
$138$	1.56009	+	0.752405i	0.132804	+	0.0640490i
$139$			21.1498i			1.79391i	0.442127	+	0.896953i	$0.354224\pi$
$139$			21.1498i			1.79391i	−0.442127	+	0.896953i	$0.645776\pi$
$140$	2.77233	+	2.63962i	0.234305	+	0.223089i
$141$	−1.47724	−	19.8655i	−0.124406	−	1.67298i
$142$	−6.20418	+	10.7460i	−0.520643	+	0.901781i
$143$	4.18597	+	7.25031i	0.350048	+	0.606301i
$144$	1.86777	+	2.34764i	0.155648	+	0.195637i
$145$	8.62111	+	4.97740i	0.715944	+	0.413350i
$146$	2.41092			0.199529
$147$	−7.30713	−	9.67501i	−0.602682	−	0.797981i
$148$	−7.17272			−0.589594
$149$	2.37873	+	1.37336i	0.194873	+	0.112510i	0.594262	−	0.804272i	$-0.297444\pi$
$149$	2.37873	+	1.37336i	0.194873	+	0.112510i	−0.399389	+	0.916782i	$0.630778\pi$
$150$	2.83363	+	4.16130i	0.231365	+	0.339769i
$151$	−4.71729	−	8.17059i	−0.383888	−	0.664914i	0.607726	−	0.794147i	$-0.292082\pi$
$151$	−4.71729	−	8.17059i	−0.383888	−	0.664914i	−0.991614	+	0.129233i	$0.958748\pi$
$152$	3.60236	−	6.23947i	0.292190	−	0.506087i
$153$	−11.5171	+	1.72240i	−0.931103	+	0.139248i
$154$	4.68956	+	4.46507i	0.377896	+	0.359806i
$155$			4.86989i			0.391159i
$156$	2.57377	−	5.33664i	0.206066	−	0.427273i
$157$	−2.66109	+	1.53638i	−0.212378	+	0.122617i	−0.602416	−	0.798182i	$-0.705795\pi$
$157$	−2.66109	+	1.53638i	−0.212378	+	0.122617i	0.390038	+	0.920799i	$0.372462\pi$
$158$	10.2711	−	5.93001i	0.817123	−	0.471766i
$159$	2.84851	−	5.90632i	0.225902	−	0.468402i
$160$			1.44684i			0.114383i
$161$	−0.747214	−	2.53804i	−0.0588887	−	0.200026i
$162$	2.63303	+	8.60623i	0.206871	+	0.676169i
$163$	−0.601674	+	1.04213i	−0.0471268	+	0.0816259i	−0.888627	−	0.458631i	$-0.848340\pi$
$163$	−0.601674	+	1.04213i	−0.0471268	+	0.0816259i	0.841500	+	0.540257i	$0.181673\pi$
$164$	−4.90256	−	8.49149i	−0.382826	−	0.663074i
$165$	−3.45206	−	5.06950i	−0.268743	−	0.394660i
$166$	−11.7212	−	6.76721i	−0.909738	−	0.525237i
$167$	−9.17724			−0.710156			−0.355078	−	0.934837i	$-0.615546\pi$
$167$	−9.17724			−0.710156			−0.355078	+	0.934837i	$0.615546\pi$
$168$	0.743914	−	4.52179i	0.0573942	−	0.348864i
$169$	1.29865			0.0998959
$170$	−4.86381	−	2.80812i	−0.373038	−	0.215373i
$171$	16.9141	−	13.4568i	1.29345	−	1.02907i
$172$	−4.12169	−	7.13898i	−0.314276	−	0.544342i
$173$	9.50912	−	16.4703i	0.722965	−	1.25221i	−0.236841	−	0.971548i	$-0.576112\pi$
$173$	9.50912	−	16.4703i	0.722965	−	1.25221i	0.959806	−	0.280664i	$-0.0905546\pi$
$174$	−0.883744	−	11.8843i	−0.0669964	−	0.900949i
$175$	1.80769	−	7.47480i	0.136649	−	0.565041i
$176$			2.44742i			0.184481i
$177$	−17.1462	−	8.26933i	−1.28879	−	0.621561i
$178$	7.52183	−	4.34273i	0.563785	−	0.325502i
$179$	−13.3216	+	7.69121i	−0.995701	+	0.574868i	−0.906973	−	0.421188i	$-0.861613\pi$
$179$	−13.3216	+	7.69121i	−0.995701	+	0.574868i	−0.0887274	+	0.996056i	$0.528280\pi$
$180$	−1.59041	+	4.03866i	−0.118542	+	0.301024i
$181$		−	19.2438i		−	1.43038i	−0.698929	−	0.715191i	$-0.746339\pi$
$181$		−	19.2438i		−	1.43038i	0.698929	−	0.715191i	$-0.253661\pi$
$182$	−8.68195	+	2.55601i	−0.643549	+	0.189464i
$183$	−3.77986	+	0.281079i	−0.279415	+	0.0207779i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−5.18890	−	8.98743i	−0.381495	−	0.660769i
$186$	4.81875	−	3.28131i	0.353328	−	0.240598i
$187$	−8.22742	−	4.75010i	−0.601649	−	0.347362i
$188$	−11.5010			−0.838799
$189$	7.04702	−	11.8042i	0.512595	−	0.858630i
$190$	10.4241			0.756242
$191$	17.0429	+	9.83973i	1.23318	+	0.711978i	0.967692	−	0.252136i	$-0.0811331\pi$
$191$	17.0429	+	9.83973i	1.23318	+	0.711978i	0.265490	+	0.964114i	$0.414466\pi$
$192$	1.43165	−	0.974877i	0.103320	−	0.0703557i
$193$	−11.6616	−	20.1985i	−0.839422	−	1.45392i	−0.890378	−	0.455221i	$-0.849560\pi$
$193$	−11.6616	−	20.1985i	−0.839422	−	1.45392i	0.0509560	−	0.998701i	$-0.483773\pi$
$194$	1.68780	−	2.92335i	0.121177	−	0.209884i
$195$	8.54874	−	0.635702i	0.612188	−	0.0455236i
$196$	−5.88334	+	3.79293i	−0.420239	+	0.270923i
$197$			12.5022i			0.890747i	0.895345	+	0.445373i	$0.146929\pi$
$197$			12.5022i			0.890747i	−0.895345	+	0.445373i	$0.853071\pi$
$198$	−2.69027	+	6.83162i	−0.191189	+	0.485502i
$199$	3.95601	−	2.28400i	0.280434	−	0.161909i	−0.353186	−	0.935553i	$-0.614902\pi$
$199$	3.95601	−	2.28400i	0.280434	−	0.161909i	0.633620	+	0.773644i	$0.281568\pi$
$200$	2.51723	−	1.45333i	0.177995	−	0.102766i
$201$	−4.00154	−	1.92987i	−0.282247	−	0.136123i
$202$			5.49421i			0.386571i
$203$	−12.5526	+	13.1837i	−0.881017	+	0.925312i
$204$	0.498586	+	6.70484i	0.0349080	+	0.469433i
$205$	7.09323	−	12.2858i	0.495413	−	0.858080i
$206$	−3.90102	−	6.75677i	−0.271797	−	0.470767i
$207$	2.34764	−	1.86777i	0.163172	−	0.129819i
$208$	−2.96243	−	1.71036i	−0.205408	−	0.118592i
$209$	17.6329			1.21970
$210$	6.20397	−	2.33903i	0.428115	−	0.161409i
$211$	12.4221			0.855174			0.427587	−	0.903974i	$-0.359364\pi$
$211$	12.4221			0.855174			0.427587	+	0.903974i	$0.359364\pi$
$212$	−3.27867	−	1.89294i	−0.225180	−	0.130008i
$213$	12.0966	+	17.7644i	0.828847	+	1.21720i
$214$	−3.30697	−	5.72784i	−0.226060	−	0.391547i
$215$	5.96343	−	10.3290i	0.406703	−	0.704430i
$216$	5.06786	−	1.14752i	0.344824	−	0.0780790i
$217$	−8.65574	−	2.09329i	−0.587590	−	0.142102i
$218$			2.92857i			0.198348i
$219$	1.81399	−	3.76126i	0.122578	−	0.254162i
$220$	−3.06661	+	1.77051i	−0.206751	+	0.119368i
$221$	11.4994	−	6.63917i	0.773531	−	0.446599i
$222$	−5.39679	+	11.1901i	−0.362209	+	0.751031i
$223$		−	4.65691i		−	0.311850i	−0.987769	−	0.155925i	$-0.950164\pi$
$223$		−	4.65691i		−	0.311850i	0.987769	−	0.155925i	$-0.0498358\pi$
$224$	−2.57162	−	0.621916i	−0.171823	−	0.0415535i
$225$	8.62404	−	1.28974i	0.574936	−	0.0859824i
$226$	8.62503	−	14.9390i	0.573728	−	0.993727i
$227$	0.120944	+	0.209482i	0.00802737	+	0.0139038i	0.870011	−	0.493032i	$-0.164111\pi$
$227$	0.120944	+	0.209482i	0.00802737	+	0.0139038i	−0.861984	+	0.506936i	$0.830778\pi$
$228$	−7.02371	−	10.3146i	−0.465156	−	0.683102i
$229$	15.8613	+	9.15753i	1.04814	+	0.605147i	0.922129	−	0.386882i	$-0.126448\pi$
$229$	15.8613	+	9.15753i	1.04814	+	0.605147i	0.126015	+	0.992028i	$0.459781\pi$
$230$	1.44684			0.0954019
$231$	10.4944	−	3.95661i	0.690479	−	0.260326i
$232$	−6.88037			−0.451718
$233$	7.97801	+	4.60611i	0.522657	+	0.301756i	0.738021	−	0.674778i	$-0.235760\pi$
$233$	7.97801	+	4.60611i	0.522657	+	0.301756i	−0.215364	+	0.976534i	$0.569094\pi$
$234$	−6.38914	−	8.03063i	−0.417671	−	0.524979i
$235$	−8.32008	−	14.4108i	−0.542742	−	0.940057i
$236$	−5.49526	+	9.51808i	−0.357711	+	0.619574i
$237$	−1.52335	−	20.4856i	−0.0989524	−	1.33068i
$238$	7.08185	−	7.43790i	0.459048	−	0.482127i
$239$		−	22.4033i		−	1.44915i	−0.689196	−	0.724575i	$-0.742036\pi$
$239$		−	22.4033i		−	1.44915i	0.689196	−	0.724575i	$-0.257964\pi$
$240$	2.25721	+	1.08861i	0.145702	+	0.0702695i
$241$	−25.7428	+	14.8626i	−1.65824	+	0.957385i	−0.684713	+	0.728813i	$0.740072\pi$
$241$	−25.7428	+	14.8626i	−1.65824	+	0.957385i	−0.973527	+	0.228572i	$0.926594\pi$
$242$	4.33892	−	2.50508i	0.278917	−	0.161033i
$243$	15.4076	+	2.36759i	0.988399	+	0.151881i
$244$			2.18833i			0.140093i
$245$	−9.00867	−	4.62795i	−0.575543	−	0.295669i
$246$	−16.9362	+	1.25941i	−1.07981	+	0.0802972i
$247$	−12.3227	+	21.3435i	−0.784073	+	1.35805i
$248$	−1.68294	−	2.91493i	−0.106867	−	0.185098i
$249$	−19.3765	+	13.1944i	−1.22794	+	0.836161i
$250$	9.90704	+	5.71983i	0.626576	+	0.361754i
$251$	13.2669			0.837396			0.418698	−	0.908125i	$-0.362487\pi$
$251$	13.2669			0.837396			0.418698	+	0.908125i	$0.362487\pi$
$252$	−6.49469	−	4.56279i	−0.409127	−	0.287429i
$253$	2.44742			0.153868
$254$	−13.5948	−	7.84898i	−0.853015	−	0.492489i
$255$	−8.04049	+	5.47515i	−0.503515	+	0.342867i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.09084	−	7.08554i	0.255180	−	0.441984i	−0.709765	−	0.704439i	$-0.751199\pi$
$257$	4.09084	−	7.08554i	0.255180	−	0.441984i	0.964944	+	0.262455i	$0.0845321\pi$
$258$	−14.2386	+	1.05882i	−0.886459	+	0.0659190i
$259$	18.2047	−	5.35956i	1.13118	−	0.333027i
$260$		−	4.94924i		−	0.306939i
$261$	−19.2056	−	7.56310i	−1.18880	−	0.468144i
$262$	11.6025	−	6.69869i	0.716803	−	0.413846i
$263$	−15.0577	+	8.69357i	−0.928498	+	0.536069i	−0.886336	−	0.463042i	$-0.846758\pi$
$263$	−15.0577	+	8.69357i	−0.928498	+	0.536069i	−0.0421620	+	0.999111i	$0.513425\pi$
$264$	3.81819	+	1.84145i	0.234994	+	0.113333i
$265$		−	5.47757i		−	0.336484i
$266$	−4.48073	+	18.5278i	−0.274731	+	1.13601i
$267$	−1.11560	−	15.0022i	−0.0682735	−	0.918122i
$268$	−1.28247	+	2.22130i	−0.0783393	+	0.135688i
$269$	5.25247	+	9.09754i	0.320249	+	0.554687i	0.980539	−	0.196323i	$-0.0629002\pi$
$269$	5.25247	+	9.09754i	0.320249	+	0.554687i	−0.660291	+	0.751010i	$0.729567\pi$
$270$	5.10404	+	5.51989i	0.310622	+	0.335930i
$271$	13.5483	+	7.82211i	0.823000	+	0.475159i	0.851450	−	0.524436i	$-0.175724\pi$
$271$	13.5483	+	7.82211i	0.823000	+	0.475159i	−0.0284501	+	0.999595i	$0.509057\pi$
$272$	3.88173			0.235365
$273$	−2.54472	+	15.4678i	−0.154014	+	0.936154i
$274$	3.15496			0.190598
$275$	6.16072	+	3.55689i	0.371505	+	0.214489i
$276$	−0.974877	−	1.43165i	−0.0586807	−	0.0861751i
$277$	2.08719	+	3.61511i	0.125407	+	0.217211i	0.921892	−	0.387447i	$-0.126643\pi$
$277$	2.08719	+	3.61511i	0.125407	+	0.217211i	−0.796485	+	0.604658i	$0.793310\pi$
$278$	10.5749	−	18.3163i	0.634241	−	1.09854i
$279$	−1.49350	−	9.98656i	−0.0894137	−	0.597880i
$280$	−1.08110	−	3.67215i	−0.0646081	−	0.219453i
$281$		−	3.31167i		−	0.197558i	−0.995109	−	0.0987788i	$-0.968506\pi$
$281$		−	3.31167i		−	0.197558i	0.995109	−	0.0987788i	$-0.0314936\pi$
$282$	−8.65343	+	17.9427i	−0.515304	+	1.06847i
$283$	−25.2731	+	14.5915i	−1.50233	+	0.867372i	−0.502336	+	0.864673i	$0.667526\pi$
$283$	−25.2731	+	14.5915i	−1.50233	+	0.867372i	−0.999996	+	0.00269944i	$0.999141\pi$
$284$	10.7460	−	6.20418i	0.637655	−	0.368150i
$285$	7.84313	−	16.2625i	0.464587	−	0.963308i
$286$		−	8.37193i		−	0.495043i
$287$	18.7879	+	17.8885i	1.10901	+	1.05593i
$288$	−0.443719	−	2.96700i	−0.0261464	−	0.174832i
$289$	0.966081	−	1.67330i	0.0568283	−	0.0984295i
$290$	−4.97740	−	8.62111i	−0.292283	−	0.506249i
$291$	−3.29079	−	4.83266i	−0.192909	−	0.283295i
$292$	−2.08792	−	1.20546i	−0.122186	−	0.0705442i
$293$	−10.5616			−0.617016			−0.308508	−	0.951222i	$-0.599830\pi$
$293$	−10.5616			−0.617016			−0.308508	+	0.951222i	$0.599830\pi$
$294$	1.49066	+	12.0324i	0.0869370	+	0.701742i
$295$	−15.9015			−0.925824
$296$	6.21176	+	3.58636i	0.361051	+	0.208453i
$297$	8.63378	+	9.33722i	0.500983	+	0.541800i
$298$	−1.37336	−	2.37873i	−0.0795566	−	0.137796i
$299$	−1.71036	+	2.96243i	−0.0989128	+	0.171322i
$300$	−0.373343	−	5.02060i	−0.0215550	−	0.289865i
$301$	15.7954	+	15.0393i	0.910430	+	0.866848i
$302$			9.43459i			0.542900i
$303$	8.57147	+	4.13387i	0.492418	+	0.237484i
$304$	−6.23947	+	3.60236i	−0.357858	+	0.206609i
$305$	−2.74198	+	1.58308i	−0.157005	+	0.0906471i
$306$	10.8353	+	4.26692i	0.619413	+	0.243923i
$307$			4.53097i			0.258596i	0.991606	+	0.129298i	$0.0412724\pi$
$307$			4.53097i			0.258596i	−0.991606	+	0.129298i	$0.958728\pi$
$308$	−1.82874	−	6.21165i	−0.104202	−	0.353942i
$309$	−13.4763	+	1.00213i	−0.766642	+	0.0570091i
$310$	2.43494	−	4.21745i	0.138295	−	0.239535i
$311$	−0.131501	−	0.227766i	−0.00745672	−	0.0129154i	0.862273	−	0.506444i	$-0.169040\pi$
$311$	−0.131501	−	0.227766i	−0.00745672	−	0.0129154i	−0.869730	+	0.493528i	$0.835707\pi$
$312$	−4.89727	+	3.33478i	−0.277253	+	0.188795i
$313$	6.49269	+	3.74855i	0.366988	+	0.211881i	0.672142	−	0.740422i	$-0.265374\pi$
$313$	6.49269	+	3.74855i	0.366988	+	0.211881i	−0.305154	+	0.952303i	$0.598708\pi$
$314$	3.07277			0.173406
$315$	1.01879	−	11.4387i	0.0574026	−	0.644496i
$316$	−11.8600			−0.667179
$317$	−25.8522	−	14.9258i	−1.45201	−	0.838316i	−0.453411	−	0.891302i	$-0.649793\pi$
$317$	−25.8522	−	14.9258i	−1.45201	−	0.838316i	−0.998595	+	0.0529853i	$0.983126\pi$
$318$	−5.42004	+	3.69077i	−0.303941	+	0.206968i
$319$	−8.41956	−	14.5831i	−0.471405	−	0.816497i
$320$	0.723421	−	1.25300i	0.0404404	−	0.0700449i
$321$	−11.4241	+	0.849522i	−0.637633	+	0.0474157i
$322$	−0.621916	+	2.57162i	−0.0346580	+	0.143311i
$323$		−	27.9668i		−	1.55611i
$324$	2.02284	−	8.76973i	0.112380	−	0.487207i
$325$	−8.61076	+	4.97142i	−0.477639	+	0.275765i
$326$	1.04213	−	0.601674i	0.0577183	−	0.0333237i
$327$	4.56883	+	2.20347i	0.252657	+	0.121852i
$328$			9.80512i			0.541397i
$329$	29.1901	−	8.59373i	1.60930	−	0.473788i
$330$	0.454824	+	6.11634i	0.0250372	+	0.336694i
$331$	−5.72774	+	9.92074i	−0.314825	+	0.545293i	−0.979400	−	0.201928i	$-0.935279\pi$
$331$	−5.72774	+	9.92074i	−0.314825	+	0.545293i	0.664575	+	0.747221i	$0.268613\pi$
$332$	6.76721	+	11.7212i	0.371399	+	0.643282i
$333$	13.3970	+	16.8390i	0.734152	+	0.922770i
$334$	7.94772	+	4.58862i	0.434880	+	0.251078i
$335$	−3.71106			−0.202757
$336$	−2.90514	+	3.54403i	−0.158489	+	0.193343i
$337$	−27.3588			−1.49033			−0.745164	−	0.666882i	$-0.767629\pi$
$337$	−27.3588			−1.49033			−0.745164	+	0.666882i	$0.767629\pi$
$338$	−1.12466	−	0.649323i	−0.0611735	−	0.0353185i
$339$	−16.8167	−	24.6960i	−0.913357	−	1.34130i
$340$	2.80812	+	4.86381i	0.152292	+	0.263777i
$341$	4.11885	−	7.13405i	0.223048	−	0.386331i
$342$	−21.3764	+	3.19687i	−1.15590	+	0.172867i
$343$	12.0981	−	14.0227i	0.653234	−	0.757156i
$344$			8.24338i			0.444453i
$345$	1.08861	−	2.25721i	0.0586088	−	0.121524i
$346$	−16.4703	+	9.50912i	−0.885448	+	0.511214i
$347$	31.3790	−	18.1167i	1.68451	−	0.972554i	0.725918	−	0.687781i	$-0.241415\pi$
$347$	31.3790	−	18.1167i	1.68451	−	0.972554i	0.958595	−	0.284773i	$-0.0919181\pi$
$348$	−5.17682	+	10.7340i	−0.277507	+	0.575403i
$349$		−	12.0514i		−	0.645098i	−0.946553	−	0.322549i	$-0.895460\pi$
$349$		−	12.0514i		−	0.645098i	0.946553	−	0.322549i	$-0.104540\pi$
$350$	−5.30290	+	5.56952i	−0.283452	+	0.297703i
$351$	−17.3357	+	3.92536i	−0.925314	+	0.209520i
$352$	1.22371	−	2.11952i	0.0652238	−	0.112971i
$353$	6.98889	+	12.1051i	0.371981	+	0.644290i	0.989870	−	0.141975i	$-0.0453454\pi$
$353$	6.98889	+	12.1051i	0.371981	+	0.644290i	−0.617889	+	0.786265i	$0.712012\pi$
$354$	10.7144	+	15.7346i	0.569465	+	0.836283i
$355$	15.5477	+	8.97646i	0.825186	+	0.476421i
$356$	−8.68546			−0.460329
$357$	−6.27539	−	16.6446i	−0.332129	−	0.880928i
$358$	15.3824			0.812986
$359$	3.84620	+	2.22060i	0.202995	+	0.117199i	0.598052	−	0.801458i	$-0.295942\pi$
$359$	3.84620	+	2.22060i	0.202995	+	0.117199i	−0.395057	+	0.918657i	$0.629275\pi$
$360$	3.39666	−	2.70237i	0.179020	−	0.142428i
$361$	16.4539	+	28.4991i	0.865997	+	1.49995i
$362$	−9.62192	+	16.6656i	−0.505717	+	0.875927i
$363$	−0.643526	−	8.65395i	−0.0337764	−	0.454215i
$364$	8.79680	+	2.12740i	0.461077	+	0.111506i
$365$		−	3.48822i		−	0.182582i
$366$	3.41400	+	1.64651i	0.178452	+	0.0860645i
$367$	11.2829	−	6.51420i	0.588963	−	0.340038i	−0.175724	−	0.984439i	$-0.556227\pi$
$367$	11.2829	−	6.51420i	0.588963	−	0.340038i	0.764688	+	0.644401i	$0.222893\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	−10.7781	+	27.3696i	−0.561085	+	1.42481i
$370$			10.3778i			0.539516i
$371$	9.73583	+	2.35450i	0.505459	+	0.122239i
$372$	−5.81381	+	0.432327i	−0.301432	+	0.0224151i
$373$	10.0316	−	17.3753i	0.519417	−	0.899657i	−0.480328	−	0.877089i	$-0.659482\pi$
$373$	10.0316	−	17.3753i	0.519417	−	0.899657i	0.999745	−	0.0225681i	$-0.00718425\pi$
$374$	4.75010	+	8.22742i	0.245622	+	0.425430i
$375$	16.3776	−	11.1523i	0.845734	−	0.575901i
$376$	9.96019	+	5.75052i	0.513657	+	0.296560i
$377$	23.5358			1.21216
$378$	−12.0050	+	6.69924i	−0.617471	+	0.344572i
$379$	12.5836			0.646378			0.323189	−	0.946334i	$-0.395245\pi$
$379$	12.5836			0.646378			0.323189	+	0.946334i	$0.395245\pi$
$380$	−9.02752	−	5.21204i	−0.463102	−	0.267372i
$381$	−22.4739	+	15.3036i	−1.15137	+	0.784026i
$382$	−9.83973	−	17.0429i	−0.503444	−	0.871991i
$383$	−3.35063	+	5.80345i	−0.171209	+	0.296543i	−0.938843	−	0.344346i	$-0.888101\pi$
$383$	−3.35063	+	5.80345i	−0.171209	+	0.296543i	0.767634	+	0.640889i	$0.221434\pi$
$384$	−1.72728	+	0.128444i	−0.0881450	+	0.00655465i
$385$	6.46025	−	6.78505i	0.329245	−	0.345798i
$386$			23.3233i			1.18712i
$387$	−9.06137	+	23.0102i	−0.460615	+	1.16968i
$388$	−2.92335	+	1.68780i	−0.148411	+	0.0856849i
$389$	−20.5683	+	11.8751i	−1.04285	+	0.602092i	−0.920641	−	0.390411i	$-0.872333\pi$
$389$	−20.5683	+	11.8751i	−1.04285	+	0.602092i	−0.122214	+	0.992504i	$0.538999\pi$
$390$	−7.72128	−	3.72384i	−0.390982	−	0.188564i
$391$		−	3.88173i		−	0.196308i
$392$	6.99159	−	0.343100i	0.353128	−	0.0173292i
$393$	−1.72082	−	23.1410i	−0.0868037	−	1.16731i
$394$	6.25111	−	10.8272i	0.314926	−	0.545469i
$395$	−8.57979	−	14.8606i	−0.431696	−	0.747719i
$396$	5.74565	−	4.57122i	0.288730	−	0.229712i
$397$	−2.05223	−	1.18485i	−0.102998	−	0.0594661i	0.447616	−	0.894226i	$-0.352273\pi$
$397$	−2.05223	−	1.18485i	−0.102998	−	0.0594661i	−0.550614	+	0.834760i	$0.685606\pi$
$398$	−4.56801			−0.228974
$399$	25.5337	+	20.9307i	1.27828	+	1.04785i
$400$	−2.90665			−0.145333
$401$	16.0596	+	9.27203i	0.801980	+	0.463023i	0.844163	−	0.536087i	$-0.180098\pi$
$401$	16.0596	+	9.27203i	0.801980	+	0.463023i	−0.0421831	+	0.999110i	$0.513431\pi$
$402$	2.50050	+	3.67209i	0.124714	+	0.183147i
$403$	5.75686	+	9.97118i	0.286770	+	0.496700i
$404$	2.74710	−	4.75812i	0.136673	−	0.236725i
$405$	12.4518	−	3.80958i	0.618737	−	0.189300i
$406$	17.4627	−	5.14111i	0.866658	−	0.255149i
$407$			17.5546i			0.870151i
$408$	2.92063	−	6.05586i	0.144593	−	0.299810i
$409$	29.3001	−	16.9164i	1.44879	−	0.836462i	0.450385	−	0.892835i	$-0.351287\pi$
$409$	29.3001	−	16.9164i	1.44879	−	0.836462i	0.998410	+	0.0563727i	$0.0179535\pi$
$410$	−12.2858	+	7.09323i	−0.606754	+	0.350310i
$411$	2.37381	−	4.92203i	0.117091	−	0.242786i
$412$			7.80205i			0.384379i
$413$	6.83518	−	28.2634i	0.336337	−	1.39075i
$414$	−2.96700	+	0.443719i	−0.145820	+	0.0218076i
$415$	−9.79108	+	16.9586i	−0.480625	+	0.832467i
$416$	1.71036	+	2.96243i	0.0838574	+	0.145245i
$417$	−20.6185	−	30.2791i	−1.00969	−	1.48277i
$418$	−15.2706	−	8.81646i	−0.746908	−	0.431227i
$419$	−17.9477			−0.876803			−0.438402	−	0.898779i	$-0.644455\pi$
$419$	−17.9477			−0.876803			−0.438402	+	0.898779i	$0.644455\pi$
$420$	−6.54231	−	1.07633i	−0.319232	−	0.0525193i
$421$	−7.19559			−0.350691			−0.175346	−	0.984507i	$-0.556104\pi$
$421$	−7.19559			−0.350691			−0.175346	+	0.984507i	$0.556104\pi$
$422$	−10.7579	−	6.21106i	−0.523685	−	0.302350i
$423$	21.4813	+	27.0003i	1.04446	+	1.31280i
$424$	1.89294	+	3.27867i	0.0919293	+	0.159226i
$425$	5.64142	−	9.77122i	0.273649	−	0.473974i
$426$	−1.59378	−	21.4327i	−0.0772191	−	1.03842i
$427$	−1.63515	−	5.55408i	−0.0791305	−	0.268781i
$428$			6.61393i			0.319697i
$429$	−13.0610	−	6.29908i	−0.630590	−	0.304123i
$430$	−10.3290	+	5.96343i	−0.498107	+	0.287582i
$431$	−23.9684	+	13.8382i	−1.15452	+	0.666561i	−0.949984	−	0.312299i	$-0.898901\pi$
$431$	−23.9684	+	13.8382i	−1.15452	+	0.666561i	−0.204533	+	0.978860i	$0.565568\pi$
$432$	−4.96266	−	1.54015i	−0.238766	−	0.0741003i
$433$			14.2435i			0.684500i	0.939609	+	0.342250i	$0.111189\pi$
$433$			14.2435i			0.684500i	−0.939609	+	0.342250i	$0.888811\pi$
$434$	6.44945	+	6.14072i	0.309583	+	0.294764i
$435$	−17.1947	+	1.27864i	−0.824425	+	0.0613059i
$436$	1.46428	−	2.53621i	0.0701265	−	0.121463i
$437$	3.60236	+	6.23947i	0.172324	+	0.298474i
$438$	−3.45159	+	2.35035i	−0.164923	+	0.112304i
$439$	−18.6271	−	10.7544i	−0.889025	−	0.513279i	−0.0154017	−	0.999881i	$-0.504903\pi$
$439$	−18.6271	−	10.7544i	−0.889025	−	0.513279i	−0.873624	+	0.486602i	$0.838236\pi$
$440$	3.54102			0.168812
$441$	19.8932	+	6.72765i	0.947294	+	0.320364i
$442$	−13.2783			−0.631586
$443$	18.2078	+	10.5123i	0.865079	+	0.499454i	0.865710	−	0.500546i	$-0.166867\pi$
$443$	18.2078	+	10.5123i	0.865079	+	0.499454i	−0.000630757		1.00000i	$0.500201\pi$
$444$	10.2688	−	6.99252i	0.487336	−	0.331850i
$445$	−6.28324	−	10.8829i	−0.297854	−	0.515899i
$446$	−2.32846	+	4.03300i	−0.110256	+	0.190968i
$447$	−4.74436	+	0.352801i	−0.224401	+	0.0166869i
$448$	1.91613	+	1.82440i	0.0905286	+	0.0861950i
$449$			16.6184i			0.784269i	0.919908	+	0.392134i	$0.128263\pi$
$449$			16.6184i			0.784269i	−0.919908	+	0.392134i	$0.871737\pi$
$450$	−8.11351	−	3.19508i	−0.382474	−	0.150617i
$451$	−20.7822	+	11.9986i	−0.978595	+	0.564992i
$452$	−14.9390	+	8.62503i	−0.702671	+	0.405687i
$453$	14.7188	+	7.09863i	0.691551	+	0.333523i
$454$		−	0.241889i		−	0.0113524i
$455$	3.69815	+	12.5614i	0.173372	+	0.588888i
$456$	0.925404	+	12.4446i	0.0433360	+	0.582770i
$457$	2.74544	−	4.75524i	0.128426	−	0.222441i	−0.794641	−	0.607080i	$-0.792341\pi$
$457$	2.74544	−	4.75524i	0.128426	−	0.222441i	0.923067	+	0.384639i	$0.125674\pi$
$458$	−9.15753	−	15.8613i	−0.427903	−	0.741150i
$459$	14.8093	−	13.6936i	0.691240	−	0.639164i
$460$	−1.25300	−	0.723421i	−0.0584215	−	0.0337297i
$461$	−19.7605			−0.920339			−0.460170	−	0.887831i	$-0.652211\pi$
$461$	−19.7605			−0.920339			−0.460170	+	0.887831i	$0.652211\pi$
$462$	−11.0667	−	1.82067i	−0.514870	−	0.0847051i
$463$	26.2725			1.22098			0.610492	−	0.792022i	$-0.290972\pi$
$463$	26.2725			1.22098			0.610492	+	0.792022i	$0.290972\pi$
$464$	5.95857	+	3.44018i	0.276620	+	0.159706i
$465$	−4.74754	−	6.97196i	−0.220162	−	0.323317i
$466$	−4.60611	−	7.97801i	−0.213374	−	0.369574i
$467$	5.19590	−	8.99957i	0.240438	−	0.416450i	−0.720401	−	0.693557i	$-0.756042\pi$
$467$	5.19590	−	8.99957i	0.240438	−	0.416450i	0.960839	+	0.277107i	$0.0893757\pi$
$468$	1.51784	+	10.1493i	0.0701622	+	0.469152i
$469$	1.59518	−	6.59604i	0.0736584	−	0.304577i
$470$			16.6402i			0.767554i
$471$	2.31196	−	4.79380i	0.106530	−	0.220887i
$472$	9.51808	−	5.49526i	0.438105	−	0.252940i
$473$	−17.4720	+	10.0875i	−0.803365	+	0.463823i
$474$	−8.92354	+	18.5027i	−0.409872	+	0.849859i
$475$			20.9416i			0.960866i
$476$	−9.85201	+	2.90049i	−0.451566	+	0.132944i
$477$	1.67987	+	11.2327i	0.0769158	+	0.514311i
$478$	−11.2017	+	19.4018i	−0.512352	+	0.887420i
$479$	8.56433	+	14.8339i	0.391314	+	0.677776i	0.992623	−	0.121240i	$-0.0386872\pi$
$479$	8.56433	+	14.8339i	0.391314	+	0.677776i	−0.601309	+	0.799017i	$0.705354\pi$
$480$	−1.41049	−	2.07137i	−0.0643799	−	0.0945445i
$481$	−21.2487	−	12.2680i	−0.968858	−	0.559370i
$482$	29.7252			1.35395
$483$	3.54403	+	2.90514i	0.161259	+	0.132189i
$484$	−5.01016			−0.227734
$485$	−4.22962	−	2.44197i	−0.192057	−	0.110884i
$486$	−12.1596	−	9.75420i	−0.551570	−	0.442460i
$487$	8.16266	+	14.1381i	0.369885	+	0.640660i	0.989547	−	0.144209i	$-0.0460637\pi$
$487$	8.16266	+	14.1381i	0.369885	+	0.640660i	−0.619662	+	0.784869i	$0.712730\pi$
$488$	1.09417	−	1.89515i	0.0495305	−	0.0857894i
$489$	−0.154563	−	2.07852i	−0.00698959	−	0.0939940i
$490$	5.48776	+	8.51226i	0.247912	+	0.384545i
$491$		−	18.5093i		−	0.835313i	−0.908605	−	0.417657i	$-0.862852\pi$
$491$		−	18.5093i		−	0.835313i	0.908605	−	0.417657i	$-0.137148\pi$
$492$	15.2969	+	7.37742i	0.689637	+	0.332600i
$493$	−23.1296	+	13.3539i	−1.04170	+	0.601428i
$494$	21.3435	−	12.3227i	0.960289	−	0.554423i
$495$	9.88427	+	3.89240i	0.444265	+	0.174950i
$496$			3.36587i			0.151132i
$497$	−22.6379	+	23.7760i	−1.01545	+	1.06650i
$498$	23.3778	−	1.73842i	1.04758	−	0.0779004i
$499$	5.20048	−	9.00749i	0.232805	−	0.403231i	−0.725827	−	0.687877i	$-0.758543\pi$
$499$	5.20048	−	9.00749i	0.232805	−	0.403231i	0.958633	+	0.284646i	$0.0918762\pi$
$500$	−5.71983	−	9.90704i	−0.255799	−	0.443056i
$501$	13.1386	−	8.94668i	0.586988	−	0.399708i
$502$	−11.4894	−	6.63343i	−0.512798	−	0.296064i
$503$	30.4653			1.35838			0.679191	−	0.733961i	$-0.262331\pi$
$503$	30.4653			1.35838			0.679191	+	0.733961i	$0.262331\pi$
$504$	3.34317	+	7.19884i	0.148916	+	0.320662i
$505$	7.94924			0.353737
$506$	−2.11952	−	1.22371i	−0.0942243	−	0.0544004i
$507$	−1.85920	+	1.26602i	−0.0825702	+	0.0562260i
$508$	7.84898	+	13.5948i	0.348242	+	0.603173i
$509$	−14.2418	+	24.6675i	−0.631257	+	1.09337i	0.356038	+	0.934471i	$0.384127\pi$
$509$	−14.2418	+	24.6675i	−0.631257	+	1.09337i	−0.987295	+	0.158897i	$0.949206\pi$
$510$	9.70084	−	0.721375i	0.429561	−	0.0319430i
$511$	6.19996	+	1.49939i	0.274270	+	0.0663290i
$512$			1.00000i			0.0441942i
$513$	−11.0963	+	35.7545i	−0.489914	+	1.57860i
$514$	−7.08554	+	4.09084i	−0.312530	+	0.180439i
$515$	−9.77598	+	5.64416i	−0.430781	+	0.248712i
$516$	12.8604	+	6.20236i	0.566149	+	0.273044i
$517$			28.1478i			1.23794i
$518$	−18.4455	−	4.46083i	−0.810449	−	0.195998i
$519$	2.44278	+	32.8499i	0.107226	+	1.44195i
$520$	−2.47462	+	4.28617i	−0.108519	+	0.187961i
$521$	9.07394	+	15.7165i	0.397537	+	0.688554i	0.993421	−	0.114516i	$-0.0365318\pi$
$521$	9.07394	+	15.7165i	0.397537	+	0.688554i	−0.595885	+	0.803070i	$0.703198\pi$
$522$	12.8510	+	16.1526i	0.562472	+	0.706981i
$523$	−10.1577	−	5.86458i	−0.444167	−	0.256440i	0.261196	−	0.965286i	$-0.415883\pi$
$523$	−10.1577	−	5.86458i	−0.444167	−	0.256440i	−0.705364	+	0.708846i	$0.749216\pi$
$524$	−13.3974			−0.585267
$525$	4.69903	+	12.4636i	0.205082	+	0.543954i
$526$	17.3871			0.758116
$527$	−11.3150	−	6.53271i	−0.492889	−	0.284569i
$528$	−2.38593	−	3.50384i	−0.103834	−	0.152485i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−2.73878	+	4.74371i	−0.118965	+	0.206054i
$531$	32.6089	−	4.87671i	1.41511	−	0.211631i
$532$	13.1443	−	13.8052i	0.569878	−	0.598530i
$533$		−	33.5406i		−	1.45281i
$534$	−6.53498	+	13.5501i	−0.282796	+	0.586371i
$535$	−8.28727	+	4.78466i	−0.358290	+	0.206859i
$536$	2.22130	−	1.28247i	0.0959456	−	0.0553942i
$537$	11.5738	−	23.9980i	0.499447	−	1.03559i
$538$		−	10.5049i		−	0.452900i
$539$	9.28287	+	14.3990i	0.399841	+	0.620208i
$540$	−1.66028	−	7.33239i	−0.0714472	−	0.315536i
$541$	−11.4735	+	19.8727i	−0.493286	+	0.854396i	−0.999970	−	0.00773560i	$-0.997538\pi$
$541$	−11.4735	+	19.8727i	−0.493286	+	0.854396i	0.506684	+	0.862132i	$0.330871\pi$
$542$	−7.82211	−	13.5483i	−0.335988	−	0.581949i
$543$	18.7604	+	27.5504i	0.805084	+	1.18230i
$544$	−3.36168	−	1.94087i	−0.144131	−	0.0832139i
$545$	4.23717			0.181501
$546$	9.93770	−	12.1231i	0.425294	−	0.518823i
$547$	−10.5205			−0.449824			−0.224912	−	0.974379i	$-0.572209\pi$
$547$	−10.5205			−0.449824			−0.224912	+	0.974379i	$0.572209\pi$
$548$	−2.73228	−	1.57748i	−0.116717	−	0.0673867i
$549$	5.13741	−	4.08731i	0.219260	−	0.174442i
$550$	−3.55689	−	6.16072i	−0.151666	−	0.262694i
$551$	24.7855	−	42.9298i	1.05590	−	1.82887i
$552$	0.128444	+	1.72728i	0.00546695	+	0.0735180i
$553$	30.1013	−	8.86198i	1.28004	−	0.376850i
$554$		−	4.17437i		−	0.177352i
$555$	16.1903	+	7.80830i	0.687240	+	0.331444i
$556$	−18.3163	+	10.5749i	−0.776784	+	0.448476i
$557$	4.62535	−	2.67044i	0.195982	−	0.113150i	−0.398798	−	0.917039i	$-0.630572\pi$
$557$	4.62535	−	2.67044i	0.195982	−	0.113150i	0.594780	+	0.803888i	$0.297239\pi$
$558$	−3.69987	+	9.39537i	−0.156628	+	0.397738i
$559$		−	28.1983i		−	1.19266i
$560$	−0.899813	+	3.72072i	−0.0380241	+	0.157229i
$561$	16.4095	−	1.22025i	0.692811	−	0.0515189i
$562$	−1.65583	+	2.86799i	−0.0698471	+	0.120979i
$563$	−12.2178	−	21.1619i	−0.514919	−	0.891867i	−0.999850	−	0.0173140i	$-0.994489\pi$
$563$	−12.2178	−	21.1619i	−0.514919	−	0.891867i	0.484931	−	0.874553i	$-0.338845\pi$
$564$	16.4654	−	11.2121i	0.693319	−	0.472114i
$565$	−21.6143	−	12.4790i	−0.909322	−	0.524997i
$566$	29.1829			1.22665
$567$	1.41881	+	23.7695i	0.0595842	+	0.998223i
$568$	−12.4084			−0.520643
$569$	19.7524	+	11.4040i	0.828063	+	0.478082i	0.853189	−	0.521602i	$-0.174665\pi$
$569$	19.7524	+	11.4040i	0.828063	+	0.478082i	−0.0251263	+	0.999684i	$0.507999\pi$
$570$	−14.9236	+	10.1622i	−0.625081	+	0.425647i
$571$	−5.56651	−	9.64147i	−0.232951	−	0.403483i	0.725724	−	0.687986i	$-0.241505\pi$
$571$	−5.56651	−	9.64147i	−0.232951	−	0.403483i	−0.958675	+	0.284503i	$0.908172\pi$
$572$	−4.18597	+	7.25031i	−0.175024	+	0.303151i
$573$	−33.9920	+	2.52771i	−1.42003	+	0.105597i
$574$	−7.32653	−	24.8858i	−0.305803	−	1.03872i
$575$			2.90665i			0.121216i
$576$	−1.09923	+	2.79136i	−0.0458013	+	0.116307i
$577$	−3.46746	+	2.00194i	−0.144352	+	0.0833419i	−0.570437	−	0.821342i	$-0.693226\pi$
$577$	−3.46746	+	2.00194i	−0.144352	+	0.0833419i	0.426084	+	0.904683i	$0.359893\pi$
$578$	−1.67330	+	0.966081i	−0.0696002	+	0.0401837i
$579$	36.3864	+	17.5485i	1.51217	+	0.729292i
$580$			9.95480i			0.413350i
$581$	−25.9337	−	24.6922i	−1.07591	−	1.02441i
$582$	0.433576	+	5.83060i	0.0179723	+	0.241686i
$583$	−4.63281	+	8.02426i	−0.191871	+	0.332331i
$584$	1.20546	+	2.08792i	0.0498823	+	0.0863986i
$585$	−11.6191	+	9.24407i	−0.480389	+	0.382195i
$586$	9.14662	+	5.28080i	0.377843	+	0.218148i
$587$	−3.59374			−0.148330			−0.0741648	−	0.997246i	$-0.523629\pi$
$587$	−3.59374			−0.148330			−0.0741648	+	0.997246i	$0.523629\pi$
$588$	4.72524	−	11.1657i	0.194865	−	0.460464i
$589$	24.2502			0.999211
$590$	13.7711	+	7.95077i	0.566949	+	0.327328i
$591$	−12.1881	−	17.8988i	−0.501353	−	0.736257i
$592$	−3.58636	−	6.21176i	−0.147399	−	0.255302i
$593$	−16.3362	+	28.2952i	−0.670849	+	1.16194i	0.306815	+	0.951769i	$0.400737\pi$
$593$	−16.3362	+	28.2952i	−0.670849	+	1.16194i	−0.977664	+	0.210175i	$0.932596\pi$
$594$	−2.80846	−	12.4032i	−0.115233	−	0.508908i
$595$	−10.7615	−	10.2463i	−0.441177	−	0.420058i
$596$			2.74672i			0.112510i
$597$	−3.43699	+	7.12652i	−0.140667	+	0.291669i
$598$	2.96243	−	1.71036i	0.121143	−	0.0699419i
$599$	−32.9491	+	19.0232i	−1.34627	+	0.777266i	−0.987718	−	0.156245i	$-0.950061\pi$
$599$	−32.9491	+	19.0232i	−1.34627	+	0.777266i	−0.358547	+	0.933512i	$0.616728\pi$
$600$	−2.18698	+	4.53464i	−0.0892830	+	0.185126i
$601$		−	15.3195i		−	0.624895i	−0.949935	−	0.312447i	$-0.898851\pi$
$601$		−	15.3195i		−	0.624895i	0.949935	−	0.312447i	$-0.101149\pi$
$602$	−6.15957	−	20.9221i	−0.251045	−	0.852720i
$603$	7.61018	−	1.13811i	0.309911	−	0.0463475i
$604$	4.71729	−	8.17059i	0.191944	−	0.332457i
$605$	−3.62445	−	6.27773i	−0.147355	−	0.255226i
$606$	−5.35617	−	7.86577i	−0.217580	−	0.319525i
$607$	−33.0295	−	19.0696i	−1.34062	−	0.774010i	−0.353726	−	0.935349i	$-0.615085\pi$
$607$	−33.0295	−	19.0696i	−1.34062	−	0.774010i	−0.986899	+	0.161339i	$0.948419\pi$
$608$	7.20471			0.292190
$609$	5.11840	−	31.1116i	0.207408	−	1.26070i
$610$	3.16617			0.128194
$611$	−34.0710	−	19.6709i	−1.37837	−	0.795801i
$612$	−7.25020	−	9.11291i	−0.293072	−	0.368368i
$613$	−18.9794	−	32.8733i	−0.766571	−	1.32774i	−0.939412	−	0.342790i	$-0.888628\pi$
$613$	−18.9794	−	32.8733i	−0.766571	−	1.32774i	0.172841	−	0.984950i	$-0.444705\pi$
$614$	2.26548	−	3.92393i	0.0914275	−	0.158357i
$615$	1.82217	+	24.5040i	0.0734770	+	0.988097i
$616$	−1.52209	+	6.29382i	−0.0613266	+	0.253585i
$617$			8.17554i			0.329135i	0.986366	+	0.164567i	$0.0526228\pi$
$617$			8.17554i			0.329135i	−0.986366	+	0.164567i	$0.947377\pi$
$618$	12.1719	+	5.87030i	0.489626	+	0.236138i
$619$	29.7243	−	17.1613i	1.19472	−	0.689772i	0.235347	−	0.971911i	$-0.424377\pi$
$619$	29.7243	−	17.1613i	1.19472	−	0.689772i	0.959374	+	0.282139i	$0.0910440\pi$
$620$	−4.21745	+	2.43494i	−0.169377	+	0.0977897i
$621$	−1.54015	+	4.96266i	−0.0618039	+	0.199145i
$622$			0.263002i			0.0105454i
$623$	22.0441	−	6.48990i	0.883178	−	0.260012i
$624$	5.90855	−	0.439373i	0.236531	−	0.0175890i
$625$	1.00907	−	1.74775i	0.0403626	−	0.0699101i
$626$	−3.74855	−	6.49269i	−0.149822	−	0.259500i
$627$	−25.2441	+	17.1899i	−1.00815	+	0.686500i
$628$	−2.66109	−	1.53638i	−0.106189	−	0.0613084i
$629$	27.8426			1.11016
$630$	−6.60163	+	9.39678i	−0.263015	+	0.374377i
$631$	8.25964			0.328811			0.164406	−	0.986393i	$-0.447429\pi$
$631$	8.25964			0.328811			0.164406	+	0.986393i	$0.447429\pi$
$632$	10.2711	+	5.93001i	0.408562	+	0.235883i
$633$	−17.7841	+	12.1100i	−0.706855	+	0.481331i
$634$	14.9258	+	25.8522i	0.592779	+	1.02672i
$635$	−11.3562	+	19.6696i	−0.450658	+	0.780563i
$636$	6.53928	−	0.486275i	0.259299	−	0.0192820i
$637$	−23.9163	+	1.17365i	−0.947598	+	0.0465017i
$638$			16.8391i			0.666667i
$639$	−34.6362	−	13.6396i	−1.37019	−	0.539576i
$640$	−1.25300	+	0.723421i	−0.0495292	+	0.0285957i
$641$	18.7316	−	10.8147i	0.739852	−	0.427154i	−0.0821634	−	0.996619i	$-0.526183\pi$
$641$	18.7316	−	10.8147i	0.739852	−	0.427154i	0.822016	+	0.569465i	$0.192850\pi$
$642$	10.3183	+	4.97636i	0.407233	+	0.196401i
$643$		−	12.7991i		−	0.504746i	−0.967630	−	0.252373i	$-0.918789\pi$
$643$		−	12.7991i		−	0.504746i	0.967630	−	0.252373i	$-0.0812109\pi$
$644$	1.82440	−	1.91613i	0.0718916	−	0.0755061i
$645$	1.53194	+	20.6010i	0.0603200	+	0.811165i
$646$	−13.9834	+	24.2199i	−0.550169	+	0.952920i
$647$	−22.7515	−	39.4067i	−0.894453	−	1.54924i	−0.834480	−	0.551039i	$-0.814232\pi$
$647$	−22.7515	−	39.4067i	−0.894453	−	1.54924i	−0.0599736	−	0.998200i	$-0.519102\pi$
$648$	−6.13669	+	6.58339i	−0.241072	+	0.258620i
$649$	23.2947	+	13.4492i	0.914396	+	0.527927i
$650$	9.94285			0.389991
$651$	14.4327	−	5.44143i	0.565661	−	0.213266i
$652$	−1.20335			−0.0471268
$653$	−16.4102	−	9.47445i	−0.642182	−	0.370764i	0.143273	−	0.989683i	$-0.454237\pi$
$653$	−16.4102	−	9.47445i	−0.642182	−	0.370764i	−0.785455	+	0.618919i	$0.787571\pi$
$654$	−2.85499	−	4.19268i	−0.111639	−	0.163947i
$655$	−9.69194	−	16.7869i	−0.378695	−	0.655920i
$656$	4.90256	−	8.49149i	0.191413	−	0.331537i
$657$	1.06977	+	7.15321i	0.0417357	+	0.279073i
$658$	−29.5763	−	7.15267i	−1.15300	−	0.278840i
$659$		−	36.9553i		−	1.43958i	−0.694194	−	0.719788i	$-0.744239\pi$
$659$		−	36.9553i		−	1.43958i	0.694194	−	0.719788i	$-0.255761\pi$
$660$	2.66428	−	5.52432i	0.103707	−	0.215034i
$661$	22.4021	−	12.9339i	0.871341	−	0.503069i	0.00354723	−	0.999994i	$-0.498871\pi$
$661$	22.4021	−	12.9339i	0.871341	−	0.503069i	0.867794	+	0.496925i	$0.165538\pi$
$662$	9.92074	−	5.72774i	0.385580	−	0.222615i
$663$	−9.99068	+	20.7154i	−0.388006	+	0.804520i
$664$		−	13.5344i		−	0.525237i
$665$	26.8067	+	6.48290i	1.03952	+	0.251396i
$666$	−3.18267	−	21.2815i	−0.123326	−	0.824641i
$667$	3.44018	−	5.95857i	0.133204	−	0.230717i
$668$	−4.58862	−	7.94772i	−0.177539	−	0.307507i
$669$	4.53992	+	6.66706i	0.175523	+	0.257763i
$670$	3.21387	+	1.85553i	0.124163	+	0.0716853i
$671$	5.35575			0.206757
$672$	4.28794	−	1.61665i	0.165411	−	0.0623635i
$673$	−0.993438			−0.0382942			−0.0191471	−	0.999817i	$-0.506095\pi$
$673$	−0.993438			−0.0382942			−0.0191471	+	0.999817i	$0.506095\pi$
$674$	23.6934	+	13.6794i	0.912635	+	0.526910i
$675$	−11.0893	+	10.2538i	−0.426826	+	0.394670i
$676$	0.649323	+	1.12466i	0.0249740	+	0.0432562i
$677$	−23.4253	+	40.5738i	−0.900307	+	1.55938i	−0.0732114	+	0.997316i	$0.523325\pi$
$677$	−23.4253	+	40.5738i	−0.900307	+	1.55938i	−0.827096	+	0.562061i	$0.810009\pi$
$678$	2.21567	+	29.7957i	0.0850924	+	1.14430i
$679$	6.15844	−	6.46807i	0.236339	−	0.248222i
$680$		−	5.61625i		−	0.215373i
$681$	−0.377369	−	0.181998i	−0.0144608	−	0.00697420i
$682$	−7.13405	+	4.11885i	−0.273177	+	0.157719i
$683$	28.9057	−	16.6887i	1.10605	−	0.638576i	0.168244	−	0.985745i	$-0.446190\pi$
$683$	28.9057	−	16.6887i	1.10605	−	0.638576i	0.937803	+	0.347169i	$0.112857\pi$
$684$	20.1110	+	7.91964i	0.768962	+	0.302815i
$685$		−	4.56473i		−	0.174409i
$686$	−17.4886	+	6.09502i	−0.667717	+	0.232709i
$687$	−31.6353	+	2.35247i	−1.20696	+	0.0897522i
$688$	4.12169	−	7.13898i	0.157138	−	0.272171i
$689$	−6.47522	−	11.2154i	−0.246686	−	0.427273i
$690$	−2.07137	+	1.41049i	−0.0788556	+	0.0536965i
$691$	−25.2447	−	14.5750i	−0.960354	−	0.554461i	−0.0640721	−	0.997945i	$-0.520409\pi$
$691$	−25.2447	−	14.5750i	−0.960354	−	0.554461i	−0.896282	+	0.443485i	$0.853742\pi$
$692$	19.0182			0.722965
$693$	−11.1670	+	15.8952i	−0.424201	+	0.603808i
$694$	−36.2333			−1.37540
$695$	−26.5008	−	15.3002i	−1.00523	−	0.580371i
$696$	9.85026	−	6.70751i	0.373373	−	0.254247i
$697$	19.0304	+	32.9617i	0.720829	+	1.24851i
$698$	−6.02571	+	10.4368i	−0.228076	+	0.395040i
$699$	−15.9121	+	1.18326i	−0.601851	+	0.0447549i
$700$	7.37721	−	2.17189i	0.278832	−	0.0820898i
$701$		−	13.3764i		−	0.505220i	−0.967568	−	0.252610i	$-0.918711\pi$
$701$		−	13.3764i		−	0.505220i	0.967568	−	0.252610i	$-0.0812889\pi$
$702$	16.9759	+	5.26841i	0.640713	+	0.198843i
$703$	−44.7540	+	25.8387i	−1.68793	+	0.974525i
$704$	−2.11952	+	1.22371i	−0.0798826	+	0.0461202i
$705$	25.9602	+	12.5201i	0.977717	+	0.471536i
$706$		−	13.9778i		−	0.526060i
$707$	−3.41693	+	14.1290i	−0.128507	+	0.531376i
$708$	−1.41167	−	18.9837i	−0.0530538	−	0.713452i
$709$	−17.9255	+	31.0479i	−0.673206	+	1.16603i	0.303784	+	0.952741i	$0.401750\pi$
$709$	−17.9255	+	31.0479i	−0.673206	+	1.16603i	−0.976990	+	0.213286i	$0.931583\pi$
$710$	−8.97646	−	15.5477i	−0.336881	−	0.583495i
$711$	22.1518	+	27.8431i	0.830759	+	1.04420i
$712$	7.52183	+	4.34273i	0.281893	+	0.162751i
$713$	3.36587			0.126053
$714$	−2.88767	+	17.5524i	−0.108068	+	0.656881i
$715$	−12.1129			−0.452995
$716$	−13.3216	−	7.69121i	−0.497850	−	0.287434i
$717$	21.8405	+	32.0737i	0.815648	+	1.19781i
$718$	−2.22060	−	3.84620i	−0.0828722	−	0.143539i
$719$	−25.3910	+	43.9785i	−0.946923	+	1.64012i	−0.195070	+	0.980789i	$0.562493\pi$
$719$	−25.3910	+	43.9785i	−0.946923	+	1.64012i	−0.751854	+	0.659330i	$0.770840\pi$
$720$	−4.29278	+	0.641991i	−0.159983	+	0.0239256i
$721$	−5.82980	−	19.8019i	−0.217113	−	0.737463i
$722$		−	32.9079i		−	1.22471i
$723$	22.3654	−	46.3741i	0.831778	−	1.72467i
$724$	16.6656	−	9.62192i	0.619374	−	0.357596i
$725$	17.3195	−	9.99941i	0.643229	−	0.371369i
$726$	−3.76967	+	7.81631i	−0.139905	+	0.290090i
$727$			1.26742i			0.0470062i	0.999724	+	0.0235031i	$0.00748195\pi$
$727$			1.26742i			0.0470062i	−0.999724	+	0.0235031i	$0.992518\pi$
$728$	−6.55455	−	6.24078i	−0.242928	−	0.231299i
$729$	−24.3664	+	11.6310i	−0.902459	+	0.430776i
$730$	−1.74411	+	3.02088i	−0.0645524	+	0.111808i
$731$	15.9993	+	27.7116i	0.591755	+	1.02495i
$732$	−2.13335	−	3.13292i	−0.0788510	−	0.115796i
$733$	15.8708	+	9.16302i	0.586202	+	0.338444i	0.763594	−	0.645696i	$-0.223433\pi$
$733$	15.8708	+	9.16302i	0.586202	+	0.338444i	−0.177392	+	0.984140i	$0.556766\pi$
$734$	−13.0284			−0.480887
$735$	17.4089	−	2.15675i	0.642138	−	0.0795529i
$736$	1.00000			0.0368605
$737$	5.43645	+	3.13873i	0.200254	+	0.115617i
$738$	23.0189	−	18.3138i	0.847338	−	0.674139i
$739$	17.3186	+	29.9968i	0.637076	+	1.10345i	0.986071	+	0.166324i	$0.0531898\pi$
$739$	17.3186	+	29.9968i	0.637076	+	1.10345i	−0.348995	+	0.937125i	$0.613477\pi$
$740$	5.18890	−	8.98743i	0.190748	−	0.330385i
$741$	−3.16555	−	42.5694i	−0.116290	−	1.56383i
$742$	−7.25423	−	6.90697i	−0.266311	−	0.253563i
$743$			4.55621i			0.167151i	0.996501	+	0.0835756i	$0.0266340\pi$
$743$			4.55621i			0.167151i	−0.996501	+	0.0835756i	$0.973366\pi$
$744$	5.25107	+	2.53250i	0.192514	+	0.0928460i
$745$	−3.44165	+	1.98703i	−0.126092	+	0.0727993i
$746$	−17.3753	+	10.0316i	−0.636154	+	0.367283i
$747$	14.8774	−	37.7794i	0.544337	−	1.38228i
$748$		−	9.50021i		−	0.347362i
$749$	−4.94203	−	16.7865i	−0.180578	−	0.613364i
$750$	−19.7595	+	1.46936i	−0.721516	+	0.0536535i
$751$	2.28060	−	3.95011i	0.0832202	−	0.144142i	−0.821411	−	0.570336i	$-0.806813\pi$
$751$	2.28060	−	3.95011i	0.0832202	−	0.144142i	0.904631	+	0.426195i	$0.140146\pi$
$752$	−5.75052	−	9.96019i	−0.209700	−	0.363211i
$753$	−18.9935	+	12.9335i	−0.692160	+	0.471325i
$754$	−20.3826	−	11.7679i	−0.742292	−	0.428562i
$755$	13.6504			0.496787
$756$	13.7463	+	0.200791i	0.499947	+	0.00730271i
$757$	−7.75387			−0.281819			−0.140910	−	0.990022i	$-0.545003\pi$
$757$	−7.75387			−0.281819			−0.140910	+	0.990022i	$0.545003\pi$
$758$	−10.8977	−	6.29182i	−0.395824	−	0.228529i
$759$	−3.50384	+	2.38593i	−0.127181	+	0.0866037i
$760$	5.21204	+	9.02752i	0.189061	+	0.327462i
$761$	17.4653	−	30.2507i	0.633115	−	1.09659i	−0.353796	−	0.935323i	$-0.615109\pi$
$761$	17.4653	−	30.2507i	0.633115	−	1.09659i	0.986911	−	0.161265i	$-0.0515575\pi$
$762$	27.1148	−	2.01631i	0.982265	−	0.0730433i
$763$	−1.82132	+	7.53116i	−0.0659363	+	0.272646i
$764$			19.6795i			0.711978i
$765$	6.17355	−	15.6770i	0.223205	−	0.566802i
$766$	5.80345	−	3.35063i	0.209687	−	0.121063i
$767$	−32.5587	+	18.7978i	−1.17563	+	0.678748i
$768$	1.56009	+	0.752405i	0.0562950	+	0.0271501i
$769$			19.8213i			0.714774i	0.933956	+	0.357387i	$0.116332\pi$
$769$			19.8213i			0.714774i	−0.933956	+	0.357387i	$0.883668\pi$
$770$	−8.98727	+	2.64590i	−0.323879	+	0.0953517i
$771$	1.05089	+	14.1321i	0.0378469	+	0.508954i
$772$	11.6616	−	20.1985i	0.419711	−	0.726961i
$773$	11.5793	+	20.0559i	0.416477	+	0.721359i	0.995582	−	0.0938937i	$-0.0299314\pi$
$773$	11.5793	+	20.0559i	0.416477	+	0.721359i	−0.579105	+	0.815253i	$0.696598\pi$
$774$	19.3525	−	15.3968i	0.695611	−	0.553425i
$775$	8.47269	+	4.89171i	0.304348	+	0.175715i
$776$	3.37559			0.121177
$777$	−20.8378	+	25.4203i	−0.747552	+	0.911949i
$778$	23.7502			0.851487
$779$	−61.1787	−	35.3216i	−2.19196	−	1.26553i
$780$	4.82490	+	7.08557i	0.172759	+	0.253704i
$781$	−15.1842	−	26.2998i	−0.543334	−	0.941082i
$782$	−1.94087	+	3.36168i	−0.0694052	+	0.120213i
$783$	34.8687	−	7.89537i	1.24611	−	0.282158i
$784$	−6.22644	−	3.19866i	−0.222373	−	0.114238i
$785$		−	4.44580i		−	0.158678i
$786$	−10.0803	+	20.9011i	−0.359551	+	0.745519i
$787$	22.6414	−	13.0720i	0.807080	−	0.465968i	−0.0388610	−	0.999245i	$-0.512373\pi$
$787$	22.6414	−	13.0720i	0.807080	−	0.465968i	0.845941	+	0.533277i	$0.179040\pi$
$788$	−10.8272	+	6.25111i	−0.385705	+	0.222687i
$789$	13.0822	−	27.1256i	0.465738	−	0.965695i
$790$			17.1596i			0.610510i
$791$	31.4711	−	33.0533i	1.11898	−	1.17524i
$792$	−7.26149	+	1.08596i	−0.258026	+	0.0385881i
$793$	−3.74284	+	6.48278i	−0.132912	+	0.230210i
$794$	1.18485	+	2.05223i	0.0420489	+	0.0728308i
$795$	5.33995	+	7.84194i	0.189389	+	0.278125i
$796$	3.95601	+	2.28400i	0.140217	+	0.0809544i
$797$	−28.3000			−1.00244			−0.501218	−	0.865321i	$-0.667115\pi$
$797$	−28.3000			−1.00244			−0.501218	+	0.865321i	$0.667115\pi$
$798$	−11.6475	−	30.8934i	−0.412316	−	1.09361i
$799$	44.6439			1.57939
$800$	2.51723	+	1.45333i	0.0889976	+	0.0513828i
$801$	16.2225	+	20.3904i	0.573193	+	0.720458i
$802$	−9.27203	−	16.0596i	−0.327407	−	0.567085i
$803$	−2.95026	+	5.11000i	−0.104112	+	0.180328i
$804$	−0.329452	−	4.43037i	−0.0116189	−	0.156247i
$805$	3.72072	+	0.899813i	0.131138	+	0.0317143i
$806$		−	11.5137i		−	0.405554i
$807$	−16.3887	−	7.90397i	−0.576909	−	0.278233i
$808$	−4.75812	+	2.74710i	−0.167390	+	0.0966428i
$809$	−0.830641	+	0.479571i	−0.0292038	+	0.0168608i	−0.514531	−	0.857472i	$-0.672034\pi$
$809$	−0.830641	+	0.479571i	−0.0292038	+	0.0168608i	0.485327	+	0.874333i	$0.338701\pi$
$810$	−12.6884	−	2.92673i	−0.445825	−	0.102835i
$811$		−	2.35197i		−	0.0825889i	−0.999147	−	0.0412944i	$-0.986852\pi$
$811$		−	2.35197i		−	0.0825889i	0.999147	−	0.0412944i	$-0.0131482\pi$
$812$	−17.6937	−	4.27901i	−0.620926	−	0.150164i
$813$	−27.0220	+	2.00941i	−0.947701	+	0.0704731i
$814$	8.77732	−	15.2028i	0.307645	−	0.532856i
$815$	−0.870527	−	1.50780i	−0.0304932	−	0.0528158i
$816$	−5.55727	+	3.78421i	−0.194543	+	0.132474i
$817$	−51.4343	−	29.6956i	−1.79946	−	1.03892i
$818$	−33.8328			−1.18294
$819$	−11.4361	−	24.6252i	−0.399608	−	0.860475i
$820$	14.1865			0.495413
$821$	24.6815	+	14.2499i	0.861391	+	0.497324i	0.864478	−	0.502671i	$-0.167649\pi$
$821$	24.6815	+	14.2499i	0.861391	+	0.497324i	−0.00308670	+	0.999995i	$0.500983\pi$
$822$	−4.51680	+	3.07570i	−0.157541	+	0.107277i
$823$	−16.6608	−	28.8574i	−0.580760	−	1.00591i	−0.995389	−	0.0959155i	$-0.969422\pi$
$823$	−16.6608	−	28.8574i	−0.580760	−	1.00591i	0.414629	−	0.909990i	$-0.363911\pi$
$824$	3.90102	−	6.75677i	0.135899	−	0.235383i
$825$	−12.2875	+	0.913725i	−0.427796	+	0.0318118i
$826$	−20.0512	+	21.0593i	−0.697669	+	0.732746i
$827$			1.02702i			0.0357129i	0.999841	+	0.0178564i	$0.00568418\pi$
$827$			1.02702i			0.0357129i	−0.999841	+	0.0178564i	$0.994316\pi$
$828$	2.79136	+	1.09923i	0.0970065	+	0.0382009i
$829$	35.9104	−	20.7329i	1.24722	−	0.720083i	0.276666	−	0.960966i	$-0.410770\pi$
$829$	35.9104	−	20.7329i	1.24722	−	0.720083i	0.970554	+	0.240883i	$0.0774371\pi$
$830$	16.9586	−	9.79108i	0.588643	−	0.339853i
$831$	−6.51240	−	3.14082i	−0.225913	−	0.108954i
$832$		−	3.42072i		−	0.118592i
$833$	22.8376	−	14.7231i	0.791274	−	0.510126i
$834$	2.71658	+	36.5317i	0.0940673	+	1.26499i
$835$	6.63900	−	11.4991i	0.229752	−	0.397942i
$836$	8.81646	+	15.2706i	0.304924	+	0.528144i
$837$	11.8738	+	12.8413i	0.410420	+	0.443859i
$838$	15.5432	+	8.97386i	0.536930	+	0.309997i
$839$	−35.2868			−1.21823			−0.609117	−	0.793080i	$-0.708476\pi$
$839$	−35.2868			−1.21823			−0.609117	+	0.793080i	$0.708476\pi$
$840$	5.12765	+	4.20328i	0.176921	+	0.145027i
$841$	−18.3394			−0.632394
$842$	6.23156	+	3.59779i	0.214754	+	0.123988i
$843$	3.22847	+	4.74114i	0.111194	+	0.163294i
$844$	6.21106	+	10.7579i	0.213794	+	0.370301i
$845$	−0.939468	+	1.62721i	−0.0323187	+	0.0559776i
$846$	−5.10323	−	34.1236i	−0.175453	−	1.17319i
$847$	12.7160	−	3.74366i	0.436927	−	0.128634i
$848$		−	3.78588i		−	0.130008i
$849$	21.9574	−	45.5280i	0.753575	−	1.56252i
$850$	−9.77122	+	5.64142i	−0.335150	+	0.193499i
$851$	−6.21176	+	3.58636i	−0.212936	+	0.122939i
$852$	−9.33611	+	19.3582i	−0.319850	+	0.663200i
$853$			8.56089i			0.293119i	0.989202	+	0.146560i	$0.0468200\pi$
$853$			8.56089i			0.293119i	−0.989202	+	0.146560i	$0.953180\pi$
$854$	−1.36096	+	5.62755i	−0.0465710	+	0.192571i
$855$	4.62536	+	30.9283i	0.158184	+	1.05772i
$856$	3.30697	−	5.72784i	0.113030	−	0.195773i
$857$	−0.873753	−	1.51338i	−0.0298468	−	0.0516962i	0.850716	−	0.525625i	$-0.176169\pi$
$857$	−0.873753	−	1.51338i	−0.0298468	−	0.0516962i	−0.880563	+	0.473929i	$0.842835\pi$
$858$	8.16160	+	11.9857i	0.278633	+	0.409184i
$859$	3.44538	+	1.98919i	0.117555	+	0.0678704i	0.557625	−	0.830093i	$-0.311713\pi$
$859$	3.44538	+	1.98919i	0.117555	+	0.0678704i	−0.440070	+	0.897964i	$0.645046\pi$
$860$	11.9269			0.406703
$861$	−44.3367	−	7.29417i	−1.51099	−	0.248585i
$862$	27.6763			0.942660
$863$	8.66323	+	5.00172i	0.294900	+	0.170261i	0.640150	−	0.768250i	$-0.278872\pi$
$863$	8.66323	+	5.00172i	0.294900	+	0.170261i	−0.345250	+	0.938511i	$0.612206\pi$
$864$	3.52771	+	3.81513i	0.120015	+	0.129793i
$865$	13.7582	+	23.8299i	0.467792	+	0.810240i
$866$	7.12176	−	12.3353i	0.242007	−	0.419169i
$867$	0.248175	+	3.33739i	0.00842848	+	0.113344i
$868$	−2.51503	−	8.54274i	−0.0853657	−	0.289959i
$869$			29.0264i			0.984654i
$870$	15.5304	+	7.49004i	0.526530	+	0.253936i
$871$	−7.59846	+	4.38697i	−0.257464	+	0.148647i
$872$	−2.53621	+	1.46428i	−0.0858870	+	0.0495869i
$873$	9.42249	+	3.71055i	0.318903	+	0.125583i
$874$		−	7.20471i		−	0.243703i
$875$	21.9199	+	20.8706i	0.741027	+	0.705554i
$876$	4.16434	−	0.309669i	0.140700	−	0.0104627i
$877$	−9.85284	+	17.0656i	−0.332707	+	0.576265i	−0.983042	−	0.183383i	$-0.941295\pi$
$877$	−9.85284	+	17.0656i	−0.332707	+	0.576265i	0.650335	+	0.759648i	$0.274629\pi$
$878$	10.7544	+	18.6271i	0.362943	+	0.628636i
$879$	15.1205	−	10.2963i	0.510002	−	0.347285i
$880$	−3.06661	−	1.77051i	−0.103376	−	0.0596839i
$881$	−17.8121			−0.600105			−0.300053	−	0.953923i	$-0.597004\pi$
$881$	−17.8121			−0.600105			−0.300053	+	0.953923i	$0.597004\pi$
$882$	−13.8642	−	15.7729i	−0.466831	−	0.531101i
$883$	24.2005			0.814410			0.407205	−	0.913337i	$-0.366503\pi$
$883$	24.2005			0.814410			0.407205	+	0.913337i	$0.366503\pi$
$884$	11.4994	+	6.63917i	0.386766	+	0.223299i
$885$	22.7654	−	15.5021i	0.765251	−	0.521096i
$886$	−10.5123	−	18.2078i	−0.353167	−	0.611703i
$887$	21.0312	−	36.4271i	0.706158	−	1.22310i	−0.260114	−	0.965578i	$-0.583760\pi$
$887$	21.0312	−	36.4271i	0.706158	−	1.22310i	0.966272	−	0.257524i	$-0.0829066\pi$
$888$	−12.3893	+	0.921295i	−0.415758	+	0.0309167i
$889$	−30.0793	−	28.6394i	−1.00883	−	0.960535i
$890$			12.5665i			0.421230i
$891$	−21.4632	−	4.95073i	−0.719043	−	0.165856i
$892$	4.03300	−	2.32846i	0.135035	−	0.0779625i
$893$	−71.7603	+	41.4308i	−2.40137	+	1.38643i
$894$	4.28514	+	2.06665i	0.143316	+	0.0691190i
$895$		−	22.2559i		−	0.743934i
$896$	−0.747214	−	2.53804i	−0.0249627	−	0.0847901i
$897$	−0.439373	−	5.90855i	−0.0146702	−	0.197281i
$898$	8.30918	−	14.3919i	0.277281	−	0.480265i
$899$	−11.5792	−	20.0558i	−0.386189	−	0.668898i
$900$	5.42897	+	6.82377i	0.180966	+	0.227459i
$901$	12.7269	+	7.34788i	0.423995	+	0.244793i
$902$	23.9972			0.799020
$903$	−37.2748	−	6.13236i	−1.24043	−	0.204072i
$904$	17.2501			0.573728
$905$	24.1125	+	13.9214i	0.801528	+	0.462763i
$906$	−9.19756	−	13.5070i	−0.305569	−	0.448740i
$907$	−29.2429	−	50.6502i	−0.970995	−	1.68181i	−0.692565	−	0.721356i	$-0.743519\pi$
$907$	−29.2429	−	50.6502i	−0.970995	−	1.68181i	−0.278430	−	0.960456i	$-0.589814\pi$
$908$	−0.120944	+	0.209482i	−0.00401368	+	0.00695190i
$909$	−16.3013	+	2.43788i	−0.540681	+	0.0808595i
$910$	3.07801	−	12.7276i	0.102035	−	0.421915i
$911$		−	33.2372i		−	1.10120i	−0.834770	−	0.550599i	$-0.814399\pi$
$911$		−	33.2372i		−	1.10120i	0.834770	−	0.550599i	$-0.185601\pi$
$912$	5.42086	−	11.2400i	0.179503	−	0.372194i
$913$	28.6865	−	16.5622i	0.949385	−	0.548128i
$914$	−4.75524	+	2.74544i	−0.157289	+	0.0908110i
$915$	2.38224	−	4.93951i	0.0787544	−	0.163295i
$916$			18.3151i			0.605147i
$917$	34.0031	−	10.0107i	1.12288	−	0.330583i
$918$	−19.6721	+	4.45437i	−0.649275	+	0.147016i
$919$	23.6889	−	41.0305i	0.781426	−	1.35347i	−0.149685	−	0.988734i	$-0.547826\pi$
$919$	23.6889	−	41.0305i	0.781426	−	1.35347i	0.931111	−	0.364736i	$-0.118841\pi$
$920$	0.723421	+	1.25300i	0.0238505	+	0.0413102i
$921$	−4.41714	−	6.48675i	−0.145550	−	0.213746i
$922$	17.1131	+	9.88026i	0.563590	+	0.325389i
$923$	42.4456			1.39711
$924$	8.67371	+	7.11009i	0.285344	+	0.233905i
$925$	−20.8486			−0.685498
$926$	−22.7526	−	13.1362i	−0.747697	−	0.431683i
$927$	18.3164	−	14.5725i	0.601590	−	0.478623i
$928$	−3.44018	−	5.95857i	−0.112930	−	0.195600i
$929$	10.9618	−	18.9864i	0.359646	−	0.622925i	−0.628256	−	0.778007i	$-0.716231\pi$
$929$	10.9618	−	18.9864i	0.359646	−	0.622925i	0.987902	+	0.155082i	$0.0495642\pi$
$930$	0.625509	+	8.41167i	0.0205113	+	0.275829i
$931$	−23.0454	+	44.8597i	−0.755283	+	1.47022i
$932$			9.21222i			0.301756i
$933$	0.410307	+	0.197884i	0.0134328	+	0.00647842i
$934$	−8.99957	+	5.19590i	−0.294475	+	0.170015i
$935$	11.9038	−	6.87265i	0.389295	−	0.224760i
$936$	3.76016	−	9.54847i	0.122905	−	0.312102i
$937$		−	30.2316i		−	0.987625i	−0.869568	−	0.493812i	$-0.835603\pi$
$937$		−	30.2316i		−	0.987625i	0.869568	−	0.493812i	$-0.164397\pi$
$938$	−4.67948	+	4.91475i	−0.152791	+	0.160472i
$939$	−12.9496	+	0.962961i	−0.422595	+	0.0314250i
$940$	8.32008	−	14.4108i	0.271371	−	0.470029i
$941$	−1.14371	−	1.98096i	−0.0372839	−	0.0645776i	0.846781	−	0.531941i	$-0.178537\pi$
$941$	−1.14371	−	1.98096i	−0.0372839	−	0.0645776i	−0.884065	+	0.467364i	$0.845204\pi$
$942$	−4.39912	+	2.99557i	−0.143331	+	0.0976009i
$943$	−8.49149	−	4.90256i	−0.276521	−	0.159649i
$944$	−10.9905			−0.357711
$945$	9.69274	+	17.3693i	0.315305	+	0.565025i
$946$	20.1750			0.655945
$947$	18.1446	+	10.4758i	0.589622	+	0.340418i	0.764948	−	0.644092i	$-0.222765\pi$
$947$	18.1446	+	10.4758i	0.589622	+	0.340418i	−0.175326	+	0.984510i	$0.556098\pi$
$948$	16.9794	−	11.5621i	0.551465	−	0.375518i
$949$	−4.12354	−	7.14219i	−0.133856	−	0.231845i
$950$	10.4708	−	18.1359i	0.339717	−	0.588408i
$951$	51.5621	−	3.83427i	1.67202	−	0.124335i
$952$	9.98233	+	2.41411i	0.323529	+	0.0782417i
$953$			0.303311i			0.00982520i	0.999988	+	0.00491260i	$0.00156374\pi$
$953$			0.303311i			0.00982520i	−0.999988	+	0.00491260i	$0.998436\pi$
$954$	4.16155	−	10.5678i	0.134735	−	0.342144i
$955$	−24.6584	+	14.2365i	−0.797926	+	0.460683i
$956$	19.4018	−	11.2017i	0.627501	−	0.362288i
$957$	26.2706	+	12.6698i	0.849207	+	0.409557i
$958$		−	17.1287i		−	0.553402i
$959$	8.11336	+	1.96212i	0.261994	+	0.0633602i
$960$	0.185839	+	2.49910i	0.00599791	+	0.0806582i
$961$	−9.83544	+	17.0355i	−0.317272	+	0.549532i
$962$	12.2680	+	21.2487i	0.395535	+	0.685086i
$963$	15.5271	−	12.3533i	0.500355	−	0.398081i
$964$	−25.7428	−	14.8626i	−0.829120	−	0.478693i
$965$	33.7450			1.08629
$966$	−1.61665	−	4.28794i	−0.0520148	−	0.137962i
$967$	17.1539			0.551633			0.275817	−	0.961210i	$-0.411052\pi$
$967$	17.1539			0.551633			0.275817	+	0.961210i	$0.411052\pi$
$968$	4.33892	+	2.50508i	0.139458	+	0.0805163i
$969$	27.2641	+	40.0385i	0.875851	+	1.28622i
$970$	2.44197	+	4.22962i	0.0784070	+	0.135805i
$971$	−21.3853	+	37.0404i	−0.686287	+	1.18868i	0.286743	+	0.958007i	$0.407427\pi$
$971$	−21.3853	+	37.0404i	−0.686287	+	1.18868i	−0.973030	+	0.230677i	$0.925906\pi$
$972$	5.65341	+	14.5272i	0.181333	+	0.465960i
$973$	38.5858	−	40.5258i	1.23700	−	1.29920i
$974$		−	16.3253i		−	0.523097i
$975$	7.48105	−	15.5118i	0.239585	−	0.496774i
$976$	−1.89515	+	1.09417i	−0.0606623	+	0.0350234i
$977$	−27.8828	+	16.0981i	−0.892050	+	0.515025i	−0.874613	−	0.484823i	$-0.838884\pi$
$977$	−27.8828	+	16.0981i	−0.892050	+	0.515025i	−0.0174376	+	0.999848i	$0.505551\pi$
$978$	−0.905405	+	1.87733i	−0.0289517	+	0.0600305i
$979$			21.2569i			0.679375i
$980$	−0.496411	−	10.1157i	−0.0158573	−	0.323135i
$981$	−8.68907	+	1.29946i	−0.277421	+	0.0414886i
$982$	−9.25465	+	16.0295i	−0.295328	+	0.511523i
$983$	16.8936	+	29.2606i	0.538822	+	0.933268i	0.998968	+	0.0454241i	$0.0144639\pi$
$983$	16.8936	+	29.2606i	0.538822	+	0.933268i	−0.460145	+	0.887844i	$0.652203\pi$
$984$	−9.55879	−	14.0375i	−0.304723	−	0.447499i
$985$	−15.6653	−	9.04437i	−0.499138	−	0.288177i
$986$	26.7077			0.850547
$987$	−33.4121	+	40.7600i	−1.06352	+	1.29740i
$988$	−24.6453			−0.784073
$989$	−7.13898	−	4.12169i	−0.227006	−	0.131062i
$990$	−6.61383	−	8.31305i	−0.210201	−	0.264206i
$991$	−6.50216	−	11.2621i	−0.206548	−	0.357752i	0.744077	−	0.668094i	$-0.232890\pi$
$991$	−6.50216	−	11.2621i	−0.206548	−	0.357752i	−0.950625	+	0.310342i	$0.899556\pi$
$992$	1.68294	−	2.91493i	0.0534333	−	0.0925492i
$993$	−1.47139	−	19.7868i	−0.0466932	−	0.627916i
$994$	31.4930	−	9.27171i	0.998897	−	0.294081i
$995$			6.60918i			0.209525i
$996$	−21.1149	−	10.1834i	−0.669052	−	0.322672i
$997$	19.0599	−	11.0042i	0.603633	−	0.348508i	−0.166836	−	0.985985i	$-0.553355\pi$
$997$	19.0599	−	11.0042i	0.603633	−	0.348508i	0.770470	+	0.637477i	$0.220022\pi$
$998$	−9.00749	+	5.20048i	−0.285127	+	0.164618i
$999$	−35.5958	−	11.0470i	−1.12620	−	0.349513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.3	✓	56
3.2	odd	2	inner	966.2.l.c.47.17	yes	56
7.3	odd	6	inner	966.2.l.c.185.17	yes	56
21.17	even	6	inner	966.2.l.c.185.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.3	✓	56	1.1	even	1	trivial
966.2.l.c.47.17	yes	56	3.2	odd	2	inner
966.2.l.c.185.3	yes	56	21.17	even	6	inner
966.2.l.c.185.17	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.43165 + 0.974877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.723421 + 1.25300i) q^{5} +(1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} -1.00000i q^{8} +(1.09923 - 2.79136i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.43165 + 0.974877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.723421 + 1.25300i) q^{5} +(1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} -1.00000i q^{8} +(1.09923 - 2.79136i) q^{9} +(1.25300 - 0.723421i) q^{10} +(2.11952 - 1.22371i) q^{11} +(-1.56009 - 0.752405i) q^{12} +3.42072i q^{13} +(0.747214 + 2.53804i) q^{14} +(-0.185839 - 2.49910i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.94087 - 3.36168i) q^{17} +(-2.34764 + 1.86777i) q^{18} +(6.23947 + 3.60236i) q^{19} -1.44684 q^{20} +(4.52179 + 0.743914i) q^{21} -2.44742 q^{22} +(0.866025 + 0.500000i) q^{23} +(0.974877 + 1.43165i) q^{24} +(1.45333 + 2.51723i) q^{25} +(1.71036 - 2.96243i) q^{26} +(1.14752 + 5.06786i) q^{27} +(0.621916 - 2.57162i) q^{28} -6.88037i q^{29} +(-1.08861 + 2.25721i) q^{30} +(2.91493 - 1.68294i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.84145 + 3.81819i) q^{33} +3.88173i q^{34} +(3.67215 - 1.08110i) q^{35} +(2.96700 - 0.443719i) q^{36} +(-3.58636 + 6.21176i) q^{37} +(-3.60236 - 6.23947i) q^{38} +(-3.33478 - 4.89727i) q^{39} +(1.25300 + 0.723421i) q^{40} -9.80512 q^{41} +(-3.54403 - 2.90514i) q^{42} -8.24338 q^{43} +(2.11952 + 1.22371i) q^{44} +(2.70237 + 3.39666i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-5.75052 + 9.96019i) q^{47} +(-0.128444 - 1.72728i) q^{48} +(0.343100 + 6.99159i) q^{49} -2.90665i q^{50} +(6.05586 + 2.92063i) q^{51} +(-2.96243 + 1.71036i) q^{52} +(-3.27867 + 1.89294i) q^{53} +(1.54015 - 4.96266i) q^{54} +3.54102i q^{55} +(-1.82440 + 1.91613i) q^{56} +(-12.4446 + 0.925404i) q^{57} +(-3.44018 + 5.95857i) q^{58} +(5.49526 + 9.51808i) q^{59} +(2.07137 - 1.41049i) q^{60} +(1.89515 + 1.09417i) q^{61} -3.36587 q^{62} +(-7.19884 + 3.34317i) q^{63} -1.00000 q^{64} +(-4.28617 - 2.47462i) q^{65} +(3.50384 - 2.38593i) q^{66} +(1.28247 + 2.22130i) q^{67} +(1.94087 - 3.36168i) q^{68} +(-1.72728 + 0.128444i) q^{69} +(-3.72072 - 0.899813i) q^{70} -12.4084i q^{71} +(-2.79136 - 1.09923i) q^{72} +(-2.08792 + 1.20546i) q^{73} +(6.21176 - 3.58636i) q^{74} +(-4.53464 - 2.18698i) q^{75} +7.20471i q^{76} +(-6.29382 - 1.52209i) q^{77} +(0.439373 + 5.90855i) q^{78} +(-5.93001 + 10.2711i) q^{79} +(-0.723421 - 1.25300i) q^{80} +(-6.58339 - 6.13669i) q^{81} +(8.49149 + 4.90256i) q^{82} +13.5344 q^{83} +(1.61665 + 4.28794i) q^{84} +5.61625 q^{85} +(7.13898 + 4.12169i) q^{86} +(6.70751 + 9.85026i) q^{87} +(-1.22371 - 2.11952i) q^{88} +(-4.34273 + 7.52183i) q^{89} +(-0.641991 - 4.29278i) q^{90} +(6.24078 - 6.55455i) q^{91} +1.00000i q^{92} +(-2.53250 + 5.25107i) q^{93} +(9.96019 - 5.75052i) q^{94} +(-9.02752 + 5.21204i) q^{95} +(-0.752405 + 1.56009i) q^{96} +3.37559i q^{97} +(3.19866 - 6.22644i) q^{98} +(-1.08596 - 7.26149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Introduction

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