LMFDB - Embedded newform 966.2.l.c.47.17

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			47.17
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.56009 + 0.752405i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.723421 - 1.25300i) q^{5} +(-1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} +1.00000i q^{8} +(1.86777 - 2.34764i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.56009 + 0.752405i) 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} +(1.86777 - 2.34764i) q^{9} +(1.25300 - 0.723421i) q^{10} +(-2.11952 + 1.22371i) q^{11} +(-1.43165 - 0.974877i) 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} +(2.79136 - 1.09923i) q^{18} +(6.23947 + 3.60236i) q^{19} +1.44684 q^{20} +(4.36203 + 1.40453i) q^{21} -2.44742 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-0.752405 - 1.56009i) 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} +(-1.41049 + 2.07137i) q^{30} +(2.91493 - 1.68294i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.38593 - 3.50384i) 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} +(-2.57377 - 5.33664i) q^{39} +(1.25300 + 0.723421i) q^{40} +9.80512 q^{41} +(3.07536 + 3.39738i) q^{42} -8.24338 q^{43} +(-2.11952 - 1.22371i) q^{44} +(-1.59041 - 4.03866i) 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} +(-5.55727 - 3.78421i) q^{51} +(-2.96243 + 1.71036i) q^{52} +(3.27867 - 1.89294i) q^{53} +(-3.52771 + 3.81513i) 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} +(-2.25721 + 1.08861i) q^{60} +(1.89515 + 1.09417i) q^{61} +3.36587 q^{62} +(-7.86194 + 1.09081i) q^{63} -1.00000 q^{64} +(4.28617 + 2.47462i) q^{65} +(3.81819 - 1.84145i) 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} +(2.34764 + 1.86777i) q^{72} +(-2.08792 + 1.20546i) q^{73} +(-6.21176 + 3.58636i) q^{74} +(-4.16130 - 2.83363i) 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} +(-2.02284 - 8.76973i) q^{81} +(8.49149 + 4.90256i) q^{82} -13.5344 q^{83} +(0.964652 + 4.47989i) q^{84} +5.61625 q^{85} +(-7.13898 - 4.12169i) q^{86} +(-5.17682 - 10.7340i) 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} +(-3.28131 + 4.81875i) q^{93} +(9.96019 - 5.75052i) q^{94} +(9.02752 - 5.21204i) q^{95} +(0.974877 - 1.43165i) 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
$3$	−1.56009	+	0.752405i	−0.900720	+	0.434401i
$3$	−1.56009	+	0.752405i	−0.900720	+	0.434401i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.723421	−	1.25300i	0.323524	−	0.560359i	−0.657689	−	0.753290i	$-0.728466\pi$
$5$	0.723421	−	1.25300i	0.323524	−	0.560359i	0.981212	+	0.192930i	$0.0617992\pi$
$6$	−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
$9$	1.86777	−	2.34764i	0.622591	−	0.782547i
$10$	1.25300	−	0.723421i	0.396234	−	0.228766i
$11$	−2.11952	+	1.22371i	−0.639061	+	0.368962i	−0.784253	−	0.620442i	$-0.786953\pi$
$11$	−2.11952	+	1.22371i	−0.639061	+	0.368962i	0.145192	+	0.989403i	$0.453620\pi$
$12$	−1.43165	−	0.974877i	−0.413281	−	0.281423i
$13$			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	0.999440	−	0.0334756i	$-0.0106576\pi$
$17$	1.94087	+	3.36168i	0.470729	+	0.815327i	−0.528710	+	0.848802i	$0.677324\pi$
$18$	2.79136	−	1.09923i	0.657930	−	0.259091i
$19$	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
$21$	4.36203	+	1.40453i	0.951872	+	0.306494i
$22$	−2.44742			−0.521791
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	−0.752405	−	1.56009i	−0.153584	−	0.318452i
$25$	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	$0.220580\pi$
$29$			6.88037i			1.27765i	−0.769351	+	0.638826i	$0.779420\pi$
$30$	−1.41049	+	2.07137i	−0.257519	+	0.378178i
$31$	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
$33$	2.38593	−	3.50384i	0.415337	−	0.609940i
$34$			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
$39$	−2.57377	−	5.33664i	−0.412133	−	0.854547i
$40$	1.25300	+	0.723421i	0.198117	+	0.114383i
$41$	9.80512			1.53130			0.765652	−	0.643255i	$-0.222417\pi$
$41$	9.80512			1.53130			0.765652	+	0.643255i	$0.222417\pi$
$42$	3.07536	+	3.39738i	0.474538	+	0.524226i
$43$	−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
$45$	−1.59041	−	4.03866i	−0.237085	−	0.602047i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	5.75052	−	9.96019i	0.838799	−	1.45284i	−0.0521006	−	0.998642i	$-0.516592\pi$
$47$	5.75052	−	9.96019i	0.838799	−	1.45284i	0.890900	−	0.454200i	$-0.150075\pi$
$48$	0.128444	−	1.72728i	0.0185393	−	0.249312i
$49$	0.343100	+	6.99159i	0.0490143	+	0.998798i
$50$			2.90665i			0.411062i
$51$	−5.55727	−	3.78421i	−0.778174	−	0.529895i
$52$	−2.96243	+	1.71036i	−0.410816	+	0.237185i
$53$	3.27867	−	1.89294i	0.450360	−	0.260015i	−0.257622	−	0.966246i	$-0.582939\pi$
$53$	3.27867	−	1.89294i	0.450360	−	0.260015i	0.707982	+	0.706230i	$0.249606\pi$
$54$	−3.52771	+	3.81513i	−0.480061	+	0.519174i
$55$			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	$-0.912901\pi$
$59$	−5.49526	−	9.51808i	−0.715422	−	1.23915i	0.247374	−	0.968920i	$-0.420432\pi$
$60$	−2.25721	+	1.08861i	−0.291404	+	0.140539i
$61$	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
$63$	−7.86194	+	1.09081i	−0.990512	+	0.137429i
$64$	−1.00000			−0.125000
$65$	4.28617	+	2.47462i	0.531634	+	0.306939i
$66$	3.81819	−	1.84145i	0.469987	−	0.226666i
$67$	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	$0.263429\pi$
$71$			12.4084i			1.47260i	−0.676654	+	0.736301i	$0.736571\pi$
$72$	2.34764	+	1.86777i	0.276672	+	0.220119i
$73$	−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
$75$	−4.16130	−	2.83363i	−0.480505	−	0.327199i
$76$			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
$81$	−2.02284	−	8.76973i	−0.224760	−	0.974414i
$82$	8.49149	+	4.90256i	0.937728	+	0.541397i
$83$	−13.5344			−1.48560			−0.742798	−	0.669516i	$-0.766502\pi$
$83$	−13.5344			−1.48560			−0.742798	+	0.669516i	$0.766502\pi$
$84$	0.964652	+	4.47989i	0.105252	+	0.488796i
$85$	5.61625			0.609168
$86$	−7.13898	−	4.12169i	−0.769816	−	0.444453i
$87$	−5.17682	−	10.7340i	−0.555013	−	1.15081i
$88$	−1.22371	−	2.11952i	−0.130448	−	0.225942i
$89$	4.34273	−	7.52183i	0.460329	−	0.797313i	−0.538648	−	0.842531i	$-0.681065\pi$
$89$	4.34273	−	7.52183i	0.460329	−	0.797313i	0.998977	+	0.0452180i	$0.0143982\pi$
$90$	0.641991	−	4.29278i	0.0676718	−	0.452499i
$91$	6.24078	−	6.55455i	0.654212	−	0.687103i
$92$		−	1.00000i		−	0.104257i
$93$	−3.28131	+	4.81875i	−0.340256	+	0.499681i
$94$	9.96019	−	5.75052i	1.02731	−	0.593120i
$95$	9.02752	−	5.21204i	0.926204	−	0.534744i
$96$	0.974877	−	1.43165i	0.0994980	−	0.146117i
$97$			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	0.969717	−	0.244232i	$-0.0785359\pi$
$101$	2.74710	+	4.75812i	0.273347	+	0.473451i	−0.696370	+	0.717683i	$0.745203\pi$
$102$	−2.92063	−	6.05586i	−0.289186	−	0.599619i
$103$	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
$105$	4.91546	−	4.44956i	0.479700	−	0.434232i
$106$	3.78588			0.367717
$107$	−5.72784	−	3.30697i	−0.553731	−	0.319697i	0.196895	−	0.980425i	$-0.436914\pi$
$107$	−5.72784	−	3.30697i	−0.553731	−	0.319697i	−0.750625	+	0.660728i	$0.770248\pi$
$108$	−4.96266	+	1.54015i	−0.477532	+	0.148201i
$109$	−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	$-0.698720\pi$
$113$		−	17.2501i		−	1.62275i	0.584527	−	0.811374i	$-0.301280\pi$
$114$	−10.3146	−	7.02371i	−0.966052	−	0.657831i
$115$	−1.25300	+	0.723421i	−0.116843	+	0.0674593i
$116$	−5.95857	+	3.44018i	−0.553239	+	0.319413i
$117$	8.03063	+	6.38914i	0.742432	+	0.590676i
$118$		−	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
$123$	−15.2969	+	7.37742i	−1.37927	+	0.665200i
$124$	2.91493	+	1.68294i	0.261769	+	0.151132i
$125$	11.4397			1.02320
$126$	−7.35405	−	2.98630i	−0.655151	−	0.266041i
$127$	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
$129$	12.8604	−	6.20236i	1.13230	−	0.546087i
$130$	2.47462	+	4.28617i	0.217039	+	0.375922i
$131$	6.69869	−	11.6025i	0.585267	−	1.01371i	−0.409575	−	0.912276i	$-0.634323\pi$
$131$	6.69869	−	11.6025i	0.585267	−	1.01371i	0.994842	−	0.101436i	$-0.0323437\pi$
$132$	4.22738	+	0.314357i	0.367946	+	0.0273612i
$133$	−5.38347	−	18.2859i	−0.466806	−	1.58559i
$134$			2.56494i			0.221577i
$135$	5.51989	+	5.10404i	0.475077	+	0.439286i
$136$	−3.36168	+	1.94087i	−0.288261	+	0.166428i
$137$	2.73228	−	1.57748i	0.233434	−	0.134773i	−0.378721	−	0.925511i	$-0.623636\pi$
$137$	2.73228	−	1.57748i	0.233434	−	0.134773i	0.612155	+	0.790737i	$0.290303\pi$
$138$	1.43165	+	0.974877i	0.121870	+	0.0829870i
$139$			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
$144$	1.09923	+	2.79136i	0.0916025	+	0.232613i
$145$	8.62111	+	4.97740i	0.715944	+	0.413350i
$146$	−2.41092			−0.199529
$147$	−5.79577	−	10.6494i	−0.478027	−	0.878345i
$148$	−7.17272			−0.589594
$149$	−2.37873	−	1.37336i	−0.194873	−	0.112510i	0.399389	−	0.916782i	$-0.369222\pi$
$149$	−2.37873	−	1.37336i	−0.194873	−	0.112510i	−0.594262	+	0.804272i	$0.702556\pi$
$150$	−2.18698	−	4.53464i	−0.178566	−	0.370252i
$151$	−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
$156$	3.33478	−	4.89727i	0.266996	−	0.392096i
$157$	−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
$159$	−3.69077	+	5.42004i	−0.292697	+	0.429837i
$160$			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
$165$	−2.66428	−	5.52432i	−0.207414	−	0.430068i
$166$	−11.7212	−	6.76721i	−0.909738	−	0.525237i
$167$	9.17724			0.710156			0.355078	−	0.934837i	$-0.384454\pi$
$167$	9.17724			0.710156			0.355078	+	0.934837i	$0.384454\pi$
$168$	−1.40453	+	4.36203i	−0.108362	+	0.336538i
$169$	1.29865			0.0998959
$170$	4.86381	+	2.80812i	0.373038	+	0.215373i
$171$	20.1110	−	7.91964i	1.53792	−	0.605630i
$172$	−4.12169	−	7.13898i	−0.314276	−	0.544342i
$173$	−9.50912	+	16.4703i	−0.722965	+	1.25221i	0.236841	+	0.971548i	$0.423888\pi$
$173$	−9.50912	+	16.4703i	−0.722965	+	1.25221i	−0.959806	+	0.280664i	$0.909445\pi$
$174$	0.883744	−	11.8843i	0.0669964	−	0.900949i
$175$	1.80769	−	7.47480i	0.136649	−	0.565041i
$176$		−	2.44742i		−	0.184481i
$177$	15.7346	+	10.7144i	1.18268	+	0.805344i
$178$	7.52183	−	4.34273i	0.563785	−	0.325502i
$179$	13.3216	−	7.69121i	0.995701	−	0.574868i	0.0887274	−	0.996056i	$-0.471720\pi$
$179$	13.3216	−	7.69121i	0.995701	−	0.574868i	0.906973	+	0.421188i	$0.138387\pi$
$180$	2.70237	−	3.39666i	0.201423	−	0.253172i
$181$		−	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
$186$	−5.25107	+	2.53250i	−0.385027	+	0.185692i
$187$	−8.22742	−	4.75010i	−0.601649	−	0.347362i
$188$	11.5010			0.838799
$189$	11.4446	−	7.61713i	0.832474	−	0.554064i
$190$	10.4241			0.756242
$191$	−17.0429	−	9.83973i	−1.23318	−	0.711978i	−0.265490	−	0.964114i	$-0.585534\pi$
$191$	−17.0429	−	9.83973i	−1.23318	−	0.711978i	−0.967692	+	0.252136i	$0.918867\pi$
$192$	1.56009	−	0.752405i	0.112590	−	0.0543001i
$193$	−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	$-0.853071\pi$
$197$		−	12.5022i		−	0.890747i	0.895345	−	0.445373i	$-0.146929\pi$
$198$	−4.57122	+	5.74565i	−0.324862	+	0.408326i
$199$	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
$201$	−3.67209	−	2.50050i	−0.259009	−	0.176372i
$202$			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
$207$	−2.79136	+	1.09923i	−0.194013	+	0.0764018i
$208$	−2.96243	−	1.71036i	−0.205408	−	0.118592i
$209$	−17.6329			−1.21970
$210$	6.48169	−	1.39570i	0.447279	−	0.0963124i
$211$	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
$213$	−9.33611	−	19.3582i	−0.639700	−	1.32640i
$214$	−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
$219$	2.35035	−	3.45159i	0.158822	−	0.233237i
$220$	−3.06661	+	1.77051i	−0.206751	+	0.119368i
$221$	−11.4994	+	6.63917i	−0.773531	+	0.446599i
$222$	6.99252	−	10.2688i	0.469307	−	0.689198i
$223$		−	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	0.861984	−	0.506936i	$-0.169222\pi$
$227$	−0.120944	−	0.209482i	−0.00802737	−	0.0139038i	−0.870011	+	0.493032i	$0.835889\pi$
$228$	−5.42086	−	11.2400i	−0.359005	−	0.744388i
$229$	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
$231$	−10.9642	+	2.36090i	−0.721389	+	0.155336i
$232$	−6.88037			−0.451718
$233$	−7.97801	−	4.60611i	−0.522657	−	0.301756i	0.215364	−	0.976534i	$-0.430906\pi$
$233$	−7.97801	−	4.60611i	−0.522657	−	0.301756i	−0.738021	+	0.674778i	$0.764240\pi$
$234$	3.76016	+	9.54847i	0.245810	+	0.624203i
$235$	−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	$0.257964\pi$
$239$			22.4033i			1.44915i	−0.689196	+	0.724575i	$0.742036\pi$
$240$	−2.07137	−	1.41049i	−0.133706	−	0.0910469i
$241$	−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
$243$	9.75420	+	12.1596i	0.625732	+	0.780038i
$244$			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
$249$	21.1149	−	10.1834i	1.33810	−	0.645344i
$250$	9.90704	+	5.71983i	0.626576	+	0.361754i
$251$	−13.2669			−0.837396			−0.418698	−	0.908125i	$-0.637513\pi$
$251$	−13.2669			−0.837396			−0.418698	+	0.908125i	$0.637513\pi$
$252$	−4.87564	−	6.26324i	−0.307136	−	0.394547i
$253$	2.44742			0.153868
$254$	13.5948	+	7.84898i	0.853015	+	0.492489i
$255$	−8.76186	+	4.22569i	−0.548689	+	0.264623i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.09084	+	7.08554i	−0.255180	+	0.441984i	−0.964944	−	0.262455i	$-0.915468\pi$
$257$	−4.09084	+	7.08554i	−0.255180	+	0.441984i	0.709765	+	0.704439i	$0.248801\pi$
$258$	14.2386	+	1.05882i	0.886459	+	0.0659190i
$259$	18.2047	−	5.35956i	1.13118	−	0.333027i
$260$			4.94924i			0.306939i
$261$	16.1526	+	12.8510i	0.999823	+	0.795455i
$262$	11.6025	−	6.69869i	0.716803	−	0.413846i
$263$	15.0577	−	8.69357i	0.928498	−	0.536069i	0.0421620	−	0.999111i	$-0.486575\pi$
$263$	15.0577	−	8.69357i	0.928498	−	0.536069i	0.886336	+	0.463042i	$0.153242\pi$
$264$	3.50384	+	2.38593i	0.215646	+	0.146844i
$265$		−	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	0.660291	−	0.751010i	$-0.270433\pi$
$269$	−5.25247	−	9.09754i	−0.320249	−	0.554687i	−0.980539	+	0.196323i	$0.937100\pi$
$270$	2.22835	+	7.18017i	0.135613	+	0.436972i
$271$	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
$273$	−4.80452	+	14.9213i	−0.290783	+	0.903078i
$274$	3.15496			0.190598
$275$	−6.16072	−	3.55689i	−0.371505	−	0.214489i
$276$	0.752405	+	1.56009i	0.0452894	+	0.0939065i
$277$	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	$0.0314936\pi$
$281$			3.31167i			0.197558i	−0.995109	+	0.0987788i	$0.968506\pi$
$282$	−11.2121	+	16.4654i	−0.667670	+	0.980502i
$283$	−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
$285$	−10.1622	+	14.9236i	−0.601956	+	0.883998i
$286$		−	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
$291$	−2.53981	−	5.26623i	−0.148886	−	0.308712i
$292$	−2.08792	−	1.20546i	−0.122186	−	0.0705442i
$293$	10.5616			0.617016			0.308508	−	0.951222i	$-0.400170\pi$
$293$	10.5616			0.617016			0.308508	+	0.951222i	$0.400170\pi$
$294$	0.305399	−	12.1205i	0.0178112	−	0.706882i
$295$	−15.9015			−0.925824
$296$	−6.21176	−	3.58636i	−0.361051	−	0.208453i
$297$	−3.76938	−	12.1457i	−0.218721	−	0.704764i
$298$	−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
$303$	−7.86577	−	5.35617i	−0.451877	−	0.307704i
$304$	−6.23947	+	3.60236i	−0.357858	+	0.206609i
$305$	2.74198	−	1.58308i	0.157005	−	0.0906471i
$306$	9.11291	+	7.25020i	0.520951	+	0.414466i
$307$			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	0.869730	−	0.493528i	$-0.164293\pi$
$311$	0.131501	+	0.227766i	0.00745672	+	0.0129154i	−0.862273	+	0.506444i	$0.830960\pi$
$312$	5.33664	−	2.57377i	0.302128	−	0.145711i
$313$	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
$315$	−4.32071	+	10.6401i	−0.243444	+	0.599504i
$316$	−11.8600			−0.667179
$317$	25.8522	+	14.9258i	1.45201	+	0.838316i	0.998595	−	0.0529853i	$-0.0168736\pi$
$317$	25.8522	+	14.9258i	1.45201	+	0.838316i	0.453411	+	0.891302i	$0.350207\pi$
$318$	−5.90632	+	2.84851i	−0.331210	+	0.159737i
$319$	−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
$324$	6.58339	−	6.13669i	0.365744	−	0.340927i
$325$	−8.61076	+	4.97142i	−0.477639	+	0.275765i
$326$	−1.04213	+	0.601674i	−0.0577183	+	0.0333237i
$327$	4.19268	+	2.85499i	0.231856	+	0.157881i
$328$			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
$333$	7.88447	+	20.0217i	0.432066	+	1.09718i
$334$	7.94772	+	4.58862i	0.434880	+	0.251078i
$335$	3.71106			0.202757
$336$	−3.39738	+	3.07536i	−0.185342	+	0.167775i
$337$	−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
$339$	12.9790	+	26.9117i	0.704924	+	1.46164i
$340$	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
$345$	1.41049	−	2.07137i	0.0759383	−	0.111519i
$346$	−16.4703	+	9.50912i	−0.885448	+	0.511214i
$347$	−31.3790	+	18.1167i	−1.68451	+	0.972554i	−0.725918	+	0.687781i	$0.758585\pi$
$347$	−31.3790	+	18.1167i	−1.68451	+	0.972554i	−0.958595	+	0.284773i	$0.908082\pi$
$348$	6.70751	−	9.85026i	0.359560	−	0.528029i
$349$		−	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	0.617889	−	0.786265i	$-0.287988\pi$
$353$	−6.98889	−	12.1051i	−0.371981	−	0.644290i	−0.989870	+	0.141975i	$0.954655\pi$
$354$	8.26933	+	17.1462i	0.439510	+	0.911312i
$355$	15.5477	+	8.97646i	0.825186	+	0.476421i
$356$	8.68546			0.460329
$357$	3.74452	+	17.3897i	0.198181	+	0.920363i
$358$	15.3824			0.812986
$359$	−3.84620	−	2.22060i	−0.202995	−	0.117199i	0.395057	−	0.918657i	$-0.370725\pi$
$359$	−3.84620	−	2.22060i	−0.202995	−	0.117199i	−0.598052	+	0.801458i	$0.704058\pi$
$360$	4.03866	−	1.59041i	0.212856	−	0.0838220i
$361$	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
$366$	−3.13292	−	2.13335i	−0.163760	−	0.111512i
$367$	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
$369$	18.3138	−	23.0189i	0.953376	−	1.19832i
$370$			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
$375$	−17.8469	+	8.60726i	−0.921612	+	0.444477i
$376$	9.96019	+	5.75052i	0.513657	+	0.296560i
$377$	−23.5358			−1.21216
$378$	13.7199	−	0.874313i	0.705675	−	0.0449698i
$379$	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
$381$	−24.4903	+	11.8112i	−1.25467	+	0.605107i
$382$	−9.83973	−	17.0429i	−0.503444	−	0.871991i
$383$	3.35063	−	5.80345i	0.171209	−	0.296543i	−0.767634	−	0.640889i	$-0.778566\pi$
$383$	3.35063	−	5.80345i	0.171209	−	0.296543i	0.938843	+	0.344346i	$0.111899\pi$
$384$	1.72728	+	0.128444i	0.0881450	+	0.00655465i
$385$	6.46025	−	6.78505i	0.329245	−	0.345798i
$386$		−	23.3233i		−	1.18712i
$387$	−15.3968	+	19.3525i	−0.782662	+	0.983743i
$388$	−2.92335	+	1.68780i	−0.148411	+	0.0856849i
$389$	20.5683	−	11.8751i	1.04285	−	0.602092i	0.122214	−	0.992504i	$-0.461001\pi$
$389$	20.5683	−	11.8751i	1.04285	−	0.602092i	0.920641	+	0.390411i	$0.127667\pi$
$390$	−7.08557	−	4.82490i	−0.358792	−	0.244319i
$391$		−	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
$396$	−6.83162	+	2.69027i	−0.343302	+	0.135191i
$397$	−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
$399$	22.1571	+	24.4771i	1.10924	+	1.22539i
$400$	−2.90665			−0.145333
$401$	−16.0596	−	9.27203i	−0.801980	−	0.463023i	0.0421831	−	0.999110i	$-0.486569\pi$
$401$	−16.0596	−	9.27203i	−0.801980	−	0.463023i	−0.844163	+	0.536087i	$0.819902\pi$
$402$	−1.92987	−	4.00154i	−0.0962532	−	0.199579i
$403$	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
$408$	3.78421	−	5.55727i	0.187346	−	0.275126i
$409$	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
$411$	−3.07570	+	4.51680i	−0.151713	+	0.222797i
$412$			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
$417$	−15.9132	−	32.9957i	−0.779274	−	1.61581i
$418$	−15.2706	−	8.81646i	−0.746908	−	0.431227i
$419$	17.9477			0.876803			0.438402	−	0.898779i	$-0.355545\pi$
$419$	17.9477			0.876803			0.438402	+	0.898779i	$0.355545\pi$
$420$	6.31116	+	2.03214i	0.307953	+	0.0991581i
$421$	−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
$423$	−12.6423	−	32.1035i	−0.614689	−	1.56093i
$424$	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
$429$	11.9857	+	8.16160i	0.578673	+	0.394046i
$430$	−10.3290	+	5.96343i	−0.498107	+	0.287582i
$431$	23.9684	−	13.8382i	1.15452	−	0.666561i	0.204533	−	0.978860i	$-0.434432\pi$
$431$	23.9684	−	13.8382i	1.15452	−	0.666561i	0.949984	+	0.312299i	$0.101099\pi$
$432$	−3.81513	−	3.52771i	−0.183556	−	0.169727i
$433$			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
$438$	3.76126	−	1.81399i	0.179720	−	0.0866757i
$439$	−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
$441$	17.0546	+	12.2532i	0.812122	+	0.583487i
$442$	−13.2783			−0.631586
$443$	−18.2078	−	10.5123i	−0.865079	−	0.499454i	0.000630757	−	1.00000i	$-0.499799\pi$
$443$	−18.2078	−	10.5123i	−0.865079	−	0.499454i	−0.865710	+	0.500546i	$0.833133\pi$
$444$	11.1901	−	5.39679i	0.531059	−	0.256120i
$445$	−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	$-0.871737\pi$
$449$		−	16.6184i		−	0.784269i	0.919908	−	0.392134i	$-0.128263\pi$
$450$	6.82377	+	5.42897i	0.321676	+	0.255924i
$451$	−20.7822	+	11.9986i	−0.978595	+	0.564992i
$452$	14.9390	−	8.62503i	0.702671	−	0.405687i
$453$	13.5070	+	9.19756i	0.634615	+	0.432139i
$454$		−	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
$459$	−19.2637	+	5.97843i	−0.899152	+	0.279049i
$460$	−1.25300	−	0.723421i	−0.0584215	−	0.0337297i
$461$	19.7605			0.920339			0.460170	−	0.887831i	$-0.347789\pi$
$461$	19.7605			0.920339			0.460170	+	0.887831i	$0.347789\pi$
$462$	−10.6757	−	3.43748i	−0.496678	−	0.159926i
$463$	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
$465$	3.66413	+	7.59747i	0.169920	+	0.352324i
$466$	−4.60611	−	7.97801i	−0.213374	−	0.369574i
$467$	−5.19590	+	8.99957i	−0.240438	+	0.416450i	−0.960839	−	0.277107i	$-0.910624\pi$
$467$	−5.19590	+	8.99957i	−0.240438	+	0.416450i	0.720401	+	0.693557i	$0.243958\pi$
$468$	−1.51784	+	10.1493i	−0.0701622	+	0.469152i
$469$	1.59518	−	6.59604i	0.0736584	−	0.304577i
$470$		−	16.6402i		−	0.767554i
$471$	2.99557	−	4.39912i	0.138029	−	0.202701i
$472$	9.51808	−	5.49526i	0.438105	−	0.252940i
$473$	17.4720	−	10.0875i	0.803365	−	0.463823i
$474$	11.5621	−	16.9794i	0.531063	−	0.779889i
$475$			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	0.601309	−	0.799017i	$-0.294646\pi$
$479$	−8.56433	−	14.8339i	−0.391314	−	0.677776i	−0.992623	+	0.121240i	$0.961313\pi$
$480$	−1.08861	−	2.25721i	−0.0496880	−	0.103027i
$481$	−21.2487	−	12.2680i	−0.968858	−	0.559370i
$482$	−29.7252			−1.35395
$483$	−3.07536	−	3.39738i	−0.139934	−	0.154586i
$484$	−5.01016			−0.227734
$485$	4.22962	+	2.44197i	0.192057	+	0.110884i
$486$	2.36759	+	15.4076i	0.107396	+	0.698903i
$487$	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	$0.137148\pi$
$491$			18.5093i			0.835313i	−0.908605	+	0.417657i	$0.862852\pi$
$492$	−14.0375	−	9.55879i	−0.632859	−	0.430944i
$493$	−23.1296	+	13.3539i	−1.04170	+	0.601428i
$494$	−21.3435	+	12.3227i	−0.960289	+	0.554423i
$495$	8.31305	+	6.61383i	0.373644	+	0.297269i
$496$			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
$501$	−14.3173	+	6.90500i	−0.639651	+	0.308493i
$502$	−11.4894	−	6.63343i	−0.512798	−	0.296064i
$503$	−30.4653			−1.35838			−0.679191	−	0.733961i	$-0.737669\pi$
$503$	−30.4653			−1.35838			−0.679191	+	0.733961i	$0.737669\pi$
$504$	−1.09081	−	7.86194i	−0.0485885	−	0.350199i
$505$	7.94924			0.353737
$506$	2.11952	+	1.22371i	0.0942243	+	0.0544004i
$507$	−2.02601	+	0.977108i	−0.0899782	+	0.0433949i
$508$	7.84898	+	13.5948i	0.348242	+	0.603173i
$509$	14.2418	−	24.6675i	0.631257	−	1.09337i	−0.356038	−	0.934471i	$-0.615873\pi$
$509$	14.2418	−	24.6675i	0.631257	−	1.09337i	0.987295	−	0.158897i	$-0.0507939\pi$
$510$	−9.70084	−	0.721375i	−0.429561	−	0.0319430i
$511$	6.19996	+	1.49939i	0.274270	+	0.0663290i
$512$		−	1.00000i		−	0.0441942i
$513$	−25.4162	+	27.4869i	−1.12215	+	1.21358i
$514$	−7.08554	+	4.09084i	−0.312530	+	0.180439i
$515$	9.77598	−	5.64416i	0.430781	−	0.248712i
$516$	11.8016	+	8.03628i	0.519537	+	0.353777i
$517$			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	0.595885	−	0.803070i	$-0.296802\pi$
$521$	−9.07394	−	15.7165i	−0.397537	−	0.688554i	−0.993421	+	0.114516i	$0.963468\pi$
$522$	7.56310	+	19.2056i	0.331028	+	0.840605i
$523$	−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
$525$	2.80391	+	13.0215i	0.122373	+	0.568304i
$526$	17.3871			0.758116
$527$	11.3150	+	6.53271i	0.492889	+	0.284569i
$528$	1.84145	+	3.81819i	0.0801387	+	0.166166i
$529$	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
$534$	−8.46726	+	12.4345i	−0.366414	+	0.538094i
$535$	−8.28727	+	4.78466i	−0.358290	+	0.206859i
$536$	−2.22130	+	1.28247i	−0.0959456	+	0.0553942i
$537$	−14.9960	+	22.0222i	−0.647124	+	0.950329i
$538$		−	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
$543$	14.4792	+	30.0222i	0.621360	+	1.28837i
$544$	−3.36168	−	1.94087i	−0.144131	−	0.0832139i
$545$	−4.23717			−0.181501
$546$	−11.6215	+	10.5200i	−0.497354	+	0.450213i
$547$	−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
$549$	6.10842	−	2.40548i	0.260701	−	0.102663i
$550$	−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
$555$	−14.8573	−	10.1171i	−0.630659	−	0.429446i
$556$	−18.3163	+	10.5749i	−0.776784	+	0.448476i
$557$	−4.62535	+	2.67044i	−0.195982	+	0.113150i	−0.594780	−	0.803888i	$-0.702761\pi$
$557$	−4.62535	+	2.67044i	−0.195982	+	0.113150i	0.398798	+	0.917039i	$0.369428\pi$
$558$	6.28669	−	7.90187i	0.266137	−	0.334513i
$559$		−	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	$0.00551148\pi$
$563$	12.2178	+	21.1619i	0.514919	+	0.891867i	−0.484931	+	0.874553i	$0.661155\pi$
$564$	−17.9427	+	8.65343i	−0.755523	+	0.364375i
$565$	−21.6143	−	12.4790i	−0.909322	−	0.524997i
$566$	−29.1829			−1.22665
$567$	−12.1235	+	20.4944i	−0.509139	+	0.860684i
$568$	−12.4084			−0.520643
$569$	−19.7524	−	11.4040i	−0.828063	−	0.478082i	0.0251263	−	0.999684i	$-0.492001\pi$
$569$	−19.7524	−	11.4040i	−0.828063	−	0.478082i	−0.853189	+	0.521602i	$0.825335\pi$
$570$	−16.2625	+	7.84313i	−0.681162	+	0.328512i
$571$	−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
$576$	−1.86777	+	2.34764i	−0.0778239	+	0.0978184i
$577$	−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
$579$	33.3907	+	22.7373i	1.38767	+	0.944930i
$580$			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
$585$	13.8151	−	5.44036i	0.571185	−	0.224931i
$586$	9.14662	+	5.28080i	0.377843	+	0.218148i
$587$	3.59374			0.148330			0.0741648	−	0.997246i	$-0.476371\pi$
$587$	3.59374			0.148330			0.0741648	+	0.997246i	$0.476371\pi$
$588$	6.32474	−	10.3440i	0.260828	−	0.426578i
$589$	24.2502			0.999211
$590$	−13.7711	−	7.95077i	−0.566949	−	0.327328i
$591$	9.40673	+	19.5046i	0.386941	+	0.802313i
$592$	−3.58636	−	6.21176i	−0.147399	−	0.255302i
$593$	16.3362	−	28.2952i	0.670849	−	1.16194i	−0.306815	−	0.951769i	$-0.599263\pi$
$593$	16.3362	−	28.2952i	0.670849	−	1.16194i	0.977664	−	0.210175i	$-0.0674035\pi$
$594$	2.80846	−	12.4032i	0.115233	−	0.508908i
$595$	−10.7615	−	10.2463i	−0.441177	−	0.420058i
$596$		−	2.74672i		−	0.112510i
$597$	−4.45325	+	6.53978i	−0.182259	+	0.267655i
$598$	2.96243	−	1.71036i	0.121143	−	0.0699419i
$599$	32.9491	−	19.0232i	1.34627	−	0.777266i	0.358547	−	0.933512i	$-0.383272\pi$
$599$	32.9491	−	19.0232i	1.34627	−	0.777266i	0.987718	+	0.156245i	$0.0499390\pi$
$600$	2.83363	−	4.16130i	0.115682	−	0.169884i
$601$		−	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
$606$	−4.13387	−	8.57147i	−0.167927	−	0.348192i
$607$	−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
$609$	−9.66370	+	30.0123i	−0.391593	+	1.21616i
$610$	3.16617			0.128194
$611$	34.0710	+	19.6709i	1.37837	+	0.795801i
$612$	4.26692	+	10.8353i	0.172480	+	0.437991i
$613$	−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	$-0.947377\pi$
$617$		−	8.17554i		−	0.329135i	0.986366	−	0.164567i	$-0.0526228\pi$
$618$	−11.1698	−	7.60604i	−0.449315	−	0.305960i
$619$	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
$621$	3.52771	−	3.81513i	0.141562	−	0.153096i
$622$			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
$627$	27.5090	−	13.2671i	1.09860	−	0.529837i
$628$	−2.66109	−	1.53638i	−0.106189	−	0.0613084i
$629$	−27.8426			−1.11016
$630$	−9.06191	+	7.05428i	−0.361035	+	0.281049i
$631$	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
$633$	−19.3797	+	9.34647i	−0.770272	+	0.371489i
$634$	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
$639$	29.1304	+	23.1760i	1.15238	+	0.916829i
$640$	−1.25300	+	0.723421i	−0.0495292	+	0.0285957i
$641$	−18.7316	+	10.8147i	−0.739852	+	0.427154i	−0.822016	−	0.569465i	$-0.807150\pi$
$641$	−18.7316	+	10.8147i	−0.739852	+	0.427154i	0.0821634	+	0.996619i	$0.473817\pi$
$642$	9.46882	+	6.44777i	0.373705	+	0.254473i
$643$		−	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	$0.185768\pi$
$647$	22.7515	+	39.4067i	0.894453	+	1.54924i	0.0599736	+	0.998200i	$0.480898\pi$
$648$	8.76973	−	2.02284i	0.344507	−	0.0794647i
$649$	23.2947	+	13.4492i	0.914396	+	0.527927i
$650$	−9.94285			−0.389991
$651$	15.0788	−	3.24690i	0.590983	−	0.127256i
$652$	−1.20335			−0.0471268
$653$	16.4102	+	9.47445i	0.642182	+	0.370764i	0.785455	−	0.618919i	$-0.212429\pi$
$653$	16.4102	+	9.47445i	0.642182	+	0.370764i	−0.143273	+	0.989683i	$0.545763\pi$
$654$	2.20347	+	4.56883i	0.0861624	+	0.178656i
$655$	−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	$0.255761\pi$
$659$			36.9553i			1.43958i	−0.694194	+	0.719788i	$0.744239\pi$
$660$	3.45206	−	5.06950i	0.134371	−	0.197330i
$661$	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
$663$	12.9447	−	19.0099i	0.502732	−	0.738283i
$664$		−	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
$669$	3.50388	+	7.26521i	0.135468	+	0.280889i
$670$	3.21387	+	1.85553i	0.124163	+	0.0716853i
$671$	−5.35575			−0.206757
$672$	−4.47989	+	0.964652i	−0.172816	+	0.0372123i
$673$	−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
$675$	−14.4247	+	4.47667i	−0.555207	+	0.172307i
$676$	0.649323	+	1.12466i	0.0249740	+	0.0432562i
$677$	23.4253	−	40.5738i	0.900307	−	1.55938i	0.0732114	−	0.997316i	$-0.476675\pi$
$677$	23.4253	−	40.5738i	0.900307	−	1.55938i	0.827096	−	0.562061i	$-0.189991\pi$
$678$	−2.21567	+	29.7957i	−0.0850924	+	1.14430i
$679$	6.15844	−	6.46807i	0.236339	−	0.248222i
$680$			5.61625i			0.215373i
$681$	0.346300	+	0.235812i	0.0132702	+	0.00903633i
$682$	−7.13405	+	4.11885i	−0.273177	+	0.157719i
$683$	−28.9057	+	16.6887i	−1.10605	+	0.638576i	−0.937803	−	0.347169i	$-0.887143\pi$
$683$	−28.9057	+	16.6887i	−1.10605	+	0.638576i	−0.168244	+	0.985745i	$0.553810\pi$
$684$	16.9141	+	13.4568i	0.646726	+	0.514533i
$685$		−	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
$690$	2.25721	−	1.08861i	0.0859303	−	0.0414427i
$691$	−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
$693$	15.3287	−	11.9327i	0.582291	−	0.453286i
$694$	−36.2333			−1.37540
$695$	26.5008	+	15.3002i	1.00523	+	0.580371i
$696$	10.7340	−	5.17682i	0.406871	−	0.196227i
$697$	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	$0.0812889\pi$
$701$			13.3764i			0.505220i	−0.967568	+	0.252610i	$0.918711\pi$
$702$	−13.0505	−	12.0673i	−0.492560	−	0.455452i
$703$	−44.7540	+	25.8387i	−1.68793	+	0.974525i
$704$	2.11952	−	1.22371i	0.0798826	−	0.0461202i
$705$	23.8229	+	16.2221i	0.897221	+	0.610960i
$706$		−	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
$711$	13.0369	+	33.1056i	0.488922	+	1.24156i
$712$	7.52183	+	4.34273i	0.281893	+	0.162751i
$713$	−3.36587			−0.126053
$714$	−5.45202	+	16.9322i	−0.204037	+	0.633672i
$715$	−12.1129			−0.452995
$716$	13.3216	+	7.69121i	0.497850	+	0.287434i
$717$	−16.8564	−	34.9512i	−0.629513	−	1.30528i
$718$	−2.22060	−	3.84620i	−0.0828722	−	0.143539i
$719$	25.3910	−	43.9785i	0.946923	−	1.64012i	0.195070	−	0.980789i	$-0.437507\pi$
$719$	25.3910	−	43.9785i	0.946923	−	1.64012i	0.751854	−	0.659330i	$-0.229160\pi$
$720$	4.29278	+	0.641991i	0.159983	+	0.0239256i
$721$	−5.82980	−	19.8019i	−0.217113	−	0.737463i
$722$			32.9079i			1.22471i
$723$	28.9784	−	42.5561i	1.07772	−	1.58268i
$724$	16.6656	−	9.62192i	0.619374	−	0.357596i
$725$	−17.3195	+	9.99941i	−0.643229	+	0.371369i
$726$	4.88429	−	7.17278i	0.181273	−	0.266207i
$727$			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
$732$	−1.64651	−	3.41400i	−0.0608568	−	0.126185i
$733$	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
$735$	−17.5365	−	0.441864i	−0.646842	−	0.0162984i
$736$	1.00000			0.0368605
$737$	−5.43645	−	3.13873i	−0.200254	−	0.115617i
$738$	27.3696	−	10.7781i	1.00749	−	0.396747i
$739$	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	$-0.973366\pi$
$743$		−	4.55621i		−	0.167151i	0.996501	−	0.0835756i	$-0.0266340\pi$
$744$	−4.81875	−	3.28131i	−0.176664	−	0.120299i
$745$	−3.44165	+	1.98703i	−0.126092	+	0.0727993i
$746$	17.3753	−	10.0316i	0.636154	−	0.367283i
$747$	−25.2792	+	31.7740i	−0.924919	+	1.16255i
$748$		−	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
$753$	20.6975	−	9.98204i	0.754259	−	0.363766i
$754$	−20.3826	−	11.7679i	−0.742292	−	0.428562i
$755$	−13.6504			−0.496787
$756$	12.3189	+	6.10277i	0.448035	+	0.221956i
$757$	−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
$759$	−3.81819	+	1.84145i	−0.138592	+	0.0668403i
$760$	5.21204	+	9.02752i	0.189061	+	0.327462i
$761$	−17.4653	+	30.2507i	−0.633115	+	1.09659i	0.353796	+	0.935323i	$0.384891\pi$
$761$	−17.4653	+	30.2507i	−0.633115	+	1.09659i	−0.986911	+	0.161265i	$0.948443\pi$
$762$	−27.1148	−	2.01631i	−0.982265	−	0.0730433i
$763$	−1.82132	+	7.53116i	−0.0659363	+	0.272646i
$764$		−	19.6795i		−	0.711978i
$765$	10.4899	−	13.1849i	0.379263	−	0.476702i
$766$	5.80345	−	3.35063i	0.209687	−	0.121063i
$767$	32.5587	−	18.7978i	1.17563	−	0.678748i
$768$	1.43165	+	0.974877i	0.0516601	+	0.0351778i
$769$			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	0.579105	−	0.815253i	$-0.303402\pi$
$773$	−11.5793	−	20.0559i	−0.416477	−	0.721359i	−0.995582	+	0.0938937i	$0.970069\pi$
$774$	−23.0102	+	9.06137i	−0.827086	+	0.325704i
$775$	8.47269	+	4.89171i	0.304348	+	0.175715i
$776$	−3.37559			−0.121177
$777$	−24.3684	+	22.0587i	−0.874213	+	0.791352i
$778$	23.7502			0.851487
$779$	61.1787	+	35.3216i	2.19196	+	1.26553i
$780$	−3.72384	−	7.72128i	−0.133335	−	0.276466i
$781$	−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
$786$	−13.0608	+	19.1803i	−0.465863	+	0.684139i
$787$	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
$789$	−16.9503	+	24.8923i	−0.603448	+	0.886188i
$790$			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
$795$	4.12135	+	8.54551i	0.146169	+	0.303078i
$796$	3.95601	+	2.28400i	0.140217	+	0.0809544i
$797$	28.3000			1.00244			0.501218	−	0.865321i	$-0.332885\pi$
$797$	28.3000			1.00244			0.501218	+	0.865321i	$0.332885\pi$
$798$	6.95004	+	32.2764i	0.246029	+	1.14257i
$799$	44.6439			1.57939
$800$	−2.51723	−	1.45333i	−0.0889976	−	0.0513828i
$801$	−9.54732	−	24.2443i	−0.337338	−	0.856629i
$802$	−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
$807$	15.0394	+	10.2410i	0.529411	+	0.360501i
$808$	−4.75812	+	2.74710i	−0.167390	+	0.0966428i
$809$	0.830641	−	0.479571i	0.0292038	−	0.0168608i	−0.485327	−	0.874333i	$-0.661299\pi$
$809$	0.830641	−	0.479571i	0.0292038	−	0.0168608i	0.514531	+	0.857472i	$0.327966\pi$
$810$	−8.87882	−	9.52511i	−0.311970	−	0.334678i
$811$		−	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
$816$	6.05586	−	2.92063i	0.211997	−	0.102243i
$817$	−51.4343	−	29.6956i	−1.79946	−	1.03892i
$818$	33.8328			1.18294
$819$	−3.73136	−	26.8935i	−0.130384	−	0.939736i
$820$	14.1865			0.495413
$821$	−24.6815	−	14.2499i	−0.861391	−	0.497324i	0.00308670	−	0.999995i	$-0.499017\pi$
$821$	−24.6815	−	14.2499i	−0.861391	−	0.497324i	−0.864478	+	0.502671i	$0.832351\pi$
$822$	−4.92203	+	2.37381i	−0.171676	+	0.0827961i
$823$	−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	$-0.994316\pi$
$827$		−	1.02702i		−	0.0357129i	0.999841	−	0.0178564i	$-0.00568418\pi$
$828$	−2.34764	−	1.86777i	−0.0815862	−	0.0649096i
$829$	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
$831$	−5.97623	−	4.06950i	−0.207313	−	0.141169i
$832$		−	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
$837$	5.18394	+	16.7037i	0.179183	+	0.577364i
$838$	15.5432	+	8.97386i	0.536930	+	0.309997i
$839$	35.2868			1.21823			0.609117	−	0.793080i	$-0.291524\pi$
$839$	35.2868			1.21823			0.609117	+	0.793080i	$0.291524\pi$
$840$	4.44956	+	4.91546i	0.153524	+	0.169600i
$841$	−18.3394			−0.632394
$842$	−6.23156	−	3.59779i	−0.214754	−	0.123988i
$843$	−2.49171	−	5.16651i	−0.0858192	−	0.177944i
$844$	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
$849$	28.4497	−	41.7796i	0.976393	−	1.43387i
$850$	−9.77122	+	5.64142i	−0.335150	+	0.193499i
$851$	6.21176	−	3.58636i	0.212936	−	0.122939i
$852$	12.0966	−	17.7644i	0.414424	−	0.608598i
$853$			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	0.880563	−	0.473929i	$-0.157165\pi$
$857$	0.873753	+	1.51338i	0.0298468	+	0.0516962i	−0.850716	+	0.525625i	$0.823831\pi$
$858$	6.29908	+	13.0610i	0.215047	+	0.445895i
$859$	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
$861$	42.7702	+	13.7716i	1.45761	+	0.469336i
$862$	27.6763			0.942660
$863$	−8.66323	−	5.00172i	−0.294900	−	0.170261i	0.345250	−	0.938511i	$-0.387794\pi$
$863$	−8.66323	−	5.00172i	−0.294900	−	0.170261i	−0.640150	+	0.768250i	$0.721128\pi$
$864$	−1.54015	−	4.96266i	−0.0523968	−	0.168833i
$865$	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
$870$	−14.2518	−	9.70470i	−0.483180	−	0.329020i
$871$	−7.59846	+	4.38697i	−0.257464	+	0.148647i
$872$	2.53621	−	1.46428i	0.0858870	−	0.0495869i
$873$	7.92468	+	6.30484i	0.268210	+	0.213387i
$874$		−	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
$879$	−16.4771	+	7.94661i	−0.555758	+	0.268032i
$880$	−3.06661	−	1.77051i	−0.103376	−	0.0596839i
$881$	17.8121			0.600105			0.300053	−	0.953923i	$-0.402996\pi$
$881$	17.8121			0.600105			0.300053	+	0.953923i	$0.402996\pi$
$882$	8.64308	+	19.1389i	0.291028	+	0.644440i
$883$	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
$885$	24.8079	−	11.9644i	0.833908	−	0.402179i
$886$	−10.5123	−	18.2078i	−0.353167	−	0.611703i
$887$	−21.0312	+	36.4271i	−0.706158	+	1.22310i	0.260114	+	0.965578i	$0.416240\pi$
$887$	−21.0312	+	36.4271i	−0.706158	+	1.22310i	−0.966272	+	0.257524i	$0.917093\pi$
$888$	12.3893	+	0.921295i	0.415758	+	0.0309167i
$889$	−30.0793	−	28.6394i	−1.00883	−	0.960535i
$890$		−	12.5665i		−	0.421230i
$891$	15.0190	+	16.1123i	0.503157	+	0.539782i
$892$	4.03300	−	2.32846i	0.135035	−	0.0779625i
$893$	71.7603	−	41.4308i	2.40137	−	1.38643i
$894$	3.93234	+	2.67772i	0.131517	+	0.0895562i
$895$		−	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
$900$	3.19508	+	8.11351i	0.106503	+	0.270450i
$901$	12.7269	+	7.34788i	0.423995	+	0.244793i
$902$	−23.9972			−0.799020
$903$	−35.9578	−	11.5781i	−1.19660	−	0.385295i
$904$	17.2501			0.573728
$905$	−24.1125	−	13.9214i	−0.801528	−	0.462763i
$906$	7.09863	+	14.7188i	0.235836	+	0.489000i
$907$	−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	$0.185601\pi$
$911$			33.2372i			1.10120i	−0.834770	+	0.550599i	$0.814399\pi$
$912$	7.02371	−	10.3146i	0.232578	−	0.341551i
$913$	28.6865	−	16.5622i	0.949385	−	0.548128i
$914$	4.75524	−	2.74544i	0.157289	−	0.0908110i
$915$	−3.08662	+	4.53283i	−0.102041	+	0.149851i
$916$			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
$921$	−3.40912	−	7.06873i	−0.112334	−	0.232922i
$922$	17.1131	+	9.88026i	0.563590	+	0.325389i
$923$	−42.4456			−1.39711
$924$	−7.52668	−	8.31479i	−0.247610	−	0.273537i
$925$	−20.8486			−0.685498
$926$	22.7526	+	13.1362i	0.747697	+	0.431683i
$927$	21.7783	−	8.57625i	0.715294	−	0.281681i
$928$	−3.44018	−	5.95857i	−0.112930	−	0.195600i
$929$	−10.9618	+	18.9864i	−0.359646	+	0.622925i	−0.987902	−	0.155082i	$-0.950436\pi$
$929$	−10.9618	+	18.9864i	−0.359646	+	0.622925i	0.628256	+	0.778007i	$0.283769\pi$
$930$	−0.625509	+	8.41167i	−0.0205113	+	0.275829i
$931$	−23.0454	+	44.8597i	−0.755283	+	1.47022i
$932$		−	9.21222i		−	0.301756i
$933$	−0.376526	−	0.256394i	−0.0123269	−	0.00839397i
$934$	−8.99957	+	5.19590i	−0.294475	+	0.170015i
$935$	−11.9038	+	6.87265i	−0.389295	+	0.224760i
$936$	−6.38914	+	8.03063i	−0.208836	+	0.262489i
$937$		−	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	0.884065	−	0.467364i	$-0.154796\pi$
$941$	1.14371	+	1.98096i	0.0372839	+	0.0645776i	−0.846781	+	0.531941i	$0.821463\pi$
$942$	4.79380	−	2.31196i	0.156190	−	0.0753279i
$943$	−8.49149	−	4.90256i	−0.276521	−	0.159649i
$944$	10.9905			0.357711
$945$	−1.26499	−	19.8505i	−0.0411502	−	0.645737i
$946$	20.1750			0.655945
$947$	−18.1446	−	10.4758i	−0.589622	−	0.340418i	0.175326	−	0.984510i	$-0.443902\pi$
$947$	−18.1446	−	10.4758i	−0.589622	−	0.340418i	−0.764948	+	0.644092i	$0.777235\pi$
$948$	18.5027	−	8.92354i	0.600941	−	0.289823i
$949$	−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	$-0.998436\pi$
$953$		−	0.303311i		−	0.00982520i	0.999988	−	0.00491260i	$-0.00156374\pi$
$954$	7.07117	−	8.88789i	0.228937	−	0.287756i
$955$	−24.6584	+	14.2365i	−0.797926	+	0.460683i
$956$	−19.4018	+	11.2017i	−0.627501	+	0.362288i
$957$	24.1077	+	16.4161i	0.779291	+	0.530656i
$958$		−	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
$963$	−18.4619	+	7.27024i	−0.594926	+	0.234280i
$964$	−25.7428	−	14.8626i	−0.829120	−	0.478693i
$965$	−33.7450			−1.08629
$966$	−0.964652	−	4.47989i	−0.0310372	−	0.144138i
$967$	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
$969$	−21.0423	−	43.6307i	−0.675977	−	1.40162i
$970$	2.44197	+	4.22962i	0.0784070	+	0.135805i
$971$	21.3853	−	37.0404i	0.686287	−	1.18868i	−0.286743	−	0.958007i	$-0.592573\pi$
$971$	21.3853	−	37.0404i	0.686287	−	1.18868i	0.973030	−	0.230677i	$-0.0740940\pi$
$972$	−5.65341	+	14.5272i	−0.181333	+	0.465960i
$973$	38.5858	−	40.5258i	1.23700	−	1.29920i
$974$			16.3253i			0.523097i
$975$	9.69305	−	14.2347i	0.310426	−	0.455874i
$976$	−1.89515	+	1.09417i	−0.0606623	+	0.0350234i
$977$	27.8828	−	16.0981i	0.892050	−	0.515025i	0.0174376	−	0.999848i	$-0.494449\pi$
$977$	27.8828	−	16.0981i	0.892050	−	0.515025i	0.874613	+	0.484823i	$0.161116\pi$
$978$	1.17312	−	1.72277i	0.0375121	−	0.0550881i
$979$			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	$-0.985536\pi$
$983$	−16.8936	−	29.2606i	−0.538822	−	0.933268i	0.460145	−	0.887844i	$-0.347797\pi$
$984$	−7.37742	−	15.2969i	−0.235184	−	0.487647i
$985$	−15.6653	−	9.04437i	−0.499138	−	0.288177i
$986$	−26.7077			−0.850547
$987$	39.0733	−	35.3698i	1.24372	−	1.12583i
$988$	−24.6453			−0.784073
$989$	7.13898	+	4.12169i	0.227006	+	0.131062i
$990$	3.89240	+	9.88427i	0.123709	+	0.314143i
$991$	−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
$996$	19.3765	+	13.1944i	0.613968	+	0.418080i
$997$	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
$999$	−27.3649	−	25.3033i	−0.865787	−	0.800561i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.56009 + 0.752405i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.723421 - 1.25300i) q^{5} +(-1.72728 - 0.128444i) q^{6} +(-1.91613 - 1.82440i) q^{7} +1.00000i q^{8} +(1.86777 - 2.34764i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.56009 + 0.752405i) 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} +(1.86777 - 2.34764i) q^{9} +(1.25300 - 0.723421i) q^{10} +(-2.11952 + 1.22371i) q^{11} +(-1.43165 - 0.974877i) 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} +(2.79136 - 1.09923i) q^{18} +(6.23947 + 3.60236i) q^{19} +1.44684 q^{20} +(4.36203 + 1.40453i) q^{21} -2.44742 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-0.752405 - 1.56009i) 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} +(-1.41049 + 2.07137i) q^{30} +(2.91493 - 1.68294i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.38593 - 3.50384i) 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} +(-2.57377 - 5.33664i) q^{39} +(1.25300 + 0.723421i) q^{40} +9.80512 q^{41} +(3.07536 + 3.39738i) q^{42} -8.24338 q^{43} +(-2.11952 - 1.22371i) q^{44} +(-1.59041 - 4.03866i) 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} +(-5.55727 - 3.78421i) q^{51} +(-2.96243 + 1.71036i) q^{52} +(3.27867 - 1.89294i) q^{53} +(-3.52771 + 3.81513i) 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} +(-2.25721 + 1.08861i) q^{60} +(1.89515 + 1.09417i) q^{61} +3.36587 q^{62} +(-7.86194 + 1.09081i) q^{63} -1.00000 q^{64} +(4.28617 + 2.47462i) q^{65} +(3.81819 - 1.84145i) 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} +(2.34764 + 1.86777i) q^{72} +(-2.08792 + 1.20546i) q^{73} +(-6.21176 + 3.58636i) q^{74} +(-4.16130 - 2.83363i) 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} +(-2.02284 - 8.76973i) q^{81} +(8.49149 + 4.90256i) q^{82} -13.5344 q^{83} +(0.964652 + 4.47989i) q^{84} +5.61625 q^{85} +(-7.13898 - 4.12169i) q^{86} +(-5.17682 - 10.7340i) 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} +(-3.28131 + 4.81875i) q^{93} +(9.96019 - 5.75052i) q^{94} +(9.02752 - 5.21204i) q^{95} +(0.974877 - 1.43165i) 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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