LMFDB - Embedded newform 722.2.e.g.423.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			423.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	722.423
Dual form			722.2.e.g.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.520945 - 2.95442i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.520945 + 2.95442i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-5.63816 - 2.05212i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.520945 - 2.95442i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.520945 + 2.95442i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-5.63816 - 2.05212i) q^{9} +(-1.87939 - 0.684040i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-0.520945 - 2.95442i) q^{13} +(-2.29813 - 1.92836i) q^{14} +(4.59627 - 3.85673i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.939693 - 0.342020i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(8.45723 - 3.07818i) q^{21} +(-0.347296 + 1.96962i) q^{22} +(3.83022 - 3.21394i) q^{23} +(2.29813 + 1.92836i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(1.50000 + 2.59808i) q^{26} +(-4.50000 + 7.79423i) q^{27} +(2.81908 + 1.02606i) q^{28} +(2.81908 + 1.02606i) q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.59627 - 3.85673i) q^{33} +(-0.766044 + 0.642788i) q^{34} +(-1.04189 + 5.90885i) q^{35} +(-5.63816 + 2.05212i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(-1.87939 + 0.684040i) q^{40} +(2.08378 - 11.8177i) q^{41} +(-6.89440 + 5.78509i) q^{42} +(-7.66044 - 6.42788i) q^{43} +(-0.347296 - 1.96962i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(-2.50000 + 4.33013i) q^{46} +(7.51754 + 2.73616i) q^{47} +(-2.81908 - 1.02606i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.520945 - 2.95442i) q^{51} +(-2.29813 - 1.92836i) q^{52} +(-2.29813 + 1.92836i) q^{53} +(1.56283 - 8.86327i) q^{54} +(3.75877 - 1.36808i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(-2.81908 + 1.02606i) q^{59} +(1.04189 - 5.90885i) q^{60} +(-4.59627 - 3.85673i) q^{62} +(-3.12567 - 17.7265i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00000 - 5.19615i) q^{65} +(5.63816 + 2.05212i) q^{66} +(-14.0954 - 5.13030i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-7.50000 - 12.9904i) q^{69} +(-1.04189 - 5.90885i) q^{70} +(4.59627 - 3.85673i) q^{72} +(-1.91013 + 10.8329i) q^{73} +(-5.63816 + 2.05212i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(8.45723 - 3.07818i) q^{78} +(-2.08378 + 11.8177i) q^{79} +(1.53209 - 1.28558i) q^{80} +(6.89440 + 5.78509i) q^{81} +(2.08378 + 11.8177i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(4.50000 - 7.79423i) q^{84} +(1.87939 + 0.684040i) q^{85} +(9.39693 + 3.42020i) q^{86} +(4.50000 - 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(1.04189 + 5.90885i) q^{89} +(9.19253 + 7.71345i) q^{90} +(6.89440 - 5.78509i) q^{91} +(0.868241 - 4.92404i) q^{92} +(16.9145 - 6.15636i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(-11.2763 + 4.10424i) q^{97} +(0.347296 - 1.96962i) q^{98} +(-9.19253 + 7.71345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 9 * q^7 - 3 * q^8	$ 6 q + 9 q^{7} - 3 q^{8} + 6 q^{11} - 9 q^{12} + 36 q^{18} + 12 q^{20} + 9 q^{26} - 27 q^{27} - 18 q^{30} + 18 q^{31} + 36 q^{37} - 54 q^{39} - 36 q^{45} - 15 q^{46} - 6 q^{49} + 3 q^{50} - 18 q^{56} - 18 q^{58} - 3 q^{64} + 18 q^{65} + 3 q^{68} - 45 q^{69} - 18 q^{75} + 36 q^{77} - 6 q^{83} + 27 q^{84} + 27 q^{87} + 6 q^{88} - 48 q^{94} + 18 q^{96}+O(q^{100}) $ 6 * q + 9 * q^7 - 3 * q^8 + 6 * q^11 - 9 * q^12 + 36 * q^18 + 12 * q^20 + 9 * q^26 - 27 * q^27 - 18 * q^30 + 18 * q^31 + 36 * q^37 - 54 * q^39 - 36 * q^45 - 15 * q^46 - 6 * q^49 + 3 * q^50 - 18 * q^56 - 18 * q^58 - 3 * q^64 + 18 * q^65 + 3 * q^68 - 45 * q^69 - 18 * q^75 + 36 * q^77 - 6 * q^83 + 27 * q^84 + 27 * q^87 + 6 * q^88 - 48 * q^94 + 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.520945	−	2.95442i	0.300767	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$3$	0.520945	−	2.95442i	0.300767	−	1.70574i	0.642788	−	0.766044i	$-0.277778\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	0.917512	−	0.397708i	$-0.130194\pi$
$5$	1.53209	+	1.28558i	0.685171	+	0.574927i	−0.232341	+	0.972634i	$0.574639\pi$
$6$	0.520945	+	2.95442i	0.212675	+	1.20614i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−5.63816	−	2.05212i	−1.87939	−	0.684040i
$10$	−1.87939	−	0.684040i	−0.594314	−	0.216313i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	−0.520945	−	2.95442i	−0.144484	−	0.819410i	−0.967780	−	0.251797i	$-0.918978\pi$
$13$	−0.520945	−	2.95442i	−0.144484	−	0.819410i	0.823296	−	0.567612i	$-0.192133\pi$
$14$	−2.29813	−	1.92836i	−0.614202	−	0.515377i
$15$	4.59627	−	3.85673i	1.18675	−	0.995802i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.939693	−	0.342020i	0.227909	−	0.0829521i	−0.225542	−	0.974234i	$-0.572415\pi$
$17$	0.939693	−	0.342020i	0.227909	−	0.0829521i	0.453450	+	0.891281i	$0.350193\pi$
$18$	6.00000			1.41421
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	8.45723	−	3.07818i	1.84552	−	0.671714i
$22$	−0.347296	+	1.96962i	−0.0740438	+	0.419923i
$23$	3.83022	−	3.21394i	0.798657	−	0.670152i	−0.149215	−	0.988805i	$-0.547675\pi$
$23$	3.83022	−	3.21394i	0.798657	−	0.670152i	0.947872	+	0.318652i	$0.103230\pi$
$24$	2.29813	+	1.92836i	0.469105	+	0.393625i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$	−4.50000	+	7.79423i	−0.866025	+	1.50000i
$28$	2.81908	+	1.02606i	0.532756	+	0.193907i
$29$	2.81908	+	1.02606i	0.523490	+	0.190535i	0.590229	−	0.807236i	$-0.299037\pi$
$29$	2.81908	+	1.02606i	0.523490	+	0.190535i	−0.0667395	+	0.997770i	$0.521260\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−4.59627	−	3.85673i	−0.800107	−	0.671370i
$34$	−0.766044	+	0.642788i	−0.131376	+	0.110237i
$35$	−1.04189	+	5.90885i	−0.176111	+	0.998777i
$36$	−5.63816	+	2.05212i	−0.939693	+	0.342020i
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$	−9.00000			−1.44115
$40$	−1.87939	+	0.684040i	−0.297157	+	0.108156i
$41$	2.08378	−	11.8177i	0.325431	−	1.84561i	−0.181194	−	0.983447i	$-0.557996\pi$
$41$	2.08378	−	11.8177i	0.325431	−	1.84561i	0.506626	−	0.862166i	$-0.330893\pi$
$42$	−6.89440	+	5.78509i	−1.06383	+	0.892659i
$43$	−7.66044	−	6.42788i	−1.16821	−	0.980242i	−0.168222	−	0.985749i	$-0.553803\pi$
$43$	−7.66044	−	6.42788i	−1.16821	−	0.980242i	−0.999985	+	0.00550722i	$0.998247\pi$
$44$	−0.347296	−	1.96962i	−0.0523569	−	0.296931i
$45$	−6.00000	−	10.3923i	−0.894427	−	1.54919i
$46$	−2.50000	+	4.33013i	−0.368605	+	0.638442i
$47$	7.51754	+	2.73616i	1.09655	+	0.399110i	0.826042	−	0.563609i	$-0.190587\pi$
$47$	7.51754	+	2.73616i	1.09655	+	0.399110i	0.270504	+	0.962719i	$0.412810\pi$
$48$	−2.81908	−	1.02606i	−0.406899	−	0.148099i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.520945	−	2.95442i	−0.0729468	−	0.413702i
$52$	−2.29813	−	1.92836i	−0.318694	−	0.267416i
$53$	−2.29813	+	1.92836i	−0.315673	+	0.264881i	−0.786832	−	0.617167i	$-0.788280\pi$
$53$	−2.29813	+	1.92836i	−0.315673	+	0.264881i	0.471159	+	0.882048i	$0.343836\pi$
$54$	1.56283	−	8.86327i	0.212675	−	1.20614i
$55$	3.75877	−	1.36808i	0.506833	−	0.184472i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−3.00000			−0.393919
$59$	−2.81908	+	1.02606i	−0.367013	+	0.133582i	−0.518942	−	0.854810i	$-0.673674\pi$
$59$	−2.81908	+	1.02606i	−0.367013	+	0.133582i	0.151929	+	0.988391i	$0.451452\pi$
$60$	1.04189	−	5.90885i	0.134507	−	0.762829i
$61$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$61$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$62$	−4.59627	−	3.85673i	−0.583726	−	0.489805i
$63$	−3.12567	−	17.7265i	−0.393797	−	2.23333i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	5.63816	+	2.05212i	0.694009	+	0.252599i
$67$	−14.0954	−	5.13030i	−1.72203	−	0.626766i	−0.724014	−	0.689786i	$-0.757705\pi$
$67$	−14.0954	−	5.13030i	−1.72203	−	0.626766i	−0.998012	+	0.0630195i	$0.979927\pi$
$68$	0.500000	−	0.866025i	0.0606339	−	0.105021i
$69$	−7.50000	−	12.9904i	−0.902894	−	1.56386i
$70$	−1.04189	−	5.90885i	−0.124530	−	0.706242i
$71$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$71$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$72$	4.59627	−	3.85673i	0.541675	−	0.454519i
$73$	−1.91013	+	10.8329i	−0.223564	+	1.26789i	0.641848	+	0.766832i	$0.278168\pi$
$73$	−1.91013	+	10.8329i	−0.223564	+	1.26789i	−0.865412	+	0.501061i	$0.832943\pi$
$74$	−5.63816	+	2.05212i	−0.655422	+	0.238554i
$75$	−3.00000			−0.346410
$76$		0			0
$77$	6.00000			0.683763
$78$	8.45723	−	3.07818i	0.957593	−	0.348535i
$79$	−2.08378	+	11.8177i	−0.234443	+	1.32959i	0.609339	+	0.792909i	$0.291435\pi$
$79$	−2.08378	+	11.8177i	−0.234443	+	1.32959i	−0.843783	+	0.536685i	$0.819676\pi$
$80$	1.53209	−	1.28558i	0.171293	−	0.143732i
$81$	6.89440	+	5.78509i	0.766044	+	0.642788i
$82$	2.08378	+	11.8177i	0.230115	+	1.30505i
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$	4.50000	−	7.79423i	0.490990	−	0.850420i
$85$	1.87939	+	0.684040i	0.203848	+	0.0741946i
$86$	9.39693	+	3.42020i	1.01330	+	0.368810i
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	1.04189	+	5.90885i	0.110440	+	0.626336i	0.988907	+	0.148534i	$0.0474554\pi$
$89$	1.04189	+	5.90885i	0.110440	+	0.626336i	−0.878467	+	0.477803i	$0.841433\pi$
$90$	9.19253	+	7.71345i	0.968978	+	0.813069i
$91$	6.89440	−	5.78509i	0.722729	−	0.606442i
$92$	0.868241	−	4.92404i	0.0905204	−	0.513367i
$93$	16.9145	−	6.15636i	1.75395	−	0.638385i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	3.00000			0.306186
$97$	−11.2763	+	4.10424i	−1.14494	+	0.416723i	−0.843694	−	0.536825i	$-0.819624\pi$
$97$	−11.2763	+	4.10424i	−1.14494	+	0.416723i	−0.301242	+	0.953548i	$0.597401\pi$
$98$	0.347296	−	1.96962i	0.0350822	−	0.198961i
$99$	−9.19253	+	7.71345i	−0.923884	+	0.775231i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	1.73648	+	9.84808i	0.172786	+	0.979920i	0.940668	+	0.339328i	$0.110200\pi$
$101$	1.73648	+	9.84808i	0.172786	+	0.979920i	−0.767882	+	0.640592i	$0.778689\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$	2.81908	+	1.02606i	0.276433	+	0.100614i
$105$	16.9145	+	6.15636i	1.65068	+	0.600799i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$	1.56283	+	8.86327i	0.150384	+	0.852869i
$109$	2.29813	+	1.92836i	0.220121	+	0.184704i	0.746179	−	0.665745i	$-0.231886\pi$
$109$	2.29813	+	1.92836i	0.220121	+	0.184704i	−0.526058	+	0.850449i	$0.676331\pi$
$110$	−3.06418	+	2.57115i	−0.292158	+	0.245150i
$111$	3.12567	−	17.7265i	0.296675	−	1.68253i
$112$	2.81908	−	1.02606i	0.266378	−	0.0969536i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	10.0000			0.932505
$116$	2.81908	−	1.02606i	0.261745	−	0.0952673i
$117$	−3.12567	+	17.7265i	−0.288968	+	1.63882i
$118$	2.29813	−	1.92836i	0.211560	−	0.177520i
$119$	2.29813	+	1.92836i	0.210670	+	0.176773i
$120$	1.04189	+	5.90885i	0.0951110	+	0.539401i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−33.8289	−	12.3127i	−3.05025	−	1.11020i
$124$	5.63816	+	2.05212i	0.506321	+	0.184286i
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$	9.00000	+	15.5885i	0.801784	+	1.38873i
$127$	2.08378	+	11.8177i	0.184905	+	1.04865i	0.926077	+	0.377335i	$0.123159\pi$
$127$	2.08378	+	11.8177i	0.184905	+	1.04865i	−0.741171	+	0.671316i	$0.765729\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−22.9813	+	19.2836i	−2.02339	+	1.69783i
$130$	−1.04189	+	5.90885i	−0.0913797	+	0.518240i
$131$	−13.1557	+	4.78828i	−1.14942	+	0.418354i	−0.845306	−	0.534282i	$-0.820582\pi$
$131$	−13.1557	+	4.78828i	−1.14942	+	0.418354i	−0.304112	+	0.952636i	$0.598360\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	15.0000			1.29580
$135$	−16.9145	+	6.15636i	−1.45577	+	0.529855i
$136$	−0.173648	+	0.984808i	−0.0148902	+	0.0844466i
$137$	14.5548	−	12.2130i	1.24350	−	1.04342i	0.246262	−	0.969203i	$-0.420797\pi$
$137$	14.5548	−	12.2130i	1.24350	−	1.04342i	0.997242	−	0.0742208i	$-0.0236470\pi$
$138$	11.4907	+	9.64181i	0.978151	+	0.820766i
$139$	1.04189	+	5.90885i	0.0883719	+	0.501182i	0.996578	+	0.0826585i	$0.0263411\pi$
$139$	1.04189	+	5.90885i	0.0883719	+	0.501182i	−0.908206	+	0.418523i	$0.862548\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$		0			0
$143$	−5.63816	−	2.05212i	−0.471486	−	0.171607i
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−1.91013	−	10.8329i	−0.158083	−	0.896536i
$147$	4.59627	+	3.85673i	0.379094	+	0.318097i
$148$	4.59627	−	3.85673i	0.377811	−	0.317021i
$149$	−1.38919	+	7.87846i	−0.113807	+	0.645429i	0.873528	+	0.486774i	$0.161827\pi$
$149$	−1.38919	+	7.87846i	−0.113807	+	0.645429i	−0.987334	+	0.158654i	$0.949284\pi$
$150$	2.81908	−	1.02606i	0.230177	−	0.0837775i
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−5.63816	+	2.05212i	−0.454336	+	0.165365i
$155$	−2.08378	+	11.8177i	−0.167373	+	0.949220i
$156$	−6.89440	+	5.78509i	−0.551994	+	0.463178i
$157$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$157$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$158$	−2.08378	−	11.8177i	−0.165776	−	0.940165i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	14.0954	+	5.13030i	1.11087	+	0.404324i
$162$	−8.45723	−	3.07818i	−0.664463	−	0.241845i
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	−2.08378	−	11.8177i	−0.162222	−	0.920006i
$166$	1.53209	+	1.28558i	0.118913	+	0.0997800i
$167$	−9.19253	+	7.71345i	−0.711340	+	0.596885i	−0.924975	−	0.380029i	$-0.875914\pi$
$167$	−9.19253	+	7.71345i	−0.711340	+	0.596885i	0.213635	+	0.976914i	$0.431470\pi$
$168$	−1.56283	+	8.86327i	−0.120575	+	0.683816i
$169$	3.75877	−	1.36808i	0.289136	−	0.105237i
$170$	−2.00000			−0.153393
$171$		0			0
$172$	−10.0000			−0.762493
$173$	16.9145	−	6.15636i	1.28598	−	0.468060i	0.393577	−	0.919292i	$-0.371238\pi$
$173$	16.9145	−	6.15636i	1.28598	−	0.468060i	0.892407	+	0.451232i	$0.149015\pi$
$174$	−1.56283	+	8.86327i	−0.118478	+	0.671923i
$175$	2.29813	−	1.92836i	0.173723	−	0.145771i
$176$	−1.53209	−	1.28558i	−0.115486	−	0.0969039i
$177$	1.56283	+	8.86327i	0.117470	+	0.666204i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	−11.2763	−	4.10424i	−0.840487	−	0.305912i
$181$	−16.9145	−	6.15636i	−1.25724	−	0.457599i	−0.374400	−	0.927267i	$-0.622151\pi$
$181$	−16.9145	−	6.15636i	−1.25724	−	0.457599i	−0.882843	+	0.469669i	$0.844373\pi$
$182$	−4.50000	+	7.79423i	−0.333562	+	0.577747i
$183$		0			0
$184$	0.868241	+	4.92404i	0.0640076	+	0.363005i
$185$	9.19253	+	7.71345i	0.675848	+	0.567104i
$186$	−13.7888	+	11.5702i	−1.01104	+	0.848367i
$187$	0.347296	−	1.96962i	0.0253968	−	0.144033i
$188$	7.51754	−	2.73616i	0.548273	−	0.199555i
$189$	−27.0000			−1.96396
$190$		0			0
$191$	−11.0000			−0.795932			−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000			−0.795932			−0.397966	+	0.917400i	$0.630284\pi$
$192$	−2.81908	+	1.02606i	−0.203449	+	0.0740495i
$193$	1.04189	−	5.90885i	0.0749968	−	0.425328i	−0.924073	−	0.382215i	$-0.875161\pi$
$193$	1.04189	−	5.90885i	0.0749968	−	0.425328i	0.999070	−	0.0431130i	$-0.0137275\pi$
$194$	9.19253	−	7.71345i	0.659985	−	0.553794i
$195$	−13.7888	−	11.5702i	−0.987436	−	0.828558i
$196$	0.347296	+	1.96962i	0.0248069	+	0.140687i
$197$	−2.00000	−	3.46410i	−0.142494	−	0.246807i	0.785941	−	0.618301i	$-0.212179\pi$
$197$	−2.00000	−	3.46410i	−0.142494	−	0.246807i	−0.928435	+	0.371494i	$0.878846\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	6.57785	+	2.39414i	0.466291	+	0.169716i	0.564472	−	0.825452i	$-0.309080\pi$
$199$	6.57785	+	2.39414i	0.466291	+	0.169716i	−0.0981803	+	0.995169i	$0.531302\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	−22.5000	+	38.9711i	−1.58703	+	2.74881i
$202$	−5.00000	−	8.66025i	−0.351799	−	0.609333i
$203$	1.56283	+	8.86327i	0.109689	+	0.622080i
$204$	−2.29813	−	1.92836i	−0.160902	−	0.135012i
$205$	18.3851	−	15.4269i	1.28407	−	1.07746i
$206$	1.04189	−	5.90885i	0.0725919	−	0.411689i
$207$	−28.1908	+	10.2606i	−1.95939	+	0.713161i
$208$	−3.00000			−0.208013
$209$		0			0
$210$	−18.0000			−1.24212
$211$	−2.81908	+	1.02606i	−0.194073	+	0.0706369i	−0.437228	−	0.899351i	$-0.644040\pi$
$211$	−2.81908	+	1.02606i	−0.194073	+	0.0706369i	0.243155	+	0.969987i	$0.421818\pi$
$212$	−0.520945	+	2.95442i	−0.0357786	+	0.202911i
$213$		0			0
$214$	−2.29813	−	1.92836i	−0.157097	−	0.131820i
$215$	−3.47296	−	19.6962i	−0.236854	−	1.34327i
$216$	−4.50000	−	7.79423i	−0.306186	−	0.530330i
$217$	−9.00000	+	15.5885i	−0.610960	+	1.05821i
$218$	−2.81908	−	1.02606i	−0.190932	−	0.0694936i
$219$	31.0099	+	11.2867i	2.09545	+	0.762682i
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$	3.12567	+	17.7265i	0.209781	+	1.18973i
$223$	13.7888	+	11.5702i	0.923366	+	0.774796i	0.974615	−	0.223890i	$-0.0718755\pi$
$223$	13.7888	+	11.5702i	0.923366	+	0.774796i	−0.0512482	+	0.998686i	$0.516320\pi$
$224$	−2.29813	+	1.92836i	−0.153550	+	0.128844i
$225$	−1.04189	+	5.90885i	−0.0694593	+	0.393923i
$226$	−11.2763	+	4.10424i	−0.750089	+	0.273010i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$	−9.39693	+	3.42020i	−0.619615	+	0.225521i
$231$	3.12567	−	17.7265i	0.205654	−	1.16632i
$232$	−2.29813	+	1.92836i	−0.150880	+	0.126603i
$233$	10.7246	+	8.99903i	0.702593	+	0.589546i	0.922510	−	0.385973i	$-0.126134\pi$
$233$	10.7246	+	8.99903i	0.702593	+	0.589546i	−0.219917	+	0.975519i	$0.570579\pi$
$234$	−3.12567	−	17.7265i	−0.204331	−	1.15882i
$235$	8.00000	+	13.8564i	0.521862	+	0.903892i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	33.8289	+	12.3127i	2.19743	+	0.799797i
$238$	−2.81908	−	1.02606i	−0.182734	−	0.0665096i
$239$	−0.500000	+	0.866025i	−0.0323423	+	0.0560185i	−0.881743	−	0.471729i	$-0.843630\pi$
$239$	−0.500000	+	0.866025i	−0.0323423	+	0.0560185i	0.849401	+	0.527748i	$0.176963\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	4.16756	+	23.6354i	0.268456	+	1.52249i	0.759010	+	0.651079i	$0.225683\pi$
$241$	4.16756	+	23.6354i	0.268456	+	1.52249i	−0.490554	+	0.871411i	$0.663206\pi$
$242$	−5.36231	−	4.49951i	−0.344702	−	0.289240i
$243$		0			0
$244$		0			0
$245$	−3.75877	+	1.36808i	−0.240139	+	0.0874035i
$246$	36.0000			2.29528
$247$		0			0
$248$	−6.00000			−0.381000
$249$	−5.63816	+	2.05212i	−0.357304	+	0.130048i
$250$	−2.08378	+	11.8177i	−0.131790	+	0.747417i
$251$	−15.3209	+	12.8558i	−0.967046	+	0.811448i	−0.982085	−	0.188439i	$-0.939657\pi$
$251$	−15.3209	+	12.8558i	−0.967046	+	0.811448i	0.0150390	+	0.999887i	$0.495213\pi$
$252$	−13.7888	−	11.5702i	−0.868613	−	0.728853i
$253$	−1.73648	−	9.84808i	−0.109172	−	0.619143i
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	16.9145	+	6.15636i	1.05510	+	0.384023i	0.810584	−	0.585623i	$-0.199150\pi$
$257$	16.9145	+	6.15636i	1.05510	+	0.384023i	0.244512	+	0.969646i	$0.421372\pi$
$258$	15.0000	−	25.9808i	0.933859	−	1.61749i
$259$	9.00000	+	15.5885i	0.559233	+	0.968620i
$260$	−1.04189	−	5.90885i	−0.0646152	−	0.366451i
$261$	−13.7888	−	11.5702i	−0.853505	−	0.716176i
$262$	10.7246	−	8.99903i	0.662569	−	0.555962i
$263$	−1.38919	+	7.87846i	−0.0856608	+	0.485807i	0.911551	+	0.411187i	$0.134886\pi$
$263$	−1.38919	+	7.87846i	−0.0856608	+	0.485807i	−0.997212	+	0.0746202i	$0.976226\pi$
$264$	5.63816	−	2.05212i	0.347004	−	0.126299i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$	−14.0954	+	5.13030i	−0.861013	+	0.313383i
$269$	−1.04189	+	5.90885i	−0.0635251	+	0.360269i	0.936431	+	0.350853i	$0.114108\pi$
$269$	−1.04189	+	5.90885i	−0.0635251	+	0.360269i	−0.999956	+	0.00941580i	$0.997003\pi$
$270$	13.7888	−	11.5702i	0.839160	−	0.704139i
$271$	−8.42649	−	7.07066i	−0.511873	−	0.429512i	0.349915	−	0.936782i	$-0.386211\pi$
$271$	−8.42649	−	7.07066i	−0.511873	−	0.429512i	−0.861788	+	0.507269i	$0.830655\pi$
$272$	−0.173648	−	0.984808i	−0.0105290	−	0.0597127i
$273$	−13.5000	−	23.3827i	−0.817057	−	1.41518i
$274$	−9.50000	+	16.4545i	−0.573916	+	0.994052i
$275$	−1.87939	−	0.684040i	−0.113331	−	0.0412492i
$276$	−14.0954	−	5.13030i	−0.848443	−	0.308808i
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.0754058	+	0.997153i	$0.524025\pi$
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.825857	+	0.563880i	$0.809308\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$	−6.25133	−	35.4531i	−0.374258	−	2.12252i
$280$	−4.59627	−	3.85673i	−0.274679	−	0.230483i
$281$	9.19253	−	7.71345i	0.548381	−	0.460146i	−0.326012	−	0.945366i	$-0.605705\pi$
$281$	9.19253	−	7.71345i	0.548381	−	0.460146i	0.874392	+	0.485220i	$0.161260\pi$
$282$	−4.16756	+	23.6354i	−0.248174	+	1.40747i
$283$	13.1557	−	4.78828i	0.782025	−	0.284634i	0.0800082	−	0.996794i	$-0.474505\pi$
$283$	13.1557	−	4.78828i	0.782025	−	0.284634i	0.702017	+	0.712160i	$0.252283\pi$
$284$		0			0
$285$		0			0
$286$	6.00000			0.354787
$287$	33.8289	−	12.3127i	1.99686	−	0.726797i
$288$	1.04189	−	5.90885i	0.0613939	−	0.348182i
$289$	−12.2567	+	10.2846i	−0.720983	+	0.604977i
$290$	−4.59627	−	3.85673i	−0.269902	−	0.226475i
$291$	6.25133	+	35.4531i	0.366460	+	2.07830i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	−5.63816	−	2.05212i	−0.328824	−	0.119682i
$295$	−5.63816	−	2.05212i	−0.328266	−	0.119479i
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	9.00000	+	15.5885i	0.522233	+	0.904534i
$298$	−1.38919	−	7.87846i	−0.0804734	−	0.456387i
$299$	−11.4907	−	9.64181i	−0.664522	−	0.557601i
$300$	−2.29813	+	1.92836i	−0.132683	+	0.111334i
$301$	5.20945	−	29.5442i	0.300267	−	1.70290i
$302$	16.9145	−	6.15636i	0.973318	−	0.354259i
$303$	30.0000			1.72345
$304$		0			0
$305$		0			0
$306$	5.63816	−	2.05212i	0.322312	−	0.117312i
$307$	2.08378	−	11.8177i	0.118927	−	0.674471i	−0.865803	−	0.500385i	$-0.833192\pi$
$307$	2.08378	−	11.8177i	0.118927	−	0.674471i	0.984730	−	0.174086i	$-0.0556971\pi$
$308$	4.59627	−	3.85673i	0.261897	−	0.219757i
$309$	13.7888	+	11.5702i	0.784417	+	0.658204i
$310$	−2.08378	−	11.8177i	−0.118351	−	0.671200i
$311$	5.50000	+	9.52628i	0.311876	+	0.540186i	0.978769	−	0.204968i	$-0.0657092\pi$
$311$	5.50000	+	9.52628i	0.311876	+	0.540186i	−0.666892	+	0.745154i	$0.732376\pi$
$312$	4.50000	−	7.79423i	0.254762	−	0.441261i
$313$	−19.7335	−	7.18242i	−1.11541	−	0.405975i	−0.282432	−	0.959287i	$-0.591141\pi$
$313$	−19.7335	−	7.18242i	−1.11541	−	0.405975i	−0.832974	+	0.553313i	$0.813363\pi$
$314$		0			0
$315$	18.0000	−	31.1769i	1.01419	−	1.75662i
$316$	6.00000	+	10.3923i	0.337526	+	0.584613i
$317$	−5.73039	−	32.4987i	−0.321851	−	1.82531i	−0.530940	−	0.847410i	$-0.678161\pi$
$317$	−5.73039	−	32.4987i	−0.321851	−	1.82531i	0.209089	−	0.977897i	$-0.432950\pi$
$318$	−6.89440	−	5.78509i	−0.386619	−	0.324412i
$319$	4.59627	−	3.85673i	0.257342	−	0.215935i
$320$	0.347296	−	1.96962i	0.0194145	−	0.110105i
$321$	8.45723	−	3.07818i	0.472037	−	0.171807i
$322$	−15.0000			−0.835917
$323$		0			0
$324$	9.00000			0.500000
$325$	−2.81908	+	1.02606i	−0.156374	+	0.0569156i
$326$	−1.04189	+	5.90885i	−0.0577049	+	0.327261i
$327$	6.89440	−	5.78509i	0.381261	−	0.319916i
$328$	9.19253	+	7.71345i	0.507573	+	0.425904i
$329$	4.16756	+	23.6354i	0.229765	+	1.30306i
$330$	6.00000	+	10.3923i	0.330289	+	0.572078i
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	−0.962788	−	0.270259i	$-0.912891\pi$
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	0.715445	+	0.698669i	$0.246224\pi$
$332$	−1.87939	−	0.684040i	−0.103145	−	0.0375416i
$333$	−33.8289	−	12.3127i	−1.85381	−	0.674733i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	−15.0000	−	25.9808i	−0.819538	−	1.41948i
$336$	−1.56283	−	8.86327i	−0.0852596	−	0.483531i
$337$	13.7888	+	11.5702i	0.751124	+	0.630268i	0.935800	−	0.352532i	$-0.114679\pi$
$337$	13.7888	+	11.5702i	0.751124	+	0.630268i	−0.184676	+	0.982799i	$0.559124\pi$
$338$	−3.06418	+	2.57115i	−0.166669	+	0.139852i
$339$	6.25133	−	35.4531i	0.339526	−	1.92555i
$340$	1.87939	−	0.684040i	0.101924	−	0.0370973i
$341$	12.0000			0.649836
$342$		0			0
$343$	15.0000			0.809924
$344$	9.39693	−	3.42020i	0.506648	−	0.184405i
$345$	5.20945	−	29.5442i	0.280467	−	1.59061i
$346$	−13.7888	+	11.5702i	−0.741290	+	0.622017i
$347$	12.2567	+	10.2846i	0.657975	+	0.552106i	0.909479	−	0.415750i	$-0.136481\pi$
$347$	12.2567	+	10.2846i	0.657975	+	0.552106i	−0.251504	+	0.967856i	$0.580925\pi$
$348$	−1.56283	−	8.86327i	−0.0837767	−	0.475121i
$349$	−14.0000	−	24.2487i	−0.749403	−	1.29800i	−0.948109	−	0.317945i	$-0.897007\pi$
$349$	−14.0000	−	24.2487i	−0.749403	−	1.29800i	0.198706	−	0.980059i	$-0.436326\pi$
$350$	−1.50000	+	2.59808i	−0.0801784	+	0.138873i
$351$	25.3717	+	9.23454i	1.35424	+	0.492903i
$352$	1.87939	+	0.684040i	0.100172	+	0.0364595i
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	−0.0769515	−	0.997035i	$-0.524519\pi$
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	0.901933	−	0.431875i	$-0.142148\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$		0			0
$356$	4.59627	+	3.85673i	0.243602	+	0.204406i
$357$	6.89440	−	5.78509i	0.364890	−	0.306179i
$358$	−2.08378	+	11.8177i	−0.110131	+	0.624584i
$359$	−17.8542	+	6.49838i	−0.942307	+	0.342972i	−0.767076	−	0.641556i	$-0.778289\pi$
$359$	−17.8542	+	6.49838i	−0.942307	+	0.342972i	−0.175230	+	0.984527i	$0.556067\pi$
$360$	12.0000			0.632456
$361$		0			0
$362$	18.0000			0.946059
$363$	19.7335	−	7.18242i	1.03574	−	0.376979i
$364$	1.56283	−	8.86327i	0.0819147	−	0.464562i
$365$	−16.8530	+	14.1413i	−0.882125	+	0.740191i
$366$		0			0
$367$	1.38919	+	7.87846i	0.0725149	+	0.411252i	0.999359	+	0.0358054i	$0.0113997\pi$
$367$	1.38919	+	7.87846i	0.0725149	+	0.411252i	−0.926844	+	0.375447i	$0.877489\pi$
$368$	−2.50000	−	4.33013i	−0.130322	−	0.225723i
$369$	−36.0000	+	62.3538i	−1.87409	+	3.24601i
$370$	−11.2763	−	4.10424i	−0.586228	−	0.213369i
$371$	−8.45723	−	3.07818i	−0.439078	−	0.159811i
$372$	9.00000	−	15.5885i	0.466628	−	0.808224i
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	0.998689	+	0.0511818i	$0.0162988\pi$
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	−0.455020	+	0.890481i	$0.650368\pi$
$374$	0.347296	+	1.96962i	0.0179583	+	0.101846i
$375$	−27.5776	−	23.1404i	−1.42410	−	1.19496i
$376$	−6.12836	+	5.14230i	−0.316046	+	0.265194i
$377$	1.56283	−	8.86327i	0.0804900	−	0.456482i
$378$	25.3717	−	9.23454i	1.30498	−	0.474974i
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$		0			0
$381$	36.0000			1.84434
$382$	10.3366	−	3.76222i	0.528867	−	0.192492i
$383$	3.12567	−	17.7265i	0.159714	−	0.905784i	−0.794634	−	0.607088i	$-0.792337\pi$
$383$	3.12567	−	17.7265i	0.159714	−	0.905784i	0.954348	−	0.298696i	$-0.0965515\pi$
$384$	2.29813	−	1.92836i	0.117276	−	0.0984064i
$385$	9.19253	+	7.71345i	0.468495	+	0.393114i
$386$	1.04189	+	5.90885i	0.0530308	+	0.300752i
$387$	30.0000	+	51.9615i	1.52499	+	2.64135i
$388$	−6.00000	+	10.3923i	−0.304604	+	0.527589i
$389$	−24.4320	−	8.89252i	−1.23875	−	0.450869i	−0.362166	−	0.932114i	$-0.617963\pi$
$389$	−24.4320	−	8.89252i	−1.23875	−	0.450869i	−0.876586	+	0.481245i	$0.840185\pi$
$390$	16.9145	+	6.15636i	0.856497	+	0.311740i
$391$	2.50000	−	4.33013i	0.126430	−	0.218984i
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$	7.29322	+	41.3619i	0.367894	+	2.08643i
$394$	3.06418	+	2.57115i	0.154371	+	0.129533i
$395$	−18.3851	+	15.4269i	−0.925053	+	0.776212i
$396$	−2.08378	+	11.8177i	−0.104714	+	0.593861i
$397$	−1.87939	+	0.684040i	−0.0943236	+	0.0343310i	−0.388751	−	0.921343i	$-0.627093\pi$
$397$	−1.87939	+	0.684040i	−0.0943236	+	0.0343310i	0.294427	+	0.955674i	$0.404871\pi$
$398$	−7.00000			−0.350878
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−33.8289	+	12.3127i	−1.68934	+	0.614868i	−0.994542	−	0.104340i	$-0.966727\pi$
$401$	−33.8289	+	12.3127i	−1.68934	+	0.614868i	−0.694795	+	0.719208i	$0.744505\pi$
$402$	7.81417	−	44.3163i	0.389735	−	2.21030i
$403$	13.7888	−	11.5702i	0.686869	−	0.576352i
$404$	7.66044	+	6.42788i	0.381121	+	0.319799i
$405$	3.12567	+	17.7265i	0.155316	+	0.880839i
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	2.81908	+	1.02606i	0.139565	+	0.0507976i
$409$	−5.63816	−	2.05212i	−0.278789	−	0.101471i	0.198842	−	0.980032i	$-0.436282\pi$
$409$	−5.63816	−	2.05212i	−0.278789	−	0.101471i	−0.477631	+	0.878561i	$0.658504\pi$
$410$	−12.0000	+	20.7846i	−0.592638	+	1.02648i
$411$	−28.5000	−	49.3634i	−1.40580	−	2.43492i
$412$	1.04189	+	5.90885i	0.0513302	+	0.291108i
$413$	−6.89440	−	5.78509i	−0.339251	−	0.284666i
$414$	22.9813	−	19.2836i	1.12947	−	0.947739i
$415$	0.694593	−	3.93923i	0.0340962	−	0.193369i
$416$	2.81908	−	1.02606i	0.138217	−	0.0503068i
$417$	18.0000			0.881464
$418$		0			0
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$	16.9145	−	6.15636i	0.825341	−	0.300400i
$421$	−4.68850	+	26.5898i	−0.228504	+	1.29591i	0.627369	+	0.778722i	$0.284132\pi$
$421$	−4.68850	+	26.5898i	−0.228504	+	1.29591i	−0.855873	+	0.517186i	$0.826979\pi$
$422$	2.29813	−	1.92836i	0.111871	−	0.0938712i
$423$	−36.7701	−	30.8538i	−1.78783	−	1.50016i
$424$	−0.520945	−	2.95442i	−0.0252993	−	0.143479i
$425$	−0.500000	−	0.866025i	−0.0242536	−	0.0420084i
$426$		0			0
$427$		0			0
$428$	2.81908	+	1.02606i	0.136265	+	0.0495965i
$429$	−9.00000	+	15.5885i	−0.434524	+	0.752618i
$430$	10.0000	+	17.3205i	0.482243	+	0.835269i
$431$	4.16756	+	23.6354i	0.200744	+	1.13848i	0.903998	+	0.427537i	$0.140619\pi$
$431$	4.16756	+	23.6354i	0.200744	+	1.13848i	−0.703254	+	0.710939i	$0.748270\pi$
$432$	6.89440	+	5.78509i	0.331707	+	0.278335i
$433$	22.9813	−	19.2836i	1.10441	−	0.926712i	0.106698	−	0.994291i	$-0.465972\pi$
$433$	22.9813	−	19.2836i	1.10441	−	0.926712i	0.997714	+	0.0675794i	$0.0215276\pi$
$434$	3.12567	−	17.7265i	0.150037	−	0.850901i
$435$	16.9145	−	6.15636i	0.810987	−	0.295175i
$436$	3.00000			0.143674
$437$		0			0
$438$	−33.0000			−1.57680
$439$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$439$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$440$	−0.694593	+	3.93923i	−0.0331134	+	0.187795i
$441$	9.19253	−	7.71345i	0.437740	−	0.367307i
$442$	2.29813	+	1.92836i	0.109311	+	0.0917229i
$443$	−3.82026	−	21.6658i	−0.181506	−	1.02937i	−0.930363	−	0.366640i	$-0.880508\pi$
$443$	−3.82026	−	21.6658i	−0.181506	−	1.02937i	0.748857	−	0.662732i	$-0.230603\pi$
$444$	−9.00000	−	15.5885i	−0.427121	−	0.739795i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	−16.9145	−	6.15636i	−0.800923	−	0.291512i
$447$	22.5526	+	8.20848i	1.06670	+	0.388248i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$	−1.04189	−	5.90885i	−0.0491151	−	0.278546i
$451$	−18.3851	−	15.4269i	−0.865719	−	0.726424i
$452$	9.19253	−	7.71345i	0.432380	−	0.362810i
$453$	−9.37700	+	53.1796i	−0.440570	+	2.49860i
$454$	−2.81908	+	1.02606i	−0.132306	+	0.0481554i
$455$	18.0000			0.843853
$456$		0			0
$457$	1.00000			0.0467780			0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000			0.0467780			0.0233890	+	0.999726i	$0.492554\pi$
$458$	11.2763	−	4.10424i	0.526907	−	0.191779i
$459$	−1.56283	+	8.86327i	−0.0729468	+	0.413702i
$460$	7.66044	−	6.42788i	0.357170	−	0.299701i
$461$	3.06418	+	2.57115i	0.142713	+	0.119750i	0.711349	−	0.702839i	$-0.248084\pi$
$461$	3.06418	+	2.57115i	0.142713	+	0.119750i	−0.568636	+	0.822589i	$0.692529\pi$
$462$	3.12567	+	17.7265i	0.145419	+	0.824713i
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	−0.950854	−	0.309640i	$-0.899791\pi$
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	0.207271	−	0.978284i	$-0.433542\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	33.8289	+	12.3127i	1.56878	+	0.570989i
$466$	−13.1557	−	4.78828i	−0.609426	−	0.221813i
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$	9.00000	+	15.5885i	0.416025	+	0.720577i
$469$	−7.81417	−	44.3163i	−0.360825	−	2.04634i
$470$	−12.2567	−	10.2846i	−0.565360	−	0.474393i
$471$		0			0
$472$	0.520945	−	2.95442i	0.0239784	−	0.135988i
$473$	−18.7939	+	6.84040i	−0.864142	+	0.314522i
$474$	−36.0000			−1.65353
$475$		0			0
$476$	3.00000			0.137505
$477$	16.9145	−	6.15636i	0.774460	−	0.281880i
$478$	0.173648	−	0.984808i	0.00794248	−	0.0450441i
$479$	−30.6418	+	25.7115i	−1.40006	+	1.17479i	−0.438986	+	0.898494i	$0.644662\pi$
$479$	−30.6418	+	25.7115i	−1.40006	+	1.17479i	−0.961073	+	0.276294i	$0.910893\pi$
$480$	4.59627	+	3.85673i	0.209790	+	0.176035i
$481$	−3.12567	−	17.7265i	−0.142518	−	0.808261i
$482$	−12.0000	−	20.7846i	−0.546585	−	0.946713i
$483$	22.5000	−	38.9711i	1.02379	−	1.77325i
$484$	6.57785	+	2.39414i	0.298993	+	0.108825i
$485$	−22.5526	−	8.20848i	−1.02406	−	0.372728i
$486$		0			0
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	0.994646	−	0.103339i	$-0.0329526\pi$
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	−0.586817	+	0.809719i	$0.699619\pi$
$488$		0			0
$489$	−13.7888	−	11.5702i	−0.623551	−	0.523221i
$490$	3.06418	−	2.57115i	0.138425	−	0.116153i
$491$	1.38919	−	7.87846i	0.0626931	−	0.355550i	−0.937283	−	0.348570i	$-0.886667\pi$
$491$	1.38919	−	7.87846i	0.0626931	−	0.355550i	0.999976	−	0.00697956i	$-0.00222168\pi$
$492$	−33.8289	+	12.3127i	−1.52513	+	0.555101i
$493$	3.00000			0.135113
$494$		0			0
$495$	−24.0000			−1.07872
$496$	5.63816	−	2.05212i	0.253161	−	0.0921429i
$497$		0			0
$498$	4.59627	−	3.85673i	0.205964	−	0.172824i
$499$	13.7888	+	11.5702i	0.617271	+	0.517952i	0.896945	−	0.442143i	$-0.145782\pi$
$499$	13.7888	+	11.5702i	0.617271	+	0.517952i	−0.279673	+	0.960095i	$0.590226\pi$
$500$	−2.08378	−	11.8177i	−0.0931894	−	0.528503i
$501$	18.0000	+	31.1769i	0.804181	+	1.39288i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	−0.939693	−	0.342020i	−0.0418988	−	0.0152499i	0.320986	−	0.947084i	$-0.395986\pi$
$503$	−0.939693	−	0.342020i	−0.0418988	−	0.0152499i	−0.362885	+	0.931834i	$0.618208\pi$
$504$	16.9145	+	6.15636i	0.753430	+	0.274226i
$505$	−10.0000	+	17.3205i	−0.444994	+	0.770752i
$506$	5.00000	+	8.66025i	0.222277	+	0.384995i
$507$	−2.08378	−	11.8177i	−0.0925438	−	0.524842i
$508$	9.19253	+	7.71345i	0.407853	+	0.342229i
$509$	13.7888	−	11.5702i	0.611178	−	0.512839i	−0.283839	−	0.958872i	$-0.591608\pi$
$509$	13.7888	−	11.5702i	0.611178	−	0.512839i	0.895017	+	0.446033i	$0.147164\pi$
$510$	−1.04189	+	5.90885i	−0.0461356	+	0.261648i
$511$	−31.0099	+	11.2867i	−1.37180	+	0.499293i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.0000			−0.793946
$515$	−11.2763	+	4.10424i	−0.496894	+	0.180854i
$516$	−5.20945	+	29.5442i	−0.229333	+	1.30061i
$517$	12.2567	−	10.2846i	0.539050	−	0.452316i
$518$	−13.7888	−	11.5702i	−0.605845	−	0.508364i
$519$	−9.37700	−	53.1796i	−0.411605	−	2.33433i
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$	16.9145	+	6.15636i	0.740326	+	0.269457i
$523$	−8.45723	−	3.07818i	−0.369809	−	0.134599i	0.150429	−	0.988621i	$-0.451935\pi$
$523$	−8.45723	−	3.07818i	−0.369809	−	0.134599i	−0.520238	+	0.854021i	$0.674157\pi$
$524$	−7.00000	+	12.1244i	−0.305796	+	0.529655i
$525$	−4.50000	−	7.79423i	−0.196396	−	0.340168i
$526$	−1.38919	−	7.87846i	−0.0605714	−	0.343517i
$527$	4.59627	+	3.85673i	0.200217	+	0.168002i
$528$	−4.59627	+	3.85673i	−0.200027	+	0.167842i
$529$	0.347296	−	1.96962i	0.0150998	−	0.0856355i
$530$	5.63816	−	2.05212i	0.244906	−	0.0891384i
$531$	18.0000			0.781133
$532$		0			0
$533$	−36.0000			−1.55933
$534$	−16.9145	+	6.15636i	−0.731961	+	0.266412i
$535$	−1.04189	+	5.90885i	−0.0450448	+	0.255462i
$536$	11.4907	−	9.64181i	0.496321	−	0.416463i
$537$	−27.5776	−	23.1404i	−1.19006	−	0.998580i
$538$	−1.04189	−	5.90885i	−0.0449190	−	0.254748i
$539$	2.00000	+	3.46410i	0.0861461	+	0.149209i
$540$	−9.00000	+	15.5885i	−0.387298	+	0.670820i
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	0.301303	−	0.953528i	$-0.402578\pi$
$541$	−1.87939	−	0.684040i	−0.0808011	−	0.0294092i	−0.382104	+	0.924119i	$0.624801\pi$
$542$	10.3366	+	3.76222i	0.443996	+	0.161601i
$543$	−27.0000	+	46.7654i	−1.15868	+	2.00689i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	1.04189	+	5.90885i	0.0446296	+	0.253107i
$546$	20.6832	+	17.3553i	0.885159	+	0.742737i
$547$	−27.5776	+	23.1404i	−1.17913	+	0.989410i	−0.179149	+	0.983822i	$0.557334\pi$
$547$	−27.5776	+	23.1404i	−1.17913	+	0.989410i	−0.999984	+	0.00558807i	$0.998221\pi$
$548$	3.29932	−	18.7113i	0.140940	−	0.799309i
$549$		0			0
$550$	2.00000			0.0852803
$551$		0			0
$552$	15.0000			0.638442
$553$	−33.8289	+	12.3127i	−1.43855	+	0.523590i
$554$	5.20945	−	29.5442i	0.221328	−	1.25521i
$555$	27.5776	−	23.1404i	1.17060	−	0.982253i
$556$	4.59627	+	3.85673i	0.194925	+	0.163562i
$557$	3.82026	+	21.6658i	0.161870	+	0.918008i	0.952234	+	0.305371i	$0.0987803\pi$
$557$	3.82026	+	21.6658i	0.161870	+	0.918008i	−0.790364	+	0.612638i	$0.790109\pi$
$558$	18.0000	+	31.1769i	0.762001	+	1.31982i
$559$	−15.0000	+	25.9808i	−0.634432	+	1.09887i
$560$	5.63816	+	2.05212i	0.238256	+	0.0867179i
$561$	−5.63816	−	2.05212i	−0.238043	−	0.0866406i
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$	−4.16756	−	23.6354i	−0.175486	−	0.995229i
$565$	18.3851	+	15.4269i	0.773466	+	0.649015i
$566$	−10.7246	+	8.99903i	−0.450789	+	0.378257i
$567$	−4.68850	+	26.5898i	−0.196899	+	1.11667i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$	−5.63816	+	2.05212i	−0.235743	+	0.0858035i
$573$	−5.73039	+	32.4987i	−0.239390	+	1.35765i
$574$	−27.5776	+	23.1404i	−1.15107	+	0.965860i
$575$	−3.83022	−	3.21394i	−0.159731	−	0.134030i
$576$	1.04189	+	5.90885i	0.0434120	+	0.246202i
$577$	−7.50000	−	12.9904i	−0.312229	−	0.540797i	0.666616	−	0.745402i	$-0.267742\pi$
$577$	−7.50000	−	12.9904i	−0.312229	−	0.540797i	−0.978845	+	0.204605i	$0.934409\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	−16.9145	−	6.15636i	−0.702941	−	0.255850i
$580$	5.63816	+	2.05212i	0.234112	+	0.0852097i
$581$	3.00000	−	5.19615i	0.124461	−	0.215573i
$582$	−18.0000	−	31.1769i	−0.746124	−	1.29232i
$583$	1.04189	+	5.90885i	0.0431506	+	0.244719i
$584$	−8.42649	−	7.07066i	−0.348691	−	0.292586i
$585$	−27.5776	+	23.1404i	−1.14019	+	0.956736i
$586$	−1.56283	+	8.86327i	−0.0645601	+	0.366138i
$587$	26.3114	−	9.57656i	1.08599	−	0.395267i	0.263854	−	0.964563i	$-0.415006\pi$
$587$	26.3114	−	9.57656i	1.08599	−	0.395267i	0.822133	+	0.569295i	$0.192784\pi$
$588$	6.00000			0.247436
$589$		0			0
$590$	6.00000			0.247016
$591$	−11.2763	+	4.10424i	−0.463845	+	0.168826i
$592$	1.04189	−	5.90885i	0.0428214	−	0.242852i
$593$	−1.53209	+	1.28558i	−0.0629153	+	0.0527922i	−0.673703	−	0.739002i	$-0.735297\pi$
$593$	−1.53209	+	1.28558i	−0.0629153	+	0.0527922i	0.610788	+	0.791794i	$0.290853\pi$
$594$	−13.7888	−	11.5702i	−0.565761	−	0.474730i
$595$	1.04189	+	5.90885i	0.0427133	+	0.242239i
$596$	4.00000	+	6.92820i	0.163846	+	0.283790i
$597$	10.5000	−	18.1865i	0.429736	−	0.744325i
$598$	14.0954	+	5.13030i	0.576403	+	0.209794i
$599$	33.8289	+	12.3127i	1.38221	+	0.503084i	0.922848	−	0.385164i	$-0.125855\pi$
$599$	33.8289	+	12.3127i	1.38221	+	0.503084i	0.459364	+	0.888248i	$0.348077\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	0.920703	−	0.390264i	$-0.127616\pi$
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	−0.798330	+	0.602220i	$0.794283\pi$
$602$	5.20945	+	29.5442i	0.212321	+	1.20413i
$603$	68.9440	+	57.8509i	2.80762	+	2.35587i
$604$	−13.7888	+	11.5702i	−0.561058	+	0.470784i
$605$	−2.43107	+	13.7873i	−0.0988372	+	0.560534i
$606$	−28.1908	+	10.2606i	−1.14517	+	0.416809i
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$		0			0
$609$	27.0000			1.09410
$610$		0			0
$611$	4.16756	−	23.6354i	0.168601	−	0.956185i
$612$	−4.59627	+	3.85673i	−0.185793	+	0.155899i
$613$	13.7888	+	11.5702i	0.556924	+	0.467315i	0.877278	−	0.479983i	$-0.159357\pi$
$613$	13.7888	+	11.5702i	0.556924	+	0.467315i	−0.320353	+	0.947298i	$0.603802\pi$
$614$	2.08378	+	11.8177i	0.0840944	+	0.476923i
$615$	−36.0000	−	62.3538i	−1.45166	−	2.51435i
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	−9.39693	−	3.42020i	−0.378306	−	0.137692i	0.145866	−	0.989304i	$-0.453403\pi$
$617$	−9.39693	−	3.42020i	−0.378306	−	0.137692i	−0.524172	+	0.851612i	$0.675625\pi$
$618$	−16.9145	−	6.15636i	−0.680400	−	0.247645i
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	−0.517473	−	0.855699i	$-0.673127\pi$
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	0.999794	+	0.0202954i	$0.00646066\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	7.81417	+	44.3163i	0.313572	+	1.77835i
$622$	−8.42649	−	7.07066i	−0.337871	−	0.283508i
$623$	−13.7888	+	11.5702i	−0.552437	+	0.463549i
$624$	−1.56283	+	8.86327i	−0.0625634	+	0.354815i
$625$	17.8542	−	6.49838i	0.714166	−	0.259935i
$626$	21.0000			0.839329
$627$		0			0
$628$		0			0
$629$	5.63816	−	2.05212i	0.224808	−	0.0818234i
$630$	−6.25133	+	35.4531i	−0.249059	+	1.41248i
$631$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$631$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$632$	−9.19253	−	7.71345i	−0.365659	−	0.306825i
$633$	1.56283	+	8.86327i	0.0621171	+	0.352283i
$634$	16.5000	+	28.5788i	0.655299	+	1.13501i
$635$	−12.0000	+	20.7846i	−0.476205	+	0.824812i
$636$	8.45723	+	3.07818i	0.335351	+	0.122058i
$637$	5.63816	+	2.05212i	0.223392	+	0.0813080i
$638$	−3.00000	+	5.19615i	−0.118771	+	0.205718i
$639$		0			0
$640$	0.347296	+	1.96962i	0.0137281	+	0.0778559i
$641$	13.7888	+	11.5702i	0.544625	+	0.456995i	0.873116	−	0.487513i	$-0.162096\pi$
$641$	13.7888	+	11.5702i	0.544625	+	0.456995i	−0.328491	+	0.944507i	$0.606540\pi$
$642$	−6.89440	+	5.78509i	−0.272100	+	0.228319i
$643$	5.55674	−	31.5138i	0.219137	−	1.24278i	−0.654446	−	0.756109i	$-0.727098\pi$
$643$	5.55674	−	31.5138i	0.219137	−	1.24278i	0.873582	−	0.486676i	$-0.161791\pi$
$644$	14.0954	−	5.13030i	0.555436	−	0.202162i
$645$	−60.0000			−2.36250
$646$		0			0
$647$	−23.0000			−0.904223			−0.452112	−	0.891961i	$-0.649329\pi$
$647$	−23.0000			−0.904223			−0.452112	+	0.891961i	$0.649329\pi$
$648$	−8.45723	+	3.07818i	−0.332232	+	0.120922i
$649$	−1.04189	+	5.90885i	−0.0408977	+	0.231943i
$650$	2.29813	−	1.92836i	0.0901402	−	0.0756366i
$651$	41.3664	+	34.7105i	1.62128	+	1.36041i
$652$	−1.04189	−	5.90885i	−0.0408035	−	0.231408i
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	0.947118	−	0.320884i	$-0.103980\pi$
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	−0.751453	+	0.659786i	$0.770647\pi$
$654$	−4.50000	+	7.79423i	−0.175964	+	0.304778i
$655$	−26.3114	−	9.57656i	−1.02807	−	0.374187i
$656$	−11.2763	−	4.10424i	−0.440266	−	0.160244i
$657$	33.0000	−	57.1577i	1.28745	−	2.22993i
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	−2.60472	−	14.7721i	−0.101466	−	0.575440i	−0.992573	−	0.121648i	$-0.961182\pi$
$659$	−2.60472	−	14.7721i	−0.101466	−	0.575440i	0.891108	−	0.453792i	$-0.149929\pi$
$660$	−9.19253	−	7.71345i	−0.357819	−	0.300246i
$661$	11.4907	−	9.64181i	0.446935	−	0.375023i	−0.391362	−	0.920237i	$-0.627996\pi$
$661$	11.4907	−	9.64181i	0.446935	−	0.375023i	0.838297	+	0.545214i	$0.183552\pi$
$662$	1.56283	−	8.86327i	0.0607413	−	0.344481i
$663$	−8.45723	+	3.07818i	−0.328452	+	0.119547i
$664$	2.00000			0.0776151
$665$		0			0
$666$	36.0000			1.39497
$667$	14.0954	−	5.13030i	0.545776	−	0.198646i
$668$	−2.08378	+	11.8177i	−0.0806238	+	0.457240i
$669$	41.3664	−	34.7105i	1.59932	−	1.34199i
$670$	22.9813	+	19.2836i	0.887846	+	0.744992i
$671$		0			0
$672$	4.50000	+	7.79423i	0.173591	+	0.300669i
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.133783	−	0.991011i	$-0.457287\pi$
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.791349	−	0.611365i	$-0.209379\pi$
$674$	−16.9145	−	6.15636i	−0.651521	−	0.237134i
$675$	8.45723	+	3.07818i	0.325519	+	0.118479i
$676$	2.00000	−	3.46410i	0.0769231	−	0.133235i
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	0.835760	−	0.549095i	$-0.185027\pi$
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	−0.893410	+	0.449242i	$0.851694\pi$
$678$	6.25133	+	35.4531i	0.240081	+	1.36157i
$679$	−27.5776	−	23.1404i	−1.05833	−	0.888045i
$680$	−1.53209	+	1.28558i	−0.0587529	+	0.0492996i
$681$	1.56283	−	8.86327i	0.0598879	−	0.339641i
$682$	−11.2763	+	4.10424i	−0.431792	+	0.157160i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	38.0000			1.45191
$686$	−14.0954	+	5.13030i	−0.538164	+	0.195876i
$687$	−6.25133	+	35.4531i	−0.238503	+	1.35262i
$688$	−7.66044	+	6.42788i	−0.292052	+	0.245060i
$689$	6.89440	+	5.78509i	0.262656	+	0.220394i
$690$	5.20945	+	29.5442i	0.198320	+	1.12473i
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$	−33.8289	−	12.3127i	−1.28505	−	0.467722i
$694$	−15.0351	−	5.47232i	−0.570724	−	0.207727i
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$	−2.08378	−	11.8177i	−0.0789287	−	0.447627i
$698$	21.4492	+	17.9981i	0.811866	+	0.681236i
$699$	32.1739	−	26.9971i	1.21693	−	1.02112i
$700$	0.520945	−	2.95442i	0.0196899	−	0.111667i
$701$	37.5877	−	13.6808i	1.41967	−	0.516717i	0.485716	−	0.874116i	$-0.338559\pi$
$701$	37.5877	−	13.6808i	1.41967	−	0.516717i	0.933952	+	0.357400i	$0.116337\pi$
$702$	−27.0000			−1.01905
$703$		0			0
$704$	−2.00000			−0.0753778
$705$	45.1052	−	16.4170i	1.69876	−	0.618299i
$706$	−5.38309	+	30.5290i	−0.202595	+	1.14898i
$707$	−22.9813	+	19.2836i	−0.864302	+	0.725235i
$708$	6.89440	+	5.78509i	0.259107	+	0.217417i
$709$	−1.38919	−	7.87846i	−0.0521720	−	0.295882i	0.947546	−	0.319619i	$-0.103555\pi$
$709$	−1.38919	−	7.87846i	−0.0521720	−	0.295882i	−0.999718	+	0.0237367i	$0.992444\pi$
$710$		0			0
$711$	36.0000	−	62.3538i	1.35011	−	2.33845i
$712$	−5.63816	−	2.05212i	−0.211299	−	0.0769065i
$713$	28.1908	+	10.2606i	1.05575	+	0.384263i
$714$	−4.50000	+	7.79423i	−0.168408	+	0.291692i
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$	−2.08378	−	11.8177i	−0.0778744	−	0.441648i
$717$	2.29813	+	1.92836i	0.0858254	+	0.0720160i
$718$	14.5548	−	12.2130i	0.543182	−	0.455784i
$719$	−7.46687	+	42.3467i	−0.278467	+	1.57927i	0.449261	+	0.893401i	$0.351687\pi$
$719$	−7.46687	+	42.3467i	−0.278467	+	1.57927i	−0.727728	+	0.685866i	$0.759424\pi$
$720$	−11.2763	+	4.10424i	−0.420243	+	0.152956i
$721$	−18.0000			−0.670355
$722$		0			0
$723$	72.0000			2.67771
$724$	−16.9145	+	6.15636i	−0.628621	+	0.228799i
$725$	0.520945	−	2.95442i	0.0193474	−	0.109725i
$726$	−16.0869	+	13.4985i	−0.597042	+	0.500978i
$727$	−26.8116	−	22.4976i	−0.994386	−	0.834389i	−0.00818884	−	0.999966i	$-0.502607\pi$
$727$	−26.8116	−	22.4976i	−0.994386	−	0.834389i	−0.986197	+	0.165578i	$0.947051\pi$
$728$	1.56283	+	8.86327i	0.0579225	+	0.328495i
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	11.0000	−	19.0526i	0.407128	−	0.705167i
$731$	−9.39693	−	3.42020i	−0.347558	−	0.126501i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−4.00000	−	6.92820i	−0.147643	−	0.255725i
$735$	2.08378	+	11.8177i	0.0768613	+	0.435902i
$736$	3.83022	+	3.21394i	0.141184	+	0.118467i
$737$	−22.9813	+	19.2836i	−0.846528	+	0.710322i
$738$	12.5027	−	70.9062i	0.460230	−	2.61009i
$739$	11.2763	−	4.10424i	0.414806	−	0.150977i	−0.126183	−	0.992007i	$-0.540273\pi$
$739$	11.2763	−	4.10424i	0.414806	−	0.150977i	0.540988	+	0.841030i	$0.318050\pi$
$740$	12.0000			0.441129
$741$		0			0
$742$	9.00000			0.330400
$743$	−5.63816	+	2.05212i	−0.206844	+	0.0752850i	−0.443364	−	0.896342i	$-0.646215\pi$
$743$	−5.63816	+	2.05212i	−0.206844	+	0.0752850i	0.236520	+	0.971627i	$0.423993\pi$
$744$	−3.12567	+	17.7265i	−0.114593	+	0.649886i
$745$	−12.2567	+	10.2846i	−0.449051	+	0.376799i
$746$	−16.0869	−	13.4985i	−0.588984	−	0.494217i
$747$	2.08378	+	11.8177i	0.0762415	+	0.432387i
$748$	−1.00000	−	1.73205i	−0.0365636	−	0.0633300i
$749$	−4.50000	+	7.79423i	−0.164426	+	0.284795i
$750$	33.8289	+	12.3127i	1.23526	+	0.449597i
$751$	−11.2763	−	4.10424i	−0.411478	−	0.149766i	0.127983	−	0.991776i	$-0.459150\pi$
$751$	−11.2763	−	4.10424i	−0.411478	−	0.149766i	−0.539461	+	0.842010i	$0.681372\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$	30.0000	+	51.9615i	1.09326	+	1.89358i
$754$	1.56283	+	8.86327i	0.0569150	+	0.322781i
$755$	−27.5776	−	23.1404i	−1.00365	−	0.842164i
$756$	−20.6832	+	17.3553i	−0.752241	+	0.631205i
$757$	2.08378	−	11.8177i	0.0757362	−	0.429521i	−0.923238	−	0.384230i	$-0.874467\pi$
$757$	2.08378	−	11.8177i	0.0757362	−	0.429521i	0.998974	−	0.0452918i	$-0.0144218\pi$
$758$	−2.81908	+	1.02606i	−0.102394	+	0.0372682i
$759$	−30.0000			−1.08893
$760$		0			0
$761$	−13.0000			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$762$	−33.8289	+	12.3127i	−1.22549	+	0.446043i
$763$	−1.56283	+	8.86327i	−0.0565784	+	0.320872i
$764$	−8.42649	+	7.07066i	−0.304860	+	0.255808i
$765$	−9.19253	−	7.71345i	−0.332357	−	0.278880i
$766$	3.12567	+	17.7265i	0.112935	+	0.640486i
$767$	4.50000	+	7.79423i	0.162486	+	0.281433i
$768$	−1.50000	+	2.59808i	−0.0541266	+	0.0937500i
$769$	14.0954	+	5.13030i	0.508293	+	0.185003i	0.583420	−	0.812171i	$-0.301714\pi$
$769$	14.0954	+	5.13030i	0.508293	+	0.185003i	−0.0751274	+	0.997174i	$0.523936\pi$
$770$	−11.2763	−	4.10424i	−0.406370	−	0.147907i
$771$	27.0000	−	46.7654i	0.972381	−	1.68421i
$772$	−3.00000	−	5.19615i	−0.107972	−	0.187014i
$773$	2.60472	+	14.7721i	0.0936854	+	0.531316i	0.995142	+	0.0984472i	$0.0313876\pi$
$773$	2.60472	+	14.7721i	0.0936854	+	0.531316i	−0.901457	+	0.432869i	$0.857501\pi$
$774$	−45.9627	−	38.5673i	−1.65209	−	1.38627i
$775$	4.59627	−	3.85673i	0.165103	−	0.138538i
$776$	2.08378	−	11.8177i	0.0748033	−	0.424230i
$777$	50.7434	−	18.4691i	1.82041	−	0.662575i
$778$	26.0000			0.932145
$779$		0			0
$780$	−18.0000			−0.644503
$781$		0			0
$782$	−0.868241	+	4.92404i	−0.0310482	+	0.176083i
$783$	−20.6832	+	17.3553i	−0.739157	+	0.620227i
$784$	1.53209	+	1.28558i	0.0547175	+	0.0459134i
$785$		0			0
$786$	−21.0000	−	36.3731i	−0.749045	−	1.29738i
$787$	4.50000	−	7.79423i	0.160408	−	0.277834i	−0.774607	−	0.632443i	$-0.782052\pi$
$787$	4.50000	−	7.79423i	0.160408	−	0.277834i	0.935015	+	0.354608i	$0.115386\pi$
$788$	−3.75877	−	1.36808i	−0.133901	−	0.0487359i
$789$	22.5526	+	8.20848i	0.802895	+	0.292230i
$790$	12.0000	−	20.7846i	0.426941	−	0.739483i
$791$	18.0000	+	31.1769i	0.640006	+	1.10852i
$792$	−2.08378	−	11.8177i	−0.0740438	−	0.419923i
$793$		0			0
$794$	1.53209	−	1.28558i	0.0543718	−	0.0456234i
$795$	−3.12567	+	17.7265i	−0.110856	+	0.628696i
$796$	6.57785	−	2.39414i	0.233146	−	0.0848581i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	6.25133	−	35.4531i	0.220880	−	1.25267i
$802$	27.5776	−	23.1404i	0.973799	−	0.817114i
$803$	16.8530	+	14.1413i	0.594729	+	0.499037i
$804$	7.81417	+	44.3163i	0.275584	+	1.56292i
$805$	15.0000	+	25.9808i	0.528681	+	0.915702i
$806$	−9.00000	+	15.5885i	−0.317011	+	0.549080i
$807$	16.9145	+	6.15636i	0.595417	+	0.216714i
$808$	−9.39693	−	3.42020i	−0.330583	−	0.120322i
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	−0.752995	−	0.658026i	$-0.771392\pi$
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	0.946365	+	0.323100i	$0.104725\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	5.73039	+	32.4987i	0.201221	+	1.14118i	0.903276	+	0.429059i	$0.141155\pi$
$811$	5.73039	+	32.4987i	0.201221	+	1.14118i	−0.702055	+	0.712123i	$0.747734\pi$
$812$	6.89440	+	5.78509i	0.241946	+	0.203017i
$813$	−25.2795	+	21.2120i	−0.886590	+	0.743937i
$814$	−2.08378	+	11.8177i	−0.0730364	+	0.414210i
$815$	11.2763	−	4.10424i	0.394992	−	0.143765i
$816$	−3.00000			−0.105021
$817$		0			0
$818$	6.00000			0.209785
$819$	−50.7434	+	18.4691i	−1.77312	+	0.645362i
$820$	4.16756	−	23.6354i	0.145537	−	0.825383i
$821$	1.53209	−	1.28558i	0.0534703	−	0.0448669i	−0.615661	−	0.788011i	$-0.711111\pi$
$821$	1.53209	−	1.28558i	0.0534703	−	0.0448669i	0.669131	+	0.743144i	$0.266666\pi$
$822$	43.6645	+	36.6389i	1.52298	+	1.27793i
$823$	0.520945	+	2.95442i	0.0181590	+	0.102985i	0.992540	−	0.121918i	$-0.0389046\pi$
$823$	0.520945	+	2.95442i	0.0181590	+	0.102985i	−0.974381	+	0.224903i	$0.927793\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$	−3.00000	+	5.19615i	−0.104447	+	0.180907i
$826$	8.45723	+	3.07818i	0.294265	+	0.107104i
$827$	−14.0954	−	5.13030i	−0.490145	−	0.178398i	0.0851114	−	0.996371i	$-0.472875\pi$
$827$	−14.0954	−	5.13030i	−0.490145	−	0.178398i	−0.575256	+	0.817973i	$0.695098\pi$
$828$	−15.0000	+	25.9808i	−0.521286	+	0.902894i
$829$	−25.5000	−	44.1673i	−0.885652	−	1.53399i	−0.844965	−	0.534822i	$-0.820379\pi$
$829$	−25.5000	−	44.1673i	−0.885652	−	1.53399i	−0.0406866	−	0.999172i	$-0.512955\pi$
$830$	0.694593	+	3.93923i	0.0241097	+	0.136733i
$831$	68.9440	+	57.8509i	2.39164	+	2.00682i
$832$	−2.29813	+	1.92836i	−0.0796734	+	0.0668540i
$833$	−0.347296	+	1.96962i	−0.0120331	+	0.0682431i
$834$	−16.9145	+	6.15636i	−0.585700	+	0.213177i
$835$	−24.0000			−0.830554
$836$		0			0
$837$	−54.0000			−1.86651
$838$	13.1557	−	4.78828i	0.454456	−	0.165408i
$839$	−3.12567	+	17.7265i	−0.107910	+	0.611988i	0.882108	+	0.471047i	$0.156124\pi$
$839$	−3.12567	+	17.7265i	−0.107910	+	0.611988i	−0.990018	+	0.140941i	$0.954987\pi$
$840$	−13.7888	+	11.5702i	−0.475759	+	0.399209i
$841$	−15.3209	−	12.8558i	−0.528307	−	0.443302i
$842$	−4.68850	−	26.5898i	−0.161576	−	0.916345i
$843$	−18.0000	−	31.1769i	−0.619953	−	1.07379i
$844$	−1.50000	+	2.59808i	−0.0516321	+	0.0894295i
$845$	7.51754	+	2.73616i	0.258611	+	0.0941268i
$846$	45.1052	+	16.4170i	1.55075	+	0.564427i
$847$	−10.5000	+	18.1865i	−0.360784	+	0.624897i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	−7.29322	−	41.3619i	−0.250303	−	1.41954i
$850$	0.766044	+	0.642788i	0.0262751	+	0.0220474i
$851$	22.9813	−	19.2836i	0.787790	−	0.661034i
$852$		0			0
$853$	−43.2259	+	15.7329i	−1.48003	+	0.538685i	−0.950802	−	0.309798i	$-0.899739\pi$
$853$	−43.2259	+	15.7329i	−1.48003	+	0.538685i	−0.529223	+	0.848483i	$0.677516\pi$
$854$		0			0
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−22.5526	+	8.20848i	−0.770383	+	0.280396i	−0.697157	−	0.716919i	$-0.745552\pi$
$857$	−22.5526	+	8.20848i	−0.770383	+	0.280396i	−0.0732263	+	0.997315i	$0.523330\pi$
$858$	3.12567	−	17.7265i	0.106709	−	0.605174i
$859$	41.3664	−	34.7105i	1.41140	−	1.18431i	0.455643	−	0.890163i	$-0.349410\pi$
$859$	41.3664	−	34.7105i	1.41140	−	1.18431i	0.955761	−	0.294145i	$-0.0950349\pi$
$860$	−15.3209	−	12.8558i	−0.522438	−	0.438378i
$861$	−18.7540	−	106.359i	−0.639135	−	3.62471i
$862$	−12.0000	−	20.7846i	−0.408722	−	0.707927i
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	0.0909355	+	0.995857i	$0.471014\pi$
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	−0.907905	+	0.419176i	$0.862319\pi$
$864$	−8.45723	−	3.07818i	−0.287721	−	0.104722i
$865$	33.8289	+	12.3127i	1.15022	+	0.418645i
$866$	−15.0000	+	25.9808i	−0.509721	+	0.882862i
$867$	24.0000	+	41.5692i	0.815083	+	1.41176i
$868$	3.12567	+	17.7265i	0.106092	+	0.601678i
$869$	18.3851	+	15.4269i	0.623671	+	0.523322i
$870$	−13.7888	+	11.5702i	−0.467484	+	0.392266i
$871$	−7.81417	+	44.3163i	−0.264773	+	1.50160i
$872$	−2.81908	+	1.02606i	−0.0954660	+	0.0347468i
$873$	72.0000			2.43683
$874$		0			0
$875$	36.0000			1.21702
$876$	31.0099	−	11.2867i	1.04773	−	0.381341i
$877$	4.68850	−	26.5898i	0.158319	−	0.897874i	−0.797369	−	0.603493i	$-0.793775\pi$
$877$	4.68850	−	26.5898i	0.158319	−	0.897874i	0.955688	−	0.294381i	$-0.0951136\pi$
$878$		0			0
$879$	−20.6832	−	17.3553i	−0.697627	−	0.585379i
$880$	−0.694593	−	3.93923i	−0.0234147	−	0.132791i
$881$	−17.0000	−	29.4449i	−0.572745	−	0.992023i	−0.996283	−	0.0861444i	$-0.972545\pi$
$881$	−17.0000	−	29.4449i	−0.572745	−	0.992023i	0.423538	−	0.905878i	$-0.360788\pi$
$882$	−6.00000	+	10.3923i	−0.202031	+	0.349927i
$883$	22.5526	+	8.20848i	0.758956	+	0.276237i	0.692369	−	0.721543i	$-0.256567\pi$
$883$	22.5526	+	8.20848i	0.758956	+	0.276237i	0.0665867	+	0.997781i	$0.478789\pi$
$884$	−2.81908	−	1.02606i	−0.0948158	−	0.0345101i
$885$	−9.00000	+	15.5885i	−0.302532	+	0.524000i
$886$	11.0000	+	19.0526i	0.369552	+	0.640083i
$887$	−4.16756	−	23.6354i	−0.139933	−	0.793599i	−0.971297	−	0.237870i	$-0.923551\pi$
$887$	−4.16756	−	23.6354i	−0.139933	−	0.793599i	0.831364	−	0.555728i	$-0.187560\pi$
$888$	13.7888	+	11.5702i	0.462722	+	0.388270i
$889$	−27.5776	+	23.1404i	−0.924923	+	0.776103i
$890$	2.08378	−	11.8177i	0.0698484	−	0.396130i
$891$	16.9145	−	6.15636i	0.566656	−	0.206246i
$892$	18.0000			0.602685
$893$		0			0
$894$	−24.0000			−0.802680
$895$	22.5526	−	8.20848i	0.753851	−	0.274379i
$896$	−0.520945	+	2.95442i	−0.0174035	+	0.0987004i
$897$	−34.4720	+	28.9254i	−1.15099	+	0.965792i
$898$	4.59627	+	3.85673i	0.153379	+	0.128701i
$899$	3.12567	+	17.7265i	0.104247	+	0.591213i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$	−1.50000	+	2.59808i	−0.0499722	+	0.0865545i
$902$	22.5526	+	8.20848i	0.750920	+	0.273313i
$903$	−84.5723	−	30.7818i	−2.81439	−	1.02435i
$904$	−6.00000	+	10.3923i	−0.199557	+	0.345643i
$905$	−18.0000	−	31.1769i	−0.598340	−	1.03636i
$906$	−9.37700	−	53.1796i	−0.311530	−	1.76677i
$907$	−11.4907	−	9.64181i	−0.381541	−	0.320151i	0.431766	−	0.901986i	$-0.357891\pi$
$907$	−11.4907	−	9.64181i	−0.381541	−	0.320151i	−0.813307	+	0.581835i	$0.802335\pi$
$908$	2.29813	−	1.92836i	0.0762662	−	0.0639950i
$909$	10.4189	−	59.0885i	0.345573	−	1.95984i
$910$	−16.9145	+	6.15636i	−0.560709	+	0.204081i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$	−0.939693	+	0.342020i	−0.0310823	+	0.0113130i
$915$		0			0
$916$	−9.19253	+	7.71345i	−0.303730	+	0.254860i
$917$	−32.1739	−	26.9971i	−1.06247	−	0.891522i
$918$	−1.56283	−	8.86327i	−0.0515812	−	0.292531i
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	0.715402	−	0.698713i	$-0.246244\pi$
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	−0.962804	+	0.270200i	$0.912910\pi$
$920$	−5.00000	+	8.66025i	−0.164845	+	0.285520i
$921$	−33.8289	−	12.3127i	−1.11470	−	0.405718i
$922$	−3.75877	−	1.36808i	−0.123789	−	0.0450553i
$923$		0			0
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$	−1.04189	−	5.90885i	−0.0342571	−	0.194282i
$926$	24.5134	+	20.5692i	0.805561	+	0.675946i
$927$	27.5776	−	23.1404i	0.905767	−	0.760029i
$928$	−0.520945	+	2.95442i	−0.0171008	+	0.0969837i
$929$	−38.5274	+	14.0228i	−1.26404	+	0.460074i	−0.885124	−	0.465356i	$-0.845926\pi$
$929$	−38.5274	+	14.0228i	−1.26404	+	0.460074i	−0.378919	+	0.925430i	$0.623704\pi$
$930$	−36.0000			−1.18049
$931$		0			0
$932$	14.0000			0.458585
$933$	31.0099	−	11.2867i	1.01522	−	0.369509i
$934$	1.38919	−	7.87846i	0.0454555	−	0.257791i
$935$	3.06418	−	2.57115i	0.100209	−	0.0840856i
$936$	−13.7888	−	11.5702i	−0.450701	−	0.378183i
$937$	−8.16146	−	46.2860i	−0.266623	−	1.51210i	−0.764372	−	0.644775i	$-0.776951\pi$
$937$	−8.16146	−	46.2860i	−0.266623	−	1.51210i	0.497749	−	0.867321i	$-0.334160\pi$
$938$	22.5000	+	38.9711i	0.734651	+	1.27245i
$939$	−31.5000	+	54.5596i	−1.02796	+	1.78049i
$940$	15.0351	+	5.47232i	0.490390	+	0.178487i
$941$	25.3717	+	9.23454i	0.827094	+	0.301038i	0.720666	−	0.693283i	$-0.243836\pi$
$941$	25.3717	+	9.23454i	0.827094	+	0.301038i	0.106428	+	0.994320i	$0.466059\pi$
$942$		0			0
$943$	−30.0000	−	51.9615i	−0.976934	−	1.69210i
$944$	0.520945	+	2.95442i	0.0169553	+	0.0961583i
$945$	−41.3664	−	34.7105i	−1.34565	−	1.12913i
$946$	15.3209	−	12.8558i	0.498125	−	0.417977i
$947$	−7.98782	+	45.3012i	−0.259569	+	1.47209i	0.524497	+	0.851412i	$0.324253\pi$
$947$	−7.98782	+	45.3012i	−0.259569	+	1.47209i	−0.784066	+	0.620677i	$0.786858\pi$
$948$	33.8289	−	12.3127i	1.09871	−	0.399899i
$949$	33.0000			1.07123
$950$		0			0
$951$	−99.0000			−3.21029
$952$	−2.81908	+	1.02606i	−0.0913668	+	0.0332548i
$953$	−5.20945	+	29.5442i	−0.168750	+	0.957032i	0.776362	+	0.630287i	$0.217063\pi$
$953$	−5.20945	+	29.5442i	−0.168750	+	0.957032i	−0.945113	+	0.326745i	$0.894048\pi$
$954$	−13.7888	+	11.5702i	−0.446429	+	0.374598i
$955$	−16.8530	−	14.1413i	−0.545350	−	0.457603i
$956$	0.173648	+	0.984808i	0.00561618	+	0.0318510i
$957$	−9.00000	−	15.5885i	−0.290929	−	0.503903i
$958$	20.0000	−	34.6410i	0.646171	−	1.11920i
$959$	53.5625	+	19.4951i	1.72962	+	0.629531i
$960$	−5.63816	−	2.05212i	−0.181971	−	0.0662319i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	9.00000	+	15.5885i	0.290172	+	0.502592i
$963$	−3.12567	−	17.7265i	−0.100723	−	0.571230i
$964$	18.3851	+	15.4269i	0.592143	+	0.496867i
$965$	9.19253	−	7.71345i	0.295918	−	0.248305i
$966$	−7.81417	+	44.3163i	−0.251417	+	1.42586i
$967$	22.5526	−	8.20848i	0.725243	−	0.263967i	0.0470934	−	0.998890i	$-0.485004\pi$
$967$	22.5526	−	8.20848i	0.725243	−	0.263967i	0.678150	+	0.734923i	$0.262782\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	24.0000			0.770594
$971$	45.1052	−	16.4170i	1.44750	−	0.526846i	0.505605	−	0.862765i	$-0.331269\pi$
$971$	45.1052	−	16.4170i	1.44750	−	0.526846i	0.941891	+	0.335919i	$0.109047\pi$
$972$		0			0
$973$	−13.7888	+	11.5702i	−0.442049	+	0.370923i
$974$	−13.7888	−	11.5702i	−0.441822	−	0.370732i
$975$	1.56283	+	8.86327i	0.0500507	+	0.283852i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	16.9145	+	6.15636i	0.540865	+	0.196859i
$979$	11.2763	+	4.10424i	0.360392	+	0.131172i
$980$	−2.00000	+	3.46410i	−0.0638877	+	0.110657i
$981$	−9.00000	−	15.5885i	−0.287348	−	0.497701i
$982$	1.38919	+	7.87846i	0.0443307	+	0.251412i
$983$	−18.3851	−	15.4269i	−0.586393	−	0.492042i	0.300647	−	0.953736i	$-0.402797\pi$
$983$	−18.3851	−	15.4269i	−0.586393	−	0.492042i	−0.887039	+	0.461694i	$0.847242\pi$
$984$	27.5776	−	23.1404i	0.879142	−	0.737688i
$985$	1.38919	−	7.87846i	0.0442631	−	0.251029i
$986$	−2.81908	+	1.02606i	−0.0897777	+	0.0326764i
$987$	72.0000			2.29179
$988$		0			0
$989$	−50.0000			−1.58991
$990$	22.5526	−	8.20848i	0.716769	−	0.260883i
$991$	1.04189	−	5.90885i	0.0330967	−	0.187701i	−0.963777	−	0.266708i	$-0.914064\pi$
$991$	1.04189	−	5.90885i	0.0330967	−	0.187701i	0.996874	+	0.0790075i	$0.0251751\pi$
$992$	−4.59627	+	3.85673i	−0.145932	+	0.122451i
$993$	20.6832	+	17.3553i	0.656362	+	0.550753i
$994$		0			0
$995$	7.00000	+	12.1244i	0.221915	+	0.384368i
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	−5.63816	−	2.05212i	−0.178562	−	0.0649913i	0.251192	−	0.967937i	$-0.419178\pi$
$997$	−5.63816	−	2.05212i	−0.178562	−	0.0649913i	−0.429754	+	0.902946i	$0.641400\pi$
$998$	−16.9145	−	6.15636i	−0.535418	−	0.194876i
$999$	−27.0000	+	46.7654i	−0.854242	+	1.47959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.g.423.1		6
19.2	odd	18		722.2.a.a.1.1	✓	1
19.3	odd	18		722.2.c.g.653.1		2
19.4	even	9	inner	722.2.e.g.99.1		6
19.5	even	9		722.2.c.a.429.1		2
19.6	even	9	inner	722.2.e.g.389.1		6
19.7	even	3	inner	722.2.e.g.245.1		6
19.8	odd	6		722.2.e.h.415.1		6
19.9	even	9	inner	722.2.e.g.595.1		6
19.10	odd	18		722.2.e.h.595.1		6
19.11	even	3	inner	722.2.e.g.415.1		6
19.12	odd	6		722.2.e.h.245.1		6
19.13	odd	18		722.2.e.h.389.1		6
19.14	odd	18		722.2.c.g.429.1		2
19.15	odd	18		722.2.e.h.99.1		6
19.16	even	9		722.2.c.a.653.1		2
19.17	even	9		722.2.a.f.1.1	yes	1
19.18	odd	2		722.2.e.h.423.1		6
57.2	even	18		6498.2.a.m.1.1		1
57.17	odd	18		6498.2.a.a.1.1		1
76.55	odd	18		5776.2.a.a.1.1		1
76.59	even	18		5776.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.a.1.1	✓	1	19.2	odd	18
722.2.a.f.1.1	yes	1	19.17	even	9
722.2.c.a.429.1		2	19.5	even	9
722.2.c.a.653.1		2	19.16	even	9
722.2.c.g.429.1		2	19.14	odd	18
722.2.c.g.653.1		2	19.3	odd	18
722.2.e.g.99.1		6	19.4	even	9	inner
722.2.e.g.245.1		6	19.7	even	3	inner
722.2.e.g.389.1		6	19.6	even	9	inner
722.2.e.g.415.1		6	19.11	even	3	inner
722.2.e.g.423.1		6	1.1	even	1	trivial
722.2.e.g.595.1		6	19.9	even	9	inner
722.2.e.h.99.1		6	19.15	odd	18
722.2.e.h.245.1		6	19.12	odd	6
722.2.e.h.389.1		6	19.13	odd	18
722.2.e.h.415.1		6	19.8	odd	6
722.2.e.h.423.1		6	19.18	odd	2
722.2.e.h.595.1		6	19.10	odd	18
5776.2.a.a.1.1		1	76.55	odd	18
5776.2.a.q.1.1		1	76.59	even	18
6498.2.a.a.1.1		1	57.17	odd	18
6498.2.a.m.1.1		1	57.2	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.520945 - 2.95442i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.520945 + 2.95442i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-5.63816 - 2.05212i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.520945 - 2.95442i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.53209 + 1.28558i) q^{5} +(0.520945 + 2.95442i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-5.63816 - 2.05212i) q^{9} +(-1.87939 - 0.684040i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-0.520945 - 2.95442i) q^{13} +(-2.29813 - 1.92836i) q^{14} +(4.59627 - 3.85673i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.939693 - 0.342020i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(8.45723 - 3.07818i) q^{21} +(-0.347296 + 1.96962i) q^{22} +(3.83022 - 3.21394i) q^{23} +(2.29813 + 1.92836i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(1.50000 + 2.59808i) q^{26} +(-4.50000 + 7.79423i) q^{27} +(2.81908 + 1.02606i) q^{28} +(2.81908 + 1.02606i) q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.59627 - 3.85673i) q^{33} +(-0.766044 + 0.642788i) q^{34} +(-1.04189 + 5.90885i) q^{35} +(-5.63816 + 2.05212i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(-1.87939 + 0.684040i) q^{40} +(2.08378 - 11.8177i) q^{41} +(-6.89440 + 5.78509i) q^{42} +(-7.66044 - 6.42788i) q^{43} +(-0.347296 - 1.96962i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(-2.50000 + 4.33013i) q^{46} +(7.51754 + 2.73616i) q^{47} +(-2.81908 - 1.02606i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.520945 - 2.95442i) q^{51} +(-2.29813 - 1.92836i) q^{52} +(-2.29813 + 1.92836i) q^{53} +(1.56283 - 8.86327i) q^{54} +(3.75877 - 1.36808i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(-2.81908 + 1.02606i) q^{59} +(1.04189 - 5.90885i) q^{60} +(-4.59627 - 3.85673i) q^{62} +(-3.12567 - 17.7265i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00000 - 5.19615i) q^{65} +(5.63816 + 2.05212i) q^{66} +(-14.0954 - 5.13030i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-7.50000 - 12.9904i) q^{69} +(-1.04189 - 5.90885i) q^{70} +(4.59627 - 3.85673i) q^{72} +(-1.91013 + 10.8329i) q^{73} +(-5.63816 + 2.05212i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(8.45723 - 3.07818i) q^{78} +(-2.08378 + 11.8177i) q^{79} +(1.53209 - 1.28558i) q^{80} +(6.89440 + 5.78509i) q^{81} +(2.08378 + 11.8177i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(4.50000 - 7.79423i) q^{84} +(1.87939 + 0.684040i) q^{85} +(9.39693 + 3.42020i) q^{86} +(4.50000 - 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(1.04189 + 5.90885i) q^{89} +(9.19253 + 7.71345i) q^{90} +(6.89440 - 5.78509i) q^{91} +(0.868241 - 4.92404i) q^{92} +(16.9145 - 6.15636i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(-11.2763 + 4.10424i) q^{97} +(0.347296 - 1.96962i) q^{98} +(-9.19253 + 7.71345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 9 * q^7 - 3 * q^8	\( 6 q + 9 q^{7} - 3 q^{8} + 6 q^{11} - 9 q^{12} + 36 q^{18} + 12 q^{20} + 9 q^{26} - 27 q^{27} - 18 q^{30} + 18 q^{31} + 36 q^{37} - 54 q^{39} - 36 q^{45} - 15 q^{46} - 6 q^{49} + 3 q^{50} - 18 q^{56} - 18 q^{58} - 3 q^{64} + 18 q^{65} + 3 q^{68} - 45 q^{69} - 18 q^{75} + 36 q^{77} - 6 q^{83} + 27 q^{84} + 27 q^{87} + 6 q^{88} - 48 q^{94} + 18 q^{96}+O(q^{100}) \) 6 * q + 9 * q^7 - 3 * q^8 + 6 * q^11 - 9 * q^12 + 36 * q^18 + 12 * q^20 + 9 * q^26 - 27 * q^27 - 18 * q^30 + 18 * q^31 + 36 * q^37 - 54 * q^39 - 36 * q^45 - 15 * q^46 - 6 * q^49 + 3 * q^50 - 18 * q^56 - 18 * q^58 - 3 * q^64 + 18 * q^65 + 3 * q^68 - 45 * q^69 - 18 * q^75 + 36 * q^77 - 6 * q^83 + 27 * q^84 + 27 * q^87 + 6 * q^88 - 48 * q^94 + 18 * q^96

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