LMFDB - Embedded newform 546.2.p.d.281.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.2
Root			$1.72893 - 0.103975i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.d.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} -1.00000i q^{4} +(-0.237140 + 0.237140i) q^{5} +(1.72893 + 0.103975i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} -1.00000i q^{4} +(-0.237140 + 0.237140i) q^{5} +(1.72893 + 0.103975i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} -0.335367i q^{10} +(-2.55493 - 2.55493i) q^{11} +(-1.29606 + 1.14901i) q^{12} +(3.37961 + 1.25628i) q^{13} -1.00000i q^{14} +(0.579825 + 0.0348698i) q^{15} -1.00000 q^{16} -5.26383 q^{17} +(-1.85180 - 2.36026i) q^{18} +(0.906991 + 0.906991i) q^{19} +(0.237140 + 0.237140i) q^{20} +(1.72893 + 0.103975i) q^{21} +3.61322 q^{22} +1.48838 q^{23} +(0.103975 - 1.72893i) q^{24} +4.88753i q^{25} +(-3.27807 + 1.50142i) q^{26} +(4.27326 - 2.95623i) q^{27} +(0.707107 + 0.707107i) q^{28} +7.36454i q^{29} +(-0.434655 + 0.385342i) q^{30} +(7.20598 + 7.20598i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.375685 + 6.24699i) q^{33} +(3.72209 - 3.72209i) q^{34} -0.335367i q^{35} +(2.97838 + 0.359531i) q^{36} +(-2.83332 + 2.83332i) q^{37} -1.28268 q^{38} +(-2.25500 - 5.82365i) q^{39} -0.335367 q^{40} +(-1.32329 + 1.32329i) q^{41} +(-1.29606 + 1.14901i) q^{42} +2.75805i q^{43} +(-2.55493 + 2.55493i) q^{44} +(-0.621034 - 0.791553i) q^{45} +(-1.05244 + 1.05244i) q^{46} +(2.27264 + 2.27264i) q^{47} +(1.14901 + 1.29606i) q^{48} -1.00000i q^{49} +(-3.45600 - 3.45600i) q^{50} +(6.04822 + 6.82223i) q^{51} +(1.25628 - 3.37961i) q^{52} +8.80608i q^{53} +(-0.931280 + 5.11202i) q^{54} +1.21175 q^{55} -1.00000 q^{56} +(0.133367 - 2.21766i) q^{57} +(-5.20752 - 5.20752i) q^{58} +(0.785394 + 0.785394i) q^{59} +(0.0348698 - 0.579825i) q^{60} +8.74912 q^{61} -10.1908 q^{62} +(-1.85180 - 2.36026i) q^{63} +1.00000i q^{64} +(-1.09936 + 0.503526i) q^{65} +(-4.15164 - 4.68294i) q^{66} +(-9.68048 - 9.68048i) q^{67} +5.26383i q^{68} +(-1.71017 - 1.92903i) q^{69} +(0.237140 + 0.237140i) q^{70} +(-4.94294 + 4.94294i) q^{71} +(-2.36026 + 1.85180i) q^{72} +(-4.00560 + 4.00560i) q^{73} -4.00692i q^{74} +(6.33452 - 5.61584i) q^{75} +(0.906991 - 0.906991i) q^{76} +3.61322 q^{77} +(5.71247 + 2.52342i) q^{78} -8.50862 q^{79} +(0.237140 - 0.237140i) q^{80} +(-8.74148 - 2.14164i) q^{81} -1.87142i q^{82} +(3.05668 - 3.05668i) q^{83} +(0.103975 - 1.72893i) q^{84} +(1.24827 - 1.24827i) q^{85} +(-1.95023 - 1.95023i) q^{86} +(9.54487 - 8.46196i) q^{87} -3.61322i q^{88} +(-1.62293 - 1.62293i) q^{89} +(0.998850 + 0.120575i) q^{90} +(-3.27807 + 1.50142i) q^{91} -1.48838i q^{92} +(1.05959 - 17.6191i) q^{93} -3.21400 q^{94} -0.430168 q^{95} +(-1.72893 - 0.103975i) q^{96} +(-4.86305 - 4.86305i) q^{97} +(0.707107 + 0.707107i) q^{98} +(8.52813 - 6.69097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	$ 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.14901	−	1.29606i	−0.663384	−	0.748279i
$3$	−1.14901	−	1.29606i	−0.663384	−	0.748279i
$4$		−	1.00000i		−	0.500000i
$5$	−0.237140	+	0.237140i	−0.106052	+	0.106052i	−0.758142	−	0.652090i	$-0.773893\pi$
$5$	−0.237140	+	0.237140i	−0.106052	+	0.106052i	0.652090	+	0.758142i	$0.273893\pi$
$6$	1.72893	+	0.103975i	0.705832	+	0.0424477i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.359531	+	2.97838i	−0.119844	+	0.992793i
$10$		−	0.335367i		−	0.106052i
$11$	−2.55493	−	2.55493i	−0.770341	−	0.770341i	0.207825	−	0.978166i	$-0.433361\pi$
$11$	−2.55493	−	2.55493i	−0.770341	−	0.770341i	−0.978166	+	0.207825i	$0.933361\pi$
$12$	−1.29606	+	1.14901i	−0.374140	+	0.331692i
$13$	3.37961	+	1.25628i	0.937335	+	0.348430i
$13$	3.37961	+	1.25628i	0.937335	+	0.348430i
$14$		−	1.00000i		−	0.267261i
$15$	0.579825	+	0.0348698i	0.149710	+	0.00900335i
$16$	−1.00000			−0.250000
$17$	−5.26383			−1.27667			−0.638334	−	0.769760i	$-0.720376\pi$
$17$	−5.26383			−1.27667			−0.638334	+	0.769760i	$0.720376\pi$
$18$	−1.85180	−	2.36026i	−0.436475	−	0.556318i
$19$	0.906991	+	0.906991i	0.208078	+	0.208078i	0.803450	−	0.595372i	$-0.202995\pi$
$19$	0.906991	+	0.906991i	0.208078	+	0.208078i	−0.595372	+	0.803450i	$0.702995\pi$
$20$	0.237140	+	0.237140i	0.0530262	+	0.0530262i
$21$	1.72893	+	0.103975i	0.377283	+	0.0226892i
$22$	3.61322			0.770341
$23$	1.48838			0.310349			0.155175	−	0.987887i	$-0.450406\pi$
$23$	1.48838			0.310349			0.155175	+	0.987887i	$0.450406\pi$
$24$	0.103975	−	1.72893i	0.0212238	−	0.352916i
$25$			4.88753i			0.977506i
$26$	−3.27807	+	1.50142i	−0.642882	+	0.294452i
$27$	4.27326	−	2.95623i	0.822389	−	0.568926i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$			7.36454i			1.36756i	0.729688	+	0.683780i	$0.239665\pi$
$29$			7.36454i			1.36756i	−0.729688	+	0.683780i	$0.760335\pi$
$30$	−0.434655	+	0.385342i	−0.0793568	+	0.0703534i
$31$	7.20598	+	7.20598i	1.29423	+	1.29423i	0.932143	+	0.362089i	$0.117936\pi$
$31$	7.20598	+	7.20598i	1.29423	+	1.29423i	0.362089	+	0.932143i	$0.382064\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.375685	+	6.24699i	−0.0653983	+	1.08746i
$34$	3.72209	−	3.72209i	0.638334	−	0.638334i
$35$		−	0.335367i		−	0.0566874i
$36$	2.97838	+	0.359531i	0.496396	+	0.0599218i
$37$	−2.83332	+	2.83332i	−0.465795	+	0.465795i	−0.900549	−	0.434754i	$-0.856835\pi$
$37$	−2.83332	+	2.83332i	−0.465795	+	0.465795i	0.434754	+	0.900549i	$0.356835\pi$
$38$	−1.28268			−0.208078
$39$	−2.25500	−	5.82365i	−0.361090	−	0.932531i
$40$	−0.335367			−0.0530262
$41$	−1.32329	+	1.32329i	−0.206664	+	0.206664i	−0.802848	−	0.596184i	$-0.796683\pi$
$41$	−1.32329	+	1.32329i	−0.206664	+	0.206664i	0.596184	+	0.802848i	$0.296683\pi$
$42$	−1.29606	+	1.14901i	−0.199986	+	0.177297i
$43$			2.75805i			0.420598i	0.977637	+	0.210299i	$0.0674437\pi$
$43$			2.75805i			0.420598i	−0.977637	+	0.210299i	$0.932556\pi$
$44$	−2.55493	+	2.55493i	−0.385170	+	0.385170i
$45$	−0.621034	−	0.791553i	−0.0925783	−	0.117998i
$46$	−1.05244	+	1.05244i	−0.155175	+	0.155175i
$47$	2.27264	+	2.27264i	0.331499	+	0.331499i	0.853156	−	0.521657i	$-0.174686\pi$
$47$	2.27264	+	2.27264i	0.331499	+	0.331499i	−0.521657	+	0.853156i	$0.674686\pi$
$48$	1.14901	+	1.29606i	0.165846	+	0.187070i
$49$		−	1.00000i		−	0.142857i
$50$	−3.45600	−	3.45600i	−0.488753	−	0.488753i
$51$	6.04822	+	6.82223i	0.846920	+	0.955304i
$52$	1.25628	−	3.37961i	0.174215	−	0.468667i
$53$			8.80608i			1.20961i	0.796374	+	0.604804i	$0.206749\pi$
$53$			8.80608i			1.20961i	−0.796374	+	0.604804i	$0.793251\pi$
$54$	−0.931280	+	5.11202i	−0.126731	+	0.695657i
$55$	1.21175			0.163393
$56$	−1.00000			−0.133631
$57$	0.133367	−	2.21766i	0.0176648	−	0.293736i
$58$	−5.20752	−	5.20752i	−0.683780	−	0.683780i
$59$	0.785394	+	0.785394i	0.102250	+	0.102250i	0.756381	−	0.654131i	$-0.226966\pi$
$59$	0.785394	+	0.785394i	0.102250	+	0.102250i	−0.654131	+	0.756381i	$0.726966\pi$
$60$	0.0348698	−	0.579825i	0.00450167	−	0.0748551i
$61$	8.74912			1.12021			0.560105	−	0.828422i	$-0.310761\pi$
$61$	8.74912			1.12021			0.560105	+	0.828422i	$0.310761\pi$
$62$	−10.1908			−1.29423
$63$	−1.85180	−	2.36026i	−0.233305	−	0.297365i
$64$			1.00000i			0.125000i
$65$	−1.09936	+	0.503526i	−0.136358	+	0.0624547i
$66$	−4.15164	−	4.68294i	−0.511032	−	0.576430i
$67$	−9.68048	−	9.68048i	−1.18266	−	1.18266i	−0.979053	−	0.203606i	$-0.934734\pi$
$67$	−9.68048	−	9.68048i	−1.18266	−	1.18266i	−0.203606	−	0.979053i	$-0.565266\pi$
$68$			5.26383i			0.638334i
$69$	−1.71017	−	1.92903i	−0.205881	−	0.232228i
$70$	0.237140	+	0.237140i	0.0283437	+	0.0283437i
$71$	−4.94294	+	4.94294i	−0.586619	+	0.586619i	−0.936714	−	0.350095i	$-0.886149\pi$
$71$	−4.94294	+	4.94294i	−0.586619	+	0.586619i	0.350095	+	0.936714i	$0.386149\pi$
$72$	−2.36026	+	1.85180i	−0.278159	+	0.218237i
$73$	−4.00560	+	4.00560i	−0.468821	+	0.468821i	−0.901532	−	0.432712i	$-0.857557\pi$
$73$	−4.00560	+	4.00560i	−0.468821	+	0.468821i	0.432712	+	0.901532i	$0.357557\pi$
$74$		−	4.00692i		−	0.465795i
$75$	6.33452	−	5.61584i	0.731447	−	0.648462i
$76$	0.906991	−	0.906991i	0.104039	−	0.104039i
$77$	3.61322			0.411764
$78$	5.71247	+	2.52342i	0.646810	+	0.285721i
$79$	−8.50862			−0.957294			−0.478647	−	0.878007i	$-0.658873\pi$
$79$	−8.50862			−0.957294			−0.478647	+	0.878007i	$0.658873\pi$
$80$	0.237140	−	0.237140i	0.0265131	−	0.0265131i
$81$	−8.74148	−	2.14164i	−0.971275	−	0.237960i
$82$		−	1.87142i		−	0.206664i
$83$	3.05668	−	3.05668i	0.335515	−	0.335515i	−0.519162	−	0.854676i	$-0.673756\pi$
$83$	3.05668	−	3.05668i	0.335515	−	0.335515i	0.854676	+	0.519162i	$0.173756\pi$
$84$	0.103975	−	1.72893i	0.0113446	−	0.188641i
$85$	1.24827	−	1.24827i	0.135394	−	0.135394i
$86$	−1.95023	−	1.95023i	−0.210299	−	0.210299i
$87$	9.54487	−	8.46196i	1.02332	−	0.907218i
$88$		−	3.61322i		−	0.385170i
$89$	−1.62293	−	1.62293i	−0.172030	−	0.172030i	0.615840	−	0.787871i	$-0.288817\pi$
$89$	−1.62293	−	1.62293i	−0.172030	−	0.172030i	−0.787871	+	0.615840i	$0.788817\pi$
$90$	0.998850	+	0.120575i	0.105288	+	0.0127097i
$91$	−3.27807	+	1.50142i	−0.343635	+	0.157391i
$92$		−	1.48838i		−	0.155175i
$93$	1.05959	−	17.6191i	0.109874	−	1.82702i
$94$	−3.21400			−0.331499
$95$	−0.430168			−0.0441343
$96$	−1.72893	−	0.103975i	−0.176458	−	0.0106119i
$97$	−4.86305	−	4.86305i	−0.493768	−	0.493768i	0.415723	−	0.909491i	$-0.363529\pi$
$97$	−4.86305	−	4.86305i	−0.493768	−	0.493768i	−0.909491	+	0.415723i	$0.863529\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	8.52813	−	6.69097i	0.857109	−	0.672468i
$100$	4.88753			0.488753
$101$	18.5302			1.84382			0.921911	−	0.387402i	$-0.126627\pi$
$101$	18.5302			1.84382			0.921911	+	0.387402i	$0.126627\pi$
$102$	−9.10078	−	0.547308i	−0.901112	−	0.0541915i
$103$			5.76073i			0.567622i	0.958880	+	0.283811i	$0.0915988\pi$
$103$			5.76073i			0.567622i	−0.958880	+	0.283811i	$0.908401\pi$
$104$	1.50142	+	3.27807i	0.147226	+	0.321441i
$105$	−0.434655	+	0.385342i	−0.0424180	+	0.0376055i
$106$	−6.22684	−	6.22684i	−0.604804	−	0.604804i
$107$		−	18.3125i		−	1.77034i	−0.465270	−	0.885169i	$-0.654043\pi$
$107$		−	18.3125i		−	1.77034i	0.465270	−	0.885169i	$-0.345957\pi$
$108$	−2.95623	−	4.27326i	−0.284463	−	0.411194i
$109$	−6.72226	−	6.72226i	−0.643876	−	0.643876i	0.307630	−	0.951506i	$-0.400464\pi$
$109$	−6.72226	−	6.72226i	−0.643876	−	0.643876i	−0.951506	+	0.307630i	$0.900464\pi$
$110$	−0.856839	+	0.856839i	−0.0816964	+	0.0816964i
$111$	6.92768	+	0.416620i	0.657546	+	0.0395439i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$			15.8812i			1.49398i	0.664835	+	0.746990i	$0.268502\pi$
$113$			15.8812i			1.49398i	−0.664835	+	0.746990i	$0.731498\pi$
$114$	1.47382	+	1.66243i	0.138036	+	0.155700i
$115$	−0.352955	+	0.352955i	−0.0329132	+	0.0329132i
$116$	7.36454			0.683780
$117$	−4.95676	+	9.61408i	−0.458253	+	0.888822i
$118$	−1.11071			−0.102250
$119$	3.72209	−	3.72209i	0.341204	−	0.341204i
$120$	0.385342	+	0.434655i	0.0351767	+	0.0396784i
$121$			2.05534i			0.186849i
$122$	−6.18656	+	6.18656i	−0.560105	+	0.560105i
$123$	3.23555	+	0.194581i	0.291739	+	0.0175448i
$124$	7.20598	−	7.20598i	0.647116	−	0.647116i
$125$	−2.34473	−	2.34473i	−0.209719	−	0.209719i
$126$	2.97838	+	0.359531i	0.265335	+	0.0320295i
$127$			8.38087i			0.743682i	0.928297	+	0.371841i	$0.121273\pi$
$127$			8.38087i			0.743682i	−0.928297	+	0.371841i	$0.878727\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.57459	−	3.16903i	0.314725	−	0.279018i
$130$	0.421316	−	1.13341i	0.0369518	−	0.0994066i
$131$			14.5927i			1.27497i	0.770464	+	0.637484i	$0.220025\pi$
$131$			14.5927i			1.27497i	−0.770464	+	0.637484i	$0.779975\pi$
$132$	6.24699	+	0.375685i	0.543731	+	0.0326992i
$133$	−1.28268			−0.111222
$134$	13.6903			1.18266
$135$	−0.312321	+	1.71440i	−0.0268803	+	0.147552i
$136$	−3.72209	−	3.72209i	−0.319167	−	0.319167i
$137$	−11.5852	−	11.5852i	−0.989790	−	0.989790i	0.0101587	−	0.999948i	$-0.496766\pi$
$137$	−11.5852	−	11.5852i	−0.989790	−	0.989790i	−0.999948	+	0.0101587i	$0.996766\pi$
$138$	2.57330	+	0.154755i	0.219054	+	0.0131736i
$139$	11.9801			1.01614			0.508070	−	0.861316i	$-0.330359\pi$
$139$	11.9801			1.01614			0.508070	+	0.861316i	$0.330359\pi$
$140$	−0.335367			−0.0283437
$141$	0.334176	−	5.55677i	0.0281427	−	0.467965i
$142$		−	6.99038i		−	0.586619i
$143$	−5.42495	−	11.8444i	−0.453657	−	0.990477i
$144$	0.359531	−	2.97838i	0.0299609	−	0.248198i
$145$	−1.74643	−	1.74643i	−0.145033	−	0.145033i
$146$		−	5.66478i		−	0.468821i
$147$	−1.29606	+	1.14901i	−0.106897	+	0.0947691i
$148$	2.83332	+	2.83332i	0.232898	+	0.232898i
$149$	−2.17899	+	2.17899i	−0.178510	+	0.178510i	−0.790706	−	0.612196i	$-0.790286\pi$
$149$	−2.17899	+	2.17899i	−0.178510	+	0.178510i	0.612196	+	0.790706i	$0.290286\pi$
$150$	−0.508181	+	8.45018i	−0.0414928	+	0.689954i
$151$	9.34711	−	9.34711i	0.760657	−	0.760657i	−0.215784	−	0.976441i	$-0.569231\pi$
$151$	9.34711	−	9.34711i	0.760657	−	0.760657i	0.976441	+	0.215784i	$0.0692307\pi$
$152$			1.28268i			0.104039i
$153$	1.89251	−	15.6777i	0.153000	−	1.26747i
$154$	−2.55493	+	2.55493i	−0.205882	+	0.205882i
$155$	−3.41766			−0.274513
$156$	−5.82365	+	2.25500i	−0.466266	+	0.180545i
$157$	−17.6346			−1.40740			−0.703698	−	0.710499i	$-0.748469\pi$
$157$	−17.6346			−1.40740			−0.703698	+	0.710499i	$0.748469\pi$
$158$	6.01650	−	6.01650i	0.478647	−	0.478647i
$159$	11.4132	−	10.1183i	0.905125	−	0.802435i
$160$			0.335367i			0.0265131i
$161$	−1.05244	+	1.05244i	−0.0829443	+	0.0829443i
$162$	7.69552	−	4.66679i	0.604617	−	0.366658i
$163$	−2.26457	+	2.26457i	−0.177375	+	0.177375i	−0.790210	−	0.612836i	$-0.790029\pi$
$163$	−2.26457	+	2.26457i	−0.177375	+	0.177375i	0.612836	+	0.790210i	$0.290029\pi$
$164$	1.32329	+	1.32329i	0.103332	+	0.103332i
$165$	−1.39232	−	1.57050i	−0.108392	−	0.122263i
$166$			4.32280i			0.335515i
$167$	−12.4482	−	12.4482i	−0.963272	−	0.963272i	0.0360774	−	0.999349i	$-0.488514\pi$
$167$	−12.4482	−	12.4482i	−0.963272	−	0.963272i	−0.999349	+	0.0360774i	$0.988514\pi$
$168$	1.14901	+	1.29606i	0.0886484	+	0.0999930i
$169$	9.84351	+	8.49149i	0.757193	+	0.653192i
$170$			1.76532i			0.135394i
$171$	−3.02745	+	2.37527i	−0.231515	+	0.181641i
$172$	2.75805			0.210299
$173$	12.8517			0.977096			0.488548	−	0.872537i	$-0.337527\pi$
$173$	12.8517			0.977096			0.488548	+	0.872537i	$0.337527\pi$
$174$	−0.765729	+	12.7328i	−0.0580497	+	0.965267i
$175$	−3.45600	−	3.45600i	−0.261249	−	0.261249i
$176$	2.55493	+	2.55493i	0.192585	+	0.192585i
$177$	0.115487	−	1.92034i	0.00868051	−	0.144342i
$178$	2.29517			0.172030
$179$	13.7258			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$179$	13.7258			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$180$	−0.791553	+	0.621034i	−0.0589989	+	0.0462892i
$181$			17.7979i			1.32291i	0.749986	+	0.661454i	$0.230060\pi$
$181$			17.7979i			1.32291i	−0.749986	+	0.661454i	$0.769940\pi$
$182$	1.25628	−	3.37961i	0.0931219	−	0.250513i
$183$	−10.0529	−	11.3394i	−0.743129	−	0.838230i
$184$	1.05244	+	1.05244i	0.0775873	+	0.0775873i
$185$		−	1.34379i		−	0.0987974i
$186$	11.7094	+	13.2079i	0.858573	+	0.968447i
$187$	13.4487	+	13.4487i	0.983469	+	0.983469i
$188$	2.27264	−	2.27264i	0.165749	−	0.165749i
$189$	−0.931280	+	5.11202i	−0.0677406	+	0.371845i
$190$	0.304175	−	0.304175i	0.0220672	−	0.0220672i
$191$		−	0.449102i		−	0.0324959i	−0.999868	−	0.0162479i	$-0.994828\pi$
$191$		−	0.449102i		−	0.0324959i	0.999868	−	0.0162479i	$-0.00517211\pi$
$192$	1.29606	−	1.14901i	0.0935349	−	0.0829230i
$193$	−5.53933	+	5.53933i	−0.398730	+	0.398730i	−0.877785	−	0.479055i	$-0.840979\pi$
$193$	−5.53933	+	5.53933i	−0.398730	+	0.398730i	0.479055	+	0.877785i	$0.340979\pi$
$194$	6.87739			0.493768
$195$	1.91578	+	0.846271i	0.137192	+	0.0606027i
$196$	−1.00000			−0.0714286
$197$	−15.8126	+	15.8126i	−1.12660	+	1.12660i	−0.135878	+	0.990726i	$0.543386\pi$
$197$	−15.8126	+	15.8126i	−1.12660	+	1.12660i	−0.990726	+	0.135878i	$0.956614\pi$
$198$	−1.29906	+	10.7615i	−0.0923204	+	0.764789i
$199$		−	26.3160i		−	1.86549i	−0.360531	−	0.932747i	$-0.617405\pi$
$199$		−	26.3160i		−	1.86549i	0.360531	−	0.932747i	$-0.382595\pi$
$200$	−3.45600	+	3.45600i	−0.244376	+	0.244376i
$201$	−1.42345	+	23.6695i	−0.100402	+	1.66952i
$202$	−13.1028	+	13.1028i	−0.921911	+	0.921911i
$203$	−5.20752	−	5.20752i	−0.365496	−	0.365496i
$204$	6.82223	−	6.04822i	0.477652	−	0.423460i
$205$		−	0.627612i		−	0.0438343i
$206$	−4.07345	−	4.07345i	−0.283811	−	0.283811i
$207$	−0.535119	+	4.43296i	−0.0371933	+	0.308112i
$208$	−3.37961	−	1.25628i	−0.234334	−	0.0871076i
$209$		−	4.63460i		−	0.320582i
$210$	0.0348698	−	0.579825i	0.00240625	−	0.0400117i
$211$	−11.4416			−0.787669			−0.393835	−	0.919181i	$-0.628852\pi$
$211$	−11.4416			−0.787669			−0.393835	+	0.919181i	$0.628852\pi$
$212$	8.80608			0.604804
$213$	12.0859	+	0.726825i	0.828109	+	0.0498012i
$214$	12.9489	+	12.9489i	0.885169	+	0.885169i
$215$	−0.654044	−	0.654044i	−0.0446054	−	0.0446054i
$216$	5.11202	+	0.931280i	0.347829	+	0.0633656i
$217$	−10.1908			−0.691796
$218$	9.50671			0.643876
$219$	9.79399	+	0.588996i	0.661817	+	0.0398007i
$220$		−	1.21175i		−	0.0816964i
$221$	−17.7897	−	6.61287i	−1.19666	−	0.444829i
$222$	−5.19320	+	4.60401i	−0.348545	+	0.309001i
$223$	−9.06520	−	9.06520i	−0.607051	−	0.607051i	0.335124	−	0.942174i	$-0.391222\pi$
$223$	−9.06520	−	9.06520i	−0.607051	−	0.607051i	−0.942174	+	0.335124i	$0.891222\pi$
$224$			1.00000i			0.0668153i
$225$	−14.5569	−	1.75722i	−0.970461	−	0.117148i
$226$	−11.2297	−	11.2297i	−0.746990	−	0.746990i
$227$	−1.95892	+	1.95892i	−0.130018	+	0.130018i	−0.769121	−	0.639103i	$-0.779306\pi$
$227$	−1.95892	+	1.95892i	−0.130018	+	0.130018i	0.639103	+	0.769121i	$0.279306\pi$
$228$	−2.21766	−	0.133367i	−0.146868	−	0.00883242i
$229$	19.6908	−	19.6908i	1.30120	−	1.30120i	0.373622	−	0.927581i	$-0.378116\pi$
$229$	19.6908	−	19.6908i	1.30120	−	1.30120i	0.927581	−	0.373622i	$-0.121884\pi$
$230$		−	0.499154i		−	0.0329132i
$231$	−4.15164	−	4.68294i	−0.273158	−	0.308115i
$232$	−5.20752	+	5.20752i	−0.341890	+	0.341890i
$233$	−8.08237			−0.529494			−0.264747	−	0.964318i	$-0.585288\pi$
$233$	−8.08237			−0.529494			−0.264747	+	0.964318i	$0.585288\pi$
$234$	−3.29322	−	10.3031i	−0.215285	−	0.673537i
$235$	−1.07787			−0.0703125
$236$	0.785394	−	0.785394i	0.0511248	−	0.0511248i
$237$	9.77652	+	11.0277i	0.635053	+	0.716323i
$238$			5.26383i			0.341204i
$239$	−17.1098	+	17.1098i	−1.10674	+	1.10674i	−0.113167	+	0.993576i	$0.536099\pi$
$239$	−17.1098	+	17.1098i	−1.10674	+	1.10674i	−0.993576	+	0.113167i	$0.963901\pi$
$240$	−0.579825	−	0.0348698i	−0.0374275	−	0.00225084i
$241$	−1.64646	+	1.64646i	−0.106058	+	0.106058i	−0.758144	−	0.652087i	$-0.773894\pi$
$241$	−1.64646	+	1.64646i	−0.106058	+	0.106058i	0.652087	+	0.758144i	$0.273894\pi$
$242$	−1.45335	−	1.45335i	−0.0934247	−	0.0934247i
$243$	7.26840	+	13.7902i	0.466268	+	0.884644i
$244$		−	8.74912i		−	0.560105i
$245$	0.237140	+	0.237140i	0.0151503	+	0.0151503i
$246$	−2.42547	+	2.15029i	−0.154642	+	0.137097i
$247$	1.92584	+	4.20471i	0.122538	+	0.267539i
$248$			10.1908i			0.647116i
$249$	−7.47381	−	0.449464i	−0.473633	−	0.0284836i
$250$	3.31595			0.209719
$251$	5.59492			0.353148			0.176574	−	0.984287i	$-0.443499\pi$
$251$	5.59492			0.353148			0.176574	+	0.984287i	$0.443499\pi$
$252$	−2.36026	+	1.85180i	−0.148682	+	0.116653i
$253$	−3.80271	−	3.80271i	−0.239074	−	0.239074i
$254$	−5.92617	−	5.92617i	−0.371841	−	0.371841i
$255$	−3.05210	−	0.183549i	−0.191130	−	0.0114943i
$256$	1.00000			0.0625000
$257$	−9.37697			−0.584920			−0.292460	−	0.956278i	$-0.594474\pi$
$257$	−9.37697			−0.584920			−0.292460	+	0.956278i	$0.594474\pi$
$258$	−0.286768	+	4.76846i	−0.0178534	+	0.296871i
$259$		−	4.00692i		−	0.248978i
$260$	0.503526	+	1.09936i	0.0312274	+	0.0681792i
$261$	−21.9344	−	2.64778i	−1.35770	−	0.163893i
$262$	−10.3186	−	10.3186i	−0.637484	−	0.637484i
$263$		−	7.28774i		−	0.449382i	−0.974430	−	0.224691i	$-0.927863\pi$
$263$		−	7.28774i		−	0.449382i	0.974430	−	0.224691i	$-0.0721372\pi$
$264$	−4.68294	+	4.15164i	−0.288215	+	0.255516i
$265$	−2.08828	−	2.08828i	−0.128282	−	0.128282i
$266$	0.906991	−	0.906991i	0.0556112	−	0.0556112i
$267$	−0.238641	+	3.96818i	−0.0146046	+	0.242849i
$268$	−9.68048	+	9.68048i	−0.591330	+	0.591330i
$269$			16.4964i			1.00580i	0.864344	+	0.502901i	$0.167734\pi$
$269$			16.4964i			1.00580i	−0.864344	+	0.502901i	$0.832266\pi$
$270$	−0.991421	−	1.43311i	−0.0603360	−	0.0872162i
$271$	−2.57036	+	2.57036i	−0.156138	+	0.156138i	−0.780853	−	0.624715i	$-0.785215\pi$
$271$	−2.57036	+	2.57036i	−0.156138	+	0.156138i	0.624715	+	0.780853i	$0.285215\pi$
$272$	5.26383			0.319167
$273$	5.71247	+	2.52342i	0.345735	+	0.152724i
$274$	16.3839			0.989790
$275$	12.4873	−	12.4873i	0.753012	−	0.753012i
$276$	−1.92903	+	1.71017i	−0.116114	+	0.102940i
$277$			7.42795i			0.446302i	0.974784	+	0.223151i	$0.0716344\pi$
$277$			7.42795i			0.446302i	−0.974784	+	0.223151i	$0.928366\pi$
$278$	−8.47121	+	8.47121i	−0.508070	+	0.508070i
$279$	−24.0529	+	18.8714i	−1.44001	+	1.12980i
$280$	0.237140	−	0.237140i	0.0141718	−	0.0141718i
$281$	9.42247	+	9.42247i	0.562097	+	0.562097i	0.929903	−	0.367805i	$-0.119891\pi$
$281$	9.42247	+	9.42247i	0.562097	+	0.562097i	−0.367805	+	0.929903i	$0.619891\pi$
$282$	3.69293	+	4.16553i	0.219911	+	0.248054i
$283$			21.5878i			1.28326i	0.767014	+	0.641631i	$0.221742\pi$
$283$			21.5878i			1.28326i	−0.767014	+	0.641631i	$0.778258\pi$
$284$	4.94294	+	4.94294i	0.293310	+	0.293310i
$285$	0.494269	+	0.557523i	0.0292780	+	0.0330248i
$286$	12.2113	+	4.53922i	0.722067	+	0.268410i
$287$		−	1.87142i		−	0.110466i
$288$	1.85180	+	2.36026i	0.109119	+	0.139080i
$289$	10.7079			0.629879
$290$	2.46982			0.145033
$291$	−0.715078	+	11.8905i	−0.0419186	+	0.697034i
$292$	4.00560	+	4.00560i	0.234410	+	0.234410i
$293$	3.94771	+	3.94771i	0.230628	+	0.230628i	0.812955	−	0.582327i	$-0.197858\pi$
$293$	3.94771	+	3.94771i	0.230628	+	0.230628i	−0.582327	+	0.812955i	$0.697858\pi$
$294$	0.103975	−	1.72893i	0.00606395	−	0.100833i
$295$	−0.372497			−0.0216876
$296$	−4.00692			−0.232898
$297$	−18.4708	−	3.36492i	−1.07179	−	0.195252i
$298$		−	3.08156i		−	0.178510i
$299$	5.03015	+	1.86983i	0.290901	+	0.108135i
$300$	−5.61584	−	6.33452i	−0.324231	−	0.365724i
$301$	−1.95023	−	1.95023i	−0.112410	−	0.112410i
$302$			13.2188i			0.760657i
$303$	−21.2915	−	24.0162i	−1.22316	−	1.37969i
$304$	−0.906991	−	0.906991i	−0.0520195	−	0.0520195i
$305$	−2.07477	+	2.07477i	−0.118801	+	0.118801i
$306$	9.74759	+	12.4240i	0.557233	+	0.710233i
$307$	−11.8118	+	11.8118i	−0.674136	+	0.674136i	−0.958667	−	0.284531i	$-0.908162\pi$
$307$	−11.8118	+	11.8118i	−0.674136	+	0.674136i	0.284531	+	0.958667i	$0.408162\pi$
$308$		−	3.61322i		−	0.205882i
$309$	7.46624	−	6.61917i	0.424740	−	0.376551i
$310$	2.41665	−	2.41665i	0.137256	−	0.137256i
$311$	20.8401			1.18174			0.590868	−	0.806769i	$-0.298786\pi$
$311$	20.8401			1.18174			0.590868	+	0.806769i	$0.298786\pi$
$312$	2.52342	−	5.71247i	0.142860	−	0.323405i
$313$	9.67697			0.546975			0.273487	−	0.961876i	$-0.411823\pi$
$313$	9.67697			0.546975			0.273487	+	0.961876i	$0.411823\pi$
$314$	12.4696	−	12.4696i	0.703698	−	0.703698i
$315$	0.998850	+	0.120575i	0.0562788	+	0.00679362i
$316$			8.50862i			0.478647i
$317$	14.4793	−	14.4793i	0.813239	−	0.813239i	−0.171879	−	0.985118i	$-0.554984\pi$
$317$	14.4793	−	14.4793i	0.813239	−	0.813239i	0.985118	+	0.171879i	$0.0549838\pi$
$318$	−0.915613	+	15.2251i	−0.0513450	+	0.853780i
$319$	18.8159	−	18.8159i	1.05349	−	1.05349i
$320$	−0.237140	−	0.237140i	−0.0132565	−	0.0132565i
$321$	−23.7341	+	21.0414i	−1.32471	+	1.17441i
$322$		−	1.48838i		−	0.0829443i
$323$	−4.77425	−	4.77425i	−0.265646	−	0.265646i
$324$	−2.14164	+	8.74148i	−0.118980	+	0.485638i
$325$	−6.14012	+	16.5179i	−0.340593	+	0.916250i
$326$		−	3.20259i		−	0.177375i
$327$	−0.988462	+	16.4364i	−0.0546620	+	0.908936i
$328$	−1.87142			−0.103332
$329$	−3.21400			−0.177194
$330$	2.09503	+	0.125992i	0.115328	+	0.00693565i
$331$	23.9019	+	23.9019i	1.31377	+	1.31377i	0.918617	+	0.395149i	$0.129307\pi$
$331$	23.9019	+	23.9019i	1.31377	+	1.31377i	0.395149	+	0.918617i	$0.370693\pi$
$332$	−3.05668	−	3.05668i	−0.167757	−	0.167757i
$333$	−7.42004	−	9.45737i	−0.406616	−	0.518261i
$334$	17.6044			0.963272
$335$	4.59126			0.250848
$336$	−1.72893	−	0.103975i	−0.0943207	−	0.00567231i
$337$		−	19.1386i		−	1.04254i	−0.853390	−	0.521272i	$-0.825458\pi$
$337$		−	19.1386i		−	1.04254i	0.853390	−	0.521272i	$-0.174542\pi$
$338$	−12.9648	+	0.956020i	−0.705192	+	0.0520006i
$339$	20.5830	−	18.2478i	1.11791	−	0.991083i
$340$	−1.24827	−	1.24827i	−0.0676968	−	0.0676968i
$341$		−	36.8216i		−	1.99400i
$342$	0.461162	−	3.82030i	0.0249368	−	0.206578i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−1.95023	+	1.95023i	−0.105149	+	0.105149i
$345$	0.863001	+	0.0518996i	0.0464624	+	0.00279418i
$346$	−9.08752	+	9.08752i	−0.488548	+	0.488548i
$347$			22.2918i			1.19669i	0.801240	+	0.598343i	$0.204174\pi$
$347$			22.2918i			1.19669i	−0.801240	+	0.598343i	$0.795826\pi$
$348$	−8.46196	−	9.54487i	−0.453609	−	0.511659i
$349$	−11.5388	+	11.5388i	−0.617658	+	0.617658i	−0.944930	−	0.327272i	$-0.893871\pi$
$349$	−11.5388	+	11.5388i	−0.617658	+	0.617658i	0.327272	+	0.944930i	$0.393871\pi$
$350$	4.88753			0.261249
$351$	18.1558	−	4.62247i	0.969084	−	0.246729i
$352$	−3.61322			−0.192585
$353$	10.9867	−	10.9867i	0.584765	−	0.584765i	−0.351444	−	0.936209i	$-0.614309\pi$
$353$	10.9867	−	10.9867i	0.584765	−	0.584765i	0.936209	+	0.351444i	$0.114309\pi$
$354$	1.27623	+	1.43955i	0.0678307	+	0.0765112i
$355$		−	2.34434i		−	0.124425i
$356$	−1.62293	+	1.62293i	−0.0860152	+	0.0860152i
$357$	−9.10078	−	0.547308i	−0.481665	−	0.0289666i
$358$	−9.70564	+	9.70564i	−0.512959	+	0.512959i
$359$	12.3937	+	12.3937i	0.654116	+	0.654116i	0.953982	−	0.299865i	$-0.0969418\pi$
$359$	12.3937	+	12.3937i	0.654116	+	0.654116i	−0.299865	+	0.953982i	$0.596942\pi$
$360$	0.120575	−	0.998850i	0.00635485	−	0.0526440i
$361$		−	17.3547i		−	0.913407i
$362$	−12.5850	−	12.5850i	−0.661454	−	0.661454i
$363$	2.66384	−	2.36162i	0.139816	−	0.123953i
$364$	1.50142	+	3.27807i	0.0786957	+	0.171818i
$365$		−	1.89978i		−	0.0994390i
$366$	15.1266	+	0.909691i	0.790679	+	0.0475503i
$367$	−19.3712			−1.01117			−0.505583	−	0.862778i	$-0.668723\pi$
$367$	−19.3712			−1.01117			−0.505583	+	0.862778i	$0.668723\pi$
$368$	−1.48838			−0.0775873
$369$	−3.46550	−	4.41703i	−0.180407	−	0.229941i
$370$	0.950203	+	0.950203i	0.0493987	+	0.0493987i
$371$	−6.22684	−	6.22684i	−0.323281	−	0.323281i
$372$	−17.6191	−	1.05959i	−0.913510	−	0.0549372i
$373$	26.6583			1.38031			0.690157	−	0.723659i	$-0.257541\pi$
$373$	26.6583			1.38031			0.690157	+	0.723659i	$0.257541\pi$
$374$	−19.0194			−0.983469
$375$	−0.344776	+	5.73304i	−0.0178042	+	0.296053i
$376$			3.21400i			0.165749i
$377$	−9.25195	+	24.8893i	−0.476499	+	1.28186i
$378$	−2.95623	−	4.27326i	−0.152052	−	0.219793i
$379$	−7.17262	−	7.17262i	−0.368433	−	0.368433i	0.498473	−	0.866905i	$-0.333894\pi$
$379$	−7.17262	−	7.17262i	−0.368433	−	0.368433i	−0.866905	+	0.498473i	$0.833894\pi$
$380$			0.430168i			0.0220672i
$381$	10.8621	−	9.62974i	0.556482	−	0.493346i
$382$	0.317563	+	0.317563i	0.0162479	+	0.0162479i
$383$	−1.75953	+	1.75953i	−0.0899076	+	0.0899076i	−0.750630	−	0.660723i	$-0.770250\pi$
$383$	−1.75953	+	1.75953i	−0.0899076	+	0.0899076i	0.660723	+	0.750630i	$0.270250\pi$
$384$	−0.103975	+	1.72893i	−0.00530596	+	0.0882289i
$385$	−0.856839	+	0.856839i	−0.0436686	+	0.0436686i
$386$		−	7.83380i		−	0.398730i
$387$	−8.21450	−	0.991602i	−0.417567	−	0.0504060i
$388$	−4.86305	+	4.86305i	−0.246884	+	0.246884i
$389$	23.3995			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$389$	23.3995			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$390$	−1.95306	+	0.756254i	−0.0988971	+	0.0382944i
$391$	−7.83459			−0.396212
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	18.9130	−	16.7672i	0.954032	−	0.845793i
$394$		−	22.3624i		−	1.12660i
$395$	2.01774	−	2.01774i	0.101523	−	0.101523i
$396$	−6.69097	−	8.52813i	−0.336234	−	0.428555i
$397$	12.7022	−	12.7022i	0.637506	−	0.637506i	−0.312434	−	0.949940i	$-0.601144\pi$
$397$	12.7022	−	12.7022i	0.637506	−	0.637506i	0.949940	+	0.312434i	$0.101144\pi$
$398$	18.6082	+	18.6082i	0.932747	+	0.932747i
$399$	1.47382	+	1.66243i	0.0737831	+	0.0832254i
$400$		−	4.88753i		−	0.244376i
$401$	4.63460	+	4.63460i	0.231441	+	0.231441i	0.813294	−	0.581853i	$-0.197672\pi$
$401$	4.63460	+	4.63460i	0.231441	+	0.231441i	−0.581853	+	0.813294i	$0.697672\pi$
$402$	−15.7303	−	17.7434i	−0.784557	−	0.884959i
$403$	15.3006	+	33.4062i	0.762179	+	1.66408i
$404$		−	18.5302i		−	0.921911i
$405$	2.58082	−	1.56509i	0.128242	−	0.0777698i
$406$	7.36454			0.365496
$407$	14.4779			0.717642
$408$	−0.547308	+	9.10078i	−0.0270958	+	0.450556i
$409$	20.9632	+	20.9632i	1.03656	+	1.03656i	0.999306	+	0.0372568i	$0.0118619\pi$
$409$	20.9632	+	20.9632i	1.03656	+	1.03656i	0.0372568	+	0.999306i	$0.488138\pi$
$410$	0.443789	+	0.443789i	0.0219172	+	0.0219172i
$411$	−1.70352	+	28.3266i	−0.0840285	+	1.39725i
$412$	5.76073			0.283811
$413$	−1.11071			−0.0546547
$414$	−2.75619	−	3.51297i	−0.135459	−	0.172653i
$415$			1.44973i			0.0711642i
$416$	3.27807	−	1.50142i	0.160721	−	0.0736131i
$417$	−13.7653	−	15.5269i	−0.674091	−	0.760356i
$418$	3.27716	+	3.27716i	0.160291	+	0.160291i
$419$		−	2.30031i		−	0.112377i	−0.998420	−	0.0561886i	$-0.982105\pi$
$419$		−	2.30031i		−	0.112377i	0.998420	−	0.0561886i	$-0.0178948\pi$
$420$	0.385342	+	0.434655i	0.0188027	+	0.0212090i
$421$	−5.27352	−	5.27352i	−0.257016	−	0.257016i	0.566823	−	0.823839i	$-0.308172\pi$
$421$	−5.27352	−	5.27352i	−0.257016	−	0.257016i	−0.823839	+	0.566823i	$0.808172\pi$
$422$	8.09040	−	8.09040i	0.393835	−	0.393835i
$423$	−7.58587	+	5.95170i	−0.368838	+	0.289382i
$424$	−6.22684	+	6.22684i	−0.302402	+	0.302402i
$425$		−	25.7271i		−	1.24795i
$426$	−9.05993	+	8.03204i	−0.438955	+	0.389154i
$427$	−6.18656	+	6.18656i	−0.299389	+	0.299389i
$428$	−18.3125			−0.885169
$429$	−9.11766	+	20.6404i	−0.440205	+	0.996529i
$430$	0.924957			0.0446054
$431$	−4.81808	+	4.81808i	−0.232079	+	0.232079i	−0.813560	−	0.581481i	$-0.802473\pi$
$431$	−4.81808	+	4.81808i	−0.232079	+	0.232079i	0.581481	+	0.813560i	$0.302473\pi$
$432$	−4.27326	+	2.95623i	−0.205597	+	0.142232i
$433$		−	4.81966i		−	0.231618i	−0.993272	−	0.115809i	$-0.963054\pi$
$433$		−	4.81966i		−	0.231618i	0.993272	−	0.115809i	$-0.0369460\pi$
$434$	7.20598	−	7.20598i	0.345898	−	0.345898i
$435$	−0.256800	+	4.27014i	−0.0123126	+	0.204738i
$436$	−6.72226	+	6.72226i	−0.321938	+	0.321938i
$437$	1.34995	+	1.34995i	0.0645768	+	0.0645768i
$438$	−7.34188	+	6.50891i	−0.350809	+	0.311008i
$439$		−	13.0143i		−	0.621137i	−0.950551	−	0.310569i	$-0.899481\pi$
$439$		−	13.0143i		−	0.621137i	0.950551	−	0.310569i	$-0.100519\pi$
$440$	0.856839	+	0.856839i	0.0408482	+	0.0408482i
$441$	2.97838	+	0.359531i	0.141828	+	0.0171205i
$442$	17.2552	−	7.90321i	0.820747	−	0.375918i
$443$		−	23.1864i		−	1.10162i	−0.834631	−	0.550810i	$-0.814319\pi$
$443$		−	23.1864i		−	1.10162i	0.834631	−	0.550810i	$-0.185681\pi$
$444$	0.416620	−	6.92768i	0.0197719	−	0.328773i
$445$	0.769725			0.0364884
$446$	12.8201			0.607051
$447$	5.32779	+	0.320406i	0.251996	+	0.0151547i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−7.31378	−	7.31378i	−0.345159	−	0.345159i	0.513144	−	0.858303i	$-0.328481\pi$
$449$	−7.31378	−	7.31378i	−0.345159	−	0.345159i	−0.858303	+	0.513144i	$0.828481\pi$
$450$	11.5358	−	9.05075i	0.543804	−	0.426656i
$451$	6.76184			0.318403
$452$	15.8812			0.746990
$453$	−22.8544	−	1.37443i	−1.07379	−	0.0645762i
$454$		−	2.77033i		−	0.130018i
$455$	0.421316	−	1.13341i	0.0197516	−	0.0531350i
$456$	1.66243	−	1.47382i	0.0778502	−	0.0690178i
$457$	7.58631	+	7.58631i	0.354873	+	0.354873i	0.861919	−	0.507046i	$-0.169263\pi$
$457$	7.58631	+	7.58631i	0.354873	+	0.354873i	−0.507046	+	0.861919i	$0.669263\pi$
$458$			27.8470i			1.30120i
$459$	−22.4937	+	15.5611i	−1.04992	+	0.726329i
$460$	0.352955	+	0.352955i	0.0164566	+	0.0164566i
$461$	9.45526	−	9.45526i	0.440375	−	0.440375i	−0.451763	−	0.892138i	$-0.649205\pi$
$461$	9.45526	−	9.45526i	0.440375	−	0.440375i	0.892138	+	0.451763i	$0.149205\pi$
$462$	6.24699	+	0.375685i	0.290636	+	0.0174784i
$463$	24.1674	−	24.1674i	1.12315	−	1.12315i	0.131890	−	0.991264i	$-0.457895\pi$
$463$	24.1674	−	24.1674i	1.12315	−	1.12315i	0.991264	−	0.131890i	$-0.0421046\pi$
$464$		−	7.36454i		−	0.341890i
$465$	3.92694	+	4.42948i	0.182107	+	0.205412i
$466$	5.71510	−	5.71510i	0.264747	−	0.264747i
$467$	23.9765			1.10950			0.554750	−	0.832017i	$-0.312814\pi$
$467$	23.9765			1.10950			0.554750	+	0.832017i	$0.312814\pi$
$468$	9.61408	+	4.95676i	0.444411	+	0.229126i
$469$	13.6903			0.632158
$470$	0.762169	−	0.762169i	0.0351562	−	0.0351562i
$471$	20.2624	+	22.8555i	0.933644	+	1.05313i
$472$			1.11071i			0.0511248i
$473$	7.04661	−	7.04661i	0.324004	−	0.324004i
$474$	−14.7108	−	0.884684i	−0.675688	−	0.0406349i
$475$	−4.43294	+	4.43294i	−0.203397	+	0.203397i
$476$	−3.72209	−	3.72209i	−0.170602	−	0.170602i
$477$	−26.2278	−	3.16606i	−1.20089	−	0.144964i
$478$		−	24.1969i		−	1.10674i
$479$	−13.3006	−	13.3006i	−0.607720	−	0.607720i	0.334630	−	0.942350i	$-0.391389\pi$
$479$	−13.3006	−	13.3006i	−0.607720	−	0.607720i	−0.942350	+	0.334630i	$0.891389\pi$
$480$	0.434655	−	0.385342i	0.0198392	−	0.0175884i
$481$	−13.1350	+	6.01607i	−0.598903	+	0.274309i
$482$		−	2.32844i		−	0.106058i
$483$	2.57330	+	0.154755i	0.117089	+	0.00704158i
$484$	2.05534			0.0934247
$485$	2.30645			0.104731
$486$	−14.8907	−	4.61163i	−0.675456	−	0.209188i
$487$	−12.0715	−	12.0715i	−0.547013	−	0.547013i	0.378563	−	0.925576i	$-0.376418\pi$
$487$	−12.0715	−	12.0715i	−0.547013	−	0.547013i	−0.925576	+	0.378563i	$0.876418\pi$
$488$	6.18656	+	6.18656i	0.280052	+	0.280052i
$489$	5.53704	+	0.332989i	0.250393	+	0.0150583i
$490$	−0.335367			−0.0151503
$491$	28.9991			1.30871			0.654356	−	0.756187i	$-0.272940\pi$
$491$	28.9991			1.30871			0.654356	+	0.756187i	$0.272940\pi$
$492$	0.194581	−	3.23555i	0.00877239	−	0.145870i
$493$		−	38.7657i		−	1.74592i
$494$	−4.33495	−	1.61141i	−0.195039	−	0.0725007i
$495$	−0.435663	+	3.60906i	−0.0195816	+	0.162215i
$496$	−7.20598	−	7.20598i	−0.323558	−	0.323558i
$497$		−	6.99038i		−	0.313561i
$498$	5.60260	−	4.96696i	0.251059	−	0.222575i
$499$	−16.4961	−	16.4961i	−0.738468	−	0.738468i	0.233814	−	0.972281i	$-0.424879\pi$
$499$	−16.4961	−	16.4961i	−0.738468	−	0.738468i	−0.972281	+	0.233814i	$0.924879\pi$
$500$	−2.34473	+	2.34473i	−0.104860	+	0.104860i
$501$	−1.83042	+	30.4368i	−0.0817773	+	1.35982i
$502$	−3.95620	+	3.95620i	−0.176574	+	0.176574i
$503$			3.30047i			0.147161i	0.997289	+	0.0735804i	$0.0234425\pi$
$503$			3.30047i			0.147161i	−0.997289	+	0.0735804i	$0.976557\pi$
$504$	0.359531	−	2.97838i	0.0160148	−	0.132668i
$505$	−4.39425	+	4.39425i	−0.195542	+	0.195542i
$506$	5.37785			0.239074
$507$	−0.304872	−	22.5146i	−0.0135398	−	0.999908i
$508$	8.38087			0.371841
$509$	−4.74000	+	4.74000i	−0.210097	+	0.210097i	−0.804309	−	0.594212i	$-0.797464\pi$
$509$	−4.74000	+	4.74000i	−0.210097	+	0.210097i	0.594212	+	0.804309i	$0.297464\pi$
$510$	2.28795	−	2.02837i	0.101312	−	0.0898179i
$511$		−	5.66478i		−	0.250595i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.55708	+	1.19453i	0.289502	+	0.0527399i
$514$	6.63052	−	6.63052i	0.292460	−	0.292460i
$515$	−1.36610	−	1.36610i	−0.0601976	−	0.0601976i
$516$	−3.16903	−	3.57459i	−0.139509	−	0.157362i
$517$		−	11.6129i		−	0.510734i
$518$	2.83332	+	2.83332i	0.124489	+	0.124489i
$519$	−14.7668	−	16.6565i	−0.648190	−	0.731140i
$520$	−1.13341	−	0.421316i	−0.0497033	−	0.0184759i
$521$			23.6757i			1.03725i	0.855001	+	0.518627i	$0.173557\pi$
$521$			23.6757i			1.03725i	−0.855001	+	0.518627i	$0.826443\pi$
$522$	17.3822	−	13.6377i	0.760799	−	0.596905i
$523$	−39.0606			−1.70800			−0.854000	−	0.520272i	$-0.825830\pi$
$523$	−39.0606			−1.70800			−0.854000	+	0.520272i	$0.825830\pi$
$524$	14.5927			0.637484
$525$	−0.508181	+	8.45018i	−0.0221789	+	0.368796i
$526$	5.15321	+	5.15321i	0.224691	+	0.224691i
$527$	−37.9311	−	37.9311i	−1.65230	−	1.65230i
$528$	0.375685	−	6.24699i	0.0163496	−	0.271865i
$529$	−20.7847			−0.903683
$530$	2.95327			0.128282
$531$	−2.62157	+	2.05683i	−0.113767	+	0.0892586i
$532$			1.28268i			0.0556112i
$533$	−6.13464	+	2.80978i	−0.265721	+	0.121705i
$534$	−2.63719	−	2.97467i	−0.114122	−	0.128727i
$535$	4.34264	+	4.34264i	0.187749	+	0.187749i
$536$		−	13.6903i		−	0.591330i
$537$	−15.7712	−	17.7895i	−0.680577	−	0.767673i
$538$	−11.6647	−	11.6647i	−0.502901	−	0.502901i
$539$	−2.55493	+	2.55493i	−0.110049	+	0.110049i
$540$	1.71440	+	0.312321i	0.0737761	+	0.0134401i
$541$	−19.3541	+	19.3541i	−0.832100	+	0.832100i	−0.987804	−	0.155704i	$-0.950235\pi$
$541$	−19.3541	+	19.3541i	−0.832100	+	0.832100i	0.155704	+	0.987804i	$0.450235\pi$
$542$		−	3.63504i		−	0.156138i
$543$	23.0671	−	20.4500i	0.989904	−	0.877595i
$544$	−3.72209	+	3.72209i	−0.159583	+	0.159583i
$545$	3.18824			0.136569
$546$	−5.82365	+	2.25500i	−0.249229	+	0.0965053i
$547$	−17.0333			−0.728292			−0.364146	−	0.931342i	$-0.618639\pi$
$547$	−17.0333			−0.728292			−0.364146	+	0.931342i	$0.618639\pi$
$548$	−11.5852	+	11.5852i	−0.494895	+	0.494895i
$549$	−3.14558	+	26.0582i	−0.134250	+	1.11214i
$550$			17.6597i			0.753012i
$551$	−6.67957	+	6.67957i	−0.284559	+	0.284559i
$552$	0.154755	−	2.57330i	0.00658680	−	0.109527i
$553$	6.01650	−	6.01650i	0.255848	−	0.255848i
$554$	−5.25236	−	5.25236i	−0.223151	−	0.223151i
$555$	−1.74163	+	1.54403i	−0.0739280	+	0.0655406i
$556$		−	11.9801i		−	0.508070i
$557$	17.6970	+	17.6970i	0.749846	+	0.749846i	0.974450	−	0.224604i	$-0.0721090\pi$
$557$	17.6970	+	17.6970i	0.749846	+	0.749846i	−0.224604	+	0.974450i	$0.572109\pi$
$558$	3.66391	−	30.3521i	0.155106	−	1.28490i
$559$	−3.46489	+	9.32111i	−0.146549	+	0.394241i
$560$			0.335367i			0.0141718i
$561$	1.97754	−	32.8831i	0.0834919	−	1.38833i
$562$	−13.3254			−0.562097
$563$	−1.91330			−0.0806362			−0.0403181	−	0.999187i	$-0.512837\pi$
$563$	−1.91330			−0.0806362			−0.0403181	+	0.999187i	$0.512837\pi$
$564$	−5.55677	−	0.334176i	−0.233982	−	0.0140714i
$565$	−3.76608	−	3.76608i	−0.158440	−	0.158440i
$566$	−15.2649	−	15.2649i	−0.641631	−	0.641631i
$567$	7.69552	−	4.66679i	0.323182	−	0.195987i
$568$	−6.99038			−0.293310
$569$	16.3399			0.685003			0.342501	−	0.939517i	$-0.388726\pi$
$569$	16.3399			0.685003			0.342501	+	0.939517i	$0.388726\pi$
$570$	−0.743729	−	0.0447268i	−0.0311514	−	0.00187340i
$571$		−	42.0194i		−	1.75846i	−0.476400	−	0.879229i	$-0.658059\pi$
$571$		−	42.0194i		−	1.75846i	0.476400	−	0.879229i	$-0.341941\pi$
$572$	−11.8444	+	5.42495i	−0.495238	+	0.226829i
$573$	−0.582062	+	0.516025i	−0.0243160	+	0.0215572i
$574$	1.32329	+	1.32329i	0.0552332	+	0.0552332i
$575$			7.27451i			0.303368i
$576$	−2.97838	−	0.359531i	−0.124099	−	0.0149804i
$577$	24.8112	+	24.8112i	1.03290	+	1.03290i	0.999440	+	0.0334650i	$0.0106542\pi$
$577$	24.8112	+	24.8112i	1.03290	+	1.03290i	0.0334650	+	0.999440i	$0.489346\pi$
$578$	−7.57166	+	7.57166i	−0.314940	+	0.314940i
$579$	13.5441	+	0.814520i	0.562872	+	0.0338503i
$580$	−1.74643	+	1.74643i	−0.0725165	+	0.0725165i
$581$			4.32280i			0.179340i
$582$	−7.90223	−	8.91350i	−0.327558	−	0.369476i
$583$	22.4989	−	22.4989i	0.931810	−	0.931810i
$584$	−5.66478			−0.234410
$585$	−1.10444	−	3.45533i	−0.0456629	−	0.142860i
$586$	−5.58290			−0.230628
$587$	9.34332	−	9.34332i	0.385640	−	0.385640i	−0.487489	−	0.873129i	$-0.662087\pi$
$587$	9.34332	−	9.34332i	0.385640	−	0.385640i	0.873129	+	0.487489i	$0.162087\pi$
$588$	1.14901	+	1.29606i	0.0473846	+	0.0534485i
$589$			13.0715i			0.538603i
$590$	0.263395	−	0.263395i	0.0108438	−	0.0108438i
$591$	38.6630	+	2.32514i	1.59038	+	0.0956434i
$592$	2.83332	−	2.83332i	0.116449	−	0.116449i
$593$	−8.89198	−	8.89198i	−0.365150	−	0.365150i	0.500555	−	0.865705i	$-0.333129\pi$
$593$	−8.89198	−	8.89198i	−0.365150	−	0.365150i	−0.865705	+	0.500555i	$0.833129\pi$
$594$	15.4402	−	10.6815i	0.633519	−	0.438267i
$595$			1.76532i			0.0723709i
$596$	2.17899	+	2.17899i	0.0892550	+	0.0892550i
$597$	−34.1071	+	30.2375i	−1.39591	+	1.23754i
$598$	−4.87902	+	2.23468i	−0.199518	+	0.0913830i
$599$			39.8265i			1.62727i	0.581379	+	0.813633i	$0.302513\pi$
$599$			39.8265i			1.62727i	−0.581379	+	0.813633i	$0.697487\pi$
$600$	8.45018	+	0.508181i	0.344977	+	0.0207464i
$601$	40.3328			1.64521			0.822605	−	0.568613i	$-0.192520\pi$
$601$	40.3328			1.64521			0.822605	+	0.568613i	$0.192520\pi$
$602$	2.75805			0.112410
$603$	32.3126	−	25.3517i	1.31587	−	1.03240i
$604$	−9.34711	−	9.34711i	−0.380329	−	0.380329i
$605$	−0.487405	−	0.487405i	−0.0198158	−	0.0198158i
$606$	32.0373	+	1.92668i	1.30143	+	0.0782659i
$607$	−29.9002			−1.21361			−0.606805	−	0.794851i	$-0.707549\pi$
$607$	−29.9002			−1.21361			−0.606805	+	0.794851i	$0.707549\pi$
$608$	1.28268			0.0520195
$609$	−0.765729	+	12.7328i	−0.0310289	+	0.515957i
$610$		−	2.93417i		−	0.118801i
$611$	4.82556	+	10.5357i	0.195221	+	0.426230i
$612$	−15.6777	−	1.89251i	−0.633733	−	0.0765002i
$613$	0.240034	+	0.240034i	0.00969490	+	0.00969490i	0.711938	−	0.702243i	$-0.247818\pi$
$613$	0.240034	+	0.240034i	0.00969490	+	0.00969490i	−0.702243	+	0.711938i	$0.747818\pi$
$614$		−	16.7044i		−	0.674136i
$615$	−0.813421	+	0.721135i	−0.0328003	+	0.0290790i
$616$	2.55493	+	2.55493i	0.102941	+	0.102941i
$617$	25.7734	−	25.7734i	1.03760	−	1.03760i	0.0383316	−	0.999265i	$-0.487796\pi$
$617$	25.7734	−	25.7734i	1.03760	−	1.03760i	0.999265	−	0.0383316i	$-0.0122043\pi$
$618$	−0.598973	+	9.95989i	−0.0240942	+	0.400645i
$619$	−26.3806	+	26.3806i	−1.06033	+	1.06033i	−0.0622679	+	0.998059i	$0.519833\pi$
$619$	−26.3806	+	26.3806i	−1.06033	+	1.06033i	−0.998059	+	0.0622679i	$0.980167\pi$
$620$			3.41766i			0.137256i
$621$	6.36024	−	4.40000i	0.255227	−	0.176566i
$622$	−14.7362	+	14.7362i	−0.590868	+	0.590868i
$623$	2.29517			0.0919541
$624$	2.25500	+	5.82365i	0.0902724	+	0.233133i
$625$	−23.3256			−0.933023
$626$	−6.84265	+	6.84265i	−0.273487	+	0.273487i
$627$	−6.00671	+	5.32522i	−0.239885	+	0.212669i
$628$			17.6346i			0.703698i
$629$	14.9141	−	14.9141i	0.594666	−	0.594666i
$630$	−0.791553	+	0.621034i	−0.0315362	+	0.0247426i
$631$	−4.98978	+	4.98978i	−0.198640	+	0.198640i	−0.799417	−	0.600777i	$-0.794858\pi$
$631$	−4.98978	+	4.98978i	−0.198640	+	0.198640i	0.600777	+	0.799417i	$0.294858\pi$
$632$	−6.01650	−	6.01650i	−0.239324	−	0.239324i
$633$	13.1465	+	14.8289i	0.522527	+	0.589396i
$634$			20.4768i			0.813239i
$635$	−1.98744	−	1.98744i	−0.0788692	−	0.0788692i
$636$	−10.1183	−	11.4132i	−0.401217	−	0.452562i
$637$	1.25628	−	3.37961i	0.0497757	−	0.133905i
$638$			26.6097i			1.05349i
$639$	−12.9448	−	16.4991i	−0.512089	−	0.652694i
$640$	0.335367			0.0132565
$641$	−6.77888			−0.267750			−0.133875	−	0.990998i	$-0.542742\pi$
$641$	−6.77888			−0.267750			−0.133875	+	0.990998i	$0.542742\pi$
$642$	1.90405	−	31.6610i	0.0751467	−	1.24956i
$643$	−11.9887	−	11.9887i	−0.472790	−	0.472790i	0.430026	−	0.902816i	$-0.358504\pi$
$643$	−11.9887	−	11.9887i	−0.472790	−	0.472790i	−0.902816	+	0.430026i	$0.858504\pi$
$644$	1.05244	+	1.05244i	0.0414721	+	0.0414721i
$645$	−0.0961725	+	1.59918i	−0.00378679	+	0.0629678i
$646$	6.75181			0.265646
$647$	4.90621			0.192883			0.0964415	−	0.995339i	$-0.469254\pi$
$647$	4.90621			0.192883			0.0964415	+	0.995339i	$0.469254\pi$
$648$	−4.66679	−	7.69552i	−0.183329	−	0.302309i
$649$		−	4.01325i		−	0.157534i
$650$	−7.33822	−	16.0217i	−0.287829	−	0.628421i
$651$	11.7094	+	13.2079i	0.458927	+	0.517657i
$652$	2.26457	+	2.26457i	0.0886874	+	0.0886874i
$653$			16.9184i			0.662069i	0.943619	+	0.331035i	$0.107398\pi$
$653$			16.9184i			0.662069i	−0.943619	+	0.331035i	$0.892602\pi$
$654$	−10.9234	−	12.3212i	−0.427137	−	0.481799i
$655$	−3.46051	−	3.46051i	−0.135213	−	0.135213i
$656$	1.32329	−	1.32329i	0.0516659	−	0.0516659i
$657$	−10.4901	−	13.3703i	−0.409256	−	0.521627i
$658$	2.27264	−	2.27264i	0.0885968	−	0.0885968i
$659$			42.8877i			1.67067i	0.549744	+	0.835333i	$0.314725\pi$
$659$			42.8877i			1.67067i	−0.549744	+	0.835333i	$0.685275\pi$
$660$	−1.57050	+	1.39232i	−0.0611317	+	0.0541961i
$661$	23.1466	−	23.1466i	0.900299	−	0.900299i	−0.0951631	−	0.995462i	$-0.530337\pi$
$661$	23.1466	−	23.1466i	0.900299	−	0.900299i	0.995462	+	0.0951631i	$0.0303373\pi$
$662$	−33.8024			−1.31377
$663$	11.8700	+	30.6548i	0.460991	+	1.19053i
$664$	4.32280			0.167757
$665$	0.304175	−	0.304175i	0.0117954	−	0.0117954i
$666$	11.9341	+	1.44061i	0.462438	+	0.0558226i
$667$			10.9612i			0.424421i
$668$	−12.4482	+	12.4482i	−0.481636	+	0.481636i
$669$	−1.33297	+	22.1651i	−0.0515357	+	0.856951i
$670$	−3.24651	+	3.24651i	−0.125424	+	0.125424i
$671$	−22.3534	−	22.3534i	−0.862943	−	0.862943i
$672$	1.29606	−	1.14901i	0.0499965	−	0.0443242i
$673$			29.7951i			1.14852i	0.818674	+	0.574259i	$0.194710\pi$
$673$			29.7951i			1.14852i	−0.818674	+	0.574259i	$0.805290\pi$
$674$	13.5330	+	13.5330i	0.521272	+	0.521272i
$675$	14.4486	+	20.8857i	0.556129	+	0.803890i
$676$	8.49149	−	9.84351i	0.326596	−	0.378596i
$677$		−	21.9759i		−	0.844602i	−0.906456	−	0.422301i	$-0.861222\pi$
$677$		−	21.9759i		−	0.844602i	0.906456	−	0.422301i	$-0.138778\pi$
$678$	−1.65125	+	27.4575i	−0.0634160	+	1.05450i
$679$	6.87739			0.263930
$680$	1.76532			0.0676968
$681$	4.78970	+	0.288045i	0.183542	+	0.0110379i
$682$	26.0368	+	26.0368i	0.997000	+	0.997000i
$683$	5.21995	+	5.21995i	0.199736	+	0.199736i	0.799887	−	0.600151i	$-0.204893\pi$
$683$	5.21995	+	5.21995i	0.199736	+	0.199736i	−0.600151	+	0.799887i	$0.704893\pi$
$684$	2.37527	+	3.02745i	0.0908207	+	0.115758i
$685$	5.49463			0.209939
$686$	−1.00000			−0.0381802
$687$	−48.1454	−	2.89539i	−1.83686	−	0.110466i
$688$		−	2.75805i		−	0.105149i
$689$	−11.0629	+	29.7611i	−0.421464	+	1.13381i
$690$	−0.646932	+	0.573535i	−0.0246283	+	0.0218341i
$691$	−16.8889	−	16.8889i	−0.642485	−	0.642485i	0.308681	−	0.951166i	$-0.400112\pi$
$691$	−16.8889	−	16.8889i	−0.642485	−	0.642485i	−0.951166	+	0.308681i	$0.900112\pi$
$692$		−	12.8517i		−	0.488548i
$693$	−1.29906	+	10.7615i	−0.0493473	+	0.408797i
$694$	−15.7627	−	15.7627i	−0.598343	−	0.598343i
$695$	−2.84097	+	2.84097i	−0.107764	+	0.107764i
$696$	12.7328	+	0.765729i	0.482634	+	0.0290249i
$697$	6.96559	−	6.96559i	0.263841	−	0.263841i
$698$		−	16.3183i		−	0.617658i
$699$	9.28676	+	10.4752i	0.351258	+	0.396209i
$700$	−3.45600	+	3.45600i	−0.130625	+	0.130625i
$701$	−37.1491			−1.40310			−0.701550	−	0.712620i	$-0.747509\pi$
$701$	−37.1491			−1.40310			−0.701550	+	0.712620i	$0.747509\pi$
$702$	−9.56950	+	16.1067i	−0.361178	+	0.607907i
$703$	−5.13960			−0.193844
$704$	2.55493	−	2.55493i	0.0962926	−	0.0962926i
$705$	1.23849	+	1.39698i	0.0466442	+	0.0526134i
$706$			15.5376i			0.584765i
$707$	−13.1028	+	13.1028i	−0.492782	+	0.492782i
$708$	−1.92034	−	0.115487i	−0.0721709	−	0.00434025i
$709$	17.2343	−	17.2343i	0.647249	−	0.647249i	−0.305078	−	0.952327i	$-0.598683\pi$
$709$	17.2343	−	17.2343i	0.647249	−	0.647249i	0.952327	+	0.305078i	$0.0986826\pi$
$710$	1.65770	+	1.65770i	0.0622124	+	0.0622124i
$711$	3.05911	−	25.3419i	0.114726	−	0.950395i
$712$		−	2.29517i		−	0.0860152i
$713$	10.7253	+	10.7253i	0.401664	+	0.401664i
$714$	6.82223	−	6.04822i	0.255316	−	0.226349i
$715$	4.09525	+	1.52231i	0.153154	+	0.0569310i
$716$		−	13.7258i		−	0.512959i
$717$	41.8348	+	2.51588i	1.56235	+	0.0939573i
$718$	−17.5274			−0.654116
$719$	2.42778			0.0905411			0.0452705	−	0.998975i	$-0.485585\pi$
$719$	2.42778			0.0905411			0.0452705	+	0.998975i	$0.485585\pi$
$720$	0.621034	+	0.791553i	0.0231446	+	0.0294994i
$721$	−4.07345	−	4.07345i	−0.151703	−	0.151703i
$722$	12.2717	+	12.2717i	0.456704	+	0.456704i
$723$	4.02570	+	0.242100i	0.149718	+	0.00900379i
$724$	17.7979			0.661454
$725$	−35.9944			−1.33680
$726$	−0.213705	+	3.55354i	−0.00793132	+	0.131884i
$727$		−	2.06159i		−	0.0764603i	−0.999269	−	0.0382301i	$-0.987828\pi$
$727$		−	2.06159i		−	0.0764603i	0.999269	−	0.0382301i	$-0.0121720\pi$
$728$	−3.37961	−	1.25628i	−0.125257	−	0.0465609i
$729$	9.52144	−	25.2654i	0.352646	−	0.935757i
$730$	1.34335	+	1.34335i	0.0497195	+	0.0497195i
$731$		−	14.5179i		−	0.536964i
$732$	−11.3394	+	10.0529i	−0.419115	+	0.371565i
$733$	16.8266	+	16.8266i	0.621505	+	0.621505i	0.945916	−	0.324412i	$-0.105166\pi$
$733$	16.8266	+	16.8266i	0.621505	+	0.621505i	−0.324412	+	0.945916i	$0.605166\pi$
$734$	13.6975	−	13.6975i	0.505583	−	0.505583i
$735$	0.0348698	−	0.579825i	0.00128619	−	0.0213872i
$736$	1.05244	−	1.05244i	0.0387936	−	0.0387936i
$737$			49.4659i			1.82210i
$738$	5.57379	+	0.672833i	0.205174	+	0.0247673i
$739$	−29.5329	+	29.5329i	−1.08638	+	1.08638i	−0.0904869	+	0.995898i	$0.528842\pi$
$739$	−29.5329	+	29.5329i	−1.08638	+	1.08638i	−0.995898	+	0.0904869i	$0.971158\pi$
$740$	−1.34379			−0.0493987
$741$	3.23673	−	7.32727i	0.118904	−	0.269174i
$742$	8.80608			0.323281
$743$	−21.2462	+	21.2462i	−0.779446	+	0.779446i	−0.979737	−	0.200290i	$-0.935811\pi$
$743$	−21.2462	+	21.2462i	−0.779446	+	0.779446i	0.200290	+	0.979737i	$0.435811\pi$
$744$	13.2079	−	11.7094i	0.484224	−	0.429287i
$745$		−	1.03345i		−	0.0378628i
$746$	−18.8503	+	18.8503i	−0.690157	+	0.690157i
$747$	8.00499	+	10.2029i	0.292887	+	0.373306i
$748$	13.4487	−	13.4487i	0.491734	−	0.491734i
$749$	12.9489	+	12.9489i	0.473143	+	0.473143i
$750$	−3.81008	−	4.29766i	−0.139124	−	0.156928i
$751$			22.6437i			0.826281i	0.910667	+	0.413140i	$0.135568\pi$
$751$			22.6437i			0.826281i	−0.910667	+	0.413140i	$0.864432\pi$
$752$	−2.27264	−	2.27264i	−0.0828747	−	0.0828747i
$753$	−6.42864	−	7.25133i	−0.234273	−	0.264253i
$754$	−11.0572	−	24.1415i	−0.402681	−	0.879181i
$755$			4.43315i			0.161339i
$756$	5.11202	+	0.931280i	0.185922	+	0.0338703i
$757$	28.9363			1.05171			0.525853	−	0.850575i	$-0.323746\pi$
$757$	28.9363			1.05171			0.525853	+	0.850575i	$0.323746\pi$
$758$	10.1436			0.368433
$759$	−0.559162	+	9.29791i	−0.0202963	+	0.337493i
$760$	−0.304175	−	0.304175i	−0.0110336	−	0.0110336i
$761$	−34.0212	−	34.0212i	−1.23327	−	1.23327i	−0.962701	−	0.270567i	$-0.912789\pi$
$761$	−34.0212	−	34.0212i	−1.23327	−	1.23327i	−0.270567	−	0.962701i	$-0.587211\pi$
$762$	−0.871402	+	14.4899i	−0.0315675	+	0.524914i
$763$	9.50671			0.344166
$764$	−0.449102			−0.0162479
$765$	3.26902	+	4.16660i	0.118192	+	0.150644i
$766$		−	2.48835i		−	0.0899076i
$767$	1.66765	+	3.64100i	0.0602152	+	0.131469i
$768$	−1.14901	−	1.29606i	−0.0414615	−	0.0467675i
$769$	14.2161	+	14.2161i	0.512647	+	0.512647i	0.915337	−	0.402690i	$-0.131925\pi$
$769$	14.2161	+	14.2161i	0.512647	+	0.512647i	−0.402690	+	0.915337i	$0.631925\pi$
$770$		−	1.21175i		−	0.0436686i
$771$	10.7743	+	12.1531i	0.388026	+	0.437683i
$772$	5.53933	+	5.53933i	0.199365	+	0.199365i
$773$	29.6369	−	29.6369i	1.06596	−	1.06596i	0.0682992	−	0.997665i	$-0.478243\pi$
$773$	29.6369	−	29.6369i	1.06596	−	1.06596i	0.997665	−	0.0682992i	$-0.0217572\pi$
$774$	6.50970	−	5.10736i	0.233986	−	0.183580i
$775$	−35.2194	+	35.2194i	−1.26512	+	1.26512i
$776$		−	6.87739i		−	0.246884i
$777$	−5.19320	+	4.60401i	−0.186305	+	0.165168i
$778$	−16.5459	+	16.5459i	−0.593200	+	0.593200i
$779$	−2.40043			−0.0860043
$780$	0.846271	−	1.91578i	0.0303014	−	0.0685958i
$781$	25.2577			0.903793
$782$	5.53989	−	5.53989i	0.198106	−	0.198106i
$783$	21.7713	+	31.4706i	0.778041	+	1.12467i
$784$			1.00000i			0.0357143i
$785$	4.18188	−	4.18188i	0.149258	−	0.149258i
$786$	−1.51728	+	25.2297i	−0.0541194	+	0.899913i
$787$	37.0266	−	37.0266i	1.31986	−	1.31986i	0.405969	−	0.913887i	$-0.366934\pi$
$787$	37.0266	−	37.0266i	1.31986	−	1.31986i	0.913887	−	0.405969i	$-0.133066\pi$
$788$	15.8126	+	15.8126i	0.563302	+	0.563302i
$789$	−9.44534	+	8.37373i	−0.336263	+	0.298113i
$790$			2.85351i			0.101523i
$791$	−11.2297	−	11.2297i	−0.399283	−	0.399283i
$792$	10.7615	+	1.29906i	0.382394	+	0.0461602i
$793$	29.5686	+	10.9914i	1.05001	+	0.390315i
$794$			17.9636i			0.637506i
$795$	−0.307066	+	5.10599i	−0.0108905	+	0.181091i
$796$	−26.3160			−0.932747
$797$	16.8981			0.598562			0.299281	−	0.954165i	$-0.403253\pi$
$797$	16.8981			0.598562			0.299281	+	0.954165i	$0.403253\pi$
$798$	−2.21766	−	0.133367i	−0.0785042	−	0.00472113i
$799$	−11.9628	−	11.9628i	−0.423214	−	0.423214i
$800$	3.45600	+	3.45600i	0.122188	+	0.122188i
$801$	5.41720	−	4.25021i	0.191407	−	0.150174i
$802$	−6.55431			−0.231441
$803$	20.4681			0.722303
$804$	23.6695	+	1.42345i	0.834758	+	0.0502011i
$805$		−	0.499154i		−	0.0175929i
$806$	−34.4409	−	12.8025i	−1.21313	−	0.450950i
$807$	21.3802	−	18.9546i	0.752620	−	0.667232i
$808$	13.1028	+	13.1028i	0.460956	+	0.460956i
$809$			5.97793i			0.210173i	0.994463	+	0.105086i	$0.0335119\pi$
$809$			5.97793i			0.210173i	−0.994463	+	0.105086i	$0.966488\pi$
$810$	−0.718235	+	2.93160i	−0.0252362	+	0.103006i
$811$	−3.24299	−	3.24299i	−0.113877	−	0.113877i	0.647872	−	0.761749i	$-0.275659\pi$
$811$	−3.24299	−	3.24299i	−0.113877	−	0.113877i	−0.761749	+	0.647872i	$0.775659\pi$
$812$	−5.20752	+	5.20752i	−0.182748	+	0.182748i
$813$	6.28472	+	0.377954i	0.220415	+	0.0132554i
$814$	−10.2374	+	10.2374i	−0.358821	+	0.358821i
$815$		−	1.07404i		−	0.0376220i
$816$	−6.04822	−	6.82223i	−0.211730	−	0.238826i
$817$	−2.50152	+	2.50152i	−0.0875172	+	0.0875172i
$818$	−29.6464			−1.03656
$819$	−3.29322	−	10.3031i	−0.115075	−	0.360021i
$820$	−0.627612			−0.0219172
$821$	8.79510	−	8.79510i	0.306951	−	0.306951i	−0.536775	−	0.843726i	$-0.680357\pi$
$821$	8.79510	−	8.79510i	0.306951	−	0.306951i	0.843726	+	0.536775i	$0.180357\pi$
$822$	−18.8254	−	21.2345i	−0.656611	−	0.740639i
$823$		−	0.483844i		−	0.0168658i	−0.999964	−	0.00843288i	$-0.997316\pi$
$823$		−	0.483844i		−	0.0168658i	0.999964	−	0.00843288i	$-0.00268430\pi$
$824$	−4.07345	+	4.07345i	−0.141905	+	0.141905i
$825$	−30.5323	−	1.83617i	−1.06300	−	0.0639272i
$826$	0.785394	−	0.785394i	0.0273273	−	0.0273273i
$827$	−0.304974	−	0.304974i	−0.0106050	−	0.0106050i	0.701784	−	0.712389i	$-0.252387\pi$
$827$	−0.304974	−	0.304974i	−0.0106050	−	0.0106050i	−0.712389	+	0.701784i	$0.752387\pi$
$828$	4.43296	+	0.535119i	0.154056	+	0.0185967i
$829$			1.15353i			0.0400637i	0.999799	+	0.0200319i	$0.00637677\pi$
$829$			1.15353i			0.0400637i	−0.999799	+	0.0200319i	$0.993623\pi$
$830$	−1.02511	−	1.02511i	−0.0355821	−	0.0355821i
$831$	9.62705	−	8.53483i	0.333959	−	0.296070i
$832$	−1.25628	+	3.37961i	−0.0435538	+	0.117167i
$833$			5.26383i			0.182381i
$834$	20.7127	+	1.24563i	0.717223	+	0.0431327i
$835$	5.90395			0.204314
$836$	−4.63460			−0.160291
$837$	52.0955	+	9.49048i	1.80069	+	0.328039i
$838$	1.62656	+	1.62656i	0.0561886	+	0.0561886i
$839$	−34.5315	−	34.5315i	−1.19216	−	1.19216i	−0.976460	−	0.215701i	$-0.930796\pi$
$839$	−34.5315	−	34.5315i	−1.19216	−	1.19216i	−0.215701	−	0.976460i	$-0.569204\pi$
$840$	−0.579825	−	0.0348698i	−0.0200059	−	0.00120312i
$841$	−25.2364			−0.870222
$842$	7.45789			0.257016
$843$	1.38551	−	23.0386i	0.0477194	−	0.793492i
$844$			11.4416i			0.393835i
$845$	−4.34797	+	0.320617i	−0.149575	+	0.0110296i
$846$	1.15553	−	9.57251i	0.0397280	−	0.329110i
$847$	−1.45335	−	1.45335i	−0.0499376	−	0.0499376i
$848$		−	8.80608i		−	0.302402i
$849$	27.9790	−	24.8047i	0.960238	−	0.851295i
$850$	18.1918	+	18.1918i	0.623975	+	0.623975i
$851$	−4.21707	+	4.21707i	−0.144559	+	0.144559i
$852$	0.726825	−	12.0859i	0.0249006	−	0.414054i
$853$	33.2316	−	33.2316i	1.13783	−	1.13783i	0.148989	−	0.988839i	$-0.452398\pi$
$853$	33.2316	−	33.2316i	1.13783	−	1.13783i	0.988839	−	0.148989i	$-0.0476018\pi$
$854$		−	8.74912i		−	0.299389i
$855$	0.154659	−	1.28120i	0.00528922	−	0.0438162i
$856$	12.9489	−	12.9489i	0.442585	−	0.442585i
$857$	16.7687			0.572808			0.286404	−	0.958109i	$-0.407540\pi$
$857$	16.7687			0.572808			0.286404	+	0.958109i	$0.407540\pi$
$858$	−8.14782	−	21.0421i	−0.278162	−	0.718367i
$859$	−3.03581			−0.103581			−0.0517903	−	0.998658i	$-0.516493\pi$
$859$	−3.03581			−0.103581			−0.0517903	+	0.998658i	$0.516493\pi$
$860$	−0.654044	+	0.654044i	−0.0223027	+	0.0223027i
$861$	−2.42547	+	2.15029i	−0.0826597	+	0.0732816i
$862$		−	6.81380i		−	0.232079i
$863$	−13.1182	+	13.1182i	−0.446549	+	0.446549i	−0.894206	−	0.447656i	$-0.852259\pi$
$863$	−13.1182	+	13.1182i	−0.446549	+	0.446549i	0.447656	+	0.894206i	$0.352259\pi$
$864$	0.931280	−	5.11202i	0.0316828	−	0.173914i
$865$	−3.04765	+	3.04765i	−0.103623	+	0.103623i
$866$	3.40801	+	3.40801i	0.115809	+	0.115809i
$867$	−12.3036	−	13.8781i	−0.417852	−	0.471325i
$868$			10.1908i			0.345898i
$869$	21.7389	+	21.7389i	0.737443	+	0.737443i
$870$	−2.83786	−	3.20103i	−0.0962126	−	0.108525i
$871$	−20.5548	−	44.8777i	−0.696473	−	1.52062i
$872$		−	9.50671i		−	0.321938i
$873$	16.2324	−	12.7356i	0.549384	−	0.431034i
$874$	−1.90912			−0.0645768
$875$	3.31595			0.112100
$876$	0.588996	−	9.79399i	0.0199003	−	0.330908i
$877$	−11.1099	−	11.1099i	−0.375156	−	0.375156i	0.494195	−	0.869351i	$-0.335463\pi$
$877$	−11.1099	−	11.1099i	−0.375156	−	0.375156i	−0.869351	+	0.494195i	$0.835463\pi$
$878$	9.20248	+	9.20248i	0.310569	+	0.310569i
$879$	0.580483	−	9.65243i	0.0195792	−	0.325569i
$880$	−1.21175			−0.0408482
$881$	−42.5418			−1.43327			−0.716634	−	0.697449i	$-0.754318\pi$
$881$	−42.5418			−1.43327			−0.716634	+	0.697449i	$0.754318\pi$
$882$	−2.36026	+	1.85180i	−0.0794740	+	0.0623535i
$883$			27.0567i			0.910530i	0.890356	+	0.455265i	$0.150455\pi$
$883$			27.0567i			0.910530i	−0.890356	+	0.455265i	$0.849545\pi$
$884$	−6.61287	+	17.7897i	−0.222415	+	0.598332i
$885$	0.428004	+	0.482777i	0.0143872	+	0.0162284i
$886$	16.3953	+	16.3953i	0.550810	+	0.550810i
$887$			5.81160i			0.195134i	0.995229	+	0.0975672i	$0.0311061\pi$
$887$			5.81160i			0.195134i	−0.995229	+	0.0975672i	$0.968894\pi$
$888$	4.60401	+	5.19320i	0.154501	+	0.174273i
$889$	−5.92617	−	5.92617i	−0.198757	−	0.198757i
$890$	−0.544278	+	0.544278i	−0.0182442	+	0.0182442i
$891$	16.8621	+	27.8056i	0.564903	+	0.931523i
$892$	−9.06520	+	9.06520i	−0.303525	+	0.303525i
$893$			4.12253i			0.137955i
$894$	−3.99388	+	3.54076i	−0.133575	+	0.118421i
$895$	−3.25495	+	3.25495i	−0.108801	+	0.108801i
$896$	1.00000			0.0334077
$897$	−3.35631	−	8.66782i	−0.112064	−	0.289410i
$898$	10.3432			0.345159
$899$	−53.0687	+	53.0687i	−1.76994	+	1.76994i
$900$	−1.75722	+	14.5569i	−0.0585739	+	0.485230i
$901$		−	46.3537i		−	1.54427i
$902$	−4.78134	+	4.78134i	−0.159201	+	0.159201i
$903$	−0.286768	+	4.76846i	−0.00954304	+	0.158684i
$904$	−11.2297	+	11.2297i	−0.373495	+	0.373495i
$905$	−4.22060	−	4.22060i	−0.140297	−	0.140297i
$906$	17.1323	−	15.1886i	0.569184	−	0.504608i
$907$		−	12.1476i		−	0.403356i	−0.979452	−	0.201678i	$-0.935361\pi$
$907$		−	12.1476i		−	0.403356i	0.979452	−	0.201678i	$-0.0646394\pi$
$908$	1.95892	+	1.95892i	0.0650090	+	0.0650090i
$909$	−6.66217	+	55.1899i	−0.220970	+	1.83053i
$910$	0.503526	+	1.09936i	0.0166917	+	0.0364433i
$911$			5.85676i			0.194043i	0.995282	+	0.0970216i	$0.0309316\pi$
$911$			5.85676i			0.194043i	−0.995282	+	0.0970216i	$0.969068\pi$
$912$	−0.133367	+	2.21766i	−0.00441621	+	0.0734340i
$913$	−15.6192			−0.516921
$914$	−10.7287			−0.354873
$915$	5.07296	+	0.305080i	0.167707	+	0.0100856i
$916$	−19.6908	−	19.6908i	−0.650601	−	0.650601i
$917$	−10.3186	−	10.3186i	−0.340750	−	0.340750i
$918$	4.90210	−	26.9088i	0.161793	−	0.888123i
$919$	30.9858			1.02213			0.511064	−	0.859543i	$-0.329252\pi$
$919$	30.9858			1.02213			0.511064	+	0.859543i	$0.329252\pi$
$920$	−0.499154			−0.0164566
$921$	28.8808	+	1.73685i	0.951654	+	0.0572310i
$922$			13.3718i			0.440375i
$923$	−22.9149	+	10.4955i	−0.754255	+	0.345463i
$924$	−4.68294	+	4.15164i	−0.154057	+	0.136579i
$925$	−13.8479	−	13.8479i	−0.455318	−	0.455318i
$926$			34.1779i			1.12315i
$927$	−17.1576	−	2.07116i	−0.563531	−	0.0680258i
$928$	5.20752	+	5.20752i	0.170945	+	0.170945i
$929$	4.17792	−	4.17792i	0.137073	−	0.137073i	−0.635241	−	0.772314i	$-0.719099\pi$
$929$	4.17792	−	4.17792i	0.137073	−	0.137073i	0.772314	+	0.635241i	$0.219099\pi$
$930$	−5.90888	−	0.355351i	−0.193760	−	0.0116524i
$931$	0.906991	−	0.906991i	0.0297254	−	0.0297254i
$932$			8.08237i			0.264747i
$933$	−23.9456	−	27.0100i	−0.783944	−	0.884268i
$934$	−16.9539	+	16.9539i	−0.554750	+	0.554750i
$935$	−6.37847			−0.208598
$936$	−10.3031	+	3.29322i	−0.336769	+	0.107642i
$937$	−7.86277			−0.256865			−0.128433	−	0.991718i	$-0.540995\pi$
$937$	−7.86277			−0.256865			−0.128433	+	0.991718i	$0.540995\pi$
$938$	−9.68048	+	9.68048i	−0.316079	+	0.316079i
$939$	−11.1190	−	12.5419i	−0.362854	−	0.409290i
$940$			1.07787i			0.0351562i
$941$	−38.2300	+	38.2300i	−1.24626	+	1.24626i	−0.288904	+	0.957358i	$0.593291\pi$
$941$	−38.2300	+	38.2300i	−1.24626	+	1.24626i	−0.957358	+	0.288904i	$0.906709\pi$
$942$	−30.4890	−	1.83356i	−0.993385	−	0.0597407i
$943$	−1.96956	+	1.96956i	−0.0641378	+	0.0641378i
$944$	−0.785394	−	0.785394i	−0.0255624	−	0.0255624i
$945$	−0.991421	−	1.43311i	−0.0322509	−	0.0466190i
$946$			9.96542i			0.324004i
$947$	37.9375	+	37.9375i	1.23280	+	1.23280i	0.962883	+	0.269918i	$0.0869968\pi$
$947$	37.9375	+	37.9375i	1.23280	+	1.23280i	0.269918	+	0.962883i	$0.413003\pi$
$948$	11.0277	−	9.77652i	0.358162	−	0.317527i
$949$	−18.5695	+	8.50520i	−0.602793	+	0.276091i
$950$		−	6.26913i		−	0.203397i
$951$	−35.4030	−	2.12908i	−1.14802	−	0.0690402i
$952$	5.26383			0.170602
$953$	3.17735			0.102924			0.0514622	−	0.998675i	$-0.483612\pi$
$953$	3.17735			0.102924			0.0514622	+	0.998675i	$0.483612\pi$
$954$	20.7846	−	16.3071i	0.672927	−	0.527963i
$955$	0.106500	+	0.106500i	0.00344627	+	0.00344627i
$956$	17.1098	+	17.1098i	0.553371	+	0.553371i
$957$	−46.0062	−	2.76674i	−1.48717	−	0.0894362i
$958$	18.8099			0.607720
$959$	16.3839			0.529065
$960$	−0.0348698	+	0.579825i	−0.00112542	+	0.0187138i
$961$			72.8524i			2.35008i
$962$	5.03383	−	13.5418i	0.162297	−	0.436606i
$963$	54.5416	+	6.58391i	1.75758	+	0.212164i
$964$	1.64646	+	1.64646i	0.0530288	+	0.0530288i
$965$		−	2.62720i		−	0.0845725i
$966$	−1.92903	+	1.71017i	−0.0620655	+	0.0550239i
$967$	−9.01267	−	9.01267i	−0.289828	−	0.289828i	0.547184	−	0.837012i	$-0.315700\pi$
$967$	−9.01267	−	9.01267i	−0.289828	−	0.289828i	−0.837012	+	0.547184i	$0.815700\pi$
$968$	−1.45335	+	1.45335i	−0.0467124	+	0.0467124i
$969$	−0.702020	+	11.6734i	−0.0225521	+	0.375003i
$970$	−1.63091	+	1.63091i	−0.0523653	+	0.0523653i
$971$		−	50.8888i		−	1.63310i	−0.577276	−	0.816549i	$-0.695884\pi$
$971$		−	50.8888i		−	1.63310i	0.577276	−	0.816549i	$-0.304116\pi$
$972$	13.7902	−	7.26840i	0.442322	−	0.233134i
$973$	−8.47121	+	8.47121i	−0.271575	+	0.271575i
$974$	17.0717			0.547013
$975$	28.4633	−	11.0214i	0.911555	−	0.352967i
$976$	−8.74912			−0.280052
$977$	−22.6267	+	22.6267i	−0.723891	+	0.723891i	−0.969395	−	0.245505i	$-0.921046\pi$
$977$	−22.6267	+	22.6267i	−0.723891	+	0.723891i	0.245505	+	0.969395i	$0.421046\pi$
$978$	−4.15074	+	3.67982i	−0.132726	+	0.117668i
$979$			8.29295i			0.265044i
$980$	0.237140	−	0.237140i	0.00757517	−	0.00757517i
$981$	22.4383	−	17.6046i	0.716400	−	0.562071i
$982$	−20.5055	+	20.5055i	−0.654356	+	0.654356i
$983$	−12.3141	−	12.3141i	−0.392758	−	0.392758i	0.482911	−	0.875669i	$-0.339579\pi$
$983$	−12.3141	−	12.3141i	−0.392758	−	0.392758i	−0.875669	+	0.482911i	$0.839579\pi$
$984$	2.15029	+	2.42547i	0.0685486	+	0.0773210i
$985$		−	7.49963i		−	0.238958i
$986$	27.4115	+	27.4115i	0.872960	+	0.872960i
$987$	3.69293	+	4.16553i	0.117547	+	0.132590i
$988$	4.20471	−	1.92584i	0.133770	−	0.0612690i
$989$			4.10502i			0.130532i
$990$	−2.24393	−	2.86005i	−0.0713168	−	0.0908984i
$991$	14.7119			0.467338			0.233669	−	0.972316i	$-0.424927\pi$
$991$	14.7119			0.467338			0.233669	+	0.972316i	$0.424927\pi$
$992$	10.1908			0.323558
$993$	3.51460	−	58.4418i	0.111533	−	1.85460i
$994$	4.94294	+	4.94294i	0.156781	+	0.156781i
$995$	6.24059	+	6.24059i	0.197840	+	0.197840i
$996$	−0.449464	+	7.47381i	−0.0142418	+	0.236817i
$997$	−17.6061			−0.557591			−0.278795	−	0.960351i	$-0.589935\pi$
$997$	−17.6061			−0.557591			−0.278795	+	0.960351i	$0.589935\pi$
$998$	23.3290			0.738468
$999$	−3.73157	+	20.4835i	−0.118062	+	0.648068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.d.281.2	yes	20
3.2	odd	2		546.2.p.c.281.7	yes	20
13.5	odd	4		546.2.p.c.239.7	✓	20
39.5	even	4	inner	546.2.p.d.239.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.7	✓	20	13.5	odd	4
546.2.p.c.281.7	yes	20	3.2	odd	2
546.2.p.d.239.2	yes	20	39.5	even	4	inner
546.2.p.d.281.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} -1.00000i q^{4} +(-0.237140 + 0.237140i) q^{5} +(1.72893 + 0.103975i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} -1.00000i q^{4} +(-0.237140 + 0.237140i) q^{5} +(1.72893 + 0.103975i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} -0.335367i q^{10} +(-2.55493 - 2.55493i) q^{11} +(-1.29606 + 1.14901i) q^{12} +(3.37961 + 1.25628i) q^{13} -1.00000i q^{14} +(0.579825 + 0.0348698i) q^{15} -1.00000 q^{16} -5.26383 q^{17} +(-1.85180 - 2.36026i) q^{18} +(0.906991 + 0.906991i) q^{19} +(0.237140 + 0.237140i) q^{20} +(1.72893 + 0.103975i) q^{21} +3.61322 q^{22} +1.48838 q^{23} +(0.103975 - 1.72893i) q^{24} +4.88753i q^{25} +(-3.27807 + 1.50142i) q^{26} +(4.27326 - 2.95623i) q^{27} +(0.707107 + 0.707107i) q^{28} +7.36454i q^{29} +(-0.434655 + 0.385342i) q^{30} +(7.20598 + 7.20598i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.375685 + 6.24699i) q^{33} +(3.72209 - 3.72209i) q^{34} -0.335367i q^{35} +(2.97838 + 0.359531i) q^{36} +(-2.83332 + 2.83332i) q^{37} -1.28268 q^{38} +(-2.25500 - 5.82365i) q^{39} -0.335367 q^{40} +(-1.32329 + 1.32329i) q^{41} +(-1.29606 + 1.14901i) q^{42} +2.75805i q^{43} +(-2.55493 + 2.55493i) q^{44} +(-0.621034 - 0.791553i) q^{45} +(-1.05244 + 1.05244i) q^{46} +(2.27264 + 2.27264i) q^{47} +(1.14901 + 1.29606i) q^{48} -1.00000i q^{49} +(-3.45600 - 3.45600i) q^{50} +(6.04822 + 6.82223i) q^{51} +(1.25628 - 3.37961i) q^{52} +8.80608i q^{53} +(-0.931280 + 5.11202i) q^{54} +1.21175 q^{55} -1.00000 q^{56} +(0.133367 - 2.21766i) q^{57} +(-5.20752 - 5.20752i) q^{58} +(0.785394 + 0.785394i) q^{59} +(0.0348698 - 0.579825i) q^{60} +8.74912 q^{61} -10.1908 q^{62} +(-1.85180 - 2.36026i) q^{63} +1.00000i q^{64} +(-1.09936 + 0.503526i) q^{65} +(-4.15164 - 4.68294i) q^{66} +(-9.68048 - 9.68048i) q^{67} +5.26383i q^{68} +(-1.71017 - 1.92903i) q^{69} +(0.237140 + 0.237140i) q^{70} +(-4.94294 + 4.94294i) q^{71} +(-2.36026 + 1.85180i) q^{72} +(-4.00560 + 4.00560i) q^{73} -4.00692i q^{74} +(6.33452 - 5.61584i) q^{75} +(0.906991 - 0.906991i) q^{76} +3.61322 q^{77} +(5.71247 + 2.52342i) q^{78} -8.50862 q^{79} +(0.237140 - 0.237140i) q^{80} +(-8.74148 - 2.14164i) q^{81} -1.87142i q^{82} +(3.05668 - 3.05668i) q^{83} +(0.103975 - 1.72893i) q^{84} +(1.24827 - 1.24827i) q^{85} +(-1.95023 - 1.95023i) q^{86} +(9.54487 - 8.46196i) q^{87} -3.61322i q^{88} +(-1.62293 - 1.62293i) q^{89} +(0.998850 + 0.120575i) q^{90} +(-3.27807 + 1.50142i) q^{91} -1.48838i q^{92} +(1.05959 - 17.6191i) q^{93} -3.21400 q^{94} -0.430168 q^{95} +(-1.72893 - 0.103975i) q^{96} +(-4.86305 - 4.86305i) q^{97} +(0.707107 + 0.707107i) q^{98} +(8.52813 - 6.69097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 20 * q + 4 * q^5 + 4 * q^6 - 8 * q^9 + 16 * q^11 + 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 - 12 * q^17 - 16 * q^18 + 12 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 + 4 * q^23 - 4 * q^24 + 24 * q^27 - 12 * q^30 - 8 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * q^54 + 28 * q^55 - 20 * q^56 + 36 * q^57 - 4 * q^58 - 20 * q^59 - 4 * q^60 - 4 * q^61 - 48 * q^62 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * q^78 - 64 * q^79 - 4 * q^80 + 32 * q^81 + 24 * q^83 - 4 * q^84 + 24 * q^85 - 4 * q^86 + 4 * q^87 + 4 * q^89 + 8 * q^90 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more