LMFDB - Embedded newform 528.2.t.b.133.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(133,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("528.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.t (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:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			133.19
Character	$\chi$	$=$	528.133
Dual form			528.2.t.b.397.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40742 - 0.138462i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.96166 - 0.389747i) q^{4} +(0.582740 + 0.582740i) q^{5} +(0.897288 - 1.09310i) q^{6} +4.89753i q^{7} +(2.70691 - 0.820152i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(1.40742 - 0.138462i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.96166 - 0.389747i) q^{4} +(0.582740 + 0.582740i) q^{5} +(0.897288 - 1.09310i) q^{6} +4.89753i q^{7} +(2.70691 - 0.820152i) q^{8} -1.00000i q^{9} +(0.900847 + 0.739473i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.11151 - 1.66269i) q^{12} +(1.72543 - 1.72543i) q^{13} +(0.678119 + 6.89287i) q^{14} +0.824119 q^{15} +(3.69619 - 1.52910i) q^{16} -2.20698 q^{17} +(-0.138462 - 1.40742i) q^{18} +(-4.64217 + 4.64217i) q^{19} +(1.37026 + 0.916015i) q^{20} +(3.46307 + 3.46307i) q^{21} +(-1.09310 - 0.897288i) q^{22} -8.23649i q^{23} +(1.33414 - 2.49401i) q^{24} -4.32083i q^{25} +(2.18950 - 2.66731i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.90880 + 9.60726i) q^{28} +(-4.49302 + 4.49302i) q^{29} +(1.15988 - 0.114109i) q^{30} +3.82276 q^{31} +(4.99037 - 2.66387i) q^{32} -1.00000 q^{33} +(-3.10614 + 0.305582i) q^{34} +(-2.85399 + 2.85399i) q^{35} +(-0.389747 - 1.96166i) q^{36} +(-4.65242 - 4.65242i) q^{37} +(-5.89072 + 7.17625i) q^{38} -2.44013i q^{39} +(2.05536 + 1.09949i) q^{40} -10.2041i q^{41} +(5.35350 + 4.39449i) q^{42} +(-1.22055 - 1.22055i) q^{43} +(-1.66269 - 1.11151i) q^{44} +(0.582740 - 0.582740i) q^{45} +(-1.14044 - 11.5922i) q^{46} +9.80364 q^{47} +(1.53237 - 3.69484i) q^{48} -16.9858 q^{49} +(-0.598269 - 6.08122i) q^{50} +(-1.56057 + 1.56057i) q^{51} +(2.71222 - 4.05719i) q^{52} +(-1.14015 - 1.14015i) q^{53} +(-1.09310 - 0.897288i) q^{54} -0.824119i q^{55} +(4.01671 + 13.2572i) q^{56} +6.56503i q^{57} +(-5.70145 + 6.94567i) q^{58} +(2.17677 + 2.17677i) q^{59} +(1.61664 - 0.321198i) q^{60} +(2.35153 - 2.35153i) q^{61} +(5.38023 - 0.529306i) q^{62} +4.89753 q^{63} +(6.65470 - 4.44015i) q^{64} +2.01096 q^{65} +(-1.40742 + 0.138462i) q^{66} +(-8.69638 + 8.69638i) q^{67} +(-4.32933 + 0.860163i) q^{68} +(-5.82408 - 5.82408i) q^{69} +(-3.62159 + 4.41192i) q^{70} +9.44670i q^{71} +(-0.820152 - 2.70691i) q^{72} +14.2278i q^{73} +(-7.19209 - 5.90373i) q^{74} +(-3.05529 - 3.05529i) q^{75} +(-7.29708 + 10.9156i) q^{76} +(3.46307 - 3.46307i) q^{77} +(-0.337864 - 3.43429i) q^{78} -1.80715 q^{79} +(3.04499 + 1.26285i) q^{80} -1.00000 q^{81} +(-1.41288 - 14.3615i) q^{82} +(-3.24879 + 3.24879i) q^{83} +(8.14309 + 5.44364i) q^{84} +(-1.28609 - 1.28609i) q^{85} +(-1.88682 - 1.54882i) q^{86} +6.35409i q^{87} +(-2.49401 - 1.33414i) q^{88} +5.30085i q^{89} +(0.739473 - 0.900847i) q^{90} +(8.45035 + 8.45035i) q^{91} +(-3.21015 - 16.1572i) q^{92} +(2.70310 - 2.70310i) q^{93} +(13.7978 - 1.35743i) q^{94} -5.41036 q^{95} +(1.64509 - 5.41236i) q^{96} +7.23833 q^{97} +(-23.9061 + 2.35188i) q^{98} +(-0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{8}+O(q^{10}) $ 40 * q + 12 * q^8	$ 40 q + 12 q^{8} + 8 q^{10} + 16 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{24} - 20 q^{28} + 20 q^{30} + 8 q^{31} + 40 q^{32} - 40 q^{33} + 20 q^{34} - 24 q^{35} + 4 q^{36} - 60 q^{38} - 56 q^{40} + 20 q^{42} + 8 q^{44} + 76 q^{46} - 64 q^{47} + 32 q^{48} - 40 q^{49} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{54} - 20 q^{56} + 12 q^{58} - 16 q^{59} - 12 q^{60} - 64 q^{61} + 68 q^{62} + 24 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{67} - 4 q^{68} - 16 q^{69} - 116 q^{70} - 12 q^{76} + 28 q^{78} - 72 q^{79} + 40 q^{80} - 40 q^{81} - 24 q^{82} + 16 q^{85} - 64 q^{86} - 12 q^{90} + 16 q^{91} + 20 q^{92} + 32 q^{93} + 104 q^{94} + 128 q^{95} - 20 q^{96} - 32 q^{97} + 36 q^{98}+O(q^{100}) $ 40 * q + 12 * q^8 + 8 * q^10 + 16 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^24 - 20 * q^28 + 20 * q^30 + 8 * q^31 + 40 * q^32 - 40 * q^33 + 20 * q^34 - 24 * q^35 + 4 * q^36 - 60 * q^38 - 56 * q^40 + 20 * q^42 + 8 * q^44 + 76 * q^46 - 64 * q^47 + 32 * q^48 - 40 * q^49 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^54 - 20 * q^56 + 12 * q^58 - 16 * q^59 - 12 * q^60 - 64 * q^61 + 68 * q^62 + 24 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^67 - 4 * q^68 - 16 * q^69 - 116 * q^70 - 12 * q^76 + 28 * q^78 - 72 * q^79 + 40 * q^80 - 40 * q^81 - 24 * q^82 + 16 * q^85 - 64 * q^86 - 12 * q^90 + 16 * q^91 + 20 * q^92 + 32 * q^93 + 104 * q^94 + 128 * q^95 - 20 * q^96 - 32 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.40742	−	0.138462i	0.995196	−	0.0979072i
$2$	1.40742	−	0.138462i	0.995196	−	0.0979072i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.96166	−	0.389747i	0.980828	−	0.194874i
$5$	0.582740	+	0.582740i	0.260609	+	0.260609i	0.825302	−	0.564692i	$-0.191005\pi$
$5$	0.582740	+	0.582740i	0.260609	+	0.260609i	−0.564692	+	0.825302i	$0.691005\pi$
$6$	0.897288	−	1.09310i	0.366316	−	0.446257i
$7$			4.89753i			1.85109i	0.378637	+	0.925545i	$0.376393\pi$
$7$			4.89753i			1.85109i	−0.378637	+	0.925545i	$0.623607\pi$
$8$	2.70691	−	0.820152i	0.957037	−	0.289967i
$9$		−	1.00000i		−	0.333333i
$10$	0.900847	+	0.739473i	0.284873	+	0.233842i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	1.11151	−	1.66269i	0.320865	−	0.479978i
$13$	1.72543	−	1.72543i	0.478549	−	0.478549i	−0.426119	−	0.904667i	$-0.640119\pi$
$13$	1.72543	−	1.72543i	0.478549	−	0.478549i	0.904667	+	0.426119i	$0.140119\pi$
$14$	0.678119	+	6.89287i	0.181235	+	1.84220i
$15$	0.824119			0.212787
$16$	3.69619	−	1.52910i	0.924049	−	0.382275i
$17$	−2.20698			−0.535271			−0.267635	−	0.963520i	$-0.586242\pi$
$17$	−2.20698			−0.535271			−0.267635	+	0.963520i	$0.586242\pi$
$18$	−0.138462	−	1.40742i	−0.0326357	−	0.331732i
$19$	−4.64217	+	4.64217i	−1.06499	+	1.06499i	−0.0672519	+	0.997736i	$0.521423\pi$
$19$	−4.64217	+	4.64217i	−1.06499	+	1.06499i	−0.997736	+	0.0672519i	$0.978577\pi$
$20$	1.37026	+	0.916015i	0.306399	+	0.204827i
$21$	3.46307	+	3.46307i	0.755705	+	0.755705i
$22$	−1.09310	−	0.897288i	−0.233050	−	0.191303i
$23$		−	8.23649i		−	1.71743i	−0.512456	−	0.858714i	$-0.671264\pi$
$23$		−	8.23649i		−	1.71743i	0.512456	−	0.858714i	$-0.328736\pi$
$24$	1.33414	−	2.49401i	0.272330	−	0.509087i
$25$		−	4.32083i		−	0.864166i
$26$	2.18950	−	2.66731i	0.429396	−	0.523103i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.90880	+	9.60726i	0.360729	+	1.81560i
$29$	−4.49302	+	4.49302i	−0.834333	+	0.834333i	−0.988106	−	0.153773i	$-0.950858\pi$
$29$	−4.49302	+	4.49302i	−0.834333	+	0.834333i	0.153773	+	0.988106i	$0.450858\pi$
$30$	1.15988	−	0.114109i	0.211764	−	0.0208333i
$31$	3.82276			0.686588			0.343294	−	0.939228i	$-0.388457\pi$
$31$	3.82276			0.686588			0.343294	+	0.939228i	$0.388457\pi$
$32$	4.99037	−	2.66387i	0.882182	−	0.470909i
$33$	−1.00000			−0.174078
$34$	−3.10614	+	0.305582i	−0.532699	+	0.0524068i
$35$	−2.85399	+	2.85399i	−0.482412	+	0.482412i
$36$	−0.389747	−	1.96166i	−0.0649579	−	0.326943i
$37$	−4.65242	−	4.65242i	−0.764853	−	0.764853i	0.212342	−	0.977195i	$-0.431891\pi$
$37$	−4.65242	−	4.65242i	−0.764853	−	0.764853i	−0.977195	+	0.212342i	$0.931891\pi$
$38$	−5.89072	+	7.17625i	−0.955601	+	1.16414i
$39$		−	2.44013i		−	0.390733i
$40$	2.05536	+	1.09949i	0.324981	+	0.173844i
$41$		−	10.2041i		−	1.59361i	−0.604234	−	0.796807i	$-0.706521\pi$
$41$		−	10.2041i		−	1.59361i	0.604234	−	0.796807i	$-0.293479\pi$
$42$	5.35350	+	4.39449i	0.826063	+	0.678085i
$43$	−1.22055	−	1.22055i	−0.186131	−	0.186131i	0.607890	−	0.794021i	$-0.292016\pi$
$43$	−1.22055	−	1.22055i	−0.186131	−	0.186131i	−0.794021	+	0.607890i	$0.792016\pi$
$44$	−1.66269	−	1.11151i	−0.250660	−	0.167566i
$45$	0.582740	−	0.582740i	0.0868698	−	0.0868698i
$46$	−1.14044	−	11.5922i	−0.168148	−	1.70918i
$47$	9.80364			1.43001			0.715004	−	0.699120i	$-0.246425\pi$
$47$	9.80364			1.43001			0.715004	+	0.699120i	$0.246425\pi$
$48$	1.53237	−	3.69484i	0.221178	−	0.533304i
$49$	−16.9858			−2.42654
$50$	−0.598269	−	6.08122i	−0.0846080	−	0.860014i
$51$	−1.56057	+	1.56057i	−0.218523	+	0.218523i
$52$	2.71222	−	4.05719i	0.376118	−	0.562631i
$53$	−1.14015	−	1.14015i	−0.156611	−	0.156611i	0.624452	−	0.781063i	$-0.285322\pi$
$53$	−1.14015	−	1.14015i	−0.156611	−	0.156611i	−0.781063	+	0.624452i	$0.785322\pi$
$54$	−1.09310	−	0.897288i	−0.148752	−	0.122105i
$55$		−	0.824119i		−	0.111124i
$56$	4.01671	+	13.2572i	0.536756	+	1.77156i
$57$			6.56503i			0.869559i
$58$	−5.70145	+	6.94567i	−0.748637	+	0.912012i
$59$	2.17677	+	2.17677i	0.283392	+	0.283392i	0.834460	−	0.551068i	$-0.185780\pi$
$59$	2.17677	+	2.17677i	0.283392	+	0.283392i	−0.551068	+	0.834460i	$0.685780\pi$
$60$	1.61664	−	0.321198i	0.208707	−	0.0414665i
$61$	2.35153	−	2.35153i	0.301082	−	0.301082i	−0.540355	−	0.841437i	$-0.681710\pi$
$61$	2.35153	−	2.35153i	0.301082	−	0.301082i	0.841437	+	0.540355i	$0.181710\pi$
$62$	5.38023	−	0.529306i	0.683289	−	0.0672219i
$63$	4.89753			0.617030
$64$	6.65470	−	4.44015i	0.831838	−	0.555019i
$65$	2.01096			0.249429
$66$	−1.40742	+	0.138462i	−0.173241	+	0.0170435i
$67$	−8.69638	+	8.69638i	−1.06243	+	1.06243i	−0.0645155	+	0.997917i	$0.520550\pi$
$67$	−8.69638	+	8.69638i	−1.06243	+	1.06243i	−0.997917	+	0.0645155i	$0.979450\pi$
$68$	−4.32933	+	0.860163i	−0.525009	+	0.104310i
$69$	−5.82408	−	5.82408i	−0.701137	−	0.701137i
$70$	−3.62159	+	4.41192i	−0.432862	+	0.527325i
$71$			9.44670i			1.12112i	0.828115	+	0.560559i	$0.189414\pi$
$71$			9.44670i			1.12112i	−0.828115	+	0.560559i	$0.810586\pi$
$72$	−0.820152	−	2.70691i	−0.0966558	−	0.319012i
$73$			14.2278i			1.66524i	0.553843	+	0.832621i	$0.313161\pi$
$73$			14.2278i			1.66524i	−0.553843	+	0.832621i	$0.686839\pi$
$74$	−7.19209	−	5.90373i	−0.836063	−	0.686294i
$75$	−3.05529	−	3.05529i	−0.352794	−	0.352794i
$76$	−7.29708	+	10.9156i	−0.837032	+	1.25211i
$77$	3.46307	−	3.46307i	0.394654	−	0.394654i
$78$	−0.337864	−	3.43429i	−0.0382556	−	0.388856i
$79$	−1.80715			−0.203320			−0.101660	−	0.994819i	$-0.532415\pi$
$79$	−1.80715			−0.203320			−0.101660	+	0.994819i	$0.532415\pi$
$80$	3.04499	+	1.26285i	0.340440	+	0.141191i
$81$	−1.00000			−0.111111
$82$	−1.41288	−	14.3615i	−0.156026	−	1.58596i
$83$	−3.24879	+	3.24879i	−0.356601	+	0.356601i	−0.862558	−	0.505958i	$-0.831139\pi$
$83$	−3.24879	+	3.24879i	−0.356601	+	0.356601i	0.505958	+	0.862558i	$0.331139\pi$
$84$	8.14309	+	5.44364i	0.888483	+	0.593950i
$85$	−1.28609	−	1.28609i	−0.139497	−	0.139497i
$86$	−1.88682	−	1.54882i	−0.203461	−	0.167014i
$87$			6.35409i			0.681230i
$88$	−2.49401	−	1.33414i	−0.265862	−	0.142220i
$89$			5.30085i			0.561889i	0.959724	+	0.280945i	$0.0906477\pi$
$89$			5.30085i			0.561889i	−0.959724	+	0.280945i	$0.909352\pi$
$90$	0.739473	−	0.900847i	0.0779473	−	0.0949576i
$91$	8.45035	+	8.45035i	0.885837	+	0.885837i
$92$	−3.21015	−	16.1572i	−0.334681	−	1.68450i
$93$	2.70310	−	2.70310i	0.280298	−	0.280298i
$94$	13.7978	−	1.35743i	1.42314	−	0.140008i
$95$	−5.41036			−0.555092
$96$	1.64509	−	5.41236i	0.167901	−	0.552397i
$97$	7.23833			0.734942			0.367471	−	0.930035i	$-0.380224\pi$
$97$	7.23833			0.734942			0.367471	+	0.930035i	$0.380224\pi$
$98$	−23.9061	+	2.35188i	−2.41488	+	0.237575i
$99$	−0.707107	+	0.707107i	−0.0710669	+	0.0710669i
$100$	−1.68403	−	8.47598i	−0.168403	−	0.847598i
$101$	−7.36735	−	7.36735i	−0.733078	−	0.733078i	0.238150	−	0.971228i	$-0.423459\pi$
$101$	−7.36735	−	7.36735i	−0.733078	−	0.733078i	−0.971228	+	0.238150i	$0.923459\pi$
$102$	−1.98030	+	2.41245i	−0.196078	+	0.238868i
$103$			7.81962i			0.770490i	0.922814	+	0.385245i	$0.125883\pi$
$103$			7.81962i			0.770490i	−0.922814	+	0.385245i	$0.874117\pi$
$104$	3.25547	−	6.08570i	0.319225	−	0.596752i
$105$			4.03614i			0.393887i
$106$	−1.76253	−	1.44680i	−0.171192	−	0.140525i
$107$	1.94604	+	1.94604i	0.188131	+	0.188131i	0.794887	−	0.606757i	$-0.207530\pi$
$107$	1.94604	+	1.94604i	0.188131	+	0.188131i	−0.606757	+	0.794887i	$0.707530\pi$
$108$	−1.66269	−	1.11151i	−0.159993	−	0.106955i
$109$	−0.638617	+	0.638617i	−0.0611684	+	0.0611684i	−0.737029	−	0.675861i	$-0.763772\pi$
$109$	−0.638617	+	0.638617i	−0.0611684	+	0.0611684i	0.675861	+	0.737029i	$0.263772\pi$
$110$	−0.114109	−	1.15988i	−0.0108799	−	0.110590i
$111$	−6.57952			−0.624500
$112$	7.48881	+	18.1022i	0.707626	+	1.71050i
$113$	0.698357			0.0656959			0.0328480	−	0.999460i	$-0.489542\pi$
$113$	0.698357			0.0656959			0.0328480	+	0.999460i	$0.489542\pi$
$114$	0.909004	+	9.23974i	0.0851361	+	0.865381i
$115$	4.79974	−	4.79974i	0.447578	−	0.447578i
$116$	−7.06262	+	10.5649i	−0.655748	+	0.980927i
$117$	−1.72543	−	1.72543i	−0.159516	−	0.159516i
$118$	3.36503	+	2.76223i	0.309776	+	0.254284i
$119$		−	10.8087i		−	0.990835i
$120$	2.23081	−	0.675903i	0.203645	−	0.0617012i
$121$			1.00000i			0.0909091i
$122$	2.98399	−	3.63518i	0.270158	−	0.329114i
$123$	−7.21539	−	7.21539i	−0.650590	−	0.650590i
$124$	7.49894	−	1.48991i	0.673425	−	0.133798i
$125$	5.43162	−	5.43162i	0.485819	−	0.485819i
$126$	6.89287	−	0.678119i	0.614066	−	0.0604117i
$127$	−10.8716			−0.964696			−0.482348	−	0.875980i	$-0.660216\pi$
$127$	−10.8716			−0.964696			−0.482348	+	0.875980i	$0.660216\pi$
$128$	8.75116	−	7.17057i	0.773501	−	0.633795i
$129$	−1.72611			−0.151976
$130$	2.83026	−	0.278441i	0.248230	−	0.0244208i
$131$	10.4734	−	10.4734i	0.915062	−	0.915062i	−0.0816027	−	0.996665i	$-0.526004\pi$
$131$	10.4734	−	10.4734i	0.915062	−	0.915062i	0.996665	+	0.0816027i	$0.0260038\pi$
$132$	−1.96166	+	0.389747i	−0.170740	+	0.0339231i
$133$	−22.7352	−	22.7352i	−1.97139	−	1.97139i
$134$	−11.0353	+	13.4436i	−0.953308	+	1.16135i
$135$		−	0.824119i		−	0.0709289i
$136$	−5.97408	+	1.81006i	−0.512274	+	0.155211i
$137$		−	18.9181i		−	1.61628i	−0.588992	−	0.808139i	$-0.700475\pi$
$137$		−	18.9181i		−	1.61628i	0.588992	−	0.808139i	$-0.299525\pi$
$138$	−9.00333	−	7.39051i	−0.766415	−	0.629122i
$139$	3.03763	+	3.03763i	0.257649	+	0.257649i	0.824097	−	0.566449i	$-0.191683\pi$
$139$	3.03763	+	3.03763i	0.257649	+	0.257649i	−0.566449	+	0.824097i	$0.691683\pi$
$140$	−4.48621	+	6.71087i	−0.379154	+	0.567172i
$141$	6.93222	−	6.93222i	0.583799	−	0.583799i
$142$	1.30801	+	13.2955i	0.109765	+	1.11573i
$143$	−2.44013			−0.204054
$144$	−1.52910	−	3.69619i	−0.127425	−	0.308016i
$145$	−5.23653			−0.434870
$146$	1.97001	+	20.0245i	0.163039	+	1.65724i
$147$	−12.0107	+	12.0107i	−0.990630	+	0.990630i
$148$	−10.9397	−	7.31319i	−0.899240	−	0.601140i
$149$	11.8476	+	11.8476i	0.970592	+	0.970592i	0.999580	−	0.0289874i	$-0.00922828\pi$
$149$	11.8476	+	11.8476i	0.970592	+	0.970592i	−0.0289874	+	0.999580i	$0.509228\pi$
$150$	−4.72311	−	3.87703i	−0.385640	−	0.316558i
$151$			14.6279i			1.19040i	0.803578	+	0.595200i	$0.202927\pi$
$151$			14.6279i			1.19040i	−0.803578	+	0.595200i	$0.797073\pi$
$152$	−8.75865	+	16.3732i	−0.710421	+	1.32804i
$153$			2.20698i			0.178424i
$154$	4.39449	−	5.35350i	0.354118	−	0.431397i
$155$	2.22768	+	2.22768i	0.178931	+	0.178931i
$156$	−0.951034	−	4.78670i	−0.0761436	−	0.383242i
$157$	0.217412	−	0.217412i	0.0173514	−	0.0173514i	−0.698378	−	0.715729i	$-0.746094\pi$
$157$	0.217412	−	0.217412i	0.0173514	−	0.0173514i	0.715729	+	0.698378i	$0.246094\pi$
$158$	−2.54342	+	0.250221i	−0.202344	+	0.0199065i
$159$	−1.61241			−0.127873
$160$	4.46043	+	1.35575i	0.352628	+	0.107181i
$161$	40.3384			3.17911
$162$	−1.40742	+	0.138462i	−0.110577	+	0.0108786i
$163$	−17.0683	+	17.0683i	−1.33689	+	1.33689i	−0.437841	+	0.899053i	$0.644257\pi$
$163$	−17.0683	+	17.0683i	−1.33689	+	1.33689i	−0.899053	+	0.437841i	$0.855743\pi$
$164$	−3.97702	−	20.0170i	−0.310553	−	1.56306i
$165$	−0.582740	−	0.582740i	−0.0453663	−	0.0453663i
$166$	−4.12257	+	5.02224i	−0.319974	+	0.389801i
$167$		−	4.03060i		−	0.311897i	−0.987765	−	0.155948i	$-0.950157\pi$
$167$		−	4.03060i		−	0.311897i	0.987765	−	0.155948i	$-0.0498434\pi$
$168$	12.2145	+	6.53398i	0.942367	+	0.504107i
$169$			7.04577i			0.541982i
$170$	−1.98815	−	1.63200i	−0.152484	−	0.125169i
$171$	4.64217	+	4.64217i	0.354996	+	0.354996i
$172$	−2.87000	−	1.91859i	−0.218835	−	0.146291i
$173$	6.86259	−	6.86259i	0.521753	−	0.521753i	−0.396347	−	0.918101i	$-0.629722\pi$
$173$	6.86259	−	6.86259i	0.521753	−	0.521753i	0.918101	+	0.396347i	$0.129722\pi$
$174$	0.879798	+	8.94287i	0.0666973	+	0.677957i
$175$	21.1614			1.59965
$176$	−3.69484	−	1.53237i	−0.278509	−	0.115507i
$177$	3.07842			0.231388
$178$	0.733965	+	7.46052i	0.0550130	+	0.559190i
$179$	−4.44665	+	4.44665i	−0.332358	+	0.332358i	−0.853481	−	0.521123i	$-0.825513\pi$
$179$	−4.44665	+	4.44665i	−0.332358	+	0.332358i	0.521123	+	0.853481i	$0.325513\pi$
$180$	0.916015	−	1.37026i	0.0682757	−	0.102133i
$181$	−12.2861	−	12.2861i	−0.913218	−	0.913218i	0.0833059	−	0.996524i	$-0.473452\pi$
$181$	−12.2861	−	12.2861i	−0.913218	−	0.913218i	−0.996524	+	0.0833059i	$0.973452\pi$
$182$	13.0632	+	10.7231i	0.968311	+	0.794852i
$183$		−	3.32556i		−	0.245833i
$184$	−6.75517	−	22.2954i	−0.497998	−	1.64364i
$185$		−	5.42231i		−	0.398656i
$186$	3.43012	−	4.17867i	0.251509	−	0.306395i
$187$	1.56057	+	1.56057i	0.114120	+	0.114120i
$188$	19.2314	−	3.82094i	1.40259	−	0.278671i
$189$	3.46307	−	3.46307i	0.251902	−	0.251902i
$190$	−7.61465	+	0.749128i	−0.552425	+	0.0543475i
$191$	21.9781			1.59028			0.795140	−	0.606426i	$-0.207397\pi$
$191$	21.9781			1.59028			0.795140	+	0.606426i	$0.207397\pi$
$192$	1.56592	−	7.84525i	0.113011	−	0.566182i
$193$	7.33803			0.528203			0.264102	−	0.964495i	$-0.414925\pi$
$193$	7.33803			0.528203			0.264102	+	0.964495i	$0.414925\pi$
$194$	10.1874	−	1.00223i	0.731411	−	0.0719560i
$195$	1.42196	−	1.42196i	0.101829	−	0.101829i
$196$	−33.3202	+	6.62015i	−2.38002	+	0.472868i
$197$	−5.33250	−	5.33250i	−0.379925	−	0.379925i	0.491150	−	0.871075i	$-0.336577\pi$
$197$	−5.33250	−	5.33250i	−0.379925	−	0.379925i	−0.871075	+	0.491150i	$0.836577\pi$
$198$	−0.897288	+	1.09310i	−0.0637675	+	0.0776834i
$199$		−	21.9645i		−	1.55702i	−0.627630	−	0.778511i	$-0.715975\pi$
$199$		−	21.9645i		−	1.55702i	0.627630	−	0.778511i	$-0.284025\pi$
$200$	−3.54373	−	11.6961i	−0.250580	−	0.827038i
$201$			12.2985i			0.867472i
$202$	−11.3890	−	9.34885i	−0.801330	−	0.657783i
$203$	−22.0047	−	22.0047i	−1.54443	−	1.54443i
$204$	−2.45307	+	3.66953i	−0.171749	+	0.256918i
$205$	5.94634	−	5.94634i	0.415311	−	0.415311i
$206$	1.08272	+	11.0055i	0.0754365	+	0.766788i
$207$	−8.23649			−0.572476
$208$	3.73917	−	9.01589i	0.259265	−	0.625140i
$209$	6.56503			0.454112
$210$	0.558851	+	5.68055i	0.0385644	+	0.391995i
$211$	8.27179	−	8.27179i	0.569453	−	0.569453i	−0.362522	−	0.931975i	$-0.618084\pi$
$211$	8.27179	−	8.27179i	0.569453	−	0.569453i	0.931975	+	0.362522i	$0.118084\pi$
$212$	−2.68095	−	1.79221i	−0.184128	−	0.123089i
$213$	6.67983	+	6.67983i	0.457694	+	0.457694i
$214$	3.00834	+	2.46944i	0.205646	+	0.168807i
$215$		−	1.42252i		−	0.0970152i
$216$	−2.49401	−	1.33414i	−0.169696	−	0.0907766i
$217$			18.7221i			1.27094i
$218$	−0.810378	+	0.987226i	−0.0548857	+	0.0668634i
$219$	10.0606	+	10.0606i	0.679832	+	0.679832i
$220$	−0.321198	−	1.61664i	−0.0216552	−	0.108994i
$221$	−3.80799	+	3.80799i	−0.256153	+	0.256153i
$222$	−9.26014	+	0.911011i	−0.621500	+	0.0611430i
$223$	24.9613			1.67153			0.835767	−	0.549084i	$-0.185023\pi$
$223$	24.9613			1.67153			0.835767	+	0.549084i	$0.185023\pi$
$224$	13.0464	+	24.4405i	0.871696	+	1.63300i
$225$	−4.32083			−0.288055
$226$	0.982881	−	0.0966957i	0.0653803	−	0.00643210i
$227$	−15.9235	+	15.9235i	−1.05688	+	1.05688i	−0.0585975	+	0.998282i	$0.518663\pi$
$227$	−15.9235	+	15.9235i	−1.05688	+	1.05688i	−0.998282	+	0.0585975i	$0.981337\pi$
$228$	2.55870	+	12.8783i	0.169454	+	0.852888i
$229$	11.5279	+	11.5279i	0.761788	+	0.761788i	0.976645	−	0.214857i	$-0.0689286\pi$
$229$	11.5279	+	11.5279i	0.761788	+	0.761788i	−0.214857	+	0.976645i	$0.568929\pi$
$230$	6.09066	−	7.41982i	0.401606	−	0.489248i
$231$		−	4.89753i		−	0.322234i
$232$	−8.47724	+	15.8472i	−0.556558	+	1.04042i
$233$		−	5.87804i		−	0.385083i	−0.981289	−	0.192542i	$-0.938327\pi$
$233$		−	5.87804i		−	0.385083i	0.981289	−	0.192542i	$-0.0616731\pi$
$234$	−2.66731	−	2.18950i	−0.174368	−	0.143132i
$235$	5.71298	+	5.71298i	0.372674	+	0.372674i
$236$	5.11847	+	3.42169i	0.333184	+	0.222733i
$237$	−1.27785	+	1.27785i	−0.0830052	+	0.0830052i
$238$	−1.49659	−	15.2124i	−0.0970098	−	0.986074i
$239$	−0.0664988			−0.00430145			−0.00215072	−	0.999998i	$-0.500685\pi$
$239$	−0.0664988			−0.00430145			−0.00215072	+	0.999998i	$0.500685\pi$
$240$	3.04610	−	1.26016i	0.196625	−	0.0813430i
$241$	−23.1161			−1.48904			−0.744520	−	0.667600i	$-0.767322\pi$
$241$	−23.1161			−1.48904			−0.744520	+	0.667600i	$0.767322\pi$
$242$	0.138462	+	1.40742i	0.00890065	+	0.0904723i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.69639	−	5.52939i	0.236637	−	0.353983i
$245$	−9.89829	−	9.89829i	−0.632378	−	0.632378i
$246$	−11.1541	−	9.15603i	−0.711162	−	0.583767i
$247$			16.0195i			1.01930i
$248$	10.3479	−	3.13524i	0.657090	−	0.199088i
$249$			4.59448i			0.291163i
$250$	6.89250	−	8.39664i	0.435920	−	0.531050i
$251$	−7.72118	−	7.72118i	−0.487356	−	0.487356i	0.420115	−	0.907471i	$-0.361990\pi$
$251$	−7.72118	−	7.72118i	−0.487356	−	0.487356i	−0.907471	+	0.420115i	$0.861990\pi$
$252$	9.60726	−	1.90880i	0.605201	−	0.120243i
$253$	−5.82408	+	5.82408i	−0.366157	+	0.366157i
$254$	−15.3009	+	1.50530i	−0.960061	+	0.0944506i
$255$	−1.81881			−0.113898
$256$	11.3237	−	11.3037i	0.707732	−	0.706481i
$257$	−1.47156			−0.0917932			−0.0458966	−	0.998946i	$-0.514614\pi$
$257$	−1.47156			−0.0917932			−0.0458966	+	0.998946i	$0.514614\pi$
$258$	−2.42936	+	0.239000i	−0.151246	+	0.0148795i
$259$	22.7854	−	22.7854i	1.41581	−	1.41581i
$260$	3.94481	−	0.783765i	0.244647	−	0.0486070i
$261$	4.49302	+	4.49302i	0.278111	+	0.278111i
$262$	13.2903	−	16.1906i	0.821075	−	1.00026i
$263$			19.5129i			1.20322i	0.798790	+	0.601610i	$0.205474\pi$
$263$			19.5129i			1.20322i	−0.798790	+	0.601610i	$0.794526\pi$
$264$	−2.70691	+	0.820152i	−0.166599	+	0.0504768i
$265$		−	1.32882i		−	0.0816287i
$266$	−35.1459	−	28.8500i	−2.15493	−	1.76890i
$267$	3.74827	+	3.74827i	0.229390	+	0.229390i
$268$	−13.6699	+	20.4487i	−0.835024	+	1.24910i
$269$	5.88616	−	5.88616i	0.358886	−	0.358886i	−0.504517	−	0.863402i	$-0.668329\pi$
$269$	5.88616	−	5.88616i	0.358886	−	0.358886i	0.863402	+	0.504517i	$0.168329\pi$
$270$	−0.114109	−	1.15988i	−0.00694445	−	0.0705881i
$271$	13.3108			0.808571			0.404286	−	0.914633i	$-0.367520\pi$
$271$	13.3108			0.808571			0.404286	+	0.914633i	$0.367520\pi$
$272$	−8.15742	+	3.37469i	−0.494616	+	0.204621i
$273$	11.9506			0.723283
$274$	−2.61942	−	26.6256i	−0.158245	−	1.60851i
$275$	−3.05529	+	3.05529i	−0.184241	+	0.184241i
$276$	−13.6948	−	9.15493i	−0.824328	−	0.551062i
$277$	−0.343580	−	0.343580i	−0.0206438	−	0.0206438i	0.696710	−	0.717353i	$-0.254647\pi$
$277$	−0.343580	−	0.343580i	−0.0206438	−	0.0206438i	−0.717353	+	0.696710i	$0.754647\pi$
$278$	4.69582	+	3.85463i	0.281636	+	0.231185i
$279$		−	3.82276i		−	0.228863i
$280$	−5.38478	+	10.0662i	−0.321802	+	0.601569i
$281$			0.183598i			0.0109525i	0.999985	+	0.00547627i	$0.00174316\pi$
$281$			0.183598i			0.0109525i	−0.999985	+	0.00547627i	$0.998257\pi$
$282$	8.79670	−	10.7164i	0.523836	−	0.638152i
$283$	12.3011	+	12.3011i	0.731225	+	0.731225i	0.970863	−	0.239637i	$-0.0770285\pi$
$283$	12.3011	+	12.3011i	0.731225	+	0.731225i	−0.239637	+	0.970863i	$0.577029\pi$
$284$	3.68183	+	18.5312i	0.218476	+	1.09962i
$285$	−3.82571	+	3.82571i	−0.226615	+	0.226615i
$286$	−3.43429	+	0.337864i	−0.203074	+	0.0199783i
$287$	49.9749			2.94992
$288$	−2.66387	−	4.99037i	−0.156970	−	0.294061i
$289$	−12.1293			−0.713485
$290$	−7.36999	+	0.725058i	−0.432781	+	0.0425769i
$291$	5.11828	−	5.11828i	0.300039	−	0.300039i
$292$	5.54526	+	27.9101i	0.324512	+	1.63332i
$293$	2.19204	+	2.19204i	0.128060	+	0.128060i	0.768232	−	0.640172i	$-0.221137\pi$
$293$	2.19204	+	2.19204i	0.128060	+	0.128060i	−0.640172	+	0.768232i	$0.721137\pi$
$294$	−15.2411	+	18.5672i	−0.888880	+	1.08286i
$295$			2.53699i			0.147709i
$296$	−16.4094	−	8.77799i	−0.953775	−	0.510210i
$297$			1.00000i			0.0580259i
$298$	18.3150	+	15.0341i	1.06096	+	0.870901i
$299$	−14.2115	−	14.2115i	−0.821873	−	0.821873i
$300$	−7.18421	−	4.80263i	−0.414781	−	0.277280i
$301$	5.97765	−	5.97765i	0.344546	−	0.344546i
$302$	2.02540	+	20.5876i	0.116549	+	1.18468i
$303$	−10.4190			−0.598556
$304$	−10.0600	+	24.2567i	−0.576982	+	1.39122i
$305$	2.74066			0.156930
$306$	0.305582	+	3.10614i	0.0174689	+	0.177566i
$307$	4.73919	−	4.73919i	0.270480	−	0.270480i	−0.558814	−	0.829293i	$-0.688743\pi$
$307$	4.73919	−	4.73919i	0.270480	−	0.270480i	0.829293	+	0.558814i	$0.188743\pi$
$308$	5.44364	−	8.14309i	0.310180	−	0.463995i
$309$	5.52930	+	5.52930i	0.314551	+	0.314551i
$310$	3.44372	+	2.82683i	0.195590	+	0.160553i
$311$			1.86379i			0.105686i	0.998603	+	0.0528431i	$0.0168283\pi$
$311$			1.86379i			0.105686i	−0.998603	+	0.0528431i	$0.983172\pi$
$312$	−2.00128	−	6.60521i	−0.113300	−	0.373946i
$313$		−	2.88059i		−	0.162821i	−0.996681	−	0.0814103i	$-0.974058\pi$
$313$		−	2.88059i		−	0.162821i	0.996681	−	0.0814103i	$-0.0259424\pi$
$314$	0.275887	−	0.336093i	0.0155692	−	0.0189669i
$315$	2.85399	+	2.85399i	0.160804	+	0.160804i
$316$	−3.54501	+	0.704332i	−0.199422	+	0.0396218i
$317$	−10.6057	+	10.6057i	−0.595673	+	0.595673i	−0.939158	−	0.343485i	$-0.888393\pi$
$317$	−10.6057	+	10.6057i	−0.595673	+	0.595673i	0.343485	+	0.939158i	$0.388393\pi$
$318$	−2.26934	+	0.223257i	−0.127258	+	0.0125196i
$319$	6.35409			0.355761
$320$	6.46542	+	1.29051i	0.361428	+	0.0721416i
$321$	2.75211			0.153608
$322$	56.7731	−	5.58533i	3.16384	−	0.311258i
$323$	10.2452	−	10.2452i	0.570057	−	0.570057i
$324$	−1.96166	+	0.389747i	−0.108981	+	0.0216526i
$325$	−7.45530	−	7.45530i	−0.413545	−	0.413545i
$326$	−21.6590	+	26.3856i	−1.19958	+	1.46136i
$327$			0.903141i			0.0499438i
$328$	−8.36891	−	27.6216i	−0.462096	−	1.52515i
$329$			48.0136i			2.64708i
$330$	−0.900847	−	0.739473i	−0.0495900	−	0.0407066i
$331$	−9.01783	−	9.01783i	−0.495665	−	0.495665i	0.414421	−	0.910085i	$-0.363984\pi$
$331$	−9.01783	−	9.01783i	−0.495665	−	0.495665i	−0.910085	+	0.414421i	$0.863984\pi$
$332$	−5.10680	+	7.63921i	−0.280272	+	0.419256i
$333$	−4.65242	+	4.65242i	−0.254951	+	0.254951i
$334$	−0.558083	−	5.67274i	−0.0305369	−	0.310398i
$335$	−10.1355			−0.553760
$336$	18.0956	+	7.50481i	0.987195	+	0.409421i
$337$	19.9937			1.08913			0.544563	−	0.838720i	$-0.316695\pi$
$337$	19.9937			1.08913			0.544563	+	0.838720i	$0.316695\pi$
$338$	0.975568	+	9.91635i	0.0530639	+	0.539378i
$339$	0.493813	−	0.493813i	0.0268202	−	0.0268202i
$340$	−3.02413	−	2.02162i	−0.164006	−	0.109638i
$341$	−2.70310	−	2.70310i	−0.146381	−	0.146381i
$342$	7.17625	+	5.89072i	0.388047	+	0.318534i
$343$		−	48.9055i		−	2.64065i
$344$	−4.30494	−	2.30287i	−0.232107	−	0.124163i
$345$		−	6.78785i		−	0.365446i
$346$	8.70833	−	10.6087i	0.468163	−	0.570330i
$347$	−14.4537	−	14.4537i	−0.775916	−	0.775916i	0.203217	−	0.979134i	$-0.434860\pi$
$347$	−14.4537	−	14.4537i	−0.775916	−	0.775916i	−0.979134	+	0.203217i	$0.934860\pi$
$348$	2.47649	+	12.4645i	0.132754	+	0.668170i
$349$	20.2751	−	20.2751i	1.08530	−	1.08530i	0.0892971	−	0.996005i	$-0.471538\pi$
$349$	20.2751	−	20.2751i	1.08530	−	1.08530i	0.996005	−	0.0892971i	$-0.0284621\pi$
$350$	29.7829	−	2.93004i	1.59196	−	0.156617i
$351$	−2.44013			−0.130244
$352$	−5.41236	−	1.64509i	−0.288480	−	0.0876835i
$353$	10.2789			0.547090			0.273545	−	0.961859i	$-0.411804\pi$
$353$	10.2789			0.547090			0.273545	+	0.961859i	$0.411804\pi$
$354$	4.33263	−	0.426243i	0.230277	−	0.0226546i
$355$	−5.50497	+	5.50497i	−0.292174	+	0.292174i
$356$	2.06599	+	10.3985i	0.109497	+	0.551117i
$357$	−7.64293	−	7.64293i	−0.404507	−	0.404507i
$358$	−5.64261	+	6.87399i	−0.298221	+	0.363302i
$359$		−	11.6208i		−	0.613324i	−0.951818	−	0.306662i	$-0.900788\pi$
$359$		−	11.6208i		−	0.613324i	0.951818	−	0.306662i	$-0.0992121\pi$
$360$	1.09949	−	2.05536i	0.0579482	−	0.108327i
$361$		−	24.0996i		−	1.26840i
$362$	−18.9928	−	15.5905i	−0.998241	−	0.819420i
$363$	0.707107	+	0.707107i	0.0371135	+	0.0371135i
$364$	19.8702	+	13.2832i	1.04148	+	0.696228i
$365$	−8.29113	+	8.29113i	−0.433978	+	0.433978i
$366$	−0.460463	−	4.68046i	−0.0240688	−	0.244652i
$367$	−0.813135			−0.0424453			−0.0212226	−	0.999775i	$-0.506756\pi$
$367$	−0.813135			−0.0424453			−0.0212226	+	0.999775i	$0.506756\pi$
$368$	−12.5944	−	30.4437i	−0.656530	−	1.58699i
$369$	−10.2041			−0.531205
$370$	−0.750782	−	7.63146i	−0.0390313	−	0.396741i
$371$	5.58390	−	5.58390i	0.289902	−	0.289902i
$372$	4.24903	−	6.35608i	0.220302	−	0.329547i
$373$	22.8768	+	22.8768i	1.18451	+	1.18451i	0.978562	+	0.205953i	$0.0660294\pi$
$373$	22.8768	+	22.8768i	1.18451	+	1.18451i	0.205953	+	0.978562i	$0.433971\pi$
$374$	2.41245	+	1.98030i	0.124745	+	0.102399i
$375$		−	7.68147i		−	0.396670i
$376$	26.5376	−	8.04048i	1.36857	−	0.414656i
$377$			15.5048i			0.798538i
$378$	4.39449	−	5.35350i	0.226028	−	0.275354i
$379$	−3.21310	−	3.21310i	−0.165046	−	0.165046i	0.619752	−	0.784798i	$-0.287233\pi$
$379$	−3.21310	−	3.21310i	−0.165046	−	0.165046i	−0.784798	+	0.619752i	$0.787233\pi$
$380$	−10.6133	+	2.10867i	−0.544450	+	0.108173i
$381$	−7.68736	+	7.68736i	−0.393835	+	0.393835i
$382$	30.9324	−	3.04312i	1.58264	−	0.155700i
$383$	9.08904			0.464428			0.232214	−	0.972665i	$-0.425403\pi$
$383$	9.08904			0.464428			0.232214	+	0.972665i	$0.425403\pi$
$384$	1.11765	−	11.2584i	0.0570347	−	0.574526i
$385$	4.03614			0.205701
$386$	10.3277	−	1.01604i	0.525666	−	0.0517149i
$387$	−1.22055	+	1.22055i	−0.0620438	+	0.0620438i
$388$	14.1991	−	2.82112i	0.720852	−	0.143221i
$389$	8.32569	+	8.32569i	0.422129	+	0.422129i	0.885936	−	0.463807i	$-0.153517\pi$
$389$	8.32569	+	8.32569i	0.422129	+	0.422129i	−0.463807	+	0.885936i	$0.653517\pi$
$390$	1.80441	−	2.19818i	0.0913698	−	0.111309i
$391$			18.1778i			0.919288i
$392$	−45.9789	+	13.9309i	−2.32228	+	0.703617i
$393$		−	14.8116i		−	0.747145i
$394$	−8.24340	−	6.76671i	−0.415297	−	0.340902i
$395$	−1.05310	−	1.05310i	−0.0529872	−	0.0529872i
$396$	−1.11151	+	1.66269i	−0.0558554	+	0.0835535i
$397$	−15.4784	+	15.4784i	−0.776840	+	0.776840i	−0.979292	−	0.202452i	$-0.935109\pi$
$397$	−15.4784	+	15.4784i	−0.776840	+	0.776840i	0.202452	+	0.979292i	$0.435109\pi$
$398$	−3.04124	−	30.9133i	−0.152444	−	1.54954i
$399$	−32.1524			−1.60963
$400$	−6.60698	−	15.9706i	−0.330349	−	0.798531i
$401$	8.52766			0.425851			0.212926	−	0.977068i	$-0.431701\pi$
$401$	8.52766			0.425851			0.212926	+	0.977068i	$0.431701\pi$
$402$	1.70288	+	17.3092i	0.0849318	+	0.863305i
$403$	6.59591	−	6.59591i	0.328566	−	0.328566i
$404$	−17.3236	−	11.5808i	−0.861882	−	0.576166i
$405$	−0.582740	−	0.582740i	−0.0289566	−	0.0289566i
$406$	−34.0166	−	27.9230i	−1.68822	−	1.38580i
$407$			6.57952i			0.326135i
$408$	−2.94441	+	5.50422i	−0.145770	+	0.272499i
$409$			0.959341i			0.0474364i	0.999719	+	0.0237182i	$0.00755044\pi$
$409$			0.959341i			0.0474364i	−0.999719	+	0.0237182i	$0.992450\pi$
$410$	7.54566	−	9.19234i	0.372653	−	0.453977i
$411$	−13.3771	−	13.3771i	−0.659843	−	0.659843i
$412$	3.04767	+	15.3394i	0.150148	+	0.755718i
$413$	−10.6608	+	10.6608i	−0.524584	+	0.524584i
$414$	−11.5922	+	1.14044i	−0.569725	+	0.0560495i
$415$	−3.78640			−0.185867
$416$	4.01423	−	13.2069i	0.196814	−	0.647520i
$417$	4.29586			0.210369
$418$	9.23974	−	0.909004i	0.451931	−	0.0444609i
$419$	−15.9502	+	15.9502i	−0.779216	+	0.779216i	−0.979697	−	0.200481i	$-0.935749\pi$
$419$	−15.9502	+	15.9502i	−0.779216	+	0.779216i	0.200481	+	0.979697i	$0.435749\pi$
$420$	1.57308	+	7.91753i	0.0767582	+	0.386336i
$421$	6.78917	+	6.78917i	0.330884	+	0.330884i	0.852922	−	0.522038i	$-0.174828\pi$
$421$	6.78917	+	6.78917i	0.330884	+	0.330884i	−0.522038	+	0.852922i	$0.674828\pi$
$422$	10.4965	−	12.7872i	0.510964	−	0.622471i
$423$		−	9.80364i		−	0.476669i
$424$	−4.02137	−	2.15118i	−0.195295	−	0.104471i
$425$			9.53597i			0.462562i
$426$	10.3262	+	8.47642i	0.500307	+	0.410684i
$427$	11.5167	+	11.5167i	0.557331	+	0.557331i
$428$	4.57592	+	3.05899i	0.221185	+	0.147862i
$429$	−1.72543	+	1.72543i	−0.0833047	+	0.0833047i
$430$	−0.196965	−	2.00208i	−0.00949848	−	0.0965491i
$431$	−5.46458			−0.263219			−0.131610	−	0.991302i	$-0.542015\pi$
$431$	−5.46458			−0.263219			−0.131610	+	0.991302i	$0.542015\pi$
$432$	−3.69484	−	1.53237i	−0.177768	−	0.0737260i
$433$	33.8187			1.62522			0.812611	−	0.582806i	$-0.198045\pi$
$433$	33.8187			1.62522			0.812611	+	0.582806i	$0.198045\pi$
$434$	2.59229	+	26.3498i	0.124434	+	1.26483i
$435$	−3.70278	+	3.70278i	−0.177535	+	0.177535i
$436$	−1.00385	+	1.50165i	−0.0480756	+	0.0719158i
$437$	38.2352	+	38.2352i	1.82904	+	1.82904i
$438$	15.5525	+	12.7665i	0.743127	+	0.610006i
$439$		−	20.8628i		−	0.995729i	−0.867255	−	0.497864i	$-0.834118\pi$
$439$		−	20.8628i		−	0.995729i	0.867255	−	0.497864i	$-0.165882\pi$
$440$	−0.675903	−	2.23081i	−0.0322224	−	0.106350i
$441$			16.9858i			0.808846i
$442$	−4.83218	+	5.88670i	−0.229843	+	0.280002i
$443$	−23.9878	−	23.9878i	−1.13970	−	1.13970i	−0.988505	−	0.151191i	$-0.951689\pi$
$443$	−23.9878	−	23.9878i	−1.13970	−	1.13970i	−0.151191	−	0.988505i	$-0.548311\pi$
$444$	−12.9068	+	2.56435i	−0.612528	+	0.121699i
$445$	−3.08902	+	3.08902i	−0.146434	+	0.146434i
$446$	35.1311	−	3.45619i	1.66350	−	0.163655i
$447$	16.7550			0.792485
$448$	21.7458	+	32.5916i	1.02739	+	1.53981i
$449$	−23.6534			−1.11627			−0.558135	−	0.829750i	$-0.688483\pi$
$449$	−23.6534			−1.11627			−0.558135	+	0.829750i	$0.688483\pi$
$450$	−6.08122	+	0.598269i	−0.286671	+	0.0282027i
$451$	−7.21539	+	7.21539i	−0.339760	+	0.339760i
$452$	1.36994	−	0.272183i	0.0644364	−	0.0128024i
$453$	10.3435	+	10.3435i	0.485979	+	0.485979i
$454$	−20.2062	+	24.6158i	−0.948325	+	1.15528i
$455$			9.84872i			0.461715i
$456$	5.38432	+	17.7709i	0.252144	+	0.832200i
$457$			0.845965i			0.0395726i	0.999804	+	0.0197863i	$0.00629858\pi$
$457$			0.845965i			0.0395726i	−0.999804	+	0.0197863i	$0.993701\pi$
$458$	17.8208	+	14.6285i	0.832713	+	0.683544i
$459$	1.56057	+	1.56057i	0.0728411	+	0.0728411i
$460$	7.54475	−	11.2861i	0.351776	−	0.526218i
$461$	−7.70908	+	7.70908i	−0.359047	+	0.359047i	−0.863462	−	0.504414i	$-0.831708\pi$
$461$	−7.70908	+	7.70908i	−0.359047	+	0.359047i	0.504414	+	0.863462i	$0.331708\pi$
$462$	−0.678119	−	6.89287i	−0.0315490	−	0.320685i
$463$	−29.6331			−1.37717			−0.688584	−	0.725156i	$-0.741767\pi$
$463$	−29.6331			−1.37717			−0.688584	+	0.725156i	$0.741767\pi$
$464$	−9.73680	+	23.4774i	−0.452020	+	1.08991i
$465$	3.15041			0.146097
$466$	−0.813883	−	8.27287i	−0.0377024	−	0.383233i
$467$	−22.1239	+	22.1239i	−1.02377	+	1.02377i	−0.0240610	+	0.999710i	$0.507660\pi$
$467$	−22.1239	+	22.1239i	−1.02377	+	1.02377i	−0.999710	+	0.0240610i	$0.992340\pi$
$468$	−4.05719	−	2.71222i	−0.187544	−	0.125373i
$469$	−42.5908	−	42.5908i	−1.96666	−	1.96666i
$470$	8.83158	+	7.24953i	0.407371	+	0.334396i
$471$		−	0.307467i		−	0.0141674i
$472$	7.67761	+	4.10704i	0.353391	+	0.189042i
$473$			1.72611i			0.0793667i
$474$	−1.62154	+	1.97540i	−0.0744796	+	0.0907332i
$475$	20.0580	+	20.0580i	0.920326	+	0.920326i
$476$	−4.21267	−	21.2030i	−0.193087	−	0.971839i
$477$	−1.14015	+	1.14015i	−0.0522037	+	0.0522037i
$478$	−0.0935916	+	0.00920753i	−0.00428078	+	0.000421142i
$479$	10.8545			0.495953			0.247976	−	0.968766i	$-0.420234\pi$
$479$	10.8545			0.495953			0.247976	+	0.968766i	$0.420234\pi$
$480$	4.11266	−	2.19534i	0.187716	−	0.100203i
$481$	−16.0549			−0.732039
$482$	−32.5341	+	3.20070i	−1.48189	+	0.145788i
$483$	28.5236	−	28.5236i	1.29787	−	1.29787i
$484$	0.389747	+	1.96166i	0.0177158	+	0.0891662i
$485$	4.21807	+	4.21807i	0.191533	+	0.191533i
$486$	−0.897288	+	1.09310i	−0.0407018	+	0.0495841i
$487$			6.22316i			0.281999i	0.990010	+	0.140999i	$0.0450315\pi$
$487$			6.22316i			0.281999i	−0.990010	+	0.140999i	$0.954968\pi$
$488$	4.43676	−	8.29398i	0.200843	−	0.375451i
$489$			24.1382i			1.09157i
$490$	−15.3016	−	12.5605i	−0.691254	−	0.567426i
$491$	−26.7116	−	26.7116i	−1.20548	−	1.20548i	−0.972476	−	0.233002i	$-0.925145\pi$
$491$	−26.7116	−	26.7116i	−1.20548	−	1.20548i	−0.233002	−	0.972476i	$-0.574855\pi$
$492$	−16.9663	−	11.3419i	−0.764900	−	0.511334i
$493$	9.91600	−	9.91600i	0.446594	−	0.446594i
$494$	2.21809	+	22.5462i	0.0997965	+	1.01440i
$495$	−0.824119			−0.0370414
$496$	14.1297	−	5.84538i	0.634441	−	0.262465i
$497$	−46.2655			−2.07529
$498$	0.636159	+	6.46636i	0.0285070	+	0.289764i
$499$	11.3391	−	11.3391i	0.507607	−	0.507607i	−0.406184	−	0.913791i	$-0.633141\pi$
$499$	11.3391	−	11.3391i	0.507607	−	0.507607i	0.913791	+	0.406184i	$0.133141\pi$
$500$	8.53802	−	12.7719i	0.381832	−	0.571178i
$501$	−2.85006	−	2.85006i	−0.127331	−	0.127331i
$502$	−11.9360	−	9.79785i	−0.532731	−	0.437299i
$503$			28.6656i			1.27814i	0.769151	+	0.639068i	$0.220680\pi$
$503$			28.6656i			1.27814i	−0.769151	+	0.639068i	$0.779320\pi$
$504$	13.2572	−	4.01671i	0.590521	−	0.178919i
$505$		−	8.58650i		−	0.382094i
$506$	−7.39051	+	9.00333i	−0.328548	+	0.400247i
$507$	4.98211	+	4.98211i	0.221263	+	0.221263i
$508$	−21.3263	+	4.23716i	−0.946201	+	0.187994i
$509$	−5.69583	+	5.69583i	−0.252463	+	0.252463i	−0.821980	−	0.569517i	$-0.807130\pi$
$509$	−5.69583	+	5.69583i	−0.252463	+	0.252463i	0.569517	+	0.821980i	$0.307130\pi$
$510$	−2.55983	+	0.251836i	−0.113351	+	0.0111515i
$511$	−69.6812			−3.08251
$512$	14.3721	−	17.4769i	0.635162	−	0.772379i
$513$	6.56503			0.289853
$514$	−2.07110	+	0.203754i	−0.0913522	+	0.00898722i
$515$	−4.55681	+	4.55681i	−0.200797	+	0.200797i
$516$	−3.38604	+	0.672747i	−0.149062	+	0.0296160i
$517$	−6.93222	−	6.93222i	−0.304879	−	0.304879i
$518$	28.9136	−	35.2234i	1.27039	−	1.54763i
$519$		−	9.70517i		−	0.426010i
$520$	5.44348	−	1.64929i	0.238712	−	0.0723262i
$521$		−	3.76148i		−	0.164794i	−0.996600	−	0.0823968i	$-0.973743\pi$
$521$		−	3.76148i		−	0.164794i	0.996600	−	0.0823968i	$-0.0262575\pi$
$522$	6.94567	+	5.70145i	0.304004	+	0.249546i
$523$	−6.40138	−	6.40138i	−0.279913	−	0.279913i	0.553161	−	0.833074i	$-0.313421\pi$
$523$	−6.40138	−	6.40138i	−0.279913	−	0.279913i	−0.833074	+	0.553161i	$0.813421\pi$
$524$	16.4632	−	24.6271i	0.719198	−	1.07584i
$525$	14.9633	−	14.9633i	0.653054	−	0.653054i
$526$	2.70179	+	27.4629i	0.117804	+	1.19744i
$527$	−8.43675			−0.367510
$528$	−3.69619	+	1.52910i	−0.160856	+	0.0665455i
$529$	−44.8398			−1.94956
$530$	−0.183990	−	1.87021i	−0.00799203	−	0.0812365i
$531$	2.17677	−	2.17677i	0.0944639	−	0.0944639i
$532$	−53.4596	−	35.7376i	−2.31777	−	1.54942i
$533$	−17.6065	−	17.6065i	−0.762622	−	0.762622i
$534$	5.79438	+	4.75639i	0.250747	+	0.205829i
$535$			2.26807i			0.0980572i
$536$	−16.4080	+	30.6727i	−0.708716	+	1.32486i
$537$			6.28851i			0.271369i
$538$	7.46929	−	9.09930i	0.322024	−	0.392299i
$539$	12.0107	+	12.0107i	0.517339	+	0.517339i
$540$	−0.321198	−	1.61664i	−0.0138222	−	0.0695691i
$541$	7.83193	−	7.83193i	0.336721	−	0.336721i	−0.518411	−	0.855132i	$-0.673476\pi$
$541$	7.83193	−	7.83193i	0.336721	−	0.336721i	0.855132	+	0.518411i	$0.173476\pi$
$542$	18.7338	−	1.84303i	0.804687	−	0.0791649i
$543$	−17.3752			−0.745639
$544$	−11.0136	+	5.87909i	−0.472206	+	0.252064i
$545$	−0.744296			−0.0318821
$546$	16.8195	−	1.65470i	0.719808	−	0.0708146i
$547$	−9.88804	+	9.88804i	−0.422782	+	0.422782i	−0.886161	−	0.463378i	$-0.846637\pi$
$547$	−9.88804	+	9.88804i	−0.422782	+	0.422782i	0.463378	+	0.886161i	$0.346637\pi$
$548$	−7.37326	−	37.1107i	−0.314970	−	1.58529i
$549$	−2.35153	−	2.35153i	−0.100361	−	0.100361i
$550$	−3.87703	+	4.72311i	−0.165317	+	0.201394i
$551$		−	41.7148i		−	1.77711i
$552$	−20.5419	−	10.9886i	−0.874320	−	0.467707i
$553$		−	8.85057i		−	0.376365i
$554$	−0.531134	−	0.435989i	−0.0225657	−	0.0185234i
$555$	−3.83415	−	3.83415i	−0.162751	−	0.162751i
$556$	7.14270	+	4.77488i	0.302918	+	0.202500i
$557$	−11.7849	+	11.7849i	−0.499342	+	0.499342i	−0.911233	−	0.411891i	$-0.864868\pi$
$557$	−11.7849	+	11.7849i	−0.499342	+	0.499342i	0.411891	+	0.911233i	$0.364868\pi$
$558$	−0.529306	−	5.38023i	−0.0224073	−	0.227763i
$559$	−4.21194			−0.178146
$560$	−6.18486	+	14.9129i	−0.261358	+	0.630186i
$561$	2.20698			0.0931787
$562$	0.0254213	+	0.258399i	0.00107233	+	0.0108999i
$563$	−6.86919	+	6.86919i	−0.289502	+	0.289502i	−0.836883	−	0.547381i	$-0.815625\pi$
$563$	−6.86919	+	6.86919i	−0.289502	+	0.289502i	0.547381	+	0.836883i	$0.315625\pi$
$564$	10.8968	−	16.3005i	0.458839	−	0.686373i
$565$	0.406961	+	0.406961i	0.0171210	+	0.0171210i
$566$	19.0161	+	15.6096i	0.799304	+	0.656120i
$567$		−	4.89753i		−	0.205677i
$568$	7.74773	+	25.5714i	0.325088	+	1.07295i
$569$		−	2.65812i		−	0.111434i	−0.998447	−	0.0557170i	$-0.982256\pi$
$569$		−	2.65812i		−	0.111434i	0.998447	−	0.0557170i	$-0.0177445\pi$
$570$	−4.85466	+	5.91408i	−0.203339	+	0.247714i
$571$	−3.47521	−	3.47521i	−0.145433	−	0.145433i	0.630641	−	0.776074i	$-0.282792\pi$
$571$	−3.47521	−	3.47521i	−0.145433	−	0.145433i	−0.776074	+	0.630641i	$0.782792\pi$
$572$	−4.78670	+	0.951034i	−0.200142	+	0.0397647i
$573$	15.5409	−	15.5409i	0.649229	−	0.649229i
$574$	70.3356	−	6.91960i	2.93575	−	0.288819i
$575$	−35.5885			−1.48414
$576$	−4.44015	−	6.65470i	−0.185006	−	0.277279i
$577$	20.5740			0.856506			0.428253	−	0.903659i	$-0.359129\pi$
$577$	20.5740			0.856506			0.428253	+	0.903659i	$0.359129\pi$
$578$	−17.0709	+	1.67944i	−0.710057	+	0.0698553i
$579$	5.18877	−	5.18877i	0.215638	−	0.215638i
$580$	−10.2723	+	2.04092i	−0.426533	+	0.0847447i
$581$	−15.9110	−	15.9110i	−0.660100	−	0.660100i
$582$	6.49487	−	7.91224i	0.269221	−	0.327973i
$583$			1.61241i			0.0667792i
$584$	11.6690	+	38.5134i	0.482866	+	1.59370i
$585$		−	2.01096i		−	0.0831429i
$586$	3.38863	+	2.78160i	0.139983	+	0.114907i
$587$	3.77592	+	3.77592i	0.155849	+	0.155849i	0.780724	−	0.624875i	$-0.214850\pi$
$587$	3.77592	+	3.77592i	0.155849	+	0.155849i	−0.624875	+	0.780724i	$0.714850\pi$
$588$	−18.8798	+	28.2421i	−0.778590	+	1.16469i
$589$	−17.7459	+	17.7459i	−0.731208	+	0.731208i
$590$	0.351275	+	3.57060i	0.0144618	+	0.146999i
$591$	−7.54129			−0.310207
$592$	−24.3103	−	10.0822i	−0.999146	−	0.414377i
$593$	26.4648			1.08678			0.543390	−	0.839481i	$-0.317141\pi$
$593$	26.4648			1.08678			0.543390	+	0.839481i	$0.317141\pi$
$594$	0.138462	+	1.40742i	0.00568115	+	0.0577471i
$595$	6.29868	−	6.29868i	0.258221	−	0.258221i
$596$	27.8585	+	18.6233i	1.14113	+	0.762842i
$597$	−15.5313	−	15.5313i	−0.635652	−	0.635652i
$598$	−21.9693	−	18.0338i	−0.898391	−	0.737457i
$599$		−	6.53747i		−	0.267114i	−0.991041	−	0.133557i	$-0.957360\pi$
$599$		−	6.53747i		−	0.267114i	0.991041	−	0.133557i	$-0.0426399\pi$
$600$	−10.7762	−	5.76458i	−0.439936	−	0.235338i
$601$			13.0445i			0.532096i	0.963960	+	0.266048i	$0.0857179\pi$
$601$			13.0445i			0.532096i	−0.963960	+	0.266048i	$0.914282\pi$
$602$	7.58539	−	9.24074i	0.309157	−	0.376624i
$603$	8.69638	+	8.69638i	0.354144	+	0.354144i
$604$	5.70117	+	28.6949i	0.231977	+	1.16758i
$605$	−0.582740	+	0.582740i	−0.0236918	+	0.0236918i
$606$	−14.6639	+	1.44263i	−0.595680	+	0.0586029i
$607$	−10.2549			−0.416235			−0.208117	−	0.978104i	$-0.566734\pi$
$607$	−10.2549			−0.416235			−0.208117	+	0.978104i	$0.566734\pi$
$608$	−10.8001	+	35.5323i	−0.438000	+	1.44103i
$609$	−31.1193			−1.26102
$610$	3.85726	−	0.379476i	0.156176	−	0.0153645i
$611$	16.9155	−	16.9155i	0.684329	−	0.684329i
$612$	0.860163	+	4.32933i	0.0347700	+	0.175003i
$613$	6.91080	+	6.91080i	0.279125	+	0.279125i	0.832759	−	0.553635i	$-0.186760\pi$
$613$	6.91080	+	6.91080i	0.279125	+	0.279125i	−0.553635	+	0.832759i	$0.686760\pi$
$614$	6.01383	−	7.32622i	0.242698	−	0.295662i
$615$		−	8.40940i		−	0.339100i
$616$	6.53398	−	12.2145i	0.263261	−	0.492135i
$617$		−	2.64616i		−	0.106531i	−0.998580	−	0.0532653i	$-0.983037\pi$
$617$		−	2.64616i		−	0.106531i	0.998580	−	0.0532653i	$-0.0169629\pi$
$618$	8.54765	+	7.01645i	0.343837	+	0.282243i
$619$	−19.2581	−	19.2581i	−0.774050	−	0.774050i	0.204762	−	0.978812i	$-0.434358\pi$
$619$	−19.2581	−	19.2581i	−0.774050	−	0.774050i	−0.978812	+	0.204762i	$0.934358\pi$
$620$	5.23817	+	3.50171i	0.210370	+	0.140632i
$621$	−5.82408	+	5.82408i	−0.233712	+	0.233712i
$622$	0.258064	+	2.62314i	0.0103474	+	0.105178i
$623$	−25.9611			−1.04011
$624$	−3.73120	−	9.01919i	−0.149368	−	0.361057i
$625$	−15.2737			−0.610948
$626$	−0.398851	−	4.05420i	−0.0159413	−	0.162038i
$627$	4.64217	−	4.64217i	0.185391	−	0.185391i
$628$	0.341753	−	0.511224i	0.0136374	−	0.0204001i
$629$	10.2678	+	10.2678i	0.409404	+	0.409404i
$630$	4.41192	+	3.62159i	0.175775	+	0.144287i
$631$		−	14.1966i		−	0.565156i	−0.959244	−	0.282578i	$-0.908810\pi$
$631$		−	14.1966i		−	0.565156i	0.959244	−	0.282578i	$-0.0911896\pi$
$632$	−4.89179	+	1.48214i	−0.194585	+	0.0589563i
$633$		−	11.6981i		−	0.464957i
$634$	−13.4581	+	16.3951i	−0.534491	+	0.651132i
$635$	−6.33530	−	6.33530i	−0.251409	−	0.251409i
$636$	−3.16300	+	0.628433i	−0.125421	+	0.0249190i
$637$	−29.3078	+	29.3078i	−1.16122	+	1.16122i
$638$	8.94287	−	0.879798i	0.354052	−	0.0348315i
$639$	9.44670			0.373706
$640$	9.27824	+	0.921074i	0.366755	+	0.0364086i
$641$	−21.6912			−0.856753			−0.428376	−	0.903600i	$-0.640914\pi$
$641$	−21.6912			−0.856753			−0.428376	+	0.903600i	$0.640914\pi$
$642$	3.87338	−	0.381062i	0.152870	−	0.0150393i
$643$	32.7693	−	32.7693i	1.29229	−	1.29229i	0.358930	−	0.933365i	$-0.383142\pi$
$643$	32.7693	−	32.7693i	1.29229	−	1.29229i	0.933365	−	0.358930i	$-0.116858\pi$
$644$	79.1302	−	15.7218i	3.11817	−	0.619525i
$645$	−1.00588	−	1.00588i	−0.0396063	−	0.0396063i
$646$	13.0007	−	15.8378i	0.511505	−	0.623131i
$647$			49.5258i			1.94706i	0.228563	+	0.973529i	$0.426597\pi$
$647$			49.5258i			1.94706i	−0.228563	+	0.973529i	$0.573403\pi$
$648$	−2.70691	+	0.820152i	−0.106337	+	0.0322186i
$649$		−	3.07842i		−	0.120839i
$650$	−11.5250	−	9.46045i	−0.452048	−	0.371069i
$651$	13.2385	+	13.2385i	0.518858	+	0.518858i
$652$	−26.8298	+	40.1345i	−1.05074	+	1.57179i
$653$	−31.1015	+	31.1015i	−1.21710	+	1.21710i	−0.248450	+	0.968645i	$0.579921\pi$
$653$	−31.1015	+	31.1015i	−1.21710	+	1.21710i	−0.968645	+	0.248450i	$0.920079\pi$
$654$	0.125050	+	1.27110i	0.00488986	+	0.0497039i
$655$	12.2065			0.476948
$656$	−15.6031	−	37.7164i	−0.609199	−	1.47258i
$657$	14.2278			0.555081
$658$	6.64804	+	67.5753i	0.259168	+	2.63436i
$659$	12.4434	−	12.4434i	0.484727	−	0.484727i	−0.421911	−	0.906637i	$-0.638640\pi$
$659$	12.4434	−	12.4434i	0.484727	−	0.484727i	0.906637	+	0.421911i	$0.138640\pi$
$660$	−1.37026	−	0.916015i	−0.0533372	−	0.0356558i
$661$	22.2673	+	22.2673i	0.866098	+	0.866098i	0.992038	−	0.125940i	$-0.0401948\pi$
$661$	22.2673	+	22.2673i	0.866098	+	0.866098i	−0.125940	+	0.992038i	$0.540195\pi$
$662$	−13.9405	−	11.4432i	−0.541812	−	0.444754i
$663$			5.38531i			0.209148i
$664$	−6.12967	+	11.4587i	−0.237877	+	0.444683i
$665$		−	26.4974i		−	1.02753i
$666$	−5.90373	+	7.19209i	−0.228765	+	0.278688i
$667$	37.0067	+	37.0067i	1.43291	+	1.43291i
$668$	−1.57091	−	7.90665i	−0.0607805	−	0.305917i
$669$	17.6503	−	17.6503i	0.682401	−	0.682401i
$670$	−14.2648	+	1.40337i	−0.551099	+	0.0542170i
$671$	−3.32556			−0.128382
$672$	26.5072	+	8.05687i	1.02254	+	0.310800i
$673$	11.8771			0.457829			0.228914	−	0.973447i	$-0.426482\pi$
$673$	11.8771			0.457829			0.228914	+	0.973447i	$0.426482\pi$
$674$	28.1395	−	2.76836i	1.08389	−	0.106633i
$675$	−3.05529	+	3.05529i	−0.117598	+	0.117598i
$676$	2.74607	+	13.8214i	0.105618	+	0.531591i
$677$	−5.07654	−	5.07654i	−0.195107	−	0.195107i	0.602792	−	0.797899i	$-0.294055\pi$
$677$	−5.07654	−	5.07654i	−0.195107	−	0.195107i	−0.797899	+	0.602792i	$0.794055\pi$
$678$	0.626628	−	0.763376i	0.0240655	−	0.0293173i
$679$			35.4499i			1.36044i
$680$	−4.53613	−	2.42655i	−0.173953	−	0.0930538i
$681$			22.5192i			0.862938i
$682$	−4.17867	−	3.43012i	−0.160010	−	0.131346i
$683$	−9.91820	−	9.91820i	−0.379510	−	0.379510i	0.491416	−	0.870925i	$-0.336480\pi$
$683$	−9.91820	−	9.91820i	−0.379510	−	0.379510i	−0.870925	+	0.491416i	$0.836480\pi$
$684$	10.9156	+	7.29708i	0.417369	+	0.279011i
$685$	11.0243	−	11.0243i	0.421217	−	0.421217i
$686$	−6.77154	−	68.8306i	−0.258539	−	2.62796i
$687$	16.3030			0.621998
$688$	−6.37771	−	2.64504i	−0.243148	−	0.100841i
$689$	−3.93449			−0.149892
$690$	−0.939857	−	9.55335i	−0.0357797	−	0.363690i
$691$	−20.2640	+	20.2640i	−0.770880	+	0.770880i	−0.978260	−	0.207380i	$-0.933506\pi$
$691$	−20.2640	+	20.2640i	−0.770880	+	0.770880i	0.207380	+	0.978260i	$0.433506\pi$
$692$	10.7874	−	16.1367i	0.410074	−	0.613426i
$693$	−3.46307	−	3.46307i	−0.131551	−	0.131551i
$694$	−22.3437	−	18.3412i	−0.848156	−	0.696221i
$695$			3.54030i			0.134291i
$696$	5.21132	+	17.1999i	0.197535	+	0.651962i
$697$			22.5202i			0.853015i
$698$	25.7283	−	31.3429i	0.973829	−	1.18635i
$699$	−4.15640	−	4.15640i	−0.157210	−	0.157210i
$700$	41.5113	−	8.24758i	1.56898	−	0.311729i
$701$	3.05442	−	3.05442i	0.115364	−	0.115364i	−0.647068	−	0.762432i	$-0.724005\pi$
$701$	3.05442	−	3.05442i	0.115364	−	0.115364i	0.762432	+	0.647068i	$0.224005\pi$
$702$	−3.43429	+	0.337864i	−0.129619	+	0.0127519i
$703$	43.1947			1.62912
$704$	−7.84525	−	1.56592i	−0.295679	−	0.0590180i
$705$	8.07937			0.304287
$706$	14.4667	−	1.42323i	0.544462	−	0.0535641i
$707$	36.0818	−	36.0818i	1.35699	−	1.35699i
$708$	6.03881	−	1.19981i	0.226952	−	0.0450915i
$709$	8.62217	+	8.62217i	0.323812	+	0.323812i	0.850228	−	0.526415i	$-0.176464\pi$
$709$	8.62217	+	8.62217i	0.323812	+	0.323812i	−0.526415	+	0.850228i	$0.676464\pi$
$710$	−6.98558	+	8.51003i	−0.262164	+	0.319376i
$711$			1.80715i			0.0677735i
$712$	4.34750	+	14.3489i	0.162930	+	0.537749i
$713$		−	31.4861i		−	1.17917i
$714$	−11.8151	−	9.69855i	−0.442167	−	0.362959i
$715$	−1.42196	−	1.42196i	−0.0531784	−	0.0531784i
$716$	−6.98973	+	10.4559i	−0.261218	+	0.390754i
$717$	−0.0470217	+	0.0470217i	−0.00175606	+	0.00175606i
$718$	−1.60904	−	16.3554i	−0.0600488	−	0.610377i
$719$	24.8479			0.926670			0.463335	−	0.886183i	$-0.346653\pi$
$719$	24.8479			0.926670			0.463335	+	0.886183i	$0.346653\pi$
$720$	1.26285	−	3.04499i	0.0470638	−	0.113480i
$721$	−38.2968			−1.42625
$722$	−3.33687	−	33.9182i	−0.124185	−	1.26230i
$723$	−16.3456	+	16.3456i	−0.607898	+	0.607898i
$724$	−28.8896	−	19.3126i	−1.07367	−	0.717748i
$725$	19.4136	+	19.4136i	0.721002	+	0.721002i
$726$	1.09310	+	0.897288i	0.0405688	+	0.0333015i
$727$			14.2040i			0.526796i	0.964687	+	0.263398i	$0.0848433\pi$
$727$			14.2040i			0.526796i	−0.964687	+	0.263398i	$0.915157\pi$
$728$	29.8049	+	15.9437i	1.10464	+	0.590915i
$729$			1.00000i			0.0370370i
$730$	−10.5211	+	12.8171i	−0.389403	+	0.474382i
$731$	2.69372	+	2.69372i	0.0996307	+	0.0996307i
$732$	−1.29613	−	6.52361i	−0.0479063	−	0.241120i
$733$	7.98976	−	7.98976i	0.295109	−	0.295109i	−0.543986	−	0.839094i	$-0.683085\pi$
$733$	7.98976	−	7.98976i	0.295109	−	0.295109i	0.839094	+	0.543986i	$0.183085\pi$
$734$	−1.14442	+	0.112588i	−0.0422414	+	0.00415570i
$735$	−13.9983			−0.516335
$736$	−21.9409	−	41.1032i	−0.808753	−	1.51508i
$737$	12.2985			0.453023
$738$	−14.3615	+	1.41288i	−0.528652	+	0.0520087i
$739$	−25.9202	+	25.9202i	−0.953489	+	0.953489i	−0.998965	−	0.0454768i	$-0.985519\pi$
$739$	−25.9202	+	25.9202i	−0.953489	+	0.953489i	0.0454768	+	0.998965i	$0.485519\pi$
$740$	−2.11333	−	10.6367i	−0.0776875	−	0.391013i
$741$	11.3275	+	11.3275i	0.416126	+	0.416126i
$742$	7.08573	−	8.63204i	0.260125	−	0.316892i
$743$		−	23.5780i		−	0.864991i	−0.901636	−	0.432496i	$-0.857633\pi$
$743$		−	23.5780i		−	0.864991i	0.901636	−	0.432496i	$-0.142367\pi$
$744$	5.10009	−	9.53400i	0.186978	−	0.349533i
$745$			13.8081i			0.505891i
$746$	35.3648	+	29.0297i	1.29480	+	1.06285i
$747$	3.24879	+	3.24879i	0.118867	+	0.118867i
$748$	3.66953	+	2.45307i	0.134171	+	0.0896932i
$749$	−9.53077	+	9.53077i	−0.348247	+	0.348247i
$750$	−1.06359	−	10.8111i	−0.0388368	−	0.394764i
$751$	48.9405			1.78586			0.892931	−	0.450193i	$-0.148645\pi$
$751$	48.9405			1.78586			0.892931	+	0.450193i	$0.148645\pi$
$752$	36.2362	−	14.9908i	1.32140	−	0.546657i
$753$	−10.9194			−0.397925
$754$	2.14682	+	21.8218i	0.0781826	+	0.794702i
$755$	−8.52425	+	8.52425i	−0.310229	+	0.310229i
$756$	5.44364	−	8.14309i	0.197983	−	0.296161i
$757$	14.8100	+	14.8100i	0.538277	+	0.538277i	0.923023	−	0.384745i	$-0.125711\pi$
$757$	14.8100	+	14.8100i	0.538277	+	0.538277i	−0.384745	+	0.923023i	$0.625711\pi$
$758$	−4.96706	−	4.07728i	−0.180412	−	0.148094i
$759$			8.23649i			0.298966i
$760$	−14.6454	+	4.43732i	−0.531243	+	0.160959i
$761$		−	13.6678i		−	0.495456i	−0.968830	−	0.247728i	$-0.920316\pi$
$761$		−	13.6678i		−	0.495456i	0.968830	−	0.247728i	$-0.0796840\pi$
$762$	−9.75493	+	11.8837i	−0.353384	+	0.430503i
$763$	−3.12764	−	3.12764i	−0.113228	−	0.113228i
$764$	43.1135	−	8.56590i	1.55979	−	0.309903i
$765$	−1.28609	+	1.28609i	−0.0464988	+	0.0464988i
$766$	12.7921	−	1.25848i	0.462197	−	0.0454709i
$767$	7.51175			0.271234
$768$	0.0141446	−	16.0000i	0.000510398	−	0.577350i
$769$	7.88350			0.284286			0.142143	−	0.989846i	$-0.454601\pi$
$769$	7.88350			0.284286			0.142143	+	0.989846i	$0.454601\pi$
$770$	5.68055	−	0.558851i	0.204713	−	0.0201396i
$771$	−1.04055	+	1.04055i	−0.0374744	+	0.0374744i
$772$	14.3947	−	2.85998i	0.518077	−	0.102933i
$773$	10.1154	+	10.1154i	0.363826	+	0.363826i	0.865220	−	0.501393i	$-0.167179\pi$
$773$	10.1154	+	10.1154i	0.363826	+	0.363826i	−0.501393	+	0.865220i	$0.667179\pi$
$774$	−1.54882	+	1.88682i	−0.0556712	+	0.0678203i
$775$		−	16.5175i		−	0.593326i
$776$	19.5935	−	5.93653i	0.703366	−	0.213109i
$777$		−	32.2234i		−	1.15601i
$778$	12.8705	+	10.5649i	0.461431	+	0.378772i
$779$	47.3692	+	47.3692i	1.69718	+	1.69718i
$780$	2.23520	−	3.34361i	0.0800328	−	0.119720i
$781$	6.67983	−	6.67983i	0.239023	−	0.239023i
$782$	2.51692	+	25.5837i	0.0900049	+	0.914872i
$783$	6.35409			0.227077
$784$	−62.7827	+	25.9729i	−2.24224	+	0.927605i
$785$	0.253390			0.00904387
$786$	−2.05084	−	20.8461i	−0.0731509	−	0.743556i
$787$	−15.5278	+	15.5278i	−0.553508	+	0.553508i	−0.927452	−	0.373943i	$-0.878005\pi$
$787$	−15.5278	+	15.5278i	−0.553508	+	0.553508i	0.373943	+	0.927452i	$0.378005\pi$
$788$	−12.5389	−	8.38220i	−0.446678	−	0.298604i
$789$	13.7977	+	13.7977i	0.491212	+	0.491212i
$790$	−1.62797	−	1.33634i	−0.0579204	−	0.0475448i
$791$			3.42022i			0.121609i
$792$	−1.33414	+	2.49401i	−0.0474065	+	0.0886207i
$793$		−	8.11480i		−	0.288165i
$794$	−19.6415	+	23.9278i	−0.697050	+	0.849166i
$795$	−0.939617	−	0.939617i	−0.0333248	−	0.0333248i
$796$	−8.56060	−	43.0868i	−0.303423	−	1.52717i
$797$	31.0037	−	31.0037i	1.09821	−	1.09821i	0.103586	−	0.994620i	$-0.466968\pi$
$797$	31.0037	−	31.0037i	1.09821	−	1.09821i	0.994620	−	0.103586i	$-0.0330317\pi$
$798$	−45.2519	+	4.45187i	−1.60190	+	0.157595i
$799$	−21.6364			−0.765442
$800$	−11.5101	−	21.5625i	−0.406944	−	0.762351i
$801$	5.30085			0.187296
$802$	12.0020	−	1.18075i	0.423805	−	0.0416939i
$803$	10.0606	−	10.0606i	0.355031	−	0.355031i
$804$	4.79332	+	24.1255i	0.169047	+	0.850841i
$805$	23.5068	+	23.5068i	0.828507	+	0.828507i
$806$	8.36993	−	10.1965i	0.294818	−	0.359156i
$807$		−	8.32429i		−	0.293029i
$808$	−25.9851	−	13.9004i	−0.914152	−	0.489014i
$809$		−	31.8240i		−	1.11887i	−0.828874	−	0.559436i	$-0.811018\pi$
$809$		−	31.8240i		−	1.11887i	0.828874	−	0.559436i	$-0.188982\pi$
$810$	−0.900847	−	0.739473i	−0.0316525	−	0.0259824i
$811$	−27.7285	−	27.7285i	−0.973678	−	0.973678i	0.0259841	−	0.999662i	$-0.491728\pi$
$811$	−27.7285	−	27.7285i	−0.973678	−	0.973678i	−0.999662	+	0.0259841i	$0.991728\pi$
$812$	−51.7419	−	34.5894i	−1.81578	−	1.21385i
$813$	9.41213	−	9.41213i	0.330098	−	0.330098i
$814$	0.911011	+	9.26014i	0.0319309	+	0.324568i
$815$	−19.8928			−0.696814
$816$	−3.38190	+	8.15443i	−0.118390	+	0.285462i
$817$	11.3320			0.396456
$818$	0.132832	+	1.35020i	0.00464436	+	0.0472085i
$819$	8.45035	−	8.45035i	0.295279	−	0.295279i
$820$	9.34711	−	13.9823i	0.326415	−	0.488281i
$821$	1.84278	+	1.84278i	0.0643133	+	0.0643133i	0.738532	−	0.674219i	$-0.235519\pi$
$821$	1.84278	+	1.84278i	0.0643133	+	0.0643133i	−0.674219	+	0.738532i	$0.735519\pi$
$822$	−20.6794	−	16.9749i	−0.721276	−	0.592069i
$823$		−	47.7183i		−	1.66336i	−0.555259	−	0.831678i	$-0.687381\pi$
$823$		−	47.7183i		−	1.66336i	0.555259	−	0.831678i	$-0.312619\pi$
$824$	6.41327	+	21.1670i	0.223417	+	0.737387i
$825$			4.32083i			0.150432i
$826$	−13.5281	+	16.4803i	−0.470703	+	0.573424i
$827$	10.0174	+	10.0174i	0.348341	+	0.348341i	0.859491	−	0.511151i	$-0.170781\pi$
$827$	10.0174	+	10.0174i	0.348341	+	0.348341i	−0.511151	+	0.859491i	$0.670781\pi$
$828$	−16.1572	+	3.21015i	−0.561500	+	0.111560i
$829$	22.1564	−	22.1564i	0.769524	−	0.769524i	−0.208498	−	0.978023i	$-0.566858\pi$
$829$	22.1564	−	22.1564i	0.769524	−	0.769524i	0.978023	+	0.208498i	$0.0668576\pi$
$830$	−5.32905	+	0.524271i	−0.184974	+	0.0181977i
$831$	−0.485896			−0.0168556
$832$	3.82106	−	19.1434i	0.132471	−	0.663679i
$833$	37.4872			1.29885
$834$	6.04608	−	0.594812i	0.209358	−	0.0205966i
$835$	2.34879	−	2.34879i	0.0812833	−	0.0812833i
$836$	12.8783	−	2.55870i	0.445406	−	0.0884945i
$837$	−2.70310	−	2.70310i	−0.0934328	−	0.0934328i
$838$	−20.2401	+	24.6570i	−0.699181	+	0.851763i
$839$			1.68311i			0.0581073i	0.999578	+	0.0290537i	$0.00924937\pi$
$839$			1.68311i			0.0581073i	−0.999578	+	0.0290537i	$0.990751\pi$
$840$	3.31025	+	10.9255i	0.114215	+	0.376965i
$841$		−	11.3745i		−	0.392223i
$842$	10.4953	+	8.61517i	0.361690	+	0.296898i
$843$	0.129823	+	0.129823i	0.00447135	+	0.00447135i
$844$	13.0025	−	19.4503i	0.447565	−	0.669507i
$845$	−4.10585	+	4.10585i	−0.141246	+	0.141246i
$846$	−1.35743	−	13.7978i	−0.0466694	−	0.474379i
$847$	−4.89753			−0.168281
$848$	−5.95760	−	2.47081i	−0.204585	−	0.0848478i
$849$	17.3964			0.597043
$850$	1.32037	+	13.4211i	0.0452882	+	0.460340i
$851$	−38.3196	+	38.3196i	−1.31358	+	1.31358i
$852$	15.7070	+	10.5001i	0.538112	+	0.359727i
$853$	−10.3815	−	10.3815i	−0.355455	−	0.355455i	0.506680	−	0.862134i	$-0.330873\pi$
$853$	−10.3815	−	10.3815i	−0.355455	−	0.355455i	−0.862134	+	0.506680i	$0.830873\pi$
$854$	17.8034	+	14.6142i	0.609220	+	0.500086i
$855$			5.41036i			0.185031i
$856$	6.86379	+	3.67170i	0.234600	+	0.125496i
$857$		−	42.3908i		−	1.44804i	−0.689777	−	0.724022i	$-0.742291\pi$
$857$		−	42.3908i		−	1.44804i	0.689777	−	0.724022i	$-0.257709\pi$
$858$	−2.18950	+	2.66731i	−0.0747483	+	0.0910605i
$859$	27.7450	+	27.7450i	0.946649	+	0.946649i	0.998647	−	0.0519984i	$-0.0165591\pi$
$859$	27.7450	+	27.7450i	0.946649	+	0.946649i	−0.0519984	+	0.998647i	$0.516559\pi$
$860$	−0.554424	−	2.79050i	−0.0189057	−	0.0951553i
$861$	35.3376	−	35.3376i	1.20430	−	1.20430i
$862$	−7.69095	+	0.756634i	−0.261955	+	0.0257711i
$863$	0.888441			0.0302429			0.0151214	−	0.999886i	$-0.495187\pi$
$863$	0.888441			0.0302429			0.0151214	+	0.999886i	$0.495187\pi$
$864$	−5.41236	−	1.64509i	−0.184132	−	0.0559671i
$865$	7.99822			0.271947
$866$	47.5971	−	4.68259i	1.61741	−	0.159121i
$867$	−8.57668	+	8.57668i	−0.291279	+	0.291279i
$868$	7.29687	+	36.7263i	0.247672	+	1.24657i
$869$	1.27785	+	1.27785i	0.0433481	+	0.0433481i
$870$	−4.69868	+	5.72406i	−0.159300	+	0.194064i
$871$			30.0100i			1.01685i
$872$	−1.20491	+	2.25244i	−0.0408036	+	0.0762773i
$873$		−	7.23833i		−	0.244981i
$874$	59.1071	+	48.5189i	1.99933	+	1.64118i
$875$	26.6015	+	26.6015i	0.899295	+	0.899295i
$876$	23.6565	+	15.8144i	0.799280	+	0.534318i
$877$	21.6802	−	21.6802i	0.732089	−	0.732089i	−0.238944	−	0.971033i	$-0.576801\pi$
$877$	21.6802	−	21.6802i	0.732089	−	0.732089i	0.971033	+	0.238944i	$0.0768014\pi$
$878$	−2.88870	−	29.3628i	−0.0974890	−	0.990945i
$879$	3.10001			0.104561
$880$	−1.26016	−	3.04610i	−0.0424800	−	0.102684i
$881$	5.60419			0.188810			0.0944050	−	0.995534i	$-0.469905\pi$
$881$	5.60419			0.188810			0.0944050	+	0.995534i	$0.469905\pi$
$882$	2.35188	+	23.9061i	0.0791918	+	0.804960i
$883$	−13.8664	+	13.8664i	−0.466641	+	0.466641i	−0.900825	−	0.434183i	$-0.857037\pi$
$883$	−13.8664	+	13.8664i	−0.466641	+	0.466641i	0.434183	+	0.900825i	$0.357037\pi$
$884$	−5.98582	+	8.95412i	−0.201325	+	0.301160i
$885$	1.79392	+	1.79392i	0.0603020	+	0.0603020i
$886$	−37.0823	−	30.4395i	−1.24580	−	1.02264i
$887$			55.7634i			1.87235i	0.351533	+	0.936176i	$0.385661\pi$
$887$			55.7634i			1.87235i	−0.351533	+	0.936176i	$0.614339\pi$
$888$	−17.8102	+	5.39620i	−0.597670	+	0.181085i
$889$		−	53.2438i		−	1.78574i
$890$	−3.91984	+	4.77526i	−0.131393	+	0.160067i
$891$	0.707107	+	0.707107i	0.0236890	+	0.0236890i
$892$	48.9656	−	9.72861i	1.63949	−	0.325738i
$893$	−45.5102	+	45.5102i	−1.52294	+	1.52294i
$894$	23.5813	−	2.31993i	0.788678	−	0.0775900i
$895$	−5.18248			−0.173231
$896$	35.1181	+	42.8591i	1.17321	+	1.43182i
$897$	−20.0981			−0.671056
$898$	−33.2902	+	3.27508i	−1.11091	+	0.109291i
$899$	−17.1757	+	17.1757i	−0.572843	+	0.572843i
$900$	−8.47598	+	1.68403i	−0.282533	+	0.0561343i
$901$	2.51628	+	2.51628i	0.0838294	+	0.0838294i
$902$	−9.15603	+	11.1541i	−0.304862	+	0.371392i
$903$		−	8.45368i		−	0.281321i
$904$	1.89039	−	0.572759i	0.0628734	−	0.0190497i
$905$		−	14.3192i		−	0.475986i
$906$	15.9898	+	13.1254i	0.531225	+	0.436063i
$907$	−31.3840	−	31.3840i	−1.04209	−	1.04209i	−0.999075	−	0.0430131i	$-0.986304\pi$
$907$	−31.3840	−	31.3840i	−1.04209	−	1.04209i	−0.0430131	−	0.999075i	$-0.513696\pi$
$908$	−25.0303	+	37.4426i	−0.830659	+	1.24257i
$909$	−7.36735	+	7.36735i	−0.244359	+	0.244359i
$910$	1.36367	+	13.8613i	0.0452052	+	0.459497i
$911$	−24.5585			−0.813661			−0.406831	−	0.913504i	$-0.633366\pi$
$911$	−24.5585			−0.813661			−0.406831	+	0.913504i	$0.633366\pi$
$912$	10.0386	+	24.2656i	0.332411	+	0.803515i
$913$	4.59448			0.152055
$914$	0.117134	+	1.19063i	0.00387444	+	0.0393824i
$915$	1.93794	−	1.93794i	0.0640663	−	0.0640663i
$916$	27.1069	+	18.1209i	0.895636	+	0.598731i
$917$	51.2936	+	51.2936i	1.69386	+	1.69386i
$918$	2.41245	+	1.98030i	0.0796228	+	0.0653595i
$919$		−	55.9358i		−	1.84515i	−0.385815	−	0.922576i	$-0.626080\pi$
$919$		−	55.9358i		−	1.84515i	0.385815	−	0.922576i	$-0.373920\pi$
$920$	9.05593	−	16.9290i	0.298565	−	0.558131i
$921$		−	6.70222i		−	0.220846i
$922$	−9.78249	+	11.9173i	−0.322169	+	0.392476i
$923$	16.2996	+	16.2996i	0.536509	+	0.536509i
$924$	−1.90880	−	9.60726i	−0.0627948	−	0.316056i
$925$	−20.1023	+	20.1023i	−0.660960	+	0.660960i
$926$	−41.7062	+	4.10305i	−1.37055	+	0.134835i
$927$	7.81962			0.256830
$928$	−10.4530	+	34.3907i	−0.343138	+	1.12893i
$929$	26.9636			0.884647			0.442324	−	0.896856i	$-0.354154\pi$
$929$	26.9636			0.884647			0.442324	+	0.896856i	$0.354154\pi$
$930$	4.43395	−	0.436211i	0.145395	−	0.0143039i
$931$	78.8509	−	78.8509i	2.58423	−	2.58423i
$932$	−2.29095	−	11.5307i	−0.0750426	−	0.377701i
$933$	1.31790	+	1.31790i	0.0431462	+	0.0431462i
$934$	−28.0743	+	34.2009i	−0.918618	+	1.11909i
$935$			1.81881i			0.0594815i
$936$	−6.08570	−	3.25547i	−0.198917	−	0.106408i
$937$			46.8857i			1.53169i	0.643027	+	0.765844i	$0.277678\pi$
$937$			46.8857i			1.53169i	−0.643027	+	0.765844i	$0.722322\pi$
$938$	−65.8402	−	54.0459i	−2.14976	−	1.76466i
$939$	−2.03688	−	2.03688i	−0.0664712	−	0.0664712i
$940$	13.4335	+	8.98029i	0.438153	+	0.292905i
$941$	−26.1894	+	26.1894i	−0.853752	+	0.853752i	−0.990593	−	0.136841i	$-0.956305\pi$
$941$	−26.1894	+	26.1894i	−0.853752	+	0.853752i	0.136841	+	0.990593i	$0.456305\pi$
$942$	−0.0425724	−	0.432736i	−0.00138709	−	0.0140993i
$943$	−84.0460			−2.73692
$944$	11.3743	+	4.71727i	0.370201	+	0.153534i
$945$	4.03614			0.131296
$946$	0.239000	+	2.42936i	0.00777057	+	0.0789854i
$947$	30.1063	−	30.1063i	0.978322	−	0.978322i	−0.0214476	−	0.999770i	$-0.506828\pi$
$947$	30.1063	−	30.1063i	0.978322	−	0.978322i	0.999770	+	0.0214476i	$0.00682751\pi$
$948$	−2.00866	+	3.00474i	−0.0652383	+	0.0975894i
$949$	24.5492	+	24.5492i	0.796900	+	0.796900i
$950$	31.0073	+	25.4528i	1.00601	+	0.825798i
$951$			14.9987i			0.486365i
$952$	−8.86480	−	29.2582i	−0.287310	−	0.948265i
$953$		−	34.2473i		−	1.10938i	−0.832057	−	0.554690i	$-0.812837\pi$
$953$		−	34.2473i		−	1.10938i	0.832057	−	0.554690i	$-0.187163\pi$
$954$	−1.44680	+	1.76253i	−0.0468418	+	0.0570641i
$955$	12.8075	+	12.8075i	0.414442	+	0.414442i
$956$	−0.130448	+	0.0259177i	−0.00421898	+	0.000838238i
$957$	4.49302	−	4.49302i	0.145239	−	0.145239i
$958$	15.2768	−	1.50293i	0.493570	−	0.0485573i
$959$	92.6517			2.99188
$960$	5.48427	−	3.65921i	0.177004	−	0.118101i
$961$	−16.3865			−0.528597
$962$	−22.5959	+	2.22298i	−0.728522	+	0.0716719i
$963$	1.94604	−	1.94604i	0.0627102	−	0.0627102i
$964$	−45.3459	+	9.00944i	−1.46049	+	0.290174i
$965$	4.27617	+	4.27617i	0.137655	+	0.137655i
$966$	36.1952	−	44.0941i	1.16456	−	1.41870i
$967$			26.2775i			0.845029i	0.906356	+	0.422514i	$0.138852\pi$
$967$			26.2775i			0.845029i	−0.906356	+	0.422514i	$0.861148\pi$
$968$	0.820152	+	2.70691i	0.0263607	+	0.0870033i
$969$		−	14.4889i		−	0.465449i
$970$	6.52063	+	5.35255i	0.209365	+	0.171860i
$971$	−15.2593	−	15.2593i	−0.489695	−	0.489695i	0.418515	−	0.908210i	$-0.362551\pi$
$971$	−15.2593	−	15.2593i	−0.489695	−	0.489695i	−0.908210	+	0.418515i	$0.862551\pi$
$972$	−1.11151	+	1.66269i	−0.0356516	+	0.0533309i
$973$	−14.8769	+	14.8769i	−0.476931	+	0.476931i
$974$	0.861670	+	8.75860i	0.0276097	+	0.280644i
$975$	−10.5434			−0.337658
$976$	5.09598	−	12.2874i	0.163118	−	0.393311i
$977$	12.4229			0.397445			0.198723	−	0.980056i	$-0.436321\pi$
$977$	12.4229			0.397445			0.198723	+	0.980056i	$0.436321\pi$
$978$	3.34222	+	33.9726i	0.106872	+	1.08632i
$979$	3.74827	−	3.74827i	0.119795	−	0.119795i
$980$	−23.2749	−	15.5592i	−0.743488	−	0.497021i
$981$	0.638617	+	0.638617i	0.0203895	+	0.0203895i
$982$	−41.2930	−	33.8959i	−1.31771	−	1.08166i
$983$		−	21.4959i		−	0.685613i	−0.939406	−	0.342807i	$-0.888622\pi$
$983$		−	21.4959i		−	0.685613i	0.939406	−	0.342807i	$-0.111378\pi$
$984$	−25.4491	−	13.6137i	−0.811288	−	0.433988i
$985$		−	6.21492i		−	0.198024i
$986$	12.5830	−	15.3289i	0.400724	−	0.488173i
$987$	33.9507	+	33.9507i	1.08066	+	1.08066i
$988$	6.24356	+	31.4248i	0.198634	+	0.999756i
$989$	−10.0530	+	10.0530i	−0.319667	+	0.319667i
$990$	−1.15988	+	0.114109i	−0.0368634	+	0.00362662i
$991$	17.3220			0.550251			0.275126	−	0.961408i	$-0.411281\pi$
$991$	17.3220			0.550251			0.275126	+	0.961408i	$0.411281\pi$
$992$	19.0770	−	10.1833i	0.605695	−	0.323321i
$993$	−12.7531			−0.404708
$994$	−65.1149	+	6.40599i	−2.06532	+	0.203186i
$995$	12.7996	−	12.7996i	0.405775	−	0.405775i
$996$	1.79068	+	9.01279i	0.0567400	+	0.285581i
$997$	−8.28691	−	8.28691i	−0.262449	−	0.262449i	0.563599	−	0.826048i	$-0.309416\pi$
$997$	−8.28691	−	8.28691i	−0.262449	−	0.262449i	−0.826048	+	0.563599i	$0.809416\pi$
$998$	14.3888	−	17.5289i	0.455470	−	0.554866i
$999$			6.57952i			0.208167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.t.b.133.19	✓	40
4.3	odd	2		2112.2.t.b.1585.5		40
16.3	odd	4		2112.2.t.b.529.5		40
16.13	even	4	inner	528.2.t.b.397.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
528.2.t.b.133.19	✓	40	1.1	even	1	trivial
528.2.t.b.397.19	yes	40	16.13	even	4	inner
2112.2.t.b.529.5		40	16.3	odd	4
2112.2.t.b.1585.5		40	4.3	odd	2

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40742 - 0.138462i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.96166 - 0.389747i) q^{4} +(0.582740 + 0.582740i) q^{5} +(0.897288 - 1.09310i) q^{6} +4.89753i q^{7} +(2.70691 - 0.820152i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.40742 - 0.138462i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.96166 - 0.389747i) q^{4} +(0.582740 + 0.582740i) q^{5} +(0.897288 - 1.09310i) q^{6} +4.89753i q^{7} +(2.70691 - 0.820152i) q^{8} -1.00000i q^{9} +(0.900847 + 0.739473i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(1.11151 - 1.66269i) q^{12} +(1.72543 - 1.72543i) q^{13} +(0.678119 + 6.89287i) q^{14} +0.824119 q^{15} +(3.69619 - 1.52910i) q^{16} -2.20698 q^{17} +(-0.138462 - 1.40742i) q^{18} +(-4.64217 + 4.64217i) q^{19} +(1.37026 + 0.916015i) q^{20} +(3.46307 + 3.46307i) q^{21} +(-1.09310 - 0.897288i) q^{22} -8.23649i q^{23} +(1.33414 - 2.49401i) q^{24} -4.32083i q^{25} +(2.18950 - 2.66731i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.90880 + 9.60726i) q^{28} +(-4.49302 + 4.49302i) q^{29} +(1.15988 - 0.114109i) q^{30} +3.82276 q^{31} +(4.99037 - 2.66387i) q^{32} -1.00000 q^{33} +(-3.10614 + 0.305582i) q^{34} +(-2.85399 + 2.85399i) q^{35} +(-0.389747 - 1.96166i) q^{36} +(-4.65242 - 4.65242i) q^{37} +(-5.89072 + 7.17625i) q^{38} -2.44013i q^{39} +(2.05536 + 1.09949i) q^{40} -10.2041i q^{41} +(5.35350 + 4.39449i) q^{42} +(-1.22055 - 1.22055i) q^{43} +(-1.66269 - 1.11151i) q^{44} +(0.582740 - 0.582740i) q^{45} +(-1.14044 - 11.5922i) q^{46} +9.80364 q^{47} +(1.53237 - 3.69484i) q^{48} -16.9858 q^{49} +(-0.598269 - 6.08122i) q^{50} +(-1.56057 + 1.56057i) q^{51} +(2.71222 - 4.05719i) q^{52} +(-1.14015 - 1.14015i) q^{53} +(-1.09310 - 0.897288i) q^{54} -0.824119i q^{55} +(4.01671 + 13.2572i) q^{56} +6.56503i q^{57} +(-5.70145 + 6.94567i) q^{58} +(2.17677 + 2.17677i) q^{59} +(1.61664 - 0.321198i) q^{60} +(2.35153 - 2.35153i) q^{61} +(5.38023 - 0.529306i) q^{62} +4.89753 q^{63} +(6.65470 - 4.44015i) q^{64} +2.01096 q^{65} +(-1.40742 + 0.138462i) q^{66} +(-8.69638 + 8.69638i) q^{67} +(-4.32933 + 0.860163i) q^{68} +(-5.82408 - 5.82408i) q^{69} +(-3.62159 + 4.41192i) q^{70} +9.44670i q^{71} +(-0.820152 - 2.70691i) q^{72} +14.2278i q^{73} +(-7.19209 - 5.90373i) q^{74} +(-3.05529 - 3.05529i) q^{75} +(-7.29708 + 10.9156i) q^{76} +(3.46307 - 3.46307i) q^{77} +(-0.337864 - 3.43429i) q^{78} -1.80715 q^{79} +(3.04499 + 1.26285i) q^{80} -1.00000 q^{81} +(-1.41288 - 14.3615i) q^{82} +(-3.24879 + 3.24879i) q^{83} +(8.14309 + 5.44364i) q^{84} +(-1.28609 - 1.28609i) q^{85} +(-1.88682 - 1.54882i) q^{86} +6.35409i q^{87} +(-2.49401 - 1.33414i) q^{88} +5.30085i q^{89} +(0.739473 - 0.900847i) q^{90} +(8.45035 + 8.45035i) q^{91} +(-3.21015 - 16.1572i) q^{92} +(2.70310 - 2.70310i) q^{93} +(13.7978 - 1.35743i) q^{94} -5.41036 q^{95} +(1.64509 - 5.41236i) q^{96} +7.23833 q^{97} +(-23.9061 + 2.35188i) q^{98} +(-0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{8}+O(q^{10}) \) 40 * q + 12 * q^8	\( 40 q + 12 q^{8} + 8 q^{10} + 16 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{24} - 20 q^{28} + 20 q^{30} + 8 q^{31} + 40 q^{32} - 40 q^{33} + 20 q^{34} - 24 q^{35} + 4 q^{36} - 60 q^{38} - 56 q^{40} + 20 q^{42} + 8 q^{44} + 76 q^{46} - 64 q^{47} + 32 q^{48} - 40 q^{49} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{54} - 20 q^{56} + 12 q^{58} - 16 q^{59} - 12 q^{60} - 64 q^{61} + 68 q^{62} + 24 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{67} - 4 q^{68} - 16 q^{69} - 116 q^{70} - 12 q^{76} + 28 q^{78} - 72 q^{79} + 40 q^{80} - 40 q^{81} - 24 q^{82} + 16 q^{85} - 64 q^{86} - 12 q^{90} + 16 q^{91} + 20 q^{92} + 32 q^{93} + 104 q^{94} + 128 q^{95} - 20 q^{96} - 32 q^{97} + 36 q^{98}+O(q^{100}) \) 40 * q + 12 * q^8 + 8 * q^10 + 16 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^24 - 20 * q^28 + 20 * q^30 + 8 * q^31 + 40 * q^32 - 40 * q^33 + 20 * q^34 - 24 * q^35 + 4 * q^36 - 60 * q^38 - 56 * q^40 + 20 * q^42 + 8 * q^44 + 76 * q^46 - 64 * q^47 + 32 * q^48 - 40 * q^49 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^54 - 20 * q^56 + 12 * q^58 - 16 * q^59 - 12 * q^60 - 64 * q^61 + 68 * q^62 + 24 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^67 - 4 * q^68 - 16 * q^69 - 116 * q^70 - 12 * q^76 + 28 * q^78 - 72 * q^79 + 40 * q^80 - 40 * q^81 - 24 * q^82 + 16 * q^85 - 64 * q^86 - 12 * q^90 + 16 * q^91 + 20 * q^92 + 32 * q^93 + 104 * q^94 + 128 * q^95 - 20 * q^96 - 32 * q^97 + 36 * q^98

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