LMFDB - Embedded newform 525.2.z.a.64.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.12
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14001 + 1.56909i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.544387 + 1.67545i) q^{4} +(-1.00833 + 1.99581i) q^{5} +(0.599339 + 1.84458i) q^{6} +1.00000i q^{7} +(0.439612 - 0.142839i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.14001 + 1.56909i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.544387 + 1.67545i) q^{4} +(-1.00833 + 1.99581i) q^{5} +(0.599339 + 1.84458i) q^{6} +1.00000i q^{7} +(0.439612 - 0.142839i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.28112 + 0.693093i) q^{10} +(-0.855237 + 0.621366i) q^{11} +(-1.03549 + 1.42522i) q^{12} +(0.0443250 - 0.0610082i) q^{13} +(-1.56909 + 1.14001i) q^{14} +(-1.57572 + 1.58654i) q^{15} +(3.57574 + 2.59793i) q^{16} +(-2.01572 + 0.654946i) q^{17} +1.93950i q^{18} +(-1.04665 - 3.22124i) q^{19} +(-2.79497 - 2.77590i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(-1.94996 - 0.633580i) q^{22} +(2.76753 + 3.80918i) q^{23} +0.462236 q^{24} +(-2.96655 - 4.02487i) q^{25} +0.146258 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.67545 - 0.544387i) q^{28} +(1.27031 - 3.90962i) q^{29} +(-4.28576 - 0.663768i) q^{30} +(-0.504631 - 1.55309i) q^{31} +7.64785i q^{32} +(-1.00539 + 0.326671i) q^{33} +(-3.32561 - 2.41620i) q^{34} +(-1.99581 - 1.00833i) q^{35} +(-1.42522 + 1.03549i) q^{36} +(1.25799 - 1.73148i) q^{37} +(3.86124 - 5.31454i) q^{38} +(0.0610082 - 0.0443250i) q^{39} +(-0.158194 + 1.02141i) q^{40} +(2.55050 + 1.85304i) q^{41} +(-1.84458 + 0.599339i) q^{42} -5.25850i q^{43} +(-0.575488 - 1.77117i) q^{44} +(-1.98886 + 1.02197i) q^{45} +(-2.82193 + 8.68501i) q^{46} +(0.318103 + 0.103358i) q^{47} +(2.59793 + 3.57574i) q^{48} -1.00000 q^{49} +(2.93349 - 9.24319i) q^{50} -2.11945 q^{51} +(0.0780862 + 0.107476i) q^{52} +(12.5720 + 4.08489i) q^{53} +(-0.599339 + 1.84458i) q^{54} +(-0.377772 - 2.33343i) q^{55} +(0.142839 + 0.439612i) q^{56} -3.38701i q^{57} +(7.58272 - 2.46378i) q^{58} +(0.133678 + 0.0971226i) q^{59} +(-1.80037 - 3.50373i) q^{60} +(3.22703 - 2.34457i) q^{61} +(1.86166 - 2.56236i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(-4.84870 + 3.52279i) q^{64} +(0.0770668 + 0.149981i) q^{65} +(-1.65873 - 1.20514i) q^{66} +(0.365694 - 0.118821i) q^{67} -3.73378i q^{68} +(1.45498 + 4.47796i) q^{69} +(-0.693093 - 4.28112i) q^{70} +(2.05993 - 6.33981i) q^{71} +(0.439612 + 0.142839i) q^{72} +(-3.55355 - 4.89104i) q^{73} +4.15098 q^{74} +(-1.57760 - 4.74459i) q^{75} +5.96681 q^{76} +(-0.621366 - 0.855237i) q^{77} +(0.139100 + 0.0451963i) q^{78} +(3.27129 - 10.0680i) q^{79} +(-8.79049 + 4.51695i) q^{80} +(0.309017 + 0.951057i) q^{81} +6.11445i q^{82} +(14.5719 - 4.73471i) q^{83} +(-1.42522 - 1.03549i) q^{84} +(0.725353 - 4.68340i) q^{85} +(8.25106 - 5.99475i) q^{86} +(2.41628 - 3.32572i) q^{87} +(-0.287217 + 0.395321i) q^{88} +(-13.8211 + 10.0417i) q^{89} +(-3.87089 - 1.95566i) q^{90} +(0.0610082 + 0.0443250i) q^{91} +(-7.88870 + 2.56319i) q^{92} -1.63302i q^{93} +(0.200463 + 0.616962i) q^{94} +(7.48436 + 1.15916i) q^{95} +(-2.36332 + 7.27354i) q^{96} +(-5.03842 - 1.63708i) q^{97} +(-1.14001 - 1.56909i) q^{98} -1.05713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	1.14001	+	1.56909i	0.806110	+	1.10951i	0.991912	+	0.126928i	$0.0405117\pi$
$2$	1.14001	+	1.56909i	0.806110	+	1.10951i	−0.185802	+	0.982587i	$0.559488\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.544387	+	1.67545i	−0.272193	+	0.837725i
$5$	−1.00833	+	1.99581i	−0.450938	+	0.892555i
$5$	−1.00833	+	1.99581i	−0.450938	+	0.892555i
$6$	0.599339	+	1.84458i	0.244679	+	0.753046i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.439612	−	0.142839i	0.155426	−	0.0505011i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−4.28112	+	0.693093i	−1.35381	+	0.219175i
$11$	−0.855237	+	0.621366i	−0.257864	+	0.187349i	−0.709205	−	0.705003i	$-0.750946\pi$
$11$	−0.855237	+	0.621366i	−0.257864	+	0.187349i	0.451341	+	0.892352i	$0.350946\pi$
$12$	−1.03549	+	1.42522i	−0.298919	+	0.411427i
$13$	0.0443250	−	0.0610082i	0.0122935	−	0.0169206i	−0.802826	−	0.596213i	$-0.796671\pi$
$13$	0.0443250	−	0.0610082i	0.0122935	−	0.0169206i	0.815120	+	0.579293i	$0.196671\pi$
$14$	−1.56909	+	1.14001i	−0.419357	+	0.304681i
$15$	−1.57572	+	1.58654i	−0.406848	+	0.409643i
$16$	3.57574	+	2.59793i	0.893934	+	0.649481i
$17$	−2.01572	+	0.654946i	−0.488883	+	0.158848i	−0.543077	−	0.839683i	$-0.682741\pi$
$17$	−2.01572	+	0.654946i	−0.488883	+	0.158848i	0.0541942	+	0.998530i	$0.482741\pi$
$18$			1.93950i			0.457145i
$19$	−1.04665	−	3.22124i	−0.240117	−	0.739004i	−0.996401	−	0.0847608i	$-0.972987\pi$
$19$	−1.04665	−	3.22124i	−0.240117	−	0.739004i	0.756284	−	0.654243i	$-0.227013\pi$
$20$	−2.79497	−	2.77590i	−0.624974	−	0.620710i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	−1.94996	−	0.633580i	−0.415733	−	0.135080i
$23$	2.76753	+	3.80918i	0.577070	+	0.794268i	0.993370	−	0.114959i	$-0.0366736\pi$
$23$	2.76753	+	3.80918i	0.577070	+	0.794268i	−0.416300	+	0.909227i	$0.636674\pi$
$24$	0.462236			0.0943535
$25$	−2.96655	−	4.02487i	−0.593310	−	0.804974i
$26$	0.146258			0.0286836
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−1.67545	−	0.544387i	−0.316630	−	0.102879i
$29$	1.27031	−	3.90962i	0.235891	−	0.725998i	−0.761111	−	0.648622i	$-0.775346\pi$
$29$	1.27031	−	3.90962i	0.235891	−	0.725998i	0.997002	−	0.0773764i	$-0.0246543\pi$
$30$	−4.28576	−	0.663768i	−0.782470	−	0.121187i
$31$	−0.504631	−	1.55309i	−0.0906343	−	0.278944i	0.895457	−	0.445148i	$-0.146849\pi$
$31$	−0.504631	−	1.55309i	−0.0906343	−	0.278944i	−0.986091	+	0.166204i	$0.946849\pi$
$32$			7.64785i			1.35196i
$33$	−1.00539	+	0.326671i	−0.175016	+	0.0568662i
$34$	−3.32561	−	2.41620i	−0.570338	−	0.414375i
$35$	−1.99581	−	1.00833i	−0.337354	−	0.170439i
$36$	−1.42522	+	1.03549i	−0.237537	+	0.172581i
$37$	1.25799	−	1.73148i	0.206813	−	0.284653i	−0.692993	−	0.720945i	$-0.743708\pi$
$37$	1.25799	−	1.73148i	0.206813	−	0.284653i	0.899806	+	0.436291i	$0.143708\pi$
$38$	3.86124	−	5.31454i	0.626375	−	0.862131i
$39$	0.0610082	−	0.0443250i	0.00976912	−	0.00709768i
$40$	−0.158194	+	1.02141i	−0.0250126	+	0.161500i
$41$	2.55050	+	1.85304i	0.398320	+	0.289397i	0.768857	−	0.639421i	$-0.220826\pi$
$41$	2.55050	+	1.85304i	0.398320	+	0.289397i	−0.370536	+	0.928818i	$0.620826\pi$
$42$	−1.84458	+	0.599339i	−0.284624	+	0.0924801i
$43$		−	5.25850i		−	0.801914i	−0.916097	−	0.400957i	$-0.868678\pi$
$43$		−	5.25850i		−	0.801914i	0.916097	−	0.400957i	$-0.131322\pi$
$44$	−0.575488	−	1.77117i	−0.0867581	−	0.267014i
$45$	−1.98886	+	1.02197i	−0.296482	+	0.152346i
$46$	−2.82193	+	8.68501i	−0.416071	+	1.28054i
$47$	0.318103	+	0.103358i	0.0464001	+	0.0150763i	0.332125	−	0.943235i	$-0.392234\pi$
$47$	0.318103	+	0.103358i	0.0464001	+	0.0150763i	−0.285725	+	0.958312i	$0.592234\pi$
$48$	2.59793	+	3.57574i	0.374978	+	0.516113i
$49$	−1.00000			−0.142857
$50$	2.93349	−	9.24319i	0.414858	−	1.30718i
$51$	−2.11945			−0.296782
$52$	0.0780862	+	0.107476i	0.0108286	+	0.0149043i
$53$	12.5720	+	4.08489i	1.72690	+	0.561103i	0.992995	−	0.118153i	$-0.0376972\pi$
$53$	12.5720	+	4.08489i	1.72690	+	0.561103i	0.733902	+	0.679255i	$0.237697\pi$
$54$	−0.599339	+	1.84458i	−0.0815598	+	0.251015i
$55$	−0.377772	−	2.33343i	−0.0509387	−	0.314640i
$56$	0.142839	+	0.439612i	0.0190876	+	0.0587457i
$57$		−	3.38701i		−	0.448621i
$58$	7.58272	−	2.46378i	0.995660	−	0.323510i
$59$	0.133678	+	0.0971226i	0.0174034	+	0.0126443i	0.596453	−	0.802648i	$-0.296576\pi$
$59$	0.133678	+	0.0971226i	0.0174034	+	0.0126443i	−0.579050	+	0.815292i	$0.696576\pi$
$60$	−1.80037	−	3.50373i	−0.232427	−	0.452330i
$61$	3.22703	−	2.34457i	0.413178	−	0.300192i	−0.361709	−	0.932291i	$-0.617807\pi$
$61$	3.22703	−	2.34457i	0.413178	−	0.300192i	0.774887	+	0.632099i	$0.217807\pi$
$62$	1.86166	−	2.56236i	0.236431	−	0.325420i
$63$	−0.587785	+	0.809017i	−0.0740540	+	0.101927i
$64$	−4.84870	+	3.52279i	−0.606087	+	0.440348i
$65$	0.0770668	+	0.149981i	0.00955896	+	0.0186028i
$66$	−1.65873	−	1.20514i	−0.204176	−	0.148343i
$67$	0.365694	−	0.118821i	0.0446766	−	0.0145163i	−0.286593	−	0.958052i	$-0.592523\pi$
$67$	0.365694	−	0.118821i	0.0446766	−	0.0145163i	0.331270	+	0.943536i	$0.392523\pi$
$68$		−	3.73378i		−	0.452787i
$69$	1.45498	+	4.47796i	0.175159	+	0.539083i
$70$	−0.693093	−	4.28112i	−0.0828404	−	0.511692i
$71$	2.05993	−	6.33981i	0.244469	−	0.752397i	−0.751255	−	0.660012i	$-0.770551\pi$
$71$	2.05993	−	6.33981i	0.244469	−	0.752397i	0.995723	−	0.0923845i	$-0.0294489\pi$
$72$	0.439612	+	0.142839i	0.0518088	+	0.0168337i
$73$	−3.55355	−	4.89104i	−0.415911	−	0.572453i	0.548736	−	0.835995i	$-0.315109\pi$
$73$	−3.55355	−	4.89104i	−0.415911	−	0.572453i	−0.964648	+	0.263543i	$0.915109\pi$
$74$	4.15098			0.482541
$75$	−1.57760	−	4.74459i	−0.182166	−	0.547858i
$76$	5.96681			0.684440
$77$	−0.621366	−	0.855237i	−0.0708112	−	0.0974633i
$78$	0.139100	+	0.0451963i	0.0157500	+	0.00511748i
$79$	3.27129	−	10.0680i	0.368049	−	1.13274i	−0.580001	−	0.814616i	$-0.696948\pi$
$79$	3.27129	−	10.0680i	0.368049	−	1.13274i	0.948050	−	0.318122i	$-0.103052\pi$
$80$	−8.79049	+	4.51695i	−0.982807	+	0.505010i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			6.11445i			0.675228i
$83$	14.5719	−	4.73471i	1.59948	−	0.519702i	0.632499	−	0.774561i	$-0.282029\pi$
$83$	14.5719	−	4.73471i	1.59948	−	0.519702i	0.966978	+	0.254860i	$0.0820293\pi$
$84$	−1.42522	−	1.03549i	−0.155505	−	0.112981i
$85$	0.725353	−	4.68340i	0.0786756	−	0.507986i
$86$	8.25106	−	5.99475i	0.889735	−	0.646430i
$87$	2.41628	−	3.32572i	0.259052	−	0.356555i
$88$	−0.287217	+	0.395321i	−0.0306175	+	0.0421414i
$89$	−13.8211	+	10.0417i	−1.46504	+	1.06441i	−0.483025	+	0.875607i	$0.660462\pi$
$89$	−13.8211	+	10.0417i	−1.46504	+	1.06441i	−0.982014	+	0.188806i	$0.939538\pi$
$90$	−3.87089	−	1.95566i	−0.408027	−	0.206144i
$91$	0.0610082	+	0.0443250i	0.00639539	+	0.00464652i
$92$	−7.88870	+	2.56319i	−0.822453	+	0.267231i
$93$		−	1.63302i		−	0.169336i
$94$	0.200463	+	0.616962i	0.0206762	+	0.0636348i
$95$	7.48436	+	1.15916i	0.767880	+	0.118927i
$96$	−2.36332	+	7.27354i	−0.241205	+	0.742352i
$97$	−5.03842	−	1.63708i	−0.511574	−	0.166221i	0.0418438	−	0.999124i	$-0.486677\pi$
$97$	−5.03842	−	1.63708i	−0.511574	−	0.166221i	−0.553418	+	0.832904i	$0.686677\pi$
$98$	−1.14001	−	1.56909i	−0.115159	−	0.158502i
$99$	−1.05713			−0.106246
$100$	8.35842	−	2.77922i	0.835842	−	0.277922i
$101$	−17.5159			−1.74289			−0.871447	−	0.490490i	$-0.836818\pi$
$101$	−17.5159			−1.74289			−0.871447	+	0.490490i	$0.836818\pi$
$102$	−2.41620	−	3.32561i	−0.239239	−	0.329285i
$103$	−4.94964	−	1.60823i	−0.487702	−	0.158464i	0.0548356	−	0.998495i	$-0.482537\pi$
$103$	−4.94964	−	1.60823i	−0.487702	−	0.158464i	−0.542538	+	0.840031i	$0.682537\pi$
$104$	0.0107715	−	0.0331513i	0.00105623	−	0.00325075i
$105$	−1.58654	−	1.57572i	−0.154831	−	0.153774i
$106$	7.92266	+	24.3834i	0.769517	+	2.36833i
$107$			12.2071i			1.18011i	0.807364	+	0.590054i	$0.200894\pi$
$107$			12.2071i			1.18011i	−0.807364	+	0.590054i	$0.799106\pi$
$108$	−1.67545	+	0.544387i	−0.161220	+	0.0523837i
$109$	2.17308	+	1.57883i	0.208143	+	0.151225i	0.686973	−	0.726683i	$-0.258939\pi$
$109$	2.17308	+	1.57883i	0.208143	+	0.151225i	−0.478830	+	0.877908i	$0.658939\pi$
$110$	3.23071	−	3.25290i	0.308036	−	0.310152i
$111$	1.73148	−	1.25799i	0.164345	−	0.119403i
$112$	−2.59793	+	3.57574i	−0.245481	+	0.337875i
$113$	11.1832	−	15.3924i	1.05203	−	1.44799i	0.164989	−	0.986295i	$-0.447241\pi$
$113$	11.1832	−	15.3924i	1.05203	−	1.44799i	0.887038	−	0.461696i	$-0.152759\pi$
$114$	5.31454	−	3.86124i	0.497752	−	0.361638i
$115$	−10.3930	+	1.68258i	−0.969151	+	0.156901i
$116$	5.85883	+	4.25669i	0.543979	+	0.395224i
$117$	0.0717194	−	0.0233030i	0.00663046	−	0.00215437i
$118$			0.320473i			0.0295020i
$119$	−0.654946	−	2.01572i	−0.0600388	−	0.184781i
$120$	−0.466085	+	0.922537i	−0.0425476	+	0.0842157i
$121$	−3.05385	+	9.39879i	−0.277623	+	0.854436i
$122$	7.35769	+	2.39066i	0.666134	+	0.216440i
$123$	1.85304	+	2.55050i	0.167083	+	0.229970i
$124$	2.87685			0.258348
$125$	11.0241	−	1.86229i	0.986030	−	0.166569i
$126$	−1.93950			−0.172785
$127$	−6.25574	−	8.61029i	−0.555107	−	0.764040i	0.435587	−	0.900147i	$-0.356541\pi$
$127$	−6.25574	−	8.61029i	−0.555107	−	0.764040i	−0.990694	+	0.136107i	$0.956541\pi$
$128$	3.49193	+	1.13460i	0.308646	+	0.100285i
$129$	1.62497	−	5.00113i	0.143070	−	0.440325i
$130$	−0.147476	+	0.291905i	−0.0129345	+	0.0256017i
$131$	−1.57125	−	4.83580i	−0.137280	−	0.422506i	0.858657	−	0.512550i	$-0.171299\pi$
$131$	−1.57125	−	4.83580i	−0.137280	−	0.422506i	−0.995938	+	0.0900444i	$0.971299\pi$
$132$		−	1.86232i		−	0.162094i
$133$	3.22124	−	1.04665i	0.279317	−	0.0907556i
$134$	0.603336	+	0.438349i	0.0521203	+	0.0378676i
$135$	−2.20733	+	0.357356i	−0.189977	+	0.0307563i
$136$	−0.792583	+	0.575845i	−0.0679634	+	0.0493783i
$137$	3.38830	−	4.66359i	0.289482	−	0.398438i	−0.639364	−	0.768904i	$-0.720802\pi$
$137$	3.38830	−	4.66359i	0.289482	−	0.398438i	0.928846	+	0.370467i	$0.120802\pi$
$138$	−5.36763	+	7.38791i	−0.456923	+	0.628901i
$139$	−14.8680	+	10.8022i	−1.26109	+	0.916232i	−0.998810	−	0.0487609i	$-0.984473\pi$
$139$	−14.8680	+	10.8022i	−1.26109	+	0.916232i	−0.262275	+	0.964993i	$0.584473\pi$
$140$	2.77590	−	2.79497i	0.234606	−	0.236218i
$141$	0.270595	+	0.196598i	0.0227882	+	0.0165566i
$142$	12.2961	−	3.99524i	1.03186	−	0.335273i
$143$			0.0797185i			0.00666639i
$144$	1.36581	+	4.20353i	0.113818	+	0.350294i
$145$	6.52198	+	6.47749i	0.541621	+	0.537926i
$146$	3.62340	−	11.1517i	0.299875	−	0.922920i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	2.21617	+	3.05030i	0.182168	+	0.250733i
$149$	8.67033			0.710301			0.355150	−	0.934809i	$-0.384430\pi$
$149$	8.67033			0.710301			0.355150	+	0.934809i	$0.384430\pi$
$150$	5.64621	−	7.88429i	0.461011	−	0.643750i
$151$	−5.69927			−0.463800			−0.231900	−	0.972740i	$-0.574494\pi$
$151$	−5.69927			−0.463800			−0.231900	+	0.972740i	$0.574494\pi$
$152$	−0.920236	−	1.26660i	−0.0746410	−	0.102735i
$153$	−2.01572	−	0.654946i	−0.162961	−	0.0529493i
$154$	0.633580	−	1.94996i	0.0510553	−	0.157132i
$155$	3.60852	+	0.558878i	0.289843	+	0.0448902i
$156$	0.0410523	+	0.126346i	0.00328682	+	0.0101158i
$157$			9.24109i			0.737519i	0.929525	+	0.368760i	$0.120217\pi$
$157$			9.24109i			0.737519i	−0.929525	+	0.368760i	$0.879783\pi$
$158$	19.5269	−	6.34468i	1.55348	−	0.504755i
$159$	10.6944	+	7.76992i	0.848120	+	0.616195i
$160$	−15.2637	−	7.71154i	−1.20670	−	0.609651i
$161$	−3.80918	+	2.76753i	−0.300205	+	0.218112i
$162$	−1.14001	+	1.56909i	−0.0895678	+	0.123279i
$163$	−0.933274	+	1.28454i	−0.0730997	+	0.100613i	−0.844001	−	0.536341i	$-0.819806\pi$
$163$	−0.933274	+	1.28454i	−0.0730997	+	0.100613i	0.770902	+	0.636954i	$0.219806\pi$
$164$	−4.49314	+	3.26446i	−0.350855	+	0.254911i
$165$	0.361788	−	2.33597i	0.0281652	−	0.181855i
$166$	24.0414	+	17.4671i	1.86597	+	1.35571i
$167$	0.822808	−	0.267347i	0.0636708	−	0.0206879i	−0.277008	−	0.960867i	$-0.589343\pi$
$167$	0.822808	−	0.267347i	0.0636708	−	0.0206879i	0.340679	+	0.940180i	$0.389343\pi$
$168$			0.462236i			0.0356623i
$169$	4.01546	+	12.3583i	0.308882	+	0.950640i
$170$	8.17559	−	4.20098i	0.627039	−	0.322201i
$171$	1.04665	−	3.22124i	0.0800390	−	0.246335i
$172$	8.81036	+	2.86266i	0.671783	+	0.218276i
$173$	−7.00902	−	9.64708i	−0.532886	−	0.733454i	0.454681	−	0.890654i	$-0.349753\pi$
$173$	−7.00902	−	9.64708i	−0.532886	−	0.733454i	−0.987567	+	0.157200i	$0.949753\pi$
$174$	7.97294			0.604427
$175$	4.02487	−	2.96655i	0.304252	−	0.224250i
$176$	−4.67236			−0.352193
$177$	0.0971226	+	0.133678i	0.00730018	+	0.0100478i
$178$	−31.5125	−	10.2390i	−2.36196	−	0.767449i
$179$	−4.81362	+	14.8148i	−0.359787	+	1.10731i	0.593395	+	0.804911i	$0.297787\pi$
$179$	−4.81362	+	14.8148i	−0.359787	+	1.10731i	−0.953182	+	0.302398i	$0.902213\pi$
$180$	−0.629544	−	3.88859i	−0.0469235	−	0.289838i
$181$	−2.12430	−	6.53791i	−0.157898	−	0.485959i	0.840545	−	0.541741i	$-0.182235\pi$
$181$	−2.12430	−	6.53791i	−0.157898	−	0.485959i	−0.998443	+	0.0557821i	$0.982235\pi$
$182$			0.146258i			0.0108414i
$183$	3.79360	−	1.23261i	0.280431	−	0.0911174i
$184$	1.76074	+	1.27925i	0.129803	+	0.0943077i
$185$	2.18724	+	4.25662i	0.160809	+	0.312953i
$186$	2.56236	−	1.86166i	0.187881	−	0.136504i
$187$	1.31695	−	1.81263i	0.0963052	−	0.132553i
$188$	−0.346342	+	0.476699i	−0.0252596	+	0.0347669i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	6.71343	+	13.0651i	0.487044	+	0.947842i
$191$	−5.94263	−	4.31757i	−0.429993	−	0.312408i	0.351653	−	0.936130i	$-0.385620\pi$
$191$	−5.94263	−	4.31757i	−0.429993	−	0.312408i	−0.781646	+	0.623722i	$0.785620\pi$
$192$	−5.69999	+	1.85204i	−0.411361	+	0.133659i
$193$		−	1.50807i		−	0.108553i	−0.998526	−	0.0542765i	$-0.982715\pi$
$193$		−	1.50807i		−	0.108553i	0.998526	−	0.0542765i	$-0.0172852\pi$
$194$	−3.17513	−	9.77204i	−0.227961	−	0.701591i
$195$	0.0269483	+	0.166455i	0.00192981	+	0.0119201i
$196$	0.544387	−	1.67545i	0.0388848	−	0.119675i
$197$	−26.0002	−	8.44798i	−1.85244	−	0.601894i	−0.996380	−	0.0850142i	$-0.972906\pi$
$197$	−26.0002	−	8.44798i	−1.85244	−	0.601894i	−0.856058	−	0.516879i	$-0.827094\pi$
$198$	−1.20514	−	1.65873i	−0.0856456	−	0.117881i
$199$	16.4506			1.16615			0.583077	−	0.812417i	$-0.301848\pi$
$199$	16.4506			1.16615			0.583077	+	0.812417i	$0.301848\pi$
$200$	−1.87904	−	1.34564i	−0.132868	−	0.0951514i
$201$	0.384513			0.0271215
$202$	−19.9683	−	27.4840i	−1.40496	−	1.93377i
$203$	3.90962	+	1.27031i	0.274402	+	0.0891585i
$204$	1.15380	−	3.55103i	0.0807822	−	0.248622i
$205$	−6.27007	+	3.22184i	−0.437920	+	0.225023i
$206$	−3.11918	−	9.59984i	−0.217323	−	0.668853i
$207$			4.70840i			0.327257i
$208$	0.316989	−	0.102996i	0.0219792	−	0.00714149i
$209$	2.89670	+	2.10458i	0.200369	+	0.145576i
$210$	0.663768	−	4.28576i	0.0458044	−	0.295746i
$211$	1.94234	−	1.41119i	0.133716	−	0.0971504i	−0.518917	−	0.854825i	$-0.673664\pi$
$211$	1.94234	−	1.41119i	0.133716	−	0.0971504i	0.652633	+	0.757674i	$0.273664\pi$
$212$	−13.6881	+	18.8400i	−0.940100	+	1.29394i
$213$	3.91822	−	5.39296i	0.268472	−	0.369520i
$214$	−19.1541	+	13.9163i	−1.30935	+	0.951297i
$215$	10.4950	+	5.30229i	0.715752	+	0.361613i
$216$	0.373957	+	0.271695i	0.0254445	+	0.0184865i
$217$	1.55309	−	0.504631i	0.105431	−	0.0342566i
$218$			5.20964i			0.352841i
$219$	−1.86821	−	5.74976i	−0.126242	−	0.388533i
$220$	4.11521	+	0.637353i	0.277447	+	0.0429703i
$221$	−0.0493896	+	0.152006i	−0.00332231	+	0.0102250i
$222$	3.94781	+	1.28272i	0.264960	+	0.0860907i
$223$	−6.03105	−	8.30103i	−0.403869	−	0.555878i	0.557841	−	0.829948i	$-0.311630\pi$
$223$	−6.03105	−	8.30103i	−0.403869	−	0.555878i	−0.961710	+	0.274070i	$0.911630\pi$
$224$	−7.64785			−0.510993
$225$	−0.0342296	−	4.99988i	−0.00228198	−	0.333326i
$226$	36.9010			2.45462
$227$	8.02240	+	11.0419i	0.532465	+	0.732875i	0.987504	−	0.157596i	$-0.0503745\pi$
$227$	8.02240	+	11.0419i	0.532465	+	0.732875i	−0.455038	+	0.890472i	$0.650375\pi$
$228$	5.67478	+	1.84385i	0.375821	+	0.122112i
$229$	−6.30353	+	19.4003i	−0.416549	+	1.28201i	0.494309	+	0.869286i	$0.335421\pi$
$229$	−6.30353	+	19.4003i	−0.416549	+	1.28201i	−0.910858	+	0.412720i	$0.864579\pi$
$230$	−14.4882	−	14.3894i	−0.955326	−	0.948808i
$231$	−0.326671	−	1.00539i	−0.0214934	−	0.0661499i
$232$		−	1.90017i		−	0.124752i
$233$	−19.0388	+	6.18608i	−1.24727	+	0.405264i	−0.856943	−	0.515411i	$-0.827639\pi$
$233$	−19.0388	+	6.18608i	−1.24727	+	0.405264i	−0.390331	+	0.920675i	$0.627639\pi$
$234$	0.118326	+	0.0859685i	0.00773518	+	0.00561994i
$235$	−0.527035	+	0.530656i	−0.0343800	+	0.0346162i
$236$	−0.235497	+	0.171098i	−0.0153295	+	0.0111375i
$237$	6.22236	−	8.56435i	0.404186	−	0.556314i
$238$	2.41620	−	3.32561i	0.156619	−	0.215567i
$239$	−20.8582	+	15.1544i	−1.34920	+	0.980254i	−0.350153	+	0.936692i	$0.613870\pi$
$239$	−20.8582	+	15.1544i	−1.34920	+	0.980254i	−0.999051	+	0.0435615i	$0.986130\pi$
$240$	−9.75607	+	1.57946i	−0.629751	+	0.101954i
$241$	−18.2895	−	13.2881i	−1.17813	−	0.855963i	−0.186173	−	0.982517i	$-0.559608\pi$
$241$	−18.2895	−	13.2881i	−1.17813	−	0.855963i	−0.991960	+	0.126554i	$0.959608\pi$
$242$	−18.2290	+	5.92296i	−1.17180	+	0.380742i
$243$			1.00000i			0.0641500i
$244$	2.17146	+	6.68308i	0.139014	+	0.427840i
$245$	1.00833	−	1.99581i	0.0644197	−	0.127508i
$246$	−1.88947	+	5.81519i	−0.120468	+	0.370763i
$247$	−0.242915	−	0.0789278i	−0.0154563	−	0.00502205i
$248$	−0.443684	−	0.610678i	−0.0281739	−	0.0387781i
$249$	15.3218			0.970982
$250$	15.4898	+	15.1749i	0.979659	+	0.959742i
$251$	−14.0464			−0.886598			−0.443299	−	0.896374i	$-0.646192\pi$
$251$	−14.0464			−0.886598			−0.443299	+	0.896374i	$0.646192\pi$
$252$	−1.03549	−	1.42522i	−0.0652295	−	0.0897806i
$253$	−4.73378	−	1.53810i	−0.297611	−	0.0966995i
$254$	6.37871	−	19.6317i	0.400236	−	1.23180i
$255$	2.13710	−	4.23003i	0.133830	−	0.264895i
$256$	5.90463	+	18.1726i	0.369039	+	1.13579i
$257$			0.265615i			0.0165686i	0.999966	+	0.00828430i	$0.00263701\pi$
$257$			0.265615i			0.0165686i	−0.999966	+	0.00828430i	$0.997363\pi$
$258$	9.69971	−	3.15163i	0.603877	−	0.196212i
$259$	1.73148	+	1.25799i	0.107589	+	0.0781679i
$260$	−0.293239	+	0.0474741i	−0.0181859	+	0.00294422i
$261$	3.32572	−	2.41628i	0.205857	−	0.149564i
$262$	5.79657	−	7.97829i	0.358113	−	0.492901i
$263$	11.1912	−	15.4034i	0.690079	−	0.949812i	−0.309921	−	0.950762i	$-0.600302\pi$
$263$	11.1912	−	15.4034i	0.690079	−	0.949812i	1.00000		0.000950292i	$0.000302487\pi$
$264$	−0.395321	+	0.287217i	−0.0243303	+	0.0176770i
$265$	−20.8294	+	20.9725i	−1.27954	+	1.28833i
$266$	5.31454	+	3.86124i	0.325855	+	0.236748i
$267$	−16.2477	+	5.27921i	−0.994345	+	0.323082i
$268$			0.677386i			0.0413779i
$269$	−1.00325	−	3.08767i	−0.0611690	−	0.188259i	0.915802	−	0.401629i	$-0.131556\pi$
$269$	−1.00325	−	3.08767i	−0.0611690	−	0.188259i	−0.976971	+	0.213370i	$0.931556\pi$
$270$	−3.07710	−	3.05611i	−0.187267	−	0.185989i
$271$	8.74063	−	26.9009i	0.530955	−	1.63411i	−0.221274	−	0.975212i	$-0.571022\pi$
$271$	8.74063	−	26.9009i	0.530955	−	1.63411i	0.752230	−	0.658901i	$-0.228978\pi$
$272$	−8.90918	−	2.89477i	−0.540198	−	0.175521i
$273$	0.0443250	+	0.0610082i	0.00268267	+	0.00369238i
$274$	11.1803			0.675427
$275$	5.03802	+	1.59890i	0.303804	+	0.0964175i
$276$	−8.29467			−0.499280
$277$	−17.5755	−	24.1907i	−1.05601	−	1.45348i	−0.883478	−	0.468472i	$-0.844805\pi$
$277$	−17.5755	−	24.1907i	−1.05601	−	1.45348i	−0.172534	−	0.985004i	$-0.555195\pi$
$278$	−33.8993	−	11.0146i	−2.03315	−	0.660609i
$279$	0.504631	−	1.55309i	0.0302114	−	0.0929813i
$280$	−1.02141	−	0.158194i	−0.0610411	−	0.00945389i
$281$	0.0237239	+	0.0730147i	0.00141525	+	0.00435569i	0.951762	−	0.306838i	$-0.0992711\pi$
$281$	0.0237239	+	0.0730147i	0.00141525	+	0.00435569i	−0.950346	+	0.311194i	$0.899271\pi$
$282$			0.648712i			0.0386302i
$283$	−10.7337	+	3.48758i	−0.638050	+	0.207315i	−0.610138	−	0.792295i	$-0.708886\pi$
$283$	−10.7337	+	3.48758i	−0.638050	+	0.207315i	−0.0279121	+	0.999610i	$0.508886\pi$
$284$	9.50064	+	6.90262i	0.563759	+	0.409595i
$285$	6.75985	+	3.41522i	0.400419	+	0.202300i
$286$	−0.125086	+	0.0908799i	−0.00739646	+	0.00537384i
$287$	−1.85304	+	2.55050i	−0.109382	+	0.150551i
$288$	−4.49529	+	6.18724i	−0.264888	+	0.364587i
$289$	−10.1191	+	7.35198i	−0.595243	+	0.432469i
$290$	−2.72863	+	17.6180i	−0.160231	+	1.03456i
$291$	−4.28594	−	3.11392i	−0.251246	−	0.182541i
$292$	10.1292	−	3.29118i	0.592767	−	0.192602i
$293$			20.2356i			1.18218i	0.806607	+	0.591088i	$0.201301\pi$
$293$			20.2356i			1.18218i	−0.806607	+	0.591088i	$0.798699\pi$
$294$	−0.599339	−	1.84458i	−0.0349542	−	0.107578i
$295$	−0.328630	+	0.168865i	−0.0191336	+	0.00983168i
$296$	0.305707	−	0.940870i	0.0177689	−	0.0546870i
$297$	−1.00539	−	0.326671i	−0.0583387	−	0.0189554i
$298$	9.88427	+	13.6045i	0.572581	+	0.788090i
$299$	0.355062			0.0205337
$300$	8.80816	−	0.0603014i	0.508539	−	0.00348150i
$301$	5.25850			0.303095
$302$	−6.49723	−	8.94267i	−0.373874	−	0.514593i
$303$	−16.6586	−	5.41270i	−0.957010	−	0.310951i
$304$	4.62602	−	14.2374i	0.265320	−	0.816572i
$305$	1.42543	+	8.80464i	0.0816198	+	0.504152i
$306$	−1.27027	−	3.90949i	−0.0726165	−	0.223491i
$307$		−	3.95450i		−	0.225695i	−0.993612	−	0.112848i	$-0.964003\pi$
$307$		−	3.95450i		−	0.225695i	0.993612	−	0.112848i	$-0.0359972\pi$
$308$	1.77117	−	0.575488i	0.100922	−	0.0327915i
$309$	−4.21041	−	3.05904i	−0.239522	−	0.174023i
$310$	3.23682	+	6.29922i	0.183839	+	0.357772i
$311$	16.2897	−	11.8351i	0.923702	−	0.671109i	−0.0207410	−	0.999785i	$-0.506603\pi$
$311$	16.2897	−	11.8351i	0.923702	−	0.671109i	0.944443	+	0.328676i	$0.106603\pi$
$312$	0.0204886	−	0.0282002i	0.00115994	−	0.00159652i
$313$	−3.82221	+	5.26081i	−0.216044	+	0.297359i	−0.903260	−	0.429095i	$-0.858833\pi$
$313$	−3.82221	+	5.26081i	−0.216044	+	0.297359i	0.687216	+	0.726453i	$0.258833\pi$
$314$	−14.5001	+	10.5349i	−0.818288	+	0.594521i
$315$	−1.02197	−	1.98886i	−0.0575813	−	0.112060i
$316$	15.0876	+	10.9618i	0.848743	+	0.616648i
$317$	−31.9443	+	10.3793i	−1.79417	+	0.582961i	−0.999704	−	0.0243495i	$-0.992249\pi$
$317$	−31.9443	+	10.3793i	−1.79417	+	0.582961i	−0.794465	+	0.607310i	$0.792249\pi$
$318$			25.6383i			1.43772i
$319$	1.34289	+	4.13298i	0.0751872	+	0.231402i
$320$	−2.14175	−	13.2292i	−0.119727	−	0.739536i
$321$	−3.77221	+	11.6097i	−0.210544	+	0.647989i
$322$	−8.68501	−	2.82193i	−0.483997	−	0.157260i
$323$	4.21948	+	5.80762i	0.234778	+	0.323145i
$324$	−1.76167			−0.0978707
$325$	−0.377042	+	0.00258126i	−0.0209145	+	0.000143183i
$326$	−3.07951			−0.170558
$327$	1.57883	+	2.17308i	0.0873096	+	0.120171i
$328$	1.38592	+	0.450311i	0.0765244	+	0.0248643i
$329$	−0.103358	+	0.318103i	−0.00569831	+	0.0175376i
$330$	4.07779	−	2.09535i	0.224475	−	0.115345i
$331$	−0.746355	−	2.29704i	−0.0410234	−	0.126257i	0.928447	−	0.371464i	$-0.121144\pi$
$331$	−0.746355	−	2.29704i	−0.0410234	−	0.126257i	−0.969471	+	0.245207i	$0.921144\pi$
$332$			26.9921i			1.48138i
$333$	2.03548	−	0.661366i	0.111543	−	0.0362427i
$334$	1.35750	+	0.986283i	0.0742792	+	0.0539670i
$335$	−0.131594	+	0.849667i	−0.00718976	+	0.0464223i
$336$	−3.57574	+	2.59793i	−0.195072	+	0.141728i
$337$	16.7003	−	22.9859i	0.909721	−	1.25212i	−0.0575408	−	0.998343i	$-0.518326\pi$
$337$	16.7003	−	22.9859i	0.909721	−	1.25212i	0.967262	−	0.253780i	$-0.0816741\pi$
$338$	−14.8137	+	20.3893i	−0.805757	+	1.10903i
$339$	15.3924	−	11.1832i	0.835998	−	0.607388i
$340$	7.45193	+	3.76487i	0.404138	+	0.204179i
$341$	1.39662	+	1.01470i	0.0756311	+	0.0549492i
$342$	6.24761	−	2.02997i	0.337832	−	0.109768i
$343$		−	1.00000i		−	0.0539949i
$344$	−0.751117	−	2.31170i	−0.0404975	−	0.124639i
$345$	−10.4043	−	1.61139i	−0.560147	−	0.0867541i
$346$	7.14679	−	21.9956i	0.384214	−	1.18249i
$347$	16.1351	+	5.24260i	0.866176	+	0.281438i	0.708206	−	0.706006i	$-0.249505\pi$
$347$	16.1351	+	5.24260i	0.866176	+	0.281438i	0.157970	+	0.987444i	$0.449505\pi$
$348$	4.25669	+	5.85883i	0.228183	+	0.314066i
$349$	−26.9677			−1.44355			−0.721775	−	0.692128i	$-0.756673\pi$
$349$	−26.9677			−1.44355			−0.721775	+	0.692128i	$0.756673\pi$
$350$	9.24319	+	2.93349i	0.494069	+	0.156802i
$351$	0.0754102			0.00402510
$352$	−4.75211	−	6.54072i	−0.253288	−	0.348622i
$353$	4.14326	+	1.34623i	0.220523	+	0.0716524i	0.417195	−	0.908817i	$-0.363013\pi$
$353$	4.14326	+	1.34623i	0.220523	+	0.0716524i	−0.196671	+	0.980469i	$0.563013\pi$
$354$	−0.0990318	+	0.304788i	−0.00526348	+	0.0161993i
$355$	10.5760	+	10.5038i	0.561316	+	0.557486i
$356$	−9.30024	−	28.6232i	−0.492912	−	1.51703i
$357$		−	2.11945i		−	0.112173i
$358$	−28.7333	+	9.33603i	−1.51860	+	0.493424i
$359$	23.2293	+	16.8771i	1.22600	+	0.890738i	0.996583	−	0.0825917i	$-0.0263197\pi$
$359$	23.2293	+	16.8771i	1.22600	+	0.890738i	0.229412	+	0.973329i	$0.426320\pi$
$360$	−0.728353	+	0.733356i	−0.0383876	+	0.0386513i
$361$	6.09038	−	4.42492i	0.320547	−	0.232891i
$362$	7.83686	−	10.7865i	0.411896	−	0.566927i
$363$	−5.80877	+	7.99509i	−0.304882	+	0.419633i
$364$	−0.107476	+	0.0780862i	−0.00563330	+	0.00409283i
$365$	13.3447	−	2.16045i	0.698496	−	0.113083i
$366$	6.25883	+	4.54730i	0.327154	+	0.237691i
$367$	34.1205	−	11.0864i	1.78107	−	0.578706i	0.782064	−	0.623199i	$-0.214167\pi$
$367$	34.1205	−	11.0864i	1.78107	−	0.578706i	0.999010	+	0.0444927i	$0.0141671\pi$
$368$			20.8105i			1.08482i
$369$	0.974202	+	2.99829i	0.0507150	+	0.156085i
$370$	−4.18554	+	8.28458i	−0.217596	+	0.430695i
$371$	−4.08489	+	12.5720i	−0.212077	+	0.652706i
$372$	2.73604	+	0.888994i	0.141857	+	0.0460922i
$373$	−0.0554324	−	0.0762961i	−0.00287018	−	0.00395046i	0.807579	−	0.589759i	$-0.200777\pi$
$373$	−0.0554324	−	0.0762961i	−0.00287018	−	0.00395046i	−0.810450	+	0.585808i	$0.800777\pi$
$374$	4.34553			0.224702
$375$	11.0601	+	1.63550i	0.571140	+	0.0844570i
$376$	0.154606			0.00797317
$377$	−0.182212	−	0.250793i	−0.00938440	−	0.0129165i
$378$	−1.84458	−	0.599339i	−0.0948748	−	0.0308267i
$379$	2.12674	−	6.54542i	0.109243	−	0.336216i	−0.881460	−	0.472259i	$-0.843439\pi$
$379$	2.12674	−	6.54542i	0.109243	−	0.336216i	0.990703	+	0.136043i	$0.0434387\pi$
$380$	−6.01650	+	11.9087i	−0.308640	+	0.610901i
$381$	−3.28884	−	10.1220i	−0.168492	−	0.518566i
$382$		−	14.2466i		−	0.728920i
$383$	9.47045	−	3.07713i	0.483917	−	0.157234i	−0.0568906	−	0.998380i	$-0.518119\pi$
$383$	9.47045	−	3.07713i	0.483917	−	0.157234i	0.540808	+	0.841146i	$0.318119\pi$
$384$	2.97041	+	2.15813i	0.151583	+	0.110132i
$385$	2.33343	−	0.377772i	0.118923	−	0.0192530i
$386$	2.36629	−	1.71921i	0.120441	−	0.0875057i
$387$	3.09087	−	4.25422i	0.157118	−	0.216254i
$388$	5.48570	−	7.55042i	0.278494	−	0.383315i
$389$	−19.7207	+	14.3279i	−0.999877	+	0.726453i	−0.962062	−	0.272831i	$-0.912040\pi$
$389$	−19.7207	+	14.3279i	−0.999877	+	0.726453i	−0.0378153	+	0.999285i	$0.512040\pi$
$390$	−0.230462	+	0.232045i	−0.0116699	+	0.0117501i
$391$	−8.07336	−	5.86564i	−0.408288	−	0.296638i
$392$	−0.439612	+	0.142839i	−0.0222038	+	0.00721444i
$393$		−	5.08466i		−	0.256487i
$394$	−16.3849	−	50.4275i	−0.825458	−	2.54050i
$395$	16.7953	+	16.6807i	0.845064	+	0.839299i
$396$	0.575488	−	1.77117i	0.0289194	−	0.0890046i
$397$	18.6782	+	6.06892i	0.937433	+	0.304590i	0.737599	−	0.675239i	$-0.235960\pi$
$397$	18.6782	+	6.06892i	0.937433	+	0.304590i	0.199834	+	0.979830i	$0.435960\pi$
$398$	18.7539	+	25.8125i	0.940049	+	1.29387i
$399$	3.38701			0.169563
$400$	−0.151290	−	22.0988i	−0.00756450	−	1.10494i
$401$	−31.1421			−1.55516			−0.777582	−	0.628782i	$-0.783554\pi$
$401$	−31.1421			−1.55516			−0.777582	+	0.628782i	$0.783554\pi$
$402$	0.438349	+	0.603336i	0.0218629	+	0.0300917i
$403$	−0.117119	−	0.0380543i	−0.00583412	−	0.00189562i
$404$	9.53541	−	29.3470i	0.474404	−	1.46007i
$405$	−2.20972	−	0.342236i	−0.109802	−	0.0170059i
$406$	2.46378	+	7.58272i	0.122275	+	0.376324i
$407$			2.26250i			0.112148i
$408$	−0.931737	+	0.302740i	−0.0461278	+	0.0149878i
$409$	18.6601	+	13.5574i	0.922684	+	0.670369i	0.944191	−	0.329400i	$-0.106846\pi$
$409$	18.6601	+	13.5574i	0.922684	+	0.670369i	−0.0215066	+	0.999769i	$0.506846\pi$
$410$	−12.2033	−	6.16537i	−0.602678	−	0.304486i
$411$	4.66359	−	3.38830i	0.230038	−	0.167132i
$412$	5.38904	−	7.41737i	0.265499	−	0.365428i
$413$	−0.0971226	+	0.133678i	−0.00477909	+	0.00657785i
$414$	−7.38791	+	5.36763i	−0.363096	+	0.263805i
$415$	−5.24369	+	33.8570i	−0.257402	+	1.66197i
$416$	0.466581	+	0.338991i	0.0228760	+	0.0166204i
$417$	−17.4784	+	5.67906i	−0.855919	+	0.278105i
$418$			6.94442i			0.339663i
$419$	4.75569	+	14.6365i	0.232331	+	0.715040i	0.997464	+	0.0711686i	$0.0226728\pi$
$419$	4.75569	+	14.6365i	0.232331	+	0.715040i	−0.765134	+	0.643871i	$0.777327\pi$
$420$	3.50373	−	1.80037i	0.170964	−	0.0878492i
$421$	−0.684317	+	2.10611i	−0.0333516	+	0.102646i	−0.966347	−	0.257244i	$-0.917186\pi$
$421$	−0.684317	+	2.10611i	−0.0333516	+	0.102646i	0.932995	+	0.359890i	$0.117186\pi$
$422$	4.42858	+	1.43893i	0.215580	+	0.0700461i
$423$	0.196598	+	0.270595i	0.00955895	+	0.0131568i
$424$	6.11029			0.296742
$425$	8.61580	+	6.17007i	0.417928	+	0.299292i
$426$	12.9289			0.626405
$427$	2.34457	+	3.22703i	0.113462	+	0.156167i
$428$	−20.4524	−	6.64540i	−0.988606	−	0.321218i
$429$	−0.0246344	+	0.0758168i	−0.00118936	+	0.00366047i
$430$	3.64463	+	22.5123i	0.175760	+	1.08564i
$431$	8.71615	+	26.8255i	0.419842	+	1.29214i	0.907848	+	0.419300i	$0.137725\pi$
$431$	8.71615	+	26.8255i	0.419842	+	1.29214i	−0.488006	+	0.872841i	$0.662275\pi$
$432$			4.41985i			0.212650i
$433$	27.1355	−	8.81684i	1.30405	−	0.423711i	0.427059	−	0.904224i	$-0.359550\pi$
$433$	27.1355	−	8.81684i	1.30405	−	0.423711i	0.876988	+	0.480513i	$0.159550\pi$
$434$	2.56236	+	1.86166i	0.122997	+	0.0893626i
$435$	4.20112	+	8.17586i	0.201428	+	0.392002i
$436$	−3.82825	+	2.78139i	−0.183340	+	0.133204i
$437$	9.37366	−	12.9017i	0.448403	−	0.617174i
$438$	6.89212	−	9.48619i	0.329318	−	0.453268i
$439$	4.12375	−	2.99608i	0.196816	−	0.142995i	−0.485013	−	0.874507i	$-0.661185\pi$
$439$	4.12375	−	2.99608i	0.196816	−	0.142995i	0.681828	+	0.731512i	$0.261185\pi$
$440$	−0.499378	−	0.971846i	−0.0238069	−	0.0463309i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−0.294816	+	0.0957914i	−0.0140229	+	0.00455633i
$443$			23.9564i			1.13821i	0.822267	+	0.569103i	$0.192709\pi$
$443$			23.9564i			1.13821i	−0.822267	+	0.569103i	$0.807291\pi$
$444$	1.16511	+	3.58584i	0.0552937	+	0.170177i
$445$	−6.10502	−	37.7097i	−0.289406	−	1.78761i
$446$	6.14960	−	18.9265i	0.291192	−	0.896197i
$447$	8.24597	+	2.67928i	0.390021	+	0.126726i
$448$	−3.52279	−	4.84870i	−0.166436	−	0.229080i
$449$	−31.7468			−1.49822			−0.749112	−	0.662443i	$-0.769520\pi$
$449$	−31.7468			−1.49822			−0.749112	+	0.662443i	$0.769520\pi$
$450$	7.80625	−	5.75363i	0.367990	−	0.271229i
$451$	−3.33269			−0.156930
$452$	19.7011	+	27.1163i	0.926664	+	1.27544i
$453$	−5.42033	−	1.76117i	−0.254669	−	0.0827470i
$454$	−8.18009	+	25.1757i	−0.383911	+	1.18156i
$455$	−0.149981	+	0.0770668i	−0.00703121	+	0.00361295i
$456$	−0.483797	−	1.48897i	−0.0226559	−	0.0697276i
$457$			24.7652i			1.15846i	0.815162	+	0.579232i	$0.196648\pi$
$457$			24.7652i			1.15846i	−0.815162	+	0.579232i	$0.803352\pi$
$458$	−37.6269	+	12.2257i	−1.75819	+	0.571271i
$459$	−1.71467	−	1.24578i	−0.0800340	−	0.0581481i
$460$	2.83874	−	18.3289i	0.132357	−	0.854590i
$461$	−18.4694	+	13.4188i	−0.860207	+	0.624977i	−0.927941	−	0.372726i	$-0.878423\pi$
$461$	−18.4694	+	13.4188i	−0.860207	+	0.624977i	0.0677341	+	0.997703i	$0.478423\pi$
$462$	1.20514	−	1.65873i	0.0560682	−	0.0771713i
$463$	22.0103	−	30.2946i	1.02291	−	1.40791i	0.112761	−	0.993622i	$-0.464031\pi$
$463$	22.0103	−	30.2946i	1.02291	−	1.40791i	0.910146	−	0.414288i	$-0.135969\pi$
$464$	14.6992	−	10.6796i	0.682393	−	0.495788i
$465$	3.25920	+	1.64662i	0.151142	+	0.0763601i
$466$	−31.4110	−	22.8214i	−1.45509	−	1.05718i
$467$	−4.44938	+	1.44569i	−0.205893	+	0.0668986i	−0.410148	−	0.912019i	$-0.634523\pi$
$467$	−4.44938	+	1.44569i	−0.205893	+	0.0668986i	0.204255	+	0.978918i	$0.434523\pi$
$468$			0.132848i			0.00614091i
$469$	0.118821	+	0.365694i	0.00548665	+	0.0168862i
$470$	−1.43347	−	0.222013i	−0.0661212	−	0.0102407i
$471$	−2.85565	+	8.78880i	−0.131582	+	0.404966i
$472$	0.0726393	+	0.0236019i	0.00334349	+	0.00108637i
$473$	3.26745	+	4.49726i	0.150238	+	0.206784i
$474$	20.5318			0.943057
$475$	−9.86016	+	13.7686i	−0.452415	+	0.631746i
$476$	3.73378			0.171137
$477$	7.76992	+	10.6944i	0.355760	+	0.489662i
$478$	−47.5571	−	15.4523i	−2.17521	−	0.706770i
$479$	13.0023	−	40.0169i	0.594089	−	1.82842i	0.0348784	−	0.999392i	$-0.488896\pi$
$479$	13.0023	−	40.0169i	0.594089	−	1.82842i	0.559210	−	0.829026i	$-0.311104\pi$
$480$	−12.1336	−	12.0509i	−0.553822	−	0.550044i
$481$	−0.0498738	−	0.153496i	−0.00227405	−	0.00699880i
$482$		−	43.8466i		−	1.99716i
$483$	−4.47796	+	1.45498i	−0.203754	+	0.0662037i
$484$	−14.0847	−	10.2332i	−0.640215	−	0.465144i
$485$	8.34770	−	8.40504i	0.379049	−	0.381653i
$486$	−1.56909	+	1.14001i	−0.0711754	+	0.0517120i
$487$	20.6006	−	28.3542i	0.933501	−	1.28485i	−0.0249774	−	0.999688i	$-0.507951\pi$
$487$	20.6006	−	28.3542i	0.933501	−	1.28485i	0.958478	−	0.285166i	$-0.0920486\pi$
$488$	1.08374	−	1.49165i	0.0490588	−	0.0675237i
$489$	−1.28454	+	0.933274i	−0.0580890	+	0.0422041i
$490$	4.28112	−	0.693093i	0.193401	−	0.0313107i
$491$	11.4668	+	8.33113i	0.517490	+	0.375979i	0.815658	−	0.578535i	$-0.196375\pi$
$491$	11.4668	+	8.33113i	0.517490	+	0.375979i	−0.298167	+	0.954514i	$0.596375\pi$
$492$	−5.28200	+	1.71623i	−0.238131	+	0.0773735i
$493$			8.71268i			0.392399i
$494$	−0.153081	−	0.471134i	−0.00688742	−	0.0211973i
$495$	1.06593	−	2.10984i	0.0479102	−	0.0948301i
$496$	2.23039	−	6.86445i	0.100148	−	0.308223i
$497$	6.33981	+	2.05993i	0.284379	+	0.0924004i
$498$	17.4671	+	24.0414i	0.782718	+	1.07732i
$499$	1.48814			0.0666185			0.0333093	−	0.999445i	$-0.489395\pi$
$499$	1.48814			0.0666185			0.0333093	+	0.999445i	$0.489395\pi$
$500$	−2.88122	+	19.4842i	−0.128852	+	0.871361i
$501$	0.865152			0.0386521
$502$	−16.0130	−	22.0400i	−0.714696	−	0.983694i
$503$	6.63190	+	2.15484i	0.295702	+	0.0960794i	0.453111	−	0.891454i	$-0.350314\pi$
$503$	6.63190	+	2.15484i	0.295702	+	0.0960794i	−0.157409	+	0.987533i	$0.550314\pi$
$504$	−0.142839	+	0.439612i	−0.00636254	+	0.0195819i
$505$	17.6617	−	34.9584i	0.785937	−	1.55563i
$506$	−2.98315	−	9.18119i	−0.132617	−	0.408154i
$507$			12.9943i			0.577098i
$508$	17.8317	−	5.79386i	0.791152	−	0.257061i
$509$	2.53151	+	1.83925i	0.112207	+	0.0815235i	0.642474	−	0.766308i	$-0.277908\pi$
$509$	2.53151	+	1.83925i	0.112207	+	0.0815235i	−0.530266	+	0.847831i	$0.677908\pi$
$510$	9.07362	−	1.46898i	0.401787	−	0.0650474i
$511$	4.89104	−	3.55355i	0.216367	−	0.157200i
$512$	−17.4668	+	24.0410i	−0.771932	+	1.06247i
$513$	1.99084	−	2.74015i	0.0878976	−	0.120981i
$514$	−0.416774	+	0.302804i	−0.0183831	+	0.0133561i
$515$	8.20060	−	8.25693i	0.361361	−	0.363844i
$516$	7.49454	+	5.44510i	0.329929	+	0.239707i
$517$	−0.336276	+	0.109263i	−0.0147894	+	0.00480537i
$518$			4.15098i			0.182383i
$519$	−3.68486	−	11.3408i	−0.161747	−	0.497807i
$520$	0.0553026	+	0.0549253i	0.00242518	+	0.00240863i
$521$	3.47143	−	10.6840i	0.152086	−	0.468074i	−0.845768	−	0.533551i	$-0.820857\pi$
$521$	3.47143	−	10.6840i	0.152086	−	0.468074i	0.997854	+	0.0654778i	$0.0208571\pi$
$522$	7.58272	+	2.46378i	0.331887	+	0.107837i
$523$	8.01592	+	11.0330i	0.350512	+	0.482438i	0.947475	−	0.319831i	$-0.103626\pi$
$523$	8.01592	+	11.0330i	0.350512	+	0.482438i	−0.596963	+	0.802269i	$0.703626\pi$
$524$	8.95751			0.391311
$525$	4.74459	−	1.57760i	0.207071	−	0.0688522i
$526$	36.9274			1.61011
$527$	2.03439	+	2.80009i	0.0886192	+	0.121974i
$528$	−4.44368	−	1.44384i	−0.193386	−	0.0628350i
$529$	0.256776	−	0.790276i	0.0111642	−	0.0343598i
$530$	−56.6535	−	8.77434i	−2.46087	−	0.381133i
$531$	0.0510604	+	0.157148i	0.00221583	+	0.00681963i
$532$			5.96681i			0.258694i
$533$	0.226101	−	0.0734648i	0.00979354	−	0.00318212i
$534$	−26.8062	−	19.4758i	−1.16002	−	0.842801i
$535$	−24.3632	−	12.3088i	−1.05331	−	0.532155i
$536$	0.143791	−	0.104470i	0.00621083	−	0.00451243i
$537$	−9.15604	+	12.6022i	−0.395112	+	0.543826i
$538$	3.70113	−	5.09417i	0.159567	−	0.219625i
$539$	0.855237	−	0.621366i	0.0368376	−	0.0267641i
$540$	0.602908	−	3.89281i	0.0259450	−	0.167520i
$541$	−21.0925	−	15.3246i	−0.906839	−	0.658857i	0.0333743	−	0.999443i	$-0.489375\pi$
$541$	−21.0925	−	15.3246i	−0.906839	−	0.658857i	−0.940213	+	0.340586i	$0.889375\pi$
$542$	52.1744	−	16.9525i	2.24108	−	0.728171i
$543$		−	6.87437i		−	0.295007i
$544$	−5.00893	−	15.4159i	−0.214756	−	0.660951i
$545$	−5.34223	+	2.74508i	−0.228836	+	0.117586i
$546$	−0.0451963	+	0.139100i	−0.00193422	+	0.00595293i
$547$	33.0188	+	10.7285i	1.41178	+	0.458716i	0.912982	−	0.408000i	$-0.133774\pi$
$547$	33.0188	+	10.7285i	1.41178	+	0.458716i	0.498801	+	0.866716i	$0.333774\pi$
$548$	5.96907	+	8.21572i	0.254986	+	0.350958i
$549$	3.98882			0.170239
$550$	3.23457	+	9.72788i	0.137923	+	0.414798i
$551$	−13.9234			−0.593157
$552$	1.27925	+	1.76074i	0.0544485	+	0.0749420i
$553$	10.0680	+	3.27129i	0.428135	+	0.139109i
$554$	17.9210	−	55.1553i	0.761392	−	2.34332i
$555$	0.764822	+	4.72418i	0.0324649	+	0.200530i
$556$	−10.0047	−	30.7912i	−0.424292	−	1.30584i
$557$		−	24.5097i		−	1.03851i	−0.854620	−	0.519254i	$-0.826210\pi$
$557$		−	24.5097i		−	1.03851i	0.854620	−	0.519254i	$-0.173790\pi$
$558$	3.01223	−	0.978733i	0.127518	−	0.0414331i
$559$	−0.320811	−	0.233083i	−0.0135689	−	0.00985836i
$560$	−4.51695	−	8.79049i	−0.190876	−	0.371466i
$561$	1.81263	−	1.31695i	0.0765294	−	0.0556018i
$562$	−0.0875212	+	0.120463i	−0.00369186	+	0.00508141i
$563$	14.5313	−	20.0006i	0.612419	−	0.842923i	−0.384354	−	0.923186i	$-0.625576\pi$
$563$	14.5313	−	20.0006i	0.612419	−	0.842923i	0.996774	+	0.0802628i	$0.0255760\pi$
$564$	−0.476699	+	0.346342i	−0.0200727	+	0.0145836i
$565$	19.4440	+	37.8401i	0.818013	+	1.59195i
$566$	−17.7088	−	12.8662i	−0.744357	−	0.540807i
$567$	−0.951057	+	0.309017i	−0.0399406	+	0.0129775i
$568$		−	3.08130i		−	0.129288i
$569$	−0.609591	−	1.87613i	−0.0255554	−	0.0786514i	0.937465	−	0.348078i	$-0.113166\pi$
$569$	−0.609591	−	1.87613i	−0.0255554	−	0.0786514i	−0.963021	+	0.269427i	$0.913166\pi$
$570$	2.34752	+	14.5002i	0.0983266	+	0.607347i
$571$	2.52514	−	7.77158i	0.105674	−	0.325231i	−0.884214	−	0.467082i	$-0.845305\pi$
$571$	2.52514	−	7.77158i	0.105674	−	0.325231i	0.989888	+	0.141851i	$0.0453054\pi$
$572$	−0.133564	−	0.0433977i	−0.00558461	−	0.00181455i
$573$	−4.31757	−	5.94263i	−0.180369	−	0.248257i
$574$	−6.11445			−0.255212
$575$	7.12143	−	22.4391i	0.296984	−	0.935774i
$576$	−5.99332			−0.249722
$577$	15.5531	+	21.4070i	0.647484	+	0.891185i	0.998987	−	0.0450014i	$-0.0143292\pi$
$577$	15.5531	+	21.4070i	0.647484	+	0.891185i	−0.351503	+	0.936187i	$0.614329\pi$
$578$	−23.0718	−	7.49650i	−0.959662	−	0.311813i
$579$	0.466018	−	1.43426i	0.0193671	−	0.0596057i
$580$	−14.4032	+	7.40100i	−0.598060	+	0.307310i
$581$	4.73471	+	14.5719i	0.196429	+	0.604545i
$582$		−	10.2749i		−	0.425910i
$583$	−13.2902	+	4.31826i	−0.550426	+	0.178844i
$584$	−2.26081	−	1.64258i	−0.0935531	−	0.0679703i
$585$	−0.0258081	+	0.166636i	−0.00106703	+	0.00688954i
$586$	−31.7515	+	23.0688i	−1.31164	+	0.952963i
$587$	0.702040	−	0.966275i	0.0289763	−	0.0398824i	−0.794283	−	0.607548i	$-0.792153\pi$
$587$	0.702040	−	0.966275i	0.0289763	−	0.0398824i	0.823259	+	0.567665i	$0.192153\pi$
$588$	1.03549	−	1.42522i	0.0427027	−	0.0587752i
$589$	−4.47472	+	3.25108i	−0.184378	+	0.133958i
$590$	−0.639606	−	0.323142i	−0.0263321	−	0.0133036i
$591$	−22.1171	−	16.0690i	−0.909776	−	0.660991i
$592$	8.99651	−	2.92314i	0.369754	−	0.120140i
$593$		−	14.4166i		−	0.592017i	−0.955185	−	0.296009i	$-0.904344\pi$
$593$		−	14.4166i		−	0.592017i	0.955185	−	0.296009i	$-0.0956557\pi$
$594$	−0.633580	−	1.94996i	−0.0259961	−	0.0800078i
$595$	4.68340	+	0.725353i	0.192001	+	0.0297366i
$596$	−4.72001	+	14.5267i	−0.193339	+	0.595037i
$597$	15.6455	+	5.08353i	0.640327	+	0.208055i
$598$	0.404774	+	0.557124i	0.0165525	+	0.0227825i
$599$	18.5365			0.757379			0.378690	−	0.925524i	$-0.376375\pi$
$599$	18.5365			0.757379			0.378690	+	0.925524i	$0.376375\pi$
$600$	−1.37125	−	1.86044i	−0.0559809	−	0.0759521i
$601$	4.69848			0.191655			0.0958274	−	0.995398i	$-0.469450\pi$
$601$	4.69848			0.191655			0.0958274	+	0.995398i	$0.469450\pi$
$602$	5.99475	+	8.25106i	0.244328	+	0.336288i
$603$	0.365694	+	0.118821i	0.0148922	+	0.00483877i
$604$	3.10261	−	9.54885i	0.126243	−	0.388537i
$605$	−15.6790	−	15.5720i	−0.637440	−	0.633091i
$606$	−10.4979	−	32.3094i	−0.426450	−	1.31248i
$607$			39.2991i			1.59510i	0.603252	+	0.797551i	$0.293871\pi$
$607$			39.2991i			1.59510i	−0.603252	+	0.797551i	$0.706129\pi$
$608$	24.6356	−	8.00459i	0.999105	−	0.324629i
$609$	3.32572	+	2.41628i	0.134765	+	0.0979125i
$610$	−12.1903	+	12.2740i	−0.493570	+	0.496960i
$611$	0.0204056	−	0.0148255i	0.000825522	−	0.000599777i
$612$	2.19466	−	3.02069i	0.0887139	−	0.122104i
$613$	11.0834	−	15.2550i	0.447656	−	0.616145i	−0.524236	−	0.851573i	$-0.675649\pi$
$613$	11.0834	−	15.2550i	0.447656	−	0.616145i	0.971892	+	0.235428i	$0.0756491\pi$
$614$	6.20498	−	4.50818i	0.250413	−	0.181935i
$615$	−6.95879	+	1.12659i	−0.280605	+	0.0454287i
$616$	−0.395321	−	0.287217i	−0.0159279	−	0.0115723i
$617$	−22.2282	+	7.22238i	−0.894874	+	0.290762i	−0.720120	−	0.693850i	$-0.755913\pi$
$617$	−22.2282	+	7.22238i	−0.894874	+	0.290762i	−0.174754	+	0.984612i	$0.555913\pi$
$618$		−	10.0939i		−	0.406035i
$619$	7.56654	+	23.2874i	0.304125	+	0.936000i	0.980002	+	0.198986i	$0.0637648\pi$
$619$	7.56654	+	23.2874i	0.304125	+	0.936000i	−0.675878	+	0.737014i	$0.736235\pi$
$620$	−2.90080	+	5.74165i	−0.116499	+	0.230590i
$621$	−1.45498	+	4.47796i	−0.0583862	+	0.179694i
$622$	37.1408	+	12.0678i	1.48921	+	0.483874i
$623$	−10.0417	−	13.8211i	−0.402310	−	0.553733i
$624$	0.333302			0.0133428
$625$	−7.39917	+	23.8800i	−0.295967	+	0.955198i
$626$	−12.6121			−0.504079
$627$	2.10458	+	2.89670i	0.0840486	+	0.115683i
$628$	−15.4830	−	5.03073i	−0.617838	−	0.200748i
$629$	−1.40173	+	4.31409i	−0.0558908	+	0.172014i
$630$	1.95566	−	3.87089i	0.0779152	−	0.154220i
$631$	9.49140	+	29.2115i	0.377847	+	1.16289i	0.941538	+	0.336907i	$0.109381\pi$
$631$	9.49140	+	29.2115i	0.377847	+	1.16289i	−0.563691	+	0.825986i	$0.690619\pi$
$632$		−	4.89328i		−	0.194644i
$633$	2.28336	−	0.741907i	0.0907553	−	0.0294882i
$634$	−52.7029	−	38.2909i	−2.09310	−	1.52073i
$635$	23.4924	−	3.80330i	0.932267	−	0.150930i
$636$	−18.8400	+	13.6881i	−0.747055	+	0.542767i
$637$	−0.0443250	+	0.0610082i	−0.00175622	+	0.00241723i
$638$	−4.95411	+	6.81875i	−0.196135	+	0.269957i
$639$	5.39296	−	3.91822i	0.213342	−	0.155002i
$640$	−5.78545	+	5.82520i	−0.228690	+	0.230261i
$641$	8.94330	+	6.49769i	0.353239	+	0.256643i	0.750227	−	0.661181i	$-0.229944\pi$
$641$	8.94330	+	6.49769i	0.353239	+	0.256643i	−0.396987	+	0.917824i	$0.629944\pi$
$642$	−22.5170	+	7.31622i	−0.888675	+	0.288748i
$643$		−	3.60059i		−	0.141993i	−0.997477	−	0.0709966i	$-0.977382\pi$
$643$		−	3.60059i		−	0.141993i	0.997477	−	0.0709966i	$-0.0226180\pi$
$644$	−2.56319	−	7.88870i	−0.101004	−	0.310858i
$645$	8.34283	+	8.28591i	0.328499	+	0.326257i
$646$	−4.30242	+	13.2415i	−0.169277	+	0.520980i
$647$	32.7459	+	10.6398i	1.28738	+	0.418294i	0.871172	−	0.490978i	$-0.163360\pi$
$647$	32.7459	+	10.6398i	1.28738	+	0.418294i	0.416204	+	0.909271i	$0.363360\pi$
$648$	0.271695	+	0.373957i	0.0106732	+	0.0146904i
$649$	−0.174675			−0.00685658
$650$	−0.433883	−	0.588671i	−0.0170183	−	0.0230896i
$651$	1.63302			0.0640031
$652$	−1.64412	−	2.26294i	−0.0643889	−	0.0886237i
$653$	−8.89342	−	2.88965i	−0.348026	−	0.113081i	0.129787	−	0.991542i	$-0.458571\pi$
$653$	−8.89342	−	2.88965i	−0.348026	−	0.113081i	−0.477814	+	0.878461i	$0.658571\pi$
$654$	−1.60987	+	4.95466i	−0.0629508	+	0.193743i
$655$	11.2357	+	1.74015i	0.439015	+	0.0679935i
$656$	4.30583	+	13.2520i	0.168115	+	0.517403i
$657$		−	6.04566i		−	0.235864i
$658$	−0.616962	+	0.200463i	−0.0240517	+	0.00781486i
$659$	−17.6632	−	12.8331i	−0.688060	−	0.499905i	0.187962	−	0.982176i	$-0.439812\pi$
$659$	−17.6632	−	12.8331i	−0.688060	−	0.499905i	−0.876022	+	0.482272i	$0.839812\pi$
$660$	3.71684	+	1.87783i	0.144678	+	0.0730943i
$661$	−7.29819	+	5.30245i	−0.283867	+	0.206241i	−0.720602	−	0.693349i	$-0.756135\pi$
$661$	−7.29819	+	5.30245i	−0.283867	+	0.206241i	0.436735	+	0.899590i	$0.356135\pi$
$662$	2.75342	−	3.78975i	0.107015	−	0.147293i
$663$	−0.0939447	+	0.129304i	−0.00364851	+	0.00502174i
$664$	5.72970	−	4.16287i	0.222355	−	0.161551i
$665$	−1.15916	+	7.48436i	−0.0449503	+	0.290231i
$666$	3.35821	+	2.43988i	0.130128	+	0.0945435i
$667$	18.4081	−	5.98114i	0.712763	−	0.231591i
$668$			1.52411i			0.0589698i
$669$	−3.17071	−	9.75845i	−0.122587	−	0.377283i
$670$	−1.48322	+	0.762147i	−0.0573019	+	0.0294443i
$671$	−1.30303	+	4.01033i	−0.0503031	+	0.154817i
$672$	−7.27354	−	2.36332i	−0.280583	−	0.0911669i
$673$	5.44903	+	7.49994i	0.210045	+	0.289101i	0.901021	−	0.433776i	$-0.142819\pi$
$673$	5.44903	+	7.49994i	0.210045	+	0.289101i	−0.690976	+	0.722877i	$0.742819\pi$
$674$	55.1055			2.12258
$675$	1.51249	−	4.76575i	0.0582159	−	0.183434i
$676$	−22.8917			−0.880451
$677$	20.8198	+	28.6561i	0.800172	+	1.10134i	0.992766	+	0.120063i	$0.0383097\pi$
$677$	20.8198	+	28.6561i	0.800172	+	1.10134i	−0.192595	+	0.981278i	$0.561690\pi$
$678$	35.0949	+	11.4030i	1.34781	+	0.437931i
$679$	1.63708	−	5.03842i	0.0628255	−	0.193357i
$680$	−0.350096	−	2.16249i	−0.0134256	−	0.0829276i
$681$	4.21762	+	12.9805i	0.161620	+	0.497414i
$682$			3.34819i			0.128209i
$683$	−21.1788	+	6.88142i	−0.810385	+	0.263310i	−0.684761	−	0.728768i	$-0.740093\pi$
$683$	−21.1788	+	6.88142i	−0.810385	+	0.263310i	−0.125624	+	0.992078i	$0.540093\pi$
$684$	4.82725	+	3.50720i	0.184575	+	0.134101i
$685$	5.89115	+	11.4648i	0.225089	+	0.438049i
$686$	1.56909	−	1.14001i	0.0599082	−	0.0435258i
$687$	−11.9900	+	16.5029i	−0.457448	+	0.629623i
$688$	13.6612	−	18.8030i	0.520828	−	0.716858i
$689$	0.806466	−	0.585932i	0.0307239	−	0.0223222i
$690$	−9.33257	−	18.1622i	−0.355285	−	0.691425i
$691$	−34.1493	−	24.8109i	−1.29910	−	0.943853i	−0.299156	−	0.954204i	$-0.596705\pi$
$691$	−34.1493	−	24.8109i	−1.29910	−	0.943853i	−0.999946	+	0.0103515i	$0.996705\pi$
$692$	19.9788	−	6.49151i	0.759481	−	0.246770i
$693$		−	1.05713i		−	0.0401571i
$694$	10.1680	+	31.2940i	0.385974	+	1.18790i
$695$	−6.56743	−	40.5659i	−0.249117	−	1.53875i
$696$	0.587184	−	1.80717i	0.0222571	−	0.0685005i
$697$	−6.35472	−	2.06477i	−0.240702	−	0.0782089i
$698$	−30.7435	−	42.3148i	−1.16366	−	1.60164i
$699$	−20.0186			−0.757172
$700$	2.77922	+	8.35842i	0.105045	+	0.315919i
$701$	−6.55639			−0.247632			−0.123816	−	0.992305i	$-0.539513\pi$
$701$	−6.55639			−0.247632			−0.123816	+	0.992305i	$0.539513\pi$
$702$	0.0859685	+	0.118326i	0.00324467	+	0.00446591i
$703$	−6.89419	−	2.24006i	−0.260019	−	0.0844854i
$704$	1.95785	−	6.02563i	0.0737891	−	0.227100i
$705$	−0.665222	+	0.341821i	−0.0250537	+	0.0128737i
$706$	2.61101	+	8.03586i	0.0982667	+	0.302434i
$707$		−	17.5159i		−	0.658752i
$708$	−0.276843	+	0.0899517i	−0.0104044	+	0.00338059i
$709$	−16.2310	−	11.7925i	−0.609567	−	0.442877i	0.239695	−	0.970848i	$-0.422953\pi$
$709$	−16.2310	−	11.7925i	−0.609567	−	0.442877i	−0.849262	+	0.527972i	$0.822953\pi$
$710$	−4.42472	+	28.5692i	−0.166057	+	1.07218i
$711$	8.56435	−	6.22236i	0.321188	−	0.233357i
$712$	−4.64161	+	6.38863i	−0.173952	+	0.239424i
$713$	4.51943	−	6.22046i	0.169254	−	0.232958i
$714$	3.32561	−	2.41620i	0.124458	−	0.0904239i
$715$	−0.159103	−	0.0803823i	−0.00595012	−	0.00300613i
$716$	−22.2010	−	16.1300i	−0.829690	−	0.602805i
$717$	−24.5203	+	7.96712i	−0.915726	+	0.297537i
$718$			55.6889i			2.07829i
$719$	−14.9275	−	45.9422i	−0.556703	−	1.71335i	−0.691404	−	0.722468i	$-0.743008\pi$
$719$	−14.9275	−	45.9422i	−0.556703	−	1.71335i	0.134702	−	0.990886i	$-0.456992\pi$
$720$	−9.76665	−	1.51263i	−0.363982	−	0.0563726i
$721$	1.60823	−	4.94964i	0.0598938	−	0.184334i
$722$	13.8862	+	4.51191i	0.516791	+	0.167916i
$723$	−13.2881	−	18.2895i	−0.494191	−	0.680195i
$724$	12.1104			0.450079
$725$	−19.5042	+	6.48524i	−0.724366	+	0.240856i
$726$	−19.1671			−0.711358
$727$	26.0377	+	35.8378i	0.965684	+	1.32915i	0.944197	+	0.329381i	$0.106840\pi$
$727$	26.0377	+	35.8378i	0.965684	+	1.32915i	0.0214874	+	0.999769i	$0.493160\pi$
$728$	0.0331513	+	0.0107715i	0.00122867	+	0.000399218i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	18.6031	+	18.4762i	0.688532	+	0.683834i
$731$	3.44403	+	10.5996i	0.127382	+	0.392042i
$732$			7.02700i			0.259725i
$733$	30.0621	−	9.76778i	1.11037	−	0.360781i	0.304285	−	0.952581i	$-0.401582\pi$
$733$	30.0621	−	9.76778i	1.11037	−	0.360781i	0.806085	+	0.591800i	$0.201582\pi$
$734$	56.2933	+	40.8995i	2.07782	+	1.50963i
$735$	1.57572	−	1.58654i	0.0581212	−	0.0585205i
$736$	−29.1320	+	21.1657i	−1.07382	+	0.780176i
$737$	−0.238923	+	0.328850i	−0.00880085	+	0.0121133i
$738$	−3.59398	+	4.94669i	−0.132296	+	0.182090i
$739$	−22.7884	+	16.5568i	−0.838286	+	0.609050i	−0.921891	−	0.387449i	$-0.873356\pi$
$739$	−22.7884	+	16.5568i	−0.838286	+	0.609050i	0.0836057	+	0.996499i	$0.473356\pi$
$740$	−8.32246	+	1.34737i	−0.305940	+	0.0495302i
$741$	−0.206636	−	0.150130i	−0.00759095	−	0.00551515i
$742$	−24.3834	+	7.92266i	−0.895144	+	0.290850i
$743$			31.9736i			1.17300i	0.809950	+	0.586498i	$0.199494\pi$
$743$			31.9736i			1.17300i	−0.809950	+	0.586498i	$0.800506\pi$
$744$	−0.233258	−	0.717895i	−0.00855167	−	0.0263193i
$745$	−8.74253	+	17.3044i	−0.320302	+	0.633983i
$746$	0.0565220	−	0.173957i	0.00206942	−	0.00636901i
$747$	14.5719	+	4.73471i	0.533159	+	0.173234i
$748$	2.32004	+	3.19326i	0.0848292	+	0.116757i
$749$	−12.2071			−0.446039
$750$	10.0424	+	19.2187i	0.366695	+	0.701769i
$751$	29.3668			1.07161			0.535805	−	0.844342i	$-0.320008\pi$
$751$	29.3668			1.07161			0.535805	+	0.844342i	$0.320008\pi$
$752$	0.868937	+	1.19599i	0.0316869	+	0.0436132i
$753$	−13.3589	−	4.34056i	−0.486825	−	0.158179i
$754$	0.185794	−	0.571815i	0.00676621	−	0.0208243i
$755$	5.74673	−	11.3747i	0.209145	−	0.413967i
$756$	−0.544387	−	1.67545i	−0.0197992	−	0.0609356i
$757$			28.9811i			1.05334i	0.850071	+	0.526668i	$0.176559\pi$
$757$			28.9811i			1.05334i	−0.850071	+	0.526668i	$0.823441\pi$
$758$	12.6949	−	4.12481i	0.461098	−	0.149820i
$759$	−4.02680	−	2.92564i	−0.146164	−	0.106194i
$760$	3.45579	−	0.559476i	0.125355	−	0.0202943i
$761$	−28.5012	+	20.7074i	−1.03317	+	0.750641i	−0.968940	−	0.247294i	$-0.920459\pi$
$761$	−28.5012	+	20.7074i	−1.03317	+	0.750641i	−0.0642285	+	0.997935i	$0.520459\pi$
$762$	12.1330	−	16.6997i	0.439533	−	0.604966i
$763$	−1.57883	+	2.17308i	−0.0571576	+	0.0786706i
$764$	10.4690	−	7.60615i	0.378754	−	0.275181i
$765$	3.33966	−	3.36260i	0.120745	−	0.121575i
$766$	15.6247	+	11.3520i	0.564544	+	0.410165i
$767$	0.0118505	−	0.00385047i	0.000427898	−	0.000139033i
$768$			19.1078i			0.689493i
$769$	11.1878	+	34.4324i	0.403441	+	1.24166i	0.922190	+	0.386737i	$0.126398\pi$
$769$	11.1878	+	34.4324i	0.403441	+	1.24166i	−0.518749	+	0.854927i	$0.673602\pi$
$770$	3.25290	+	3.23071i	0.117226	+	0.116427i
$771$	−0.0820795	+	0.252615i	−0.00295602	+	0.00909770i
$772$	2.52669	+	0.820972i	0.0909376	+	0.0295474i
$773$	2.64868	+	3.64559i	0.0952663	+	0.131123i	0.853989	−	0.520291i	$-0.174176\pi$
$773$	2.64868	+	3.64559i	0.0952663	+	0.131123i	−0.758723	+	0.651413i	$0.774176\pi$
$774$	10.1989			0.366591
$775$	−4.75399	+	6.63840i	−0.170768	+	0.238458i
$776$	−2.44879			−0.0879065
$777$	1.25799	+	1.73148i	0.0451303	+	0.0621165i
$778$	−44.9636	−	14.6095i	−1.61202	−	0.523778i
$779$	3.29964	−	10.1552i	0.118222	−	0.363849i
$780$	−0.293558	−	0.0454655i	−0.0105110	−	0.00162792i
$781$	2.17761	+	6.70200i	0.0779211	+	0.239817i
$782$		−	19.3547i		−	0.692124i
$783$	3.90962	−	1.27031i	0.139718	−	0.0453973i
$784$	−3.57574	−	2.59793i	−0.127705	−	0.0927830i
$785$	−18.4435	−	9.31805i	−0.658277	−	0.332575i
$786$	7.97829	−	5.79657i	0.284576	−	0.206757i
$787$	−25.2040	+	34.6904i	−0.898427	+	1.23658i	0.0725397	+	0.997366i	$0.476890\pi$
$787$	−25.2040	+	34.6904i	−0.898427	+	1.23658i	−0.970967	+	0.239214i	$0.923110\pi$
$788$	28.3083	−	38.9631i	1.00844	−	1.38800i
$789$	15.4034	−	11.1912i	0.548374	−	0.398417i
$790$	−7.02673	+	45.3696i	−0.250000	+	1.61418i
$791$	15.3924	+	11.1832i	0.547289	+	0.397629i
$792$	−0.464728	+	0.150999i	−0.0165134	+	0.00536552i
$793$		−	0.300798i		−	0.0106816i
$794$	11.7707	+	36.2265i	0.417726	+	1.28563i
$795$	−26.2908	+	13.5094i	−0.932438	+	0.479128i
$796$	−8.95551	+	27.5622i	−0.317420	+	0.976917i
$797$	−19.3329	−	6.28164i	−0.684807	−	0.222507i	−0.0541081	−	0.998535i	$-0.517232\pi$
$797$	−19.3329	−	6.28164i	−0.684807	−	0.222507i	−0.630699	+	0.776028i	$0.717232\pi$
$798$	3.86124	+	5.31454i	0.136686	+	0.188133i
$799$	−0.708900			−0.0250791
$800$	30.7816	−	22.6877i	1.08829	−	0.802132i
$801$	−17.0839			−0.603629
$802$	−35.5024	−	48.8648i	−1.25363	−	1.72548i
$803$	6.07825	+	1.97494i	0.214497	+	0.0696942i
$804$	−0.209324	+	0.644232i	−0.00738228	+	0.0227203i
$805$	−1.68258	−	10.3930i	−0.0593030	−	0.366305i
$806$	−0.0738065	−	0.227153i	−0.00259972	−	0.00800112i
$807$		−	3.24657i		−	0.114285i
$808$	−7.70019	+	2.50194i	−0.270892	+	0.0880181i
$809$	2.07315	+	1.50623i	0.0728880	+	0.0529562i	0.623633	−	0.781718i	$-0.285656\pi$
$809$	2.07315	+	1.50623i	0.0728880	+	0.0529562i	−0.550745	+	0.834674i	$0.685656\pi$
$810$	−1.98211	−	3.85741i	−0.0696442	−	0.135536i
$811$	23.4918	−	17.0678i	0.824910	−	0.599332i	−0.0932046	−	0.995647i	$-0.529711\pi$
$811$	23.4918	−	17.0678i	0.824910	−	0.599332i	0.918115	+	0.396315i	$0.129711\pi$
$812$	−4.25669	+	5.85883i	−0.149381	+	0.205605i
$813$	16.6257	−	22.8833i	0.583087	−	0.802551i
$814$	−3.55007	+	2.57927i	−0.124430	+	0.0904035i
$815$	−1.62266	−	3.15788i	−0.0568393	−	0.110616i
$816$	−7.57860	−	5.50617i	−0.265304	−	0.192755i
$817$	−16.9389	+	5.50378i	−0.592617	+	0.192553i
$818$			44.7350i			1.56412i
$819$	0.0233030	+	0.0717194i	0.000814274	+	0.00250608i
$820$	−1.98469	−	12.2591i	−0.0693084	−	0.428107i
$821$	−11.6897	+	35.9771i	−0.407972	+	1.25561i	0.510415	+	0.859928i	$0.329492\pi$
$821$	−11.6897	+	35.9771i	−0.407972	+	1.25561i	−0.918388	+	0.395682i	$0.870508\pi$
$822$	10.6331	+	3.45490i	0.370872	+	0.120504i
$823$	−5.86613	−	8.07403i	−0.204480	−	0.281443i	0.694444	−	0.719547i	$-0.255650\pi$
$823$	−5.86613	−	8.07403i	−0.204480	−	0.281443i	−0.898925	+	0.438104i	$0.855650\pi$
$824$	−2.40564			−0.0838045
$825$	4.29735	+	3.07748i	0.149615	+	0.107144i
$826$	−0.320473			−0.0111507
$827$	17.2047	+	23.6803i	0.598267	+	0.823444i	0.995548	−	0.0942528i	$-0.0300462\pi$
$827$	17.2047	+	23.6803i	0.598267	+	0.823444i	−0.397281	+	0.917697i	$0.630046\pi$
$828$	−7.88870	−	2.56319i	−0.274151	−	0.0890771i
$829$	2.96242	−	9.11738i	0.102889	−	0.316660i	−0.886340	−	0.463035i	$-0.846761\pi$
$829$	2.96242	−	9.11738i	0.102889	−	0.316660i	0.989229	+	0.146375i	$0.0467606\pi$
$830$	−59.1026	+	30.3695i	−2.05148	+	1.05414i
$831$	−9.24001	−	28.4378i	−0.320532	−	0.986497i
$832$			0.451958i			0.0156688i
$833$	2.01572	−	0.654946i	0.0698405	−	0.0226925i
$834$	−28.8365	−	20.9509i	−0.998526	−	0.725472i
$835$	−0.296086	+	1.91175i	−0.0102465	+	0.0661587i
$836$	−5.10304	+	3.70757i	−0.176492	+	0.128229i
$837$	0.959865	−	1.32114i	0.0331778	−	0.0456653i
$838$	−17.5445	+	24.1479i	−0.606064	+	0.834175i
$839$	18.6538	−	13.5528i	0.644000	−	0.467893i	−0.217222	−	0.976122i	$-0.569700\pi$
$839$	18.6538	−	13.5528i	0.644000	−	0.467893i	0.861222	+	0.508229i	$0.169700\pi$
$840$	−0.922537	−	0.466085i	−0.0318305	−	0.0160815i
$841$	9.79006	+	7.11289i	0.337588	+	0.245272i
$842$	−4.08481	+	1.32724i	−0.140772	+	0.0457395i
$843$			0.0767722i			0.00264418i
$844$	1.30700	+	4.02253i	0.0449887	+	0.138461i
$845$	−28.7138	−	4.44713i	−0.987786	−	0.152986i
$846$	−0.200463	+	0.616962i	−0.00689206	+	0.0212116i
$847$	−9.39879	−	3.05385i	−0.322946	−	0.104932i
$848$	34.3419	+	47.2676i	1.17931	+	1.62318i
$849$	−11.2860			−0.387336
$850$	0.140707	+	20.5529i	0.00482621	+	0.704960i
$851$	10.0770			0.345437
$852$	6.90262	+	9.50064i	0.236480	+	0.325486i
$853$	30.3065	+	9.84718i	1.03768	+	0.337161i	0.777821	−	0.628486i	$-0.216325\pi$
$853$	30.3065	+	9.84718i	1.03768	+	0.337161i	0.259855	+	0.965648i	$0.416325\pi$
$854$	−2.39066	+	7.35769i	−0.0818067	+	0.251775i
$855$	5.37364	+	5.33698i	0.183775	+	0.182521i
$856$	1.74365	+	5.36641i	0.0595968	+	0.183420i
$857$		−	31.0525i		−	1.06073i	−0.847768	−	0.530367i	$-0.822054\pi$
$857$		−	31.0525i		−	1.06073i	0.847768	−	0.530367i	$-0.177946\pi$
$858$	−0.147047	+	0.0477784i	−0.00502010	+	0.00163113i
$859$	−37.5836	−	27.3061i	−1.28234	−	0.931672i	−0.282716	−	0.959204i	$-0.591235\pi$
$859$	−37.5836	−	27.3061i	−1.28234	−	0.931672i	−0.999621	+	0.0275316i	$0.991235\pi$
$860$	−14.5971	+	14.6973i	−0.497756	+	0.501175i
$861$	−2.55050	+	1.85304i	−0.0869206	+	0.0631515i
$862$	−32.1552	+	44.2579i	−1.09521	+	1.50743i
$863$	−19.5228	+	26.8708i	−0.664563	+	0.914692i	−0.999622	−	0.0275049i	$-0.991244\pi$
$863$	−19.5228	+	26.8708i	−0.664563	+	0.914692i	0.335059	+	0.942197i	$0.391244\pi$
$864$	−6.18724	+	4.49529i	−0.210494	+	0.152933i
$865$	26.3212	−	4.26127i	0.894947	−	0.144888i
$866$	44.7692	+	32.5267i	1.52132	+	1.10530i
$867$	−11.8957	+	3.86516i	−0.404001	+	0.131268i
$868$			2.87685i			0.0976465i
$869$	3.45818	+	10.6432i	0.117311	+	0.361045i
$870$	−8.03934	+	15.9125i	−0.272559	+	0.539485i
$871$	0.00896032	−	0.0275770i	0.000303609	−	0.000934412i
$872$	1.18083	+	0.383675i	0.0399879	+	0.0129929i
$873$	−3.11392	−	4.28594i	−0.105390	−	0.145057i
$874$	30.9301			1.04623
$875$	1.86229	+	11.0241i	0.0629570	+	0.372684i
$876$	10.6505			0.359846
$877$	−6.94540	−	9.55953i	−0.234530	−	0.322802i	0.675489	−	0.737370i	$-0.263933\pi$
$877$	−6.94540	−	9.55953i	−0.234530	−	0.322802i	−0.910018	+	0.414568i	$0.863933\pi$
$878$	9.40224	+	3.05497i	0.317310	+	0.103100i
$879$	−6.25314	+	19.2452i	−0.210913	+	0.649124i
$880$	4.71127	−	9.32517i	0.158817	−	0.314351i
$881$	1.20635	+	3.71277i	0.0406431	+	0.125086i	0.969319	−	0.245805i	$-0.0790522\pi$
$881$	1.20635	+	3.71277i	0.0406431	+	0.125086i	−0.928676	+	0.370891i	$0.879052\pi$
$882$		−	1.93950i		−	0.0653065i
$883$	−32.3475	+	10.5104i	−1.08858	+	0.353702i	−0.797698	−	0.603057i	$-0.793949\pi$
$883$	−32.3475	+	10.5104i	−1.08858	+	0.353702i	−0.290883	+	0.956759i	$0.593949\pi$
$884$	−0.227791	−	0.165500i	−0.00766144	−	0.00556636i
$885$	−0.364727	+	0.0590476i	−0.0122602	+	0.00198486i
$886$	−37.5898	+	27.3106i	−1.26286	+	0.917518i
$887$	22.3074	−	30.7035i	0.749009	−	1.03092i	−0.249040	−	0.968493i	$-0.580115\pi$
$887$	22.3074	−	30.7035i	0.749009	−	1.03092i	0.998049	−	0.0624296i	$-0.0198849\pi$
$888$	0.581490	−	0.800352i	0.0195135	−	0.0268580i
$889$	8.61029	−	6.25574i	0.288780	−	0.209811i
$890$	52.2102	−	52.5689i	1.75009	−	1.76211i
$891$	−0.855237	−	0.621366i	−0.0286515	−	0.0208165i
$892$	17.1912	−	5.58576i	0.575604	−	0.187025i
$893$		−	1.13287i		−	0.0379099i
$894$	5.19647	+	15.9931i	0.173796	+	0.534889i
$895$	−24.7139	−	24.5453i	−0.826093	−	0.820457i
$896$	−1.13460	+	3.49193i	−0.0379042	+	0.116657i
$897$	0.337684	+	0.109720i	0.0112749	+	0.00366345i
$898$	−36.1917	−	49.8136i	−1.20773	−	1.66230i
$899$	−6.71304			−0.223893
$900$	8.39569	+	2.66452i	0.279856	+	0.0888174i
$901$	−28.0170			−0.933381
$902$	−3.79931	−	5.22930i	−0.126503	−	0.174117i
$903$	5.00113	+	1.62497i	0.166427	+	0.0540755i
$904$	2.71765	−	8.36407i	0.0903877	−	0.278185i
$905$	15.1905	+	2.35266i	0.504948	+	0.0782050i
$906$	−3.41580	−	10.5127i	−0.113482	−	0.349263i
$907$			5.40625i			0.179512i	0.995964	+	0.0897558i	$0.0286087\pi$
$907$			5.40625i			0.179512i	−0.995964	+	0.0897558i	$0.971391\pi$
$908$	−22.8674	+	7.43007i	−0.758882	+	0.246576i
$909$	−14.1706	−	10.2956i	−0.470010	−	0.341482i
$910$	−0.291905	−	0.147476i	−0.00967654	−	0.00488880i
$911$	−4.59143	+	3.33587i	−0.152121	+	0.110522i	−0.661242	−	0.750173i	$-0.729970\pi$
$911$	−4.59143	+	3.33587i	−0.152121	+	0.110522i	0.509121	+	0.860695i	$0.329970\pi$
$912$	8.79921	−	12.1111i	0.291371	−	0.401038i
$913$	−9.52046	+	13.1038i	−0.315081	+	0.433672i
$914$	−38.8588	+	28.2326i	−1.28533	+	0.933850i
$915$	−1.36512	+	8.81419i	−0.0451295	+	0.291388i
$916$	−29.0726	−	21.1225i	−0.960587	−	0.697908i
$917$	4.83580	−	1.57125i	0.159692	−	0.0518871i
$918$		−	4.11068i		−	0.135673i
$919$	−9.40579	−	28.9481i	−0.310269	−	0.954908i	−0.977658	−	0.210200i	$-0.932589\pi$
$919$	−9.40579	−	28.9481i	−0.310269	−	0.954908i	0.667390	−	0.744708i	$-0.267411\pi$
$920$	−4.32855	+	2.22420i	−0.142708	+	0.0733298i
$921$	1.22201	−	3.76096i	0.0402666	−	0.123928i
$922$	−42.1107	−	13.6826i	−1.38684	−	0.450613i
$923$	−0.295474	−	0.406685i	−0.00972563	−	0.0133862i
$924$	1.86232			0.0612658
$925$	−10.7009	+	0.0732591i	−0.351843	+	0.00240875i
$926$	72.6270			2.38667
$927$	−3.05904	−	4.21041i	−0.100472	−	0.138288i
$928$	29.9002	+	9.71516i	0.981522	+	0.318916i
$929$	9.18937	−	28.2820i	0.301493	−	0.927901i	−0.679469	−	0.733704i	$-0.737790\pi$
$929$	9.18937	−	28.2820i	0.301493	−	0.927901i	0.980963	−	0.194197i	$-0.0622101\pi$
$930$	1.13183	+	6.99115i	0.0371143	+	0.229249i
$931$	1.04665	+	3.22124i	0.0343024	+	0.105572i
$932$		−	35.2662i		−	1.15518i
$933$	19.1496	−	6.22209i	0.626931	−	0.203702i
$934$	−7.34076	−	5.33338i	−0.240197	−	0.174513i
$935$	2.28975	+	4.45612i	0.0748830	+	0.145731i
$936$	0.0282002	−	0.0204886i	0.000921751	−	0.000669691i
$937$	−3.28753	+	4.52490i	−0.107399	+	0.147822i	−0.859333	−	0.511416i	$-0.829121\pi$
$937$	−3.28753	+	4.52490i	−0.107399	+	0.147822i	0.751934	+	0.659238i	$0.229121\pi$
$938$	−0.438349	+	0.603336i	−0.0143126	+	0.0196996i
$939$	−5.26081	+	3.82221i	−0.171680	+	0.124733i
$940$	−0.602177	−	1.17190i	−0.0196408	−	0.0382233i
$941$	40.2669	+	29.2556i	1.31266	+	0.953705i	0.999993	+	0.00384353i	$0.00122344\pi$
$941$	40.2669	+	29.2556i	1.31266	+	0.953705i	0.312670	+	0.949862i	$0.398777\pi$
$942$	−17.0459	+	5.53855i	−0.555385	+	0.180456i
$943$			14.8436i			0.483375i
$944$	0.225679	+	0.694570i	0.00734524	+	0.0226063i
$945$	−0.357356	−	2.20733i	−0.0116248	−	0.0718044i
$946$	−3.33168	+	10.2539i	−0.108322	+	0.333382i
$947$	−21.3171	−	6.92636i	−0.692714	−	0.225076i	−0.0585607	−	0.998284i	$-0.518651\pi$
$947$	−21.3171	−	6.92636i	−0.692714	−	0.225076i	−0.634153	+	0.773208i	$0.718651\pi$
$948$	10.9618	+	15.0876i	0.356022	+	0.490022i
$949$	−0.455904			−0.0147993
$950$	−32.8449	+	0.224859i	−1.06563	+	0.00729538i
$951$	−33.5882			−1.08917
$952$	−0.575845	−	0.792583i	−0.0186632	−	0.0256877i
$953$	−2.77375	−	0.901245i	−0.0898504	−	0.0291942i	0.263747	−	0.964592i	$-0.415042\pi$
$953$	−2.77375	−	0.901245i	−0.0898504	−	0.0291942i	−0.353597	+	0.935398i	$0.615042\pi$
$954$	−7.92266	+	24.3834i	−0.256506	+	0.789443i
$955$	14.6092	−	7.50685i	0.472742	−	0.242916i
$956$	−14.0355	−	43.1967i	−0.453939	−	1.39708i
$957$			4.34567i			0.140476i
$958$	77.6128	−	25.2179i	2.50756	−	0.814755i
$959$	4.66359	+	3.38830i	0.150595	+	0.109414i
$960$	2.05113	−	13.2436i	0.0662000	−	0.427435i
$961$	22.9221	−	16.6539i	0.739422	−	0.537221i
$962$	0.183992	−	0.253243i	0.00593214	−	0.00816489i
$963$	−7.17517	+	9.87578i	−0.231217	+	0.318242i
$964$	32.2202	−	23.4093i	1.03774	−	0.753964i
$965$	3.00982	+	1.52063i	0.0968896	+	0.0489507i
$966$	−7.38791	−	5.36763i	−0.237702	−	0.172701i
$967$	−5.32179	+	1.72915i	−0.171137	+	0.0556058i	−0.393332	−	0.919396i	$-0.628678\pi$
$967$	−5.32179	+	1.72915i	−0.171137	+	0.0556058i	0.222195	+	0.975002i	$0.428678\pi$
$968$			4.56803i			0.146822i
$969$	2.21831	+	6.82726i	0.0712625	+	0.219323i
$970$	22.7047	+	3.51645i	0.729005	+	0.112907i
$971$	8.93372	−	27.4952i	0.286697	−	0.882362i	−0.699188	−	0.714938i	$-0.746455\pi$
$971$	8.93372	−	27.4952i	0.286697	−	0.882362i	0.985885	−	0.167424i	$-0.0535449\pi$
$972$	−1.67545	−	0.544387i	−0.0537401	−	0.0174612i
$973$	−10.8022	−	14.8680i	−0.346303	−	0.476646i
$974$	67.9753			2.17807
$975$	−0.359386	−	0.114058i	−0.0115096	−	0.00365277i
$976$	17.6300			0.564323
$977$	−20.1866	−	27.7845i	−0.645828	−	0.888906i	0.353082	−	0.935593i	$-0.385134\pi$
$977$	−20.1866	−	27.7845i	−0.645828	−	0.888906i	−0.998910	+	0.0466866i	$0.985134\pi$
$978$	−2.92878	−	0.951620i	−0.0936522	−	0.0304294i
$979$	5.58081	−	17.1760i	0.178364	−	0.548947i
$980$	2.79497	+	2.77590i	0.0892820	+	0.0886728i
$981$	0.830041	+	2.55460i	0.0265012	+	0.0815622i
$982$			27.4901i			0.877243i
$983$	−16.2195	+	5.27005i	−0.517323	+	0.168088i	−0.556030	−	0.831162i	$-0.687676\pi$
$983$	−16.2195	+	5.27005i	−0.517323	+	0.168088i	0.0387072	+	0.999251i	$0.487676\pi$
$984$	1.17893	+	0.856543i	0.0375829	+	0.0273056i
$985$	43.0773	−	43.3733i	1.37256	−	1.38199i
$986$	−13.6710	+	9.93255i	−0.435373	+	0.316317i
$987$	−0.196598	+	0.270595i	−0.00625780	+	0.00861312i
$988$	0.264479	−	0.364024i	0.00841420	−	0.0115812i
$989$	20.0306	−	14.5531i	0.636935	−	0.462760i
$990$	4.52570	−	0.732690i	0.143836	−	0.0232864i
$991$	−10.0601	−	7.30911i	−0.319571	−	0.232182i	0.416422	−	0.909172i	$-0.363284\pi$
$991$	−10.0601	−	7.30911i	−0.319571	−	0.232182i	−0.735992	+	0.676990i	$0.763284\pi$
$992$	11.8778	−	3.85934i	0.377121	−	0.122534i
$993$		−	2.41525i		−	0.0766458i
$994$	3.99524	+	12.2961i	0.126721	+	0.390008i
$995$	−16.5876	+	32.8324i	−0.525863	+	1.04086i
$996$	−8.34100	+	25.6710i	−0.264295	+	0.813416i
$997$	−38.0370	−	12.3590i	−1.20464	−	0.391412i	−0.363176	−	0.931721i	$-0.618308\pi$
$997$	−38.0370	−	12.3590i	−1.20464	−	0.391412i	−0.841467	+	0.540308i	$0.818308\pi$
$998$	1.69650	+	2.33503i	0.0537018	+	0.0739142i
$999$	2.14023			0.0677138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.12	✓	56
25.9	even	10	inner	525.2.z.a.484.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.12	✓	56	1.1	even	1	trivial
525.2.z.a.484.12	yes	56	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14001 + 1.56909i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.544387 + 1.67545i) q^{4} +(-1.00833 + 1.99581i) q^{5} +(0.599339 + 1.84458i) q^{6} +1.00000i q^{7} +(0.439612 - 0.142839i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.14001 + 1.56909i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.544387 + 1.67545i) q^{4} +(-1.00833 + 1.99581i) q^{5} +(0.599339 + 1.84458i) q^{6} +1.00000i q^{7} +(0.439612 - 0.142839i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.28112 + 0.693093i) q^{10} +(-0.855237 + 0.621366i) q^{11} +(-1.03549 + 1.42522i) q^{12} +(0.0443250 - 0.0610082i) q^{13} +(-1.56909 + 1.14001i) q^{14} +(-1.57572 + 1.58654i) q^{15} +(3.57574 + 2.59793i) q^{16} +(-2.01572 + 0.654946i) q^{17} +1.93950i q^{18} +(-1.04665 - 3.22124i) q^{19} +(-2.79497 - 2.77590i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(-1.94996 - 0.633580i) q^{22} +(2.76753 + 3.80918i) q^{23} +0.462236 q^{24} +(-2.96655 - 4.02487i) q^{25} +0.146258 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.67545 - 0.544387i) q^{28} +(1.27031 - 3.90962i) q^{29} +(-4.28576 - 0.663768i) q^{30} +(-0.504631 - 1.55309i) q^{31} +7.64785i q^{32} +(-1.00539 + 0.326671i) q^{33} +(-3.32561 - 2.41620i) q^{34} +(-1.99581 - 1.00833i) q^{35} +(-1.42522 + 1.03549i) q^{36} +(1.25799 - 1.73148i) q^{37} +(3.86124 - 5.31454i) q^{38} +(0.0610082 - 0.0443250i) q^{39} +(-0.158194 + 1.02141i) q^{40} +(2.55050 + 1.85304i) q^{41} +(-1.84458 + 0.599339i) q^{42} -5.25850i q^{43} +(-0.575488 - 1.77117i) q^{44} +(-1.98886 + 1.02197i) q^{45} +(-2.82193 + 8.68501i) q^{46} +(0.318103 + 0.103358i) q^{47} +(2.59793 + 3.57574i) q^{48} -1.00000 q^{49} +(2.93349 - 9.24319i) q^{50} -2.11945 q^{51} +(0.0780862 + 0.107476i) q^{52} +(12.5720 + 4.08489i) q^{53} +(-0.599339 + 1.84458i) q^{54} +(-0.377772 - 2.33343i) q^{55} +(0.142839 + 0.439612i) q^{56} -3.38701i q^{57} +(7.58272 - 2.46378i) q^{58} +(0.133678 + 0.0971226i) q^{59} +(-1.80037 - 3.50373i) q^{60} +(3.22703 - 2.34457i) q^{61} +(1.86166 - 2.56236i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(-4.84870 + 3.52279i) q^{64} +(0.0770668 + 0.149981i) q^{65} +(-1.65873 - 1.20514i) q^{66} +(0.365694 - 0.118821i) q^{67} -3.73378i q^{68} +(1.45498 + 4.47796i) q^{69} +(-0.693093 - 4.28112i) q^{70} +(2.05993 - 6.33981i) q^{71} +(0.439612 + 0.142839i) q^{72} +(-3.55355 - 4.89104i) q^{73} +4.15098 q^{74} +(-1.57760 - 4.74459i) q^{75} +5.96681 q^{76} +(-0.621366 - 0.855237i) q^{77} +(0.139100 + 0.0451963i) q^{78} +(3.27129 - 10.0680i) q^{79} +(-8.79049 + 4.51695i) q^{80} +(0.309017 + 0.951057i) q^{81} +6.11445i q^{82} +(14.5719 - 4.73471i) q^{83} +(-1.42522 - 1.03549i) q^{84} +(0.725353 - 4.68340i) q^{85} +(8.25106 - 5.99475i) q^{86} +(2.41628 - 3.32572i) q^{87} +(-0.287217 + 0.395321i) q^{88} +(-13.8211 + 10.0417i) q^{89} +(-3.87089 - 1.95566i) q^{90} +(0.0610082 + 0.0443250i) q^{91} +(-7.88870 + 2.56319i) q^{92} -1.63302i q^{93} +(0.200463 + 0.616962i) q^{94} +(7.48436 + 1.15916i) q^{95} +(-2.36332 + 7.27354i) q^{96} +(-5.03842 - 1.63708i) q^{97} +(-1.14001 - 1.56909i) q^{98} -1.05713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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