LMFDB - Embedded newform 525.2.z.b.64.15

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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.15
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01102 + 1.39156i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.296223 + 0.911681i) q^{4} +(1.48832 + 1.66881i) q^{5} +(-0.531527 - 1.63587i) q^{6} +1.00000i q^{7} +(1.70360 - 0.553533i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.01102 + 1.39156i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.296223 + 0.911681i) q^{4} +(1.48832 + 1.66881i) q^{5} +(-0.531527 - 1.63587i) q^{6} +1.00000i q^{7} +(1.70360 - 0.553533i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.817513 + 3.75828i) q^{10} +(1.77104 - 1.28674i) q^{11} +(0.563450 - 0.775522i) q^{12} +(0.410313 - 0.564747i) q^{13} +(-1.39156 + 1.01102i) q^{14} +(-0.899783 - 2.04704i) q^{15} +(4.04370 + 2.93792i) q^{16} +(-3.02591 + 0.983178i) q^{17} +1.72006i q^{18} +(1.31857 + 4.05815i) q^{19} +(-1.96229 + 0.862531i) q^{20} +(0.309017 - 0.951057i) q^{21} +(3.58113 + 1.16358i) q^{22} +(-2.19964 - 3.02754i) q^{23} -1.79127 q^{24} +(-0.569831 + 4.96742i) q^{25} +1.20071 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.911681 - 0.296223i) q^{28} +(-1.03400 + 3.18232i) q^{29} +(1.93887 - 3.32171i) q^{30} +(1.33944 + 4.12237i) q^{31} +5.01480i q^{32} +(-2.08198 + 0.676477i) q^{33} +(-4.42742 - 3.21671i) q^{34} +(-1.66881 + 1.48832i) q^{35} +(-0.775522 + 0.563450i) q^{36} +(1.49326 - 2.05529i) q^{37} +(-4.31404 + 5.93776i) q^{38} +(-0.564747 + 0.410313i) q^{39} +(3.45923 + 2.01915i) q^{40} +(3.47165 + 2.52230i) q^{41} +(1.63587 - 0.531527i) q^{42} -9.45659i q^{43} +(0.648470 + 1.99578i) q^{44} +(0.223173 + 2.22490i) q^{45} +(1.98910 - 6.12183i) q^{46} +(0.385152 + 0.125144i) q^{47} +(-2.93792 - 4.04370i) q^{48} -1.00000 q^{49} +(-7.48856 + 4.22924i) q^{50} +3.18163 q^{51} +(0.393325 + 0.541366i) q^{52} +(-4.93840 - 1.60458i) q^{53} +(0.531527 - 1.63587i) q^{54} +(4.78318 + 1.04045i) q^{55} +(0.553533 + 1.70360i) q^{56} -4.26699i q^{57} +(-5.47377 + 1.77853i) q^{58} +(-9.44575 - 6.86274i) q^{59} +(2.13279 - 0.213933i) q^{60} +(-1.03833 + 0.754388i) q^{61} +(-4.38231 + 6.03173i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(1.10902 - 0.805753i) q^{64} +(1.55313 - 0.155790i) q^{65} +(-3.04629 - 2.21326i) q^{66} +(8.13363 - 2.64277i) q^{67} -3.04991i q^{68} +(1.15642 + 3.55908i) q^{69} +(-3.75828 - 0.817513i) q^{70} +(4.07431 - 12.5394i) q^{71} +(1.70360 + 0.553533i) q^{72} +(-4.93585 - 6.79361i) q^{73} +4.36977 q^{74} +(2.07696 - 4.54821i) q^{75} -4.09033 q^{76} +(1.28674 + 1.77104i) q^{77} +(-1.14195 - 0.371041i) q^{78} +(3.31483 - 10.2020i) q^{79} +(1.11548 + 11.1207i) q^{80} +(0.309017 + 0.951057i) q^{81} +7.38110i q^{82} +(-5.63904 + 1.83224i) q^{83} +(0.775522 + 0.563450i) q^{84} +(-6.14425 - 3.58638i) q^{85} +(13.1594 - 9.56085i) q^{86} +(1.96678 - 2.70704i) q^{87} +(2.30489 - 3.17241i) q^{88} +(7.95278 - 5.77803i) q^{89} +(-2.87044 + 2.55999i) q^{90} +(0.564747 + 0.410313i) q^{91} +(3.41173 - 1.10854i) q^{92} -4.33452i q^{93} +(0.215254 + 0.662484i) q^{94} +(-4.80982 + 8.24026i) q^{95} +(1.54966 - 4.76936i) q^{96} +(1.78534 + 0.580092i) q^{97} +(-1.01102 - 1.39156i) q^{98} +2.18913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * 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 $

$2$	1.01102	+	1.39156i	0.714902	+	0.983979i	0.999678	+	0.0253844i	$0.00808096\pi$
$2$	1.01102	+	1.39156i	0.714902	+	0.983979i	−0.284775	+	0.958594i	$0.591919\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.296223	+	0.911681i	−0.148112	+	0.455841i
$5$	1.48832	+	1.66881i	0.665595	+	0.746313i
$5$	1.48832	+	1.66881i	0.665595	+	0.746313i
$6$	−0.531527	−	1.63587i	−0.216995	−	0.667842i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.70360	−	0.553533i	0.602313	−	0.195704i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.817513	+	3.75828i	−0.258520	+	1.18847i
$11$	1.77104	−	1.28674i	0.533989	−	0.387965i	−0.287859	−	0.957673i	$-0.592943\pi$
$11$	1.77104	−	1.28674i	0.533989	−	0.387965i	0.821848	+	0.569707i	$0.192943\pi$
$12$	0.563450	−	0.775522i	0.162654	−	0.223874i
$13$	0.410313	−	0.564747i	0.113800	−	0.156633i	−0.748317	−	0.663341i	$-0.769138\pi$
$13$	0.410313	−	0.564747i	0.113800	−	0.156633i	0.862118	+	0.506708i	$0.169138\pi$
$14$	−1.39156	+	1.01102i	−0.371909	+	0.270208i
$15$	−0.899783	−	2.04704i	−0.232323	−	0.528545i
$16$	4.04370	+	2.93792i	1.01092	+	0.734480i
$17$	−3.02591	+	0.983178i	−0.733891	+	0.238456i	−0.652036	−	0.758188i	$-0.726085\pi$
$17$	−3.02591	+	0.983178i	−0.733891	+	0.238456i	−0.0818558	+	0.996644i	$0.526085\pi$
$18$			1.72006i			0.405421i
$19$	1.31857	+	4.05815i	0.302502	+	0.931004i	0.980598	+	0.196031i	$0.0628053\pi$
$19$	1.31857	+	4.05815i	0.302502	+	0.931004i	−0.678096	+	0.734973i	$0.737195\pi$
$20$	−1.96229	+	0.862531i	−0.438782	+	0.192868i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	3.58113	+	1.16358i	0.763499	+	0.248076i
$23$	−2.19964	−	3.02754i	−0.458656	−	0.631285i	0.515574	−	0.856845i	$-0.327579\pi$
$23$	−2.19964	−	3.02754i	−0.458656	−	0.631285i	−0.974229	+	0.225560i	$0.927579\pi$
$24$	−1.79127			−0.365642
$25$	−0.569831	+	4.96742i	−0.113966	+	0.993485i
$26$	1.20071			0.235479
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−0.911681	−	0.296223i	−0.172292	−	0.0559809i
$29$	−1.03400	+	3.18232i	−0.192008	+	0.590941i	0.807990	+	0.589196i	$0.200555\pi$
$29$	−1.03400	+	3.18232i	−0.192008	+	0.590941i	−0.999998	+	0.00174512i	$0.999445\pi$
$30$	1.93887	−	3.32171i	0.353988	−	0.606459i
$31$	1.33944	+	4.12237i	0.240571	+	0.740400i	0.996333	+	0.0855547i	$0.0272662\pi$
$31$	1.33944	+	4.12237i	0.240571	+	0.740400i	−0.755763	+	0.654845i	$0.772734\pi$
$32$			5.01480i			0.886499i
$33$	−2.08198	+	0.676477i	−0.362427	+	0.117760i
$34$	−4.42742	−	3.21671i	−0.759296	−	0.551661i
$35$	−1.66881	+	1.48832i	−0.282080	+	0.251571i
$36$	−0.775522	+	0.563450i	−0.129254	+	0.0939083i
$37$	1.49326	−	2.05529i	0.245490	−	0.337888i	−0.668435	−	0.743770i	$-0.733036\pi$
$37$	1.49326	−	2.05529i	0.245490	−	0.337888i	0.913925	+	0.405882i	$0.133036\pi$
$38$	−4.31404	+	5.93776i	−0.699829	+	0.963232i
$39$	−0.564747	+	0.410313i	−0.0904319	+	0.0657026i
$40$	3.45923	+	2.01915i	0.546953	+	0.319255i
$41$	3.47165	+	2.52230i	0.542180	+	0.393917i	0.824894	−	0.565287i	$-0.191235\pi$
$41$	3.47165	+	2.52230i	0.542180	+	0.393917i	−0.282714	+	0.959204i	$0.591235\pi$
$42$	1.63587	−	0.531527i	0.252421	−	0.0820164i
$43$		−	9.45659i		−	1.44212i	−0.692874	−	0.721059i	$-0.743656\pi$
$43$		−	9.45659i		−	1.44212i	0.692874	−	0.721059i	$-0.256344\pi$
$44$	0.648470	+	1.99578i	0.0977605	+	0.300876i
$45$	0.223173	+	2.22490i	0.0332687	+	0.331669i
$46$	1.98910	−	6.12183i	0.293277	−	0.902615i
$47$	0.385152	+	0.125144i	0.0561803	+	0.0182541i	0.336972	−	0.941515i	$-0.390597\pi$
$47$	0.385152	+	0.125144i	0.0561803	+	0.0182541i	−0.280792	+	0.959769i	$0.590597\pi$
$48$	−2.93792	−	4.04370i	−0.424052	−	0.583658i
$49$	−1.00000			−0.142857
$50$	−7.48856	+	4.22924i	−1.05904	+	0.598104i
$51$	3.18163			0.445518
$52$	0.393325	+	0.541366i	0.0545444	+	0.0750739i
$53$	−4.93840	−	1.60458i	−0.678342	−	0.220407i	−0.0504726	−	0.998725i	$-0.516073\pi$
$53$	−4.93840	−	1.60458i	−0.678342	−	0.220407i	−0.627869	+	0.778319i	$0.716073\pi$
$54$	0.531527	−	1.63587i	0.0723317	−	0.222614i
$55$	4.78318	+	1.04045i	0.644964	+	0.140295i
$56$	0.553533	+	1.70360i	0.0739690	+	0.227653i
$57$		−	4.26699i		−	0.565177i
$58$	−5.47377	+	1.77853i	−0.718741	+	0.233533i
$59$	−9.44575	−	6.86274i	−1.22973	−	0.893453i	−0.232862	−	0.972510i	$-0.574809\pi$
$59$	−9.44575	−	6.86274i	−1.22973	−	0.893453i	−0.996870	+	0.0790568i	$0.974809\pi$
$60$	2.13279	−	0.213933i	0.275342	−	0.0276187i
$61$	−1.03833	+	0.754388i	−0.132944	+	0.0965895i	−0.652270	−	0.757987i	$-0.726183\pi$
$61$	−1.03833	+	0.754388i	−0.132944	+	0.0965895i	0.519326	+	0.854576i	$0.326183\pi$
$62$	−4.38231	+	6.03173i	−0.556553	+	0.766030i
$63$	−0.587785	+	0.809017i	−0.0740540	+	0.101927i
$64$	1.10902	−	0.805753i	0.138628	−	0.100719i
$65$	1.55313	−	0.155790i	0.192642	−	0.0193233i
$66$	−3.04629	−	2.21326i	−0.374972	−	0.272433i
$67$	8.13363	−	2.64277i	0.993680	−	0.322866i	0.233343	−	0.972395i	$-0.425034\pi$
$67$	8.13363	−	2.64277i	0.993680	−	0.322866i	0.760338	+	0.649528i	$0.225034\pi$
$68$		−	3.04991i		−	0.369856i
$69$	1.15642	+	3.55908i	0.139216	+	0.428463i
$70$	−3.75828	−	0.817513i	−0.449200	−	0.0977116i
$71$	4.07431	−	12.5394i	0.483532	−	1.48816i	−0.350564	−	0.936539i	$-0.614010\pi$
$71$	4.07431	−	12.5394i	0.483532	−	1.48816i	0.834096	−	0.551619i	$-0.185990\pi$
$72$	1.70360	+	0.553533i	0.200771	+	0.0652345i
$73$	−4.93585	−	6.79361i	−0.577697	−	0.795132i	0.415743	−	0.909482i	$-0.363522\pi$
$73$	−4.93585	−	6.79361i	−0.577697	−	0.795132i	−0.993441	+	0.114350i	$0.963522\pi$
$74$	4.36977			0.507976
$75$	2.07696	−	4.54821i	0.239827	−	0.525182i
$76$	−4.09033			−0.469193
$77$	1.28674	+	1.77104i	0.146637	+	0.201829i
$78$	−1.14195	−	0.371041i	−0.129300	−	0.0420121i
$79$	3.31483	−	10.2020i	0.372948	−	1.14782i	−0.571905	−	0.820320i	$-0.693795\pi$
$79$	3.31483	−	10.2020i	0.372948	−	1.14782i	0.944853	−	0.327495i	$-0.106205\pi$
$80$	1.11548	+	11.1207i	0.124715	+	1.24333i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			7.38110i			0.815106i
$83$	−5.63904	+	1.83224i	−0.618965	+	0.201114i	−0.601681	−	0.798737i	$-0.705502\pi$
$83$	−5.63904	+	1.83224i	−0.618965	+	0.201114i	−0.0172843	+	0.999851i	$0.505502\pi$
$84$	0.775522	+	0.563450i	0.0846164	+	0.0614774i
$85$	−6.14425	−	3.58638i	−0.666437	−	0.388998i
$86$	13.1594	−	9.56085i	1.41901	−	1.03097i
$87$	1.96678	−	2.70704i	0.210861	−	0.290225i
$88$	2.30489	−	3.17241i	0.245702	−	0.338180i
$89$	7.95278	−	5.77803i	0.842993	−	0.612470i	−0.0802119	−	0.996778i	$-0.525560\pi$
$89$	7.95278	−	5.77803i	0.842993	−	0.612470i	0.923205	+	0.384307i	$0.125560\pi$
$90$	−2.87044	+	2.55999i	−0.302571	+	0.269847i
$91$	0.564747	+	0.410313i	0.0592016	+	0.0430125i
$92$	3.41173	−	1.10854i	0.355698	−	0.115573i
$93$		−	4.33452i		−	0.449469i
$94$	0.215254	+	0.662484i	0.0222018	+	0.0683300i
$95$	−4.80982	+	8.24026i	−0.493477	+	0.845433i
$96$	1.54966	−	4.76936i	0.158161	−	0.486770i
$97$	1.78534	+	0.580092i	0.181274	+	0.0588995i	0.398247	−	0.917278i	$-0.369619\pi$
$97$	1.78534	+	0.580092i	0.181274	+	0.0588995i	−0.216974	+	0.976177i	$0.569619\pi$
$98$	−1.01102	−	1.39156i	−0.102129	−	0.140568i
$99$	2.18913			0.220015
$100$	−4.35991	−	1.99097i	−0.435991	−	0.199097i
$101$	−7.53206			−0.749468			−0.374734	−	0.927132i	$-0.622266\pi$
$101$	−7.53206			−0.749468			−0.374734	+	0.927132i	$0.622266\pi$
$102$	3.21671	+	4.42742i	0.318502	+	0.438380i
$103$	−9.48670	−	3.08242i	−0.934752	−	0.303719i	−0.198248	−	0.980152i	$-0.563525\pi$
$103$	−9.48670	−	3.08242i	−0.934752	−	0.303719i	−0.736505	+	0.676432i	$0.763525\pi$
$104$	0.386403	−	1.18923i	0.0378899	−	0.116613i
$105$	2.04704	−	0.899783i	0.199771	−	0.0878098i
$106$	−2.75998	−	8.49434i	−0.268073	−	0.825043i
$107$		−	16.6751i		−	1.61205i	−0.591883	−	0.806024i	$-0.701615\pi$
$107$		−	16.6751i		−	1.61205i	0.591883	−	0.806024i	$-0.298385\pi$
$108$	0.911681	−	0.296223i	0.0877266	−	0.0285041i
$109$	2.49778	+	1.81474i	0.239244	+	0.173821i	0.700946	−	0.713214i	$-0.252761\pi$
$109$	2.49778	+	1.81474i	0.239244	+	0.173821i	−0.461702	+	0.887035i	$0.652761\pi$
$110$	3.38806	+	7.70799i	0.323039	+	0.734928i
$111$	−2.05529	+	1.49326i	−0.195080	+	0.141734i
$112$	−2.93792	+	4.04370i	−0.277607	+	0.382094i
$113$	−8.63899	+	11.8905i	−0.812687	+	1.11857i	0.178216	+	0.983991i	$0.442968\pi$
$113$	−8.63899	+	11.8905i	−0.812687	+	1.11857i	−0.990903	+	0.134577i	$0.957032\pi$
$114$	5.93776	−	4.31404i	0.556122	−	0.404046i
$115$	1.77862	−	8.17670i	0.165857	−	0.762481i
$116$	−2.59496	−	1.88535i	−0.240936	−	0.175051i
$117$	0.663900	−	0.215714i	0.0613776	−	0.0199428i
$118$		−	20.0827i		−	1.84876i
$119$	−0.983178	−	3.02591i	−0.0901278	−	0.277385i
$120$	−2.66598	−	2.98928i	−0.243369	−	0.272883i
$121$	−1.91829	+	5.90390i	−0.174390	+	0.536718i
$122$	−2.09955	−	0.682184i	−0.190084	−	0.0617621i
$123$	−2.52230	−	3.47165i	−0.227428	−	0.313028i
$124$	−4.15506			−0.373136
$125$	−9.13776	+	6.44216i	−0.817306	+	0.576204i
$126$	−1.72006			−0.153235
$127$	3.69287	+	5.08280i	0.327689	+	0.451025i	0.940795	−	0.338975i	$-0.110080\pi$
$127$	3.69287	+	5.08280i	0.327689	+	0.451025i	−0.613106	+	0.790001i	$0.710080\pi$
$128$	11.7812	+	3.82795i	1.04132	+	0.338346i
$129$	−2.92225	+	8.99376i	−0.257290	+	0.791856i
$130$	1.78704	+	2.00376i	0.156734	+	0.175741i
$131$	1.50912	+	4.64458i	0.131852	+	0.405799i	0.995087	−	0.0990031i	$-0.0315654\pi$
$131$	1.50912	+	4.64458i	0.131852	+	0.405799i	−0.863235	+	0.504802i	$0.831565\pi$
$132$		−	2.09849i		−	0.182650i
$133$	−4.05815	+	1.31857i	−0.351886	+	0.114335i
$134$	11.9009	+	8.64648i	1.02808	+	0.746942i
$135$	0.475283	−	2.18497i	0.0409058	−	0.188053i
$136$	−4.61072	+	3.34988i	−0.395366	+	0.287250i
$137$	−5.22276	+	7.18851i	−0.446211	+	0.614156i	−0.971578	−	0.236719i	$-0.923928\pi$
$137$	−5.22276	+	7.18851i	−0.446211	+	0.614156i	0.525368	+	0.850875i	$0.323928\pi$
$138$	−3.78350	+	5.20754i	−0.322073	+	0.443295i
$139$	17.5747	−	12.7688i	1.49067	−	1.08304i	0.516752	−	0.856135i	$-0.327141\pi$
$139$	17.5747	−	12.7688i	1.49067	−	1.08304i	0.973918	−	0.226900i	$-0.0728592\pi$
$140$	−0.862531	−	1.96229i	−0.0728971	−	0.165844i
$141$	−0.327630	−	0.238037i	−0.0275914	−	0.0200464i
$142$	21.5686	−	7.00805i	1.80999	−	0.588103i
$143$		−	1.52815i		−	0.127791i
$144$	1.54456	+	4.75365i	0.128713	+	0.396138i
$145$	−6.84958	+	3.01075i	−0.568827	+	0.250029i
$146$	4.46343	−	13.7370i	0.369396	−	1.13688i
$147$	0.951057	+	0.309017i	0.0784418	+	0.0254873i
$148$	1.43143	+	1.97020i	0.117663	+	0.161949i
$149$	−3.29732			−0.270127			−0.135064	−	0.990837i	$-0.543124\pi$
$149$	−3.29732			−0.270127			−0.135064	+	0.990837i	$0.543124\pi$
$150$	8.42895	−	1.70815i	0.688221	−	0.139470i
$151$	20.7437			1.68810			0.844048	−	0.536268i	$-0.180166\pi$
$151$	20.7437			1.68810			0.844048	+	0.536268i	$0.180166\pi$
$152$	4.49264	+	6.18359i	0.364401	+	0.501556i
$153$	−3.02591	−	0.983178i	−0.244630	−	0.0794852i
$154$	−1.16358	+	3.58113i	−0.0937639	+	0.288576i
$155$	−4.88593	+	8.37066i	−0.392448	+	0.672348i
$156$	−0.206783	−	0.636414i	−0.0165559	−	0.0509539i
$157$		−	13.0139i		−	1.03862i	−0.854585	−	0.519311i	$-0.826189\pi$
$157$		−	13.0139i		−	1.03862i	0.854585	−	0.519311i	$-0.173811\pi$
$158$	17.5480	−	5.70170i	1.39605	−	0.453603i
$159$	4.20086	+	3.05210i	0.333150	+	0.242047i
$160$	−8.36873	+	7.46361i	−0.661606	+	0.590050i
$161$	3.02754	−	2.19964i	0.238603	−	0.173356i
$162$	−1.01102	+	1.39156i	−0.0794336	+	0.109331i
$163$	−5.06494	+	6.97130i	−0.396717	+	0.546034i	−0.959916	−	0.280287i	$-0.909570\pi$
$163$	−5.06494	+	6.97130i	−0.396717	+	0.546034i	0.563199	+	0.826321i	$0.309570\pi$
$164$	−3.32792	+	2.41787i	−0.259867	+	0.188804i
$165$	−4.22756	−	2.46761i	−0.329115	−	0.192103i
$166$	−8.25087	−	5.99460i	−0.640391	−	0.465272i
$167$	−19.7234	+	6.40851i	−1.52624	+	0.495905i	−0.947540	−	0.319636i	$-0.896439\pi$
$167$	−19.7234	+	6.40851i	−1.52624	+	0.495905i	−0.578699	+	0.815542i	$0.696439\pi$
$168$		−	1.79127i		−	0.138200i
$169$	3.86664	+	11.9003i	0.297434	+	0.915407i
$170$	−1.22134	−	12.1760i	−0.0936721	−	0.933855i
$171$	−1.31857	+	4.05815i	−0.100834	+	0.310335i
$172$	8.62140	+	2.80126i	0.657376	+	0.213594i
$173$	9.43507	+	12.9863i	0.717335	+	0.987327i	0.999608	+	0.0279929i	$0.00891158\pi$
$173$	9.43507	+	12.9863i	0.717335	+	0.987327i	−0.282273	+	0.959334i	$0.591088\pi$
$174$	5.75546			0.436320
$175$	−4.96742	−	0.569831i	−0.375502	−	0.0430751i
$176$	10.9419			0.824775
$177$	6.86274	+	9.44575i	0.515835	+	0.709986i
$178$	16.0809	+	5.22501i	1.20532	+	0.391631i
$179$	0.810704	−	2.49509i	0.0605948	−	0.186492i	−0.916177	−	0.400774i	$-0.868741\pi$
$179$	0.810704	−	2.49509i	0.0605948	−	0.186492i	0.976772	+	0.214282i	$0.0687412\pi$
$180$	−2.09451	−	0.455605i	−0.156116	−	0.0339588i
$181$	3.76392	+	11.5842i	0.279770	+	0.861044i	0.987918	+	0.154980i	$0.0495312\pi$
$181$	3.76392	+	11.5842i	0.279770	+	0.861044i	−0.708148	+	0.706065i	$0.750469\pi$
$182$			1.20071i			0.0890028i
$183$	1.22063	−	0.396605i	0.0902313	−	0.0293179i
$184$	−5.42314	−	3.94014i	−0.399799	−	0.290471i
$185$	5.65233	−	0.566967i	0.415567	−	0.0416843i
$186$	6.03173	−	4.38231i	0.442268	−	0.321326i
$187$	−4.09392	+	5.63480i	−0.299377	+	0.412057i
$188$	−0.228182	+	0.314066i	−0.0166419	+	0.0229056i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−16.3296	+	1.63797i	−1.18468	+	0.118831i
$191$	−0.378394	−	0.274920i	−0.0273797	−	0.0198925i	0.574011	−	0.818847i	$-0.305387\pi$
$191$	−0.378394	−	0.274920i	−0.0273797	−	0.0198925i	−0.601391	+	0.798955i	$0.705387\pi$
$192$	−1.30374	+	0.423610i	−0.0940890	+	0.0305714i
$193$		−	20.7108i		−	1.49080i	−0.666618	−	0.745399i	$-0.732259\pi$
$193$		−	20.7108i		−	1.49080i	0.666618	−	0.745399i	$-0.267741\pi$
$194$	0.997793	+	3.07089i	0.0716373	+	0.220477i
$195$	−1.52526	−	0.331779i	−0.109226	−	0.0237592i
$196$	0.296223	−	0.911681i	0.0211588	−	0.0651201i
$197$	−11.6748	−	3.79337i	−0.831795	−	0.270267i	−0.137994	−	0.990433i	$-0.544065\pi$
$197$	−11.6748	−	3.79337i	−0.831795	−	0.270267i	−0.693801	+	0.720167i	$0.744065\pi$
$198$	2.21326	+	3.04629i	0.157290	+	0.216490i
$199$	−8.73013			−0.618862			−0.309431	−	0.950922i	$-0.600139\pi$
$199$	−8.73013			−0.618862			−0.309431	+	0.950922i	$0.600139\pi$
$200$	1.77887	+	8.77792i	0.125785	+	0.620693i
$201$	−8.55220			−0.603226
$202$	−7.61509	−	10.4813i	−0.535796	−	0.737460i
$203$	−3.18232	−	1.03400i	−0.223355	−	0.0725724i
$204$	−0.942473	+	2.90063i	−0.0659863	+	0.203085i
$205$	0.957679	+	9.54749i	0.0668872	+	0.666825i
$206$	−5.30193	−	16.3177i	−0.369403	−	1.13691i
$207$		−	3.74224i		−	0.260104i
$208$	3.31836	−	1.07820i	0.230087	−	0.0747598i
$209$	7.55702	+	5.49049i	0.522730	+	0.379785i
$210$	3.32171	+	1.93887i	0.229220	+	0.133795i
$211$	−20.3765	+	14.8044i	−1.40278	+	1.01918i	−0.408452	+	0.912780i	$0.633931\pi$
$211$	−20.3765	+	14.8044i	−1.40278	+	1.01918i	−0.994324	+	0.106397i	$0.966069\pi$
$212$	2.92574	−	4.02693i	0.200941	−	0.276571i
$213$	−7.74980	+	10.6667i	−0.531008	+	0.730869i
$214$	23.2044	−	16.8590i	1.58622	−	1.15246i
$215$	15.7812	−	14.0744i	1.07627	−	0.959866i
$216$	−1.44917	−	1.05288i	−0.0986034	−	0.0716396i
$217$	−4.12237	+	1.33944i	−0.279845	+	0.0909271i
$218$			5.31055i			0.359676i
$219$	2.59493	+	7.98637i	0.175349	+	0.539669i
$220$	−2.36545	+	4.05253i	−0.159479	+	0.273221i
$221$	−0.686323	+	2.11229i	−0.0461671	+	0.142088i
$222$	−4.15590	−	1.35033i	−0.278926	−	0.0906285i
$223$	−6.12864	−	8.43535i	−0.410404	−	0.564873i	0.552913	−	0.833239i	$-0.313516\pi$
$223$	−6.12864	−	8.43535i	−0.410404	−	0.564873i	−0.963317	+	0.268366i	$0.913516\pi$
$224$	−5.01480			−0.335065
$225$	−3.38078	+	3.68379i	−0.225385	+	0.245586i
$226$	−25.2806			−1.68164
$227$	−1.06010	−	1.45910i	−0.0703614	−	0.0968441i	0.772386	−	0.635154i	$-0.219063\pi$
$227$	−1.06010	−	1.45910i	−0.0703614	−	0.0968441i	−0.842747	+	0.538309i	$0.819063\pi$
$228$	3.89014	+	1.26398i	0.257631	+	0.0837093i
$229$	−1.09811	+	3.37965i	−0.0725654	+	0.223333i	−0.980761	−	0.195213i	$-0.937460\pi$
$229$	−1.09811	+	3.37965i	−0.0725654	+	0.223333i	0.908195	+	0.418546i	$0.137460\pi$
$230$	13.1766	−	5.79179i	0.868837	−	0.381899i
$231$	−0.676477	−	2.08198i	−0.0445089	−	0.136984i
$232$			5.99375i			0.393509i
$233$	−23.1031	+	7.50665i	−1.51353	+	0.491777i	−0.943931	−	0.330143i	$-0.892903\pi$
$233$	−23.1031	+	7.50665i	−1.51353	+	0.491777i	−0.569603	+	0.821920i	$0.692903\pi$
$234$	0.971398	+	0.705762i	0.0635023	+	0.0461371i
$235$	0.364388	+	0.828998i	0.0237701	+	0.0540779i
$236$	9.05469	−	6.57861i	0.589410	−	0.428231i
$237$	−6.30519	+	8.67834i	−0.409566	+	0.563719i
$238$	3.21671	−	4.42742i	0.208508	−	0.286987i
$239$	13.6612	−	9.92541i	0.883667	−	0.642021i	−0.0505524	−	0.998721i	$-0.516098\pi$
$239$	13.6612	−	9.92541i	0.883667	−	0.642021i	0.934219	+	0.356700i	$0.116098\pi$
$240$	2.37560	−	10.9211i	0.153344	−	0.704955i
$241$	−10.5318	−	7.65177i	−0.678410	−	0.492894i	0.194420	−	0.980918i	$-0.437718\pi$
$241$	−10.5318	−	7.65177i	−0.678410	−	0.492894i	−0.872830	+	0.488025i	$0.837718\pi$
$242$	−10.1550	+	3.29958i	−0.652791	+	0.212105i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.380185	−	1.17009i	−0.0243389	−	0.0749074i
$245$	−1.48832	−	1.66881i	−0.0950850	−	0.106616i
$246$	2.28088	−	7.01984i	0.145424	−	0.447569i
$247$	2.83286	+	0.920451i	0.180250	+	0.0585669i
$248$	4.56374	+	6.28145i	0.289798	+	0.398872i
$249$	5.92924			0.375750
$250$	−18.2031	−	6.20252i	−1.15127	−	0.392282i
$251$	−13.0569			−0.824143			−0.412072	−	0.911151i	$-0.635195\pi$
$251$	−13.0569			−0.824143			−0.412072	+	0.911151i	$0.635195\pi$
$252$	−0.563450	−	0.775522i	−0.0354940	−	0.0488533i
$253$	−7.79128	−	2.53154i	−0.489834	−	0.159157i
$254$	−3.33942	+	10.2777i	−0.209534	+	0.644878i
$255$	4.73527	+	5.30953i	0.296534	+	0.332496i
$256$	5.73707	+	17.6569i	0.358567	+	1.10356i
$257$		−	6.21176i		−	0.387479i	−0.981053	−	0.193739i	$-0.937938\pi$
$257$		−	6.21176i		−	0.387479i	0.981053	−	0.193739i	$-0.0620616\pi$
$258$	−15.4698	+	5.02644i	−0.963106	+	0.312932i
$259$	2.05529	+	1.49326i	0.127710	+	0.0927865i
$260$	−0.318042	+	1.46211i	−0.0197242	+	0.0906760i
$261$	−2.70704	+	1.96678i	−0.167562	+	0.121741i
$262$	−4.93744	+	6.79581i	−0.305036	+	0.419847i
$263$	5.96521	−	8.21041i	0.367831	−	0.506276i	−0.584479	−	0.811409i	$-0.698701\pi$
$263$	5.96521	−	8.21041i	0.367831	−	0.506276i	0.952310	+	0.305133i	$0.0987010\pi$
$264$	−3.17241	+	2.30489i	−0.195248	+	0.141856i
$265$	−4.67216	−	10.6294i	−0.287009	−	0.652957i
$266$	−5.93776	−	4.31404i	−0.364067	−	0.264510i
$267$	−9.34906	+	3.03769i	−0.572153	+	0.185904i
$268$			8.19812i			0.500780i
$269$	−8.48573	−	26.1164i	−0.517384	−	1.59234i	−0.778902	−	0.627146i	$-0.784223\pi$
$269$	−8.48573	−	26.1164i	−0.517384	−	1.59234i	0.261517	−	0.965199i	$-0.415777\pi$
$270$	3.52103	−	1.54768i	0.214283	−	0.0941887i
$271$	2.06157	−	6.34487i	0.125232	−	0.385424i	−0.868711	−	0.495318i	$-0.835051\pi$
$271$	2.06157	−	6.34487i	0.125232	−	0.385424i	0.993943	+	0.109895i	$0.0350514\pi$
$272$	−15.1244	−	4.91421i	−0.917050	−	0.297968i
$273$	−0.410313	−	0.564747i	−0.0248333	−	0.0341801i
$274$	−15.2836			−0.923313
$275$	5.38257	+	9.53073i	0.324581	+	0.574724i
$276$	−3.58731			−0.215931
$277$	12.5979	+	17.3395i	0.756931	+	1.04183i	0.997463	+	0.0711855i	$0.0226782\pi$
$277$	12.5979	+	17.3395i	0.756931	+	1.04183i	−0.240532	+	0.970641i	$0.577322\pi$
$278$	35.5370	+	11.5467i	2.13137	+	0.692523i
$279$	−1.33944	+	4.12237i	−0.0801902	+	0.246800i
$280$	−2.01915	+	3.45923i	−0.120667	+	0.206729i
$281$	−5.69347	−	17.5227i	−0.339644	−	1.04532i	−0.964389	−	0.264487i	$-0.914797\pi$
$281$	−5.69347	−	17.5227i	−0.339644	−	1.04532i	0.624745	−	0.780829i	$-0.285203\pi$
$282$		−	0.696577i		−	0.0414806i
$283$	16.4232	−	5.33623i	0.976259	−	0.317206i	0.222919	−	0.974837i	$-0.428442\pi$
$283$	16.4232	−	5.33623i	0.976259	−	0.317206i	0.753340	+	0.657631i	$0.228442\pi$
$284$	10.2251	+	7.42895i	0.606746	+	0.440827i
$285$	7.12079	−	6.35064i	0.421799	−	0.376179i
$286$	2.12651	−	1.54500i	0.125743	−	0.0913578i
$287$	−2.52230	+	3.47165i	−0.148887	+	0.204925i
$288$	−2.94762	+	4.05706i	−0.173690	+	0.239064i
$289$	−5.56379	+	4.04233i	−0.327282	+	0.237784i
$290$	−11.1147	−	6.48764i	−0.652679	−	0.380967i
$291$	−1.51870	−	1.10340i	−0.0890279	−	0.0646825i
$292$	7.65572	−	2.48750i	0.448017	−	0.145570i
$293$			5.11097i			0.298586i	0.988793	+	0.149293i	$0.0476997\pi$
$293$			5.11097i			0.298586i	−0.988793	+	0.149293i	$0.952300\pi$
$294$	0.531527	+	1.63587i	0.0309993	+	0.0954060i
$295$	−2.60568	−	25.9771i	−0.151708	−	1.51244i
$296$	1.40624	−	4.32796i	0.0817361	−	0.251558i
$297$	−2.08198	−	0.676477i	−0.120809	−	0.0392532i
$298$	−3.33368	−	4.58841i	−0.193115	−	0.265800i
$299$	−2.61233			−0.151075
$300$	3.53128	+	3.24081i	0.203878	+	0.187108i
$301$	9.45659			0.545069
$302$	20.9724	+	28.8660i	1.20682	+	1.66105i
$303$	7.16341	+	2.32753i	0.411527	+	0.133713i
$304$	−6.59061	+	20.2838i	−0.377997	+	1.16336i
$305$	−2.80429	−	0.609998i	−0.160573	−	0.0349284i
$306$	−1.69112	−	5.20474i	−0.0966751	−	0.297535i
$307$			19.7663i			1.12812i	0.825733	+	0.564062i	$0.190762\pi$
$307$			19.7663i			1.12812i	−0.825733	+	0.564062i	$0.809238\pi$
$308$	−1.99578	+	0.648470i	−0.113720	+	0.0369500i
$309$	8.06987	+	5.86310i	0.459079	+	0.333540i
$310$	−16.5880	+	1.66389i	−0.942137	+	0.0945029i
$311$	−21.6015	+	15.6944i	−1.22491	+	0.889949i	−0.996498	−	0.0836152i	$-0.973353\pi$
$311$	−21.6015	+	15.6944i	−1.22491	+	0.889949i	−0.228412	+	0.973565i	$0.573353\pi$
$312$	−0.734981	+	1.01162i	−0.0416101	+	0.0572714i
$313$	−4.72457	+	6.50281i	−0.267049	+	0.367561i	−0.921391	−	0.388638i	$-0.872946\pi$
$313$	−4.72457	+	6.50281i	−0.267049	+	0.367561i	0.654342	+	0.756199i	$0.272946\pi$
$314$	18.1096	−	13.1574i	1.02198	−	0.742514i
$315$	−2.22490	+	0.223173i	−0.125359	+	0.0125744i
$316$	8.31905	+	6.04414i	0.467983	+	0.340010i
$317$	−1.65959	+	0.539235i	−0.0932121	+	0.0302864i	−0.355252	−	0.934771i	$-0.615605\pi$
$317$	−1.65959	+	0.539235i	−0.0932121	+	0.0302864i	0.262040	+	0.965057i	$0.415605\pi$
$318$			8.93148i			0.500852i
$319$	2.26355	+	6.96649i	0.126734	+	0.390049i
$320$	2.99522	+	0.651531i	0.167438	+	0.0364217i
$321$	−5.15290	+	15.8590i	−0.287607	+	0.885164i
$322$	6.12183	+	1.98910i	0.341156	+	0.110848i
$323$	−7.97977	−	10.9832i	−0.444006	−	0.611122i
$324$	−0.958598			−0.0532555
$325$	2.57153	+	2.36001i	0.142643	+	0.130910i
$326$	−14.8217			−0.820900
$327$	−1.81474	−	2.49778i	−0.100356	−	0.138128i
$328$	7.31047	+	2.37532i	0.403653	+	0.131155i
$329$	−0.125144	+	0.385152i	−0.00689939	+	0.0212341i
$330$	−0.840341	−	8.37770i	−0.0462593	−	0.461177i
$331$	9.82963	+	30.2525i	0.540285	+	1.66283i	0.731943	+	0.681365i	$0.238614\pi$
$331$	9.82963	+	30.2525i	0.540285	+	1.66283i	−0.191658	+	0.981462i	$0.561386\pi$
$332$		−	5.68376i		−	0.311937i
$333$	2.41614	−	0.785052i	0.132404	−	0.0430206i
$334$	−28.8586	−	20.9670i	−1.57907	−	1.14726i
$335$	16.5157	+	9.64016i	0.902348	+	0.526698i
$336$	4.04370	−	2.93792i	0.220602	−	0.160277i
$337$	−7.60644	+	10.4694i	−0.414349	+	0.570303i	−0.964273	−	0.264912i	$-0.914657\pi$
$337$	−7.60644	+	10.4694i	−0.414349	+	0.570303i	0.549923	+	0.835215i	$0.314657\pi$
$338$	−12.6507	+	17.4121i	−0.688105	+	0.947095i
$339$	11.8905	−	8.63899i	0.645806	−	0.469205i
$340$	5.08970	−	4.53923i	0.276028	−	0.246174i
$341$	7.67661	+	5.57738i	0.415712	+	0.302032i
$342$	−6.98026	+	2.26802i	−0.377449	+	0.122641i
$343$		−	1.00000i		−	0.0539949i
$344$	−5.23454	−	16.1103i	−0.282227	−	0.868607i
$345$	−4.21831	+	7.22688i	−0.227106	+	0.389082i
$346$	−8.53202	+	26.2589i	−0.458684	+	1.41168i
$347$	−17.3115	−	5.62484i	−0.929329	−	0.301957i	−0.195040	−	0.980795i	$-0.562484\pi$
$347$	−17.3115	−	5.62484i	−0.929329	−	0.301957i	−0.734288	+	0.678838i	$0.762484\pi$
$348$	1.88535	+	2.59496i	0.101065	+	0.139105i
$349$	30.9551			1.65699			0.828494	−	0.559998i	$-0.189198\pi$
$349$	30.9551			1.65699			0.828494	+	0.559998i	$0.189198\pi$
$350$	−4.22924	−	7.48856i	−0.226062	−	0.400280i
$351$	−0.698066			−0.0372600
$352$	6.45272	+	8.88141i	0.343931	+	0.473381i
$353$	24.5482	+	7.97618i	1.30657	+	0.424529i	0.877861	−	0.478915i	$-0.158970\pi$
$353$	24.5482	+	7.97618i	1.30657	+	0.424529i	0.428706	+	0.903444i	$0.358970\pi$
$354$	−6.20589	+	19.0998i	−0.329840	+	1.01514i
$355$	26.9898	−	11.8634i	1.43247	−	0.629645i
$356$	2.91193	+	8.96199i	0.154332	+	0.474985i
$357$			3.18163i			0.168390i
$358$	4.29170	−	1.39446i	0.226823	−	0.0736994i
$359$	−7.49768	−	5.44738i	−0.395712	−	0.287502i	0.372080	−	0.928201i	$-0.378645\pi$
$359$	−7.49768	−	5.44738i	−0.395712	−	0.287502i	−0.767792	+	0.640699i	$0.778645\pi$
$360$	1.61176	+	3.66681i	0.0849470	+	0.193258i
$361$	0.641361	−	0.465976i	0.0337558	−	0.0245250i
$362$	−12.3146	+	16.9496i	−0.647241	+	0.890850i
$363$	3.64881	−	5.02216i	0.191513	−	0.263595i
$364$	−0.541366	+	0.393325i	−0.0283753	+	0.0206158i
$365$	3.99112	−	18.3480i	0.208905	−	0.960379i
$366$	1.78598	+	1.29759i	0.0933548	+	0.0678262i
$367$	34.1209	−	11.0866i	1.78110	−	0.578714i	0.782087	−	0.623169i	$-0.214155\pi$
$367$	34.1209	−	11.0866i	1.78110	−	0.578714i	0.999011	+	0.0444547i	$0.0141550\pi$
$368$		−	18.7048i		−	0.975055i
$369$	1.32605	+	4.08117i	0.0690315	+	0.212457i
$370$	6.50361	+	7.29231i	0.338106	+	0.379109i
$371$	1.60458	−	4.93840i	0.0833059	−	0.256389i
$372$	3.95170	+	1.28399i	0.204886	+	0.0665715i
$373$	18.7966	+	25.8712i	0.973249	+	1.33956i	0.940388	+	0.340102i	$0.110462\pi$
$373$	18.7966	+	25.8712i	0.973249	+	1.33956i	0.0328606	+	0.999460i	$0.489538\pi$
$374$	−11.9802			−0.619481
$375$	10.6813	−	3.30314i	0.551578	−	0.170573i
$376$	0.725417			0.0374105
$377$	1.37294	+	1.88969i	0.0707101	+	0.0973241i
$378$	1.63587	+	0.531527i	0.0841402	+	0.0273388i
$379$	−7.75380	+	23.8638i	−0.398286	+	1.22580i	0.528086	+	0.849191i	$0.322910\pi$
$379$	−7.75380	+	23.8638i	−0.398286	+	1.22580i	−0.926373	+	0.376608i	$0.877090\pi$
$380$	−6.08771	−	6.82597i	−0.312293	−	0.350165i
$381$	−1.94146	−	5.97519i	−0.0994638	−	0.306118i
$382$		−	0.804507i		−	0.0411622i
$383$	6.41409	−	2.08406i	0.327745	−	0.106491i	−0.140523	−	0.990077i	$-0.544878\pi$
$383$	6.41409	−	2.08406i	0.327745	−	0.106491i	0.468268	+	0.883587i	$0.344878\pi$
$384$	−10.0217	−	7.28119i	−0.511418	−	0.371567i
$385$	−1.04045	+	4.78318i	−0.0530264	+	0.243773i
$386$	28.8203	−	20.9392i	1.46691	−	1.06578i
$387$	5.55845	−	7.65055i	0.282552	−	0.388899i
$388$	−1.05772	+	1.45583i	−0.0536975	+	0.0739083i
$389$	21.0320	−	15.2807i	1.06637	−	0.774761i	0.0911111	−	0.995841i	$-0.470958\pi$
$389$	21.0320	−	15.2807i	1.06637	−	0.774761i	0.975256	+	0.221080i	$0.0709582\pi$
$390$	−1.08038	−	2.45791i	−0.0547073	−	0.124461i
$391$	9.63251	+	6.99843i	0.487137	+	0.353926i
$392$	−1.70360	+	0.553533i	−0.0860448	+	0.0279576i
$393$		−	4.88361i		−	0.246345i
$394$	−6.52482	−	20.0813i	−0.328716	−	1.01168i
$395$	21.9587	−	9.65200i	1.10486	−	0.485645i
$396$	−0.648470	+	1.99578i	−0.0325868	+	0.100292i
$397$	14.7266	+	4.78496i	0.739106	+	0.240150i	0.654287	−	0.756246i	$-0.272969\pi$
$397$	14.7266	+	4.78496i	0.739106	+	0.240150i	0.0848190	+	0.996396i	$0.472969\pi$
$398$	−8.82637	−	12.1485i	−0.442426	−	0.608947i
$399$	4.26699			0.213617
$400$	−16.8981	+	18.4126i	−0.844905	+	0.920632i
$401$	−3.14900			−0.157254			−0.0786269	−	0.996904i	$-0.525054\pi$
$401$	−3.14900			−0.157254			−0.0786269	+	0.996904i	$0.525054\pi$
$402$	−8.64648	−	11.9009i	−0.431247	−	0.593561i
$403$	2.87769	+	0.935018i	0.143348	+	0.0465765i
$404$	2.23117	−	6.86683i	0.111005	−	0.341638i
$405$	−1.12721	+	1.93116i	−0.0560117	+	0.0959602i
$406$	−1.77853	−	5.47377i	−0.0882672	−	0.271659i
$407$		−	5.56143i		−	0.275670i
$408$	5.42023	−	1.76114i	0.268341	−	0.0871893i
$409$	−18.6573	−	13.5553i	−0.922542	−	0.670266i	0.0216134	−	0.999766i	$-0.493120\pi$
$409$	−18.6573	−	13.5553i	−0.922542	−	0.670266i	−0.944155	+	0.329500i	$0.893120\pi$
$410$	−12.3176	+	10.9854i	−0.608324	+	0.542531i
$411$	7.18851	−	5.22276i	0.354583	−	0.257620i
$412$	5.62036	−	7.73576i	0.276895	−	0.381114i
$413$	6.86274	−	9.44575i	0.337693	−	0.464795i
$414$	5.20754	−	3.78350i	0.255937	−	0.185949i
$415$	−11.4503	−	6.68352i	−0.562074	−	0.328081i
$416$	2.83209	+	2.05764i	0.138855	+	0.100884i
$417$	−20.6603	+	6.71295i	−1.01174	+	0.328735i
$418$			16.0670i			0.785864i
$419$	7.39285	+	22.7528i	0.361164	+	1.11155i	0.952348	+	0.305013i	$0.0986607\pi$
$419$	7.39285	+	22.7528i	0.361164	+	1.11155i	−0.591184	+	0.806537i	$0.701339\pi$
$420$	0.213933	+	2.13279i	0.0104389	+	0.104069i
$421$	4.33106	−	13.3296i	0.211083	−	0.649647i	−0.788326	−	0.615258i	$-0.789052\pi$
$421$	4.33106	−	13.3296i	0.211083	−	0.649647i	0.999409	−	0.0343884i	$-0.0109483\pi$
$422$	−41.2023	−	13.3874i	−2.00570	−	0.651690i
$423$	0.238037	+	0.327630i	0.0115738	+	0.0159299i
$424$	−9.30125			−0.451709
$425$	−3.15961	−	15.5912i	−0.153263	−	0.756286i
$426$	−22.6785			−1.09878
$427$	−0.754388	−	1.03833i	−0.0365074	−	0.0502481i
$428$	15.2024	+	4.93957i	0.734837	+	0.238763i
$429$	−0.472226	+	1.45336i	−0.0227993	+	0.0701689i
$430$	35.5405	+	7.73089i	1.71392	+	0.372817i
$431$	−0.474329	−	1.45983i	−0.0228476	−	0.0703177i	0.938983	−	0.343965i	$-0.111770\pi$
$431$	−0.474329	−	1.45983i	−0.0228476	−	0.0703177i	−0.961830	+	0.273647i	$0.911770\pi$
$432$		−	4.99829i		−	0.240480i
$433$	4.64426	−	1.50901i	0.223189	−	0.0725184i	−0.195288	−	0.980746i	$-0.562564\pi$
$433$	4.64426	−	1.50901i	0.223189	−	0.0725184i	0.418477	+	0.908228i	$0.362564\pi$
$434$	−6.03173	−	4.38231i	−0.289532	−	0.210357i
$435$	7.44472	−	0.746756i	0.356947	−	0.0358042i
$436$	−2.39437	+	1.73961i	−0.114669	+	0.0833123i
$437$	9.38583	−	12.9185i	0.448985	−	0.617975i
$438$	−8.48995	+	11.6854i	−0.405665	+	0.558350i
$439$	8.32250	−	6.04665i	0.397211	−	0.288591i	−0.371193	−	0.928556i	$-0.621051\pi$
$439$	8.32250	−	6.04665i	0.397211	−	0.288591i	0.768404	+	0.639965i	$0.221051\pi$
$440$	8.72455	−	0.875133i	0.415927	−	0.0417203i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−3.63325	+	1.18052i	−0.172816	+	0.0561514i
$443$			19.3514i			0.919410i	0.888072	+	0.459705i	$0.152045\pi$
$443$			19.3514i			0.919410i	−0.888072	+	0.459705i	$0.847955\pi$
$444$	−0.752550	−	2.31611i	−0.0357144	−	0.109918i
$445$	21.4787	+	4.67211i	1.01819	+	0.221479i
$446$	5.54205	−	17.0567i	0.262424	−	0.807657i
$447$	3.13594	+	1.01893i	0.148325	+	0.0481937i
$448$	0.805753	+	1.10902i	0.0380683	+	0.0523965i
$449$	−10.7463			−0.507147			−0.253574	−	0.967316i	$-0.581606\pi$
$449$	−10.7463			−0.507147			−0.253574	+	0.967316i	$0.581606\pi$
$450$	−8.54425	−	0.980141i	−0.402780	−	0.0462043i
$451$	9.39396			0.442344
$452$	−8.28132	−	11.3983i	−0.389520	−	0.536129i
$453$	−19.7284	−	6.41014i	−0.926921	−	0.301175i
$454$	0.958636	−	2.95038i	0.0449910	−	0.138468i
$455$	0.155790	+	1.55313i	0.00730353	+	0.0728118i
$456$	−2.36192	−	7.26925i	−0.110607	−	0.340414i
$457$			24.6490i			1.15303i	0.817086	+	0.576515i	$0.195588\pi$
$457$			24.6490i			1.15303i	−0.817086	+	0.576515i	$0.804412\pi$
$458$	−5.81319	+	1.88882i	−0.271633	+	0.0882588i
$459$	2.57399	+	1.87012i	0.120144	+	0.0872895i
$460$	6.92767	+	4.04366i	0.323004	+	0.188537i
$461$	−23.2970	+	16.9263i	−1.08505	+	0.788335i	−0.978557	−	0.205978i	$-0.933962\pi$
$461$	−23.2970	+	16.9263i	−1.08505	+	0.788335i	−0.106494	+	0.994313i	$0.533962\pi$
$462$	2.21326	−	3.04629i	0.102970	−	0.141726i
$463$	−14.9849	+	20.6250i	−0.696409	+	0.958524i	0.303575	+	0.952807i	$0.401820\pi$
$463$	−14.9849	+	20.6250i	−0.696409	+	0.958524i	−0.999984	+	0.00571658i	$0.998180\pi$
$464$	−13.5306	+	9.83053i	−0.628140	+	0.456371i
$465$	7.23347	−	6.45114i	0.335444	−	0.299164i
$466$	−33.8037	−	24.5598i	−1.56593	−	1.13771i
$467$	39.1088	−	12.7072i	1.80974	−	0.588020i	0.809741	−	0.586787i	$-0.199607\pi$
$467$	39.1088	−	12.7072i	1.80974	−	0.588020i	0.999999	−	0.00123346i	$-0.000392624\pi$
$468$			0.669165i			0.0309322i
$469$	2.64277	+	8.13363i	0.122032	+	0.375576i
$470$	−0.785192	+	1.34520i	−0.0362182	+	0.0620496i
$471$	−4.02152	+	12.3770i	−0.185302	+	0.570300i
$472$	−19.8905	−	6.46283i	−0.915536	−	0.297476i
$473$	−12.1681	−	16.7480i	−0.559492	−	0.770074i
$474$	−18.4511			−0.847487
$475$	−20.9099	+	4.23745i	−0.959413	+	0.194428i
$476$	3.04991			0.139792
$477$	−3.05210	−	4.20086i	−0.139746	−	0.192344i
$478$	27.6235	+	8.97543i	1.26347	+	0.410526i
$479$	9.89226	−	30.4452i	0.451989	−	1.39108i	−0.422645	−	0.906295i	$-0.638898\pi$
$479$	9.89226	−	30.4452i	0.451989	−	1.39108i	0.874634	−	0.484783i	$-0.161102\pi$
$480$	10.2655	−	4.51223i	0.468554	−	0.205954i
$481$	−0.548018	−	1.68663i	−0.0249875	−	0.0769035i
$482$		−	22.3916i		−	1.01991i
$483$	−3.55908	+	1.15642i	−0.161944	+	0.0526188i
$484$	−4.81423	−	3.49774i	−0.218829	−	0.158988i
$485$	1.68909	+	3.84275i	0.0766976	+	0.174490i
$486$	1.39156	−	1.01102i	0.0631223	−	0.0458610i
$487$	−1.48861	+	2.04889i	−0.0674553	+	0.0928443i	−0.841412	−	0.540395i	$-0.818275\pi$
$487$	−1.48861	+	2.04889i	−0.0674553	+	0.0928443i	0.773956	+	0.633239i	$0.218275\pi$
$488$	−1.35131	+	1.85992i	−0.0611711	+	0.0841948i
$489$	6.97130	−	5.06494i	0.315253	−	0.229045i
$490$	0.817513	−	3.75828i	0.0369315	−	0.169782i
$491$	9.55675	+	6.94338i	0.431290	+	0.313351i	0.782165	−	0.623072i	$-0.214116\pi$
$491$	9.55675	+	6.94338i	0.431290	+	0.313351i	−0.350875	+	0.936422i	$0.614116\pi$
$492$	3.91220	−	1.27115i	0.176376	−	0.0573079i
$493$		−	10.6460i		−	0.479472i
$494$	1.58323	+	4.87268i	0.0712329	+	0.219232i
$495$	3.25811	+	3.65323i	0.146441	+	0.164200i
$496$	−6.69491	+	20.6048i	−0.300610	+	0.925183i
$497$	12.5394	+	4.07431i	0.562471	+	0.182758i
$498$	5.99460	+	8.25087i	0.268625	+	0.369730i
$499$	−37.5232			−1.67977			−0.839885	−	0.542765i	$-0.817377\pi$
$499$	−37.5232			−1.67977			−0.839885	+	0.542765i	$0.817377\pi$
$500$	−3.16638	−	10.2390i	−0.141605	−	0.457904i
$501$	20.7384			0.926522
$502$	−13.2008	−	18.1694i	−0.589182	−	0.810939i
$503$	−23.3532	−	7.58791i	−1.04127	−	0.338328i	−0.262032	−	0.965059i	$-0.584393\pi$
$503$	−23.3532	−	7.58791i	−1.04127	−	0.338328i	−0.779236	+	0.626731i	$0.784393\pi$
$504$	−0.553533	+	1.70360i	−0.0246563	+	0.0758844i
$505$	−11.2101	−	12.5695i	−0.498842	−	0.559337i
$506$	−4.35440	−	13.4015i	−0.193577	−	0.595767i
$507$		−	12.5127i		−	0.555709i
$508$	−5.72781	+	1.86108i	−0.254130	+	0.0825719i
$509$	12.5840	+	9.14278i	0.557774	+	0.405247i	0.830644	−	0.556804i	$-0.187973\pi$
$509$	12.5840	+	9.14278i	0.557774	+	0.405247i	−0.272869	+	0.962051i	$0.587973\pi$
$510$	−2.60103	+	11.9575i	−0.115175	+	0.529485i
$511$	6.79361	−	4.93585i	0.300532	−	0.218349i
$512$	−4.20785	+	5.79161i	−0.185963	+	0.255956i
$513$	2.50808	−	3.45207i	0.110734	−	0.152413i
$514$	8.64401	−	6.28024i	0.381271	−	0.277009i
$515$	−8.97525	−	20.4191i	−0.395497	−	0.899772i
$516$	−7.33380	−	5.32832i	−0.322853	−	0.234566i
$517$	0.843147	−	0.273955i	0.0370816	−	0.0120485i
$518$			4.36977i			0.191997i
$519$	−4.96031	−	15.2663i	−0.217733	−	0.670115i
$520$	2.55968	−	1.12511i	0.112249	−	0.0493394i
$521$	−12.3216	+	37.9220i	−0.539820	+	1.66139i	0.193179	+	0.981164i	$0.438120\pi$
$521$	−12.3216	+	37.9220i	−0.539820	+	1.66139i	−0.732998	+	0.680230i	$0.761880\pi$
$522$	−5.47377	−	1.77853i	−0.239580	−	0.0778444i
$523$	10.8245	+	14.8986i	0.473320	+	0.651470i	0.977204	−	0.212302i	$-0.0680960\pi$
$523$	10.8245	+	14.8986i	0.473320	+	0.651470i	−0.503884	+	0.863772i	$0.668096\pi$
$524$	−4.68142			−0.204509
$525$	4.54821	+	2.07696i	0.198500	+	0.0906459i
$526$	17.4562			0.761128
$527$	−8.10605	−	11.1570i	−0.353105	−	0.486008i
$528$	−10.4063	−	3.38123i	−0.452878	−	0.147149i
$529$	2.77980	−	8.55534i	0.120861	−	0.371971i
$530$	10.0677	−	17.2481i	0.437312	−	0.749211i
$531$	−3.60796	−	11.1042i	−0.156572	−	0.481879i
$532$		−	4.09033i		−	0.177338i
$533$	2.84892	−	0.925671i	0.123401	−	0.0400953i
$534$	−13.6792	−	9.93855i	−0.591959	−	0.430083i
$535$	27.8276	−	24.8179i	1.20309	−	1.07297i
$536$	12.3936	−	9.00446i	0.535321	−	0.388934i
$537$	−1.54205	+	2.12245i	−0.0665444	+	0.0915905i
$538$	27.7631	−	38.2127i	1.19695	−	1.64747i
$539$	−1.77104	+	1.28674i	−0.0762841	+	0.0554236i
$540$	1.85121	+	1.08055i	0.0796634	+	0.0464993i
$541$	9.52885	+	6.92311i	0.409677	+	0.297648i	0.773471	−	0.633832i	$-0.218519\pi$
$541$	9.52885	+	6.92311i	0.409677	+	0.297648i	−0.363794	+	0.931479i	$0.618519\pi$
$542$	10.9136	−	3.54603i	0.468777	−	0.152315i
$543$		−	12.1803i		−	0.522707i
$544$	−4.93044	−	15.1743i	−0.211391	−	0.650594i
$545$	0.689031	+	6.86923i	0.0295148	+	0.294245i
$546$	0.371041	−	1.14195i	0.0158791	−	0.0488708i
$547$	20.9959	+	6.82199i	0.897721	+	0.291687i	0.721296	−	0.692627i	$-0.243547\pi$
$547$	20.9959	+	6.82199i	0.897721	+	0.291687i	0.176425	+	0.984314i	$0.443547\pi$
$548$	−5.00653	−	6.89090i	−0.213868	−	0.294365i
$549$	−1.28344			−0.0547760
$550$	−7.82063	+	17.1259i	−0.333473	+	0.730253i
$551$	−14.2777			−0.608252
$552$	3.94014	+	5.42314i	0.167704	+	0.230824i
$553$	10.2020	+	3.31483i	0.433833	+	0.140961i
$554$	−11.3921	+	35.0612i	−0.484003	+	1.48961i
$555$	−5.55088	−	1.20745i	−0.235622	−	0.0512533i
$556$	6.43503	+	19.8050i	0.272906	+	0.839918i
$557$		−	39.4246i		−	1.67048i	−0.549889	−	0.835238i	$-0.685330\pi$
$557$		−	39.4246i		−	1.67048i	0.549889	−	0.835238i	$-0.314670\pi$
$558$	−7.09072	+	2.30391i	−0.300174	+	0.0975325i
$559$	−5.34059	−	3.88016i	−0.225883	−	0.164113i
$560$	−11.1207	+	1.11548i	−0.469935	+	0.0471378i
$561$	5.63480	−	4.09392i	0.237901	−	0.172845i
$562$	18.6276	−	25.6386i	0.785756	−	1.08150i
$563$	−9.58549	+	13.1933i	−0.403980	+	0.556031i	−0.961737	−	0.273973i	$-0.911662\pi$
$563$	−9.58549	+	13.1933i	−0.403980	+	0.556031i	0.557757	+	0.830004i	$0.311662\pi$
$564$	0.314066	−	0.228182i	0.0132246	−	0.00960820i
$565$	−32.7006	+	3.28009i	−1.37572	+	0.137994i
$566$	24.0299	+	17.4588i	1.01005	+	0.733847i
$567$	−0.951057	+	0.309017i	−0.0399406	+	0.0129775i
$568$		−	23.6175i		−	0.990967i
$569$	10.4078	+	32.0318i	0.436316	+	1.34284i	0.891732	+	0.452565i	$0.149491\pi$
$569$	10.4078	+	32.0318i	0.436316	+	1.34284i	−0.455415	+	0.890279i	$0.650509\pi$
$570$	16.0366	+	3.48832i	0.671697	+	0.146110i
$571$	−5.34161	+	16.4398i	−0.223539	+	0.687983i	0.774897	+	0.632087i	$0.217802\pi$
$571$	−5.34161	+	16.4398i	−0.223539	+	0.687983i	−0.998437	+	0.0558962i	$0.982198\pi$
$572$	1.39319	+	0.452675i	0.0582522	+	0.0189273i
$573$	0.274920	+	0.378394i	0.0114849	+	0.0158077i
$574$	−7.38110			−0.308081
$575$	16.2925	−	9.20133i	0.679443	−	0.383722i
$576$	1.37083			0.0571179
$577$	−23.3226	−	32.1008i	−0.970931	−	1.33637i	−0.941575	−	0.336803i	$-0.890654\pi$
$577$	−23.3226	−	32.1008i	−0.970931	−	1.33637i	−0.0293558	−	0.999569i	$-0.509346\pi$
$578$	−11.2503	−	3.65543i	−0.467949	−	0.152046i
$579$	−6.40000	+	19.6972i	−0.265975	+	0.818587i
$580$	−0.715839	−	7.13649i	−0.0297236	−	0.296327i
$581$	−1.83224	−	5.63904i	−0.0760139	−	0.233947i
$582$		−	3.22892i		−	0.133843i
$583$	−10.8108	+	3.51264i	−0.447737	+	0.145479i
$584$	−12.1692	−	8.84144i	−0.503565	−	0.365862i
$585$	1.34808	+	0.786870i	0.0557362	+	0.0325331i
$586$	−7.11220	+	5.16731i	−0.293802	+	0.213460i
$587$	9.73783	−	13.4030i	0.401923	−	0.553200i	−0.559302	−	0.828964i	$-0.688931\pi$
$587$	9.73783	−	13.4030i	0.401923	−	0.553200i	0.961225	+	0.275764i	$0.0889308\pi$
$588$	−0.563450	+	0.775522i	−0.0232363	+	0.0319820i
$589$	−14.9631	+	10.8713i	−0.616542	+	0.447944i
$590$	33.5141	−	29.8894i	1.37976	−	1.23053i
$591$	9.93118	+	7.21542i	0.408514	+	0.296803i
$592$	12.0766	−	3.92391i	0.496344	−	0.161272i
$593$		−	43.2800i		−	1.77730i	−0.458588	−	0.888649i	$-0.651644\pi$
$593$		−	43.2800i		−	1.77730i	0.458588	−	0.888649i	$-0.348356\pi$
$594$	−1.16358	−	3.58113i	−0.0477422	−	0.146936i
$595$	3.58638	−	6.14425i	0.147027	−	0.251890i
$596$	0.976744	−	3.00611i	0.0400090	−	0.123135i
$597$	8.30284	+	2.69776i	0.339813	+	0.110412i
$598$	−2.64113	−	3.63521i	−0.108004	−	0.148655i
$599$	−47.9358			−1.95860			−0.979302	−	0.202403i	$-0.935125\pi$
$599$	−47.9358			−1.95860			−0.979302	+	0.202403i	$0.935125\pi$
$600$	1.02072	−	8.89800i	0.0416707	−	0.363259i
$601$	23.0440			0.939984			0.469992	−	0.882671i	$-0.344257\pi$
$601$	23.0440			0.939984			0.469992	+	0.882671i	$0.344257\pi$
$602$	9.56085	+	13.1594i	0.389671	+	0.536336i
$603$	8.13363	+	2.64277i	0.331227	+	0.107622i
$604$	−6.14475	+	18.9116i	−0.250026	+	0.769502i
$605$	−12.7075	+	5.58561i	−0.516633	+	0.227087i
$606$	4.00349	+	12.3215i	0.162631	+	0.500526i
$607$		−	24.9148i		−	1.01126i	−0.862750	−	0.505630i	$-0.831260\pi$
$607$		−	24.9148i		−	1.01126i	0.862750	−	0.505630i	$-0.168740\pi$
$608$	−20.3508	+	6.61238i	−0.825335	+	0.268167i
$609$	2.70704	+	1.96678i	0.109695	+	0.0796979i
$610$	−1.98636	−	4.51904i	−0.0804252	−	0.182971i
$611$	0.228707	−	0.166166i	0.00925252	−	0.00672235i
$612$	1.79269	−	2.46743i	0.0724652	−	0.0997398i
$613$	−16.5496	+	22.7786i	−0.668434	+	0.920020i	−0.999724	−	0.0235088i	$-0.992516\pi$
$613$	−16.5496	+	22.7786i	−0.668434	+	0.920020i	0.331290	+	0.943529i	$0.392516\pi$
$614$	−27.5059	+	19.9842i	−1.11005	+	0.806498i
$615$	2.03953	−	9.37614i	0.0822417	−	0.378082i
$616$	3.17241	+	2.30489i	0.127820	+	0.0928668i
$617$	19.2233	−	6.24602i	0.773900	−	0.251455i	0.104666	−	0.994507i	$-0.466623\pi$
$617$	19.2233	−	6.24602i	0.773900	−	0.251455i	0.669234	+	0.743052i	$0.266623\pi$
$618$			17.1574i			0.690172i
$619$	−12.1878	−	37.5103i	−0.489870	−	1.50767i	−0.824801	−	0.565423i	$-0.808713\pi$
$619$	−12.1878	−	37.5103i	−0.489870	−	1.50767i	0.334931	−	0.942243i	$-0.391287\pi$
$620$	−6.18405	−	6.93400i	−0.248357	−	0.278476i
$621$	−1.15642	+	3.55908i	−0.0464054	+	0.142821i
$622$	−43.6793	−	14.1923i	−1.75138	−	0.569059i
$623$	5.77803	+	7.95278i	0.231492	+	0.318621i
$624$	−3.48913			−0.139677
$625$	−24.3506	−	5.66118i	−0.974023	−	0.226447i
$626$	−13.8257			−0.552586
$627$	−5.49049	−	7.55702i	−0.219269	−	0.301798i
$628$	11.8645	+	3.85502i	0.473446	+	0.153832i
$629$	−2.49775	+	7.68727i	−0.0995917	+	0.306512i
$630$	−2.55999	−	2.87044i	−0.101992	−	0.114361i
$631$	5.31543	+	16.3592i	0.211604	+	0.651249i	0.999377	+	0.0352844i	$0.0112337\pi$
$631$	5.31543	+	16.3592i	0.211604	+	0.651249i	−0.787774	+	0.615965i	$0.788766\pi$
$632$		−	19.2150i		−	0.764332i
$633$	23.9540	−	7.78313i	0.952086	−	0.309352i
$634$	−2.42827	−	1.76424i	−0.0964387	−	0.0700668i
$635$	−2.98605	+	13.7275i	−0.118498	+	0.544759i
$636$	−4.02693	+	2.92574i	−0.159678	+	0.116013i
$637$	−0.410313	+	0.564747i	−0.0162572	+	0.0223761i
$638$	−7.40576	+	10.1931i	−0.293197	+	0.403551i
$639$	10.6667	−	7.74980i	0.421968	−	0.306577i
$640$	11.1461	+	25.3578i	0.440587	+	1.00235i
$641$	11.5078	+	8.36093i	0.454532	+	0.330237i	0.791383	−	0.611321i	$-0.209362\pi$
$641$	11.5078	+	8.36093i	0.454532	+	0.330237i	−0.336850	+	0.941558i	$0.609362\pi$
$642$	−27.2784	+	8.86329i	−1.07659	+	0.349806i
$643$		−	18.5514i		−	0.731597i	−0.930694	−	0.365798i	$-0.880796\pi$
$643$		−	18.5514i		−	0.731597i	0.930694	−	0.365798i	$-0.119204\pi$
$644$	1.10854	+	3.41173i	0.0436826	+	0.134441i
$645$	−19.3581	+	8.50888i	−0.762223	+	0.335037i
$646$	7.21601	−	22.2086i	0.283910	−	0.873786i
$647$	4.09160	+	1.32944i	0.160857	+	0.0522657i	0.388339	−	0.921517i	$-0.373049\pi$
$647$	4.09160	+	1.32944i	0.160857	+	0.0522657i	−0.227481	+	0.973782i	$0.573049\pi$
$648$	1.05288	+	1.44917i	0.0413611	+	0.0569287i
$649$	−25.5593			−1.00329
$650$	−0.684203	+	5.96445i	−0.0268367	+	0.233945i
$651$	4.33452			0.169883
$652$	−4.85525	−	6.68267i	−0.190146	−	0.261714i
$653$	10.3375	+	3.35885i	0.404536	+	0.131442i	0.504216	−	0.863578i	$-0.331782\pi$
$653$	10.3375	+	3.35885i	0.404536	+	0.131442i	−0.0996793	+	0.995020i	$0.531782\pi$
$654$	1.64105	−	5.05064i	0.0641702	−	0.197496i
$655$	−5.50487	+	9.43103i	−0.215093	+	0.368501i
$656$	6.62798	+	20.3988i	0.258779	+	0.796441i
$657$		−	8.39737i		−	0.327613i
$658$	−0.662484	+	0.215254i	−0.0258263	+	0.00839148i
$659$	30.3684	+	22.0640i	1.18299	+	0.859490i	0.992505	−	0.122201i	$-0.0389952\pi$
$659$	30.3684	+	22.0640i	1.18299	+	0.859490i	0.190481	+	0.981691i	$0.438995\pi$
$660$	3.50198	−	3.12322i	0.136314	−	0.121571i
$661$	−9.51392	+	6.91227i	−0.370049	+	0.268856i	−0.757231	−	0.653147i	$-0.773448\pi$
$661$	−9.51392	+	6.91227i	−0.370049	+	0.268856i	0.387182	+	0.922003i	$0.373448\pi$
$662$	−32.1600	+	44.2645i	−1.24994	+	1.72039i
$663$	1.30546	−	1.79682i	0.0507000	−	0.0697826i
$664$	−8.59246	+	6.24279i	−0.333452	+	0.242267i
$665$	−8.24026	−	4.80982i	−0.319543	−	0.186517i
$666$	3.53522	+	2.56849i	0.136987	+	0.0995269i
$667$	11.9090	−	3.86947i	0.461118	−	0.149826i
$668$		−	19.8798i		−	0.769171i
$669$	3.22202	+	9.91635i	0.124570	+	0.383388i
$670$	3.28294	+	32.7289i	0.126831	+	1.26443i
$671$	−0.868219	+	2.67210i	−0.0335172	+	0.103155i
$672$	4.76936	+	1.54966i	0.183982	+	0.0597794i
$673$	−22.9055	−	31.5267i	−0.882943	−	1.21527i	−0.975597	−	0.219568i	$-0.929535\pi$
$673$	−22.9055	−	31.5267i	−0.882943	−	1.21527i	0.0926546	−	0.995698i	$-0.470465\pi$
$674$	−22.2590			−0.857385
$675$	4.35367	−	2.45878i	0.167573	−	0.0946383i
$676$	−11.9947			−0.461333
$677$	14.5106	+	19.9721i	0.557686	+	0.767589i	0.991030	−	0.133640i	$-0.0426664\pi$
$677$	14.5106	+	19.9721i	0.557686	+	0.767589i	−0.433344	+	0.901229i	$0.642666\pi$
$678$	24.0433	+	7.81213i	0.923376	+	0.300023i
$679$	−0.580092	+	1.78534i	−0.0222619	+	0.0685151i
$680$	−12.4525	−	2.70871i	−0.477532	−	0.103874i
$681$	0.557328	+	1.71528i	0.0213569	+	0.0657296i
$682$			16.3213i			0.624975i
$683$	−16.2633	+	5.28427i	−0.622298	+	0.202197i	−0.603160	−	0.797620i	$-0.706092\pi$
$683$	−16.2633	+	5.28427i	−0.622298	+	0.202197i	−0.0191377	+	0.999817i	$0.506092\pi$
$684$	−3.30915	−	2.40424i	−0.126528	−	0.0919283i
$685$	−19.7694	+	1.98300i	−0.755348	+	0.0757666i
$686$	1.39156	−	1.01102i	0.0531299	−	0.0386011i
$687$	2.08874	−	2.87490i	0.0796903	−	0.109684i
$688$	27.7827	−	38.2396i	1.05921	−	1.45787i
$689$	−2.93247	+	2.13057i	−0.111718	+	0.0811682i
$690$	−14.3214	+	1.43654i	−0.545207	+	0.0546880i
$691$	−0.985572	−	0.716060i	−0.0374929	−	0.0272402i	0.568881	−	0.822420i	$-0.307377\pi$
$691$	−0.985572	−	0.716060i	−0.0374929	−	0.0272402i	−0.606374	+	0.795180i	$0.707377\pi$
$692$	−14.6342	+	4.75494i	−0.556309	+	0.180756i
$693$			2.18913i			0.0831580i
$694$	−9.67505	−	29.7767i	−0.367260	−	1.13031i
$695$	47.4654	+	10.3248i	1.80047	+	0.391643i
$696$	1.85217	−	5.70039i	0.0702063	−	0.216073i
$697$	−12.9848	−	4.21901i	−0.491833	−	0.159806i
$698$	31.2964	+	43.0758i	1.18458	+	1.63044i
$699$	24.2920			0.918809
$700$	1.99097	−	4.35991i	0.0752516	−	0.164789i
$701$	17.3517			0.655364			0.327682	−	0.944788i	$-0.393732\pi$
$701$	17.3517			0.655364			0.327682	+	0.944788i	$0.393732\pi$
$702$	−0.705762	−	0.971398i	−0.0266373	−	0.0366630i
$703$	10.3097	+	3.34981i	0.388836	+	0.126341i
$704$	0.927335	−	2.85404i	0.0349502	−	0.107566i
$705$	−0.0903791	−	0.901026i	−0.00340388	−	0.0339346i
$706$	13.7195	+	42.2243i	0.516340	+	1.58913i
$707$		−	7.53206i		−	0.283272i
$708$	−10.6444	+	3.45858i	−0.400042	+	0.129981i
$709$	2.12125	+	1.54118i	0.0796651	+	0.0578801i	0.626905	−	0.779096i	$-0.284321\pi$
$709$	2.12125	+	1.54118i	0.0796651	+	0.0578801i	−0.547240	+	0.836976i	$0.684321\pi$
$710$	43.7959	+	25.5636i	1.64363	+	0.959384i
$711$	8.67834	−	6.30519i	0.325463	−	0.236463i
$712$	10.3500	−	14.2456i	0.387884	−	0.533876i
$713$	9.53436	−	13.1229i	0.357065	−	0.491457i
$714$	−4.42742	+	3.21671i	−0.165692	+	0.120382i
$715$	2.55019	−	2.27438i	0.0953718	−	0.0850569i
$716$	2.03458	+	1.47821i	0.0760357	+	0.0552432i
$717$	−16.0596	+	5.21810i	−0.599759	+	0.194873i
$718$		−	15.9409i		−	0.594908i
$719$	5.28313	+	16.2598i	0.197028	+	0.606388i	0.999947	+	0.0103008i	$0.00327890\pi$
$719$	5.28313	+	16.2598i	0.197028	+	0.606388i	−0.802919	+	0.596088i	$0.796721\pi$
$720$	−5.63414	+	9.65250i	−0.209972	+	0.359727i
$721$	3.08242	−	9.48670i	0.114795	−	0.353303i
$722$	1.29686	+	0.421376i	0.0482642	+	0.0156820i
$723$	7.65177	+	10.5318i	0.284572	+	0.391680i
$724$	−11.6760			−0.433936
$725$	−15.2187	−	6.94968i	−0.565209	−	0.258105i
$726$	10.6777			0.396285
$727$	−19.0547	−	26.2266i	−0.706702	−	0.972691i	−0.999862	−	0.0166279i	$-0.994707\pi$
$727$	−19.0547	−	26.2266i	−0.706702	−	0.972691i	0.293160	−	0.956063i	$-0.405293\pi$
$728$	1.18923	+	0.386403i	0.0440756	+	0.0143210i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	29.5674	−	12.9964i	1.09434	−	0.481019i
$731$	9.29752	+	28.6148i	0.343881	+	1.05836i
$732$			1.23031i			0.0454734i
$733$	−21.1624	+	6.87608i	−0.781652	+	0.253974i	−0.672545	−	0.740056i	$-0.734799\pi$
$733$	−21.1624	+	6.87608i	−0.781652	+	0.253974i	−0.109106	+	0.994030i	$0.534799\pi$
$734$	49.9247	+	36.2724i	1.84275	+	1.33884i
$735$	0.899783	+	2.04704i	0.0331890	+	0.0755064i
$736$	15.1825	−	11.0307i	0.559634	−	0.406598i
$737$	11.0044	−	15.1463i	0.405353	−	0.557921i
$738$	−4.33850	+	5.97143i	−0.159702	+	0.219811i
$739$	10.9875	−	7.98285i	0.404180	−	0.293654i	−0.367061	−	0.930197i	$-0.619636\pi$
$739$	10.9875	−	7.98285i	0.404180	−	0.293654i	0.771241	+	0.636543i	$0.219636\pi$
$740$	−1.15746	+	5.32107i	−0.0425489	+	0.195606i
$741$	−2.40977	−	1.75080i	−0.0885252	−	0.0643173i
$742$	8.49434	−	2.75998i	0.311837	−	0.101322i
$743$			38.0676i			1.39656i	0.715822	+	0.698282i	$0.246052\pi$
$743$			38.0676i			1.39656i	−0.715822	+	0.698282i	$0.753948\pi$
$744$	−2.39930	−	7.38429i	−0.0879626	−	0.270721i
$745$	−4.90746	−	5.50260i	−0.179795	−	0.201600i
$746$	−16.9975	+	52.3129i	−0.622323	+	1.91531i
$747$	−5.63904	−	1.83224i	−0.206322	−	0.0670380i
$748$	−3.92442	−	5.40151i	−0.143491	−	0.197499i
$749$	16.6751			0.609297
$750$	15.3955	+	11.5240i	0.562165	+	0.420798i
$751$	16.4363			0.599768			0.299884	−	0.953976i	$-0.403052\pi$
$751$	16.4363			0.599768			0.299884	+	0.953976i	$0.403052\pi$
$752$	1.18978	+	1.63759i	0.0433868	+	0.0597167i
$753$	12.4178	+	4.03480i	0.452531	+	0.147036i
$754$	−1.24153	+	3.82105i	−0.0452140	+	0.139154i
$755$	30.8731	+	34.6172i	1.12359	+	1.25985i
$756$	0.296223	+	0.911681i	0.0107735	+	0.0331575i
$757$			28.4659i			1.03461i	0.855800	+	0.517306i	$0.173065\pi$
$757$			28.4659i			1.03461i	−0.855800	+	0.517306i	$0.826935\pi$
$758$	−41.0470	+	13.3370i	−1.49090	+	0.484421i
$759$	6.62766	+	4.81528i	0.240569	+	0.174784i
$760$	−3.63275	+	16.7005i	−0.131774	+	0.605791i
$761$	−34.2185	+	24.8612i	−1.24042	+	0.901217i	−0.997626	−	0.0688619i	$-0.978063\pi$
$761$	−34.2185	+	24.8612i	−1.24042	+	0.901217i	−0.242792	+	0.970078i	$0.578063\pi$
$762$	6.35195	−	8.74271i	0.230107	−	0.316715i
$763$	−1.81474	+	2.49778i	−0.0656982	+	0.0904258i
$764$	0.362728	−	0.263537i	0.0131230	−	0.00953445i
$765$	−2.86278	−	6.51294i	−0.103504	−	0.235476i
$766$	9.38490	+	6.81853i	0.339090	+	0.246363i
$767$	−7.75143	+	2.51859i	−0.279888	+	0.0909411i
$768$		−	18.5656i		−	0.669927i
$769$	5.03323	+	15.4907i	0.181503	+	0.558609i	0.999871	−	0.0160862i	$-0.00512061\pi$
$769$	5.03323	+	15.4907i	0.181503	+	0.558609i	−0.818368	+	0.574695i	$0.805121\pi$
$770$	−7.70799	+	3.38806i	−0.277777	+	0.122097i
$771$	−1.91954	+	5.90773i	−0.0691305	+	0.212762i
$772$	18.8817	+	6.13503i	0.679567	+	0.220805i
$773$	7.76223	+	10.6838i	0.279188	+	0.384269i	0.925465	−	0.378834i	$-0.123675\pi$
$773$	7.76223	+	10.6838i	0.279188	+	0.384269i	−0.646277	+	0.763103i	$0.723675\pi$
$774$	16.2659			0.584665
$775$	−21.2408	+	4.30451i	−0.762993	+	0.154623i
$776$	3.36261			0.120711
$777$	−1.49326	−	2.05529i	−0.0535703	−	0.0737332i
$778$	42.5278	+	13.8181i	1.52470	+	0.495404i
$779$	−5.65825	+	17.4143i	−0.202728	+	0.623932i
$780$	0.754292	−	1.29227i	0.0270080	−	0.0462705i
$781$	−8.91918	−	27.4504i	−0.319153	−	0.982253i
$782$			20.4798i			0.732355i
$783$	3.18232	−	1.03400i	0.113727	−	0.0369520i
$784$	−4.04370	−	2.93792i	−0.144418	−	0.104926i
$785$	21.7177	−	19.3688i	0.775138	−	0.691302i
$786$	6.79581	−	4.93744i	0.242399	−	0.176113i
$787$	−0.766539	+	1.05505i	−0.0273242	+	0.0376085i	−0.822461	−	0.568822i	$-0.807399\pi$
$787$	−0.766539	+	1.05505i	−0.0273242	+	0.0376085i	0.795136	+	0.606431i	$0.207399\pi$
$788$	6.91669	−	9.52001i	0.246397	−	0.339136i
$789$	−8.21041	+	5.96521i	−0.292298	+	0.212367i
$790$	35.6321	+	20.7983i	1.26773	+	0.739972i
$791$	−11.8905	−	8.63899i	−0.422779	−	0.307167i
$792$	3.72939	−	1.21175i	0.132518	−	0.0430578i
$793$			0.895927i			0.0318153i
$794$	8.23040	+	25.3306i	0.292086	+	0.898949i
$795$	1.15884	+	11.5529i	0.0410997	+	0.409739i
$796$	2.58607	−	7.95909i	0.0916607	−	0.282103i
$797$	5.59642	+	1.81839i	0.198235	+	0.0644105i	0.406452	−	0.913672i	$-0.366766\pi$
$797$	5.59642	+	1.81839i	0.198235	+	0.0644105i	−0.208217	+	0.978083i	$0.566766\pi$
$798$	4.31404	+	5.93776i	0.152715	+	0.210194i
$799$	−1.28848			−0.0455830
$800$	−24.9106	−	2.85759i	−0.880724	−	0.101031i
$801$	9.83018			0.347332
$802$	−3.18372	−	4.38201i	−0.112421	−	0.154734i
$803$	−17.4832	−	5.68063i	−0.616968	−	0.200465i
$804$	2.53336	−	7.79688i	0.0893447	−	0.274975i
$805$	8.17670	+	1.77862i	0.288191	+	0.0626882i
$806$	1.60828	+	4.94979i	0.0566494	+	0.174349i
$807$			27.4604i			0.966652i
$808$	−12.8316	+	4.16924i	−0.451414	+	0.146673i
$809$	34.8318	+	25.3068i	1.22462	+	0.889739i	0.996475	−	0.0838883i	$-0.0267339\pi$
$809$	34.8318	+	25.3068i	1.22462	+	0.889739i	0.228145	+	0.973627i	$0.426734\pi$
$810$	−3.82696	+	0.383871i	−0.134466	+	0.0134878i
$811$	−25.6090	+	18.6060i	−0.899254	+	0.653346i	−0.938274	−	0.345892i	$-0.887576\pi$
$811$	−25.6090	+	18.6060i	−0.899254	+	0.653346i	0.0390203	+	0.999238i	$0.487576\pi$
$812$	1.88535	−	2.59496i	0.0661629	−	0.0910654i
$813$	−3.92135	+	5.39727i	−0.137528	+	0.189291i
$814$	7.73905	−	5.62275i	0.271253	−	0.197077i
$815$	−19.1720	+	1.92308i	−0.671565	+	0.0673626i
$816$	12.8656	+	9.34738i	0.450385	+	0.327224i
$817$	38.3763	−	12.4692i	1.34262	−	0.436243i
$818$		−	39.6674i		−	1.38694i
$819$	0.215714	+	0.663900i	0.00753767	+	0.0231985i
$820$	−8.98795	−	1.95509i	−0.313873	−	0.0682747i
$821$	8.09812	−	24.9234i	0.282626	−	0.869834i	−0.704474	−	0.709730i	$-0.748817\pi$
$821$	8.09812	−	24.9234i	0.282626	−	0.869834i	0.987100	−	0.160104i	$-0.0511831\pi$
$822$	14.5355	+	4.72288i	0.506985	+	0.164729i
$823$	−1.83080	−	2.51989i	−0.0638178	−	0.0878377i	0.775915	−	0.630837i	$-0.217288\pi$
$823$	−1.83080	−	2.51989i	−0.0638178	−	0.0878377i	−0.839733	+	0.543000i	$0.817288\pi$
$824$	−17.8678			−0.622453
$825$	−2.17397	−	10.7276i	−0.0756879	−	0.373486i
$826$	20.0827			0.698766
$827$	−3.30619	−	4.55058i	−0.114968	−	0.158239i	0.747655	−	0.664087i	$-0.231180\pi$
$827$	−3.30619	−	4.55058i	−0.114968	−	0.158239i	−0.862623	+	0.505848i	$0.831180\pi$
$828$	3.41173	+	1.10854i	0.118566	+	0.0385244i
$829$	−10.6250	+	32.7004i	−0.369022	+	1.13573i	0.578402	+	0.815752i	$0.303676\pi$
$829$	−10.6250	+	32.7004i	−0.369022	+	1.13573i	−0.947424	+	0.319981i	$0.896324\pi$
$830$	−2.27606	−	22.6910i	−0.0790032	−	0.787615i
$831$	−6.62308	−	20.3838i	−0.229752	−	0.707104i
$832$		−	0.956929i		−	0.0331756i
$833$	3.02591	−	0.983178i	0.104842	−	0.0340651i
$834$	−30.2296	−	21.9631i	−1.04676	−	0.760519i
$835$	−40.0491	−	23.3766i	−1.38596	−	0.808980i
$836$	−7.24414	+	5.26318i	−0.250544	+	0.182031i
$837$	2.54777	−	3.50670i	0.0880637	−	0.121209i
$838$	−24.1875	+	33.2912i	−0.835544	+	1.15003i
$839$	−8.85891	+	6.43637i	−0.305844	+	0.222208i	−0.730111	−	0.683329i	$-0.760532\pi$
$839$	−8.85891	+	6.43637i	−0.305844	+	0.222208i	0.424267	+	0.905537i	$0.360532\pi$
$840$	2.98928	−	2.66598i	0.103140	−	0.0919850i
$841$	14.4035	+	10.4648i	0.496673	+	0.360854i
$842$	22.9277	−	7.44968i	0.790142	−	0.256733i
$843$			18.4244i			0.634572i
$844$	−7.46090	−	22.9623i	−0.256815	−	0.790394i
$845$	−14.1045	+	24.1641i	−0.485210	+	0.831269i
$846$	−0.215254	+	0.662484i	−0.00740059	+	0.0227767i
$847$	−5.90390	−	1.91829i	−0.202860	−	0.0659133i
$848$	−15.2553	−	20.9971i	−0.523868	−	0.721043i
$849$	−17.2684			−0.592650
$850$	18.5016	−	20.1599i	0.634601	−	0.691478i
$851$	−9.50710			−0.325899
$852$	−7.42895	−	10.2251i	−0.254512	−	0.350305i
$853$	1.57641	+	0.512207i	0.0539753	+	0.0175376i	0.335880	−	0.941905i	$-0.390966\pi$
$853$	1.57641	+	0.512207i	0.0539753	+	0.0175376i	−0.281905	+	0.959442i	$0.590966\pi$
$854$	0.682184	−	2.09955i	0.0233439	−	0.0718450i
$855$	−8.73472	+	3.83937i	−0.298721	+	0.131304i
$856$	−9.23025	−	28.4078i	−0.315483	−	0.970958i
$857$			24.3421i			0.831511i	0.909476	+	0.415756i	$0.136483\pi$
$857$			24.3421i			0.831511i	−0.909476	+	0.415756i	$0.863517\pi$
$858$	−2.49986	+	0.812255i	−0.0853440	+	0.0277299i
$859$	−15.9288	−	11.5730i	−0.543485	−	0.394865i	0.281893	−	0.959446i	$-0.409038\pi$
$859$	−15.9288	−	11.5730i	−0.543485	−	0.394865i	−0.825378	+	0.564581i	$0.809038\pi$
$860$	8.15660	+	18.5566i	0.278138	+	0.632775i
$861$	3.47165	−	2.52230i	0.118313	−	0.0859597i
$862$	1.55188	−	2.13598i	0.0528573	−	0.0727519i
$863$	−24.6819	+	33.9717i	−0.840181	+	1.15641i	0.145760	+	0.989320i	$0.453437\pi$
$863$	−24.6819	+	33.9717i	−0.840181	+	1.15641i	−0.985942	+	0.167091i	$0.946563\pi$
$864$	4.05706	−	2.94762i	0.138024	−	0.100280i
$865$	−7.62919	+	35.0730i	−0.259400	+	1.19252i
$866$	6.79533	+	4.93710i	0.230915	+	0.167769i
$867$	6.54063	−	2.12518i	0.222131	−	0.0721748i
$868$		−	4.15506i		−	0.141032i
$869$	−7.25659	−	22.3335i	−0.246163	−	0.757611i
$870$	8.56594	+	9.60475i	0.290413	+	0.325631i
$871$	1.84483	−	5.67781i	0.0625097	−	0.192385i
$872$	5.25974	+	1.70899i	0.178117	+	0.0578738i
$873$	1.10340	+	1.51870i	0.0373445	+	0.0514003i
$874$	27.4661			0.929055
$875$	−6.44216	−	9.13776i	−0.217785	−	0.308913i
$876$	−8.04970			−0.271974
$877$	−3.97083	−	5.46538i	−0.134086	−	0.184553i	0.736694	−	0.676226i	$-0.236386\pi$
$877$	−3.97083	−	5.46538i	−0.134086	−	0.184553i	−0.870780	+	0.491673i	$0.836386\pi$
$878$	16.8285	+	5.46791i	0.567934	+	0.184533i
$879$	1.57938	−	4.86082i	0.0532710	−	0.163951i
$880$	16.2850	+	18.2599i	0.548966	+	0.615540i
$881$	−8.14414	−	25.0651i	−0.274383	−	0.844465i	−0.989382	−	0.145339i	$-0.953573\pi$
$881$	−8.14414	−	25.0651i	−0.274383	−	0.844465i	0.714999	−	0.699126i	$-0.246427\pi$
$882$		−	1.72006i		−	0.0579174i
$883$	39.9247	−	12.9723i	1.34357	−	0.436553i	0.453047	−	0.891487i	$-0.350337\pi$
$883$	39.9247	−	12.9723i	1.34357	−	0.436553i	0.890525	+	0.454934i	$0.150337\pi$
$884$	−1.72243	−	1.25142i	−0.0579315	−	0.0420897i
$885$	−5.54921	+	25.5109i	−0.186535	+	0.857538i
$886$	−26.9285	+	19.5647i	−0.904680	+	0.657289i
$887$	25.3412	−	34.8791i	0.850873	−	1.17113i	−0.132797	−	0.991143i	$-0.542396\pi$
$887$	25.3412	−	34.8791i	0.850873	−	1.17113i	0.983670	−	0.179983i	$-0.0576043\pi$
$888$	−2.67483	+	3.68159i	−0.0897614	+	0.123546i
$889$	−5.08280	+	3.69287i	−0.170472	+	0.123855i
$890$	15.2140	+	34.6124i	0.509973	+	1.16021i
$891$	1.77104	+	1.28674i	0.0593321	+	0.0431073i
$892$	9.50579	−	3.08862i	0.318277	−	0.103415i
$893$			1.72802i			0.0578259i
$894$	1.75262	+	5.39400i	0.0586163	+	0.180402i
$895$	5.37041	−	2.36057i	0.179513	−	0.0789053i
$896$	−3.82795	+	11.7812i	−0.127883	+	0.393583i
$897$	2.48448	+	0.807255i	0.0829542	+	0.0269535i
$898$	−10.8647	−	14.9540i	−0.362561	−	0.499022i
$899$	−14.5037			−0.483725
$900$	−2.35698	−	4.17342i	−0.0785659	−	0.139114i
$901$	16.5208			0.550386
$902$	9.49752	+	13.0722i	0.316233	+	0.435257i
$903$	−8.99376	−	2.92225i	−0.299293	−	0.0972463i
$904$	−8.13556	+	25.0387i	−0.270585	+	0.832775i
$905$	−13.7298	+	23.5222i	−0.456395	+	0.781903i
$906$	−11.0258	−	33.9340i	−0.366308	−	1.12738i
$907$			14.7954i			0.491274i	0.969362	+	0.245637i	$0.0789971\pi$
$907$			14.7954i			0.491274i	−0.969362	+	0.245637i	$0.921003\pi$
$908$	1.64426	−	0.534254i	0.0545668	−	0.0177298i
$909$	−6.09356	−	4.42723i	−0.202111	−	0.146842i
$910$	−2.00376	+	1.78704i	−0.0664240	+	0.0592398i
$911$	−26.1292	+	18.9840i	−0.865698	+	0.628966i	−0.929429	−	0.369001i	$-0.879700\pi$
$911$	−26.1292	+	18.9840i	−0.865698	+	0.628966i	0.0637311	+	0.997967i	$0.479700\pi$
$912$	12.5361	−	17.2544i	0.415111	−	0.571351i
$913$	−7.62936	+	10.5009i	−0.252495	+	0.347530i
$914$	−34.3004	+	24.9207i	−1.13456	+	0.824304i
$915$	2.47854	+	1.44671i	0.0819379	+	0.0478269i
$916$	−2.75588	−	2.00226i	−0.0910567	−	0.0661566i
$917$	−4.64458	+	1.50912i	−0.153378	+	0.0498354i
$918$			5.47259i			0.180622i
$919$	−16.5981	−	51.0837i	−0.547521	−	1.68510i	−0.714919	−	0.699207i	$-0.753536\pi$
$919$	−16.5981	−	51.0837i	−0.547521	−	1.68510i	0.167398	−	0.985889i	$-0.446464\pi$
$920$	−1.49601	−	14.9143i	−0.0493221	−	0.491712i
$921$	6.10813	−	18.7989i	0.201270	−	0.619444i
$922$	−47.1077	−	15.3062i	−1.55141	−	0.504084i
$923$	−5.40987	−	7.44605i	−0.178068	−	0.245090i
$924$	2.09849			0.0690353
$925$	9.35861	+	8.58881i	0.307709	+	0.282398i
$926$	−43.8509			−1.44103
$927$	−5.86310	−	8.06987i	−0.192570	−	0.265049i
$928$	−15.9587	−	5.18529i	−0.523869	−	0.170215i
$929$	6.01242	−	18.5043i	0.197261	−	0.607108i	−0.802682	−	0.596408i	$-0.796594\pi$
$929$	6.01242	−	18.5043i	0.197261	−	0.607108i	0.999943	−	0.0106998i	$-0.00340591\pi$
$930$	16.2903	+	3.54353i	0.534181	+	0.116197i
$931$	−1.31857	−	4.05815i	−0.0432145	−	0.133001i
$932$		−	23.2863i		−	0.762768i
$933$	25.3941	−	8.25105i	0.831366	−	0.270127i
$934$	57.2228	+	41.5748i	1.87239	+	1.36037i
$935$	−15.4964	+	1.55440i	−0.506787	+	0.0508343i
$936$	1.01162	−	0.734981i	0.0330657	−	0.0240236i
$937$	−24.2071	+	33.3182i	−0.790810	+	1.08846i	0.203197	+	0.979138i	$0.434867\pi$
$937$	−24.2071	+	33.3182i	−0.790810	+	1.08846i	−0.994007	+	0.109319i	$0.965133\pi$
$938$	−8.64648	+	11.9009i	−0.282318	+	0.388577i
$939$	6.50281	−	4.72457i	0.212211	−	0.154181i
$940$	−0.863722	+	0.0866373i	−0.0281715	+	0.00282580i
$941$	−14.4281	−	10.4826i	−0.470341	−	0.341723i	0.327233	−	0.944944i	$-0.393884\pi$
$941$	−14.4281	−	10.4826i	−0.470341	−	0.341723i	−0.797574	+	0.603221i	$0.793884\pi$
$942$	−21.2891	+	6.91724i	−0.693636	+	0.225376i
$943$		−	16.0587i		−	0.522943i
$944$	−18.0336	−	55.5017i	−0.586944	−	1.80643i
$945$	2.18497	+	0.475283i	0.0710772	+	0.0154609i
$946$	11.0035	−	33.8653i	0.357755	−	1.10106i
$947$	15.3124	+	4.97530i	0.497586	+	0.161675i	0.547049	−	0.837100i	$-0.315751\pi$
$947$	15.3124	+	4.97530i	0.497586	+	0.161675i	−0.0494632	+	0.998776i	$0.515751\pi$
$948$	−6.04414	−	8.31905i	−0.196305	−	0.270190i
$949$	−5.86192			−0.190286
$950$	−27.0371	−	24.8132i	−0.877199	−	0.805045i
$951$	1.74500			0.0565855
$952$	−3.34988	−	4.61072i	−0.108570	−	0.149434i
$953$	7.53406	+	2.44796i	0.244052	+	0.0792973i	0.428489	−	0.903547i	$-0.359046\pi$
$953$	7.53406	+	2.44796i	0.244052	+	0.0792973i	−0.184437	+	0.982844i	$0.559046\pi$
$954$	2.75998	−	8.49434i	0.0893576	−	0.275014i
$955$	−0.104383	−	1.04063i	−0.00337775	−	0.0336741i
$956$	5.00206	+	15.3948i	0.161778	+	0.497902i
$957$		−	7.32500i		−	0.236784i
$958$	52.3676	−	17.0153i	1.69192	−	0.549738i
$959$	−7.18851	−	5.22276i	−0.232129	−	0.168652i
$960$	−2.64729	−	1.54522i	−0.0854410	−	0.0498717i
$961$	9.87967	−	7.17800i	0.318699	−	0.231548i
$962$	1.79297	−	2.46782i	0.0578078	−	0.0795657i
$963$	9.80141	−	13.4905i	0.315846	−	0.434725i
$964$	10.0957	−	7.33497i	0.325161	−	0.236244i
$965$	34.5624	−	30.8243i	1.11260	−	0.992269i
$966$	−5.20754	−	3.78350i	−0.167550	−	0.121732i
$967$	17.5953	−	5.71706i	0.565827	−	0.183848i	−0.0121146	−	0.999927i	$-0.503856\pi$
$967$	17.5953	−	5.71706i	0.565827	−	0.183848i	0.577941	+	0.816078i	$0.303856\pi$
$968$			11.1197i			0.357401i
$969$	4.19522	+	12.9115i	0.134770	+	0.414779i
$970$	−3.63969	+	6.23558i	−0.116863	+	0.200212i
$971$	−17.2462	+	53.0785i	−0.553458	+	1.70337i	0.146523	+	0.989207i	$0.453192\pi$
$971$	−17.2462	+	53.0785i	−0.553458	+	1.70337i	−0.699981	+	0.714162i	$0.746808\pi$
$972$	0.911681	+	0.296223i	0.0292422	+	0.00950136i
$973$	12.7688	+	17.5747i	0.409349	+	0.563420i
$974$	−4.35617			−0.139581
$975$	−1.71639	−	3.03915i	−0.0549684	−	0.0973306i
$976$	−6.41501			−0.205340
$977$	3.43704	+	4.73067i	0.109961	+	0.151348i	0.860450	−	0.509534i	$-0.170182\pi$
$977$	3.43704	+	4.73067i	0.109961	+	0.151348i	−0.750490	+	0.660882i	$0.770182\pi$
$978$	14.0963	+	4.58017i	0.450750	+	0.146458i
$979$	6.64989	−	20.4663i	0.212531	−	0.654105i
$980$	1.96229	−	0.862531i	0.0626832	−	0.0275525i
$981$	0.954068	+	2.93632i	0.0304610	+	0.0937494i
$982$			20.3187i			0.648395i
$983$	9.28131	−	3.01568i	0.296028	−	0.0961853i	−0.157238	−	0.987561i	$-0.550259\pi$
$983$	9.28131	−	3.01568i	0.296028	−	0.0961853i	0.453266	+	0.891375i	$0.350259\pi$
$984$	−6.21866	−	4.51812i	−0.198244	−	0.144032i
$985$	−11.0454	−	25.1287i	−0.351935	−	0.800668i
$986$	14.8145	−	10.7634i	0.471790	−	0.342776i
$987$	0.238037	−	0.327630i	0.00757681	−	0.0104286i
$988$	−1.67832	+	2.31000i	−0.0533944	+	0.0734910i
$989$	−28.6302	+	20.8011i	−0.910387	+	0.661435i
$990$	−1.78964	+	8.22735i	−0.0568785	+	0.261482i
$991$	−44.4345	−	32.2836i	−1.41151	−	1.02552i	−0.993101	−	0.117262i	$-0.962588\pi$
$991$	−44.4345	−	32.2836i	−1.41151	−	1.02552i	−0.418408	−	0.908259i	$-0.637412\pi$
$992$	−20.6729	+	6.71702i	−0.656364	+	0.213266i
$993$		−	31.8093i		−	1.00944i
$994$	7.00805	+	21.5686i	0.222282	+	0.684113i
$995$	−12.9932	−	14.5689i	−0.411912	−	0.461865i
$996$	−1.75638	+	5.40557i	−0.0556530	+	0.171282i
$997$	−26.7644	−	8.69628i	−0.847637	−	0.275414i	−0.147181	−	0.989110i	$-0.547020\pi$
$997$	−26.7644	−	8.69628i	−0.847637	−	0.275414i	−0.700456	+	0.713696i	$0.747020\pi$
$998$	−37.9369	−	52.2156i	−1.20087	−	1.65286i
$999$	−2.54048			−0.0803773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.15	✓	72
25.9	even	10	inner	525.2.z.b.484.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.15	✓	72	1.1	even	1	trivial
525.2.z.b.484.15	yes	72	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)

\(f(q)\)	\(=\)	\(q+(1.01102 + 1.39156i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.296223 + 0.911681i) q^{4} +(1.48832 + 1.66881i) q^{5} +(-0.531527 - 1.63587i) q^{6} +1.00000i q^{7} +(1.70360 - 0.553533i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.01102 + 1.39156i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.296223 + 0.911681i) q^{4} +(1.48832 + 1.66881i) q^{5} +(-0.531527 - 1.63587i) q^{6} +1.00000i q^{7} +(1.70360 - 0.553533i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.817513 + 3.75828i) q^{10} +(1.77104 - 1.28674i) q^{11} +(0.563450 - 0.775522i) q^{12} +(0.410313 - 0.564747i) q^{13} +(-1.39156 + 1.01102i) q^{14} +(-0.899783 - 2.04704i) q^{15} +(4.04370 + 2.93792i) q^{16} +(-3.02591 + 0.983178i) q^{17} +1.72006i q^{18} +(1.31857 + 4.05815i) q^{19} +(-1.96229 + 0.862531i) q^{20} +(0.309017 - 0.951057i) q^{21} +(3.58113 + 1.16358i) q^{22} +(-2.19964 - 3.02754i) q^{23} -1.79127 q^{24} +(-0.569831 + 4.96742i) q^{25} +1.20071 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.911681 - 0.296223i) q^{28} +(-1.03400 + 3.18232i) q^{29} +(1.93887 - 3.32171i) q^{30} +(1.33944 + 4.12237i) q^{31} +5.01480i q^{32} +(-2.08198 + 0.676477i) q^{33} +(-4.42742 - 3.21671i) q^{34} +(-1.66881 + 1.48832i) q^{35} +(-0.775522 + 0.563450i) q^{36} +(1.49326 - 2.05529i) q^{37} +(-4.31404 + 5.93776i) q^{38} +(-0.564747 + 0.410313i) q^{39} +(3.45923 + 2.01915i) q^{40} +(3.47165 + 2.52230i) q^{41} +(1.63587 - 0.531527i) q^{42} -9.45659i q^{43} +(0.648470 + 1.99578i) q^{44} +(0.223173 + 2.22490i) q^{45} +(1.98910 - 6.12183i) q^{46} +(0.385152 + 0.125144i) q^{47} +(-2.93792 - 4.04370i) q^{48} -1.00000 q^{49} +(-7.48856 + 4.22924i) q^{50} +3.18163 q^{51} +(0.393325 + 0.541366i) q^{52} +(-4.93840 - 1.60458i) q^{53} +(0.531527 - 1.63587i) q^{54} +(4.78318 + 1.04045i) q^{55} +(0.553533 + 1.70360i) q^{56} -4.26699i q^{57} +(-5.47377 + 1.77853i) q^{58} +(-9.44575 - 6.86274i) q^{59} +(2.13279 - 0.213933i) q^{60} +(-1.03833 + 0.754388i) q^{61} +(-4.38231 + 6.03173i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(1.10902 - 0.805753i) q^{64} +(1.55313 - 0.155790i) q^{65} +(-3.04629 - 2.21326i) q^{66} +(8.13363 - 2.64277i) q^{67} -3.04991i q^{68} +(1.15642 + 3.55908i) q^{69} +(-3.75828 - 0.817513i) q^{70} +(4.07431 - 12.5394i) q^{71} +(1.70360 + 0.553533i) q^{72} +(-4.93585 - 6.79361i) q^{73} +4.36977 q^{74} +(2.07696 - 4.54821i) q^{75} -4.09033 q^{76} +(1.28674 + 1.77104i) q^{77} +(-1.14195 - 0.371041i) q^{78} +(3.31483 - 10.2020i) q^{79} +(1.11548 + 11.1207i) q^{80} +(0.309017 + 0.951057i) q^{81} +7.38110i q^{82} +(-5.63904 + 1.83224i) q^{83} +(0.775522 + 0.563450i) q^{84} +(-6.14425 - 3.58638i) q^{85} +(13.1594 - 9.56085i) q^{86} +(1.96678 - 2.70704i) q^{87} +(2.30489 - 3.17241i) q^{88} +(7.95278 - 5.77803i) q^{89} +(-2.87044 + 2.55999i) q^{90} +(0.564747 + 0.410313i) q^{91} +(3.41173 - 1.10854i) q^{92} -4.33452i q^{93} +(0.215254 + 0.662484i) q^{94} +(-4.80982 + 8.24026i) q^{95} +(1.54966 - 4.76936i) q^{96} +(1.78534 + 0.580092i) q^{97} +(-1.01102 - 1.39156i) q^{98} +2.18913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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