LMFDB - Embedded newform 357.2.bj.a.26.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(26,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 20, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bj (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$44$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			26.7
Character	$\chi$	$=$	357.26
Dual form			357.2.bj.a.206.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.15355 + 0.577042i) q^{2} +(0.879586 - 1.49209i) q^{3} +(2.57275 - 1.48538i) q^{4} +(0.469021 + 0.611240i) q^{5} +(-1.03323 + 3.72084i) q^{6} +(0.376382 - 2.61884i) q^{7} +(-1.53040 + 1.53040i) q^{8} +(-1.45266 - 2.62484i) q^{9} +(-1.36277 - 1.04569i) q^{10} +(0.745683 - 0.971793i) q^{11} +(0.0466401 - 5.14528i) q^{12} -0.918607 q^{13} +(0.700626 + 5.85699i) q^{14} +(1.32457 - 0.162182i) q^{15} +(-0.558068 + 0.966602i) q^{16} +(4.12262 - 0.0634107i) q^{17} +(4.64301 + 4.81448i) q^{18} +(-2.96790 + 0.795248i) q^{19} +(2.11459 + 0.875893i) q^{20} +(-3.57649 - 2.86509i) q^{21} +(-1.04510 + 2.52309i) q^{22} +(-4.99071 - 0.657040i) q^{23} +(0.937372 + 3.62961i) q^{24} +(1.14046 - 4.25626i) q^{25} +(1.97827 - 0.530075i) q^{26} +(-5.19423 - 0.141283i) q^{27} +(-2.92163 - 7.29669i) q^{28} +(0.788160 + 0.326467i) q^{29} +(-2.75894 + 1.11360i) q^{30} +(-1.56607 + 0.206177i) q^{31} +(1.76439 - 6.58478i) q^{32} +(-0.794108 - 1.96740i) q^{33} +(-8.84167 + 2.51548i) q^{34} +(1.77727 - 0.998232i) q^{35} +(-7.63619 - 4.59531i) q^{36} +(6.94564 - 5.32958i) q^{37} +(5.93264 - 3.42521i) q^{38} +(-0.807994 + 1.37064i) q^{39} +(-1.65323 - 0.217652i) q^{40} +(-3.83356 - 9.25504i) q^{41} +(9.35542 + 4.10634i) q^{42} +(0.699131 + 0.699131i) q^{43} +(0.474975 - 3.60780i) q^{44} +(0.923081 - 2.11903i) q^{45} +(11.1269 - 1.46488i) q^{46} +(7.53949 + 4.35293i) q^{47} +(0.951387 + 1.68290i) q^{48} +(-6.71667 - 1.97137i) q^{49} +9.82416i q^{50} +(3.53158 - 6.20709i) q^{51} +(-2.36334 + 1.36448i) q^{52} +(0.572918 - 2.13816i) q^{53} +(11.2676 - 2.69303i) q^{54} +0.943739 q^{55} +(3.43186 + 4.58389i) q^{56} +(-1.42395 + 5.12786i) q^{57} +(-1.88573 - 0.248261i) q^{58} +(0.0323169 - 0.120608i) q^{59} +(3.16688 - 2.38474i) q^{60} +(1.42709 - 10.8398i) q^{61} +(3.25363 - 1.34770i) q^{62} +(-7.42080 + 2.81634i) q^{63} +12.9665i q^{64} +(-0.430846 - 0.561489i) q^{65} +(2.84542 + 3.77866i) q^{66} +(-1.45058 - 2.51248i) q^{67} +(10.5123 - 6.28678i) q^{68} +(-5.37013 + 6.86866i) q^{69} +(-3.25142 + 3.17530i) q^{70} +(-3.39434 + 8.19466i) q^{71} +(6.24019 + 1.79391i) q^{72} +(0.172249 + 1.30836i) q^{73} +(-11.8824 + 15.4854i) q^{74} +(-5.34758 - 5.44542i) q^{75} +(-6.45442 + 6.45442i) q^{76} +(-2.26431 - 2.31859i) q^{77} +(0.949137 - 3.41799i) q^{78} +(-0.899342 + 6.83118i) q^{79} +(-0.852571 + 0.112243i) q^{80} +(-4.77958 + 7.62598i) q^{81} +(13.5963 + 17.7191i) q^{82} +(-4.23223 + 4.23223i) q^{83} +(-13.4571 - 2.05873i) q^{84} +(1.97235 + 2.49017i) q^{85} +(-1.90904 - 1.10219i) q^{86} +(1.18037 - 0.888849i) q^{87} +(0.346038 + 2.62842i) q^{88} +(12.1356 + 7.00646i) q^{89} +(-0.765135 + 5.09608i) q^{90} +(-0.345747 + 2.40569i) q^{91} +(-13.8158 + 5.72269i) q^{92} +(-1.06986 + 2.51806i) q^{93} +(-18.7485 - 5.02364i) q^{94} +(-1.87810 - 1.44111i) q^{95} +(-8.27314 - 8.42450i) q^{96} +(16.2113 + 6.71494i) q^{97} +(15.6023 + 0.369636i) q^{98} +(-3.63402 - 0.545618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) $ 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$-1$

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 $

$2$	−2.15355	+	0.577042i	−1.52279	+	0.408030i	−0.920659	−	0.390368i	$-0.872348\pi$
$2$	−2.15355	+	0.577042i	−1.52279	+	0.408030i	−0.602130	+	0.798398i	$0.705681\pi$
$3$	0.879586	−	1.49209i	0.507829	−	0.861458i
$3$	0.879586	−	1.49209i	0.507829	−	0.861458i
$4$	2.57275	−	1.48538i	1.28637	−	0.742688i
$5$	0.469021	+	0.611240i	0.209752	+	0.273355i	0.886368	−	0.462982i	$-0.153221\pi$
$5$	0.469021	+	0.611240i	0.209752	+	0.273355i	−0.676615	+	0.736337i	$0.736554\pi$
$6$	−1.03323	+	3.72084i	−0.421816	+	1.51903i
$7$	0.376382	−	2.61884i	0.142259	−	0.989829i
$7$	0.376382	−	2.61884i	0.142259	−	0.989829i
$8$	−1.53040	+	1.53040i	−0.541077	+	0.541077i
$9$	−1.45266	−	2.62484i	−0.484219	−	0.874947i
$10$	−1.36277	−	1.04569i	−0.430946	−	0.330676i
$11$	0.745683	−	0.971793i	0.224832	−	0.293006i	−0.667293	−	0.744795i	$-0.732547\pi$
$11$	0.745683	−	0.971793i	0.224832	−	0.293006i	0.892125	+	0.451789i	$0.149214\pi$
$12$	0.0466401	−	5.14528i	0.0134638	−	1.48532i
$13$	−0.918607			−0.254776			−0.127388	−	0.991853i	$-0.540659\pi$
$13$	−0.918607			−0.254776			−0.127388	+	0.991853i	$0.540659\pi$
$14$	0.700626	+	5.85699i	0.187250	+	1.56535i
$15$	1.32457	−	0.162182i	0.342002	−	0.0418753i
$16$	−0.558068	+	0.966602i	−0.139517	+	0.241651i
$17$	4.12262	−	0.0634107i	0.999882	−	0.0153794i
$17$	4.12262	−	0.0634107i	0.999882	−	0.0153794i
$18$	4.64301	+	4.81448i	1.09437	+	1.13478i
$19$	−2.96790	+	0.795248i	−0.680884	+	0.182442i	−0.582653	−	0.812721i	$-0.697985\pi$
$19$	−2.96790	+	0.795248i	−0.680884	+	0.182442i	−0.0982313	+	0.995164i	$0.531319\pi$
$20$	2.11459	+	0.875893i	0.472837	+	0.195856i
$21$	−3.57649	−	2.86509i	−0.780453	−	0.625214i
$22$	−1.04510	+	2.52309i	−0.222816	+	0.537925i
$23$	−4.99071	−	0.657040i	−1.04064	−	0.137002i	−0.409211	−	0.912440i	$-0.634196\pi$
$23$	−4.99071	−	0.657040i	−1.04064	−	0.137002i	−0.631425	+	0.775437i	$0.717529\pi$
$24$	0.937372	+	3.62961i	0.191340	+	0.740890i
$25$	1.14046	−	4.25626i	0.228092	−	0.851252i
$26$	1.97827	−	0.530075i	0.387970	−	0.103956i
$27$	−5.19423	−	0.141283i	−0.999630	−	0.0271898i
$28$	−2.92163	−	7.29669i	−0.552137	−	1.37894i
$29$	0.788160	+	0.326467i	0.146358	+	0.0606233i	0.454660	−	0.890665i	$-0.349761\pi$
$29$	0.788160	+	0.326467i	0.146358	+	0.0606233i	−0.308302	+	0.951288i	$0.599761\pi$
$30$	−2.75894	+	1.11360i	−0.503711	+	0.203314i
$31$	−1.56607	+	0.206177i	−0.281274	+	0.0370304i	−0.269843	−	0.962904i	$-0.586972\pi$
$31$	−1.56607	+	0.206177i	−0.281274	+	0.0370304i	−0.0114307	+	0.999935i	$0.503639\pi$
$32$	1.76439	−	6.58478i	0.311902	−	1.16404i
$33$	−0.794108	−	1.96740i	−0.138237	−	0.342480i
$34$	−8.84167	+	2.51548i	−1.51633	+	0.431401i
$35$	1.77727	−	0.998232i	0.300414	−	0.168732i
$36$	−7.63619	−	4.59531i	−1.27270	−	0.765885i
$37$	6.94564	−	5.32958i	1.14186	−	0.876177i	0.148236	−	0.988952i	$-0.452641\pi$
$37$	6.94564	−	5.32958i	1.14186	−	0.876177i	0.993621	+	0.112775i	$0.0359739\pi$
$38$	5.93264	−	3.42521i	0.962401	−	0.555642i
$39$	−0.807994	+	1.37064i	−0.129383	+	0.219479i
$40$	−1.65323	−	0.217652i	−0.261398	−	0.0344138i
$41$	−3.83356	−	9.25504i	−0.598702	−	1.44539i	−0.874905	−	0.484295i	$-0.839076\pi$
$41$	−3.83356	−	9.25504i	−0.598702	−	1.44539i	0.276202	−	0.961099i	$-0.410924\pi$
$42$	9.35542	+	4.10634i	1.44357	+	0.633622i
$43$	0.699131	+	0.699131i	0.106617	+	0.106617i	0.758403	−	0.651786i	$-0.225980\pi$
$43$	0.699131	+	0.699131i	0.106617	+	0.106617i	−0.651786	+	0.758403i	$0.725980\pi$
$44$	0.474975	−	3.60780i	0.0716052	−	0.543896i
$45$	0.923081	−	2.11903i	0.137605	−	0.315886i
$46$	11.1269	−	1.46488i	1.64057	−	0.215985i
$47$	7.53949	+	4.35293i	1.09975	+	0.634940i	0.936155	−	0.351588i	$-0.114358\pi$
$47$	7.53949	+	4.35293i	1.09975	+	0.634940i	0.163593	+	0.986528i	$0.447692\pi$
$48$	0.951387	+	1.68290i	0.137321	+	0.242905i
$49$	−6.71667	−	1.97137i	−0.959525	−	0.281624i
$50$			9.82416i			1.38935i
$51$	3.53158	−	6.20709i	0.494521	−	0.869166i
$52$	−2.36334	+	1.36448i	−0.327737	+	0.189219i
$53$	0.572918	−	2.13816i	0.0786963	−	0.293699i	−0.915350	−	0.402660i	$-0.868086\pi$
$53$	0.572918	−	2.13816i	0.0786963	−	0.293699i	0.994046	+	0.108961i	$0.0347524\pi$
$54$	11.2676	−	2.69303i	1.53332	−	0.366475i
$55$	0.943739			0.127254
$56$	3.43186	+	4.58389i	0.458601	+	0.612547i
$57$	−1.42395	+	5.12786i	−0.188607	+	0.679202i
$58$	−1.88573	−	0.248261i	−0.247608	−	0.0325982i
$59$	0.0323169	−	0.120608i	0.00420730	−	0.0157018i	−0.963790	−	0.266661i	$-0.914079\pi$
$59$	0.0323169	−	0.120608i	0.00420730	−	0.0157018i	0.967998	+	0.250960i	$0.0807461\pi$
$60$	3.16688	−	2.38474i	0.408842	−	0.307868i
$61$	1.42709	−	10.8398i	0.182720	−	1.38790i	−0.616733	−	0.787172i	$-0.711544\pi$
$61$	1.42709	−	10.8398i	0.182720	−	1.38790i	0.799454	−	0.600728i	$-0.205122\pi$
$62$	3.25363	−	1.34770i	0.413212	−	0.171158i
$63$	−7.42080	+	2.81634i	−0.934933	+	0.354825i
$64$			12.9665i			1.62081i
$65$	−0.430846	−	0.561489i	−0.0534399	−	0.0696442i
$66$	2.84542	+	3.77866i	0.350247	+	0.465121i
$67$	−1.45058	−	2.51248i	−0.177217	−	0.306949i	0.763709	−	0.645560i	$-0.223376\pi$
$67$	−1.45058	−	2.51248i	−0.177217	−	0.306949i	−0.940926	+	0.338611i	$0.890043\pi$
$68$	10.5123	−	6.28678i	1.27480	−	0.762384i
$69$	−5.37013	+	6.86866i	−0.646487	+	0.826890i
$70$	−3.25142	+	3.17530i	−0.388619	+	0.379521i
$71$	−3.39434	+	8.19466i	−0.402834	+	0.972527i	0.584141	+	0.811652i	$0.301432\pi$
$71$	−3.39434	+	8.19466i	−0.402834	+	0.972527i	−0.986975	+	0.160875i	$0.948568\pi$
$72$	6.24019	+	1.79391i	0.735414	+	0.211414i
$73$	0.172249	+	1.30836i	0.0201603	+	0.153132i	0.998564	−	0.0535701i	$-0.0170601\pi$
$73$	0.172249	+	1.30836i	0.0201603	+	0.153132i	−0.978404	+	0.206703i	$0.933727\pi$
$74$	−11.8824	+	15.4854i	−1.38130	+	1.80015i
$75$	−5.34758	−	5.44542i	−0.617486	−	0.628783i
$76$	−6.45442	+	6.45442i	−0.740373	+	0.740373i
$77$	−2.26431	−	2.31859i	−0.258042	−	0.264228i
$78$	0.949137	−	3.41799i	0.107469	−	0.387012i
$79$	−0.899342	+	6.83118i	−0.101184	+	0.768568i	0.863349	+	0.504607i	$0.168362\pi$
$79$	−0.899342	+	6.83118i	−0.101184	+	0.768568i	−0.964533	+	0.263961i	$0.914971\pi$
$80$	−0.852571	+	0.112243i	−0.0953204	+	0.0125492i
$81$	−4.77958	+	7.62598i	−0.531064	+	0.847331i
$82$	13.5963	+	17.7191i	1.50146	+	1.95674i
$83$	−4.23223	+	4.23223i	−0.464548	+	0.464548i	−0.900143	−	0.435595i	$-0.856538\pi$
$83$	−4.23223	+	4.23223i	−0.464548	+	0.464548i	0.435595	+	0.900143i	$0.356538\pi$
$84$	−13.4571	−	2.05873i	−1.46829	−	0.224626i
$85$	1.97235	+	2.49017i	0.213932	+	0.270097i
$86$	−1.90904	−	1.10219i	−0.205857	−	0.118852i
$87$	1.18037	−	0.888849i	0.126549	−	0.0952946i
$88$	0.346038	+	2.62842i	0.0368878	+	0.280191i
$89$	12.1356	+	7.00646i	1.28637	+	0.742684i	0.978004	−	0.208586i	$-0.0668860\pi$
$89$	12.1356	+	7.00646i	1.28637	+	0.742684i	0.308362	+	0.951269i	$0.400219\pi$
$90$	−0.765135	+	5.09608i	−0.0806523	+	0.537174i
$91$	−0.345747	+	2.40569i	−0.0362441	+	0.252185i
$92$	−13.8158	+	5.72269i	−1.44040	+	0.596632i
$93$	−1.06986	+	2.51806i	−0.110939	+	0.261111i
$94$	−18.7485	−	5.02364i	−1.93376	−	0.518149i
$95$	−1.87810	−	1.44111i	−0.192689	−	0.147855i
$96$	−8.27314	−	8.42450i	−0.844374	−	0.859822i
$97$	16.2113	+	6.71494i	1.64601	+	0.681799i	0.996884	−	0.0788835i	$-0.0251355\pi$
$97$	16.2113	+	6.71494i	1.64601	+	0.681799i	0.649124	+	0.760682i	$0.275136\pi$
$98$	15.6023	+	0.369636i	1.57607	+	0.0373389i
$99$	−3.63402	−	0.545618i	−0.365233	−	0.0548367i
$100$	−3.38803	−	12.6443i	−0.338803	−	1.26443i
$101$	−0.160827	−	0.278560i	−0.0160028	−	0.0277177i	0.857913	−	0.513795i	$-0.171761\pi$
$101$	−0.160827	−	0.278560i	−0.0160028	−	0.0277177i	−0.873916	+	0.486077i	$0.838427\pi$
$102$	−4.02369	+	15.4051i	−0.398405	+	1.52534i
$103$	9.94801	+	5.74349i	0.980207	+	0.565923i	0.902333	−	0.431041i	$-0.141853\pi$
$103$	9.94801	+	5.74349i	0.980207	+	0.565923i	0.0778742	+	0.996963i	$0.475187\pi$
$104$	1.40583	−	1.40583i	0.137853	−	0.137853i
$105$	0.0738127	−	3.52988i	0.00720338	−	0.344481i
$106$			4.93523i			0.479352i
$107$	−12.9890	+	9.96682i	−1.25570	+	0.963529i	−0.999995	−	0.00322704i	$-0.998973\pi$
$107$	−12.9890	+	9.96682i	−1.25570	+	0.963529i	−0.255701	+	0.966756i	$0.582306\pi$
$108$	−13.5733	+	7.35190i	−1.30609	+	0.707437i
$109$	−1.26908	+	1.65390i	−0.121556	+	0.158415i	−0.850167	−	0.526512i	$-0.823499\pi$
$109$	−1.26908	+	1.65390i	−0.121556	+	0.158415i	0.728611	+	0.684927i	$0.240166\pi$
$110$	−2.03239	+	0.544577i	−0.193781	+	0.0519234i
$111$	−1.84291	−	15.0513i	−0.174921	−	1.42861i
$112$	2.32133	+	1.82530i	0.219345	+	0.172475i
$113$	−0.796848	−	1.92376i	−0.0749612	−	0.180972i	0.881957	−	0.471330i	$-0.156226\pi$
$113$	−0.796848	−	1.92376i	−0.0749612	−	0.180972i	−0.956918	+	0.290357i	$0.906226\pi$
$114$	0.107550	−	11.8648i	0.0100730	−	1.11124i
$115$	−1.93914	−	3.35869i	−0.180826	−	0.313199i
$116$	2.51266	−	0.330798i	0.233295	−	0.0307138i
$117$	1.33442	+	2.41120i	0.123367	+	0.222915i
$118$			0.278384i			0.0256273i
$119$	1.38561	−	10.8204i	0.127019	−	0.991900i
$120$	−1.77891	+	2.27532i	−0.162392	+	0.207707i
$121$	2.45867	+	9.17589i	0.223516	+	0.834171i
$122$	3.18173	+	24.1676i	0.288060	+	2.18803i
$123$	−17.1813	−	2.42059i	−1.54918	−	0.218257i
$124$	−3.72285	+	2.85664i	−0.334321	+	0.256534i
$125$	6.69552	−	2.77337i	0.598865	−	0.248058i
$126$	14.3559	−	10.3472i	1.27893	−	0.921805i
$127$	14.3672	+	14.3672i	1.27488	+	1.27488i	0.943495	+	0.331386i	$0.107516\pi$
$127$	14.3672	+	14.3672i	1.27488	+	1.27488i	0.331386	+	0.943495i	$0.392484\pi$
$128$	−3.95344	−	14.7544i	−0.349438	−	1.30412i
$129$	1.65811	−	0.428219i	0.145989	−	0.0377026i
$130$	1.25185	+	0.960579i	0.109795	+	0.0842483i
$131$	−7.77115	−	10.1276i	−0.678968	−	0.884849i	0.319052	−	0.947737i	$-0.396635\pi$
$131$	−7.77115	−	10.1276i	−0.678968	−	0.884849i	−0.998021	+	0.0628885i	$0.979969\pi$
$132$	−4.96537	−	3.88207i	−0.432180	−	0.337891i
$133$	0.965564	+	8.07179i	0.0837250	+	0.699913i
$134$	4.57371	+	4.57371i	0.395109	+	0.395109i
$135$	−2.34985	−	3.24119i	−0.202242	−	0.278957i
$136$	−6.21220	+	6.40629i	−0.532692	+	0.549335i
$137$	11.4275	−	6.59768i	0.976319	−	0.563678i	0.0751621	−	0.997171i	$-0.476053\pi$
$137$	11.4275	−	6.59768i	0.976319	−	0.563678i	0.901157	+	0.433493i	$0.142719\pi$
$138$	7.60132	−	17.8908i	0.647068	−	1.52297i
$139$	4.08863	−	9.87083i	0.346793	−	0.837232i	−0.650202	−	0.759762i	$-0.725316\pi$
$139$	4.08863	−	9.87083i	0.346793	−	0.837232i	0.996995	−	0.0774707i	$-0.0246844\pi$
$140$	3.08972	−	5.20812i	0.261129	−	0.440166i
$141$	13.1266	−	7.42081i	1.10546	−	0.624945i
$142$	2.58122	−	19.6063i	0.216611	−	1.64532i
$143$	−0.684990	+	0.892696i	−0.0572817	+	0.0746510i
$144$	3.34786	+	0.0606993i	0.278988	+	0.00505827i
$145$	0.170114	+	0.634874i	0.0141272	+	0.0527234i
$146$	−1.12593	−	2.71823i	−0.0931825	−	0.224962i
$147$	−8.84935	+	8.28788i	−0.729882	+	0.683573i
$148$	9.95295	−	24.0285i	0.818127	−	1.97513i
$149$	1.38110	−	2.39214i	0.113144	−	0.195972i	−0.803892	−	0.594775i	$-0.797241\pi$
$149$	1.38110	−	2.39214i	0.113144	−	0.195972i	0.917036	+	0.398803i	$0.130574\pi$
$150$	14.6585	+	8.64120i	1.19686	+	0.705551i
$151$	−5.10617	−	1.36819i	−0.415534	−	0.111342i	0.0449938	−	0.998987i	$-0.485673\pi$
$151$	−5.10617	−	1.36819i	−0.415534	−	0.111342i	−0.460528	+	0.887645i	$0.652340\pi$
$152$	3.32503	−	5.75912i	0.269696	−	0.467126i
$153$	−6.15519	−	10.7291i	−0.497618	−	0.867397i
$154$	6.21423	+	3.68660i	0.500757	+	0.297074i
$155$	−0.860542	−	0.860542i	−0.0691204	−	0.0691204i
$156$	−0.0428440	+	4.72649i	−0.00343026	+	0.378422i
$157$	0.417544	+	0.723207i	0.0333236	+	0.0577182i	0.882206	−	0.470863i	$-0.156057\pi$
$157$	0.417544	+	0.723207i	0.0333236	+	0.0577182i	−0.848883	+	0.528581i	$0.822724\pi$
$158$	−2.00510	−	15.2302i	−0.159517	−	1.21165i
$159$	−2.68639	−	2.73554i	−0.213045	−	0.216942i
$160$	4.85241	−	2.00994i	0.383617	−	0.158899i
$161$	−3.59910	+	12.8226i	−0.283649	+	1.01056i
$162$	5.89255	−	19.1809i	0.462963	−	1.50700i
$163$	19.1883	+	2.52619i	1.50295	+	0.197867i	0.836616	−	0.547790i	$-0.184531\pi$
$163$	19.1883	+	2.52619i	1.50295	+	0.197867i	0.666331	+	0.745656i	$0.267864\pi$
$164$	−23.6100	−	18.1166i	−1.84363	−	1.41467i
$165$	0.830100	−	1.40814i	0.0646232	−	0.109624i
$166$	6.67215	−	11.5565i	0.517859	−	0.896958i
$167$	15.8924	+	6.58285i	1.22979	+	0.509396i	0.900510	−	0.434836i	$-0.143194\pi$
$167$	15.8924	+	6.58285i	1.22979	+	0.509396i	0.329281	+	0.944232i	$0.393194\pi$
$168$	9.85818	−	1.08871i	0.760575	−	0.0839961i
$169$	−12.1562			−0.935089
$170$	−5.68449	−	4.22457i	−0.435980	−	0.324010i
$171$	6.39874	+	6.63506i	0.489324	+	0.507395i
$172$	2.83716	+	0.760215i	0.216331	+	0.0579658i
$173$	−1.54518	+	1.18566i	−0.117478	+	0.0901441i	−0.665830	−	0.746104i	$-0.731922\pi$
$173$	−1.54518	+	1.18566i	−0.117478	+	0.0901441i	0.548352	+	0.836248i	$0.315256\pi$
$174$	−2.02909	+	2.59530i	−0.153825	+	0.196749i
$175$	−10.7172	−	4.58867i	−0.810146	−	0.346871i
$176$	0.523195	+	1.26310i	0.0394373	+	0.0952101i
$177$	−0.151533	−	0.154305i	−0.0113899	−	0.0115983i
$178$	−30.1775	−	8.08604i	−2.26190	−	0.606075i
$179$	4.67768	+	1.25338i	0.349627	+	0.0936821i	0.429358	−	0.903134i	$-0.358740\pi$
$179$	4.67768	+	1.25338i	0.349627	+	0.0936821i	−0.0797318	+	0.996816i	$0.525406\pi$
$180$	−0.772696	−	6.82284i	−0.0575934	−	0.508545i
$181$	9.02665	+	21.7923i	0.670946	+	1.61981i	0.780007	+	0.625771i	$0.215216\pi$
$181$	9.02665	+	21.7923i	0.670946	+	1.61981i	−0.109061	+	0.994035i	$0.534784\pi$
$182$	−0.643600	−	5.38028i	−0.0477068	−	0.398813i
$183$	−14.9188	−	11.6639i	−1.10283	−	0.862222i
$184$	8.64331	−	6.63225i	0.637193	−	0.488936i
$185$	6.51530	+	1.74577i	0.479014	+	0.128352i
$186$	0.850964	−	6.04012i	0.0623957	−	0.442883i
$187$	3.01254	−	4.05361i	0.220299	−	0.296430i
$188$	25.8629			1.88625
$189$	−2.32501	+	13.5497i	−0.169120	+	0.985596i
$190$	4.87616	+	2.01977i	0.353754	+	0.146529i
$191$	−11.4816	+	19.8867i	−0.830779	+	1.43895i	0.0666426	+	0.997777i	$0.478771\pi$
$191$	−11.4816	+	19.8867i	−0.830779	+	1.43895i	−0.897421	+	0.441174i	$0.854562\pi$
$192$	19.3472	+	11.4052i	1.39626	+	0.823096i
$193$	−19.0013	−	14.5802i	−1.36774	−	1.04950i	−0.992457	−	0.122594i	$-0.960879\pi$
$193$	−19.0013	−	14.5802i	−1.36774	−	1.04950i	−0.375283	−	0.926910i	$-0.622455\pi$
$194$	−38.7866	−	5.10636i	−2.78472	−	0.366615i
$195$	−1.21676	+	0.148982i	−0.0871338	+	0.0106688i
$196$	−20.2085	+	4.90496i	−1.44347	+	0.350354i
$197$	0.00399018	−	0.00165279i	0.000284288	−	0.000117756i	−0.382541	−	0.923938i	$-0.624951\pi$
$197$	0.00399018	−	0.00165279i	0.000284288	−	0.000117756i	0.382826	+	0.923821i	$0.374951\pi$
$198$	8.14089	−	0.921967i	0.578548	−	0.0655213i
$199$	−1.63448	−	12.4151i	−0.115865	−	0.880083i	−0.946373	−	0.323076i	$-0.895283\pi$
$199$	−1.63448	−	12.4151i	−0.115865	−	0.880083i	0.830508	−	0.557007i	$-0.188050\pi$
$200$	4.76841	+	8.25913i	0.337178	+	0.584009i
$201$	−5.02476	−	0.0455477i	−0.354419	−	0.00321269i
$202$	0.507089	+	0.507089i	0.0356786	+	0.0356786i
$203$	1.15161	−	1.94119i	0.0808274	−	0.136245i
$204$	−0.133986	−	21.2150i	−0.00938093	−	1.48535i
$205$	3.85903	−	6.68403i	0.269526	−	0.466833i
$206$	−24.7378	−	6.62846i	−1.72356	−	0.461827i
$207$	5.52517	+	14.0543i	0.384026	+	0.976840i
$208$	0.512645	−	0.887928i	0.0355456	−	0.0615667i
$209$	−1.44030	+	3.47719i	−0.0996276	+	0.240522i
$210$	1.87793	+	7.64436i	0.129589	+	0.527511i
$211$	−6.72083	−	16.2255i	−0.462681	−	1.11701i	−0.967292	−	0.253665i	$-0.918364\pi$
$211$	−6.72083	−	16.2255i	−0.462681	−	1.11701i	0.504611	−	0.863347i	$-0.331636\pi$
$212$	−1.70200	−	6.35194i	−0.116894	−	0.436253i
$213$	9.24155	+	12.2726i	0.633220	+	0.840902i
$214$	22.2212	−	28.9592i	1.51901	−	1.97961i
$215$	−0.0994298	+	0.755244i	−0.00678105	+	0.0515072i
$216$	8.16546	−	7.73302i	0.555589	−	0.526166i
$217$	−0.0494945	+	4.17889i	−0.00335991	+	0.283681i
$218$	1.77866	−	4.29407i	0.120466	−	0.290831i
$219$	2.10370	+	0.893808i	0.142155	+	0.0603979i
$220$	2.42800	−	1.40181i	0.163696	−	0.0945098i
$221$	−3.78707	+	0.0582495i	−0.254746	+	0.00391829i
$222$	12.6540	+	31.3504i	0.849284	+	2.10410i
$223$	−1.06184	−	1.06184i	−0.0711063	−	0.0711063i	0.670659	−	0.741766i	$-0.266011\pi$
$223$	−1.06184	−	1.06184i	−0.0711063	−	0.0711063i	−0.741766	+	0.670659i	$0.766011\pi$
$224$	−16.5804	−	7.09904i	−1.10783	−	0.474325i
$225$	−12.8287	+	3.18935i	−0.855247	+	0.212624i
$226$	2.82614	+	3.68310i	0.187992	+	0.244996i
$227$	10.6242	+	8.15226i	0.705155	+	0.541085i	0.897919	−	0.440161i	$-0.145078\pi$
$227$	10.6242	+	8.15226i	0.705155	+	0.541085i	−0.192764	+	0.981245i	$0.561745\pi$
$228$	3.95335	+	15.3078i	0.261817	+	1.01378i
$229$	5.31725	+	19.8443i	0.351374	+	1.31135i	0.884987	+	0.465616i	$0.154167\pi$
$229$	5.31725	+	19.8443i	0.351374	+	1.31135i	−0.533613	+	0.845729i	$0.679166\pi$
$230$	6.11414	+	6.11414i	0.403154	+	0.403154i
$231$	−5.45120	+	1.33915i	−0.358663	+	0.0881097i
$232$	−1.70582	+	0.706575i	−0.111993	+	0.0463889i
$233$	19.2024	−	14.7345i	1.25799	−	0.965290i	0.257990	−	0.966148i	$-0.416940\pi$
$233$	19.2024	−	14.7345i	1.25799	−	0.965290i	1.00000		0.000858040i	$0.000273123\pi$
$234$	−4.26510	−	4.42262i	−0.278818	−	0.289116i
$235$	0.875496	+	6.65005i	0.0571111	+	0.433802i
$236$	−0.0960054	−	0.358297i	−0.00624942	−	0.0233231i
$237$	9.40168	+	7.35051i	0.610705	+	0.477467i
$238$	3.25981	+	24.1017i	0.211302	+	1.56228i
$239$		−	16.1765i		−	1.04637i	−0.852219	−	0.523185i	$-0.824744\pi$
$239$		−	16.1765i		−	1.04637i	0.852219	−	0.523185i	$-0.175256\pi$
$240$	−0.582433	+	1.37084i	−0.0375959	+	0.0884873i
$241$	−0.538854	+	0.0709414i	−0.0347106	+	0.00456974i	−0.147862	−	0.989008i	$-0.547239\pi$
$241$	−0.538854	+	0.0709414i	−0.0347106	+	0.00456974i	0.113151	+	0.993578i	$0.463906\pi$
$242$	−10.5897	−	18.3420i	−0.680734	−	1.17907i
$243$	7.17459	+	13.8393i	0.460250	+	0.887789i
$244$	−12.4297	−	30.0079i	−0.795730	−	1.92106i
$245$	−1.94528	−	5.03011i	−0.124279	−	0.321362i
$246$	38.3975	−	4.70146i	2.44814	−	0.299754i
$247$	2.72634	−	0.730520i	0.173473	−	0.0464819i
$248$	2.08117	−	2.71224i	0.132155	−	0.172227i
$249$	2.59225	+	10.0375i	0.164277	+	0.636099i
$250$	−12.8188	+	9.83619i	−0.810730	+	0.622095i
$251$			13.5484i			0.855165i	0.903976	+	0.427582i	$0.140635\pi$
$251$			13.5484i			0.855165i	−0.903976	+	0.427582i	$0.859365\pi$
$252$	−14.9085	+	18.2684i	−0.939148	+	1.15080i
$253$	−4.36000	+	4.36000i	−0.274111	+	0.274111i
$254$	−39.2309	−	22.6500i	−2.46157	−	1.42119i
$255$	5.45040	−	0.752608i	0.341318	−	0.0471301i
$256$	4.06136	+	7.03448i	0.253835	+	0.439655i
$257$	1.79444	+	6.69694i	0.111934	+	0.417744i	0.999039	−	0.0438236i	$-0.0139540\pi$
$257$	1.79444	+	6.69694i	0.111934	+	0.417744i	−0.887105	+	0.461567i	$0.847287\pi$
$258$	−3.32373	+	1.87899i	−0.206926	+	0.116981i
$259$	−11.3431	−	20.1955i	−0.704827	−	1.25489i
$260$	−1.94248	−	0.804602i	−0.120468	−	0.0498993i
$261$	−0.288003	−	2.54304i	−0.0178269	−	0.157410i
$262$	22.5796	+	17.3259i	1.39497	+	1.07040i
$263$	−18.4021	−	4.93082i	−1.13472	−	0.304048i	−0.357894	−	0.933762i	$-0.616505\pi$
$263$	−18.4021	−	4.93082i	−1.13472	−	0.304048i	−0.776827	+	0.629715i	$0.783172\pi$
$264$	4.22621	+	1.79560i	0.260105	+	0.110512i
$265$	1.57564	−	0.652651i	0.0967907	−	0.0400920i
$266$	−6.73715	−	16.8258i	−0.413081	−	1.03166i
$267$	21.1285	−	11.9445i	1.29304	−	0.730993i
$268$	−7.46397	−	4.30933i	−0.455935	−	0.263234i
$269$	−1.78751	−	13.5775i	−0.108986	−	0.827833i	−0.955402	−	0.295310i	$-0.904577\pi$
$269$	−1.78751	−	13.5775i	−0.108986	−	0.827833i	0.846415	−	0.532523i	$-0.178756\pi$
$270$	6.93081	+	5.62409i	0.421796	+	0.342271i
$271$	5.56375	+	3.21224i	0.337974	+	0.195129i	0.659376	−	0.751814i	$-0.270821\pi$
$271$	5.56375	+	3.21224i	0.337974	+	0.195129i	−0.321402	+	0.946943i	$0.604154\pi$
$272$	−2.23941	+	4.02032i	−0.135784	+	0.243768i
$273$	3.28539	+	2.63189i	0.198841	+	0.159290i
$274$	−20.8026	+	20.8026i	−1.25673	+	1.25673i
$275$	−3.28578	−	4.28211i	−0.198140	−	0.258221i
$276$	−3.61342	+	25.6480i	−0.217503	+	1.54383i
$277$	−9.44833	+	1.24390i	−0.567695	+	0.0747385i	−0.408910	−	0.912575i	$-0.634091\pi$
$277$	−9.44833	+	1.24390i	−0.567695	+	0.0747385i	−0.158785	+	0.987313i	$0.550758\pi$
$278$	−3.10919	+	23.6166i	−0.186477	+	1.41643i
$279$	2.81614	+	3.81117i	0.168598	+	0.228169i
$280$	−1.19224	+	4.24763i	−0.0712500	+	0.253844i
$281$	5.08394	−	5.08394i	0.303283	−	0.303283i	−0.539014	−	0.842297i	$-0.681203\pi$
$281$	5.08394	−	5.08394i	0.303283	−	0.303283i	0.842297	+	0.539014i	$0.181203\pi$
$282$	−23.9866	+	23.5557i	−1.42838	+	1.40272i
$283$	−5.58544	+	7.27908i	−0.332020	+	0.432696i	−0.929294	−	0.369340i	$-0.879584\pi$
$283$	−5.58544	+	7.27908i	−0.332020	+	0.432696i	0.597274	+	0.802037i	$0.296250\pi$
$284$	3.43938	+	26.1247i	0.204089	+	1.55021i
$285$	−3.80222	+	1.53470i	−0.225224	+	0.0909079i
$286$	0.960036	−	2.31773i	0.0567681	−	0.137050i
$287$	−25.6804	+	6.55607i	−1.51587	+	0.386993i
$288$	−19.8470	+	4.93419i	−1.16950	+	0.290750i
$289$	16.9920	−	0.522836i	0.999527	−	0.0307551i
$290$	−0.732698	−	1.26907i	−0.0430255	−	0.0745224i
$291$	24.2785	−	18.2823i	1.42323	−	1.07173i
$292$	2.38657	+	3.11024i	0.139663	+	0.182013i
$293$			17.4199i			1.01768i	0.860861	+	0.508840i	$0.169925\pi$
$293$			17.4199i			1.01768i	−0.860861	+	0.508840i	$0.830075\pi$
$294$	14.2751	−	22.9548i	0.832538	−	1.33875i
$295$	0.0888778	−	0.0368144i	0.00517467	−	0.00214342i
$296$	−2.47322	+	18.7860i	−0.143753	+	1.09191i
$297$	−4.01055	+	4.94236i	−0.232715	+	0.286785i
$298$	−1.59391	+	5.94855i	−0.0923327	+	0.344590i
$299$	4.58451	+	0.603562i	0.265129	+	0.0349049i
$300$	−21.8465	−	6.06651i	−1.26131	−	0.350250i
$301$	2.09405	−	1.56777i	0.120699	−	0.0903650i
$302$	11.7859			0.678202
$303$	−0.557097	−	0.00504988i	−0.0320044	−	0.000290108i
$304$	0.887605	−	3.31259i	0.0509076	−	0.189990i
$305$	7.29508	−	4.21182i	0.417715	−	0.241168i
$306$	19.4466	+	19.5539i	1.11169	+	1.11782i
$307$		−	22.8162i		−	1.30219i	−0.758997	−	0.651094i	$-0.774310\pi$
$307$		−	22.8162i		−	1.30219i	0.758997	−	0.651094i	$-0.225690\pi$
$308$	−9.26948	−	2.60179i	−0.528177	−	0.148251i
$309$	17.3199	−	9.79142i	0.985296	−	0.557015i
$310$	2.34979	+	1.35665i	0.133459	+	0.0770526i
$311$	17.3609	−	2.28561i	0.984447	−	0.129605i	0.378920	−	0.925429i	$-0.376296\pi$
$311$	17.3609	−	2.28561i	0.984447	−	0.129605i	0.605527	+	0.795824i	$0.292962\pi$
$312$	−0.861077	−	3.33418i	−0.0487489	−	0.188761i
$313$	−0.669524	+	5.08554i	−0.0378437	+	0.287452i	0.962050	+	0.272873i	$0.0879740\pi$
$313$	−0.669524	+	5.08554i	−0.0378437	+	0.287452i	−0.999894	+	0.0145785i	$0.995359\pi$
$314$	−1.31652	−	1.31652i	−0.0742956	−	0.0742956i
$315$	−5.20197	−	3.21497i	−0.293098	−	0.181143i
$316$	7.83309	+	18.9108i	0.440646	+	1.06381i
$317$	21.3072	+	2.80514i	1.19673	+	0.157553i	0.702439	−	0.711744i	$-0.252094\pi$
$317$	21.3072	+	2.80514i	1.19673	+	0.157553i	0.494291	+	0.869296i	$0.335428\pi$
$318$	7.36380	+	4.34096i	0.412941	+	0.243429i
$319$	0.904975	−	0.522488i	0.0506689	−	0.0292537i
$320$	−7.92564	+	6.08156i	−0.443057	+	0.339969i
$321$	3.44642	+	28.1474i	0.192360	+	1.57104i
$322$	0.351658	−	29.6909i	0.0195971	−	1.65461i
$323$	−12.1851	+	3.46670i	−0.677998	+	0.192892i
$324$	−0.969198	+	26.7192i	−0.0538443	+	1.48440i
$325$	−1.04764	+	3.90983i	−0.0581124	+	0.216878i
$326$	−42.7808	+	5.63219i	−2.36941	+	0.311938i
$327$	1.35150	+	3.34833i	0.0747380	+	0.185163i
$328$	20.0308	+	8.29702i	1.10601	+	0.458126i
$329$	14.2374	−	18.1064i	0.784931	−	0.998237i
$330$	−0.975104	+	3.51151i	−0.0536777	+	0.193302i
$331$	−30.6780	+	8.22014i	−1.68621	+	0.451820i	−0.969408	−	0.245454i	$-0.921063\pi$
$331$	−30.6780	+	8.22014i	−1.68621	+	0.451820i	−0.716805	+	0.697273i	$0.754396\pi$
$332$	−4.60201	+	17.1749i	−0.252568	+	0.942596i
$333$	−24.0789	−	10.4892i	−1.31952	−	0.574802i
$334$	−38.0237	−	5.00591i	−2.08056	−	0.273911i
$335$	0.855377	−	2.06506i	0.0467342	−	0.112826i
$336$	4.76533	−	1.85812i	0.259970	−	0.101369i
$337$	−23.6423	−	9.79298i	−1.28788	−	0.533457i	−0.369527	−	0.929220i	$-0.620480\pi$
$337$	−23.6423	−	9.79298i	−1.28788	−	0.533457i	−0.918353	+	0.395762i	$0.870480\pi$
$338$	26.1789	−	7.01461i	1.42394	−	0.381545i
$339$	−3.57132	−	0.503146i	−0.193967	−	0.0273272i
$340$	8.77320	+	3.47688i	0.475794	+	0.188561i
$341$	−0.967428	+	1.67564i	−0.0523892	+	0.0907407i
$342$	−17.6087	−	10.5966i	−0.952170	−	0.572997i
$343$	−7.69073	+	16.8479i	−0.415261	+	0.909702i
$344$	−2.13990			−0.115376
$345$	−6.71710	−	0.0608881i	−0.361637	−	0.00327811i
$346$	2.64345	−	3.44501i	0.142113	−	0.185205i
$347$	17.0048	+	13.0483i	0.912868	+	0.700468i	0.954356	−	0.298671i	$-0.0965432\pi$
$347$	17.0048	+	13.0483i	0.912868	+	0.700468i	−0.0414882	+	0.999139i	$0.513210\pi$
$348$	1.71652	−	4.04008i	0.0920153	−	0.216571i
$349$	5.34423	−	5.34423i	0.286070	−	0.286070i	−0.549454	−	0.835524i	$-0.685164\pi$
$349$	5.34423	−	5.34423i	0.286070	−	0.286070i	0.835524	+	0.549454i	$0.185164\pi$
$350$	25.7279	+	3.69763i	1.37522	+	0.197647i
$351$	4.77146	+	0.129783i	0.254682	+	0.00692731i
$352$	−5.08337	−	6.62477i	−0.270944	−	0.353102i
$353$	24.8205	−	14.3301i	1.32106	−	0.762716i	0.337165	−	0.941446i	$-0.390532\pi$
$353$	24.8205	−	14.3301i	1.32106	−	0.762716i	0.983898	+	0.178730i	$0.0571987\pi$
$354$	0.415373	+	0.244863i	0.0220768	+	0.0130143i
$355$	−6.60092	+	1.76871i	−0.350340	+	0.0938734i
$356$	41.6289			2.20633
$357$	−14.9262	−	11.5849i	−0.789976	−	0.613138i
$358$	−10.7969			−0.570633
$359$	19.8727	−	5.32486i	1.04884	−	0.281036i	0.307067	−	0.951688i	$-0.400652\pi$
$359$	19.8727	−	5.32486i	1.04884	−	0.281036i	0.741772	+	0.670652i	$0.233986\pi$
$360$	1.83027	+	4.65564i	0.0964638	+	0.245374i
$361$	−8.27844	+	4.77956i	−0.435708	+	0.251556i
$362$	−32.0144	−	41.7220i	−1.68264	−	2.19286i
$363$	15.8538	+	4.40243i	0.832111	+	0.231068i
$364$	2.68383	+	6.70279i	0.140671	+	0.351322i
$365$	−0.718936	+	0.718936i	−0.0376308	+	0.0376308i
$366$	38.8588	+	16.5101i	2.03118	+	0.862996i
$367$	−4.88273	−	3.74665i	−0.254876	−	0.195573i	0.473418	−	0.880838i	$-0.343020\pi$
$367$	−4.88273	−	3.74665i	−0.254876	−	0.195573i	−0.728294	+	0.685264i	$0.759687\pi$
$368$	3.42025	−	4.45736i	0.178293	−	0.232356i
$369$	−18.7242	+	23.5069i	−0.974741	+	1.22372i
$370$	−15.0384			−0.781809
$371$	−5.38387	−	2.30515i	−0.279516	−	0.119677i
$372$	0.987796	+	8.06748i	0.0512148	+	0.418279i
$373$	−14.7764	+	25.5934i	−0.765091	+	1.32518i	0.175108	+	0.984549i	$0.443973\pi$
$373$	−14.7764	+	25.5934i	−0.765091	+	1.32518i	−0.940199	+	0.340627i	$0.889361\pi$
$374$	−4.14855	+	10.4680i	−0.214517	+	0.541288i
$375$	1.75116	−	12.4297i	0.0904298	−	0.641868i
$376$	−18.2001	+	4.87671i	−0.938600	+	0.251497i
$377$	−0.724009	−	0.299895i	−0.0372884	−	0.0154454i
$378$	−2.81172	−	30.5216i	−0.144619	−	1.56986i
$379$	13.4639	−	32.5047i	0.691594	−	1.66966i	−0.0499497	−	0.998752i	$-0.515906\pi$
$379$	13.4639	−	32.5047i	0.691594	−	1.66966i	0.741544	−	0.670904i	$-0.234094\pi$
$380$	−6.97246	−	0.917942i	−0.357680	−	0.0470894i
$381$	34.0743	−	8.79993i	1.74568	−	0.450834i
$382$	13.2507	−	49.4523i	0.677966	−	2.53020i
$383$	23.2077	−	6.21848i	1.18586	−	0.317749i	0.388610	−	0.921402i	$-0.372955\pi$
$383$	23.2077	−	6.21848i	1.18586	−	0.317749i	0.797247	+	0.603653i	$0.206289\pi$
$384$	−25.4923	−	7.07892i	−1.30090	−	0.361245i
$385$	0.355206	−	2.47150i	0.0181030	−	0.125960i
$386$	49.3335	+	20.4346i	2.51101	+	1.04009i
$387$	0.819511	−	2.85071i	0.0416581	−	0.144910i
$388$	51.6818	−	6.80404i	2.62374	−	0.345423i
$389$	−3.18901	+	11.9015i	−0.161689	+	0.603432i	0.836750	+	0.547585i	$0.184453\pi$
$389$	−3.18901	+	11.9015i	−0.161689	+	0.603432i	−0.998439	+	0.0558471i	$0.982214\pi$
$390$	2.53438	−	1.02296i	0.128333	−	0.0517996i
$391$	−20.6165	−	2.39226i	−1.04262	−	0.120982i
$392$	13.2962	−	7.26221i	0.671558	−	0.366797i
$393$	−21.9466	+	2.68718i	−1.10706	+	0.135550i
$394$	−0.00763932	+	0.00586185i	−0.000384863	+	0.000295316i
$395$	−4.59730	+	2.65425i	−0.231315	+	0.133550i
$396$	−10.1599	+	3.99415i	−0.510552	+	0.200714i
$397$	35.0898	+	4.61966i	1.76111	+	0.231854i	0.940536	−	0.339693i	$-0.110323\pi$
$397$	35.0898	+	4.61966i	1.76111	+	0.231854i	0.820569	+	0.571547i	$0.193657\pi$
$398$	10.6840	+	25.7934i	0.535539	+	1.29290i
$399$	12.8931	+	5.65913i	0.645464	+	0.283311i
$400$	3.47766	+	3.47766i	0.173883	+	0.173883i
$401$	0.116060	−	0.881561i	0.00579574	−	0.0440231i	−0.988303	−	0.152506i	$-0.951266\pi$
$401$	0.116060	−	0.881561i	0.00579574	−	0.0440231i	0.994098	+	0.108482i	$0.0345991\pi$
$402$	10.8474	−	2.80141i	0.541017	−	0.139722i
$403$	1.43860	−	0.189395i	0.0716618	−	0.00943446i
$404$	−0.827532	−	0.477776i	−0.0411713	−	0.0237702i
$405$	−6.90303	+	0.655275i	−0.343014	+	0.0325609i
$406$	−1.35991	+	4.84498i	−0.0674911	+	0.240452i
$407$		−	10.7239i		−	0.531564i
$408$	4.09458	+	14.9040i	0.202712	+	0.737860i
$409$	14.0819	−	8.13021i	0.696307	−	0.402013i	−0.109663	−	0.993969i	$-0.534977\pi$
$409$	14.0819	−	8.13021i	0.696307	−	0.402013i	0.805971	+	0.591956i	$0.201644\pi$
$410$	−4.45364	+	16.6212i	−0.219950	+	0.820864i
$411$	0.207164	−	22.8541i	0.0102187	−	1.12731i
$412$	34.1250			1.68122
$413$	−0.303690	−	0.130027i	−0.0149436	−	0.00639823i
$414$	−20.0086	−	27.0783i	−0.983370	−	1.33083i
$415$	−4.57191	−	0.601904i	−0.224426	−	0.0295463i
$416$	−1.62078	+	6.04883i	−0.0794652	+	0.296568i
$417$	−11.1318	−	14.7828i	−0.545129	−	0.723919i
$418$	1.09527	−	8.31941i	0.0535715	−	0.406916i
$419$	−25.1938	+	10.4356i	−1.23080	+	0.509813i	−0.900827	−	0.434178i	$-0.857039\pi$
$419$	−25.1938	+	10.4356i	−1.23080	+	0.509813i	−0.329971	+	0.943991i	$0.607039\pi$
$420$	−5.05330	−	9.19112i	−0.246576	−	0.448481i
$421$			13.3076i			0.648573i	0.945959	+	0.324286i	$0.105124\pi$
$421$			13.3076i			0.648573i	−0.945959	+	0.324286i	$0.894876\pi$
$422$	23.8365	+	31.0643i	1.16034	+	1.51219i
$423$	0.473454	−	26.1133i	0.0230201	−	1.26967i
$424$	2.39544	+	4.14903i	0.116333	+	0.201495i
$425$	4.43180	−	17.6193i	0.214974	−	0.854659i
$426$	−26.9839	−	21.0968i	−1.30737	−	1.02214i
$427$	−27.8507	−	7.81725i	−1.34779	−	0.378303i
$428$	−18.6130	+	44.9357i	−0.899692	+	2.17205i
$429$	0.729474	+	1.80727i	0.0352193	+	0.0872557i
$430$	−0.221680	−	1.68383i	−0.0106904	−	0.0812015i
$431$	10.3727	−	13.5180i	0.499635	−	0.651137i	−0.473657	−	0.880710i	$-0.657066\pi$
$431$	10.3727	−	13.5180i	0.499635	−	0.651137i	0.973291	+	0.229573i	$0.0737329\pi$
$432$	3.03530	−	4.94191i	0.146036	−	0.237768i
$433$	−6.52355	+	6.52355i	−0.313502	+	0.313502i	−0.846265	−	0.532763i	$-0.821154\pi$
$433$	−6.52355	+	6.52355i	−0.313502	+	0.313502i	0.532763	+	0.846265i	$0.321154\pi$
$434$	−2.30480	−	9.02800i	−0.110634	−	0.433358i
$435$	1.09692	+	0.304601i	0.0525932	+	0.0146045i
$436$	−0.808363	+	6.14013i	−0.0387136	+	0.294059i
$437$	15.3345	−	2.01882i	0.733547	−	0.0965733i
$438$	−5.04619	−	0.710934i	−0.241116	−	0.0339698i
$439$	3.06174	+	3.99014i	0.146129	+	0.190439i	0.860683	−	0.509141i	$-0.170037\pi$
$439$	3.06174	+	3.99014i	0.146129	+	0.190439i	−0.714554	+	0.699580i	$0.753370\pi$
$440$	−1.44430	+	1.44430i	−0.0688541	+	0.0688541i
$441$	4.58249	+	20.4939i	0.218214	+	0.975901i
$442$	8.12202	−	2.31074i	0.386325	−	0.109911i
$443$	−25.8094	−	14.9011i	−1.22624	−	0.707971i	−0.260000	−	0.965609i	$-0.583723\pi$
$443$	−25.8094	−	14.9011i	−1.22624	−	0.707971i	−0.966242	+	0.257638i	$0.917056\pi$
$444$	−27.0982	−	35.9859i	−1.28603	−	1.70781i
$445$	1.40920	+	10.7039i	0.0668023	+	0.507414i
$446$	2.89946	+	1.67400i	0.137293	+	0.0792664i
$447$	−2.35449	−	4.16482i	−0.111363	−	0.196989i
$448$	33.9572	+	4.88035i	1.60433	+	0.230575i
$449$	−27.1347	+	11.2396i	−1.28057	+	0.530428i	−0.916160	−	0.400812i	$-0.868728\pi$
$449$	−27.1347	+	11.2396i	−1.28057	+	0.530428i	−0.364406	+	0.931240i	$0.618728\pi$
$450$	25.7869	−	14.2711i	1.21560	−	0.672747i
$451$	−11.8526	−	3.17590i	−0.558117	−	0.149547i
$452$	−4.90760	−	3.76573i	−0.230834	−	0.177125i
$453$	−6.53278	+	6.41541i	−0.306937	+	0.301422i
$454$	−27.5840	−	11.4257i	−1.29458	−	0.536233i
$455$	−1.63261	+	0.916984i	−0.0765382	+	0.0429889i
$456$	−5.66847	−	10.0269i	−0.265450	−	0.469552i
$457$	−0.0841752	−	0.314146i	−0.00393755	−	0.0146951i	0.963929	−	0.266159i	$-0.0857547\pi$
$457$	−0.0841752	−	0.314146i	−0.00393755	−	0.0146951i	−0.967867	+	0.251464i	$0.919088\pi$
$458$	−22.9019	−	39.6673i	−1.07014	−	1.85353i
$459$	−21.4228	−	0.253084i	−0.999930	−	0.0118129i
$460$	−9.97783	−	5.76070i	−0.465219	−	0.268594i
$461$	6.96135	−	6.96135i	0.324222	−	0.324222i	−0.526162	−	0.850384i	$-0.676369\pi$
$461$	6.96135	−	6.96135i	0.324222	−	0.324222i	0.850384	+	0.526162i	$0.176369\pi$
$462$	10.9667	−	6.02950i	0.510216	−	0.280518i
$463$		−	13.8172i		−	0.642140i	−0.947056	−	0.321070i	$-0.895958\pi$
$463$		−	13.8172i		−	0.642140i	0.947056	−	0.321070i	$-0.104042\pi$
$464$	−0.755410	+	0.579647i	−0.0350690	+	0.0269094i
$465$	−2.04093	+	0.527084i	−0.0946456	+	0.0244429i
$466$	−32.8508	+	42.8121i	−1.52179	+	1.98323i
$467$	−26.7663	+	7.17201i	−1.23860	+	0.331881i	−0.817921	−	0.575330i	$-0.804874\pi$
$467$	−26.7663	+	7.17201i	−1.23860	+	0.331881i	−0.420676	+	0.907211i	$0.638207\pi$
$468$	7.01466	+	4.22129i	0.324253	+	0.195129i
$469$	−7.12578	+	2.85320i	−0.329038	+	0.131748i
$470$	−5.72278	−	13.8160i	−0.263972	−	0.637285i
$471$	1.44636	+	0.0131107i	0.0666445	+	0.000604109i
$472$	0.135121	+	0.234036i	0.00621944	+	0.0107724i
$473$	1.20074	−	0.158081i	0.0552101	−	0.00726855i
$474$	−24.4885	−	10.4045i	−1.12480	−	0.477896i
$475$			13.5391i			0.621218i
$476$	−12.5075	−	29.8962i	−0.573278	−	1.37029i
$477$	−6.44458	+	1.60219i	−0.295077	+	0.0733593i
$478$	9.33451	+	34.8369i	0.426951	+	1.59340i
$479$	3.35003	+	25.4460i	0.153067	+	1.16266i	0.879665	+	0.475594i	$0.157767\pi$
$479$	3.35003	+	25.4460i	0.153067	+	1.16266i	−0.726598	+	0.687063i	$0.758900\pi$
$480$	1.26911	−	9.00814i	0.0579269	−	0.411164i
$481$	−6.38032	+	4.89579i	−0.290917	+	0.223229i
$482$	1.11951	−	0.463717i	0.0509924	−	0.0211217i
$483$	15.9667	+	16.6488i	0.726512	+	0.757544i
$484$	19.9552	+	19.9552i	0.907054	+	0.907054i
$485$	3.49900	+	13.0584i	0.158881	+	0.592953i
$486$	−23.4367	−	25.6635i	−1.06311	−	1.16412i
$487$	12.8739	+	9.87846i	0.583370	+	0.447636i	0.857809	−	0.513969i	$-0.171825\pi$
$487$	12.8739	+	9.87846i	0.583370	+	0.447636i	−0.274439	+	0.961605i	$0.588492\pi$
$488$	14.4053	+	18.7733i	0.652095	+	0.849827i
$489$	20.6471	−	26.4087i	0.933694	−	1.19424i
$490$	7.09184	+	9.71008i	0.320377	+	0.438657i
$491$	3.21810	+	3.21810i	0.145231	+	0.145231i	0.775984	−	0.630753i	$-0.217254\pi$
$491$	3.21810	+	3.21810i	0.145231	+	0.145231i	−0.630753	+	0.775984i	$0.717254\pi$
$492$	−47.7986	+	19.2931i	−2.15493	+	0.869801i
$493$	3.26998	+	1.29592i	0.147273	+	0.0583653i
$494$	−5.44976	+	3.14642i	−0.245196	+	0.141564i
$495$	−1.37093	−	2.47717i	−0.0616186	−	0.111340i
$496$	0.674681	−	1.62882i	0.0302941	−	0.0731364i
$497$	20.1830	+	11.9736i	0.905330	+	0.537088i
$498$	−11.3746	−	20.1204i	−0.509707	−	0.901615i
$499$	−3.26796	+	24.8226i	−0.146294	+	1.11121i	0.747989	+	0.663711i	$0.231020\pi$
$499$	−3.26796	+	24.8226i	−0.146294	+	1.11121i	−0.894283	+	0.447502i	$0.852314\pi$
$500$	13.1064	−	17.0805i	0.586134	−	0.763865i
$501$	23.8009	−	17.9227i	1.06335	−	0.800727i
$502$	−7.81797	−	29.1771i	−0.348933	−	1.30224i
$503$	−5.23837	−	12.6465i	−0.233567	−	0.563882i	0.763025	−	0.646369i	$-0.223713\pi$
$503$	−5.23837	−	12.6465i	−0.233567	−	0.563882i	−0.996592	+	0.0824877i	$0.973713\pi$
$504$	7.04666	−	15.6669i	0.313883	−	0.697859i
$505$	0.0948359	−	0.228954i	0.00422014	−	0.0101883i
$506$	6.87357	−	11.9054i	0.305567	−	0.529258i
$507$	−10.6924	+	18.1381i	−0.474866	+	0.805540i
$508$	58.3038	+	15.6225i	2.58681	+	0.693134i
$509$	−11.3809	+	19.7122i	−0.504447	+	0.873728i	0.495539	+	0.868585i	$0.334970\pi$
$509$	−11.3809	+	19.7122i	−0.504447	+	0.873728i	−0.999987	+	0.00514296i	$0.998363\pi$
$510$	−11.3034	+	4.76589i	−0.500524	+	0.211037i
$511$	3.49123	+	0.0413500i	0.154443	+	0.00182922i
$512$	8.79648	+	8.79648i	0.388753	+	0.388753i
$513$	15.5283	−	3.71139i	0.685593	−	0.163862i
$514$	−7.72883	−	13.3867i	−0.340904	−	0.590463i
$515$	1.15518	+	8.77444i	0.0509032	+	0.386648i
$516$	3.62984	−	3.56462i	0.159795	−	0.156924i
$517$	9.85221	−	4.08092i	0.433300	−	0.179479i
$518$	36.0816	+	36.9465i	1.58533	+	1.62334i
$519$	0.409989	+	3.34844i	0.0179965	+	0.146980i
$520$	1.51867	+	0.199936i	0.0665980	+	0.00876779i
$521$	−2.31037	−	1.77281i	−0.101219	−	0.0776681i	0.556912	−	0.830572i	$-0.311986\pi$
$521$	−2.31037	−	1.77281i	−0.101219	−	0.0776681i	−0.658131	+	0.752903i	$0.728653\pi$
$522$	2.08767	+	5.31037i	0.0913747	+	0.232429i
$523$	4.86555	−	8.42738i	0.212756	−	0.368504i	−0.739820	−	0.672805i	$-0.765089\pi$
$523$	4.86555	−	8.42738i	0.212756	−	0.368504i	0.952576	+	0.304301i	$0.0984228\pi$
$524$	−35.0364	−	14.5126i	−1.53057	−	0.633984i
$525$	−16.2734	+	11.9549i	−0.710230	+	0.521756i
$526$	42.4751			1.85200
$527$	−6.44322	+	0.949293i	−0.280671	+	0.0413519i
$528$	2.34486	+	0.330356i	0.102047	+	0.0143769i
$529$	2.25923	+	0.605359i	0.0982274	+	0.0263200i
$530$	−3.01661	+	2.31473i	−0.131033	+	0.100545i
$531$	−0.363523	+	0.0903756i	−0.0157755	+	0.00392197i
$532$	14.4738	+	19.3324i	0.627519	+	0.838168i
$533$	3.52154	+	8.50175i	0.152535	+	0.368252i
$534$	−38.6088	+	37.9152i	−1.67077	+	1.64075i
$535$	−12.1842	−	3.26476i	−0.526770	−	0.141148i
$536$	6.06507	+	1.62513i	0.261971	+	0.0701950i
$537$	5.98458	−	5.87706i	0.258254	−	0.253614i
$538$	11.6843	+	28.2083i	0.503744	+	1.21615i
$539$	−6.92427	+	5.05720i	−0.298249	+	0.217829i
$540$	−10.8599	−	4.84835i	−0.467337	−	0.208640i
$541$	−8.66053	+	6.64546i	−0.372345	+	0.285711i	−0.777935	−	0.628345i	$-0.783733\pi$
$541$	−8.66053	+	6.64546i	−0.372345	+	0.285711i	0.405590	+	0.914055i	$0.367066\pi$
$542$	−13.8354	−	3.70719i	−0.594282	−	0.159237i
$543$	40.4557	+	5.69961i	1.73612	+	0.244594i
$544$	6.85635	−	27.2584i	0.293963	−	1.16869i
$545$	−1.60616			−0.0688001
$546$	−8.59395	−	3.77211i	−0.367787	−	0.161431i
$547$	−12.1534	−	5.03411i	−0.519642	−	0.215243i	0.107417	−	0.994214i	$-0.465742\pi$
$547$	−12.1534	−	5.03411i	−0.519642	−	0.215243i	−0.627060	+	0.778971i	$0.715742\pi$
$548$	19.6001	−	33.9483i	0.837274	−	1.45020i
$549$	−30.5259	+	12.0007i	−1.30282	+	0.512176i
$550$	9.54705	+	7.32571i	0.407087	+	0.312369i
$551$	−2.59881	−	0.342139i	−0.110713	−	0.0145756i
$552$	−2.29336	−	18.7302i	−0.0976119	−	0.797211i
$553$	17.5513	+	4.92637i	0.746357	+	0.209490i
$554$	19.6297	−	8.13087i	0.833984	−	0.345448i
$555$	8.33561	−	8.18585i	0.353827	−	0.347470i
$556$	−4.14288	−	31.4683i	−0.175697	−	1.33455i
$557$	−4.98099	−	8.62733i	−0.211051	−	0.365552i	0.740993	−	0.671513i	$-0.234355\pi$
$557$	−4.98099	−	8.62733i	−0.211051	−	0.365552i	−0.952044	+	0.305962i	$0.901022\pi$
$558$	−8.26390	−	6.58252i	−0.349839	−	0.278660i
$559$	−0.642227	−	0.642227i	−0.0271633	−	0.0271633i
$560$	−0.0269449	+	2.27500i	−0.00113863	+	0.0961361i
$561$	−3.39856	−	8.06048i	−0.143487	−	0.340314i
$562$	−8.01487	+	13.8822i	−0.338087	+	0.585584i
$563$	−7.44866	−	1.99586i	−0.313924	−	0.0841156i	0.0984171	−	0.995145i	$-0.468622\pi$
$563$	−7.44866	−	1.99586i	−0.313924	−	0.0841156i	−0.412341	+	0.911030i	$0.635289\pi$
$564$	22.7487	−	38.5898i	0.957892	−	1.62492i
$565$	0.802142	−	1.38935i	0.0337463	−	0.0584504i
$566$	7.82818	−	18.8989i	0.329043	−	0.794380i
$567$	18.1723	+	15.3872i	0.763165	+	0.646204i
$568$	−7.34640	−	17.7358i	−0.308248	−	0.744177i
$569$	−6.94991	−	25.9374i	−0.291355	−	1.08735i	−0.944069	−	0.329748i	$-0.893036\pi$
$569$	−6.94991	−	25.9374i	−0.291355	−	1.08735i	0.652714	−	0.757605i	$-0.273630\pi$
$570$	7.30267	−	5.49909i	0.305875	−	0.230332i
$571$	−19.3456	+	25.2117i	−0.809589	+	1.05508i	0.187753	+	0.982216i	$0.439880\pi$
$571$	−19.3456	+	25.2117i	−0.809589	+	1.05508i	−0.997342	+	0.0728611i	$0.976787\pi$
$572$	−0.436316	+	3.31415i	−0.0182433	+	0.138571i
$573$	19.5737	+	34.6236i	0.817702	+	1.44642i
$574$	51.5208	−	28.9375i	2.15044	−	1.20783i
$575$	−8.48825	+	20.4925i	−0.353985	+	0.854594i
$576$	34.0350	−	18.8359i	1.41813	−	0.784828i
$577$	10.0579	−	5.80693i	0.418716	−	0.241746i	−0.275812	−	0.961212i	$-0.588947\pi$
$577$	10.0579	−	5.80693i	0.418716	−	0.241746i	0.694528	+	0.719466i	$0.255613\pi$
$578$	−36.2913	+	10.9310i	−1.50952	+	0.454671i
$579$	−38.4682	+	15.5270i	−1.59868	+	0.645281i
$580$	1.38069	+	1.38069i	0.0573299	+	0.0573299i
$581$	9.49062	+	12.6765i	0.393737	+	0.525909i
$582$	−41.7353	+	53.3816i	−1.72999	+	2.21274i
$583$	−1.65063	−	2.15115i	−0.0683622	−	0.0890913i
$584$	−2.26593	−	1.73871i	−0.0937648	−	0.0719483i
$585$	−0.847949	+	1.94655i	−0.0350584	+	0.0804801i
$586$	−10.0520	−	37.5146i	−0.415244	−	1.54971i
$587$	−26.4364	−	26.4364i	−1.09115	−	1.09115i	−0.995406	−	0.0957425i	$-0.969477\pi$
$587$	−26.4364	−	26.4364i	−1.09115	−	1.09115i	−0.0957425	−	0.995406i	$-0.530523\pi$
$588$	−10.4565	+	34.4672i	−0.431219	+	1.42140i
$589$	4.48398	−	1.85732i	0.184759	−	0.0765297i
$590$	−0.170159	+	0.130568i	−0.00700535	+	0.00537539i
$591$	0.00104360	−	0.00740747i	4.29281e−5	−	0.000304702i
$592$	1.27544	+	9.68794i	0.0524203	+	0.398172i
$593$	−8.73017	−	32.5814i	−0.358505	−	1.33796i	−0.876016	−	0.482283i	$-0.839808\pi$
$593$	−8.73017	−	32.5814i	−0.358505	−	1.33796i	0.517510	−	0.855677i	$-0.326859\pi$
$594$	5.78496	−	12.9579i	0.237360	−	0.531668i
$595$	7.26371	−	4.22803i	0.297783	−	0.173332i
$596$		−	8.20583i		−	0.336124i
$597$	−19.9621	−	8.48137i	−0.816994	−	0.347119i
$598$	−10.2212	+	1.34565i	−0.417978	+	0.0550278i
$599$	19.9462	+	34.5478i	0.814980	+	1.41159i	0.909343	+	0.416048i	$0.136585\pi$
$599$	19.9462	+	34.5478i	0.814980	+	1.41159i	−0.0943630	+	0.995538i	$0.530081\pi$
$600$	16.5176	+	0.149726i	0.674328	+	0.00611254i
$601$	6.50176	+	15.6966i	0.265212	+	0.640279i	0.999246	−	0.0388343i	$-0.0123644\pi$
$601$	6.50176	+	15.6966i	0.265212	+	0.640279i	−0.734033	+	0.679113i	$0.762364\pi$
$602$	−3.60498	+	4.58464i	−0.146928	+	0.186856i
$603$	−4.48767	+	7.45733i	−0.182752	+	0.303686i
$604$	−15.1692	+	4.06456i	−0.617224	+	0.165385i
$605$	−4.45550	+	5.80652i	−0.181142	+	0.236069i
$606$	1.20265	−	0.310593i	0.0488543	−	0.0126170i
$607$	8.25598	−	6.33504i	0.335100	−	0.257131i	−0.427481	−	0.904025i	$-0.640599\pi$
$607$	8.25598	−	6.33504i	0.335100	−	0.257131i	0.762581	+	0.646893i	$0.223932\pi$
$608$			20.9461i			0.849477i
$609$	−1.88349	−	3.42575i	−0.0763227	−	0.138819i
$610$	−13.2799	+	13.2799i	−0.537688	+	0.537688i
$611$	−6.92583	−	3.99863i	−0.280189	−	0.161767i
$612$	−31.7725	−	18.4605i	−1.28433	−	0.746221i
$613$	−17.2531	−	29.8833i	−0.696847	−	1.20697i	−0.969554	−	0.244877i	$-0.921252\pi$
$613$	−17.2531	−	29.8833i	−0.696847	−	1.20697i	0.272707	−	0.962097i	$-0.412081\pi$
$614$	13.1659	+	49.1358i	0.531332	+	1.98296i
$615$	−6.57882	−	11.6372i	−0.265284	−	0.469257i
$616$	7.01366	+	0.0830695i	0.282589	+	0.00334697i
$617$	−11.7149	−	4.85246i	−0.471623	−	0.195353i	0.134196	−	0.990955i	$-0.457155\pi$
$617$	−11.7149	−	4.85246i	−0.471623	−	0.195353i	−0.605820	+	0.795602i	$0.707155\pi$
$618$	−31.6493	+	31.0806i	−1.27312	+	1.25025i
$619$	33.2946	+	25.5479i	1.33822	+	1.02686i	0.996194	+	0.0871661i	$0.0277811\pi$
$619$	33.2946	+	25.5479i	1.33822	+	1.02686i	0.342030	+	0.939689i	$0.388886\pi$
$620$	−3.49218	−	0.935728i	−0.140249	−	0.0375797i
$621$	25.8301	+	4.11792i	1.03653	+	0.165246i
$622$	−36.0687	+	14.9401i	−1.44622	+	0.599045i
$623$	22.9164	−	29.1440i	0.918127	−	1.16763i
$624$	−0.873951	−	1.54592i	−0.0349860	−	0.0618864i
$625$	−14.2448	−	8.22422i	−0.569790	−	0.328969i
$626$	−1.49272	−	11.3383i	−0.0596609	−	0.453170i
$627$	3.92141	+	5.20754i	0.156606	+	0.207969i
$628$	2.14847	+	1.24042i	0.0857333	+	0.0494981i
$629$	28.2963	−	22.4122i	1.12825	−	0.893635i
$630$	13.0579	+	3.92184i	0.520238	+	0.156250i
$631$	13.2622	−	13.2622i	0.527960	−	0.527960i	−0.392003	−	0.919964i	$-0.628218\pi$
$631$	13.2622	−	13.2622i	0.527960	−	0.527960i	0.919964	+	0.392003i	$0.128218\pi$
$632$	−9.07808	−	11.8308i	−0.361106	−	0.470603i
$633$	−30.1215	−	4.24367i	−1.19722	−	0.168671i
$634$	−47.5048	+	6.25412i	−1.88665	+	0.248383i
$635$	−2.04329	+	15.5203i	−0.0810853	+	0.615904i
$636$	−10.9747	−	3.04755i	−0.435176	−	0.120843i
$637$	6.16999	+	1.81091i	0.244464	+	0.0717510i
$638$	−1.64741	+	1.64741i	−0.0652216	+	0.0652216i
$639$	26.4405	−	2.99442i	1.04597	−	0.118458i
$640$	7.16426	−	9.33664i	0.283192	−	0.369063i
$641$	5.38203	+	40.8806i	0.212577	+	1.61469i	0.681754	+	0.731581i	$0.261217\pi$
$641$	5.38203	+	40.8806i	0.212577	+	1.61469i	−0.469177	+	0.883104i	$0.655449\pi$
$642$	−23.6643	−	58.6282i	−0.933955	−	2.31387i
$643$	17.4718	−	42.1806i	0.689020	−	1.66344i	−0.0577255	−	0.998332i	$-0.518385\pi$
$643$	17.4718	−	42.1806i	0.689020	−	1.66344i	0.746746	−	0.665110i	$-0.231615\pi$
$644$	9.78681	+	38.3353i	0.385655	+	1.51062i
$645$	1.03943	+	0.812660i	0.0409277	+	0.0319985i
$646$	24.2408	−	14.4970i	0.953742	−	0.570378i
$647$	−22.3600	−	38.7287i	−0.879063	−	1.52258i	−0.852370	−	0.522938i	$-0.824836\pi$
$647$	−22.3600	−	38.7287i	−0.879063	−	1.52258i	−0.0266928	−	0.999644i	$-0.508498\pi$
$648$	−4.35613	−	18.9854i	−0.171125	−	0.745819i
$649$	−0.0931080	−	0.121341i	−0.00365481	−	0.00476304i
$650$		−	9.02455i		−	0.353972i
$651$	6.19173	+	3.74954i	0.242673	+	0.146956i
$652$	53.1191	−	22.0026i	2.08030	−	0.861690i
$653$	3.52806	−	26.7982i	0.138064	−	1.04870i	−0.772409	−	0.635126i	$-0.780948\pi$
$653$	3.52806	−	26.7982i	0.138064	−	1.04870i	0.910472	−	0.413570i	$-0.135718\pi$
$654$	−4.84264	−	6.43092i	−0.189362	−	0.251469i
$655$	2.54554	−	9.50007i	0.0994623	−	0.371198i
$656$	11.0853	+	1.45941i	0.432810	+	0.0569805i
$657$	3.18403	−	2.35273i	0.124221	−	0.0917888i
$658$	−20.2127	+	47.2085i	−0.787974	+	1.84038i
$659$	−48.0030			−1.86993			−0.934965	−	0.354740i	$-0.884569\pi$
$659$	−48.0030			−1.86993			−0.934965	+	0.354740i	$0.884569\pi$
$660$	0.0440161	−	4.85580i	0.00171333	−	0.189012i
$661$	9.83013	−	36.6866i	0.382348	−	1.42694i	−0.459957	−	0.887941i	$-0.652135\pi$
$661$	9.83013	−	36.6866i	0.382348	−	1.42694i	0.842305	−	0.539001i	$-0.181198\pi$
$662$	61.3232	−	35.4049i	2.38339	−	1.37605i
$663$	−3.24414	+	5.70187i	−0.125992	+	0.221442i
$664$		−	12.9540i		−	0.502713i
$665$	−4.48093	+	4.37603i	−0.173763	+	0.169695i
$666$	57.9078	+	8.69438i	2.24388	+	0.336900i
$667$	−3.71898	−	2.14715i	−0.143999	−	0.0831381i
$668$	50.6651	−	6.67019i	1.96029	−	0.258077i
$669$	−2.51835	+	0.650381i	−0.0973649	+	0.0251452i
$670$	−0.650469	+	4.94080i	−0.0251298	+	0.190880i
$671$	−9.46992	−	9.46992i	−0.365582	−	0.365582i
$672$	−25.1763	+	18.4952i	−0.971197	+	0.713469i
$673$	14.6408	+	35.3460i	0.564362	+	1.36249i	0.906247	+	0.422748i	$0.138934\pi$
$673$	14.6408	+	35.3460i	0.564362	+	1.36249i	−0.341886	+	0.939742i	$0.611066\pi$
$674$	56.5659	+	7.44704i	2.17884	+	0.286849i
$675$	−6.52516	+	21.9469i	−0.251153	+	0.844736i
$676$	−31.2747	+	18.0565i	−1.20287	+	0.694480i
$677$	−5.18739	+	3.98042i	−0.199368	+	0.152980i	−0.703621	−	0.710576i	$-0.748435\pi$
$677$	−5.18739	+	3.98042i	−0.199368	+	0.152980i	0.504253	+	0.863556i	$0.331768\pi$
$678$	7.98135	−	0.977250i	0.306522	−	0.0375311i
$679$	23.6870	−	39.9275i	0.909024	−	1.53228i
$680$	−6.82943	−	0.792462i	−0.261897	−	0.0303895i
$681$	21.5088	−	8.68168i	0.824220	−	0.332683i
$682$	1.11649	−	4.16681i	0.0427527	−	0.159555i
$683$	−13.4588	+	1.77189i	−0.514987	+	0.0677993i	−0.383541	−	0.923524i	$-0.625295\pi$
$683$	−13.4588	+	1.77189i	−0.514987	+	0.0677993i	−0.131446	+	0.991323i	$0.541962\pi$
$684$	26.3179	+	7.56578i	1.00629	+	0.289285i
$685$	9.39251	+	3.89050i	0.358869	+	0.148649i
$686$	6.84042	−	40.7207i	0.261168	−	1.55472i
$687$	34.2864	+	9.52092i	1.30811	+	0.363246i
$688$	−1.06594	+	0.285619i	−0.0406388	+	0.0108891i
$689$	−0.526287	+	1.96413i	−0.0200499	+	0.0748273i
$690$	14.5007	−	3.74492i	0.552034	−	0.142567i
$691$	−19.3561	−	2.54828i	−0.736342	−	0.0969412i	−0.246978	−	0.969021i	$-0.579438\pi$
$691$	−19.3561	−	2.54828i	−0.736342	−	0.0969412i	−0.489364	+	0.872080i	$0.662771\pi$
$692$	−2.21421	+	5.34558i	−0.0841718	+	0.203209i
$693$	−2.79667	+	9.31157i	−0.106237	+	0.353717i
$694$	−44.1502	−	18.2876i	−1.67592	−	0.694188i
$695$	7.95109	−	2.13049i	0.301602	−	0.0808141i
$696$	−0.446146	+	3.16673i	−0.0169111	+	0.120035i
$697$	−16.3912	−	37.9119i	−0.620861	−	1.43602i
$698$	−8.42523	+	14.5929i	−0.318900	+	0.552350i
$699$	−5.09504	−	41.6119i	−0.192712	−	1.57391i
$700$	−34.3886	+	4.11364i	−1.29977	+	0.155481i
$701$	−4.10795			−0.155155			−0.0775776	−	0.996986i	$-0.524719\pi$
$701$	−4.10795			−0.155155			−0.0775776	+	0.996986i	$0.524719\pi$
$702$	−10.3505	+	2.47384i	−0.390653	+	0.0933690i
$703$	−16.3757	+	21.3412i	−0.617620	+	0.804898i
$704$	12.6007	+	9.66889i	0.474909	+	0.364410i
$705$	10.6925	+	4.54298i	0.402704	+	0.171098i
$706$	−45.1831	+	45.1831i	−1.70049	+	1.70049i
$707$	−0.790037	+	0.316335i	−0.0297124	+	0.0118970i
$708$	−0.619056	−	0.171905i	−0.0232655	−	0.00646057i
$709$	−5.40008	−	7.03752i	−0.202804	−	0.264300i	0.680868	−	0.732407i	$-0.261603\pi$
$709$	−5.40008	−	7.03752i	−0.202804	−	0.264300i	−0.883672	+	0.468107i	$0.844936\pi$
$710$	13.1948	−	7.61801i	0.495192	−	0.285899i
$711$	19.2372	−	7.56273i	0.721451	−	0.283624i
$712$	−29.2949	+	7.84955i	−1.09787	+	0.294174i
$713$	7.95126			0.297777
$714$	38.8292	+	16.3356i	1.45315	+	0.611345i
$715$	−0.866926			−0.0324212
$716$	13.8962	−	3.72349i	0.519327	−	0.139153i
$717$	−24.1368	−	14.2286i	−0.901404	−	0.531378i
$718$	−39.7241	+	22.9347i	−1.48249	+	0.855916i
$719$	6.50980	+	8.48374i	0.242775	+	0.316390i	0.898809	−	0.438341i	$-0.144434\pi$
$719$	6.50980	+	8.48374i	0.242775	+	0.316390i	−0.656034	+	0.754731i	$0.727767\pi$
$720$	1.53311	+	2.07481i	0.0571358	+	0.0773237i
$721$	18.7855	−	23.8905i	0.699610	−	0.889730i
$722$	15.0700	−	15.0700i	0.560849	−	0.560849i
$723$	−0.368117	+	0.866417i	−0.0136904	+	0.0322224i
$724$	55.5930	+	42.6580i	2.06610	+	1.58537i
$725$	2.28839	−	2.98229i	0.0849888	−	0.110760i
$726$	−36.6824	−	0.332513i	−1.36141	−	0.0123407i
$727$	26.2706			0.974322			0.487161	−	0.873312i	$-0.338032\pi$
$727$	26.2706			0.974322			0.487161	+	0.873312i	$0.338032\pi$
$728$	−3.15253	−	4.21079i	−0.116841	−	0.156062i
$729$	26.9601	+	1.46771i	0.998521	+	0.0543596i
$730$	1.13341	−	1.96312i	0.0419493	−	0.0726583i
$731$	2.92658	+	2.83792i	0.108244	+	0.104964i
$732$	−55.7075	−	7.84836i	−2.05901	−	0.290084i
$733$	−34.8834	+	9.34698i	−1.28845	+	0.345239i	−0.837071	−	0.547094i	$-0.815734\pi$
$733$	−34.8834	+	9.34698i	−1.28845	+	0.345239i	−0.451378	+	0.892333i	$0.649067\pi$
$734$	12.6772	+	5.25105i	0.467923	+	0.193820i
$735$	−9.21641	−	1.52188i	−0.339953	−	0.0561356i
$736$	−13.1320	+	31.7035i	−0.484052	+	1.16861i
$737$	−3.52329	−	0.463850i	−0.129782	−	0.0170861i
$738$	26.7590	−	61.4279i	0.985011	−	2.26119i
$739$	6.37029	−	23.7743i	0.234335	−	0.874550i	−0.744112	−	0.668054i	$-0.767127\pi$
$739$	6.37029	−	23.7743i	0.234335	−	0.874550i	0.978447	−	0.206496i	$-0.0662060\pi$
$740$	19.3553	−	5.18625i	0.711517	−	0.190650i
$741$	1.30805	−	4.71049i	0.0480524	−	0.173044i
$742$	12.9246	+	1.85753i	0.474477	+	0.0681920i
$743$	−1.26724	−	0.524908i	−0.0464905	−	0.0192570i	0.359317	−	0.933216i	$-0.383010\pi$
$743$	−1.26724	−	0.524908i	−0.0464905	−	0.0192570i	−0.405808	+	0.913959i	$0.633010\pi$
$744$	−2.21633	−	5.49094i	−0.0812545	−	0.201308i
$745$	2.10994	−	0.277779i	0.0773022	−	0.0101770i
$746$	17.0532	−	63.6432i	0.624360	−	2.33014i
$747$	17.2569	+	4.96096i	0.631397	+	0.181512i
$748$	1.72937	−	14.9037i	0.0632320	−	0.544933i
$749$	21.2127	+	37.7675i	0.775096	+	1.37999i
$750$	3.40125	+	27.7785i	0.124196	+	1.01433i
$751$	29.3024	−	22.4845i	1.06926	−	0.820471i	0.0848543	−	0.996393i	$-0.472958\pi$
$751$	29.3024	−	22.4845i	1.06926	−	0.820471i	0.984404	+	0.175923i	$0.0562909\pi$
$752$	−8.41510	+	4.85846i	−0.306867	+	0.177170i
$753$	20.2153	+	11.9169i	0.736688	+	0.434278i
$754$	1.73224	+	0.228054i	0.0630845	+	0.00830523i
$755$	−1.55861	−	3.76281i	−0.0567234	−	0.136943i
$756$	14.1447	+	38.3135i	0.514439	+	1.39345i
$757$	−24.4377	−	24.4377i	−0.888203	−	0.888203i	0.106148	−	0.994350i	$-0.466148\pi$
$757$	−24.4377	−	24.4377i	−0.888203	−	0.888203i	−0.994350	+	0.106148i	$0.966148\pi$
$758$	−10.2386	+	77.7698i	−0.371882	+	2.82473i
$759$	2.67051	+	10.3405i	0.0969333	+	0.375336i
$760$	5.07971	−	0.668757i	0.184261	−	0.0242584i
$761$	15.9149	+	9.18850i	0.576916	+	0.333083i	0.759907	−	0.650032i	$-0.225244\pi$
$761$	15.9149	+	9.18850i	0.576916	+	0.333083i	−0.182991	+	0.983115i	$0.558578\pi$
$762$	−68.3027	+	38.6134i	−2.47435	+	1.39881i
$763$	3.85364	+	3.94602i	0.139511	+	0.142856i
$764$			68.2179i			2.46804i
$765$	3.67114	−	8.79447i	0.132730	−	0.317965i
$766$	−46.3906	+	26.7836i	−1.67616	+	0.967731i
$767$	−0.0296865	+	0.110792i	−0.00107192	+	0.00400045i
$768$	14.0684	+	0.127525i	0.507649	+	0.00460165i
$769$	−53.9288			−1.94472			−0.972362	−	0.233479i	$-0.924989\pi$
$769$	−53.9288			−1.94472			−0.972362	+	0.233479i	$0.924989\pi$
$770$	0.661208	+	5.52747i	0.0238283	+	0.199196i
$771$	11.5708	+	3.21307i	0.416712	+	0.115716i
$772$	−70.5425	−	9.28709i	−2.53888	−	0.334250i
$773$	−4.23162	+	15.7926i	−0.152201	+	0.568021i	0.847128	+	0.531389i	$0.178330\pi$
$773$	−4.23162	+	15.7926i	−0.152201	+	0.568021i	−0.999329	+	0.0366321i	$0.988337\pi$
$774$	−0.119881	+	6.61203i	−0.00430904	+	0.237664i
$775$	−0.908498	+	6.90073i	−0.0326342	+	0.247881i
$776$	−35.0863	+	14.5332i	−1.25952	+	0.521712i
$777$	−40.1107	−	0.838749i	−1.43896	−	0.0300899i
$778$		−	27.4707i		−	0.984874i
$779$	18.7377	+	24.4194i	0.671348	+	0.874918i
$780$	−2.90912	+	2.19064i	−0.104163	+	0.0784374i
$781$	5.43241	+	9.40921i	0.194387	+	0.336688i
$782$	45.7790	−	6.74472i	1.63705	−	0.241191i
$783$	−4.04776	−	1.80710i	−0.144655	−	0.0645803i
$784$	5.65389	−	5.39219i	0.201925	−	0.192578i
$785$	−0.246216	+	0.594419i	−0.00878784	+	0.0212157i
$786$	45.7125	−	18.4511i	1.63051	−	0.658128i
$787$	6.87774	+	52.2416i	0.245165	+	1.86221i	0.463176	+	0.886266i	$0.346710\pi$
$787$	6.87774	+	52.2416i	0.245165	+	1.86221i	−0.218011	+	0.975946i	$0.569957\pi$
$788$	0.00781071	−	0.0101791i	0.000278245	−	0.000362616i
$789$	−23.5434	+	23.1204i	−0.838169	+	0.823110i
$790$	8.36890	−	8.36890i	0.297752	−	0.297752i
$791$	−5.33795	+	1.36275i	−0.189796	+	0.0484539i
$792$	6.39651	−	4.72649i	0.227290	−	0.167948i
$793$	−1.31094	+	9.95756i	−0.0465528	+	0.353603i
$794$	−78.2333	+	10.2996i	−2.77640	+	0.365519i
$795$	0.412097	−	2.92505i	0.0146156	−	0.103741i
$796$	−22.6462	−	29.5131i	−0.802673	−	1.04606i
$797$	16.8270	−	16.8270i	0.596042	−	0.596042i	−0.343215	−	0.939257i	$-0.611516\pi$
$797$	16.8270	−	16.8270i	0.596042	−	0.596042i	0.939257	+	0.343215i	$0.111516\pi$
$798$	−31.0315	−	4.74734i	−1.09850	−	0.168054i
$799$	31.3585	+	17.4674i	1.10938	+	0.617951i
$800$	−26.0143	−	15.0194i	−0.919745	−	0.531015i
$801$	0.762070	−	42.0319i	0.0269264	−	1.48512i
$802$	0.258757	+	1.96546i	0.00913704	+	0.0694027i
$803$	1.39990	+	0.808234i	0.0494015	+	0.0285220i
$804$	−12.9951	+	7.34648i	−0.458302	+	0.259090i
$805$	−9.52573	+	3.81415i	−0.335738	+	0.134431i
$806$	−2.98881	+	1.23801i	−0.105276	+	0.0436069i
$807$	−21.8311	−	9.27544i	−0.768490	−	0.326511i
$808$	0.672436	+	0.180179i	0.0236562	+	0.00633867i
$809$	−0.848735	−	0.651257i	−0.0298399	−	0.0228970i	0.593734	−	0.804662i	$-0.297653\pi$
$809$	−0.848735	−	0.651257i	−0.0298399	−	0.0228970i	−0.623574	+	0.781765i	$0.714320\pi$
$810$	14.4879	−	5.39450i	0.509053	−	0.189543i
$811$	−38.6625	−	16.0145i	−1.35762	−	0.562347i	−0.419220	−	0.907885i	$-0.637696\pi$
$811$	−38.6625	−	16.0145i	−1.35762	−	0.562347i	−0.938405	+	0.345538i	$0.887696\pi$
$812$	0.0794110	−	6.70477i	0.00278678	−	0.235291i
$813$	9.68674	−	5.47618i	0.339729	−	0.192058i
$814$	6.18814	+	23.0944i	0.216894	+	0.809460i
$815$	7.45562	+	12.9135i	0.261159	+	0.452341i
$816$	4.02892	+	6.87761i	0.141040	+	0.240765i
$817$	−2.63094	−	1.51897i	−0.0920448	−	0.0531421i
$818$	−25.6347	+	25.6347i	−0.896296	+	0.896296i
$819$	6.81680	−	2.58711i	0.238198	−	0.0904008i
$820$		−	22.9284i		−	0.800696i
$821$	−35.4268	+	27.1839i	−1.23640	+	0.948725i	−0.999739	−	0.0228663i	$-0.992721\pi$
$821$	−35.4268	+	27.1839i	−1.23640	+	0.948725i	−0.236664	+	0.971591i	$0.576054\pi$
$822$	12.7416	+	49.3370i	0.444415	+	1.72082i
$823$	−7.78613	+	10.1471i	−0.271407	+	0.353705i	−0.909094	−	0.416591i	$-0.863225\pi$
$823$	−7.78613	+	10.1471i	−0.271407	+	0.353705i	0.637687	+	0.770296i	$0.279891\pi$
$824$	−24.0142	+	6.43460i	−0.836576	+	0.224160i
$825$	−9.27942	+	1.13619i	−0.323068	+	0.0395570i
$826$	0.729044	+	0.104779i	0.0253667	+	0.00364571i
$827$	9.35175	+	22.5771i	0.325192	+	0.785083i	0.998936	+	0.0461182i	$0.0146851\pi$
$827$	9.35175	+	22.5771i	0.325192	+	0.785083i	−0.673744	+	0.738965i	$0.735315\pi$
$828$	35.0907	+	27.9512i	1.21949	+	0.971370i
$829$	17.8704	+	30.9524i	0.620663	+	1.07502i	0.989362	+	0.145471i	$0.0464699\pi$
$829$	17.8704	+	30.9524i	0.620663	+	1.07502i	−0.368699	+	0.929549i	$0.620197\pi$
$830$	10.1932	−	1.34196i	0.353810	−	0.0465800i
$831$	−6.45462	+	15.1919i	−0.223908	+	0.527000i
$832$		−	11.9111i		−	0.412944i
$833$	−27.8153	−	7.70129i	−0.963743	−	0.266834i
$834$	32.5033	+	25.4120i	1.12550	+	0.879947i
$835$	3.43017	+	12.8016i	0.118706	+	0.443016i
$836$	1.45941	+	11.0853i	0.0504747	+	0.383394i
$837$	8.16365	−	0.849672i	0.282177	−	0.0293689i
$838$	48.2343	−	37.0115i	1.66623	−	1.27854i
$839$	−39.3736	+	16.3091i	−1.35933	+	0.563053i	−0.938874	−	0.344261i	$-0.888130\pi$
$839$	−39.3736	+	16.3091i	−1.35933	+	0.563053i	−0.420455	+	0.907313i	$0.638130\pi$
$840$	5.28916	+	5.51508i	0.182493	+	0.190288i
$841$	−19.9915	−	19.9915i	−0.689361	−	0.689361i
$842$	−7.67904	−	28.6586i	−0.264637	−	0.987639i
$843$	−3.11393	−	12.0575i	−0.107249	−	0.415281i
$844$	−41.3920	−	31.7612i	−1.42477	−	1.09327i
$845$	−5.70149	−	7.43033i	−0.196137	−	0.255611i
$846$	14.0488	+	56.5094i	0.483009	+	1.94283i
$847$	24.9556	−	2.98524i	0.857485	−	0.102574i
$848$	1.74702	+	1.74702i	0.0599930	+	0.0599930i
$849$	5.94816	+	14.7365i	0.204140	+	0.505757i
$850$	0.622957	+	40.5013i	0.0213672	+	1.38918i
$851$	−38.1655	+	22.0348i	−1.30829	+	0.755344i
$852$	42.0055	+	17.8470i	1.43909	+	0.611429i
$853$	6.12998	−	14.7991i	0.209886	−	0.506711i	−0.783519	−	0.621368i	$-0.786577\pi$
$853$	6.12998	−	14.7991i	0.209886	−	0.506711i	0.993405	+	0.114658i	$0.0365771\pi$
$854$	64.4888	+	0.763802i	2.20676	+	0.0261368i
$855$	−1.05447	+	7.02315i	−0.0360620	+	0.240187i
$856$	4.62516	−	35.1316i	0.158085	−	1.20077i
$857$	23.6767	−	30.8560i	0.808779	−	1.05402i	−0.188627	−	0.982049i	$-0.560404\pi$
$857$	23.6767	−	30.8560i	0.808779	−	1.05402i	0.997407	−	0.0719730i	$-0.0229295\pi$
$858$	−2.61383	−	3.47110i	−0.0892346	−	0.118502i
$859$	1.57887	+	5.89243i	0.0538704	+	0.201047i	0.987616	−	0.156890i	$-0.0501468\pi$
$859$	1.57887	+	5.89243i	0.0538704	+	0.201047i	−0.933746	+	0.357937i	$0.883480\pi$
$860$	0.866014	+	2.09074i	0.0295308	+	0.0712937i
$861$	−12.8059	+	44.0840i	−0.436423	+	1.50238i
$862$	−14.5377	+	35.0970i	−0.495155	+	1.19541i
$863$	−16.6347	+	28.8121i	−0.566251	+	0.980775i	0.430681	+	0.902504i	$0.358273\pi$
$863$	−16.6347	+	28.8121i	−0.566251	+	0.980775i	−0.996932	+	0.0782710i	$0.975060\pi$
$864$	−10.0949	+	33.9536i	−0.343437	+	1.15512i
$865$	−1.44945	−	0.388378i	−0.0492827	−	0.0132052i
$866$	10.2844	−	17.8131i	0.349479	−	0.605315i
$867$	14.1658	−	25.8134i	0.481095	−	0.876669i
$868$	6.07988	+	10.8247i	0.206365	+	0.367415i
$869$	5.96787	+	5.96787i	0.202446	+	0.202446i
$870$	−2.53804	−	0.0230064i	−0.0860475	−	0.000779990i
$871$	1.33252	+	2.30799i	0.0451506	+	0.0782032i
$872$	−0.588925	−	4.47333i	−0.0199435	−	0.151486i
$873$	−5.92379	−	52.3066i	−0.200490	−	1.77031i
$874$	−31.8586	+	13.1963i	−1.07763	+	0.446370i
$875$	−4.74296	−	18.5783i	−0.160341	−	0.628063i
$876$	6.73994	−	0.825250i	0.227721	−	0.0278826i
$877$	−20.4809	−	2.69636i	−0.691591	−	0.0910496i	−0.223466	−	0.974712i	$-0.571737\pi$
$877$	−20.4809	−	2.69636i	−0.691591	−	0.0910496i	−0.468125	+	0.883662i	$0.655070\pi$
$878$	−8.89609	−	6.82621i	−0.300228	−	0.230373i
$879$	25.9920	+	15.3223i	0.876688	+	0.516808i
$880$	−0.526671	+	0.912220i	−0.0177541	+	0.0307509i
$881$	−5.55102	−	2.29931i	−0.187019	−	0.0774656i	0.287209	−	0.957868i	$-0.407273\pi$
$881$	−5.55102	−	2.29931i	−0.187019	−	0.0774656i	−0.474228	+	0.880402i	$0.657273\pi$
$882$	−21.6945	−	41.4904i	−0.730491	−	1.39705i
$883$	−26.1297			−0.879336			−0.439668	−	0.898160i	$-0.644904\pi$
$883$	−26.1297			−0.879336			−0.439668	+	0.898160i	$0.644904\pi$
$884$	−9.65664	+	5.77508i	−0.324788	+	0.194237i
$885$	0.0232454	−	0.164995i	0.000781384	−	0.00554625i
$886$	64.1804	+	17.1971i	2.15618	+	0.577747i
$887$	22.0638	−	16.9301i	0.740828	−	0.568458i	−0.167921	−	0.985801i	$-0.553705\pi$
$887$	22.0638	−	16.9301i	0.740828	−	0.568458i	0.908749	+	0.417343i	$0.137039\pi$
$888$	25.8549	+	20.2141i	0.867634	+	0.678342i
$889$	43.0329	−	32.2178i	1.44328	−	1.08055i
$890$	−9.21138	−	22.2382i	−0.308766	−	0.745427i
$891$	3.84682	+	10.3313i	0.128873	+	0.346112i
$892$	−4.30909	−	1.15462i	−0.144279	−	0.0386594i
$893$	−25.8381	−	6.92331i	−0.864641	−	0.231680i
$894$	7.47378	+	7.61052i	0.249961	+	0.254534i
$895$	1.42781	+	3.44705i	0.0477266	+	0.115222i
$896$	−40.1276	+	4.80014i	−1.34057	+	0.160361i
$897$	4.93304	−	6.30960i	0.164709	−	0.210672i
$898$	51.9502	−	39.8628i	1.73360	−	1.33024i
$899$	−1.30162	−	0.348768i	−0.0434115	−	0.0116321i
$900$	−28.2676	+	27.2608i	−0.942254	+	0.908695i
$901$	2.22634	−	8.85114i	0.0741701	−	0.294874i
$902$	27.3578			0.910915
$903$	−0.497357	−	4.50351i	−0.0165510	−	0.149867i
$904$	4.16362	+	1.72463i	0.138480	+	0.0573602i
$905$	−9.08661	+	15.7385i	−0.302049	+	0.523165i
$906$	10.3667	−	17.5856i	0.344411	−	0.584242i
$907$	0.603877	+	0.463371i	0.0200514	+	0.0153860i	0.618739	−	0.785597i	$-0.287644\pi$
$907$	0.603877	+	0.463371i	0.0200514	+	0.0153860i	−0.598687	+	0.800983i	$0.704311\pi$
$908$	39.4426	+	5.19272i	1.30895	+	0.172327i
$909$	−0.497550	+	0.826796i	−0.0165027	+	0.0274231i
$910$	2.98678	−	2.91686i	0.0990107	−	0.0966928i
$911$	15.1451	−	6.27332i	0.501781	−	0.207844i	−0.117412	−	0.993083i	$-0.537460\pi$
$911$	15.1451	−	6.27332i	0.501781	−	0.207844i	0.619193	+	0.785239i	$0.287460\pi$
$912$	−4.16195	−	4.23809i	−0.137816	−	0.140337i
$913$	0.956950	+	7.26875i	0.0316704	+	0.240561i
$914$	0.362551	+	0.627957i	0.0119921	+	0.0207710i
$915$	0.132249	−	14.5896i	0.00437202	−	0.482316i
$916$	43.1561	+	43.1561i	1.42592	+	1.42592i
$917$	−29.4474	+	16.5396i	−0.972439	+	0.546185i
$918$	46.2811	−	11.8168i	1.52750	−	0.390013i
$919$	−6.79324	+	11.7662i	−0.224088	+	0.388132i	−0.956046	−	0.293218i	$-0.905274\pi$
$919$	−6.79324	+	11.7662i	−0.224088	+	0.388132i	0.731957	+	0.681351i	$0.238607\pi$
$920$	8.10779	+	2.17247i	0.267306	+	0.0716244i
$921$	−34.0438	−	20.0688i	−1.12178	−	0.661290i
$922$	−10.9746	+	19.0086i	−0.361430	+	0.626015i
$923$	3.11807	−	7.52768i	0.102632	−	0.247776i
$924$	−12.0354	+	11.5424i	−0.395936	+	0.379716i
$925$	−14.7628	−	35.6406i	−0.485399	−	1.17186i
$926$	7.97310	+	29.7560i	0.262012	+	0.977843i
$927$	0.624701	−	34.4553i	0.0205179	−	1.13166i
$928$	3.54033	−	4.61385i	0.116217	−	0.151457i
$929$	−1.35934	+	10.3252i	−0.0445986	+	0.338760i	0.954570	+	0.297987i	$0.0963152\pi$
$929$	−1.35934	+	10.3252i	−0.0445986	+	0.338760i	−0.999168	+	0.0407726i	$0.987018\pi$
$930$	4.09108	−	2.31280i	0.134152	−	0.0758397i
$931$	21.5022	+	0.509413i	0.704705	+	0.0166953i
$932$	27.5166	−	66.4309i	0.901336	−	2.17602i
$933$	11.8601	−	27.9144i	0.388282	−	0.913877i
$934$	53.5040	−	30.8906i	1.75071	−	1.01077i
$935$	3.89068	−	0.0598432i	0.127239	−	0.00195708i
$936$	−5.73229	−	1.64790i	−0.187366	−	0.0538632i
$937$	26.2120	+	26.2120i	0.856308	+	0.856308i	0.990901	−	0.134593i	$-0.0429726\pi$
$937$	26.2120	+	26.2120i	0.856308	+	0.856308i	−0.134593	+	0.990901i	$0.542973\pi$
$938$	13.6993	−	10.2564i	0.447298	−	0.334882i
$939$	6.99917	+	5.47216i	0.228409	+	0.178577i
$940$	12.1303	+	15.8085i	0.395645	+	0.515615i
$941$	6.71636	+	5.15365i	0.218947	+	0.168004i	0.712412	−	0.701762i	$-0.247603\pi$
$941$	6.71636	+	5.15365i	0.218947	+	0.168004i	−0.493464	+	0.869766i	$0.664270\pi$
$942$	−3.12236	+	0.806373i	−0.101732	+	0.0262730i
$943$	13.0513	+	48.7081i	0.425008	+	1.58615i
$944$	0.0985451	+	0.0985451i	0.00320737	+	0.00320737i
$945$	−9.37259	+	4.93395i	−0.304890	+	0.160501i
$946$	−2.49464	+	1.03331i	−0.0811076	+	0.0335959i
$947$	11.6283	−	8.92275i	0.377871	−	0.289950i	−0.402311	−	0.915503i	$-0.631793\pi$
$947$	11.6283	−	8.92275i	0.377871	−	0.289950i	0.780182	+	0.625553i	$0.215126\pi$
$948$	35.1064	+	4.94598i	1.14020	+	0.160638i
$949$	−0.158230	−	1.20187i	−0.00513635	−	0.0390144i
$950$	−7.81264	−	29.1572i	−0.253476	−	0.945984i
$951$	22.9270	−	29.3248i	0.743460	−	0.950923i
$952$	14.4389	+	18.6800i	0.467968	+	0.605422i
$953$		−	3.68962i		−	0.119519i	−0.998213	−	0.0597593i	$-0.980967\pi$
$953$		−	3.68962i		−	0.119519i	0.998213	−	0.0597593i	$-0.0190333\pi$
$954$	12.9542	−	7.16919i	0.419407	−	0.232111i
$955$	−17.5406	+	2.30927i	−0.567602	+	0.0747262i
$956$	−24.0282	−	41.6180i	−0.777127	−	1.34602i
$957$	0.0164059	−	1.80988i	0.000530327	−	0.0585050i
$958$	−21.8978	−	52.8661i	−0.707487	−	1.70803i
$959$	−12.9772	−	32.4101i	−0.419055	−	1.04658i
$960$	2.10294	+	17.1750i	0.0678720	+	0.554321i
$961$	−27.5336	+	7.37762i	−0.888182	+	0.237988i
$962$	10.9153	−	14.2250i	0.351922	−	0.458633i
$963$	45.0299	+	19.6157i	1.45107	+	0.632108i
$964$	−1.28096	+	0.982915i	−0.0412569	+	0.0316576i
$965$		−	18.4527i		−	0.594014i
$966$	−43.9922	−	26.6404i	−1.41543	−	0.857142i
$967$	−21.0195	+	21.0195i	−0.675942	+	0.675942i	−0.959079	−	0.283138i	$-0.908625\pi$
$967$	−21.0195	+	21.0195i	−0.675942	+	0.675942i	0.283138	+	0.959079i	$0.408625\pi$
$968$	−17.8055	−	10.2800i	−0.572291	−	0.330412i
$969$	−5.54523	+	21.2305i	−0.178139	+	0.682023i
$970$	−15.0705	−	26.1029i	−0.483886	−	0.838114i
$971$	0.594700	+	2.21945i	0.0190848	+	0.0712256i	0.974812	−	0.223030i	$-0.0715949\pi$
$971$	0.594700	+	2.21945i	0.0190848	+	0.0712256i	−0.955727	+	0.294256i	$0.904928\pi$
$972$	39.0149	+	24.9480i	1.25140	+	0.800206i
$973$	−24.3113	−	14.4227i	−0.779383	−	0.462370i
$974$	−33.4248	−	13.8450i	−1.07100	−	0.443622i
$975$	4.91233	+	5.00220i	0.157320	+	0.160199i
$976$	9.68140	+	7.42880i	0.309894	+	0.237790i
$977$	−34.6509	−	9.28468i	−1.10858	−	0.297043i	−0.342327	−	0.939581i	$-0.611215\pi$
$977$	−34.6509	−	9.28468i	−1.10858	−	0.297043i	−0.766254	+	0.642538i	$0.777882\pi$
$978$	−29.2256	+	68.7867i	−0.934533	+	2.19956i
$979$	15.8581	−	6.56864i	0.506827	−	0.209935i
$980$	−12.4763	−	10.0517i	−0.398542	−	0.321091i
$981$	6.18476	+	0.928591i	0.197464	+	0.0296476i
$982$	−8.78731	−	5.07335i	−0.280414	−	0.161897i
$983$	−2.83276	−	21.5169i	−0.0903510	−	0.686284i	−0.975346	−	0.220683i	$-0.929171\pi$
$983$	−2.83276	−	21.5169i	−0.0903510	−	0.686284i	0.884995	−	0.465601i	$-0.154162\pi$
$984$	29.9987	−	22.5897i	0.956323	−	0.720135i
$985$	0.00288172	+	0.00166376i	9.18194e−5	+	5.30119e-5i
$986$	−7.78987	−	0.903908i	−0.248080	−	0.0287863i
$987$	−14.4933	−	37.1695i	−0.461328	−	1.18312i
$988$	5.92908	−	5.92908i	0.188629	−	0.188629i
$989$	−3.02981	−	3.94852i	−0.0963423	−	0.125556i
$990$	4.38179	+	4.54361i	0.139262	+	0.144406i
$991$	37.2650	−	4.90603i	1.18376	−	0.155845i	0.487166	−	0.873309i	$-0.338031\pi$
$991$	37.2650	−	4.90603i	1.18376	−	0.155845i	0.696596	+	0.717464i	$0.254697\pi$
$992$	−1.40552	+	10.6760i	−0.0446253	+	0.338963i
$993$	−14.7187	+	53.0046i	−0.467085	+	1.68205i
$994$	−50.3743	−	14.1392i	−1.59777	−	0.448470i
$995$	6.82200	−	6.82200i	0.216272	−	0.216272i
$996$	21.5786	+	21.9734i	0.683745	+	0.696254i
$997$	12.9101	−	16.8247i	0.408866	−	0.532844i	−0.542848	−	0.839831i	$-0.682654\pi$
$997$	12.9101	−	16.8247i	0.408866	−	0.532844i	0.951714	+	0.306987i	$0.0993207\pi$
$998$	−7.28598	−	55.3425i	−0.230634	−	1.75184i
$999$	−36.8302	+	26.7018i	−1.16526	+	0.844806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bj.a.26.7	✓	352
3.2	odd	2	inner	357.2.bj.a.26.38	yes	352
7.3	odd	6	inner	357.2.bj.a.332.38	yes	352
17.2	even	8	inner	357.2.bj.a.257.7	yes	352
21.17	even	6	inner	357.2.bj.a.332.7	yes	352
51.2	odd	8	inner	357.2.bj.a.257.38	yes	352
119.87	odd	24	inner	357.2.bj.a.206.38	yes	352
357.206	even	24	inner	357.2.bj.a.206.7	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.7	✓	352	1.1	even	1	trivial
357.2.bj.a.26.38	yes	352	3.2	odd	2	inner
357.2.bj.a.206.7	yes	352	357.206	even	24	inner
357.2.bj.a.206.38	yes	352	119.87	odd	24	inner
357.2.bj.a.257.7	yes	352	17.2	even	8	inner
357.2.bj.a.257.38	yes	352	51.2	odd	8	inner
357.2.bj.a.332.7	yes	352	21.17	even	6	inner
357.2.bj.a.332.38	yes	352	7.3	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bj (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15355 + 0.577042i) q^{2} +(0.879586 - 1.49209i) q^{3} +(2.57275 - 1.48538i) q^{4} +(0.469021 + 0.611240i) q^{5} +(-1.03323 + 3.72084i) q^{6} +(0.376382 - 2.61884i) q^{7} +(-1.53040 + 1.53040i) q^{8} +(-1.45266 - 2.62484i) q^{9} +(-1.36277 - 1.04569i) q^{10} +(0.745683 - 0.971793i) q^{11} +(0.0466401 - 5.14528i) q^{12} -0.918607 q^{13} +(0.700626 + 5.85699i) q^{14} +(1.32457 - 0.162182i) q^{15} +(-0.558068 + 0.966602i) q^{16} +(4.12262 - 0.0634107i) q^{17} +(4.64301 + 4.81448i) q^{18} +(-2.96790 + 0.795248i) q^{19} +(2.11459 + 0.875893i) q^{20} +(-3.57649 - 2.86509i) q^{21} +(-1.04510 + 2.52309i) q^{22} +(-4.99071 - 0.657040i) q^{23} +(0.937372 + 3.62961i) q^{24} +(1.14046 - 4.25626i) q^{25} +(1.97827 - 0.530075i) q^{26} +(-5.19423 - 0.141283i) q^{27} +(-2.92163 - 7.29669i) q^{28} +(0.788160 + 0.326467i) q^{29} +(-2.75894 + 1.11360i) q^{30} +(-1.56607 + 0.206177i) q^{31} +(1.76439 - 6.58478i) q^{32} +(-0.794108 - 1.96740i) q^{33} +(-8.84167 + 2.51548i) q^{34} +(1.77727 - 0.998232i) q^{35} +(-7.63619 - 4.59531i) q^{36} +(6.94564 - 5.32958i) q^{37} +(5.93264 - 3.42521i) q^{38} +(-0.807994 + 1.37064i) q^{39} +(-1.65323 - 0.217652i) q^{40} +(-3.83356 - 9.25504i) q^{41} +(9.35542 + 4.10634i) q^{42} +(0.699131 + 0.699131i) q^{43} +(0.474975 - 3.60780i) q^{44} +(0.923081 - 2.11903i) q^{45} +(11.1269 - 1.46488i) q^{46} +(7.53949 + 4.35293i) q^{47} +(0.951387 + 1.68290i) q^{48} +(-6.71667 - 1.97137i) q^{49} +9.82416i q^{50} +(3.53158 - 6.20709i) q^{51} +(-2.36334 + 1.36448i) q^{52} +(0.572918 - 2.13816i) q^{53} +(11.2676 - 2.69303i) q^{54} +0.943739 q^{55} +(3.43186 + 4.58389i) q^{56} +(-1.42395 + 5.12786i) q^{57} +(-1.88573 - 0.248261i) q^{58} +(0.0323169 - 0.120608i) q^{59} +(3.16688 - 2.38474i) q^{60} +(1.42709 - 10.8398i) q^{61} +(3.25363 - 1.34770i) q^{62} +(-7.42080 + 2.81634i) q^{63} +12.9665i q^{64} +(-0.430846 - 0.561489i) q^{65} +(2.84542 + 3.77866i) q^{66} +(-1.45058 - 2.51248i) q^{67} +(10.5123 - 6.28678i) q^{68} +(-5.37013 + 6.86866i) q^{69} +(-3.25142 + 3.17530i) q^{70} +(-3.39434 + 8.19466i) q^{71} +(6.24019 + 1.79391i) q^{72} +(0.172249 + 1.30836i) q^{73} +(-11.8824 + 15.4854i) q^{74} +(-5.34758 - 5.44542i) q^{75} +(-6.45442 + 6.45442i) q^{76} +(-2.26431 - 2.31859i) q^{77} +(0.949137 - 3.41799i) q^{78} +(-0.899342 + 6.83118i) q^{79} +(-0.852571 + 0.112243i) q^{80} +(-4.77958 + 7.62598i) q^{81} +(13.5963 + 17.7191i) q^{82} +(-4.23223 + 4.23223i) q^{83} +(-13.4571 - 2.05873i) q^{84} +(1.97235 + 2.49017i) q^{85} +(-1.90904 - 1.10219i) q^{86} +(1.18037 - 0.888849i) q^{87} +(0.346038 + 2.62842i) q^{88} +(12.1356 + 7.00646i) q^{89} +(-0.765135 + 5.09608i) q^{90} +(-0.345747 + 2.40569i) q^{91} +(-13.8158 + 5.72269i) q^{92} +(-1.06986 + 2.51806i) q^{93} +(-18.7485 - 5.02364i) q^{94} +(-1.87810 - 1.44111i) q^{95} +(-8.27314 - 8.42450i) q^{96} +(16.2113 + 6.71494i) q^{97} +(15.6023 + 0.369636i) q^{98} +(-3.63402 - 0.545618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) \) 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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