LMFDB - Embedded newform 160.2.z.a.109.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(29,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	160.109
Dual form			160.2.z.a.69.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.654098 + 1.25386i) q^{2} +(1.44059 + 0.596710i) q^{3} +(-1.14431 - 1.64029i) q^{4} +(1.94969 - 1.09485i) q^{5} +(-1.69047 + 1.41598i) q^{6} +(1.37373 + 1.37373i) q^{7} +(2.80518 - 0.361890i) q^{8} +(-0.402097 - 0.402097i) q^{9} +(0.0974914 + 3.16077i) q^{10} +(0.378268 + 0.913219i) q^{11} +(-0.669700 - 3.04580i) q^{12} +(-0.275521 + 0.665167i) q^{13} +(-2.62102 + 0.823906i) q^{14} +(3.46201 - 0.413821i) q^{15} +(-1.38111 + 3.75400i) q^{16} -5.52634 q^{17} +(0.767183 - 0.241161i) q^{18} +(-1.19548 - 0.495182i) q^{19} +(-4.02693 - 1.94522i) q^{20} +(1.15926 + 2.79870i) q^{21} +(-1.39247 - 0.123042i) q^{22} +(-2.90780 + 2.90780i) q^{23} +(4.25704 + 1.15255i) q^{24} +(2.60261 - 4.26924i) q^{25} +(-0.653806 - 0.780549i) q^{26} +(-2.12945 - 5.14095i) q^{27} +(0.681342 - 3.82529i) q^{28} +(-1.57338 + 3.79846i) q^{29} +(-1.74562 + 4.61154i) q^{30} +10.1211 q^{31} +(-3.80360 - 4.18720i) q^{32} +1.54129i q^{33} +(3.61477 - 6.92923i) q^{34} +(4.18238 + 1.17433i) q^{35} +(-0.199432 + 1.11968i) q^{36} +(-2.86828 - 6.92465i) q^{37} +(1.40285 - 1.17506i) q^{38} +(-0.793824 + 0.793824i) q^{39} +(5.07303 - 3.77682i) q^{40} +(-6.22154 - 6.22154i) q^{41} +(-4.26743 - 0.377080i) q^{42} +(-0.568391 + 0.235435i) q^{43} +(1.06509 - 1.66547i) q^{44} +(-1.22420 - 0.343731i) q^{45} +(-1.74398 - 5.54795i) q^{46} +5.99048 q^{47} +(-4.22965 + 4.58384i) q^{48} -3.22573i q^{49} +(3.65065 + 6.05580i) q^{50} +(-7.96116 - 3.29762i) q^{51} +(1.40635 - 0.309223i) q^{52} +(-2.78382 + 1.15310i) q^{53} +(7.83888 + 0.692660i) q^{54} +(1.73734 + 1.36635i) q^{55} +(4.35070 + 3.35642i) q^{56} +(-1.42670 - 1.42670i) q^{57} +(-3.73359 - 4.45736i) q^{58} +(-10.8796 + 4.50647i) q^{59} +(-4.64040 - 5.20516i) q^{60} +(-4.13274 + 9.97733i) q^{61} +(-6.62018 + 12.6904i) q^{62} -1.10475i q^{63} +(7.73807 - 2.03033i) q^{64} +(0.191075 + 1.59853i) q^{65} +(-1.93255 - 1.00815i) q^{66} +(2.14498 + 0.888479i) q^{67} +(6.32385 + 9.06480i) q^{68} +(-5.92404 + 2.45382i) q^{69} +(-4.20813 + 4.47598i) q^{70} +(5.00709 - 5.00709i) q^{71} +(-1.27347 - 0.982440i) q^{72} +(10.5719 - 10.5719i) q^{73} +(10.5587 + 0.932986i) q^{74} +(6.29678 - 4.59720i) q^{75} +(0.555753 + 2.52757i) q^{76} +(-0.734879 + 1.77415i) q^{77} +(-0.476102 - 1.51458i) q^{78} +11.4150i q^{79} +(1.41733 + 8.83126i) q^{80} -6.97068i q^{81} +(11.8704 - 3.73142i) q^{82} +(-4.21565 + 10.1775i) q^{83} +(3.26412 - 5.10410i) q^{84} +(-10.7747 + 6.05051i) q^{85} +(0.0765816 - 0.866678i) q^{86} +(-4.53316 + 4.53316i) q^{87} +(1.39159 + 2.42485i) q^{88} +(-4.84017 + 4.84017i) q^{89} +(1.23174 - 1.31014i) q^{90} +(-1.29225 + 0.535269i) q^{91} +(8.09706 + 1.44221i) q^{92} +(14.5803 + 6.03935i) q^{93} +(-3.91837 + 7.51121i) q^{94} +(-2.87296 + 0.343411i) q^{95} +(-2.98087 - 8.30166i) q^{96} +14.5940i q^{97} +(4.04460 + 2.10994i) q^{98} +(0.215102 - 0.519303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34}+ \cdots - 48 q^{99}+O(q^{100}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−0.654098	+	1.25386i	−0.462517	+	0.886610i
$2$	−0.654098	+	1.25386i	−0.462517	+	0.886610i
$3$	1.44059	+	0.596710i	0.831722	+	0.344511i	0.757584	−	0.652737i	$-0.226379\pi$
$3$	1.44059	+	0.596710i	0.831722	+	0.344511i	0.0741380	+	0.997248i	$0.476379\pi$
$4$	−1.14431	−	1.64029i	−0.572155	−	0.820145i
$5$	1.94969	−	1.09485i	0.871930	−	0.489631i
$5$	1.94969	−	1.09485i	0.871930	−	0.489631i
$6$	−1.69047	+	1.41598i	−0.690133	+	0.578071i
$7$	1.37373	+	1.37373i	0.519222	+	0.519222i	0.917336	−	0.398114i	$-0.130335\pi$
$7$	1.37373	+	1.37373i	0.519222	+	0.519222i	−0.398114	+	0.917336i	$0.630335\pi$
$8$	2.80518	−	0.361890i	0.991781	−	0.127948i
$9$	−0.402097	−	0.402097i	−0.134032	−	0.134032i
$10$	0.0974914	+	3.16077i	0.0308295	+	0.999525i
$11$	0.378268	+	0.913219i	0.114052	+	0.275346i	0.970590	−	0.240738i	$-0.0773894\pi$
$11$	0.378268	+	0.913219i	0.114052	+	0.275346i	−0.856538	+	0.516084i	$0.827389\pi$
$12$	−0.669700	−	3.04580i	−0.193326	−	0.879247i
$13$	−0.275521	+	0.665167i	−0.0764159	+	0.184484i	−0.957471	−	0.288529i	$-0.906834\pi$
$13$	−0.275521	+	0.665167i	−0.0764159	+	0.184484i	0.881055	+	0.473013i	$0.156834\pi$
$14$	−2.62102	+	0.823906i	−0.700496	+	0.220198i
$15$	3.46201	−	0.413821i	0.893886	−	0.106848i
$16$	−1.38111	+	3.75400i	−0.345276	+	0.938501i
$17$	−5.52634			−1.34033			−0.670167	−	0.742210i	$-0.733778\pi$
$17$	−5.52634			−1.34033			−0.670167	+	0.742210i	$0.733778\pi$
$18$	0.767183	−	0.241161i	0.180827	−	0.0568422i
$19$	−1.19548	−	0.495182i	−0.274261	−	0.113603i	0.241314	−	0.970447i	$-0.422422\pi$
$19$	−1.19548	−	0.495182i	−0.274261	−	0.113603i	−0.515575	+	0.856845i	$0.672422\pi$
$20$	−4.02693	−	1.94522i	−0.900448	−	0.434964i
$21$	1.15926	+	2.79870i	0.252971	+	0.610725i
$22$	−1.39247	−	0.123042i	−0.296875	−	0.0262326i
$23$	−2.90780	+	2.90780i	−0.606318	+	0.606318i	−0.941982	−	0.335664i	$-0.891039\pi$
$23$	−2.90780	+	2.90780i	−0.606318	+	0.606318i	0.335664	+	0.941982i	$0.391039\pi$
$24$	4.25704	+	1.15255i	0.868966	+	0.235262i
$25$	2.60261	−	4.26924i	0.520523	−	0.853848i
$26$	−0.653806	−	0.780549i	−0.128222	−	0.153078i
$27$	−2.12945	−	5.14095i	−0.409813	−	0.989376i
$28$	0.681342	−	3.82529i	0.128762	−	0.722912i
$29$	−1.57338	+	3.79846i	−0.292168	+	0.705357i	−0.999999	−	0.00102470i	$-0.999674\pi$
$29$	−1.57338	+	3.79846i	−0.292168	+	0.705357i	0.707831	+	0.706382i	$0.249674\pi$
$30$	−1.74562	+	4.61154i	−0.318705	+	0.841948i
$31$	10.1211			1.81780			0.908899	−	0.417016i	$-0.136924\pi$
$31$	10.1211			1.81780			0.908899	+	0.417016i	$0.136924\pi$
$32$	−3.80360	−	4.18720i	−0.672388	−	0.740199i
$33$			1.54129i			0.268303i
$34$	3.61477	−	6.92923i	0.619928	−	1.18835i
$35$	4.18238	+	1.17433i	0.706952	+	0.198498i
$36$	−0.199432	+	1.11968i	−0.0332387	+	0.186613i
$37$	−2.86828	−	6.92465i	−0.471543	−	1.13841i	−0.963481	−	0.267775i	$-0.913711\pi$
$37$	−2.86828	−	6.92465i	−0.471543	−	1.13841i	0.491938	−	0.870630i	$-0.336289\pi$
$38$	1.40285	−	1.17506i	0.227572	−	0.190619i
$39$	−0.793824	+	0.793824i	−0.127114	+	0.127114i
$40$	5.07303	−	3.77682i	0.802116	−	0.597168i
$41$	−6.22154	−	6.22154i	−0.971642	−	0.971642i	0.0279672	−	0.999609i	$-0.491097\pi$
$41$	−6.22154	−	6.22154i	−0.971642	−	0.971642i	−0.999609	+	0.0279672i	$0.991097\pi$
$42$	−4.26743	−	0.377080i	−0.658479	−	0.0581846i
$43$	−0.568391	+	0.235435i	−0.0866788	+	0.0359035i	−0.425602	−	0.904911i	$-0.639937\pi$
$43$	−0.568391	+	0.235435i	−0.0866788	+	0.0359035i	0.338923	+	0.940814i	$0.389937\pi$
$44$	1.06509	−	1.66547i	0.160568	−	0.251080i
$45$	−1.22420	−	0.343731i	−0.182493	−	0.0512404i
$46$	−1.74398	−	5.54795i	−0.257135	−	0.818000i
$47$	5.99048			0.873802			0.436901	−	0.899510i	$-0.356076\pi$
$47$	5.99048			0.873802			0.436901	+	0.899510i	$0.356076\pi$
$48$	−4.22965	+	4.58384i	−0.610498	+	0.661621i
$49$		−	3.22573i		−	0.460818i
$50$	3.65065	+	6.05580i	0.516280	+	0.856420i
$51$	−7.96116	−	3.29762i	−1.11479	−	0.461759i
$52$	1.40635	−	0.309223i	0.195026	−	0.0428815i
$53$	−2.78382	+	1.15310i	−0.382387	+	0.158390i	−0.565593	−	0.824685i	$-0.691353\pi$
$53$	−2.78382	+	1.15310i	−0.382387	+	0.158390i	0.183205	+	0.983075i	$0.441353\pi$
$54$	7.83888	+	0.692660i	1.06674	+	0.0942591i
$55$	1.73734	+	1.36635i	0.234263	+	0.184239i
$56$	4.35070	+	3.35642i	0.581387	+	0.448521i
$57$	−1.42670	−	1.42670i	−0.188972	−	0.188972i
$58$	−3.73359	−	4.45736i	−0.490244	−	0.585279i
$59$	−10.8796	+	4.50647i	−1.41640	+	0.586692i	−0.953953	−	0.299955i	$-0.903028\pi$
$59$	−10.8796	+	4.50647i	−1.41640	+	0.586692i	−0.462447	+	0.886647i	$0.653028\pi$
$60$	−4.64040	−	5.20516i	−0.599073	−	0.671983i
$61$	−4.13274	+	9.97733i	−0.529144	+	1.27747i	0.402941	+	0.915226i	$0.367988\pi$
$61$	−4.13274	+	9.97733i	−0.529144	+	1.27747i	−0.932085	+	0.362240i	$0.882012\pi$
$62$	−6.62018	+	12.6904i	−0.840763	+	1.61168i
$63$		−	1.10475i		−	0.139185i
$64$	7.73807	−	2.03033i	0.967259	−	0.253792i
$65$	0.191075	+	1.59853i	0.0237000	+	0.198273i
$66$	−1.93255	−	1.00815i	−0.237880	−	0.124095i
$67$	2.14498	+	0.888479i	0.262051	+	0.108545i	0.509841	−	0.860269i	$-0.329704\pi$
$67$	2.14498	+	0.888479i	0.262051	+	0.108545i	−0.247790	+	0.968814i	$0.579704\pi$
$68$	6.32385	+	9.06480i	0.766879	+	1.09927i
$69$	−5.92404	+	2.45382i	−0.713171	+	0.295405i
$70$	−4.20813	+	4.47598i	−0.502967	+	0.534982i
$71$	5.00709	−	5.00709i	0.594232	−	0.594232i	−0.344539	−	0.938772i	$-0.611965\pi$
$71$	5.00709	−	5.00709i	0.594232	−	0.594232i	0.938772	+	0.344539i	$0.111965\pi$
$72$	−1.27347	−	0.982440i	−0.150080	−	0.115782i
$73$	10.5719	−	10.5719i	1.23735	−	1.23735i	0.276272	−	0.961080i	$-0.410901\pi$
$73$	10.5719	−	10.5719i	1.23735	−	1.23735i	0.961080	−	0.276272i	$-0.0890990\pi$
$74$	10.5587	+	0.932986i	1.22742	+	0.108457i
$75$	6.29678	−	4.59720i	0.727090	−	0.530839i
$76$	0.555753	+	2.52757i	0.0637492	+	0.289932i
$77$	−0.734879	+	1.77415i	−0.0837472	+	0.202184i
$78$	−0.476102	−	1.51458i	−0.0539080	−	0.171492i
$79$			11.4150i			1.28429i	0.766583	+	0.642146i	$0.221956\pi$
$79$			11.4150i			1.28429i	−0.766583	+	0.642146i	$0.778044\pi$
$80$	1.41733	+	8.83126i	0.158463	+	0.987365i
$81$		−	6.97068i		−	0.774520i
$82$	11.8704	−	3.73142i	1.31087	−	0.412066i
$83$	−4.21565	+	10.1775i	−0.462728	+	1.11712i	0.504545	+	0.863385i	$0.331660\pi$
$83$	−4.21565	+	10.1775i	−0.462728	+	1.11712i	−0.967273	+	0.253739i	$0.918340\pi$
$84$	3.26412	−	5.10410i	0.356145	−	0.556903i
$85$	−10.7747	+	6.05051i	−1.16868	+	0.656269i
$86$	0.0765816	−	0.866678i	0.00825801	−	0.0934563i
$87$	−4.53316	+	4.53316i	−0.486006	+	0.486006i
$88$	1.39159	+	2.42485i	0.148344	+	0.258490i
$89$	−4.84017	+	4.84017i	−0.513057	+	0.513057i	−0.915462	−	0.402405i	$-0.868174\pi$
$89$	−4.84017	+	4.84017i	−0.513057	+	0.513057i	0.402405	+	0.915462i	$0.368174\pi$
$90$	1.23174	−	1.31014i	0.129837	−	0.138101i
$91$	−1.29225	+	0.535269i	−0.135465	+	0.0561114i
$92$	8.09706	+	1.44221i	0.844177	+	0.150361i
$93$	14.5803	+	6.03935i	1.51190	+	0.626251i
$94$	−3.91837	+	7.51121i	−0.404149	+	0.774722i
$95$	−2.87296	+	0.343411i	−0.294759	+	0.0352332i
$96$	−2.98087	−	8.30166i	−0.304234	−	0.847285i
$97$			14.5940i			1.48179i	0.671620	+	0.740896i	$0.265599\pi$
$97$			14.5940i			1.48179i	−0.671620	+	0.740896i	$0.734401\pi$
$98$	4.04460	+	2.10994i	0.408566	+	0.213136i
$99$	0.215102	−	0.519303i	0.0216186	−	0.0521919i
$100$	−9.98099	+	0.616297i	−0.998099	+	0.0616297i
$101$	3.61198	−	1.49613i	0.359406	−	0.148871i	−0.195672	−	0.980669i	$-0.562689\pi$
$101$	3.61198	−	1.49613i	0.359406	−	0.148871i	0.555077	+	0.831799i	$0.312689\pi$
$102$	9.34213	−	7.82518i	0.925008	−	0.774809i
$103$	−12.5941	−	12.5941i	−1.24093	−	1.24093i	−0.959616	−	0.281314i	$-0.909230\pi$
$103$	−12.5941	−	12.5941i	−1.24093	−	1.24093i	−0.281314	−	0.959616i	$-0.590770\pi$
$104$	−0.532169	+	1.96562i	−0.0521835	+	0.192745i
$105$	5.32435	+	4.18739i	0.519603	+	0.408647i
$106$	0.375076	−	4.24475i	0.0364306	−	0.412287i
$107$	−5.04046	+	2.08783i	−0.487280	+	0.201838i	−0.612777	−	0.790256i	$-0.709948\pi$
$107$	−5.04046	+	2.08783i	−0.487280	+	0.201838i	0.125497	+	0.992094i	$0.459948\pi$
$108$	−5.99589	+	9.37576i	−0.576955	+	0.902183i
$109$	3.49388	+	1.44721i	0.334653	+	0.138618i	0.543681	−	0.839292i	$-0.317030\pi$
$109$	3.49388	+	1.44721i	0.334653	+	0.138618i	−0.209028	+	0.977910i	$0.567030\pi$
$110$	−2.84960	+	1.28465i	−0.271699	+	0.122487i
$111$		−	11.6871i		−	1.10929i
$112$	−7.05426	+	3.25973i	−0.666565	+	0.308015i
$113$	11.4644			1.07848			0.539242	−	0.842151i	$-0.318711\pi$
$113$	11.4644			1.07848			0.539242	+	0.842151i	$0.318711\pi$
$114$	2.72209	−	0.855677i	0.254947	−	0.0801415i
$115$	−2.48572	+	8.85292i	−0.231794	+	0.825539i
$116$	8.03102	−	1.76583i	0.745661	−	0.163953i
$117$	0.378248	−	0.156676i	0.0349691	−	0.0144847i
$118$	1.46585	−	16.5891i	0.134942	−	1.52715i
$119$	−7.59170	−	7.59170i	−0.695930	−	0.695930i
$120$	9.56180	−	2.41371i	0.872869	−	0.220341i
$121$	7.08729	−	7.08729i	0.644299	−	0.644299i
$122$	−9.80691	−	11.7080i	−0.887876	−	1.05999i
$123$	−5.25021	−	12.6751i	−0.473395	−	1.14288i
$124$	−11.5817	−	16.6015i	−1.04006	−	1.49086i
$125$	0.400127	−	11.1732i	0.0357884	−	0.999359i
$126$	1.38519	+	0.722613i	0.123403	+	0.0643755i
$127$		−	5.65269i		−	0.501595i	−0.968040	−	0.250798i	$-0.919307\pi$
$127$		−	5.65269i		−	0.501595i	0.968040	−	0.250798i	$-0.0806929\pi$
$128$	−2.51571	+	11.0305i	−0.222360	+	0.974965i
$129$	−0.959302			−0.0844619
$130$	−2.12930	−	0.806013i	−0.186752	−	0.0706920i
$131$	−2.63661	+	6.36535i	−0.230362	+	0.556143i	−0.996220	−	0.0868668i	$-0.972315\pi$
$131$	−2.63661	+	6.36535i	−0.230362	+	0.556143i	0.765858	+	0.643010i	$0.222315\pi$
$132$	2.52816	−	1.76371i	0.220048	−	0.153511i
$133$	−0.962014	−	2.32251i	−0.0834172	−	0.201387i
$134$	−2.51705	+	2.10834i	−0.217440	+	0.182133i
$135$	−9.78033	−	7.69185i	−0.841757	−	0.662009i
$136$	−15.5024	+	1.99993i	−1.32932	+	0.171492i
$137$	6.57530	−	6.57530i	0.561765	−	0.561765i	−0.368043	−	0.929809i	$-0.619972\pi$
$137$	6.57530	−	6.57530i	0.561765	−	0.561765i	0.929809	+	0.368043i	$0.119972\pi$
$138$	0.798170	−	9.03294i	0.0679448	−	0.768935i
$139$	−1.18195	−	2.85348i	−0.100252	−	0.242029i	0.865794	−	0.500401i	$-0.166814\pi$
$139$	−1.18195	−	2.85348i	−0.100252	−	0.242029i	−0.966046	+	0.258372i	$0.916814\pi$
$140$	−2.85971	−	8.20412i	−0.241689	−	0.693374i
$141$	8.62980	+	3.57458i	0.726761	+	0.301034i
$142$	3.00304	+	9.55330i	0.252010	+	0.801695i
$143$	−0.711664			−0.0595123
$144$	2.06481	−	0.954136i	0.172068	−	0.0795113i
$145$	1.09114	+	9.12845i	0.0906145	+	0.758077i
$146$	6.34060	+	20.1708i	0.524752	+	1.66934i
$147$	1.92482	−	4.64693i	0.158757	−	0.383273i
$148$	−8.07623	+	12.6288i	−0.663862	+	1.03808i
$149$	−3.33033	−	8.04013i	−0.272831	−	0.658673i	0.726771	−	0.686880i	$-0.241020\pi$
$149$	−3.33033	−	8.04013i	−0.272831	−	0.658673i	−0.999602	+	0.0282070i	$0.991020\pi$
$150$	1.64551	+	10.9023i	0.134355	+	0.890168i
$151$	12.4035	+	12.4035i	1.00938	+	1.00938i	0.999956	+	0.00942371i	$0.00299971\pi$
$151$	12.4035	+	12.4035i	1.00938	+	1.00938i	0.00942371	+	0.999956i	$0.497000\pi$
$152$	−3.53272	−	0.956444i	−0.286542	−	0.0775779i
$153$	2.22213	+	2.22213i	0.179648	+	0.179648i
$154$	−1.74385	−	2.08190i	−0.140524	−	0.167765i
$155$	19.7330	−	11.0810i	1.58499	−	0.890051i
$156$	2.21048	+	0.393720i	0.176980	+	0.0315229i
$157$	20.3501	+	8.42931i	1.62412	+	0.672732i	0.994555	−	0.104217i	$-0.0332336\pi$
$157$	20.3501	+	8.42931i	1.62412	+	0.672732i	0.629564	+	0.776949i	$0.283234\pi$
$158$	−14.3128	−	7.46655i	−1.13867	−	0.594007i
$159$	−4.69840			−0.372607
$160$	−12.0002	−	3.99938i	−0.948700	−	0.316179i
$161$	−7.98907			−0.629627
$162$	8.74023	+	4.55951i	0.686698	+	0.358229i
$163$	−11.1090	−	4.60152i	−0.870128	−	0.360419i	−0.0974676	−	0.995239i	$-0.531074\pi$
$163$	−11.1090	−	4.60152i	−0.870128	−	0.360419i	−0.772660	+	0.634820i	$0.781074\pi$
$164$	−3.08576	+	17.3245i	−0.240957	+	1.35282i
$165$	1.68747	+	3.00503i	0.131370	+	0.233942i
$166$	−10.0037	−	11.9429i	−0.776434	−	0.926948i
$167$	12.2387	+	12.2387i	0.947057	+	0.947057i	0.998667	−	0.0516101i	$-0.0164353\pi$
$167$	12.2387	+	12.2387i	0.947057	+	0.947057i	−0.0516101	+	0.998667i	$0.516435\pi$
$168$	4.26475	+	7.43132i	0.329032	+	0.573339i
$169$	8.82585	+	8.82585i	0.678912	+	0.678912i
$170$	−0.538771	−	17.4675i	−0.0413218	−	1.33970i
$171$	0.281586	+	0.679808i	0.0215334	+	0.0519862i
$172$	1.03660	+	0.662915i	0.0790399	+	0.0505468i
$173$	4.84722	−	11.7022i	0.368527	−	0.889703i	−0.625465	−	0.780252i	$-0.715091\pi$
$173$	4.84722	−	11.7022i	0.368527	−	0.889703i	0.993992	−	0.109451i	$-0.0349092\pi$
$174$	−2.71880	−	8.64907i	−0.206112	−	0.655684i
$175$	9.44008	−	2.28950i	0.713603	−	0.173070i
$176$	−3.95065	+	0.158767i	−0.297792	+	0.0119675i
$177$	−18.3620			−1.38017
$178$	−2.90293	−	9.23482i	−0.217584	−	0.692179i
$179$	15.1421	+	6.27205i	1.13177	+	0.468795i	0.868383	−	0.495895i	$-0.165160\pi$
$179$	15.1421	+	6.27205i	1.13177	+	0.468795i	0.263389	+	0.964690i	$0.415160\pi$
$180$	0.837049	+	2.40138i	0.0623900	+	0.178988i
$181$	4.45192	+	10.7479i	0.330909	+	0.798884i	0.998521	+	0.0543749i	$0.0173166\pi$
$181$	4.45192	+	10.7479i	0.330909	+	0.798884i	−0.667612	+	0.744510i	$0.732683\pi$
$182$	0.174110	−	1.97042i	0.0129059	−	0.146057i
$183$	−11.9071	+	11.9071i	−0.880201	+	0.880201i
$184$	−7.10459	+	9.20920i	−0.523758	+	0.678911i
$185$	−13.1737	−	10.3606i	−0.968551	−	0.761727i
$186$	−17.1094	+	14.3312i	−1.25452	+	1.05082i
$187$	−2.09043	−	5.04676i	−0.152868	−	0.369055i
$188$	−6.85498	−	9.82613i	−0.499951	−	0.716645i
$189$	4.13699	−	9.98757i	0.300921	−	0.726489i
$190$	1.44861	−	3.82690i	0.105093	−	0.277633i
$191$	−5.61545			−0.406320			−0.203160	−	0.979146i	$-0.565121\pi$
$191$	−5.61545			−0.406320			−0.203160	+	0.979146i	$0.565121\pi$
$192$	12.3589	+	1.69251i	0.891925	+	0.122147i
$193$			11.7323i			0.844509i	0.906477	+	0.422255i	$0.138761\pi$
$193$			11.7323i			0.844509i	−0.906477	+	0.422255i	$0.861239\pi$
$194$	−18.2987	−	9.54589i	−1.31377	−	0.685355i
$195$	−0.678597	+	2.41683i	−0.0485953	+	0.173073i
$196$	−5.29113	+	3.69123i	−0.377938	+	0.263660i
$197$	−5.01964	−	12.1185i	−0.357634	−	0.863405i	−0.995632	−	0.0933670i	$-0.970237\pi$
$197$	−5.01964	−	12.1185i	−0.357634	−	0.863405i	0.637998	−	0.770038i	$-0.279763\pi$
$198$	0.510433	+	0.609382i	0.0362749	+	0.0433069i
$199$	6.03200	−	6.03200i	0.427597	−	0.427597i	−0.460212	−	0.887809i	$-0.652227\pi$
$199$	6.03200	−	6.03200i	0.427597	−	0.427597i	0.887809	+	0.460212i	$0.152227\pi$
$200$	5.75580	−	12.9178i	0.406997	−	0.913430i
$201$	2.55986	+	2.55986i	0.180559	+	0.180559i
$202$	−0.486657	+	5.50752i	−0.0342411	+	0.387508i
$203$	−7.37946	+	3.05667i	−0.517937	+	0.214536i
$204$	3.70099	+	16.8321i	0.259121	+	1.17848i
$205$	−18.9418	−	5.31846i	−1.32295	−	0.371457i
$206$	24.0289	−	7.55339i	1.67417	−	0.526269i
$207$	2.33843			0.162532
$208$	−2.11652	−	1.95297i	−0.146754	−	0.135414i
$209$		−	1.27904i		−	0.0884731i
$210$	−8.73303	+	3.93700i	−0.602636	+	0.271679i
$211$	−5.32066	−	2.20389i	−0.366289	−	0.151722i	0.191944	−	0.981406i	$-0.438521\pi$
$211$	−5.32066	−	2.20389i	−0.366289	−	0.151722i	−0.558234	+	0.829684i	$0.688521\pi$
$212$	5.07697	+	3.24678i	0.348688	+	0.222989i
$213$	10.2009	−	4.22536i	0.698956	−	0.289517i
$214$	0.679122	−	7.68566i	0.0464238	−	0.525381i
$215$	−0.850422	+	1.08133i	−0.0579983	+	0.0737460i
$216$	−7.83395	−	13.6507i	−0.533033	−	0.928809i
$217$	13.9036	+	13.9036i	0.943840	+	0.943840i
$218$	−4.09993	+	3.43420i	−0.277682	+	0.232593i
$219$	21.5382	−	8.92139i	1.45541	−	0.602852i
$220$	0.253153	−	4.41328i	0.0170676	−	0.297543i
$221$	1.52262	−	3.67594i	0.102423	−	0.247270i
$222$	14.6539	+	7.64450i	0.983507	+	0.513065i
$223$			4.15640i			0.278333i	0.990269	+	0.139167i	$0.0444424\pi$
$223$			4.15640i			0.278333i	−0.990269	+	0.139167i	$0.955558\pi$
$224$	0.526952	−	10.9772i	0.0352085	−	0.733446i
$225$	−2.76315	+	0.670146i	−0.184210	+	0.0446764i
$226$	−7.49887	+	14.3748i	−0.498817	+	0.956194i
$227$	17.9728	+	7.44459i	1.19290	+	0.494115i	0.888698	−	0.458493i	$-0.151611\pi$
$227$	17.9728	+	7.44459i	1.19290	+	0.494115i	0.304200	+	0.952608i	$0.401611\pi$
$228$	−0.707616	+	3.97280i	−0.0468630	+	0.263105i
$229$	−5.93964	+	2.46028i	−0.392502	+	0.162580i	−0.570201	−	0.821505i	$-0.693135\pi$
$229$	−5.93964	+	2.46028i	−0.392502	+	0.162580i	0.177699	+	0.984085i	$0.443135\pi$
$230$	−9.47438	−	8.90741i	−0.624722	−	0.587337i
$231$	−2.11731	+	2.11731i	−0.139309	+	0.139309i
$232$	−3.03897	+	11.2248i	−0.199518	+	0.736942i
$233$	−7.86399	+	7.86399i	−0.515187	+	0.515187i	−0.916111	−	0.400924i	$-0.868689\pi$
$233$	−7.86399	+	7.86399i	−0.515187	+	0.515187i	0.400924	+	0.916111i	$0.368689\pi$
$234$	−0.0509629	+	0.576750i	−0.00333155	+	0.0377033i
$235$	11.6796	−	6.55867i	0.761894	−	0.427841i
$236$	19.8415	+	12.6889i	1.29157	+	0.825975i
$237$	−6.81146	+	16.4443i	−0.442452	+	1.06817i
$238$	14.4846	−	4.55318i	0.938899	−	0.295139i
$239$			2.44629i			0.158237i	0.996865	+	0.0791185i	$0.0252106\pi$
$239$			2.44629i			0.158237i	−0.996865	+	0.0791185i	$0.974789\pi$
$240$	−3.22791	+	13.5679i	−0.208361	+	0.875806i
$241$		−	7.75381i		−	0.499467i	−0.968315	−	0.249733i	$-0.919657\pi$
$241$		−	7.75381i		−	0.499467i	0.968315	−	0.249733i	$-0.0803430\pi$
$242$	4.25066	+	13.5222i	0.273243	+	0.869242i
$243$	−2.22887	+	5.38098i	−0.142982	+	0.345190i
$244$	21.0949	−	4.63826i	1.35046	−	0.296934i
$245$	−3.53168	−	6.28918i	−0.225631	−	0.401801i
$246$	19.3269	+	1.70777i	1.23224	+	0.108883i
$247$	0.658758	−	0.658758i	0.0419158	−	0.0419158i
$248$	28.3914	−	3.66272i	1.80286	−	0.232583i
$249$	−12.1460	+	12.1460i	−0.769722	+	0.769722i
$250$	13.7478	+	7.81006i	0.869490	+	0.493951i
$251$	−19.4308	+	8.04851i	−1.22646	+	0.508017i	−0.899459	−	0.437006i	$-0.856039\pi$
$251$	−19.4308	+	8.04851i	−1.22646	+	0.508017i	−0.327004	+	0.945023i	$0.606039\pi$
$252$	−1.81211	+	1.26417i	−0.114152	+	0.0796354i
$253$	−3.75538	−	1.55553i	−0.236099	−	0.0977953i
$254$	7.08766	+	3.69742i	0.444720	+	0.231997i
$255$	−19.1322	+	2.28692i	−1.19811	+	0.143212i
$256$	−12.1851	−	10.3693i	−0.761569	−	0.648084i
$257$		−	19.0271i		−	1.18688i	−0.804878	−	0.593440i	$-0.797769\pi$
$257$		−	19.0271i		−	1.18688i	0.804878	−	0.593440i	$-0.202231\pi$
$258$	0.627478	−	1.20283i	0.0390651	−	0.0748847i
$259$	5.57236	−	13.4529i	0.346249	−	0.835920i
$260$	2.40340	−	2.14263i	0.149052	−	0.132880i
$261$	2.16000	−	0.894702i	0.133701	−	0.0553807i
$262$	−6.25663	−	7.46950i	−0.386536	−	0.461467i
$263$	5.06770	+	5.06770i	0.312488	+	0.312488i	0.845873	−	0.533385i	$-0.179080\pi$
$263$	5.06770	+	5.06770i	0.312488	+	0.312488i	−0.533385	+	0.845873i	$0.679080\pi$
$264$	0.557776	+	4.32358i	0.0343287	+	0.266098i
$265$	−4.16513	+	5.29605i	−0.255862	+	0.325334i
$266$	3.54134	+	0.312921i	0.217134	+	0.0191864i
$267$	−9.86085	+	4.08450i	−0.603474	+	0.249967i
$268$	−0.997158	−	4.53508i	−0.0609111	−	0.277024i
$269$	6.09262	+	2.52364i	0.371473	+	0.153869i	0.560607	−	0.828082i	$-0.310568\pi$
$269$	6.09262	+	2.52364i	0.371473	+	0.153869i	−0.189134	+	0.981951i	$0.560568\pi$
$270$	16.0418	−	7.23191i	0.976271	−	0.440120i
$271$			5.87746i			0.357030i	0.983937	+	0.178515i	$0.0571293\pi$
$271$			5.87746i			0.357030i	−0.983937	+	0.178515i	$0.942871\pi$
$272$	7.63246	−	20.7459i	0.462786	−	1.25790i
$273$	−2.18100			−0.132000
$274$	3.94359	+	12.5454i	0.238241	+	0.757893i
$275$	4.88323	+	0.761840i	0.294470	+	0.0459407i
$276$	10.8039	+	6.90922i	0.650320	+	0.415886i
$277$	4.94092	−	2.04659i	0.296871	−	0.122968i	−0.229277	−	0.973361i	$-0.573636\pi$
$277$	4.94092	−	2.04659i	0.296871	−	0.122968i	0.526147	+	0.850393i	$0.323636\pi$
$278$	4.35097	+	0.384461i	0.260954	+	0.0230584i
$279$	−4.06965	−	4.06965i	−0.243644	−	0.243644i
$280$	12.1573	+	1.78064i	0.726538	+	0.106413i
$281$	0.624853	−	0.624853i	0.0372756	−	0.0372756i	−0.688223	−	0.725499i	$-0.741609\pi$
$281$	0.624853	−	0.624853i	0.0372756	−	0.0372756i	0.725499	+	0.688223i	$0.241609\pi$
$282$	−10.1268	+	8.48241i	−0.603039	+	0.505120i
$283$	0.215731	+	0.520821i	0.0128239	+	0.0309596i	0.930162	−	0.367150i	$-0.119666\pi$
$283$	0.215731	+	0.520821i	0.0128239	+	0.0309596i	−0.917338	+	0.398110i	$0.869666\pi$
$284$	−13.9428	−	2.48341i	−0.827350	−	0.147364i
$285$	−4.34366	−	1.21961i	−0.257296	−	0.0722435i
$286$	0.465498	−	0.892324i	0.0275255	−	0.0527642i
$287$		−	17.0935i		−	1.00899i
$288$	−0.154241	+	3.21308i	−0.00908875	+	0.189332i
$289$	13.5404			0.796495
$290$	−12.1595	−	4.60277i	−0.714029	−	0.270284i
$291$	−8.70836	+	21.0238i	−0.510493	+	1.23244i
$292$	−29.4386	−	5.24346i	−1.72277	−	0.306850i
$293$	3.41872	+	8.25352i	0.199724	+	0.482176i	0.991731	−	0.128336i	$-0.0409636\pi$
$293$	3.41872	+	8.25352i	0.199724	+	0.482176i	−0.792007	+	0.610512i	$0.790964\pi$
$294$	4.56756	+	5.45300i	0.266386	+	0.318026i
$295$	−16.2779	+	20.6977i	−0.947738	+	1.20507i
$296$	−10.5520	−	18.3869i	−0.613323	−	1.06872i
$297$	3.88931	−	3.88931i	0.225680	−	0.225680i
$298$	12.2595	+	1.08328i	0.710175	+	0.0627527i
$299$	−1.13301	−	2.73533i	−0.0655238	−	0.158188i
$300$	−14.7462	−	5.06793i	−0.851373	−	0.292597i
$301$	−1.10424	−	0.457392i	−0.0636474	−	0.0263636i
$302$	−23.6652	+	7.43907i	−1.36178	+	0.428071i
$303$	6.09613			0.350213
$304$	3.50999	−	3.80392i	0.201312	−	0.218170i
$305$	2.86608	+	23.9775i	0.164111	+	1.37295i
$306$	−4.23971	+	1.33274i	−0.242368	+	0.0761875i
$307$	6.86308	−	16.5689i	0.391697	−	0.945639i	−0.597874	−	0.801590i	$-0.703988\pi$
$307$	6.86308	−	16.5689i	0.391697	−	0.945639i	0.989571	−	0.144049i	$-0.0460123\pi$
$308$	3.75106	−	0.824770i	0.213736	−	0.0469956i
$309$	−10.6278	−	25.6578i	−0.604595	−	1.45962i
$310$	0.986718	+	31.9904i	0.0560418	+	1.81693i
$311$	−18.8663	−	18.8663i	−1.06981	−	1.06981i	−0.997373	−	0.0724385i	$-0.976922\pi$
$311$	−18.8663	−	18.8663i	−1.06981	−	1.06981i	−0.0724385	−	0.997373i	$-0.523078\pi$
$312$	−1.93954	+	2.51410i	−0.109805	+	0.142333i
$313$	−8.81659	−	8.81659i	−0.498343	−	0.498343i	0.412579	−	0.910922i	$-0.364628\pi$
$313$	−8.81659	−	8.81659i	−0.498343	−	0.498343i	−0.910922	+	0.412579i	$0.864628\pi$
$314$	−23.8801	+	20.0026i	−1.34763	+	1.12881i
$315$	−1.20953	−	2.15392i	−0.0681493	−	0.121360i
$316$	18.7240	−	13.0623i	1.05331	−	0.734814i
$317$	−24.1479	−	10.0024i	−1.35628	−	0.561789i	−0.418245	−	0.908334i	$-0.637355\pi$
$317$	−24.1479	−	10.0024i	−1.35628	−	0.561789i	−0.938033	+	0.346545i	$0.887355\pi$
$318$	3.07321	−	5.89112i	0.172337	−	0.330357i
$319$	−4.06399			−0.227539
$320$	12.8640	−	12.4305i	0.719117	−	0.694889i
$321$	−8.50704			−0.474817
$322$	5.22563	−	10.0171i	0.291213	−	0.558233i
$323$	6.60660	+	2.73654i	0.367601	+	0.152265i
$324$	−11.4339	+	7.97663i	−0.635219	+	0.443146i
$325$	2.12268	+	2.90744i	0.117745	+	0.161276i
$326$	13.0360	−	10.9193i	0.722000	−	0.604764i
$327$	4.16966	+	4.16966i	0.230583	+	0.230583i
$328$	−19.7041	−	15.2010i	−1.08797	−	0.839337i
$329$	8.22931	+	8.22931i	0.453697	+	0.453697i
$330$	−4.87166	+	0.150262i	−0.268176	+	0.00827166i
$331$	0.351197	+	0.847864i	0.0193035	+	0.0466028i	0.933237	−	0.359260i	$-0.116971\pi$
$331$	0.351197	+	0.847864i	0.0193035	+	0.0466028i	−0.913934	+	0.405863i	$0.866971\pi$
$332$	21.5180	−	4.73131i	1.18096	−	0.259664i
$333$	−1.63105	+	3.93771i	−0.0893812	+	0.215785i
$334$	−23.3508	+	7.34024i	−1.27770	+	0.401640i
$335$	5.15480	−	0.616164i	0.281637	−	0.0336647i
$336$	−12.1074	+	0.486565i	−0.660511	+	0.0265443i
$337$	−18.1579			−0.989122			−0.494561	−	0.869143i	$-0.664671\pi$
$337$	−18.1579			−0.989122			−0.494561	+	0.869143i	$0.664671\pi$
$338$	−16.8393	+	5.29338i	−0.915939	+	0.287922i
$339$	16.5155	+	6.84094i	0.896999	+	0.371549i
$340$	22.2542	+	10.7499i	1.20690	+	0.582997i
$341$	3.82847	+	9.24275i	0.207323	+	0.500523i
$342$	−1.03657	−	0.0915933i	−0.0560511	−	0.00495280i
$343$	14.0474	−	14.0474i	0.758488	−	0.758488i
$344$	−1.50924	+	0.866133i	−0.0813726	+	0.0466988i
$345$	−8.86351	+	11.2701i	−0.477195	+	0.606763i
$346$	11.5023	+	13.7321i	0.618370	+	0.738243i
$347$	12.3815	+	29.8916i	0.664673	+	1.60466i	0.790395	+	0.612597i	$0.209875\pi$
$347$	12.3815	+	29.8916i	0.664673	+	1.60466i	−0.125722	+	0.992065i	$0.540125\pi$
$348$	12.6231	+	2.24836i	0.676667	+	0.120525i
$349$	3.86987	−	9.34270i	0.207150	−	0.500103i	−0.785823	−	0.618452i	$-0.787760\pi$
$349$	3.86987	−	9.34270i	0.207150	−	0.500103i	0.992972	+	0.118349i	$0.0377601\pi$
$350$	−3.30404	+	13.3341i	−0.176608	+	0.712735i
$351$	4.00630			0.213840
$352$	2.38504	−	5.05740i	0.127123	−	0.269560i
$353$		−	20.2353i		−	1.07701i	−0.842621	−	0.538507i	$-0.818989\pi$
$353$		−	20.2353i		−	1.07701i	0.842621	−	0.538507i	$-0.181011\pi$
$354$	12.0106	−	23.0233i	0.638354	−	1.22368i
$355$	4.28029	−	15.2443i	0.227174	−	0.809084i
$356$	13.4779	+	2.40062i	0.714329	+	0.127233i
$357$	−6.40645	−	15.4665i	−0.339065	−	0.818576i
$358$	−17.7687	+	14.8834i	−0.939102	+	0.786614i
$359$	−15.0409	+	15.0409i	−0.793829	+	0.793829i	−0.982114	−	0.188285i	$-0.939707\pi$
$359$	−15.0409	+	15.0409i	−0.793829	+	0.793829i	0.188285	+	0.982114i	$0.439707\pi$
$360$	−3.55850	−	0.521200i	−0.187549	−	0.0274697i
$361$	−12.2511	−	12.2511i	−0.644793	−	0.644793i
$362$	−16.3883	−	1.44811i	−0.861350	−	0.0761108i
$363$	14.4389	−	5.98079i	0.757846	−	0.313910i
$364$	2.35674	+	1.50716i	0.123526	+	0.0789965i
$365$	9.03737	−	32.1867i	0.473037	−	1.68473i
$366$	−7.14140	−	22.7183i	−0.373287	−	1.18750i
$367$	−26.5268			−1.38469			−0.692344	−	0.721567i	$-0.743422\pi$
$367$	−26.5268			−1.38469			−0.692344	+	0.721567i	$0.743422\pi$
$368$	−6.89991	−	14.9319i	−0.359683	−	0.778377i
$369$			5.00333i			0.260463i
$370$	21.6076	−	9.74109i	1.12333	−	0.506415i
$371$	−5.40827	−	2.24018i	−0.280783	−	0.116304i
$372$	−6.77808	−	30.8268i	−0.351427	−	1.59829i
$373$	−13.4197	+	5.55861i	−0.694844	+	0.287814i	−0.702017	−	0.712160i	$-0.747717\pi$
$373$	−13.4197	+	5.55861i	−0.694844	+	0.287814i	0.00717252	+	0.999974i	$0.497717\pi$
$374$	7.69526	+	0.679970i	0.397912	+	0.0351604i
$375$	7.24356	−	15.8572i	0.374056	−	0.818860i
$376$	16.8044	−	2.16790i	0.866620	−	0.111801i
$377$	−2.09312	−	2.09312i	−0.107801	−	0.107801i
$378$	9.81698	+	11.7200i	0.504931	+	0.602814i
$379$	−8.88128	+	3.67875i	−0.456201	+	0.188965i	−0.598937	−	0.800796i	$-0.704410\pi$
$379$	−8.88128	+	3.67875i	−0.456201	+	0.188965i	0.142736	+	0.989761i	$0.454410\pi$
$380$	3.85085	+	4.31952i	0.197545	+	0.221587i
$381$	3.37302	−	8.14318i	0.172805	−	0.417188i
$382$	3.67305	−	7.04096i	0.187930	−	0.360247i
$383$			6.69931i			0.342319i	0.985243	+	0.171159i	$0.0547513\pi$
$383$			6.69931i			0.342319i	−0.985243	+	0.171159i	$0.945249\pi$
$384$	−10.2061	+	14.3892i	−0.520827	+	0.734295i
$385$	0.509642	+	4.26364i	0.0259738	+	0.217295i
$386$	−14.7106	−	7.67407i	−0.748750	−	0.390600i
$387$	0.323216	+	0.133881i	0.0164300	+	0.00680553i
$388$	23.9383	−	16.7000i	1.21528	−	0.847816i
$389$	21.9633	−	9.09749i	1.11358	−	0.461261i	0.251413	−	0.967880i	$-0.419105\pi$
$389$	21.9633	−	9.09749i	1.11358	−	0.461261i	0.862170	+	0.506619i	$0.169105\pi$
$390$	−2.58649	−	2.43171i	−0.130972	−	0.123134i
$391$	16.0695	−	16.0695i	0.812669	−	0.812669i
$392$	−1.16736	−	9.04874i	−0.0589605	−	0.457031i
$393$	−7.59653	+	7.59653i	−0.383194	+	0.383194i
$394$	18.4782	+	1.63277i	0.930916	+	0.0822578i
$395$	12.4977	+	22.2558i	0.628829	+	1.11981i
$396$	−1.09795	+	0.241414i	−0.0551741	+	0.0121315i
$397$	−10.7505	+	25.9539i	−0.539550	+	1.30259i	0.385487	+	0.922713i	$0.374034\pi$
$397$	−10.7505	+	25.9539i	−0.539550	+	1.30259i	−0.925037	+	0.379876i	$0.875966\pi$
$398$	3.61774	+	11.5088i	0.181341	+	0.576883i
$399$		−	3.91981i		−	0.196236i
$400$	12.4323	+	15.6665i	0.621613	+	0.783324i
$401$			7.02488i			0.350806i	0.984497	+	0.175403i	$0.0561228\pi$
$401$			7.02488i			0.350806i	−0.984497	+	0.175403i	$0.943877\pi$
$402$	−4.88410	+	1.53530i	−0.243597	+	0.0765736i
$403$	−2.78857	+	6.73221i	−0.138909	+	0.335355i
$404$	−6.58732	−	4.21266i	−0.327732	−	0.209588i
$405$	−7.63184	−	13.5907i	−0.379229	−	0.675327i
$406$	0.994265	−	11.2522i	0.0493445	−	0.558435i
$407$	5.23874	−	5.23874i	0.259675	−	0.259675i
$408$	−23.5259	−	6.36936i	−1.16470	−	0.315330i
$409$	6.78466	−	6.78466i	0.335480	−	0.335480i	−0.519183	−	0.854663i	$-0.673764\pi$
$409$	6.78466	−	6.78466i	0.335480	−	0.335480i	0.854663	+	0.519183i	$0.173764\pi$
$410$	19.0583	−	20.2714i	0.941225	−	1.00114i
$411$	13.3958	−	5.54873i	0.660767	−	0.273699i
$412$	−6.24639	+	35.0694i	−0.307738	+	1.72775i
$413$	−21.1363	−	8.75494i	−1.04005	−	0.430802i
$414$	−1.52957	+	2.93206i	−0.0751741	+	0.144103i
$415$	2.92357	+	24.4585i	0.143513	+	1.20062i
$416$	3.83316	−	1.37637i	0.187936	−	0.0674821i
$417$		−	4.81597i		−	0.235839i
$418$	1.60373	+	0.836619i	0.0784412	+	0.0409204i
$419$	9.42784	−	22.7608i	0.460580	−	1.11194i	−0.507579	−	0.861605i	$-0.669460\pi$
$419$	9.42784	−	22.7608i	0.460580	−	1.11194i	0.968160	−	0.250334i	$-0.0805404\pi$
$420$	0.775825	−	13.5251i	0.0378564	−	0.659960i
$421$	−2.93732	+	1.21668i	−0.143156	+	0.0592972i	−0.453111	−	0.891454i	$-0.649686\pi$
$421$	−2.93732	+	1.21668i	−0.143156	+	0.0592972i	0.309955	+	0.950751i	$0.399686\pi$
$422$	6.24360	−	5.22978i	0.303934	−	0.254582i
$423$	−2.40876	−	2.40876i	−0.117118	−	0.117118i
$424$	−7.39183	+	4.24208i	−0.358979	+	0.206014i
$425$	−14.3829	+	23.5933i	−0.697674	+	1.14444i
$426$	−1.37441	+	15.5543i	−0.0665905	+	0.753608i
$427$	−19.3834	+	8.02889i	−0.938031	+	0.388545i
$428$	9.19250	+	5.87870i	0.444336	+	0.284158i
$429$	−1.02521	−	0.424657i	−0.0494977	−	0.0205026i
$430$	−0.799571	−	1.77360i	−0.0385587	−	0.0855307i
$431$			1.56057i			0.0751699i	0.999293	+	0.0375850i	$0.0119665\pi$
$431$			1.56057i			0.0751699i	−0.999293	+	0.0375850i	$0.988034\pi$
$432$	22.2401	−	0.893776i	1.07003	−	0.0430018i
$433$	11.7548			0.564899			0.282449	−	0.959282i	$-0.408853\pi$
$433$	11.7548			0.564899			0.282449	+	0.959282i	$0.408853\pi$
$434$	−26.5275	+	8.33881i	−1.27336	+	0.400276i
$435$	−3.87515	+	13.8014i	−0.185799	+	0.661727i
$436$	−1.62423	−	7.38703i	−0.0777867	−	0.353775i
$437$	4.91609	−	2.03631i	0.235169	−	0.0974100i
$438$	−2.90192	+	32.8412i	−0.138659	+	1.56921i
$439$	−6.33547	−	6.33547i	−0.302376	−	0.302376i	0.539567	−	0.841943i	$-0.318588\pi$
$439$	−6.33547	−	6.33547i	−0.302376	−	0.302376i	−0.841943	+	0.539567i	$0.818588\pi$
$440$	5.36803	+	3.20413i	0.255911	+	0.152751i
$441$	−1.29706	+	1.29706i	−0.0617645	+	0.0617645i
$442$	3.61315	+	4.31358i	0.171860	+	0.205176i
$443$	8.63740	+	20.8525i	0.410375	+	0.990734i	0.985037	+	0.172343i	$0.0551337\pi$
$443$	8.63740	+	20.8525i	0.410375	+	0.990734i	−0.574662	+	0.818391i	$0.694866\pi$
$444$	−19.1702	+	13.3737i	−0.909778	+	0.634686i
$445$	−4.13759	+	14.7361i	−0.196141	+	0.698558i
$446$	−5.21153	−	2.71870i	−0.246773	−	0.128734i
$447$		−	13.5697i		−	0.641826i
$448$	13.4192	+	7.84089i	0.633996	+	0.370447i
$449$	16.5751			0.782228			0.391114	−	0.920342i	$-0.372090\pi$
$449$	16.5751			0.782228			0.391114	+	0.920342i	$0.372090\pi$
$450$	0.967106	−	3.90294i	0.0455898	−	0.183986i
$451$	3.32822	−	8.03504i	0.156720	−	0.378355i
$452$	−13.1189	−	18.8050i	−0.617060	−	0.884513i
$453$	10.4670	+	25.2695i	0.491781	+	1.18727i
$454$	−21.0904	+	17.6658i	−0.989823	+	0.829099i
$455$	−1.93346	+	2.45843i	−0.0906420	+	0.115253i
$456$	−4.51847	−	3.48585i	−0.211597	−	0.163240i
$457$	13.1674	−	13.1674i	0.615946	−	0.615946i	−0.328543	−	0.944489i	$-0.606558\pi$
$457$	13.1674	−	13.1674i	0.615946	−	0.615946i	0.944489	+	0.328543i	$0.106558\pi$
$458$	0.800271	−	9.05672i	0.0373942	−	0.423193i
$459$	11.7681	+	28.4106i	0.549286	+	1.32609i
$460$	17.3658	−	6.05319i	0.809684	−	0.282231i
$461$	−7.73451	−	3.20374i	−0.360232	−	0.149213i	0.195225	−	0.980759i	$-0.437456\pi$
$461$	−7.73451	−	3.20374i	−0.360232	−	0.149213i	−0.555456	+	0.831546i	$0.687456\pi$
$462$	−1.26987	−	4.03973i	−0.0590799	−	0.187945i
$463$	3.13983			0.145920			0.0729602	−	0.997335i	$-0.476755\pi$
$463$	3.13983			0.145920			0.0729602	+	0.997335i	$0.476755\pi$
$464$	−12.0865	−	11.1525i	−0.561100	−	0.517744i
$465$	35.0392	−	4.18831i	1.62491	−	0.194228i
$466$	−4.71649	−	15.0041i	−0.218487	−	0.695053i
$467$	10.4175	−	25.1501i	0.482065	−	1.16381i	−0.476561	−	0.879141i	$-0.658117\pi$
$467$	10.4175	−	25.1501i	0.482065	−	1.16381i	0.958626	−	0.284667i	$-0.0918831\pi$
$468$	−0.689827	−	0.441151i	−0.0318873	−	0.0203922i
$469$	1.72609	+	4.16715i	0.0797035	+	0.192421i
$470$	0.584021	+	18.9346i	0.0269389	+	0.873387i
$471$	24.2863	+	24.2863i	1.11905	+	1.11905i
$472$	−28.8883	+	16.5787i	−1.32969	+	0.763095i
$473$	−0.430008	−	0.430008i	−0.0197718	−	0.0197718i
$474$	−16.1635	−	19.2968i	−0.742412	−	0.886331i
$475$	−5.22541	+	3.81500i	−0.239758	+	0.175044i
$476$	−3.76533	+	21.1399i	−0.172584	+	0.968944i
$477$	1.58302	+	0.655710i	0.0724817	+	0.0300229i
$478$	−3.06729	−	1.60011i	−0.140295	−	0.0731874i
$479$	17.1811			0.785026			0.392513	−	0.919746i	$-0.371606\pi$
$479$	17.1811			0.785026			0.392513	+	0.919746i	$0.371606\pi$
$480$	−14.9009	−	12.9221i	−0.680128	−	0.589810i
$481$	5.39632			0.246051
$482$	9.72217	+	5.07176i	0.442833	+	0.231012i
$483$	−11.5089	−	4.76716i	−0.523674	−	0.216913i
$484$	−19.7353	−	3.51515i	−0.897058	−	0.159780i
$485$	15.9782	+	28.4538i	0.725532	+	1.29202i
$486$	−5.28907	−	6.31438i	−0.239917	−	0.286426i
$487$	2.27177	+	2.27177i	0.102944	+	0.102944i	0.756703	−	0.653759i	$-0.226809\pi$
$487$	2.27177	+	2.27177i	0.102944	+	0.102944i	−0.653759	+	0.756703i	$0.726809\pi$
$488$	−7.98240	+	29.4838i	−0.361346	+	1.33467i
$489$	−13.2578	−	13.2578i	−0.599536	−	0.599536i
$490$	10.1958	−	0.314481i	0.460599	−	0.0142068i
$491$	−7.16933	−	17.3083i	−0.323547	−	0.781112i	−0.999043	−	0.0437479i	$-0.986070\pi$
$491$	−7.16933	−	17.3083i	−0.323547	−	0.781112i	0.675495	−	0.737364i	$-0.263930\pi$
$492$	−14.7830	+	23.1161i	−0.666469	+	1.04216i
$493$	8.69501	−	20.9916i	0.391603	−	0.945414i
$494$	0.395095	+	1.25688i	0.0177762	+	0.0565497i
$495$	−0.149174	−	1.24799i	−0.00670489	−	0.0560928i
$496$	−13.9783	+	37.9946i	−0.627643	+	1.70601i
$497$	13.7568			0.617077
$498$	−7.28467	−	23.1740i	−0.326434	−	1.03845i
$499$	−12.8831	−	5.33636i	−0.576727	−	0.238888i	0.0752016	−	0.997168i	$-0.476040\pi$
$499$	−12.8831	−	5.33636i	−0.576727	−	0.238888i	−0.651929	+	0.758280i	$0.726040\pi$
$500$	−18.7851	+	12.1293i	−0.840096	+	0.542437i
$501$	10.3279	+	24.9338i	0.461417	+	1.11396i
$502$	2.61799	−	29.6280i	0.116847	−	1.32236i
$503$	15.2756	−	15.2756i	0.681104	−	0.681104i	−0.279145	−	0.960249i	$-0.590051\pi$
$503$	15.2756	−	15.2756i	0.681104	−	0.681104i	0.960249	+	0.279145i	$0.0900509\pi$
$504$	−0.399797	−	3.09901i	−0.0178084	−	0.138041i
$505$	5.40422	−	6.87157i	0.240485	−	0.305781i
$506$	4.40680	−	3.69124i	0.195906	−	0.164096i
$507$	7.44792	+	17.9809i	0.330774	+	0.798558i
$508$	−9.27206	+	6.46844i	−0.411381	+	0.286990i
$509$	−4.32972	+	10.4529i	−0.191911	+	0.463315i	−0.990320	−	0.138801i	$-0.955675\pi$
$509$	−4.32972	+	10.4529i	−0.191911	+	0.463315i	0.798409	+	0.602115i	$0.205675\pi$
$510$	9.64689	−	25.4849i	0.427172	−	1.12849i
$511$	29.0460			1.28492
$512$	20.9719	−	8.49579i	0.926837	−	0.375464i
$513$			7.20034i			0.317903i
$514$	23.8573	+	12.4456i	1.05230	+	0.548953i
$515$	−38.3431	−	10.7660i	−1.68960	−	0.474405i
$516$	1.09774	+	1.57353i	0.0483253	+	0.0692710i
$517$	2.26601	+	5.47062i	0.0996588	+	0.240598i
$518$	13.2231	+	15.7864i	0.580989	+	0.693616i
$519$	13.9657	−	13.9657i	0.613024	−	0.613024i
$520$	1.11449	+	4.41501i	0.0488737	+	0.193611i
$521$	−17.3931	−	17.3931i	−0.762006	−	0.762006i	0.214679	−	0.976685i	$-0.431130\pi$
$521$	−17.3931	−	17.3931i	−0.762006	−	0.762006i	−0.976685	+	0.214679i	$0.931130\pi$
$522$	−0.291026	+	3.29355i	−0.0127378	+	0.144155i
$523$	31.5147	−	13.0538i	1.37804	−	0.570804i	0.434085	−	0.900872i	$-0.357072\pi$
$523$	31.5147	−	13.0538i	1.37804	−	0.570804i	0.943957	+	0.330069i	$0.107072\pi$
$524$	13.4581	−	2.95913i	0.587921	−	0.129270i
$525$	14.9654	+	2.33477i	0.653144	+	0.101898i
$526$	−9.66894	+	3.03939i	−0.421586	+	0.132524i
$527$	−55.9325			−2.43646
$528$	−5.78599	−	2.12868i	−0.251803	−	0.0926388i
$529$			6.08942i			0.264757i
$530$	−3.91608	−	8.68662i	−0.170104	−	0.377323i
$531$	6.18668	+	2.56261i	0.268479	+	0.111208i
$532$	−2.70874	+	4.23565i	−0.117439	+	0.183639i
$533$	5.85253	−	2.42420i	0.253501	−	0.105004i
$534$	1.32859	−	15.0357i	0.0574938	−	0.650660i
$535$	−7.54150	+	9.58917i	−0.326048	+	0.414576i
$536$	6.33858	+	1.71610i	0.273785	+	0.0741241i
$537$	18.0708	+	18.0708i	0.779815	+	0.779815i
$538$	−7.14946	+	5.98855i	−0.308235	+	0.258185i
$539$	2.94579	−	1.22019i	0.126884	−	0.0525572i
$540$	−1.42512	+	24.8445i	−0.0613274	+	1.06913i
$541$	−14.7474	+	35.6035i	−0.634042	+	1.53071i	0.200456	+	0.979703i	$0.435758\pi$
$541$	−14.7474	+	35.6035i	−0.634042	+	1.53071i	−0.834498	+	0.551010i	$0.814242\pi$
$542$	−7.36949	−	3.84444i	−0.316547	−	0.165133i
$543$			18.1398i			0.778452i
$544$	21.0200	+	23.1399i	0.901225	+	0.992113i
$545$	8.39647	−	1.00365i	0.359665	−	0.0429915i
$546$	1.42659	−	2.73466i	0.0610524	−	0.117033i
$547$	−9.39628	−	3.89207i	−0.401756	−	0.166413i	0.172650	−	0.984983i	$-0.444767\pi$
$547$	−9.39628	−	3.89207i	−0.401756	−	0.166413i	−0.574406	+	0.818570i	$0.694767\pi$
$548$	−18.3096	−	3.26121i	−0.782146	−	0.139312i
$549$	5.67362	−	2.35009i	0.242144	−	0.100299i
$550$	−4.14935	+	5.62455i	−0.176929	+	0.239832i
$551$	3.76186	−	3.76186i	0.160261	−	0.160261i
$552$	−15.7300	+	9.02726i	−0.669513	+	0.384226i
$553$	−15.6812	+	15.6812i	−0.666832	+	0.666832i
$554$	−0.665710	+	7.53387i	−0.0282833	+	0.320084i
$555$	−12.7956	−	22.7862i	−0.543142	−	0.967222i
$556$	−3.32802	+	5.20401i	−0.141139	+	0.220699i
$557$	−1.90473	+	4.59841i	−0.0807058	+	0.194841i	−0.959082	−	0.283129i	$-0.908627\pi$
$557$	−1.90473	+	4.59841i	−0.0807058	+	0.194841i	0.878376	+	0.477970i	$0.158627\pi$
$558$	7.76472	−	2.44081i	0.328707	−	0.103328i
$559$		−	0.442943i		−	0.0187345i
$560$	−10.1847	+	14.0788i	−0.430384	+	0.594938i
$561$		−	8.51766i		−	0.359616i
$562$	0.374761	+	1.19219i	0.0158083	+	0.0502896i
$563$	14.6484	−	35.3644i	0.617357	−	1.49043i	−0.237404	−	0.971411i	$-0.576297\pi$
$563$	14.6484	−	35.3644i	0.617357	−	1.49043i	0.854761	−	0.519021i	$-0.173703\pi$
$564$	−4.01183	−	18.2458i	−0.168928	−	0.768288i
$565$	22.3521	−	12.5518i	0.940362	−	0.528059i
$566$	−0.794144	−	0.0701723i	−0.0333804	−	0.00294956i
$567$	9.57584	−	9.57584i	0.402148	−	0.402148i
$568$	12.2338	−	15.8578i	0.513318	−	0.665379i
$569$	21.9217	−	21.9217i	0.919005	−	0.919005i	−0.0779525	−	0.996957i	$-0.524838\pi$
$569$	21.9217	−	21.9217i	0.919005	−	0.919005i	0.996957	+	0.0779525i	$0.0248383\pi$
$570$	4.37040	−	4.64858i	0.183056	−	0.194708i
$571$	−32.3232	+	13.3887i	−1.35268	+	0.560299i	−0.937038	−	0.349228i	$-0.886444\pi$
$571$	−32.3232	+	13.3887i	−1.35268	+	0.560299i	−0.415644	+	0.909527i	$0.636444\pi$
$572$	0.814365	+	1.16734i	0.0340503	+	0.0488087i
$573$	−8.08953	−	3.35079i	−0.337945	−	0.139981i
$574$	21.4327	+	11.1808i	0.894585	+	0.466677i
$575$	4.84622	+	19.9820i	0.202101	+	0.833305i
$576$	−3.92785	−	2.29506i	−0.163660	−	0.0956277i
$577$		−	22.1174i		−	0.920760i	−0.887722	−	0.460380i	$-0.847713\pi$
$577$		−	22.1174i		−	0.920760i	0.887722	−	0.460380i	$-0.152287\pi$
$578$	−8.85677	+	16.9777i	−0.368393	+	0.706181i
$579$	−7.00078	+	16.9014i	−0.290942	+	0.702397i
$580$	13.7247	−	12.2356i	0.569887	−	0.508055i
$581$	−19.7723	+	8.18995i	−0.820293	+	0.339777i
$582$	−20.6648	−	24.6707i	−0.856582	−	1.02263i
$583$	−2.10606	−	2.10606i	−0.0872241	−	0.0872241i
$584$	25.8303	−	33.4821i	1.06887	−	1.38550i
$585$	0.565932	−	0.719594i	0.0233984	−	0.0297515i
$586$	−12.5849	−	1.11203i	−0.519878	−	0.0459376i
$587$	−29.6698	+	12.2896i	−1.22460	+	0.507248i	−0.898871	−	0.438214i	$-0.855611\pi$
$587$	−29.6698	+	12.2896i	−1.22460	+	0.507248i	−0.325734	+	0.945462i	$0.605611\pi$
$588$	−9.82492	+	2.16027i	−0.405173	+	0.0890880i
$589$	−12.0995	−	5.01177i	−0.498551	−	0.206507i
$590$	−15.3046	−	33.9485i	−0.630080	−	1.39764i
$591$		−	20.4530i		−	0.841322i
$592$	29.9566	−	1.20388i	1.23121	−	0.0494792i
$593$	14.2999			0.587228			0.293614	−	0.955924i	$-0.405142\pi$
$593$	14.2999			0.587228			0.293614	+	0.955924i	$0.405142\pi$
$594$	2.33264	+	7.42062i	0.0957095	+	0.304472i
$595$	−23.1133	−	6.48973i	−0.947551	−	0.266053i
$596$	−9.37721	+	14.6631i	−0.384106	+	0.600625i
$597$	12.2890	−	5.09025i	0.502954	−	0.208330i
$598$	4.17082	+	0.368542i	0.170557	+	0.0150708i
$599$	23.8858	+	23.8858i	0.975945	+	0.975945i	0.999717	−	0.0237720i	$-0.00756758\pi$
$599$	23.8858	+	23.8858i	0.975945	+	0.975945i	−0.0237720	+	0.999717i	$0.507568\pi$
$600$	15.9999	−	15.1747i	0.653194	−	0.619505i
$601$	11.8634	−	11.8634i	0.483917	−	0.483917i	−0.422463	−	0.906380i	$-0.638834\pi$
$601$	11.8634	−	11.8634i	0.483917	−	0.483917i	0.906380	+	0.422463i	$0.138834\pi$
$602$	1.29579	−	1.08538i	0.0528123	−	0.0442368i
$603$	−0.505235	−	1.21974i	−0.0205747	−	0.0496718i
$604$	6.15186	−	34.5387i	0.250316	−	1.40536i
$605$	6.05854	−	21.5776i	0.246315	−	0.877253i
$606$	−3.98747	+	7.64367i	−0.161980	+	0.310503i
$607$		−	16.0302i		−	0.650647i	−0.945603	−	0.325324i	$-0.894527\pi$
$607$		−	16.0302i		−	0.650647i	0.945603	−	0.325324i	$-0.105473\pi$
$608$	2.47369	+	6.88916i	0.100321	+	0.279392i
$609$	−12.4547			−0.504690
$610$	−31.9390	−	12.0900i	−1.29317	−	0.489509i
$611$	−1.65051	+	3.98467i	−0.0667723	+	0.161203i
$612$	1.10213	−	6.18773i	0.0445509	−	0.250124i
$613$	−5.96490	−	14.4005i	−0.240920	−	0.581632i	0.756455	−	0.654046i	$-0.226930\pi$
$613$	−5.96490	−	14.4005i	−0.240920	−	0.581632i	−0.997375	+	0.0724139i	$0.976930\pi$
$614$	16.2859	+	19.4430i	0.657247	+	0.784657i
$615$	−24.1136	−	18.9644i	−0.972356	−	0.764719i
$616$	−1.41942	+	5.24277i	−0.0571900	+	0.211237i
$617$	−5.74233	+	5.74233i	−0.231177	+	0.231177i	−0.813184	−	0.582007i	$-0.802268\pi$
$617$	−5.74233	+	5.74233i	−0.231177	+	0.231177i	0.582007	+	0.813184i	$0.302268\pi$
$618$	39.1228	+	3.45698i	1.57375	+	0.139060i
$619$	−15.1568	−	36.5918i	−0.609203	−	1.47075i	−0.863868	−	0.503718i	$-0.831965\pi$
$619$	−15.1568	−	36.5918i	−0.609203	−	1.47075i	0.254665	−	0.967029i	$-0.418035\pi$
$620$	−40.7568	−	19.6877i	−1.63683	−	0.790676i
$621$	21.1408	+	8.75683i	0.848353	+	0.351399i
$622$	35.9961	−	11.3152i	1.44331	−	0.453699i
$623$	−13.2982			−0.532780
$624$	−1.88366	−	4.07637i	−0.0754069	−	0.163185i
$625$	−11.4528	−	22.2224i	−0.458113	−	0.888894i
$626$	16.8217	−	5.28782i	0.672328	−	0.211344i
$627$	0.763217	−	1.84257i	0.0304799	−	0.0735851i
$628$	−9.46038	−	43.0259i	−0.377510	−	1.71692i
$629$	15.8511	+	38.2680i	0.632025	+	1.52584i
$630$	3.49185	−	0.107703i	0.139119	−	0.00429100i
$631$	−8.27454	−	8.27454i	−0.329404	−	0.329404i	0.522956	−	0.852360i	$-0.324829\pi$
$631$	−8.27454	−	8.27454i	−0.329404	−	0.329404i	−0.852360	+	0.522956i	$0.824829\pi$
$632$	4.13099	+	32.0212i	0.164322	+	1.27374i
$633$	−6.34978	−	6.34978i	−0.252381	−	0.252381i
$634$	28.3366	−	23.7354i	1.12539	−	0.942653i
$635$	−6.18884	−	11.0210i	−0.245597	−	0.437356i
$636$	5.37643	+	7.70674i	0.213189	+	0.305592i
$637$	2.14565	+	0.888756i	0.0850137	+	0.0352138i
$638$	2.65825	−	5.09565i	0.105241	−	0.201739i
$639$	−4.02667			−0.159293
$640$	7.17183	+	24.2604i	0.283491	+	0.958975i
$641$	−19.5785			−0.773303			−0.386651	−	0.922226i	$-0.626368\pi$
$641$	−19.5785			−0.773303			−0.386651	+	0.922226i	$0.626368\pi$
$642$	5.56444	−	10.6666i	0.219611	−	0.420978i
$643$	−7.50877	−	3.11024i	−0.296117	−	0.122656i	0.229679	−	0.973266i	$-0.426232\pi$
$643$	−7.50877	−	3.11024i	−0.296117	−	0.122656i	−0.525796	+	0.850611i	$0.676232\pi$
$644$	9.14197	+	13.1044i	0.360244	+	0.516385i
$645$	−1.87035	+	1.05029i	−0.0736448	+	0.0413552i
$646$	−7.75260	+	6.49376i	−0.305022	+	0.255494i
$647$	33.5826	+	33.5826i	1.32027	+	1.32027i	0.913558	+	0.406709i	$0.133324\pi$
$647$	33.5826	+	33.5826i	1.32027	+	1.32027i	0.406709	+	0.913558i	$0.366676\pi$
$648$	−2.52262	−	19.5540i	−0.0990979	−	0.768154i
$649$	−8.23078	−	8.23078i	−0.323086	−	0.323086i
$650$	−5.03395	+	0.759789i	−0.197448	+	0.0298014i
$651$	11.7329	+	28.3258i	0.459850	+	1.11018i
$652$	5.16438	+	23.4876i	0.202253	+	0.919846i
$653$	−3.76501	+	9.08954i	−0.147336	+	0.355701i	−0.980268	−	0.197675i	$-0.936661\pi$
$653$	−3.76501	+	9.08954i	−0.147336	+	0.355701i	0.832931	+	0.553376i	$0.186661\pi$
$654$	−7.95552	+	2.50079i	−0.311086	+	0.0977885i
$655$	1.82850	+	15.2972i	0.0714455	+	0.597710i
$656$	31.9483	−	14.7631i	1.24737	−	0.576402i
$657$	−8.50189			−0.331690
$658$	−15.7012	+	4.93560i	−0.612095	+	0.192410i
$659$	−33.0023	−	13.6700i	−1.28559	−	0.532507i	−0.367919	−	0.929858i	$-0.619930\pi$
$659$	−33.0023	−	13.6700i	−1.28559	−	0.532507i	−0.917667	+	0.397351i	$0.869930\pi$
$660$	2.99813	−	6.20664i	0.116702	−	0.241593i
$661$	−2.64914	−	6.39559i	−0.103040	−	0.248760i	0.863949	−	0.503579i	$-0.167984\pi$
$661$	−2.64914	−	6.39559i	−0.103040	−	0.248760i	−0.966989	+	0.254820i	$0.917984\pi$
$662$	−1.29282	−	0.114236i	−0.0502468	−	0.00443991i
$663$	4.38694	−	4.38694i	0.170375	−	0.170375i
$664$	−8.14253	+	30.0753i	−0.315991	+	1.16715i
$665$	−4.41843	−	3.47492i	−0.171339	−	0.134752i
$666$	−3.87045	−	4.62076i	−0.149977	−	0.179051i
$667$	−6.47011	−	15.6202i	−0.250524	−	0.604818i
$668$	6.07013	−	34.0798i	0.234860	−	1.31859i
$669$	−2.48017	+	5.98766i	−0.0958888	+	0.231496i
$670$	−2.59916	+	6.86641i	−0.100414	+	0.265273i
$671$	−10.6748			−0.412095
$672$	7.30933	−	15.4992i	0.281963	−	0.597893i
$673$		−	24.6788i		−	0.951299i	−0.879635	−	0.475649i	$-0.842213\pi$
$673$		−	24.6788i		−	0.951299i	0.879635	−	0.475649i	$-0.157787\pi$
$674$	11.8770	−	22.7673i	0.457486	−	0.876965i
$675$	−27.4901	−	4.28876i	−1.05809	−	0.165074i
$676$	4.37744	−	24.5765i	0.168363	−	0.945249i
$677$	9.39264	+	22.6758i	0.360988	+	0.871503i	0.995156	+	0.0983076i	$0.0313429\pi$
$677$	9.39264	+	22.6758i	0.360988	+	0.871503i	−0.634168	+	0.773196i	$0.718657\pi$
$678$	−19.3803	+	16.2334i	−0.744297	+	0.623440i
$679$	−20.0482	+	20.0482i	−0.769378	+	0.769378i
$680$	−28.0353	+	20.8720i	−1.07510	+	0.800405i
$681$	21.4491	+	21.4491i	0.821932	+	0.821932i
$682$	−14.0933	−	1.24531i	−0.539660	−	0.0476855i
$683$	−19.6320	+	8.13182i	−0.751196	+	0.311155i	−0.725229	−	0.688507i	$-0.758266\pi$
$683$	−19.6320	+	8.13182i	−0.751196	+	0.311155i	−0.0259664	+	0.999663i	$0.508266\pi$
$684$	0.792861	−	1.23979i	0.0303158	−	0.0474047i
$685$	5.62086	−	20.0188i	0.214762	−	0.764878i
$686$	8.42504	+	26.8018i	0.321669	+	1.02330i
$687$	−10.0246			−0.382463
$688$	−0.0988172	−	2.45890i	−0.00376737	−	0.0937448i
$689$		−	2.16941i		−	0.0826480i
$690$	−8.33351	−	18.4853i	−0.317251	−	0.703725i
$691$	−10.4060	−	4.31032i	−0.395864	−	0.163972i	0.175866	−	0.984414i	$-0.443727\pi$
$691$	−10.4060	−	4.31032i	−0.395864	−	0.163972i	−0.571730	+	0.820442i	$0.693727\pi$
$692$	−24.7418	+	5.44013i	−0.940540	+	0.206803i
$693$	1.00888	−	0.417890i	0.0383240	−	0.0158743i
$694$	−45.5784	−	4.02741i	−1.73013	−	0.152878i
$695$	−5.42857	−	4.26936i	−0.205918	−	0.161946i
$696$	−11.0758	+	14.3568i	−0.419828	+	0.544195i
$697$	34.3824	+	34.3824i	1.30232	+	1.30232i
$698$	9.18312	+	10.9633i	0.347586	+	0.414967i
$699$	−16.0213	+	6.63623i	−0.605980	+	0.251005i
$700$	−14.5578	−	12.8646i	−0.550234	−	0.486235i
$701$	0.140166	−	0.338390i	0.00529399	−	0.0127808i	−0.921210	−	0.389065i	$-0.872798\pi$
$701$	0.140166	−	0.338390i	0.00529399	−	0.0127808i	0.926504	+	0.376284i	$0.122798\pi$
$702$	−2.62051	+	5.02332i	−0.0989049	+	0.189593i
$703$			9.69857i			0.365788i
$704$	4.78120	+	6.29854i	0.180198	+	0.237385i
$705$	20.7391	−	2.47899i	0.781080	−	0.0933641i
$706$	25.3721	+	13.2358i	0.954892	+	0.498138i
$707$	7.01718	+	2.90661i	0.263908	+	0.109314i
$708$	21.0118	+	30.1190i	0.789674	+	1.13194i
$709$	−33.0748	+	13.7000i	−1.24215	+	0.514516i	−0.904386	−	0.426715i	$-0.859671\pi$
$709$	−33.0748	+	13.7000i	−1.24215	+	0.514516i	−0.337764	+	0.941231i	$0.609671\pi$
$710$	16.3144	+	15.3381i	0.612270	+	0.575630i
$711$	4.58995	−	4.58995i	0.172137	−	0.172137i
$712$	−11.8259	+	15.3291i	−0.443195	+	0.574484i
$713$	−29.4300	+	29.4300i	−1.10216	+	1.10216i
$714$	23.5833	+	2.08387i	0.882582	+	0.0779868i
$715$	−1.38753	+	0.779164i	−0.0518906	+	0.0291391i
$716$	−7.03925	−	32.0146i	−0.263069	−	1.19644i
$717$	−1.45972	+	3.52408i	−0.0545144	+	0.131609i
$718$	−9.02091	−	28.6974i	−0.336657	−	1.07098i
$719$		−	23.5195i		−	0.877131i	−0.898699	−	0.438566i	$-0.855487\pi$
$719$		−	23.5195i		−	0.877131i	0.898699	−	0.438566i	$-0.144513\pi$
$720$	2.98112	−	4.12093i	0.111100	−	0.153578i
$721$		−	34.6017i		−	1.28863i
$722$	23.3745	−	7.34768i	0.869908	−	0.273452i
$723$	4.62678	−	11.1700i	0.172072	−	0.415418i
$724$	12.5353	−	19.6014i	0.465870	−	0.728479i
$725$	12.1217	+	16.6030i	0.450187	+	0.616622i
$726$	−1.94541	+	22.0163i	−0.0722010	+	0.817103i
$727$	−15.0961	+	15.0961i	−0.559883	+	0.559883i	−0.929274	−	0.369391i	$-0.879566\pi$
$727$	−15.0961	+	15.0961i	−0.559883	+	0.559883i	0.369391	+	0.929274i	$0.379566\pi$
$728$	−3.43129	+	1.96918i	−0.127172	+	0.0729826i
$729$	−21.2088	+	21.2088i	−0.785512	+	0.785512i
$730$	34.4462	+	32.3848i	1.27491	+	1.19862i
$731$	3.14112	−	1.30110i	0.116179	−	0.0481227i
$732$	33.1566	+	5.90570i	1.22550	+	0.218281i
$733$	−26.7808	−	11.0930i	−0.989171	−	0.409728i	−0.171356	−	0.985209i	$-0.554815\pi$
$733$	−26.7808	−	11.0930i	−0.989171	−	0.409728i	−0.817815	+	0.575481i	$0.804815\pi$
$734$	17.3511	−	33.2608i	0.640442	−	1.22768i
$735$	−1.33487	−	11.1675i	−0.0492376	−	0.411919i
$736$	23.2356	+	1.11541i	0.856477	+	0.0411145i
$737$			2.29492i			0.0845343i
$738$	−6.27345	−	3.27267i	−0.230929	−	0.120469i
$739$	−14.9921	+	36.1941i	−0.551493	+	1.33142i	0.364864	+	0.931061i	$0.381115\pi$
$739$	−14.9921	+	36.1941i	−0.551493	+	1.33142i	−0.916357	+	0.400362i	$0.868885\pi$
$740$	−1.91958	+	33.4645i	−0.0705651	+	1.23018i
$741$	1.34208	−	0.555909i	0.0493027	−	0.0204218i
$742$	6.34640	−	5.31589i	0.232984	−	0.195153i
$743$	19.3126	+	19.3126i	0.708509	+	0.708509i	0.966222	−	0.257712i	$-0.0829687\pi$
$743$	19.3126	+	19.3126i	0.708509	+	0.708509i	−0.257712	+	0.966222i	$0.582969\pi$
$744$	43.0859	+	11.6650i	1.57960	+	0.427659i
$745$	−15.2959	−	12.0296i	−0.560397	−	0.440730i
$746$	1.80809	−	20.4622i	0.0661988	−	0.749175i
$747$	5.78744	−	2.39724i	0.211751	−	0.0877103i
$748$	−5.88604	+	9.20398i	−0.215215	+	0.336531i
$749$	−9.79235	−	4.05613i	−0.357805	−	0.148208i
$750$	15.1446	+	19.4545i	0.553002	+	0.710379i
$751$			25.2860i			0.922699i	0.887219	+	0.461349i	$0.152635\pi$
$751$			25.2860i			0.922699i	−0.887219	+	0.461349i	$0.847365\pi$
$752$	−8.27349	+	22.4883i	−0.301703	+	0.820064i
$753$	−32.7944			−1.19509
$754$	3.99357	−	1.25536i	0.145437	−	0.0457176i
$755$	37.7629	+	10.6030i	1.37433	+	0.385884i
$756$	−21.1165	+	4.64302i	−0.768000	+	0.168865i
$757$	50.8293	−	21.0542i	1.84742	−	0.765228i	0.916413	−	0.400235i	$-0.131071\pi$
$757$	50.8293	−	21.0542i	1.84742	−	0.765228i	0.931010	−	0.364993i	$-0.118929\pi$
$758$	1.19661	−	13.5421i	0.0434628	−	0.491872i
$759$	−4.48175	−	4.48175i	−0.162677	−	0.162677i
$760$	−7.93489	+	2.00303i	−0.287829	+	0.0726574i
$761$	−21.5700	+	21.5700i	−0.781911	+	0.781911i	−0.980153	−	0.198242i	$-0.936477\pi$
$761$	−21.5700	+	21.5700i	−0.781911	+	0.781911i	0.198242	+	0.980153i	$0.436477\pi$
$762$	8.00410	+	9.55572i	0.289958	+	0.346167i
$763$	2.81157	+	6.78772i	0.101786	+	0.245732i
$764$	6.42582	+	9.21097i	0.232478	+	0.333241i
$765$	6.76535	+	1.89957i	0.244602	+	0.0686792i
$766$	−8.39997	−	4.38201i	−0.303503	−	0.158328i
$767$		−	8.47837i		−	0.306136i
$768$	−11.3662	−	22.2089i	−0.410142	−	0.801395i
$769$	−30.0941			−1.08522			−0.542611	−	0.839984i	$-0.682564\pi$
$769$	−30.0941			−1.08522			−0.542611	+	0.839984i	$0.682564\pi$
$770$	−5.67935	−	2.14982i	−0.204669	−	0.0774742i
$771$	11.3537	−	27.4102i	0.408893	−	0.987155i
$772$	19.2444	−	13.4254i	0.692620	−	0.483190i
$773$	12.2463	+	29.5651i	0.440468	+	1.06338i	0.975785	+	0.218732i	$0.0701921\pi$
$773$	12.2463	+	29.5651i	0.440468	+	1.06338i	−0.535317	+	0.844651i	$0.679808\pi$
$774$	−0.379282	+	0.317696i	−0.0136330	+	0.0114193i
$775$	26.3412	−	43.2093i	0.946205	−	1.55212i
$776$	5.28141	+	40.9387i	0.189592	+	1.46961i
$777$	16.0549	−	16.0549i	0.575967	−	0.575967i
$778$	−2.95920	+	33.4894i	−0.106092	+	1.20065i
$779$	4.35690	+	10.5185i	0.156102	+	0.376864i
$780$	4.74083	−	1.65251i	0.169749	−	0.0591694i
$781$	6.46659	+	2.67855i	0.231393	+	0.0958460i
$782$	9.63780	+	30.6598i	0.344647	+	1.09639i
$783$	22.8781			0.817598
$784$	12.1094	+	4.45507i	0.432478	+	0.159110i
$785$	48.9054	−	5.84576i	1.74551	−	0.208644i
$786$	−4.55608	−	14.4938i	−0.162510	−	0.516978i
$787$	7.29972	−	17.6231i	0.260207	−	0.628195i	−0.738744	−	0.673986i	$-0.764581\pi$
$787$	7.29972	−	17.6231i	0.260207	−	0.628195i	0.998951	+	0.0457908i	$0.0145808\pi$
$788$	−14.1338	+	22.1010i	−0.503495	+	0.787314i
$789$	4.27651	+	10.3244i	0.152248	+	0.367559i
$790$	−36.0803	+	1.11287i	−1.28368	+	0.0395941i
$791$	15.7490	+	15.7490i	0.559972	+	0.559972i
$792$	0.415470	−	1.53458i	0.0147631	−	0.0545290i
$793$	−5.49793	−	5.49793i	−0.195237	−	0.195237i
$794$	−25.5106	−	30.4560i	−0.905338	−	1.08084i
$795$	−9.16044	+	5.14404i	−0.324887	+	0.182440i
$796$	−16.7967	−	2.99175i	−0.595343	−	0.106040i
$797$	11.8909	+	4.92536i	0.421196	+	0.174465i	0.583207	−	0.812324i	$-0.301798\pi$
$797$	11.8909	+	4.92536i	0.421196	+	0.174465i	−0.162010	+	0.986789i	$0.551798\pi$
$798$	4.91488	+	2.56394i	0.173985	+	0.0907626i
$799$	−33.1055			−1.17119
$800$	−27.7754	+	5.34085i	−0.982010	+	0.188827i
$801$	3.89243			0.137532
$802$	−8.80819	−	4.59496i	−0.311028	−	0.162254i
$803$	13.6535	+	5.65547i	0.481822	+	0.199577i
$804$	1.26964	−	7.12819i	0.0447767	−	0.251392i
$805$	−15.5762	+	8.74682i	−0.548990	+	0.308285i
$806$	−6.61722	−	7.89999i	−0.233082	−	0.278265i
$807$	7.27105	+	7.27105i	0.255953	+	0.255953i
$808$	9.59083	−	5.50406i	0.337404	−	0.193632i
$809$	−1.56855	−	1.56855i	−0.0551472	−	0.0551472i	0.678995	−	0.734143i	$-0.262416\pi$
$809$	−1.56855	−	1.56855i	−0.0551472	−	0.0551472i	−0.734143	+	0.678995i	$0.762416\pi$
$810$	22.0328	−	0.679582i	0.774152	−	0.0238781i
$811$	−18.0512	−	43.5794i	−0.633862	−	1.53028i	−0.834730	−	0.550660i	$-0.814376\pi$
$811$	−18.0512	−	43.5794i	−0.633862	−	1.53028i	0.200868	−	0.979618i	$-0.435624\pi$
$812$	13.4582	+	8.60668i	0.472291	+	0.302035i
$813$	−3.50714	+	8.46698i	−0.123001	+	0.296950i
$814$	3.14198	+	9.99528i	0.110126	+	0.350334i
$815$	−26.6972	+	3.19117i	−0.935162	+	0.111782i
$816$	23.3745	−	25.3319i	0.818271	−	0.886793i
$817$	0.796081			0.0278513
$818$	4.06915	+	12.9448i	0.142275	+	0.452605i
$819$	0.734841	+	0.304381i	0.0256774	+	0.0106359i
$820$	12.9514	+	37.1559i	0.452284	+	1.29754i
$821$	−18.2083	−	43.9588i	−0.635475	−	1.53417i	−0.832648	−	0.553803i	$-0.813176\pi$
$821$	−18.2083	−	43.9588i	−0.635475	−	1.53417i	0.197173	−	0.980369i	$-0.436824\pi$
$822$	−1.80487	+	20.4258i	−0.0629522	+	0.712433i
$823$	9.34794	−	9.34794i	0.325849	−	0.325849i	−0.525157	−	0.851005i	$-0.675993\pi$
$823$	9.34794	−	9.34794i	0.325849	−	0.325849i	0.851005	+	0.525157i	$0.175993\pi$
$824$	−39.8863	−	30.7709i	−1.38950	−	1.07196i
$825$	6.58012	+	4.01137i	0.229090	+	0.139658i
$826$	24.8026	−	20.7753i	0.862994	−	0.722864i
$827$	9.43175	+	22.7703i	0.327974	+	0.791800i	0.998743	+	0.0501328i	$0.0159644\pi$
$827$	9.43175	+	22.7703i	0.327974	+	0.791800i	−0.670768	+	0.741667i	$0.734036\pi$
$828$	−2.67590	−	3.83571i	−0.0929938	−	0.133300i
$829$	−0.0118029	+	0.0284948i	−0.000409932	+	0.000989664i	−0.924084	−	0.382189i	$-0.875170\pi$
$829$	−0.0118029	+	0.0284948i	−0.000409932	+	0.000989664i	0.923674	+	0.383178i	$0.125170\pi$
$830$	−32.5797	−	12.3325i	−1.13086	−	0.428068i
$831$	8.33904			0.289278
$832$	−0.781491	+	5.70651i	−0.0270933	+	0.197838i
$833$			17.8265i			0.617650i
$834$	6.03853	+	3.15012i	0.209097	+	0.109080i
$835$	37.2612	+	10.4622i	1.28948	+	0.362058i
$836$	−2.09800	+	1.46362i	−0.0725608	+	0.0506204i
$837$	−21.5523	−	52.0319i	−0.744957	−	1.79849i
$838$	22.3721	+	26.7090i	0.772830	+	0.922646i
$839$	20.9932	−	20.9932i	0.724767	−	0.724767i	−0.244805	−	0.969572i	$-0.578724\pi$
$839$	20.9932	−	20.9932i	0.724767	−	0.724767i	0.969572	+	0.244805i	$0.0787239\pi$
$840$	16.4511	+	9.81955i	0.567618	+	0.338807i
$841$	8.55328	+	8.55328i	0.294941	+	0.294941i
$842$	0.395757	−	4.47880i	0.0136387	−	0.154350i
$843$	1.27301	−	0.527298i	0.0438448	−	0.0181611i
$844$	2.47347	+	11.2494i	0.0851404	+	0.387219i
$845$	26.8707	+	7.54474i	0.924380	+	0.259547i
$846$	4.59580	−	1.44467i	0.158007	−	0.0496688i
$847$	19.4721			0.669068
$848$	−0.483980	−	12.0430i	−0.0166199	−	0.413559i
$849$			0.879016i			0.0301678i
$850$	−20.1747	−	33.4664i	−0.691987	−	1.14789i
$851$	28.4759	+	11.7951i	0.976140	+	0.404331i
$852$	−18.6038	−	11.8974i	−0.637357	−	0.407597i
$853$	−34.8407	+	14.4315i	−1.19292	+	0.494125i	−0.888706	−	0.458478i	$-0.848395\pi$
$853$	−34.8407	+	14.4315i	−1.19292	+	0.494125i	−0.304217	+	0.952603i	$0.598395\pi$
$854$	2.61161	−	29.5557i	0.0893674	−	1.01138i
$855$	1.29329	+	1.01712i	0.0442297	+	0.0347849i
$856$	−13.3838	+	7.68083i	−0.457450	+	0.262525i
$857$	−11.2012	−	11.2012i	−0.382626	−	0.382626i	0.489422	−	0.872047i	$-0.337208\pi$
$857$	−11.2012	−	11.2012i	−0.382626	−	0.382626i	−0.872047	+	0.489422i	$0.837208\pi$
$858$	1.20305	−	1.00770i	0.0410714	−	0.0344024i
$859$	27.0813	−	11.2175i	0.924003	−	0.382735i	0.130603	−	0.991435i	$-0.458309\pi$
$859$	27.0813	−	11.2175i	0.924003	−	0.382735i	0.793400	+	0.608700i	$0.208309\pi$
$860$	2.74684	+	0.157563i	0.0936665	+	0.00537287i
$861$	10.1998	−	24.6246i	0.347609	−	0.839203i
$862$	−1.95673	−	1.02077i	−0.0666464	−	0.0347674i
$863$		−	28.5569i		−	0.972089i	−0.873934	−	0.486045i	$-0.838439\pi$
$863$		−	28.5569i		−	0.972089i	0.873934	−	0.486045i	$-0.161561\pi$
$864$	−13.4266	+	28.4705i	−0.456781	+	0.968588i
$865$	−3.36157	−	28.1227i	−0.114297	−	0.956201i
$866$	−7.68878	+	14.7388i	−0.261275	+	0.500845i
$867$	19.5061	+	8.07971i	0.662463	+	0.274401i
$868$	6.89592	−	38.7161i	0.234063	−	1.31411i
$869$	−10.4244	+	4.31794i	−0.353624	+	0.146476i
$870$	−14.7703	−	13.8864i	−0.500758	−	0.470792i
$871$	−1.18197	+	1.18197i	−0.0400497	+	0.0400497i
$872$	10.3247	+	2.79529i	0.349638	+	0.0946604i
$873$	5.86819	−	5.86819i	0.198608	−	0.198608i
$874$	−0.662365	+	7.49602i	−0.0224048	+	0.253557i
$875$	15.8986	−	14.7993i	0.537471	−	0.500307i
$876$	−39.2800	−	25.1200i	−1.32715	−	0.848725i
$877$	−22.5473	+	54.4339i	−0.761367	+	1.83810i	−0.286353	+	0.958124i	$0.592443\pi$
$877$	−22.5473	+	54.4339i	−0.761367	+	1.83810i	−0.475014	+	0.879978i	$0.657557\pi$
$878$	12.0878	−	3.79975i	0.407943	−	0.128235i
$879$			13.9299i			0.469844i
$880$	−7.52874	+	4.63492i	−0.253794	+	0.156243i
$881$			1.46830i			0.0494683i	0.999694	+	0.0247342i	$0.00787393\pi$
$881$			1.46830i			0.0494683i	−0.999694	+	0.0247342i	$0.992126\pi$
$882$	−0.777919	−	2.47472i	−0.0261939	−	0.0833282i
$883$	−21.6029	+	52.1540i	−0.726995	+	1.75512i	−0.0746368	+	0.997211i	$0.523780\pi$
$883$	−21.6029	+	52.1540i	−0.726995	+	1.75512i	−0.652358	+	0.757911i	$0.726220\pi$
$884$	−7.77196	+	1.70887i	−0.261399	+	0.0574756i
$885$	−35.8003	+	20.1036i	−1.20341	+	0.675776i
$886$	−31.7958	−	2.80955i	−1.06820	−	0.0943886i
$887$	−0.932364	+	0.932364i	−0.0313057	+	0.0313057i	−0.722586	−	0.691281i	$-0.757047\pi$
$887$	−0.932364	+	0.932364i	−0.0313057	+	0.0313057i	0.691281	+	0.722586i	$0.257047\pi$
$888$	−4.22944	−	32.7844i	−0.141931	−	1.10017i
$889$	7.76528	−	7.76528i	0.260439	−	0.260439i
$890$	−15.7705	−	14.8268i	−0.528630	−	0.496995i
$891$	6.36576	−	2.63678i	0.213261	−	0.0883355i
$892$	6.81771	−	4.75622i	0.228274	−	0.159250i
$893$	−7.16148	−	2.96638i	−0.239650	−	0.0992661i
$894$	17.0145	+	8.87594i	0.569050	+	0.296856i
$895$	36.3893	−	4.34970i	1.21636	−	0.145394i
$896$	−18.6088	+	11.6970i	−0.621677	+	0.390769i
$897$		−	4.61656i		−	0.154142i
$898$	−10.8418	+	20.7828i	−0.361794	+	0.693532i
$899$	−15.9242	+	38.4445i	−0.531103	+	1.28220i
$900$	4.26114	+	3.76552i	0.142038	+	0.125517i
$901$	15.3843	−	6.37241i	0.512527	−	0.212296i
$902$	7.89780	+	9.42881i	0.262968	+	0.313945i
$903$	−1.31782	−	1.31782i	−0.0438544	−	0.0438544i
$904$	32.1598	−	4.14887i	1.06962	−	0.137989i
$905$	20.4472	+	16.0809i	0.679688	+	0.534548i
$906$	−38.5308	−	3.40466i	−1.28010	−	0.113112i
$907$	−19.1541	+	7.93389i	−0.636001	+	0.263440i	−0.677301	−	0.735706i	$-0.736850\pi$
$907$	−19.1541	+	7.93389i	−0.636001	+	0.263440i	0.0412992	+	0.999147i	$0.486850\pi$
$908$	−8.35521	−	37.9996i	−0.277277	−	1.26106i
$909$	−2.05396	−	0.850777i	−0.0681255	−	0.0282185i
$910$	−1.81785	−	4.03234i	−0.0602611	−	0.133671i
$911$		−	13.5372i		−	0.448507i	−0.974531	−	0.224254i	$-0.928006\pi$
$911$		−	13.5372i		−	0.448507i	0.974531	−	0.224254i	$-0.0719944\pi$
$912$	7.32628	−	3.38542i	0.242597	−	0.112103i
$913$	−10.8889			−0.360370
$914$	7.89727	+	25.1229i	0.261218	+	0.830990i
$915$	−10.1788	+	36.2518i	−0.336500	+	1.19845i
$916$	10.8324	+	6.92741i	0.357911	+	0.228888i
$917$	−12.3663	+	5.12228i	−0.408370	+	0.169153i
$918$	−43.3203	−	3.82788i	−1.42978	−	0.126339i
$919$	30.9063	+	30.9063i	1.01950	+	1.01950i	0.999806	+	0.0196980i	$0.00627048\pi$
$919$	30.9063	+	30.9063i	1.01950	+	1.01950i	0.0196980	+	0.999806i	$0.493730\pi$
$920$	−3.76910	+	25.7336i	−0.124264	+	0.848411i
$921$	19.7737	−	19.7737i	0.651566	−	0.651566i
$922$	9.07615	−	7.60240i	0.298907	−	0.250372i
$923$	1.95099	+	4.71011i	0.0642177	+	0.155035i
$924$	5.89587	+	1.05014i	0.193960	+	0.0345472i
$925$	−37.0280	−	5.77679i	−1.21747	−	0.189940i
$926$	−2.05376	+	3.93690i	−0.0674907	+	0.129374i
$927$			10.1281i			0.332649i
$928$	21.8894	−	7.85982i	0.718555	−	0.258011i
$929$	−17.1760			−0.563527			−0.281763	−	0.959484i	$-0.590919\pi$
$929$	−17.1760			−0.563527			−0.281763	+	0.959484i	$0.590919\pi$
$930$	−17.6676	+	46.6737i	−0.579342	+	1.53049i
$931$	−1.59732	+	3.85628i	−0.0523501	+	0.126384i
$932$	21.8981	+	3.90038i	0.717295	+	0.127761i
$933$	−15.9208	−	38.4363i	−0.521225	−	1.25835i
$934$	24.7205	+	29.5127i	0.808881	+	0.965686i
$935$	−9.60114	−	7.55092i	−0.313991	−	0.246941i
$936$	1.00435	−	0.576387i	0.0328284	−	0.0188398i
$937$	10.2273	−	10.2273i	0.334111	−	0.334111i	−0.520035	−	0.854145i	$-0.674081\pi$
$937$	10.2273	−	10.2273i	0.334111	−	0.334111i	0.854145	+	0.520035i	$0.174081\pi$
$938$	−6.35405	−	0.561457i	−0.207467	−	0.0183322i
$939$	−7.44010	−	17.9620i	−0.242799	−	0.586168i
$940$	−24.1232	−	11.6528i	−0.786813	−	0.380072i
$941$	7.59138	+	3.14445i	0.247472	+	0.102506i	0.502972	−	0.864303i	$-0.332240\pi$
$941$	7.59138	+	3.14445i	0.247472	+	0.102506i	−0.255500	+	0.966809i	$0.582240\pi$
$942$	−46.3371	+	14.5659i	−1.50974	+	0.474582i
$943$	36.1820			1.17825
$944$	−1.89146	−	47.0659i	−0.0615618	−	1.53186i
$945$	−2.86902	−	24.0021i	−0.0933292	−	0.780788i
$946$	0.820435	−	0.257901i	0.0266746	−	0.00838507i
$947$	14.7657	−	35.6476i	0.479821	−	1.15839i	−0.479871	−	0.877339i	$-0.659317\pi$
$947$	14.7657	−	35.6476i	0.479821	−	1.15839i	0.959693	−	0.281052i	$-0.0906834\pi$
$948$	34.7679	−	7.64464i	1.12921	−	0.248287i
$949$	4.11931	+	9.94490i	0.133719	+	0.322825i
$950$	−1.36553	−	9.04730i	−0.0443038	−	0.293533i
$951$	−28.8185	−	28.8185i	−0.934505	−	0.934505i
$952$	−24.0435	−	18.5487i	−0.779253	−	0.601168i
$953$	−9.41143	−	9.41143i	−0.304866	−	0.304866i	0.538048	−	0.842914i	$-0.319162\pi$
$953$	−9.41143	−	9.41143i	−0.304866	−	0.304866i	−0.842914	+	0.538048i	$0.819162\pi$
$954$	−1.85762	+	1.55599i	−0.0601426	+	0.0503769i
$955$	−10.9484	+	6.14807i	−0.354282	+	0.198947i
$956$	4.01262	−	2.79931i	0.129777	−	0.0905362i
$957$	−5.85452	−	2.42502i	−0.189250	−	0.0783898i
$958$	−11.2382	+	21.5427i	−0.363088	+	0.696012i
$959$	18.0654			0.583361
$960$	25.9491	−	10.2312i	0.837502	−	0.330211i
$961$	71.4361			2.30439
$962$	−3.52973	+	6.76621i	−0.113803	+	0.218151i
$963$	2.86627	+	1.18725i	0.0923641	+	0.0382585i
$964$	−12.7185	+	8.87277i	−0.409635	+	0.285773i
$965$	12.8451	+	22.8744i	0.413498	+	0.736353i
$966$	13.5053	−	11.3124i	0.434526	−	0.363969i
$967$	−6.51158	−	6.51158i	−0.209398	−	0.209398i	0.594613	−	0.804012i	$-0.297305\pi$
$967$	−6.51158	−	6.51158i	−0.209398	−	0.209398i	−0.804012	+	0.594613i	$0.797305\pi$
$968$	17.3163	−	22.4460i	0.556567	−	0.721440i
$969$	7.88445	+	7.88445i	0.253285	+	0.253285i
$970$	−46.1282	+	1.42279i	−1.48109	+	0.0456829i
$971$	16.4380	+	39.6849i	0.527521	+	1.27355i	0.933142	+	0.359507i	$0.117055\pi$
$971$	16.4380	+	39.6849i	0.527521	+	1.27355i	−0.405621	+	0.914041i	$0.632945\pi$
$972$	11.3769	−	2.50151i	0.364914	−	0.0802360i
$973$	2.29623	−	5.54360i	0.0736139	−	0.177720i
$974$	−4.33444	+	1.36251i	−0.138885	+	0.0436578i
$975$	1.32301	+	5.45504i	0.0423702	+	0.174701i
$976$	−31.7472	−	29.2941i	−1.01620	−	0.937681i
$977$	−43.9377			−1.40569			−0.702845	−	0.711343i	$-0.748087\pi$
$977$	−43.9377			−1.40569			−0.702845	+	0.711343i	$0.748087\pi$
$978$	25.2952	−	7.95144i	0.808851	−	0.254259i
$979$	−6.25101	−	2.58925i	−0.199783	−	0.0827529i
$980$	−6.27474	+	12.9898i	−0.200439	+	0.414943i
$981$	−0.822958	−	1.98680i	−0.0262750	−	0.0634335i
$982$	26.3915	+	2.33202i	0.842188	+	0.0744176i
$983$	−3.47583	+	3.47583i	−0.110862	+	0.110862i	−0.760362	−	0.649500i	$-0.774978\pi$
$983$	−3.47583	+	3.47583i	−0.110862	+	0.110862i	0.649500	+	0.760362i	$0.274978\pi$
$984$	−19.3148	−	33.6560i	−0.615733	−	1.07291i
$985$	−23.0546	−	18.1316i	−0.734582	−	0.577720i
$986$	20.6331	+	24.6329i	0.657091	+	0.784470i
$987$	6.94452	+	16.7655i	0.221046	+	0.533653i
$988$	−1.83438	−	0.326730i	−0.0583593	−	0.0103947i
$989$	0.968168	−	2.33736i	0.0307860	−	0.0743239i
$990$	1.66237	+	0.629262i	0.0528336	+	0.0199993i
$991$	−21.3950			−0.679636			−0.339818	−	0.940491i	$-0.610365\pi$
$991$	−21.3950			−0.679636			−0.339818	+	0.940491i	$0.610365\pi$
$992$	−38.4965	−	42.3789i	−1.22227	−	1.34553i
$993$			1.43098i			0.0454109i
$994$	−8.99829	+	17.2490i	−0.285409	+	0.547106i
$995$	5.15642	−	18.3647i	0.163470	−	0.582199i
$996$	33.8218	+	6.02417i	1.07168	+	0.190883i
$997$	−5.61012	−	13.5440i	−0.177674	−	0.428944i	0.809804	−	0.586701i	$-0.199574\pi$
$997$	−5.61012	−	13.5440i	−0.177674	−	0.428944i	−0.987478	+	0.157757i	$0.949574\pi$
$998$	15.1178	−	12.6631i	0.478547	−	0.400842i
$999$	−29.4914	+	29.4914i	−0.933066	+	0.933066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.z.a.109.9	yes	88
4.3	odd	2		640.2.z.a.529.6		88
5.2	odd	4		800.2.y.f.301.3		88
5.3	odd	4		800.2.y.f.301.20		88
5.4	even	2	inner	160.2.z.a.109.14	yes	88
20.19	odd	2		640.2.z.a.529.17		88
32.5	even	8	inner	160.2.z.a.69.14	yes	88
32.27	odd	8		640.2.z.a.369.17		88
160.37	odd	8		800.2.y.f.101.3		88
160.59	odd	8		640.2.z.a.369.6		88
160.69	even	8	inner	160.2.z.a.69.9	✓	88
160.133	odd	8		800.2.y.f.101.20		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.69.9	✓	88	160.69	even	8	inner
160.2.z.a.69.14	yes	88	32.5	even	8	inner
160.2.z.a.109.9	yes	88	1.1	even	1	trivial
160.2.z.a.109.14	yes	88	5.4	even	2	inner
640.2.z.a.369.6		88	160.59	odd	8
640.2.z.a.369.17		88	32.27	odd	8
640.2.z.a.529.6		88	4.3	odd	2
640.2.z.a.529.17		88	20.19	odd	2
800.2.y.f.101.3		88	160.37	odd	8
800.2.y.f.101.20		88	160.133	odd	8
800.2.y.f.301.3		88	5.2	odd	4
800.2.y.f.301.20		88	5.3	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654098 + 1.25386i) q^{2} +(1.44059 + 0.596710i) q^{3} +(-1.14431 - 1.64029i) q^{4} +(1.94969 - 1.09485i) q^{5} +(-1.69047 + 1.41598i) q^{6} +(1.37373 + 1.37373i) q^{7} +(2.80518 - 0.361890i) q^{8} +(-0.402097 - 0.402097i) q^{9} +(0.0974914 + 3.16077i) q^{10} +(0.378268 + 0.913219i) q^{11} +(-0.669700 - 3.04580i) q^{12} +(-0.275521 + 0.665167i) q^{13} +(-2.62102 + 0.823906i) q^{14} +(3.46201 - 0.413821i) q^{15} +(-1.38111 + 3.75400i) q^{16} -5.52634 q^{17} +(0.767183 - 0.241161i) q^{18} +(-1.19548 - 0.495182i) q^{19} +(-4.02693 - 1.94522i) q^{20} +(1.15926 + 2.79870i) q^{21} +(-1.39247 - 0.123042i) q^{22} +(-2.90780 + 2.90780i) q^{23} +(4.25704 + 1.15255i) q^{24} +(2.60261 - 4.26924i) q^{25} +(-0.653806 - 0.780549i) q^{26} +(-2.12945 - 5.14095i) q^{27} +(0.681342 - 3.82529i) q^{28} +(-1.57338 + 3.79846i) q^{29} +(-1.74562 + 4.61154i) q^{30} +10.1211 q^{31} +(-3.80360 - 4.18720i) q^{32} +1.54129i q^{33} +(3.61477 - 6.92923i) q^{34} +(4.18238 + 1.17433i) q^{35} +(-0.199432 + 1.11968i) q^{36} +(-2.86828 - 6.92465i) q^{37} +(1.40285 - 1.17506i) q^{38} +(-0.793824 + 0.793824i) q^{39} +(5.07303 - 3.77682i) q^{40} +(-6.22154 - 6.22154i) q^{41} +(-4.26743 - 0.377080i) q^{42} +(-0.568391 + 0.235435i) q^{43} +(1.06509 - 1.66547i) q^{44} +(-1.22420 - 0.343731i) q^{45} +(-1.74398 - 5.54795i) q^{46} +5.99048 q^{47} +(-4.22965 + 4.58384i) q^{48} -3.22573i q^{49} +(3.65065 + 6.05580i) q^{50} +(-7.96116 - 3.29762i) q^{51} +(1.40635 - 0.309223i) q^{52} +(-2.78382 + 1.15310i) q^{53} +(7.83888 + 0.692660i) q^{54} +(1.73734 + 1.36635i) q^{55} +(4.35070 + 3.35642i) q^{56} +(-1.42670 - 1.42670i) q^{57} +(-3.73359 - 4.45736i) q^{58} +(-10.8796 + 4.50647i) q^{59} +(-4.64040 - 5.20516i) q^{60} +(-4.13274 + 9.97733i) q^{61} +(-6.62018 + 12.6904i) q^{62} -1.10475i q^{63} +(7.73807 - 2.03033i) q^{64} +(0.191075 + 1.59853i) q^{65} +(-1.93255 - 1.00815i) q^{66} +(2.14498 + 0.888479i) q^{67} +(6.32385 + 9.06480i) q^{68} +(-5.92404 + 2.45382i) q^{69} +(-4.20813 + 4.47598i) q^{70} +(5.00709 - 5.00709i) q^{71} +(-1.27347 - 0.982440i) q^{72} +(10.5719 - 10.5719i) q^{73} +(10.5587 + 0.932986i) q^{74} +(6.29678 - 4.59720i) q^{75} +(0.555753 + 2.52757i) q^{76} +(-0.734879 + 1.77415i) q^{77} +(-0.476102 - 1.51458i) q^{78} +11.4150i q^{79} +(1.41733 + 8.83126i) q^{80} -6.97068i q^{81} +(11.8704 - 3.73142i) q^{82} +(-4.21565 + 10.1775i) q^{83} +(3.26412 - 5.10410i) q^{84} +(-10.7747 + 6.05051i) q^{85} +(0.0765816 - 0.866678i) q^{86} +(-4.53316 + 4.53316i) q^{87} +(1.39159 + 2.42485i) q^{88} +(-4.84017 + 4.84017i) q^{89} +(1.23174 - 1.31014i) q^{90} +(-1.29225 + 0.535269i) q^{91} +(8.09706 + 1.44221i) q^{92} +(14.5803 + 6.03935i) q^{93} +(-3.91837 + 7.51121i) q^{94} +(-2.87296 + 0.343411i) q^{95} +(-2.98087 - 8.30166i) q^{96} +14.5940i q^{97} +(4.04460 + 2.10994i) q^{98} +(0.215102 - 0.519303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34}+ \cdots - 48 q^{99}+O(q^{100}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Introduction

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