LMFDB - Embedded newform 560.2.cp.a.501.46

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(221,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.221"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			501.46
Character	$\chi$	$=$	560.501
Dual form			560.2.cp.a.541.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.821747 + 1.15097i) q^{2} +(-0.559657 - 2.08867i) q^{3} +(-0.649464 + 1.89161i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(1.94410 - 2.36050i) q^{6} +(-2.29347 - 1.31908i) q^{7} +(-2.71088 + 0.806912i) q^{8} +(-1.45124 + 0.837872i) q^{9} +(-1.32444 + 0.495854i) q^{10} +(5.37294 - 1.43967i) q^{11} +(4.31442 + 0.297861i) q^{12} +(4.14901 - 4.14901i) q^{13} +(-0.366427 - 3.72367i) q^{14} +2.16235 q^{15} +(-3.15639 - 2.45707i) q^{16} +(0.489834 - 0.848418i) q^{17} +(-2.15692 - 0.981812i) q^{18} +(3.89965 + 1.04491i) q^{19} +(-1.65906 - 1.11692i) q^{20} +(-1.47157 + 5.52853i) q^{21} +(6.07221 + 5.00104i) q^{22} +(4.22416 - 2.43882i) q^{23} +(3.20253 + 5.21054i) q^{24} +(-0.866025 - 0.500000i) q^{25} +(8.18483 + 1.36595i) q^{26} +(-2.02480 - 2.02480i) q^{27} +(3.98473 - 3.48166i) q^{28} +(-7.28641 + 7.28641i) q^{29} +(1.77690 + 2.48880i) q^{30} +(4.25600 - 7.37160i) q^{31} +(0.234258 - 5.65200i) q^{32} +(-6.01400 - 10.4165i) q^{33} +(1.37902 - 0.133400i) q^{34} +(1.86773 - 1.87392i) q^{35} +(-0.642402 - 3.28935i) q^{36} +(-0.498557 + 1.86064i) q^{37} +(2.00187 + 5.34702i) q^{38} +(-10.9879 - 6.34388i) q^{39} +(-0.0777889 - 2.82736i) q^{40} +0.00229279i q^{41} +(-7.57244 + 2.84932i) q^{42} +(-3.71185 - 3.71185i) q^{43} +(-0.766226 + 11.0985i) q^{44} +(-0.433715 - 1.61864i) q^{45} +(6.27820 + 2.85779i) q^{46} +(0.793555 + 1.37448i) q^{47} +(-3.36550 + 7.96777i) q^{48} +(3.52003 + 6.05057i) q^{49} +(-0.136169 - 1.40764i) q^{50} +(-2.04620 - 0.548278i) q^{51} +(5.15369 + 10.5430i) q^{52} +(-6.86340 + 1.83904i) q^{53} +(0.666611 - 3.99436i) q^{54} +5.56247i q^{55} +(7.28172 + 1.72526i) q^{56} -8.72985i q^{57} +(-14.3740 - 2.39886i) q^{58} +(7.88705 - 2.11333i) q^{59} +(-1.40437 + 4.09032i) q^{60} +(-3.69584 - 0.990298i) q^{61} +(11.9818 - 1.15907i) q^{62} +(4.43360 - 0.00733180i) q^{63} +(6.69779 - 4.37489i) q^{64} +(2.93380 + 5.08148i) q^{65} +(7.04715 - 15.4817i) q^{66} +(0.634479 + 2.36791i) q^{67} +(1.28675 + 1.47759i) q^{68} +(-7.45796 - 7.45796i) q^{69} +(3.69163 + 0.609816i) q^{70} +14.4957i q^{71} +(3.25805 - 3.44240i) q^{72} +(6.53559 + 3.77332i) q^{73} +(-2.55123 + 0.955150i) q^{74} +(-0.559657 + 2.08867i) q^{75} +(-4.50924 + 6.69799i) q^{76} +(-14.2217 - 3.78551i) q^{77} +(-1.72768 - 17.8598i) q^{78} +(-4.91056 - 8.50534i) q^{79} +(3.19028 - 2.41290i) q^{80} +(-5.60956 + 9.71604i) q^{81} +(-0.00263893 + 0.00188409i) q^{82} +(0.0507297 - 0.0507297i) q^{83} +(-9.50211 - 6.37423i) q^{84} +(0.692730 + 0.692730i) q^{85} +(1.22203 - 7.32244i) q^{86} +(19.2968 + 11.1410i) q^{87} +(-13.4037 + 8.23828i) q^{88} +(7.78910 - 4.49704i) q^{89} +(1.50661 - 1.82931i) q^{90} +(-14.9885 + 4.04275i) q^{91} +(1.86986 + 9.57440i) q^{92} +(-17.7787 - 4.76379i) q^{93} +(-0.929882 + 2.04283i) q^{94} +(-2.01861 + 3.49633i) q^{95} +(-11.9363 + 2.67389i) q^{96} -4.00212 q^{97} +(-4.07145 + 9.02349i) q^{98} +(-6.59114 + 6.59114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.821747	+	1.15097i	0.581063	+	0.813859i
$2$	0.821747	+	1.15097i	0.581063	+	0.813859i
$3$	−0.559657	−	2.08867i	−0.323118	−	1.20589i	−0.916190	−	0.400743i	$-0.868752\pi$
$3$	−0.559657	−	2.08867i	−0.323118	−	1.20589i	0.593073	−	0.805149i	$-0.297915\pi$
$4$	−0.649464	+	1.89161i	−0.324732	+	0.945806i
$5$	−0.258819	+	0.965926i	−0.115747	+	0.431975i
$5$	−0.258819	+	0.965926i	−0.115747	+	0.431975i
$6$	1.94410	−	2.36050i	0.793674	−	0.963671i
$7$	−2.29347	−	1.31908i	−0.866851	−	0.498567i
$7$	−2.29347	−	1.31908i	−0.866851	−	0.498567i
$8$	−2.71088	+	0.806912i	−0.958442	+	0.285287i
$9$	−1.45124	+	0.837872i	−0.483746	+	0.279291i
$10$	−1.32444	+	0.495854i	−0.418823	+	0.156803i
$11$	5.37294	−	1.43967i	1.62000	−	0.434078i	0.668999	−	0.743263i	$-0.266723\pi$
$11$	5.37294	−	1.43967i	1.62000	−	0.434078i	0.951002	+	0.309185i	$0.100056\pi$
$12$	4.31442	+	0.297861i	1.24547	+	0.0859852i
$13$	4.14901	−	4.14901i	1.15073	−	1.15073i	0.164323	−	0.986407i	$-0.447456\pi$
$13$	4.14901	−	4.14901i	1.15073	−	1.15073i	0.986407	−	0.164323i	$-0.0525438\pi$
$14$	−0.366427	−	3.72367i	−0.0979316	−	0.995193i
$15$	2.16235			0.558316
$16$	−3.15639	−	2.45707i	−0.789098	−	0.614267i
$17$	0.489834	−	0.848418i	0.118802	−	0.205772i	−0.800491	−	0.599345i	$-0.795428\pi$
$17$	0.489834	−	0.848418i	0.118802	−	0.205772i	0.919293	+	0.393573i	$0.128761\pi$
$18$	−2.15692	−	0.981812i	−0.508390	−	0.231415i
$19$	3.89965	+	1.04491i	0.894640	+	0.239718i	0.676713	−	0.736247i	$-0.263404\pi$
$19$	3.89965	+	1.04491i	0.894640	+	0.239718i	0.217927	+	0.975965i	$0.430070\pi$
$20$	−1.65906	−	1.11692i	−0.370978	−	0.249751i
$21$	−1.47157	+	5.52853i	−0.321123	+	1.20643i
$22$	6.07221	+	5.00104i	1.29460	+	1.06623i
$23$	4.22416	−	2.43882i	0.880798	−	0.508529i	0.00987662	−	0.999951i	$-0.496856\pi$
$23$	4.22416	−	2.43882i	0.880798	−	0.508529i	0.870921	+	0.491422i	$0.163523\pi$
$24$	3.20253	+	5.21054i	0.653715	+	1.06360i
$25$	−0.866025	−	0.500000i	−0.173205	−	0.100000i
$26$	8.18483	+	1.36595i	1.60518	+	0.267885i
$27$	−2.02480	−	2.02480i	−0.389673	−	0.389673i
$28$	3.98473	−	3.48166i	0.753042	−	0.657972i
$29$	−7.28641	+	7.28641i	−1.35305	+	1.35305i	−0.470828	+	0.882225i	$0.656045\pi$
$29$	−7.28641	+	7.28641i	−1.35305	+	1.35305i	−0.882225	+	0.470828i	$0.843955\pi$
$30$	1.77690	+	2.48880i	0.324416	+	0.454390i
$31$	4.25600	−	7.37160i	0.764399	−	1.32398i	−0.176164	−	0.984361i	$-0.556369\pi$
$31$	4.25600	−	7.37160i	0.764399	−	1.32398i	0.940564	−	0.339618i	$-0.110298\pi$
$32$	0.234258	−	5.65200i	0.0414113	−	0.999142i
$33$	−6.01400	−	10.4165i	−1.04690	−	1.81329i
$34$	1.37902	−	0.133400i	0.236501	−	0.0228779i
$35$	1.86773	−	1.87392i	0.315704	−	0.316750i
$36$	−0.642402	−	3.28935i	−0.107067	−	0.548224i
$37$	−0.498557	+	1.86064i	−0.0819622	+	0.305887i	−0.994722	−	0.102610i	$-0.967281\pi$
$37$	−0.498557	+	1.86064i	−0.0819622	+	0.305887i	0.912759	+	0.408498i	$0.133947\pi$
$38$	2.00187	+	5.34702i	0.324745	+	0.867402i
$39$	−10.9879	−	6.34388i	−1.75948	−	1.01583i
$40$	−0.0777889	−	2.82736i	−0.0122995	−	0.447044i
$41$			0.00229279i			0.000358073i	1.00000		0.000179037i	$5.69891e-5\pi$
$41$			0.00229279i			0.000358073i	−1.00000		0.000179037i	$0.999943\pi$
$42$	−7.57244	+	2.84932i	−1.16845	+	0.439660i
$43$	−3.71185	−	3.71185i	−0.566052	−	0.566052i	0.364968	−	0.931020i	$-0.381080\pi$
$43$	−3.71185	−	3.71185i	−0.566052	−	0.566052i	−0.931020	+	0.364968i	$0.881080\pi$
$44$	−0.766226	+	11.0985i	−0.115513	+	1.67317i
$45$	−0.433715	−	1.61864i	−0.0646543	−	0.241293i
$46$	6.27820	+	2.85779i	0.925670	+	0.421358i
$47$	0.793555	+	1.37448i	0.115752	+	0.200488i	0.918080	−	0.396395i	$-0.129739\pi$
$47$	0.793555	+	1.37448i	0.115752	+	0.200488i	−0.802328	+	0.596883i	$0.796406\pi$
$48$	−3.36550	+	7.96777i	−0.485768	+	1.15005i
$49$	3.52003	+	6.05057i	0.502862	+	0.864367i
$50$	−0.136169	−	1.40764i	−0.0192571	−	0.199071i
$51$	−2.04620	−	0.548278i	−0.286526	−	0.0767743i
$52$	5.15369	+	10.5430i	0.714688	+	1.46205i
$53$	−6.86340	+	1.83904i	−0.942761	+	0.252612i	−0.697288	−	0.716791i	$-0.745610\pi$
$53$	−6.86340	+	1.83904i	−0.942761	+	0.252612i	−0.245473	+	0.969403i	$0.578943\pi$
$54$	0.666611	−	3.99436i	0.0907143	−	0.543563i
$55$			5.56247i			0.750044i
$56$	7.28172	+	1.72526i	0.973061	+	0.230547i
$57$		−	8.72985i		−	1.15630i
$58$	−14.3740	−	2.39886i	−1.88740	−	0.314985i
$59$	7.88705	−	2.11333i	1.02681	−	0.275132i	0.294171	−	0.955753i	$-0.404956\pi$
$59$	7.88705	−	2.11333i	1.02681	−	0.275132i	0.732636	+	0.680621i	$0.238290\pi$
$60$	−1.40437	+	4.09032i	−0.181303	+	0.528058i
$61$	−3.69584	−	0.990298i	−0.473204	−	0.126795i	0.0143324	−	0.999897i	$-0.495438\pi$
$61$	−3.69584	−	0.990298i	−0.473204	−	0.126795i	−0.487536	+	0.873103i	$0.662104\pi$
$62$	11.9818	−	1.15907i	1.52170	−	0.147202i
$63$	4.43360	−	0.00733180i	0.558581	−	0.000923720i
$64$	6.69779	−	4.37489i	0.837223	−	0.546861i
$65$	2.93380	+	5.08148i	0.363893	+	0.630280i
$66$	7.04715	−	15.4817i	0.867445	−	1.90567i
$67$	0.634479	+	2.36791i	0.0775139	+	0.289286i	0.993792	−	0.111258i	$-0.0354879\pi$
$67$	0.634479	+	2.36791i	0.0775139	+	0.289286i	−0.916278	+	0.400544i	$0.868821\pi$
$68$	1.28675	+	1.47759i	0.156041	+	0.179185i
$69$	−7.45796	−	7.45796i	−0.897833	−	0.897833i
$70$	3.69163	+	0.609816i	0.441234	+	0.0728870i
$71$			14.4957i			1.72033i	0.510017	+	0.860164i	$0.329639\pi$
$71$			14.4957i			1.72033i	−0.510017	+	0.860164i	$0.670361\pi$
$72$	3.25805	−	3.44240i	0.383964	−	0.405690i
$73$	6.53559	+	3.77332i	0.764933	+	0.441634i	0.831064	−	0.556177i	$-0.187732\pi$
$73$	6.53559	+	3.77332i	0.764933	+	0.441634i	−0.0661312	+	0.997811i	$0.521066\pi$
$74$	−2.55123	+	0.955150i	−0.296574	+	0.111034i
$75$	−0.559657	+	2.08867i	−0.0646236	+	0.241178i
$76$	−4.50924	+	6.69799i	−0.517245	+	0.768312i
$77$	−14.2217	−	3.78551i	−1.62072	−	0.431398i
$78$	−1.72768	−	17.8598i	−0.195621	−	2.02223i
$79$	−4.91056	−	8.50534i	−0.552481	−	0.956925i	−0.998095	−	0.0616999i	$-0.980348\pi$
$79$	−4.91056	−	8.50534i	−0.552481	−	0.956925i	0.445614	−	0.895225i	$-0.352986\pi$
$80$	3.19028	−	2.41290i	0.356684	−	0.269771i
$81$	−5.60956	+	9.71604i	−0.623284	+	1.07956i
$82$	−0.00263893	+	0.00188409i	−0.000291421	+	0.000208063i
$83$	0.0507297	−	0.0507297i	0.00556831	−	0.00556831i	−0.704317	−	0.709885i	$-0.748747\pi$
$83$	0.0507297	−	0.0507297i	0.00556831	−	0.00556831i	0.709885	+	0.704317i	$0.248747\pi$
$84$	−9.50211	−	6.37423i	−1.03676	−	0.695485i
$85$	0.692730	+	0.692730i	0.0751372	+	0.0751372i
$86$	1.22203	−	7.32244i	0.131775	−	0.789599i
$87$	19.2968	+	11.1410i	2.06883	+	1.19444i
$88$	−13.4037	+	8.23828i	−1.42884	+	0.878203i
$89$	7.78910	−	4.49704i	0.825642	−	0.476685i	−0.0267159	−	0.999643i	$-0.508505\pi$
$89$	7.78910	−	4.49704i	0.825642	−	0.476685i	0.852358	+	0.522958i	$0.175172\pi$
$90$	1.50661	−	1.82931i	0.158810	−	0.192826i
$91$	−14.9885	+	4.04275i	−1.57123	+	0.423795i
$92$	1.86986	+	9.57440i	0.194946	+	0.998200i
$93$	−17.7787	−	4.76379i	−1.84357	−	0.493982i
$94$	−0.929882	+	2.04283i	−0.0959100	+	0.210702i
$95$	−2.01861	+	3.49633i	−0.207105	+	0.358716i
$96$	−11.9363	+	2.67389i	−1.21824	+	0.272903i
$97$	−4.00212			−0.406354			−0.203177	−	0.979142i	$-0.565127\pi$
$97$	−4.00212			−0.406354			−0.203177	+	0.979142i	$0.565127\pi$
$98$	−4.07145	+	9.02349i	−0.411279	+	0.911510i
$99$	−6.59114	+	6.59114i	−0.662435	+	0.662435i
$100$	1.50826	−	1.31345i	0.150826	−	0.131345i
$101$	−6.96314	+	1.86577i	−0.692858	+	0.185651i	−0.588029	−	0.808840i	$-0.700096\pi$
$101$	−6.96314	+	1.86577i	−0.692858	+	0.185651i	−0.104829	+	0.994490i	$0.533429\pi$
$102$	−1.05041	−	2.80566i	−0.104006	−	0.277802i
$103$	−13.5257	+	7.80905i	−1.33272	+	0.769448i	−0.985716	−	0.168414i	$-0.946135\pi$
$103$	−13.5257	+	7.80905i	−1.33272	+	0.769448i	−0.347007	+	0.937863i	$0.612802\pi$
$104$	−7.89960	+	14.5954i	−0.774620	+	1.43120i
$105$	−4.95928	−	2.85232i	−0.483976	−	0.278358i
$106$	−7.75666	−	6.38834i	−0.753394	−	0.620491i
$107$	1.14139	−	4.25971i	0.110342	−	0.411802i	−0.888554	−	0.458772i	$-0.848290\pi$
$107$	1.14139	−	4.25971i	0.110342	−	0.411802i	0.998896	+	0.0469694i	$0.0149563\pi$
$108$	5.14517	−	2.51510i	0.495094	−	0.242016i
$109$	1.51680	+	5.66078i	0.145283	+	0.542204i	0.999743	+	0.0226862i	$0.00722186\pi$
$109$	1.51680	+	5.66078i	0.145283	+	0.542204i	−0.854459	+	0.519518i	$0.826111\pi$
$110$	−6.40224	+	4.57094i	−0.610429	+	0.435822i
$111$	4.16528			0.395351
$112$	3.99802	+	9.79877i	0.377777	+	0.925897i
$113$	18.1951			1.71165			0.855824	−	0.517266i	$-0.173050\pi$
$113$	18.1951			1.71165			0.855824	+	0.517266i	$0.173050\pi$
$114$	10.0478	−	7.17373i	0.941062	−	0.671881i
$115$	1.26243	+	4.71144i	0.117722	+	0.439344i
$116$	−9.05080	−	18.5153i	−0.840346	−	1.71911i
$117$	−2.54486	+	9.49755i	−0.235272	+	0.878048i
$118$	8.91354	+	7.34114i	0.820558	+	0.675807i
$119$	−2.24256	+	1.29969i	−0.205575	+	0.119142i
$120$	−5.86187	+	1.74482i	−0.535113	+	0.159280i
$121$	17.2695	−	9.97055i	1.56995	−	0.906413i
$122$	−1.89724	−	5.06758i	−0.171768	−	0.458797i
$123$	0.00478887	−	0.00128317i	0.000431797	−	0.000115700i
$124$	11.1801	+	12.8383i	1.00400	+	1.15291i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	3.65173	+	5.09691i	0.325322	+	0.454069i
$127$	2.19170			0.194482			0.0972410	−	0.995261i	$-0.468998\pi$
$127$	2.19170			0.194482			0.0972410	+	0.995261i	$0.468998\pi$
$128$	10.5393	+	4.11390i	0.931547	+	0.363621i
$129$	−5.67546	+	9.83019i	−0.499697	+	0.865500i
$130$	−3.43780	+	7.55240i	−0.301515	+	0.662390i
$131$	−10.4607	−	2.80294i	−0.913956	−	0.244894i	−0.228956	−	0.973437i	$-0.573531\pi$
$131$	−10.4607	−	2.80294i	−0.913956	−	0.244894i	−0.685000	+	0.728543i	$0.740198\pi$
$132$	23.6099	−	4.61097i	2.05498	−	0.401334i
$133$	−7.56541	−	7.54043i	−0.656004	−	0.653838i
$134$	−2.20401	+	2.67609i	−0.190397	+	0.231179i
$135$	2.47986	−	1.43175i	0.213433	−	0.123225i
$136$	−0.643285	+	2.69522i	−0.0551613	+	0.231113i
$137$	−4.12267	−	2.38022i	−0.352223	−	0.203356i	0.313441	−	0.949608i	$-0.398518\pi$
$137$	−4.12267	−	2.38022i	−0.352223	−	0.203356i	−0.665664	+	0.746252i	$0.731852\pi$
$138$	2.45533	−	14.7124i	0.209012	−	1.25241i
$139$	4.75866	+	4.75866i	0.403625	+	0.403625i	0.879508	−	0.475884i	$-0.157872\pi$
$139$	4.75866	+	4.75866i	0.403625	+	0.403625i	−0.475884	+	0.879508i	$0.657872\pi$
$140$	2.33170	+	4.75007i	0.197065	+	0.401454i
$141$	2.42671	−	2.42671i	0.204366	−	0.204366i
$142$	−16.6842	+	11.9118i	−1.40010	+	0.999619i
$143$	16.3192	−	28.2656i	1.36468	−	2.36369i
$144$	6.63938	+	0.921137i	0.553282	+	0.0767614i
$145$	−5.15227	−	8.92400i	−0.427873	−	0.741098i
$146$	1.02762	+	10.6230i	0.0850461	+	0.879165i
$147$	10.6676	−	10.7384i	0.879850	−	0.885689i
$148$	−3.19581	−	2.15149i	−0.262694	−	0.176852i
$149$	−1.77707	+	6.63213i	−0.145584	+	0.543326i	0.854145	+	0.520035i	$0.174081\pi$
$149$	−1.77707	+	6.63213i	−0.145584	+	0.543326i	−0.999729	+	0.0232908i	$0.992586\pi$
$150$	−2.86389	+	1.07221i	−0.233836	+	0.0875454i
$151$	1.76089	+	1.01665i	0.143300	+	0.0827340i	0.569936	−	0.821689i	$-0.306968\pi$
$151$	1.76089	+	1.01665i	0.143300	+	0.0827340i	−0.426636	+	0.904423i	$0.640301\pi$
$152$	−11.4146	+	0.314050i	−0.925849	+	0.0254728i
$153$			1.64167i			0.132721i
$154$	−7.32966	−	19.4795i	−0.590641	−	1.56970i
$155$	6.01889	+	6.01889i	0.483449	+	0.483449i
$156$	19.1364	−	16.6648i	1.53214	−	1.33425i
$157$	3.00871	+	11.2287i	0.240121	+	0.896145i	0.975773	+	0.218785i	$0.0702094\pi$
$157$	3.00871	+	11.2287i	0.240121	+	0.896145i	−0.735652	+	0.677360i	$0.763124\pi$
$158$	5.75415	−	12.6411i	0.457776	−	1.00568i
$159$	7.68230	+	13.3061i	0.609246	+	1.05524i
$160$	5.39878	+	1.68912i	0.426811	+	0.133537i
$161$	−12.9050	+	0.0213409i	−1.01706	+	0.00168190i
$162$	−15.7925	+	1.52769i	−1.24078	+	0.120027i
$163$	−12.2253	−	3.27577i	−0.957562	−	0.256578i	−0.253994	−	0.967206i	$-0.581744\pi$
$163$	−12.2253	−	3.27577i	−0.957562	−	0.256578i	−0.703568	+	0.710628i	$0.748411\pi$
$164$	−0.00433706	−	0.00148908i	−0.000338668	−	0.000116278i
$165$	11.6181	−	3.11307i	0.904472	−	0.242352i
$166$	0.100075	+	0.0167014i	0.00776736	+	0.00129628i
$167$		−	18.0603i		−	1.39755i	−0.715341	−	0.698776i	$-0.753729\pi$
$167$		−	18.0603i		−	1.39755i	0.715341	−	0.698776i	$-0.246271\pi$
$168$	−0.471781	−	16.1746i	−0.0363987	−	1.24790i
$169$		−	21.4286i		−	1.64836i
$170$	−0.228063	+	1.36656i	−0.0174916	+	0.104810i
$171$	−6.53481	+	1.75100i	−0.499729	+	0.133902i
$172$	9.43210	−	4.61067i	0.719191	−	0.351560i
$173$	−1.00509	−	0.269313i	−0.0764157	−	0.0204755i	0.220409	−	0.975408i	$-0.429261\pi$
$173$	−1.00509	−	0.269313i	−0.0764157	−	0.0204755i	−0.296824	+	0.954932i	$0.595928\pi$
$174$	3.03411	+	31.3651i	0.230015	+	2.37778i
$175$	1.32666	+	2.28910i	0.100286	+	0.173039i
$176$	−20.4965	−	8.65750i	−1.54498	−	0.652583i
$177$	−8.82808	−	15.2907i	−0.663559	−	1.14932i
$178$	11.5766	+	5.26959i	0.867704	+	0.394973i
$179$	2.23790	+	8.35197i	0.167269	+	0.624256i	0.997740	+	0.0671940i	$0.0214046\pi$
$179$	2.23790	+	8.35197i	0.167269	+	0.624256i	−0.830471	+	0.557062i	$0.811929\pi$
$180$	3.34353	+	0.230832i	0.249212	+	0.0172052i
$181$	−5.90851	−	5.90851i	−0.439176	−	0.439176i	0.452558	−	0.891735i	$-0.350511\pi$
$181$	−5.90851	−	5.90851i	−0.439176	−	0.439176i	−0.891735	+	0.452558i	$0.850511\pi$
$182$	−16.9699	−	13.9293i	−1.25789	−	1.03251i
$183$			8.27361i			0.611603i
$184$	−9.48329	+	10.0199i	−0.699118	+	0.738676i
$185$	−1.66820	−	0.963138i	−0.122649	−	0.0708113i
$186$	−9.12662	−	24.3774i	−0.669196	−	1.78744i
$187$	1.41040	−	5.26370i	0.103139	−	0.384920i
$188$	−3.11537	+	0.608424i	−0.227211	+	0.0443739i
$189$	1.97294	+	7.31471i	0.143510	+	0.532067i
$190$	−5.68295	+	0.549741i	−0.412285	+	0.0398824i
$191$	11.7486	+	20.3492i	0.850102	+	1.47242i	0.881116	+	0.472901i	$0.156793\pi$
$191$	11.7486	+	20.3492i	0.850102	+	1.47242i	−0.0310140	+	0.999519i	$0.509874\pi$
$192$	−12.8861	−	11.5410i	−0.929978	−	0.832900i
$193$	−2.31055	+	4.00198i	−0.166317	+	0.288069i	−0.937122	−	0.349002i	$-0.886521\pi$
$193$	−2.31055	+	4.00198i	−0.166317	+	0.288069i	0.770805	+	0.637071i	$0.219854\pi$
$194$	−3.28873	−	4.60632i	−0.236117	−	0.330715i
$195$	8.97161	−	8.97161i	0.642470	−	0.642470i
$196$	−13.7315	+	2.72890i	−0.980819	+	0.194922i
$197$	3.33197	+	3.33197i	0.237393	+	0.237393i	0.815770	−	0.578377i	$-0.196314\pi$
$197$	3.33197	+	3.33197i	0.237393	+	0.237393i	−0.578377	+	0.815770i	$0.696314\pi$
$198$	−13.0025	−	2.16996i	−0.924044	−	0.154212i
$199$	−19.2764	−	11.1293i	−1.36647	−	0.788932i	−0.375995	−	0.926622i	$-0.622699\pi$
$199$	−19.2764	−	11.1293i	−1.36647	−	0.788932i	−0.990475	+	0.137690i	$0.956032\pi$
$200$	2.75115	+	0.656636i	0.194536	+	0.0464311i
$201$	4.59068	−	2.65043i	0.323802	−	0.186947i
$202$	−7.86938	−	6.48117i	−0.553687	−	0.456014i
$203$	26.3226	−	7.09979i	1.84748	−	0.498308i
$204$	2.36606	−	3.51453i	0.165658	−	0.246066i
$205$	−0.00221466		0.000593417i	−0.000154679		4.14460e-5i
$206$	−20.1026	−	9.15058i	−1.40062	−	0.637551i
$207$	−4.08684	+	7.07861i	−0.284055	+	0.491997i
$208$	−23.2903	+	2.90150i	−1.61489	+	0.201183i
$209$	22.4569			1.55337
$210$	−0.792341	−	8.05187i	−0.0546767	−	0.555632i
$211$	−14.5010	+	14.5010i	−0.998292	+	0.998292i	−0.999999	−	0.00170639i	$-0.999457\pi$
$211$	−14.5010	+	14.5010i	−0.998292	+	0.998292i	0.00170639	+	0.999999i	$0.499457\pi$
$212$	0.978779	−	14.1773i	0.0672228	−	0.973700i
$213$	30.2768	−	8.11264i	2.07453	−	0.555869i
$214$	5.84074	−	2.18670i	0.399264	−	0.149480i
$215$	4.54607	−	2.62468i	0.310040	−	0.179001i
$216$	7.12284	+	3.85516i	0.484648	+	0.262311i
$217$	−19.4848	+	11.2925i	−1.32271	+	0.766588i
$218$	−5.26896	+	6.39752i	−0.356859	+	0.433295i
$219$	4.22353	−	15.7624i	0.285400	−	1.06513i
$220$	−10.5220	−	3.61263i	−0.709396	−	0.243563i
$221$	−1.48777	−	5.55243i	−0.100078	−	0.373497i
$222$	3.42280	+	4.79411i	0.229723	+	0.321759i
$223$	15.9510			1.06816			0.534080	−	0.845434i	$-0.320658\pi$
$223$	15.9510			1.06816			0.534080	+	0.845434i	$0.320658\pi$
$224$	−7.99273	+	12.6537i	−0.534037	+	0.845461i
$225$	1.67574			0.111716
$226$	14.9517	+	20.9420i	0.994575	+	1.39304i
$227$	3.36241	+	12.5487i	0.223171	+	0.832885i	0.983129	+	0.182913i	$0.0585527\pi$
$227$	3.36241	+	12.5487i	0.223171	+	0.832885i	−0.759958	+	0.649972i	$0.774781\pi$
$228$	16.5135	+	5.66973i	1.09363	+	0.375487i
$229$	−0.978844	+	3.65309i	−0.0646838	+	0.241403i	−0.990697	−	0.136089i	$-0.956547\pi$
$229$	−0.978844	+	3.65309i	−0.0646838	+	0.241403i	0.926013	+	0.377492i	$0.123213\pi$
$230$	−4.38533	+	5.32462i	−0.289160	+	0.351095i
$231$	0.0526255	+	31.8230i	0.00346250	+	2.09380i
$232$	13.8731	−	25.6321i	0.910815	−	1.68283i
$233$	20.0996	−	11.6045i	1.31677	−	0.760237i	0.333562	−	0.942728i	$-0.391749\pi$
$233$	20.0996	−	11.6045i	1.31677	−	0.760237i	0.983208	+	0.182491i	$0.0584160\pi$
$234$	−13.0226	+	4.87552i	−0.851315	+	0.318723i
$235$	−1.53303	+	0.410774i	−0.100004	+	0.0267960i
$236$	−1.12476	+	16.2918i	−0.0732156	+	1.06050i
$237$	−15.0166	+	15.0166i	−0.975432	+	0.975432i
$238$	−3.33872	−	1.51310i	−0.216417	−	0.0980797i
$239$	7.75884			0.501878			0.250939	−	0.968003i	$-0.419261\pi$
$239$	7.75884			0.501878			0.250939	+	0.968003i	$0.419261\pi$
$240$	−6.82522	−	5.31304i	−0.440566	−	0.342955i
$241$	−2.99642	+	5.18995i	−0.193016	+	0.334314i	−0.946248	−	0.323441i	$-0.895160\pi$
$241$	−2.99642	+	5.18995i	−0.193016	+	0.334314i	0.753232	+	0.657755i	$0.228494\pi$
$242$	25.6670	+	11.6834i	1.64993	+	0.751038i
$243$	15.1352	+	4.05547i	0.970924	+	0.260158i
$244$	4.27358	−	6.34793i	0.273588	−	0.406385i
$245$	−6.75545	+	1.83409i	−0.431590	+	0.117175i
$246$	0.00541213	+	0.00445740i	0.000345065	+	0.000284193i
$247$	20.5150	−	11.8443i	1.30534	−	0.753638i
$248$	−5.58928	+	23.4178i	−0.354919	+	1.48703i
$249$	−0.134349	−	0.0775663i	−0.00851401	−	0.00491556i
$250$	1.39492	+	0.232796i	0.0882226	+	0.0147233i
$251$	−5.43145	−	5.43145i	−0.342830	−	0.342830i	0.514600	−	0.857430i	$-0.327940\pi$
$251$	−5.43145	−	5.43145i	−0.342830	−	0.342830i	−0.857430	+	0.514600i	$0.827940\pi$
$252$	−2.86559	+	8.39141i	−0.180515	+	0.528609i
$253$	19.1850	−	19.1850i	1.20615	−	1.20615i
$254$	1.80102	+	2.52258i	0.113006	+	0.158281i
$255$	1.05919	−	1.83457i	0.0663292	−	0.114885i
$256$	3.92562	+	15.5109i	0.245352	+	0.969434i
$257$	1.05716	+	1.83106i	0.0659439	+	0.114218i	0.897112	−	0.441803i	$-0.145661\pi$
$257$	1.05716	+	1.83106i	0.0659439	+	0.114218i	−0.831168	+	0.556021i	$0.812328\pi$
$258$	−15.9780	+	1.54564i	−0.994750	+	0.0962273i
$259$	3.59777	−	3.60969i	0.223554	−	0.224295i
$260$	−11.5176	+	2.24936i	−0.714291	+	0.139499i
$261$	4.46923	−	16.6794i	0.276638	−	1.03243i
$262$	−5.36995	−	14.3433i	−0.331757	−	0.886129i
$263$	6.95771	+	4.01704i	0.429031	+	0.247701i	0.698934	−	0.715186i	$-0.253658\pi$
$263$	6.95771	+	4.01704i	0.429031	+	0.247701i	−0.269903	+	0.962888i	$0.586992\pi$
$264$	24.7085	+	23.3853i	1.52070	+	1.43926i
$265$		−	7.10552i		−	0.436488i
$266$	2.46196	−	14.9039i	0.150952	−	0.913816i
$267$	−13.7520	−	13.7520i	−0.841611	−	0.841611i
$268$	−4.89123	−	0.337683i	−0.298780	−	0.0206273i
$269$	7.59396	+	28.3411i	0.463012	+	1.72798i	0.663397	+	0.748267i	$0.269114\pi$
$269$	7.59396	+	28.3411i	0.463012	+	1.72798i	−0.200385	+	0.979717i	$0.564219\pi$
$270$	3.68572	+	1.67771i	0.224306	+	0.102102i
$271$	3.96790	+	6.87261i	0.241033	+	0.417481i	0.961009	−	0.276518i	$-0.0891804\pi$
$271$	3.96790	+	6.87261i	0.241033	+	0.417481i	−0.719976	+	0.693999i	$0.755847\pi$
$272$	−3.63073	+	1.47438i	−0.220145	+	0.0893976i
$273$	16.8324	+	29.0435i	1.01874	+	1.75779i
$274$	−0.648223	−	6.70101i	−0.0391606	−	0.404823i
$275$	−5.37294	−	1.43967i	−0.324000	−	0.0868156i
$276$	18.9512	−	9.26389i	1.14073	−	0.557621i
$277$	−27.1205	+	7.26691i	−1.62951	+	0.436627i	−0.953776	−	0.300517i	$-0.902841\pi$
$277$	−27.1205	+	7.26691i	−1.62951	+	0.436627i	−0.675736	+	0.737144i	$0.736174\pi$
$278$	−1.56666	+	9.38749i	−0.0939622	+	0.563025i
$279$			14.2639i			0.853959i
$280$	−3.55112	+	6.58708i	−0.212220	+	0.393653i
$281$		−	11.8315i		−	0.705810i	−0.935659	−	0.352905i	$-0.885194\pi$
$281$		−	11.8315i		−	0.705810i	0.935659	−	0.352905i	$-0.114806\pi$
$282$	4.78721	+	0.798929i	0.285074	+	0.0475755i
$283$	−11.5122	+	3.08468i	−0.684328	+	0.183365i	−0.584201	−	0.811609i	$-0.698592\pi$
$283$	−11.5122	+	3.08468i	−0.684328	+	0.183365i	−0.100128	+	0.994975i	$0.531925\pi$
$284$	−27.4203	−	9.41447i	−1.62710	−	0.558646i
$285$	8.43239	+	2.25945i	0.499492	+	0.133838i
$286$	45.9431	−	4.44431i	2.71667	−	0.262798i
$287$	0.00302438	−	0.00525844i	0.000178523	−	0.000310396i
$288$	4.39569	+	8.39867i	0.259019	+	0.494897i
$289$	8.02012	+	13.8913i	0.471772	+	0.817133i
$290$	6.03739	−	13.2634i	0.354528	−	0.778852i
$291$	2.23981	+	8.35909i	0.131300	+	0.490019i
$292$	−11.3823	+	9.91216i	−0.666099	+	0.580065i
$293$	10.4438	+	10.4438i	0.610133	+	0.610133i	0.942981	−	0.332847i	$-0.108009\pi$
$293$	10.4438	+	10.4438i	0.610133	+	0.610133i	−0.332847	+	0.942981i	$0.608009\pi$
$294$	21.1257	+	3.45385i	1.23207	+	0.201433i
$295$			8.16528i			0.475401i
$296$	−0.149843	−	5.44627i	−0.00870944	−	0.316558i
$297$	−13.7942	−	7.96407i	−0.800419	−	0.462122i
$298$	−9.09369	+	3.40457i	−0.526784	+	0.197222i
$299$	7.40740	−	27.6448i	0.428381	−	1.59874i
$300$	−3.58747	−	2.41517i	−0.207123	−	0.139440i
$301$	3.61678	+	13.4093i	0.208468	+	0.772898i
$302$	0.276872	+	2.86217i	0.0159322	+	0.164699i
$303$	7.79393	+	13.4995i	0.447750	+	0.775525i
$304$	−9.74140	−	12.8798i	−0.558708	−	0.738709i
$305$	1.91311	−	3.31360i	0.109544	−	0.189736i
$306$	−1.88952	+	1.34904i	−0.108017	+	0.0771195i
$307$	−16.1597	+	16.1597i	−0.922283	+	0.922283i	−0.997190	−	0.0749078i	$-0.976134\pi$
$307$	−16.1597	+	16.1597i	−0.922283	+	0.922283i	0.0749078	+	0.997190i	$0.476134\pi$
$308$	16.3972	−	24.4434i	0.934318	−	1.39279i
$309$	23.8802	+	23.8802i	1.35850	+	1.35850i
$310$	−1.98156	+	11.8736i	−0.112545	+	0.674373i
$311$	−21.5297	−	12.4302i	−1.22083	−	0.704849i	−0.255739	−	0.966746i	$-0.582319\pi$
$311$	−21.5297	−	12.4302i	−1.22083	−	0.704849i	−0.965096	+	0.261897i	$0.915652\pi$
$312$	34.9060	+	8.33124i	1.97616	+	0.471664i
$313$	−4.73165	+	2.73182i	−0.267449	+	0.154412i	−0.627728	−	0.778433i	$-0.716015\pi$
$313$	−4.73165	+	2.73182i	−0.267449	+	0.154412i	0.360279	+	0.932845i	$0.382682\pi$
$314$	−10.4515	+	12.6901i	−0.589810	+	0.716141i
$315$	−1.14042	+	4.28442i	−0.0642552	+	0.241400i
$316$	19.2780	−	3.76496i	1.08447	−	0.211796i
$317$	19.0749	+	5.11110i	1.07135	+	0.287068i	0.751049	−	0.660247i	$-0.229548\pi$
$317$	19.0749	+	5.11110i	1.07135	+	0.287068i	0.320304	+	0.947315i	$0.396215\pi$
$318$	−9.00205	+	19.7764i	−0.504810	+	1.10900i
$319$	−28.6594	+	49.6395i	−1.60462	+	2.77928i
$320$	2.49231	+	7.60187i	0.139324	+	0.424957i
$321$	−9.53591			−0.532243
$322$	−10.6292	−	14.8357i	−0.592343	−	0.826763i
$323$	2.79670	−	2.79670i	0.155612	−	0.155612i
$324$	−14.7358	−	16.9213i	−0.818654	−	0.940074i
$325$	−5.66766	+	1.51864i	−0.314385	+	0.0842392i
$326$	−6.27582	−	16.7628i	−0.347585	−	0.928408i
$327$	10.9746	−	6.33619i	0.606896	−	0.350392i
$328$	−0.00185008	−	0.00621548i	−0.000102153	−	0.000343192i
$329$	−0.00694401	−	4.19909i	−0.000382836	−	0.231504i
$330$	13.1302	+	10.8140i	0.722796	+	0.595290i
$331$	3.05916	−	11.4169i	0.168146	−	0.627531i	−0.829471	−	0.558549i	$-0.811358\pi$
$331$	3.05916	−	11.4169i	0.168146	−	0.627531i	0.997618	−	0.0689820i	$-0.0219751\pi$
$332$	0.0630138	+	0.128908i	0.00345833	+	0.00707475i
$333$	−0.835454	−	3.11796i	−0.0457826	−	0.170863i
$334$	20.7869	−	14.8410i	1.13741	−	0.812065i
$335$	−2.45144			−0.133936
$336$	18.2288	−	13.8345i	0.994465	−	0.754732i
$337$	19.7639			1.07661			0.538303	−	0.842751i	$-0.319065\pi$
$337$	19.7639			1.07661			0.538303	+	0.842751i	$0.319065\pi$
$338$	24.6637	−	17.6089i	1.34153	−	0.957798i
$339$	−10.1830	−	38.0035i	−0.553064	−	2.06406i
$340$	−1.76028	+	0.860473i	−0.0954646	+	0.0466657i
$341$	12.2545	−	45.7344i	0.663618	−	2.47666i
$342$	−7.38530	−	6.08249i	−0.399352	−	0.328904i
$343$	−0.0918799	−	18.5200i	−0.00496105	−	0.999988i
$344$	13.0575	+	7.06727i	0.704016	+	0.381041i
$345$	9.13410	−	5.27357i	0.491763	−	0.283920i
$346$	−0.515959	−	1.37814i	−0.0277381	−	0.0740891i
$347$	−12.3993	+	3.32239i	−0.665631	+	0.178355i	−0.575786	−	0.817600i	$-0.695304\pi$
$347$	−12.3993	+	3.32239i	−0.665631	+	0.178355i	−0.0898450	+	0.995956i	$0.528637\pi$
$348$	−33.6070	+	29.2663i	−1.80153	+	1.56884i
$349$	−3.63719	+	3.63719i	−0.194695	+	0.194695i	−0.797721	−	0.603027i	$-0.793961\pi$
$349$	−3.63719	+	3.63719i	−0.194695	+	0.194695i	0.603027	+	0.797721i	$0.293961\pi$
$350$	−1.54450	+	3.40801i	−0.0825571	+	0.182166i
$351$	−16.8018			−0.896816
$352$	−6.87839	−	30.7051i	−0.366619	−	1.63659i
$353$	−5.48000	+	9.49165i	−0.291671	+	0.505189i	−0.974205	−	0.225665i	$-0.927545\pi$
$353$	−5.48000	+	9.49165i	−0.291671	+	0.505189i	0.682534	+	0.730854i	$0.260878\pi$
$354$	10.3447	−	22.7259i	0.549813	−	1.20787i
$355$	−14.0018	−	3.75177i	−0.743139	−	0.199124i
$356$	3.44791	+	17.6546i	0.182739	+	0.935693i
$357$	3.96968	+	3.95657i	0.210098	+	0.209404i
$358$	−7.77388	+	9.43897i	−0.410862	+	0.498865i
$359$	−2.22990	+	1.28743i	−0.117689	+	0.0679480i	−0.557689	−	0.830050i	$-0.688312\pi$
$359$	−2.22990	+	1.28743i	−0.117689	+	0.0679480i	0.440000	+	0.897998i	$0.354979\pi$
$360$	2.48185	+	4.03799i	0.130805	+	0.212821i
$361$	−2.33907	−	1.35047i	−0.123109	−	0.0710771i
$362$	1.94522	−	11.6558i	0.102238	−	0.612617i
$363$	−30.4901	−	30.4901i	−1.60032	−	1.60032i
$364$	2.08722	−	30.9781i	0.109400	−	1.62370i
$365$	−5.33629	+	5.33629i	−0.279314	+	0.279314i
$366$	−9.52267	+	6.79881i	−0.497758	+	0.355379i
$367$	−3.64873	+	6.31979i	−0.190462	+	0.329890i	−0.945403	−	0.325902i	$-0.894332\pi$
$367$	−3.64873	+	6.31979i	−0.190462	+	0.329890i	0.754941	+	0.655792i	$0.227665\pi$
$368$	−19.3255	−	2.68118i	−1.00741	−	0.139766i
$369$	−0.00192106	−	0.00332738i	−0.000100006	−	0.000173216i
$370$	−0.262298	−	2.71151i	−0.0136362	−	0.140965i
$371$	18.1669	+	4.83561i	0.943177	+	0.251053i
$372$	20.5579	−	30.5365i	1.06588	−	1.58324i
$373$	−4.08478	+	15.2446i	−0.211502	+	0.789335i	0.775867	+	0.630896i	$0.217313\pi$
$373$	−4.08478	+	15.2446i	−0.211502	+	0.789335i	−0.987369	+	0.158439i	$0.949354\pi$
$374$	7.21735	−	2.70209i	0.373200	−	0.139722i
$375$	−1.87265	−	1.08117i	−0.0967031	−	0.0558316i
$376$	−3.26032	−	3.08572i	−0.168138	−	0.159134i
$377$			60.4629i			3.11400i
$378$	−6.79775	+	8.28163i	−0.349639	+	0.425961i
$379$	6.33681	+	6.33681i	0.325500	+	0.325500i	0.850872	−	0.525372i	$-0.176074\pi$
$379$	6.33681	+	6.33681i	0.325500	+	0.325500i	−0.525372	+	0.850872i	$0.676074\pi$
$380$	−5.30268	−	6.08916i	−0.272022	−	0.312367i
$381$	−1.22660	−	4.57773i	−0.0628406	−	0.234524i
$382$	−13.7670	+	30.2443i	−0.704379	+	1.54743i
$383$	−2.98343	−	5.16745i	−0.152446	−	0.264044i	0.779680	−	0.626178i	$-0.215382\pi$
$383$	−2.98343	−	5.16745i	−0.152446	−	0.264044i	−0.932126	+	0.362134i	$0.882048\pi$
$384$	2.69420	−	24.3154i	0.137488	−	1.24084i
$385$	7.33737	−	12.7574i	0.373947	−	0.650176i
$386$	−6.50485	+	0.629247i	−0.331088	+	0.0320279i
$387$	8.49684	+	2.27672i	0.431919	+	0.115732i
$388$	2.59923	−	7.57046i	0.131956	−	0.384332i
$389$	33.3509	−	8.93635i	1.69096	−	0.453091i	0.720321	−	0.693641i	$-0.243994\pi$
$389$	33.3509	−	8.93635i	1.69096	−	0.453091i	0.970637	+	0.240550i	$0.0773277\pi$
$390$	17.6984	+	2.95366i	0.896195	+	0.149564i
$391$		−	4.77847i		−	0.241658i
$392$	−14.4247	−	13.5620i	−0.728556	−	0.684986i
$393$			23.4176i			1.18126i
$394$	−1.09696	+	6.57303i	−0.0552641	+	0.331144i
$395$	9.48647	−	2.54189i	0.477316	−	0.127896i
$396$	−8.18717	−	16.7486i	−0.411421	−	0.841648i
$397$	−13.8931	−	3.72265i	−0.697275	−	0.186834i	−0.107265	−	0.994230i	$-0.534209\pi$
$397$	−13.8931	−	3.72265i	−0.697275	−	0.186834i	−0.590010	+	0.807396i	$0.700876\pi$
$398$	−3.03091	−	31.3320i	−0.151926	−	1.57053i
$399$	−11.5154	+	20.0217i	−0.576492	+	1.00234i
$400$	1.50498	+	3.70608i	0.0752491	+	0.185304i
$401$	0.404065	+	0.699861i	0.0201780	+	0.0349494i	0.875938	−	0.482424i	$-0.160243\pi$
$401$	0.404065	+	0.699861i	0.0201780	+	0.0349494i	−0.855760	+	0.517373i	$0.826910\pi$
$402$	6.82294	+	3.10575i	0.340297	+	0.154901i
$403$	−12.9267	−	48.2431i	−0.643924	−	2.40316i
$404$	0.993001	−	14.3833i	0.0494037	−	0.715596i
$405$	−7.93311	−	7.93311i	−0.394199	−	0.394199i
$406$	29.8021	+	24.4623i	1.47906	+	1.21404i
$407$			10.7149i			0.531116i
$408$	5.98943	−	0.164787i	0.296521	−	0.00815816i
$409$	−14.9845	−	8.65132i	−0.740937	−	0.427780i	0.0814726	−	0.996676i	$-0.474038\pi$
$409$	−14.9845	−	8.65132i	−0.740937	−	0.427780i	−0.822410	+	0.568895i	$0.807371\pi$
$410$	−0.00113689	−	0.00303665i	−5.61468e−5	−	0.000149969i
$411$	−2.66421	+	9.94298i	−0.131416	+	0.490451i
$412$	−5.98725	−	30.6570i	−0.294971	−	1.51036i
$413$	−20.8764	−	5.55683i	−1.02726	−	0.273434i
$414$	−11.5056	+	1.11300i	−0.565470	+	0.0547009i
$415$	0.0358713	+	0.0621310i	0.00176085	+	0.00304989i
$416$	−22.4783	−	24.4222i	−1.10209	−	1.19740i
$417$	7.27604	−	12.6025i	0.356309	−	0.617146i
$418$	18.4539	+	25.8472i	0.902608	+	1.26423i
$419$	15.4043	−	15.4043i	0.752550	−	0.752550i	−0.222404	−	0.974954i	$-0.571391\pi$
$419$	15.4043	−	15.4043i	0.752550	−	0.752550i	0.974954	+	0.222404i	$0.0713905\pi$
$420$	8.61636	−	7.52856i	0.420435	−	0.367356i
$421$	11.9156	+	11.9156i	0.580732	+	0.580732i	0.935104	−	0.354372i	$-0.115305\pi$
$421$	11.9156	+	11.9156i	0.580732	+	0.580732i	−0.354372	+	0.935104i	$0.615305\pi$
$422$	−28.6064	−	4.77408i	−1.39254	−	0.232398i
$423$	−2.30327	−	1.32980i	−0.111989	−	0.0646569i
$424$	17.1219	−	10.5236i	0.831515	−	0.511071i
$425$	−0.848418	+	0.489834i	−0.0411543	+	0.0237605i
$426$	34.2173	+	28.1811i	1.65783	+	1.36538i
$427$	7.17002	+	7.14635i	0.346982	+	0.345836i
$428$	7.31644	+	4.92559i	0.353653	+	0.238088i
$429$	−68.1706	−	18.2662i	−3.29131	−	0.881903i
$430$	6.75665	+	3.07558i	0.325834	+	0.148317i
$431$	−4.17242	+	7.22684i	−0.200978	+	0.348105i	−0.948844	−	0.315746i	$-0.897745\pi$
$431$	−4.17242	+	7.22684i	−0.200978	+	0.348105i	0.747866	+	0.663850i	$0.231079\pi$
$432$	1.41599	+	11.3661i	0.0681269	+	0.546854i
$433$	−16.0940			−0.773430			−0.386715	−	0.922199i	$-0.626390\pi$
$433$	−16.0940			−0.773430			−0.386715	+	0.922199i	$0.626390\pi$
$434$	−29.0089	−	13.1468i	−1.39247	−	0.631066i
$435$	−15.7558	+	15.7558i	−0.755431	+	0.755431i
$436$	−11.6931	−	0.807275i	−0.559998	−	0.0386614i
$437$	19.0211	−	5.09668i	0.909901	−	0.243807i
$438$	21.6128	−	8.09157i	1.03270	−	0.386630i
$439$	27.9502	−	16.1370i	1.33399	−	0.770179i	0.348080	−	0.937465i	$-0.386834\pi$
$439$	27.9502	−	16.1370i	1.33399	−	0.770179i	0.985908	+	0.167286i	$0.0535003\pi$
$440$	−4.48843	−	15.0792i	−0.213977	−	0.718873i
$441$	−10.1780	−	5.83147i	−0.484667	−	0.277689i
$442$	5.16811	−	6.27507i	0.245822	−	0.298474i
$443$	−0.439759	+	1.64120i	−0.0208936	+	0.0779759i	−0.975585	−	0.219620i	$-0.929518\pi$
$443$	−0.439759	+	1.64120i	−0.0208936	+	0.0779759i	0.954692	+	0.297596i	$0.0961849\pi$
$444$	−2.70520	+	7.87909i	−0.128383	+	0.373925i
$445$	2.32784	+	8.68761i	0.110350	+	0.411832i
$446$	13.1077	+	18.3592i	0.620668	+	0.869331i
$447$	14.8469			0.702233
$448$	−21.1320	+	1.19875i	−0.998395	+	0.0566354i
$449$	6.83191			0.322418			0.161209	−	0.986920i	$-0.448461\pi$
$449$	6.83191			0.322418			0.161209	+	0.986920i	$0.448461\pi$
$450$	1.37704	+	1.92873i	0.0649142	+	0.0909213i
$451$	0.00330086	+	0.0123190i	0.000155432	+	0.000580079i
$452$	−11.8171	+	34.4180i	−0.555827	+	1.61889i
$453$	1.13795	−	4.24690i	0.0534657	−	0.199537i
$454$	−11.6801	+	14.1819i	−0.548174	+	0.665588i
$455$	−0.0256722	−	15.5242i	−0.00120353	−	0.727784i
$456$	7.04422	+	23.6656i	0.329876	+	1.10824i
$457$	11.4777	−	6.62667i	0.536905	−	0.309982i	−0.206919	−	0.978358i	$-0.566343\pi$
$457$	11.4777	−	6.62667i	0.536905	−	0.309982i	0.743824	+	0.668376i	$0.233010\pi$
$458$	−5.00896	+	1.87530i	−0.234054	+	0.0876270i
$459$	−2.70969	+	0.726060i	−0.126478	+	0.0338896i
$460$	−9.73211	−	0.671890i	−0.453762	−	0.0313271i
$461$	20.2943	−	20.2943i	0.945200	−	0.945200i	−0.0533748	−	0.998575i	$-0.516998\pi$
$461$	20.2943	−	20.2943i	0.945200	−	0.945200i	0.998575	+	0.0533748i	$0.0169978\pi$
$462$	−36.5841	+	26.2111i	−1.70205	+	1.21945i
$463$	14.1275			0.656561			0.328280	−	0.944580i	$-0.393531\pi$
$463$	14.1275			0.656561			0.328280	+	0.944580i	$0.393531\pi$
$464$	40.9020	−	5.09556i	1.89883	−	0.236555i
$465$	9.20294	−	15.9400i	0.426776	−	0.739198i
$466$	29.8732	+	13.5981i	1.38385	+	0.629919i
$467$	−12.4416	−	3.33371i	−0.575727	−	0.154266i	−0.0408053	−	0.999167i	$-0.512992\pi$
$467$	−12.4416	−	3.33371i	−0.575727	−	0.154266i	−0.534922	+	0.844901i	$0.679659\pi$
$468$	−16.3129	−	10.9822i	−0.754063	−	0.507653i
$469$	1.66831	−	6.26766i	0.0770354	−	0.289414i
$470$	−1.73255	−	1.42692i	−0.0799167	−	0.0658189i
$471$	21.7691	−	12.5684i	1.00307	−	0.579121i
$472$	−19.6756	+	12.0932i	−0.905644	+	0.556632i
$473$	−25.2874	−	14.5997i	−1.16272	−	0.671295i
$474$	−29.6235	−	4.94381i	−1.36065	−	0.227077i
$475$	−2.85474	−	2.85474i	−0.130984	−	0.130984i
$476$	−1.00205	−	5.08615i	−0.0459288	−	0.233123i
$477$	8.41954	−	8.41954i	0.385504	−	0.385504i
$478$	6.37580	+	8.93019i	0.291622	+	0.408458i
$479$	16.8162	−	29.1266i	0.768353	−	1.33083i	−0.170102	−	0.985426i	$-0.554410\pi$
$479$	16.8162	−	29.1266i	0.768353	−	1.33083i	0.938455	−	0.345401i	$-0.112257\pi$
$480$	0.506546	−	12.2216i	0.0231206	−	0.557837i
$481$	5.65130	+	9.78834i	0.257677	+	0.446310i
$482$	−8.43577	+	0.816036i	−0.384239	+	0.0371694i
$483$	7.26694	+	26.9423i	0.330657	+	1.22592i
$484$	7.64449	+	39.1427i	0.347477	+	1.77921i
$485$	1.03582	−	3.86575i	0.0470344	−	0.175535i
$486$	7.76959	+	20.7527i	0.352436	+	0.941363i
$487$	−20.5754	−	11.8792i	−0.932361	−	0.538299i	−0.0448032	−	0.998996i	$-0.514266\pi$
$487$	−20.5754	−	11.8792i	−0.932361	−	0.538299i	−0.887557	+	0.460697i	$0.847599\pi$
$488$	10.8181	−	0.297637i	0.489711	−	0.0134734i
$489$			27.3679i			1.23762i
$490$	−7.66225	−	6.26817i	−0.346145	−	0.283167i
$491$	−5.98912	−	5.98912i	−0.270285	−	0.270285i	0.558930	−	0.829215i	$-0.311212\pi$
$491$	−5.98912	−	5.98912i	−0.270285	−	0.270285i	−0.829215	+	0.558930i	$0.811212\pi$
$492$	−0.000682932		0.00989205i	−3.07890e−5		0.000445968i
$493$	2.61279	+	9.75106i	0.117674	+	0.439166i
$494$	30.4906	+	13.8791i	1.37184	+	0.624451i
$495$	−4.66064	−	8.07247i	−0.209480	−	0.362830i
$496$	−31.5461	+	12.8104i	−1.41646	+	0.575203i
$497$	19.1211	−	33.2456i	0.857699	−	1.49127i
$498$	−0.0211242	−	0.218371i	−0.000946597	−	0.00978545i
$499$	−0.585390	−	0.156855i	−0.0262056	−	0.00702178i	0.245692	−	0.969348i	$-0.420985\pi$
$499$	−0.585390	−	0.156855i	−0.0262056	−	0.00702178i	−0.271898	+	0.962326i	$0.587651\pi$
$500$	0.878331	+	1.79681i	0.0392802	+	0.0803559i
$501$	−37.7220	+	10.1076i	−1.68530	+	0.451574i
$502$	1.78816	−	10.7147i	0.0798095	−	0.478221i
$503$			5.16116i			0.230125i	0.993358	+	0.115062i	$0.0367068\pi$
$503$			5.16116i			0.230125i	−0.993358	+	0.115062i	$0.963293\pi$
$504$	−12.0131	+	3.59740i	−0.535104	+	0.160241i
$505$		−	7.20877i		−	0.320786i
$506$	37.8466	+	6.31616i	1.68249	+	0.280787i
$507$	−44.7573	+	11.9927i	−1.98774	+	0.532613i
$508$	−1.42343	+	4.14585i	−0.0631545	+	0.183942i
$509$	−8.00447	−	2.14479i	−0.354792	−	0.0950662i	0.0770209	−	0.997029i	$-0.475459\pi$
$509$	−8.00447	−	2.14479i	−0.354792	−	0.0950662i	−0.431813	+	0.901963i	$0.642126\pi$
$510$	2.98193	−	0.288457i	0.132042	−	0.0127731i
$511$	−10.0119	−	17.2750i	−0.442899	−	0.764202i
$512$	−14.6268	+	17.2643i	−0.646418	+	0.762984i
$513$	−5.78028	−	10.0117i	−0.255205	−	0.442029i
$514$	−1.23877	+	2.72142i	−0.0546399	+	0.120037i
$515$	−4.04226	−	15.0859i	−0.178123	−	0.664765i
$516$	−14.9089	−	17.1201i	−0.656327	−	0.753672i
$517$	6.24252	+	6.24252i	0.274546	+	0.274546i
$518$	7.11109	+	1.17467i	0.312444	+	0.0516122i
$519$			2.25002i			0.0987651i
$520$	−12.0535	−	11.4080i	−0.528581	−	0.500274i
$521$	19.3759	+	11.1867i	0.848876	+	0.490099i	0.860271	−	0.509836i	$-0.170294\pi$
$521$	19.3759	+	11.1867i	0.848876	+	0.490099i	−0.0113956	+	0.999935i	$0.503627\pi$
$522$	22.8701	−	8.56229i	1.00100	−	0.374761i
$523$	−0.407119	+	1.51939i	−0.0178021	+	0.0664382i	−0.974255	−	0.225447i	$-0.927616\pi$
$523$	−0.407119	+	1.51939i	−0.0178021	+	0.0664382i	0.956453	+	0.291885i	$0.0942825\pi$
$524$	12.0959	−	17.9672i	0.528413	−	0.784900i
$525$	4.03869	−	4.05207i	0.176263	−	0.176847i
$526$	1.09399	+	11.3091i	0.0477002	+	0.493101i
$527$	−4.16947	−	7.22173i	−0.181625	−	0.314583i
$528$	−6.61164	+	47.6555i	−0.287735	+	2.07394i
$529$	0.395681	−	0.685340i	0.0172035	−	0.0297974i
$530$	8.17824	−	5.83894i	0.355240	−	0.253627i
$531$	−9.67529	+	9.67529i	−0.419872	+	0.419872i
$532$	19.1770	−	9.41358i	0.831430	−	0.408130i
$533$	0.00951280	+	0.00951280i	0.000412045	+	0.000412045i
$534$	4.52749	−	27.1289i	0.195924	−	1.17398i
$535$	3.81916	+	2.20499i	0.165116	+	0.0953301i
$536$	−3.63069	−	5.90715i	−0.156822	−	0.255150i
$537$	16.1920	−	9.34847i	0.698738	−	0.403416i
$538$	−26.3794	+	32.0296i	−1.13730	+	1.38089i
$539$	27.6237	+	27.4416i	1.18984	+	1.18199i
$540$	1.09773	+	5.62081i	0.0472389	+	0.241881i
$541$	−6.22334	−	1.66754i	−0.267562	−	0.0716931i	0.122543	−	0.992463i	$-0.460895\pi$
$541$	−6.22334	−	1.66754i	−0.267562	−	0.0716931i	−0.390106	+	0.920770i	$0.627562\pi$
$542$	−4.64956	+	10.2145i	−0.199716	+	0.438750i
$543$	−9.03418	+	15.6477i	−0.387694	+	0.671505i
$544$	−4.68051	−	2.96729i	−0.200675	−	0.127222i
$545$	−5.86047			−0.251035
$546$	−19.5963	+	43.2400i	−0.838643	+	1.85050i
$547$	−4.01088	+	4.01088i	−0.171493	+	0.171493i	−0.787635	−	0.616142i	$-0.788695\pi$
$547$	−4.01088	+	4.01088i	−0.171493	+	0.171493i	0.616142	+	0.787635i	$0.288695\pi$
$548$	7.17998	−	6.25262i	0.306714	−	0.267098i
$549$	6.19328	−	1.65949i	0.264323	−	0.0708251i
$550$	−2.75817	−	7.36713i	−0.117609	−	0.314136i
$551$	−36.0281	+	20.8008i	−1.53485	+	0.886144i
$552$	26.2356	+	14.1997i	1.11666	+	0.604381i
$553$	0.0429699	+	25.9842i	0.00182726	+	1.10496i
$554$	−30.6502	−	25.2433i	−1.30220	−	1.07249i
$555$	−1.07805	+	4.02335i	−0.0457608	+	0.170782i
$556$	−12.0921	+	5.91096i	−0.512820	+	0.250681i
$557$	6.65815	+	24.8486i	0.282115	+	1.05287i	0.950922	+	0.309431i	$0.100139\pi$
$557$	6.65815	+	24.8486i	0.282115	+	1.05287i	−0.668807	+	0.743436i	$0.733195\pi$
$558$	−16.4173	+	11.7213i	−0.695002	+	0.496204i
$559$	−30.8011			−1.30275
$560$	−10.4996	+	1.32568i	−0.443691	+	0.0560202i
$561$	−11.7834			−0.497498
$562$	13.6177	−	9.72252i	0.574429	−	0.410120i
$563$	10.5769	+	39.4734i	0.445762	+	1.66361i	0.713918	+	0.700230i	$0.246919\pi$
$563$	10.5769	+	39.4734i	0.445762	+	1.66361i	−0.268156	+	0.963375i	$0.586414\pi$
$564$	3.01433	+	6.16645i	0.126926	+	0.259654i
$565$	−4.70923	+	17.5751i	−0.198119	+	0.739390i
$566$	−13.0105	−	10.7154i	−0.546871	−	0.450400i
$567$	25.6816	−	14.8840i	1.07853	−	0.625069i
$568$	−11.6968	−	39.2963i	−0.490787	−	1.64884i
$569$	−40.2776	+	23.2543i	−1.68852	+	0.974870i	−0.732874	+	0.680365i	$0.761821\pi$
$569$	−40.2776	+	23.2543i	−1.68852	+	0.974870i	−0.955650	+	0.294505i	$0.904845\pi$
$570$	4.32873	+	11.5621i	0.181310	+	0.484284i
$571$	−4.16645	+	1.11640i	−0.174360	+	0.0467197i	−0.344943	−	0.938624i	$-0.612102\pi$
$571$	−4.16645	+	1.11640i	−0.174360	+	0.0467197i	0.170582	+	0.985343i	$0.445435\pi$
$572$	42.8688	+	49.2270i	1.79244	+	2.05828i
$573$	35.9276	−	35.9276i	1.50090	−	1.50090i
$574$	0.00853758		0.000840138i	0.000356352		3.50667e-5i
$575$	−4.87764			−0.203412
$576$	−6.05448	+	11.9609i	−0.252270	+	0.498371i
$577$	−2.08274	+	3.60741i	−0.0867056	+	0.150178i	−0.906117	−	0.423028i	$-0.860967\pi$
$577$	−2.08274	+	3.60741i	−0.0867056	+	0.150178i	0.819411	+	0.573206i	$0.194301\pi$
$578$	−9.39792	+	20.6460i	−0.390902	+	0.858761i
$579$	9.65192	+	2.58622i	0.401120	+	0.107480i
$580$	20.2270	−	3.95028i	0.839879	−	0.164027i
$581$	−0.183264	+	0.0494304i	−0.00760307	+	0.00205072i
$582$	−7.78051	+	9.44702i	−0.322512	+	0.391591i
$583$	−34.2290	+	19.7621i	−1.41762	+	0.818463i
$584$	−20.7620	−	4.95540i	−0.859136	−	0.205056i
$585$	−8.51527	−	4.91629i	−0.352063	−	0.203264i
$586$	−3.43834	+	20.6027i	−0.142037	+	0.851088i
$587$	−8.30891	−	8.30891i	−0.342946	−	0.342946i	0.514528	−	0.857474i	$-0.327967\pi$
$587$	−8.30891	−	8.30891i	−0.342946	−	0.342946i	−0.857474	+	0.514528i	$0.827967\pi$
$588$	13.3847	+	27.1532i	0.551975	+	1.11978i
$589$	24.2995	−	24.2995i	1.00124	−	1.00124i
$590$	−9.39799	+	6.70979i	−0.386909	+	0.276238i
$591$	5.09461	−	8.82413i	0.209564	−	0.362976i
$592$	6.14536	−	4.64792i	0.252573	−	0.191028i
$593$	1.48361	+	2.56969i	0.0609247	+	0.105525i	0.894879	−	0.446309i	$-0.147262\pi$
$593$	1.48361	+	2.56969i	0.0609247	+	0.105525i	−0.833954	+	0.551834i	$0.813928\pi$
$594$	−2.16891	−	22.4211i	−0.0889915	−	0.919950i
$595$	−0.674988	−	2.50253i	−0.0276718	−	0.102594i
$596$	−11.3913	−	7.66887i	−0.466605	−	0.314129i
$597$	−12.4571	+	46.4906i	−0.509836	+	1.90273i
$598$	37.9053	−	14.1913i	1.55006	−	0.580326i
$599$	−29.9291	−	17.2796i	−1.22287	−	0.706025i	−0.257341	−	0.966321i	$-0.582847\pi$
$599$	−29.9291	−	17.2796i	−1.22287	−	0.706025i	−0.965529	+	0.260296i	$0.916180\pi$
$600$	−0.168207	−	6.11373i	−0.00686701	−	0.249592i
$601$			4.28545i			0.174807i	0.996173	+	0.0874035i	$0.0278569\pi$
$601$			4.28545i			0.174807i	−0.996173	+	0.0874035i	$0.972143\pi$
$602$	−12.4616	+	15.1818i	−0.507897	+	0.618766i
$603$	−2.90478	−	2.90478i	−0.118292	−	0.118292i
$604$	−3.06675	+	2.67065i	−0.124784	+	0.108667i
$605$	5.16113	+	19.2616i	0.209830	+	0.783096i
$606$	−9.13286	+	20.0637i	−0.370997	+	0.815034i
$607$	−13.2152	−	22.8894i	−0.536388	−	0.929052i	−0.999095	−	0.0425404i	$-0.986455\pi$
$607$	−13.2152	−	22.8894i	−0.536388	−	0.929052i	0.462706	−	0.886512i	$-0.346878\pi$
$608$	6.81934	−	21.7960i	0.276561	−	0.883946i
$609$	−29.5607	−	51.0057i	−1.19786	−	2.06685i
$610$	5.38595	−	0.521010i	0.218071	−	0.0210951i
$611$	8.99520	+	2.41026i	0.363907	+	0.0975085i
$612$	−3.10541	−	1.06621i	−0.125529	−	0.0430989i
$613$	−16.0632	+	4.30412i	−0.648786	+	0.173842i	−0.568180	−	0.822904i	$-0.692352\pi$
$613$	−16.0632	+	4.30412i	−0.648786	+	0.173842i	−0.0806063	+	0.996746i	$0.525686\pi$
$614$	−31.8785	−	5.32015i	−1.28651	−	0.214704i
$615$			0.00495780i			0.000199918i
$616$	41.6080	−	1.21362i	1.67644	−	0.0488982i
$617$			12.3217i			0.496054i	0.968753	+	0.248027i	$0.0797822\pi$
$617$			12.3217i			0.496054i	−0.968753	+	0.248027i	$0.920218\pi$
$618$	−7.86192	+	47.1089i	−0.316253	+	1.89500i
$619$	24.5527	−	6.57887i	0.986855	−	0.264427i	0.270926	−	0.962600i	$-0.412670\pi$
$619$	24.5527	−	6.57887i	0.986855	−	0.264427i	0.715929	+	0.698173i	$0.246003\pi$
$620$	−15.2945	+	7.47635i	−0.614240	+	0.300257i
$621$	−13.4912	−	3.61496i	−0.541383	−	0.145063i
$622$	−3.38519	−	34.9944i	−0.135734	−	1.40315i
$623$	−23.7960	+	0.0393513i	−0.953369	+	0.00157658i
$624$	19.0949	+	47.0219i	0.764406	+	1.88238i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−7.03246	−	3.20112i	−0.281074	−	0.127943i
$627$	−12.5681	−	46.9049i	−0.501923	−	1.87320i
$628$	−23.1943	−	1.60130i	−0.925555	−	0.0638989i
$629$	1.33439	+	1.33439i	0.0532056	+	0.0532056i
$630$	−5.86838	+	2.20813i	−0.233802	+	0.0879738i
$631$			26.2371i			1.04448i	0.852797	+	0.522242i	$0.174904\pi$
$631$			26.2371i			1.04448i	−0.852797	+	0.522242i	$0.825096\pi$
$632$	20.1750	+	19.0946i	0.802519	+	0.759542i
$633$	38.4034	+	22.1722i	1.52640	+	0.881267i
$634$	9.79201	+	26.1547i	0.388890	+	1.03873i
$635$	−0.567254	+	2.11702i	−0.0225108	+	0.0840114i
$636$	−30.1594	+	5.89007i	−1.19590	+	0.233556i
$637$	39.7085	+	10.4992i	1.57331	+	0.415995i
$638$	−80.6843	+	7.80501i	−3.19432	+	0.309003i
$639$	−12.1456	−	21.0368i	−0.480472	−	0.832202i
$640$	−6.70148	+	9.11538i	−0.264899	+	0.360317i
$641$	16.2691	−	28.1788i	0.642589	−	1.11300i	−0.342264	−	0.939604i	$-0.611194\pi$
$641$	16.2691	−	28.1788i	0.642589	−	1.11300i	0.984853	−	0.173393i	$-0.0554730\pi$
$642$	−7.83610	−	10.9755i	−0.309266	−	0.433170i
$643$	−2.48346	+	2.48346i	−0.0979382	+	0.0979382i	−0.754378	−	0.656440i	$-0.772062\pi$
$643$	−2.48346	+	2.48346i	−0.0979382	+	0.0979382i	0.656440	+	0.754378i	$0.272062\pi$
$644$	8.34097	−	24.4251i	0.328680	−	0.962484i
$645$	−8.02632	−	8.02632i	−0.316036	−	0.316036i
$646$	5.51709	+	0.920738i	0.217067	+	0.0362260i
$647$	−11.6915	−	6.75011i	−0.459642	−	0.265374i	0.252252	−	0.967662i	$-0.418829\pi$
$647$	−11.6915	−	6.75011i	−0.459642	−	0.265374i	−0.711894	+	0.702287i	$0.752162\pi$
$648$	7.36687	−	30.8655i	0.289398	−	1.21251i
$649$	39.3341	−	22.7096i	1.54400	−	0.891429i
$650$	−6.40529	−	5.27536i	−0.251236	−	0.206917i
$651$	34.4911	+	34.3773i	1.35181	+	1.34735i
$652$	14.1364	−	20.9981i	0.553624	−	0.822349i
$653$	−46.1006	−	12.3526i	−1.80406	−	0.483395i	−0.809455	−	0.587181i	$-0.800238\pi$
$653$	−46.1006	−	12.3526i	−1.80406	−	0.483395i	−0.994600	+	0.103786i	$0.966904\pi$
$654$	16.3111	+	7.42469i	0.637814	+	0.290328i
$655$	5.41486	−	9.37881i	0.211576	−	0.366460i
$656$	0.00563353	−	0.00723693i	0.000219953	−	0.000282555i
$657$	−12.6463			−0.493377
$658$	4.82733	−	3.45859i	0.188189	−	0.134830i
$659$	−8.68312	+	8.68312i	−0.338246	+	0.338246i	−0.855707	−	0.517461i	$-0.826877\pi$
$659$	−8.68312	+	8.68312i	−0.338246	+	0.338246i	0.517461	+	0.855707i	$0.326877\pi$
$660$	−1.65685	+	23.9989i	−0.0644926	+	0.934154i
$661$	11.0823	−	2.96949i	0.431051	−	0.115500i	−0.0367682	−	0.999324i	$-0.511706\pi$
$661$	11.0823	−	2.96949i	0.431051	−	0.115500i	0.467820	+	0.883824i	$0.345040\pi$
$662$	15.6544	−	5.86083i	0.608425	−	0.227788i
$663$	−10.7645	+	6.21490i	−0.418060	+	0.241367i
$664$	−0.0965880	+	0.178457i	−0.00374834	+	0.00692547i
$665$	9.24157	−	5.35602i	0.358373	−	0.207697i
$666$	2.90214	−	3.52375i	0.112456	−	0.136543i
$667$	−13.0087	+	48.5492i	−0.503700	+	1.87983i
$668$	34.1632	+	11.7295i	1.32181	+	0.453830i
$669$	−8.92710	−	33.3164i	−0.345142	−	1.28809i
$670$	−2.01446	−	2.82153i	−0.0778254	−	0.109005i
$671$	−21.2832			−0.821630
$672$	30.9026	+	9.61243i	1.19209	+	0.370807i
$673$	4.31660			0.166393			0.0831963	−	0.996533i	$-0.473487\pi$
$673$	4.31660			0.166393			0.0831963	+	0.996533i	$0.473487\pi$
$674$	16.2409	+	22.7476i	0.625576	+	0.876206i
$675$	0.741128	+	2.76593i	0.0285260	+	0.106461i
$676$	40.5346	+	13.9171i	1.55902	+	0.535274i
$677$	3.36587	−	12.5616i	0.129361	−	0.482781i	−0.870597	−	0.491997i	$-0.836267\pi$
$677$	3.36587	−	12.5616i	0.129361	−	0.482781i	0.999958	+	0.00921600i	$0.00293358\pi$
$678$	35.3730	−	42.9495i	1.35849	−	1.64947i
$679$	9.17875	+	5.27914i	0.352248	+	0.202595i
$680$	−2.43688	−	1.31894i	−0.0934502	−	0.0505790i
$681$	24.3282	−	14.0459i	0.932259	−	0.538240i
$682$	62.7090	−	23.4775i	2.40125	−	0.899001i
$683$	−20.7439	+	5.55831i	−0.793743	+	0.212683i	−0.632835	−	0.774287i	$-0.718109\pi$
$683$	−20.7439	+	5.55831i	−0.793743	+	0.212683i	−0.160908	+	0.986969i	$0.551442\pi$
$684$	0.931919	−	13.4985i	0.0356328	−	0.516129i
$685$	3.36614	−	3.36614i	0.128614	−	0.128614i
$686$	21.2405	−	15.3245i	0.810966	−	0.585093i
$687$	8.17791			0.312007
$688$	2.59579	+	20.8363i	0.0989634	+	0.794378i
$689$	−20.8461	+	36.1066i	−0.794174	+	1.37555i
$690$	13.5756	+	6.17953i	0.516816	+	0.235251i
$691$	−34.7961	−	9.32359i	−1.32371	−	0.354686i	−0.473341	−	0.880879i	$-0.656952\pi$
$691$	−34.7961	−	9.32359i	−1.32371	−	0.354686i	−0.850365	+	0.526193i	$0.823619\pi$
$692$	1.16221	−	1.72633i	0.0441805	−	0.0656254i
$693$	23.8109	−	6.42233i	0.904500	−	0.243964i
$694$	−14.0131	−	11.5411i	−0.531929	−	0.438094i
$695$	−5.82815	+	3.36488i	−0.221074	+	0.127637i
$696$	−61.3011	−	14.6312i	−2.32361	−	0.554592i
$697$	0.00194524	+	0.00112309i	7.36812e−5	+	4.25399e-5i
$698$	−7.17515	−	1.19745i	−0.271584	−	0.0453241i
$699$	−35.4869	−	35.4869i	−1.34224	−	1.34224i
$700$	−5.19170	+	1.02284i	−0.196228	+	0.0386599i
$701$	14.5097	−	14.5097i	0.548026	−	0.548026i	−0.377844	−	0.925869i	$-0.623334\pi$
$701$	14.5097	−	14.5097i	0.548026	−	0.548026i	0.925869	+	0.377844i	$0.123334\pi$
$702$	−13.8069	−	19.3384i	−0.521107	−	0.729882i
$703$	−3.88839	+	6.73489i	−0.146653	+	0.254011i
$704$	29.6884	−	33.1486i	1.11892	−	1.24934i
$705$	1.71594	+	2.97210i	0.0646261	+	0.111936i
$706$	−15.4278	+	1.49241i	−0.580632	+	0.0561675i
$707$	18.4309	+	4.90588i	0.693164	+	0.184505i
$708$	34.6576	−	6.76855i	1.30251	−	0.254378i
$709$	−0.0124137	+	0.0463286i	−0.000466206	+	0.00173991i	−0.966159	−	0.257949i	$-0.916953\pi$
$709$	−0.0124137	+	0.0463286i	−0.000466206	+	0.00173991i	0.965692	+	0.259689i	$0.0836200\pi$
$710$	−7.18777	−	19.1987i	−0.269752	−	0.720514i
$711$	14.2528	+	8.22884i	0.534521	+	0.308606i
$712$	−17.4866	+	18.4761i	−0.655339	+	0.692420i
$713$		−	41.5184i		−	1.55488i
$714$	−1.29182	+	7.82029i	−0.0483453	+	0.292667i
$715$	23.0788	+	23.0788i	0.863097	+	0.863097i
$716$	−17.2521	−	1.19106i	−0.644742	−	0.0445120i
$717$	−4.34229	−	16.2056i	−0.162166	−	0.605210i
$718$	−3.31421	−	1.50860i	−0.123685	−	0.0563005i
$719$	−8.55464	−	14.8171i	−0.319034	−	0.552584i	0.661253	−	0.750163i	$-0.270025\pi$
$719$	−8.55464	−	14.8171i	−0.319034	−	0.552584i	−0.980287	+	0.197580i	$0.936692\pi$
$720$	−2.60815	+	6.17474i	−0.0972000	+	0.230119i
$721$	41.3215	−	0.0683331i	1.53889	−	0.00254486i
$722$	−0.367782	−	3.80195i	−0.0136874	−	0.141494i
$723$	12.5170	+	3.35393i	0.465514	+	0.124734i
$724$	15.0140	−	7.33925i	0.557990	−	0.272761i
$725$	9.95343	−	2.66701i	0.369661	−	0.0990504i
$726$	10.0381	−	60.1484i	0.372547	−	2.23232i
$727$			48.7603i			1.80842i	0.427091	+	0.904209i	$0.359539\pi$
$727$			48.7603i			1.80842i	−0.427091	+	0.904209i	$0.640461\pi$
$728$	37.3701	−	23.0539i	1.38503	−	0.854433i
$729$		−	0.224724i		−	0.00832313i
$730$	−10.5270	−	1.75683i	−0.389621	−	0.0650232i
$731$	−4.96740	+	1.33101i	−0.183726	+	0.0492292i
$732$	−15.6505	−	5.37341i	−0.578457	−	0.198607i
$733$	−1.64747	−	0.441440i	−0.0608509	−	0.0163049i	0.228265	−	0.973599i	$-0.426695\pi$
$733$	−1.64747	−	0.441440i	−0.0608509	−	0.0163049i	−0.289116	+	0.957294i	$0.593361\pi$
$734$	−10.2722	+	0.993685i	−0.379154	+	0.0366776i
$735$	7.61153	+	13.0834i	0.280755	+	0.482590i
$736$	−12.7947	−	24.4463i	−0.471618	−	0.901101i
$737$	6.81803	+	11.8092i	0.251145	+	0.434996i
$738$	0.00225108	−	0.00494535i	8.28636e−5	−	0.000182041i
$739$	11.9314	+	44.5287i	0.438904	+	1.63801i	0.731547	+	0.681791i	$0.238799\pi$
$739$	11.9314	+	44.5287i	0.438904	+	1.63801i	−0.292643	+	0.956222i	$0.594535\pi$
$740$	2.90532	−	2.53007i	0.106802	−	0.0930072i
$741$	−36.2203	−	36.2203i	−1.33058	−	1.33058i
$742$	9.36292	+	24.8832i	0.343724	+	0.913490i
$743$		−	26.8815i		−	0.986188i	−0.869976	−	0.493094i	$-0.835866\pi$
$743$		−	26.8815i		−	0.986188i	0.869976	−	0.493094i	$-0.164134\pi$
$744$	52.0400	−	1.43177i	1.90788	−	0.0524914i
$745$	−5.94621	−	3.43305i	−0.217852	−	0.125777i
$746$	−20.9027	+	7.82574i	−0.765303	+	0.286521i
$747$	−0.0311158	+	0.116126i	−0.00113847	+	0.00424883i
$748$	9.04086	+	6.08652i	0.330567	+	0.222545i
$749$	−8.23666	+	8.26395i	−0.300961	+	0.301958i
$750$	−0.294444	−	3.04381i	−0.0107516	−	0.111144i
$751$	−23.5699	−	40.8243i	−0.860079	−	1.48970i	−0.871852	−	0.489770i	$-0.837081\pi$
$751$	−23.5699	−	40.8243i	−0.860079	−	1.48970i	0.0117727	−	0.999931i	$-0.496253\pi$
$752$	0.872416	−	6.28821i	0.0318137	−	0.229308i
$753$	−8.30474	+	14.3842i	−0.302642	+	0.524191i
$754$	−69.5909	+	49.6852i	−2.53435	+	1.80943i
$755$	−1.43776	+	1.43776i	−0.0523256	+	0.0523256i
$756$	−15.1179	−	1.01860i	−0.549834	−	0.0370462i
$757$	10.9623	+	10.9623i	0.398433	+	0.398433i	0.877680	−	0.479247i	$-0.159090\pi$
$757$	10.9623	+	10.9623i	0.398433	+	0.398433i	−0.479247	+	0.877680i	$0.659090\pi$
$758$	−2.08622	+	12.5007i	−0.0757751	+	0.454047i
$759$	−50.8082	−	29.3341i	−1.84422	−	1.06476i
$760$	2.65098	−	11.1070i	0.0961610	−	0.402892i
$761$	−17.6917	+	10.2143i	−0.641325	+	0.370269i	−0.785125	−	0.619337i	$-0.787401\pi$
$761$	−17.6917	+	10.2143i	−0.641325	+	0.370269i	0.143800	+	0.989607i	$0.454068\pi$
$762$	4.26088	−	5.17352i	0.154355	−	0.187417i
$763$	3.98831	−	14.9836i	0.144386	−	0.542444i
$764$	−46.1232	+	9.00776i	−1.66868	+	0.325889i
$765$	−1.58574	−	0.424897i	−0.0573324	−	0.0153622i
$766$	3.49596	−	7.68017i	0.126314	−	0.277496i
$767$	23.9553	−	41.4917i	0.864974	−	1.49818i
$768$	30.2002	−	16.8801i	1.08976	−	0.609109i
$769$	7.35969			0.265397			0.132699	−	0.991156i	$-0.457636\pi$
$769$	7.35969			0.265397			0.132699	+	0.991156i	$0.457636\pi$
$770$	20.7128	−	2.03824i	0.746438	−	0.0734530i
$771$	3.23282	−	3.23282i	0.116427	−	0.116427i
$772$	−6.06958	−	6.96980i	−0.218449	−	0.250849i
$773$	5.23213	−	1.40194i	0.188186	−	0.0504244i	−0.163495	−	0.986544i	$-0.552277\pi$
$773$	5.23213	−	1.40194i	0.188186	−	0.0504244i	0.351681	+	0.936120i	$0.385610\pi$
$774$	4.36181	+	11.6505i	0.156782	+	0.418768i
$775$	−7.37160	+	4.25600i	−0.264796	+	0.152880i
$776$	10.8493	−	3.22936i	0.389467	−	0.115927i
$777$	−9.55295	−	5.49435i	−0.342710	−	0.197109i
$778$	37.6915	+	31.0425i	1.35130	+	1.11293i
$779$	−0.00239575	+	0.00894105i	−8.58366e−5	+	0.000320346i
$780$	11.1441	+	22.7975i	0.399021	+	0.816283i
$781$	20.8691	+	77.8847i	0.746757	+	2.78693i
$782$	5.49988	−	3.92669i	0.196675	−	0.140418i
$783$	29.5071			1.05450
$784$	3.75607	−	27.7469i	0.134145	−	0.990962i
$785$	−11.6248			−0.414906
$786$	−26.9530	+	19.2433i	−0.961380	+	0.686387i
$787$	−10.1879	−	38.0216i	−0.363158	−	1.35532i	−0.869901	−	0.493227i	$-0.835817\pi$
$787$	−10.1879	−	38.0216i	−0.363158	−	1.35532i	0.506742	−	0.862098i	$-0.330850\pi$
$788$	−8.46679	+	4.13880i	−0.301617	+	0.147439i
$789$	4.49632	−	16.7805i	0.160073	−	0.597402i
$790$	10.7211	+	8.82985i	0.381440	+	0.314152i
$791$	−41.7299	−	24.0008i	−1.48374	−	0.853372i
$792$	12.5493	−	23.1863i	0.445922	−	0.823889i
$793$	−19.4429	+	11.2253i	−0.690436	+	0.398623i
$794$	−7.13196	−	19.0496i	−0.253104	−	0.676046i
$795$	−14.8411	+	3.97665i	−0.526358	+	0.141037i
$796$	33.5716	−	29.2355i	1.18991	−	1.03622i
$797$	−13.8004	+	13.8004i	−0.488837	+	0.488837i	−0.907939	−	0.419102i	$-0.862345\pi$
$797$	−13.8004	+	13.8004i	−0.488837	+	0.488837i	0.419102	+	0.907939i	$0.362345\pi$
$798$	−32.5071	+	3.19885i	−1.15074	+	0.113238i
$799$	1.55484			0.0550064
$800$	−3.02887	+	4.77765i	−0.107087	+	0.168915i
$801$	−7.53588	+	13.0525i	−0.266267	+	0.461189i
$802$	−0.473480	+	1.04018i	−0.0167192	+	0.0367299i
$803$	40.5477	+	10.8647i	1.43090	+	0.383407i
$804$	2.03210	+	10.4051i	0.0716667	+	0.366961i
$805$	3.31945	−	12.4708i	0.116995	−	0.439538i
$806$	44.9038	−	54.5218i	1.58167	−	1.92045i
$807$	54.9450	−	31.7225i	1.93416	−	1.11669i
$808$	17.3707	−	10.6765i	0.611101	−	0.375599i
$809$	0.784939	+	0.453185i	0.0275970	+	0.0159331i	0.513735	−	0.857949i	$-0.328261\pi$
$809$	0.784939	+	0.453185i	0.0275970	+	0.0159331i	−0.486138	+	0.873882i	$0.661595\pi$
$810$	2.61176	−	15.6498i	0.0917681	−	0.549877i
$811$	32.9654	+	32.9654i	1.15757	+	1.15757i	0.984996	+	0.172577i	$0.0552094\pi$
$811$	32.9654	+	32.9654i	1.15757	+	1.15757i	0.172577	+	0.984996i	$0.444791\pi$
$812$	−3.66553	+	54.4032i	−0.128635	+	1.90918i
$813$	12.1339	−	12.1339i	0.425556	−	0.425556i
$814$	−12.3325	+	8.80490i	−0.432253	+	0.308611i
$815$	6.32830	−	10.9609i	0.221671	−	0.383945i
$816$	5.11146	+	6.75824i	0.178937	+	0.236586i
$817$	−10.5964	−	18.3535i	−0.370720	−	0.642106i
$818$	−2.35608	−	24.3559i	−0.0823783	−	0.851586i
$819$	18.3646	−	18.4255i	0.641712	−	0.643838i
$820$	0.00256086	−	0.00380388i	8.94290e−5	−	0.000132837i
$821$	−9.41788	+	35.1480i	−0.328686	+	1.22667i	0.581867	+	0.813284i	$0.302322\pi$
$821$	−9.41788	+	35.1480i	−0.328686	+	1.22667i	−0.910554	+	0.413391i	$0.864344\pi$
$822$	−13.6334	+	5.10418i	−0.475519	+	0.178029i
$823$	33.8765	+	19.5586i	1.18086	+	0.681770i	0.956213	−	0.292670i	$-0.0945438\pi$
$823$	33.8765	+	19.5586i	1.18086	+	0.681770i	0.224647	+	0.974440i	$0.427877\pi$
$824$	30.3653	−	32.0834i	1.05783	−	1.11768i
$825$			12.0280i			0.418761i
$826$	−10.7594	−	28.5944i	−0.374366	−	0.994927i
$827$	0.906684	+	0.906684i	0.0315285	+	0.0315285i	0.722695	−	0.691167i	$-0.242903\pi$
$827$	0.906684	+	0.906684i	0.0315285	+	0.0315285i	−0.691167	+	0.722695i	$0.742903\pi$
$828$	−10.7357	−	12.3280i	−0.373092	−	0.428428i
$829$	−10.2315	−	38.1846i	−0.355356	−	1.32621i	−0.880036	−	0.474907i	$-0.842482\pi$
$829$	−10.2315	−	38.1846i	−0.355356	−	1.32621i	0.524680	−	0.851300i	$-0.324185\pi$
$830$	−0.0420337	+	0.0923428i	−0.00145901	+	0.00320526i
$831$	30.3563	+	52.5787i	1.05305	+	1.82393i
$832$	9.63772	−	45.9407i	0.334128	−	1.59271i
$833$	6.85764	−	0.0226809i	0.237603	−	0.000785847i
$834$	20.4841	−	1.98154i	0.709308	−	0.0686150i
$835$	17.4450	+	4.67436i	0.603708	+	0.161763i
$836$	−14.5849	+	42.4797i	−0.504431	+	1.46919i
$837$	−23.5436	+	6.30848i	−0.813785	+	0.218053i
$838$	30.3884	+	5.07146i	1.04975	+	0.175191i
$839$			28.7218i			0.991586i	0.868441	+	0.495793i	$0.165123\pi$
$839$			28.7218i			0.991586i	−0.868441	+	0.495793i	$0.834877\pi$
$840$	15.7456	+	3.73060i	0.543275	+	0.128718i
$841$		−	77.1836i		−	2.66150i
$842$	−3.92290	+	23.5062i	−0.135192	+	0.810076i
$843$	−24.7121	+	6.62159i	−0.851130	+	0.228060i
$844$	−18.0124	−	36.8482i	−0.620013	−	1.26837i
$845$	20.6985	+	5.54614i	0.712049	+	0.190793i
$846$	−0.362153	−	3.74376i	−0.0124511	−	0.128713i
$847$	−52.7591	+	0.0872473i	−1.81282	+	0.00299785i
$848$	26.1822	+	11.0591i	0.899102	+	0.379771i
$849$	12.8857	+	22.3188i	0.442237	+	0.765978i
$850$	−1.26097	−	0.573984i	−0.0432509	−	0.0196875i
$851$	2.43178	+	9.07553i	0.0833603	+	0.311105i
$852$	−4.31772	+	62.5408i	−0.147923	+	2.14261i
$853$	−30.7987	−	30.7987i	−1.05453	−	1.05453i	−0.998425	−	0.0561038i	$-0.982132\pi$
$853$	−30.7987	−	30.7987i	−1.05453	−	1.05453i	−0.0561038	−	0.998425i	$-0.517868\pi$
$854$	−2.33329	+	14.1250i	−0.0798435	+	0.483347i
$855$		−	6.76533i		−	0.231369i
$856$	0.343048	+	12.4686i	0.0117251	+	0.426168i
$857$	8.34203	+	4.81627i	0.284958	+	0.164521i	0.635666	−	0.771964i	$-0.280726\pi$
$857$	8.34203	+	4.81627i	0.284958	+	0.164521i	−0.350708	+	0.936485i	$0.614059\pi$
$858$	−34.9950	−	93.4725i	−1.19471	−	3.19110i
$859$	11.6551	−	43.4973i	0.397666	−	1.48411i	−0.419525	−	0.907744i	$-0.637804\pi$
$859$	11.6551	−	43.4973i	0.397666	−	1.48411i	0.817192	−	0.576366i	$-0.195530\pi$
$860$	2.01236	+	10.3040i	0.0686208	+	0.351365i
$861$	−0.0126757	−	0.00337400i	−0.000431988	−	0.000114986i
$862$	−11.7465	+	1.13630i	−0.400089	+	0.0387027i
$863$	8.41186	+	14.5698i	0.286343	+	0.495961i	0.972934	−	0.231083i	$-0.0742269\pi$
$863$	8.41186	+	14.5698i	0.286343	+	0.495961i	−0.686591	+	0.727044i	$0.740894\pi$
$864$	−11.9185	+	10.9699i	−0.405476	+	0.373202i
$865$	0.520274	−	0.901140i	0.0176898	−	0.0306397i
$866$	−13.2252	−	18.5238i	−0.449411	−	0.629463i
$867$	24.5257	−	24.5257i	0.832937	−	0.832937i
$868$	−8.70645	−	44.1917i	−0.295516	−	1.49997i
$869$	−38.6290	−	38.6290i	−1.31040	−	1.31040i
$870$	−31.0816	−	5.18716i	−1.05377	−	0.175861i
$871$	12.4569	+	7.19202i	0.422087	+	0.243692i
$872$	−8.67962	−	14.1218i	−0.293929	−	0.478224i
$873$	5.80802	−	3.35326i	0.196572	−	0.113491i
$874$	21.4966	+	17.7045i	0.727134	+	0.598864i
$875$	−2.55446	+	0.688996i	−0.0863566	+	0.0232923i
$876$	27.0734	+	18.2264i	0.914725	+	0.615814i
$877$	8.19106	+	2.19479i	0.276593	+	0.0741128i	0.394449	−	0.918918i	$-0.370936\pi$
$877$	8.19106	+	2.19479i	0.276593	+	0.0741128i	−0.117856	+	0.993031i	$0.537602\pi$
$878$	41.5412	+	18.9093i	1.40195	+	0.638156i
$879$	15.9687	−	27.6586i	0.538610	−	0.932900i
$880$	13.6674	−	17.5573i	0.460727	−	0.591858i
$881$	−13.5692			−0.457158			−0.228579	−	0.973525i	$-0.573408\pi$
$881$	−13.5692			−0.457158			−0.228579	+	0.973525i	$0.573408\pi$
$882$	−1.65189	−	16.5066i	−0.0556220	−	0.555805i
$883$	−39.1099	+	39.1099i	−1.31615	+	1.31615i	−0.399356	+	0.916796i	$0.630766\pi$
$883$	−39.1099	+	39.1099i	−1.31615	+	1.31615i	−0.916796	+	0.399356i	$0.869234\pi$
$884$	11.4693	+	0.791823i	0.385754	+	0.0266319i
$885$	17.0545	−	4.56975i	0.573282	−	0.153611i
$886$	−2.25035	+	0.842504i	−0.0756019	+	0.0283045i
$887$	28.2991	−	16.3385i	0.950190	−	0.548593i	0.0570504	−	0.998371i	$-0.481830\pi$
$887$	28.2991	−	16.3385i	0.950190	−	0.548593i	0.893140	+	0.449779i	$0.148497\pi$
$888$	−11.2916	+	3.36101i	−0.378921	+	0.112788i
$889$	−5.02660	−	2.89104i	−0.168587	−	0.0969623i
$890$	−8.08628	+	9.81828i	−0.271053	+	0.329110i
$891$	−16.1519	+	60.2796i	−0.541108	+	2.01944i
$892$	−10.3596	+	30.1732i	−0.346866	+	1.01027i
$893$	1.65838	+	6.18917i	0.0554957	+	0.207113i
$894$	12.2004	+	17.0883i	0.408041	+	0.571518i
$895$	−8.64660			−0.289024
$896$	−18.7449	−	23.3373i	−0.626223	−	0.779644i
$897$	−61.8863			−2.06633
$898$	5.61410	+	7.86332i	0.187345	+	0.262402i
$899$	22.7016	+	84.7235i	0.757140	+	2.82569i
$900$	−1.08834	+	3.16986i	−0.0362779	+	0.105662i
$901$	−1.80165	+	6.72386i	−0.0600218	+	0.224004i
$902$	−0.0114663	+	0.0139223i	−0.000381787	+	0.000463561i
$903$	25.9834	−	15.0589i	0.864672	−	0.501127i
$904$	−49.3247	+	14.6818i	−1.64052	+	0.488310i
$905$	7.23642	−	4.17795i	0.240547	−	0.138880i
$906$	5.82316	−	2.18013i	0.193462	−	0.0724298i
$907$	2.30659	−	0.618048i	0.0765890	−	0.0205220i	−0.220321	−	0.975427i	$-0.570711\pi$
$907$	2.30659	−	0.618048i	0.0765890	−	0.0205220i	0.296910	+	0.954905i	$0.404044\pi$
$908$	−25.9210	−	1.78955i	−0.860218	−	0.0593882i
$909$	8.54189	−	8.54189i	0.283317	−	0.283317i
$910$	17.8468	−	12.7865i	0.591614	−	0.423868i
$911$	39.0190			1.29276			0.646378	−	0.763018i	$-0.276283\pi$
$911$	39.0190			1.29276			0.646378	+	0.763018i	$0.276283\pi$
$912$	−21.4498	+	27.5548i	−0.710275	+	0.912432i
$913$	0.199533	−	0.345602i	0.00660359	−	0.0114378i
$914$	17.0589	+	7.76507i	0.564258	+	0.256846i
$915$	−7.99169	−	2.14137i	−0.264197	−	0.0707914i
$916$	−6.27451	−	4.22415i	−0.207316	−	0.139570i
$917$	20.2940	+	20.2270i	0.670167	+	0.667955i
$918$	−3.06236	−	2.52214i	−0.101073	−	0.0832430i
$919$	2.69526	−	1.55611i	0.0889086	−	0.0513314i	−0.454887	−	0.890549i	$-0.650320\pi$
$919$	2.69526	−	1.55611i	0.0889086	−	0.0513314i	0.543795	+	0.839218i	$0.316987\pi$
$920$	−7.22401	−	11.7535i	−0.238168	−	0.387501i
$921$	42.7961	+	24.7083i	1.41018	+	0.814168i
$922$	40.0349	+	6.68136i	1.31848	+	0.220039i
$923$	60.1430	+	60.1430i	1.97963	+	1.97963i
$924$	−60.2310	−	20.5684i	−1.98146	−	0.676650i
$925$	1.36208	−	1.36208i	0.0447850	−	0.0447850i
$926$	11.6092	+	16.2603i	0.381503	+	0.534348i
$927$	13.0860	−	22.6656i	0.429799	−	0.744435i
$928$	39.4759	+	42.8897i	1.29586	+	1.40792i
$929$	14.0919	+	24.4079i	0.462340	+	0.800796i	0.999077	−	0.0429537i	$-0.0136768\pi$
$929$	14.0919	+	24.4079i	0.462340	+	0.800796i	−0.536738	+	0.843749i	$0.680343\pi$
$930$	25.9089	−	2.50630i	0.849586	−	0.0821849i
$931$	7.40459	+	27.2732i	0.242676	+	0.893842i
$932$	8.89726	+	45.5574i	0.291440	+	1.49228i
$933$	−13.9132	+	51.9249i	−0.455499	+	1.69994i
$934$	−6.38682	−	17.0593i	−0.208983	−	0.558199i
$935$	4.71930	+	2.72469i	0.154338	+	0.0891069i
$936$	−0.764866	−	27.8002i	−0.0250004	−	0.908679i
$937$			30.7794i			1.00552i	0.864426	+	0.502759i	$0.167682\pi$
$937$			30.7794i			1.00552i	−0.864426	+	0.502759i	$0.832318\pi$
$938$	8.58482	−	3.23025i	0.280304	−	0.105472i
$939$	8.35396	+	8.35396i	0.272621	+	0.272621i
$940$	0.218623	−	3.16668i	0.00713070	−	0.103286i
$941$	−14.1576	−	52.8370i	−0.461526	−	1.72244i	−0.668158	−	0.744019i	$-0.732917\pi$
$941$	−14.1576	−	52.8370i	−0.461526	−	1.72244i	0.206633	−	0.978419i	$-0.433749\pi$
$942$	32.3545	+	14.7275i	1.05417	+	0.479849i
$943$	0.00559169	+	0.00968509i	0.000182091	+	0.000315390i
$944$	−30.0872	−	12.7085i	−0.979256	−	0.413628i
$945$	−7.57610	+	0.0125285i	−0.246451	+	0.000407553i
$946$	−3.97604	−	41.1023i	−0.129272	−	1.33635i
$947$	18.2037	+	4.87766i	0.591540	+	0.158503i	0.542157	−	0.840277i	$-0.317608\pi$
$947$	18.2037	+	4.87766i	0.591540	+	0.158503i	0.0493829	+	0.998780i	$0.484275\pi$
$948$	−18.6528	−	38.1583i	−0.605816	−	1.23932i
$949$	42.7718	−	11.4607i	1.38843	−	0.372029i
$950$	0.939846	−	5.63159i	0.0304926	−	0.182713i
$951$		−	42.7016i		−	1.38469i
$952$	5.03058	−	5.33286i	0.163042	−	0.172839i
$953$			39.4220i			1.27700i	0.769621	+	0.638501i	$0.220445\pi$
$953$			39.4220i			1.27700i	−0.769621	+	0.638501i	$0.779555\pi$
$954$	16.6094	+	2.77191i	0.537748	+	0.0897439i
$955$	−22.6966	+	6.08154i	−0.734446	+	0.196794i
$956$	−5.03909	+	14.6767i	−0.162976	+	0.474679i
$957$	119.720	+	32.0788i	3.86999	+	1.03696i
$958$	47.3425	−	4.57969i	1.52957	−	0.147963i
$959$	6.31551	+	10.8971i	0.203938	+	0.351886i
$960$	14.4829	−	9.46003i	0.467435	−	0.305321i
$961$	−20.7270	−	35.9002i	−0.668613	−	1.15807i
$962$	−6.62215	+	14.5480i	−0.213507	+	0.469047i
$963$	1.91267	+	7.13819i	0.0616350	+	0.230025i
$964$	−7.87130	−	9.03875i	−0.253518	−	0.291119i
$965$	−3.26760	−	3.26760i	−0.105188	−	0.105188i
$966$	−25.0382	+	30.5038i	−0.805591	+	0.981443i
$967$		−	37.7738i		−	1.21472i	−0.794425	−	0.607362i	$-0.792228\pi$
$967$		−	37.7738i		−	1.21472i	0.794425	−	0.607362i	$-0.207772\pi$
$968$	−38.7702	+	40.9640i	−1.24612	+	1.31663i
$969$	−7.40656	−	4.27618i	−0.237933	−	0.137371i
$970$	5.30055	−	1.98447i	0.170190	−	0.0637173i
$971$	−1.40218	+	5.23302i	−0.0449982	+	0.167936i	−0.984768	−	0.173871i	$-0.944372\pi$
$971$	−1.40218	+	5.23302i	−0.0449982	+	0.167936i	0.939770	+	0.341807i	$0.111039\pi$
$972$	−17.5011	+	25.9961i	−0.561349	+	0.833824i
$973$	−4.63678	−	17.1909i	−0.148648	−	0.551116i
$974$	−3.23515	−	33.4434i	−0.103661	−	1.07160i
$975$	6.34388	+	10.9879i	0.203167	+	0.351895i
$976$	9.23229	+	12.2067i	0.295519	+	0.390727i
$977$	0.685293	−	1.18696i	0.0219245	−	0.0379743i	−0.854855	−	0.518867i	$-0.826354\pi$
$977$	0.685293	−	1.18696i	0.0219245	−	0.0379743i	0.876779	+	0.480893i	$0.159687\pi$
$978$	−31.4997	+	22.4895i	−1.00725	+	0.719136i
$979$	35.3760	−	35.3760i	1.13062	−	1.13062i
$980$	0.918045	−	13.9699i	0.0293259	−	0.446251i
$981$	−6.94425	−	6.94425i	−0.221713	−	0.221713i
$982$	1.97176	−	11.8148i	0.0629213	−	0.377027i
$983$	27.6067	+	15.9387i	0.880516	+	0.508366i	0.870829	−	0.491587i	$-0.163583\pi$
$983$	27.6067	+	15.9387i	0.880516	+	0.508366i	0.00968747	+	0.999953i	$0.496916\pi$
$984$	−0.0119467	+	0.00734273i	−0.000380845	+	0.000234078i
$985$	−4.08081	+	2.35606i	−0.130025	+	0.0750702i
$986$	−9.07613	+	11.0201i	−0.289043	+	0.350953i
$987$	−8.76662	+	2.36455i	−0.279045	+	0.0752646i
$988$	9.08114	+	46.4989i	0.288910	+	1.47933i
$989$	−24.7320	−	6.62692i	−0.786432	−	0.210724i
$990$	5.46130	−	11.9978i	0.173572	−	0.381315i
$991$	−2.14173	+	3.70958i	−0.0680342	+	0.117839i	−0.898036	−	0.439922i	$-0.855006\pi$
$991$	−2.14173	+	3.70958i	−0.0680342	+	0.117839i	0.830002	+	0.557761i	$0.188339\pi$
$992$	−40.6673	−	25.7817i	−1.29119	−	0.818571i
$993$	−25.5582			−0.811066
$994$	53.9774	−	5.31163i	1.71206	−	0.168475i
$995$	15.7391	−	15.7391i	0.498964	−	0.498964i
$996$	0.233980	−	0.203759i	0.00741394	−	0.00645636i
$997$	−28.2745	+	7.57613i	−0.895462	+	0.239938i	−0.677066	−	0.735922i	$-0.736749\pi$
$997$	−28.2745	+	7.57613i	−0.895462	+	0.239938i	−0.218396	+	0.975860i	$0.570082\pi$
$998$	−0.300507	−	0.802661i	−0.00951239	−	0.0254078i
$999$	4.77690	−	2.75795i	0.151134	−	0.0872575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.501.46	yes	256
7.2	even	3	inner	560.2.cp.a.261.41	yes	256
16.13	even	4	inner	560.2.cp.a.221.41	✓	256
112.93	even	12	inner	560.2.cp.a.541.46	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.41	✓	256	16.13	even	4	inner
560.2.cp.a.261.41	yes	256	7.2	even	3	inner
560.2.cp.a.501.46	yes	256	1.1	even	1	trivial
560.2.cp.a.541.46	yes	256	112.93	even	12	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.821747 + 1.15097i) q^{2} +(-0.559657 - 2.08867i) q^{3} +(-0.649464 + 1.89161i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(1.94410 - 2.36050i) q^{6} +(-2.29347 - 1.31908i) q^{7} +(-2.71088 + 0.806912i) q^{8} +(-1.45124 + 0.837872i) q^{9} +(-1.32444 + 0.495854i) q^{10} +(5.37294 - 1.43967i) q^{11} +(4.31442 + 0.297861i) q^{12} +(4.14901 - 4.14901i) q^{13} +(-0.366427 - 3.72367i) q^{14} +2.16235 q^{15} +(-3.15639 - 2.45707i) q^{16} +(0.489834 - 0.848418i) q^{17} +(-2.15692 - 0.981812i) q^{18} +(3.89965 + 1.04491i) q^{19} +(-1.65906 - 1.11692i) q^{20} +(-1.47157 + 5.52853i) q^{21} +(6.07221 + 5.00104i) q^{22} +(4.22416 - 2.43882i) q^{23} +(3.20253 + 5.21054i) q^{24} +(-0.866025 - 0.500000i) q^{25} +(8.18483 + 1.36595i) q^{26} +(-2.02480 - 2.02480i) q^{27} +(3.98473 - 3.48166i) q^{28} +(-7.28641 + 7.28641i) q^{29} +(1.77690 + 2.48880i) q^{30} +(4.25600 - 7.37160i) q^{31} +(0.234258 - 5.65200i) q^{32} +(-6.01400 - 10.4165i) q^{33} +(1.37902 - 0.133400i) q^{34} +(1.86773 - 1.87392i) q^{35} +(-0.642402 - 3.28935i) q^{36} +(-0.498557 + 1.86064i) q^{37} +(2.00187 + 5.34702i) q^{38} +(-10.9879 - 6.34388i) q^{39} +(-0.0777889 - 2.82736i) q^{40} +0.00229279i q^{41} +(-7.57244 + 2.84932i) q^{42} +(-3.71185 - 3.71185i) q^{43} +(-0.766226 + 11.0985i) q^{44} +(-0.433715 - 1.61864i) q^{45} +(6.27820 + 2.85779i) q^{46} +(0.793555 + 1.37448i) q^{47} +(-3.36550 + 7.96777i) q^{48} +(3.52003 + 6.05057i) q^{49} +(-0.136169 - 1.40764i) q^{50} +(-2.04620 - 0.548278i) q^{51} +(5.15369 + 10.5430i) q^{52} +(-6.86340 + 1.83904i) q^{53} +(0.666611 - 3.99436i) q^{54} +5.56247i q^{55} +(7.28172 + 1.72526i) q^{56} -8.72985i q^{57} +(-14.3740 - 2.39886i) q^{58} +(7.88705 - 2.11333i) q^{59} +(-1.40437 + 4.09032i) q^{60} +(-3.69584 - 0.990298i) q^{61} +(11.9818 - 1.15907i) q^{62} +(4.43360 - 0.00733180i) q^{63} +(6.69779 - 4.37489i) q^{64} +(2.93380 + 5.08148i) q^{65} +(7.04715 - 15.4817i) q^{66} +(0.634479 + 2.36791i) q^{67} +(1.28675 + 1.47759i) q^{68} +(-7.45796 - 7.45796i) q^{69} +(3.69163 + 0.609816i) q^{70} +14.4957i q^{71} +(3.25805 - 3.44240i) q^{72} +(6.53559 + 3.77332i) q^{73} +(-2.55123 + 0.955150i) q^{74} +(-0.559657 + 2.08867i) q^{75} +(-4.50924 + 6.69799i) q^{76} +(-14.2217 - 3.78551i) q^{77} +(-1.72768 - 17.8598i) q^{78} +(-4.91056 - 8.50534i) q^{79} +(3.19028 - 2.41290i) q^{80} +(-5.60956 + 9.71604i) q^{81} +(-0.00263893 + 0.00188409i) q^{82} +(0.0507297 - 0.0507297i) q^{83} +(-9.50211 - 6.37423i) q^{84} +(0.692730 + 0.692730i) q^{85} +(1.22203 - 7.32244i) q^{86} +(19.2968 + 11.1410i) q^{87} +(-13.4037 + 8.23828i) q^{88} +(7.78910 - 4.49704i) q^{89} +(1.50661 - 1.82931i) q^{90} +(-14.9885 + 4.04275i) q^{91} +(1.86986 + 9.57440i) q^{92} +(-17.7787 - 4.76379i) q^{93} +(-0.929882 + 2.04283i) q^{94} +(-2.01861 + 3.49633i) q^{95} +(-11.9363 + 2.67389i) q^{96} -4.00212 q^{97} +(-4.07145 + 9.02349i) q^{98} +(-6.59114 + 6.59114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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