LMFDB - Embedded newform 560.2.cp.a.221.41

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			221.41
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.41

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.585896 + 1.28714i) q^{2} +(2.08867 - 0.559657i) q^{3} +(-1.31345 + 1.50826i) q^{4} +(0.965926 + 0.258819i) 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} +(0.232796 + 1.39492i) q^{10} +(-1.43967 - 5.37294i) q^{11} +(-1.89926 + 3.88533i) q^{12} +(4.14901 + 4.14901i) q^{13} +(-0.354109 + 3.72486i) q^{14} +2.16235 q^{15} +(-0.549688 - 3.96205i) q^{16} +(0.489834 - 0.848418i) q^{17} +(1.92873 + 1.37704i) q^{18} +(-1.04491 + 3.89965i) q^{19} +(-1.65906 + 1.11692i) q^{20} +(5.52853 + 1.47157i) q^{21} +(6.07221 - 5.00104i) q^{22} +(-4.22416 + 2.43882i) q^{23} +(-6.11373 - 0.168207i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.90947 + 7.77125i) q^{26} +(-2.02480 + 2.02480i) q^{27} +(-5.00189 + 1.72659i) q^{28} +(-7.28641 - 7.28641i) q^{29} +(1.26691 + 2.78324i) q^{30} +(4.25600 - 7.37160i) q^{31} +(4.77765 - 3.02887i) q^{32} +(-6.01400 - 10.4165i) q^{33} +(1.37902 + 0.133400i) q^{34} +(1.87392 + 1.86773i) q^{35} +(-0.642402 + 3.28935i) q^{36} +(1.86064 + 0.498557i) q^{37} +(-5.63159 + 0.939846i) q^{38} +(10.9879 + 6.34388i) q^{39} +(-2.40967 - 1.48105i) q^{40} -0.00229279i q^{41} +(1.34503 + 7.97818i) q^{42} +(-3.71185 + 3.71185i) q^{43} +(9.99472 + 4.88569i) q^{44} +(1.61864 - 0.433715i) q^{45} +(-5.61402 - 4.00818i) 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} +(0.548278 - 2.04620i) q^{51} +(-11.7073 + 0.808255i) q^{52} +(1.83904 + 6.86340i) q^{53} +(-3.79252 - 1.41988i) q^{54} -5.56247i q^{55} +(-5.15295 - 5.42652i) q^{56} +8.72985i q^{57} +(5.10954 - 13.6477i) q^{58} +(-2.11333 - 7.88705i) q^{59} +(-2.84014 + 3.26138i) q^{60} +(0.990298 - 3.69584i) 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} +(9.88397 - 13.8439i) q^{66} +(-2.36791 + 0.634479i) q^{67} +(0.636260 + 1.85315i) q^{68} +(-7.45796 + 7.45796i) q^{69} +(-1.30611 + 3.50629i) q^{70} -14.4957i q^{71} +(-4.61023 + 1.10035i) q^{72} +(-6.53559 - 3.77332i) q^{73} +(0.448429 + 2.68700i) q^{74} +(2.08867 + 0.559657i) q^{75} +(-4.50924 - 6.69799i) q^{76} +(3.78551 - 14.2217i) q^{77} +(-1.72768 + 17.8598i) q^{78} +(-4.91056 - 8.50534i) q^{79} +(0.494496 - 3.96932i) q^{80} +(-5.60956 + 9.71604i) q^{81} +(0.00295113 - 0.00134333i) q^{82} +(0.0507297 + 0.0507297i) q^{83} +(-9.48097 + 6.40562i) q^{84} +(0.692730 - 0.692730i) q^{85} +(-6.95243 - 2.60291i) q^{86} +(-19.2968 - 11.1410i) q^{87} +(-0.432699 + 15.7271i) q^{88} +(-7.78910 + 4.49704i) q^{89} +(1.50661 + 1.82931i) q^{90} +(4.04275 + 14.9885i) q^{91} +(1.86986 - 9.57440i) q^{92} +(4.76379 - 17.7787i) q^{93} +(-1.30420 + 1.82672i) q^{94} +(-2.01861 + 3.49633i) q^{95} +(8.28379 - 9.00015i) q^{96} -4.00212 q^{97} +(-5.72555 + 8.07577i) 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.585896	+	1.28714i	0.414291	+	0.910144i
$2$	0.585896	+	1.28714i	0.414291	+	0.910144i
$3$	2.08867	−	0.559657i	1.20589	−	0.323118i	0.400743	−	0.916190i	$-0.368752\pi$
$3$	2.08867	−	0.559657i	1.20589	−	0.323118i	0.805149	+	0.593073i	$0.202085\pi$
$4$	−1.31345	+	1.50826i	−0.656726	+	0.754129i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	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
$10$	0.232796	+	1.39492i	0.0736166	+	0.441113i
$11$	−1.43967	−	5.37294i	−0.434078	−	1.62000i	−0.743263	−	0.668999i	$-0.766723\pi$
$11$	−1.43967	−	5.37294i	−0.434078	−	1.62000i	0.309185	−	0.951002i	$-0.399944\pi$
$12$	−1.89926	+	3.88533i	−0.548268	+	1.12160i
$13$	4.14901	+	4.14901i	1.15073	+	1.15073i	0.986407	+	0.164323i	$0.0525438\pi$
$13$	4.14901	+	4.14901i	1.15073	+	1.15073i	0.164323	+	0.986407i	$0.447456\pi$
$14$	−0.354109	+	3.72486i	−0.0946396	+	0.995512i
$15$	2.16235			0.558316
$16$	−0.549688	−	3.96205i	−0.137422	−	0.990513i
$17$	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	$0.128761\pi$
$18$	1.92873	+	1.37704i	0.454606	+	0.324571i
$19$	−1.04491	+	3.89965i	−0.239718	+	0.894640i	0.736247	+	0.676713i	$0.236596\pi$
$19$	−1.04491	+	3.89965i	−0.239718	+	0.894640i	−0.975965	+	0.217927i	$0.930070\pi$
$20$	−1.65906	+	1.11692i	−0.370978	+	0.249751i
$21$	5.52853	+	1.47157i	1.20643	+	0.321123i
$22$	6.07221	−	5.00104i	1.29460	−	1.06623i
$23$	−4.22416	+	2.43882i	−0.880798	+	0.508529i	−0.870921	−	0.491422i	$-0.836477\pi$
$23$	−4.22416	+	2.43882i	−0.880798	+	0.508529i	−0.00987662	+	0.999951i	$0.503144\pi$
$24$	−6.11373	−	0.168207i	−1.24796	−	0.0343350i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.90947	+	7.77125i	−0.570593	+	1.52407i
$27$	−2.02480	+	2.02480i	−0.389673	+	0.389673i
$28$	−5.00189	+	1.72659i	−0.945268	+	0.326296i
$29$	−7.28641	−	7.28641i	−1.35305	−	1.35305i	−0.882225	−	0.470828i	$-0.843955\pi$
$29$	−7.28641	−	7.28641i	−1.35305	−	1.35305i	−0.470828	−	0.882225i	$-0.656045\pi$
$30$	1.26691	+	2.78324i	0.231305	+	0.508148i
$31$	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	$-0.110298\pi$
$32$	4.77765	−	3.02887i	0.844577	−	0.535434i
$33$	−6.01400	−	10.4165i	−1.04690	−	1.81329i
$34$	1.37902	+	0.133400i	0.236501	+	0.0228779i
$35$	1.87392	+	1.86773i	0.316750	+	0.315704i
$36$	−0.642402	+	3.28935i	−0.107067	+	0.548224i
$37$	1.86064	+	0.498557i	0.305887	+	0.0819622i	0.408498	−	0.912759i	$-0.366053\pi$
$37$	1.86064	+	0.498557i	0.305887	+	0.0819622i	−0.102610	+	0.994722i	$0.532719\pi$
$38$	−5.63159	+	0.939846i	−0.913565	+	0.152463i
$39$	10.9879	+	6.34388i	1.75948	+	1.01583i
$40$	−2.40967	−	1.48105i	−0.381002	−	0.234174i
$41$		−	0.00229279i		−	0.000358073i	−1.00000		0.000179037i	$-0.999943\pi$
$41$		−	0.00229279i		−	0.000358073i	1.00000		0.000179037i	$-5.69891e-5\pi$
$42$	1.34503	+	7.97818i	0.207542	+	1.23106i
$43$	−3.71185	+	3.71185i	−0.566052	+	0.566052i	−0.931020	−	0.364968i	$-0.881080\pi$
$43$	−3.71185	+	3.71185i	−0.566052	+	0.566052i	0.364968	+	0.931020i	$0.381080\pi$
$44$	9.99472	+	4.88569i	1.50676	+	0.736546i
$45$	1.61864	−	0.433715i	0.241293	−	0.0646543i
$46$	−5.61402	−	4.00818i	−0.827742	−	0.590975i
$47$	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
$51$	0.548278	−	2.04620i	0.0767743	−	0.286526i
$52$	−11.7073	+	0.808255i	−1.62351	+	0.112085i
$53$	1.83904	+	6.86340i	0.252612	+	0.942761i	0.969403	+	0.245473i	$0.0789433\pi$
$53$	1.83904	+	6.86340i	0.252612	+	0.942761i	−0.716791	+	0.697288i	$0.754390\pi$
$54$	−3.79252	−	1.41988i	−0.516097	−	0.193221i
$55$		−	5.56247i		−	0.750044i
$56$	−5.15295	−	5.42652i	−0.688592	−	0.725149i
$57$			8.72985i			1.15630i
$58$	5.10954	−	13.6477i	0.670916	−	1.79203i
$59$	−2.11333	−	7.88705i	−0.275132	−	1.02681i	−0.955753	−	0.294171i	$-0.904956\pi$
$59$	−2.11333	−	7.88705i	−0.275132	−	1.02681i	0.680621	−	0.732636i	$-0.261710\pi$
$60$	−2.84014	+	3.26138i	−0.366660	+	0.421042i
$61$	0.990298	−	3.69584i	0.126795	−	0.473204i	−0.873103	−	0.487536i	$-0.837896\pi$
$61$	0.990298	−	3.69584i	0.126795	−	0.473204i	0.999897	+	0.0143324i	$0.00456232\pi$
$62$	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
$66$	9.88397	−	13.8439i	1.21663	−	1.70406i
$67$	−2.36791	+	0.634479i	−0.289286	+	0.0775139i	−0.400544	−	0.916278i	$-0.631179\pi$
$67$	−2.36791	+	0.634479i	−0.289286	+	0.0775139i	0.111258	+	0.993792i	$0.464512\pi$
$68$	0.636260	+	1.85315i	0.0771578	+	0.224728i
$69$	−7.45796	+	7.45796i	−0.897833	+	0.897833i
$70$	−1.30611	+	3.50629i	−0.156110	+	0.419082i
$71$		−	14.4957i		−	1.72033i	−0.510017	−	0.860164i	$-0.670361\pi$
$71$		−	14.4957i		−	1.72033i	0.510017	−	0.860164i	$-0.329639\pi$
$72$	−4.61023	+	1.10035i	−0.543320	+	0.129678i
$73$	−6.53559	−	3.77332i	−0.764933	−	0.441634i	0.0661312	−	0.997811i	$-0.478934\pi$
$73$	−6.53559	−	3.77332i	−0.764933	−	0.441634i	−0.831064	+	0.556177i	$0.812268\pi$
$74$	0.448429	+	2.68700i	0.0521288	+	0.312358i
$75$	2.08867	+	0.559657i	0.241178	+	0.0646236i
$76$	−4.50924	−	6.69799i	−0.517245	−	0.768312i
$77$	3.78551	−	14.2217i	0.431398	−	1.62072i
$78$	−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	$-0.352986\pi$
$80$	0.494496	−	3.96932i	0.0552864	−	0.443783i
$81$	−5.60956	+	9.71604i	−0.623284	+	1.07956i
$82$	0.00295113	−	0.00134333i	0.000325898	−	0.000148346i
$83$	0.0507297	+	0.0507297i	0.00556831	+	0.00556831i	0.709885	−	0.704317i	$-0.248747\pi$
$83$	0.0507297	+	0.0507297i	0.00556831	+	0.00556831i	−0.704317	+	0.709885i	$0.748747\pi$
$84$	−9.48097	+	6.40562i	−1.03446	+	0.698910i
$85$	0.692730	−	0.692730i	0.0751372	−	0.0751372i
$86$	−6.95243	−	2.60291i	−0.749700	−	0.280679i
$87$	−19.2968	−	11.1410i	−2.06883	−	1.19444i
$88$	−0.432699	+	15.7271i	−0.0461258	+	1.67651i
$89$	−7.78910	+	4.49704i	−0.825642	+	0.476685i	−0.852358	−	0.522958i	$-0.824828\pi$
$89$	−7.78910	+	4.49704i	−0.825642	+	0.476685i	0.0267159	+	0.999643i	$0.491495\pi$
$90$	1.50661	+	1.82931i	0.158810	+	0.192826i
$91$	4.04275	+	14.9885i	0.423795	+	1.57123i
$92$	1.86986	−	9.57440i	0.194946	−	0.998200i
$93$	4.76379	−	17.7787i	0.493982	−	1.84357i
$94$	−1.30420	+	1.82672i	−0.134518	+	0.188411i
$95$	−2.01861	+	3.49633i	−0.207105	+	0.358716i
$96$	8.28379	−	9.00015i	0.845460	−	0.918574i
$97$	−4.00212			−0.406354			−0.203177	−	0.979142i	$-0.565127\pi$
$97$	−4.00212			−0.406354			−0.203177	+	0.979142i	$0.565127\pi$
$98$	−5.72555	+	8.07577i	−0.578368	+	0.815776i
$99$	−6.59114	−	6.59114i	−0.662435	−	0.662435i
$100$	−1.89161	+	0.649464i	−0.189161	+	0.0649464i
$101$	1.86577	+	6.96314i	0.185651	+	0.692858i	0.994490	+	0.104829i	$0.0334294\pi$
$101$	1.86577	+	6.96314i	0.185651	+	0.692858i	−0.808840	+	0.588029i	$0.799904\pi$
$102$	2.95498	−	0.493151i	0.292587	−	0.0488292i
$103$	13.5257	−	7.80905i	1.33272	−	0.769448i	0.347007	−	0.937863i	$-0.387198\pi$
$103$	13.5257	−	7.80905i	1.33272	−	0.769448i	0.985716	+	0.168414i	$0.0538647\pi$
$104$	−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
$107$	−4.25971	−	1.14139i	−0.411802	−	0.110342i	0.0469694	−	0.998896i	$-0.485044\pi$
$107$	−4.25971	−	1.14139i	−0.411802	−	0.110342i	−0.458772	+	0.888554i	$0.651710\pi$
$108$	−0.394445	−	5.71340i	−0.0379554	−	0.549772i
$109$	−5.66078	+	1.51680i	−0.542204	+	0.145283i	−0.519518	−	0.854459i	$-0.673889\pi$
$109$	−5.66078	+	1.51680i	−0.542204	+	0.145283i	−0.0226862	+	0.999743i	$0.507222\pi$
$110$	7.15967	−	3.25903i	0.682648	−	0.310736i
$111$	4.16528			0.395351
$112$	3.96559	−	9.81194i	0.374713	−	0.927141i
$113$	18.1951			1.71165			0.855824	−	0.517266i	$-0.173050\pi$
$113$	18.1951			1.71165			0.855824	+	0.517266i	$0.173050\pi$
$114$	−11.2365	+	5.11478i	−1.05240	+	0.479043i
$115$	−4.71144	+	1.26243i	−0.439344	+	0.117722i
$116$	20.5601	−	1.41944i	1.90896	−	0.131792i
$117$	9.49755	+	2.54486i	0.878048	+	0.235272i
$118$	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
$122$	5.33727	−	0.890728i	0.483214	−	0.0806427i
$123$	−0.00128317	−	0.00478887i	−0.000115700	−	0.000431797i
$124$	5.52823	+	16.1014i	0.496450	+	1.44595i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	2.60706	+	5.70236i	0.232256	+	0.508006i
$127$	2.19170			0.194482			0.0972410	−	0.995261i	$-0.468998\pi$
$127$	2.19170			0.194482			0.0972410	+	0.995261i	$0.468998\pi$
$128$	−1.70689	+	11.1842i	−0.150869	+	0.988554i
$129$	−5.67546	+	9.83019i	−0.499697	+	0.865500i
$130$	−4.82167	+	6.75342i	−0.422889	+	0.592314i
$131$	2.80294	−	10.4607i	0.244894	−	0.913956i	−0.728543	−	0.685000i	$-0.759802\pi$
$131$	2.80294	−	10.4607i	0.244894	−	0.913956i	0.973437	−	0.228956i	$-0.0735311\pi$
$132$	23.6099	+	4.61097i	2.05498	+	0.401334i
$133$	−7.54043	+	7.56541i	−0.653838	+	0.656004i
$134$	−2.20401	−	2.67609i	−0.190397	−	0.231179i
$135$	−2.47986	+	1.43175i	−0.213433	+	0.123225i
$136$	−2.01248	+	1.90471i	−0.172569	+	0.163327i
$137$	4.12267	+	2.38022i	0.352223	+	0.203356i	0.665664	−	0.746252i	$-0.268148\pi$
$137$	4.12267	+	2.38022i	0.352223	+	0.203356i	−0.313441	+	0.949608i	$0.601482\pi$
$138$	−13.9690	−	5.22984i	−1.18912	−	0.445194i
$139$	4.75866	−	4.75866i	0.403625	−	0.403625i	−0.475884	−	0.879508i	$-0.657872\pi$
$139$	4.75866	−	4.75866i	0.403625	−	0.403625i	0.879508	+	0.475884i	$0.157872\pi$
$140$	−5.27833	+	0.373179i	−0.446100	+	0.0315394i
$141$	2.42671	+	2.42671i	0.204366	+	0.204366i
$142$	18.6580	−	8.49300i	1.56575	−	0.712717i
$143$	16.3192	−	28.2656i	1.36468	−	2.36369i
$144$	−4.11742	−	5.28931i	−0.343118	−	0.440776i
$145$	−5.15227	−	8.92400i	−0.427873	−	0.741098i
$146$	1.02762	−	10.6230i	0.0850461	−	0.879165i
$147$	10.7384	+	10.6676i	0.885689	+	0.879850i
$148$	−3.19581	+	2.15149i	−0.262694	+	0.176852i
$149$	6.63213	+	1.77707i	0.543326	+	0.145584i	0.520035	−	0.854145i	$-0.325919\pi$
$149$	6.63213	+	1.77707i	0.543326	+	0.145584i	0.0232908	+	0.999729i	$0.492586\pi$
$150$	0.503386	+	3.01630i	0.0411013	+	0.246280i
$151$	−1.76089	−	1.01665i	−0.143300	−	0.0827340i	0.426636	−	0.904423i	$-0.359699\pi$
$151$	−1.76089	−	1.01665i	−0.143300	−	0.0827340i	−0.569936	+	0.821689i	$0.693032\pi$
$152$	5.97929	−	9.72834i	0.484985	−	0.789073i
$153$		−	1.64167i		−	0.132721i
$154$	20.5233	−	3.45998i	1.65381	−	0.278813i
$155$	6.01889	−	6.01889i	0.483449	−	0.483449i
$156$	−24.0003	+	8.24025i	−1.92156	+	0.659748i
$157$	−11.2287	+	3.00871i	−0.896145	+	0.240121i	−0.677360	−	0.735652i	$-0.736876\pi$
$157$	−11.2287	+	3.00871i	−0.896145	+	0.240121i	−0.218785	+	0.975773i	$0.570209\pi$
$158$	8.07047	−	11.3038i	0.642052	−	0.899283i
$159$	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
$163$	3.27577	−	12.2253i	0.256578	−	0.957562i	−0.710628	−	0.703568i	$-0.751589\pi$
$163$	3.27577	−	12.2253i	0.256578	−	0.957562i	0.967206	−	0.253994i	$-0.0817443\pi$
$164$	0.00345811	+	0.00301146i	0.000270033	+	0.000235156i
$165$	−3.11307	−	11.6181i	−0.242352	−	0.904472i
$166$	−0.0355739	+	0.0950186i	−0.00276107	+	0.00737487i
$167$			18.0603i			1.39755i	0.715341	+	0.698776i	$0.246271\pi$
$167$			18.0603i			1.39755i	−0.715341	+	0.698776i	$0.753729\pi$
$168$	−13.7998	−	8.45030i	−1.06468	−	0.651955i
$169$			21.4286i			1.64836i
$170$	1.29751	+	0.485772i	0.0995143	+	0.0372570i
$171$	1.75100	+	6.53481i	0.133902	+	0.499729i
$172$	−0.723094	−	10.4738i	−0.0551354	−	0.798618i
$173$	0.269313	−	1.00509i	0.0204755	−	0.0764157i	−0.954932	−	0.296824i	$-0.904072\pi$
$173$	0.269313	−	1.00509i	0.0204755	−	0.0764157i	0.975408	+	0.220409i	$0.0707391\pi$
$174$	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
$178$	−10.3519	−	7.39085i	−0.775908	−	0.553968i
$179$	−8.35197	+	2.23790i	−0.624256	+	0.167269i	−0.557062	−	0.830471i	$-0.688071\pi$
$179$	−8.35197	+	2.23790i	−0.624256	+	0.167269i	−0.0671940	+	0.997740i	$0.521405\pi$
$180$	−1.47186	+	3.01100i	−0.109706	+	0.224427i
$181$	−5.90851	+	5.90851i	−0.439176	+	0.439176i	−0.891735	−	0.452558i	$-0.850511\pi$
$181$	−5.90851	+	5.90851i	−0.439176	+	0.439176i	0.452558	+	0.891735i	$0.350511\pi$
$182$	−16.9237	+	13.9853i	−1.25447	+	1.03666i
$183$		−	8.27361i		−	0.611603i
$184$	13.4191	−	3.20283i	0.989271	−	0.236116i
$185$	1.66820	+	0.963138i	0.122649	+	0.0708113i
$186$	25.6748	−	4.28481i	1.88256	−	0.314178i
$187$	−5.26370	−	1.41040i	−0.384920	−	0.103139i
$188$	−3.11537	−	0.608424i	−0.227211	−	0.0443739i
$189$	−7.31471	+	1.97294i	−0.532067	+	0.143510i
$190$	−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	$0.509874\pi$
$192$	16.4379	+	5.38923i	1.18630	+	0.388934i
$193$	−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	$0.219854\pi$
$194$	−2.34483	−	5.15128i	−0.168349	−	0.369841i
$195$	8.97161	+	8.97161i	0.642470	+	0.642470i
$196$	−13.7492	−	2.63801i	−0.982087	−	0.188430i
$197$	3.33197	−	3.33197i	0.237393	−	0.237393i	−0.578377	−	0.815770i	$-0.696314\pi$
$197$	3.33197	−	3.33197i	0.237393	−	0.237393i	0.815770	+	0.578377i	$0.196314\pi$
$198$	4.62199	−	12.3454i	0.328471	−	0.877352i
$199$	19.2764	+	11.1293i	1.36647	+	0.788932i	0.990475	−	0.137690i	$-0.0439678\pi$
$199$	19.2764	+	11.1293i	1.36647	+	0.788932i	0.375995	+	0.926622i	$0.377301\pi$
$200$	−1.94424	−	2.05425i	−0.137478	−	0.145257i
$201$	−4.59068	+	2.65043i	−0.323802	+	0.186947i
$202$	−7.86938	+	6.48117i	−0.553687	+	0.456014i
$203$	−7.09979	−	26.3226i	−0.498308	−	1.84748i
$204$	2.36606	+	3.51453i	0.165658	+	0.246066i
$205$	0.000593417	−	0.00221466i	4.14460e−5	−	0.000154679i
$206$	17.9760	+	12.8341i	1.25244	+	0.894195i
$207$	−4.08684	+	7.07861i	−0.284055	+	0.491997i
$208$	14.1579	−	18.7193i	0.981676	−	1.29795i
$209$	22.4569			1.55337
$210$	−0.765706	+	8.05445i	−0.0528388	+	0.555810i
$211$	−14.5010	−	14.5010i	−0.998292	−	0.998292i	0.00170639	−	0.999999i	$-0.499457\pi$
$211$	−14.5010	−	14.5010i	−0.998292	−	0.998292i	−0.999999	+	0.00170639i	$0.999457\pi$
$212$	−12.7673	−	6.24100i	−0.876860	−	0.428633i
$213$	−8.11264	−	30.2768i	−0.555869	−	2.07453i
$214$	−1.02663	−	6.15158i	−0.0701787	−	0.420513i
$215$	−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
$219$	−15.7624	−	4.22353i	−1.06513	−	0.285400i
$220$	8.38965	+	7.30604i	0.565630	+	0.492573i
$221$	5.55243	−	1.48777i	0.373497	−	0.100078i
$222$	2.44042	+	5.36129i	0.163790	+	0.359826i
$223$	15.9510			1.06816			0.534080	−	0.845434i	$-0.320658\pi$
$223$	15.9510			1.06816			0.534080	+	0.845434i	$0.320658\pi$
$224$	14.9527	−	0.644515i	0.999072	−	0.0430635i
$225$	1.67574			0.111716
$226$	10.6604	+	23.4196i	0.709121	+	1.55785i
$227$	−12.5487	+	3.36241i	−0.832885	+	0.223171i	−0.649972	−	0.759958i	$-0.725219\pi$
$227$	−12.5487	+	3.36241i	−0.832885	+	0.223171i	−0.182913	+	0.983129i	$0.558553\pi$
$228$	−13.1669	−	11.4662i	−0.871997	−	0.759370i
$229$	3.65309	+	0.978844i	0.241403	+	0.0646838i	0.377492	−	0.926013i	$-0.376787\pi$
$229$	3.65309	+	0.978844i	0.241403	+	0.0646838i	−0.136089	+	0.990697i	$0.543453\pi$
$230$	−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	−0.983208	−	0.182491i	$-0.941584\pi$
$233$	−20.0996	+	11.6045i	−1.31677	+	0.760237i	−0.333562	+	0.942728i	$0.608251\pi$
$234$	2.28899	+	13.7157i	0.149636	+	0.896622i
$235$	0.410774	+	1.53303i	0.0267960	+	0.100004i
$236$	14.6715	+	7.17182i	0.955032	+	0.466846i
$237$	−15.0166	−	15.0166i	−0.975432	−	0.975432i
$238$	2.98679	+	2.12500i	0.193605	+	0.137743i
$239$	7.75884			0.501878			0.250939	−	0.968003i	$-0.419261\pi$
$239$	7.75884			0.501878			0.250939	+	0.968003i	$0.419261\pi$
$240$	−1.18862	−	8.56733i	−0.0767248	−	0.553019i
$241$	−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	$0.228494\pi$
$242$	−22.9516	−	16.3865i	−1.47538	−	1.05337i
$243$	−4.05547	+	15.1352i	−0.260158	+	0.970924i
$244$	4.27358	+	6.34793i	0.273588	+	0.406385i
$245$	1.83409	+	6.75545i	0.117175	+	0.431590i
$246$	0.00541213	−	0.00445740i	0.000345065	−	0.000284193i
$247$	−20.5150	+	11.8443i	−1.30534	+	0.753638i
$248$	−17.4857	+	16.5493i	−1.11035	+	1.05088i
$249$	0.134349	+	0.0775663i	0.00851401	+	0.00491556i
$250$	−0.495854	+	1.32444i	−0.0313605	+	0.0837647i
$251$	−5.43145	+	5.43145i	−0.342830	+	0.342830i	−0.857430	−	0.514600i	$-0.827940\pi$
$251$	−5.43145	+	5.43145i	−0.342830	+	0.342830i	0.514600	+	0.857430i	$0.327940\pi$
$252$	−5.81226	+	6.69664i	−0.366138	+	0.421849i
$253$	19.1850	+	19.1850i	1.20615	+	1.20615i
$254$	1.28411	+	2.82102i	0.0805721	+	0.177007i
$255$	1.05919	−	1.83457i	0.0663292	−	0.114885i
$256$	−15.3957	+	4.35578i	−0.962230	+	0.272236i
$257$	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
$259$	3.60969	+	3.59777i	0.224295	+	0.223554i
$260$	−11.5176	−	2.24936i	−0.714291	−	0.139499i
$261$	−16.6794	−	4.46923i	−1.03243	−	0.276638i
$262$	15.1066	−	2.52111i	0.933289	−	0.155755i
$263$	−6.95771	−	4.01704i	−0.429031	−	0.247701i	0.269903	−	0.962888i	$-0.413008\pi$
$263$	−6.95771	−	4.01704i	−0.429031	−	0.247701i	−0.698934	+	0.715186i	$0.746342\pi$
$264$	7.89801	+	33.0908i	0.486089	+	2.03660i
$265$			7.10552i			0.436488i
$266$	−14.1556	−	5.27304i	−0.867938	−	0.323311i
$267$	−13.7520	+	13.7520i	−0.841611	+	0.841611i
$268$	2.15317	−	4.40477i	0.131526	−	0.269064i
$269$	−28.3411	+	7.59396i	−1.72798	+	0.463012i	−0.979717	−	0.200385i	$-0.935781\pi$
$269$	−28.3411	+	7.59396i	−1.72798	+	0.463012i	−0.748267	+	0.663397i	$0.769114\pi$
$270$	−3.29580	−	2.35307i	−0.200576	−	0.143203i
$271$	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
$275$	1.43967	−	5.37294i	0.0868156	−	0.324000i
$276$	−1.45286	−	21.0442i	−0.0874519	−	1.26671i
$277$	7.26691	+	27.1205i	0.436627	+	1.62951i	0.737144	+	0.675736i	$0.236174\pi$
$277$	7.26691	+	27.1205i	0.436627	+	1.62951i	−0.300517	+	0.953776i	$0.597159\pi$
$278$	8.91314	+	3.33698i	0.534575	+	0.200139i
$279$		−	14.2639i		−	0.853959i
$280$	−3.57288	−	6.57529i	−0.213521	−	0.392949i
$281$			11.8315i			0.705810i	0.935659	+	0.352905i	$0.114806\pi$
$281$			11.8315i			0.705810i	−0.935659	+	0.352905i	$0.885194\pi$
$282$	−1.70171	+	4.54531i	−0.101335	+	0.270669i
$283$	3.08468	+	11.5122i	0.183365	+	0.684328i	0.994975	+	0.100128i	$0.0319252\pi$
$283$	3.08468	+	11.5122i	0.183365	+	0.684328i	−0.811609	+	0.584201i	$0.801408\pi$
$284$	21.8633	+	19.0395i	1.29735	+	1.12978i
$285$	−2.25945	+	8.43239i	−0.133838	+	0.499492i
$286$	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
$290$	8.46773	−	11.8602i	0.497242	−	0.696456i
$291$	−8.35909	+	2.23981i	−0.490019	+	0.131300i
$292$	14.2753	−	4.90128i	0.835401	−	0.286826i
$293$	10.4438	−	10.4438i	0.610133	−	0.610133i	−0.332847	−	0.942981i	$-0.608009\pi$
$293$	10.4438	−	10.4438i	0.610133	−	0.610133i	0.942981	+	0.332847i	$0.108009\pi$
$294$	−7.43911	+	20.0719i	−0.433858	+	1.17062i
$295$		−	8.16528i		−	0.475401i
$296$	−4.64169	−	2.85290i	−0.269793	−	0.165822i
$297$	13.7942	+	7.96407i	0.800419	+	0.462122i
$298$	1.59840	+	9.57766i	0.0925927	+	0.554819i
$299$	−27.6448	−	7.40740i	−1.59874	−	0.428381i
$300$	−3.58747	+	2.41517i	−0.207123	+	0.139440i
$301$	−13.4093	+	3.61678i	−0.772898	+	0.208468i
$302$	0.276872	−	2.86217i	0.0159322	−	0.164699i
$303$	7.79393	+	13.4995i	0.447750	+	0.775525i
$304$	16.0250	+	1.99639i	0.919095	+	0.114501i
$305$	1.91311	−	3.31360i	0.109544	−	0.189736i
$306$	2.11306	−	0.961850i	0.120796	−	0.0549853i
$307$	−16.1597	−	16.1597i	−0.922283	−	0.922283i	0.0749078	−	0.997190i	$-0.476134\pi$
$307$	−16.1597	−	16.1597i	−0.922283	−	0.922283i	−0.997190	+	0.0749078i	$0.976134\pi$
$308$	16.4780	+	24.3891i	0.938919	+	1.38970i
$309$	23.8802	−	23.8802i	1.35850	−	1.35850i
$310$	11.2736	+	4.22070i	0.640296	+	0.239720i
$311$	21.5297	+	12.4302i	1.22083	+	0.704849i	0.965096	−	0.261897i	$-0.0843479\pi$
$311$	21.5297	+	12.4302i	1.22083	+	0.704849i	0.255739	+	0.966746i	$0.417681\pi$
$312$	−24.6680	−	26.0638i	−1.39655	−	1.47557i
$313$	4.73165	−	2.73182i	0.267449	−	0.154412i	−0.360279	−	0.932845i	$-0.617318\pi$
$313$	4.73165	−	2.73182i	0.267449	−	0.154412i	0.627728	+	0.778433i	$0.283985\pi$
$314$	−10.4515	−	12.6901i	−0.589810	−	0.716141i
$315$	4.28442	+	1.14042i	0.241400	+	0.0642552i
$316$	19.2780	+	3.76496i	1.08447	+	0.211796i
$317$	−5.11110	+	19.0749i	−0.287068	+	1.07135i	0.660247	+	0.751049i	$0.270452\pi$
$317$	−5.11110	+	19.0749i	−0.287068	+	1.07135i	−0.947315	+	0.320304i	$0.896215\pi$
$318$	−12.6258	+	17.6842i	−0.708020	+	0.991680i
$319$	−28.6594	+	49.6395i	−1.60462	+	2.77928i
$320$	5.33726	+	5.95933i	0.298362	+	0.333137i
$321$	−9.53591			−0.532243
$322$	−7.58846	−	16.5980i	−0.422888	−	0.924972i
$323$	2.79670	+	2.79670i	0.155612	+	0.155612i
$324$	−7.28641	−	21.2222i	−0.404801	−	1.17901i
$325$	1.51864	+	5.66766i	0.0842392	+	0.314385i
$326$	17.6550	−	2.94640i	0.977818	−	0.163186i
$327$	−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
$331$	−11.4169	−	3.05916i	−0.627531	−	0.168146i	−0.0689820	−	0.997618i	$-0.521975\pi$
$331$	−11.4169	−	3.05916i	−0.627531	−	0.168146i	−0.558549	+	0.829471i	$0.688642\pi$
$332$	−0.143145	+	0.00988249i	−0.00785608	+	0.000542372i
$333$	3.11796	−	0.835454i	0.170863	−	0.0457826i
$334$	−23.2462	+	10.5815i	−1.27197	+	0.578993i
$335$	−2.45144			−0.133936
$336$	2.79147	−	22.7132i	0.152287	−	1.23911i
$337$	19.7639			1.07661			0.538303	−	0.842751i	$-0.319065\pi$
$337$	19.7639			1.07661			0.538303	+	0.842751i	$0.319065\pi$
$338$	−27.5816	+	12.5549i	−1.50024	+	0.682899i
$339$	38.0035	−	10.1830i	2.06406	−	0.553064i
$340$	0.134948	+	1.95468i	0.00731861	+	0.106008i
$341$	−45.7344	−	12.2545i	−2.47666	−	0.663618i
$342$	−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
$346$	1.45148	−	0.242235i	0.0780321	−	0.0130226i
$347$	3.32239	+	12.3993i	0.178355	+	0.665631i	0.995956	+	0.0898450i	$0.0286372\pi$
$347$	3.32239	+	12.3993i	0.178355	+	0.665631i	−0.817600	+	0.575786i	$0.804696\pi$
$348$	42.1489	−	14.4714i	2.25942	−	0.775747i
$349$	−3.63719	−	3.63719i	−0.194695	−	0.194695i	0.603027	−	0.797721i	$-0.293961\pi$
$349$	−3.63719	−	3.63719i	−0.194695	−	0.194695i	−0.797721	+	0.603027i	$0.793961\pi$
$350$	−2.16910	+	3.04877i	−0.115943	+	0.162964i
$351$	−16.8018			−0.896816
$352$	−23.1522	−	21.3094i	−1.23402	−	1.13580i
$353$	−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	$0.260878\pi$
$354$	14.5089	−	20.3217i	0.771139	−	1.08009i
$355$	3.75177	−	14.0018i	0.199124	−	0.743139i
$356$	3.44791	−	17.6546i	0.182739	−	0.935693i
$357$	3.95657	−	3.96968i	0.209404	−	0.210098i
$358$	−7.77388	−	9.43897i	−0.410862	−	0.498865i
$359$	2.22990	−	1.28743i	0.117689	−	0.0679480i	−0.440000	−	0.897998i	$-0.645021\pi$
$359$	2.22990	−	1.28743i	0.117689	−	0.0679480i	0.557689	+	0.830050i	$0.311688\pi$
$360$	−4.73793	−	0.130354i	−0.249711	−	0.00687028i
$361$	2.33907	+	1.35047i	0.123109	+	0.0710771i
$362$	−11.0668	−	4.14330i	−0.581661	−	0.217767i
$363$	−30.4901	+	30.4901i	−1.60032	+	1.60032i
$364$	−27.9166	−	13.5892i	−1.46323	−	0.712269i
$365$	−5.33629	−	5.33629i	−0.279314	−	0.279314i
$366$	10.6493	−	4.84747i	0.556647	−	0.253381i
$367$	−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	$0.227665\pi$
$368$	11.9847	+	15.3957i	0.624745	+	0.802559i
$369$	−0.00192106	−	0.00332738i	−0.000100006	−	0.000173216i
$370$	−0.262298	+	2.71151i	−0.0136362	+	0.140965i
$371$	−4.83561	+	18.1669i	−0.251053	+	0.943177i
$372$	20.5579	+	30.5365i	1.06588	+	1.58324i
$373$	15.2446	+	4.08478i	0.789335	+	0.211502i	0.630896	−	0.775867i	$-0.282687\pi$
$373$	15.2446	+	4.08478i	0.789335	+	0.211502i	0.158439	+	0.987369i	$0.449354\pi$
$374$	−1.26859	−	7.60146i	−0.0655974	−	0.393062i
$375$	1.87265	+	1.08117i	0.0967031	+	0.0558316i
$376$	−1.04215	−	4.36638i	−0.0537450	−	0.225179i
$377$		−	60.4629i		−	3.11400i
$378$	−6.82510	−	8.25910i	−0.351046	−	0.424803i
$379$	6.33681	−	6.33681i	0.325500	−	0.325500i	−0.525372	−	0.850872i	$-0.676074\pi$
$379$	6.33681	−	6.33681i	0.325500	−	0.325500i	0.850872	+	0.525372i	$0.176074\pi$
$380$	−2.62202	−	7.63684i	−0.134507	−	0.391761i
$381$	4.57773	−	1.22660i	0.234524	−	0.0628406i
$382$	−19.3088	+	27.0447i	−0.987925	+	1.38373i
$383$	−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
$387$	−2.27672	+	8.49684i	−0.115732	+	0.431919i
$388$	5.25659	−	6.03623i	0.266863	−	0.306443i
$389$	−8.93635	−	33.3509i	−0.453091	−	1.69096i	−0.693641	−	0.720321i	$-0.743994\pi$
$389$	−8.93635	−	33.3509i	−0.453091	−	1.69096i	0.240550	−	0.970637i	$-0.422672\pi$
$390$	−6.29127	+	16.8041i	−0.318571	+	0.850910i
$391$			4.77847i			0.241658i
$392$	−4.66012	−	19.2427i	−0.235371	−	0.971905i
$393$		−	23.4176i		−	1.18126i
$394$	6.24089	+	2.33652i	0.314412	+	0.117712i
$395$	−2.54189	−	9.48647i	−0.127896	−	0.477316i
$396$	18.5983	−	1.28400i	0.934599	−	0.0645233i
$397$	3.72265	−	13.8931i	0.186834	−	0.697275i	−0.807396	−	0.590010i	$-0.799124\pi$
$397$	3.72265	−	13.8931i	0.186834	−	0.697275i	0.994230	−	0.107265i	$-0.0342094\pi$
$398$	−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	$0.826910\pi$
$402$	−6.10113	−	4.35596i	−0.304297	−	0.217256i
$403$	48.2431	−	12.9267i	2.40316	−	0.643924i
$404$	−12.9528	−	6.33169i	−0.644426	−	0.315013i
$405$	−7.93311	+	7.93311i	−0.394199	+	0.394199i
$406$	29.7211	−	24.5607i	1.47503	−	1.21893i
$407$		−	10.7149i		−	0.531116i
$408$	−3.13742	+	5.10460i	−0.155326	+	0.252715i
$409$	14.9845	+	8.65132i	0.740937	+	0.427780i	0.822410	−	0.568895i	$-0.192629\pi$
$409$	14.9845	+	8.65132i	0.740937	+	0.427780i	−0.0814726	+	0.996676i	$0.525962\pi$
$410$	0.00319826		0.000533751i	0.000157951		2.63601e-5i
$411$	9.94298	+	2.66421i	0.490451	+	0.131416i
$412$	−5.98725	+	30.6570i	−0.294971	+	1.51036i
$413$	5.55683	−	20.8764i	0.273434	−	1.02726i
$414$	−11.5056	−	1.11300i	−0.565470	−	0.0547009i
$415$	0.0358713	+	0.0621310i	0.00176085	+	0.00304989i
$416$	32.3894	+	7.25569i	1.58802	+	0.355739i
$417$	7.27604	−	12.6025i	0.356309	−	0.617146i
$418$	13.1574	+	28.9051i	0.643549	+	1.41379i
$419$	15.4043	+	15.4043i	0.752550	+	0.752550i	0.974954	−	0.222404i	$-0.0713905\pi$
$419$	15.4043	+	15.4043i	0.752550	+	0.752550i	−0.222404	+	0.974954i	$0.571391\pi$
$420$	−10.8158	+	3.73350i	−0.527758	+	0.182176i
$421$	11.9156	−	11.9156i	0.580732	−	0.580732i	−0.354372	−	0.935104i	$-0.615305\pi$
$421$	11.9156	−	11.9156i	0.580732	−	0.580732i	0.935104	+	0.354372i	$0.115305\pi$
$422$	10.1687	−	27.1609i	0.495007	−	1.32217i
$423$	2.30327	+	1.32980i	0.111989	+	0.0646569i
$424$	0.552731	−	20.0898i	0.0268430	−	0.975649i
$425$	0.848418	−	0.489834i	0.0411543	−	0.0237605i
$426$	34.2173	−	28.1811i	1.65783	−	1.36538i
$427$	7.14635	−	7.17002i	0.345836	−	0.346982i
$428$	7.31644	−	4.92559i	0.353653	−	0.238088i
$429$	18.2662	−	68.1706i	0.881903	−	3.29131i
$430$	−6.04185	−	4.31364i	−0.291364	−	0.208022i
$431$	−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	$0.231079\pi$
$432$	9.13537	+	6.90935i	0.439526	+	0.332426i
$433$	−16.0940			−0.773430			−0.386715	−	0.922199i	$-0.626390\pi$
$433$	−16.0940			−0.773430			−0.386715	+	0.922199i	$0.626390\pi$
$434$	25.9511	+	18.4634i	1.24569	+	0.886269i
$435$	−15.7558	−	15.7558i	−0.755431	−	0.755431i
$436$	5.14743	−	10.5302i	0.246517	−	0.504303i
$437$	−5.09668	−	19.0211i	−0.243807	−	0.909901i
$438$	−3.79888	−	22.7630i	−0.181517	−	1.08766i
$439$	−27.9502	+	16.1370i	−1.33399	+	0.770179i	−0.985908	−	0.167286i	$-0.946500\pi$
$439$	−27.9502	+	16.1370i	−1.33399	+	0.770179i	−0.348080	+	0.937465i	$0.613166\pi$
$440$	−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
$443$	1.64120	+	0.439759i	0.0779759	+	0.0208936i	0.297596	−	0.954692i	$-0.403815\pi$
$443$	1.64120	+	0.439759i	0.0779759	+	0.0208936i	−0.219620	+	0.975585i	$0.570482\pi$
$444$	−5.47089	+	6.28231i	−0.259637	+	0.298145i
$445$	−8.68761	+	2.32784i	−0.411832	+	0.110350i
$446$	9.34564	+	20.5312i	0.442529	+	0.972180i
$447$	14.8469			0.702233
$448$	9.59033	+	18.8686i	0.453101	+	0.891459i
$449$	6.83191			0.322418			0.161209	−	0.986920i	$-0.448461\pi$
$449$	6.83191			0.322418			0.161209	+	0.986920i	$0.448461\pi$
$450$	0.981812	+	2.15692i	0.0462831	+	0.101678i
$451$	−0.0123190	+	0.00330086i	−0.000580079	+	0.000155432i
$452$	−23.8984	+	27.4429i	−1.12408	+	1.29080i
$453$	−4.24690	−	1.13795i	−0.199537	−	0.0534657i
$454$	−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	−0.743824	−	0.668376i	$-0.766990\pi$
$457$	−11.4777	+	6.62667i	−0.536905	+	0.309982i	0.206919	+	0.978358i	$0.433657\pi$
$458$	0.880426	+	5.27554i	0.0411396	+	0.246510i
$459$	0.726060	+	2.70969i	0.0338896	+	0.126478i
$460$	4.28418	−	8.76420i	0.199751	−	0.408633i
$461$	20.2943	+	20.2943i	0.945200	+	0.945200i	0.998575	−	0.0533748i	$-0.0169978\pi$
$461$	20.2943	+	20.2943i	0.945200	+	0.945200i	−0.0533748	+	0.998575i	$0.516998\pi$
$462$	40.9298	−	18.7127i	1.90423	−	0.870595i
$463$	14.1275			0.656561			0.328280	−	0.944580i	$-0.393531\pi$
$463$	14.1275			0.656561			0.328280	+	0.944580i	$0.393531\pi$
$464$	−24.8639	+	32.8744i	−1.15428	+	1.52616i
$465$	9.20294	−	15.9400i	0.426776	−	0.739198i
$466$	−26.7129	−	19.0720i	−1.23745	−	0.883491i
$467$	3.33371	−	12.4416i	0.154266	−	0.575727i	−0.844901	−	0.534922i	$-0.820341\pi$
$467$	3.33371	−	12.4416i	0.154266	−	0.575727i	0.999167	−	0.0408053i	$-0.0129923\pi$
$468$	−16.3129	+	10.9822i	−0.754063	+	0.507653i
$469$	−6.26766	−	1.66831i	−0.289414	−	0.0770354i
$470$	−1.73255	+	1.42692i	−0.0799167	+	0.0658189i
$471$	−21.7691	+	12.5684i	−1.00307	+	0.579121i
$472$	−0.635168	+	23.0862i	−0.0292360	+	1.06263i
$473$	25.2874	+	14.5997i	1.16272	+	0.671295i
$474$	10.5303	−	28.1266i	0.483672	−	1.29190i
$475$	−2.85474	+	2.85474i	−0.130984	+	0.130984i
$476$	−0.985222	+	5.08944i	−0.0451576	+	0.233274i
$477$	8.41954	+	8.41954i	0.385504	+	0.385504i
$478$	4.54587	+	9.98670i	0.207923	+	0.456781i
$479$	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	$-0.112257\pi$
$480$	10.3309	−	6.54948i	0.471540	−	0.298941i
$481$	5.65130	+	9.78834i	0.257677	+	0.446310i
$482$	−8.43577	−	0.816036i	−0.384239	−	0.0371694i
$483$	−26.9423	+	7.26694i	−1.22592	+	0.330657i
$484$	7.64449	−	39.1427i	0.347477	−	1.77921i
$485$	−3.86575	−	1.03582i	−0.175535	−	0.0470344i
$486$	−21.8572	+	3.64771i	−0.991462	+	0.165463i
$487$	20.5754	+	11.8792i	0.932361	+	0.538299i	0.887557	−	0.460697i	$-0.152401\pi$
$487$	20.5754	+	11.8792i	0.932361	+	0.538299i	0.0448032	+	0.998996i	$0.485734\pi$
$488$	−5.66680	+	9.21991i	−0.256524	+	0.417366i
$489$		−	27.3679i		−	1.23762i
$490$	−7.62062	+	6.31871i	−0.344265	+	0.285450i
$491$	−5.98912	+	5.98912i	−0.270285	+	0.270285i	−0.829215	−	0.558930i	$-0.811212\pi$
$491$	−5.98912	+	5.98912i	−0.270285	+	0.270285i	0.558930	+	0.829215i	$0.311212\pi$
$492$	0.00890823	+	0.00435459i	0.000401614	+	0.000196320i
$493$	−9.75106	+	2.61279i	−0.439166	+	0.117674i
$494$	−27.2650	−	19.4661i	−1.22671	−	0.875822i
$495$	−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
$499$	0.156855	−	0.585390i	0.00702178	−	0.0262056i	−0.962326	−	0.271898i	$-0.912349\pi$
$499$	0.156855	−	0.585390i	0.00702178	−	0.0262056i	0.969348	+	0.245692i	$0.0790153\pi$
$500$	−1.99525	+	0.137749i	−0.0892303	+	0.00616033i
$501$	10.1076	+	37.7220i	0.451574	+	1.68530i
$502$	−10.1733	−	3.80876i	−0.454056	−	0.169993i
$503$		−	5.16116i		−	0.230125i	−0.993358	−	0.115062i	$-0.963293\pi$
$503$		−	5.16116i		−	0.230125i	0.993358	−	0.115062i	$-0.0367068\pi$
$504$	−12.0249	−	3.55765i	−0.535631	−	0.158470i
$505$			7.20877i			0.320786i
$506$	−13.4534	+	35.9342i	−0.598075	+	1.59747i
$507$	11.9927	+	44.7573i	0.532613	+	1.98774i
$508$	−2.87869	+	3.30565i	−0.127721	+	0.146665i
$509$	2.14479	−	8.00447i	0.0950662	−	0.354792i	−0.901963	−	0.431813i	$-0.857874\pi$
$509$	2.14479	−	8.00447i	0.0950662	−	0.354792i	0.997029	+	0.0770209i	$0.0245408\pi$
$510$	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
$514$	−1.73744	+	2.43352i	−0.0766350	+	0.107338i
$515$	15.0859	−	4.04226i	0.664765	−	0.178123i
$516$	−7.37202	−	21.4715i	−0.324535	−	0.945232i
$517$	6.24252	−	6.24252i	0.274546	−	0.274546i
$518$	−2.51592	+	6.75408i	−0.110543	+	0.296757i
$519$		−	2.25002i		−	0.0987651i
$520$	−3.85287	−	16.1426i	−0.168959	−	0.707901i
$521$	−19.3759	−	11.1867i	−0.848876	−	0.490099i	0.0113956	−	0.999935i	$-0.496373\pi$
$521$	−19.3759	−	11.1867i	−0.848876	−	0.490099i	−0.860271	+	0.509836i	$0.829706\pi$
$522$	−4.01987	−	24.0872i	−0.175945	−	1.05427i
$523$	1.51939	+	0.407119i	0.0664382	+	0.0178021i	0.291885	−	0.956453i	$-0.405718\pi$
$523$	1.51939	+	0.407119i	0.0664382	+	0.0178021i	−0.225447	+	0.974255i	$0.572384\pi$
$524$	12.0959	+	17.9672i	0.528413	+	0.784900i
$525$	4.05207	+	4.03869i	0.176847	+	0.176263i
$526$	1.09399	−	11.3091i	0.0477002	−	0.493101i
$527$	−4.16947	−	7.22173i	−0.181625	−	0.314583i
$528$	−37.9651	+	29.5536i	−1.65222	+	1.28616i
$529$	0.395681	−	0.685340i	0.0172035	−	0.0297974i
$530$	−9.14579	+	4.16309i	−0.397268	+	0.180833i
$531$	−9.67529	−	9.67529i	−0.419872	−	0.419872i
$532$	−1.50660	−	21.3097i	−0.0653195	−	0.923893i
$533$	0.00951280	−	0.00951280i	0.000412045	−	0.000412045i
$534$	−25.7580	−	9.64351i	−1.11466	−	0.417316i
$535$	−3.81916	−	2.20499i	−0.165116	−	0.0953301i
$536$	6.93109	+	0.190695i	0.299378	+	0.00823676i
$537$	−16.1920	+	9.34847i	−0.698738	+	0.403416i
$538$	−26.3794	−	32.0296i	−1.13730	−	1.38089i
$539$	27.4416	−	27.6237i	1.18199	−	1.18984i
$540$	1.09773	−	5.62081i	0.0472389	−	0.241881i
$541$	1.66754	−	6.22334i	0.0716931	−	0.267562i	−0.920770	−	0.390106i	$-0.872438\pi$
$541$	1.66754	−	6.22334i	0.0716931	−	0.267562i	0.992463	+	0.122543i	$0.0391051\pi$
$542$	−6.52123	+	9.13388i	−0.280111	+	0.392334i
$543$	−9.03418	+	15.6477i	−0.387694	+	0.671505i
$544$	−0.229495	−	5.53709i	−0.00983951	−	0.237401i
$545$	−5.86047			−0.251035
$546$	−27.5210	+	38.6821i	−1.17779	+	1.65544i
$547$	−4.01088	−	4.01088i	−0.171493	−	0.171493i	0.616142	−	0.787635i	$-0.288695\pi$
$547$	−4.01088	−	4.01088i	−0.171493	−	0.171493i	−0.787635	+	0.616142i	$0.788695\pi$
$548$	−9.00491	+	3.09174i	−0.384671	+	0.132073i
$549$	−1.65949	−	6.19328i	−0.0708251	−	0.264323i
$550$	7.75921	−	1.29492i	0.330854	−	0.0552156i
$551$	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
$555$	4.02335	+	1.07805i	0.170782	+	0.0457608i
$556$	0.927019	+	13.4276i	0.0393144	+	0.569456i
$557$	−24.8486	+	6.65815i	−1.05287	+	0.282115i	−0.743436	−	0.668807i	$-0.766805\pi$
$557$	−24.8486	+	6.65815i	−1.05287	+	0.282115i	−0.309431	+	0.950922i	$0.600139\pi$
$558$	18.3596	−	8.35717i	0.777226	−	0.353787i
$559$	−30.8011			−1.30275
$560$	6.36998	−	8.45124i	0.269181	−	0.357130i
$561$	−11.7834			−0.497498
$562$	−15.2288	+	6.93204i	−0.642389	+	0.292411i
$563$	−39.4734	+	10.5769i	−1.66361	+	0.445762i	−0.963375	−	0.268156i	$-0.913586\pi$
$563$	−39.4734	+	10.5769i	−1.66361	+	0.445762i	−0.700230	+	0.713918i	$0.746919\pi$
$564$	−6.84747	+	0.472739i	−0.288330	+	0.0199059i
$565$	17.5751	+	4.70923i	0.739390	+	0.198119i
$566$	−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	$-0.238179\pi$
$569$	40.2776	−	23.2543i	1.68852	−	0.974870i	0.955650	−	0.294505i	$-0.0951547\pi$
$570$	−12.1775	+	2.03227i	−0.510057	+	0.0851226i
$571$	1.11640	+	4.16645i	0.0467197	+	0.174360i	0.985343	−	0.170582i	$-0.0545649\pi$
$571$	1.11640	+	4.16645i	0.0467197	+	0.174360i	−0.938624	+	0.344943i	$0.887898\pi$
$572$	21.1974	+	61.7390i	0.886308	+	2.58144i
$573$	35.9276	+	35.9276i	1.50090	+	1.50090i
$574$	0.00854031		0.000811896i	0.000356466		3.38879e-5i
$575$	−4.87764			−0.203412
$576$	13.3857	+	0.737117i	0.557736	+	0.0307132i
$577$	−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	$0.194301\pi$
$578$	−13.1810	+	18.4618i	−0.548258	+	0.767912i
$579$	−2.58622	+	9.65192i	−0.107480	+	0.401120i
$580$	20.2270	+	3.95028i	0.839879	+	0.164027i
$581$	0.0494304	+	0.183264i	0.00205072	+	0.00760307i
$582$	−7.78051	−	9.44702i	−0.322512	−	0.391591i
$583$	34.2290	−	19.7621i	1.41762	−	0.818463i
$584$	14.6725	+	15.5027i	0.607152	+	0.641506i
$585$	8.51527	+	4.91629i	0.352063	+	0.203264i
$586$	19.5616	+	7.32364i	0.808082	+	0.302537i
$587$	−8.30891	+	8.30891i	−0.342946	+	0.342946i	−0.857474	−	0.514528i	$-0.827967\pi$
$587$	−8.30891	+	8.30891i	−0.342946	+	0.342946i	0.514528	+	0.857474i	$0.327967\pi$
$588$	−30.1939	+	2.18490i	−1.24518	+	0.0901039i
$589$	24.2995	+	24.2995i	1.00124	+	1.00124i
$590$	10.5098	−	4.78400i	0.432684	−	0.196954i
$591$	5.09461	−	8.82413i	0.209564	−	0.362976i
$592$	0.952536	−	7.64600i	0.0391490	−	0.314249i
$593$	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
$595$	2.50253	−	0.674988i	0.102594	−	0.0276718i
$596$	−11.3913	+	7.66887i	−0.466605	+	0.314129i
$597$	46.4906	+	12.4571i	1.90273	+	0.509836i
$598$	−6.66262	−	39.9226i	−0.272455	−	1.63256i
$599$	29.9291	+	17.2796i	1.22287	+	0.706025i	0.965529	−	0.260296i	$-0.0838201\pi$
$599$	29.9291	+	17.2796i	1.22287	+	0.706025i	0.257341	+	0.966321i	$0.417153\pi$
$600$	−5.21054	−	3.20253i	−0.212719	−	0.130743i
$601$		−	4.28545i		−	0.174807i	−0.996173	−	0.0874035i	$-0.972143\pi$
$601$		−	4.28545i		−	0.174807i	0.996173	−	0.0874035i	$-0.0278569\pi$
$602$	−12.5117	−	15.1405i	−0.509941	−	0.617083i
$603$	−2.90478	+	2.90478i	−0.118292	+	0.118292i
$604$	3.84623	−	1.32056i	0.156501	−	0.0537328i
$605$	−19.2616	+	5.16113i	−0.783096	+	0.209830i
$606$	−12.8093	+	17.9412i	−0.520341	+	0.728810i
$607$	−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
$611$	−2.41026	+	8.99520i	−0.0975085	+	0.363907i
$612$	2.47607	+	2.15626i	0.100089	+	0.0871617i
$613$	4.30412	+	16.0632i	0.173842	+	0.648786i	0.996746	+	0.0806063i	$0.0256857\pi$
$613$	4.30412	+	16.0632i	0.173842	+	0.648786i	−0.822904	+	0.568180i	$0.807648\pi$
$614$	11.3319	−	30.2677i	0.457317	−	1.22150i
$615$		−	0.00495780i		−	0.000199918i
$616$	−21.7378	+	35.4989i	−0.875839	+	1.43029i
$617$		−	12.3217i		−	0.496054i	−0.968753	−	0.248027i	$-0.920218\pi$
$617$		−	12.3217i		−	0.496054i	0.968753	−	0.248027i	$-0.0797822\pi$
$618$	44.7285	+	16.7458i	1.79924	+	0.673616i
$619$	−6.57887	−	24.5527i	−0.264427	−	0.986855i	−0.962600	−	0.270926i	$-0.912670\pi$
$619$	−6.57887	−	24.5527i	−0.264427	−	0.986855i	0.698173	−	0.715929i	$-0.253997\pi$
$620$	1.17252	+	16.9836i	0.0470895	+	0.682076i
$621$	3.61496	−	13.4912i	0.145063	−	0.541383i
$622$	−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
$626$	6.28849	+	4.48973i	0.251338	+	0.179446i
$627$	46.9049	−	12.5681i	1.87320	−	0.501923i
$628$	10.2104	−	20.8875i	0.407439	−	0.833503i
$629$	1.33439	−	1.33439i	0.0532056	−	0.0532056i
$630$	1.04235	+	6.18281i	0.0415283	+	0.246329i
$631$		−	26.2371i		−	1.04448i	−0.852797	−	0.522242i	$-0.825096\pi$
$631$		−	26.2371i		−	1.04448i	0.852797	−	0.522242i	$-0.174904\pi$
$632$	6.44890	+	27.0194i	0.256523	+	1.07477i
$633$	−38.4034	−	22.1722i	−1.52640	−	0.881267i
$634$	−27.5466	+	4.59720i	−1.09402	+	0.182578i
$635$	2.11702	+	0.567254i	0.0840114	+	0.0225108i
$636$	−30.1594	−	5.89007i	−1.19590	−	0.233556i
$637$	−10.4992	+	39.7085i	−0.415995	+	1.57331i
$638$	−80.6843	−	7.80501i	−3.19432	−	0.309003i
$639$	−12.1456	−	21.0368i	−0.480472	−	0.832202i
$640$	−4.54341	+	10.3613i	−0.179594	+	0.409568i
$641$	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	$-0.0554730\pi$
$642$	−5.58705	−	12.2740i	−0.220503	−	0.484418i
$643$	−2.48346	−	2.48346i	−0.0979382	−	0.0979382i	0.656440	−	0.754378i	$-0.272062\pi$
$643$	−2.48346	−	2.48346i	−0.0979382	−	0.0979382i	−0.754378	+	0.656440i	$0.772062\pi$
$644$	16.9179	−	19.4921i	0.666659	−	0.768097i
$645$	−8.02632	+	8.02632i	−0.316036	+	0.316036i
$646$	−1.96116	+	5.23831i	−0.0771610	+	0.206099i
$647$	11.6915	+	6.75011i	0.459642	+	0.265374i	0.711894	−	0.702287i	$-0.247838\pi$
$647$	11.6915	+	6.75011i	0.459642	+	0.265374i	−0.252252	+	0.967662i	$0.581171\pi$
$648$	23.0468	−	21.8126i	0.905366	−	0.856881i
$649$	−39.3341	+	22.7096i	−1.54400	+	0.891429i
$650$	−6.40529	+	5.27536i	−0.251236	+	0.206917i
$651$	34.3773	−	34.4911i	1.34735	−	1.35181i
$652$	14.1364	+	20.9981i	0.553624	+	0.822349i
$653$	12.3526	−	46.1006i	0.483395	−	1.80406i	−0.103786	−	0.994600i	$-0.533096\pi$
$653$	12.3526	−	46.1006i	0.483395	−	1.80406i	0.587181	−	0.809455i	$-0.300238\pi$
$654$	−14.5855	−	10.4135i	−0.570339	−	0.407199i
$655$	5.41486	−	9.37881i	0.211576	−	0.366460i
$656$	−0.00908413	+	0.00126032i	−0.000354676	+	4.92071e-5i
$657$	−12.6463			−0.493377
$658$	−5.40075	+	2.46917i	−0.210543	+	0.0962583i
$659$	−8.68312	−	8.68312i	−0.338246	−	0.338246i	0.517461	−	0.855707i	$-0.326877\pi$
$659$	−8.68312	−	8.68312i	−0.338246	−	0.338246i	−0.855707	+	0.517461i	$0.826877\pi$
$660$	21.6120	+	10.5646i	0.841248	+	0.411225i
$661$	−2.96949	−	11.0823i	−0.115500	−	0.431051i	0.883824	−	0.467820i	$-0.154960\pi$
$661$	−2.96949	−	11.0823i	−0.115500	−	0.431051i	−0.999324	+	0.0367682i	$0.988294\pi$
$662$	−2.75157	−	16.4875i	−0.106943	−	0.640806i
$663$	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
$667$	48.5492	+	13.0087i	1.87983	+	0.503700i
$668$	−27.2397	−	23.7214i	−1.05393	−	0.917808i
$669$	33.3164	−	8.92710i	1.28809	−	0.345142i
$670$	−1.43629	−	3.15534i	−0.0554886	−	0.121901i
$671$	−21.2832			−0.821630
$672$	30.8706	−	9.71458i	1.19086	−	0.374748i
$673$	4.31660			0.166393			0.0831963	−	0.996533i	$-0.473487\pi$
$673$	4.31660			0.166393			0.0831963	+	0.996533i	$0.473487\pi$
$674$	11.5796	+	25.4388i	0.446028	+	0.979868i
$675$	−2.76593	+	0.741128i	−0.106461	+	0.0285260i
$676$	−32.3199	−	28.1455i	−1.24307	−	1.08252i
$677$	−12.5616	−	3.36587i	−0.482781	−	0.129361i	0.00921600	−	0.999958i	$-0.497066\pi$
$677$	−12.5616	−	3.36587i	−0.482781	−	0.129361i	−0.491997	+	0.870597i	$0.663733\pi$
$678$	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
$682$	−11.0224	−	66.0463i	−0.422068	−	2.52905i
$683$	5.55831	+	20.7439i	0.212683	+	0.793743i	0.986969	+	0.160908i	$0.0514422\pi$
$683$	5.55831	+	20.7439i	0.212683	+	0.793743i	−0.774287	+	0.632835i	$0.781891\pi$
$684$	−12.1560	−	5.94220i	−0.464798	−	0.227206i
$685$	3.36614	+	3.36614i	0.128614	+	0.128614i
$686$	−23.7840	+	10.9691i	−0.908078	+	0.418801i
$687$	8.17791			0.312007
$688$	16.7469	+	12.6662i	0.638470	+	0.482894i
$689$	−20.8461	+	36.1066i	−0.794174	+	1.37555i
$690$	−12.1395	−	8.66709i	−0.462141	−	0.329950i
$691$	9.32359	−	34.7961i	0.354686	−	1.32371i	−0.526193	−	0.850365i	$-0.676381\pi$
$691$	9.32359	−	34.7961i	0.354686	−	1.32371i	0.880879	−	0.473341i	$-0.156952\pi$
$692$	1.16221	+	1.72633i	0.0441805	+	0.0656254i
$693$	−6.42233	−	23.8109i	−0.243964	−	0.904500i
$694$	−14.0131	+	11.5411i	−0.531929	+	0.438094i
$695$	5.82815	−	3.36488i	0.221074	−	0.127637i
$696$	43.3215	+	45.7728i	1.64210	+	1.73501i
$697$	−0.00194524	−	0.00112309i	−7.36812e−5	−	4.25399e-5i
$698$	2.55056	−	6.81259i	0.0965400	−	0.257860i
$699$	−35.4869	+	35.4869i	−1.34224	+	1.34224i
$700$	−5.19506	−	1.00567i	−0.196355	−	0.0380107i
$701$	14.5097	+	14.5097i	0.548026	+	0.548026i	0.925869	−	0.377844i	$-0.123334\pi$
$701$	14.5097	+	14.5097i	0.548026	+	0.548026i	−0.377844	+	0.925869i	$0.623334\pi$
$702$	−9.84413	−	21.6263i	−0.371543	−	0.816232i
$703$	−3.88839	+	6.73489i	−0.146653	+	0.254011i
$704$	13.8634	−	42.2852i	0.522496	−	1.59368i
$705$	1.71594	+	2.97210i	0.0646261	+	0.111936i
$706$	−15.4278	−	1.49241i	−0.580632	−	0.0561675i
$707$	−4.90588	+	18.4309i	−0.184505	+	0.693164i
$708$	34.6576	+	6.76855i	1.30251	+	0.254378i
$709$	0.0463286	+	0.0124137i	0.00173991	+	0.000466206i	0.259689	−	0.965692i	$-0.416380\pi$
$709$	0.0463286	+	0.0124137i	0.00173991	+	0.000466206i	−0.257949	+	0.966159i	$0.583047\pi$
$710$	20.2204	−	3.37455i	0.758859	−	0.126645i
$711$	−14.2528	−	8.22884i	−0.534521	−	0.308606i
$712$	24.7440	−	5.90583i	0.927322	−	0.221330i
$713$			41.5184i			1.55488i
$714$	7.42767	+	2.76684i	0.277974	+	0.103546i
$715$	23.0788	−	23.0788i	0.863097	−	0.863097i
$716$	7.59458	−	15.5363i	0.283823	−	0.580619i
$717$	16.2056	−	4.34229i	0.605210	−	0.162166i
$718$	2.96359	+	2.11589i	0.110600	+	0.0789641i
$719$	−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
$723$	−3.35393	+	12.5170i	−0.124734	+	0.465514i
$724$	−1.15102	−	16.6721i	−0.0427772	−	0.619614i
$725$	−2.66701	−	9.95343i	−0.0990504	−	0.369661i
$726$	−57.1091	−	21.3810i	−2.11952	−	0.793523i
$727$		−	48.7603i		−	1.80842i	−0.427091	−	0.904209i	$-0.640461\pi$
$727$		−	48.7603i		−	1.80842i	0.427091	−	0.904209i	$-0.359539\pi$
$728$	1.13502	−	43.8944i	0.0420668	−	1.62683i
$729$			0.224724i			0.00832313i
$730$	3.74203	−	9.99505i	0.138499	−	0.369933i
$731$	1.33101	+	4.96740i	0.0492292	+	0.183726i
$732$	12.4787	+	10.8670i	0.461227	+	0.401655i
$733$	0.441440	−	1.64747i	0.0163049	−	0.0608509i	−0.957294	−	0.289116i	$-0.906639\pi$
$733$	0.441440	−	1.64747i	0.0163049	−	0.0608509i	0.973599	+	0.228265i	$0.0733053\pi$
$734$	−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
$738$	0.00315725	−	0.00442217i	0.000116220	−	0.000162782i
$739$	−44.5287	+	11.9314i	−1.63801	+	0.438904i	−0.956222	−	0.292643i	$-0.905465\pi$
$739$	−44.5287	+	11.9314i	−1.63801	+	0.438904i	−0.681791	+	0.731547i	$0.738799\pi$
$740$	−3.64377	+	1.25105i	−0.133948	+	0.0459894i
$741$	−36.2203	+	36.2203i	−1.33058	+	1.33058i
$742$	−26.2165	+	4.41979i	−0.962436	+	0.162256i
$743$			26.8815i			0.986188i	0.869976	+	0.493094i	$0.164134\pi$
$743$			26.8815i			0.986188i	−0.869976	+	0.493094i	$0.835866\pi$
$744$	−27.2599	+	44.3521i	−0.999398	+	1.62603i
$745$	5.94621	+	3.43305i	0.217852	+	0.125777i
$746$	3.67407	+	22.0152i	0.134517	+	0.806032i
$747$	0.116126	+	0.0311158i	0.00424883	+	0.00113847i
$748$	9.04086	−	6.08652i	0.330567	−	0.222545i
$749$	−8.26395	−	8.23666i	−0.301958	−	0.300961i
$750$	−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	$-0.496253\pi$
$752$	5.00954	−	3.89964i	0.182679	−	0.142205i
$753$	−8.30474	+	14.3842i	−0.302642	+	0.524191i
$754$	77.8241	−	35.4249i	2.83419	−	1.29010i
$755$	−1.43776	−	1.43776i	−0.0523256	−	0.0523256i
$756$	6.63181	−	13.6238i	0.241197	−	0.495494i
$757$	10.9623	−	10.9623i	0.398433	−	0.398433i	−0.479247	−	0.877680i	$-0.659090\pi$
$757$	10.9623	−	10.9623i	0.398433	−	0.398433i	0.877680	+	0.479247i	$0.159090\pi$
$758$	11.8691	+	4.44364i	0.431104	+	0.161400i
$759$	50.8082	+	29.3341i	1.84422	+	1.06476i
$760$	8.29343	−	7.84930i	0.300834	−	0.284724i
$761$	17.6917	−	10.2143i	0.641325	−	0.370269i	−0.143800	−	0.989607i	$-0.545932\pi$
$761$	17.6917	−	10.2143i	0.641325	−	0.370269i	0.785125	+	0.619337i	$0.212599\pi$
$762$	4.26088	+	5.17352i	0.154355	+	0.187417i
$763$	−14.9836	−	3.98831i	−0.542444	−	0.144386i
$764$	−46.1232	−	9.00776i	−1.66868	−	0.325889i
$765$	0.424897	−	1.58574i	0.0153622	−	0.0573324i
$766$	4.90324	−	6.86767i	0.177161	−	0.248139i
$767$	23.9553	−	41.4917i	0.864974	−	1.49818i
$768$	−29.7187	+	17.7141i	−1.07238	+	0.639202i
$769$	7.35969			0.265397			0.132699	−	0.991156i	$-0.457636\pi$
$769$	7.35969			0.265397			0.132699	+	0.991156i	$0.457636\pi$
$770$	20.7194	+	1.96972i	0.746677	+	0.0709838i
$771$	3.23282	+	3.23282i	0.116427	+	0.116427i
$772$	−3.00123	−	8.74131i	−0.108017	−	0.314607i
$773$	−1.40194	−	5.23213i	−0.0504244	−	0.188186i	0.936120	−	0.351681i	$-0.114390\pi$
$773$	−1.40194	−	5.23213i	−0.0504244	−	0.188186i	−0.986544	+	0.163495i	$0.947723\pi$
$774$	−12.2705	+	2.04781i	−0.441055	+	0.0736069i
$775$	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
$779$	0.00894105	+	0.00239575i	0.000320346	+	8.58366e-5i
$780$	−25.3153	+	1.74773i	−0.906432	+	0.0625787i
$781$	−77.8847	+	20.8691i	−2.78693	+	0.746757i
$782$	−6.15055	+	2.79969i	−0.219943	+	0.100117i
$783$	29.5071			1.05450
$784$	22.0377	−	17.2725i	0.787062	−	0.616874i
$785$	−11.6248			−0.414906
$786$	30.1417	−	13.7203i	1.07512	−	0.489386i
$787$	38.0216	−	10.1879i	1.35532	−	0.363158i	0.493227	−	0.869901i	$-0.335817\pi$
$787$	38.0216	−	10.1879i	1.35532	−	0.363158i	0.862098	+	0.506742i	$0.169150\pi$
$788$	0.649090	+	9.40185i	0.0231229	+	0.334927i
$789$	−16.7805	−	4.49632i	−0.597402	−	0.160073i
$790$	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
$794$	20.0634	−	3.34835i	0.712025	−	0.118829i
$795$	3.97665	+	14.8411i	0.141037	+	0.526358i
$796$	−42.1045	+	14.4561i	−1.49235	+	0.512383i
$797$	−13.8004	−	13.8004i	−0.488837	−	0.488837i	0.419102	−	0.907939i	$-0.362345\pi$
$797$	−13.8004	−	13.8004i	−0.488837	−	0.488837i	−0.907939	+	0.419102i	$0.862345\pi$
$798$	−32.5175	−	3.09132i	−1.15111	−	0.109431i
$799$	1.55484			0.0550064
$800$	5.65200	−	0.234258i	0.199828	−	0.00828225i
$801$	−7.53588	+	13.0525i	−0.266267	+	0.461189i
$802$	−0.664078	+	0.930134i	−0.0234494	+	0.0328442i
$803$	−10.8647	+	40.5477i	−0.383407	+	1.43090i
$804$	2.03210	−	10.4051i	0.0716667	−	0.366961i
$805$	−12.4708	−	3.31945i	−0.439538	−	0.116995i
$806$	44.9038	+	54.5218i	1.58167	+	1.92045i
$807$	−54.9450	+	31.7225i	−1.93416	+	1.11669i
$808$	0.560762	−	20.3818i	0.0197276	−	0.717028i
$809$	−0.784939	−	0.453185i	−0.0275970	−	0.0159331i	0.486138	−	0.873882i	$-0.338405\pi$
$809$	−0.784939	−	0.453185i	−0.0275970	−	0.0159331i	−0.513735	+	0.857949i	$0.671739\pi$
$810$	−14.8590	−	5.56304i	−0.522092	−	0.195465i
$811$	32.9654	−	32.9654i	1.15757	−	1.15757i	0.172577	−	0.984996i	$-0.444791\pi$
$811$	32.9654	−	32.9654i	1.15757	−	1.15757i	0.984996	−	0.172577i	$-0.0552094\pi$
$812$	49.0265	+	23.8651i	1.72049	+	0.837502i
$813$	12.1339	+	12.1339i	0.425556	+	0.425556i
$814$	13.7915	−	6.27779i	0.483392	−	0.220036i
$815$	6.32830	−	10.9609i	0.221671	−	0.383945i
$816$	−8.40854	−	1.04753i	−0.294358	−	0.0366710i
$817$	−10.5964	−	18.3535i	−0.370720	−	0.642106i
$818$	−2.35608	+	24.3559i	−0.0823783	+	0.851586i
$819$	18.4255	+	18.3646i	0.643838	+	0.641712i
$820$	0.00256086	+	0.00380388i	8.94290e−5	+	0.000132837i
$821$	35.1480	+	9.41788i	1.22667	+	0.328686i	0.813284	−	0.581867i	$-0.197678\pi$
$821$	35.1480	+	9.41788i	1.22667	+	0.328686i	0.413391	+	0.910554i	$0.364344\pi$
$822$	2.39634	+	14.3590i	0.0835820	+	0.500826i
$823$	−33.8765	−	19.5586i	−1.18086	−	0.681770i	−0.224647	−	0.974440i	$-0.572123\pi$
$823$	−33.8765	−	19.5586i	−1.18086	−	0.681770i	−0.956213	+	0.292670i	$0.905456\pi$
$824$	−42.9677	+	10.2554i	−1.49685	+	0.357264i
$825$		−	12.0280i		−	0.418761i
$826$	30.1265	−	5.07899i	1.04824	−	0.176721i
$827$	0.906684	−	0.906684i	0.0315285	−	0.0315285i	−0.691167	−	0.722695i	$-0.742903\pi$
$827$	0.906684	−	0.906684i	0.0315285	−	0.0315285i	0.722695	+	0.691167i	$0.242903\pi$
$828$	−5.30851	−	15.4614i	−0.184483	−	0.537322i
$829$	38.1846	−	10.2315i	1.32621	−	0.355356i	0.474907	−	0.880036i	$-0.342482\pi$
$829$	38.1846	−	10.2315i	1.32621	−	0.355356i	0.851300	+	0.524680i	$0.175815\pi$
$830$	−0.0589543	+	0.0825737i	−0.00204633	+	0.00286617i
$831$	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
$835$	−4.67436	+	17.4450i	−0.161763	+	0.603708i
$836$	−29.4960	+	33.8708i	−1.02014	+	1.17144i
$837$	6.30848	+	23.5436i	0.218053	+	0.813785i
$838$	−10.8022	+	28.8528i	−0.373155	+	0.996704i
$839$		−	28.7218i		−	0.991586i	−0.868441	−	0.495793i	$-0.834877\pi$
$839$		−	28.7218i		−	0.991586i	0.868441	−	0.495793i	$-0.165123\pi$
$840$	−11.1425	−	11.7340i	−0.384452	−	0.404862i
$841$			77.1836i			2.66150i
$842$	22.3184	+	8.35575i	0.769142	+	0.287958i
$843$	6.62159	+	24.7121i	0.228060	+	0.851130i
$844$	40.9177	−	2.82490i	1.40845	−	0.0972370i
$845$	−5.54614	+	20.6985i	−0.190793	+	0.712049i
$846$	−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
$850$	1.12757	+	0.805040i	0.0386753	+	0.0276126i
$851$	−9.07553	+	2.43178i	−0.311105	+	0.0833603i
$852$	56.3208	+	27.5311i	1.92952	+	0.943201i
$853$	−30.7987	+	30.7987i	−1.05453	+	1.05453i	−0.0561038	+	0.998425i	$0.517868\pi$
$853$	−30.7987	+	30.7987i	−1.05453	+	1.05453i	−0.998425	+	0.0561038i	$0.982132\pi$
$854$	13.4158	+	4.99745i	0.459080	+	0.171009i
$855$			6.76533i			0.231369i
$856$	10.6266	+	6.53138i	0.363209	+	0.223238i
$857$	−8.34203	−	4.81627i	−0.284958	−	0.164521i	0.350708	−	0.936485i	$-0.385941\pi$
$857$	−8.34203	−	4.81627i	−0.284958	−	0.164521i	−0.635666	+	0.771964i	$0.719274\pi$
$858$	98.4471	−	16.4297i	3.36093	−	0.560899i
$859$	−43.4973	−	11.6551i	−1.48411	−	0.397666i	−0.576366	−	0.817192i	$-0.695530\pi$
$859$	−43.4973	−	11.6551i	−1.48411	−	0.397666i	−0.907744	+	0.419525i	$0.862196\pi$
$860$	2.01236	−	10.3040i	0.0686208	−	0.351365i
$861$	0.00337400	−	0.0126757i	0.000114986	−	0.000431988i
$862$	−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	$0.740894\pi$
$864$	−3.54092	+	15.8066i	−0.120465	+	0.537753i
$865$	0.520274	−	0.901140i	0.0176898	−	0.0306397i
$866$	−9.42943	−	20.7153i	−0.320425	−	0.703933i
$867$	24.5257	+	24.5257i	0.832937	+	0.832937i
$868$	−8.56024	+	44.2203i	−0.290553	+	1.50093i
$869$	−38.6290	+	38.6290i	−1.31040	+	1.31040i
$870$	11.0486	−	29.5111i	0.374583	−	1.00052i
$871$	−12.4569	−	7.19202i	−0.422087	−	0.243692i
$872$	16.5696	+	0.455880i	0.561119	+	0.0154380i
$873$	−5.80802	+	3.35326i	−0.196572	+	0.113491i
$874$	21.4966	−	17.7045i	0.727134	−	0.598864i
$875$	0.688996	+	2.55446i	0.0232923	+	0.0863566i
$876$	27.0734	−	18.2264i	0.914725	−	0.615814i
$877$	−2.19479	+	8.19106i	−0.0741128	+	0.276593i	−0.993031	−	0.117856i	$-0.962398\pi$
$877$	−2.19479	+	8.19106i	−0.0741128	+	0.276593i	0.918918	+	0.394449i	$0.129064\pi$
$878$	−37.1465	−	26.5211i	−1.25363	−	0.895044i
$879$	15.9687	−	27.6586i	0.538610	−	0.932900i
$880$	−22.0388	+	3.05762i	−0.742928	+	0.103072i
$881$	−13.5692			−0.457158			−0.228579	−	0.973525i	$-0.573408\pi$
$881$	−13.5692			−0.457158			−0.228579	+	0.973525i	$0.573408\pi$
$882$	−1.54267	+	16.5171i	−0.0519443	+	0.556161i
$883$	−39.1099	−	39.1099i	−1.31615	−	1.31615i	−0.916796	−	0.399356i	$-0.869234\pi$
$883$	−39.1099	−	39.1099i	−1.31615	−	1.31615i	−0.399356	−	0.916796i	$-0.630766\pi$
$884$	−5.04891	+	10.3286i	−0.169813	+	0.347389i
$885$	−4.56975	−	17.0545i	−0.153611	−	0.573282i
$886$	0.395543	+	2.37011i	0.0132885	+	0.0796254i
$887$	−28.2991	+	16.3385i	−0.950190	+	0.548593i	−0.893140	−	0.449779i	$-0.851503\pi$
$887$	−28.2991	+	16.3385i	−0.950190	+	0.548593i	−0.0570504	+	0.998371i	$0.518170\pi$
$888$	−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
$891$	60.2796	+	16.1519i	2.01944	+	0.541108i
$892$	−20.9509	+	24.0583i	−0.701488	+	0.805531i
$893$	−6.18917	+	1.65838i	−0.207113	+	0.0554957i
$894$	8.69872	+	19.1100i	0.290929	+	0.639133i
$895$	−8.64660			−0.289024
$896$	−18.6676	+	23.3991i	−0.623641	+	0.781711i
$897$	−61.8863			−2.06633
$898$	4.00279	+	8.79361i	0.133575	+	0.293447i
$899$	−84.7235	+	22.7016i	−2.82569	+	0.757140i
$900$	−2.20101	+	2.52746i	−0.0733670	+	0.0842485i
$901$	6.72386	+	1.80165i	0.224004	+	0.0600218i
$902$	−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
$906$	−1.02354	−	6.13307i	−0.0340047	−	0.203758i
$907$	−0.618048	−	2.30659i	−0.0205220	−	0.0765890i	0.954905	−	0.296910i	$-0.0959562\pi$
$907$	−0.618048	−	2.30659i	−0.0205220	−	0.0765890i	−0.975427	+	0.220321i	$0.929289\pi$
$908$	11.4107	−	23.3430i	0.378677	−	0.774665i
$909$	8.54189	+	8.54189i	0.283317	+	0.283317i
$910$	−19.9667	+	9.12859i	−0.661890	+	0.302610i
$911$	39.0190			1.29276			0.646378	−	0.763018i	$-0.276283\pi$
$911$	39.0190			1.29276			0.646378	+	0.763018i	$0.276283\pi$
$912$	34.5881	−	4.79869i	1.14533	−	0.158901i
$913$	0.199533	−	0.345602i	0.00660359	−	0.0114378i
$914$	−15.2542	−	10.8909i	−0.504564	−	0.360238i
$915$	2.14137	−	7.99169i	0.0707914	−	0.264197i
$916$	−6.27451	+	4.22415i	−0.207316	+	0.139570i
$917$	20.2270	−	20.2940i	0.667955	−	0.670167i
$918$	−3.06236	+	2.52214i	−0.101073	+	0.0832430i
$919$	−2.69526	+	1.55611i	−0.0889086	+	0.0513314i	−0.543795	−	0.839218i	$-0.683013\pi$
$919$	−2.69526	+	1.55611i	−0.0889086	+	0.0513314i	0.454887	+	0.890549i	$0.349680\pi$
$920$	13.7908	+	0.379426i	0.454670	+	0.0125093i
$921$	−42.7961	−	24.7083i	−1.41018	−	0.814168i
$922$	−14.2312	+	38.0119i	−0.468681	+	1.25186i
$923$	60.1430	−	60.1430i	1.97963	−	1.97963i
$924$	48.0665	+	41.7187i	1.58127	+	1.37244i
$925$	1.36208	+	1.36208i	0.0447850	+	0.0447850i
$926$	8.27724	+	18.1840i	0.272007	+	0.597565i
$927$	13.0860	−	22.6656i	0.429799	−	0.744435i
$928$	−56.8815	−	12.7423i	−1.86723	−	0.418286i
$929$	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
$931$	−27.2732	+	7.40459i	−0.893842	+	0.242676i
$932$	8.89726	−	45.5574i	0.291440	−	1.49228i
$933$	51.9249	+	13.9132i	1.69994	+	0.455499i
$934$	17.9672	−	2.99852i	0.587906	−	0.0981146i
$935$	−4.71930	−	2.72469i	−0.154338	−	0.0891069i
$936$	−23.6933	−	14.5625i	−0.774439	−	0.475990i
$937$		−	30.7794i		−	1.00552i	−0.864426	−	0.502759i	$-0.832318\pi$
$937$		−	30.7794i		−	1.00552i	0.864426	−	0.502759i	$-0.167682\pi$
$938$	−1.52485	−	9.04481i	−0.0497881	−	0.295323i
$939$	8.35396	−	8.35396i	0.272621	−	0.272621i
$940$	−2.85174	−	1.39401i	−0.0930135	−	0.0454676i
$941$	52.8370	−	14.1576i	1.72244	−	0.461526i	0.744019	−	0.668158i	$-0.232917\pi$
$941$	52.8370	−	14.1576i	1.72244	−	0.461526i	0.978419	+	0.206633i	$0.0662505\pi$
$942$	−28.9317	−	20.6561i	−0.942645	−	0.673011i
$943$	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
$947$	−4.87766	+	18.2037i	−0.158503	+	0.591540i	0.840277	+	0.542157i	$0.182392\pi$
$947$	−4.87766	+	18.2037i	−0.158503	+	0.591540i	−0.998780	+	0.0493829i	$0.984275\pi$
$948$	42.3725	−	2.92533i	1.37619	−	0.0950104i
$949$	−11.4607	−	42.7718i	−0.372029	−	1.38843i
$950$	−5.34702	−	2.00187i	−0.173480	−	0.0649491i
$951$			42.7016i			1.38469i
$952$	−7.12805	+	1.71376i	−0.231021	+	0.0555434i
$953$		−	39.4220i		−	1.27700i	−0.769621	−	0.638501i	$-0.779555\pi$
$953$		−	39.4220i		−	1.27700i	0.769621	−	0.638501i	$-0.220445\pi$
$954$	−5.90414	+	15.7701i	−0.191154	+	0.510576i
$955$	6.08154	+	22.6966i	0.196794	+	0.734446i
$956$	−10.1909	+	11.7023i	−0.329596	+	0.378481i
$957$	−32.0788	+	119.720i	−1.03696	+	3.86999i
$958$	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
$962$	−9.28787	+	13.0090i	−0.299453	+	0.419425i
$963$	−7.13819	+	1.91267i	−0.230025	+	0.0616350i
$964$	−3.89213	−	11.3361i	−0.125357	−	0.365112i
$965$	−3.26760	+	3.26760i	−0.105188	+	0.105188i
$966$	−25.1390	−	30.4208i	−0.808832	−	0.978774i
$967$			37.7738i			1.21472i	0.794425	+	0.607362i	$0.207772\pi$
$967$			37.7738i			1.21472i	−0.794425	+	0.607362i	$0.792228\pi$
$968$	54.8609	−	13.0940i	1.76330	−	0.420858i
$969$	7.40656	+	4.27618i	0.237933	+	0.137371i
$970$	−0.931677	−	5.58264i	−0.0299144	−	0.179248i
$971$	5.23302	+	1.40218i	0.167936	+	0.0449982i	0.341807	−	0.939770i	$-0.388961\pi$
$971$	5.23302	+	1.40218i	0.167936	+	0.0449982i	−0.173871	+	0.984768i	$0.555628\pi$
$972$	−17.5011	−	25.9961i	−0.561349	−	0.833824i
$973$	17.1909	−	4.63678i	0.551116	−	0.148648i
$974$	−3.23515	+	33.4434i	−0.103661	+	1.07160i
$975$	6.34388	+	10.9879i	0.203167	+	0.351895i
$976$	−15.1875	−	1.89205i	−0.486139	−	0.0605630i
$977$	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	$0.159687\pi$
$978$	35.2263	−	16.0348i	1.12641	−	0.512735i
$979$	35.3760	+	35.3760i	1.13062	+	1.13062i
$980$	−12.5980	−	6.10668i	−0.402427	−	0.195071i
$981$	−6.94425	+	6.94425i	−0.221713	+	0.221713i
$982$	−11.2178	−	4.19983i	−0.357975	−	0.134022i
$983$	−27.6067	−	15.9387i	−0.880516	−	0.508366i	−0.00968747	−	0.999953i	$-0.503084\pi$
$983$	−27.6067	−	15.9387i	−0.880516	−	0.508366i	−0.870829	+	0.491587i	$0.836417\pi$
$984$	−0.000385662		0.0140175i	−1.22945e−5		0.000446861i
$985$	4.08081	−	2.35606i	0.130025	−	0.0750702i
$986$	−9.07613	−	11.0201i	−0.289043	−	0.350953i
$987$	2.36455	+	8.76662i	0.0752646	+	0.279045i
$988$	9.08114	−	46.4989i	0.288910	−	1.47933i
$989$	6.62692	−	24.7320i	0.210724	−	0.786432i
$990$	7.65973	−	10.7285i	0.243442	−	0.340975i
$991$	−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	$0.188339\pi$
$992$	−1.99400	−	48.1098i	−0.0633095	−	1.52749i
$993$	−25.5582			−0.811066
$994$	53.9947	+	5.13307i	1.71261	+	0.162811i
$995$	15.7391	+	15.7391i	0.498964	+	0.498964i
$996$	−0.293451	+	0.100753i	−0.00929834	+	0.00319248i
$997$	7.57613	+	28.2745i	0.239938	+	0.895462i	0.975860	+	0.218396i	$0.0700824\pi$
$997$	7.57613	+	28.2745i	0.239938	+	0.895462i	−0.735922	+	0.677066i	$0.763251\pi$
$998$	0.845378	−	0.141084i	0.0267600	−	0.00446593i
$999$	−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.221.41	✓	256
7.2	even	3	inner	560.2.cp.a.541.46	yes	256
16.5	even	4	inner	560.2.cp.a.501.46	yes	256
112.37	even	12	inner	560.2.cp.a.261.41	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.41	✓	256	1.1	even	1	trivial
560.2.cp.a.261.41	yes	256	112.37	even	12	inner
560.2.cp.a.501.46	yes	256	16.5	even	4	inner
560.2.cp.a.541.46	yes	256	7.2	even	3	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+(0.585896 + 1.28714i) q^{2} +(2.08867 - 0.559657i) q^{3} +(-1.31345 + 1.50826i) q^{4} +(0.965926 + 0.258819i) 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} +(0.232796 + 1.39492i) q^{10} +(-1.43967 - 5.37294i) q^{11} +(-1.89926 + 3.88533i) q^{12} +(4.14901 + 4.14901i) q^{13} +(-0.354109 + 3.72486i) q^{14} +2.16235 q^{15} +(-0.549688 - 3.96205i) q^{16} +(0.489834 - 0.848418i) q^{17} +(1.92873 + 1.37704i) q^{18} +(-1.04491 + 3.89965i) q^{19} +(-1.65906 + 1.11692i) q^{20} +(5.52853 + 1.47157i) q^{21} +(6.07221 - 5.00104i) q^{22} +(-4.22416 + 2.43882i) q^{23} +(-6.11373 - 0.168207i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.90947 + 7.77125i) q^{26} +(-2.02480 + 2.02480i) q^{27} +(-5.00189 + 1.72659i) q^{28} +(-7.28641 - 7.28641i) q^{29} +(1.26691 + 2.78324i) q^{30} +(4.25600 - 7.37160i) q^{31} +(4.77765 - 3.02887i) q^{32} +(-6.01400 - 10.4165i) q^{33} +(1.37902 + 0.133400i) q^{34} +(1.87392 + 1.86773i) q^{35} +(-0.642402 + 3.28935i) q^{36} +(1.86064 + 0.498557i) q^{37} +(-5.63159 + 0.939846i) q^{38} +(10.9879 + 6.34388i) q^{39} +(-2.40967 - 1.48105i) q^{40} -0.00229279i q^{41} +(1.34503 + 7.97818i) q^{42} +(-3.71185 + 3.71185i) q^{43} +(9.99472 + 4.88569i) q^{44} +(1.61864 - 0.433715i) q^{45} +(-5.61402 - 4.00818i) 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} +(0.548278 - 2.04620i) q^{51} +(-11.7073 + 0.808255i) q^{52} +(1.83904 + 6.86340i) q^{53} +(-3.79252 - 1.41988i) q^{54} -5.56247i q^{55} +(-5.15295 - 5.42652i) q^{56} +8.72985i q^{57} +(5.10954 - 13.6477i) q^{58} +(-2.11333 - 7.88705i) q^{59} +(-2.84014 + 3.26138i) q^{60} +(0.990298 - 3.69584i) 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} +(9.88397 - 13.8439i) q^{66} +(-2.36791 + 0.634479i) q^{67} +(0.636260 + 1.85315i) q^{68} +(-7.45796 + 7.45796i) q^{69} +(-1.30611 + 3.50629i) q^{70} -14.4957i q^{71} +(-4.61023 + 1.10035i) q^{72} +(-6.53559 - 3.77332i) q^{73} +(0.448429 + 2.68700i) q^{74} +(2.08867 + 0.559657i) q^{75} +(-4.50924 - 6.69799i) q^{76} +(3.78551 - 14.2217i) q^{77} +(-1.72768 + 17.8598i) q^{78} +(-4.91056 - 8.50534i) q^{79} +(0.494496 - 3.96932i) q^{80} +(-5.60956 + 9.71604i) q^{81} +(0.00295113 - 0.00134333i) q^{82} +(0.0507297 + 0.0507297i) q^{83} +(-9.48097 + 6.40562i) q^{84} +(0.692730 - 0.692730i) q^{85} +(-6.95243 - 2.60291i) q^{86} +(-19.2968 - 11.1410i) q^{87} +(-0.432699 + 15.7271i) q^{88} +(-7.78910 + 4.49704i) q^{89} +(1.50661 + 1.82931i) q^{90} +(4.04275 + 14.9885i) q^{91} +(1.86986 - 9.57440i) q^{92} +(4.76379 - 17.7787i) q^{93} +(-1.30420 + 1.82672i) q^{94} +(-2.01861 + 3.49633i) q^{95} +(8.28379 - 9.00015i) q^{96} -4.00212 q^{97} +(-5.72555 + 8.07577i) 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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