LMFDB - Embedded newform 560.2.cp.a.221.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47162251319$
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			221.63
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39430 + 0.236474i) q^{2} +(-2.75340 + 0.737770i) q^{3} +(1.88816 + 0.659433i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-4.01353 + 0.377568i) q^{6} +(0.122153 - 2.64293i) q^{7} +(2.47673 + 1.36595i) q^{8} +(4.43881 - 2.56275i) q^{9} +O(q^{10})$	\(q+(1.39430 + 0.236474i) q^{2} +(-2.75340 + 0.737770i) q^{3} +(1.88816 + 0.659433i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-4.01353 + 0.377568i) q^{6} +(0.122153 - 2.64293i) q^{7} +(2.47673 + 1.36595i) q^{8} +(4.43881 - 2.56275i) q^{9} +(1.28559 + 0.589289i) q^{10} +(0.994369 + 3.71103i) q^{11} +(-5.68536 - 0.422652i) q^{12} +(1.34667 + 1.34667i) q^{13} +(0.795302 - 3.65616i) q^{14} -2.85052 q^{15} +(3.13030 + 2.49023i) q^{16} +(1.37117 - 2.37494i) q^{17} +(6.79506 - 2.52358i) q^{18} +(-0.643079 + 2.40000i) q^{19} +(1.65315 + 1.12566i) q^{20} +(1.61354 + 7.36715i) q^{21} +(0.508887 + 5.40945i) q^{22} +(1.14567 - 0.661452i) q^{23} +(-7.82717 - 1.93375i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.55922 + 2.19612i) q^{26} +(-4.28420 + 4.28420i) q^{27} +(1.97348 - 4.90972i) q^{28} +(3.59715 + 3.59715i) q^{29} +(-3.97449 - 0.674075i) q^{30} +(-3.71816 + 6.44004i) q^{31} +(3.77571 + 4.21237i) q^{32} +(-5.47578 - 9.48433i) q^{33} +(2.47344 - 2.98714i) q^{34} +(0.802031 - 2.52126i) q^{35} +(10.0711 - 1.91178i) q^{36} +(7.72035 + 2.06866i) q^{37} +(-1.46418 + 3.19426i) q^{38} +(-4.70146 - 2.71439i) q^{39} +(2.03880 + 1.96043i) q^{40} +5.99585i q^{41} +(0.507622 + 10.6536i) q^{42} +(-1.43694 + 1.43694i) q^{43} +(-0.569651 + 7.66275i) q^{44} +(4.95085 - 1.32657i) q^{45} +(1.75383 - 0.651344i) q^{46} +(-0.326196 - 0.564987i) q^{47} +(-10.4562 - 4.54715i) q^{48} +(-6.97016 - 0.645683i) q^{49} +(1.08926 + 0.901944i) q^{50} +(-2.02322 + 7.55076i) q^{51} +(1.65469 + 3.43077i) q^{52} +(-3.33974 - 12.4641i) q^{53} +(-6.98657 + 4.96036i) q^{54} +3.84195i q^{55} +(3.91265 - 6.37896i) q^{56} -7.08260i q^{57} +(4.16489 + 5.86615i) q^{58} +(-3.74685 - 13.9834i) q^{59} +(-5.38225 - 1.87973i) q^{60} +(1.75953 - 6.56667i) q^{61} +(-6.70714 + 8.10011i) q^{62} +(-6.23095 - 12.0445i) q^{63} +(4.26836 + 6.76617i) q^{64} +(0.952241 + 1.64933i) q^{65} +(-5.39210 - 14.5189i) q^{66} +(0.104421 - 0.0279795i) q^{67} +(4.15511 - 3.58007i) q^{68} +(-2.66648 + 2.66648i) q^{69} +(1.71449 - 3.32574i) q^{70} -15.9256i q^{71} +(14.4943 - 0.284036i) q^{72} +(-6.31294 - 3.64478i) q^{73} +(10.2753 + 4.71000i) q^{74} +(-2.75340 - 0.737770i) q^{75} +(-2.79688 + 4.10752i) q^{76} +(9.92947 - 2.17473i) q^{77} +(-5.91337 - 4.89645i) q^{78} +(1.57758 + 2.73244i) q^{79} +(2.37912 + 3.21556i) q^{80} +(0.947096 - 1.64042i) q^{81} +(-1.41786 + 8.36003i) q^{82} +(0.732560 + 0.732560i) q^{83} +(-1.81152 + 14.9744i) q^{84} +(1.93913 - 1.93913i) q^{85} +(-2.34333 + 1.66373i) q^{86} +(-12.5583 - 7.25051i) q^{87} +(-2.60631 + 10.5495i) q^{88} +(8.80695 - 5.08470i) q^{89} +(7.21668 - 0.678900i) q^{90} +(3.72366 - 3.39466i) q^{91} +(2.59939 - 0.493436i) q^{92} +(5.48629 - 20.4751i) q^{93} +(-0.321211 - 0.864900i) q^{94} +(-1.24233 + 2.15178i) q^{95} +(-13.5038 - 8.81271i) q^{96} +1.96535 q^{97} +(-9.56582 - 2.54854i) q^{98} +(13.9242 + 13.9242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4}+O(q^{10}) $ 256 * q + 4 * q^4	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	1.39430	+	0.236474i	0.985921	+	0.167212i
$2$	1.39430	+	0.236474i	0.985921	+	0.167212i
$3$	−2.75340	+	0.737770i	−1.58967	+	0.425952i	−0.941903	−	0.335884i	$-0.890965\pi$
$3$	−2.75340	+	0.737770i	−1.58967	+	0.425952i	−0.647770	+	0.761836i	$0.724298\pi$
$4$	1.88816	+	0.659433i	0.944080	+	0.329716i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−4.01353	+	0.377568i	−1.63852	+	0.154142i
$7$	0.122153	−	2.64293i	0.0461694	−	0.998934i
$7$	0.122153	−	2.64293i	0.0461694	−	0.998934i
$8$	2.47673	+	1.36595i	0.875655	+	0.482936i
$9$	4.43881	−	2.56275i	1.47960	−	0.854249i
$10$	1.28559	+	0.589289i	0.406539	+	0.186349i
$11$	0.994369	+	3.71103i	0.299813	+	1.11892i	0.937319	+	0.348473i	$0.113300\pi$
$11$	0.994369	+	3.71103i	0.299813	+	1.11892i	−0.637505	+	0.770446i	$0.720034\pi$
$12$	−5.68536	−	0.422652i	−1.64122	−	0.122009i
$13$	1.34667	+	1.34667i	0.373500	+	0.373500i	0.868750	−	0.495251i	$-0.164924\pi$
$13$	1.34667	+	1.34667i	0.373500	+	0.373500i	−0.495251	+	0.868750i	$0.664924\pi$
$14$	0.795302	−	3.65616i	0.212554	−	0.977149i
$15$	−2.85052			−0.736002
$16$	3.13030	+	2.49023i	0.782574	+	0.622557i
$17$	1.37117	−	2.37494i	0.332558	−	0.576008i	−0.650454	−	0.759545i	$-0.725422\pi$
$17$	1.37117	−	2.37494i	0.332558	−	0.576008i	0.983013	+	0.183537i	$0.0587548\pi$
$18$	6.79506	−	2.52358i	1.60161	−	0.594814i
$19$	−0.643079	+	2.40000i	−0.147532	+	0.550598i	0.852097	+	0.523383i	$0.175330\pi$
$19$	−0.643079	+	2.40000i	−0.147532	+	0.550598i	−0.999630	+	0.0272148i	$0.991336\pi$
$20$	1.65315	+	1.12566i	0.369655	+	0.251704i
$21$	1.61354	+	7.36715i	0.352103	+	1.60764i
$22$	0.508887	+	5.40945i	0.108495	+	1.15330i
$23$	1.14567	−	0.661452i	0.238888	−	0.137922i	−0.375777	−	0.926710i	$-0.622624\pi$
$23$	1.14567	−	0.661452i	0.238888	−	0.137922i	0.614666	+	0.788788i	$0.289291\pi$
$24$	−7.82717	−	1.93375i	−1.59771	−	0.394724i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	1.55922	+	2.19612i	0.305787	+	0.430695i
$27$	−4.28420	+	4.28420i	−0.824494	+	0.824494i
$28$	1.97348	−	4.90972i	0.372952	−	0.927850i
$29$	3.59715	+	3.59715i	0.667975	+	0.667975i	0.957247	−	0.289272i	$-0.0934133\pi$
$29$	3.59715	+	3.59715i	0.667975	+	0.667975i	−0.289272	+	0.957247i	$0.593413\pi$
$30$	−3.97449	−	0.674075i	−0.725640	−	0.123069i
$31$	−3.71816	+	6.44004i	−0.667801	+	1.15666i	0.310717	+	0.950502i	$0.399431\pi$
$31$	−3.71816	+	6.44004i	−0.667801	+	1.15666i	−0.978518	+	0.206162i	$0.933903\pi$
$32$	3.77571	+	4.21237i	0.667457	+	0.744649i
$33$	−5.47578	−	9.48433i	−0.953211	−	1.65101i
$34$	2.47344	−	2.98714i	0.424192	−	0.512290i
$35$	0.802031	−	2.52126i	0.135568	−	0.426171i
$36$	10.0711	−	1.91178i	1.67852	−	0.318630i
$37$	7.72035	+	2.06866i	1.26922	+	0.340086i	0.829731	−	0.558163i	$-0.188494\pi$
$37$	7.72035	+	2.06866i	1.26922	+	0.340086i	0.439486	+	0.898249i	$0.355160\pi$
$38$	−1.46418	+	3.19426i	−0.237522	+	0.518177i
$39$	−4.70146	−	2.71439i	−0.752835	−	0.434650i
$40$	2.03880	+	1.96043i	0.322363	+	0.309971i
$41$			5.99585i			0.936395i	0.883624	+	0.468197i	$0.155096\pi$
$41$			5.99585i			0.936395i	−0.883624	+	0.468197i	$0.844904\pi$
$42$	0.507622	+	10.6536i	0.0783278	+	1.64389i
$43$	−1.43694	+	1.43694i	−0.219131	+	0.219131i	−0.808132	−	0.589001i	$-0.799521\pi$
$43$	−1.43694	+	1.43694i	−0.219131	+	0.219131i	0.589001	+	0.808132i	$0.299521\pi$
$44$	−0.569651	+	7.66275i	−0.0858781	+	1.15520i
$45$	4.95085	−	1.32657i	0.738028	−	0.197754i
$46$	1.75383	−	0.651344i	0.258587	−	0.0960354i
$47$	−0.326196	−	0.564987i	−0.0475805	−	0.0824119i	0.841254	−	0.540640i	$-0.181818\pi$
$47$	−0.326196	−	0.564987i	−0.0475805	−	0.0824119i	−0.888835	+	0.458228i	$0.848484\pi$
$48$	−10.4562	−	4.54715i	−1.50922	−	0.656324i
$49$	−6.97016	−	0.645683i	−0.995737	−	0.0922404i
$50$	1.08926	+	0.901944i	0.154045	+	0.127554i
$51$	−2.02322	+	7.55076i	−0.283308	+	1.05732i
$52$	1.65469	+	3.43077i	0.229465	+	0.475763i
$53$	−3.33974	−	12.4641i	−0.458748	−	1.71207i	−0.676828	−	0.736141i	$-0.736646\pi$
$53$	−3.33974	−	12.4641i	−0.458748	−	1.71207i	0.218080	−	0.975931i	$-0.430021\pi$
$54$	−6.98657	+	4.96036i	−0.950751	+	0.675020i
$55$			3.84195i			0.518048i
$56$	3.91265	−	6.37896i	0.522850	−	0.852425i
$57$		−	7.08260i		−	0.938113i
$58$	4.16489	+	5.86615i	0.546876	+	0.770264i
$59$	−3.74685	−	13.9834i	−0.487798	−	1.82049i	−0.567116	−	0.823638i	$-0.691941\pi$
$59$	−3.74685	−	13.9834i	−0.487798	−	1.82049i	0.0793181	−	0.996849i	$-0.474726\pi$
$60$	−5.38225	−	1.87973i	−0.694845	−	0.242672i
$61$	1.75953	−	6.56667i	0.225285	−	0.840776i	−0.757005	−	0.653409i	$-0.773338\pi$
$61$	1.75953	−	6.56667i	0.225285	−	0.840776i	0.982290	−	0.187366i	$-0.0599952\pi$
$62$	−6.70714	+	8.10011i	−0.851807	+	1.02872i
$63$	−6.23095	−	12.0445i	−0.785025	−	1.51746i
$64$	4.26836	+	6.76617i	0.533545	+	0.845772i
$65$	0.952241	+	1.64933i	0.118111	+	0.204574i
$66$	−5.39210	−	14.5189i	−0.663721	−	1.78715i
$67$	0.104421	−	0.0279795i	0.0127571	−	0.00341824i	−0.252435	−	0.967614i	$-0.581231\pi$
$67$	0.104421	−	0.0279795i	0.0127571	−	0.00341824i	0.265192	+	0.964196i	$0.414565\pi$
$68$	4.15511	−	3.58007i	0.503881	−	0.434148i
$69$	−2.66648	+	2.66648i	−0.321006	+	0.321006i
$70$	1.71449	−	3.32574i	0.204920	−	0.397502i
$71$		−	15.9256i		−	1.89002i	−0.327037	−	0.945012i	$-0.606050\pi$
$71$		−	15.9256i		−	1.89002i	0.327037	−	0.945012i	$-0.393950\pi$
$72$	14.4943	−	0.284036i	1.70817	−	0.0334740i
$73$	−6.31294	−	3.64478i	−0.738873	−	0.426589i	0.0827862	−	0.996567i	$-0.473618\pi$
$73$	−6.31294	−	3.64478i	−0.738873	−	0.426589i	−0.821660	+	0.569979i	$0.806951\pi$
$74$	10.2753	+	4.71000i	1.19448	+	0.547527i
$75$	−2.75340	−	0.737770i	−0.317935	−	0.0851904i
$76$	−2.79688	+	4.10752i	−0.320824	+	0.471165i
$77$	9.92947	−	2.17473i	1.13157	−	0.247834i
$78$	−5.91337	−	4.89645i	−0.669557	−	0.554414i
$79$	1.57758	+	2.73244i	0.177491	+	0.307424i	0.941021	−	0.338349i	$-0.109869\pi$
$79$	1.57758	+	2.73244i	0.177491	+	0.307424i	−0.763529	+	0.645773i	$0.776535\pi$
$80$	2.37912	+	3.21556i	0.265993	+	0.359510i
$81$	0.947096	−	1.64042i	0.105233	−	0.182269i
$82$	−1.41786	+	8.36003i	−0.156577	+	0.923211i
$83$	0.732560	+	0.732560i	0.0804089	+	0.0804089i	0.746167	−	0.665758i	$-0.231892\pi$
$83$	0.732560	+	0.732560i	0.0804089	+	0.0804089i	−0.665758	+	0.746167i	$0.731892\pi$
$84$	−1.81152	+	14.9744i	−0.197653	+	1.63384i
$85$	1.93913	−	1.93913i	0.210328	−	0.210328i
$86$	−2.34333	+	1.66373i	−0.252688	+	0.179405i
$87$	−12.5583	−	7.25051i	−1.34639	−	0.777337i
$88$	−2.60631	+	10.5495i	−0.277833	+	1.12458i
$89$	8.80695	−	5.08470i	0.933535	−	0.538977i	0.0456072	−	0.998959i	$-0.485478\pi$
$89$	8.80695	−	5.08470i	0.933535	−	0.538977i	0.887928	+	0.459983i	$0.152144\pi$
$90$	7.21668	−	0.678900i	0.760705	−	0.0715624i
$91$	3.72366	−	3.39466i	0.390346	−	0.355857i
$92$	2.59939	−	0.493436i	0.271005	−	0.0514442i
$93$	5.48629	−	20.4751i	0.568902	−	2.12317i
$94$	−0.321211	−	0.864900i	−0.0331303	−	0.0892077i
$95$	−1.24233	+	2.15178i	−0.127461	+	0.220768i
$96$	−13.5038	−	8.81271i	−1.37822	−	0.899444i
$97$	1.96535			0.199551			0.0997756	−	0.995010i	$-0.468188\pi$
$97$	1.96535			0.199551			0.0997756	+	0.995010i	$0.468188\pi$
$98$	−9.56582	−	2.54854i	−0.966294	−	0.257441i
$99$	13.9242	+	13.9242i	1.39944	+	1.39944i
$100$	1.30548	+	1.51517i	0.130548	+	0.151517i
$101$	5.06213	+	18.8921i	0.503701	+	1.87984i	0.474481	+	0.880265i	$0.342636\pi$
$101$	5.06213	+	18.8921i	0.503701	+	1.87984i	0.0292198	+	0.999573i	$0.490698\pi$
$102$	−4.60654	+	10.0496i	−0.456116	+	0.995060i
$103$	16.6443	−	9.60961i	1.64001	−	0.946863i	0.659189	−	0.751977i	$-0.270900\pi$
$103$	16.6443	−	9.60961i	1.64001	−	0.946863i	0.980826	−	0.194886i	$-0.0624336\pi$
$104$	1.49585	+	5.17483i	0.146680	+	0.507434i
$105$	−0.348200	+	7.53374i	−0.0339808	+	0.735218i
$106$	−1.70918	−	18.1684i	−0.166010	−	1.76468i
$107$	−12.4442	−	3.33441i	−1.20302	−	0.322349i	−0.399003	−	0.916950i	$-0.630644\pi$
$107$	−12.4442	−	3.33441i	−1.20302	−	0.322349i	−0.804022	+	0.594600i	$0.797310\pi$
$108$	−10.9144	+	5.26411i	−1.05024	+	0.506539i
$109$	−15.2121	+	4.07606i	−1.45705	+	0.390415i	−0.898470	−	0.439035i	$-0.855320\pi$
$109$	−15.2121	+	4.07606i	−1.45705	+	0.390415i	−0.558580	+	0.829450i	$0.688654\pi$
$110$	−0.908521	+	5.35683i	−0.0866240	+	0.510754i
$111$	−22.7834			−2.16250
$112$	6.96388	−	7.96897i	0.658025	−	0.752996i
$113$	−16.5528			−1.55716			−0.778578	−	0.627548i	$-0.784059\pi$
$113$	−16.5528			−1.55716			−0.778578	+	0.627548i	$0.784059\pi$
$114$	1.67485	−	9.87529i	0.156864	−	0.924905i
$115$	1.27783	−	0.342393i	0.119158	−	0.0319283i
$116$	4.41992	+	9.16408i	0.410379	+	0.850864i
$117$	9.42880	+	2.52644i	0.871692	+	0.233569i
$118$	−1.91752	−	20.3832i	−0.176522	−	1.87642i
$119$	−6.10931	−	3.91402i	−0.560040	−	0.358798i
$120$	−7.05997	−	3.89367i	−0.644485	−	0.355442i
$121$	−3.25673	+	1.88027i	−0.296066	+	0.170934i
$122$	4.00617	−	8.73984i	0.362701	−	0.791268i
$123$	−4.42356	−	16.5090i	−0.398859	−	1.48856i
$124$	−11.2672	+	9.70794i	−1.01183	+	0.871799i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−5.83961	−	18.2671i	−0.520234	−	1.62737i
$127$	−3.47001			−0.307913			−0.153957	−	0.988078i	$-0.549202\pi$
$127$	−3.47001			−0.307913			−0.153957	+	0.988078i	$0.549202\pi$
$128$	4.35136	+	10.4434i	0.384610	+	0.923079i
$129$	2.89633	−	5.01660i	0.255008	−	0.441687i
$130$	0.937688	+	2.52485i	0.0822407	+	0.221444i
$131$	−0.562137	+	2.09792i	−0.0491141	+	0.183296i	−0.986125	−	0.166003i	$-0.946914\pi$
$131$	−0.562137	+	2.09792i	−0.0491141	+	0.183296i	0.937011	+	0.349300i	$0.113580\pi$
$132$	−4.08487	−	21.5188i	−0.355542	−	1.87297i
$133$	6.26448	+	1.99278i	0.543200	+	0.172796i
$134$	0.152211	−	0.0143191i	0.0131490	−	0.00123698i
$135$	−5.24705	+	3.02938i	−0.451594	+	0.260728i
$136$	6.64007	−	4.00913i	0.569382	−	0.343780i
$137$	−14.8106	−	8.55091i	−1.26536	−	0.730554i	−0.291251	−	0.956647i	$-0.594071\pi$
$137$	−14.8106	−	8.55091i	−1.26536	−	0.730554i	−0.974106	+	0.226093i	$0.927405\pi$
$138$	−4.34843	+	3.08733i	−0.370163	+	0.262811i
$139$	2.80951	−	2.80951i	0.238299	−	0.238299i	−0.577846	−	0.816146i	$-0.696107\pi$
$139$	2.80951	−	2.80951i	0.238299	−	0.238299i	0.816146	+	0.577846i	$0.196107\pi$
$140$	3.17696	−	4.23165i	0.268502	−	0.357640i
$141$	1.31498	+	1.31498i	0.110741	+	0.110741i
$142$	3.76600	−	22.2051i	0.316035	−	1.86341i
$143$	−3.65846	+	6.33663i	−0.305936	+	0.529896i
$144$	20.2766	+	3.03149i	1.68972	+	0.252624i
$145$	2.54357	+	4.40559i	0.211232	+	0.365865i
$146$	−7.94025	−	6.57477i	−0.657140	−	0.544132i
$147$	19.6680	−	3.36455i	1.62219	−	0.277504i
$148$	13.2131	+	8.99701i	1.08611	+	0.739550i
$149$	−9.39738	−	2.51802i	−0.769864	−	0.206284i	−0.147552	−	0.989054i	$-0.547139\pi$
$149$	−9.39738	−	2.51802i	−0.769864	−	0.206284i	−0.622311	+	0.782770i	$0.713806\pi$
$150$	−3.66460	−	1.67978i	−0.299214	−	0.137154i
$151$	1.07943	+	0.623207i	0.0878425	+	0.0507159i	0.543278	−	0.839553i	$-0.317183\pi$
$151$	1.07943	+	0.623207i	0.0878425	+	0.0507159i	−0.455435	+	0.890269i	$0.650516\pi$
$152$	−4.87101	+	5.06574i	−0.395091	+	0.410886i
$153$		−	14.0559i		−	1.13635i
$154$	14.3590	−	0.684174i	1.15708	−	0.0551324i
$155$	−5.25827	+	5.25827i	−0.422354	+	0.422354i
$156$	−7.08714	−	8.22549i	−0.567426	−	0.658566i
$157$	−15.7107	+	4.20966i	−1.25385	+	0.335968i	−0.823822	−	0.566849i	$-0.808162\pi$
$157$	−15.7107	+	4.20966i	−1.25385	+	0.335968i	−0.430026	+	0.902816i	$0.641496\pi$
$158$	1.55347	+	4.18291i	0.123587	+	0.332774i
$159$	18.3912	+	31.8546i	1.45852	+	2.52623i
$160$	2.55681	+	5.04606i	0.202134	+	0.398926i
$161$	−1.60823	−	3.10872i	−0.126746	−	0.245002i
$162$	1.70846	−	2.06328i	0.134229	−	0.162106i
$163$	−4.86554	+	18.1585i	−0.381099	+	1.42228i	0.463127	+	0.886292i	$0.346727\pi$
$163$	−4.86554	+	18.1585i	−0.381099	+	1.42228i	−0.844226	+	0.535988i	$0.819939\pi$
$164$	−3.95386	+	11.3211i	−0.308745	+	0.884032i
$165$	−2.83447	−	10.5784i	−0.220663	−	0.823527i
$166$	0.848179	+	1.19464i	0.0658315	+	0.0927222i
$167$			8.84486i			0.684436i	0.939621	+	0.342218i	$0.111178\pi$
$167$			8.84486i			0.684436i	−0.939621	+	0.342218i	$0.888822\pi$
$168$	−6.06686	+	20.4504i	−0.468069	+	1.57779i
$169$		−	9.37295i		−	0.720996i
$170$	3.16229	−	2.24518i	0.242537	−	0.172198i
$171$	3.29609	+	12.3012i	0.252059	+	0.940696i
$172$	−3.66074	+	1.76561i	−0.279129	+	0.134626i
$173$	−2.17385	+	8.11293i	−0.165275	+	0.616815i	0.832730	+	0.553679i	$0.186777\pi$
$173$	−2.17385	+	8.11293i	−0.165275	+	0.616815i	−0.998005	+	0.0631355i	$0.979890\pi$
$174$	−15.7955	−	13.0791i	−1.19745	−	0.991525i
$175$	1.42725	−	2.22777i	0.107890	−	0.168403i
$176$	−6.12866	+	14.0928i	−0.461965	+	1.06229i
$177$	20.6331	+	35.7376i	1.55088	+	2.68620i
$178$	13.4820	−	5.00699i	1.01052	−	0.375290i
$179$	13.0054	−	3.48478i	0.972069	−	0.260465i	0.262368	−	0.964968i	$-0.415497\pi$
$179$	13.0054	−	3.48478i	0.972069	−	0.260465i	0.709701	+	0.704503i	$0.248830\pi$
$180$	10.2228	+	0.759965i	0.761961	+	0.0566444i
$181$	3.43752	−	3.43752i	0.255509	−	0.255509i	−0.567716	−	0.823225i	$-0.692173\pi$
$181$	3.43752	−	3.43752i	0.255509	−	0.255509i	0.823225	+	0.567716i	$0.192173\pi$
$182$	5.99466	−	3.85264i	0.444354	−	0.285576i
$183$			19.3788i			1.43252i
$184$	3.74102	−	0.0733106i	0.275792	−	0.00540453i
$185$	6.92187	+	3.99635i	0.508906	+	0.293817i
$186$	12.4914	−	27.2511i	0.915913	−	1.99815i
$187$	10.1769	+	2.72690i	0.744212	+	0.199411i
$188$	−0.243338	−	1.28189i	−0.0177473	−	0.0934915i
$189$	10.7995	+	11.8462i	0.785548	+	0.861681i
$190$	−2.24103	+	2.70646i	−0.162581	+	0.196347i
$191$	1.87817	+	3.25308i	0.135899	+	0.235385i	0.925941	−	0.377669i	$-0.123274\pi$
$191$	1.87817	+	3.25308i	0.135899	+	0.235385i	−0.790041	+	0.613054i	$0.789941\pi$
$192$	−16.7444	−	15.4809i	−1.20842	−	1.11724i
$193$	10.4866	−	18.1633i	0.754840	−	1.30742i	−0.190613	−	0.981665i	$-0.561048\pi$
$193$	10.4866	−	18.1633i	0.754840	−	1.30742i	0.945454	−	0.325757i	$-0.105619\pi$
$194$	2.74030	+	0.464755i	0.196742	+	0.0333674i
$195$	−3.83872	−	3.83872i	−0.274897	−	0.274897i
$196$	−12.7350	−	5.81550i	−0.909642	−	0.415393i
$197$	−7.53878	+	7.53878i	−0.537116	+	0.537116i	−0.922681	−	0.385565i	$-0.874007\pi$
$197$	−7.53878	+	7.53878i	−0.537116	+	0.537116i	0.385565	+	0.922681i	$0.374007\pi$
$198$	16.1219	+	22.7073i	1.14573	+	1.61374i
$199$	−6.16507	−	3.55941i	−0.437030	−	0.252320i	0.265307	−	0.964164i	$-0.414527\pi$
$199$	−6.16507	−	3.55941i	−0.437030	−	0.252320i	−0.702337	+	0.711844i	$0.747860\pi$
$200$	1.46193	+	2.42131i	0.103374	+	0.171213i
$201$	−0.266870	+	0.154077i	−0.0188236	+	0.0108678i
$202$	2.59065	+	27.5384i	0.182277	+	1.93760i
$203$	9.94643	−	9.06762i	0.698102	−	0.636422i
$204$	−8.79939	+	12.9229i	−0.616080	+	0.904782i
$205$	−1.55184	+	5.79155i	−0.108385	+	0.404499i
$206$	25.4797	−	9.46275i	1.77525	−	0.659301i
$207$	3.39027	−	5.87212i	0.235640	−	0.408140i
$208$	0.861960	+	7.56901i	0.0597662	+	0.524816i
$209$	−9.54595			−0.660307
$210$	−2.26703	+	10.4220i	−0.156440	+	0.719184i
$211$	11.2631	+	11.2631i	0.775382	+	0.775382i	0.979042	−	0.203660i	$-0.0652837\pi$
$211$	11.2631	+	11.2631i	0.775382	+	0.775382i	−0.203660	+	0.979042i	$0.565284\pi$
$212$	1.91326	−	25.7365i	0.131403	−	1.76759i
$213$	11.7494	+	43.8495i	0.805059	+	3.00452i
$214$	−16.5625	−	7.59190i	−1.13219	−	0.518972i
$215$	−1.75988	+	1.01607i	−0.120023	+	0.0692954i
$216$	−16.4628	+	4.75879i	−1.12015	+	0.323795i
$217$	16.5664	+	10.6135i	1.12460	+	0.720491i
$218$	−22.1741	+	2.08600i	−1.50182	+	0.141282i
$219$	20.0710	+	5.37801i	1.35627	+	0.363412i
$220$	−2.53351	+	7.25421i	−0.170809	+	0.489079i
$221$	5.04479	−	1.35175i	0.339349	−	0.0909283i
$222$	−31.7669	−	5.38768i	−2.13206	−	0.361597i
$223$	23.4439			1.56992			0.784961	−	0.619545i	$-0.212683\pi$
$223$	23.4439			1.56992			0.784961	+	0.619545i	$0.212683\pi$
$224$	11.5942	−	9.46437i	0.774671	−	0.632365i
$225$	5.12549			0.341699
$226$	−23.0796	−	3.91431i	−1.53523	−	0.260376i
$227$	3.28730	−	0.880830i	0.218186	−	0.0584628i	−0.148070	−	0.988977i	$-0.547306\pi$
$227$	3.28730	−	0.880830i	0.218186	−	0.0584628i	0.366256	+	0.930514i	$0.380639\pi$
$228$	4.67050	−	13.3731i	0.309311	−	0.885654i
$229$	−19.0580	−	5.10656i	−1.25938	−	0.337451i	−0.433430	−	0.901187i	$-0.642697\pi$
$229$	−19.0580	−	5.10656i	−1.25938	−	0.337451i	−0.825955	+	0.563736i	$0.809363\pi$
$230$	1.86265	−	0.175226i	0.122819	−	0.0115541i
$231$	−25.7353	+	13.3136i	−1.69326	+	0.875968i
$232$	3.99564	+	13.8227i	0.262326	+	0.907505i
$233$	−5.55295	+	3.20600i	−0.363786	+	0.210032i	−0.670740	−	0.741692i	$-0.734023\pi$
$233$	−5.55295	+	3.20600i	−0.363786	+	0.210032i	0.306954	+	0.951724i	$0.400690\pi$
$234$	12.5492	+	5.75229i	0.820364	+	0.376039i
$235$	−0.168851	−	0.630162i	−0.0110146	−	0.0411072i
$236$	2.14648	−	28.8737i	0.139724	−	1.87952i
$237$	−6.35961	−	6.35961i	−0.413101	−	0.413101i
$238$	−7.59266	−	6.90202i	−0.492159	−	0.447392i
$239$	−0.983140			−0.0635941			−0.0317970	−	0.999494i	$-0.510123\pi$
$239$	−0.983140			−0.0635941			−0.0317970	+	0.999494i	$0.510123\pi$
$240$	−8.92299	−	7.09846i	−0.575976	−	0.458204i
$241$	9.47833	−	16.4170i	0.610553	−	1.05751i	−0.380594	−	0.924742i	$-0.624281\pi$
$241$	9.47833	−	16.4170i	0.610553	−	1.05751i	0.991147	−	0.132767i	$-0.0423862\pi$
$242$	−4.98550	+	1.85154i	−0.320480	+	0.119021i
$243$	3.30689	−	12.3415i	0.212137	−	0.791708i
$244$	7.65256	−	11.2386i	0.489905	−	0.719479i
$245$	−6.56554	−	2.42769i	−0.419457	−	0.155099i
$246$	−2.26384	−	24.0645i	−0.144337	−	1.53430i
$247$	−4.09803	+	2.36600i	−0.260752	+	0.150545i
$248$	−18.0056	+	10.8714i	−1.14336	+	0.690335i
$249$	−2.55749	−	1.47657i	−0.162074	−	0.0935736i
$250$	0.818708	+	1.15313i	0.0517797	+	0.0729306i
$251$	7.88867	−	7.88867i	0.497929	−	0.497929i	−0.412864	−	0.910793i	$-0.635472\pi$
$251$	7.88867	−	7.88867i	0.497929	−	0.497929i	0.910793	+	0.412864i	$0.135472\pi$
$252$	−3.82248	−	26.8508i	−0.240794	−	1.69144i
$253$	3.59389	+	3.59389i	0.225946	+	0.225946i
$254$	−4.83824	−	0.820567i	−0.303578	−	0.0514870i
$255$	−3.90856	+	6.76983i	−0.244764	+	0.423943i
$256$	3.59751	+	15.5903i	0.224844	+	0.974395i
$257$	−11.0907	−	19.2096i	−0.691816	−	1.19826i	−0.971242	−	0.238093i	$-0.923478\pi$
$257$	−11.0907	−	19.2096i	−0.691816	−	1.19826i	0.279426	−	0.960167i	$-0.409856\pi$
$258$	5.22466	−	6.30974i	0.325273	−	0.392828i
$259$	6.41039	−	20.1516i	0.398322	−	1.25216i
$260$	0.710361	+	3.74214i	0.0440547	+	0.232078i
$261$	25.1857	+	6.74848i	1.55895	+	0.417720i
$262$	−1.27989	+	2.79221i	−0.0790720	+	0.172503i
$263$	−21.4558	−	12.3875i	−1.32302	−	0.763846i	−0.338811	−	0.940855i	$-0.610025\pi$
$263$	−21.4558	−	12.3875i	−1.32302	−	0.763846i	−0.984209	+	0.177009i	$0.943358\pi$
$264$	−0.606896	−	30.9697i	−0.0373519	−	1.90606i
$265$		−	12.9038i		−	0.792671i
$266$	8.26335	+	4.25992i	0.506658	+	0.261193i
$267$	−20.4977	+	20.4977i	−1.25444	+	1.25444i
$268$	0.215614	+	0.0160288i	0.0131707	+	0.000979117i
$269$	−7.70247	+	2.06387i	−0.469628	+	0.125836i	−0.485869	−	0.874032i	$-0.661497\pi$
$269$	−7.70247	+	2.06387i	−0.469628	+	0.125836i	0.0162412	+	0.999868i	$0.494830\pi$
$270$	−8.03234	+	2.98309i	−0.488833	+	0.181545i
$271$	3.39084	+	5.87310i	0.205979	+	0.356765i	0.950444	−	0.310896i	$-0.100629\pi$
$271$	3.39084	+	5.87310i	0.205979	+	0.356765i	−0.744465	+	0.667661i	$0.767296\pi$
$272$	10.2063	−	4.01973i	0.618850	−	0.243732i
$273$	−7.74823	+	12.0940i	−0.468944	+	0.731965i
$274$	−18.6284	−	15.4249i	−1.12538	−	0.931852i
$275$	−0.994369	+	3.71103i	−0.0599627	+	0.223784i
$276$	−6.79311	+	3.27638i	−0.408897	+	0.197215i
$277$	−0.607068	−	2.26561i	−0.0364752	−	0.136127i	0.945287	−	0.326239i	$-0.105782\pi$
$277$	−0.607068	−	2.26561i	−0.0364752	−	0.136127i	−0.981762	+	0.190112i	$0.939115\pi$
$278$	4.58168	−	3.25293i	0.274791	−	0.195098i
$279$			38.1148i			2.28187i
$280$	5.43033	−	5.14894i	0.324524	−	0.307708i
$281$		−	20.6323i		−	1.23082i	−0.788207	−	0.615410i	$-0.788990\pi$
$281$		−	20.6323i		−	1.23082i	0.788207	−	0.615410i	$-0.211010\pi$
$282$	1.52252	+	2.14443i	0.0906646	+	0.127699i
$283$	4.34099	+	16.2008i	0.258045	+	0.963038i	0.966371	+	0.257152i	$0.0827842\pi$
$283$	4.34099	+	16.2008i	0.258045	+	0.963038i	−0.708326	+	0.705886i	$0.750549\pi$
$284$	10.5019	−	30.0701i	0.623172	−	1.78433i
$285$	1.83311	−	6.84127i	0.108584	−	0.405242i
$286$	−6.59945	+	7.97006i	−0.390234	+	0.471279i
$287$	15.8466	+	0.732410i	0.935396	+	0.0432328i
$288$	27.5549	+	9.02171i	1.62369	+	0.531609i
$289$	4.73977	+	8.20952i	0.278810	+	0.482913i
$290$	2.50470	+	6.74422i	0.147081	+	0.396034i
$291$	−5.41139	+	1.44998i	−0.317221	+	0.0849992i
$292$	−9.51635	−	11.0449i	−0.556902	−	0.646353i
$293$	−7.39524	+	7.39524i	−0.432035	+	0.432035i	−0.889320	−	0.457285i	$-0.848822\pi$
$293$	−7.39524	+	7.39524i	−0.432035	+	0.432035i	0.457285	+	0.889320i	$0.348822\pi$
$294$	28.2187	−	0.0402426i	1.64575	−	0.00234699i
$295$		−	14.4767i		−	0.842867i
$296$	16.2955	+	15.6691i	0.947157	+	0.910749i
$297$	−20.1589	−	11.6387i	−1.16974	−	0.675347i
$298$	−12.5073	−	5.73312i	−0.724531	−	0.332111i
$299$	2.43360	+	0.652081i	0.140739	+	0.0377108i
$300$	−4.71234	−	3.20871i	−0.272067	−	0.185255i
$301$	3.62221	+	3.97326i	0.208780	+	0.229015i
$302$	1.35768	+	1.12420i	0.0781254	+	0.0646902i
$303$	−27.8761	−	48.2829i	−1.60144	−	2.77378i
$304$	−7.98958	+	5.91130i	−0.458234	+	0.339037i
$305$	3.39916	−	5.88751i	0.194635	−	0.337118i
$306$	3.32385	−	19.5981i	0.190012	−	1.12035i
$307$	−21.3961	−	21.3961i	−1.22114	−	1.22114i	−0.967226	−	0.253915i	$-0.918282\pi$
$307$	−21.3961	−	21.3961i	−1.22114	−	1.22114i	−0.253915	−	0.967226i	$-0.581718\pi$
$308$	20.1825	+	2.44157i	1.15001	+	0.139122i
$309$	−38.7388	+	38.7388i	−2.20377	+	2.20377i
$310$	−8.57506	+	6.08817i	−0.487031	+	0.345785i
$311$	3.64364	+	2.10366i	0.206612	+	0.119287i	0.599736	−	0.800198i	$-0.295272\pi$
$311$	3.64364	+	2.10366i	0.206612	+	0.119287i	−0.393124	+	0.919485i	$0.628606\pi$
$312$	−7.93651	−	13.1448i	−0.449316	−	0.744175i
$313$	−21.9898	+	12.6958i	−1.24294	+	0.717612i	−0.969692	−	0.244332i	$-0.921431\pi$
$313$	−21.9898	+	12.6958i	−1.24294	+	0.717612i	−0.273248	+	0.961944i	$0.588098\pi$
$314$	−22.9009	+	2.15438i	−1.29237	+	0.121578i
$315$	−2.90129	−	13.2468i	−0.163469	−	0.746372i
$316$	1.17685	+	6.19959i	0.0662032	+	0.348754i
$317$	−4.25632	+	15.8848i	−0.239059	+	0.892179i	0.737218	+	0.675655i	$0.236139\pi$
$317$	−4.25632	+	15.8848i	−0.239059	+	0.892179i	−0.976277	+	0.216525i	$0.930528\pi$
$318$	18.1102	+	48.7639i	1.01557	+	2.73455i
$319$	−9.77226	+	16.9261i	−0.547142	+	0.947677i
$320$	2.37171	+	7.64035i	0.132582	+	0.427109i
$321$	36.7238			2.04972
$322$	−1.50722	−	4.71480i	−0.0839941	−	0.262746i
$323$	4.81809	+	4.81809i	0.268086	+	0.268086i
$324$	2.87002	−	2.47283i	0.159445	−	0.137379i
$325$	0.492916	+	1.83959i	0.0273421	+	0.102042i
$326$	−11.0780	+	24.1678i	−0.613556	+	1.33853i
$327$	38.8776	−	22.4460i	2.14994	−	1.24127i
$328$	−8.19004	+	14.8501i	−0.452219	+	0.819959i
$329$	−1.53307	+	0.793098i	−0.0845208	+	0.0437249i
$330$	−1.45060	−	15.4198i	−0.0798527	−	0.848830i
$331$	−11.4207	−	3.06017i	−0.627740	−	0.168202i	−0.0690958	−	0.997610i	$-0.522011\pi$
$331$	−11.4207	−	3.06017i	−0.627740	−	0.168202i	−0.558644	+	0.829408i	$0.688678\pi$
$332$	0.900117	+	1.86627i	0.0494003	+	0.102425i
$333$	39.5706	−	10.6029i	2.16845	−	0.581036i
$334$	−2.09158	+	12.3324i	−0.114446	+	0.674800i
$335$	0.108105			0.00590639
$336$	−13.2950	+	27.0795i	−0.725304	+	1.47731i
$337$	22.7230			1.23780			0.618901	−	0.785469i	$-0.287578\pi$
$337$	22.7230			1.23780			0.618901	+	0.785469i	$0.287578\pi$
$338$	2.21646	−	13.0687i	0.120560	−	0.710845i
$339$	45.5764	−	12.2122i	2.47537	−	0.663273i
$340$	4.94012	−	2.38266i	0.267916	−	0.129218i
$341$	−27.5964	−	7.39444i	−1.49443	−	0.400431i
$342$	1.68684	+	17.9310i	0.0912139	+	0.969599i
$343$	−2.55792	+	18.3428i	−0.138115	+	0.990416i
$344$	−5.52170	+	1.59612i	−0.297710	+	0.0860571i
$345$	−3.26576	+	1.88549i	−0.175822	+	0.101511i
$346$	−4.94951	+	10.7978i	−0.266087	+	0.580495i
$347$	−5.90975	−	22.0555i	−0.317252	−	1.18400i	−0.921874	−	0.387489i	$-0.873343\pi$
$347$	−5.90975	−	22.0555i	−0.317252	−	1.18400i	0.604622	−	0.796512i	$-0.293324\pi$
$348$	−18.9308	−	21.9715i	−1.01480	−	1.17779i
$349$	11.4833	+	11.4833i	0.614686	+	0.614686i	0.944164	−	0.329477i	$-0.106872\pi$
$349$	11.4833	+	11.4833i	0.614686	+	0.614686i	−0.329477	+	0.944164i	$0.606872\pi$
$350$	2.51683	−	2.76867i	0.134530	−	0.147992i
$351$	−11.5388			−0.615896
$352$	−11.8778	+	18.2004i	−0.633089	+	0.970086i
$353$	12.3164	−	21.3327i	0.655537	−	1.13542i	−0.326221	−	0.945293i	$-0.605775\pi$
$353$	12.3164	−	21.3327i	0.655537	−	1.13542i	0.981759	−	0.190131i	$-0.0608912\pi$
$354$	20.3178	+	54.7082i	1.07988	+	2.90771i
$355$	4.12185	−	15.3830i	0.218765	−	0.816443i
$356$	19.9820	−	3.79313i	1.05904	−	0.201035i
$357$	19.7090	+	6.26958i	1.04311	+	0.331821i
$358$	18.9575	−	1.78341i	1.00194	−	0.0942559i
$359$	1.72433	−	0.995543i	0.0910067	−	0.0525428i	−0.453806	−	0.891101i	$-0.649934\pi$
$359$	1.72433	−	0.995543i	0.0910067	−	0.0525428i	0.544813	+	0.838558i	$0.316601\pi$
$360$	14.0739	+	3.47704i	0.741761	+	0.183256i
$361$	11.1080	+	6.41322i	0.584633	+	0.337538i
$362$	5.60583	−	3.98006i	0.294636	−	0.209188i
$363$	7.57985	−	7.57985i	0.397839	−	0.397839i
$364$	9.26942	−	3.95416i	0.485849	−	0.207254i
$365$	−5.15449	−	5.15449i	−0.269798	−	0.269798i
$366$	−4.58258	+	27.0199i	−0.239535	+	1.41235i
$367$	−10.0877	+	17.4724i	−0.526574	+	0.912053i	0.472947	+	0.881091i	$0.343190\pi$
$367$	−10.0877	+	17.4724i	−0.526574	+	0.912053i	−0.999521	+	0.0309618i	$0.990143\pi$
$368$	5.23345	+	0.782437i	0.272813	+	0.0407874i
$369$	15.3658	+	26.6144i	0.799914	+	1.38549i
$370$	8.70616	+	7.20896i	0.452611	+	0.374776i
$371$	−33.3496	+	7.30417i	−1.73143	+	0.379214i
$372$	23.8610	−	35.0424i	1.23713	−	1.81687i
$373$	−18.1335	−	4.85886i	−0.938917	−	0.251582i	−0.243264	−	0.969960i	$-0.578218\pi$
$373$	−18.1335	−	4.85886i	−0.938917	−	0.251582i	−0.695653	+	0.718378i	$0.744885\pi$
$374$	13.5449	+	6.20871i	0.700390	+	0.321045i
$375$	−2.46863	−	1.42526i	−0.127479	−	0.0736002i
$376$	−0.0361532	−	1.84489i	−0.00186446	−	0.0951428i
$377$			9.68837i			0.498977i
$378$	12.2565	+	19.0709i	0.630405	+	0.980903i
$379$	7.07175	−	7.07175i	0.363251	−	0.363251i	−0.501757	−	0.865009i	$-0.667313\pi$
$379$	7.07175	−	7.07175i	0.363251	−	0.363251i	0.865009	+	0.501757i	$0.167313\pi$
$380$	−3.76468	+	3.24368i	−0.193124	+	0.166397i
$381$	9.55431	−	2.56007i	0.489482	−	0.131156i
$382$	1.84947	+	4.97992i	0.0946269	+	0.254795i
$383$	−9.99813	−	17.3173i	−0.510881	−	0.884871i	−0.999920	−	0.0126098i	$-0.995986\pi$
$383$	−9.99813	−	17.3173i	−0.510881	−	0.884871i	0.489040	−	0.872261i	$-0.337347\pi$
$384$	−19.6859	−	25.5446i	−1.00459	−	1.30357i
$385$	10.1540	+	0.469304i	0.517495	+	0.0239180i
$386$	18.9166	−	22.8453i	0.962830	−	1.16280i
$387$	−2.69579	+	10.0608i	−0.137034	+	0.511420i
$388$	3.71090	+	1.29602i	0.188392	+	0.0657953i
$389$	−7.87896	−	29.4047i	−0.399479	−	1.49088i	−0.814016	−	0.580843i	$-0.802723\pi$
$389$	−7.87896	−	29.4047i	−0.399479	−	1.49088i	0.414537	−	0.910033i	$-0.363944\pi$
$390$	−4.44458	−	6.26010i	−0.225060	−	0.316992i
$391$		−	3.62786i		−	0.183469i
$392$	−16.3812	−	11.1201i	−0.827376	−	0.561648i
$393$		−	6.19114i		−	0.312302i
$394$	−12.2941	+	8.72861i	−0.619366	+	0.439741i
$395$	0.816614	+	3.04764i	0.0410883	+	0.153344i
$396$	17.1091	+	35.4733i	0.859765	+	1.78260i
$397$	1.63170	−	6.08958i	0.0818925	−	0.305627i	−0.912815	−	0.408373i	$-0.866096\pi$
$397$	1.63170	−	6.08958i	0.0818925	−	0.305627i	0.994708	+	0.102746i	$0.0327629\pi$
$398$	−7.75427	−	6.42077i	−0.388686	−	0.321844i
$399$	−18.7188	−	0.865159i	−0.937113	−	0.0433121i
$400$	1.46580	+	3.72175i	0.0732901	+	0.186088i
$401$	7.77766	+	13.4713i	0.388398	+	0.672725i	0.992234	−	0.124383i	$-0.0396953\pi$
$401$	7.77766	+	13.4713i	0.388398	+	0.672725i	−0.603836	+	0.797108i	$0.706362\pi$
$402$	−0.408533	+	0.151723i	−0.0203758	+	0.00756724i
$403$	−13.6798	+	3.66548i	−0.681437	+	0.182591i
$404$	−2.89998	+	39.0095i	−0.144279	+	1.94080i
$405$	1.33940	−	1.33940i	0.0665551	−	0.0665551i
$406$	16.0126	−	10.2909i	0.794691	−	0.510731i
$407$			30.7075i			1.52211i
$408$	−15.3249	+	15.9376i	−0.758697	+	0.789027i
$409$	23.4748	+	13.5532i	1.16076	+	0.670163i	0.951485	−	0.307695i	$-0.0995576\pi$
$409$	23.4748	+	13.5532i	1.16076	+	0.670163i	0.209271	+	0.977858i	$0.432891\pi$
$410$	−3.53329	+	7.70820i	−0.174497	+	0.380681i
$411$	47.0881	+	12.6172i	2.32268	+	0.622362i
$412$	37.7641	−	7.16866i	1.86050	−	0.353175i
$413$	−37.4149	+	8.19454i	−1.84107	+	0.403227i
$414$	6.11566	−	7.38580i	0.300568	−	0.362992i
$415$	0.517998	+	0.897199i	0.0254275	+	0.0440418i
$416$	−0.588041	+	10.7573i	−0.0288311	+	0.527421i
$417$	−5.66292	+	9.80846i	−0.277314	+	0.480322i
$418$	−13.3099	−	2.25737i	−0.651010	−	0.110412i
$419$	−7.85228	−	7.85228i	−0.383609	−	0.383609i	0.488792	−	0.872401i	$-0.337438\pi$
$419$	−7.85228	−	7.85228i	−0.383609	−	0.383609i	−0.872401	+	0.488792i	$0.837438\pi$
$420$	−5.62545	+	13.9953i	−0.274494	+	0.682900i
$421$	9.06035	−	9.06035i	0.441574	−	0.441574i	−0.450966	−	0.892541i	$-0.648921\pi$
$421$	9.06035	−	9.06035i	0.441574	−	0.441574i	0.892541	+	0.450966i	$0.148921\pi$
$422$	13.0407	+	18.3676i	0.634812	+	0.894119i
$423$	−2.89584	−	1.67191i	−0.140801	−	0.0812912i
$424$	8.75368	−	35.4320i	0.425116	−	1.72073i
$425$	2.37494	−	1.37117i	0.115202	−	0.0665117i
$426$	6.01301	+	63.9180i	0.291331	+	3.09684i
$427$	−17.1403	−	5.45246i	−0.829478	−	0.263863i
$428$	−21.2978	−	14.5020i	−1.02947	−	0.700981i
$429$	5.39820	−	20.1464i	0.260628	−	0.972676i
$430$	−2.69409	+	1.00054i	−0.129920	+	0.0482504i
$431$	−4.10665	+	7.11293i	−0.197810	+	0.342618i	−0.947818	−	0.318811i	$-0.896716\pi$
$431$	−4.10665	+	7.11293i	−0.197810	+	0.342618i	0.750008	+	0.661429i	$0.230050\pi$
$432$	−24.0794	+	2.74217i	−1.15852	+	0.131933i
$433$	15.7652			0.757625			0.378813	−	0.925473i	$-0.376332\pi$
$433$	15.7652			0.757625			0.378813	+	0.925473i	$0.376332\pi$
$434$	20.5887	+	18.7159i	0.988291	+	0.898394i
$435$	−10.2538	−	10.2538i	−0.491631	−	0.491631i
$436$	−31.4107	−	2.33508i	−1.50430	−	0.111830i
$437$	0.850732	+	3.17497i	0.0406960	+	0.151880i
$438$	26.7133	+	12.2449i	1.27641	+	0.585082i
$439$	−2.58622	+	1.49315i	−0.123434	+	0.0712644i	−0.560446	−	0.828191i	$-0.689370\pi$
$439$	−2.58622	+	1.49315i	−0.123434	+	0.0712644i	0.437012	+	0.899456i	$0.356037\pi$
$440$	−5.24791	+	9.51545i	−0.250184	+	0.453631i
$441$	−32.5939	+	14.9967i	−1.55209	+	0.714128i
$442$	7.35362	−	0.691783i	0.349776	−	0.0329047i
$443$	−3.09932	−	0.830460i	−0.147253	−	0.0394564i	0.184440	−	0.982844i	$-0.440953\pi$
$443$	−3.09932	−	0.830460i	−0.147253	−	0.0394564i	−0.331693	+	0.943388i	$0.607620\pi$
$444$	−43.0186	−	15.0241i	−2.04157	−	0.713012i
$445$	9.82288	−	2.63203i	0.465649	−	0.124770i
$446$	32.6879	+	5.54388i	1.54782	+	0.262510i
$447$	27.7324			1.31170
$448$	18.4039	−	10.4545i	0.869503	−	0.493927i
$449$	−16.9147			−0.798253			−0.399127	−	0.916896i	$-0.630687\pi$
$449$	−16.9147			−0.798253			−0.399127	+	0.916896i	$0.630687\pi$
$450$	7.14649	+	1.21205i	0.336889	+	0.0571364i
$451$	−22.2508	+	5.96209i	−1.04775	+	0.280744i
$452$	−31.2543	−	10.9155i	−1.47008	−	0.513420i
$453$	−3.43187	−	0.919567i	−0.161243	−	0.0432050i
$454$	4.79179	−	0.450782i	0.224890	−	0.0211562i
$455$	4.47538	−	2.31524i	0.209809	−	0.108540i
$456$	9.67448	−	17.5417i	0.453049	−	0.821464i
$457$	−11.5526	+	6.66990i	−0.540408	+	0.312005i	−0.745244	−	0.666792i	$-0.767667\pi$
$457$	−11.5526	+	6.66990i	−0.540408	+	0.312005i	0.204836	+	0.978796i	$0.434334\pi$
$458$	−25.3650	−	11.6268i	−1.18523	−	0.543285i
$459$	4.30034	+	16.0491i	0.200723	+	0.749107i
$460$	2.63853	+	0.196149i	0.123022	+	0.00914550i
$461$	21.1350	+	21.1350i	0.984356	+	0.984356i	0.999879	−	0.0155239i	$-0.00494161\pi$
$461$	21.1350	+	21.1350i	0.984356	+	0.984356i	−0.0155239	+	0.999879i	$0.504942\pi$
$462$	−39.0311	+	12.4774i	−1.81589	+	0.580502i
$463$	13.2477			0.615674			0.307837	−	0.951439i	$-0.400395\pi$
$463$	13.2477			0.615674			0.307837	+	0.951439i	$0.400395\pi$
$464$	2.30242	+	20.2179i	0.106887	+	0.938592i
$465$	10.5987	−	18.3575i	0.491503	−	0.851308i
$466$	−8.50063	+	3.15700i	−0.393784	+	0.146245i
$467$	0.324365	−	1.21055i	0.0150098	−	0.0560175i	−0.958015	−	0.286719i	$-0.907435\pi$
$467$	0.324365	−	1.21055i	0.0150098	−	0.0560175i	0.973025	+	0.230701i	$0.0741021\pi$
$468$	16.1371	+	10.9880i	0.745936	+	0.507919i
$469$	−0.0611926	−	0.279395i	−0.00282561	−	0.0129013i
$470$	−0.0864129	−	0.918565i	−0.00398593	−	0.0423702i
$471$	40.1519	−	23.1817i	1.85010	−	1.06816i
$472$	9.82074	−	39.7512i	0.452036	−	1.82970i
$473$	−6.76138	−	3.90368i	−0.310889	−	0.179492i
$474$	−7.36333	−	10.3711i	−0.338209	−	0.476360i
$475$	−1.75692	+	1.75692i	−0.0806132	+	0.0806132i
$476$	−8.95432	−	11.4190i	−0.410421	−	0.523388i
$477$	−46.7667	−	46.7667i	−2.14130	−	2.14130i
$478$	−1.37079	−	0.232487i	−0.0626987	−	0.0106337i
$479$	−3.50622	+	6.07296i	−0.160203	+	0.277481i	−0.934942	−	0.354802i	$-0.884548\pi$
$479$	−3.50622	+	6.07296i	−0.160203	+	0.277481i	0.774738	+	0.632282i	$0.217882\pi$
$480$	−10.7627	−	12.0075i	−0.491250	−	0.548063i
$481$	7.61097	+	13.1826i	0.347030	+	0.601074i
$482$	17.0979	−	20.6488i	0.778786	−	0.940528i
$483$	6.72160	+	7.37304i	0.305843	+	0.335485i
$484$	−7.38913	+	1.40266i	−0.335870	+	0.0637573i
$485$	1.89838	+	0.508670i	0.0862012	+	0.0230975i
$486$	7.52926	−	16.4258i	0.341534	−	0.745089i
$487$	29.4316	+	16.9923i	1.33367	+	0.769996i	0.985861	−	0.167568i	$-0.0535913\pi$
$487$	29.4316	+	16.9923i	1.33367	+	0.769996i	0.347812	+	0.937564i	$0.386925\pi$
$488$	13.3276	−	13.8604i	0.603313	−	0.627431i
$489$		−	53.5871i		−	2.42329i
$490$	−8.58026	−	4.93752i	−0.387617	−	0.223054i
$491$	5.77150	−	5.77150i	0.260464	−	0.260464i	−0.564778	−	0.825243i	$-0.691038\pi$
$491$	5.77150	−	5.77150i	0.260464	−	0.260464i	0.825243	+	0.564778i	$0.191038\pi$
$492$	2.53416	−	34.0886i	0.114249	−	1.53683i
$493$	13.4753	−	3.61071i	0.606899	−	0.162618i
$494$	−6.27339	+	2.32984i	−0.282253	+	0.104825i
$495$	9.84593	+	17.0537i	0.442542	+	0.766505i
$496$	−27.6761	+	10.9002i	−1.24269	+	0.489432i
$497$	−42.0903	−	1.94536i	−1.88801	−	0.0872613i
$498$	−3.21674	−	2.66356i	−0.144146	−	0.119357i
$499$	6.85291	−	25.5754i	0.306778	−	1.14491i	−0.624625	−	0.780925i	$-0.714748\pi$
$499$	6.85291	−	25.5754i	0.306778	−	1.14491i	0.931404	−	0.363988i	$-0.118585\pi$
$500$	0.868841	+	1.80142i	0.0388558	+	0.0805620i
$501$	−6.52548	−	24.3534i	−0.291537	−	1.08803i
$502$	12.8647	−	9.13373i	0.574178	−	0.407658i
$503$		−	17.4177i		−	0.776616i	−0.921530	−	0.388308i	$-0.873060\pi$
$503$		−	17.4177i		−	0.776616i	0.921530	−	0.388308i	$-0.126940\pi$
$504$	1.01983	−	38.3421i	0.0454269	−	1.70789i
$505$			19.5586i			0.870346i
$506$	4.16111	+	5.86083i	0.184984	+	0.260546i
$507$	6.91508	+	25.8074i	0.307110	+	1.14615i
$508$	−6.55193	−	2.28824i	−0.290695	−	0.101524i
$509$	−1.51126	+	5.64010i	−0.0669854	+	0.249993i	−0.991297	−	0.131646i	$-0.957974\pi$
$509$	−1.51126	+	5.64010i	−0.0669854	+	0.249993i	0.924311	+	0.381639i	$0.124640\pi$
$510$	−7.05061	+	8.51492i	−0.312206	+	0.377047i
$511$	−10.4040	+	16.2394i	−0.460247	+	0.718390i
$512$	1.32931	+	22.5883i	0.0587479	+	0.998273i
$513$	−7.52700	−	13.0372i	−0.332325	−	0.575604i
$514$	−10.9212	−	29.4066i	−0.481712	−	1.29707i
$515$	18.5643	−	4.97430i	0.818043	−	0.219194i
$516$	8.77685	−	7.56220i	0.386379	−	0.332907i
$517$	1.77233	−	1.77233i	0.0779469	−	0.0779469i
$518$	13.7034	−	26.5816i	0.602091	−	1.16793i
$519$		−	23.9419i		−	1.05093i
$520$	0.105540	+	5.38565i	0.00462822	+	0.236177i
$521$	−6.19544	−	3.57694i	−0.271427	−	0.156709i	0.358109	−	0.933680i	$-0.383422\pi$
$521$	−6.19544	−	3.57694i	−0.271427	−	0.156709i	−0.629536	+	0.776971i	$0.716755\pi$
$522$	33.5206	+	15.3652i	1.46716	+	0.672515i
$523$	9.62852	+	2.57995i	0.421026	+	0.112814i	0.463111	−	0.886301i	$-0.346733\pi$
$523$	9.62852	+	2.57995i	0.421026	+	0.112814i	−0.0420847	+	0.999114i	$0.513400\pi$
$524$	−2.44484	+	3.59052i	−0.106803	+	0.156853i
$525$	−2.28621	+	7.18691i	−0.0997784	+	0.313663i
$526$	−26.9865	−	22.3457i	−1.17667	−	0.974317i
$527$	10.1965	+	17.6608i	0.444165	+	0.769317i
$528$	6.47735	−	43.3247i	0.281890	−	1.88547i
$529$	−10.6250	+	18.4030i	−0.461955	+	0.800129i
$530$	3.05140	−	17.9917i	0.132545	−	0.781511i
$531$	−52.4675	−	52.4675i	−2.27690	−	2.27690i
$532$	10.5142	+	7.89369i	0.455850	+	0.342235i
$533$	−8.07445	+	8.07445i	−0.349743	+	0.349743i
$534$	−33.4272	+	23.7328i	−1.44653	+	1.02702i
$535$	−11.1571	−	6.44158i	−0.482366	−	0.278494i
$536$	0.296841	+	0.0733362i	0.0128216	+	0.00316764i
$537$	−33.2380	+	19.1900i	−1.43433	+	0.828109i
$538$	−11.2276	+	1.05623i	−0.484057	+	0.0455371i
$539$	−4.53476	−	26.5085i	−0.195326	−	1.14180i
$540$	−11.9049	+	2.25989i	−0.512307	+	0.0972500i
$541$	−2.88972	+	10.7846i	−0.124239	+	0.463665i	−0.999811	−	0.0194215i	$-0.993818\pi$
$541$	−2.88972	+	10.7846i	−0.124239	+	0.463665i	0.875573	+	0.483086i	$0.160484\pi$
$542$	3.33902	+	8.99072i	0.143423	+	0.386185i
$543$	−6.92876	+	12.0010i	−0.297342	+	0.515011i
$544$	15.1813	−	3.19119i	0.650892	−	0.136821i
$545$	−15.7487			−0.674599
$546$	−13.6633	+	15.0305i	−0.584736	+	0.643246i
$547$	17.6653	+	17.6653i	0.755315	+	0.755315i	0.975466	−	0.220151i	$-0.0706549\pi$
$547$	17.6653	+	17.6653i	0.755315	+	0.755315i	−0.220151	+	0.975466i	$0.570655\pi$
$548$	−22.3261	−	25.9121i	−0.953722	−	1.10691i
$549$	−9.01847	−	33.6574i	−0.384899	−	1.43646i
$550$	−2.26401	+	4.93916i	−0.0965379	+	0.210607i
$551$	−10.9464	+	6.31992i	−0.466333	+	0.269238i
$552$	−10.2464	+	2.96187i	−0.436117	+	0.126065i
$553$	7.41436	−	3.83565i	0.315291	−	0.163108i
$554$	−0.310679	−	3.30250i	−0.0131995	−	0.140310i
$555$	−22.0070	−	5.89677i	−0.934147	−	0.250304i
$556$	7.15748	−	3.45212i	0.303545	−	0.146402i
$557$	−8.13652	+	2.18017i	−0.344756	+	0.0923770i	−0.427042	−	0.904232i	$-0.640444\pi$
$557$	−8.13652	+	2.18017i	−0.344756	+	0.0923770i	0.0822866	+	0.996609i	$0.473778\pi$
$558$	−9.01315	+	53.1435i	−0.381557	+	2.24974i
$559$	−3.87017			−0.163691
$560$	8.78911	−	5.89505i	0.371408	−	0.249111i
$561$	−30.0330			−1.26799
$562$	4.87901	−	28.7677i	0.205809	−	1.21349i
$563$	37.9966	−	10.1812i	1.60137	−	0.429085i	0.655912	−	0.754837i	$-0.272284\pi$
$563$	37.9966	−	10.1812i	1.60137	−	0.429085i	0.945455	+	0.325752i	$0.105617\pi$
$564$	1.61575	+	3.35003i	0.0680352	+	0.141062i
$565$	−15.9888	−	4.28418i	−0.672652	−	0.180237i
$566$	2.22159	+	23.6154i	0.0933803	+	0.992628i
$567$	−4.21982	−	2.70349i	−0.177216	−	0.113536i
$568$	21.7536	−	39.4434i	0.912761	−	1.65501i
$569$	27.8119	−	16.0572i	1.16593	−	0.673152i	0.213215	−	0.977005i	$-0.431607\pi$
$569$	27.8119	−	16.0572i	1.16593	−	0.673152i	0.952719	+	0.303853i	$0.0982732\pi$
$570$	4.17369	−	9.10531i	0.174817	−	0.381380i
$571$	−0.497049	−	1.85501i	−0.0208009	−	0.0776299i	0.954745	−	0.297425i	$-0.0961278\pi$
$571$	−0.497049	−	1.85501i	−0.0208009	−	0.0776299i	−0.975546	+	0.219795i	$0.929461\pi$
$572$	−11.0863	+	9.55207i	−0.463543	+	0.399392i
$573$	−7.57137	−	7.57137i	−0.316298	−	0.316298i
$574$	21.9218	+	4.76852i	0.914998	+	0.199034i
$575$	1.32290			0.0551689
$576$	36.2864	+	19.0950i	1.51193	+	0.795625i
$577$	−6.28850	+	10.8920i	−0.261794	+	0.453440i	−0.966719	−	0.255842i	$-0.917647\pi$
$577$	−6.28850	+	10.8920i	−0.261794	+	0.453440i	0.704925	+	0.709282i	$0.250981\pi$
$578$	4.66733	+	12.5674i	0.194135	+	0.522734i
$579$	−15.4734	+	57.7474i	−0.643051	+	2.39990i
$580$	1.89748	+	9.99578i	0.0787884	+	0.415052i
$581$	2.02559	−	1.84662i	0.0840356	−	0.0766108i
$582$	−7.88800	+	0.742054i	−0.326968	+	0.0307591i
$583$	42.9337	−	24.7878i	1.77813	−	1.02660i
$584$	−10.6568	−	17.6503i	−0.440983	−	0.730373i
$585$	8.45363	+	4.88070i	0.349514	+	0.201792i
$586$	−12.0600	+	8.56242i	−0.498194	+	0.353710i
$587$	−7.07670	+	7.07670i	−0.292087	+	0.292087i	−0.837904	−	0.545818i	$-0.816219\pi$
$587$	−7.07670	+	7.07670i	−0.292087	+	0.292087i	0.545818	+	0.837904i	$0.316219\pi$
$588$	39.3550	+	6.61689i	1.62297	+	0.272876i
$589$	−13.0650	−	13.0650i	−0.538335	−	0.538335i
$590$	3.42337	−	20.1849i	0.140938	−	0.831000i
$591$	15.1954	−	26.3191i	0.625053	−	1.08262i
$592$	19.0155	+	25.7010i	0.781534	+	1.05630i
$593$	−8.48572	−	14.6977i	−0.348467	−	0.603562i	0.637511	−	0.770442i	$-0.279964\pi$
$593$	−8.48572	−	14.6977i	−0.348467	−	0.603562i	−0.985977	+	0.166880i	$0.946631\pi$
$594$	−25.3553	−	20.9950i	−1.04034	−	0.861434i
$595$	−4.88812	−	5.36186i	−0.200393	−	0.219815i
$596$	−16.0833	−	10.9514i	−0.658797	−	0.448586i
$597$	19.6009	+	5.25205i	0.802212	+	0.214952i
$598$	3.23897	+	1.48468i	0.132452	+	0.0607132i
$599$	4.48723	+	2.59071i	0.183343	+	0.105853i	0.588863	−	0.808233i	$-0.299576\pi$
$599$	4.48723	+	2.59071i	0.183343	+	0.105853i	−0.405519	+	0.914087i	$0.632909\pi$
$600$	−5.81165	−	5.58826i	−0.237260	−	0.228140i
$601$			5.64070i			0.230089i	0.993360	+	0.115045i	$0.0367011\pi$
$601$			5.64070i			0.230089i	−0.993360	+	0.115045i	$0.963299\pi$
$602$	4.11088	+	6.39648i	0.167547	+	0.260701i
$603$	0.391800	−	0.391800i	0.0159553	−	0.0159553i
$604$	1.62717	+	1.88852i	0.0662085	+	0.0768430i
$605$	−3.63241	+	0.973300i	−0.147678	+	0.0395703i
$606$	−27.4501	−	73.9129i	−1.11508	−	3.00251i
$607$	3.50378	+	6.06873i	0.142214	+	0.246322i	0.928330	−	0.371757i	$-0.121245\pi$
$607$	3.50378	+	6.06873i	0.142214	+	0.246322i	−0.786116	+	0.618079i	$0.787911\pi$
$608$	−12.5378	+	6.35282i	−0.508474	+	0.257641i
$609$	−20.6966	+	32.3049i	−0.838670	+	1.30906i
$610$	6.13170	−	7.40516i	0.248265	−	0.299826i
$611$	0.321574	−	1.20013i	0.0130095	−	0.0485521i
$612$	9.26891	−	26.5397i	0.374673	−	1.07281i
$613$	4.67719	+	17.4555i	0.188910	+	0.705021i	0.993760	+	0.111542i	$0.0355791\pi$
$613$	4.67719	+	17.4555i	0.188910	+	0.705021i	−0.804850	+	0.593478i	$0.797754\pi$
$614$	−24.7731	−	34.8923i	−0.999759	−	1.40814i
$615$		−	17.0913i		−	0.689189i
$616$	27.5632	+	8.17694i	1.11055	+	0.329458i
$617$			18.3215i			0.737594i	0.929510	+	0.368797i	$0.120230\pi$
$617$			18.3215i			0.737594i	−0.929510	+	0.368797i	$0.879770\pi$
$618$	−63.1743	+	44.8528i	−2.54124	+	1.80425i
$619$	6.36405	+	23.7510i	0.255793	+	0.954632i	0.967648	+	0.252305i	$0.0811886\pi$
$619$	6.36405	+	23.7510i	0.255793	+	0.954632i	−0.711855	+	0.702326i	$0.752145\pi$
$620$	−13.3959	+	6.46098i	−0.537993	+	0.259479i
$621$	−2.07448	+	7.74206i	−0.0832460	+	0.310678i
$622$	4.58288	+	3.79476i	0.183757	+	0.152156i
$623$	−12.3627	−	23.8973i	−0.495301	−	0.957424i
$624$	−7.95750	−	20.2045i	−0.318555	−	0.808829i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−33.6627	+	12.5018i	−1.34543	+	0.499673i
$627$	26.2838	−	7.04271i	1.04967	−	0.281259i
$628$	−32.4402	−	2.41162i	−1.29451	−	0.0962341i
$629$	15.4989	−	15.4989i	0.617981	−	0.617981i
$630$	−0.912749	−	19.1561i	−0.0363648	−	0.763197i
$631$		−	23.6718i		−	0.942360i	−0.882037	−	0.471180i	$-0.843828\pi$
$631$		−	23.6718i		−	0.942360i	0.882037	−	0.471180i	$-0.156172\pi$
$632$	0.174847	+	8.92241i	0.00695505	+	0.354914i
$633$	−39.3212	−	22.7021i	−1.56288	−	0.902329i
$634$	−9.69094	+	21.1417i	−0.384877	+	0.839645i
$635$	−3.35177	−	0.898104i	−0.133011	−	0.0356402i
$636$	13.7197	+	72.2743i	0.544020	+	2.86586i
$637$	−8.51699	−	10.2560i	−0.337456	−	0.406359i
$638$	−17.6281	+	21.2892i	−0.697902	+	0.842846i
$639$	−40.8133	−	70.6907i	−1.61455	−	2.79648i
$640$	1.50013	+	11.2138i	0.0592978	+	0.443265i
$641$	−12.2914	+	21.2893i	−0.485481	+	0.840878i	−0.999861	−	0.0166848i	$-0.994689\pi$
$641$	−12.2914	+	21.2893i	−0.485481	+	0.840878i	0.514380	+	0.857562i	$0.328022\pi$
$642$	51.2041	+	8.68422i	2.02086	+	0.342739i
$643$	21.5872	+	21.5872i	0.851317	+	0.851317i	0.990295	−	0.138979i	$-0.0443819\pi$
$643$	21.5872	+	21.5872i	0.851317	+	0.851317i	−0.138979	+	0.990295i	$0.544382\pi$
$644$	−0.986594	−	6.93028i	−0.0388772	−	0.273091i
$645$	4.09603	−	4.09603i	0.161281	−	0.161281i
$646$	5.57853	+	7.85723i	0.219484	+	0.309139i
$647$	−10.4499	−	6.03325i	−0.410828	−	0.237192i	0.280318	−	0.959907i	$-0.409560\pi$
$647$	−10.4499	−	6.03325i	−0.410828	−	0.237192i	−0.691145	+	0.722716i	$0.742894\pi$
$648$	4.58643	−	2.76919i	0.180172	−	0.108784i
$649$	48.1672	−	27.8094i	1.89073	−	1.09161i
$650$	0.252259	+	2.68151i	0.00989443	+	0.105177i
$651$	−53.4441	−	17.0010i	−2.09464	−	0.666321i
$652$	−21.1612	+	31.0776i	−0.828737	+	1.21709i
$653$	−7.91273	+	29.5307i	−0.309649	+	1.15563i	0.619220	+	0.785218i	$0.287449\pi$
$653$	−7.91273	+	29.5307i	−0.309649	+	1.15563i	−0.928869	+	0.370408i	$0.879218\pi$
$654$	59.5150	−	22.1030i	2.32722	−	0.864294i
$655$	−1.08596	+	1.88095i	−0.0424321	+	0.0734946i
$656$	−14.9311	+	18.7688i	−0.582960	+	0.732798i
$657$	−37.3625			−1.45765
$658$	−2.32511	+	0.743287i	−0.0906421	+	0.0289763i
$659$	−33.6290	−	33.6290i	−1.31000	−	1.31000i	−0.921412	−	0.388586i	$-0.872964\pi$
$659$	−33.6290	−	33.6290i	−1.31000	−	1.31000i	−0.388586	−	0.921412i	$-0.627036\pi$
$660$	1.62380	−	21.8428i	0.0632065	−	0.850232i
$661$	−3.64663	−	13.6094i	−0.141837	−	0.529345i	−0.999876	−	0.0157590i	$-0.994984\pi$
$661$	−3.64663	−	13.6094i	−0.141837	−	0.529345i	0.858038	−	0.513586i	$-0.171683\pi$
$662$	−15.2003	−	6.96751i	−0.590776	−	0.270800i
$663$	−12.8930	+	7.44379i	−0.500723	+	0.289093i
$664$	0.813712	+	2.81499i	0.0315781	+	0.109243i
$665$	5.53526	+	3.54624i	0.214648	+	0.137517i
$666$	57.6807	−	5.42624i	2.23508	−	0.210263i
$667$	6.50049	+	1.74180i	0.251700	+	0.0674428i
$668$	−5.83259	+	16.7005i	−0.225670	+	0.646162i
$669$	−64.5504	+	17.2962i	−2.49566	+	0.668711i
$670$	0.150731	+	0.0255639i	0.00582323	+	0.000987621i
$671$	26.1188			1.00830
$672$	−24.9409	+	34.6130i	−0.962116	+	1.33523i
$673$	26.8735			1.03590			0.517948	−	0.855412i	$-0.326696\pi$
$673$	26.8735			1.03590			0.517948	+	0.855412i	$0.326696\pi$
$674$	31.6828	+	5.37341i	1.22038	+	0.206976i
$675$	−5.85232	+	1.56812i	−0.225256	+	0.0603571i
$676$	6.18083	−	17.6976i	0.237724	−	0.680678i
$677$	−10.9418	−	2.93184i	−0.420527	−	0.112680i	0.0423490	−	0.999103i	$-0.486516\pi$
$677$	−10.9418	−	2.93184i	−0.420527	−	0.112680i	−0.462876	+	0.886423i	$0.653183\pi$
$678$	66.4351	−	6.24981i	2.55143	−	0.240022i
$679$	0.240073	−	5.19429i	0.00921316	−	0.199338i
$680$	7.45146	−	2.15394i	0.285750	−	0.0826000i
$681$	−8.40140	+	4.85055i	−0.321942	+	0.185873i
$682$	−36.7292	−	16.8359i	−1.40643	−	0.644681i
$683$	−1.31399	−	4.90388i	−0.0502784	−	0.187642i	0.936219	−	0.351416i	$-0.114300\pi$
$683$	−1.31399	−	4.90388i	−0.0502784	−	0.187642i	−0.986498	+	0.163774i	$0.947633\pi$
$684$	−1.88826	+	25.4002i	−0.0721993	+	0.971200i
$685$	−12.0928	−	12.0928i	−0.462043	−	0.462043i
$686$	−7.90410	+	24.9705i	−0.301780	+	0.953378i
$687$	56.2415			2.14575
$688$	−8.07636	+	0.919737i	−0.307908	+	0.0350646i
$689$	12.2875	−	21.2825i	0.468116	−	0.810800i
$690$	−4.99932	+	1.85667i	−0.190321	+	0.0706823i
$691$	0.716871	−	2.67540i	0.0272711	−	0.101777i	−0.950949	−	0.309348i	$-0.899889\pi$
$691$	0.716871	−	2.67540i	0.0272711	−	0.101777i	0.978220	+	0.207571i	$0.0665558\pi$
$692$	−9.45452	+	13.8850i	−0.359407	+	0.527829i
$693$	38.5017	−	35.0999i	1.46256	−	1.33334i
$694$	−3.02443	−	32.1495i	−0.114806	−	1.22038i
$695$	3.44093	−	1.98662i	0.130522	−	0.0753569i
$696$	−21.1995	−	35.1115i	−0.803567	−	1.33090i
$697$	14.2398	+	8.22135i	0.539371	+	0.311406i
$698$	13.2957	+	18.7267i	0.503249	+	0.708815i
$699$	12.9242	−	12.9242i	0.488837	−	0.488837i
$700$	4.16394	−	3.26521i	0.157382	−	0.123413i
$701$	30.6372	+	30.6372i	1.15715	+	1.15715i	0.985086	+	0.172066i	$0.0550441\pi$
$701$	30.6372	+	30.6372i	1.15715	+	1.15715i	0.172066	+	0.985086i	$0.444956\pi$
$702$	−16.0886	−	2.72863i	−0.607225	−	0.102986i
$703$	−9.92958	+	17.1985i	−0.374501	+	0.648655i
$704$	−20.8652	+	22.5681i	−0.786386	+	0.850567i
$705$	0.929829	+	1.61051i	0.0350194	+	0.0606553i
$706$	22.2175	−	26.8317i	0.836165	−	1.00982i
$707$	50.5490	−	11.0711i	1.90109	−	0.416373i
$708$	15.3921	+	81.0844i	0.578469	+	3.04734i
$709$	7.42098	+	1.98844i	0.278701	+	0.0746776i	0.395462	−	0.918482i	$-0.370585\pi$
$709$	7.42098	+	1.98844i	0.278701	+	0.0746776i	−0.116761	+	0.993160i	$0.537251\pi$
$710$	9.38478	−	20.4738i	0.352205	−	0.768368i
$711$	14.0051	+	8.08586i	0.525233	+	0.303243i
$712$	28.7579	−	0.563551i	1.07775	−	0.0211200i
$713$			9.83753i			0.368418i
$714$	25.9977	+	13.4024i	0.972940	+	0.501571i
$715$	−5.17384	+	5.17384i	−0.193491	+	0.193491i
$716$	26.8542	+	1.99635i	1.00359	+	0.0746072i
$717$	2.70697	−	0.725331i	0.101094	−	0.0270880i
$718$	2.63966	−	0.980329i	0.0985112	−	0.0365855i
$719$	−25.7654	−	44.6270i	−0.960887	−	1.66431i	−0.720281	−	0.693682i	$-0.755987\pi$
$719$	−25.7654	−	44.6270i	−0.960887	−	1.66431i	−0.240606	−	0.970623i	$-0.577346\pi$
$720$	18.8011	+	8.17617i	0.700675	+	0.304708i
$721$	−23.3644	−	45.1637i	−0.870135	−	1.68198i
$722$	13.9714	+	11.5687i	0.519961	+	0.430544i
$723$	−13.9857	+	52.1952i	−0.520132	+	1.94116i
$724$	8.75741	−	4.22378i	0.325467	−	0.156976i
$725$	1.31665	+	4.91380i	0.0488991	+	0.182494i
$726$	12.3610	−	8.77616i	0.458761	−	0.325714i
$727$			9.75386i			0.361751i	0.983506	+	0.180875i	$0.0578931\pi$
$727$			9.75386i			0.361751i	−0.983506	+	0.180875i	$0.942107\pi$
$728$	13.8594	−	3.32132i	0.513665	−	0.123096i
$729$			42.1033i			1.55938i
$730$	−5.96802	−	8.40582i	−0.220886	−	0.311114i
$731$	1.44235	+	5.38294i	0.0533474	+	0.199095i
$732$	−12.7790	+	36.5902i	−0.472325	+	1.35241i
$733$	−11.8141	+	44.0906i	−0.436362	+	1.62853i	0.301424	+	0.953490i	$0.402538\pi$
$733$	−11.8141	+	44.0906i	−0.436362	+	1.62853i	−0.737786	+	0.675035i	$0.764129\pi$
$734$	−18.1971	+	21.9764i	−0.671667	+	0.811162i
$735$	19.8686	+	1.84053i	0.732865	+	0.0678891i
$736$	7.11199	+	2.32853i	0.262151	+	0.0858308i
$737$	0.207666	+	0.359688i	0.00764948	+	0.0132493i
$738$	15.1310	+	40.7422i	0.556981	+	1.49974i
$739$	20.3789	−	5.46050i	0.749648	−	0.200868i	0.136286	−	0.990670i	$-0.456483\pi$
$739$	20.3789	−	5.46050i	0.749648	−	0.200868i	0.613362	+	0.789802i	$0.289817\pi$
$740$	10.4343	+	12.1103i	0.383572	+	0.445182i
$741$	9.53794	−	9.53794i	0.350385	−	0.350385i
$742$	−48.2267	+	2.29790i	−1.77046	+	0.0843587i
$743$			15.4751i			0.567726i	0.958865	+	0.283863i	$0.0916160\pi$
$743$			15.4751i			0.567726i	−0.958865	+	0.283863i	$0.908384\pi$
$744$	41.5560	−	43.2173i	1.52352	−	1.58442i
$745$	−8.42546	−	4.86444i	−0.308685	−	0.178219i
$746$	−24.1346	−	11.0628i	−0.883631	−	0.405039i
$747$	5.12906	+	1.37433i	0.187662	+	0.0502840i
$748$	17.4175	+	11.8598i	0.636846	+	0.433639i
$749$	−10.3327	+	32.4818i	−0.377549	+	1.18686i
$750$	−3.10498	−	2.57101i	−0.113378	−	0.0938801i
$751$	−9.83777	−	17.0395i	−0.358985	−	0.621781i	0.628806	−	0.777562i	$-0.283544\pi$
$751$	−9.83777	−	17.0395i	−0.358985	−	0.621781i	−0.987792	+	0.155781i	$0.950211\pi$
$752$	0.385860	−	2.58088i	0.0140709	−	0.0941150i
$753$	−15.9006	+	27.5407i	−0.579450	+	1.00364i
$754$	−2.29105	+	13.5085i	−0.0834351	+	0.491951i
$755$	0.881348	+	0.881348i	0.0320755	+	0.0320755i
$756$	12.5794	+	29.4890i	0.457510	+	1.07250i
$757$	−6.25528	+	6.25528i	−0.227352	+	0.227352i	−0.811586	−	0.584234i	$-0.801395\pi$
$757$	−6.25528	+	6.25528i	−0.227352	+	0.227352i	0.584234	+	0.811586i	$0.301395\pi$
$758$	11.5324	−	8.18788i	0.418877	−	0.297397i
$759$	−12.5469	−	7.24393i	−0.455422	−	0.262938i
$760$	−6.01615	+	3.63242i	−0.218229	+	0.131762i
$761$	30.4697	−	17.5917i	1.10452	−	0.637698i	0.167119	−	0.985937i	$-0.446554\pi$
$761$	30.4697	−	17.5917i	1.10452	−	0.637698i	0.937406	+	0.348239i	$0.113220\pi$
$762$	13.9270	−	1.31016i	0.504521	−	0.0474623i
$763$	8.91454	+	40.7023i	0.322728	+	1.47352i
$764$	1.40109	+	7.38087i	0.0506897	+	0.267030i
$765$	3.63793	−	13.5769i	0.131530	−	0.490875i
$766$	−9.84534	−	26.5098i	−0.355726	−	0.957839i
$767$	13.7853	−	23.8769i	0.497759	−	0.862144i
$768$	−21.4074	−	40.2722i	−0.772474	−	1.45320i
$769$	3.03556			0.109465			0.0547325	−	0.998501i	$-0.482569\pi$
$769$	3.03556			0.109465			0.0547325	+	0.998501i	$0.482569\pi$
$770$	14.0468	+	3.05551i	0.506210	+	0.110113i
$771$	44.7092	+	44.7092i	1.61016	+	1.61016i
$772$	31.7778	−	27.3800i	1.14371	−	0.985428i
$773$	−0.826224	−	3.08351i	−0.0297172	−	0.110906i	0.949474	−	0.313845i	$-0.101617\pi$
$773$	−0.826224	−	3.08351i	−0.0297172	−	0.110906i	−0.979191	+	0.202939i	$0.934951\pi$
$774$	−6.13786	+	13.3903i	−0.220621	+	0.481305i
$775$	−6.44004	+	3.71816i	−0.231333	+	0.133560i
$776$	4.86764	+	2.68457i	0.174738	+	0.0963705i
$777$	−2.78305	+	60.2148i	−0.0998414	+	2.16020i
$778$	−4.03221	−	42.8622i	−0.144562	−	1.53668i
$779$	−14.3901	−	3.85580i	−0.515577	−	0.138149i
$780$	−4.71674	−	9.77950i	−0.168886	−	0.350162i
$781$	59.1005	−	15.8359i	2.11478	−	0.566654i
$782$	0.857895	−	5.05834i	0.0306783	−	0.180886i
$783$	−30.8218			−1.10148
$784$	−20.2108	−	19.3785i	−0.721813	−	0.692088i
$785$	−16.2649			−0.580519
$786$	1.46404	−	8.63232i	0.0522207	−	0.307905i
$787$	−39.9922	+	10.7159i	−1.42557	+	0.381980i	−0.887455	−	0.460894i	$-0.847529\pi$
$787$	−39.9922	+	10.7159i	−1.42557	+	0.381980i	−0.538112	+	0.842874i	$0.680862\pi$
$788$	−19.2057	+	9.26310i	−0.684176	+	0.329984i
$789$	68.2154	+	18.2783i	2.42853	+	0.650723i
$790$	0.417918	+	4.44245i	0.0148688	+	0.158055i
$791$	−2.02197	+	43.7479i	−0.0718930	+	1.55549i
$792$	15.4667	+	53.5064i	0.549587	+	1.90127i
$793$	11.2127	−	6.47363i	0.398173	−	0.229885i
$794$	3.71511	−	8.10486i	0.131844	−	0.287631i
$795$	9.52000	+	35.5291i	0.337640	+	1.26009i
$796$	−9.29345	−	10.7862i	−0.329398	−	0.382306i
$797$	−25.1265	−	25.1265i	−0.890026	−	0.890026i	0.104499	−	0.994525i	$-0.466676\pi$
$797$	−25.1265	−	25.1265i	−0.890026	−	0.890026i	−0.994525	+	0.104499i	$0.966676\pi$
$798$	−25.8951	−	5.63281i	−0.916677	−	0.199399i
$799$	−1.78908			−0.0632932
$800$	1.16367	+	5.53587i	0.0411421	+	0.195723i
$801$	26.0616	−	45.1400i	0.920840	−	1.59494i
$802$	7.65880	+	20.6223i	0.270442	+	0.728198i
$803$	7.24850	−	27.0518i	0.255794	−	0.954636i
$804$	−0.605497	+	0.114940i	−0.0213542	+	0.00405362i
$805$	−0.748830	−	3.41903i	−0.0263928	−	0.120505i
$806$	−19.9405	+	1.87588i	−0.702375	+	0.0660751i
$807$	19.6853	−	11.3653i	0.692954	−	0.400077i
$808$	−13.2682	+	53.7053i	−0.466773	+	1.88935i
$809$	−48.0383	−	27.7349i	−1.68894	−	0.975108i	−0.955333	−	0.295531i	$-0.904503\pi$
$809$	−48.0383	−	27.7349i	−1.68894	−	0.975108i	−0.733604	−	0.679577i	$-0.762163\pi$
$810$	2.18426	−	1.55079i	0.0767470	−	0.0544893i
$811$	−33.6346	+	33.6346i	−1.18107	+	1.18107i	−0.201601	+	0.979468i	$0.564615\pi$
$811$	−33.6346	+	33.6346i	−1.18107	+	1.18107i	−0.979468	+	0.201601i	$0.935385\pi$
$812$	24.7599	−	10.5621i	0.868903	−	0.370658i
$813$	−13.6693	−	13.6693i	−0.479404	−	0.479404i
$814$	−7.26152	+	42.8155i	−0.254516	+	1.50068i
$815$	−9.39951	+	16.2804i	−0.329250	+	0.570278i
$816$	−25.1364	+	18.5978i	−0.879951	+	0.651055i
$817$	−2.52459	−	4.37272i	−0.0883243	−	0.152982i
$818$	29.5261	+	24.4485i	1.03235	+	0.854820i
$819$	7.82895	−	24.6110i	0.273566	−	0.859979i
$820$	−6.74926	+	9.91204i	−0.235694	+	0.346143i
$821$	44.2663	+	11.8611i	1.54490	+	0.413955i	0.927846	−	0.372963i	$-0.121658\pi$
$821$	44.2663	+	11.8611i	1.54490	+	0.413955i	0.617057	+	0.786919i	$0.288325\pi$
$822$	62.6714	+	28.7273i	2.18592	+	1.00198i
$823$	6.33657	+	3.65842i	0.220879	+	0.127524i	0.606357	−	0.795192i	$-0.292630\pi$
$823$	6.33657	+	3.65842i	0.220879	+	0.127524i	−0.385478	+	0.922717i	$0.625964\pi$
$824$	54.3497	−	1.06506i	1.89336	−	0.0371031i
$825$		−	10.9516i		−	0.381284i
$826$	−54.1055	+	2.57802i	−1.88257	+	0.0897006i
$827$	36.2891	−	36.2891i	1.26190	−	1.26190i	0.311722	−	0.950173i	$-0.399094\pi$
$827$	36.2891	−	36.2891i	1.26190	−	1.26190i	0.950173	−	0.311722i	$-0.100906\pi$
$828$	10.2736	−	8.85184i	0.357034	−	0.307623i
$829$	21.3930	−	5.73224i	0.743010	−	0.199089i	0.132594	−	0.991170i	$-0.457669\pi$
$829$	21.3930	−	5.73224i	0.743010	−	0.199089i	0.610415	+	0.792082i	$0.291003\pi$
$830$	0.510082	+	1.37346i	0.0177052	+	0.0476735i
$831$	3.34300	+	5.79024i	0.115967	+	0.200861i
$832$	−3.36373	+	14.8599i	−0.116616	+	0.515174i
$833$	−11.0908	+	15.6684i	−0.384272	+	0.542877i
$834$	−10.2153	+	12.3368i	−0.353726	+	0.427189i
$835$	−2.28922	+	8.54348i	−0.0792217	+	0.295659i
$836$	−18.0243	−	6.29491i	−0.623383	−	0.217714i
$837$	−11.6611	−	43.5197i	−0.403065	−	1.50426i
$838$	−9.09159	−	12.8053i	−0.314064	−	0.442352i
$839$			43.9307i			1.51666i	0.651873	+	0.758328i	$0.273983\pi$
$839$			43.9307i			1.51666i	−0.651873	+	0.758328i	$0.726017\pi$
$840$	−11.1531	+	18.1834i	−0.384819	+	0.627387i
$841$		−	3.12098i		−	0.107620i
$842$	14.7754	−	10.4903i	0.509194	−	0.361521i
$843$	15.2219	+	56.8089i	0.524270	+	1.95660i
$844$	13.8392	+	28.6937i	0.476366	+	0.987679i
$845$	2.42590	−	9.05357i	0.0834534	−	0.311452i
$846$	−3.64231	−	3.01594i	−0.125225	−	0.103690i
$847$	4.57161	+	8.83698i	0.157082	+	0.303642i
$848$	20.5840	−	47.3329i	0.706859	−	1.62542i
$849$	−23.9050	−	41.4046i	−0.820416	−	1.42100i
$850$	3.63563	−	1.35022i	0.124701	−	0.0463121i
$851$	10.2133	−	2.73664i	0.350107	−	0.0938108i
$852$	−6.73099	+	90.5429i	−0.230600	+	3.10195i
$853$	18.4664	−	18.4664i	0.632278	−	0.632278i	−0.316361	−	0.948639i	$-0.602461\pi$
$853$	18.4664	−	18.4664i	0.632278	−	0.632278i	0.948639	+	0.316361i	$0.102461\pi$
$854$	−22.6094	−	11.6556i	−0.773678	−	0.398847i
$855$			12.7351i			0.435532i
$856$	−26.2662	−	25.2566i	−0.897761	−	0.863251i
$857$	19.4892	+	11.2521i	0.665739	+	0.384365i	0.794460	−	0.607316i	$-0.207754\pi$
$857$	19.4892	+	11.2521i	0.665739	+	0.384365i	−0.128721	+	0.991681i	$0.541087\pi$
$858$	12.2908	−	26.8136i	0.419602	−	0.915401i
$859$	−44.0953	−	11.8153i	−1.50451	−	0.403132i	−0.589903	−	0.807474i	$-0.700834\pi$
$859$	−44.0953	−	11.8153i	−1.50451	−	0.403132i	−0.914608	+	0.404342i	$0.867501\pi$
$860$	−3.99297	+	0.757977i	−0.136159	+	0.0258468i
$861$	−44.1724	+	9.67455i	−1.50539	+	0.329708i
$862$	−7.40794	+	8.94646i	−0.252315	+	0.304718i
$863$	12.2601	+	21.2352i	0.417340	+	0.722854i	0.995671	−	0.0929482i	$-0.0296291\pi$
$863$	12.2601	+	21.2352i	0.417340	+	0.722854i	−0.578331	+	0.815802i	$0.696296\pi$
$864$	−34.2225	−	1.87075i	−1.16427	−	0.0636441i
$865$	−4.19956	+	7.27386i	−0.142789	+	0.247319i
$866$	21.9814	+	3.72805i	0.746959	+	0.126684i
$867$	−19.1072	−	19.1072i	−0.648914	−	0.648914i
$868$	24.2811	+	30.9644i	0.824154	+	1.05100i
$869$	−8.57150	+	8.57150i	−0.290768	+	0.290768i
$870$	−11.8721	−	16.7216i	−0.402502	−	0.566916i
$871$	0.178300	+	0.102942i	0.00604147	+	0.00348805i
$872$	−43.2438	−	10.6836i	−1.46442	−	0.361793i
$873$	8.72382	−	5.03670i	0.295256	−	0.170466i
$874$	0.435378	+	4.62805i	0.0147269	+	0.156546i
$875$	1.95521	−	1.78246i	0.0660981	−	0.0602581i
$876$	34.3509	+	23.3900i	1.16061	+	0.790276i
$877$	8.17164	−	30.4970i	0.275937	−	1.02981i	−0.679274	−	0.733884i	$-0.737705\pi$
$877$	8.17164	−	30.4970i	0.275937	−	1.02981i	0.955211	−	0.295925i	$-0.0956279\pi$
$878$	−3.95907	+	1.47034i	−0.133612	+	0.0496214i
$879$	14.9060	−	25.8180i	0.502768	−	0.870820i
$880$	−9.56733	+	12.0264i	−0.322515	+	0.405411i
$881$	−49.3117			−1.66135			−0.830676	−	0.556756i	$-0.812046\pi$
$881$	−49.3117			−1.66135			−0.830676	+	0.556756i	$0.812046\pi$
$882$	−48.9921	+	13.2023i	−1.64965	+	0.444545i
$883$	−16.1006	−	16.1006i	−0.541828	−	0.541828i	0.382237	−	0.924064i	$-0.375154\pi$
$883$	−16.1006	−	16.1006i	−0.541828	−	0.541828i	−0.924064	+	0.382237i	$0.875154\pi$
$884$	10.4168	+	0.774385i	0.350353	+	0.0260454i
$885$	10.6805	+	39.8601i	0.359021	+	1.33988i
$886$	−4.12501	−	1.89082i	−0.138582	−	0.0635234i
$887$	14.2102	−	8.20424i	0.477130	−	0.275471i	−0.242089	−	0.970254i	$-0.577833\pi$
$887$	14.2102	−	8.20424i	0.477130	−	0.275471i	0.719220	+	0.694783i	$0.244499\pi$
$888$	−56.4282	−	31.1209i	−1.89361	−	1.04435i
$889$	−0.423871	+	9.17099i	−0.0142162	+	0.307585i
$890$	14.3185	−	1.34699i	0.479956	−	0.0451513i
$891$	7.02941	+	1.88353i	0.235494	+	0.0631005i
$892$	44.2659	+	15.4597i	1.48213	+	0.517629i
$893$	1.56574	−	0.419539i	0.0523955	−	0.0140393i
$894$	38.6674	+	6.55800i	1.29323	+	0.219332i
$895$	13.4642			0.450058
$896$	28.1328	−	10.2246i	0.939852	−	0.341582i
$897$	−7.18175			−0.239792
$898$	−23.5842	−	3.99988i	−0.787014	−	0.133478i
$899$	−36.5406	+	9.79102i	−1.21870	+	0.326549i
$900$	9.67775	+	3.37992i	0.322592	+	0.112664i
$901$	−34.1808	−	9.15872i	−1.13873	−	0.305121i
$902$	−32.4342	+	3.05121i	−1.07994	+	0.101594i
$903$	−12.9047	−	8.26760i	−0.429442	−	0.275128i
$904$	−40.9967	−	22.6103i	−1.36353	−	0.752007i
$905$	4.21009	−	2.43070i	0.139948	−	0.0807991i
$906$	−4.56762	−	2.09370i	−0.151749	−	0.0695587i
$907$	−4.29995	−	16.0476i	−0.142777	−	0.532852i	−0.999844	−	0.0176473i	$-0.994382\pi$
$907$	−4.29995	−	16.0476i	−0.142777	−	0.532852i	0.857067	−	0.515205i	$-0.172284\pi$
$908$	6.78780	+	0.504608i	0.225261	+	0.0167460i
$909$	70.8856	+	70.8856i	2.35113	+	2.35113i
$910$	6.78753	−	2.16983i	0.225004	−	0.0719291i
$911$	2.22761			0.0738039			0.0369019	−	0.999319i	$-0.488251\pi$
$911$	2.22761			0.0738039			0.0369019	+	0.999319i	$0.488251\pi$
$912$	17.6373	−	22.1706i	0.584029	−	0.734143i
$913$	−1.99012	+	3.44699i	−0.0658634	+	0.114079i
$914$	−17.6851	+	6.56797i	−0.584971	+	0.217249i
$915$	−5.01559	+	18.7184i	−0.165810	+	0.618813i
$916$	−32.6170	−	22.2094i	−1.07770	−	0.733821i
$917$	5.47599	+	1.74195i	0.180833	+	0.0575244i
$918$	2.20078	+	23.3942i	0.0726366	+	0.772124i
$919$	11.0338	−	6.37039i	0.363973	−	0.210140i	−0.306849	−	0.951758i	$-0.599275\pi$
$919$	11.0338	−	6.37039i	0.363973	−	0.210140i	0.670822	+	0.741618i	$0.265941\pi$
$920$	3.63252	+	0.897435i	0.119761	+	0.0295875i
$921$	74.6974	+	43.1266i	2.46136	+	1.42107i
$922$	24.4707	+	34.4665i	0.805900	+	1.13509i
$923$	21.4466	−	21.4466i	0.705923	−	0.705923i
$924$	−57.3718	+	8.16744i	−1.88739	+	0.268689i
$925$	5.65169	+	5.65169i	0.185826	+	0.185826i
$926$	18.4713	+	3.13274i	0.607005	+	0.102948i
$927$	49.2540	−	85.3104i	1.61771	−	2.80196i
$928$	−1.57074	+	28.7343i	−0.0515621	+	0.943250i
$929$	−11.5803	−	20.0578i	−0.379939	−	0.658073i	0.611114	−	0.791543i	$-0.290722\pi$
$929$	−11.5803	−	20.0578i	−0.379939	−	0.658073i	−0.991053	+	0.133469i	$0.957388\pi$
$930$	19.1189	−	23.0896i	0.626932	−	0.757137i
$931$	6.03200	−	16.3132i	0.197691	−	0.534642i
$932$	−12.5990	+	2.39164i	−0.412694	+	0.0783407i
$933$	−11.5844	−	3.10403i	−0.379256	−	0.101621i
$934$	0.738527	−	1.61117i	0.0241653	−	0.0527190i
$935$	9.12439	+	5.26797i	0.298400	+	0.172281i
$936$	19.9016	+	19.1366i	0.650503	+	0.625498i
$937$			4.05078i			0.132333i	0.997809	+	0.0661665i	$0.0210769\pi$
$937$			4.05078i			0.132333i	−0.997809	+	0.0661665i	$0.978923\pi$
$938$	−0.0192513	−	0.404032i	−0.000628577	−	0.0131921i
$939$	51.1801	−	51.1801i	1.67020	−	1.67020i
$940$	0.0967311	−	1.30119i	0.00315502	−	0.0424402i
$941$	8.28634	−	2.22032i	0.270127	−	0.0723803i	−0.121213	−	0.992627i	$-0.538678\pi$
$941$	8.28634	−	2.22032i	0.270127	−	0.0723803i	0.391340	+	0.920246i	$0.372012\pi$
$942$	61.4658	−	22.8275i	2.00266	−	0.743759i
$943$	3.96597	+	6.86926i	0.129150	+	0.223694i
$944$	23.0932	−	53.1028i	0.751620	−	1.72835i
$945$	7.36551	+	14.2376i	0.239600	+	0.463150i
$946$	−8.50429	−	7.04181i	−0.276498	−	0.228949i
$947$	−10.2558	+	38.2750i	−0.333267	+	1.24377i	0.572468	+	0.819927i	$0.305986\pi$
$947$	−10.2558	+	38.2750i	−0.333267	+	1.24377i	−0.905736	+	0.423843i	$0.860681\pi$
$948$	−7.81422	−	16.2017i	−0.253794	−	0.526206i
$949$	−3.59314	−	13.4098i	−0.116638	−	0.435300i
$950$	−2.86515	+	2.03422i	−0.0929577	+	0.0659987i
$951$		−	46.8773i		−	1.52010i
$952$	−9.78474	−	18.0390i	−0.317125	−	0.584647i
$953$			49.0855i			1.59004i	0.606586	+	0.795018i	$0.292539\pi$
$953$			49.0855i			1.59004i	−0.606586	+	0.795018i	$0.707461\pi$
$954$	−54.1478	−	76.2660i	−1.75310	−	2.46920i
$955$	0.972211	+	3.62834i	0.0314600	+	0.117410i
$956$	−1.85633	−	0.648315i	−0.0600379	−	0.0209680i
$957$	14.4194	−	53.8138i	0.466112	−	1.73955i
$958$	−6.32484	+	7.63841i	−0.204346	+	0.246786i
$959$	−24.4086	+	38.0989i	−0.788196	+	1.23028i
$960$	−12.1671	−	19.2871i	−0.392690	−	0.622490i
$961$	−12.1494	−	21.0433i	−0.391915	−	0.678817i
$962$	7.49466	+	20.1803i	0.241637	+	0.650639i
$963$	−63.7826	+	17.0905i	−2.05536	+	0.550733i
$964$	28.7225	−	24.7475i	0.925089	−	0.797064i
$965$	14.8303	−	14.8303i	0.477403	−	0.477403i
$966$	7.62842	+	11.8697i	0.245440	+	0.381902i
$967$		−	37.0892i		−	1.19271i	−0.802721	−	0.596355i	$-0.796615\pi$
$967$		−	37.0892i		−	1.19271i	0.802721	−	0.596355i	$-0.203385\pi$
$968$	−10.6344	+	0.208396i	−0.341802	+	0.00669809i
$969$	−16.8208	−	9.71147i	−0.540361	−	0.311977i
$970$	2.52663	+	1.15816i	0.0811253	+	0.0371863i
$971$	−9.85116	−	2.63961i	−0.316139	−	0.0847092i	0.0972605	−	0.995259i	$-0.468992\pi$
$971$	−9.85116	−	2.63961i	−0.316139	−	0.0847092i	−0.413399	+	0.910550i	$0.635659\pi$
$972$	14.3823	−	21.1221i	0.461314	−	0.677490i
$973$	−7.08214	−	7.76852i	−0.227043	−	0.249047i
$974$	37.0183	+	30.6523i	1.18614	+	0.982162i
$975$	−2.71439	−	4.70146i	−0.0869299	−	0.150567i
$976$	21.8604	−	16.1740i	0.699733	−	0.517716i
$977$	11.6516	−	20.1812i	0.372768	−	0.645653i	−0.617222	−	0.786789i	$-0.711742\pi$
$977$	11.6516	−	20.1812i	0.372768	−	0.645653i	0.989990	+	0.141136i	$0.0450754\pi$
$978$	12.6720	−	74.7166i	0.405204	−	2.38917i
$979$	27.6268	+	27.6268i	0.882958	+	0.882958i
$980$	−10.7959	−	8.91340i	−0.344862	−	0.284728i
$981$	−57.0775	+	57.0775i	−1.82234	+	1.82234i
$982$	9.41203	−	6.68241i	0.300350	−	0.213244i
$983$	18.6384	+	10.7609i	0.594473	+	0.343219i	0.766864	−	0.641809i	$-0.221816\pi$
$983$	18.6384	+	10.7609i	0.594473	+	0.343219i	−0.172391	+	0.985029i	$0.555149\pi$
$984$	11.5945	−	46.9306i	0.369618	−	1.49609i
$985$	−9.23308	+	5.33072i	−0.294190	+	0.169851i
$986$	19.6426	−	1.84785i	0.625546	−	0.0588475i
$987$	3.63602	−	3.31476i	0.115736	−	0.105510i
$988$	−9.29796	+	1.76501i	−0.295807	+	0.0561524i
$989$	−0.695790	+	2.59672i	−0.0221248	+	0.0825710i
$990$	9.69546	+	26.1063i	0.308142	+	0.829711i
$991$	−17.9580	+	31.1042i	−0.570455	+	0.988057i	0.426064	+	0.904693i	$0.359900\pi$
$991$	−17.9580	+	31.1042i	−0.570455	+	0.988057i	−0.996519	+	0.0833641i	$0.973434\pi$
$992$	−41.1665	+	8.65344i	−1.30704	+	0.274747i
$993$	33.7035			1.06955
$994$	−58.2266	−	12.6657i	−1.84684	−	0.401731i
$995$	−5.03376	−	5.03376i	−0.159581	−	0.159581i
$996$	−3.85525	−	4.47449i	−0.122158	−	0.141780i
$997$	−11.9315	−	44.5291i	−0.377875	−	1.41025i	−0.849098	−	0.528236i	$-0.822854\pi$
$997$	−11.9315	−	44.5291i	−0.377875	−	1.41025i	0.471223	−	0.882014i	$-0.343813\pi$
$998$	15.6030	−	34.0393i	0.493903	−	1.07750i
$999$	−41.9380	+	24.2129i	−1.32686	+	0.766063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.221.63	✓	256
7.2	even	3	inner	560.2.cp.a.541.24	yes	256
16.5	even	4	inner	560.2.cp.a.501.24	yes	256
112.37	even	12	inner	560.2.cp.a.261.63	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.63	✓	256	1.1	even	1	trivial
560.2.cp.a.261.63	yes	256	112.37	even	12	inner
560.2.cp.a.501.24	yes	256	16.5	even	4	inner
560.2.cp.a.541.24	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39430 + 0.236474i) q^{2} +(-2.75340 + 0.737770i) q^{3} +(1.88816 + 0.659433i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-4.01353 + 0.377568i) q^{6} +(0.122153 - 2.64293i) q^{7} +(2.47673 + 1.36595i) q^{8} +(4.43881 - 2.56275i) q^{9} +O(q^{10})\)	\(q+(1.39430 + 0.236474i) q^{2} +(-2.75340 + 0.737770i) q^{3} +(1.88816 + 0.659433i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-4.01353 + 0.377568i) q^{6} +(0.122153 - 2.64293i) q^{7} +(2.47673 + 1.36595i) q^{8} +(4.43881 - 2.56275i) q^{9} +(1.28559 + 0.589289i) q^{10} +(0.994369 + 3.71103i) q^{11} +(-5.68536 - 0.422652i) q^{12} +(1.34667 + 1.34667i) q^{13} +(0.795302 - 3.65616i) q^{14} -2.85052 q^{15} +(3.13030 + 2.49023i) q^{16} +(1.37117 - 2.37494i) q^{17} +(6.79506 - 2.52358i) q^{18} +(-0.643079 + 2.40000i) q^{19} +(1.65315 + 1.12566i) q^{20} +(1.61354 + 7.36715i) q^{21} +(0.508887 + 5.40945i) q^{22} +(1.14567 - 0.661452i) q^{23} +(-7.82717 - 1.93375i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.55922 + 2.19612i) q^{26} +(-4.28420 + 4.28420i) q^{27} +(1.97348 - 4.90972i) q^{28} +(3.59715 + 3.59715i) q^{29} +(-3.97449 - 0.674075i) q^{30} +(-3.71816 + 6.44004i) q^{31} +(3.77571 + 4.21237i) q^{32} +(-5.47578 - 9.48433i) q^{33} +(2.47344 - 2.98714i) q^{34} +(0.802031 - 2.52126i) q^{35} +(10.0711 - 1.91178i) q^{36} +(7.72035 + 2.06866i) q^{37} +(-1.46418 + 3.19426i) q^{38} +(-4.70146 - 2.71439i) q^{39} +(2.03880 + 1.96043i) q^{40} +5.99585i q^{41} +(0.507622 + 10.6536i) q^{42} +(-1.43694 + 1.43694i) q^{43} +(-0.569651 + 7.66275i) q^{44} +(4.95085 - 1.32657i) q^{45} +(1.75383 - 0.651344i) q^{46} +(-0.326196 - 0.564987i) q^{47} +(-10.4562 - 4.54715i) q^{48} +(-6.97016 - 0.645683i) q^{49} +(1.08926 + 0.901944i) q^{50} +(-2.02322 + 7.55076i) q^{51} +(1.65469 + 3.43077i) q^{52} +(-3.33974 - 12.4641i) q^{53} +(-6.98657 + 4.96036i) q^{54} +3.84195i q^{55} +(3.91265 - 6.37896i) q^{56} -7.08260i q^{57} +(4.16489 + 5.86615i) q^{58} +(-3.74685 - 13.9834i) q^{59} +(-5.38225 - 1.87973i) q^{60} +(1.75953 - 6.56667i) q^{61} +(-6.70714 + 8.10011i) q^{62} +(-6.23095 - 12.0445i) q^{63} +(4.26836 + 6.76617i) q^{64} +(0.952241 + 1.64933i) q^{65} +(-5.39210 - 14.5189i) q^{66} +(0.104421 - 0.0279795i) q^{67} +(4.15511 - 3.58007i) q^{68} +(-2.66648 + 2.66648i) q^{69} +(1.71449 - 3.32574i) q^{70} -15.9256i q^{71} +(14.4943 - 0.284036i) q^{72} +(-6.31294 - 3.64478i) q^{73} +(10.2753 + 4.71000i) q^{74} +(-2.75340 - 0.737770i) q^{75} +(-2.79688 + 4.10752i) q^{76} +(9.92947 - 2.17473i) q^{77} +(-5.91337 - 4.89645i) q^{78} +(1.57758 + 2.73244i) q^{79} +(2.37912 + 3.21556i) q^{80} +(0.947096 - 1.64042i) q^{81} +(-1.41786 + 8.36003i) q^{82} +(0.732560 + 0.732560i) q^{83} +(-1.81152 + 14.9744i) q^{84} +(1.93913 - 1.93913i) q^{85} +(-2.34333 + 1.66373i) q^{86} +(-12.5583 - 7.25051i) q^{87} +(-2.60631 + 10.5495i) q^{88} +(8.80695 - 5.08470i) q^{89} +(7.21668 - 0.678900i) q^{90} +(3.72366 - 3.39466i) q^{91} +(2.59939 - 0.493436i) q^{92} +(5.48629 - 20.4751i) q^{93} +(-0.321211 - 0.864900i) q^{94} +(-1.24233 + 2.15178i) q^{95} +(-13.5038 - 8.81271i) q^{96} +1.96535 q^{97} +(-9.56582 - 2.54854i) q^{98} +(13.9242 + 13.9242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4}+O(q^{10}) \) 256 * q + 4 * q^4	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46} + 80 q^{47} - 160 q^{48} - 8 q^{50} - 40 q^{51} + 24 q^{52} - 16 q^{53} - 116 q^{54} - 96 q^{56} - 8 q^{58} + 16 q^{59} - 28 q^{60} + 88 q^{62} - 56 q^{64} - 16 q^{66} - 40 q^{67} - 20 q^{68} - 16 q^{70} + 76 q^{72} + 52 q^{74} - 48 q^{78} + 128 q^{81} - 80 q^{83} - 68 q^{84} + 52 q^{86} + 20 q^{88} - 72 q^{90} - 32 q^{91} - 112 q^{92} + 120 q^{94} + 140 q^{96} + 24 q^{98} - 80 q^{99}+O(q^{100}) \) 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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