LMFDB - Embedded newform 600.2.bm.a.61.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(61,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bm (of order $10$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.20
Character	$\chi$	$=$	600.61
Dual form			600.2.bm.a.541.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.871359 + 1.11388i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.481467 - 1.94118i) q^{4} +(-2.21490 - 0.306977i) q^{5} +(-1.17292 + 0.790100i) q^{6} -1.70149 q^{7} +(2.58178 + 1.15517i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.27191 - 2.19965i) q^{10} +(0.338166 + 0.465445i) q^{11} +(0.141956 - 1.99496i) q^{12} +(3.68774 - 5.07574i) q^{13} +(1.48261 - 1.89526i) q^{14} +(-2.01163 - 0.976393i) q^{15} +(-3.53638 + 1.86923i) q^{16} +(0.990565 + 3.04865i) q^{17} +(-1.35967 + 0.388978i) q^{18} +(2.79857 - 0.909312i) q^{19} +(0.470503 + 4.44732i) q^{20} +(-1.61822 - 0.525790i) q^{21} +(-0.813115 - 0.0288930i) q^{22} +(4.14655 - 3.01264i) q^{23} +(2.09845 + 1.89644i) q^{24} +(4.81153 + 1.35984i) q^{25} +(2.44043 + 8.53050i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.819214 + 3.30291i) q^{28} +(1.59423 + 0.517995i) q^{29} +(2.84044 - 1.38993i) q^{30} +(0.715382 + 2.20172i) q^{31} +(0.999349 - 5.56788i) q^{32} +(0.177784 + 0.547164i) q^{33} +(-4.25897 - 1.55309i) q^{34} +(3.76863 + 0.522319i) q^{35} +(0.751483 - 1.85345i) q^{36} +(6.11207 - 8.41254i) q^{37} +(-1.42570 + 3.90962i) q^{38} +(5.07574 - 3.68774i) q^{39} +(-5.36376 - 3.35112i) q^{40} +(6.62758 + 4.81522i) q^{41} +(1.99572 - 1.34435i) q^{42} -3.58773i q^{43} +(0.740698 - 0.880538i) q^{44} +(-1.61145 - 1.55023i) q^{45} +(-0.257401 + 7.24386i) q^{46} +(0.471444 - 1.45095i) q^{47} +(-3.94092 + 0.684945i) q^{48} -4.10492 q^{49} +(-5.70727 + 4.17457i) q^{50} +3.20554i q^{51} +(-11.6285 - 4.71477i) q^{52} +(-0.674573 - 0.219182i) q^{53} +(-1.41332 - 0.0502205i) q^{54} +(-0.606121 - 1.13472i) q^{55} +(-4.39288 - 1.96551i) q^{56} +2.94260 q^{57} +(-1.96613 + 1.32442i) q^{58} +(2.31991 - 3.19308i) q^{59} +(-0.926822 + 4.37504i) q^{60} +(-4.53982 - 6.24853i) q^{61} +(-3.07581 - 1.12164i) q^{62} +(-1.37654 - 1.00011i) q^{63} +(5.33117 + 5.96478i) q^{64} +(-9.72610 + 10.1102i) q^{65} +(-0.764390 - 0.278745i) q^{66} +(5.09198 - 1.65449i) q^{67} +(5.44105 - 3.39069i) q^{68} +(4.87456 - 1.58384i) q^{69} +(-3.86563 + 3.74269i) q^{70} +(-4.57507 + 14.0806i) q^{71} +(1.40971 + 2.45208i) q^{72} +(1.88002 - 1.36592i) q^{73} +(4.04477 + 14.1385i) q^{74} +(4.15582 + 2.78013i) q^{75} +(-3.11256 - 4.99474i) q^{76} +(-0.575387 - 0.791952i) q^{77} +(-0.315082 + 8.86712i) q^{78} +(-2.66676 + 8.20745i) q^{79} +(8.40652 - 3.05457i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-11.1386 + 3.18656i) q^{82} +(-4.23182 + 1.37500i) q^{83} +(-0.241536 + 3.39440i) q^{84} +(-1.25814 - 7.05652i) q^{85} +(3.99631 + 3.12620i) q^{86} +(1.35613 + 0.985286i) q^{87} +(0.335402 + 1.59232i) q^{88} +(8.62683 - 6.26776i) q^{89} +(3.13093 - 0.444159i) q^{90} +(-6.27467 + 8.63634i) q^{91} +(-7.84452 - 6.59872i) q^{92} +2.31502i q^{93} +(1.20540 + 1.78943i) q^{94} +(-6.47769 + 1.15493i) q^{95} +(2.67101 - 4.98655i) q^{96} +(3.98300 - 12.2584i) q^{97} +(3.57686 - 4.57240i) q^{98} +0.575322i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) $ 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.871359	+	1.11388i	−0.616144	+	0.787634i
$2$	−0.871359	+	1.11388i	−0.616144	+	0.787634i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.481467	−	1.94118i	−0.240734	−	0.970591i
$5$	−2.21490	−	0.306977i	−0.990532	−	0.137284i
$5$	−2.21490	−	0.306977i	−0.990532	−	0.137284i
$6$	−1.17292	+	0.790100i	−0.478843	+	0.322557i
$7$	−1.70149			−0.643104			−0.321552	−	0.946892i	$-0.604205\pi$
$7$	−1.70149			−0.643104			−0.321552	+	0.946892i	$0.604205\pi$
$8$	2.58178	+	1.15517i	0.912797	+	0.408414i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	2.27191	−	2.19965i	0.718440	−	0.695589i
$11$	0.338166	+	0.465445i	0.101961	+	0.140337i	0.856949	−	0.515402i	$-0.172357\pi$
$11$	0.338166	+	0.465445i	0.101961	+	0.140337i	−0.754988	+	0.655739i	$0.772357\pi$
$12$	0.141956	−	1.99496i	0.0409790	−	0.575894i
$13$	3.68774	−	5.07574i	1.02280	−	1.40776i	0.112570	−	0.993644i	$-0.464092\pi$
$13$	3.68774	−	5.07574i	1.02280	−	1.40776i	0.910225	−	0.414113i	$-0.135908\pi$
$14$	1.48261	−	1.89526i	0.396245	−	0.506530i
$15$	−2.01163	−	0.976393i	−0.519401	−	0.252104i
$16$	−3.53638	+	1.86923i	−0.884095	+	0.467308i
$17$	0.990565	+	3.04865i	0.240247	+	0.739405i	0.996382	+	0.0849892i	$0.0270856\pi$
$17$	0.990565	+	3.04865i	0.240247	+	0.739405i	−0.756134	+	0.654416i	$0.772914\pi$
$18$	−1.35967	+	0.388978i	−0.320477	+	0.0916830i
$19$	2.79857	−	0.909312i	0.642037	−	0.208610i	0.0301372	−	0.999546i	$-0.490406\pi$
$19$	2.79857	−	0.909312i	0.642037	−	0.208610i	0.611900	+	0.790935i	$0.290406\pi$
$20$	0.470503	+	4.44732i	0.105208	+	0.994450i
$21$	−1.61822	−	0.525790i	−0.353124	−	0.114737i
$22$	−0.813115	−	0.0288930i	−0.173357	−	0.00616000i
$23$	4.14655	−	3.01264i	0.864615	−	0.628180i	−0.0645213	−	0.997916i	$-0.520552\pi$
$23$	4.14655	−	3.01264i	0.864615	−	0.628180i	0.929137	+	0.369736i	$0.120552\pi$
$24$	2.09845	+	1.89644i	0.428345	+	0.387110i
$25$	4.81153	+	1.35984i	0.962306	+	0.271969i
$26$	2.44043	+	8.53050i	0.478608	+	1.67297i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	0.819214	+	3.30291i	0.154817	+	0.624191i
$29$	1.59423	+	0.517995i	0.296040	+	0.0961893i	0.453272	−	0.891372i	$-0.350257\pi$
$29$	1.59423	+	0.517995i	0.296040	+	0.0961893i	−0.157231	+	0.987562i	$0.550257\pi$
$30$	2.84044	−	1.38993i	0.518591	−	0.253766i
$31$	0.715382	+	2.20172i	0.128486	+	0.395440i	0.994520	−	0.104545i	$-0.0333386\pi$
$31$	0.715382	+	2.20172i	0.128486	+	0.395440i	−0.866034	+	0.499986i	$0.833339\pi$
$32$	0.999349	−	5.56788i	0.176662	−	0.984272i
$33$	0.177784	+	0.547164i	0.0309483	+	0.0952490i
$34$	−4.25897	−	1.55309i	−0.730408	−	0.266353i
$35$	3.76863	+	0.522319i	0.637015	+	0.0882880i
$36$	0.751483	−	1.85345i	0.125247	−	0.308908i
$37$	6.11207	−	8.41254i	1.00482	−	1.38301i	0.0824951	−	0.996591i	$-0.473711\pi$
$37$	6.11207	−	8.41254i	1.00482	−	1.38301i	0.922322	−	0.386421i	$-0.126289\pi$
$38$	−1.42570	+	3.90962i	−0.231278	+	0.634224i
$39$	5.07574	−	3.68774i	0.812769	−	0.590511i
$40$	−5.36376	−	3.35112i	−0.848086	−	0.529859i
$41$	6.62758	+	4.81522i	1.03505	+	0.752011i	0.969314	−	0.245826i	$-0.0790591\pi$
$41$	6.62758	+	4.81522i	1.03505	+	0.752011i	0.0657403	+	0.997837i	$0.479059\pi$
$42$	1.99572	−	1.34435i	0.307946	−	0.207438i
$43$		−	3.58773i		−	0.547124i	−0.961854	−	0.273562i	$-0.911798\pi$
$43$		−	3.58773i		−	0.547124i	0.961854	−	0.273562i	$-0.0882019\pi$
$44$	0.740698	−	0.880538i	0.111664	−	0.132746i
$45$	−1.61145	−	1.55023i	−0.240221	−	0.231095i
$46$	−0.257401	+	7.24386i	−0.0379517	+	1.06805i
$47$	0.471444	−	1.45095i	0.0687671	−	0.211643i	−0.910767	−	0.412920i	$-0.864509\pi$
$47$	0.471444	−	1.45095i	0.0687671	−	0.211643i	0.979534	+	0.201276i	$0.0645090\pi$
$48$	−3.94092	+	0.684945i	−0.568823	+	0.0988633i
$49$	−4.10492			−0.586417
$50$	−5.70727	+	4.17457i	−0.807130	+	0.590373i
$51$			3.20554i			0.448865i
$52$	−11.6285	−	4.71477i	−1.61258	−	0.653821i
$53$	−0.674573	−	0.219182i	−0.0926598	−	0.0301070i	0.262320	−	0.964981i	$-0.415512\pi$
$53$	−0.674573	−	0.219182i	−0.0926598	−	0.0301070i	−0.354980	+	0.934874i	$0.615512\pi$
$54$	−1.41332	−	0.0502205i	−0.192329	−	0.00683415i
$55$	−0.606121	−	1.13472i	−0.0817294	−	0.153006i
$56$	−4.39288	−	1.96551i	−0.587023	−	0.262653i
$57$	2.94260			0.389756
$58$	−1.96613	+	1.32442i	−0.258165	+	0.173905i
$59$	2.31991	−	3.19308i	0.302026	−	0.415703i	−0.630848	−	0.775907i	$-0.717293\pi$
$59$	2.31991	−	3.19308i	0.302026	−	0.415703i	0.932874	+	0.360203i	$0.117293\pi$
$60$	−0.926822	+	4.37504i	−0.119652	+	0.564816i
$61$	−4.53982	−	6.24853i	−0.581265	−	0.800042i	0.412568	−	0.910927i	$-0.364632\pi$
$61$	−4.53982	−	6.24853i	−0.581265	−	0.800042i	−0.993833	+	0.110884i	$0.964632\pi$
$62$	−3.07581	−	1.12164i	−0.390628	−	0.142448i
$63$	−1.37654	−	1.00011i	−0.173427	−	0.126002i
$64$	5.33117	+	5.96478i	0.666397	+	0.745598i
$65$	−9.72610	+	10.1102i	−1.20637	+	1.25401i
$66$	−0.764390	−	0.278745i	−0.0940899	−	0.0343112i
$67$	5.09198	−	1.65449i	0.622085	−	0.202128i	0.0190192	−	0.999819i	$-0.493946\pi$
$67$	5.09198	−	1.65449i	0.622085	−	0.202128i	0.603066	+	0.797691i	$0.293946\pi$
$68$	5.44105	−	3.39069i	0.659825	−	0.411182i
$69$	4.87456	−	1.58384i	0.586828	−	0.190672i
$70$	−3.86563	+	3.74269i	−0.462031	+	0.447336i
$71$	−4.57507	+	14.0806i	−0.542961	+	1.67106i	0.182828	+	0.983145i	$0.441475\pi$
$71$	−4.57507	+	14.0806i	−0.542961	+	1.67106i	−0.725789	+	0.687917i	$0.758525\pi$
$72$	1.40971	+	2.45208i	0.166136	+	0.288981i
$73$	1.88002	−	1.36592i	0.220040	−	0.159868i	−0.472305	−	0.881435i	$-0.656578\pi$
$73$	1.88002	−	1.36592i	0.220040	−	0.159868i	0.692345	+	0.721567i	$0.256578\pi$
$74$	4.04477	+	14.1385i	0.470195	+	1.64356i
$75$	4.15582	+	2.78013i	0.479873	+	0.321022i
$76$	−3.11256	−	4.99474i	−0.357035	−	0.572936i
$77$	−0.575387	−	0.791952i	−0.0655714	−	0.0902513i
$78$	−0.315082	+	8.86712i	−0.0356760	+	1.00400i
$79$	−2.66676	+	8.20745i	−0.300034	+	0.923410i	0.681450	+	0.731865i	$0.261350\pi$
$79$	−2.66676	+	8.20745i	−0.300034	+	0.923410i	−0.981484	+	0.191545i	$0.938650\pi$
$80$	8.40652	−	3.05457i	0.939878	−	0.341511i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−11.1386	+	3.18656i	−1.23005	+	0.351897i
$83$	−4.23182	+	1.37500i	−0.464503	+	0.150926i	−0.531913	−	0.846799i	$-0.678527\pi$
$83$	−4.23182	+	1.37500i	−0.464503	+	0.150926i	0.0674097	+	0.997725i	$0.478527\pi$
$84$	−0.241536	+	3.39440i	−0.0263538	+	0.370360i
$85$	−1.25814	−	7.05652i	−0.136464	−	0.765387i
$86$	3.99631	+	3.12620i	0.430933	+	0.337107i
$87$	1.35613	+	0.985286i	0.145392	+	0.105634i
$88$	0.335402	+	1.59232i	0.0357540	+	0.169741i
$89$	8.62683	−	6.26776i	0.914442	−	0.664381i	−0.0276923	−	0.999616i	$-0.508816\pi$
$89$	8.62683	−	6.26776i	0.914442	−	0.664381i	0.942134	+	0.335235i	$0.108816\pi$
$90$	3.13093	−	0.444159i	0.330029	−	0.0468185i
$91$	−6.27467	+	8.63634i	−0.657764	+	0.905334i
$92$	−7.84452	−	6.59872i	−0.817848	−	0.687964i
$93$			2.31502i			0.240057i
$94$	1.20540	+	1.78943i	0.124327	+	0.184566i
$95$	−6.47769	+	1.15493i	−0.664597	+	0.118494i
$96$	2.67101	−	4.98655i	0.272609	−	0.508938i
$97$	3.98300	−	12.2584i	0.404412	−	1.24465i	−0.516973	−	0.856002i	$-0.672941\pi$
$97$	3.98300	−	12.2584i	0.404412	−	1.24465i	0.921385	−	0.388651i	$-0.127059\pi$
$98$	3.57686	−	4.57240i	0.361317	−	0.461882i
$99$			0.575322i			0.0578220i
$100$	0.323107	−	9.99478i	0.0323107	−	0.999478i
$101$			0.668293i			0.0664976i	0.999447	+	0.0332488i	$0.0105854\pi$
$101$			0.668293i			0.0664976i	−0.999447	+	0.0332488i	$0.989415\pi$
$102$	−3.57059	−	2.79317i	−0.353541	−	0.276565i
$103$	−2.18393	+	6.72145i	−0.215189	+	0.662284i	0.783951	+	0.620823i	$0.213201\pi$
$103$	−2.18393	+	6.72145i	−0.215189	+	0.662284i	−0.999140	+	0.0414612i	$0.986799\pi$
$104$	15.3843	−	8.84448i	1.50855	−	0.867273i
$105$	3.42278	+	1.66133i	0.334029	+	0.162129i
$106$	0.831939	−	0.560409i	0.0808050	−	0.0544317i
$107$		−	0.457727i		−	0.0442502i	−0.999755	−	0.0221251i	$-0.992957\pi$
$107$		−	0.457727i		−	0.0442502i	0.999755	−	0.0221251i	$-0.00704320\pi$
$108$	1.28745	−	1.53051i	0.123885	−	0.147274i
$109$	−0.903279	+	1.24326i	−0.0865185	+	0.119082i	−0.850082	−	0.526650i	$-0.823448\pi$
$109$	−0.903279	+	1.24326i	−0.0865185	+	0.119082i	0.763564	+	0.645732i	$0.223448\pi$
$110$	1.79210	+	0.313602i	0.170870	+	0.0299008i
$111$	8.41254	−	6.11207i	0.798483	−	0.580132i
$112$	6.01712	−	3.18049i	0.568565	−	0.300528i
$113$	−12.7927	−	9.29446i	−1.20344	−	0.874349i	−0.208820	−	0.977954i	$-0.566962\pi$
$113$	−12.7927	−	9.29446i	−1.20344	−	0.874349i	−0.994619	+	0.103605i	$0.966962\pi$
$114$	−2.56406	+	3.27770i	−0.240146	+	0.306985i
$115$	−10.1090	+	5.39980i	−0.942668	+	0.503534i
$116$	0.237956	−	3.34408i	0.0220936	−	0.310490i
$117$	5.96689	−	1.93876i	0.551639	−	0.179238i
$118$	1.53524	+	5.36642i	0.141330	+	0.494019i
$119$	−1.68544	−	5.18725i	−0.154504	−	0.475515i
$120$	−4.06569	−	4.84460i	−0.371145	−	0.442250i
$121$	3.29690	−	10.1468i	0.299719	−	0.922439i
$122$	10.9159	+	0.387884i	0.988283	+	0.0351174i
$123$	4.81522	+	6.62758i	0.434174	+	0.597589i
$124$	3.92951	−	2.44874i	0.352880	−	0.219904i
$125$	−10.2396	−	4.48894i	−0.915858	−	0.401503i
$126$	2.31347	−	0.661843i	0.206100	−	0.0589617i
$127$	−9.14351	+	6.64315i	−0.811356	+	0.589484i	−0.914223	−	0.405211i	$-0.867198\pi$
$127$	−9.14351	+	6.64315i	−0.811356	+	0.589484i	0.102868	+	0.994695i	$0.467198\pi$
$128$	−11.2894	+	0.740834i	−0.997854	+	0.0654811i
$129$	1.10867	−	3.41214i	0.0976130	−	0.300422i
$130$	−2.78664	−	19.6433i	−0.244404	−	1.72283i
$131$	−18.8992	+	6.14073i	−1.65123	+	0.536518i	−0.979007	−	0.203827i	$-0.934662\pi$
$131$	−18.8992	+	6.14073i	−1.65123	+	0.536518i	−0.672226	+	0.740346i	$0.734662\pi$
$132$	0.976547	−	0.608553i	0.0849975	−	0.0529678i
$133$	−4.76176	+	1.54719i	−0.412897	+	0.134158i
$134$	−2.59404	+	7.11352i	−0.224091	+	0.614515i
$135$	−1.05353	−	1.97233i	−0.0906738	−	0.169751i
$136$	−0.964279	+	9.01520i	−0.0826862	+	0.773047i
$137$	8.24133	+	5.98768i	0.704105	+	0.511562i	0.881266	−	0.472620i	$-0.156692\pi$
$137$	8.24133	+	5.98768i	0.704105	+	0.511562i	−0.177162	+	0.984182i	$0.556692\pi$
$138$	−2.48328	+	6.80978i	−0.211391	+	0.579687i
$139$	8.50477	+	11.7058i	0.721365	+	0.992874i	0.999477	+	0.0323253i	$0.0102912\pi$
$139$	8.50477	+	11.7058i	0.721365	+	0.992874i	−0.278112	+	0.960549i	$0.589709\pi$
$140$	−0.800558	−	7.56708i	−0.0676595	−	0.639535i
$141$	0.896739	−	1.23426i	0.0755191	−	0.103943i
$142$	−11.6976	−	17.3654i	−0.981643	−	1.45727i
$143$	3.60955			0.301845
$144$	−3.95970	−	0.566390i	−0.329975	−	0.0471992i
$145$	−3.37203	−	1.63670i	−0.280032	−	0.135920i
$146$	−0.116704	+	3.28433i	−0.00965852	+	0.271813i
$147$	−3.90401	−	1.26849i	−0.321997	−	0.104623i
$148$	−19.2730	−	7.81427i	−1.58423	−	0.642329i
$149$		−	22.2446i		−	1.82235i	−0.412021	−	0.911174i	$-0.635177\pi$
$149$		−	22.2446i		−	1.82235i	0.412021	−	0.911174i	$-0.364823\pi$
$150$	−6.71795	+	2.20661i	−0.548519	+	0.180169i
$151$	21.6484			1.76172			0.880861	−	0.473374i	$-0.156964\pi$
$151$	21.6484			1.76172			0.880861	+	0.473374i	$0.156964\pi$
$152$	8.27571	+	0.885181i	0.671249	+	0.0717977i
$153$	−0.990565	+	3.04865i	−0.0800825	+	0.246468i
$154$	1.38351	+	0.0491612i	0.111486	+	0.00396152i
$155$	−0.908621	−	5.09619i	−0.0729822	−	0.409335i
$156$	−9.60238	−	8.07741i	−0.768806	−	0.646710i
$157$			18.4006i			1.46852i	0.678866	+	0.734262i	$0.262472\pi$
$157$			18.4006i			1.46852i	−0.678866	+	0.734262i	$0.737528\pi$
$158$	−6.81843	−	10.1221i	−0.542445	−	0.805271i
$159$	−0.573826	−	0.416909i	−0.0455074	−	0.0330631i
$160$	−3.92266	+	12.0255i	−0.310114	+	0.950699i
$161$	−7.05533	+	5.12600i	−0.556038	+	0.403985i
$162$	−1.32863	−	0.484503i	−0.104387	−	0.0380661i
$163$	0.316401	−	0.435489i	0.0247825	−	0.0341101i	−0.796446	−	0.604710i	$-0.793289\pi$
$163$	0.316401	−	0.435489i	0.0247825	−	0.0341101i	0.821228	+	0.570600i	$0.193289\pi$
$164$	6.15625	−	15.1837i	0.480723	−	1.18565i
$165$	−0.225807	−	1.26649i	−0.0175791	−	0.0985958i
$166$	2.15585	−	5.91187i	0.167326	−	0.458850i
$167$	−6.02110	−	18.5310i	−0.465927	−	1.43397i	−0.857814	−	0.513961i	$-0.828178\pi$
$167$	−6.02110	−	18.5310i	−0.465927	−	1.43397i	0.391887	−	0.920013i	$-0.371822\pi$
$168$	−3.57050	−	3.22679i	−0.275470	−	0.248952i
$169$	−8.14648	−	25.0723i	−0.626652	−	1.92864i
$170$	8.95642	+	4.74734i	0.686926	+	0.364105i
$171$	2.79857	+	0.909312i	0.214012	+	0.0695368i
$172$	−6.96444	+	1.72738i	−0.531034	+	0.131711i
$173$	−10.9922	−	15.1294i	−0.835719	−	1.15027i	−0.986832	−	0.161752i	$-0.948286\pi$
$173$	−10.9922	−	15.1294i	−0.835719	−	1.15027i	0.151113	−	0.988517i	$-0.451714\pi$
$174$	−2.27917	+	0.652031i	−0.172783	+	0.0494304i
$175$	−8.18679	−	2.31376i	−0.618863	−	0.174904i
$176$	−2.06591	−	1.01388i	−0.155724	−	0.0764241i
$177$	3.19308	−	2.31991i	0.240007	−	0.174375i
$178$	−0.535519	+	15.0707i	−0.0401389	+	1.12960i
$179$	18.2381	+	5.92592i	1.36318	+	0.442924i	0.897104	−	0.441820i	$-0.145667\pi$
$179$	18.2381	+	5.92592i	1.36318	+	0.442924i	0.466077	+	0.884744i	$0.345667\pi$
$180$	−2.23342	+	3.87451i	−0.166469	+	0.288789i
$181$	−3.22106	+	1.04659i	−0.239420	+	0.0777922i	−0.426269	−	0.904596i	$-0.640172\pi$
$181$	−3.22106	+	1.04659i	−0.239420	+	0.0777922i	0.186849	+	0.982389i	$0.440172\pi$
$182$	−4.15238	−	14.5146i	−0.307795	−	1.07589i
$183$	−2.38673	−	7.34559i	−0.176432	−	0.543002i
$184$	14.1856	−	2.98802i	1.04578	−	0.220280i
$185$	−16.1200	+	16.7566i	−1.18517	+	1.23197i
$186$	−2.57867	−	2.01722i	−0.189077	−	0.147910i
$187$	−1.08400	+	1.49200i	−0.0792701	+	0.109106i
$188$	−3.04355	−	0.216571i	−0.221974	−	0.0157950i
$189$	−1.00011	−	1.37654i	−0.0727475	−	0.100128i
$190$	4.35793	−	8.22175i	0.316158	−	0.596468i
$191$	3.02319	+	2.19648i	0.218751	+	0.158932i	0.691764	−	0.722124i	$-0.256834\pi$
$191$	3.02319	+	2.19648i	0.218751	+	0.158932i	−0.473014	+	0.881055i	$0.656834\pi$
$192$	3.22703	+	7.32027i	0.232891	+	0.528295i
$193$	−0.575154			−0.0414005			−0.0207002	−	0.999786i	$-0.506590\pi$
$193$	−0.575154			−0.0414005			−0.0207002	+	0.999786i	$0.506590\pi$
$194$	10.1838	+	15.1181i	0.731154	+	1.08541i
$195$	−12.3743	+	6.60983i	−0.886141	+	0.473340i
$196$	1.97639	+	7.96840i	0.141170	+	0.569171i
$197$	1.48969	+	0.484030i	0.106136	+	0.0344857i	0.361604	−	0.932332i	$-0.382229\pi$
$197$	1.48969	+	0.484030i	0.106136	+	0.0344857i	−0.255467	+	0.966818i	$0.582229\pi$
$198$	−0.640841	−	0.501312i	−0.0455426	−	0.0356267i
$199$	−23.4316			−1.66102			−0.830510	−	0.557003i	$-0.811951\pi$
$199$	−23.4316			−1.66102			−0.830510	+	0.557003i	$0.811951\pi$
$200$	10.8515	+	9.06894i	0.767314	+	0.641271i
$201$	5.35403			0.377644
$202$	−0.744400	−	0.582323i	−0.0523758	−	0.0409721i
$203$	−2.71257	−	0.881366i	−0.190385	−	0.0618598i
$204$	6.22253	−	1.54336i	0.435664	−	0.108057i
$205$	−13.2012	−	12.6997i	−0.922015	−	0.886987i
$206$	−5.58391	−	8.28943i	−0.389050	−	0.577552i
$207$	5.12542			0.356241
$208$	−3.55351	+	24.8430i	−0.246391	+	1.72255i
$209$	1.36962	+	0.995085i	0.0947384	+	0.0688315i
$210$	−4.83299	+	2.36496i	−0.333508	+	0.163198i
$211$	−1.56804	−	2.15823i	−0.107949	−	0.148578i	0.751625	−	0.659591i	$-0.229271\pi$
$211$	−1.56804	−	2.15823i	−0.107949	−	0.148578i	−0.859573	+	0.511013i	$0.829271\pi$
$212$	−0.100687	+	1.41500i	−0.00691524	+	0.0971825i
$213$	−8.70230	+	11.9777i	−0.596272	+	0.820698i
$214$	0.509854	+	0.398845i	0.0348529	+	0.0272645i
$215$	−1.10135	+	7.94646i	−0.0751114	+	0.541944i
$216$	0.582981	+	2.76769i	0.0396668	+	0.188318i
$217$	−1.21722	−	3.74621i	−0.0826301	−	0.254309i
$218$	−0.597762	−	2.08947i	−0.0404855	−	0.141517i
$219$	2.21010	−	0.718105i	0.149345	−	0.0485250i
$220$	−1.91087	+	1.72292i	−0.128831	+	0.116159i
$221$	19.1271	+	6.21477i	1.28663	+	0.418050i
$222$	−0.522217	+	14.6964i	−0.0350489	+	0.986356i
$223$	17.9809	−	13.0639i	1.20409	−	0.874822i	0.209408	−	0.977828i	$-0.432846\pi$
$223$	17.9809	−	13.0639i	1.20409	−	0.874822i	0.994681	+	0.103007i	$0.0328463\pi$
$224$	−1.70039	+	9.47371i	−0.113612	+	0.632989i
$225$	3.09331	+	3.92828i	0.206221	+	0.261886i
$226$	21.5000	−	6.15078i	1.43016	−	0.409144i
$227$	7.58017	+	10.4332i	0.503113	+	0.692476i	0.982739	−	0.184997i	$-0.0592276\pi$
$227$	7.58017	+	10.4332i	0.503113	+	0.692476i	−0.479626	+	0.877473i	$0.659228\pi$
$228$	−1.41676	−	5.71211i	−0.0938275	−	0.378294i
$229$	16.8973	+	5.49025i	1.11660	+	0.362806i	0.808470	−	0.588537i	$-0.200296\pi$
$229$	16.8973	+	5.49025i	1.11660	+	0.362806i	0.308132	+	0.951344i	$0.400296\pi$
$230$	2.79381	−	15.9654i	0.184219	−	1.05273i
$231$	−0.302499	−	0.930996i	−0.0199030	−	0.0612550i
$232$	3.51757	+	3.17895i	0.230940	+	0.208708i
$233$	−3.21413	−	9.89207i	−0.210565	−	0.648051i	−0.999439	−	0.0334964i	$-0.989336\pi$
$233$	−3.21413	−	9.89207i	−0.210565	−	0.648051i	0.788874	−	0.614555i	$-0.210664\pi$
$234$	−3.03975	+	8.33577i	−0.198715	+	0.544926i
$235$	−1.48961	+	3.06899i	−0.0971713	+	0.200199i
$236$	−7.31531	−	2.96600i	−0.476186	−	0.193070i
$237$	−5.07248	+	6.98168i	−0.329493	+	0.453509i
$238$	7.24661	+	2.64258i	0.469728	+	0.171293i
$239$	−17.8588	+	12.9751i	−1.15519	+	0.839293i	−0.989162	−	0.146829i	$-0.953093\pi$
$239$	−17.8588	+	12.9751i	−1.15519	+	0.839293i	−0.166025	+	0.986122i	$0.553093\pi$
$240$	8.93899	−	0.307311i	0.577009	−	0.0198369i
$241$	12.5397	+	9.11060i	0.807751	+	0.586865i	0.913178	−	0.407562i	$-0.133621\pi$
$241$	12.5397	+	9.11060i	0.807751	+	0.586865i	−0.105427	+	0.994427i	$0.533621\pi$
$242$	8.42958	+	12.5139i	0.541874	+	0.804423i
$243$			1.00000i			0.0641500i
$244$	−9.94376	+	11.8211i	−0.636584	+	0.756768i
$245$	9.09197	+	1.26011i	0.580865	+	0.0805057i
$246$	−11.5781	−	0.411414i	−0.738195	−	0.0262308i
$247$	5.70499	−	17.5581i	0.363000	−	1.11720i
$248$	−0.696398	+	6.51074i	−0.0442213	+	0.413432i
$249$	−4.44960			−0.281982
$250$	13.9225	−	7.49424i	0.880537	−	0.473977i
$251$			16.0233i			1.01138i	0.862714	+	0.505692i	$0.168763\pi$
$251$			16.0233i			1.01138i	−0.862714	+	0.505692i	$0.831237\pi$
$252$	−1.27864	+	3.15363i	−0.0805470	+	0.198660i
$253$	2.80444	+	0.911219i	0.176314	+	0.0572878i
$254$	0.567593	−	15.9734i	0.0356139	−	1.00226i
$255$	0.984025	−	7.09993i	0.0616220	−	0.444615i
$256$	9.01194	−	13.2206i	0.563246	−	0.826289i
$257$	3.61812			0.225692			0.112846	−	0.993612i	$-0.464003\pi$
$257$	3.61812			0.225692			0.112846	+	0.993612i	$0.464003\pi$
$258$	2.83467	+	4.20812i	0.176479	+	0.261986i
$259$	−10.3996	+	14.3139i	−0.646202	+	0.889421i
$260$	24.3085	+	14.0124i	1.50755	+	0.869012i
$261$	0.985286	+	1.35613i	0.0609877	+	0.0839423i
$262$	9.62796	−	26.4023i	0.594817	−	1.63114i
$263$	5.65938	+	4.11178i	0.348972	+	0.253543i	0.748438	−	0.663205i	$-0.230804\pi$
$263$	5.65938	+	4.11178i	0.348972	+	0.253543i	−0.399465	+	0.916748i	$0.630804\pi$
$264$	−0.173066	+	1.61803i	−0.0106515	+	0.0995827i
$265$	1.42683	+	0.692544i	0.0876492	+	0.0425426i
$266$	2.42581	−	6.65219i	0.148736	−	0.407872i
$267$	10.1414	−	3.29516i	0.620646	−	0.201660i
$268$	−5.66328	−	9.08789i	−0.345940	−	0.555131i
$269$	−13.8235	+	4.49154i	−0.842836	+	0.273854i	−0.698442	−	0.715667i	$-0.746123\pi$
$269$	−13.8235	+	4.49154i	−0.842836	+	0.273854i	−0.144393	+	0.989520i	$0.546123\pi$
$270$	3.11494	+	0.545090i	0.189569	+	0.0331731i
$271$	−9.75275	+	30.0159i	−0.592437	+	1.82333i	−0.0253472	+	0.999679i	$0.508069\pi$
$271$	−9.75275	+	30.0159i	−0.592437	+	1.82333i	−0.567090	+	0.823656i	$0.691931\pi$
$272$	−9.20164	−	8.92957i	−0.557932	−	0.541435i
$273$	−8.63634	+	6.27467i	−0.522695	+	0.379760i
$274$	−13.8507	+	3.96246i	−0.836753	+	0.239381i
$275$	0.994163	+	2.69936i	0.0599503	+	0.162777i
$276$	−5.42147	−	8.69985i	−0.326334	−	0.523669i
$277$	16.4940	+	22.7021i	0.991031	+	1.36404i	0.930670	+	0.365861i	$0.119225\pi$
$277$	16.4940	+	22.7021i	0.991031	+	1.36404i	0.0603616	+	0.998177i	$0.480775\pi$
$278$	−20.4496	−	0.726650i	−1.22649	−	0.0435816i
$279$	−0.715382	+	2.20172i	−0.0428288	+	0.131813i
$280$	9.12641	+	5.70192i	0.545407	+	0.340755i
$281$	−3.24975	−	10.0017i	−0.193864	−	0.596651i	−0.999988	−	0.00490475i	$-0.998439\pi$
$281$	−3.24975	−	10.0017i	−0.193864	−	0.596651i	0.806124	−	0.591746i	$-0.201561\pi$
$282$	0.593434	+	2.07434i	0.0353385	+	0.123525i
$283$	7.94284	−	2.58078i	0.472153	−	0.153412i	−0.0632692	−	0.997996i	$-0.520153\pi$
$283$	7.94284	−	2.58078i	0.472153	−	0.153412i	0.535422	+	0.844585i	$0.320153\pi$
$284$	29.5358	+	2.10169i	1.75263	+	0.124712i
$285$	−6.51754	−	0.903308i	−0.386066	−	0.0535073i
$286$	−3.14521	+	4.02061i	−0.185980	+	0.237744i
$287$	−11.2768	−	8.19307i	−0.665648	−	0.483621i
$288$	4.08121	−	3.91711i	0.240488	−	0.230818i
$289$	5.44026	−	3.95258i	0.320015	−	0.232505i
$290$	4.76134	−	2.32990i	0.279595	−	0.136816i
$291$	7.57611	−	10.4276i	0.444119	−	0.611278i
$292$	−3.55666	−	2.99182i	−0.208138	−	0.175083i
$293$			13.2927i			0.776568i	0.921540	+	0.388284i	$0.126932\pi$
$293$			13.2927i			0.776568i	−0.921540	+	0.388284i	$0.873068\pi$
$294$	4.81474	−	3.24330i	0.280801	−	0.189153i
$295$	−6.11856	+	6.36018i	−0.356236	+	0.370304i
$296$	25.4979	−	14.6589i	1.48204	−	0.852029i
$297$	−0.177784	+	0.547164i	−0.0103161	+	0.0317497i
$298$	24.7779	+	19.3830i	1.43534	+	1.12283i
$299$		−	32.1567i		−	1.85967i
$300$	3.39585	−	9.40575i	0.196059	−	0.543041i
$301$			6.10450i			0.351858i
$302$	−18.8635	+	24.1138i	−1.08547	+	1.38759i
$303$	−0.206514	+	0.635584i	−0.0118639	+	0.0365134i
$304$	−8.19710	+	8.44686i	−0.470136	+	0.484460i
$305$	8.13709	+	15.2335i	0.465928	+	0.872266i
$306$	−2.53270	−	3.75984i	−0.144785	−	0.214936i
$307$		−	0.326456i		−	0.0186318i	−0.999957	−	0.00931592i	$-0.997035\pi$
$307$		−	0.326456i		−	0.0186318i	0.999957	−	0.00931592i	$-0.00296539\pi$
$308$	−1.26029	+	1.49823i	−0.0718119	+	0.0853696i
$309$	−4.15408	+	5.71760i	−0.236318	+	0.325263i
$310$	6.46829	+	3.42851i	0.367374	+	0.194726i
$311$	9.23242	−	6.70774i	0.523522	−	0.380361i	−0.294407	−	0.955680i	$-0.595122\pi$
$311$	9.23242	−	6.70774i	0.523522	−	0.380361i	0.817929	+	0.575319i	$0.195122\pi$
$312$	17.3644	−	3.65760i	0.983066	−	0.207071i
$313$	2.28219	+	1.65811i	0.128997	+	0.0937219i	0.650413	−	0.759581i	$-0.274596\pi$
$313$	2.28219	+	1.65811i	0.128997	+	0.0937219i	−0.521416	+	0.853303i	$0.674596\pi$
$314$	−20.4961	−	16.0335i	−1.15666	−	0.904822i
$315$	2.74188	+	2.63771i	0.154487	+	0.148618i
$316$	17.2161	+	1.22505i	0.968482	+	0.0689145i
$317$	−16.9744	+	5.51532i	−0.953379	+	0.309771i	−0.744088	−	0.668082i	$-0.767116\pi$
$317$	−16.9744	+	5.51532i	−0.953379	+	0.309771i	−0.209291	+	0.977853i	$0.567116\pi$
$318$	0.964397	−	0.275897i	0.0540807	−	0.0154716i
$319$	0.298014	+	0.917193i	0.0166856	+	0.0513530i
$320$	−9.97695	−	14.8479i	−0.557728	−	0.830024i
$321$	0.141445	−	0.435324i	0.00789472	−	0.0242974i
$322$	0.437967	−	12.3254i	0.0244069	−	0.686867i
$323$	5.54434	+	7.63113i	0.308495	+	0.424608i
$324$	1.69739	−	1.05776i	0.0942996	−	0.0587645i
$325$	24.6459	−	19.4073i	1.36711	−	1.07652i
$326$	0.209384	+	0.731901i	0.0115967	+	0.0405362i
$327$	−1.24326	+	0.903279i	−0.0687523	+	0.0499515i
$328$	11.5486	+	20.0878i	0.637663	+	1.10916i
$329$	−0.802158	+	2.46879i	−0.0442244	+	0.136109i
$330$	1.60748	+	0.852041i	0.0884886	+	0.0469033i
$331$	−13.7566	+	4.46980i	−0.756134	+	0.245683i	−0.661618	−	0.749841i	$-0.730130\pi$
$331$	−13.7566	+	4.46980i	−0.756134	+	0.245683i	−0.0945152	+	0.995523i	$0.530130\pi$
$332$	4.70662	+	7.55272i	0.258309	+	0.414509i
$333$	9.88953	−	3.21330i	0.541943	−	0.176088i
$334$	25.8879	+	9.44039i	1.41652	+	0.516555i
$335$	−11.7861	+	2.10139i	−0.643944	+	0.114811i
$336$	6.70545	−	1.16543i	0.365812	−	0.0635794i
$337$	18.0349	+	13.1031i	0.982424	+	0.713773i	0.958249	−	0.285935i	$-0.0923042\pi$
$337$	18.0349	+	13.1031i	0.982424	+	0.713773i	0.0241747	+	0.999708i	$0.492304\pi$
$338$	35.0261	+	12.7727i	1.90517	+	0.694745i
$339$	−9.29446	−	12.7927i	−0.504806	−	0.694806i
$340$	−13.0922	+	5.83976i	−0.710026	+	0.316705i
$341$	−0.782862	+	1.07752i	−0.0423944	+	0.0583508i
$342$	−3.45143	+	2.32495i	−0.186632	+	0.125719i
$343$	18.8949			1.02023
$344$	4.14444	−	9.26274i	0.223453	−	0.499413i
$345$	−11.2829	+	2.01167i	−0.607448	+	0.108305i
$346$	26.4305	+	0.939174i	1.42091	+	0.0504903i
$347$	−23.9217	−	7.77264i	−1.28419	−	0.417257i	−0.414134	−	0.910216i	$-0.635915\pi$
$347$	−23.9217	−	7.77264i	−1.28419	−	0.417257i	−0.870053	+	0.492959i	$0.835915\pi$
$348$	1.25969	−	3.10688i	0.0675263	−	0.166546i
$349$			28.9692i			1.55069i	0.631540	+	0.775343i	$0.282423\pi$
$349$			28.9692i			1.55069i	−0.631540	+	0.775343i	$0.717577\pi$
$350$	9.71089	−	7.10300i	0.519069	−	0.379671i
$351$	6.27396			0.334879
$352$	2.92949	−	1.41772i	0.156142	−	0.0755650i
$353$	−9.62344	+	29.6179i	−0.512204	+	1.57640i	0.276108	+	0.961127i	$0.410955\pi$
$353$	−9.62344	+	29.6179i	−0.512204	+	1.57640i	−0.788312	+	0.615275i	$0.789045\pi$
$354$	−0.198214	+	5.57819i	−0.0105349	+	0.296477i
$355$	14.4557	−	29.7827i	0.767230	−	1.58070i
$356$	−16.3204	−	13.7285i	−0.864979	−	0.727610i
$357$		−	5.45420i		−	0.288667i
$358$	−22.4927	+	15.1515i	−1.18878	+	0.800782i
$359$	5.03269	+	3.65646i	0.265615	+	0.192981i	0.712619	−	0.701551i	$-0.247509\pi$
$359$	5.03269	+	3.65646i	0.265615	+	0.192981i	−0.447004	+	0.894532i	$0.647509\pi$
$360$	−2.36964	−	5.86386i	−0.124891	−	0.309052i
$361$	−8.36615	+	6.07837i	−0.440324	+	0.319914i
$362$	1.64093	−	4.49984i	0.0862452	−	0.236506i
$363$	6.27108	−	8.63141i	0.329147	−	0.453031i
$364$	19.7858	+	8.02216i	1.03706	+	0.420475i
$365$	−4.58336	+	2.44824i	−0.239904	+	0.128147i
$366$	10.2618	+	3.74211i	0.536394	+	0.195603i
$367$	7.26322	+	22.3539i	0.379137	+	1.16686i	0.940645	+	0.339392i	$0.110221\pi$
$367$	7.26322	+	22.3539i	0.379137	+	1.16686i	−0.561508	+	0.827471i	$0.689779\pi$
$368$	−9.03243	+	18.4047i	−0.470848	+	0.959412i
$369$	2.53151	+	7.79119i	0.131785	+	0.405593i
$370$	−4.61858	−	32.5569i	−0.240108	−	1.69255i
$371$	1.14778	+	0.372937i	0.0595899	+	0.0193619i
$372$	4.49389	−	1.11461i	0.232997	−	0.0577898i
$373$	1.25551	+	1.72806i	0.0650079	+	0.0894757i	0.840283	−	0.542148i	$-0.182389\pi$
$373$	1.25551	+	1.72806i	0.0650079	+	0.0894757i	−0.775275	+	0.631624i	$0.782389\pi$
$374$	−0.717359	−	2.50752i	−0.0370938	−	0.129661i
$375$	−8.35128	−	7.43344i	−0.431258	−	0.383861i
$376$	2.89326	−	3.20145i	0.149208	−	0.165102i
$377$	8.50830	−	6.18164i	0.438200	−	0.318371i
$378$	2.40476	+	0.0854499i	0.123687	+	0.00439507i
$379$	−30.7971	−	10.0066i	−1.58194	−	0.514003i	−0.619384	−	0.785088i	$-0.712618\pi$
$379$	−30.7971	−	10.0066i	−1.58194	−	0.514003i	−0.962555	+	0.271085i	$0.912618\pi$
$380$	5.36074	+	12.0183i	0.275000	+	0.616526i
$381$	−10.7488	+	3.49251i	−0.550680	+	0.178927i
$382$	−5.08090	+	1.45356i	−0.259962	+	0.0743706i
$383$	−11.1937	−	34.4505i	−0.571969	−	1.76034i	−0.646275	−	0.763105i	$-0.723674\pi$
$383$	−11.1937	−	34.4505i	−0.571969	−	1.76034i	0.0743058	−	0.997235i	$-0.476326\pi$
$384$	−10.9658	−	2.78405i	−0.559597	−	0.142073i
$385$	1.03131	+	1.93072i	0.0525605	+	0.0983987i
$386$	0.501165	−	0.640654i	0.0255086	−	0.0326084i
$387$	2.10882	−	2.90254i	0.107197	−	0.147544i
$388$	−25.7135	−	1.82970i	−1.30540	−	0.0928890i
$389$	−15.2713	−	21.0192i	−0.774288	−	1.06572i	−0.995889	−	0.0905786i	$-0.971128\pi$
$389$	−15.2713	−	21.0192i	−0.774288	−	1.06572i	0.221601	−	0.975137i	$-0.428872\pi$
$390$	3.41987	−	19.5430i	0.173172	−	0.989600i
$391$	13.2919	+	9.65714i	0.672201	+	0.488383i
$392$	−10.5980	−	4.74187i	−0.535280	−	0.239501i
$393$	−19.8718			−1.00240
$394$	−1.83721	+	1.23758i	−0.0925573	+	0.0623483i
$395$	8.42610	−	17.3600i	0.423963	−	0.873477i
$396$	1.11680	−	0.276999i	0.0561216	−	0.0139197i
$397$	−0.0929904	−	0.0302144i	−0.00466705	−	0.00151642i	0.306683	−	0.951812i	$-0.400781\pi$
$397$	−0.0929904	−	0.0302144i	−0.00466705	−	0.00151642i	−0.311350	+	0.950295i	$0.600781\pi$
$398$	20.4173	−	26.1000i	1.02343	−	1.30828i
$399$	−5.00681			−0.250654
$400$	−19.5573	+	4.18495i	−0.977863	+	0.209248i
$401$	−32.0997			−1.60298			−0.801492	−	0.598005i	$-0.795960\pi$
$401$	−32.0997			−1.60298			−0.801492	+	0.598005i	$0.795960\pi$
$402$	−4.66528	+	5.96376i	−0.232683	+	0.297445i
$403$	13.8135	+	4.48828i	0.688099	+	0.223577i
$404$	1.29728	−	0.321761i	0.0645420	−	0.0160082i
$405$	−0.392489	−	2.20135i	−0.0195029	−	0.109386i
$406$	3.34536	−	2.25349i	0.166027	−	0.111839i
$407$	5.98247			0.296540
$408$	−3.70293	+	8.27599i	−0.183323	+	0.409723i
$409$	−15.5937	−	11.3295i	−0.771058	−	0.560207i	0.131224	−	0.991353i	$-0.458109\pi$
$409$	−15.5937	−	11.3295i	−0.771058	−	0.560207i	−0.902282	+	0.431146i	$0.858109\pi$
$410$	25.6490	−	3.63862i	1.26671	−	0.179698i
$411$	5.98768	+	8.24133i	0.295350	+	0.406515i
$412$	14.0990	+	1.00325i	0.694610	+	0.0494265i
$413$	−3.94731	+	5.43300i	−0.194234	+	0.267341i
$414$	−4.46608	+	5.70911i	−0.219496	+	0.280588i
$415$	9.79514	−	1.74642i	0.480825	−	0.0857283i
$416$	−24.5758	−	25.6053i	−1.20493	−	1.25541i
$417$	4.47122	+	13.7610i	0.218957	+	0.673879i
$418$	−2.30184	+	0.658516i	−0.112586	+	0.0322091i
$419$	−6.03770	+	1.96177i	−0.294961	+	0.0958386i	−0.452759	−	0.891633i	$-0.649560\pi$
$419$	−6.03770	+	1.96177i	−0.294961	+	0.0958386i	0.157799	+	0.987471i	$0.449560\pi$
$420$	1.57698	−	7.44411i	0.0769488	−	0.363235i
$421$	−5.06038	−	1.64422i	−0.246628	−	0.0801343i	0.183094	−	0.983095i	$-0.441389\pi$
$421$	−5.06038	−	1.64422i	−0.246628	−	0.0801343i	−0.429722	+	0.902961i	$0.641389\pi$
$422$	3.77034	+	0.133974i	0.183537	+	0.00652175i
$423$	1.23426	−	0.896739i	0.0600116	−	0.0436009i
$424$	−1.48841	−	1.34513i	−0.0722835	−	0.0653251i
$425$	0.620456	+	16.0157i	0.0300965	+	0.776874i
$426$	−5.75891	−	20.1302i	−0.279020	−	0.975312i
$427$	7.72448	+	10.6318i	0.373814	+	0.514511i
$428$	−0.888532	+	0.220381i	−0.0429488	+	0.0106525i
$429$	3.43288	+	1.11541i	0.165741	+	0.0538526i
$430$	−7.89175	−	8.15099i	−0.380574	−	0.393076i
$431$	2.34333	+	7.21202i	0.112874	+	0.347391i	0.991498	−	0.130124i	$-0.0415376\pi$
$431$	2.34333	+	7.21202i	0.112874	+	0.347391i	−0.878624	+	0.477515i	$0.841538\pi$
$432$	−3.59087	−	1.76228i	−0.172766	−	0.0847879i
$433$	−7.50892	−	23.1101i	−0.360855	−	1.11060i	−0.952536	−	0.304426i	$-0.901535\pi$
$433$	−7.50892	−	23.1101i	−0.360855	−	1.11060i	0.591680	−	0.806173i	$-0.298465\pi$
$434$	5.23347	+	1.90846i	0.251215	+	0.0916089i
$435$	−2.70123	−	2.59861i	−0.129514	−	0.124594i
$436$	2.84829	+	1.15484i	0.136408	+	0.0553069i
$437$	8.86499	−	12.2016i	0.424070	−	0.583683i
$438$	−1.12591	+	3.08752i	−0.0537978	+	0.147527i
$439$	−22.8771	+	16.6212i	−1.09187	+	0.793286i	−0.979713	−	0.200405i	$-0.935774\pi$
$439$	−22.8771	+	16.6212i	−1.09187	+	0.793286i	−0.112152	+	0.993691i	$0.535774\pi$
$440$	−0.254077	−	3.62977i	−0.0121126	−	0.173043i
$441$	−3.32095	−	2.41281i	−0.158140	−	0.114896i
$442$	−23.5891	+	15.8900i	−1.12202	+	0.755812i
$443$			29.3826i			1.39601i	0.716092	+	0.698006i	$0.245929\pi$
$443$			29.3826i			1.39601i	−0.716092	+	0.698006i	$0.754071\pi$
$444$	−15.9150	−	13.3875i	−0.755292	−	0.635343i
$445$	−21.0316	+	11.2342i	−0.996993	+	0.532552i
$446$	−1.11618	+	31.4119i	−0.0528527	+	1.48740i
$447$	6.87396	−	21.1559i	0.325127	−	1.00064i
$448$	−9.07096	−	10.1490i	−0.428562	−	0.479497i
$449$	24.6437			1.16301			0.581505	−	0.813543i	$-0.302464\pi$
$449$	24.6437			1.16301			0.581505	+	0.813543i	$0.302464\pi$
$450$	−7.07103	+	0.0226447i	−0.333332	+	0.00106748i
$451$			4.71312i			0.221932i
$452$	−11.8830	+	29.3080i	−0.558928	+	1.37853i
$453$	20.5889	+	6.68973i	0.967349	+	0.314311i
$454$	−18.2264	−	0.647652i	−0.855408	−	0.0303958i
$455$	16.5489	−	17.2024i	0.775824	−	0.806462i
$456$	7.59713	+	3.39919i	0.355768	+	0.159182i
$457$	38.7436			1.81235			0.906175	−	0.422903i	$-0.138989\pi$
$457$	38.7436			1.81235			0.906175	+	0.422903i	$0.138989\pi$
$458$	−20.8391	+	14.0376i	−0.973746	+	0.655933i
$459$	−1.88417	+	2.59333i	−0.0879454	+	0.121046i
$460$	15.3491	+	17.0236i	0.715658	+	0.793728i
$461$	10.9931	+	15.1308i	0.512002	+	0.704710i	0.984255	−	0.176753i	$-0.0565593\pi$
$461$	10.9931	+	15.1308i	0.512002	+	0.704710i	−0.472254	+	0.881463i	$0.656559\pi$
$462$	1.30060	+	0.474283i	0.0605096	+	0.0220656i
$463$	16.1923	+	11.7644i	0.752520	+	0.546738i	0.896607	−	0.442827i	$-0.146024\pi$
$463$	16.1923	+	11.7644i	0.752520	+	0.546738i	−0.144087	+	0.989565i	$0.546024\pi$
$464$	−6.60604	+	1.14815i	−0.306678	+	0.0533016i
$465$	0.710658	−	5.12754i	0.0329560	−	0.237784i
$466$	13.8193	+	5.03938i	0.640165	+	0.233445i
$467$	−20.0870	+	6.52668i	−0.929518	+	0.302019i	−0.734365	−	0.678754i	$-0.762520\pi$
$467$	−20.0870	+	6.52668i	−0.929518	+	0.302019i	−0.195152	+	0.980773i	$0.562520\pi$
$468$	−6.63635	−	10.6494i	−0.306765	−	0.492267i
$469$	−8.66398	+	2.81510i	−0.400065	+	0.129989i
$470$	−2.12051	−	4.33344i	−0.0978119	−	0.199887i
$471$	−5.68608	+	17.5000i	−0.262001	+	0.806356i
$472$	9.67803	−	5.56394i	0.445468	−	0.256101i
$473$	1.66989	−	1.21325i	0.0767818	−	0.0557852i
$474$	−3.35681	−	11.7337i	−0.154183	−	0.538946i
$475$	14.7019	−	0.569562i	0.674572	−	0.0261333i
$476$	−9.25792	+	5.76924i	−0.424336	+	0.264433i
$477$	−0.416909	−	0.573826i	−0.0190890	−	0.0262737i
$478$	1.10860	−	31.1986i	0.0507062	−	1.42699i
$479$	−6.70942	+	20.6495i	−0.306561	+	0.943498i	0.672529	+	0.740071i	$0.265208\pi$
$479$	−6.70942	+	20.6495i	−0.306561	+	0.943498i	−0.979090	+	0.203427i	$0.934792\pi$
$480$	−7.44676	+	10.2248i	−0.339897	+	0.466694i
$481$	−20.1601	−	62.0465i	−0.919223	−	2.82908i
$482$	−21.0747	+	6.02911i	−0.959925	+	0.274618i
$483$	−8.29404	+	2.69490i	−0.377392	+	0.122622i
$484$	−21.2842	−	1.51452i	−0.967463	−	0.0688420i
$485$	−12.5850	+	25.9284i	−0.571454	+	1.17735i
$486$	−1.11388	−	0.871359i	−0.0505267	−	0.0395256i
$487$	−2.39264	−	1.73835i	−0.108421	−	0.0787722i	0.532254	−	0.846585i	$-0.321345\pi$
$487$	−2.39264	−	1.73835i	−0.108421	−	0.0787722i	−0.640675	+	0.767813i	$0.721345\pi$
$488$	−4.50272	−	21.3766i	−0.203829	−	0.967673i
$489$	0.435489	−	0.316401i	0.0196935	−	0.0143082i
$490$	−9.32599	+	9.02937i	−0.421305	+	0.407906i
$491$	6.52712	−	8.98381i	0.294565	−	0.405434i	−0.635925	−	0.771751i	$-0.719381\pi$
$491$	6.52712	−	8.98381i	0.294565	−	0.405434i	0.930490	+	0.366317i	$0.119381\pi$
$492$	10.5470	−	12.5382i	0.475494	−	0.565265i
$493$			5.37334i			0.242003i
$494$	14.5866	+	21.6541i	0.656283	+	0.974265i
$495$	0.176610	−	1.27428i	0.00793805	−	0.0572746i
$496$	−6.64539	−	6.44890i	−0.298387	−	0.289564i
$497$	7.78445	−	23.9581i	0.349181	−	1.07467i
$498$	3.87720	−	4.95633i	0.173742	−	0.222099i
$499$		−	41.0256i		−	1.83656i	−0.395932	−	0.918280i	$-0.629578\pi$
$499$		−	41.0256i		−	1.83656i	0.395932	−	0.918280i	$-0.370422\pi$
$500$	−3.78381	+	22.0382i	−0.169217	+	0.985579i
$501$		−	19.4847i		−	0.870511i
$502$	−17.8481	−	13.9621i	−0.796600	−	0.623158i
$503$	9.28140	−	28.5652i	0.413837	−	1.27366i	−0.499449	−	0.866343i	$-0.666464\pi$
$503$	9.28140	−	28.5652i	0.413837	−	1.27366i	0.913287	−	0.407317i	$-0.133536\pi$
$504$	−2.39862	−	4.17220i	−0.106843	−	0.185845i
$505$	0.205150	−	1.48020i	0.00912907	−	0.0658680i
$506$	−3.45867	+	2.32982i	−0.153756	+	0.103573i
$507$		−	26.3626i		−	1.17080i
$508$	17.2979	+	14.5508i	0.767469	+	0.645586i
$509$	−5.73544	+	7.89415i	−0.254219	+	0.349902i	−0.916983	−	0.398926i	$-0.869383\pi$
$509$	−5.73544	+	7.89415i	−0.254219	+	0.349902i	0.662764	+	0.748828i	$0.269383\pi$
$510$	7.05105	+	7.28268i	0.312226	+	0.322482i
$511$	−3.19885	+	2.32410i	−0.141509	+	0.102812i
$512$	6.87359	+	21.5581i	0.303772	+	0.952745i
$513$	2.38061	+	1.72961i	0.105106	+	0.0763643i
$514$	−3.15268	+	4.03016i	−0.139059	+	0.177763i
$515$	6.90051	−	14.2169i	0.304073	−	0.626471i
$516$	−7.15737	−	0.509299i	−0.315086	−	0.0224206i
$517$	0.834766	−	0.271232i	0.0367130	−	0.0119288i
$518$	−6.88216	−	24.0565i	−0.302385	−	1.05698i
$519$	−5.77892	−	17.7857i	−0.253667	−	0.780705i
$520$	−36.7896	+	14.8670i	−1.61333	+	0.651961i
$521$	−6.06709	+	18.6726i	−0.265804	+	0.818060i	0.725703	+	0.688008i	$0.241515\pi$
$521$	−6.06709	+	18.6726i	−0.265804	+	0.818060i	−0.991507	+	0.130052i	$0.958485\pi$
$522$	−2.36911	−	0.0841831i	−0.103693	−	0.00368459i
$523$	−16.8652	−	23.2130i	−0.737466	−	1.01503i	−0.998760	−	0.0497753i	$-0.984149\pi$
$523$	−16.8652	−	23.2130i	−0.737466	−	1.01503i	0.261295	−	0.965259i	$-0.415851\pi$
$524$	21.0196	+	33.7303i	0.918247	+	1.47351i
$525$	−7.07111	−	4.73038i	−0.308608	−	0.206451i
$526$	−9.51139	+	2.72105i	−0.414716	+	0.118643i
$527$	−6.00363	+	4.36189i	−0.261522	+	0.190007i
$528$	−1.65149	−	1.60266i	−0.0718718	−	0.0697467i
$529$	1.01046	−	3.10986i	0.0439329	−	0.135211i
$530$	−2.01469	+	0.985862i	−0.0875125	+	0.0428231i
$531$	3.75369	−	1.21965i	0.162896	−	0.0529282i
$532$	5.29601	+	8.49852i	0.229611	+	0.368457i
$533$	48.8816	−	15.8826i	2.11730	−	0.687952i
$534$	−5.16642	+	14.1676i	−0.223573	+	0.613094i
$535$	−0.140512	+	1.01382i	−0.00607484	+	0.0438312i
$536$	15.0576	+	1.61058i	0.650389	+	0.0695665i
$537$	15.5143	+	11.2718i	0.669490	+	0.486413i
$538$	7.04221	−	19.3115i	0.303611	−	0.832579i
$539$	−1.38814	−	1.91062i	−0.0597916	−	0.0822960i
$540$	−3.32140	+	2.99471i	−0.142930	+	0.128872i
$541$	−3.46724	+	4.77225i	−0.149068	+	0.205175i	−0.877020	−	0.480453i	$-0.840472\pi$
$541$	−3.46724	+	4.77225i	−0.149068	+	0.205175i	0.727952	+	0.685628i	$0.240472\pi$
$542$	−24.9360	−	37.0180i	−1.07109	−	1.59006i
$543$	−3.38683			−0.145343
$544$	17.9644	−	2.46869i	0.770218	−	0.105844i
$545$	2.38232	−	2.47640i	0.102047	−	0.106077i
$546$	0.536109	−	15.0874i	0.0229434	−	0.645679i
$547$	14.6413	+	4.75725i	0.626018	+	0.203405i	0.604810	−	0.796370i	$-0.293249\pi$
$547$	14.6413	+	4.75725i	0.626018	+	0.203405i	0.0212074	+	0.999775i	$0.493249\pi$
$548$	7.65524	−	18.8808i	0.327016	−	0.806548i
$549$		−	7.72361i		−	0.329636i
$550$	−3.87304	−	1.24473i	−0.165147	−	0.0530754i
$551$	4.93258			0.210135
$552$	14.4146	+	1.54181i	0.613528	+	0.0656238i
$553$	4.53748	−	13.9649i	0.192953	−	0.593849i
$554$	−39.6597	−	1.40926i	−1.68498	−	0.0598736i
$555$	−20.5092	+	10.9551i	−0.870565	+	0.465020i
$556$	18.6283	−	22.1453i	0.790018	−	0.939169i
$557$			8.23329i			0.348855i	0.984670	+	0.174428i	$0.0558075\pi$
$557$			8.23329i			0.348855i	−0.984670	+	0.174428i	$0.944192\pi$
$558$	−1.82910	−	2.71534i	−0.0774321	−	0.114949i
$559$	−18.2104	−	13.2306i	−0.770218	−	0.559596i
$560$	−14.3036	+	5.19733i	−0.604439	+	0.219627i
$561$	−1.49200	+	1.08400i	−0.0629924	+	0.0457666i
$562$	13.9724	+	5.09523i	0.589390	+	0.214929i
$563$	15.3024	−	21.0620i	0.644921	−	0.887657i	−0.353945	−	0.935266i	$-0.615160\pi$
$563$	15.3024	−	21.0620i	0.644921	−	0.887657i	0.998866	+	0.0476090i	$0.0151601\pi$
$564$	−2.82767	−	1.14648i	−0.119066	−	0.0482755i
$565$	25.4814	+	24.5133i	1.07201	+	1.03128i
$566$	−4.04637	+	11.0962i	−0.170082	+	0.466407i
$567$	−0.525790	−	1.61822i	−0.0220811	−	0.0679587i
$568$	−28.0773	+	31.0681i	−1.17810	+	1.30359i
$569$	−8.53254	−	26.2605i	−0.357703	−	1.10090i	−0.954426	−	0.298449i	$-0.903531\pi$
$569$	−8.53254	−	26.2605i	−0.357703	−	1.10090i	0.596723	−	0.802447i	$-0.296469\pi$
$570$	6.68530	−	6.47267i	0.280016	−	0.271110i
$571$	−10.3089	−	3.34955i	−0.431412	−	0.140174i	0.0852579	−	0.996359i	$-0.472829\pi$
$571$	−10.3089	−	3.34955i	−0.431412	−	0.140174i	−0.516670	+	0.856185i	$0.672829\pi$
$572$	−1.73788	−	7.00679i	−0.0726644	−	0.292969i
$573$	2.19648	+	3.02319i	0.0917592	+	0.126296i
$574$	18.9522	−	5.42191i	0.791051	−	0.226306i
$575$	24.0480	−	8.85678i	1.00287	−	0.369353i
$576$	0.806999	+	7.95919i	0.0336250	+	0.331633i
$577$	−21.9848	+	15.9729i	−0.915238	+	0.664960i	−0.942334	−	0.334673i	$-0.891374\pi$
$577$	−21.9848	+	15.9729i	−0.915238	+	0.664960i	0.0270958	+	0.999633i	$0.491374\pi$
$578$	−0.337710	+	9.50393i	−0.0140469	+	0.395311i
$579$	−0.547004	−	0.177732i	−0.0227327	−	0.00738630i
$580$	−1.55360	+	7.33375i	−0.0645098	+	0.304517i
$581$	7.20042	−	2.33956i	0.298724	−	0.0970612i
$582$	5.01363	+	17.5251i	0.207822	+	0.726439i
$583$	−0.126100	−	0.388097i	−0.00522254	−	0.0160733i
$584$	6.43167	−	1.35475i	0.266144	−	0.0560601i
$585$	−13.8112	+	2.46246i	−0.571023	+	0.101810i
$586$	−14.8065	−	11.5827i	−0.611651	−	0.478477i
$587$	−4.78527	+	6.58636i	−0.197509	+	0.271848i	−0.896271	−	0.443506i	$-0.853735\pi$
$587$	−4.78527	+	6.58636i	−0.197509	+	0.271848i	0.698762	+	0.715354i	$0.253735\pi$
$588$	−0.582716	+	8.18913i	−0.0240308	+	0.337714i
$589$	4.00410	+	5.51117i	0.164986	+	0.227084i
$590$	−1.75304	−	12.3574i	−0.0721713	−	0.508744i
$591$	1.26721	+	0.920680i	0.0521260	+	0.0378717i
$592$	−5.88959	+	41.1748i	−0.242061	+	1.69227i
$593$	8.70655			0.357535			0.178768	−	0.983891i	$-0.442789\pi$
$593$	8.70655			0.357535			0.178768	+	0.983891i	$0.442789\pi$
$594$	−0.454562	−	0.674807i	−0.0186509	−	0.0276877i
$595$	2.14071	+	12.0066i	0.0877606	+	0.492223i
$596$	−43.1808	+	10.7101i	−1.76876	+	0.438701i
$597$	−22.2848	−	7.24076i	−0.912054	−	0.296344i
$598$	35.8187	+	28.0200i	1.46474	+	1.14582i
$599$	41.4476			1.69350			0.846751	−	0.531990i	$-0.178556\pi$
$599$	41.4476			1.69350			0.846751	+	0.531990i	$0.178556\pi$
$600$	7.51790	+	11.9784i	0.306917	+	0.489015i
$601$	3.62930			0.148042			0.0740211	−	0.997257i	$-0.476417\pi$
$601$	3.62930			0.148042			0.0740211	+	0.997257i	$0.476417\pi$
$602$	−6.79970	−	5.31921i	−0.277135	−	0.216795i
$603$	5.09198	+	1.65449i	0.207362	+	0.0673759i
$604$	−10.4230	−	42.0235i	−0.424106	−	1.70991i
$605$	−10.4171	+	21.4621i	−0.423517	+	0.872558i
$606$	−0.528019	−	0.783854i	−0.0214493	−	0.0318419i
$607$	−14.8735			−0.603699			−0.301849	−	0.953356i	$-0.597604\pi$
$607$	−14.8735			−0.603699			−0.301849	+	0.953356i	$0.597604\pi$
$608$	−2.26619	−	16.4908i	−0.0919060	−	0.668792i
$609$	−2.30745	−	1.67646i	−0.0935024	−	0.0679335i
$610$	−24.0586	−	4.21006i	−0.974105	−	0.170460i
$611$	−5.62610	−	7.74367i	−0.227608	−	0.313275i
$612$	6.39490	+	0.455044i	0.258499	+	0.0183941i
$613$	16.4036	−	22.5776i	0.662533	−	0.911899i	−0.337029	−	0.941494i	$-0.609422\pi$
$613$	16.4036	−	22.5776i	0.662533	−	0.911899i	0.999562	+	0.0295956i	$0.00942195\pi$
$614$	0.363634	+	0.284460i	0.0146751	+	0.0114799i
$615$	−8.63070	−	16.1576i	−0.348023	−	0.651536i
$616$	−0.570684	−	2.70931i	−0.0229935	−	0.109161i
$617$	2.99460	+	9.21643i	0.120558	+	0.371039i	0.993066	−	0.117561i	$-0.0375076\pi$
$617$	2.99460	+	9.21643i	0.120558	+	0.371039i	−0.872508	+	0.488600i	$0.837508\pi$
$618$	−2.74904	−	9.60924i	−0.110583	−	0.386541i
$619$	−31.0648	+	10.0936i	−1.24860	+	0.405695i	−0.857419	−	0.514619i	$-0.827933\pi$
$619$	−31.0648	+	10.0936i	−1.24860	+	0.405695i	−0.391181	+	0.920314i	$0.627933\pi$
$620$	−9.45515	+	4.21745i	−0.379728	+	0.169377i
$621$	4.87456	+	1.58384i	0.195609	+	0.0635574i
$622$	−0.573112	+	16.1287i	−0.0229797	+	0.646701i
$623$	−14.6785	+	10.6646i	−0.588081	+	0.427266i
$624$	−11.0565	+	22.5290i	−0.442614	+	0.901881i
$625$	21.3017	+	13.0858i	0.852066	+	0.523434i
$626$	−3.83555	+	1.09728i	−0.153299	+	0.0438563i
$627$	0.995085	+	1.36962i	0.0397399	+	0.0546972i
$628$	35.7188	−	8.85927i	1.42534	−	0.353523i
$629$	31.7013	+	10.3004i	1.26401	+	0.410702i
$630$	−5.32726	+	0.755734i	−0.212243	+	0.0301092i
$631$	1.19215	+	3.66906i	0.0474588	+	0.146063i	0.971978	−	0.235073i	$-0.0755329\pi$
$631$	1.19215	+	3.66906i	0.0474588	+	0.146063i	−0.924519	+	0.381136i	$0.875533\pi$
$632$	−16.3660	+	18.1093i	−0.651004	+	0.720348i
$633$	−0.824369	−	2.53715i	−0.0327657	−	0.100843i
$634$	8.64739	−	23.7133i	0.343432	−	0.941777i
$635$	22.2912	−	11.9070i	0.884600	−	0.472517i
$636$	−0.533018	+	1.31463i	−0.0211355	+	0.0521285i
$637$	−15.1379	+	20.8355i	−0.599785	+	0.825533i
$638$	−1.28132	−	0.467252i	−0.0507280	−	0.0184987i
$639$	−11.9777	+	8.70230i	−0.473830	+	0.344258i
$640$	25.2323	+	1.82472i	0.997395	+	0.0721283i
$641$	3.20127	+	2.32586i	0.126443	+	0.0918660i	0.649209	−	0.760610i	$-0.275100\pi$
$641$	3.20127	+	2.32586i	0.126443	+	0.0918660i	−0.522766	+	0.852476i	$0.675100\pi$
$642$	0.361650	+	0.536877i	0.0142732	+	0.0211889i
$643$		−	32.3110i		−	1.27422i	−0.770772	−	0.637111i	$-0.780129\pi$
$643$		−	32.3110i		−	1.27422i	0.770772	−	0.637111i	$-0.219871\pi$
$644$	13.3474	+	11.2277i	0.525961	+	0.442432i
$645$	−3.50304	+	7.21719i	−0.137932	+	0.284177i
$646$	−13.3313	−	0.473710i	−0.524513	−	0.0186379i
$647$	−0.851559	+	2.62083i	−0.0334782	+	0.103035i	−0.966399	−	0.257046i	$-0.917251\pi$
$647$	−0.851559	+	2.62083i	−0.0334782	+	0.103035i	0.932921	+	0.360081i	$0.117251\pi$
$648$	−0.300817	+	2.81238i	−0.0118172	+	0.110481i
$649$	2.27072			0.0891334
$650$	0.142072	+	44.3634i	0.00557252	+	1.74007i
$651$		−	3.93900i		−	0.154382i
$652$	−0.997700	−	0.404519i	−0.0390730	−	0.0158422i
$653$	−28.5370	−	9.27222i	−1.11674	−	0.362850i	−0.308216	−	0.951316i	$-0.599732\pi$
$653$	−28.5370	−	9.27222i	−1.11674	−	0.362850i	−0.808522	+	0.588466i	$0.799732\pi$
$654$	0.0771765	−	2.17192i	0.00301784	−	0.0849289i
$655$	43.7449	−	7.79946i	1.70925	−	0.304750i
$656$	−32.4384	−	4.63995i	−1.26651	−	0.181160i
$657$	2.32384			0.0906615
$658$	−2.05097	−	3.04471i	−0.0799553	−	0.118695i
$659$	18.8036	−	25.8810i	0.732486	−	1.00818i	−0.266530	−	0.963827i	$-0.585877\pi$
$659$	18.8036	−	25.8810i	0.732486	−	1.00818i	0.999016	−	0.0443536i	$-0.0141228\pi$
$660$	−2.34976	+	1.04811i	−0.0914644	+	0.0407974i
$661$	−13.4865	−	18.5625i	−0.524563	−	0.721999i	0.461727	−	0.887022i	$-0.347230\pi$
$661$	−13.4865	−	18.5625i	−0.524563	−	0.721999i	−0.986290	+	0.165024i	$0.947230\pi$
$662$	7.00814	−	19.2181i	0.272379	−	0.746932i
$663$	16.2705	+	11.8212i	0.631893	+	0.459097i
$664$	−12.5140	−	1.33851i	−0.485637	−	0.0519444i
$665$	11.0217	−	1.96511i	0.427405	−	0.0762039i
$666$	−5.03809	+	13.8157i	−0.195222	+	0.535348i
$667$	8.17107	−	2.65494i	0.316385	−	0.102800i
$668$	−33.0732	+	20.6101i	−1.27964	+	0.797430i
$669$	21.1378	−	6.86808i	0.817234	−	0.265535i
$670$	7.92922	−	14.9594i	0.306333	−	0.577932i
$671$	1.37314	−	4.22608i	0.0530093	−	0.163146i
$672$	−4.54470	+	8.48459i	−0.175316	+	0.327300i
$673$	−13.9445	+	10.1313i	−0.537521	+	0.390532i	−0.823163	−	0.567804i	$-0.807793\pi$
$673$	−13.9445	+	10.1313i	−0.537521	+	0.390532i	0.285643	+	0.958336i	$0.407793\pi$
$674$	−30.3102	+	8.67124i	−1.16751	+	0.334003i
$675$	1.72801	+	4.69191i	0.0665112	+	0.180592i
$676$	−44.7476	+	27.8853i	−1.72106	+	1.07251i
$677$	19.2697	+	26.5225i	0.740594	+	1.01934i	0.998584	+	0.0531931i	$0.0169399\pi$
$677$	19.2697	+	26.5225i	0.740594	+	1.01934i	−0.257990	+	0.966148i	$0.583060\pi$
$678$	22.3484	+	0.794121i	0.858285	+	0.0304981i
$679$	−6.77704	+	20.8576i	−0.260079	+	0.800441i
$680$	4.90323	−	19.6717i	0.188030	−	0.754376i
$681$	3.98513	+	12.2650i	0.152710	+	0.469995i
$682$	−0.518074	−	1.81092i	−0.0198381	−	0.0693437i
$683$	5.03030	−	1.63444i	0.192479	−	0.0625402i	−0.211191	−	0.977445i	$-0.567734\pi$
$683$	5.03030	−	1.63444i	0.192479	−	0.0625402i	0.403670	+	0.914905i	$0.367734\pi$
$684$	0.417718	−	5.87035i	0.0159718	−	0.224458i
$685$	−16.4156	−	15.7920i	−0.627209	−	0.603381i
$686$	−16.4643	+	21.0467i	−0.628609	+	0.803569i
$687$	14.3737	+	10.4431i	0.548390	+	0.398428i
$688$	6.70631	+	12.6876i	0.255676	+	0.483709i
$689$	−3.60016	+	2.61567i	−0.137155	+	0.0996492i
$690$	7.59065	−	14.3207i	0.288971	−	0.545178i
$691$	13.0452	−	17.9552i	0.496265	−	0.683050i	−0.485263	−	0.874368i	$-0.661276\pi$
$691$	13.0452	−	17.9552i	0.496265	−	0.683050i	0.981528	+	0.191318i	$0.0612763\pi$
$692$	−24.0766	+	28.6221i	−0.915254	+	1.08805i
$693$		−	0.978907i		−	0.0371856i
$694$	29.5022	−	19.8732i	1.11989	−	0.754378i
$695$	−15.2438	−	28.5379i	−0.578229	−	1.08250i
$696$	2.36306	+	4.11035i	0.0895714	+	0.155802i
$697$	−8.11485	+	24.9749i	−0.307372	+	0.945993i
$698$	−32.2683	−	25.2426i	−1.22137	−	0.955446i
$699$		−	10.4011i		−	0.393407i
$700$	−0.549764	+	17.0061i	−0.0207791	+	0.642768i
$701$			3.06563i			0.115787i	0.998323	+	0.0578935i	$0.0184384\pi$
$701$			3.06563i			0.115787i	−0.998323	+	0.0578935i	$0.981562\pi$
$702$	−5.46687	+	6.98845i	−0.206334	+	0.263762i
$703$	9.45545	−	29.1009i	0.356619	−	1.09756i
$704$	−0.973459	+	4.49845i	−0.0366886	+	0.169542i
$705$	−2.36507	+	2.45847i	−0.0890737	+	0.0925913i
$706$	−24.6054	−	36.5272i	−0.926036	−	1.37472i
$707$		−	1.13710i		−	0.0427649i
$708$	−6.04073	−	5.08139i	−0.227024	−	0.190970i
$709$	8.33466	−	11.4717i	0.313015	−	0.430828i	−0.623304	−	0.781980i	$-0.714210\pi$
$709$	8.33466	−	11.4717i	0.313015	−	0.430828i	0.936318	+	0.351152i	$0.114210\pi$
$710$	20.5783	+	42.0534i	0.772289	+	1.57824i
$711$	−6.98168	+	5.07248i	−0.261833	+	0.190233i
$712$	29.5129	−	6.21653i	1.10604	−	0.232974i
$713$	9.59937	+	6.97435i	0.359499	+	0.261191i
$714$	6.07534	+	4.75257i	0.227364	+	0.177860i
$715$	−7.99477	−	1.10805i	−0.298987	−	0.0414386i
$716$	2.72224	−	38.2566i	0.101735	−	1.42972i
$717$	−20.9942	+	6.82144i	−0.784044	+	0.254751i
$718$	−8.45815	+	2.41973i	−0.315655	+	0.0903036i
$719$	8.01328	+	24.6623i	0.298845	+	0.919750i	0.981903	+	0.189386i	$0.0606497\pi$
$719$	8.01328	+	24.6623i	0.298845	+	0.919750i	−0.683058	+	0.730364i	$0.739350\pi$
$720$	8.59645	+	2.47003i	0.320371	+	0.0920526i
$721$	3.71594	−	11.4365i	0.138389	−	0.425918i
$722$	0.519337	−	14.6153i	0.0193277	−	0.543927i
$723$	9.11060	+	12.5397i	0.338827	+	0.466355i
$724$	3.58245	+	5.74877i	0.133141	+	0.213652i
$725$	6.96628	+	4.66025i	0.258721	+	0.173077i
$726$	4.15001	+	14.5063i	0.154021	+	0.538379i
$727$	−30.8824	+	22.4374i	−1.14537	+	0.832157i	−0.987858	−	0.155361i	$-0.950346\pi$
$727$	−30.8824	+	22.4374i	−1.14537	+	0.832157i	−0.157508	+	0.987518i	$0.550346\pi$
$728$	−26.1762	+	15.0488i	−0.970156	+	0.557747i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	1.26670	−	7.23862i	0.0468827	−	0.267913i
$731$	10.9377	−	3.55388i	0.404547	−	0.131445i
$732$	−13.1100	+	8.16973i	−0.484559	+	0.301962i
$733$	9.82683	−	3.19293i	0.362962	−	0.117934i	−0.121858	−	0.992548i	$-0.538885\pi$
$733$	9.82683	−	3.19293i	0.362962	−	0.117934i	0.484820	+	0.874614i	$0.338885\pi$
$734$	−31.2285	−	11.3879i	−1.15266	−	0.420335i
$735$	8.25758	+	4.00801i	0.304585	+	0.147838i
$736$	−12.6302	−	26.0982i	−0.465555	−	0.961992i
$737$	2.49201	+	1.81055i	0.0917943	+	0.0666924i
$738$	−10.8843	−	3.96912i	−0.400657	−	0.146105i
$739$	19.7296	+	27.1555i	0.725765	+	0.998930i	0.999313	+	0.0370717i	$0.0118030\pi$
$739$	19.7296	+	27.1555i	0.725765	+	0.998930i	−0.273547	+	0.961859i	$0.588197\pi$
$740$	40.2890	+	23.2242i	1.48105	+	0.853738i
$741$	10.8515	−	14.9358i	0.398641	−	0.548682i
$742$	−1.41554	+	0.953532i	−0.0519660	+	0.0350053i
$743$	39.7829			1.45949			0.729746	−	0.683719i	$-0.239638\pi$
$743$	39.7829			1.45949			0.729746	+	0.683719i	$0.239638\pi$
$744$	−2.67424	+	5.97688i	−0.0980425	+	0.219123i
$745$	−6.82857	+	49.2695i	−0.250180	+	1.80509i
$746$	−3.01886	−	0.107271i	−0.110528	−	0.00392748i
$747$	−4.23182	−	1.37500i	−0.154834	−	0.0503087i
$748$	3.41816	+	1.38590i	0.124980	+	0.0506734i
$749$			0.778820i			0.0284575i
$750$	15.5569	−	2.82515i	0.568059	−	0.103160i
$751$	−9.99993			−0.364903			−0.182451	−	0.983215i	$-0.558403\pi$
$751$	−9.99993			−0.364903			−0.182451	+	0.983215i	$0.558403\pi$
$752$	1.04497	+	6.01236i	0.0381061	+	0.219248i
$753$	−4.95148	+	15.2391i	−0.180442	+	0.555344i
$754$	−0.528161	+	14.8637i	−0.0192345	+	0.541303i
$755$	−47.9490	−	6.64555i	−1.74504	−	0.241856i
$756$	−2.19059	+	2.60416i	−0.0796709	+	0.0947124i
$757$		−	17.1991i		−	0.625111i	−0.949899	−	0.312556i	$-0.898815\pi$
$757$		−	17.1991i		−	0.625111i	0.949899	−	0.312556i	$-0.101185\pi$
$758$	37.9814	−	25.5850i	1.37955	−	0.929289i
$759$	2.38560	+	1.73324i	0.0865918	+	0.0629127i
$760$	−18.0581	−	4.50103i	−0.655037	−	0.163270i
$761$	−12.0870	+	8.78174i	−0.438154	+	0.318338i	−0.784901	−	0.619621i	$-0.787286\pi$
$761$	−12.0870	+	8.78174i	−0.438154	+	0.318338i	0.346747	+	0.937959i	$0.387286\pi$
$762$	5.47586	−	15.0162i	0.198369	−	0.543979i
$763$	1.53692	−	2.11539i	0.0556404	−	0.0765824i
$764$	2.80820	−	6.92610i	0.101597	−	0.250578i
$765$	3.12986	−	6.44836i	0.113160	−	0.233141i
$766$	48.1275	+	17.5504i	1.73892	+	0.634120i
$767$	−7.65202	−	23.5505i	−0.276298	−	0.850359i
$768$	12.6563	−	9.78872i	0.456694	−	0.353220i
$769$	2.06806	+	6.36482i	0.0745760	+	0.229521i	0.981395	−	0.191998i	$-0.0614968\pi$
$769$	2.06806	+	6.36482i	0.0745760	+	0.229521i	−0.906819	+	0.421520i	$0.861497\pi$
$770$	−3.04924	−	0.533592i	−0.109887	−	0.0192293i
$771$	3.44104	+	1.11806i	0.123926	+	0.0402660i
$772$	0.276918	+	1.11648i	0.00996649	+	0.0401829i
$773$	−22.9953	−	31.6504i	−0.827085	−	1.13838i	−0.988459	−	0.151491i	$-0.951593\pi$
$773$	−22.9953	−	31.6504i	−0.827085	−	1.13838i	0.161374	−	0.986893i	$-0.448407\pi$
$774$	1.39555	+	4.87812i	0.0501620	+	0.175341i
$775$	0.448091	+	11.5664i	0.0160959	+	0.415479i
$776$	24.4437	−	27.0475i	0.877479	−	0.970947i
$777$	−14.3139	+	10.3996i	−0.513508	+	0.373085i
$778$	36.7197	+	1.30479i	1.31647	+	0.0467789i
$779$	22.9263	+	7.44921i	0.821420	+	0.266896i
$780$	18.7887	+	20.8383i	0.672743	+	0.746132i
$781$	−8.10089	+	2.63214i	−0.289873	+	0.0941853i
$782$	−22.3390	+	6.39079i	−0.798839	+	0.228534i
$783$	0.517995	+	1.59423i	0.0185116	+	0.0569730i
$784$	14.5165	−	7.67305i	0.518448	−	0.274037i
$785$	5.64854	−	40.7553i	0.201605	−	1.45462i
$786$	17.3155	−	22.1349i	0.617623	−	0.789525i
$787$	17.9730	−	24.7377i	0.640669	−	0.881806i	−0.357982	−	0.933729i	$-0.616535\pi$
$787$	17.9730	−	24.7377i	0.640669	−	0.881806i	0.998651	+	0.0519230i	$0.0165350\pi$
$788$	0.222353	−	3.12481i	0.00792099	−	0.111317i
$789$	4.11178	+	5.65938i	0.146383	+	0.201479i
$790$	11.9949	+	24.5125i	0.426758	+	0.872115i
$791$	21.7667	+	15.8145i	0.773936	+	0.562298i
$792$	−0.664594	+	1.48535i	−0.0236153	+	0.0527798i
$793$	−48.4576			−1.72078
$794$	0.114683	−	0.0772528i	0.00406996	−	0.00274160i
$795$	1.14298	+	1.09956i	0.0405375	+	0.0389974i
$796$	11.2815	+	45.4850i	0.399864	+	1.61217i
$797$	−37.5316	−	12.1948i	−1.32944	−	0.431960i	−0.443712	−	0.896170i	$-0.646339\pi$
$797$	−37.5316	−	12.1948i	−1.32944	−	0.431960i	−0.885726	+	0.464209i	$0.846339\pi$
$798$	4.36273	−	5.57699i	0.154439	−	0.197423i
$799$	4.89044			0.173011
$800$	12.3798	−	25.4311i	0.437694	−	0.899124i
$801$	10.6633			0.376771
$802$	27.9704	−	35.7553i	0.987669	−	1.26256i
$803$	1.27152	+	0.413141i	0.0448709	+	0.0145794i
$804$	−2.57779	−	10.3931i	−0.0909117	−	0.366538i
$805$	17.2004	−	9.18773i	0.606234	−	0.323825i
$806$	−17.0359	+	11.4757i	−0.600065	+	0.404215i
$807$	−14.5349			−0.511653
$808$	−0.771991	+	1.72539i	−0.0271585	+	0.0606988i
$809$	1.06053	+	0.770523i	0.0372864	+	0.0270901i	0.606272	−	0.795257i	$-0.292664\pi$
$809$	1.06053	+	0.770523i	0.0372864	+	0.0270901i	−0.568986	+	0.822347i	$0.692664\pi$
$810$	2.79405	+	1.48098i	0.0981728	+	0.0520364i
$811$	−19.9098	−	27.4034i	−0.699126	−	0.962265i	−0.999963	−	0.00858912i	$-0.997266\pi$
$811$	−19.9098	−	27.4034i	−0.699126	−	0.962265i	0.300837	−	0.953676i	$-0.402734\pi$
$812$	−0.404880	+	5.68993i	−0.0142085	+	0.199678i
$813$	−18.5508	+	25.5330i	−0.650606	+	0.895482i
$814$	−5.21288	+	6.66376i	−0.182711	+	0.233565i
$815$	−0.834481	+	0.867435i	−0.0292306	+	0.0303849i
$816$	−5.99189	−	11.3360i	−0.209758	−	0.396839i
$817$	−3.26237	−	10.0405i	−0.114136	−	0.351274i
$818$	26.2074	−	7.49749i	0.916320	−	0.262144i
$819$	−10.1526	+	3.29879i	−0.354761	+	0.115269i
$820$	−18.2965	+	31.7405i	−0.638942	+	1.10843i
$821$	33.0968	+	10.7538i	1.15509	+	0.375310i	0.823057	−	0.567959i	$-0.192267\pi$
$821$	33.0968	+	10.7538i	1.15509	+	0.375310i	0.332029	+	0.943269i	$0.392267\pi$
$822$	−14.3973	−	0.511589i	−0.502163	−	0.0178437i
$823$	−30.3292	+	22.0354i	−1.05721	+	0.768107i	−0.973570	−	0.228389i	$-0.926654\pi$
$823$	−30.3292	+	22.0354i	−1.05721	+	0.768107i	−0.0836391	+	0.996496i	$0.526654\pi$
$824$	−13.4028	+	14.8305i	−0.466910	+	0.516645i
$825$	0.111358	+	2.87445i	0.00387699	+	0.100076i
$826$	−2.61220	−	9.13093i	−0.0908902	−	0.317706i
$827$	4.31426	+	5.93806i	0.150021	+	0.206487i	0.877413	−	0.479736i	$-0.159268\pi$
$827$	4.31426	+	5.93806i	0.150021	+	0.206487i	−0.727392	+	0.686223i	$0.759268\pi$
$828$	−2.46772	−	9.94937i	−0.0857593	−	0.345765i
$829$	11.1495	+	3.62269i	0.387237	+	0.125821i	0.496164	−	0.868229i	$-0.334741\pi$
$829$	11.1495	+	3.62269i	0.387237	+	0.125821i	−0.108927	+	0.994050i	$0.534741\pi$
$830$	−6.58978	+	12.4324i	−0.228735	+	0.431535i
$831$	8.67143	+	26.6879i	0.300809	+	0.925794i
$832$	49.9356	−	5.06308i	1.73121	−	0.175531i
$833$	−4.06619	−	12.5145i	−0.140885	−	0.433600i
$834$	−19.2242	−	7.01036i	−0.665679	−	0.242749i
$835$	7.64751	+	42.8927i	0.264653	+	1.48436i
$836$	1.27222	−	3.13778i	0.0440005	−	0.108522i
$837$	−1.36074	+	1.87289i	−0.0470340	+	0.0647367i
$838$	3.07582	−	8.43469i	0.106253	−	0.291372i
$839$	11.7342	−	8.52541i	0.405110	−	0.294330i	−0.366509	−	0.930414i	$-0.619447\pi$
$839$	11.7342	−	8.52541i	0.405110	−	0.294330i	0.771619	+	0.636085i	$0.219447\pi$
$840$	6.91774	+	8.24306i	0.238685	+	0.284413i
$841$	−21.1883	−	15.3942i	−0.730629	−	0.530833i
$842$	6.24087	−	4.20397i	0.215075	−	0.144878i
$843$		−	10.5164i		−	0.362204i
$844$	−3.43455	+	4.08297i	−0.118222	+	0.140542i
$845$	10.3470	+	58.0333i	0.355948	+	1.99641i
$846$	−0.0766176	+	2.15620i	−0.00263417	+	0.0741316i
$847$	−5.60966	+	17.2648i	−0.192750	+	0.593224i
$848$	2.79525	−	0.485823i	0.0959892	−	0.0166832i
$849$	8.35159			0.286626
$850$	−18.3802	−	13.2643i	−0.630436	−	0.454961i
$851$		−	53.2965i		−	1.82698i
$852$	27.4408	+	11.1259i	0.940105	+	0.381167i
$853$	−11.4034	−	3.70518i	−0.390444	−	0.126863i	0.107215	−	0.994236i	$-0.465807\pi$
$853$	−11.4034	−	3.70518i	−0.390444	−	0.126863i	−0.497659	+	0.867373i	$0.665807\pi$
$854$	−18.5734	−	0.659982i	−0.635569	−	0.0225841i
$855$	−5.91941	−	2.87313i	−0.202440	−	0.0982589i
$856$	0.528752	−	1.18175i	0.0180724	−	0.0403914i
$857$	31.1919			1.06550			0.532748	−	0.846274i	$-0.321159\pi$
$857$	31.1919			1.06550			0.532748	+	0.846274i	$0.321159\pi$
$858$	−4.23371	+	2.85190i	−0.144536	+	0.0973624i
$859$	−32.9741	+	45.3849i	−1.12506	+	1.54851i	−0.327937	+	0.944700i	$0.606353\pi$
$859$	−32.9741	+	45.3849i	−1.12506	+	1.54851i	−0.797125	+	0.603815i	$0.793647\pi$
$860$	15.9558	−	1.68804i	0.544088	−	0.0575617i
$861$	−8.19307	−	11.2768i	−0.279219	−	0.384312i
$862$	−10.0752	−	3.67407i	−0.343164	−	0.125139i
$863$	−3.99891	−	2.90538i	−0.136124	−	0.0989002i	0.517639	−	0.855599i	$-0.326811\pi$
$863$	−3.99891	−	2.90538i	−0.136124	−	0.0989002i	−0.653764	+	0.756699i	$0.726811\pi$
$864$	5.09191	−	2.46423i	0.173230	−	0.0838347i
$865$	19.7021	+	36.8844i	0.669892	+	1.25411i
$866$	32.2849	+	11.7731i	1.09708	+	0.400067i
$867$	6.39541	−	2.07799i	0.217200	−	0.0705724i
$868$	−6.68603	+	4.16652i	−0.226939	+	0.141421i
$869$	−4.72193	+	1.53425i	−0.160180	+	0.0520458i
$870$	5.24828	−	0.744530i	0.177933	−	0.0252419i
$871$	10.3802	−	31.9469i	0.351719	−	1.08248i
$872$	−3.76824	+	2.16638i	−0.127609	+	0.0733628i
$873$	10.4276	−	7.57611i	0.352921	−	0.256412i
$874$	5.86657	+	20.5065i	0.198440	+	0.693644i
$875$	17.4226	+	7.63790i	0.588992	+	0.258208i
$876$	−2.45806	−	3.94446i	−0.0830503	−	0.133271i
$877$	−2.73780	−	3.76827i	−0.0924491	−	0.127245i	0.760287	−	0.649587i	$-0.225058\pi$
$877$	−2.73780	−	3.76827i	−0.0924491	−	0.127245i	−0.852736	+	0.522342i	$0.825058\pi$
$878$	1.42012	−	39.9654i	0.0479267	−	1.34877i
$879$	−4.10767	+	12.6421i	−0.138548	+	0.426408i
$880$	4.26453	+	2.87982i	0.143757	+	0.0970788i
$881$	−8.67553	−	26.7005i	−0.292286	−	0.899564i	−0.984120	−	0.177507i	$-0.943197\pi$
$881$	−8.67553	−	26.7005i	−0.292286	−	0.899564i	0.691834	−	0.722057i	$-0.256803\pi$
$882$	5.58133	−	1.59672i	0.187933	−	0.0537644i
$883$	−49.8647	+	16.2020i	−1.67808	+	0.545242i	−0.984538	−	0.175173i	$-0.943951\pi$
$883$	−49.8647	+	16.2020i	−1.67808	+	0.545242i	−0.693543	+	0.720415i	$0.743951\pi$
$884$	2.85493	−	40.1214i	0.0960215	−	1.34943i
$885$	−7.78450	+	4.15815i	−0.261673	+	0.139775i
$886$	−32.7288	−	25.6028i	−1.09955	−	0.860144i
$887$	−18.1903	−	13.2160i	−0.610770	−	0.443751i	0.238915	−	0.971040i	$-0.423208\pi$
$887$	−18.1903	−	13.2160i	−0.610770	−	0.443751i	−0.849685	+	0.527290i	$0.823208\pi$
$888$	28.7798	−	6.06211i	0.965786	−	0.203431i
$889$	15.5576	−	11.3033i	0.521786	−	0.379100i
$890$	5.81248	−	33.2157i	0.194835	−	1.11339i
$891$	−0.338166	+	0.465445i	−0.0113290	+	0.0155930i
$892$	−34.0166	−	28.6143i	−1.13896	−	0.958079i
$893$		−	4.48929i		−	0.150228i
$894$	17.5755	+	26.0911i	0.587812	+	0.872618i
$895$	−38.5764	−	18.7240i	−1.28947	−	0.625873i
$896$	19.2089	−	1.26052i	0.641724	−	0.0421112i
$897$	9.93695	−	30.5828i	0.331785	−	1.02113i
$898$	−21.4735	+	27.4502i	−0.716581	+	0.916026i
$899$			3.88060i			0.129425i
$900$	6.13618	−	7.89603i	0.204539	−	0.263201i
$901$		−	2.27365i		−	0.0757463i
$902$	−5.24986	−	4.10682i	−0.174801	−	0.136742i
$903$	−1.88640	+	5.80573i	−0.0627753	+	0.193203i
$904$	−22.2913	−	38.7740i	−0.741399	−	1.28960i
$905$	7.45560	−	1.32929i	0.247833	−	0.0441871i
$906$	−25.3919	+	17.1044i	−0.843588	+	0.568256i
$907$		−	38.2782i		−	1.27101i	−0.772097	−	0.635504i	$-0.780792\pi$
$907$		−	38.2782i		−	1.27101i	0.772097	−	0.635504i	$-0.219208\pi$
$908$	16.6031	−	19.7377i	0.550995	−	0.655020i
$909$	−0.392813	+	0.540660i	−0.0130288	+	0.0179326i
$910$	4.74145	+	33.4230i	0.157177	+	1.10796i
$911$	9.21195	−	6.69288i	0.305206	−	0.221745i	−0.424631	−	0.905367i	$-0.639596\pi$
$911$	9.21195	−	6.69288i	0.305206	−	0.221745i	0.729837	+	0.683622i	$0.239596\pi$
$912$	−10.4061	+	5.50039i	−0.344581	+	0.182136i
$913$	−2.07105	−	1.50470i	−0.0685416	−	0.0497984i
$914$	−33.7596	+	43.1558i	−1.11667	+	1.42747i
$915$	3.03143	+	17.0024i	0.100216	+	0.562082i
$916$	2.52210	−	35.4440i	0.0833325	−	1.17110i
$917$	32.1569	−	10.4484i	1.06191	−	0.345037i
$918$	−1.24688	−	4.35847i	−0.0411533	−	0.143851i
$919$	5.93823	+	18.2760i	0.195884	+	0.602870i	0.999965	+	0.00834980i	$0.00265786\pi$
$919$	5.93823	+	18.2760i	0.195884	+	0.602870i	−0.804081	+	0.594520i	$0.797342\pi$
$920$	−32.3369	+	2.26351i	−1.06611	+	0.0746259i
$921$	0.100880	−	0.310478i	0.00332412	−	0.0102306i
$922$	−26.4329	−	0.939257i	−0.870520	−	0.0309328i
$923$	54.5979	+	75.1475i	1.79711	+	2.47351i
$924$	−1.66159	+	1.03545i	−0.0546623	+	0.0340638i
$925$	40.8481	−	32.1657i	1.34308	−	1.05760i
$926$	−27.2135	+	7.78531i	−0.894290	+	0.255841i
$927$	−5.71760	+	4.15408i	−0.187791	+	0.136438i
$928$	4.47733	−	8.35880i	0.146975	−	0.274391i
$929$	7.42542	−	22.8531i	0.243620	−	0.749785i	−0.752240	−	0.658889i	$-0.771027\pi$
$929$	7.42542	−	22.8531i	0.243620	−	0.749785i	0.995860	−	0.0908966i	$-0.0289733\pi$
$930$	5.09224	+	5.25952i	0.166981	+	0.172466i
$931$	−11.4879	+	3.73265i	−0.376501	+	0.122333i
$932$	−17.6548	+	11.0019i	−0.578303	+	0.360380i
$933$	10.8534	−	3.52647i	0.355323	−	0.115451i
$934$	10.2331	−	28.0617i	0.334836	−	0.918206i
$935$	2.85896	−	2.97187i	0.0934981	−	0.0971904i
$936$	17.6448	+	1.88731i	0.576738	+	0.0616887i
$937$	12.3176	+	8.94927i	0.402399	+	0.292360i	0.770517	−	0.637419i	$-0.219998\pi$
$937$	12.3176	+	8.94927i	0.402399	+	0.292360i	−0.368119	+	0.929779i	$0.619998\pi$
$938$	4.41375	−	12.1036i	0.144114	−	0.395197i
$939$	1.65811	+	2.28219i	0.0541104	+	0.0744765i
$940$	6.67467	+	1.41398i	0.217704	+	0.0461190i
$941$	0.0360454	−	0.0496123i	0.00117505	−	0.00161731i	−0.808429	−	0.588594i	$-0.799682\pi$
$941$	0.0360454	−	0.0496123i	0.00117505	−	0.00161731i	0.809604	+	0.586976i	$0.199682\pi$
$942$	−14.5383	−	21.5824i	−0.473683	−	0.703192i
$943$	41.9881			1.36732
$944$	−2.23546	+	15.6284i	−0.0727582	+	0.508660i
$945$	1.79258	+	3.35590i	0.0583127	+	0.109167i
$946$	−0.103660	+	2.91724i	−0.00337029	+	0.0948476i
$947$	−55.1298	−	17.9128i	−1.79148	−	0.582086i	−0.791886	−	0.610669i	$-0.790901\pi$
$947$	−55.1298	−	17.9128i	−1.79148	−	0.582086i	−0.999591	+	0.0285826i	$0.990901\pi$
$948$	15.9949	+	6.48517i	0.519492	+	0.210628i
$949$		−	14.5797i		−	0.473275i
$950$	−12.1762	+	16.8725i	−0.395050	+	0.547417i
$951$	−17.8480			−0.578760
$952$	1.64071	−	15.3393i	0.0531758	−	0.497150i
$953$	8.50788	−	26.1846i	0.275597	−	0.848201i	−0.713464	−	0.700692i	$-0.752875\pi$
$953$	8.50788	−	26.1846i	0.275597	−	0.848201i	0.989061	−	0.147509i	$-0.0471254\pi$
$954$	1.00245	+	0.0356208i	0.0324556	+	0.00115327i
$955$	−6.02179	−	5.79302i	−0.194861	−	0.187458i
$956$	33.7855	+	28.4200i	1.09270	+	0.919168i
$957$			0.964394i			0.0311744i
$958$	−17.1548	−	25.4666i	−0.554245	−	0.822788i
$959$	−14.0226	−	10.1880i	−0.452813	−	0.328988i
$960$	−4.90038	−	17.2043i	−0.158159	−	0.555265i
$961$	20.7437	−	15.0712i	0.669153	−	0.486168i
$962$	86.6792	+	31.6088i	2.79465	+	1.01911i
$963$	0.269045	−	0.370309i	0.00866986	−	0.0119330i
$964$	11.6479	−	28.7282i	0.375153	−	0.925274i
$965$	1.27391	+	0.176559i	0.0410085	+	0.00568363i
$966$	4.22528	−	11.5868i	0.135946	−	0.372799i
$967$	1.86832	+	5.75010i	0.0600811	+	0.184911i	0.976592	−	0.215098i	$-0.0690071\pi$
$967$	1.86832	+	5.75010i	0.0600811	+	0.184911i	−0.916511	+	0.400009i	$0.869007\pi$
$968$	20.2332	−	22.3884i	0.650319	−	0.719590i
$969$	2.91483	+	8.97093i	0.0936379	+	0.288188i
$970$	−17.9152	−	36.6111i	−0.575221	−	1.17551i
$971$	−17.1812	−	5.58252i	−0.551372	−	0.179152i	0.0200634	−	0.999799i	$-0.493613\pi$
$971$	−17.1812	−	5.58252i	−0.551372	−	0.179152i	−0.571435	+	0.820647i	$0.693613\pi$
$972$	1.94118	−	0.481467i	0.0622635	−	0.0154431i
$973$	−14.4708	−	19.9174i	−0.463913	−	0.638521i
$974$	4.02116	−	1.15039i	0.128846	−	0.0368608i
$975$	29.4368	−	10.8415i	0.942733	−	0.347205i
$976$	27.7345	+	13.6112i	0.887759	+	0.435683i
$977$	−4.75557	+	3.45512i	−0.152144	+	0.110539i	−0.661253	−	0.750163i	$-0.729975\pi$
$977$	−4.75557	+	3.45512i	−0.152144	+	0.110539i	0.509109	+	0.860702i	$0.329975\pi$
$978$	−0.0270334	+	0.760782i	−0.000864433	+	0.0243271i
$979$	5.83460	+	1.89578i	0.186475	+	0.0605892i
$980$	−1.93138	−	18.2559i	−0.0616956	−	0.583163i
$981$	−1.46154	+	0.474882i	−0.0466633	+	0.0151618i
$982$	4.31944	+	15.0986i	0.137839	+	0.481815i
$983$	10.1444	+	31.2213i	0.323557	+	0.995806i	0.972088	+	0.234617i	$0.0753837\pi$
$983$	10.1444	+	31.2213i	0.323557	+	0.995806i	−0.648531	+	0.761188i	$0.724616\pi$
$984$	4.77586	+	22.6733i	0.152249	+	0.722800i
$985$	−3.15093	−	1.52938i	−0.100397	−	0.0487300i
$986$	−5.98527	−	4.68211i	−0.190610	−	0.149109i
$987$	−1.52580	+	2.10008i	−0.0485666	+	0.0668462i
$988$	−36.8303	−	2.62074i	−1.17173	−	0.0833770i
$989$	−10.8086	−	14.8767i	−0.343692	−	0.473052i
$990$	1.26551	+	1.30708i	0.0402204	+	0.0415416i
$991$	−19.4806	−	14.1535i	−0.618821	−	0.449600i	0.233689	−	0.972311i	$-0.424920\pi$
$991$	−19.4806	−	14.1535i	−0.618821	−	0.449600i	−0.852509	+	0.522712i	$0.824920\pi$
$992$	12.9738	−	1.78287i	0.411919	−	0.0566063i
$993$	−14.4646			−0.459020
$994$	19.9034	+	29.5471i	0.631299	+	0.937176i
$995$	51.8985	+	7.19295i	1.64529	+	0.228032i
$996$	2.14234	+	8.63749i	0.0678826	+	0.273689i
$997$	−5.20280	−	1.69049i	−0.164774	−	0.0535384i	0.225468	−	0.974251i	$-0.427609\pi$
$997$	−5.20280	−	1.69049i	−0.164774	−	0.0535384i	−0.390242	+	0.920712i	$0.627609\pi$
$998$	45.6977	+	35.7481i	1.44654	+	1.13159i
$999$	10.3985			0.328993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bm.a.61.20	yes	240
8.5	even	2	inner	600.2.bm.a.61.7	✓	240
25.16	even	5	inner	600.2.bm.a.541.7	yes	240
200.141	even	10	inner	600.2.bm.a.541.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bm.a.61.7	✓	240	8.5	even	2	inner
600.2.bm.a.61.20	yes	240	1.1	even	1	trivial
600.2.bm.a.541.7	yes	240	25.16	even	5	inner
600.2.bm.a.541.20	yes	240	200.141	even	10	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bm (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.871359 + 1.11388i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.481467 - 1.94118i) q^{4} +(-2.21490 - 0.306977i) q^{5} +(-1.17292 + 0.790100i) q^{6} -1.70149 q^{7} +(2.58178 + 1.15517i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.27191 - 2.19965i) q^{10} +(0.338166 + 0.465445i) q^{11} +(0.141956 - 1.99496i) q^{12} +(3.68774 - 5.07574i) q^{13} +(1.48261 - 1.89526i) q^{14} +(-2.01163 - 0.976393i) q^{15} +(-3.53638 + 1.86923i) q^{16} +(0.990565 + 3.04865i) q^{17} +(-1.35967 + 0.388978i) q^{18} +(2.79857 - 0.909312i) q^{19} +(0.470503 + 4.44732i) q^{20} +(-1.61822 - 0.525790i) q^{21} +(-0.813115 - 0.0288930i) q^{22} +(4.14655 - 3.01264i) q^{23} +(2.09845 + 1.89644i) q^{24} +(4.81153 + 1.35984i) q^{25} +(2.44043 + 8.53050i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.819214 + 3.30291i) q^{28} +(1.59423 + 0.517995i) q^{29} +(2.84044 - 1.38993i) q^{30} +(0.715382 + 2.20172i) q^{31} +(0.999349 - 5.56788i) q^{32} +(0.177784 + 0.547164i) q^{33} +(-4.25897 - 1.55309i) q^{34} +(3.76863 + 0.522319i) q^{35} +(0.751483 - 1.85345i) q^{36} +(6.11207 - 8.41254i) q^{37} +(-1.42570 + 3.90962i) q^{38} +(5.07574 - 3.68774i) q^{39} +(-5.36376 - 3.35112i) q^{40} +(6.62758 + 4.81522i) q^{41} +(1.99572 - 1.34435i) q^{42} -3.58773i q^{43} +(0.740698 - 0.880538i) q^{44} +(-1.61145 - 1.55023i) q^{45} +(-0.257401 + 7.24386i) q^{46} +(0.471444 - 1.45095i) q^{47} +(-3.94092 + 0.684945i) q^{48} -4.10492 q^{49} +(-5.70727 + 4.17457i) q^{50} +3.20554i q^{51} +(-11.6285 - 4.71477i) q^{52} +(-0.674573 - 0.219182i) q^{53} +(-1.41332 - 0.0502205i) q^{54} +(-0.606121 - 1.13472i) q^{55} +(-4.39288 - 1.96551i) q^{56} +2.94260 q^{57} +(-1.96613 + 1.32442i) q^{58} +(2.31991 - 3.19308i) q^{59} +(-0.926822 + 4.37504i) q^{60} +(-4.53982 - 6.24853i) q^{61} +(-3.07581 - 1.12164i) q^{62} +(-1.37654 - 1.00011i) q^{63} +(5.33117 + 5.96478i) q^{64} +(-9.72610 + 10.1102i) q^{65} +(-0.764390 - 0.278745i) q^{66} +(5.09198 - 1.65449i) q^{67} +(5.44105 - 3.39069i) q^{68} +(4.87456 - 1.58384i) q^{69} +(-3.86563 + 3.74269i) q^{70} +(-4.57507 + 14.0806i) q^{71} +(1.40971 + 2.45208i) q^{72} +(1.88002 - 1.36592i) q^{73} +(4.04477 + 14.1385i) q^{74} +(4.15582 + 2.78013i) q^{75} +(-3.11256 - 4.99474i) q^{76} +(-0.575387 - 0.791952i) q^{77} +(-0.315082 + 8.86712i) q^{78} +(-2.66676 + 8.20745i) q^{79} +(8.40652 - 3.05457i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-11.1386 + 3.18656i) q^{82} +(-4.23182 + 1.37500i) q^{83} +(-0.241536 + 3.39440i) q^{84} +(-1.25814 - 7.05652i) q^{85} +(3.99631 + 3.12620i) q^{86} +(1.35613 + 0.985286i) q^{87} +(0.335402 + 1.59232i) q^{88} +(8.62683 - 6.26776i) q^{89} +(3.13093 - 0.444159i) q^{90} +(-6.27467 + 8.63634i) q^{91} +(-7.84452 - 6.59872i) q^{92} +2.31502i q^{93} +(1.20540 + 1.78943i) q^{94} +(-6.47769 + 1.15493i) q^{95} +(2.67101 - 4.98655i) q^{96} +(3.98300 - 12.2584i) q^{97} +(3.57686 - 4.57240i) q^{98} +0.575322i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) \) 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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