LMFDB - Embedded newform 546.2.bk.b.25.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,2,Mod(25,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.752609431977984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.6
Root			$0.385124 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.b.415.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.25312 - 1.30084i) q^{5} +1.00000i q^{6} +(-1.49160 + 2.18521i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.30084 - 2.25312i) q^{10} +(3.11915 + 1.80084i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.60168 + 0.167055i) q^{13} +(-0.199160 + 2.63824i) q^{14} +2.60168i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.41647 - 2.45340i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.15537 + 0.667055i) q^{19} -2.60168i q^{20} +(-1.14664 - 2.38437i) q^{21} +3.60168 q^{22} +(-1.46789 - 2.54247i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.884367 - 1.53177i) q^{25} +(3.20267 - 1.65617i) q^{26} +1.00000 q^{27} +(1.14664 + 2.38437i) q^{28} +8.97209 q^{29} +(1.30084 + 2.25312i) q^{30} +(-3.46410 - 2.00000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.11915 + 1.80084i) q^{33} -2.83294i q^{34} +(-0.518152 + 6.86387i) q^{35} -1.00000 q^{36} +(-0.144674 + 0.0835276i) q^{37} +(-0.667055 + 1.15537i) q^{38} +(-1.94551 + 3.03562i) q^{39} +(-1.30084 - 2.25312i) q^{40} +3.03630i q^{41} +(-2.18521 - 1.49160i) q^{42} +2.33411 q^{43} +(3.11915 - 1.80084i) q^{44} +(-2.25312 - 1.30084i) q^{45} +(-2.54247 - 1.46789i) q^{46} +(-8.43580 + 4.87041i) q^{47} +1.00000 q^{48} +(-2.55026 - 6.51891i) q^{49} -1.76873i q^{50} +(1.41647 + 2.45340i) q^{51} +(1.94551 - 3.03562i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.866025 - 0.500000i) q^{54} +9.37041 q^{55} +(2.18521 + 1.49160i) q^{56} -1.33411i q^{57} +(7.77006 - 4.48605i) q^{58} +(-10.0232 - 5.78689i) q^{59} +(2.25312 + 1.30084i) q^{60} +(-2.01815 - 3.49554i) q^{61} -4.00000 q^{62} +(2.63824 + 0.199160i) q^{63} -1.00000 q^{64} +(8.33233 - 4.30881i) q^{65} +(-1.80084 + 3.11915i) q^{66} +(10.1679 + 5.87041i) q^{67} +(-1.41647 - 2.45340i) q^{68} +2.93579 q^{69} +(2.98320 + 6.20336i) q^{70} +5.76873i q^{71} +(-0.866025 + 0.500000i) q^{72} +(-9.93411 - 5.73546i) q^{73} +(-0.0835276 + 0.144674i) q^{74} +(0.884367 + 1.53177i) q^{75} +1.33411i q^{76} +(-8.58773 + 4.12985i) q^{77} +(-0.167055 + 3.60168i) q^{78} +(-3.37041 - 5.83773i) q^{79} +(-2.25312 - 1.30084i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.51815 + 2.62952i) q^{82} +8.10051i q^{83} +(-2.63824 - 0.199160i) q^{84} -7.37041i q^{85} +(2.02140 - 1.16706i) q^{86} +(-4.48605 + 7.77006i) q^{87} +(1.80084 - 3.11915i) q^{88} +(-7.07288 + 4.08353i) q^{89} -2.60168 q^{90} +(-5.73732 + 7.62123i) q^{91} -2.93579 q^{92} +(3.46410 - 2.00000i) q^{93} +(-4.87041 + 8.43580i) q^{94} +(-1.73546 + 3.00591i) q^{95} +(0.866025 - 0.500000i) q^{96} -0.139148i q^{97} +(-5.46804 - 4.37041i) q^{98} -3.60168i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43}+ \cdots + 24 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.25312	−	1.30084i	1.00763	−	0.581753i	0.0971303	−	0.995272i	$-0.469034\pi$
$5$	2.25312	−	1.30084i	1.00763	−	0.581753i	0.910496	+	0.413519i	$0.135700\pi$
$6$			1.00000i			0.408248i
$7$	−1.49160	+	2.18521i	−0.563772	+	0.825931i
$7$	−1.49160	+	2.18521i	−0.563772	+	0.825931i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.30084	−	2.25312i	0.411362	−	0.712499i
$11$	3.11915	+	1.80084i	0.940458	+	0.542974i	0.890104	−	0.455758i	$-0.150632\pi$
$11$	3.11915	+	1.80084i	0.940458	+	0.542974i	0.0503540	+	0.998731i	$0.483965\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.60168	+	0.167055i	0.998926	+	0.0463328i
$13$	3.60168	+	0.167055i	0.998926	+	0.0463328i
$14$	−0.199160	+	2.63824i	−0.0532279	+	0.705101i
$15$			2.60168i			0.671751i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.41647	−	2.45340i	0.343545	−	0.595037i	−0.641543	−	0.767087i	$-0.721706\pi$
$17$	1.41647	−	2.45340i	0.343545	−	0.595037i	0.985088	+	0.172049i	$0.0550389\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.15537	+	0.667055i	−0.265061	+	0.153033i	−0.626641	−	0.779308i	$-0.715571\pi$
$19$	−1.15537	+	0.667055i	−0.265061	+	0.153033i	0.361580	+	0.932341i	$0.382237\pi$
$20$		−	2.60168i		−	0.581753i
$21$	−1.14664	−	2.38437i	−0.250218	−	0.520312i
$22$	3.60168			0.767881
$23$	−1.46789	−	2.54247i	−0.306077	−	0.530141i	0.671423	−	0.741074i	$-0.265683\pi$
$23$	−1.46789	−	2.54247i	−0.306077	−	0.530141i	−0.977501	+	0.210933i	$0.932350\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.884367	−	1.53177i	0.176873	−	0.306354i
$26$	3.20267	−	1.65617i	0.628096	−	0.324801i
$27$	1.00000			0.192450
$28$	1.14664	+	2.38437i	0.216695	+	0.450603i
$29$	8.97209			1.66608			0.833038	−	0.553216i	$-0.186600\pi$
$29$	8.97209			1.66608			0.833038	+	0.553216i	$0.186600\pi$
$30$	1.30084	+	2.25312i	0.237500	+	0.411362i
$31$	−3.46410	−	2.00000i	−0.622171	−	0.359211i	0.155543	−	0.987829i	$-0.450287\pi$
$31$	−3.46410	−	2.00000i	−0.622171	−	0.359211i	−0.777714	+	0.628619i	$0.783621\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−3.11915	+	1.80084i	−0.542974	+	0.313486i
$34$		−	2.83294i		−	0.485846i
$35$	−0.518152	+	6.86387i	−0.0875836	+	1.16021i
$36$	−1.00000			−0.166667
$37$	−0.144674	+	0.0835276i	−0.0237843	+	0.0137319i	−0.511845	−	0.859078i	$-0.671038\pi$
$37$	−0.144674	+	0.0835276i	−0.0237843	+	0.0137319i	0.488061	+	0.872810i	$0.337704\pi$
$38$	−0.667055	+	1.15537i	−0.108211	+	0.187426i
$39$	−1.94551	+	3.03562i	−0.311531	+	0.486088i
$40$	−1.30084	−	2.25312i	−0.205681	−	0.356250i
$41$			3.03630i			0.474191i	0.971486	+	0.237095i	$0.0761954\pi$
$41$			3.03630i			0.474191i	−0.971486	+	0.237095i	$0.923805\pi$
$42$	−2.18521	−	1.49160i	−0.337185	−	0.230159i
$43$	2.33411			0.355948			0.177974	−	0.984035i	$-0.443046\pi$
$43$	2.33411			0.355948			0.177974	+	0.984035i	$0.443046\pi$
$44$	3.11915	−	1.80084i	0.470229	−	0.271487i
$45$	−2.25312	−	1.30084i	−0.335875	−	0.193918i
$46$	−2.54247	−	1.46789i	−0.374866	−	0.216429i
$47$	−8.43580	+	4.87041i	−1.23049	+	0.710423i	−0.967132	−	0.254276i	$-0.918163\pi$
$47$	−8.43580	+	4.87041i	−1.23049	+	0.710423i	−0.263357	+	0.964699i	$0.584830\pi$
$48$	1.00000			0.144338
$49$	−2.55026	−	6.51891i	−0.364322	−	0.931273i
$50$		−	1.76873i		−	0.250137i
$51$	1.41647	+	2.45340i	0.198346	+	0.343545i
$52$	1.94551	−	3.03562i	0.269794	−	0.420964i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	9.37041			1.26351
$56$	2.18521	+	1.49160i	0.292011	+	0.199323i
$57$		−	1.33411i		−	0.176707i
$58$	7.77006	−	4.48605i	1.02026	−	0.589047i
$59$	−10.0232	−	5.78689i	−1.30491	−	0.753388i	−0.323666	−	0.946172i	$-0.604915\pi$
$59$	−10.0232	−	5.78689i	−1.30491	−	0.753388i	−0.981241	+	0.192783i	$0.938249\pi$
$60$	2.25312	+	1.30084i	0.290877	+	0.167938i
$61$	−2.01815	−	3.49554i	−0.258398	−	0.447558i	0.707415	−	0.706798i	$-0.249861\pi$
$61$	−2.01815	−	3.49554i	−0.258398	−	0.447558i	−0.965813	+	0.259240i	$0.916528\pi$
$62$	−4.00000			−0.508001
$63$	2.63824	+	0.199160i	0.332388	+	0.0250919i
$64$	−1.00000			−0.125000
$65$	8.33233	−	4.30881i	1.03350	−	0.534442i
$66$	−1.80084	+	3.11915i	−0.221668	+	0.383940i
$67$	10.1679	+	5.87041i	1.24220	+	0.717185i	0.969542	−	0.244926i	$-0.0787635\pi$
$67$	10.1679	+	5.87041i	1.24220	+	0.717185i	0.272659	+	0.962111i	$0.412097\pi$
$68$	−1.41647	−	2.45340i	−0.171773	−	0.297519i
$69$	2.93579			0.353428
$70$	2.98320	+	6.20336i	0.356561	+	0.741443i
$71$			5.76873i			0.684623i	0.939587	+	0.342311i	$0.111210\pi$
$71$			5.76873i			0.684623i	−0.939587	+	0.342311i	$0.888790\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−9.93411	−	5.73546i	−1.16270	−	0.671285i	−0.210751	−	0.977540i	$-0.567591\pi$
$73$	−9.93411	−	5.73546i	−1.16270	−	0.671285i	−0.951950	+	0.306255i	$0.900924\pi$
$74$	−0.0835276	+	0.144674i	−0.00970988	+	0.0168180i
$75$	0.884367	+	1.53177i	0.102118	+	0.176873i
$76$			1.33411i			0.153033i
$77$	−8.58773	+	4.12985i	−0.978662	+	0.470640i
$78$	−0.167055	+	3.60168i	−0.0189153	+	0.407810i
$79$	−3.37041	−	5.83773i	−0.379201	−	0.656796i	0.611745	−	0.791055i	$-0.290468\pi$
$79$	−3.37041	−	5.83773i	−0.379201	−	0.656796i	−0.990946	+	0.134259i	$0.957134\pi$
$80$	−2.25312	−	1.30084i	−0.251906	−	0.145438i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.51815	+	2.62952i	0.167652	+	0.290381i
$83$			8.10051i			0.889147i	0.895742	+	0.444573i	$0.146645\pi$
$83$			8.10051i			0.889147i	−0.895742	+	0.444573i	$0.853355\pi$
$84$	−2.63824	−	0.199160i	−0.287856	−	0.0217302i
$85$		−	7.37041i		−	0.799434i
$86$	2.02140	−	1.16706i	0.217973	−	0.125847i
$87$	−4.48605	+	7.77006i	−0.480955	+	0.833038i
$88$	1.80084	−	3.11915i	0.191970	−	0.332502i
$89$	−7.07288	+	4.08353i	−0.749723	+	0.432853i	−0.825594	−	0.564265i	$-0.809160\pi$
$89$	−7.07288	+	4.08353i	−0.749723	+	0.432853i	0.0758705	+	0.997118i	$0.475826\pi$
$90$	−2.60168			−0.274241
$91$	−5.73732	+	7.62123i	−0.601434	+	0.798922i
$92$	−2.93579			−0.306077
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	−4.87041	+	8.43580i	−0.502345	+	0.870087i
$95$	−1.73546	+	3.00591i	−0.178055	+	0.308400i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	0.139148i		−	0.0141283i	−0.999975	−	0.00706416i	$-0.997751\pi$
$97$		−	0.139148i		−	0.0141283i	0.999975	−	0.00706416i	$-0.00224861\pi$
$98$	−5.46804	−	4.37041i	−0.552356	−	0.441478i
$99$		−	3.60168i		−	0.361982i
$100$	−0.884367	−	1.53177i	−0.0884367	−	0.153177i
$101$	−1.78269	+	3.08771i	−0.177384	+	0.307238i	−0.940984	−	0.338452i	$-0.890097\pi$
$101$	−1.78269	+	3.08771i	−0.177384	+	0.307238i	0.763600	+	0.645690i	$0.223430\pi$
$102$	2.45340	+	1.41647i	0.242923	+	0.140252i
$103$	−9.53747	−	16.5194i	−0.939755	−	1.62770i	−0.765928	−	0.642927i	$-0.777720\pi$
$103$	−9.53747	−	16.5194i	−0.939755	−	1.62770i	−0.173827	−	0.984776i	$-0.555613\pi$
$104$	0.167055	−	3.60168i	0.0163811	−	0.353174i
$105$	−5.68521	−	3.88067i	−0.554819	−	0.378714i
$106$			3.00000i			0.291386i
$107$	4.03630	+	6.99108i	0.390204	+	0.675853i	0.992476	−	0.122437i	$-0.0390711\pi$
$107$	4.03630	+	6.99108i	0.390204	+	0.675853i	−0.602272	+	0.798291i	$0.705738\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−11.1451	−	6.43462i	−1.06751	−	0.616325i	−0.140007	−	0.990150i	$-0.544713\pi$
$109$	−11.1451	−	6.43462i	−1.06751	−	0.616325i	−0.927499	+	0.373825i	$0.878046\pi$
$110$	8.11502	−	4.68521i	0.773736	−	0.446717i
$111$		−	0.167055i		−	0.0158562i
$112$	2.63824	+	0.199160i	0.249291	+	0.0188189i
$113$	−19.8800			−1.87015			−0.935075	−	0.354449i	$-0.884668\pi$
$113$	−19.8800			−1.87015			−0.935075	+	0.354449i	$0.884668\pi$
$114$	−0.667055	−	1.15537i	−0.0624754	−	0.108211i
$115$	−6.61469	−	3.81899i	−0.616823	−	0.356123i
$116$	4.48605	−	7.77006i	0.416519	−	0.721432i
$117$	−1.65617	−	3.20267i	−0.153113	−	0.296087i
$118$	−11.5738			−1.06545
$119$	3.24838	+	6.75478i	0.297779	+	0.619210i
$120$	2.60168			0.237500
$121$	0.986046	+	1.70788i	0.0896406	+	0.155262i
$122$	−3.49554	−	2.01815i	−0.316471	−	0.182715i
$123$	−2.62952	−	1.51815i	−0.237095	−	0.136887i
$124$	−3.46410	+	2.00000i	−0.311086	+	0.179605i
$125$			8.40672i			0.751920i
$126$	2.38437	−	1.14664i	0.212416	−	0.102151i
$127$	−10.0386			−0.890785			−0.445392	−	0.895335i	$-0.646936\pi$
$127$	−10.0386			−0.890785			−0.445392	+	0.895335i	$0.646936\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.16706	+	2.02140i	−0.102753	+	0.177974i
$130$	5.06160	−	7.89770i	0.443932	−	0.692674i
$131$	−4.05562	−	7.02454i	−0.354341	−	0.613737i	0.632664	−	0.774427i	$-0.281962\pi$
$131$	−4.05562	−	7.02454i	−0.354341	−	0.613737i	−0.987005	+	0.160690i	$0.948628\pi$
$132$			3.60168i			0.313486i
$133$	0.265702	−	3.51971i	0.0230393	−	0.305198i
$134$	11.7408			1.01425
$135$	2.25312	−	1.30084i	0.193918	−	0.111958i
$136$	−2.45340	−	1.41647i	−0.210378	−	0.121462i
$137$	4.00934	+	2.31479i	0.342541	+	0.197766i	0.661395	−	0.750038i	$-0.269965\pi$
$137$	4.00934	+	2.31479i	0.342541	+	0.197766i	−0.318854	+	0.947804i	$0.603298\pi$
$138$	2.54247	−	1.46789i	0.216429	−	0.124955i
$139$	−0.935789			−0.0793726			−0.0396863	−	0.999212i	$-0.512636\pi$
$139$	−0.935789			−0.0793726			−0.0396863	+	0.999212i	$0.512636\pi$
$140$	5.68521	+	3.88067i	0.480488	+	0.327976i
$141$		−	9.74083i		−	0.820326i
$142$	2.88437	+	4.99587i	0.242051	+	0.419244i
$143$	10.9333	+	7.00712i	0.914290	+	0.585964i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	20.2152	−	11.6713i	1.67878	−	0.969245i
$146$	−11.4709			−0.949341
$147$	6.92067	+	1.05087i	0.570807	+	0.0866741i
$148$			0.167055i			0.0137319i
$149$	7.04871	−	4.06957i	0.577453	−	0.333392i	−0.182668	−	0.983175i	$-0.558473\pi$
$149$	7.04871	−	4.06957i	0.577453	−	0.333392i	0.760120	+	0.649782i	$0.225140\pi$
$150$	1.53177	+	0.884367i	0.125068	+	0.0722083i
$151$	17.3278	+	10.0042i	1.41011	+	0.814130i	0.995399	−	0.0958208i	$-0.0305476\pi$
$151$	17.3278	+	10.0042i	1.41011	+	0.814130i	0.414716	+	0.909951i	$0.363881\pi$
$152$	0.667055	+	1.15537i	0.0541053	+	0.0937132i
$153$	−2.83294			−0.229030
$154$	−5.37227	+	7.87041i	−0.432910	+	0.634216i
$155$	−10.4067			−0.835888
$156$	1.65617	+	3.20267i	0.132599	+	0.256419i
$157$	−10.6724	+	18.4852i	−0.851752	+	1.47528i	0.0278743	+	0.999611i	$0.491126\pi$
$157$	−10.6724	+	18.4852i	−0.851752	+	1.47528i	−0.879626	+	0.475666i	$0.842207\pi$
$158$	−5.83773	−	3.37041i	−0.464425	−	0.268136i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$	−2.60168			−0.205681
$161$	7.74533	+	0.584693i	0.610418	+	0.0460803i
$162$			1.00000i			0.0785674i
$163$	−0.890194	+	0.513954i	−0.0697254	+	0.0402560i	−0.534457	−	0.845195i	$-0.679484\pi$
$163$	−0.890194	+	0.513954i	−0.0697254	+	0.0402560i	0.464732	+	0.885451i	$0.346151\pi$
$164$	2.62952	+	1.51815i	0.205331	+	0.118548i
$165$	−4.68521	+	8.11502i	−0.364743	+	0.631753i
$166$	4.05026	+	7.01525i	0.314361	+	0.544489i
$167$			5.96976i			0.461954i	0.972959	+	0.230977i	$0.0741922\pi$
$167$			5.96976i			0.461954i	−0.972959	+	0.230977i	$0.925808\pi$
$168$	−2.38437	+	1.14664i	−0.183958	+	0.0884655i
$169$	12.9442	+	1.20336i	0.995707	+	0.0925660i
$170$	−3.68521	−	6.38297i	−0.282642	−	0.489551i
$171$	1.15537	+	0.667055i	0.0883536	+	0.0510110i
$172$	1.16706	−	2.02140i	0.0889871	−	0.154130i
$173$	8.29108	+	14.3606i	0.630359	+	1.09181i	0.987478	+	0.157756i	$0.0504258\pi$
$173$	8.29108	+	14.3606i	0.630359	+	1.09181i	−0.357119	+	0.934059i	$0.616241\pi$
$174$			8.97209i			0.680173i
$175$	2.02811	+	4.21731i	0.153311	+	0.318799i
$176$		−	3.60168i		−	0.271487i
$177$	10.0232	−	5.78689i	0.753388	−	0.434969i
$178$	−4.08353	+	7.07288i	−0.306073	+	0.530135i
$179$	9.37041	−	16.2300i	0.700378	−	1.21309i	−0.267956	−	0.963431i	$-0.586348\pi$
$179$	9.37041	−	16.2300i	0.700378	−	1.21309i	0.968334	−	0.249659i	$-0.0803184\pi$
$180$	−2.25312	+	1.30084i	−0.167938	+	0.0969589i
$181$	−0.426228			−0.0316813			−0.0158406	−	0.999875i	$-0.505042\pi$
$181$	−0.426228			−0.0316813			−0.0158406	+	0.999875i	$0.505042\pi$
$182$	−1.15804	+	9.46884i	−0.0858400	+	0.701877i
$183$	4.03630			0.298372
$184$	−2.54247	+	1.46789i	−0.187433	+	0.108215i
$185$	−0.217312	+	0.376395i	−0.0159771	+	0.0276731i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	8.83637	−	5.10168i	0.646179	−	0.373072i
$188$			9.74083i			0.710423i
$189$	−1.49160	+	2.18521i	−0.108498	+	0.158950i
$190$			3.47093i			0.251808i
$191$	4.43462	+	7.68099i	0.320878	+	0.555777i	0.980669	−	0.195672i	$-0.0626887\pi$
$191$	4.43462	+	7.68099i	0.320878	+	0.555777i	−0.659791	+	0.751449i	$0.729355\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−6.06945	−	3.50420i	−0.436888	−	0.252238i	0.265388	−	0.964142i	$-0.414500\pi$
$193$	−6.06945	−	3.50420i	−0.436888	−	0.252238i	−0.702277	+	0.711904i	$0.747833\pi$
$194$	−0.0695739	−	0.120505i	−0.00499511	−	0.00865179i
$195$	−0.434624	+	9.37041i	−0.0311241	+	0.671029i
$196$	−6.92067	−	1.05087i	−0.494334	−	0.0750620i
$197$		−	17.8050i		−	1.26856i	−0.773105	−	0.634278i	$-0.781297\pi$
$197$		−	17.8050i		−	1.26856i	0.773105	−	0.634278i	$-0.218703\pi$
$198$	−1.80084	−	3.11915i	−0.127980	−	0.221668i
$199$	13.5545	−	23.4770i	0.960850	−	1.66424i	0.240475	−	0.970655i	$-0.422697\pi$
$199$	13.5545	−	23.4770i	0.960850	−	1.66424i	0.720374	−	0.693585i	$-0.243970\pi$
$200$	−1.53177	−	0.884367i	−0.108312	−	0.0625342i
$201$	−10.1679	+	5.87041i	−0.717185	+	0.414067i
$202$			3.56538i			0.250859i
$203$	−13.3828	+	19.6059i	−0.939287	+	1.37606i
$204$	2.83294			0.198346
$205$	3.94974	+	6.84116i	0.275862	+	0.477807i
$206$	−16.5194	−	9.53747i	−1.15096	−	0.664507i
$207$	−1.46789	+	2.54247i	−0.102026	+	0.176714i
$208$	−1.65617	−	3.20267i	−0.114834	−	0.222065i
$209$	−4.80504			−0.332371
$210$	−6.86387	−	0.518152i	−0.473652	−	0.0357559i
$211$	22.6743			1.56096			0.780481	−	0.625179i	$-0.214974\pi$
$211$	22.6743			1.56096			0.780481	+	0.625179i	$0.214974\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	−4.99587	−	2.88437i	−0.342311	−	0.197634i
$214$	6.99108	+	4.03630i	0.477901	+	0.275916i
$215$	5.25903	−	3.03630i	0.358663	−	0.207074i
$216$		−	1.00000i		−	0.0680414i
$217$	9.53747	−	4.58658i	0.647446	−	0.311357i
$218$	−12.8692			−0.871615
$219$	9.93411	−	5.73546i	0.671285	−	0.387567i
$220$	4.68521	−	8.11502i	0.315877	−	0.547114i
$221$	5.51153	−	8.59974i	0.370746	−	0.578481i
$222$	−0.0835276	−	0.144674i	−0.00560600	−	0.00970988i
$223$		−	9.19496i		−	0.615740i	−0.951428	−	0.307870i	$-0.900384\pi$
$223$		−	9.19496i		−	0.615740i	0.951428	−	0.307870i	$-0.0996162\pi$
$224$	2.38437	−	1.14664i	0.159312	−	0.0766134i
$225$	−1.76873			−0.117916
$226$	−17.2166	+	9.93999i	−1.14523	+	0.661198i
$227$	−11.7238	−	6.76873i	−0.778135	−	0.449257i	0.0576337	−	0.998338i	$-0.481644\pi$
$227$	−11.7238	−	6.76873i	−0.778135	−	0.449257i	−0.835769	+	0.549081i	$0.814978\pi$
$228$	−1.15537	−	0.667055i	−0.0765165	−	0.0441768i
$229$	15.9407	−	9.20336i	1.05339	−	0.608175i	0.129794	−	0.991541i	$-0.458569\pi$
$229$	15.9407	−	9.20336i	1.05339	−	0.608175i	0.923597	+	0.383366i	$0.125235\pi$
$230$	−7.63798			−0.503634
$231$	0.717312	−	9.50211i	0.0471957	−	0.625193i
$232$		−	8.97209i		−	0.589047i
$233$	5.86505	+	10.1586i	0.384232	+	0.665510i	0.991662	−	0.128863i	$-0.0411329\pi$
$233$	5.86505	+	10.1586i	0.384232	+	0.665510i	−0.607430	+	0.794373i	$0.707800\pi$
$234$	−3.03562	−	1.94551i	−0.198445	−	0.127182i
$235$	−12.6713	+	21.9473i	−0.826581	+	1.43168i
$236$	−10.0232	+	5.78689i	−0.652453	+	0.376694i
$237$	6.74083			0.437864
$238$	6.19057	+	4.22562i	0.401275	+	0.273906i
$239$		−	11.1731i		−	0.722729i	−0.932425	−	0.361365i	$-0.882311\pi$
$239$		−	11.1731i		−	0.722729i	0.932425	−	0.361365i	$-0.117689\pi$
$240$	2.25312	−	1.30084i	0.145438	−	0.0839688i
$241$	−12.7659	−	7.37041i	−0.822326	−	0.474770i	0.0288920	−	0.999583i	$-0.490802\pi$
$241$	−12.7659	−	7.37041i	−0.822326	−	0.474770i	−0.851218	+	0.524812i	$0.824135\pi$
$242$	1.70788	+	0.986046i	0.109787	+	0.0633855i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.03630			−0.258398
$245$	−14.2261	−	11.3704i	−0.908872	−	0.726429i
$246$	−3.03630			−0.193588
$247$	−4.27272	+	2.20951i	−0.271867	+	0.140588i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−7.01525	−	4.05026i	−0.444573	−	0.256675i
$250$	4.20336	+	7.28043i	0.265844	+	0.460455i
$251$	22.9465			1.44837			0.724186	−	0.689605i	$-0.242216\pi$
$251$	22.9465			1.44837			0.724186	+	0.689605i	$0.242216\pi$
$252$	1.49160	−	2.18521i	0.0939620	−	0.137655i
$253$		−	10.5738i		−	0.664767i
$254$	−8.69371	+	5.01932i	−0.545492	+	0.314940i
$255$	6.38297	+	3.68521i	0.399717	+	0.230777i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.370413	+	0.641575i	0.0231058	+	0.0400203i	0.877347	−	0.479856i	$-0.159311\pi$
$257$	0.370413	+	0.641575i	0.0231058	+	0.0400203i	−0.854241	+	0.519877i	$0.825978\pi$
$258$			2.33411i			0.145315i
$259$	0.0332708	−	0.440732i	0.00206735	−	0.0273858i
$260$	0.434624	−	9.37041i	0.0269542	−	0.581128i
$261$	−4.48605	−	7.77006i	−0.277679	−	0.480955i
$262$	−7.02454	−	4.05562i	−0.433978	−	0.250557i
$263$	10.5042	−	18.1938i	0.647717	−	1.12188i	−0.335950	−	0.941880i	$-0.609057\pi$
$263$	10.5042	−	18.1938i	0.647717	−	1.12188i	0.983667	−	0.179998i	$-0.0576092\pi$
$264$	1.80084	+	3.11915i	0.110834	+	0.191970i
$265$			7.80504i			0.479460i
$266$	−1.52975	−	3.18101i	−0.0937950	−	0.195040i
$267$		−	8.16706i		−	0.499816i
$268$	10.1679	−	5.87041i	0.621101	−	0.358593i
$269$	15.5587	−	26.9484i	0.948628	−	1.64307i	0.200308	−	0.979733i	$-0.435806\pi$
$269$	15.5587	−	26.9484i	0.948628	−	1.64307i	0.748319	−	0.663339i	$-0.230861\pi$
$270$	1.30084	−	2.25312i	0.0791666	−	0.137121i
$271$	1.73932	−	1.00420i	0.105656	−	0.0610007i	−0.446241	−	0.894913i	$-0.647237\pi$
$271$	1.73932	−	1.00420i	0.105656	−	0.0610007i	0.551897	+	0.833912i	$0.313904\pi$
$272$	−2.83294			−0.171773
$273$	−3.73152	−	8.77928i	−0.225842	−	0.531346i
$274$	4.62959			0.279684
$275$	5.51694	−	3.18521i	0.332684	−	0.192075i
$276$	1.46789	−	2.54247i	0.0883569	−	0.153039i
$277$	−7.68404	+	13.3091i	−0.461689	+	0.799669i	−0.999045	−	0.0436862i	$-0.986090\pi$
$277$	−7.68404	+	13.3091i	−0.461689	+	0.799669i	0.537356	+	0.843356i	$0.319423\pi$
$278$	−0.810417	+	0.467895i	−0.0486056	+	0.0280625i
$279$			4.00000i			0.239474i
$280$	6.86387	+	0.518152i	0.410194	+	0.0309655i
$281$			16.6682i			0.994343i	0.867652	+	0.497171i	$0.165628\pi$
$281$			16.6682i			0.994343i	−0.867652	+	0.497171i	$0.834372\pi$
$282$	−4.87041	−	8.43580i	−0.290029	−	0.502345i
$283$	−8.90252	+	15.4196i	−0.529200	+	0.916601i	0.470220	+	0.882549i	$0.344174\pi$
$283$	−8.90252	+	15.4196i	−0.529200	+	0.916601i	−0.999420	+	0.0340519i	$0.989159\pi$
$284$	4.99587	+	2.88437i	0.296450	+	0.171156i
$285$	−1.73546	−	3.00591i	−0.102800	−	0.178055i
$286$	12.9721	+	0.601679i	0.767056	+	0.0355780i
$287$	−6.63495	−	4.52895i	−0.391649	−	0.267336i
$288$			1.00000i			0.0589256i
$289$	4.48721	+	7.77208i	0.263954	+	0.457181i
$290$	11.6713	−	20.2152i	0.685360	−	1.18708i
$291$	0.120505	+	0.0695739i	0.00706416	+	0.00407849i
$292$	−9.93411	+	5.73546i	−0.581350	+	0.335643i
$293$			26.4733i			1.54658i	0.634050	+	0.773292i	$0.281391\pi$
$293$			26.4733i			1.54658i	−0.634050	+	0.773292i	$0.718609\pi$
$294$	6.51891	−	2.55026i	0.380191	−	0.148734i
$295$	−30.1112			−1.75314
$296$	0.0835276	+	0.144674i	0.00485494	+	0.00840901i
$297$	3.11915	+	1.80084i	0.180991	+	0.104495i
$298$	4.06957	−	7.04871i	0.235744	−	0.408321i
$299$	−4.86215	−	9.40237i	−0.281186	−	0.543753i
$300$	1.76873			0.102118
$301$	−3.48156	+	5.10051i	−0.200674	+	0.293989i
$302$	20.0084			1.15135
$303$	−1.78269	−	3.08771i	−0.102413	−	0.177384i
$304$	1.15537	+	0.667055i	0.0662652	+	0.0382582i
$305$	−9.09428	−	5.25058i	−0.520737	−	0.300647i
$306$	−2.45340	+	1.41647i	−0.140252	+	0.0809743i
$307$		−	23.2783i		−	1.32856i	−0.747483	−	0.664281i	$-0.768738\pi$
$307$		−	23.2783i		−	1.32856i	0.747483	−	0.664281i	$-0.231262\pi$
$308$	−0.717312	+	9.50211i	−0.0408726	+	0.541433i
$309$	19.0749			1.08514
$310$	−9.01248	+	5.20336i	−0.511875	+	0.295531i
$311$	−8.27293	+	14.3291i	−0.469115	+	0.812531i	−0.999377	−	0.0353031i	$-0.988760\pi$
$311$	−8.27293	+	14.3291i	−0.469115	+	0.812531i	0.530262	+	0.847834i	$0.322094\pi$
$312$	3.03562	+	1.94551i	0.171858	+	0.110143i
$313$	5.01395	+	8.68442i	0.283405	+	0.490873i	0.972221	−	0.234064i	$-0.0752025\pi$
$313$	5.01395	+	8.68442i	0.283405	+	0.490873i	−0.688816	+	0.724936i	$0.741869\pi$
$314$			21.3448i			1.20456i
$315$	6.20336	−	2.98320i	0.349520	−	0.168084i
$316$	−6.74083			−0.379201
$317$	18.5408	−	10.7045i	1.04135	−	0.601226i	0.121137	−	0.992636i	$-0.461346\pi$
$317$	18.5408	−	10.7045i	1.04135	−	0.601226i	0.920216	+	0.391410i	$0.128012\pi$
$318$	−2.59808	−	1.50000i	−0.145693	−	0.0841158i
$319$	27.9853	+	16.1573i	1.56687	+	0.904635i
$320$	−2.25312	+	1.30084i	−0.125953	+	0.0727191i
$321$	−8.07261			−0.450569
$322$	7.00000	−	3.36631i	0.390095	−	0.187597i
$323$			3.77946i			0.210295i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	3.44110	−	5.36920i	0.190878	−	0.297830i
$326$	−0.513954	+	0.890194i	−0.0284653	+	0.0493033i
$327$	11.1451	−	6.43462i	0.616325	−	0.355836i
$328$	3.03630			0.167652
$329$	1.93999	−	25.6987i	0.106955	−	1.41681i
$330$			9.37041i			0.515824i
$331$	−31.0561	+	17.9302i	−1.70700	+	0.985535i	−0.768761	+	0.639536i	$0.779126\pi$
$331$	−31.0561	+	17.9302i	−1.70700	+	0.985535i	−0.938235	+	0.345998i	$0.887540\pi$
$332$	7.01525	+	4.05026i	0.385012	+	0.222287i
$333$	0.144674	+	0.0835276i	0.00792809	+	0.00457728i
$334$	2.98488	+	5.16997i	0.163325	+	0.282888i
$335$	30.5459			1.66890
$336$	−1.49160	+	2.18521i	−0.0813735	+	0.119213i
$337$	6.73850			0.367069			0.183535	−	0.983013i	$-0.441246\pi$
$337$	6.73850			0.367069			0.183535	+	0.983013i	$0.441246\pi$
$338$	11.8117	−	5.42995i	0.642470	−	0.295351i
$339$	9.93999	−	17.2166i	0.539866	−	0.935075i
$340$	−6.38297	−	3.68521i	−0.346165	−	0.199858i
$341$	−7.20336	−	12.4766i	−0.390084	−	0.675645i
$342$	1.33411			0.0721404
$343$	18.0491	+	4.15077i	0.974561	+	0.224121i
$344$		−	2.33411i		−	0.125847i
$345$	6.61469	−	3.81899i	0.356123	−	0.205608i
$346$	14.3606	+	8.29108i	0.772029	+	0.445731i
$347$	−17.2869	+	29.9418i	−0.928009	+	1.60736i	−0.141359	+	0.989958i	$0.545147\pi$
$347$	−17.2869	+	29.9418i	−0.928009	+	1.60736i	−0.786650	+	0.617400i	$0.788186\pi$
$348$	4.48605	+	7.77006i	0.240477	+	0.416519i
$349$		−	21.7771i		−	1.16570i	−0.812579	−	0.582852i	$-0.801937\pi$
$349$		−	21.7771i		−	1.16570i	0.812579	−	0.582852i	$-0.198063\pi$
$350$	3.86505	+	2.63824i	0.206596	+	0.141020i
$351$	3.60168	+	0.167055i	0.192243	+	0.00891675i
$352$	−1.80084	−	3.11915i	−0.0959851	−	0.166251i
$353$	17.6244	+	10.1755i	0.938052	+	0.541585i	0.889349	−	0.457229i	$-0.151158\pi$
$353$	17.6244	+	10.1755i	0.938052	+	0.541585i	0.0487029	+	0.998813i	$0.484491\pi$
$354$	5.78689	−	10.0232i	0.307570	−	0.532726i
$355$	7.50420	+	12.9977i	0.398281	+	0.689844i
$356$			8.16706i			0.432853i
$357$	−7.47400	−	0.564211i	−0.395566	−	0.0298612i
$358$		−	18.7408i		−	0.990483i
$359$	1.24040	−	0.716146i	0.0654659	−	0.0377968i	−0.466910	−	0.884305i	$-0.654633\pi$
$359$	1.24040	−	0.716146i	0.0654659	−	0.0377968i	0.532376	+	0.846508i	$0.321299\pi$
$360$	−1.30084	+	2.25312i	−0.0685603	+	0.118750i
$361$	−8.61007	+	14.9131i	−0.453162	+	0.784899i
$362$	−0.369125	+	0.213114i	−0.0194008	+	0.0112010i
$363$	−1.97209			−0.103508
$364$	3.73152	+	8.77928i	0.195585	+	0.460159i
$365$	−29.8437			−1.56209
$366$	3.49554	−	2.01815i	0.182715	−	0.105490i
$367$	−12.1755	+	21.0885i	−0.635553	+	1.10081i	0.350844	+	0.936434i	$0.385895\pi$
$367$	−12.1755	+	21.0885i	−0.635553	+	1.10081i	−0.986398	+	0.164377i	$0.947439\pi$
$368$	−1.46789	+	2.54247i	−0.0765193	+	0.132535i
$369$	2.62952	−	1.51815i	0.136887	−	0.0790318i
$370$			0.434624i			0.0225950i
$371$	−3.43993	−	7.15310i	−0.178592	−	0.371371i
$372$		−	4.00000i		−	0.207390i
$373$	−15.9763	−	27.6717i	−0.827221	−	1.43279i	−0.900210	−	0.435456i	$-0.856587\pi$
$373$	−15.9763	−	27.6717i	−0.827221	−	1.43279i	0.0729891	−	0.997333i	$-0.476746\pi$
$374$	5.10168	−	8.83637i	0.263802	−	0.456918i
$375$	−7.28043	−	4.20336i	−0.375960	−	0.217060i
$376$	4.87041	+	8.43580i	0.251172	+	0.435043i
$377$	32.3146	+	1.49883i	1.66429	+	0.0771939i
$378$	−0.199160	+	2.63824i	−0.0102437	+	0.135697i
$379$			2.79664i			0.143654i	0.997417	+	0.0718269i	$0.0228829\pi$
$379$			2.79664i			0.143654i	−0.997417	+	0.0718269i	$0.977117\pi$
$380$	1.73546	+	3.00591i	0.0890274	+	0.154200i
$381$	5.01932	−	8.69371i	0.257147	−	0.445392i
$382$	7.68099	+	4.43462i	0.392994	+	0.226895i
$383$	8.52487	−	4.92184i	0.435600	−	0.251494i	−0.266129	−	0.963937i	$-0.585745\pi$
$383$	8.52487	−	4.92184i	0.435600	−	0.251494i	0.701730	+	0.712443i	$0.252411\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−13.9769	+	20.4763i	−0.712329	+	1.04357i
$386$	−7.00840			−0.356718
$387$	−1.16706	−	2.02140i	−0.0593247	−	0.102753i
$388$	−0.120505	−	0.0695739i	−0.00611774	−	0.00353208i
$389$	−8.19057	+	14.1865i	−0.415278	+	0.719283i	−0.995458	−	0.0952056i	$-0.969649\pi$
$389$	−8.19057	+	14.1865i	−0.415278	+	0.719283i	0.580179	+	0.814489i	$0.302982\pi$
$390$	4.30881	+	8.33233i	0.218185	+	0.421924i
$391$	−8.31693			−0.420605
$392$	−6.51891	+	2.55026i	−0.329255	+	0.128807i
$393$	8.11124			0.409158
$394$	−8.90252	−	15.4196i	−0.448502	−	0.776829i
$395$	−15.1879	−	8.76873i	−0.764186	−	0.441203i
$396$	−3.11915	−	1.80084i	−0.156743	−	0.0904956i
$397$	−4.71379	+	2.72151i	−0.236579	+	0.136589i	−0.613603	−	0.789615i	$-0.710281\pi$
$397$	−4.71379	+	2.72151i	−0.236579	+	0.136589i	0.377025	+	0.926203i	$0.376947\pi$
$398$		−	27.1089i		−	1.35885i
$399$	2.91531	+	1.98996i	0.145948	+	0.0996226i
$400$	−1.76873			−0.0884367
$401$	15.2214	−	8.78805i	0.760118	−	0.438854i	−0.0692201	−	0.997601i	$-0.522051\pi$
$401$	15.2214	−	8.78805i	0.760118	−	0.438854i	0.829338	+	0.558747i	$0.188718\pi$
$402$	−5.87041	+	10.1679i	−0.292790	+	0.507126i
$403$	−12.1425	−	7.78205i	−0.604860	−	0.387652i
$404$	1.78269	+	3.08771i	0.0886920	+	0.153619i
$405$			2.60168i			0.129278i
$406$	−1.78689	+	23.6706i	−0.0886817	+	1.17475i
$407$	−0.601679			−0.0298241
$408$	2.45340	−	1.41647i	0.121462	−	0.0701258i
$409$	−16.4618	−	9.50420i	−0.813981	−	0.469952i	0.0343552	−	0.999410i	$-0.489062\pi$
$409$	−16.4618	−	9.50420i	−0.813981	−	0.469952i	−0.848337	+	0.529457i	$0.822396\pi$
$410$	6.84116	+	3.94974i	0.337861	+	0.195064i
$411$	−4.00934	+	2.31479i	−0.197766	+	0.114180i
$412$	−19.0749			−0.939755
$413$	27.5961	−	13.2710i	1.35792	−	0.653023i
$414$			2.93579i			0.144286i
$415$	10.5375	+	18.2514i	0.517264	+	0.895928i
$416$	−3.03562	−	1.94551i	−0.148833	−	0.0953867i
$417$	0.467895	−	0.810417i	0.0229129	−	0.0396863i
$418$	−4.16128	+	2.40252i	−0.203535	+	0.117511i
$419$	5.48165			0.267796			0.133898	−	0.990995i	$-0.457250\pi$
$419$	5.48165			0.267796			0.133898	+	0.990995i	$0.457250\pi$
$420$	−6.20336	+	2.98320i	−0.302693	+	0.145565i
$421$			3.16472i			0.154239i	0.997022	+	0.0771196i	$0.0245723\pi$
$421$			3.16472i			0.154239i	−0.997022	+	0.0771196i	$0.975428\pi$
$422$	19.6365	−	11.3371i	0.955890	−	0.551883i
$423$	8.43580	+	4.87041i	0.410163	+	0.236808i
$424$	2.59808	+	1.50000i	0.126174	+	0.0728464i
$425$	−2.50536	−	4.33942i	−0.121528	−	0.210493i
$426$	−5.76873			−0.279496
$427$	10.6488	+	0.803872i	0.515329	+	0.0389021i
$428$	8.07261			0.390204
$429$	−11.5350	+	5.96498i	−0.556915	+	0.287992i
$430$	3.03630	−	5.25903i	0.146424	−	0.253613i
$431$	−13.3688	−	7.71848i	−0.643952	−	0.371786i	0.142183	−	0.989840i	$-0.454588\pi$
$431$	−13.3688	−	7.71848i	−0.643952	−	0.371786i	−0.786135	+	0.618054i	$0.787921\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	13.9419			0.670003			0.335001	−	0.942218i	$-0.391263\pi$
$433$	13.9419			0.670003			0.335001	+	0.942218i	$0.391263\pi$
$434$	5.96640	−	8.74083i	0.286396	−	0.419573i
$435$			23.3425i			1.11919i
$436$	−11.1451	+	6.43462i	−0.533753	+	0.308163i
$437$	3.39193	+	1.95833i	0.162258	+	0.0936798i
$438$	5.73546	−	9.93411i	0.274051	−	0.474670i
$439$	13.6936	+	23.7180i	0.653560	+	1.13200i	0.982253	+	0.187562i	$0.0600586\pi$
$439$	13.6936	+	23.7180i	0.653560	+	1.13200i	−0.328693	+	0.944437i	$0.606608\pi$
$440$		−	9.37041i		−	0.446717i
$441$	−4.37041	+	5.46804i	−0.208115	+	0.260383i
$442$	0.473258	−	10.2034i	0.0225106	−	0.485324i
$443$	−12.0556	−	20.8809i	−0.572780	−	0.992084i	−0.996279	−	0.0861872i	$-0.972532\pi$
$443$	−12.0556	−	20.8809i	−0.572780	−	0.992084i	0.423499	−	0.905896i	$-0.360802\pi$
$444$	−0.144674	−	0.0835276i	−0.00686593	−	0.00396404i
$445$	−10.6240	+	18.4014i	−0.503627	+	0.872308i
$446$	−4.59748	−	7.96307i	−0.217697	−	0.377062i
$447$			8.13915i			0.384968i
$448$	1.49160	−	2.18521i	0.0704715	−	0.103241i
$449$		−	2.59095i		−	0.122275i	−0.998129	−	0.0611373i	$-0.980527\pi$
$449$		−	2.59095i		−	0.122275i	0.998129	−	0.0611373i	$-0.0194728\pi$
$450$	−1.53177	+	0.884367i	−0.0722083	+	0.0416895i
$451$	−5.46789	+	9.47067i	−0.257473	+	0.445957i
$452$	−9.93999	+	17.2166i	−0.467538	+	0.809799i
$453$	−17.3278	+	10.0042i	−0.814130	+	0.470038i
$454$	−13.5375			−0.635345
$455$	−3.01286	+	24.6349i	−0.141245	+	1.15490i
$456$	−1.33411			−0.0624754
$457$	−9.06607	+	5.23430i	−0.424093	+	0.244850i	−0.696827	−	0.717239i	$-0.745405\pi$
$457$	−9.06607	+	5.23430i	−0.424093	+	0.244850i	0.272734	+	0.962089i	$0.412072\pi$
$458$	9.20336	−	15.9407i	0.430045	−	0.744859i
$459$	1.41647	−	2.45340i	0.0661153	−	0.114515i
$460$	−6.61469	+	3.81899i	−0.308411	+	0.178061i
$461$		−	30.0168i		−	1.39802i	−0.715111	−	0.699011i	$-0.753624\pi$
$461$		−	30.0168i		−	1.39802i	0.715111	−	0.699011i	$-0.246376\pi$
$462$	−4.12985	−	8.58773i	−0.192138	−	0.399537i
$463$			19.4649i			0.904609i	0.891864	+	0.452304i	$0.149398\pi$
$463$			19.4649i			0.904609i	−0.891864	+	0.452304i	$0.850602\pi$
$464$	−4.48605	−	7.77006i	−0.208259	−	0.360716i
$465$	5.20336	−	9.01248i	0.241300	−	0.417944i
$466$	10.1586	+	5.86505i	0.470586	+	0.271693i
$467$	0.150069	+	0.259927i	0.00694437	+	0.0120280i	0.869477	−	0.493974i	$-0.164456\pi$
$467$	0.150069	+	0.259927i	0.00694437	+	0.0120280i	−0.862532	+	0.506002i	$0.831123\pi$
$468$	−3.60168	−	0.167055i	−0.166488	−	0.00772213i
$469$	−27.9944	+	13.4626i	−1.29266	+	0.621643i
$470$			25.3425i			1.16896i
$471$	−10.6724	−	18.4852i	−0.491759	−	0.851752i
$472$	−5.78689	+	10.0232i	−0.266363	+	0.461354i
$473$	7.28043	+	4.20336i	0.334755	+	0.193271i
$474$	5.83773	−	3.37041i	0.268136	−	0.154808i
$475$			2.35969i			0.108270i
$476$	7.47400	+	0.564211i	0.342570	+	0.0258605i
$477$	3.00000			0.137361
$478$	−5.58656	−	9.67621i	−0.255523	−	0.442579i
$479$	20.4248	+	11.7922i	0.933232	+	0.538802i	0.887832	−	0.460167i	$-0.152211\pi$
$479$	20.4248	+	11.7922i	0.933232	+	0.538802i	0.0453996	+	0.998969i	$0.485544\pi$
$480$	1.30084	−	2.25312i	0.0593749	−	0.102840i
$481$	−0.535023	+	0.276671i	−0.0243950	+	0.0126151i
$482$	−14.7408			−0.671426
$483$	−4.37902	+	6.41531i	−0.199253	+	0.291907i
$484$	1.97209			0.0896406
$485$	−0.181009	−	0.313517i	−0.00821919	−	0.0142361i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	29.6544	+	17.1210i	1.34377	+	0.775826i	0.987359	−	0.158502i	$-0.0506666\pi$
$487$	29.6544	+	17.1210i	1.34377	+	0.775826i	0.356412	+	0.934329i	$0.384000\pi$
$488$	−3.49554	+	2.01815i	−0.158236	+	0.0913574i
$489$		−	1.02791i		−	0.0464836i
$490$	−18.0054	−	2.73402i	−0.813399	−	0.123510i
$491$	−39.7553			−1.79413			−0.897065	−	0.441898i	$-0.854305\pi$
$491$	−39.7553			−1.79413			−0.897065	+	0.441898i	$0.854305\pi$
$492$	−2.62952	+	1.51815i	−0.118548	+	0.0684436i
$493$	12.7087	−	22.0122i	0.572372	−	0.991377i
$494$	−2.59553	+	4.04985i	−0.116778	+	0.182211i
$495$	−4.68521	−	8.11502i	−0.210584	−	0.364743i
$496$			4.00000i			0.179605i
$497$	−12.6059	−	8.60465i	−0.565451	−	0.385971i
$498$	−8.10051			−0.362993
$499$	10.6091	−	6.12519i	0.474931	−	0.274201i	−0.243371	−	0.969933i	$-0.578253\pi$
$499$	10.6091	−	6.12519i	0.474931	−	0.274201i	0.718301	+	0.695732i	$0.244920\pi$
$500$	7.28043	+	4.20336i	0.325591	+	0.187980i
$501$	−5.16997	−	2.98488i	−0.230977	−	0.133355i
$502$	19.8723	−	11.4733i	0.886943	−	0.512077i
$503$	2.12842			0.0949016			0.0474508	−	0.998874i	$-0.484890\pi$
$503$	2.12842			0.0949016			0.0474508	+	0.998874i	$0.484890\pi$
$504$	0.199160	−	2.63824i	0.00887131	−	0.117517i
$505$			9.27596i			0.412775i
$506$	−5.28689	−	9.15715i	−0.235031	−	0.407085i
$507$	−7.51423	+	10.6083i	−0.333719	+	0.471132i
$508$	−5.01932	+	8.69371i	−0.222696	+	0.385721i
$509$	29.1741	−	16.8437i	1.29312	−	0.746583i	0.313913	−	0.949452i	$-0.398360\pi$
$509$	29.1741	−	16.8437i	1.29312	−	0.746583i	0.979206	+	0.202869i	$0.0650266\pi$
$510$	7.37041			0.326367
$511$	27.3509	−	13.1531i	1.20993	−	0.581858i
$512$			1.00000i			0.0441942i
$513$	−1.15537	+	0.667055i	−0.0510110	+	0.0294512i
$514$	0.641575	+	0.370413i	0.0282987	+	0.0163382i
$515$	−42.9781	−	24.8134i	−1.89384	−	1.09341i
$516$	1.16706	+	2.02140i	0.0513767	+	0.0889871i
$517$	−35.0833			−1.54296
$518$	−0.191553	−	0.398321i	−0.00841635	−	0.0175012i
$519$	−16.5822			−0.727876
$520$	−4.30881	−	8.33233i	−0.188954	−	0.365397i
$521$	0.130752	−	0.226469i	0.00572835	−	0.00992180i	−0.863147	−	0.504953i	$-0.831510\pi$
$521$	0.130752	−	0.226469i	0.00572835	−	0.00992180i	0.868875	+	0.495031i	$0.164843\pi$
$522$	−7.77006	−	4.48605i	−0.340086	−	0.196349i
$523$	−5.23966	−	9.07536i	−0.229114	−	0.396838i	0.728432	−	0.685119i	$-0.240250\pi$
$523$	−5.23966	−	9.07536i	−0.229114	−	0.396838i	−0.957546	+	0.288281i	$0.906916\pi$
$524$	−8.11124			−0.354341
$525$	−4.66635	−	0.352262i	−0.203656	−	0.0153740i
$526$		−	21.0084i		−	0.916010i
$527$	−9.81361	+	5.66589i	−0.427488	+	0.246810i
$528$	3.11915	+	1.80084i	0.135743	+	0.0783715i
$529$	7.19057	−	12.4544i	0.312633	−	0.541497i
$530$	3.90252	+	6.75936i	0.169515	+	0.293608i
$531$			11.5738i			0.502259i
$532$	−2.91531	−	1.98996i	−0.126395	−	0.0862757i
$533$	−0.507230	+	10.9358i	−0.0219706	+	0.473682i
$534$	−4.08353	−	7.07288i	−0.176712	−	0.306073i
$535$	18.1886	+	10.5012i	0.786360	+	0.454005i
$536$	5.87041	−	10.1679i	0.253563	−	0.439184i
$537$	9.37041	+	16.2300i	0.404363	+	0.700378i
$538$		−	31.1173i		−	1.34156i
$539$	3.78489	−	24.9260i	0.163027	−	1.07364i
$540$		−	2.60168i		−	0.111958i
$541$	−18.8112	+	10.8607i	−0.808757	+	0.466936i	−0.846524	−	0.532350i	$-0.821309\pi$
$541$	−18.8112	+	10.8607i	−0.808757	+	0.466936i	0.0377670	+	0.999287i	$0.487976\pi$
$542$	1.00420	−	1.73932i	0.0431340	−	0.0747103i
$543$	0.213114	−	0.369125i	0.00914560	−	0.0158406i
$544$	−2.45340	+	1.41647i	−0.105189	+	0.0607308i
$545$	−33.4817			−1.43420
$546$	−7.62123	−	5.73732i	−0.326159	−	0.245534i
$547$	−33.3593			−1.42634			−0.713170	−	0.700991i	$-0.752741\pi$
$547$	−33.3593			−1.42634			−0.713170	+	0.700991i	$0.752741\pi$
$548$	4.00934	−	2.31479i	0.171270	−	0.0988831i
$549$	−2.01815	+	3.49554i	−0.0861326	+	0.149186i
$550$	3.18521	−	5.51694i	0.135818	−	0.235243i
$551$	−10.3661	+	5.98488i	−0.441611	+	0.254964i
$552$		−	2.93579i		−	0.124955i
$553$	17.7840	+	1.34251i	0.756251	+	0.0570892i
$554$			15.3681i			0.652927i
$555$	−0.217312	−	0.376395i	−0.00922438	−	0.0159771i
$556$	−0.467895	+	0.810417i	−0.0198432	+	0.0343694i
$557$	33.2612	+	19.2034i	1.40932	+	0.813672i	0.995323	−	0.0966049i	$-0.0307983\pi$
$557$	33.2612	+	19.2034i	1.40932	+	0.813672i	0.413999	+	0.910277i	$0.364132\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	8.40672	+	0.389925i	0.355566	+	0.0164921i
$560$	6.20336	−	2.98320i	0.262140	−	0.126063i
$561$			10.2034i			0.430786i
$562$	8.33411	+	14.4351i	0.351553	+	0.608908i
$563$	−1.93346	+	3.34885i	−0.0814856	+	0.141137i	−0.903888	−	0.427769i	$-0.859300\pi$
$563$	−1.93346	+	3.34885i	−0.0814856	+	0.141137i	0.822403	+	0.568906i	$0.192633\pi$
$564$	−8.43580	−	4.87041i	−0.355211	−	0.205081i
$565$	−44.7920	+	25.8607i	−1.88441	+	1.08797i
$566$			17.8050i			0.748402i
$567$	−1.14664	−	2.38437i	−0.0481545	−	0.100134i
$568$	5.76873			0.242051
$569$	13.8371	+	23.9666i	0.580083	+	1.00473i	0.995469	+	0.0950882i	$0.0303133\pi$
$569$	13.8371	+	23.9666i	0.580083	+	1.00473i	−0.415386	+	0.909645i	$0.636353\pi$
$570$	−3.00591	−	1.73546i	−0.125904	−	0.0726906i
$571$	20.0470	−	34.7225i	0.838942	−	1.45309i	−0.0518379	−	0.998656i	$-0.516508\pi$
$571$	20.0470	−	34.7225i	0.838942	−	1.45309i	0.890780	−	0.454435i	$-0.150159\pi$
$572$	11.5350	−	5.96498i	0.482303	−	0.249408i
$573$	−8.86925			−0.370518
$574$	−8.01051	−	0.604711i	−0.334352	−	0.0252402i
$575$	−5.19263			−0.216548
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.352227	+	0.203358i	0.0146634	+	0.00846592i	0.507314	−	0.861761i	$-0.330639\pi$
$577$	0.352227	+	0.203358i	0.0146634	+	0.00846592i	−0.492650	+	0.870227i	$0.663972\pi$
$578$	7.77208	+	4.48721i	0.323276	+	0.186643i
$579$	6.06945	−	3.50420i	0.252238	−	0.145629i
$580$		−	23.3425i		−	0.969245i
$581$	−17.7013	−	12.0827i	−0.734374	−	0.501276i
$582$	0.139148			0.00576786
$583$	−9.35744	+	5.40252i	−0.387545	+	0.223749i
$584$	−5.73546	+	9.93411i	−0.237335	+	0.411077i
$585$	−7.89770	−	5.06160i	−0.326530	−	0.209271i
$586$	13.2366	+	22.9265i	0.546800	+	0.947086i
$587$		−	22.0131i		−	0.908576i	−0.890855	−	0.454288i	$-0.849894\pi$
$587$		−	22.0131i		−	0.908576i	0.890855	−	0.454288i	$-0.150106\pi$
$588$	4.37041	−	5.46804i	0.180233	−	0.225498i
$589$	5.33644			0.219884
$590$	−26.0771	+	15.0556i	−1.07358	+	0.619830i
$591$	15.4196	+	8.90252i	0.634278	+	0.366201i
$592$	0.144674	+	0.0835276i	0.00594607	+	0.00343296i
$593$	−27.0080	+	15.5931i	−1.10909	+	0.640331i	−0.938593	−	0.345027i	$-0.887870\pi$
$593$	−27.0080	+	15.5931i	−1.10909	+	0.640331i	−0.170494	+	0.985359i	$0.554536\pi$
$594$	3.60168			0.147779
$595$	16.1059	+	10.9937i	0.660277	+	0.450698i
$596$		−	8.13915i		−	0.333392i
$597$	13.5545	+	23.4770i	0.554747	+	0.960850i
$598$	−8.91194	−	5.71162i	−0.364436	−	0.233565i
$599$	3.17009	−	5.49075i	0.129526	−	0.224346i	−0.793967	−	0.607961i	$-0.791988\pi$
$599$	3.17009	−	5.49075i	0.129526	−	0.224346i	0.923493	+	0.383615i	$0.125321\pi$
$600$	1.53177	−	0.884367i	0.0625342	−	0.0361041i
$601$	−23.5566			−0.960893			−0.480447	−	0.877024i	$-0.659525\pi$
$601$	−23.5566			−0.960893			−0.480447	+	0.877024i	$0.659525\pi$
$602$	−0.464862	+	6.15795i	−0.0189464	+	0.250979i
$603$		−	11.7408i		−	0.478123i
$604$	17.3278	−	10.0042i	0.705057	−	0.407065i
$605$	4.44336	+	2.56538i	0.180648	+	0.104297i
$606$	−3.08771	−	1.78269i	−0.125429	−	0.0724168i
$607$	−8.01932	−	13.8899i	−0.325494	−	0.563772i	0.656118	−	0.754658i	$-0.272197\pi$
$607$	−8.01932	−	13.8899i	−0.325494	−	0.563772i	−0.981612	+	0.190886i	$0.938864\pi$
$608$	1.33411			0.0541053
$609$	−10.2878	−	21.3928i	−0.416883	−	0.866878i
$610$	−10.5012			−0.425180
$611$	−31.1967	+	16.1324i	−1.26208	+	0.652648i
$612$	−1.41647	+	2.45340i	−0.0572575	+	0.0991729i
$613$	−7.37710	−	4.25917i	−0.297958	−	0.172026i	0.343567	−	0.939128i	$-0.388365\pi$
$613$	−7.37710	−	4.25917i	−0.297958	−	0.172026i	−0.641525	+	0.767102i	$0.721698\pi$
$614$	−11.6391	−	20.1596i	−0.469718	−	0.813575i
$615$	−7.89949			−0.318538
$616$	4.12985	+	8.58773i	0.166396	+	0.346009i
$617$		−	1.40905i		−	0.0567261i	−0.999598	−	0.0283631i	$-0.990971\pi$
$617$		−	1.40905i		−	0.0567261i	0.999598	−	0.0283631i	$-0.00902945\pi$
$618$	16.5194	−	9.53747i	0.664507	−	0.383653i
$619$	−39.3641	−	22.7269i	−1.58218	−	0.913470i	−0.994541	−	0.104344i	$-0.966726\pi$
$619$	−39.3641	−	22.7269i	−1.58218	−	0.913470i	−0.587635	−	0.809126i	$-0.699941\pi$
$620$	−5.20336	+	9.01248i	−0.208972	+	0.361950i
$621$	−1.46789	−	2.54247i	−0.0589046	−	0.102026i
$622$			16.5459i			0.663429i
$623$	1.62655	−	21.5467i	0.0651665	−	0.863250i
$624$	3.60168	+	0.167055i	0.144183	+	0.00668756i
$625$	15.3576	+	26.6002i	0.614305	+	1.06401i
$626$	8.68442	+	5.01395i	0.347099	+	0.200398i
$627$	2.40252	−	4.16128i	0.0959474	−	0.166186i
$628$	10.6724	+	18.4852i	0.425876	+	0.737639i
$629$			0.473258i			0.0188700i
$630$	3.88067	−	5.68521i	0.154609	−	0.226504i
$631$		−	35.2313i		−	1.40253i	−0.712898	−	0.701267i	$-0.752618\pi$
$631$		−	35.2313i		−	1.40253i	0.712898	−	0.701267i	$-0.247382\pi$
$632$	−5.83773	+	3.37041i	−0.232212	+	0.134068i
$633$	−11.3371	+	19.6365i	−0.450611	+	0.780481i
$634$	10.7045	−	18.5408i	0.425131	−	0.736348i
$635$	−22.6182	+	13.0587i	−0.897578	+	0.518217i
$636$	−3.00000			−0.118958
$637$	−8.09619	−	23.9051i	−0.320783	−	0.947153i
$638$	32.3146			1.27935
$639$	4.99587	−	2.88437i	0.197634	−	0.114104i
$640$	−1.30084	+	2.25312i	−0.0514202	+	0.0890624i
$641$	−11.1168	+	19.2549i	−0.439087	+	0.760521i	−0.997619	−	0.0689616i	$-0.978031\pi$
$641$	−11.1168	+	19.2549i	−0.439087	+	0.760521i	0.558532	+	0.829483i	$0.311365\pi$
$642$	−6.99108	+	4.03630i	−0.275916	+	0.159300i
$643$			3.64031i			0.143560i	0.997420	+	0.0717800i	$0.0228679\pi$
$643$			3.64031i			0.143560i	−0.997420	+	0.0717800i	$0.977132\pi$
$644$	4.37902	−	6.41531i	0.172558	−	0.252799i
$645$			6.07261i			0.239109i
$646$	1.88973	+	3.27311i	0.0743505	+	0.128779i
$647$	−7.02791	+	12.1727i	−0.276296	+	0.478558i	−0.970461	−	0.241257i	$-0.922440\pi$
$647$	−7.02791	+	12.1727i	−0.276296	+	0.478558i	0.694166	+	0.719815i	$0.255774\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−20.8425	−	36.1003i	−0.818140	−	1.41706i
$650$	0.295476	−	6.37041i	0.0115895	−	0.249868i
$651$	−0.796642	+	10.5530i	−0.0312229	+	0.413604i
$652$			1.02791i			0.0402560i
$653$	8.62403	+	14.9373i	0.337484	+	0.584540i	0.983959	−	0.178396i	$-0.0570907\pi$
$653$	8.62403	+	14.9373i	0.337484	+	0.584540i	−0.646475	+	0.762936i	$0.723757\pi$
$654$	6.43462	−	11.1451i	0.251614	−	0.435808i
$655$	−18.2756	−	10.5514i	−0.714087	−	0.412278i
$656$	2.62952	−	1.51815i	0.102665	−	0.0592739i
$657$			11.4709i			0.447523i
$658$	−11.1693	−	23.2257i	−0.435423	−	0.905432i
$659$	−21.6999			−0.845307			−0.422653	−	0.906291i	$-0.638901\pi$
$659$	−21.6999			−0.845307			−0.422653	+	0.906291i	$0.638901\pi$
$660$	4.68521	+	8.11502i	0.182371	+	0.315877i
$661$	20.0758	+	11.5908i	0.780857	+	0.450828i	0.836734	−	0.547609i	$-0.184462\pi$
$661$	20.0758	+	11.5908i	0.780857	+	0.450828i	−0.0558767	+	0.998438i	$0.517795\pi$
$662$	−17.9302	+	31.0561i	−0.696878	+	1.20703i
$663$	4.69183	+	9.07300i	0.182215	+	0.352366i
$664$	8.10051			0.314361
$665$	−3.97992	−	8.27596i	−0.154335	−	0.320928i
$666$	0.167055			0.00647326
$667$	−13.1701	−	22.8113i	−0.509948	−	0.883256i
$668$	5.16997	+	2.98488i	0.200032	+	0.115489i
$669$	7.96307	+	4.59748i	0.307870	+	0.177749i
$670$	26.4535	−	15.2729i	1.02199	−	0.590045i
$671$		−	14.5375i		−	0.561213i
$672$	−0.199160	+	2.63824i	−0.00768278	+	0.101772i
$673$	7.56538			0.291624			0.145812	−	0.989312i	$-0.453421\pi$
$673$	7.56538			0.291624			0.145812	+	0.989312i	$0.453421\pi$
$674$	5.83571	−	3.36925i	0.224783	−	0.129779i
$675$	0.884367	−	1.53177i	0.0340393	−	0.0589578i
$676$	7.51423	−	10.6083i	0.289009	−	0.408012i
$677$	10.4581	+	18.1140i	0.401939	+	0.696179i	0.993960	−	0.109744i	$-0.0350031\pi$
$677$	10.4581	+	18.1140i	0.401939	+	0.696179i	−0.592021	+	0.805923i	$0.701670\pi$
$678$		−	19.8800i		−	0.763486i
$679$	0.304067	+	0.207553i	0.0116690	+	0.00796515i
$680$	−7.37041			−0.282642
$681$	11.7238	−	6.76873i	0.449257	−	0.259378i
$682$	−12.4766	−	7.20336i	−0.477753	−	0.275831i
$683$	−17.0981	−	9.87158i	−0.654240	−	0.377725i	0.135839	−	0.990731i	$-0.456627\pi$
$683$	−17.0981	−	9.87158i	−0.654240	−	0.377725i	−0.790079	+	0.613005i	$0.789960\pi$
$684$	1.15537	−	0.667055i	0.0441768	−	0.0255055i
$685$	12.0447			0.460204
$686$	17.7064	−	5.42989i	0.676033	−	0.207314i
$687$			18.4067i			0.702260i
$688$	−1.16706	−	2.02140i	−0.0444936	−	0.0770651i
$689$	−5.83654	+	9.10685i	−0.222354	+	0.346944i
$690$	3.81899	−	6.61469i	0.145387	−	0.251817i
$691$	−23.4013	+	13.5107i	−0.890226	+	0.513972i	−0.874016	−	0.485896i	$-0.838493\pi$
$691$	−23.4013	+	13.5107i	−0.890226	+	0.513972i	−0.0162096	+	0.999869i	$0.505160\pi$
$692$	16.5822			0.630359
$693$	7.87041	+	5.37227i	0.298972	+	0.204076i
$694$			34.5738i			1.31240i
$695$	−2.10845	+	1.21731i	−0.0799779	+	0.0461753i
$696$	7.77006	+	4.48605i	0.294523	+	0.170043i
$697$	7.44927	+	4.30084i	0.282161	+	0.162906i
$698$	−10.8886	−	18.8595i	−0.412138	−	0.713844i
$699$	−11.7301			−0.443673
$700$	4.66635	+	0.352262i	0.176372	+	0.0133142i
$701$	46.3956			1.75234			0.876169	−	0.482004i	$-0.160091\pi$
$701$	46.3956			1.75234			0.876169	+	0.482004i	$0.160091\pi$
$702$	3.20267	−	1.65617i	0.120877	−	0.0625079i
$703$	0.111435	−	0.193011i	0.00420285	−	0.00727955i
$704$	−3.11915	−	1.80084i	−0.117557	−	0.0678717i
$705$	−12.6713	−	21.9473i	−0.477227	−	0.826581i
$706$	20.3509			0.765916
$707$	−4.08822	−	8.50117i	−0.153753	−	0.319719i
$708$		−	11.5738i		−	0.434969i
$709$	−35.7795	+	20.6573i	−1.34373	+	0.775801i	−0.987352	−	0.158542i	$-0.949321\pi$
$709$	−35.7795	+	20.6573i	−1.34373	+	0.775801i	−0.356375	+	0.934343i	$0.615987\pi$
$710$	12.9977	+	7.50420i	0.487793	+	0.281628i
$711$	−3.37041	+	5.83773i	−0.126400	+	0.218932i
$712$	4.08353	+	7.07288i	0.153037	+	0.265067i
$713$			11.7432i			0.439785i
$714$	−6.75478	+	3.24838i	−0.252791	+	0.121568i
$715$	33.7492	+	1.56538i	1.26215	+	0.0585417i
$716$	−9.37041	−	16.2300i	−0.350189	−	0.606545i
$717$	9.67621	+	5.58656i	0.361365	+	0.208634i
$718$	0.716146	−	1.24040i	0.0267263	−	0.0462914i
$719$	14.9721	+	25.9324i	0.558365	+	0.967116i	0.997633	+	0.0687604i	$0.0219044\pi$
$719$	14.9721	+	25.9324i	0.558365	+	0.967116i	−0.439268	+	0.898356i	$0.644762\pi$
$720$			2.60168i			0.0969589i
$721$	50.3244	+	3.79897i	1.87418	+	0.141481i
$722$			17.2201i			0.640868i
$723$	12.7659	−	7.37041i	0.474770	−	0.274109i
$724$	−0.213114	+	0.369125i	−0.00792032	+	0.0137184i
$725$	7.93462	−	13.7432i	0.294685	−	0.510409i
$726$	−1.70788	+	0.986046i	−0.0633855	+	0.0365956i
$727$	22.8860			0.848796			0.424398	−	0.905476i	$-0.360486\pi$
$727$	22.8860			0.848796			0.424398	+	0.905476i	$0.360486\pi$
$728$	7.62123	+	5.73732i	0.282462	+	0.212639i
$729$	1.00000			0.0370370
$730$	−25.8454	+	14.9218i	−0.956580	+	0.552282i
$731$	3.30620	−	5.72651i	0.122284	−	0.211803i
$732$	2.01815	−	3.49554i	0.0745930	−	0.129199i
$733$	33.8210	−	19.5265i	1.24921	−	0.721229i	0.278255	−	0.960507i	$-0.410244\pi$
$733$	33.8210	−	19.5265i	1.24921	−	0.721229i	0.970951	+	0.239278i	$0.0769107\pi$
$734$			24.3509i			0.898808i
$735$	16.9601	−	6.63495i	0.625583	−	0.244734i
$736$			2.93579i			0.108215i
$737$	21.1433	+	36.6213i	0.778825	+	1.34896i
$738$	1.51815	−	2.62952i	0.0558839	−	0.0967938i
$739$	42.8282	+	24.7269i	1.57546	+	0.909593i	0.995481	+	0.0949620i	$0.0302729\pi$
$739$	42.8282	+	24.7269i	1.57546	+	0.909593i	0.579980	+	0.814631i	$0.303060\pi$
$740$	0.217312	+	0.376395i	0.00798855	+	0.0138366i
$741$	0.222870	−	4.80504i	0.00818734	−	0.176517i
$742$	−6.55562	−	4.47480i	−0.240664	−	0.164275i
$743$		−	0.203358i		−	0.00746049i	−0.999993	−	0.00373025i	$-0.998813\pi$
$743$		−	0.203358i		−	0.00746049i	0.999993	−	0.00373025i	$-0.00118738\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	10.5877	−	18.3385i	0.387904	−	0.671870i
$746$	−27.6717	−	15.9763i	−1.01313	−	0.584934i
$747$	7.01525	−	4.05026i	0.256675	−	0.148191i
$748$		−	10.2034i		−	0.373072i
$749$	−21.2975	−	1.60774i	−0.778194	−	0.0587457i
$750$	−8.40672			−0.306970
$751$	21.4733	+	37.1928i	0.783570	+	1.35718i	0.929849	+	0.367940i	$0.119937\pi$
$751$	21.4733	+	37.1928i	0.783570	+	1.35718i	−0.146279	+	0.989243i	$0.546730\pi$
$752$	8.43580	+	4.87041i	0.307622	+	0.177606i
$753$	−11.4733	+	19.8723i	−0.418109	+	0.724186i
$754$	28.7347	−	14.8593i	1.04646	−	0.541143i
$755$	52.0554			1.89449
$756$	1.14664	+	2.38437i	0.0417031	+	0.0867186i
$757$	−19.5180			−0.709392			−0.354696	−	0.934982i	$-0.615416\pi$
$757$	−19.5180			−0.709392			−0.354696	+	0.934982i	$0.615416\pi$
$758$	1.39832	+	2.42196i	0.0507893	+	0.0879696i
$759$	9.15715	+	5.28689i	0.332384	+	0.191902i
$760$	3.00591	+	1.73546i	0.109036	+	0.0629519i
$761$	−36.3876	+	21.0084i	−1.31905	+	0.761554i	−0.983576	−	0.180496i	$-0.942230\pi$
$761$	−36.3876	+	21.0084i	−1.31905	+	0.761554i	−0.335474	+	0.942049i	$0.608896\pi$
$762$		−	10.0386i		−	0.363661i
$763$	30.6850	−	14.7565i	1.11087	−	0.534219i
$764$	8.86925			0.320878
$765$	−6.38297	+	3.68521i	−0.230777	+	0.133239i
$766$	4.92184	−	8.52487i	0.177833	−	0.308016i
$767$	−35.1336	−	22.5169i	−1.26860	−	0.813039i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	51.9502i		−	1.87337i	−0.350168	−	0.936687i	$-0.613875\pi$
$769$		−	51.9502i		−	1.87337i	0.350168	−	0.936687i	$-0.386125\pi$
$770$	−1.86622	+	24.7214i	−0.0672537	+	0.890899i
$771$	−0.740827			−0.0266802
$772$	−6.06945	+	3.50420i	−0.218444	+	0.126119i
$773$	36.4022	+	21.0168i	1.30929	+	0.755921i	0.981978	−	0.188993i	$-0.0605225\pi$
$773$	36.4022	+	21.0168i	1.30929	+	0.755921i	0.327316	+	0.944915i	$0.393856\pi$
$774$	−2.02140	−	1.16706i	−0.0726577	−	0.0419489i
$775$	−6.12708	+	3.53747i	−0.220091	+	0.127070i
$776$	−0.139148			−0.00499511
$777$	0.365050	+	0.249180i	0.0130961	+	0.00893927i
$778$			16.3811i			0.587292i
$779$	−2.02538	−	3.50806i	−0.0725668	−	0.125689i
$780$	7.89770	+	5.06160i	0.282783	+	0.181234i
$781$	−10.3886	+	17.9935i	−0.371732	+	0.643859i
$782$	−7.20267	+	4.15846i	−0.257567	+	0.148706i
$783$	8.97209			0.320636
$784$	−4.37041	+	5.46804i	−0.156086	+	0.195287i
$785$			55.5324i			1.98204i
$786$	7.02454	−	4.05562i	0.250557	−	0.144659i
$787$	−7.61610	−	4.39716i	−0.271485	−	0.156742i	0.358078	−	0.933692i	$-0.383432\pi$
$787$	−7.61610	−	4.39716i	−0.271485	−	0.156742i	−0.629562	+	0.776950i	$0.716766\pi$
$788$	−15.4196	−	8.90252i	−0.549301	−	0.317139i
$789$	10.5042	+	18.1938i	0.373959	+	0.647717i
$790$	−17.5375			−0.623955
$791$	29.6530	−	43.4419i	1.05434	−	1.54461i
$792$	−3.60168			−0.127980
$793$	−6.68479	−	12.9270i	−0.237384	−	0.459050i
$794$	−2.72151	+	4.71379i	−0.0965828	+	0.167286i
$795$	−6.75936	−	3.90252i	−0.239730	−	0.138408i
$796$	−13.5545	−	23.4770i	−0.480425	−	0.832120i
$797$	−6.25039			−0.221400			−0.110700	−	0.993854i	$-0.535309\pi$
$797$	−6.25039			−0.221400			−0.110700	+	0.993854i	$0.535309\pi$
$798$	3.51971	+	0.265702i	0.124596	+	0.00940575i
$799$			27.5952i			0.976249i
$800$	−1.53177	+	0.884367i	−0.0541562	+	0.0312671i
$801$	7.07288	+	4.08353i	0.249908	+	0.144284i
$802$	8.78805	−	15.2214i	0.310317	−	0.537485i
$803$	−20.6573	−	35.7795i	−0.728980	−	1.26263i
$804$			11.7408i			0.414067i
$805$	18.2118	−	8.75805i	0.641880	−	0.308681i
$806$	−14.4067	−	0.668221i	−0.507455	−	0.0235371i
$807$	15.5587	+	26.9484i	0.547691	+	0.948628i
$808$	3.08771	+	1.78269i	0.108625	+	0.0627147i
$809$	22.9260	−	39.7091i	0.806036	−	1.39610i	−0.109553	−	0.993981i	$-0.534942\pi$
$809$	22.9260	−	39.7091i	0.806036	−	1.39610i	0.915589	−	0.402115i	$-0.131725\pi$
$810$	1.30084	+	2.25312i	0.0457068	+	0.0791666i
$811$		−	29.5096i		−	1.03622i	−0.855314	−	0.518110i	$-0.826636\pi$
$811$		−	29.5096i		−	1.03622i	0.855314	−	0.518110i	$-0.173364\pi$
$812$	10.2878	+	21.3928i	0.361031	+	0.750739i
$813$			2.00840i			0.0704375i
$814$	−0.521069	+	0.300840i	−0.0182635	+	0.0105444i
$815$	−1.33714	+	2.31600i	−0.0468381	+	0.0811259i
$816$	1.41647	−	2.45340i	0.0495865	−	0.0858863i
$817$	−2.69677	+	1.55698i	−0.0943480	+	0.0544718i
$818$	−19.0084			−0.664613
$819$	9.46884	+	1.15804i	0.330868	+	0.0404653i
$820$	7.89949			0.275862
$821$	20.9197	−	12.0780i	0.730101	−	0.421524i	−0.0883581	−	0.996089i	$-0.528162\pi$
$821$	20.9197	−	12.0780i	0.730101	−	0.421524i	0.818459	+	0.574565i	$0.194829\pi$
$822$	−2.31479	+	4.00934i	−0.0807377	+	0.139842i
$823$	15.3511	−	26.5889i	0.535106	−	0.926830i	−0.464053	−	0.885808i	$-0.653605\pi$
$823$	15.3511	−	26.5889i	0.535106	−	0.926830i	0.999158	−	0.0410224i	$-0.0130615\pi$
$824$	−16.5194	+	9.53747i	−0.575480	+	0.332253i
$825$			6.37041i			0.221789i
$826$	17.2634	−	25.2911i	0.600672	−	0.879989i
$827$			3.32338i			0.115565i	0.998329	+	0.0577827i	$0.0184031\pi$
$827$			3.32338i			0.115565i	−0.998329	+	0.0577827i	$0.981597\pi$
$828$	1.46789	+	2.54247i	0.0510129	+	0.0883569i
$829$	14.8232	−	25.6745i	0.514831	−	0.891713i	−0.485021	−	0.874502i	$-0.661188\pi$
$829$	14.8232	−	25.6745i	0.514831	−	0.891713i	0.999852	−	0.0172105i	$-0.00547853\pi$
$830$	18.2514	+	10.5375i	0.633516	+	0.365761i
$831$	−7.68404	−	13.3091i	−0.266556	−	0.461689i
$832$	−3.60168	−	0.167055i	−0.124866	−	0.00579160i
$833$	−19.6059	−	2.97705i	−0.679303	−	0.103149i
$834$		−	0.935789i		−	0.0324037i
$835$	7.76570	+	13.4506i	0.268743	+	0.465477i
$836$	−2.40252	+	4.16128i	−0.0830928	+	0.143921i
$837$	−3.46410	−	2.00000i	−0.119737	−	0.0691301i
$838$	4.74725	−	2.74083i	0.163991	−	0.0946803i
$839$		−	5.51189i		−	0.190292i	−0.995463	−	0.0951458i	$-0.969668\pi$
$839$		−	5.51189i		−	0.190292i	0.995463	−	0.0951458i	$-0.0303317\pi$
$840$	−3.88067	+	5.68521i	−0.133896	+	0.196158i
$841$	51.4984			1.77581
$842$	1.58236	+	2.74073i	0.0545318	+	0.0944518i
$843$	−14.4351	−	8.33411i	−0.497171	−	0.287042i
$844$	11.3371	−	19.6365i	0.390241	−	0.675916i
$845$	30.7302	−	14.1270i	1.05715	−	0.485983i
$846$	9.74083			0.334897
$847$	−5.20286	−	0.392763i	−0.178772	−	0.0134955i
$848$	3.00000			0.103020
$849$	−8.90252	−	15.4196i	−0.305534	−	0.529200i
$850$	−4.33942	−	2.50536i	−0.148841	−	0.0859333i
$851$	0.424732	+	0.245219i	0.0145596	+	0.00840601i
$852$	−4.99587	+	2.88437i	−0.171156	+	0.0988168i
$853$			34.2611i			1.17308i	0.809921	+	0.586539i	$0.199510\pi$
$853$			34.2611i			1.17308i	−0.809921	+	0.586539i	$0.800490\pi$
$854$	9.62403	−	4.62820i	0.329327	−	0.158374i
$855$	3.47093			0.118703
$856$	6.99108	−	4.03630i	0.238950	−	0.137958i
$857$	−18.2299	+	31.5751i	−0.622722	+	1.07859i	0.366255	+	0.930515i	$0.380640\pi$
$857$	−18.2299	+	31.5751i	−0.622722	+	1.07859i	−0.988977	+	0.148071i	$0.952694\pi$
$858$	−7.00712	+	10.9333i	−0.239219	+	0.373257i
$859$	−21.6743	−	37.5410i	−0.739517	−	1.28088i	−0.952713	−	0.303872i	$-0.901721\pi$
$859$	−21.6743	−	37.5410i	−0.739517	−	1.28088i	0.213196	−	0.977009i	$-0.431613\pi$
$860$		−	6.07261i		−	0.207074i
$861$	7.23966	−	3.48156i	0.246727	−	0.118651i
$862$	−15.4370			−0.525785
$863$	−11.7907	+	6.80737i	−0.401360	+	0.231726i	−0.687071	−	0.726590i	$-0.741104\pi$
$863$	−11.7907	+	6.80737i	−0.401360	+	0.231726i	0.285710	+	0.958316i	$0.407770\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	37.3616	+	21.5707i	1.27033	+	0.733427i
$866$	12.0740	−	6.97093i	0.410291	−	0.236882i
$867$	−8.97442			−0.304787
$868$	0.796642	−	10.5530i	0.0270398	−	0.358191i
$869$		−	24.2783i		−	0.823585i
$870$	11.6713	+	20.2152i	0.395693	+	0.685360i
$871$	35.6407	+	22.8419i	1.20764	+	0.773970i
$872$	−6.43462	+	11.1451i	−0.217904	+	0.377421i
$873$	−0.120505	+	0.0695739i	−0.00407849	+	0.00235472i
$874$	3.91667			0.132483
$875$	−18.3704	−	12.5395i	−0.621033	−	0.423911i
$876$		−	11.4709i		−	0.387567i
$877$	−23.8292	+	13.7578i	−0.804656	+	0.464568i	−0.845097	−	0.534614i	$-0.820457\pi$
$877$	−23.8292	+	13.7578i	−0.804656	+	0.464568i	0.0404407	+	0.999182i	$0.487124\pi$
$878$	23.7180	+	13.6936i	0.800444	+	0.462137i
$879$	−22.9265	−	13.2366i	−0.773292	−	0.446460i
$880$	−4.68521	−	8.11502i	−0.157938	−	0.273557i
$881$	−22.3341			−0.752455			−0.376228	−	0.926527i	$-0.622779\pi$
$881$	−22.3341			−0.752455			−0.376228	+	0.926527i	$0.622779\pi$
$882$	−1.05087	+	6.92067i	−0.0353846	+	0.233031i
$883$	9.28669			0.312522			0.156261	−	0.987716i	$-0.450056\pi$
$883$	9.28669			0.312522			0.156261	+	0.987716i	$0.450056\pi$
$884$	−4.69183	−	9.07300i	−0.157803	−	0.305158i
$885$	15.0556	−	26.0771i	0.506089	−	0.876572i
$886$	−20.8809	−	12.0556i	−0.701509	−	0.405016i
$887$	6.97209	+	12.0760i	0.234100	+	0.405473i	0.959011	−	0.283370i	$-0.0914524\pi$
$887$	6.97209	+	12.0760i	0.234100	+	0.405473i	−0.724911	+	0.688843i	$0.758119\pi$
$888$	−0.167055			−0.00560600
$889$	14.9736	−	21.9365i	0.502199	−	0.735726i
$890$			21.2481i			0.712236i
$891$	−3.11915	+	1.80084i	−0.104495	+	0.0603304i
$892$	−7.96307	−	4.59748i	−0.266623	−	0.153935i
$893$	6.49767	−	11.2543i	0.217436	−	0.376611i
$894$	4.06957	+	7.04871i	0.136107	+	0.235744i
$895$		−	48.7576i		−	1.62979i
$896$	0.199160	−	2.63824i	0.00665348	−	0.0881376i
$897$	10.5738	+	0.490439i	0.353048	+	0.0163753i
$898$	−1.29548	−	2.24383i	−0.0432306	−	0.0748776i
$899$	−31.0802	−	17.9442i	−1.03658	−	0.598472i
$900$	−0.884367	+	1.53177i	−0.0294789	+	0.0510590i
$901$	4.24942	+	7.36021i	0.141569	+	0.245204i
$902$			10.9358i			0.364122i
$903$	−2.67639	−	5.56538i	−0.0890648	−	0.185204i
$904$			19.8800i			0.661198i
$905$	−0.960344	+	0.554455i	−0.0319229	+	0.0184307i
$906$	−10.0042	+	17.3278i	−0.332367	+	0.575677i
$907$	−2.06957	+	3.58461i	−0.0687191	+	0.119025i	−0.898338	−	0.439306i	$-0.855225\pi$
$907$	−2.06957	+	3.58461i	−0.0687191	+	0.119025i	0.829619	+	0.558330i	$0.188558\pi$
$908$	−11.7238	+	6.76873i	−0.389068	+	0.224628i
$909$	3.56538			0.118256
$910$	9.70823	+	22.8409i	0.321825	+	0.757167i
$911$	18.5566			0.614807			0.307404	−	0.951579i	$-0.400540\pi$
$911$	18.5566			0.614807			0.307404	+	0.951579i	$0.400540\pi$
$912$	−1.15537	+	0.667055i	−0.0382582	+	0.0220884i
$913$	−14.5877	+	25.2667i	−0.482783	+	0.836205i
$914$	−5.23430	+	9.06607i	−0.173135	+	0.299879i
$915$	9.09428	−	5.25058i	0.300647	−	0.173579i
$916$		−	18.4067i		−	0.608175i
$917$	21.3994	+	1.61544i	0.706672	+	0.0533465i
$918$		−	2.83294i		−	0.0935011i
$919$	−25.6743	−	44.4692i	−0.846917	−	1.46690i	−0.883946	−	0.467588i	$-0.845123\pi$
$919$	−25.6743	−	44.4692i	−0.846917	−	1.46690i	0.0370298	−	0.999314i	$-0.488210\pi$
$920$	−3.81899	+	6.61469i	−0.125908	+	0.218080i
$921$	20.1596	+	11.6391i	0.664281	+	0.383523i
$922$	−15.0084	−	25.9953i	−0.494275	−	0.856110i
$923$	−0.963697	+	20.7771i	−0.0317205	+	0.683888i
$924$	−7.87041	−	5.37227i	−0.258918	−	0.176735i
$925$			0.295476i			0.00971520i
$926$	9.73243	+	16.8571i	0.319828	+	0.553958i
$927$	−9.53747	+	16.5194i	−0.313252	+	0.542568i
$928$	−7.77006	−	4.48605i	−0.255065	−	0.147262i
$929$	6.01182	−	3.47093i	0.197241	−	0.113877i	−0.398127	−	0.917330i	$-0.630340\pi$
$929$	6.01182	−	3.47093i	0.197241	−	0.113877i	0.595368	+	0.803453i	$0.297006\pi$
$930$		−	10.4067i		−	0.341250i
$931$	7.29497	+	5.83061i	0.239083	+	0.191091i
$932$	11.7301			0.384232
$933$	−8.27293	−	14.3291i	−0.270844	−	0.469115i
$934$	0.259927	+	0.150069i	0.00850508	+	0.00491041i
$935$	13.2729	−	22.9894i	0.434071	−	0.751834i
$936$	−3.20267	+	1.65617i	−0.104683	+	0.0541335i
$937$	37.1005			1.21202			0.606010	−	0.795457i	$-0.292769\pi$
$937$	37.1005			1.21202			0.606010	+	0.795457i	$0.292769\pi$
$938$	−17.5126	+	25.6561i	−0.571807	+	0.837702i
$939$	−10.0279			−0.327248
$940$	12.6713	+	21.9473i	0.413291	+	0.715840i
$941$	7.28447	+	4.20569i	0.237467	+	0.137102i	0.614012	−	0.789297i	$-0.289555\pi$
$941$	7.28447	+	4.20569i	0.237467	+	0.137102i	−0.376545	+	0.926398i	$0.622888\pi$
$942$	−18.4852	−	10.6724i	−0.602279	−	0.347726i
$943$	7.71970	−	4.45697i	0.251388	−	0.145139i
$944$			11.5738i			0.376694i
$945$	−0.518152	+	6.86387i	−0.0168555	+	0.223282i
$946$	8.40672			0.273326
$947$	21.7953	−	12.5835i	0.708252	−	0.408910i	−0.102161	−	0.994768i	$-0.532576\pi$
$947$	21.7953	−	12.5835i	0.708252	−	0.408910i	0.810414	+	0.585858i	$0.199242\pi$
$948$	3.37041	−	5.83773i	0.109466	−	0.189601i
$949$	−34.8214	−	22.3168i	−1.13035	−	0.724435i
$950$	1.17984	+	2.04355i	0.0382792	+	0.0663015i
$951$			21.4090i			0.694236i
$952$	6.75478	−	3.24838i	0.218924	−	0.105281i
$953$	35.3681			1.14568			0.572842	−	0.819666i	$-0.305841\pi$
$953$	35.3681			1.14568			0.572842	+	0.819666i	$0.305841\pi$
$954$	2.59808	−	1.50000i	0.0841158	−	0.0485643i
$955$	19.9835	+	11.5375i	0.646650	+	0.373344i
$956$	−9.67621	−	5.58656i	−0.312951	−	0.180682i
$957$	−27.9853	+	16.1573i	−0.904635	+	0.522291i
$958$	23.5845			0.761981
$959$	−11.0386	+	5.30849i	−0.356456	+	0.171420i
$960$		−	2.60168i		−	0.0839688i
$961$	−7.50000	−	12.9904i	−0.241935	−	0.419045i
$962$	−0.325008	+	0.507116i	−0.0104787	+	0.0163501i
$963$	4.03630	−	6.99108i	0.130068	−	0.225284i
$964$	−12.7659	+	7.37041i	−0.411163	+	0.237385i
$965$	−18.2336			−0.586960
$966$	−0.584693	+	7.74533i	−0.0188122	+	0.249202i
$967$		−	17.3123i		−	0.556725i	−0.960476	−	0.278362i	$-0.910208\pi$
$967$		−	17.3123i		−	0.556725i	0.960476	−	0.278362i	$-0.0897917\pi$
$968$	1.70788	−	0.986046i	0.0548934	−	0.0316927i
$969$	−3.27311	−	1.88973i	−0.105147	−	0.0607069i
$970$	−0.313517	−	0.181009i	−0.0100664	−	0.00581185i
$971$	26.6959	+	46.2387i	0.856713	+	1.48387i	0.875046	+	0.484039i	$0.160831\pi$
$971$	26.6959	+	46.2387i	0.856713	+	1.48387i	−0.0183332	+	0.999832i	$0.505836\pi$
$972$	−1.00000			−0.0320750
$973$	1.39582	−	2.04489i	0.0447481	−	0.0655563i
$974$	34.2420			1.09718
$975$	2.92932	+	5.66468i	0.0938132	+	0.181415i
$976$	−2.01815	+	3.49554i	−0.0645995	+	0.111890i
$977$	−28.4656	−	16.4346i	−0.910695	−	0.525790i	−0.0300405	−	0.999549i	$-0.509564\pi$
$977$	−28.4656	−	16.4346i	−0.910695	−	0.525790i	−0.880655	+	0.473758i	$0.842897\pi$
$978$	−0.513954	−	0.890194i	−0.0164344	−	0.0284653i
$979$	−29.4151			−0.940111
$980$	−16.9601	+	6.63495i	−0.541771	+	0.211946i
$981$			12.8692i			0.410883i
$982$	−34.4291	+	19.8776i	−1.09868	+	0.634321i
$983$	8.42126	+	4.86202i	0.268597	+	0.155074i	0.628250	−	0.778012i	$-0.283772\pi$
$983$	8.42126	+	4.86202i	0.268597	+	0.155074i	−0.359653	+	0.933086i	$0.617105\pi$
$984$	−1.51815	+	2.62952i	−0.0483969	+	0.0838259i
$985$	−23.1615	−	40.1169i	−0.737987	−	1.27823i
$986$		−	25.4174i		−	0.809456i
$987$	21.2857	+	14.5294i	0.677532	+	0.462477i
$988$	−0.222870	+	4.80504i	−0.00709044	+	0.152869i
$989$	−3.42623	−	5.93440i	−0.108948	−	0.188703i
$990$	−8.11502	−	4.68521i	−0.257912	−	0.148906i
$991$	−16.2057	+	28.0691i	−0.514791	+	0.891644i	0.485062	+	0.874480i	$0.338797\pi$
$991$	−16.2057	+	28.0691i	−0.514791	+	0.891644i	−0.999853	+	0.0171639i	$0.994536\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		−	35.8605i		−	1.13800i
$994$	−15.2193	−	1.14890i	−0.482728	−	0.0364410i
$995$		−	70.5287i		−	2.23591i
$996$	−7.01525	+	4.05026i	−0.222287	+	0.128337i
$997$	22.8395	−	39.5591i	0.723333	−	1.25285i	−0.236323	−	0.971675i	$-0.575942\pi$
$997$	22.8395	−	39.5591i	0.723333	−	1.25285i	0.959656	−	0.281176i	$-0.0907243\pi$
$998$	6.12519	−	10.6091i	0.193890	−	0.335827i
$999$	−0.144674	+	0.0835276i	−0.00457728	+	0.00264270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.b.25.6	yes	12
3.2	odd	2		1638.2.dm.c.1117.1		12
7.2	even	3	inner	546.2.bk.b.415.1	yes	12
7.3	odd	6		3822.2.c.j.883.4		6
7.4	even	3		3822.2.c.k.883.6		6
13.12	even	2	inner	546.2.bk.b.25.1	✓	12
21.2	odd	6		1638.2.dm.c.415.6		12
39.38	odd	2		1638.2.dm.c.1117.6		12
91.25	even	6		3822.2.c.k.883.1		6
91.38	odd	6		3822.2.c.j.883.3		6
91.51	even	6	inner	546.2.bk.b.415.6	yes	12
273.233	odd	6		1638.2.dm.c.415.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.1	✓	12	13.12	even	2	inner
546.2.bk.b.25.6	yes	12	1.1	even	1	trivial
546.2.bk.b.415.1	yes	12	7.2	even	3	inner
546.2.bk.b.415.6	yes	12	91.51	even	6	inner
1638.2.dm.c.415.1		12	273.233	odd	6
1638.2.dm.c.415.6		12	21.2	odd	6
1638.2.dm.c.1117.1		12	3.2	odd	2
1638.2.dm.c.1117.6		12	39.38	odd	2
3822.2.c.j.883.3		6	91.38	odd	6
3822.2.c.j.883.4		6	7.3	odd	6
3822.2.c.k.883.1		6	91.25	even	6
3822.2.c.k.883.6		6	7.4	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.25312 - 1.30084i) q^{5} +1.00000i q^{6} +(-1.49160 + 2.18521i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.30084 - 2.25312i) q^{10} +(3.11915 + 1.80084i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.60168 + 0.167055i) q^{13} +(-0.199160 + 2.63824i) q^{14} +2.60168i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.41647 - 2.45340i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.15537 + 0.667055i) q^{19} -2.60168i q^{20} +(-1.14664 - 2.38437i) q^{21} +3.60168 q^{22} +(-1.46789 - 2.54247i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.884367 - 1.53177i) q^{25} +(3.20267 - 1.65617i) q^{26} +1.00000 q^{27} +(1.14664 + 2.38437i) q^{28} +8.97209 q^{29} +(1.30084 + 2.25312i) q^{30} +(-3.46410 - 2.00000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.11915 + 1.80084i) q^{33} -2.83294i q^{34} +(-0.518152 + 6.86387i) q^{35} -1.00000 q^{36} +(-0.144674 + 0.0835276i) q^{37} +(-0.667055 + 1.15537i) q^{38} +(-1.94551 + 3.03562i) q^{39} +(-1.30084 - 2.25312i) q^{40} +3.03630i q^{41} +(-2.18521 - 1.49160i) q^{42} +2.33411 q^{43} +(3.11915 - 1.80084i) q^{44} +(-2.25312 - 1.30084i) q^{45} +(-2.54247 - 1.46789i) q^{46} +(-8.43580 + 4.87041i) q^{47} +1.00000 q^{48} +(-2.55026 - 6.51891i) q^{49} -1.76873i q^{50} +(1.41647 + 2.45340i) q^{51} +(1.94551 - 3.03562i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.866025 - 0.500000i) q^{54} +9.37041 q^{55} +(2.18521 + 1.49160i) q^{56} -1.33411i q^{57} +(7.77006 - 4.48605i) q^{58} +(-10.0232 - 5.78689i) q^{59} +(2.25312 + 1.30084i) q^{60} +(-2.01815 - 3.49554i) q^{61} -4.00000 q^{62} +(2.63824 + 0.199160i) q^{63} -1.00000 q^{64} +(8.33233 - 4.30881i) q^{65} +(-1.80084 + 3.11915i) q^{66} +(10.1679 + 5.87041i) q^{67} +(-1.41647 - 2.45340i) q^{68} +2.93579 q^{69} +(2.98320 + 6.20336i) q^{70} +5.76873i q^{71} +(-0.866025 + 0.500000i) q^{72} +(-9.93411 - 5.73546i) q^{73} +(-0.0835276 + 0.144674i) q^{74} +(0.884367 + 1.53177i) q^{75} +1.33411i q^{76} +(-8.58773 + 4.12985i) q^{77} +(-0.167055 + 3.60168i) q^{78} +(-3.37041 - 5.83773i) q^{79} +(-2.25312 - 1.30084i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.51815 + 2.62952i) q^{82} +8.10051i q^{83} +(-2.63824 - 0.199160i) q^{84} -7.37041i q^{85} +(2.02140 - 1.16706i) q^{86} +(-4.48605 + 7.77006i) q^{87} +(1.80084 - 3.11915i) q^{88} +(-7.07288 + 4.08353i) q^{89} -2.60168 q^{90} +(-5.73732 + 7.62123i) q^{91} -2.93579 q^{92} +(3.46410 - 2.00000i) q^{93} +(-4.87041 + 8.43580i) q^{94} +(-1.73546 + 3.00591i) q^{95} +(0.866025 - 0.500000i) q^{96} -0.139148i q^{97} +(-5.46804 - 4.37041i) q^{98} -3.60168i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43}+ \cdots + 24 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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