LMFDB - Embedded newform 726.2.e.f.565.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,1,-1,-7,1,-1,-1,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			565.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	726.565
Dual form			726.2.e.f.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.42705 + 4.39201i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +2.85410 q^{10} -1.00000 q^{12} +(2.61803 + 1.90211i) q^{13} +(1.42705 - 4.39201i) q^{14} +(-0.881966 - 2.71441i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.00000 - 1.45309i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.00000 + 3.07768i) q^{19} +(-2.30902 - 1.67760i) q^{20} -4.61803 q^{21} -3.23607 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.972136 - 2.99193i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.73607 + 2.71441i) q^{28} +(-0.118034 - 0.363271i) q^{29} +(-0.881966 + 2.71441i) q^{30} +(-6.97214 - 5.06555i) q^{31} +1.00000 q^{32} -2.47214 q^{34} +(-10.6631 - 7.74721i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.472136 + 1.45309i) q^{37} +(2.61803 - 1.90211i) q^{38} +(-2.61803 + 1.90211i) q^{39} +(0.881966 + 2.71441i) q^{40} +(-1.00000 + 3.07768i) q^{41} +(3.73607 + 2.71441i) q^{42} -3.23607 q^{43} +2.85410 q^{45} +(2.61803 + 1.90211i) q^{46} +(0.763932 - 2.35114i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-11.5902 + 8.42075i) q^{49} +(-2.54508 + 1.84911i) q^{50} +(0.763932 + 2.35114i) q^{51} +(-1.00000 + 3.07768i) q^{52} +(3.11803 + 2.26538i) q^{53} -1.00000 q^{54} +4.61803 q^{56} +(-2.61803 - 1.90211i) q^{57} +(-0.118034 + 0.363271i) q^{58} +(-1.19098 - 3.66547i) q^{59} +(2.30902 - 1.67760i) q^{60} +(5.47214 - 3.97574i) q^{61} +(2.66312 + 8.19624i) q^{62} +(1.42705 - 4.39201i) q^{63} +(-0.809017 - 0.587785i) q^{64} -9.23607 q^{65} +4.00000 q^{67} +(2.00000 + 1.45309i) q^{68} +(1.00000 - 3.07768i) q^{69} +(4.07295 + 12.5352i) q^{70} +(-10.0902 + 7.33094i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(0.472136 - 1.45309i) q^{74} +(2.54508 + 1.84911i) q^{75} -3.23607 q^{76} +3.23607 q^{78} +(7.54508 + 5.48183i) q^{79} +(0.881966 - 2.71441i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.61803 - 1.90211i) q^{82} +(0.545085 - 0.396027i) q^{83} +(-1.42705 - 4.39201i) q^{84} +(-2.18034 + 6.71040i) q^{85} +(2.61803 + 1.90211i) q^{86} +0.381966 q^{87} -11.7082 q^{89} +(-2.30902 - 1.67760i) q^{90} +(-4.61803 + 14.2128i) q^{91} +(-1.00000 - 3.07768i) q^{92} +(6.97214 - 5.06555i) q^{93} +(-2.00000 + 1.45309i) q^{94} +(-2.85410 - 8.78402i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-9.16312 - 6.65740i) q^{97} +14.3262 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - 7 q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{12} + 6 q^{13} - q^{14} - 8 q^{15} - q^{16} + 8 q^{17} - q^{18} - 4 q^{19} - 7 q^{20} - 14 q^{21} - 4 q^{23}+ \cdots + 26 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 - 7 * q^5 + q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^12 + 6 * q^13 - q^14 - 8 * q^15 - q^16 + 8 * q^17 - q^18 - 4 * q^19 - 7 * q^20 - 14 * q^21 - 4 * q^23 + q^24 - 14 * q^25 - 4 * q^26 + q^27 - 6 * q^28 + 4 * q^29 - 8 * q^30 - 10 * q^31 + 4 * q^32 + 8 * q^34 - 27 * q^35 - q^36 - 16 * q^37 + 6 * q^38 - 6 * q^39 + 8 * q^40 - 4 * q^41 + 6 * q^42 - 4 * q^43 - 2 * q^45 + 6 * q^46 + 12 * q^47 + q^48 - 24 * q^49 + q^50 + 12 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 14 * q^56 - 6 * q^57 + 4 * q^58 - 7 * q^59 + 7 * q^60 + 4 * q^61 - 5 * q^62 - q^63 - q^64 - 28 * q^65 + 16 * q^67 + 8 * q^68 + 4 * q^69 + 23 * q^70 - 18 * q^71 - q^72 - 14 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + 19 * q^79 + 8 * q^80 - q^81 + 6 * q^82 - 9 * q^83 + q^84 + 36 * q^85 + 6 * q^86 + 6 * q^87 - 20 * q^89 - 7 * q^90 - 14 * q^91 - 4 * q^92 + 10 * q^93 - 8 * q^94 + 2 * q^95 + q^96 - 21 * q^97 + 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.30902	+	1.67760i	−1.03262	+	0.750245i	−0.968832	−	0.247718i	$-0.920319\pi$
$5$	−2.30902	+	1.67760i	−1.03262	+	0.750245i	−0.0637916	+	0.997963i	$0.520319\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	1.42705	+	4.39201i	0.539375	+	1.66002i	0.734002	+	0.679147i	$0.237650\pi$
$7$	1.42705	+	4.39201i	0.539375	+	1.66002i	−0.194628	+	0.980877i	$0.562350\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	2.85410			0.902546
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	2.61803	+	1.90211i	0.726112	+	0.527551i	0.888331	−	0.459204i	$-0.151865\pi$
$13$	2.61803	+	1.90211i	0.726112	+	0.527551i	−0.162219	+	0.986755i	$0.551865\pi$
$14$	1.42705	−	4.39201i	0.381395	−	1.17381i
$15$	−0.881966	−	2.71441i	−0.227723	−	0.700858i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.00000	−	1.45309i	0.485071	−	0.352425i	−0.318214	−	0.948019i	$-0.603083\pi$
$17$	2.00000	−	1.45309i	0.485071	−	0.352425i	0.803286	+	0.595594i	$0.203083\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	−1.00000	+	3.07768i	−0.229416	+	0.706069i	0.768398	+	0.639973i	$0.221054\pi$
$19$	−1.00000	+	3.07768i	−0.229416	+	0.706069i	−0.997813	+	0.0660962i	$0.978946\pi$
$20$	−2.30902	−	1.67760i	−0.516312	−	0.375123i
$21$	−4.61803			−1.00774
$22$		0			0
$23$	−3.23607			−0.674767			−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607			−0.674767			−0.337383	+	0.941367i	$0.609542\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	0.972136	−	2.99193i	0.194427	−	0.598385i
$26$	−1.00000	−	3.07768i	−0.196116	−	0.603583i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−3.73607	+	2.71441i	−0.706050	+	0.512976i
$29$	−0.118034	−	0.363271i	−0.0219184	−	0.0674578i	0.939499	−	0.342551i	$-0.111291\pi$
$29$	−0.118034	−	0.363271i	−0.0219184	−	0.0674578i	−0.961417	+	0.275094i	$0.911291\pi$
$30$	−0.881966	+	2.71441i	−0.161024	+	0.495582i
$31$	−6.97214	−	5.06555i	−1.25223	−	0.909800i	−0.253883	−	0.967235i	$-0.581708\pi$
$31$	−6.97214	−	5.06555i	−1.25223	−	0.909800i	−0.998349	+	0.0574346i	$0.981708\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.47214			−0.423968
$35$	−10.6631	−	7.74721i	−1.80240	−	1.30952i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.472136	+	1.45309i	0.0776187	+	0.238886i	0.982336	−	0.187127i	$-0.0599177\pi$
$37$	0.472136	+	1.45309i	0.0776187	+	0.238886i	−0.904717	+	0.426013i	$0.859918\pi$
$38$	2.61803	−	1.90211i	0.424701	−	0.308563i
$39$	−2.61803	+	1.90211i	−0.419221	+	0.304582i
$40$	0.881966	+	2.71441i	0.139451	+	0.429186i
$41$	−1.00000	+	3.07768i	−0.156174	+	0.480653i	−0.998278	−	0.0586615i	$-0.981317\pi$
$41$	−1.00000	+	3.07768i	−0.156174	+	0.480653i	0.842104	+	0.539315i	$0.181317\pi$
$42$	3.73607	+	2.71441i	0.576488	+	0.418843i
$43$	−3.23607			−0.493496			−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607			−0.493496			−0.246748	+	0.969080i	$0.579362\pi$
$44$		0			0
$45$	2.85410			0.425464
$46$	2.61803	+	1.90211i	0.386008	+	0.280451i
$47$	0.763932	−	2.35114i	0.111431	−	0.342949i	−0.879755	−	0.475427i	$-0.842293\pi$
$47$	0.763932	−	2.35114i	0.111431	−	0.342949i	0.991186	+	0.132478i	$0.0422935\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−11.5902	+	8.42075i	−1.65574	+	1.20296i
$50$	−2.54508	+	1.84911i	−0.359929	+	0.261504i
$51$	0.763932	+	2.35114i	0.106972	+	0.329226i
$52$	−1.00000	+	3.07768i	−0.138675	+	0.426798i
$53$	3.11803	+	2.26538i	0.428295	+	0.311174i	0.780967	−	0.624573i	$-0.214727\pi$
$53$	3.11803	+	2.26538i	0.428295	+	0.311174i	−0.352672	+	0.935747i	$0.614727\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	4.61803			0.617111
$57$	−2.61803	−	1.90211i	−0.346767	−	0.251941i
$58$	−0.118034	+	0.363271i	−0.0154986	+	0.0476999i
$59$	−1.19098	−	3.66547i	−0.155053	−	0.477203i	0.843113	−	0.537736i	$-0.180720\pi$
$59$	−1.19098	−	3.66547i	−0.155053	−	0.477203i	−0.998166	+	0.0605323i	$0.980720\pi$
$60$	2.30902	−	1.67760i	0.298093	−	0.216577i
$61$	5.47214	−	3.97574i	0.700635	−	0.509041i	−0.179504	−	0.983757i	$-0.557449\pi$
$61$	5.47214	−	3.97574i	0.700635	−	0.509041i	0.880139	+	0.474716i	$0.157449\pi$
$62$	2.66312	+	8.19624i	0.338216	+	1.04092i
$63$	1.42705	−	4.39201i	0.179792	−	0.553341i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−9.23607			−1.14559
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	2.00000	+	1.45309i	0.242536	+	0.176212i
$69$	1.00000	−	3.07768i	0.120386	−	0.370510i
$70$	4.07295	+	12.5352i	0.486811	+	1.49825i
$71$	−10.0902	+	7.33094i	−1.19748	+	0.870022i	−0.994035	−	0.109064i	$-0.965215\pi$
$71$	−10.0902	+	7.33094i	−1.19748	+	0.870022i	−0.203448	+	0.979086i	$0.565215\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	−3.50000	−	10.7719i	−0.409644	−	1.26075i	−0.916955	−	0.398991i	$-0.869360\pi$
$73$	−3.50000	−	10.7719i	−0.409644	−	1.26075i	0.507311	−	0.861763i	$-0.330640\pi$
$74$	0.472136	−	1.45309i	0.0548847	−	0.168918i
$75$	2.54508	+	1.84911i	0.293881	+	0.213517i
$76$	−3.23607			−0.371202
$77$		0			0
$78$	3.23607			0.366413
$79$	7.54508	+	5.48183i	0.848888	+	0.616754i	0.924839	−	0.380358i	$-0.124199\pi$
$79$	7.54508	+	5.48183i	0.848888	+	0.616754i	−0.0759509	+	0.997112i	$0.524199\pi$
$80$	0.881966	−	2.71441i	0.0986068	−	0.303481i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.61803	−	1.90211i	0.289113	−	0.210053i
$83$	0.545085	−	0.396027i	0.0598308	−	0.0434697i	−0.557468	−	0.830199i	$-0.688227\pi$
$83$	0.545085	−	0.396027i	0.0598308	−	0.0434697i	0.617299	+	0.786729i	$0.288227\pi$
$84$	−1.42705	−	4.39201i	−0.155704	−	0.479208i
$85$	−2.18034	+	6.71040i	−0.236491	+	0.727845i
$86$	2.61803	+	1.90211i	0.282310	+	0.205110i
$87$	0.381966			0.0409511
$88$		0			0
$89$	−11.7082			−1.24107			−0.620534	−	0.784180i	$-0.713084\pi$
$89$	−11.7082			−1.24107			−0.620534	+	0.784180i	$0.713084\pi$
$90$	−2.30902	−	1.67760i	−0.243392	−	0.176834i
$91$	−4.61803	+	14.2128i	−0.484102	+	1.48991i
$92$	−1.00000	−	3.07768i	−0.104257	−	0.320871i
$93$	6.97214	−	5.06555i	0.722977	−	0.525273i
$94$	−2.00000	+	1.45309i	−0.206284	+	0.149874i
$95$	−2.85410	−	8.78402i	−0.292825	−	0.901222i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−9.16312	−	6.65740i	−0.930374	−	0.675956i	0.0157105	−	0.999877i	$-0.494999\pi$
$97$	−9.16312	−	6.65740i	−0.930374	−	0.675956i	−0.946084	+	0.323920i	$0.894999\pi$
$98$	14.3262			1.44717
$99$		0			0
$100$	3.14590			0.314590
$101$	10.0172	+	7.27794i	0.996751	+	0.724182i	0.961389	−	0.275193i	$-0.0887417\pi$
$101$	10.0172	+	7.27794i	0.996751	+	0.724182i	0.0353617	+	0.999375i	$0.488742\pi$
$102$	0.763932	−	2.35114i	0.0756405	−	0.232798i
$103$	3.71885	+	11.4454i	0.366429	+	1.12775i	0.949081	+	0.315031i	$0.102015\pi$
$103$	3.71885	+	11.4454i	0.366429	+	1.12775i	−0.582653	+	0.812721i	$0.697985\pi$
$104$	2.61803	−	1.90211i	0.256719	−	0.186518i
$105$	10.6631	−	7.74721i	1.04061	−	0.756050i
$106$	−1.19098	−	3.66547i	−0.115678	−	0.356022i
$107$	1.66312	−	5.11855i	0.160780	−	0.494829i	−0.837921	−	0.545792i	$-0.816229\pi$
$107$	1.66312	−	5.11855i	0.160780	−	0.494829i	0.998701	+	0.0509626i	$0.0162289\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	17.4164			1.66819			0.834095	−	0.551621i	$-0.185991\pi$
$109$	17.4164			1.66819			0.834095	+	0.551621i	$0.185991\pi$
$110$		0			0
$111$	−1.52786			−0.145018
$112$	−3.73607	−	2.71441i	−0.353025	−	0.256488i
$113$	−3.85410	+	11.8617i	−0.362563	+	1.11586i	0.588929	+	0.808184i	$0.299550\pi$
$113$	−3.85410	+	11.8617i	−0.362563	+	1.11586i	−0.951493	+	0.307671i	$0.900450\pi$
$114$	1.00000	+	3.07768i	0.0936586	+	0.288251i
$115$	7.47214	−	5.42882i	0.696780	−	0.506240i
$116$	0.309017	−	0.224514i	0.0286915	−	0.0208456i
$117$	−1.00000	−	3.07768i	−0.0924500	−	0.284532i
$118$	−1.19098	+	3.66547i	−0.109639	+	0.337434i
$119$	9.23607	+	6.71040i	0.846669	+	0.615141i
$120$	−2.85410			−0.260543
$121$		0			0
$122$	−6.76393			−0.612378
$123$	−2.61803	−	1.90211i	−0.236060	−	0.171508i
$124$	2.66312	−	8.19624i	0.239155	−	0.736044i
$125$	−1.63525	−	5.03280i	−0.146262	−	0.450147i
$126$	−3.73607	+	2.71441i	−0.332835	+	0.241819i
$127$	−9.70820	+	7.05342i	−0.861464	+	0.625890i	−0.928283	−	0.371875i	$-0.878715\pi$
$127$	−9.70820	+	7.05342i	−0.861464	+	0.625890i	0.0668190	+	0.997765i	$0.478715\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	1.00000	−	3.07768i	0.0880451	−	0.270975i
$130$	7.47214	+	5.42882i	0.655350	+	0.476139i
$131$	−15.2705			−1.33419			−0.667095	−	0.744972i	$-0.732463\pi$
$131$	−15.2705			−1.33419			−0.667095	+	0.744972i	$0.732463\pi$
$132$		0			0
$133$	−14.9443			−1.29583
$134$	−3.23607	−	2.35114i	−0.279554	−	0.203108i
$135$	−0.881966	+	2.71441i	−0.0759075	+	0.233619i
$136$	−0.763932	−	2.35114i	−0.0655066	−	0.201609i
$137$	18.7082	−	13.5923i	1.59835	−	1.16127i	0.707769	−	0.706444i	$-0.249702\pi$
$137$	18.7082	−	13.5923i	1.59835	−	1.16127i	0.890581	−	0.454825i	$-0.150298\pi$
$138$	−2.61803	+	1.90211i	−0.222862	+	0.161919i
$139$	4.09017	+	12.5882i	0.346924	+	1.06772i	0.960546	+	0.278122i	$0.0897118\pi$
$139$	4.09017	+	12.5882i	0.346924	+	1.06772i	−0.613622	+	0.789600i	$0.710288\pi$
$140$	4.07295	−	12.5352i	0.344227	−	1.05942i
$141$	2.00000	+	1.45309i	0.168430	+	0.122372i
$142$	12.4721			1.04664
$143$		0			0
$144$	1.00000			0.0833333
$145$	0.881966	+	0.640786i	0.0732433	+	0.0532144i
$146$	−3.50000	+	10.7719i	−0.289662	+	0.891488i
$147$	−4.42705	−	13.6251i	−0.365137	−	1.12378i
$148$	−1.23607	+	0.898056i	−0.101604	+	0.0738197i
$149$	−1.11803	+	0.812299i	−0.0915929	+	0.0665461i	−0.632639	−	0.774447i	$-0.718028\pi$
$149$	−1.11803	+	0.812299i	−0.0915929	+	0.0665461i	0.541046	+	0.840993i	$0.318028\pi$
$150$	−0.972136	−	2.99193i	−0.0793746	−	0.244290i
$151$	2.88197	−	8.86978i	0.234531	−	0.721812i	−0.762652	−	0.646809i	$-0.776103\pi$
$151$	2.88197	−	8.86978i	0.234531	−	0.721812i	0.997183	−	0.0750036i	$-0.0238968\pi$
$152$	2.61803	+	1.90211i	0.212351	+	0.154282i
$153$	−2.47214			−0.199860
$154$		0			0
$155$	24.5967			1.97566
$156$	−2.61803	−	1.90211i	−0.209610	−	0.152291i
$157$	1.38197	−	4.25325i	0.110293	−	0.339447i	−0.880643	−	0.473780i	$-0.842889\pi$
$157$	1.38197	−	4.25325i	0.110293	−	0.339447i	0.990936	+	0.134333i	$0.0428892\pi$
$158$	−2.88197	−	8.86978i	−0.229277	−	0.705642i
$159$	−3.11803	+	2.26538i	−0.247276	+	0.179657i
$160$	−2.30902	+	1.67760i	−0.182544	+	0.132626i
$161$	−4.61803	−	14.2128i	−0.363952	−	1.12013i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	10.8541	+	7.88597i	0.850159	+	0.617677i	0.925190	−	0.379505i	$-0.123906\pi$
$163$	10.8541	+	7.88597i	0.850159	+	0.617677i	−0.0750310	+	0.997181i	$0.523906\pi$
$164$	−3.23607			−0.252694
$165$		0			0
$166$	−0.673762			−0.0522941
$167$	−5.85410	−	4.25325i	−0.453004	−	0.329127i	0.337777	−	0.941226i	$-0.390325\pi$
$167$	−5.85410	−	4.25325i	−0.453004	−	0.329127i	−0.790781	+	0.612100i	$0.790325\pi$
$168$	−1.42705	+	4.39201i	−0.110099	+	0.338851i
$169$	−0.781153	−	2.40414i	−0.0600887	−	0.184934i
$170$	5.70820	−	4.14725i	0.437799	−	0.318080i
$171$	2.61803	−	1.90211i	0.200206	−	0.145458i
$172$	−1.00000	−	3.07768i	−0.0762493	−	0.234671i
$173$	−1.28115	+	3.94298i	−0.0974043	+	0.299779i	−0.987873	−	0.155265i	$-0.950377\pi$
$173$	−1.28115	+	3.94298i	−0.0974043	+	0.299779i	0.890469	+	0.455045i	$0.150377\pi$
$174$	−0.309017	−	0.224514i	−0.0234265	−	0.0170204i
$175$	14.5279			1.09820
$176$		0			0
$177$	3.85410			0.289692
$178$	9.47214	+	6.88191i	0.709967	+	0.515821i
$179$	−1.97214	+	6.06961i	−0.147404	+	0.453664i	−0.997312	−	0.0732671i	$-0.976657\pi$
$179$	−1.97214	+	6.06961i	−0.147404	+	0.453664i	0.849908	+	0.526931i	$0.176657\pi$
$180$	0.881966	+	2.71441i	0.0657379	+	0.202320i
$181$	13.3262	−	9.68208i	0.990531	−	0.719663i	0.0304941	−	0.999535i	$-0.490292\pi$
$181$	13.3262	−	9.68208i	0.990531	−	0.719663i	0.960037	+	0.279872i	$0.0902919\pi$
$182$	12.0902	−	8.78402i	0.896183	−	0.651115i
$183$	2.09017	+	6.43288i	0.154510	+	0.475532i
$184$	−1.00000	+	3.07768i	−0.0737210	+	0.226890i
$185$	−3.52786	−	2.56314i	−0.259374	−	0.188446i
$186$	−8.61803			−0.631905
$187$		0			0
$188$	2.47214			0.180299
$189$	3.73607	+	2.71441i	0.271759	+	0.197444i
$190$	−2.85410	+	8.78402i	−0.207058	+	0.637260i
$191$	6.94427	+	21.3723i	0.502470	+	1.54644i	0.804983	+	0.593298i	$0.202174\pi$
$191$	6.94427	+	21.3723i	0.502470	+	1.54644i	−0.302513	+	0.953145i	$0.597826\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	−0.263932	+	0.191758i	−0.0189982	+	0.0138030i	−0.597244	−	0.802060i	$-0.703738\pi$
$193$	−0.263932	+	0.191758i	−0.0189982	+	0.0138030i	0.578246	+	0.815863i	$0.303738\pi$
$194$	3.50000	+	10.7719i	0.251285	+	0.773377i
$195$	2.85410	−	8.78402i	0.204386	−	0.629037i
$196$	−11.5902	−	8.42075i	−0.827869	−	0.601482i
$197$	6.09017			0.433907			0.216953	−	0.976182i	$-0.430388\pi$
$197$	6.09017			0.433907			0.216953	+	0.976182i	$0.430388\pi$
$198$		0			0
$199$	13.1459			0.931888			0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459			0.931888			0.465944	+	0.884814i	$0.345715\pi$
$200$	−2.54508	−	1.84911i	−0.179965	−	0.130752i
$201$	−1.23607	+	3.80423i	−0.0871855	+	0.268329i
$202$	−3.82624	−	11.7759i	−0.269213	−	0.828553i
$203$	1.42705	−	1.03681i	0.100159	−	0.0727700i
$204$	−2.00000	+	1.45309i	−0.140028	+	0.101736i
$205$	−2.85410	−	8.78402i	−0.199339	−	0.613503i
$206$	3.71885	−	11.4454i	0.259104	−	0.797441i
$207$	2.61803	+	1.90211i	0.181966	+	0.132206i
$208$	−3.23607			−0.224381
$209$		0			0
$210$	−13.1803			−0.909530
$211$	3.76393	+	2.73466i	0.259120	+	0.188262i	0.709759	−	0.704445i	$-0.248804\pi$
$211$	3.76393	+	2.73466i	0.259120	+	0.188262i	−0.450639	+	0.892706i	$0.648804\pi$
$212$	−1.19098	+	3.66547i	−0.0817970	+	0.251745i
$213$	−3.85410	−	11.8617i	−0.264079	−	0.812751i
$214$	−4.35410	+	3.16344i	−0.297640	+	0.216248i
$215$	7.47214	−	5.42882i	0.509595	−	0.370243i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	12.2984	−	37.8505i	0.834868	−	2.56946i
$218$	−14.0902	−	10.2371i	−0.954307	−	0.693344i
$219$	11.3262			0.765356
$220$		0			0
$221$	8.00000			0.538138
$222$	1.23607	+	0.898056i	0.0829595	+	0.0602736i
$223$	−0.590170	+	1.81636i	−0.0395207	+	0.121632i	−0.968870	−	0.247568i	$-0.920368\pi$
$223$	−0.590170	+	1.81636i	−0.0395207	+	0.121632i	0.929350	+	0.369201i	$0.120368\pi$
$224$	1.42705	+	4.39201i	0.0953489	+	0.293454i
$225$	−2.54508	+	1.84911i	−0.169672	+	0.123274i
$226$	10.0902	−	7.33094i	0.671188	−	0.487647i
$227$	−2.20820	−	6.79615i	−0.146564	−	0.451077i	0.850645	−	0.525740i	$-0.176212\pi$
$227$	−2.20820	−	6.79615i	−0.146564	−	0.451077i	−0.997209	+	0.0746638i	$0.976212\pi$
$228$	1.00000	−	3.07768i	0.0662266	−	0.203825i
$229$	−18.5623	−	13.4863i	−1.22663	−	0.891200i	−0.229999	−	0.973191i	$-0.573872\pi$
$229$	−18.5623	−	13.4863i	−1.22663	−	0.891200i	−0.996633	+	0.0819909i	$0.973872\pi$
$230$	−9.23607			−0.609008
$231$		0			0
$232$	−0.381966			−0.0250773
$233$	7.23607	+	5.25731i	0.474051	+	0.344418i	0.799018	−	0.601307i	$-0.205353\pi$
$233$	7.23607	+	5.25731i	0.474051	+	0.344418i	−0.324967	+	0.945725i	$0.605353\pi$
$234$	−1.00000	+	3.07768i	−0.0653720	+	0.201194i
$235$	2.18034	+	6.71040i	0.142230	+	0.437738i
$236$	3.11803	−	2.26538i	0.202967	−	0.147464i
$237$	−7.54508	+	5.48183i	−0.490106	+	0.356083i
$238$	−3.52786	−	10.8576i	−0.228677	−	0.703797i
$239$	−5.09017	+	15.6659i	−0.329256	+	1.01334i	0.640227	+	0.768186i	$0.278840\pi$
$239$	−5.09017	+	15.6659i	−0.329256	+	1.01334i	−0.969483	+	0.245159i	$0.921160\pi$
$240$	2.30902	+	1.67760i	0.149046	+	0.108289i
$241$	−2.43769			−0.157026			−0.0785128	−	0.996913i	$-0.525017\pi$
$241$	−2.43769			−0.157026			−0.0785128	+	0.996913i	$0.525017\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	5.47214	+	3.97574i	0.350318	+	0.254521i
$245$	12.6353	−	38.8873i	0.807237	−	2.48442i
$246$	1.00000	+	3.07768i	0.0637577	+	0.196226i
$247$	−8.47214	+	6.15537i	−0.539069	+	0.391657i
$248$	−6.97214	+	5.06555i	−0.442731	+	0.321663i
$249$	0.208204	+	0.640786i	0.0131944	+	0.0406082i
$250$	−1.63525	+	5.03280i	−0.103423	+	0.318302i
$251$	15.6353	+	11.3597i	0.986889	+	0.717016i	0.959238	−	0.282601i	$-0.0911973\pi$
$251$	15.6353	+	11.3597i	0.986889	+	0.717016i	0.0276510	+	0.999618i	$0.491197\pi$
$252$	4.61803			0.290909
$253$		0			0
$254$	12.0000			0.752947
$255$	−5.70820	−	4.14725i	−0.357462	−	0.259711i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.562306	−	1.73060i	−0.0350757	−	0.107952i	0.931986	−	0.362495i	$-0.118075\pi$
$257$	−0.562306	−	1.73060i	−0.0350757	−	0.107952i	−0.967061	+	0.254543i	$0.918075\pi$
$258$	−2.61803	+	1.90211i	−0.162992	+	0.118420i
$259$	−5.70820	+	4.14725i	−0.354691	+	0.257698i
$260$	−2.85410	−	8.78402i	−0.177004	−	0.544762i
$261$	−0.118034	+	0.363271i	−0.00730612	+	0.0224859i
$262$	12.3541	+	8.97578i	0.763239	+	0.554526i
$263$	7.70820			0.475308			0.237654	−	0.971350i	$-0.423622\pi$
$263$	7.70820			0.475308			0.237654	+	0.971350i	$0.423622\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$	12.0902	+	8.78402i	0.741296	+	0.538583i
$267$	3.61803	−	11.1352i	0.221420	−	0.681461i
$268$	1.23607	+	3.80423i	0.0755049	+	0.232380i
$269$	2.38197	−	1.73060i	0.145231	−	0.105517i	−0.512797	−	0.858510i	$-0.671391\pi$
$269$	2.38197	−	1.73060i	0.145231	−	0.105517i	0.658028	+	0.752993i	$0.271391\pi$
$270$	2.30902	−	1.67760i	0.140522	−	0.102095i
$271$	7.23607	+	22.2703i	0.439560	+	1.35283i	0.888341	+	0.459184i	$0.151858\pi$
$271$	7.23607	+	22.2703i	0.439560	+	1.35283i	−0.448781	+	0.893642i	$0.648142\pi$
$272$	−0.763932	+	2.35114i	−0.0463202	+	0.142559i
$273$	−12.0902	−	8.78402i	−0.731730	−	0.531633i
$274$	−23.1246			−1.39701
$275$		0			0
$276$	3.23607			0.194788
$277$	−9.00000	−	6.53888i	−0.540758	−	0.392883i	0.283609	−	0.958940i	$-0.408468\pi$
$277$	−9.00000	−	6.53888i	−0.540758	−	0.392883i	−0.824366	+	0.566057i	$0.808468\pi$
$278$	4.09017	−	12.5882i	0.245312	−	0.754993i
$279$	2.66312	+	8.19624i	0.159437	+	0.490696i
$280$	−10.6631	+	7.74721i	−0.637243	+	0.462984i
$281$	−18.7082	+	13.5923i	−1.11604	+	0.810849i	−0.983604	−	0.180343i	$-0.942279\pi$
$281$	−18.7082	+	13.5923i	−1.11604	+	0.810849i	−0.132434	+	0.991192i	$0.542279\pi$
$282$	−0.763932	−	2.35114i	−0.0454915	−	0.140008i
$283$	−7.38197	+	22.7194i	−0.438812	+	1.35053i	0.450317	+	0.892869i	$0.351311\pi$
$283$	−7.38197	+	22.7194i	−0.438812	+	1.35053i	−0.889129	+	0.457657i	$0.848689\pi$
$284$	−10.0902	−	7.33094i	−0.598741	−	0.435011i
$285$	9.23607			0.547097
$286$		0			0
$287$	−14.9443			−0.882132
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−3.36475	+	10.3556i	−0.197926	+	0.609154i
$290$	−0.336881	−	1.03681i	−0.0197823	−	0.0608838i
$291$	9.16312	−	6.65740i	0.537152	−	0.390263i
$292$	9.16312	−	6.65740i	0.536231	−	0.389595i
$293$	7.10081	+	21.8541i	0.414834	+	1.27673i	0.912399	+	0.409301i	$0.134227\pi$
$293$	7.10081	+	21.8541i	0.414834	+	1.27673i	−0.497565	+	0.867426i	$0.665773\pi$
$294$	−4.42705	+	13.6251i	−0.258191	+	0.794630i
$295$	8.89919	+	6.46564i	0.518131	+	0.376444i
$296$	1.52786			0.0888053
$297$		0			0
$298$	1.38197			0.0800551
$299$	−8.47214	−	6.15537i	−0.489956	−	0.355974i
$300$	−0.972136	+	2.99193i	−0.0561263	+	0.172739i
$301$	−4.61803	−	14.2128i	−0.266179	−	0.819215i
$302$	−7.54508	+	5.48183i	−0.434171	+	0.315444i
$303$	−10.0172	+	7.27794i	−0.575474	+	0.418107i
$304$	−1.00000	−	3.07768i	−0.0573539	−	0.176517i
$305$	−5.96556	+	18.3601i	−0.341587	+	1.05130i
$306$	2.00000	+	1.45309i	0.114332	+	0.0830673i
$307$	−16.6525			−0.950407			−0.475203	−	0.879876i	$-0.657626\pi$
$307$	−16.6525			−0.950407			−0.475203	+	0.879876i	$0.657626\pi$
$308$		0			0
$309$	−12.0344			−0.684615
$310$	−19.8992	−	14.4576i	−1.13020	−	0.821137i
$311$	−7.38197	+	22.7194i	−0.418593	+	1.28830i	0.490405	+	0.871495i	$0.336849\pi$
$311$	−7.38197	+	22.7194i	−0.418593	+	1.28830i	−0.908997	+	0.416802i	$0.863151\pi$
$312$	1.00000	+	3.07768i	0.0566139	+	0.174240i
$313$	−12.2533	+	8.90254i	−0.692597	+	0.503201i	−0.877513	−	0.479553i	$-0.840799\pi$
$313$	−12.2533	+	8.90254i	−0.692597	+	0.503201i	0.184916	+	0.982754i	$0.440799\pi$
$314$	−3.61803	+	2.62866i	−0.204177	+	0.148344i
$315$	4.07295	+	12.5352i	0.229485	+	0.706281i
$316$	−2.88197	+	8.86978i	−0.162123	+	0.498964i
$317$	16.0902	+	11.6902i	0.903714	+	0.656587i	0.939417	−	0.342776i	$-0.111367\pi$
$317$	16.0902	+	11.6902i	0.903714	+	0.656587i	−0.0357033	+	0.999362i	$0.511367\pi$
$318$	3.85410			0.216127
$319$		0			0
$320$	2.85410			0.159549
$321$	4.35410	+	3.16344i	0.243022	+	0.176566i
$322$	−4.61803	+	14.2128i	−0.257353	+	0.792051i
$323$	2.47214	+	7.60845i	0.137553	+	0.423346i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	8.23607	−	5.98385i	0.456855	−	0.331924i
$326$	−4.14590	−	12.7598i	−0.229620	−	0.706698i
$327$	−5.38197	+	16.5640i	−0.297623	+	0.915991i
$328$	2.61803	+	1.90211i	0.144557	+	0.105027i
$329$	11.4164			0.629407
$330$		0			0
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$	0.545085	+	0.396027i	0.0299154	+	0.0217348i
$333$	0.472136	−	1.45309i	0.0258729	−	0.0796286i
$334$	2.23607	+	6.88191i	0.122352	+	0.376561i
$335$	−9.23607	+	6.71040i	−0.504620	+	0.366628i
$336$	3.73607	−	2.71441i	0.203819	−	0.148083i
$337$	2.14590	+	6.60440i	0.116895	+	0.359764i	0.992337	−	0.123557i	$-0.0394302\pi$
$337$	2.14590	+	6.60440i	0.116895	+	0.359764i	−0.875443	+	0.483321i	$0.839430\pi$
$338$	−0.781153	+	2.40414i	−0.0424891	+	0.130768i
$339$	−10.0902	−	7.33094i	−0.548023	−	0.398162i
$340$	−7.05573			−0.382651
$341$		0			0
$342$	−3.23607			−0.174987
$343$	−27.3713	−	19.8864i	−1.47791	−	1.07377i
$344$	−1.00000	+	3.07768i	−0.0539164	+	0.165938i
$345$	2.85410	+	8.78402i	0.153660	+	0.472916i
$346$	3.35410	−	2.43690i	0.180318	−	0.131008i
$347$	−9.59017	+	6.96767i	−0.514827	+	0.374044i	−0.814652	−	0.579950i	$-0.803072\pi$
$347$	−9.59017	+	6.96767i	−0.514827	+	0.374044i	0.299824	+	0.953994i	$0.403072\pi$
$348$	0.118034	+	0.363271i	0.00632729	+	0.0194734i
$349$	−4.09017	+	12.5882i	−0.218942	+	0.673834i	0.779908	+	0.625894i	$0.215266\pi$
$349$	−4.09017	+	12.5882i	−0.218942	+	0.673834i	−0.998850	+	0.0479399i	$0.984734\pi$
$350$	−11.7533	−	8.53926i	−0.628240	−	0.456443i
$351$	3.23607			0.172729
$352$		0			0
$353$	−21.5967			−1.14948			−0.574739	−	0.818336i	$-0.694897\pi$
$353$	−21.5967			−1.14948			−0.574739	+	0.818336i	$0.694897\pi$
$354$	−3.11803	−	2.26538i	−0.165722	−	0.120404i
$355$	11.0000	−	33.8545i	0.583819	−	1.79681i
$356$	−3.61803	−	11.1352i	−0.191755	−	0.590162i
$357$	−9.23607	+	6.71040i	−0.488825	+	0.355152i
$358$	5.16312	−	3.75123i	0.272879	−	0.198258i
$359$	3.94427	+	12.1392i	0.208171	+	0.640684i	0.999568	+	0.0293817i	$0.00935385\pi$
$359$	3.94427	+	12.1392i	0.208171	+	0.640684i	−0.791398	+	0.611302i	$0.790646\pi$
$360$	0.881966	−	2.71441i	0.0464837	−	0.143062i
$361$	6.89919	+	5.01255i	0.363115	+	0.263819i
$362$	−16.4721			−0.865756
$363$		0			0
$364$	−14.9443			−0.783293
$365$	26.1525	+	19.0009i	1.36888	+	0.994552i
$366$	2.09017	−	6.43288i	0.109255	−	0.336252i
$367$	−11.5902	−	35.6709i	−0.605002	−	1.86200i	−0.496777	−	0.867878i	$-0.665483\pi$
$367$	−11.5902	−	35.6709i	−0.605002	−	1.86200i	−0.108225	−	0.994126i	$-0.534517\pi$
$368$	2.61803	−	1.90211i	0.136474	−	0.0991545i
$369$	2.61803	−	1.90211i	0.136289	−	0.0990200i
$370$	1.34752	+	4.14725i	0.0700544	+	0.215605i
$371$	−5.50000	+	16.9273i	−0.285546	+	0.878820i
$372$	6.97214	+	5.06555i	0.361488	+	0.262637i
$373$	−9.52786			−0.493334			−0.246667	−	0.969100i	$-0.579335\pi$
$373$	−9.52786			−0.493334			−0.246667	+	0.969100i	$0.579335\pi$
$374$		0			0
$375$	5.29180			0.273267
$376$	−2.00000	−	1.45309i	−0.103142	−	0.0749371i
$377$	0.381966	−	1.17557i	0.0196723	−	0.0605450i
$378$	−1.42705	−	4.39201i	−0.0733996	−	0.225901i
$379$	−3.00000	+	2.17963i	−0.154100	+	0.111960i	−0.662163	−	0.749360i	$-0.730361\pi$
$379$	−3.00000	+	2.17963i	−0.154100	+	0.111960i	0.508064	+	0.861320i	$0.330361\pi$
$380$	7.47214	−	5.42882i	0.383312	−	0.278493i
$381$	−3.70820	−	11.4127i	−0.189977	−	0.584689i
$382$	6.94427	−	21.3723i	0.355300	−	1.09350i
$383$	−10.7082	−	7.77997i	−0.547164	−	0.397538i	0.279575	−	0.960124i	$-0.409806\pi$
$383$	−10.7082	−	7.77997i	−0.547164	−	0.397538i	−0.826739	+	0.562586i	$0.809806\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	0.326238			0.0166051
$387$	2.61803	+	1.90211i	0.133082	+	0.0966898i
$388$	3.50000	−	10.7719i	0.177686	−	0.546860i
$389$	12.0344	+	37.0382i	0.610170	+	1.87791i	0.456316	+	0.889818i	$0.349169\pi$
$389$	12.0344	+	37.0382i	0.610170	+	1.87791i	0.153855	+	0.988093i	$0.450831\pi$
$390$	−7.47214	+	5.42882i	−0.378366	+	0.274899i
$391$	−6.47214	+	4.70228i	−0.327310	+	0.237805i
$392$	4.42705	+	13.6251i	0.223600	+	0.688170i
$393$	4.71885	−	14.5231i	0.238034	−	0.732594i
$394$	−4.92705	−	3.57971i	−0.248221	−	0.180343i
$395$	−26.6180			−1.33930
$396$		0			0
$397$	9.88854			0.496292			0.248146	−	0.968723i	$-0.420179\pi$
$397$	9.88854			0.496292			0.248146	+	0.968723i	$0.420179\pi$
$398$	−10.6353	−	7.72696i	−0.533097	−	0.387318i
$399$	4.61803	−	14.2128i	0.231191	−	0.711532i
$400$	0.972136	+	2.99193i	0.0486068	+	0.149596i
$401$	−8.32624	+	6.04937i	−0.415792	+	0.302091i	−0.775943	−	0.630803i	$-0.782725\pi$
$401$	−8.32624	+	6.04937i	−0.415792	+	0.302091i	0.360150	+	0.932894i	$0.382725\pi$
$402$	3.23607	−	2.35114i	0.161400	−	0.117264i
$403$	−8.61803	−	26.5236i	−0.429295	−	1.32123i
$404$	−3.82624	+	11.7759i	−0.190362	+	0.585875i
$405$	−2.30902	−	1.67760i	−0.114736	−	0.0833606i
$406$	−1.76393			−0.0875425
$407$		0			0
$408$	2.47214			0.122389
$409$	9.78115	+	7.10642i	0.483647	+	0.351390i	0.802736	−	0.596335i	$-0.203377\pi$
$409$	9.78115	+	7.10642i	0.483647	+	0.351390i	−0.319089	+	0.947725i	$0.603377\pi$
$410$	−2.85410	+	8.78402i	−0.140954	+	0.433812i
$411$	7.14590	+	21.9928i	0.352481	+	1.08483i
$412$	−9.73607	+	7.07367i	−0.479662	+	0.348495i
$413$	14.3992	−	10.4616i	0.708538	−	0.514783i
$414$	−1.00000	−	3.07768i	−0.0491473	−	0.151260i
$415$	−0.594235	+	1.82887i	−0.0291699	+	0.0897756i
$416$	2.61803	+	1.90211i	0.128360	+	0.0932588i
$417$	−13.2361			−0.648173
$418$		0			0
$419$	−17.9787			−0.878318			−0.439159	−	0.898409i	$-0.644723\pi$
$419$	−17.9787			−0.878318			−0.439159	+	0.898409i	$0.644723\pi$
$420$	10.6631	+	7.74721i	0.520307	+	0.378025i
$421$	10.8541	−	33.4055i	0.528997	−	1.62808i	−0.227278	−	0.973830i	$-0.572983\pi$
$421$	10.8541	−	33.4055i	0.528997	−	1.62808i	0.756275	−	0.654254i	$-0.227017\pi$
$422$	−1.43769	−	4.42477i	−0.0699859	−	0.215394i
$423$	−2.00000	+	1.45309i	−0.0972433	+	0.0706514i
$424$	3.11803	−	2.26538i	0.151425	−	0.110017i
$425$	−2.40325	−	7.39645i	−0.116575	−	0.358781i
$426$	−3.85410	+	11.8617i	−0.186732	+	0.574702i
$427$	25.2705	+	18.3601i	1.22293	+	0.888508i
$428$	5.38197			0.260147
$429$		0			0
$430$	−9.23607			−0.445403
$431$	5.85410	+	4.25325i	0.281982	+	0.204872i	0.719782	−	0.694201i	$-0.244242\pi$
$431$	5.85410	+	4.25325i	0.281982	+	0.204872i	−0.437799	+	0.899073i	$0.644242\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	3.80902	+	11.7229i	0.183050	+	0.563369i	0.999909	−	0.0134675i	$-0.00428697\pi$
$433$	3.80902	+	11.7229i	0.183050	+	0.563369i	−0.816860	+	0.576836i	$0.804287\pi$
$434$	−32.1976	+	23.3929i	−1.54553	+	1.12290i
$435$	−0.881966	+	0.640786i	−0.0422870	+	0.0307233i
$436$	5.38197	+	16.5640i	0.257749	+	0.793271i
$437$	3.23607	−	9.95959i	0.154802	−	0.476432i
$438$	−9.16312	−	6.65740i	−0.437831	−	0.318103i
$439$	16.0344			0.765282			0.382641	−	0.923897i	$-0.375015\pi$
$439$	16.0344			0.765282			0.382641	+	0.923897i	$0.375015\pi$
$440$		0			0
$441$	14.3262			0.682202
$442$	−6.47214	−	4.70228i	−0.307848	−	0.223665i
$443$	−0.517221	+	1.59184i	−0.0245739	+	0.0756307i	−0.962591	−	0.270957i	$-0.912660\pi$
$443$	−0.517221	+	1.59184i	−0.0245739	+	0.0756307i	0.938017	+	0.346588i	$0.112660\pi$
$444$	−0.472136	−	1.45309i	−0.0224066	−	0.0689604i
$445$	27.0344	−	19.6417i	1.28156	−	0.931105i
$446$	1.54508	−	1.12257i	0.0731619	−	0.0531552i
$447$	−0.427051	−	1.31433i	−0.0201988	−	0.0621656i
$448$	1.42705	−	4.39201i	0.0674218	−	0.207503i
$449$	−29.0344	−	21.0948i	−1.37022	−	0.995523i	−0.997720	−	0.0674910i	$-0.978501\pi$
$449$	−29.0344	−	21.0948i	−1.37022	−	0.995523i	−0.372500	−	0.928032i	$-0.621499\pi$
$450$	3.14590			0.148299
$451$		0			0
$452$	−12.4721			−0.586640
$453$	7.54508	+	5.48183i	0.354499	+	0.257559i
$454$	−2.20820	+	6.79615i	−0.103636	+	0.318959i
$455$	−13.1803	−	40.5649i	−0.617904	−	1.90171i
$456$	−2.61803	+	1.90211i	−0.122601	+	0.0890746i
$457$	17.7812	−	12.9188i	0.831767	−	0.604314i	−0.0882915	−	0.996095i	$-0.528141\pi$
$457$	17.7812	−	12.9188i	0.831767	−	0.604314i	0.920059	+	0.391780i	$0.128141\pi$
$458$	7.09017	+	21.8213i	0.331302	+	1.01964i
$459$	0.763932	−	2.35114i	0.0356573	−	0.109742i
$460$	7.47214	+	5.42882i	0.348390	+	0.253120i
$461$	40.8328			1.90177			0.950887	−	0.309538i	$-0.100175\pi$
$461$	40.8328			1.90177			0.950887	+	0.309538i	$0.100175\pi$
$462$		0			0
$463$	19.0902			0.887195			0.443598	−	0.896226i	$-0.353702\pi$
$463$	19.0902			0.887195			0.443598	+	0.896226i	$0.353702\pi$
$464$	0.309017	+	0.224514i	0.0143458	+	0.0104228i
$465$	−7.60081	+	23.3929i	−0.352479	+	1.08482i
$466$	−2.76393	−	8.50651i	−0.128037	−	0.394056i
$467$	−15.8262	+	11.4984i	−0.732351	+	0.532084i	−0.890306	−	0.455362i	$-0.849510\pi$
$467$	−15.8262	+	11.4984i	−0.732351	+	0.532084i	0.157955	+	0.987446i	$0.449510\pi$
$468$	2.61803	−	1.90211i	0.121019	−	0.0879252i
$469$	5.70820	+	17.5680i	0.263580	+	0.811217i
$470$	2.18034	−	6.71040i	0.100572	−	0.309527i
$471$	3.61803	+	2.62866i	0.166710	+	0.121122i
$472$	−3.85410			−0.177399
$473$		0			0
$474$	9.32624			0.428368
$475$	8.23607	+	5.98385i	0.377897	+	0.274558i
$476$	−3.52786	+	10.8576i	−0.161699	+	0.497660i
$477$	−1.19098	−	3.66547i	−0.0545314	−	0.167830i
$478$	13.3262	−	9.68208i	0.609528	−	0.442848i
$479$	5.85410	−	4.25325i	0.267481	−	0.194336i	−0.445958	−	0.895054i	$-0.647137\pi$
$479$	5.85410	−	4.25325i	0.267481	−	0.194336i	0.713438	+	0.700718i	$0.247137\pi$
$480$	−0.881966	−	2.71441i	−0.0402561	−	0.123895i
$481$	−1.52786	+	4.70228i	−0.0696646	+	0.214406i
$482$	1.97214	+	1.43284i	0.0898283	+	0.0652641i
$483$	14.9443			0.679988
$484$		0			0
$485$	32.3262			1.46786
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	7.71885	−	23.7562i	0.349774	−	1.07649i	−0.609204	−	0.793014i	$-0.708511\pi$
$487$	7.71885	−	23.7562i	0.349774	−	1.07649i	0.958978	−	0.283481i	$-0.0914892\pi$
$488$	−2.09017	−	6.43288i	−0.0946175	−	0.291203i
$489$	−10.8541	+	7.88597i	−0.490839	+	0.356616i
$490$	−33.0795	+	24.0337i	−1.49438	+	1.08573i
$491$	13.0557	+	40.1814i	0.589197	+	1.81336i	0.581720	+	0.813389i	$0.302380\pi$
$491$	13.0557	+	40.1814i	0.589197	+	1.81336i	0.00747678	+	0.999972i	$0.497620\pi$
$492$	1.00000	−	3.07768i	0.0450835	−	0.138753i
$493$	−0.763932	−	0.555029i	−0.0344058	−	0.0249973i
$494$	10.4721			0.471164
$495$		0			0
$496$	8.61803			0.386961
$497$	−46.5967	−	33.8545i	−2.09015	−	1.51858i
$498$	0.208204	−	0.640786i	0.00932984	−	0.0287143i
$499$	−2.29180	−	7.05342i	−0.102595	−	0.315755i	0.886564	−	0.462607i	$-0.153086\pi$
$499$	−2.29180	−	7.05342i	−0.102595	−	0.315755i	−0.989158	+	0.146852i	$0.953086\pi$
$500$	4.28115	−	3.11044i	0.191459	−	0.139103i
$501$	5.85410	−	4.25325i	0.261542	−	0.190021i
$502$	−5.97214	−	18.3803i	−0.266549	−	0.820355i
$503$	1.34752	−	4.14725i	0.0600831	−	0.184917i	−0.916510	−	0.400012i	$-0.869006\pi$
$503$	1.34752	−	4.14725i	0.0600831	−	0.184917i	0.976593	+	0.215095i	$0.0690061\pi$
$504$	−3.73607	−	2.71441i	−0.166418	−	0.120910i
$505$	−35.3394			−1.57258
$506$		0			0
$507$	2.52786			0.112266
$508$	−9.70820	−	7.05342i	−0.430732	−	0.312945i
$509$	0.989357	−	3.04493i	0.0438525	−	0.134964i	−0.926733	−	0.375720i	$-0.877395\pi$
$509$	0.989357	−	3.04493i	0.0438525	−	0.134964i	0.970586	+	0.240756i	$0.0773954\pi$
$510$	2.18034	+	6.71040i	0.0965471	+	0.297141i
$511$	42.3156	−	30.7441i	1.87193	−	1.36004i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.00000	+	3.07768i	0.0441511	+	0.135883i
$514$	−0.562306	+	1.73060i	−0.0248022	+	0.0763335i
$515$	−27.7877	−	20.1890i	−1.22447	−	0.889632i
$516$	3.23607			0.142460
$517$		0			0
$518$	7.05573			0.310011
$519$	−3.35410	−	2.43690i	−0.147229	−	0.106968i
$520$	−2.85410	+	8.78402i	−0.125161	+	0.385205i
$521$	9.70820	+	29.8788i	0.425324	+	1.30901i	0.902684	+	0.430305i	$0.141594\pi$
$521$	9.70820	+	29.8788i	0.425324	+	1.30901i	−0.477359	+	0.878708i	$0.658406\pi$
$522$	0.309017	−	0.224514i	0.0135253	−	0.00982671i
$523$	−15.8541	+	11.5187i	−0.693251	+	0.503677i	−0.877727	−	0.479160i	$-0.840941\pi$
$523$	−15.8541	+	11.5187i	−0.693251	+	0.503677i	0.184476	+	0.982837i	$0.440941\pi$
$524$	−4.71885	−	14.5231i	−0.206144	−	0.634445i
$525$	−4.48936	+	13.8168i	−0.195932	+	0.603015i
$526$	−6.23607	−	4.53077i	−0.271905	−	0.197551i
$527$	−21.3050			−0.928058
$528$		0			0
$529$	−12.5279			−0.544690
$530$	8.89919	+	6.46564i	0.386556	+	0.280849i
$531$	−1.19098	+	3.66547i	−0.0516843	+	0.159068i
$532$	−4.61803	−	14.2128i	−0.200217	−	0.616205i
$533$	−8.47214	+	6.15537i	−0.366969	+	0.266619i
$534$	−9.47214	+	6.88191i	−0.409899	+	0.297809i
$535$	4.74671	+	14.6089i	0.205218	+	0.631597i
$536$	1.23607	−	3.80423i	0.0533900	−	0.164318i
$537$	−5.16312	−	3.75123i	−0.222805	−	0.161877i
$538$	−2.94427			−0.126937
$539$		0			0
$540$	−2.85410			−0.122821
$541$	−6.09017	−	4.42477i	−0.261837	−	0.190236i	0.449120	−	0.893472i	$-0.351738\pi$
$541$	−6.09017	−	4.42477i	−0.261837	−	0.190236i	−0.710956	+	0.703236i	$0.751738\pi$
$542$	7.23607	−	22.2703i	0.310816	−	0.956592i
$543$	5.09017	+	15.6659i	0.218440	+	0.672290i
$544$	2.00000	−	1.45309i	0.0857493	−	0.0623005i
$545$	−40.2148	+	29.2177i	−1.72261	+	1.25155i
$546$	4.61803	+	14.2128i	0.197634	+	0.608254i
$547$	5.61803	−	17.2905i	0.240210	−	0.739290i	−0.756178	−	0.654366i	$-0.772935\pi$
$547$	5.61803	−	17.2905i	0.240210	−	0.739290i	0.996387	−	0.0849234i	$-0.0270646\pi$
$548$	18.7082	+	13.5923i	0.799175	+	0.580635i
$549$	−6.76393			−0.288678
$550$		0			0
$551$	1.23607			0.0526583
$552$	−2.61803	−	1.90211i	−0.111431	−	0.0809593i
$553$	−13.3090	+	40.9609i	−0.565957	+	1.74184i
$554$	3.43769	+	10.5801i	0.146054	+	0.449507i
$555$	3.52786	−	2.56314i	0.149749	−	0.108799i
$556$	−10.7082	+	7.77997i	−0.454129	+	0.329944i
$557$	−12.9894	−	39.9771i	−0.550377	−	1.69389i	−0.707851	−	0.706362i	$-0.750335\pi$
$557$	−12.9894	−	39.9771i	−0.550377	−	1.69389i	0.157474	−	0.987523i	$-0.449665\pi$
$558$	2.66312	−	8.19624i	0.112739	−	0.346974i
$559$	−8.47214	−	6.15537i	−0.358333	−	0.260344i
$560$	13.1803			0.556971
$561$		0			0
$562$	23.1246			0.975453
$563$	37.8885	+	27.5276i	1.59681	+	1.16015i	0.893293	+	0.449475i	$0.148389\pi$
$563$	37.8885	+	27.5276i	1.59681	+	1.16015i	0.703519	+	0.710677i	$0.251611\pi$
$564$	−0.763932	+	2.35114i	−0.0321673	+	0.0990009i
$565$	−11.0000	−	33.8545i	−0.462773	−	1.42427i
$566$	19.3262	−	14.0413i	0.812342	−	0.590201i
$567$	−3.73607	+	2.71441i	−0.156900	+	0.113995i
$568$	3.85410	+	11.8617i	0.161715	+	0.497706i
$569$	11.3820	−	35.0301i	0.477157	−	1.46854i	−0.365870	−	0.930666i	$-0.619228\pi$
$569$	11.3820	−	35.0301i	0.477157	−	1.46854i	0.843027	−	0.537872i	$-0.180772\pi$
$570$	−7.47214	−	5.42882i	−0.312973	−	0.227388i
$571$	9.59675			0.401611			0.200806	−	0.979631i	$-0.435644\pi$
$571$	9.59675			0.401611			0.200806	+	0.979631i	$0.435644\pi$
$572$		0			0
$573$	−22.4721			−0.938787
$574$	12.0902	+	8.78402i	0.504634	+	0.366638i
$575$	−3.14590	+	9.68208i	−0.131193	+	0.403771i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−5.73607	+	4.16750i	−0.238796	+	0.173495i	−0.700747	−	0.713410i	$-0.747150\pi$
$577$	−5.73607	+	4.16750i	−0.238796	+	0.173495i	0.461951	+	0.886905i	$0.347150\pi$
$578$	8.80902	−	6.40013i	0.366407	−	0.266210i
$579$	−0.100813	−	0.310271i	−0.00418965	−	0.0128944i
$580$	−0.336881	+	1.03681i	−0.0139882	+	0.0430513i
$581$	2.51722	+	1.82887i	0.104432	+	0.0758742i
$582$	−11.3262			−0.469488
$583$		0			0
$584$	−11.3262			−0.468683
$585$	7.47214	+	5.42882i	0.308935	+	0.224454i
$586$	7.10081	−	21.8541i	0.293332	−	0.902783i
$587$	−7.44427	−	22.9111i	−0.307258	−	0.945643i	−0.978825	−	0.204699i	$-0.934378\pi$
$587$	−7.44427	−	22.9111i	−0.307258	−	0.945643i	0.671567	−	0.740944i	$-0.265622\pi$
$588$	11.5902	−	8.42075i	0.477971	−	0.347266i
$589$	22.5623	−	16.3925i	0.929664	−	0.675440i
$590$	−3.39919	−	10.4616i	−0.139942	−	0.430698i
$591$	−1.88197	+	5.79210i	−0.0774137	+	0.238255i
$592$	−1.23607	−	0.898056i	−0.0508021	−	0.0369099i
$593$	24.4721			1.00495			0.502475	−	0.864592i	$-0.332423\pi$
$593$	24.4721			1.00495			0.502475	+	0.864592i	$0.332423\pi$
$594$		0			0
$595$	−32.5836			−1.33580
$596$	−1.11803	−	0.812299i	−0.0457965	−	0.0332731i
$597$	−4.06231	+	12.5025i	−0.166259	+	0.511693i
$598$	3.23607	+	9.95959i	0.132333	+	0.407278i
$599$	−6.76393	+	4.91428i	−0.276367	+	0.200792i	−0.717331	−	0.696732i	$-0.754637\pi$
$599$	−6.76393	+	4.91428i	−0.276367	+	0.200792i	0.440964	+	0.897525i	$0.354637\pi$
$600$	2.54508	−	1.84911i	0.103903	−	0.0754897i
$601$	−7.33688	−	22.5806i	−0.299278	−	0.921082i	−0.981751	−	0.190171i	$-0.939096\pi$
$601$	−7.33688	−	22.5806i	−0.299278	−	0.921082i	0.682473	−	0.730911i	$-0.260904\pi$
$602$	−4.61803	+	14.2128i	−0.188217	+	0.579272i
$603$	−3.23607	−	2.35114i	−0.131783	−	0.0957459i
$604$	9.32624			0.379479
$605$		0			0
$606$	12.3820			0.502983
$607$	−19.2361	−	13.9758i	−0.780768	−	0.567261i	0.124441	−	0.992227i	$-0.460286\pi$
$607$	−19.2361	−	13.9758i	−0.780768	−	0.567261i	−0.905209	+	0.424966i	$0.860286\pi$
$608$	−1.00000	+	3.07768i	−0.0405554	+	0.124817i
$609$	0.545085	+	1.67760i	0.0220880	+	0.0679797i
$610$	15.6180	−	11.3472i	0.632356	−	0.459433i
$611$	6.47214	−	4.70228i	0.261835	−	0.190234i
$612$	−0.763932	−	2.35114i	−0.0308801	−	0.0950392i
$613$	−4.41641	+	13.5923i	−0.178377	+	0.548988i	−0.999772	−	0.0213723i	$-0.993196\pi$
$613$	−4.41641	+	13.5923i	−0.178377	+	0.548988i	0.821395	+	0.570360i	$0.193196\pi$
$614$	13.4721	+	9.78808i	0.543691	+	0.395015i
$615$	9.23607			0.372434
$616$		0			0
$617$	−30.2918			−1.21950			−0.609751	−	0.792593i	$-0.708731\pi$
$617$	−30.2918			−1.21950			−0.609751	+	0.792593i	$0.708731\pi$
$618$	9.73607	+	7.07367i	0.391642	+	0.284545i
$619$	−7.81966	+	24.0664i	−0.314299	+	0.967312i	0.661743	+	0.749730i	$0.269817\pi$
$619$	−7.81966	+	24.0664i	−0.314299	+	0.967312i	−0.976042	+	0.217582i	$0.930183\pi$
$620$	7.60081	+	23.3929i	0.305256	+	0.939481i
$621$	−2.61803	+	1.90211i	−0.105058	+	0.0763292i
$622$	19.3262	−	14.0413i	0.774912	−	0.563006i
$623$	−16.7082	−	51.4226i	−0.669400	−	2.06020i
$624$	1.00000	−	3.07768i	0.0400320	−	0.123206i
$625$	24.9443	+	18.1231i	0.997771	+	0.724923i
$626$	15.1459			0.605352
$627$		0			0
$628$	4.47214			0.178458
$629$	3.05573	+	2.22012i	0.121840	+	0.0885218i
$630$	4.07295	−	12.5352i	0.162270	−	0.499416i
$631$	−5.29837	−	16.3067i	−0.210925	−	0.649160i	−0.999418	−	0.0341164i	$-0.989138\pi$
$631$	−5.29837	−	16.3067i	−0.210925	−	0.649160i	0.788493	−	0.615044i	$-0.210862\pi$
$632$	7.54508	−	5.48183i	0.300127	−	0.218055i
$633$	−3.76393	+	2.73466i	−0.149603	+	0.108693i
$634$	−6.14590	−	18.9151i	−0.244085	−	0.751216i
$635$	10.5836	−	32.5729i	0.419997	−	1.29262i
$636$	−3.11803	−	2.26538i	−0.123638	−	0.0898283i
$637$	−46.3607			−1.83688
$638$		0			0
$639$	12.4721			0.493390
$640$	−2.30902	−	1.67760i	−0.0912719	−	0.0663129i
$641$	14.5623	−	44.8182i	0.575177	−	1.77021i	−0.0604010	−	0.998174i	$-0.519238\pi$
$641$	14.5623	−	44.8182i	0.575177	−	1.77021i	0.635578	−	0.772037i	$-0.280762\pi$
$642$	−1.66312	−	5.11855i	−0.0656381	−	0.202013i
$643$	−8.85410	+	6.43288i	−0.349172	+	0.253688i	−0.748521	−	0.663111i	$-0.769236\pi$
$643$	−8.85410	+	6.43288i	−0.349172	+	0.253688i	0.399350	+	0.916799i	$0.369236\pi$
$644$	12.0902	−	8.78402i	0.476419	−	0.346139i
$645$	2.85410	+	8.78402i	0.112380	+	0.345871i
$646$	2.47214	−	7.60845i	0.0972649	−	0.299351i
$647$	2.32624	+	1.69011i	0.0914538	+	0.0664451i	0.632573	−	0.774501i	$-0.281999\pi$
$647$	2.32624	+	1.69011i	0.0914538	+	0.0664451i	−0.541119	+	0.840946i	$0.681999\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−10.1803			−0.399306
$651$	32.1976	+	23.3929i	1.26192	+	0.916840i
$652$	−4.14590	+	12.7598i	−0.162366	+	0.499711i
$653$	−6.53444	−	20.1109i	−0.255712	−	0.787002i	−0.993688	−	0.112175i	$-0.964218\pi$
$653$	−6.53444	−	20.1109i	−0.255712	−	0.787002i	0.737976	−	0.674827i	$-0.235782\pi$
$654$	14.0902	−	10.2371i	0.550969	−	0.400303i
$655$	35.2599	−	25.6178i	1.37772	−	1.00097i
$656$	−1.00000	−	3.07768i	−0.0390434	−	0.120163i
$657$	−3.50000	+	10.7719i	−0.136548	+	0.420252i
$658$	−9.23607	−	6.71040i	−0.360059	−	0.261598i
$659$	43.1459			1.68073			0.840363	−	0.542024i	$-0.182342\pi$
$659$	43.1459			1.68073			0.840363	+	0.542024i	$0.182342\pi$
$660$		0			0
$661$	5.81966			0.226359			0.113179	−	0.993575i	$-0.463897\pi$
$661$	5.81966			0.226359			0.113179	+	0.993575i	$0.463897\pi$
$662$	−7.23607	−	5.25731i	−0.281238	−	0.204331i
$663$	−2.47214	+	7.60845i	−0.0960098	+	0.295488i
$664$	−0.208204	−	0.640786i	−0.00807988	−	0.0248673i
$665$	34.5066	−	25.0705i	1.33811	−	0.972192i
$666$	−1.23607	+	0.898056i	−0.0478967	+	0.0347990i
$667$	0.381966	+	1.17557i	0.0147898	+	0.0455183i
$668$	2.23607	−	6.88191i	0.0865161	−	0.266269i
$669$	−1.54508	−	1.12257i	−0.0597364	−	0.0434011i
$670$	11.4164			0.441054
$671$		0			0
$672$	−4.61803			−0.178145
$673$	5.63525	+	4.09425i	0.217223	+	0.157822i	0.691076	−	0.722782i	$-0.257137\pi$
$673$	5.63525	+	4.09425i	0.217223	+	0.157822i	−0.473853	+	0.880604i	$0.657137\pi$
$674$	2.14590	−	6.60440i	0.0826569	−	0.254392i
$675$	−0.972136	−	2.99193i	−0.0374175	−	0.115159i
$676$	2.04508	−	1.48584i	0.0786571	−	0.0571477i
$677$	32.7705	−	23.8092i	1.25947	−	0.915061i	0.260741	−	0.965409i	$-0.416033\pi$
$677$	32.7705	−	23.8092i	1.25947	−	0.915061i	0.998732	+	0.0503480i	$0.0160330\pi$
$678$	3.85410	+	11.8617i	0.148016	+	0.455546i
$679$	16.1631	−	49.7450i	0.620284	−	1.90904i
$680$	5.70820	+	4.14725i	0.218900	+	0.159040i
$681$	7.14590			0.273831
$682$		0			0
$683$	45.7426			1.75029			0.875147	−	0.483857i	$-0.160765\pi$
$683$	45.7426			1.75029			0.875147	+	0.483857i	$0.160765\pi$
$684$	2.61803	+	1.90211i	0.100103	+	0.0727291i
$685$	−20.3951	+	62.7697i	−0.779258	+	2.39831i
$686$	10.4549	+	32.1769i	0.399171	+	1.22852i
$687$	18.5623	−	13.4863i	0.708196	−	0.514535i
$688$	2.61803	−	1.90211i	0.0998116	−	0.0725174i
$689$	3.85410	+	11.8617i	0.146830	+	0.451895i
$690$	2.85410	−	8.78402i	0.108654	−	0.334402i
$691$	0.236068	+	0.171513i	0.00898045	+	0.00652468i	0.592266	−	0.805742i	$-0.298233\pi$
$691$	0.236068	+	0.171513i	0.00898045	+	0.00652468i	−0.583286	+	0.812267i	$0.698233\pi$
$692$	−4.14590			−0.157603
$693$		0			0
$694$	11.8541			0.449976
$695$	−30.5623	−	22.2048i	−1.15929	−	0.842277i
$696$	0.118034	−	0.363271i	0.00447407	−	0.0137698i
$697$	2.47214	+	7.60845i	0.0936388	+	0.288191i
$698$	10.7082	−	7.77997i	0.405311	−	0.294476i
$699$	−7.23607	+	5.25731i	−0.273693	+	0.198850i
$700$	4.48936	+	13.8168i	0.169682	+	0.522227i
$701$	0.326238	−	1.00406i	0.0123218	−	0.0379227i	−0.944707	−	0.327917i	$-0.893653\pi$
$701$	0.326238	−	1.00406i	0.0123218	−	0.0379227i	0.957028	+	0.289994i	$0.0936534\pi$
$702$	−2.61803	−	1.90211i	−0.0988113	−	0.0717906i
$703$	−4.94427			−0.186477
$704$		0			0
$705$	−7.05573			−0.265734
$706$	17.4721	+	12.6942i	0.657573	+	0.477754i
$707$	−17.6697	+	54.3817i	−0.664537	+	2.04524i
$708$	1.19098	+	3.66547i	0.0447599	+	0.137757i
$709$	−28.3262	+	20.5802i	−1.06381	+	0.772906i	−0.974790	−	0.223123i	$-0.928375\pi$
$709$	−28.3262	+	20.5802i	−1.06381	+	0.772906i	−0.0890239	+	0.996029i	$0.528375\pi$
$710$	−28.7984	+	20.9232i	−1.08078	+	0.785235i
$711$	−2.88197	−	8.86978i	−0.108082	−	0.332643i
$712$	−3.61803	+	11.1352i	−0.135592	+	0.417308i
$713$	22.5623	+	16.3925i	0.844965	+	0.613903i
$714$	11.4164			0.427248
$715$		0			0
$716$	−6.38197			−0.238505
$717$	−13.3262	−	9.68208i	−0.497677	−	0.361584i
$718$	3.94427	−	12.1392i	0.147199	−	0.453032i
$719$	3.38197	+	10.4086i	0.126126	+	0.388176i	0.994105	−	0.108426i	$-0.0345810\pi$
$719$	3.38197	+	10.4086i	0.126126	+	0.388176i	−0.867979	+	0.496602i	$0.834581\pi$
$720$	−2.30902	+	1.67760i	−0.0860520	+	0.0625204i
$721$	−44.9615	+	32.6664i	−1.67445	+	1.21656i
$722$	−2.63525	−	8.11048i	−0.0980740	−	0.301841i
$723$	0.753289	−	2.31838i	0.0280151	−	0.0862217i
$724$	13.3262	+	9.68208i	0.495266	+	0.359832i
$725$	−1.20163			−0.0446273
$726$		0			0
$727$	3.41641			0.126708			0.0633538	−	0.997991i	$-0.479820\pi$
$727$	3.41641			0.126708			0.0633538	+	0.997991i	$0.479820\pi$
$728$	12.0902	+	8.78402i	0.448092	+	0.325558i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−9.98936	−	30.7441i	−0.369723	−	1.13789i
$731$	−6.47214	+	4.70228i	−0.239381	+	0.173920i
$732$	−5.47214	+	3.97574i	−0.202256	+	0.146948i
$733$	−13.5066	−	41.5690i	−0.498877	−	1.53539i	−0.810827	−	0.585286i	$-0.800982\pi$
$733$	−13.5066	−	41.5690i	−0.498877	−	1.53539i	0.311950	−	0.950099i	$-0.399018\pi$
$734$	−11.5902	+	35.6709i	−0.427801	+	1.31664i
$735$	33.0795	+	24.0337i	1.22016	+	0.886496i
$736$	−3.23607			−0.119283
$737$		0			0
$738$	−3.23607			−0.119121
$739$	−12.1803	−	8.84953i	−0.448061	−	0.325535i	0.340769	−	0.940147i	$-0.389313\pi$
$739$	−12.1803	−	8.84953i	−0.448061	−	0.325535i	−0.788830	+	0.614612i	$0.789313\pi$
$740$	1.34752	−	4.14725i	0.0495360	−	0.152456i
$741$	−3.23607	−	9.95959i	−0.118880	−	0.365875i
$742$	14.3992	−	10.4616i	0.528611	−	0.384058i
$743$	30.5623	−	22.2048i	1.12122	−	0.814616i	0.136828	−	0.990595i	$-0.456309\pi$
$743$	30.5623	−	22.2048i	1.12122	−	0.814616i	0.984394	+	0.175979i	$0.0563091\pi$
$744$	−2.66312	−	8.19624i	−0.0976347	−	0.300489i
$745$	1.21885	−	3.75123i	0.0446551	−	0.137434i
$746$	7.70820	+	5.60034i	0.282217	+	0.205043i
$747$	−0.673762			−0.0246517
$748$		0			0
$749$	24.8541			0.908149
$750$	−4.28115	−	3.11044i	−0.156326	−	0.113577i
$751$	−3.12461	+	9.61657i	−0.114019	+	0.350913i	−0.991741	−	0.128256i	$-0.959062\pi$
$751$	−3.12461	+	9.61657i	−0.114019	+	0.350913i	0.877722	+	0.479169i	$0.159062\pi$
$752$	0.763932	+	2.35114i	0.0278577	+	0.0857373i
$753$	−15.6353	+	11.3597i	−0.569780	+	0.413970i
$754$	−1.00000	+	0.726543i	−0.0364179	+	0.0264591i
$755$	8.22542	+	25.3153i	0.299354	+	0.921316i
$756$	−1.42705	+	4.39201i	−0.0519013	+	0.159736i
$757$	24.7082	+	17.9516i	0.898035	+	0.652461i	0.937961	−	0.346742i	$-0.112712\pi$
$757$	24.7082	+	17.9516i	0.898035	+	0.652461i	−0.0399256	+	0.999203i	$0.512712\pi$
$758$	3.70820			0.134688
$759$		0			0
$760$	−9.23607			−0.335027
$761$	−8.32624	−	6.04937i	−0.301826	−	0.219289i	0.426555	−	0.904461i	$-0.359727\pi$
$761$	−8.32624	−	6.04937i	−0.301826	−	0.219289i	−0.728381	+	0.685172i	$0.759727\pi$
$762$	−3.70820	+	11.4127i	−0.134334	+	0.413438i
$763$	24.8541	+	76.4931i	0.899779	+	2.76923i
$764$	−18.1803	+	13.2088i	−0.657742	+	0.477877i
$765$	5.70820	−	4.14725i	0.206381	−	0.149944i
$766$	4.09017	+	12.5882i	0.147784	+	0.454832i
$767$	3.85410	−	11.8617i	0.139164	−	0.428301i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	−4.27051			−0.153999			−0.0769993	−	0.997031i	$-0.524534\pi$
$769$	−4.27051			−0.153999			−0.0769993	+	0.997031i	$0.524534\pi$
$770$		0			0
$771$	1.81966			0.0655335
$772$	−0.263932	−	0.191758i	−0.00949912	−	0.00690152i
$773$	2.93769	−	9.04129i	0.105662	−	0.325193i	−0.884224	−	0.467064i	$-0.845312\pi$
$773$	2.93769	−	9.04129i	0.105662	−	0.325193i	0.989885	+	0.141871i	$0.0453118\pi$
$774$	−1.00000	−	3.07768i	−0.0359443	−	0.110625i
$775$	−21.9336	+	15.9357i	−0.787879	+	0.572428i
$776$	−9.16312	+	6.65740i	−0.328937	+	0.238987i
$777$	−2.18034	−	6.71040i	−0.0782193	−	0.240734i
$778$	12.0344	−	37.0382i	0.431456	−	1.32788i
$779$	−8.47214	−	6.15537i	−0.303546	−	0.220539i
$780$	9.23607			0.330704
$781$		0			0
$782$	8.00000			0.286079
$783$	−0.309017	−	0.224514i	−0.0110434	−	0.00802348i
$784$	4.42705	−	13.6251i	0.158109	−	0.486609i
$785$	3.94427	+	12.1392i	0.140777	+	0.433267i
$786$	−12.3541	+	8.97578i	−0.440656	+	0.320155i
$787$	30.3262	−	22.0333i	1.08101	−	0.785402i	0.103154	−	0.994665i	$-0.467106\pi$
$787$	30.3262	−	22.0333i	1.08101	−	0.785402i	0.977859	+	0.209263i	$0.0671065\pi$
$788$	1.88197	+	5.79210i	0.0670423	+	0.206335i
$789$	−2.38197	+	7.33094i	−0.0848002	+	0.260988i
$790$	21.5344	+	15.6457i	0.766161	+	0.556649i
$791$	−57.5967			−2.04790
$792$		0			0
$793$	21.8885			0.777285
$794$	−8.00000	−	5.81234i	−0.283909	−	0.206272i
$795$	3.39919	−	10.4616i	0.120557	−	0.371035i
$796$	4.06231	+	12.5025i	0.143985	+	0.443139i
$797$	18.2984	−	13.2945i	0.648162	−	0.470917i	−0.214483	−	0.976728i	$-0.568807\pi$
$797$	18.2984	−	13.2945i	0.648162	−	0.470917i	0.862644	+	0.505811i	$0.168807\pi$
$798$	−12.0902	+	8.78402i	−0.427987	+	0.310951i
$799$	−1.88854	−	5.81234i	−0.0668119	−	0.205626i
$800$	0.972136	−	2.99193i	0.0343702	−	0.105781i
$801$	9.47214	+	6.88191i	0.334681	+	0.243160i
$802$	10.2918			0.363416
$803$		0			0
$804$	−4.00000			−0.141069
$805$	34.5066	+	25.0705i	1.21620	+	0.883619i
$806$	−8.61803	+	26.5236i	−0.303557	+	0.934253i
$807$	0.909830	+	2.80017i	0.0320275	+	0.0985706i
$808$	10.0172	−	7.27794i	0.352405	−	0.256037i
$809$	−24.4721	+	17.7800i	−0.860394	+	0.625113i	−0.927992	−	0.372599i	$-0.878467\pi$
$809$	−24.4721	+	17.7800i	−0.860394	+	0.625113i	0.0675978	+	0.997713i	$0.478467\pi$
$810$	0.881966	+	2.71441i	0.0309891	+	0.0953747i
$811$	−12.5967	+	38.7688i	−0.442332	+	1.36136i	0.443052	+	0.896496i	$0.353896\pi$
$811$	−12.5967	+	38.7688i	−0.442332	+	1.36136i	−0.885384	+	0.464861i	$0.846104\pi$
$812$	1.42705	+	1.03681i	0.0500797	+	0.0363850i
$813$	−23.4164			−0.821249
$814$		0			0
$815$	−38.2918			−1.34130
$816$	−2.00000	−	1.45309i	−0.0700140	−	0.0508682i
$817$	3.23607	−	9.95959i	0.113216	−	0.348442i
$818$	−3.73607	−	11.4984i	−0.130629	−	0.402033i
$819$	12.0902	−	8.78402i	0.422465	−	0.306939i
$820$	7.47214	−	5.42882i	0.260938	−	0.189583i
$821$	6.51722	+	20.0579i	0.227453	+	0.700027i	0.998033	+	0.0626847i	$0.0199663\pi$
$821$	6.51722	+	20.0579i	0.227453	+	0.700027i	−0.770581	+	0.637342i	$0.780034\pi$
$822$	7.14590	−	21.9928i	0.249242	−	0.767087i
$823$	2.60081	+	1.88960i	0.0906586	+	0.0658674i	0.632191	−	0.774812i	$-0.282156\pi$
$823$	2.60081	+	1.88960i	0.0906586	+	0.0658674i	−0.541533	+	0.840680i	$0.682156\pi$
$824$	12.0344			0.419240
$825$		0			0
$826$	−17.7984			−0.619285
$827$	−8.64590	−	6.28161i	−0.300647	−	0.218433i	0.427226	−	0.904145i	$-0.359491\pi$
$827$	−8.64590	−	6.28161i	−0.300647	−	0.218433i	−0.727873	+	0.685712i	$0.759491\pi$
$828$	−1.00000	+	3.07768i	−0.0347524	+	0.106957i
$829$	2.25735	+	6.94742i	0.0784012	+	0.241294i	0.982574	−	0.185874i	$-0.0595115\pi$
$829$	2.25735	+	6.94742i	0.0784012	+	0.241294i	−0.904173	+	0.427167i	$0.859511\pi$
$830$	1.55573	−	1.13030i	0.0540001	−	0.0392334i
$831$	9.00000	−	6.53888i	0.312207	−	0.226831i
$832$	−1.00000	−	3.07768i	−0.0346688	−	0.106699i
$833$	−10.9443	+	33.6830i	−0.379197	+	1.16705i
$834$	10.7082	+	7.77997i	0.370795	+	0.269398i
$835$	20.6525			0.714708
$836$		0			0
$837$	−8.61803			−0.297883
$838$	14.5451	+	10.5676i	0.502452	+	0.365052i
$839$	−0.965558	+	2.97168i	−0.0333348	+	0.102594i	−0.966339	−	0.257270i	$-0.917177\pi$
$839$	−0.965558	+	2.97168i	−0.0333348	+	0.102594i	0.933005	+	0.359864i	$0.117177\pi$
$840$	−4.07295	−	12.5352i	−0.140530	−	0.432507i
$841$	23.3435	−	16.9600i	0.804947	−	0.584828i
$842$	−28.4164	+	20.6457i	−0.979294	+	0.711499i
$843$	−7.14590	−	21.9928i	−0.246118	−	0.757473i
$844$	−1.43769	+	4.42477i	−0.0494875	+	0.152307i
$845$	5.83688	+	4.24074i	0.200795	+	0.145886i
$846$	2.47214			0.0849938
$847$		0			0
$848$	−3.85410			−0.132350
$849$	−19.3262	−	14.0413i	−0.663275	−	0.481897i
$850$	−2.40325	+	7.39645i	−0.0824309	+	0.253696i
$851$	−1.52786	−	4.70228i	−0.0523745	−	0.161192i
$852$	10.0902	−	7.33094i	0.345684	−	0.251154i
$853$	−12.1803	+	8.84953i	−0.417047	+	0.303002i	−0.776449	−	0.630181i	$-0.782981\pi$
$853$	−12.1803	+	8.84953i	−0.417047	+	0.303002i	0.359402	+	0.933183i	$0.382981\pi$
$854$	−9.65248	−	29.7073i	−0.330301	−	1.01656i
$855$	−2.85410	+	8.78402i	−0.0976082	+	0.300407i
$856$	−4.35410	−	3.16344i	−0.148820	−	0.108124i
$857$	8.76393			0.299370			0.149685	−	0.988734i	$-0.452174\pi$
$857$	8.76393			0.299370			0.149685	+	0.988734i	$0.452174\pi$
$858$		0			0
$859$	4.40325			0.150237			0.0751185	−	0.997175i	$-0.476066\pi$
$859$	4.40325			0.150237			0.0751185	+	0.997175i	$0.476066\pi$
$860$	7.47214	+	5.42882i	0.254798	+	0.185121i
$861$	4.61803	−	14.2128i	0.157382	−	0.484373i
$862$	−2.23607	−	6.88191i	−0.0761608	−	0.234399i
$863$	−2.23607	+	1.62460i	−0.0761166	+	0.0553020i	−0.625193	−	0.780470i	$-0.714980\pi$
$863$	−2.23607	+	1.62460i	−0.0761166	+	0.0553020i	0.549076	+	0.835772i	$0.314980\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−3.65654	−	11.2537i	−0.124326	−	0.382636i
$866$	3.80902	−	11.7229i	0.129436	−	0.398362i
$867$	−8.80902	−	6.40013i	−0.299170	−	0.217360i
$868$	39.7984			1.35084
$869$		0			0
$870$	1.09017			0.0369602
$871$	10.4721	+	7.60845i	0.354835	+	0.257803i
$872$	5.38197	−	16.5640i	0.182256	−	0.560927i
$873$	3.50000	+	10.7719i	0.118457	+	0.364573i
$874$	−8.47214	+	6.15537i	−0.286574	+	0.208208i
$875$	19.7705	−	14.3641i	0.668365	−	0.485596i
$876$	3.50000	+	10.7719i	0.118254	+	0.363949i
$877$	−9.38197	+	28.8747i	−0.316806	+	0.975030i	0.658198	+	0.752845i	$0.271319\pi$
$877$	−9.38197	+	28.8747i	−0.316806	+	0.975030i	−0.975004	+	0.222185i	$0.928681\pi$
$878$	−12.9721	−	9.42481i	−0.437788	−	0.318072i
$879$	−22.9787			−0.775053
$880$		0			0
$881$	−12.2918			−0.414121			−0.207061	−	0.978328i	$-0.566390\pi$
$881$	−12.2918			−0.414121			−0.207061	+	0.978328i	$0.566390\pi$
$882$	−11.5902	−	8.42075i	−0.390261	−	0.283541i
$883$	8.59675	−	26.4581i	0.289304	−	0.890385i	−0.695772	−	0.718263i	$-0.744938\pi$
$883$	8.59675	−	26.4581i	0.289304	−	0.890385i	0.985076	−	0.172122i	$-0.0550624\pi$
$884$	2.47214	+	7.60845i	0.0831469	+	0.255900i
$885$	−8.89919	+	6.46564i	−0.299143	+	0.217340i
$886$	1.35410	−	0.983813i	0.0454919	−	0.0330518i
$887$	−8.81966	−	27.1441i	−0.296135	−	0.911410i	−0.982838	−	0.184472i	$-0.940943\pi$
$887$	−8.81966	−	27.1441i	−0.296135	−	0.911410i	0.686703	−	0.726938i	$-0.259057\pi$
$888$	−0.472136	+	1.45309i	−0.0158438	+	0.0487623i
$889$	−44.8328	−	32.5729i	−1.50364	−	1.09246i
$890$	−33.4164			−1.12012
$891$		0			0
$892$	−1.90983			−0.0639458
$893$	6.47214	+	4.70228i	0.216582	+	0.157356i
$894$	−0.427051	+	1.31433i	−0.0142827	+	0.0439577i
$895$	−5.62868	−	17.3233i	−0.188146	−	0.579054i
$896$	−3.73607	+	2.71441i	−0.124813	+	0.0906821i
$897$	8.47214	−	6.15537i	0.282876	−	0.205522i
$898$	11.0902	+	34.1320i	0.370084	+	1.13900i
$899$	−1.01722	+	3.13068i	−0.0339262	+	0.104414i
$900$	−2.54508	−	1.84911i	−0.0848362	−	0.0616371i
$901$	9.52786			0.317419
$902$		0			0
$903$	14.9443			0.497314
$904$	10.0902	+	7.33094i	0.335594	+	0.243823i
$905$	−14.5279	+	44.7122i	−0.482923	+	1.48628i
$906$	−2.88197	−	8.86978i	−0.0957469	−	0.294679i
$907$	6.61803	−	4.80828i	0.219748	−	0.159656i	−0.472465	−	0.881349i	$-0.656636\pi$
$907$	6.61803	−	4.80828i	0.219748	−	0.159656i	0.692213	+	0.721693i	$0.256636\pi$
$908$	5.78115	−	4.20025i	0.191854	−	0.139390i
$909$	−3.82624	−	11.7759i	−0.126908	−	0.390584i
$910$	−13.1803	+	40.5649i	−0.436924	+	1.34471i
$911$	−35.3607	−	25.6910i	−1.17155	−	0.851182i	−0.180358	−	0.983601i	$-0.557726\pi$
$911$	−35.3607	−	25.6910i	−1.17155	−	0.851182i	−0.991194	+	0.132419i	$0.957726\pi$
$912$	3.23607			0.107157
$913$		0			0
$914$	−21.9787			−0.726991
$915$	−15.6180	−	11.3472i	−0.516316	−	0.375126i
$916$	7.09017	−	21.8213i	0.234266	−	0.720996i
$917$	−21.7918	−	67.0683i	−0.719629	−	2.21479i
$918$	−2.00000	+	1.45309i	−0.0660098	+	0.0479590i
$919$	−40.6697	+	29.5483i	−1.34157	+	0.974707i	−0.342185	+	0.939633i	$0.611167\pi$
$919$	−40.6697	+	29.5483i	−1.34157	+	0.974707i	−0.999385	+	0.0350746i	$0.988833\pi$
$920$	−2.85410	−	8.78402i	−0.0940970	−	0.289601i
$921$	5.14590	−	15.8374i	0.169563	−	0.521862i
$922$	−33.0344	−	24.0009i	−1.08793	−	0.790428i
$923$	−40.3607			−1.32849
$924$		0			0
$925$	4.80650			0.158037
$926$	−15.4443	−	11.2209i	−0.507530	−	0.368742i
$927$	3.71885	−	11.4454i	0.122143	−	0.375917i
$928$	−0.118034	−	0.363271i	−0.00387466	−	0.0119250i
$929$	18.7082	−	13.5923i	0.613796	−	0.445949i	−0.236953	−	0.971521i	$-0.576149\pi$
$929$	18.7082	−	13.5923i	0.613796	−	0.445949i	0.850749	+	0.525572i	$0.176149\pi$
$930$	19.8992	−	14.4576i	0.652520	−	0.474084i
$931$	−14.3262	−	44.0916i	−0.469523	−	1.44504i
$932$	−2.76393	+	8.50651i	−0.0905356	+	0.278640i
$933$	−19.3262	−	14.0413i	−0.632713	−	0.459693i
$934$	19.5623			0.640098
$935$		0			0
$936$	−3.23607			−0.105774
$937$	−22.2082	−	16.1352i	−0.725510	−	0.527114i	0.162630	−	0.986687i	$-0.448002\pi$
$937$	−22.2082	−	16.1352i	−0.725510	−	0.527114i	−0.888140	+	0.459573i	$0.848002\pi$
$938$	5.70820	−	17.5680i	0.186379	−	0.573617i
$939$	−4.68034	−	14.4046i	−0.152737	−	0.470077i
$940$	−5.70820	+	4.14725i	−0.186181	+	0.135268i
$941$	7.14590	−	5.19180i	0.232950	−	0.169248i	−0.465187	−	0.885213i	$-0.654013\pi$
$941$	7.14590	−	5.19180i	0.232950	−	0.169248i	0.698136	+	0.715965i	$0.254013\pi$
$942$	−1.38197	−	4.25325i	−0.0450269	−	0.138579i
$943$	3.23607	−	9.95959i	0.105381	−	0.324329i
$944$	3.11803	+	2.26538i	0.101483	+	0.0737320i
$945$	−13.1803			−0.428756
$946$		0			0
$947$	2.32624			0.0755926			0.0377963	−	0.999285i	$-0.487966\pi$
$947$	2.32624			0.0755926			0.0377963	+	0.999285i	$0.487966\pi$
$948$	−7.54508	−	5.48183i	−0.245053	−	0.178041i
$949$	11.3262	−	34.8586i	0.367665	−	1.13156i
$950$	−3.14590	−	9.68208i	−0.102066	−	0.314128i
$951$	−16.0902	+	11.6902i	−0.521760	+	0.379080i
$952$	9.23607	−	6.71040i	0.299343	−	0.217485i
$953$	15.0557	+	46.3368i	0.487703	+	1.50100i	0.828028	+	0.560687i	$0.189463\pi$
$953$	15.0557	+	46.3368i	0.487703	+	1.50100i	−0.340325	+	0.940308i	$0.610537\pi$
$954$	−1.19098	+	3.66547i	−0.0385595	+	0.118674i
$955$	−51.8885	−	37.6992i	−1.67907	−	1.21992i
$956$	−16.4721			−0.532747
$957$		0			0
$958$	−7.23607			−0.233787
$959$	86.3951	+	62.7697i	2.78984	+	2.02694i
$960$	−0.881966	+	2.71441i	−0.0284653	+	0.0876073i
$961$	13.3713	+	41.1527i	0.431333	+	1.32751i
$962$	4.00000	−	2.90617i	0.128965	−	0.0936987i
$963$	−4.35410	+	3.16344i	−0.140309	+	0.101940i
$964$	−0.753289	−	2.31838i	−0.0242618	−	0.0746701i
$965$	0.287731	−	0.885544i	0.00926238	−	0.0285067i
$966$	−12.0902	−	8.78402i	−0.388995	−	0.282621i
$967$	13.6869			0.440142			0.220071	−	0.975484i	$-0.429371\pi$
$967$	13.6869			0.440142			0.220071	+	0.975484i	$0.429371\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$	−26.1525	−	19.0009i	−0.839705	−	0.610082i
$971$	−2.87539	+	8.84953i	−0.0922756	+	0.283995i	−0.986534	−	0.163556i	$-0.947704\pi$
$971$	−2.87539	+	8.84953i	−0.0922756	+	0.283995i	0.894258	+	0.447551i	$0.147704\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−49.4508	+	35.9281i	−1.58532	+	1.15180i
$974$	−20.2082	+	14.6821i	−0.647513	+	0.470445i
$975$	3.14590	+	9.68208i	0.100749	+	0.310075i
$976$	−2.09017	+	6.43288i	−0.0669047	+	0.205912i
$977$	29.7426	+	21.6093i	0.951552	+	0.691343i	0.951173	−	0.308657i	$-0.0998796\pi$
$977$	29.7426	+	21.6093i	0.951552	+	0.691343i	0.000378218		1.00000i	$0.499880\pi$
$978$	13.4164			0.429009
$979$		0			0
$980$	40.8885			1.30614
$981$	−14.0902	−	10.2371i	−0.449865	−	0.326846i
$982$	13.0557	−	40.1814i	0.416625	−	1.28224i
$983$	−2.81966	−	8.67802i	−0.0899332	−	0.276786i	0.895967	−	0.444121i	$-0.146484\pi$
$983$	−2.81966	−	8.67802i	−0.0899332	−	0.276786i	−0.985900	+	0.167335i	$0.946484\pi$
$984$	−2.61803	+	1.90211i	−0.0834599	+	0.0606371i
$985$	−14.0623	+	10.2169i	−0.448062	+	0.325536i
$986$	0.291796	+	0.898056i	0.00929268	+	0.0285999i
$987$	−3.52786	+	10.8576i	−0.112293	+	0.345603i
$988$	−8.47214	−	6.15537i	−0.269535	−	0.195828i
$989$	10.4721			0.332995
$990$		0			0
$991$	−45.6869			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$991$	−45.6869			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$992$	−6.97214	−	5.06555i	−0.221366	−	0.160831i
$993$	−2.76393	+	8.50651i	−0.0877107	+	0.269946i
$994$	17.7984	+	54.7778i	0.564530	+	1.73745i
$995$	−30.3541	+	22.0535i	−0.962290	+	0.699144i
$996$	−0.545085	+	0.396027i	−0.0172717	+	0.0125486i
$997$	17.9098	+	55.1208i	0.567210	+	1.74569i	0.661292	+	0.750128i	$0.270008\pi$
$997$	17.9098	+	55.1208i	0.567210	+	1.74569i	−0.0940821	+	0.995564i	$0.529992\pi$
$998$	−2.29180	+	7.05342i	−0.0725455	+	0.223272i
$999$	1.23607	+	0.898056i	0.0391075	+	0.0284132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.f.565.1		4
11.2	odd	10		726.2.e.r.511.1		4
11.3	even	5	inner	726.2.e.f.487.1		4
11.4	even	5		66.2.e.a.31.1	✓	4
11.5	even	5		726.2.a.l.1.2		2
11.6	odd	10		726.2.a.j.1.2		2
11.7	odd	10		726.2.e.r.493.1		4
11.8	odd	10		726.2.e.n.487.1		4
11.9	even	5		66.2.e.a.49.1	yes	4
11.10	odd	2		726.2.e.n.565.1		4
33.5	odd	10		2178.2.a.t.1.1		2
33.17	even	10		2178.2.a.bb.1.1		2
33.20	odd	10		198.2.f.c.181.1		4
33.26	odd	10		198.2.f.c.163.1		4
44.15	odd	10		528.2.y.d.97.1		4
44.27	odd	10		5808.2.a.cb.1.2		2
44.31	odd	10		528.2.y.d.49.1		4
44.39	even	10		5808.2.a.cg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.31.1	✓	4	11.4	even	5
66.2.e.a.49.1	yes	4	11.9	even	5
198.2.f.c.163.1		4	33.26	odd	10
198.2.f.c.181.1		4	33.20	odd	10
528.2.y.d.49.1		4	44.31	odd	10
528.2.y.d.97.1		4	44.15	odd	10
726.2.a.j.1.2		2	11.6	odd	10
726.2.a.l.1.2		2	11.5	even	5
726.2.e.f.487.1		4	11.3	even	5	inner
726.2.e.f.565.1		4	1.1	even	1	trivial
726.2.e.n.487.1		4	11.8	odd	10
726.2.e.n.565.1		4	11.10	odd	2
726.2.e.r.493.1		4	11.7	odd	10
726.2.e.r.511.1		4	11.2	odd	10
2178.2.a.t.1.1		2	33.5	odd	10
2178.2.a.bb.1.1		2	33.17	even	10
5808.2.a.cb.1.2		2	44.27	odd	10
5808.2.a.cg.1.2		2	44.39	even	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.42705 + 4.39201i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +2.85410 q^{10} -1.00000 q^{12} +(2.61803 + 1.90211i) q^{13} +(1.42705 - 4.39201i) q^{14} +(-0.881966 - 2.71441i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.00000 - 1.45309i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.00000 + 3.07768i) q^{19} +(-2.30902 - 1.67760i) q^{20} -4.61803 q^{21} -3.23607 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.972136 - 2.99193i) q^{25} +(-1.00000 - 3.07768i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.73607 + 2.71441i) q^{28} +(-0.118034 - 0.363271i) q^{29} +(-0.881966 + 2.71441i) q^{30} +(-6.97214 - 5.06555i) q^{31} +1.00000 q^{32} -2.47214 q^{34} +(-10.6631 - 7.74721i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.472136 + 1.45309i) q^{37} +(2.61803 - 1.90211i) q^{38} +(-2.61803 + 1.90211i) q^{39} +(0.881966 + 2.71441i) q^{40} +(-1.00000 + 3.07768i) q^{41} +(3.73607 + 2.71441i) q^{42} -3.23607 q^{43} +2.85410 q^{45} +(2.61803 + 1.90211i) q^{46} +(0.763932 - 2.35114i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-11.5902 + 8.42075i) q^{49} +(-2.54508 + 1.84911i) q^{50} +(0.763932 + 2.35114i) q^{51} +(-1.00000 + 3.07768i) q^{52} +(3.11803 + 2.26538i) q^{53} -1.00000 q^{54} +4.61803 q^{56} +(-2.61803 - 1.90211i) q^{57} +(-0.118034 + 0.363271i) q^{58} +(-1.19098 - 3.66547i) q^{59} +(2.30902 - 1.67760i) q^{60} +(5.47214 - 3.97574i) q^{61} +(2.66312 + 8.19624i) q^{62} +(1.42705 - 4.39201i) q^{63} +(-0.809017 - 0.587785i) q^{64} -9.23607 q^{65} +4.00000 q^{67} +(2.00000 + 1.45309i) q^{68} +(1.00000 - 3.07768i) q^{69} +(4.07295 + 12.5352i) q^{70} +(-10.0902 + 7.33094i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-3.50000 - 10.7719i) q^{73} +(0.472136 - 1.45309i) q^{74} +(2.54508 + 1.84911i) q^{75} -3.23607 q^{76} +3.23607 q^{78} +(7.54508 + 5.48183i) q^{79} +(0.881966 - 2.71441i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.61803 - 1.90211i) q^{82} +(0.545085 - 0.396027i) q^{83} +(-1.42705 - 4.39201i) q^{84} +(-2.18034 + 6.71040i) q^{85} +(2.61803 + 1.90211i) q^{86} +0.381966 q^{87} -11.7082 q^{89} +(-2.30902 - 1.67760i) q^{90} +(-4.61803 + 14.2128i) q^{91} +(-1.00000 - 3.07768i) q^{92} +(6.97214 - 5.06555i) q^{93} +(-2.00000 + 1.45309i) q^{94} +(-2.85410 - 8.78402i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-9.16312 - 6.65740i) q^{97} +14.3262 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - 7 q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{12} + 6 q^{13} - q^{14} - 8 q^{15} - q^{16} + 8 q^{17} - q^{18} - 4 q^{19} - 7 q^{20} - 14 q^{21} - 4 q^{23}+ \cdots + 26 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - 7 * q^5 + q^6 - q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^12 + 6 * q^13 - q^14 - 8 * q^15 - q^16 + 8 * q^17 - q^18 - 4 * q^19 - 7 * q^20 - 14 * q^21 - 4 * q^23 + q^24 - 14 * q^25 - 4 * q^26 + q^27 - 6 * q^28 + 4 * q^29 - 8 * q^30 - 10 * q^31 + 4 * q^32 + 8 * q^34 - 27 * q^35 - q^36 - 16 * q^37 + 6 * q^38 - 6 * q^39 + 8 * q^40 - 4 * q^41 + 6 * q^42 - 4 * q^43 - 2 * q^45 + 6 * q^46 + 12 * q^47 + q^48 - 24 * q^49 + q^50 + 12 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 14 * q^56 - 6 * q^57 + 4 * q^58 - 7 * q^59 + 7 * q^60 + 4 * q^61 - 5 * q^62 - q^63 - q^64 - 28 * q^65 + 16 * q^67 + 8 * q^68 + 4 * q^69 + 23 * q^70 - 18 * q^71 - q^72 - 14 * q^73 - 16 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + 19 * q^79 + 8 * q^80 - q^81 + 6 * q^82 - 9 * q^83 + q^84 + 36 * q^85 + 6 * q^86 + 6 * q^87 - 20 * q^89 - 7 * q^90 - 14 * q^91 - 4 * q^92 + 10 * q^93 - 8 * q^94 + 2 * q^95 + q^96 - 21 * q^97 + 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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