LMFDB - Embedded newform 266.2.e.d.39.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [266,2,Mod(39,266)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("266.39"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(266, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 266 = 2 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	266.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.12402069377$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			39.1
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	266.39
Dual form			266.2.e.d.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.45611 + 2.52206i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91223 + 3.31208i) q^{5} -2.91223 q^{6} +(2.58392 - 0.568650i) q^{7} -1.00000 q^{8} +(-2.74054 - 4.74675i) q^{9} +(-1.91223 + 3.31208i) q^{10} +(0.656620 - 1.13730i) q^{11} +(-1.45611 - 2.52206i) q^{12} +1.34338 q^{13} +(1.78442 + 1.95341i) q^{14} -11.1377 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.78442 - 4.82277i) q^{17} +(2.74054 - 4.74675i) q^{18} +(-0.500000 - 0.866025i) q^{19} -3.82446 q^{20} +(-2.32831 + 7.34483i) q^{21} +1.31324 q^{22} +(-4.04003 - 6.99754i) q^{23} +(1.45611 - 2.52206i) q^{24} +(-4.81324 + 8.33678i) q^{25} +(0.671690 + 1.16340i) q^{26} +7.22547 q^{27} +(-0.799494 + 2.52206i) q^{28} +6.22547 q^{29} +(-5.56885 - 9.64553i) q^{30} +(-3.56885 + 6.18143i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.91223 + 3.31208i) q^{33} +5.56885 q^{34} +(6.82446 + 7.47075i) q^{35} +5.48108 q^{36} +(-0.587771 - 1.01805i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.95611 + 3.38809i) q^{39} +(-1.91223 - 3.31208i) q^{40} +6.00000 q^{41} +(-7.52496 + 1.65604i) q^{42} -1.82446 q^{43} +(0.656620 + 1.13730i) q^{44} +(10.4811 - 18.1538i) q^{45} +(4.04003 - 6.99754i) q^{46} +(-2.15662 - 3.73538i) q^{47} +2.91223 q^{48} +(6.35327 - 2.93869i) q^{49} -9.62648 q^{50} +(8.10888 + 14.0450i) q^{51} +(-0.671690 + 1.16340i) q^{52} +(-1.52882 + 2.64799i) q^{53} +(3.61274 + 6.25744i) q^{54} +5.02243 q^{55} +(-2.58392 + 0.568650i) q^{56} +2.91223 q^{57} +(3.11274 + 5.39142i) q^{58} +(2.78442 - 4.82277i) q^{59} +(5.56885 - 9.64553i) q^{60} +(-2.25561 - 3.90683i) q^{61} -7.13770 q^{62} +(-9.78057 - 10.7068i) q^{63} +1.00000 q^{64} +(2.56885 + 4.44938i) q^{65} +(-1.91223 + 3.31208i) q^{66} +(-5.96733 + 10.3357i) q^{67} +(2.78442 + 4.82277i) q^{68} +23.5310 q^{69} +(-3.05763 + 9.64553i) q^{70} -12.7866 q^{71} +(2.74054 + 4.74675i) q^{72} +(-5.21040 + 9.02468i) q^{73} +(0.587771 - 1.01805i) q^{74} +(-14.0173 - 24.2786i) q^{75} +1.00000 q^{76} +(1.04993 - 3.31208i) q^{77} -3.91223 q^{78} +(-2.74439 - 4.75343i) q^{79} +(1.91223 - 3.31208i) q^{80} +(-2.29949 + 3.98284i) q^{81} +(3.00000 + 5.19615i) q^{82} -0.862301 q^{83} +(-5.19665 - 5.68879i) q^{84} +21.2978 q^{85} +(-0.912229 - 1.58003i) q^{86} +(-9.06500 + 15.7010i) q^{87} +(-0.656620 + 1.13730i) q^{88} +(1.96986 + 3.41190i) q^{89} +20.9622 q^{90} +(3.47118 - 0.763913i) q^{91} +8.08007 q^{92} +(-10.3933 - 18.0017i) q^{93} +(2.15662 - 3.73538i) q^{94} +(1.91223 - 3.31208i) q^{95} +(1.45611 + 2.52206i) q^{96} -15.5886 q^{97} +(5.72162 + 4.03275i) q^{98} -7.19798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 2 q^{10} - 2 q^{12} + 12 q^{13} + 2 q^{14} - 32 q^{15} - 3 q^{16} + 8 q^{17} + q^{18} - 3 q^{19} + 4 q^{20} - 12 q^{21}+ \cdots - 32 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 - q^9 + 2 * q^10 - 2 * q^12 + 12 * q^13 + 2 * q^14 - 32 * q^15 - 3 * q^16 + 8 * q^17 + q^18 - 3 * q^19 + 4 * q^20 - 12 * q^21 - 6 * q^23 + 2 * q^24 - 21 * q^25 + 6 * q^26 + 22 * q^27 - 2 * q^28 + 16 * q^29 - 16 * q^30 - 4 * q^31 + 3 * q^32 - 2 * q^33 + 16 * q^34 + 14 * q^35 + 2 * q^36 - 17 * q^37 + 3 * q^38 - 5 * q^39 + 2 * q^40 + 36 * q^41 - 21 * q^42 + 16 * q^43 + 32 * q^45 + 6 * q^46 - 9 * q^47 + 4 * q^48 + 12 * q^49 - 42 * q^50 + 13 * q^51 - 6 * q^52 - 10 * q^53 + 11 * q^54 - 8 * q^55 - 4 * q^56 + 4 * q^57 + 8 * q^58 + 8 * q^59 + 16 * q^60 - 4 * q^61 - 8 * q^62 - 25 * q^63 + 6 * q^64 - 2 * q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 62 * q^69 - 20 * q^70 + 12 * q^71 + q^72 - 4 * q^73 + 17 * q^74 - 10 * q^75 + 6 * q^76 - 42 * q^77 - 10 * q^78 - 26 * q^79 - 2 * q^80 - 11 * q^81 + 18 * q^82 - 40 * q^83 - 9 * q^84 + 20 * q^85 + 8 * q^86 - 12 * q^87 + 64 * q^90 + 20 * q^91 + 12 * q^92 - 18 * q^93 + 9 * q^94 - 2 * q^95 + 2 * q^96 - 16 * q^97 - 12 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/266\mathbb{Z}\right)^\times$.

$n$	$115$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.45611	+	2.52206i	−0.840688	+	1.45611i	0.0486256	+	0.998817i	$0.484516\pi$
$3$	−1.45611	+	2.52206i	−0.840688	+	1.45611i	−0.889314	+	0.457298i	$0.848817\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.91223	+	3.31208i	0.855175	+	1.48121i	0.876483	+	0.481433i	$0.159884\pi$
$5$	1.91223	+	3.31208i	0.855175	+	1.48121i	−0.0213078	+	0.999773i	$0.506783\pi$
$6$	−2.91223			−1.18891
$7$	2.58392	−	0.568650i	0.976630	−	0.214929i
$7$	2.58392	−	0.568650i	0.976630	−	0.214929i
$8$	−1.00000			−0.353553
$9$	−2.74054	−	4.74675i	−0.913513	−	1.58225i
$10$	−1.91223	+	3.31208i	−0.604700	+	1.04737i
$11$	0.656620	−	1.13730i	0.197979	−	0.342909i	−0.749894	−	0.661558i	$-0.769896\pi$
$11$	0.656620	−	1.13730i	0.197979	−	0.342909i	0.947873	+	0.318649i	$0.103229\pi$
$12$	−1.45611	−	2.52206i	−0.420344	−	0.728057i
$13$	1.34338			0.372586			0.186293	−	0.982494i	$-0.440353\pi$
$13$	1.34338			0.372586			0.186293	+	0.982494i	$0.440353\pi$
$14$	1.78442	+	1.95341i	0.476908	+	0.522072i
$15$	−11.1377			−2.87574
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.78442	−	4.82277i	0.675322	−	1.16969i	−0.301052	−	0.953608i	$-0.597338\pi$
$17$	2.78442	−	4.82277i	0.675322	−	1.16969i	0.976375	−	0.216085i	$-0.0693288\pi$
$18$	2.74054	−	4.74675i	0.645951	−	1.11882i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	−3.82446			−0.855175
$21$	−2.32831	+	7.34483i	−0.508079	+	1.60277i
$22$	1.31324			0.279984
$23$	−4.04003	−	6.99754i	−0.842405	−	1.45909i	−0.887856	−	0.460122i	$-0.847806\pi$
$23$	−4.04003	−	6.99754i	−0.842405	−	1.45909i	0.0454504	−	0.998967i	$-0.485528\pi$
$24$	1.45611	−	2.52206i	0.297228	−	0.514814i
$25$	−4.81324	+	8.33678i	−0.962648	+	1.66736i
$26$	0.671690	+	1.16340i	0.131729	+	0.228162i
$27$	7.22547			1.39054
$28$	−0.799494	+	2.52206i	−0.151090	+	0.476625i
$29$	6.22547			1.15604			0.578020	−	0.816022i	$-0.303825\pi$
$29$	6.22547			1.15604			0.578020	+	0.816022i	$0.303825\pi$
$30$	−5.56885	−	9.64553i	−1.01673	−	1.76102i
$31$	−3.56885	+	6.18143i	−0.640984	+	1.11022i	0.344229	+	0.938886i	$0.388140\pi$
$31$	−3.56885	+	6.18143i	−0.640984	+	1.11022i	−0.985213	+	0.171332i	$0.945193\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.91223	+	3.31208i	0.332876	+	0.576559i
$34$	5.56885			0.955050
$35$	6.82446	+	7.47075i	1.15354	+	1.26279i
$36$	5.48108			0.913513
$37$	−0.587771	−	1.01805i	−0.0966289	−	0.167366i	0.813658	−	0.581343i	$-0.197473\pi$
$37$	−0.587771	−	1.01805i	−0.0966289	−	0.167366i	−0.910287	+	0.413977i	$0.864139\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$	−1.95611	+	3.38809i	−0.313229	+	0.542529i
$40$	−1.91223	−	3.31208i	−0.302350	−	0.523686i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	−7.52496	+	1.65604i	−1.16113	+	0.255532i
$43$	−1.82446			−0.278227			−0.139114	−	0.990276i	$-0.544425\pi$
$43$	−1.82446			−0.278227			−0.139114	+	0.990276i	$0.544425\pi$
$44$	0.656620	+	1.13730i	0.0989893	+	0.171454i
$45$	10.4811	−	18.1538i	1.56243	−	2.70620i
$46$	4.04003	−	6.99754i	0.595670	−	1.03173i
$47$	−2.15662	−	3.73538i	−0.314575	−	0.544861i	0.664772	−	0.747047i	$-0.268529\pi$
$47$	−2.15662	−	3.73538i	−0.314575	−	0.544861i	−0.979347	+	0.202186i	$0.935195\pi$
$48$	2.91223			0.420344
$49$	6.35327	−	2.93869i	0.907611	−	0.419813i
$50$	−9.62648			−1.36139
$51$	8.10888	+	14.0450i	1.13547	+	1.96669i
$52$	−0.671690	+	1.16340i	−0.0931466	+	0.161335i
$53$	−1.52882	+	2.64799i	−0.209999	+	0.363729i	−0.951714	−	0.306986i	$-0.900679\pi$
$53$	−1.52882	+	2.64799i	−0.209999	+	0.363729i	0.741715	+	0.670715i	$0.234013\pi$
$54$	3.61274	+	6.25744i	0.491631	+	0.851530i
$55$	5.02243			0.677225
$56$	−2.58392	+	0.568650i	−0.345291	+	0.0759890i
$57$	2.91223			0.385734
$58$	3.11274	+	5.39142i	0.408722	+	0.707927i
$59$	2.78442	−	4.82277i	0.362501	−	0.627871i	−0.625871	−	0.779927i	$-0.715256\pi$
$59$	2.78442	−	4.82277i	0.362501	−	0.627871i	0.988372	+	0.152056i	$0.0485895\pi$
$60$	5.56885	−	9.64553i	0.718935	−	1.24523i
$61$	−2.25561	−	3.90683i	−0.288801	−	0.500218i	0.684723	−	0.728804i	$-0.259923\pi$
$61$	−2.25561	−	3.90683i	−0.288801	−	0.500218i	−0.973524	+	0.228585i	$0.926590\pi$
$62$	−7.13770			−0.906489
$63$	−9.78057	−	10.7068i	−1.23224	−	1.34893i
$64$	1.00000			0.125000
$65$	2.56885	+	4.44938i	0.318627	+	0.551877i
$66$	−1.91223	+	3.31208i	−0.235379	+	0.407689i
$67$	−5.96733	+	10.3357i	−0.729026	+	1.26271i	0.228270	+	0.973598i	$0.426693\pi$
$67$	−5.96733	+	10.3357i	−0.729026	+	1.26271i	−0.957295	+	0.289112i	$0.906640\pi$
$68$	2.78442	+	4.82277i	0.337661	+	0.584846i
$69$	23.5310			2.83280
$70$	−3.05763	+	9.64553i	−0.365457	+	1.15286i
$71$	−12.7866			−1.51749			−0.758746	−	0.651387i	$-0.774188\pi$
$71$	−12.7866			−1.51749			−0.758746	+	0.651387i	$0.774188\pi$
$72$	2.74054	+	4.74675i	0.322976	+	0.559410i
$73$	−5.21040	+	9.02468i	−0.609831	+	1.05626i	0.381437	+	0.924395i	$0.375429\pi$
$73$	−5.21040	+	9.02468i	−0.609831	+	1.05626i	−0.991268	+	0.131864i	$0.957904\pi$
$74$	0.587771	−	1.01805i	0.0683270	−	0.118346i
$75$	−14.0173	−	24.2786i	−1.61857	−	2.80345i
$76$	1.00000			0.114708
$77$	1.04993	−	3.31208i	0.119650	−	0.377446i
$78$	−3.91223			−0.442973
$79$	−2.74439	−	4.75343i	−0.308768	−	0.534802i	0.669325	−	0.742970i	$-0.266583\pi$
$79$	−2.74439	−	4.75343i	−0.308768	−	0.534802i	−0.978093	+	0.208168i	$0.933250\pi$
$80$	1.91223	−	3.31208i	0.213794	−	0.370302i
$81$	−2.29949	+	3.98284i	−0.255499	+	0.442538i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	−0.862301			−0.0946498			−0.0473249	−	0.998880i	$-0.515070\pi$
$83$	−0.862301			−0.0946498			−0.0473249	+	0.998880i	$0.515070\pi$
$84$	−5.19665	−	5.68879i	−0.567001	−	0.620698i
$85$	21.2978			2.31007
$86$	−0.912229	−	1.58003i	−0.0983682	−	0.170379i
$87$	−9.06500	+	15.7010i	−0.971870	+	1.68333i
$88$	−0.656620	+	1.13730i	−0.0699960	+	0.121237i
$89$	1.96986	+	3.41190i	0.208805	+	0.361661i	0.951338	−	0.308148i	$-0.0997093\pi$
$89$	1.96986	+	3.41190i	0.208805	+	0.361661i	−0.742533	+	0.669809i	$0.766376\pi$
$90$	20.9622			2.20961
$91$	3.47118	−	0.763913i	0.363879	−	0.0800798i
$92$	8.08007			0.842405
$93$	−10.3933	−	18.0017i	−1.07774	−	1.86669i
$94$	2.15662	−	3.73538i	0.222438	−	0.385275i
$95$	1.91223	−	3.31208i	0.196191	−	0.339812i
$96$	1.45611	+	2.52206i	0.148614	+	0.257407i
$97$	−15.5886			−1.58279			−0.791393	−	0.611307i	$-0.790644\pi$
$97$	−15.5886			−1.58279			−0.791393	+	0.611307i	$0.790644\pi$
$98$	5.72162	+	4.03275i	0.577971	+	0.407369i
$99$	−7.19798			−0.723424
$100$	−4.81324	−	8.33678i	−0.481324	−	0.833678i
$101$	−2.56885	+	4.44938i	−0.255610	+	0.442730i	−0.965061	−	0.262025i	$-0.915610\pi$
$101$	−2.56885	+	4.44938i	−0.255610	+	0.442730i	0.709451	+	0.704755i	$0.248943\pi$
$102$	−8.10888	+	14.0450i	−0.802899	+	1.39066i
$103$	0.686759	+	1.18950i	0.0676684	+	0.117205i	0.897875	−	0.440251i	$-0.145111\pi$
$103$	0.686759	+	1.18950i	0.0676684	+	0.117205i	−0.830206	+	0.557456i	$0.811777\pi$
$104$	−1.34338			−0.131729
$105$	−28.7789	+	6.33345i	−2.80853	+	0.618082i
$106$	−3.05763			−0.296983
$107$	−7.80939	−	13.5263i	−0.754962	−	1.30763i	−0.945393	−	0.325932i	$-0.894322\pi$
$107$	−7.80939	−	13.5263i	−0.754962	−	1.30763i	0.190431	−	0.981701i	$-0.439011\pi$
$108$	−3.61274	+	6.25744i	−0.347636	+	0.602123i
$109$	−1.32831	+	2.30070i	−0.127229	+	0.220367i	−0.922602	−	0.385753i	$-0.873942\pi$
$109$	−1.32831	+	2.30070i	−0.127229	+	0.220367i	0.795373	+	0.606120i	$0.207275\pi$
$110$	2.51122	+	4.34956i	0.239435	+	0.414714i
$111$	3.42345			0.324939
$112$	−1.78442	−	1.95341i	−0.168612	−	0.184580i
$113$	−1.19798			−0.112696			−0.0563481	−	0.998411i	$-0.517946\pi$
$113$	−1.19798			−0.112696			−0.0563481	+	0.998411i	$0.517946\pi$
$114$	1.45611	+	2.52206i	0.136378	+	0.236213i
$115$	15.4509	−	26.7618i	1.44081	−	2.49555i
$116$	−3.11274	+	5.39142i	−0.289010	+	0.500580i
$117$	−3.68158	−	6.37669i	−0.340363	−	0.589525i
$118$	5.56885			0.512654
$119$	4.45226	−	14.0450i	0.408138	−	1.28750i
$120$	11.1377			1.01673
$121$	4.63770	+	8.03273i	0.421609	+	0.730248i
$122$	2.25561	−	3.90683i	0.204213	−	0.353708i
$123$	−8.73669	+	15.1324i	−0.787761	+	1.36444i
$124$	−3.56885	−	6.18143i	−0.320492	−	0.555109i
$125$	−17.6938			−1.58258
$126$	4.38209	−	13.8236i	0.390388	−	1.23151i
$127$	20.3357			1.80450			0.902250	−	0.431214i	$-0.141915\pi$
$127$	20.3357			1.80450			0.902250	+	0.431214i	$0.141915\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.65662	−	4.60140i	0.233902	−	0.405131i
$130$	−2.56885	+	4.44938i	−0.225303	+	0.390236i
$131$	10.0499	+	17.4070i	0.878066	+	1.52086i	0.853460	+	0.521158i	$0.174500\pi$
$131$	10.0499	+	17.4070i	0.878066	+	1.52086i	0.0246063	+	0.999697i	$0.492167\pi$
$132$	−3.82446			−0.332876
$133$	−1.78442	−	1.95341i	−0.154729	−	0.169383i
$134$	−11.9347			−1.03100
$135$	13.8168	+	23.9313i	1.18916	+	2.05968i
$136$	−2.78442	+	4.82277i	−0.238762	+	0.413549i
$137$	8.90705	−	15.4275i	0.760981	−	1.31806i	−0.181364	−	0.983416i	$-0.558051\pi$
$137$	8.90705	−	15.4275i	0.760981	−	1.31806i	0.942345	−	0.334642i	$-0.108615\pi$
$138$	11.7655	+	20.3784i	1.00155	+	1.73473i
$139$	15.7642			1.33710			0.668550	−	0.743667i	$-0.266915\pi$
$139$	15.7642			1.33710			0.668550	+	0.743667i	$0.266915\pi$
$140$	−9.88209	+	2.17478i	−0.835189	+	0.183802i
$141$	12.5611			1.05784
$142$	−6.39331	−	11.0735i	−0.536514	−	0.929270i
$143$	0.882090	−	1.52783i	0.0737641	−	0.127763i
$144$	−2.74054	+	4.74675i	−0.228378	+	0.395563i
$145$	11.9045	+	20.6192i	0.988617	+	1.71233i
$146$	−10.4208			−0.862432
$147$	−1.83953	+	20.3024i	−0.151722	+	1.67452i
$148$	1.17554			0.0966289
$149$	−8.73669	−	15.1324i	−0.715737	−	1.23969i	−0.962674	−	0.270662i	$-0.912757\pi$
$149$	−8.73669	−	15.1324i	−0.715737	−	1.23969i	0.246937	−	0.969032i	$-0.420576\pi$
$150$	14.0173	−	24.2786i	1.14450	−	1.98234i
$151$	−0.774530	+	1.34153i	−0.0630304	+	0.109172i	−0.895819	−	0.444420i	$-0.853410\pi$
$151$	−0.774530	+	1.34153i	−0.0630304	+	0.109172i	0.832788	+	0.553592i	$0.186743\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	−30.5233			−2.46766
$154$	3.39331	−	0.746774i	0.273441	−	0.0601768i
$155$	−27.2978			−2.19261
$156$	−1.95611	−	3.38809i	−0.156615	−	0.271264i
$157$	1.56885	−	2.71733i	0.125208	−	0.216866i	−0.796606	−	0.604498i	$-0.793374\pi$
$157$	1.56885	−	2.71733i	0.125208	−	0.216866i	0.921814	+	0.387632i	$0.126707\pi$
$158$	2.74439	−	4.75343i	0.218332	−	0.378162i
$159$	−4.45226	−	7.71155i	−0.353087	−	0.611565i
$160$	3.82446			0.302350
$161$	−14.4183	−	15.7837i	−1.13632	−	1.24393i
$162$	−4.59899			−0.361331
$163$	−4.59899	−	7.96568i	−0.360221	−	0.623920i	0.627776	−	0.778394i	$-0.283965\pi$
$163$	−4.59899	−	7.96568i	−0.360221	−	0.623920i	−0.987997	+	0.154473i	$0.950632\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	−7.31324	+	12.6669i	−0.569335	+	0.986117i
$166$	−0.431150	−	0.746774i	−0.0334638	−	0.0579609i
$167$	−8.96216			−0.693513			−0.346756	−	0.937955i	$-0.612717\pi$
$167$	−8.96216			−0.693513			−0.346756	+	0.937955i	$0.612717\pi$
$168$	2.32831	−	7.34483i	0.179633	−	0.566666i
$169$	−11.1953			−0.861179
$170$	10.6489	+	18.4445i	0.816735	+	1.41463i
$171$	−2.74054	+	4.74675i	−0.209574	+	0.362993i
$172$	0.912229	−	1.58003i	0.0695568	−	0.120476i
$173$	5.09899	+	8.83171i	0.387669	+	0.671462i	0.992136	−	0.125168i	$-0.0399471\pi$
$173$	5.09899	+	8.83171i	0.387669	+	0.671462i	−0.604467	+	0.796630i	$0.706614\pi$
$174$	−18.1300			−1.37443
$175$	−7.69632	+	24.2786i	−0.581787	+	1.83529i
$176$	−1.31324			−0.0989893
$177$	8.10888	+	14.0450i	0.609501	+	1.05569i
$178$	−1.96986	+	3.41190i	−0.147647	+	0.255733i
$179$	4.44237	−	7.69441i	0.332038	−	0.575107i	−0.650873	−	0.759186i	$-0.725597\pi$
$179$	4.44237	−	7.69441i	0.332038	−	0.575107i	0.982911	+	0.184079i	$0.0589304\pi$
$180$	10.4811	+	18.1538i	0.781213	+	1.35310i
$181$	−13.4509			−0.999801			−0.499900	−	0.866083i	$-0.666630\pi$
$181$	−13.4509			−0.999801			−0.499900	+	0.866083i	$0.666630\pi$
$182$	2.39716	+	2.62418i	0.177689	+	0.194517i
$183$	13.1377			0.971167
$184$	4.04003	+	6.99754i	0.297835	+	0.515866i
$185$	2.24791	−	3.89349i	0.165269	−	0.286255i
$186$	10.3933	−	18.0017i	0.762074	−	1.31995i
$187$	−3.65662	−	6.33345i	−0.267399	−	0.463148i
$188$	4.31324			0.314575
$189$	18.6700	−	4.10876i	1.35804	−	0.298869i
$190$	3.82446			0.277455
$191$	0.975036	+	1.68881i	0.0705511	+	0.122198i	0.899143	−	0.437655i	$-0.144191\pi$
$191$	0.975036	+	1.68881i	0.0705511	+	0.122198i	−0.828592	+	0.559853i	$0.810858\pi$
$192$	−1.45611	+	2.52206i	−0.105086	+	0.182014i
$193$	4.30554	−	7.45741i	0.309919	−	0.536796i	−0.668425	−	0.743779i	$-0.733031\pi$
$193$	4.30554	−	7.45741i	0.309919	−	0.536796i	0.978344	+	0.206983i	$0.0663646\pi$
$194$	−7.79432	−	13.5002i	−0.559600	−	0.969255i
$195$	−14.9622			−1.07146
$196$	−0.631656	+	6.97144i	−0.0451183	+	0.497960i
$197$	5.54906			0.395354			0.197677	−	0.980267i	$-0.436660\pi$
$197$	5.54906			0.395354			0.197677	+	0.980267i	$0.436660\pi$
$198$	−3.59899	−	6.23363i	−0.255769	−	0.443005i
$199$	−3.35327	+	5.80804i	−0.237707	+	0.411721i	−0.960056	−	0.279808i	$-0.909729\pi$
$199$	−3.35327	+	5.80804i	−0.237707	+	0.411721i	0.722349	+	0.691529i	$0.243063\pi$
$200$	4.81324	−	8.33678i	0.340348	−	0.589499i
$201$	−17.3782	−	30.1000i	−1.22577	−	2.12309i
$202$	−5.13770			−0.361487
$203$	16.0861	−	3.54011i	1.12902	−	0.248467i
$204$	−16.2178			−1.13547
$205$	11.4734	+	19.8725i	0.801335	+	1.38795i
$206$	−0.686759	+	1.18950i	−0.0478488	+	0.0828765i
$207$	−22.1437	+	38.3541i	−1.53910	+	2.66579i
$208$	−0.671690	−	1.16340i	−0.0465733	−	0.0806673i
$209$	−1.31324			−0.0908388
$210$	−19.8744	−	21.7565i	−1.37146	−	1.50134i
$211$	19.6791			1.35476			0.677381	−	0.735632i	$-0.263115\pi$
$211$	19.6791			1.35476			0.677381	+	0.735632i	$0.263115\pi$
$212$	−1.52882	−	2.64799i	−0.105000	−	0.181864i
$213$	18.6188	−	32.2487i	1.27574	−	2.20964i
$214$	7.80939	−	13.5263i	0.533839	−	0.924636i
$215$	−3.48878	−	6.04275i	−0.237933	−	0.412112i
$216$	−7.22547			−0.491631
$217$	−5.70655	+	18.0017i	−0.387386	+	1.22204i
$218$	−2.65662			−0.179929
$219$	−15.1739	−	26.2819i	−1.02536	−	1.77597i
$220$	−2.51122	+	4.34956i	−0.169306	+	0.293247i
$221$	3.74054	−	6.47880i	0.251616	−	0.435812i
$222$	1.71172	+	2.96479i	0.114883	+	0.198984i
$223$	−1.03784			−0.0694991			−0.0347495	−	0.999396i	$-0.511063\pi$
$223$	−1.03784			−0.0694991			−0.0347495	+	0.999396i	$0.511063\pi$
$224$	0.799494	−	2.52206i	0.0534185	−	0.168513i
$225$	52.7635			3.51757
$226$	−0.598988	−	1.03748i	−0.0398441	−	0.0690120i
$227$	−7.15277	+	12.3890i	−0.474746	+	0.822284i	−0.999582	−	0.0289194i	$-0.990793\pi$
$227$	−7.15277	+	12.3890i	−0.474746	+	0.822284i	0.524836	+	0.851203i	$0.324127\pi$
$228$	−1.45611	+	2.52206i	−0.0964335	+	0.167028i
$229$	5.28310	+	9.15060i	0.349117	+	0.604689i	0.986093	−	0.166195i	$-0.0531482\pi$
$229$	5.28310	+	9.15060i	0.349117	+	0.604689i	−0.636976	+	0.770884i	$0.719815\pi$
$230$	30.9019			2.03761
$231$	6.82446	+	7.47075i	0.449016	+	0.491539i
$232$	−6.22547			−0.408722
$233$	−11.3245	−	19.6145i	−0.741890	−	1.28499i	−0.951634	−	0.307235i	$-0.900596\pi$
$233$	−11.3245	−	19.6145i	−0.741890	−	1.28499i	0.209744	−	0.977756i	$-0.432737\pi$
$234$	3.68158	−	6.37669i	0.240673	−	0.416857i
$235$	8.24791	−	14.2858i	0.538034	−	0.931902i
$236$	2.78442	+	4.82277i	0.181251	+	0.313935i
$237$	15.9846			1.03831
$238$	14.3895	−	3.16673i	0.932730	−	0.205268i
$239$	22.0697			1.42757			0.713786	−	0.700364i	$-0.246979\pi$
$239$	22.0697			1.42757			0.713786	+	0.700364i	$0.246979\pi$
$240$	5.56885	+	9.64553i	0.359468	+	0.622616i
$241$	10.6791	−	18.4967i	0.687898	−	1.19148i	−0.284618	−	0.958641i	$-0.591867\pi$
$241$	10.6791	−	18.4967i	0.687898	−	1.19148i	0.972516	−	0.232834i	$-0.0747999\pi$
$242$	−4.63770	+	8.03273i	−0.298123	+	0.516363i
$243$	4.14155	+	7.17338i	0.265681	+	0.460172i
$244$	4.51122			0.288801
$245$	21.8821	+	15.4231i	1.39800	+	0.985345i
$246$	−17.4734			−1.11406
$247$	−0.671690	−	1.16340i	−0.0427386	−	0.0740254i
$248$	3.56885	−	6.18143i	0.226622	−	0.392521i
$249$	1.25561	−	2.17478i	0.0795710	−	0.137821i
$250$	−8.84689	−	15.3233i	−0.559527	−	0.969129i
$251$	20.8865			1.31834			0.659171	−	0.751993i	$-0.270907\pi$
$251$	20.8865			1.31834			0.659171	+	0.751993i	$0.270907\pi$
$252$	14.1627	−	3.11682i	0.892164	−	0.196341i
$253$	−10.6111			−0.667113
$254$	10.1678	+	17.6112i	0.637987	+	1.10503i
$255$	−31.0121	+	53.7145i	−1.94205	+	3.36373i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.77453	−	4.80563i	−0.173070	−	0.299767i	0.766421	−	0.642338i	$-0.222035\pi$
$257$	−2.77453	−	4.80563i	−0.173070	−	0.299767i	−0.939492	+	0.342571i	$0.888702\pi$
$258$	5.31324			0.330788
$259$	−2.09767	−	2.29632i	−0.130343	−	0.142686i
$260$	−5.13770			−0.318627
$261$	−17.0611	−	29.5508i	−1.05606	−	1.82915i
$262$	−10.0499	+	17.4070i	−0.620887	+	1.07541i
$263$	1.33216	−	2.30737i	0.0821446	−	0.142279i	−0.822026	−	0.569450i	$-0.807156\pi$
$263$	1.33216	−	2.30737i	0.0821446	−	0.142279i	0.904171	+	0.427171i	$0.140490\pi$
$264$	−1.91223	−	3.31208i	−0.117690	−	0.203844i
$265$	−11.6938			−0.718344
$266$	0.799494	−	2.52206i	0.0490201	−	0.154638i
$267$	−11.4734			−0.702159
$268$	−5.96733	−	10.3357i	−0.364513	−	0.631355i
$269$	−4.64892	+	8.05216i	−0.283449	+	0.490949i	−0.972232	−	0.234019i	$-0.924812\pi$
$269$	−4.64892	+	8.05216i	−0.283449	+	0.490949i	0.688783	+	0.724968i	$0.258145\pi$
$270$	−13.8168	+	23.9313i	−0.840861	+	1.45641i
$271$	8.55378	+	14.8156i	0.519605	+	0.899983i	0.999740	+	0.0227880i	$0.00725427\pi$
$271$	8.55378	+	14.8156i	0.519605	+	0.899983i	−0.480135	+	0.877195i	$0.659412\pi$
$272$	−5.56885			−0.337661
$273$	−3.12780	+	9.86689i	−0.189303	+	0.597172i
$274$	17.8141			1.07619
$275$	6.32094	+	10.9482i	0.381167	+	0.660201i
$276$	−11.7655	+	20.3784i	−0.708200	+	1.22664i
$277$	−5.74439	+	9.94958i	−0.345147	+	0.597812i	−0.985380	−	0.170368i	$-0.945504\pi$
$277$	−5.74439	+	9.94958i	−0.345147	+	0.597812i	0.640233	+	0.768180i	$0.278838\pi$
$278$	7.88209	+	13.6522i	0.472736	+	0.818803i
$279$	39.1223			2.34219
$280$	−6.82446	−	7.47075i	−0.407839	−	0.446463i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	6.28057	+	10.8783i	0.374003	+	0.647792i
$283$	1.08007	−	1.87073i	0.0642033	−	0.111203i	−0.832137	−	0.554570i	$-0.812883\pi$
$283$	1.08007	−	1.87073i	0.0642033	−	0.111203i	0.896340	+	0.443367i	$0.146216\pi$
$284$	6.39331	−	11.0735i	0.379373	−	0.657093i
$285$	5.56885	+	9.64553i	0.329870	+	0.571352i
$286$	1.76418			0.104318
$287$	15.5035	−	3.41190i	0.915143	−	0.201398i
$288$	−5.48108			−0.322976
$289$	−7.00604	−	12.1348i	−0.412120	−	0.713813i
$290$	−11.9045	+	20.6192i	−0.699058	+	1.21080i
$291$	22.6988	−	39.3156i	1.33063	−	2.30472i
$292$	−5.21040	−	9.02468i	−0.304916	−	0.528129i
$293$	−17.6841			−1.03312			−0.516558	−	0.856252i	$-0.672787\pi$
$293$	−17.6841			−1.03312			−0.516558	+	0.856252i	$0.672787\pi$
$294$	−18.5022	+	8.55814i	−1.07907	+	0.499121i
$295$	21.2978			1.24001
$296$	0.587771	+	1.01805i	0.0341635	+	0.0591729i
$297$	4.74439	−	8.21753i	0.275298	−	0.476829i
$298$	8.73669	−	15.1324i	0.506103	−	0.876596i
$299$	−5.42730	−	9.40036i	−0.313869	−	0.543637i
$300$	28.0345			1.61857
$301$	−4.71425	+	1.03748i	−0.271725	+	0.0597992i
$302$	−1.54906			−0.0891384
$303$	−7.48108	−	12.9576i	−0.429777	−	0.744395i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	8.62648	−	14.9415i	0.493951	−	0.855548i
$306$	−15.2617	−	26.4340i	−0.872451	−	1.51113i
$307$	−18.1377			−1.03517			−0.517587	−	0.855631i	$-0.673169\pi$
$307$	−18.1377			−1.03517			−0.517587	+	0.855631i	$0.673169\pi$
$308$	2.34338	+	2.56530i	0.133526	+	0.146172i
$309$	−4.00000			−0.227552
$310$	−13.6489	−	23.6406i	−0.775206	−	1.34270i
$311$	0.975036	−	1.68881i	0.0552892	−	0.0957637i	−0.837056	−	0.547117i	$-0.815725\pi$
$311$	0.975036	−	1.68881i	0.0552892	−	0.0957637i	0.892345	+	0.451353i	$0.149059\pi$
$312$	1.95611	−	3.38809i	0.110743	−	0.191813i
$313$	5.87956	+	10.1837i	0.332332	+	0.575617i	0.982969	−	0.183773i	$-0.0588311\pi$
$313$	5.87956	+	10.1837i	0.332332	+	0.575617i	−0.650636	+	0.759390i	$0.725498\pi$
$314$	3.13770			0.177071
$315$	16.7591	−	52.8679i	0.944270	−	2.97877i
$316$	5.48878			0.308768
$317$	6.49615	+	11.2517i	0.364860	+	0.631956i	0.988754	−	0.149553i	$-0.0477835\pi$
$317$	6.49615	+	11.2517i	0.364860	+	0.631956i	−0.623894	+	0.781509i	$0.714450\pi$
$318$	4.45226	−	7.71155i	0.249670	−	0.432442i
$319$	4.08777	−	7.08023i	0.228871	−	0.396417i
$320$	1.91223	+	3.31208i	0.106897	+	0.185151i
$321$	45.4855			2.53875
$322$	6.45997	−	20.3784i	0.360000	−	1.13565i
$323$	−5.56885			−0.309859
$324$	−2.29949	−	3.98284i	−0.127750	−	0.221269i
$325$	−6.46601	+	11.1995i	−0.358670	+	0.621234i
$326$	4.59899	−	7.96568i	0.254714	−	0.441178i
$327$	−3.86834	−	6.70017i	−0.213920	−	0.370520i
$328$	−6.00000			−0.331295
$329$	−7.69665	−	8.42555i	−0.424330	−	0.464515i
$330$	−14.6265			−0.805161
$331$	−3.29817	−	5.71260i	−0.181284	−	0.313993i	0.761034	−	0.648712i	$-0.224692\pi$
$331$	−3.29817	−	5.71260i	−0.181284	−	0.313993i	−0.942318	+	0.334719i	$0.891359\pi$
$332$	0.431150	−	0.746774i	0.0236625	−	0.0409846i
$333$	−3.22162	+	5.58001i	−0.176544	+	0.305782i
$334$	−4.48108	−	7.76146i	−0.245194	−	0.424688i
$335$	−45.6436			−2.49378
$336$	7.52496	−	1.65604i	0.410520	−	0.0903443i
$337$	−8.16013			−0.444511			−0.222255	−	0.974988i	$-0.571342\pi$
$337$	−8.16013			−0.444511			−0.222255	+	0.974988i	$0.571342\pi$
$338$	−5.59767	−	9.69544i	−0.304473	−	0.527362i
$339$	1.74439	−	3.02137i	0.0947423	−	0.164099i
$340$	−10.6489	+	18.4445i	−0.577519	+	1.00029i
$341$	4.68676	+	8.11770i	0.253802	+	0.439598i
$342$	−5.48108			−0.296383
$343$	14.7453	−	11.2061i	0.796169	−	0.605074i
$344$	1.82446			0.0983682
$345$	44.9967	+	77.9365i	2.42254	+	4.19596i
$346$	−5.09899	+	8.83171i	−0.274123	+	0.474796i
$347$	−4.10756	+	7.11450i	−0.220505	+	0.381927i	−0.954962	−	0.296730i	$-0.904104\pi$
$347$	−4.10756	+	7.11450i	−0.220505	+	0.381927i	0.734456	+	0.678656i	$0.237437\pi$
$348$	−9.06500	−	15.7010i	−0.485935	−	0.841664i
$349$	−12.0603			−0.645572			−0.322786	−	0.946472i	$-0.604619\pi$
$349$	−12.0603			−0.645572			−0.322786	+	0.946472i	$0.604619\pi$
$350$	−24.8740	+	5.47410i	−1.32957	+	0.292603i
$351$	9.70655			0.518097
$352$	−0.656620	−	1.13730i	−0.0349980	−	0.0606183i
$353$	−5.82963	+	10.0972i	−0.310280	+	0.537421i	−0.978423	−	0.206612i	$-0.933756\pi$
$353$	−5.82963	+	10.0972i	−0.310280	+	0.537421i	0.668143	+	0.744033i	$0.267089\pi$
$354$	−8.10888	+	14.0450i	−0.430982	+	0.746483i
$355$	−24.4509	−	42.3503i	−1.29772	−	2.24772i
$356$	−3.93972			−0.208805
$357$	28.9394	+	31.6800i	1.53163	+	1.67668i
$358$	8.88474			0.469573
$359$	4.24824	+	7.35817i	0.224214	+	0.388350i	0.956083	−	0.293095i	$-0.0946853\pi$
$359$	4.24824	+	7.35817i	0.224214	+	0.388350i	−0.731870	+	0.681445i	$0.761352\pi$
$360$	−10.4811	+	18.1538i	−0.552401	+	0.956787i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	−6.72547	−	11.6489i	−0.353483	−	0.612250i
$363$	−27.0121			−1.41777
$364$	−1.07402	+	3.38809i	−0.0562942	+	0.177584i
$365$	−39.8539			−2.08605
$366$	6.56885	+	11.3776i	0.343359	+	0.594716i
$367$	−18.0035	+	31.1830i	−0.939776	+	1.62774i	−0.173888	+	0.984765i	$0.555633\pi$
$367$	−18.0035	+	31.1830i	−0.939776	+	1.62774i	−0.765888	+	0.642974i	$0.777700\pi$
$368$	−4.04003	+	6.99754i	−0.210601	+	0.364772i
$369$	−16.4432	−	28.4805i	−0.856001	−	1.48264i
$370$	4.49581			0.233726
$371$	−2.44456	+	7.71155i	−0.126915	+	0.400363i
$372$	20.7866			1.07774
$373$	−0.295642	−	0.512067i	−0.0153078	−	0.0265138i	0.858270	−	0.513198i	$-0.171539\pi$
$373$	−0.295642	−	0.512067i	−0.0153078	−	0.0265138i	−0.873578	+	0.486684i	$0.838206\pi$
$374$	3.65662	−	6.33345i	0.189079	−	0.327495i
$375$	25.7642	−	44.6249i	1.33046	−	2.30442i
$376$	2.15662	+	3.73538i	0.111219	+	0.192637i
$377$	8.36317			0.430725
$378$	12.8933	+	14.1143i	0.663160	+	0.725963i
$379$	−11.2935			−0.580106			−0.290053	−	0.957011i	$-0.593673\pi$
$379$	−11.2935			−0.580106			−0.290053	+	0.957011i	$0.593673\pi$
$380$	1.91223	+	3.31208i	0.0980953	+	0.169906i
$381$	−29.6111	+	51.2879i	−1.51702	+	2.62756i
$382$	−0.975036	+	1.68881i	−0.0498872	+	0.0864071i
$383$	3.59899	+	6.23363i	0.183900	+	0.318524i	0.943205	−	0.332211i	$-0.107795\pi$
$383$	3.59899	+	6.23363i	0.183900	+	0.318524i	−0.759305	+	0.650734i	$0.774461\pi$
$384$	−2.91223			−0.148614
$385$	12.9776	−	2.85601i	0.661398	−	0.145556i
$386$	8.61107			0.438292
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$	7.79432	−	13.5002i	0.395697	−	0.685367i
$389$	−14.3055	+	24.7779i	−0.725320	+	1.25629i	0.233523	+	0.972351i	$0.424975\pi$
$389$	−14.3055	+	24.7779i	−0.725320	+	1.25629i	−0.958842	+	0.283939i	$0.908359\pi$
$390$	−7.48108	−	12.9576i	−0.378819	−	0.656134i
$391$	−44.9967			−2.27558
$392$	−6.35327	+	2.93869i	−0.320889	+	0.148426i
$393$	−58.5354			−2.95272
$394$	2.77453	+	4.80563i	0.139779	+	0.242104i
$395$	10.4958	−	18.1793i	0.528102	−	0.914699i
$396$	3.59899	−	6.23363i	0.180856	−	0.313252i
$397$	−2.37087	−	4.10647i	−0.118991	−	0.206098i	0.800377	−	0.599497i	$-0.204633\pi$
$397$	−2.37087	−	4.10647i	−0.118991	−	0.206098i	−0.919368	+	0.393399i	$0.871299\pi$
$398$	−6.70655			−0.336169
$399$	7.52496	−	1.65604i	0.376719	−	0.0829056i
$400$	9.62648			0.481324
$401$	17.4734	+	30.2648i	0.872579	+	1.51135i	0.859320	+	0.511439i	$0.170887\pi$
$401$	17.4734	+	30.2648i	0.872579	+	1.51135i	0.0132589	+	0.999912i	$0.495779\pi$
$402$	17.3782	−	30.1000i	0.866748	−	1.50125i
$403$	−4.79432	+	8.30401i	−0.238822	+	0.413652i
$404$	−2.56885	−	4.44938i	−0.127805	−	0.221365i
$405$	−17.5886			−0.873987
$406$	11.1089	+	12.1609i	0.551325	+	0.603536i
$407$	−1.54377			−0.0765218
$408$	−8.10888	−	14.0450i	−0.401450	−	0.695331i
$409$	9.87439	−	17.1029i	0.488257	−	0.845686i	−0.511652	−	0.859193i	$-0.670966\pi$
$409$	9.87439	−	17.1029i	0.488257	−	0.845686i	0.999909	+	0.0135070i	$0.00429954\pi$
$410$	−11.4734	+	19.8725i	−0.566630	+	0.981431i
$411$	25.9394	+	44.9283i	1.27950	+	2.21615i
$412$	−1.37352			−0.0676684
$413$	4.45226	−	14.0450i	0.219082	−	0.691109i
$414$	−44.2875			−2.17661
$415$	−1.64892	−	2.85601i	−0.0809421	−	0.140196i
$416$	0.671690	−	1.16340i	0.0329323	−	0.0570404i
$417$	−22.9545	+	39.7583i	−1.12408	+	1.94697i
$418$	−0.656620	−	1.13730i	−0.0321164	−	0.0556272i
$419$	−4.57149			−0.223332			−0.111666	−	0.993746i	$-0.535619\pi$
$419$	−4.57149			−0.223332			−0.111666	+	0.993746i	$0.535619\pi$
$420$	8.90453	−	28.0900i	0.434496	−	1.37065i
$421$	−1.07236			−0.0522638			−0.0261319	−	0.999659i	$-0.508319\pi$
$421$	−1.07236			−0.0522638			−0.0261319	+	0.999659i	$0.508319\pi$
$422$	9.83953	+	17.0426i	0.478981	+	0.829619i
$423$	−11.8206	+	20.4739i	−0.574738	+	0.995475i
$424$	1.52882	−	2.64799i	0.0742459	−	0.128598i
$425$	26.8042	+	46.4263i	1.30020	+	2.25200i
$426$	37.2376			1.80417
$427$	−8.04993	−	8.81228i	−0.389563	−	0.426456i
$428$	15.6188			0.754962
$429$	2.56885	+	4.44938i	0.124025	+	0.214818i
$430$	3.48878	−	6.04275i	0.168244	−	0.291407i
$431$	12.1678	−	21.0753i	0.586104	−	1.01516i	−0.408633	−	0.912699i	$-0.633994\pi$
$431$	12.1678	−	21.0753i	0.586104	−	1.01516i	0.994737	−	0.102463i	$-0.0326724\pi$
$432$	−3.61274	−	6.25744i	−0.173818	−	0.301061i
$433$	2.07568			0.0997510			0.0498755	−	0.998755i	$-0.484118\pi$
$433$	2.07568			0.0997510			0.0498755	+	0.998755i	$0.484118\pi$
$434$	−18.4432	+	4.05885i	−0.885304	+	0.194831i
$435$	−69.3374			−3.32447
$436$	−1.32831	−	2.30070i	−0.0636145	−	0.110184i
$437$	−4.04003	+	6.99754i	−0.193261	+	0.334738i
$438$	15.1739	−	26.2819i	0.725036	−	1.25580i
$439$	−4.86230	−	8.42175i	−0.232065	−	0.401948i	0.726351	−	0.687324i	$-0.241215\pi$
$439$	−4.86230	−	8.42175i	−0.232065	−	0.401948i	−0.958416	+	0.285376i	$0.907882\pi$
$440$	−5.02243			−0.239435
$441$	−31.3606	−	22.1038i	−1.49336	−	1.05256i
$442$	7.48108			0.355839
$443$	4.19798	+	7.27111i	0.199452	+	0.345461i	0.948351	−	0.317223i	$-0.102751\pi$
$443$	4.19798	+	7.27111i	0.199452	+	0.345461i	−0.748899	+	0.662684i	$0.769417\pi$
$444$	−1.71172	+	2.96479i	−0.0812348	+	0.140703i
$445$	−7.53365	+	13.0487i	−0.357129	+	0.618566i
$446$	−0.518921	−	0.898798i	−0.0245716	−	0.0425593i
$447$	50.8865			2.40685
$448$	2.58392	−	0.568650i	0.122079	−	0.0268662i
$449$	5.47338			0.258305			0.129152	−	0.991625i	$-0.458774\pi$
$449$	5.47338			0.258305			0.129152	+	0.991625i	$0.458774\pi$
$450$	26.3818	+	45.6945i	1.24365	+	2.15406i
$451$	3.93972	−	6.82380i	0.185514	−	0.321320i
$452$	0.598988	−	1.03748i	0.0281740	−	0.0487989i
$453$	−2.25561	−	3.90683i	−0.105978	−	0.183559i
$454$	−14.3055			−0.671392
$455$	9.16784	+	10.0361i	0.429795	+	0.470498i
$456$	−2.91223			−0.136378
$457$	−14.5486	−	25.1989i	−0.680555	−	1.17876i	−0.974812	−	0.223030i	$-0.928405\pi$
$457$	−14.5486	−	25.1989i	−0.680555	−	1.17876i	0.294257	−	0.955726i	$-0.404928\pi$
$458$	−5.28310	+	9.15060i	−0.246863	+	0.427580i
$459$	20.1188	−	34.8467i	0.939064	−	1.62651i
$460$	15.4509	+	26.7618i	0.720404	+	1.24778i
$461$	14.9622			0.696857			0.348429	−	0.937335i	$-0.386715\pi$
$461$	14.9622			0.696857			0.348429	+	0.937335i	$0.386715\pi$
$462$	−3.05763	+	9.64553i	−0.142254	+	0.448751i
$463$	5.56620			0.258683			0.129342	−	0.991600i	$-0.458714\pi$
$463$	5.56620			0.258683			0.129342	+	0.991600i	$0.458714\pi$
$464$	−3.11274	−	5.39142i	−0.144505	−	0.250290i
$465$	39.7488	−	68.8469i	1.84331	−	3.19270i
$466$	11.3245	−	19.6145i	0.524595	−	0.908626i
$467$	−2.51122	−	4.34956i	−0.116205	−	0.201273i	0.802056	−	0.597249i	$-0.203740\pi$
$467$	−2.51122	−	4.34956i	−0.116205	−	0.201273i	−0.918261	+	0.395976i	$0.870406\pi$
$468$	7.36317			0.340363
$469$	−9.54169	+	30.1000i	−0.440595	+	1.38989i
$470$	16.4958			0.760895
$471$	4.56885	+	7.91348i	0.210521	+	0.364634i
$472$	−2.78442	+	4.82277i	−0.128164	+	0.221986i
$473$	−1.19798	+	2.07496i	−0.0550830	+	0.0954066i
$474$	7.99230	+	13.8431i	0.367098	+	0.635833i
$475$	9.62648			0.441693
$476$	9.93719	+	10.8783i	0.455471	+	0.498605i
$477$	16.7591			0.767348
$478$	11.0349	+	19.1129i	0.504723	+	0.874205i
$479$	−11.2530	+	19.4907i	−0.514161	+	0.890553i	0.485704	+	0.874123i	$0.338563\pi$
$479$	−11.2530	+	19.4907i	−0.514161	+	0.890553i	−0.999865	+	0.0164297i	$0.994770\pi$
$480$	−5.56885	+	9.64553i	−0.254182	+	0.440256i
$481$	−0.789599	−	1.36763i	−0.0360026	−	0.0623584i
$482$	21.3581			0.972835
$483$	60.8022	−	13.3809i	2.76660	−	0.608852i
$484$	−9.27540			−0.421609
$485$	−29.8091	−	51.6308i	−1.35356	−	2.34443i
$486$	−4.14155	+	7.17338i	−0.187865	+	0.325391i
$487$	0.217766	−	0.377182i	0.00986793	−	0.0170918i	−0.861049	−	0.508522i	$-0.830192\pi$
$487$	0.217766	−	0.377182i	0.00986793	−	0.0170918i	0.870917	+	0.491430i	$0.163526\pi$
$488$	2.25561	+	3.90683i	0.102107	+	0.176854i
$489$	26.7866			1.21133
$490$	−2.41574	+	26.6620i	−0.109132	+	1.20447i
$491$	−2.39595			−0.108128			−0.0540639	−	0.998537i	$-0.517217\pi$
$491$	−2.39595			−0.108128			−0.0540639	+	0.998537i	$0.517217\pi$
$492$	−8.73669	−	15.1324i	−0.393880	−	0.682221i
$493$	17.3344	−	30.0240i	0.780700	−	1.35221i
$494$	0.671690	−	1.16340i	0.0302208	−	0.0523439i
$495$	−13.7642	−	23.8403i	−0.618654	−	1.07154i
$496$	7.13770			0.320492
$497$	−33.0396	+	7.27111i	−1.48203	+	0.326154i
$498$	2.51122			0.112530
$499$	4.85195	+	8.40383i	0.217203	+	0.376207i	0.953952	−	0.299960i	$-0.0969732\pi$
$499$	4.85195	+	8.40383i	0.217203	+	0.376207i	−0.736749	+	0.676167i	$0.763640\pi$
$500$	8.84689	−	15.3233i	0.395645	−	0.685277i
$501$	13.0499	−	22.6031i	0.583028	−	1.00983i
$502$	10.4432	+	18.0882i	0.466104	+	0.807317i
$503$	−4.34602			−0.193780			−0.0968898	−	0.995295i	$-0.530889\pi$
$503$	−4.34602			−0.193780			−0.0968898	+	0.995295i	$0.530889\pi$
$504$	9.78057	+	10.7068i	0.435661	+	0.476920i
$505$	−19.6489			−0.874365
$506$	−5.30554	−	9.18946i	−0.235860	−	0.408521i
$507$	16.3017	−	28.2353i	0.723983	−	1.25398i
$508$	−10.1678	+	17.6112i	−0.451125	+	0.781371i
$509$	−21.7101	−	37.6029i	−0.962282	−	1.66672i	−0.716748	−	0.697333i	$-0.754370\pi$
$509$	−21.7101	−	37.6029i	−0.962282	−	1.66672i	−0.245534	−	0.969388i	$-0.578963\pi$
$510$	−62.0242			−2.74648
$511$	−8.33137	+	26.2819i	−0.368558	+	1.16264i
$512$	−1.00000			−0.0441942
$513$	−3.61274	−	6.25744i	−0.159506	−	0.276273i
$514$	2.77453	−	4.80563i	0.122379	−	0.211967i
$515$	−2.62648	+	4.54920i	−0.115737	+	0.200462i
$516$	2.65662	+	4.60140i	0.116951	+	0.202565i
$517$	−5.66432			−0.249117
$518$	0.939839	−	2.96479i	0.0412941	−	0.130265i
$519$	−29.6988			−1.30363
$520$	−2.56885	−	4.44938i	−0.112652	−	0.195118i
$521$	11.8520	−	20.5282i	0.519243	−	0.899356i	−0.480506	−	0.876991i	$-0.659547\pi$
$521$	11.8520	−	20.5282i	0.519243	−	0.899356i	0.999750	−	0.0223648i	$-0.00711953\pi$
$522$	17.0611	−	29.5508i	0.746746	−	1.29340i
$523$	0.864492	+	1.49734i	0.0378016	+	0.0654743i	0.884307	−	0.466905i	$-0.154631\pi$
$523$	0.864492	+	1.49734i	0.0378016	+	0.0654743i	−0.846506	+	0.532380i	$0.821298\pi$
$524$	−20.0999			−0.878066
$525$	−50.0255	−	54.7630i	−2.18329	−	2.39005i
$526$	2.66432			0.116170
$527$	19.8744	+	34.4234i	0.865742	+	1.49951i
$528$	1.91223	−	3.31208i	0.0832191	−	0.144140i
$529$	−21.1437	+	36.6220i	−0.919293	+	1.59226i
$530$	−5.84689	−	10.1271i	−0.253973	−	0.439894i
$531$	−30.5233			−1.32460
$532$	2.58392	−	0.568650i	0.112027	−	0.0246541i
$533$	8.06028			0.349129
$534$	−5.73669	−	9.93623i	−0.248251	−	0.429983i
$535$	29.8667	−	51.7306i	1.29125	−	2.23651i
$536$	5.96733	−	10.3357i	0.257749	−	0.446435i
$537$	12.9372	+	22.4079i	0.558281	+	0.966971i
$538$	−9.29783			−0.400858
$539$	0.829517	−	9.15518i	0.0357298	−	0.394342i
$540$	−27.6335			−1.18916
$541$	15.3132	+	26.5233i	0.658368	+	1.14033i	0.981038	+	0.193815i	$0.0620861\pi$
$541$	15.3132	+	26.5233i	0.658368	+	1.14033i	−0.322670	+	0.946511i	$0.604581\pi$
$542$	−8.55378	+	14.8156i	−0.367416	+	0.636384i
$543$	19.5861	−	33.9241i	0.840520	−	1.45582i
$544$	−2.78442	−	4.82277i	−0.119381	−	0.206774i
$545$	−10.1601			−0.435212
$546$	−10.1089	+	2.22469i	−0.432620	+	0.0952079i
$547$	−16.2583			−0.695153			−0.347576	−	0.937652i	$-0.612995\pi$
$547$	−16.2583			−0.695153			−0.347576	+	0.937652i	$0.612995\pi$
$548$	8.90705	+	15.4275i	0.380491	+	0.659029i
$549$	−12.3632	+	21.4136i	−0.527647	+	0.913912i
$550$	−6.32094	+	10.9482i	−0.269526	+	0.466833i
$551$	−3.11274	−	5.39142i	−0.132607	−	0.229682i
$552$	−23.5310			−1.00155
$553$	−9.79432	−	10.7219i	−0.416497	−	0.455940i
$554$	−11.4888			−0.488112
$555$	6.54641	+	11.3387i	0.277880	+	0.481302i
$556$	−7.88209	+	13.6522i	−0.334275	+	0.578981i
$557$	15.1300	−	26.2059i	0.641078	−	1.11038i	−0.344114	−	0.938928i	$-0.611821\pi$
$557$	15.1300	−	26.2059i	0.641078	−	1.11038i	0.985192	−	0.171453i	$-0.0548460\pi$
$558$	19.5611	+	33.8809i	0.828089	+	1.43429i
$559$	−2.45094			−0.103664
$560$	3.05763	−	9.64553i	0.129209	−	0.407598i
$561$	21.2978			0.899195
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	0.862301	−	1.49355i	0.0363416	−	0.0629456i	−0.847283	−	0.531142i	$-0.821763\pi$
$563$	0.862301	−	1.49355i	0.0363416	−	0.0629456i	0.883624	+	0.468197i	$0.155096\pi$
$564$	−6.28057	+	10.8783i	−0.264460	+	0.458058i
$565$	−2.29081	−	3.96779i	−0.0963749	−	0.166926i
$566$	2.16013			0.0907972
$567$	−3.67686	+	11.5989i	−0.154414	+	0.487110i
$568$	12.7866			0.536514
$569$	5.62648	+	9.74535i	0.235874	+	0.408546i	0.959526	−	0.281619i	$-0.0908713\pi$
$569$	5.62648	+	9.74535i	0.235874	+	0.408546i	−0.723652	+	0.690165i	$0.757538\pi$
$570$	−5.56885	+	9.64553i	−0.233253	+	0.404007i
$571$	−20.0499	+	34.7275i	−0.839063	+	1.45330i	0.0516153	+	0.998667i	$0.483563\pi$
$571$	−20.0499	+	34.7275i	−0.839063	+	1.45330i	−0.890679	+	0.454633i	$0.849770\pi$
$572$	0.882090	+	1.52783i	0.0368821	+	0.0638816i
$573$	−5.67906			−0.237246
$574$	10.7065	+	11.7205i	0.446883	+	0.489204i
$575$	77.7826			3.24376
$576$	−2.74054	−	4.74675i	−0.114189	−	0.197781i
$577$	12.6317	−	21.8787i	0.525863	−	0.910821i	−0.473683	−	0.880695i	$-0.657076\pi$
$577$	12.6317	−	21.8787i	0.525863	−	0.910821i	0.999546	−	0.0301258i	$-0.00959078\pi$
$578$	7.00604	−	12.1348i	0.291413	−	0.504742i
$579$	12.5387	+	21.7177i	0.521091	+	0.902556i
$580$	−23.8091			−0.988617
$581$	−2.22812	+	0.490347i	−0.0924378	+	0.0203430i
$582$	45.3977			1.88179
$583$	2.00770	+	3.47744i	0.0831506	+	0.144021i
$584$	5.21040	−	9.02468i	0.215608	−	0.373444i
$585$	14.0801	−	24.3874i	0.582139	−	1.00829i
$586$	−8.84206	−	15.3149i	−0.365262	−	0.632652i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$	−16.6627	−	11.7443i	−0.687157	−	0.484327i
$589$	7.13770			0.294104
$590$	10.6489	+	18.4445i	0.438409	+	0.759347i
$591$	−8.08007	+	13.9951i	−0.332370	+	0.575681i
$592$	−0.587771	+	1.01805i	−0.0241572	+	0.0418416i
$593$	−0.488783	−	0.846596i	−0.0200719	−	0.0347655i	0.855815	−	0.517282i	$-0.173056\pi$
$593$	−0.488783	−	0.846596i	−0.0200719	−	0.0347655i	−0.875887	+	0.482517i	$0.839723\pi$
$594$	9.48878			0.389329
$595$	55.0319	−	12.1110i	2.25609	−	0.496503i
$596$	17.4734			0.715737
$597$	−9.76550	−	16.9143i	−0.399675	−	0.692258i
$598$	5.42730	−	9.40036i	0.221939	−	0.384409i
$599$	18.3357	−	31.7583i	0.749175	−	1.29761i	−0.199043	−	0.979991i	$-0.563783\pi$
$599$	18.3357	−	31.7583i	0.749175	−	1.29761i	0.948218	−	0.317619i	$-0.102883\pi$
$600$	14.0173	+	24.2786i	0.572252	+	0.991170i
$601$	−13.9296			−0.568200			−0.284100	−	0.958795i	$-0.591695\pi$
$601$	−13.9296			−0.568200			−0.284100	+	0.958795i	$0.591695\pi$
$602$	−3.25561	−	3.56392i	−0.132689	−	0.145255i
$603$	65.4148			2.66390
$604$	−0.774530	−	1.34153i	−0.0315152	−	0.0545859i
$605$	−17.7367	+	30.7208i	−0.721099	+	1.24898i
$606$	7.48108	−	12.9576i	0.303898	−	0.526367i
$607$	−13.6714	−	23.6795i	−0.554903	−	0.961120i	−0.997911	−	0.0646026i	$-0.979422\pi$
$607$	−13.6714	−	23.6795i	−0.554903	−	0.961120i	0.443008	−	0.896518i	$-0.353911\pi$
$608$	−1.00000			−0.0405554
$609$	−14.4948	+	45.7250i	−0.587360	+	1.85287i
$610$	17.2530			0.698552
$611$	−2.89716	−	5.01803i	−0.117207	−	0.203008i
$612$	15.2617	−	26.4340i	0.616916	−	1.06853i
$613$	0.576553	−	0.998620i	0.0232868	−	0.0403339i	−0.854147	−	0.520031i	$-0.825920\pi$
$613$	0.576553	−	0.998620i	0.0232868	−	0.0403339i	0.877434	+	0.479697i	$0.159254\pi$
$614$	−9.06885	−	15.7077i	−0.365989	−	0.633912i
$615$	−66.8262			−2.69469
$616$	−1.04993	+	3.31208i	−0.0423028	+	0.133447i
$617$	−0.604047			−0.0243180			−0.0121590	−	0.999926i	$-0.503870\pi$
$617$	−0.604047			−0.0243180			−0.0121590	+	0.999926i	$0.503870\pi$
$618$	−2.00000	−	3.46410i	−0.0804518	−	0.139347i
$619$	9.91223	−	17.1685i	0.398406	−	0.690060i	−0.595123	−	0.803634i	$-0.702897\pi$
$619$	9.91223	−	17.1685i	0.398406	−	0.690060i	0.993529	+	0.113575i	$0.0362301\pi$
$620$	13.6489	−	23.6406i	0.548154	−	0.949430i
$621$	−29.1911	−	50.5605i	−1.17140	−	2.02892i
$622$	1.95007			0.0781907
$623$	7.03014	+	7.69591i	0.281657	+	0.308330i
$624$	3.91223			0.156615
$625$	−9.76837	−	16.9193i	−0.390735	−	0.676773i
$626$	−5.87956	+	10.1837i	−0.234995	+	0.407022i
$627$	1.91223	−	3.31208i	0.0763671	−	0.132272i
$628$	1.56885	+	2.71733i	0.0626039	+	0.108433i
$629$	−6.54641			−0.261023
$630$	54.1645	−	11.9201i	2.15797	−	0.474909i
$631$	−29.8416			−1.18798			−0.593988	−	0.804474i	$-0.702447\pi$
$631$	−29.8416			−1.18798			−0.593988	+	0.804474i	$0.702447\pi$
$632$	2.74439	+	4.75343i	0.109166	+	0.189081i
$633$	−28.6550	+	49.6318i	−1.13893	+	1.97269i
$634$	−6.49615	+	11.2517i	−0.257995	+	0.446860i
$635$	38.8865	+	67.3533i	1.54316	+	2.67284i
$636$	8.90453			0.353087
$637$	8.53486	−	3.94778i	0.338163	−	0.156417i
$638$	8.17554			0.323673
$639$	35.0422	+	60.6949i	1.38625	+	2.40105i
$640$	−1.91223	+	3.31208i	−0.0755875	+	0.130921i
$641$	−7.33303	+	12.7012i	−0.289637	+	0.501667i	−0.973723	−	0.227735i	$-0.926868\pi$
$641$	−7.33303	+	12.7012i	−0.289637	+	0.501667i	0.684086	+	0.729401i	$0.260201\pi$
$642$	22.7427	+	39.3916i	0.897584	+	1.55466i
$643$	−31.2978			−1.23427			−0.617133	−	0.786859i	$-0.711706\pi$
$643$	−31.2978			−1.23427			−0.617133	+	0.786859i	$0.711706\pi$
$644$	20.8782	−	4.59473i	0.822718	−	0.181058i
$645$	20.3203			0.800110
$646$	−2.78442	−	4.82277i	−0.109552	−	0.189749i
$647$	13.7518	−	23.8187i	0.540637	−	0.936411i	−0.458230	−	0.888834i	$-0.651516\pi$
$647$	13.7518	−	23.8187i	0.540637	−	0.936411i	0.998868	−	0.0475778i	$-0.0151502\pi$
$648$	2.29949	−	3.98284i	0.0903327	−	0.156461i
$649$	−3.65662	−	6.33345i	−0.143535	−	0.248610i
$650$	−12.9320			−0.507236
$651$	−37.0922	−	40.6049i	−1.45376	−	1.59143i
$652$	9.19798			0.360221
$653$	1.62913	+	2.82173i	0.0637527	+	0.110423i	0.896140	−	0.443771i	$-0.146360\pi$
$653$	1.62913	+	2.82173i	0.0637527	+	0.110423i	−0.832387	+	0.554194i	$0.813026\pi$
$654$	3.86834	−	6.70017i	0.151264	−	0.261997i
$655$	−38.4355	+	66.5723i	−1.50180	+	2.60119i
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	57.1172			2.22836
$658$	3.44841	−	10.8783i	0.134433	−	0.424079i
$659$	27.6188			1.07587			0.537937	−	0.842985i	$-0.319204\pi$
$659$	27.6188			1.07587			0.537937	+	0.842985i	$0.319204\pi$
$660$	−7.31324	−	12.6669i	−0.284668	−	0.493059i
$661$	0.761652	−	1.31922i	0.0296248	−	0.0513117i	−0.850833	−	0.525436i	$-0.823902\pi$
$661$	0.761652	−	1.31922i	0.0296248	−	0.0513117i	0.880458	+	0.474125i	$0.157235\pi$
$662$	3.29817	−	5.71260i	0.128187	−	0.222027i
$663$	10.8933	+	18.8678i	0.423061	+	0.732763i
$664$	0.862301			0.0334638
$665$	3.05763	−	9.64553i	0.118570	−	0.374038i
$666$	−6.44324			−0.249670
$667$	−25.1511	−	43.5630i	−0.973855	−	1.68677i
$668$	4.48108	−	7.76146i	0.173378	−	0.300300i
$669$	1.51122	−	2.61751i	0.0584270	−	0.101199i
$670$	−22.8218	−	39.5285i	−0.881684	−	1.52712i
$671$	−5.92432			−0.228706
$672$	5.19665	+	5.68879i	0.200465	+	0.219450i
$673$	−6.06028			−0.233607			−0.116803	−	0.993155i	$-0.537265\pi$
$673$	−6.06028			−0.233607			−0.116803	+	0.993155i	$0.537265\pi$
$674$	−4.08007	−	7.06688i	−0.157158	−	0.272206i
$675$	−34.7779	+	60.2371i	−1.33860	+	2.31853i
$676$	5.59767	−	9.69544i	0.215295	−	0.372902i
$677$	−17.4381	−	30.2036i	−0.670199	−	1.16082i	−0.977847	−	0.209319i	$-0.932875\pi$
$677$	−17.4381	−	30.2036i	−0.670199	−	1.16082i	0.307648	−	0.951500i	$-0.400458\pi$
$678$	3.48878			0.133986
$679$	−40.2798	+	8.86448i	−1.54580	+	0.340187i
$680$	−21.2978			−0.816735
$681$	−20.8305	−	36.0795i	−0.798227	−	1.38257i
$682$	−4.68676	+	8.11770i	−0.179465	+	0.310843i
$683$	17.3821	−	30.1067i	0.665107	−	1.15200i	−0.314149	−	0.949374i	$-0.601719\pi$
$683$	17.3821	−	30.1067i	0.665107	−	1.15200i	0.979256	−	0.202626i	$-0.0649475\pi$
$684$	−2.74054	−	4.74675i	−0.104787	−	0.181497i
$685$	68.1293			2.60309
$686$	17.0774	+	7.16671i	0.652019	+	0.273626i
$687$	−30.7712			−1.17399
$688$	0.912229	+	1.58003i	0.0347784	+	0.0602380i
$689$	−2.05378	+	3.55725i	−0.0782428	+	0.135520i
$690$	−44.9967	+	77.9365i	−1.71299	+	2.96699i
$691$	−17.6111	−	30.5033i	−0.669957	−	1.16040i	−0.977916	−	0.209000i	$-0.932979\pi$
$691$	−17.6111	−	30.5033i	−0.669957	−	1.16040i	0.307959	−	0.951400i	$-0.400354\pi$
$692$	−10.1980			−0.387669
$693$	−18.5990	+	4.09313i	−0.706517	+	0.155485i
$694$	−8.21512			−0.311842
$695$	30.1447	+	52.2122i	1.14345	+	1.98052i
$696$	9.06500	−	15.7010i	0.343608	−	0.595146i
$697$	16.7065	−	28.9366i	0.632806	−	1.09605i
$698$	−6.03014	−	10.4445i	−0.228244	−	0.395330i
$699$	65.9588			2.49479
$700$	−17.1777	−	18.8045i	−0.649257	−	0.710744i
$701$	28.3150			1.06944			0.534721	−	0.845029i	$-0.320417\pi$
$701$	28.3150			1.06944			0.534721	+	0.845029i	$0.320417\pi$
$702$	4.85327	+	8.40612i	0.183175	+	0.317268i
$703$	−0.587771	+	1.01805i	−0.0221682	+	0.0383964i
$704$	0.656620	−	1.13730i	0.0247473	−	0.0428636i
$705$	24.0198	+	41.6035i	0.904638	+	1.56688i
$706$	−11.6593			−0.438802
$707$	−4.10756	+	12.9576i	−0.154481	+	0.487321i
$708$	−16.2178			−0.609501
$709$	13.0422	+	22.5898i	0.489811	+	0.848378i	0.999931	−	0.0117255i	$-0.00373243\pi$
$709$	13.0422	+	22.5898i	0.489811	+	0.848378i	−0.510120	+	0.860103i	$0.670399\pi$
$710$	24.4509	−	42.3503i	0.917627	−	1.58938i
$711$	−15.0422	+	26.0539i	−0.564127	+	0.977097i
$712$	−1.96986	−	3.41190i	−0.0738237	−	0.127866i
$713$	57.6731			2.15987
$714$	−12.9660	+	40.9023i	−0.485241	+	1.53073i
$715$	6.74704			0.252325
$716$	4.44237	+	7.69441i	0.166019	+	0.287553i
$717$	−32.1360	+	55.6613i	−1.20014	+	2.07871i
$718$	−4.24824	+	7.35817i	−0.158543	+	0.274605i
$719$	9.92730	+	17.1946i	0.370226	+	0.641250i	0.989600	−	0.143846i	$-0.0459470\pi$
$719$	9.92730	+	17.1946i	0.370226	+	0.641250i	−0.619374	+	0.785096i	$0.712614\pi$
$720$	−20.9622			−0.781213
$721$	2.45094	+	2.68305i	0.0912778	+	0.0999220i
$722$	−1.00000			−0.0372161
$723$	31.0999	+	53.8665i	1.15662	+	2.00332i
$724$	6.72547	−	11.6489i	0.249950	−	0.432926i
$725$	−29.9647	+	51.9004i	−1.11286	+	1.92753i
$726$	−13.5060	−	23.3932i	−0.501256	−	0.868201i
$727$	−35.6439			−1.32196			−0.660979	−	0.750405i	$-0.729859\pi$
$727$	−35.6439			−1.32196			−0.660979	+	0.750405i	$0.729859\pi$
$728$	−3.47118	+	0.763913i	−0.128651	+	0.0283125i
$729$	−37.9193			−1.40442
$730$	−19.9270	−	34.5145i	−0.737530	−	1.27744i
$731$	−5.08007	+	8.79893i	−0.187893	+	0.325440i
$732$	−6.56885	+	11.3776i	−0.242792	+	0.420528i
$733$	22.0473	+	38.1870i	0.814335	+	1.41047i	0.909804	+	0.415037i	$0.136231\pi$
$733$	22.0473	+	38.1870i	0.814335	+	1.41047i	−0.0954695	+	0.995432i	$0.530435\pi$
$734$	−36.0070			−1.32904
$735$	−70.7609	+	32.7303i	−2.61005	+	1.20727i
$736$	−8.08007			−0.297835
$737$	7.83654	+	13.5733i	0.288663	+	0.499979i
$738$	16.4432	−	28.4805i	0.605284	−	1.04838i
$739$	14.8442	−	25.7110i	0.546054	−	0.945794i	−0.452485	−	0.891772i	$-0.649462\pi$
$739$	14.8442	−	25.7110i	0.546054	−	0.945794i	0.998540	−	0.0540222i	$-0.0172042\pi$
$740$	2.24791	+	3.89349i	0.0826346	+	0.143127i
$741$	3.91223			0.143719
$742$	−7.90067	+	1.73872i	−0.290043	+	0.0638305i
$743$	1.72460			0.0632695			0.0316347	−	0.999499i	$-0.489929\pi$
$743$	1.72460			0.0632695			0.0316347	+	0.999499i	$0.489929\pi$
$744$	10.3933	+	18.0017i	0.381037	+	0.659976i
$745$	33.4131	−	57.8732i	1.22416	−	2.12031i
$746$	0.295642	−	0.512067i	0.0108242	−	0.0187481i
$747$	2.36317	+	4.09313i	0.0864638	+	0.149760i
$748$	7.31324			0.267399
$749$	−27.8705	−	30.5099i	−1.01837	−	1.11481i
$750$	51.5284			1.88155
$751$	16.6988	+	28.9232i	0.609350	+	1.05542i	0.991348	+	0.131261i	$0.0419027\pi$
$751$	16.6988	+	28.9232i	0.609350	+	1.05542i	−0.381998	+	0.924163i	$0.624764\pi$
$752$	−2.15662	+	3.73538i	−0.0786439	+	0.136215i
$753$	−30.4131	+	52.6770i	−1.10831	+	1.91966i
$754$	4.18158	+	7.24272i	0.152284	+	0.263764i
$755$	−5.92432			−0.215608
$756$	−5.77672	+	18.2231i	−0.210097	+	0.662768i
$757$	−3.92432			−0.142632			−0.0713158	−	0.997454i	$-0.522720\pi$
$757$	−3.92432			−0.142632			−0.0713158	+	0.997454i	$0.522720\pi$
$758$	−5.64673	−	9.78042i	−0.205098	−	0.355241i
$759$	15.4509	−	26.7618i	0.560834	−	0.971392i
$760$	−1.91223	+	3.31208i	−0.0693638	+	0.120142i
$761$	−20.6059	−	35.6905i	−0.746963	−	1.29378i	−0.949272	−	0.314457i	$-0.898178\pi$
$761$	−20.6059	−	35.6905i	−0.746963	−	1.29378i	0.202309	−	0.979322i	$-0.435156\pi$
$762$	−59.2221			−2.14539
$763$	−2.12395	+	6.70017i	−0.0768922	+	0.242562i
$764$	−1.95007			−0.0705511
$765$	−58.3676	−	101.096i	−2.11028	−	3.65512i
$766$	−3.59899	+	6.23363i	−0.130037	+	0.225230i
$767$	3.74054	−	6.47880i	0.135063	−	0.233936i
$768$	−1.45611	−	2.52206i	−0.0525430	−	0.0910072i
$769$	10.7118			0.386279			0.193139	−	0.981171i	$-0.438133\pi$
$769$	10.7118			0.386279			0.193139	+	0.981171i	$0.438133\pi$
$770$	8.96216	+	9.81090i	0.322974	+	0.353560i
$771$	16.1601			0.581993
$772$	4.30554	+	7.45741i	0.154960	+	0.268398i
$773$	−26.6864	+	46.2222i	−0.959844	+	1.66250i	−0.236972	+	0.971517i	$0.576155\pi$
$773$	−26.6864	+	46.2222i	−0.959844	+	1.66250i	−0.722872	+	0.690982i	$0.757178\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	−34.3555	−	59.5054i	−1.23408	−	2.13750i
$776$	15.5886			0.559600
$777$	8.84591	−	1.94674i	0.317345	−	0.0698390i
$778$	−28.6111			−1.02576
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$	7.48108	−	12.9576i	0.267866	−	0.463957i
$781$	−8.39595	+	14.5422i	−0.300431	+	0.520361i
$782$	−22.4983	−	38.9683i	−0.804539	−	1.39350i
$783$	44.9819			1.60752
$784$	−5.72162	−	4.03275i	−0.204344	−	0.144027i
$785$	12.0000			0.428298
$786$	−29.2677	−	50.6931i	−1.04394	−	1.80816i
$787$	−0.0175986	+	0.0304816i	−0.000627321	+	0.00108655i	−0.866339	−	0.499457i	$-0.833533\pi$
$787$	−0.0175986	+	0.0304816i	−0.000627321	+	0.00108655i	0.865712	+	0.500543i	$0.166866\pi$
$788$	−2.77453	+	4.80563i	−0.0988385	+	0.171193i
$789$	3.87956	+	6.71960i	0.138116	+	0.239224i
$790$	20.9916			0.746848
$791$	−3.09547	+	0.681229i	−0.110062	+	0.0242217i
$792$	7.19798			0.255769
$793$	−3.03014	−	5.24835i	−0.107603	−	0.186375i
$794$	2.37087	−	4.10647i	0.0841391	−	0.145733i
$795$	17.0275	−	29.4925i	0.603903	−	1.04599i
$796$	−3.35327	−	5.80804i	−0.118854	−	0.205861i
$797$	40.9417			1.45023			0.725115	−	0.688628i	$-0.241787\pi$
$797$	40.9417			1.45023			0.725115	+	0.688628i	$0.241787\pi$
$798$	5.19665	+	5.68879i	0.183960	+	0.201381i
$799$	−24.0198			−0.849759
$800$	4.81324	+	8.33678i	0.170174	+	0.294750i
$801$	10.7970	−	18.7009i	0.381492	−	0.660764i
$802$	−17.4734	+	30.2648i	−0.617006	+	1.06869i
$803$	6.84251	+	11.8516i	0.241467	+	0.418233i
$804$	34.7565			1.22577
$805$	24.7059	−	77.9365i	0.870768	−	2.74690i
$806$	−9.58864			−0.337745
$807$	−13.5387	−	23.4497i	−0.476585	−	0.825470i
$808$	2.56885	−	4.44938i	0.0903718	−	0.156529i
$809$	16.9798	−	29.4098i	0.596976	−	1.03399i	−0.396288	−	0.918126i	$-0.629702\pi$
$809$	16.9798	−	29.4098i	0.596976	−	1.03399i	0.993265	−	0.115867i	$-0.0369648\pi$
$810$	−8.79432	−	15.2322i	−0.309001	−	0.535205i
$811$	−1.88035			−0.0660281			−0.0330141	−	0.999455i	$-0.510511\pi$
$811$	−1.88035			−0.0660281			−0.0330141	+	0.999455i	$0.510511\pi$
$812$	−4.97723	+	15.7010i	−0.174666	+	0.550998i
$813$	−49.8211			−1.74730
$814$	−0.771885	−	1.33694i	−0.0270545	−	0.0468598i
$815$	17.5886	−	30.4644i	0.616103	−	1.06712i
$816$	8.10888	−	14.0450i	0.283868	−	0.491673i
$817$	0.912229	+	1.58003i	0.0319149	+	0.0552782i
$818$	19.7488			0.690500
$819$	−13.1390	−	14.3833i	−0.459115	−	0.502594i
$820$	−22.9468			−0.801335
$821$	8.69885	+	15.0668i	0.303592	+	0.525836i	0.976947	−	0.213483i	$-0.0684808\pi$
$821$	8.69885	+	15.0668i	0.303592	+	0.525836i	−0.673355	+	0.739319i	$0.735147\pi$
$822$	−25.9394	+	44.9283i	−0.904740	+	1.56706i
$823$	12.1627	−	21.0664i	0.423964	−	0.734327i	−0.572359	−	0.820003i	$-0.693972\pi$
$823$	12.1627	−	21.0664i	0.423964	−	0.734327i	0.996323	+	0.0856762i	$0.0273050\pi$
$824$	−0.686759	−	1.18950i	−0.0239244	−	0.0414383i
$825$	−36.8161			−1.28177
$826$	14.3895	−	3.16673i	0.500673	−	0.110184i
$827$	−41.9588			−1.45905			−0.729526	−	0.683953i	$-0.760259\pi$
$827$	−41.9588			−1.45905			−0.729526	+	0.683953i	$0.760259\pi$
$828$	−22.1437	−	38.3541i	−0.769548	−	1.33290i
$829$	−22.6360	+	39.2068i	−0.786182	+	1.36171i	0.142108	+	0.989851i	$0.454612\pi$
$829$	−22.6360	+	39.2068i	−0.786182	+	1.36171i	−0.928290	+	0.371856i	$0.878721\pi$
$830$	1.64892	−	2.85601i	0.0572347	−	0.0991335i
$831$	−16.7290	−	28.9754i	−0.580322	−	1.00515i
$832$	1.34338			0.0465733
$833$	3.51760	−	38.8229i	0.121878	−	1.34513i
$834$	−45.9089			−1.58970
$835$	−17.1377	−	29.6834i	−0.593075	−	1.02724i
$836$	0.656620	−	1.13730i	0.0227097	−	0.0393343i
$837$	−25.7866	+	44.6637i	−0.891316	+	1.54380i
$838$	−2.28575	−	3.95903i	−0.0789598	−	0.136762i
$839$	39.8539			1.37591			0.687955	−	0.725753i	$-0.258509\pi$
$839$	39.8539			1.37591			0.687955	+	0.725753i	$0.258509\pi$
$840$	28.7789	−	6.33345i	0.992967	−	0.218525i
$841$	9.75648			0.336430
$842$	−0.536182	−	0.928694i	−0.0184780	−	0.0320049i
$843$	17.4734	−	30.2648i	0.601815	−	1.04237i
$844$	−9.83953	+	17.0426i	−0.338691	+	0.586629i
$845$	−21.4080	−	37.0798i	−0.736459	−	1.27558i
$846$	−23.6412			−0.812802
$847$	16.5513	+	18.1187i	0.568708	+	0.622566i
$848$	3.05763			0.105000
$849$	3.14540	+	5.44800i	0.107950	+	0.186975i
$850$	−26.8042	+	46.4263i	−0.919377	+	1.59241i
$851$	−4.74923	+	8.22590i	−0.162801	+	0.281980i
$852$	18.6188	+	32.2487i	0.637869	+	1.10482i
$853$	25.3581			0.868245			0.434123	−	0.900854i	$-0.357058\pi$
$853$	25.3581			0.868245			0.434123	+	0.900854i	$0.357058\pi$
$854$	3.60669	−	11.3776i	0.123418	−	0.389333i
$855$	−20.9622			−0.716891
$856$	7.80939	+	13.5263i	0.266919	+	0.462318i
$857$	−4.75912	+	8.24304i	−0.162569	+	0.281577i	−0.935789	−	0.352560i	$-0.885311\pi$
$857$	−4.75912	+	8.24304i	−0.162569	+	0.281577i	0.773221	+	0.634137i	$0.218645\pi$
$858$	−2.56885	+	4.44938i	−0.0876991	+	0.151899i
$859$	18.5913	+	32.2010i	0.634326	+	1.09869i	0.986657	+	0.162810i	$0.0520558\pi$
$859$	18.5913	+	32.2010i	0.634326	+	1.09869i	−0.352331	+	0.935875i	$0.614611\pi$
$860$	6.97757			0.237933
$861$	−13.9699	+	44.0690i	−0.476092	+	1.50187i
$862$	24.3357			0.828876
$863$	−12.8821	−	22.3124i	−0.438511	−	0.759524i	0.559063	−	0.829125i	$-0.311161\pi$
$863$	−12.8821	−	22.3124i	−0.438511	−	0.759524i	−0.997575	+	0.0696007i	$0.977827\pi$
$864$	3.61274	−	6.25744i	0.122908	−	0.212882i
$865$	−19.5009	+	33.7765i	−0.663049	+	1.14844i
$866$	1.03784	+	1.79760i	0.0352673	+	0.0610848i
$867$	40.8064			1.38586
$868$	−12.7367	−	13.9429i	−0.432311	−	0.473252i
$869$	−7.20809			−0.244518
$870$	−34.6687	−	60.0480i	−1.17538	−	2.03582i
$871$	−8.01639	+	13.8848i	−0.271625	+	0.470468i
$872$	1.32831	−	2.30070i	0.0449823	−	0.0779116i
$873$	42.7213	+	73.9954i	1.44590	+	2.50437i
$874$	−8.08007			−0.273312
$875$	−45.7193	+	10.0616i	−1.54559	+	0.340143i
$876$	30.3478			1.02536
$877$	−7.21305	−	12.4934i	−0.243567	−	0.421871i	0.718161	−	0.695877i	$-0.244984\pi$
$877$	−7.21305	−	12.4934i	−0.243567	−	0.421871i	−0.961728	+	0.274007i	$0.911651\pi$
$878$	4.86230	−	8.42175i	0.164095	−	0.284220i
$879$	25.7501	−	44.6005i	0.868529	−	1.50434i
$880$	−2.51122	−	4.34956i	−0.0846531	−	0.146624i
$881$	−54.2978			−1.82934			−0.914670	−	0.404201i	$-0.867550\pi$
$881$	−54.2978			−1.82934			−0.914670	+	0.404201i	$0.867550\pi$
$882$	3.46216	−	38.2110i	0.116577	−	1.28663i
$883$	9.31324			0.313416			0.156708	−	0.987645i	$-0.449912\pi$
$883$	9.31324			0.313416			0.156708	+	0.987645i	$0.449912\pi$
$884$	3.74054	+	6.47880i	0.125808	+	0.217906i
$885$	−31.0121	+	53.7145i	−1.04246	+	1.80559i
$886$	−4.19798	+	7.27111i	−0.141034	+	0.244278i
$887$	19.2754	+	33.3860i	0.647205	+	1.12099i	0.983788	+	0.179337i	$0.0573954\pi$
$887$	19.2754	+	33.3860i	0.647205	+	1.12099i	−0.336583	+	0.941654i	$0.609271\pi$
$888$	−3.42345			−0.114883
$889$	52.5457	−	11.5639i	1.76233	−	0.387840i
$890$	−15.0673			−0.505057
$891$	3.01979	+	5.23043i	0.101167	+	0.175226i
$892$	0.518921	−	0.898798i	0.0173748	−	0.0300940i
$893$	−2.15662	+	3.73538i	−0.0721686	+	0.125000i
$894$	25.4432	+	44.0690i	0.850949	+	1.47389i
$895$	33.9793			1.13580
$896$	1.78442	+	1.95341i	0.0596134	+	0.0652590i
$897$	31.6111			1.05546
$898$	2.73669	+	4.74008i	0.0913244	+	0.158179i
$899$	−22.2178	+	38.4823i	−0.741004	+	1.28346i
$900$	−26.3818	+	45.6945i	−0.879392	+	1.52315i
$901$	8.51375	+	14.7462i	0.283634	+	0.491269i
$902$	7.87945			0.262357
$903$	4.24791	−	13.4003i	0.141361	−	0.445935i
$904$	1.19798			0.0398441
$905$	−25.7213	−	44.5506i	−0.855004	−	1.48091i
$906$	2.25561	−	3.90683i	0.0749376	−	0.129796i
$907$	−8.09767	+	14.0256i	−0.268879	+	0.465711i	−0.968573	−	0.248731i	$-0.919986\pi$
$907$	−8.09767	+	14.0256i	−0.268879	+	0.465711i	0.699694	+	0.714443i	$0.253320\pi$
$908$	−7.15277	−	12.3890i	−0.237373	−	0.411142i
$909$	28.1601			0.934013
$910$	−4.10756	+	12.9576i	−0.136164	+	0.429541i
$911$	33.4030			1.10669			0.553345	−	0.832952i	$-0.313351\pi$
$911$	33.4030			1.10669			0.553345	+	0.832952i	$0.313351\pi$
$912$	−1.45611	−	2.52206i	−0.0482168	−	0.0835139i
$913$	−0.566204	+	0.980695i	−0.0187386	+	0.0324563i
$914$	14.5486	−	25.1989i	0.481225	−	0.833506i
$915$	25.1223	+	43.5131i	0.830517	+	1.43850i
$916$	−10.5662			−0.349117
$917$	35.8667	+	39.2634i	1.18442	+	1.29659i
$918$	40.2376			1.32804
$919$	25.8042	+	44.6942i	0.851202	+	1.47433i	0.880124	+	0.474744i	$0.157459\pi$
$919$	25.8042	+	44.6942i	0.851202	+	1.47433i	−0.0289213	+	0.999582i	$0.509207\pi$
$920$	−15.4509	+	26.7618i	−0.509402	+	0.882311i
$921$	26.4106	−	45.7444i	0.870258	−	1.50733i
$922$	7.48108	+	12.9576i	0.246376	+	0.426736i
$923$	−17.1773			−0.565397
$924$	−9.88209	+	2.17478i	−0.325097	+	0.0715449i
$925$	11.3163			0.372079
$926$	2.78310	+	4.82047i	0.0914584	+	0.158411i
$927$	3.76418	−	6.51975i	0.123632	−	0.214137i
$928$	3.11274	−	5.39142i	0.102181	−	0.176982i
$929$	−30.1572	−	52.2337i	−0.989424	−	1.71373i	−0.620331	−	0.784340i	$-0.713002\pi$
$929$	−30.1572	−	52.2337i	−0.989424	−	1.71373i	−0.369093	−	0.929392i	$-0.620332\pi$
$930$	79.4975			2.60683
$931$	−5.72162	−	4.03275i	−0.187518	−	0.132168i
$932$	22.6489			0.741890
$933$	2.83953	+	4.91821i	0.0929620	+	0.161015i
$934$	2.51122	−	4.34956i	0.0821695	−	0.142322i
$935$	13.9846	−	24.2220i	0.457345	−	0.792145i
$936$	3.68158	+	6.37669i	0.120336	+	0.208429i
$937$	25.4881			0.832660			0.416330	−	0.909214i	$-0.363316\pi$
$937$	25.4881			0.832660			0.416330	+	0.909214i	$0.363316\pi$
$938$	−30.8382	+	6.78665i	−1.00690	+	0.221592i
$939$	−34.2453			−1.11755
$940$	8.24791	+	14.2858i	0.269017	+	0.465951i
$941$	18.3004	−	31.6972i	0.596575	−	1.03330i	−0.396748	−	0.917928i	$-0.629861\pi$
$941$	18.3004	−	31.6972i	0.596575	−	1.03330i	0.993323	−	0.115370i	$-0.0368054\pi$
$942$	−4.56885	+	7.91348i	−0.148861	+	0.257835i
$943$	−24.2402	−	41.9853i	−0.789370	−	1.36723i
$944$	−5.56885			−0.181251
$945$	49.3099	+	53.9797i	1.60405	+	1.75596i
$946$	−2.39595			−0.0778992
$947$	−25.0499	−	43.3877i	−0.814013	−	1.40991i	−0.910034	−	0.414533i	$-0.863945\pi$
$947$	−25.0499	−	43.3877i	−0.814013	−	1.40991i	0.0960209	−	0.995379i	$-0.469388\pi$
$948$	−7.99230	+	13.8431i	−0.259578	+	0.449602i
$949$	−6.99955	+	12.1236i	−0.227215	+	0.393548i
$950$	4.81324	+	8.33678i	0.156162	+	0.270481i
$951$	−37.8365			−1.22693
$952$	−4.45226	+	14.0450i	−0.144299	+	0.455201i
$953$	−51.3374			−1.66298			−0.831491	−	0.555538i	$-0.812512\pi$
$953$	−51.3374			−1.66298			−0.831491	+	0.555538i	$0.812512\pi$
$954$	8.37956	+	14.5138i	0.271298	+	0.469902i
$955$	−3.72898	+	6.45879i	−0.120667	+	0.209002i
$956$	−11.0349	+	19.1129i	−0.356893	+	0.618157i
$957$	11.9045	+	20.6192i	0.384819	+	0.666525i
$958$	−22.5059			−0.727133
$959$	14.2423	−	44.9283i	0.459907	−	1.45081i
$960$	−11.1377			−0.359468
$961$	−9.97338	−	17.2744i	−0.321722	−	0.557238i
$962$	0.789599	−	1.36763i	0.0254577	−	0.0440940i
$963$	−42.8039	+	74.1385i	−1.37934	+	2.38908i
$964$	10.6791	+	18.4967i	0.343949	+	0.595738i
$965$	32.9327			1.06014
$966$	41.9893	+	45.9658i	1.35098	+	1.47893i
$967$	−1.33568			−0.0429524			−0.0214762	−	0.999769i	$-0.506837\pi$
$967$	−1.33568			−0.0429524			−0.0214762	+	0.999769i	$0.506837\pi$
$968$	−4.63770	−	8.03273i	−0.149061	−	0.258182i
$969$	8.10888	−	14.0450i	0.260495	−	0.451190i
$970$	29.8091	−	51.6308i	0.957111	−	1.65776i
$971$	5.64034	+	9.76936i	0.181007	+	0.313514i	0.942224	−	0.334984i	$-0.108731\pi$
$971$	5.64034	+	9.76936i	0.181007	+	0.313514i	−0.761217	+	0.648498i	$0.775398\pi$
$972$	−8.28310			−0.265681
$973$	40.7334	−	8.96430i	1.30585	−	0.287382i
$974$	0.435533			0.0139554
$975$	−18.8305	−	32.6154i	−0.603059	−	1.04453i
$976$	−2.25561	+	3.90683i	−0.0722003	+	0.125055i
$977$	9.56115	−	16.5604i	0.305888	−	0.529814i	−0.671571	−	0.740941i	$-0.734380\pi$
$977$	9.56115	−	16.5604i	0.305888	−	0.529814i	0.977459	+	0.211127i	$0.0677133\pi$
$978$	13.3933	+	23.1979i	0.428271	+	0.741787i
$979$	5.17380			0.165356
$980$	−24.2978	+	11.2389i	−0.776166	+	0.359014i
$981$	14.5611			0.464902
$982$	−1.19798	−	2.07496i	−0.0382290	−	0.0662145i
$983$	−28.5387	+	49.4305i	−0.910244	+	1.57659i	−0.0965237	+	0.995331i	$0.530772\pi$
$983$	−28.5387	+	49.4305i	−0.910244	+	1.57659i	−0.813720	+	0.581257i	$0.802561\pi$
$984$	8.73669	−	15.1324i	0.278515	−	0.482403i
$985$	10.6111	+	18.3789i	0.338097	+	0.585601i
$986$	34.6687			1.10408
$987$	32.4570	−	7.14290i	1.03312	−	0.227361i
$988$	1.34338			0.0427386
$989$	7.37087	+	12.7667i	0.234380	+	0.405958i
$990$	13.7642	−	23.8403i	0.437454	−	0.757693i
$991$	−2.21777	+	3.84128i	−0.0704497	+	0.122022i	−0.899098	−	0.437746i	$-0.855777\pi$
$991$	−2.21777	+	3.84128i	−0.0704497	+	0.122022i	0.828649	+	0.559769i	$0.189110\pi$
$992$	3.56885	+	6.18143i	0.113311	+	0.196261i
$993$	19.2101			0.609613
$994$	−22.8168	−	24.9776i	−0.723704	−	0.792240i
$995$	−25.6489			−0.813125
$996$	1.25561	+	2.17478i	0.0397855	+	0.0689105i
$997$	−9.15749	+	15.8612i	−0.290021	+	0.502330i	−0.973814	−	0.227345i	$-0.926995\pi$
$997$	−9.15749	+	15.8612i	−0.290021	+	0.502330i	0.683794	+	0.729675i	$0.260329\pi$
$998$	−4.85195	+	8.40383i	−0.153586	+	0.266018i
$999$	−4.24692	−	7.35588i	−0.134367	−	0.232730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	266.2.e.d.39.1	✓	6
7.2	even	3	inner	266.2.e.d.191.1	yes	6
7.3	odd	6		1862.2.a.n.1.1		3
7.4	even	3		1862.2.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.e.d.39.1	✓	6	1.1	even	1	trivial
266.2.e.d.191.1	yes	6	7.2	even	3	inner
1862.2.a.n.1.1		3	7.3	odd	6
1862.2.a.q.1.3		3	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:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	266.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.45611 + 2.52206i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91223 + 3.31208i) q^{5} -2.91223 q^{6} +(2.58392 - 0.568650i) q^{7} -1.00000 q^{8} +(-2.74054 - 4.74675i) q^{9} +(-1.91223 + 3.31208i) q^{10} +(0.656620 - 1.13730i) q^{11} +(-1.45611 - 2.52206i) q^{12} +1.34338 q^{13} +(1.78442 + 1.95341i) q^{14} -11.1377 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.78442 - 4.82277i) q^{17} +(2.74054 - 4.74675i) q^{18} +(-0.500000 - 0.866025i) q^{19} -3.82446 q^{20} +(-2.32831 + 7.34483i) q^{21} +1.31324 q^{22} +(-4.04003 - 6.99754i) q^{23} +(1.45611 - 2.52206i) q^{24} +(-4.81324 + 8.33678i) q^{25} +(0.671690 + 1.16340i) q^{26} +7.22547 q^{27} +(-0.799494 + 2.52206i) q^{28} +6.22547 q^{29} +(-5.56885 - 9.64553i) q^{30} +(-3.56885 + 6.18143i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.91223 + 3.31208i) q^{33} +5.56885 q^{34} +(6.82446 + 7.47075i) q^{35} +5.48108 q^{36} +(-0.587771 - 1.01805i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.95611 + 3.38809i) q^{39} +(-1.91223 - 3.31208i) q^{40} +6.00000 q^{41} +(-7.52496 + 1.65604i) q^{42} -1.82446 q^{43} +(0.656620 + 1.13730i) q^{44} +(10.4811 - 18.1538i) q^{45} +(4.04003 - 6.99754i) q^{46} +(-2.15662 - 3.73538i) q^{47} +2.91223 q^{48} +(6.35327 - 2.93869i) q^{49} -9.62648 q^{50} +(8.10888 + 14.0450i) q^{51} +(-0.671690 + 1.16340i) q^{52} +(-1.52882 + 2.64799i) q^{53} +(3.61274 + 6.25744i) q^{54} +5.02243 q^{55} +(-2.58392 + 0.568650i) q^{56} +2.91223 q^{57} +(3.11274 + 5.39142i) q^{58} +(2.78442 - 4.82277i) q^{59} +(5.56885 - 9.64553i) q^{60} +(-2.25561 - 3.90683i) q^{61} -7.13770 q^{62} +(-9.78057 - 10.7068i) q^{63} +1.00000 q^{64} +(2.56885 + 4.44938i) q^{65} +(-1.91223 + 3.31208i) q^{66} +(-5.96733 + 10.3357i) q^{67} +(2.78442 + 4.82277i) q^{68} +23.5310 q^{69} +(-3.05763 + 9.64553i) q^{70} -12.7866 q^{71} +(2.74054 + 4.74675i) q^{72} +(-5.21040 + 9.02468i) q^{73} +(0.587771 - 1.01805i) q^{74} +(-14.0173 - 24.2786i) q^{75} +1.00000 q^{76} +(1.04993 - 3.31208i) q^{77} -3.91223 q^{78} +(-2.74439 - 4.75343i) q^{79} +(1.91223 - 3.31208i) q^{80} +(-2.29949 + 3.98284i) q^{81} +(3.00000 + 5.19615i) q^{82} -0.862301 q^{83} +(-5.19665 - 5.68879i) q^{84} +21.2978 q^{85} +(-0.912229 - 1.58003i) q^{86} +(-9.06500 + 15.7010i) q^{87} +(-0.656620 + 1.13730i) q^{88} +(1.96986 + 3.41190i) q^{89} +20.9622 q^{90} +(3.47118 - 0.763913i) q^{91} +8.08007 q^{92} +(-10.3933 - 18.0017i) q^{93} +(2.15662 - 3.73538i) q^{94} +(1.91223 - 3.31208i) q^{95} +(1.45611 + 2.52206i) q^{96} -15.5886 q^{97} +(5.72162 + 4.03275i) q^{98} -7.19798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 2 q^{10} - 2 q^{12} + 12 q^{13} + 2 q^{14} - 32 q^{15} - 3 q^{16} + 8 q^{17} + q^{18} - 3 q^{19} + 4 q^{20} - 12 q^{21}+ \cdots - 32 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 - q^9 + 2 * q^10 - 2 * q^12 + 12 * q^13 + 2 * q^14 - 32 * q^15 - 3 * q^16 + 8 * q^17 + q^18 - 3 * q^19 + 4 * q^20 - 12 * q^21 - 6 * q^23 + 2 * q^24 - 21 * q^25 + 6 * q^26 + 22 * q^27 - 2 * q^28 + 16 * q^29 - 16 * q^30 - 4 * q^31 + 3 * q^32 - 2 * q^33 + 16 * q^34 + 14 * q^35 + 2 * q^36 - 17 * q^37 + 3 * q^38 - 5 * q^39 + 2 * q^40 + 36 * q^41 - 21 * q^42 + 16 * q^43 + 32 * q^45 + 6 * q^46 - 9 * q^47 + 4 * q^48 + 12 * q^49 - 42 * q^50 + 13 * q^51 - 6 * q^52 - 10 * q^53 + 11 * q^54 - 8 * q^55 - 4 * q^56 + 4 * q^57 + 8 * q^58 + 8 * q^59 + 16 * q^60 - 4 * q^61 - 8 * q^62 - 25 * q^63 + 6 * q^64 - 2 * q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 62 * q^69 - 20 * q^70 + 12 * q^71 + q^72 - 4 * q^73 + 17 * q^74 - 10 * q^75 + 6 * q^76 - 42 * q^77 - 10 * q^78 - 26 * q^79 - 2 * q^80 - 11 * q^81 + 18 * q^82 - 40 * q^83 - 9 * q^84 + 20 * q^85 + 8 * q^86 - 12 * q^87 + 64 * q^90 + 20 * q^91 + 12 * q^92 - 18 * q^93 + 9 * q^94 - 2 * q^95 + 2 * q^96 - 16 * q^97 - 12 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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