Properties

Label 462.2.i.a.67.1
Level $462$
Weight $2$
Character 462.67
Analytic conductor $3.689$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.a.331.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.00000 - 5.19615i) q^{19} +3.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(-2.50000 - 4.33013i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} -6.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +5.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} +5.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.50000 - 4.33013i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(2.50000 + 4.33013i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +6.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(2.50000 + 4.33013i) q^{61} -4.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(2.50000 + 4.33013i) q^{68} +5.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-6.00000 + 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +1.00000 q^{83} +(0.500000 + 2.59808i) q^{84} -15.0000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} -3.00000 q^{90} +(-15.0000 - 5.19615i) q^{91} +5.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-9.00000 + 15.5885i) q^{95} +(0.500000 + 0.866025i) q^{96} +9.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + q^{11} - q^{12} + 12 q^{13} - q^{14} + 6 q^{15} - q^{16} + 5 q^{17} + q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} - 4 q^{25} + 6 q^{26} + 2 q^{27} + 4 q^{28} - 12 q^{29} + 3 q^{30} - 4 q^{31} + q^{32} + q^{33} + 10 q^{34} + 3 q^{35} + 2 q^{36} + 2 q^{37} + 6 q^{38} - 6 q^{39} + 3 q^{40} + 10 q^{41} + 5 q^{42} - 20 q^{43} + q^{44} - 3 q^{45} + 5 q^{46} - 9 q^{47} + 2 q^{48} + 11 q^{49} - 8 q^{50} + 5 q^{51} - 6 q^{52} - 2 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 12 q^{57} - 6 q^{58} + 12 q^{59} - 3 q^{60} + 5 q^{61} - 8 q^{62} + q^{63} + 2 q^{64} - 18 q^{65} - q^{66} - 5 q^{67} + 5 q^{68} + 10 q^{69} - 12 q^{70} + 8 q^{71} + q^{72} - 12 q^{73} - 2 q^{74} - 4 q^{75} + 12 q^{76} - 4 q^{77} - 12 q^{78} + q^{79} - 3 q^{80} - q^{81} + 5 q^{82} + 2 q^{83} + q^{84} - 30 q^{85} - 10 q^{86} + 6 q^{87} - q^{88} - 6 q^{89} - 6 q^{90} - 30 q^{91} + 10 q^{92} - 4 q^{93} + 9 q^{94} - 18 q^{95} + q^{96} + 18 q^{97} - 2 q^{98} - 2 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 3.00000 0.774597
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i \(-0.625971\pi\)
0.991838 0.127502i \(-0.0406959\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 3.00000 0.670820
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) 1.00000 0.213201
\(23\) −2.50000 4.33013i −0.521286 0.902894i −0.999694 0.0247559i \(-0.992119\pi\)
0.478407 0.878138i \(-0.341214\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) 1.00000 0.192450
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) 5.00000 0.857493
\(35\) 1.50000 + 7.79423i 0.253546 + 1.31747i
\(36\) 1.00000 0.166667
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 2.50000 + 0.866025i 0.385758 + 0.133631i
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 2.50000 4.33013i 0.368605 0.638442i
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −4.00000 −0.565685
\(51\) 2.50000 + 4.33013i 0.350070 + 0.606339i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i \(-0.877195\pi\)
0.789136 + 0.614218i \(0.210529\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −3.00000 −0.404520
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 6.00000 0.794719
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) −1.50000 + 2.59808i −0.193649 + 0.335410i
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0.500000 + 2.59808i 0.0629941 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) −9.00000 15.5885i −1.11631 1.93351i
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 2.50000 + 4.33013i 0.303170 + 0.525105i
\(69\) 5.00000 0.601929
\(70\) −6.00000 + 5.19615i −0.717137 + 0.621059i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −6.00000 + 10.3923i −0.702247 + 1.21633i 0.265429 + 0.964130i \(0.414486\pi\)
−0.967676 + 0.252197i \(0.918847\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 6.00000 0.688247
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) −6.00000 −0.679366
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.50000 + 4.33013i 0.276079 + 0.478183i
\(83\) 1.00000 0.109764 0.0548821 0.998493i \(-0.482522\pi\)
0.0548821 + 0.998493i \(0.482522\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) −15.0000 −1.62698
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) −3.00000 −0.316228
\(91\) −15.0000 5.19615i −1.57243 0.544705i
\(92\) 5.00000 0.521286
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) −9.00000 + 15.5885i −0.923381 + 1.59934i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) −1.00000 −0.100504
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 4.00000 6.92820i 0.398015 0.689382i −0.595466 0.803380i \(-0.703033\pi\)
0.993481 + 0.113998i \(0.0363659\pi\)
\(102\) −2.50000 + 4.33013i −0.247537 + 0.428746i
\(103\) 1.00000 + 1.73205i 0.0985329 + 0.170664i 0.911078 0.412235i \(-0.135252\pi\)
−0.812545 + 0.582899i \(0.801918\pi\)
\(104\) −6.00000 −0.588348
\(105\) −7.50000 2.59808i −0.731925 0.253546i
\(106\) −2.00000 −0.194257
\(107\) 6.50000 + 11.2583i 0.628379 + 1.08838i 0.987877 + 0.155238i \(0.0496145\pi\)
−0.359498 + 0.933146i \(0.617052\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) −2.00000 −0.189832
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) −7.50000 + 12.9904i −0.699379 + 1.21136i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) −3.00000 5.19615i −0.277350 0.480384i
\(118\) 12.0000 1.10469
\(119\) −10.0000 + 8.66025i −0.916698 + 0.793884i
\(120\) −3.00000 −0.273861
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.50000 + 4.33013i −0.226339 + 0.392031i
\(123\) −2.50000 + 4.33013i −0.225417 + 0.390434i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) −3.00000 −0.268328
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 5.00000 8.66025i 0.440225 0.762493i
\(130\) 9.00000 15.5885i 0.789352 1.36720i
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 3.00000 + 15.5885i 0.260133 + 1.35169i
\(134\) −5.00000 −0.431934
\(135\) −1.50000 2.59808i −0.129099 0.223607i
\(136\) −2.50000 + 4.33013i −0.214373 + 0.371305i
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 2.50000 + 4.33013i 0.212814 + 0.368605i
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) −7.50000 2.59808i −0.633866 0.219578i
\(141\) 9.00000 0.757937
\(142\) 2.00000 + 3.46410i 0.167836 + 0.290701i
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 9.00000 + 15.5885i 0.747409 + 1.29455i
\(146\) −12.0000 −0.993127
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) −2.00000 −0.164399
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −4.50000 + 7.79423i −0.366205 + 0.634285i −0.988969 0.148124i \(-0.952676\pi\)
0.622764 + 0.782410i \(0.286010\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −5.00000 −0.404226
\(154\) −2.50000 0.866025i −0.201456 0.0697863i
\(155\) 12.0000 0.963863
\(156\) −3.00000 5.19615i −0.240192 0.416025i
\(157\) 12.0000 20.7846i 0.957704 1.65879i 0.229650 0.973273i \(-0.426242\pi\)
0.728055 0.685519i \(-0.240425\pi\)
\(158\) −0.500000 + 0.866025i −0.0397779 + 0.0688973i
\(159\) −1.00000 1.73205i −0.0793052 0.137361i
\(160\) −3.00000 −0.237171
\(161\) 2.50000 + 12.9904i 0.197028 + 1.02379i
\(162\) −1.00000 −0.0785674
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −2.50000 + 4.33013i −0.195217 + 0.338126i
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0.500000 + 0.866025i 0.0388075 + 0.0672166i
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) −2.00000 + 1.73205i −0.154303 + 0.133631i
\(169\) 23.0000 1.76923
\(170\) −7.50000 12.9904i −0.575224 0.996317i
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 6.00000 0.454859
\(175\) 8.00000 6.92820i 0.604743 0.523723i
\(176\) −1.00000 −0.0753778
\(177\) 6.00000 + 10.3923i 0.450988 + 0.781133i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 4.00000 6.92820i 0.298974 0.517838i −0.676927 0.736050i \(-0.736689\pi\)
0.975901 + 0.218212i \(0.0700223\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −3.00000 15.5885i −0.222375 1.15549i
\(183\) −5.00000 −0.369611
\(184\) 2.50000 + 4.33013i 0.184302 + 0.319221i
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −2.50000 4.33013i −0.182818 0.316650i
\(188\) 9.00000 0.656392
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) −18.0000 −1.30586
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −3.00000 + 5.19615i −0.215945 + 0.374027i −0.953564 0.301189i \(-0.902616\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(194\) 4.50000 + 7.79423i 0.323081 + 0.559593i
\(195\) 18.0000 1.28901
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) 8.00000 0.562878
\(203\) 15.0000 + 5.19615i 1.05279 + 0.364698i
\(204\) −5.00000 −0.350070
\(205\) −7.50000 12.9904i −0.523823 0.907288i
\(206\) −1.00000 + 1.73205i −0.0696733 + 0.120678i
\(207\) −2.50000 + 4.33013i −0.173762 + 0.300965i
\(208\) −3.00000 5.19615i −0.208013 0.360288i
\(209\) −6.00000 −0.415029
\(210\) −1.50000 7.79423i −0.103510 0.537853i
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −1.00000 1.73205i −0.0686803 0.118958i
\(213\) −2.00000 + 3.46410i −0.137038 + 0.237356i
\(214\) −6.50000 + 11.2583i −0.444331 + 0.769604i
\(215\) 15.0000 + 25.9808i 1.02299 + 1.77187i
\(216\) −1.00000 −0.0680414
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 11.0000 0.745014
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) −1.00000 1.73205i −0.0671156 0.116248i
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 4.00000 0.266667
\(226\) 5.00000 + 8.66025i 0.332595 + 0.576072i
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) −3.00000 + 5.19615i −0.198680 + 0.344124i
\(229\) −13.0000 22.5167i −0.859064 1.48794i −0.872823 0.488037i \(-0.837713\pi\)
0.0137585 0.999905i \(-0.495620\pi\)
\(230\) −15.0000 −0.989071
\(231\) −0.500000 2.59808i −0.0328976 0.170941i
\(232\) 6.00000 0.393919
\(233\) 14.5000 + 25.1147i 0.949927 + 1.64532i 0.745573 + 0.666424i \(0.232176\pi\)
0.204354 + 0.978897i \(0.434491\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) −13.5000 + 23.3827i −0.880643 + 1.52532i
\(236\) 6.00000 + 10.3923i 0.390567 + 0.676481i
\(237\) −1.00000 −0.0649570
\(238\) −12.5000 4.33013i −0.810255 0.280680i
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i \(-0.517406\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −5.00000 −0.320092
\(245\) 3.00000 20.7846i 0.191663 1.32788i
\(246\) −5.00000 −0.318788
\(247\) −18.0000 31.1769i −1.14531 1.98374i
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) −0.500000 + 0.866025i −0.0316862 + 0.0548821i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −2.50000 0.866025i −0.157485 0.0545545i
\(253\) −5.00000 −0.314347
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) 7.50000 12.9904i 0.469668 0.813489i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.00000 + 12.1244i 0.436648 + 0.756297i 0.997429 0.0716680i \(-0.0228322\pi\)
−0.560781 + 0.827964i \(0.689499\pi\)
\(258\) 10.0000 0.622573
\(259\) −1.00000 5.19615i −0.0621370 0.322873i
\(260\) 18.0000 1.11631
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) −2.00000 + 3.46410i −0.123560 + 0.214013i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 6.00000 0.368577
\(266\) −12.0000 + 10.3923i −0.735767 + 0.637193i
\(267\) 6.00000 0.367194
\(268\) −2.50000 4.33013i −0.152712 0.264505i
\(269\) 4.50000 7.79423i 0.274370 0.475223i −0.695606 0.718423i \(-0.744864\pi\)
0.969976 + 0.243201i \(0.0781974\pi\)
\(270\) 1.50000 2.59808i 0.0912871 0.158114i
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) −5.00000 −0.303170
\(273\) 12.0000 10.3923i 0.726273 0.628971i
\(274\) 2.00000 0.120824
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) −2.50000 + 4.33013i −0.150482 + 0.260643i
\(277\) −9.00000 + 15.5885i −0.540758 + 0.936620i 0.458103 + 0.888899i \(0.348529\pi\)
−0.998861 + 0.0477206i \(0.984804\pi\)
\(278\) 11.0000 + 19.0526i 0.659736 + 1.14270i
\(279\) 4.00000 0.239474
\(280\) −1.50000 7.79423i −0.0896421 0.465794i
\(281\) 11.0000 0.656205 0.328102 0.944642i \(-0.393591\pi\)
0.328102 + 0.944642i \(0.393591\pi\)
\(282\) 4.50000 + 7.79423i 0.267971 + 0.464140i
\(283\) 3.00000 5.19615i 0.178331 0.308879i −0.762978 0.646425i \(-0.776263\pi\)
0.941309 + 0.337546i \(0.109597\pi\)
\(284\) −2.00000 + 3.46410i −0.118678 + 0.205557i
\(285\) −9.00000 15.5885i −0.533114 0.923381i
\(286\) 6.00000 0.354787
\(287\) −12.5000 4.33013i −0.737852 0.255599i
\(288\) −1.00000 −0.0589256
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) −9.00000 + 15.5885i −0.528498 + 0.915386i
\(291\) −4.50000 + 7.79423i −0.263795 + 0.456906i
\(292\) −6.00000 10.3923i −0.351123 0.608164i
\(293\) 8.00000 0.467365 0.233682 0.972313i \(-0.424922\pi\)
0.233682 + 0.972313i \(0.424922\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) −36.0000 −2.09600
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 9.00000 15.5885i 0.521356 0.903015i
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) 4.00000 0.230940
\(301\) 25.0000 + 8.66025i 1.44098 + 0.499169i
\(302\) −9.00000 −0.517892
\(303\) 4.00000 + 6.92820i 0.229794 + 0.398015i
\(304\) −3.00000 + 5.19615i −0.172062 + 0.298020i
\(305\) 7.50000 12.9904i 0.429449 0.743827i
\(306\) −2.50000 4.33013i −0.142915 0.247537i
\(307\) 18.0000 1.02731 0.513657 0.857996i \(-0.328290\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) −2.00000 −0.113776
\(310\) 6.00000 + 10.3923i 0.340777 + 0.590243i
\(311\) 10.5000 18.1865i 0.595400 1.03126i −0.398090 0.917346i \(-0.630327\pi\)
0.993490 0.113917i \(-0.0363399\pi\)
\(312\) 3.00000 5.19615i 0.169842 0.294174i
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) 24.0000 1.35440
\(315\) 6.00000 5.19615i 0.338062 0.292770i
\(316\) −1.00000 −0.0562544
\(317\) −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i \(-0.248000\pi\)
−0.964281 + 0.264883i \(0.914667\pi\)
\(318\) 1.00000 1.73205i 0.0560772 0.0971286i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) −13.0000 −0.725589
\(322\) −10.0000 + 8.66025i −0.557278 + 0.482617i
\(323\) −30.0000 −1.66924
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −12.0000 + 20.7846i −0.665640 + 1.15292i
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 5.50000 + 9.52628i 0.304151 + 0.526804i
\(328\) −5.00000 −0.276079
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) 3.00000 0.165145
\(331\) −17.5000 30.3109i −0.961887 1.66604i −0.717756 0.696295i \(-0.754831\pi\)
−0.244131 0.969742i \(-0.578503\pi\)
\(332\) −0.500000 + 0.866025i −0.0274411 + 0.0475293i
\(333\) 1.00000 1.73205i 0.0547997 0.0949158i
\(334\) −12.0000 20.7846i −0.656611 1.13728i
\(335\) 15.0000 0.819538
\(336\) −2.50000 0.866025i −0.136386 0.0472456i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 11.5000 + 19.9186i 0.625518 + 1.08343i
\(339\) −5.00000 + 8.66025i −0.271563 + 0.470360i
\(340\) 7.50000 12.9904i 0.406745 0.704502i
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) −6.00000 −0.324443
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 10.0000 0.539164
\(345\) −7.50000 12.9904i −0.403786 0.699379i
\(346\) −6.00000 + 10.3923i −0.322562 + 0.558694i
\(347\) −3.50000 + 6.06218i −0.187890 + 0.325435i −0.944547 0.328378i \(-0.893498\pi\)
0.756657 + 0.653812i \(0.226831\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 10.0000 + 3.46410i 0.534522 + 0.185164i
\(351\) 6.00000 0.320256
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 6.00000 0.317999
\(357\) −2.50000 12.9904i −0.132314 0.687524i
\(358\) 8.00000 0.422813
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 1.50000 2.59808i 0.0790569 0.136931i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −11.0000 19.0526i −0.578147 1.00138i
\(363\) 1.00000 0.0524864
\(364\) 12.0000 10.3923i 0.628971 0.544705i
\(365\) 36.0000 1.88433
\(366\) −2.50000 4.33013i −0.130677 0.226339i
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) −2.50000 + 4.33013i −0.130322 + 0.225723i
\(369\) −2.50000 4.33013i −0.130145 0.225417i
\(370\) 6.00000 0.311925
\(371\) 4.00000 3.46410i 0.207670 0.179847i
\(372\) 4.00000 0.207390
\(373\) 3.50000 + 6.06218i 0.181223 + 0.313888i 0.942297 0.334777i \(-0.108661\pi\)
−0.761074 + 0.648665i \(0.775328\pi\)
\(374\) 2.50000 4.33013i 0.129272 0.223906i
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) 4.50000 + 7.79423i 0.232070 + 0.401957i
\(377\) −36.0000 −1.85409
\(378\) −0.500000 2.59808i −0.0257172 0.133631i
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) −9.00000 15.5885i −0.461690 0.799671i
\(381\) −2.50000 + 4.33013i −0.128079 + 0.221839i
\(382\) 0 0
\(383\) −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i \(-0.232188\pi\)
−0.949938 + 0.312437i \(0.898855\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 7.50000 + 2.59808i 0.382235 + 0.132410i
\(386\) −6.00000 −0.305392
\(387\) 5.00000 + 8.66025i 0.254164 + 0.440225i
\(388\) −4.50000 + 7.79423i −0.228453 + 0.395692i
\(389\) 10.5000 18.1865i 0.532371 0.922094i −0.466915 0.884302i \(-0.654634\pi\)
0.999286 0.0377914i \(-0.0120322\pi\)
\(390\) 9.00000 + 15.5885i 0.455733 + 0.789352i
\(391\) −25.0000 −1.26430
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) −4.00000 −0.201773
\(394\) −12.0000 20.7846i −0.604551 1.04711i
\(395\) 1.50000 2.59808i 0.0754732 0.130723i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i \(-0.940407\pi\)
0.330075 0.943955i \(-0.392926\pi\)
\(398\) −10.0000 −0.501255
\(399\) −15.0000 5.19615i −0.750939 0.260133i
\(400\) 4.00000 0.200000
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 2.50000 4.33013i 0.124689 0.215967i
\(403\) −12.0000 + 20.7846i −0.597763 + 1.03536i
\(404\) 4.00000 + 6.92820i 0.199007 + 0.344691i
\(405\) 3.00000 0.149071
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 2.00000 0.0991363
\(408\) −2.50000 4.33013i −0.123768 0.214373i
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 7.50000 12.9904i 0.370399 0.641549i
\(411\) 1.00000 + 1.73205i 0.0493264 + 0.0854358i
\(412\) −2.00000 −0.0985329
\(413\) −24.0000 + 20.7846i −1.18096 + 1.02274i
\(414\) −5.00000 −0.245737
\(415\) −1.50000 2.59808i −0.0736321 0.127535i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) −11.0000 + 19.0526i −0.538672 + 0.933008i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 6.00000 5.19615i 0.292770 0.253546i
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 7.00000 + 12.1244i 0.340755 + 0.590204i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) 10.0000 + 17.3205i 0.485071 + 0.840168i
\(426\) −4.00000 −0.193801
\(427\) −2.50000 12.9904i −0.120983 0.628649i
\(428\) −13.0000 −0.628379
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) −15.0000 + 25.9808i −0.723364 + 1.25290i
\(431\) −11.0000 + 19.0526i −0.529851 + 0.917729i 0.469542 + 0.882910i \(0.344419\pi\)
−0.999394 + 0.0348195i \(0.988914\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 10.0000 + 3.46410i 0.480015 + 0.166282i
\(435\) −18.0000 −0.863034
\(436\) 5.50000 + 9.52628i 0.263402 + 0.456226i
\(437\) −15.0000 + 25.9808i −0.717547 + 1.24283i
\(438\) 6.00000 10.3923i 0.286691 0.496564i
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) 3.00000 0.143019
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 30.0000 1.42695
\(443\) −1.00000 1.73205i −0.0475114 0.0822922i 0.841292 0.540581i \(-0.181796\pi\)
−0.888803 + 0.458289i \(0.848462\pi\)
\(444\) 1.00000 1.73205i 0.0474579 0.0821995i
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 18.0000 0.851371
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 2.00000 + 3.46410i 0.0942809 + 0.163299i
\(451\) 2.50000 4.33013i 0.117720 0.203898i
\(452\) −5.00000 + 8.66025i −0.235180 + 0.407344i
\(453\) −4.50000 7.79423i −0.211428 0.366205i
\(454\) −3.00000 −0.140797
\(455\) 9.00000 + 46.7654i 0.421927 + 2.19239i
\(456\) −6.00000 −0.280976
\(457\) 13.0000 + 22.5167i 0.608114 + 1.05328i 0.991551 + 0.129718i \(0.0414071\pi\)
−0.383437 + 0.923567i \(0.625260\pi\)
\(458\) 13.0000 22.5167i 0.607450 1.05213i
\(459\) 2.50000 4.33013i 0.116690 0.202113i
\(460\) −7.50000 12.9904i −0.349689 0.605680i
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 2.00000 1.73205i 0.0930484 0.0805823i
\(463\) 28.0000 1.30127 0.650635 0.759390i \(-0.274503\pi\)
0.650635 + 0.759390i \(0.274503\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) −14.5000 + 25.1147i −0.671700 + 1.16342i
\(467\) −8.00000 13.8564i −0.370196 0.641198i 0.619400 0.785076i \(-0.287376\pi\)
−0.989595 + 0.143878i \(0.954043\pi\)
\(468\) 6.00000 0.277350
\(469\) 10.0000 8.66025i 0.461757 0.399893i
\(470\) −27.0000 −1.24542
\(471\) 12.0000 + 20.7846i 0.552931 + 0.957704i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −5.00000 + 8.66025i −0.229900 + 0.398199i
\(474\) −0.500000 0.866025i −0.0229658 0.0397779i
\(475\) 24.0000 1.10120
\(476\) −2.50000 12.9904i −0.114587 0.595413i
\(477\) 2.00000 0.0915737
\(478\) 13.0000 + 22.5167i 0.594606 + 1.02989i
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 1.50000 2.59808i 0.0684653 0.118585i
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 26.0000 1.18427
\(483\) −12.5000 4.33013i −0.568770 0.197028i
\(484\) 1.00000 0.0454545
\(485\) −13.5000 23.3827i −0.613003 1.06175i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 2.00000 3.46410i 0.0906287 0.156973i −0.817147 0.576429i \(-0.804446\pi\)
0.907776 + 0.419456i \(0.137779\pi\)
\(488\) −2.50000 4.33013i −0.113170 0.196016i
\(489\) −1.00000 −0.0452216
\(490\) 19.5000 7.79423i 0.880920 0.352107i
\(491\) −3.00000 −0.135388 −0.0676941 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) −2.50000 4.33013i −0.112709 0.195217i
\(493\) −15.0000 + 25.9808i −0.675566 + 1.17011i
\(494\) 18.0000 31.1769i 0.809858 1.40272i
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 4.00000 0.179605
\(497\) −10.0000 3.46410i −0.448561 0.155386i
\(498\) −1.00000 −0.0448111
\(499\) −6.00000 10.3923i −0.268597 0.465223i 0.699903 0.714238i \(-0.253227\pi\)
−0.968500 + 0.249015i \(0.919893\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) −0.500000 2.59808i −0.0222718 0.115728i
\(505\) −24.0000 −1.06799
\(506\) −2.50000 4.33013i −0.111139 0.192498i
\(507\) −11.5000 + 19.9186i −0.510733 + 0.884615i
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i \(-0.180780\pi\)
−0.887336 + 0.461123i \(0.847447\pi\)
\(510\) 15.0000 0.664211
\(511\) 24.0000 20.7846i 1.06170 0.919457i
\(512\) −1.00000 −0.0441942
\(513\) −3.00000 5.19615i −0.132453 0.229416i
\(514\) −7.00000 + 12.1244i −0.308757 + 0.534782i
\(515\) 3.00000 5.19615i 0.132196 0.228970i
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) −9.00000 −0.395820
\(518\) 4.00000 3.46410i 0.175750 0.152204i
\(519\) −12.0000 −0.526742
\(520\) 9.00000 + 15.5885i 0.394676 + 0.683599i
\(521\) −1.00000 + 1.73205i −0.0438108 + 0.0758825i −0.887099 0.461579i \(-0.847283\pi\)
0.843288 + 0.537461i \(0.180617\pi\)
\(522\) −3.00000 + 5.19615i −0.131306 + 0.227429i
\(523\) −3.00000 5.19615i −0.131181 0.227212i 0.792951 0.609285i \(-0.208544\pi\)
−0.924132 + 0.382073i \(0.875210\pi\)
\(524\) −4.00000 −0.174741
\(525\) 2.00000 + 10.3923i 0.0872872 + 0.453557i
\(526\) −24.0000 −1.04645
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) 3.00000 + 5.19615i 0.130312 + 0.225706i
\(531\) −12.0000 −0.520756
\(532\) −15.0000 5.19615i −0.650332 0.225282i
\(533\) 30.0000 1.29944
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) 19.5000 33.7750i 0.843059 1.46022i
\(536\) 2.50000 4.33013i 0.107984 0.187033i
\(537\) 4.00000 + 6.92820i 0.172613 + 0.298974i
\(538\) 9.00000 0.388018
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 3.00000 0.129099
\(541\) 19.5000 + 33.7750i 0.838370 + 1.45210i 0.891256 + 0.453500i \(0.149825\pi\)
−0.0528859 + 0.998601i \(0.516842\pi\)
\(542\) −12.0000 + 20.7846i −0.515444 + 0.892775i
\(543\) 11.0000 19.0526i 0.472055 0.817624i
\(544\) −2.50000 4.33013i −0.107187 0.185653i
\(545\) −33.0000 −1.41356
\(546\) 15.0000 + 5.19615i 0.641941 + 0.222375i
\(547\) −42.0000 −1.79579 −0.897895 0.440209i \(-0.854904\pi\)
−0.897895 + 0.440209i \(0.854904\pi\)
\(548\) 1.00000 + 1.73205i 0.0427179 + 0.0739895i
\(549\) 2.50000 4.33013i 0.106697 0.184805i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 18.0000 + 31.1769i 0.766826 + 1.32818i
\(552\) −5.00000 −0.212814
\(553\) −0.500000 2.59808i −0.0212622 0.110481i
\(554\) −18.0000 −0.764747
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) −11.0000 + 19.0526i −0.466504 + 0.808008i
\(557\) 16.0000 27.7128i 0.677942 1.17423i −0.297658 0.954673i \(-0.596205\pi\)
0.975600 0.219557i \(-0.0704612\pi\)
\(558\) 2.00000 + 3.46410i 0.0846668 + 0.146647i
\(559\) −60.0000 −2.53773
\(560\) 6.00000 5.19615i 0.253546 0.219578i
\(561\) 5.00000 0.211100
\(562\) 5.50000 + 9.52628i 0.232003 + 0.401842i
\(563\) 8.00000 13.8564i 0.337160 0.583978i −0.646737 0.762713i \(-0.723867\pi\)
0.983897 + 0.178735i \(0.0572004\pi\)
\(564\) −4.50000 + 7.79423i −0.189484 + 0.328196i
\(565\) −15.0000 25.9808i −0.631055 1.09302i
\(566\) 6.00000 0.252199
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) −4.00000 −0.167836
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 9.00000 15.5885i 0.376969 0.652929i
\(571\) 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i \(-0.581382\pi\)
0.964321 0.264735i \(-0.0852845\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) −2.50000 12.9904i −0.104348 0.542208i
\(575\) 20.0000 0.834058
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 3.50000 6.06218i 0.145707 0.252372i −0.783930 0.620850i \(-0.786788\pi\)
0.929636 + 0.368478i \(0.120121\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −3.00000 5.19615i −0.124676 0.215945i
\(580\) −18.0000 −0.747409
\(581\) −2.50000 0.866025i −0.103717 0.0359288i
\(582\) −9.00000 −0.373062
\(583\) 1.00000 + 1.73205i 0.0414158 + 0.0717342i
\(584\) 6.00000 10.3923i 0.248282 0.430037i
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 4.00000 + 6.92820i 0.165238 + 0.286201i
\(587\) −24.0000 −0.990586 −0.495293 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) 1.00000 6.92820i 0.0412393 0.285714i
\(589\) 24.0000 0.988903
\(590\) −18.0000 31.1769i −0.741048 1.28353i
\(591\) 12.0000 20.7846i 0.493614 0.854965i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −7.00000 12.1244i −0.287456 0.497888i 0.685746 0.727841i \(-0.259476\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(594\) 1.00000 0.0410305
\(595\) 37.5000 + 12.9904i 1.53735 + 0.532554i
\(596\) 18.0000 0.737309
\(597\) −5.00000 8.66025i −0.204636 0.354441i
\(598\) 15.0000 25.9808i 0.613396 1.06243i
\(599\) 1.50000 2.59808i 0.0612883 0.106155i −0.833753 0.552137i \(-0.813812\pi\)
0.895042 + 0.445983i \(0.147146\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 5.00000 + 25.9808i 0.203785 + 1.05890i
\(603\) 5.00000 0.203616
\(604\) −4.50000 7.79423i −0.183102 0.317143i
\(605\) −1.50000 + 2.59808i −0.0609837 + 0.105627i
\(606\) −4.00000 + 6.92820i −0.162489 + 0.281439i
\(607\) −16.5000 28.5788i −0.669714 1.15998i −0.977984 0.208680i \(-0.933083\pi\)
0.308270 0.951299i \(-0.400250\pi\)
\(608\) −6.00000 −0.243332
\(609\) −12.0000 + 10.3923i −0.486265 + 0.421117i
\(610\) 15.0000 0.607332
\(611\) −27.0000 46.7654i −1.09230 1.89192i
\(612\) 2.50000 4.33013i 0.101057 0.175035i
\(613\) 20.5000 35.5070i 0.827987 1.43412i −0.0716275 0.997431i \(-0.522819\pi\)
0.899615 0.436684i \(-0.143847\pi\)
\(614\) 9.00000 + 15.5885i 0.363210 + 0.629099i
\(615\) 15.0000 0.604858
\(616\) 2.00000 1.73205i 0.0805823 0.0697863i
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −1.00000 1.73205i −0.0402259 0.0696733i
\(619\) 14.5000 25.1147i 0.582804 1.00945i −0.412341 0.911030i \(-0.635289\pi\)
0.995145 0.0984169i \(-0.0313779\pi\)
\(620\) −6.00000 + 10.3923i −0.240966 + 0.417365i
\(621\) −2.50000 4.33013i −0.100322 0.173762i
\(622\) 21.0000 0.842023
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) 6.00000 0.240192
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 12.0000 + 20.7846i 0.478852 + 0.829396i
\(629\) 10.0000 0.398726
\(630\) 7.50000 + 2.59808i 0.298807 + 0.103510i
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) −0.500000 0.866025i −0.0198889 0.0344486i
\(633\) −7.00000 + 12.1244i −0.278225 + 0.481900i
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) −7.50000 12.9904i −0.297628 0.515508i
\(636\) 2.00000 0.0793052
\(637\) 33.0000 + 25.9808i 1.30751 + 1.02940i
\(638\) −6.00000 −0.237542
\(639\) −2.00000 3.46410i −0.0791188 0.137038i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) 20.0000 34.6410i 0.789953 1.36824i −0.136043 0.990703i \(-0.543438\pi\)
0.925995 0.377535i \(-0.123228\pi\)
\(642\) −6.50000 11.2583i −0.256535 0.444331i
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) −12.5000 4.33013i −0.492569 0.170631i
\(645\) −30.0000 −1.18125
\(646\) −15.0000 25.9808i −0.590167 1.02220i
\(647\) −8.50000 + 14.7224i −0.334169 + 0.578799i −0.983325 0.181857i \(-0.941789\pi\)
0.649155 + 0.760656i \(0.275122\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) −24.0000 −0.941357
\(651\) 2.00000 + 10.3923i 0.0783862 + 0.407307i
\(652\) −1.00000 −0.0391630
\(653\) 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i \(0.0105021\pi\)
−0.471160 + 0.882048i \(0.656165\pi\)
\(654\) −5.50000 + 9.52628i −0.215067 + 0.372507i
\(655\) 6.00000 10.3923i 0.234439 0.406061i
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) 12.0000 0.468165
\(658\) −18.0000 + 15.5885i −0.701713 + 0.607701i
\(659\) 31.0000 1.20759 0.603794 0.797140i \(-0.293655\pi\)
0.603794 + 0.797140i \(0.293655\pi\)
\(660\) 1.50000 + 2.59808i 0.0583874 + 0.101130i
\(661\) −2.00000 + 3.46410i −0.0777910 + 0.134738i −0.902297 0.431116i \(-0.858120\pi\)
0.824506 + 0.565854i \(0.191453\pi\)
\(662\) 17.5000 30.3109i 0.680157 1.17807i
\(663\) 15.0000 + 25.9808i 0.582552 + 1.00901i
\(664\) −1.00000 −0.0388075
\(665\) 36.0000 31.1769i 1.39602 1.20899i
\(666\) 2.00000 0.0774984
\(667\) 15.0000 + 25.9808i 0.580802 + 1.00598i
\(668\) 12.0000 20.7846i 0.464294 0.804181i
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 7.50000 + 12.9904i 0.289750 + 0.501862i
\(671\) 5.00000 0.193023
\(672\) −0.500000 2.59808i −0.0192879 0.100223i
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) −1.00000 1.73205i −0.0385186 0.0667161i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) −10.0000 −0.384048
\(679\) −22.5000 7.79423i −0.863471 0.299115i
\(680\) 15.0000 0.575224
\(681\) −1.50000 2.59808i −0.0574801 0.0995585i
\(682\) −2.00000 + 3.46410i −0.0765840 + 0.132647i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −3.00000 5.19615i −0.114708 0.198680i
\(685\) −6.00000 −0.229248
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 26.0000 0.991962
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 7.50000 12.9904i 0.285520 0.494535i
\(691\) 13.5000 + 23.3827i 0.513564 + 0.889519i 0.999876 + 0.0157341i \(0.00500851\pi\)
−0.486312 + 0.873785i \(0.661658\pi\)
\(692\) −12.0000 −0.456172
\(693\) 2.50000 + 0.866025i 0.0949671 + 0.0328976i
\(694\) −7.00000 −0.265716
\(695\) −33.0000 57.1577i −1.25176 2.16811i
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) 12.5000 21.6506i 0.473471 0.820076i
\(698\) −9.50000 16.4545i −0.359580 0.622811i
\(699\) −29.0000 −1.09688
\(700\) 2.00000 + 10.3923i 0.0755929 + 0.392792i
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 3.00000 + 5.19615i 0.113228 + 0.196116i
\(703\) 6.00000 10.3923i 0.226294 0.391953i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −13.5000 23.3827i −0.508439 0.880643i
\(706\) −24.0000 −0.903252
\(707\) −16.0000 + 13.8564i −0.601742 + 0.521124i
\(708\) −12.0000 −0.450988
\(709\) −10.0000 17.3205i −0.375558 0.650485i 0.614852 0.788642i \(-0.289216\pi\)
−0.990410 + 0.138157i \(0.955882\pi\)
\(710\) 6.00000 10.3923i 0.225176 0.390016i
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 20.0000 0.749006
\(714\) 10.0000 8.66025i 0.374241 0.324102i
\(715\) −18.0000 −0.673162
\(716\) 4.00000 + 6.92820i 0.149487 + 0.258919i
\(717\) −13.0000 + 22.5167i −0.485494 + 0.840900i
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) −18.5000 32.0429i −0.689934 1.19500i −0.971859 0.235564i \(-0.924306\pi\)
0.281925 0.959436i \(-0.409027\pi\)
\(720\) 3.00000 0.111803
\(721\) −1.00000 5.19615i −0.0372419 0.193515i
\(722\) −17.0000 −0.632674
\(723\) 13.0000 + 22.5167i 0.483475 + 0.837404i
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) 22.0000 0.815935 0.407967 0.912996i \(-0.366238\pi\)
0.407967 + 0.912996i \(0.366238\pi\)
\(728\) 15.0000 + 5.19615i 0.555937 + 0.192582i
\(729\) 1.00000 0.0370370
\(730\) 18.0000 + 31.1769i 0.666210 + 1.15391i
\(731\) −25.0000 + 43.3013i −0.924658 + 1.60156i
\(732\) 2.50000 4.33013i 0.0924027 0.160046i
\(733\) 7.50000 + 12.9904i 0.277019 + 0.479811i 0.970642 0.240527i \(-0.0773202\pi\)
−0.693624 + 0.720338i \(0.743987\pi\)
\(734\) 14.0000 0.516749
\(735\) 16.5000 + 12.9904i 0.608612 + 0.479157i
\(736\) −5.00000 −0.184302
\(737\) 2.50000 + 4.33013i 0.0920887 + 0.159502i
\(738\) 2.50000 4.33013i 0.0920263 0.159394i
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) 3.00000 + 5.19615i 0.110282 + 0.191014i
\(741\) 36.0000 1.32249
\(742\) 5.00000 + 1.73205i 0.183556 + 0.0635856i
\(743\) 22.0000 0.807102 0.403551 0.914957i \(-0.367776\pi\)
0.403551 + 0.914957i \(0.367776\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) −27.0000 + 46.7654i −0.989203 + 1.71335i
\(746\) −3.50000 + 6.06218i −0.128144 + 0.221952i
\(747\) −0.500000 0.866025i −0.0182940 0.0316862i
\(748\) 5.00000 0.182818
\(749\) −6.50000 33.7750i −0.237505 1.23411i
\(750\) 3.00000 0.109545
\(751\) 1.00000 + 1.73205i 0.0364905 + 0.0632034i 0.883694 0.468065i \(-0.155049\pi\)
−0.847203 + 0.531269i \(0.821715\pi\)
\(752\) −4.50000 + 7.79423i −0.164098 + 0.284226i
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) −18.0000 31.1769i −0.655521 1.13540i
\(755\) 27.0000 0.982631
\(756\) 2.00000 1.73205i 0.0727393 0.0629941i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 6.50000 + 11.2583i 0.236091 + 0.408921i
\(759\) 2.50000 4.33013i 0.0907443 0.157174i
\(760\) 9.00000 15.5885i 0.326464 0.565453i
\(761\) −23.5000 40.7032i −0.851874 1.47549i −0.879515 0.475872i \(-0.842133\pi\)
0.0276404 0.999618i \(-0.491201\pi\)
\(762\) −5.00000 −0.181131
\(763\) −22.0000 + 19.0526i −0.796453 + 0.689749i
\(764\) 0 0
\(765\) 7.50000 + 12.9904i 0.271163 + 0.469668i
\(766\) 4.00000 6.92820i 0.144526 0.250326i
\(767\) 36.0000 62.3538i 1.29988 2.25147i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 1.50000 + 7.79423i 0.0540562 + 0.280885i
\(771\) −14.0000 −0.504198
\(772\) −3.00000 5.19615i −0.107972 0.187014i
\(773\) −5.50000 + 9.52628i −0.197821 + 0.342636i −0.947822 0.318801i \(-0.896720\pi\)
0.750000 + 0.661437i \(0.230053\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) −8.00000 13.8564i −0.287368 0.497737i