Properties

Label 1386.2.k.c.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
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: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.c.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.00000 - 1.73205i) q^{19} +3.00000 q^{20} +1.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.00000 + 1.73205i) q^{28} +6.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-1.50000 - 7.79423i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-1.50000 - 2.59808i) q^{40} +3.00000 q^{41} +2.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-4.50000 - 7.79423i) q^{47} +(5.50000 + 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +3.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-2.50000 - 4.33013i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-6.00000 + 5.19615i) q^{70} -12.0000 q^{71} +(8.00000 - 13.8564i) q^{73} +(-1.00000 + 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(-8.50000 - 14.7224i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-1.50000 - 2.59808i) q^{82} -9.00000 q^{83} -9.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(5.00000 + 1.73205i) q^{91} -3.00000 q^{92} +(-4.50000 + 7.79423i) q^{94} +(-3.00000 + 5.19615i) q^{95} +17.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 3q^{5} + 5q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 3q^{5} + 5q^{7} + 2q^{8} - 3q^{10} - q^{11} + 4q^{13} - q^{14} - q^{16} + 3q^{17} - 2q^{19} + 6q^{20} + 2q^{22} + 3q^{23} - 4q^{25} - 2q^{26} - 4q^{28} + 12q^{29} + 4q^{31} - q^{32} - 6q^{34} - 3q^{35} - 2q^{37} - 2q^{38} - 3q^{40} + 6q^{41} + 4q^{43} - q^{44} + 3q^{46} - 9q^{47} + 11q^{49} + 8q^{50} - 2q^{52} + 6q^{53} + 6q^{55} + 5q^{56} - 6q^{58} - 12q^{59} - 5q^{61} - 8q^{62} + 2q^{64} - 6q^{65} - 5q^{67} + 3q^{68} - 12q^{70} - 24q^{71} + 16q^{73} - 2q^{74} + 4q^{76} - 4q^{77} - 17q^{79} - 3q^{80} - 3q^{82} - 18q^{83} - 18q^{85} - 2q^{86} - q^{88} - 6q^{89} + 10q^{91} - 6q^{92} - 9q^{94} - 6q^{95} + 34q^{97} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(4\) −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 \(-0.400725\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −1.50000 7.79423i −0.253546 1.31747i
\(36\) 0 0
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 0 0
\(70\) −6.00000 + 5.19615i −0.717137 + 0.621059i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 8.00000 13.8564i 0.936329 1.62177i 0.164083 0.986447i \(-0.447534\pi\)
0.772246 0.635323i \(-0.219133\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 0 0
\(79\) −8.50000 14.7224i −0.956325 1.65640i −0.731307 0.682048i \(-0.761089\pi\)
−0.225018 0.974355i \(-0.572244\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) −9.00000 −0.976187
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) −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 \(0.936344\pi\)
\(90\) 0 0
\(91\) 5.00000 + 1.73205i 0.524142 + 0.181568i
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −4.50000 + 7.79423i −0.464140 + 0.803913i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 0 0
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) 0 0
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 6.00000 5.19615i 0.550019 0.476331i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.50000 + 4.33013i −0.226339 + 0.392031i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) −1.00000 5.19615i −0.0867110 0.450564i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 7.50000 + 2.59808i 0.633866 + 0.219578i
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 0 0
\(145\) −9.00000 15.5885i −0.747409 1.29455i
\(146\) −16.0000 −1.32417
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) 0 0
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) −12.0000 −0.963863
\(156\) 0 0
\(157\) −10.0000 + 17.3205i −0.798087 + 1.38233i 0.122774 + 0.992435i \(0.460821\pi\)
−0.920860 + 0.389892i \(0.872512\pi\)
\(158\) −8.50000 + 14.7224i −0.676224 + 1.17125i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) 1.50000 + 7.79423i 0.118217 + 0.614271i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 0 0
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 4.50000 + 7.79423i 0.345134 + 0.597790i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −1.00000 5.19615i −0.0741249 0.385164i
\(183\) 0 0
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 1.50000 + 2.59808i 0.109691 + 0.189990i
\(188\) 9.00000 0.656392
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −8.50000 14.7224i −0.610264 1.05701i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) 15.0000 + 5.19615i 1.05279 + 0.364698i
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 0 0
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 11.0000 0.745014
\(219\) 0 0
\(220\) −1.50000 + 2.59808i −0.101130 + 0.175162i
\(221\) 3.00000 5.19615i 0.201802 0.349531i
\(222\) 0 0
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) −10.5000 + 18.1865i −0.696909 + 1.20708i 0.272623 + 0.962121i \(0.412109\pi\)
−0.969533 + 0.244962i \(0.921225\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) −9.00000 −0.593442
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 13.5000 + 23.3827i 0.884414 + 1.53185i 0.846383 + 0.532574i \(0.178775\pi\)
0.0380310 + 0.999277i \(0.487891\pi\)
\(234\) 0 0
\(235\) −13.5000 + 23.3827i −0.880643 + 1.52532i
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 0 0
\(238\) −7.50000 2.59808i −0.486153 0.168408i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 5.00000 0.320092
\(245\) 3.00000 20.7846i 0.191663 1.32788i
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) −5.50000 9.52628i −0.345101 0.597732i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) −1.00000 5.19615i −0.0621370 0.322873i
\(260\) 6.00000 0.372104
\(261\) 0 0
\(262\) −6.00000 + 10.3923i −0.370681 + 0.642039i
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) −18.0000 −1.10573
\(266\) −4.00000 + 3.46410i −0.245256 + 0.212398i
\(267\) 0 0
\(268\) −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 \(0.0781974\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −7.00000 12.1244i −0.419832 0.727171i
\(279\) 0 0
\(280\) −1.50000 7.79423i −0.0896421 0.465794i
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 7.50000 + 2.59808i 0.442711 + 0.153360i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −9.00000 + 15.5885i −0.528498 + 0.915386i
\(291\) 0 0
\(292\) 8.00000 + 13.8564i 0.468165 + 0.810885i
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 36.0000 2.09600
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 5.00000 + 1.73205i 0.288195 + 0.0998337i
\(302\) −1.00000 −0.0575435
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) −7.50000 + 12.9904i −0.429449 + 0.743827i
\(306\) 0 0
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) 0 0
\(310\) 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 \(-0.0363399\pi\)
\(312\) 0 0
\(313\) −1.00000 1.73205i −0.0565233 0.0979013i 0.836379 0.548151i \(-0.184668\pi\)
−0.892903 + 0.450250i \(0.851335\pi\)
\(314\) 20.0000 1.12867
\(315\) 0 0
\(316\) 17.0000 0.956325
\(317\) −16.5000 28.5788i −0.926732 1.60515i −0.788751 0.614713i \(-0.789272\pi\)
−0.137981 0.990435i \(-0.544061\pi\)
\(318\) 0 0
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) 6.00000 5.19615i 0.334367 0.289570i
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 0.500000 0.866025i 0.0276924 0.0479647i
\(327\) 0 0
\(328\) 3.00000 0.165647
\(329\) −4.50000 23.3827i −0.248093 1.28913i
\(330\) 0 0
\(331\) −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i \(-0.264424\pi\)
−0.976658 + 0.214799i \(0.931090\pi\)
\(332\) 4.50000 7.79423i 0.246970 0.427764i
\(333\) 0 0
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) 15.0000 0.819538
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) 4.50000 7.79423i 0.244047 0.422701i
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) −16.5000 + 28.5788i −0.885766 + 1.53419i −0.0409337 + 0.999162i \(0.513033\pi\)
−0.844833 + 0.535031i \(0.820300\pi\)
\(348\) 0 0
\(349\) 11.0000 0.588817 0.294408 0.955680i \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(350\) 10.0000 + 3.46410i 0.534522 + 0.185164i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −6.00000 + 10.3923i −0.319348 + 0.553127i −0.980352 0.197256i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(354\) 0 0
\(355\) 18.0000 + 31.1769i 0.955341 + 1.65470i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i \(0.124121\pi\)
−0.133263 + 0.991081i \(0.542545\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) −4.00000 + 3.46410i −0.209657 + 0.181568i
\(365\) −48.0000 −2.51243
\(366\) 0 0
\(367\) 5.00000 8.66025i 0.260998 0.452062i −0.705509 0.708700i \(-0.749282\pi\)
0.966507 + 0.256639i \(0.0826151\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) 1.50000 2.59808i 0.0775632 0.134343i
\(375\) 0 0
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 0 0
\(382\) 12.0000 20.7846i 0.613973 1.06343i
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0 0
\(385\) 7.50000 + 2.59808i 0.382235 + 0.132410i
\(386\) 2.00000 0.101797
\(387\) 0 0
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) 10.5000 18.1865i 0.532371 0.922094i −0.466915 0.884302i \(-0.654634\pi\)
0.999286 0.0377914i \(-0.0120322\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) −25.5000 + 44.1673i −1.28304 + 2.22230i
\(396\) 0 0
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) 2.00000 0.100251
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) −3.00000 15.5885i −0.148888 0.773642i
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 0 0
\(412\) 14.0000 0.689730
\(413\) −24.0000 + 20.7846i −1.18096 + 1.02274i
\(414\) 0 0
\(415\) 13.5000 + 23.3827i 0.662689 + 1.14781i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) −1.00000 1.73205i −0.0489116 0.0847174i
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 11.0000 + 19.0526i 0.535472 + 0.927464i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 0 0
\(427\) −2.50000 12.9904i −0.120983 0.628649i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i \(-0.879492\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(432\) 0 0
\(433\) 35.0000 1.68199 0.840996 0.541041i \(-0.181970\pi\)
0.840996 + 0.541041i \(0.181970\pi\)
\(434\) −10.0000 3.46410i −0.480015 0.166282i
\(435\) 0 0
\(436\) −5.50000 9.52628i −0.263402 0.456226i
\(437\) 3.00000 5.19615i 0.143509 0.248566i
\(438\) 0 0
\(439\) 9.50000 + 16.4545i 0.453410 + 0.785330i 0.998595 0.0529862i \(-0.0168739\pi\)
−0.545185 + 0.838316i \(0.683541\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i \(-0.0260248\pi\)
−0.569057 + 0.822298i \(0.692691\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) −10.0000 17.3205i −0.473514 0.820150i
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −1.50000 + 2.59808i −0.0706322 + 0.122339i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 0 0
\(454\) 21.0000 0.985579
\(455\) −3.00000 15.5885i −0.140642 0.730798i
\(456\) 0 0
\(457\) −19.0000 32.9090i −0.888783 1.53942i −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) 0 0
\(460\) 4.50000 + 7.79423i 0.209814 + 0.363408i
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) 13.5000 23.3827i 0.625375 1.08318i
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0 0
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) 27.0000 1.24542
\(471\) 0 0
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 1.50000 + 7.79423i 0.0687524 + 0.357248i
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −25.5000 44.1673i −1.15790 2.00553i
\(486\) 0 0
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) −2.50000 4.33013i −0.113170 0.196016i
\(489\) 0 0
\(490\) −19.5000 + 7.79423i −0.880920 + 0.352107i
\(491\) 3.00000 0.135388 0.0676941 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −2.00000 + 3.46410i −0.0899843 + 0.155857i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −30.0000 10.3923i −1.34568 0.466159i
\(498\) 0 0
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 1.50000 + 2.59808i 0.0666831 + 0.115499i
\(507\) 0 0
\(508\) −5.50000 + 9.52628i −0.244023 + 0.422660i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) 32.0000 27.7128i 1.41560 1.22594i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) −21.0000 + 36.3731i −0.925371 + 1.60279i
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) −4.00000 + 3.46410i −0.175750 + 0.152204i
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 0 0
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 9.00000 + 15.5885i 0.390935 + 0.677119i
\(531\) 0 0
\(532\) 5.00000 + 1.73205i 0.216777 + 0.0750939i
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) −2.50000 + 4.33013i −0.107984 + 0.187033i
\(537\) 0 0
\(538\) −9.00000 −0.388018
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) 0 0
\(541\) −11.5000 19.9186i −0.494424 0.856367i 0.505556 0.862794i \(-0.331288\pi\)
−0.999979 + 0.00642713i \(0.997954\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 33.0000 1.41356
\(546\) 0 0
\(547\) −46.0000 −1.96682 −0.983409 0.181402i \(-0.941936\pi\)
−0.983409 + 0.181402i \(0.941936\pi\)
\(548\) 9.00000 + 15.5885i 0.384461 + 0.665906i
\(549\) 0 0
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) −6.00000 10.3923i −0.255609 0.442727i
\(552\) 0 0
\(553\) −8.50000 44.1673i −0.361457 1.87818i
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −18.0000 + 31.1769i −0.762684 + 1.32101i 0.178778 + 0.983890i \(0.442786\pi\)
−0.941462 + 0.337119i \(0.890548\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) −6.00000 + 5.19615i −0.253546 + 0.219578i
\(561\) 0 0
\(562\) 1.50000 + 2.59808i 0.0632737 + 0.109593i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −19.0000 + 32.9090i −0.795125 + 1.37720i 0.127634 + 0.991821i \(0.459262\pi\)
−0.922760 + 0.385376i \(0.874072\pi\)
\(572\) −1.00000 1.73205i −0.0418121 0.0724207i
\(573\) 0 0
\(574\) −1.50000 7.79423i −0.0626088 0.325325i
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −8.50000 + 14.7224i −0.353860 + 0.612903i −0.986922 0.161198i \(-0.948464\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 0 0
\(580\) 18.0000 0.747409
\(581\) −22.5000 7.79423i −0.933457 0.323359i
\(582\) 0 0
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) 8.00000 13.8564i 0.331042 0.573382i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) −36.0000 −1.48588 −0.742940 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) −18.0000 31.1769i −0.741048 1.28353i
\(591\) 0 0
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 0 0
\(595\) −22.5000 7.79423i −0.922410 0.319532i
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) 13.5000 23.3827i 0.551595 0.955391i −0.446565 0.894751i \(-0.647353\pi\)
0.998160 0.0606393i \(-0.0193139\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) −1.00000 5.19615i −0.0407570 0.211779i
\(603\) 0 0
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) −1.50000 + 2.59808i −0.0609837 + 0.105627i
\(606\) 0 0
\(607\) 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i \(-0.160206\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 15.0000 0.607332
\(611\) −9.00000 15.5885i −0.364101 0.630641i
\(612\) 0 0
\(613\) 15.5000 26.8468i 0.626039 1.08433i −0.362300 0.932062i \(-0.618008\pi\)
0.988339 0.152270i \(-0.0486583\pi\)
\(614\) 11.0000 + 19.0526i 0.443924 + 0.768899i
\(615\) 0 0
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i \(-0.904286\pi\)
0.734068 + 0.679076i \(0.237620\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 0 0
\(622\) −21.0000 −0.842023
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −1.00000 + 1.73205i −0.0399680 + 0.0692267i
\(627\) 0 0
\(628\) −10.0000 17.3205i −0.399043 0.691164i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.50000 14.7224i −0.338112 0.585627i
\(633\) 0 0
\(634\) −16.5000 + 28.5788i −0.655299 + 1.13501i
\(635\) −16.5000 28.5788i −0.654783 1.13412i
\(636\) 0 0
\(637\) 11.0000 + 8.66025i 0.435836 + 0.343132i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) −7.50000 2.59808i −0.295541 0.102379i
\(645\) 0 0
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) 19.5000 33.7750i 0.766624 1.32783i −0.172760 0.984964i \(-0.555268\pi\)
0.939384 0.342868i \(-0.111398\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 8.00000 0.313786
\(651\) 0 0
\(652\) −1.00000 −0.0391630
\(653\) −10.5000 18.1865i −0.410897 0.711694i 0.584091 0.811688i \(-0.301451\pi\)
−0.994988 + 0.0999939i \(0.968118\pi\)
\(654\) 0 0
\(655\) −18.0000 + 31.1769i −0.703318 + 1.21818i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) 0 0
\(658\) −18.0000 + 15.5885i −0.701713 + 0.607701i
\(659\) 33.0000 1.28550 0.642749 0.766077i \(-0.277794\pi\)
0.642749 + 0.766077i \(0.277794\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) −5.50000 + 9.52628i −0.213764 + 0.370249i
\(663\) 0 0
\(664\) −9.00000 −0.349268
\(665\) −12.0000 + 10.3923i −0.465340 + 0.402996i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 0 0
\(670\) −7.50000 12.9904i −0.289750 0.501862i
\(671\) 5.00000 0.193023
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 11.0000 + 19.0526i 0.423704 + 0.733877i
\(675\) 0 0
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −15.0000 25.9808i −0.576497 0.998522i −0.995877 0.0907112i \(-0.971086\pi\)
0.419380 0.907811i \(-0.362247\pi\)
\(678\) 0 0
\(679\) 42.5000 + 14.7224i 1.63100 + 0.564995i
\(680\) −9.00000 −0.345134
\(681\) 0 0
\(682\) 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 \(0.0929302\pi\)
\(684\) 0 0
\(685\) −54.0000 −2.06323
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 9.50000 + 16.4545i 0.361397 + 0.625958i 0.988191 0.153227i \(-0.0489666\pi\)
−0.626794 + 0.779185i \(0.715633\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) −21.0000 36.3731i −0.796575 1.37971i
\(696\) 0 0
\(697\) 4.50000 7.79423i 0.170450 0.295227i
\(698\) −5.50000 9.52628i −0.208178 0.360575i
\(699\) 0 0
\(700\) −2.00000 10.3923i −0.0755929 0.392792i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 12.0000 0.451626
\(707\) 24.0000 20.7846i 0.902613 0.781686i
\(708\) 0 0
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 18.0000 31.1769i 0.675528 1.17005i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) −10.5000 18.1865i −0.391584 0.678243i 0.601075 0.799193i \(-0.294739\pi\)
−0.992659 + 0.120950i \(0.961406\pi\)
\(720\) 0 0
\(721\) −7.00000 36.3731i −0.260694 1.35460i
\(722\) −15.0000 −0.558242
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) −12.0000 + 20.7846i −0.445669 + 0.771921i
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 5.00000 + 1.73205i 0.185312 + 0.0641941i
\(729\) 0 0
\(730\) 24.0000 + 41.5692i 0.888280 + 1.53855i
\(731\) 3.00000 5.19615i 0.110959 0.192187i
\(732\) 0 0
\(733\) 24.5000 + 42.4352i 0.904928 + 1.56738i 0.821014 + 0.570909i \(0.193409\pi\)
0.0839145 + 0.996473i \(0.473258\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −2.50000 4.33013i −0.0920887 0.159502i
\(738\) 0 0
\(739\) −19.0000 + 32.9090i −0.698926 + 1.21058i 0.269913 + 0.962885i \(0.413005\pi\)
−0.968839 + 0.247691i \(0.920328\pi\)
\(740\) −3.00000 5.19615i −0.110282 0.191014i
\(741\) 0 0
\(742\) −15.0000 5.19615i −0.550667 0.190757i
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 0.500000 0.866025i 0.0183063 0.0317074i
\(747\) 0 0
\(748\) −3.00000 −0.109691
\(749\) 1.50000 + 7.79423i 0.0548088 + 0.284795i
\(750\) 0 0
\(751\) −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i \(-0.178285\pi\)
−0.883694 + 0.468065i \(0.844951\pi\)
\(752\) −4.50000 + 7.79423i −0.164098 + 0.284226i
\(753\) 0 0
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) −3.00000 −0.109181
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) −14.5000 25.1147i −0.526664 0.912208i
\(759\) 0 0
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) 7.50000 + 12.9904i 0.271875 + 0.470901i 0.969342 0.245716i \(-0.0790230\pi\)
−0.697467 + 0.716617i \(0.745690\pi\)
\(762\) 0 0
\(763\) −22.0000 + 19.0526i −0.796453 + 0.689749i
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0 0
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) −1.50000 7.79423i −0.0540562 0.280885i
\(771\) 0 0
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) −13.5000 + 23.3827i −0.485561 + 0.841017i −0.999862 0.0165929i \(-0.994718\pi\)
0.514301 + 0.857610i \(0.328051\pi\)
\(774\) 0 0
\(775\) 8.00000 + 13.8564i 0.287368 + 0.497737i
\(776\) 17.0000 0.610264
\(777\) 0 0
\(778\) −21.0000 −0.752886
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 0 0
\(781\) 6.00000 10.3923i 0.214697 0.371866i
\(782\) −4.50000 7.79423i −0.160920 0.278721i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 60.0000 2.14149
\(786\) 0 0
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) 6.00000 10.3923i 0.213741 0.370211i
\(789\) 0 0