Properties

Label 260.2.bg.a.43.1
Level $260$
Weight $2$
Character 260.43
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM discriminant -4
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bg (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label 43.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.43
Dual form 260.2.bg.a.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-3.00000 - 1.00000i) q^{10} +(-3.59808 + 0.232051i) q^{13} +(2.00000 - 3.46410i) q^{16} +(6.96410 + 1.86603i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(4.46410 + 0.267949i) q^{20} +(1.96410 + 4.59808i) q^{25} +(4.83013 - 1.63397i) q^{26} +(5.76795 + 3.33013i) q^{29} +(-1.46410 + 5.46410i) q^{32} -10.1962 q^{34} +(3.00000 - 5.19615i) q^{36} +(-1.13397 + 0.303848i) q^{37} +(-6.19615 + 1.26795i) q^{40} +(1.66987 + 0.964102i) q^{41} +(6.69615 + 0.401924i) q^{45} +(-6.06218 - 3.50000i) q^{49} +(-4.36603 - 5.56218i) q^{50} +(-6.00000 + 4.00000i) q^{52} +(-10.2942 - 10.2942i) q^{53} +(-9.09808 - 2.43782i) q^{58} +(-7.33013 - 12.6962i) q^{61} -8.00000i q^{64} +(-7.00000 - 4.00000i) q^{65} +(13.9282 - 3.73205i) q^{68} +(-2.19615 + 8.19615i) q^{72} +(-9.83013 + 9.83013i) q^{73} +(1.43782 - 0.830127i) q^{74} +(8.00000 - 4.00000i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-2.63397 - 0.705771i) q^{82} +(10.6962 + 12.0622i) q^{85} +(-5.00000 + 8.66025i) q^{89} +(-9.29423 + 1.90192i) q^{90} +(4.75833 - 17.7583i) q^{97} +(9.56218 + 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.965926 + 0.258819i
\(3\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 1.86603 + 1.23205i 0.834512 + 0.550990i
\(6\) 0 0
\(7\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) −3.00000 1.00000i −0.948683 0.316228i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) −3.59808 + 0.232051i −0.997927 + 0.0643593i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 6.96410 + 1.86603i 1.68904 + 0.452578i 0.970143 0.242536i \(-0.0779791\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −3.00000 + 3.00000i −0.707107 + 0.707107i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 4.46410 + 0.267949i 0.998203 + 0.0599153i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(24\) 0 0
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) 4.83013 1.63397i 0.947266 0.320449i
\(27\) 0 0
\(28\) 0 0
\(29\) 5.76795 + 3.33013i 1.07108 + 0.618389i 0.928477 0.371391i \(-0.121119\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.46410 + 5.46410i −0.258819 + 0.965926i
\(33\) 0 0
\(34\) −10.1962 −1.74863
\(35\) 0 0
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) −1.13397 + 0.303848i −0.186424 + 0.0499522i −0.350823 0.936442i \(-0.614098\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.19615 + 1.26795i −0.979698 + 0.200480i
\(41\) 1.66987 + 0.964102i 0.260790 + 0.150567i 0.624695 0.780869i \(-0.285223\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 0 0
\(43\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(44\) 0 0
\(45\) 6.69615 + 0.401924i 0.998203 + 0.0599153i
\(46\) 0 0
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) 0 0
\(49\) −6.06218 3.50000i −0.866025 0.500000i
\(50\) −4.36603 5.56218i −0.617449 0.786611i
\(51\) 0 0
\(52\) −6.00000 + 4.00000i −0.832050 + 0.554700i
\(53\) −10.2942 10.2942i −1.41402 1.41402i −0.718677 0.695344i \(-0.755252\pi\)
−0.695344 0.718677i \(-0.744748\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −9.09808 2.43782i −1.19464 0.320102i
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) −7.33013 12.6962i −0.938527 1.62558i −0.768221 0.640184i \(-0.778858\pi\)
−0.170305 0.985391i \(-0.554475\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −7.00000 4.00000i −0.868243 0.496139i
\(66\) 0 0
\(67\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) 13.9282 3.73205i 1.68904 0.452578i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) −2.19615 + 8.19615i −0.258819 + 0.965926i
\(73\) −9.83013 + 9.83013i −1.15053 + 1.15053i −0.164083 + 0.986447i \(0.552466\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 1.43782 0.830127i 0.167143 0.0965003i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 8.00000 4.00000i 0.894427 0.447214i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −2.63397 0.705771i −0.290874 0.0779394i
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) 10.6962 + 12.0622i 1.16016 + 1.30833i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) −9.29423 + 1.90192i −0.979698 + 0.200480i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 4.75833 17.7583i 0.483135 1.80309i −0.105180 0.994453i \(-0.533542\pi\)
0.588315 0.808632i \(-0.299792\pi\)
\(98\) 9.56218 + 2.56218i 0.965926 + 0.258819i
\(99\) 0 0
\(100\) 8.00000 + 6.00000i 0.800000 + 0.600000i
\(101\) −8.16025 + 14.1340i −0.811976 + 1.40638i 0.0995037 + 0.995037i \(0.468274\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) 6.73205 7.66025i 0.660132 0.751150i
\(105\) 0 0
\(106\) 17.8301 + 10.2942i 1.73182 + 0.999864i
\(107\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(108\) 0 0
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.06218 11.4282i 0.288065 1.07507i −0.658505 0.752577i \(-0.728811\pi\)
0.946570 0.322498i \(-0.104523\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 13.3205 1.23678
\(117\) −9.00000 + 6.00000i −0.832050 + 0.554700i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 14.6603 + 14.6603i 1.32728 + 1.32728i
\(123\) 0 0
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(128\) 2.92820 + 10.9282i 0.258819 + 0.965926i
\(129\) 0 0
\(130\) 11.0263 + 2.90192i 0.967069 + 0.254516i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −17.6603 + 10.1962i −1.51435 + 0.874313i
\(137\) 6.03590 22.5263i 0.515682 1.92455i 0.173939 0.984757i \(-0.444351\pi\)
0.341743 0.939793i \(-0.388983\pi\)
\(138\) 0 0
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) 6.66025 + 13.3205i 0.553104 + 1.10621i
\(146\) 9.83013 17.0263i 0.813547 1.40910i
\(147\) 0 0
\(148\) −1.66025 + 1.66025i −0.136472 + 0.136472i
\(149\) 1.06218 + 1.83975i 0.0870170 + 0.150718i 0.906249 0.422744i \(-0.138933\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 20.8923 5.59808i 1.68904 0.452578i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.2224 12.2224i 0.975456 0.975456i −0.0242497 0.999706i \(-0.507720\pi\)
0.999706 + 0.0242497i \(0.00771967\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −9.46410 + 8.39230i −0.748203 + 0.663470i
\(161\) 0 0
\(162\) −3.29423 + 12.2942i −0.258819 + 0.965926i
\(163\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(164\) 3.85641 0.301135
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(168\) 0 0
\(169\) 12.8923 1.66987i 0.991716 0.128452i
\(170\) −19.0263 12.5622i −1.45925 0.963475i
\(171\) 0 0
\(172\) 0 0
\(173\) −5.49038 + 20.4904i −0.417426 + 1.55785i 0.362500 + 0.931984i \(0.381923\pi\)
−0.779926 + 0.625871i \(0.784744\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 3.66025 13.6603i 0.274348 1.02388i
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 12.0000 6.00000i 0.894427 0.447214i
\(181\) −26.3205 −1.95639 −0.978194 0.207693i \(-0.933404\pi\)
−0.978194 + 0.207693i \(0.933404\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.49038 0.830127i −0.183096 0.0610322i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 0 0
\(193\) −5.06218 18.8923i −0.364384 1.35990i −0.868255 0.496119i \(-0.834758\pi\)
0.503871 0.863779i \(-0.331909\pi\)
\(194\) 26.0000i 1.86669i
\(195\) 0 0
\(196\) −14.0000 −1.00000
\(197\) −17.7583 + 4.75833i −1.26523 + 0.339017i −0.828201 0.560431i \(-0.810635\pi\)
−0.437028 + 0.899448i \(0.643969\pi\)
\(198\) 0 0
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) −13.1244 5.26795i −0.928032 0.372500i
\(201\) 0 0
\(202\) 5.97372 22.2942i 0.420310 1.56862i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.92820 + 3.85641i 0.134672 + 0.269343i
\(206\) 0 0
\(207\) 0 0
\(208\) −6.39230 + 12.9282i −0.443227 + 0.896410i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) −28.1244 7.53590i −1.93159 0.517568i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 27.3205 7.32051i 1.85038 0.495807i
\(219\) 0 0
\(220\) 0 0
\(221\) −25.4904 5.09808i −1.71467 0.342934i
\(222\) 0 0
\(223\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(224\) 0 0
\(225\) 12.0000 + 9.00000i 0.800000 + 0.600000i
\(226\) 16.7321i 1.11300i
\(227\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(228\) 0 0
\(229\) 30.0000 1.98246 0.991228 0.132164i \(-0.0421925\pi\)
0.991228 + 0.132164i \(0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −18.1962 + 4.87564i −1.19464 + 0.320102i
\(233\) −5.00000 5.00000i −0.327561 0.327561i 0.524097 0.851658i \(-0.324403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 10.0981 11.4904i 0.660132 0.751150i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 6.99038 4.03590i 0.450290 0.259975i −0.257663 0.966235i \(-0.582952\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) −11.0000 11.0000i −0.707107 0.707107i
\(243\) 0 0
\(244\) −25.3923 14.6603i −1.62558 0.938527i
\(245\) −7.00000 14.0000i −0.447214 0.894427i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −1.29423 15.7583i −0.0818542 0.996644i
\(251\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 2.64359 + 9.86603i 0.164903 + 0.615426i 0.998053 + 0.0623783i \(0.0198685\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −16.1244 + 0.0717968i −0.999990 + 0.00445265i
\(261\) 19.9808 1.23678
\(262\) 0 0
\(263\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(264\) 0 0
\(265\) −6.52628 31.8923i −0.400906 1.95913i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −22.5167 + 13.0000i −1.37287 + 0.792624i −0.991288 0.131713i \(-0.957952\pi\)
−0.381577 + 0.924337i \(0.624619\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 20.3923 20.3923i 1.23647 1.23647i
\(273\) 0 0
\(274\) 32.9808i 1.99244i
\(275\) 0 0
\(276\) 0 0
\(277\) 23.7942 + 6.37564i 1.42966 + 0.383075i 0.888899 0.458103i \(-0.151471\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 32.7128i 1.95148i 0.218926 + 0.975741i \(0.429745\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 4.39230 + 16.3923i 0.258819 + 0.965926i
\(289\) 30.2942 + 17.4904i 1.78201 + 1.02885i
\(290\) −13.9737 15.7583i −0.820565 0.925361i
\(291\) 0 0
\(292\) −7.19615 + 26.8564i −0.421123 + 1.57165i
\(293\) 4.76795 + 1.27757i 0.278547 + 0.0746363i 0.395388 0.918514i \(-0.370610\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.66025 2.87564i 0.0965003 0.167143i
\(297\) 0 0
\(298\) −2.12436 2.12436i −0.123061 0.123061i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.96410 32.7224i 0.112464 1.87368i
\(306\) −26.4904 + 15.2942i −1.51435 + 0.874313i
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 25.0000 + 25.0000i 1.41308 + 1.41308i 0.734803 + 0.678280i \(0.237274\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) −12.2224 + 21.1699i −0.689752 + 1.19469i
\(315\) 0 0
\(316\) 0 0
\(317\) 23.1506 + 23.1506i 1.30027 + 1.30027i 0.928208 + 0.372061i \(0.121349\pi\)
0.372061 + 0.928208i \(0.378651\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 9.85641 14.9282i 0.550990 0.834512i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) −8.13397 16.0885i −0.451192 0.892427i
\(326\) 0 0
\(327\) 0 0
\(328\) −5.26795 + 1.41154i −0.290874 + 0.0779394i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) −2.49038 + 2.49038i −0.136472 + 0.136472i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6.43782 6.43782i 0.350691 0.350691i −0.509676 0.860366i \(-0.670235\pi\)
0.860366 + 0.509676i \(0.170235\pi\)
\(338\) −17.0000 + 7.00000i −0.924678 + 0.380750i
\(339\) 0 0
\(340\) 30.5885 + 10.1962i 1.65889 + 0.552964i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 30.0000i 1.61281i
\(347\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.27757 23.4282i −0.334121 1.24696i −0.904819 0.425797i \(-0.859994\pi\)
0.570697 0.821160i \(-0.306673\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.0000i 1.06000i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −14.1962 + 12.5885i −0.748203 + 0.663470i
\(361\) −9.50000 + 16.4545i −0.500000 + 0.866025i
\(362\) 35.9545 9.63397i 1.88973 0.506350i
\(363\) 0 0
\(364\) 0 0
\(365\) −30.4545 + 6.23205i −1.59406 + 0.326200i
\(366\) 0 0
\(367\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(368\) 0 0
\(369\) 5.78461 0.301135
\(370\) 3.70577 + 0.222432i 0.192654 + 0.0115637i
\(371\) 0 0
\(372\) 0 0
\(373\) 1.08846 4.06218i 0.0563582 0.210332i −0.932005 0.362446i \(-0.881942\pi\)
0.988363 + 0.152115i \(0.0486083\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −21.5263 10.6436i −1.10866 0.548173i
\(378\) 0 0
\(379\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.8301 + 23.9545i 0.703935 + 1.21925i
\(387\) 0 0
\(388\) −9.51666 35.5167i −0.483135 1.80309i
\(389\) 0.320508i 0.0162504i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.999967 + 0.00812520i \(0.997414\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 19.1244 5.12436i 0.965926 0.258819i
\(393\) 0 0
\(394\) 22.5167 13.0000i 1.13437 0.654931i
\(395\) 0 0
\(396\) 0 0
\(397\) −4.75833 + 17.7583i −0.238814 + 0.891265i 0.737579 + 0.675261i \(0.235969\pi\)
−0.976392 + 0.216004i \(0.930698\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 19.8564 + 2.39230i 0.992820 + 0.119615i
\(401\) 15.8205 + 9.13397i 0.790038 + 0.456129i 0.839976 0.542623i \(-0.182569\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 32.6410i 1.62395i
\(405\) 18.0000 9.00000i 0.894427 0.447214i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −7.40192 12.8205i −0.366002 0.633933i 0.622935 0.782274i \(-0.285940\pi\)
−0.988936 + 0.148340i \(0.952607\pi\)
\(410\) −4.04552 4.56218i −0.199794 0.225310i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 20.0000i 0.196116 0.980581i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) 39.2487i 1.91287i −0.291953 0.956433i \(-0.594305\pi\)
0.291953 0.956433i \(-0.405695\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 41.1769 1.99973
\(425\) 5.09808 + 35.6865i 0.247293 + 1.73105i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0 0
\(433\) −10.1077 + 37.7224i −0.485745 + 1.81282i 0.0909384 + 0.995857i \(0.471013\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −34.6410 + 20.0000i −1.65900 + 0.957826i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 36.6865 2.36603i 1.74500 0.112540i
\(443\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) −20.0000 + 10.0000i −0.948091 + 0.474045i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.0000 34.6410i −0.943858 1.63481i −0.758021 0.652230i \(-0.773834\pi\)
−0.185837 0.982581i \(-0.559500\pi\)
\(450\) −19.6865 7.90192i −0.928032 0.372500i
\(451\) 0 0
\(452\) −6.12436 22.8564i −0.288065 1.07507i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −41.1865 + 11.0359i −1.92662 + 0.516238i −0.944286 + 0.329125i \(0.893246\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) −40.9808 + 10.9808i −1.91491 + 0.513097i
\(459\) 0 0
\(460\) 0 0
\(461\) 37.1603 21.4545i 1.73073 0.999235i 0.845807 0.533488i \(-0.179119\pi\)
0.884918 0.465746i \(-0.154214\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 23.0718 13.3205i 1.07108 0.618389i
\(465\) 0 0
\(466\) 8.66025 + 5.00000i 0.401179 + 0.231621i
\(467\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) −9.58846 + 19.3923i −0.443227 + 0.896410i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −42.1865 11.3038i −1.93159 0.517568i
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 4.00962 1.35641i 0.182823 0.0618468i
\(482\) −8.07180 + 8.07180i −0.367660 + 0.367660i
\(483\) 0 0
\(484\) 19.0526 + 11.0000i 0.866025 + 0.500000i
\(485\) 30.7583 27.2750i 1.39666 1.23849i
\(486\) 0 0
\(487\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(488\) 40.0526 + 10.7321i 1.81309 + 0.485817i
\(489\) 0 0
\(490\) 14.6865 + 16.5622i 0.663470 + 0.748203i
\(491\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 33.9545 + 33.9545i 1.52923 + 1.52923i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 7.53590 + 21.0526i 0.337016 + 0.941499i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(504\) 0 0
\(505\) −32.6410 + 16.3205i −1.45251 + 0.726253i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −21.5526 + 37.3301i −0.955300 + 1.65463i −0.221621 + 0.975133i \(0.571135\pi\)
−0.733679 + 0.679496i \(0.762199\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) −7.22243 12.5096i −0.318568 0.551776i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 22.0000 6.00000i 0.964764 0.263117i
\(521\) 45.6410 1.99957 0.999785 0.0207541i \(-0.00660670\pi\)
0.999785 + 0.0207541i \(0.00660670\pi\)
\(522\) −27.2942 + 7.31347i −1.19464 + 0.320102i
\(523\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 19.9186 11.5000i 0.866025 0.500000i
\(530\) 20.5885 + 41.1769i 0.894305 + 1.78861i
\(531\) 0 0
\(532\) 0 0
\(533\) −6.23205 3.08142i −0.269940 0.133471i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 26.0000 26.0000i 1.12094 1.12094i
\(539\) 0 0
\(540\) 0 0
\(541\) 26.3731i 1.13387i −0.823764 0.566933i \(-0.808130\pi\)
0.823764 0.566933i \(-0.191870\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −20.3923 + 35.3205i −0.874313 + 1.51435i
\(545\) −37.3205 24.6410i −1.59863 1.05551i
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) −12.0718 45.0526i −0.515682 1.92455i
\(549\) −38.0885 21.9904i −1.62558 0.938527i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −34.8372 −1.48009
\(555\) 0 0
\(556\) 0 0
\(557\) −16.6244 + 4.45448i −0.704397 + 0.188742i −0.593199 0.805056i \(-0.702135\pi\)
−0.111198 + 0.993798i \(0.535469\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −11.9737 44.6865i −0.505081 1.88499i
\(563\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(564\) 0 0
\(565\) 19.7942 17.5526i 0.832749 0.738442i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.5167 13.0000i −0.943948 0.544988i −0.0527519 0.998608i \(-0.516799\pi\)
−0.891196 + 0.453619i \(0.850133\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) −10.1506 10.1506i −0.422576 0.422576i 0.463513 0.886090i \(-0.346589\pi\)
−0.886090 + 0.463513i \(0.846589\pi\)
\(578\) −47.7846 12.8038i −1.98758 0.532570i
\(579\) 0 0
\(580\) 24.8564 + 16.4115i 1.03211 + 0.681452i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 39.3205i 1.62709i
\(585\) −24.1865 + 0.107695i −0.999990 + 0.00445265i
\(586\) −6.98076 −0.288373
\(587\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.21539 + 4.53590i −0.0499522 + 0.186424i
\(593\) 28.4904 28.4904i 1.16996 1.16996i 0.187741 0.982219i \(-0.439883\pi\)
0.982219 0.187741i \(-0.0601166\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.67949 + 2.12436i 0.150718 + 0.0870170i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −16.3301 + 28.2846i −0.666120 + 1.15375i 0.312861 + 0.949799i \(0.398713\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.47372 + 24.5526i −0.0599153 + 0.998203i
\(606\) 0 0
\(607\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 9.29423 + 45.4186i 0.376312 + 1.83894i
\(611\) 0 0
\(612\) 30.5885 30.5885i 1.23647 1.23647i
\(613\) −10.9115 40.7224i −0.440713 1.64476i −0.727013 0.686624i \(-0.759092\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.6436 + 43.4545i −0.468753 + 1.74941i 0.175382 + 0.984500i \(0.443884\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) −43.3013 25.0000i −1.73067 0.999201i
\(627\) 0 0
\(628\) 8.94744 33.3923i 0.357042 1.33250i
\(629\) −8.46410 −0.337486
\(630\) 0 0
\(631\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −40.0981 23.1506i −1.59250 0.919429i
\(635\) 0 0
\(636\) 0 0
\(637\) 22.6244 + 11.1865i 0.896410 + 0.443227i
\(638\) 0 0
\(639\) 0 0
\(640\) −8.00000 + 24.0000i −0.316228 + 0.948683i
\(641\) −23.6506 40.9641i −0.934144 1.61798i −0.776153 0.630544i \(-0.782832\pi\)
−0.157991 0.987441i \(-0.550502\pi\)
\(642\) 0 0
\(643\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(648\) 6.58846 + 24.5885i 0.258819 + 0.965926i
\(649\) 0 0
\(650\) 17.0000 + 19.0000i 0.666795 + 0.745241i
\(651\) 0 0
\(652\) 0 0
\(653\) −47.8109 + 12.8109i −1.87098 + 0.501329i −0.871036 + 0.491220i \(0.836551\pi\)
−0.999949 + 0.0101092i \(0.996782\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.67949 3.85641i 0.260790 0.150567i
\(657\) −10.7942 + 40.2846i −0.421123 + 1.57165i
\(658\) 0 0
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 30.6506 + 17.6962i 1.19217 + 0.688301i 0.958799 0.284087i \(-0.0916904\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 2.49038 4.31347i 0.0965003 0.167143i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 36.9186 9.89230i 1.42311 0.381320i 0.536522 0.843886i \(-0.319738\pi\)
0.886585 + 0.462566i \(0.153071\pi\)
\(674\) −6.43782 + 11.1506i −0.247976 + 0.429506i
\(675\) 0 0
\(676\) 20.6603 15.7846i 0.794625 0.607100i
\(677\) 25.0000 25.0000i 0.960828 0.960828i −0.0384331 0.999261i \(-0.512237\pi\)
0.999261 + 0.0384331i \(0.0122367\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −45.5167 2.73205i −1.74548 0.104769i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(684\) 0 0
\(685\) 39.0167 34.5981i 1.49075 1.32192i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 39.4282 + 34.6506i 1.50209 + 1.32008i
\(690\) 0 0
\(691\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 10.9808 + 40.9808i 0.417426 + 1.55785i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.83013 + 9.83013i 0.372343 + 0.372343i
\(698\) −3.66025 + 13.6603i −0.138543 + 0.517048i
\(699\) 0 0
\(700\) 0 0
\(701\) 52.0000 1.96401 0.982006 0.188847i \(-0.0604752\pi\)
0.982006 + 0.188847i \(0.0604752\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 17.1506 + 29.7058i 0.645473 + 1.11799i
\(707\) 0 0
\(708\) 0 0
\(709\) −26.5526 45.9904i −0.997202 1.72721i −0.563337 0.826227i \(-0.690483\pi\)
−0.433865 0.900978i \(-0.642851\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7.32051 27.3205i −0.274348 1.02388i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 14.7846 22.3923i 0.550990 0.834512i
\(721\) 0 0
\(722\) 6.95448 25.9545i 0.258819 0.965926i
\(723\) 0 0
\(724\) −45.5885 + 26.3205i −1.69428 + 0.978194i
\(725\) −3.98334 + 33.0622i −0.147938 + 1.22790i
\(726\) 0 0
\(727\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 39.3205 19.6603i 1.45532 0.727659i
\(731\) 0 0
\(732\) 0 0
\(733\) −36.1506 + 36.1506i −1.33525 + 1.33525i −0.434659 + 0.900595i \(0.643131\pi\)
−0.900595 + 0.434659i \(0.856869\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −7.90192 + 2.11731i −0.290874 + 0.0779394i
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) −5.14359 + 1.05256i −0.189082 + 0.0386928i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(744\) 0 0
\(745\) −0.284610 + 4.74167i −0.0104273 + 0.173721i
\(746\) 5.94744i 0.217751i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 33.3013 + 6.66025i 1.21276 + 0.242552i
\(755\) 0 0
\(756\) 0 0
\(757\) 12.8109 + 47.8109i 0.465620 + 1.73772i 0.654827 + 0.755779i \(0.272742\pi\)
−0.189207 + 0.981937i \(0.560592\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.6410 20.0000i 1.25574 0.724999i 0.283493 0.958974i \(-0.408507\pi\)
0.972243 + 0.233975i \(0.0751733\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 45.8827 + 15.2942i 1.65889 + 0.552964i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 25.0000 43.3013i 0.901523 1.56148i 0.0760054 0.997107i \(-0.475783\pi\)
0.825518 0.564376i \(-0.190883\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −27.6603 27.6603i −0.995514 0.995514i
\(773\) 53.2750 + 14.2750i 1.91617 + 0.513436i 0.990997 + 0.133887i \(0.0427458\pi\)
0.925172 + 0.379549i \(0.123921\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 26.0000 + 45.0333i 0.933346 + 1.61660i
\(777\) 0 0
\(778\) −0.117314 0.437822i −0.00420591 0.0156967i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −24.2487 + 14.0000i −0.866025 + 0.500000i
\(785\) 37.8660 7.74871i 1.35150 0.276563i
\(786\) 0 0
\(787\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(788\) −26.0000 + 26.0000i −0.926212 + 0.926212i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 29.3205 + 43.9808i 1.04120 + 1.56180i
\(794\) 26.0000i 0.922705i
\(795\) 0 0
\(796\) 0 0
\(797\) 20.4904 + 5.49038i 0.725807 + 0.194479i 0.602761 0.797922i \(-0.294067\pi\)
0.123045 + 0.992401i \(0.460734\pi\)
\(798\) 0 0
\(799\)