Properties

Label 260.2.bg.b.23.1
Level $260$
Weight $2$
Character 260.23
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 23.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.23
Dual form 260.2.bg.b.147.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(2.36603 - 2.09808i) q^{10} +(0.232051 - 3.59808i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-1.86603 - 6.96410i) q^{17} +(3.00000 - 3.00000i) q^{18} +(2.00000 + 4.00000i) q^{20} +(1.96410 + 4.59808i) q^{25} +(4.83013 + 1.63397i) q^{26} +(-5.76795 + 3.33013i) q^{29} +(-5.46410 + 1.46410i) q^{32} +10.1962 q^{34} +(3.00000 + 5.19615i) q^{36} +(-0.303848 + 1.13397i) q^{37} +(-6.19615 + 1.26795i) q^{40} +(1.66987 - 0.964102i) q^{41} +(3.00000 + 6.00000i) q^{45} +(6.06218 - 3.50000i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(-4.00000 + 6.00000i) q^{52} +(-10.2942 - 10.2942i) q^{53} +(-2.43782 - 9.09808i) q^{58} +(-7.33013 + 12.6962i) q^{61} -8.00000i q^{64} +(-4.86603 + 6.42820i) q^{65} +(-3.73205 + 13.9282i) q^{68} +(-8.19615 + 2.19615i) q^{72} +(9.83013 - 9.83013i) q^{73} +(-1.43782 - 0.830127i) q^{74} +(0.535898 - 8.92820i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.705771 + 2.63397i) q^{82} +(-5.09808 + 15.2942i) q^{85} +(5.00000 + 8.66025i) q^{89} +(-9.29423 + 1.90192i) q^{90} +(17.7583 - 4.75833i) q^{97} +(2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 4 q^{5} + 8 q^{8} + 6 q^{10} - 6 q^{13} + 8 q^{16} - 4 q^{17} + 12 q^{18} + 8 q^{20} - 6 q^{25} + 2 q^{26} - 30 q^{29} - 8 q^{32} + 20 q^{34} + 12 q^{36} - 22 q^{37} - 4 q^{40} + 24 q^{41} + 12 q^{45} - 28 q^{50} - 16 q^{52} - 10 q^{53} - 34 q^{58} - 12 q^{61} - 16 q^{65} - 8 q^{68} - 12 q^{72} + 22 q^{73} - 30 q^{74} + 16 q^{80} + 18 q^{81} + 34 q^{82} - 10 q^{85} + 20 q^{89} - 6 q^{90} + 26 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) −1.86603 1.23205i −0.834512 0.550990i
\(6\) 0 0
\(7\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −2.59808 1.50000i −0.866025 0.500000i
\(10\) 2.36603 2.09808i 0.748203 0.663470i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 0.232051 3.59808i 0.0643593 0.997927i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −1.86603 6.96410i −0.452578 1.68904i −0.695113 0.718900i \(-0.744646\pi\)
0.242536 0.970143i \(-0.422021\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 2.00000 + 4.00000i 0.447214 + 0.894427i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(24\) 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 \(-0.878881\pi\)
−0.142605 + 0.989780i \(0.545548\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) 0 0
\(34\) 10.1962 1.74863
\(35\) 0 0
\(36\) 3.00000 + 5.19615i 0.500000 + 0.866025i
\(37\) −0.303848 + 1.13397i −0.0499522 + 0.186424i −0.986394 0.164399i \(-0.947432\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.19615 + 1.26795i −0.979698 + 0.200480i
\(41\) 1.66987 0.964102i 0.260790 0.150567i −0.363905 0.931436i \(-0.618557\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(44\) 0 0
\(45\) 3.00000 + 6.00000i 0.447214 + 0.894427i
\(46\) 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
\(50\) −7.00000 + 1.00000i −0.989949 + 0.141421i
\(51\) 0 0
\(52\) −4.00000 + 6.00000i −0.554700 + 0.832050i
\(53\) −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
\(58\) −2.43782 9.09808i −0.320102 1.19464i
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) −7.33013 + 12.6962i −0.938527 + 1.62558i −0.170305 + 0.985391i \(0.554475\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −4.86603 + 6.42820i −0.603556 + 0.797320i
\(66\) 0 0
\(67\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) −3.73205 + 13.9282i −0.452578 + 1.68904i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −8.19615 + 2.19615i −0.965926 + 0.258819i
\(73\) 9.83013 9.83013i 1.15053 1.15053i 0.164083 0.986447i \(-0.447534\pi\)
0.986447 0.164083i \(-0.0524664\pi\)
\(74\) −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 \(0.5\pi\)
\(80\) 0.535898 8.92820i 0.0599153 0.998203i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 0.705771 + 2.63397i 0.0779394 + 0.290874i
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) −5.09808 + 15.2942i −0.552964 + 1.65889i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) −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
\(97\) 17.7583 4.75833i 1.80309 0.483135i 0.808632 0.588315i \(-0.200208\pi\)
0.994453 + 0.105180i \(0.0335417\pi\)
\(98\) 2.56218 + 9.56218i 0.258819 + 0.965926i
\(99\) 0 0
\(100\) 1.19615 9.92820i 0.119615 0.992820i
\(101\) −8.16025 14.1340i −0.811976 1.40638i −0.911479 0.411346i \(-0.865059\pi\)
0.0995037 0.995037i \(-0.468274\pi\)
\(102\) 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 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(108\) 0 0
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.4282 + 3.06218i −1.07507 + 0.288065i −0.752577 0.658505i \(-0.771189\pi\)
−0.322498 + 0.946570i \(0.604523\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 13.3205 1.23678
\(117\) −6.00000 + 9.00000i −0.554700 + 0.832050i
\(118\) 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 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) 0 0
\(130\) −7.00000 9.00000i −0.613941 0.789352i
\(131\) 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
\(137\) 22.5263 6.03590i 1.92455 0.515682i 0.939793 0.341743i \(-0.111017\pi\)
0.984757 0.173939i \(-0.0556494\pi\)
\(138\) 0 0
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) 14.8660 + 0.892305i 1.23456 + 0.0741019i
\(146\) 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 \(-0.861067\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −5.59808 + 20.8923i −0.452578 + 1.68904i
\(154\) 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
\(160\) 12.0000 + 4.00000i 0.948683 + 0.316228i
\(161\) 0 0
\(162\) −12.2942 + 3.29423i −0.965926 + 0.258819i
\(163\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(164\) −3.85641 −0.301135
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(168\) 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
\(173\) 20.4904 5.49038i 1.55785 0.417426i 0.625871 0.779926i \(-0.284744\pi\)
0.931984 + 0.362500i \(0.118077\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −13.6603 + 3.66025i −1.02388 + 0.274348i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0.803848 13.3923i 0.0599153 0.998203i
\(181\) −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
\(185\) 1.96410 1.74167i 0.144404 0.128050i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) −18.8923 5.06218i −1.35990 0.364384i −0.496119 0.868255i \(-0.665242\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 26.0000i 1.86669i
\(195\) 0 0
\(196\) −14.0000 −1.00000
\(197\) −4.75833 + 17.7583i −0.339017 + 1.26523i 0.560431 + 0.828201i \(0.310635\pi\)
−0.899448 + 0.437028i \(0.856031\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 13.1244 + 5.26795i 0.928032 + 0.372500i
\(201\) 0 0
\(202\) 22.2942 5.97372i 1.56862 0.420310i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.30385 0.258330i −0.300594 0.0180426i
\(206\) 0 0
\(207\) 0 0
\(208\) 12.9282 6.39230i 0.896410 0.443227i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 7.53590 + 28.1244i 0.517568 + 1.93159i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −7.32051 + 27.3205i −0.495807 + 1.85038i
\(219\) 0 0
\(220\) 0 0
\(221\) −25.4904 + 5.09808i −1.71467 + 0.342934i
\(222\) 0 0
\(223\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(224\) 0 0
\(225\) 1.79423 14.8923i 0.119615 0.992820i
\(226\) 16.7321i 1.11300i
\(227\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(228\) 0 0
\(229\) −30.0000 −1.98246 −0.991228 0.132164i \(-0.957808\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.87564 + 18.1962i −0.320102 + 1.19464i
\(233\) −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 0.707953 0.706260i \(-0.249619\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) 11.0000 + 11.0000i 0.707107 + 0.707107i
\(243\) 0 0
\(244\) 25.3923 14.6603i 1.62558 0.938527i
\(245\) −15.6244 0.937822i −0.998203 0.0599153i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 14.2942 + 6.75833i 0.904046 + 0.427434i
\(251\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −9.86603 2.64359i −0.615426 0.164903i −0.0623783 0.998053i \(-0.519869\pi\)
−0.553047 + 0.833150i \(0.686535\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 14.8564 6.26795i 0.921355 0.388722i
\(261\) 19.9808 1.23678
\(262\) 0 0
\(263\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(264\) 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 \(-0.0420477\pi\)
0.381577 + 0.924337i \(0.375381\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 20.3923 20.3923i 1.23647 1.23647i
\(273\) 0 0
\(274\) 32.9808i 1.99244i
\(275\) 0 0
\(276\) 0 0
\(277\) −6.37564 23.7942i −0.383075 1.42966i −0.841178 0.540758i \(-0.818138\pi\)
0.458103 0.888899i \(-0.348529\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 32.7128i 1.95148i −0.218926 0.975741i \(-0.570255\pi\)
0.218926 0.975741i \(-0.429745\pi\)
\(282\) 0 0
\(283\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 16.3923 + 4.39230i 0.965926 + 0.258819i
\(289\) −30.2942 + 17.4904i −1.78201 + 1.02885i
\(290\) −6.66025 + 19.9808i −0.391104 + 1.17331i
\(291\) 0 0
\(292\) −26.8564 + 7.19615i −1.57165 + 0.421123i
\(293\) 1.27757 + 4.76795i 0.0746363 + 0.278547i 0.993151 0.116841i \(-0.0372769\pi\)
−0.918514 + 0.395388i \(0.870610\pi\)
\(294\) 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
\(305\) 29.3205 14.6603i 1.67889 0.839444i
\(306\) −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 \(-0.878651\pi\)
−0.372061 0.928208i \(-0.621349\pi\)
\(318\) 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
\(325\) 17.0000 6.00000i 0.942990 0.332820i
\(326\) 0 0
\(327\) 0 0
\(328\) 1.41154 5.26795i 0.0779394 0.290874i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 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 \(0.170235\pi\)
\(338\) 7.00000 17.0000i 0.380750 0.924678i
\(339\) 0 0
\(340\) 24.1244 21.3923i 1.30833 1.16016i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 30.0000i 1.61281i
\(347\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(348\) 0 0
\(349\) −5.00000 8.66025i −0.267644 0.463573i 0.700609 0.713545i \(-0.252912\pi\)
−0.968253 + 0.249973i \(0.919578\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −23.4282 6.27757i −1.24696 0.334121i −0.425797 0.904819i \(-0.640006\pi\)
−0.821160 + 0.570697i \(0.806673\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.0000i 1.06000i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 18.0000 + 6.00000i 0.948683 + 0.316228i
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) 9.63397 35.9545i 0.506350 1.88973i
\(363\) 0 0
\(364\) 0 0
\(365\) −30.4545 + 6.23205i −1.59406 + 0.326200i
\(366\) 0 0
\(367\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(368\) 0 0
\(369\) −5.78461 −0.301135
\(370\) 1.66025 + 3.32051i 0.0863125 + 0.172625i
\(371\) 0 0
\(372\) 0 0
\(373\) −4.06218 + 1.08846i −0.210332 + 0.0563582i −0.362446 0.932005i \(-0.618058\pi\)
0.152115 + 0.988363i \(0.451392\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.6436 + 21.5263i 0.548173 + 1.10866i
\(378\) 0 0
\(379\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.8301 23.9545i 0.703935 1.21925i
\(387\) 0 0
\(388\) −35.5167 9.51666i −1.80309 0.483135i
\(389\) 0.320508i 0.0162504i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.999967 + 0.00812520i \(0.997414\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.12436 19.1244i 0.258819 0.965926i
\(393\) 0 0
\(394\) −22.5167 13.0000i −1.13437 0.654931i
\(395\) 0 0
\(396\) 0 0
\(397\) −17.7583 + 4.75833i −0.891265 + 0.238814i −0.675261 0.737579i \(-0.735969\pi\)
−0.216004 + 0.976392i \(0.569302\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −12.0000 + 16.0000i −0.600000 + 0.800000i
\(401\) 15.8205 9.13397i 0.790038 0.456129i −0.0499376 0.998752i \(-0.515902\pi\)
0.839976 + 0.542623i \(0.182569\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 32.6410i 1.62395i
\(405\) 1.20577 20.0885i 0.0599153 0.998203i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 7.40192 12.8205i 0.366002 0.633933i −0.622935 0.782274i \(-0.714060\pi\)
0.988936 + 0.148340i \(0.0473931\pi\)
\(410\) 1.92820 5.78461i 0.0952272 0.285682i
\(411\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 39.2487i 1.91287i 0.291953 + 0.956433i \(0.405695\pi\)
−0.291953 + 0.956433i \(0.594305\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −41.1769 −1.99973
\(425\) 28.3564 22.2583i 1.37549 1.07969i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) 37.7224 10.1077i 1.81282 0.485745i 0.816968 0.576683i \(-0.195653\pi\)
0.995857 + 0.0909384i \(0.0289866\pi\)
\(434\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 2.36603 36.6865i 0.112540 1.74500i
\(443\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) 1.33975 22.3205i 0.0635100 1.05809i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.0000 34.6410i 0.943858 1.63481i 0.185837 0.982581i \(-0.440500\pi\)
0.758021 0.652230i \(-0.226166\pi\)
\(450\) 19.6865 + 7.90192i 0.928032 + 0.372500i
\(451\) 0 0
\(452\) 22.8564 + 6.12436i 1.07507 + 0.288065i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0359 + 41.1865i −0.516238 + 1.92662i −0.187112 + 0.982339i \(0.559913\pi\)
−0.329125 + 0.944286i \(0.606754\pi\)
\(458\) 10.9808 40.9808i 0.513097 1.91491i
\(459\) 0 0
\(460\) 0 0
\(461\) 37.1603 + 21.4545i 1.73073 + 0.999235i 0.884918 + 0.465746i \(0.154214\pi\)
0.845807 + 0.533488i \(0.179119\pi\)
\(462\) 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 \(0.750000\pi\)
\(468\) 19.3923 9.58846i 0.896410 0.443227i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 11.3038 + 42.1865i 0.517568 + 1.93159i
\(478\) 0 0
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 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
\(485\) −39.0000 13.0000i −1.77090 0.590300i
\(486\) 0 0
\(487\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(488\) 10.7321 + 40.0526i 0.485817 + 1.81309i
\(489\) 0 0
\(490\) 7.00000 21.0000i 0.316228 0.948683i
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 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 \(\pi\)
\(500\) −14.4641 + 17.0526i −0.646854 + 0.762614i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(504\) 0 0
\(505\) −2.18653 + 36.4282i −0.0972995 + 1.62103i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 21.5526 + 37.3301i 0.955300 + 1.65463i 0.733679 + 0.679496i \(0.237801\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) 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
\(520\) 3.12436 + 22.5885i 0.137012 + 0.990569i
\(521\) 45.6410 1.99957 0.999785 0.0207541i \(-0.00660670\pi\)
0.999785 + 0.0207541i \(0.00660670\pi\)
\(522\) −7.31347 + 27.2942i −0.320102 + 1.19464i
\(523\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −19.9186 11.5000i −0.866025 0.500000i
\(530\) −45.9545 2.75833i −1.99614 0.119814i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.08142 6.23205i −0.133471 0.269940i
\(534\) 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 \(0.191870\pi\)
−0.823764 + 0.566933i \(0.808130\pi\)
\(542\) 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 \(0.750000\pi\)
\(548\) −45.0526 12.0718i −1.92455 0.515682i
\(549\) 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
\(557\) −4.45448 + 16.6244i −0.188742 + 0.704397i 0.805056 + 0.593199i \(0.202135\pi\)
−0.993798 + 0.111198i \(0.964531\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 44.6865 + 11.9737i 1.88499 + 0.505081i
\(563\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(564\) 0 0
\(565\) 25.0981 + 8.36603i 1.05588 + 0.351961i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.5167 13.0000i 0.943948 0.544988i 0.0527519 0.998608i \(-0.483201\pi\)
0.891196 + 0.453619i \(0.149867\pi\)
\(570\) 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 0.886090 0.463513i \(-0.153411\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(578\) −12.8038 47.7846i −0.532570 1.98758i
\(579\) 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
\(585\) 22.2846 9.40192i 0.921355 0.388722i
\(586\) −6.98076 −0.288373
\(587\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −4.53590 + 1.21539i −0.186424 + 0.0499522i
\(593\) −28.4904 + 28.4904i −1.16996 + 1.16996i −0.187741 + 0.982219i \(0.560117\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(594\) 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 −0.978980 0.203954i \(-0.934621\pi\)
0.312861 0.949799i \(-0.398713\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −22.0000 + 11.0000i −0.894427 + 0.447214i
\(606\) 0 0
\(607\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(608\) 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
\(613\) −40.7224 10.9115i −1.64476 0.440713i −0.686624 0.727013i \(-0.740908\pi\)
−0.958140 + 0.286300i \(0.907575\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −43.4545 + 11.6436i −1.74941 + 0.468753i −0.984500 0.175382i \(-0.943884\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 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
\(628\) −33.3923 + 8.94744i −1.33250 + 0.357042i
\(629\) 8.46410 0.337486
\(630\) 0 0
\(631\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 40.0981 23.1506i 1.59250 0.919429i
\(635\) 0 0
\(636\) 0 0
\(637\) −11.1865 22.6244i −0.443227 0.896410i
\(638\) 0 0
\(639\) 0 0
\(640\) −16.7846 18.9282i −0.663470 0.748203i
\(641\) −23.6506 + 40.9641i −0.934144 + 1.61798i −0.157991 + 0.987441i \(0.550502\pi\)
−0.776153 + 0.630544i \(0.782832\pi\)
\(642\) 0 0
\(643\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(648\) 24.5885 + 6.58846i 0.965926 + 0.258819i
\(649\) 0 0
\(650\) 1.97372 + 25.4186i 0.0774157 + 0.996999i
\(651\) 0 0
\(652\) 0 0
\(653\) 12.8109 47.8109i 0.501329 1.87098i 0.0101092 0.999949i \(-0.496782\pi\)
0.491220 0.871036i \(-0.336551\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.67949 + 3.85641i 0.260790 + 0.150567i
\(657\) −40.2846 + 10.7942i −1.57165 + 0.421123i
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 30.6506 17.6962i 1.19217 0.688301i 0.233373 0.972387i \(-0.425024\pi\)
0.958799 + 0.284087i \(0.0916904\pi\)
\(662\) 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
\(673\) −9.89230 + 36.9186i −0.381320 + 1.42311i 0.462566 + 0.886585i \(0.346929\pi\)
−0.843886 + 0.536522i \(0.819738\pi\)
\(674\) 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
\(680\) 20.3923 + 40.7846i 0.782009 + 1.56402i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(684\) 0 0
\(685\) −49.4711 16.4904i −1.89020 0.630065i
\(686\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) −40.9808 10.9808i −1.55785 0.417426i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.83013 9.83013i −0.372343 0.372343i
\(698\) 13.6603 3.66025i 0.517048 0.138543i
\(699\) 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 0.433865 0.900978i \(-0.357149\pi\)
0.563337 0.826227i \(-0.309517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 27.3205 + 7.32051i 1.02388 + 0.274348i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −14.7846 + 22.3923i −0.550990 + 0.834512i
\(721\) 0 0
\(722\) 25.9545 6.95448i 0.965926 0.258819i
\(723\) 0 0
\(724\) 45.5885 + 26.3205i 1.69428 + 0.978194i
\(725\) −26.6410 19.9808i −0.989423 0.742067i
\(726\) 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
\(730\) 2.63397 43.8827i 0.0974878 1.62417i
\(731\) 0 0
\(732\) 0 0
\(733\) 36.1506 36.1506i 1.33525 1.33525i 0.434659 0.900595i \(-0.356869\pi\)
0.900595 0.434659i \(-0.143131\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 2.11731 7.90192i 0.0779394 0.290874i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) −5.14359 + 1.05256i −0.189082 + 0.0386928i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(744\) 0 0
\(745\) 4.24871 2.12436i 0.155661 0.0778304i
\(746\) 5.94744i 0.217751i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −33.3013 + 6.66025i −1.21276 + 0.242552i
\(755\) 0 0
\(756\) 0 0
\(757\) −47.8109 12.8109i −1.73772 0.465620i −0.755779 0.654827i \(-0.772742\pi\)
−0.981937 + 0.189207i \(0.939408\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.6410 + 20.0000i 1.25574 + 0.724999i 0.972243 0.233975i \(-0.0751733\pi\)
0.283493 + 0.958974i \(0.408507\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 36.1865 32.0885i 1.30833 1.16016i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −25.0000 43.3013i −0.901523 1.56148i −0.825518 0.564376i \(-0.809117\pi\)
−0.0760054 0.997107i \(-0.524217\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 27.6603 + 27.6603i 0.995514 + 0.995514i
\(773\) 14.2750 + 53.2750i 0.513436 + 1.91617i 0.379549 + 0.925172i \(0.376079\pi\)
0.133887 + 0.990997i \(0.457254\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 26.0000 45.0333i 0.933346 1.61660i
\(777\) 0 0
\(778\) −0.437822 0.117314i −0.0156967 0.00420591i
\(779\) 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 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(788\) 26.0000 26.0000i 0.926212 0.926212i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 43.9808 + 29.3205i 1.56180 + 1.04120i
\(794\) 26.0000i 0.922705i
\(795\) 0 0
\(796\) 0 0
\(797\) −5.49038 20.4904i −0.194479 0.725807i −0.992401 0.123045i \(-0.960734\pi\)
0.797922 0.602761i \(-0.205933\pi\)
\(798\) 0 0
\(799