Properties

Label 260.2.bg.a.23.1
Level $260$
Weight $2$
Character 260.23
Analytic conductor $2.076$
Analytic rank $0$
Dimension $4$
CM discriminant -4
Inner twists $4$

Related objects

Downloads

Learn more

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.a.147.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(0.133975 - 2.23205i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-3.00000 - 1.00000i) q^{10} +(1.59808 - 3.23205i) q^{13} +(2.00000 + 3.46410i) q^{16} +(0.0358984 + 0.133975i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-2.46410 + 3.73205i) q^{20} +(-4.96410 - 0.598076i) q^{25} +(-3.83013 - 3.36603i) q^{26} +(9.23205 - 5.33013i) q^{29} +(5.46410 - 1.46410i) q^{32} +0.196152 q^{34} +(3.00000 + 5.19615i) q^{36} +(-2.86603 + 10.6962i) q^{37} +(4.19615 + 4.73205i) q^{40} +(10.3301 - 5.96410i) q^{41} +(-3.69615 + 5.59808i) q^{45} +(6.06218 - 3.50000i) q^{49} +(-2.63397 + 6.56218i) q^{50} +(-6.00000 + 4.00000i) q^{52} +(5.29423 + 5.29423i) q^{53} +(-3.90192 - 14.5622i) q^{58} +(1.33013 - 2.30385i) q^{61} -8.00000i q^{64} +(-7.00000 - 4.00000i) q^{65} +(0.0717968 - 0.267949i) q^{68} +(8.19615 - 2.19615i) q^{72} +(-1.16987 + 1.16987i) q^{73} +(13.5622 + 7.83013i) q^{74} +(8.00000 - 4.00000i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-4.36603 - 16.2942i) q^{82} +(0.303848 - 0.0621778i) q^{85} +(-5.00000 - 8.66025i) q^{89} +(6.29423 + 7.09808i) q^{90} +(-17.7583 + 4.75833i) q^{97} +(-2.56218 - 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) 0.133975 2.23205i 0.0599153 0.998203i
\(6\) 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
\(10\) −3.00000 1.00000i −0.948683 0.316228i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 1.59808 3.23205i 0.443227 0.896410i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0.0358984 + 0.133975i 0.00870664 + 0.0324936i 0.970143 0.242536i \(-0.0779791\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) −3.00000 + 3.00000i −0.707107 + 0.707107i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) −2.46410 + 3.73205i −0.550990 + 0.834512i
\(21\) 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
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) −3.83013 3.36603i −0.751150 0.660132i
\(27\) 0 0
\(28\) 0 0
\(29\) 9.23205 5.33013i 1.71435 0.989780i 0.785872 0.618389i \(-0.212214\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 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
\(34\) 0.196152 0.0336399
\(35\) 0 0
\(36\) 3.00000 + 5.19615i 0.500000 + 0.866025i
\(37\) −2.86603 + 10.6962i −0.471172 + 1.75844i 0.164399 + 0.986394i \(0.447432\pi\)
−0.635571 + 0.772043i \(0.719235\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 4.19615 + 4.73205i 0.663470 + 0.748203i
\(41\) 10.3301 5.96410i 1.61329 0.931436i 0.624695 0.780869i \(-0.285223\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) 0 0
\(43\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(44\) 0 0
\(45\) −3.69615 + 5.59808i −0.550990 + 0.834512i
\(46\) 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
\(50\) −2.63397 + 6.56218i −0.372500 + 0.928032i
\(51\) 0 0
\(52\) −6.00000 + 4.00000i −0.832050 + 0.554700i
\(53\) 5.29423 + 5.29423i 0.727218 + 0.727218i 0.970065 0.242846i \(-0.0780811\pi\)
−0.242846 + 0.970065i \(0.578081\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −3.90192 14.5622i −0.512348 1.91211i
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.33013 2.30385i 0.170305 0.294977i −0.768221 0.640184i \(-0.778858\pi\)
0.938527 + 0.345207i \(0.112191\pi\)
\(62\) 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 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) 0.0717968 0.267949i 0.00870664 0.0324936i
\(69\) 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
\(73\) −1.16987 + 1.16987i −0.136923 + 0.136923i −0.772246 0.635323i \(-0.780867\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 13.5622 + 7.83013i 1.57657 + 0.910234i
\(75\) 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
\(82\) −4.36603 16.2942i −0.482147 1.79940i
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) 0.303848 0.0621778i 0.0329569 0.00674413i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 6.29423 + 7.09808i 0.663470 + 0.748203i
\(91\) 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 −0.994453 0.105180i \(-0.966458\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(98\) −2.56218 9.56218i −0.258819 0.965926i
\(99\) 0 0
\(100\) 8.00000 + 6.00000i 0.800000 + 0.600000i
\(101\) 9.16025 + 15.8660i 0.911479 + 1.57873i 0.811976 + 0.583691i \(0.198392\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) 3.26795 + 9.66025i 0.320449 + 0.947266i
\(105\) 0 0
\(106\) 9.16987 5.29423i 0.890657 0.514221i
\(107\) 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 \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.06218 + 2.42820i −0.852498 + 0.228426i −0.658505 0.752577i \(-0.728811\pi\)
−0.193993 + 0.981003i \(0.562144\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −21.3205 −1.97956
\(117\) −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
\(122\) −2.66025 2.66025i −0.240848 0.240848i
\(123\) 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
\(130\) −8.02628 + 8.09808i −0.703951 + 0.710248i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.339746 0.196152i −0.0291330 0.0168199i
\(137\) 12.9641 3.47372i 1.10760 0.296780i 0.341743 0.939793i \(-0.388983\pi\)
0.765855 + 0.643013i \(0.222316\pi\)
\(138\) 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
\(145\) −10.6603 21.3205i −0.885286 1.77057i
\(146\) 1.16987 + 2.02628i 0.0968194 + 0.167696i
\(147\) 0 0
\(148\) 15.6603 15.6603i 1.28726 1.28726i
\(149\) −11.0622 + 19.1603i −0.906249 + 1.56967i −0.0870170 + 0.996207i \(0.527733\pi\)
−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
\(153\) 0.107695 0.401924i 0.00870664 0.0324936i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −17.2224 + 17.2224i −1.37450 + 1.37450i −0.520854 + 0.853646i \(0.674386\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −2.53590 12.3923i −0.200480 0.979698i
\(161\) 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 \(0.416667\pi\)
\(164\) −23.8564 −1.86287
\(165\) 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
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) 0.0262794 0.437822i 0.00201554 0.0335794i
\(171\) 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 \(0.833333\pi\)
\(180\) 12.0000 6.00000i 0.894427 0.447214i
\(181\) 8.32051 0.618458 0.309229 0.950988i \(-0.399929\pi\)
0.309229 + 0.950988i \(0.399929\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 23.4904 + 7.83013i 1.72705 + 0.575682i
\(186\) 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
\(193\) 7.06218 + 1.89230i 0.508347 + 0.136211i 0.503871 0.863779i \(-0.331909\pi\)
0.00447566 + 0.999990i \(0.498575\pi\)
\(194\) 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 \(-0.689365\pi\)
0.899448 0.437028i \(-0.143969\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 11.1244 8.73205i 0.786611 0.617449i
\(201\) 0 0
\(202\) 25.0263 6.70577i 1.76084 0.471816i
\(203\) 0 0
\(204\) 0 0
\(205\) −11.9282 23.8564i −0.833102 1.66620i
\(206\) 0 0
\(207\) 0 0
\(208\) 14.3923 0.928203i 0.997927 0.0643593i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −3.87564 14.4641i −0.266180 0.993399i
\(213\) 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
\(221\) 0.490381 + 0.0980762i 0.0329866 + 0.00659732i
\(222\) 0 0
\(223\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(224\) 0 0
\(225\) 12.0000 + 9.00000i 0.800000 + 0.600000i
\(226\) 13.2679i 0.882571i
\(227\) 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 \(-0.0421925\pi\)
0.991228 + 0.132164i \(0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −7.80385 + 29.1244i −0.512348 + 1.91211i
\(233\) −5.00000 5.00000i −0.327561 0.327561i 0.524097 0.851658i \(-0.324403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.90192 + 14.4904i 0.320449 + 0.947266i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −18.9904 10.9641i −1.22328 0.706260i −0.257663 0.966235i \(-0.582952\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) −11.0000 11.0000i −0.707107 0.707107i
\(243\) 0 0
\(244\) −4.60770 + 2.66025i −0.294977 + 0.170305i
\(245\) −7.00000 14.0000i −0.447214 0.894427i
\(246\) 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
\(257\) 30.3564 + 8.13397i 1.89358 + 0.507383i 0.998053 + 0.0623783i \(0.0198685\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.12436 + 13.9282i 0.503851 + 0.863790i
\(261\) −31.9808 −1.97956
\(262\) 0 0
\(263\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(264\) 0 0
\(265\) 12.5263 11.1077i 0.769483 0.682340i
\(266\) 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 \(0.833333\pi\)
\(272\) −0.392305 + 0.392305i −0.0237870 + 0.0237870i
\(273\) 0 0
\(274\) 18.9808i 1.14667i
\(275\) 0 0
\(276\) 0 0
\(277\) 8.20577 + 30.6244i 0.493037 + 1.84004i 0.540758 + 0.841178i \(0.318138\pi\)
−0.0477206 + 0.998861i \(0.515196\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.7128i 1.35493i −0.735554 0.677466i \(-0.763078\pi\)
0.735554 0.677466i \(-0.236922\pi\)
\(282\) 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
\(289\) 14.7058 8.49038i 0.865045 0.499434i
\(290\) −33.0263 + 6.75833i −1.93937 + 0.396863i
\(291\) 0 0
\(292\) 3.19615 0.856406i 0.187041 0.0501174i
\(293\) 8.23205 + 30.7224i 0.480922 + 1.79482i 0.597763 + 0.801673i \(0.296056\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −15.6603 27.1244i −0.910234 1.57657i
\(297\) 0 0
\(298\) 22.1244 + 22.1244i 1.28163 + 1.28163i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.96410 3.27757i −0.284244 0.187673i
\(306\) −0.509619 0.294229i −0.0291330 0.0168199i
\(307\) 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 \(0.262726\pi\)
\(314\) 17.2224 + 29.8301i 0.971918 + 1.68341i
\(315\) 0 0
\(316\) 0 0
\(317\) −20.1506 20.1506i −1.13177 1.13177i −0.989882 0.141890i \(-0.954682\pi\)
−0.141890 0.989882i \(-0.545318\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −17.8564 1.07180i −0.998203 0.0599153i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) −9.86603 + 15.0885i −0.547269 + 0.836957i
\(326\) 0 0
\(327\) 0 0
\(328\) −8.73205 + 32.5885i −0.482147 + 1.79940i
\(329\) 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
\(333\) 23.4904 23.4904i 1.28726 1.28726i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.5622 18.5622i 1.01115 1.01115i 0.0112091 0.999937i \(-0.496432\pi\)
0.999937 0.0112091i \(-0.00356804\pi\)
\(338\) −17.0000 + 7.00000i −0.924678 + 0.380750i
\(339\) 0 0
\(340\) −0.588457 0.196152i −0.0319136 0.0106379i
\(341\) 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 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −35.7224 9.57180i −1.90131 0.509455i −0.996495 0.0836583i \(-0.973340\pi\)
−0.904819 0.425797i \(-0.859994\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.0000i 1.06000i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −3.80385 18.5885i −0.200480 0.979698i
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) 3.04552 11.3660i 0.160069 0.597385i
\(363\) 0 0
\(364\) 0 0
\(365\) 2.45448 + 2.76795i 0.128473 + 0.144881i
\(366\) 0 0
\(367\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(368\) 0 0
\(369\) −35.7846 −1.86287
\(370\) 19.2942 29.2224i 1.00306 1.51920i
\(371\) 0 0
\(372\) 0 0
\(373\) −30.0885 + 8.06218i −1.55792 + 0.417444i −0.932005 0.362446i \(-0.881942\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.47372 38.3564i −0.127403 1.97546i
\(378\) 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
\(386\) 5.16987 8.95448i 0.263140 0.455771i
\(387\) 0 0
\(388\) 35.5167 + 9.51666i 1.80309 + 0.483135i
\(389\) 34.3205i 1.74012i −0.492947 0.870059i \(-0.664080\pi\)
0.492947 0.870059i \(-0.335920\pi\)
\(390\) 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 0.216004 0.976392i \(-0.430698\pi\)
0.675261 + 0.737579i \(0.264031\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −7.85641 18.3923i −0.392820 0.919615i
\(401\) −18.8205 + 10.8660i −0.939851 + 0.542623i −0.889914 0.456129i \(-0.849236\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 36.6410i 1.82296i
\(405\) 18.0000 9.00000i 0.894427 0.447214i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −12.5981 + 21.8205i −0.622935 + 1.07895i 0.366002 + 0.930614i \(0.380726\pi\)
−0.988936 + 0.148340i \(0.952607\pi\)
\(410\) −36.9545 + 7.56218i −1.82505 + 0.373469i
\(411\) 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
\(421\) 9.24871i 0.450755i 0.974272 + 0.225377i \(0.0723615\pi\)
−0.974272 + 0.225377i \(0.927639\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −21.1769 −1.02844
\(425\) −0.0980762 0.686533i −0.00475740 0.0333018i
\(426\) 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
\(433\) −30.8923 + 8.27757i −1.48459 + 0.397795i −0.907906 0.419173i \(-0.862320\pi\)
−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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 0.313467 0.633975i 0.0149101 0.0301551i
\(443\) 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 −0.185837 + 0.982581i \(0.559500\pi\)
−0.758021 + 0.652230i \(0.773834\pi\)
\(450\) 16.6865 13.0981i 0.786611 0.617449i
\(451\) 0 0
\(452\) 18.1244 + 4.85641i 0.852498 + 0.228426i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.81347 + 17.9641i −0.225164 + 0.840325i 0.757174 + 0.653213i \(0.226579\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 10.9808 40.9808i 0.513097 1.91491i
\(459\) 0 0
\(460\) 0 0
\(461\) 19.8397 + 11.4545i 0.924029 + 0.533488i 0.884918 0.465746i \(-0.154214\pi\)
0.0391109 + 0.999235i \(0.487547\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 36.9282 + 21.3205i 1.71435 + 0.989780i
\(465\) 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 \(0.750000\pi\)
\(468\) 21.5885 1.39230i 0.997927 0.0643593i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5.81347 21.6962i −0.266180 0.993399i
\(478\) 0 0
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 29.9904 + 26.3564i 1.36744 + 1.20175i
\(482\) −21.9282 + 21.9282i −0.998802 + 0.998802i
\(483\) 0 0
\(484\) −19.0526 + 11.0000i −0.866025 + 0.500000i
\(485\) 8.24167 + 40.2750i 0.374235 + 1.82879i
\(486\) 0 0
\(487\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(488\) 1.94744 + 7.26795i 0.0881565 + 0.329005i
\(489\) 0 0
\(490\) −21.6865 + 4.43782i −0.979698 + 0.200480i
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 1.04552 + 1.04552i 0.0470877 + 0.0470877i
\(494\) 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
\(505\) 36.6410 18.3205i 1.63050 0.815252i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16.5526 + 28.6699i 0.733679 + 1.27077i 0.955300 + 0.295637i \(0.0955319\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) 22.2224 38.4904i 0.980189 1.69774i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 22.0000 6.00000i 0.964764 0.263117i
\(521\) −23.6410 −1.03573 −0.517866 0.855462i \(-0.673273\pi\)
−0.517866 + 0.855462i \(0.673273\pi\)
\(522\) −11.7058 + 43.6865i −0.512348 + 1.91211i
\(523\) 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
\(530\) −10.5885 21.1769i −0.459933 0.919866i
\(531\) 0 0
\(532\) 0 0
\(533\) −2.76795 42.9186i −0.119893 1.85901i
\(534\) 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
\(541\) 46.3731i 1.99373i 0.0790969 + 0.996867i \(0.474796\pi\)
−0.0790969 + 0.996867i \(0.525204\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.392305 + 0.679492i 0.0168199 + 0.0291330i
\(545\) −2.67949 + 44.6410i −0.114777 + 1.91221i
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) −25.9282 6.94744i −1.10760 0.296780i
\(549\) −6.91154 + 3.99038i −0.294977 + 0.170305i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 44.8372 1.90495
\(555\) 0 0
\(556\) 0 0
\(557\) 7.62436 28.4545i 0.323054 1.20566i −0.593199 0.805056i \(-0.702135\pi\)
0.916253 0.400599i \(-0.131198\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −31.0263 8.31347i −1.30876 0.350682i
\(563\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(564\) 0 0
\(565\) 4.20577 + 20.5526i 0.176938 + 0.864653i
\(566\) 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
\(577\) 33.1506 + 33.1506i 1.38008 + 1.38008i 0.844459 + 0.535620i \(0.179922\pi\)
0.535620 + 0.844459i \(0.320078\pi\)
\(578\) −6.21539 23.1962i −0.258526 0.964833i
\(579\) 0 0
\(580\) −2.85641 + 47.5885i −0.118606 + 1.97600i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 4.67949i 0.193639i
\(585\) 12.1865 + 20.8923i 0.503851 + 0.863790i
\(586\) 44.9808 1.85814
\(587\) 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
\(592\) −42.7846 + 11.4641i −1.75844 + 0.471172i
\(593\) 2.50962 2.50962i 0.103058 0.103058i −0.653698 0.756756i \(-0.726783\pi\)
0.756756 + 0.653698i \(0.226783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 38.3205 22.1244i 1.56967 0.906249i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −7.66987 13.2846i −0.312861 0.541891i 0.666120 0.745845i \(-0.267954\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −20.5263 13.5526i −0.834512 0.550990i
\(606\) 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
\(610\) −6.29423 + 5.58142i −0.254846 + 0.225985i
\(611\) 0 0
\(612\) −0.588457 + 0.588457i −0.0237870 + 0.0237870i
\(613\) −42.0885 11.2776i −1.69994 0.455497i −0.727013 0.686624i \(-0.759092\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −39.3564 + 10.5455i −1.58443 + 0.424547i −0.940294 0.340365i \(-0.889449\pi\)
−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
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 43.3013 25.0000i 1.73067 0.999201i
\(627\) 0 0
\(628\) 47.0526 12.6077i 1.87760 0.503102i
\(629\) −1.53590 −0.0612403
\(630\) 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
\(634\) −34.9019 + 20.1506i −1.38613 + 0.800284i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.62436 25.1865i −0.0643593 0.997927i
\(638\) 0 0
\(639\) 0 0
\(640\) −8.00000 + 24.0000i −0.316228 + 0.948683i
\(641\) 19.6506 34.0359i 0.776153 1.34434i −0.157991 0.987441i \(-0.550502\pi\)
0.934144 0.356897i \(-0.116165\pi\)
\(642\) 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
\(650\) 17.0000 + 19.0000i 0.666795 + 0.745241i
\(651\) 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
\(656\) 41.3205 + 23.8564i 1.61329 + 0.931436i
\(657\) 4.79423 1.28461i 0.187041 0.0501174i
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) −12.6506 + 7.30385i −0.492053 + 0.284087i −0.725426 0.688301i \(-0.758357\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −23.4904 40.6865i −0.910234 1.57657i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −2.91858 + 10.8923i −0.112503 + 0.419867i −0.999088 0.0426985i \(-0.986405\pi\)
0.886585 + 0.462566i \(0.153071\pi\)
\(674\) −18.5622 32.1506i −0.714988 1.23840i
\(675\) 0 0
\(676\) 3.33975 + 25.7846i 0.128452 + 0.991716i
\(677\) 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
\(680\) −0.483340 + 0.732051i −0.0185352 + 0.0280729i
\(681\) 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
\(685\) −6.01666 29.4019i −0.229885 1.12339i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 25.5718 8.65064i 0.974208 0.329563i
\(690\) 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
\(697\) 1.16987 + 1.16987i 0.0443121 + 0.0443121i
\(698\) 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
\(706\) −26.1506 + 45.2942i −0.984192 + 1.70467i
\(707\) 0 0
\(708\) 0 0
\(709\) 11.5526 20.0096i 0.433865 0.751477i −0.563337 0.826227i \(-0.690483\pi\)
0.997202 + 0.0747503i \(0.0238160\pi\)
\(710\) 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 \(0.166667\pi\)
\(720\) −26.7846 1.60770i −0.998203 0.0599153i
\(721\) 0 0
\(722\) −25.9545 + 6.95448i −0.965926 + 0.258819i
\(723\) 0 0
\(724\) −14.4115 8.32051i −0.535601 0.309229i
\(725\) −49.0167 + 20.9378i −1.82043 + 0.777611i
\(726\) 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
\(730\) 4.67949 2.33975i 0.173196 0.0865979i
\(731\) 0 0
\(732\) 0 0
\(733\) 7.15064 7.15064i 0.264115 0.264115i −0.562609 0.826723i \(-0.690202\pi\)
0.826723 + 0.562609i \(0.190202\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −13.0981 + 48.8827i −0.482147 + 1.79940i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) −32.8564 37.0526i −1.20783 1.36208i
\(741\) 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
\(745\) 41.2846 + 27.2583i 1.51255 + 0.998668i
\(746\) 44.0526i 1.61288i
\(747\) 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
\(754\) −53.3013 10.6603i −1.94112 0.388224i
\(755\) 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 −0.283493 0.958974i \(-0.591493\pi\)
−0.972243 + 0.233975i \(0.924827\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.882686 0.294229i −0.0319136 0.0106379i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 25.0000 + 43.3013i 0.901523 + 1.56148i 0.825518 + 0.564376i \(0.190883\pi\)
0.0760054 + 0.997107i \(0.475783\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.3397 10.3397i −0.372136 0.372136i
\(773\) −14.2750 53.2750i −0.513436 1.91617i −0.379549 0.925172i \(-0.623921\pi\)
−0.133887 0.990997i \(-0.542746\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 26.0000 45.0333i 0.933346 1.61660i
\(777\) 0 0
\(778\) −46.8827 12.5622i −1.68083 0.450376i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 24.2487 + 14.0000i 0.866025 + 0.500000i
\(785\) 36.1340 + 40.7487i 1.28968 + 1.45438i
\(786\) 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
\(793\) −5.32051 7.98076i −0.188937 0.283405i
\(794\) 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