Properties

Label 1344.2.s.b.239.1
Level 1344
Weight 2
Character 1344.239
Analytic conductor 10.732
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.s (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 336)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.1
Root \(0.707107 + 0.707107i\)
Character \(\chi\) = 1344.239
Dual form 1344.2.s.b.911.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.41421i) q^{3} +(0.414214 + 0.414214i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.41421i) q^{3} +(0.414214 + 0.414214i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +(3.82843 - 3.82843i) q^{11} +(-4.41421 - 4.41421i) q^{13} +(1.00000 - 0.171573i) q^{15} +1.17157i q^{17} +(-0.414214 + 0.414214i) q^{19} +(1.00000 - 1.41421i) q^{21} +7.65685i q^{23} -4.65685i q^{25} +(-5.00000 - 1.41421i) q^{27} +(-3.00000 + 3.00000i) q^{29} -6.48528i q^{31} +(-1.58579 - 9.24264i) q^{33} +(0.414214 + 0.414214i) q^{35} +(1.82843 - 1.82843i) q^{37} +(-10.6569 + 1.82843i) q^{39} -0.343146 q^{41} +(3.82843 + 3.82843i) q^{43} +(0.757359 - 1.58579i) q^{45} +5.65685 q^{47} +1.00000 q^{49} +(1.65685 + 1.17157i) q^{51} +(-5.82843 - 5.82843i) q^{53} +3.17157 q^{55} +(0.171573 + 1.00000i) q^{57} +(10.0711 - 10.0711i) q^{59} +(2.41421 + 2.41421i) q^{61} +(-1.00000 - 2.82843i) q^{63} -3.65685i q^{65} +(7.00000 - 7.00000i) q^{67} +(10.8284 + 7.65685i) q^{69} +6.00000i q^{71} +5.17157i q^{73} +(-6.58579 - 4.65685i) q^{75} +(3.82843 - 3.82843i) q^{77} -2.00000i q^{79} +(-7.00000 + 5.65685i) q^{81} +(-8.89949 - 8.89949i) q^{83} +(-0.485281 + 0.485281i) q^{85} +(1.24264 + 7.24264i) q^{87} -15.6569 q^{89} +(-4.41421 - 4.41421i) q^{91} +(-9.17157 - 6.48528i) q^{93} -0.343146 q^{95} -2.00000 q^{97} +(-14.6569 - 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 12q^{13} + 4q^{15} + 4q^{19} + 4q^{21} - 20q^{27} - 12q^{29} - 12q^{33} - 4q^{35} - 4q^{37} - 20q^{39} - 24q^{41} + 4q^{43} + 20q^{45} + 4q^{49} - 16q^{51} - 12q^{53} + 24q^{55} + 12q^{57} + 12q^{59} + 4q^{61} - 4q^{63} + 28q^{67} + 32q^{69} - 32q^{75} + 4q^{77} - 28q^{81} + 4q^{83} + 32q^{85} - 12q^{87} - 40q^{89} - 12q^{91} - 48q^{93} - 24q^{95} - 8q^{97} - 36q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 0 0
\(5\) 0.414214 + 0.414214i 0.185242 + 0.185242i 0.793635 0.608394i \(-0.208186\pi\)
−0.608394 + 0.793635i \(0.708186\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0 0
\(11\) 3.82843 3.82843i 1.15431 1.15431i 0.168636 0.985678i \(-0.446064\pi\)
0.985678 0.168636i \(-0.0539362\pi\)
\(12\) 0 0
\(13\) −4.41421 4.41421i −1.22428 1.22428i −0.966095 0.258188i \(-0.916875\pi\)
−0.258188 0.966095i \(-0.583125\pi\)
\(14\) 0 0
\(15\) 1.00000 0.171573i 0.258199 0.0442999i
\(16\) 0 0
\(17\) 1.17157i 0.284148i 0.989856 + 0.142074i \(0.0453771\pi\)
−0.989856 + 0.142074i \(0.954623\pi\)
\(18\) 0 0
\(19\) −0.414214 + 0.414214i −0.0950271 + 0.0950271i −0.753022 0.657995i \(-0.771405\pi\)
0.657995 + 0.753022i \(0.271405\pi\)
\(20\) 0 0
\(21\) 1.00000 1.41421i 0.218218 0.308607i
\(22\) 0 0
\(23\) 7.65685i 1.59656i 0.602284 + 0.798282i \(0.294258\pi\)
−0.602284 + 0.798282i \(0.705742\pi\)
\(24\) 0 0
\(25\) 4.65685i 0.931371i
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i \(-0.878881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 6.48528i 1.16479i −0.812906 0.582395i \(-0.802116\pi\)
0.812906 0.582395i \(-0.197884\pi\)
\(32\) 0 0
\(33\) −1.58579 9.24264i −0.276050 1.60894i
\(34\) 0 0
\(35\) 0.414214 + 0.414214i 0.0700149 + 0.0700149i
\(36\) 0 0
\(37\) 1.82843 1.82843i 0.300592 0.300592i −0.540654 0.841245i \(-0.681823\pi\)
0.841245 + 0.540654i \(0.181823\pi\)
\(38\) 0 0
\(39\) −10.6569 + 1.82843i −1.70646 + 0.292783i
\(40\) 0 0
\(41\) −0.343146 −0.0535904 −0.0267952 0.999641i \(-0.508530\pi\)
−0.0267952 + 0.999641i \(0.508530\pi\)
\(42\) 0 0
\(43\) 3.82843 + 3.82843i 0.583830 + 0.583830i 0.935953 0.352124i \(-0.114540\pi\)
−0.352124 + 0.935953i \(0.614540\pi\)
\(44\) 0 0
\(45\) 0.757359 1.58579i 0.112900 0.236395i
\(46\) 0 0
\(47\) 5.65685 0.825137 0.412568 0.910927i \(-0.364632\pi\)
0.412568 + 0.910927i \(0.364632\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.65685 + 1.17157i 0.232006 + 0.164053i
\(52\) 0 0
\(53\) −5.82843 5.82843i −0.800596 0.800596i 0.182593 0.983189i \(-0.441551\pi\)
−0.983189 + 0.182593i \(0.941551\pi\)
\(54\) 0 0
\(55\) 3.17157 0.427655
\(56\) 0 0
\(57\) 0.171573 + 1.00000i 0.0227254 + 0.132453i
\(58\) 0 0
\(59\) 10.0711 10.0711i 1.31114 1.31114i 0.390567 0.920575i \(-0.372279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 0 0
\(61\) 2.41421 + 2.41421i 0.309108 + 0.309108i 0.844564 0.535455i \(-0.179860\pi\)
−0.535455 + 0.844564i \(0.679860\pi\)
\(62\) 0 0
\(63\) −1.00000 2.82843i −0.125988 0.356348i
\(64\) 0 0
\(65\) 3.65685i 0.453577i
\(66\) 0 0
\(67\) 7.00000 7.00000i 0.855186 0.855186i −0.135580 0.990766i \(-0.543290\pi\)
0.990766 + 0.135580i \(0.0432899\pi\)
\(68\) 0 0
\(69\) 10.8284 + 7.65685i 1.30359 + 0.921777i
\(70\) 0 0
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) 5.17157i 0.605287i 0.953104 + 0.302643i \(0.0978691\pi\)
−0.953104 + 0.302643i \(0.902131\pi\)
\(74\) 0 0
\(75\) −6.58579 4.65685i −0.760461 0.537727i
\(76\) 0 0
\(77\) 3.82843 3.82843i 0.436290 0.436290i
\(78\) 0 0
\(79\) 2.00000i 0.225018i −0.993651 0.112509i \(-0.964111\pi\)
0.993651 0.112509i \(-0.0358886\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) −8.89949 8.89949i −0.976846 0.976846i 0.0228915 0.999738i \(-0.492713\pi\)
−0.999738 + 0.0228915i \(0.992713\pi\)
\(84\) 0 0
\(85\) −0.485281 + 0.485281i −0.0526362 + 0.0526362i
\(86\) 0 0
\(87\) 1.24264 + 7.24264i 0.133225 + 0.776493i
\(88\) 0 0
\(89\) −15.6569 −1.65962 −0.829812 0.558044i \(-0.811552\pi\)
−0.829812 + 0.558044i \(0.811552\pi\)
\(90\) 0 0
\(91\) −4.41421 4.41421i −0.462735 0.462735i
\(92\) 0 0
\(93\) −9.17157 6.48528i −0.951048 0.672492i
\(94\) 0 0
\(95\) −0.343146 −0.0352060
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −14.6569 7.00000i −1.47307 0.703526i
\(100\) 0 0
\(101\) 10.0711 + 10.0711i 1.00211 + 1.00211i 0.999998 + 0.00211093i \(0.000671930\pi\)
0.00211093 + 0.999998i \(0.499328\pi\)
\(102\) 0 0
\(103\) −11.3137 −1.11477 −0.557386 0.830253i \(-0.688196\pi\)
−0.557386 + 0.830253i \(0.688196\pi\)
\(104\) 0 0
\(105\) 1.00000 0.171573i 0.0975900 0.0167438i
\(106\) 0 0
\(107\) 5.00000 5.00000i 0.483368 0.483368i −0.422837 0.906206i \(-0.638966\pi\)
0.906206 + 0.422837i \(0.138966\pi\)
\(108\) 0 0
\(109\) 5.82843 + 5.82843i 0.558262 + 0.558262i 0.928812 0.370550i \(-0.120831\pi\)
−0.370550 + 0.928812i \(0.620831\pi\)
\(110\) 0 0
\(111\) −0.757359 4.41421i −0.0718854 0.418979i
\(112\) 0 0
\(113\) 1.65685i 0.155864i 0.996959 + 0.0779319i \(0.0248317\pi\)
−0.996959 + 0.0779319i \(0.975168\pi\)
\(114\) 0 0
\(115\) −3.17157 + 3.17157i −0.295751 + 0.295751i
\(116\) 0 0
\(117\) −8.07107 + 16.8995i −0.746170 + 1.56236i
\(118\) 0 0
\(119\) 1.17157i 0.107398i
\(120\) 0 0
\(121\) 18.3137i 1.66488i
\(122\) 0 0
\(123\) −0.343146 + 0.485281i −0.0309404 + 0.0437563i
\(124\) 0 0
\(125\) 4.00000 4.00000i 0.357771 0.357771i
\(126\) 0 0
\(127\) 15.6569i 1.38932i 0.719338 + 0.694661i \(0.244445\pi\)
−0.719338 + 0.694661i \(0.755555\pi\)
\(128\) 0 0
\(129\) 9.24264 1.58579i 0.813769 0.139621i
\(130\) 0 0
\(131\) 4.07107 + 4.07107i 0.355691 + 0.355691i 0.862222 0.506531i \(-0.169072\pi\)
−0.506531 + 0.862222i \(0.669072\pi\)
\(132\) 0 0
\(133\) −0.414214 + 0.414214i −0.0359169 + 0.0359169i
\(134\) 0 0
\(135\) −1.48528 2.65685i −0.127833 0.228666i
\(136\) 0 0
\(137\) −7.65685 −0.654169 −0.327085 0.944995i \(-0.606066\pi\)
−0.327085 + 0.944995i \(0.606066\pi\)
\(138\) 0 0
\(139\) 4.41421 + 4.41421i 0.374409 + 0.374409i 0.869080 0.494671i \(-0.164712\pi\)
−0.494671 + 0.869080i \(0.664712\pi\)
\(140\) 0 0
\(141\) 5.65685 8.00000i 0.476393 0.673722i
\(142\) 0 0
\(143\) −33.7990 −2.82641
\(144\) 0 0
\(145\) −2.48528 −0.206391
\(146\) 0 0
\(147\) 1.00000 1.41421i 0.0824786 0.116642i
\(148\) 0 0
\(149\) 9.48528 + 9.48528i 0.777065 + 0.777065i 0.979331 0.202266i \(-0.0648306\pi\)
−0.202266 + 0.979331i \(0.564831\pi\)
\(150\) 0 0
\(151\) 17.6569 1.43689 0.718447 0.695581i \(-0.244853\pi\)
0.718447 + 0.695581i \(0.244853\pi\)
\(152\) 0 0
\(153\) 3.31371 1.17157i 0.267897 0.0947161i
\(154\) 0 0
\(155\) 2.68629 2.68629i 0.215768 0.215768i
\(156\) 0 0
\(157\) 2.89949 + 2.89949i 0.231405 + 0.231405i 0.813279 0.581874i \(-0.197680\pi\)
−0.581874 + 0.813279i \(0.697680\pi\)
\(158\) 0 0
\(159\) −14.0711 + 2.41421i −1.11591 + 0.191460i
\(160\) 0 0
\(161\) 7.65685i 0.603445i
\(162\) 0 0
\(163\) 1.82843 1.82843i 0.143213 0.143213i −0.631865 0.775078i \(-0.717710\pi\)
0.775078 + 0.631865i \(0.217710\pi\)
\(164\) 0 0
\(165\) 3.17157 4.48528i 0.246907 0.349179i
\(166\) 0 0
\(167\) 7.17157i 0.554953i −0.960732 0.277476i \(-0.910502\pi\)
0.960732 0.277476i \(-0.0894981\pi\)
\(168\) 0 0
\(169\) 25.9706i 1.99774i
\(170\) 0 0
\(171\) 1.58579 + 0.757359i 0.121268 + 0.0579167i
\(172\) 0 0
\(173\) 4.89949 4.89949i 0.372502 0.372502i −0.495886 0.868388i \(-0.665157\pi\)
0.868388 + 0.495886i \(0.165157\pi\)
\(174\) 0 0
\(175\) 4.65685i 0.352025i
\(176\) 0 0
\(177\) −4.17157 24.3137i −0.313555 1.82753i
\(178\) 0 0
\(179\) 15.0000 + 15.0000i 1.12115 + 1.12115i 0.991568 + 0.129584i \(0.0413643\pi\)
0.129584 + 0.991568i \(0.458636\pi\)
\(180\) 0 0
\(181\) −2.07107 + 2.07107i −0.153941 + 0.153941i −0.779876 0.625934i \(-0.784718\pi\)
0.625934 + 0.779876i \(0.284718\pi\)
\(182\) 0 0
\(183\) 5.82843 1.00000i 0.430850 0.0739221i
\(184\) 0 0
\(185\) 1.51472 0.111364
\(186\) 0 0
\(187\) 4.48528 + 4.48528i 0.327996 + 0.327996i
\(188\) 0 0
\(189\) −5.00000 1.41421i −0.363696 0.102869i
\(190\) 0 0
\(191\) 6.34315 0.458974 0.229487 0.973312i \(-0.426295\pi\)
0.229487 + 0.973312i \(0.426295\pi\)
\(192\) 0 0
\(193\) 15.6569 1.12701 0.563503 0.826114i \(-0.309454\pi\)
0.563503 + 0.826114i \(0.309454\pi\)
\(194\) 0 0
\(195\) −5.17157 3.65685i −0.370344 0.261873i
\(196\) 0 0
\(197\) −5.82843 5.82843i −0.415258 0.415258i 0.468307 0.883566i \(-0.344864\pi\)
−0.883566 + 0.468307i \(0.844864\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −2.89949 16.8995i −0.204515 1.19200i
\(202\) 0 0
\(203\) −3.00000 + 3.00000i −0.210559 + 0.210559i
\(204\) 0 0
\(205\) −0.142136 0.142136i −0.00992718 0.00992718i
\(206\) 0 0
\(207\) 21.6569 7.65685i 1.50526 0.532188i
\(208\) 0 0
\(209\) 3.17157i 0.219382i
\(210\) 0 0
\(211\) −5.00000 + 5.00000i −0.344214 + 0.344214i −0.857949 0.513735i \(-0.828262\pi\)
0.513735 + 0.857949i \(0.328262\pi\)
\(212\) 0 0
\(213\) 8.48528 + 6.00000i 0.581402 + 0.411113i
\(214\) 0 0
\(215\) 3.17157i 0.216299i
\(216\) 0 0
\(217\) 6.48528i 0.440250i
\(218\) 0 0
\(219\) 7.31371 + 5.17157i 0.494215 + 0.349463i
\(220\) 0 0
\(221\) 5.17157 5.17157i 0.347878 0.347878i
\(222\) 0 0
\(223\) 7.17157i 0.480244i 0.970743 + 0.240122i \(0.0771875\pi\)
−0.970743 + 0.240122i \(0.922813\pi\)
\(224\) 0 0
\(225\) −13.1716 + 4.65685i −0.878105 + 0.310457i
\(226\) 0 0
\(227\) 8.07107 + 8.07107i 0.535696 + 0.535696i 0.922262 0.386566i \(-0.126339\pi\)
−0.386566 + 0.922262i \(0.626339\pi\)
\(228\) 0 0
\(229\) 10.8995 10.8995i 0.720259 0.720259i −0.248399 0.968658i \(-0.579904\pi\)
0.968658 + 0.248399i \(0.0799044\pi\)
\(230\) 0 0
\(231\) −1.58579 9.24264i −0.104337 0.608121i
\(232\) 0 0
\(233\) −1.31371 −0.0860639 −0.0430320 0.999074i \(-0.513702\pi\)
−0.0430320 + 0.999074i \(0.513702\pi\)
\(234\) 0 0
\(235\) 2.34315 + 2.34315i 0.152850 + 0.152850i
\(236\) 0 0
\(237\) −2.82843 2.00000i −0.183726 0.129914i
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 0 0
\(241\) 0.343146 0.0221040 0.0110520 0.999939i \(-0.496482\pi\)
0.0110520 + 0.999939i \(0.496482\pi\)
\(242\) 0 0
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 0 0
\(245\) 0.414214 + 0.414214i 0.0264631 + 0.0264631i
\(246\) 0 0
\(247\) 3.65685 0.232680
\(248\) 0 0
\(249\) −21.4853 + 3.68629i −1.36157 + 0.233609i
\(250\) 0 0
\(251\) −2.41421 + 2.41421i −0.152384 + 0.152384i −0.779182 0.626798i \(-0.784365\pi\)
0.626798 + 0.779182i \(0.284365\pi\)
\(252\) 0 0
\(253\) 29.3137 + 29.3137i 1.84294 + 1.84294i
\(254\) 0 0
\(255\) 0.201010 + 1.17157i 0.0125877 + 0.0733667i
\(256\) 0 0
\(257\) 26.8284i 1.67351i 0.547576 + 0.836756i \(0.315551\pi\)
−0.547576 + 0.836756i \(0.684449\pi\)
\(258\) 0 0
\(259\) 1.82843 1.82843i 0.113613 0.113613i
\(260\) 0 0
\(261\) 11.4853 + 5.48528i 0.710921 + 0.339530i
\(262\) 0 0
\(263\) 11.6569i 0.718792i 0.933185 + 0.359396i \(0.117017\pi\)
−0.933185 + 0.359396i \(0.882983\pi\)
\(264\) 0 0
\(265\) 4.82843i 0.296608i
\(266\) 0 0
\(267\) −15.6569 + 22.1421i −0.958184 + 1.35508i
\(268\) 0 0
\(269\) 5.58579 5.58579i 0.340571 0.340571i −0.516011 0.856582i \(-0.672584\pi\)
0.856582 + 0.516011i \(0.172584\pi\)
\(270\) 0 0
\(271\) 16.8284i 1.02225i −0.859505 0.511127i \(-0.829228\pi\)
0.859505 0.511127i \(-0.170772\pi\)
\(272\) 0 0
\(273\) −10.6569 + 1.82843i −0.644982 + 0.110661i
\(274\) 0 0
\(275\) −17.8284 17.8284i −1.07509 1.07509i
\(276\) 0 0
\(277\) 6.31371 6.31371i 0.379354 0.379354i −0.491515 0.870869i \(-0.663557\pi\)
0.870869 + 0.491515i \(0.163557\pi\)
\(278\) 0 0
\(279\) −18.3431 + 6.48528i −1.09818 + 0.388264i
\(280\) 0 0
\(281\) 6.68629 0.398871 0.199435 0.979911i \(-0.436089\pi\)
0.199435 + 0.979911i \(0.436089\pi\)
\(282\) 0 0
\(283\) 12.8995 + 12.8995i 0.766795 + 0.766795i 0.977541 0.210746i \(-0.0675892\pi\)
−0.210746 + 0.977541i \(0.567589\pi\)
\(284\) 0 0
\(285\) −0.343146 + 0.485281i −0.0203262 + 0.0287456i
\(286\) 0 0
\(287\) −0.343146 −0.0202553
\(288\) 0 0
\(289\) 15.6274 0.919260
\(290\) 0 0
\(291\) −2.00000 + 2.82843i −0.117242 + 0.165805i
\(292\) 0 0
\(293\) −9.24264 9.24264i −0.539961 0.539961i 0.383557 0.923517i \(-0.374699\pi\)
−0.923517 + 0.383557i \(0.874699\pi\)
\(294\) 0 0
\(295\) 8.34315 0.485757
\(296\) 0 0
\(297\) −24.5563 + 13.7279i −1.42490 + 0.796575i
\(298\) 0 0
\(299\) 33.7990 33.7990i 1.95465 1.95465i
\(300\) 0 0
\(301\) 3.82843 + 3.82843i 0.220667 + 0.220667i
\(302\) 0 0
\(303\) 24.3137 4.17157i 1.39679 0.239651i
\(304\) 0 0
\(305\) 2.00000i 0.114520i
\(306\) 0 0
\(307\) 14.8995 14.8995i 0.850359 0.850359i −0.139818 0.990177i \(-0.544652\pi\)
0.990177 + 0.139818i \(0.0446518\pi\)
\(308\) 0 0
\(309\) −11.3137 + 16.0000i −0.643614 + 0.910208i
\(310\) 0 0
\(311\) 1.51472i 0.0858918i −0.999077 0.0429459i \(-0.986326\pi\)
0.999077 0.0429459i \(-0.0136743\pi\)
\(312\) 0 0
\(313\) 20.4853i 1.15790i 0.815364 + 0.578948i \(0.196537\pi\)
−0.815364 + 0.578948i \(0.803463\pi\)
\(314\) 0 0
\(315\) 0.757359 1.58579i 0.0426724 0.0893489i
\(316\) 0 0
\(317\) −13.1421 + 13.1421i −0.738136 + 0.738136i −0.972217 0.234081i \(-0.924792\pi\)
0.234081 + 0.972217i \(0.424792\pi\)
\(318\) 0 0
\(319\) 22.9706i 1.28610i
\(320\) 0 0
\(321\) −2.07107 12.0711i −0.115596 0.673741i
\(322\) 0 0
\(323\) −0.485281 0.485281i −0.0270018 0.0270018i
\(324\) 0 0
\(325\) −20.5563 + 20.5563i −1.14026 + 1.14026i
\(326\) 0 0
\(327\) 14.0711 2.41421i 0.778132 0.133506i
\(328\) 0 0
\(329\) 5.65685 0.311872
\(330\) 0 0
\(331\) −17.1421 17.1421i −0.942217 0.942217i 0.0562024 0.998419i \(-0.482101\pi\)
−0.998419 + 0.0562024i \(0.982101\pi\)
\(332\) 0 0
\(333\) −7.00000 3.34315i −0.383598 0.183203i
\(334\) 0 0
\(335\) 5.79899 0.316833
\(336\) 0 0
\(337\) 25.3137 1.37893 0.689463 0.724321i \(-0.257847\pi\)
0.689463 + 0.724321i \(0.257847\pi\)
\(338\) 0 0
\(339\) 2.34315 + 1.65685i 0.127262 + 0.0899880i
\(340\) 0 0
\(341\) −24.8284 24.8284i −1.34453 1.34453i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 1.31371 + 7.65685i 0.0707277 + 0.412231i
\(346\) 0 0
\(347\) −13.1421 + 13.1421i −0.705507 + 0.705507i −0.965587 0.260080i \(-0.916251\pi\)
0.260080 + 0.965587i \(0.416251\pi\)
\(348\) 0 0
\(349\) −2.07107 2.07107i −0.110862 0.110862i 0.649500 0.760362i \(-0.274978\pi\)
−0.760362 + 0.649500i \(0.774978\pi\)
\(350\) 0 0
\(351\) 15.8284 + 28.3137i 0.844859 + 1.51127i
\(352\) 0 0
\(353\) 8.48528i 0.451626i −0.974171 0.225813i \(-0.927496\pi\)
0.974171 0.225813i \(-0.0725038\pi\)
\(354\) 0 0
\(355\) −2.48528 + 2.48528i −0.131905 + 0.131905i
\(356\) 0 0
\(357\) 1.65685 + 1.17157i 0.0876900 + 0.0620062i
\(358\) 0 0
\(359\) 20.3431i 1.07367i 0.843687 + 0.536835i \(0.180380\pi\)
−0.843687 + 0.536835i \(0.819620\pi\)
\(360\) 0 0
\(361\) 18.6569i 0.981940i
\(362\) 0 0
\(363\) −25.8995 18.3137i −1.35937 0.961220i
\(364\) 0 0
\(365\) −2.14214 + 2.14214i −0.112125 + 0.112125i
\(366\) 0 0
\(367\) 16.1421i 0.842613i 0.906918 + 0.421306i \(0.138428\pi\)
−0.906918 + 0.421306i \(0.861572\pi\)
\(368\) 0 0
\(369\) 0.343146 + 0.970563i 0.0178635 + 0.0505255i
\(370\) 0 0
\(371\) −5.82843 5.82843i −0.302597 0.302597i
\(372\) 0 0
\(373\) −8.31371 + 8.31371i −0.430468 + 0.430468i −0.888787 0.458320i \(-0.848451\pi\)
0.458320 + 0.888787i \(0.348451\pi\)
\(374\) 0 0
\(375\) −1.65685 9.65685i −0.0855596 0.498678i
\(376\) 0 0
\(377\) 26.4853 1.36406
\(378\) 0 0
\(379\) 27.1421 + 27.1421i 1.39420 + 1.39420i 0.815645 + 0.578553i \(0.196382\pi\)
0.578553 + 0.815645i \(0.303618\pi\)
\(380\) 0 0
\(381\) 22.1421 + 15.6569i 1.13438 + 0.802125i
\(382\) 0 0
\(383\) −19.3137 −0.986884 −0.493442 0.869779i \(-0.664262\pi\)
−0.493442 + 0.869779i \(0.664262\pi\)
\(384\) 0 0
\(385\) 3.17157 0.161638
\(386\) 0 0
\(387\) 7.00000 14.6569i 0.355830 0.745050i
\(388\) 0 0
\(389\) −19.9706 19.9706i −1.01255 1.01255i −0.999920 0.0126275i \(-0.995980\pi\)
−0.0126275 0.999920i \(1.49598\pi\)
\(390\) 0 0
\(391\) −8.97056 −0.453661
\(392\) 0 0
\(393\) 9.82843 1.68629i 0.495779 0.0850622i
\(394\) 0 0
\(395\) 0.828427 0.828427i 0.0416827 0.0416827i
\(396\) 0 0
\(397\) −23.7279 23.7279i −1.19087 1.19087i −0.976823 0.214047i \(-0.931335\pi\)
−0.214047 0.976823i \(-0.568665\pi\)
\(398\) 0 0
\(399\) 0.171573 + 1.00000i 0.00858939 + 0.0500626i
\(400\) 0 0
\(401\) 19.3137i 0.964481i −0.876039 0.482240i \(-0.839823\pi\)
0.876039 0.482240i \(-0.160177\pi\)
\(402\) 0 0
\(403\) −28.6274 + 28.6274i −1.42603 + 1.42603i
\(404\) 0 0
\(405\) −5.24264 0.556349i −0.260509 0.0276452i
\(406\) 0 0
\(407\) 14.0000i 0.693954i
\(408\) 0 0
\(409\) 25.1716i 1.24465i −0.782757 0.622327i \(-0.786187\pi\)
0.782757 0.622327i \(-0.213813\pi\)
\(410\) 0 0
\(411\) −7.65685 + 10.8284i −0.377685 + 0.534127i
\(412\) 0 0
\(413\) 10.0711 10.0711i 0.495565 0.495565i
\(414\) 0 0
\(415\) 7.37258i 0.361906i
\(416\) 0 0
\(417\) 10.6569 1.82843i 0.521868 0.0895385i
\(418\) 0 0
\(419\) 13.2426 + 13.2426i 0.646945 + 0.646945i 0.952254 0.305308i \(-0.0987595\pi\)
−0.305308 + 0.952254i \(0.598759\pi\)
\(420\) 0 0
\(421\) −1.68629 + 1.68629i −0.0821848 + 0.0821848i −0.747004 0.664819i \(-0.768509\pi\)
0.664819 + 0.747004i \(0.268509\pi\)
\(422\) 0 0
\(423\) −5.65685 16.0000i −0.275046 0.777947i
\(424\) 0 0
\(425\) 5.45584 0.264647
\(426\) 0 0
\(427\) 2.41421 + 2.41421i 0.116832 + 0.116832i
\(428\) 0 0
\(429\) −33.7990 + 47.7990i −1.63183 + 2.30776i
\(430\) 0 0
\(431\) 3.31371 0.159616 0.0798079 0.996810i \(-0.474569\pi\)
0.0798079 + 0.996810i \(0.474569\pi\)
\(432\) 0 0
\(433\) −14.6863 −0.705778 −0.352889 0.935665i \(-0.614801\pi\)
−0.352889 + 0.935665i \(0.614801\pi\)
\(434\) 0 0
\(435\) −2.48528 + 3.51472i −0.119160 + 0.168518i
\(436\) 0 0
\(437\) −3.17157 3.17157i −0.151717 0.151717i
\(438\) 0 0
\(439\) 0.970563 0.0463224 0.0231612 0.999732i \(-0.492627\pi\)
0.0231612 + 0.999732i \(0.492627\pi\)
\(440\) 0 0
\(441\) −1.00000 2.82843i −0.0476190 0.134687i
\(442\) 0 0
\(443\) −16.6569 + 16.6569i −0.791391 + 0.791391i −0.981720 0.190329i \(-0.939044\pi\)
0.190329 + 0.981720i \(0.439044\pi\)
\(444\) 0 0
\(445\) −6.48528 6.48528i −0.307432 0.307432i
\(446\) 0 0
\(447\) 22.8995 3.92893i 1.08311 0.185832i
\(448\) 0 0
\(449\) 12.9706i 0.612119i 0.952012 + 0.306059i \(0.0990106\pi\)
−0.952012 + 0.306059i \(0.900989\pi\)
\(450\) 0 0
\(451\) −1.31371 + 1.31371i −0.0618601 + 0.0618601i
\(452\) 0 0
\(453\) 17.6569 24.9706i 0.829591 1.17322i
\(454\) 0 0
\(455\) 3.65685i 0.171436i
\(456\) 0 0
\(457\) 29.9411i 1.40059i 0.713855 + 0.700293i \(0.246947\pi\)
−0.713855 + 0.700293i \(0.753053\pi\)
\(458\) 0 0
\(459\) 1.65685 5.85786i 0.0773353 0.273422i
\(460\) 0 0
\(461\) −22.4142 + 22.4142i −1.04393 + 1.04393i −0.0449445 + 0.998989i \(0.514311\pi\)
−0.998989 + 0.0449445i \(0.985689\pi\)
\(462\) 0 0
\(463\) 11.6569i 0.541740i 0.962616 + 0.270870i \(0.0873113\pi\)
−0.962616 + 0.270870i \(0.912689\pi\)
\(464\) 0 0
\(465\) −1.11270 6.48528i −0.0516002 0.300748i
\(466\) 0 0
\(467\) 14.4142 + 14.4142i 0.667010 + 0.667010i 0.957023 0.290013i \(-0.0936595\pi\)
−0.290013 + 0.957023i \(0.593659\pi\)
\(468\) 0 0
\(469\) 7.00000 7.00000i 0.323230 0.323230i
\(470\) 0 0
\(471\) 7.00000 1.20101i 0.322543 0.0553396i
\(472\) 0 0
\(473\) 29.3137 1.34785
\(474\) 0 0
\(475\) 1.92893 + 1.92893i 0.0885055 + 0.0885055i
\(476\) 0 0
\(477\) −10.6569 + 22.3137i −0.487944 + 1.02167i
\(478\) 0 0
\(479\) −27.3137 −1.24800 −0.623998 0.781426i \(-0.714493\pi\)
−0.623998 + 0.781426i \(0.714493\pi\)
\(480\) 0 0
\(481\) −16.1421 −0.736018
\(482\) 0 0
\(483\) 10.8284 + 7.65685i 0.492710 + 0.348399i
\(484\) 0 0
\(485\) −0.828427 0.828427i −0.0376169 0.0376169i
\(486\) 0 0
\(487\) 16.2843 0.737911 0.368955 0.929447i \(-0.379716\pi\)
0.368955 + 0.929447i \(0.379716\pi\)
\(488\) 0 0
\(489\) −0.757359 4.41421i −0.0342490 0.199618i
\(490\) 0 0
\(491\) −10.3137 + 10.3137i −0.465451 + 0.465451i −0.900437 0.434986i \(-0.856753\pi\)
0.434986 + 0.900437i \(0.356753\pi\)
\(492\) 0 0
\(493\) −3.51472 3.51472i −0.158295 0.158295i
\(494\) 0 0
\(495\) −3.17157 8.97056i −0.142552 0.403197i
\(496\) 0 0
\(497\) 6.00000i 0.269137i
\(498\) 0 0
\(499\) −5.68629 + 5.68629i −0.254553 + 0.254553i −0.822834 0.568281i \(-0.807609\pi\)
0.568281 + 0.822834i \(0.307609\pi\)
\(500\) 0 0
\(501\) −10.1421 7.17157i −0.453117 0.320402i
\(502\) 0 0
\(503\) 16.8284i 0.750342i 0.926956 + 0.375171i \(0.122416\pi\)
−0.926956 + 0.375171i \(0.877584\pi\)
\(504\) 0 0
\(505\) 8.34315i 0.371265i
\(506\) 0 0
\(507\) 36.7279 + 25.9706i 1.63114 + 1.15339i
\(508\) 0 0
\(509\) 7.24264 7.24264i 0.321024 0.321024i −0.528136 0.849160i \(-0.677109\pi\)
0.849160 + 0.528136i \(0.177109\pi\)
\(510\) 0 0
\(511\) 5.17157i 0.228777i
\(512\) 0 0
\(513\) 2.65685 1.48528i 0.117303 0.0655768i
\(514\) 0 0
\(515\) −4.68629 4.68629i −0.206503 0.206503i
\(516\) 0 0
\(517\) 21.6569 21.6569i 0.952467 0.952467i
\(518\) 0 0
\(519\) −2.02944 11.8284i −0.0890824 0.519210i
\(520\) 0 0
\(521\) 13.3137 0.583284 0.291642 0.956528i \(-0.405798\pi\)
0.291642 + 0.956528i \(0.405798\pi\)
\(522\) 0 0
\(523\) −21.0416 21.0416i −0.920086 0.920086i 0.0769488 0.997035i \(-0.475482\pi\)
−0.997035 + 0.0769488i \(0.975482\pi\)
\(524\) 0 0
\(525\) −6.58579 4.65685i −0.287427 0.203242i
\(526\) 0 0
\(527\) 7.59798 0.330973
\(528\) 0 0
\(529\) −35.6274 −1.54902
\(530\) 0 0
\(531\) −38.5563 18.4142i −1.67320 0.799109i
\(532\) 0 0
\(533\) 1.51472 + 1.51472i 0.0656097 + 0.0656097i
\(534\) 0 0
\(535\) 4.14214 0.179080
\(536\) 0 0
\(537\) 36.2132 6.21320i 1.56272 0.268120i
\(538\) 0 0
\(539\) 3.82843 3.82843i 0.164902 0.164902i
\(540\) 0 0
\(541\) −21.0000 21.0000i −0.902861 0.902861i 0.0928222 0.995683i \(-0.470411\pi\)
−0.995683 + 0.0928222i \(0.970411\pi\)
\(542\) 0 0
\(543\) 0.857864 + 5.00000i 0.0368145 + 0.214571i
\(544\) 0 0
\(545\) 4.82843i 0.206827i
\(546\) 0 0
\(547\) 17.1421 17.1421i 0.732945 0.732945i −0.238257 0.971202i \(-0.576576\pi\)
0.971202 + 0.238257i \(0.0765761\pi\)
\(548\) 0 0
\(549\) 4.41421 9.24264i 0.188394 0.394466i
\(550\) 0 0
\(551\) 2.48528i 0.105877i
\(552\) 0 0
\(553\) 2.00000i 0.0850487i
\(554\) 0 0
\(555\) 1.51472 2.14214i 0.0642962 0.0909286i
\(556\) 0 0
\(557\) 15.1421 15.1421i 0.641593 0.641593i −0.309354 0.950947i \(-0.600113\pi\)
0.950947 + 0.309354i \(0.100113\pi\)
\(558\) 0 0
\(559\) 33.7990i 1.42954i
\(560\) 0 0
\(561\) 10.8284 1.85786i 0.457177 0.0784391i
\(562\) 0 0
\(563\) 19.5858 + 19.5858i 0.825442 + 0.825442i 0.986883 0.161440i \(-0.0516138\pi\)
−0.161440 + 0.986883i \(0.551614\pi\)
\(564\) 0 0
\(565\) −0.686292 + 0.686292i −0.0288725 + 0.0288725i
\(566\) 0 0
\(567\) −7.00000 + 5.65685i −0.293972 + 0.237566i
\(568\) 0 0
\(569\) 32.6274 1.36781 0.683906 0.729570i \(-0.260280\pi\)
0.683906 + 0.729570i \(0.260280\pi\)
\(570\) 0 0
\(571\) 6.17157 + 6.17157i 0.258272 + 0.258272i 0.824351 0.566079i \(-0.191540\pi\)
−0.566079 + 0.824351i \(0.691540\pi\)
\(572\) 0 0
\(573\) 6.34315 8.97056i 0.264989 0.374751i
\(574\) 0 0
\(575\) 35.6569 1.48699
\(576\) 0 0
\(577\) −0.343146 −0.0142853 −0.00714267 0.999974i \(-0.502274\pi\)
−0.00714267 + 0.999974i \(0.502274\pi\)
\(578\) 0 0
\(579\) 15.6569 22.1421i 0.650677 0.920196i
\(580\) 0 0
\(581\) −8.89949 8.89949i −0.369213 0.369213i
\(582\) 0 0
\(583\) −44.6274 −1.84828
\(584\) 0 0
\(585\) −10.3431 + 3.65685i −0.427636 + 0.151192i
\(586\) 0 0
\(587\) −16.0711 + 16.0711i −0.663324 + 0.663324i −0.956162 0.292838i \(-0.905400\pi\)
0.292838 + 0.956162i \(0.405400\pi\)
\(588\) 0 0
\(589\) 2.68629 + 2.68629i 0.110687 + 0.110687i
\(590\) 0 0
\(591\) −14.0711 + 2.41421i −0.578806 + 0.0993075i
\(592\) 0 0
\(593\) 1.85786i 0.0762933i 0.999272 + 0.0381467i \(0.0121454\pi\)
−0.999272 + 0.0381467i \(0.987855\pi\)
\(594\) 0 0
\(595\) −0.485281 + 0.485281i −0.0198946 + 0.0198946i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 42.9706i 1.75573i −0.478909 0.877865i \(-0.658967\pi\)
0.478909 0.877865i \(-0.341033\pi\)
\(600\) 0 0
\(601\) 16.4853i 0.672449i −0.941782 0.336224i \(-0.890850\pi\)
0.941782 0.336224i \(-0.109150\pi\)
\(602\) 0 0
\(603\) −26.7990 12.7990i −1.09134 0.521215i
\(604\) 0 0
\(605\) 7.58579 7.58579i 0.308406 0.308406i
\(606\) 0 0
\(607\) 21.1127i 0.856938i −0.903556 0.428469i \(-0.859053\pi\)
0.903556 0.428469i \(-0.140947\pi\)
\(608\) 0 0
\(609\) 1.24264 + 7.24264i 0.0503543 + 0.293487i
\(610\) 0 0
\(611\) −24.9706 24.9706i −1.01020 1.01020i
\(612\) 0 0
\(613\) −14.1716 + 14.1716i −0.572384 + 0.572384i −0.932794 0.360410i \(-0.882637\pi\)
0.360410 + 0.932794i \(0.382637\pi\)
\(614\) 0 0
\(615\) −0.343146 + 0.0588745i −0.0138370 + 0.00237405i
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) −26.4142 26.4142i −1.06168 1.06168i −0.997969 0.0637083i \(-0.979707\pi\)
−0.0637083 0.997969i \(-0.520293\pi\)
\(620\) 0 0
\(621\) 10.8284 38.2843i 0.434530 1.53629i
\(622\) 0 0
\(623\) −15.6569 −0.627279
\(624\) 0 0
\(625\) −19.9706 −0.798823
\(626\) 0 0
\(627\) 4.48528 + 3.17157i 0.179125 + 0.126660i
\(628\) 0 0
\(629\) 2.14214 + 2.14214i 0.0854125 + 0.0854125i
\(630\) 0 0
\(631\) 13.6569 0.543671 0.271835 0.962344i \(-0.412369\pi\)
0.271835 + 0.962344i \(0.412369\pi\)
\(632\) 0 0
\(633\) 2.07107 + 12.0711i 0.0823176 + 0.479782i
\(634\) 0 0
\(635\) −6.48528 + 6.48528i −0.257361 + 0.257361i
\(636\) 0 0
\(637\) −4.41421 4.41421i −0.174898 0.174898i
\(638\) 0 0
\(639\) 16.9706 6.00000i 0.671345 0.237356i
\(640\) 0 0
\(641\) 45.2548i 1.78746i 0.448607 + 0.893729i \(0.351920\pi\)
−0.448607 + 0.893729i \(0.648080\pi\)
\(642\) 0 0
\(643\) 21.0416 21.0416i 0.829801 0.829801i −0.157688 0.987489i \(-0.550404\pi\)
0.987489 + 0.157688i \(0.0504040\pi\)
\(644\) 0 0
\(645\) 4.48528 + 3.17157i 0.176608 + 0.124881i
\(646\) 0 0
\(647\) 16.1421i 0.634613i −0.948323 0.317306i \(-0.897222\pi\)
0.948323 0.317306i \(-0.102778\pi\)
\(648\) 0 0
\(649\) 77.1127i 3.02694i
\(650\) 0 0
\(651\) −9.17157 6.48528i −0.359462 0.254178i
\(652\) 0 0
\(653\) 11.3431 11.3431i 0.443892 0.443892i −0.449426 0.893318i \(-0.648371\pi\)
0.893318 + 0.449426i \(0.148371\pi\)
\(654\) 0 0
\(655\) 3.37258i 0.131778i
\(656\) 0 0
\(657\) 14.6274 5.17157i 0.570670 0.201762i
\(658\) 0 0
\(659\) −25.4853 25.4853i −0.992766 0.992766i 0.00720841 0.999974i \(-0.497705\pi\)
−0.999974 + 0.00720841i \(0.997705\pi\)
\(660\) 0 0
\(661\) 11.3848 11.3848i 0.442816 0.442816i −0.450141 0.892957i \(-0.648626\pi\)
0.892957 + 0.450141i \(0.148626\pi\)
\(662\) 0 0
\(663\) −2.14214 12.4853i −0.0831937 0.484888i
\(664\) 0 0
\(665\) −0.343146 −0.0133066
\(666\) 0 0
\(667\) −22.9706 22.9706i −0.889424 0.889424i
\(668\) 0 0
\(669\) 10.1421 + 7.17157i 0.392118 + 0.277269i
\(670\) 0 0
\(671\) 18.4853 0.713616
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) −6.58579 + 23.2843i −0.253487 + 0.896212i
\(676\) 0 0
\(677\) 20.8995 + 20.8995i 0.803233 + 0.803233i 0.983599 0.180367i \(-0.0577284\pi\)
−0.180367 + 0.983599i \(0.557728\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) 0 0
\(681\) 19.4853 3.34315i 0.746678 0.128110i
\(682\) 0 0
\(683\) 0.313708 0.313708i 0.0120037 0.0120037i −0.701079 0.713083i \(-0.747298\pi\)
0.713083 + 0.701079i \(0.247298\pi\)
\(684\) 0 0
\(685\) −3.17157 3.17157i −0.121180 0.121180i
\(686\) 0 0
\(687\) −4.51472 26.3137i −0.172247 1.00393i
\(688\) 0 0
\(689\) 51.4558i 1.96031i
\(690\) 0 0
\(691\) 14.8995 14.8995i 0.566803 0.566803i −0.364428 0.931232i \(-0.618735\pi\)
0.931232 + 0.364428i \(0.118735\pi\)
\(692\) 0 0
\(693\) −14.6569 7.00000i −0.556768 0.265908i
\(694\) 0 0
\(695\) 3.65685i 0.138712i
\(696\) 0 0
\(697\) 0.402020i 0.0152276i
\(698\) 0 0
\(699\) −1.31371 + 1.85786i −0.0496890 + 0.0702709i
\(700\) 0 0
\(701\) −0.656854 + 0.656854i −0.0248090 + 0.0248090i −0.719402 0.694593i \(-0.755584\pi\)
0.694593 + 0.719402i \(0.255584\pi\)
\(702\) 0 0
\(703\) 1.51472i 0.0571287i
\(704\) 0 0
\(705\) 5.65685 0.970563i 0.213049 0.0365535i
\(706\) 0 0
\(707\) 10.0711 + 10.0711i 0.378761 + 0.378761i
\(708\) 0 0
\(709\) −2.17157 + 2.17157i −0.0815551 + 0.0815551i −0.746708 0.665152i \(-0.768367\pi\)
0.665152 + 0.746708i \(0.268367\pi\)
\(710\) 0 0
\(711\) −5.65685 + 2.00000i −0.212149 + 0.0750059i
\(712\) 0 0
\(713\) 49.6569 1.85966
\(714\) 0 0
\(715\) −14.0000 14.0000i −0.523570 0.523570i
\(716\) 0 0
\(717\) −11.3137 + 16.0000i −0.422518 + 0.597531i
\(718\) 0 0
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) −11.3137 −0.421345
\(722\) 0 0
\(723\) 0.343146 0.485281i 0.0127617 0.0180478i
\(724\) 0 0
\(725\) 13.9706 + 13.9706i 0.518854 + 0.518854i
\(726\) 0 0
\(727\) 35.3137 1.30971 0.654856 0.755753i \(-0.272729\pi\)
0.654856 + 0.755753i \(0.272729\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) −4.48528 + 4.48528i −0.165894 + 0.165894i
\(732\) 0 0
\(733\) −2.27208 2.27208i −0.0839211 0.0839211i 0.663900 0.747821i \(-0.268900\pi\)
−0.747821 + 0.663900i \(0.768900\pi\)
\(734\) 0 0
\(735\) 1.00000 0.171573i 0.0368856 0.00632856i
\(736\) 0 0
\(737\) 53.5980i 1.97431i
\(738\) 0 0
\(739\) 21.8284 21.8284i 0.802972 0.802972i −0.180587 0.983559i \(-0.557800\pi\)
0.983559 + 0.180587i \(0.0577998\pi\)
\(740\) 0 0
\(741\) 3.65685 5.17157i 0.134338 0.189982i
\(742\) 0 0
\(743\) 4.34315i 0.159335i 0.996822 + 0.0796673i \(0.0253858\pi\)
−0.996822 + 0.0796673i \(0.974614\pi\)
\(744\) 0 0
\(745\) 7.85786i 0.287890i
\(746\) 0 0
\(747\) −16.2721 + 34.0711i −0.595364 + 1.24660i
\(748\) 0 0
\(749\) 5.00000 5.00000i 0.182696 0.182696i
\(750\) 0 0
\(751\) 18.6863i 0.681872i −0.940086 0.340936i \(-0.889256\pi\)
0.940086 0.340936i \(-0.110744\pi\)
\(752\) 0 0
\(753\) 1.00000 + 5.82843i 0.0364420 + 0.212400i
\(754\) 0 0
\(755\) 7.31371 + 7.31371i 0.266173 + 0.266173i
\(756\) 0 0
\(757\) 14.5147 14.5147i 0.527546 0.527546i −0.392294 0.919840i \(-0.628318\pi\)
0.919840 + 0.392294i \(0.128318\pi\)
\(758\) 0 0
\(759\) 70.7696 12.1421i 2.56877 0.440732i
\(760\) 0 0
\(761\) −36.6274 −1.32774 −0.663871 0.747847i \(-0.731088\pi\)
−0.663871 + 0.747847i \(0.731088\pi\)
\(762\) 0 0
\(763\) 5.82843 + 5.82843i 0.211003 + 0.211003i
\(764\) 0 0
\(765\) 1.85786 + 0.887302i 0.0671712 + 0.0320805i
\(766\) 0 0
\(767\) −88.9117 −3.21041
\(768\) 0 0
\(769\) 24.3431 0.877836 0.438918 0.898527i \(-0.355362\pi\)
0.438918 + 0.898527i \(0.355362\pi\)
\(770\) 0 0
\(771\) 37.9411 + 26.8284i 1.36642 + 0.966202i
\(772\) 0 0
\(773\) −36.5563 36.5563i −1.31484 1.31484i −0.917802 0.397039i \(-0.870038\pi\)
−0.397039 0.917802i \(1.37004\pi\)
\(774\) 0 0
\(775\) −30.2010 −1.08485
\(776\) 0 0
\(777\) −0.757359 4.41421i −0.0271701 0.158359i
\(778\) 0 0
\(779\) 0.142136 0.142136i 0.00509254 0.00509254i
\(780\) 0 0
\(781\) 22.9706 + 22.9706i 0.821951 + 0.821951i
\(782\) 0 0
\(783\) 19.2426 10.7574i 0.687676 0.384437i
\(784\) 0 0
\(785\) 2.40202i 0.0857318i
\(786\) 0 0
\(787\) −23.0416 + 23.0416i −0.821345 + 0.821345i −0.986301 0.164956i \(-0.947252\pi\)
0.164956 + 0.986301i \(0.447252\pi\)
\(788\) 0 0
\(789\) 16.4853 + 11.6569i 0.586892 + 0.414995i
\(790\) 0 0
\(791\) 1.65685i 0.0589110i
\(792\) 0 0
\(793\) 21.3137i 0.756872i
\(794\) 0 0
\(795\) −6.82843 4.82843i −0.242179 0.171247i
\(796\) 0 0
\(797\) −34.4142 + 34.4142i −1.21901 + 1.21901i −0.251036 + 0.967978i \(0.580771\pi\)
−0.967978 + 0.251036i \(0.919229\pi\)
\(798\) 0 0
\(799\) 6.62742i 0.234461i
\(800\) 0 0
\(801\) 15.6569 + 44.2843i 0.553208 + 1.56471i
\(802\) 0 0
\(803\) 19.7990