Properties

Label 768.2.o.b.287.4
Level 768
Weight 2
Character 768.287
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 287.4
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +O(q^{10})\) \(q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +(-1.85010 + 4.46654i) q^{11} +(-3.76813 + 1.56081i) q^{13} +(-4.15344 + 1.43465i) q^{15} +3.52935 q^{17} +(1.87141 + 4.51799i) q^{19} +(3.92609 + 0.236307i) q^{21} +(-2.48603 + 2.48603i) q^{23} +(-1.01571 - 1.01571i) q^{25} +(4.27370 - 2.95558i) q^{27} +(0.681149 - 0.282141i) q^{29} -4.63882i q^{31} +(7.91483 - 2.73389i) q^{33} +(2.20469 + 5.32259i) q^{35} +(-4.35102 - 1.80225i) q^{37} +(6.35238 + 3.09064i) q^{39} +(0.606628 + 0.606628i) q^{41} +(-0.565994 - 0.234442i) q^{43} +(6.63157 + 3.73499i) q^{45} -1.04074i q^{47} +1.84333i q^{49} +(-4.05505 - 4.57445i) q^{51} +(5.29738 + 2.19425i) q^{53} +(8.67289 + 8.67289i) q^{55} +(3.70568 - 7.61652i) q^{57} +(2.26739 + 0.939185i) q^{59} +(5.63874 + 13.6131i) q^{61} +(-4.20460 - 5.36017i) q^{63} +10.3474i q^{65} +(-10.1483 + 4.20357i) q^{67} +(6.07851 + 0.365859i) q^{69} +(-1.52242 - 1.52242i) q^{71} +(-10.0596 + 10.0596i) q^{73} +(-0.149478 + 2.48349i) q^{75} +(-4.20127 - 10.1428i) q^{77} -5.48744 q^{79} +(-8.74105 - 2.14339i) q^{81} +(-3.39246 + 1.40520i) q^{83} +(3.42655 - 8.27243i) q^{85} +(-1.14829 - 0.558681i) q^{87} +(-0.460940 + 0.460940i) q^{89} +(3.54433 - 8.55678i) q^{91} +(-6.01245 + 5.32977i) q^{93} +12.4066 q^{95} -3.50976 q^{97} +(-12.6372 - 7.11743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(3\) −1.14895 1.29612i −0.663346 0.748312i
\(4\) 0 0
\(5\) 0.970873 2.34389i 0.434188 1.04822i −0.543736 0.839257i \(-0.682991\pi\)
0.977923 0.208965i \(-0.0670095\pi\)
\(6\) 0 0
\(7\) −1.60572 + 1.60572i −0.606905 + 0.606905i −0.942136 0.335231i \(-0.891186\pi\)
0.335231 + 0.942136i \(0.391186\pi\)
\(8\) 0 0
\(9\) −0.359830 + 2.97834i −0.119943 + 0.992781i
\(10\) 0 0
\(11\) −1.85010 + 4.46654i −0.557827 + 1.34671i 0.353657 + 0.935375i \(0.384938\pi\)
−0.911483 + 0.411337i \(0.865062\pi\)
\(12\) 0 0
\(13\) −3.76813 + 1.56081i −1.04509 + 0.432891i −0.838137 0.545460i \(-0.816355\pi\)
−0.206954 + 0.978351i \(0.566355\pi\)
\(14\) 0 0
\(15\) −4.15344 + 1.43465i −1.07241 + 0.370426i
\(16\) 0 0
\(17\) 3.52935 0.855994 0.427997 0.903780i \(-0.359219\pi\)
0.427997 + 0.903780i \(0.359219\pi\)
\(18\) 0 0
\(19\) 1.87141 + 4.51799i 0.429332 + 1.03650i 0.979500 + 0.201445i \(0.0645637\pi\)
−0.550168 + 0.835054i \(0.685436\pi\)
\(20\) 0 0
\(21\) 3.92609 + 0.236307i 0.856743 + 0.0515663i
\(22\) 0 0
\(23\) −2.48603 + 2.48603i −0.518374 + 0.518374i −0.917079 0.398705i \(-0.869460\pi\)
0.398705 + 0.917079i \(0.369460\pi\)
\(24\) 0 0
\(25\) −1.01571 1.01571i −0.203143 0.203143i
\(26\) 0 0
\(27\) 4.27370 2.95558i 0.822474 0.568803i
\(28\) 0 0
\(29\) 0.681149 0.282141i 0.126486 0.0523923i −0.318543 0.947909i \(-0.603193\pi\)
0.445029 + 0.895516i \(0.353193\pi\)
\(30\) 0 0
\(31\) 4.63882i 0.833157i −0.909100 0.416578i \(-0.863229\pi\)
0.909100 0.416578i \(-0.136771\pi\)
\(32\) 0 0
\(33\) 7.91483 2.73389i 1.37779 0.475908i
\(34\) 0 0
\(35\) 2.20469 + 5.32259i 0.372660 + 0.899681i
\(36\) 0 0
\(37\) −4.35102 1.80225i −0.715304 0.296289i −0.00480655 0.999988i \(-0.501530\pi\)
−0.710497 + 0.703700i \(0.751530\pi\)
\(38\) 0 0
\(39\) 6.35238 + 3.09064i 1.01719 + 0.494898i
\(40\) 0 0
\(41\) 0.606628 + 0.606628i 0.0947393 + 0.0947393i 0.752888 0.658149i \(-0.228660\pi\)
−0.658149 + 0.752888i \(0.728660\pi\)
\(42\) 0 0
\(43\) −0.565994 0.234442i −0.0863133 0.0357521i 0.339109 0.940747i \(-0.389874\pi\)
−0.425422 + 0.904995i \(0.639874\pi\)
\(44\) 0 0
\(45\) 6.63157 + 3.73499i 0.988576 + 0.556780i
\(46\) 0 0
\(47\) 1.04074i 0.151808i −0.997115 0.0759039i \(-0.975816\pi\)
0.997115 0.0759039i \(-0.0241842\pi\)
\(48\) 0 0
\(49\) 1.84333i 0.263333i
\(50\) 0 0
\(51\) −4.05505 4.57445i −0.567820 0.640551i
\(52\) 0 0
\(53\) 5.29738 + 2.19425i 0.727651 + 0.301403i 0.715586 0.698524i \(-0.246160\pi\)
0.0120644 + 0.999927i \(0.496160\pi\)
\(54\) 0 0
\(55\) 8.67289 + 8.67289i 1.16945 + 1.16945i
\(56\) 0 0
\(57\) 3.70568 7.61652i 0.490829 1.00883i
\(58\) 0 0
\(59\) 2.26739 + 0.939185i 0.295189 + 0.122271i 0.525363 0.850878i \(-0.323929\pi\)
−0.230174 + 0.973150i \(0.573929\pi\)
\(60\) 0 0
\(61\) 5.63874 + 13.6131i 0.721967 + 1.74298i 0.667670 + 0.744457i \(0.267292\pi\)
0.0542969 + 0.998525i \(0.482708\pi\)
\(62\) 0 0
\(63\) −4.20460 5.36017i −0.529729 0.675318i
\(64\) 0 0
\(65\) 10.3474i 1.28344i
\(66\) 0 0
\(67\) −10.1483 + 4.20357i −1.23981 + 0.513548i −0.903656 0.428258i \(-0.859127\pi\)
−0.336157 + 0.941806i \(0.609127\pi\)
\(68\) 0 0
\(69\) 6.07851 + 0.365859i 0.731767 + 0.0440442i
\(70\) 0 0
\(71\) −1.52242 1.52242i −0.180678 0.180678i 0.610973 0.791651i \(-0.290778\pi\)
−0.791651 + 0.610973i \(0.790778\pi\)
\(72\) 0 0
\(73\) −10.0596 + 10.0596i −1.17739 + 1.17739i −0.196979 + 0.980408i \(0.563113\pi\)
−0.980408 + 0.196979i \(0.936887\pi\)
\(74\) 0 0
\(75\) −0.149478 + 2.48349i −0.0172603 + 0.286769i
\(76\) 0 0
\(77\) −4.20127 10.1428i −0.478779 1.15587i
\(78\) 0 0
\(79\) −5.48744 −0.617385 −0.308693 0.951162i \(-0.599891\pi\)
−0.308693 + 0.951162i \(0.599891\pi\)
\(80\) 0 0
\(81\) −8.74105 2.14339i −0.971227 0.238155i
\(82\) 0 0
\(83\) −3.39246 + 1.40520i −0.372371 + 0.154241i −0.561018 0.827804i \(-0.689590\pi\)
0.188646 + 0.982045i \(0.439590\pi\)
\(84\) 0 0
\(85\) 3.42655 8.27243i 0.371662 0.897271i
\(86\) 0 0
\(87\) −1.14829 0.558681i −0.123110 0.0598969i
\(88\) 0 0
\(89\) −0.460940 + 0.460940i −0.0488596 + 0.0488596i −0.731114 0.682255i \(-0.760999\pi\)
0.682255 + 0.731114i \(0.260999\pi\)
\(90\) 0 0
\(91\) 3.54433 8.55678i 0.371547 0.896994i
\(92\) 0 0
\(93\) −6.01245 + 5.32977i −0.623462 + 0.552672i
\(94\) 0 0
\(95\) 12.4066 1.27289
\(96\) 0 0
\(97\) −3.50976 −0.356362 −0.178181 0.983998i \(-0.557021\pi\)
−0.178181 + 0.983998i \(0.557021\pi\)
\(98\) 0 0
\(99\) −12.6372 7.11743i −1.27008 0.715329i
\(100\) 0 0
\(101\) −4.59506 + 11.0935i −0.457225 + 1.10384i 0.512291 + 0.858812i \(0.328797\pi\)
−0.969516 + 0.245028i \(0.921203\pi\)
\(102\) 0 0
\(103\) 0.531901 0.531901i 0.0524097 0.0524097i −0.680416 0.732826i \(-0.738201\pi\)
0.732826 + 0.680416i \(0.238201\pi\)
\(104\) 0 0
\(105\) 4.36561 8.97291i 0.426040 0.875667i
\(106\) 0 0
\(107\) 6.91982 16.7059i 0.668964 1.61502i −0.114382 0.993437i \(-0.536489\pi\)
0.783346 0.621586i \(-0.213511\pi\)
\(108\) 0 0
\(109\) −4.18161 + 1.73208i −0.400526 + 0.165903i −0.573848 0.818962i \(-0.694550\pi\)
0.173322 + 0.984865i \(0.444550\pi\)
\(110\) 0 0
\(111\) 2.66318 + 7.71013i 0.252778 + 0.731813i
\(112\) 0 0
\(113\) 11.4007 1.07248 0.536242 0.844064i \(-0.319844\pi\)
0.536242 + 0.844064i \(0.319844\pi\)
\(114\) 0 0
\(115\) 3.41338 + 8.24062i 0.318299 + 0.768442i
\(116\) 0 0
\(117\) −3.29274 11.7844i −0.304414 1.08947i
\(118\) 0 0
\(119\) −5.66715 + 5.66715i −0.519507 + 0.519507i
\(120\) 0 0
\(121\) −8.74893 8.74893i −0.795358 0.795358i
\(122\) 0 0
\(123\) 0.0892747 1.48324i 0.00804963 0.133740i
\(124\) 0 0
\(125\) 8.35262 3.45977i 0.747081 0.309451i
\(126\) 0 0
\(127\) 17.0225i 1.51051i 0.655434 + 0.755253i \(0.272486\pi\)
−0.655434 + 0.755253i \(0.727514\pi\)
\(128\) 0 0
\(129\) 0.346434 + 1.00296i 0.0305018 + 0.0883053i
\(130\) 0 0
\(131\) 1.01086 + 2.44044i 0.0883195 + 0.213222i 0.961867 0.273516i \(-0.0881866\pi\)
−0.873548 + 0.486738i \(0.838187\pi\)
\(132\) 0 0
\(133\) −10.2596 4.24966i −0.889620 0.368493i
\(134\) 0 0
\(135\) −2.77836 12.8866i −0.239123 1.10910i
\(136\) 0 0
\(137\) −14.5134 14.5134i −1.23997 1.23997i −0.960014 0.279953i \(-0.909681\pi\)
−0.279953 0.960014i \(1.40968\pi\)
\(138\) 0 0
\(139\) 15.9809 + 6.61950i 1.35548 + 0.561459i 0.937813 0.347141i \(-0.112847\pi\)
0.417669 + 0.908599i \(0.362847\pi\)
\(140\) 0 0
\(141\) −1.34892 + 1.19576i −0.113600 + 0.100701i
\(142\) 0 0
\(143\) 19.7182i 1.64891i
\(144\) 0 0
\(145\) 1.87046i 0.155334i
\(146\) 0 0
\(147\) 2.38917 2.11790i 0.197055 0.174681i
\(148\) 0 0
\(149\) −12.5382 5.19348i −1.02717 0.425466i −0.195477 0.980708i \(-0.562626\pi\)
−0.831689 + 0.555242i \(0.812626\pi\)
\(150\) 0 0
\(151\) 3.63118 + 3.63118i 0.295501 + 0.295501i 0.839249 0.543748i \(-0.182995\pi\)
−0.543748 + 0.839249i \(0.682995\pi\)
\(152\) 0 0
\(153\) −1.26997 + 10.5116i −0.102671 + 0.849814i
\(154\) 0 0
\(155\) −10.8729 4.50371i −0.873333 0.361746i
\(156\) 0 0
\(157\) −6.88058 16.6112i −0.549130 1.32572i −0.918127 0.396286i \(-0.870299\pi\)
0.368997 0.929431i \(-0.379701\pi\)
\(158\) 0 0
\(159\) −3.24242 9.38709i −0.257141 0.744444i
\(160\) 0 0
\(161\) 7.98374i 0.629207i
\(162\) 0 0
\(163\) 9.77028 4.04698i 0.765268 0.316984i 0.0343138 0.999411i \(-0.489075\pi\)
0.730954 + 0.682427i \(0.239075\pi\)
\(164\) 0 0
\(165\) 1.27635 21.2058i 0.0993638 1.65087i
\(166\) 0 0
\(167\) −9.39415 9.39415i −0.726941 0.726941i 0.243068 0.970009i \(-0.421846\pi\)
−0.970009 + 0.243068i \(0.921846\pi\)
\(168\) 0 0
\(169\) 2.57027 2.57027i 0.197713 0.197713i
\(170\) 0 0
\(171\) −14.1295 + 3.94800i −1.08051 + 0.301911i
\(172\) 0 0
\(173\) 2.32375 + 5.61003i 0.176671 + 0.426522i 0.987265 0.159087i \(-0.0508551\pi\)
−0.810593 + 0.585610i \(0.800855\pi\)
\(174\) 0 0
\(175\) 3.26190 0.246577
\(176\) 0 0
\(177\) −1.38783 4.01788i −0.104316 0.302002i
\(178\) 0 0
\(179\) 6.06280 2.51129i 0.453155 0.187703i −0.144419 0.989517i \(-0.546131\pi\)
0.597574 + 0.801814i \(0.296131\pi\)
\(180\) 0 0
\(181\) −4.36208 + 10.5310i −0.324231 + 0.782763i 0.674768 + 0.738030i \(0.264244\pi\)
−0.998999 + 0.0447329i \(0.985756\pi\)
\(182\) 0 0
\(183\) 11.1656 22.9493i 0.825381 1.69646i
\(184\) 0 0
\(185\) −8.44858 + 8.44858i −0.621152 + 0.621152i
\(186\) 0 0
\(187\) −6.52966 + 15.7640i −0.477496 + 1.15278i
\(188\) 0 0
\(189\) −2.11652 + 11.6082i −0.153954 + 0.844372i
\(190\) 0 0
\(191\) 3.01629 0.218251 0.109126 0.994028i \(-0.465195\pi\)
0.109126 + 0.994028i \(0.465195\pi\)
\(192\) 0 0
\(193\) 4.88422 0.351574 0.175787 0.984428i \(-0.443753\pi\)
0.175787 + 0.984428i \(0.443753\pi\)
\(194\) 0 0
\(195\) 13.4115 11.8887i 0.960416 0.851367i
\(196\) 0 0
\(197\) −5.02958 + 12.1425i −0.358343 + 0.865116i 0.637191 + 0.770706i \(0.280096\pi\)
−0.995533 + 0.0944095i \(0.969904\pi\)
\(198\) 0 0
\(199\) 0.383062 0.383062i 0.0271545 0.0271545i −0.693399 0.720554i \(-0.743888\pi\)
0.720554 + 0.693399i \(0.243888\pi\)
\(200\) 0 0
\(201\) 17.1082 + 8.32370i 1.20672 + 0.587108i
\(202\) 0 0
\(203\) −0.640694 + 1.54677i −0.0449679 + 0.108562i
\(204\) 0 0
\(205\) 2.01083 0.832913i 0.140442 0.0581732i
\(206\) 0 0
\(207\) −6.50971 8.29880i −0.452456 0.576807i
\(208\) 0 0
\(209\) −23.6421 −1.63536
\(210\) 0 0
\(211\) −4.15639 10.0344i −0.286138 0.690798i 0.713817 0.700332i \(-0.246965\pi\)
−0.999955 + 0.00953483i \(0.996965\pi\)
\(212\) 0 0
\(213\) −0.224048 + 3.72242i −0.0153515 + 0.255056i
\(214\) 0 0
\(215\) −1.09902 + 1.09902i −0.0749523 + 0.0749523i
\(216\) 0 0
\(217\) 7.44864 + 7.44864i 0.505647 + 0.505647i
\(218\) 0 0
\(219\) 24.5964 + 1.48043i 1.66207 + 0.100038i
\(220\) 0 0
\(221\) −13.2991 + 5.50865i −0.894591 + 0.370552i
\(222\) 0 0
\(223\) 8.46207i 0.566662i −0.959022 0.283331i \(-0.908560\pi\)
0.959022 0.283331i \(-0.0914395\pi\)
\(224\) 0 0
\(225\) 3.39063 2.65966i 0.226042 0.177311i
\(226\) 0 0
\(227\) −1.09044 2.63257i −0.0723754 0.174730i 0.883552 0.468333i \(-0.155145\pi\)
−0.955927 + 0.293604i \(0.905145\pi\)
\(228\) 0 0
\(229\) 19.1182 + 7.91903i 1.26337 + 0.523305i 0.910942 0.412535i \(-0.135356\pi\)
0.352427 + 0.935839i \(0.385356\pi\)
\(230\) 0 0
\(231\) −8.31913 + 17.0988i −0.547359 + 1.12502i
\(232\) 0 0
\(233\) −0.892522 0.892522i −0.0584710 0.0584710i 0.677267 0.735738i \(-0.263164\pi\)
−0.735738 + 0.677267i \(0.763164\pi\)
\(234\) 0 0
\(235\) −2.43939 1.01043i −0.159128 0.0659131i
\(236\) 0 0
\(237\) 6.30479 + 7.11236i 0.409540 + 0.461997i
\(238\) 0 0
\(239\) 11.6414i 0.753017i 0.926413 + 0.376509i \(0.122876\pi\)
−0.926413 + 0.376509i \(0.877124\pi\)
\(240\) 0 0
\(241\) 10.7911i 0.695116i 0.937659 + 0.347558i \(0.112989\pi\)
−0.937659 + 0.347558i \(0.887011\pi\)
\(242\) 0 0
\(243\) 7.26494 + 13.7921i 0.466046 + 0.884760i
\(244\) 0 0
\(245\) 4.32058 + 1.78964i 0.276031 + 0.114336i
\(246\) 0 0
\(247\) −14.1035 14.1035i −0.897381 0.897381i
\(248\) 0 0
\(249\) 5.71908 + 2.78252i 0.362432 + 0.176335i
\(250\) 0 0
\(251\) −16.4676 6.82109i −1.03942 0.430543i −0.203318 0.979113i \(-0.565173\pi\)
−0.836105 + 0.548570i \(0.815173\pi\)
\(252\) 0 0
\(253\) −6.50455 15.7034i −0.408938 0.987263i
\(254\) 0 0
\(255\) −14.6590 + 5.06340i −0.917980 + 0.317082i
\(256\) 0 0
\(257\) 1.65839i 0.103448i 0.998661 + 0.0517239i \(0.0164716\pi\)
−0.998661 + 0.0517239i \(0.983528\pi\)
\(258\) 0 0
\(259\) 9.88043 4.09261i 0.613940 0.254302i
\(260\) 0 0
\(261\) 0.595215 + 2.13022i 0.0368429 + 0.131857i
\(262\) 0 0
\(263\) 19.0749 + 19.0749i 1.17621 + 1.17621i 0.980703 + 0.195503i \(0.0626339\pi\)
0.195503 + 0.980703i \(0.437366\pi\)
\(264\) 0 0
\(265\) 10.2862 10.2862i 0.631874 0.631874i
\(266\) 0 0
\(267\) 1.12703 + 0.0678346i 0.0689731 + 0.00415141i
\(268\) 0 0
\(269\) −10.0864 24.3507i −0.614979 1.48469i −0.857469 0.514536i \(-0.827964\pi\)
0.242490 0.970154i \(1.57796\pi\)
\(270\) 0 0
\(271\) 10.5104 0.638463 0.319231 0.947677i \(-0.396575\pi\)
0.319231 + 0.947677i \(0.396575\pi\)
\(272\) 0 0
\(273\) −15.1628 + 5.23744i −0.917696 + 0.316984i
\(274\) 0 0
\(275\) 6.41591 2.65756i 0.386894 0.160257i
\(276\) 0 0
\(277\) −8.45233 + 20.4057i −0.507851 + 1.22606i 0.437267 + 0.899332i \(0.355947\pi\)
−0.945118 + 0.326729i \(0.894053\pi\)
\(278\) 0 0
\(279\) 13.8160 + 1.66918i 0.827142 + 0.0999315i
\(280\) 0 0
\(281\) 3.13790 3.13790i 0.187191 0.187191i −0.607289 0.794481i \(-0.707743\pi\)
0.794481 + 0.607289i \(0.207743\pi\)
\(282\) 0 0
\(283\) −3.61311 + 8.72283i −0.214777 + 0.518518i −0.994146 0.108048i \(-0.965540\pi\)
0.779368 + 0.626566i \(0.215540\pi\)
\(284\) 0 0
\(285\) −14.2546 16.0804i −0.844368 0.952520i
\(286\) 0 0
\(287\) −1.94815 −0.114995
\(288\) 0 0
\(289\) −4.54367 −0.267275
\(290\) 0 0
\(291\) 4.03254 + 4.54905i 0.236392 + 0.266670i
\(292\) 0 0
\(293\) −1.40313 + 3.38745i −0.0819716 + 0.197897i −0.959551 0.281534i \(-0.909157\pi\)
0.877580 + 0.479431i \(0.159157\pi\)
\(294\) 0 0
\(295\) 4.40270 4.40270i 0.256335 0.256335i
\(296\) 0 0
\(297\) 5.29446 + 24.5568i 0.307216 + 1.42493i
\(298\) 0 0
\(299\) 5.48746 13.2479i 0.317348 0.766146i
\(300\) 0 0
\(301\) 1.28528 0.532379i 0.0740821 0.0306858i
\(302\) 0 0
\(303\) 19.6579 6.79009i 1.12932 0.390081i
\(304\) 0 0
\(305\) 37.3822 2.14050
\(306\) 0 0
\(307\) −6.27230 15.1427i −0.357979 0.864238i −0.995584 0.0938743i \(-0.970075\pi\)
0.637605 0.770363i \(-0.279925\pi\)
\(308\) 0 0
\(309\) −1.30053 0.0782775i −0.0739847 0.00445305i
\(310\) 0 0
\(311\) −11.1566 + 11.1566i −0.632635 + 0.632635i −0.948728 0.316094i \(-0.897629\pi\)
0.316094 + 0.948728i \(0.397629\pi\)
\(312\) 0 0
\(313\) 7.05760 + 7.05760i 0.398919 + 0.398919i 0.877852 0.478933i \(-0.158976\pi\)
−0.478933 + 0.877852i \(0.658976\pi\)
\(314\) 0 0
\(315\) −16.6458 + 4.65109i −0.937884 + 0.262059i
\(316\) 0 0
\(317\) 26.1796 10.8440i 1.47039 0.609057i 0.503446 0.864027i \(-0.332065\pi\)
0.966949 + 0.254969i \(0.0820654\pi\)
\(318\) 0 0
\(319\) 3.56437i 0.199566i
\(320\) 0 0
\(321\) −29.6033 + 10.2254i −1.65230 + 0.570725i
\(322\) 0 0
\(323\) 6.60488 + 15.9456i 0.367505 + 0.887237i
\(324\) 0 0
\(325\) 5.41268 + 2.24201i 0.300241 + 0.124364i
\(326\) 0 0
\(327\) 7.04944 + 3.42978i 0.389835 + 0.189667i
\(328\) 0 0
\(329\) 1.67114 + 1.67114i 0.0921329 + 0.0921329i
\(330\) 0 0
\(331\) −20.9565 8.68047i −1.15187 0.477122i −0.276713 0.960953i \(-0.589245\pi\)
−0.875162 + 0.483831i \(0.839245\pi\)
\(332\) 0 0
\(333\) 6.93335 12.3103i 0.379945 0.674602i
\(334\) 0 0
\(335\) 27.8677i 1.52258i
\(336\) 0 0
\(337\) 31.4720i 1.71439i −0.514992 0.857195i \(-0.672205\pi\)
0.514992 0.857195i \(-0.327795\pi\)
\(338\) 0 0
\(339\) −13.0988 14.7766i −0.711428 0.802553i
\(340\) 0 0
\(341\) 20.7195 + 8.58229i 1.12202 + 0.464757i
\(342\) 0 0
\(343\) −14.1999 14.1999i −0.766723 0.766723i
\(344\) 0 0
\(345\) 6.75900 13.8922i 0.363892 0.747930i
\(346\) 0 0
\(347\) 1.28308 + 0.531467i 0.0688791 + 0.0285307i 0.416857 0.908972i \(-0.363132\pi\)
−0.347978 + 0.937503i \(0.613132\pi\)
\(348\) 0 0
\(349\) 3.87192 + 9.34765i 0.207259 + 0.500368i 0.992990 0.118201i \(-0.0377127\pi\)
−0.785730 + 0.618569i \(0.787713\pi\)
\(350\) 0 0
\(351\) −11.4907 + 17.8075i −0.613331 + 0.950492i
\(352\) 0 0
\(353\) 30.0966i 1.60188i −0.598744 0.800941i \(-0.704333\pi\)
0.598744 0.800941i \(-0.295667\pi\)
\(354\) 0 0
\(355\) −5.04648 + 2.09032i −0.267839 + 0.110943i
\(356\) 0 0
\(357\) 13.8565 + 0.834010i 0.733366 + 0.0441405i
\(358\) 0 0
\(359\) −6.32903 6.32903i −0.334034 0.334034i 0.520082 0.854116i \(-0.325901\pi\)
−0.854116 + 0.520082i \(0.825901\pi\)
\(360\) 0 0
\(361\) −3.47505 + 3.47505i −0.182897 + 0.182897i
\(362\) 0 0
\(363\) −1.28754 + 21.3917i −0.0675785 + 1.12277i
\(364\) 0 0
\(365\) 13.8120 + 33.3452i 0.722956 + 1.74537i
\(366\) 0 0
\(367\) 14.6156 0.762928 0.381464 0.924384i \(-0.375420\pi\)
0.381464 + 0.924384i \(0.375420\pi\)
\(368\) 0 0
\(369\) −2.02503 + 1.58846i −0.105419 + 0.0826920i
\(370\) 0 0
\(371\) −12.0294 + 4.98276i −0.624537 + 0.258692i
\(372\) 0 0
\(373\) −0.624034 + 1.50655i −0.0323113 + 0.0780063i −0.939212 0.343339i \(-0.888442\pi\)
0.906900 + 0.421345i \(0.138442\pi\)
\(374\) 0 0
\(375\) −14.0810 6.85086i −0.727139 0.353777i
\(376\) 0 0
\(377\) −2.12629 + 2.12629i −0.109509 + 0.109509i
\(378\) 0 0
\(379\) −0.943771 + 2.27846i −0.0484782 + 0.117037i −0.946264 0.323397i \(-0.895175\pi\)
0.897785 + 0.440433i \(0.145175\pi\)
\(380\) 0 0
\(381\) 22.0632 19.5580i 1.13033 1.00199i
\(382\) 0 0
\(383\) −4.75455 −0.242946 −0.121473 0.992595i \(-0.538762\pi\)
−0.121473 + 0.992595i \(0.538762\pi\)
\(384\) 0 0
\(385\) −27.8524 −1.41949
\(386\) 0 0
\(387\) 0.901911 1.60136i 0.0458467 0.0814019i
\(388\) 0 0
\(389\) 1.83890 4.43949i 0.0932357 0.225091i −0.870381 0.492379i \(-0.836127\pi\)
0.963617 + 0.267288i \(0.0861275\pi\)
\(390\) 0 0
\(391\) −8.77409 + 8.77409i −0.443725 + 0.443725i
\(392\) 0 0
\(393\) 2.00166 4.11413i 0.100970 0.207531i
\(394\) 0 0
\(395\) −5.32761 + 12.8620i −0.268061 + 0.647157i
\(396\) 0 0
\(397\) 18.6101 7.70855i 0.934014 0.386881i 0.136814 0.990597i \(-0.456314\pi\)
0.797200 + 0.603716i \(0.206314\pi\)
\(398\) 0 0
\(399\) 6.27970 + 18.1803i 0.314378 + 0.910152i
\(400\) 0 0
\(401\) 12.1070 0.604595 0.302297 0.953214i \(-0.402246\pi\)
0.302297 + 0.953214i \(0.402246\pi\)
\(402\) 0 0
\(403\) 7.24032 + 17.4797i 0.360666 + 0.870724i
\(404\) 0 0
\(405\) −13.5103 + 18.4071i −0.671334 + 0.914658i
\(406\) 0 0
\(407\) 16.0997 16.0997i 0.798031 0.798031i
\(408\) 0 0
\(409\) 0.903424 + 0.903424i 0.0446714 + 0.0446714i 0.729090 0.684418i \(-0.239944\pi\)
−0.684418 + 0.729090i \(0.739944\pi\)
\(410\) 0 0
\(411\) −2.13588 + 35.4863i −0.105355 + 1.75041i
\(412\) 0 0
\(413\) −5.14886 + 2.13273i −0.253359 + 0.104945i
\(414\) 0 0
\(415\) 9.31585i 0.457297i
\(416\) 0 0
\(417\) −9.78160 28.3186i −0.479007 1.38677i
\(418\) 0 0
\(419\) 6.08627 + 14.6935i 0.297334 + 0.717827i 0.999980 + 0.00628784i \(0.00200150\pi\)
−0.702647 + 0.711539i \(0.747999\pi\)
\(420\) 0 0
\(421\) −1.96867 0.815452i −0.0959473 0.0397427i 0.334194 0.942504i \(-0.391536\pi\)
−0.430141 + 0.902762i \(0.641536\pi\)
\(422\) 0 0
\(423\) 3.09969 + 0.374490i 0.150712 + 0.0182083i
\(424\) 0 0
\(425\) −3.58482 3.58482i −0.173889 0.173889i
\(426\) 0 0
\(427\) −30.9131 12.8046i −1.49599 0.619659i
\(428\) 0 0
\(429\) −25.5570 + 22.6552i −1.23390 + 1.09380i
\(430\) 0 0
\(431\) 10.3316i 0.497658i −0.968547 0.248829i \(-0.919954\pi\)
0.968547 0.248829i \(-0.0800457\pi\)
\(432\) 0 0
\(433\) 28.8197i 1.38499i 0.721423 + 0.692494i \(0.243488\pi\)
−0.721423 + 0.692494i \(0.756512\pi\)
\(434\) 0 0
\(435\) −2.42434 + 2.14907i −0.116238 + 0.103040i
\(436\) 0 0
\(437\) −15.8843 6.57948i −0.759848 0.314739i
\(438\) 0 0
\(439\) 8.85668 + 8.85668i 0.422706 + 0.422706i 0.886135 0.463428i \(-0.153381\pi\)
−0.463428 + 0.886135i \(0.653381\pi\)
\(440\) 0 0
\(441\) −5.49007 0.663285i −0.261432 0.0315850i
\(442\) 0 0
\(443\) 5.89186 + 2.44049i 0.279931 + 0.115951i 0.518232 0.855240i \(-0.326590\pi\)
−0.238301 + 0.971191i \(0.576590\pi\)
\(444\) 0 0
\(445\) 0.632881 + 1.52791i 0.0300014 + 0.0724299i
\(446\) 0 0
\(447\) 7.67437 + 22.2179i 0.362985 + 1.05087i
\(448\) 0 0
\(449\) 36.3009i 1.71315i 0.516025 + 0.856574i \(0.327411\pi\)
−0.516025 + 0.856574i \(0.672589\pi\)
\(450\) 0 0
\(451\) −3.83185 + 1.58720i −0.180435 + 0.0747385i
\(452\) 0 0
\(453\) 0.534384 8.87846i 0.0251076 0.417147i
\(454\) 0 0
\(455\) −16.6151 16.6151i −0.778927 0.778927i
\(456\) 0 0
\(457\) 23.9408 23.9408i 1.11990 1.11990i 0.128149 0.991755i \(-0.459096\pi\)
0.991755 0.128149i \(-0.0409037\pi\)
\(458\) 0 0
\(459\) 15.0834 10.4313i 0.704033 0.486891i
\(460\) 0 0
\(461\) 3.52528 + 8.51078i 0.164189 + 0.396387i 0.984465 0.175581i \(-0.0561804\pi\)
−0.820276 + 0.571967i \(0.806180\pi\)
\(462\) 0 0
\(463\) −23.3090 −1.08326 −0.541630 0.840617i \(-0.682193\pi\)
−0.541630 + 0.840617i \(0.682193\pi\)
\(464\) 0 0
\(465\) 6.65510 + 19.2671i 0.308623 + 0.893489i
\(466\) 0 0
\(467\) 13.7618 5.70032i 0.636819 0.263779i −0.0408280 0.999166i \(-0.513000\pi\)
0.677647 + 0.735387i \(0.263000\pi\)
\(468\) 0 0
\(469\) 9.54559 23.0451i 0.440774 1.06412i
\(470\) 0 0
\(471\) −13.6246 + 28.0034i −0.627787 + 1.29033i
\(472\) 0 0
\(473\) 2.09429 2.09429i 0.0962957 0.0962957i
\(474\) 0 0
\(475\) 2.68817 6.48982i 0.123342 0.297773i
\(476\) 0 0
\(477\) −8.44137 + 14.9878i −0.386504 + 0.686246i
\(478\) 0 0
\(479\) 27.5679 1.25961 0.629805 0.776753i \(-0.283135\pi\)
0.629805 + 0.776753i \(0.283135\pi\)
\(480\) 0 0
\(481\) 19.2082 0.875818
\(482\) 0 0
\(483\) −10.3478 + 9.17291i −0.470843 + 0.417382i
\(484\) 0 0
\(485\) −3.40753 + 8.22651i −0.154728 + 0.373547i
\(486\) 0 0
\(487\) 14.7280 14.7280i 0.667392 0.667392i −0.289720 0.957111i \(-0.593562\pi\)
0.957111 + 0.289720i \(0.0935622\pi\)
\(488\) 0 0
\(489\) −16.4709 8.01363i −0.744841 0.362389i
\(490\) 0 0
\(491\) −5.50514 + 13.2906i −0.248444 + 0.599796i −0.998072 0.0620627i \(-0.980232\pi\)
0.749629 + 0.661859i \(0.230232\pi\)
\(492\) 0 0
\(493\) 2.40401 0.995775i 0.108271 0.0448475i
\(494\) 0 0
\(495\) −28.9516 + 22.7101i −1.30128 + 1.02074i
\(496\) 0 0
\(497\) 4.88917 0.219309
\(498\) 0 0
\(499\) −14.9661 36.1315i −0.669977 1.61747i −0.781647 0.623721i \(-0.785620\pi\)
0.111670 0.993745i \(-0.464380\pi\)
\(500\) 0 0
\(501\) −1.38250 + 22.9693i −0.0617654 + 1.02619i
\(502\) 0 0
\(503\) −24.0188 + 24.0188i −1.07095 + 1.07095i −0.0736641 + 0.997283i \(0.523469\pi\)
−0.997283 + 0.0736641i \(0.976531\pi\)
\(504\) 0 0
\(505\) 21.5407 + 21.5407i 0.958547 + 0.958547i
\(506\) 0 0
\(507\) −6.28448 0.378256i −0.279104 0.0167989i
\(508\) 0 0
\(509\) 34.0535 14.1054i 1.50940 0.625213i 0.533963 0.845508i \(-0.320702\pi\)
0.975433 + 0.220295i \(0.0707020\pi\)
\(510\) 0 0
\(511\) 32.3058i 1.42912i
\(512\) 0 0
\(513\) 21.3512 + 13.7774i 0.942678 + 0.608288i
\(514\) 0 0
\(515\) −0.730311 1.76313i −0.0321814 0.0776927i
\(516\) 0 0
\(517\) 4.64852 + 1.92548i 0.204442 + 0.0846824i
\(518\) 0 0
\(519\) 4.60137 9.45748i 0.201978 0.415137i
\(520\) 0 0
\(521\) 16.9782 + 16.9782i 0.743826 + 0.743826i 0.973312 0.229486i \(-0.0737044\pi\)
−0.229486 + 0.973312i \(0.573704\pi\)
\(522\) 0 0
\(523\) 25.0460 + 10.3744i 1.09519 + 0.453641i 0.855812 0.517286i \(-0.173058\pi\)
0.239374 + 0.970927i \(0.423058\pi\)
\(524\) 0 0
\(525\) −3.74776 4.22780i −0.163566 0.184517i
\(526\) 0 0
\(527\) 16.3720i 0.713177i
\(528\) 0 0
\(529\) 10.6393i 0.462578i
\(530\) 0 0
\(531\) −3.61309 + 6.41513i −0.156795 + 0.278393i
\(532\) 0 0
\(533\) −3.23268 1.33902i −0.140023 0.0579994i
\(534\) 0 0
\(535\) −32.4387 32.4387i −1.40245 1.40245i
\(536\) 0 0
\(537\) −10.2208 4.97273i −0.441059 0.214589i
\(538\) 0 0
\(539\) −8.23332 3.41035i −0.354634 0.146894i
\(540\) 0 0
\(541\) 6.82494 + 16.4769i 0.293427 + 0.708396i 1.00000 0.000755337i \(0.000240431\pi\)
−0.706572 + 0.707641i \(0.749760\pi\)
\(542\) 0 0
\(543\) 18.6612 6.44582i 0.800829 0.276617i
\(544\) 0 0
\(545\) 11.4829i 0.491873i
\(546\) 0 0
\(547\) 41.1024 17.0252i 1.75741 0.727943i 0.760505 0.649332i \(-0.224952\pi\)
0.996905 0.0786106i \(-0.0250484\pi\)
\(548\) 0 0
\(549\) −42.5735 + 11.8957i −1.81699 + 0.507696i
\(550\) 0 0
\(551\) 2.54942 + 2.54942i 0.108609 + 0.108609i
\(552\) 0 0
\(553\) 8.81129 8.81129i 0.374694 0.374694i
\(554\) 0 0
\(555\) 20.6573 + 1.24334i 0.876855 + 0.0527769i
\(556\) 0 0
\(557\) −12.0200 29.0188i −0.509303 1.22957i −0.944286 0.329127i \(-0.893246\pi\)
0.434983 0.900439i \(1.64325\pi\)
\(558\) 0 0
\(559\) 2.49866 0.105682
\(560\) 0 0
\(561\) 27.9342 9.64885i 1.17938 0.407375i
\(562\) 0 0
\(563\) −1.38276 + 0.572760i −0.0582766 + 0.0241389i −0.411631 0.911350i \(-0.635041\pi\)
0.353355 + 0.935489i \(0.385041\pi\)
\(564\) 0 0
\(565\) 11.0686 26.7219i 0.465659 1.12420i
\(566\) 0 0
\(567\) 17.4773 10.5940i 0.733980 0.444905i
\(568\) 0 0
\(569\) 7.17341 7.17341i 0.300725 0.300725i −0.540573 0.841297i \(-0.681792\pi\)
0.841297 + 0.540573i \(0.181792\pi\)
\(570\) 0 0
\(571\) 14.0237 33.8562i 0.586874 1.41684i −0.299602 0.954064i \(-0.596854\pi\)
0.886476 0.462775i \(-0.153146\pi\)
\(572\) 0 0
\(573\) −3.46556 3.90946i −0.144776 0.163320i
\(574\) 0 0
\(575\) 5.05020 0.210608
\(576\) 0 0
\(577\) 0.998741 0.0415781 0.0207891 0.999784i \(-0.493382\pi\)
0.0207891 + 0.999784i \(0.493382\pi\)
\(578\) 0 0
\(579\) −5.61173 6.33052i −0.233215 0.263087i
\(580\) 0 0
\(581\) 3.19098 7.70371i 0.132384 0.319604i
\(582\) 0 0
\(583\) −19.6014 + 19.6014i −0.811806 + 0.811806i
\(584\) 0 0
\(585\) −30.8182 3.72332i −1.27418 0.153940i
\(586\) 0 0
\(587\) 6.37457 15.3896i 0.263106 0.635195i −0.736021 0.676959i \(-0.763298\pi\)
0.999128 + 0.0417634i \(0.0132976\pi\)
\(588\) 0 0
\(589\) 20.9582 8.68116i 0.863566 0.357701i
\(590\) 0 0
\(591\) 21.5168 7.43218i 0.885082 0.305719i
\(592\) 0 0
\(593\) −35.6688 −1.46474 −0.732371 0.680906i \(-0.761586\pi\)
−0.732371 + 0.680906i \(0.761586\pi\)
\(594\) 0 0
\(595\) 7.78112 + 18.7853i 0.318995 + 0.770122i
\(596\) 0 0
\(597\) −0.936611 0.0563736i −0.0383329 0.00230722i
\(598\) 0 0
\(599\) 18.1105 18.1105i 0.739973 0.739973i −0.232600 0.972573i \(-0.574723\pi\)
0.972573 + 0.232600i \(0.0747232\pi\)
\(600\) 0 0
\(601\) −10.0737 10.0737i −0.410916 0.410916i 0.471141 0.882058i \(-0.343842\pi\)
−0.882058 + 0.471141i \(0.843842\pi\)
\(602\) 0 0
\(603\) −8.86801 31.7377i −0.361133 1.29246i
\(604\) 0 0
\(605\) −29.0007 + 12.0125i −1.17905 + 0.488377i
\(606\) 0 0
\(607\) 7.28221i 0.295576i 0.989019 + 0.147788i \(0.0472153\pi\)
−0.989019 + 0.147788i \(0.952785\pi\)
\(608\) 0 0
\(609\) 2.74092 0.946750i 0.111068 0.0383643i
\(610\) 0 0
\(611\) 1.62440 + 3.92165i 0.0657162 + 0.158653i
\(612\) 0 0
\(613\) −0.372820 0.154427i −0.0150581 0.00623725i 0.375142 0.926967i \(-0.377594\pi\)
−0.390200 + 0.920730i \(0.627594\pi\)
\(614\) 0 0
\(615\) −3.38989 1.64929i −0.136694 0.0665059i
\(616\) 0 0
\(617\) 0.952724 + 0.952724i 0.0383552 + 0.0383552i 0.726024 0.687669i \(-0.241366\pi\)
−0.687669 + 0.726024i \(0.741366\pi\)
\(618\) 0 0
\(619\) 29.7961 + 12.3419i 1.19761 + 0.496065i 0.890225 0.455522i \(-0.150547\pi\)
0.307381 + 0.951586i \(0.400547\pi\)
\(620\) 0 0
\(621\) −3.27688 + 17.9722i −0.131497 + 0.721201i
\(622\) 0 0
\(623\) 1.48028i 0.0593062i
\(624\) 0 0
\(625\) 30.1188i 1.20475i
\(626\) 0 0
\(627\) 27.1636 + 30.6429i 1.08481 + 1.22376i
\(628\) 0 0
\(629\) −15.3563 6.36079i −0.612296 0.253621i
\(630\) 0 0
\(631\) 20.1478 + 20.1478i 0.802070 + 0.802070i 0.983419 0.181349i \(-0.0580463\pi\)
−0.181349 + 0.983419i \(0.558046\pi\)
\(632\) 0 0
\(633\) −8.23028 + 16.9162i −0.327124 + 0.672359i
\(634\) 0 0
\(635\) 39.8990 + 16.5267i 1.58334 + 0.655843i
\(636\) 0 0
\(637\) −2.87709 6.94591i −0.113994 0.275207i
\(638\) 0 0
\(639\) 5.08211 3.98649i 0.201045 0.157703i
\(640\) 0 0
\(641\) 14.0316i 0.554215i 0.960839 + 0.277108i \(0.0893758\pi\)
−0.960839 + 0.277108i \(0.910624\pi\)
\(642\) 0 0
\(643\) −29.2893 + 12.1320i −1.15506 + 0.478441i −0.876227 0.481899i \(-0.839947\pi\)
−0.278832 + 0.960340i \(0.589947\pi\)
\(644\) 0 0
\(645\) 2.68717 + 0.161737i 0.105807 + 0.00636841i
\(646\) 0 0
\(647\) 22.8248 + 22.8248i 0.897334 + 0.897334i 0.995200 0.0978653i \(-0.0312014\pi\)
−0.0978653 + 0.995200i \(0.531201\pi\)
\(648\) 0 0
\(649\) −8.38982 + 8.38982i −0.329329 + 0.329329i
\(650\) 0 0
\(651\) 1.09618 18.2124i 0.0429629 0.713801i
\(652\) 0 0
\(653\) −15.1160 36.4932i −0.591534 1.42809i −0.882021 0.471211i \(-0.843817\pi\)
0.290486 0.956879i \(1.59382\pi\)
\(654\) 0 0
\(655\) 6.70155 0.261851
\(656\) 0 0
\(657\) −26.3412 33.5807i −1.02767 1.31011i
\(658\) 0 0
\(659\) −35.1778 + 14.5711i −1.37033 + 0.567611i −0.941879 0.335952i \(-0.890942\pi\)
−0.428455 + 0.903563i \(0.640942\pi\)
\(660\) 0 0
\(661\) 4.52621 10.9272i 0.176049 0.425021i −0.811082 0.584932i \(-0.801121\pi\)
0.987131 + 0.159912i \(0.0511210\pi\)
\(662\) 0 0
\(663\) 22.4198 + 10.9079i 0.870712 + 0.423630i
\(664\) 0 0
\(665\) −19.9215 + 19.9215i −0.772524 + 0.772524i
\(666\) 0 0
\(667\) −0.991946 + 2.39477i −0.0384083 + 0.0927258i
\(668\) 0 0
\(669\) −10.9678 + 9.72249i −0.424040 + 0.375893i
\(670\) 0 0
\(671\) −71.2358 −2.75003
\(672\) 0 0
\(673\) 24.6062 0.948499 0.474249 0.880391i \(-0.342719\pi\)
0.474249 + 0.880391i \(0.342719\pi\)
\(674\) 0 0
\(675\) −7.34289 1.33883i −0.282628 0.0515316i
\(676\) 0 0
\(677\) 15.9784 38.5753i 0.614100 1.48257i −0.244359 0.969685i \(-0.578577\pi\)
0.858458 0.512883i \(-0.171423\pi\)
\(678\) 0 0
\(679\) 5.63569 5.63569i 0.216278 0.216278i
\(680\) 0 0
\(681\) −2.15924 + 4.43803i −0.0827424 + 0.170066i
\(682\) 0 0
\(683\) −3.00142 + 7.24607i −0.114846 + 0.277263i −0.970842 0.239719i \(-0.922945\pi\)
0.855996 + 0.516982i \(0.172945\pi\)
\(684\) 0 0
\(685\) −48.1087 + 19.9273i −1.83814 + 0.761382i
\(686\) 0 0
\(687\) −11.7019 33.8780i −0.446456 1.29253i
\(688\) 0 0
\(689\) −23.3860 −0.890935
\(690\) 0 0
\(691\) −6.64017 16.0308i −0.252604 0.609840i 0.745809 0.666160i \(-0.232063\pi\)
−0.998413 + 0.0563199i \(0.982063\pi\)
\(692\) 0 0
\(693\) 31.7203 8.86315i 1.20496 0.336683i
\(694\) 0 0
\(695\) 31.0308 31.0308i 1.17707 1.17707i
\(696\) 0 0
\(697\) 2.14100 + 2.14100i 0.0810963 + 0.0810963i
\(698\) 0 0
\(699\) −0.131349 + 2.18227i −0.00496806 + 0.0825412i
\(700\) 0 0
\(701\) −30.4348 + 12.6065i −1.14951 + 0.476142i −0.874369 0.485262i \(-0.838724\pi\)
−0.275140 + 0.961404i \(0.588724\pi\)
\(702\) 0 0
\(703\) 23.0307i 0.868618i
\(704\) 0 0
\(705\) 1.49310 + 4.32266i 0.0562336 + 0.162801i
\(706\) 0 0
\(707\) −10.4346 25.1913i −0.392433 0.947418i
\(708\) 0 0
\(709\) 1.50725 + 0.624323i 0.0566059 + 0.0234469i 0.410807 0.911722i \(-0.365247\pi\)
−0.354201 + 0.935169i \(0.615247\pi\)
\(710\) 0 0
\(711\) 1.97454 16.3435i 0.0740512 0.612928i
\(712\) 0 0
\(713\) 11.5323 + 11.5323i 0.431887 + 0.431887i
\(714\) 0 0
\(715\) −46.2173 19.1438i −1.72843 0.715938i
\(716\) 0 0
\(717\) 15.0886 13.3753i 0.563492 0.499511i
\(718\) 0 0
\(719\) 23.0397i 0.859235i −0.903011 0.429617i \(-0.858648\pi\)
0.903011 0.429617i \(-0.141352\pi\)
\(720\) 0 0
\(721\) 1.70817i 0.0636154i
\(722\) 0 0
\(723\) 13.9865 12.3984i 0.520164 0.461102i
\(724\) 0 0
\(725\) −0.978427 0.405278i −0.0363379 0.0150516i
\(726\) 0 0
\(727\) 14.9321 + 14.9321i 0.553800 + 0.553800i 0.927535 0.373735i \(-0.121923\pi\)
−0.373735 + 0.927535i \(0.621923\pi\)
\(728\) 0 0
\(729\) 9.52904 25.2626i 0.352927 0.935651i
\(730\) 0 0
\(731\) −1.99759 0.827430i −0.0738836 0.0306036i
\(732\) 0 0
\(733\) −9.10293 21.9764i −0.336224 0.811717i −0.998071 0.0620784i \(-0.980227\pi\)
0.661847 0.749639i \(-0.269773\pi\)
\(734\) 0 0
\(735\) −2.64454 7.65617i −0.0975454 0.282402i
\(736\) 0 0
\(737\) 53.1049i 1.95614i
\(738\) 0 0
\(739\) −20.9490 + 8.67734i −0.770620 + 0.319201i −0.733123 0.680096i \(-0.761938\pi\)
−0.0374963 + 0.999297i \(0.511938\pi\)
\(740\) 0 0
\(741\) −2.07554 + 34.4839i −0.0762470 + 1.26680i
\(742\) 0 0
\(743\) −6.18457 6.18457i −0.226890 0.226890i 0.584502 0.811392i \(-0.301290\pi\)
−0.811392 + 0.584502i \(0.801290\pi\)
\(744\) 0 0
\(745\) −24.3459 + 24.3459i −0.891966 + 0.891966i
\(746\) 0 0
\(747\) −2.96447 10.6096i −0.108464 0.388183i
\(748\) 0 0
\(749\) 15.7137 + 37.9363i 0.574167 + 1.38616i
\(750\) 0 0
\(751\) −45.6086 −1.66428 −0.832140 0.554565i \(-0.812885\pi\)
−0.832140 + 0.554565i \(0.812885\pi\)
\(752\) 0 0
\(753\) 10.0795 + 29.1809i 0.367317 + 1.06341i
\(754\) 0 0
\(755\) 12.0365 4.98569i 0.438053 0.181448i
\(756\) 0 0
\(757\) −15.2177 + 36.7389i −0.553098 + 1.33530i 0.362042 + 0.932162i \(0.382080\pi\)
−0.915140 + 0.403135i \(0.867920\pi\)
\(758\) 0 0
\(759\) −12.8800 + 26.4730i −0.467514 + 0.960910i
\(760\) 0 0
\(761\) 22.7252 22.7252i 0.823790 0.823790i −0.162860 0.986649i \(-0.552072\pi\)
0.986649 + 0.162860i \(0.0520718\pi\)
\(762\) 0 0
\(763\) 3.93326 9.49573i 0.142394 0.343769i
\(764\) 0 0
\(765\) 23.4052 + 13.1821i 0.846215 + 0.476600i
\(766\) 0 0
\(767\) −10.0097 −0.361430
\(768\) 0 0
\(769\) 31.6105 1.13990 0.569951 0.821679i \(-0.306962\pi\)
0.569951 + 0.821679i \(0.306962\pi\)
\(770\) 0 0
\(771\) 2.14947 1.90541i 0.0774112 0.0686217i
\(772\) 0 0
\(773\) −6.78635 + 16.3837i −0.244088 + 0.589280i −0.997681 0.0680606i \(-0.978319\pi\)
0.753593 + 0.657341i \(0.228319\pi\)
\(774\) 0 0
\(775\) −4.71172 + 4.71172i −0.169250 + 0.169250i
\(776\) 0 0
\(777\) −16.6566 8.10398i −0.597553 0.290729i
\(778\) 0 0
\(779\) −1.60549 + 3.87599i −0.0575226 + 0.138872i
\(780\) 0 0
\(781\) 9.61661 3.98333i 0.344109 0.142535i
\(782\) 0 0
\(783\) 2.07713 3.21898i