Properties

Label 1008.2.r.m.337.3
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.508277025.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 21 x^{4} + 3 x^{3} - 22 x^{2} + 3 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.3
Root \(1.86526 + 0.199842i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.m.673.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60570 - 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +O(q^{10})\) \(q+(1.60570 - 0.649414i) q^{3} +(-0.468293 + 0.811107i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.15652 - 2.08552i) q^{9} +(2.48741 + 4.30833i) q^{11} +(-0.622156 + 1.07761i) q^{13} +(-0.225193 + 1.60651i) q^{15} +5.22446 q^{17} -5.18622 q^{19} +(1.36526 + 1.06587i) q^{21} +(-1.00266 + 1.73666i) q^{23} +(2.06140 + 3.57046i) q^{25} +(2.10836 - 4.74919i) q^{27} +(-3.43925 - 5.95695i) q^{29} +(-2.86526 + 4.96277i) q^{31} +(6.79192 + 5.30251i) q^{33} -0.936586 q^{35} +9.73051 q^{37} +(-0.299182 + 2.13435i) q^{39} +(5.73705 - 9.93686i) q^{41} +(4.80184 + 8.31704i) q^{43} +(0.681697 + 2.72581i) q^{45} +(-0.984753 - 1.70564i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(8.38890 - 3.39284i) q^{51} -7.63418 q^{53} -4.65935 q^{55} +(-8.32750 + 3.36800i) q^{57} +(2.43925 - 4.22490i) q^{59} +(1.52178 + 2.63580i) q^{61} +(2.88438 + 0.824844i) q^{63} +(-0.582703 - 1.00927i) q^{65} +(-0.573990 + 0.994179i) q^{67} +(-0.482159 + 3.43969i) q^{69} +8.83749 q^{71} +6.10698 q^{73} +(5.62869 + 4.39437i) q^{75} +(-2.48741 + 4.30833i) q^{77} +(-6.05414 - 10.4861i) q^{79} +(0.301193 - 8.99496i) q^{81} +(-0.431332 - 0.747088i) q^{83} +(-2.44658 + 4.23760i) q^{85} +(-9.39091 - 7.33156i) q^{87} -10.8480 q^{89} -1.24431 q^{91} +(-1.37784 + 9.82944i) q^{93} +(2.42867 - 4.20658i) q^{95} +(-3.78521 - 6.55618i) q^{97} +(14.3493 + 4.10345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + 6q^{11} - 3q^{13} - 4q^{15} - 16q^{17} + 4q^{19} - q^{21} + 5q^{23} - 14q^{25} - 5q^{27} + q^{29} - 11q^{31} + 8q^{35} + 54q^{37} + 12q^{39} + 2q^{41} + 11q^{43} + 26q^{45} - 7q^{47} - 4q^{49} - 17q^{51} - 8q^{53} - 12q^{55} - 13q^{57} - 9q^{59} - 7q^{61} + 5q^{63} - 9q^{65} + 12q^{67} + 4q^{69} + 24q^{71} + 26q^{73} + 23q^{75} - 6q^{77} + 22q^{79} + 34q^{81} + 6q^{83} - 11q^{85} - 37q^{87} - 28q^{89} - 6q^{91} - 13q^{93} + 23q^{95} - q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.60570 0.649414i 0.927049 0.374939i
\(4\) 0 0
\(5\) −0.468293 + 0.811107i −0.209427 + 0.362738i −0.951534 0.307543i \(-0.900493\pi\)
0.742107 + 0.670281i \(0.233827\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.15652 2.08552i 0.718841 0.695174i
\(10\) 0 0
\(11\) 2.48741 + 4.30833i 0.749983 + 1.29901i 0.947830 + 0.318776i \(0.103272\pi\)
−0.197847 + 0.980233i \(0.563395\pi\)
\(12\) 0 0
\(13\) −0.622156 + 1.07761i −0.172555 + 0.298874i −0.939312 0.343063i \(-0.888536\pi\)
0.766757 + 0.641937i \(0.221869\pi\)
\(14\) 0 0
\(15\) −0.225193 + 1.60651i −0.0581445 + 0.414799i
\(16\) 0 0
\(17\) 5.22446 1.26712 0.633559 0.773694i \(-0.281593\pi\)
0.633559 + 0.773694i \(0.281593\pi\)
\(18\) 0 0
\(19\) −5.18622 −1.18980 −0.594900 0.803800i \(-0.702808\pi\)
−0.594900 + 0.803800i \(0.702808\pi\)
\(20\) 0 0
\(21\) 1.36526 + 1.06587i 0.297923 + 0.232591i
\(22\) 0 0
\(23\) −1.00266 + 1.73666i −0.209069 + 0.362118i −0.951422 0.307891i \(-0.900377\pi\)
0.742352 + 0.670010i \(0.233710\pi\)
\(24\) 0 0
\(25\) 2.06140 + 3.57046i 0.412281 + 0.714091i
\(26\) 0 0
\(27\) 2.10836 4.74919i 0.405754 0.913983i
\(28\) 0 0
\(29\) −3.43925 5.95695i −0.638652 1.10618i −0.985729 0.168341i \(-0.946159\pi\)
0.347077 0.937837i \(-0.387174\pi\)
\(30\) 0 0
\(31\) −2.86526 + 4.96277i −0.514615 + 0.891340i 0.485241 + 0.874381i \(0.338732\pi\)
−0.999856 + 0.0169594i \(0.994601\pi\)
\(32\) 0 0
\(33\) 6.79192 + 5.30251i 1.18232 + 0.923048i
\(34\) 0 0
\(35\) −0.936586 −0.158312
\(36\) 0 0
\(37\) 9.73051 1.59969 0.799843 0.600209i \(-0.204916\pi\)
0.799843 + 0.600209i \(0.204916\pi\)
\(38\) 0 0
\(39\) −0.299182 + 2.13435i −0.0479075 + 0.341769i
\(40\) 0 0
\(41\) 5.73705 9.93686i 0.895976 1.55188i 0.0633848 0.997989i \(-0.479810\pi\)
0.832592 0.553887i \(-0.186856\pi\)
\(42\) 0 0
\(43\) 4.80184 + 8.31704i 0.732274 + 1.26834i 0.955909 + 0.293663i \(0.0948744\pi\)
−0.223635 + 0.974673i \(0.571792\pi\)
\(44\) 0 0
\(45\) 0.681697 + 2.72581i 0.101621 + 0.406339i
\(46\) 0 0
\(47\) −0.984753 1.70564i −0.143641 0.248793i 0.785224 0.619212i \(-0.212548\pi\)
−0.928865 + 0.370418i \(0.879214\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 8.38890 3.39284i 1.17468 0.475092i
\(52\) 0 0
\(53\) −7.63418 −1.04864 −0.524318 0.851523i \(-0.675680\pi\)
−0.524318 + 0.851523i \(0.675680\pi\)
\(54\) 0 0
\(55\) −4.65935 −0.628267
\(56\) 0 0
\(57\) −8.32750 + 3.36800i −1.10300 + 0.446103i
\(58\) 0 0
\(59\) 2.43925 4.22490i 0.317563 0.550035i −0.662416 0.749136i \(-0.730469\pi\)
0.979979 + 0.199101i \(0.0638022\pi\)
\(60\) 0 0
\(61\) 1.52178 + 2.63580i 0.194844 + 0.337480i 0.946849 0.321677i \(-0.104247\pi\)
−0.752005 + 0.659157i \(0.770913\pi\)
\(62\) 0 0
\(63\) 2.88438 + 0.824844i 0.363397 + 0.103921i
\(64\) 0 0
\(65\) −0.582703 1.00927i −0.0722754 0.125185i
\(66\) 0 0
\(67\) −0.573990 + 0.994179i −0.0701240 + 0.121458i −0.898955 0.438040i \(-0.855673\pi\)
0.828831 + 0.559498i \(0.189006\pi\)
\(68\) 0 0
\(69\) −0.482159 + 3.43969i −0.0580451 + 0.414090i
\(70\) 0 0
\(71\) 8.83749 1.04882 0.524409 0.851467i \(-0.324286\pi\)
0.524409 + 0.851467i \(0.324286\pi\)
\(72\) 0 0
\(73\) 6.10698 0.714768 0.357384 0.933958i \(-0.383669\pi\)
0.357384 + 0.933958i \(0.383669\pi\)
\(74\) 0 0
\(75\) 5.62869 + 4.39437i 0.649945 + 0.507418i
\(76\) 0 0
\(77\) −2.48741 + 4.30833i −0.283467 + 0.490979i
\(78\) 0 0
\(79\) −6.05414 10.4861i −0.681144 1.17978i −0.974632 0.223813i \(-0.928150\pi\)
0.293488 0.955963i \(-0.405184\pi\)
\(80\) 0 0
\(81\) 0.301193 8.99496i 0.0334659 0.999440i
\(82\) 0 0
\(83\) −0.431332 0.747088i −0.0473448 0.0820036i 0.841382 0.540441i \(-0.181743\pi\)
−0.888727 + 0.458438i \(0.848409\pi\)
\(84\) 0 0
\(85\) −2.44658 + 4.23760i −0.265369 + 0.459632i
\(86\) 0 0
\(87\) −9.39091 7.33156i −1.00681 0.786026i
\(88\) 0 0
\(89\) −10.8480 −1.14989 −0.574943 0.818194i \(-0.694976\pi\)
−0.574943 + 0.818194i \(0.694976\pi\)
\(90\) 0 0
\(91\) −1.24431 −0.130439
\(92\) 0 0
\(93\) −1.37784 + 9.82944i −0.142876 + 1.01927i
\(94\) 0 0
\(95\) 2.42867 4.20658i 0.249176 0.431586i
\(96\) 0 0
\(97\) −3.78521 6.55618i −0.384330 0.665680i 0.607346 0.794438i \(-0.292234\pi\)
−0.991676 + 0.128758i \(0.958901\pi\)
\(98\) 0 0
\(99\) 14.3493 + 4.10345i 1.44216 + 0.412413i
\(100\) 0 0
\(101\) −2.52970 4.38156i −0.251714 0.435982i 0.712284 0.701892i \(-0.247661\pi\)
−0.963998 + 0.265910i \(0.914328\pi\)
\(102\) 0 0
\(103\) 0.119496 0.206973i 0.0117743 0.0203936i −0.860078 0.510162i \(-0.829585\pi\)
0.871853 + 0.489769i \(0.162919\pi\)
\(104\) 0 0
\(105\) −1.50387 + 0.608232i −0.146763 + 0.0593573i
\(106\) 0 0
\(107\) −9.25496 −0.894710 −0.447355 0.894356i \(-0.647634\pi\)
−0.447355 + 0.894356i \(0.647634\pi\)
\(108\) 0 0
\(109\) −10.5453 −1.01005 −0.505026 0.863104i \(-0.668517\pi\)
−0.505026 + 0.863104i \(0.668517\pi\)
\(110\) 0 0
\(111\) 15.6243 6.31913i 1.48299 0.599785i
\(112\) 0 0
\(113\) 5.06406 8.77122i 0.476387 0.825127i −0.523247 0.852181i \(-0.675279\pi\)
0.999634 + 0.0270545i \(0.00861278\pi\)
\(114\) 0 0
\(115\) −0.939078 1.62653i −0.0875695 0.151675i
\(116\) 0 0
\(117\) 0.905677 + 3.62141i 0.0837299 + 0.334799i
\(118\) 0 0
\(119\) 2.61223 + 4.52452i 0.239463 + 0.414762i
\(120\) 0 0
\(121\) −6.87445 + 11.9069i −0.624950 + 1.08245i
\(122\) 0 0
\(123\) 2.75883 19.6813i 0.248755 1.77460i
\(124\) 0 0
\(125\) −8.54429 −0.764225
\(126\) 0 0
\(127\) −6.52720 −0.579196 −0.289598 0.957148i \(-0.593522\pi\)
−0.289598 + 0.957148i \(0.593522\pi\)
\(128\) 0 0
\(129\) 13.1115 + 10.2363i 1.15440 + 0.901252i
\(130\) 0 0
\(131\) −1.76748 + 3.06136i −0.154425 + 0.267472i −0.932850 0.360266i \(-0.882686\pi\)
0.778424 + 0.627738i \(0.216019\pi\)
\(132\) 0 0
\(133\) −2.59311 4.49140i −0.224851 0.389454i
\(134\) 0 0
\(135\) 2.86478 + 3.93412i 0.246561 + 0.338595i
\(136\) 0 0
\(137\) −2.48603 4.30593i −0.212396 0.367881i 0.740068 0.672532i \(-0.234793\pi\)
−0.952464 + 0.304651i \(0.901460\pi\)
\(138\) 0 0
\(139\) 4.87566 8.44490i 0.413548 0.716287i −0.581726 0.813385i \(-0.697623\pi\)
0.995275 + 0.0970976i \(0.0309559\pi\)
\(140\) 0 0
\(141\) −2.68888 2.09923i −0.226445 0.176787i
\(142\) 0 0
\(143\) −6.19024 −0.517654
\(144\) 0 0
\(145\) 6.44230 0.535004
\(146\) 0 0
\(147\) −0.240440 + 1.71528i −0.0198311 + 0.141474i
\(148\) 0 0
\(149\) 6.39108 11.0697i 0.523578 0.906863i −0.476046 0.879421i \(-0.657930\pi\)
0.999623 0.0274426i \(-0.00873635\pi\)
\(150\) 0 0
\(151\) 11.4781 + 19.8807i 0.934078 + 1.61787i 0.776271 + 0.630400i \(0.217109\pi\)
0.157807 + 0.987470i \(0.449558\pi\)
\(152\) 0 0
\(153\) 11.2667 10.8957i 0.910857 0.880868i
\(154\) 0 0
\(155\) −2.68356 4.64806i −0.215549 0.373341i
\(156\) 0 0
\(157\) −8.25489 + 14.2979i −0.658812 + 1.14110i 0.322112 + 0.946702i \(0.395607\pi\)
−0.980924 + 0.194394i \(0.937726\pi\)
\(158\) 0 0
\(159\) −12.2582 + 4.95774i −0.972137 + 0.393174i
\(160\) 0 0
\(161\) −2.00532 −0.158041
\(162\) 0 0
\(163\) −17.2245 −1.34912 −0.674562 0.738218i \(-0.735667\pi\)
−0.674562 + 0.738218i \(0.735667\pi\)
\(164\) 0 0
\(165\) −7.48151 + 3.02585i −0.582435 + 0.235562i
\(166\) 0 0
\(167\) 6.56406 11.3693i 0.507943 0.879782i −0.492015 0.870587i \(-0.663740\pi\)
0.999958 0.00919564i \(-0.00292711\pi\)
\(168\) 0 0
\(169\) 5.72584 + 9.91745i 0.440449 + 0.762881i
\(170\) 0 0
\(171\) −11.1842 + 10.8160i −0.855278 + 0.827119i
\(172\) 0 0
\(173\) 9.49412 + 16.4443i 0.721824 + 1.25024i 0.960268 + 0.279080i \(0.0900295\pi\)
−0.238444 + 0.971156i \(0.576637\pi\)
\(174\) 0 0
\(175\) −2.06140 + 3.57046i −0.155827 + 0.269901i
\(176\) 0 0
\(177\) 1.17298 8.36799i 0.0881669 0.628976i
\(178\) 0 0
\(179\) −7.61835 −0.569422 −0.284711 0.958613i \(-0.591898\pi\)
−0.284711 + 0.958613i \(0.591898\pi\)
\(180\) 0 0
\(181\) −9.27737 −0.689581 −0.344791 0.938680i \(-0.612050\pi\)
−0.344791 + 0.938680i \(0.612050\pi\)
\(182\) 0 0
\(183\) 4.15524 + 3.24403i 0.307165 + 0.239806i
\(184\) 0 0
\(185\) −4.55673 + 7.89249i −0.335018 + 0.580267i
\(186\) 0 0
\(187\) 12.9954 + 22.5087i 0.950317 + 1.64600i
\(188\) 0 0
\(189\) 5.16710 0.548705i 0.375851 0.0399124i
\(190\) 0 0
\(191\) 4.80119 + 8.31591i 0.347402 + 0.601718i 0.985787 0.167999i \(-0.0537306\pi\)
−0.638385 + 0.769717i \(0.720397\pi\)
\(192\) 0 0
\(193\) 7.54155 13.0624i 0.542853 0.940249i −0.455886 0.890038i \(-0.650677\pi\)
0.998739 0.0502103i \(-0.0159892\pi\)
\(194\) 0 0
\(195\) −1.59108 1.24217i −0.113940 0.0889535i
\(196\) 0 0
\(197\) −11.0712 −0.788788 −0.394394 0.918942i \(-0.629045\pi\)
−0.394394 + 0.918942i \(0.629045\pi\)
\(198\) 0 0
\(199\) −18.3368 −1.29986 −0.649929 0.759995i \(-0.725201\pi\)
−0.649929 + 0.759995i \(0.725201\pi\)
\(200\) 0 0
\(201\) −0.276020 + 1.96911i −0.0194689 + 0.138890i
\(202\) 0 0
\(203\) 3.43925 5.95695i 0.241388 0.418096i
\(204\) 0 0
\(205\) 5.37324 + 9.30672i 0.375283 + 0.650010i
\(206\) 0 0
\(207\) 1.45958 + 5.83622i 0.101448 + 0.405645i
\(208\) 0 0
\(209\) −12.9003 22.3439i −0.892331 1.54556i
\(210\) 0 0
\(211\) 1.30911 2.26744i 0.0901227 0.156097i −0.817440 0.576014i \(-0.804607\pi\)
0.907563 + 0.419917i \(0.137941\pi\)
\(212\) 0 0
\(213\) 14.1903 5.73919i 0.972305 0.393243i
\(214\) 0 0
\(215\) −8.99468 −0.613432
\(216\) 0 0
\(217\) −5.73051 −0.389013
\(218\) 0 0
\(219\) 9.80595 3.96595i 0.662625 0.267994i
\(220\) 0 0
\(221\) −3.25043 + 5.62991i −0.218648 + 0.378709i
\(222\) 0 0
\(223\) −12.5442 21.7272i −0.840023 1.45496i −0.889875 0.456205i \(-0.849208\pi\)
0.0498520 0.998757i \(-0.484125\pi\)
\(224\) 0 0
\(225\) 11.8917 + 3.40067i 0.792782 + 0.226711i
\(226\) 0 0
\(227\) −12.7781 22.1323i −0.848113 1.46898i −0.882890 0.469581i \(-0.844405\pi\)
0.0347761 0.999395i \(-0.488928\pi\)
\(228\) 0 0
\(229\) −2.73657 + 4.73987i −0.180837 + 0.313220i −0.942166 0.335147i \(-0.891214\pi\)
0.761329 + 0.648366i \(0.224547\pi\)
\(230\) 0 0
\(231\) −1.19615 + 8.53323i −0.0787006 + 0.561445i
\(232\) 0 0
\(233\) 10.6774 0.699500 0.349750 0.936843i \(-0.386267\pi\)
0.349750 + 0.936843i \(0.386267\pi\)
\(234\) 0 0
\(235\) 1.84461 0.120329
\(236\) 0 0
\(237\) −16.5309 12.9058i −1.07380 0.838323i
\(238\) 0 0
\(239\) 2.50000 4.33013i 0.161712 0.280093i −0.773771 0.633465i \(-0.781632\pi\)
0.935483 + 0.353373i \(0.114965\pi\)
\(240\) 0 0
\(241\) −10.1684 17.6121i −0.655003 1.13450i −0.981893 0.189436i \(-0.939334\pi\)
0.326890 0.945062i \(-0.393999\pi\)
\(242\) 0 0
\(243\) −5.35782 14.6388i −0.343705 0.939078i
\(244\) 0 0
\(245\) −0.468293 0.811107i −0.0299181 0.0518197i
\(246\) 0 0
\(247\) 3.22664 5.58871i 0.205306 0.355601i
\(248\) 0 0
\(249\) −1.17776 0.919485i −0.0746373 0.0582700i
\(250\) 0 0
\(251\) −19.8151 −1.25072 −0.625358 0.780338i \(-0.715047\pi\)
−0.625358 + 0.780338i \(0.715047\pi\)
\(252\) 0 0
\(253\) −9.97613 −0.627194
\(254\) 0 0
\(255\) −1.17651 + 8.39314i −0.0736759 + 0.525599i
\(256\) 0 0
\(257\) 0.969506 1.67923i 0.0604761 0.104748i −0.834202 0.551459i \(-0.814071\pi\)
0.894678 + 0.446711i \(0.147405\pi\)
\(258\) 0 0
\(259\) 4.86526 + 8.42687i 0.302312 + 0.523620i
\(260\) 0 0
\(261\) −19.8402 5.67368i −1.22808 0.351192i
\(262\) 0 0
\(263\) −6.67768 11.5661i −0.411763 0.713195i 0.583320 0.812243i \(-0.301754\pi\)
−0.995083 + 0.0990481i \(0.968420\pi\)
\(264\) 0 0
\(265\) 3.57503 6.19214i 0.219613 0.380380i
\(266\) 0 0
\(267\) −17.4186 + 7.04484i −1.06600 + 0.431137i
\(268\) 0 0
\(269\) 4.15040 0.253055 0.126527 0.991963i \(-0.459617\pi\)
0.126527 + 0.991963i \(0.459617\pi\)
\(270\) 0 0
\(271\) 16.6050 1.00868 0.504341 0.863505i \(-0.331736\pi\)
0.504341 + 0.863505i \(0.331736\pi\)
\(272\) 0 0
\(273\) −1.99799 + 0.808074i −0.120924 + 0.0489068i
\(274\) 0 0
\(275\) −10.2551 + 17.7624i −0.618407 + 1.07111i
\(276\) 0 0
\(277\) −8.55414 14.8162i −0.513968 0.890219i −0.999869 0.0162051i \(-0.994842\pi\)
0.485900 0.874014i \(-0.338492\pi\)
\(278\) 0 0
\(279\) 4.17097 + 16.6779i 0.249710 + 0.998479i
\(280\) 0 0
\(281\) 7.49007 + 12.9732i 0.446820 + 0.773916i 0.998177 0.0603541i \(-0.0192230\pi\)
−0.551357 + 0.834270i \(0.685890\pi\)
\(282\) 0 0
\(283\) −9.00580 + 15.5985i −0.535339 + 0.927235i 0.463807 + 0.885936i \(0.346483\pi\)
−0.999147 + 0.0412990i \(0.986850\pi\)
\(284\) 0 0
\(285\) 1.16790 8.33171i 0.0691803 0.493528i
\(286\) 0 0
\(287\) 11.4741 0.677294
\(288\) 0 0
\(289\) 10.2950 0.605588
\(290\) 0 0
\(291\) −10.3356 8.06907i −0.605883 0.473017i
\(292\) 0 0
\(293\) 13.8362 23.9650i 0.808320 1.40005i −0.105707 0.994397i \(-0.533710\pi\)
0.914027 0.405654i \(-0.132956\pi\)
\(294\) 0 0
\(295\) 2.28456 + 3.95698i 0.133012 + 0.230384i
\(296\) 0 0
\(297\) 25.7054 2.72971i 1.49158 0.158394i
\(298\) 0 0
\(299\) −1.24762 2.16095i −0.0721519 0.124971i
\(300\) 0 0
\(301\) −4.80184 + 8.31704i −0.276774 + 0.479386i
\(302\) 0 0
\(303\) −6.90737 5.39264i −0.396818 0.309799i
\(304\) 0 0
\(305\) −2.85056 −0.163222
\(306\) 0 0
\(307\) 6.10040 0.348168 0.174084 0.984731i \(-0.444304\pi\)
0.174084 + 0.984731i \(0.444304\pi\)
\(308\) 0 0
\(309\) 0.0574631 0.409938i 0.00326896 0.0233205i
\(310\) 0 0
\(311\) 13.3277 23.0842i 0.755743 1.30898i −0.189262 0.981927i \(-0.560609\pi\)
0.945004 0.327058i \(-0.106057\pi\)
\(312\) 0 0
\(313\) −12.0681 20.9026i −0.682130 1.18148i −0.974330 0.225126i \(-0.927721\pi\)
0.292200 0.956357i \(-0.405613\pi\)
\(314\) 0 0
\(315\) −2.01977 + 1.95327i −0.113801 + 0.110054i
\(316\) 0 0
\(317\) 8.80046 + 15.2428i 0.494283 + 0.856124i 0.999978 0.00658868i \(-0.00209726\pi\)
−0.505695 + 0.862712i \(0.668764\pi\)
\(318\) 0 0
\(319\) 17.1097 29.6348i 0.957957 1.65923i
\(320\) 0 0
\(321\) −14.8607 + 6.01029i −0.829441 + 0.335462i
\(322\) 0 0
\(323\) −27.0952 −1.50762
\(324\) 0 0
\(325\) −5.13006 −0.284565
\(326\) 0 0
\(327\) −16.9325 + 6.84823i −0.936368 + 0.378708i
\(328\) 0 0
\(329\) 0.984753 1.70564i 0.0542912 0.0940351i
\(330\) 0 0
\(331\) 12.1497 + 21.0440i 0.667810 + 1.15668i 0.978515 + 0.206175i \(0.0661015\pi\)
−0.310705 + 0.950506i \(0.600565\pi\)
\(332\) 0 0
\(333\) 20.9841 20.2932i 1.14992 1.11206i
\(334\) 0 0
\(335\) −0.537591 0.931135i −0.0293717 0.0508733i
\(336\) 0 0
\(337\) −11.4722 + 19.8704i −0.624929 + 1.08241i 0.363626 + 0.931545i \(0.381539\pi\)
−0.988555 + 0.150863i \(0.951795\pi\)
\(338\) 0 0
\(339\) 2.43520 17.3726i 0.132262 0.943549i
\(340\) 0 0
\(341\) −28.5083 −1.54381
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −2.56417 2.00187i −0.138050 0.107777i
\(346\) 0 0
\(347\) −6.36930 + 11.0319i −0.341922 + 0.592226i −0.984790 0.173751i \(-0.944411\pi\)
0.642868 + 0.765977i \(0.277744\pi\)
\(348\) 0 0
\(349\) 3.99468 + 6.91899i 0.213830 + 0.370365i 0.952910 0.303253i \(-0.0980727\pi\)
−0.739080 + 0.673618i \(0.764739\pi\)
\(350\) 0 0
\(351\) 3.80603 + 5.22672i 0.203151 + 0.278982i
\(352\) 0 0
\(353\) 10.9781 + 19.0147i 0.584307 + 1.01205i 0.994961 + 0.100259i \(0.0319671\pi\)
−0.410654 + 0.911791i \(0.634700\pi\)
\(354\) 0 0
\(355\) −4.13854 + 7.16815i −0.219651 + 0.380446i
\(356\) 0 0
\(357\) 7.13273 + 5.56858i 0.377504 + 0.294721i
\(358\) 0 0
\(359\) −20.4673 −1.08022 −0.540112 0.841593i \(-0.681618\pi\)
−0.540112 + 0.841593i \(0.681618\pi\)
\(360\) 0 0
\(361\) 7.89688 0.415625
\(362\) 0 0
\(363\) −3.30578 + 23.5832i −0.173509 + 1.23780i
\(364\) 0 0
\(365\) −2.85985 + 4.95341i −0.149692 + 0.259273i
\(366\) 0 0
\(367\) −9.94174 17.2196i −0.518955 0.898856i −0.999757 0.0220269i \(-0.992988\pi\)
0.480803 0.876829i \(-0.340345\pi\)
\(368\) 0 0
\(369\) −8.35146 33.3938i −0.434760 1.73841i
\(370\) 0 0
\(371\) −3.81709 6.61139i −0.198173 0.343246i
\(372\) 0 0
\(373\) −17.1438 + 29.6939i −0.887672 + 1.53749i −0.0450513 + 0.998985i \(0.514345\pi\)
−0.842620 + 0.538508i \(0.818988\pi\)
\(374\) 0 0
\(375\) −13.7195 + 5.54878i −0.708474 + 0.286538i
\(376\) 0 0
\(377\) 8.55900 0.440811
\(378\) 0 0
\(379\) −18.6248 −0.956694 −0.478347 0.878171i \(-0.658764\pi\)
−0.478347 + 0.878171i \(0.658764\pi\)
\(380\) 0 0
\(381\) −10.4807 + 4.23885i −0.536943 + 0.217163i
\(382\) 0 0
\(383\) 16.4360 28.4680i 0.839842 1.45465i −0.0501852 0.998740i \(-0.515981\pi\)
0.890027 0.455908i \(-0.150686\pi\)
\(384\) 0 0
\(385\) −2.32968 4.03512i −0.118731 0.205649i
\(386\) 0 0
\(387\) 27.7007 + 7.92154i 1.40810 + 0.402674i
\(388\) 0 0
\(389\) 10.8250 + 18.7495i 0.548850 + 0.950635i 0.998354 + 0.0573571i \(0.0182674\pi\)
−0.449504 + 0.893278i \(0.648399\pi\)
\(390\) 0 0
\(391\) −5.23836 + 9.07311i −0.264915 + 0.458847i
\(392\) 0 0
\(393\) −0.849943 + 6.06343i −0.0428739 + 0.305860i
\(394\) 0 0
\(395\) 11.3404 0.570600
\(396\) 0 0
\(397\) 16.2721 0.816673 0.408336 0.912832i \(-0.366109\pi\)
0.408336 + 0.912832i \(0.366109\pi\)
\(398\) 0 0
\(399\) −7.08052 5.52782i −0.354470 0.276737i
\(400\) 0 0
\(401\) 4.57133 7.91777i 0.228281 0.395395i −0.729018 0.684495i \(-0.760023\pi\)
0.957299 + 0.289100i \(0.0933561\pi\)
\(402\) 0 0
\(403\) −3.56528 6.17524i −0.177599 0.307611i
\(404\) 0 0
\(405\) 7.15483 + 4.45658i 0.355526 + 0.221449i
\(406\) 0 0
\(407\) 24.2038 + 41.9222i 1.19974 + 2.07801i
\(408\) 0 0
\(409\) 11.0976 19.2217i 0.548743 0.950450i −0.449618 0.893221i \(-0.648440\pi\)
0.998361 0.0572294i \(-0.0182266\pi\)
\(410\) 0 0
\(411\) −6.78815 5.29956i −0.334835 0.261408i
\(412\) 0 0
\(413\) 4.87849 0.240055
\(414\) 0 0
\(415\) 0.807958 0.0396611
\(416\) 0 0
\(417\) 2.34461 16.7263i 0.114816 0.819089i
\(418\) 0 0
\(419\) 13.9601 24.1795i 0.681994 1.18125i −0.292378 0.956303i \(-0.594447\pi\)
0.974372 0.224945i \(-0.0722202\pi\)
\(420\) 0 0
\(421\) −12.0441 20.8611i −0.586996 1.01671i −0.994623 0.103558i \(-0.966977\pi\)
0.407628 0.913148i \(-0.366356\pi\)
\(422\) 0 0
\(423\) −5.68080 1.62453i −0.276210 0.0789875i
\(424\) 0 0
\(425\) 10.7697 + 18.6537i 0.522408 + 0.904838i
\(426\) 0 0
\(427\) −1.52178 + 2.63580i −0.0736442 + 0.127555i
\(428\) 0 0
\(429\) −9.93965 + 4.02003i −0.479891 + 0.194089i
\(430\) 0 0
\(431\) 26.1623 1.26020 0.630098 0.776516i \(-0.283015\pi\)
0.630098 + 0.776516i \(0.283015\pi\)
\(432\) 0 0
\(433\) −18.5630 −0.892082 −0.446041 0.895013i \(-0.647166\pi\)
−0.446041 + 0.895013i \(0.647166\pi\)
\(434\) 0 0
\(435\) 10.3444 4.18372i 0.495975 0.200594i
\(436\) 0 0
\(437\) 5.20002 9.00670i 0.248751 0.430849i
\(438\) 0 0
\(439\) 3.85395 + 6.67524i 0.183939 + 0.318592i 0.943218 0.332173i \(-0.107782\pi\)
−0.759279 + 0.650765i \(0.774448\pi\)
\(440\) 0 0
\(441\) 0.727853 + 2.91037i 0.0346597 + 0.138589i
\(442\) 0 0
\(443\) 16.5204 + 28.6142i 0.784909 + 1.35950i 0.929053 + 0.369945i \(0.120624\pi\)
−0.144145 + 0.989557i \(0.546043\pi\)
\(444\) 0 0
\(445\) 5.08004 8.79889i 0.240817 0.417107i
\(446\) 0 0
\(447\) 3.07334 21.9250i 0.145364 1.03702i
\(448\) 0 0
\(449\) 19.9283 0.940477 0.470238 0.882540i \(-0.344168\pi\)
0.470238 + 0.882540i \(0.344168\pi\)
\(450\) 0 0
\(451\) 57.0816 2.68787
\(452\) 0 0
\(453\) 31.3412 + 24.4683i 1.47254 + 1.14962i
\(454\) 0 0
\(455\) 0.582703 1.00927i 0.0273175 0.0473154i
\(456\) 0 0
\(457\) 16.9326 + 29.3282i 0.792075 + 1.37191i 0.924680 + 0.380745i \(0.124333\pi\)
−0.132605 + 0.991169i \(0.542334\pi\)
\(458\) 0 0
\(459\) 11.0150 24.8120i 0.514138 1.15812i
\(460\) 0 0
\(461\) 7.25351 + 12.5634i 0.337830 + 0.585138i 0.984024 0.178035i \(-0.0569739\pi\)
−0.646195 + 0.763173i \(0.723641\pi\)
\(462\) 0 0
\(463\) 12.5348 21.7110i 0.582544 1.00900i −0.412633 0.910897i \(-0.635391\pi\)
0.995177 0.0980981i \(-0.0312759\pi\)
\(464\) 0 0
\(465\) −7.32750 5.72064i −0.339805 0.265288i
\(466\) 0 0
\(467\) 0.102955 0.00476419 0.00238209 0.999997i \(-0.499242\pi\)
0.00238209 + 0.999997i \(0.499242\pi\)
\(468\) 0 0
\(469\) −1.14798 −0.0530088
\(470\) 0 0
\(471\) −3.96961 + 28.3189i −0.182910 + 1.30487i
\(472\) 0 0
\(473\) −23.8883 + 41.3758i −1.09839 + 1.90246i
\(474\) 0 0
\(475\) −10.6909 18.5172i −0.490532 0.849626i
\(476\) 0 0
\(477\) −16.4633 + 15.9213i −0.753802 + 0.728984i
\(478\) 0 0
\(479\) 2.62668 + 4.54954i 0.120016 + 0.207874i 0.919774 0.392449i \(-0.128372\pi\)
−0.799758 + 0.600323i \(0.795039\pi\)
\(480\) 0 0
\(481\) −6.05390 + 10.4857i −0.276034 + 0.478105i
\(482\) 0 0
\(483\) −3.21994 + 1.30228i −0.146512 + 0.0592559i
\(484\) 0 0
\(485\) 7.09036 0.321957
\(486\) 0 0
\(487\) 30.7319 1.39260 0.696299 0.717752i \(-0.254829\pi\)
0.696299 + 0.717752i \(0.254829\pi\)
\(488\) 0 0
\(489\) −27.6573 + 11.1858i −1.25070 + 0.505839i
\(490\) 0 0
\(491\) −2.35920 + 4.08626i −0.106469 + 0.184410i −0.914338 0.404953i \(-0.867288\pi\)
0.807868 + 0.589363i \(0.200621\pi\)
\(492\) 0 0
\(493\) −17.9682 31.1219i −0.809248 1.40166i
\(494\) 0 0
\(495\) −10.0480 + 9.71719i −0.451624 + 0.436755i
\(496\) 0 0
\(497\) 4.41875 + 7.65349i 0.198208 + 0.343306i
\(498\) 0 0
\(499\) 12.3566 21.4023i 0.553158 0.958098i −0.444886 0.895587i \(-0.646756\pi\)
0.998044 0.0625105i \(-0.0199107\pi\)
\(500\) 0 0
\(501\) 3.15652 22.5184i 0.141023 1.00605i
\(502\) 0 0
\(503\) 19.4083 0.865371 0.432686 0.901545i \(-0.357566\pi\)
0.432686 + 0.901545i \(0.357566\pi\)
\(504\) 0 0
\(505\) 4.73856 0.210863
\(506\) 0 0
\(507\) 15.6345 + 12.2060i 0.694352 + 0.542087i
\(508\) 0 0
\(509\) −2.72850 + 4.72591i −0.120939 + 0.209472i −0.920138 0.391594i \(-0.871924\pi\)
0.799199 + 0.601066i \(0.205257\pi\)
\(510\) 0 0
\(511\) 3.05349 + 5.28880i 0.135078 + 0.233963i
\(512\) 0 0
\(513\) −10.9344 + 24.6304i −0.482766 + 1.08746i
\(514\) 0 0
\(515\) 0.111918 + 0.193848i 0.00493170 + 0.00854196i
\(516\) 0 0
\(517\) 4.89897 8.48527i 0.215457 0.373182i
\(518\) 0 0
\(519\) 25.9238 + 20.2389i 1.13793 + 0.888391i
\(520\) 0 0
\(521\) −24.7683 −1.08512 −0.542558 0.840018i \(-0.682544\pi\)
−0.542558 + 0.840018i \(0.682544\pi\)
\(522\) 0 0
\(523\) 32.7530 1.43219 0.716094 0.698004i \(-0.245928\pi\)
0.716094 + 0.698004i \(0.245928\pi\)
\(524\) 0 0
\(525\) −0.991287 + 7.07177i −0.0432633 + 0.308637i
\(526\) 0 0
\(527\) −14.9694 + 25.9278i −0.652078 + 1.12943i
\(528\) 0 0
\(529\) 9.48934 + 16.4360i 0.412580 + 0.714610i
\(530\) 0 0
\(531\) −3.55083 14.1982i −0.154093 0.616149i
\(532\) 0 0
\(533\) 7.13868 + 12.3646i 0.309211 + 0.535569i
\(534\) 0 0
\(535\) 4.33403 7.50676i 0.187377 0.324546i
\(536\) 0 0
\(537\) −12.2328 + 4.94746i −0.527883 + 0.213499i
\(538\) 0 0
\(539\) −4.97483 −0.214281
\(540\) 0 0
\(541\) 37.8575 1.62762 0.813811 0.581130i \(-0.197389\pi\)
0.813811 + 0.581130i \(0.197389\pi\)
\(542\) 0 0
\(543\) −14.8966 + 6.02485i −0.639276 + 0.258551i
\(544\) 0 0
\(545\) 4.93827 8.55333i 0.211532 0.366385i
\(546\) 0 0
\(547\) 1.74835 + 3.02824i 0.0747543 + 0.129478i 0.900979 0.433862i \(-0.142849\pi\)
−0.826225 + 0.563340i \(0.809516\pi\)
\(548\) 0 0
\(549\) 8.77878 + 2.51046i 0.374669 + 0.107144i
\(550\) 0 0
\(551\) 17.8367 + 30.8941i 0.759869 + 1.31613i
\(552\) 0 0
\(553\) 6.05414 10.4861i 0.257448 0.445913i
\(554\) 0 0
\(555\) −2.19124 + 15.6322i −0.0930129 + 0.663548i
\(556\) 0 0
\(557\) −34.1226 −1.44582 −0.722911 0.690941i \(-0.757197\pi\)
−0.722911 + 0.690941i \(0.757197\pi\)
\(558\) 0 0
\(559\) −11.9500 −0.505431
\(560\) 0 0
\(561\) 35.4841 + 27.7027i 1.49814 + 1.16961i
\(562\) 0 0
\(563\) 7.65071 13.2514i 0.322439 0.558481i −0.658552 0.752535i \(-0.728831\pi\)
0.980991 + 0.194055i \(0.0621640\pi\)
\(564\) 0 0
\(565\) 4.74293 + 8.21500i 0.199537 + 0.345608i
\(566\) 0 0
\(567\) 7.94046 4.23664i 0.333468 0.177922i
\(568\) 0 0
\(569\) −16.4953 28.5707i −0.691520 1.19775i −0.971340 0.237695i \(-0.923608\pi\)
0.279820 0.960053i \(-0.409725\pi\)
\(570\) 0 0
\(571\) −10.7150 + 18.5590i −0.448410 + 0.776668i −0.998283 0.0585801i \(-0.981343\pi\)
0.549873 + 0.835248i \(0.314676\pi\)
\(572\) 0 0
\(573\) 13.1097 + 10.2349i 0.547667 + 0.427568i
\(574\) 0 0
\(575\) −8.26755 −0.344781
\(576\) 0 0
\(577\) −38.4188 −1.59939 −0.799697 0.600404i \(-0.795007\pi\)
−0.799697 + 0.600404i \(0.795007\pi\)
\(578\) 0 0
\(579\) 3.62658 25.8718i 0.150715 1.07519i
\(580\) 0 0
\(581\) 0.431332 0.747088i 0.0178947 0.0309944i
\(582\) 0 0
\(583\) −18.9894 32.8905i −0.786459 1.36219i
\(584\) 0 0
\(585\) −3.36147 0.961278i −0.138980 0.0397439i
\(586\) 0 0
\(587\) −8.43772 14.6146i −0.348262 0.603207i 0.637679 0.770302i \(-0.279895\pi\)
−0.985941 + 0.167095i \(0.946561\pi\)
\(588\) 0 0
\(589\) 14.8599 25.7380i 0.612290 1.06052i
\(590\) 0 0
\(591\) −17.7769 + 7.18976i −0.731245 + 0.295747i
\(592\) 0 0
\(593\) 21.7817 0.894467 0.447233 0.894417i \(-0.352409\pi\)
0.447233 + 0.894417i \(0.352409\pi\)
\(594\) 0 0
\(595\) −4.89316 −0.200600
\(596\) 0 0
\(597\) −29.4433 + 11.9081i −1.20503 + 0.487368i
\(598\) 0 0
\(599\) −13.3778 + 23.1710i −0.546601 + 0.946740i 0.451904 + 0.892067i \(0.350745\pi\)
−0.998504 + 0.0546732i \(0.982588\pi\)
\(600\) 0 0
\(601\) 12.5615 + 21.7571i 0.512393 + 0.887491i 0.999897 + 0.0143699i \(0.00457423\pi\)
−0.487504 + 0.873121i \(0.662092\pi\)
\(602\) 0 0
\(603\) 0.835561 + 3.34104i 0.0340267 + 0.136058i
\(604\) 0 0
\(605\) −6.43852 11.1518i −0.261763 0.453387i
\(606\) 0 0
\(607\) 4.31975 7.48203i 0.175333 0.303686i −0.764943 0.644098i \(-0.777233\pi\)
0.940277 + 0.340411i \(0.110566\pi\)
\(608\) 0 0
\(609\) 1.65386 11.7985i 0.0670179 0.478101i
\(610\) 0 0
\(611\) 2.45068 0.0991440
\(612\) 0 0
\(613\) 46.1789 1.86515 0.932575 0.360977i \(-0.117557\pi\)
0.932575 + 0.360977i \(0.117557\pi\)
\(614\) 0 0
\(615\) 14.6717 + 11.4543i 0.591620 + 0.461883i
\(616\) 0 0
\(617\) 5.76222 9.98046i 0.231978 0.401798i −0.726412 0.687260i \(-0.758814\pi\)
0.958390 + 0.285461i \(0.0921468\pi\)
\(618\) 0 0
\(619\) 19.6325 + 34.0045i 0.789096 + 1.36675i 0.926521 + 0.376242i \(0.122784\pi\)
−0.137425 + 0.990512i \(0.543883\pi\)
\(620\) 0 0
\(621\) 6.13376 + 8.42333i 0.246139 + 0.338016i
\(622\) 0 0
\(623\) −5.42400 9.39464i −0.217308 0.376388i
\(624\) 0 0
\(625\) −6.30578 + 10.9219i −0.252231 + 0.436877i
\(626\) 0 0
\(627\) −35.2244 27.5000i −1.40673 1.09824i
\(628\) 0 0
\(629\) 50.8367 2.02699
\(630\) 0 0
\(631\) −22.8387 −0.909193 −0.454596 0.890698i \(-0.650216\pi\)
−0.454596 + 0.890698i \(0.650216\pi\)
\(632\) 0 0
\(633\) 0.629523 4.49098i 0.0250213 0.178500i
\(634\) 0 0
\(635\) 3.05664 5.29426i 0.121299 0.210096i
\(636\) 0 0
\(637\) −0.622156 1.07761i −0.0246507 0.0426963i
\(638\) 0 0
\(639\) 19.0583 18.4308i 0.753933 0.729111i
\(640\) 0 0
\(641\) 9.04899 + 15.6733i 0.357413 + 0.619058i 0.987528 0.157444i \(-0.0503254\pi\)
−0.630114 + 0.776502i \(0.716992\pi\)
\(642\) 0 0
\(643\) −15.0416 + 26.0529i −0.593184 + 1.02742i 0.400616 + 0.916246i \(0.368796\pi\)
−0.993800 + 0.111179i \(0.964537\pi\)
\(644\) 0 0
\(645\) −14.4427 + 5.84127i −0.568682 + 0.230000i
\(646\) 0 0
\(647\) 25.1323 0.988054 0.494027 0.869447i \(-0.335524\pi\)
0.494027 + 0.869447i \(0.335524\pi\)
\(648\) 0 0
\(649\) 24.2697 0.952668
\(650\) 0 0
\(651\) −9.20147 + 3.72147i −0.360634 + 0.145856i
\(652\) 0 0
\(653\) −5.24884 + 9.09125i −0.205403 + 0.355768i −0.950261 0.311455i \(-0.899184\pi\)
0.744858 + 0.667223i \(0.232517\pi\)
\(654\) 0 0
\(655\) −1.65539 2.86722i −0.0646815 0.112032i
\(656\) 0 0
\(657\) 13.1698 12.7362i 0.513804 0.496888i
\(658\) 0 0
\(659\) −4.04138 6.99988i −0.157430 0.272677i 0.776511 0.630103i \(-0.216988\pi\)
−0.933941 + 0.357427i \(0.883654\pi\)
\(660\) 0 0
\(661\) 13.4530 23.3012i 0.523260 0.906312i −0.476374 0.879243i \(-0.658049\pi\)
0.999634 0.0270695i \(-0.00861755\pi\)
\(662\) 0 0
\(663\) −1.56307 + 11.1508i −0.0607045 + 0.433062i
\(664\) 0 0
\(665\) 4.85734 0.188360
\(666\) 0 0
\(667\) 13.7936 0.534090
\(668\) 0 0
\(669\) −34.2521 26.7409i −1.32426 1.03386i
\(670\) 0 0
\(671\) −7.57060 + 13.1127i −0.292260 + 0.506209i
\(672\) 0 0
\(673\) 6.11160 + 10.5856i 0.235585 + 0.408045i 0.959443 0.281904i \(-0.0909661\pi\)
−0.723858 + 0.689949i \(0.757633\pi\)
\(674\) 0 0
\(675\) 21.3030 2.26220i 0.819951 0.0870723i
\(676\) 0 0
\(677\) −3.34015 5.78531i −0.128372 0.222348i 0.794674 0.607037i \(-0.207642\pi\)
−0.923046 + 0.384689i \(0.874309\pi\)
\(678\) 0 0
\(679\) 3.78521 6.55618i 0.145263 0.251603i
\(680\) 0 0
\(681\) −34.8908 27.2396i −1.33702 1.04382i
\(682\) 0 0
\(683\) −19.2125 −0.735146 −0.367573 0.929995i \(-0.619811\pi\)
−0.367573 + 0.929995i \(0.619811\pi\)
\(684\) 0 0
\(685\) 4.65677 0.177926
\(686\) 0 0
\(687\) −1.31596 + 9.38796i −0.0502070 + 0.358173i
\(688\) 0 0
\(689\) 4.74966 8.22664i 0.180947 0.313410i
\(690\) 0 0
\(691\) −5.72706 9.91955i −0.217867 0.377357i 0.736288 0.676668i \(-0.236577\pi\)
−0.954156 + 0.299310i \(0.903243\pi\)
\(692\) 0 0
\(693\) 3.62094 + 14.4786i 0.137548 + 0.549995i
\(694\) 0 0
\(695\) 4.56648 + 7.90937i 0.173216 + 0.300020i
\(696\) 0 0
\(697\) 29.9730 51.9147i 1.13531 1.96641i
\(698\) 0 0
\(699\) 17.1447 6.93405i 0.648471 0.262270i
\(700\) 0 0
\(701\) −4.29596 −0.162256 −0.0811281 0.996704i \(-0.525852\pi\)
−0.0811281 + 0.996704i \(0.525852\pi\)
\(702\) 0 0
\(703\) −50.4646 −1.90331
\(704\) 0 0
\(705\) 2.96189 1.19792i 0.111551 0.0451161i
\(706\) 0 0
\(707\) 2.52970 4.38156i 0.0951390 0.164786i
\(708\) 0 0
\(709\) −6.44506 11.1632i −0.242049 0.419242i 0.719248 0.694753i \(-0.244486\pi\)
−0.961298 + 0.275511i \(0.911153\pi\)
\(710\) 0 0
\(711\) −34.9248 9.98743i −1.30978 0.374558i
\(712\) 0 0
\(713\) −5.74576 9.95195i −0.215180 0.372703i
\(714\) 0 0
\(715\) 2.89885 5.02095i 0.108411 0.187773i
\(716\) 0 0
\(717\) 1.20220 8.57640i 0.0448969 0.320292i
\(718\) 0 0
\(719\) −5.46489 −0.203806 −0.101903 0.994794i \(-0.532493\pi\)
−0.101903 + 0.994794i \(0.532493\pi\)
\(720\) 0 0
\(721\) 0.238992 0.00890051
\(722\) 0 0
\(723\) −27.7649 21.6763i −1.03259 0.806150i
\(724\) 0 0
\(725\) 14.1793 24.5594i 0.526608 0.912111i
\(726\) 0 0
\(727\) −24.9300 43.1800i −0.924601 1.60146i −0.792201 0.610260i \(-0.791065\pi\)
−0.132401 0.991196i \(-0.542269\pi\)
\(728\) 0 0
\(729\) −18.1097 20.0260i −0.670728 0.741703i
\(730\) 0 0
\(731\) 25.0870 + 43.4520i 0.927878 + 1.60713i
\(732\) 0 0
\(733\) 17.6123 30.5054i 0.650525 1.12674i −0.332471 0.943114i \(-0.607882\pi\)
0.982996 0.183629i \(-0.0587844\pi\)
\(734\) 0 0
\(735\) −1.27868 0.998277i −0.0471648 0.0368220i
\(736\) 0 0
\(737\) −5.71100 −0.210367
\(738\) 0 0
\(739\) 35.7209 1.31401 0.657007 0.753885i \(-0.271822\pi\)
0.657007 + 0.753885i \(0.271822\pi\)
\(740\) 0 0
\(741\) 1.55163 11.0692i 0.0570004 0.406637i
\(742\) 0 0
\(743\) 6.53043 11.3110i 0.239578 0.414962i −0.721015 0.692919i \(-0.756324\pi\)
0.960593 + 0.277958i \(0.0896575\pi\)
\(744\) 0 0
\(745\) 5.98580 + 10.3677i 0.219303 + 0.379843i
\(746\) 0 0
\(747\) −2.48825 0.711562i −0.0910402 0.0260347i
\(748\) 0 0
\(749\) −4.62748 8.01503i −0.169084 0.292863i
\(750\) 0 0
\(751\) −1.11223 + 1.92644i −0.0405859 + 0.0702968i −0.885605 0.464440i \(-0.846256\pi\)
0.845019 + 0.534736i \(0.179589\pi\)
\(752\) 0 0
\(753\) −31.8170 + 12.8682i −1.15948 + 0.468943i
\(754\) 0 0
\(755\) −21.5005 −0.782484
\(756\) 0 0
\(757\) 4.27335 0.155317 0.0776587 0.996980i \(-0.475256\pi\)
0.0776587 + 0.996980i \(0.475256\pi\)
\(758\) 0 0
\(759\) −16.0186 + 6.47863i −0.581440 + 0.235159i
\(760\) 0 0
\(761\) −25.2206 + 43.6833i −0.914245 + 1.58352i −0.106242 + 0.994340i \(0.533882\pi\)
−0.808003 + 0.589179i \(0.799451\pi\)
\(762\) 0 0
\(763\) −5.27263 9.13246i −0.190882 0.330617i
\(764\) 0 0
\(765\) 3.56150 + 14.2409i 0.128766 + 0.514880i
\(766\) 0 0
\(767\) 3.03519 + 5.25710i 0.109594 + 0.189823i
\(768\) 0 0
\(769\) 1.03493 1.79255i 0.0373205 0.0646411i −0.846762 0.531972i \(-0.821451\pi\)
0.884082 + 0.467331i \(0.154784\pi\)
\(770\) 0 0
\(771\) 0.466215 3.32595i 0.0167903 0.119781i
\(772\) 0 0
\(773\) −28.3739 −1.02054 −0.510269 0.860015i \(-0.670454\pi\)
−0.510269 + 0.860015i \(0.670454\pi\)
\(774\) 0 0
\(775\) −23.6258 −0.848664
\(776\) 0 0
\(777\) 13.2847 + 10.3714i 0.476584 + 0.372073i
\(778\) 0 0
\(779\) −29.7536 + 51.5347i −1.06603 + 1.84642i
\(780\) 0 0
\(781\) 21.9825 + 38.0748i 0.786595 + 1.36242i
\(782\) 0 0
\(783\) −35.5419 + 3.77426i −1.27016 + 0.134881i
\(784\) 0 0
\(785\) −7.73141 13.3912i −0.275946 0.477952i
\(786\) 0 0
\(787\) −1.72536 + 2.98841i −0.0615025 + 0.106525i −0.895137 0.445791i \(-0.852923\pi\)
0.833635 + 0.552316i \(0.186256\pi\)
\(788\) 0 0
\(789\) −18.2335 14.2350i −0.649129 0.506781i
\(790\) 0 0
\(791\) 10.1281 0.360115
\(792\) 0 0
\(793\) −3.78714 −0.134485
\(794\) 0 0
\(795\) 1.71916 12.2644i 0.0609723 0.434973i
\(796\) 0 0
\(797\) 11.2230 19.4388i 0.397540 0.688559i −0.595882 0.803072i \(-0.703197\pi\)
0.993422 + 0.114513i \(0.0365308\pi\)
\(798\)