Properties

Label 74.2.b.a.73.2
Level $74$
Weight $2$
Character 74.73
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{21})\)
Defining polynomial: \( x^{4} + 11x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 73.2
Root \(-1.79129i\) of defining polynomial
Character \(\chi\) \(=\) 74.73
Dual form 74.2.b.a.73.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} +0.791288i q^{5} -1.79129i q^{6} -2.00000 q^{7} +1.00000i q^{8} +0.208712 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.79129 q^{3} -1.00000 q^{4} +0.791288i q^{5} -1.79129i q^{6} -2.00000 q^{7} +1.00000i q^{8} +0.208712 q^{9} +0.791288 q^{10} -0.791288 q^{11} -1.79129 q^{12} -3.79129i q^{13} +2.00000i q^{14} +1.41742i q^{15} +1.00000 q^{16} +7.58258i q^{17} -0.208712i q^{18} +1.58258i q^{19} -0.791288i q^{20} -3.58258 q^{21} +0.791288i q^{22} -3.79129i q^{23} +1.79129i q^{24} +4.37386 q^{25} -3.79129 q^{26} -5.00000 q^{27} +2.00000 q^{28} +3.79129i q^{29} +1.41742 q^{30} -8.37386i q^{31} -1.00000i q^{32} -1.41742 q^{33} +7.58258 q^{34} -1.58258i q^{35} -0.208712 q^{36} +(4.00000 - 4.58258i) q^{37} +1.58258 q^{38} -6.79129i q^{39} -0.791288 q^{40} +9.79129 q^{41} +3.58258i q^{42} -6.00000i q^{43} +0.791288 q^{44} +0.165151i q^{45} -3.79129 q^{46} -7.58258 q^{47} +1.79129 q^{48} -3.00000 q^{49} -4.37386i q^{50} +13.5826i q^{51} +3.79129i q^{52} -1.58258 q^{53} +5.00000i q^{54} -0.626136i q^{55} -2.00000i q^{56} +2.83485i q^{57} +3.79129 q^{58} +1.58258i q^{59} -1.41742i q^{60} +12.7913i q^{61} -8.37386 q^{62} -0.417424 q^{63} -1.00000 q^{64} +3.00000 q^{65} +1.41742i q^{66} +6.37386 q^{67} -7.58258i q^{68} -6.79129i q^{69} -1.58258 q^{70} -9.16515 q^{71} +0.208712i q^{72} -4.37386 q^{73} +(-4.58258 - 4.00000i) q^{74} +7.83485 q^{75} -1.58258i q^{76} +1.58258 q^{77} -6.79129 q^{78} +8.20871i q^{79} +0.791288i q^{80} -9.58258 q^{81} -9.79129i q^{82} +15.1652 q^{83} +3.58258 q^{84} -6.00000 q^{85} -6.00000 q^{86} +6.79129i q^{87} -0.791288i q^{88} +6.00000i q^{89} +0.165151 q^{90} +7.58258i q^{91} +3.79129i q^{92} -15.0000i q^{93} +7.58258i q^{94} -1.25227 q^{95} -1.79129i q^{96} -13.5826i q^{97} +3.00000i q^{98} -0.165151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 4 q^{4} - 8 q^{7} + 10 q^{9} - 6 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{16} + 4 q^{21} - 10 q^{25} - 6 q^{26} - 20 q^{27} + 8 q^{28} + 24 q^{30} - 24 q^{33} + 12 q^{34} - 10 q^{36} + 16 q^{37} - 12 q^{38} + 6 q^{40} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 12 q^{47} - 2 q^{48} - 12 q^{49} + 12 q^{53} + 6 q^{58} - 6 q^{62} - 20 q^{63} - 4 q^{64} + 12 q^{65} - 2 q^{67} + 12 q^{70} + 10 q^{73} + 68 q^{75} - 12 q^{77} - 18 q^{78} - 20 q^{81} + 24 q^{83} - 4 q^{84} - 24 q^{85} - 24 q^{86} - 36 q^{90} - 60 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.79129 1.03420 0.517100 0.855925i \(-0.327011\pi\)
0.517100 + 0.855925i \(0.327011\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.791288i 0.353875i 0.984222 + 0.176937i \(0.0566190\pi\)
−0.984222 + 0.176937i \(0.943381\pi\)
\(6\) 1.79129i 0.731290i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.208712 0.0695707
\(10\) 0.791288 0.250227
\(11\) −0.791288 −0.238582 −0.119291 0.992859i \(-0.538062\pi\)
−0.119291 + 0.992859i \(0.538062\pi\)
\(12\) −1.79129 −0.517100
\(13\) 3.79129i 1.05151i −0.850635 0.525757i \(-0.823782\pi\)
0.850635 0.525757i \(-0.176218\pi\)
\(14\) 2.00000i 0.534522i
\(15\) 1.41742i 0.365977i
\(16\) 1.00000 0.250000
\(17\) 7.58258i 1.83904i 0.393038 + 0.919522i \(0.371424\pi\)
−0.393038 + 0.919522i \(0.628576\pi\)
\(18\) 0.208712i 0.0491939i
\(19\) 1.58258i 0.363068i 0.983385 + 0.181534i \(0.0581062\pi\)
−0.983385 + 0.181534i \(0.941894\pi\)
\(20\) 0.791288i 0.176937i
\(21\) −3.58258 −0.781782
\(22\) 0.791288i 0.168703i
\(23\) 3.79129i 0.790538i −0.918565 0.395269i \(-0.870651\pi\)
0.918565 0.395269i \(-0.129349\pi\)
\(24\) 1.79129i 0.365645i
\(25\) 4.37386 0.874773
\(26\) −3.79129 −0.743533
\(27\) −5.00000 −0.962250
\(28\) 2.00000 0.377964
\(29\) 3.79129i 0.704024i 0.935995 + 0.352012i \(0.114502\pi\)
−0.935995 + 0.352012i \(0.885498\pi\)
\(30\) 1.41742 0.258785
\(31\) 8.37386i 1.50399i −0.659169 0.751995i \(-0.729092\pi\)
0.659169 0.751995i \(-0.270908\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −1.41742 −0.246742
\(34\) 7.58258 1.30040
\(35\) 1.58258i 0.267504i
\(36\) −0.208712 −0.0347854
\(37\) 4.00000 4.58258i 0.657596 0.753371i
\(38\) 1.58258 0.256728
\(39\) 6.79129i 1.08748i
\(40\) −0.791288 −0.125114
\(41\) 9.79129 1.52914 0.764571 0.644539i \(-0.222951\pi\)
0.764571 + 0.644539i \(0.222951\pi\)
\(42\) 3.58258i 0.552803i
\(43\) 6.00000i 0.914991i −0.889212 0.457496i \(-0.848747\pi\)
0.889212 0.457496i \(-0.151253\pi\)
\(44\) 0.791288 0.119291
\(45\) 0.165151i 0.0246193i
\(46\) −3.79129 −0.558995
\(47\) −7.58258 −1.10603 −0.553016 0.833171i \(-0.686523\pi\)
−0.553016 + 0.833171i \(0.686523\pi\)
\(48\) 1.79129 0.258550
\(49\) −3.00000 −0.428571
\(50\) 4.37386i 0.618558i
\(51\) 13.5826i 1.90194i
\(52\) 3.79129i 0.525757i
\(53\) −1.58258 −0.217383 −0.108692 0.994076i \(-0.534666\pi\)
−0.108692 + 0.994076i \(0.534666\pi\)
\(54\) 5.00000i 0.680414i
\(55\) 0.626136i 0.0844282i
\(56\) 2.00000i 0.267261i
\(57\) 2.83485i 0.375485i
\(58\) 3.79129 0.497820
\(59\) 1.58258i 0.206034i 0.994680 + 0.103017i \(0.0328496\pi\)
−0.994680 + 0.103017i \(0.967150\pi\)
\(60\) 1.41742i 0.182989i
\(61\) 12.7913i 1.63776i 0.573967 + 0.818878i \(0.305404\pi\)
−0.573967 + 0.818878i \(0.694596\pi\)
\(62\) −8.37386 −1.06348
\(63\) −0.417424 −0.0525905
\(64\) −1.00000 −0.125000
\(65\) 3.00000 0.372104
\(66\) 1.41742i 0.174473i
\(67\) 6.37386 0.778691 0.389346 0.921092i \(-0.372701\pi\)
0.389346 + 0.921092i \(0.372701\pi\)
\(68\) 7.58258i 0.919522i
\(69\) 6.79129i 0.817575i
\(70\) −1.58258 −0.189154
\(71\) −9.16515 −1.08770 −0.543852 0.839181i \(-0.683035\pi\)
−0.543852 + 0.839181i \(0.683035\pi\)
\(72\) 0.208712i 0.0245970i
\(73\) −4.37386 −0.511922 −0.255961 0.966687i \(-0.582392\pi\)
−0.255961 + 0.966687i \(0.582392\pi\)
\(74\) −4.58258 4.00000i −0.532714 0.464991i
\(75\) 7.83485 0.904690
\(76\) 1.58258i 0.181534i
\(77\) 1.58258 0.180351
\(78\) −6.79129 −0.768962
\(79\) 8.20871i 0.923552i 0.886997 + 0.461776i \(0.152788\pi\)
−0.886997 + 0.461776i \(0.847212\pi\)
\(80\) 0.791288i 0.0884687i
\(81\) −9.58258 −1.06473
\(82\) 9.79129i 1.08127i
\(83\) 15.1652 1.66459 0.832296 0.554332i \(-0.187026\pi\)
0.832296 + 0.554332i \(0.187026\pi\)
\(84\) 3.58258 0.390891
\(85\) −6.00000 −0.650791
\(86\) −6.00000 −0.646997
\(87\) 6.79129i 0.728102i
\(88\) 0.791288i 0.0843516i
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 0.165151 0.0174085
\(91\) 7.58258i 0.794870i
\(92\) 3.79129i 0.395269i
\(93\) 15.0000i 1.55543i
\(94\) 7.58258i 0.782083i
\(95\) −1.25227 −0.128480
\(96\) 1.79129i 0.182823i
\(97\) 13.5826i 1.37910i −0.724237 0.689551i \(-0.757808\pi\)
0.724237 0.689551i \(-0.242192\pi\)
\(98\) 3.00000i 0.303046i
\(99\) −0.165151 −0.0165983
\(100\) −4.37386 −0.437386
\(101\) 7.58258 0.754494 0.377247 0.926113i \(-0.376871\pi\)
0.377247 + 0.926113i \(0.376871\pi\)
\(102\) 13.5826 1.34488
\(103\) 6.79129i 0.669165i 0.942366 + 0.334583i \(0.108595\pi\)
−0.942366 + 0.334583i \(0.891405\pi\)
\(104\) 3.79129 0.371766
\(105\) 2.83485i 0.276653i
\(106\) 1.58258i 0.153713i
\(107\) −5.37386 −0.519511 −0.259755 0.965674i \(-0.583642\pi\)
−0.259755 + 0.965674i \(0.583642\pi\)
\(108\) 5.00000 0.481125
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) −0.626136 −0.0596998
\(111\) 7.16515 8.20871i 0.680086 0.779136i
\(112\) −2.00000 −0.188982
\(113\) 10.4174i 0.979989i −0.871726 0.489994i \(-0.836999\pi\)
0.871726 0.489994i \(-0.163001\pi\)
\(114\) 2.83485 0.265508
\(115\) 3.00000 0.279751
\(116\) 3.79129i 0.352012i
\(117\) 0.791288i 0.0731546i
\(118\) 1.58258 0.145688
\(119\) 15.1652i 1.39019i
\(120\) −1.41742 −0.129393
\(121\) −10.3739 −0.943079
\(122\) 12.7913 1.15807
\(123\) 17.5390 1.58144
\(124\) 8.37386i 0.751995i
\(125\) 7.41742i 0.663435i
\(126\) 0.417424i 0.0371871i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.7477i 0.946285i
\(130\) 3.00000i 0.263117i
\(131\) 16.7477i 1.46326i 0.681704 + 0.731628i \(0.261239\pi\)
−0.681704 + 0.731628i \(0.738761\pi\)
\(132\) 1.41742 0.123371
\(133\) 3.16515i 0.274453i
\(134\) 6.37386i 0.550618i
\(135\) 3.95644i 0.340516i
\(136\) −7.58258 −0.650201
\(137\) −3.62614 −0.309802 −0.154901 0.987930i \(-0.549506\pi\)
−0.154901 + 0.987930i \(0.549506\pi\)
\(138\) −6.79129 −0.578113
\(139\) −13.3739 −1.13436 −0.567178 0.823595i \(-0.691965\pi\)
−0.567178 + 0.823595i \(0.691965\pi\)
\(140\) 1.58258i 0.133752i
\(141\) −13.5826 −1.14386
\(142\) 9.16515i 0.769122i
\(143\) 3.00000i 0.250873i
\(144\) 0.208712 0.0173927
\(145\) −3.00000 −0.249136
\(146\) 4.37386i 0.361984i
\(147\) −5.37386 −0.443229
\(148\) −4.00000 + 4.58258i −0.328798 + 0.376685i
\(149\) −4.41742 −0.361889 −0.180945 0.983493i \(-0.557916\pi\)
−0.180945 + 0.983493i \(0.557916\pi\)
\(150\) 7.83485i 0.639713i
\(151\) −14.7477 −1.20015 −0.600077 0.799943i \(-0.704863\pi\)
−0.600077 + 0.799943i \(0.704863\pi\)
\(152\) −1.58258 −0.128364
\(153\) 1.58258i 0.127944i
\(154\) 1.58258i 0.127528i
\(155\) 6.62614 0.532224
\(156\) 6.79129i 0.543738i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 8.20871 0.653050
\(159\) −2.83485 −0.224818
\(160\) 0.791288 0.0625568
\(161\) 7.58258i 0.597591i
\(162\) 9.58258i 0.752878i
\(163\) 19.5826i 1.53383i 0.641751 + 0.766913i \(0.278208\pi\)
−0.641751 + 0.766913i \(0.721792\pi\)
\(164\) −9.79129 −0.764571
\(165\) 1.12159i 0.0873157i
\(166\) 15.1652i 1.17704i
\(167\) 21.9564i 1.69904i −0.527556 0.849520i \(-0.676892\pi\)
0.527556 0.849520i \(-0.323108\pi\)
\(168\) 3.58258i 0.276402i
\(169\) −1.37386 −0.105682
\(170\) 6.00000i 0.460179i
\(171\) 0.330303i 0.0252589i
\(172\) 6.00000i 0.457496i
\(173\) 15.1652 1.15299 0.576493 0.817102i \(-0.304421\pi\)
0.576493 + 0.817102i \(0.304421\pi\)
\(174\) 6.79129 0.514846
\(175\) −8.74773 −0.661266
\(176\) −0.791288 −0.0596456
\(177\) 2.83485i 0.213080i
\(178\) 6.00000 0.449719
\(179\) 1.58258i 0.118287i 0.998249 + 0.0591436i \(0.0188370\pi\)
−0.998249 + 0.0591436i \(0.981163\pi\)
\(180\) 0.165151i 0.0123097i
\(181\) 8.74773 0.650213 0.325107 0.945677i \(-0.394600\pi\)
0.325107 + 0.945677i \(0.394600\pi\)
\(182\) 7.58258 0.562058
\(183\) 22.9129i 1.69377i
\(184\) 3.79129 0.279497
\(185\) 3.62614 + 3.16515i 0.266599 + 0.232707i
\(186\) −15.0000 −1.09985
\(187\) 6.00000i 0.438763i
\(188\) 7.58258 0.553016
\(189\) 10.0000 0.727393
\(190\) 1.25227i 0.0908494i
\(191\) 8.37386i 0.605912i 0.953005 + 0.302956i \(0.0979734\pi\)
−0.953005 + 0.302956i \(0.902027\pi\)
\(192\) −1.79129 −0.129275
\(193\) 18.3303i 1.31944i −0.751510 0.659722i \(-0.770674\pi\)
0.751510 0.659722i \(-0.229326\pi\)
\(194\) −13.5826 −0.975172
\(195\) 5.37386 0.384830
\(196\) 3.00000 0.214286
\(197\) −19.9129 −1.41873 −0.709367 0.704839i \(-0.751019\pi\)
−0.709367 + 0.704839i \(0.751019\pi\)
\(198\) 0.165151i 0.0117368i
\(199\) 15.1652i 1.07503i −0.843254 0.537515i \(-0.819363\pi\)
0.843254 0.537515i \(-0.180637\pi\)
\(200\) 4.37386i 0.309279i
\(201\) 11.4174 0.805323
\(202\) 7.58258i 0.533508i
\(203\) 7.58258i 0.532192i
\(204\) 13.5826i 0.950971i
\(205\) 7.74773i 0.541125i
\(206\) 6.79129 0.473171
\(207\) 0.791288i 0.0549983i
\(208\) 3.79129i 0.262879i
\(209\) 1.25227i 0.0866215i
\(210\) −2.83485 −0.195623
\(211\) 10.3739 0.714166 0.357083 0.934073i \(-0.383771\pi\)
0.357083 + 0.934073i \(0.383771\pi\)
\(212\) 1.58258 0.108692
\(213\) −16.4174 −1.12490
\(214\) 5.37386i 0.367350i
\(215\) 4.74773 0.323792
\(216\) 5.00000i 0.340207i
\(217\) 16.7477i 1.13691i
\(218\) 6.00000 0.406371
\(219\) −7.83485 −0.529430
\(220\) 0.626136i 0.0422141i
\(221\) 28.7477 1.93378
\(222\) −8.20871 7.16515i −0.550933 0.480893i
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 2.00000i 0.133631i
\(225\) 0.912878 0.0608586
\(226\) −10.4174 −0.692957
\(227\) 25.9129i 1.71990i −0.510380 0.859949i \(-0.670495\pi\)
0.510380 0.859949i \(-0.329505\pi\)
\(228\) 2.83485i 0.187742i
\(229\) 6.74773 0.445902 0.222951 0.974830i \(-0.428431\pi\)
0.222951 + 0.974830i \(0.428431\pi\)
\(230\) 3.00000i 0.197814i
\(231\) 2.83485 0.186519
\(232\) −3.79129 −0.248910
\(233\) −16.1216 −1.05616 −0.528080 0.849194i \(-0.677088\pi\)
−0.528080 + 0.849194i \(0.677088\pi\)
\(234\) −0.791288 −0.0517281
\(235\) 6.00000i 0.391397i
\(236\) 1.58258i 0.103017i
\(237\) 14.7042i 0.955138i
\(238\) −15.1652 −0.983011
\(239\) 2.04356i 0.132187i 0.997813 + 0.0660935i \(0.0210536\pi\)
−0.997813 + 0.0660935i \(0.978946\pi\)
\(240\) 1.41742i 0.0914943i
\(241\) 4.41742i 0.284551i 0.989827 + 0.142276i \(0.0454419\pi\)
−0.989827 + 0.142276i \(0.954558\pi\)
\(242\) 10.3739i 0.666857i
\(243\) −2.16515 −0.138895
\(244\) 12.7913i 0.818878i
\(245\) 2.37386i 0.151661i
\(246\) 17.5390i 1.11825i
\(247\) 6.00000 0.381771
\(248\) 8.37386 0.531741
\(249\) 27.1652 1.72152
\(250\) 7.41742 0.469119
\(251\) 4.41742i 0.278825i 0.990234 + 0.139413i \(0.0445215\pi\)
−0.990234 + 0.139413i \(0.955479\pi\)
\(252\) 0.417424 0.0262953
\(253\) 3.00000i 0.188608i
\(254\) 8.00000i 0.501965i
\(255\) −10.7477 −0.673049
\(256\) 1.00000 0.0625000
\(257\) 4.74773i 0.296155i −0.988976 0.148078i \(-0.952691\pi\)
0.988976 0.148078i \(-0.0473085\pi\)
\(258\) −10.7477 −0.669124
\(259\) −8.00000 + 9.16515i −0.497096 + 0.569495i
\(260\) −3.00000 −0.186052
\(261\) 0.791288i 0.0489795i
\(262\) 16.7477 1.03468
\(263\) −27.1652 −1.67507 −0.837537 0.546380i \(-0.816006\pi\)
−0.837537 + 0.546380i \(0.816006\pi\)
\(264\) 1.41742i 0.0872364i
\(265\) 1.25227i 0.0769265i
\(266\) −3.16515 −0.194068
\(267\) 10.7477i 0.657750i
\(268\) −6.37386 −0.389346
\(269\) 16.7477 1.02113 0.510563 0.859840i \(-0.329437\pi\)
0.510563 + 0.859840i \(0.329437\pi\)
\(270\) −3.95644 −0.240781
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 7.58258i 0.459761i
\(273\) 13.5826i 0.822055i
\(274\) 3.62614i 0.219063i
\(275\) −3.46099 −0.208705
\(276\) 6.79129i 0.408787i
\(277\) 9.62614i 0.578378i −0.957272 0.289189i \(-0.906614\pi\)
0.957272 0.289189i \(-0.0933857\pi\)
\(278\) 13.3739i 0.802111i
\(279\) 1.74773i 0.104634i
\(280\) 1.58258 0.0945770
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 13.5826i 0.808831i
\(283\) 24.0000i 1.42665i 0.700832 + 0.713326i \(0.252812\pi\)
−0.700832 + 0.713326i \(0.747188\pi\)
\(284\) 9.16515 0.543852
\(285\) −2.24318 −0.132875
\(286\) 3.00000 0.177394
\(287\) −19.5826 −1.15592
\(288\) 0.208712i 0.0122985i
\(289\) −40.4955 −2.38209
\(290\) 3.00000i 0.176166i
\(291\) 24.3303i 1.42627i
\(292\) 4.37386 0.255961
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 5.37386i 0.313410i
\(295\) −1.25227 −0.0729101
\(296\) 4.58258 + 4.00000i 0.266357 + 0.232495i
\(297\) 3.95644 0.229576
\(298\) 4.41742i 0.255895i
\(299\) −14.3739 −0.831262
\(300\) −7.83485 −0.452345
\(301\) 12.0000i 0.691669i
\(302\) 14.7477i 0.848636i
\(303\) 13.5826 0.780299
\(304\) 1.58258i 0.0907669i
\(305\) −10.1216 −0.579561
\(306\) 1.58258 0.0904698
\(307\) 1.37386 0.0784105 0.0392053 0.999231i \(-0.487517\pi\)
0.0392053 + 0.999231i \(0.487517\pi\)
\(308\) −1.58258 −0.0901756
\(309\) 12.1652i 0.692051i
\(310\) 6.62614i 0.376339i
\(311\) 23.3739i 1.32541i −0.748880 0.662705i \(-0.769408\pi\)
0.748880 0.662705i \(-0.230592\pi\)
\(312\) 6.79129 0.384481
\(313\) 14.8348i 0.838515i −0.907867 0.419258i \(-0.862290\pi\)
0.907867 0.419258i \(-0.137710\pi\)
\(314\) 2.00000i 0.112867i
\(315\) 0.330303i 0.0186105i
\(316\) 8.20871i 0.461776i
\(317\) −28.7477 −1.61463 −0.807317 0.590119i \(-0.799081\pi\)
−0.807317 + 0.590119i \(0.799081\pi\)
\(318\) 2.83485i 0.158970i
\(319\) 3.00000i 0.167968i
\(320\) 0.791288i 0.0442343i
\(321\) −9.62614 −0.537279
\(322\) 7.58258 0.422560
\(323\) −12.0000 −0.667698
\(324\) 9.58258 0.532365
\(325\) 16.5826i 0.919836i
\(326\) 19.5826 1.08458
\(327\) 10.7477i 0.594351i
\(328\) 9.79129i 0.540633i
\(329\) 15.1652 0.836082
\(330\) −1.12159 −0.0617415
\(331\) 25.5826i 1.40615i −0.711118 0.703073i \(-0.751811\pi\)
0.711118 0.703073i \(-0.248189\pi\)
\(332\) −15.1652 −0.832296
\(333\) 0.834849 0.956439i 0.0457494 0.0524125i
\(334\) −21.9564 −1.20140
\(335\) 5.04356i 0.275559i
\(336\) −3.58258 −0.195446
\(337\) 33.1216 1.80425 0.902124 0.431477i \(-0.142007\pi\)
0.902124 + 0.431477i \(0.142007\pi\)
\(338\) 1.37386i 0.0747283i
\(339\) 18.6606i 1.01350i
\(340\) 6.00000 0.325396
\(341\) 6.62614i 0.358825i
\(342\) 0.330303 0.0178607
\(343\) 20.0000 1.07990
\(344\) 6.00000 0.323498
\(345\) 5.37386 0.289319
\(346\) 15.1652i 0.815284i
\(347\) 7.58258i 0.407054i 0.979069 + 0.203527i \(0.0652405\pi\)
−0.979069 + 0.203527i \(0.934760\pi\)
\(348\) 6.79129i 0.364051i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 8.74773i 0.467586i
\(351\) 18.9564i 1.01182i
\(352\) 0.791288i 0.0421758i
\(353\) 1.58258i 0.0842320i −0.999113 0.0421160i \(-0.986590\pi\)
0.999113 0.0421160i \(-0.0134099\pi\)
\(354\) 2.83485 0.150671
\(355\) 7.25227i 0.384911i
\(356\) 6.00000i 0.317999i
\(357\) 27.1652i 1.43773i
\(358\) 1.58258 0.0836417
\(359\) −8.83485 −0.466285 −0.233143 0.972443i \(-0.574901\pi\)
−0.233143 + 0.972443i \(0.574901\pi\)
\(360\) −0.165151 −0.00870424
\(361\) 16.4955 0.868182
\(362\) 8.74773i 0.459770i
\(363\) −18.5826 −0.975332
\(364\) 7.58258i 0.397435i
\(365\) 3.46099i 0.181156i
\(366\) 22.9129 1.19768
\(367\) −5.25227 −0.274166 −0.137083 0.990560i \(-0.543773\pi\)
−0.137083 + 0.990560i \(0.543773\pi\)
\(368\) 3.79129i 0.197635i
\(369\) 2.04356 0.106384
\(370\) 3.16515 3.62614i 0.164548 0.188514i
\(371\) 3.16515 0.164326
\(372\) 15.0000i 0.777714i
\(373\) −12.7477 −0.660052 −0.330026 0.943972i \(-0.607058\pi\)
−0.330026 + 0.943972i \(0.607058\pi\)
\(374\) −6.00000 −0.310253
\(375\) 13.2867i 0.686124i
\(376\) 7.58258i 0.391041i
\(377\) 14.3739 0.740292
\(378\) 10.0000i 0.514344i
\(379\) 20.1216 1.03358 0.516788 0.856113i \(-0.327127\pi\)
0.516788 + 0.856113i \(0.327127\pi\)
\(380\) 1.25227 0.0642402
\(381\) 14.3303 0.734164
\(382\) 8.37386 0.428444
\(383\) 18.3303i 0.936635i −0.883560 0.468317i \(-0.844860\pi\)
0.883560 0.468317i \(-0.155140\pi\)
\(384\) 1.79129i 0.0914113i
\(385\) 1.25227i 0.0638217i
\(386\) −18.3303 −0.932988
\(387\) 1.25227i 0.0636566i
\(388\) 13.5826i 0.689551i
\(389\) 32.8693i 1.66654i 0.552866 + 0.833270i \(0.313534\pi\)
−0.552866 + 0.833270i \(0.686466\pi\)
\(390\) 5.37386i 0.272116i
\(391\) 28.7477 1.45384
\(392\) 3.00000i 0.151523i
\(393\) 30.0000i 1.51330i
\(394\) 19.9129i 1.00320i
\(395\) −6.49545 −0.326822
\(396\) 0.165151 0.00829917
\(397\) 14.7477 0.740167 0.370084 0.928998i \(-0.379329\pi\)
0.370084 + 0.928998i \(0.379329\pi\)
\(398\) −15.1652 −0.760160
\(399\) 5.66970i 0.283840i
\(400\) 4.37386 0.218693
\(401\) 16.7477i 0.836342i −0.908368 0.418171i \(-0.862671\pi\)
0.908368 0.418171i \(-0.137329\pi\)
\(402\) 11.4174i 0.569449i
\(403\) −31.7477 −1.58147
\(404\) −7.58258 −0.377247
\(405\) 7.58258i 0.376781i
\(406\) −7.58258 −0.376317
\(407\) −3.16515 + 3.62614i −0.156891 + 0.179741i
\(408\) −13.5826 −0.672438
\(409\) 27.1652i 1.34323i 0.740900 + 0.671615i \(0.234399\pi\)
−0.740900 + 0.671615i \(0.765601\pi\)
\(410\) 7.74773 0.382633
\(411\) −6.49545 −0.320397
\(412\) 6.79129i 0.334583i
\(413\) 3.16515i 0.155747i
\(414\) −0.791288 −0.0388897
\(415\) 12.0000i 0.589057i
\(416\) −3.79129 −0.185883
\(417\) −23.9564 −1.17315
\(418\) −1.25227 −0.0612507
\(419\) 2.20871 0.107903 0.0539513 0.998544i \(-0.482818\pi\)
0.0539513 + 0.998544i \(0.482818\pi\)
\(420\) 2.83485i 0.138326i
\(421\) 18.9564i 0.923880i −0.886911 0.461940i \(-0.847153\pi\)
0.886911 0.461940i \(-0.152847\pi\)
\(422\) 10.3739i 0.504992i
\(423\) −1.58258 −0.0769475
\(424\) 1.58258i 0.0768567i
\(425\) 33.1652i 1.60875i
\(426\) 16.4174i 0.795427i
\(427\) 25.5826i 1.23803i
\(428\) 5.37386 0.259755
\(429\) 5.37386i 0.259453i
\(430\) 4.74773i 0.228956i
\(431\) 8.83485i 0.425560i −0.977100 0.212780i \(-0.931748\pi\)
0.977100 0.212780i \(-0.0682517\pi\)
\(432\) −5.00000 −0.240563
\(433\) 10.6261 0.510660 0.255330 0.966854i \(-0.417816\pi\)
0.255330 + 0.966854i \(0.417816\pi\)
\(434\) 16.7477 0.803917
\(435\) −5.37386 −0.257657
\(436\) 6.00000i 0.287348i
\(437\) 6.00000 0.287019
\(438\) 7.83485i 0.374364i
\(439\) 12.6261i 0.602613i 0.953527 + 0.301306i \(0.0974227\pi\)
−0.953527 + 0.301306i \(0.902577\pi\)
\(440\) 0.626136 0.0298499
\(441\) −0.626136 −0.0298160
\(442\) 28.7477i 1.36739i
\(443\) 27.9564 1.32825 0.664125 0.747621i \(-0.268804\pi\)
0.664125 + 0.747621i \(0.268804\pi\)
\(444\) −7.16515 + 8.20871i −0.340043 + 0.389568i
\(445\) −4.74773 −0.225064
\(446\) 14.0000i 0.662919i
\(447\) −7.91288 −0.374266
\(448\) 2.00000 0.0944911
\(449\) 2.83485i 0.133785i −0.997760 0.0668924i \(-0.978692\pi\)
0.997760 0.0668924i \(-0.0213084\pi\)
\(450\) 0.912878i 0.0430335i
\(451\) −7.74773 −0.364826
\(452\) 10.4174i 0.489994i
\(453\) −26.4174 −1.24120
\(454\) −25.9129 −1.21615
\(455\) −6.00000 −0.281284
\(456\) −2.83485 −0.132754
\(457\) 21.4955i 1.00551i −0.864428 0.502757i \(-0.832319\pi\)
0.864428 0.502757i \(-0.167681\pi\)
\(458\) 6.74773i 0.315301i
\(459\) 37.9129i 1.76962i
\(460\) −3.00000 −0.139876
\(461\) 12.3303i 0.574279i 0.957889 + 0.287140i \(0.0927044\pi\)
−0.957889 + 0.287140i \(0.907296\pi\)
\(462\) 2.83485i 0.131889i
\(463\) 29.7042i 1.38047i 0.723585 + 0.690235i \(0.242493\pi\)
−0.723585 + 0.690235i \(0.757507\pi\)
\(464\) 3.79129i 0.176006i
\(465\) 11.8693 0.550426
\(466\) 16.1216i 0.746818i
\(467\) 16.4174i 0.759708i 0.925046 + 0.379854i \(0.124026\pi\)
−0.925046 + 0.379854i \(0.875974\pi\)
\(468\) 0.791288i 0.0365773i
\(469\) −12.7477 −0.588635
\(470\) −6.00000 −0.276759
\(471\) −3.58258 −0.165076
\(472\) −1.58258 −0.0728440
\(473\) 4.74773i 0.218301i
\(474\) 14.7042 0.675385
\(475\) 6.92197i 0.317602i
\(476\) 15.1652i 0.695094i
\(477\) −0.330303 −0.0151235
\(478\) 2.04356 0.0934703
\(479\) 3.79129i 0.173228i 0.996242 + 0.0866142i \(0.0276047\pi\)
−0.996242 + 0.0866142i \(0.972395\pi\)
\(480\) 1.41742 0.0646963
\(481\) −17.3739 15.1652i −0.792180 0.691471i
\(482\) 4.41742 0.201208
\(483\) 13.5826i 0.618029i
\(484\) 10.3739 0.471539
\(485\) 10.7477 0.488029
\(486\) 2.16515i 0.0982133i
\(487\) 36.6606i 1.66125i 0.556832 + 0.830625i \(0.312017\pi\)
−0.556832 + 0.830625i \(0.687983\pi\)
\(488\) −12.7913 −0.579034
\(489\) 35.0780i 1.58628i
\(490\) −2.37386 −0.107240
\(491\) 5.37386 0.242519 0.121260 0.992621i \(-0.461307\pi\)
0.121260 + 0.992621i \(0.461307\pi\)
\(492\) −17.5390 −0.790720
\(493\) −28.7477 −1.29473
\(494\) 6.00000i 0.269953i
\(495\) 0.130682i 0.00587373i
\(496\) 8.37386i 0.375998i
\(497\) 18.3303 0.822226
\(498\) 27.1652i 1.21730i
\(499\) 10.7477i 0.481134i −0.970632 0.240567i \(-0.922667\pi\)
0.970632 0.240567i \(-0.0773334\pi\)
\(500\) 7.41742i 0.331717i
\(501\) 39.3303i 1.75715i
\(502\) 4.41742 0.197159
\(503\) 15.6261i 0.696735i 0.937358 + 0.348367i \(0.113264\pi\)
−0.937358 + 0.348367i \(0.886736\pi\)
\(504\) 0.417424i 0.0185936i
\(505\) 6.00000i 0.266996i
\(506\) 3.00000 0.133366
\(507\) −2.46099 −0.109296
\(508\) −8.00000 −0.354943
\(509\) 4.41742 0.195799 0.0978994 0.995196i \(-0.468788\pi\)
0.0978994 + 0.995196i \(0.468788\pi\)
\(510\) 10.7477i 0.475917i
\(511\) 8.74773 0.386977
\(512\) 1.00000i 0.0441942i
\(513\) 7.91288i 0.349362i
\(514\) −4.74773 −0.209413
\(515\) −5.37386 −0.236801
\(516\) 10.7477i 0.473142i
\(517\) 6.00000 0.263880
\(518\) 9.16515 + 8.00000i 0.402694 + 0.351500i
\(519\) 27.1652 1.19242
\(520\) 3.00000i 0.131559i
\(521\) −9.16515 −0.401533 −0.200766 0.979639i \(-0.564343\pi\)
−0.200766 + 0.979639i \(0.564343\pi\)
\(522\) 0.791288 0.0346337
\(523\) 15.1652i 0.663126i 0.943433 + 0.331563i \(0.107576\pi\)
−0.943433 + 0.331563i \(0.892424\pi\)
\(524\) 16.7477i 0.731628i
\(525\) −15.6697 −0.683882
\(526\) 27.1652i 1.18446i
\(527\) 63.4955 2.76591
\(528\) −1.41742 −0.0616855
\(529\) 8.62614 0.375049
\(530\) −1.25227 −0.0543953
\(531\) 0.330303i 0.0143339i
\(532\) 3.16515i 0.137227i
\(533\) 37.1216i 1.60791i
\(534\) 10.7477 0.465100
\(535\) 4.25227i 0.183842i
\(536\) 6.37386i 0.275309i
\(537\) 2.83485i 0.122333i
\(538\) 16.7477i 0.722046i
\(539\) 2.37386 0.102250
\(540\) 3.95644i 0.170258i
\(541\) 12.7913i 0.549940i −0.961453 0.274970i \(-0.911332\pi\)
0.961453 0.274970i \(-0.0886680\pi\)
\(542\) 22.0000i 0.944981i
\(543\) 15.6697 0.672451
\(544\) 7.58258 0.325100
\(545\) −4.74773 −0.203370
\(546\) 13.5826 0.581281
\(547\) 25.9129i 1.10795i −0.832532 0.553977i \(-0.813109\pi\)
0.832532 0.553977i \(-0.186891\pi\)
\(548\) 3.62614 0.154901
\(549\) 2.66970i 0.113940i
\(550\) 3.46099i 0.147577i
\(551\) −6.00000 −0.255609
\(552\) 6.79129 0.289056
\(553\) 16.4174i 0.698140i
\(554\) −9.62614 −0.408975
\(555\) 6.49545 + 5.66970i 0.275717 + 0.240665i
\(556\) 13.3739 0.567178
\(557\) 8.70417i 0.368807i −0.982851 0.184404i \(-0.940965\pi\)
0.982851 0.184404i \(-0.0590354\pi\)
\(558\) −1.74773 −0.0739872
\(559\) −22.7477 −0.962126
\(560\) 1.58258i 0.0668760i
\(561\) 10.7477i 0.453769i
\(562\) 0 0
\(563\) 10.7477i 0.452963i 0.974016 + 0.226481i \(0.0727222\pi\)
−0.974016 + 0.226481i \(0.927278\pi\)
\(564\) 13.5826 0.571930
\(565\) 8.24318 0.346793
\(566\) 24.0000 1.00880
\(567\) 19.1652 0.804861
\(568\) 9.16515i 0.384561i
\(569\) 45.1652i 1.89342i −0.322085 0.946711i \(-0.604384\pi\)
0.322085 0.946711i \(-0.395616\pi\)
\(570\) 2.24318i 0.0939565i
\(571\) −14.6261 −0.612085 −0.306042 0.952018i \(-0.599005\pi\)
−0.306042 + 0.952018i \(0.599005\pi\)
\(572\) 3.00000i 0.125436i
\(573\) 15.0000i 0.626634i
\(574\) 19.5826i 0.817361i
\(575\) 16.5826i 0.691541i
\(576\) −0.208712 −0.00869634
\(577\) 13.5826i 0.565450i −0.959201 0.282725i \(-0.908762\pi\)
0.959201 0.282725i \(-0.0912384\pi\)
\(578\) 40.4955i 1.68439i
\(579\) 32.8348i 1.36457i
\(580\) 3.00000 0.124568
\(581\) −30.3303 −1.25831
\(582\) −24.3303 −1.00852
\(583\) 1.25227 0.0518638
\(584\) 4.37386i 0.180992i
\(585\) 0.626136 0.0258876
\(586\) 6.00000i 0.247858i
\(587\) 19.9129i 0.821892i 0.911660 + 0.410946i \(0.134802\pi\)
−0.911660 + 0.410946i \(0.865198\pi\)
\(588\) 5.37386 0.221614
\(589\) 13.2523 0.546050
\(590\) 1.25227i 0.0515553i
\(591\) −35.6697 −1.46726
\(592\) 4.00000 4.58258i 0.164399 0.188343i
\(593\) −18.7913 −0.771666 −0.385833 0.922569i \(-0.626086\pi\)
−0.385833 + 0.922569i \(0.626086\pi\)
\(594\) 3.95644i 0.162335i
\(595\) 12.0000 0.491952
\(596\) 4.41742 0.180945
\(597\) 27.1652i 1.11180i
\(598\) 14.3739i 0.587791i
\(599\) 8.83485 0.360982 0.180491 0.983577i \(-0.442231\pi\)
0.180491 + 0.983577i \(0.442231\pi\)
\(600\) 7.83485i 0.319856i
\(601\) −33.1216 −1.35106 −0.675529 0.737333i \(-0.736085\pi\)
−0.675529 + 0.737333i \(0.736085\pi\)
\(602\) 12.0000 0.489083
\(603\) 1.33030 0.0541741
\(604\) 14.7477 0.600077
\(605\) 8.20871i 0.333732i
\(606\) 13.5826i 0.551754i
\(607\) 26.5390i 1.07719i 0.842566 + 0.538593i \(0.181044\pi\)
−0.842566 + 0.538593i \(0.818956\pi\)
\(608\) 1.58258 0.0641819
\(609\) 13.5826i 0.550394i
\(610\) 10.1216i 0.409811i
\(611\) 28.7477i 1.16301i
\(612\) 1.58258i 0.0639718i
\(613\) −49.4955 −1.99910 −0.999551 0.0299539i \(-0.990464\pi\)
−0.999551 + 0.0299539i \(0.990464\pi\)
\(614\) 1.37386i 0.0554446i
\(615\) 13.8784i 0.559631i
\(616\) 1.58258i 0.0637638i
\(617\) −23.0436 −0.927699 −0.463849 0.885914i \(-0.653532\pi\)
−0.463849 + 0.885914i \(0.653532\pi\)
\(618\) 12.1652 0.489354
\(619\) −35.1216 −1.41166 −0.705828 0.708383i \(-0.749425\pi\)
−0.705828 + 0.708383i \(0.749425\pi\)
\(620\) −6.62614 −0.266112
\(621\) 18.9564i 0.760696i
\(622\) −23.3739 −0.937207
\(623\) 12.0000i 0.480770i
\(624\) 6.79129i 0.271869i
\(625\) 16.0000 0.640000
\(626\) −14.8348 −0.592920
\(627\) 2.24318i 0.0895840i
\(628\) 2.00000 0.0798087
\(629\) 34.7477 + 30.3303i 1.38548 + 1.20935i
\(630\) −0.330303 −0.0131596
\(631\) 18.9564i 0.754644i 0.926082 + 0.377322i \(0.123155\pi\)
−0.926082 + 0.377322i \(0.876845\pi\)
\(632\) −8.20871 −0.326525
\(633\) 18.5826 0.738591
\(634\) 28.7477i 1.14172i
\(635\) 6.33030i 0.251210i
\(636\) 2.83485 0.112409
\(637\) 11.3739i 0.450649i
\(638\) −3.00000 −0.118771
\(639\) −1.91288 −0.0756723
\(640\) −0.791288 −0.0312784
\(641\) −3.46099 −0.136701 −0.0683503 0.997661i \(-0.521774\pi\)
−0.0683503 + 0.997661i \(0.521774\pi\)
\(642\) 9.62614i 0.379913i
\(643\) 39.4955i 1.55755i −0.627304 0.778774i \(-0.715842\pi\)
0.627304 0.778774i \(-0.284158\pi\)
\(644\) 7.58258i 0.298795i
\(645\) 8.50455 0.334866
\(646\) 12.0000i 0.472134i
\(647\) 17.7042i 0.696023i 0.937490 + 0.348011i \(0.113143\pi\)
−0.937490 + 0.348011i \(0.886857\pi\)
\(648\) 9.58258i 0.376439i
\(649\) 1.25227i 0.0491560i
\(650\) −16.5826 −0.650422
\(651\) 30.0000i 1.17579i
\(652\) 19.5826i 0.766913i
\(653\) 0.626136i 0.0245026i 0.999925 + 0.0122513i \(0.00389981\pi\)
−0.999925 + 0.0122513i \(0.996100\pi\)
\(654\) 10.7477 0.420269
\(655\) −13.2523 −0.517809
\(656\) 9.79129 0.382286
\(657\) −0.912878 −0.0356148
\(658\) 15.1652i 0.591199i
\(659\) 11.0436 0.430196 0.215098 0.976592i \(-0.430993\pi\)
0.215098 + 0.976592i \(0.430993\pi\)
\(660\) 1.12159i 0.0436579i
\(661\) 32.2087i 1.25277i 0.779512 + 0.626387i \(0.215467\pi\)
−0.779512 + 0.626387i \(0.784533\pi\)
\(662\) −25.5826 −0.994295
\(663\) 51.4955 1.99992
\(664\) 15.1652i 0.588522i
\(665\) 2.50455 0.0971221
\(666\) −0.956439 0.834849i −0.0370613 0.0323497i
\(667\) 14.3739 0.556558
\(668\) 21.9564i 0.849520i
\(669\) 25.0780 0.969573
\(670\) 5.04356 0.194850
\(671\) 10.1216i 0.390740i
\(672\) 3.58258i 0.138201i
\(673\) −36.1216 −1.39238 −0.696192 0.717855i \(-0.745124\pi\)
−0.696192 + 0.717855i \(0.745124\pi\)
\(674\) 33.1216i 1.27580i
\(675\) −21.8693 −0.841750
\(676\) 1.37386 0.0528409
\(677\) 9.16515 0.352245 0.176123 0.984368i \(-0.443644\pi\)
0.176123 + 0.984368i \(0.443644\pi\)
\(678\) −18.6606 −0.716656
\(679\) 27.1652i 1.04250i
\(680\) 6.00000i 0.230089i
\(681\) 46.4174i 1.77872i
\(682\) 6.62614 0.253728
\(683\) 31.5826i 1.20847i −0.796805 0.604237i \(-0.793478\pi\)
0.796805 0.604237i \(-0.206522\pi\)
\(684\) 0.330303i 0.0126294i
\(685\) 2.86932i 0.109631i
\(686\) 20.0000i 0.763604i
\(687\) 12.0871 0.461152
\(688\) 6.00000i 0.228748i
\(689\) 6.00000i 0.228582i
\(690\) 5.37386i 0.204579i
\(691\) 25.4955 0.969893 0.484946 0.874544i \(-0.338839\pi\)
0.484946 + 0.874544i \(0.338839\pi\)
\(692\) −15.1652 −0.576493
\(693\) 0.330303 0.0125472
\(694\) 7.58258 0.287831
\(695\) 10.5826i 0.401420i
\(696\) −6.79129 −0.257423
\(697\) 74.2432i 2.81216i
\(698\) 10.0000i 0.378506i
\(699\) −28.8784 −1.09228
\(700\) 8.74773 0.330633
\(701\) 3.95644i 0.149433i 0.997205 + 0.0747163i \(0.0238051\pi\)
−0.997205 + 0.0747163i \(0.976195\pi\)
\(702\) 18.9564 0.715465
\(703\) 7.25227 + 6.33030i 0.273525 + 0.238752i
\(704\) 0.791288 0.0298228
\(705\) 10.7477i 0.404783i
\(706\) −1.58258 −0.0595610
\(707\) −15.1652 −0.570344
\(708\) 2.83485i 0.106540i
\(709\) 23.2087i 0.871621i 0.900038 + 0.435811i \(0.143538\pi\)
−0.900038 + 0.435811i \(0.856462\pi\)
\(710\) −7.25227 −0.272173
\(711\) 1.71326i 0.0642522i
\(712\) −6.00000 −0.224860
\(713\) −31.7477 −1.18896
\(714\) −27.1652 −1.01663
\(715\) −2.37386 −0.0887775
\(716\) 1.58258i 0.0591436i
\(717\) 3.66061i 0.136708i
\(718\) 8.83485i 0.329714i
\(719\) −21.1652 −0.789327 −0.394663 0.918826i \(-0.629139\pi\)
−0.394663 + 0.918826i \(0.629139\pi\)
\(720\) 0.165151i 0.00615483i
\(721\) 13.5826i 0.505842i
\(722\) 16.4955i 0.613897i
\(723\) 7.91288i 0.294283i
\(724\) −8.74773 −0.325107
\(725\) 16.5826i 0.615861i
\(726\) 18.5826i 0.689664i
\(727\) 13.1216i 0.486653i −0.969944 0.243326i \(-0.921761\pi\)
0.969944 0.243326i \(-0.0782386\pi\)
\(728\) −7.58258 −0.281029
\(729\) 24.8693 0.921086
\(730\) −3.46099 −0.128097
\(731\) 45.4955 1.68271
\(732\) 22.9129i 0.846884i
\(733\) 47.4955 1.75428 0.877142 0.480231i \(-0.159447\pi\)
0.877142 + 0.480231i \(0.159447\pi\)
\(734\) 5.25227i 0.193865i
\(735\) 4.25227i 0.156847i
\(736\) −3.79129 −0.139749
\(737\) −5.04356 −0.185782
\(738\) 2.04356i 0.0752245i
\(739\) −35.1216 −1.29197 −0.645984 0.763351i \(-0.723553\pi\)
−0.645984 + 0.763351i \(0.723553\pi\)
\(740\) −3.62614 3.16515i −0.133299 0.116353i
\(741\) 10.7477 0.394828
\(742\) 3.16515i 0.116196i
\(743\) 15.1652 0.556355 0.278178 0.960530i \(-0.410270\pi\)
0.278178 + 0.960530i \(0.410270\pi\)
\(744\) 15.0000 0.549927
\(745\) 3.49545i 0.128064i
\(746\) 12.7477i 0.466727i
\(747\) 3.16515 0.115807
\(748\) 6.00000i 0.219382i
\(749\) 10.7477 0.392713
\(750\) 13.2867 0.485163
\(751\) −41.4955 −1.51419 −0.757095 0.653304i \(-0.773382\pi\)
−0.757095 + 0.653304i \(0.773382\pi\)
\(752\) −7.58258 −0.276508
\(753\) 7.91288i 0.288361i
\(754\) 14.3739i 0.523465i
\(755\) 11.6697i 0.424704i
\(756\) −10.0000 −0.363696
\(757\) 35.2087i 1.27968i −0.768507 0.639841i \(-0.779000\pi\)
0.768507 0.639841i \(-0.221000\pi\)
\(758\) 20.1216i 0.730849i
\(759\) 5.37386i 0.195059i
\(760\) 1.25227i 0.0454247i
\(761\) 14.2087 0.515065 0.257533 0.966270i \(-0.417090\pi\)
0.257533 + 0.966270i \(0.417090\pi\)
\(762\) 14.3303i 0.519132i
\(763\) 12.0000i 0.434429i
\(764\) 8.37386i 0.302956i
\(765\) −1.25227 −0.0452760
\(766\) −18.3303 −0.662301
\(767\) 6.00000 0.216647
\(768\) 1.79129 0.0646375
\(769\) 11.6697i 0.420820i −0.977613 0.210410i \(-0.932520\pi\)
0.977613 0.210410i \(-0.0674799\pi\)
\(770\) 1.25227 0.0451288
\(771\) 8.50455i 0.306284i
\(772\) 18.3303i 0.659722i
\(773\) 31.9129 1.14783 0.573913 0.818916i \(-0.305425\pi\)
0.573913 + 0.818916i \(0.305425\pi\)
\(774\) −1.25227 −0.0450120
\(775\) 36.6261i 1.31565i
\(776\) 13.5826 0.487586
\(777\) −14.3303 + 16.4174i −0.514097 + 0.588972i
\(778\) 32.8693 1.17842
\(779\) 15.4955i 0.555182i
\(780\) −5.37386 −0.192415
\(781\) 7.25227 0.259507
\(782\) 28.7477i 1.02802i
\(783\) 18.9564i 0.677448i
\(784\) −3.00000 −0.107143
\(785\) 1.58258i 0.0564845i
\(786\) 30.0000 1.07006
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) 19.9129 0.709367
\(789\) −48.6606 −1.73236
\(790\)