Properties

Label 19.3.b.b.18.1
Level $19$
Weight $3$
Character 19.18
Analytic conductor $0.518$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 19.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.517712502285\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-13}) \)
Defining polynomial: \(x^{2} + 13\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 18.1
Root \(-3.60555i\) of defining polynomial
Character \(\chi\) \(=\) 19.18
Dual form 19.3.b.b.18.2

$q$-expansion

\(f(q)\) \(=\) \(q-3.60555i q^{2} +3.60555i q^{3} -9.00000 q^{4} +4.00000 q^{5} +13.0000 q^{6} -5.00000 q^{7} +18.0278i q^{8} -4.00000 q^{9} +O(q^{10})\) \(q-3.60555i q^{2} +3.60555i q^{3} -9.00000 q^{4} +4.00000 q^{5} +13.0000 q^{6} -5.00000 q^{7} +18.0278i q^{8} -4.00000 q^{9} -14.4222i q^{10} -10.0000 q^{11} -32.4500i q^{12} -3.60555i q^{13} +18.0278i q^{14} +14.4222i q^{15} +29.0000 q^{16} +15.0000 q^{17} +14.4222i q^{18} +(-6.00000 - 18.0278i) q^{19} -36.0000 q^{20} -18.0278i q^{21} +36.0555i q^{22} +35.0000 q^{23} -65.0000 q^{24} -9.00000 q^{25} -13.0000 q^{26} +18.0278i q^{27} +45.0000 q^{28} -18.0278i q^{29} +52.0000 q^{30} +36.0555i q^{31} -32.4500i q^{32} -36.0555i q^{33} -54.0833i q^{34} -20.0000 q^{35} +36.0000 q^{36} +21.6333i q^{37} +(-65.0000 + 21.6333i) q^{38} +13.0000 q^{39} +72.1110i q^{40} -36.0555i q^{41} -65.0000 q^{42} -20.0000 q^{43} +90.0000 q^{44} -16.0000 q^{45} -126.194i q^{46} +10.0000 q^{47} +104.561i q^{48} -24.0000 q^{49} +32.4500i q^{50} +54.0833i q^{51} +32.4500i q^{52} +75.7166i q^{53} +65.0000 q^{54} -40.0000 q^{55} -90.1388i q^{56} +(65.0000 - 21.6333i) q^{57} -65.0000 q^{58} -18.0278i q^{59} -129.800i q^{60} -40.0000 q^{61} +130.000 q^{62} +20.0000 q^{63} -1.00000 q^{64} -14.4222i q^{65} -130.000 q^{66} -39.6611i q^{67} -135.000 q^{68} +126.194i q^{69} +72.1110i q^{70} -108.167i q^{71} -72.1110i q^{72} +105.000 q^{73} +78.0000 q^{74} -32.4500i q^{75} +(54.0000 + 162.250i) q^{76} +50.0000 q^{77} -46.8722i q^{78} +36.0555i q^{79} +116.000 q^{80} -101.000 q^{81} -130.000 q^{82} -40.0000 q^{83} +162.250i q^{84} +60.0000 q^{85} +72.1110i q^{86} +65.0000 q^{87} -180.278i q^{88} +57.6888i q^{90} +18.0278i q^{91} -315.000 q^{92} -130.000 q^{93} -36.0555i q^{94} +(-24.0000 - 72.1110i) q^{95} +117.000 q^{96} -122.589i q^{97} +86.5332i q^{98} +40.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 18q^{4} + 8q^{5} + 26q^{6} - 10q^{7} - 8q^{9} + O(q^{10}) \) \( 2q - 18q^{4} + 8q^{5} + 26q^{6} - 10q^{7} - 8q^{9} - 20q^{11} + 58q^{16} + 30q^{17} - 12q^{19} - 72q^{20} + 70q^{23} - 130q^{24} - 18q^{25} - 26q^{26} + 90q^{28} + 104q^{30} - 40q^{35} + 72q^{36} - 130q^{38} + 26q^{39} - 130q^{42} - 40q^{43} + 180q^{44} - 32q^{45} + 20q^{47} - 48q^{49} + 130q^{54} - 80q^{55} + 130q^{57} - 130q^{58} - 80q^{61} + 260q^{62} + 40q^{63} - 2q^{64} - 260q^{66} - 270q^{68} + 210q^{73} + 156q^{74} + 108q^{76} + 100q^{77} + 232q^{80} - 202q^{81} - 260q^{82} - 80q^{83} + 120q^{85} + 130q^{87} - 630q^{92} - 260q^{93} - 48q^{95} + 234q^{96} + 80q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.60555i 1.80278i −0.433013 0.901388i \(-0.642549\pi\)
0.433013 0.901388i \(-0.357451\pi\)
\(3\) 3.60555i 1.20185i 0.799305 + 0.600925i \(0.205201\pi\)
−0.799305 + 0.600925i \(0.794799\pi\)
\(4\) −9.00000 −2.25000
\(5\) 4.00000 0.800000 0.400000 0.916515i \(-0.369010\pi\)
0.400000 + 0.916515i \(0.369010\pi\)
\(6\) 13.0000 2.16667
\(7\) −5.00000 −0.714286 −0.357143 0.934050i \(-0.616249\pi\)
−0.357143 + 0.934050i \(0.616249\pi\)
\(8\) 18.0278i 2.25347i
\(9\) −4.00000 −0.444444
\(10\) 14.4222i 1.44222i
\(11\) −10.0000 −0.909091 −0.454545 0.890724i \(-0.650198\pi\)
−0.454545 + 0.890724i \(0.650198\pi\)
\(12\) 32.4500i 2.70416i
\(13\) 3.60555i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) 18.0278i 1.28770i
\(15\) 14.4222i 0.961480i
\(16\) 29.0000 1.81250
\(17\) 15.0000 0.882353 0.441176 0.897420i \(-0.354561\pi\)
0.441176 + 0.897420i \(0.354561\pi\)
\(18\) 14.4222i 0.801234i
\(19\) −6.00000 18.0278i −0.315789 0.948829i
\(20\) −36.0000 −1.80000
\(21\) 18.0278i 0.858465i
\(22\) 36.0555i 1.63889i
\(23\) 35.0000 1.52174 0.760870 0.648905i \(-0.224773\pi\)
0.760870 + 0.648905i \(0.224773\pi\)
\(24\) −65.0000 −2.70833
\(25\) −9.00000 −0.360000
\(26\) −13.0000 −0.500000
\(27\) 18.0278i 0.667695i
\(28\) 45.0000 1.60714
\(29\) 18.0278i 0.621647i −0.950468 0.310823i \(-0.899395\pi\)
0.950468 0.310823i \(-0.100605\pi\)
\(30\) 52.0000 1.73333
\(31\) 36.0555i 1.16308i 0.813517 + 0.581541i \(0.197550\pi\)
−0.813517 + 0.581541i \(0.802450\pi\)
\(32\) 32.4500i 1.01406i
\(33\) 36.0555i 1.09259i
\(34\) 54.0833i 1.59068i
\(35\) −20.0000 −0.571429
\(36\) 36.0000 1.00000
\(37\) 21.6333i 0.584684i 0.956314 + 0.292342i \(0.0944346\pi\)
−0.956314 + 0.292342i \(0.905565\pi\)
\(38\) −65.0000 + 21.6333i −1.71053 + 0.569298i
\(39\) 13.0000 0.333333
\(40\) 72.1110i 1.80278i
\(41\) 36.0555i 0.879403i −0.898144 0.439701i \(-0.855084\pi\)
0.898144 0.439701i \(-0.144916\pi\)
\(42\) −65.0000 −1.54762
\(43\) −20.0000 −0.465116 −0.232558 0.972582i \(-0.574710\pi\)
−0.232558 + 0.972582i \(0.574710\pi\)
\(44\) 90.0000 2.04545
\(45\) −16.0000 −0.355556
\(46\) 126.194i 2.74335i
\(47\) 10.0000 0.212766 0.106383 0.994325i \(-0.466073\pi\)
0.106383 + 0.994325i \(0.466073\pi\)
\(48\) 104.561i 2.17835i
\(49\) −24.0000 −0.489796
\(50\) 32.4500i 0.648999i
\(51\) 54.0833i 1.06046i
\(52\) 32.4500i 0.624038i
\(53\) 75.7166i 1.42861i 0.699832 + 0.714307i \(0.253258\pi\)
−0.699832 + 0.714307i \(0.746742\pi\)
\(54\) 65.0000 1.20370
\(55\) −40.0000 −0.727273
\(56\) 90.1388i 1.60962i
\(57\) 65.0000 21.6333i 1.14035 0.379532i
\(58\) −65.0000 −1.12069
\(59\) 18.0278i 0.305555i −0.988261 0.152778i \(-0.951178\pi\)
0.988261 0.152778i \(-0.0488218\pi\)
\(60\) 129.800i 2.16333i
\(61\) −40.0000 −0.655738 −0.327869 0.944723i \(-0.606330\pi\)
−0.327869 + 0.944723i \(0.606330\pi\)
\(62\) 130.000 2.09677
\(63\) 20.0000 0.317460
\(64\) −1.00000 −0.0156250
\(65\) 14.4222i 0.221880i
\(66\) −130.000 −1.96970
\(67\) 39.6611i 0.591956i −0.955195 0.295978i \(-0.904354\pi\)
0.955195 0.295978i \(-0.0956455\pi\)
\(68\) −135.000 −1.98529
\(69\) 126.194i 1.82890i
\(70\) 72.1110i 1.03016i
\(71\) 108.167i 1.52347i −0.647887 0.761736i \(-0.724347\pi\)
0.647887 0.761736i \(-0.275653\pi\)
\(72\) 72.1110i 1.00154i
\(73\) 105.000 1.43836 0.719178 0.694826i \(-0.244519\pi\)
0.719178 + 0.694826i \(0.244519\pi\)
\(74\) 78.0000 1.05405
\(75\) 32.4500i 0.432666i
\(76\) 54.0000 + 162.250i 0.710526 + 2.13487i
\(77\) 50.0000 0.649351
\(78\) 46.8722i 0.600925i
\(79\) 36.0555i 0.456399i 0.973614 + 0.228199i \(0.0732838\pi\)
−0.973614 + 0.228199i \(0.926716\pi\)
\(80\) 116.000 1.45000
\(81\) −101.000 −1.24691
\(82\) −130.000 −1.58537
\(83\) −40.0000 −0.481928 −0.240964 0.970534i \(-0.577464\pi\)
−0.240964 + 0.970534i \(0.577464\pi\)
\(84\) 162.250i 1.93155i
\(85\) 60.0000 0.705882
\(86\) 72.1110i 0.838500i
\(87\) 65.0000 0.747126
\(88\) 180.278i 2.04861i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 57.6888i 0.640987i
\(91\) 18.0278i 0.198107i
\(92\) −315.000 −3.42391
\(93\) −130.000 −1.39785
\(94\) 36.0555i 0.383569i
\(95\) −24.0000 72.1110i −0.252632 0.759063i
\(96\) 117.000 1.21875
\(97\) 122.589i 1.26380i −0.775049 0.631901i \(-0.782275\pi\)
0.775049 0.631901i \(-0.217725\pi\)
\(98\) 86.5332i 0.882992i
\(99\) 40.0000 0.404040
\(100\) 81.0000 0.810000
\(101\) −50.0000 −0.495050 −0.247525 0.968882i \(-0.579617\pi\)
−0.247525 + 0.968882i \(0.579617\pi\)
\(102\) 195.000 1.91176
\(103\) 57.6888i 0.560086i −0.959988 0.280043i \(-0.909651\pi\)
0.959988 0.280043i \(-0.0903487\pi\)
\(104\) 65.0000 0.625000
\(105\) 72.1110i 0.686772i
\(106\) 273.000 2.57547
\(107\) 75.7166i 0.707632i −0.935315 0.353816i \(-0.884884\pi\)
0.935315 0.353816i \(-0.115116\pi\)
\(108\) 162.250i 1.50231i
\(109\) 198.305i 1.81931i 0.415359 + 0.909657i \(0.363656\pi\)
−0.415359 + 0.909657i \(0.636344\pi\)
\(110\) 144.222i 1.31111i
\(111\) −78.0000 −0.702703
\(112\) −145.000 −1.29464
\(113\) 122.589i 1.08486i 0.840102 + 0.542428i \(0.182495\pi\)
−0.840102 + 0.542428i \(0.817505\pi\)
\(114\) −78.0000 234.361i −0.684211 2.05580i
\(115\) 140.000 1.21739
\(116\) 162.250i 1.39871i
\(117\) 14.4222i 0.123267i
\(118\) −65.0000 −0.550847
\(119\) −75.0000 −0.630252
\(120\) −260.000 −2.16667
\(121\) −21.0000 −0.173554
\(122\) 144.222i 1.18215i
\(123\) 130.000 1.05691
\(124\) 324.500i 2.61693i
\(125\) −136.000 −1.08800
\(126\) 72.1110i 0.572310i
\(127\) 129.800i 1.02205i 0.859567 + 0.511023i \(0.170733\pi\)
−0.859567 + 0.511023i \(0.829267\pi\)
\(128\) 126.194i 0.985893i
\(129\) 72.1110i 0.559000i
\(130\) −52.0000 −0.400000
\(131\) 112.000 0.854962 0.427481 0.904024i \(-0.359401\pi\)
0.427481 + 0.904024i \(0.359401\pi\)
\(132\) 324.500i 2.45833i
\(133\) 30.0000 + 90.1388i 0.225564 + 0.677735i
\(134\) −143.000 −1.06716
\(135\) 72.1110i 0.534156i
\(136\) 270.416i 1.98836i
\(137\) 125.000 0.912409 0.456204 0.889875i \(-0.349209\pi\)
0.456204 + 0.889875i \(0.349209\pi\)
\(138\) 455.000 3.29710
\(139\) 50.0000 0.359712 0.179856 0.983693i \(-0.442437\pi\)
0.179856 + 0.983693i \(0.442437\pi\)
\(140\) 180.000 1.28571
\(141\) 36.0555i 0.255713i
\(142\) −390.000 −2.74648
\(143\) 36.0555i 0.252136i
\(144\) −116.000 −0.805556
\(145\) 72.1110i 0.497317i
\(146\) 378.583i 2.59303i
\(147\) 86.5332i 0.588661i
\(148\) 194.700i 1.31554i
\(149\) 70.0000 0.469799 0.234899 0.972020i \(-0.424524\pi\)
0.234899 + 0.972020i \(0.424524\pi\)
\(150\) −117.000 −0.780000
\(151\) 36.0555i 0.238778i −0.992848 0.119389i \(-0.961906\pi\)
0.992848 0.119389i \(-0.0380936\pi\)
\(152\) 325.000 108.167i 2.13816 0.711622i
\(153\) −60.0000 −0.392157
\(154\) 180.278i 1.17063i
\(155\) 144.222i 0.930465i
\(156\) −117.000 −0.750000
\(157\) 10.0000 0.0636943 0.0318471 0.999493i \(-0.489861\pi\)
0.0318471 + 0.999493i \(0.489861\pi\)
\(158\) 130.000 0.822785
\(159\) −273.000 −1.71698
\(160\) 129.800i 0.811249i
\(161\) −175.000 −1.08696
\(162\) 364.161i 2.24791i
\(163\) −270.000 −1.65644 −0.828221 0.560402i \(-0.810647\pi\)
−0.828221 + 0.560402i \(0.810647\pi\)
\(164\) 324.500i 1.97866i
\(165\) 144.222i 0.874073i
\(166\) 144.222i 0.868808i
\(167\) 122.589i 0.734064i −0.930208 0.367032i \(-0.880374\pi\)
0.930208 0.367032i \(-0.119626\pi\)
\(168\) 325.000 1.93452
\(169\) 156.000 0.923077
\(170\) 216.333i 1.27255i
\(171\) 24.0000 + 72.1110i 0.140351 + 0.421702i
\(172\) 180.000 1.04651
\(173\) 122.589i 0.708605i 0.935131 + 0.354303i \(0.115282\pi\)
−0.935131 + 0.354303i \(0.884718\pi\)
\(174\) 234.361i 1.34690i
\(175\) 45.0000 0.257143
\(176\) −290.000 −1.64773
\(177\) 65.0000 0.367232
\(178\) 0 0
\(179\) 36.0555i 0.201427i −0.994915 0.100714i \(-0.967887\pi\)
0.994915 0.100714i \(-0.0321126\pi\)
\(180\) 144.000 0.800000
\(181\) 108.167i 0.597605i −0.954315 0.298803i \(-0.903413\pi\)
0.954315 0.298803i \(-0.0965872\pi\)
\(182\) 65.0000 0.357143
\(183\) 144.222i 0.788099i
\(184\) 630.971i 3.42919i
\(185\) 86.5332i 0.467747i
\(186\) 468.722i 2.52001i
\(187\) −150.000 −0.802139
\(188\) −90.0000 −0.478723
\(189\) 90.1388i 0.476925i
\(190\) −260.000 + 86.5332i −1.36842 + 0.455438i
\(191\) 193.000 1.01047 0.505236 0.862981i \(-0.331406\pi\)
0.505236 + 0.862981i \(0.331406\pi\)
\(192\) 3.60555i 0.0187789i
\(193\) 266.811i 1.38244i −0.722645 0.691220i \(-0.757074\pi\)
0.722645 0.691220i \(-0.242926\pi\)
\(194\) −442.000 −2.27835
\(195\) 52.0000 0.266667
\(196\) 216.000 1.10204
\(197\) 90.0000 0.456853 0.228426 0.973561i \(-0.426642\pi\)
0.228426 + 0.973561i \(0.426642\pi\)
\(198\) 144.222i 0.728394i
\(199\) 123.000 0.618090 0.309045 0.951047i \(-0.399991\pi\)
0.309045 + 0.951047i \(0.399991\pi\)
\(200\) 162.250i 0.811249i
\(201\) 143.000 0.711443
\(202\) 180.278i 0.892463i
\(203\) 90.1388i 0.444033i
\(204\) 486.749i 2.38603i
\(205\) 144.222i 0.703522i
\(206\) −208.000 −1.00971
\(207\) −140.000 −0.676329
\(208\) 104.561i 0.502697i
\(209\) 60.0000 + 180.278i 0.287081 + 0.862572i
\(210\) −260.000 −1.23810
\(211\) 234.361i 1.11071i 0.831612 + 0.555357i \(0.187419\pi\)
−0.831612 + 0.555357i \(0.812581\pi\)
\(212\) 681.449i 3.21438i
\(213\) 390.000 1.83099
\(214\) −273.000 −1.27570
\(215\) −80.0000 −0.372093
\(216\) −325.000 −1.50463
\(217\) 180.278i 0.830772i
\(218\) 715.000 3.27982
\(219\) 378.583i 1.72869i
\(220\) 360.000 1.63636
\(221\) 54.0833i 0.244721i
\(222\) 281.233i 1.26682i
\(223\) 201.911i 0.905430i 0.891655 + 0.452715i \(0.149544\pi\)
−0.891655 + 0.452715i \(0.850456\pi\)
\(224\) 162.250i 0.724329i
\(225\) 36.0000 0.160000
\(226\) 442.000 1.95575
\(227\) 255.994i 1.12773i −0.825868 0.563864i \(-0.809314\pi\)
0.825868 0.563864i \(-0.190686\pi\)
\(228\) −585.000 + 194.700i −2.56579 + 0.853946i
\(229\) −160.000 −0.698690 −0.349345 0.936994i \(-0.613596\pi\)
−0.349345 + 0.936994i \(0.613596\pi\)
\(230\) 504.777i 2.19468i
\(231\) 180.278i 0.780422i
\(232\) 325.000 1.40086
\(233\) −270.000 −1.15880 −0.579399 0.815044i \(-0.696713\pi\)
−0.579399 + 0.815044i \(0.696713\pi\)
\(234\) 52.0000 0.222222
\(235\) 40.0000 0.170213
\(236\) 162.250i 0.687499i
\(237\) −130.000 −0.548523
\(238\) 270.416i 1.13620i
\(239\) 197.000 0.824268 0.412134 0.911123i \(-0.364784\pi\)
0.412134 + 0.911123i \(0.364784\pi\)
\(240\) 418.244i 1.74268i
\(241\) 396.611i 1.64569i −0.568268 0.822844i \(-0.692386\pi\)
0.568268 0.822844i \(-0.307614\pi\)
\(242\) 75.7166i 0.312878i
\(243\) 201.911i 0.830909i
\(244\) 360.000 1.47541
\(245\) −96.0000 −0.391837
\(246\) 468.722i 1.90537i
\(247\) −65.0000 + 21.6333i −0.263158 + 0.0875842i
\(248\) −650.000 −2.62097
\(249\) 144.222i 0.579205i
\(250\) 490.355i 1.96142i
\(251\) −402.000 −1.60159 −0.800797 0.598936i \(-0.795590\pi\)
−0.800797 + 0.598936i \(0.795590\pi\)
\(252\) −180.000 −0.714286
\(253\) −350.000 −1.38340
\(254\) 468.000 1.84252
\(255\) 216.333i 0.848365i
\(256\) −459.000 −1.79297
\(257\) 418.244i 1.62741i 0.581279 + 0.813704i \(0.302552\pi\)
−0.581279 + 0.813704i \(0.697448\pi\)
\(258\) −260.000 −1.00775
\(259\) 108.167i 0.417631i
\(260\) 129.800i 0.499230i
\(261\) 72.1110i 0.276287i
\(262\) 403.822i 1.54130i
\(263\) 310.000 1.17871 0.589354 0.807875i \(-0.299382\pi\)
0.589354 + 0.807875i \(0.299382\pi\)
\(264\) 650.000 2.46212
\(265\) 302.866i 1.14289i
\(266\) 325.000 108.167i 1.22180 0.406641i
\(267\) 0 0
\(268\) 356.950i 1.33190i
\(269\) 108.167i 0.402106i −0.979580 0.201053i \(-0.935564\pi\)
0.979580 0.201053i \(-0.0644364\pi\)
\(270\) 260.000 0.962963
\(271\) 105.000 0.387454 0.193727 0.981055i \(-0.437942\pi\)
0.193727 + 0.981055i \(0.437942\pi\)
\(272\) 435.000 1.59926
\(273\) −65.0000 −0.238095
\(274\) 450.694i 1.64487i
\(275\) 90.0000 0.327273
\(276\) 1135.75i 4.11503i
\(277\) −50.0000 −0.180505 −0.0902527 0.995919i \(-0.528767\pi\)
−0.0902527 + 0.995919i \(0.528767\pi\)
\(278\) 180.278i 0.648480i
\(279\) 144.222i 0.516925i
\(280\) 360.555i 1.28770i
\(281\) 288.444i 1.02649i 0.858242 + 0.513246i \(0.171557\pi\)
−0.858242 + 0.513246i \(0.828443\pi\)
\(282\) 130.000 0.460993
\(283\) −320.000 −1.13074 −0.565371 0.824837i \(-0.691267\pi\)
−0.565371 + 0.824837i \(0.691267\pi\)
\(284\) 973.499i 3.42781i
\(285\) 260.000 86.5332i 0.912281 0.303625i
\(286\) 130.000 0.454545
\(287\) 180.278i 0.628145i
\(288\) 129.800i 0.450694i
\(289\) −64.0000 −0.221453
\(290\) −260.000 −0.896552
\(291\) 442.000 1.51890
\(292\) −945.000 −3.23630
\(293\) 219.939i 0.750644i 0.926895 + 0.375322i \(0.122468\pi\)
−0.926895 + 0.375322i \(0.877532\pi\)
\(294\) −312.000 −1.06122
\(295\) 72.1110i 0.244444i
\(296\) −390.000 −1.31757
\(297\) 180.278i 0.606995i
\(298\) 252.389i 0.846942i
\(299\) 126.194i 0.422054i
\(300\) 292.050i 0.973499i
\(301\) 100.000 0.332226
\(302\) −130.000 −0.430464
\(303\) 180.278i 0.594975i
\(304\) −174.000 522.805i −0.572368 1.71975i
\(305\) −160.000 −0.524590
\(306\) 216.333i 0.706971i
\(307\) 237.966i 0.775135i −0.921841 0.387567i \(-0.873315\pi\)
0.921841 0.387567i \(-0.126685\pi\)
\(308\) −450.000 −1.46104
\(309\) 208.000 0.673139
\(310\) 520.000 1.67742
\(311\) 395.000 1.27010 0.635048 0.772472i \(-0.280980\pi\)
0.635048 + 0.772472i \(0.280980\pi\)
\(312\) 234.361i 0.751157i
\(313\) 125.000 0.399361 0.199681 0.979861i \(-0.436010\pi\)
0.199681 + 0.979861i \(0.436010\pi\)
\(314\) 36.0555i 0.114826i
\(315\) 80.0000 0.253968
\(316\) 324.500i 1.02690i
\(317\) 3.60555i 0.0113740i −0.999984 0.00568699i \(-0.998190\pi\)
0.999984 0.00568699i \(-0.00181023\pi\)
\(318\) 984.315i 3.09533i
\(319\) 180.278i 0.565133i
\(320\) −4.00000 −0.0125000
\(321\) 273.000 0.850467
\(322\) 630.971i 1.95954i
\(323\) −90.0000 270.416i −0.278638 0.837202i
\(324\) 909.000 2.80556
\(325\) 32.4500i 0.0998460i
\(326\) 973.499i 2.98619i
\(327\) −715.000 −2.18654
\(328\) 650.000 1.98171
\(329\) −50.0000 −0.151976
\(330\) −520.000 −1.57576
\(331\) 198.305i 0.599110i 0.954079 + 0.299555i \(0.0968382\pi\)
−0.954079 + 0.299555i \(0.903162\pi\)
\(332\) 360.000 1.08434
\(333\) 86.5332i 0.259860i
\(334\) −442.000 −1.32335
\(335\) 158.644i 0.473565i
\(336\) 522.805i 1.55597i
\(337\) 57.6888i 0.171183i −0.996330 0.0855917i \(-0.972722\pi\)
0.996330 0.0855917i \(-0.0272781\pi\)
\(338\) 562.466i 1.66410i
\(339\) −442.000 −1.30383
\(340\) −540.000 −1.58824
\(341\) 360.555i 1.05735i
\(342\) 260.000 86.5332i 0.760234 0.253021i
\(343\) 365.000 1.06414
\(344\) 360.555i 1.04813i
\(345\) 504.777i 1.46312i
\(346\) 442.000 1.27746
\(347\) −40.0000 −0.115274 −0.0576369 0.998338i \(-0.518357\pi\)
−0.0576369 + 0.998338i \(0.518357\pi\)
\(348\) −585.000 −1.68103
\(349\) 98.0000 0.280802 0.140401 0.990095i \(-0.455161\pi\)
0.140401 + 0.990095i \(0.455161\pi\)
\(350\) 162.250i 0.463571i
\(351\) 65.0000 0.185185
\(352\) 324.500i 0.921874i
\(353\) −185.000 −0.524079 −0.262040 0.965057i \(-0.584395\pi\)
−0.262040 + 0.965057i \(0.584395\pi\)
\(354\) 234.361i 0.662036i
\(355\) 432.666i 1.21878i
\(356\) 0 0
\(357\) 270.416i 0.757469i
\(358\) −130.000 −0.363128
\(359\) −225.000 −0.626741 −0.313370 0.949631i \(-0.601458\pi\)
−0.313370 + 0.949631i \(0.601458\pi\)
\(360\) 288.444i 0.801234i
\(361\) −289.000 + 216.333i −0.800554 + 0.599261i
\(362\) −390.000 −1.07735
\(363\) 75.7166i 0.208586i
\(364\) 162.250i 0.445741i
\(365\) 420.000 1.15068
\(366\) −520.000 −1.42077
\(367\) 50.0000 0.136240 0.0681199 0.997677i \(-0.478300\pi\)
0.0681199 + 0.997677i \(0.478300\pi\)
\(368\) 1015.00 2.75815
\(369\) 144.222i 0.390846i
\(370\) 312.000 0.843243
\(371\) 378.583i 1.02044i
\(372\) 1170.00 3.14516
\(373\) 436.272i 1.16963i 0.811167 + 0.584815i \(0.198833\pi\)
−0.811167 + 0.584815i \(0.801167\pi\)
\(374\) 540.833i 1.44608i
\(375\) 490.355i 1.30761i
\(376\) 180.278i 0.479462i
\(377\) −65.0000 −0.172414
\(378\) −325.000 −0.859788
\(379\) 486.749i 1.28430i 0.766579 + 0.642150i \(0.221957\pi\)
−0.766579 + 0.642150i \(0.778043\pi\)
\(380\) 216.000 + 648.999i 0.568421 + 1.70789i
\(381\) −468.000 −1.22835
\(382\) 695.871i 1.82165i
\(383\) 201.911i 0.527182i −0.964634 0.263591i \(-0.915093\pi\)
0.964634 0.263591i \(-0.0849070\pi\)
\(384\) 455.000 1.18490
\(385\) 200.000 0.519481
\(386\) −962.000 −2.49223
\(387\) 80.0000 0.206718
\(388\) 1103.30i 2.84355i
\(389\) −478.000 −1.22879 −0.614396 0.788998i \(-0.710600\pi\)
−0.614396 + 0.788998i \(0.710600\pi\)
\(390\) 187.489i 0.480740i
\(391\) 525.000 1.34271
\(392\) 432.666i 1.10374i
\(393\) 403.822i 1.02754i
\(394\) 324.500i 0.823603i
\(395\) 144.222i 0.365119i
\(396\) −360.000 −0.909091
\(397\) 750.000 1.88917 0.944584 0.328269i \(-0.106465\pi\)
0.944584 + 0.328269i \(0.106465\pi\)
\(398\) 443.483i 1.11428i
\(399\) −325.000 + 108.167i −0.814536 + 0.271094i
\(400\) −261.000 −0.652500
\(401\) 288.444i 0.719312i 0.933085 + 0.359656i \(0.117106\pi\)
−0.933085 + 0.359656i \(0.882894\pi\)
\(402\) 515.594i 1.28257i
\(403\) 130.000 0.322581
\(404\) 450.000 1.11386
\(405\) −404.000 −0.997531
\(406\) 325.000 0.800493
\(407\) 216.333i 0.531531i
\(408\) −975.000 −2.38971
\(409\) 36.0555i 0.0881553i 0.999028 + 0.0440776i \(0.0140349\pi\)
−0.999028 + 0.0440776i \(0.985965\pi\)
\(410\) −520.000 −1.26829
\(411\) 450.694i 1.09658i
\(412\) 519.199i 1.26019i
\(413\) 90.1388i 0.218254i
\(414\) 504.777i 1.21927i
\(415\) −160.000 −0.385542
\(416\) −117.000 −0.281250
\(417\) 180.278i 0.432320i
\(418\) 650.000 216.333i 1.55502 0.517543i
\(419\) 112.000 0.267303 0.133652 0.991028i \(-0.457330\pi\)
0.133652 + 0.991028i \(0.457330\pi\)
\(420\) 648.999i 1.54524i
\(421\) 630.971i 1.49874i −0.662149 0.749372i \(-0.730355\pi\)
0.662149 0.749372i \(-0.269645\pi\)
\(422\) 845.000 2.00237
\(423\) −40.0000 −0.0945626
\(424\) −1365.00 −3.21934
\(425\) −135.000 −0.317647
\(426\) 1406.16i 3.30086i
\(427\) 200.000 0.468384
\(428\) 681.449i 1.59217i
\(429\) −130.000 −0.303030
\(430\) 288.444i 0.670800i
\(431\) 432.666i 1.00387i 0.864907 + 0.501933i \(0.167378\pi\)
−0.864907 + 0.501933i \(0.832622\pi\)
\(432\) 522.805i 1.21020i
\(433\) 735.532i 1.69869i 0.527839 + 0.849345i \(0.323003\pi\)
−0.527839 + 0.849345i \(0.676997\pi\)
\(434\) −650.000 −1.49770
\(435\) 260.000 0.597701
\(436\) 1784.75i 4.09346i
\(437\) −210.000 630.971i −0.480549 1.44387i
\(438\) 1365.00 3.11644
\(439\) 793.221i 1.80688i −0.428712 0.903441i \(-0.641033\pi\)
0.428712 0.903441i \(-0.358967\pi\)
\(440\) 721.110i 1.63889i
\(441\) 96.0000 0.217687
\(442\) −195.000 −0.441176
\(443\) 670.000 1.51242 0.756208 0.654332i \(-0.227050\pi\)
0.756208 + 0.654332i \(0.227050\pi\)
\(444\) 702.000 1.58108
\(445\) 0 0
\(446\) 728.000 1.63229
\(447\) 252.389i 0.564628i
\(448\) 5.00000 0.0111607
\(449\) 36.0555i 0.0803018i 0.999194 + 0.0401509i \(0.0127839\pi\)
−0.999194 + 0.0401509i \(0.987216\pi\)
\(450\) 129.800i 0.288444i
\(451\) 360.555i 0.799457i
\(452\) 1103.30i 2.44093i
\(453\) 130.000 0.286976
\(454\) −923.000 −2.03304
\(455\) 72.1110i 0.158486i
\(456\) 390.000 + 1171.80i 0.855263 + 2.56975i
\(457\) −755.000 −1.65208 −0.826039 0.563612i \(-0.809411\pi\)
−0.826039 + 0.563612i \(0.809411\pi\)
\(458\) 576.888i 1.25958i
\(459\) 270.416i 0.589142i
\(460\) −1260.00 −2.73913
\(461\) 772.000 1.67462 0.837310 0.546728i \(-0.184127\pi\)
0.837310 + 0.546728i \(0.184127\pi\)
\(462\) 650.000 1.40693
\(463\) −350.000 −0.755940 −0.377970 0.925818i \(-0.623378\pi\)
−0.377970 + 0.925818i \(0.623378\pi\)
\(464\) 522.805i 1.12673i
\(465\) −520.000 −1.11828
\(466\) 973.499i 2.08905i
\(467\) 70.0000 0.149893 0.0749465 0.997188i \(-0.476121\pi\)
0.0749465 + 0.997188i \(0.476121\pi\)
\(468\) 129.800i 0.277350i
\(469\) 198.305i 0.422826i
\(470\) 144.222i 0.306855i
\(471\) 36.0555i 0.0765510i
\(472\) 325.000 0.688559
\(473\) 200.000 0.422833
\(474\) 468.722i 0.988864i
\(475\) 54.0000 + 162.250i 0.113684 + 0.341579i
\(476\) 675.000 1.41807
\(477\) 302.866i 0.634940i
\(478\) 710.294i 1.48597i
\(479\) −370.000 −0.772443 −0.386221 0.922406i \(-0.626220\pi\)
−0.386221 + 0.922406i \(0.626220\pi\)
\(480\) 468.000 0.975000
\(481\) 78.0000 0.162162
\(482\) −1430.00 −2.96680
\(483\) 630.971i 1.30636i
\(484\) 189.000 0.390496
\(485\) 490.355i 1.01104i
\(486\) −728.000 −1.49794
\(487\) 519.199i 1.06612i 0.846078 + 0.533059i \(0.178958\pi\)
−0.846078 + 0.533059i \(0.821042\pi\)
\(488\) 721.110i 1.47768i
\(489\) 973.499i 1.99080i
\(490\) 346.133i 0.706394i
\(491\) −632.000 −1.28717 −0.643585 0.765375i \(-0.722554\pi\)
−0.643585 + 0.765375i \(0.722554\pi\)
\(492\) −1170.00 −2.37805
\(493\) 270.416i 0.548512i
\(494\) 78.0000 + 234.361i 0.157895 + 0.474415i
\(495\) 160.000 0.323232
\(496\) 1045.61i 2.10808i
\(497\) 540.833i 1.08819i
\(498\) −520.000 −1.04418
\(499\) 380.000 0.761523 0.380762 0.924673i \(-0.375662\pi\)
0.380762 + 0.924673i \(0.375662\pi\)
\(500\) 1224.00 2.44800
\(501\) 442.000 0.882236
\(502\) 1449.43i 2.88731i
\(503\) −45.0000 −0.0894632 −0.0447316 0.998999i \(-0.514243\pi\)
−0.0447316 + 0.998999i \(0.514243\pi\)
\(504\) 360.555i 0.715387i
\(505\) −200.000 −0.396040
\(506\) 1261.94i 2.49396i
\(507\) 562.466i 1.10940i
\(508\) 1168.20i 2.29960i
\(509\) 829.277i 1.62923i −0.580004 0.814614i \(-0.696949\pi\)
0.580004 0.814614i \(-0.303051\pi\)
\(510\) 780.000 1.52941
\(511\) −525.000 −1.02740
\(512\) 1150.17i 2.24643i
\(513\) 325.000 108.167i 0.633528 0.210851i
\(514\) 1508.00 2.93385
\(515\) 230.755i 0.448069i
\(516\) 648.999i 1.25775i
\(517\) −100.000 −0.193424
\(518\) −390.000 −0.752896
\(519\) −442.000 −0.851638
\(520\) 260.000 0.500000
\(521\) 612.944i 1.17648i −0.808688 0.588238i \(-0.799822\pi\)
0.808688 0.588238i \(-0.200178\pi\)
\(522\) 260.000 0.498084
\(523\) 465.116i 0.889323i −0.895699 0.444662i \(-0.853324\pi\)
0.895699 0.444662i \(-0.146676\pi\)
\(524\) −1008.00 −1.92366
\(525\) 162.250i 0.309047i
\(526\) 1117.72i 2.12494i
\(527\) 540.833i 1.02625i
\(528\) 1045.61i 1.98032i
\(529\) 696.000 1.31569
\(530\) 1092.00 2.06038
\(531\) 72.1110i 0.135802i
\(532\) −270.000 811.249i −0.507519 1.52490i
\(533\) −130.000 −0.243902
\(534\) 0 0
\(535\) 302.866i 0.566105i
\(536\) 715.000 1.33396
\(537\) 130.000 0.242086
\(538\) −390.000 −0.724907
\(539\) 240.000 0.445269
\(540\) 648.999i 1.20185i
\(541\) −600.000 −1.10906 −0.554529 0.832165i \(-0.687101\pi\)
−0.554529 + 0.832165i \(0.687101\pi\)
\(542\) 378.583i 0.698492i
\(543\) 390.000 0.718232
\(544\) 486.749i 0.894760i
\(545\) 793.221i 1.45545i
\(546\) 234.361i 0.429232i
\(547\) 598.522i 1.09419i 0.837071 + 0.547095i \(0.184266\pi\)
−0.837071 + 0.547095i \(0.815734\pi\)
\(548\) −1125.00 −2.05292
\(549\) 160.000 0.291439
\(550\) 324.500i 0.589999i
\(551\) −325.000 + 108.167i −0.589837 + 0.196310i
\(552\) −2275.00 −4.12138
\(553\) 180.278i 0.325999i
\(554\) 180.278i 0.325411i
\(555\) −312.000 −0.562162
\(556\) −450.000 −0.809353
\(557\) 380.000 0.682226 0.341113 0.940022i \(-0.389196\pi\)
0.341113 + 0.940022i \(0.389196\pi\)
\(558\) −520.000 −0.931900
\(559\) 72.1110i 0.129000i
\(560\) −580.000 −1.03571
\(561\) 540.833i 0.964051i
\(562\) 1040.00 1.85053
\(563\) 122.589i 0.217742i −0.994056 0.108871i \(-0.965276\pi\)
0.994056 0.108871i \(-0.0347235\pi\)
\(564\) 324.500i 0.575354i
\(565\) 490.355i 0.867885i
\(566\) 1153.78i 2.03847i
\(567\) 505.000 0.890653
\(568\) 1950.00 3.43310
\(569\) 36.0555i 0.0633665i −0.999498 0.0316832i \(-0.989913\pi\)
0.999498 0.0316832i \(-0.0100868\pi\)
\(570\) −312.000 937.443i −0.547368 1.64464i
\(571\) −790.000 −1.38354 −0.691769 0.722119i \(-0.743168\pi\)
−0.691769 + 0.722119i \(0.743168\pi\)
\(572\) 324.500i 0.567307i
\(573\) 695.871i 1.21444i
\(574\) 650.000 1.13240
\(575\) −315.000 −0.547826
\(576\) 4.00000 0.00694444
\(577\) 675.000 1.16984 0.584922 0.811090i \(-0.301125\pi\)
0.584922 + 0.811090i \(0.301125\pi\)
\(578\) 230.755i 0.399231i
\(579\) 962.000 1.66149
\(580\) 648.999i 1.11896i
\(581\) 200.000 0.344234
\(582\) 1593.65i 2.73824i
\(583\) 757.166i 1.29874i
\(584\) 1892.91i 3.24129i
\(585\) 57.6888i 0.0986134i
\(586\) 793.000 1.35324
\(587\) −280.000 −0.477002 −0.238501 0.971142i \(-0.576656\pi\)
−0.238501 + 0.971142i \(0.576656\pi\)
\(588\) 778.799i 1.32449i
\(589\) 650.000 216.333i 1.10357 0.367289i
\(590\) −260.000 −0.440678
\(591\) 324.500i 0.549069i
\(592\) 627.366i 1.05974i
\(593\) 750.000 1.26476 0.632378 0.774660i \(-0.282079\pi\)
0.632378 + 0.774660i \(0.282079\pi\)
\(594\) −650.000 −1.09428
\(595\) −300.000 −0.504202
\(596\) −630.000 −1.05705
\(597\) 443.483i 0.742852i
\(598\) −455.000 −0.760870
\(599\) 504.777i 0.842700i −0.906898 0.421350i \(-0.861556\pi\)
0.906898 0.421350i \(-0.138444\pi\)
\(600\) 585.000 0.975000
\(601\) 612.944i 1.01987i −0.860212 0.509937i \(-0.829669\pi\)
0.860212 0.509937i \(-0.170331\pi\)
\(602\) 360.555i 0.598929i
\(603\) 158.644i 0.263092i
\(604\) 324.500i 0.537251i
\(605\) −84.0000 −0.138843
\(606\) −650.000 −1.07261
\(607\) 987.921i 1.62755i 0.581182 + 0.813774i \(0.302590\pi\)
−0.581182 + 0.813774i \(0.697410\pi\)
\(608\) −585.000 + 194.700i −0.962171 + 0.320230i
\(609\) −325.000 −0.533662
\(610\) 576.888i 0.945718i
\(611\) 36.0555i 0.0590107i
\(612\) 540.000 0.882353
\(613\) −1200.00 −1.95759 −0.978793 0.204853i \(-0.934328\pi\)
−0.978793 + 0.204853i \(0.934328\pi\)
\(614\) −858.000 −1.39739
\(615\) 520.000 0.845528
\(616\) 901.388i 1.46329i
\(617\) −350.000 −0.567261 −0.283630 0.958934i \(-0.591539\pi\)
−0.283630 + 0.958934i \(0.591539\pi\)
\(618\) 749.955i 1.21352i
\(619\) 560.000 0.904685 0.452342 0.891844i \(-0.350588\pi\)
0.452342 + 0.891844i \(0.350588\pi\)
\(620\) 1298.00i 2.09355i
\(621\) 630.971i 1.01606i
\(622\) 1424.19i 2.28970i
\(623\) 0 0
\(624\) 377.000 0.604167
\(625\) −319.000 −0.510400
\(626\) 450.694i 0.719958i
\(627\) −650.000 + 216.333i −1.03668 + 0.345029i
\(628\) −90.0000 −0.143312
\(629\) 324.500i 0.515898i
\(630\) 288.444i 0.457848i
\(631\) −1050.00 −1.66403 −0.832013 0.554757i \(-0.812811\pi\)
−0.832013 + 0.554757i \(0.812811\pi\)
\(632\) −650.000 −1.02848
\(633\) −845.000 −1.33491
\(634\) −13.0000 −0.0205047
\(635\) 519.199i 0.817637i
\(636\) 2457.00 3.86321
\(637\) 86.5332i 0.135845i
\(638\) 650.000 1.01881
\(639\) 432.666i 0.677099i
\(640\) 504.777i 0.788714i
\(641\) 1225.89i 1.91246i −0.292615 0.956230i \(-0.594525\pi\)
0.292615 0.956230i \(-0.405475\pi\)
\(642\) 984.315i 1.53320i
\(643\) −1030.00 −1.60187 −0.800933 0.598754i \(-0.795663\pi\)
−0.800933 + 0.598754i \(0.795663\pi\)
\(644\) 1575.00 2.44565
\(645\) 288.444i 0.447200i
\(646\) −975.000 + 324.500i −1.50929 + 0.502321i
\(647\) 555.000 0.857805 0.428903 0.903351i \(-0.358900\pi\)
0.428903 + 0.903351i \(0.358900\pi\)
\(648\) 1820.80i 2.80988i
\(649\) 180.278i 0.277777i
\(650\) 117.000 0.180000
\(651\) 650.000 0.998464
\(652\) 2430.00 3.72699
\(653\) 50.0000 0.0765697 0.0382848 0.999267i \(-0.487811\pi\)
0.0382848 + 0.999267i \(0.487811\pi\)
\(654\) 2577.97i 3.94185i
\(655\) 448.000 0.683969
\(656\) 1045.61i 1.59392i
\(657\) −420.000 −0.639269
\(658\) 180.278i 0.273978i
\(659\) 198.305i 0.300919i −0.988616 0.150459i \(-0.951925\pi\)
0.988616 0.150459i \(-0.0480752\pi\)
\(660\) 1298.00i 1.96666i
\(661\) 198.305i 0.300008i −0.988685 0.150004i \(-0.952071\pi\)
0.988685 0.150004i \(-0.0479287\pi\)
\(662\) 715.000 1.08006
\(663\) 195.000 0.294118
\(664\) 721.110i 1.08601i
\(665\) 120.000 + 360.555i 0.180451 + 0.542188i
\(666\) −312.000 −0.468468
\(667\) 630.971i 0.945984i
\(668\) 1103.30i 1.65164i
\(669\) −728.000 −1.08819
\(670\) −572.000 −0.853731
\(671\) 400.000 0.596125
\(672\) −585.000 −0.870536
\(673\) 598.522i 0.889334i −0.895696 0.444667i \(-0.853322\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(674\) −208.000 −0.308605
\(675\) 162.250i 0.240370i
\(676\) −1404.00 −2.07692
\(677\) 68.5055i 0.101190i −0.998719 0.0505949i \(-0.983888\pi\)
0.998719 0.0505949i \(-0.0161117\pi\)
\(678\) 1593.65i 2.35052i
\(679\) 612.944i 0.902715i
\(680\) 1081.67i 1.59068i
\(681\) 923.000 1.35536
\(682\) −1300.00 −1.90616
\(683\) 237.966i 0.348413i 0.984709 + 0.174207i \(0.0557361\pi\)
−0.984709 + 0.174207i \(0.944264\pi\)
\(684\) −216.000 648.999i −0.315789 0.948829i
\(685\) 500.000 0.729927
\(686\) 1316.03i 1.91841i
\(687\) 576.888i 0.839721i
\(688\) −580.000 −0.843023
\(689\) 273.000 0.396226
\(690\) 1820.00 2.63768
\(691\) −820.000 −1.18669 −0.593343 0.804950i \(-0.702192\pi\)
−0.593343 + 0.804950i \(0.702192\pi\)
\(692\) 1103.30i 1.59436i
\(693\) −200.000 −0.288600
\(694\) 144.222i 0.207813i
\(695\) 200.000 0.287770
\(696\) 1171.80i 1.68363i
\(697\) 540.833i 0.775944i
\(698\) 353.344i 0.506224i
\(699\) 973.499i 1.39270i
\(700\) −405.000 −0.578571
\(701\) −540.000 −0.770328 −0.385164 0.922848i \(-0.625855\pi\)
−0.385164 + 0.922848i \(0.625855\pi\)
\(702\) 234.361i 0.333847i
\(703\) 390.000 129.800i 0.554765 0.184637i
\(704\) 10.0000 0.0142045
\(705\) 144.222i 0.204570i
\(706\) 667.027i 0.944797i
\(707\) 250.000 0.353607
\(708\) −585.000 −0.826271
\(709\) 268.000 0.377997 0.188999 0.981977i \(-0.439476\pi\)
0.188999 + 0.981977i \(0.439476\pi\)
\(710\) −1560.00 −2.19718
\(711\) 144.222i 0.202844i
\(712\) 0 0
\(713\) 1261.94i 1.76991i
\(714\) −975.000 −1.36555
\(715\) 144.222i 0.201709i
\(716\) 324.500i 0.453212i
\(717\) 710.294i 0.990647i
\(718\) 811.249i 1.12987i
\(719\) 105.000 0.146036 0.0730181 0.997331i \(-0.476737\pi\)
0.0730181 + 0.997331i \(0.476737\pi\)
\(720\) −464.000 −0.644444
\(721\) 288.444i 0.400061i
\(722\) 780.000 + 1042.00i 1.08033 + 1.44322i
\(723\) 1430.00 1.97787
\(724\) 973.499i 1.34461i
\(725\) 162.250i 0.223793i
\(726\) −273.000 −0.376033
\(727\) 695.000 0.955983 0.477992 0.878364i \(-0.341365\pi\)
0.477992 + 0.878364i \(0.341365\pi\)
\(728\) −325.000 −0.446429
\(729\) −181.000 −0.248285
\(730\) 1514.33i 2.07443i
\(731\) −300.000 −0.410397
\(732\) 1298.00i 1.77322i
\(733\) 160.000 0.218281 0.109141 0.994026i \(-0.465190\pi\)
0.109141 + 0.994026i \(0.465190\pi\)
\(734\) 180.278i 0.245610i
\(735\) 346.133i 0.470929i
\(736\) 1135.75i 1.54314i
\(737\) 396.611i 0.538142i
\(738\) 520.000 0.704607
\(739\) 1028.00 1.39107 0.695535 0.718493i \(-0.255168\pi\)
0.695535 + 0.718493i \(0.255168\pi\)
\(740\) 778.799i 1.05243i
\(741\) −78.0000 234.361i −0.105263 0.316276i
\(742\) −1365.00 −1.83962
\(743\) 526.410i 0.708493i 0.935152 + 0.354247i \(0.115263\pi\)
−0.935152 + 0.354247i \(0.884737\pi\)
\(744\) 2343.61i 3.15001i
\(745\) 280.000 0.375839
\(746\) 1573.00 2.10858
\(747\) 160.000 0.214190
\(748\) 1350.00 1.80481
\(749\) 378.583i 0.505451i
\(750\) −1768.00 −2.35733
\(751\) 36.0555i 0.0480100i −0.999712 0.0240050i \(-0.992358\pi\)
0.999712 0.0240050i \(-0.00764176\pi\)
\(752\) 290.000 0.385638
\(753\) 1449.43i 1.92488i
\(754\) 234.361i 0.310823i
\(755\) 144.222i 0.191023i
\(756\) 811.249i 1.07308i
\(757\) 60.0000 0.0792602 0.0396301 0.999214i \(-0.487382\pi\)
0.0396301 + 0.999214i \(0.487382\pi\)
\(758\) 1755.00 2.31530
\(759\) 1261.94i 1.66264i
\(760\) 1300.00 432.666i 1.71053 0.569298i
\(761\) −655.000 −0.860710 −0.430355 0.902660i \(-0.641612\pi\)
−0.430355 + 0.902660i \(0.641612\pi\)
\(762\) 1687.40i 2.21443i
\(763\) 991.527i 1.29951i
\(764\) −1737.00 −2.27356
\(765\) −240.000 −0.313725
\(766\) −728.000 −0.950392
\(767\) −65.0000 −0.0847458
\(768\) 1654.95i 2.15488i
\(769\) −185.000 −0.240572 −0.120286 0.992739i \(-0.538381\pi\)
−0.120286 + 0.992739i \(0.538381\pi\)
\(770\) 721.110i 0.936507i
\(771\) −1508.00 −1.95590
\(772\) 2401.30i 3.11049i
\(773\) 320.894i 0.415128i 0.978221 + 0.207564i \(0.0665536\pi\)
−0.978221 + 0.207564i \(0.933446\pi\)
\(774\) 288.444i 0.372667i
\(775\) 324.500i 0.418709i
\(776\) 2210.00 2.84794
\(777\) 390.000 0.501931
\(778\) 1723.45i 2.21524i
\(779\) −650.000 + 216.333i −0.834403 + 0.277706i
\(780\) −468.000 −0.600000
\(781\) 1081.67i 1.38497i
\(782\) 1892.91i 2.42061i
\(783\) 325.000 0.415070
\(784\) −696.000 −0.887755
\(785\) 40.0000 0.0509554
\(786\) 1456.00 1.85242
\(787\) 68.5055i 0.0870463i −0.999052 0.0435232i \(-0.986142\pi\)
0.999052 0.0435232i \(-0.0138582\pi\)
\(788\) −810.000