Properties

Label 475.3.d.b.474.2
Level $475$
Weight $3$
Character 475.474
Analytic conductor $12.943$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.9428125571\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{13})\)
Defining polynomial: \(x^{4} + 7 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 474.2
Root \(-2.30278i\) of defining polynomial
Character \(\chi\) \(=\) 475.474
Dual form 475.3.d.b.474.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.60555 q^{2} -3.60555 q^{3} +9.00000 q^{4} +13.0000 q^{6} +5.00000i q^{7} -18.0278 q^{8} +4.00000 q^{9} +O(q^{10})\) \(q-3.60555 q^{2} -3.60555 q^{3} +9.00000 q^{4} +13.0000 q^{6} +5.00000i q^{7} -18.0278 q^{8} +4.00000 q^{9} -10.0000 q^{11} -32.4500 q^{12} +3.60555 q^{13} -18.0278i q^{14} +29.0000 q^{16} -15.0000i q^{17} -14.4222 q^{18} +(6.00000 + 18.0278i) q^{19} -18.0278i q^{21} +36.0555 q^{22} +35.0000i q^{23} +65.0000 q^{24} -13.0000 q^{26} +18.0278 q^{27} +45.0000i q^{28} +18.0278i q^{29} +36.0555i q^{31} -32.4500 q^{32} +36.0555 q^{33} +54.0833i q^{34} +36.0000 q^{36} +21.6333 q^{37} +(-21.6333 - 65.0000i) q^{38} -13.0000 q^{39} -36.0555i q^{41} +65.0000i q^{42} -20.0000i q^{43} -90.0000 q^{44} -126.194i q^{46} -10.0000i q^{47} -104.561 q^{48} +24.0000 q^{49} +54.0833i q^{51} +32.4500 q^{52} -75.7166 q^{53} -65.0000 q^{54} -90.1388i q^{56} +(-21.6333 - 65.0000i) q^{57} -65.0000i q^{58} +18.0278i q^{59} -40.0000 q^{61} -130.000i q^{62} +20.0000i q^{63} +1.00000 q^{64} -130.000 q^{66} -39.6611 q^{67} -135.000i q^{68} -126.194i q^{69} -108.167i q^{71} -72.1110 q^{72} +105.000i q^{73} -78.0000 q^{74} +(54.0000 + 162.250i) q^{76} -50.0000i q^{77} +46.8722 q^{78} -36.0555i q^{79} -101.000 q^{81} +130.000i q^{82} -40.0000i q^{83} -162.250i q^{84} +72.1110i q^{86} -65.0000i q^{87} +180.278 q^{88} +18.0278i q^{91} +315.000i q^{92} -130.000i q^{93} +36.0555i q^{94} +117.000 q^{96} -122.589 q^{97} -86.5332 q^{98} -40.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 36q^{4} + 52q^{6} + 16q^{9} + O(q^{10}) \) \( 4q + 36q^{4} + 52q^{6} + 16q^{9} - 40q^{11} + 116q^{16} + 24q^{19} + 260q^{24} - 52q^{26} + 144q^{36} - 52q^{39} - 360q^{44} + 96q^{49} - 260q^{54} - 160q^{61} + 4q^{64} - 520q^{66} - 312q^{74} + 216q^{76} - 404q^{81} + 468q^{96} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.60555 −1.80278 −0.901388 0.433013i \(-0.857451\pi\)
−0.901388 + 0.433013i \(0.857451\pi\)
\(3\) −3.60555 −1.20185 −0.600925 0.799305i \(-0.705201\pi\)
−0.600925 + 0.799305i \(0.705201\pi\)
\(4\) 9.00000 2.25000
\(5\) 0 0
\(6\) 13.0000 2.16667
\(7\) 5.00000i 0.714286i 0.934050 + 0.357143i \(0.116249\pi\)
−0.934050 + 0.357143i \(0.883751\pi\)
\(8\) −18.0278 −2.25347
\(9\) 4.00000 0.444444
\(10\) 0 0
\(11\) −10.0000 −0.909091 −0.454545 0.890724i \(-0.650198\pi\)
−0.454545 + 0.890724i \(0.650198\pi\)
\(12\) −32.4500 −2.70416
\(13\) 3.60555 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 18.0278i 1.28770i
\(15\) 0 0
\(16\) 29.0000 1.81250
\(17\) 15.0000i 0.882353i −0.897420 0.441176i \(-0.854561\pi\)
0.897420 0.441176i \(-0.145439\pi\)
\(18\) −14.4222 −0.801234
\(19\) 6.00000 + 18.0278i 0.315789 + 0.948829i
\(20\) 0 0
\(21\) 18.0278i 0.858465i
\(22\) 36.0555 1.63889
\(23\) 35.0000i 1.52174i 0.648905 + 0.760870i \(0.275227\pi\)
−0.648905 + 0.760870i \(0.724773\pi\)
\(24\) 65.0000 2.70833
\(25\) 0 0
\(26\) −13.0000 −0.500000
\(27\) 18.0278 0.667695
\(28\) 45.0000i 1.60714i
\(29\) 18.0278i 0.621647i 0.950468 + 0.310823i \(0.100605\pi\)
−0.950468 + 0.310823i \(0.899395\pi\)
\(30\) 0 0
\(31\) 36.0555i 1.16308i 0.813517 + 0.581541i \(0.197550\pi\)
−0.813517 + 0.581541i \(0.802450\pi\)
\(32\) −32.4500 −1.01406
\(33\) 36.0555 1.09259
\(34\) 54.0833i 1.59068i
\(35\) 0 0
\(36\) 36.0000 1.00000
\(37\) 21.6333 0.584684 0.292342 0.956314i \(-0.405565\pi\)
0.292342 + 0.956314i \(0.405565\pi\)
\(38\) −21.6333 65.0000i −0.569298 1.71053i
\(39\) −13.0000 −0.333333
\(40\) 0 0
\(41\) 36.0555i 0.879403i −0.898144 0.439701i \(-0.855084\pi\)
0.898144 0.439701i \(-0.144916\pi\)
\(42\) 65.0000i 1.54762i
\(43\) 20.0000i 0.465116i −0.972582 0.232558i \(-0.925290\pi\)
0.972582 0.232558i \(-0.0747096\pi\)
\(44\) −90.0000 −2.04545
\(45\) 0 0
\(46\) 126.194i 2.74335i
\(47\) 10.0000i 0.212766i −0.994325 0.106383i \(-0.966073\pi\)
0.994325 0.106383i \(-0.0339270\pi\)
\(48\) −104.561 −2.17835
\(49\) 24.0000 0.489796
\(50\) 0 0
\(51\) 54.0833i 1.06046i
\(52\) 32.4500 0.624038
\(53\) −75.7166 −1.42861 −0.714307 0.699832i \(-0.753258\pi\)
−0.714307 + 0.699832i \(0.753258\pi\)
\(54\) −65.0000 −1.20370
\(55\) 0 0
\(56\) 90.1388i 1.60962i
\(57\) −21.6333 65.0000i −0.379532 1.14035i
\(58\) 65.0000i 1.12069i
\(59\) 18.0278i 0.305555i 0.988261 + 0.152778i \(0.0488218\pi\)
−0.988261 + 0.152778i \(0.951178\pi\)
\(60\) 0 0
\(61\) −40.0000 −0.655738 −0.327869 0.944723i \(-0.606330\pi\)
−0.327869 + 0.944723i \(0.606330\pi\)
\(62\) 130.000i 2.09677i
\(63\) 20.0000i 0.317460i
\(64\) 1.00000 0.0156250
\(65\) 0 0
\(66\) −130.000 −1.96970
\(67\) −39.6611 −0.591956 −0.295978 0.955195i \(-0.595646\pi\)
−0.295978 + 0.955195i \(0.595646\pi\)
\(68\) 135.000i 1.98529i
\(69\) 126.194i 1.82890i
\(70\) 0 0
\(71\) 108.167i 1.52347i −0.647887 0.761736i \(-0.724347\pi\)
0.647887 0.761736i \(-0.275653\pi\)
\(72\) −72.1110 −1.00154
\(73\) 105.000i 1.43836i 0.694826 + 0.719178i \(0.255481\pi\)
−0.694826 + 0.719178i \(0.744519\pi\)
\(74\) −78.0000 −1.05405
\(75\) 0 0
\(76\) 54.0000 + 162.250i 0.710526 + 2.13487i
\(77\) 50.0000i 0.649351i
\(78\) 46.8722 0.600925
\(79\) 36.0555i 0.456399i −0.973614 0.228199i \(-0.926716\pi\)
0.973614 0.228199i \(-0.0732838\pi\)
\(80\) 0 0
\(81\) −101.000 −1.24691
\(82\) 130.000i 1.58537i
\(83\) 40.0000i 0.481928i −0.970534 0.240964i \(-0.922536\pi\)
0.970534 0.240964i \(-0.0774635\pi\)
\(84\) 162.250i 1.93155i
\(85\) 0 0
\(86\) 72.1110i 0.838500i
\(87\) 65.0000i 0.747126i
\(88\) 180.278 2.04861
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 18.0278i 0.198107i
\(92\) 315.000i 3.42391i
\(93\) 130.000i 1.39785i
\(94\) 36.0555i 0.383569i
\(95\) 0 0
\(96\) 117.000 1.21875
\(97\) −122.589 −1.26380 −0.631901 0.775049i \(-0.717725\pi\)
−0.631901 + 0.775049i \(0.717725\pi\)
\(98\) −86.5332 −0.882992
\(99\) −40.0000 −0.404040
\(100\) 0 0
\(101\) −50.0000 −0.495050 −0.247525 0.968882i \(-0.579617\pi\)
−0.247525 + 0.968882i \(0.579617\pi\)
\(102\) 195.000i 1.91176i
\(103\) 57.6888 0.560086 0.280043 0.959988i \(-0.409651\pi\)
0.280043 + 0.959988i \(0.409651\pi\)
\(104\) −65.0000 −0.625000
\(105\) 0 0
\(106\) 273.000 2.57547
\(107\) −75.7166 −0.707632 −0.353816 0.935315i \(-0.615116\pi\)
−0.353816 + 0.935315i \(0.615116\pi\)
\(108\) 162.250 1.50231
\(109\) 198.305i 1.81931i −0.415359 0.909657i \(-0.636344\pi\)
0.415359 0.909657i \(-0.363656\pi\)
\(110\) 0 0
\(111\) −78.0000 −0.702703
\(112\) 145.000i 1.29464i
\(113\) −122.589 −1.08486 −0.542428 0.840102i \(-0.682495\pi\)
−0.542428 + 0.840102i \(0.682495\pi\)
\(114\) 78.0000 + 234.361i 0.684211 + 2.05580i
\(115\) 0 0
\(116\) 162.250i 1.39871i
\(117\) 14.4222 0.123267
\(118\) 65.0000i 0.550847i
\(119\) 75.0000 0.630252
\(120\) 0 0
\(121\) −21.0000 −0.173554
\(122\) 144.222 1.18215
\(123\) 130.000i 1.05691i
\(124\) 324.500i 2.61693i
\(125\) 0 0
\(126\) 72.1110i 0.572310i
\(127\) 129.800 1.02205 0.511023 0.859567i \(-0.329267\pi\)
0.511023 + 0.859567i \(0.329267\pi\)
\(128\) 126.194 0.985893
\(129\) 72.1110i 0.559000i
\(130\) 0 0
\(131\) 112.000 0.854962 0.427481 0.904024i \(-0.359401\pi\)
0.427481 + 0.904024i \(0.359401\pi\)
\(132\) 324.500 2.45833
\(133\) −90.1388 + 30.0000i −0.677735 + 0.225564i
\(134\) 143.000 1.06716
\(135\) 0 0
\(136\) 270.416i 1.98836i
\(137\) 125.000i 0.912409i −0.889875 0.456204i \(-0.849209\pi\)
0.889875 0.456204i \(-0.150791\pi\)
\(138\) 455.000i 3.29710i
\(139\) −50.0000 −0.359712 −0.179856 0.983693i \(-0.557563\pi\)
−0.179856 + 0.983693i \(0.557563\pi\)
\(140\) 0 0
\(141\) 36.0555i 0.255713i
\(142\) 390.000i 2.74648i
\(143\) −36.0555 −0.252136
\(144\) 116.000 0.805556
\(145\) 0 0
\(146\) 378.583i 2.59303i
\(147\) −86.5332 −0.588661
\(148\) 194.700 1.31554
\(149\) −70.0000 −0.469799 −0.234899 0.972020i \(-0.575476\pi\)
−0.234899 + 0.972020i \(0.575476\pi\)
\(150\) 0 0
\(151\) 36.0555i 0.238778i −0.992848 0.119389i \(-0.961906\pi\)
0.992848 0.119389i \(-0.0380936\pi\)
\(152\) −108.167 325.000i −0.711622 2.13816i
\(153\) 60.0000i 0.392157i
\(154\) 180.278i 1.17063i
\(155\) 0 0
\(156\) −117.000 −0.750000
\(157\) 10.0000i 0.0636943i −0.999493 0.0318471i \(-0.989861\pi\)
0.999493 0.0318471i \(-0.0101390\pi\)
\(158\) 130.000i 0.822785i
\(159\) 273.000 1.71698
\(160\) 0 0
\(161\) −175.000 −1.08696
\(162\) 364.161 2.24791
\(163\) 270.000i 1.65644i −0.560402 0.828221i \(-0.689353\pi\)
0.560402 0.828221i \(-0.310647\pi\)
\(164\) 324.500i 1.97866i
\(165\) 0 0
\(166\) 144.222i 0.868808i
\(167\) −122.589 −0.734064 −0.367032 0.930208i \(-0.619626\pi\)
−0.367032 + 0.930208i \(0.619626\pi\)
\(168\) 325.000i 1.93452i
\(169\) −156.000 −0.923077
\(170\) 0 0
\(171\) 24.0000 + 72.1110i 0.140351 + 0.421702i
\(172\) 180.000i 1.04651i
\(173\) −122.589 −0.708605 −0.354303 0.935131i \(-0.615282\pi\)
−0.354303 + 0.935131i \(0.615282\pi\)
\(174\) 234.361i 1.34690i
\(175\) 0 0
\(176\) −290.000 −1.64773
\(177\) 65.0000i 0.367232i
\(178\) 0 0
\(179\) 36.0555i 0.201427i 0.994915 + 0.100714i \(0.0321126\pi\)
−0.994915 + 0.100714i \(0.967887\pi\)
\(180\) 0 0
\(181\) 108.167i 0.597605i −0.954315 0.298803i \(-0.903413\pi\)
0.954315 0.298803i \(-0.0965872\pi\)
\(182\) 65.0000i 0.357143i
\(183\) 144.222 0.788099
\(184\) 630.971i 3.42919i
\(185\) 0 0
\(186\) 468.722i 2.52001i
\(187\) 150.000i 0.802139i
\(188\) 90.0000i 0.478723i
\(189\) 90.1388i 0.476925i
\(190\) 0 0
\(191\) 193.000 1.01047 0.505236 0.862981i \(-0.331406\pi\)
0.505236 + 0.862981i \(0.331406\pi\)
\(192\) −3.60555 −0.0187789
\(193\) 266.811 1.38244 0.691220 0.722645i \(-0.257074\pi\)
0.691220 + 0.722645i \(0.257074\pi\)
\(194\) 442.000 2.27835
\(195\) 0 0
\(196\) 216.000 1.10204
\(197\) 90.0000i 0.456853i −0.973561 0.228426i \(-0.926642\pi\)
0.973561 0.228426i \(-0.0733580\pi\)
\(198\) 144.222 0.728394
\(199\) −123.000 −0.618090 −0.309045 0.951047i \(-0.600009\pi\)
−0.309045 + 0.951047i \(0.600009\pi\)
\(200\) 0 0
\(201\) 143.000 0.711443
\(202\) 180.278 0.892463
\(203\) −90.1388 −0.444033
\(204\) 486.749i 2.38603i
\(205\) 0 0
\(206\) −208.000 −1.00971
\(207\) 140.000i 0.676329i
\(208\) 104.561 0.502697
\(209\) −60.0000 180.278i −0.287081 0.862572i
\(210\) 0 0
\(211\) 234.361i 1.11071i 0.831612 + 0.555357i \(0.187419\pi\)
−0.831612 + 0.555357i \(0.812581\pi\)
\(212\) −681.449 −3.21438
\(213\) 390.000i 1.83099i
\(214\) 273.000 1.27570
\(215\) 0 0
\(216\) −325.000 −1.50463
\(217\) −180.278 −0.830772
\(218\) 715.000i 3.27982i
\(219\) 378.583i 1.72869i
\(220\) 0 0
\(221\) 54.0833i 0.244721i
\(222\) 281.233 1.26682
\(223\) −201.911 −0.905430 −0.452715 0.891655i \(-0.649544\pi\)
−0.452715 + 0.891655i \(0.649544\pi\)
\(224\) 162.250i 0.724329i
\(225\) 0 0
\(226\) 442.000 1.95575
\(227\) −255.994 −1.12773 −0.563864 0.825868i \(-0.690686\pi\)
−0.563864 + 0.825868i \(0.690686\pi\)
\(228\) −194.700 585.000i −0.853946 2.56579i
\(229\) 160.000 0.698690 0.349345 0.936994i \(-0.386404\pi\)
0.349345 + 0.936994i \(0.386404\pi\)
\(230\) 0 0
\(231\) 180.278i 0.780422i
\(232\) 325.000i 1.40086i
\(233\) 270.000i 1.15880i −0.815044 0.579399i \(-0.803287\pi\)
0.815044 0.579399i \(-0.196713\pi\)
\(234\) −52.0000 −0.222222
\(235\) 0 0
\(236\) 162.250i 0.687499i
\(237\) 130.000i 0.548523i
\(238\) −270.416 −1.13620
\(239\) −197.000 −0.824268 −0.412134 0.911123i \(-0.635216\pi\)
−0.412134 + 0.911123i \(0.635216\pi\)
\(240\) 0 0
\(241\) 396.611i 1.64569i −0.568268 0.822844i \(-0.692386\pi\)
0.568268 0.822844i \(-0.307614\pi\)
\(242\) 75.7166 0.312878
\(243\) 201.911 0.830909
\(244\) −360.000 −1.47541
\(245\) 0 0
\(246\) 468.722i 1.90537i
\(247\) 21.6333 + 65.0000i 0.0875842 + 0.263158i
\(248\) 650.000i 2.62097i
\(249\) 144.222i 0.579205i
\(250\) 0 0
\(251\) −402.000 −1.60159 −0.800797 0.598936i \(-0.795590\pi\)
−0.800797 + 0.598936i \(0.795590\pi\)
\(252\) 180.000i 0.714286i
\(253\) 350.000i 1.38340i
\(254\) −468.000 −1.84252
\(255\) 0 0
\(256\) −459.000 −1.79297
\(257\) 418.244 1.62741 0.813704 0.581279i \(-0.197448\pi\)
0.813704 + 0.581279i \(0.197448\pi\)
\(258\) 260.000i 1.00775i
\(259\) 108.167i 0.417631i
\(260\) 0 0
\(261\) 72.1110i 0.276287i
\(262\) −403.822 −1.54130
\(263\) 310.000i 1.17871i 0.807875 + 0.589354i \(0.200618\pi\)
−0.807875 + 0.589354i \(0.799382\pi\)
\(264\) −650.000 −2.46212
\(265\) 0 0
\(266\) 325.000 108.167i 1.22180 0.406641i
\(267\) 0 0
\(268\) −356.950 −1.33190
\(269\) 108.167i 0.402106i 0.979580 + 0.201053i \(0.0644364\pi\)
−0.979580 + 0.201053i \(0.935564\pi\)
\(270\) 0 0
\(271\) 105.000 0.387454 0.193727 0.981055i \(-0.437942\pi\)
0.193727 + 0.981055i \(0.437942\pi\)
\(272\) 435.000i 1.59926i
\(273\) 65.0000i 0.238095i
\(274\) 450.694i 1.64487i
\(275\) 0 0
\(276\) 1135.75i 4.11503i
\(277\) 50.0000i 0.180505i 0.995919 + 0.0902527i \(0.0287675\pi\)
−0.995919 + 0.0902527i \(0.971233\pi\)
\(278\) 180.278 0.648480
\(279\) 144.222i 0.516925i
\(280\) 0 0
\(281\) 288.444i 1.02649i 0.858242 + 0.513246i \(0.171557\pi\)
−0.858242 + 0.513246i \(0.828443\pi\)
\(282\) 130.000i 0.460993i
\(283\) 320.000i 1.13074i −0.824837 0.565371i \(-0.808733\pi\)
0.824837 0.565371i \(-0.191267\pi\)
\(284\) 973.499i 3.42781i
\(285\) 0 0
\(286\) 130.000 0.454545
\(287\) 180.278 0.628145
\(288\) −129.800 −0.450694
\(289\) 64.0000 0.221453
\(290\) 0 0
\(291\) 442.000 1.51890
\(292\) 945.000i 3.23630i
\(293\) −219.939 −0.750644 −0.375322 0.926895i \(-0.622468\pi\)
−0.375322 + 0.926895i \(0.622468\pi\)
\(294\) 312.000 1.06122
\(295\) 0 0
\(296\) −390.000 −1.31757
\(297\) −180.278 −0.606995
\(298\) 252.389 0.846942
\(299\) 126.194i 0.422054i
\(300\) 0 0
\(301\) 100.000 0.332226
\(302\) 130.000i 0.430464i
\(303\) 180.278 0.594975
\(304\) 174.000 + 522.805i 0.572368 + 1.71975i
\(305\) 0 0
\(306\) 216.333i 0.706971i
\(307\) −237.966 −0.775135 −0.387567 0.921841i \(-0.626685\pi\)
−0.387567 + 0.921841i \(0.626685\pi\)
\(308\) 450.000i 1.46104i
\(309\) −208.000 −0.673139
\(310\) 0 0
\(311\) 395.000 1.27010 0.635048 0.772472i \(-0.280980\pi\)
0.635048 + 0.772472i \(0.280980\pi\)
\(312\) 234.361 0.751157
\(313\) 125.000i 0.399361i 0.979861 + 0.199681i \(0.0639904\pi\)
−0.979861 + 0.199681i \(0.936010\pi\)
\(314\) 36.0555i 0.114826i
\(315\) 0 0
\(316\) 324.500i 1.02690i
\(317\) −3.60555 −0.0113740 −0.00568699 0.999984i \(-0.501810\pi\)
−0.00568699 + 0.999984i \(0.501810\pi\)
\(318\) −984.315 −3.09533
\(319\) 180.278i 0.565133i
\(320\) 0 0
\(321\) 273.000 0.850467
\(322\) 630.971 1.95954
\(323\) 270.416 90.0000i 0.837202 0.278638i
\(324\) −909.000 −2.80556
\(325\) 0 0
\(326\) 973.499i 2.98619i
\(327\) 715.000i 2.18654i
\(328\) 650.000i 1.98171i
\(329\) 50.0000 0.151976
\(330\) 0 0
\(331\) 198.305i 0.599110i 0.954079 + 0.299555i \(0.0968382\pi\)
−0.954079 + 0.299555i \(0.903162\pi\)
\(332\) 360.000i 1.08434i
\(333\) 86.5332 0.259860
\(334\) 442.000 1.32335
\(335\) 0 0
\(336\) 522.805i 1.55597i
\(337\) −57.6888 −0.171183 −0.0855917 0.996330i \(-0.527278\pi\)
−0.0855917 + 0.996330i \(0.527278\pi\)
\(338\) 562.466 1.66410
\(339\) 442.000 1.30383
\(340\) 0 0
\(341\) 360.555i 1.05735i
\(342\) −86.5332 260.000i −0.253021 0.760234i
\(343\) 365.000i 1.06414i
\(344\) 360.555i 1.04813i
\(345\) 0 0
\(346\) 442.000 1.27746
\(347\) 40.0000i 0.115274i 0.998338 + 0.0576369i \(0.0183566\pi\)
−0.998338 + 0.0576369i \(0.981643\pi\)
\(348\) 585.000i 1.68103i
\(349\) −98.0000 −0.280802 −0.140401 0.990095i \(-0.544839\pi\)
−0.140401 + 0.990095i \(0.544839\pi\)
\(350\) 0 0
\(351\) 65.0000 0.185185
\(352\) 324.500 0.921874
\(353\) 185.000i 0.524079i −0.965057 0.262040i \(-0.915605\pi\)
0.965057 0.262040i \(-0.0843951\pi\)
\(354\) 234.361i 0.662036i
\(355\) 0 0
\(356\) 0 0
\(357\) −270.416 −0.757469
\(358\) 130.000i 0.363128i
\(359\) 225.000 0.626741 0.313370 0.949631i \(-0.398542\pi\)
0.313370 + 0.949631i \(0.398542\pi\)
\(360\) 0 0
\(361\) −289.000 + 216.333i −0.800554 + 0.599261i
\(362\) 390.000i 1.07735i
\(363\) 75.7166 0.208586
\(364\) 162.250i 0.445741i
\(365\) 0 0
\(366\) −520.000 −1.42077
\(367\) 50.0000i 0.136240i −0.997677 0.0681199i \(-0.978300\pi\)
0.997677 0.0681199i \(-0.0217000\pi\)
\(368\) 1015.00i 2.75815i
\(369\) 144.222i 0.390846i
\(370\) 0 0
\(371\) 378.583i 1.02044i
\(372\) 1170.00i 3.14516i
\(373\) −436.272 −1.16963 −0.584815 0.811167i \(-0.698833\pi\)
−0.584815 + 0.811167i \(0.698833\pi\)
\(374\) 540.833i 1.44608i
\(375\) 0 0
\(376\) 180.278i 0.479462i
\(377\) 65.0000i 0.172414i
\(378\) 325.000i 0.859788i
\(379\) 486.749i 1.28430i −0.766579 0.642150i \(-0.778043\pi\)
0.766579 0.642150i \(-0.221957\pi\)
\(380\) 0 0
\(381\) −468.000 −1.22835
\(382\) −695.871 −1.82165
\(383\) 201.911 0.527182 0.263591 0.964634i \(-0.415093\pi\)
0.263591 + 0.964634i \(0.415093\pi\)
\(384\) −455.000 −1.18490
\(385\) 0 0
\(386\) −962.000 −2.49223
\(387\) 80.0000i 0.206718i
\(388\) −1103.30 −2.84355
\(389\) 478.000 1.22879 0.614396 0.788998i \(-0.289400\pi\)
0.614396 + 0.788998i \(0.289400\pi\)
\(390\) 0 0
\(391\) 525.000 1.34271
\(392\) −432.666 −1.10374
\(393\) −403.822 −1.02754
\(394\) 324.500i 0.823603i
\(395\) 0 0
\(396\) −360.000 −0.909091
\(397\) 750.000i 1.88917i −0.328269 0.944584i \(-0.606465\pi\)
0.328269 0.944584i \(-0.393535\pi\)
\(398\) 443.483 1.11428
\(399\) 325.000 108.167i 0.814536 0.271094i
\(400\) 0 0
\(401\) 288.444i 0.719312i 0.933085 + 0.359656i \(0.117106\pi\)
−0.933085 + 0.359656i \(0.882894\pi\)
\(402\) −515.594 −1.28257
\(403\) 130.000i 0.322581i
\(404\) −450.000 −1.11386
\(405\) 0 0
\(406\) 325.000 0.800493
\(407\) −216.333 −0.531531
\(408\) 975.000i 2.38971i
\(409\) 36.0555i 0.0881553i −0.999028 0.0440776i \(-0.985965\pi\)
0.999028 0.0440776i \(-0.0140349\pi\)
\(410\) 0 0
\(411\) 450.694i 1.09658i
\(412\) 519.199 1.26019
\(413\) −90.1388 −0.218254
\(414\) 504.777i 1.21927i
\(415\) 0 0
\(416\) −117.000 −0.281250
\(417\) 180.278 0.432320
\(418\) 216.333 + 650.000i 0.517543 + 1.55502i
\(419\) −112.000 −0.267303 −0.133652 0.991028i \(-0.542670\pi\)
−0.133652 + 0.991028i \(0.542670\pi\)
\(420\) 0 0
\(421\) 630.971i 1.49874i −0.662149 0.749372i \(-0.730355\pi\)
0.662149 0.749372i \(-0.269645\pi\)
\(422\) 845.000i 2.00237i
\(423\) 40.0000i 0.0945626i
\(424\) 1365.00 3.21934
\(425\) 0 0
\(426\) 1406.16i 3.30086i
\(427\) 200.000i 0.468384i
\(428\) −681.449 −1.59217
\(429\) 130.000 0.303030
\(430\) 0 0
\(431\) 432.666i 1.00387i 0.864907 + 0.501933i \(0.167378\pi\)
−0.864907 + 0.501933i \(0.832622\pi\)
\(432\) 522.805 1.21020
\(433\) −735.532 −1.69869 −0.849345 0.527839i \(-0.823003\pi\)
−0.849345 + 0.527839i \(0.823003\pi\)
\(434\) 650.000 1.49770
\(435\) 0 0
\(436\) 1784.75i 4.09346i
\(437\) −630.971 + 210.000i −1.44387 + 0.480549i
\(438\) 1365.00i 3.11644i
\(439\) 793.221i 1.80688i 0.428712 + 0.903441i \(0.358967\pi\)
−0.428712 + 0.903441i \(0.641033\pi\)
\(440\) 0 0
\(441\) 96.0000 0.217687
\(442\) 195.000i 0.441176i
\(443\) 670.000i 1.51242i 0.654332 + 0.756208i \(0.272950\pi\)
−0.654332 + 0.756208i \(0.727050\pi\)
\(444\) −702.000 −1.58108
\(445\) 0 0
\(446\) 728.000 1.63229
\(447\) 252.389 0.564628
\(448\) 5.00000i 0.0111607i
\(449\) 36.0555i 0.0803018i −0.999194 0.0401509i \(-0.987216\pi\)
0.999194 0.0401509i \(-0.0127839\pi\)
\(450\) 0 0
\(451\) 360.555i 0.799457i
\(452\) −1103.30 −2.44093
\(453\) 130.000i 0.286976i
\(454\) 923.000 2.03304
\(455\) 0 0
\(456\) 390.000 + 1171.80i 0.855263 + 2.56975i
\(457\) 755.000i 1.65208i 0.563612 + 0.826039i \(0.309411\pi\)
−0.563612 + 0.826039i \(0.690589\pi\)
\(458\) −576.888 −1.25958
\(459\) 270.416i 0.589142i
\(460\) 0 0
\(461\) 772.000 1.67462 0.837310 0.546728i \(-0.184127\pi\)
0.837310 + 0.546728i \(0.184127\pi\)
\(462\) 650.000i 1.40693i
\(463\) 350.000i 0.755940i −0.925818 0.377970i \(-0.876622\pi\)
0.925818 0.377970i \(-0.123378\pi\)
\(464\) 522.805i 1.12673i
\(465\) 0 0
\(466\) 973.499i 2.08905i
\(467\) 70.0000i 0.149893i −0.997188 0.0749465i \(-0.976121\pi\)
0.997188 0.0749465i \(-0.0238786\pi\)
\(468\) 129.800 0.277350
\(469\) 198.305i 0.422826i
\(470\) 0 0
\(471\) 36.0555i 0.0765510i
\(472\) 325.000i 0.688559i
\(473\) 200.000i 0.422833i
\(474\) 468.722i 0.988864i
\(475\) 0 0
\(476\) 675.000 1.41807
\(477\) −302.866 −0.634940
\(478\) 710.294 1.48597
\(479\) 370.000 0.772443 0.386221 0.922406i \(-0.373780\pi\)
0.386221 + 0.922406i \(0.373780\pi\)
\(480\) 0 0
\(481\) 78.0000 0.162162
\(482\) 1430.00i 2.96680i
\(483\) 630.971 1.30636
\(484\) −189.000 −0.390496
\(485\) 0 0
\(486\) −728.000 −1.49794
\(487\) 519.199 1.06612 0.533059 0.846078i \(-0.321042\pi\)
0.533059 + 0.846078i \(0.321042\pi\)
\(488\) 721.110 1.47768
\(489\) 973.499i 1.99080i
\(490\) 0 0
\(491\) −632.000 −1.28717 −0.643585 0.765375i \(-0.722554\pi\)
−0.643585 + 0.765375i \(0.722554\pi\)
\(492\) 1170.00i 2.37805i
\(493\) 270.416 0.548512
\(494\) −78.0000 234.361i −0.157895 0.474415i
\(495\) 0 0
\(496\) 1045.61i 2.10808i
\(497\) 540.833 1.08819
\(498\) 520.000i 1.04418i
\(499\) −380.000 −0.761523 −0.380762 0.924673i \(-0.624338\pi\)
−0.380762 + 0.924673i \(0.624338\pi\)
\(500\) 0 0
\(501\) 442.000 0.882236
\(502\) 1449.43 2.88731
\(503\) 45.0000i 0.0894632i −0.998999 0.0447316i \(-0.985757\pi\)
0.998999 0.0447316i \(-0.0142433\pi\)
\(504\) 360.555i 0.715387i
\(505\) 0 0
\(506\) 1261.94i 2.49396i
\(507\) 562.466 1.10940
\(508\) 1168.20 2.29960
\(509\) 829.277i 1.62923i 0.580004 + 0.814614i \(0.303051\pi\)
−0.580004 + 0.814614i \(0.696949\pi\)
\(510\) 0 0
\(511\) −525.000 −1.02740
\(512\) 1150.17 2.24643
\(513\) 108.167 + 325.000i 0.210851 + 0.633528i
\(514\) −1508.00 −2.93385
\(515\) 0 0
\(516\) 648.999i 1.25775i
\(517\) 100.000i 0.193424i
\(518\) 390.000i 0.752896i
\(519\) 442.000 0.851638
\(520\) 0 0
\(521\) 612.944i 1.17648i −0.808688 0.588238i \(-0.799822\pi\)
0.808688 0.588238i \(-0.200178\pi\)
\(522\) 260.000i 0.498084i
\(523\) 465.116 0.889323 0.444662 0.895699i \(-0.353324\pi\)
0.444662 + 0.895699i \(0.353324\pi\)
\(524\) 1008.00 1.92366
\(525\) 0 0
\(526\) 1117.72i 2.12494i
\(527\) 540.833 1.02625
\(528\) 1045.61 1.98032
\(529\) −696.000 −1.31569
\(530\) 0 0
\(531\) 72.1110i 0.135802i
\(532\) −811.249 + 270.000i −1.52490 + 0.507519i
\(533\) 130.000i 0.243902i
\(534\) 0 0
\(535\) 0 0
\(536\) 715.000 1.33396
\(537\) 130.000i 0.242086i
\(538\) 390.000i 0.724907i
\(539\) −240.000 −0.445269
\(540\) 0 0
\(541\) −600.000 −1.10906 −0.554529 0.832165i \(-0.687101\pi\)
−0.554529 + 0.832165i \(0.687101\pi\)
\(542\) −378.583 −0.698492
\(543\) 390.000i 0.718232i
\(544\) 486.749i 0.894760i
\(545\) 0 0
\(546\) 234.361i 0.429232i
\(547\) 598.522 1.09419 0.547095 0.837071i \(-0.315734\pi\)
0.547095 + 0.837071i \(0.315734\pi\)
\(548\) 1125.00i 2.05292i
\(549\) −160.000 −0.291439
\(550\) 0 0
\(551\) −325.000 + 108.167i −0.589837 + 0.196310i
\(552\) 2275.00i 4.12138i
\(553\) 180.278 0.325999
\(554\) 180.278i 0.325411i
\(555\) 0 0
\(556\) −450.000 −0.809353
\(557\) 380.000i 0.682226i −0.940022 0.341113i \(-0.889196\pi\)
0.940022 0.341113i \(-0.110804\pi\)
\(558\) 520.000i 0.931900i
\(559\) 72.1110i 0.129000i
\(560\) 0 0
\(561\) 540.833i 0.964051i
\(562\) 1040.00i 1.85053i
\(563\) 122.589 0.217742 0.108871 0.994056i \(-0.465276\pi\)
0.108871 + 0.994056i \(0.465276\pi\)
\(564\) 324.500i 0.575354i
\(565\) 0 0
\(566\) 1153.78i 2.03847i
\(567\) 505.000i 0.890653i
\(568\) 1950.00i 3.43310i
\(569\) 36.0555i 0.0633665i 0.999498 + 0.0316832i \(0.0100868\pi\)
−0.999498 + 0.0316832i \(0.989913\pi\)
\(570\) 0 0
\(571\) −790.000 −1.38354 −0.691769 0.722119i \(-0.743168\pi\)
−0.691769 + 0.722119i \(0.743168\pi\)
\(572\) −324.500 −0.567307
\(573\) −695.871 −1.21444
\(574\) −650.000 −1.13240
\(575\) 0 0
\(576\) 4.00000 0.00694444
\(577\) 675.000i 1.16984i −0.811090 0.584922i \(-0.801125\pi\)
0.811090 0.584922i \(-0.198875\pi\)
\(578\) −230.755 −0.399231
\(579\) −962.000 −1.66149
\(580\) 0 0
\(581\) 200.000 0.344234
\(582\) −1593.65 −2.73824
\(583\) 757.166 1.29874
\(584\) 1892.91i 3.24129i
\(585\) 0 0
\(586\) 793.000 1.35324
\(587\) 280.000i 0.477002i 0.971142 + 0.238501i \(0.0766560\pi\)
−0.971142 + 0.238501i \(0.923344\pi\)
\(588\) −778.799 −1.32449
\(589\) −650.000 + 216.333i −1.10357 + 0.367289i
\(590\) 0 0
\(591\) 324.500i 0.549069i
\(592\) 627.366 1.05974
\(593\) 750.000i 1.26476i 0.774660 + 0.632378i \(0.217921\pi\)
−0.774660 + 0.632378i \(0.782079\pi\)
\(594\) 650.000 1.09428
\(595\) 0 0
\(596\) −630.000 −1.05705
\(597\) 443.483 0.742852
\(598\) 455.000i 0.760870i
\(599\) 504.777i 0.842700i 0.906898 + 0.421350i \(0.138444\pi\)
−0.906898 + 0.421350i \(0.861556\pi\)
\(600\) 0 0
\(601\) 612.944i 1.01987i −0.860212 0.509937i \(-0.829669\pi\)
0.860212 0.509937i \(-0.170331\pi\)
\(602\) −360.555 −0.598929
\(603\) −158.644 −0.263092
\(604\) 324.500i 0.537251i
\(605\) 0 0
\(606\) −650.000 −1.07261
\(607\) 987.921 1.62755 0.813774 0.581182i \(-0.197410\pi\)
0.813774 + 0.581182i \(0.197410\pi\)
\(608\) −194.700 585.000i −0.320230 0.962171i
\(609\) 325.000 0.533662
\(610\) 0 0
\(611\) 36.0555i 0.0590107i
\(612\) 540.000i 0.882353i
\(613\) 1200.00i 1.95759i −0.204853 0.978793i \(-0.565672\pi\)
0.204853 0.978793i \(-0.434328\pi\)
\(614\) 858.000 1.39739
\(615\) 0 0
\(616\) 901.388i 1.46329i
\(617\) 350.000i 0.567261i 0.958934 + 0.283630i \(0.0915389\pi\)
−0.958934 + 0.283630i \(0.908461\pi\)
\(618\) 749.955 1.21352
\(619\) −560.000 −0.904685 −0.452342 0.891844i \(-0.649412\pi\)
−0.452342 + 0.891844i \(0.649412\pi\)
\(620\) 0 0
\(621\) 630.971i 1.01606i
\(622\) −1424.19 −2.28970
\(623\) 0 0
\(624\) −377.000 −0.604167
\(625\) 0 0
\(626\) 450.694i 0.719958i
\(627\) 216.333 + 650.000i 0.345029 + 1.03668i
\(628\) 90.0000i 0.143312i
\(629\) 324.500i 0.515898i
\(630\) 0 0
\(631\) −1050.00 −1.66403 −0.832013 0.554757i \(-0.812811\pi\)
−0.832013 + 0.554757i \(0.812811\pi\)
\(632\) 650.000i 1.02848i
\(633\) 845.000i 1.33491i
\(634\) 13.0000 0.0205047
\(635\) 0 0
\(636\) 2457.00 3.86321
\(637\) 86.5332 0.135845
\(638\) 650.000i 1.01881i
\(639\) 432.666i 0.677099i
\(640\) 0 0
\(641\) 1225.89i 1.91246i −0.292615 0.956230i \(-0.594525\pi\)
0.292615 0.956230i \(-0.405475\pi\)
\(642\) −984.315 −1.53320
\(643\) 1030.00i 1.60187i −0.598754 0.800933i \(-0.704337\pi\)
0.598754 0.800933i \(-0.295663\pi\)
\(644\) −1575.00 −2.44565
\(645\) 0 0
\(646\) −975.000 + 324.500i −1.50929 + 0.502321i
\(647\) 555.000i 0.857805i −0.903351 0.428903i \(-0.858900\pi\)
0.903351 0.428903i \(-0.141100\pi\)
\(648\) 1820.80 2.80988
\(649\) 180.278i 0.277777i
\(650\) 0 0
\(651\) 650.000 0.998464
\(652\) 2430.00i 3.72699i
\(653\) 50.0000i 0.0765697i 0.999267 + 0.0382848i \(0.0121894\pi\)
−0.999267 + 0.0382848i \(0.987811\pi\)
\(654\) 2577.97i 3.94185i
\(655\) 0 0
\(656\) 1045.61i 1.59392i
\(657\) 420.000i 0.639269i
\(658\) −180.278 −0.273978
\(659\) 198.305i 0.300919i 0.988616 + 0.150459i \(0.0480752\pi\)
−0.988616 + 0.150459i \(0.951925\pi\)
\(660\) 0 0
\(661\) 198.305i 0.300008i −0.988685 0.150004i \(-0.952071\pi\)
0.988685 0.150004i \(-0.0479287\pi\)
\(662\) 715.000i 1.08006i
\(663\) 195.000i 0.294118i
\(664\) 721.110i 1.08601i
\(665\) 0 0
\(666\) −312.000 −0.468468
\(667\) −630.971 −0.945984
\(668\) −1103.30 −1.65164
\(669\) 728.000 1.08819
\(670\) 0 0
\(671\) 400.000 0.596125
\(672\) 585.000i 0.870536i
\(673\) 598.522 0.889334 0.444667 0.895696i \(-0.353322\pi\)
0.444667 + 0.895696i \(0.353322\pi\)
\(674\) 208.000 0.308605
\(675\) 0 0
\(676\) −1404.00 −2.07692
\(677\) −68.5055 −0.101190 −0.0505949 0.998719i \(-0.516112\pi\)
−0.0505949 + 0.998719i \(0.516112\pi\)
\(678\) −1593.65 −2.35052
\(679\) 612.944i 0.902715i
\(680\) 0 0
\(681\) 923.000 1.35536
\(682\) 1300.00i 1.90616i
\(683\) −237.966 −0.348413 −0.174207 0.984709i \(-0.555736\pi\)
−0.174207 + 0.984709i \(0.555736\pi\)
\(684\) 216.000 + 648.999i 0.315789 + 0.948829i
\(685\) 0 0
\(686\) 1316.03i 1.91841i
\(687\) −576.888 −0.839721
\(688\) 580.000i 0.843023i
\(689\) −273.000 −0.396226
\(690\) 0 0
\(691\) −820.000 −1.18669 −0.593343 0.804950i \(-0.702192\pi\)
−0.593343 + 0.804950i \(0.702192\pi\)
\(692\) −1103.30 −1.59436
\(693\) 200.000i 0.288600i
\(694\) 144.222i 0.207813i
\(695\) 0 0
\(696\) 1171.80i 1.68363i
\(697\) −540.833 −0.775944
\(698\) 353.344 0.506224
\(699\) 973.499i 1.39270i
\(700\) 0 0
\(701\) −540.000 −0.770328 −0.385164 0.922848i \(-0.625855\pi\)
−0.385164 + 0.922848i \(0.625855\pi\)
\(702\) −234.361 −0.333847
\(703\) 129.800 + 390.000i 0.184637 + 0.554765i
\(704\) −10.0000 −0.0142045
\(705\) 0 0
\(706\) 667.027i 0.944797i
\(707\) 250.000i 0.353607i
\(708\) 585.000i 0.826271i
\(709\) −268.000 −0.377997 −0.188999 0.981977i \(-0.560524\pi\)
−0.188999 + 0.981977i \(0.560524\pi\)
\(710\) 0 0
\(711\) 144.222i 0.202844i
\(712\) 0 0
\(713\) −1261.94 −1.76991
\(714\) 975.000 1.36555
\(715\) 0 0
\(716\) 324.500i 0.453212i
\(717\) 710.294 0.990647
\(718\) −811.249 −1.12987
\(719\) −105.000 −0.146036 −0.0730181 0.997331i \(-0.523263\pi\)
−0.0730181 + 0.997331i \(0.523263\pi\)
\(720\) 0 0
\(721\) 288.444i 0.400061i
\(722\) 1042.00 780.000i 1.44322 1.08033i
\(723\) 1430.00i 1.97787i
\(724\) 973.499i 1.34461i
\(725\) 0 0
\(726\) −273.000 −0.376033
\(727\) 695.000i 0.955983i −0.878364 0.477992i \(-0.841365\pi\)
0.878364 0.477992i \(-0.158635\pi\)
\(728\) 325.000i 0.446429i
\(729\) 181.000 0.248285
\(730\) 0 0
\(731\) −300.000 −0.410397
\(732\) 1298.00 1.77322
\(733\) 160.000i 0.218281i 0.994026 + 0.109141i \(0.0348098\pi\)
−0.994026 + 0.109141i \(0.965190\pi\)
\(734\) 180.278i 0.245610i
\(735\) 0 0
\(736\) 1135.75i 1.54314i
\(737\) 396.611 0.538142
\(738\) 520.000i 0.704607i
\(739\) −1028.00 −1.39107 −0.695535 0.718493i \(-0.744832\pi\)
−0.695535 + 0.718493i \(0.744832\pi\)
\(740\) 0 0
\(741\) −78.0000 234.361i −0.105263 0.316276i
\(742\) 1365.00i 1.83962i
\(743\) −526.410 −0.708493 −0.354247 0.935152i \(-0.615263\pi\)
−0.354247 + 0.935152i \(0.615263\pi\)
\(744\) 2343.61i 3.15001i
\(745\) 0 0
\(746\) 1573.00 2.10858
\(747\) 160.000i 0.214190i
\(748\) 1350.00i 1.80481i
\(749\) 378.583i 0.505451i
\(750\) 0 0
\(751\) 36.0555i 0.0480100i −0.999712 0.0240050i \(-0.992358\pi\)
0.999712 0.0240050i \(-0.00764176\pi\)
\(752\) 290.000i 0.385638i
\(753\) 1449.43 1.92488
\(754\) 234.361i 0.310823i
\(755\) 0 0
\(756\) 811.249i 1.07308i
\(757\) 60.0000i 0.0792602i −0.999214 0.0396301i \(-0.987382\pi\)
0.999214 0.0396301i \(-0.0126180\pi\)
\(758\) 1755.00i 2.31530i
\(759\) 1261.94i 1.66264i
\(760\) 0 0
\(761\) −655.000 −0.860710 −0.430355 0.902660i \(-0.641612\pi\)
−0.430355 + 0.902660i \(0.641612\pi\)
\(762\) 1687.40 2.21443
\(763\) 991.527 1.29951
\(764\) 1737.00 2.27356
\(765\) 0 0
\(766\) −728.000 −0.950392
\(767\) 65.0000i 0.0847458i
\(768\) 1654.95 2.15488
\(769\) 185.000 0.240572 0.120286 0.992739i \(-0.461619\pi\)
0.120286 + 0.992739i \(0.461619\pi\)
\(770\) 0 0
\(771\) −1508.00 −1.95590
\(772\) 2401.30 3.11049
\(773\) −320.894 −0.415128 −0.207564 0.978221i \(-0.566554\pi\)
−0.207564 + 0.978221i \(0.566554\pi\)
\(774\) 288.444i 0.372667i
\(775\) 0 0
\(776\) 2210.00 2.84794
\(777\) 390.000i 0.501931i
\(778\) −1723.45 −2.21524
\(779\) 650.000 216.333i 0.834403 0.277706i
\(780\) 0 0
\(781\) 1081.67i 1.38497i
\(782\) −1892.91 −2.42061
\(783\) 325.000i 0.415070i
\(784\) 696.000 0.887755
\(785\) 0 0
\(786\) 1456.00 1.85242
\(787\) −68.5055 −0.0870463 −0.0435232 0.999052i \(-0.513858\pi\)
−0.0435232 + 0.999052i \(0.513858\pi\)
\(788\) 810.000i 1.02792i
\(789\) 1117.72i 1.41663i
\(790\) 0 0
\(791\) 612.944i 0.774897i
\(792\) 721.110 0.910493
\(793\) −144.222