Properties

Label 475.3.d.b.474.3
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 474.3
Root \(-1.30278i\) of defining polynomial
Character \(\chi\) \(=\) 475.474
Dual form 475.3.d.b.474.4

$q$-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 \(-0.142549\pi\)
0.901388 + 0.433013i \(0.142549\pi\)
\(3\) 3.60555 1.20185 0.600925 0.799305i \(-0.294799\pi\)
0.600925 + 0.799305i \(0.294799\pi\)
\(4\) 9.00000 2.25000
\(5\) 0 0
\(6\) 13.0000 2.16667
\(7\) 5.00000i 0.714286i −0.934050 0.357143i \(-0.883751\pi\)
0.934050 0.357143i \(-0.116249\pi\)
\(8\) 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 \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 18.0278i 1.28770i
\(15\) 0 0
\(16\) 29.0000 1.81250
\(17\) 15.0000i 0.882353i 0.897420 + 0.441176i \(0.145439\pi\)
−0.897420 + 0.441176i \(0.854561\pi\)
\(18\) 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 \(-0.724773\pi\)
0.648905 0.760870i \(-0.275227\pi\)
\(24\) 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 \(-0.594435\pi\)
−0.292342 + 0.956314i \(0.594435\pi\)
\(38\) 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 \(0.0747096\pi\)
−0.972582 + 0.232558i \(0.925290\pi\)
\(44\) −90.0000 −2.04545
\(45\) 0 0
\(46\) 126.194i 2.74335i
\(47\) 10.0000i 0.212766i 0.994325 + 0.106383i \(0.0339270\pi\)
−0.994325 + 0.106383i \(0.966073\pi\)
\(48\) 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 \(-0.246742\pi\)
0.714307 + 0.699832i \(0.246742\pi\)
\(54\) −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 \(-0.404354\pi\)
0.295978 + 0.955195i \(0.404354\pi\)
\(68\) 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 \(-0.744519\pi\)
0.694826 0.719178i \(-0.255481\pi\)
\(74\) −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 \(0.0774635\pi\)
−0.970534 + 0.240964i \(0.922536\pi\)
\(84\) 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 \(-0.282275\pi\)
0.631901 + 0.775049i \(0.282275\pi\)
\(98\) 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 \(-0.590349\pi\)
−0.280043 + 0.959988i \(0.590349\pi\)
\(104\) −65.0000 −0.625000
\(105\) 0 0
\(106\) 273.000 2.57547
\(107\) 75.7166 0.707632 0.353816 0.935315i \(-0.384884\pi\)
0.353816 + 0.935315i \(0.384884\pi\)
\(108\) −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 \(-0.317505\pi\)
0.542428 + 0.840102i \(0.317505\pi\)
\(114\) 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 \(-0.670733\pi\)
−0.511023 + 0.859567i \(0.670733\pi\)
\(128\) −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 \(0.150791\pi\)
−0.889875 + 0.456204i \(0.849209\pi\)
\(138\) 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 \(0.0101390\pi\)
−0.999493 + 0.0318471i \(0.989861\pi\)
\(158\) 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 \(0.310647\pi\)
−0.560402 + 0.828221i \(0.689353\pi\)
\(164\) 324.500i 1.97866i
\(165\) 0 0
\(166\) 144.222i 0.868808i
\(167\) 122.589 0.734064 0.367032 0.930208i \(-0.380374\pi\)
0.367032 + 0.930208i \(0.380374\pi\)
\(168\) 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 \(-0.384718\pi\)
0.354303 + 0.935131i \(0.384718\pi\)
\(174\) 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 \(-0.742926\pi\)
−0.691220 + 0.722645i \(0.742926\pi\)
\(194\) 442.000 2.27835
\(195\) 0 0
\(196\) 216.000 1.10204
\(197\) 90.0000i 0.456853i 0.973561 + 0.228426i \(0.0733580\pi\)
−0.973561 + 0.228426i \(0.926642\pi\)
\(198\) −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 \(-0.350456\pi\)
0.452715 + 0.891655i \(0.350456\pi\)
\(224\) 162.250i 0.724329i
\(225\) 0 0
\(226\) 442.000 1.95575
\(227\) 255.994 1.12773 0.563864 0.825868i \(-0.309314\pi\)
0.563864 + 0.825868i \(0.309314\pi\)
\(228\) 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 \(0.196713\pi\)
−0.815044 + 0.579399i \(0.803287\pi\)
\(234\) −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 \(-0.802552\pi\)
−0.813704 + 0.581279i \(0.802552\pi\)
\(258\) 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 \(-0.799382\pi\)
0.807875 0.589354i \(-0.200618\pi\)
\(264\) −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 \(-0.971233\pi\)
0.995919 0.0902527i \(-0.0287675\pi\)
\(278\) −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 \(0.191267\pi\)
−0.824837 + 0.565371i \(0.808733\pi\)
\(284\) 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 \(-0.377532\pi\)
0.375322 + 0.926895i \(0.377532\pi\)
\(294\) 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 \(-0.373315\pi\)
0.387567 + 0.921841i \(0.373315\pi\)
\(308\) 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 \(-0.936010\pi\)
0.979861 0.199681i \(-0.0639904\pi\)
\(314\) 36.0555i 0.114826i
\(315\) 0 0
\(316\) 324.500i 1.02690i
\(317\) 3.60555 0.0113740 0.00568699 0.999984i \(-0.498190\pi\)
0.00568699 + 0.999984i \(0.498190\pi\)
\(318\) 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 \(-0.472722\pi\)
0.0855917 + 0.996330i \(0.472722\pi\)
\(338\) −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 \(-0.981643\pi\)
0.998338 0.0576369i \(-0.0183566\pi\)
\(348\) 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 \(0.0843951\pi\)
−0.965057 + 0.262040i \(0.915605\pi\)
\(354\) 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 \(0.0217000\pi\)
−0.997677 + 0.0681199i \(0.978300\pi\)
\(368\) 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 \(-0.301167\pi\)
0.584815 + 0.811167i \(0.301167\pi\)
\(374\) 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 \(-0.584907\pi\)
−0.263591 + 0.964634i \(0.584907\pi\)
\(384\) −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 \(0.393535\pi\)
−0.328269 + 0.944584i \(0.606465\pi\)
\(398\) −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 \(-0.176997\pi\)
0.849345 + 0.527839i \(0.176997\pi\)
\(434\) 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 \(-0.727050\pi\)
0.654332 0.756208i \(-0.272950\pi\)
\(444\) −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 \(-0.690589\pi\)
0.563612 0.826039i \(-0.309411\pi\)
\(458\) 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 \(0.123378\pi\)
−0.925818 + 0.377970i \(0.876622\pi\)
\(464\) 522.805i 1.12673i
\(465\) 0 0
\(466\) 973.499i 2.08905i
\(467\) 70.0000i 0.149893i 0.997188 + 0.0749465i \(0.0238786\pi\)
−0.997188 + 0.0749465i \(0.976121\pi\)
\(468\) −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 \(-0.678958\pi\)
−0.533059 + 0.846078i \(0.678958\pi\)
\(488\) −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 \(0.0142433\pi\)
−0.998999 + 0.0447316i \(0.985757\pi\)
\(504\) 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 \(-0.646676\pi\)
−0.444662 + 0.895699i \(0.646676\pi\)
\(524\) 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 \(-0.684266\pi\)
−0.547095 + 0.837071i \(0.684266\pi\)
\(548\) 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 \(0.110804\pi\)
−0.940022 + 0.341113i \(0.889196\pi\)
\(558\) 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 \(-0.534724\pi\)
−0.108871 + 0.994056i \(0.534724\pi\)
\(564\) 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 \(0.198875\pi\)
−0.811090 + 0.584922i \(0.801125\pi\)
\(578\) 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 \(-0.923344\pi\)
0.971142 0.238501i \(-0.0766560\pi\)
\(588\) 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 \(-0.782079\pi\)
0.774660 0.632378i \(-0.217921\pi\)
\(594\) 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 \(-0.802590\pi\)
−0.813774 + 0.581182i \(0.802590\pi\)
\(608\) 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 \(0.434328\pi\)
−0.204853 + 0.978793i \(0.565672\pi\)
\(614\) 858.000 1.39739
\(615\) 0 0
\(616\) 901.388i 1.46329i
\(617\) 350.000i 0.567261i −0.958934 0.283630i \(-0.908461\pi\)
0.958934 0.283630i \(-0.0915389\pi\)
\(618\) −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 \(0.295663\pi\)
−0.598754 + 0.800933i \(0.704337\pi\)
\(644\) −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 \(0.141100\pi\)
−0.903351 + 0.428903i \(0.858900\pi\)
\(648\) −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 \(-0.987811\pi\)
0.999267 0.0382848i \(-0.0121894\pi\)
\(654\) 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 \(-0.646678\pi\)
−0.444667 + 0.895696i \(0.646678\pi\)
\(674\) 208.000 0.308605
\(675\) 0 0
\(676\) −1404.00 −2.07692
\(677\) 68.5055 0.101190 0.0505949 0.998719i \(-0.483888\pi\)
0.0505949 + 0.998719i \(0.483888\pi\)
\(678\) 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 \(-0.444264\pi\)
0.174207 + 0.984709i \(0.444264\pi\)
\(684\) 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 \(0.158635\pi\)
−0.878364 + 0.477992i \(0.841365\pi\)
\(728\) 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 \(-0.965190\pi\)
0.994026 0.109141i \(-0.0348098\pi\)
\(734\) 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 \(-0.384737\pi\)
0.354247 + 0.935152i \(0.384737\pi\)
\(744\) 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 \(0.0126180\pi\)
−0.999214 + 0.0396301i \(0.987382\pi\)
\(758\) 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 \(-0.433446\pi\)
0.207564 + 0.978221i \(0.433446\pi\)
\(774\) 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 \(-0.486142\pi\)
0.0435232 + 0.999052i \(0.486142\pi\)
\(788\) 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 0.181869