Properties

Label 483.3.f.a.22.5
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.5
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.6

$q$-expansion

\(f(q)\) \(=\) \(q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} -9.14952i q^{10} +7.34623i q^{11} +11.7304 q^{12} +3.74384 q^{13} -8.68378i q^{14} +4.82836i q^{15} +2.77741 q^{16} +19.4029i q^{17} -9.84648 q^{18} -7.40141i q^{19} +18.8796i q^{20} +4.58258i q^{21} -24.1115i q^{22} +(-19.1329 + 12.7646i) q^{23} -15.7617 q^{24} +17.2290 q^{25} -12.2879 q^{26} +5.19615 q^{27} +17.9185i q^{28} -40.6316 q^{29} -15.8474i q^{30} +8.80682 q^{31} +27.2841 q^{32} +12.7240i q^{33} -63.6834i q^{34} -7.37544 q^{35} +20.3177 q^{36} -22.4788i q^{37} +24.2926i q^{38} +6.48451 q^{39} -25.3677i q^{40} -0.856967 q^{41} -15.0407i q^{42} -40.9123i q^{43} +49.7528i q^{44} +8.36296i q^{45} +(62.7971 - 41.8953i) q^{46} +16.9402 q^{47} +4.81062 q^{48} -7.00000 q^{49} -56.5483 q^{50} +33.6068i q^{51} +25.3554 q^{52} +34.8928i q^{53} -17.0546 q^{54} -20.4787 q^{55} -24.0764i q^{56} -12.8196i q^{57} +133.359 q^{58} -27.4908 q^{59} +32.7004i q^{60} +94.2762i q^{61} -28.9054 q^{62} +7.93725i q^{63} -100.661 q^{64} +10.4365i q^{65} -41.7623i q^{66} +61.9795i q^{67} +131.407i q^{68} +(-33.1391 + 22.1089i) q^{69} +24.2074 q^{70} -77.3081 q^{71} -27.3000 q^{72} -132.608 q^{73} +73.7790i q^{74} +29.8415 q^{75} -50.1265i q^{76} -19.4363 q^{77} -21.2832 q^{78} +124.048i q^{79} +7.74246i q^{80} +9.00000 q^{81} +2.81270 q^{82} +59.1946i q^{83} +31.0358i q^{84} -54.0885 q^{85} +134.281i q^{86} -70.3760 q^{87} -66.8508i q^{88} +66.6559i q^{89} -27.4486i q^{90} +9.90526i q^{91} +(-129.579 + 86.4489i) q^{92} +15.2539 q^{93} -55.6003 q^{94} +20.6325 q^{95} +47.2575 q^{96} +7.24707i q^{97} +22.9751 q^{98} +22.0387i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.28216 −1.64108 −0.820540 0.571589i \(-0.806327\pi\)
−0.820540 + 0.571589i \(0.806327\pi\)
\(3\) 1.73205 0.577350
\(4\) 6.77257 1.69314
\(5\) 2.78765i 0.557530i 0.960359 + 0.278765i \(0.0899251\pi\)
−0.960359 + 0.278765i \(0.910075\pi\)
\(6\) −5.68487 −0.947478
\(7\) 2.64575i 0.377964i
\(8\) −9.10001 −1.13750
\(9\) 3.00000 0.333333
\(10\) 9.14952i 0.914952i
\(11\) 7.34623i 0.667839i 0.942602 + 0.333919i \(0.108371\pi\)
−0.942602 + 0.333919i \(0.891629\pi\)
\(12\) 11.7304 0.977536
\(13\) 3.74384 0.287987 0.143994 0.989579i \(-0.454006\pi\)
0.143994 + 0.989579i \(0.454006\pi\)
\(14\) 8.68378i 0.620270i
\(15\) 4.82836i 0.321890i
\(16\) 2.77741 0.173588
\(17\) 19.4029i 1.14135i 0.821177 + 0.570673i \(0.193318\pi\)
−0.821177 + 0.570673i \(0.806682\pi\)
\(18\) −9.84648 −0.547027
\(19\) 7.40141i 0.389548i −0.980848 0.194774i \(-0.937603\pi\)
0.980848 0.194774i \(-0.0623973\pi\)
\(20\) 18.8796i 0.943978i
\(21\) 4.58258i 0.218218i
\(22\) 24.1115i 1.09598i
\(23\) −19.1329 + 12.7646i −0.831863 + 0.554981i
\(24\) −15.7617 −0.656737
\(25\) 17.2290 0.689160
\(26\) −12.2879 −0.472610
\(27\) 5.19615 0.192450
\(28\) 17.9185i 0.639948i
\(29\) −40.6316 −1.40109 −0.700544 0.713609i \(-0.747059\pi\)
−0.700544 + 0.713609i \(0.747059\pi\)
\(30\) 15.8474i 0.528248i
\(31\) 8.80682 0.284091 0.142045 0.989860i \(-0.454632\pi\)
0.142045 + 0.989860i \(0.454632\pi\)
\(32\) 27.2841 0.852629
\(33\) 12.7240i 0.385577i
\(34\) 63.6834i 1.87304i
\(35\) −7.37544 −0.210727
\(36\) 20.3177 0.564381
\(37\) 22.4788i 0.607535i −0.952746 0.303767i \(-0.901755\pi\)
0.952746 0.303767i \(-0.0982446\pi\)
\(38\) 24.2926i 0.639279i
\(39\) 6.48451 0.166270
\(40\) 25.3677i 0.634192i
\(41\) −0.856967 −0.0209016 −0.0104508 0.999945i \(-0.503327\pi\)
−0.0104508 + 0.999945i \(0.503327\pi\)
\(42\) 15.0407i 0.358113i
\(43\) 40.9123i 0.951448i −0.879595 0.475724i \(-0.842186\pi\)
0.879595 0.475724i \(-0.157814\pi\)
\(44\) 49.7528i 1.13075i
\(45\) 8.36296i 0.185843i
\(46\) 62.7971 41.8953i 1.36515 0.910768i
\(47\) 16.9402 0.360429 0.180214 0.983627i \(-0.442321\pi\)
0.180214 + 0.983627i \(0.442321\pi\)
\(48\) 4.81062 0.100221
\(49\) −7.00000 −0.142857
\(50\) −56.5483 −1.13097
\(51\) 33.6068i 0.658957i
\(52\) 25.3554 0.487604
\(53\) 34.8928i 0.658354i 0.944268 + 0.329177i \(0.106771\pi\)
−0.944268 + 0.329177i \(0.893229\pi\)
\(54\) −17.0546 −0.315826
\(55\) −20.4787 −0.372341
\(56\) 24.0764i 0.429935i
\(57\) 12.8196i 0.224905i
\(58\) 133.359 2.29930
\(59\) −27.4908 −0.465945 −0.232973 0.972483i \(-0.574845\pi\)
−0.232973 + 0.972483i \(0.574845\pi\)
\(60\) 32.7004i 0.545006i
\(61\) 94.2762i 1.54551i 0.634704 + 0.772756i \(0.281122\pi\)
−0.634704 + 0.772756i \(0.718878\pi\)
\(62\) −28.9054 −0.466216
\(63\) 7.93725i 0.125988i
\(64\) −100.661 −1.57282
\(65\) 10.4365i 0.160562i
\(66\) 41.7623i 0.632762i
\(67\) 61.9795i 0.925067i 0.886602 + 0.462533i \(0.153059\pi\)
−0.886602 + 0.462533i \(0.846941\pi\)
\(68\) 131.407i 1.93246i
\(69\) −33.1391 + 22.1089i −0.480276 + 0.320418i
\(70\) 24.2074 0.345819
\(71\) −77.3081 −1.08885 −0.544423 0.838811i \(-0.683251\pi\)
−0.544423 + 0.838811i \(0.683251\pi\)
\(72\) −27.3000 −0.379167
\(73\) −132.608 −1.81654 −0.908272 0.418379i \(-0.862598\pi\)
−0.908272 + 0.418379i \(0.862598\pi\)
\(74\) 73.7790i 0.997013i
\(75\) 29.8415 0.397887
\(76\) 50.1265i 0.659560i
\(77\) −19.4363 −0.252419
\(78\) −21.2832 −0.272862
\(79\) 124.048i 1.57023i 0.619351 + 0.785114i \(0.287396\pi\)
−0.619351 + 0.785114i \(0.712604\pi\)
\(80\) 7.74246i 0.0967808i
\(81\) 9.00000 0.111111
\(82\) 2.81270 0.0343012
\(83\) 59.1946i 0.713188i 0.934259 + 0.356594i \(0.116062\pi\)
−0.934259 + 0.356594i \(0.883938\pi\)
\(84\) 31.0358i 0.369474i
\(85\) −54.0885 −0.636335
\(86\) 134.281i 1.56140i
\(87\) −70.3760 −0.808919
\(88\) 66.8508i 0.759668i
\(89\) 66.6559i 0.748943i 0.927238 + 0.374471i \(0.122176\pi\)
−0.927238 + 0.374471i \(0.877824\pi\)
\(90\) 27.4486i 0.304984i
\(91\) 9.90526i 0.108849i
\(92\) −129.579 + 86.4489i −1.40846 + 0.939662i
\(93\) 15.2539 0.164020
\(94\) −55.6003 −0.591492
\(95\) 20.6325 0.217185
\(96\) 47.2575 0.492266
\(97\) 7.24707i 0.0747120i 0.999302 + 0.0373560i \(0.0118936\pi\)
−0.999302 + 0.0373560i \(0.988106\pi\)
\(98\) 22.9751 0.234440
\(99\) 22.0387i 0.222613i
\(100\) 116.685 1.16685
\(101\) 20.6541 0.204496 0.102248 0.994759i \(-0.467396\pi\)
0.102248 + 0.994759i \(0.467396\pi\)
\(102\) 110.303i 1.08140i
\(103\) 117.447i 1.14026i −0.821553 0.570132i \(-0.806892\pi\)
0.821553 0.570132i \(-0.193108\pi\)
\(104\) −34.0689 −0.327586
\(105\) −12.7746 −0.121663
\(106\) 114.524i 1.08041i
\(107\) 85.9178i 0.802970i 0.915866 + 0.401485i \(0.131506\pi\)
−0.915866 + 0.401485i \(0.868494\pi\)
\(108\) 35.1913 0.325845
\(109\) 191.485i 1.75674i 0.477977 + 0.878372i \(0.341370\pi\)
−0.477977 + 0.878372i \(0.658630\pi\)
\(110\) 67.2144 0.611040
\(111\) 38.9344i 0.350760i
\(112\) 7.34834i 0.0656102i
\(113\) 133.624i 1.18251i −0.806483 0.591257i \(-0.798632\pi\)
0.806483 0.591257i \(-0.201368\pi\)
\(114\) 42.0760i 0.369088i
\(115\) −35.5832 53.3357i −0.309419 0.463789i
\(116\) −275.180 −2.37224
\(117\) 11.2315 0.0959958
\(118\) 90.2291 0.764654
\(119\) −51.3352 −0.431388
\(120\) 43.9381i 0.366151i
\(121\) 67.0329 0.553991
\(122\) 309.429i 2.53631i
\(123\) −1.48431 −0.0120676
\(124\) 59.6448 0.481006
\(125\) 117.720i 0.941758i
\(126\) 26.0513i 0.206757i
\(127\) −5.96059 −0.0469337 −0.0234669 0.999725i \(-0.507470\pi\)
−0.0234669 + 0.999725i \(0.507470\pi\)
\(128\) 221.247 1.72849
\(129\) 70.8621i 0.549319i
\(130\) 34.2543i 0.263495i
\(131\) 67.0342 0.511711 0.255856 0.966715i \(-0.417643\pi\)
0.255856 + 0.966715i \(0.417643\pi\)
\(132\) 86.1744i 0.652837i
\(133\) 19.5823 0.147235
\(134\) 203.427i 1.51811i
\(135\) 14.4851i 0.107297i
\(136\) 176.567i 1.29828i
\(137\) 2.58095i 0.0188391i 0.999956 + 0.00941953i \(0.00299837\pi\)
−0.999956 + 0.00941953i \(0.997002\pi\)
\(138\) 108.768 72.5648i 0.788172 0.525832i
\(139\) 22.8055 0.164069 0.0820343 0.996630i \(-0.473858\pi\)
0.0820343 + 0.996630i \(0.473858\pi\)
\(140\) −49.9506 −0.356790
\(141\) 29.3412 0.208094
\(142\) 253.738 1.78688
\(143\) 27.5031i 0.192329i
\(144\) 8.33224 0.0578628
\(145\) 113.267i 0.781150i
\(146\) 435.240 2.98109
\(147\) −12.1244 −0.0824786
\(148\) 152.239i 1.02864i
\(149\) 131.419i 0.882006i −0.897506 0.441003i \(-0.854623\pi\)
0.897506 0.441003i \(-0.145377\pi\)
\(150\) −97.9445 −0.652964
\(151\) −99.7634 −0.660685 −0.330342 0.943861i \(-0.607164\pi\)
−0.330342 + 0.943861i \(0.607164\pi\)
\(152\) 67.3529i 0.443111i
\(153\) 58.2087i 0.380449i
\(154\) 63.7930 0.414240
\(155\) 24.5503i 0.158389i
\(156\) 43.9168 0.281518
\(157\) 31.6630i 0.201675i −0.994903 0.100838i \(-0.967848\pi\)
0.994903 0.100838i \(-0.0321523\pi\)
\(158\) 407.145i 2.57687i
\(159\) 60.4361i 0.380101i
\(160\) 76.0587i 0.475367i
\(161\) −33.7719 50.6208i −0.209763 0.314415i
\(162\) −29.5394 −0.182342
\(163\) 105.168 0.645201 0.322601 0.946535i \(-0.395443\pi\)
0.322601 + 0.946535i \(0.395443\pi\)
\(164\) −5.80387 −0.0353894
\(165\) −35.4702 −0.214971
\(166\) 194.286i 1.17040i
\(167\) 69.6119 0.416837 0.208419 0.978040i \(-0.433168\pi\)
0.208419 + 0.978040i \(0.433168\pi\)
\(168\) 41.7015i 0.248223i
\(169\) −154.984 −0.917063
\(170\) 177.527 1.04428
\(171\) 22.2042i 0.129849i
\(172\) 277.081i 1.61094i
\(173\) 93.3923 0.539840 0.269920 0.962883i \(-0.413003\pi\)
0.269920 + 0.962883i \(0.413003\pi\)
\(174\) 230.985 1.32750
\(175\) 45.5836i 0.260478i
\(176\) 20.4035i 0.115929i
\(177\) −47.6154 −0.269014
\(178\) 218.775i 1.22907i
\(179\) −18.6887 −0.104406 −0.0522032 0.998636i \(-0.516624\pi\)
−0.0522032 + 0.998636i \(0.516624\pi\)
\(180\) 56.6387i 0.314659i
\(181\) 141.499i 0.781761i −0.920441 0.390881i \(-0.872171\pi\)
0.920441 0.390881i \(-0.127829\pi\)
\(182\) 32.5106i 0.178630i
\(183\) 163.291i 0.892301i
\(184\) 174.109 116.158i 0.946246 0.631292i
\(185\) 62.6630 0.338719
\(186\) −50.0656 −0.269170
\(187\) −142.538 −0.762235
\(188\) 114.728 0.610257
\(189\) 13.7477i 0.0727393i
\(190\) −67.7193 −0.356417
\(191\) 289.469i 1.51554i −0.652519 0.757772i \(-0.726288\pi\)
0.652519 0.757772i \(-0.273712\pi\)
\(192\) −174.349 −0.908069
\(193\) 157.578 0.816465 0.408233 0.912878i \(-0.366145\pi\)
0.408233 + 0.912878i \(0.366145\pi\)
\(194\) 23.7860i 0.122608i
\(195\) 18.0766i 0.0927004i
\(196\) −47.4080 −0.241877
\(197\) −7.97780 −0.0404964 −0.0202482 0.999795i \(-0.506446\pi\)
−0.0202482 + 0.999795i \(0.506446\pi\)
\(198\) 72.3345i 0.365326i
\(199\) 299.579i 1.50542i 0.658350 + 0.752712i \(0.271255\pi\)
−0.658350 + 0.752712i \(0.728745\pi\)
\(200\) −156.784 −0.783920
\(201\) 107.352i 0.534088i
\(202\) −67.7900 −0.335594
\(203\) 107.501i 0.529562i
\(204\) 227.604i 1.11571i
\(205\) 2.38893i 0.0116533i
\(206\) 385.480i 1.87126i
\(207\) −57.3986 + 38.2937i −0.277288 + 0.184994i
\(208\) 10.3982 0.0499912
\(209\) 54.3724 0.260155
\(210\) 41.9284 0.199659
\(211\) 141.461 0.670433 0.335216 0.942141i \(-0.391191\pi\)
0.335216 + 0.942141i \(0.391191\pi\)
\(212\) 236.314i 1.11469i
\(213\) −133.902 −0.628646
\(214\) 281.996i 1.31774i
\(215\) 114.049 0.530461
\(216\) −47.2850 −0.218912
\(217\) 23.3006i 0.107376i
\(218\) 628.485i 2.88296i
\(219\) −229.683 −1.04878
\(220\) −138.694 −0.630425
\(221\) 72.6412i 0.328693i
\(222\) 127.789i 0.575626i
\(223\) 142.812 0.640412 0.320206 0.947348i \(-0.396248\pi\)
0.320206 + 0.947348i \(0.396248\pi\)
\(224\) 72.1870i 0.322264i
\(225\) 51.6870 0.229720
\(226\) 438.576i 1.94060i
\(227\) 220.920i 0.973218i −0.873620 0.486609i \(-0.838234\pi\)
0.873620 0.486609i \(-0.161766\pi\)
\(228\) 86.8217i 0.380797i
\(229\) 342.678i 1.49641i 0.663468 + 0.748205i \(0.269084\pi\)
−0.663468 + 0.748205i \(0.730916\pi\)
\(230\) 116.790 + 175.056i 0.507781 + 0.761115i
\(231\) −33.6646 −0.145734
\(232\) 369.748 1.59374
\(233\) −57.8140 −0.248129 −0.124064 0.992274i \(-0.539593\pi\)
−0.124064 + 0.992274i \(0.539593\pi\)
\(234\) −36.8636 −0.157537
\(235\) 47.2233i 0.200950i
\(236\) −186.183 −0.788912
\(237\) 214.857i 0.906572i
\(238\) 168.490 0.707943
\(239\) −369.300 −1.54519 −0.772595 0.634899i \(-0.781042\pi\)
−0.772595 + 0.634899i \(0.781042\pi\)
\(240\) 13.4103i 0.0558764i
\(241\) 37.1026i 0.153953i 0.997033 + 0.0769763i \(0.0245266\pi\)
−0.997033 + 0.0769763i \(0.975473\pi\)
\(242\) −220.013 −0.909144
\(243\) 15.5885 0.0641500
\(244\) 638.492i 2.61677i
\(245\) 19.5136i 0.0796472i
\(246\) 4.87174 0.0198038
\(247\) 27.7096i 0.112185i
\(248\) −80.1421 −0.323154
\(249\) 102.528i 0.411759i
\(250\) 386.375i 1.54550i
\(251\) 196.331i 0.782196i −0.920349 0.391098i \(-0.872095\pi\)
0.920349 0.391098i \(-0.127905\pi\)
\(252\) 53.7556i 0.213316i
\(253\) −93.7714 140.554i −0.370638 0.555551i
\(254\) 19.5636 0.0770220
\(255\) −93.6841 −0.367388
\(256\) −323.527 −1.26378
\(257\) 319.634 1.24371 0.621856 0.783131i \(-0.286379\pi\)
0.621856 + 0.783131i \(0.286379\pi\)
\(258\) 232.581i 0.901476i
\(259\) 59.4733 0.229627
\(260\) 70.6820i 0.271854i
\(261\) −121.895 −0.467030
\(262\) −220.017 −0.839759
\(263\) 208.330i 0.792131i −0.918222 0.396065i \(-0.870375\pi\)
0.918222 0.396065i \(-0.129625\pi\)
\(264\) 115.789i 0.438594i
\(265\) −97.2690 −0.367053
\(266\) −64.2722 −0.241625
\(267\) 115.451i 0.432402i
\(268\) 419.760i 1.56627i
\(269\) −17.4800 −0.0649815 −0.0324908 0.999472i \(-0.510344\pi\)
−0.0324908 + 0.999472i \(0.510344\pi\)
\(270\) 47.5423i 0.176083i
\(271\) −76.9658 −0.284007 −0.142003 0.989866i \(-0.545354\pi\)
−0.142003 + 0.989866i \(0.545354\pi\)
\(272\) 53.8898i 0.198124i
\(273\) 17.1564i 0.0628440i
\(274\) 8.47109i 0.0309164i
\(275\) 126.568i 0.460248i
\(276\) −224.437 + 149.734i −0.813176 + 0.542514i
\(277\) 326.944 1.18031 0.590153 0.807292i \(-0.299068\pi\)
0.590153 + 0.807292i \(0.299068\pi\)
\(278\) −74.8514 −0.269250
\(279\) 26.4204 0.0946969
\(280\) 67.1165 0.239702
\(281\) 195.830i 0.696903i 0.937327 + 0.348452i \(0.113292\pi\)
−0.937327 + 0.348452i \(0.886708\pi\)
\(282\) −96.3025 −0.341498
\(283\) 359.211i 1.26930i −0.772802 0.634648i \(-0.781145\pi\)
0.772802 0.634648i \(-0.218855\pi\)
\(284\) −523.575 −1.84357
\(285\) 35.7366 0.125392
\(286\) 90.2694i 0.315627i
\(287\) 2.26732i 0.00790007i
\(288\) 81.8524 0.284210
\(289\) −87.4721 −0.302672
\(290\) 371.759i 1.28193i
\(291\) 12.5523i 0.0431350i
\(292\) −898.095 −3.07567
\(293\) 59.6930i 0.203730i −0.994798 0.101865i \(-0.967519\pi\)
0.994798 0.101865i \(-0.0324810\pi\)
\(294\) 39.7941 0.135354
\(295\) 76.6347i 0.259779i
\(296\) 204.557i 0.691072i
\(297\) 38.1721i 0.128526i
\(298\) 431.338i 1.44744i
\(299\) −71.6303 + 47.7884i −0.239566 + 0.159827i
\(300\) 202.104 0.673679
\(301\) 108.244 0.359614
\(302\) 327.439 1.08424
\(303\) 35.7739 0.118066
\(304\) 20.5568i 0.0676209i
\(305\) −262.809 −0.861670
\(306\) 191.050i 0.624347i
\(307\) 168.152 0.547727 0.273864 0.961769i \(-0.411698\pi\)
0.273864 + 0.961769i \(0.411698\pi\)
\(308\) −131.634 −0.427382
\(309\) 203.424i 0.658331i
\(310\) 80.5781i 0.259929i
\(311\) 495.245 1.59243 0.796214 0.605015i \(-0.206833\pi\)
0.796214 + 0.605015i \(0.206833\pi\)
\(312\) −59.0092 −0.189132
\(313\) 370.674i 1.18426i −0.805842 0.592130i \(-0.798287\pi\)
0.805842 0.592130i \(-0.201713\pi\)
\(314\) 103.923i 0.330965i
\(315\) −22.1263 −0.0702422
\(316\) 840.124i 2.65862i
\(317\) 275.198 0.868131 0.434066 0.900881i \(-0.357079\pi\)
0.434066 + 0.900881i \(0.357079\pi\)
\(318\) 198.361i 0.623776i
\(319\) 298.489i 0.935702i
\(320\) 280.607i 0.876896i
\(321\) 148.814i 0.463595i
\(322\) 110.845 + 166.145i 0.344238 + 0.515980i
\(323\) 143.609 0.444609
\(324\) 60.9531 0.188127
\(325\) 64.5025 0.198469
\(326\) −345.177 −1.05883
\(327\) 331.662i 1.01426i
\(328\) 7.79841 0.0237756
\(329\) 44.8194i 0.136229i
\(330\) 116.419 0.352784
\(331\) 83.7782 0.253106 0.126553 0.991960i \(-0.459609\pi\)
0.126553 + 0.991960i \(0.459609\pi\)
\(332\) 400.900i 1.20753i
\(333\) 67.4364i 0.202512i
\(334\) −228.477 −0.684064
\(335\) −172.777 −0.515753
\(336\) 12.7277i 0.0378801i
\(337\) 519.798i 1.54243i 0.636576 + 0.771214i \(0.280350\pi\)
−0.636576 + 0.771214i \(0.719650\pi\)
\(338\) 508.681 1.50497
\(339\) 231.444i 0.682725i
\(340\) −366.318 −1.07741
\(341\) 64.6969i 0.189727i
\(342\) 72.8778i 0.213093i
\(343\) 18.5203i 0.0539949i
\(344\) 372.302i 1.08227i
\(345\) −61.6318 92.3802i −0.178643 0.267769i
\(346\) −306.528 −0.885920
\(347\) 47.0383 0.135557 0.0677785 0.997700i \(-0.478409\pi\)
0.0677785 + 0.997700i \(0.478409\pi\)
\(348\) −476.626 −1.36961
\(349\) −149.404 −0.428092 −0.214046 0.976824i \(-0.568664\pi\)
−0.214046 + 0.976824i \(0.568664\pi\)
\(350\) 149.613i 0.427465i
\(351\) 19.4535 0.0554232
\(352\) 200.435i 0.569419i
\(353\) 311.382 0.882102 0.441051 0.897482i \(-0.354606\pi\)
0.441051 + 0.897482i \(0.354606\pi\)
\(354\) 156.281 0.441473
\(355\) 215.508i 0.607065i
\(356\) 451.432i 1.26807i
\(357\) −88.9152 −0.249062
\(358\) 61.3394 0.171339
\(359\) 309.900i 0.863230i 0.902058 + 0.431615i \(0.142056\pi\)
−0.902058 + 0.431615i \(0.857944\pi\)
\(360\) 76.1030i 0.211397i
\(361\) 306.219 0.848253
\(362\) 464.422i 1.28293i
\(363\) 116.104 0.319847
\(364\) 67.0840i 0.184297i
\(365\) 369.664i 1.01278i
\(366\) 535.947i 1.46434i
\(367\) 60.4009i 0.164580i −0.996608 0.0822900i \(-0.973777\pi\)
0.996608 0.0822900i \(-0.0262234\pi\)
\(368\) −53.1398 + 35.4525i −0.144402 + 0.0963382i
\(369\) −2.57090 −0.00696721
\(370\) −205.670 −0.555865
\(371\) −92.3176 −0.248835
\(372\) 103.308 0.277709
\(373\) 160.463i 0.430196i −0.976592 0.215098i \(-0.930993\pi\)
0.976592 0.215098i \(-0.0690070\pi\)
\(374\) 467.833 1.25089
\(375\) 203.897i 0.543724i
\(376\) −154.156 −0.409988
\(377\) −152.118 −0.403496
\(378\) 45.1222i 0.119371i
\(379\) 190.016i 0.501362i 0.968070 + 0.250681i \(0.0806546\pi\)
−0.968070 + 0.250681i \(0.919345\pi\)
\(380\) 139.735 0.367725
\(381\) −10.3240 −0.0270972
\(382\) 950.083i 2.48713i
\(383\) 513.529i 1.34081i −0.741997 0.670404i \(-0.766121\pi\)
0.741997 0.670404i \(-0.233879\pi\)
\(384\) 383.212 0.997947
\(385\) 54.1816i 0.140731i
\(386\) −517.195 −1.33988
\(387\) 122.737i 0.317149i
\(388\) 49.0812i 0.126498i
\(389\) 390.284i 1.00330i −0.865070 0.501651i \(-0.832726\pi\)
0.865070 0.501651i \(-0.167274\pi\)
\(390\) 59.3302i 0.152129i
\(391\) −247.669 371.233i −0.633425 0.949444i
\(392\) 63.7001 0.162500
\(393\) 116.107 0.295437
\(394\) 26.1844 0.0664579
\(395\) −345.803 −0.875450
\(396\) 149.258i 0.376915i
\(397\) −552.158 −1.39082 −0.695412 0.718611i \(-0.744778\pi\)
−0.695412 + 0.718611i \(0.744778\pi\)
\(398\) 983.267i 2.47052i
\(399\) 33.9175 0.0850063
\(400\) 47.8520 0.119630
\(401\) 41.0185i 0.102291i −0.998691 0.0511453i \(-0.983713\pi\)
0.998691 0.0511453i \(-0.0162871\pi\)
\(402\) 352.345i 0.876480i
\(403\) 32.9713 0.0818146
\(404\) 139.881 0.346241
\(405\) 25.0889i 0.0619478i
\(406\) 352.836i 0.869053i
\(407\) 165.134 0.405735
\(408\) 305.822i 0.749564i
\(409\) −211.284 −0.516586 −0.258293 0.966067i \(-0.583160\pi\)
−0.258293 + 0.966067i \(0.583160\pi\)
\(410\) 7.84083i 0.0191240i
\(411\) 4.47034i 0.0108767i
\(412\) 795.419i 1.93063i
\(413\) 72.7338i 0.176111i
\(414\) 188.391 125.686i 0.455051 0.303589i
\(415\) −165.014 −0.397624
\(416\) 102.147 0.245546
\(417\) 39.5004 0.0947251
\(418\) −178.459 −0.426935
\(419\) 48.5428i 0.115854i 0.998321 + 0.0579270i \(0.0184491\pi\)
−0.998321 + 0.0579270i \(0.981551\pi\)
\(420\) −86.5170 −0.205993
\(421\) 190.130i 0.451616i 0.974172 + 0.225808i \(0.0725022\pi\)
−0.974172 + 0.225808i \(0.927498\pi\)
\(422\) −464.299 −1.10023
\(423\) 50.8205 0.120143
\(424\) 317.525i 0.748879i
\(425\) 334.292i 0.786570i
\(426\) 439.486 1.03166
\(427\) −249.431 −0.584148
\(428\) 581.884i 1.35954i
\(429\) 47.6367i 0.111041i
\(430\) −374.328 −0.870529
\(431\) 528.069i 1.22522i 0.790386 + 0.612609i \(0.209880\pi\)
−0.790386 + 0.612609i \(0.790120\pi\)
\(432\) 14.4319 0.0334071
\(433\) 570.370i 1.31725i 0.752471 + 0.658625i \(0.228862\pi\)
−0.752471 + 0.658625i \(0.771138\pi\)
\(434\) 76.4764i 0.176213i
\(435\) 196.184i 0.450997i
\(436\) 1296.85i 2.97442i
\(437\) 94.4757 + 141.610i 0.216192 + 0.324050i
\(438\) 753.858 1.72114
\(439\) 477.624 1.08798 0.543991 0.839091i \(-0.316913\pi\)
0.543991 + 0.839091i \(0.316913\pi\)
\(440\) 186.357 0.423538
\(441\) −21.0000 −0.0476190
\(442\) 238.420i 0.539412i
\(443\) 665.292 1.50179 0.750894 0.660423i \(-0.229623\pi\)
0.750894 + 0.660423i \(0.229623\pi\)
\(444\) 263.686i 0.593887i
\(445\) −185.814 −0.417558
\(446\) −468.731 −1.05097
\(447\) 227.624i 0.509227i
\(448\) 266.323i 0.594470i
\(449\) 576.679 1.28436 0.642181 0.766553i \(-0.278030\pi\)
0.642181 + 0.766553i \(0.278030\pi\)
\(450\) −169.645 −0.376989
\(451\) 6.29547i 0.0139589i
\(452\) 904.978i 2.00216i
\(453\) −172.795 −0.381446
\(454\) 725.096i 1.59713i
\(455\) −27.6124 −0.0606866
\(456\) 116.659i 0.255830i
\(457\) 505.790i 1.10676i −0.832928 0.553381i \(-0.813337\pi\)
0.832928 0.553381i \(-0.186663\pi\)
\(458\) 1124.72i 2.45573i
\(459\) 100.820i 0.219652i
\(460\) −240.989 361.220i −0.523890 0.785261i
\(461\) −723.295 −1.56897 −0.784485 0.620148i \(-0.787073\pi\)
−0.784485 + 0.620148i \(0.787073\pi\)
\(462\) 110.493 0.239162
\(463\) 622.083 1.34359 0.671796 0.740737i \(-0.265523\pi\)
0.671796 + 0.740737i \(0.265523\pi\)
\(464\) −112.851 −0.243213
\(465\) 42.5224i 0.0914461i
\(466\) 189.755 0.407199
\(467\) 401.686i 0.860140i −0.902795 0.430070i \(-0.858489\pi\)
0.902795 0.430070i \(-0.141511\pi\)
\(468\) 76.0662 0.162535
\(469\) −163.982 −0.349642
\(470\) 154.994i 0.329775i
\(471\) 54.8420i 0.116437i
\(472\) 250.166 0.530014
\(473\) 300.551 0.635414
\(474\) 705.196i 1.48776i
\(475\) 127.519i 0.268461i
\(476\) −347.671 −0.730402
\(477\) 104.678i 0.219451i
\(478\) 1212.10 2.53578
\(479\) 52.7804i 0.110189i 0.998481 + 0.0550944i \(0.0175460\pi\)
−0.998481 + 0.0550944i \(0.982454\pi\)
\(480\) 131.738i 0.274453i
\(481\) 84.1569i 0.174962i
\(482\) 121.777i 0.252649i
\(483\) −58.4946 87.6777i −0.121107 0.181527i
\(484\) 453.985 0.937986
\(485\) −20.2023 −0.0416542
\(486\) −51.1638 −0.105275
\(487\) 629.626 1.29287 0.646434 0.762970i \(-0.276260\pi\)
0.646434 + 0.762970i \(0.276260\pi\)
\(488\) 857.914i 1.75802i
\(489\) 182.156 0.372507
\(490\) 64.0466i 0.130707i
\(491\) 25.7496 0.0524432 0.0262216 0.999656i \(-0.491652\pi\)
0.0262216 + 0.999656i \(0.491652\pi\)
\(492\) −10.0526 −0.0204321
\(493\) 788.370i 1.59913i
\(494\) 90.9475i 0.184104i
\(495\) −61.4362 −0.124114
\(496\) 24.4602 0.0493148
\(497\) 204.538i 0.411545i
\(498\) 336.514i 0.675730i
\(499\) 262.836 0.526725 0.263363 0.964697i \(-0.415168\pi\)
0.263363 + 0.964697i \(0.415168\pi\)
\(500\) 797.265i 1.59453i
\(501\) 120.571 0.240661
\(502\) 644.390i 1.28365i
\(503\) 757.291i 1.50555i −0.658279 0.752774i \(-0.728715\pi\)
0.658279 0.752774i \(-0.271285\pi\)
\(504\) 72.2291i 0.143312i
\(505\) 57.5764i 0.114013i
\(506\) 307.773 + 461.322i 0.608246 + 0.911703i
\(507\) −268.440 −0.529467
\(508\) −40.3685 −0.0794655
\(509\) −460.495 −0.904706 −0.452353 0.891839i \(-0.649415\pi\)
−0.452353 + 0.891839i \(0.649415\pi\)
\(510\) 307.486 0.602914
\(511\) 350.847i 0.686589i
\(512\) 176.877 0.345463
\(513\) 38.4588i 0.0749685i
\(514\) −1049.09 −2.04103
\(515\) 327.402 0.635732
\(516\) 479.919i 0.930075i
\(517\) 124.446i 0.240708i
\(518\) −195.201 −0.376835
\(519\) 161.760 0.311677
\(520\) 94.9724i 0.182639i
\(521\) 292.391i 0.561211i −0.959823 0.280606i \(-0.909465\pi\)
0.959823 0.280606i \(-0.0905353\pi\)
\(522\) 400.078 0.766433
\(523\) 128.901i 0.246465i 0.992378 + 0.123233i \(0.0393262\pi\)
−0.992378 + 0.123233i \(0.960674\pi\)
\(524\) 453.994 0.866400
\(525\) 78.9532i 0.150387i
\(526\) 683.773i 1.29995i
\(527\) 170.878i 0.324246i
\(528\) 35.3399i 0.0669316i
\(529\) 203.132 488.445i 0.383992 0.923336i
\(530\) 319.252 0.602363
\(531\) −82.4723 −0.155315
\(532\) 132.622 0.249290
\(533\) −3.20834 −0.00601940
\(534\) 378.930i 0.709607i
\(535\) −239.509 −0.447680
\(536\) 564.014i 1.05226i
\(537\) −32.3698 −0.0602790
\(538\) 57.3722 0.106640
\(539\) 51.4236i 0.0954056i
\(540\) 98.1011i 0.181669i
\(541\) −890.548 −1.64612 −0.823058 0.567958i \(-0.807734\pi\)
−0.823058 + 0.567958i \(0.807734\pi\)
\(542\) 252.614 0.466078
\(543\) 245.083i 0.451350i
\(544\) 529.391i 0.973145i
\(545\) −533.794 −0.979439
\(546\) 56.3101i 0.103132i
\(547\) 451.013 0.824522 0.412261 0.911066i \(-0.364739\pi\)
0.412261 + 0.911066i \(0.364739\pi\)
\(548\) 17.4797i 0.0318972i
\(549\) 282.829i 0.515170i
\(550\) 415.417i 0.755303i
\(551\) 300.731i 0.545791i
\(552\) 301.566 201.191i 0.546315 0.364476i
\(553\) −328.200 −0.593490
\(554\) −1073.08 −1.93697
\(555\) 108.536 0.195560
\(556\) 154.452 0.277792
\(557\) 798.237i 1.43310i 0.697536 + 0.716550i \(0.254280\pi\)
−0.697536 + 0.716550i \(0.745720\pi\)
\(558\) −86.7161 −0.155405
\(559\) 153.169i 0.274005i
\(560\) −20.4846 −0.0365797
\(561\) −246.883 −0.440077
\(562\) 642.745i 1.14367i
\(563\) 743.196i 1.32006i 0.751238 + 0.660032i \(0.229457\pi\)
−0.751238 + 0.660032i \(0.770543\pi\)
\(564\) 198.715 0.352332
\(565\) 372.498 0.659288
\(566\) 1178.99i 2.08301i
\(567\) 23.8118i 0.0419961i
\(568\) 703.505 1.23856
\(569\) 1101.92i 1.93658i 0.249824 + 0.968291i \(0.419627\pi\)
−0.249824 + 0.968291i \(0.580373\pi\)
\(570\) −117.293 −0.205778
\(571\) 713.916i 1.25029i 0.780509 + 0.625145i \(0.214960\pi\)
−0.780509 + 0.625145i \(0.785040\pi\)
\(572\) 186.266i 0.325641i
\(573\) 501.375i 0.875000i
\(574\) 7.44171i 0.0129646i
\(575\) −329.640 + 219.921i −0.573287 + 0.382470i
\(576\) −301.982 −0.524274
\(577\) −606.046 −1.05034 −0.525170 0.850997i \(-0.675998\pi\)
−0.525170 + 0.850997i \(0.675998\pi\)
\(578\) 287.097 0.496708
\(579\) 272.933 0.471386
\(580\) 767.107i 1.32260i
\(581\) −156.614 −0.269560
\(582\) 41.1986i 0.0707880i
\(583\) −256.330 −0.439675
\(584\) 1206.73 2.06632
\(585\) 31.3095i 0.0535206i
\(586\) 195.922i 0.334338i
\(587\) −1038.80 −1.76967 −0.884835 0.465905i \(-0.845729\pi\)
−0.884835 + 0.465905i \(0.845729\pi\)
\(588\) −82.1130 −0.139648
\(589\) 65.1828i 0.110667i
\(590\) 251.527i 0.426318i
\(591\) −13.8180 −0.0233806
\(592\) 62.4329i 0.105461i
\(593\) −623.644 −1.05168 −0.525838 0.850585i \(-0.676248\pi\)
−0.525838 + 0.850585i \(0.676248\pi\)
\(594\) 125.287i 0.210921i
\(595\) 143.105i 0.240512i
\(596\) 890.044i 1.49336i
\(597\) 518.887i 0.869157i
\(598\) 235.102 156.849i 0.393147 0.262290i
\(599\) 932.541 1.55683 0.778415 0.627750i \(-0.216024\pi\)
0.778415 + 0.627750i \(0.216024\pi\)
\(600\) −271.558 −0.452597
\(601\) −321.981 −0.535742 −0.267871 0.963455i \(-0.586320\pi\)
−0.267871 + 0.963455i \(0.586320\pi\)
\(602\) −355.273 −0.590154
\(603\) 185.938i 0.308356i
\(604\) −675.654 −1.11863
\(605\) 186.865i 0.308867i
\(606\) −117.416 −0.193755
\(607\) 1116.54 1.83944 0.919722 0.392571i \(-0.128414\pi\)
0.919722 + 0.392571i \(0.128414\pi\)
\(608\) 201.941i 0.332140i
\(609\) 186.197i 0.305743i
\(610\) 862.582 1.41407
\(611\) 63.4212 0.103799
\(612\) 394.222i 0.644154i
\(613\) 984.755i 1.60645i 0.595675 + 0.803226i \(0.296885\pi\)
−0.595675 + 0.803226i \(0.703115\pi\)
\(614\) −551.903 −0.898864
\(615\) 4.13774i 0.00672803i
\(616\) 176.870 0.287127
\(617\) 308.789i 0.500469i 0.968185 + 0.250235i \(0.0805077\pi\)
−0.968185 + 0.250235i \(0.919492\pi\)
\(618\) 667.671i 1.08037i
\(619\) 889.616i 1.43718i −0.695432 0.718591i \(-0.744787\pi\)
0.695432 0.718591i \(-0.255213\pi\)
\(620\) 166.269i 0.268176i
\(621\) −99.4172 + 66.3266i −0.160092 + 0.106806i
\(622\) −1625.47 −2.61330
\(623\) −176.355 −0.283074
\(624\) 18.0102 0.0288625
\(625\) 102.563 0.164101
\(626\) 1216.61i 1.94347i
\(627\) 94.1758 0.150201
\(628\) 214.440i 0.341465i
\(629\) 436.153 0.693408
\(630\) 72.6221 0.115273
\(631\) 55.1014i 0.0873240i 0.999046 + 0.0436620i \(0.0139025\pi\)
−0.999046 + 0.0436620i \(0.986098\pi\)
\(632\) 1128.84i 1.78614i
\(633\) 245.018 0.387075
\(634\) −903.242 −1.42467
\(635\) 16.6160i 0.0261670i
\(636\) 409.307i 0.643565i
\(637\) −26.2068 −0.0411411
\(638\) 979.688i 1.53556i
\(639\) −231.924 −0.362949
\(640\) 616.761i 0.963689i
\(641\) 146.120i 0.227957i 0.993483 + 0.113978i \(0.0363595\pi\)
−0.993483 + 0.113978i \(0.963641\pi\)
\(642\) 488.431i 0.760796i
\(643\) 1114.71i 1.73360i −0.498653 0.866802i \(-0.666172\pi\)
0.498653 0.866802i \(-0.333828\pi\)
\(644\) −228.722 342.833i −0.355159 0.532349i
\(645\) 197.539 0.306262
\(646\) −471.347 −0.729639
\(647\) −362.955 −0.560981 −0.280491 0.959857i \(-0.590497\pi\)
−0.280491 + 0.959857i \(0.590497\pi\)
\(648\) −81.9001 −0.126389
\(649\) 201.954i 0.311176i
\(650\) −211.708 −0.325704
\(651\) 40.3579i 0.0619937i
\(652\) 712.256 1.09242
\(653\) −231.202 −0.354061 −0.177030 0.984205i \(-0.556649\pi\)
−0.177030 + 0.984205i \(0.556649\pi\)
\(654\) 1088.57i 1.66448i
\(655\) 186.868i 0.285295i
\(656\) −2.38015 −0.00362828
\(657\) −397.823 −0.605515
\(658\) 147.105i 0.223563i
\(659\) 348.022i 0.528107i −0.964508 0.264053i \(-0.914941\pi\)
0.964508 0.264053i \(-0.0850595\pi\)
\(660\) −240.224 −0.363976
\(661\) 1125.69i 1.70302i 0.524340 + 0.851509i \(0.324312\pi\)
−0.524340 + 0.851509i \(0.675688\pi\)
\(662\) −274.973 −0.415368
\(663\) 125.818i 0.189771i
\(664\) 538.672i 0.811253i
\(665\) 54.5886i 0.0820881i
\(666\) 221.337i 0.332338i
\(667\) 777.398 518.644i 1.16551 0.777578i
\(668\) 471.451 0.705765
\(669\) 247.357 0.369742
\(670\) 567.082 0.846392
\(671\) −692.574 −1.03215
\(672\) 125.032i 0.186059i
\(673\) 971.764 1.44393 0.721964 0.691930i \(-0.243239\pi\)
0.721964 + 0.691930i \(0.243239\pi\)
\(674\) 1706.06i 2.53125i
\(675\) 89.5245 0.132629
\(676\) −1049.64 −1.55272
\(677\) 432.134i 0.638307i 0.947703 + 0.319154i \(0.103399\pi\)
−0.947703 + 0.319154i \(0.896601\pi\)
\(678\) 759.635i 1.12041i
\(679\) −19.1739 −0.0282385
\(680\) 492.206 0.723833
\(681\) 382.645i 0.561888i
\(682\) 212.345i 0.311357i
\(683\) 924.855 1.35411 0.677054 0.735934i \(-0.263257\pi\)
0.677054 + 0.735934i \(0.263257\pi\)
\(684\) 150.380i 0.219853i
\(685\) −7.19479 −0.0105033
\(686\) 60.7864i 0.0886100i
\(687\) 593.535i 0.863952i
\(688\) 113.630i 0.165160i
\(689\) 130.633i 0.189598i
\(690\) 202.285 + 303.207i 0.293167 + 0.439430i
\(691\) 604.638 0.875019 0.437510 0.899214i \(-0.355861\pi\)
0.437510 + 0.899214i \(0.355861\pi\)
\(692\) 632.506 0.914026
\(693\) −58.3089 −0.0841398
\(694\) −154.387 −0.222460
\(695\) 63.5739i 0.0914733i
\(696\) 640.422 0.920147
\(697\) 16.6276i 0.0238560i
\(698\) 490.368 0.702533
\(699\) −100.137 −0.143257
\(700\) 308.718i 0.441026i
\(701\) 711.153i 1.01448i 0.861804 + 0.507242i \(0.169335\pi\)
−0.861804 + 0.507242i \(0.830665\pi\)
\(702\) −63.8496 −0.0909539
\(703\) −166.375 −0.236664
\(704\) 739.475i 1.05039i
\(705\) 81.7931i 0.116019i
\(706\) −1022.01 −1.44760
\(707\) 54.6456i 0.0772922i
\(708\) −322.479 −0.455478
\(709\) 331.156i 0.467075i −0.972348 0.233537i \(-0.924970\pi\)
0.972348 0.233537i \(-0.0750301\pi\)
\(710\) 707.332i 0.996242i
\(711\) 372.144i 0.523409i
\(712\) 606.570i 0.851924i
\(713\) −168.499 + 112.415i −0.236325 + 0.157665i
\(714\) 291.834 0.408731
\(715\) −76.6690 −0.107229
\(716\) −126.571 −0.176775
\(717\) −639.647 −0.892116
\(718\) 1017.14i 1.41663i
\(719\) −576.485 −0.801787 −0.400894 0.916125i \(-0.631300\pi\)
−0.400894 + 0.916125i \(0.631300\pi\)
\(720\) 23.2274i 0.0322603i
\(721\) 310.736 0.430979
\(722\) −1005.06 −1.39205
\(723\) 64.2636i 0.0888846i
\(724\) 958.310i 1.32363i
\(725\) −700.041 −0.965574
\(726\) −381.073 −0.524894
\(727\) 1023.00i 1.40715i −0.710621 0.703575i \(-0.751586\pi\)
0.710621 0.703575i \(-0.248414\pi\)
\(728\) 90.1380i 0.123816i
\(729\) 27.0000 0.0370370
\(730\) 1213.30i 1.66205i
\(731\) 793.816 1.08593
\(732\) 1105.90i 1.51079i
\(733\) 1229.83i 1.67780i 0.544284 + 0.838901i \(0.316801\pi\)
−0.544284 + 0.838901i \(0.683199\pi\)
\(734\) 198.245i 0.270089i
\(735\) 33.7985i 0.0459843i
\(736\) −522.023 + 348.270i −0.709271 + 0.473193i
\(737\) −455.315 −0.617796
\(738\) 8.43810 0.0114337
\(739\) 293.034 0.396527 0.198264 0.980149i \(-0.436470\pi\)
0.198264 + 0.980149i \(0.436470\pi\)
\(740\) 424.390 0.573500
\(741\) 47.9945i 0.0647699i
\(742\) 303.001 0.408357
\(743\) 1145.14i 1.54124i −0.637294 0.770621i \(-0.719946\pi\)
0.637294 0.770621i \(-0.280054\pi\)
\(744\) −138.810 −0.186573
\(745\) 366.350 0.491745
\(746\) 526.665i 0.705985i
\(747\) 177.584i 0.237729i
\(748\) −965.349 −1.29057
\(749\) −227.317 −0.303494
\(750\) 669.221i 0.892295i
\(751\) 909.316i 1.21081i −0.795919 0.605404i \(-0.793012\pi\)
0.795919 0.605404i \(-0.206988\pi\)
\(752\) 47.0498 0.0625662
\(753\) 340.056i 0.451601i
\(754\) 499.275 0.662169
\(755\) 278.106i 0.368352i
\(756\) 93.1074i 0.123158i
\(757\) 703.956i 0.929929i 0.885329 + 0.464964i \(0.153933\pi\)
−0.885329 + 0.464964i \(0.846067\pi\)
\(758\) 623.664i 0.822775i
\(759\) −162.417 243.447i −0.213988 0.320747i
\(760\) −187.756 −0.247048
\(761\) 261.889 0.344138 0.172069 0.985085i \(-0.444955\pi\)
0.172069 + 0.985085i \(0.444955\pi\)
\(762\) 33.8851 0.0444687
\(763\) −506.622 −0.663987
\(764\) 1960.45i 2.56603i
\(765\) −162.266 −0.212112
\(766\) 1685.48i 2.20037i
\(767\) −102.921 −0.134186
\(768\) −560.365 −0.729642
\(769\) 438.046i 0.569631i −0.958582 0.284816i \(-0.908068\pi\)
0.958582 0.284816i \(-0.0919324\pi\)
\(770\) 177.833i 0.230952i
\(771\) 553.623 0.718058
\(772\) 1067.21 1.38239
\(773\) 837.173i 1.08302i −0.840695 0.541509i \(-0.817853\pi\)
0.840695 0.541509i \(-0.182147\pi\)
\(774\) 402.842i 0.520467i
\(775\) 151.733 0.195784
\(776\) 65.9484i 0.0849850i
\(777\) 103.011 0.132575
\(778\) 1280.98i 1.64650i
\(779\) 6.34276i 0.00814218i
\(780\) 122.425i 0.156955i
\(781\) 567.923i 0.727174i
\(782\) 812.890 + 1218.44i 1.03950 + 1.55811i
\(783\) −211.128 −0.269640
\(784\) −19.4419 −0.0247983
\(785\) 88.2656 0.112440
\(786\) −381.080 −0.484835
\(787\) 1233.03i 1.56675i −0.621549 0.783375i \(-0.713497\pi\)
0.621549 0.783375i \(-0.286503\pi\)
\(788\) −54.0302 −0.0685662
\(789\) 360.839i 0.457337i
\(790\) 1134.98 1.43668
\(791\) 353.536 0.446948