Properties

Label 483.3.f.a.22.22
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 22.22
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.21

$q$-expansion

\(f(q)\) \(=\) \(q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} -8.10909i q^{5} +1.29170 q^{6} +2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} -8.10909i q^{5} +1.29170 q^{6} +2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} +6.04744i q^{10} -17.3590i q^{11} +5.96491 q^{12} +11.7963 q^{13} -1.97310i q^{14} +14.0453i q^{15} +9.63540 q^{16} -14.5159i q^{17} -2.23728 q^{18} +7.64785i q^{19} +27.9264i q^{20} -4.58258i q^{21} +12.9456i q^{22} +(-0.920715 - 22.9816i) q^{23} -9.61518 q^{24} -40.7573 q^{25} -8.79723 q^{26} -5.19615 q^{27} -9.11155i q^{28} +4.85267 q^{29} -10.4745i q^{30} +3.69740 q^{31} -29.3910 q^{32} +30.0666i q^{33} +10.8254i q^{34} +21.4546 q^{35} -10.3315 q^{36} +27.2098i q^{37} -5.70347i q^{38} -20.4318 q^{39} -45.0162i q^{40} -75.2950 q^{41} +3.41751i q^{42} +10.9461i q^{43} +59.7815i q^{44} -24.3273i q^{45} +(0.686633 + 17.1387i) q^{46} -63.8078 q^{47} -16.6890 q^{48} -7.00000 q^{49} +30.3952 q^{50} +25.1422i q^{51} -40.6246 q^{52} +0.265774i q^{53} +3.87509 q^{54} -140.765 q^{55} +14.6874i q^{56} -13.2465i q^{57} -3.61893 q^{58} +109.616 q^{59} -48.3699i q^{60} -94.2884i q^{61} -2.75737 q^{62} +7.93725i q^{63} -16.6230 q^{64} -95.6573i q^{65} -22.4225i q^{66} -50.6910i q^{67} +49.9903i q^{68} +(1.59472 + 39.8052i) q^{69} -16.0000 q^{70} +32.1216 q^{71} +16.6540 q^{72} -125.902 q^{73} -20.2920i q^{74} +70.5937 q^{75} -26.3380i q^{76} +45.9275 q^{77} +15.2372 q^{78} +45.1325i q^{79} -78.1343i q^{80} +9.00000 q^{81} +56.1521 q^{82} +119.398i q^{83} +15.7817i q^{84} -117.710 q^{85} -8.16319i q^{86} -8.40507 q^{87} -96.3653i q^{88} -94.1931i q^{89} +18.1423i q^{90} +31.2101i q^{91} +(3.17080 + 79.1449i) q^{92} -6.40408 q^{93} +47.5853 q^{94} +62.0171 q^{95} +50.9067 q^{96} +53.8983i q^{97} +5.22033 q^{98} -52.0769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.745761 −0.372880 −0.186440 0.982466i \(-0.559695\pi\)
−0.186440 + 0.982466i \(0.559695\pi\)
\(3\) −1.73205 −0.577350
\(4\) −3.44384 −0.860960
\(5\) 8.10909i 1.62182i −0.585173 0.810909i \(-0.698973\pi\)
0.585173 0.810909i \(-0.301027\pi\)
\(6\) 1.29170 0.215283
\(7\) 2.64575i 0.377964i
\(8\) 5.55132 0.693916
\(9\) 3.00000 0.333333
\(10\) 6.04744i 0.604744i
\(11\) 17.3590i 1.57809i −0.614337 0.789044i \(-0.710576\pi\)
0.614337 0.789044i \(-0.289424\pi\)
\(12\) 5.96491 0.497076
\(13\) 11.7963 0.907409 0.453704 0.891152i \(-0.350102\pi\)
0.453704 + 0.891152i \(0.350102\pi\)
\(14\) 1.97310i 0.140936i
\(15\) 14.0453i 0.936357i
\(16\) 9.63540 0.602213
\(17\) 14.5159i 0.853874i −0.904281 0.426937i \(-0.859593\pi\)
0.904281 0.426937i \(-0.140407\pi\)
\(18\) −2.23728 −0.124293
\(19\) 7.64785i 0.402519i 0.979538 + 0.201259i \(0.0645034\pi\)
−0.979538 + 0.201259i \(0.935497\pi\)
\(20\) 27.9264i 1.39632i
\(21\) 4.58258i 0.218218i
\(22\) 12.9456i 0.588438i
\(23\) −0.920715 22.9816i −0.0400311 0.999198i
\(24\) −9.61518 −0.400632
\(25\) −40.7573 −1.63029
\(26\) −8.79723 −0.338355
\(27\) −5.19615 −0.192450
\(28\) 9.11155i 0.325412i
\(29\) 4.85267 0.167333 0.0836667 0.996494i \(-0.473337\pi\)
0.0836667 + 0.996494i \(0.473337\pi\)
\(30\) 10.4745i 0.349149i
\(31\) 3.69740 0.119271 0.0596355 0.998220i \(-0.481006\pi\)
0.0596355 + 0.998220i \(0.481006\pi\)
\(32\) −29.3910 −0.918469
\(33\) 30.0666i 0.911110i
\(34\) 10.8254i 0.318393i
\(35\) 21.4546 0.612989
\(36\) −10.3315 −0.286987
\(37\) 27.2098i 0.735399i 0.929945 + 0.367700i \(0.119855\pi\)
−0.929945 + 0.367700i \(0.880145\pi\)
\(38\) 5.70347i 0.150091i
\(39\) −20.4318 −0.523893
\(40\) 45.0162i 1.12540i
\(41\) −75.2950 −1.83646 −0.918232 0.396043i \(-0.870383\pi\)
−0.918232 + 0.396043i \(0.870383\pi\)
\(42\) 3.41751i 0.0813692i
\(43\) 10.9461i 0.254561i 0.991867 + 0.127281i \(0.0406248\pi\)
−0.991867 + 0.127281i \(0.959375\pi\)
\(44\) 59.7815i 1.35867i
\(45\) 24.3273i 0.540606i
\(46\) 0.686633 + 17.1387i 0.0149268 + 0.372581i
\(47\) −63.8078 −1.35761 −0.678806 0.734317i \(-0.737502\pi\)
−0.678806 + 0.734317i \(0.737502\pi\)
\(48\) −16.6890 −0.347688
\(49\) −7.00000 −0.142857
\(50\) 30.3952 0.607903
\(51\) 25.1422i 0.492984i
\(52\) −40.6246 −0.781243
\(53\) 0.265774i 0.00501460i 0.999997 + 0.00250730i \(0.000798099\pi\)
−0.999997 + 0.00250730i \(0.999202\pi\)
\(54\) 3.87509 0.0717609
\(55\) −140.765 −2.55937
\(56\) 14.6874i 0.262275i
\(57\) 13.2465i 0.232394i
\(58\) −3.61893 −0.0623953
\(59\) 109.616 1.85790 0.928950 0.370206i \(-0.120713\pi\)
0.928950 + 0.370206i \(0.120713\pi\)
\(60\) 48.3699i 0.806166i
\(61\) 94.2884i 1.54571i −0.634582 0.772855i \(-0.718828\pi\)
0.634582 0.772855i \(-0.281172\pi\)
\(62\) −2.75737 −0.0444738
\(63\) 7.93725i 0.125988i
\(64\) −16.6230 −0.259734
\(65\) 95.6573i 1.47165i
\(66\) 22.4225i 0.339735i
\(67\) 50.6910i 0.756581i −0.925687 0.378291i \(-0.876512\pi\)
0.925687 0.378291i \(-0.123488\pi\)
\(68\) 49.9903i 0.735151i
\(69\) 1.59472 + 39.8052i 0.0231120 + 0.576887i
\(70\) −16.0000 −0.228572
\(71\) 32.1216 0.452416 0.226208 0.974079i \(-0.427367\pi\)
0.226208 + 0.974079i \(0.427367\pi\)
\(72\) 16.6540 0.231305
\(73\) −125.902 −1.72468 −0.862342 0.506327i \(-0.831003\pi\)
−0.862342 + 0.506327i \(0.831003\pi\)
\(74\) 20.2920i 0.274216i
\(75\) 70.5937 0.941249
\(76\) 26.3380i 0.346553i
\(77\) 45.9275 0.596461
\(78\) 15.2372 0.195349
\(79\) 45.1325i 0.571297i 0.958334 + 0.285648i \(0.0922090\pi\)
−0.958334 + 0.285648i \(0.907791\pi\)
\(80\) 78.1343i 0.976679i
\(81\) 9.00000 0.111111
\(82\) 56.1521 0.684781
\(83\) 119.398i 1.43853i 0.694738 + 0.719263i \(0.255520\pi\)
−0.694738 + 0.719263i \(0.744480\pi\)
\(84\) 15.7817i 0.187877i
\(85\) −117.710 −1.38483
\(86\) 8.16319i 0.0949208i
\(87\) −8.40507 −0.0966100
\(88\) 96.3653i 1.09506i
\(89\) 94.1931i 1.05835i −0.848513 0.529175i \(-0.822502\pi\)
0.848513 0.529175i \(-0.177498\pi\)
\(90\) 18.1423i 0.201581i
\(91\) 31.2101i 0.342968i
\(92\) 3.17080 + 79.1449i 0.0344652 + 0.860270i
\(93\) −6.40408 −0.0688611
\(94\) 47.5853 0.506227
\(95\) 62.0171 0.652812
\(96\) 50.9067 0.530278
\(97\) 53.8983i 0.555652i 0.960631 + 0.277826i \(0.0896139\pi\)
−0.960631 + 0.277826i \(0.910386\pi\)
\(98\) 5.22033 0.0532686
\(99\) 52.0769i 0.526029i
\(100\) 140.362 1.40362
\(101\) −26.2570 −0.259970 −0.129985 0.991516i \(-0.541493\pi\)
−0.129985 + 0.991516i \(0.541493\pi\)
\(102\) 18.7501i 0.183824i
\(103\) 51.4015i 0.499043i 0.968369 + 0.249522i \(0.0802734\pi\)
−0.968369 + 0.249522i \(0.919727\pi\)
\(104\) 65.4851 0.629665
\(105\) −37.1605 −0.353910
\(106\) 0.198204i 0.00186984i
\(107\) 187.789i 1.75504i 0.479540 + 0.877520i \(0.340804\pi\)
−0.479540 + 0.877520i \(0.659196\pi\)
\(108\) 17.8947 0.165692
\(109\) 79.7085i 0.731271i 0.930758 + 0.365635i \(0.119148\pi\)
−0.930758 + 0.365635i \(0.880852\pi\)
\(110\) 104.977 0.954339
\(111\) 47.1287i 0.424583i
\(112\) 25.4929i 0.227615i
\(113\) 1.05462i 0.00933291i −0.999989 0.00466645i \(-0.998515\pi\)
0.999989 0.00466645i \(-0.00148538\pi\)
\(114\) 9.87870i 0.0866553i
\(115\) −186.359 + 7.46616i −1.62052 + 0.0649231i
\(116\) −16.7118 −0.144067
\(117\) 35.3889 0.302470
\(118\) −81.7474 −0.692774
\(119\) 38.4053 0.322734
\(120\) 77.9703i 0.649752i
\(121\) −180.334 −1.49036
\(122\) 70.3166i 0.576365i
\(123\) 130.415 1.06028
\(124\) −12.7333 −0.102688
\(125\) 127.777i 1.02222i
\(126\) 5.91929i 0.0469785i
\(127\) 221.052 1.74057 0.870285 0.492549i \(-0.163935\pi\)
0.870285 + 0.492549i \(0.163935\pi\)
\(128\) 129.961 1.01532
\(129\) 18.9592i 0.146971i
\(130\) 71.3375i 0.548750i
\(131\) −120.544 −0.920183 −0.460091 0.887872i \(-0.652183\pi\)
−0.460091 + 0.887872i \(0.652183\pi\)
\(132\) 103.545i 0.784429i
\(133\) −20.2343 −0.152138
\(134\) 37.8033i 0.282114i
\(135\) 42.1360i 0.312119i
\(136\) 80.5822i 0.592516i
\(137\) 6.29977i 0.0459837i −0.999736 0.0229919i \(-0.992681\pi\)
0.999736 0.0229919i \(-0.00731918\pi\)
\(138\) −1.18928 29.6852i −0.00861799 0.215110i
\(139\) 87.3445 0.628378 0.314189 0.949361i \(-0.398268\pi\)
0.314189 + 0.949361i \(0.398268\pi\)
\(140\) −73.8863 −0.527759
\(141\) 110.518 0.783818
\(142\) −23.9550 −0.168697
\(143\) 204.772i 1.43197i
\(144\) 28.9062 0.200738
\(145\) 39.3507i 0.271384i
\(146\) 93.8927 0.643101
\(147\) 12.1244 0.0824786
\(148\) 93.7061i 0.633150i
\(149\) 75.8390i 0.508986i −0.967075 0.254493i \(-0.918091\pi\)
0.967075 0.254493i \(-0.0819086\pi\)
\(150\) −52.6460 −0.350973
\(151\) 17.1909 0.113847 0.0569237 0.998379i \(-0.481871\pi\)
0.0569237 + 0.998379i \(0.481871\pi\)
\(152\) 42.4557i 0.279314i
\(153\) 43.5476i 0.284625i
\(154\) −34.2509 −0.222409
\(155\) 29.9825i 0.193436i
\(156\) 70.3639 0.451051
\(157\) 173.915i 1.10774i −0.832603 0.553870i \(-0.813151\pi\)
0.832603 0.553870i \(-0.186849\pi\)
\(158\) 33.6580i 0.213025i
\(159\) 0.460333i 0.00289518i
\(160\) 238.334i 1.48959i
\(161\) 60.8035 2.43598i 0.377662 0.0151303i
\(162\) −6.71185 −0.0414312
\(163\) −61.4799 −0.377177 −0.188589 0.982056i \(-0.560391\pi\)
−0.188589 + 0.982056i \(0.560391\pi\)
\(164\) 259.304 1.58112
\(165\) 243.813 1.47765
\(166\) 89.0421i 0.536398i
\(167\) 194.339 1.16371 0.581853 0.813294i \(-0.302328\pi\)
0.581853 + 0.813294i \(0.302328\pi\)
\(168\) 25.4394i 0.151425i
\(169\) −29.8470 −0.176610
\(170\) 87.7837 0.516375
\(171\) 22.9436i 0.134173i
\(172\) 37.6967i 0.219167i
\(173\) −51.7714 −0.299257 −0.149628 0.988742i \(-0.547808\pi\)
−0.149628 + 0.988742i \(0.547808\pi\)
\(174\) 6.26817 0.0360240
\(175\) 107.834i 0.616192i
\(176\) 167.261i 0.950345i
\(177\) −189.861 −1.07266
\(178\) 70.2455i 0.394638i
\(179\) −288.189 −1.60999 −0.804997 0.593279i \(-0.797833\pi\)
−0.804997 + 0.593279i \(0.797833\pi\)
\(180\) 83.7792i 0.465440i
\(181\) 85.6046i 0.472954i −0.971637 0.236477i \(-0.924007\pi\)
0.971637 0.236477i \(-0.0759927\pi\)
\(182\) 23.2753i 0.127886i
\(183\) 163.312i 0.892416i
\(184\) −5.11119 127.578i −0.0277782 0.693359i
\(185\) 220.646 1.19268
\(186\) 4.77591 0.0256770
\(187\) −251.980 −1.34749
\(188\) 219.744 1.16885
\(189\) 13.7477i 0.0727393i
\(190\) −46.2499 −0.243421
\(191\) 33.4941i 0.175362i 0.996149 + 0.0876810i \(0.0279456\pi\)
−0.996149 + 0.0876810i \(0.972054\pi\)
\(192\) 28.7918 0.149957
\(193\) 185.943 0.963434 0.481717 0.876327i \(-0.340013\pi\)
0.481717 + 0.876327i \(0.340013\pi\)
\(194\) 40.1952i 0.207192i
\(195\) 165.683i 0.849658i
\(196\) 24.1069 0.122994
\(197\) −192.754 −0.978449 −0.489224 0.872158i \(-0.662720\pi\)
−0.489224 + 0.872158i \(0.662720\pi\)
\(198\) 38.8369i 0.196146i
\(199\) 85.6702i 0.430503i 0.976559 + 0.215252i \(0.0690572\pi\)
−0.976559 + 0.215252i \(0.930943\pi\)
\(200\) −226.257 −1.13128
\(201\) 87.7993i 0.436813i
\(202\) 19.5814 0.0969377
\(203\) 12.8390i 0.0632461i
\(204\) 86.5857i 0.424440i
\(205\) 610.574i 2.97841i
\(206\) 38.3332i 0.186083i
\(207\) −2.76214 68.9447i −0.0133437 0.333066i
\(208\) 113.662 0.546453
\(209\) 132.759 0.635210
\(210\) 27.7128 0.131966
\(211\) −125.041 −0.592613 −0.296307 0.955093i \(-0.595755\pi\)
−0.296307 + 0.955093i \(0.595755\pi\)
\(212\) 0.915282i 0.00431737i
\(213\) −55.6362 −0.261203
\(214\) 140.046i 0.654420i
\(215\) 88.7631 0.412851
\(216\) −28.8455 −0.133544
\(217\) 9.78240i 0.0450802i
\(218\) 59.4435i 0.272676i
\(219\) 218.068 0.995746
\(220\) 484.774 2.20352
\(221\) 171.234i 0.774812i
\(222\) 35.1467i 0.158319i
\(223\) 38.1190 0.170937 0.0854687 0.996341i \(-0.472761\pi\)
0.0854687 + 0.996341i \(0.472761\pi\)
\(224\) 77.7613i 0.347149i
\(225\) −122.272 −0.543430
\(226\) 0.786493i 0.00348006i
\(227\) 388.681i 1.71225i −0.516768 0.856126i \(-0.672865\pi\)
0.516768 0.856126i \(-0.327135\pi\)
\(228\) 45.6187i 0.200082i
\(229\) 347.374i 1.51692i −0.651722 0.758458i \(-0.725953\pi\)
0.651722 0.758458i \(-0.274047\pi\)
\(230\) 138.980 5.56797i 0.604259 0.0242085i
\(231\) −79.5488 −0.344367
\(232\) 26.9387 0.116115
\(233\) −382.241 −1.64052 −0.820260 0.571991i \(-0.806171\pi\)
−0.820260 + 0.571991i \(0.806171\pi\)
\(234\) −26.3917 −0.112785
\(235\) 517.423i 2.20180i
\(236\) −377.500 −1.59958
\(237\) 78.1717i 0.329838i
\(238\) −28.6412 −0.120341
\(239\) 331.712 1.38792 0.693958 0.720015i \(-0.255865\pi\)
0.693958 + 0.720015i \(0.255865\pi\)
\(240\) 135.333i 0.563886i
\(241\) 265.451i 1.10146i −0.834685 0.550728i \(-0.814350\pi\)
0.834685 0.550728i \(-0.185650\pi\)
\(242\) 134.486 0.555727
\(243\) −15.5885 −0.0641500
\(244\) 324.714i 1.33080i
\(245\) 56.7636i 0.231688i
\(246\) −97.2583 −0.395359
\(247\) 90.2165i 0.365249i
\(248\) 20.5255 0.0827639
\(249\) 206.803i 0.830534i
\(250\) 95.2911i 0.381164i
\(251\) 229.727i 0.915248i 0.889146 + 0.457624i \(0.151299\pi\)
−0.889146 + 0.457624i \(0.848701\pi\)
\(252\) 27.3346i 0.108471i
\(253\) −398.936 + 15.9827i −1.57682 + 0.0631726i
\(254\) −164.852 −0.649024
\(255\) 203.880 0.799530
\(256\) −30.4278 −0.118859
\(257\) 294.228 1.14486 0.572428 0.819955i \(-0.306001\pi\)
0.572428 + 0.819955i \(0.306001\pi\)
\(258\) 14.1391i 0.0548026i
\(259\) −71.9903 −0.277955
\(260\) 329.429i 1.26703i
\(261\) 14.5580 0.0557778
\(262\) 89.8969 0.343118
\(263\) 49.5368i 0.188353i 0.995556 + 0.0941764i \(0.0300218\pi\)
−0.995556 + 0.0941764i \(0.969978\pi\)
\(264\) 166.910i 0.632233i
\(265\) 2.15518 0.00813276
\(266\) 15.0900 0.0567292
\(267\) 163.147i 0.611038i
\(268\) 174.572i 0.651387i
\(269\) −407.228 −1.51386 −0.756929 0.653498i \(-0.773301\pi\)
−0.756929 + 0.653498i \(0.773301\pi\)
\(270\) 31.4234i 0.116383i
\(271\) −136.566 −0.503932 −0.251966 0.967736i \(-0.581077\pi\)
−0.251966 + 0.967736i \(0.581077\pi\)
\(272\) 139.866i 0.514214i
\(273\) 54.0575i 0.198013i
\(274\) 4.69812i 0.0171464i
\(275\) 707.504i 2.57274i
\(276\) −5.49198 137.083i −0.0198985 0.496677i
\(277\) 108.086 0.390202 0.195101 0.980783i \(-0.437497\pi\)
0.195101 + 0.980783i \(0.437497\pi\)
\(278\) −65.1381 −0.234310
\(279\) 11.0922 0.0397570
\(280\) 119.102 0.425363
\(281\) 256.248i 0.911915i 0.890001 + 0.455958i \(0.150703\pi\)
−0.890001 + 0.455958i \(0.849297\pi\)
\(282\) −82.4202 −0.292270
\(283\) 87.9114i 0.310641i 0.987864 + 0.155321i \(0.0496410\pi\)
−0.987864 + 0.155321i \(0.950359\pi\)
\(284\) −110.622 −0.389513
\(285\) −107.417 −0.376901
\(286\) 152.711i 0.533954i
\(287\) 199.212i 0.694118i
\(288\) −88.1730 −0.306156
\(289\) 78.2899 0.270899
\(290\) 29.3462i 0.101194i
\(291\) 93.3545i 0.320806i
\(292\) 433.586 1.48488
\(293\) 553.764i 1.88998i −0.327101 0.944989i \(-0.606072\pi\)
0.327101 0.944989i \(-0.393928\pi\)
\(294\) −9.04187 −0.0307547
\(295\) 888.886i 3.01317i
\(296\) 151.050i 0.510305i
\(297\) 90.1999i 0.303703i
\(298\) 56.5577i 0.189791i
\(299\) −10.8610 271.098i −0.0363245 0.906681i
\(300\) −243.113 −0.810378
\(301\) −28.9607 −0.0962150
\(302\) −12.8203 −0.0424514
\(303\) 45.4784 0.150094
\(304\) 73.6902i 0.242402i
\(305\) −764.592 −2.50686
\(306\) 32.4761i 0.106131i
\(307\) 166.279 0.541627 0.270813 0.962632i \(-0.412707\pi\)
0.270813 + 0.962632i \(0.412707\pi\)
\(308\) −158.167 −0.513529
\(309\) 89.0299i 0.288123i
\(310\) 22.3598i 0.0721283i
\(311\) −343.603 −1.10483 −0.552417 0.833568i \(-0.686294\pi\)
−0.552417 + 0.833568i \(0.686294\pi\)
\(312\) −113.424 −0.363537
\(313\) 314.795i 1.00574i −0.864363 0.502868i \(-0.832278\pi\)
0.864363 0.502868i \(-0.167722\pi\)
\(314\) 129.699i 0.413054i
\(315\) 64.3639 0.204330
\(316\) 155.429i 0.491864i
\(317\) −401.581 −1.26682 −0.633409 0.773818i \(-0.718345\pi\)
−0.633409 + 0.773818i \(0.718345\pi\)
\(318\) 0.343299i 0.00107956i
\(319\) 84.2373i 0.264067i
\(320\) 134.797i 0.421241i
\(321\) 325.261i 1.01327i
\(322\) −45.3449 + 1.81666i −0.140823 + 0.00564180i
\(323\) 111.015 0.343700
\(324\) −30.9946 −0.0956622
\(325\) −480.785 −1.47934
\(326\) 45.8493 0.140642
\(327\) 138.059i 0.422199i
\(328\) −417.987 −1.27435
\(329\) 168.820i 0.513129i
\(330\) −181.826 −0.550988
\(331\) −497.047 −1.50165 −0.750827 0.660499i \(-0.770345\pi\)
−0.750827 + 0.660499i \(0.770345\pi\)
\(332\) 411.187i 1.23851i
\(333\) 81.6293i 0.245133i
\(334\) −144.930 −0.433923
\(335\) −411.057 −1.22704
\(336\) 44.1550i 0.131414i
\(337\) 357.790i 1.06169i −0.847468 0.530846i \(-0.821874\pi\)
0.847468 0.530846i \(-0.178126\pi\)
\(338\) 22.2588 0.0658543
\(339\) 1.82665i 0.00538836i
\(340\) 405.376 1.19228
\(341\) 64.1830i 0.188220i
\(342\) 17.1104i 0.0500304i
\(343\) 18.5203i 0.0539949i
\(344\) 60.7655i 0.176644i
\(345\) 322.784 12.9318i 0.935606 0.0374834i
\(346\) 38.6091 0.111587
\(347\) 529.547 1.52607 0.763035 0.646357i \(-0.223708\pi\)
0.763035 + 0.646357i \(0.223708\pi\)
\(348\) 28.9457 0.0831773
\(349\) 324.799 0.930657 0.465328 0.885138i \(-0.345936\pi\)
0.465328 + 0.885138i \(0.345936\pi\)
\(350\) 80.4181i 0.229766i
\(351\) −61.2954 −0.174631
\(352\) 510.198i 1.44942i
\(353\) −119.472 −0.338447 −0.169224 0.985578i \(-0.554126\pi\)
−0.169224 + 0.985578i \(0.554126\pi\)
\(354\) 141.591 0.399973
\(355\) 260.477i 0.733737i
\(356\) 324.386i 0.911197i
\(357\) −66.5200 −0.186331
\(358\) 214.920 0.600335
\(359\) 32.2603i 0.0898616i −0.998990 0.0449308i \(-0.985693\pi\)
0.998990 0.0449308i \(-0.0143067\pi\)
\(360\) 135.048i 0.375135i
\(361\) 302.510 0.837979
\(362\) 63.8406i 0.176355i
\(363\) 312.347 0.860461
\(364\) 107.483i 0.295282i
\(365\) 1020.95i 2.79712i
\(366\) 121.792i 0.332765i
\(367\) 10.7331i 0.0292455i −0.999893 0.0146228i \(-0.995345\pi\)
0.999893 0.0146228i \(-0.00465474\pi\)
\(368\) −8.87146 221.437i −0.0241072 0.601730i
\(369\) −225.885 −0.612155
\(370\) −164.549 −0.444728
\(371\) −0.703171 −0.00189534
\(372\) 22.0546 0.0592867
\(373\) 209.138i 0.560693i 0.959899 + 0.280346i \(0.0904493\pi\)
−0.959899 + 0.280346i \(0.909551\pi\)
\(374\) 187.917 0.502452
\(375\) 221.316i 0.590177i
\(376\) −354.218 −0.942069
\(377\) 57.2436 0.151840
\(378\) 10.2525i 0.0271231i
\(379\) 227.488i 0.600232i 0.953903 + 0.300116i \(0.0970254\pi\)
−0.953903 + 0.300116i \(0.902975\pi\)
\(380\) −213.577 −0.562045
\(381\) −382.874 −1.00492
\(382\) 24.9786i 0.0653891i
\(383\) 358.454i 0.935910i 0.883752 + 0.467955i \(0.155009\pi\)
−0.883752 + 0.467955i \(0.844991\pi\)
\(384\) −225.099 −0.586194
\(385\) 372.430i 0.967351i
\(386\) −138.669 −0.359246
\(387\) 32.8384i 0.0848537i
\(388\) 185.617i 0.478394i
\(389\) 320.157i 0.823025i 0.911404 + 0.411512i \(0.134999\pi\)
−0.911404 + 0.411512i \(0.865001\pi\)
\(390\) 123.560i 0.316821i
\(391\) −333.597 + 13.3650i −0.853189 + 0.0341815i
\(392\) −38.8593 −0.0991308
\(393\) 208.788 0.531268
\(394\) 143.749 0.364844
\(395\) 365.983 0.926539
\(396\) 179.345i 0.452890i
\(397\) 636.060 1.60217 0.801083 0.598554i \(-0.204258\pi\)
0.801083 + 0.598554i \(0.204258\pi\)
\(398\) 63.8894i 0.160526i
\(399\) 35.0469 0.0878368
\(400\) −392.713 −0.981782
\(401\) 491.403i 1.22544i 0.790299 + 0.612721i \(0.209925\pi\)
−0.790299 + 0.612721i \(0.790075\pi\)
\(402\) 65.4773i 0.162879i
\(403\) 43.6157 0.108227
\(404\) 90.4248 0.223824
\(405\) 72.9818i 0.180202i
\(406\) 9.57479i 0.0235832i
\(407\) 472.334 1.16053
\(408\) 139.573i 0.342089i
\(409\) −519.008 −1.26897 −0.634484 0.772936i \(-0.718787\pi\)
−0.634484 + 0.772936i \(0.718787\pi\)
\(410\) 455.342i 1.11059i
\(411\) 10.9115i 0.0265487i
\(412\) 177.018i 0.429656i
\(413\) 290.017i 0.702220i
\(414\) 2.05990 + 51.4162i 0.00497560 + 0.124194i
\(415\) 968.206 2.33303
\(416\) −346.705 −0.833426
\(417\) −151.285 −0.362794
\(418\) −99.0064 −0.236857
\(419\) 287.924i 0.687170i −0.939122 0.343585i \(-0.888359\pi\)
0.939122 0.343585i \(-0.111641\pi\)
\(420\) 127.975 0.304702
\(421\) 534.001i 1.26841i 0.773165 + 0.634206i \(0.218673\pi\)
−0.773165 + 0.634206i \(0.781327\pi\)
\(422\) 93.2509 0.220974
\(423\) −191.423 −0.452538
\(424\) 1.47540i 0.00347971i
\(425\) 591.627i 1.39206i
\(426\) 41.4913 0.0973974
\(427\) 249.464 0.584224
\(428\) 646.717i 1.51102i
\(429\) 354.675i 0.826749i
\(430\) −66.1960 −0.153944
\(431\) 513.030i 1.19033i −0.803605 0.595163i \(-0.797088\pi\)
0.803605 0.595163i \(-0.202912\pi\)
\(432\) −50.0670 −0.115896
\(433\) 762.021i 1.75986i 0.475101 + 0.879931i \(0.342412\pi\)
−0.475101 + 0.879931i \(0.657588\pi\)
\(434\) 7.29533i 0.0168095i
\(435\) 68.1574i 0.156684i
\(436\) 274.503i 0.629595i
\(437\) 175.760 7.04149i 0.402196 0.0161133i
\(438\) −162.627 −0.371294
\(439\) −486.445 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(440\) −781.434 −1.77599
\(441\) −21.0000 −0.0476190
\(442\) 127.699i 0.288912i
\(443\) 568.520 1.28334 0.641670 0.766981i \(-0.278242\pi\)
0.641670 + 0.766981i \(0.278242\pi\)
\(444\) 162.304i 0.365549i
\(445\) −763.820 −1.71645
\(446\) −28.4277 −0.0637392
\(447\) 131.357i 0.293863i
\(448\) 43.9802i 0.0981701i
\(449\) 181.778 0.404850 0.202425 0.979298i \(-0.435118\pi\)
0.202425 + 0.979298i \(0.435118\pi\)
\(450\) 91.1855 0.202634
\(451\) 1307.04i 2.89810i
\(452\) 3.63194i 0.00803526i
\(453\) −29.7756 −0.0657298
\(454\) 289.863i 0.638465i
\(455\) 253.085 0.556232
\(456\) 73.5355i 0.161262i
\(457\) 842.429i 1.84339i −0.387915 0.921695i \(-0.626805\pi\)
0.387915 0.921695i \(-0.373195\pi\)
\(458\) 259.058i 0.565628i
\(459\) 75.4266i 0.164328i
\(460\) 641.792 25.7123i 1.39520 0.0558962i
\(461\) −819.955 −1.77865 −0.889323 0.457281i \(-0.848824\pi\)
−0.889323 + 0.457281i \(0.848824\pi\)
\(462\) 59.3244 0.128408
\(463\) 598.844 1.29340 0.646700 0.762745i \(-0.276149\pi\)
0.646700 + 0.762745i \(0.276149\pi\)
\(464\) 46.7574 0.100770
\(465\) 51.9313i 0.111680i
\(466\) 285.060 0.611718
\(467\) 688.578i 1.47447i −0.675636 0.737236i \(-0.736131\pi\)
0.675636 0.737236i \(-0.263869\pi\)
\(468\) −121.874 −0.260414
\(469\) 134.116 0.285961
\(470\) 385.874i 0.821008i
\(471\) 301.230i 0.639554i
\(472\) 608.514 1.28923
\(473\) 190.013 0.401720
\(474\) 58.2974i 0.122990i
\(475\) 311.706i 0.656223i
\(476\) −132.262 −0.277861
\(477\) 0.797321i 0.00167153i
\(478\) −247.378 −0.517527
\(479\) 515.560i 1.07633i −0.842841 0.538163i \(-0.819118\pi\)
0.842841 0.538163i \(-0.180882\pi\)
\(480\) 412.807i 0.860014i
\(481\) 320.975i 0.667308i
\(482\) 197.963i 0.410712i
\(483\) −105.315 + 4.21925i −0.218043 + 0.00873550i
\(484\) 621.041 1.28314
\(485\) 437.066 0.901166
\(486\) 11.6253 0.0239203
\(487\) 42.9540 0.0882013 0.0441007 0.999027i \(-0.485958\pi\)
0.0441007 + 0.999027i \(0.485958\pi\)
\(488\) 523.425i 1.07259i
\(489\) 106.486 0.217763
\(490\) 42.3321i 0.0863920i
\(491\) 16.5663 0.0337400 0.0168700 0.999858i \(-0.494630\pi\)
0.0168700 + 0.999858i \(0.494630\pi\)
\(492\) −449.128 −0.912862
\(493\) 70.4406i 0.142882i
\(494\) 67.2799i 0.136194i
\(495\) −422.296 −0.853123
\(496\) 35.6259 0.0718265
\(497\) 84.9857i 0.170997i
\(498\) 154.225i 0.309690i
\(499\) 410.775 0.823196 0.411598 0.911366i \(-0.364971\pi\)
0.411598 + 0.911366i \(0.364971\pi\)
\(500\) 440.044i 0.880088i
\(501\) −336.605 −0.671866
\(502\) 171.322i 0.341278i
\(503\) 707.969i 1.40749i −0.710452 0.703746i \(-0.751509\pi\)
0.710452 0.703746i \(-0.248491\pi\)
\(504\) 44.0623i 0.0874251i
\(505\) 212.920i 0.421624i
\(506\) 297.511 11.9192i 0.587966 0.0235558i
\(507\) 51.6966 0.101966
\(508\) −761.269 −1.49856
\(509\) 928.365 1.82390 0.911950 0.410301i \(-0.134576\pi\)
0.911950 + 0.410301i \(0.134576\pi\)
\(510\) −152.046 −0.298129
\(511\) 333.105i 0.651869i
\(512\) −497.151 −0.970998
\(513\) 39.7394i 0.0774648i
\(514\) −219.424 −0.426895
\(515\) 416.819 0.809357
\(516\) 65.2926i 0.126536i
\(517\) 1107.64i 2.14243i
\(518\) 53.6875 0.103644
\(519\) 89.6707 0.172776
\(520\) 531.025i 1.02120i
\(521\) 268.873i 0.516070i −0.966136 0.258035i \(-0.916925\pi\)
0.966136 0.258035i \(-0.0830750\pi\)
\(522\) −10.8568 −0.0207984
\(523\) 807.315i 1.54362i −0.635851 0.771812i \(-0.719351\pi\)
0.635851 0.771812i \(-0.280649\pi\)
\(524\) 415.134 0.792241
\(525\) 186.773i 0.355759i
\(526\) 36.9426i 0.0702330i
\(527\) 53.6709i 0.101842i
\(528\) 289.704i 0.548682i
\(529\) −527.305 + 42.3189i −0.996795 + 0.0799980i
\(530\) −1.60725 −0.00303255
\(531\) 328.848 0.619300
\(532\) 69.6838 0.130985
\(533\) −888.204 −1.66642
\(534\) 121.669i 0.227844i
\(535\) 1522.80 2.84635
\(536\) 281.402i 0.525004i
\(537\) 499.158 0.929530
\(538\) 303.694 0.564488
\(539\) 121.513i 0.225441i
\(540\) 145.110i 0.268722i
\(541\) −78.0316 −0.144236 −0.0721179 0.997396i \(-0.522976\pi\)
−0.0721179 + 0.997396i \(0.522976\pi\)
\(542\) 101.845 0.187906
\(543\) 148.272i 0.273060i
\(544\) 426.636i 0.784257i
\(545\) 646.363 1.18599
\(546\) 40.3140i 0.0738351i
\(547\) 417.888 0.763963 0.381982 0.924170i \(-0.375242\pi\)
0.381982 + 0.924170i \(0.375242\pi\)
\(548\) 21.6954i 0.0395902i
\(549\) 282.865i 0.515237i
\(550\) 527.629i 0.959325i
\(551\) 37.1125i 0.0673548i
\(552\) 8.85284 + 220.972i 0.0160377 + 0.400311i
\(553\) −119.409 −0.215930
\(554\) −80.6063 −0.145499
\(555\) −382.171 −0.688596
\(556\) −300.801 −0.541008
\(557\) 895.207i 1.60719i 0.595173 + 0.803597i \(0.297083\pi\)
−0.595173 + 0.803597i \(0.702917\pi\)
\(558\) −8.27212 −0.0148246
\(559\) 129.124i 0.230991i
\(560\) 206.724 0.369150
\(561\) 436.443 0.777973
\(562\) 191.100i 0.340035i
\(563\) 537.325i 0.954396i −0.878796 0.477198i \(-0.841653\pi\)
0.878796 0.477198i \(-0.158347\pi\)
\(564\) −380.608 −0.674836
\(565\) −8.55199 −0.0151363
\(566\) 65.5609i 0.115832i
\(567\) 23.8118i 0.0419961i
\(568\) 178.317 0.313939
\(569\) 348.018i 0.611632i −0.952091 0.305816i \(-0.901071\pi\)
0.952091 0.305816i \(-0.0989292\pi\)
\(570\) 80.1072 0.140539
\(571\) 660.161i 1.15615i −0.815984 0.578075i \(-0.803804\pi\)
0.815984 0.578075i \(-0.196196\pi\)
\(572\) 705.202i 1.23287i
\(573\) 58.0136i 0.101245i
\(574\) 148.564i 0.258823i
\(575\) 37.5258 + 936.666i 0.0652623 + 1.62898i
\(576\) −49.8689 −0.0865779
\(577\) 285.015 0.493960 0.246980 0.969021i \(-0.420562\pi\)
0.246980 + 0.969021i \(0.420562\pi\)
\(578\) −58.3856 −0.101013
\(579\) −322.062 −0.556239
\(580\) 135.518i 0.233651i
\(581\) −315.897 −0.543712
\(582\) 69.6201i 0.119622i
\(583\) 4.61356 0.00791347
\(584\) −698.922 −1.19678
\(585\) 286.972i 0.490550i
\(586\) 412.975i 0.704736i
\(587\) −446.694 −0.760978 −0.380489 0.924785i \(-0.624244\pi\)
−0.380489 + 0.924785i \(0.624244\pi\)
\(588\) −41.7544 −0.0710108
\(589\) 28.2772i 0.0480088i
\(590\) 662.896i 1.12355i
\(591\) 333.860 0.564908
\(592\) 262.177i 0.442867i
\(593\) 19.3952 0.0327069 0.0163534 0.999866i \(-0.494794\pi\)
0.0163534 + 0.999866i \(0.494794\pi\)
\(594\) 67.2675i 0.113245i
\(595\) 311.432i 0.523416i
\(596\) 261.177i 0.438217i
\(597\) 148.385i 0.248551i
\(598\) 8.09974 + 202.174i 0.0135447 + 0.338084i
\(599\) 506.473 0.845530 0.422765 0.906239i \(-0.361059\pi\)
0.422765 + 0.906239i \(0.361059\pi\)
\(600\) 391.888 0.653147
\(601\) 425.353 0.707742 0.353871 0.935294i \(-0.384865\pi\)
0.353871 + 0.935294i \(0.384865\pi\)
\(602\) 21.5978 0.0358767
\(603\) 152.073i 0.252194i
\(604\) −59.2029 −0.0980180
\(605\) 1462.34i 2.41710i
\(606\) −33.9160 −0.0559670
\(607\) 633.633 1.04388 0.521938 0.852983i \(-0.325209\pi\)
0.521938 + 0.852983i \(0.325209\pi\)
\(608\) 224.778i 0.369701i
\(609\) 22.2377i 0.0365151i
\(610\) 570.203 0.934759
\(611\) −752.697 −1.23191
\(612\) 149.971i 0.245050i
\(613\) 25.9856i 0.0423909i 0.999775 + 0.0211954i \(0.00674722\pi\)
−0.999775 + 0.0211954i \(0.993253\pi\)
\(614\) −124.005 −0.201962
\(615\) 1057.54i 1.71959i
\(616\) 254.959 0.413894
\(617\) 158.782i 0.257345i 0.991687 + 0.128672i \(0.0410715\pi\)
−0.991687 + 0.128672i \(0.958928\pi\)
\(618\) 66.3950i 0.107435i
\(619\) 801.920i 1.29551i 0.761849 + 0.647755i \(0.224292\pi\)
−0.761849 + 0.647755i \(0.775708\pi\)
\(620\) 103.255i 0.166540i
\(621\) 4.78417 + 119.416i 0.00770399 + 0.192296i
\(622\) 256.246 0.411971
\(623\) 249.212 0.400018
\(624\) −196.869 −0.315495
\(625\) 17.2234 0.0275574
\(626\) 234.762i 0.375019i
\(627\) −229.945 −0.366739
\(628\) 598.936i 0.953720i
\(629\) 394.973 0.627938
\(630\) −48.0000 −0.0761906
\(631\) 755.002i 1.19652i −0.801303 0.598258i \(-0.795860\pi\)
0.801303 0.598258i \(-0.204140\pi\)
\(632\) 250.545i 0.396432i
\(633\) 216.578 0.342145
\(634\) 299.483 0.472371
\(635\) 1792.53i 2.82289i
\(636\) 1.58531i 0.00249263i
\(637\) −82.5742 −0.129630
\(638\) 62.8209i 0.0984653i
\(639\) 96.3647 0.150805
\(640\) 1053.86i 1.64666i
\(641\) 474.103i 0.739631i −0.929105 0.369815i \(-0.879421\pi\)
0.929105 0.369815i \(-0.120579\pi\)
\(642\) 242.567i 0.377830i
\(643\) 92.0437i 0.143147i 0.997435 + 0.0715737i \(0.0228021\pi\)
−0.997435 + 0.0715737i \(0.977198\pi\)
\(644\) −209.398 + 8.38914i −0.325152 + 0.0130266i
\(645\) −153.742 −0.238360
\(646\) −82.7907 −0.128159
\(647\) 861.523 1.33156 0.665782 0.746146i \(-0.268098\pi\)
0.665782 + 0.746146i \(0.268098\pi\)
\(648\) 49.9619 0.0771017
\(649\) 1902.82i 2.93193i
\(650\) 358.551 0.551617
\(651\) 16.9436i 0.0260270i
\(652\) 211.727 0.324735
\(653\) 946.887 1.45006 0.725028 0.688719i \(-0.241827\pi\)
0.725028 + 0.688719i \(0.241827\pi\)
\(654\) 102.959i 0.157430i
\(655\) 977.501i 1.49237i
\(656\) −725.498 −1.10594
\(657\) −377.706 −0.574894
\(658\) 125.899i 0.191336i
\(659\) 284.771i 0.432126i 0.976379 + 0.216063i \(0.0693217\pi\)
−0.976379 + 0.216063i \(0.930678\pi\)
\(660\) −839.652 −1.27220
\(661\) 193.575i 0.292852i −0.989222 0.146426i \(-0.953223\pi\)
0.989222 0.146426i \(-0.0467771\pi\)
\(662\) 370.678 0.559937
\(663\) 296.585i 0.447338i
\(664\) 662.815i 0.998216i
\(665\) 164.082i 0.246740i
\(666\) 60.8759i 0.0914053i
\(667\) −4.46792 111.522i −0.00669854 0.167199i
\(668\) −669.272 −1.00190
\(669\) −66.0241 −0.0986907
\(670\) 306.550 0.457538
\(671\) −1636.75 −2.43927
\(672\) 134.686i 0.200426i
\(673\) 913.275 1.35702 0.678511 0.734590i \(-0.262626\pi\)
0.678511 + 0.734590i \(0.262626\pi\)
\(674\) 266.826i 0.395884i
\(675\) 211.781 0.313750
\(676\) 102.788 0.152054
\(677\) 286.078i 0.422567i −0.977425 0.211284i \(-0.932236\pi\)
0.977425 0.211284i \(-0.0677644\pi\)
\(678\) 1.36225i 0.00200921i
\(679\) −142.601 −0.210017
\(680\) −653.448 −0.960953
\(681\) 673.215i 0.988569i
\(682\) 47.8652i 0.0701836i
\(683\) 950.616 1.39182 0.695912 0.718127i \(-0.255000\pi\)
0.695912 + 0.718127i \(0.255000\pi\)
\(684\) 79.0140i 0.115518i
\(685\) −51.0854 −0.0745772
\(686\) 13.8117i 0.0201336i
\(687\) 601.669i 0.875791i
\(688\) 105.470i 0.153300i
\(689\) 3.13515i 0.00455029i
\(690\) −240.720 + 9.64400i −0.348869 + 0.0139768i
\(691\) −742.374 −1.07435 −0.537174 0.843472i \(-0.680508\pi\)
−0.537174 + 0.843472i \(0.680508\pi\)
\(692\) 178.292 0.257648
\(693\) 137.783 0.198820
\(694\) −394.915 −0.569042
\(695\) 708.284i 1.01911i
\(696\) −46.6592 −0.0670391
\(697\) 1092.97i 1.56811i
\(698\) −242.223 −0.347024
\(699\) 662.061 0.947155
\(700\) 371.362i 0.530517i
\(701\) 270.705i 0.386169i −0.981182 0.193085i \(-0.938151\pi\)
0.981182 0.193085i \(-0.0618492\pi\)
\(702\) 45.7117 0.0651164
\(703\) −208.096 −0.296012
\(704\) 288.557i 0.409883i
\(705\) 896.203i 1.27121i
\(706\) 89.0974 0.126200
\(707\) 69.4694i 0.0982594i
\(708\) 653.850 0.923517
\(709\) 392.483i 0.553572i −0.960932 0.276786i \(-0.910731\pi\)
0.960932 0.276786i \(-0.0892694\pi\)
\(710\) 194.253i 0.273596i
\(711\) 135.397i 0.190432i
\(712\) 522.896i 0.734405i
\(713\) −3.40425 84.9720i −0.00477454 0.119175i
\(714\) 49.6080 0.0694790
\(715\) −1660.51 −2.32239
\(716\) 992.477 1.38614
\(717\) −574.542 −0.801314
\(718\) 24.0585i 0.0335076i
\(719\) 126.909 0.176507 0.0882536 0.996098i \(-0.471871\pi\)
0.0882536 + 0.996098i \(0.471871\pi\)
\(720\) 234.403i 0.325560i
\(721\) −135.995 −0.188621
\(722\) −225.600 −0.312466
\(723\) 459.775i 0.635926i
\(724\) 294.809i 0.407194i
\(725\) −197.781 −0.272802
\(726\) −232.936 −0.320849
\(727\) 335.134i 0.460982i 0.973075 + 0.230491i \(0.0740332\pi\)
−0.973075 + 0.230491i \(0.925967\pi\)
\(728\) 173.257i 0.237991i
\(729\) 27.0000 0.0370370
\(730\) 761.384i 1.04299i
\(731\) 158.892 0.217363
\(732\) 562.421i 0.768335i
\(733\) 839.520i 1.14532i 0.819793 + 0.572660i \(0.194089\pi\)
−0.819793 + 0.572660i \(0.805911\pi\)
\(734\) 8.00433i 0.0109051i
\(735\) 98.3174i 0.133765i
\(736\) 27.0607 + 675.451i 0.0367673 + 0.917733i
\(737\) −879.943 −1.19395
\(738\) 168.456 0.228260
\(739\) 146.458 0.198184 0.0990921 0.995078i \(-0.468406\pi\)
0.0990921 + 0.995078i \(0.468406\pi\)
\(740\) −759.871 −1.02685
\(741\) 156.260i 0.210877i
\(742\) 0.524397 0.000706735
\(743\) 1227.58i 1.65219i 0.563531 + 0.826095i \(0.309442\pi\)
−0.563531 + 0.826095i \(0.690558\pi\)
\(744\) −35.5511 −0.0477838
\(745\) −614.985 −0.825483
\(746\) 155.967i 0.209071i
\(747\) 358.193i 0.479509i
\(748\) 867.780 1.16013
\(749\) −496.844 −0.663343
\(750\) 165.049i 0.220065i
\(751\) 5.77510i 0.00768987i 0.999993 + 0.00384494i \(0.00122388\pi\)
−0.999993 + 0.00384494i \(0.998776\pi\)
\(752\) −614.814 −0.817572
\(753\) 397.899i 0.528419i
\(754\) −42.6900 −0.0566180
\(755\) 139.403i 0.184640i
\(756\) 47.3450i 0.0626256i
\(757\) 451.516i 0.596455i 0.954495 + 0.298227i \(0.0963954\pi\)
−0.954495 + 0.298227i \(0.903605\pi\)
\(758\) 169.652i 0.223815i
\(759\) 690.978 27.6828i 0.910379 0.0364727i
\(760\) 344.277 0.452996
\(761\) 258.765 0.340033 0.170016 0.985441i \(-0.445618\pi\)
0.170016 + 0.985441i \(0.445618\pi\)
\(762\) 285.532 0.374714
\(763\) −210.889 −0.276394
\(764\) 115.349i 0.150980i
\(765\) −353.131 −0.461609
\(766\) 267.321i 0.348983i
\(767\) 1293.07 1.68587
\(768\) 52.7025 0.0686230
\(769\) 295.640i 0.384447i −0.981351 0.192223i \(-0.938430\pi\)
0.981351 0.192223i \(-0.0615698\pi\)
\(770\) 277.744i 0.360706i
\(771\) −509.618 −0.660983
\(772\) −640.357 −0.829478
\(773\) 1385.11i 1.79186i −0.444195 0.895930i \(-0.646510\pi\)
0.444195 0.895930i \(-0.353490\pi\)
\(774\) 24.4896i 0.0316403i
\(775\) −150.696 −0.194446
\(776\) 299.207i 0.385576i
\(777\) 124.691 0.160477
\(778\) 238.760i 0.306890i
\(779\) 575.845i 0.739211i
\(780\) 570.587i 0.731522i
\(781\) 557.597i 0.713953i
\(782\) 248.784 9.96707i 0.318138 0.0127456i
\(783\) −25.2152 −0.0322033
\(784\) −67.4478 −0.0860304
\(785\) −1410.29 −1.79655
\(786\) −155.706 −0.198099
\(787\) 548.275i 0.696665i 0.937371 + 0.348332i \(0.113252\pi\)
−0.937371 + 0.348332i \(0.886748\pi\)
\(788\) 663.815 0.842405
\(789\) 85.8002i 0.108746i
\(790\) −272.936 −0.345488
\(791\) 2.79026 0.00352751