Properties

Label 690.3.c.a.91.19
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.19
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.22

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +1.37049i q^{7} +2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +1.37049i q^{7} +2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} +12.6432i q^{11} -3.46410 q^{12} -17.1953 q^{13} +1.93817i q^{14} +3.87298i q^{15} +4.00000 q^{16} +17.1987i q^{17} +4.24264 q^{18} +5.73865i q^{19} -4.47214i q^{20} -2.37376i q^{21} +17.8802i q^{22} +(22.4818 + 4.85478i) q^{23} -4.89898 q^{24} -5.00000 q^{25} -24.3178 q^{26} -5.19615 q^{27} +2.74098i q^{28} +19.0719 q^{29} +5.47723i q^{30} +27.6139 q^{31} +5.65685 q^{32} -21.8987i q^{33} +24.3226i q^{34} +3.06451 q^{35} +6.00000 q^{36} +28.5685i q^{37} +8.11568i q^{38} +29.7831 q^{39} -6.32456i q^{40} -40.8110 q^{41} -3.35700i q^{42} +33.6014i q^{43} +25.2864i q^{44} -6.70820i q^{45} +(31.7941 + 6.86570i) q^{46} -36.0593 q^{47} -6.92820 q^{48} +47.1218 q^{49} -7.07107 q^{50} -29.7890i q^{51} -34.3906 q^{52} +72.1605i q^{53} -7.34847 q^{54} +28.2711 q^{55} +3.87633i q^{56} -9.93963i q^{57} +26.9718 q^{58} +33.0861 q^{59} +7.74597i q^{60} +102.589i q^{61} +39.0519 q^{62} +4.11147i q^{63} +8.00000 q^{64} +38.4498i q^{65} -30.9694i q^{66} +83.7272i q^{67} +34.3974i q^{68} +(-38.9396 - 8.40873i) q^{69} +4.33387 q^{70} -53.3503 q^{71} +8.48528 q^{72} -6.09068 q^{73} +40.4019i q^{74} +8.66025 q^{75} +11.4773i q^{76} -17.3274 q^{77} +42.1197 q^{78} -16.0407i q^{79} -8.94427i q^{80} +9.00000 q^{81} -57.7155 q^{82} -119.789i q^{83} -4.74752i q^{84} +38.4574 q^{85} +47.5196i q^{86} -33.0335 q^{87} +35.7604i q^{88} -71.6620i q^{89} -9.48683i q^{90} -23.5660i q^{91} +(44.9636 + 9.70956i) q^{92} -47.8286 q^{93} -50.9955 q^{94} +12.8320 q^{95} -9.79796 q^{96} -47.4489i q^{97} +66.6402 q^{98} +37.9297i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −1.73205 −0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −2.44949 −0.408248
\(7\) 1.37049i 0.195784i 0.995197 + 0.0978922i \(0.0312100\pi\)
−0.995197 + 0.0978922i \(0.968790\pi\)
\(8\) 2.82843 0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 12.6432i 1.14938i 0.818370 + 0.574692i \(0.194878\pi\)
−0.818370 + 0.574692i \(0.805122\pi\)
\(12\) −3.46410 −0.288675
\(13\) −17.1953 −1.32271 −0.661357 0.750071i \(-0.730019\pi\)
−0.661357 + 0.750071i \(0.730019\pi\)
\(14\) 1.93817i 0.138440i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 17.1987i 1.01169i 0.862625 + 0.505844i \(0.168819\pi\)
−0.862625 + 0.505844i \(0.831181\pi\)
\(18\) 4.24264 0.235702
\(19\) 5.73865i 0.302034i 0.988531 + 0.151017i \(0.0482548\pi\)
−0.988531 + 0.151017i \(0.951745\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 2.37376i 0.113036i
\(22\) 17.8802i 0.812737i
\(23\) 22.4818 + 4.85478i 0.977469 + 0.211077i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) −24.3178 −0.935301
\(27\) −5.19615 −0.192450
\(28\) 2.74098i 0.0978922i
\(29\) 19.0719 0.657653 0.328826 0.944390i \(-0.393347\pi\)
0.328826 + 0.944390i \(0.393347\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 27.6139 0.890770 0.445385 0.895339i \(-0.353067\pi\)
0.445385 + 0.895339i \(0.353067\pi\)
\(32\) 5.65685 0.176777
\(33\) 21.8987i 0.663597i
\(34\) 24.3226i 0.715371i
\(35\) 3.06451 0.0875574
\(36\) 6.00000 0.166667
\(37\) 28.5685i 0.772120i 0.922474 + 0.386060i \(0.126164\pi\)
−0.922474 + 0.386060i \(0.873836\pi\)
\(38\) 8.11568i 0.213570i
\(39\) 29.7831 0.763670
\(40\) 6.32456i 0.158114i
\(41\) −40.8110 −0.995391 −0.497695 0.867352i \(-0.665820\pi\)
−0.497695 + 0.867352i \(0.665820\pi\)
\(42\) 3.35700i 0.0799286i
\(43\) 33.6014i 0.781428i 0.920512 + 0.390714i \(0.127772\pi\)
−0.920512 + 0.390714i \(0.872228\pi\)
\(44\) 25.2864i 0.574692i
\(45\) 6.70820i 0.149071i
\(46\) 31.7941 + 6.86570i 0.691175 + 0.149254i
\(47\) −36.0593 −0.767218 −0.383609 0.923496i \(-0.625319\pi\)
−0.383609 + 0.923496i \(0.625319\pi\)
\(48\) −6.92820 −0.144338
\(49\) 47.1218 0.961668
\(50\) −7.07107 −0.141421
\(51\) 29.7890i 0.584098i
\(52\) −34.3906 −0.661357
\(53\) 72.1605i 1.36152i 0.732507 + 0.680760i \(0.238350\pi\)
−0.732507 + 0.680760i \(0.761650\pi\)
\(54\) −7.34847 −0.136083
\(55\) 28.2711 0.514020
\(56\) 3.87633i 0.0692202i
\(57\) 9.93963i 0.174380i
\(58\) 26.9718 0.465031
\(59\) 33.0861 0.560781 0.280391 0.959886i \(-0.409536\pi\)
0.280391 + 0.959886i \(0.409536\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 102.589i 1.68179i 0.541196 + 0.840896i \(0.317972\pi\)
−0.541196 + 0.840896i \(0.682028\pi\)
\(62\) 39.0519 0.629869
\(63\) 4.11147i 0.0652615i
\(64\) 8.00000 0.125000
\(65\) 38.4498i 0.591536i
\(66\) 30.9694i 0.469234i
\(67\) 83.7272i 1.24966i 0.780761 + 0.624830i \(0.214832\pi\)
−0.780761 + 0.624830i \(0.785168\pi\)
\(68\) 34.3974i 0.505844i
\(69\) −38.9396 8.40873i −0.564342 0.121866i
\(70\) 4.33387 0.0619125
\(71\) −53.3503 −0.751413 −0.375706 0.926739i \(-0.622600\pi\)
−0.375706 + 0.926739i \(0.622600\pi\)
\(72\) 8.48528 0.117851
\(73\) −6.09068 −0.0834340 −0.0417170 0.999129i \(-0.513283\pi\)
−0.0417170 + 0.999129i \(0.513283\pi\)
\(74\) 40.4019i 0.545971i
\(75\) 8.66025 0.115470
\(76\) 11.4773i 0.151017i
\(77\) −17.3274 −0.225031
\(78\) 42.1197 0.539996
\(79\) 16.0407i 0.203047i −0.994833 0.101524i \(-0.967628\pi\)
0.994833 0.101524i \(-0.0323718\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −57.7155 −0.703848
\(83\) 119.789i 1.44325i −0.692287 0.721623i \(-0.743397\pi\)
0.692287 0.721623i \(-0.256603\pi\)
\(84\) 4.74752i 0.0565181i
\(85\) 38.4574 0.452440
\(86\) 47.5196i 0.552553i
\(87\) −33.0335 −0.379696
\(88\) 35.7604i 0.406369i
\(89\) 71.6620i 0.805191i −0.915378 0.402596i \(-0.868108\pi\)
0.915378 0.402596i \(-0.131892\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 23.5660i 0.258967i
\(92\) 44.9636 + 9.70956i 0.488735 + 0.105539i
\(93\) −47.8286 −0.514286
\(94\) −50.9955 −0.542505
\(95\) 12.8320 0.135074
\(96\) −9.79796 −0.102062
\(97\) 47.4489i 0.489164i −0.969629 0.244582i \(-0.921349\pi\)
0.969629 0.244582i \(-0.0786507\pi\)
\(98\) 66.6402 0.680002
\(99\) 37.9297i 0.383128i
\(100\) −10.0000 −0.100000
\(101\) −25.2315 −0.249817 −0.124908 0.992168i \(-0.539864\pi\)
−0.124908 + 0.992168i \(0.539864\pi\)
\(102\) 42.1280i 0.413020i
\(103\) 102.361i 0.993800i −0.867808 0.496900i \(-0.834471\pi\)
0.867808 0.496900i \(-0.165529\pi\)
\(104\) −48.6356 −0.467650
\(105\) −5.30789 −0.0505513
\(106\) 102.050i 0.962740i
\(107\) 99.6919i 0.931700i −0.884864 0.465850i \(-0.845749\pi\)
0.884864 0.465850i \(-0.154251\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 70.6544i 0.648205i 0.946022 + 0.324103i \(0.105062\pi\)
−0.946022 + 0.324103i \(0.894938\pi\)
\(110\) 39.9814 0.363467
\(111\) 49.4820i 0.445784i
\(112\) 5.48196i 0.0489461i
\(113\) 117.729i 1.04185i 0.853603 + 0.520924i \(0.174413\pi\)
−0.853603 + 0.520924i \(0.825587\pi\)
\(114\) 14.0568i 0.123305i
\(115\) 10.8556 50.2708i 0.0943967 0.437138i
\(116\) 38.1438 0.328826
\(117\) −51.5859 −0.440905
\(118\) 46.7908 0.396532
\(119\) −23.5706 −0.198073
\(120\) 10.9545i 0.0912871i
\(121\) −38.8511 −0.321084
\(122\) 145.083i 1.18921i
\(123\) 70.6868 0.574689
\(124\) 55.2277 0.445385
\(125\) 11.1803i 0.0894427i
\(126\) 5.81450i 0.0461468i
\(127\) −210.520 −1.65764 −0.828819 0.559516i \(-0.810987\pi\)
−0.828819 + 0.559516i \(0.810987\pi\)
\(128\) 11.3137 0.0883883
\(129\) 58.1994i 0.451158i
\(130\) 54.3763i 0.418279i
\(131\) 179.091 1.36711 0.683553 0.729901i \(-0.260434\pi\)
0.683553 + 0.729901i \(0.260434\pi\)
\(132\) 43.7974i 0.331799i
\(133\) −7.86477 −0.0591336
\(134\) 118.408i 0.883643i
\(135\) 11.6190i 0.0860663i
\(136\) 48.6452i 0.357685i
\(137\) 68.6261i 0.500921i −0.968127 0.250460i \(-0.919418\pi\)
0.968127 0.250460i \(-0.0805820\pi\)
\(138\) −55.0689 11.8917i −0.399050 0.0861720i
\(139\) 35.6149 0.256222 0.128111 0.991760i \(-0.459109\pi\)
0.128111 + 0.991760i \(0.459109\pi\)
\(140\) 6.12902 0.0437787
\(141\) 62.4565 0.442954
\(142\) −75.4487 −0.531329
\(143\) 217.404i 1.52031i
\(144\) 12.0000 0.0833333
\(145\) 42.6461i 0.294111i
\(146\) −8.61352 −0.0589967
\(147\) −81.6173 −0.555220
\(148\) 57.1369i 0.386060i
\(149\) 169.122i 1.13505i −0.823356 0.567525i \(-0.807901\pi\)
0.823356 0.567525i \(-0.192099\pi\)
\(150\) 12.2474 0.0816497
\(151\) 51.9046 0.343739 0.171870 0.985120i \(-0.445019\pi\)
0.171870 + 0.985120i \(0.445019\pi\)
\(152\) 16.2314i 0.106785i
\(153\) 51.5960i 0.337229i
\(154\) −24.5047 −0.159121
\(155\) 61.7465i 0.398364i
\(156\) 59.5662 0.381835
\(157\) 103.070i 0.656500i 0.944591 + 0.328250i \(0.106459\pi\)
−0.944591 + 0.328250i \(0.893541\pi\)
\(158\) 22.6850i 0.143576i
\(159\) 124.986i 0.786074i
\(160\) 12.6491i 0.0790569i
\(161\) −6.65343 + 30.8111i −0.0413257 + 0.191373i
\(162\) 12.7279 0.0785674
\(163\) 56.7509 0.348165 0.174083 0.984731i \(-0.444304\pi\)
0.174083 + 0.984731i \(0.444304\pi\)
\(164\) −81.6220 −0.497695
\(165\) −48.9670 −0.296770
\(166\) 169.408i 1.02053i
\(167\) −309.988 −1.85622 −0.928108 0.372310i \(-0.878566\pi\)
−0.928108 + 0.372310i \(0.878566\pi\)
\(168\) 6.71401i 0.0399643i
\(169\) 126.678 0.749575
\(170\) 54.3870 0.319924
\(171\) 17.2159i 0.100678i
\(172\) 67.2028i 0.390714i
\(173\) 301.774 1.74436 0.872179 0.489186i \(-0.162706\pi\)
0.872179 + 0.489186i \(0.162706\pi\)
\(174\) −46.7165 −0.268486
\(175\) 6.85245i 0.0391569i
\(176\) 50.5729i 0.287346i
\(177\) −57.3068 −0.323767
\(178\) 101.345i 0.569356i
\(179\) −66.8168 −0.373278 −0.186639 0.982429i \(-0.559760\pi\)
−0.186639 + 0.982429i \(0.559760\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 140.236i 0.774785i −0.921915 0.387392i \(-0.873376\pi\)
0.921915 0.387392i \(-0.126624\pi\)
\(182\) 33.3273i 0.183117i
\(183\) 177.690i 0.970983i
\(184\) 63.5881 + 13.7314i 0.345588 + 0.0746271i
\(185\) 63.8810 0.345303
\(186\) −67.6399 −0.363655
\(187\) −217.447 −1.16282
\(188\) −72.1185 −0.383609
\(189\) 7.12128i 0.0376787i
\(190\) 18.1472 0.0955116
\(191\) 345.209i 1.80738i −0.428190 0.903689i \(-0.640849\pi\)
0.428190 0.903689i \(-0.359151\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 186.257 0.965062 0.482531 0.875879i \(-0.339718\pi\)
0.482531 + 0.875879i \(0.339718\pi\)
\(194\) 67.1028i 0.345891i
\(195\) 66.5971i 0.341524i
\(196\) 94.2435 0.480834
\(197\) −279.423 −1.41839 −0.709196 0.705012i \(-0.750942\pi\)
−0.709196 + 0.705012i \(0.750942\pi\)
\(198\) 53.6407i 0.270912i
\(199\) 45.7328i 0.229813i −0.993376 0.114907i \(-0.963343\pi\)
0.993376 0.114907i \(-0.0366569\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 145.020i 0.721491i
\(202\) −35.6827 −0.176647
\(203\) 26.1379i 0.128758i
\(204\) 59.5780i 0.292049i
\(205\) 91.2562i 0.445152i
\(206\) 144.761i 0.702723i
\(207\) 67.4454 + 14.5643i 0.325823 + 0.0703591i
\(208\) −68.7812 −0.330679
\(209\) −72.5550 −0.347153
\(210\) −7.50649 −0.0357452
\(211\) 307.575 1.45770 0.728851 0.684673i \(-0.240055\pi\)
0.728851 + 0.684673i \(0.240055\pi\)
\(212\) 144.321i 0.680760i
\(213\) 92.4055 0.433828
\(214\) 140.986i 0.658811i
\(215\) 75.1351 0.349465
\(216\) −14.6969 −0.0680414
\(217\) 37.8445i 0.174399i
\(218\) 99.9204i 0.458350i
\(219\) 10.5494 0.0481706
\(220\) 56.5422 0.257010
\(221\) 295.736i 1.33817i
\(222\) 69.9781i 0.315217i
\(223\) −356.509 −1.59870 −0.799348 0.600869i \(-0.794821\pi\)
−0.799348 + 0.600869i \(0.794821\pi\)
\(224\) 7.75267i 0.0346101i
\(225\) −15.0000 −0.0666667
\(226\) 166.494i 0.736698i
\(227\) 167.195i 0.736542i −0.929719 0.368271i \(-0.879950\pi\)
0.929719 0.368271i \(-0.120050\pi\)
\(228\) 19.8793i 0.0871898i
\(229\) 281.250i 1.22817i 0.789242 + 0.614083i \(0.210474\pi\)
−0.789242 + 0.614083i \(0.789526\pi\)
\(230\) 15.3522 71.0937i 0.0667485 0.309103i
\(231\) 30.0120 0.129922
\(232\) 53.9435 0.232515
\(233\) 60.2115 0.258419 0.129209 0.991617i \(-0.458756\pi\)
0.129209 + 0.991617i \(0.458756\pi\)
\(234\) −72.9535 −0.311767
\(235\) 80.6309i 0.343110i
\(236\) 66.1722 0.280391
\(237\) 27.7834i 0.117229i
\(238\) −33.3339 −0.140058
\(239\) 44.8445 0.187634 0.0938170 0.995589i \(-0.470093\pi\)
0.0938170 + 0.995589i \(0.470093\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 0.284271i 0.00117955i 1.00000 0.000589774i \(0.000187731\pi\)
−1.00000 0.000589774i \(0.999812\pi\)
\(242\) −54.9438 −0.227040
\(243\) −15.5885 −0.0641500
\(244\) 205.179i 0.840896i
\(245\) 105.367i 0.430071i
\(246\) 99.9662 0.406367
\(247\) 98.6778i 0.399505i
\(248\) 78.1038 0.314935
\(249\) 207.481i 0.833258i
\(250\) 15.8114i 0.0632456i
\(251\) 219.635i 0.875041i 0.899208 + 0.437521i \(0.144143\pi\)
−0.899208 + 0.437521i \(0.855857\pi\)
\(252\) 8.22294i 0.0326307i
\(253\) −61.3801 + 284.242i −0.242609 + 1.12349i
\(254\) −297.720 −1.17213
\(255\) −66.6102 −0.261216
\(256\) 16.0000 0.0625000
\(257\) −83.7888 −0.326026 −0.163013 0.986624i \(-0.552121\pi\)
−0.163013 + 0.986624i \(0.552121\pi\)
\(258\) 82.3063i 0.319017i
\(259\) −39.1528 −0.151169
\(260\) 76.8997i 0.295768i
\(261\) 57.2158 0.219218
\(262\) 253.273 0.966690
\(263\) 52.1022i 0.198107i −0.995082 0.0990536i \(-0.968418\pi\)
0.995082 0.0990536i \(-0.0315815\pi\)
\(264\) 61.9389i 0.234617i
\(265\) 161.356 0.608890
\(266\) −11.1225 −0.0418138
\(267\) 124.122i 0.464877i
\(268\) 167.454i 0.624830i
\(269\) −317.806 −1.18143 −0.590717 0.806879i \(-0.701155\pi\)
−0.590717 + 0.806879i \(0.701155\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −249.647 −0.921207 −0.460604 0.887606i \(-0.652367\pi\)
−0.460604 + 0.887606i \(0.652367\pi\)
\(272\) 68.7947i 0.252922i
\(273\) 40.8175i 0.149515i
\(274\) 97.0520i 0.354204i
\(275\) 63.2161i 0.229877i
\(276\) −77.8792 16.8175i −0.282171 0.0609328i
\(277\) −35.6857 −0.128829 −0.0644146 0.997923i \(-0.520518\pi\)
−0.0644146 + 0.997923i \(0.520518\pi\)
\(278\) 50.3670 0.181176
\(279\) 82.8416 0.296923
\(280\) 8.66774 0.0309562
\(281\) 237.163i 0.843996i 0.906597 + 0.421998i \(0.138671\pi\)
−0.906597 + 0.421998i \(0.861329\pi\)
\(282\) 88.3268 0.313215
\(283\) 284.190i 1.00420i 0.864809 + 0.502102i \(0.167440\pi\)
−0.864809 + 0.502102i \(0.832560\pi\)
\(284\) −106.701 −0.375706
\(285\) −22.2257 −0.0779849
\(286\) 307.456i 1.07502i
\(287\) 55.9311i 0.194882i
\(288\) 16.9706 0.0589256
\(289\) −6.79461 −0.0235108
\(290\) 60.3107i 0.207968i
\(291\) 82.1839i 0.282419i
\(292\) −12.1814 −0.0417170
\(293\) 551.696i 1.88292i −0.337124 0.941460i \(-0.609454\pi\)
0.337124 0.941460i \(-0.390546\pi\)
\(294\) −115.424 −0.392600
\(295\) 73.9828i 0.250789i
\(296\) 80.8038i 0.272986i
\(297\) 65.6961i 0.221199i
\(298\) 239.175i 0.802601i
\(299\) −386.581 83.4794i −1.29291 0.279195i
\(300\) 17.3205 0.0577350
\(301\) −46.0504 −0.152991
\(302\) 73.4042 0.243060
\(303\) 43.7022 0.144232
\(304\) 22.9546i 0.0755085i
\(305\) 229.397 0.752120
\(306\) 72.9678i 0.238457i
\(307\) 96.3675 0.313901 0.156950 0.987606i \(-0.449834\pi\)
0.156950 + 0.987606i \(0.449834\pi\)
\(308\) −34.6548 −0.112516
\(309\) 177.295i 0.573771i
\(310\) 87.3227i 0.281686i
\(311\) 423.308 1.36112 0.680560 0.732693i \(-0.261737\pi\)
0.680560 + 0.732693i \(0.261737\pi\)
\(312\) 84.2394 0.269998
\(313\) 58.3745i 0.186500i −0.995643 0.0932500i \(-0.970274\pi\)
0.995643 0.0932500i \(-0.0297256\pi\)
\(314\) 145.764i 0.464215i
\(315\) 9.19353 0.0291858
\(316\) 32.0815i 0.101524i
\(317\) 60.9213 0.192181 0.0960904 0.995373i \(-0.469366\pi\)
0.0960904 + 0.995373i \(0.469366\pi\)
\(318\) 176.757i 0.555838i
\(319\) 241.131i 0.755895i
\(320\) 17.8885i 0.0559017i
\(321\) 172.671i 0.537917i
\(322\) −9.40937 + 43.5735i −0.0292217 + 0.135321i
\(323\) −98.6972 −0.305564
\(324\) 18.0000 0.0555556
\(325\) 85.9765 0.264543
\(326\) 80.2579 0.246190
\(327\) 122.377i 0.374242i
\(328\) −115.431 −0.351924
\(329\) 49.4189i 0.150209i
\(330\) −69.2498 −0.209848
\(331\) 245.050 0.740332 0.370166 0.928966i \(-0.379301\pi\)
0.370166 + 0.928966i \(0.379301\pi\)
\(332\) 239.579i 0.721623i
\(333\) 85.7054i 0.257373i
\(334\) −438.390 −1.31254
\(335\) 187.220 0.558865
\(336\) 9.49504i 0.0282590i
\(337\) 570.626i 1.69325i 0.532188 + 0.846626i \(0.321370\pi\)
−0.532188 + 0.846626i \(0.678630\pi\)
\(338\) 179.150 0.530029
\(339\) 203.912i 0.601512i
\(340\) 76.9148 0.226220
\(341\) 349.128i 1.02384i
\(342\) 24.3470i 0.0711901i
\(343\) 131.734i 0.384064i
\(344\) 95.0392i 0.276277i
\(345\) −18.8025 + 87.0716i −0.0545000 + 0.252381i
\(346\) 426.773 1.23345
\(347\) 72.5341 0.209032 0.104516 0.994523i \(-0.466671\pi\)
0.104516 + 0.994523i \(0.466671\pi\)
\(348\) −66.0671 −0.189848
\(349\) 436.542 1.25084 0.625418 0.780290i \(-0.284928\pi\)
0.625418 + 0.780290i \(0.284928\pi\)
\(350\) 9.69083i 0.0276881i
\(351\) 89.3494 0.254557
\(352\) 71.5209i 0.203184i
\(353\) −33.3967 −0.0946081 −0.0473040 0.998881i \(-0.515063\pi\)
−0.0473040 + 0.998881i \(0.515063\pi\)
\(354\) −81.0441 −0.228938
\(355\) 119.295i 0.336042i
\(356\) 143.324i 0.402596i
\(357\) 40.8255 0.114357
\(358\) −94.4932 −0.263948
\(359\) 348.492i 0.970730i −0.874312 0.485365i \(-0.838687\pi\)
0.874312 0.485365i \(-0.161313\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 328.068 0.908775
\(362\) 198.324i 0.547855i
\(363\) 67.2921 0.185378
\(364\) 47.1320i 0.129483i
\(365\) 13.6192i 0.0373128i
\(366\) 251.292i 0.686589i
\(367\) 42.8645i 0.116797i 0.998293 + 0.0583985i \(0.0185994\pi\)
−0.998293 + 0.0583985i \(0.981401\pi\)
\(368\) 89.9272 + 19.4191i 0.244367 + 0.0527694i
\(369\) −122.433 −0.331797
\(370\) 90.3414 0.244166
\(371\) −98.8954 −0.266564
\(372\) −95.6572 −0.257143
\(373\) 548.173i 1.46963i 0.678266 + 0.734817i \(0.262732\pi\)
−0.678266 + 0.734817i \(0.737268\pi\)
\(374\) −307.516 −0.822236
\(375\) 19.3649i 0.0516398i
\(376\) −101.991 −0.271253
\(377\) −327.947 −0.869887
\(378\) 10.0710i 0.0266429i
\(379\) 575.949i 1.51966i −0.650125 0.759828i \(-0.725283\pi\)
0.650125 0.759828i \(-0.274717\pi\)
\(380\) 25.6640 0.0675369
\(381\) 364.632 0.957038
\(382\) 488.199i 1.27801i
\(383\) 485.343i 1.26721i −0.773655 0.633607i \(-0.781574\pi\)
0.773655 0.633607i \(-0.218426\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 38.7453i 0.100637i
\(386\) 263.407 0.682402
\(387\) 100.804i 0.260476i
\(388\) 94.8977i 0.244582i
\(389\) 34.6469i 0.0890666i 0.999008 + 0.0445333i \(0.0141801\pi\)
−0.999008 + 0.0445333i \(0.985820\pi\)
\(390\) 94.1825i 0.241494i
\(391\) −83.4958 + 386.657i −0.213544 + 0.988893i
\(392\) 133.280 0.340001
\(393\) −310.194 −0.789299
\(394\) −395.164 −1.00295
\(395\) −35.8682 −0.0908055
\(396\) 75.8593i 0.191564i
\(397\) −576.948 −1.45327 −0.726635 0.687024i \(-0.758917\pi\)
−0.726635 + 0.687024i \(0.758917\pi\)
\(398\) 64.6760i 0.162502i
\(399\) 13.6222 0.0341408
\(400\) −20.0000 −0.0500000
\(401\) 627.475i 1.56477i −0.622792 0.782387i \(-0.714002\pi\)
0.622792 0.782387i \(-0.285998\pi\)
\(402\) 205.089i 0.510171i
\(403\) −474.828 −1.17823
\(404\) −50.4630 −0.124908
\(405\) 20.1246i 0.0496904i
\(406\) 36.9646i 0.0910457i
\(407\) −361.197 −0.887463
\(408\) 84.2560i 0.206510i
\(409\) 22.7131 0.0555333 0.0277666 0.999614i \(-0.491160\pi\)
0.0277666 + 0.999614i \(0.491160\pi\)
\(410\) 129.056i 0.314770i
\(411\) 118.864i 0.289207i
\(412\) 204.723i 0.496900i
\(413\) 45.3442i 0.109792i
\(414\) 95.3822 + 20.5971i 0.230392 + 0.0497514i
\(415\) −267.857 −0.645439
\(416\) −97.2713 −0.233825
\(417\) −61.6868 −0.147930
\(418\) −102.608 −0.245474
\(419\) 212.213i 0.506474i 0.967404 + 0.253237i \(0.0814952\pi\)
−0.967404 + 0.253237i \(0.918505\pi\)
\(420\) −10.6158 −0.0252757
\(421\) 592.278i 1.40684i 0.710776 + 0.703419i \(0.248344\pi\)
−0.710776 + 0.703419i \(0.751656\pi\)
\(422\) 434.977 1.03075
\(423\) −108.178 −0.255739
\(424\) 204.101i 0.481370i
\(425\) 85.9934i 0.202337i
\(426\) 130.681 0.306763
\(427\) −140.598 −0.329269
\(428\) 199.384i 0.465850i
\(429\) 376.555i 0.877750i
\(430\) 106.257 0.247109
\(431\) 333.504i 0.773791i −0.922124 0.386895i \(-0.873547\pi\)
0.922124 0.386895i \(-0.126453\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 61.7200i 0.142540i 0.997457 + 0.0712702i \(0.0227053\pi\)
−0.997457 + 0.0712702i \(0.977295\pi\)
\(434\) 53.5203i 0.123319i
\(435\) 73.8652i 0.169805i
\(436\) 141.309i 0.324103i
\(437\) −27.8599 + 129.015i −0.0637526 + 0.295229i
\(438\) 14.9191 0.0340618
\(439\) 858.490 1.95556 0.977779 0.209640i \(-0.0672293\pi\)
0.977779 + 0.209640i \(0.0672293\pi\)
\(440\) 79.9628 0.181734
\(441\) 141.365 0.320556
\(442\) 418.234i 0.946232i
\(443\) 707.452 1.59696 0.798479 0.602023i \(-0.205638\pi\)
0.798479 + 0.602023i \(0.205638\pi\)
\(444\) 98.9640i 0.222892i
\(445\) −160.241 −0.360092
\(446\) −504.180 −1.13045
\(447\) 292.929i 0.655321i
\(448\) 10.9639i 0.0244730i
\(449\) −27.9221 −0.0621873 −0.0310936 0.999516i \(-0.509899\pi\)
−0.0310936 + 0.999516i \(0.509899\pi\)
\(450\) −21.2132 −0.0471405
\(451\) 515.983i 1.14409i
\(452\) 235.458i 0.520924i
\(453\) −89.9014 −0.198458
\(454\) 236.449i 0.520813i
\(455\) −52.6952 −0.115814
\(456\) 28.1135i 0.0616525i
\(457\) 391.345i 0.856335i 0.903699 + 0.428167i \(0.140841\pi\)
−0.903699 + 0.428167i \(0.859159\pi\)
\(458\) 397.748i 0.868444i
\(459\) 89.3670i 0.194699i
\(460\) 21.7112 100.542i 0.0471983 0.218569i
\(461\) 358.584 0.777841 0.388920 0.921271i \(-0.372848\pi\)
0.388920 + 0.921271i \(0.372848\pi\)
\(462\) 42.4433 0.0918687
\(463\) −49.7419 −0.107434 −0.0537169 0.998556i \(-0.517107\pi\)
−0.0537169 + 0.998556i \(0.517107\pi\)
\(464\) 76.2877 0.164413
\(465\) 106.948i 0.229996i
\(466\) 85.1519 0.182729
\(467\) 7.85966i 0.0168301i −0.999965 0.00841505i \(-0.997321\pi\)
0.999965 0.00841505i \(-0.00267863\pi\)
\(468\) −103.172 −0.220452
\(469\) −114.747 −0.244664
\(470\) 114.029i 0.242616i
\(471\) 178.523i 0.379030i
\(472\) 93.5816 0.198266
\(473\) −424.830 −0.898161
\(474\) 39.2916i 0.0828937i
\(475\) 28.6932i 0.0604068i
\(476\) −47.1413 −0.0990363
\(477\) 216.482i 0.453840i
\(478\) 63.4197 0.132677
\(479\) 567.601i 1.18497i 0.805581 + 0.592486i \(0.201853\pi\)
−0.805581 + 0.592486i \(0.798147\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 491.243i 1.02129i
\(482\) 0.402020i 0.000834067i
\(483\) 11.5241 53.3664i 0.0238594 0.110489i
\(484\) −77.7022 −0.160542
\(485\) −106.099 −0.218761
\(486\) −22.0454 −0.0453609
\(487\) 374.905 0.769825 0.384913 0.922953i \(-0.374232\pi\)
0.384913 + 0.922953i \(0.374232\pi\)
\(488\) 290.166i 0.594603i
\(489\) −98.2955 −0.201013
\(490\) 149.012i 0.304106i
\(491\) −412.426 −0.839971 −0.419985 0.907531i \(-0.637965\pi\)
−0.419985 + 0.907531i \(0.637965\pi\)
\(492\) 141.374 0.287345
\(493\) 328.012i 0.665339i
\(494\) 139.551i 0.282493i
\(495\) 84.8133 0.171340
\(496\) 110.455 0.222692
\(497\) 73.1161i 0.147115i
\(498\) 293.423i 0.589202i
\(499\) 327.529 0.656370 0.328185 0.944613i \(-0.393563\pi\)
0.328185 + 0.944613i \(0.393563\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 536.915 1.07169
\(502\) 310.611i 0.618748i
\(503\) 636.770i 1.26595i 0.774174 + 0.632973i \(0.218165\pi\)
−0.774174 + 0.632973i \(0.781835\pi\)
\(504\) 11.6290i 0.0230734i
\(505\) 56.4193i 0.111721i
\(506\) −86.8045 + 401.979i −0.171550 + 0.794426i
\(507\) −219.413 −0.432767
\(508\) −421.040 −0.828819
\(509\) 125.717 0.246988 0.123494 0.992345i \(-0.460590\pi\)
0.123494 + 0.992345i \(0.460590\pi\)
\(510\) −94.2011 −0.184708
\(511\) 8.34722i 0.0163351i
\(512\) 22.6274 0.0441942
\(513\) 29.8189i 0.0581265i
\(514\) −118.495 −0.230535
\(515\) −228.887 −0.444441
\(516\) 116.399i 0.225579i
\(517\) 455.905i 0.881828i
\(518\) −55.3704 −0.106893
\(519\) −522.688 −1.00711
\(520\) 108.753i 0.209140i
\(521\) 668.477i 1.28306i 0.767096 + 0.641532i \(0.221701\pi\)
−0.767096 + 0.641532i \(0.778299\pi\)
\(522\) 80.9153 0.155010
\(523\) 421.745i 0.806396i −0.915113 0.403198i \(-0.867899\pi\)
0.915113 0.403198i \(-0.132101\pi\)
\(524\) 358.182 0.683553
\(525\) 11.8688i 0.0226072i
\(526\) 73.6837i 0.140083i
\(527\) 474.922i 0.901180i
\(528\) 87.5948i 0.165899i
\(529\) 481.862 + 218.288i 0.910893 + 0.412643i
\(530\) 228.192 0.430550
\(531\) 99.2583 0.186927
\(532\) −15.7295 −0.0295668
\(533\) 701.757 1.31662
\(534\) 175.535i 0.328718i
\(535\) −222.918 −0.416669
\(536\) 236.816i 0.441821i
\(537\) 115.730 0.215512
\(538\) −449.445 −0.835400
\(539\) 595.771i 1.10533i
\(540\) 23.2379i 0.0430331i
\(541\) 769.598 1.42255 0.711273 0.702916i \(-0.248119\pi\)
0.711273 + 0.702916i \(0.248119\pi\)
\(542\) −353.054 −0.651392
\(543\) 242.896i 0.447322i
\(544\) 97.2904i 0.178843i
\(545\) 157.988 0.289886
\(546\) 57.7246i 0.105723i
\(547\) 406.464 0.743079 0.371539 0.928417i \(-0.378830\pi\)
0.371539 + 0.928417i \(0.378830\pi\)
\(548\) 137.252i 0.250460i
\(549\) 307.768i 0.560597i
\(550\) 89.4011i 0.162547i
\(551\) 109.447i 0.198634i
\(552\) −110.138 23.7835i −0.199525 0.0430860i
\(553\) 21.9837 0.0397535
\(554\) −50.4672 −0.0910960
\(555\) −110.645 −0.199361
\(556\) 71.2297 0.128111
\(557\) 753.052i 1.35198i 0.736912 + 0.675989i \(0.236283\pi\)
−0.736912 + 0.675989i \(0.763717\pi\)
\(558\) 117.156 0.209956
\(559\) 577.786i 1.03361i
\(560\) 12.2580 0.0218894
\(561\) 376.629 0.671353
\(562\) 335.399i 0.596796i
\(563\) 79.5409i 0.141280i 0.997502 + 0.0706402i \(0.0225042\pi\)
−0.997502 + 0.0706402i \(0.977496\pi\)
\(564\) 124.913 0.221477
\(565\) 263.250 0.465929
\(566\) 401.905i 0.710079i
\(567\) 12.3344i 0.0217538i
\(568\) −150.897 −0.265665
\(569\) 210.524i 0.369989i 0.982740 + 0.184994i \(0.0592267\pi\)
−0.982740 + 0.184994i \(0.940773\pi\)
\(570\) −31.4319 −0.0551436
\(571\) 243.033i 0.425626i 0.977093 + 0.212813i \(0.0682626\pi\)
−0.977093 + 0.212813i \(0.931737\pi\)
\(572\) 434.808i 0.760154i
\(573\) 597.920i 1.04349i
\(574\) 79.0986i 0.137802i
\(575\) −112.409 24.2739i −0.195494 0.0422155i
\(576\) 24.0000 0.0416667
\(577\) −343.119 −0.594661 −0.297330 0.954775i \(-0.596096\pi\)
−0.297330 + 0.954775i \(0.596096\pi\)
\(578\) −9.60903 −0.0166246
\(579\) −322.606 −0.557179
\(580\) 85.2922i 0.147056i
\(581\) 164.170 0.282565
\(582\) 116.226i 0.199700i
\(583\) −912.342 −1.56491
\(584\) −17.2270 −0.0294984
\(585\) 115.350i 0.197179i
\(586\) 780.216i 1.33143i
\(587\) −664.216 −1.13154 −0.565772 0.824562i \(-0.691422\pi\)
−0.565772 + 0.824562i \(0.691422\pi\)
\(588\) −163.235 −0.277610
\(589\) 158.466i 0.269043i
\(590\) 104.627i 0.177335i
\(591\) 483.975 0.818908
\(592\) 114.274i 0.193030i
\(593\) 614.904 1.03694 0.518469 0.855097i \(-0.326502\pi\)
0.518469 + 0.855097i \(0.326502\pi\)
\(594\) 92.9083i 0.156411i
\(595\) 52.7055i 0.0885807i
\(596\) 338.245i 0.567525i
\(597\) 79.2116i 0.132683i
\(598\) −546.708 118.058i −0.914228 0.197421i
\(599\) 606.007 1.01170 0.505849 0.862622i \(-0.331179\pi\)
0.505849 + 0.862622i \(0.331179\pi\)
\(600\) 24.4949 0.0408248
\(601\) −281.807 −0.468896 −0.234448 0.972129i \(-0.575328\pi\)
−0.234448 + 0.972129i \(0.575328\pi\)
\(602\) −65.1252 −0.108181
\(603\) 251.182i 0.416553i
\(604\) 103.809 0.171870
\(605\) 86.8737i 0.143593i
\(606\) 61.8042 0.101987
\(607\) 2.23403 0.00368044 0.00184022 0.999998i \(-0.499414\pi\)
0.00184022 + 0.999998i \(0.499414\pi\)
\(608\) 32.4627i 0.0533926i
\(609\) 45.2722i 0.0743385i
\(610\) 324.416 0.531829
\(611\) 620.049 1.01481
\(612\) 103.192i 0.168615i
\(613\) 24.5222i 0.0400035i −0.999800 0.0200018i \(-0.993633\pi\)
0.999800 0.0200018i \(-0.00636719\pi\)
\(614\) 136.284 0.221961
\(615\) 158.060i 0.257009i
\(616\) −49.0093 −0.0795606
\(617\) 1084.85i 1.75827i 0.476570 + 0.879137i \(0.341880\pi\)
−0.476570 + 0.879137i \(0.658120\pi\)
\(618\) 250.733i 0.405717i
\(619\) 817.729i 1.32105i −0.750804 0.660525i \(-0.770334\pi\)
0.750804 0.660525i \(-0.229666\pi\)
\(620\) 123.493i 0.199182i
\(621\) −116.819 25.2262i −0.188114 0.0406219i
\(622\) 598.648 0.962457
\(623\) 98.2121 0.157644
\(624\) 119.132 0.190917
\(625\) 25.0000 0.0400000
\(626\) 82.5540i 0.131875i
\(627\) 125.669 0.200429
\(628\) 206.141i 0.328250i
\(629\) −491.340 −0.781144
\(630\) 13.0016 0.0206375
\(631\) 393.978i 0.624371i −0.950021 0.312185i \(-0.898939\pi\)
0.950021 0.312185i \(-0.101061\pi\)
\(632\) 45.3701i 0.0717881i
\(633\) −532.736 −0.841604
\(634\) 86.1558 0.135892
\(635\) 470.737i 0.741319i
\(636\) 249.971i 0.393037i
\(637\) −810.272 −1.27201
\(638\) 341.010i 0.534499i
\(639\) −160.051 −0.250471
\(640\) 25.2982i 0.0395285i
\(641\) 803.224i 1.25308i −0.779389 0.626540i \(-0.784471\pi\)
0.779389 0.626540i \(-0.215529\pi\)
\(642\) 244.194i 0.380365i
\(643\) 590.715i 0.918686i −0.888259 0.459343i \(-0.848085\pi\)
0.888259 0.459343i \(-0.151915\pi\)
\(644\) −13.3069 + 61.6222i −0.0206628 + 0.0956866i
\(645\) −130.138 −0.201764
\(646\) −139.579 −0.216066
\(647\) 328.095 0.507102 0.253551 0.967322i \(-0.418401\pi\)
0.253551 + 0.967322i \(0.418401\pi\)
\(648\) 25.4558 0.0392837
\(649\) 418.315i 0.644553i
\(650\) 121.589 0.187060
\(651\) 65.5487i 0.100689i
\(652\) 113.502 0.174083
\(653\) 291.306 0.446104 0.223052 0.974806i \(-0.428398\pi\)
0.223052 + 0.974806i \(0.428398\pi\)
\(654\) 173.067i 0.264629i
\(655\) 400.459i 0.611388i
\(656\) −163.244 −0.248848
\(657\) −18.2720 −0.0278113
\(658\) 69.8888i 0.106214i
\(659\) 500.076i 0.758841i 0.925224 + 0.379420i \(0.123877\pi\)
−0.925224 + 0.379420i \(0.876123\pi\)
\(660\) −97.9340 −0.148385
\(661\) 803.159i 1.21507i 0.794294 + 0.607533i \(0.207841\pi\)
−0.794294 + 0.607533i \(0.792159\pi\)
\(662\) 346.553 0.523494
\(663\) 512.230i 0.772595i
\(664\) 338.815i 0.510264i
\(665\) 17.5862i 0.0264453i
\(666\) 121.206i 0.181990i
\(667\) 428.771 + 92.5900i 0.642835 + 0.138816i
\(668\) −619.976 −0.928108
\(669\) 617.492 0.923007
\(670\) 264.769 0.395177
\(671\) −1297.06 −1.93303
\(672\) 13.4280i 0.0199822i
\(673\) −908.196 −1.34947 −0.674737 0.738058i \(-0.735743\pi\)
−0.674737 + 0.738058i \(0.735743\pi\)
\(674\) 806.987i 1.19731i
\(675\) 25.9808 0.0384900
\(676\) 253.356 0.374787
\(677\) 968.574i 1.43069i −0.698774 0.715343i \(-0.746271\pi\)
0.698774 0.715343i \(-0.253729\pi\)
\(678\) 288.376i 0.425333i
\(679\) 65.0282 0.0957706
\(680\) 108.774 0.159962
\(681\) 289.590i 0.425242i
\(682\) 493.742i 0.723962i
\(683\) 455.566 0.667008 0.333504 0.942749i \(-0.391769\pi\)
0.333504 + 0.942749i \(0.391769\pi\)
\(684\) 34.4319i 0.0503390i
\(685\) −153.453 −0.224019
\(686\) 186.300i 0.271574i
\(687\) 487.139i 0.709082i
\(688\) 134.406i 0.195357i
\(689\) 1240.82i 1.80090i
\(690\) −26.5907 + 123.138i −0.0385373 + 0.178461i
\(691\) 47.1105 0.0681772 0.0340886 0.999419i \(-0.489147\pi\)
0.0340886 + 0.999419i \(0.489147\pi\)
\(692\) 603.548 0.872179
\(693\) −51.9823 −0.0750105
\(694\) 102.579 0.147808
\(695\) 79.6373i 0.114586i
\(696\) −93.4330 −0.134243
\(697\) 701.896i 1.00702i
\(698\) 617.364 0.884475
\(699\) −104.289 −0.149198
\(700\) 13.7049i 0.0195784i
\(701\) 364.053i 0.519334i 0.965698 + 0.259667i \(0.0836127\pi\)
−0.965698 + 0.259667i \(0.916387\pi\)
\(702\) 126.359 0.179999
\(703\) −163.944 −0.233207
\(704\) 101.146i 0.143673i
\(705\) 139.657i 0.198095i
\(706\) −47.2300 −0.0668980
\(707\) 34.5795i 0.0489102i
\(708\) −114.614 −0.161884
\(709\) 853.680i 1.20406i 0.798472 + 0.602031i \(0.205642\pi\)
−0.798472 + 0.602031i \(0.794358\pi\)
\(710\) 168.709i 0.237618i
\(711\) 48.1222i 0.0676824i
\(712\) 202.691i 0.284678i
\(713\) 620.809 + 134.059i 0.870700 + 0.188021i
\(714\) 57.7360 0.0808628
\(715\) −486.130 −0.679902
\(716\) −133.634 −0.186639
\(717\) −77.6730 −0.108330
\(718\) 492.842i 0.686410i
\(719\) 825.637 1.14831 0.574157 0.818745i \(-0.305330\pi\)
0.574157 + 0.818745i \(0.305330\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 140.285 0.194571
\(722\) 463.958 0.642601
\(723\) 0.492372i 0.000681013i
\(724\) 280.472i 0.387392i
\(725\) −95.3596 −0.131531
\(726\) 95.1654 0.131082
\(727\) 1157.96i 1.59279i −0.604778 0.796394i \(-0.706738\pi\)
0.604778 0.796394i \(-0.293262\pi\)
\(728\) 66.6547i 0.0915586i
\(729\) 27.0000 0.0370370
\(730\) 19.2604i 0.0263841i
\(731\) −577.900 −0.790561
\(732\) 355.380i 0.485492i
\(733\) 937.923i 1.27957i −0.768555 0.639784i \(-0.779024\pi\)
0.768555 0.639784i \(-0.220976\pi\)
\(734\) 60.6195i 0.0825879i
\(735\) 182.502i 0.248302i
\(736\) 127.176 + 27.4628i 0.172794 + 0.0373136i
\(737\) −1058.58 −1.43634
\(738\) −173.146 −0.234616
\(739\) 276.870 0.374655 0.187327 0.982298i \(-0.440017\pi\)
0.187327 + 0.982298i \(0.440017\pi\)
\(740\) 127.762 0.172651
\(741\) 170.915i 0.230654i
\(742\) −139.859 −0.188489
\(743\) 953.464i 1.28326i 0.767013 + 0.641631i \(0.221742\pi\)
−0.767013 + 0.641631i \(0.778258\pi\)
\(744\) −135.280 −0.181828
\(745\) −378.169 −0.507610
\(746\) 775.234i 1.03919i
\(747\) 359.368i 0.481082i
\(748\) −434.894 −0.581408
\(749\) 136.627 0.182412
\(750\) 27.3861i 0.0365148i
\(751\) 101.682i 0.135396i 0.997706 + 0.0676980i \(0.0215654\pi\)
−0.997706 + 0.0676980i \(0.978435\pi\)
\(752\) −144.237 −0.191805
\(753\) 380.420i 0.505205i
\(754\) −463.788 −0.615103
\(755\) 116.062i 0.153725i
\(756\) 14.2426i 0.0188394i
\(757\) 979.734i 1.29423i −0.762391 0.647116i \(-0.775975\pi\)
0.762391 0.647116i \(-0.224025\pi\)
\(758\) 814.515i 1.07456i
\(759\) 106.313 492.322i 0.140070 0.648646i
\(760\) 36.2944 0.0477558
\(761\) −113.842 −0.149595 −0.0747974 0.997199i \(-0.523831\pi\)
−0.0747974 + 0.997199i \(0.523831\pi\)
\(762\) 515.667 0.676728
\(763\) −96.8312 −0.126908
\(764\) 690.418i 0.903689i
\(765\) 115.372 0.150813
\(766\) 686.378i 0.896055i
\(767\) −568.925 −0.741754
\(768\) −27.7128 −0.0360844
\(769\) 683.546i 0.888876i −0.895810 0.444438i \(-0.853403\pi\)
0.895810 0.444438i \(-0.146597\pi\)
\(770\) 54.7941i 0.0711612i
\(771\) 145.126 0.188231
\(772\) 372.514 0.482531
\(773\) 1180.64i 1.52735i −0.645600 0.763676i \(-0.723393\pi\)
0.645600 0.763676i \(-0.276607\pi\)
\(774\) 142.559i 0.184184i
\(775\) −138.069 −0.178154
\(776\) 134.206i 0.172945i
\(777\) 67.8146 0.0872775
\(778\) 48.9981i 0.0629796i
\(779\) 234.200i 0.300642i
\(780\) 133.194i 0.170762i
\(781\) 674.520i 0.863662i
\(782\) −118.081 + 546.816i −0.150999 + 0.699253i
\(783\) −99.1006 −0.126565
\(784\) 188.487 0.240417
\(785\) 230.473 0.293596
\(786\) −438.681 −0.558119
\(787\) 838.063i 1.06488i 0.846467 + 0.532442i \(0.178725\pi\)
−0.846467 + 0.532442i \(0.821275\pi\)
\(788\) −558.846 −0.709196
\(789\) 90.2437i 0.114377i
\(790\) −50.7253 −0.0642092
\(791\) −161.346 −0.203978
\(792\) 107.281i 0.135456i