Properties

Label 177.3.c.a.58.8
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.8
Root \(-1.39995i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.13

$q$-expansion

\(f(q)\) \(=\) \(q-1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} +2.42478i q^{6} -10.8938 q^{7} -8.45589i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.39995i q^{2} -1.73205 q^{3} +2.04015 q^{4} +0.273484 q^{5} +2.42478i q^{6} -10.8938 q^{7} -8.45589i q^{8} +3.00000 q^{9} -0.382863i q^{10} -15.0527i q^{11} -3.53364 q^{12} -11.1132i q^{13} +15.2508i q^{14} -0.473689 q^{15} -3.67721 q^{16} -3.40920 q^{17} -4.19984i q^{18} -15.7121 q^{19} +0.557948 q^{20} +18.8687 q^{21} -21.0729 q^{22} +15.2765i q^{23} +14.6460i q^{24} -24.9252 q^{25} -15.5578 q^{26} -5.19615 q^{27} -22.2251 q^{28} +22.5689 q^{29} +0.663139i q^{30} -59.5188i q^{31} -28.6757i q^{32} +26.0720i q^{33} +4.77271i q^{34} -2.97929 q^{35} +6.12044 q^{36} +42.4500i q^{37} +21.9961i q^{38} +19.2485i q^{39} -2.31255i q^{40} +78.4822 q^{41} -26.4152i q^{42} +78.3986i q^{43} -30.7096i q^{44} +0.820453 q^{45} +21.3862 q^{46} -35.3465i q^{47} +6.36911 q^{48} +69.6759 q^{49} +34.8940i q^{50} +5.90491 q^{51} -22.6725i q^{52} +37.2779 q^{53} +7.27434i q^{54} -4.11666i q^{55} +92.1171i q^{56} +27.2142 q^{57} -31.5952i q^{58} +(52.6472 - 26.6321i) q^{59} -0.966395 q^{60} -44.2464i q^{61} -83.3232 q^{62} -32.6815 q^{63} -54.8532 q^{64} -3.03927i q^{65} +36.4994 q^{66} +17.3224i q^{67} -6.95528 q^{68} -26.4596i q^{69} +4.17086i q^{70} -59.0750 q^{71} -25.3677i q^{72} -85.3122i q^{73} +59.4278 q^{74} +43.1717 q^{75} -32.0550 q^{76} +163.981i q^{77} +26.9470 q^{78} +62.2163 q^{79} -1.00566 q^{80} +9.00000 q^{81} -109.871i q^{82} -98.9653i q^{83} +38.4949 q^{84} -0.932363 q^{85} +109.754 q^{86} -39.0904 q^{87} -127.284 q^{88} +35.9346i q^{89} -1.14859i q^{90} +121.065i q^{91} +31.1663i q^{92} +103.090i q^{93} -49.4833 q^{94} -4.29702 q^{95} +49.6677i q^{96} -11.0179i q^{97} -97.5426i q^{98} -45.1580i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39995i 0.699974i −0.936755 0.349987i \(-0.886186\pi\)
0.936755 0.349987i \(-0.113814\pi\)
\(3\) −1.73205 −0.577350
\(4\) 2.04015 0.510037
\(5\) 0.273484 0.0546968 0.0273484 0.999626i \(-0.491294\pi\)
0.0273484 + 0.999626i \(0.491294\pi\)
\(6\) 2.42478i 0.404130i
\(7\) −10.8938 −1.55626 −0.778132 0.628101i \(-0.783832\pi\)
−0.778132 + 0.628101i \(0.783832\pi\)
\(8\) 8.45589i 1.05699i
\(9\) 3.00000 0.333333
\(10\) 0.382863i 0.0382863i
\(11\) 15.0527i 1.36842i −0.729284 0.684212i \(-0.760146\pi\)
0.729284 0.684212i \(-0.239854\pi\)
\(12\) −3.53364 −0.294470
\(13\) 11.1132i 0.854858i −0.904049 0.427429i \(-0.859419\pi\)
0.904049 0.427429i \(-0.140581\pi\)
\(14\) 15.2508i 1.08934i
\(15\) −0.473689 −0.0315792
\(16\) −3.67721 −0.229825
\(17\) −3.40920 −0.200541 −0.100271 0.994960i \(-0.531971\pi\)
−0.100271 + 0.994960i \(0.531971\pi\)
\(18\) 4.19984i 0.233325i
\(19\) −15.7121 −0.826954 −0.413477 0.910515i \(-0.635686\pi\)
−0.413477 + 0.910515i \(0.635686\pi\)
\(20\) 0.557948 0.0278974
\(21\) 18.8687 0.898509
\(22\) −21.0729 −0.957860
\(23\) 15.2765i 0.664194i 0.943245 + 0.332097i \(0.107756\pi\)
−0.943245 + 0.332097i \(0.892244\pi\)
\(24\) 14.6460i 0.610251i
\(25\) −24.9252 −0.997008
\(26\) −15.5578 −0.598378
\(27\) −5.19615 −0.192450
\(28\) −22.2251 −0.793752
\(29\) 22.5689 0.778237 0.389118 0.921188i \(-0.372780\pi\)
0.389118 + 0.921188i \(0.372780\pi\)
\(30\) 0.663139i 0.0221046i
\(31\) 59.5188i 1.91996i −0.280067 0.959981i \(-0.590357\pi\)
0.280067 0.959981i \(-0.409643\pi\)
\(32\) 28.6757i 0.896114i
\(33\) 26.0720i 0.790060i
\(34\) 4.77271i 0.140374i
\(35\) −2.97929 −0.0851227
\(36\) 6.12044 0.170012
\(37\) 42.4500i 1.14730i 0.819101 + 0.573649i \(0.194473\pi\)
−0.819101 + 0.573649i \(0.805527\pi\)
\(38\) 21.9961i 0.578846i
\(39\) 19.2485i 0.493553i
\(40\) 2.31255i 0.0578138i
\(41\) 78.4822 1.91420 0.957101 0.289756i \(-0.0935741\pi\)
0.957101 + 0.289756i \(0.0935741\pi\)
\(42\) 26.4152i 0.628933i
\(43\) 78.3986i 1.82322i 0.411052 + 0.911612i \(0.365162\pi\)
−0.411052 + 0.911612i \(0.634838\pi\)
\(44\) 30.7096i 0.697946i
\(45\) 0.820453 0.0182323
\(46\) 21.3862 0.464918
\(47\) 35.3465i 0.752054i −0.926609 0.376027i \(-0.877290\pi\)
0.926609 0.376027i \(-0.122710\pi\)
\(48\) 6.36911 0.132690
\(49\) 69.6759 1.42196
\(50\) 34.8940i 0.697879i
\(51\) 5.90491 0.115783
\(52\) 22.6725i 0.436009i
\(53\) 37.2779 0.703357 0.351678 0.936121i \(-0.385611\pi\)
0.351678 + 0.936121i \(0.385611\pi\)
\(54\) 7.27434i 0.134710i
\(55\) 4.11666i 0.0748484i
\(56\) 92.1171i 1.64495i
\(57\) 27.2142 0.477442
\(58\) 31.5952i 0.544745i
\(59\) 52.6472 26.6321i 0.892326 0.451392i
\(60\) −0.966395 −0.0161066
\(61\) 44.2464i 0.725350i −0.931916 0.362675i \(-0.881864\pi\)
0.931916 0.362675i \(-0.118136\pi\)
\(62\) −83.3232 −1.34392
\(63\) −32.6815 −0.518755
\(64\) −54.8532 −0.857082
\(65\) 3.03927i 0.0467580i
\(66\) 36.4994 0.553021
\(67\) 17.3224i 0.258544i 0.991609 + 0.129272i \(0.0412640\pi\)
−0.991609 + 0.129272i \(0.958736\pi\)
\(68\) −6.95528 −0.102284
\(69\) 26.4596i 0.383473i
\(70\) 4.17086i 0.0595836i
\(71\) −59.0750 −0.832043 −0.416021 0.909355i \(-0.636576\pi\)
−0.416021 + 0.909355i \(0.636576\pi\)
\(72\) 25.3677i 0.352329i
\(73\) 85.3122i 1.16866i −0.811516 0.584330i \(-0.801357\pi\)
0.811516 0.584330i \(-0.198643\pi\)
\(74\) 59.4278 0.803079
\(75\) 43.1717 0.575623
\(76\) −32.0550 −0.421777
\(77\) 163.981i 2.12963i
\(78\) 26.9470 0.345474
\(79\) 62.2163 0.787548 0.393774 0.919207i \(-0.371169\pi\)
0.393774 + 0.919207i \(0.371169\pi\)
\(80\) −1.00566 −0.0125707
\(81\) 9.00000 0.111111
\(82\) 109.871i 1.33989i
\(83\) 98.9653i 1.19235i −0.802853 0.596177i \(-0.796686\pi\)
0.802853 0.596177i \(-0.203314\pi\)
\(84\) 38.4949 0.458273
\(85\) −0.932363 −0.0109690
\(86\) 109.754 1.27621
\(87\) −39.0904 −0.449315
\(88\) −127.284 −1.44640
\(89\) 35.9346i 0.403759i 0.979410 + 0.201880i \(0.0647050\pi\)
−0.979410 + 0.201880i \(0.935295\pi\)
\(90\) 1.14859i 0.0127621i
\(91\) 121.065i 1.33038i
\(92\) 31.1663i 0.338764i
\(93\) 103.090i 1.10849i
\(94\) −49.4833 −0.526418
\(95\) −4.29702 −0.0452318
\(96\) 49.6677i 0.517372i
\(97\) 11.0179i 0.113587i −0.998386 0.0567935i \(-0.981912\pi\)
0.998386 0.0567935i \(-0.0180877\pi\)
\(98\) 97.5426i 0.995332i
\(99\) 45.1580i 0.456141i
\(100\) −50.8511 −0.508511
\(101\) 110.774i 1.09677i 0.836227 + 0.548384i \(0.184757\pi\)
−0.836227 + 0.548384i \(0.815243\pi\)
\(102\) 8.26657i 0.0810448i
\(103\) 43.0668i 0.418125i 0.977902 + 0.209062i \(0.0670412\pi\)
−0.977902 + 0.209062i \(0.932959\pi\)
\(104\) −93.9716 −0.903573
\(105\) 5.16029 0.0491456
\(106\) 52.1871i 0.492331i
\(107\) −146.405 −1.36827 −0.684137 0.729353i \(-0.739821\pi\)
−0.684137 + 0.729353i \(0.739821\pi\)
\(108\) −10.6009 −0.0981567
\(109\) 141.124i 1.29472i 0.762185 + 0.647359i \(0.224127\pi\)
−0.762185 + 0.647359i \(0.775873\pi\)
\(110\) −5.76311 −0.0523919
\(111\) 73.5256i 0.662393i
\(112\) 40.0589 0.357669
\(113\) 21.1887i 0.187511i −0.995595 0.0937555i \(-0.970113\pi\)
0.995595 0.0937555i \(-0.0298872\pi\)
\(114\) 38.0984i 0.334197i
\(115\) 4.17787i 0.0363293i
\(116\) 46.0438 0.396929
\(117\) 33.3395i 0.284953i
\(118\) −37.2836 73.7033i −0.315963 0.624604i
\(119\) 37.1393 0.312095
\(120\) 4.00546i 0.0333788i
\(121\) −105.582 −0.872582
\(122\) −61.9426 −0.507726
\(123\) −135.935 −1.10516
\(124\) 121.427i 0.979251i
\(125\) −13.6538 −0.109230
\(126\) 45.7524i 0.363115i
\(127\) 215.084 1.69358 0.846789 0.531929i \(-0.178533\pi\)
0.846789 + 0.531929i \(0.178533\pi\)
\(128\) 37.9110i 0.296180i
\(129\) 135.790i 1.05264i
\(130\) −4.25482 −0.0327294
\(131\) 79.8202i 0.609314i −0.952462 0.304657i \(-0.901458\pi\)
0.952462 0.304657i \(-0.0985419\pi\)
\(132\) 53.1907i 0.402960i
\(133\) 171.165 1.28696
\(134\) 24.2505 0.180974
\(135\) −1.42107 −0.0105264
\(136\) 28.8278i 0.211969i
\(137\) −138.442 −1.01053 −0.505265 0.862965i \(-0.668605\pi\)
−0.505265 + 0.862965i \(0.668605\pi\)
\(138\) −37.0421 −0.268421
\(139\) 59.8615 0.430658 0.215329 0.976542i \(-0.430918\pi\)
0.215329 + 0.976542i \(0.430918\pi\)
\(140\) −6.07820 −0.0434157
\(141\) 61.2220i 0.434198i
\(142\) 82.7019i 0.582408i
\(143\) −167.282 −1.16981
\(144\) −11.0316 −0.0766085
\(145\) 6.17223 0.0425671
\(146\) −119.433 −0.818031
\(147\) −120.682 −0.820967
\(148\) 86.6044i 0.585165i
\(149\) 218.369i 1.46556i −0.680464 0.732782i \(-0.738222\pi\)
0.680464 0.732782i \(-0.261778\pi\)
\(150\) 60.4381i 0.402921i
\(151\) 26.4104i 0.174904i 0.996169 + 0.0874518i \(0.0278724\pi\)
−0.996169 + 0.0874518i \(0.972128\pi\)
\(152\) 132.860i 0.874078i
\(153\) −10.2276 −0.0668471
\(154\) 229.565 1.49068
\(155\) 16.2774i 0.105016i
\(156\) 39.2699i 0.251730i
\(157\) 18.4659i 0.117617i −0.998269 0.0588087i \(-0.981270\pi\)
0.998269 0.0588087i \(-0.0187302\pi\)
\(158\) 87.0995i 0.551263i
\(159\) −64.5672 −0.406083
\(160\) 7.84234i 0.0490146i
\(161\) 166.419i 1.03366i
\(162\) 12.5995i 0.0777748i
\(163\) −247.452 −1.51811 −0.759055 0.651026i \(-0.774339\pi\)
−0.759055 + 0.651026i \(0.774339\pi\)
\(164\) 160.115 0.976313
\(165\) 7.13027i 0.0432138i
\(166\) −138.546 −0.834616
\(167\) 63.0046 0.377273 0.188637 0.982047i \(-0.439593\pi\)
0.188637 + 0.982047i \(0.439593\pi\)
\(168\) 159.552i 0.949712i
\(169\) 45.4978 0.269218
\(170\) 1.30526i 0.00767800i
\(171\) −47.1364 −0.275651
\(172\) 159.945i 0.929912i
\(173\) 163.258i 0.943690i −0.881681 0.471845i \(-0.843588\pi\)
0.881681 0.471845i \(-0.156412\pi\)
\(174\) 54.7245i 0.314509i
\(175\) 271.531 1.55161
\(176\) 55.3517i 0.314498i
\(177\) −91.1876 + 46.1282i −0.515184 + 0.260611i
\(178\) 50.3065 0.282621
\(179\) 80.5355i 0.449919i −0.974368 0.224960i \(-0.927775\pi\)
0.974368 0.224960i \(-0.0722250\pi\)
\(180\) 1.67384 0.00929914
\(181\) −130.162 −0.719125 −0.359563 0.933121i \(-0.617074\pi\)
−0.359563 + 0.933121i \(0.617074\pi\)
\(182\) 169.485 0.931234
\(183\) 76.6369i 0.418781i
\(184\) 129.176 0.702044
\(185\) 11.6094i 0.0627536i
\(186\) 144.320 0.775914
\(187\) 51.3176i 0.274426i
\(188\) 72.1121i 0.383575i
\(189\) 56.6061 0.299503
\(190\) 6.01560i 0.0316610i
\(191\) 206.275i 1.07997i 0.841674 + 0.539987i \(0.181571\pi\)
−0.841674 + 0.539987i \(0.818429\pi\)
\(192\) 95.0086 0.494836
\(193\) 174.658 0.904964 0.452482 0.891773i \(-0.350539\pi\)
0.452482 + 0.891773i \(0.350539\pi\)
\(194\) −15.4245 −0.0795079
\(195\) 5.26417i 0.0269958i
\(196\) 142.149 0.725250
\(197\) 262.732 1.33367 0.666833 0.745207i \(-0.267649\pi\)
0.666833 + 0.745207i \(0.267649\pi\)
\(198\) −63.2188 −0.319287
\(199\) −36.7705 −0.184776 −0.0923882 0.995723i \(-0.529450\pi\)
−0.0923882 + 0.995723i \(0.529450\pi\)
\(200\) 210.765i 1.05382i
\(201\) 30.0033i 0.149270i
\(202\) 155.077 0.767709
\(203\) −245.862 −1.21114
\(204\) 12.0469 0.0590534
\(205\) 21.4637 0.104701
\(206\) 60.2913 0.292676
\(207\) 45.8294i 0.221398i
\(208\) 40.8654i 0.196468i
\(209\) 236.509i 1.13162i
\(210\) 7.22413i 0.0344006i
\(211\) 332.832i 1.57740i −0.614775 0.788702i \(-0.710753\pi\)
0.614775 0.788702i \(-0.289247\pi\)
\(212\) 76.0525 0.358738
\(213\) 102.321 0.480380
\(214\) 204.960i 0.957756i
\(215\) 21.4408i 0.0997246i
\(216\) 43.9381i 0.203417i
\(217\) 648.389i 2.98797i
\(218\) 197.567 0.906269
\(219\) 147.765i 0.674726i
\(220\) 8.39860i 0.0381755i
\(221\) 37.8870i 0.171434i
\(222\) −102.932 −0.463658
\(223\) −68.0441 −0.305131 −0.152565 0.988293i \(-0.548753\pi\)
−0.152565 + 0.988293i \(0.548753\pi\)
\(224\) 312.388i 1.39459i
\(225\) −74.7756 −0.332336
\(226\) −29.6631 −0.131253
\(227\) 297.497i 1.31056i −0.755386 0.655280i \(-0.772551\pi\)
0.755386 0.655280i \(-0.227449\pi\)
\(228\) 55.5210 0.243513
\(229\) 27.5954i 0.120504i 0.998183 + 0.0602519i \(0.0191904\pi\)
−0.998183 + 0.0602519i \(0.980810\pi\)
\(230\) 5.84880 0.0254296
\(231\) 284.024i 1.22954i
\(232\) 190.840i 0.822585i
\(233\) 359.245i 1.54182i −0.636943 0.770911i \(-0.719801\pi\)
0.636943 0.770911i \(-0.280199\pi\)
\(234\) −46.6735 −0.199459
\(235\) 9.66672i 0.0411350i
\(236\) 107.408 54.3335i 0.455119 0.230227i
\(237\) −107.762 −0.454691
\(238\) 51.9931i 0.218458i
\(239\) −265.127 −1.10932 −0.554659 0.832078i \(-0.687151\pi\)
−0.554659 + 0.832078i \(0.687151\pi\)
\(240\) 1.74185 0.00725771
\(241\) −58.8858 −0.244340 −0.122170 0.992509i \(-0.538985\pi\)
−0.122170 + 0.992509i \(0.538985\pi\)
\(242\) 147.810i 0.610784i
\(243\) −15.5885 −0.0641500
\(244\) 90.2691i 0.369955i
\(245\) 19.0553 0.0777765
\(246\) 190.302i 0.773586i
\(247\) 174.611i 0.706928i
\(248\) −503.284 −2.02937
\(249\) 171.413i 0.688406i
\(250\) 19.1145i 0.0764581i
\(251\) 1.34813 0.00537104 0.00268552 0.999996i \(-0.499145\pi\)
0.00268552 + 0.999996i \(0.499145\pi\)
\(252\) −66.6752 −0.264584
\(253\) 229.951 0.908899
\(254\) 301.107i 1.18546i
\(255\) 1.61490 0.00633294
\(256\) −272.486 −1.06440
\(257\) 301.120 1.17167 0.585837 0.810429i \(-0.300766\pi\)
0.585837 + 0.810429i \(0.300766\pi\)
\(258\) −190.099 −0.736819
\(259\) 462.444i 1.78550i
\(260\) 6.20056i 0.0238483i
\(261\) 67.7066 0.259412
\(262\) −111.744 −0.426504
\(263\) 82.6739 0.314350 0.157175 0.987571i \(-0.449761\pi\)
0.157175 + 0.987571i \(0.449761\pi\)
\(264\) 220.462 0.835082
\(265\) 10.1949 0.0384714
\(266\) 239.623i 0.900837i
\(267\) 62.2405i 0.233111i
\(268\) 35.3403i 0.131867i
\(269\) 208.155i 0.773810i 0.922120 + 0.386905i \(0.126456\pi\)
−0.922120 + 0.386905i \(0.873544\pi\)
\(270\) 1.98942i 0.00736821i
\(271\) 38.7081 0.142834 0.0714171 0.997447i \(-0.477248\pi\)
0.0714171 + 0.997447i \(0.477248\pi\)
\(272\) 12.5363 0.0460895
\(273\) 209.691i 0.768098i
\(274\) 193.812i 0.707344i
\(275\) 375.191i 1.36433i
\(276\) 53.9815i 0.195585i
\(277\) 209.375 0.755866 0.377933 0.925833i \(-0.376635\pi\)
0.377933 + 0.925833i \(0.376635\pi\)
\(278\) 83.8030i 0.301450i
\(279\) 178.556i 0.639987i
\(280\) 25.1926i 0.0899735i
\(281\) 307.082 1.09282 0.546409 0.837519i \(-0.315995\pi\)
0.546409 + 0.837519i \(0.315995\pi\)
\(282\) 85.7075 0.303927
\(283\) 229.159i 0.809749i 0.914372 + 0.404875i \(0.132685\pi\)
−0.914372 + 0.404875i \(0.867315\pi\)
\(284\) −120.522 −0.424373
\(285\) 7.44265 0.0261146
\(286\) 234.187i 0.818834i
\(287\) −854.974 −2.97900
\(288\) 86.0270i 0.298705i
\(289\) −277.377 −0.959783
\(290\) 8.64079i 0.0297958i
\(291\) 19.0836i 0.0655795i
\(292\) 174.049i 0.596060i
\(293\) 56.5578 0.193030 0.0965150 0.995332i \(-0.469230\pi\)
0.0965150 + 0.995332i \(0.469230\pi\)
\(294\) 168.949i 0.574655i
\(295\) 14.3982 7.28347i 0.0488074 0.0246897i
\(296\) 358.953 1.21268
\(297\) 78.2159i 0.263353i
\(298\) −305.705 −1.02586
\(299\) 169.770 0.567792
\(300\) 88.0767 0.293589
\(301\) 854.063i 2.83742i
\(302\) 36.9732 0.122428
\(303\) 191.865i 0.633219i
\(304\) 57.7767 0.190055
\(305\) 12.1007i 0.0396744i
\(306\) 14.3181i 0.0467912i
\(307\) −38.1615 −0.124305 −0.0621523 0.998067i \(-0.519796\pi\)
−0.0621523 + 0.998067i \(0.519796\pi\)
\(308\) 334.546i 1.08619i
\(309\) 74.5940i 0.241404i
\(310\) −22.7876 −0.0735083
\(311\) −237.381 −0.763282 −0.381641 0.924311i \(-0.624641\pi\)
−0.381641 + 0.924311i \(0.624641\pi\)
\(312\) 162.764 0.521678
\(313\) 468.363i 1.49637i −0.663491 0.748184i \(-0.730926\pi\)
0.663491 0.748184i \(-0.269074\pi\)
\(314\) −25.8513 −0.0823291
\(315\) −8.93788 −0.0283742
\(316\) 126.930 0.401679
\(317\) −97.7779 −0.308447 −0.154224 0.988036i \(-0.549288\pi\)
−0.154224 + 0.988036i \(0.549288\pi\)
\(318\) 90.3907i 0.284248i
\(319\) 339.721i 1.06496i
\(320\) −15.0015 −0.0468797
\(321\) 253.582 0.789974
\(322\) −232.978 −0.723536
\(323\) 53.5658 0.165838
\(324\) 18.3613 0.0566708
\(325\) 276.998i 0.852300i
\(326\) 346.420i 1.06264i
\(327\) 244.434i 0.747506i
\(328\) 663.637i 2.02328i
\(329\) 385.060i 1.17039i
\(330\) 9.98200 0.0302485
\(331\) −248.132 −0.749644 −0.374822 0.927097i \(-0.622296\pi\)
−0.374822 + 0.927097i \(0.622296\pi\)
\(332\) 201.904i 0.608144i
\(333\) 127.350i 0.382433i
\(334\) 88.2032i 0.264081i
\(335\) 4.73741i 0.0141415i
\(336\) −69.3841 −0.206500
\(337\) 84.1105i 0.249586i 0.992183 + 0.124793i \(0.0398267\pi\)
−0.992183 + 0.124793i \(0.960173\pi\)
\(338\) 63.6945i 0.188445i
\(339\) 36.7000i 0.108260i
\(340\) −1.90216 −0.00559459
\(341\) −895.916 −2.62732
\(342\) 65.9884i 0.192949i
\(343\) −225.240 −0.656676
\(344\) 662.930 1.92712
\(345\) 7.23629i 0.0209747i
\(346\) −228.553 −0.660558
\(347\) 521.687i 1.50342i −0.659493 0.751711i \(-0.729229\pi\)
0.659493 0.751711i \(-0.270771\pi\)
\(348\) −79.7502 −0.229167
\(349\) 299.873i 0.859234i 0.903011 + 0.429617i \(0.141351\pi\)
−0.903011 + 0.429617i \(0.858649\pi\)
\(350\) 380.130i 1.08608i
\(351\) 57.7456i 0.164518i
\(352\) −431.645 −1.22626
\(353\) 633.470i 1.79453i 0.441491 + 0.897266i \(0.354450\pi\)
−0.441491 + 0.897266i \(0.645550\pi\)
\(354\) 64.5771 + 127.658i 0.182421 + 0.360616i
\(355\) −16.1561 −0.0455101
\(356\) 73.3119i 0.205932i
\(357\) −64.3272 −0.180188
\(358\) −112.745 −0.314932
\(359\) 456.186 1.27071 0.635356 0.772219i \(-0.280853\pi\)
0.635356 + 0.772219i \(0.280853\pi\)
\(360\) 6.93765i 0.0192713i
\(361\) −114.129 −0.316148
\(362\) 182.220i 0.503369i
\(363\) 182.874 0.503786
\(364\) 246.990i 0.678545i
\(365\) 23.3315i 0.0639220i
\(366\) 107.288 0.293136
\(367\) 505.395i 1.37710i 0.725190 + 0.688549i \(0.241752\pi\)
−0.725190 + 0.688549i \(0.758248\pi\)
\(368\) 56.1747i 0.152649i
\(369\) 235.447 0.638067
\(370\) 16.2526 0.0439259
\(371\) −406.100 −1.09461
\(372\) 210.318i 0.565371i
\(373\) −262.292 −0.703195 −0.351598 0.936151i \(-0.614361\pi\)
−0.351598 + 0.936151i \(0.614361\pi\)
\(374\) 71.8419 0.192091
\(375\) 23.6490 0.0630640
\(376\) −298.886 −0.794910
\(377\) 250.811i 0.665282i
\(378\) 79.2455i 0.209644i
\(379\) 532.499 1.40501 0.702505 0.711679i \(-0.252065\pi\)
0.702505 + 0.711679i \(0.252065\pi\)
\(380\) −8.76655 −0.0230699
\(381\) −372.537 −0.977787
\(382\) 288.774 0.755953
\(383\) 286.541 0.748150 0.374075 0.927398i \(-0.377960\pi\)
0.374075 + 0.927398i \(0.377960\pi\)
\(384\) 65.6638i 0.170999i
\(385\) 44.8463i 0.116484i
\(386\) 244.512i 0.633451i
\(387\) 235.196i 0.607741i
\(388\) 22.4782i 0.0579336i
\(389\) 620.394 1.59484 0.797421 0.603423i \(-0.206197\pi\)
0.797421 + 0.603423i \(0.206197\pi\)
\(390\) 7.36956 0.0188963
\(391\) 52.0806i 0.133198i
\(392\) 589.171i 1.50299i
\(393\) 138.253i 0.351788i
\(394\) 367.811i 0.933531i
\(395\) 17.0152 0.0430764
\(396\) 92.1289i 0.232649i
\(397\) 434.013i 1.09323i −0.837383 0.546616i \(-0.815916\pi\)
0.837383 0.546616i \(-0.184084\pi\)
\(398\) 51.4767i 0.129339i
\(399\) −296.467 −0.743026
\(400\) 91.6551 0.229138
\(401\) 107.207i 0.267350i 0.991025 + 0.133675i \(0.0426778\pi\)
−0.991025 + 0.133675i \(0.957322\pi\)
\(402\) −42.0031 −0.104485
\(403\) −661.442 −1.64129
\(404\) 225.994i 0.559392i
\(405\) 2.46136 0.00607743
\(406\) 344.193i 0.847767i
\(407\) 638.986 1.56999
\(408\) 49.9313i 0.122381i
\(409\) 550.503i 1.34597i 0.739654 + 0.672987i \(0.234989\pi\)
−0.739654 + 0.672987i \(0.765011\pi\)
\(410\) 30.0480i 0.0732878i
\(411\) 239.789 0.583429
\(412\) 87.8627i 0.213259i
\(413\) −573.531 + 290.126i −1.38869 + 0.702485i
\(414\) 64.1587 0.154973
\(415\) 27.0655i 0.0652180i
\(416\) −318.677 −0.766050
\(417\) −103.683 −0.248641
\(418\) 331.100 0.792106
\(419\) 274.431i 0.654967i 0.944857 + 0.327483i \(0.106201\pi\)
−0.944857 + 0.327483i \(0.893799\pi\)
\(420\) 10.5278 0.0250661
\(421\) 46.0928i 0.109484i 0.998501 + 0.0547420i \(0.0174336\pi\)
−0.998501 + 0.0547420i \(0.982566\pi\)
\(422\) −465.948 −1.10414
\(423\) 106.040i 0.250685i
\(424\) 315.218i 0.743438i
\(425\) 84.9751 0.199941
\(426\) 143.244i 0.336253i
\(427\) 482.013i 1.12884i
\(428\) −298.689 −0.697871
\(429\) 289.742 0.675389
\(430\) 30.0160 0.0698046
\(431\) 256.182i 0.594389i 0.954817 + 0.297195i \(0.0960510\pi\)
−0.954817 + 0.297195i \(0.903949\pi\)
\(432\) 19.1073 0.0442299
\(433\) 76.7056 0.177149 0.0885746 0.996070i \(-0.471769\pi\)
0.0885746 + 0.996070i \(0.471769\pi\)
\(434\) 907.710 2.09150
\(435\) −10.6906 −0.0245761
\(436\) 287.914i 0.660354i
\(437\) 240.026i 0.549258i
\(438\) 206.863 0.472291
\(439\) 622.390 1.41775 0.708873 0.705336i \(-0.249204\pi\)
0.708873 + 0.705336i \(0.249204\pi\)
\(440\) −34.8100 −0.0791137
\(441\) 209.028 0.473986
\(442\) 53.0398 0.120000
\(443\) 682.698i 1.54108i 0.637392 + 0.770540i \(0.280013\pi\)
−0.637392 + 0.770540i \(0.719987\pi\)
\(444\) 150.003i 0.337845i
\(445\) 9.82754i 0.0220844i
\(446\) 95.2582i 0.213583i
\(447\) 378.226i 0.846144i
\(448\) 597.563 1.33385
\(449\) −144.491 −0.321806 −0.160903 0.986970i \(-0.551441\pi\)
−0.160903 + 0.986970i \(0.551441\pi\)
\(450\) 104.682i 0.232626i
\(451\) 1181.37i 2.61944i
\(452\) 43.2282i 0.0956375i
\(453\) 45.7442i 0.100981i
\(454\) −416.480 −0.917358
\(455\) 33.1094i 0.0727678i
\(456\) 230.120i 0.504649i
\(457\) 293.853i 0.643004i −0.946909 0.321502i \(-0.895812\pi\)
0.946909 0.321502i \(-0.104188\pi\)
\(458\) 38.6321 0.0843495
\(459\) 17.7147 0.0385942
\(460\) 8.52348i 0.0185293i
\(461\) 457.634 0.992698 0.496349 0.868123i \(-0.334674\pi\)
0.496349 + 0.868123i \(0.334674\pi\)
\(462\) −397.619 −0.860646
\(463\) 671.285i 1.44986i 0.688822 + 0.724930i \(0.258128\pi\)
−0.688822 + 0.724930i \(0.741872\pi\)
\(464\) −82.9904 −0.178859
\(465\) 28.1934i 0.0606309i
\(466\) −502.923 −1.07923
\(467\) 358.075i 0.766756i −0.923592 0.383378i \(-0.874761\pi\)
0.923592 0.383378i \(-0.125239\pi\)
\(468\) 68.0174i 0.145336i
\(469\) 188.708i 0.402362i
\(470\) −13.5329 −0.0287934
\(471\) 31.9839i 0.0679065i
\(472\) −225.198 445.179i −0.477115 0.943176i
\(473\) 1180.11 2.49494
\(474\) 150.861i 0.318272i
\(475\) 391.628 0.824480
\(476\) 75.7697 0.159180
\(477\) 111.834 0.234452
\(478\) 371.164i 0.776493i
\(479\) −23.3301 −0.0487059 −0.0243530 0.999703i \(-0.507753\pi\)
−0.0243530 + 0.999703i \(0.507753\pi\)
\(480\) 13.5833i 0.0282986i
\(481\) 471.754 0.980777
\(482\) 82.4371i 0.171031i
\(483\) 288.247i 0.596785i
\(484\) −215.404 −0.445049
\(485\) 3.01323i 0.00621285i
\(486\) 21.8230i 0.0449033i
\(487\) 718.517 1.47539 0.737697 0.675132i \(-0.235913\pi\)
0.737697 + 0.675132i \(0.235913\pi\)
\(488\) −374.142 −0.766685
\(489\) 428.600 0.876482
\(490\) 26.6763i 0.0544415i
\(491\) 406.760 0.828431 0.414215 0.910179i \(-0.364056\pi\)
0.414215 + 0.910179i \(0.364056\pi\)
\(492\) −277.328 −0.563675
\(493\) −76.9419 −0.156069
\(494\) 244.446 0.494831
\(495\) 12.3500i 0.0249495i
\(496\) 218.863i 0.441256i
\(497\) 643.554 1.29488
\(498\) 239.969 0.481866
\(499\) −828.694 −1.66071 −0.830355 0.557235i \(-0.811862\pi\)
−0.830355 + 0.557235i \(0.811862\pi\)
\(500\) −27.8557 −0.0557114
\(501\) −109.127 −0.217819
\(502\) 1.88731i 0.00375959i
\(503\) 491.016i 0.976175i −0.872795 0.488088i \(-0.837695\pi\)
0.872795 0.488088i \(-0.162305\pi\)
\(504\) 276.351i 0.548316i
\(505\) 30.2948i 0.0599897i
\(506\) 321.920i 0.636205i
\(507\) −78.8045 −0.155433
\(508\) 438.804 0.863787
\(509\) 299.875i 0.589146i −0.955629 0.294573i \(-0.904823\pi\)
0.955629 0.294573i \(-0.0951774\pi\)
\(510\) 2.26078i 0.00443289i
\(511\) 929.378i 1.81874i
\(512\) 229.822i 0.448872i
\(513\) 81.6426 0.159147
\(514\) 421.553i 0.820141i
\(515\) 11.7781i 0.0228701i
\(516\) 277.033i 0.536885i
\(517\) −532.059 −1.02913
\(518\) −647.398 −1.24980
\(519\) 282.772i 0.544840i
\(520\) −25.6997 −0.0494226
\(521\) −793.658 −1.52334 −0.761668 0.647967i \(-0.775619\pi\)
−0.761668 + 0.647967i \(0.775619\pi\)
\(522\) 94.7857i 0.181582i
\(523\) −991.881 −1.89652 −0.948261 0.317493i \(-0.897159\pi\)
−0.948261 + 0.317493i \(0.897159\pi\)
\(524\) 162.845i 0.310773i
\(525\) −470.306 −0.895821
\(526\) 115.739i 0.220036i
\(527\) 202.912i 0.385032i
\(528\) 95.8720i 0.181576i
\(529\) 295.630 0.558846
\(530\) 14.2723i 0.0269290i
\(531\) 157.942 79.8964i 0.297442 0.150464i
\(532\) 349.203 0.656396
\(533\) 872.185i 1.63637i
\(534\) −87.1335 −0.163171
\(535\) −40.0396 −0.0748403
\(536\) 146.477 0.273277
\(537\) 139.492i 0.259761i
\(538\) 291.406 0.541646
\(539\) 1048.81i 1.94584i
\(540\) −2.89918 −0.00536886
\(541\) 200.875i 0.371303i −0.982616 0.185652i \(-0.940560\pi\)
0.982616 0.185652i \(-0.0594396\pi\)
\(542\) 54.1893i 0.0999802i
\(543\) 225.447 0.415187
\(544\) 97.7612i 0.179708i
\(545\) 38.5953i 0.0708170i
\(546\) −293.556 −0.537648
\(547\) −412.389 −0.753911 −0.376955 0.926231i \(-0.623029\pi\)
−0.376955 + 0.926231i \(0.623029\pi\)
\(548\) −282.443 −0.515407
\(549\) 132.739i 0.241783i
\(550\) 525.247 0.954994
\(551\) −354.605 −0.643566
\(552\) −223.740 −0.405325
\(553\) −677.775 −1.22563
\(554\) 293.114i 0.529086i
\(555\) 20.1081i 0.0362308i
\(556\) 122.126 0.219652
\(557\) −214.797 −0.385632 −0.192816 0.981235i \(-0.561762\pi\)
−0.192816 + 0.981235i \(0.561762\pi\)
\(558\) −249.970 −0.447974
\(559\) 871.256 1.55860
\(560\) 10.9555 0.0195634
\(561\) 88.8846i 0.158440i
\(562\) 429.898i 0.764943i
\(563\) 104.763i 0.186079i −0.995662 0.0930396i \(-0.970342\pi\)
0.995662 0.0930396i \(-0.0296583\pi\)
\(564\) 124.902i 0.221457i
\(565\) 5.79479i 0.0102563i
\(566\) 320.810 0.566803
\(567\) −98.0446 −0.172918
\(568\) 499.532i 0.879458i
\(569\) 765.436i 1.34523i 0.739992 + 0.672615i \(0.234829\pi\)
−0.739992 + 0.672615i \(0.765171\pi\)
\(570\) 10.4193i 0.0182795i
\(571\) 249.624i 0.437170i 0.975818 + 0.218585i \(0.0701441\pi\)
−0.975818 + 0.218585i \(0.929856\pi\)
\(572\) −341.281 −0.596645
\(573\) 357.279i 0.623523i
\(574\) 1196.92i 2.08522i
\(575\) 380.769i 0.662207i
\(576\) −164.560 −0.285694
\(577\) −268.842 −0.465930 −0.232965 0.972485i \(-0.574843\pi\)
−0.232965 + 0.972485i \(0.574843\pi\)
\(578\) 388.314i 0.671823i
\(579\) −302.517 −0.522481
\(580\) 12.5923 0.0217108
\(581\) 1078.11i 1.85562i
\(582\) 26.7161 0.0459039
\(583\) 561.132i 0.962490i
\(584\) −721.390 −1.23526
\(585\) 9.11782i 0.0155860i
\(586\) 79.1779i 0.135116i
\(587\) 793.085i 1.35108i 0.737322 + 0.675541i \(0.236090\pi\)
−0.737322 + 0.675541i \(0.763910\pi\)
\(588\) −246.209 −0.418724
\(589\) 935.166i 1.58772i
\(590\) −10.1965 20.1567i −0.0172822 0.0341639i
\(591\) −455.066 −0.769993
\(592\) 156.098i 0.263678i
\(593\) −108.147 −0.182373 −0.0911866 0.995834i \(-0.529066\pi\)
−0.0911866 + 0.995834i \(0.529066\pi\)
\(594\) 109.498 0.184340
\(595\) 10.1570 0.0170706
\(596\) 445.505i 0.747492i
\(597\) 63.6884 0.106681
\(598\) 237.669i 0.397439i
\(599\) 21.0152 0.0350837 0.0175419 0.999846i \(-0.494416\pi\)
0.0175419 + 0.999846i \(0.494416\pi\)
\(600\) 365.055i 0.608425i
\(601\) 792.854i 1.31922i −0.751606 0.659612i \(-0.770721\pi\)
0.751606 0.659612i \(-0.229279\pi\)
\(602\) −1195.64 −1.98612
\(603\) 51.9673i 0.0861813i
\(604\) 53.8812i 0.0892073i
\(605\) −28.8751 −0.0477275
\(606\) −268.602 −0.443237
\(607\) 848.008 1.39705 0.698524 0.715587i \(-0.253841\pi\)
0.698524 + 0.715587i \(0.253841\pi\)
\(608\) 450.555i 0.741045i
\(609\) 425.845 0.699253
\(610\) −16.9403 −0.0277710
\(611\) −392.811 −0.642899
\(612\) −20.8658 −0.0340945
\(613\) 355.689i 0.580243i 0.956990 + 0.290121i \(0.0936957\pi\)
−0.956990 + 0.290121i \(0.906304\pi\)
\(614\) 53.4241i 0.0870100i
\(615\) −37.1761 −0.0604490
\(616\) 1386.61 2.25099
\(617\) 120.858 0.195880 0.0979402 0.995192i \(-0.468775\pi\)
0.0979402 + 0.995192i \(0.468775\pi\)
\(618\) −104.428 −0.168977
\(619\) −112.377 −0.181546 −0.0907732 0.995872i \(-0.528934\pi\)
−0.0907732 + 0.995872i \(0.528934\pi\)
\(620\) 33.2084i 0.0535619i
\(621\) 79.3789i 0.127824i
\(622\) 332.320i 0.534277i
\(623\) 391.466i 0.628356i
\(624\) 70.7809i 0.113431i
\(625\) 619.396 0.991034
\(626\) −655.684 −1.04742
\(627\) 409.646i 0.653343i
\(628\) 37.6732i 0.0599892i
\(629\) 144.721i 0.230081i
\(630\) 12.5126i 0.0198612i
\(631\) 467.803 0.741368 0.370684 0.928759i \(-0.379123\pi\)
0.370684 + 0.928759i \(0.379123\pi\)
\(632\) 526.094i 0.832427i
\(633\) 576.483i 0.910715i
\(634\) 136.884i 0.215905i
\(635\) 58.8222 0.0926333
\(636\) −131.727 −0.207117
\(637\) 774.319i 1.21557i
\(638\) −475.592 −0.745442
\(639\) −177.225 −0.277348
\(640\) 10.3681i 0.0162001i
\(641\) −1006.77 −1.57062 −0.785311 0.619102i \(-0.787497\pi\)
−0.785311 + 0.619102i \(0.787497\pi\)
\(642\) 355.001i 0.552961i
\(643\) 65.4231 0.101747 0.0508734 0.998705i \(-0.483800\pi\)
0.0508734 + 0.998705i \(0.483800\pi\)
\(644\) 339.520i 0.527205i
\(645\) 37.1365i 0.0575760i
\(646\) 74.9893i 0.116083i
\(647\) 1000.16 1.54584 0.772920 0.634503i \(-0.218795\pi\)
0.772920 + 0.634503i \(0.218795\pi\)
\(648\) 76.1030i 0.117443i
\(649\) −400.884 792.480i −0.617696 1.22108i
\(650\) 387.782 0.596588
\(651\) 1123.04i 1.72510i
\(652\) −504.839 −0.774293
\(653\) −635.037 −0.972492 −0.486246 0.873822i \(-0.661634\pi\)
−0.486246 + 0.873822i \(0.661634\pi\)
\(654\) −342.195 −0.523234
\(655\) 21.8296i 0.0333276i
\(656\) −288.595 −0.439932
\(657\) 255.937i 0.389553i
\(658\) 539.063 0.819245
\(659\) 445.774i 0.676440i 0.941067 + 0.338220i \(0.109825\pi\)
−0.941067 + 0.338220i \(0.890175\pi\)
\(660\) 14.5468i 0.0220406i
\(661\) 4.13501 0.00625568 0.00312784 0.999995i \(-0.499004\pi\)
0.00312784 + 0.999995i \(0.499004\pi\)
\(662\) 347.372i 0.524731i
\(663\) 65.6222i 0.0989777i
\(664\) −836.840 −1.26030
\(665\) 46.8110 0.0703925
\(666\) 178.283 0.267693
\(667\) 344.773i 0.516900i
\(668\) 128.539 0.192423
\(669\) 117.856 0.176167
\(670\) 6.63213 0.00989870
\(671\) −666.025 −0.992586
\(672\) 541.072i 0.805167i
\(673\) 144.454i 0.214641i −0.994224 0.107321i \(-0.965773\pi\)
0.994224 0.107321i \(-0.0342271\pi\)
\(674\) 117.750 0.174704
\(675\) 129.515 0.191874
\(676\) 92.8222 0.137311
\(677\) 567.757 0.838637 0.419318 0.907839i \(-0.362269\pi\)
0.419318 + 0.907839i \(0.362269\pi\)
\(678\) 51.3780 0.0757788
\(679\) 120.028i 0.176771i
\(680\) 7.88396i 0.0115941i
\(681\) 515.280i 0.756652i
\(682\) 1254.24i 1.83905i
\(683\) 505.717i 0.740435i 0.928945 + 0.370218i \(0.120717\pi\)
−0.928945 + 0.370218i \(0.879283\pi\)
\(684\) −96.1651 −0.140592
\(685\) −37.8618 −0.0552727
\(686\) 315.324i 0.459656i
\(687\) 47.7966i 0.0695729i
\(688\) 288.288i 0.419023i
\(689\) 414.275i 0.601270i
\(690\) −10.1304 −0.0146818
\(691\) 843.080i 1.22009i 0.792368 + 0.610044i \(0.208848\pi\)
−0.792368 + 0.610044i \(0.791152\pi\)
\(692\) 333.071i 0.481317i
\(693\) 491.944i 0.709876i
\(694\) −730.334 −1.05236
\(695\) 16.3712 0.0235557
\(696\) 330.544i 0.474920i
\(697\) −267.562 −0.383877
\(698\) 419.806 0.601441
\(699\) 622.230i 0.890171i
\(700\) 553.964 0.791377
\(701\) 873.826i 1.24654i 0.782006 + 0.623271i \(0.214197\pi\)
−0.782006 + 0.623271i \(0.785803\pi\)
\(702\) 80.8409 0.115158
\(703\) 666.980i 0.948763i
\(704\) 825.687i 1.17285i
\(705\) 16.7432i 0.0237493i
\(706\) 886.824 1.25612
\(707\) 1206.75i 1.70686i
\(708\) −186.036 + 94.1084i −0.262763 + 0.132921i
\(709\) 159.514 0.224985 0.112492 0.993653i \(-0.464117\pi\)
0.112492 + 0.993653i \(0.464117\pi\)
\(710\) 22.6177i 0.0318559i
\(711\) 186.649 0.262516
\(712\) 303.859 0.426768
\(713\) 909.237 1.27523
\(714\) 90.0547i 0.126127i
\(715\) −45.7491 −0.0639848
\(716\) 164.304i 0.229475i
\(717\) 459.213 0.640465
\(718\) 638.636i 0.889465i
\(719\) 35.0202i 0.0487068i −0.999703 0.0243534i \(-0.992247\pi\)
0.999703 0.0243534i \(-0.00775270\pi\)
\(720\) −3.01697 −0.00419024
\(721\) 469.164i 0.650712i
\(722\) 159.775i 0.221295i
\(723\) 101.993 0.141070
\(724\) −265.549 −0.366781
\(725\) −562.534 −0.775908
\(726\) 256.014i 0.352637i
\(727\) 1123.28 1.54509 0.772544 0.634961i \(-0.218984\pi\)
0.772544 + 0.634961i \(0.218984\pi\)
\(728\) 1023.71 1.40620
\(729\) 27.0000 0.0370370
\(730\) −32.6629 −0.0447437
\(731\) 267.277i 0.365632i
\(732\) 156.351i 0.213594i
\(733\) −1337.07 −1.82411 −0.912053 0.410073i \(-0.865503\pi\)
−0.912053 + 0.410073i \(0.865503\pi\)
\(734\) 707.526 0.963932
\(735\) −33.0047 −0.0449043
\(736\) 438.063 0.595194
\(737\) 260.749 0.353797
\(738\) 329.613i 0.446630i
\(739\) 393.835i 0.532930i 0.963845 + 0.266465i \(0.0858556\pi\)
−0.963845 + 0.266465i \(0.914144\pi\)
\(740\) 23.6849i 0.0320067i
\(741\) 302.435i 0.408145i
\(742\) 568.518i 0.766197i
\(743\) −42.0432 −0.0565857 −0.0282929 0.999600i \(-0.509007\pi\)
−0.0282929 + 0.999600i \(0.509007\pi\)
\(744\) 871.714 1.17166
\(745\) 59.7205i 0.0801617i
\(746\) 367.195i 0.492218i
\(747\) 296.896i 0.397451i
\(748\) 104.695i 0.139967i
\(749\) 1594.92 2.12940
\(750\) 33.1073i 0.0441431i
\(751\) 1078.71i 1.43636i −0.695858 0.718180i \(-0.744975\pi\)
0.695858 0.718180i \(-0.255025\pi\)
\(752\) 129.976i 0.172841i
\(753\) −2.33503 −0.00310097
\(754\) −351.123 −0.465680
\(755\) 7.22284i 0.00956667i
\(756\) 115.485 0.152758
\(757\) −247.277 −0.326654 −0.163327 0.986572i \(-0.552223\pi\)
−0.163327 + 0.986572i \(0.552223\pi\)
\(758\) 745.470i 0.983470i
\(759\) −398.288 −0.524753
\(760\) 36.3351i 0.0478093i
\(761\) 681.030 0.894914 0.447457 0.894305i \(-0.352330\pi\)
0.447457 + 0.894305i \(0.352330\pi\)
\(762\) 521.532i 0.684425i
\(763\) 1537.39i 2.01492i
\(764\) 420.831i 0.550826i
\(765\) −2.79709 −0.00365633
\(766\) 401.143i 0.523685i
\(767\) −295.967 585.077i −0.385876 0.762812i
\(768\) 471.960 0.614531
\(769\) 1018.02i 1.32382i 0.749582 + 0.661912i \(0.230255\pi\)
−0.749582 + 0.661912i \(0.769745\pi\)
\(770\) 62.7824 0.0815356
\(771\) −521.556 −0.676466
\(772\) 356.328 0.461565
\(773\) 1082.79i 1.40076i −0.713770 0.700380i \(-0.753014\pi\)
0.713770 0.700380i \(-0.246986\pi\)
\(774\) 329.262 0.425403
\(775\) 1483.52i 1.91422i
\(776\) −93.1664 −0.120060
\(777\) 800.977i 1.03086i
\(778\) 868.518i 1.11635i
\(779\) −1233.12 −1.58296
\(780\) 10.7397i 0.0137688i
\(781\) 889.236i 1.13859i
\(782\) −72.9101 −0.0932354
\(783\) −117.271 −0.149772
\(784\) −256.213 −0.326802
\(785\) 5.05014i 0.00643330i
\(786\) 193.546 0.246242
\(787\) 302.623 0.384527 0.192263 0.981343i \(-0.438417\pi\)
0.192263 + 0.981343i \(0.438417\pi\)
\(788\) 536.013 0.680219
\(789\) −143.195 −0.181490
\(790\) 23.8203i 0.0301523i
\(791\) 230.827i 0.291817i
\(792\) −381.851