Properties

Label 1053.2.e.m.352.1
Level $1053$
Weight $2$
Character 1053.352
Analytic conductor $8.408$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.40824733284\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1053.352
Dual form 1053.2.e.m.703.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 - 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(1.41421 - 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} -1.58579 q^{8} +O(q^{10})\) \(q+(-0.207107 - 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(1.41421 - 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} -1.58579 q^{8} -1.17157 q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.585786 + 1.01461i) q^{14} +(-1.50000 - 2.59808i) q^{16} +7.65685 q^{17} -2.82843 q^{19} +(-2.58579 - 4.47871i) q^{20} +(0.414214 - 0.717439i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{25} -0.414214 q^{26} -5.17157 q^{28} +(-1.00000 - 1.73205i) q^{29} +(0.585786 - 1.01461i) q^{31} +(-2.20711 + 3.82282i) q^{32} +(-1.58579 - 2.74666i) q^{34} -8.00000 q^{35} -7.65685 q^{37} +(0.585786 + 1.01461i) q^{38} +(-2.24264 + 3.88437i) q^{40} +(-2.58579 + 4.47871i) q^{41} +(0.828427 + 1.43488i) q^{43} +3.65685 q^{44} -1.65685 q^{46} +(5.82843 + 10.0951i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.621320 + 1.07616i) q^{50} +(-0.914214 - 1.58346i) q^{52} -2.00000 q^{53} +5.65685 q^{55} +(2.24264 + 3.88437i) q^{56} +(-0.414214 + 0.717439i) q^{58} +(-3.82843 + 6.63103i) q^{59} +(-6.65685 - 11.5300i) q^{61} -0.485281 q^{62} -4.17157 q^{64} +(-1.41421 - 2.44949i) q^{65} +(-3.41421 + 5.91359i) q^{67} +(7.00000 - 12.1244i) q^{68} +(1.65685 + 2.86976i) q^{70} +2.00000 q^{71} +0.343146 q^{73} +(1.58579 + 2.74666i) q^{74} +(-2.58579 + 4.47871i) q^{76} +(2.82843 - 4.89898i) q^{77} +(5.65685 + 9.79796i) q^{79} -8.48528 q^{80} +2.14214 q^{82} +(-1.82843 - 3.16693i) q^{83} +(10.8284 - 18.7554i) q^{85} +(0.343146 - 0.594346i) q^{86} +(-1.58579 - 2.74666i) q^{88} +14.8284 q^{89} -2.82843 q^{91} +(-3.65685 - 6.33386i) q^{92} +(2.41421 - 4.18154i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(-1.82843 - 3.16693i) q^{97} +0.414214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 12q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 12q^{8} - 16q^{10} + 4q^{11} + 2q^{13} - 8q^{14} - 6q^{16} + 8q^{17} - 16q^{20} - 4q^{22} + 8q^{23} - 6q^{25} + 4q^{26} - 32q^{28} - 4q^{29} + 8q^{31} - 6q^{32} - 12q^{34} - 32q^{35} - 8q^{37} + 8q^{38} + 8q^{40} - 16q^{41} - 8q^{43} - 8q^{44} + 16q^{46} + 12q^{47} - 2q^{49} + 6q^{50} + 2q^{52} - 8q^{53} - 8q^{56} + 4q^{58} - 4q^{59} - 4q^{61} + 32q^{62} - 28q^{64} - 8q^{67} + 28q^{68} - 16q^{70} + 8q^{71} + 24q^{73} + 12q^{74} - 16q^{76} - 48q^{82} + 4q^{83} + 32q^{85} + 24q^{86} - 12q^{88} + 48q^{89} + 8q^{92} + 4q^{94} - 16q^{95} + 4q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(730\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 0.358719i −0.146447 0.253653i 0.783465 0.621436i \(-0.213450\pi\)
−0.929912 + 0.367783i \(0.880117\pi\)
\(3\) 0 0
\(4\) 0.914214 1.58346i 0.457107 0.791732i
\(5\) 1.41421 2.44949i 0.632456 1.09545i −0.354593 0.935021i \(-0.615380\pi\)
0.987048 0.160424i \(-0.0512862\pi\)
\(6\) 0 0
\(7\) −1.41421 2.44949i −0.534522 0.925820i −0.999186 0.0403329i \(-0.987158\pi\)
0.464664 0.885487i \(-0.346175\pi\)
\(8\) −1.58579 −0.560660
\(9\) 0 0
\(10\) −1.17157 −0.370484
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) −0.585786 + 1.01461i −0.156558 + 0.271166i
\(15\) 0 0
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 7.65685 1.85706 0.928530 0.371257i \(-0.121073\pi\)
0.928530 + 0.371257i \(0.121073\pi\)
\(18\) 0 0
\(19\) −2.82843 −0.648886 −0.324443 0.945905i \(-0.605177\pi\)
−0.324443 + 0.945905i \(0.605177\pi\)
\(20\) −2.58579 4.47871i −0.578199 1.00147i
\(21\) 0 0
\(22\) 0.414214 0.717439i 0.0883106 0.152958i
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) −0.414214 −0.0812340
\(27\) 0 0
\(28\) −5.17157 −0.977335
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0 0
\(31\) 0.585786 1.01461i 0.105210 0.182230i −0.808614 0.588340i \(-0.799782\pi\)
0.913824 + 0.406110i \(0.133115\pi\)
\(32\) −2.20711 + 3.82282i −0.390165 + 0.675786i
\(33\) 0 0
\(34\) −1.58579 2.74666i −0.271960 0.471049i
\(35\) −8.00000 −1.35225
\(36\) 0 0
\(37\) −7.65685 −1.25878 −0.629390 0.777090i \(-0.716695\pi\)
−0.629390 + 0.777090i \(0.716695\pi\)
\(38\) 0.585786 + 1.01461i 0.0950271 + 0.164592i
\(39\) 0 0
\(40\) −2.24264 + 3.88437i −0.354593 + 0.614172i
\(41\) −2.58579 + 4.47871i −0.403832 + 0.699458i −0.994185 0.107688i \(-0.965655\pi\)
0.590353 + 0.807145i \(0.298989\pi\)
\(42\) 0 0
\(43\) 0.828427 + 1.43488i 0.126334 + 0.218817i 0.922254 0.386585i \(-0.126346\pi\)
−0.795920 + 0.605402i \(0.793012\pi\)
\(44\) 3.65685 0.551292
\(45\) 0 0
\(46\) −1.65685 −0.244290
\(47\) 5.82843 + 10.0951i 0.850163 + 1.47253i 0.881060 + 0.473004i \(0.156830\pi\)
−0.0308969 + 0.999523i \(0.509836\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −0.621320 + 1.07616i −0.0878680 + 0.152192i
\(51\) 0 0
\(52\) −0.914214 1.58346i −0.126779 0.219587i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 5.65685 0.762770
\(56\) 2.24264 + 3.88437i 0.299685 + 0.519070i
\(57\) 0 0
\(58\) −0.414214 + 0.717439i −0.0543889 + 0.0942043i
\(59\) −3.82843 + 6.63103i −0.498419 + 0.863287i −0.999998 0.00182490i \(-0.999419\pi\)
0.501580 + 0.865112i \(0.332752\pi\)
\(60\) 0 0
\(61\) −6.65685 11.5300i −0.852323 1.47627i −0.879107 0.476625i \(-0.841860\pi\)
0.0267837 0.999641i \(-0.491473\pi\)
\(62\) −0.485281 −0.0616308
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) −1.41421 2.44949i −0.175412 0.303822i
\(66\) 0 0
\(67\) −3.41421 + 5.91359i −0.417113 + 0.722460i −0.995648 0.0931973i \(-0.970291\pi\)
0.578535 + 0.815657i \(0.303625\pi\)
\(68\) 7.00000 12.1244i 0.848875 1.47029i
\(69\) 0 0
\(70\) 1.65685 + 2.86976i 0.198032 + 0.343001i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) 0.343146 0.0401622 0.0200811 0.999798i \(-0.493608\pi\)
0.0200811 + 0.999798i \(0.493608\pi\)
\(74\) 1.58579 + 2.74666i 0.184344 + 0.319293i
\(75\) 0 0
\(76\) −2.58579 + 4.47871i −0.296610 + 0.513744i
\(77\) 2.82843 4.89898i 0.322329 0.558291i
\(78\) 0 0
\(79\) 5.65685 + 9.79796i 0.636446 + 1.10236i 0.986207 + 0.165518i \(0.0529295\pi\)
−0.349761 + 0.936839i \(0.613737\pi\)
\(80\) −8.48528 −0.948683
\(81\) 0 0
\(82\) 2.14214 0.236559
\(83\) −1.82843 3.16693i −0.200696 0.347616i 0.748057 0.663635i \(-0.230987\pi\)
−0.948753 + 0.316019i \(0.897654\pi\)
\(84\) 0 0
\(85\) 10.8284 18.7554i 1.17451 2.03431i
\(86\) 0.343146 0.594346i 0.0370024 0.0640900i
\(87\) 0 0
\(88\) −1.58579 2.74666i −0.169045 0.292795i
\(89\) 14.8284 1.57181 0.785905 0.618347i \(-0.212197\pi\)
0.785905 + 0.618347i \(0.212197\pi\)
\(90\) 0 0
\(91\) −2.82843 −0.296500
\(92\) −3.65685 6.33386i −0.381253 0.660350i
\(93\) 0 0
\(94\) 2.41421 4.18154i 0.249007 0.431293i
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0 0
\(97\) −1.82843 3.16693i −0.185649 0.321553i 0.758146 0.652085i \(-0.226105\pi\)
−0.943795 + 0.330532i \(0.892772\pi\)
\(98\) 0.414214 0.0418419
\(99\) 0 0
\(100\) −5.48528 −0.548528
\(101\) −3.82843 6.63103i −0.380943 0.659812i 0.610255 0.792205i \(-0.291067\pi\)
−0.991197 + 0.132393i \(0.957734\pi\)
\(102\) 0 0
\(103\) −1.17157 + 2.02922i −0.115439 + 0.199945i −0.917955 0.396685i \(-0.870161\pi\)
0.802516 + 0.596630i \(0.203494\pi\)
\(104\) −0.792893 + 1.37333i −0.0777496 + 0.134666i
\(105\) 0 0
\(106\) 0.414214 + 0.717439i 0.0402320 + 0.0696838i
\(107\) −11.3137 −1.09374 −0.546869 0.837218i \(-0.684180\pi\)
−0.546869 + 0.837218i \(0.684180\pi\)
\(108\) 0 0
\(109\) 5.31371 0.508961 0.254480 0.967078i \(-0.418096\pi\)
0.254480 + 0.967078i \(0.418096\pi\)
\(110\) −1.17157 2.02922i −0.111705 0.193479i
\(111\) 0 0
\(112\) −4.24264 + 7.34847i −0.400892 + 0.694365i
\(113\) 2.65685 4.60181i 0.249936 0.432902i −0.713572 0.700582i \(-0.752924\pi\)
0.963508 + 0.267680i \(0.0862571\pi\)
\(114\) 0 0
\(115\) −5.65685 9.79796i −0.527504 0.913664i
\(116\) −3.65685 −0.339530
\(117\) 0 0
\(118\) 3.17157 0.291967
\(119\) −10.8284 18.7554i −0.992640 1.71930i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −2.75736 + 4.77589i −0.249640 + 0.432388i
\(123\) 0 0
\(124\) −1.07107 1.85514i −0.0961847 0.166597i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 5.65685 0.501965 0.250982 0.967992i \(-0.419246\pi\)
0.250982 + 0.967992i \(0.419246\pi\)
\(128\) 5.27817 + 9.14207i 0.466529 + 0.808052i
\(129\) 0 0
\(130\) −0.585786 + 1.01461i −0.0513769 + 0.0889873i
\(131\) 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 0 0
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) 2.82843 0.244339
\(135\) 0 0
\(136\) −12.1421 −1.04118
\(137\) 5.41421 + 9.37769i 0.462567 + 0.801190i 0.999088 0.0426968i \(-0.0135950\pi\)
−0.536521 + 0.843887i \(0.680262\pi\)
\(138\) 0 0
\(139\) 3.65685 6.33386i 0.310170 0.537231i −0.668229 0.743956i \(-0.732947\pi\)
0.978399 + 0.206725i \(0.0662806\pi\)
\(140\) −7.31371 + 12.6677i −0.618121 + 1.07062i
\(141\) 0 0
\(142\) −0.414214 0.717439i −0.0347600 0.0602061i
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −5.65685 −0.469776
\(146\) −0.0710678 0.123093i −0.00588161 0.0101873i
\(147\) 0 0
\(148\) −7.00000 + 12.1244i −0.575396 + 0.996616i
\(149\) 4.58579 7.94282i 0.375682 0.650701i −0.614747 0.788725i \(-0.710742\pi\)
0.990429 + 0.138024i \(0.0440751\pi\)
\(150\) 0 0
\(151\) 1.75736 + 3.04384i 0.143012 + 0.247704i 0.928629 0.371009i \(-0.120988\pi\)
−0.785618 + 0.618712i \(0.787655\pi\)
\(152\) 4.48528 0.363804
\(153\) 0 0
\(154\) −2.34315 −0.188816
\(155\) −1.65685 2.86976i −0.133082 0.230504i
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 2.34315 4.05845i 0.186411 0.322873i
\(159\) 0 0
\(160\) 6.24264 + 10.8126i 0.493524 + 0.854809i
\(161\) −11.3137 −0.891645
\(162\) 0 0
\(163\) 18.8284 1.47476 0.737378 0.675480i \(-0.236064\pi\)
0.737378 + 0.675480i \(0.236064\pi\)
\(164\) 4.72792 + 8.18900i 0.369189 + 0.639454i
\(165\) 0 0
\(166\) −0.757359 + 1.31178i −0.0587825 + 0.101814i
\(167\) 1.82843 3.16693i 0.141488 0.245064i −0.786569 0.617502i \(-0.788145\pi\)
0.928057 + 0.372438i \(0.121478\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −8.97056 −0.688011
\(171\) 0 0
\(172\) 3.02944 0.230992
\(173\) 5.82843 + 10.0951i 0.443127 + 0.767519i 0.997920 0.0644701i \(-0.0205357\pi\)
−0.554793 + 0.831989i \(0.687202\pi\)
\(174\) 0 0
\(175\) −4.24264 + 7.34847i −0.320713 + 0.555492i
\(176\) 3.00000 5.19615i 0.226134 0.391675i
\(177\) 0 0
\(178\) −3.07107 5.31925i −0.230186 0.398694i
\(179\) −23.3137 −1.74255 −0.871274 0.490797i \(-0.836706\pi\)
−0.871274 + 0.490797i \(0.836706\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0.585786 + 1.01461i 0.0434214 + 0.0752080i
\(183\) 0 0
\(184\) −3.17157 + 5.49333i −0.233811 + 0.404973i
\(185\) −10.8284 + 18.7554i −0.796122 + 1.37892i
\(186\) 0 0
\(187\) 7.65685 + 13.2621i 0.559925 + 0.969818i
\(188\) 21.3137 1.55446
\(189\) 0 0
\(190\) 3.31371 0.240402
\(191\) −1.65685 2.86976i −0.119886 0.207648i 0.799836 0.600218i \(-0.204919\pi\)
−0.919722 + 0.392570i \(0.871586\pi\)
\(192\) 0 0
\(193\) −2.65685 + 4.60181i −0.191245 + 0.331245i −0.945663 0.325149i \(-0.894586\pi\)
0.754418 + 0.656394i \(0.227919\pi\)
\(194\) −0.757359 + 1.31178i −0.0543752 + 0.0941807i
\(195\) 0 0
\(196\) 0.914214 + 1.58346i 0.0653010 + 0.113105i
\(197\) 0.485281 0.0345749 0.0172874 0.999851i \(-0.494497\pi\)
0.0172874 + 0.999851i \(0.494497\pi\)
\(198\) 0 0
\(199\) 21.6569 1.53521 0.767607 0.640921i \(-0.221447\pi\)
0.767607 + 0.640921i \(0.221447\pi\)
\(200\) 2.37868 + 4.11999i 0.168198 + 0.291328i
\(201\) 0 0
\(202\) −1.58579 + 2.74666i −0.111576 + 0.193255i
\(203\) −2.82843 + 4.89898i −0.198517 + 0.343841i
\(204\) 0 0
\(205\) 7.31371 + 12.6677i 0.510812 + 0.884752i
\(206\) 0.970563 0.0676223
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) −2.82843 4.89898i −0.195646 0.338869i
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) −1.82843 + 3.16693i −0.125577 + 0.217506i
\(213\) 0 0
\(214\) 2.34315 + 4.05845i 0.160174 + 0.277430i
\(215\) 4.68629 0.319602
\(216\) 0 0
\(217\) −3.31371 −0.224949
\(218\) −1.10051 1.90613i −0.0745356 0.129099i
\(219\) 0 0
\(220\) 5.17157 8.95743i 0.348667 0.603910i
\(221\) 3.82843 6.63103i 0.257528 0.446051i
\(222\) 0 0
\(223\) 6.24264 + 10.8126i 0.418038 + 0.724063i 0.995742 0.0921831i \(-0.0293845\pi\)
−0.577704 + 0.816246i \(0.696051\pi\)
\(224\) 12.4853 0.834208
\(225\) 0 0
\(226\) −2.20101 −0.146409
\(227\) 8.65685 + 14.9941i 0.574576 + 0.995194i 0.996088 + 0.0883713i \(0.0281662\pi\)
−0.421512 + 0.906823i \(0.638500\pi\)
\(228\) 0 0
\(229\) 0.656854 1.13770i 0.0434062 0.0751817i −0.843506 0.537120i \(-0.819512\pi\)
0.886912 + 0.461938i \(0.152846\pi\)
\(230\) −2.34315 + 4.05845i −0.154502 + 0.267606i
\(231\) 0 0
\(232\) 1.58579 + 2.74666i 0.104112 + 0.180327i
\(233\) 6.97056 0.456657 0.228328 0.973584i \(-0.426674\pi\)
0.228328 + 0.973584i \(0.426674\pi\)
\(234\) 0 0
\(235\) 32.9706 2.15076
\(236\) 7.00000 + 12.1244i 0.455661 + 0.789228i
\(237\) 0 0
\(238\) −4.48528 + 7.76874i −0.290738 + 0.503572i
\(239\) −1.00000 + 1.73205i −0.0646846 + 0.112037i −0.896554 0.442934i \(-0.853937\pi\)
0.831869 + 0.554971i \(0.187271\pi\)
\(240\) 0 0
\(241\) −0.171573 0.297173i −0.0110520 0.0191426i 0.860447 0.509541i \(-0.170185\pi\)
−0.871499 + 0.490398i \(0.836851\pi\)
\(242\) −2.89949 −0.186387
\(243\) 0 0
\(244\) −24.3431 −1.55841
\(245\) 1.41421 + 2.44949i 0.0903508 + 0.156492i
\(246\) 0 0
\(247\) −1.41421 + 2.44949i −0.0899843 + 0.155857i
\(248\) −0.928932 + 1.60896i −0.0589873 + 0.102169i
\(249\) 0 0
\(250\) −1.17157 2.02922i −0.0740968 0.128339i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −1.17157 2.02922i −0.0735110 0.127325i
\(255\) 0 0
\(256\) −1.98528 + 3.43861i −0.124080 + 0.214913i
\(257\) 2.17157 3.76127i 0.135459 0.234622i −0.790314 0.612702i \(-0.790082\pi\)
0.925773 + 0.378081i \(0.123416\pi\)
\(258\) 0 0
\(259\) 10.8284 + 18.7554i 0.672846 + 1.16540i
\(260\) −5.17157 −0.320727
\(261\) 0 0
\(262\) −3.31371 −0.204722
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) −2.82843 + 4.89898i −0.173749 + 0.300942i
\(266\) 1.65685 2.86976i 0.101588 0.175956i
\(267\) 0 0
\(268\) 6.24264 + 10.8126i 0.381330 + 0.660483i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −27.7990 −1.68867 −0.844334 0.535817i \(-0.820004\pi\)
−0.844334 + 0.535817i \(0.820004\pi\)
\(272\) −11.4853 19.8931i −0.696397 1.20620i
\(273\) 0 0
\(274\) 2.24264 3.88437i 0.135483 0.234663i
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 0 0
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) −3.02944 −0.181694
\(279\) 0 0
\(280\) 12.6863 0.758151
\(281\) −10.5858 18.3351i −0.631495 1.09378i −0.987246 0.159201i \(-0.949108\pi\)
0.355751 0.934581i \(-0.384225\pi\)
\(282\) 0 0
\(283\) −14.4853 + 25.0892i −0.861061 + 1.49140i 0.00984565 + 0.999952i \(0.496866\pi\)
−0.870906 + 0.491449i \(0.836467\pi\)
\(284\) 1.82843 3.16693i 0.108497 0.187923i
\(285\) 0 0
\(286\) −0.414214 0.717439i −0.0244930 0.0424231i
\(287\) 14.6274 0.863429
\(288\) 0 0
\(289\) 41.6274 2.44867
\(290\) 1.17157 + 2.02922i 0.0687971 + 0.119160i
\(291\) 0 0
\(292\) 0.313708 0.543359i 0.0183584 0.0317977i
\(293\) −1.07107 + 1.85514i −0.0625724 + 0.108379i −0.895615 0.444831i \(-0.853264\pi\)
0.833042 + 0.553210i \(0.186597\pi\)
\(294\) 0 0
\(295\) 10.8284 + 18.7554i 0.630455 + 1.09198i
\(296\) 12.1421 0.705747
\(297\) 0 0
\(298\) −3.79899 −0.220070
\(299\) −2.00000 3.46410i −0.115663 0.200334i
\(300\) 0 0
\(301\) 2.34315 4.05845i 0.135057 0.233925i
\(302\) 0.727922 1.26080i 0.0418872 0.0725508i
\(303\) 0 0
\(304\) 4.24264 + 7.34847i 0.243332 + 0.421464i
\(305\) −37.6569 −2.15623
\(306\) 0 0
\(307\) −22.8284 −1.30289 −0.651444 0.758697i \(-0.725836\pi\)
−0.651444 + 0.758697i \(0.725836\pi\)
\(308\) −5.17157 8.95743i −0.294678 0.510397i
\(309\) 0 0
\(310\) −0.686292 + 1.18869i −0.0389787 + 0.0675132i
\(311\) 5.31371 9.20361i 0.301313 0.521889i −0.675121 0.737707i \(-0.735909\pi\)
0.976434 + 0.215818i \(0.0692418\pi\)
\(312\) 0 0
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) −4.14214 −0.233754
\(315\) 0 0
\(316\) 20.6863 1.16369
\(317\) −4.24264 7.34847i −0.238290 0.412731i 0.721933 0.691963i \(-0.243254\pi\)
−0.960224 + 0.279231i \(0.909920\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) −5.89949 + 10.2182i −0.329792 + 0.571216i
\(321\) 0 0
\(322\) 2.34315 + 4.05845i 0.130578 + 0.226168i
\(323\) −21.6569 −1.20502
\(324\) 0 0
\(325\) −3.00000 −0.166410
\(326\) −3.89949 6.75412i −0.215973 0.374076i
\(327\) 0 0
\(328\) 4.10051 7.10228i 0.226413 0.392158i
\(329\) 16.4853 28.5533i 0.908863 1.57420i
\(330\) 0 0
\(331\) −13.0711 22.6398i −0.718451 1.24439i −0.961613 0.274408i \(-0.911518\pi\)
0.243163 0.969986i \(-0.421815\pi\)
\(332\) −6.68629 −0.366958
\(333\) 0 0
\(334\) −1.51472 −0.0828817
\(335\) 9.65685 + 16.7262i 0.527610 + 0.913848i
\(336\) 0 0
\(337\) −4.65685 + 8.06591i −0.253675 + 0.439378i −0.964535 0.263956i \(-0.914973\pi\)
0.710860 + 0.703334i \(0.248306\pi\)
\(338\) −0.207107 + 0.358719i −0.0112651 + 0.0195118i
\(339\) 0 0
\(340\) −19.7990 34.2929i −1.07375 1.85979i
\(341\) 2.34315 0.126888
\(342\) 0 0
\(343\) −16.9706 −0.916324
\(344\) −1.31371 2.27541i −0.0708304 0.122682i
\(345\) 0 0
\(346\) 2.41421 4.18154i 0.129789 0.224801i
\(347\) 4.34315 7.52255i 0.233152 0.403832i −0.725582 0.688136i \(-0.758429\pi\)
0.958734 + 0.284304i \(0.0917626\pi\)
\(348\) 0 0
\(349\) −1.82843 3.16693i −0.0978735 0.169522i 0.812931 0.582360i \(-0.197871\pi\)
−0.910804 + 0.412839i \(0.864537\pi\)
\(350\) 3.51472 0.187870
\(351\) 0 0
\(352\) −8.82843 −0.470557
\(353\) 16.7279 + 28.9736i 0.890337 + 1.54211i 0.839471 + 0.543404i \(0.182865\pi\)
0.0508663 + 0.998705i \(0.483802\pi\)
\(354\) 0 0
\(355\) 2.82843 4.89898i 0.150117 0.260011i
\(356\) 13.5563 23.4803i 0.718485 1.24445i
\(357\) 0 0
\(358\) 4.82843 + 8.36308i 0.255190 + 0.442003i
\(359\) 34.9706 1.84568 0.922838 0.385189i \(-0.125864\pi\)
0.922838 + 0.385189i \(0.125864\pi\)
\(360\) 0 0
\(361\) −11.0000 −0.578947
\(362\) −2.89949 5.02207i −0.152394 0.263954i
\(363\) 0 0
\(364\) −2.58579 + 4.47871i −0.135532 + 0.234748i
\(365\) 0.485281 0.840532i 0.0254008 0.0439955i
\(366\) 0 0
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) −12.0000 −0.625543
\(369\) 0 0
\(370\) 8.97056 0.466357
\(371\) 2.82843 + 4.89898i 0.146845 + 0.254342i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 3.17157 5.49333i 0.163998 0.284053i
\(375\) 0 0
\(376\) −9.24264 16.0087i −0.476653 0.825587i
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) 0.485281 0.0249272 0.0124636 0.999922i \(-0.496033\pi\)
0.0124636 + 0.999922i \(0.496033\pi\)
\(380\) 7.31371 + 12.6677i 0.375185 + 0.649840i
\(381\) 0 0
\(382\) −0.686292 + 1.18869i −0.0351137 + 0.0608188i
\(383\) −15.4853 + 26.8213i −0.791261 + 1.37050i 0.133926 + 0.990991i \(0.457242\pi\)
−0.925187 + 0.379513i \(0.876092\pi\)
\(384\) 0 0
\(385\) −8.00000 13.8564i −0.407718 0.706188i
\(386\) 2.20101 0.112028
\(387\) 0 0
\(388\) −6.68629 −0.339445
\(389\) 13.4853 + 23.3572i 0.683731 + 1.18426i 0.973834 + 0.227261i \(0.0729771\pi\)
−0.290103 + 0.956995i \(0.593690\pi\)
\(390\) 0 0
\(391\) 15.3137 26.5241i 0.774448 1.34138i
\(392\) 0.792893 1.37333i 0.0400472 0.0693637i
\(393\) 0 0
\(394\) −0.100505 0.174080i −0.00506337 0.00877002i
\(395\) 32.0000 1.61009
\(396\) 0 0
\(397\) 30.9706 1.55437 0.777184 0.629273i \(-0.216647\pi\)
0.777184 + 0.629273i \(0.216647\pi\)
\(398\) −4.48528 7.76874i −0.224827 0.389412i
\(399\) 0 0
\(400\) −4.50000 + 7.79423i −0.225000 + 0.389711i
\(401\) −13.0711 + 22.6398i −0.652738 + 1.13058i 0.329718 + 0.944080i \(0.393046\pi\)
−0.982456 + 0.186496i \(0.940287\pi\)
\(402\) 0 0
\(403\) −0.585786 1.01461i −0.0291801 0.0505414i
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) 2.34315 0.116288
\(407\) −7.65685 13.2621i −0.379536 0.657376i
\(408\) 0 0
\(409\) 17.4853 30.2854i 0.864592 1.49752i −0.00286068 0.999996i \(-0.500911\pi\)
0.867452 0.497521i \(-0.165756\pi\)
\(410\) 3.02944 5.24714i 0.149613 0.259138i
\(411\) 0 0
\(412\) 2.14214 + 3.71029i 0.105535 + 0.182793i
\(413\) 21.6569 1.06566
\(414\) 0 0
\(415\) −10.3431 −0.507725
\(416\) 2.20711 + 3.82282i 0.108212 + 0.187429i
\(417\) 0 0
\(418\) −1.17157 + 2.02922i −0.0573035 + 0.0992526i
\(419\) −7.31371 + 12.6677i −0.357298 + 0.618858i −0.987508 0.157566i \(-0.949635\pi\)
0.630210 + 0.776424i \(0.282969\pi\)
\(420\) 0 0
\(421\) −18.6569 32.3146i −0.909279 1.57492i −0.815067 0.579366i \(-0.803300\pi\)
−0.0942120 0.995552i \(-0.530033\pi\)
\(422\) −4.97056 −0.241963
\(423\) 0 0
\(424\) 3.17157 0.154025
\(425\) −11.4853 19.8931i −0.557118 0.964957i
\(426\) 0 0
\(427\) −18.8284 + 32.6118i −0.911171 + 1.57820i
\(428\) −10.3431 + 17.9149i −0.499955 + 0.865947i
\(429\) 0 0
\(430\) −0.970563 1.68106i −0.0468047 0.0810681i
\(431\) 8.34315 0.401875 0.200938 0.979604i \(-0.435601\pi\)
0.200938 + 0.979604i \(0.435601\pi\)
\(432\) 0 0
\(433\) −21.3137 −1.02427 −0.512136 0.858905i \(-0.671146\pi\)
−0.512136 + 0.858905i \(0.671146\pi\)
\(434\) 0.686292 + 1.18869i 0.0329430 + 0.0570590i
\(435\) 0 0
\(436\) 4.85786 8.41407i 0.232650 0.402961i
\(437\) −5.65685 + 9.79796i −0.270604 + 0.468700i
\(438\) 0 0
\(439\) −8.48528 14.6969i −0.404980 0.701447i 0.589339 0.807886i \(-0.299388\pi\)
−0.994319 + 0.106439i \(0.966055\pi\)
\(440\) −8.97056 −0.427655
\(441\) 0 0
\(442\) −3.17157 −0.150856
\(443\) 12.9706 + 22.4657i 0.616250 + 1.06738i 0.990164 + 0.139913i \(0.0446823\pi\)
−0.373914 + 0.927463i \(0.621984\pi\)
\(444\) 0 0
\(445\) 20.9706 36.3221i 0.994100 1.72183i
\(446\) 2.58579 4.47871i 0.122441 0.212073i
\(447\) 0 0
\(448\) 5.89949 + 10.2182i 0.278725 + 0.482766i
\(449\) −31.7990 −1.50069 −0.750344 0.661048i \(-0.770112\pi\)
−0.750344 + 0.661048i \(0.770112\pi\)
\(450\) 0 0
\(451\) −10.3431 −0.487040
\(452\) −4.85786 8.41407i −0.228495 0.395764i
\(453\) 0 0
\(454\) 3.58579 6.21076i 0.168289 0.291486i
\(455\) −4.00000 + 6.92820i −0.187523 + 0.324799i
\(456\) 0 0
\(457\) 3.82843 + 6.63103i 0.179086 + 0.310187i 0.941568 0.336823i \(-0.109353\pi\)
−0.762482 + 0.647010i \(0.776019\pi\)
\(458\) −0.544156 −0.0254267
\(459\) 0 0
\(460\) −20.6863 −0.964503
\(461\) −2.58579 4.47871i −0.120432 0.208594i 0.799506 0.600658i \(-0.205095\pi\)
−0.919938 + 0.392064i \(0.871761\pi\)
\(462\) 0 0
\(463\) 12.2426 21.2049i 0.568964 0.985474i −0.427705 0.903918i \(-0.640678\pi\)
0.996669 0.0815558i \(-0.0259889\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) −1.44365 2.50048i −0.0668758 0.115832i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) 19.3137 0.891824
\(470\) −6.82843 11.8272i −0.314972 0.545547i
\(471\) 0 0
\(472\) 6.07107 10.5154i 0.279444 0.484010i
\(473\) −1.65685 + 2.86976i −0.0761822 + 0.131952i
\(474\) 0 0
\(475\) 4.24264 + 7.34847i 0.194666 + 0.337171i
\(476\) −39.5980 −1.81497
\(477\) 0 0
\(478\) 0.828427 0.0378914
\(479\) −12.6569 21.9223i −0.578306 1.00166i −0.995674 0.0929182i \(-0.970380\pi\)
0.417367 0.908738i \(-0.362953\pi\)
\(480\) 0 0
\(481\) −3.82843 + 6.63103i −0.174561 + 0.302349i
\(482\) −0.0710678 + 0.123093i −0.00323705 + 0.00560674i
\(483\) 0 0
\(484\) −6.39949 11.0843i −0.290886 0.503830i
\(485\) −10.3431 −0.469658
\(486\) 0 0
\(487\) −7.79899 −0.353406 −0.176703 0.984264i \(-0.556543\pi\)
−0.176703 + 0.984264i \(0.556543\pi\)
\(488\) 10.5563 + 18.2841i 0.477863 + 0.827684i
\(489\) 0 0
\(490\) 0.585786 1.01461i 0.0264631 0.0458355i
\(491\) −15.3137 + 26.5241i −0.691098 + 1.19702i 0.280380 + 0.959889i \(0.409539\pi\)
−0.971478 + 0.237128i \(0.923794\pi\)
\(492\) 0 0
\(493\) −7.65685 13.2621i −0.344847 0.597293i
\(494\) 1.17157 0.0527116
\(495\) 0 0
\(496\) −3.51472 −0.157816
\(497\) −2.82843 4.89898i −0.126872 0.219749i
\(498\) 0 0
\(499\) −13.0711 + 22.6398i −0.585141 + 1.01349i 0.409716 + 0.912213i \(0.365628\pi\)
−0.994858 + 0.101282i \(0.967706\pi\)
\(500\) 5.17157 8.95743i 0.231280 0.400588i
\(501\) 0 0
\(502\) 0 0
\(503\) −7.31371 −0.326102 −0.163051 0.986618i \(-0.552134\pi\)
−0.163051 + 0.986618i \(0.552134\pi\)
\(504\) 0 0
\(505\) −21.6569 −0.963717
\(506\) −1.65685 2.86976i −0.0736562 0.127576i
\(507\) 0 0
\(508\) 5.17157 8.95743i 0.229451 0.397422i
\(509\) −5.89949 + 10.2182i −0.261491 + 0.452915i −0.966638 0.256146i \(-0.917547\pi\)
0.705148 + 0.709060i \(0.250881\pi\)
\(510\) 0 0
\(511\) −0.485281 0.840532i −0.0214676 0.0371829i
\(512\) 22.7574 1.00574
\(513\) 0 0
\(514\) −1.79899 −0.0793500
\(515\) 3.31371 + 5.73951i 0.146019 + 0.252913i
\(516\) 0 0
\(517\) −11.6569 + 20.1903i −0.512668 + 0.887967i
\(518\) 4.48528 7.76874i 0.197072 0.341339i
\(519\) 0 0
\(520\) 2.24264 + 3.88437i 0.0983463 + 0.170341i
\(521\) 25.3137 1.10901 0.554507 0.832179i \(-0.312907\pi\)
0.554507 + 0.832179i \(0.312907\pi\)
\(522\) 0 0
\(523\) −15.3137 −0.669622 −0.334811 0.942285i \(-0.608672\pi\)
−0.334811 + 0.942285i \(0.608672\pi\)
\(524\) −7.31371 12.6677i −0.319501 0.553392i
\(525\) 0 0
\(526\) −2.48528 + 4.30463i −0.108363 + 0.187691i
\(527\) 4.48528 7.76874i 0.195382 0.338411i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 2.34315 0.101780
\(531\) 0 0
\(532\) 14.6274 0.634179
\(533\) 2.58579 + 4.47871i 0.112003 + 0.193995i
\(534\) 0 0
\(535\) −16.0000 + 27.7128i −0.691740 + 1.19813i
\(536\) 5.41421 9.37769i 0.233858 0.405055i
\(537\) 0 0
\(538\) −3.72792 6.45695i −0.160722 0.278379i
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 5.75736 + 9.97204i 0.247300 + 0.428336i
\(543\) 0 0
\(544\) −16.8995 + 29.2708i −0.724560 + 1.25497i
\(545\) 7.51472 13.0159i 0.321895 0.557539i
\(546\) 0 0
\(547\) −11.6569 20.1903i −0.498411 0.863273i 0.501587 0.865107i \(-0.332750\pi\)
−0.999998 + 0.00183374i \(0.999416\pi\)
\(548\) 19.7990 0.845771
\(549\) 0 0
\(550\) −2.48528 −0.105973
\(551\) 2.82843 + 4.89898i 0.120495 + 0.208704i
\(552\) 0 0
\(553\) 16.0000 27.7128i 0.680389 1.17847i
\(554\) 0.414214 0.717439i 0.0175982 0.0304811i
\(555\) 0 0
\(556\) −6.68629 11.5810i −0.283562 0.491144i
\(557\) −7.79899 −0.330454 −0.165227 0.986256i \(-0.552836\pi\)
−0.165227 + 0.986256i \(0.552836\pi\)
\(558\) 0 0
\(559\) 1.65685 0.0700775
\(560\) 12.0000 + 20.7846i 0.507093 + 0.878310i
\(561\) 0 0
\(562\) −4.38478 + 7.59466i −0.184961 + 0.320361i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) 0 0
\(565\) −7.51472 13.0159i −0.316147 0.547582i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) −3.17157 −0.133076
\(569\) 21.4853 + 37.2136i 0.900710 + 1.56008i 0.826575 + 0.562827i \(0.190286\pi\)
0.0741351 + 0.997248i \(0.476380\pi\)
\(570\) 0 0
\(571\) 6.48528 11.2328i 0.271401 0.470080i −0.697820 0.716273i \(-0.745847\pi\)
0.969221 + 0.246193i \(0.0791799\pi\)
\(572\) 1.82843 3.16693i 0.0764504 0.132416i
\(573\) 0 0
\(574\) −3.02944 5.24714i −0.126446 0.219011i
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −31.9411 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(578\) −8.62132 14.9326i −0.358600 0.621113i
\(579\) 0 0
\(580\) −5.17157 + 8.95743i −0.214738 + 0.371937i
\(581\) −5.17157 + 8.95743i −0.214553 + 0.371617i
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) −0.544156 −0.0225173
\(585\) 0 0
\(586\) 0.887302 0.0366541
\(587\) 5.48528 + 9.50079i 0.226402 + 0.392139i 0.956739 0.290947i \(-0.0939704\pi\)
−0.730337 + 0.683087i \(0.760637\pi\)
\(588\) 0 0
\(589\) −1.65685 + 2.86976i −0.0682695 + 0.118246i
\(590\) 4.48528 7.76874i 0.184656 0.319834i
\(591\) 0 0
\(592\) 11.4853 + 19.8931i 0.472042 + 0.817601i
\(593\) −20.4853 −0.841230 −0.420615 0.907239i \(-0.638186\pi\)
−0.420615 + 0.907239i \(0.638186\pi\)
\(594\) 0 0
\(595\) −61.2548 −2.51120
\(596\) −8.38478 14.5229i −0.343454 0.594879i
\(597\) 0 0
\(598\) −0.828427 + 1.43488i −0.0338769 + 0.0586765i
\(599\) 11.6569 20.1903i 0.476286 0.824952i −0.523345 0.852121i \(-0.675316\pi\)
0.999631 + 0.0271693i \(0.00864931\pi\)
\(600\) 0 0
\(601\) 0.313708 + 0.543359i 0.0127964 + 0.0221641i 0.872353 0.488877i \(-0.162593\pi\)
−0.859556 + 0.511041i \(0.829260\pi\)
\(602\) −1.94113 −0.0791144
\(603\) 0 0
\(604\) 6.42641 0.261487
\(605\) −9.89949 17.1464i −0.402472 0.697101i
\(606\) 0 0
\(607\) −20.9706 + 36.3221i −0.851169 + 1.47427i 0.0289853 + 0.999580i \(0.490772\pi\)
−0.880154 + 0.474688i \(0.842561\pi\)
\(608\) 6.24264 10.8126i 0.253173 0.438508i
\(609\) 0 0
\(610\) 7.79899 + 13.5082i 0.315772 + 0.546933i
\(611\) 11.6569 0.471586
\(612\) 0 0
\(613\) −47.6569 −1.92484 −0.962421 0.271561i \(-0.912460\pi\)
−0.962421 + 0.271561i \(0.912460\pi\)
\(614\) 4.72792 + 8.18900i 0.190803 + 0.330481i
\(615\) 0 0
\(616\) −4.48528 + 7.76874i −0.180717 + 0.313011i
\(617\) 17.4142 30.1623i 0.701070 1.21429i −0.267021 0.963691i \(-0.586039\pi\)
0.968091 0.250598i \(-0.0806272\pi\)
\(618\) 0 0
\(619\) −11.8995 20.6105i −0.478281 0.828407i 0.521409 0.853307i \(-0.325407\pi\)
−0.999690 + 0.0248998i \(0.992073\pi\)
\(620\) −6.05887 −0.243330
\(621\) 0 0
\(622\) −4.40202 −0.176505
\(623\) −20.9706 36.3221i −0.840168 1.45521i
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) −1.24264 + 2.15232i −0.0496659 + 0.0860239i
\(627\) 0 0
\(628\) −9.14214 15.8346i −0.364811 0.631871i
\(629\) −58.6274 −2.33763
\(630\) 0 0
\(631\) 43.1127 1.71629 0.858145 0.513408i \(-0.171617\pi\)
0.858145 + 0.513408i \(0.171617\pi\)
\(632\) −8.97056 15.5375i −0.356830 0.618047i
\(633\) 0 0
\(634\) −1.75736 + 3.04384i −0.0697937 + 0.120886i
\(635\) 8.00000 13.8564i 0.317470 0.549875i
\(636\) 0 0
\(637\) 0.500000 + 0.866025i 0.0198107 + 0.0343132i
\(638\) −1.65685 −0.0655955
\(639\) 0 0
\(640\) 29.8579 1.18024
\(641\) −15.1421 26.2269i −0.598078 1.03590i −0.993105 0.117232i \(-0.962598\pi\)
0.395026 0.918670i \(-0.370736\pi\)
\(642\) 0 0
\(643\) −11.4142 + 19.7700i −0.450133 + 0.779653i −0.998394 0.0566545i \(-0.981957\pi\)
0.548261 + 0.836307i \(0.315290\pi\)
\(644\) −10.3431 + 17.9149i −0.407577 + 0.705944i
\(645\) 0 0
\(646\) 4.48528 + 7.76874i 0.176471 + 0.305657i
\(647\) 11.3137 0.444788 0.222394 0.974957i \(-0.428613\pi\)
0.222394 + 0.974957i \(0.428613\pi\)
\(648\) 0 0
\(649\) −15.3137 −0.601116
\(650\) 0.621320 + 1.07616i 0.0243702 + 0.0422104i
\(651\) 0 0
\(652\) 17.2132 29.8141i 0.674121 1.16761i
\(653\) 12.6569 21.9223i 0.495301 0.857886i −0.504684 0.863304i \(-0.668391\pi\)
0.999985 + 0.00541749i \(0.00172445\pi\)
\(654\) 0 0
\(655\) −11.3137 19.5959i −0.442063 0.765676i
\(656\) 15.5147 0.605748
\(657\) 0 0
\(658\) −13.6569 −0.532400
\(659\) 23.6569 + 40.9749i 0.921540 + 1.59615i 0.797033 + 0.603936i \(0.206402\pi\)
0.124507 + 0.992219i \(0.460265\pi\)
\(660\) 0 0
\(661\) 17.4853 30.2854i 0.680099 1.17797i −0.294852 0.955543i \(-0.595270\pi\)
0.974950 0.222422i \(-0.0713964\pi\)
\(662\) −5.41421 + 9.37769i −0.210429 + 0.364474i
\(663\) 0 0
\(664\) 2.89949 + 5.02207i 0.112522 + 0.194894i
\(665\) 22.6274 0.877454
\(666\) 0 0
\(667\) −8.00000 −0.309761
\(668\) −3.34315 5.79050i −0.129350 0.224041i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) 13.3137 23.0600i 0.513970 0.890222i
\(672\) 0 0
\(673\) −8.31371 14.3998i −0.320470 0.555070i 0.660115 0.751164i \(-0.270507\pi\)
−0.980585 + 0.196094i \(0.937174\pi\)
\(674\) 3.85786 0.148599
\(675\) 0 0
\(676\) −1.82843 −0.0703241
\(677\) −13.3431 23.1110i −0.512819 0.888228i −0.999890 0.0148656i \(-0.995268\pi\)
0.487071 0.873363i \(-0.338065\pi\)
\(678\) 0 0
\(679\) −5.17157 + 8.95743i −0.198467 + 0.343754i
\(680\) −17.1716 + 29.7420i −0.658500 + 1.14056i
\(681\) 0 0
\(682\) −0.485281 0.840532i −0.0185824 0.0321856i
\(683\) 47.9411 1.83442 0.917208 0.398408i \(-0.130437\pi\)
0.917208 + 0.398408i \(0.130437\pi\)
\(684\) 0 0
\(685\) 30.6274 1.17021
\(686\) 3.51472 + 6.08767i 0.134193 + 0.232428i
\(687\) 0 0
\(688\) 2.48528 4.30463i 0.0947505 0.164113i
\(689\) −1.00000 + 1.73205i −0.0380970 + 0.0659859i
\(690\) 0 0
\(691\) 2.92893 + 5.07306i 0.111422 + 0.192988i 0.916344 0.400392i \(-0.131126\pi\)
−0.804922 + 0.593381i \(0.797793\pi\)
\(692\) 21.3137 0.810226
\(693\) 0 0
\(694\) −3.59798 −0.136577
\(695\) −10.3431 17.9149i −0.392338 0.679549i
\(696\) 0 0
\(697\) −19.7990 + 34.2929i −0.749940 + 1.29893i
\(698\) −0.757359 + 1.31178i −0.0286665 + 0.0496518i
\(699\) 0 0
\(700\) 7.75736 + 13.4361i 0.293201 + 0.507838i
\(701\) 5.02944 0.189959 0.0949796 0.995479i \(-0.469721\pi\)
0.0949796 + 0.995479i \(0.469721\pi\)
\(702\) 0 0
\(703\) 21.6569 0.816804
\(704\) −4.17157 7.22538i −0.157222 0.272317i
\(705\) 0 0
\(706\) 6.92893 12.0013i 0.260774 0.451673i
\(707\) −10.8284 + 18.7554i −0.407245 + 0.705369i
\(708\) 0 0
\(709\) 2.31371 + 4.00746i 0.0868931 + 0.150503i 0.906196 0.422857i \(-0.138973\pi\)
−0.819303 + 0.573360i \(0.805639\pi\)
\(710\) −2.34315 −0.0879367
\(711\) 0 0
\(712\) −23.5147 −0.881251
\(713\) −2.34315 4.05845i −0.0877515 0.151990i
\(714\) 0 0
\(715\) 2.82843 4.89898i 0.105777 0.183211i
\(716\) −21.3137 + 36.9164i −0.796531 + 1.37963i
\(717\) 0 0
\(718\) −7.24264 12.5446i −0.270293 0.468161i
\(719\) −29.9411 −1.11662 −0.558308 0.829634i \(-0.688549\pi\)
−0.558308 + 0.829634i \(0.688549\pi\)
\(720\) 0 0
\(721\) 6.62742 0.246818
\(722\) 2.27817 + 3.94591i 0.0847849 + 0.146852i
\(723\) 0 0
\(724\) 12.7990 22.1685i 0.475671 0.823886i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 0 0
\(727\) 5.17157 + 8.95743i 0.191803 + 0.332213i 0.945848 0.324610i \(-0.105233\pi\)
−0.754045 + 0.656823i \(0.771900\pi\)
\(728\) 4.48528 0.166236
\(729\) 0 0
\(730\) −0.402020 −0.0148794
\(731\) 6.34315 + 10.9867i 0.234610 + 0.406356i
\(732\) 0 0
\(733\) 18.3137 31.7203i 0.676432 1.17162i −0.299616 0.954060i \(-0.596858\pi\)
0.976048 0.217555i \(-0.0698082\pi\)
\(734\) 4.97056 8.60927i 0.183467 0.317774i
\(735\) 0 0
\(736\) 8.82843 + 15.2913i 0.325420 + 0.563644i
\(737\) −13.6569 −0.503057
\(738\) 0 0
\(739\) −18.1421 −0.667369 −0.333685 0.942685i \(-0.608292\pi\)
−0.333685 + 0.942685i \(0.608292\pi\)
\(740\) 19.7990 + 34.2929i 0.727825 + 1.26063i
\(741\) 0 0
\(742\) 1.17157 2.02922i 0.0430098 0.0744951i
\(743\) −1.00000 + 1.73205i −0.0366864 + 0.0635428i −0.883786 0.467892i \(-0.845014\pi\)
0.847099 + 0.531435i \(0.178347\pi\)
\(744\) 0 0
\(745\) −12.9706 22.4657i −0.475205 0.823079i
\(746\) 4.14214 0.151654
\(747\) 0 0
\(748\) 28.0000 1.02378
\(749\) 16.0000 + 27.7128i 0.584627 + 1.01260i
\(750\) 0 0
\(751\) 0.485281 0.840532i 0.0177082 0.0306714i −0.857036 0.515257i \(-0.827696\pi\)
0.874744 + 0.484586i \(0.161030\pi\)
\(752\) 17.4853 30.2854i 0.637623 1.10439i
\(753\) 0 0
\(754\) 0.414214 + 0.717439i 0.0150848 + 0.0261276i
\(755\) 9.94113 0.361795
\(756\) 0 0
\(757\) 51.9411 1.88783 0.943916 0.330185i \(-0.107111\pi\)
0.943916 + 0.330185i \(0.107111\pi\)
\(758\) −0.100505 0.174080i −0.00365051 0.00632287i
\(759\) 0 0
\(760\) 6.34315 10.9867i 0.230090 0.398528i
\(761\) −16.2426 + 28.1331i −0.588795 + 1.01982i 0.405595 + 0.914053i \(0.367064\pi\)
−0.994391 + 0.105771i \(0.966269\pi\)
\(762\) 0 0
\(763\) −7.51472 13.0159i −0.272051 0.471206i
\(764\) −6.05887 −0.219202
\(765\) 0 0
\(766\) 12.8284 0.463510
\(767\) 3.82843 + 6.63103i 0.138236 + 0.239433i
\(768\) 0 0
\(769\) −21.0000 + 36.3731i −0.757279 + 1.31165i 0.186954 + 0.982369i \(0.440139\pi\)
−0.944233 + 0.329278i \(0.893195\pi\)
\(770\) −3.31371 + 5.73951i −0.119418 + 0.206838i
\(771\) 0 0
\(772\) 4.85786 + 8.41407i 0.174838 + 0.302829i
\(773\) 34.1421 1.22801 0.614004 0.789303i \(-0.289558\pi\)
0.614004 + 0.789303i \(0.289558\pi\)
\(774\) 0 0
\(775\) −3.51472 −0.126252
\(776\) 2.89949 + 5.02207i 0.104086 + 0.180282i
\(777\) 0 0
\(778\) 5.58579 9.67487i 0.200260 0.346861i
\(779\) 7.31371 12.6677i 0.262041 0.453868i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) −12.6863 −0.453661
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −14.1421 24.4949i −0.504754 0.874260i
\(786\) 0 0
\(787\) 20.3848 35.3075i 0.726639 1.25858i −0.231657 0.972798i \(-0.574415\pi\)
0.958296 0.285778i \(-0.0922519\pi\)
\(788\) 0.443651 0.768426i 0.0158044 0.0273740i
\(789\) 0 0