Properties

Label 1344.2.q.x.961.2
Level $1344$
Weight $2$
Character 1344.961
Analytic conductor $10.732$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 1344.961
Dual form 1344.2.q.x.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(1.63746 - 2.83616i) q^{5} +(1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(1.63746 - 2.83616i) q^{5} +(1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.63746 - 2.83616i) q^{11} -6.27492 q^{13} +3.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(3.13746 - 5.43424i) q^{19} +(2.63746 + 0.209313i) q^{21} +(2.00000 - 3.46410i) q^{23} +(-2.86254 - 4.95807i) q^{25} -1.00000 q^{27} -5.27492 q^{29} +(-0.500000 - 0.866025i) q^{31} +(1.63746 - 2.83616i) q^{33} +(-3.72508 - 7.82300i) q^{35} +(-1.13746 + 1.97014i) q^{37} +(-3.13746 - 5.43424i) q^{39} -4.54983 q^{41} +0.274917 q^{43} +(1.63746 + 2.83616i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-2.50000 - 6.53835i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(4.63746 + 8.03231i) q^{53} -10.7251 q^{55} +6.27492 q^{57} +(0.637459 + 1.10411i) q^{59} +(5.00000 - 8.66025i) q^{61} +(1.13746 + 2.38876i) q^{63} +(-10.2749 + 17.7967i) q^{65} +(0.137459 + 0.238085i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(2.13746 + 3.70219i) q^{73} +(2.86254 - 4.95807i) q^{75} +(-8.63746 - 0.685484i) q^{77} +(5.77492 - 10.0025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.27492 q^{83} +13.0997 q^{85} +(-2.63746 - 4.56821i) q^{87} +(5.27492 - 9.13642i) q^{89} +(-9.41238 + 13.6759i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-10.2749 - 17.7967i) q^{95} +8.72508 q^{97} +3.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - q^{5} + 6q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} - q^{5} + 6q^{7} - 2q^{9} + q^{11} - 10q^{13} - 2q^{15} + 8q^{17} + 5q^{19} + 3q^{21} + 8q^{23} - 19q^{25} - 4q^{27} - 6q^{29} - 2q^{31} - q^{33} - 30q^{35} + 3q^{37} - 5q^{39} + 12q^{41} - 14q^{43} - q^{45} - 12q^{47} - 10q^{49} - 8q^{51} + 11q^{53} - 58q^{55} + 10q^{57} - 5q^{59} + 20q^{61} - 3q^{63} - 26q^{65} - 7q^{67} + 16q^{69} - 8q^{71} + q^{73} + 19q^{75} - 27q^{77} + 8q^{79} - 2q^{81} + 14q^{83} - 8q^{85} - 3q^{87} + 6q^{89} - 15q^{91} + 2q^{93} - 26q^{95} + 50q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.63746 2.83616i 0.732294 1.26837i −0.223607 0.974679i \(-0.571783\pi\)
0.955901 0.293691i \(-0.0948835\pi\)
\(6\) 0 0
\(7\) 1.50000 2.17945i 0.566947 0.823754i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.63746 2.83616i −0.493712 0.855135i 0.506261 0.862380i \(-0.331027\pi\)
−0.999974 + 0.00724520i \(0.997694\pi\)
\(12\) 0 0
\(13\) −6.27492 −1.74035 −0.870174 0.492744i \(-0.835994\pi\)
−0.870174 + 0.492744i \(0.835994\pi\)
\(14\) 0 0
\(15\) 3.27492 0.845580
\(16\) 0 0
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) 3.13746 5.43424i 0.719782 1.24670i −0.241303 0.970450i \(-0.577575\pi\)
0.961086 0.276250i \(-0.0890918\pi\)
\(20\) 0 0
\(21\) 2.63746 + 0.209313i 0.575541 + 0.0456759i
\(22\) 0 0
\(23\) 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
\(25\) −2.86254 4.95807i −0.572508 0.991613i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.27492 −0.979528 −0.489764 0.871855i \(-0.662917\pi\)
−0.489764 + 0.871855i \(0.662917\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 1.63746 2.83616i 0.285045 0.493712i
\(34\) 0 0
\(35\) −3.72508 7.82300i −0.629654 1.32233i
\(36\) 0 0
\(37\) −1.13746 + 1.97014i −0.186997 + 0.323888i −0.944248 0.329236i \(-0.893209\pi\)
0.757251 + 0.653124i \(0.226542\pi\)
\(38\) 0 0
\(39\) −3.13746 5.43424i −0.502395 0.870174i
\(40\) 0 0
\(41\) −4.54983 −0.710565 −0.355282 0.934759i \(-0.615615\pi\)
−0.355282 + 0.934759i \(0.615615\pi\)
\(42\) 0 0
\(43\) 0.274917 0.0419245 0.0209622 0.999780i \(-0.493327\pi\)
0.0209622 + 0.999780i \(0.493327\pi\)
\(44\) 0 0
\(45\) 1.63746 + 2.83616i 0.244098 + 0.422790i
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) −2.50000 6.53835i −0.357143 0.934050i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 4.63746 + 8.03231i 0.637004 + 1.10332i 0.986087 + 0.166231i \(0.0531598\pi\)
−0.349083 + 0.937092i \(0.613507\pi\)
\(54\) 0 0
\(55\) −10.7251 −1.44617
\(56\) 0 0
\(57\) 6.27492 0.831133
\(58\) 0 0
\(59\) 0.637459 + 1.10411i 0.0829900 + 0.143743i 0.904533 0.426404i \(-0.140220\pi\)
−0.821543 + 0.570147i \(0.806886\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 0 0
\(63\) 1.13746 + 2.38876i 0.143306 + 0.300956i
\(64\) 0 0
\(65\) −10.2749 + 17.7967i −1.27445 + 2.20741i
\(66\) 0 0
\(67\) 0.137459 + 0.238085i 0.0167932 + 0.0290867i 0.874300 0.485386i \(-0.161321\pi\)
−0.857507 + 0.514473i \(0.827988\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 2.13746 + 3.70219i 0.250171 + 0.433308i 0.963573 0.267447i \(-0.0861800\pi\)
−0.713402 + 0.700755i \(0.752847\pi\)
\(74\) 0 0
\(75\) 2.86254 4.95807i 0.330538 0.572508i
\(76\) 0 0
\(77\) −8.63746 0.685484i −0.984330 0.0781181i
\(78\) 0 0
\(79\) 5.77492 10.0025i 0.649729 1.12536i −0.333459 0.942765i \(-0.608216\pi\)
0.983188 0.182599i \(-0.0584509\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.27492 0.798526 0.399263 0.916836i \(-0.369266\pi\)
0.399263 + 0.916836i \(0.369266\pi\)
\(84\) 0 0
\(85\) 13.0997 1.42086
\(86\) 0 0
\(87\) −2.63746 4.56821i −0.282765 0.489764i
\(88\) 0 0
\(89\) 5.27492 9.13642i 0.559140 0.968459i −0.438428 0.898766i \(-0.644465\pi\)
0.997568 0.0696929i \(-0.0222020\pi\)
\(90\) 0 0
\(91\) −9.41238 + 13.6759i −0.986685 + 1.43362i
\(92\) 0 0
\(93\) 0.500000 0.866025i 0.0518476 0.0898027i
\(94\) 0 0
\(95\) −10.2749 17.7967i −1.05418 1.82590i
\(96\) 0 0
\(97\) 8.72508 0.885898 0.442949 0.896547i \(-0.353932\pi\)
0.442949 + 0.896547i \(0.353932\pi\)
\(98\) 0 0
\(99\) 3.27492 0.329142
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 5.41238 9.37451i 0.533297 0.923698i −0.465946 0.884813i \(-0.654286\pi\)
0.999244 0.0388850i \(-0.0123806\pi\)
\(104\) 0 0
\(105\) 4.91238 7.13752i 0.479399 0.696550i
\(106\) 0 0
\(107\) 7.91238 13.7046i 0.764918 1.32488i −0.175372 0.984502i \(-0.556113\pi\)
0.940290 0.340375i \(-0.110554\pi\)
\(108\) 0 0
\(109\) 8.41238 + 14.5707i 0.805759 + 1.39562i 0.915777 + 0.401687i \(0.131576\pi\)
−0.110018 + 0.993930i \(0.535091\pi\)
\(110\) 0 0
\(111\) −2.27492 −0.215926
\(112\) 0 0
\(113\) −4.54983 −0.428012 −0.214006 0.976832i \(-0.568651\pi\)
−0.214006 + 0.976832i \(0.568651\pi\)
\(114\) 0 0
\(115\) −6.54983 11.3446i −0.610775 1.05789i
\(116\) 0 0
\(117\) 3.13746 5.43424i 0.290058 0.502395i
\(118\) 0 0
\(119\) 10.5498 + 0.837253i 0.967102 + 0.0767509i
\(120\) 0 0
\(121\) 0.137459 0.238085i 0.0124962 0.0216441i
\(122\) 0 0
\(123\) −2.27492 3.94027i −0.205122 0.355282i
\(124\) 0 0
\(125\) −2.37459 −0.212389
\(126\) 0 0
\(127\) 6.45017 0.572360 0.286180 0.958176i \(-0.407615\pi\)
0.286180 + 0.958176i \(0.407615\pi\)
\(128\) 0 0
\(129\) 0.137459 + 0.238085i 0.0121026 + 0.0209622i
\(130\) 0 0
\(131\) −3.63746 + 6.30026i −0.317806 + 0.550457i −0.980030 0.198850i \(-0.936279\pi\)
0.662224 + 0.749306i \(0.269613\pi\)
\(132\) 0 0
\(133\) −7.13746 14.9893i −0.618896 1.29974i
\(134\) 0 0
\(135\) −1.63746 + 2.83616i −0.140930 + 0.244098i
\(136\) 0 0
\(137\) −0.725083 1.25588i −0.0619480 0.107297i 0.833388 0.552688i \(-0.186398\pi\)
−0.895336 + 0.445391i \(0.853065\pi\)
\(138\) 0 0
\(139\) 8.27492 0.701869 0.350935 0.936400i \(-0.385864\pi\)
0.350935 + 0.936400i \(0.385864\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 10.2749 + 17.7967i 0.859232 + 1.48823i
\(144\) 0 0
\(145\) −8.63746 + 14.9605i −0.717302 + 1.24240i
\(146\) 0 0
\(147\) 4.41238 5.43424i 0.363927 0.448208i
\(148\) 0 0
\(149\) −7.27492 + 12.6005i −0.595984 + 1.03228i 0.397423 + 0.917636i \(0.369905\pi\)
−0.993407 + 0.114640i \(0.963429\pi\)
\(150\) 0 0
\(151\) 11.1873 + 19.3770i 0.910409 + 1.57687i 0.813487 + 0.581583i \(0.197566\pi\)
0.0969217 + 0.995292i \(0.469100\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −3.27492 −0.263048
\(156\) 0 0
\(157\) −0.274917 0.476171i −0.0219408 0.0380026i 0.854847 0.518881i \(-0.173651\pi\)
−0.876787 + 0.480878i \(0.840318\pi\)
\(158\) 0 0
\(159\) −4.63746 + 8.03231i −0.367774 + 0.637004i
\(160\) 0 0
\(161\) −4.54983 9.55505i −0.358577 0.753044i
\(162\) 0 0
\(163\) 6.00000 10.3923i 0.469956 0.813988i −0.529454 0.848339i \(-0.677603\pi\)
0.999410 + 0.0343508i \(0.0109363\pi\)
\(164\) 0 0
\(165\) −5.36254 9.28819i −0.417473 0.723085i
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 26.3746 2.02881
\(170\) 0 0
\(171\) 3.13746 + 5.43424i 0.239927 + 0.415567i
\(172\) 0 0
\(173\) −11.2749 + 19.5287i −0.857216 + 1.48474i 0.0173577 + 0.999849i \(0.494475\pi\)
−0.874574 + 0.484892i \(0.838859\pi\)
\(174\) 0 0
\(175\) −15.0997 1.19834i −1.14143 0.0905857i
\(176\) 0 0
\(177\) −0.637459 + 1.10411i −0.0479143 + 0.0829900i
\(178\) 0 0
\(179\) 8.27492 + 14.3326i 0.618496 + 1.07127i 0.989760 + 0.142740i \(0.0455912\pi\)
−0.371264 + 0.928527i \(0.621075\pi\)
\(180\) 0 0
\(181\) 18.8248 1.39923 0.699616 0.714519i \(-0.253354\pi\)
0.699616 + 0.714519i \(0.253354\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 3.72508 + 6.45203i 0.273874 + 0.474363i
\(186\) 0 0
\(187\) 6.54983 11.3446i 0.478971 0.829603i
\(188\) 0 0
\(189\) −1.50000 + 2.17945i −0.109109 + 0.158532i
\(190\) 0 0
\(191\) 2.27492 3.94027i 0.164607 0.285108i −0.771909 0.635734i \(-0.780698\pi\)
0.936516 + 0.350626i \(0.114031\pi\)
\(192\) 0 0
\(193\) −0.225083 0.389855i −0.0162018 0.0280624i 0.857811 0.513966i \(-0.171824\pi\)
−0.874013 + 0.485903i \(0.838491\pi\)
\(194\) 0 0
\(195\) −20.5498 −1.47160
\(196\) 0 0
\(197\) 1.45017 0.103320 0.0516600 0.998665i \(-0.483549\pi\)
0.0516600 + 0.998665i \(0.483549\pi\)
\(198\) 0 0
\(199\) −2.54983 4.41644i −0.180753 0.313073i 0.761384 0.648301i \(-0.224520\pi\)
−0.942137 + 0.335228i \(0.891187\pi\)
\(200\) 0 0
\(201\) −0.137459 + 0.238085i −0.00969558 + 0.0167932i
\(202\) 0 0
\(203\) −7.91238 + 11.4964i −0.555340 + 0.806890i
\(204\) 0 0
\(205\) −7.45017 + 12.9041i −0.520342 + 0.901259i
\(206\) 0 0
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) 0 0
\(209\) −20.5498 −1.42146
\(210\) 0 0
\(211\) −27.6495 −1.90347 −0.951735 0.306921i \(-0.900701\pi\)
−0.951735 + 0.306921i \(0.900701\pi\)
\(212\) 0 0
\(213\) −1.00000 1.73205i −0.0685189 0.118678i
\(214\) 0 0
\(215\) 0.450166 0.779710i 0.0307010 0.0531758i
\(216\) 0 0
\(217\) −2.63746 0.209313i −0.179042 0.0142091i
\(218\) 0 0
\(219\) −2.13746 + 3.70219i −0.144436 + 0.250171i
\(220\) 0 0
\(221\) −12.5498 21.7370i −0.844193 1.46219i
\(222\) 0 0
\(223\) 1.27492 0.0853748 0.0426874 0.999088i \(-0.486408\pi\)
0.0426874 + 0.999088i \(0.486408\pi\)
\(224\) 0 0
\(225\) 5.72508 0.381672
\(226\) 0 0
\(227\) 5.63746 + 9.76436i 0.374171 + 0.648084i 0.990203 0.139638i \(-0.0445939\pi\)
−0.616031 + 0.787722i \(0.711261\pi\)
\(228\) 0 0
\(229\) 9.13746 15.8265i 0.603820 1.04585i −0.388416 0.921484i \(-0.626978\pi\)
0.992237 0.124363i \(-0.0396889\pi\)
\(230\) 0 0
\(231\) −3.72508 7.82300i −0.245092 0.514716i
\(232\) 0 0
\(233\) 0.274917 0.476171i 0.0180104 0.0311950i −0.856880 0.515516i \(-0.827600\pi\)
0.874890 + 0.484321i \(0.160933\pi\)
\(234\) 0 0
\(235\) 9.82475 + 17.0170i 0.640896 + 1.11006i
\(236\) 0 0
\(237\) 11.5498 0.750242
\(238\) 0 0
\(239\) −15.4502 −0.999388 −0.499694 0.866202i \(-0.666554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(240\) 0 0
\(241\) −4.91238 8.50848i −0.316434 0.548080i 0.663307 0.748347i \(-0.269152\pi\)
−0.979741 + 0.200267i \(0.935819\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −22.6375 3.61587i −1.44625 0.231010i
\(246\) 0 0
\(247\) −19.6873 + 34.0994i −1.25267 + 2.16969i
\(248\) 0 0
\(249\) 3.63746 + 6.30026i 0.230515 + 0.399263i
\(250\) 0 0
\(251\) −18.3746 −1.15979 −0.579897 0.814690i \(-0.696907\pi\)
−0.579897 + 0.814690i \(0.696907\pi\)
\(252\) 0 0
\(253\) −13.0997 −0.823569
\(254\) 0 0
\(255\) 6.54983 + 11.3446i 0.410167 + 0.710429i
\(256\) 0 0
\(257\) −5.54983 + 9.61260i −0.346189 + 0.599617i −0.985569 0.169274i \(-0.945858\pi\)
0.639380 + 0.768891i \(0.279191\pi\)
\(258\) 0 0
\(259\) 2.58762 + 5.43424i 0.160787 + 0.337667i
\(260\) 0 0
\(261\) 2.63746 4.56821i 0.163255 0.282765i
\(262\) 0 0
\(263\) −4.72508 8.18408i −0.291361 0.504652i 0.682771 0.730633i \(-0.260775\pi\)
−0.974132 + 0.225980i \(0.927441\pi\)
\(264\) 0 0
\(265\) 30.3746 1.86590
\(266\) 0 0
\(267\) 10.5498 0.645639
\(268\) 0 0
\(269\) 10.3625 + 17.9484i 0.631815 + 1.09434i 0.987180 + 0.159609i \(0.0510232\pi\)
−0.355365 + 0.934728i \(0.615643\pi\)
\(270\) 0 0
\(271\) 0.637459 1.10411i 0.0387229 0.0670699i −0.846014 0.533160i \(-0.821004\pi\)
0.884737 + 0.466090i \(0.154338\pi\)
\(272\) 0 0
\(273\) −16.5498 1.31342i −1.00164 0.0794920i
\(274\) 0 0
\(275\) −9.37459 + 16.2373i −0.565309 + 0.979144i
\(276\) 0 0
\(277\) −13.4124 23.2309i −0.805872 1.39581i −0.915701 0.401860i \(-0.868364\pi\)
0.109830 0.993950i \(-0.464970\pi\)
\(278\) 0 0
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −26.5498 −1.58383 −0.791915 0.610631i \(-0.790916\pi\)
−0.791915 + 0.610631i \(0.790916\pi\)
\(282\) 0 0
\(283\) 12.9622 + 22.4512i 0.770523 + 1.33459i 0.937276 + 0.348587i \(0.113338\pi\)
−0.166753 + 0.985999i \(0.553328\pi\)
\(284\) 0 0
\(285\) 10.2749 17.7967i 0.608634 1.05418i
\(286\) 0 0
\(287\) −6.82475 + 9.91613i −0.402852 + 0.585331i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 4.36254 + 7.55614i 0.255737 + 0.442949i
\(292\) 0 0
\(293\) 27.8248 1.62554 0.812770 0.582585i \(-0.197959\pi\)
0.812770 + 0.582585i \(0.197959\pi\)
\(294\) 0 0
\(295\) 4.17525 0.243092
\(296\) 0 0
\(297\) 1.63746 + 2.83616i 0.0950150 + 0.164571i
\(298\) 0 0
\(299\) −12.5498 + 21.7370i −0.725776 + 1.25708i
\(300\) 0 0
\(301\) 0.412376 0.599168i 0.0237689 0.0345355i
\(302\) 0 0
\(303\) 3.00000 5.19615i 0.172345 0.298511i
\(304\) 0 0
\(305\) −16.3746 28.3616i −0.937606 1.62398i
\(306\) 0 0
\(307\) 11.3746 0.649182 0.324591 0.945854i \(-0.394773\pi\)
0.324591 + 0.945854i \(0.394773\pi\)
\(308\) 0 0
\(309\) 10.8248 0.615799
\(310\) 0 0
\(311\) −2.27492 3.94027i −0.128999 0.223432i 0.794290 0.607539i \(-0.207843\pi\)
−0.923289 + 0.384106i \(0.874510\pi\)
\(312\) 0 0
\(313\) 9.77492 16.9307i 0.552511 0.956977i −0.445582 0.895241i \(-0.647003\pi\)
0.998093 0.0617357i \(-0.0196636\pi\)
\(314\) 0 0
\(315\) 8.63746 + 0.685484i 0.486666 + 0.0386226i
\(316\) 0 0
\(317\) −13.9124 + 24.0969i −0.781397 + 1.35342i 0.149731 + 0.988727i \(0.452159\pi\)
−0.931128 + 0.364692i \(0.881174\pi\)
\(318\) 0 0
\(319\) 8.63746 + 14.9605i 0.483605 + 0.837628i
\(320\) 0 0
\(321\) 15.8248 0.883252
\(322\) 0 0
\(323\) 25.0997 1.39658
\(324\) 0 0
\(325\) 17.9622 + 31.1115i 0.996364 + 1.72575i
\(326\) 0 0
\(327\) −8.41238 + 14.5707i −0.465205 + 0.805759i
\(328\) 0 0
\(329\) 6.82475 + 14.3326i 0.376261 + 0.790181i
\(330\) 0 0
\(331\) −0.587624 + 1.01779i −0.0322987 + 0.0559431i −0.881723 0.471768i \(-0.843616\pi\)
0.849424 + 0.527711i \(0.176949\pi\)
\(332\) 0 0
\(333\) −1.13746 1.97014i −0.0623323 0.107963i
\(334\) 0 0
\(335\) 0.900331 0.0491903
\(336\) 0 0
\(337\) −24.0997 −1.31279 −0.656396 0.754416i \(-0.727920\pi\)
−0.656396 + 0.754416i \(0.727920\pi\)
\(338\) 0 0
\(339\) −2.27492 3.94027i −0.123557 0.214006i
\(340\) 0 0
\(341\) −1.63746 + 2.83616i −0.0886734 + 0.153587i
\(342\) 0 0
\(343\) −18.0000 4.35890i −0.971909 0.235358i
\(344\) 0 0
\(345\) 6.54983 11.3446i 0.352631 0.610775i
\(346\) 0 0
\(347\) −15.0997 26.1534i −0.810593 1.40399i −0.912450 0.409189i \(-0.865812\pi\)
0.101857 0.994799i \(-0.467522\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) 6.27492 0.334930
\(352\) 0 0
\(353\) 10.2749 + 17.7967i 0.546879 + 0.947222i 0.998486 + 0.0550049i \(0.0175174\pi\)
−0.451607 + 0.892217i \(0.649149\pi\)
\(354\) 0 0
\(355\) −3.27492 + 5.67232i −0.173815 + 0.301056i
\(356\) 0 0
\(357\) 4.54983 + 9.55505i 0.240803 + 0.505707i
\(358\) 0 0
\(359\) −9.82475 + 17.0170i −0.518531 + 0.898121i 0.481238 + 0.876590i \(0.340187\pi\)
−0.999768 + 0.0215311i \(0.993146\pi\)
\(360\) 0 0
\(361\) −10.1873 17.6449i −0.536173 0.928679i
\(362\) 0 0
\(363\) 0.274917 0.0144294
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) 11.0498 + 19.1389i 0.576797 + 0.999041i 0.995844 + 0.0910767i \(0.0290308\pi\)
−0.419047 + 0.907964i \(0.637636\pi\)
\(368\) 0 0
\(369\) 2.27492 3.94027i 0.118427 0.205122i
\(370\) 0 0
\(371\) 24.4622 + 1.94136i 1.27001 + 0.100791i
\(372\) 0 0
\(373\) −3.13746 + 5.43424i −0.162451 + 0.281374i −0.935747 0.352671i \(-0.885273\pi\)
0.773296 + 0.634045i \(0.218607\pi\)
\(374\) 0 0
\(375\) −1.18729 2.05645i −0.0613115 0.106195i
\(376\) 0 0
\(377\) 33.0997 1.70472
\(378\) 0 0
\(379\) 13.1752 0.676767 0.338384 0.941008i \(-0.390120\pi\)
0.338384 + 0.941008i \(0.390120\pi\)
\(380\) 0 0
\(381\) 3.22508 + 5.58601i 0.165226 + 0.286180i
\(382\) 0 0
\(383\) 5.27492 9.13642i 0.269536 0.466849i −0.699206 0.714920i \(-0.746463\pi\)
0.968742 + 0.248070i \(0.0797965\pi\)
\(384\) 0 0
\(385\) −16.0876 + 23.3748i −0.819901 + 1.19129i
\(386\) 0 0
\(387\) −0.137459 + 0.238085i −0.00698741 + 0.0121026i
\(388\) 0 0
\(389\) −1.00000 1.73205i −0.0507020 0.0878185i 0.839561 0.543266i \(-0.182813\pi\)
−0.890263 + 0.455448i \(0.849479\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) −7.27492 −0.366971
\(394\) 0 0
\(395\) −18.9124 32.7572i −0.951585 1.64819i
\(396\) 0 0
\(397\) −1.68729 + 2.92248i −0.0846828 + 0.146675i −0.905256 0.424867i \(-0.860321\pi\)
0.820573 + 0.571541i \(0.193654\pi\)
\(398\) 0 0
\(399\) 9.41238 13.6759i 0.471208 0.684650i
\(400\) 0 0
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 0 0
\(403\) 3.13746 + 5.43424i 0.156288 + 0.270699i
\(404\) 0 0
\(405\) −3.27492 −0.162732
\(406\) 0 0
\(407\) 7.45017 0.369291
\(408\) 0 0
\(409\) −5.22508 9.05011i −0.258364 0.447499i 0.707440 0.706773i \(-0.249850\pi\)
−0.965804 + 0.259274i \(0.916517\pi\)
\(410\) 0 0
\(411\) 0.725083 1.25588i 0.0357657 0.0619480i
\(412\) 0 0
\(413\) 3.36254 + 0.266857i 0.165460 + 0.0131312i
\(414\) 0 0
\(415\) 11.9124 20.6328i 0.584756 1.01283i
\(416\) 0 0
\(417\) 4.13746 + 7.16629i 0.202612 + 0.350935i
\(418\) 0 0
\(419\) 28.5498 1.39475 0.697375 0.716706i \(-0.254351\pi\)
0.697375 + 0.716706i \(0.254351\pi\)
\(420\) 0 0
\(421\) −8.82475 −0.430092 −0.215046 0.976604i \(-0.568990\pi\)
−0.215046 + 0.976604i \(0.568990\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) 11.4502 19.8323i 0.555415 0.962006i
\(426\) 0 0
\(427\) −11.3746 23.8876i −0.550455 1.15600i
\(428\) 0 0
\(429\) −10.2749 + 17.7967i −0.496078 + 0.859232i
\(430\) 0 0
\(431\) −8.82475 15.2849i −0.425073 0.736249i 0.571354 0.820704i \(-0.306418\pi\)
−0.996427 + 0.0844552i \(0.973085\pi\)
\(432\) 0 0
\(433\) 3.17525 0.152593 0.0762963 0.997085i \(-0.475690\pi\)
0.0762963 + 0.997085i \(0.475690\pi\)
\(434\) 0 0
\(435\) −17.2749 −0.828269
\(436\) 0 0
\(437\) −12.5498 21.7370i −0.600340 1.03982i
\(438\) 0 0
\(439\) 8.63746 14.9605i 0.412243 0.714027i −0.582891 0.812550i \(-0.698079\pi\)
0.995135 + 0.0985236i \(0.0314120\pi\)
\(440\) 0 0
\(441\) 6.91238 + 1.10411i 0.329161 + 0.0525767i
\(442\) 0 0
\(443\) 3.18729 5.52055i 0.151433 0.262289i −0.780322 0.625378i \(-0.784945\pi\)
0.931754 + 0.363089i \(0.118278\pi\)
\(444\) 0 0
\(445\) −17.2749 29.9210i −0.818910 1.41839i
\(446\) 0 0
\(447\) −14.5498 −0.688184
\(448\) 0 0
\(449\) 20.5498 0.969807 0.484903 0.874568i \(-0.338855\pi\)
0.484903 + 0.874568i \(0.338855\pi\)
\(450\) 0 0
\(451\) 7.45017 + 12.9041i 0.350815 + 0.607629i
\(452\) 0 0
\(453\) −11.1873 + 19.3770i −0.525625 + 0.910409i
\(454\) 0 0
\(455\) 23.3746 + 49.0887i 1.09582 + 2.30131i
\(456\) 0 0
\(457\) −18.3248 + 31.7394i −0.857196 + 1.48471i 0.0173972 + 0.999849i \(0.494462\pi\)
−0.874593 + 0.484858i \(0.838871\pi\)
\(458\) 0 0
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 3.64950 0.169974 0.0849872 0.996382i \(-0.472915\pi\)
0.0849872 + 0.996382i \(0.472915\pi\)
\(462\) 0 0
\(463\) −13.1752 −0.612306 −0.306153 0.951982i \(-0.599042\pi\)
−0.306153 + 0.951982i \(0.599042\pi\)
\(464\) 0 0
\(465\) −1.63746 2.83616i −0.0759353 0.131524i
\(466\) 0 0
\(467\) −20.2749 + 35.1172i −0.938211 + 1.62503i −0.169406 + 0.985546i \(0.554185\pi\)
−0.768805 + 0.639483i \(0.779148\pi\)
\(468\) 0 0
\(469\) 0.725083 + 0.0575438i 0.0334812 + 0.00265713i
\(470\) 0 0
\(471\) 0.274917 0.476171i 0.0126675 0.0219408i
\(472\) 0 0
\(473\) −0.450166 0.779710i −0.0206986 0.0358511i
\(474\) 0 0
\(475\) −35.9244 −1.64833
\(476\) 0 0
\(477\) −9.27492 −0.424669
\(478\) 0 0
\(479\) −2.72508 4.71998i −0.124512 0.215661i 0.797030 0.603940i \(-0.206403\pi\)
−0.921542 + 0.388278i \(0.873070\pi\)
\(480\) 0 0
\(481\) 7.13746 12.3624i 0.325440 0.563679i
\(482\) 0 0
\(483\) 6.00000 8.71780i 0.273009 0.396674i
\(484\) 0 0
\(485\) 14.2870 24.7457i 0.648738 1.12365i
\(486\) 0 0
\(487\) 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i \(-0.159454\pi\)
−0.854475 + 0.519493i \(0.826121\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) 36.9244 1.66638 0.833188 0.552990i \(-0.186513\pi\)
0.833188 + 0.552990i \(0.186513\pi\)
\(492\) 0 0
\(493\) −10.5498 18.2728i −0.475141 0.822968i
\(494\) 0 0
\(495\) 5.36254 9.28819i 0.241028 0.417473i
\(496\) 0 0
\(497\) −3.00000 + 4.35890i −0.134568 + 0.195523i
\(498\) 0 0
\(499\) −16.1375 + 27.9509i −0.722412 + 1.25125i 0.237619 + 0.971359i \(0.423633\pi\)
−0.960030 + 0.279896i \(0.909700\pi\)
\(500\) 0 0
\(501\) 3.00000 + 5.19615i 0.134030 + 0.232147i
\(502\) 0 0
\(503\) 37.6495 1.67871 0.839354 0.543585i \(-0.182933\pi\)
0.839354 + 0.543585i \(0.182933\pi\)
\(504\) 0 0
\(505\) −19.6495 −0.874391
\(506\) 0 0
\(507\) 13.1873 + 22.8411i 0.585668 + 1.01441i
\(508\) 0 0
\(509\) −5.63746 + 9.76436i −0.249876 + 0.432798i −0.963491 0.267740i \(-0.913723\pi\)
0.713615 + 0.700538i \(0.247057\pi\)
\(510\) 0 0
\(511\) 11.2749 + 0.894797i 0.498773 + 0.0395835i
\(512\) 0 0
\(513\) −3.13746 + 5.43424i −0.138522 + 0.239927i
\(514\) 0 0
\(515\) −17.7251 30.7007i −0.781060 1.35284i
\(516\) 0 0
\(517\) 19.6495 0.864184
\(518\) 0 0
\(519\) −22.5498 −0.989828
\(520\) 0 0
\(521\) 7.27492 + 12.6005i 0.318720 + 0.552039i 0.980221 0.197905i \(-0.0634137\pi\)
−0.661501 + 0.749944i \(0.730080\pi\)
\(522\) 0 0
\(523\) 8.86254 15.3504i 0.387532 0.671225i −0.604585 0.796541i \(-0.706661\pi\)
0.992117 + 0.125316i \(0.0399944\pi\)
\(524\) 0 0
\(525\) −6.51204 13.6759i −0.284209 0.596864i
\(526\) 0 0
\(527\) 2.00000 3.46410i 0.0871214 0.150899i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −1.27492 −0.0553267
\(532\) 0 0
\(533\) 28.5498 1.23663
\(534\) 0 0
\(535\) −25.9124 44.8816i −1.12029 1.94040i
\(536\) 0 0
\(537\) −8.27492 + 14.3326i −0.357089 + 0.618496i
\(538\) 0 0
\(539\) −14.4502 + 17.7967i −0.622413 + 0.766557i
\(540\) 0 0
\(541\) −4.13746 + 7.16629i −0.177883 + 0.308103i −0.941155 0.337974i \(-0.890258\pi\)
0.763272 + 0.646077i \(0.223592\pi\)
\(542\) 0 0
\(543\) 9.41238 + 16.3027i 0.403924 + 0.699616i
\(544\) 0 0
\(545\) 55.0997 2.36021
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) 0 0
\(551\) −16.5498 + 28.6652i −0.705047 + 1.22118i
\(552\) 0 0
\(553\) −13.1375 27.5898i −0.558662 1.17324i
\(554\) 0 0
\(555\) −3.72508 + 6.45203i −0.158121 + 0.273874i
\(556\) 0 0
\(557\) −14.9124 25.8290i −0.631858 1.09441i −0.987172 0.159663i \(-0.948959\pi\)
0.355314 0.934747i \(-0.384374\pi\)
\(558\) 0 0
\(559\) −1.72508 −0.0729632
\(560\) 0 0
\(561\) 13.0997 0.553068
\(562\) 0 0
\(563\) −7.63746 13.2285i −0.321881 0.557513i 0.658996 0.752147i \(-0.270982\pi\)
−0.980876 + 0.194633i \(0.937648\pi\)
\(564\) 0 0
\(565\) −7.45017 + 12.9041i −0.313431 + 0.542878i
\(566\) 0 0
\(567\) −2.63746 0.209313i −0.110763 0.00879034i
\(568\) 0 0
\(569\) −5.72508 + 9.91613i −0.240008 + 0.415706i −0.960716 0.277532i \(-0.910483\pi\)
0.720708 + 0.693238i \(0.243817\pi\)
\(570\) 0 0
\(571\) −4.13746 7.16629i −0.173147 0.299900i 0.766371 0.642398i \(-0.222060\pi\)
−0.939519 + 0.342498i \(0.888727\pi\)
\(572\) 0 0
\(573\) 4.54983 0.190072
\(574\) 0 0
\(575\) −22.9003 −0.955010
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 0 0
\(579\) 0.225083 0.389855i 0.00935412 0.0162018i
\(580\) 0 0
\(581\) 10.9124 15.8553i 0.452722 0.657789i
\(582\) 0 0
\(583\) 15.1873 26.3052i 0.628993 1.08945i
\(584\) 0 0
\(585\) −10.2749 17.7967i −0.424816 0.735802i
\(586\) 0 0
\(587\) 9.27492 0.382817 0.191408 0.981510i \(-0.438695\pi\)
0.191408 + 0.981510i \(0.438695\pi\)
\(588\) 0 0
\(589\) −6.27492 −0.258553
\(590\) 0 0
\(591\) 0.725083 + 1.25588i 0.0298259 + 0.0516600i
\(592\) 0 0
\(593\) 0.274917 0.476171i 0.0112895 0.0195540i −0.860325 0.509745i \(-0.829740\pi\)
0.871615 + 0.490191i \(0.163073\pi\)
\(594\) 0 0
\(595\) 19.6495 28.5501i 0.805551 1.17044i
\(596\) 0 0
\(597\) 2.54983 4.41644i 0.104358 0.180753i
\(598\) 0 0
\(599\) 11.2749 + 19.5287i 0.460681 + 0.797922i 0.998995 0.0448219i \(-0.0142720\pi\)
−0.538314 + 0.842744i \(0.680939\pi\)
\(600\) 0 0
\(601\) 4.09967 0.167229 0.0836145 0.996498i \(-0.473354\pi\)
0.0836145 + 0.996498i \(0.473354\pi\)
\(602\) 0 0
\(603\) −0.274917 −0.0111955
\(604\) 0 0
\(605\) −0.450166 0.779710i −0.0183018 0.0316997i
\(606\) 0 0
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 0 0
\(609\) −13.9124 1.10411i −0.563758 0.0447408i
\(610\) 0 0
\(611\) 18.8248 32.6054i 0.761568 1.31907i
\(612\) 0 0
\(613\) −4.27492 7.40437i −0.172662 0.299060i 0.766688 0.642020i \(-0.221904\pi\)
−0.939350 + 0.342961i \(0.888570\pi\)
\(614\) 0 0
\(615\) −14.9003 −0.600839
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −14.4124 24.9630i −0.579282 1.00335i −0.995562 0.0941097i \(-0.970000\pi\)
0.416280 0.909237i \(-0.363334\pi\)
\(620\) 0 0
\(621\) −2.00000 + 3.46410i −0.0802572 + 0.139010i
\(622\) 0 0
\(623\) −12.0000 25.2011i −0.480770 1.00966i
\(624\) 0 0
\(625\) 10.4244 18.0556i 0.416977 0.722225i
\(626\) 0 0
\(627\) −10.2749 17.7967i −0.410341 0.710731i
\(628\) 0 0
\(629\) −9.09967 −0.362828
\(630\) 0 0
\(631\) −19.8248 −0.789211 −0.394605 0.918851i \(-0.629119\pi\)
−0.394605 + 0.918851i \(0.629119\pi\)
\(632\) 0 0
\(633\) −13.8248 23.9452i −0.549485 0.951735i
\(634\) 0 0
\(635\) 10.5619 18.2937i 0.419135 0.725964i
\(636\) 0 0
\(637\) 15.6873 + 41.0276i 0.621553 + 1.62557i
\(638\) 0 0
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) 0 0
\(641\) 1.82475 + 3.16056i 0.0720734 + 0.124835i 0.899810 0.436282i \(-0.143705\pi\)
−0.827736 + 0.561117i \(0.810372\pi\)
\(642\) 0 0
\(643\) 5.37459 0.211953 0.105976 0.994369i \(-0.466203\pi\)
0.105976 + 0.994369i \(0.466203\pi\)
\(644\) 0 0
\(645\) 0.900331 0.0354505
\(646\) 0 0
\(647\) −17.0000 29.4449i −0.668339 1.15760i −0.978368 0.206870i \(-0.933672\pi\)
0.310029 0.950727i \(-0.399661\pi\)
\(648\) 0 0
\(649\) 2.08762 3.61587i 0.0819464 0.141935i
\(650\) 0 0
\(651\) −1.13746 2.38876i −0.0445805 0.0936230i
\(652\) 0 0
\(653\) −3.46221 + 5.99672i −0.135487 + 0.234670i −0.925783 0.378055i \(-0.876593\pi\)
0.790297 + 0.612725i \(0.209926\pi\)
\(654\) 0 0
\(655\) 11.9124 + 20.6328i 0.465455 + 0.806192i
\(656\) 0 0
\(657\) −4.27492 −0.166780
\(658\) 0 0
\(659\) −42.1993 −1.64385 −0.821926 0.569594i \(-0.807101\pi\)
−0.821926 + 0.569594i \(0.807101\pi\)
\(660\) 0 0
\(661\) 3.58762 + 6.21395i 0.139542 + 0.241695i 0.927323 0.374261i \(-0.122104\pi\)
−0.787781 + 0.615955i \(0.788770\pi\)
\(662\) 0 0
\(663\) 12.5498 21.7370i 0.487395 0.844193i
\(664\) 0 0
\(665\) −54.1993 4.30136i −2.10176 0.166799i
\(666\) 0 0
\(667\) −10.5498 + 18.2728i −0.408491 + 0.707528i
\(668\) 0 0
\(669\) 0.637459 + 1.10411i 0.0246456 + 0.0426874i
\(670\) 0 0
\(671\) −32.7492 −1.26427
\(672\) 0 0
\(673\) 41.5498 1.60163 0.800814 0.598913i \(-0.204400\pi\)
0.800814 + 0.598913i \(0.204400\pi\)
\(674\) 0 0
\(675\) 2.86254 + 4.95807i 0.110179 + 0.190836i
\(676\) 0 0
\(677\) −6.63746 + 11.4964i −0.255098 + 0.441843i −0.964922 0.262536i \(-0.915441\pi\)
0.709824 + 0.704379i \(0.248774\pi\)
\(678\) 0 0
\(679\) 13.0876 19.0159i 0.502257 0.729762i
\(680\) 0 0
\(681\) −5.63746 + 9.76436i −0.216028 + 0.374171i
\(682\) 0 0
\(683\) −6.08762 10.5441i −0.232936 0.403458i 0.725735 0.687975i \(-0.241500\pi\)
−0.958671 + 0.284517i \(0.908167\pi\)
\(684\) 0 0
\(685\) −4.74917 −0.181457
\(686\) 0 0
\(687\) 18.2749 0.697232
\(688\) 0 0
\(689\) −29.0997 50.4021i −1.10861 1.92017i
\(690\) 0 0
\(691\) 5.41238 9.37451i 0.205896 0.356623i −0.744522 0.667598i \(-0.767322\pi\)
0.950418 + 0.310975i \(0.100656\pi\)
\(692\) 0 0
\(693\) 4.91238 7.13752i 0.186606 0.271132i
\(694\) 0 0
\(695\) 13.5498 23.4690i 0.513975 0.890230i
\(696\) 0 0
\(697\) −9.09967 15.7611i −0.344675 0.596994i
\(698\) 0 0
\(699\) 0.549834 0.0207966
\(700\) 0 0
\(701\) 12.9244 0.488149 0.244074 0.969757i \(-0.421516\pi\)
0.244074 + 0.969757i \(0.421516\pi\)
\(702\) 0 0
\(703\) 7.13746 + 12.3624i 0.269194 + 0.466258i
\(704\) 0 0
\(705\) −9.82475 + 17.0170i −0.370022 + 0.640896i
\(706\) 0 0
\(707\) −15.8248 1.25588i −0.595151 0.0472322i
\(708\) 0 0
\(709\) −14.0997 + 24.4213i −0.529524 + 0.917163i 0.469883 + 0.882729i \(0.344296\pi\)
−0.999407 + 0.0344340i \(0.989037\pi\)
\(710\) 0 0
\(711\) 5.77492 + 10.0025i 0.216576 + 0.375121i
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 67.2990 2.51684
\(716\) 0 0
\(717\) −7.72508 13.3802i −0.288499 0.499694i
\(718\) 0 0
\(719\) 14.0997 24.4213i 0.525829 0.910762i −0.473718 0.880676i \(-0.657089\pi\)
0.999547 0.0300860i \(-0.00957813\pi\)
\(720\) 0 0
\(721\) −12.3127 25.8578i −0.458549 0.962993i
\(722\) 0 0
\(723\) 4.91238 8.50848i 0.182693 0.316434i
\(724\) 0 0
\(725\) 15.0997 + 26.1534i 0.560788 + 0.971313i
\(726\) 0 0
\(727\) −31.5498 −1.17012 −0.585059 0.810991i \(-0.698929\pi\)
−0.585059 + 0.810991i \(0.698929\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.549834 + 0.952341i 0.0203364 + 0.0352236i
\(732\) 0 0
\(733\) 2.96221 5.13070i 0.109412 0.189507i −0.806120 0.591752i \(-0.798437\pi\)
0.915532 + 0.402245i \(0.131770\pi\)
\(734\) 0 0
\(735\) −8.18729 21.4125i −0.301993 0.789814i
\(736\) 0 0
\(737\) 0.450166 0.779710i 0.0165821 0.0287210i
\(738\) 0 0
\(739\) −0.687293 1.19043i −0.0252825 0.0437905i 0.853107 0.521735i \(-0.174715\pi\)
−0.878390 + 0.477945i \(0.841382\pi\)
\(740\) 0 0
\(741\) −39.3746 −1.44646
\(742\) 0 0
\(743\) 44.1993 1.62152 0.810758 0.585381i \(-0.199055\pi\)
0.810758 + 0.585381i \(0.199055\pi\)
\(744\) 0 0
\(745\) 23.8248 + 41.2657i 0.872871 + 1.51186i
\(746\) 0 0
\(747\) −3.63746 + 6.30026i −0.133088 + 0.230515i
\(748\) 0 0
\(749\) −18.0000 37.8016i −0.657706 1.38124i
\(750\) 0 0
\(751\) −5.22508 + 9.05011i −0.190666 + 0.330243i −0.945471 0.325706i \(-0.894398\pi\)
0.754805 + 0.655949i \(0.227731\pi\)
\(752\) 0 0
\(753\) −9.18729 15.9129i −0.334804 0.579897i
\(754\) 0 0
\(755\) 73.2749 2.66675
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 0 0
\(759\) −6.54983 11.3446i −0.237744 0.411785i
\(760\) 0 0
\(761\) 12.5498 21.7370i 0.454931 0.787964i −0.543753 0.839245i \(-0.682997\pi\)
0.998684 + 0.0512814i \(0.0163305\pi\)
\(762\) 0 0
\(763\) 44.3746 + 3.52165i 1.60647 + 0.127492i
\(764\) 0 0
\(765\) −6.54983 + 11.3446i −0.236810 + 0.410167i
\(766\) 0 0
\(767\) −4.00000 6.92820i −0.144432 0.250163i
\(768\) 0 0
\(769\) −32.6495 −1.17737 −0.588686 0.808362i \(-0.700354\pi\)
−0.588686 + 0.808362i \(0.700354\pi\)
\(770\) 0 0
\(771\) −11.0997 −0.399745
\(772\) 0 0
\(773\) 1.54983 + 2.68439i 0.0557437 + 0.0965509i 0.892551 0.450947i \(-0.148914\pi\)
−0.836807 + 0.547498i \(0.815580\pi\)
\(774\) 0 0
\(775\) −2.86254 + 4.95807i −0.102826 + 0.178099i
\(776\) 0 0
\(777\) −3.41238 + 4.95807i −0.122418 + 0.177870i
\(778\) 0 0
\(779\) −14.2749 + 24.7249i −0.511452 + 0.885861i
\(780\) 0 0
\(781\) 3.27492 + 5.67232i 0.117186 + 0.202972i
\(782\) 0 0
\(783\) 5.27492 0.188510
\(784\) 0 0
\(785\) −1.80066 −0.0642684
\(786\) 0 0
\(787\) −1.27492 2.20822i −0.0454459 0.0787146i 0.842408 0.538841i \(-0.181138\pi\)
−0.887854 + 0.460126i \(0.847804\pi\)
\(788\) 0 0
\(789\) 4.72508 8.18408i 0.168217 0.291361i
\(790\) 0 0
\(791\) −6.82475 + 9.91613i −0.242660 + 0.352577i
\(792\) 0 0
\(793\) −31.3746 + 54.3424i −1.11414 + 1.92975i
\(794\) 0 0
\(795\) 15.1873 + 26.3052i 0.538638 + 0.932948i
\(796\) 0 0
\(797\) 31.