Properties

Label 1512.2.c.f.757.9
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.9
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.671239 - 1.24476i) q^{2} +(-1.09888 + 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(2.81770 + 0.246156i) q^{8} +O(q^{10})\) \(q+(-0.671239 - 1.24476i) q^{2} +(-1.09888 + 1.67107i) q^{4} +3.66698i q^{5} +1.00000 q^{7} +(2.81770 + 0.246156i) q^{8} +(4.56453 - 2.46142i) q^{10} +4.45794i q^{11} +1.51546i q^{13} +(-0.671239 - 1.24476i) q^{14} +(-1.58494 - 3.67260i) q^{16} +3.45516 q^{17} +2.29933i q^{19} +(-6.12778 - 4.02956i) q^{20} +(5.54908 - 2.99234i) q^{22} +8.76326 q^{23} -8.44677 q^{25} +(1.88640 - 1.01724i) q^{26} +(-1.09888 + 1.67107i) q^{28} -1.62037i q^{29} -9.26498 q^{31} +(-3.50764 + 4.43807i) q^{32} +(-2.31924 - 4.30086i) q^{34} +3.66698i q^{35} -5.69381i q^{37} +(2.86213 - 1.54340i) q^{38} +(-0.902651 + 10.3324i) q^{40} +6.86926 q^{41} +0.880042i q^{43} +(-7.44952 - 4.89872i) q^{44} +(-5.88224 - 10.9082i) q^{46} -10.5955 q^{47} +1.00000 q^{49} +(5.66980 + 10.5142i) q^{50} +(-2.53244 - 1.66531i) q^{52} +11.5036i q^{53} -16.3472 q^{55} +(2.81770 + 0.246156i) q^{56} +(-2.01698 + 1.08766i) q^{58} -2.99426i q^{59} -8.51202i q^{61} +(6.21902 + 11.5327i) q^{62} +(7.87881 + 1.38719i) q^{64} -5.55718 q^{65} +10.6629i q^{67} +(-3.79680 + 5.77381i) q^{68} +(4.56453 - 2.46142i) q^{70} -10.6172 q^{71} +7.85523 q^{73} +(-7.08745 + 3.82191i) q^{74} +(-3.84235 - 2.52668i) q^{76} +4.45794i q^{77} +4.57730 q^{79} +(13.4674 - 5.81195i) q^{80} +(-4.61091 - 8.55061i) q^{82} +2.60500i q^{83} +12.6700i q^{85} +(1.09545 - 0.590719i) q^{86} +(-1.09735 + 12.5611i) q^{88} +2.14381 q^{89} +1.51546i q^{91} +(-9.62974 + 14.6440i) q^{92} +(7.11208 + 13.1888i) q^{94} -8.43162 q^{95} -13.8317 q^{97} +(-0.671239 - 1.24476i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.671239 1.24476i −0.474638 0.880181i
\(3\) 0 0
\(4\) −1.09888 + 1.67107i −0.549438 + 0.835534i
\(5\) 3.66698i 1.63993i 0.572417 + 0.819963i \(0.306006\pi\)
−0.572417 + 0.819963i \(0.693994\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.81770 + 0.246156i 0.996206 + 0.0870294i
\(9\) 0 0
\(10\) 4.56453 2.46142i 1.44343 0.778370i
\(11\) 4.45794i 1.34412i 0.740498 + 0.672059i \(0.234590\pi\)
−0.740498 + 0.672059i \(0.765410\pi\)
\(12\) 0 0
\(13\) 1.51546i 0.420314i 0.977668 + 0.210157i \(0.0673975\pi\)
−0.977668 + 0.210157i \(0.932602\pi\)
\(14\) −0.671239 1.24476i −0.179396 0.332677i
\(15\) 0 0
\(16\) −1.58494 3.67260i −0.396235 0.918149i
\(17\) 3.45516 0.838000 0.419000 0.907986i \(-0.362381\pi\)
0.419000 + 0.907986i \(0.362381\pi\)
\(18\) 0 0
\(19\) 2.29933i 0.527503i 0.964591 + 0.263752i \(0.0849600\pi\)
−0.964591 + 0.263752i \(0.915040\pi\)
\(20\) −6.12778 4.02956i −1.37021 0.901038i
\(21\) 0 0
\(22\) 5.54908 2.99234i 1.18307 0.637969i
\(23\) 8.76326 1.82727 0.913633 0.406539i \(-0.133265\pi\)
0.913633 + 0.406539i \(0.133265\pi\)
\(24\) 0 0
\(25\) −8.44677 −1.68935
\(26\) 1.88640 1.01724i 0.369953 0.199497i
\(27\) 0 0
\(28\) −1.09888 + 1.67107i −0.207668 + 0.315802i
\(29\) 1.62037i 0.300895i −0.988618 0.150448i \(-0.951928\pi\)
0.988618 0.150448i \(-0.0480715\pi\)
\(30\) 0 0
\(31\) −9.26498 −1.66404 −0.832020 0.554746i \(-0.812816\pi\)
−0.832020 + 0.554746i \(0.812816\pi\)
\(32\) −3.50764 + 4.43807i −0.620070 + 0.784547i
\(33\) 0 0
\(34\) −2.31924 4.30086i −0.397746 0.737592i
\(35\) 3.66698i 0.619833i
\(36\) 0 0
\(37\) 5.69381i 0.936056i −0.883714 0.468028i \(-0.844965\pi\)
0.883714 0.468028i \(-0.155035\pi\)
\(38\) 2.86213 1.54340i 0.464299 0.250373i
\(39\) 0 0
\(40\) −0.902651 + 10.3324i −0.142722 + 1.63370i
\(41\) 6.86926 1.07280 0.536399 0.843965i \(-0.319784\pi\)
0.536399 + 0.843965i \(0.319784\pi\)
\(42\) 0 0
\(43\) 0.880042i 0.134205i 0.997746 + 0.0671026i \(0.0213755\pi\)
−0.997746 + 0.0671026i \(0.978625\pi\)
\(44\) −7.44952 4.89872i −1.12306 0.738510i
\(45\) 0 0
\(46\) −5.88224 10.9082i −0.867289 1.60833i
\(47\) −10.5955 −1.54551 −0.772753 0.634707i \(-0.781121\pi\)
−0.772753 + 0.634707i \(0.781121\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.66980 + 10.5142i 0.801831 + 1.48694i
\(51\) 0 0
\(52\) −2.53244 1.66531i −0.351187 0.230937i
\(53\) 11.5036i 1.58014i 0.613014 + 0.790072i \(0.289957\pi\)
−0.613014 + 0.790072i \(0.710043\pi\)
\(54\) 0 0
\(55\) −16.3472 −2.20425
\(56\) 2.81770 + 0.246156i 0.376530 + 0.0328940i
\(57\) 0 0
\(58\) −2.01698 + 1.08766i −0.264843 + 0.142816i
\(59\) 2.99426i 0.389819i −0.980821 0.194909i \(-0.937559\pi\)
0.980821 0.194909i \(-0.0624413\pi\)
\(60\) 0 0
\(61\) 8.51202i 1.08985i −0.838484 0.544926i \(-0.816558\pi\)
0.838484 0.544926i \(-0.183442\pi\)
\(62\) 6.21902 + 11.5327i 0.789816 + 1.46466i
\(63\) 0 0
\(64\) 7.87881 + 1.38719i 0.984852 + 0.173398i
\(65\) −5.55718 −0.689284
\(66\) 0 0
\(67\) 10.6629i 1.30268i 0.758786 + 0.651341i \(0.225793\pi\)
−0.758786 + 0.651341i \(0.774207\pi\)
\(68\) −3.79680 + 5.77381i −0.460429 + 0.700178i
\(69\) 0 0
\(70\) 4.56453 2.46142i 0.545566 0.294196i
\(71\) −10.6172 −1.26003 −0.630015 0.776583i \(-0.716951\pi\)
−0.630015 + 0.776583i \(0.716951\pi\)
\(72\) 0 0
\(73\) 7.85523 0.919385 0.459692 0.888078i \(-0.347960\pi\)
0.459692 + 0.888078i \(0.347960\pi\)
\(74\) −7.08745 + 3.82191i −0.823899 + 0.444288i
\(75\) 0 0
\(76\) −3.84235 2.52668i −0.440747 0.289831i
\(77\) 4.45794i 0.508029i
\(78\) 0 0
\(79\) 4.57730 0.514986 0.257493 0.966280i \(-0.417104\pi\)
0.257493 + 0.966280i \(0.417104\pi\)
\(80\) 13.4674 5.81195i 1.50570 0.649796i
\(81\) 0 0
\(82\) −4.61091 8.55061i −0.509190 0.944257i
\(83\) 2.60500i 0.285936i 0.989727 + 0.142968i \(0.0456645\pi\)
−0.989727 + 0.142968i \(0.954335\pi\)
\(84\) 0 0
\(85\) 12.6700i 1.37426i
\(86\) 1.09545 0.590719i 0.118125 0.0636988i
\(87\) 0 0
\(88\) −1.09735 + 12.5611i −0.116978 + 1.33902i
\(89\) 2.14381 0.227244 0.113622 0.993524i \(-0.463755\pi\)
0.113622 + 0.993524i \(0.463755\pi\)
\(90\) 0 0
\(91\) 1.51546i 0.158864i
\(92\) −9.62974 + 14.6440i −1.00397 + 1.52674i
\(93\) 0 0
\(94\) 7.11208 + 13.1888i 0.733555 + 1.36033i
\(95\) −8.43162 −0.865066
\(96\) 0 0
\(97\) −13.8317 −1.40440 −0.702199 0.711981i \(-0.747798\pi\)
−0.702199 + 0.711981i \(0.747798\pi\)
\(98\) −0.671239 1.24476i −0.0678054 0.125740i
\(99\) 0 0
\(100\) 9.28196 14.1151i 0.928196 1.41151i
\(101\) 10.2333i 1.01826i 0.860691 + 0.509128i \(0.170032\pi\)
−0.860691 + 0.509128i \(0.829968\pi\)
\(102\) 0 0
\(103\) −12.7223 −1.25357 −0.626784 0.779193i \(-0.715629\pi\)
−0.626784 + 0.779193i \(0.715629\pi\)
\(104\) −0.373041 + 4.27012i −0.0365797 + 0.418719i
\(105\) 0 0
\(106\) 14.3193 7.72168i 1.39081 0.749996i
\(107\) 6.40575i 0.619268i 0.950856 + 0.309634i \(0.100206\pi\)
−0.950856 + 0.309634i \(0.899794\pi\)
\(108\) 0 0
\(109\) 3.38839i 0.324549i −0.986746 0.162274i \(-0.948117\pi\)
0.986746 0.162274i \(-0.0518829\pi\)
\(110\) 10.9729 + 20.3484i 1.04622 + 1.94014i
\(111\) 0 0
\(112\) −1.58494 3.67260i −0.149763 0.347028i
\(113\) 1.40668 0.132329 0.0661644 0.997809i \(-0.478924\pi\)
0.0661644 + 0.997809i \(0.478924\pi\)
\(114\) 0 0
\(115\) 32.1347i 2.99658i
\(116\) 2.70775 + 1.78059i 0.251408 + 0.165323i
\(117\) 0 0
\(118\) −3.72714 + 2.00986i −0.343111 + 0.185023i
\(119\) 3.45516 0.316734
\(120\) 0 0
\(121\) −8.87319 −0.806653
\(122\) −10.5955 + 5.71360i −0.959268 + 0.517285i
\(123\) 0 0
\(124\) 10.1811 15.4824i 0.914287 1.39036i
\(125\) 12.6393i 1.13049i
\(126\) 0 0
\(127\) 10.4597 0.928152 0.464076 0.885795i \(-0.346386\pi\)
0.464076 + 0.885795i \(0.346386\pi\)
\(128\) −3.56185 10.7384i −0.314826 0.949150i
\(129\) 0 0
\(130\) 3.73020 + 6.91738i 0.327160 + 0.606695i
\(131\) 12.6638i 1.10644i −0.833034 0.553221i \(-0.813398\pi\)
0.833034 0.553221i \(-0.186602\pi\)
\(132\) 0 0
\(133\) 2.29933i 0.199378i
\(134\) 13.2728 7.15736i 1.14660 0.618301i
\(135\) 0 0
\(136\) 9.73559 + 0.850510i 0.834820 + 0.0729306i
\(137\) 6.87026 0.586966 0.293483 0.955964i \(-0.405186\pi\)
0.293483 + 0.955964i \(0.405186\pi\)
\(138\) 0 0
\(139\) 13.4362i 1.13964i −0.821768 0.569822i \(-0.807012\pi\)
0.821768 0.569822i \(-0.192988\pi\)
\(140\) −6.12778 4.02956i −0.517892 0.340560i
\(141\) 0 0
\(142\) 7.12668 + 13.2159i 0.598058 + 1.10905i
\(143\) −6.75584 −0.564952
\(144\) 0 0
\(145\) 5.94188 0.493446
\(146\) −5.27273 9.77790i −0.436374 0.809225i
\(147\) 0 0
\(148\) 9.51475 + 6.25679i 0.782107 + 0.514305i
\(149\) 6.35294i 0.520453i 0.965548 + 0.260227i \(0.0837973\pi\)
−0.965548 + 0.260227i \(0.916203\pi\)
\(150\) 0 0
\(151\) 19.5918 1.59436 0.797179 0.603743i \(-0.206325\pi\)
0.797179 + 0.603743i \(0.206325\pi\)
\(152\) −0.565996 + 6.47882i −0.0459083 + 0.525502i
\(153\) 0 0
\(154\) 5.54908 2.99234i 0.447158 0.241130i
\(155\) 33.9745i 2.72890i
\(156\) 0 0
\(157\) 22.6978i 1.81148i −0.423834 0.905740i \(-0.639316\pi\)
0.423834 0.905740i \(-0.360684\pi\)
\(158\) −3.07246 5.69766i −0.244432 0.453281i
\(159\) 0 0
\(160\) −16.2743 12.8625i −1.28660 1.01687i
\(161\) 8.76326 0.690642
\(162\) 0 0
\(163\) 3.60107i 0.282058i −0.990005 0.141029i \(-0.954959\pi\)
0.990005 0.141029i \(-0.0450410\pi\)
\(164\) −7.54847 + 11.4790i −0.589436 + 0.896359i
\(165\) 0 0
\(166\) 3.24261 1.74857i 0.251675 0.135716i
\(167\) 5.46351 0.422779 0.211390 0.977402i \(-0.432201\pi\)
0.211390 + 0.977402i \(0.432201\pi\)
\(168\) 0 0
\(169\) 10.7034 0.823336
\(170\) 15.7712 8.50461i 1.20960 0.652274i
\(171\) 0 0
\(172\) −1.47061 0.967058i −0.112133 0.0737375i
\(173\) 1.71944i 0.130727i 0.997862 + 0.0653634i \(0.0208207\pi\)
−0.997862 + 0.0653634i \(0.979179\pi\)
\(174\) 0 0
\(175\) −8.44677 −0.638516
\(176\) 16.3722 7.06556i 1.23410 0.532587i
\(177\) 0 0
\(178\) −1.43901 2.66854i −0.107858 0.200016i
\(179\) 10.9956i 0.821846i 0.911670 + 0.410923i \(0.134794\pi\)
−0.911670 + 0.410923i \(0.865206\pi\)
\(180\) 0 0
\(181\) 26.6227i 1.97885i 0.145040 + 0.989426i \(0.453669\pi\)
−0.145040 + 0.989426i \(0.546331\pi\)
\(182\) 1.88640 1.01724i 0.139829 0.0754027i
\(183\) 0 0
\(184\) 24.6922 + 2.15713i 1.82033 + 0.159026i
\(185\) 20.8791 1.53506
\(186\) 0 0
\(187\) 15.4029i 1.12637i
\(188\) 11.6431 17.7057i 0.849160 1.29132i
\(189\) 0 0
\(190\) 5.65963 + 10.4954i 0.410593 + 0.761415i
\(191\) −22.1581 −1.60330 −0.801652 0.597791i \(-0.796045\pi\)
−0.801652 + 0.597791i \(0.796045\pi\)
\(192\) 0 0
\(193\) 11.5599 0.832098 0.416049 0.909342i \(-0.363414\pi\)
0.416049 + 0.909342i \(0.363414\pi\)
\(194\) 9.28438 + 17.2172i 0.666580 + 1.23612i
\(195\) 0 0
\(196\) −1.09888 + 1.67107i −0.0784912 + 0.119362i
\(197\) 13.1740i 0.938611i −0.883036 0.469305i \(-0.844504\pi\)
0.883036 0.469305i \(-0.155496\pi\)
\(198\) 0 0
\(199\) −12.1012 −0.857828 −0.428914 0.903345i \(-0.641104\pi\)
−0.428914 + 0.903345i \(0.641104\pi\)
\(200\) −23.8004 2.07923i −1.68294 0.147024i
\(201\) 0 0
\(202\) 12.7381 6.86902i 0.896250 0.483302i
\(203\) 1.62037i 0.113728i
\(204\) 0 0
\(205\) 25.1895i 1.75931i
\(206\) 8.53972 + 15.8363i 0.594990 + 1.10337i
\(207\) 0 0
\(208\) 5.56569 2.40192i 0.385911 0.166543i
\(209\) −10.2503 −0.709027
\(210\) 0 0
\(211\) 21.7501i 1.49734i −0.662944 0.748669i \(-0.730693\pi\)
0.662944 0.748669i \(-0.269307\pi\)
\(212\) −19.2233 12.6411i −1.32027 0.868192i
\(213\) 0 0
\(214\) 7.97365 4.29979i 0.545068 0.293928i
\(215\) −3.22710 −0.220086
\(216\) 0 0
\(217\) −9.26498 −0.628948
\(218\) −4.21774 + 2.27442i −0.285662 + 0.154043i
\(219\) 0 0
\(220\) 17.9635 27.3173i 1.21110 1.84173i
\(221\) 5.23617i 0.352223i
\(222\) 0 0
\(223\) −3.00739 −0.201390 −0.100695 0.994917i \(-0.532107\pi\)
−0.100695 + 0.994917i \(0.532107\pi\)
\(224\) −3.50764 + 4.43807i −0.234364 + 0.296531i
\(225\) 0 0
\(226\) −0.944215 1.75098i −0.0628083 0.116473i
\(227\) 11.1508i 0.740102i 0.929011 + 0.370051i \(0.120660\pi\)
−0.929011 + 0.370051i \(0.879340\pi\)
\(228\) 0 0
\(229\) 2.46317i 0.162771i 0.996683 + 0.0813853i \(0.0259344\pi\)
−0.996683 + 0.0813853i \(0.974066\pi\)
\(230\) 40.0002 21.5701i 2.63753 1.42229i
\(231\) 0 0
\(232\) 0.398865 4.56571i 0.0261867 0.299754i
\(233\) 26.1143 1.71080 0.855401 0.517966i \(-0.173311\pi\)
0.855401 + 0.517966i \(0.173311\pi\)
\(234\) 0 0
\(235\) 38.8534i 2.53451i
\(236\) 5.00361 + 3.29032i 0.325707 + 0.214181i
\(237\) 0 0
\(238\) −2.31924 4.30086i −0.150334 0.278783i
\(239\) −24.4496 −1.58151 −0.790757 0.612130i \(-0.790313\pi\)
−0.790757 + 0.612130i \(0.790313\pi\)
\(240\) 0 0
\(241\) −9.01348 −0.580609 −0.290305 0.956934i \(-0.593757\pi\)
−0.290305 + 0.956934i \(0.593757\pi\)
\(242\) 5.95603 + 11.0450i 0.382868 + 0.710001i
\(243\) 0 0
\(244\) 14.2242 + 9.35366i 0.910609 + 0.598807i
\(245\) 3.66698i 0.234275i
\(246\) 0 0
\(247\) −3.48456 −0.221717
\(248\) −26.1059 2.28063i −1.65773 0.144820i
\(249\) 0 0
\(250\) −15.7329 + 8.48397i −0.995036 + 0.536573i
\(251\) 24.7649i 1.56315i −0.623814 0.781573i \(-0.714418\pi\)
0.623814 0.781573i \(-0.285582\pi\)
\(252\) 0 0
\(253\) 39.0661i 2.45606i
\(254\) −7.02099 13.0199i −0.440536 0.816942i
\(255\) 0 0
\(256\) −10.9759 + 11.6417i −0.685996 + 0.727606i
\(257\) −17.1618 −1.07052 −0.535262 0.844686i \(-0.679787\pi\)
−0.535262 + 0.844686i \(0.679787\pi\)
\(258\) 0 0
\(259\) 5.69381i 0.353796i
\(260\) 6.10666 9.28644i 0.378719 0.575920i
\(261\) 0 0
\(262\) −15.7635 + 8.50045i −0.973870 + 0.525159i
\(263\) −4.02861 −0.248415 −0.124207 0.992256i \(-0.539639\pi\)
−0.124207 + 0.992256i \(0.539639\pi\)
\(264\) 0 0
\(265\) −42.1836 −2.59132
\(266\) 2.86213 1.54340i 0.175488 0.0946321i
\(267\) 0 0
\(268\) −17.8184 11.7172i −1.08843 0.715743i
\(269\) 24.4193i 1.48887i 0.667693 + 0.744436i \(0.267282\pi\)
−0.667693 + 0.744436i \(0.732718\pi\)
\(270\) 0 0
\(271\) −1.21510 −0.0738120 −0.0369060 0.999319i \(-0.511750\pi\)
−0.0369060 + 0.999319i \(0.511750\pi\)
\(272\) −5.47622 12.6894i −0.332045 0.769409i
\(273\) 0 0
\(274\) −4.61159 8.55185i −0.278596 0.516636i
\(275\) 37.6552i 2.27069i
\(276\) 0 0
\(277\) 11.1239i 0.668371i 0.942507 + 0.334185i \(0.108461\pi\)
−0.942507 + 0.334185i \(0.891539\pi\)
\(278\) −16.7249 + 9.01890i −1.00309 + 0.540918i
\(279\) 0 0
\(280\) −0.902651 + 10.3324i −0.0539437 + 0.617482i
\(281\) 29.4678 1.75790 0.878952 0.476910i \(-0.158243\pi\)
0.878952 + 0.476910i \(0.158243\pi\)
\(282\) 0 0
\(283\) 13.0312i 0.774624i 0.921949 + 0.387312i \(0.126596\pi\)
−0.921949 + 0.387312i \(0.873404\pi\)
\(284\) 11.6670 17.7421i 0.692309 1.05280i
\(285\) 0 0
\(286\) 4.53478 + 8.40943i 0.268147 + 0.497260i
\(287\) 6.86926 0.405479
\(288\) 0 0
\(289\) −5.06186 −0.297756
\(290\) −3.98842 7.39624i −0.234208 0.434322i
\(291\) 0 0
\(292\) −8.63192 + 13.1266i −0.505145 + 0.768177i
\(293\) 4.86503i 0.284218i −0.989851 0.142109i \(-0.954612\pi\)
0.989851 0.142109i \(-0.0453883\pi\)
\(294\) 0 0
\(295\) 10.9799 0.639274
\(296\) 1.40157 16.0434i 0.0814644 0.932505i
\(297\) 0 0
\(298\) 7.90792 4.26434i 0.458093 0.247027i
\(299\) 13.2804i 0.768026i
\(300\) 0 0
\(301\) 0.880042i 0.0507248i
\(302\) −13.1508 24.3872i −0.756742 1.40332i
\(303\) 0 0
\(304\) 8.44453 3.64431i 0.484327 0.209015i
\(305\) 31.2134 1.78728
\(306\) 0 0
\(307\) 9.07611i 0.518001i 0.965877 + 0.259000i \(0.0833931\pi\)
−0.965877 + 0.259000i \(0.916607\pi\)
\(308\) −7.44952 4.89872i −0.424476 0.279131i
\(309\) 0 0
\(310\) −42.2903 + 22.8050i −2.40193 + 1.29524i
\(311\) −1.21020 −0.0686240 −0.0343120 0.999411i \(-0.510924\pi\)
−0.0343120 + 0.999411i \(0.510924\pi\)
\(312\) 0 0
\(313\) −3.15697 −0.178443 −0.0892214 0.996012i \(-0.528438\pi\)
−0.0892214 + 0.996012i \(0.528438\pi\)
\(314\) −28.2534 + 15.2356i −1.59443 + 0.859796i
\(315\) 0 0
\(316\) −5.02989 + 7.64898i −0.282953 + 0.430289i
\(317\) 7.08197i 0.397763i −0.980024 0.198882i \(-0.936269\pi\)
0.980024 0.198882i \(-0.0637309\pi\)
\(318\) 0 0
\(319\) 7.22351 0.404439
\(320\) −5.08679 + 28.8915i −0.284360 + 1.61508i
\(321\) 0 0
\(322\) −5.88224 10.9082i −0.327805 0.607890i
\(323\) 7.94457i 0.442048i
\(324\) 0 0
\(325\) 12.8008i 0.710060i
\(326\) −4.48248 + 2.41718i −0.248262 + 0.133875i
\(327\) 0 0
\(328\) 19.3555 + 1.69091i 1.06873 + 0.0933649i
\(329\) −10.5955 −0.584146
\(330\) 0 0
\(331\) 7.34765i 0.403863i −0.979400 0.201932i \(-0.935278\pi\)
0.979400 0.201932i \(-0.0647219\pi\)
\(332\) −4.35313 2.86257i −0.238909 0.157104i
\(333\) 0 0
\(334\) −3.66732 6.80078i −0.200667 0.372122i
\(335\) −39.1007 −2.13630
\(336\) 0 0
\(337\) −26.9873 −1.47009 −0.735046 0.678017i \(-0.762840\pi\)
−0.735046 + 0.678017i \(0.762840\pi\)
\(338\) −7.18452 13.3232i −0.390786 0.724685i
\(339\) 0 0
\(340\) −21.1725 13.9228i −1.14824 0.755069i
\(341\) 41.3027i 2.23667i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −0.216628 + 2.47969i −0.0116798 + 0.133696i
\(345\) 0 0
\(346\) 2.14030 1.15416i 0.115063 0.0620479i
\(347\) 9.06776i 0.486783i 0.969928 + 0.243391i \(0.0782599\pi\)
−0.969928 + 0.243391i \(0.921740\pi\)
\(348\) 0 0
\(349\) 13.6784i 0.732191i 0.930577 + 0.366095i \(0.119306\pi\)
−0.930577 + 0.366095i \(0.880694\pi\)
\(350\) 5.66980 + 10.5142i 0.303064 + 0.562010i
\(351\) 0 0
\(352\) −19.7846 15.6368i −1.05452 0.833447i
\(353\) 0.949067 0.0505138 0.0252569 0.999681i \(-0.491960\pi\)
0.0252569 + 0.999681i \(0.491960\pi\)
\(354\) 0 0
\(355\) 38.9331i 2.06636i
\(356\) −2.35578 + 3.58246i −0.124856 + 0.189870i
\(357\) 0 0
\(358\) 13.6869 7.38064i 0.723374 0.390079i
\(359\) 15.0508 0.794351 0.397175 0.917743i \(-0.369991\pi\)
0.397175 + 0.917743i \(0.369991\pi\)
\(360\) 0 0
\(361\) 13.7131 0.721740
\(362\) 33.1390 17.8702i 1.74175 0.939237i
\(363\) 0 0
\(364\) −2.53244 1.66531i −0.132736 0.0872859i
\(365\) 28.8050i 1.50772i
\(366\) 0 0
\(367\) −3.70674 −0.193490 −0.0967451 0.995309i \(-0.530843\pi\)
−0.0967451 + 0.995309i \(0.530843\pi\)
\(368\) −13.8892 32.1839i −0.724027 1.67770i
\(369\) 0 0
\(370\) −14.0149 25.9896i −0.728598 1.35113i
\(371\) 11.5036i 0.597239i
\(372\) 0 0
\(373\) 31.3688i 1.62421i −0.583508 0.812107i \(-0.698320\pi\)
0.583508 0.812107i \(-0.301680\pi\)
\(374\) 19.1730 10.3390i 0.991410 0.534618i
\(375\) 0 0
\(376\) −29.8548 2.60814i −1.53964 0.134504i
\(377\) 2.45562 0.126471
\(378\) 0 0
\(379\) 17.6560i 0.906930i 0.891274 + 0.453465i \(0.149812\pi\)
−0.891274 + 0.453465i \(0.850188\pi\)
\(380\) 9.26531 14.0898i 0.475301 0.722792i
\(381\) 0 0
\(382\) 14.8734 + 27.5816i 0.760989 + 1.41120i
\(383\) 17.7974 0.909402 0.454701 0.890644i \(-0.349746\pi\)
0.454701 + 0.890644i \(0.349746\pi\)
\(384\) 0 0
\(385\) −16.3472 −0.833129
\(386\) −7.75944 14.3893i −0.394945 0.732397i
\(387\) 0 0
\(388\) 15.1993 23.1137i 0.771630 1.17342i
\(389\) 25.1886i 1.27711i 0.769574 + 0.638557i \(0.220468\pi\)
−0.769574 + 0.638557i \(0.779532\pi\)
\(390\) 0 0
\(391\) 30.2785 1.53125
\(392\) 2.81770 + 0.246156i 0.142315 + 0.0124328i
\(393\) 0 0
\(394\) −16.3986 + 8.84292i −0.826148 + 0.445500i
\(395\) 16.7849i 0.844539i
\(396\) 0 0
\(397\) 34.3710i 1.72503i −0.506032 0.862515i \(-0.668888\pi\)
0.506032 0.862515i \(-0.331112\pi\)
\(398\) 8.12276 + 15.0631i 0.407157 + 0.755044i
\(399\) 0 0
\(400\) 13.3876 + 31.0216i 0.669382 + 1.55108i
\(401\) −9.65560 −0.482178 −0.241089 0.970503i \(-0.577505\pi\)
−0.241089 + 0.970503i \(0.577505\pi\)
\(402\) 0 0
\(403\) 14.0408i 0.699420i
\(404\) −17.1006 11.2452i −0.850788 0.559469i
\(405\) 0 0
\(406\) −2.01698 + 1.08766i −0.100101 + 0.0539795i
\(407\) 25.3826 1.25817
\(408\) 0 0
\(409\) 28.4161 1.40509 0.702543 0.711642i \(-0.252048\pi\)
0.702543 + 0.711642i \(0.252048\pi\)
\(410\) 31.3549 16.9081i 1.54851 0.835034i
\(411\) 0 0
\(412\) 13.9803 21.2599i 0.688758 1.04740i
\(413\) 2.99426i 0.147338i
\(414\) 0 0
\(415\) −9.55248 −0.468913
\(416\) −6.72573 5.31571i −0.329756 0.260624i
\(417\) 0 0
\(418\) 6.88039 + 12.7592i 0.336531 + 0.624072i
\(419\) 11.5381i 0.563673i −0.959462 0.281837i \(-0.909056\pi\)
0.959462 0.281837i \(-0.0909436\pi\)
\(420\) 0 0
\(421\) 6.84814i 0.333758i −0.985977 0.166879i \(-0.946631\pi\)
0.985977 0.166879i \(-0.0533689\pi\)
\(422\) −27.0737 + 14.5995i −1.31793 + 0.710692i
\(423\) 0 0
\(424\) −2.83169 + 32.4137i −0.137519 + 1.57415i
\(425\) −29.1850 −1.41568
\(426\) 0 0
\(427\) 8.51202i 0.411925i
\(428\) −10.7045 7.03913i −0.517419 0.340249i
\(429\) 0 0
\(430\) 2.16616 + 4.01698i 0.104461 + 0.193716i
\(431\) −10.4500 −0.503357 −0.251679 0.967811i \(-0.580983\pi\)
−0.251679 + 0.967811i \(0.580983\pi\)
\(432\) 0 0
\(433\) 18.1818 0.873763 0.436882 0.899519i \(-0.356083\pi\)
0.436882 + 0.899519i \(0.356083\pi\)
\(434\) 6.21902 + 11.5327i 0.298522 + 0.553588i
\(435\) 0 0
\(436\) 5.66223 + 3.72342i 0.271171 + 0.178319i
\(437\) 20.1497i 0.963889i
\(438\) 0 0
\(439\) 7.91836 0.377923 0.188961 0.981985i \(-0.439488\pi\)
0.188961 + 0.981985i \(0.439488\pi\)
\(440\) −46.0614 4.02396i −2.19589 0.191835i
\(441\) 0 0
\(442\) 6.51780 3.51472i 0.310020 0.167178i
\(443\) 18.2916i 0.869062i −0.900657 0.434531i \(-0.856914\pi\)
0.900657 0.434531i \(-0.143086\pi\)
\(444\) 0 0
\(445\) 7.86132i 0.372662i
\(446\) 2.01868 + 3.74350i 0.0955873 + 0.177260i
\(447\) 0 0
\(448\) 7.87881 + 1.38719i 0.372239 + 0.0655384i
\(449\) 15.2172 0.718144 0.359072 0.933310i \(-0.383093\pi\)
0.359072 + 0.933310i \(0.383093\pi\)
\(450\) 0 0
\(451\) 30.6227i 1.44197i
\(452\) −1.54576 + 2.35065i −0.0727066 + 0.110565i
\(453\) 0 0
\(454\) 13.8801 7.48482i 0.651424 0.351280i
\(455\) −5.55718 −0.260525
\(456\) 0 0
\(457\) 38.6658 1.80871 0.904354 0.426783i \(-0.140353\pi\)
0.904354 + 0.426783i \(0.140353\pi\)
\(458\) 3.06606 1.65337i 0.143268 0.0772570i
\(459\) 0 0
\(460\) −53.6994 35.3121i −2.50375 1.64644i
\(461\) 5.18888i 0.241670i −0.992673 0.120835i \(-0.961443\pi\)
0.992673 0.120835i \(-0.0385572\pi\)
\(462\) 0 0
\(463\) −3.81583 −0.177337 −0.0886683 0.996061i \(-0.528261\pi\)
−0.0886683 + 0.996061i \(0.528261\pi\)
\(464\) −5.95097 + 2.56819i −0.276267 + 0.119225i
\(465\) 0 0
\(466\) −17.5289 32.5061i −0.812011 1.50582i
\(467\) 7.29246i 0.337455i −0.985663 0.168727i \(-0.946034\pi\)
0.985663 0.168727i \(-0.0539657\pi\)
\(468\) 0 0
\(469\) 10.6629i 0.492367i
\(470\) −48.3633 + 26.0799i −2.23083 + 1.20298i
\(471\) 0 0
\(472\) 0.737055 8.43690i 0.0339257 0.388340i
\(473\) −3.92317 −0.180388
\(474\) 0 0
\(475\) 19.4220i 0.891140i
\(476\) −3.79680 + 5.77381i −0.174026 + 0.264642i
\(477\) 0 0
\(478\) 16.4115 + 30.4340i 0.750646 + 1.39202i
\(479\) −16.2695 −0.743371 −0.371686 0.928359i \(-0.621220\pi\)
−0.371686 + 0.928359i \(0.621220\pi\)
\(480\) 0 0
\(481\) 8.62876 0.393438
\(482\) 6.05020 + 11.2197i 0.275579 + 0.511042i
\(483\) 0 0
\(484\) 9.75054 14.8277i 0.443206 0.673986i
\(485\) 50.7207i 2.30311i
\(486\) 0 0
\(487\) 7.16667 0.324753 0.162376 0.986729i \(-0.448084\pi\)
0.162376 + 0.986729i \(0.448084\pi\)
\(488\) 2.09529 23.9843i 0.0948492 1.08572i
\(489\) 0 0
\(490\) 4.56453 2.46142i 0.206205 0.111196i
\(491\) 17.8247i 0.804418i −0.915548 0.402209i \(-0.868243\pi\)
0.915548 0.402209i \(-0.131757\pi\)
\(492\) 0 0
\(493\) 5.59864i 0.252150i
\(494\) 2.33897 + 4.33746i 0.105235 + 0.195151i
\(495\) 0 0
\(496\) 14.6844 + 34.0265i 0.659351 + 1.52784i
\(497\) −10.6172 −0.476247
\(498\) 0 0
\(499\) 37.6121i 1.68375i 0.539673 + 0.841875i \(0.318548\pi\)
−0.539673 + 0.841875i \(0.681452\pi\)
\(500\) 21.1211 + 13.8890i 0.944563 + 0.621135i
\(501\) 0 0
\(502\) −30.8265 + 16.6232i −1.37585 + 0.741928i
\(503\) 20.3707 0.908286 0.454143 0.890929i \(-0.349945\pi\)
0.454143 + 0.890929i \(0.349945\pi\)
\(504\) 0 0
\(505\) −37.5255 −1.66986
\(506\) 48.6280 26.2227i 2.16178 1.16574i
\(507\) 0 0
\(508\) −11.4940 + 17.4789i −0.509962 + 0.775503i
\(509\) 26.6481i 1.18116i 0.806980 + 0.590578i \(0.201100\pi\)
−0.806980 + 0.590578i \(0.798900\pi\)
\(510\) 0 0
\(511\) 7.85523 0.347495
\(512\) 21.8586 + 5.84809i 0.966024 + 0.258451i
\(513\) 0 0
\(514\) 11.5197 + 21.3624i 0.508111 + 0.942256i
\(515\) 46.6526i 2.05576i
\(516\) 0 0
\(517\) 47.2339i 2.07734i
\(518\) −7.08745 + 3.82191i −0.311405 + 0.167925i
\(519\) 0 0
\(520\) −15.6585 1.36794i −0.686669 0.0599880i
\(521\) 13.2614 0.580992 0.290496 0.956876i \(-0.406180\pi\)
0.290496 + 0.956876i \(0.406180\pi\)
\(522\) 0 0
\(523\) 21.3786i 0.934821i 0.884040 + 0.467411i \(0.154813\pi\)
−0.884040 + 0.467411i \(0.845187\pi\)
\(524\) 21.1621 + 13.9160i 0.924471 + 0.607922i
\(525\) 0 0
\(526\) 2.70416 + 5.01467i 0.117907 + 0.218650i
\(527\) −32.0120 −1.39447
\(528\) 0 0
\(529\) 53.7948 2.33890
\(530\) 28.3153 + 52.5087i 1.22994 + 2.28083i
\(531\) 0 0
\(532\) −3.84235 2.52668i −0.166587 0.109546i
\(533\) 10.4101i 0.450912i
\(534\) 0 0
\(535\) −23.4898 −1.01555
\(536\) −2.62474 + 30.0448i −0.113372 + 1.29774i
\(537\) 0 0
\(538\) 30.3963 16.3912i 1.31048 0.706675i
\(539\) 4.45794i 0.192017i
\(540\) 0 0
\(541\) 31.4969i 1.35416i −0.735910 0.677080i \(-0.763245\pi\)
0.735910 0.677080i \(-0.236755\pi\)
\(542\) 0.815621 + 1.51251i 0.0350339 + 0.0649679i
\(543\) 0 0
\(544\) −12.1195 + 15.3342i −0.519618 + 0.657450i
\(545\) 12.4252 0.532235
\(546\) 0 0
\(547\) 1.38840i 0.0593637i 0.999559 + 0.0296819i \(0.00944942\pi\)
−0.999559 + 0.0296819i \(0.990551\pi\)
\(548\) −7.54957 + 11.4807i −0.322502 + 0.490430i
\(549\) 0 0
\(550\) −46.8718 + 25.2756i −1.99862 + 1.07776i
\(551\) 3.72578 0.158723
\(552\) 0 0
\(553\) 4.57730 0.194647
\(554\) 13.8466 7.46680i 0.588287 0.317234i
\(555\) 0 0
\(556\) 22.4528 + 14.7647i 0.952212 + 0.626164i
\(557\) 10.8246i 0.458654i −0.973349 0.229327i \(-0.926347\pi\)
0.973349 0.229327i \(-0.0736525\pi\)
\(558\) 0 0
\(559\) −1.33367 −0.0564083
\(560\) 13.4674 5.81195i 0.569100 0.245600i
\(561\) 0 0
\(562\) −19.7800 36.6805i −0.834367 1.54727i
\(563\) 7.56473i 0.318816i −0.987213 0.159408i \(-0.949042\pi\)
0.987213 0.159408i \(-0.0509585\pi\)
\(564\) 0 0
\(565\) 5.15826i 0.217009i
\(566\) 16.2208 8.74704i 0.681810 0.367666i
\(567\) 0 0
\(568\) −29.9160 2.61349i −1.25525 0.109660i
\(569\) 21.9063 0.918360 0.459180 0.888343i \(-0.348143\pi\)
0.459180 + 0.888343i \(0.348143\pi\)
\(570\) 0 0
\(571\) 43.6061i 1.82486i −0.409235 0.912429i \(-0.634204\pi\)
0.409235 0.912429i \(-0.365796\pi\)
\(572\) 7.42384 11.2895i 0.310406 0.472037i
\(573\) 0 0
\(574\) −4.61091 8.55061i −0.192456 0.356895i
\(575\) −74.0213 −3.08690
\(576\) 0 0
\(577\) 12.6116 0.525028 0.262514 0.964928i \(-0.415448\pi\)
0.262514 + 0.964928i \(0.415448\pi\)
\(578\) 3.39772 + 6.30082i 0.141326 + 0.262080i
\(579\) 0 0
\(580\) −6.52939 + 9.92928i −0.271118 + 0.412291i
\(581\) 2.60500i 0.108073i
\(582\) 0 0
\(583\) −51.2824 −2.12390
\(584\) 22.1336 + 1.93361i 0.915896 + 0.0800135i
\(585\) 0 0
\(586\) −6.05581 + 3.26560i −0.250163 + 0.134901i
\(587\) 10.5118i 0.433866i −0.976186 0.216933i \(-0.930395\pi\)
0.976186 0.216933i \(-0.0696054\pi\)
\(588\) 0 0
\(589\) 21.3033i 0.877787i
\(590\) −7.37013 13.6674i −0.303423 0.562677i
\(591\) 0 0
\(592\) −20.9111 + 9.02435i −0.859439 + 0.370898i
\(593\) 23.9765 0.984598 0.492299 0.870426i \(-0.336157\pi\)
0.492299 + 0.870426i \(0.336157\pi\)
\(594\) 0 0
\(595\) 12.6700i 0.519420i
\(596\) −10.6162 6.98110i −0.434857 0.285957i
\(597\) 0 0
\(598\) 16.5310 8.91433i 0.676002 0.364534i
\(599\) 32.2302 1.31689 0.658446 0.752628i \(-0.271214\pi\)
0.658446 + 0.752628i \(0.271214\pi\)
\(600\) 0 0
\(601\) 43.3405 1.76790 0.883949 0.467584i \(-0.154875\pi\)
0.883949 + 0.467584i \(0.154875\pi\)
\(602\) 1.09545 0.590719i 0.0446470 0.0240759i
\(603\) 0 0
\(604\) −21.5290 + 32.7392i −0.876001 + 1.33214i
\(605\) 32.5378i 1.32285i
\(606\) 0 0
\(607\) −13.2372 −0.537283 −0.268642 0.963240i \(-0.586575\pi\)
−0.268642 + 0.963240i \(0.586575\pi\)
\(608\) −10.2046 8.06525i −0.413851 0.327089i
\(609\) 0 0
\(610\) −20.9517 38.8534i −0.848308 1.57313i
\(611\) 16.0570i 0.649598i
\(612\) 0 0
\(613\) 6.23612i 0.251874i −0.992038 0.125937i \(-0.959806\pi\)
0.992038 0.125937i \(-0.0401938\pi\)
\(614\) 11.2976 6.09224i 0.455935 0.245863i
\(615\) 0 0
\(616\) −1.09735 + 12.5611i −0.0442134 + 0.506101i
\(617\) −7.66713 −0.308667 −0.154334 0.988019i \(-0.549323\pi\)
−0.154334 + 0.988019i \(0.549323\pi\)
\(618\) 0 0
\(619\) 27.9974i 1.12531i 0.826692 + 0.562655i \(0.190220\pi\)
−0.826692 + 0.562655i \(0.809780\pi\)
\(620\) 56.7738 + 37.3338i 2.28009 + 1.49936i
\(621\) 0 0
\(622\) 0.812332 + 1.50641i 0.0325715 + 0.0604016i
\(623\) 2.14381 0.0858900
\(624\) 0 0
\(625\) 4.11412 0.164565
\(626\) 2.11908 + 3.92969i 0.0846956 + 0.157062i
\(627\) 0 0
\(628\) 37.9295 + 24.9421i 1.51355 + 0.995297i
\(629\) 19.6730i 0.784415i
\(630\) 0 0
\(631\) 18.2806 0.727739 0.363869 0.931450i \(-0.381455\pi\)
0.363869 + 0.931450i \(0.381455\pi\)
\(632\) 12.8974 + 1.12673i 0.513032 + 0.0448189i
\(633\) 0 0
\(634\) −8.81539 + 4.75370i −0.350104 + 0.188793i
\(635\) 38.3557i 1.52210i
\(636\) 0 0
\(637\) 1.51546i 0.0600449i
\(638\) −4.84870 8.99157i −0.191962 0.355980i
\(639\) 0 0
\(640\) 39.3775 13.0612i 1.55653 0.516291i
\(641\) −5.99361 −0.236733 −0.118367 0.992970i \(-0.537766\pi\)
−0.118367 + 0.992970i \(0.537766\pi\)
\(642\) 0 0
\(643\) 29.0547i 1.14581i 0.819623 + 0.572903i \(0.194183\pi\)
−0.819623 + 0.572903i \(0.805817\pi\)
\(644\) −9.62974 + 14.6440i −0.379465 + 0.577055i
\(645\) 0 0
\(646\) 9.88912 5.33271i 0.389082 0.209812i
\(647\) −26.7288 −1.05082 −0.525408 0.850850i \(-0.676087\pi\)
−0.525408 + 0.850850i \(0.676087\pi\)
\(648\) 0 0
\(649\) 13.3482 0.523963
\(650\) −15.9340 + 8.59238i −0.624981 + 0.337021i
\(651\) 0 0
\(652\) 6.01763 + 3.95713i 0.235669 + 0.154973i
\(653\) 41.0011i 1.60450i −0.596991 0.802248i \(-0.703637\pi\)
0.596991 0.802248i \(-0.296363\pi\)
\(654\) 0 0
\(655\) 46.4380 1.81448
\(656\) −10.8874 25.2280i −0.425080 0.984988i
\(657\) 0 0
\(658\) 7.11208 + 13.1888i 0.277258 + 0.514155i
\(659\) 1.91818i 0.0747219i 0.999302 + 0.0373609i \(0.0118951\pi\)
−0.999302 + 0.0373609i \(0.988105\pi\)
\(660\) 0 0
\(661\) 10.9347i 0.425312i 0.977127 + 0.212656i \(0.0682114\pi\)
−0.977127 + 0.212656i \(0.931789\pi\)
\(662\) −9.14609 + 4.93203i −0.355473 + 0.191689i
\(663\) 0 0
\(664\) −0.641236 + 7.34009i −0.0248848 + 0.284851i
\(665\) −8.43162 −0.326964
\(666\) 0 0
\(667\) 14.1997i 0.549816i
\(668\) −6.00373 + 9.12990i −0.232291 + 0.353247i
\(669\) 0 0
\(670\) 26.2459 + 48.6712i 1.01397 + 1.88033i
\(671\) 37.9460 1.46489
\(672\) 0 0
\(673\) 10.0071 0.385745 0.192872 0.981224i \(-0.438220\pi\)
0.192872 + 0.981224i \(0.438220\pi\)
\(674\) 18.1149 + 33.5928i 0.697761 + 1.29395i
\(675\) 0 0
\(676\) −11.7617 + 17.8861i −0.452372 + 0.687925i
\(677\) 35.4441i 1.36223i 0.732178 + 0.681113i \(0.238504\pi\)
−0.732178 + 0.681113i \(0.761496\pi\)
\(678\) 0 0
\(679\) −13.8317 −0.530812
\(680\) −3.11881 + 35.7003i −0.119601 + 1.36904i
\(681\) 0 0
\(682\) −51.4121 + 27.7240i −1.96867 + 1.06161i
\(683\) 34.8397i 1.33310i 0.745459 + 0.666551i \(0.232230\pi\)
−0.745459 + 0.666551i \(0.767770\pi\)
\(684\) 0 0
\(685\) 25.1931i 0.962580i
\(686\) −0.671239 1.24476i −0.0256280 0.0475253i
\(687\) 0 0
\(688\) 3.23204 1.39481i 0.123220 0.0531768i
\(689\) −17.4333 −0.664157
\(690\) 0 0
\(691\) 16.2381i 0.617727i 0.951106 + 0.308864i \(0.0999486\pi\)
−0.951106 + 0.308864i \(0.900051\pi\)
\(692\) −2.87331 1.88946i −0.109227 0.0718263i
\(693\) 0 0
\(694\) 11.2872 6.08663i 0.428457 0.231045i
\(695\) 49.2704 1.86893
\(696\) 0 0
\(697\) 23.7344 0.899004
\(698\) 17.0264 9.18151i 0.644461 0.347525i
\(699\) 0 0
\(700\) 9.28196 14.1151i 0.350825 0.533502i
\(701\) 28.8081i 1.08807i 0.839064 + 0.544033i \(0.183103\pi\)
−0.839064 + 0.544033i \(0.816897\pi\)
\(702\) 0 0
\(703\) 13.0920 0.493773
\(704\) −6.18399 + 35.1232i −0.233068 + 1.32376i
\(705\) 0 0
\(706\) −0.637051 1.18137i −0.0239757 0.0444613i
\(707\) 10.2333i 0.384864i
\(708\) 0 0
\(709\) 18.1039i 0.679906i −0.940442 0.339953i \(-0.889589\pi\)
0.940442 0.339953i \(-0.110411\pi\)
\(710\) −48.4626 + 26.1334i −1.81877 + 0.980770i
\(711\) 0 0
\(712\) 6.04061 + 0.527713i 0.226381 + 0.0197769i
\(713\) −81.1915 −3.04064
\(714\) 0 0
\(715\) 24.7736i 0.926479i
\(716\) −18.3743 12.0828i −0.686681 0.451554i
\(717\) 0 0
\(718\) −10.1027 18.7347i −0.377029 0.699173i
\(719\) 12.7731 0.476357 0.238179 0.971221i \(-0.423450\pi\)
0.238179 + 0.971221i \(0.423450\pi\)
\(720\) 0 0
\(721\) −12.7223 −0.473804
\(722\) −9.20474 17.0695i −0.342565 0.635262i
\(723\) 0 0
\(724\) −44.4884 29.2551i −1.65340 1.08726i
\(725\) 13.6869i 0.508319i
\(726\) 0 0
\(727\) −10.1654 −0.377012 −0.188506 0.982072i \(-0.560365\pi\)
−0.188506 + 0.982072i \(0.560365\pi\)
\(728\) −0.373041 + 4.27012i −0.0138258 + 0.158261i
\(729\) 0 0
\(730\) 35.8554 19.3350i 1.32707 0.715621i
\(731\) 3.04069i 0.112464i
\(732\) 0 0
\(733\) 26.1041i 0.964178i −0.876122 0.482089i \(-0.839878\pi\)
0.876122 0.482089i \(-0.160122\pi\)
\(734\) 2.48811 + 4.61402i 0.0918377 + 0.170307i
\(735\) 0 0
\(736\) −30.7384 + 38.8919i −1.13303 + 1.43358i
\(737\) −47.5345 −1.75096
\(738\) 0 0
\(739\) 9.90517i 0.364368i 0.983264 + 0.182184i \(0.0583166\pi\)
−0.983264 + 0.182184i \(0.941683\pi\)
\(740\) −22.9436 + 34.8904i −0.843422 + 1.28260i
\(741\) 0 0
\(742\) 14.3193 7.72168i 0.525678 0.283472i
\(743\) −33.5353 −1.23029 −0.615146 0.788413i \(-0.710903\pi\)
−0.615146 + 0.788413i \(0.710903\pi\)
\(744\) 0 0
\(745\) −23.2961 −0.853504
\(746\) −39.0468 + 21.0560i −1.42960 + 0.770913i
\(747\) 0 0
\(748\) −25.7393 16.9259i −0.941121 0.618871i
\(749\) 6.40575i 0.234061i
\(750\) 0 0
\(751\) 53.8436 1.96478 0.982391 0.186839i \(-0.0598243\pi\)
0.982391 + 0.186839i \(0.0598243\pi\)
\(752\) 16.7932 + 38.9128i 0.612384 + 1.41901i
\(753\) 0 0
\(754\) −1.64830 3.05666i −0.0600277 0.111317i
\(755\) 71.8428i 2.61463i
\(756\) 0 0
\(757\) 1.18921i 0.0432225i 0.999766 + 0.0216113i \(0.00687962\pi\)
−0.999766 + 0.0216113i \(0.993120\pi\)
\(758\) 21.9776 11.8514i 0.798262 0.430463i
\(759\) 0 0
\(760\) −23.7577 2.07550i −0.861784 0.0752862i
\(761\) 38.0810 1.38043 0.690217 0.723602i \(-0.257515\pi\)
0.690217 + 0.723602i \(0.257515\pi\)
\(762\) 0 0
\(763\) 3.38839i 0.122668i
\(764\) 24.3490 37.0277i 0.880917 1.33962i
\(765\) 0 0
\(766\) −11.9463 22.1535i −0.431637 0.800439i
\(767\) 4.53769 0.163846
\(768\) 0 0
\(769\) −38.6053 −1.39214 −0.696071 0.717973i \(-0.745070\pi\)
−0.696071 + 0.717973i \(0.745070\pi\)
\(770\) 10.9729 + 20.3484i 0.395434 + 0.733305i
\(771\) 0 0
\(772\) −12.7029 + 19.3173i −0.457187 + 0.695246i
\(773\) 18.5902i 0.668642i 0.942459 + 0.334321i \(0.108507\pi\)
−0.942459 + 0.334321i \(0.891493\pi\)
\(774\) 0 0
\(775\) 78.2592 2.81115
\(776\) −38.9736 3.40476i −1.39907 0.122224i
\(777\) 0 0
\(778\) 31.3539 16.9076i 1.12409 0.606166i
\(779\) 15.7947i 0.565905i
\(780\) 0 0
\(781\) 47.3308i 1.69363i
\(782\) −20.3241 37.6896i −0.726788 1.34778i
\(783\) 0 0
\(784\) −1.58494 3.67260i −0.0566050 0.131164i
\(785\) 83.2324 2.97069
\(786\) 0 0