Properties

Label 168.2.u.a.89.4
Level 168
Weight 2
Character 168.89
Analytic conductor 1.341
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.4
Root \(0.934861 - 1.45809i\) of \(x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} - 13122 x + 6561\)
Character \(\chi\) \(=\) 168.89
Dual form 168.2.u.a.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0805675 + 1.73018i) q^{3} +(1.90017 - 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(-2.98702 + 0.278792i) q^{9} +O(q^{10})\) \(q+(0.0805675 + 1.73018i) q^{3} +(1.90017 - 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(-2.98702 + 0.278792i) q^{9} +(0.309539 - 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 + 3.02246i) q^{15} +(0.0519689 + 0.0900129i) q^{17} +(-2.12615 - 1.22753i) q^{19} +(-2.26983 + 3.98094i) q^{21} +(-1.15188 - 0.665037i) q^{23} +(-4.72127 - 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(-6.83007 + 3.94335i) q^{31} +(0.334142 + 0.521158i) q^{33} +(8.90704 - 4.66504i) q^{35} +(5.45622 - 9.45046i) q^{37} +(-6.99976 + 0.325951i) q^{39} -6.15464 q^{41} +0.502751 q^{43} +(-4.75828 + 10.3606i) q^{45} +(-5.72578 + 9.91734i) q^{47} +(2.99000 + 6.32929i) q^{49} +(-0.151551 + 0.0971675i) q^{51} +(-5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 - 6.53614i) q^{59} +(8.20485 + 4.73707i) q^{61} +(-7.07060 - 3.60647i) q^{63} +(13.3151 + 7.68750i) q^{65} +(-1.34375 - 2.32744i) q^{67} +(1.05783 - 2.04653i) q^{69} -5.78975i q^{71} +(-0.203925 + 0.117736i) q^{73} +(13.7681 - 8.82748i) q^{75} +(0.944856 + 0.0388878i) q^{77} +(-1.61247 + 2.79289i) q^{79} +(8.84455 - 1.66551i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(8.60356 - 0.400634i) q^{87} +(-3.41213 + 5.90999i) q^{89} +(-5.72862 + 9.04192i) q^{91} +(-7.37296 - 11.4995i) q^{93} +(-8.08008 + 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 + 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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 0
\(3\) 0.0805675 + 1.73018i 0.0465156 + 0.998918i
\(4\) 0 0
\(5\) 1.90017 3.29119i 0.849781 1.47186i −0.0316229 0.999500i \(-0.510068\pi\)
0.881404 0.472364i \(-0.156599\pi\)
\(6\) 0 0
\(7\) 2.23495 + 1.41598i 0.844732 + 0.535190i
\(8\) 0 0
\(9\) −2.98702 + 0.278792i −0.995673 + 0.0929306i
\(10\) 0 0
\(11\) 0.309539 0.178712i 0.0933294 0.0538838i −0.452609 0.891709i \(-0.649507\pi\)
0.545938 + 0.837825i \(0.316173\pi\)
\(12\) 0 0
\(13\) 4.04570i 1.12207i 0.827791 + 0.561037i \(0.189597\pi\)
−0.827791 + 0.561037i \(0.810403\pi\)
\(14\) 0 0
\(15\) 5.84742 + 3.02246i 1.50980 + 0.780396i
\(16\) 0 0
\(17\) 0.0519689 + 0.0900129i 0.0126043 + 0.0218313i 0.872259 0.489045i \(-0.162654\pi\)
−0.859654 + 0.510876i \(0.829321\pi\)
\(18\) 0 0
\(19\) −2.12615 1.22753i −0.487772 0.281615i 0.235878 0.971783i \(-0.424204\pi\)
−0.723650 + 0.690167i \(0.757537\pi\)
\(20\) 0 0
\(21\) −2.26983 + 3.98094i −0.495318 + 0.868712i
\(22\) 0 0
\(23\) −1.15188 0.665037i −0.240183 0.138670i 0.375078 0.926993i \(-0.377616\pi\)
−0.615261 + 0.788323i \(0.710949\pi\)
\(24\) 0 0
\(25\) −4.72127 8.17749i −0.944255 1.63550i
\(26\) 0 0
\(27\) −0.723015 5.14560i −0.139144 0.990272i
\(28\) 0 0
\(29\) 4.97265i 0.923398i −0.887037 0.461699i \(-0.847240\pi\)
0.887037 0.461699i \(-0.152760\pi\)
\(30\) 0 0
\(31\) −6.83007 + 3.94335i −1.22672 + 0.708246i −0.966342 0.257262i \(-0.917180\pi\)
−0.260376 + 0.965507i \(0.583846\pi\)
\(32\) 0 0
\(33\) 0.334142 + 0.521158i 0.0581667 + 0.0907220i
\(34\) 0 0
\(35\) 8.90704 4.66504i 1.50556 0.788535i
\(36\) 0 0
\(37\) 5.45622 9.45046i 0.896998 1.55365i 0.0656853 0.997840i \(-0.479077\pi\)
0.831312 0.555805i \(-0.187590\pi\)
\(38\) 0 0
\(39\) −6.99976 + 0.325951i −1.12086 + 0.0521940i
\(40\) 0 0
\(41\) −6.15464 −0.961193 −0.480597 0.876942i \(-0.659580\pi\)
−0.480597 + 0.876942i \(0.659580\pi\)
\(42\) 0 0
\(43\) 0.502751 0.0766688 0.0383344 0.999265i \(-0.487795\pi\)
0.0383344 + 0.999265i \(0.487795\pi\)
\(44\) 0 0
\(45\) −4.75828 + 10.3606i −0.709322 + 1.54446i
\(46\) 0 0
\(47\) −5.72578 + 9.91734i −0.835190 + 1.44659i 0.0586849 + 0.998277i \(0.481309\pi\)
−0.893875 + 0.448316i \(0.852024\pi\)
\(48\) 0 0
\(49\) 2.99000 + 6.32929i 0.427143 + 0.904184i
\(50\) 0 0
\(51\) −0.151551 + 0.0971675i −0.0212214 + 0.0136062i
\(52\) 0 0
\(53\) −5.08143 + 2.93376i −0.697988 + 0.402983i −0.806597 0.591101i \(-0.798693\pi\)
0.108610 + 0.994084i \(0.465360\pi\)
\(54\) 0 0
\(55\) 1.35833i 0.183158i
\(56\) 0 0
\(57\) 1.95255 3.77751i 0.258622 0.500344i
\(58\) 0 0
\(59\) −3.77364 6.53614i −0.491286 0.850933i 0.508664 0.860965i \(-0.330140\pi\)
−0.999950 + 0.0100329i \(0.996806\pi\)
\(60\) 0 0
\(61\) 8.20485 + 4.73707i 1.05052 + 0.606520i 0.922796 0.385289i \(-0.125898\pi\)
0.127727 + 0.991809i \(0.459232\pi\)
\(62\) 0 0
\(63\) −7.07060 3.60647i −0.890812 0.454373i
\(64\) 0 0
\(65\) 13.3151 + 7.68750i 1.65154 + 0.953517i
\(66\) 0 0
\(67\) −1.34375 2.32744i −0.164165 0.284342i 0.772193 0.635388i \(-0.219160\pi\)
−0.936358 + 0.351045i \(0.885826\pi\)
\(68\) 0 0
\(69\) 1.05783 2.04653i 0.127348 0.246374i
\(70\) 0 0
\(71\) 5.78975i 0.687117i −0.939131 0.343558i \(-0.888368\pi\)
0.939131 0.343558i \(-0.111632\pi\)
\(72\) 0 0
\(73\) −0.203925 + 0.117736i −0.0238676 + 0.0137800i −0.511886 0.859053i \(-0.671053\pi\)
0.488019 + 0.872833i \(0.337720\pi\)
\(74\) 0 0
\(75\) 13.7681 8.82748i 1.58980 1.01931i
\(76\) 0 0
\(77\) 0.944856 + 0.0388878i 0.107676 + 0.00443168i
\(78\) 0 0
\(79\) −1.61247 + 2.79289i −0.181418 + 0.314224i −0.942364 0.334591i \(-0.891402\pi\)
0.760946 + 0.648815i \(0.224735\pi\)
\(80\) 0 0
\(81\) 8.84455 1.66551i 0.982728 0.185057i
\(82\) 0 0
\(83\) 9.07747 0.996382 0.498191 0.867067i \(-0.333998\pi\)
0.498191 + 0.867067i \(0.333998\pi\)
\(84\) 0 0
\(85\) 0.394999 0.0428436
\(86\) 0 0
\(87\) 8.60356 0.400634i 0.922398 0.0429525i
\(88\) 0 0
\(89\) −3.41213 + 5.90999i −0.361685 + 0.626457i −0.988238 0.152921i \(-0.951132\pi\)
0.626553 + 0.779379i \(0.284465\pi\)
\(90\) 0 0
\(91\) −5.72862 + 9.04192i −0.600523 + 0.947851i
\(92\) 0 0
\(93\) −7.37296 11.4995i −0.764541 1.19245i
\(94\) 0 0
\(95\) −8.08008 + 4.66504i −0.828999 + 0.478623i
\(96\) 0 0
\(97\) 5.14243i 0.522134i −0.965321 0.261067i \(-0.915926\pi\)
0.965321 0.261067i \(-0.0840744\pi\)
\(98\) 0 0
\(99\) −0.874774 + 0.620114i −0.0879181 + 0.0623238i
\(100\) 0 0
\(101\) 6.43891 + 11.1525i 0.640695 + 1.10972i 0.985278 + 0.170960i \(0.0546870\pi\)
−0.344583 + 0.938756i \(0.611980\pi\)
\(102\) 0 0
\(103\) 4.88120 + 2.81816i 0.480959 + 0.277682i 0.720816 0.693126i \(-0.243767\pi\)
−0.239857 + 0.970808i \(0.577101\pi\)
\(104\) 0 0
\(105\) 8.78895 + 15.0349i 0.857714 + 1.46725i
\(106\) 0 0
\(107\) −7.62737 4.40366i −0.737365 0.425718i 0.0837453 0.996487i \(-0.473312\pi\)
−0.821111 + 0.570769i \(0.806645\pi\)
\(108\) 0 0
\(109\) 2.23862 + 3.87741i 0.214421 + 0.371389i 0.953093 0.302676i \(-0.0978801\pi\)
−0.738672 + 0.674065i \(0.764547\pi\)
\(110\) 0 0
\(111\) 16.7905 + 8.67883i 1.59369 + 0.823758i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) −4.37753 + 2.52737i −0.408206 + 0.235678i
\(116\) 0 0
\(117\) −1.12791 12.0846i −0.104275 1.11722i
\(118\) 0 0
\(119\) −0.0113084 + 0.274761i −0.00103664 + 0.0251873i
\(120\) 0 0
\(121\) −5.43612 + 9.41564i −0.494193 + 0.855968i
\(122\) 0 0
\(123\) −0.495864 10.6486i −0.0447105 0.960153i
\(124\) 0 0
\(125\) −16.8832 −1.51008
\(126\) 0 0
\(127\) 12.9198 1.14645 0.573223 0.819399i \(-0.305693\pi\)
0.573223 + 0.819399i \(0.305693\pi\)
\(128\) 0 0
\(129\) 0.0405054 + 0.869848i 0.00356630 + 0.0765858i
\(130\) 0 0
\(131\) −2.66384 + 4.61391i −0.232741 + 0.403119i −0.958614 0.284710i \(-0.908103\pi\)
0.725873 + 0.687829i \(0.241436\pi\)
\(132\) 0 0
\(133\) −3.01367 5.75406i −0.261319 0.498940i
\(134\) 0 0
\(135\) −18.3090 7.39793i −1.57579 0.636713i
\(136\) 0 0
\(137\) 4.37380 2.52521i 0.373679 0.215744i −0.301386 0.953502i \(-0.597449\pi\)
0.675064 + 0.737759i \(0.264116\pi\)
\(138\) 0 0
\(139\) 21.2651i 1.80368i −0.432067 0.901841i \(-0.642216\pi\)
0.432067 0.901841i \(-0.357784\pi\)
\(140\) 0 0
\(141\) −17.6200 9.10759i −1.48388 0.766997i
\(142\) 0 0
\(143\) 0.723015 + 1.25230i 0.0604616 + 0.104723i
\(144\) 0 0
\(145\) −16.3659 9.44887i −1.35912 0.784686i
\(146\) 0 0
\(147\) −10.7099 + 5.68316i −0.883337 + 0.468739i
\(148\) 0 0
\(149\) 10.5482 + 6.09001i 0.864143 + 0.498913i 0.865398 0.501086i \(-0.167066\pi\)
−0.00125437 + 0.999999i \(0.500399\pi\)
\(150\) 0 0
\(151\) 4.10880 + 7.11665i 0.334369 + 0.579145i 0.983363 0.181649i \(-0.0581434\pi\)
−0.648994 + 0.760793i \(0.724810\pi\)
\(152\) 0 0
\(153\) −0.180327 0.254381i −0.0145786 0.0205655i
\(154\) 0 0
\(155\) 29.9721i 2.40741i
\(156\) 0 0
\(157\) 11.2104 6.47230i 0.894683 0.516546i 0.0192119 0.999815i \(-0.493884\pi\)
0.875472 + 0.483270i \(0.160551\pi\)
\(158\) 0 0
\(159\) −5.48532 8.55539i −0.435014 0.678487i
\(160\) 0 0
\(161\) −1.63271 3.11736i −0.128676 0.245683i
\(162\) 0 0
\(163\) 1.09237 1.89205i 0.0855613 0.148197i −0.820069 0.572265i \(-0.806065\pi\)
0.905630 + 0.424068i \(0.139398\pi\)
\(164\) 0 0
\(165\) 2.35016 0.109437i 0.182959 0.00851969i
\(166\) 0 0
\(167\) −0.464592 −0.0359512 −0.0179756 0.999838i \(-0.505722\pi\)
−0.0179756 + 0.999838i \(0.505722\pi\)
\(168\) 0 0
\(169\) −3.36765 −0.259050
\(170\) 0 0
\(171\) 6.69307 + 3.07391i 0.511832 + 0.235068i
\(172\) 0 0
\(173\) −4.62587 + 8.01224i −0.351698 + 0.609159i −0.986547 0.163477i \(-0.947729\pi\)
0.634849 + 0.772636i \(0.281062\pi\)
\(174\) 0 0
\(175\) 1.02735 24.9615i 0.0776603 1.88691i
\(176\) 0 0
\(177\) 11.0046 7.05566i 0.827159 0.530336i
\(178\) 0 0
\(179\) −1.77096 + 1.02246i −0.132367 + 0.0764224i −0.564722 0.825282i \(-0.691016\pi\)
0.432354 + 0.901704i \(0.357683\pi\)
\(180\) 0 0
\(181\) 17.6193i 1.30963i 0.755790 + 0.654815i \(0.227253\pi\)
−0.755790 + 0.654815i \(0.772747\pi\)
\(182\) 0 0
\(183\) −7.53492 + 14.5775i −0.556998 + 1.07760i
\(184\) 0 0
\(185\) −20.7355 35.9149i −1.52450 2.64052i
\(186\) 0 0
\(187\) 0.0321728 + 0.0185750i 0.00235271 + 0.00135834i
\(188\) 0 0
\(189\) 5.67017 12.5239i 0.412444 0.910983i
\(190\) 0 0
\(191\) 19.4811 + 11.2474i 1.40960 + 0.813834i 0.995350 0.0963279i \(-0.0307097\pi\)
0.414252 + 0.910162i \(0.364043\pi\)
\(192\) 0 0
\(193\) −4.81985 8.34823i −0.346940 0.600918i 0.638764 0.769403i \(-0.279446\pi\)
−0.985704 + 0.168484i \(0.946113\pi\)
\(194\) 0 0
\(195\) −12.2280 + 23.6569i −0.875662 + 1.69411i
\(196\) 0 0
\(197\) 15.3750i 1.09542i −0.836667 0.547712i \(-0.815499\pi\)
0.836667 0.547712i \(-0.184501\pi\)
\(198\) 0 0
\(199\) −3.96967 + 2.29189i −0.281403 + 0.162468i −0.634058 0.773285i \(-0.718612\pi\)
0.352656 + 0.935753i \(0.385279\pi\)
\(200\) 0 0
\(201\) 3.91862 2.51244i 0.276398 0.177214i
\(202\) 0 0
\(203\) 7.04117 11.1136i 0.494194 0.780023i
\(204\) 0 0
\(205\) −11.6948 + 20.2561i −0.816804 + 1.41475i
\(206\) 0 0
\(207\) 3.62609 + 1.66534i 0.252031 + 0.115749i
\(208\) 0 0
\(209\) −0.877501 −0.0606980
\(210\) 0 0
\(211\) −0.870400 −0.0599208 −0.0299604 0.999551i \(-0.509538\pi\)
−0.0299604 + 0.999551i \(0.509538\pi\)
\(212\) 0 0
\(213\) 10.0173 0.466465i 0.686373 0.0319617i
\(214\) 0 0
\(215\) 0.955311 1.65465i 0.0651517 0.112846i
\(216\) 0 0
\(217\) −20.8486 0.858072i −1.41529 0.0582497i
\(218\) 0 0
\(219\) −0.220134 0.343341i −0.0148753 0.0232008i
\(220\) 0 0
\(221\) −0.364165 + 0.210251i −0.0244964 + 0.0141430i
\(222\) 0 0
\(223\) 1.21373i 0.0812777i 0.999174 + 0.0406388i \(0.0129393\pi\)
−0.999174 + 0.0406388i \(0.987061\pi\)
\(224\) 0 0
\(225\) 16.3823 + 23.1100i 1.09216 + 1.54067i
\(226\) 0 0
\(227\) −6.67205 11.5563i −0.442840 0.767021i 0.555059 0.831811i \(-0.312696\pi\)
−0.997899 + 0.0647898i \(0.979362\pi\)
\(228\) 0 0
\(229\) 9.60627 + 5.54618i 0.634800 + 0.366502i 0.782609 0.622514i \(-0.213889\pi\)
−0.147808 + 0.989016i \(0.547222\pi\)
\(230\) 0 0
\(231\) 0.00884196 + 1.63790i 0.000581758 + 0.107766i
\(232\) 0 0
\(233\) 7.08411 + 4.09001i 0.464095 + 0.267946i 0.713765 0.700386i \(-0.246989\pi\)
−0.249669 + 0.968331i \(0.580322\pi\)
\(234\) 0 0
\(235\) 21.7599 + 37.6892i 1.41946 + 2.45857i
\(236\) 0 0
\(237\) −4.96210 2.56485i −0.322323 0.166605i
\(238\) 0 0
\(239\) 22.5944i 1.46151i −0.682638 0.730757i \(-0.739167\pi\)
0.682638 0.730757i \(-0.260833\pi\)
\(240\) 0 0
\(241\) 4.24127 2.44870i 0.273205 0.157735i −0.357138 0.934051i \(-0.616248\pi\)
0.630343 + 0.776317i \(0.282914\pi\)
\(242\) 0 0
\(243\) 3.59421 + 15.1684i 0.230569 + 0.973056i
\(244\) 0 0
\(245\) 26.5124 + 2.18606i 1.69381 + 0.139662i
\(246\) 0 0
\(247\) 4.96622 8.60175i 0.315993 0.547316i
\(248\) 0 0
\(249\) 0.731349 + 15.7056i 0.0463474 + 0.995304i
\(250\) 0 0
\(251\) −9.17857 −0.579346 −0.289673 0.957126i \(-0.593547\pi\)
−0.289673 + 0.957126i \(0.593547\pi\)
\(252\) 0 0
\(253\) −0.475401 −0.0298882
\(254\) 0 0
\(255\) 0.0318241 + 0.683418i 0.00199290 + 0.0427973i
\(256\) 0 0
\(257\) −6.31055 + 10.9302i −0.393641 + 0.681806i −0.992927 0.118729i \(-0.962118\pi\)
0.599286 + 0.800535i \(0.295451\pi\)
\(258\) 0 0
\(259\) 25.5760 13.3954i 1.58922 0.832349i
\(260\) 0 0
\(261\) 1.38633 + 14.8534i 0.0858119 + 0.919402i
\(262\) 0 0
\(263\) 25.2489 14.5775i 1.55692 0.898886i 0.559367 0.828920i \(-0.311044\pi\)
0.997549 0.0699665i \(-0.0222892\pi\)
\(264\) 0 0
\(265\) 22.2986i 1.36979i
\(266\) 0 0
\(267\) −10.5002 5.42744i −0.642603 0.332154i
\(268\) 0 0
\(269\) −2.23640 3.87356i −0.136356 0.236175i 0.789759 0.613418i \(-0.210206\pi\)
−0.926115 + 0.377242i \(0.876872\pi\)
\(270\) 0 0
\(271\) −14.4985 8.37071i −0.880721 0.508485i −0.00982495 0.999952i \(-0.503127\pi\)
−0.870896 + 0.491467i \(0.836461\pi\)
\(272\) 0 0
\(273\) −16.1057 9.18304i −0.974759 0.555783i
\(274\) 0 0
\(275\) −2.92283 1.68750i −0.176254 0.101760i
\(276\) 0 0
\(277\) −0.510924 0.884946i −0.0306984 0.0531713i 0.850268 0.526350i \(-0.176440\pi\)
−0.880966 + 0.473179i \(0.843106\pi\)
\(278\) 0 0
\(279\) 19.3022 13.6830i 1.15559 0.819181i
\(280\) 0 0
\(281\) 13.9453i 0.831907i 0.909386 + 0.415953i \(0.136552\pi\)
−0.909386 + 0.415953i \(0.863448\pi\)
\(282\) 0 0
\(283\) 14.0386 8.10519i 0.834508 0.481803i −0.0208856 0.999782i \(-0.506649\pi\)
0.855394 + 0.517978i \(0.173315\pi\)
\(284\) 0 0
\(285\) −8.72233 13.6041i −0.516666 0.805838i
\(286\) 0 0
\(287\) −13.7553 8.71485i −0.811950 0.514421i
\(288\) 0 0
\(289\) 8.49460 14.7131i 0.499682 0.865475i
\(290\) 0 0
\(291\) 8.89731 0.414312i 0.521569 0.0242874i
\(292\) 0 0
\(293\) 19.2067 1.12207 0.561034 0.827793i \(-0.310404\pi\)
0.561034 + 0.827793i \(0.310404\pi\)
\(294\) 0 0
\(295\) −28.6822 −1.66994
\(296\) 0 0
\(297\) −1.14338 1.46355i −0.0663459 0.0849239i
\(298\) 0 0
\(299\) 2.69054 4.66015i 0.155598 0.269503i
\(300\) 0 0
\(301\) 1.12362 + 0.711886i 0.0647646 + 0.0410324i
\(302\) 0 0
\(303\) −18.7770 + 12.0390i −1.07871 + 0.691621i
\(304\) 0 0
\(305\) 31.1812 18.0025i 1.78543 1.03082i
\(306\) 0 0
\(307\) 0.480498i 0.0274235i 0.999906 + 0.0137117i \(0.00436472\pi\)
−0.999906 + 0.0137117i \(0.995635\pi\)
\(308\) 0 0
\(309\) −4.48265 + 8.67239i −0.255009 + 0.493355i
\(310\) 0 0
\(311\) −4.66653 8.08266i −0.264615 0.458326i 0.702848 0.711340i \(-0.251911\pi\)
−0.967463 + 0.253014i \(0.918578\pi\)
\(312\) 0 0
\(313\) 15.5147 + 8.95742i 0.876943 + 0.506303i 0.869649 0.493670i \(-0.164345\pi\)
0.00729351 + 0.999973i \(0.497678\pi\)
\(314\) 0 0
\(315\) −25.3049 + 16.4178i −1.42577 + 0.925036i
\(316\) 0 0
\(317\) −19.3275 11.1587i −1.08554 0.626736i −0.153153 0.988202i \(-0.548943\pi\)
−0.932385 + 0.361467i \(0.882276\pi\)
\(318\) 0 0
\(319\) −0.888674 1.53923i −0.0497562 0.0861802i
\(320\) 0 0
\(321\) 7.00459 13.5515i 0.390958 0.756370i
\(322\) 0 0
\(323\) 0.255174i 0.0141983i
\(324\) 0 0
\(325\) 33.0836 19.1008i 1.83515 1.05952i
\(326\) 0 0
\(327\) −6.52824 + 4.18561i −0.361013 + 0.231465i
\(328\) 0 0
\(329\) −26.8396 + 14.0572i −1.47971 + 0.774996i
\(330\) 0 0
\(331\) −7.05860 + 12.2259i −0.387976 + 0.671994i −0.992177 0.124838i \(-0.960159\pi\)
0.604201 + 0.796832i \(0.293492\pi\)
\(332\) 0 0
\(333\) −13.6631 + 29.7498i −0.748735 + 1.63028i
\(334\) 0 0
\(335\) −10.2134 −0.558018
\(336\) 0 0
\(337\) −18.4042 −1.00254 −0.501270 0.865291i \(-0.667134\pi\)
−0.501270 + 0.865291i \(0.667134\pi\)
\(338\) 0 0
\(339\) 6.92070 0.322270i 0.375881 0.0175033i
\(340\) 0 0
\(341\) −1.40945 + 2.44124i −0.0763259 + 0.132200i
\(342\) 0 0
\(343\) −2.27965 + 18.3794i −0.123089 + 0.992396i
\(344\) 0 0
\(345\) −4.72547 7.37027i −0.254411 0.396802i
\(346\) 0 0
\(347\) −27.6474 + 15.9623i −1.48419 + 0.856899i −0.999838 0.0179729i \(-0.994279\pi\)
−0.484354 + 0.874872i \(0.660945\pi\)
\(348\) 0 0
\(349\) 14.7367i 0.788840i −0.918930 0.394420i \(-0.870945\pi\)
0.918930 0.394420i \(-0.129055\pi\)
\(350\) 0 0
\(351\) 20.8175 2.92510i 1.11116 0.156130i
\(352\) 0 0
\(353\) 13.5686 + 23.5016i 0.722185 + 1.25086i 0.960122 + 0.279581i \(0.0901956\pi\)
−0.237937 + 0.971281i \(0.576471\pi\)
\(354\) 0 0
\(355\) −19.0551 11.0015i −1.01134 0.583899i
\(356\) 0 0
\(357\) −0.476296 + 0.00257121i −0.0252083 + 0.000136083i
\(358\) 0 0
\(359\) 16.9479 + 9.78486i 0.894475 + 0.516425i 0.875404 0.483393i \(-0.160596\pi\)
0.0190713 + 0.999818i \(0.493929\pi\)
\(360\) 0 0
\(361\) −6.48633 11.2346i −0.341386 0.591297i
\(362\) 0 0
\(363\) −16.7287 8.64686i −0.878029 0.453842i
\(364\) 0 0
\(365\) 0.894875i 0.0468399i
\(366\) 0 0
\(367\) −1.16258 + 0.671213i −0.0606860 + 0.0350371i −0.530036 0.847975i \(-0.677822\pi\)
0.469350 + 0.883012i \(0.344488\pi\)
\(368\) 0 0
\(369\) 18.3840 1.71586i 0.957034 0.0893243i
\(370\) 0 0
\(371\) −15.5109 0.638387i −0.805285 0.0331434i
\(372\) 0 0
\(373\) −6.52378 + 11.2995i −0.337788 + 0.585066i −0.984016 0.178078i \(-0.943012\pi\)
0.646228 + 0.763144i \(0.276345\pi\)
\(374\) 0 0
\(375\) −1.36023 29.2109i −0.0702422 1.50844i
\(376\) 0 0
\(377\) 20.1178 1.03612
\(378\) 0 0
\(379\) −20.0822 −1.03156 −0.515778 0.856722i \(-0.672497\pi\)
−0.515778 + 0.856722i \(0.672497\pi\)
\(380\) 0 0
\(381\) 1.04092 + 22.3535i 0.0533277 + 1.14521i
\(382\) 0 0
\(383\) 11.2613 19.5052i 0.575428 0.996670i −0.420567 0.907261i \(-0.638169\pi\)
0.995995 0.0894085i \(-0.0284977\pi\)
\(384\) 0 0
\(385\) 1.92337 3.03581i 0.0980242 0.154719i
\(386\) 0 0
\(387\) −1.50173 + 0.140163i −0.0763370 + 0.00712488i
\(388\) 0 0
\(389\) −32.1899 + 18.5848i −1.63209 + 0.942289i −0.648645 + 0.761091i \(0.724664\pi\)
−0.983447 + 0.181197i \(0.942003\pi\)
\(390\) 0 0
\(391\) 0.138245i 0.00699136i
\(392\) 0 0
\(393\) −8.19750 4.23719i −0.413509 0.213738i
\(394\) 0 0
\(395\) 6.12795 + 10.6139i 0.308330 + 0.534044i
\(396\) 0 0
\(397\) −24.0288 13.8730i −1.20597 0.696268i −0.244095 0.969751i \(-0.578491\pi\)
−0.961877 + 0.273483i \(0.911824\pi\)
\(398\) 0 0
\(399\) 9.71273 5.67778i 0.486245 0.284244i
\(400\) 0 0
\(401\) −19.7233 11.3872i −0.984933 0.568651i −0.0811773 0.996700i \(-0.525868\pi\)
−0.903756 + 0.428048i \(0.859201\pi\)
\(402\) 0 0
\(403\) −15.9536 27.6324i −0.794704 1.37647i
\(404\) 0 0
\(405\) 11.3246 32.2738i 0.562725 1.60370i
\(406\) 0 0
\(407\) 3.90038i 0.193334i
\(408\) 0 0
\(409\) −22.6849 + 13.0972i −1.12170 + 0.647613i −0.941834 0.336078i \(-0.890899\pi\)
−0.179865 + 0.983691i \(0.557566\pi\)
\(410\) 0 0
\(411\) 4.72145 + 7.36399i 0.232892 + 0.363239i
\(412\) 0 0
\(413\) 0.821144 19.9513i 0.0404059 0.981741i
\(414\) 0 0
\(415\) 17.2487 29.8757i 0.846707 1.46654i
\(416\) 0 0
\(417\) 36.7924 1.71328i 1.80173 0.0838995i
\(418\) 0 0
\(419\) 8.93992 0.436744 0.218372 0.975866i \(-0.429925\pi\)
0.218372 + 0.975866i \(0.429925\pi\)
\(420\) 0 0
\(421\) −5.00735 −0.244043 −0.122022 0.992527i \(-0.538938\pi\)
−0.122022 + 0.992527i \(0.538938\pi\)
\(422\) 0 0
\(423\) 14.3381 31.2196i 0.697144 1.51795i
\(424\) 0 0
\(425\) 0.490719 0.849951i 0.0238034 0.0412287i
\(426\) 0 0
\(427\) 11.6298 + 22.2050i 0.562807 + 1.07458i
\(428\) 0 0
\(429\) −2.10845 + 1.35184i −0.101797 + 0.0652674i
\(430\) 0 0
\(431\) −5.62468 + 3.24741i −0.270931 + 0.156422i −0.629311 0.777154i \(-0.716663\pi\)
0.358379 + 0.933576i \(0.383329\pi\)
\(432\) 0 0
\(433\) 1.05254i 0.0505818i −0.999680 0.0252909i \(-0.991949\pi\)
0.999680 0.0252909i \(-0.00805120\pi\)
\(434\) 0 0
\(435\) 15.0296 29.0772i 0.720616 1.39414i
\(436\) 0 0
\(437\) 1.63271 + 2.82794i 0.0781032 + 0.135279i
\(438\) 0 0
\(439\) 25.8990 + 14.9528i 1.23609 + 0.713658i 0.968293 0.249817i \(-0.0803705\pi\)
0.267799 + 0.963475i \(0.413704\pi\)
\(440\) 0 0
\(441\) −10.6957 18.0721i −0.509321 0.860577i
\(442\) 0 0
\(443\) 26.7104 + 15.4212i 1.26905 + 0.732685i 0.974808 0.223047i \(-0.0716002\pi\)
0.294240 + 0.955732i \(0.404934\pi\)
\(444\) 0 0
\(445\) 12.9672 + 22.4599i 0.614707 + 1.06470i
\(446\) 0 0
\(447\) −9.68695 + 18.7409i −0.458177 + 0.886415i
\(448\) 0 0
\(449\) 36.6953i 1.73176i 0.500253 + 0.865879i \(0.333240\pi\)
−0.500253 + 0.865879i \(0.666760\pi\)
\(450\) 0 0
\(451\) −1.90510 + 1.09991i −0.0897076 + 0.0517927i
\(452\) 0 0
\(453\) −11.9820 + 7.68232i −0.562964 + 0.360947i
\(454\) 0 0
\(455\) 18.8733 + 36.0351i 0.884795 + 1.68935i
\(456\) 0 0
\(457\) 11.8750 20.5681i 0.555489 0.962135i −0.442376 0.896830i \(-0.645864\pi\)
0.997865 0.0653057i \(-0.0208022\pi\)
\(458\) 0 0
\(459\) 0.425596 0.332492i 0.0198651 0.0155194i
\(460\) 0 0
\(461\) −10.5938 −0.493404 −0.246702 0.969091i \(-0.579347\pi\)
−0.246702 + 0.969091i \(0.579347\pi\)
\(462\) 0 0
\(463\) −0.367649 −0.0170861 −0.00854305 0.999964i \(-0.502719\pi\)
−0.00854305 + 0.999964i \(0.502719\pi\)
\(464\) 0 0
\(465\) −51.8570 + 2.41477i −2.40481 + 0.111982i
\(466\) 0 0
\(467\) −15.7847 + 27.3399i −0.730428 + 1.26514i 0.226272 + 0.974064i \(0.427346\pi\)
−0.956700 + 0.291075i \(0.905987\pi\)
\(468\) 0 0
\(469\) 0.292400 7.10444i 0.0135018 0.328053i
\(470\) 0 0
\(471\) 12.1014 + 18.8744i 0.557603 + 0.869688i
\(472\) 0 0
\(473\) 0.155621 0.0898478i 0.00715546 0.00413120i
\(474\) 0 0
\(475\) 23.1821i 1.06367i
\(476\) 0 0
\(477\) 14.3604 10.1799i 0.657518 0.466104i
\(478\) 0 0
\(479\) 6.01497 + 10.4182i 0.274831 + 0.476022i 0.970093 0.242735i \(-0.0780447\pi\)
−0.695261 + 0.718757i \(0.744711\pi\)
\(480\) 0 0
\(481\) 38.2337 + 22.0742i 1.74331 + 1.00650i
\(482\) 0 0
\(483\) 5.26204 3.07604i 0.239431 0.139964i
\(484\) 0 0
\(485\) −16.9247 9.77148i −0.768511 0.443700i
\(486\) 0 0
\(487\) 9.47737 + 16.4153i 0.429461 + 0.743848i 0.996825 0.0796188i \(-0.0253703\pi\)
−0.567365 + 0.823467i \(0.692037\pi\)
\(488\) 0 0
\(489\) 3.36159 + 1.73756i 0.152016 + 0.0785753i
\(490\) 0 0
\(491\) 15.8373i 0.714727i −0.933965 0.357364i \(-0.883676\pi\)
0.933965 0.357364i \(-0.116324\pi\)
\(492\) 0 0
\(493\) 0.447602 0.258423i 0.0201590 0.0116388i
\(494\) 0 0
\(495\) 0.378692 + 4.05736i 0.0170209 + 0.182365i
\(496\) 0 0
\(497\) 8.19817 12.9398i 0.367738 0.580429i
\(498\) 0 0
\(499\) −10.0988 + 17.4916i −0.452084 + 0.783033i −0.998515 0.0544710i \(-0.982653\pi\)
0.546431 + 0.837504i \(0.315986\pi\)
\(500\) 0 0
\(501\) −0.0374310 0.803826i −0.00167229 0.0359123i
\(502\) 0 0
\(503\) −36.8663 −1.64379 −0.821893 0.569641i \(-0.807082\pi\)
−0.821893 + 0.569641i \(0.807082\pi\)
\(504\) 0 0
\(505\) 48.9400 2.17780
\(506\) 0 0
\(507\) −0.271323 5.82663i −0.0120499 0.258770i
\(508\) 0 0
\(509\) 5.13197 8.88884i 0.227471 0.393991i −0.729587 0.683888i \(-0.760288\pi\)
0.957058 + 0.289897i \(0.0936211\pi\)
\(510\) 0 0
\(511\) −0.622475 0.0256194i −0.0275367 0.00113334i
\(512\) 0 0
\(513\) −4.77916 + 11.8279i −0.211005 + 0.522212i
\(514\) 0 0
\(515\) 18.5502 10.7100i 0.817419 0.471937i
\(516\) 0 0
\(517\) 4.09307i 0.180013i
\(518\) 0 0
\(519\) −14.2353 7.35804i −0.624859 0.322982i
\(520\) 0 0
\(521\) −7.98887 13.8371i −0.349999 0.606216i 0.636250 0.771483i \(-0.280485\pi\)
−0.986249 + 0.165267i \(0.947151\pi\)
\(522\) 0 0
\(523\) 0.676700 + 0.390693i 0.0295900 + 0.0170838i 0.514722 0.857357i \(-0.327895\pi\)
−0.485132 + 0.874441i \(0.661228\pi\)
\(524\) 0 0
\(525\) 43.2706 0.233590i 1.88848 0.0101947i
\(526\) 0 0
\(527\) −0.709904 0.409863i −0.0309239 0.0178539i
\(528\) 0 0
\(529\) −10.6155 18.3865i −0.461541 0.799413i
\(530\) 0 0
\(531\) 13.0942 + 18.4715i 0.568238 + 0.801595i
\(532\) 0 0
\(533\) 24.8998i 1.07853i
\(534\) 0 0
\(535\) −28.9865 + 16.7354i −1.25320 + 0.723534i
\(536\) 0 0
\(537\) −1.91172 2.98169i −0.0824968 0.128669i
\(538\) 0 0
\(539\) 2.05664 + 1.42481i 0.0885859 + 0.0613709i
\(540\) 0 0
\(541\) 3.63362 6.29362i 0.156222 0.270584i −0.777282 0.629153i \(-0.783402\pi\)
0.933503 + 0.358569i \(0.116735\pi\)
\(542\) 0 0
\(543\) −30.4844 + 1.41954i −1.30821 + 0.0609182i
\(544\) 0 0
\(545\) 17.0150 0.728845
\(546\) 0 0
\(547\) 41.2546 1.76392 0.881960 0.471325i \(-0.156224\pi\)
0.881960 + 0.471325i \(0.156224\pi\)
\(548\) 0 0
\(549\) −25.8287 11.8623i −1.10234 0.506269i
\(550\) 0 0
\(551\) −6.10409 + 10.5726i −0.260043 + 0.450408i
\(552\) 0 0
\(553\) −7.55847 + 3.95873i −0.321419 + 0.168342i
\(554\) 0 0
\(555\) 60.4685 38.7696i 2.56675 1.64568i
\(556\) 0 0
\(557\) 5.48798 3.16849i 0.232533 0.134253i −0.379207 0.925312i \(-0.623803\pi\)
0.611740 + 0.791059i \(0.290470\pi\)
\(558\) 0 0
\(559\) 2.03398i 0.0860281i
\(560\) 0 0
\(561\) −0.0295459 + 0.0571611i −0.00124743 + 0.00241335i
\(562\) 0 0
\(563\) 7.73130 + 13.3910i 0.325836 + 0.564364i 0.981681 0.190531i \(-0.0610211\pi\)
−0.655846 + 0.754895i \(0.727688\pi\)
\(564\) 0 0
\(565\) −13.1647 7.60067i −0.553845 0.319763i
\(566\) 0 0
\(567\) 22.1255 + 8.80137i 0.929182 + 0.369623i
\(568\) 0 0
\(569\) −10.2364 5.90999i −0.429132 0.247760i 0.269845 0.962904i \(-0.413028\pi\)
−0.698977 + 0.715144i \(0.746361\pi\)
\(570\) 0 0
\(571\) −18.0386 31.2438i −0.754892 1.30751i −0.945428 0.325831i \(-0.894356\pi\)
0.190536 0.981680i \(-0.438977\pi\)
\(572\) 0 0
\(573\) −17.8905 + 34.6119i −0.747385 + 1.44593i
\(574\) 0 0
\(575\) 12.5593i 0.523759i
\(576\) 0 0
\(577\) −20.4253 + 11.7926i −0.850316 + 0.490930i −0.860758 0.509015i \(-0.830010\pi\)
0.0104412 + 0.999945i \(0.496676\pi\)
\(578\) 0 0
\(579\) 14.0556 9.01178i 0.584130 0.374517i
\(580\) 0 0
\(581\) 20.2877 + 12.8535i 0.841676 + 0.533254i
\(582\) 0 0
\(583\) −1.04860 + 1.81623i −0.0434285 + 0.0752204i
\(584\) 0 0
\(585\) −41.9158 19.2505i −1.73300 0.795912i
\(586\) 0 0
\(587\) −0.287490 −0.0118660 −0.00593298 0.999982i \(-0.501889\pi\)
−0.00593298 + 0.999982i \(0.501889\pi\)
\(588\) 0 0
\(589\) 19.3623 0.797812
\(590\) 0 0
\(591\) 26.6015 1.23872i 1.09424 0.0509543i
\(592\) 0 0
\(593\) 5.71589 9.90021i 0.234723 0.406553i −0.724469 0.689308i \(-0.757915\pi\)
0.959192 + 0.282755i \(0.0912482\pi\)
\(594\) 0 0
\(595\) 0.882803 + 0.559311i 0.0361914 + 0.0229295i
\(596\) 0 0
\(597\) −4.28520 6.68358i −0.175382 0.273541i
\(598\) 0 0
\(599\) −18.7842 + 10.8451i −0.767502 + 0.443117i −0.831983 0.554802i \(-0.812794\pi\)
0.0644810 + 0.997919i \(0.479461\pi\)
\(600\) 0 0
\(601\) 23.7036i 0.966889i −0.875375 0.483445i \(-0.839385\pi\)
0.875375 0.483445i \(-0.160615\pi\)
\(602\) 0 0
\(603\) 4.66268 + 6.57749i 0.189879 + 0.267856i
\(604\) 0 0
\(605\) 20.6591 + 35.7826i 0.839912 + 1.45477i
\(606\) 0 0
\(607\) −18.5031 10.6828i −0.751017 0.433600i 0.0750445 0.997180i \(-0.476090\pi\)
−0.826061 + 0.563580i \(0.809423\pi\)
\(608\) 0 0
\(609\) 19.7958 + 11.2871i 0.802167 + 0.457375i
\(610\) 0 0
\(611\) −40.1225 23.1647i −1.62318 0.937145i
\(612\) 0 0
\(613\) −19.8248 34.3376i −0.800716 1.38688i −0.919145 0.393918i \(-0.871119\pi\)
0.118429 0.992962i \(-0.462214\pi\)
\(614\) 0 0
\(615\) −35.9888 18.6022i −1.45121 0.750112i
\(616\) 0 0
\(617\) 28.6296i 1.15258i 0.817244 + 0.576292i \(0.195501\pi\)
−0.817244 + 0.576292i \(0.804499\pi\)
\(618\) 0 0
\(619\) −32.9529 + 19.0254i −1.32449 + 0.764694i −0.984441 0.175714i \(-0.943776\pi\)
−0.340047 + 0.940408i \(0.610443\pi\)
\(620\) 0 0
\(621\) −2.58919 + 6.40794i −0.103901 + 0.257142i
\(622\) 0 0
\(623\) −15.9944 + 8.37701i −0.640801 + 0.335618i
\(624\) 0 0
\(625\) −8.47450 + 14.6783i −0.338980 + 0.587130i
\(626\) 0 0
\(627\) −0.0706980 1.51823i −0.00282341 0.0606323i
\(628\) 0 0
\(629\) 1.13422 0.0452242
\(630\) 0 0
\(631\) −3.65235 −0.145398 −0.0726989 0.997354i \(-0.523161\pi\)
−0.0726989 + 0.997354i \(0.523161\pi\)
\(632\) 0 0
\(633\) −0.0701259 1.50595i −0.00278726 0.0598560i
\(634\) 0 0
\(635\) 24.5498 42.5215i 0.974228 1.68741i
\(636\) 0 0
\(637\) −25.6064 + 12.0966i −1.01456 + 0.479286i
\(638\) 0 0
\(639\) 1.61413 + 17.2941i 0.0638542 + 0.684143i
\(640\) 0 0
\(641\) −21.2563 + 12.2723i −0.839574 + 0.484728i −0.857119 0.515118i \(-0.827748\pi\)
0.0175456 + 0.999846i \(0.494415\pi\)
\(642\) 0 0
\(643\) 27.3936i 1.08030i −0.841569 0.540149i \(-0.818368\pi\)
0.841569 0.540149i \(-0.181632\pi\)
\(644\) 0 0
\(645\) 2.93980 + 1.51955i 0.115754 + 0.0598321i
\(646\) 0 0
\(647\) 16.1181 + 27.9173i 0.633667 + 1.09754i 0.986796 + 0.161969i \(0.0517845\pi\)
−0.353129 + 0.935575i \(0.614882\pi\)
\(648\) 0 0
\(649\) −2.33618 1.34879i −0.0917029 0.0529447i
\(650\) 0 0
\(651\) −0.195101 36.1408i −0.00764660 1.41647i
\(652\) 0 0
\(653\) 13.5027 + 7.79579i 0.528401 + 0.305073i 0.740365 0.672205i \(-0.234653\pi\)
−0.211964 + 0.977278i \(0.567986\pi\)
\(654\) 0 0
\(655\) 10.1235 + 17.5344i 0.395558 + 0.685126i
\(656\) 0 0
\(657\) 0.576304 0.408533i 0.0224838 0.0159384i
\(658\) 0 0
\(659\) 35.1100i 1.36769i −0.729626 0.683847i \(-0.760306\pi\)
0.729626 0.683847i \(-0.239694\pi\)
\(660\) 0 0
\(661\) 6.96082 4.01883i 0.270745 0.156314i −0.358481 0.933537i \(-0.616705\pi\)
0.629226 + 0.777222i \(0.283372\pi\)
\(662\) 0 0
\(663\) −0.393110 0.613129i −0.0152671 0.0238120i
\(664\) 0 0
\(665\) −24.6642 1.01511i −0.956436 0.0393644i
\(666\) 0 0
\(667\) −3.30700 + 5.72789i −0.128047 + 0.221785i
\(668\) 0 0
\(669\) −2.09997 + 0.0977875i −0.0811897 + 0.00378068i
\(670\) 0 0
\(671\) 3.38629 0.130726
\(672\) 0 0
\(673\) 28.1744 1.08604 0.543022 0.839719i \(-0.317280\pi\)
0.543022 + 0.839719i \(0.317280\pi\)
\(674\) 0 0
\(675\) −38.6646 + 30.2063i −1.48820 + 1.16264i
\(676\) 0 0
\(677\) 17.3844 30.1106i 0.668135 1.15724i −0.310290 0.950642i \(-0.600426\pi\)
0.978425 0.206602i \(-0.0662405\pi\)
\(678\) 0 0
\(679\) 7.28158 11.4931i 0.279441 0.441063i
\(680\) 0 0
\(681\) 19.4569 12.4749i 0.745592 0.478039i
\(682\) 0 0
\(683\) 40.7393 23.5209i 1.55885 0.900001i 0.561479 0.827491i \(-0.310232\pi\)
0.997368 0.0725098i \(-0.0231009\pi\)
\(684\) 0 0
\(685\) 19.1933i 0.733339i
\(686\) 0 0
\(687\) −8.82192 + 17.0674i −0.336577 + 0.651161i
\(688\) 0 0
\(689\) −11.8691 20.5579i −0.452177 0.783194i
\(690\) 0 0
\(691\) −27.1758 15.6900i −1.03382 0.596874i −0.115740 0.993279i \(-0.536924\pi\)
−0.918076 + 0.396406i \(0.870257\pi\)
\(692\) 0 0
\(693\) −2.83314 + 0.147260i −0.107622 + 0.00559393i
\(694\) 0 0
\(695\) −69.9874 40.4073i −2.65478 1.53274i
\(696\) 0 0
\(697\) −0.319850 0.553997i −0.0121152 0.0209841i
\(698\) 0 0
\(699\) −6.50569 + 12.5863i −0.246068 + 0.476057i
\(700\) 0 0
\(701\) 29.9818i 1.13240i 0.824268 + 0.566199i \(0.191587\pi\)
−0.824268 + 0.566199i \(0.808413\pi\)
\(702\) 0 0
\(703\) −23.2015 + 13.3954i −0.875061 + 0.505217i
\(704\) 0 0
\(705\) −63.4558 + 40.6849i −2.38988 + 1.53228i
\(706\) 0 0
\(707\) −1.40111 + 34.0427i −0.0526940 + 1.28031i
\(708\) 0 0
\(709\) −11.5451 + 19.9968i −0.433587 + 0.750995i −0.997179 0.0750583i \(-0.976086\pi\)
0.563592 + 0.826053i \(0.309419\pi\)
\(710\) 0 0
\(711\) 4.03786 8.79195i 0.151431 0.329724i
\(712\) 0 0
\(713\) 10.4899 0.392849
\(714\) 0 0
\(715\) 5.49540 0.205516
\(716\) 0 0
\(717\) 39.0924 1.82038i 1.45993 0.0679832i
\(718\) 0 0
\(719\) 22.5340 39.0300i 0.840376 1.45557i −0.0492012 0.998789i \(-0.515668\pi\)
0.889577 0.456785i \(-0.150999\pi\)
\(720\) 0 0
\(721\) 6.91877 + 13.2101i 0.257669 + 0.491971i
\(722\) 0 0
\(723\) 4.57839 + 7.14087i 0.170272 + 0.265572i
\(724\) 0 0
\(725\) −40.6638 + 23.4772i −1.51022 + 0.871923i
\(726\) 0 0
\(727\) 3.14662i 0.116702i −0.998296 0.0583508i \(-0.981416\pi\)
0.998296 0.0583508i \(-0.0185842\pi\)
\(728\) 0 0
\(729\) −25.9545 + 7.44070i −0.961278 + 0.275582i
\(730\) 0 0
\(731\) 0.0261274 + 0.0452541i 0.000966358 + 0.00167378i
\(732\) 0 0
\(733\) 14.9590 + 8.63657i 0.552522 + 0.318999i 0.750139 0.661281i \(-0.229987\pi\)
−0.197616 + 0.980279i \(0.563320\pi\)
\(734\) 0 0
\(735\) −1.64624 + 46.0472i −0.0607224 + 1.69848i
\(736\) 0 0
\(737\) −0.831885 0.480289i −0.0306429 0.0176917i
\(738\) 0 0
\(739\) −0.996550 1.72607i −0.0366587 0.0634947i 0.847114 0.531411i \(-0.178338\pi\)
−0.883773 + 0.467917i \(0.845005\pi\)
\(740\) 0 0
\(741\) 15.2827 + 7.89942i 0.561423 + 0.290192i
\(742\) 0 0
\(743\) 5.54435i 0.203402i 0.994815 + 0.101701i \(0.0324286\pi\)
−0.994815 + 0.101701i \(0.967571\pi\)
\(744\) 0 0
\(745\) 40.0867 23.1441i 1.46866 0.847934i
\(746\) 0 0
\(747\) −27.1146 + 2.53073i −0.992071 + 0.0925944i
\(748\) 0 0
\(749\) −10.8113 20.6422i −0.395036 0.754248i
\(750\) 0 0
\(751\) 22.0897 38.2605i 0.806065 1.39615i −0.109504 0.993986i \(-0.534926\pi\)
0.915569 0.402160i \(-0.131740\pi\)
\(752\) 0 0
\(753\) −0.739494 15.8805i −0.0269487 0.578719i
\(754\) 0 0
\(755\) 31.2296 1.13656
\(756\) 0 0
\(757\) 10.6250 0.386172 0.193086 0.981182i \(-0.438150\pi\)
0.193086 + 0.981182i \(0.438150\pi\)
\(758\) 0 0
\(759\) −0.0383019 0.822528i −0.00139027 0.0298559i
\(760\) 0 0
\(761\) 13.9084 24.0900i 0.504178 0.873262i −0.495810 0.868431i \(-0.665129\pi\)
0.999988 0.00483132i \(-0.00153786\pi\)
\(762\) 0 0
\(763\) −0.487125 + 11.8357i −0.0176351 + 0.428480i
\(764\) 0 0
\(765\) −1.17987 + 0.110122i −0.0426582 + 0.00398149i
\(766\) 0 0
\(767\) 26.4432 15.2670i 0.954809 0.551259i
\(768\) 0 0
\(769\) 10.2707i 0.370369i −0.982704 0.185185i \(-0.940712\pi\)
0.982704 0.185185i \(-0.0592883\pi\)
\(770\) 0 0
\(771\) −19.4196 10.0377i −0.699379 0.361500i
\(772\) 0 0
\(773\) 20.2953 + 35.1525i 0.729972 + 1.26435i 0.956895 + 0.290435i \(0.0938001\pi\)
−0.226923 + 0.973913i \(0.572867\pi\)
\(774\) 0 0
\(775\) 64.4933 + 37.2352i 2.31667 + 1.33753i
\(776\) 0 0
\(777\) 25.2370 + 43.1718i 0.905372 + 1.54878i
\(778\) 0 0
\(779\) 13.0857 + 7.55502i 0.468843 + 0.270687i
\(780\) 0 0
\(781\) −1.03470 1.79215i −0.0370244 0.0641282i
\(782\) 0 0
\(783\) −25.5873 + 3.59530i −0.914415 + 0.128486i
\(784\) 0 0
\(785\) 49.1938i 1.75580i
\(786\) 0 0
\(787\) 22.6225 13.0611i 0.806404 0.465578i −0.0393014 0.999227i \(-0.512513\pi\)
0.845706 + 0.533650i \(0.179180\pi\)
\(788\) 0 0
\(789\) 27.2559 + 42.5107i