Properties

Label 168.2.u.a.89.3
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 89.3
Root \(-0.441628 - 1.67480i\)
Character \(\chi\) = 168.89
Dual form 168.2.u.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.21986 + 1.22961i) q^{3} +(-1.40397 + 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(-0.0238727 - 2.99991i) q^{9} +O(q^{10})\) \(q+(-1.21986 + 1.22961i) q^{3} +(-1.40397 + 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(-0.0238727 - 2.99991i) q^{9} +(-4.74645 + 2.74036i) q^{11} +1.35669i q^{13} +(-1.27745 - 4.69274i) q^{15} +(2.88753 + 5.00135i) q^{17} +(1.71973 + 0.992889i) q^{19} +(4.54574 - 0.579855i) q^{21} +(2.09928 + 1.21202i) q^{23} +(-1.44228 - 2.49811i) q^{25} +(3.71783 + 3.63012i) q^{27} -7.05668i q^{29} +(-3.07596 + 1.77591i) q^{31} +(2.42044 - 9.17913i) q^{33} +(6.88616 - 2.78798i) q^{35} +(-2.14377 + 3.71312i) q^{37} +(-1.66820 - 1.65498i) q^{39} -1.81976 q^{41} +11.2288 q^{43} +(7.32855 + 4.15374i) q^{45} +(-0.201213 + 0.348512i) q^{47} +(1.70327 + 6.78961i) q^{49} +(-9.67209 - 2.55043i) q^{51} +(-5.28097 + 3.04897i) q^{53} -15.3896i q^{55} +(-3.31870 + 0.903412i) q^{57} +(1.28234 + 2.22108i) q^{59} +(-4.75817 - 2.74713i) q^{61} +(-4.83218 + 6.29682i) q^{63} +(-3.29914 - 1.90476i) q^{65} +(3.45238 + 5.97970i) q^{67} +(-4.05114 + 1.10279i) q^{69} -2.08251i q^{71} +(-0.295696 + 0.170720i) q^{73} +(4.83108 + 1.27390i) q^{75} +(14.3610 + 2.00772i) q^{77} +(1.19139 - 2.06355i) q^{79} +(-8.99886 + 0.143232i) q^{81} -11.8717 q^{83} -16.2161 q^{85} +(8.67696 + 8.60818i) q^{87} +(-0.576571 + 0.998650i) q^{89} +(2.20785 - 2.83014i) q^{91} +(1.56858 - 5.94859i) q^{93} +(-4.82892 + 2.78798i) q^{95} +16.0187i q^{97} +(8.33413 + 14.1735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

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
\(3\) −1.21986 + 1.22961i −0.704288 + 0.709915i
\(4\) 0 0
\(5\) −1.40397 + 2.43175i −0.627876 + 1.08751i 0.360101 + 0.932913i \(0.382742\pi\)
−0.987977 + 0.154600i \(0.950591\pi\)
\(6\) 0 0
\(7\) −2.08606 1.62738i −0.788456 0.615092i
\(8\) 0 0
\(9\) −0.0238727 2.99991i −0.00795756 0.999968i
\(10\) 0 0
\(11\) −4.74645 + 2.74036i −1.43111 + 0.826250i −0.997205 0.0747101i \(-0.976197\pi\)
−0.433902 + 0.900960i \(0.642864\pi\)
\(12\) 0 0
\(13\) 1.35669i 0.376279i 0.982142 + 0.188139i \(0.0602457\pi\)
−0.982142 + 0.188139i \(0.939754\pi\)
\(14\) 0 0
\(15\) −1.27745 4.69274i −0.329836 1.21166i
\(16\) 0 0
\(17\) 2.88753 + 5.00135i 0.700329 + 1.21301i 0.968351 + 0.249593i \(0.0802967\pi\)
−0.268022 + 0.963413i \(0.586370\pi\)
\(18\) 0 0
\(19\) 1.71973 + 0.992889i 0.394534 + 0.227784i 0.684123 0.729367i \(-0.260185\pi\)
−0.289589 + 0.957151i \(0.593519\pi\)
\(20\) 0 0
\(21\) 4.54574 0.579855i 0.991962 0.126535i
\(22\) 0 0
\(23\) 2.09928 + 1.21202i 0.437730 + 0.252723i 0.702634 0.711551i \(-0.252007\pi\)
−0.264904 + 0.964275i \(0.585340\pi\)
\(24\) 0 0
\(25\) −1.44228 2.49811i −0.288457 0.499622i
\(26\) 0 0
\(27\) 3.71783 + 3.63012i 0.715497 + 0.698616i
\(28\) 0 0
\(29\) 7.05668i 1.31039i −0.755458 0.655197i \(-0.772586\pi\)
0.755458 0.655197i \(-0.227414\pi\)
\(30\) 0 0
\(31\) −3.07596 + 1.77591i −0.552459 + 0.318962i −0.750113 0.661309i \(-0.770001\pi\)
0.197654 + 0.980272i \(0.436668\pi\)
\(32\) 0 0
\(33\) 2.42044 9.17913i 0.421344 1.59788i
\(34\) 0 0
\(35\) 6.88616 2.78798i 1.16397 0.471255i
\(36\) 0 0
\(37\) −2.14377 + 3.71312i −0.352434 + 0.610434i −0.986675 0.162701i \(-0.947979\pi\)
0.634241 + 0.773135i \(0.281313\pi\)
\(38\) 0 0
\(39\) −1.66820 1.65498i −0.267126 0.265009i
\(40\) 0 0
\(41\) −1.81976 −0.284199 −0.142100 0.989852i \(-0.545385\pi\)
−0.142100 + 0.989852i \(0.545385\pi\)
\(42\) 0 0
\(43\) 11.2288 1.71238 0.856188 0.516665i \(-0.172827\pi\)
0.856188 + 0.516665i \(0.172827\pi\)
\(44\) 0 0
\(45\) 7.32855 + 4.15374i 1.09248 + 0.619202i
\(46\) 0 0
\(47\) −0.201213 + 0.348512i −0.0293500 + 0.0508356i −0.880327 0.474367i \(-0.842677\pi\)
0.850977 + 0.525202i \(0.176010\pi\)
\(48\) 0 0
\(49\) 1.70327 + 6.78961i 0.243325 + 0.969945i
\(50\) 0 0
\(51\) −9.67209 2.55043i −1.35436 0.357131i
\(52\) 0 0
\(53\) −5.28097 + 3.04897i −0.725397 + 0.418808i −0.816736 0.577012i \(-0.804219\pi\)
0.0913389 + 0.995820i \(0.470885\pi\)
\(54\) 0 0
\(55\) 15.3896i 2.07513i
\(56\) 0 0
\(57\) −3.31870 + 0.903412i −0.439573 + 0.119660i
\(58\) 0 0
\(59\) 1.28234 + 2.22108i 0.166947 + 0.289161i 0.937345 0.348403i \(-0.113276\pi\)
−0.770398 + 0.637563i \(0.779942\pi\)
\(60\) 0 0
\(61\) −4.75817 2.74713i −0.609222 0.351734i 0.163439 0.986553i \(-0.447741\pi\)
−0.772661 + 0.634819i \(0.781075\pi\)
\(62\) 0 0
\(63\) −4.83218 + 6.29682i −0.608798 + 0.793325i
\(64\) 0 0
\(65\) −3.29914 1.90476i −0.409208 0.236257i
\(66\) 0 0
\(67\) 3.45238 + 5.97970i 0.421775 + 0.730536i 0.996113 0.0880819i \(-0.0280737\pi\)
−0.574338 + 0.818618i \(0.694740\pi\)
\(68\) 0 0
\(69\) −4.05114 + 1.10279i −0.487700 + 0.132761i
\(70\) 0 0
\(71\) 2.08251i 0.247148i −0.992335 0.123574i \(-0.960564\pi\)
0.992335 0.123574i \(-0.0394357\pi\)
\(72\) 0 0
\(73\) −0.295696 + 0.170720i −0.0346086 + 0.0199813i −0.517204 0.855862i \(-0.673027\pi\)
0.482596 + 0.875843i \(0.339694\pi\)
\(74\) 0 0
\(75\) 4.83108 + 1.27390i 0.557846 + 0.147098i
\(76\) 0 0
\(77\) 14.3610 + 2.00772i 1.63658 + 0.228800i
\(78\) 0 0
\(79\) 1.19139 2.06355i 0.134042 0.232168i −0.791189 0.611572i \(-0.790538\pi\)
0.925231 + 0.379404i \(0.123871\pi\)
\(80\) 0 0
\(81\) −8.99886 + 0.143232i −0.999873 + 0.0159146i
\(82\) 0 0
\(83\) −11.8717 −1.30309 −0.651543 0.758611i \(-0.725878\pi\)
−0.651543 + 0.758611i \(0.725878\pi\)
\(84\) 0 0
\(85\) −16.2161 −1.75888
\(86\) 0 0
\(87\) 8.67696 + 8.60818i 0.930267 + 0.922894i
\(88\) 0 0
\(89\) −0.576571 + 0.998650i −0.0611164 + 0.105857i −0.894965 0.446137i \(-0.852799\pi\)
0.833848 + 0.551994i \(0.186133\pi\)
\(90\) 0 0
\(91\) 2.20785 2.83014i 0.231446 0.296679i
\(92\) 0 0
\(93\) 1.56858 5.94859i 0.162654 0.616840i
\(94\) 0 0
\(95\) −4.82892 + 2.78798i −0.495437 + 0.286041i
\(96\) 0 0
\(97\) 16.0187i 1.62645i 0.581950 + 0.813225i \(0.302290\pi\)
−0.581950 + 0.813225i \(0.697710\pi\)
\(98\) 0 0
\(99\) 8.33413 + 14.1735i 0.837612 + 1.42449i
\(100\) 0 0
\(101\) −7.33982 12.7129i −0.730339 1.26498i −0.956738 0.290950i \(-0.906029\pi\)
0.226399 0.974035i \(-0.427305\pi\)
\(102\) 0 0
\(103\) 4.06960 + 2.34958i 0.400989 + 0.231511i 0.686911 0.726742i \(-0.258966\pi\)
−0.285922 + 0.958253i \(0.592300\pi\)
\(104\) 0 0
\(105\) −4.97204 + 11.8682i −0.485221 + 1.15822i
\(106\) 0 0
\(107\) 7.14150 + 4.12315i 0.690395 + 0.398600i 0.803760 0.594954i \(-0.202830\pi\)
−0.113365 + 0.993553i \(0.536163\pi\)
\(108\) 0 0
\(109\) −4.41113 7.64030i −0.422509 0.731808i 0.573675 0.819083i \(-0.305517\pi\)
−0.996184 + 0.0872755i \(0.972184\pi\)
\(110\) 0 0
\(111\) −1.95058 7.16550i −0.185141 0.680119i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) −5.89467 + 3.40329i −0.549680 + 0.317358i
\(116\) 0 0
\(117\) 4.06995 0.0323879i 0.376267 0.00299426i
\(118\) 0 0
\(119\) 2.11554 15.1322i 0.193931 1.38717i
\(120\) 0 0
\(121\) 9.51916 16.4877i 0.865378 1.49888i
\(122\) 0 0
\(123\) 2.21986 2.23760i 0.200158 0.201757i
\(124\) 0 0
\(125\) −5.94002 −0.531291
\(126\) 0 0
\(127\) −6.93769 −0.615620 −0.307810 0.951448i \(-0.599596\pi\)
−0.307810 + 0.951448i \(0.599596\pi\)
\(128\) 0 0
\(129\) −13.6976 + 13.8070i −1.20601 + 1.21564i
\(130\) 0 0
\(131\) 0.118734 0.205654i 0.0103739 0.0179680i −0.860792 0.508957i \(-0.830031\pi\)
0.871166 + 0.490989i \(0.163365\pi\)
\(132\) 0 0
\(133\) −1.97166 4.86988i −0.170964 0.422273i
\(134\) 0 0
\(135\) −14.0473 + 3.94426i −1.20900 + 0.339468i
\(136\) 0 0
\(137\) 9.58873 5.53606i 0.819221 0.472977i −0.0309270 0.999522i \(-0.509846\pi\)
0.850148 + 0.526544i \(0.176513\pi\)
\(138\) 0 0
\(139\) 1.02466i 0.0869108i −0.999055 0.0434554i \(-0.986163\pi\)
0.999055 0.0434554i \(-0.0138366\pi\)
\(140\) 0 0
\(141\) −0.183080 0.672550i −0.0154181 0.0566389i
\(142\) 0 0
\(143\) −3.71783 6.43947i −0.310900 0.538495i
\(144\) 0 0
\(145\) 17.1601 + 9.90740i 1.42507 + 0.822765i
\(146\) 0 0
\(147\) −10.4263 6.18804i −0.859949 0.510381i
\(148\) 0 0
\(149\) 19.0549 + 11.0013i 1.56104 + 0.901266i 0.997152 + 0.0754127i \(0.0240274\pi\)
0.563886 + 0.825853i \(0.309306\pi\)
\(150\) 0 0
\(151\) 3.63368 + 6.29371i 0.295704 + 0.512175i 0.975149 0.221552i \(-0.0711123\pi\)
−0.679444 + 0.733727i \(0.737779\pi\)
\(152\) 0 0
\(153\) 14.9346 8.78171i 1.20739 0.709959i
\(154\) 0 0
\(155\) 9.97331i 0.801075i
\(156\) 0 0
\(157\) 19.6994 11.3735i 1.57219 0.907702i 0.576285 0.817249i \(-0.304502\pi\)
0.995901 0.0904525i \(-0.0288313\pi\)
\(158\) 0 0
\(159\) 2.69302 10.2128i 0.213570 0.809931i
\(160\) 0 0
\(161\) −2.40680 5.94467i −0.189683 0.468505i
\(162\) 0 0
\(163\) −9.06678 + 15.7041i −0.710165 + 1.23004i 0.254630 + 0.967039i \(0.418046\pi\)
−0.964795 + 0.263003i \(0.915287\pi\)
\(164\) 0 0
\(165\) 18.9232 + 18.7732i 1.47317 + 1.46149i
\(166\) 0 0
\(167\) 24.0942 1.86447 0.932233 0.361858i \(-0.117857\pi\)
0.932233 + 0.361858i \(0.117857\pi\)
\(168\) 0 0
\(169\) 11.1594 0.858414
\(170\) 0 0
\(171\) 2.93752 5.18274i 0.224638 0.396334i
\(172\) 0 0
\(173\) −5.18802 + 8.98592i −0.394438 + 0.683187i −0.993029 0.117868i \(-0.962394\pi\)
0.598591 + 0.801055i \(0.295727\pi\)
\(174\) 0 0
\(175\) −1.05668 + 7.55835i −0.0798778 + 0.571357i
\(176\) 0 0
\(177\) −4.29535 1.13264i −0.322858 0.0851342i
\(178\) 0 0
\(179\) 11.5922 6.69274i 0.866439 0.500239i 0.000276030 1.00000i \(-0.499912\pi\)
0.866163 + 0.499761i \(0.166579\pi\)
\(180\) 0 0
\(181\) 18.4339i 1.37018i 0.728457 + 0.685092i \(0.240238\pi\)
−0.728457 + 0.685092i \(0.759762\pi\)
\(182\) 0 0
\(183\) 9.18221 2.49957i 0.678769 0.184773i
\(184\) 0 0
\(185\) −6.01960 10.4263i −0.442570 0.766554i
\(186\) 0 0
\(187\) −27.4110 15.8258i −2.00449 1.15729i
\(188\) 0 0
\(189\) −1.84803 13.6230i −0.134424 0.990924i
\(190\) 0 0
\(191\) −3.59492 2.07553i −0.260119 0.150180i 0.364270 0.931293i \(-0.381319\pi\)
−0.624389 + 0.781114i \(0.714652\pi\)
\(192\) 0 0
\(193\) −9.75462 16.8955i −0.702153 1.21616i −0.967709 0.252069i \(-0.918889\pi\)
0.265556 0.964095i \(-0.414444\pi\)
\(194\) 0 0
\(195\) 6.36661 1.73311i 0.455922 0.124110i
\(196\) 0 0
\(197\) 3.80952i 0.271417i 0.990749 + 0.135709i \(0.0433311\pi\)
−0.990749 + 0.135709i \(0.956669\pi\)
\(198\) 0 0
\(199\) −5.30327 + 3.06185i −0.375939 + 0.217049i −0.676050 0.736856i \(-0.736310\pi\)
0.300111 + 0.953904i \(0.402976\pi\)
\(200\) 0 0
\(201\) −11.5641 3.04933i −0.815670 0.215083i
\(202\) 0 0
\(203\) −11.4839 + 14.7206i −0.806012 + 1.03319i
\(204\) 0 0
\(205\) 2.55490 4.42522i 0.178442 0.309071i
\(206\) 0 0
\(207\) 3.58583 6.32657i 0.249232 0.439727i
\(208\) 0 0
\(209\) −10.8835 −0.752827
\(210\) 0 0
\(211\) 2.93058 0.201750 0.100875 0.994899i \(-0.467836\pi\)
0.100875 + 0.994899i \(0.467836\pi\)
\(212\) 0 0
\(213\) 2.56067 + 2.54037i 0.175454 + 0.174063i
\(214\) 0 0
\(215\) −15.7649 + 27.3057i −1.07516 + 1.86223i
\(216\) 0 0
\(217\) 9.30671 + 1.30111i 0.631780 + 0.0883252i
\(218\) 0 0
\(219\) 0.150789 0.571845i 0.0101894 0.0386417i
\(220\) 0 0
\(221\) −6.78530 + 3.91749i −0.456428 + 0.263519i
\(222\) 0 0
\(223\) 4.61145i 0.308806i 0.988008 + 0.154403i \(0.0493454\pi\)
−0.988008 + 0.154403i \(0.950655\pi\)
\(224\) 0 0
\(225\) −7.45966 + 4.38635i −0.497311 + 0.292424i
\(226\) 0 0
\(227\) −8.62344 14.9362i −0.572358 0.991353i −0.996323 0.0856745i \(-0.972695\pi\)
0.423965 0.905678i \(-0.360638\pi\)
\(228\) 0 0
\(229\) −11.5705 6.68024i −0.764601 0.441443i 0.0663443 0.997797i \(-0.478866\pi\)
−0.830945 + 0.556354i \(0.812200\pi\)
\(230\) 0 0
\(231\) −19.9871 + 15.2092i −1.31505 + 1.00069i
\(232\) 0 0
\(233\) 15.5908 + 9.00135i 1.02139 + 0.589698i 0.914505 0.404574i \(-0.132580\pi\)
0.106882 + 0.994272i \(0.465913\pi\)
\(234\) 0 0
\(235\) −0.564996 0.978602i −0.0368563 0.0638370i
\(236\) 0 0
\(237\) 1.08403 + 3.98220i 0.0704151 + 0.258671i
\(238\) 0 0
\(239\) 23.6499i 1.52979i 0.644158 + 0.764893i \(0.277208\pi\)
−0.644158 + 0.764893i \(0.722792\pi\)
\(240\) 0 0
\(241\) 3.53574 2.04136i 0.227757 0.131496i −0.381780 0.924253i \(-0.624689\pi\)
0.609537 + 0.792758i \(0.291355\pi\)
\(242\) 0 0
\(243\) 10.8013 11.2398i 0.692901 0.721033i
\(244\) 0 0
\(245\) −18.9020 5.39050i −1.20761 0.344386i
\(246\) 0 0
\(247\) −1.34705 + 2.33315i −0.0857105 + 0.148455i
\(248\) 0 0
\(249\) 14.4818 14.5975i 0.917748 0.925080i
\(250\) 0 0
\(251\) −5.78085 −0.364884 −0.182442 0.983217i \(-0.558400\pi\)
−0.182442 + 0.983217i \(0.558400\pi\)
\(252\) 0 0
\(253\) −13.2855 −0.835251
\(254\) 0 0
\(255\) 19.7814 19.9394i 1.23876 1.24865i
\(256\) 0 0
\(257\) −10.4824 + 18.1560i −0.653871 + 1.13254i 0.328304 + 0.944572i \(0.393523\pi\)
−0.982175 + 0.187966i \(0.939810\pi\)
\(258\) 0 0
\(259\) 10.5147 4.25706i 0.653351 0.264521i
\(260\) 0 0
\(261\) −21.1694 + 0.168462i −1.31035 + 0.0104275i
\(262\) 0 0
\(263\) −4.32937 + 2.49957i −0.266961 + 0.154130i −0.627506 0.778612i \(-0.715924\pi\)
0.360545 + 0.932742i \(0.382591\pi\)
\(264\) 0 0
\(265\) 17.1227i 1.05184i
\(266\) 0 0
\(267\) −0.524611 1.92717i −0.0321057 0.117941i
\(268\) 0 0
\(269\) 7.67602 + 13.2953i 0.468015 + 0.810626i 0.999332 0.0365470i \(-0.0116359\pi\)
−0.531317 + 0.847173i \(0.678303\pi\)
\(270\) 0 0
\(271\) 14.4761 + 8.35779i 0.879362 + 0.507700i 0.870448 0.492260i \(-0.163829\pi\)
0.00891391 + 0.999960i \(0.497163\pi\)
\(272\) 0 0
\(273\) 0.786685 + 6.16718i 0.0476124 + 0.373254i
\(274\) 0 0
\(275\) 13.6914 + 7.90476i 0.825625 + 0.476675i
\(276\) 0 0
\(277\) 11.2571 + 19.4979i 0.676376 + 1.17152i 0.976065 + 0.217481i \(0.0697839\pi\)
−0.299689 + 0.954037i \(0.596883\pi\)
\(278\) 0 0
\(279\) 5.40098 + 9.18520i 0.323348 + 0.549903i
\(280\) 0 0
\(281\) 18.1134i 1.08055i 0.841488 + 0.540276i \(0.181680\pi\)
−0.841488 + 0.540276i \(0.818320\pi\)
\(282\) 0 0
\(283\) −5.00728 + 2.89095i −0.297652 + 0.171849i −0.641388 0.767217i \(-0.721641\pi\)
0.343736 + 0.939066i \(0.388308\pi\)
\(284\) 0 0
\(285\) 2.46250 9.33864i 0.145866 0.553173i
\(286\) 0 0
\(287\) 3.79613 + 2.96145i 0.224079 + 0.174809i
\(288\) 0 0
\(289\) −8.17567 + 14.1607i −0.480921 + 0.832980i
\(290\) 0 0
\(291\) −19.6967 19.5406i −1.15464 1.14549i
\(292\) 0 0
\(293\) 9.38786 0.548445 0.274222 0.961666i \(-0.411580\pi\)
0.274222 + 0.961666i \(0.411580\pi\)
\(294\) 0 0
\(295\) −7.20151 −0.419288
\(296\) 0 0
\(297\) −27.5943 7.04195i −1.60118 0.408616i
\(298\) 0 0
\(299\) −1.64434 + 2.84808i −0.0950945 + 0.164709i
\(300\) 0 0
\(301\) −23.4239 18.2735i −1.35013 1.05327i
\(302\) 0 0
\(303\) 24.5855 + 6.48293i 1.41240 + 0.372435i
\(304\) 0 0
\(305\) 13.3607 7.71380i 0.765031 0.441691i
\(306\) 0 0
\(307\) 19.7599i 1.12776i −0.825857 0.563880i \(-0.809308\pi\)
0.825857 0.563880i \(-0.190692\pi\)
\(308\) 0 0
\(309\) −7.85341 + 2.13784i −0.446765 + 0.121618i
\(310\) 0 0
\(311\) −10.1911 17.6515i −0.577884 1.00092i −0.995722 0.0924025i \(-0.970545\pi\)
0.417838 0.908522i \(-0.362788\pi\)
\(312\) 0 0
\(313\) 6.19972 + 3.57941i 0.350429 + 0.202320i 0.664874 0.746955i \(-0.268485\pi\)
−0.314445 + 0.949276i \(0.601818\pi\)
\(314\) 0 0
\(315\) −8.52807 20.5913i −0.480502 1.16019i
\(316\) 0 0
\(317\) −9.81412 5.66618i −0.551216 0.318245i 0.198396 0.980122i \(-0.436427\pi\)
−0.749612 + 0.661877i \(0.769760\pi\)
\(318\) 0 0
\(319\) 19.3379 + 33.4942i 1.08271 + 1.87531i
\(320\) 0 0
\(321\) −13.7815 + 3.75158i −0.769208 + 0.209393i
\(322\) 0 0
\(323\) 11.4680i 0.638096i
\(324\) 0 0
\(325\) 3.38917 1.95674i 0.187997 0.108540i
\(326\) 0 0
\(327\) 14.7755 + 3.89615i 0.817089 + 0.215458i
\(328\) 0 0
\(329\) 0.986903 0.399565i 0.0544097 0.0220287i
\(330\) 0 0
\(331\) 9.41383 16.3052i 0.517431 0.896216i −0.482364 0.875971i \(-0.660222\pi\)
0.999795 0.0202456i \(-0.00644480\pi\)
\(332\) 0 0
\(333\) 11.1902 + 6.34247i 0.613219 + 0.347565i
\(334\) 0 0
\(335\) −19.3882 −1.05929
\(336\) 0 0
\(337\) 28.9739 1.57831 0.789156 0.614193i \(-0.210518\pi\)
0.789156 + 0.614193i \(0.210518\pi\)
\(338\) 0 0
\(339\) 4.91843 + 4.87945i 0.267133 + 0.265015i
\(340\) 0 0
\(341\) 9.73325 16.8585i 0.527085 0.912939i
\(342\) 0 0
\(343\) 7.49615 16.9354i 0.404754 0.914426i
\(344\) 0 0
\(345\) 3.00597 11.3997i 0.161836 0.613738i
\(346\) 0 0
\(347\) 15.6525 9.03697i 0.840270 0.485130i −0.0170860 0.999854i \(-0.505439\pi\)
0.857356 + 0.514724i \(0.172106\pi\)
\(348\) 0 0
\(349\) 12.8624i 0.688510i −0.938876 0.344255i \(-0.888132\pi\)
0.938876 0.344255i \(-0.111868\pi\)
\(350\) 0 0
\(351\) −4.92495 + 5.04395i −0.262875 + 0.269226i
\(352\) 0 0
\(353\) −13.6386 23.6227i −0.725909 1.25731i −0.958599 0.284760i \(-0.908086\pi\)
0.232690 0.972551i \(-0.425247\pi\)
\(354\) 0 0
\(355\) 5.06415 + 2.92379i 0.268777 + 0.155178i
\(356\) 0 0
\(357\) 16.0260 + 21.0605i 0.848187 + 1.11464i
\(358\) 0 0
\(359\) 0.773273 + 0.446450i 0.0408118 + 0.0235627i 0.520267 0.854004i \(-0.325832\pi\)
−0.479455 + 0.877566i \(0.659166\pi\)
\(360\) 0 0
\(361\) −7.52834 13.0395i −0.396229 0.686288i
\(362\) 0 0
\(363\) 8.66131 + 31.8175i 0.454601 + 1.66999i
\(364\) 0 0
\(365\) 0.958746i 0.0501831i
\(366\) 0 0
\(367\) −9.57418 + 5.52765i −0.499768 + 0.288541i −0.728618 0.684921i \(-0.759837\pi\)
0.228850 + 0.973462i \(0.426504\pi\)
\(368\) 0 0
\(369\) 0.0434426 + 5.45912i 0.00226153 + 0.284190i
\(370\) 0 0
\(371\) 15.9782 + 2.23382i 0.829549 + 0.115974i
\(372\) 0 0
\(373\) −11.5503 + 20.0057i −0.598053 + 1.03586i 0.395055 + 0.918657i \(0.370725\pi\)
−0.993108 + 0.117201i \(0.962608\pi\)
\(374\) 0 0
\(375\) 7.24600 7.30390i 0.374182 0.377172i
\(376\) 0 0
\(377\) 9.57375 0.493073
\(378\) 0 0
\(379\) −23.3938 −1.20166 −0.600830 0.799377i \(-0.705163\pi\)
−0.600830 + 0.799377i \(0.705163\pi\)
\(380\) 0 0
\(381\) 8.46302 8.53063i 0.433574 0.437038i
\(382\) 0 0
\(383\) 11.5139 19.9426i 0.588331 1.01902i −0.406120 0.913820i \(-0.633119\pi\)
0.994451 0.105200i \(-0.0335482\pi\)
\(384\) 0 0
\(385\) −25.0447 + 32.1036i −1.27640 + 1.63615i
\(386\) 0 0
\(387\) −0.268062 33.6853i −0.0136263 1.71232i
\(388\) 0 0
\(389\) 5.45545 3.14970i 0.276602 0.159696i −0.355282 0.934759i \(-0.615615\pi\)
0.631884 + 0.775063i \(0.282282\pi\)
\(390\) 0 0
\(391\) 13.9990i 0.707958i
\(392\) 0 0
\(393\) 0.108034 + 0.396866i 0.00544960 + 0.0200192i
\(394\) 0 0
\(395\) 3.34537 + 5.79435i 0.168324 + 0.291545i
\(396\) 0 0
\(397\) 6.27940 + 3.62541i 0.315154 + 0.181954i 0.649230 0.760592i \(-0.275091\pi\)
−0.334077 + 0.942546i \(0.608424\pi\)
\(398\) 0 0
\(399\) 8.39320 + 3.51622i 0.420186 + 0.176031i
\(400\) 0 0
\(401\) 11.8188 + 6.82360i 0.590204 + 0.340755i 0.765178 0.643819i \(-0.222651\pi\)
−0.174974 + 0.984573i \(0.555984\pi\)
\(402\) 0 0
\(403\) −2.40936 4.17314i −0.120019 0.207879i
\(404\) 0 0
\(405\) 12.2859 22.0841i 0.610489 1.09737i
\(406\) 0 0
\(407\) 23.4989i 1.16479i
\(408\) 0 0
\(409\) −11.9303 + 6.88797i −0.589916 + 0.340588i −0.765064 0.643954i \(-0.777293\pi\)
0.175148 + 0.984542i \(0.443959\pi\)
\(410\) 0 0
\(411\) −4.88975 + 18.5436i −0.241194 + 0.914689i
\(412\) 0 0
\(413\) 0.939504 6.72017i 0.0462300 0.330678i
\(414\) 0 0
\(415\) 16.6675 28.8690i 0.818177 1.41712i
\(416\) 0 0
\(417\) 1.25993 + 1.24995i 0.0616992 + 0.0612102i
\(418\) 0 0
\(419\) −6.94914 −0.339488 −0.169744 0.985488i \(-0.554294\pi\)
−0.169744 + 0.985488i \(0.554294\pi\)
\(420\) 0 0
\(421\) −0.349861 −0.0170512 −0.00852560 0.999964i \(-0.502714\pi\)
−0.00852560 + 0.999964i \(0.502714\pi\)
\(422\) 0 0
\(423\) 1.05031 + 0.595301i 0.0510676 + 0.0289445i
\(424\) 0 0
\(425\) 8.32928 14.4267i 0.404029 0.699800i
\(426\) 0 0
\(427\) 5.45520 + 13.4740i 0.263995 + 0.652054i
\(428\) 0 0
\(429\) 12.4533 + 3.28379i 0.601249 + 0.158543i
\(430\) 0 0
\(431\) 17.4513 10.0755i 0.840601 0.485321i −0.0168676 0.999858i \(-0.505369\pi\)
0.857468 + 0.514537i \(0.172036\pi\)
\(432\) 0 0
\(433\) 1.42453i 0.0684585i 0.999414 + 0.0342292i \(0.0108976\pi\)
−0.999414 + 0.0342292i \(0.989102\pi\)
\(434\) 0 0
\(435\) −33.1152 + 9.01456i −1.58775 + 0.432215i
\(436\) 0 0
\(437\) 2.40680 + 4.16870i 0.115133 + 0.199416i
\(438\) 0 0
\(439\) 1.76541 + 1.01926i 0.0842583 + 0.0486465i 0.541537 0.840677i \(-0.317843\pi\)
−0.457279 + 0.889323i \(0.651176\pi\)
\(440\) 0 0
\(441\) 20.3275 5.27174i 0.967978 0.251035i
\(442\) 0 0
\(443\) −11.1751 6.45195i −0.530945 0.306541i 0.210456 0.977603i \(-0.432505\pi\)
−0.741401 + 0.671062i \(0.765838\pi\)
\(444\) 0 0
\(445\) −1.61898 2.80416i −0.0767471 0.132930i
\(446\) 0 0
\(447\) −36.7717 + 10.0099i −1.73924 + 0.473453i
\(448\) 0 0
\(449\) 2.49432i 0.117714i 0.998266 + 0.0588572i \(0.0187457\pi\)
−0.998266 + 0.0588572i \(0.981254\pi\)
\(450\) 0 0
\(451\) 8.63741 4.98681i 0.406720 0.234820i
\(452\) 0 0
\(453\) −12.1714 3.20946i −0.571862 0.150794i
\(454\) 0 0
\(455\) 3.78243 + 9.34240i 0.177323 + 0.437978i
\(456\) 0 0
\(457\) −7.30952 + 12.6605i −0.341925 + 0.592232i −0.984790 0.173748i \(-0.944412\pi\)
0.642865 + 0.765979i \(0.277746\pi\)
\(458\) 0 0
\(459\) −7.42014 + 29.0762i −0.346342 + 1.35716i
\(460\) 0 0
\(461\) 2.83467 0.132024 0.0660120 0.997819i \(-0.478972\pi\)
0.0660120 + 0.997819i \(0.478972\pi\)
\(462\) 0 0
\(463\) 14.1594 0.658042 0.329021 0.944323i \(-0.393281\pi\)
0.329021 + 0.944323i \(0.393281\pi\)
\(464\) 0 0
\(465\) 12.2633 + 12.1661i 0.568695 + 0.564188i
\(466\) 0 0
\(467\) −4.98809 + 8.63963i −0.230821 + 0.399794i −0.958050 0.286601i \(-0.907475\pi\)
0.727229 + 0.686395i \(0.240808\pi\)
\(468\) 0 0
\(469\) 2.52937 18.0923i 0.116796 0.835426i
\(470\) 0 0
\(471\) −10.0457 + 38.0966i −0.462880 + 1.75540i
\(472\) 0 0
\(473\) −53.2969 + 30.7710i −2.45059 + 1.41485i
\(474\) 0 0
\(475\) 5.72811i 0.262824i
\(476\) 0 0
\(477\) 9.27269 + 15.7696i 0.424567 + 0.722041i
\(478\) 0 0
\(479\) 21.7575 + 37.6850i 0.994124 + 1.72187i 0.590805 + 0.806815i \(0.298810\pi\)
0.403320 + 0.915059i \(0.367856\pi\)
\(480\) 0 0
\(481\) −5.03757 2.90844i −0.229693 0.132614i
\(482\) 0 0
\(483\) 10.2456 + 4.29225i 0.466190 + 0.195304i
\(484\) 0 0
\(485\) −38.9535 22.4898i −1.76879 1.02121i
\(486\) 0 0
\(487\) −18.5796 32.1808i −0.841921 1.45825i −0.888269 0.459324i \(-0.848092\pi\)
0.0463476 0.998925i \(-0.485242\pi\)
\(488\) 0 0
\(489\) −8.24970 30.3055i −0.373064 1.37046i
\(490\) 0 0
\(491\) 22.1831i 1.00111i −0.865704 0.500556i \(-0.833129\pi\)
0.865704 0.500556i \(-0.166871\pi\)
\(492\) 0 0
\(493\) 35.2929 20.3764i 1.58951 0.917707i
\(494\) 0 0
\(495\) −46.1673 + 0.367391i −2.07507 + 0.0165130i
\(496\) 0 0
\(497\) −3.38903 + 4.34423i −0.152019 + 0.194865i
\(498\) 0 0
\(499\) −8.33695 + 14.4400i −0.373213 + 0.646424i −0.990058 0.140661i \(-0.955077\pi\)
0.616845 + 0.787085i \(0.288411\pi\)
\(500\) 0 0
\(501\) −29.3916 + 29.6265i −1.31312 + 1.32361i
\(502\) 0 0
\(503\) −8.55884 −0.381620 −0.190810 0.981627i \(-0.561111\pi\)
−0.190810 + 0.981627i \(0.561111\pi\)
\(504\) 0 0
\(505\) 41.2196 1.83425
\(506\) 0 0
\(507\) −13.6129 + 13.7217i −0.604571 + 0.609401i
\(508\) 0 0
\(509\) 14.1072 24.4345i 0.625292 1.08304i −0.363192 0.931714i \(-0.618313\pi\)
0.988484 0.151324i \(-0.0483536\pi\)
\(510\) 0 0
\(511\) 0.894665 + 0.125077i 0.0395777 + 0.00553310i
\(512\) 0 0
\(513\) 2.78938 + 9.93423i 0.123154 + 0.438607i
\(514\) 0 0
\(515\) −11.4272 + 6.59750i −0.503543 + 0.290721i
\(516\) 0 0
\(517\) 2.20559i 0.0970017i
\(518\) 0 0
\(519\) −4.72049 17.3408i −0.207206 0.761177i
\(520\) 0 0
\(521\) 9.00041 + 15.5892i 0.394315 + 0.682974i 0.993014 0.118001i \(-0.0376485\pi\)
−0.598698 + 0.800975i \(0.704315\pi\)
\(522\) 0 0
\(523\) −11.9049 6.87332i −0.520567 0.300549i 0.216600 0.976260i \(-0.430503\pi\)
−0.737167 + 0.675711i \(0.763837\pi\)
\(524\) 0 0
\(525\) −8.00479 10.5194i −0.349358 0.459106i
\(526\) 0 0
\(527\) −17.7639 10.2560i −0.773806 0.446757i
\(528\) 0 0
\(529\) −8.56202 14.8299i −0.372262 0.644776i
\(530\) 0 0
\(531\) 6.63243 3.89993i 0.287823 0.169243i
\(532\) 0 0
\(533\) 2.46886i 0.106938i
\(534\) 0 0
\(535\) −20.0530 + 11.5776i −0.866965 + 0.500542i
\(536\) 0 0
\(537\) −5.91140 + 22.4180i −0.255096 + 0.967410i
\(538\) 0 0
\(539\) −26.6905 27.5589i −1.14964 1.18705i
\(540\) 0 0
\(541\) −19.6272 + 33.9953i −0.843839 + 1.46157i 0.0427866 + 0.999084i \(0.486376\pi\)
−0.886626 + 0.462488i \(0.846957\pi\)
\(542\) 0 0
\(543\) −22.6665 22.4869i −0.972714 0.965004i
\(544\) 0 0
\(545\) 24.7724 1.06113
\(546\) 0 0
\(547\) −12.4980 −0.534375 −0.267188 0.963645i \(-0.586094\pi\)
−0.267188 + 0.963645i \(0.586094\pi\)
\(548\) 0 0
\(549\) −8.12755 + 14.3396i −0.346875 + 0.612001i
\(550\) 0 0
\(551\) 7.00651 12.1356i 0.298487 0.516995i
\(552\) 0 0
\(553\) −5.84350 + 2.36584i −0.248491 + 0.100606i
\(554\) 0 0
\(555\) 20.1633 + 5.31684i 0.855884 + 0.225687i
\(556\) 0 0
\(557\) 15.4816 8.93830i 0.655976 0.378728i −0.134766 0.990877i \(-0.543028\pi\)
0.790742 + 0.612150i \(0.209695\pi\)
\(558\) 0 0
\(559\) 15.2340i 0.644331i
\(560\) 0 0
\(561\) 52.8971 14.3996i 2.23332 0.607950i
\(562\) 0 0
\(563\) −1.36644 2.36674i −0.0575885 0.0997462i 0.835794 0.549043i \(-0.185008\pi\)
−0.893382 + 0.449297i \(0.851674\pi\)
\(564\) 0 0
\(565\) 9.72702 + 5.61589i 0.409219 + 0.236262i
\(566\) 0 0
\(567\) 19.0052 + 14.3458i 0.798145 + 0.602466i
\(568\) 0 0
\(569\) −1.72971 0.998650i −0.0725133 0.0418656i 0.463305 0.886199i \(-0.346663\pi\)
−0.535818 + 0.844333i \(0.679997\pi\)
\(570\) 0 0
\(571\) 1.00728 + 1.74466i 0.0421534 + 0.0730118i 0.886332 0.463050i \(-0.153245\pi\)
−0.844179 + 0.536061i \(0.819912\pi\)
\(572\) 0 0
\(573\) 6.93739 1.88848i 0.289814 0.0788926i
\(574\) 0 0
\(575\) 6.99231i 0.291599i
\(576\) 0 0
\(577\) −22.0199 + 12.7132i −0.916701 + 0.529258i −0.882581 0.470160i \(-0.844196\pi\)
−0.0341199 + 0.999418i \(0.510863\pi\)
\(578\) 0 0
\(579\) 32.6741 + 8.61582i 1.35789 + 0.358061i
\(580\) 0 0
\(581\) 24.7650 + 19.3197i 1.02743 + 0.801518i
\(582\) 0 0
\(583\) 16.7106 28.9435i 0.692080 1.19872i
\(584\) 0 0
\(585\) −5.63534 + 9.94259i −0.232993 + 0.411075i
\(586\) 0 0
\(587\) 34.4645 1.42250 0.711251 0.702939i \(-0.248129\pi\)
0.711251 + 0.702939i \(0.248129\pi\)
\(588\) 0 0
\(589\) −7.05312 −0.290619
\(590\) 0 0
\(591\) −4.68422 4.64709i −0.192683 0.191156i
\(592\) 0 0
\(593\) −3.62199 + 6.27347i −0.148737 + 0.257620i −0.930761 0.365628i \(-0.880854\pi\)
0.782024 + 0.623249i \(0.214188\pi\)
\(594\) 0 0
\(595\) 33.8277 + 26.3897i 1.38680 + 1.08187i
\(596\) 0 0
\(597\) 2.70439 10.2560i 0.110683 0.419749i
\(598\) 0 0
\(599\) −32.5464 + 18.7907i −1.32981 + 0.767766i −0.985270 0.171005i \(-0.945299\pi\)
−0.344540 + 0.938772i \(0.611965\pi\)
\(600\) 0 0
\(601\) 3.78103i 0.154232i −0.997022 0.0771158i \(-0.975429\pi\)
0.997022 0.0771158i \(-0.0245711\pi\)
\(602\) 0 0
\(603\) 17.8561 10.4996i 0.727157 0.427575i
\(604\) 0 0
\(605\) 26.7293 + 46.2965i 1.08670 + 1.88222i
\(606\) 0 0
\(607\) −24.0353 13.8768i −0.975565 0.563242i −0.0746364 0.997211i \(-0.523780\pi\)
−0.900928 + 0.433968i \(0.857113\pi\)
\(608\) 0 0
\(609\) −4.09185 32.0779i −0.165810 1.29986i
\(610\) 0 0
\(611\) −0.472823 0.272985i −0.0191284 0.0110438i
\(612\) 0 0
\(613\) 15.3570 + 26.5991i 0.620264 + 1.07433i 0.989436 + 0.144968i \(0.0463080\pi\)
−0.369172 + 0.929361i \(0.620359\pi\)
\(614\) 0 0
\(615\) 2.32466 + 8.53968i 0.0937392 + 0.344353i
\(616\) 0 0
\(617\) 44.3075i 1.78375i −0.452279 0.891877i \(-0.649389\pi\)
0.452279 0.891877i \(-0.350611\pi\)
\(618\) 0 0
\(619\) 27.4026 15.8209i 1.10140 0.635895i 0.164813 0.986325i \(-0.447298\pi\)
0.936589 + 0.350430i \(0.113965\pi\)
\(620\) 0 0
\(621\) 3.40499 + 12.1267i 0.136638 + 0.486628i
\(622\) 0 0
\(623\) 2.82794 1.14494i 0.113299 0.0458711i
\(624\) 0 0
\(625\) 15.5511 26.9352i 0.622042 1.07741i
\(626\) 0 0
\(627\) 13.2764 13.3824i 0.530207 0.534443i
\(628\) 0 0
\(629\) −24.7608 −0.987279
\(630\) 0 0
\(631\) −20.7528 −0.826157 −0.413079 0.910695i \(-0.635547\pi\)
−0.413079 + 0.910695i \(0.635547\pi\)
\(632\) 0 0
\(633\) −3.57491 + 3.60347i −0.142090 + 0.143225i
\(634\) 0 0
\(635\) 9.74033 16.8707i 0.386533 0.669495i
\(636\) 0 0
\(637\) −9.21142 + 2.31082i −0.364970 + 0.0915580i
\(638\) 0 0
\(639\) −6.24732 + 0.0497150i −0.247140 + 0.00196670i
\(640\) 0 0
\(641\) 33.0033 19.0545i 1.30355 0.752606i 0.322541 0.946556i \(-0.395463\pi\)
0.981012 + 0.193949i \(0.0621298\pi\)
\(642\) 0 0
\(643\) 29.5791i 1.16648i 0.812298 + 0.583242i \(0.198216\pi\)
−0.812298 + 0.583242i \(0.801784\pi\)
\(644\) 0 0
\(645\) −14.3442 52.6939i −0.564804 2.07482i
\(646\) 0 0
\(647\) 10.5935 + 18.3485i 0.416474 + 0.721354i 0.995582 0.0938966i \(-0.0299323\pi\)
−0.579108 + 0.815251i \(0.696599\pi\)
\(648\) 0 0
\(649\) −12.1731 7.02817i −0.477838 0.275880i
\(650\) 0 0
\(651\) −12.9528 + 9.85643i −0.507659 + 0.386304i
\(652\) 0 0
\(653\) −23.0548 13.3107i −0.902204 0.520888i −0.0242893 0.999705i \(-0.507732\pi\)
−0.877915 + 0.478817i \(0.841066\pi\)
\(654\) 0 0
\(655\) 0.333399 + 0.577465i 0.0130270 + 0.0225634i
\(656\) 0 0
\(657\) 0.519203 + 0.882984i 0.0202560 + 0.0344485i
\(658\) 0 0
\(659\) 16.3864i 0.638322i −0.947701 0.319161i \(-0.896599\pi\)
0.947701 0.319161i \(-0.103401\pi\)
\(660\) 0 0
\(661\) −16.0227 + 9.25072i −0.623211 + 0.359811i −0.778118 0.628118i \(-0.783826\pi\)
0.154907 + 0.987929i \(0.450492\pi\)
\(662\) 0 0
\(663\) 3.46014 13.1221i 0.134381 0.509618i
\(664\) 0 0
\(665\) 14.6105 + 2.04260i 0.566572 + 0.0792088i
\(666\) 0 0
\(667\) 8.55284 14.8139i 0.331167 0.573598i
\(668\) 0 0
\(669\) −5.67028 5.62534i −0.219226 0.217488i
\(670\) 0 0
\(671\) 30.1125 1.16248
\(672\) 0 0
\(673\) −45.4357 −1.75142 −0.875708 0.482841i \(-0.839605\pi\)
−0.875708 + 0.482841i \(0.839605\pi\)
\(674\) 0 0
\(675\) 3.70626 14.5232i 0.142654 0.558998i
\(676\) 0 0
\(677\) −15.8566 + 27.4644i −0.609419 + 1.05554i 0.381917 + 0.924196i \(0.375264\pi\)
−0.991336 + 0.131348i \(0.958069\pi\)
\(678\) 0 0
\(679\) 26.0684 33.4159i 1.00042 1.28238i
\(680\) 0 0
\(681\) 28.8851 + 7.61670i 1.10688 + 0.291872i
\(682\) 0 0
\(683\) −31.0917 + 17.9508i −1.18969 + 0.686868i −0.958236 0.285978i \(-0.907682\pi\)
−0.231454 + 0.972846i \(0.574348\pi\)
\(684\) 0 0
\(685\) 31.0899i 1.18788i
\(686\) 0 0
\(687\) 22.3285 6.07823i 0.851886 0.231899i
\(688\) 0 0
\(689\) −4.13651 7.16465i −0.157589 0.272952i
\(690\) 0 0
\(691\) 22.2415 + 12.8411i 0.846106 + 0.488499i 0.859335 0.511413i \(-0.170878\pi\)
−0.0132293 + 0.999912i \(0.504211\pi\)
\(692\) 0 0
\(693\) 5.68012 43.1295i 0.215770 1.63835i
\(694\) 0 0
\(695\) 2.49173 + 1.43860i 0.0945167 + 0.0545692i
\(696\) 0 0
\(697\) −5.25462 9.10127i −0.199033 0.344735i
\(698\) 0 0
\(699\) −30.0868 + 8.19016i −1.13799 + 0.309780i
\(700\) 0 0
\(701\) 1.29881i 0.0490553i 0.999699 + 0.0245276i \(0.00780818\pi\)
−0.999699 + 0.0245276i \(0.992192\pi\)
\(702\) 0 0
\(703\) −7.37344 + 4.25706i −0.278095 + 0.160558i
\(704\) 0 0
\(705\) 1.89252 + 0.499036i 0.0712762 + 0.0187948i
\(706\) 0 0
\(707\) −5.37749 + 38.4646i −0.202241 + 1.44661i
\(708\) 0 0
\(709\) 13.8609 24.0077i 0.520556 0.901629i −0.479158 0.877728i \(-0.659058\pi\)
0.999714 0.0239010i \(-0.00760863\pi\)
\(710\) 0 0
\(711\) −6.21890 3.52480i −0.233227 0.132190i
\(712\) 0 0
\(713\) −8.60973 −0.322437
\(714\) 0 0
\(715\) 20.8789 0.780828
\(716\) 0 0
\(717\) −29.0801 28.8496i −1.08602 1.07741i
\(718\) 0 0
\(719\) 20.9122 36.2210i 0.779893 1.35081i −0.152109 0.988364i \(-0.548607\pi\)
0.932003 0.362451i \(-0.118060\pi\)
\(720\) 0 0
\(721\) −4.66575 11.5241i −0.173762 0.429181i
\(722\) 0 0
\(723\) −1.80304 + 6.83775i −0.0670558 + 0.254299i
\(724\) 0 0
\(725\) −17.6284 + 10.1777i −0.654701 + 0.377992i
\(726\) 0 0
\(727\) 2.19295i 0.0813319i −0.999173 0.0406660i \(-0.987052\pi\)
0.999173 0.0406660i \(-0.0129479\pi\)
\(728\) 0 0
\(729\) 0.644508 + 26.9923i 0.0238707 + 0.999715i
\(730\) 0 0
\(731\) 32.4235 + 56.1592i 1.19923 + 2.07712i
\(732\) 0 0
\(733\) 18.0850 + 10.4414i 0.667986 + 0.385662i 0.795313 0.606199i \(-0.207307\pi\)
−0.127327 + 0.991861i \(0.540640\pi\)
\(734\) 0 0
\(735\) 29.6861 16.6664i 1.09499 0.614750i
\(736\) 0 0
\(737\) −32.7731 18.9215i −1.20721 0.696984i
\(738\) 0 0
\(739\) 6.65032 + 11.5187i 0.244636 + 0.423722i 0.962029 0.272947i \(-0.0879982\pi\)
−0.717393 + 0.696668i \(0.754665\pi\)
\(740\) 0 0
\(741\) −1.22565 4.50246i −0.0450255 0.165402i
\(742\) 0 0
\(743\) 24.8226i 0.910653i 0.890324 + 0.455327i \(0.150478\pi\)
−0.890324 + 0.455327i \(0.849522\pi\)
\(744\) 0 0
\(745\) −53.5051 + 30.8912i −1.96028 + 1.13177i
\(746\) 0 0
\(747\) 0.283409 + 35.6139i 0.0103694 + 1.30305i
\(748\) 0 0
\(749\) −8.18765 20.2230i −0.299170 0.738934i
\(750\) 0 0
\(751\) 5.98635 10.3687i 0.218445 0.378358i −0.735888 0.677104i \(-0.763235\pi\)
0.954333 + 0.298746i \(0.0965682\pi\)
\(752\) 0 0
\(753\) 7.05184 7.10818i 0.256983 0.259037i
\(754\) 0 0
\(755\) −20.4063 −0.742663
\(756\) 0 0
\(757\) 29.8095 1.08345 0.541723 0.840557i \(-0.317772\pi\)
0.541723 + 0.840557i \(0.317772\pi\)
\(758\) 0 0
\(759\) 16.2065 16.3359i 0.588257 0.592957i
\(760\) 0 0
\(761\) 16.7439 29.0013i 0.606967 1.05130i −0.384770 0.923012i \(-0.625719\pi\)
0.991737 0.128286i \(-0.0409474\pi\)
\(762\) 0 0
\(763\) −3.23180 + 23.1167i −0.116999 + 0.836880i
\(764\) 0 0
\(765\) 0.387121 + 48.6467i 0.0139964 + 1.75882i
\(766\) 0 0
\(767\) −3.01333 + 1.73975i −0.108805 + 0.0628186i
\(768\) 0 0
\(769\) 19.6491i 0.708566i −0.935138 0.354283i \(-0.884725\pi\)
0.935138 0.354283i \(-0.115275\pi\)
\(770\) 0 0
\(771\) −9.53770 35.0370i −0.343492 1.26183i
\(772\) 0 0
\(773\) 6.51659 + 11.2871i 0.234385 + 0.405968i 0.959094 0.283088i \(-0.0913589\pi\)
−0.724708 + 0.689056i \(0.758026\pi\)
\(774\) 0 0
\(775\) 8.87282 + 5.12273i 0.318721 + 0.184014i
\(776\) 0 0
\(777\) −7.59197 + 18.1220i −0.272360 + 0.650122i
\(778\) 0 0
\(779\) −3.12951 1.80682i −0.112126 0.0647362i
\(780\) 0 0
\(781\) 5.70682 + 9.88451i 0.204206 + 0.353695i
\(782\) 0 0
\(783\) 25.6166 26.2355i 0.915462 0.937582i
\(784\) 0 0
\(785\) 63.8722i 2.27970i
\(786\) 0 0
\(787\) 21.1053 12.1852i 0.752324 0.434354i −0.0742091 0.997243i \(-0.523643\pi\)
0.826533 + 0.562888i \(0.190310\pi\)
\(788\) 0 0
\(789\) 2.20775 8.37256i 0.0785981 0.298071i
\(790\)