Properties

Label 168.2.u.a.17.3
Level 168
Weight 2
Character 168.17
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 17.3
Root \(-0.441628 + 1.67480i\) 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 \(\chi\) \(=\) 168.17
Dual form 168.2.u.a.89.3

$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

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

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 −0.987977 0.154600i \(-0.950591\pi\)
0.360101 0.932913i \(-0.382742\pi\)
\(6\) 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 −0.433902 0.900960i \(-0.642864\pi\)
−0.997205 + 0.0747101i \(0.976197\pi\)
\(12\) 0 0
\(13\) 1.35669i 0.376279i −0.982142 0.188139i \(-0.939754\pi\)
0.982142 0.188139i \(-0.0602457\pi\)
\(14\) 0 0
\(15\) −1.27745 + 4.69274i −0.329836 + 1.21166i
\(16\) 0 0
\(17\) 2.88753 5.00135i 0.700329 1.21301i −0.268022 0.963413i \(-0.586370\pi\)
0.968351 0.249593i \(-0.0802967\pi\)
\(18\) 0 0
\(19\) 1.71973 0.992889i 0.394534 0.227784i −0.289589 0.957151i \(-0.593519\pi\)
0.684123 + 0.729367i \(0.260185\pi\)
\(20\) 0 0
\(21\) 4.54574 + 0.579855i 0.991962 + 0.126535i
\(22\) 0 0
\(23\) 2.09928 1.21202i 0.437730 0.252723i −0.264904 0.964275i \(-0.585340\pi\)
0.702634 + 0.711551i \(0.252007\pi\)
\(24\) 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 \(0.227414\pi\)
−0.755458 + 0.655197i \(0.772586\pi\)
\(30\) 0 0
\(31\) −3.07596 1.77591i −0.552459 0.318962i 0.197654 0.980272i \(-0.436668\pi\)
−0.750113 + 0.661309i \(0.770001\pi\)
\(32\) 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 0.634241 0.773135i \(-0.281313\pi\)
−0.986675 + 0.162701i \(0.947979\pi\)
\(38\) 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 0.850977 0.525202i \(-0.176010\pi\)
−0.880327 + 0.474367i \(0.842677\pi\)
\(48\) 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 0.0913389 0.995820i \(-0.470885\pi\)
−0.816736 + 0.577012i \(0.804219\pi\)
\(54\) 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 −0.770398 0.637563i \(-0.779942\pi\)
0.937345 + 0.348403i \(0.113276\pi\)
\(60\) 0 0
\(61\) −4.75817 + 2.74713i −0.609222 + 0.351734i −0.772661 0.634819i \(-0.781075\pi\)
0.163439 + 0.986553i \(0.447741\pi\)
\(62\) 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 −0.574338 0.818618i \(-0.694740\pi\)
0.996113 + 0.0880819i \(0.0280737\pi\)
\(68\) 0 0
\(69\) −4.05114 1.10279i −0.487700 0.132761i
\(70\) 0 0
\(71\) 2.08251i 0.247148i 0.992335 + 0.123574i \(0.0394357\pi\)
−0.992335 + 0.123574i \(0.960564\pi\)
\(72\) 0 0
\(73\) −0.295696 0.170720i −0.0346086 0.0199813i 0.482596 0.875843i \(-0.339694\pi\)
−0.517204 + 0.855862i \(0.673027\pi\)
\(74\) 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 0.925231 0.379404i \(-0.123871\pi\)
−0.791189 + 0.611572i \(0.790538\pi\)
\(80\) 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 0.833848 0.551994i \(-0.186133\pi\)
−0.894965 + 0.446137i \(0.852799\pi\)
\(90\) 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 \(-0.697710\pi\)
0.581950 0.813225i \(-0.302290\pi\)
\(98\) 0 0
\(99\) 8.33413 14.1735i 0.837612 1.42449i
\(100\) 0 0
\(101\) −7.33982 + 12.7129i −0.730339 + 1.26498i 0.226399 + 0.974035i \(0.427305\pi\)
−0.956738 + 0.290950i \(0.906029\pi\)
\(102\) 0 0
\(103\) 4.06960 2.34958i 0.400989 0.231511i −0.285922 0.958253i \(-0.592300\pi\)
0.686911 + 0.726742i \(0.258966\pi\)
\(104\) 0 0
\(105\) −4.97204 11.8682i −0.485221 1.15822i
\(106\) 0 0
\(107\) 7.14150 4.12315i 0.690395 0.398600i −0.113365 0.993553i \(-0.536163\pi\)
0.803760 + 0.594954i \(0.202830\pi\)
\(108\) 0 0
\(109\) −4.41113 + 7.64030i −0.422509 + 0.731808i −0.996184 0.0872755i \(-0.972184\pi\)
0.573675 + 0.819083i \(0.305517\pi\)
\(110\) 0 0
\(111\) −1.95058 + 7.16550i −0.185141 + 0.680119i
\(112\) 0 0
\(113\) 4.00000i 0.376288i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 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 0.871166 0.490989i \(-0.163365\pi\)
−0.860792 + 0.508957i \(0.830031\pi\)
\(132\) 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 0.850148 0.526544i \(-0.176513\pi\)
−0.0309270 + 0.999522i \(0.509846\pi\)
\(138\) 0 0
\(139\) 1.02466i 0.0869108i 0.999055 + 0.0434554i \(0.0138366\pi\)
−0.999055 + 0.0434554i \(0.986163\pi\)
\(140\) 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 0.563886 0.825853i \(-0.309306\pi\)
0.997152 0.0754127i \(-0.0240274\pi\)
\(150\) 0 0
\(151\) 3.63368 6.29371i 0.295704 0.512175i −0.679444 0.733727i \(-0.737779\pi\)
0.975149 + 0.221552i \(0.0711123\pi\)
\(152\) 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 0.995901 + 0.0904525i \(0.0288313\pi\)
0.576285 + 0.817249i \(0.304502\pi\)
\(158\) 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 −0.964795 0.263003i \(-0.915287\pi\)
0.254630 0.967039i \(-0.418046\pi\)
\(164\) 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 0.598591 0.801055i \(-0.295727\pi\)
−0.993029 + 0.117868i \(0.962394\pi\)
\(174\) 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 0.866163 0.499761i \(-0.166579\pi\)
0.000276030 1.00000i \(0.499912\pi\)
\(180\) 0 0
\(181\) 18.4339i 1.37018i −0.728457 0.685092i \(-0.759762\pi\)
0.728457 0.685092i \(-0.240238\pi\)
\(182\) 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 −0.624389 0.781114i \(-0.714652\pi\)
0.364270 + 0.931293i \(0.381319\pi\)
\(192\) 0 0
\(193\) −9.75462 + 16.8955i −0.702153 + 1.21616i 0.265556 + 0.964095i \(0.414444\pi\)
−0.967709 + 0.252069i \(0.918889\pi\)
\(194\) 0 0
\(195\) 6.36661 + 1.73311i 0.455922 + 0.124110i
\(196\) 0 0
\(197\) 3.80952i 0.271417i −0.990749 0.135709i \(-0.956669\pi\)
0.990749 0.135709i \(-0.0433311\pi\)
\(198\) 0 0
\(199\) −5.30327 3.06185i −0.375939 0.217049i 0.300111 0.953904i \(-0.402976\pi\)
−0.676050 + 0.736856i \(0.736310\pi\)
\(200\) 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 \(-0.950655\pi\)
0.988008 0.154403i \(-0.0493454\pi\)
\(224\) 0 0
\(225\) −7.45966 4.38635i −0.497311 0.292424i
\(226\) 0 0
\(227\) −8.62344 + 14.9362i −0.572358 + 0.991353i 0.423965 + 0.905678i \(0.360638\pi\)
−0.996323 + 0.0856745i \(0.972695\pi\)
\(228\) 0 0
\(229\) −11.5705 + 6.68024i −0.764601 + 0.441443i −0.830945 0.556354i \(-0.812200\pi\)
0.0663443 + 0.997797i \(0.478866\pi\)
\(230\) 0 0
\(231\) −19.9871 15.2092i −1.31505 1.00069i
\(232\) 0 0
\(233\) 15.5908 9.00135i 1.02139 0.589698i 0.106882 0.994272i \(-0.465913\pi\)
0.914505 + 0.404574i \(0.132580\pi\)
\(234\) 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 \(-0.722792\pi\)
0.644158 0.764893i \(-0.277208\pi\)
\(240\) 0 0
\(241\) 3.53574 + 2.04136i 0.227757 + 0.131496i 0.609537 0.792758i \(-0.291355\pi\)
−0.381780 + 0.924253i \(0.624689\pi\)
\(242\) 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 −0.982175 0.187966i \(-0.939810\pi\)
0.328304 0.944572i \(-0.393523\pi\)
\(258\) 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 0.360545 0.932742i \(-0.382591\pi\)
−0.627506 + 0.778612i \(0.715924\pi\)
\(264\) 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 −0.531317 0.847173i \(-0.678303\pi\)
0.999332 + 0.0365470i \(0.0116359\pi\)
\(270\) 0 0
\(271\) 14.4761 8.35779i 0.879362 0.507700i 0.00891391 0.999960i \(-0.497163\pi\)
0.870448 + 0.492260i \(0.163829\pi\)
\(272\) 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 −0.299689 0.954037i \(-0.596883\pi\)
0.976065 0.217481i \(-0.0697839\pi\)
\(278\) 0 0
\(279\) 5.40098 9.18520i 0.323348 0.549903i
\(280\) 0 0
\(281\) 18.1134i 1.08055i −0.841488 0.540276i \(-0.818320\pi\)
0.841488 0.540276i \(-0.181680\pi\)
\(282\) 0 0
\(283\) −5.00728 2.89095i −0.297652 0.171849i 0.343736 0.939066i \(-0.388308\pi\)
−0.641388 + 0.767217i \(0.721641\pi\)
\(284\) 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 \(0.190692\pi\)
−0.825857 + 0.563880i \(0.809308\pi\)
\(308\) 0 0
\(309\) −7.85341 2.13784i −0.446765 0.121618i
\(310\) 0 0
\(311\) −10.1911 + 17.6515i −0.577884 + 1.00092i 0.417838 + 0.908522i \(0.362788\pi\)
−0.995722 + 0.0924025i \(0.970545\pi\)
\(312\) 0 0
\(313\) 6.19972 3.57941i 0.350429 0.202320i −0.314445 0.949276i \(-0.601818\pi\)
0.664874 + 0.746955i \(0.268485\pi\)
\(314\) 0 0
\(315\) −8.52807 + 20.5913i −0.480502 + 1.16019i
\(316\) 0 0
\(317\) −9.81412 + 5.66618i −0.551216 + 0.318245i −0.749612 0.661877i \(-0.769760\pi\)
0.198396 + 0.980122i \(0.436427\pi\)
\(318\) 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 0.999795 + 0.0202456i \(0.00644480\pi\)
−0.482364 + 0.875971i \(0.660222\pi\)
\(332\) 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 0.857356 0.514724i \(-0.172106\pi\)
−0.0170860 + 0.999854i \(0.505439\pi\)
\(348\) 0 0
\(349\) 12.8624i 0.688510i 0.938876 + 0.344255i \(0.111868\pi\)
−0.938876 + 0.344255i \(0.888132\pi\)
\(350\) 0 0
\(351\) −4.92495 5.04395i −0.262875 0.269226i
\(352\) 0 0
\(353\) −13.6386 + 23.6227i −0.725909 + 1.25731i 0.232690 + 0.972551i \(0.425247\pi\)
−0.958599 + 0.284760i \(0.908086\pi\)
\(354\) 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 −0.479455 0.877566i \(-0.659166\pi\)
0.520267 + 0.854004i \(0.325832\pi\)
\(360\) 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 0.228850 0.973462i \(-0.426504\pi\)
−0.728618 + 0.684921i \(0.759837\pi\)
\(368\) 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 −0.993108 0.117201i \(-0.962608\pi\)
0.395055 0.918657i \(-0.370725\pi\)
\(374\) 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 0.994451 + 0.105200i \(0.0335482\pi\)
−0.406120 + 0.913820i \(0.633119\pi\)
\(384\) 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 0.631884 0.775063i \(-0.282282\pi\)
−0.355282 + 0.934759i \(0.615615\pi\)
\(390\) 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 −0.334077 0.942546i \(-0.608424\pi\)
0.649230 + 0.760592i \(0.275091\pi\)
\(398\) 0 0
\(399\) 8.39320 3.51622i 0.420186 0.176031i
\(400\) 0 0
\(401\) 11.8188 6.82360i 0.590204 0.340755i −0.174974 0.984573i \(-0.555984\pi\)
0.765178 + 0.643819i \(0.222651\pi\)
\(402\) 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 0.175148 0.984542i \(-0.443959\pi\)
−0.765064 + 0.643954i \(0.777293\pi\)
\(410\) 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 0.857468 0.514537i \(-0.172036\pi\)
−0.0168676 + 0.999858i \(0.505369\pi\)
\(432\) 0 0
\(433\) 1.42453i 0.0684585i −0.999414 0.0342292i \(-0.989102\pi\)
0.999414 0.0342292i \(-0.0108976\pi\)
\(434\) 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 −0.457279 0.889323i \(-0.651176\pi\)
0.541537 + 0.840677i \(0.317843\pi\)
\(440\) 0 0
\(441\) 20.3275 + 5.27174i 0.967978 + 0.251035i
\(442\) 0 0
\(443\) −11.1751 + 6.45195i −0.530945 + 0.306541i −0.741401 0.671062i \(-0.765838\pi\)
0.210456 + 0.977603i \(0.432505\pi\)
\(444\) 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 \(-0.981254\pi\)
0.998266 0.0588572i \(-0.0187457\pi\)
\(450\) 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 0.642865 0.765979i \(-0.277746\pi\)
−0.984790 + 0.173748i \(0.944412\pi\)
\(458\) 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 0.727229 0.686395i \(-0.240808\pi\)
−0.958050 + 0.286601i \(0.907475\pi\)
\(468\) 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 0.403320 0.915059i \(-0.367856\pi\)
0.590805 0.806815i \(-0.298810\pi\)
\(480\) 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 0.0463476 + 0.998925i \(0.485242\pi\)
−0.888269 + 0.459324i \(0.848092\pi\)
\(488\) 0 0
\(489\) −8.24970 + 30.3055i −0.373064 + 1.37046i
\(490\) 0 0
\(491\) 22.1831i 1.00111i 0.865704 + 0.500556i \(0.166871\pi\)
−0.865704 + 0.500556i \(0.833129\pi\)
\(492\) 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 0.616845 0.787085i \(-0.288411\pi\)
−0.990058 + 0.140661i \(0.955077\pi\)
\(500\) 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 0.988484 + 0.151324i \(0.0483536\pi\)
−0.363192 + 0.931714i \(0.618313\pi\)
\(510\) 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 −0.598698 0.800975i \(-0.704315\pi\)
0.993014 + 0.118001i \(0.0376485\pi\)
\(522\) 0 0
\(523\) −11.9049 + 6.87332i −0.520567 + 0.300549i −0.737167 0.675711i \(-0.763837\pi\)
0.216600 + 0.976260i \(0.430503\pi\)
\(524\) 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 −0.886626 0.462488i \(-0.846957\pi\)
0.0427866 0.999084i \(-0.486376\pi\)
\(542\) 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 0.790742 0.612150i \(-0.209695\pi\)
−0.134766 + 0.990877i \(0.543028\pi\)
\(558\) 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 −0.893382 0.449297i \(-0.851674\pi\)
0.835794 + 0.549043i \(0.185008\pi\)
\(564\) 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 −0.535818 0.844333i \(-0.679997\pi\)
0.463305 + 0.886199i \(0.346663\pi\)
\(570\) 0 0
\(571\) 1.00728 1.74466i 0.0421534 0.0730118i −0.844179 0.536061i \(-0.819912\pi\)
0.886332 + 0.463050i \(0.153245\pi\)
\(572\) 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 −0.0341199 0.999418i \(-0.510863\pi\)
−0.882581 + 0.470160i \(0.844196\pi\)
\(578\) 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 0.782024 0.623249i \(-0.214188\pi\)
−0.930761 + 0.365628i \(0.880854\pi\)
\(594\) 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 −0.344540 0.938772i \(-0.611965\pi\)
−0.985270 + 0.171005i \(0.945299\pi\)
\(600\) 0 0
\(601\) 3.78103i 0.154232i 0.997022 + 0.0771158i \(0.0245711\pi\)
−0.997022 + 0.0771158i \(0.975429\pi\)
\(602\) 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 −0.900928 0.433968i \(-0.857113\pi\)
−0.0746364 + 0.997211i \(0.523780\pi\)
\(608\) 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 −0.369172 0.929361i \(-0.620359\pi\)
0.989436 0.144968i \(-0.0463080\pi\)
\(614\) 0 0
\(615\) 2.32466 8.53968i 0.0937392 0.344353i
\(616\) 0 0
\(617\) 44.3075i 1.78375i 0.452279 + 0.891877i \(0.350611\pi\)
−0.452279 + 0.891877i \(0.649389\pi\)
\(618\) 0 0
\(619\) 27.4026 + 15.8209i 1.10140 + 0.635895i 0.936589 0.350430i \(-0.113965\pi\)
0.164813 + 0.986325i \(0.447298\pi\)
\(620\) 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 0.981012 0.193949i \(-0.0621298\pi\)
0.322541 + 0.946556i \(0.395463\pi\)
\(642\) 0 0
\(643\) 29.5791i 1.16648i −0.812298 0.583242i \(-0.801784\pi\)
0.812298 0.583242i \(-0.198216\pi\)
\(644\) 0 0
\(645\) −14.3442 + 52.6939i −0.564804 + 2.07482i
\(646\) 0 0
\(647\) 10.5935 18.3485i 0.416474 0.721354i −0.579108 0.815251i \(-0.696599\pi\)
0.995582 + 0.0938966i \(0.0299323\pi\)
\(648\) 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 −0.877915 0.478817i \(-0.841066\pi\)
−0.0242893 + 0.999705i \(0.507732\pi\)
\(654\) 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 \(0.103401\pi\)
−0.947701 + 0.319161i \(0.896599\pi\)
\(660\) 0 0
\(661\) −16.0227 9.25072i −0.623211 0.359811i 0.154907 0.987929i \(-0.450492\pi\)
−0.778118 + 0.628118i \(0.783826\pi\)
\(662\) 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 −0.991336 0.131348i \(-0.958069\pi\)
0.381917 0.924196i \(-0.375264\pi\)
\(678\) 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 −0.231454 0.972846i \(-0.574348\pi\)
−0.958236 + 0.285978i \(0.907682\pi\)
\(684\) 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 −0.0132293 0.999912i \(-0.504211\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(692\) 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 \(-0.992192\pi\)
0.999699 0.0245276i \(-0.00780818\pi\)
\(702\) 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 0.999714 + 0.0239010i \(0.00760863\pi\)
−0.479158 + 0.877728i \(0.659058\pi\)
\(710\) 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 0.932003 + 0.362451i \(0.118060\pi\)
−0.152109 + 0.988364i \(0.548607\pi\)
\(720\) 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 \(0.0129479\pi\)
−0.999173 + 0.0406660i \(0.987052\pi\)
\(728\) 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 −0.127327 0.991861i \(-0.540640\pi\)
0.795313 + 0.606199i \(0.207307\pi\)
\(734\) 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 −0.717393 0.696668i \(-0.754665\pi\)
0.962029 + 0.272947i \(0.0879982\pi\)
\(740\) 0 0
\(741\) −1.22565 + 4.50246i −0.0450255 + 0.165402i
\(742\) 0 0
\(743\) 24.8226i 0.910653i −0.890324 0.455327i \(-0.849522\pi\)
0.890324 0.455327i \(-0.150478\pi\)
\(744\) 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 0.954333 0.298746i \(-0.0965682\pi\)
−0.735888 + 0.677104i \(0.763235\pi\)
\(752\) 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 0.991737 + 0.128286i \(0.0409474\pi\)
−0.384770 + 0.923012i \(0.625719\pi\)
\(762\) 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 \(0.115275\pi\)
−0.935138 + 0.354283i \(0.884725\pi\)
\(770\) 0 0
\(771\) −9.53770 + 35.0370i −0.343492 + 1.26183i
\(772\) 0 0
\(773\) 6.51659 11.2871i 0.234385 0.405968i −0.724708 0.689056i \(-0.758026\pi\)
0.959094 + 0.283088i \(0.0913589\pi\)
\(774\) 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 0.826533 0.562888i \(-0.190310\pi\)
−0.0742091 + 0.997243i \(0.523643\pi\)
\(788\) 0 0
\(789\) 2.20775 + 8.37256i 0.0785981 + 0.298071i