Properties

Label 168.2.u.a.89.1
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 89.1
Root \(1.22961 + 1.21986i\)
Character \(\chi\) = 168.89
Dual form 168.2.u.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67480 + 0.441628i) q^{3} +(1.40397 - 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(2.60993 - 1.47928i) q^{9} +O(q^{10})\) \(q+(-1.67480 + 0.441628i) q^{3} +(1.40397 - 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(2.60993 - 1.47928i) q^{9} +(4.74645 - 2.74036i) q^{11} +1.35669i q^{13} +(-1.27745 + 4.69274i) q^{15} +(-2.88753 - 5.00135i) q^{17} +(1.71973 + 0.992889i) q^{19} +(4.21243 + 1.80428i) q^{21} +(-2.09928 - 1.21202i) q^{23} +(-1.44228 - 2.49811i) q^{25} +(-3.71783 + 3.63012i) q^{27} +7.05668i q^{29} +(-3.07596 + 1.77591i) q^{31} +(-6.73914 + 6.68573i) q^{33} +(-6.88616 + 2.78798i) q^{35} +(-2.14377 + 3.71312i) q^{37} +(-0.599153 - 2.27219i) q^{39} +1.81976 q^{41} +11.2288 q^{43} +(0.0670332 - 8.42358i) q^{45} +(0.201213 - 0.348512i) q^{47} +(1.70327 + 6.78961i) q^{49} +(7.04478 + 7.10106i) q^{51} +(5.28097 - 3.04897i) q^{53} -15.3896i q^{55} +(-3.31870 - 0.903412i) q^{57} +(-1.28234 - 2.22108i) q^{59} +(-4.75817 - 2.74713i) q^{61} +(-7.85181 - 1.16149i) q^{63} +(3.29914 + 1.90476i) q^{65} +(3.45238 + 5.97970i) q^{67} +(4.05114 + 1.10279i) q^{69} +2.08251i q^{71} +(-0.295696 + 0.170720i) q^{73} +(3.51878 + 3.54689i) q^{75} +(-14.3610 - 2.00772i) q^{77} +(1.19139 - 2.06355i) q^{79} +(4.62347 - 7.72163i) q^{81} +11.8717 q^{83} -16.2161 q^{85} +(-3.11643 - 11.8186i) q^{87} +(0.576571 - 0.998650i) q^{89} +(2.20785 - 2.83014i) q^{91} +(4.36734 - 4.33272i) q^{93} +(4.82892 - 2.78798i) q^{95} +16.0187i q^{97} +(8.33413 - 14.1735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

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
\(3\) −1.67480 + 0.441628i −0.966948 + 0.254974i
\(4\) 0 0
\(5\) 1.40397 2.43175i 0.627876 1.08751i −0.360101 0.932913i \(-0.617258\pi\)
0.987977 0.154600i \(-0.0494089\pi\)
\(6\) 0 0
\(7\) −2.08606 1.62738i −0.788456 0.615092i
\(8\) 0 0
\(9\) 2.60993 1.47928i 0.869977 0.493093i
\(10\) 0 0
\(11\) 4.74645 2.74036i 1.43111 0.826250i 0.433902 0.900960i \(-0.357136\pi\)
0.997205 + 0.0747101i \(0.0238032\pi\)
\(12\) 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 \(-0.919703\pi\)
0.268022 0.963413i \(-0.413630\pi\)
\(18\) 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
\(21\) 4.21243 + 1.80428i 0.919228 + 0.393726i
\(22\) 0 0
\(23\) −2.09928 1.21202i −0.437730 0.252723i 0.264904 0.964275i \(-0.414660\pi\)
−0.702634 + 0.711551i \(0.747993\pi\)
\(24\) 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 −0.750113 0.661309i \(-0.770001\pi\)
0.197654 + 0.980272i \(0.436668\pi\)
\(32\) 0 0
\(33\) −6.73914 + 6.68573i −1.17313 + 1.16384i
\(34\) 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
\(39\) −0.599153 2.27219i −0.0959413 0.363842i
\(40\) 0 0
\(41\) 1.81976 0.284199 0.142100 0.989852i \(-0.454615\pi\)
0.142100 + 0.989852i \(0.454615\pi\)
\(42\) 0 0
\(43\) 11.2288 1.71238 0.856188 0.516665i \(-0.172827\pi\)
0.856188 + 0.516665i \(0.172827\pi\)
\(44\) 0 0
\(45\) 0.0670332 8.42358i 0.00999272 1.25571i
\(46\) 0 0
\(47\) 0.201213 0.348512i 0.0293500 0.0508356i −0.850977 0.525202i \(-0.823990\pi\)
0.880327 + 0.474367i \(0.157323\pi\)
\(48\) 0 0
\(49\) 1.70327 + 6.78961i 0.243325 + 0.969945i
\(50\) 0 0
\(51\) 7.04478 + 7.10106i 0.986466 + 0.994348i
\(52\) 0 0
\(53\) 5.28097 3.04897i 0.725397 0.418808i −0.0913389 0.995820i \(-0.529115\pi\)
0.816736 + 0.577012i \(0.195781\pi\)
\(54\) 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 \(-0.220058\pi\)
−0.937345 + 0.348403i \(0.886724\pi\)
\(60\) 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
\(63\) −7.85181 1.16149i −0.989235 0.146334i
\(64\) 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 \(0.0394357\pi\)
−0.992335 + 0.123574i \(0.960564\pi\)
\(72\) 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
\(75\) 3.51878 + 3.54689i 0.406313 + 0.409560i
\(76\) 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
\(81\) 4.62347 7.72163i 0.513719 0.857958i
\(82\) 0 0
\(83\) 11.8717 1.30309 0.651543 0.758611i \(-0.274122\pi\)
0.651543 + 0.758611i \(0.274122\pi\)
\(84\) 0 0
\(85\) −16.2161 −1.75888
\(86\) 0 0
\(87\) −3.11643 11.8186i −0.334116 1.26708i
\(88\) 0 0
\(89\) 0.576571 0.998650i 0.0611164 0.105857i −0.833848 0.551994i \(-0.813867\pi\)
0.894965 + 0.446137i \(0.147201\pi\)
\(90\) 0 0
\(91\) 2.20785 2.83014i 0.231446 0.296679i
\(92\) 0 0
\(93\) 4.36734 4.33272i 0.452872 0.449283i
\(94\) 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 \(0.0939712\pi\)
−0.226399 + 0.974035i \(0.572695\pi\)
\(102\) 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
\(105\) 10.3017 7.71043i 1.00534 0.752461i
\(106\) 0 0
\(107\) −7.14150 4.12315i −0.690395 0.398600i 0.113365 0.993553i \(-0.463837\pi\)
−0.803760 + 0.594954i \(0.797170\pi\)
\(108\) 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 \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 0 0
\(115\) −5.89467 + 3.40329i −0.549680 + 0.317358i
\(116\) 0 0
\(117\) 2.00693 + 3.54087i 0.185540 + 0.327354i
\(118\) 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
\(123\) −3.04775 + 0.803658i −0.274806 + 0.0724634i
\(124\) 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
\(129\) −18.8060 + 4.95895i −1.65578 + 0.436611i
\(130\) 0 0
\(131\) −0.118734 + 0.205654i −0.0103739 + 0.0179680i −0.871166 0.490989i \(-0.836635\pi\)
0.860792 + 0.508957i \(0.169969\pi\)
\(132\) 0 0
\(133\) −1.97166 4.86988i −0.170964 0.422273i
\(134\) 0 0
\(135\) 3.60782 + 14.1374i 0.310511 + 1.21676i
\(136\) 0 0
\(137\) −9.58873 + 5.53606i −0.819221 + 0.472977i −0.850148 0.526544i \(-0.823487\pi\)
0.0309270 + 0.999522i \(0.490154\pi\)
\(138\) 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
\(147\) −5.85113 10.6191i −0.482593 0.875845i
\(148\) 0 0
\(149\) −19.0549 11.0013i −1.56104 0.901266i −0.997152 0.0754127i \(-0.975973\pi\)
−0.563886 0.825853i \(-0.690694\pi\)
\(150\) 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
\(159\) −7.49807 + 7.43864i −0.594636 + 0.589923i
\(160\) 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
\(165\) 6.79646 + 25.7745i 0.529104 + 2.00654i
\(166\) 0 0
\(167\) −24.0942 −1.86447 −0.932233 0.361858i \(-0.882143\pi\)
−0.932233 + 0.361858i \(0.882143\pi\)
\(168\) 0 0
\(169\) 11.1594 0.858414
\(170\) 0 0
\(171\) 5.95715 + 0.0474059i 0.455554 + 0.00362522i
\(172\) 0 0
\(173\) 5.18802 8.98592i 0.394438 0.683187i −0.598591 0.801055i \(-0.704273\pi\)
0.993029 + 0.117868i \(0.0376059\pi\)
\(174\) 0 0
\(175\) −1.05668 + 7.55835i −0.0798778 + 0.571357i
\(176\) 0 0
\(177\) 3.12856 + 3.15356i 0.235157 + 0.237036i
\(178\) 0 0
\(179\) −11.5922 + 6.69274i −0.866439 + 0.500239i −0.866163 0.499761i \(-0.833421\pi\)
−0.000276030 1.00000i \(0.500088\pi\)
\(180\) 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
\(189\) 13.6632 1.52231i 0.993850 0.110732i
\(190\) 0 0
\(191\) 3.59492 + 2.07553i 0.260119 + 0.150180i 0.624389 0.781114i \(-0.285348\pi\)
−0.364270 + 0.931293i \(0.618681\pi\)
\(192\) 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 \(-0.956669\pi\)
0.990749 0.135709i \(-0.0433311\pi\)
\(198\) 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
\(201\) −8.42286 8.49015i −0.594103 0.598849i
\(202\) 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
\(207\) −7.27189 0.0578683i −0.505431 0.00402212i
\(208\) 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
\(213\) −0.919693 3.48779i −0.0630163 0.238979i
\(214\) 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
\(219\) 0.419838 0.416510i 0.0283700 0.0281451i
\(220\) 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 \(0.0273045\pi\)
−0.423965 + 0.905678i \(0.639362\pi\)
\(228\) 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
\(231\) 24.9385 2.97967i 1.64083 0.196048i
\(232\) 0 0
\(233\) −15.5908 9.00135i −1.02139 0.589698i −0.106882 0.994272i \(-0.534087\pi\)
−0.914505 + 0.404574i \(0.867420\pi\)
\(234\) 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 −0.381780 0.924253i \(-0.624689\pi\)
0.609537 + 0.792758i \(0.291355\pi\)
\(242\) 0 0
\(243\) −4.33332 + 14.9741i −0.277983 + 0.960586i
\(244\) 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
\(249\) −19.8827 + 5.24286i −1.26002 + 0.332253i
\(250\) 0 0
\(251\) 5.78085 0.364884 0.182442 0.983217i \(-0.441600\pi\)
0.182442 + 0.983217i \(0.441600\pi\)
\(252\) 0 0
\(253\) −13.2855 −0.835251
\(254\) 0 0
\(255\) 27.1587 7.16146i 1.70075 0.448468i
\(256\) 0 0
\(257\) 10.4824 18.1560i 0.653871 1.13254i −0.328304 0.944572i \(-0.606477\pi\)
0.982175 0.187966i \(-0.0601896\pi\)
\(258\) 0 0
\(259\) 10.5147 4.25706i 0.653351 0.264521i
\(260\) 0 0
\(261\) 10.4388 + 18.4175i 0.646145 + 1.14001i
\(262\) 0 0
\(263\) 4.32937 2.49957i 0.266961 0.154130i −0.360545 0.932742i \(-0.617409\pi\)
0.627506 + 0.778612i \(0.284076\pi\)
\(264\) 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 \(-0.321697\pi\)
−0.999332 + 0.0365470i \(0.988364\pi\)
\(270\) 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
\(273\) −2.44785 + 5.71498i −0.148151 + 0.345886i
\(274\) 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 \(-0.818320\pi\)
0.841488 0.540276i \(-0.181680\pi\)
\(282\) 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
\(285\) −6.85625 + 6.80190i −0.406129 + 0.402910i
\(286\) 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
\(291\) −7.07428 26.8281i −0.414702 1.57269i
\(292\) 0 0
\(293\) −9.38786 −0.548445 −0.274222 0.961666i \(-0.588420\pi\)
−0.274222 + 0.961666i \(0.588420\pi\)
\(294\) 0 0
\(295\) −7.20151 −0.419288
\(296\) 0 0
\(297\) −7.69864 + 27.4183i −0.446720 + 1.59097i
\(298\) 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
\(303\) −17.9071 18.0502i −1.02874 1.03696i
\(304\) 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 \(0.0294546\pi\)
−0.417838 + 0.908522i \(0.637212\pi\)
\(312\) 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
\(315\) −13.8482 + 17.4630i −0.780257 + 0.983927i
\(316\) 0 0
\(317\) 9.81412 + 5.66618i 0.551216 + 0.318245i 0.749612 0.661877i \(-0.230240\pi\)
−0.198396 + 0.980122i \(0.563573\pi\)
\(318\) 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
\(327\) 10.7619 + 10.8479i 0.595136 + 0.599891i
\(328\) 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
\(333\) −0.102355 + 12.8622i −0.00560903 + 0.704846i
\(334\) 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
\(339\) −1.76651 6.69921i −0.0959437 0.363851i
\(340\) 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
\(345\) 8.36942 8.30308i 0.450594 0.447023i
\(346\) 0 0
\(347\) −15.6525 + 9.03697i −0.840270 + 0.485130i −0.857356 0.514724i \(-0.827894\pi\)
0.0170860 + 0.999854i \(0.494561\pi\)
\(348\) 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 \(0.0919140\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(354\) 0 0
\(355\) 5.06415 + 2.92379i 0.268777 + 0.155178i
\(356\) 0 0
\(357\) −3.13969 26.2778i −0.166170 1.39077i
\(358\) 0 0
\(359\) −0.773273 0.446450i −0.0408118 0.0235627i 0.479455 0.877566i \(-0.340834\pi\)
−0.520267 + 0.854004i \(0.674168\pi\)
\(360\) 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
\(369\) 4.74946 2.69194i 0.247247 0.140137i
\(370\) 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
\(375\) −9.94836 + 2.62328i −0.513731 + 0.135465i
\(376\) 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
\(381\) 11.6193 3.06387i 0.595273 0.156967i
\(382\) 0 0
\(383\) −11.5139 + 19.9426i −0.588331 + 1.01902i 0.406120 + 0.913820i \(0.366881\pi\)
−0.994451 + 0.105200i \(0.966452\pi\)
\(384\) 0 0
\(385\) −25.0447 + 32.1036i −1.27640 + 1.63615i
\(386\) 0 0
\(387\) 29.3064 16.6105i 1.48973 0.844360i
\(388\) 0 0
\(389\) −5.45545 + 3.14970i −0.276602 + 0.159696i −0.631884 0.775063i \(-0.717718\pi\)
0.355282 + 0.934759i \(0.384385\pi\)
\(390\) 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
\(399\) 5.45281 + 7.28536i 0.272982 + 0.364724i
\(400\) 0 0
\(401\) −11.8188 6.82360i −0.590204 0.340755i 0.174974 0.984573i \(-0.444016\pi\)
−0.765178 + 0.643819i \(0.777349\pi\)
\(402\) 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
\(411\) 13.6144 13.5065i 0.671547 0.666224i
\(412\) 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
\(417\) 0.452519 + 1.71611i 0.0221600 + 0.0840382i
\(418\) 0 0
\(419\) 6.94914 0.339488 0.169744 0.985488i \(-0.445706\pi\)
0.169744 + 0.985488i \(0.445706\pi\)
\(420\) 0 0
\(421\) −0.349861 −0.0170512 −0.00852560 0.999964i \(-0.502714\pi\)
−0.00852560 + 0.999964i \(0.502714\pi\)
\(422\) 0 0
\(423\) 0.00960700 1.20724i 0.000467108 0.0586981i
\(424\) 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
\(429\) −9.07048 9.14295i −0.437927 0.441426i
\(430\) 0 0
\(431\) −17.4513 + 10.0755i −0.840601 + 0.485321i −0.857468 0.514537i \(-0.827964\pi\)
0.0168676 + 0.999858i \(0.494631\pi\)
\(432\) 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
\(441\) 14.4892 + 15.2008i 0.689960 + 0.723848i
\(442\) 0 0
\(443\) 11.1751 + 6.45195i 0.530945 + 0.306541i 0.741401 0.671062i \(-0.234162\pi\)
−0.210456 + 0.977603i \(0.567495\pi\)
\(444\) 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
\(453\) −8.86517 8.93600i −0.416522 0.419850i
\(454\) 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
\(459\) 28.8908 + 8.11209i 1.34851 + 0.378640i
\(460\) 0 0
\(461\) −2.83467 −0.132024 −0.0660120 0.997819i \(-0.521028\pi\)
−0.0660120 + 0.997819i \(0.521028\pi\)
\(462\) 0 0
\(463\) 14.1594 0.658042 0.329021 0.944323i \(-0.393281\pi\)
0.329021 + 0.944323i \(0.393281\pi\)
\(464\) 0 0
\(465\) −4.40449 16.7033i −0.204253 0.774598i
\(466\) 0 0
\(467\) 4.98809 8.63963i 0.230821 0.399794i −0.727229 0.686395i \(-0.759192\pi\)
0.958050 + 0.286601i \(0.0925254\pi\)
\(468\) 0 0
\(469\) 2.52937 18.0923i 0.116796 0.835426i
\(470\) 0 0
\(471\) −27.9698 + 27.7481i −1.28878 + 1.27857i
\(472\) 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 \(-0.701190\pi\)
−0.403320 0.915059i \(-0.632144\pi\)
\(480\) 0 0
\(481\) −5.03757 2.90844i −0.229693 0.132614i
\(482\) 0 0
\(483\) −6.65625 8.89323i −0.302870 0.404656i
\(484\) 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 \(0.166871\pi\)
−0.865704 + 0.500556i \(0.833129\pi\)
\(492\) 0 0
\(493\) 35.2929 20.3764i 1.58951 0.917707i
\(494\) 0 0
\(495\) −22.7655 40.1657i −1.02323 1.80532i
\(496\) 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
\(501\) 40.3531 10.6407i 1.80284 0.475390i
\(502\) 0 0
\(503\) 8.55884 0.381620 0.190810 0.981627i \(-0.438889\pi\)
0.190810 + 0.981627i \(0.438889\pi\)
\(504\) 0 0
\(505\) 41.2196 1.83425
\(506\) 0 0
\(507\) −18.6898 + 4.92829i −0.830042 + 0.218873i
\(508\) 0 0
\(509\) −14.1072 + 24.4345i −0.625292 + 1.08304i 0.363192 + 0.931714i \(0.381687\pi\)
−0.988484 + 0.151324i \(0.951646\pi\)
\(510\) 0 0
\(511\) 0.894665 + 0.125077i 0.0395777 + 0.00553310i
\(512\) 0 0
\(513\) −9.99798 + 2.55144i −0.441422 + 0.112649i
\(514\) 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 \(-0.295685\pi\)
−0.993014 + 0.118001i \(0.962352\pi\)
\(522\) 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
\(525\) −1.56824 13.1254i −0.0684434 0.572839i
\(526\) 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
\(537\) 16.4589 16.3284i 0.710254 0.704624i
\(538\) 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
\(543\) −8.14094 30.8732i −0.349361 1.32490i
\(544\) 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
\(549\) −16.4823 0.131163i −0.703446 0.00559789i
\(550\) 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
\(555\) −14.6862 14.8035i −0.623393 0.628374i
\(556\) 0 0
\(557\) −15.4816 + 8.93830i −0.655976 + 0.378728i −0.790742 0.612150i \(-0.790305\pi\)
0.134766 + 0.990877i \(0.456972\pi\)
\(558\) 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 \(-0.148326\pi\)
−0.835794 + 0.549043i \(0.814992\pi\)
\(564\) 0 0
\(565\) 9.72702 + 5.61589i 0.409219 + 0.236262i
\(566\) 0 0
\(567\) −22.2108 + 8.58361i −0.932768 + 0.360478i
\(568\) 0 0
\(569\) 1.72971 + 0.998650i 0.0725133 + 0.0418656i 0.535818 0.844333i \(-0.320003\pi\)
−0.463305 + 0.886199i \(0.653337\pi\)
\(570\) 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
\(579\) 23.7986 + 23.9887i 0.989036 + 0.996938i
\(580\) 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
\(585\) 11.4282 + 0.0909435i 0.472498 + 0.00376005i
\(586\) 0 0
\(587\) −34.4645 −1.42250 −0.711251 0.702939i \(-0.751871\pi\)
−0.711251 + 0.702939i \(0.751871\pi\)
\(588\) 0 0
\(589\) −7.05312 −0.290619
\(590\) 0 0
\(591\) 1.68239 + 6.38020i 0.0692043 + 0.262446i
\(592\) 0 0
\(593\) 3.62199 6.27347i 0.148737 0.257620i −0.782024 0.623249i \(-0.785812\pi\)
0.930761 + 0.365628i \(0.119146\pi\)
\(594\) 0 0
\(595\) 33.8277 + 26.3897i 1.38680 + 1.08187i
\(596\) 0 0
\(597\) 7.52974 7.47006i 0.308172 0.305729i
\(598\) 0 0
\(599\) 32.5464 18.7907i 1.32981 0.767766i 0.344540 0.938772i \(-0.388035\pi\)
0.985270 + 0.171005i \(0.0547015\pi\)
\(600\) 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
\(609\) −12.7322 + 29.7258i −0.515936 + 1.20455i
\(610\) 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 \(0.350611\pi\)
−0.452279 + 0.891877i \(0.649389\pi\)
\(618\) 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
\(621\) 12.2045 3.11455i 0.489751 0.124982i
\(622\) 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
\(627\) −18.2277 + 4.80645i −0.727945 + 0.191951i
\(628\) 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
\(633\) −4.90815 + 1.29423i −0.195082 + 0.0514409i
\(634\) 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
\(639\) 3.08061 + 5.43520i 0.121867 + 0.215013i
\(640\) 0 0
\(641\) −33.0033 + 19.0545i −1.30355 + 0.752606i −0.981012 0.193949i \(-0.937870\pi\)
−0.322541 + 0.946556i \(0.604537\pi\)
\(642\) 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 0.579108 0.815251i \(-0.303401\pi\)
−0.995582 + 0.0938966i \(0.970068\pi\)
\(648\) 0 0
\(649\) −12.1731 7.02817i −0.477838 0.275880i
\(650\) 0 0
\(651\) −16.1615 + 1.93099i −0.633419 + 0.0756816i
\(652\) 0 0
\(653\) 23.0548 + 13.3107i 0.902204 + 0.520888i 0.877915 0.478817i \(-0.158934\pi\)
0.0242893 + 0.999705i \(0.492268\pi\)
\(654\) 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 −0.778118 0.628118i \(-0.783826\pi\)
0.154907 + 0.987929i \(0.450492\pi\)
\(662\) 0 0
\(663\) −9.63396 + 9.55760i −0.374152 + 0.371186i
\(664\) 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
\(669\) −2.03654 7.72327i −0.0787373 0.298599i
\(670\) 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
\(675\) 14.4306 + 4.05189i 0.555434 + 0.155957i
\(676\) 0 0
\(677\) 15.8566 27.4644i 0.609419 1.05554i −0.381917 0.924196i \(-0.624736\pi\)
0.991336 0.131348i \(-0.0419305\pi\)
\(678\) 0 0
\(679\) 26.0684 33.4159i 1.00042 1.28238i
\(680\) 0 0
\(681\) −21.0388 21.2069i −0.806209 0.812650i
\(682\) 0 0
\(683\) 31.0917 17.9508i 1.18969 0.686868i 0.231454 0.972846i \(-0.425652\pi\)
0.958236 + 0.285978i \(0.0923183\pi\)
\(684\) 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
\(693\) −40.4511 + 16.0039i −1.53661 + 0.607937i
\(694\) 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
\(705\) 1.37844 + 1.38945i 0.0519149 + 0.0523296i
\(706\) 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
\(711\) 0.0568835 7.14813i 0.00213330 0.268076i
\(712\) 0 0
\(713\) 8.60973 0.322437
\(714\) 0 0
\(715\) 20.8789 0.780828
\(716\) 0 0
\(717\) 10.4444 + 39.6089i 0.390055 + 1.47922i
\(718\) 0 0
\(719\) −20.9122 + 36.2210i −0.779893 + 1.35081i 0.152109 + 0.988364i \(0.451393\pi\)
−0.932003 + 0.362451i \(0.881940\pi\)
\(720\) 0 0
\(721\) −4.66575 11.5241i −0.173762 0.429181i
\(722\) 0 0
\(723\) −5.02015 + 4.98036i −0.186701 + 0.185221i
\(724\) 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
\(735\) −34.0378 0.680374i −1.25550 0.0250960i
\(736\) 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 \(-0.849522\pi\)
0.890324 0.455327i \(-0.150478\pi\)
\(744\) 0 0
\(745\) −53.5051 + 30.8912i −1.96028 + 1.13177i
\(746\) 0 0
\(747\) 30.9843 17.5615i 1.13366 0.642543i
\(748\) 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
\(753\) −9.68179 + 2.55298i −0.352824 + 0.0930359i
\(754\) 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
\(759\) 22.2506 5.86723i 0.807644 0.212967i
\(760\) 0 0
\(761\) −16.7439 + 29.0013i −0.606967 + 1.05130i 0.384770 + 0.923012i \(0.374281\pi\)
−0.991737 + 0.128286i \(0.959053\pi\)
\(762\) 0 0
\(763\) −3.23180 + 23.1167i −0.116999 + 0.836880i
\(764\) 0 0
\(765\) −42.3228 + 23.9881i −1.53018 + 0.867291i
\(766\) 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 0.724708 0.689056i \(-0.241974\pi\)
−0.959094 + 0.283088i \(0.908641\pi\)
\(774\) 0 0
\(775\) 8.87282 + 5.12273i 0.318721 + 0.184014i
\(776\) 0 0
\(777\) −15.7300 + 11.7733i −0.564311 + 0.422365i
\(778\) 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
\(789\) −6.14697 + 6.09825i −0.218838 + 0.217103i
\(790\)