Properties

Label 336.2.bc.f.17.8
Level 336
Weight 2
Character 336.17
Analytic conductor 2.683
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
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: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.8
Root \(-0.441628 + 1.67480i\)
Character \(\chi\) = 336.17
Dual form 336.2.bc.f.257.8

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0.987977 + 0.154600i \(0.0494089\pi\)
−0.360101 + 0.932913i \(0.617258\pi\)
\(6\) 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 \(-0.642864\pi\)
−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 \(0.413630\pi\)
−0.968351 + 0.249593i \(0.919703\pi\)
\(18\) 0 0
\(19\) −1.71973 + 0.992889i −0.394534 + 0.227784i −0.684123 0.729367i \(-0.739815\pi\)
0.289589 + 0.957151i \(0.406481\pi\)
\(20\) 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 \(-0.585340\pi\)
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 \(-0.772586\pi\)
0.755458 0.655197i \(-0.227414\pi\)
\(30\) 0 0
\(31\) 3.07596 + 1.77591i 0.552459 + 0.318962i 0.750113 0.661309i \(-0.229999\pi\)
−0.197654 + 0.980272i \(0.563332\pi\)
\(32\) 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 0.634241 0.773135i \(-0.281313\pi\)
−0.986675 + 0.162701i \(0.947979\pi\)
\(38\) 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 \(-0.827173\pi\)
−0.856188 + 0.516665i \(0.827173\pi\)
\(44\) 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 \(-0.176010\pi\)
−0.880327 + 0.474367i \(0.842677\pi\)
\(48\) 0 0
\(49\) 1.70327 6.78961i 0.243325 0.969945i
\(50\) 0 0
\(51\) −7.04478 + 7.10106i −0.986466 + 0.994348i
\(52\) 0 0
\(53\) 5.28097 + 3.04897i 0.725397 + 0.418808i 0.816736 0.577012i \(-0.195781\pi\)
−0.0913389 + 0.995820i \(0.529115\pi\)
\(54\) 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
\(63\) 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 \(-0.971926\pi\)
0.574338 + 0.818618i \(0.305260\pi\)
\(68\) 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
\(75\) −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 \(-0.209462\pi\)
−0.925231 + 0.379404i \(0.876129\pi\)
\(80\) 0 0
\(81\) 4.62347 + 7.72163i 0.513719 + 0.857958i
\(82\) 0 0
\(83\) −11.8717 −1.30309 −0.651543 0.758611i \(-0.725878\pi\)
−0.651543 + 0.758611i \(0.725878\pi\)
\(84\) 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 0.894965 0.446137i \(-0.147201\pi\)
−0.833848 + 0.551994i \(0.813867\pi\)
\(90\) 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 \(-0.697710\pi\)
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 \(-0.572695\pi\)
0.956738 0.290950i \(-0.0939712\pi\)
\(102\) 0 0
\(103\) −4.06960 + 2.34958i −0.400989 + 0.231511i −0.686911 0.726742i \(-0.741034\pi\)
0.285922 + 0.958253i \(0.407700\pi\)
\(104\) 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 \(-0.536163\pi\)
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 \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) 5.89467 + 3.40329i 0.549680 + 0.317358i
\(116\) 0 0
\(117\) 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 \(-0.400404\pi\)
0.307810 + 0.951448i \(0.400404\pi\)
\(128\) 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 \(-0.163365\pi\)
−0.860792 + 0.508957i \(0.830031\pi\)
\(132\) 0 0
\(133\) −1.97166 + 4.86988i −0.170964 + 0.422273i
\(134\) 0 0
\(135\) −3.60782 + 14.1374i −0.310511 + 1.21676i
\(136\) 0 0
\(137\) −9.58873 5.53606i −0.819221 0.472977i 0.0309270 0.999522i \(-0.490154\pi\)
−0.850148 + 0.526544i \(0.823487\pi\)
\(138\) 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 −0.563886 + 0.825853i \(0.690694\pi\)
−0.997152 + 0.0754127i \(0.975973\pi\)
\(150\) 0 0
\(151\) −3.63368 + 6.29371i −0.295704 + 0.512175i −0.975149 0.221552i \(-0.928888\pi\)
0.679444 + 0.733727i \(0.262221\pi\)
\(152\) 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
\(159\) 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 0.964795 + 0.263003i \(0.0847130\pi\)
−0.254630 + 0.967039i \(0.581954\pi\)
\(164\) 0 0
\(165\) 6.79646 25.7745i 0.529104 2.00654i
\(166\) 0 0
\(167\) 24.0942 1.86447 0.932233 0.361858i \(-0.117857\pi\)
0.932233 + 0.361858i \(0.117857\pi\)
\(168\) 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 0.993029 0.117868i \(-0.0376059\pi\)
−0.598591 + 0.801055i \(0.704273\pi\)
\(174\) 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 \(-0.166579\pi\)
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
\(189\) 13.6632 + 1.52231i 0.993850 + 0.110732i
\(190\) 0 0
\(191\) −3.59492 + 2.07553i −0.260119 + 0.150180i −0.624389 0.781114i \(-0.714652\pi\)
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 \(0.0433311\pi\)
−0.990749 + 0.135709i \(0.956669\pi\)
\(198\) 0 0
\(199\) 5.30327 + 3.06185i 0.375939 + 0.217049i 0.676050 0.736856i \(-0.263690\pi\)
−0.300111 + 0.953904i \(0.597024\pi\)
\(200\) 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 \(-0.532164\pi\)
−0.100875 + 0.994899i \(0.532164\pi\)
\(212\) 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 0.423965 + 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
\(231\) −24.9385 2.97967i −1.64083 0.196048i
\(232\) 0 0
\(233\) −15.5908 + 9.00135i −1.02139 + 0.589698i −0.914505 0.404574i \(-0.867420\pi\)
−0.106882 + 0.994272i \(0.534087\pi\)
\(234\) 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
\(243\) 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 \(-0.558400\pi\)
−0.182442 + 0.983217i \(0.558400\pi\)
\(252\) 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 0.982175 + 0.187966i \(0.0601896\pi\)
−0.328304 + 0.944572i \(0.606477\pi\)
\(258\) 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 \(-0.382591\pi\)
−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 −0.999332 0.0365470i \(-0.988364\pi\)
0.531317 + 0.847173i \(0.321697\pi\)
\(270\) 0 0
\(271\) −14.4761 + 8.35779i −0.879362 + 0.507700i −0.870448 0.492260i \(-0.836171\pi\)
−0.00891391 + 0.999960i \(0.502837\pi\)
\(272\) 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 −0.299689 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 \(0.181680\pi\)
−0.841488 + 0.540276i \(0.818320\pi\)
\(282\) 0 0
\(283\) 5.00728 + 2.89095i 0.297652 + 0.171849i 0.641388 0.767217i \(-0.278359\pi\)
−0.343736 + 0.939066i \(0.611692\pi\)
\(284\) 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 0.417838 + 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
\(315\) 13.8482 + 17.4630i 0.780257 + 0.983927i
\(316\) 0 0
\(317\) 9.81412 5.66618i 0.551216 0.318245i −0.198396 0.980122i \(-0.563573\pi\)
0.749612 + 0.661877i \(0.230240\pi\)
\(318\) 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 −0.999795 0.0202456i \(-0.993555\pi\)
0.482364 0.875971i \(-0.339778\pi\)
\(332\) 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 \(-0.172106\pi\)
−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 \(-0.574753\pi\)
0.958599 0.284760i \(-0.0919140\pi\)
\(354\) 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 \(-0.659166\pi\)
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 0.728618 0.684921i \(-0.240163\pi\)
−0.228850 + 0.973462i \(0.573496\pi\)
\(368\) 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 −0.993108 0.117201i \(-0.962608\pi\)
0.395055 0.918657i \(-0.370725\pi\)
\(374\) 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 \(-0.294837\pi\)
0.600830 + 0.799377i \(0.294837\pi\)
\(380\) 0 0
\(381\) 11.6193 + 3.06387i 0.595273 + 0.156967i
\(382\) 0 0
\(383\) 11.5139 + 19.9426i 0.588331 + 1.01902i 0.994451 + 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
\(387\) −29.3064 16.6105i −1.48973 0.844360i
\(388\) 0 0
\(389\) −5.45545 3.14970i −0.276602 0.159696i 0.355282 0.934759i \(-0.384385\pi\)
−0.631884 + 0.775063i \(0.717718\pi\)
\(390\) 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
\(399\) −5.45281 + 7.28536i −0.272982 + 0.364724i
\(400\) 0 0
\(401\) −11.8188 + 6.82360i −0.590204 + 0.340755i −0.765178 0.643819i \(-0.777349\pi\)
0.174974 + 0.984573i \(0.444016\pi\)
\(402\) 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
\(411\) −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 \(-0.554294\pi\)
−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
\(423\) −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 \(-0.172036\pi\)
−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 −0.541537 0.840677i \(-0.682157\pi\)
0.457279 + 0.889323i \(0.348824\pi\)
\(440\) 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 \(-0.765838\pi\)
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 \(0.0187457\pi\)
−0.998266 + 0.0588572i \(0.981254\pi\)
\(450\) 0 0
\(451\) −8.63741 4.98681i −0.406720 0.234820i
\(452\) 0 0
\(453\) −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 0.642865 0.765979i \(-0.277746\pi\)
−0.984790 + 0.173748i \(0.944412\pi\)
\(458\) 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 \(-0.606719\pi\)
−0.329021 + 0.944323i \(0.606719\pi\)
\(464\) 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 \(-0.240808\pi\)
−0.958050 + 0.286601i \(0.907475\pi\)
\(468\) 0 0
\(469\) 2.52937 + 18.0923i 0.116796 + 0.835426i
\(470\) 0 0
\(471\) 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 0.403320 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
\(483\) 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 −0.0463476 0.998925i \(-0.514758\pi\)
0.888269 0.459324i \(-0.151908\pi\)
\(488\) 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 \(-0.0449227\pi\)
−0.616845 + 0.787085i \(0.711589\pi\)
\(500\) 0 0
\(501\) 40.3531 + 10.6407i 1.80284 + 0.475390i
\(502\) 0 0
\(503\) −8.55884 −0.381620 −0.190810 0.981627i \(-0.561111\pi\)
−0.190810 + 0.981627i \(0.561111\pi\)
\(504\) 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 −0.988484 0.151324i \(-0.951646\pi\)
0.363192 0.931714i \(-0.381687\pi\)
\(510\) 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 −0.993014 0.118001i \(-0.962352\pi\)
0.598698 + 0.800975i \(0.295685\pi\)
\(522\) 0 0
\(523\) 11.9049 6.87332i 0.520567 0.300549i −0.216600 0.976260i \(-0.569497\pi\)
0.737167 + 0.675711i \(0.236163\pi\)
\(524\) 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 −0.886626 0.462488i \(-0.846957\pi\)
0.0427866 0.999084i \(-0.486376\pi\)
\(542\) 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 \(-0.413906\pi\)
0.267188 + 0.963645i \(0.413906\pi\)
\(548\) 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 0.134766 0.990877i \(-0.456972\pi\)
−0.790742 + 0.612150i \(0.790305\pi\)
\(558\) 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
\(567\) 22.2108 + 8.58361i 0.932768 + 0.360478i
\(568\) 0 0
\(569\) 1.72971 0.998650i 0.0725133 0.0418656i −0.463305 0.886199i \(-0.653337\pi\)
0.535818 + 0.844333i \(0.320003\pi\)
\(570\) 0 0
\(571\) −1.00728 + 1.74466i −0.0421534 + 0.0730118i −0.886332 0.463050i \(-0.846755\pi\)
0.844179 + 0.536061i \(0.180088\pi\)
\(572\) 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
\(579\) −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 \(-0.248129\pi\)
0.711251 + 0.702939i \(0.248129\pi\)
\(588\) 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 0.930761 0.365628i \(-0.119146\pi\)
−0.782024 + 0.623249i \(0.785812\pi\)
\(594\) 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 \(-0.611965\pi\)
−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 0.0746364 0.997211i \(-0.476220\pi\)
0.900928 + 0.433968i \(0.142887\pi\)
\(608\) 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 −0.369172 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 \(-0.649389\pi\)
0.452279 0.891877i \(-0.350611\pi\)
\(618\) 0 0
\(619\) −27.4026 15.8209i −1.10140 0.635895i −0.164813 0.986325i \(-0.552702\pi\)
−0.936589 + 0.350430i \(0.886035\pi\)
\(620\) 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 \(-0.364453\pi\)
0.413079 + 0.910695i \(0.364453\pi\)
\(632\) 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 −0.322541 0.946556i \(-0.604537\pi\)
−0.981012 + 0.193949i \(0.937870\pi\)
\(642\) 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 \(-0.696599\pi\)
0.995582 + 0.0938966i \(0.0299323\pi\)
\(648\) 0 0
\(649\) −12.1731 + 7.02817i −0.477838 + 0.275880i
\(650\) 0 0
\(651\) 16.1615 + 1.93099i 0.633419 + 0.0756816i
\(652\) 0 0
\(653\) 23.0548 13.3107i 0.902204 0.520888i 0.0242893 0.999705i \(-0.492268\pi\)
0.877915 + 0.478817i \(0.158934\pi\)
\(654\) 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
\(663\) 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 0.991336 + 0.131348i \(0.0419305\pi\)
−0.381917 + 0.924196i \(0.624736\pi\)
\(678\) 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 \(-0.574348\pi\)
−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 −0.859335 0.511413i \(-0.829122\pi\)
0.0132293 + 0.999912i \(0.495789\pi\)
\(692\) 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 \(0.00780818\pi\)
−0.999699 + 0.0245276i \(0.992192\pi\)
\(702\) 0 0
\(703\) 7.37344 + 4.25706i 0.278095 + 0.160558i
\(704\) 0 0
\(705\) 1.37844 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 0.999714 + 0.0239010i \(0.00760863\pi\)
−0.479158 + 0.877728i \(0.659058\pi\)
\(710\) 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 0.932003 + 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
\(723\) 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 −0.127327 0.991861i \(-0.540640\pi\)
0.795313 + 0.606199i \(0.207307\pi\)
\(734\) 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 \(-0.912002\pi\)
0.717393 + 0.696668i \(0.245335\pi\)
\(740\) 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 \(-0.236765\pi\)
−0.954333 + 0.298746i \(0.903432\pi\)
\(752\) 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 −0.991737 0.128286i \(-0.959053\pi\)
0.384770 0.923012i \(-0.374281\pi\)
\(762\) 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 \(0.115275\pi\)
−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 −0.959094 0.283088i \(-0.908641\pi\)
0.724708 + 0.689056i \(0.241974\pi\)
\(774\) 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 \(-0.476357\pi\)
−0.826533 + 0.562888i \(0.809690\pi\)
\(788\) 0 0
\(789\) −6.14697 6.09825i −0.218838 0.217103i