Properties

Label 336.2.bc.f.257.4
Level 336
Weight 2
Character 336.257
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 257.4
Root \(-1.70742 - 0.291063i\)
Character \(\chi\) = 336.257
Dual form 336.2.bc.f.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.291063 + 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(-1.05451 + 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +O(q^{10})\) \(q+(-0.291063 + 1.70742i) q^{3} +(-0.0726693 + 0.125867i) q^{5} +(-1.05451 + 2.42652i) q^{7} +(-2.83056 - 0.993934i) q^{9} +(-2.13889 + 1.23489i) q^{11} +2.04143i q^{13} +(-0.193756 - 0.160712i) q^{15} +(-0.878419 - 1.52147i) q^{17} +(3.68319 + 2.12649i) q^{19} +(-3.83616 - 2.50676i) q^{21} +(-7.46351 - 4.30906i) q^{23} +(2.48944 + 4.31183i) q^{25} +(2.52094 - 4.54366i) q^{27} +7.08790i q^{29} +(-3.11812 + 1.80025i) q^{31} +(-1.48592 - 4.01141i) q^{33} +(-0.228788 - 0.309061i) q^{35} +(-2.93493 + 5.08345i) q^{37} +(-3.48558 - 0.594185i) q^{39} +5.33255 q^{41} +9.19692 q^{43} +(0.330798 - 0.284046i) q^{45} +(4.65190 - 8.05733i) q^{47} +(-4.77602 - 5.11758i) q^{49} +(2.85346 - 1.05699i) q^{51} +(4.49578 - 2.59564i) q^{53} -0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(5.60299 + 9.70466i) q^{59} +(4.66353 + 2.69249i) q^{61} +(5.39666 - 5.82031i) q^{63} +(-0.256949 - 0.148349i) q^{65} +(-2.57417 - 4.45860i) q^{67} +(9.52973 - 11.4891i) q^{69} +7.79323i q^{71} +(11.3013 - 6.52482i) q^{73} +(-8.08669 + 2.99550i) q^{75} +(-0.741003 - 6.49226i) q^{77} +(-2.86075 + 4.95497i) q^{79} +(7.02419 + 5.62679i) q^{81} +15.9818 q^{83} +0.255336 q^{85} +(-12.1020 - 2.06303i) q^{87} +(-4.34252 + 7.52147i) q^{89} +(-4.95358 - 2.15271i) q^{91} +(-2.16621 - 5.84793i) q^{93} +(-0.535310 + 0.309061i) q^{95} -6.65337i q^{97} +(7.28165 - 1.36951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q - 4q^{7} + 2q^{9} - 8q^{15} + 6q^{19} + 14q^{21} - 18q^{25} + 48q^{31} - 12q^{33} - 2q^{37} + 22q^{39} - 20q^{43} - 42q^{45} - 28q^{49} - 6q^{51} - 8q^{57} + 36q^{61} + 32q^{63} - 14q^{67} + 30q^{73} - 54q^{75} - 28q^{79} + 30q^{81} + 16q^{85} - 78q^{87} - 66q^{91} + 16q^{93} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) −0.291063 + 1.70742i −0.168045 + 0.985779i
\(4\) 0 0
\(5\) −0.0726693 + 0.125867i −0.0324987 + 0.0562894i −0.881817 0.471591i \(-0.843680\pi\)
0.849319 + 0.527881i \(0.177013\pi\)
\(6\) 0 0
\(7\) −1.05451 + 2.42652i −0.398567 + 0.917139i
\(8\) 0 0
\(9\) −2.83056 0.993934i −0.943521 0.331311i
\(10\) 0 0
\(11\) −2.13889 + 1.23489i −0.644899 + 0.372332i −0.786499 0.617592i \(-0.788109\pi\)
0.141600 + 0.989924i \(0.454775\pi\)
\(12\) 0 0
\(13\) 2.04143i 0.566191i 0.959092 + 0.283096i \(0.0913613\pi\)
−0.959092 + 0.283096i \(0.908639\pi\)
\(14\) 0 0
\(15\) −0.193756 0.160712i −0.0500276 0.0414957i
\(16\) 0 0
\(17\) −0.878419 1.52147i −0.213048 0.369010i 0.739619 0.673026i \(-0.235006\pi\)
−0.952667 + 0.304016i \(0.901672\pi\)
\(18\) 0 0
\(19\) 3.68319 + 2.12649i 0.844983 + 0.487851i 0.858955 0.512051i \(-0.171114\pi\)
−0.0139720 + 0.999902i \(0.504448\pi\)
\(20\) 0 0
\(21\) −3.83616 2.50676i −0.837119 0.547020i
\(22\) 0 0
\(23\) −7.46351 4.30906i −1.55625 0.898501i −0.997610 0.0690910i \(-0.977990\pi\)
−0.558640 0.829410i \(-0.688677\pi\)
\(24\) 0 0
\(25\) 2.48944 + 4.31183i 0.497888 + 0.862367i
\(26\) 0 0
\(27\) 2.52094 4.54366i 0.485154 0.874429i
\(28\) 0 0
\(29\) 7.08790i 1.31619i 0.752935 + 0.658095i \(0.228637\pi\)
−0.752935 + 0.658095i \(0.771363\pi\)
\(30\) 0 0
\(31\) −3.11812 + 1.80025i −0.560031 + 0.323334i −0.753158 0.657840i \(-0.771470\pi\)
0.193127 + 0.981174i \(0.438137\pi\)
\(32\) 0 0
\(33\) −1.48592 4.01141i −0.258665 0.698296i
\(34\) 0 0
\(35\) −0.228788 0.309061i −0.0386723 0.0522409i
\(36\) 0 0
\(37\) −2.93493 + 5.08345i −0.482499 + 0.835713i −0.999798 0.0200916i \(-0.993604\pi\)
0.517299 + 0.855805i \(0.326938\pi\)
\(38\) 0 0
\(39\) −3.48558 0.594185i −0.558139 0.0951458i
\(40\) 0 0
\(41\) 5.33255 0.832804 0.416402 0.909181i \(-0.363291\pi\)
0.416402 + 0.909181i \(0.363291\pi\)
\(42\) 0 0
\(43\) 9.19692 1.40252 0.701258 0.712907i \(-0.252622\pi\)
0.701258 + 0.712907i \(0.252622\pi\)
\(44\) 0 0
\(45\) 0.330798 0.284046i 0.0493125 0.0423431i
\(46\) 0 0
\(47\) 4.65190 8.05733i 0.678549 1.17528i −0.296868 0.954918i \(-0.595942\pi\)
0.975418 0.220364i \(-0.0707244\pi\)
\(48\) 0 0
\(49\) −4.77602 5.11758i −0.682288 0.731083i
\(50\) 0 0
\(51\) 2.85346 1.05699i 0.399564 0.148008i
\(52\) 0 0
\(53\) 4.49578 2.59564i 0.617543 0.356539i −0.158369 0.987380i \(-0.550623\pi\)
0.775912 + 0.630841i \(0.217290\pi\)
\(54\) 0 0
\(55\) 0.358953i 0.0484013i
\(56\) 0 0
\(57\) −4.70286 + 5.66982i −0.622909 + 0.750985i
\(58\) 0 0
\(59\) 5.60299 + 9.70466i 0.729447 + 1.26344i 0.957117 + 0.289701i \(0.0935558\pi\)
−0.227670 + 0.973738i \(0.573111\pi\)
\(60\) 0 0
\(61\) 4.66353 + 2.69249i 0.597104 + 0.344738i 0.767901 0.640568i \(-0.221301\pi\)
−0.170798 + 0.985306i \(0.554634\pi\)
\(62\) 0 0
\(63\) 5.39666 5.82031i 0.679915 0.733291i
\(64\) 0 0
\(65\) −0.256949 0.148349i −0.0318705 0.0184005i
\(66\) 0 0
\(67\) −2.57417 4.45860i −0.314485 0.544705i 0.664843 0.746984i \(-0.268499\pi\)
−0.979328 + 0.202279i \(0.935165\pi\)
\(68\) 0 0
\(69\) 9.52973 11.4891i 1.14724 1.38313i
\(70\) 0 0
\(71\) 7.79323i 0.924886i 0.886649 + 0.462443i \(0.153027\pi\)
−0.886649 + 0.462443i \(0.846973\pi\)
\(72\) 0 0
\(73\) 11.3013 6.52482i 1.32272 0.763672i 0.338558 0.940946i \(-0.390061\pi\)
0.984162 + 0.177273i \(0.0567277\pi\)
\(74\) 0 0
\(75\) −8.08669 + 2.99550i −0.933771 + 0.345891i
\(76\) 0 0
\(77\) −0.741003 6.49226i −0.0844451 0.739861i
\(78\) 0 0
\(79\) −2.86075 + 4.95497i −0.321860 + 0.557478i −0.980872 0.194655i \(-0.937641\pi\)
0.659012 + 0.752133i \(0.270975\pi\)
\(80\) 0 0
\(81\) 7.02419 + 5.62679i 0.780466 + 0.625199i
\(82\) 0 0
\(83\) 15.9818 1.75423 0.877115 0.480280i \(-0.159465\pi\)
0.877115 + 0.480280i \(0.159465\pi\)
\(84\) 0 0
\(85\) 0.255336 0.0276951
\(86\) 0 0
\(87\) −12.1020 2.06303i −1.29747 0.221180i
\(88\) 0 0
\(89\) −4.34252 + 7.52147i −0.460306 + 0.797274i −0.998976 0.0452432i \(-0.985594\pi\)
0.538670 + 0.842517i \(0.318927\pi\)
\(90\) 0 0
\(91\) −4.95358 2.15271i −0.519276 0.225665i
\(92\) 0 0
\(93\) −2.16621 5.84793i −0.224626 0.606402i
\(94\) 0 0
\(95\) −0.535310 + 0.309061i −0.0549217 + 0.0317090i
\(96\) 0 0
\(97\) 6.65337i 0.675547i −0.941227 0.337774i \(-0.890326\pi\)
0.941227 0.337774i \(-0.109674\pi\)
\(98\) 0 0
\(99\) 7.28165 1.36951i 0.731834 0.137641i
\(100\) 0 0
\(101\) −8.06357 13.9665i −0.802355 1.38972i −0.918062 0.396437i \(-0.870247\pi\)
0.115707 0.993283i \(-0.463087\pi\)
\(102\) 0 0
\(103\) 0.147333 + 0.0850626i 0.0145171 + 0.00838147i 0.507241 0.861804i \(-0.330665\pi\)
−0.492724 + 0.870186i \(0.663999\pi\)
\(104\) 0 0
\(105\) 0.594290 0.300681i 0.0579967 0.0293435i
\(106\) 0 0
\(107\) −6.03900 3.48662i −0.583813 0.337064i 0.178835 0.983879i \(-0.442767\pi\)
−0.762647 + 0.646815i \(0.776101\pi\)
\(108\) 0 0
\(109\) −0.677559 1.17357i −0.0648984 0.112407i 0.831751 0.555150i \(-0.187339\pi\)
−0.896649 + 0.442742i \(0.854006\pi\)
\(110\) 0 0
\(111\) −7.82532 6.49076i −0.742747 0.616076i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) 1.08474 0.626273i 0.101152 0.0584002i
\(116\) 0 0
\(117\) 2.02905 5.77840i 0.187586 0.534213i
\(118\) 0 0
\(119\) 4.61817 0.527101i 0.423347 0.0483193i
\(120\) 0 0
\(121\) −2.45011 + 4.24371i −0.222737 + 0.385792i
\(122\) 0 0
\(123\) −1.55211 + 9.10490i −0.139949 + 0.820961i
\(124\) 0 0
\(125\) −1.45032 −0.129720
\(126\) 0 0
\(127\) 7.33399 0.650787 0.325393 0.945579i \(-0.394503\pi\)
0.325393 + 0.945579i \(0.394503\pi\)
\(128\) 0 0
\(129\) −2.67688 + 15.7030i −0.235687 + 1.38257i
\(130\) 0 0
\(131\) −3.04832 + 5.27985i −0.266333 + 0.461303i −0.967912 0.251289i \(-0.919146\pi\)
0.701579 + 0.712592i \(0.252479\pi\)
\(132\) 0 0
\(133\) −9.04395 + 6.69494i −0.784210 + 0.580525i
\(134\) 0 0
\(135\) 0.388702 + 0.647487i 0.0334542 + 0.0557268i
\(136\) 0 0
\(137\) −17.3832 + 10.0362i −1.48515 + 0.857451i −0.999857 0.0169018i \(-0.994620\pi\)
−0.485291 + 0.874353i \(0.661286\pi\)
\(138\) 0 0
\(139\) 0.117694i 0.00998266i −0.999988 0.00499133i \(-0.998411\pi\)
0.999988 0.00499133i \(-0.00158880\pi\)
\(140\) 0 0
\(141\) 12.4032 + 10.2879i 1.04454 + 0.866401i
\(142\) 0 0
\(143\) −2.52094 4.36639i −0.210811 0.365136i
\(144\) 0 0
\(145\) −0.892131 0.515072i −0.0740875 0.0427744i
\(146\) 0 0
\(147\) 10.1280 6.66513i 0.835342 0.549730i
\(148\) 0 0
\(149\) 7.75705 + 4.47853i 0.635482 + 0.366896i 0.782872 0.622183i \(-0.213754\pi\)
−0.147390 + 0.989078i \(0.547087\pi\)
\(150\) 0 0
\(151\) −1.37132 2.37519i −0.111596 0.193290i 0.804818 0.593522i \(-0.202263\pi\)
−0.916414 + 0.400232i \(0.868930\pi\)
\(152\) 0 0
\(153\) 0.974184 + 5.17970i 0.0787581 + 0.418754i
\(154\) 0 0
\(155\) 0.523291i 0.0420318i
\(156\) 0 0
\(157\) −11.7303 + 6.77249i −0.936180 + 0.540504i −0.888761 0.458371i \(-0.848433\pi\)
−0.0474193 + 0.998875i \(0.515100\pi\)
\(158\) 0 0
\(159\) 3.12329 + 8.43168i 0.247693 + 0.668676i
\(160\) 0 0
\(161\) 18.3264 13.5664i 1.44432 1.06918i
\(162\) 0 0
\(163\) −2.02428 + 3.50616i −0.158554 + 0.274624i −0.934347 0.356363i \(-0.884017\pi\)
0.775793 + 0.630987i \(0.217350\pi\)
\(164\) 0 0
\(165\) 0.612884 + 0.104478i 0.0477130 + 0.00813361i
\(166\) 0 0
\(167\) −3.70521 −0.286717 −0.143359 0.989671i \(-0.545790\pi\)
−0.143359 + 0.989671i \(0.545790\pi\)
\(168\) 0 0
\(169\) 8.83256 0.679428
\(170\) 0 0
\(171\) −8.31193 9.68003i −0.635629 0.740250i
\(172\) 0 0
\(173\) −11.2370 + 19.4630i −0.854333 + 1.47975i 0.0229296 + 0.999737i \(0.492701\pi\)
−0.877263 + 0.480011i \(0.840633\pi\)
\(174\) 0 0
\(175\) −13.0879 + 1.49381i −0.989352 + 0.112921i
\(176\) 0 0
\(177\) −18.2008 + 6.74198i −1.36805 + 0.506758i
\(178\) 0 0
\(179\) −3.18574 + 1.83929i −0.238113 + 0.137475i −0.614309 0.789065i \(-0.710565\pi\)
0.376196 + 0.926540i \(0.377232\pi\)
\(180\) 0 0
\(181\) 8.01062i 0.595425i 0.954656 + 0.297712i \(0.0962237\pi\)
−0.954656 + 0.297712i \(0.903776\pi\)
\(182\) 0 0
\(183\) −5.95459 + 7.17892i −0.440176 + 0.530681i
\(184\) 0 0
\(185\) −0.426558 0.738821i −0.0313612 0.0543192i
\(186\) 0 0
\(187\) 3.75768 + 2.16950i 0.274789 + 0.158649i
\(188\) 0 0
\(189\) 8.36695 + 10.9084i 0.608606 + 0.793473i
\(190\) 0 0
\(191\) 0.971326 + 0.560795i 0.0702827 + 0.0405777i 0.534730 0.845023i \(-0.320413\pi\)
−0.464447 + 0.885601i \(0.653747\pi\)
\(192\) 0 0
\(193\) −9.18421 15.9075i −0.661094 1.14505i −0.980329 0.197373i \(-0.936759\pi\)
0.319235 0.947676i \(-0.396574\pi\)
\(194\) 0 0
\(195\) 0.328083 0.395540i 0.0234945 0.0283252i
\(196\) 0 0
\(197\) 0.296699i 0.0211389i 0.999944 + 0.0105695i \(0.00336442\pi\)
−0.999944 + 0.0105695i \(0.996636\pi\)
\(198\) 0 0
\(199\) 23.6874 13.6759i 1.67915 0.969460i 0.716951 0.697124i \(-0.245537\pi\)
0.962202 0.272336i \(-0.0877962\pi\)
\(200\) 0 0
\(201\) 8.36195 3.09746i 0.589807 0.218478i
\(202\) 0 0
\(203\) −17.1989 7.47426i −1.20713 0.524590i
\(204\) 0 0
\(205\) −0.387513 + 0.671191i −0.0270650 + 0.0468780i
\(206\) 0 0
\(207\) 16.8430 + 19.6153i 1.17067 + 1.36336i
\(208\) 0 0
\(209\) −10.5039 −0.726571
\(210\) 0 0
\(211\) −21.0295 −1.44773 −0.723864 0.689942i \(-0.757636\pi\)
−0.723864 + 0.689942i \(0.757636\pi\)
\(212\) 0 0
\(213\) −13.3063 2.26832i −0.911734 0.155423i
\(214\) 0 0
\(215\) −0.668333 + 1.15759i −0.0455800 + 0.0789468i
\(216\) 0 0
\(217\) −1.08025 9.46457i −0.0733323 0.642497i
\(218\) 0 0
\(219\) 7.85121 + 21.1952i 0.530535 + 1.43224i
\(220\) 0 0
\(221\) 3.10597 1.79323i 0.208930 0.120626i
\(222\) 0 0
\(223\) 6.89447i 0.461688i −0.972991 0.230844i \(-0.925851\pi\)
0.972991 0.230844i \(-0.0741487\pi\)
\(224\) 0 0
\(225\) −2.76084 14.6793i −0.184056 0.978617i
\(226\) 0 0
\(227\) −6.70734 11.6174i −0.445182 0.771077i 0.552883 0.833259i \(-0.313528\pi\)
−0.998065 + 0.0621816i \(0.980194\pi\)
\(228\) 0 0
\(229\) −5.51012 3.18127i −0.364119 0.210224i 0.306767 0.951785i \(-0.400753\pi\)
−0.670886 + 0.741560i \(0.734086\pi\)
\(230\) 0 0
\(231\) 11.3007 + 0.624454i 0.743530 + 0.0410861i
\(232\) 0 0
\(233\) 4.29295 + 2.47853i 0.281240 + 0.162374i 0.633985 0.773346i \(-0.281418\pi\)
−0.352744 + 0.935720i \(0.614752\pi\)
\(234\) 0 0
\(235\) 0.676100 + 1.17104i 0.0441039 + 0.0763903i
\(236\) 0 0
\(237\) −7.62755 6.32672i −0.495463 0.410964i
\(238\) 0 0
\(239\) 17.3756i 1.12394i 0.827159 + 0.561968i \(0.189956\pi\)
−0.827159 + 0.561968i \(0.810044\pi\)
\(240\) 0 0
\(241\) 12.5626 7.25302i 0.809228 0.467208i −0.0374597 0.999298i \(-0.511927\pi\)
0.846688 + 0.532090i \(0.178593\pi\)
\(242\) 0 0
\(243\) −11.6518 + 10.3555i −0.747462 + 0.664305i
\(244\) 0 0
\(245\) 0.991204 0.229251i 0.0633257 0.0146463i
\(246\) 0 0
\(247\) −4.34109 + 7.51899i −0.276217 + 0.478422i
\(248\) 0 0
\(249\) −4.65171 + 27.2876i −0.294790 + 1.72928i
\(250\) 0 0
\(251\) 3.49783 0.220781 0.110391 0.993888i \(-0.464790\pi\)
0.110391 + 0.993888i \(0.464790\pi\)
\(252\) 0 0
\(253\) 21.2848 1.33816
\(254\) 0 0
\(255\) −0.0743190 + 0.435966i −0.00465404 + 0.0273013i
\(256\) 0 0
\(257\) 7.96781 13.8006i 0.497018 0.860861i −0.502976 0.864300i \(-0.667762\pi\)
0.999994 + 0.00343985i \(0.00109494\pi\)
\(258\) 0 0
\(259\) −9.24018 12.4822i −0.574157 0.775607i
\(260\) 0 0
\(261\) 7.04490 20.0627i 0.436069 1.24185i
\(262\) 0 0
\(263\) 12.4343 7.17892i 0.766729 0.442671i −0.0649777 0.997887i \(-0.520698\pi\)
0.831706 + 0.555216i \(0.187364\pi\)
\(264\) 0 0
\(265\) 0.754493i 0.0463482i
\(266\) 0 0
\(267\) −11.5784 9.60373i −0.708584 0.587739i
\(268\) 0 0
\(269\) 3.68211 + 6.37760i 0.224502 + 0.388849i 0.956170 0.292812i \(-0.0945911\pi\)
−0.731668 + 0.681661i \(0.761258\pi\)
\(270\) 0 0
\(271\) −10.8537 6.26636i −0.659313 0.380654i 0.132702 0.991156i \(-0.457635\pi\)
−0.792015 + 0.610501i \(0.790968\pi\)
\(272\) 0 0
\(273\) 5.11738 7.83126i 0.309718 0.473969i
\(274\) 0 0
\(275\) −10.6493 6.14835i −0.642174 0.370759i
\(276\) 0 0
\(277\) −16.2409 28.1300i −0.975819 1.69017i −0.677205 0.735794i \(-0.736809\pi\)
−0.298614 0.954374i \(-0.596524\pi\)
\(278\) 0 0
\(279\) 10.6154 1.99651i 0.635526 0.119528i
\(280\) 0 0
\(281\) 10.1758i 0.607037i −0.952826 0.303518i \(-0.901839\pi\)
0.952826 0.303518i \(-0.0981614\pi\)
\(282\) 0 0
\(283\) 1.18666 0.685120i 0.0705397 0.0407261i −0.464315 0.885670i \(-0.653700\pi\)
0.534855 + 0.844944i \(0.320366\pi\)
\(284\) 0 0
\(285\) −0.371889 1.00396i −0.0220288 0.0594692i
\(286\) 0 0
\(287\) −5.62323 + 12.9395i −0.331929 + 0.763797i
\(288\) 0 0
\(289\) 6.95676 12.0495i 0.409221 0.708792i
\(290\) 0 0
\(291\) 11.3601 + 1.93655i 0.665941 + 0.113523i
\(292\) 0 0
\(293\) 16.9961 0.992923 0.496461 0.868059i \(-0.334632\pi\)
0.496461 + 0.868059i \(0.334632\pi\)
\(294\) 0 0
\(295\) −1.62866 −0.0948243
\(296\) 0 0
\(297\) 0.218914 + 12.8315i 0.0127027 + 0.744556i
\(298\) 0 0
\(299\) 8.79665 15.2362i 0.508723 0.881135i
\(300\) 0 0
\(301\) −9.69824 + 22.3165i −0.558997 + 1.28630i
\(302\) 0 0
\(303\) 26.1937 9.70276i 1.50479 0.557409i
\(304\) 0 0
\(305\) −0.677791 + 0.391323i −0.0388102 + 0.0224071i
\(306\) 0 0
\(307\) 20.9023i 1.19296i 0.802629 + 0.596479i \(0.203434\pi\)
−0.802629 + 0.596479i \(0.796566\pi\)
\(308\) 0 0
\(309\) −0.188121 + 0.226800i −0.0107018 + 0.0129022i
\(310\) 0 0
\(311\) 5.74040 + 9.94267i 0.325508 + 0.563797i 0.981615 0.190871i \(-0.0611312\pi\)
−0.656107 + 0.754668i \(0.727798\pi\)
\(312\) 0 0
\(313\) 8.57172 + 4.94889i 0.484502 + 0.279728i 0.722291 0.691589i \(-0.243089\pi\)
−0.237788 + 0.971317i \(0.576423\pi\)
\(314\) 0 0
\(315\) 0.340413 + 1.10222i 0.0191801 + 0.0621030i
\(316\) 0 0
\(317\) 5.74547 + 3.31715i 0.322698 + 0.186310i 0.652594 0.757707i \(-0.273681\pi\)
−0.329897 + 0.944017i \(0.607014\pi\)
\(318\) 0 0
\(319\) −8.75275 15.1602i −0.490060 0.848809i
\(320\) 0 0
\(321\) 7.71086 9.29629i 0.430378 0.518868i
\(322\) 0 0
\(323\) 7.47181i 0.415742i
\(324\) 0 0
\(325\) −8.80231 + 5.08202i −0.488264 + 0.281900i
\(326\) 0 0
\(327\) 2.20098 0.815296i 0.121715 0.0450860i
\(328\) 0 0
\(329\) 14.6458 + 19.7845i 0.807449 + 1.09075i
\(330\) 0 0
\(331\) 7.36537 12.7572i 0.404837 0.701199i −0.589465 0.807794i \(-0.700661\pi\)
0.994303 + 0.106595i \(0.0339948\pi\)
\(332\) 0 0
\(333\) 13.3601 11.4719i 0.732130 0.628656i
\(334\) 0 0
\(335\) 0.748254 0.0408815
\(336\) 0 0
\(337\) −30.7209 −1.67347 −0.836737 0.547605i \(-0.815540\pi\)
−0.836737 + 0.547605i \(0.815540\pi\)
\(338\) 0 0
\(339\) 6.82968 + 1.16425i 0.370937 + 0.0632335i
\(340\) 0 0
\(341\) 4.44621 7.70106i 0.240776 0.417036i
\(342\) 0 0
\(343\) 17.4543 6.19257i 0.942443 0.334367i
\(344\) 0 0
\(345\) 0.753584 + 2.03439i 0.0405716 + 0.109528i
\(346\) 0 0
\(347\) 14.5124 8.37875i 0.779068 0.449795i −0.0570320 0.998372i \(-0.518164\pi\)
0.836100 + 0.548577i \(0.184830\pi\)
\(348\) 0 0
\(349\) 3.12385i 0.167216i −0.996499 0.0836080i \(-0.973356\pi\)
0.996499 0.0836080i \(-0.0266443\pi\)
\(350\) 0 0
\(351\) 9.27558 + 5.14632i 0.495094 + 0.274690i
\(352\) 0 0
\(353\) 17.7450 + 30.7353i 0.944473 + 1.63587i 0.756804 + 0.653642i \(0.226760\pi\)
0.187669 + 0.982232i \(0.439907\pi\)
\(354\) 0 0
\(355\) −0.980910 0.566328i −0.0520613 0.0300576i
\(356\) 0 0
\(357\) −0.444197 + 8.03858i −0.0235094 + 0.425447i
\(358\) 0 0
\(359\) 5.42817 + 3.13395i 0.286488 + 0.165404i 0.636357 0.771395i \(-0.280441\pi\)
−0.349869 + 0.936799i \(0.613774\pi\)
\(360\) 0 0
\(361\) −0.456052 0.789905i −0.0240027 0.0415739i
\(362\) 0 0
\(363\) −6.53266 5.41855i −0.342876 0.284400i
\(364\) 0 0
\(365\) 1.89662i 0.0992734i
\(366\) 0 0
\(367\) 14.5823 8.41907i 0.761188 0.439472i −0.0685342 0.997649i \(-0.521832\pi\)
0.829722 + 0.558177i \(0.188499\pi\)
\(368\) 0 0
\(369\) −15.0941 5.30020i −0.785769 0.275918i
\(370\) 0 0
\(371\) 1.55753 + 13.6462i 0.0808631 + 0.708478i
\(372\) 0 0
\(373\) 0.617106 1.06886i 0.0319526 0.0553435i −0.849607 0.527416i \(-0.823161\pi\)
0.881559 + 0.472073i \(0.156494\pi\)
\(374\) 0 0
\(375\) 0.422134 2.47630i 0.0217989 0.127875i
\(376\) 0 0
\(377\) −14.4695 −0.745215
\(378\) 0 0
\(379\) 14.3895 0.739141 0.369571 0.929203i \(-0.379505\pi\)
0.369571 + 0.929203i \(0.379505\pi\)
\(380\) 0 0
\(381\) −2.13466 + 12.5222i −0.109362 + 0.641532i
\(382\) 0 0
\(383\) 4.95842 8.58824i 0.253364 0.438839i −0.711086 0.703105i \(-0.751796\pi\)
0.964450 + 0.264266i \(0.0851298\pi\)
\(384\) 0 0
\(385\) 0.871008 + 0.378520i 0.0443907 + 0.0192912i
\(386\) 0 0
\(387\) −26.0325 9.14113i −1.32330 0.464670i
\(388\) 0 0
\(389\) 11.5061 6.64306i 0.583383 0.336816i −0.179094 0.983832i \(-0.557317\pi\)
0.762477 + 0.647016i \(0.223983\pi\)
\(390\) 0 0
\(391\) 15.1406i 0.765695i
\(392\) 0 0
\(393\) −8.12767 6.74154i −0.409987 0.340066i
\(394\) 0 0
\(395\) −0.415778 0.720148i −0.0209201 0.0362346i
\(396\) 0 0
\(397\) 21.0410 + 12.1480i 1.05602 + 0.609693i 0.924328 0.381598i \(-0.124626\pi\)
0.131691 + 0.991291i \(0.457959\pi\)
\(398\) 0 0
\(399\) −8.79872 17.3905i −0.440487 0.870612i
\(400\) 0 0
\(401\) −12.4125 7.16635i −0.619850 0.357870i 0.156961 0.987605i \(-0.449830\pi\)
−0.776810 + 0.629735i \(0.783164\pi\)
\(402\) 0 0
\(403\) −3.67508 6.36543i −0.183069 0.317085i
\(404\) 0 0
\(405\) −1.21867 + 0.475218i −0.0605562 + 0.0236138i
\(406\) 0 0
\(407\) 14.4972i 0.718600i
\(408\) 0 0
\(409\) 17.3256 10.0029i 0.856695 0.494613i −0.00620937 0.999981i \(-0.501977\pi\)
0.862904 + 0.505368i \(0.168643\pi\)
\(410\) 0 0
\(411\) −12.0764 32.6016i −0.595685 1.60812i
\(412\) 0 0
\(413\) −29.4570 + 3.36211i −1.44948 + 0.165439i
\(414\) 0 0
\(415\) −1.16139 + 2.01158i −0.0570102 + 0.0987446i
\(416\) 0 0
\(417\) 0.200953 + 0.0342563i 0.00984070 + 0.00167754i
\(418\) 0 0
\(419\) −27.7445 −1.35541 −0.677704 0.735335i \(-0.737025\pi\)
−0.677704 + 0.735335i \(0.737025\pi\)
\(420\) 0 0
\(421\) −1.53586 −0.0748533 −0.0374267 0.999299i \(-0.511916\pi\)
−0.0374267 + 0.999299i \(0.511916\pi\)
\(422\) 0 0
\(423\) −21.1760 + 18.1831i −1.02961 + 0.884093i
\(424\) 0 0
\(425\) 4.37354 7.57519i 0.212148 0.367451i
\(426\) 0 0
\(427\) −11.4511 + 8.47690i −0.554159 + 0.410226i
\(428\) 0 0
\(429\) 8.18901 3.03340i 0.395369 0.146454i
\(430\) 0 0
\(431\) −14.8277 + 8.56080i −0.714227 + 0.412359i −0.812624 0.582788i \(-0.801962\pi\)
0.0983974 + 0.995147i \(0.468628\pi\)
\(432\) 0 0
\(433\) 27.5219i 1.32262i 0.750113 + 0.661310i \(0.229999\pi\)
−0.750113 + 0.661310i \(0.770001\pi\)
\(434\) 0 0
\(435\) 1.13911 1.37332i 0.0546162 0.0658459i
\(436\) 0 0
\(437\) −18.3264 31.7422i −0.876670 1.51844i
\(438\) 0 0
\(439\) 18.9922 + 10.9651i 0.906446 + 0.523337i 0.879286 0.476294i \(-0.158020\pi\)
0.0271602 + 0.999631i \(0.491354\pi\)
\(440\) 0 0
\(441\) 8.43228 + 19.2327i 0.401537 + 0.915843i
\(442\) 0 0
\(443\) 17.7589 + 10.2531i 0.843750 + 0.487139i 0.858537 0.512752i \(-0.171374\pi\)
−0.0147873 + 0.999891i \(0.504707\pi\)
\(444\) 0 0
\(445\) −0.631136 1.09316i −0.0299187 0.0518207i
\(446\) 0 0
\(447\) −9.90453 + 11.9410i −0.468468 + 0.564790i
\(448\) 0 0
\(449\) 18.7692i 0.885773i −0.896578 0.442886i \(-0.853954\pi\)
0.896578 0.442886i \(-0.146046\pi\)
\(450\) 0 0
\(451\) −11.4057 + 6.58509i −0.537074 + 0.310080i
\(452\) 0 0
\(453\) 4.45458 1.65008i 0.209295 0.0775276i
\(454\) 0 0
\(455\) 0.630928 0.467055i 0.0295783 0.0218959i
\(456\) 0 0
\(457\) −3.79670 + 6.57607i −0.177602 + 0.307616i −0.941059 0.338243i \(-0.890167\pi\)
0.763457 + 0.645859i \(0.223501\pi\)
\(458\) 0 0
\(459\) −9.12747 + 0.155721i −0.426034 + 0.00726845i
\(460\) 0 0
\(461\) −29.2727 −1.36337 −0.681683 0.731648i \(-0.738752\pi\)
−0.681683 + 0.731648i \(0.738752\pi\)
\(462\) 0 0
\(463\) −11.8326 −0.549906 −0.274953 0.961458i \(-0.588662\pi\)
−0.274953 + 0.961458i \(0.588662\pi\)
\(464\) 0 0
\(465\) 0.893478 + 0.152311i 0.0414340 + 0.00706325i
\(466\) 0 0
\(467\) −2.58282 + 4.47358i −0.119519 + 0.207013i −0.919577 0.392910i \(-0.871469\pi\)
0.800058 + 0.599922i \(0.204802\pi\)
\(468\) 0 0
\(469\) 13.5334 1.54465i 0.624914 0.0713254i
\(470\) 0 0
\(471\) −8.14923 21.9998i −0.375497 1.01370i
\(472\) 0 0
\(473\) −19.6712 + 11.3572i −0.904481 + 0.522202i
\(474\) 0 0
\(475\) 21.1751i 0.971580i
\(476\) 0 0
\(477\) −15.3055 + 2.87862i −0.700790 + 0.131803i
\(478\) 0 0
\(479\) 9.85496 + 17.0693i 0.450284 + 0.779915i 0.998403 0.0564848i \(-0.0179893\pi\)
−0.548119 + 0.836400i \(0.684656\pi\)
\(480\) 0 0
\(481\) −10.3775 5.99145i −0.473173 0.273187i
\(482\) 0 0
\(483\) 17.8295 + 35.2395i 0.811268 + 1.60345i
\(484\) 0 0
\(485\) 0.837439 + 0.483496i 0.0380261 + 0.0219544i
\(486\) 0 0
\(487\) −2.50360 4.33637i −0.113449 0.196500i 0.803710 0.595022i \(-0.202857\pi\)
−0.917159 + 0.398522i \(0.869523\pi\)
\(488\) 0 0
\(489\) −5.39730 4.47682i −0.244074 0.202449i
\(490\) 0 0
\(491\) 3.55902i 0.160616i 0.996770 + 0.0803081i \(0.0255904\pi\)
−0.996770 + 0.0803081i \(0.974410\pi\)
\(492\) 0 0
\(493\) 10.7840 6.22614i 0.485687 0.280411i
\(494\) 0 0
\(495\) −0.356776 + 1.01604i −0.0160359 + 0.0456676i
\(496\) 0 0
\(497\) −18.9104 8.21804i −0.848249 0.368629i
\(498\) 0 0
\(499\) −0.404702 + 0.700965i −0.0181170 + 0.0313795i −0.874942 0.484228i \(-0.839100\pi\)
0.856825 + 0.515608i \(0.172434\pi\)
\(500\) 0 0
\(501\) 1.07845 6.32634i 0.0481815 0.282640i
\(502\) 0 0
\(503\) 9.47070 0.422278 0.211139 0.977456i \(-0.432283\pi\)
0.211139 + 0.977456i \(0.432283\pi\)
\(504\) 0 0
\(505\) 2.34390 0.104302
\(506\) 0 0
\(507\) −2.57083 + 15.0809i −0.114175 + 0.669766i
\(508\) 0 0
\(509\) 5.24404 9.08294i 0.232438 0.402594i −0.726087 0.687603i \(-0.758663\pi\)
0.958525 + 0.285009i \(0.0919965\pi\)
\(510\) 0 0
\(511\) 3.91526 + 34.3034i 0.173201 + 1.51749i
\(512\) 0 0
\(513\) 18.9472 11.3744i 0.836538 0.502194i
\(514\) 0 0
\(515\) −0.0214131 + 0.0123629i −0.000943576 + 0.000544774i
\(516\) 0 0
\(517\) 22.9783i 1.01058i
\(518\) 0 0
\(519\) −29.9609 24.8512i −1.31514 1.09085i
\(520\) 0 0
\(521\) 4.77854 + 8.27667i 0.209351 + 0.362607i 0.951510 0.307617i \(-0.0995314\pi\)
−0.742159 + 0.670224i \(0.766198\pi\)
\(522\) 0 0
\(523\) 24.0305 + 13.8740i 1.05078 + 0.606668i 0.922868 0.385117i \(-0.125839\pi\)
0.127912 + 0.991785i \(0.459172\pi\)
\(524\) 0 0
\(525\) 1.25885 22.7813i 0.0549408 0.994259i
\(526\) 0 0
\(527\) 5.47804 + 3.16275i 0.238627 + 0.137771i
\(528\) 0 0
\(529\) 25.6360 + 44.4029i 1.11461 + 1.93056i
\(530\) 0 0
\(531\) −6.21383 33.0387i −0.269657 1.43376i
\(532\) 0 0
\(533\) 10.8860i 0.471526i
\(534\) 0 0
\(535\) 0.877700 0.506740i 0.0379463 0.0219083i
\(536\) 0 0
\(537\) −2.21318 5.97474i −0.0955060 0.257829i
\(538\) 0 0
\(539\) 16.5350 + 5.04809i 0.712213 + 0.217437i
\(540\) 0 0
\(541\) 0.577777 1.00074i 0.0248406 0.0430251i −0.853338 0.521358i \(-0.825426\pi\)
0.878178 + 0.478333i \(0.158759\pi\)
\(542\) 0 0
\(543\) −13.6775 2.33160i −0.586958 0.100058i
\(544\) 0 0
\(545\) 0.196951 0.00843645
\(546\) 0 0
\(547\) −16.1394 −0.690070 −0.345035 0.938590i \(-0.612133\pi\)
−0.345035 + 0.938590i \(0.612133\pi\)
\(548\) 0 0
\(549\) −10.5243 12.2565i −0.449165 0.523095i
\(550\) 0 0
\(551\) −15.0724 + 26.1061i −0.642104 + 1.11216i
\(552\) 0 0
\(553\) −9.00665 12.1667i −0.383002 0.517383i
\(554\) 0 0
\(555\) 1.38563 0.513271i 0.0588168 0.0217871i
\(556\) 0 0
\(557\) 32.1074 18.5372i 1.36043 0.785447i 0.370753 0.928732i \(-0.379100\pi\)
0.989682 + 0.143284i \(0.0457663\pi\)
\(558\) 0 0
\(559\) 18.7749i 0.794092i
\(560\) 0 0
\(561\) −4.79796 + 5.78447i −0.202570 + 0.244221i
\(562\) 0 0
\(563\) 7.79584 + 13.5028i 0.328556 + 0.569075i 0.982225 0.187705i \(-0.0601049\pi\)
−0.653670 + 0.756780i \(0.726772\pi\)
\(564\) 0 0
\(565\) 0.503468 + 0.290677i 0.0211810 + 0.0122289i
\(566\) 0 0
\(567\) −21.0606 + 11.1108i −0.884462 + 0.466612i
\(568\) 0 0
\(569\) −13.0276 7.52147i −0.546144 0.315316i 0.201421 0.979505i \(-0.435444\pi\)
−0.747565 + 0.664188i \(0.768777\pi\)
\(570\) 0 0
\(571\) 2.81334 + 4.87284i 0.117735 + 0.203922i 0.918870 0.394561i \(-0.129103\pi\)
−0.801135 + 0.598484i \(0.795770\pi\)
\(572\) 0 0
\(573\) −1.24023 + 1.49523i −0.0518114 + 0.0624643i
\(574\) 0 0
\(575\) 42.9086i 1.78941i
\(576\) 0 0
\(577\) 19.2278 11.1012i 0.800465 0.462149i −0.0431688 0.999068i \(-0.513745\pi\)
0.843634 + 0.536919i \(0.180412\pi\)
\(578\) 0 0
\(579\) 29.8340 11.0512i 1.23986 0.459273i
\(580\) 0 0
\(581\) −16.8530 + 38.7802i −0.699179 + 1.60887i
\(582\) 0 0
\(583\) −6.41064 + 11.1036i −0.265502 + 0.459863i
\(584\) 0 0
\(585\) 0.579860 + 0.675302i 0.0239743 + 0.0279203i
\(586\) 0 0
\(587\) −20.9245 −0.863648 −0.431824 0.901958i \(-0.642130\pi\)
−0.431824 + 0.901958i \(0.642130\pi\)
\(588\) 0 0
\(589\) −15.3129 −0.630956
\(590\) 0 0
\(591\) −0.506589 0.0863581i −0.0208383 0.00355230i
\(592\) 0 0
\(593\) −10.5845 + 18.3329i −0.434654 + 0.752842i −0.997267 0.0738778i \(-0.976463\pi\)
0.562614 + 0.826720i \(0.309796\pi\)
\(594\) 0 0
\(595\) −0.269255 + 0.619579i −0.0110384 + 0.0254003i
\(596\) 0 0
\(597\) 16.4560 + 44.4248i 0.673499 + 1.81819i
\(598\) 0 0
\(599\) 4.58648 2.64801i 0.187399 0.108195i −0.403366 0.915039i \(-0.632160\pi\)
0.590764 + 0.806844i \(0.298826\pi\)
\(600\) 0 0
\(601\) 37.5346i 1.53107i 0.643396 + 0.765533i \(0.277525\pi\)
−0.643396 + 0.765533i \(0.722475\pi\)
\(602\) 0 0
\(603\) 2.85481 + 15.1789i 0.116257 + 0.618133i
\(604\) 0 0
\(605\) −0.356095 0.616775i −0.0144773 0.0250755i
\(606\) 0 0
\(607\) −34.2123 19.7525i −1.38864 0.801729i −0.395474 0.918477i \(-0.629420\pi\)
−0.993162 + 0.116748i \(0.962753\pi\)
\(608\) 0 0
\(609\) 17.7677 27.1903i 0.719982 1.10181i
\(610\) 0 0
\(611\) 16.4485 + 9.49653i 0.665434 + 0.384189i
\(612\) 0 0
\(613\) −7.19736 12.4662i −0.290699 0.503505i 0.683277 0.730160i \(-0.260554\pi\)
−0.973975 + 0.226655i \(0.927221\pi\)
\(614\) 0 0
\(615\) −1.03321 0.857006i −0.0416632 0.0345578i
\(616\) 0 0
\(617\) 12.1573i 0.489435i −0.969594 0.244718i \(-0.921305\pi\)
0.969594 0.244718i \(-0.0786952\pi\)
\(618\) 0 0
\(619\) 16.8732 9.74173i 0.678190 0.391553i −0.120983 0.992655i \(-0.538605\pi\)
0.799173 + 0.601101i \(0.205271\pi\)
\(620\) 0 0
\(621\) −38.3940 + 23.0488i −1.54070 + 0.924918i
\(622\) 0 0
\(623\) −13.6718 18.4687i −0.547748 0.739932i
\(624\) 0 0
\(625\) −12.3418 + 21.3766i −0.493672 + 0.855065i
\(626\) 0 0
\(627\) 3.05730 17.9346i 0.122097 0.716239i
\(628\) 0 0
\(629\) 10.3124 0.411182
\(630\) 0 0
\(631\) 31.3846 1.24940 0.624701 0.780864i \(-0.285221\pi\)
0.624701 + 0.780864i \(0.285221\pi\)
\(632\) 0 0
\(633\) 6.12091 35.9061i 0.243284 1.42714i
\(634\) 0 0
\(635\) −0.532956 + 0.923107i −0.0211497 + 0.0366324i
\(636\) 0 0
\(637\) 10.4472 9.74991i 0.413933 0.386305i
\(638\) 0 0
\(639\) 7.74596 22.0592i 0.306425 0.872650i
\(640\) 0 0
\(641\) 36.0118 20.7914i 1.42238 0.821211i 0.425878 0.904781i \(-0.359965\pi\)
0.996502 + 0.0835697i \(0.0266321\pi\)
\(642\) 0 0
\(643\) 13.5290i 0.533531i −0.963761 0.266766i \(-0.914045\pi\)
0.963761 0.266766i \(-0.0859549\pi\)
\(644\) 0 0
\(645\) −1.78196 1.47806i −0.0701646 0.0581984i
\(646\) 0 0
\(647\) −15.0442 26.0573i −0.591449 1.02442i −0.994038 0.109038i \(-0.965223\pi\)
0.402589 0.915381i \(-0.368110\pi\)
\(648\) 0 0
\(649\) −23.9683 13.8381i −0.940839 0.543193i
\(650\) 0 0
\(651\) 16.4744 + 0.910345i 0.645684 + 0.0356793i
\(652\) 0 0
\(653\) 18.3717 + 10.6069i 0.718941 + 0.415081i 0.814363 0.580356i \(-0.197087\pi\)
−0.0954221 + 0.995437i \(0.530420\pi\)
\(654\) 0 0
\(655\) −0.443039 0.767366i −0.0173110 0.0299835i
\(656\) 0 0
\(657\) −38.4743 + 7.23615i −1.50103 + 0.282309i
\(658\) 0 0
\(659\) 2.67926i 0.104369i −0.998637 0.0521846i \(-0.983382\pi\)
0.998637 0.0521846i \(-0.0166184\pi\)
\(660\) 0 0
\(661\) 4.79785 2.77004i 0.186615 0.107742i −0.403782 0.914855i \(-0.632305\pi\)
0.590397 + 0.807113i \(0.298971\pi\)
\(662\) 0 0
\(663\) 2.15777 + 5.82513i 0.0838007 + 0.226229i
\(664\) 0 0
\(665\) −0.185455 1.62485i −0.00719162 0.0630090i
\(666\) 0 0
\(667\) 30.5422 52.9006i 1.18260 2.04832i
\(668\) 0 0
\(669\) 11.7718 + 2.00673i 0.455123 + 0.0775846i
\(670\) 0 0
\(671\) −13.2997 −0.513429
\(672\) 0 0
\(673\) −17.1946 −0.662804 −0.331402 0.943490i \(-0.607522\pi\)
−0.331402 + 0.943490i \(0.607522\pi\)
\(674\) 0 0
\(675\) 25.8672 0.441314i 0.995630 0.0169862i
\(676\) 0 0
\(677\) 7.23319 12.5283i 0.277994 0.481500i −0.692892 0.721041i \(-0.743664\pi\)
0.970886 + 0.239541i \(0.0769971\pi\)
\(678\) 0 0
\(679\) 16.1446 + 7.01605i 0.619571 + 0.269251i
\(680\) 0 0
\(681\) 21.7881 8.07083i 0.834923 0.309275i
\(682\) 0 0
\(683\) −28.1356 + 16.2441i −1.07658 + 0.621564i −0.929972 0.367630i \(-0.880169\pi\)
−0.146609 + 0.989195i \(0.546836\pi\)
\(684\) 0 0
\(685\) 2.91730i 0.111464i
\(686\) 0 0
\(687\) 7.03555 8.48214i 0.268423 0.323614i
\(688\) 0 0
\(689\) 5.29882 + 9.17783i 0.201869 + 0.349647i
\(690\) 0 0
\(691\) 28.0961 + 16.2213i 1.06883 + 0.617087i 0.927861 0.372927i \(-0.121646\pi\)
0.140966 + 0.990014i \(0.454979\pi\)
\(692\) 0 0
\(693\) −4.35542 + 19.1133i −0.165449 + 0.726053i
\(694\) 0 0
\(695\) 0.0148138 + 0.00855273i 0.000561918 + 0.000324423i
\(696\) 0 0
\(697\) −4.68421 8.11329i −0.177427 0.307313i
\(698\) 0 0
\(699\) −5.48142 + 6.60845i −0.207326 + 0.249955i
\(700\) 0 0
\(701\) 30.3777i 1.14735i 0.819084 + 0.573674i \(0.194482\pi\)
−0.819084 + 0.573674i \(0.805518\pi\)
\(702\) 0 0
\(703\) −21.6198 + 12.4822i −0.815407 + 0.470776i
\(704\) 0 0
\(705\) −2.19625 + 0.813541i −0.0827154 + 0.0306397i
\(706\) 0 0
\(707\) 42.3932 4.83860i 1.59436 0.181974i
\(708\) 0 0
\(709\) 16.2569 28.1578i 0.610542 1.05749i −0.380607 0.924737i \(-0.624285\pi\)
0.991149 0.132753i \(-0.0423816\pi\)
\(710\) 0 0
\(711\) 13.0225 11.1820i 0.488380 0.419356i
\(712\) 0 0
\(713\) 31.0295 1.16207
\(714\) 0 0
\(715\) 0.732778 0.0274044
\(716\) 0 0
\(717\) −29.6675 5.05741i −1.10795 0.188872i
\(718\) 0 0
\(719\) 5.29867 9.17757i 0.197607 0.342266i −0.750145 0.661273i \(-0.770016\pi\)
0.947752 + 0.319008i \(0.103350\pi\)
\(720\) 0 0
\(721\) −0.361770 + 0.267807i −0.0134730 + 0.00997365i
\(722\) 0 0
\(723\) 8.72744 + 23.5607i 0.324577 + 0.876232i
\(724\) 0 0
\(725\) −30.5618 + 17.6449i −1.13504 + 0.655314i
\(726\) 0 0
\(727\) 31.3600i 1.16308i −0.813518 0.581540i \(-0.802451\pi\)
0.813518 0.581540i \(-0.197549\pi\)
\(728\) 0 0
\(729\) −14.2898 22.9086i −0.529251 0.848466i
\(730\) 0 0
\(731\) −8.07874 13.9928i −0.298803 0.517542i
\(732\) 0 0
\(733\) −3.13184 1.80817i −0.115677 0.0667863i 0.441045 0.897485i \(-0.354608\pi\)
−0.556722 + 0.830699i \(0.687941\pi\)
\(734\) 0 0
\(735\) 0.102925 + 1.75913i 0.00379646 + 0.0648864i
\(736\) 0 0
\(737\) 11.0117 + 6.35763i 0.405623 + 0.234186i
\(738\) 0 0
\(739\) −19.3463 33.5087i −0.711665 1.23264i −0.964232 0.265060i \(-0.914608\pi\)
0.252567 0.967579i \(-0.418725\pi\)
\(740\) 0 0
\(741\) −11.5745 9.60056i −0.425201 0.352685i
\(742\) 0 0
\(743\) 45.1194i 1.65527i −0.561266 0.827635i \(-0.689686\pi\)
0.561266 0.827635i \(-0.310314\pi\)
\(744\) 0 0
\(745\) −1.12740 + 0.650904i −0.0413047 + 0.0238473i
\(746\) 0 0
\(747\) −45.2375 15.8849i −1.65515 0.581197i
\(748\) 0 0
\(749\) 14.8286 10.9771i 0.541823 0.401094i
\(750\) 0 0
\(751\) −11.7841 + 20.4107i −0.430009 + 0.744797i −0.996874 0.0790136i \(-0.974823\pi\)
0.566865 + 0.823811i \(0.308156\pi\)
\(752\) 0 0
\(753\) −1.01809 + 5.97226i −0.0371013 + 0.217641i
\(754\) 0 0
\(755\) 0.398610 0.0145069
\(756\) 0 0
\(757\) 26.2967 0.955770 0.477885 0.878422i \(-0.341404\pi\)
0.477885 + 0.878422i \(0.341404\pi\)
\(758\) 0 0
\(759\) −6.19523 + 36.3421i −0.224872 + 1.31914i
\(760\) 0 0
\(761\) 12.9780 22.4785i 0.470452 0.814846i −0.528977 0.848636i \(-0.677424\pi\)
0.999429 + 0.0337898i \(0.0107577\pi\)
\(762\) 0 0
\(763\) 3.56218 0.406574i 0.128960 0.0147190i
\(764\) 0 0
\(765\) −0.722746 0.253787i −0.0261309 0.00917570i
\(766\) 0 0
\(767\) −19.8114 + 11.4381i −0.715348 + 0.413006i
\(768\) 0 0
\(769\) 36.9215i 1.33142i −0.746209 0.665712i \(-0.768128\pi\)
0.746209 0.665712i \(-0.231872\pi\)
\(770\) 0 0
\(771\) 21.2444 + 17.6212i 0.765097 + 0.634614i
\(772\) 0 0
\(773\) 5.79284 + 10.0335i 0.208354 + 0.360879i 0.951196 0.308587i \(-0.0998561\pi\)
−0.742842 + 0.669466i \(0.766523\pi\)
\(774\) 0 0
\(775\) −15.5247 8.96322i −0.557665 0.321968i
\(776\) 0 0
\(777\) 24.0019 12.1438i 0.861062 0.435655i
\(778\) 0 0
\(779\) 19.6408 + 11.3396i 0.703705 + 0.406284i
\(780\) 0 0
\(781\) −9.62376 16.6688i −0.344365 0.596458i
\(782\) 0 0
\(783\) 32.2050 + 17.8681i 1.15091 + 0.638555i
\(784\) 0 0
\(785\) 1.96861i 0.0702627i
\(786\) 0 0
\(787\) −25.9153 + 14.9622i −0.923779 + 0.533344i −0.884839 0.465897i \(-0.845732\pi\)
−0.0389406 + 0.999242i \(0.512398\pi\)
\(788\) 0 0
\(789\) 8.63827 + 23.3200i 0.307531 +