Properties

Label 336.2.bc.f.17.4
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 17.4
Root \(-1.70742 + 0.291063i\)
Character \(\chi\) = 336.17
Dual form 336.2.bc.f.257.4

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

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

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
\(3\) −0.291063 1.70742i −0.168045 0.985779i
\(4\) 0 0
\(5\) −0.0726693 0.125867i −0.0324987 0.0562894i 0.849319 0.527881i \(-0.177013\pi\)
−0.881817 + 0.471591i \(0.843680\pi\)
\(6\) 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 0.141600 0.989924i \(-0.454775\pi\)
−0.786499 + 0.617592i \(0.788109\pi\)
\(12\) 0 0
\(13\) 2.04143i 0.566191i −0.959092 0.283096i \(-0.908639\pi\)
0.959092 0.283096i \(-0.0913613\pi\)
\(14\) 0 0
\(15\) −0.193756 + 0.160712i −0.0500276 + 0.0414957i
\(16\) 0 0
\(17\) −0.878419 + 1.52147i −0.213048 + 0.369010i −0.952667 0.304016i \(-0.901672\pi\)
0.739619 + 0.673026i \(0.235006\pi\)
\(18\) 0 0
\(19\) 3.68319 2.12649i 0.844983 0.487851i −0.0139720 0.999902i \(-0.504448\pi\)
0.858955 + 0.512051i \(0.171114\pi\)
\(20\) 0 0
\(21\) −3.83616 + 2.50676i −0.837119 + 0.547020i
\(22\) 0 0
\(23\) −7.46351 + 4.30906i −1.55625 + 0.898501i −0.558640 + 0.829410i \(0.688677\pi\)
−0.997610 + 0.0690910i \(0.977990\pi\)
\(24\) 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 \(-0.771363\pi\)
0.752935 0.658095i \(-0.228637\pi\)
\(30\) 0 0
\(31\) −3.11812 1.80025i −0.560031 0.323334i 0.193127 0.981174i \(-0.438137\pi\)
−0.753158 + 0.657840i \(0.771470\pi\)
\(32\) 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 0.517299 0.855805i \(-0.326938\pi\)
−0.999798 + 0.0200916i \(0.993604\pi\)
\(38\) 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 0.975418 + 0.220364i \(0.0707244\pi\)
−0.296868 + 0.954918i \(0.595942\pi\)
\(48\) 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 0.775912 0.630841i \(-0.217290\pi\)
−0.158369 + 0.987380i \(0.550623\pi\)
\(54\) 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 −0.227670 0.973738i \(-0.573111\pi\)
0.957117 0.289701i \(-0.0935558\pi\)
\(60\) 0 0
\(61\) 4.66353 2.69249i 0.597104 0.344738i −0.170798 0.985306i \(-0.554634\pi\)
0.767901 + 0.640568i \(0.221301\pi\)
\(62\) 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 −0.979328 0.202279i \(-0.935165\pi\)
0.664843 + 0.746984i \(0.268499\pi\)
\(68\) 0 0
\(69\) 9.52973 + 11.4891i 1.14724 + 1.38313i
\(70\) 0 0
\(71\) 7.79323i 0.924886i −0.886649 0.462443i \(-0.846973\pi\)
0.886649 0.462443i \(-0.153027\pi\)
\(72\) 0 0
\(73\) 11.3013 + 6.52482i 1.32272 + 0.763672i 0.984162 0.177273i \(-0.0567277\pi\)
0.338558 + 0.940946i \(0.390061\pi\)
\(74\) 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 0.659012 0.752133i \(-0.270975\pi\)
−0.980872 + 0.194655i \(0.937641\pi\)
\(80\) 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 0.538670 0.842517i \(-0.318927\pi\)
−0.998976 + 0.0452432i \(0.985594\pi\)
\(90\) 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 \(0.109674\pi\)
−0.941227 + 0.337774i \(0.890326\pi\)
\(98\) 0 0
\(99\) 7.28165 + 1.36951i 0.731834 + 0.137641i
\(100\) 0 0
\(101\) −8.06357 + 13.9665i −0.802355 + 1.38972i 0.115707 + 0.993283i \(0.463087\pi\)
−0.918062 + 0.396437i \(0.870247\pi\)
\(102\) 0 0
\(103\) 0.147333 0.0850626i 0.0145171 0.00838147i −0.492724 0.870186i \(-0.663999\pi\)
0.507241 + 0.861804i \(0.330665\pi\)
\(104\) 0 0
\(105\) 0.594290 + 0.300681i 0.0579967 + 0.0293435i
\(106\) 0 0
\(107\) −6.03900 + 3.48662i −0.583813 + 0.337064i −0.762647 0.646815i \(-0.776101\pi\)
0.178835 + 0.983879i \(0.442767\pi\)
\(108\) 0 0
\(109\) −0.677559 + 1.17357i −0.0648984 + 0.112407i −0.896649 0.442742i \(-0.854006\pi\)
0.831751 + 0.555150i \(0.187339\pi\)
\(110\) 0 0
\(111\) −7.82532 + 6.49076i −0.742747 + 0.616076i
\(112\) 0 0
\(113\) 4.00000i 0.376288i 0.982141 + 0.188144i \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 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 0.701579 0.712592i \(-0.252479\pi\)
−0.967912 + 0.251289i \(0.919146\pi\)
\(132\) 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 −0.485291 0.874353i \(-0.661286\pi\)
−0.999857 + 0.0169018i \(0.994620\pi\)
\(138\) 0 0
\(139\) 0.117694i 0.00998266i 0.999988 + 0.00499133i \(0.00158880\pi\)
−0.999988 + 0.00499133i \(0.998411\pi\)
\(140\) 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 −0.147390 0.989078i \(-0.547087\pi\)
0.782872 + 0.622183i \(0.213754\pi\)
\(150\) 0 0
\(151\) −1.37132 + 2.37519i −0.111596 + 0.193290i −0.916414 0.400232i \(-0.868930\pi\)
0.804818 + 0.593522i \(0.202263\pi\)
\(152\) 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 −0.0474193 0.998875i \(-0.515100\pi\)
−0.888761 + 0.458371i \(0.848433\pi\)
\(158\) 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 0.775793 0.630987i \(-0.217350\pi\)
−0.934347 + 0.356363i \(0.884017\pi\)
\(164\) 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 −0.877263 0.480011i \(-0.840633\pi\)
0.0229296 0.999737i \(-0.492701\pi\)
\(174\) 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 0.376196 0.926540i \(-0.377232\pi\)
−0.614309 + 0.789065i \(0.710565\pi\)
\(180\) 0 0
\(181\) 8.01062i 0.595425i −0.954656 0.297712i \(-0.903776\pi\)
0.954656 0.297712i \(-0.0962237\pi\)
\(182\) 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 −0.464447 0.885601i \(-0.653747\pi\)
0.534730 + 0.845023i \(0.320413\pi\)
\(192\) 0 0
\(193\) −9.18421 + 15.9075i −0.661094 + 1.14505i 0.319235 + 0.947676i \(0.396574\pi\)
−0.980329 + 0.197373i \(0.936759\pi\)
\(194\) 0 0
\(195\) 0.328083 + 0.395540i 0.0234945 + 0.0283252i
\(196\) 0 0
\(197\) 0.296699i 0.0211389i −0.999944 0.0105695i \(-0.996636\pi\)
0.999944 0.0105695i \(-0.00336442\pi\)
\(198\) 0 0
\(199\) 23.6874 + 13.6759i 1.67915 + 0.969460i 0.962202 + 0.272336i \(0.0877962\pi\)
0.716951 + 0.697124i \(0.245537\pi\)
\(200\) 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 \(0.0741487\pi\)
−0.972991 + 0.230844i \(0.925851\pi\)
\(224\) 0 0
\(225\) −2.76084 + 14.6793i −0.184056 + 0.978617i
\(226\) 0 0
\(227\) −6.70734 + 11.6174i −0.445182 + 0.771077i −0.998065 0.0621816i \(-0.980194\pi\)
0.552883 + 0.833259i \(0.313528\pi\)
\(228\) 0 0
\(229\) −5.51012 + 3.18127i −0.364119 + 0.210224i −0.670886 0.741560i \(-0.734086\pi\)
0.306767 + 0.951785i \(0.400753\pi\)
\(230\) 0 0
\(231\) 11.3007 0.624454i 0.743530 0.0410861i
\(232\) 0 0
\(233\) 4.29295 2.47853i 0.281240 0.162374i −0.352744 0.935720i \(-0.614752\pi\)
0.633985 + 0.773346i \(0.281418\pi\)
\(234\) 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 \(-0.810044\pi\)
0.827159 0.561968i \(-0.189956\pi\)
\(240\) 0 0
\(241\) 12.5626 + 7.25302i 0.809228 + 0.467208i 0.846688 0.532090i \(-0.178593\pi\)
−0.0374597 + 0.999298i \(0.511927\pi\)
\(242\) 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 0.999994 0.00343985i \(-0.00109494\pi\)
−0.502976 + 0.864300i \(0.667762\pi\)
\(258\) 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 0.831706 0.555216i \(-0.187364\pi\)
−0.0649777 + 0.997887i \(0.520698\pi\)
\(264\) 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 −0.731668 0.681661i \(-0.761258\pi\)
0.956170 + 0.292812i \(0.0945911\pi\)
\(270\) 0 0
\(271\) −10.8537 + 6.26636i −0.659313 + 0.380654i −0.792015 0.610501i \(-0.790968\pi\)
0.132702 + 0.991156i \(0.457635\pi\)
\(272\) 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 −0.298614 + 0.954374i \(0.596524\pi\)
−0.677205 + 0.735794i \(0.736809\pi\)
\(278\) 0 0
\(279\) 10.6154 + 1.99651i 0.635526 + 0.119528i
\(280\) 0 0
\(281\) 10.1758i 0.607037i 0.952826 + 0.303518i \(0.0981614\pi\)
−0.952826 + 0.303518i \(0.901839\pi\)
\(282\) 0 0
\(283\) 1.18666 + 0.685120i 0.0705397 + 0.0407261i 0.534855 0.844944i \(-0.320366\pi\)
−0.464315 + 0.885670i \(0.653700\pi\)
\(284\) 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 \(-0.796566\pi\)
0.802629 0.596479i \(-0.203434\pi\)
\(308\) 0 0
\(309\) −0.188121 0.226800i −0.0107018 0.0129022i
\(310\) 0 0
\(311\) 5.74040 9.94267i 0.325508 0.563797i −0.656107 0.754668i \(-0.727798\pi\)
0.981615 + 0.190871i \(0.0611312\pi\)
\(312\) 0 0
\(313\) 8.57172 4.94889i 0.484502 0.279728i −0.237788 0.971317i \(-0.576423\pi\)
0.722291 + 0.691589i \(0.243089\pi\)
\(314\) 0 0
\(315\) 0.340413 1.10222i 0.0191801 0.0621030i
\(316\) 0 0
\(317\) 5.74547 3.31715i 0.322698 0.186310i −0.329897 0.944017i \(-0.607014\pi\)
0.652594 + 0.757707i \(0.273681\pi\)
\(318\) 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 0.994303 0.106595i \(-0.0339948\pi\)
−0.589465 + 0.807794i \(0.700661\pi\)
\(332\) 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 0.836100 0.548577i \(-0.184830\pi\)
−0.0570320 + 0.998372i \(0.518164\pi\)
\(348\) 0 0
\(349\) 3.12385i 0.167216i 0.996499 + 0.0836080i \(0.0266443\pi\)
−0.996499 + 0.0836080i \(0.973356\pi\)
\(350\) 0 0
\(351\) 9.27558 5.14632i 0.495094 0.274690i
\(352\) 0 0
\(353\) 17.7450 30.7353i 0.944473 1.63587i 0.187669 0.982232i \(-0.439907\pi\)
0.756804 0.653642i \(-0.226760\pi\)
\(354\) 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 −0.349869 0.936799i \(-0.613774\pi\)
0.636357 + 0.771395i \(0.280441\pi\)
\(360\) 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 0.829722 0.558177i \(-0.188499\pi\)
−0.0685342 + 0.997649i \(0.521832\pi\)
\(368\) 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 0.881559 0.472073i \(-0.156494\pi\)
−0.849607 + 0.527416i \(0.823161\pi\)
\(374\) 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 0.964450 0.264266i \(-0.0851298\pi\)
−0.711086 + 0.703105i \(0.751796\pi\)
\(384\) 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 0.762477 0.647016i \(-0.223983\pi\)
−0.179094 + 0.983832i \(0.557317\pi\)
\(390\) 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 0.131691 0.991291i \(-0.457959\pi\)
0.924328 + 0.381598i \(0.124626\pi\)
\(398\) 0 0
\(399\) −8.79872 + 17.3905i −0.440487 + 0.870612i
\(400\) 0 0
\(401\) −12.4125 + 7.16635i −0.619850 + 0.357870i −0.776810 0.629735i \(-0.783164\pi\)
0.156961 + 0.987605i \(0.449830\pi\)
\(402\) 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 0.862904 0.505368i \(-0.168643\pi\)
−0.00620937 + 0.999981i \(0.501977\pi\)
\(410\) 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 0.0983974 0.995147i \(-0.468628\pi\)
−0.812624 + 0.582788i \(0.801962\pi\)
\(432\) 0 0
\(433\) 27.5219i 1.32262i −0.750113 0.661310i \(-0.770001\pi\)
0.750113 0.661310i \(-0.229999\pi\)
\(434\) 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 0.0271602 0.999631i \(-0.491354\pi\)
0.879286 + 0.476294i \(0.158020\pi\)
\(440\) 0 0
\(441\) 8.43228 19.2327i 0.401537 0.915843i
\(442\) 0 0
\(443\) 17.7589 10.2531i 0.843750 0.487139i −0.0147873 0.999891i \(-0.504707\pi\)
0.858537 + 0.512752i \(0.171374\pi\)
\(444\) 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 \(0.146046\pi\)
−0.896578 + 0.442886i \(0.853954\pi\)
\(450\) 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 0.763457 0.645859i \(-0.223501\pi\)
−0.941059 + 0.338243i \(0.890167\pi\)
\(458\) 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 0.800058 0.599922i \(-0.204802\pi\)
−0.919577 + 0.392910i \(0.871469\pi\)
\(468\) 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 −0.548119 0.836400i \(-0.684656\pi\)
0.998403 + 0.0564848i \(0.0179893\pi\)
\(480\) 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 −0.917159 0.398522i \(-0.869523\pi\)
0.803710 + 0.595022i \(0.202857\pi\)
\(488\) 0 0
\(489\) −5.39730 + 4.47682i −0.244074 + 0.202449i
\(490\) 0 0
\(491\) 3.55902i 0.160616i −0.996770 0.0803081i \(-0.974410\pi\)
0.996770 0.0803081i \(-0.0255904\pi\)
\(492\) 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 0.856825 0.515608i \(-0.172434\pi\)
−0.874942 + 0.484228i \(0.839100\pi\)
\(500\) 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 0.958525 0.285009i \(-0.0919965\pi\)
−0.726087 + 0.687603i \(0.758663\pi\)
\(510\) 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 −0.742159 0.670224i \(-0.766198\pi\)
0.951510 + 0.307617i \(0.0995314\pi\)
\(522\) 0 0
\(523\) 24.0305 13.8740i 1.05078 0.606668i 0.127912 0.991785i \(-0.459172\pi\)
0.922868 + 0.385117i \(0.125839\pi\)
\(524\) 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 0.878178 0.478333i \(-0.158759\pi\)
−0.853338 + 0.521358i \(0.825426\pi\)
\(542\) 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 0.989682 0.143284i \(-0.0457663\pi\)
0.370753 + 0.928732i \(0.379100\pi\)
\(558\) 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 −0.653670 0.756780i \(-0.726772\pi\)
0.982225 + 0.187705i \(0.0601049\pi\)
\(564\) 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 −0.747565 0.664188i \(-0.768777\pi\)
0.201421 + 0.979505i \(0.435444\pi\)
\(570\) 0 0
\(571\) 2.81334 4.87284i 0.117735 0.203922i −0.801135 0.598484i \(-0.795770\pi\)
0.918870 + 0.394561i \(0.129103\pi\)
\(572\) 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 0.843634 0.536919i \(-0.180412\pi\)
−0.0431688 + 0.999068i \(0.513745\pi\)
\(578\) 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 0.562614 0.826720i \(-0.309796\pi\)
−0.997267 + 0.0738778i \(0.976463\pi\)
\(594\) 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 0.590764 0.806844i \(-0.298826\pi\)
−0.403366 + 0.915039i \(0.632160\pi\)
\(600\) 0 0
\(601\) 37.5346i 1.53107i −0.643396 0.765533i \(-0.722475\pi\)
0.643396 0.765533i \(-0.277525\pi\)
\(602\) 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 −0.993162 0.116748i \(-0.962753\pi\)
−0.395474 + 0.918477i \(0.629420\pi\)
\(608\) 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 −0.973975 0.226655i \(-0.927221\pi\)
0.683277 + 0.730160i \(0.260554\pi\)
\(614\) 0 0
\(615\) −1.03321 + 0.857006i −0.0416632 + 0.0345578i
\(616\) 0 0
\(617\) 12.1573i 0.489435i 0.969594 + 0.244718i \(0.0786952\pi\)
−0.969594 + 0.244718i \(0.921305\pi\)
\(618\) 0 0
\(619\) 16.8732 + 9.74173i 0.678190 + 0.391553i 0.799173 0.601101i \(-0.205271\pi\)
−0.120983 + 0.992655i \(0.538605\pi\)
\(620\) 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 0.996502 0.0835697i \(-0.0266321\pi\)
0.425878 + 0.904781i \(0.359965\pi\)
\(642\) 0 0
\(643\) 13.5290i 0.533531i 0.963761 + 0.266766i \(0.0859549\pi\)
−0.963761 + 0.266766i \(0.914045\pi\)
\(644\) 0 0
\(645\) −1.78196 + 1.47806i −0.0701646 + 0.0581984i
\(646\) 0 0
\(647\) −15.0442 + 26.0573i −0.591449 + 1.02442i 0.402589 + 0.915381i \(0.368110\pi\)
−0.994038 + 0.109038i \(0.965223\pi\)
\(648\) 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 −0.0954221 0.995437i \(-0.530420\pi\)
0.814363 + 0.580356i \(0.197087\pi\)
\(654\) 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 \(0.0166184\pi\)
−0.998637 + 0.0521846i \(0.983382\pi\)
\(660\) 0 0
\(661\) 4.79785 + 2.77004i 0.186615 + 0.107742i 0.590397 0.807113i \(-0.298971\pi\)
−0.403782 + 0.914855i \(0.632305\pi\)
\(662\) 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 0.970886 0.239541i \(-0.0769971\pi\)
−0.692892 + 0.721041i \(0.743664\pi\)
\(678\) 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 −0.146609 0.989195i \(-0.546836\pi\)
−0.929972 + 0.367630i \(0.880169\pi\)
\(684\) 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 0.140966 0.990014i \(-0.454979\pi\)
0.927861 + 0.372927i \(0.121646\pi\)
\(692\) 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 \(-0.805518\pi\)
0.819084 0.573674i \(-0.194482\pi\)
\(702\) 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 0.991149 + 0.132753i \(0.0423816\pi\)
−0.380607 + 0.924737i \(0.624285\pi\)
\(710\) 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 0.947752 0.319008i \(-0.103350\pi\)
−0.750145 + 0.661273i \(0.770016\pi\)
\(720\) 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 \(0.197549\pi\)
−0.813518 + 0.581540i \(0.802451\pi\)
\(728\) 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 −0.556722 0.830699i \(-0.687941\pi\)
0.441045 + 0.897485i \(0.354608\pi\)
\(734\) 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 0.252567 + 0.967579i \(0.418725\pi\)
−0.964232 + 0.265060i \(0.914608\pi\)
\(740\) 0 0
\(741\) −11.5745 + 9.60056i −0.425201 + 0.352685i
\(742\) 0 0
\(743\) 45.1194i 1.65527i 0.561266 + 0.827635i \(0.310314\pi\)
−0.561266 + 0.827635i \(0.689686\pi\)
\(744\) 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 0.566865 0.823811i \(-0.308156\pi\)
−0.996874 + 0.0790136i \(0.974823\pi\)
\(752\) 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 0.999429 0.0337898i \(-0.0107577\pi\)
−0.528977 + 0.848636i \(0.677424\pi\)
\(762\) 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 \(0.231872\pi\)
−0.746209 + 0.665712i \(0.768128\pi\)
\(770\) 0 0
\(771\) 21.2444 17.6212i 0.765097 0.634614i
\(772\) 0 0
\(773\) 5.79284 10.0335i 0.208354 0.360879i −0.742842 0.669466i \(-0.766523\pi\)
0.951196 + 0.308587i \(0.0998561\pi\)
\(774\) 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 −0.0389406 0.999242i \(-0.512398\pi\)
−0.884839 + 0.465897i \(0.845732\pi\)
\(788\) 0 0
\(789\) 8.63827 23.3200i 0.307531 0.830214i