Properties

Label 168.2.u.a.17.7
Level 168
Weight 2
Character 168.17
Analytic conductor 1.341
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 168.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.7
Root \(-1.70742 + 0.291063i\)
Character \(\chi\) = 168.17
Dual form 168.2.u.a.89.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +O(q^{10})\) \(q+(1.62420 - 0.601642i) q^{3} +(0.0726693 + 0.125867i) q^{5} +(1.05451 + 2.42652i) q^{7} +(2.27605 - 1.95437i) q^{9} +(-2.13889 - 1.23489i) q^{11} -2.04143i q^{13} +(0.193756 + 0.160712i) q^{15} +(0.878419 - 1.52147i) q^{17} +(-3.68319 + 2.12649i) q^{19} +(3.17263 + 3.30672i) q^{21} +(-7.46351 + 4.30906i) q^{23} +(2.48944 - 4.31183i) q^{25} +(2.52094 - 4.54366i) q^{27} +7.08790i q^{29} +(3.11812 + 1.80025i) q^{31} +(-4.21694 - 0.718860i) q^{33} +(-0.228788 + 0.309061i) q^{35} +(-2.93493 - 5.08345i) q^{37} +(-1.22821 - 3.31569i) q^{39} -5.33255 q^{41} -9.19692 q^{43} +(0.411390 + 0.144457i) q^{45} +(4.65190 + 8.05733i) q^{47} +(-4.77602 + 5.11758i) q^{49} +(0.511351 - 2.99966i) q^{51} +(-4.49578 - 2.59564i) q^{53} -0.358953i q^{55} +(-4.70286 + 5.66982i) q^{57} +(5.60299 - 9.70466i) q^{59} +(4.66353 - 2.69249i) q^{61} +(7.14245 + 3.46199i) q^{63} +(0.256949 - 0.148349i) q^{65} +(2.57417 - 4.45860i) q^{67} +(-9.52973 + 11.4891i) q^{69} -7.79323i q^{71} +(11.3013 + 6.52482i) q^{73} +(1.44917 - 8.50103i) q^{75} +(0.741003 - 6.49226i) q^{77} +(2.86075 + 4.95497i) q^{79} +(1.36085 - 8.89652i) q^{81} +15.9818 q^{83} +0.255336 q^{85} +(4.26437 + 11.5122i) q^{87} +(4.34252 + 7.52147i) q^{89} +(4.95358 - 2.15271i) q^{91} +(6.14756 + 1.04797i) q^{93} +(-0.535310 - 0.309061i) q^{95} +6.65337i q^{97} +(-7.28165 + 1.36951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 16q + 4q^{7} + 2q^{9} + 8q^{15} - 6q^{19} + 14q^{21} - 18q^{25} - 48q^{31} - 12q^{33} - 2q^{37} - 22q^{39} + 20q^{43} - 42q^{45} - 28q^{49} + 6q^{51} - 8q^{57} + 36q^{61} - 32q^{63} + 14q^{67} + 30q^{73} + 54q^{75} + 28q^{79} + 30q^{81} + 16q^{85} + 78q^{87} + 66q^{91} + 16q^{93} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.62420 0.601642i 0.937733 0.347358i
\(4\) 0 0
\(5\) 0.0726693 + 0.125867i 0.0324987 + 0.0562894i 0.881817 0.471591i \(-0.156320\pi\)
−0.849319 + 0.527881i \(0.822987\pi\)
\(6\) 0 0
\(7\) 1.05451 + 2.42652i 0.398567 + 0.917139i
\(8\) 0 0
\(9\) 2.27605 1.95437i 0.758685 0.651458i
\(10\) 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 −0.739619 0.673026i \(-0.764994\pi\)
0.952667 + 0.304016i \(0.0983276\pi\)
\(18\) 0 0
\(19\) −3.68319 + 2.12649i −0.844983 + 0.487851i −0.858955 0.512051i \(-0.828886\pi\)
0.0139720 + 0.999902i \(0.495552\pi\)
\(20\) 0 0
\(21\) 3.17263 + 3.30672i 0.692325 + 0.721586i
\(22\) 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 \(0.228637\pi\)
−0.752935 + 0.658095i \(0.771363\pi\)
\(30\) 0 0
\(31\) 3.11812 + 1.80025i 0.560031 + 0.323334i 0.753158 0.657840i \(-0.228530\pi\)
−0.193127 + 0.981174i \(0.561863\pi\)
\(32\) 0 0
\(33\) −4.21694 0.718860i −0.734075 0.125138i
\(34\) 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
\(39\) −1.22821 3.31569i −0.196671 0.530936i
\(40\) 0 0
\(41\) −5.33255 −0.832804 −0.416402 0.909181i \(-0.636709\pi\)
−0.416402 + 0.909181i \(0.636709\pi\)
\(42\) 0 0
\(43\) −9.19692 −1.40252 −0.701258 0.712907i \(-0.747378\pi\)
−0.701258 + 0.712907i \(0.747378\pi\)
\(44\) 0 0
\(45\) 0.411390 + 0.144457i 0.0613264 + 0.0215344i
\(46\) 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
\(51\) 0.511351 2.99966i 0.0716034 0.420036i
\(52\) 0 0
\(53\) −4.49578 2.59564i −0.617543 0.356539i 0.158369 0.987380i \(-0.449377\pi\)
−0.775912 + 0.630841i \(0.782710\pi\)
\(54\) 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
\(63\) 7.14245 + 3.46199i 0.899864 + 0.436170i
\(64\) 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 \(-0.731501\pi\)
0.979328 + 0.202279i \(0.0648347\pi\)
\(68\) 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
\(75\) 1.44917 8.50103i 0.167335 0.981615i
\(76\) 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 \(-0.0623586\pi\)
−0.659012 + 0.752133i \(0.729025\pi\)
\(80\) 0 0
\(81\) 1.36085 8.89652i 0.151205 0.988502i
\(82\) 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
\(87\) 4.26437 + 11.5122i 0.457189 + 1.23423i
\(88\) 0 0
\(89\) 4.34252 + 7.52147i 0.460306 + 0.797274i 0.998976 0.0452432i \(-0.0144063\pi\)
−0.538670 + 0.842517i \(0.681073\pi\)
\(90\) 0 0
\(91\) 4.95358 2.15271i 0.519276 0.225665i
\(92\) 0 0
\(93\) 6.14756 + 1.04797i 0.637472 + 0.108670i
\(94\) 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 \(-0.536913\pi\)
0.918062 0.396437i \(-0.129753\pi\)
\(102\) 0 0
\(103\) −0.147333 + 0.0850626i −0.0145171 + 0.00838147i −0.507241 0.861804i \(-0.669335\pi\)
0.492724 + 0.870186i \(0.336001\pi\)
\(104\) 0 0
\(105\) −0.185654 + 0.639626i −0.0181179 + 0.0624211i
\(106\) 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 \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) −1.08474 0.626273i −0.101152 0.0584002i
\(116\) 0 0
\(117\) −3.98972 4.64641i −0.368850 0.429561i
\(118\) 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
\(123\) −8.66113 + 3.20828i −0.780948 + 0.289281i
\(124\) 0 0
\(125\) 1.45032 0.129720
\(126\) 0 0
\(127\) −7.33399 −0.650787 −0.325393 0.945579i \(-0.605497\pi\)
−0.325393 + 0.945579i \(0.605497\pi\)
\(128\) 0 0
\(129\) −14.9376 + 5.53325i −1.31519 + 0.487175i
\(130\) 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
\(135\) 0.755091 0.0128824i 0.0649879 0.00110874i
\(136\) 0 0
\(137\) 17.3832 + 10.0362i 1.48515 + 0.857451i 0.999857 0.0169018i \(-0.00538026\pi\)
0.485291 + 0.874353i \(0.338714\pi\)
\(138\) 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
\(147\) −4.67826 + 11.1854i −0.385856 + 0.922559i
\(148\) 0 0
\(149\) −7.75705 + 4.47853i −0.635482 + 0.366896i −0.782872 0.622183i \(-0.786246\pi\)
0.147390 + 0.989078i \(0.452913\pi\)
\(150\) 0 0
\(151\) 1.37132 2.37519i 0.111596 0.193290i −0.804818 0.593522i \(-0.797737\pi\)
0.916414 + 0.400232i \(0.131070\pi\)
\(152\) 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
\(159\) −8.86370 1.51099i −0.702937 0.119829i
\(160\) 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 \(-0.115983\pi\)
−0.775793 + 0.630987i \(0.782650\pi\)
\(164\) 0 0
\(165\) −0.215961 0.583012i −0.0168126 0.0453874i
\(166\) 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
\(171\) −4.22719 + 12.0384i −0.323261 + 0.920596i
\(172\) 0 0
\(173\) 11.2370 + 19.4630i 0.854333 + 1.47975i 0.877263 + 0.480011i \(0.159367\pi\)
−0.0229296 + 0.999737i \(0.507299\pi\)
\(174\) 0 0
\(175\) 13.0879 + 1.49381i 0.989352 + 0.112921i
\(176\) 0 0
\(177\) 3.26165 19.1333i 0.245160 1.43815i
\(178\) 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
\(189\) 13.6837 + 1.32577i 0.995339 + 0.0964354i
\(190\) 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 \(0.00336442\pi\)
−0.999944 + 0.0105695i \(0.996636\pi\)
\(198\) 0 0
\(199\) −23.6874 13.6759i −1.67915 0.969460i −0.962202 0.272336i \(-0.912204\pi\)
−0.716951 0.697124i \(-0.754463\pi\)
\(200\) 0 0
\(201\) 1.49850 8.79039i 0.105696 0.620027i
\(202\) 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
\(207\) −8.56585 + 24.3942i −0.595368 + 1.69551i
\(208\) 0 0
\(209\) 10.5039 0.726571
\(210\) 0 0
\(211\) 21.0295 1.44773 0.723864 0.689942i \(-0.242364\pi\)
0.723864 + 0.689942i \(0.242364\pi\)
\(212\) 0 0
\(213\) −4.68873 12.6578i −0.321267 0.867296i
\(214\) 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
\(219\) 22.2812 + 3.79827i 1.50562 + 0.256663i
\(220\) 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 −0.998065 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
\(231\) −2.70248 10.9905i −0.177810 0.723125i
\(232\) 0 0
\(233\) −4.29295 + 2.47853i −0.281240 + 0.162374i −0.633985 0.773346i \(-0.718582\pi\)
0.352744 + 0.935720i \(0.385248\pi\)
\(234\) 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
\(243\) −3.14223 15.2685i −0.201574 0.979473i
\(244\) 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
\(249\) 25.9577 9.61532i 1.64500 0.609346i
\(250\) 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
\(255\) 0.414717 0.153621i 0.0259706 0.00962012i
\(256\) 0 0
\(257\) −7.96781 13.8006i −0.497018 0.860861i 0.502976 0.864300i \(-0.332238\pi\)
−0.999994 + 0.00343985i \(0.998905\pi\)
\(258\) 0 0
\(259\) 9.24018 12.4822i 0.574157 0.775607i
\(260\) 0 0
\(261\) 13.8524 + 16.1324i 0.857442 + 0.998573i
\(262\) 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 −0.956170 0.292812i \(-0.905409\pi\)
0.731668 + 0.681661i \(0.238742\pi\)
\(270\) 0 0
\(271\) 10.8537 6.26636i 0.659313 0.380654i −0.132702 0.991156i \(-0.542365\pi\)
0.792015 + 0.610501i \(0.209032\pi\)
\(272\) 0 0
\(273\) 6.75044 6.47671i 0.408555 0.391988i
\(274\) 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 \(-0.901839\pi\)
0.952826 0.303518i \(-0.0981614\pi\)
\(282\) 0 0
\(283\) −1.18666 0.685120i −0.0705397 0.0407261i 0.464315 0.885670i \(-0.346300\pi\)
−0.534855 + 0.844944i \(0.679634\pi\)
\(284\) 0 0
\(285\) −1.05540 0.179913i −0.0625162 0.0106571i
\(286\) 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
\(291\) 4.00295 + 10.8064i 0.234657 + 0.633483i
\(292\) 0 0
\(293\) −16.9961 −0.992923 −0.496461 0.868059i \(-0.665368\pi\)
−0.496461 + 0.868059i \(0.665368\pi\)
\(294\) 0 0
\(295\) 1.62866 0.0948243
\(296\) 0 0
\(297\) −11.0029 + 6.60531i −0.638453 + 0.383279i
\(298\) 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
\(303\) 4.69402 27.5358i 0.269664 1.58189i
\(304\) 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 −0.656107 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
\(315\) 0.0832870 + 1.15058i 0.00469269 + 0.0648278i
\(316\) 0 0
\(317\) −5.74547 + 3.31715i −0.322698 + 0.186310i −0.652594 0.757707i \(-0.726319\pi\)
0.329897 + 0.944017i \(0.392986\pi\)
\(318\) 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
\(327\) −0.394425 + 2.31376i −0.0218118 + 0.127951i
\(328\) 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 \(-0.299339\pi\)
−0.994303 + 0.106595i \(0.966005\pi\)
\(332\) 0 0
\(333\) −16.6150 5.83425i −0.910497 0.319715i
\(334\) 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
\(339\) −2.40657 6.49680i −0.130707 0.352858i
\(340\) 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
\(345\) −2.13862 0.364570i −0.115139 0.0196278i
\(346\) 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 \(0.560093\pi\)
−0.756804 + 0.653642i \(0.773240\pi\)
\(354\) 0 0
\(355\) 0.980910 0.566328i 0.0520613 0.0300576i
\(356\) 0 0
\(357\) 7.81796 1.92237i 0.413770 0.101742i
\(358\) 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 0.0685342 0.997649i \(-0.478168\pi\)
−0.829722 + 0.558177i \(0.811501\pi\)
\(368\) 0 0
\(369\) −12.1372 + 10.4218i −0.631836 + 0.542537i
\(370\) 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
\(375\) 2.35560 0.872570i 0.121643 0.0450593i
\(376\) 0 0
\(377\) 14.4695 0.745215
\(378\) 0 0
\(379\) −14.3895 −0.739141 −0.369571 0.929203i \(-0.620495\pi\)
−0.369571 + 0.929203i \(0.620495\pi\)
\(380\) 0 0
\(381\) −11.9119 + 4.41244i −0.610264 + 0.226056i
\(382\) 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
\(387\) −20.9327 + 17.9742i −1.06407 + 0.913680i
\(388\) 0 0
\(389\) −11.5061 6.64306i −0.583383 0.336816i 0.179094 0.983832i \(-0.442683\pi\)
−0.762477 + 0.647016i \(0.776017\pi\)
\(390\) 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
\(399\) −18.7171 5.43271i −0.937029 0.271976i
\(400\) 0 0
\(401\) 12.4125 7.16635i 0.619850 0.357870i −0.156961 0.987605i \(-0.550170\pi\)
0.776810 + 0.629735i \(0.216836\pi\)
\(402\) 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
\(411\) 34.2720 + 5.84234i 1.69051 + 0.288181i
\(412\) 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
\(417\) −0.0708095 0.191158i −0.00346756 0.00936107i
\(418\) 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
\(423\) 26.3350 + 9.24737i 1.28045 + 0.449622i
\(424\) 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
\(429\) −1.46750 + 8.60859i −0.0708517 + 0.415627i
\(430\) 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 −0.879286 0.476294i \(-0.841980\pi\)
−0.0271602 + 0.999631i \(0.508646\pi\)
\(440\) 0 0
\(441\) −0.868806 + 20.9820i −0.0413717 + 0.999144i
\(442\) 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 \(-0.853954\pi\)
0.896578 0.442886i \(-0.146046\pi\)
\(450\) 0 0
\(451\) 11.4057 + 6.58509i 0.537074 + 0.310080i
\(452\) 0 0
\(453\) 0.798279 4.68282i 0.0375064 0.220018i
\(454\) 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
\(459\) −4.69859 7.82676i −0.219312 0.365322i
\(460\) 0 0
\(461\) 29.2727 1.36337 0.681683 0.731648i \(-0.261248\pi\)
0.681683 + 0.731648i \(0.261248\pi\)
\(462\) 0 0
\(463\) 11.8326 0.549906 0.274953 0.961458i \(-0.411338\pi\)
0.274953 + 0.961458i \(0.411338\pi\)
\(464\) 0 0
\(465\) 0.314834 + 0.849930i 0.0146001 + 0.0394146i
\(466\) 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
\(471\) −23.1270 3.94245i −1.06563 0.181658i
\(472\) 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
\(483\) −37.9278 11.0087i −1.72578 0.500913i
\(484\) 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 \(-0.797143\pi\)
0.917159 + 0.398522i \(0.130477\pi\)
\(488\) 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
\(495\) −0.701529 0.816997i −0.0315314 0.0367213i
\(496\) 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 \(-0.160900\pi\)
−0.856825 + 0.515608i \(0.827566\pi\)
\(500\) 0 0
\(501\) −6.01800 + 2.22921i −0.268864 + 0.0995936i
\(502\) 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
\(507\) 14.3458 5.31404i 0.637122 0.236005i
\(508\) 0 0
\(509\) −5.24404 9.08294i −0.232438 0.402594i 0.726087 0.687603i \(-0.241337\pi\)
−0.958525 + 0.285009i \(0.908004\pi\)
\(510\) 0 0
\(511\) −3.91526 + 34.3034i −0.173201 + 1.51749i
\(512\) 0 0
\(513\) 0.376973 + 22.0960i 0.0166438 + 0.975560i
\(514\) 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 \(-0.900469\pi\)
0.742159 + 0.670224i \(0.233802\pi\)
\(522\) 0 0
\(523\) −24.0305 + 13.8740i −1.05078 + 0.606668i −0.922868 0.385117i \(-0.874161\pi\)
−0.127912 + 0.991785i \(0.540828\pi\)
\(524\) 0 0
\(525\) 22.1561 5.44799i 0.966972 0.237770i
\(526\) 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
\(537\) −6.28087 1.07070i −0.271040 0.0462040i
\(538\) 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
\(543\) −4.81953 13.0109i −0.206826 0.558349i
\(544\) 0 0
\(545\) −0.196951 −0.00843645
\(546\) 0 0
\(547\) 16.1394 0.690070 0.345035 0.938590i \(-0.387867\pi\)
0.345035 + 0.938590i \(0.387867\pi\)
\(548\) 0 0
\(549\) 5.35232 15.2425i 0.228431 0.650536i
\(550\) 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
\(555\) 0.248311 1.45663i 0.0105402 0.0618304i
\(556\) 0 0
\(557\) −32.1074 18.5372i −1.36043 0.785447i −0.370753 0.928732i \(-0.620900\pi\)
−0.989682 + 0.143284i \(0.954234\pi\)
\(558\) 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
\(567\) 23.0226 6.07934i 0.966860 0.255308i
\(568\) 0 0
\(569\) 13.0276 7.52147i 0.546144 0.315316i −0.201421 0.979505i \(-0.564556\pi\)
0.747565 + 0.664188i \(0.231223\pi\)
\(570\) 0 0
\(571\) −2.81334 + 4.87284i −0.117735 + 0.203922i −0.918870 0.394561i \(-0.870897\pi\)
0.801135 + 0.598484i \(0.204230\pi\)
\(572\) 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
\(579\) −5.34637 + 31.3626i −0.222188 + 1.30339i
\(580\) 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
\(585\) 0.294899 0.839825i 0.0121926 0.0347225i
\(586\) 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
\(591\) 0.178506 + 0.481898i 0.00734277 + 0.0198226i
\(592\) 0 0
\(593\) 10.5845 + 18.3329i 0.434654 + 0.752842i 0.997267 0.0738778i \(-0.0235375\pi\)
−0.562614 + 0.826720i \(0.690204\pi\)
\(594\) 0 0
\(595\) 0.269255 + 0.619579i 0.0110384 + 0.0254003i
\(596\) 0 0
\(597\) −46.7010 7.96111i −1.91135 0.325826i
\(598\) 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 0.395474 0.918477i \(-0.370580\pi\)
0.993162 + 0.116748i \(0.0372469\pi\)
\(608\) 0 0
\(609\) −23.4377 + 22.4873i −0.949743 + 0.911231i
\(610\) 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 \(-0.921305\pi\)
0.969594 0.244718i \(-0.0786952\pi\)
\(618\) 0 0
\(619\) −16.8732 9.74173i −0.678190 0.391553i 0.120983 0.992655i \(-0.461395\pi\)
−0.799173 + 0.601101i \(0.794729\pi\)
\(620\) 0 0
\(621\) 0.763888 + 44.7746i 0.0306538 + 1.79674i
\(622\) 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
\(627\) 17.0605 6.31959i 0.681329 0.252380i
\(628\) 0 0
\(629\) −10.3124 −0.411182
\(630\) 0 0
\(631\) −31.3846 −1.24940 −0.624701 0.780864i \(-0.714779\pi\)
−0.624701 + 0.780864i \(0.714779\pi\)
\(632\) 0 0
\(633\) 34.1561 12.6522i 1.35758 0.502880i
\(634\) 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
\(639\) −15.2309 17.7378i −0.602525 0.701697i
\(640\) 0 0
\(641\) −36.0118 20.7914i −1.42238 0.821211i −0.425878 0.904781i \(-0.640035\pi\)
−0.996502 + 0.0835697i \(0.973368\pi\)
\(642\) 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 0.402589 + 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
\(651\) 3.93974 + 16.0223i 0.154410 + 0.627963i
\(652\) 0 0
\(653\) −18.3717 + 10.6069i −0.718941 + 0.415081i −0.814363 0.580356i \(-0.802913\pi\)
0.0954221 + 0.995437i \(0.469580\pi\)
\(654\) 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
\(663\) −6.12360 1.04389i −0.237821 0.0405412i
\(664\) 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
\(669\) −4.14800 11.1980i −0.160371 0.432940i
\(670\) 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
\(675\) −13.3158 22.1810i −0.512526 0.853748i
\(676\) 0 0
\(677\) −7.23319 12.5283i −0.277994 0.481500i 0.692892 0.721041i \(-0.256336\pi\)
−0.970886 + 0.239541i \(0.923003\pi\)
\(678\) 0 0
\(679\) −16.1446 + 7.01605i −0.619571 + 0.269251i
\(680\) 0 0
\(681\) −3.90452 + 22.9045i −0.149621 + 0.877702i
\(682\) 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 −0.927861 0.372927i \(-0.878354\pi\)
−0.140966 + 0.990014i \(0.545021\pi\)
\(692\) 0 0
\(693\) −11.0017 16.2249i −0.417921 0.616334i
\(694\) 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
\(705\) −0.393576 + 2.30877i −0.0148229 + 0.0869535i
\(706\) 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
\(711\) 16.1951 + 5.68680i 0.607364 + 0.213272i
\(712\) 0 0
\(713\) −31.0295 −1.16207
\(714\) 0 0
\(715\) −0.732778 −0.0274044
\(716\) 0 0
\(717\) −10.4539 28.2215i −0.390408 1.05395i
\(718\) 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
\(723\) 24.7679 + 4.22217i 0.921128 + 0.157024i
\(724\) 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 −0.556722 0.830699i \(-0.687941\pi\)
0.441045 + 0.897485i \(0.354608\pi\)
\(734\) 0 0
\(735\) −1.74784 + 0.224000i −0.0644701 + 0.00826235i
\(736\) 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 \(-0.581275\pi\)
0.964232 0.265060i \(-0.0853917\pi\)
\(740\) 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
\(747\) 36.3755 31.2344i 1.33091 1.14281i
\(748\) 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 \(-0.0251771\pi\)
−0.566865 + 0.823811i \(0.691844\pi\)
\(752\) 0 0
\(753\) 5.68118 2.10444i 0.207034 0.0766901i
\(754\) 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
\(759\) 34.5708 12.8058i 1.25484 0.464822i
\(760\) 0 0
\(761\) −12.9780 22.4785i −0.470452 0.814846i 0.528977 0.848636i \(-0.322576\pi\)
−0.999429 + 0.0337898i \(0.989242\pi\)
\(762\) 0 0
\(763\) −3.56218 0.406574i −0.128960 0.0147190i
\(764\) 0 0
\(765\) 0.581159 0.499022i 0.0210119 0.0180422i
\(766\) 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 −0.951196 0.308587i \(-0.900144\pi\)
0.742842 + 0.669466i \(0.233477\pi\)
\(774\) 0 0
\(775\) 15.5247 8.96322i 0.557665 0.321968i
\(776\) 0 0
\(777\) 7.49808 25.8329i 0.268992 0.926750i
\(778\) 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 \(-0.154268\pi\)
0.0389406 + 0.999242i \(0.487602\pi\)
\(788\) 0 0
\(789\) 24.5149 + 4.17904i 0.872752 + 0.148778i