Properties

Label 168.2.u.a.89.7
Level 168
Weight 2
Character 168.89
Analytic conductor 1.341
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 89.7
Root \(-1.70742 - 0.291063i\) of \(x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} - 13122 x + 6561\)
Character \(\chi\) \(=\) 168.89
Dual form 168.2.u.a.17.7

$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.62420 + 0.601642i 0.937733 + 0.347358i
\(4\) 0 0
\(5\) 0.0726693 0.125867i 0.0324987 0.0562894i −0.849319 0.527881i \(-0.822987\pi\)
0.881817 + 0.471591i \(0.156320\pi\)
\(6\) 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 −0.786499 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 0.952667 0.304016i \(-0.0983276\pi\)
−0.739619 + 0.673026i \(0.764994\pi\)
\(18\) 0 0
\(19\) −3.68319 2.12649i −0.844983 0.487851i 0.0139720 0.999902i \(-0.495552\pi\)
−0.858955 + 0.512051i \(0.828886\pi\)
\(20\) 0 0
\(21\) 3.17263 3.30672i 0.692325 0.721586i
\(22\) 0 0
\(23\) −7.46351 4.30906i −1.55625 0.898501i −0.997610 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 \(-0.771363\pi\)
0.752935 0.658095i \(-0.228637\pi\)
\(30\) 0 0
\(31\) 3.11812 1.80025i 0.560031 0.323334i −0.193127 0.981174i \(-0.561863\pi\)
0.753158 + 0.657840i \(0.228530\pi\)
\(32\) 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 −0.999798 0.0200916i \(-0.993604\pi\)
0.517299 + 0.855805i \(0.326938\pi\)
\(38\) 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 −0.296868 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
\(51\) 0.511351 + 2.99966i 0.0716034 + 0.420036i
\(52\) 0 0
\(53\) −4.49578 + 2.59564i −0.617543 + 0.356539i −0.775912 0.630841i \(-0.782710\pi\)
0.158369 + 0.987380i \(0.449377\pi\)
\(54\) 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
\(63\) 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 0.979328 0.202279i \(-0.0648347\pi\)
−0.664843 + 0.746984i \(0.731501\pi\)
\(68\) 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
\(75\) 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 −0.659012 0.752133i \(-0.729025\pi\)
0.980872 + 0.194655i \(0.0623586\pi\)
\(80\) 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 −0.538670 0.842517i \(-0.681073\pi\)
0.998976 + 0.0452432i \(0.0144063\pi\)
\(90\) 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 \(-0.890326\pi\)
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 \(0.129753\pi\)
−0.115707 + 0.993283i \(0.536913\pi\)
\(102\) 0 0
\(103\) −0.147333 0.0850626i −0.0145171 0.00838147i 0.492724 0.870186i \(-0.336001\pi\)
−0.507241 + 0.861804i \(0.669335\pi\)
\(104\) 0 0
\(105\) −0.185654 0.639626i −0.0181179 0.0624211i
\(106\) 0 0
\(107\) −6.03900 3.48662i −0.583813 0.337064i 0.178835 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 \(0.0602472\pi\)
−0.982141 + 0.188144i \(0.939753\pi\)
\(114\) 0 0
\(115\) −1.08474 + 0.626273i −0.101152 + 0.0584002i
\(116\) 0 0
\(117\) −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 −0.967912 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
\(135\) 0.755091 + 0.0128824i 0.0649879 + 0.00110874i
\(136\) 0 0
\(137\) 17.3832 10.0362i 1.48515 0.857451i 0.485291 0.874353i \(-0.338714\pi\)
0.999857 + 0.0169018i \(0.00538026\pi\)
\(138\) 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
\(147\) −4.67826 11.1854i −0.385856 0.922559i
\(148\) 0 0
\(149\) −7.75705 4.47853i −0.635482 0.366896i 0.147390 0.989078i \(-0.452913\pi\)
−0.782872 + 0.622183i \(0.786246\pi\)
\(150\) 0 0
\(151\) 1.37132 + 2.37519i 0.111596 + 0.193290i 0.916414 0.400232i \(-0.131070\pi\)
−0.804818 + 0.593522i \(0.797737\pi\)
\(152\) 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
\(159\) −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 −0.775793 0.630987i \(-0.782650\pi\)
0.934347 + 0.356363i \(0.115983\pi\)
\(164\) 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 −0.0229296 0.999737i \(-0.507299\pi\)
0.877263 0.480011i \(-0.159367\pi\)
\(174\) 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 −0.614309 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
\(189\) 13.6837 1.32577i 0.995339 0.0964354i
\(190\) 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 \(-0.996636\pi\)
0.999944 0.0105695i \(-0.00336442\pi\)
\(198\) 0 0
\(199\) −23.6874 + 13.6759i −1.67915 + 0.969460i −0.716951 + 0.697124i \(0.754463\pi\)
−0.962202 + 0.272336i \(0.912204\pi\)
\(200\) 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 \(0.0741487\pi\)
−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 0.552883 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
\(231\) −2.70248 + 10.9905i −0.177810 + 0.723125i
\(232\) 0 0
\(233\) −4.29295 2.47853i −0.281240 0.162374i 0.352744 0.935720i \(-0.385248\pi\)
−0.633985 + 0.773346i \(0.718582\pi\)
\(234\) 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
\(243\) −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 −0.999994 0.00343985i \(-0.998905\pi\)
0.502976 + 0.864300i \(0.332238\pi\)
\(258\) 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 −0.0649777 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 0.731668 0.681661i \(-0.238742\pi\)
−0.956170 + 0.292812i \(0.905409\pi\)
\(270\) 0 0
\(271\) 10.8537 + 6.26636i 0.659313 + 0.380654i 0.792015 0.610501i \(-0.209032\pi\)
−0.132702 + 0.991156i \(0.542365\pi\)
\(272\) 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 −0.677205 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 \(0.0981614\pi\)
−0.952826 + 0.303518i \(0.901839\pi\)
\(282\) 0 0
\(283\) −1.18666 + 0.685120i −0.0705397 + 0.0407261i −0.534855 0.844944i \(-0.679634\pi\)
0.464315 + 0.885670i \(0.346300\pi\)
\(284\) 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 \(-0.796566\pi\)
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 0.981615 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
\(315\) 0.0832870 1.15058i 0.00469269 0.0648278i
\(316\) 0 0
\(317\) −5.74547 3.31715i −0.322698 0.186310i 0.329897 0.944017i \(-0.392986\pi\)
−0.652594 + 0.757707i \(0.726319\pi\)
\(318\) 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 −0.994303 0.106595i \(-0.966005\pi\)
0.589465 + 0.807794i \(0.299339\pi\)
\(332\) 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 −0.0570320 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 \(-0.773240\pi\)
−0.187669 0.982232i \(-0.560093\pi\)
\(354\) 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 0.636357 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 −0.829722 0.558177i \(-0.811501\pi\)
0.0685342 + 0.997649i \(0.478168\pi\)
\(368\) 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 −0.849607 0.527416i \(-0.823161\pi\)
0.881559 + 0.472073i \(0.156494\pi\)
\(374\) 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 −0.711086 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
\(387\) −20.9327 17.9742i −1.06407 0.913680i
\(388\) 0 0
\(389\) −11.5061 + 6.64306i −0.583383 + 0.336816i −0.762477 0.647016i \(-0.776017\pi\)
0.179094 + 0.983832i \(0.442683\pi\)
\(390\) 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
\(399\) −18.7171 + 5.43271i −0.937029 + 0.271976i
\(400\) 0 0
\(401\) 12.4125 + 7.16635i 0.619850 + 0.357870i 0.776810 0.629735i \(-0.216836\pi\)
−0.156961 + 0.987605i \(0.550170\pi\)
\(402\) 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
\(411\) 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 −0.812624 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 −0.0271602 0.999631i \(-0.508646\pi\)
−0.879286 + 0.476294i \(0.841980\pi\)
\(440\) 0 0
\(441\) −0.868806 20.9820i −0.0413717 0.999144i
\(442\) 0 0
\(443\) 17.7589 + 10.2531i 0.843750 + 0.487139i 0.858537 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 \(0.146046\pi\)
−0.896578 + 0.442886i \(0.853954\pi\)
\(450\) 0 0
\(451\) 11.4057 6.58509i 0.537074 0.310080i
\(452\) 0 0
\(453\) 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 −0.941059 0.338243i \(-0.890167\pi\)
0.763457 + 0.645859i \(0.223501\pi\)
\(458\) 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 −0.919577 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
\(471\) −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 0.998403 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
\(483\) −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 0.917159 0.398522i \(-0.130477\pi\)
−0.803710 + 0.595022i \(0.797143\pi\)
\(488\) 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
\(495\) −0.701529 + 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 −0.856825 0.515608i \(-0.827566\pi\)
0.874942 + 0.484228i \(0.160900\pi\)
\(500\) 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 −0.958525 0.285009i \(-0.908004\pi\)
0.726087 + 0.687603i \(0.241337\pi\)
\(510\) 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 0.742159 0.670224i \(-0.233802\pi\)
−0.951510 + 0.307617i \(0.900469\pi\)
\(522\) 0 0
\(523\) −24.0305 13.8740i −1.05078 0.606668i −0.127912 0.991785i \(-0.540828\pi\)
−0.922868 + 0.385117i \(0.874161\pi\)
\(524\) 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 −0.853338 0.521358i \(-0.825426\pi\)
0.878178 + 0.478333i \(0.158759\pi\)
\(542\) 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 −0.989682 0.143284i \(-0.954234\pi\)
−0.370753 + 0.928732i \(0.620900\pi\)
\(558\) 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
\(567\) 23.0226 + 6.07934i 0.966860 + 0.255308i
\(568\) 0 0
\(569\) 13.0276 + 7.52147i 0.546144 + 0.315316i 0.747565 0.664188i \(-0.231223\pi\)
−0.201421 + 0.979505i \(0.564556\pi\)
\(570\) 0 0
\(571\) −2.81334 4.87284i −0.117735 0.203922i 0.801135 0.598484i \(-0.204230\pi\)
−0.918870 + 0.394561i \(0.870897\pi\)
\(572\) 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
\(579\) −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 −0.562614 0.826720i \(-0.690204\pi\)
0.997267 + 0.0738778i \(0.0235375\pi\)
\(594\) 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 −0.403366 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 0.993162 0.116748i \(-0.0372469\pi\)
0.395474 + 0.918477i \(0.370580\pi\)
\(608\) 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 0.683277 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 \(0.0786952\pi\)
−0.969594 + 0.244718i \(0.921305\pi\)
\(618\) 0 0
\(619\) −16.8732 + 9.74173i −0.678190 + 0.391553i −0.799173 0.601101i \(-0.794729\pi\)
0.120983 + 0.992655i \(0.461395\pi\)
\(620\) 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 −0.996502 0.0835697i \(-0.973368\pi\)
−0.425878 + 0.904781i \(0.640035\pi\)
\(642\) 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 −0.994038 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
\(651\) 3.93974 16.0223i 0.154410 0.627963i
\(652\) 0 0
\(653\) −18.3717 10.6069i −0.718941 0.415081i 0.0954221 0.995437i \(-0.469580\pi\)
−0.814363 + 0.580356i \(0.802913\pi\)
\(654\) 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
\(663\) −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 −0.970886 0.239541i \(-0.923003\pi\)
0.692892 + 0.721041i \(0.256336\pi\)
\(678\) 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 −0.929972 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 −0.140966 0.990014i \(-0.545021\pi\)
−0.927861 + 0.372927i \(0.878354\pi\)
\(692\) 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 \(-0.805518\pi\)
0.819084 0.573674i \(-0.194482\pi\)
\(702\) 0 0
\(703\) 21.6198 12.4822i 0.815407 0.470776i
\(704\) 0 0
\(705\) −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 −0.380607 0.924737i \(-0.624285\pi\)
0.991149 0.132753i \(-0.0423816\pi\)
\(710\) 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 −0.750145 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
\(723\) 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 \(0.197549\pi\)
−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 0.441045 0.897485i \(-0.354608\pi\)
−0.556722 + 0.830699i \(0.687941\pi\)
\(734\) 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 0.964232 + 0.265060i \(0.0853917\pi\)
−0.252567 + 0.967579i \(0.581275\pi\)
\(740\) 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
\(747\) 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 −0.566865 0.823811i \(-0.691844\pi\)
0.996874 + 0.0790136i \(0.0251771\pi\)
\(752\) 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 −0.999429 0.0337898i \(-0.989242\pi\)
0.528977 + 0.848636i \(0.322576\pi\)
\(762\) 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 \(-0.768128\pi\)
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 0.742842 0.669466i \(-0.233477\pi\)
−0.951196 + 0.308587i \(0.900144\pi\)
\(774\) 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 0.0389406 0.999242i \(-0.487602\pi\)
0.884839 + 0.465897i \(0.154268\pi\)
\(788\) 0 0
\(789\) 24.5149 4.17904i 0.872752