Properties

Label 168.2.u.a.89.5
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 89.5
Root \(-0.601642 + 1.62420i\)
Character \(\chi\) = 168.89
Dual form 168.2.u.a.17.5

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

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

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
\(3\) 0.291063 1.70742i 0.168045 0.985779i
\(4\) 0 0
\(5\) −0.0726693 + 0.125867i −0.0324987 + 0.0562894i −0.881817 0.471591i \(-0.843680\pi\)
0.849319 + 0.527881i \(0.177013\pi\)
\(6\) 0 0
\(7\) 1.05451 2.42652i 0.398567 0.917139i
\(8\) 0 0
\(9\) −2.83056 0.993934i −0.943521 0.331311i
\(10\) 0 0
\(11\) 2.13889 1.23489i 0.644899 0.372332i −0.141600 0.989924i \(-0.545225\pi\)
0.786499 + 0.617592i \(0.211891\pi\)
\(12\) 0 0
\(13\) 2.04143i 0.566191i 0.959092 + 0.283096i \(0.0913613\pi\)
−0.959092 + 0.283096i \(0.908639\pi\)
\(14\) 0 0
\(15\) 0.193756 + 0.160712i 0.0500276 + 0.0414957i
\(16\) 0 0
\(17\) −0.878419 1.52147i −0.213048 0.369010i 0.739619 0.673026i \(-0.235006\pi\)
−0.952667 + 0.304016i \(0.901672\pi\)
\(18\) 0 0
\(19\) −3.68319 2.12649i −0.844983 0.487851i 0.0139720 0.999902i \(-0.495552\pi\)
−0.858955 + 0.512051i \(0.828886\pi\)
\(20\) 0 0
\(21\) −3.83616 2.50676i −0.837119 0.547020i
\(22\) 0 0
\(23\) 7.46351 + 4.30906i 1.55625 + 0.898501i 0.997610 + 0.0690910i \(0.0220099\pi\)
0.558640 + 0.829410i \(0.311323\pi\)
\(24\) 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 −0.193127 0.981174i \(-0.561863\pi\)
0.753158 + 0.657840i \(0.228530\pi\)
\(32\) 0 0
\(33\) −1.48592 4.01141i −0.258665 0.698296i
\(34\) 0 0
\(35\) 0.228788 + 0.309061i 0.0386723 + 0.0522409i
\(36\) 0 0
\(37\) −2.93493 + 5.08345i −0.482499 + 0.835713i −0.999798 0.0200916i \(-0.993604\pi\)
0.517299 + 0.855805i \(0.326938\pi\)
\(38\) 0 0
\(39\) 3.48558 + 0.594185i 0.558139 + 0.0951458i
\(40\) 0 0
\(41\) 5.33255 0.832804 0.416402 0.909181i \(-0.363291\pi\)
0.416402 + 0.909181i \(0.363291\pi\)
\(42\) 0 0
\(43\) −9.19692 −1.40252 −0.701258 0.712907i \(-0.747378\pi\)
−0.701258 + 0.712907i \(0.747378\pi\)
\(44\) 0 0
\(45\) 0.330798 0.284046i 0.0493125 0.0423431i
\(46\) 0 0
\(47\) −4.65190 + 8.05733i −0.678549 + 1.17528i 0.296868 + 0.954918i \(0.404058\pi\)
−0.975418 + 0.220364i \(0.929276\pi\)
\(48\) 0 0
\(49\) −4.77602 5.11758i −0.682288 0.731083i
\(50\) 0 0
\(51\) −2.85346 + 1.05699i −0.399564 + 0.148008i
\(52\) 0 0
\(53\) 4.49578 2.59564i 0.617543 0.356539i −0.158369 0.987380i \(-0.550623\pi\)
0.775912 + 0.630841i \(0.217290\pi\)
\(54\) 0 0
\(55\) 0.358953i 0.0484013i
\(56\) 0 0
\(57\) −4.70286 + 5.66982i −0.622909 + 0.750985i
\(58\) 0 0
\(59\) −5.60299 9.70466i −0.729447 1.26344i −0.957117 0.289701i \(-0.906444\pi\)
0.227670 0.973738i \(-0.426889\pi\)
\(60\) 0 0
\(61\) 4.66353 + 2.69249i 0.597104 + 0.344738i 0.767901 0.640568i \(-0.221301\pi\)
−0.170798 + 0.985306i \(0.554634\pi\)
\(62\) 0 0
\(63\) −5.39666 + 5.82031i −0.679915 + 0.733291i
\(64\) 0 0
\(65\) −0.256949 0.148349i −0.0318705 0.0184005i
\(66\) 0 0
\(67\) 2.57417 + 4.45860i 0.314485 + 0.544705i 0.979328 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 \(-0.846973\pi\)
0.886649 0.462443i \(-0.153027\pi\)
\(72\) 0 0
\(73\) 11.3013 6.52482i 1.32272 0.763672i 0.338558 0.940946i \(-0.390061\pi\)
0.984162 + 0.177273i \(0.0567277\pi\)
\(74\) 0 0
\(75\) 8.08669 2.99550i 0.933771 0.345891i
\(76\) 0 0
\(77\) −0.741003 6.49226i −0.0844451 0.739861i
\(78\) 0 0
\(79\) 2.86075 4.95497i 0.321860 0.557478i −0.659012 0.752133i \(-0.729025\pi\)
0.980872 + 0.194655i \(0.0623586\pi\)
\(80\) 0 0
\(81\) 7.02419 + 5.62679i 0.780466 + 0.625199i
\(82\) 0 0
\(83\) −15.9818 −1.75423 −0.877115 0.480280i \(-0.840535\pi\)
−0.877115 + 0.480280i \(0.840535\pi\)
\(84\) 0 0
\(85\) 0.255336 0.0276951
\(86\) 0 0
\(87\) 12.1020 + 2.06303i 1.29747 + 0.221180i
\(88\) 0 0
\(89\) −4.34252 + 7.52147i −0.460306 + 0.797274i −0.998976 0.0452432i \(-0.985594\pi\)
0.538670 + 0.842517i \(0.318927\pi\)
\(90\) 0 0
\(91\) 4.95358 + 2.15271i 0.519276 + 0.225665i
\(92\) 0 0
\(93\) −2.16621 5.84793i −0.224626 0.606402i
\(94\) 0 0
\(95\) 0.535310 0.309061i 0.0549217 0.0317090i
\(96\) 0 0
\(97\) 6.65337i 0.675547i −0.941227 0.337774i \(-0.890326\pi\)
0.941227 0.337774i \(-0.109674\pi\)
\(98\) 0 0
\(99\) −7.28165 + 1.36951i −0.731834 + 0.137641i
\(100\) 0 0
\(101\) −8.06357 13.9665i −0.802355 1.38972i −0.918062 0.396437i \(-0.870247\pi\)
0.115707 0.993283i \(-0.463087\pi\)
\(102\) 0 0
\(103\) −0.147333 0.0850626i −0.0145171 0.00838147i 0.492724 0.870186i \(-0.336001\pi\)
−0.507241 + 0.861804i \(0.669335\pi\)
\(104\) 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 \(-0.223899\pi\)
−0.178835 + 0.983879i \(0.557233\pi\)
\(108\) 0 0
\(109\) −0.677559 1.17357i −0.0648984 0.112407i 0.831751 0.555150i \(-0.187339\pi\)
−0.896649 + 0.442742i \(0.854006\pi\)
\(110\) 0 0
\(111\) 7.82532 + 6.49076i 0.742747 + 0.616076i
\(112\) 0 0
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) 0 0
\(115\) −1.08474 + 0.626273i −0.101152 + 0.0584002i
\(116\) 0 0
\(117\) 2.02905 5.77840i 0.187586 0.534213i
\(118\) 0 0
\(119\) −4.61817 + 0.527101i −0.423347 + 0.0483193i
\(120\) 0 0
\(121\) −2.45011 + 4.24371i −0.222737 + 0.385792i
\(122\) 0 0
\(123\) 1.55211 9.10490i 0.139949 0.820961i
\(124\) 0 0
\(125\) −1.45032 −0.129720
\(126\) 0 0
\(127\) −7.33399 −0.650787 −0.325393 0.945579i \(-0.605497\pi\)
−0.325393 + 0.945579i \(0.605497\pi\)
\(128\) 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 \(-0.747521\pi\)
0.967912 + 0.251289i \(0.0808545\pi\)
\(132\) 0 0
\(133\) −9.04395 + 6.69494i −0.784210 + 0.580525i
\(134\) 0 0
\(135\) −0.388702 0.647487i −0.0334542 0.0557268i
\(136\) 0 0
\(137\) −17.3832 + 10.0362i −1.48515 + 0.857451i −0.999857 0.0169018i \(-0.994620\pi\)
−0.485291 + 0.874353i \(0.661286\pi\)
\(138\) 0 0
\(139\) 0.117694i 0.00998266i 0.999988 + 0.00499133i \(0.00158880\pi\)
−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 0.782872 0.622183i \(-0.213754\pi\)
−0.147390 + 0.989078i \(0.547087\pi\)
\(150\) 0 0
\(151\) 1.37132 + 2.37519i 0.111596 + 0.193290i 0.916414 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
\(159\) −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 \(-0.782650\pi\)
0.934347 + 0.356363i \(0.115983\pi\)
\(164\) 0 0
\(165\) 0.612884 + 0.104478i 0.0477130 + 0.00813361i
\(166\) 0 0
\(167\) 3.70521 0.286717 0.143359 0.989671i \(-0.454210\pi\)
0.143359 + 0.989671i \(0.454210\pi\)
\(168\) 0 0
\(169\) 8.83256 0.679428
\(170\) 0 0
\(171\) 8.31193 + 9.68003i 0.635629 + 0.740250i
\(172\) 0 0
\(173\) −11.2370 + 19.4630i −0.854333 + 1.47975i 0.0229296 + 0.999737i \(0.492701\pi\)
−0.877263 + 0.480011i \(0.840633\pi\)
\(174\) 0 0
\(175\) 13.0879 1.49381i 0.989352 0.112921i
\(176\) 0 0
\(177\) −18.2008 + 6.74198i −1.36805 + 0.506758i
\(178\) 0 0
\(179\) 3.18574 1.83929i 0.238113 0.137475i −0.376196 0.926540i \(-0.622768\pi\)
0.614309 + 0.789065i \(0.289435\pi\)
\(180\) 0 0
\(181\) 8.01062i 0.595425i 0.954656 + 0.297712i \(0.0962237\pi\)
−0.954656 + 0.297712i \(0.903776\pi\)
\(182\) 0 0
\(183\) 5.95459 7.17892i 0.440176 0.530681i
\(184\) 0 0
\(185\) −0.426558 0.738821i −0.0313612 0.0543192i
\(186\) 0 0
\(187\) −3.75768 2.16950i −0.274789 0.158649i
\(188\) 0 0
\(189\) 8.36695 + 10.9084i 0.608606 + 0.793473i
\(190\) 0 0
\(191\) −0.971326 0.560795i −0.0702827 0.0405777i 0.464447 0.885601i \(-0.346253\pi\)
−0.534730 + 0.845023i \(0.679587\pi\)
\(192\) 0 0
\(193\) −9.18421 15.9075i −0.661094 1.14505i −0.980329 0.197373i \(-0.936759\pi\)
0.319235 0.947676i \(-0.396574\pi\)
\(194\) 0 0
\(195\) −0.328083 + 0.395540i −0.0234945 + 0.0283252i
\(196\) 0 0
\(197\) 0.296699i 0.0211389i 0.999944 + 0.0105695i \(0.00336442\pi\)
−0.999944 + 0.0105695i \(0.996636\pi\)
\(198\) 0 0
\(199\) −23.6874 + 13.6759i −1.67915 + 0.969460i −0.716951 + 0.697124i \(0.754463\pi\)
−0.962202 + 0.272336i \(0.912204\pi\)
\(200\) 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 \(-0.242364\pi\)
0.723864 + 0.689942i \(0.242364\pi\)
\(212\) 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 \(-0.0198058\pi\)
−0.552883 + 0.833259i \(0.686472\pi\)
\(228\) 0 0
\(229\) −5.51012 3.18127i −0.364119 0.210224i 0.306767 0.951785i \(-0.400753\pi\)
−0.670886 + 0.741560i \(0.734086\pi\)
\(230\) 0 0
\(231\) −11.3007 0.624454i −0.743530 0.0410861i
\(232\) 0 0
\(233\) 4.29295 + 2.47853i 0.281240 + 0.162374i 0.633985 0.773346i \(-0.281418\pi\)
−0.352744 + 0.935720i \(0.614752\pi\)
\(234\) 0 0
\(235\) −0.676100 1.17104i −0.0441039 0.0763903i
\(236\) 0 0
\(237\) −7.62755 6.32672i −0.495463 0.410964i
\(238\) 0 0
\(239\) 17.3756i 1.12394i −0.827159 0.561968i \(-0.810044\pi\)
0.827159 0.561968i \(-0.189956\pi\)
\(240\) 0 0
\(241\) 12.5626 7.25302i 0.809228 0.467208i −0.0374597 0.999298i \(-0.511927\pi\)
0.846688 + 0.532090i \(0.178593\pi\)
\(242\) 0 0
\(243\) 11.6518 10.3555i 0.747462 0.664305i
\(244\) 0 0
\(245\) 0.991204 0.229251i 0.0633257 0.0146463i
\(246\) 0 0
\(247\) 4.34109 7.51899i 0.276217 0.478422i
\(248\) 0 0
\(249\) −4.65171 + 27.2876i −0.294790 + 1.72928i
\(250\) 0 0
\(251\) −3.49783 −0.220781 −0.110391 0.993888i \(-0.535210\pi\)
−0.110391 + 0.993888i \(0.535210\pi\)
\(252\) 0 0
\(253\) 21.2848 1.33816
\(254\) 0 0
\(255\) 0.0743190 0.435966i 0.00465404 0.0273013i
\(256\) 0 0
\(257\) 7.96781 13.8006i 0.497018 0.860861i −0.502976 0.864300i \(-0.667762\pi\)
0.999994 + 0.00343985i \(0.00109494\pi\)
\(258\) 0 0
\(259\) 9.24018 + 12.4822i 0.574157 + 0.775607i
\(260\) 0 0
\(261\) 7.04490 20.0627i 0.436069 1.24185i
\(262\) 0 0
\(263\) −12.4343 + 7.17892i −0.766729 + 0.442671i −0.831706 0.555216i \(-0.812636\pi\)
0.0649777 + 0.997887i \(0.479302\pi\)
\(264\) 0 0
\(265\) 0.754493i 0.0463482i
\(266\) 0 0
\(267\) 11.5784 + 9.60373i 0.708584 + 0.587739i
\(268\) 0 0
\(269\) 3.68211 + 6.37760i 0.224502 + 0.388849i 0.956170 0.292812i \(-0.0945911\pi\)
−0.731668 + 0.681661i \(0.761258\pi\)
\(270\) 0 0
\(271\) 10.8537 + 6.26636i 0.659313 + 0.380654i 0.792015 0.610501i \(-0.209032\pi\)
−0.132702 + 0.991156i \(0.542365\pi\)
\(272\) 0 0
\(273\) 5.11738 7.83126i 0.309718 0.473969i
\(274\) 0 0
\(275\) 10.6493 + 6.14835i 0.642174 + 0.370759i
\(276\) 0 0
\(277\) −16.2409 28.1300i −0.975819 1.69017i −0.677205 0.735794i \(-0.736809\pi\)
−0.298614 0.954374i \(-0.596524\pi\)
\(278\) 0 0
\(279\) −10.6154 + 1.99651i −0.635526 + 0.119528i
\(280\) 0 0
\(281\) 10.1758i 0.607037i −0.952826 0.303518i \(-0.901839\pi\)
0.952826 0.303518i \(-0.0981614\pi\)
\(282\) 0 0
\(283\) −1.18666 + 0.685120i −0.0705397 + 0.0407261i −0.534855 0.844944i \(-0.679634\pi\)
0.464315 + 0.885670i \(0.346300\pi\)
\(284\) 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 \(-0.272202\pi\)
−0.981615 + 0.190871i \(0.938869\pi\)
\(312\) 0 0
\(313\) 8.57172 + 4.94889i 0.484502 + 0.279728i 0.722291 0.691589i \(-0.243089\pi\)
−0.237788 + 0.971317i \(0.576423\pi\)
\(314\) 0 0
\(315\) −0.340413 1.10222i −0.0191801 0.0621030i
\(316\) 0 0
\(317\) 5.74547 + 3.31715i 0.322698 + 0.186310i 0.652594 0.757707i \(-0.273681\pi\)
−0.329897 + 0.944017i \(0.607014\pi\)
\(318\) 0 0
\(319\) 8.75275 + 15.1602i 0.490060 + 0.848809i
\(320\) 0 0
\(321\) 7.71086 9.29629i 0.430378 0.518868i
\(322\) 0 0
\(323\) 7.47181i 0.415742i
\(324\) 0 0
\(325\) −8.80231 + 5.08202i −0.488264 + 0.281900i
\(326\) 0 0
\(327\) −2.20098 + 0.815296i −0.121715 + 0.0450860i
\(328\) 0 0
\(329\) 14.6458 + 19.7845i 0.807449 + 1.09075i
\(330\) 0 0
\(331\) −7.36537 + 12.7572i −0.404837 + 0.701199i −0.994303 0.106595i \(-0.966005\pi\)
0.589465 + 0.807794i \(0.299339\pi\)
\(332\) 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 \(-0.815170\pi\)
0.0570320 + 0.998372i \(0.481836\pi\)
\(348\) 0 0
\(349\) 3.12385i 0.167216i −0.996499 0.0836080i \(-0.973356\pi\)
0.996499 0.0836080i \(-0.0266443\pi\)
\(350\) 0 0
\(351\) −9.27558 5.14632i −0.495094 0.274690i
\(352\) 0 0
\(353\) 17.7450 + 30.7353i 0.944473 + 1.63587i 0.756804 + 0.653642i \(0.226760\pi\)
0.187669 + 0.982232i \(0.439907\pi\)
\(354\) 0 0
\(355\) 0.980910 + 0.566328i 0.0520613 + 0.0300576i
\(356\) 0 0
\(357\) −0.444197 + 8.03858i −0.0235094 + 0.425447i
\(358\) 0 0
\(359\) −5.42817 3.13395i −0.286488 0.165404i 0.349869 0.936799i \(-0.386226\pi\)
−0.636357 + 0.771395i \(0.719559\pi\)
\(360\) 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
\(369\) −15.0941 5.30020i −0.785769 0.275918i
\(370\) 0 0
\(371\) −1.55753 13.6462i −0.0808631 0.708478i
\(372\) 0 0
\(373\) 0.617106 1.06886i 0.0319526 0.0553435i −0.849607 0.527416i \(-0.823161\pi\)
0.881559 + 0.472073i \(0.156494\pi\)
\(374\) 0 0
\(375\) −0.422134 + 2.47630i −0.0217989 + 0.127875i
\(376\) 0 0
\(377\) −14.4695 −0.745215
\(378\) 0 0
\(379\) −14.3895 −0.739141 −0.369571 0.929203i \(-0.620495\pi\)
−0.369571 + 0.929203i \(0.620495\pi\)
\(380\) 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 \(-0.914870\pi\)
0.711086 + 0.703105i \(0.248204\pi\)
\(384\) 0 0
\(385\) 0.871008 + 0.378520i 0.0443907 + 0.0192912i
\(386\) 0 0
\(387\) 26.0325 + 9.14113i 1.32330 + 0.464670i
\(388\) 0 0
\(389\) 11.5061 6.64306i 0.583383 0.336816i −0.179094 0.983832i \(-0.557317\pi\)
0.762477 + 0.647016i \(0.223983\pi\)
\(390\) 0 0
\(391\) 15.1406i 0.765695i
\(392\) 0 0
\(393\) −8.12767 6.74154i −0.409987 0.340066i
\(394\) 0 0
\(395\) 0.415778 + 0.720148i 0.0209201 + 0.0362346i
\(396\) 0 0
\(397\) 21.0410 + 12.1480i 1.05602 + 0.609693i 0.924328 0.381598i \(-0.124626\pi\)
0.131691 + 0.991291i \(0.457959\pi\)
\(398\) 0 0
\(399\) 8.79872 + 17.3905i 0.440487 + 0.870612i
\(400\) 0 0
\(401\) −12.4125 7.16635i −0.619850 0.357870i 0.156961 0.987605i \(-0.449830\pi\)
−0.776810 + 0.629735i \(0.783164\pi\)
\(402\) 0 0
\(403\) 3.67508 + 6.36543i 0.183069 + 0.317085i
\(404\) 0 0
\(405\) −1.21867 + 0.475218i −0.0605562 + 0.0236138i
\(406\) 0 0
\(407\) 14.4972i 0.718600i
\(408\) 0 0
\(409\) 17.3256 10.0029i 0.856695 0.494613i −0.00620937 0.999981i \(-0.501977\pi\)
0.862904 + 0.505368i \(0.168643\pi\)
\(410\) 0 0
\(411\) 12.0764 + 32.6016i 0.595685 + 1.60812i
\(412\) 0 0
\(413\) −29.4570 + 3.36211i −1.44948 + 0.165439i
\(414\) 0 0
\(415\) 1.16139 2.01158i 0.0570102 0.0987446i
\(416\) 0 0
\(417\) 0.200953 + 0.0342563i 0.00984070 + 0.00167754i
\(418\) 0 0
\(419\) 27.7445 1.35541 0.677704 0.735335i \(-0.262975\pi\)
0.677704 + 0.735335i \(0.262975\pi\)
\(420\) 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 \(-0.531372\pi\)
0.812624 + 0.582788i \(0.198038\pi\)
\(432\) 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
\(441\) 8.43228 + 19.2327i 0.401537 + 0.915843i
\(442\) 0 0
\(443\) −17.7589 10.2531i −0.843750 0.487139i 0.0147873 0.999891i \(-0.495293\pi\)
−0.858537 + 0.512752i \(0.828626\pi\)
\(444\) 0 0
\(445\) −0.631136 1.09316i −0.0299187 0.0518207i
\(446\) 0 0
\(447\) 9.90453 11.9410i 0.468468 0.564790i
\(448\) 0 0
\(449\) 18.7692i 0.885773i −0.896578 0.442886i \(-0.853954\pi\)
0.896578 0.442886i \(-0.146046\pi\)
\(450\) 0 0
\(451\) 11.4057 6.58509i 0.537074 0.310080i
\(452\) 0 0
\(453\) 4.45458 1.65008i 0.209295 0.0775276i
\(454\) 0 0
\(455\) −0.630928 + 0.467055i −0.0295783 + 0.0218959i
\(456\) 0 0
\(457\) −3.79670 + 6.57607i −0.177602 + 0.307616i −0.941059 0.338243i \(-0.890167\pi\)
0.763457 + 0.645859i \(0.223501\pi\)
\(458\) 0 0
\(459\) 9.12747 0.155721i 0.426034 0.00726845i
\(460\) 0 0
\(461\) −29.2727 −1.36337 −0.681683 0.731648i \(-0.738752\pi\)
−0.681683 + 0.731648i \(0.738752\pi\)
\(462\) 0 0
\(463\) 11.8326 0.549906 0.274953 0.961458i \(-0.411338\pi\)
0.274953 + 0.961458i \(0.411338\pi\)
\(464\) 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 \(-0.795198\pi\)
0.919577 + 0.392910i \(0.128531\pi\)
\(468\) 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 \(-0.315344\pi\)
−0.998403 + 0.0564848i \(0.982011\pi\)
\(480\) 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 \(-0.130477\pi\)
−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 \(-0.974410\pi\)
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 \(-0.827566\pi\)
0.874942 + 0.484228i \(0.160900\pi\)
\(500\) 0 0
\(501\) 1.07845 6.32634i 0.0481815 0.282640i
\(502\) 0 0
\(503\) −9.47070 −0.422278 −0.211139 0.977456i \(-0.567717\pi\)
−0.211139 + 0.977456i \(0.567717\pi\)
\(504\) 0 0
\(505\) 2.34390 0.104302
\(506\) 0 0
\(507\) 2.57083 15.0809i 0.114175 0.669766i
\(508\) 0 0
\(509\) 5.24404 9.08294i 0.232438 0.402594i −0.726087 0.687603i \(-0.758663\pi\)
0.958525 + 0.285009i \(0.0919965\pi\)
\(510\) 0 0
\(511\) −3.91526 34.3034i −0.173201 1.51749i
\(512\) 0 0
\(513\) 18.9472 11.3744i 0.836538 0.502194i
\(514\) 0 0
\(515\) 0.0214131 0.0123629i 0.000943576 0.000544774i
\(516\) 0 0
\(517\) 22.9783i 1.01058i
\(518\) 0 0
\(519\) 29.9609 + 24.8512i 1.31514 + 1.09085i
\(520\) 0 0
\(521\) 4.77854 + 8.27667i 0.209351 + 0.362607i 0.951510 0.307617i \(-0.0995314\pi\)
−0.742159 + 0.670224i \(0.766198\pi\)
\(522\) 0 0
\(523\) −24.0305 13.8740i −1.05078 0.606668i −0.127912 0.991785i \(-0.540828\pi\)
−0.922868 + 0.385117i \(0.874161\pi\)
\(524\) 0 0
\(525\) 1.25885 22.7813i 0.0549408 0.994259i
\(526\) 0 0
\(527\) −5.47804 3.16275i −0.238627 0.137771i
\(528\) 0 0
\(529\) 25.6360 + 44.4029i 1.11461 + 1.93056i
\(530\) 0 0
\(531\) 6.21383 + 33.0387i 0.269657 + 1.43376i
\(532\) 0 0
\(533\) 10.8860i 0.471526i
\(534\) 0 0
\(535\) −0.877700 + 0.506740i −0.0379463 + 0.0219083i
\(536\) 0 0
\(537\) −2.21318 5.97474i −0.0955060 0.257829i
\(538\) 0 0
\(539\) −16.5350 5.04809i −0.712213 0.217437i
\(540\) 0 0
\(541\) 0.577777 1.00074i 0.0248406 0.0430251i −0.853338 0.521358i \(-0.825426\pi\)
0.878178 + 0.478333i \(0.158759\pi\)
\(542\) 0 0
\(543\) 13.6775 + 2.33160i 0.586958 + 0.100058i
\(544\) 0 0
\(545\) 0.196951 0.00843645
\(546\) 0 0
\(547\) 16.1394 0.690070 0.345035 0.938590i \(-0.387867\pi\)
0.345035 + 0.938590i \(0.387867\pi\)
\(548\) 0 0
\(549\) −10.5243 12.2565i −0.449165 0.523095i
\(550\) 0 0
\(551\) 15.0724 26.1061i 0.642104 1.11216i
\(552\) 0 0
\(553\) −9.00665 12.1667i −0.383002 0.517383i
\(554\) 0 0
\(555\) −1.38563 + 0.513271i −0.0588168 + 0.0217871i
\(556\) 0 0
\(557\) 32.1074 18.5372i 1.36043 0.785447i 0.370753 0.928732i \(-0.379100\pi\)
0.989682 + 0.143284i \(0.0457663\pi\)
\(558\) 0 0
\(559\) 18.7749i 0.794092i
\(560\) 0 0
\(561\) −4.79796 + 5.78447i −0.202570 + 0.244221i
\(562\) 0 0
\(563\) −7.79584 13.5028i −0.328556 0.569075i 0.653670 0.756780i \(-0.273228\pi\)
−0.982225 + 0.187705i \(0.939895\pi\)
\(564\) 0 0
\(565\) 0.503468 + 0.290677i 0.0211810 + 0.0122289i
\(566\) 0 0
\(567\) 21.0606 11.1108i 0.884462 0.466612i
\(568\) 0 0
\(569\) −13.0276 7.52147i −0.546144 0.315316i 0.201421 0.979505i \(-0.435444\pi\)
−0.747565 + 0.664188i \(0.768777\pi\)
\(570\) 0 0
\(571\) −2.81334 4.87284i −0.117735 0.203922i 0.801135 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
\(579\) −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 \(-0.357870\pi\)
0.431824 + 0.901958i \(0.357870\pi\)
\(588\) 0 0
\(589\) −15.3129 −0.630956
\(590\) 0 0
\(591\) 0.506589 + 0.0863581i 0.0208383 + 0.00355230i
\(592\) 0 0
\(593\) −10.5845 + 18.3329i −0.434654 + 0.752842i −0.997267 0.0738778i \(-0.976463\pi\)
0.562614 + 0.826720i \(0.309796\pi\)
\(594\) 0 0
\(595\) 0.269255 0.619579i 0.0110384 0.0254003i
\(596\) 0 0
\(597\) 16.4560 + 44.4248i 0.673499 + 1.81819i
\(598\) 0 0
\(599\) −4.58648 + 2.64801i −0.187399 + 0.108195i −0.590764 0.806844i \(-0.701174\pi\)
0.403366 + 0.915039i \(0.367840\pi\)
\(600\) 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
\(609\) 17.7677 27.1903i 0.719982 1.10181i
\(610\) 0 0
\(611\) −16.4485 9.49653i −0.665434 0.384189i
\(612\) 0 0
\(613\) −7.19736 12.4662i −0.290699 0.503505i 0.683277 0.730160i \(-0.260554\pi\)
−0.973975 + 0.226655i \(0.927221\pi\)
\(614\) 0 0
\(615\) 1.03321 + 0.857006i 0.0416632 + 0.0345578i
\(616\) 0 0
\(617\) 12.1573i 0.489435i −0.969594 0.244718i \(-0.921305\pi\)
0.969594 0.244718i \(-0.0786952\pi\)
\(618\) 0 0
\(619\) −16.8732 + 9.74173i −0.678190 + 0.391553i −0.799173 0.601101i \(-0.794729\pi\)
0.120983 + 0.992655i \(0.461395\pi\)
\(620\) 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 \(-0.714779\pi\)
−0.624701 + 0.780864i \(0.714779\pi\)
\(632\) 0 0
\(633\) 6.12091 35.9061i 0.243284 1.42714i
\(634\) 0 0
\(635\) 0.532956 0.923107i 0.0211497 0.0366324i
\(636\) 0 0
\(637\) 10.4472 9.74991i 0.413933 0.386305i
\(638\) 0 0
\(639\) −7.74596 + 22.0592i −0.306425 + 0.872650i
\(640\) 0 0
\(641\) 36.0118 20.7914i 1.42238 0.821211i 0.425878 0.904781i \(-0.359965\pi\)
0.996502 + 0.0835697i \(0.0266321\pi\)
\(642\) 0 0
\(643\) 13.5290i 0.533531i 0.963761 + 0.266766i \(0.0859549\pi\)
−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 \(0.0347771\pi\)
−0.402589 + 0.915381i \(0.631890\pi\)
\(648\) 0 0
\(649\) −23.9683 13.8381i −0.940839 0.543193i
\(650\) 0 0
\(651\) −16.4744 0.910345i −0.645684 0.0356793i
\(652\) 0 0
\(653\) 18.3717 + 10.6069i 0.718941 + 0.415081i 0.814363 0.580356i \(-0.197087\pi\)
−0.0954221 + 0.995437i \(0.530420\pi\)
\(654\) 0 0
\(655\) 0.443039 + 0.767366i 0.0173110 + 0.0299835i
\(656\) 0 0
\(657\) −38.4743 + 7.23615i −1.50103 + 0.282309i
\(658\) 0 0
\(659\) 2.67926i 0.104369i 0.998637 + 0.0521846i \(0.0166184\pi\)
−0.998637 + 0.0521846i \(0.983382\pi\)
\(660\) 0 0
\(661\) 4.79785 2.77004i 0.186615 0.107742i −0.403782 0.914855i \(-0.632305\pi\)
0.590397 + 0.807113i \(0.298971\pi\)
\(662\) 0 0
\(663\) −2.15777 5.82513i −0.0838007 0.226229i
\(664\) 0 0
\(665\) −0.185455 1.62485i −0.00719162 0.0630090i
\(666\) 0 0
\(667\) −30.5422 + 52.9006i −1.18260 + 2.04832i
\(668\) 0 0
\(669\) 11.7718 + 2.00673i 0.455123 + 0.0775846i
\(670\) 0 0
\(671\) 13.2997 0.513429
\(672\) 0 0
\(673\) −17.1946 −0.662804 −0.331402 0.943490i \(-0.607522\pi\)
−0.331402 + 0.943490i \(0.607522\pi\)
\(674\) 0 0
\(675\) −25.8672 + 0.441314i −0.995630 + 0.0169862i
\(676\) 0 0
\(677\) 7.23319 12.5283i 0.277994 0.481500i −0.692892 0.721041i \(-0.743664\pi\)
0.970886 + 0.239541i \(0.0769971\pi\)
\(678\) 0 0
\(679\) −16.1446 7.01605i −0.619571 0.269251i
\(680\) 0 0
\(681\) 21.7881 8.07083i 0.834923 0.309275i
\(682\) 0 0
\(683\) 28.1356 16.2441i 1.07658 0.621564i 0.146609 0.989195i \(-0.453164\pi\)
0.929972 + 0.367630i \(0.119831\pi\)
\(684\) 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
\(693\) −4.35542 + 19.1133i −0.165449 + 0.726053i
\(694\) 0 0
\(695\) −0.0148138 0.00855273i −0.000561918 0.000324423i
\(696\) 0 0
\(697\) −4.68421 8.11329i −0.177427 0.307313i
\(698\) 0 0
\(699\) 5.48142 6.60845i 0.207326 0.249955i
\(700\) 0 0
\(701\) 30.3777i 1.14735i 0.819084 + 0.573674i \(0.194482\pi\)
−0.819084 + 0.573674i \(0.805518\pi\)
\(702\) 0 0
\(703\) 21.6198 12.4822i 0.815407 0.470776i
\(704\) 0 0
\(705\) −2.19625 + 0.813541i −0.0827154 + 0.0306397i
\(706\) 0 0
\(707\) −42.3932 + 4.83860i −1.59436 + 0.181974i
\(708\) 0 0
\(709\) 16.2569 28.1578i 0.610542 1.05749i −0.380607 0.924737i \(-0.624285\pi\)
0.991149 0.132753i \(-0.0423816\pi\)
\(710\) 0 0
\(711\) −13.0225 + 11.1820i −0.488380 + 0.419356i
\(712\) 0 0
\(713\) 31.0295 1.16207
\(714\) 0 0
\(715\) −0.732778 −0.0274044
\(716\) 0 0
\(717\) −29.6675 5.05741i −1.10795 0.188872i
\(718\) 0 0
\(719\) −5.29867 + 9.17757i −0.197607 + 0.342266i −0.947752 0.319008i \(-0.896650\pi\)
0.750145 + 0.661273i \(0.229984\pi\)
\(720\) 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 0.441045 0.897485i \(-0.354608\pi\)
−0.556722 + 0.830699i \(0.687941\pi\)
\(734\) 0 0
\(735\) −0.102925 1.75913i −0.00379646 0.0648864i
\(736\) 0 0
\(737\) 11.0117 + 6.35763i 0.405623 + 0.234186i
\(738\) 0 0
\(739\) 19.3463 + 33.5087i 0.711665 + 1.23264i 0.964232 + 0.265060i \(0.0853917\pi\)
−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 \(0.310314\pi\)
−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 \(-0.691844\pi\)
0.996874 + 0.0790136i \(0.0251771\pi\)
\(752\) 0 0
\(753\) −1.01809 + 5.97226i −0.0371013 + 0.217641i
\(754\) 0 0
\(755\) −0.398610 −0.0145069
\(756\) 0 0
\(757\) 26.2967 0.955770 0.477885 0.878422i \(-0.341404\pi\)
0.477885 + 0.878422i \(0.341404\pi\)
\(758\) 0 0
\(759\) 6.19523 36.3421i 0.224872 1.31914i
\(760\) 0 0
\(761\) 12.9780 22.4785i 0.470452 0.814846i −0.528977 0.848636i \(-0.677424\pi\)
0.999429 + 0.0337898i \(0.0107577\pi\)
\(762\) 0 0
\(763\) −3.56218 + 0.406574i −0.128960 + 0.0147190i
\(764\) 0 0
\(765\) −0.722746 0.253787i −0.0261309 0.00917570i
\(766\) 0 0
\(767\) 19.8114 11.4381i 0.715348 0.413006i
\(768\) 0 0
\(769\) 36.9215i 1.33142i −0.746209 0.665712i \(-0.768128\pi\)
0.746209 0.665712i \(-0.231872\pi\)
\(770\) 0 0
\(771\) −21.2444 17.6212i −0.765097 0.634614i
\(772\) 0 0
\(773\) 5.79284 + 10.0335i 0.208354 + 0.360879i 0.951196 0.308587i \(-0.0998561\pi\)
−0.742842 + 0.669466i \(0.766523\pi\)
\(774\) 0 0
\(775\) 15.5247 + 8.96322i 0.557665 + 0.321968i
\(776\) 0 0
\(777\) 24.0019 12.1438i 0.861062 0.435655i
\(778\) 0 0
\(779\) −19.6408 11.3396i −0.703705 0.406284i
\(780\) 0 0
\(781\) −9.62376 16.6688i −0.344365 0.596458i
\(782\) 0 0
\(783\) −32.2050 17.8681i −1.15091 0.638555i
\(784\) 0 0
\(785\) 1.96861i 0.0702627i
\(786\) 0 0
\(787\) 25.9153 14.9622i 0.923779 0.533344i 0.0389406 0.999242i \(-0.487602\pi\)
0.884839 + 0.465897i \(0.154268\pi\)
\(788\) 0 0
\(789\) 8.63827 + 23.3200i 0.307531 + 0.830214i