Properties

Label 147.4.e.b.67.1
Level $147$
Weight $4$
Character 147.67
Analytic conductor $8.673$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.b.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-2.00000 - 3.46410i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-2.00000 - 3.46410i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +(-8.00000 + 13.8564i) q^{10} +(-31.0000 + 53.6936i) q^{11} +(-12.0000 - 20.7846i) q^{12} +62.0000 q^{13} +12.0000 q^{15} +(32.0000 + 55.4256i) q^{16} +(42.0000 - 72.7461i) q^{17} +(-18.0000 + 31.1769i) q^{18} +(50.0000 + 86.6025i) q^{19} +32.0000 q^{20} +248.000 q^{22} +(21.0000 + 36.3731i) q^{23} +(54.5000 - 94.3968i) q^{25} +(-124.000 - 214.774i) q^{26} +27.0000 q^{27} -10.0000 q^{29} +(-24.0000 - 41.5692i) q^{30} +(-24.0000 + 41.5692i) q^{31} +(128.000 - 221.703i) q^{32} +(-93.0000 - 161.081i) q^{33} -336.000 q^{34} +72.0000 q^{36} +(123.000 + 213.042i) q^{37} +(200.000 - 346.410i) q^{38} +(-93.0000 + 161.081i) q^{39} +248.000 q^{41} +68.0000 q^{43} +(-248.000 - 429.549i) q^{44} +(-18.0000 + 31.1769i) q^{45} +(84.0000 - 145.492i) q^{46} +(162.000 + 280.592i) q^{47} -192.000 q^{48} -436.000 q^{50} +(126.000 + 218.238i) q^{51} +(-248.000 + 429.549i) q^{52} +(-129.000 + 223.435i) q^{53} +(-54.0000 - 93.5307i) q^{54} +248.000 q^{55} -300.000 q^{57} +(20.0000 + 34.6410i) q^{58} +(60.0000 - 103.923i) q^{59} +(-48.0000 + 83.1384i) q^{60} +(311.000 + 538.668i) q^{61} +192.000 q^{62} -512.000 q^{64} +(-124.000 - 214.774i) q^{65} +(-372.000 + 644.323i) q^{66} +(-452.000 + 782.887i) q^{67} +(336.000 + 581.969i) q^{68} -126.000 q^{69} -678.000 q^{71} +(-321.000 + 555.988i) q^{73} +(492.000 - 852.169i) q^{74} +(163.500 + 283.190i) q^{75} -800.000 q^{76} +744.000 q^{78} +(-370.000 - 640.859i) q^{79} +(128.000 - 221.703i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-496.000 - 859.097i) q^{82} -468.000 q^{83} -336.000 q^{85} +(-136.000 - 235.559i) q^{86} +(15.0000 - 25.9808i) q^{87} +(100.000 + 173.205i) q^{89} +144.000 q^{90} -336.000 q^{92} +(-72.0000 - 124.708i) q^{93} +(648.000 - 1122.37i) q^{94} +(200.000 - 346.410i) q^{95} +(384.000 + 665.108i) q^{96} +1266.00 q^{97} +558.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} - 3q^{3} - 8q^{4} - 4q^{5} + 24q^{6} - 9q^{9} + O(q^{10}) \) \( 2q - 4q^{2} - 3q^{3} - 8q^{4} - 4q^{5} + 24q^{6} - 9q^{9} - 16q^{10} - 62q^{11} - 24q^{12} + 124q^{13} + 24q^{15} + 64q^{16} + 84q^{17} - 36q^{18} + 100q^{19} + 64q^{20} + 496q^{22} + 42q^{23} + 109q^{25} - 248q^{26} + 54q^{27} - 20q^{29} - 48q^{30} - 48q^{31} + 256q^{32} - 186q^{33} - 672q^{34} + 144q^{36} + 246q^{37} + 400q^{38} - 186q^{39} + 496q^{41} + 136q^{43} - 496q^{44} - 36q^{45} + 168q^{46} + 324q^{47} - 384q^{48} - 872q^{50} + 252q^{51} - 496q^{52} - 258q^{53} - 108q^{54} + 496q^{55} - 600q^{57} + 40q^{58} + 120q^{59} - 96q^{60} + 622q^{61} + 384q^{62} - 1024q^{64} - 248q^{65} - 744q^{66} - 904q^{67} + 672q^{68} - 252q^{69} - 1356q^{71} - 642q^{73} + 984q^{74} + 327q^{75} - 1600q^{76} + 1488q^{78} - 740q^{79} + 256q^{80} - 81q^{81} - 992q^{82} - 936q^{83} - 672q^{85} - 272q^{86} + 30q^{87} + 200q^{89} + 288q^{90} - 672q^{92} - 144q^{93} + 1296q^{94} + 400q^{95} + 768q^{96} + 2532q^{97} + 1116q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 3.46410i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −4.00000 + 6.92820i −0.500000 + 0.866025i
\(5\) −2.00000 3.46410i −0.178885 0.309839i 0.762614 0.646854i \(-0.223916\pi\)
−0.941499 + 0.337016i \(0.890582\pi\)
\(6\) 12.0000 0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −8.00000 + 13.8564i −0.252982 + 0.438178i
\(11\) −31.0000 + 53.6936i −0.849714 + 1.47175i 0.0317500 + 0.999496i \(0.489892\pi\)
−0.881464 + 0.472252i \(0.843441\pi\)
\(12\) −12.0000 20.7846i −0.288675 0.500000i
\(13\) 62.0000 1.32275 0.661373 0.750057i \(-0.269974\pi\)
0.661373 + 0.750057i \(0.269974\pi\)
\(14\) 0 0
\(15\) 12.0000 0.206559
\(16\) 32.0000 + 55.4256i 0.500000 + 0.866025i
\(17\) 42.0000 72.7461i 0.599206 1.03785i −0.393733 0.919225i \(-0.628817\pi\)
0.992939 0.118630i \(-0.0378502\pi\)
\(18\) −18.0000 + 31.1769i −0.235702 + 0.408248i
\(19\) 50.0000 + 86.6025i 0.603726 + 1.04568i 0.992251 + 0.124246i \(0.0396511\pi\)
−0.388526 + 0.921438i \(0.627016\pi\)
\(20\) 32.0000 0.357771
\(21\) 0 0
\(22\) 248.000 2.40335
\(23\) 21.0000 + 36.3731i 0.190383 + 0.329753i 0.945377 0.325979i \(-0.105694\pi\)
−0.754994 + 0.655731i \(0.772360\pi\)
\(24\) 0 0
\(25\) 54.5000 94.3968i 0.436000 0.755174i
\(26\) −124.000 214.774i −0.935323 1.62003i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −10.0000 −0.0640329 −0.0320164 0.999487i \(-0.510193\pi\)
−0.0320164 + 0.999487i \(0.510193\pi\)
\(30\) −24.0000 41.5692i −0.146059 0.252982i
\(31\) −24.0000 + 41.5692i −0.139049 + 0.240840i −0.927137 0.374723i \(-0.877738\pi\)
0.788088 + 0.615563i \(0.211071\pi\)
\(32\) 128.000 221.703i 0.707107 1.22474i
\(33\) −93.0000 161.081i −0.490582 0.849714i
\(34\) −336.000 −1.69481
\(35\) 0 0
\(36\) 72.0000 0.333333
\(37\) 123.000 + 213.042i 0.546516 + 0.946593i 0.998510 + 0.0545719i \(0.0173794\pi\)
−0.451994 + 0.892021i \(0.649287\pi\)
\(38\) 200.000 346.410i 0.853797 1.47882i
\(39\) −93.0000 + 161.081i −0.381844 + 0.661373i
\(40\) 0 0
\(41\) 248.000 0.944661 0.472330 0.881422i \(-0.343413\pi\)
0.472330 + 0.881422i \(0.343413\pi\)
\(42\) 0 0
\(43\) 68.0000 0.241161 0.120580 0.992704i \(-0.461524\pi\)
0.120580 + 0.992704i \(0.461524\pi\)
\(44\) −248.000 429.549i −0.849714 1.47175i
\(45\) −18.0000 + 31.1769i −0.0596285 + 0.103280i
\(46\) 84.0000 145.492i 0.269242 0.466341i
\(47\) 162.000 + 280.592i 0.502769 + 0.870821i 0.999995 + 0.00319997i \(0.00101858\pi\)
−0.497226 + 0.867621i \(0.665648\pi\)
\(48\) −192.000 −0.577350
\(49\) 0 0
\(50\) −436.000 −1.23319
\(51\) 126.000 + 218.238i 0.345952 + 0.599206i
\(52\) −248.000 + 429.549i −0.661373 + 1.14553i
\(53\) −129.000 + 223.435i −0.334330 + 0.579077i −0.983356 0.181689i \(-0.941843\pi\)
0.649026 + 0.760767i \(0.275177\pi\)
\(54\) −54.0000 93.5307i −0.136083 0.235702i
\(55\) 248.000 0.608006
\(56\) 0 0
\(57\) −300.000 −0.697122
\(58\) 20.0000 + 34.6410i 0.0452781 + 0.0784239i
\(59\) 60.0000 103.923i 0.132396 0.229316i −0.792204 0.610256i \(-0.791066\pi\)
0.924600 + 0.380941i \(0.124400\pi\)
\(60\) −48.0000 + 83.1384i −0.103280 + 0.178885i
\(61\) 311.000 + 538.668i 0.652778 + 1.13064i 0.982446 + 0.186548i \(0.0597300\pi\)
−0.329668 + 0.944097i \(0.606937\pi\)
\(62\) 192.000 0.393291
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) −124.000 214.774i −0.236620 0.409838i
\(66\) −372.000 + 644.323i −0.693788 + 1.20168i
\(67\) −452.000 + 782.887i −0.824188 + 1.42754i 0.0783505 + 0.996926i \(0.475035\pi\)
−0.902538 + 0.430609i \(0.858299\pi\)
\(68\) 336.000 + 581.969i 0.599206 + 1.03785i
\(69\) −126.000 −0.219835
\(70\) 0 0
\(71\) −678.000 −1.13329 −0.566646 0.823961i \(-0.691759\pi\)
−0.566646 + 0.823961i \(0.691759\pi\)
\(72\) 0 0
\(73\) −321.000 + 555.988i −0.514660 + 0.891418i 0.485195 + 0.874406i \(0.338749\pi\)
−0.999855 + 0.0170119i \(0.994585\pi\)
\(74\) 492.000 852.169i 0.772890 1.33868i
\(75\) 163.500 + 283.190i 0.251725 + 0.436000i
\(76\) −800.000 −1.20745
\(77\) 0 0
\(78\) 744.000 1.08002
\(79\) −370.000 640.859i −0.526940 0.912687i −0.999507 0.0313921i \(-0.990006\pi\)
0.472567 0.881295i \(-0.343327\pi\)
\(80\) 128.000 221.703i 0.178885 0.309839i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −496.000 859.097i −0.667976 1.15697i
\(83\) −468.000 −0.618912 −0.309456 0.950914i \(-0.600147\pi\)
−0.309456 + 0.950914i \(0.600147\pi\)
\(84\) 0 0
\(85\) −336.000 −0.428757
\(86\) −136.000 235.559i −0.170526 0.295360i
\(87\) 15.0000 25.9808i 0.0184847 0.0320164i
\(88\) 0 0
\(89\) 100.000 + 173.205i 0.119101 + 0.206289i 0.919412 0.393297i \(-0.128665\pi\)
−0.800311 + 0.599585i \(0.795332\pi\)
\(90\) 144.000 0.168655
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) −72.0000 124.708i −0.0802801 0.139049i
\(94\) 648.000 1122.37i 0.711022 1.23153i
\(95\) 200.000 346.410i 0.215995 0.374115i
\(96\) 384.000 + 665.108i 0.408248 + 0.707107i
\(97\) 1266.00 1.32518 0.662592 0.748981i \(-0.269456\pi\)
0.662592 + 0.748981i \(0.269456\pi\)
\(98\) 0 0
\(99\) 558.000 0.566476
\(100\) 436.000 + 755.174i 0.436000 + 0.755174i
\(101\) 116.000 200.918i 0.114281 0.197941i −0.803211 0.595695i \(-0.796877\pi\)
0.917492 + 0.397754i \(0.130210\pi\)
\(102\) 504.000 872.954i 0.489249 0.847405i
\(103\) −896.000 1551.92i −0.857141 1.48461i −0.874645 0.484765i \(-0.838905\pi\)
0.0175038 0.999847i \(-0.494428\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1032.00 0.945629
\(107\) 953.000 + 1650.64i 0.861028 + 1.49134i 0.870938 + 0.491393i \(0.163512\pi\)
−0.00990992 + 0.999951i \(0.503154\pi\)
\(108\) −108.000 + 187.061i −0.0962250 + 0.166667i
\(109\) 45.0000 77.9423i 0.0395433 0.0684910i −0.845576 0.533854i \(-0.820743\pi\)
0.885120 + 0.465363i \(0.154076\pi\)
\(110\) −496.000 859.097i −0.429925 0.744652i
\(111\) −738.000 −0.631062
\(112\) 0 0
\(113\) 458.000 0.381283 0.190642 0.981660i \(-0.438943\pi\)
0.190642 + 0.981660i \(0.438943\pi\)
\(114\) 600.000 + 1039.23i 0.492940 + 0.853797i
\(115\) 84.0000 145.492i 0.0681134 0.117976i
\(116\) 40.0000 69.2820i 0.0320164 0.0554541i
\(117\) −279.000 483.242i −0.220458 0.381844i
\(118\) −480.000 −0.374471
\(119\) 0 0
\(120\) 0 0
\(121\) −1256.50 2176.32i −0.944027 1.63510i
\(122\) 1244.00 2154.67i 0.923168 1.59897i
\(123\) −372.000 + 644.323i −0.272700 + 0.472330i
\(124\) −192.000 332.554i −0.139049 0.240840i
\(125\) −936.000 −0.669747
\(126\) 0 0
\(127\) 804.000 0.561760 0.280880 0.959743i \(-0.409374\pi\)
0.280880 + 0.959743i \(0.409374\pi\)
\(128\) 0 0
\(129\) −102.000 + 176.669i −0.0696170 + 0.120580i
\(130\) −496.000 + 859.097i −0.334631 + 0.579599i
\(131\) 406.000 + 703.213i 0.270782 + 0.469007i 0.969062 0.246817i \(-0.0793846\pi\)
−0.698281 + 0.715824i \(0.746051\pi\)
\(132\) 1488.00 0.981165
\(133\) 0 0
\(134\) 3616.00 2.33116
\(135\) −54.0000 93.5307i −0.0344265 0.0596285i
\(136\) 0 0
\(137\) −207.000 + 358.535i −0.129089 + 0.223589i −0.923324 0.384022i \(-0.874539\pi\)
0.794235 + 0.607611i \(0.207872\pi\)
\(138\) 252.000 + 436.477i 0.155447 + 0.269242i
\(139\) 1620.00 0.988537 0.494268 0.869309i \(-0.335436\pi\)
0.494268 + 0.869309i \(0.335436\pi\)
\(140\) 0 0
\(141\) −972.000 −0.580547
\(142\) 1356.00 + 2348.66i 0.801359 + 1.38799i
\(143\) −1922.00 + 3329.00i −1.12396 + 1.94675i
\(144\) 288.000 498.831i 0.166667 0.288675i
\(145\) 20.0000 + 34.6410i 0.0114545 + 0.0198399i
\(146\) 2568.00 1.45568
\(147\) 0 0
\(148\) −1968.00 −1.09303
\(149\) −1185.00 2052.48i −0.651537 1.12849i −0.982750 0.184939i \(-0.940791\pi\)
0.331213 0.943556i \(-0.392542\pi\)
\(150\) 654.000 1132.76i 0.355993 0.616597i
\(151\) 284.000 491.902i 0.153057 0.265102i −0.779293 0.626660i \(-0.784422\pi\)
0.932350 + 0.361558i \(0.117755\pi\)
\(152\) 0 0
\(153\) −756.000 −0.399470
\(154\) 0 0
\(155\) 192.000 0.0994956
\(156\) −744.000 1288.65i −0.381844 0.661373i
\(157\) −133.000 + 230.363i −0.0676086 + 0.117102i −0.897848 0.440305i \(-0.854870\pi\)
0.830240 + 0.557407i \(0.188204\pi\)
\(158\) −1480.00 + 2563.44i −0.745206 + 1.29073i
\(159\) −387.000 670.304i −0.193026 0.334330i
\(160\) −1024.00 −0.505964
\(161\) 0 0
\(162\) 324.000 0.157135
\(163\) 136.000 + 235.559i 0.0653518 + 0.113193i 0.896850 0.442335i \(-0.145850\pi\)
−0.831498 + 0.555527i \(0.812516\pi\)
\(164\) −992.000 + 1718.19i −0.472330 + 0.818100i
\(165\) −372.000 + 644.323i −0.175516 + 0.304003i
\(166\) 936.000 + 1621.20i 0.437637 + 0.758009i
\(167\) 1876.00 0.869277 0.434638 0.900605i \(-0.356876\pi\)
0.434638 + 0.900605i \(0.356876\pi\)
\(168\) 0 0
\(169\) 1647.00 0.749659
\(170\) 672.000 + 1163.94i 0.303177 + 0.525118i
\(171\) 450.000 779.423i 0.201242 0.348561i
\(172\) −272.000 + 471.118i −0.120580 + 0.208851i
\(173\) −76.0000 131.636i −0.0333998 0.0578502i 0.848842 0.528646i \(-0.177300\pi\)
−0.882242 + 0.470796i \(0.843967\pi\)
\(174\) −120.000 −0.0522826
\(175\) 0 0
\(176\) −3968.00 −1.69943
\(177\) 180.000 + 311.769i 0.0764386 + 0.132396i
\(178\) 400.000 692.820i 0.168434 0.291736i
\(179\) −305.000 + 528.275i −0.127356 + 0.220588i −0.922652 0.385635i \(-0.873982\pi\)
0.795295 + 0.606222i \(0.207316\pi\)
\(180\) −144.000 249.415i −0.0596285 0.103280i
\(181\) −1042.00 −0.427907 −0.213954 0.976844i \(-0.568634\pi\)
−0.213954 + 0.976844i \(0.568634\pi\)
\(182\) 0 0
\(183\) −1866.00 −0.753763
\(184\) 0 0
\(185\) 492.000 852.169i 0.195527 0.338663i
\(186\) −288.000 + 498.831i −0.113533 + 0.196645i
\(187\) 2604.00 + 4510.26i 1.01831 + 1.76376i
\(188\) −2592.00 −1.00554
\(189\) 0 0
\(190\) −1600.00 −0.610927
\(191\) 1019.00 + 1764.96i 0.386033 + 0.668628i 0.991912 0.126928i \(-0.0405118\pi\)
−0.605879 + 0.795557i \(0.707179\pi\)
\(192\) 768.000 1330.22i 0.288675 0.500000i
\(193\) 1301.00 2253.40i 0.485223 0.840431i −0.514633 0.857411i \(-0.672072\pi\)
0.999856 + 0.0169798i \(0.00540511\pi\)
\(194\) −2532.00 4385.55i −0.937046 1.62301i
\(195\) 744.000 0.273225
\(196\) 0 0
\(197\) 2354.00 0.851348 0.425674 0.904877i \(-0.360037\pi\)
0.425674 + 0.904877i \(0.360037\pi\)
\(198\) −1116.00 1932.97i −0.400559 0.693788i
\(199\) 840.000 1454.92i 0.299226 0.518275i −0.676733 0.736229i \(-0.736605\pi\)
0.975959 + 0.217954i \(0.0699381\pi\)
\(200\) 0 0
\(201\) −1356.00 2348.66i −0.475845 0.824188i
\(202\) −928.000 −0.323237
\(203\) 0 0
\(204\) −2016.00 −0.691903
\(205\) −496.000 859.097i −0.168986 0.292692i
\(206\) −3584.00 + 6207.67i −1.21218 + 2.09956i
\(207\) 189.000 327.358i 0.0634609 0.109918i
\(208\) 1984.00 + 3436.39i 0.661373 + 1.14553i
\(209\) −6200.00 −2.05198
\(210\) 0 0
\(211\) −668.000 −0.217948 −0.108974 0.994045i \(-0.534757\pi\)
−0.108974 + 0.994045i \(0.534757\pi\)
\(212\) −1032.00 1787.48i −0.334330 0.579077i
\(213\) 1017.00 1761.50i 0.327153 0.566646i
\(214\) 3812.00 6602.58i 1.21768 2.10908i
\(215\) −136.000 235.559i −0.0431401 0.0747209i
\(216\) 0 0
\(217\) 0 0
\(218\) −360.000 −0.111845
\(219\) −963.000 1667.96i −0.297139 0.514660i
\(220\) −992.000 + 1718.19i −0.304003 + 0.526548i
\(221\) 2604.00 4510.26i 0.792597 1.37282i
\(222\) 1476.00 + 2556.51i 0.446228 + 0.772890i
\(223\) 1832.00 0.550134 0.275067 0.961425i \(-0.411300\pi\)
0.275067 + 0.961425i \(0.411300\pi\)
\(224\) 0 0
\(225\) −981.000 −0.290667
\(226\) −916.000 1586.56i −0.269608 0.466975i
\(227\) 2472.00 4281.63i 0.722786 1.25190i −0.237093 0.971487i \(-0.576195\pi\)
0.959879 0.280415i \(-0.0904721\pi\)
\(228\) 1200.00 2078.46i 0.348561 0.603726i
\(229\) −2735.00 4737.16i −0.789231 1.36699i −0.926439 0.376446i \(-0.877146\pi\)
0.137208 0.990542i \(-0.456187\pi\)
\(230\) −672.000 −0.192654
\(231\) 0 0
\(232\) 0 0
\(233\) 1401.00 + 2426.60i 0.393917 + 0.682284i 0.992962 0.118431i \(-0.0377866\pi\)
−0.599046 + 0.800715i \(0.704453\pi\)
\(234\) −1116.00 + 1932.97i −0.311774 + 0.540009i
\(235\) 648.000 1122.37i 0.179876 0.311554i
\(236\) 480.000 + 831.384i 0.132396 + 0.229316i
\(237\) 2220.00 0.608458
\(238\) 0 0
\(239\) −1170.00 −0.316657 −0.158328 0.987386i \(-0.550610\pi\)
−0.158328 + 0.987386i \(0.550610\pi\)
\(240\) 384.000 + 665.108i 0.103280 + 0.178885i
\(241\) −1169.00 + 2024.77i −0.312456 + 0.541190i −0.978893 0.204371i \(-0.934485\pi\)
0.666437 + 0.745561i \(0.267818\pi\)
\(242\) −5026.00 + 8705.29i −1.33506 + 2.31238i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) −4976.00 −1.30556
\(245\) 0 0
\(246\) 2976.00 0.771312
\(247\) 3100.00 + 5369.36i 0.798576 + 1.38317i
\(248\) 0 0
\(249\) 702.000 1215.90i 0.178664 0.309456i
\(250\) 1872.00 + 3242.40i 0.473583 + 0.820269i
\(251\) −2792.00 −0.702109 −0.351055 0.936355i \(-0.614177\pi\)
−0.351055 + 0.936355i \(0.614177\pi\)
\(252\) 0 0
\(253\) −2604.00 −0.647083
\(254\) −1608.00 2785.14i −0.397224 0.688012i
\(255\) 504.000 872.954i 0.123771 0.214378i
\(256\) −2048.00 + 3547.24i −0.500000 + 0.866025i
\(257\) 3512.00 + 6082.96i 0.852422 + 1.47644i 0.879016 + 0.476792i \(0.158201\pi\)
−0.0265936 + 0.999646i \(0.508466\pi\)
\(258\) 816.000 0.196907
\(259\) 0 0
\(260\) 1984.00 0.473240
\(261\) 45.0000 + 77.9423i 0.0106721 + 0.0184847i
\(262\) 1624.00 2812.85i 0.382943 0.663277i
\(263\) −1219.00 + 2111.37i −0.285805 + 0.495029i −0.972804 0.231629i \(-0.925594\pi\)
0.686999 + 0.726658i \(0.258928\pi\)
\(264\) 0 0
\(265\) 1032.00 0.239227
\(266\) 0 0
\(267\) −600.000 −0.137526
\(268\) −3616.00 6263.10i −0.824188 1.42754i
\(269\) −3390.00 + 5871.65i −0.768372 + 1.33086i 0.170074 + 0.985431i \(0.445599\pi\)
−0.938446 + 0.345427i \(0.887734\pi\)
\(270\) −216.000 + 374.123i −0.0486864 + 0.0843274i
\(271\) −964.000 1669.70i −0.216084 0.374269i 0.737523 0.675322i \(-0.235995\pi\)
−0.953607 + 0.301053i \(0.902662\pi\)
\(272\) 5376.00 1.19841
\(273\) 0 0
\(274\) 1656.00 0.365119
\(275\) 3379.00 + 5852.60i 0.740950 + 1.28336i
\(276\) 504.000 872.954i 0.109918 0.190383i
\(277\) −2777.00 + 4809.91i −0.602360 + 1.04332i 0.390103 + 0.920771i \(0.372440\pi\)
−0.992463 + 0.122547i \(0.960894\pi\)
\(278\) −3240.00 5611.84i −0.699001 1.21071i
\(279\) 432.000 0.0926995
\(280\) 0 0
\(281\) 1942.00 0.412278 0.206139 0.978523i \(-0.433910\pi\)
0.206139 + 0.978523i \(0.433910\pi\)
\(282\) 1944.00 + 3367.11i 0.410509 + 0.711022i
\(283\) 2414.00 4181.17i 0.507058 0.878250i −0.492909 0.870081i \(-0.664066\pi\)
0.999967 0.00816911i \(-0.00260034\pi\)
\(284\) 2712.00 4697.32i 0.566646 0.981460i
\(285\) 600.000 + 1039.23i 0.124705 + 0.215995i
\(286\) 15376.0 3.17903
\(287\) 0 0
\(288\) −2304.00 −0.471405
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) 80.0000 138.564i 0.0161992 0.0280578i
\(291\) −1899.00 + 3289.16i −0.382548 + 0.662592i
\(292\) −2568.00 4447.91i −0.514660 0.891418i
\(293\) 6152.00 1.22663 0.613317 0.789837i \(-0.289835\pi\)
0.613317 + 0.789837i \(0.289835\pi\)
\(294\) 0 0
\(295\) −480.000 −0.0947345
\(296\) 0 0
\(297\) −837.000 + 1449.73i −0.163527 + 0.283238i
\(298\) −4740.00 + 8209.92i −0.921412 + 1.59593i
\(299\) 1302.00 + 2255.13i 0.251828 + 0.436179i
\(300\) −2616.00 −0.503449
\(301\) 0 0
\(302\) −2272.00 −0.432910
\(303\) 348.000 + 602.754i 0.0659805 + 0.114281i
\(304\) −3200.00 + 5542.56i −0.603726 + 1.04568i
\(305\) 1244.00 2154.67i 0.233545 0.404512i
\(306\) 1512.00 + 2618.86i 0.282468 + 0.489249i
\(307\) −5884.00 −1.09387 −0.546934 0.837176i \(-0.684205\pi\)
−0.546934 + 0.837176i \(0.684205\pi\)
\(308\) 0 0
\(309\) 5376.00 0.989741
\(310\) −384.000 665.108i −0.0703540 0.121857i
\(311\) 4566.00 7908.54i 0.832521 1.44197i −0.0635115 0.997981i \(-0.520230\pi\)
0.896033 0.443988i \(-0.146437\pi\)
\(312\) 0 0
\(313\) −4691.00 8125.05i −0.847128 1.46727i −0.883760 0.467940i \(-0.844996\pi\)
0.0366327 0.999329i \(-0.488337\pi\)
\(314\) 1064.00 0.191226
\(315\) 0 0
\(316\) 5920.00 1.05388
\(317\) −1557.00 2696.80i −0.275867 0.477816i 0.694487 0.719506i \(-0.255632\pi\)
−0.970353 + 0.241690i \(0.922298\pi\)
\(318\) −1548.00 + 2681.21i −0.272980 + 0.472815i
\(319\) 310.000 536.936i 0.0544096 0.0942402i
\(320\) 1024.00 + 1773.62i 0.178885 + 0.309839i
\(321\) −5718.00 −0.994229
\(322\) 0 0
\(323\) 8400.00 1.44702
\(324\) −324.000 561.184i −0.0555556 0.0962250i
\(325\) 3379.00 5852.60i 0.576718 0.998904i
\(326\) 544.000 942.236i 0.0924214 0.160079i
\(327\) 135.000 + 233.827i 0.0228303 + 0.0395433i
\(328\) 0 0
\(329\) 0 0
\(330\) 2976.00 0.496435
\(331\) −766.000 1326.75i −0.127200 0.220317i 0.795391 0.606097i \(-0.207266\pi\)
−0.922591 + 0.385780i \(0.873932\pi\)
\(332\) 1872.00 3242.40i 0.309456 0.535993i
\(333\) 1107.00 1917.38i 0.182172 0.315531i
\(334\) −3752.00 6498.65i −0.614672 1.06464i
\(335\) 3616.00 0.589741
\(336\) 0 0
\(337\) −4166.00 −0.673402 −0.336701 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(338\) −3294.00 5705.38i −0.530089 0.918141i
\(339\) −687.000 + 1189.92i −0.110067 + 0.190642i
\(340\) 1344.00 2327.88i 0.214378 0.371314i
\(341\) −1488.00 2577.29i −0.236304 0.409291i
\(342\) −3600.00 −0.569198
\(343\) 0 0
\(344\) 0 0
\(345\) 252.000 + 436.477i 0.0393253 + 0.0681134i
\(346\) −304.000 + 526.543i −0.0472345 + 0.0818126i
\(347\) 5683.00 9843.24i 0.879191 1.52280i 0.0269617 0.999636i \(-0.491417\pi\)
0.852230 0.523168i \(-0.175250\pi\)
\(348\) 120.000 + 207.846i 0.0184847 + 0.0320164i
\(349\) −9310.00 −1.42795 −0.713973 0.700174i \(-0.753106\pi\)
−0.713973 + 0.700174i \(0.753106\pi\)
\(350\) 0 0
\(351\) 1674.00 0.254563
\(352\) 7936.00 + 13745.6i 1.20168 + 2.08137i
\(353\) −4286.00 + 7423.57i −0.646234 + 1.11931i 0.337780 + 0.941225i \(0.390324\pi\)
−0.984015 + 0.178086i \(0.943009\pi\)
\(354\) 720.000 1247.08i 0.108100 0.187236i
\(355\) 1356.00 + 2348.66i 0.202730 + 0.351138i
\(356\) −1600.00 −0.238202
\(357\) 0 0
\(358\) 2440.00 0.360218
\(359\) 2395.00 + 4148.26i 0.352098 + 0.609852i 0.986617 0.163056i \(-0.0521350\pi\)
−0.634519 + 0.772908i \(0.718802\pi\)
\(360\) 0 0
\(361\) −1570.50 + 2720.19i −0.228969 + 0.396586i
\(362\) 2084.00 + 3609.59i 0.302576 + 0.524077i
\(363\) 7539.00 1.09007
\(364\) 0 0
\(365\) 2568.00 0.368261
\(366\) 3732.00 + 6464.01i 0.532991 + 0.923168i
\(367\) 2712.00 4697.32i 0.385736 0.668115i −0.606135 0.795362i \(-0.707281\pi\)
0.991871 + 0.127247i \(0.0406141\pi\)
\(368\) −1344.00 + 2327.88i −0.190383 + 0.329753i
\(369\) −1116.00 1932.97i −0.157443 0.272700i
\(370\) −3936.00 −0.553035
\(371\) 0 0
\(372\) 1152.00 0.160560
\(373\) −919.000 1591.75i −0.127571 0.220960i 0.795164 0.606395i \(-0.207385\pi\)
−0.922735 + 0.385435i \(0.874051\pi\)
\(374\) 10416.0 18041.0i 1.44010 2.49433i
\(375\) 1404.00 2431.80i 0.193339 0.334874i
\(376\) 0 0
\(377\) −620.000 −0.0846993
\(378\) 0 0
\(379\) −4260.00 −0.577365 −0.288683 0.957425i \(-0.593217\pi\)
−0.288683 + 0.957425i \(0.593217\pi\)
\(380\) 1600.00 + 2771.28i 0.215995 + 0.374115i
\(381\) −1206.00 + 2088.85i −0.162166 + 0.280880i
\(382\) 4076.00 7059.84i 0.545933 0.945583i
\(383\) 4524.00 + 7835.80i 0.603566 + 1.04541i 0.992276 + 0.124046i \(0.0395872\pi\)
−0.388711 + 0.921360i \(0.627080\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10408.0 −1.37242
\(387\) −306.000 530.008i −0.0401934 0.0696170i
\(388\) −5064.00 + 8771.11i −0.662592 + 1.14764i
\(389\) 5745.00 9950.63i 0.748800 1.29696i −0.199599 0.979878i \(-0.563964\pi\)
0.948398 0.317081i \(-0.102703\pi\)
\(390\) −1488.00 2577.29i −0.193200 0.334631i
\(391\) 3528.00 0.456314
\(392\) 0 0
\(393\) −2436.00 −0.312672
\(394\) −4708.00 8154.50i −0.601994 1.04268i
\(395\) −1480.00 + 2563.44i −0.188524 + 0.326533i
\(396\) −2232.00 + 3865.94i −0.283238 + 0.490582i
\(397\) −933.000 1616.00i −0.117949 0.204294i 0.801005 0.598657i \(-0.204299\pi\)
−0.918955 + 0.394363i \(0.870965\pi\)
\(398\) −6720.00 −0.846340
\(399\) 0 0
\(400\) 6976.00 0.872000
\(401\) −6831.00 11831.6i −0.850683 1.47343i −0.880593 0.473873i \(-0.842855\pi\)
0.0299100 0.999553i \(-0.490478\pi\)
\(402\) −5424.00 + 9394.64i −0.672947 + 1.16558i
\(403\) −1488.00 + 2577.29i −0.183927 + 0.318571i
\(404\) 928.000 + 1607.34i 0.114281 + 0.197941i
\(405\) 324.000 0.0397523
\(406\) 0 0
\(407\) −15252.0 −1.85753
\(408\) 0 0
\(409\) −6605.00 + 11440.2i −0.798524 + 1.38308i 0.122054 + 0.992524i \(0.461052\pi\)
−0.920577 + 0.390560i \(0.872281\pi\)
\(410\) −1984.00 + 3436.39i −0.238982 + 0.413930i
\(411\) −621.000 1075.60i −0.0745296 0.129089i
\(412\) 14336.0 1.71428
\(413\) 0 0
\(414\) −1512.00 −0.179495
\(415\) 936.000 + 1621.20i 0.110714 + 0.191763i
\(416\) 7936.00 13745.6i 0.935323 1.62003i
\(417\) −2430.00 + 4208.88i −0.285366 + 0.494268i
\(418\) 12400.0 + 21477.4i 1.45097 + 2.51315i
\(419\) −6960.00 −0.811499 −0.405750 0.913984i \(-0.632990\pi\)
−0.405750 + 0.913984i \(0.632990\pi\)
\(420\) 0 0
\(421\) 8162.00 0.944873 0.472437 0.881365i \(-0.343375\pi\)
0.472437 + 0.881365i \(0.343375\pi\)
\(422\) 1336.00 + 2314.02i 0.154112 + 0.266931i
\(423\) 1458.00 2525.33i 0.167590 0.290274i
\(424\) 0 0
\(425\) −4578.00 7929.33i −0.522507 0.905009i
\(426\) −8136.00 −0.925330
\(427\) 0 0
\(428\) −15248.0 −1.72206
\(429\) −5766.00 9987.00i −0.648916 1.12396i
\(430\) −544.000 + 942.236i −0.0610093 + 0.105671i
\(431\) −8301.00 + 14377.8i −0.927715 + 1.60685i −0.140579 + 0.990069i \(0.544896\pi\)
−0.787136 + 0.616780i \(0.788437\pi\)
\(432\) 864.000 + 1496.49i 0.0962250 + 0.166667i
\(433\) −7738.00 −0.858810 −0.429405 0.903112i \(-0.641277\pi\)
−0.429405 + 0.903112i \(0.641277\pi\)
\(434\) 0 0
\(435\) −120.000 −0.0132266
\(436\) 360.000 + 623.538i 0.0395433 + 0.0684910i
\(437\) −2100.00 + 3637.31i −0.229878 + 0.398160i
\(438\) −3852.00 + 6671.86i −0.420218 + 0.727840i
\(439\) −420.000 727.461i −0.0456617 0.0790885i 0.842291 0.539023i \(-0.181206\pi\)
−0.887953 + 0.459934i \(0.847873\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −20832.0 −2.24180
\(443\) −3309.00 5731.36i −0.354888 0.614684i 0.632211 0.774796i \(-0.282148\pi\)
−0.987099 + 0.160113i \(0.948814\pi\)
\(444\) 2952.00 5113.01i 0.315531 0.546516i
\(445\) 400.000 692.820i 0.0426108 0.0738041i
\(446\) −3664.00 6346.23i −0.389003 0.673773i
\(447\) 7110.00 0.752330
\(448\) 0 0
\(449\) 3090.00 0.324780 0.162390 0.986727i \(-0.448080\pi\)
0.162390 + 0.986727i \(0.448080\pi\)
\(450\) 1962.00 + 3398.28i 0.205532 + 0.355993i
\(451\) −7688.00 + 13316.0i −0.802691 + 1.39030i
\(452\) −1832.00 + 3173.12i −0.190642 + 0.330201i
\(453\) 852.000 + 1475.71i 0.0883674 + 0.153057i
\(454\) −19776.0 −2.04435
\(455\) 0 0
\(456\) 0 0
\(457\) −2957.00 5121.67i −0.302675 0.524249i 0.674066 0.738671i \(-0.264546\pi\)
−0.976741 + 0.214422i \(0.931213\pi\)
\(458\) −10940.0 + 18948.6i −1.11614 + 1.93321i
\(459\) 1134.00 1964.15i 0.115317 0.199735i
\(460\) 672.000 + 1163.94i 0.0681134 + 0.117976i
\(461\) 15968.0 1.61324 0.806620 0.591070i \(-0.201294\pi\)
0.806620 + 0.591070i \(0.201294\pi\)
\(462\) 0 0
\(463\) −1172.00 −0.117640 −0.0588202 0.998269i \(-0.518734\pi\)
−0.0588202 + 0.998269i \(0.518734\pi\)
\(464\) −320.000 554.256i −0.0320164 0.0554541i
\(465\) −288.000 + 498.831i −0.0287219 + 0.0497478i
\(466\) 5604.00 9706.41i 0.557082 0.964895i
\(467\) 2652.00 + 4593.40i 0.262784 + 0.455154i 0.966981 0.254850i \(-0.0820261\pi\)
−0.704197 + 0.710005i \(0.748693\pi\)
\(468\) 4464.00 0.440916
\(469\) 0 0
\(470\) −5184.00 −0.508766
\(471\) −399.000 691.088i −0.0390339 0.0676086i
\(472\) 0 0
\(473\) −2108.00 + 3651.16i −0.204917 + 0.354927i
\(474\) −4440.00 7690.31i −0.430245 0.745206i
\(475\) 10900.0 1.05290
\(476\) 0 0
\(477\) 2322.00 0.222887
\(478\) 2340.00 + 4053.00i 0.223910 + 0.387824i
\(479\) 2870.00 4970.99i 0.273765 0.474176i −0.696057 0.717986i \(-0.745064\pi\)
0.969823 + 0.243810i \(0.0783975\pi\)
\(480\) 1536.00 2660.43i 0.146059 0.252982i
\(481\) 7626.00 + 13208.6i 0.722902 + 1.25210i
\(482\) 9352.00 0.883759
\(483\) 0 0
\(484\) 20104.0 1.88805
\(485\) −2532.00 4385.55i −0.237056 0.410593i
\(486\) −486.000 + 841.777i −0.0453609 + 0.0785674i
\(487\) −4472.00 + 7745.73i −0.416110 + 0.720724i −0.995544 0.0942951i \(-0.969940\pi\)
0.579434 + 0.815019i \(0.303274\pi\)
\(488\) 0 0
\(489\) −816.000 −0.0754617
\(490\) 0 0
\(491\) −5558.00 −0.510853 −0.255427 0.966828i \(-0.582216\pi\)
−0.255427 + 0.966828i \(0.582216\pi\)
\(492\) −2976.00 5154.58i −0.272700 0.472330i
\(493\) −420.000 + 727.461i −0.0383689 + 0.0664568i
\(494\) 12400.0 21477.4i 1.12936 1.95610i
\(495\) −1116.00 1932.97i −0.101334 0.175516i
\(496\) −3072.00 −0.278099
\(497\) 0 0
\(498\) −5616.00 −0.505339
\(499\) 9910.00 + 17164.6i 0.889043 + 1.53987i 0.841008 + 0.541022i \(0.181963\pi\)
0.0480349 + 0.998846i \(0.484704\pi\)
\(500\) 3744.00 6484.80i 0.334874 0.580018i
\(501\) −2814.00 + 4873.99i −0.250939 + 0.434638i
\(502\) 5584.00 + 9671.77i 0.496466 + 0.859905i
\(503\) −1848.00 −0.163814 −0.0819068 0.996640i \(-0.526101\pi\)
−0.0819068 + 0.996640i \(0.526101\pi\)
\(504\) 0 0
\(505\) −928.000 −0.0817732
\(506\) 5208.00 + 9020.52i 0.457557 + 0.792512i
\(507\) −2470.50 + 4279.03i −0.216408 + 0.374829i
\(508\) −3216.00 + 5570.28i −0.280880 + 0.486498i
\(509\) 170.000 + 294.449i 0.0148038 + 0.0256409i 0.873332 0.487125i \(-0.161954\pi\)
−0.858529 + 0.512766i \(0.828621\pi\)
\(510\) −4032.00 −0.350078
\(511\) 0 0
\(512\) 16384.0 1.41421
\(513\) 1350.00 + 2338.27i 0.116187 + 0.201242i
\(514\) 14048.0 24331.8i 1.20551 2.08800i
\(515\) −3584.00 + 6207.67i −0.306660 + 0.531151i
\(516\) −816.000 1413.35i −0.0696170 0.120580i
\(517\) −20088.0 −1.70884
\(518\) 0 0
\(519\) 456.000 0.0385668
\(520\) 0 0
\(521\) 5106.00 8843.85i 0.429363 0.743678i −0.567454 0.823405i \(-0.692072\pi\)
0.996817 + 0.0797272i \(0.0254049\pi\)
\(522\) 180.000 311.769i 0.0150927 0.0261413i
\(523\) −4666.00 8081.75i −0.390115 0.675698i 0.602350 0.798232i \(-0.294231\pi\)
−0.992464 + 0.122534i \(0.960898\pi\)
\(524\) −6496.00 −0.541563
\(525\) 0 0
\(526\) 9752.00 0.808379
\(527\) 2016.00 + 3491.81i 0.166638 + 0.288626i
\(528\) 5952.00 10309.2i 0.490582 0.849714i
\(529\) 5201.50 9009.26i 0.427509 0.740467i
\(530\) −2064.00 3574.95i −0.169159 0.292993i
\(531\) −1080.00 −0.0882637
\(532\) 0 0
\(533\) 15376.0 1.24955
\(534\) 1200.00 + 2078.46i 0.0972455 + 0.168434i
\(535\) 3812.00 6602.58i 0.308051 0.533559i
\(536\) 0 0
\(537\) −915.000 1584.83i −0.0735292 0.127356i
\(538\) 27120.0 2.17328
\(539\) 0 0
\(540\) 864.000 0.0688530
\(541\) 4499.00 + 7792.50i 0.357536 + 0.619271i 0.987549 0.157314i \(-0.0502835\pi\)
−0.630012 + 0.776585i \(0.716950\pi\)
\(542\) −3856.00 + 6678.79i −0.305589 + 0.529296i
\(543\) 1563.00 2707.20i 0.123526 0.213954i
\(544\) −10752.0 18623.0i −0.847405 1.46775i
\(545\) −360.000 −0.0282949
\(546\) 0 0
\(547\) −3416.00 −0.267016 −0.133508 0.991048i \(-0.542624\pi\)
−0.133508 + 0.991048i \(0.542624\pi\)
\(548\) −1656.00 2868.28i −0.129089 0.223589i
\(549\) 2799.00 4848.01i 0.217593 0.376882i
\(550\) 13516.0 23410.4i 1.04786 1.81495i
\(551\) −500.000 866.025i −0.0386583 0.0669581i
\(552\) 0 0
\(553\) 0 0
\(554\) 22216.0 1.70373
\(555\) 1476.00 + 2556.51i 0.112888 + 0.195527i
\(556\) −6480.00 + 11223.7i −0.494268 + 0.856098i
\(557\) 263.000 455.529i 0.0200066 0.0346524i −0.855849 0.517226i \(-0.826965\pi\)
0.875855 + 0.482574i \(0.160298\pi\)
\(558\) −864.000 1496.49i −0.0655485 0.113533i
\(559\) 4216.00 0.318994
\(560\) 0 0
\(561\) −15624.0 −1.17584
\(562\) −3884.00 6727.29i −0.291524 0.504935i
\(563\) −3356.00 + 5812.76i −0.251223 + 0.435131i −0.963863 0.266399i \(-0.914166\pi\)
0.712640 + 0.701530i \(0.247499\pi\)
\(564\) 3888.00 6734.21i 0.290274 0.502769i
\(565\) −916.000 1586.56i −0.0682060 0.118136i
\(566\) −19312.0 −1.43418
\(567\) 0 0
\(568\) 0 0
\(569\) −2095.00 3628.65i −0.154353 0.267348i 0.778470 0.627682i \(-0.215996\pi\)
−0.932823 + 0.360334i \(0.882663\pi\)
\(570\) 2400.00 4156.92i 0.176360 0.305464i
\(571\) −1516.00 + 2625.79i −0.111108 + 0.192445i −0.916217 0.400682i \(-0.868773\pi\)
0.805109 + 0.593126i \(0.202107\pi\)
\(572\) −15376.0 26632.0i −1.12396 1.94675i
\(573\) −6114.00 −0.445752
\(574\) 0 0
\(575\) 4578.00 0.332027
\(576\) 2304.00 + 3990.65i 0.166667 + 0.288675i
\(577\) 2717.00 4705.98i 0.196032 0.339537i −0.751207 0.660067i \(-0.770528\pi\)
0.947238 + 0.320531i \(0.103861\pi\)
\(578\) −4286.00 + 7423.57i −0.308433 + 0.534221i
\(579\) 3903.00 + 6760.19i 0.280144 + 0.485223i
\(580\) −320.000 −0.0229091
\(581\) 0 0
\(582\) 15192.0 1.08201
\(583\) −7998.00 13852.9i −0.568170 0.984100i
\(584\) 0 0
\(585\) −1116.00 + 1932.97i −0.0788734 + 0.136613i
\(586\) −12304.0 21311.2i −0.867361 1.50231i
\(587\) −464.000 −0.0326258 −0.0163129 0.999867i \(-0.505193\pi\)
−0.0163129 + 0.999867i \(0.505193\pi\)
\(588\) 0 0
\(589\) −4800.00 −0.335790
\(590\) 960.000 + 1662.77i 0.0669874 + 0.116026i
\(591\) −3531.00 + 6115.87i −0.245763 + 0.425674i
\(592\) −7872.00 + 13634.7i −0.546516 + 0.946593i
\(593\) 5874.00 + 10174.1i 0.406773 + 0.704551i 0.994526 0.104489i \(-0.0333207\pi\)
−0.587753 + 0.809040i \(0.699987\pi\)
\(594\) 6696.00 0.462526
\(595\) 0 0
\(596\) 18960.0 1.30307
\(597\) 2520.00 + 4364.77i 0.172758 + 0.299226i
\(598\) 5208.00 9020.52i 0.356139 0.616850i
\(599\) −3825.00 + 6625.09i −0.260910 + 0.451910i −0.966484 0.256727i \(-0.917356\pi\)
0.705574 + 0.708636i \(0.250689\pi\)
\(600\) 0 0
\(601\) 22878.0 1.55277 0.776384 0.630261i \(-0.217052\pi\)
0.776384 + 0.630261i \(0.217052\pi\)
\(602\) 0 0
\(603\) 8136.00 0.549459
\(604\) 2272.00 + 3935.22i 0.153057 + 0.265102i
\(605\) −5026.00 + 8705.29i −0.337745 + 0.584992i
\(606\) 1392.00 2411.01i 0.0933105 0.161618i
\(607\) 352.000 + 609.682i 0.0235375 + 0.0407681i 0.877554 0.479477i \(-0.159174\pi\)
−0.854017 + 0.520246i \(0.825840\pi\)
\(608\) 25600.0 1.70759
\(609\) 0 0
\(610\) −9952.00 −0.660565
\(611\) 10044.0 + 17396.7i 0.665036 + 1.15188i
\(612\) 3024.00 5237.72i 0.199735 0.345952i
\(613\) −12479.0 + 21614.3i −0.822222 + 1.42413i 0.0818021 + 0.996649i \(0.473932\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(614\) 11768.0 + 20382.8i 0.773482 + 1.33971i
\(615\) 2976.00 0.195128
\(616\) 0 0
\(617\) −8826.00 −0.575886 −0.287943 0.957648i \(-0.592971\pi\)
−0.287943 + 0.957648i \(0.592971\pi\)
\(618\) −10752.0 18623.0i −0.699853 1.21218i
\(619\) 10610.0 18377.1i 0.688937 1.19327i −0.283245 0.959047i \(-0.591411\pi\)
0.972182 0.234226i \(-0.0752556\pi\)
\(620\) −768.000 + 1330.22i −0.0497478 + 0.0861657i
\(621\) 567.000 + 982.073i 0.0366392 + 0.0634609i
\(622\) −36528.0 −2.35473
\(623\) 0 0
\(624\) −11904.0 −0.763688
\(625\) −4940.50 8557.20i −0.316192 0.547661i
\(626\) −18764.0 + 32500.2i −1.19802 + 2.07503i
\(627\) 9300.00 16108.1i 0.592354 1.02599i
\(628\) −1064.00 1842.90i −0.0676086 0.117102i
\(629\) 20664.0 1.30990
\(630\) 0 0
\(631\) −3268.00 −0.206176 −0.103088 0.994672i \(-0.532872\pi\)
−0.103088 + 0.994672i \(0.532872\pi\)
\(632\) 0 0
\(633\) 1002.00 1735.51i 0.0629162 0.108974i
\(634\) −6228.00 + 10787.2i −0.390135 + 0.675733i
\(635\) −1608.00 2785.14i −0.100491 0.174055i
\(636\) 6192.00 0.386052
\(637\) 0 0
\(638\) −2480.00 −0.153894
\(639\) 3051.00 + 5284.49i 0.188882 + 0.327153i
\(640\) 0 0
\(641\) −6531.00 + 11312.0i −0.402432 + 0.697033i −0.994019 0.109208i \(-0.965168\pi\)
0.591587 + 0.806241i \(0.298502\pi\)
\(642\) 11436.0 + 19807.7i 0.703026 + 1.21768i
\(643\) 28012.0 1.71802 0.859009 0.511961i \(-0.171081\pi\)
0.859009 + 0.511961i \(0.171081\pi\)
\(644\) 0 0
\(645\) 816.000 0.0498139
\(646\) −16800.0 29098.5i −1.02320 1.77223i
\(647\) 1922.00 3329.00i 0.116788 0.202282i −0.801705 0.597720i \(-0.796074\pi\)
0.918493 + 0.395437i \(0.129407\pi\)
\(648\) 0 0
\(649\) 3720.00 + 6443.23i 0.224997 + 0.389705i
\(650\) −27032.0 −1.63120
\(651\) 0 0
\(652\) −2176.00 −0.130704
\(653\) 14241.0 + 24666.1i 0.853436 + 1.47819i 0.878089 + 0.478498i \(0.158818\pi\)
−0.0246533 + 0.999696i \(0.507848\pi\)
\(654\) 540.000 935.307i 0.0322870 0.0559227i
\(655\) 1624.00 2812.85i 0.0968778 0.167797i
\(656\) 7936.00 + 13745.6i 0.472330 + 0.818100i
\(657\) 5778.00 0.343107
\(658\) 0 0
\(659\) −9330.00 −0.551510 −0.275755 0.961228i \(-0.588928\pi\)
−0.275755 + 0.961228i \(0.588928\pi\)
\(660\) −2976.00 5154.58i −0.175516 0.304003i
\(661\) 4391.00 7605.44i 0.258381 0.447530i −0.707427 0.706786i \(-0.750144\pi\)
0.965808 + 0.259257i \(0.0834775\pi\)
\(662\) −3064.00 + 5307.00i −0.179888 + 0.311575i
\(663\) 7812.00 + 13530.8i 0.457606 + 0.792597i
\(664\) 0 0
\(665\) 0 0
\(666\) −8856.00 −0.515260
\(667\) −210.000 363.731i −0.0121908 0.0211150i
\(668\) −7504.00 + 12997.3i −0.434638 + 0.752816i
\(669\) −2748.00 + 4759.68i −0.158810 + 0.275067i
\(670\) −7232.00 12526.2i −0.417010 0.722282i
\(671\) −38564.0 −2.21870
\(672\) 0 0
\(673\) −10562.0 −0.604956 −0.302478 0.953156i \(-0.597814\pi\)
−0.302478 + 0.953156i \(0.597814\pi\)
\(674\) 8332.00 + 14431.4i 0.476167 + 0.824746i
\(675\) 1471.50 2548.71i 0.0839082 0.145333i
\(676\) −6588.00 + 11410.8i −0.374829 + 0.649223i
\(677\) −13008.0 22530.5i −0.738461 1.27905i −0.953188 0.302378i \(-0.902220\pi\)
0.214727 0.976674i \(-0.431114\pi\)
\(678\) 5496.00 0.311317
\(679\) 0 0
\(680\) 0 0
\(681\) 7416.00 + 12844.9i 0.417301 + 0.722786i
\(682\) −5952.00 + 10309.2i −0.334185 + 0.578825i
\(683\) −4449.00 + 7705.89i −0.249248 + 0.431710i −0.963317 0.268365i \(-0.913517\pi\)
0.714070 + 0.700075i \(0.246850\pi\)
\(684\) 3600.00 + 6235.38i 0.201242 + 0.348561i
\(685\) 1656.00 0.0923686
\(686\) 0 0
\(687\) 16410.0 0.911325
\(688\) 2176.00 + 3768.94i 0.120580 + 0.208851i
\(689\) −7998.00 + 13852.9i −0.442234 + 0.765973i
\(690\) 1008.00 1745.91i 0.0556144 0.0963269i
\(691\) 15286.0 + 26476.1i 0.841544 + 1.45760i 0.888589 + 0.458704i \(0.151686\pi\)
−0.0470452 + 0.998893i \(0.514980\pi\)
\(692\) 1216.00 0.0667997
\(693\) 0 0
\(694\) −45464.0 −2.48673
\(695\) −3240.00 5611.84i −0.176835 0.306287i
\(696\) 0 0
\(697\) 10416.0 18041.0i 0.566046 0.980421i
\(698\) 18620.0 + 32250.8i 1.00971 + 1.74887i
\(699\) −8406.00 −0.454856
\(700\) 0 0
\(701\) −30618.0 −1.64968 −0.824840 0.565366i \(-0.808735\pi\)
−0.824840 + 0.565366i \(0.808735\pi\)
\(702\) −3348.00 5798.91i −0.180003 0.311774i
\(703\) −12300.0 + 21304.2i −0.659891 + 1.14296i
\(704\) 15872.0 27491.1i 0.849714 1.47175i
\(705\) 1944.00 + 3367.11i 0.103851 + 0.179876i
\(706\) 34288.0 1.82783
\(707\) 0 0
\(708\) −2880.00 −0.152877
\(709\) 4065.00 + 7040.79i 0.215323 + 0.372951i 0.953373 0.301796i \(-0.0975861\pi\)
−0.738049 + 0.674747i \(0.764253\pi\)
\(710\) 5424.00 9394.64i 0.286703 0.496584i
\(711\) −3330.00 + 5767.73i −0.175647 + 0.304229i
\(712\) 0 0
\(713\) −2016.00 −0.105890
\(714\) 0 0
\(715\) 15376.0 0.804237
\(716\) −2440.00 4226.20i −0.127356 0.220588i
\(717\) 1755.00 3039.75i 0.0914110 0.158328i
\(718\) 9580.00 16593.0i 0.497942 0.862461i
\(719\) −13920.0 24110.1i −0.722014 1.25057i −0.960191 0.279344i \(-0.909883\pi\)
0.238177 0.971222i \(-0.423450\pi\)
\(720\) −2304.00 −0.119257
\(721\) 0 0
\(722\) 12564.0 0.647623
\(723\) −3507.00 6074.30i −0.180397 0.312456i
\(724\) 4168.00 7219.19i 0.213954 0.370579i
\(725\) −545.000 + 943.968i −0.0279183 + 0.0483560i
\(726\) −15078.0 26115.9i −0.770795 1.33506i
\(727\) −14624.0 −0.746044 −0.373022 0.927822i \(-0.621678\pi\)
−0.373022 + 0.927822i \(0.621678\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −5136.00 8895.81i −0.260400 0.451026i
\(731\) 2856.00 4946.74i 0.144505 0.250290i
\(732\) 7464.00 12928.0i 0.376882 0.652778i
\(733\) −10431.0 18067.0i −0.525618 0.910397i −0.999555 0.0298378i \(-0.990501\pi\)
0.473937 0.880559i \(-0.342832\pi\)
\(734\) −21696.0 −1.09103
\(735\) 0 0
\(736\) 10752.0 0.538484
\(737\) −28024.0 48539.0i −1.40065 2.42599i
\(738\) −4464.00 + 7731.87i −0.222659 + 0.385656i
\(739\) 6960.00 12055.1i 0.346452 0.600072i −0.639165 0.769070i \(-0.720720\pi\)
0.985616 + 0.168998i \(0.0540532\pi\)
\(740\) 3936.00 + 6817.35i 0.195527 + 0.338663i
\(741\) −18600.0 −0.922116
\(742\) 0 0
\(743\) 25578.0 1.26294 0.631471 0.775400i \(-0.282452\pi\)
0.631471 + 0.775400i \(0.282452\pi\)
\(744\) 0 0
\(745\) −4740.00 + 8209.92i −0.233101 + 0.403743i
\(746\) −3676.00 + 6367.02i −0.180413 + 0.312484i
\(747\) 2106.00 + 3647.70i 0.103152 + 0.178664i
\(748\) −41664.0 −2.03661
\(749\) 0 0
\(750\) −11232.0 −0.546846
\(751\) −16736.0 28987.6i −0.813189 1.40849i −0.910621 0.413243i \(-0.864396\pi\)
0.0974312 0.995242i \(-0.468937\pi\)
\(752\) −10368.0 + 17957.9i −0.502769 + 0.870821i
\(753\) 4188.00 7253.83i 0.202682 0.351055i
\(754\) 1240.00 + 2147.74i 0.0598914 + 0.103735i
\(755\) −2272.00 −0.109519
\(756\) 0 0
\(757\) 25934.0 1.24516 0.622581 0.782556i \(-0.286084\pi\)
0.622581 + 0.782556i \(0.286084\pi\)
\(758\) 8520.00 + 14757.1i 0.408259 + 0.707125i
\(759\) 3906.00 6765.39i 0.186797 0.323542i
\(760\) 0 0
\(761\) 13476.0 + 23341.1i 0.641925 + 1.11185i 0.985003 + 0.172539i \(0.0551971\pi\)
−0.343078 + 0.939307i \(0.611470\pi\)
\(762\) 9648.00 0.458675
\(763\) 0 0
\(764\) −16304.0 −0.772065
\(765\) 1512.00 + 2618.86i 0.0714594 + 0.123771i
\(766\) 18096.0 31343.2i 0.853571 1.47843i
\(767\) 3720.00 6443.23i 0.175126 0.303327i
\(768\) −6144.00 10641.7i −0.288675 0.500000i
\(769\) −23450.0 −1.09965 −0.549824 0.835281i \(-0.685305\pi\)
−0.549824 + 0.835281i \(0.685305\pi\)
\(770\) 0 0
\(771\) −21072.0 −0.984293
\(772\) 10408.0 + 18027.2i 0.485223 + 0.840431i
\(773\) 19784.0 34266.9i 0.920545 1.59443i 0.121970 0.992534i \(-0.461079\pi\)
0.798574 0.601896i \(-0.205588\pi\)
\(774\) −1224.00 + 2120.03i −0.0568421 + 0.0984534i
\(775\) 2616.00 + 4531.04i 0.121251 + 0.210013i
\(776\) 0 0
\(777\) 0 0
\(778\) −45960.0 −2.11793
\(779\) 12400.0 + 21477.4i 0.570316 + 0.987816i
\(780\) −2976.00 + 5154.58i −0.136613 + 0.236620i
\(781\) 21018.0 36404.2i 0.962975