Properties

Label 147.4.e.b.79.1
Level $147$
Weight $4$
Character 147.79
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.b.67.1

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

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

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 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −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 −0.941499 0.337016i \(-0.890582\pi\)
0.762614 + 0.646854i \(0.223916\pi\)
\(6\) 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 −0.881464 0.472252i \(-0.843441\pi\)
0.0317500 0.999496i \(-0.489892\pi\)
\(12\) −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 0.992939 + 0.118630i \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) −18.0000 31.1769i −0.235702 0.408248i
\(19\) 50.0000 86.6025i 0.603726 1.04568i −0.388526 0.921438i \(-0.627016\pi\)
0.992251 0.124246i \(-0.0396511\pi\)
\(20\) 32.0000 0.357771
\(21\) 0 0
\(22\) 248.000 2.40335
\(23\) 21.0000 36.3731i 0.190383 0.329753i −0.754994 0.655731i \(-0.772360\pi\)
0.945377 + 0.325979i \(0.105694\pi\)
\(24\) 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 0.788088 0.615563i \(-0.211071\pi\)
−0.927137 + 0.374723i \(0.877738\pi\)
\(32\) 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 −0.451994 0.892021i \(-0.649287\pi\)
0.998510 0.0545719i \(-0.0173794\pi\)
\(38\) 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 −0.497226 0.867621i \(-0.665648\pi\)
0.999995 0.00319997i \(-0.00101858\pi\)
\(48\) −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 0.649026 0.760767i \(-0.275177\pi\)
−0.983356 + 0.181689i \(0.941843\pi\)
\(54\) −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 0.924600 0.380941i \(-0.124400\pi\)
−0.792204 + 0.610256i \(0.791066\pi\)
\(60\) −48.0000 83.1384i −0.103280 0.178885i
\(61\) 311.000 538.668i 0.652778 1.13064i −0.329668 0.944097i \(-0.606937\pi\)
0.982446 0.186548i \(-0.0597300\pi\)
\(62\) 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 −0.902538 0.430609i \(-0.858299\pi\)
0.0783505 0.996926i \(-0.475035\pi\)
\(68\) 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 −0.999855 0.0170119i \(-0.994585\pi\)
0.485195 0.874406i \(-0.338749\pi\)
\(74\) 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 0.472567 + 0.881295i \(0.343327\pi\)
−0.999507 + 0.0313921i \(0.990006\pi\)
\(80\) 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 −0.800311 0.599585i \(-0.795332\pi\)
0.919412 + 0.393297i \(0.128665\pi\)
\(90\) 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 0.917492 0.397754i \(-0.130210\pi\)
−0.803211 + 0.595695i \(0.796877\pi\)
\(102\) 504.000 + 872.954i 0.489249 + 0.847405i
\(103\) −896.000 + 1551.92i −0.857141 + 1.48461i 0.0175038 + 0.999847i \(0.494428\pi\)
−0.874645 + 0.484765i \(0.838905\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1032.00 0.945629
\(107\) 953.000 1650.64i 0.861028 1.49134i −0.00990992 0.999951i \(-0.503154\pi\)
0.870938 0.491393i \(-0.163512\pi\)
\(108\) −108.000 187.061i −0.0962250 0.166667i
\(109\) 45.0000 + 77.9423i 0.0395433 + 0.0684910i 0.885120 0.465363i \(-0.154076\pi\)
−0.845576 + 0.533854i \(0.820743\pi\)
\(110\) −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 −0.698281 0.715824i \(-0.746051\pi\)
0.969062 + 0.246817i \(0.0793846\pi\)
\(132\) 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 0.794235 0.607611i \(-0.207872\pi\)
−0.923324 + 0.384022i \(0.874539\pi\)
\(138\) 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 0.331213 + 0.943556i \(0.392542\pi\)
−0.982750 + 0.184939i \(0.940791\pi\)
\(150\) 654.000 + 1132.76i 0.355993 + 0.616597i
\(151\) 284.000 + 491.902i 0.153057 + 0.265102i 0.932350 0.361558i \(-0.117755\pi\)
−0.779293 + 0.626660i \(0.784422\pi\)
\(152\) 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 0.830240 0.557407i \(-0.188204\pi\)
−0.897848 + 0.440305i \(0.854870\pi\)
\(158\) −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 −0.831498 0.555527i \(-0.812516\pi\)
0.896850 + 0.442335i \(0.145850\pi\)
\(164\) −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 −0.882242 0.470796i \(-0.843967\pi\)
0.848842 + 0.528646i \(0.177300\pi\)
\(174\) −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 0.795295 0.606222i \(-0.207316\pi\)
−0.922652 + 0.385635i \(0.873982\pi\)
\(180\) −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 −0.605879 0.795557i \(-0.707179\pi\)
0.991912 + 0.126928i \(0.0405118\pi\)
\(192\) 768.000 + 1330.22i 0.288675 + 0.500000i
\(193\) 1301.00 + 2253.40i 0.485223 + 0.840431i 0.999856 0.0169798i \(-0.00540511\pi\)
−0.514633 + 0.857411i \(0.672072\pi\)
\(194\) −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 0.975959 0.217954i \(-0.0699381\pi\)
−0.676733 + 0.736229i \(0.736605\pi\)
\(200\) 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 0.959879 + 0.280415i \(0.0904721\pi\)
−0.237093 + 0.971487i \(0.576195\pi\)
\(228\) 1200.00 + 2078.46i 0.348561 + 0.603726i
\(229\) −2735.00 + 4737.16i −0.789231 + 1.36699i 0.137208 + 0.990542i \(0.456187\pi\)
−0.926439 + 0.376446i \(0.877146\pi\)
\(230\) −672.000 −0.192654
\(231\) 0 0
\(232\) 0 0
\(233\) 1401.00 2426.60i 0.393917 0.682284i −0.599046 0.800715i \(-0.704453\pi\)
0.992962 + 0.118431i \(0.0377866\pi\)
\(234\) −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 0.666437 0.745561i \(-0.267818\pi\)
−0.978893 + 0.204371i \(0.934485\pi\)
\(242\) −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 −0.0265936 0.999646i \(-0.508466\pi\)
0.879016 0.476792i \(-0.158201\pi\)
\(258\) 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 0.686999 0.726658i \(-0.258928\pi\)
−0.972804 + 0.231629i \(0.925594\pi\)
\(264\) 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 −0.938446 0.345427i \(-0.887734\pi\)
0.170074 0.985431i \(-0.445599\pi\)
\(270\) −216.000 374.123i −0.0486864 0.0843274i
\(271\) −964.000 + 1669.70i −0.216084 + 0.374269i −0.953607 0.301053i \(-0.902662\pi\)
0.737523 + 0.675322i \(0.235995\pi\)
\(272\) 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 −0.992463 0.122547i \(-0.960894\pi\)
0.390103 0.920771i \(-0.372440\pi\)
\(278\) −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 0.999967 + 0.00816911i \(0.00260034\pi\)
−0.492909 + 0.870081i \(0.664066\pi\)
\(284\) 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 0.896033 + 0.443988i \(0.146437\pi\)
−0.0635115 + 0.997981i \(0.520230\pi\)
\(312\) 0 0
\(313\) −4691.00 + 8125.05i −0.847128 + 1.46727i 0.0366327 + 0.999329i \(0.488337\pi\)
−0.883760 + 0.467940i \(0.844996\pi\)
\(314\) 1064.00 0.191226
\(315\) 0 0
\(316\) 5920.00 1.05388
\(317\) −1557.00 + 2696.80i −0.275867 + 0.477816i −0.970353 0.241690i \(-0.922298\pi\)
0.694487 + 0.719506i \(0.255632\pi\)
\(318\) −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 −0.922591 0.385780i \(-0.873932\pi\)
0.795391 + 0.606097i \(0.207266\pi\)
\(332\) 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 0.852230 + 0.523168i \(0.175250\pi\)
0.0269617 + 0.999636i \(0.491417\pi\)
\(348\) 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 −0.984015 0.178086i \(-0.943009\pi\)
0.337780 0.941225i \(-0.390324\pi\)
\(354\) 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 −0.634519 0.772908i \(-0.718802\pi\)
0.986617 + 0.163056i \(0.0521350\pi\)
\(360\) 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 0.991871 0.127247i \(-0.0406141\pi\)
−0.606135 + 0.795362i \(0.707281\pi\)
\(368\) −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 −0.922735 0.385435i \(-0.874051\pi\)
0.795164 + 0.606395i \(0.207385\pi\)
\(374\) 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 −0.388711 0.921360i \(-0.627080\pi\)
0.992276 0.124046i \(-0.0395872\pi\)
\(384\) 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 0.948398 + 0.317081i \(0.102703\pi\)
−0.199599 + 0.979878i \(0.563964\pi\)
\(390\) −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 −0.918955 0.394363i \(-0.870965\pi\)
0.801005 + 0.598657i \(0.204299\pi\)
\(398\) −6720.00 −0.846340
\(399\) 0 0
\(400\) 6976.00 0.872000
\(401\) −6831.00 + 11831.6i −0.850683 + 1.47343i 0.0299100 + 0.999553i \(0.490478\pi\)
−0.880593 + 0.473873i \(0.842855\pi\)
\(402\) −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 −0.920577 0.390560i \(-0.872281\pi\)
0.122054 0.992524i \(-0.461052\pi\)
\(410\) −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 −0.787136 0.616780i \(-0.788437\pi\)
−0.140579 0.990069i \(-0.544896\pi\)
\(432\) 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 −0.887953 0.459934i \(-0.847873\pi\)
0.842291 + 0.539023i \(0.181206\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −20832.0 −2.24180
\(443\) −3309.00 + 5731.36i −0.354888 + 0.614684i −0.987099 0.160113i \(-0.948814\pi\)
0.632211 + 0.774796i \(0.282148\pi\)
\(444\) 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 −0.976741 0.214422i \(-0.931213\pi\)
0.674066 + 0.738671i \(0.264546\pi\)
\(458\) −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 −0.704197 0.710005i \(-0.748693\pi\)
0.966981 + 0.254850i \(0.0820261\pi\)
\(468\) 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 0.969823 0.243810i \(-0.0783975\pi\)
−0.696057 + 0.717986i \(0.745064\pi\)
\(480\) 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 0.579434 0.815019i \(-0.303274\pi\)
−0.995544 + 0.0942951i \(0.969940\pi\)
\(488\) 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 0.0480349 0.998846i \(-0.484704\pi\)
0.841008 0.541022i \(-0.181963\pi\)
\(500\) 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 −0.858529 0.512766i \(-0.828621\pi\)
0.873332 + 0.487125i \(0.161954\pi\)
\(510\) −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 0.996817 0.0797272i \(-0.0254049\pi\)
−0.567454 + 0.823405i \(0.692072\pi\)
\(522\) 180.000 + 311.769i 0.0150927 + 0.0261413i
\(523\) −4666.00 + 8081.75i −0.390115 + 0.675698i −0.992464 0.122534i \(-0.960898\pi\)
0.602350 + 0.798232i \(0.294231\pi\)
\(524\) −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 −0.630012 0.776585i \(-0.716950\pi\)
0.987549 + 0.157314i \(0.0502835\pi\)
\(542\) −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 0.875855 0.482574i \(-0.160298\pi\)
−0.855849 + 0.517226i \(0.826965\pi\)
\(558\) −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 0.712640 0.701530i \(-0.247499\pi\)
−0.963863 + 0.266399i \(0.914166\pi\)
\(564\) 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 −0.932823 0.360334i \(-0.882663\pi\)
0.778470 + 0.627682i \(0.215996\pi\)
\(570\) 2400.00 + 4156.92i 0.176360 + 0.305464i
\(571\) −1516.00 2625.79i −0.111108 0.192445i 0.805109 0.593126i \(-0.202107\pi\)
−0.916217 + 0.400682i \(0.868773\pi\)
\(572\) −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 0.947238 0.320531i \(-0.103861\pi\)
−0.751207 + 0.660067i \(0.770528\pi\)
\(578\) −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 −0.587753 0.809040i \(-0.699987\pi\)
0.994526 + 0.104489i \(0.0333207\pi\)
\(594\) 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 0.705574 0.708636i \(-0.250689\pi\)
−0.966484 + 0.256727i \(0.917356\pi\)
\(600\) 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 −0.854017 0.520246i \(-0.825840\pi\)
0.877554 + 0.479477i \(0.159174\pi\)
\(608\) 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 −0.904024 0.427482i \(-0.859401\pi\)
0.0818021 0.996649i \(-0.473932\pi\)
\(614\) 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 0.972182 + 0.234226i \(0.0752556\pi\)
−0.283245 + 0.959047i \(0.591411\pi\)
\(620\) −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 0.591587 0.806241i \(-0.298502\pi\)
−0.994019 + 0.109208i \(0.965168\pi\)
\(642\) 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 0.918493 0.395437i \(-0.129407\pi\)
−0.801705 + 0.597720i \(0.796074\pi\)
\(648\) 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 −0.0246533 0.999696i \(-0.507848\pi\)
0.878089 0.478498i \(-0.158818\pi\)
\(654\) 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 0.965808 0.259257i \(-0.0834775\pi\)
−0.707427 + 0.706786i \(0.750144\pi\)
\(662\) −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 0.214727 + 0.976674i \(0.431114\pi\)
−0.953188 + 0.302378i \(0.902220\pi\)
\(678\) 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 0.714070 0.700075i \(-0.246850\pi\)
−0.963317 + 0.268365i \(0.913517\pi\)
\(684\) 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 −0.0470452 0.998893i \(-0.514980\pi\)
0.888589 0.458704i \(-0.151686\pi\)
\(692\) 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 −0.738049 0.674747i \(-0.764253\pi\)
0.953373 + 0.301796i \(0.0975861\pi\)
\(710\) 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 0.238177 + 0.971222i \(0.423450\pi\)
−0.960191 + 0.279344i \(0.909883\pi\)
\(720\) −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 0.473937 + 0.880559i \(0.342832\pi\)
−0.999555 + 0.0298378i \(0.990501\pi\)
\(734\) −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 0.985616 0.168998i \(-0.0540532\pi\)
−0.639165 + 0.769070i \(0.720720\pi\)
\(740\) 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 0.0974312 + 0.995242i \(0.468937\pi\)
−0.910621 + 0.413243i \(0.864396\pi\)
\(752\) −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 −0.343078 0.939307i \(-0.611470\pi\)
0.985003 0.172539i \(-0.0551971\pi\)
\(762\) 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 0.798574 + 0.601896i \(0.205588\pi\)
0.121970 + 0.992534i \(0.461079\pi\)
\(774\) −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