Properties

Label 441.4.e.n.226.1
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.n.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(2.00000 - 3.46410i) q^{5} +(-8.00000 - 13.8564i) q^{10} +(31.0000 + 53.6936i) q^{11} +62.0000 q^{13} +(32.0000 - 55.4256i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(50.0000 - 86.6025i) q^{19} -32.0000 q^{20} +248.000 q^{22} +(-21.0000 + 36.3731i) q^{23} +(54.5000 + 94.3968i) q^{25} +(124.000 - 214.774i) q^{26} +10.0000 q^{29} +(-24.0000 - 41.5692i) q^{31} +(-128.000 - 221.703i) q^{32} -336.000 q^{34} +(123.000 - 213.042i) q^{37} +(-200.000 - 346.410i) q^{38} -248.000 q^{41} +68.0000 q^{43} +(248.000 - 429.549i) q^{44} +(84.0000 + 145.492i) q^{46} +(-162.000 + 280.592i) q^{47} +436.000 q^{50} +(-248.000 - 429.549i) q^{52} +(129.000 + 223.435i) q^{53} +248.000 q^{55} +(20.0000 - 34.6410i) q^{58} +(-60.0000 - 103.923i) q^{59} +(311.000 - 538.668i) q^{61} -192.000 q^{62} -512.000 q^{64} +(124.000 - 214.774i) q^{65} +(-452.000 - 782.887i) q^{67} +(-336.000 + 581.969i) q^{68} +678.000 q^{71} +(-321.000 - 555.988i) q^{73} +(-492.000 - 852.169i) q^{74} -800.000 q^{76} +(-370.000 + 640.859i) q^{79} +(-128.000 - 221.703i) q^{80} +(-496.000 + 859.097i) q^{82} +468.000 q^{83} -336.000 q^{85} +(136.000 - 235.559i) q^{86} +(-100.000 + 173.205i) q^{89} +336.000 q^{92} +(648.000 + 1122.37i) q^{94} +(-200.000 - 346.410i) q^{95} +1266.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{2} - 8q^{4} + 4q^{5} + O(q^{10}) \) \( 2q + 4q^{2} - 8q^{4} + 4q^{5} - 16q^{10} + 62q^{11} + 124q^{13} + 64q^{16} - 84q^{17} + 100q^{19} - 64q^{20} + 496q^{22} - 42q^{23} + 109q^{25} + 248q^{26} + 20q^{29} - 48q^{31} - 256q^{32} - 672q^{34} + 246q^{37} - 400q^{38} - 496q^{41} + 136q^{43} + 496q^{44} + 168q^{46} - 324q^{47} + 872q^{50} - 496q^{52} + 258q^{53} + 496q^{55} + 40q^{58} - 120q^{59} + 622q^{61} - 384q^{62} - 1024q^{64} + 248q^{65} - 904q^{67} - 672q^{68} + 1356q^{71} - 642q^{73} - 984q^{74} - 1600q^{76} - 740q^{79} - 256q^{80} - 992q^{82} + 936q^{83} - 672q^{85} + 272q^{86} - 200q^{89} + 672q^{92} + 1296q^{94} - 400q^{95} + 2532q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 3.46410i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0 0
\(4\) −4.00000 6.92820i −0.500000 0.866025i
\(5\) 2.00000 3.46410i 0.178885 0.309839i −0.762614 0.646854i \(-0.776084\pi\)
0.941499 + 0.337016i \(0.109418\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) −8.00000 13.8564i −0.252982 0.438178i
\(11\) 31.0000 + 53.6936i 0.849714 + 1.47175i 0.881464 + 0.472252i \(0.156559\pi\)
−0.0317500 + 0.999496i \(0.510108\pi\)
\(12\) 0 0
\(13\) 62.0000 1.32275 0.661373 0.750057i \(-0.269974\pi\)
0.661373 + 0.750057i \(0.269974\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 32.0000 55.4256i 0.500000 0.866025i
\(17\) −42.0000 72.7461i −0.599206 1.03785i −0.992939 0.118630i \(-0.962150\pi\)
0.393733 0.919225i \(-0.371183\pi\)
\(18\) 0 0
\(19\) 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 −0.945377 0.325979i \(-0.894306\pi\)
0.754994 + 0.655731i \(0.227640\pi\)
\(24\) 0 0
\(25\) 54.5000 + 94.3968i 0.436000 + 0.755174i
\(26\) 124.000 214.774i 0.935323 1.62003i
\(27\) 0 0
\(28\) 0 0
\(29\) 10.0000 0.0640329 0.0320164 0.999487i \(-0.489807\pi\)
0.0320164 + 0.999487i \(0.489807\pi\)
\(30\) 0 0
\(31\) −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
\(33\) 0 0
\(34\) −336.000 −1.69481
\(35\) 0 0
\(36\) 0 0
\(37\) 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
\(39\) 0 0
\(40\) 0 0
\(41\) −248.000 −0.944661 −0.472330 0.881422i \(-0.656587\pi\)
−0.472330 + 0.881422i \(0.656587\pi\)
\(42\) 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
\(45\) 0 0
\(46\) 84.0000 + 145.492i 0.269242 + 0.466341i
\(47\) −162.000 + 280.592i −0.502769 + 0.870821i 0.497226 + 0.867621i \(0.334352\pi\)
−0.999995 + 0.00319997i \(0.998981\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 436.000 1.23319
\(51\) 0 0
\(52\) −248.000 429.549i −0.661373 1.14553i
\(53\) 129.000 + 223.435i 0.334330 + 0.579077i 0.983356 0.181689i \(-0.0581565\pi\)
−0.649026 + 0.760767i \(0.724823\pi\)
\(54\) 0 0
\(55\) 248.000 0.608006
\(56\) 0 0
\(57\) 0 0
\(58\) 20.0000 34.6410i 0.0452781 0.0784239i
\(59\) −60.0000 103.923i −0.132396 0.229316i 0.792204 0.610256i \(-0.208934\pi\)
−0.924600 + 0.380941i \(0.875600\pi\)
\(60\) 0 0
\(61\) 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
\(66\) 0 0
\(67\) −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
\(69\) 0 0
\(70\) 0 0
\(71\) 678.000 1.13329 0.566646 0.823961i \(-0.308241\pi\)
0.566646 + 0.823961i \(0.308241\pi\)
\(72\) 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
\(75\) 0 0
\(76\) −800.000 −1.20745
\(77\) 0 0
\(78\) 0 0
\(79\) −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
\(81\) 0 0
\(82\) −496.000 + 859.097i −0.667976 + 1.15697i
\(83\) 468.000 0.618912 0.309456 0.950914i \(-0.399853\pi\)
0.309456 + 0.950914i \(0.399853\pi\)
\(84\) 0 0
\(85\) −336.000 −0.428757
\(86\) 136.000 235.559i 0.170526 0.295360i
\(87\) 0 0
\(88\) 0 0
\(89\) −100.000 + 173.205i −0.119101 + 0.206289i −0.919412 0.393297i \(-0.871335\pi\)
0.800311 + 0.599585i \(0.204668\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 336.000 0.380765
\(93\) 0 0
\(94\) 648.000 + 1122.37i 0.711022 + 1.23153i
\(95\) −200.000 346.410i −0.215995 0.374115i
\(96\) 0 0
\(97\) 1266.00 1.32518 0.662592 0.748981i \(-0.269456\pi\)
0.662592 + 0.748981i \(0.269456\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 436.000 755.174i 0.436000 0.755174i
\(101\) −116.000 200.918i −0.114281 0.197941i 0.803211 0.595695i \(-0.203123\pi\)
−0.917492 + 0.397754i \(0.869790\pi\)
\(102\) 0 0
\(103\) −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 \(0.496846\pi\)
−0.870938 + 0.491393i \(0.836488\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) 0 0
\(113\) −458.000 −0.381283 −0.190642 0.981660i \(-0.561057\pi\)
−0.190642 + 0.981660i \(0.561057\pi\)
\(114\) 0 0
\(115\) 84.0000 + 145.492i 0.0681134 + 0.117976i
\(116\) −40.0000 69.2820i −0.0320164 0.0554541i
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) −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
\(129\) 0 0
\(130\) −496.000 859.097i −0.334631 0.579599i
\(131\) −406.000 + 703.213i −0.270782 + 0.469007i −0.969062 0.246817i \(-0.920615\pi\)
0.698281 + 0.715824i \(0.253949\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3616.00 −2.33116
\(135\) 0 0
\(136\) 0 0
\(137\) 207.000 + 358.535i 0.129089 + 0.223589i 0.923324 0.384022i \(-0.125461\pi\)
−0.794235 + 0.607611i \(0.792128\pi\)
\(138\) 0 0
\(139\) 1620.00 0.988537 0.494268 0.869309i \(-0.335436\pi\)
0.494268 + 0.869309i \(0.335436\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1356.00 2348.66i 0.801359 1.38799i
\(143\) 1922.00 + 3329.00i 1.12396 + 1.94675i
\(144\) 0 0
\(145\) 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 \(-0.607458\pi\)
0.982750 0.184939i \(-0.0592087\pi\)
\(150\) 0 0
\(151\) 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
\(153\) 0 0
\(154\) 0 0
\(155\) −192.000 −0.0994956
\(156\) 0 0
\(157\) −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
\(159\) 0 0
\(160\) −1024.00 −0.505964
\(161\) 0 0
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) 936.000 1621.20i 0.437637 0.758009i
\(167\) −1876.00 −0.869277 −0.434638 0.900605i \(-0.643124\pi\)
−0.434638 + 0.900605i \(0.643124\pi\)
\(168\) 0 0
\(169\) 1647.00 0.749659
\(170\) −672.000 + 1163.94i −0.303177 + 0.525118i
\(171\) 0 0
\(172\) −272.000 471.118i −0.120580 0.208851i
\(173\) 76.0000 131.636i 0.0333998 0.0578502i −0.848842 0.528646i \(-0.822700\pi\)
0.882242 + 0.470796i \(0.156033\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3968.00 1.69943
\(177\) 0 0
\(178\) 400.000 + 692.820i 0.168434 + 0.291736i
\(179\) 305.000 + 528.275i 0.127356 + 0.220588i 0.922652 0.385635i \(-0.126018\pi\)
−0.795295 + 0.606222i \(0.792684\pi\)
\(180\) 0 0
\(181\) −1042.00 −0.427907 −0.213954 0.976844i \(-0.568634\pi\)
−0.213954 + 0.976844i \(0.568634\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −492.000 852.169i −0.195527 0.338663i
\(186\) 0 0
\(187\) 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 \(-0.959488\pi\)
0.605879 + 0.795557i \(0.292821\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) 0 0
\(197\) −2354.00 −0.851348 −0.425674 0.904877i \(-0.639963\pi\)
−0.425674 + 0.904877i \(0.639963\pi\)
\(198\) 0 0
\(199\) 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
\(201\) 0 0
\(202\) −928.000 −0.323237
\(203\) 0 0
\(204\) 0 0
\(205\) −496.000 + 859.097i −0.168986 + 0.292692i
\(206\) 3584.00 + 6207.67i 1.21218 + 2.09956i
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 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
\(219\) 0 0
\(220\) −992.000 1718.19i −0.304003 0.526548i
\(221\) −2604.00 4510.26i −0.792597 1.37282i
\(222\) 0 0
\(223\) 1832.00 0.550134 0.275067 0.961425i \(-0.411300\pi\)
0.275067 + 0.961425i \(0.411300\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −916.000 + 1586.56i −0.269608 + 0.466975i
\(227\) −2472.00 4281.63i −0.722786 1.25190i −0.959879 0.280415i \(-0.909528\pi\)
0.237093 0.971487i \(-0.423805\pi\)
\(228\) 0 0
\(229\) −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 −0.992962 0.118431i \(-0.962213\pi\)
0.599046 + 0.800715i \(0.295547\pi\)
\(234\) 0 0
\(235\) 648.000 + 1122.37i 0.179876 + 0.311554i
\(236\) −480.000 + 831.384i −0.132396 + 0.229316i
\(237\) 0 0
\(238\) 0 0
\(239\) 1170.00 0.316657 0.158328 0.987386i \(-0.449390\pi\)
0.158328 + 0.987386i \(0.449390\pi\)
\(240\) 0 0
\(241\) −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
\(243\) 0 0
\(244\) −4976.00 −1.30556
\(245\) 0 0
\(246\) 0 0
\(247\) 3100.00 5369.36i 0.798576 1.38317i
\(248\) 0 0
\(249\) 0 0
\(250\) 1872.00 3242.40i 0.473583 0.820269i
\(251\) 2792.00 0.702109 0.351055 0.936355i \(-0.385823\pi\)
0.351055 + 0.936355i \(0.385823\pi\)
\(252\) 0 0
\(253\) −2604.00 −0.647083
\(254\) 1608.00 2785.14i 0.397224 0.688012i
\(255\) 0 0
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) −3512.00 + 6082.96i −0.852422 + 1.47644i 0.0265936 + 0.999646i \(0.491534\pi\)
−0.879016 + 0.476792i \(0.841799\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1984.00 −0.473240
\(261\) 0 0
\(262\) 1624.00 + 2812.85i 0.382943 + 0.663277i
\(263\) 1219.00 + 2111.37i 0.285805 + 0.495029i 0.972804 0.231629i \(-0.0744056\pi\)
−0.686999 + 0.726658i \(0.741072\pi\)
\(264\) 0 0
\(265\) 1032.00 0.239227
\(266\) 0 0
\(267\) 0 0
\(268\) −3616.00 + 6263.10i −0.824188 + 1.42754i
\(269\) 3390.00 + 5871.65i 0.768372 + 1.33086i 0.938446 + 0.345427i \(0.112266\pi\)
−0.170074 + 0.985431i \(0.554401\pi\)
\(270\) 0 0
\(271\) −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
\(276\) 0 0
\(277\) −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
\(279\) 0 0
\(280\) 0 0
\(281\) −1942.00 −0.412278 −0.206139 0.978523i \(-0.566090\pi\)
−0.206139 + 0.978523i \(0.566090\pi\)
\(282\) 0 0
\(283\) 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
\(285\) 0 0
\(286\) 15376.0 3.17903
\(287\) 0 0
\(288\) 0 0
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) −80.0000 138.564i −0.0161992 0.0280578i
\(291\) 0 0
\(292\) −2568.00 + 4447.91i −0.514660 + 0.891418i
\(293\) −6152.00 −1.22663 −0.613317 0.789837i \(-0.710165\pi\)
−0.613317 + 0.789837i \(0.710165\pi\)
\(294\) 0 0
\(295\) −480.000 −0.0947345
\(296\) 0 0
\(297\) 0 0
\(298\) −4740.00 8209.92i −0.921412 1.59593i
\(299\) −1302.00 + 2255.13i −0.251828 + 0.436179i
\(300\) 0 0
\(301\) 0 0
\(302\) 2272.00 0.432910
\(303\) 0 0
\(304\) −3200.00 5542.56i −0.603726 1.04568i
\(305\) −1244.00 2154.67i −0.233545 0.404512i
\(306\) 0 0
\(307\) −5884.00 −1.09387 −0.546934 0.837176i \(-0.684205\pi\)
−0.546934 + 0.837176i \(0.684205\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −384.000 + 665.108i −0.0703540 + 0.121857i
\(311\) −4566.00 7908.54i −0.832521 1.44197i −0.896033 0.443988i \(-0.853563\pi\)
0.0635115 0.997981i \(-0.479770\pi\)
\(312\) 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 −0.694487 0.719506i \(-0.744368\pi\)
0.970353 + 0.241690i \(0.0777017\pi\)
\(318\) 0 0
\(319\) 310.000 + 536.936i 0.0544096 + 0.0942402i
\(320\) −1024.00 + 1773.62i −0.178885 + 0.309839i
\(321\) 0 0
\(322\) 0 0
\(323\) −8400.00 −1.44702
\(324\) 0 0
\(325\) 3379.00 + 5852.60i 0.576718 + 0.998904i
\(326\) −544.000 942.236i −0.0924214 0.160079i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −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
\(333\) 0 0
\(334\) −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
\(339\) 0 0
\(340\) 1344.00 + 2327.88i 0.214378 + 0.371314i
\(341\) 1488.00 2577.29i 0.236304 0.409291i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −304.000 526.543i −0.0472345 0.0818126i
\(347\) −5683.00 9843.24i −0.879191 1.52280i −0.852230 0.523168i \(-0.824750\pi\)
−0.0269617 0.999636i \(-0.508583\pi\)
\(348\) 0 0
\(349\) −9310.00 −1.42795 −0.713973 0.700174i \(-0.753106\pi\)
−0.713973 + 0.700174i \(0.753106\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 7936.00 13745.6i 1.20168 2.08137i
\(353\) 4286.00 + 7423.57i 0.646234 + 1.11931i 0.984015 + 0.178086i \(0.0569905\pi\)
−0.337780 + 0.941225i \(0.609676\pi\)
\(354\) 0 0
\(355\) 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 \(-0.947865\pi\)
0.634519 + 0.772908i \(0.281198\pi\)
\(360\) 0 0
\(361\) −1570.50 2720.19i −0.228969 0.396586i
\(362\) −2084.00 + 3609.59i −0.302576 + 0.524077i
\(363\) 0 0
\(364\) 0 0
\(365\) −2568.00 −0.368261
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) −3936.00 −0.553035
\(371\) 0 0
\(372\) 0 0
\(373\) −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
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 4076.00 + 7059.84i 0.545933 + 0.945583i
\(383\) −4524.00 + 7835.80i −0.603566 + 1.04541i 0.388711 + 0.921360i \(0.372920\pi\)
−0.992276 + 0.124046i \(0.960413\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10408.0 1.37242
\(387\) 0 0
\(388\) −5064.00 8771.11i −0.662592 1.14764i
\(389\) −5745.00 9950.63i −0.748800 1.29696i −0.948398 0.317081i \(-0.897297\pi\)
0.199599 0.979878i \(-0.436036\pi\)
\(390\) 0 0
\(391\) 3528.00 0.456314
\(392\) 0 0
\(393\) 0 0
\(394\) −4708.00 + 8154.50i −0.601994 + 1.04268i
\(395\) 1480.00 + 2563.44i 0.188524 + 0.326533i
\(396\) 0 0
\(397\) −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 \(-0.509522\pi\)
0.880593 0.473873i \(-0.157145\pi\)
\(402\) 0 0
\(403\) −1488.00 2577.29i −0.183927 0.318571i
\(404\) −928.000 + 1607.34i −0.114281 + 0.197941i
\(405\) 0 0
\(406\) 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
\(411\) 0 0
\(412\) 14336.0 1.71428
\(413\) 0 0
\(414\) 0 0
\(415\) 936.000 1621.20i 0.110714 0.191763i
\(416\) −7936.00 13745.6i −0.935323 1.62003i
\(417\) 0 0
\(418\) 12400.0 21477.4i 1.45097 2.51315i
\(419\) 6960.00 0.811499 0.405750 0.913984i \(-0.367010\pi\)
0.405750 + 0.913984i \(0.367010\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 0 0
\(425\) 4578.00 7929.33i 0.522507 0.905009i
\(426\) 0 0
\(427\) 0 0
\(428\) 15248.0 1.72206
\(429\) 0 0
\(430\) −544.000 942.236i −0.0610093 0.105671i
\(431\) 8301.00 + 14377.8i 0.927715 + 1.60685i 0.787136 + 0.616780i \(0.211563\pi\)
0.140579 + 0.990069i \(0.455104\pi\)
\(432\) 0 0
\(433\) −7738.00 −0.858810 −0.429405 0.903112i \(-0.641277\pi\)
−0.429405 + 0.903112i \(0.641277\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 360.000 623.538i 0.0395433 0.0684910i
\(437\) 2100.00 + 3637.31i 0.229878 + 0.398160i
\(438\) 0 0
\(439\) −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 −0.632211 0.774796i \(-0.717852\pi\)
0.987099 + 0.160113i \(0.0511857\pi\)
\(444\) 0 0
\(445\) 400.000 + 692.820i 0.0426108 + 0.0738041i
\(446\) 3664.00 6346.23i 0.389003 0.673773i
\(447\) 0 0
\(448\) 0 0
\(449\) −3090.00 −0.324780 −0.162390 0.986727i \(-0.551920\pi\)
−0.162390 + 0.986727i \(0.551920\pi\)
\(450\) 0 0
\(451\) −7688.00 13316.0i −0.802691 1.39030i
\(452\) 1832.00 + 3173.12i 0.190642 + 0.330201i
\(453\) 0 0
\(454\) −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
\(459\) 0 0
\(460\) 672.000 1163.94i 0.0681134 0.117976i
\(461\) −15968.0 −1.61324 −0.806620 0.591070i \(-0.798706\pi\)
−0.806620 + 0.591070i \(0.798706\pi\)
\(462\) 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
\(465\) 0 0
\(466\) 5604.00 + 9706.41i 0.557082 + 0.964895i
\(467\) −2652.00 + 4593.40i −0.262784 + 0.455154i −0.966981 0.254850i \(-0.917974\pi\)
0.704197 + 0.710005i \(0.251307\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 5184.00 0.508766
\(471\) 0 0
\(472\) 0 0
\(473\) 2108.00 + 3651.16i 0.204917 + 0.354927i
\(474\) 0 0
\(475\) 10900.0 1.05290
\(476\) 0 0
\(477\) 0 0
\(478\) 2340.00 4053.00i 0.223910 0.387824i
\(479\) −2870.00 4970.99i −0.273765 0.474176i 0.696057 0.717986i \(-0.254936\pi\)
−0.969823 + 0.243810i \(0.921603\pi\)
\(480\) 0 0
\(481\) 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
\(486\) 0 0
\(487\) −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
\(489\) 0 0
\(490\) 0 0
\(491\) 5558.00 0.510853 0.255427 0.966828i \(-0.417784\pi\)
0.255427 + 0.966828i \(0.417784\pi\)
\(492\) 0 0
\(493\) −420.000 727.461i −0.0383689 0.0664568i
\(494\) −12400.0 21477.4i −1.12936 1.95610i
\(495\) 0 0
\(496\) −3072.00 −0.278099
\(497\) 0 0
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 5584.00 9671.77i 0.496466 0.859905i
\(503\) 1848.00 0.163814 0.0819068 0.996640i \(-0.473899\pi\)
0.0819068 + 0.996640i \(0.473899\pi\)
\(504\) 0 0
\(505\) −928.000 −0.0817732
\(506\) −5208.00 + 9020.52i −0.457557 + 0.792512i
\(507\) 0 0
\(508\) −3216.00 5570.28i −0.280880 0.486498i
\(509\) −170.000 + 294.449i −0.0148038 + 0.0256409i −0.873332 0.487125i \(-0.838046\pi\)
0.858529 + 0.512766i \(0.171379\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16384.0 −1.41421
\(513\) 0 0
\(514\) 14048.0 + 24331.8i 1.20551 + 2.08800i
\(515\) 3584.00 + 6207.67i 0.306660 + 0.531151i
\(516\) 0 0
\(517\) −20088.0 −1.70884
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5106.00 8843.85i −0.429363 0.743678i 0.567454 0.823405i \(-0.307928\pi\)
−0.996817 + 0.0797272i \(0.974595\pi\)
\(522\) 0 0
\(523\) −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
\(528\) 0 0
\(529\) 5201.50 + 9009.26i 0.427509 + 0.740467i
\(530\) 2064.00 3574.95i 0.169159 0.292993i
\(531\) 0 0
\(532\) 0 0
\(533\) −15376.0 −1.24955
\(534\) 0 0
\(535\) 3812.00 + 6602.58i 0.308051 + 0.533559i
\(536\) 0 0
\(537\) 0 0
\(538\) 27120.0 2.17328
\(539\) 0 0
\(540\) 0 0
\(541\) 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
\(543\) 0 0
\(544\) −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
\(549\) 0 0
\(550\) 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
\(555\) 0 0
\(556\) −6480.00 11223.7i −0.494268 0.856098i
\(557\) −263.000 455.529i −0.0200066 0.0346524i 0.855849 0.517226i \(-0.173035\pi\)
−0.875855 + 0.482574i \(0.839702\pi\)
\(558\) 0 0
\(559\) 4216.00 0.318994
\(560\) 0 0
\(561\) 0 0
\(562\) −3884.00 + 6727.29i −0.291524 + 0.504935i
\(563\) 3356.00 + 5812.76i 0.251223 + 0.435131i 0.963863 0.266399i \(-0.0858339\pi\)
−0.712640 + 0.701530i \(0.752501\pi\)
\(564\) 0 0
\(565\) −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 \(-0.784004\pi\)
0.932823 + 0.360334i \(0.117337\pi\)
\(570\) 0 0
\(571\) −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
\(573\) 0 0
\(574\) 0 0
\(575\) −4578.00 −0.332027
\(576\) 0 0
\(577\) 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
\(579\) 0 0
\(580\) −320.000 −0.0229091
\(581\) 0 0
\(582\) 0 0
\(583\) −7998.00 + 13852.9i −0.568170 + 0.984100i
\(584\) 0 0
\(585\) 0 0
\(586\) −12304.0 + 21311.2i −0.867361 + 1.50231i
\(587\) 464.000 0.0326258 0.0163129 0.999867i \(-0.494807\pi\)
0.0163129 + 0.999867i \(0.494807\pi\)
\(588\) 0 0
\(589\) −4800.00 −0.335790
\(590\) −960.000 + 1662.77i −0.0669874 + 0.116026i
\(591\) 0 0
\(592\) −7872.00 13634.7i −0.546516 0.946593i
\(593\) −5874.00 + 10174.1i −0.406773 + 0.704551i −0.994526 0.104489i \(-0.966679\pi\)
0.587753 + 0.809040i \(0.300013\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18960.0 −1.30307
\(597\) 0 0
\(598\) 5208.00 + 9020.52i 0.356139 + 0.616850i
\(599\) 3825.00 + 6625.09i 0.260910 + 0.451910i 0.966484 0.256727i \(-0.0826440\pi\)
−0.705574 + 0.708636i \(0.749311\pi\)
\(600\) 0 0
\(601\) 22878.0 1.55277 0.776384 0.630261i \(-0.217052\pi\)
0.776384 + 0.630261i \(0.217052\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2272.00 3935.22i 0.153057 0.265102i
\(605\) 5026.00 + 8705.29i 0.337745 + 0.584992i
\(606\) 0 0
\(607\) 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
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) 0 0
\(617\) 8826.00 0.575886 0.287943 0.957648i \(-0.407029\pi\)
0.287943 + 0.957648i \(0.407029\pi\)
\(618\) 0 0
\(619\) 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
\(621\) 0 0
\(622\) −36528.0 −2.35473
\(623\) 0 0
\(624\) 0 0
\(625\) −4940.50 + 8557.20i −0.316192 + 0.547661i
\(626\) 18764.0 + 32500.2i 1.19802 + 2.07503i
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) −6228.00 10787.2i −0.390135 0.675733i
\(635\) 1608.00 2785.14i 0.100491 0.174055i
\(636\) 0 0
\(637\) 0 0
\(638\) 2480.00 0.153894
\(639\) 0 0
\(640\) 0 0
\(641\) 6531.00 + 11312.0i 0.402432 + 0.697033i 0.994019 0.109208i \(-0.0348316\pi\)
−0.591587 + 0.806241i \(0.701498\pi\)
\(642\) 0 0
\(643\) 28012.0 1.71802 0.859009 0.511961i \(-0.171081\pi\)
0.859009 + 0.511961i \(0.171081\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −16800.0 + 29098.5i −1.02320 + 1.77223i
\(647\) −1922.00 3329.00i −0.116788 0.202282i 0.801705 0.597720i \(-0.203926\pi\)
−0.918493 + 0.395437i \(0.870593\pi\)
\(648\) 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 \(0.492152\pi\)
−0.878089 + 0.478498i \(0.841182\pi\)
\(654\) 0 0
\(655\) 1624.00 + 2812.85i 0.0968778 + 0.167797i
\(656\) −7936.00 + 13745.6i −0.472330 + 0.818100i
\(657\) 0 0
\(658\) 0 0
\(659\) 9330.00 0.551510 0.275755 0.961228i \(-0.411072\pi\)
0.275755 + 0.961228i \(0.411072\pi\)
\(660\) 0 0
\(661\) 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
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −210.000 + 363.731i −0.0121908 + 0.0211150i
\(668\) 7504.00 + 12997.3i 0.434638 + 0.752816i
\(669\) 0 0
\(670\) −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
\(675\) 0 0
\(676\) −6588.00 11410.8i −0.374829 0.649223i
\(677\) 13008.0 22530.5i 0.738461 1.27905i −0.214727 0.976674i \(-0.568886\pi\)
0.953188 0.302378i \(-0.0977804\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −5952.00 10309.2i −0.334185 0.578825i
\(683\) 4449.00 + 7705.89i 0.249248 + 0.431710i 0.963317 0.268365i \(-0.0864833\pi\)
−0.714070 + 0.700075i \(0.753150\pi\)
\(684\) 0 0
\(685\) 1656.00 0.0923686
\(686\) 0 0
\(687\) 0 0
\(688\) 2176.00 3768.94i 0.120580 0.208851i
\(689\) 7998.00 + 13852.9i 0.442234 + 0.765973i
\(690\) 0 0
\(691\) 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
\(699\) 0 0
\(700\) 0 0
\(701\) 30618.0 1.64968 0.824840 0.565366i \(-0.191265\pi\)
0.824840 + 0.565366i \(0.191265\pi\)
\(702\) 0 0
\(703\) −12300.0 21304.2i −0.659891 1.14296i
\(704\) −15872.0 27491.1i −0.849714 1.47175i
\(705\) 0 0
\(706\) 34288.0 1.82783
\(707\) 0 0
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 0 0
\(713\) 2016.00 0.105890
\(714\) 0 0
\(715\) 15376.0 0.804237
\(716\) 2440.00 4226.20i 0.127356 0.220588i
\(717\) 0 0
\(718\) 9580.00 + 16593.0i 0.497942 + 0.862461i
\(719\) 13920.0 24110.1i 0.722014 1.25057i −0.238177 0.971222i \(-0.576550\pi\)
0.960191 0.279344i \(-0.0901169\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −12564.0 −0.647623
\(723\) 0 0
\(724\) 4168.00 + 7219.19i 0.213954 + 0.370579i
\(725\) 545.000 + 943.968i 0.0279183 + 0.0483560i
\(726\) 0 0
\(727\) −14624.0 −0.746044 −0.373022 0.927822i \(-0.621678\pi\)
−0.373022 + 0.927822i \(0.621678\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5136.00 + 8895.81i −0.260400 + 0.451026i
\(731\) −2856.00 4946.74i −0.144505 0.250290i
\(732\) 0 0
\(733\) −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
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 0 0
\(743\) −25578.0 −1.26294 −0.631471 0.775400i \(-0.717548\pi\)
−0.631471 + 0.775400i \(0.717548\pi\)
\(744\) 0 0
\(745\) −4740.00 8209.92i −0.233101 0.403743i
\(746\) 3676.00 + 6367.02i 0.180413 + 0.312484i
\(747\) 0 0
\(748\) −41664.0 −2.03661
\(749\) 0 0
\(750\) 0 0
\(751\) −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
\(753\) 0 0
\(754\) 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
\(759\) 0 0
\(760\) 0 0
\(761\) −13476.0 + 23341.1i −0.641925 + 1.11185i 0.343078 + 0.939307i \(0.388530\pi\)
−0.985003 + 0.172539i \(0.944803\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16304.0 0.772065
\(765\) 0 0
\(766\) 18096.0 + 31343.2i 0.853571 + 1.47843i
\(767\) −3720.00 6443.23i −0.175126 0.303327i
\(768\) 0 0
\(769\) −23450.0 −1.09965 −0.549824 0.835281i \(-0.685305\pi\)
−0.549824 + 0.835281i \(0.685305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10408.0 18027.2i 0.485223 0.840431i
\(773\) −19784.0 34266.9i −0.920545 1.59443i −0.798574 0.601896i \(-0.794412\pi\)
−0.121970 0.992534i \(-0.538921\pi\)
\(774\) 0 0
\(775\) 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
\(780\) 0 0
\(781\) 21018.0 + 36404.2i 0.962975 + 1.66792i
\(782\) 7056.00 12221.4i 0.322662 0.558868i
\(783\) 0 0
\(784\) 0 0
\(785\) −1064.00 −0.0483768
\(786\) 0 0
\(787\) −6178.00 10700.6i −0.279825 0.484670i 0.691516 0.722361i \(-0.256943\pi\)
−0.971341 + 0.237690i \(0.923610\pi\)
\(788\) 9416.00 + 16309.0i 0.425674 + 0.737289i
\(789\) 0 0
\(790\) 11840.0 0.533226
\(791\) 0 0