Properties

Label 441.4.e.m.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.m.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 −0.941499 0.337016i \(-0.890582\pi\)
0.762614 + 0.646854i \(0.223916\pi\)
\(6\) 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 \(-0.730026\pi\)
−0.661373 + 0.750057i \(0.730026\pi\)
\(14\) 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 \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) 0 0
\(19\) −50.0000 + 86.6025i −0.603726 + 1.04568i 0.388526 + 0.921438i \(0.372984\pi\)
−0.992251 + 0.124246i \(0.960349\pi\)
\(20\) 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 0.927137 0.374723i \(-0.122262\pi\)
−0.788088 + 0.615563i \(0.788929\pi\)
\(32\) −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 \(-0.343413\pi\)
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
\(45\) 0 0
\(46\) 84.0000 + 145.492i 0.269242 + 0.466341i
\(47\) 162.000 280.592i 0.502769 0.870821i −0.497226 0.867621i \(-0.665648\pi\)
0.999995 0.00319997i \(-0.00101858\pi\)
\(48\) 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 0.924600 0.380941i \(-0.124400\pi\)
−0.792204 + 0.610256i \(0.791066\pi\)
\(60\) 0 0
\(61\) −311.000 + 538.668i −0.652778 + 1.13064i 0.329668 + 0.944097i \(0.393063\pi\)
−0.982446 + 0.186548i \(0.940270\pi\)
\(62\) 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 \(0.00541532\pi\)
−0.485195 + 0.874406i \(0.661251\pi\)
\(74\) −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 \(-0.600147\pi\)
−0.309456 + 0.950914i \(0.600147\pi\)
\(84\) 0 0
\(85\) −336.000 −0.428757
\(86\) 136.000 235.559i 0.170526 0.295360i
\(87\) 0 0
\(88\) 0 0
\(89\) 100.000 173.205i 0.119101 0.206289i −0.800311 0.599585i \(-0.795332\pi\)
0.919412 + 0.393297i \(0.128665\pi\)
\(90\) 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 \(-0.730544\pi\)
−0.662592 + 0.748981i \(0.730544\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 436.000 755.174i 0.436000 0.755174i
\(101\) 116.000 + 200.918i 0.114281 + 0.197941i 0.917492 0.397754i \(-0.130210\pi\)
−0.803211 + 0.595695i \(0.796877\pi\)
\(102\) 0 0
\(103\) 896.000 1551.92i 0.857141 1.48461i −0.0175038 0.999847i \(-0.505572\pi\)
0.874645 0.484765i \(-0.161095\pi\)
\(104\) 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 −0.698281 0.715824i \(-0.746051\pi\)
0.969062 + 0.246817i \(0.0793846\pi\)
\(132\) 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 \(-0.664564\pi\)
−0.494268 + 0.869309i \(0.664564\pi\)
\(140\) 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 0.897848 0.440305i \(-0.145130\pi\)
−0.830240 + 0.557407i \(0.811796\pi\)
\(158\) 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 \(-0.356876\pi\)
0.434638 + 0.900605i \(0.356876\pi\)
\(168\) 0 0
\(169\) 1647.00 0.749659
\(170\) −672.000 + 1163.94i −0.303177 + 0.525118i
\(171\) 0 0
\(172\) −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 \(0.177300\pi\)
\(174\) 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 \(-0.431366\pi\)
0.213954 + 0.976844i \(0.431366\pi\)
\(182\) 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 0.676733 0.736229i \(-0.263395\pi\)
−0.975959 + 0.217954i \(0.930062\pi\)
\(200\) 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 \(-0.588700\pi\)
−0.275067 + 0.961425i \(0.588700\pi\)
\(224\) 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 \(0.0904721\pi\)
−0.237093 + 0.971487i \(0.576195\pi\)
\(228\) 0 0
\(229\) 2735.00 4737.16i 0.789231 1.36699i −0.137208 0.990542i \(-0.543813\pi\)
0.926439 0.376446i \(-0.122854\pi\)
\(230\) −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 0.978893 0.204371i \(-0.0655150\pi\)
−0.666437 + 0.745561i \(0.732182\pi\)
\(242\) 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 \(-0.614177\pi\)
−0.351055 + 0.936355i \(0.614177\pi\)
\(252\) 0 0
\(253\) −2604.00 −0.647083
\(254\) 1608.00 2785.14i 0.397224 0.688012i
\(255\) 0 0
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) 3512.00 6082.96i 0.852422 1.47644i −0.0265936 0.999646i \(-0.508466\pi\)
0.879016 0.476792i \(-0.158201\pi\)
\(258\) 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 \(-0.887734\pi\)
0.170074 0.985431i \(-0.445599\pi\)
\(270\) 0 0
\(271\) 964.000 1669.70i 0.216084 0.374269i −0.737523 0.675322i \(-0.764005\pi\)
0.953607 + 0.301053i \(0.0973381\pi\)
\(272\) 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 \(-0.997400\pi\)
0.492909 0.870081i \(-0.335934\pi\)
\(284\) −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 \(-0.289835\pi\)
0.613317 + 0.789837i \(0.289835\pi\)
\(294\) 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 \(-0.315795\pi\)
0.546934 + 0.837176i \(0.315795\pi\)
\(308\) 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 \(0.146437\pi\)
−0.0635115 + 0.997981i \(0.520230\pi\)
\(312\) 0 0
\(313\) 4691.00 8125.05i 0.847128 1.46727i −0.0366327 0.999329i \(-0.511663\pi\)
0.883760 0.467940i \(-0.155004\pi\)
\(314\) 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 \(-0.246894\pi\)
0.713973 + 0.700174i \(0.246894\pi\)
\(350\) 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 \(-0.943009\pi\)
0.337780 0.941225i \(-0.390324\pi\)
\(354\) 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 0.606135 0.795362i \(-0.292719\pi\)
−0.991871 + 0.127247i \(0.959386\pi\)
\(368\) 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 \(-0.627080\pi\)
0.992276 0.124046i \(-0.0395872\pi\)
\(384\) 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 −0.801005 0.598657i \(-0.795701\pi\)
0.918955 + 0.394363i \(0.129035\pi\)
\(398\) −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 \(0.127719\pi\)
−0.122054 + 0.992524i \(0.538948\pi\)
\(410\) 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 \(-0.632990\pi\)
−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
\(423\) 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 \(-0.358723\pi\)
0.429405 + 0.903112i \(0.358723\pi\)
\(434\) 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 −0.842291 0.539023i \(-0.818794\pi\)
0.887953 + 0.459934i \(0.152127\pi\)
\(440\) 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 \(-0.201294\pi\)
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
\(465\) 0 0
\(466\) 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 \(0.0820261\pi\)
\(468\) 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 0.969823 0.243810i \(-0.0783975\pi\)
−0.696057 + 0.717986i \(0.745064\pi\)
\(480\) 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 \(-0.526101\pi\)
−0.0819068 + 0.996640i \(0.526101\pi\)
\(504\) 0 0
\(505\) −928.000 −0.0817732
\(506\) −5208.00 + 9020.52i −0.457557 + 0.792512i
\(507\) 0 0
\(508\) −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 \(0.161954\pi\)
\(510\) 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 0.996817 0.0797272i \(-0.0254049\pi\)
−0.567454 + 0.823405i \(0.692072\pi\)
\(522\) 0 0
\(523\) 4666.00 8081.75i 0.390115 0.675698i −0.602350 0.798232i \(-0.705769\pi\)
0.992464 + 0.122534i \(0.0391021\pi\)
\(524\) −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 0.712640 0.701530i \(-0.247499\pi\)
−0.963863 + 0.266399i \(0.914166\pi\)
\(564\) 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 0.751207 0.660067i \(-0.229472\pi\)
−0.947238 + 0.320531i \(0.896139\pi\)
\(578\) 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 \(-0.505193\pi\)
−0.0163129 + 0.999867i \(0.505193\pi\)
\(588\) 0 0
\(589\) −4800.00 −0.335790
\(590\) −960.000 + 1662.77i −0.0669874 + 0.116026i
\(591\) 0 0
\(592\) −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 \(0.0333207\pi\)
\(594\) 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 \(-0.782948\pi\)
−0.776384 + 0.630261i \(0.782948\pi\)
\(602\) 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 −0.877554 0.479477i \(-0.840826\pi\)
0.854017 + 0.520246i \(0.174160\pi\)
\(608\) 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 \(-0.924744\pi\)
0.283245 0.959047i \(-0.408589\pi\)
\(620\) 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 \(-0.828919\pi\)
−0.859009 + 0.511961i \(0.828919\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −16800.0 + 29098.5i −1.02320 + 1.77223i
\(647\) 1922.00 + 3329.00i 0.116788 + 0.202282i 0.918493 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 \(0.492152\pi\)
−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 0.707427 0.706786i \(-0.249856\pi\)
−0.965808 + 0.259257i \(0.916522\pi\)
\(662\) 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 \(0.431114\pi\)
−0.953188 + 0.302378i \(0.902220\pi\)
\(678\) 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 \(0.485020\pi\)
−0.888589 + 0.458704i \(0.848314\pi\)
\(692\) 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 \(0.423450\pi\)
−0.960191 + 0.279344i \(0.909883\pi\)
\(720\) 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 \(-0.378322\pi\)
0.373022 + 0.927822i \(0.378322\pi\)
\(728\) 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 \(-0.657168\pi\)
0.999555 0.0298378i \(-0.00949909\pi\)
\(734\) −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 \(-0.611470\pi\)
0.985003 0.172539i \(-0.0551971\pi\)
\(762\) 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 \(-0.314695\pi\)
0.549824 + 0.835281i \(0.314695\pi\)
\(770\) 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 \(0.205588\pi\)
0.121970 + 0.992534i \(0.461079\pi\)
\(774\) 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 0.971341 0.237690i \(-0.0763904\pi\)
−0.691516 + 0.722361i \(0.743057\pi\)
\(788\) 9416.00 + 16309.0i 0.425674 + 0.737289i
\(789\) 0 0
\(790\) −11840.0 −0.533226
\(791\)