Properties

Label 225.4.f.c.107.3
Level $225$
Weight $4$
Character 225.107
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 16 x^{10} - 14 x^{8} - 512 x^{6} + 3889 x^{4} + 126224 x^{2} + 506944\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.3
Root \(2.02004 - 2.30794i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.c.143.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.287902 + 0.287902i) q^{2} +7.83422i q^{4} +(-15.0557 - 15.0557i) q^{7} +(-4.55871 - 4.55871i) q^{8} +O(q^{10})\) \(q+(-0.287902 + 0.287902i) q^{2} +7.83422i q^{4} +(-15.0557 - 15.0557i) q^{7} +(-4.55871 - 4.55871i) q^{8} -27.9992i q^{11} +(-2.49862 + 2.49862i) q^{13} +8.66913 q^{14} -60.0489 q^{16} +(67.9104 - 67.9104i) q^{17} -95.2200i q^{19} +(8.06104 + 8.06104i) q^{22} +(121.994 + 121.994i) q^{23} -1.43872i q^{26} +(117.950 - 117.950i) q^{28} +99.0852 q^{29} -28.7800 q^{31} +(53.7578 - 53.7578i) q^{32} +39.1031i q^{34} +(-271.064 - 271.064i) q^{37} +(27.4140 + 27.4140i) q^{38} -453.748i q^{41} +(-30.5679 + 30.5679i) q^{43} +219.352 q^{44} -70.2445 q^{46} +(254.600 - 254.600i) q^{47} +110.348i q^{49} +(-19.5748 - 19.5748i) q^{52} +(-224.021 - 224.021i) q^{53} +137.269i q^{56} +(-28.5268 + 28.5268i) q^{58} -483.263 q^{59} -264.372 q^{61} +(8.28582 - 8.28582i) q^{62} -449.437i q^{64} +(498.817 + 498.817i) q^{67} +(532.025 + 532.025i) q^{68} +609.904i q^{71} +(74.6843 - 74.6843i) q^{73} +156.080 q^{74} +745.975 q^{76} +(-421.548 + 421.548i) q^{77} +406.574i q^{79} +(130.635 + 130.635i) q^{82} +(-652.278 - 652.278i) q^{83} -17.6011i q^{86} +(-127.640 + 127.640i) q^{88} +139.860 q^{89} +75.2369 q^{91} +(-955.726 + 955.726i) q^{92} +146.600i q^{94} +(-557.633 - 557.633i) q^{97} +(-31.7693 - 31.7693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 24 q^{7} + O(q^{10}) \) \( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.287902 + 0.287902i −0.101789 + 0.101789i −0.756167 0.654378i \(-0.772930\pi\)
0.654378 + 0.756167i \(0.272930\pi\)
\(3\) 0 0
\(4\) 7.83422i 0.979278i
\(5\) 0 0
\(6\) 0 0
\(7\) −15.0557 15.0557i −0.812931 0.812931i 0.172141 0.985072i \(-0.444931\pi\)
−0.985072 + 0.172141i \(0.944931\pi\)
\(8\) −4.55871 4.55871i −0.201468 0.201468i
\(9\) 0 0
\(10\) 0 0
\(11\) 27.9992i 0.767462i −0.923445 0.383731i \(-0.874639\pi\)
0.923445 0.383731i \(-0.125361\pi\)
\(12\) 0 0
\(13\) −2.49862 + 2.49862i −0.0533071 + 0.0533071i −0.733258 0.679951i \(-0.762001\pi\)
0.679951 + 0.733258i \(0.262001\pi\)
\(14\) 8.66913 0.165494
\(15\) 0 0
\(16\) −60.0489 −0.938264
\(17\) 67.9104 67.9104i 0.968864 0.968864i −0.0306653 0.999530i \(-0.509763\pi\)
0.999530 + 0.0306653i \(0.00976260\pi\)
\(18\) 0 0
\(19\) 95.2200i 1.14974i −0.818246 0.574868i \(-0.805054\pi\)
0.818246 0.574868i \(-0.194946\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 8.06104 + 8.06104i 0.0781191 + 0.0781191i
\(23\) 121.994 + 121.994i 1.10598 + 1.10598i 0.993674 + 0.112302i \(0.0358224\pi\)
0.112302 + 0.993674i \(0.464178\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.43872i 0.0108521i
\(27\) 0 0
\(28\) 117.950 117.950i 0.796085 0.796085i
\(29\) 99.0852 0.634471 0.317235 0.948347i \(-0.397245\pi\)
0.317235 + 0.948347i \(0.397245\pi\)
\(30\) 0 0
\(31\) −28.7800 −0.166743 −0.0833716 0.996519i \(-0.526569\pi\)
−0.0833716 + 0.996519i \(0.526569\pi\)
\(32\) 53.7578 53.7578i 0.296973 0.296973i
\(33\) 0 0
\(34\) 39.1031i 0.197239i
\(35\) 0 0
\(36\) 0 0
\(37\) −271.064 271.064i −1.20439 1.20439i −0.972816 0.231578i \(-0.925611\pi\)
−0.231578 0.972816i \(-0.574389\pi\)
\(38\) 27.4140 + 27.4140i 0.117030 + 0.117030i
\(39\) 0 0
\(40\) 0 0
\(41\) 453.748i 1.72838i −0.503166 0.864190i \(-0.667832\pi\)
0.503166 0.864190i \(-0.332168\pi\)
\(42\) 0 0
\(43\) −30.5679 + 30.5679i −0.108409 + 0.108409i −0.759230 0.650822i \(-0.774424\pi\)
0.650822 + 0.759230i \(0.274424\pi\)
\(44\) 219.352 0.751559
\(45\) 0 0
\(46\) −70.2445 −0.225152
\(47\) 254.600 254.600i 0.790153 0.790153i −0.191365 0.981519i \(-0.561292\pi\)
0.981519 + 0.191365i \(0.0612915\pi\)
\(48\) 0 0
\(49\) 110.348i 0.321713i
\(50\) 0 0
\(51\) 0 0
\(52\) −19.5748 19.5748i −0.0522025 0.0522025i
\(53\) −224.021 224.021i −0.580598 0.580598i 0.354470 0.935068i \(-0.384661\pi\)
−0.935068 + 0.354470i \(0.884661\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 137.269i 0.327560i
\(57\) 0 0
\(58\) −28.5268 + 28.5268i −0.0645820 + 0.0645820i
\(59\) −483.263 −1.06636 −0.533182 0.846001i \(-0.679004\pi\)
−0.533182 + 0.846001i \(0.679004\pi\)
\(60\) 0 0
\(61\) −264.372 −0.554908 −0.277454 0.960739i \(-0.589491\pi\)
−0.277454 + 0.960739i \(0.589491\pi\)
\(62\) 8.28582 8.28582i 0.0169726 0.0169726i
\(63\) 0 0
\(64\) 449.437i 0.877807i
\(65\) 0 0
\(66\) 0 0
\(67\) 498.817 + 498.817i 0.909556 + 0.909556i 0.996236 0.0866805i \(-0.0276259\pi\)
−0.0866805 + 0.996236i \(0.527626\pi\)
\(68\) 532.025 + 532.025i 0.948788 + 0.948788i
\(69\) 0 0
\(70\) 0 0
\(71\) 609.904i 1.01947i 0.860332 + 0.509735i \(0.170256\pi\)
−0.860332 + 0.509735i \(0.829744\pi\)
\(72\) 0 0
\(73\) 74.6843 74.6843i 0.119742 0.119742i −0.644697 0.764438i \(-0.723016\pi\)
0.764438 + 0.644697i \(0.223016\pi\)
\(74\) 156.080 0.245188
\(75\) 0 0
\(76\) 745.975 1.12591
\(77\) −421.548 + 421.548i −0.623894 + 0.623894i
\(78\) 0 0
\(79\) 406.574i 0.579027i 0.957174 + 0.289513i \(0.0934935\pi\)
−0.957174 + 0.289513i \(0.906507\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 130.635 + 130.635i 0.175930 + 0.175930i
\(83\) −652.278 652.278i −0.862613 0.862613i 0.129028 0.991641i \(-0.458814\pi\)
−0.991641 + 0.129028i \(0.958814\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 17.6011i 0.0220695i
\(87\) 0 0
\(88\) −127.640 + 127.640i −0.154619 + 0.154619i
\(89\) 139.860 0.166575 0.0832873 0.996526i \(-0.473458\pi\)
0.0832873 + 0.996526i \(0.473458\pi\)
\(90\) 0 0
\(91\) 75.2369 0.0866700
\(92\) −955.726 + 955.726i −1.08306 + 1.08306i
\(93\) 0 0
\(94\) 146.600i 0.160857i
\(95\) 0 0
\(96\) 0 0
\(97\) −557.633 557.633i −0.583701 0.583701i 0.352217 0.935918i \(-0.385428\pi\)
−0.935918 + 0.352217i \(0.885428\pi\)
\(98\) −31.7693 31.7693i −0.0327468 0.0327468i
\(99\) 0 0
\(100\) 0 0
\(101\) 299.833i 0.295391i 0.989033 + 0.147695i \(0.0471855\pi\)
−0.989033 + 0.147695i \(0.952814\pi\)
\(102\) 0 0
\(103\) −577.974 + 577.974i −0.552907 + 0.552907i −0.927279 0.374372i \(-0.877858\pi\)
0.374372 + 0.927279i \(0.377858\pi\)
\(104\) 22.7810 0.0214794
\(105\) 0 0
\(106\) 128.992 0.118197
\(107\) −216.994 + 216.994i −0.196053 + 0.196053i −0.798305 0.602253i \(-0.794270\pi\)
0.602253 + 0.798305i \(0.294270\pi\)
\(108\) 0 0
\(109\) 936.415i 0.822865i 0.911440 + 0.411432i \(0.134971\pi\)
−0.911440 + 0.411432i \(0.865029\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 904.077 + 904.077i 0.762743 + 0.762743i
\(113\) −1084.00 1084.00i −0.902428 0.902428i 0.0932173 0.995646i \(-0.470285\pi\)
−0.995646 + 0.0932173i \(0.970285\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 776.256i 0.621323i
\(117\) 0 0
\(118\) 139.132 139.132i 0.108544 0.108544i
\(119\) −2044.88 −1.57524
\(120\) 0 0
\(121\) 547.043 0.411001
\(122\) 76.1133 76.1133i 0.0564834 0.0564834i
\(123\) 0 0
\(124\) 225.469i 0.163288i
\(125\) 0 0
\(126\) 0 0
\(127\) 915.574 + 915.574i 0.639717 + 0.639717i 0.950486 0.310769i \(-0.100586\pi\)
−0.310769 + 0.950486i \(0.600586\pi\)
\(128\) 559.457 + 559.457i 0.386324 + 0.386324i
\(129\) 0 0
\(130\) 0 0
\(131\) 629.329i 0.419731i 0.977730 + 0.209865i \(0.0673026\pi\)
−0.977730 + 0.209865i \(0.932697\pi\)
\(132\) 0 0
\(133\) −1433.60 + 1433.60i −0.934655 + 0.934655i
\(134\) −287.221 −0.185165
\(135\) 0 0
\(136\) −619.167 −0.390391
\(137\) 660.931 660.931i 0.412169 0.412169i −0.470325 0.882494i \(-0.655863\pi\)
0.882494 + 0.470325i \(0.155863\pi\)
\(138\) 0 0
\(139\) 1378.35i 0.841081i −0.907274 0.420540i \(-0.861840\pi\)
0.907274 0.420540i \(-0.138160\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −175.593 175.593i −0.103771 0.103771i
\(143\) 69.9595 + 69.9595i 0.0409112 + 0.0409112i
\(144\) 0 0
\(145\) 0 0
\(146\) 43.0035i 0.0243767i
\(147\) 0 0
\(148\) 2123.57 2123.57i 1.17944 1.17944i
\(149\) 924.719 0.508429 0.254215 0.967148i \(-0.418183\pi\)
0.254215 + 0.967148i \(0.418183\pi\)
\(150\) 0 0
\(151\) −401.768 −0.216526 −0.108263 0.994122i \(-0.534529\pi\)
−0.108263 + 0.994122i \(0.534529\pi\)
\(152\) −434.080 + 434.080i −0.231635 + 0.231635i
\(153\) 0 0
\(154\) 242.729i 0.127011i
\(155\) 0 0
\(156\) 0 0
\(157\) −1305.55 1305.55i −0.663659 0.663659i 0.292582 0.956240i \(-0.405486\pi\)
−0.956240 + 0.292582i \(0.905486\pi\)
\(158\) −117.053 117.053i −0.0589384 0.0589384i
\(159\) 0 0
\(160\) 0 0
\(161\) 3673.40i 1.79816i
\(162\) 0 0
\(163\) 78.8393 78.8393i 0.0378845 0.0378845i −0.687911 0.725795i \(-0.741472\pi\)
0.725795 + 0.687911i \(0.241472\pi\)
\(164\) 3554.77 1.69256
\(165\) 0 0
\(166\) 375.585 0.175609
\(167\) 428.116 428.116i 0.198375 0.198375i −0.600928 0.799303i \(-0.705202\pi\)
0.799303 + 0.600928i \(0.205202\pi\)
\(168\) 0 0
\(169\) 2184.51i 0.994317i
\(170\) 0 0
\(171\) 0 0
\(172\) −239.476 239.476i −0.106162 0.106162i
\(173\) 1390.57 + 1390.57i 0.611114 + 0.611114i 0.943236 0.332122i \(-0.107765\pi\)
−0.332122 + 0.943236i \(0.607765\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1681.32i 0.720082i
\(177\) 0 0
\(178\) −40.2660 + 40.2660i −0.0169554 + 0.0169554i
\(179\) −110.674 −0.0462131 −0.0231065 0.999733i \(-0.507356\pi\)
−0.0231065 + 0.999733i \(0.507356\pi\)
\(180\) 0 0
\(181\) 700.593 0.287706 0.143853 0.989599i \(-0.454051\pi\)
0.143853 + 0.989599i \(0.454051\pi\)
\(182\) −21.6609 + 21.6609i −0.00882203 + 0.00882203i
\(183\) 0 0
\(184\) 1112.27i 0.445638i
\(185\) 0 0
\(186\) 0 0
\(187\) −1901.44 1901.44i −0.743567 0.743567i
\(188\) 1994.59 + 1994.59i 0.773780 + 0.773780i
\(189\) 0 0
\(190\) 0 0
\(191\) 2214.32i 0.838862i −0.907787 0.419431i \(-0.862230\pi\)
0.907787 0.419431i \(-0.137770\pi\)
\(192\) 0 0
\(193\) 1964.16 1964.16i 0.732556 0.732556i −0.238569 0.971125i \(-0.576678\pi\)
0.971125 + 0.238569i \(0.0766785\pi\)
\(194\) 321.087 0.118828
\(195\) 0 0
\(196\) −864.488 −0.315047
\(197\) 2700.70 2700.70i 0.976735 0.976735i −0.0230004 0.999735i \(-0.507322\pi\)
0.999735 + 0.0230004i \(0.00732189\pi\)
\(198\) 0 0
\(199\) 841.195i 0.299652i −0.988712 0.149826i \(-0.952129\pi\)
0.988712 0.149826i \(-0.0478713\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −86.3224 86.3224i −0.0300674 0.0300674i
\(203\) −1491.80 1491.80i −0.515781 0.515781i
\(204\) 0 0
\(205\) 0 0
\(206\) 332.800i 0.112559i
\(207\) 0 0
\(208\) 150.039 150.039i 0.0500161 0.0500161i
\(209\) −2666.09 −0.882379
\(210\) 0 0
\(211\) −3970.06 −1.29531 −0.647654 0.761934i \(-0.724250\pi\)
−0.647654 + 0.761934i \(0.724250\pi\)
\(212\) 1755.03 1755.03i 0.568567 0.568567i
\(213\) 0 0
\(214\) 124.946i 0.0399119i
\(215\) 0 0
\(216\) 0 0
\(217\) 433.303 + 433.303i 0.135551 + 0.135551i
\(218\) −269.596 269.596i −0.0837584 0.0837584i
\(219\) 0 0
\(220\) 0 0
\(221\) 339.365i 0.103295i
\(222\) 0 0
\(223\) −3600.34 + 3600.34i −1.08115 + 1.08115i −0.0847496 + 0.996402i \(0.527009\pi\)
−0.996402 + 0.0847496i \(0.972991\pi\)
\(224\) −1618.72 −0.482837
\(225\) 0 0
\(226\) 624.173 0.183714
\(227\) 1734.81 1734.81i 0.507239 0.507239i −0.406439 0.913678i \(-0.633230\pi\)
0.913678 + 0.406439i \(0.133230\pi\)
\(228\) 0 0
\(229\) 3467.74i 1.00067i −0.865831 0.500337i \(-0.833209\pi\)
0.865831 0.500337i \(-0.166791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −451.700 451.700i −0.127826 0.127826i
\(233\) 1070.17 + 1070.17i 0.300899 + 0.300899i 0.841365 0.540467i \(-0.181752\pi\)
−0.540467 + 0.841365i \(0.681752\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3785.99i 1.04427i
\(237\) 0 0
\(238\) 588.724 588.724i 0.160342 0.160342i
\(239\) 3909.44 1.05808 0.529038 0.848598i \(-0.322553\pi\)
0.529038 + 0.848598i \(0.322553\pi\)
\(240\) 0 0
\(241\) −4787.09 −1.27952 −0.639759 0.768576i \(-0.720966\pi\)
−0.639759 + 0.768576i \(0.720966\pi\)
\(242\) −157.495 + 157.495i −0.0418353 + 0.0418353i
\(243\) 0 0
\(244\) 2071.15i 0.543409i
\(245\) 0 0
\(246\) 0 0
\(247\) 237.919 + 237.919i 0.0612891 + 0.0612891i
\(248\) 131.200 + 131.200i 0.0335935 + 0.0335935i
\(249\) 0 0
\(250\) 0 0
\(251\) 2337.42i 0.587794i 0.955837 + 0.293897i \(0.0949523\pi\)
−0.955837 + 0.293897i \(0.905048\pi\)
\(252\) 0 0
\(253\) 3415.73 3415.73i 0.848795 0.848795i
\(254\) −527.191 −0.130232
\(255\) 0 0
\(256\) 3273.36 0.799160
\(257\) −977.764 + 977.764i −0.237320 + 0.237320i −0.815740 0.578419i \(-0.803670\pi\)
0.578419 + 0.815740i \(0.303670\pi\)
\(258\) 0 0
\(259\) 8162.10i 1.95818i
\(260\) 0 0
\(261\) 0 0
\(262\) −181.185 181.185i −0.0427239 0.0427239i
\(263\) −790.690 790.690i −0.185384 0.185384i 0.608313 0.793697i \(-0.291847\pi\)
−0.793697 + 0.608313i \(0.791847\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 825.474i 0.190275i
\(267\) 0 0
\(268\) −3907.85 + 3907.85i −0.890708 + 0.890708i
\(269\) 3954.49 0.896317 0.448159 0.893954i \(-0.352080\pi\)
0.448159 + 0.893954i \(0.352080\pi\)
\(270\) 0 0
\(271\) 7863.30 1.76259 0.881295 0.472567i \(-0.156673\pi\)
0.881295 + 0.472567i \(0.156673\pi\)
\(272\) −4077.94 + 4077.94i −0.909050 + 0.909050i
\(273\) 0 0
\(274\) 380.567i 0.0839083i
\(275\) 0 0
\(276\) 0 0
\(277\) −908.009 908.009i −0.196957 0.196957i 0.601737 0.798694i \(-0.294475\pi\)
−0.798694 + 0.601737i \(0.794475\pi\)
\(278\) 396.830 + 396.830i 0.0856126 + 0.0856126i
\(279\) 0 0
\(280\) 0 0
\(281\) 7102.70i 1.50787i 0.656949 + 0.753935i \(0.271847\pi\)
−0.656949 + 0.753935i \(0.728153\pi\)
\(282\) 0 0
\(283\) 4721.93 4721.93i 0.991837 0.991837i −0.00813014 0.999967i \(-0.502588\pi\)
0.999967 + 0.00813014i \(0.00258793\pi\)
\(284\) −4778.13 −0.998344
\(285\) 0 0
\(286\) −40.2829 −0.00832860
\(287\) −6831.49 + 6831.49i −1.40505 + 1.40505i
\(288\) 0 0
\(289\) 4310.65i 0.877396i
\(290\) 0 0
\(291\) 0 0
\(292\) 585.094 + 585.094i 0.117260 + 0.117260i
\(293\) 2078.57 + 2078.57i 0.414442 + 0.414442i 0.883283 0.468841i \(-0.155328\pi\)
−0.468841 + 0.883283i \(0.655328\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2471.40i 0.485294i
\(297\) 0 0
\(298\) −266.229 + 266.229i −0.0517524 + 0.0517524i
\(299\) −609.632 −0.117913
\(300\) 0 0
\(301\) 920.443 0.176257
\(302\) 115.670 115.670i 0.0220399 0.0220399i
\(303\) 0 0
\(304\) 5717.85i 1.07875i
\(305\) 0 0
\(306\) 0 0
\(307\) 5325.58 + 5325.58i 0.990056 + 0.990056i 0.999951 0.00989542i \(-0.00314986\pi\)
−0.00989542 + 0.999951i \(0.503150\pi\)
\(308\) −3302.50 3302.50i −0.610966 0.610966i
\(309\) 0 0
\(310\) 0 0
\(311\) 2005.56i 0.365676i −0.983143 0.182838i \(-0.941472\pi\)
0.983143 0.182838i \(-0.0585283\pi\)
\(312\) 0 0
\(313\) −5026.49 + 5026.49i −0.907713 + 0.907713i −0.996087 0.0883746i \(-0.971833\pi\)
0.0883746 + 0.996087i \(0.471833\pi\)
\(314\) 751.742 0.135106
\(315\) 0 0
\(316\) −3185.19 −0.567028
\(317\) 3137.15 3137.15i 0.555836 0.555836i −0.372283 0.928119i \(-0.621425\pi\)
0.928119 + 0.372283i \(0.121425\pi\)
\(318\) 0 0
\(319\) 2774.31i 0.486933i
\(320\) 0 0
\(321\) 0 0
\(322\) 1057.58 + 1057.58i 0.183033 + 0.183033i
\(323\) −6466.43 6466.43i −1.11394 1.11394i
\(324\) 0 0
\(325\) 0 0
\(326\) 45.3960i 0.00771243i
\(327\) 0 0
\(328\) −2068.50 + 2068.50i −0.348214 + 0.348214i
\(329\) −7666.35 −1.28468
\(330\) 0 0
\(331\) 2978.02 0.494523 0.247261 0.968949i \(-0.420469\pi\)
0.247261 + 0.968949i \(0.420469\pi\)
\(332\) 5110.10 5110.10i 0.844738 0.844738i
\(333\) 0 0
\(334\) 246.511i 0.0403847i
\(335\) 0 0
\(336\) 0 0
\(337\) 5985.73 + 5985.73i 0.967547 + 0.967547i 0.999490 0.0319428i \(-0.0101694\pi\)
−0.0319428 + 0.999490i \(0.510169\pi\)
\(338\) −628.926 628.926i −0.101210 0.101210i
\(339\) 0 0
\(340\) 0 0
\(341\) 805.818i 0.127969i
\(342\) 0 0
\(343\) −3502.74 + 3502.74i −0.551400 + 0.551400i
\(344\) 278.701 0.0436818
\(345\) 0 0
\(346\) −800.693 −0.124409
\(347\) −8183.37 + 8183.37i −1.26601 + 1.26601i −0.317881 + 0.948130i \(0.602971\pi\)
−0.948130 + 0.317881i \(0.897029\pi\)
\(348\) 0 0
\(349\) 1421.22i 0.217983i −0.994043 0.108991i \(-0.965238\pi\)
0.994043 0.108991i \(-0.0347621\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1505.18 1505.18i −0.227916 0.227916i
\(353\) 1399.56 + 1399.56i 0.211023 + 0.211023i 0.804702 0.593679i \(-0.202325\pi\)
−0.593679 + 0.804702i \(0.702325\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1095.70i 0.163123i
\(357\) 0 0
\(358\) 31.8632 31.8632i 0.00470397 0.00470397i
\(359\) −4313.98 −0.634215 −0.317108 0.948390i \(-0.602712\pi\)
−0.317108 + 0.948390i \(0.602712\pi\)
\(360\) 0 0
\(361\) −2207.85 −0.321891
\(362\) −201.702 + 201.702i −0.0292852 + 0.0292852i
\(363\) 0 0
\(364\) 589.423i 0.0848740i
\(365\) 0 0
\(366\) 0 0
\(367\) −4533.34 4533.34i −0.644792 0.644792i 0.306938 0.951730i \(-0.400696\pi\)
−0.951730 + 0.306938i \(0.900696\pi\)
\(368\) −7325.59 7325.59i −1.03770 1.03770i
\(369\) 0 0
\(370\) 0 0
\(371\) 6745.59i 0.943972i
\(372\) 0 0
\(373\) 2787.95 2787.95i 0.387010 0.387010i −0.486609 0.873620i \(-0.661766\pi\)
0.873620 + 0.486609i \(0.161766\pi\)
\(374\) 1094.86 0.151374
\(375\) 0 0
\(376\) −2321.29 −0.318382
\(377\) −247.576 + 247.576i −0.0338218 + 0.0338218i
\(378\) 0 0
\(379\) 8409.09i 1.13970i 0.821749 + 0.569849i \(0.192998\pi\)
−0.821749 + 0.569849i \(0.807002\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 637.508 + 637.508i 0.0853868 + 0.0853868i
\(383\) 8507.38 + 8507.38i 1.13500 + 1.13500i 0.989333 + 0.145672i \(0.0465343\pi\)
0.145672 + 0.989333i \(0.453466\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1130.97i 0.149132i
\(387\) 0 0
\(388\) 4368.62 4368.62i 0.571606 0.571606i
\(389\) 8641.23 1.12629 0.563146 0.826357i \(-0.309591\pi\)
0.563146 + 0.826357i \(0.309591\pi\)
\(390\) 0 0
\(391\) 16569.3 2.14308
\(392\) 503.042 503.042i 0.0648150 0.0648150i
\(393\) 0 0
\(394\) 1555.07i 0.198841i
\(395\) 0 0
\(396\) 0 0
\(397\) −1902.21 1902.21i −0.240476 0.240476i 0.576571 0.817047i \(-0.304390\pi\)
−0.817047 + 0.576571i \(0.804390\pi\)
\(398\) 242.182 + 242.182i 0.0305012 + 0.0305012i
\(399\) 0 0
\(400\) 0 0
\(401\) 13640.1i 1.69864i −0.527882 0.849318i \(-0.677014\pi\)
0.527882 0.849318i \(-0.322986\pi\)
\(402\) 0 0
\(403\) 71.9103 71.9103i 0.00888860 0.00888860i
\(404\) −2348.96 −0.289270
\(405\) 0 0
\(406\) 858.982 0.105001
\(407\) −7589.57 + 7589.57i −0.924327 + 0.924327i
\(408\) 0 0
\(409\) 6395.02i 0.773138i −0.922260 0.386569i \(-0.873660\pi\)
0.922260 0.386569i \(-0.126340\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4527.98 4527.98i −0.541450 0.541450i
\(413\) 7275.86 + 7275.86i 0.866880 + 0.866880i
\(414\) 0 0
\(415\) 0 0
\(416\) 268.641i 0.0316615i
\(417\) 0 0
\(418\) 767.572 767.572i 0.0898162 0.0898162i
\(419\) 8474.94 0.988133 0.494067 0.869424i \(-0.335510\pi\)
0.494067 + 0.869424i \(0.335510\pi\)
\(420\) 0 0
\(421\) −9069.21 −1.04990 −0.524948 0.851134i \(-0.675915\pi\)
−0.524948 + 0.851134i \(0.675915\pi\)
\(422\) 1142.99 1142.99i 0.131848 0.131848i
\(423\) 0 0
\(424\) 2042.49i 0.233944i
\(425\) 0 0
\(426\) 0 0
\(427\) 3980.30 + 3980.30i 0.451102 + 0.451102i
\(428\) −1699.98 1699.98i −0.191990 0.191990i
\(429\) 0 0
\(430\) 0 0
\(431\) 8388.11i 0.937450i 0.883344 + 0.468725i \(0.155287\pi\)
−0.883344 + 0.468725i \(0.844713\pi\)
\(432\) 0 0
\(433\) 4132.17 4132.17i 0.458613 0.458613i −0.439587 0.898200i \(-0.644875\pi\)
0.898200 + 0.439587i \(0.144875\pi\)
\(434\) −249.498 −0.0275951
\(435\) 0 0
\(436\) −7336.08 −0.805814
\(437\) 11616.2 11616.2i 1.27158 1.27158i
\(438\) 0 0
\(439\) 10498.9i 1.14143i −0.821149 0.570714i \(-0.806667\pi\)
0.821149 0.570714i \(-0.193333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −97.7038 97.7038i −0.0105142 0.0105142i
\(443\) 1465.93 + 1465.93i 0.157220 + 0.157220i 0.781333 0.624114i \(-0.214540\pi\)
−0.624114 + 0.781333i \(0.714540\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2073.09i 0.220098i
\(447\) 0 0
\(448\) −6766.58 + 6766.58i −0.713596 + 0.713596i
\(449\) 6295.42 0.661691 0.330846 0.943685i \(-0.392666\pi\)
0.330846 + 0.943685i \(0.392666\pi\)
\(450\) 0 0
\(451\) −12704.6 −1.32647
\(452\) 8492.32 8492.32i 0.883728 0.883728i
\(453\) 0 0
\(454\) 998.909i 0.103262i
\(455\) 0 0
\(456\) 0 0
\(457\) −9065.09 9065.09i −0.927893 0.927893i 0.0696767 0.997570i \(-0.477803\pi\)
−0.997570 + 0.0696767i \(0.977803\pi\)
\(458\) 998.368 + 998.368i 0.101857 + 0.101857i
\(459\) 0 0
\(460\) 0 0
\(461\) 13305.5i 1.34424i −0.740440 0.672122i \(-0.765383\pi\)
0.740440 0.672122i \(-0.234617\pi\)
\(462\) 0 0
\(463\) 3124.86 3124.86i 0.313660 0.313660i −0.532666 0.846326i \(-0.678810\pi\)
0.846326 + 0.532666i \(0.178810\pi\)
\(464\) −5949.95 −0.595301
\(465\) 0 0
\(466\) −616.210 −0.0612562
\(467\) 4255.07 4255.07i 0.421629 0.421629i −0.464135 0.885764i \(-0.653635\pi\)
0.885764 + 0.464135i \(0.153635\pi\)
\(468\) 0 0
\(469\) 15020.1i 1.47881i
\(470\) 0 0
\(471\) 0 0
\(472\) 2203.05 + 2203.05i 0.214838 + 0.214838i
\(473\) 855.879 + 855.879i 0.0831995 + 0.0831995i
\(474\) 0 0
\(475\) 0 0
\(476\) 16020.0i 1.54260i
\(477\) 0 0
\(478\) −1125.53 + 1125.53i −0.107700 + 0.107700i
\(479\) −10625.2 −1.01352 −0.506761 0.862087i \(-0.669157\pi\)
−0.506761 + 0.862087i \(0.669157\pi\)
\(480\) 0 0
\(481\) 1354.57 0.128406
\(482\) 1378.21 1378.21i 0.130241 0.130241i
\(483\) 0 0
\(484\) 4285.66i 0.402485i
\(485\) 0 0
\(486\) 0 0
\(487\) 3269.03 + 3269.03i 0.304177 + 0.304177i 0.842645 0.538469i \(-0.180997\pi\)
−0.538469 + 0.842645i \(0.680997\pi\)
\(488\) 1205.19 + 1205.19i 0.111796 + 0.111796i
\(489\) 0 0
\(490\) 0 0
\(491\) 18791.1i 1.72715i 0.504220 + 0.863575i \(0.331780\pi\)
−0.504220 + 0.863575i \(0.668220\pi\)
\(492\) 0 0
\(493\) 6728.92 6728.92i 0.614716 0.614716i
\(494\) −136.995 −0.0124771
\(495\) 0 0
\(496\) 1728.21 0.156449
\(497\) 9182.53 9182.53i 0.828758 0.828758i
\(498\) 0 0
\(499\) 7220.67i 0.647778i 0.946095 + 0.323889i \(0.104990\pi\)
−0.946095 + 0.323889i \(0.895010\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −672.947 672.947i −0.0598308 0.0598308i
\(503\) 2081.38 + 2081.38i 0.184501 + 0.184501i 0.793314 0.608813i \(-0.208354\pi\)
−0.608813 + 0.793314i \(0.708354\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1966.79i 0.172796i
\(507\) 0 0
\(508\) −7172.81 + 7172.81i −0.626461 + 0.626461i
\(509\) 12624.1 1.09932 0.549659 0.835389i \(-0.314758\pi\)
0.549659 + 0.835389i \(0.314758\pi\)
\(510\) 0 0
\(511\) −2248.85 −0.194683
\(512\) −5418.06 + 5418.06i −0.467669 + 0.467669i
\(513\) 0 0
\(514\) 563.001i 0.0483130i
\(515\) 0 0
\(516\) 0 0
\(517\) −7128.60 7128.60i −0.606413 0.606413i
\(518\) −2349.89 2349.89i −0.199321 0.199321i
\(519\) 0 0
\(520\) 0 0
\(521\) 11837.5i 0.995409i −0.867347 0.497705i \(-0.834176\pi\)
0.867347 0.497705i \(-0.165824\pi\)
\(522\) 0 0
\(523\) 5538.72 5538.72i 0.463081 0.463081i −0.436583 0.899664i \(-0.643811\pi\)
0.899664 + 0.436583i \(0.143811\pi\)
\(524\) −4930.31 −0.411033
\(525\) 0 0
\(526\) 455.282 0.0377400
\(527\) −1954.46 + 1954.46i −0.161552 + 0.161552i
\(528\) 0 0
\(529\) 17597.9i 1.44637i
\(530\) 0 0
\(531\) 0 0
\(532\) −11231.2 11231.2i −0.915287 0.915287i
\(533\) 1133.74 + 1133.74i 0.0921349 + 0.0921349i
\(534\) 0 0
\(535\) 0 0
\(536\) 4547.92i 0.366493i
\(537\) 0 0
\(538\) −1138.51 + 1138.51i −0.0912350 + 0.0912350i
\(539\) 3089.65 0.246903
\(540\) 0 0
\(541\) 5207.24 0.413820 0.206910 0.978360i \(-0.433659\pi\)
0.206910 + 0.978360i \(0.433659\pi\)
\(542\) −2263.86 + 2263.86i −0.179412 + 0.179412i
\(543\) 0 0
\(544\) 7301.44i 0.575453i
\(545\) 0 0
\(546\) 0 0
\(547\) 3940.59 + 3940.59i 0.308021 + 0.308021i 0.844141 0.536121i \(-0.180111\pi\)
−0.536121 + 0.844141i \(0.680111\pi\)
\(548\) 5177.88 + 5177.88i 0.403628 + 0.403628i
\(549\) 0 0
\(550\) 0 0
\(551\) 9434.89i 0.729473i
\(552\) 0 0
\(553\) 6121.25 6121.25i 0.470709 0.470709i
\(554\) 522.836 0.0400959
\(555\) 0 0
\(556\) 10798.3 0.823652
\(557\) −2850.64 + 2850.64i −0.216850 + 0.216850i −0.807170 0.590320i \(-0.799002\pi\)
0.590320 + 0.807170i \(0.299002\pi\)
\(558\) 0 0
\(559\) 152.755i 0.0115579i
\(560\) 0 0
\(561\) 0 0
\(562\) −2044.88 2044.88i −0.153484 0.153484i
\(563\) −12845.3 12845.3i −0.961569 0.961569i 0.0377198 0.999288i \(-0.487991\pi\)
−0.999288 + 0.0377198i \(0.987991\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2718.91i 0.201916i
\(567\) 0 0
\(568\) 2780.38 2780.38i 0.205391 0.205391i
\(569\) 25072.7 1.84728 0.923639 0.383263i \(-0.125200\pi\)
0.923639 + 0.383263i \(0.125200\pi\)
\(570\) 0 0
\(571\) −3587.24 −0.262909 −0.131455 0.991322i \(-0.541965\pi\)
−0.131455 + 0.991322i \(0.541965\pi\)
\(572\) −548.078 + 548.078i −0.0400635 + 0.0400635i
\(573\) 0 0
\(574\) 3933.60i 0.286037i
\(575\) 0 0
\(576\) 0 0
\(577\) −760.083 760.083i −0.0548400 0.0548400i 0.679155 0.733995i \(-0.262346\pi\)
−0.733995 + 0.679155i \(0.762346\pi\)
\(578\) 1241.04 + 1241.04i 0.0893091 + 0.0893091i
\(579\) 0 0
\(580\) 0 0
\(581\) 19641.0i 1.40249i
\(582\) 0 0
\(583\) −6272.43 + 6272.43i −0.445587 + 0.445587i
\(584\) −680.928 −0.0482483
\(585\) 0 0
\(586\) −1196.85 −0.0843711
\(587\) −8165.43 + 8165.43i −0.574146 + 0.574146i −0.933284 0.359139i \(-0.883071\pi\)
0.359139 + 0.933284i \(0.383071\pi\)
\(588\) 0 0
\(589\) 2740.43i 0.191711i
\(590\) 0 0
\(591\) 0 0
\(592\) 16277.1 + 16277.1i 1.13004 + 1.13004i
\(593\) 9861.32 + 9861.32i 0.682893 + 0.682893i 0.960651 0.277758i \(-0.0895913\pi\)
−0.277758 + 0.960651i \(0.589591\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7244.46i 0.497893i
\(597\) 0 0
\(598\) 175.514 175.514i 0.0120022 0.0120022i
\(599\) −20769.5 −1.41673 −0.708363 0.705848i \(-0.750566\pi\)
−0.708363 + 0.705848i \(0.750566\pi\)
\(600\) 0 0
\(601\) −11642.9 −0.790222 −0.395111 0.918633i \(-0.629294\pi\)
−0.395111 + 0.918633i \(0.629294\pi\)
\(602\) −264.997 + 264.997i −0.0179410 + 0.0179410i
\(603\) 0 0
\(604\) 3147.54i 0.212039i
\(605\) 0 0
\(606\) 0 0
\(607\) 17174.6 + 17174.6i 1.14843 + 1.14843i 0.986862 + 0.161565i \(0.0516540\pi\)
0.161565 + 0.986862i \(0.448346\pi\)
\(608\) −5118.82 5118.82i −0.341440 0.341440i
\(609\) 0 0
\(610\) 0 0
\(611\) 1272.30i 0.0842416i
\(612\) 0 0
\(613\) −11694.1 + 11694.1i −0.770504 + 0.770504i −0.978195 0.207691i \(-0.933405\pi\)
0.207691 + 0.978195i \(0.433405\pi\)
\(614\) −3066.49 −0.201553
\(615\) 0 0
\(616\) 3843.43 0.251390
\(617\) −5586.69 + 5586.69i −0.364525 + 0.364525i −0.865476 0.500951i \(-0.832984\pi\)
0.500951 + 0.865476i \(0.332984\pi\)
\(618\) 0 0
\(619\) 16137.1i 1.04783i −0.851771 0.523914i \(-0.824471\pi\)
0.851771 0.523914i \(-0.175529\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 577.406 + 577.406i 0.0372217 + 0.0372217i
\(623\) −2105.69 2105.69i −0.135414 0.135414i
\(624\) 0 0
\(625\) 0 0
\(626\) 2894.27i 0.184790i
\(627\) 0 0
\(628\) 10228.0 10228.0i 0.649906 0.649906i
\(629\) −36816.1 −2.33379
\(630\) 0 0
\(631\) 25292.3 1.59567 0.797837 0.602874i \(-0.205978\pi\)
0.797837 + 0.602874i \(0.205978\pi\)
\(632\) 1853.45 1853.45i 0.116656 0.116656i
\(633\) 0 0
\(634\) 1806.38i 0.113156i
\(635\) 0 0
\(636\) 0 0
\(637\) −275.717 275.717i −0.0171496 0.0171496i
\(638\) 798.729 + 798.729i 0.0495643 + 0.0495643i
\(639\) 0 0
\(640\) 0 0
\(641\) 8057.35i 0.496484i 0.968698 + 0.248242i \(0.0798528\pi\)
−0.968698 + 0.248242i \(0.920147\pi\)
\(642\) 0 0
\(643\) −15024.4 + 15024.4i −0.921471 + 0.921471i −0.997133 0.0756629i \(-0.975893\pi\)
0.0756629 + 0.997133i \(0.475893\pi\)
\(644\) 28778.2 1.76090
\(645\) 0 0
\(646\) 3723.40 0.226773
\(647\) −2396.69 + 2396.69i −0.145631 + 0.145631i −0.776163 0.630532i \(-0.782837\pi\)
0.630532 + 0.776163i \(0.282837\pi\)
\(648\) 0 0
\(649\) 13531.0i 0.818394i
\(650\) 0 0
\(651\) 0 0
\(652\) 617.645 + 617.645i 0.0370995 + 0.0370995i
\(653\) −10852.1 10852.1i −0.650343 0.650343i 0.302732 0.953076i \(-0.402101\pi\)
−0.953076 + 0.302732i \(0.902101\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 27247.1i 1.62168i
\(657\) 0 0
\(658\) 2207.16 2207.16i 0.130766 0.130766i
\(659\) −21164.7 −1.25108 −0.625538 0.780193i \(-0.715121\pi\)
−0.625538 + 0.780193i \(0.715121\pi\)
\(660\) 0 0
\(661\) −6399.33 −0.376558 −0.188279 0.982116i \(-0.560291\pi\)
−0.188279 + 0.982116i \(0.560291\pi\)
\(662\) −857.380 + 857.380i −0.0503369 + 0.0503369i
\(663\) 0 0
\(664\) 5947.09i 0.347578i
\(665\) 0 0
\(666\) 0 0
\(667\) 12087.8 + 12087.8i 0.701710 + 0.701710i
\(668\) 3353.96 + 3353.96i 0.194264 + 0.194264i
\(669\) 0 0
\(670\) 0 0
\(671\) 7402.22i 0.425871i
\(672\) 0 0
\(673\) 1618.29 1618.29i 0.0926903 0.0926903i −0.659241 0.751932i \(-0.729122\pi\)
0.751932 + 0.659241i \(0.229122\pi\)
\(674\) −3446.61 −0.196971
\(675\) 0 0
\(676\) −17114.0 −0.973713
\(677\) −16119.8 + 16119.8i −0.915118 + 0.915118i −0.996669 0.0815511i \(-0.974013\pi\)
0.0815511 + 0.996669i \(0.474013\pi\)
\(678\) 0 0
\(679\) 16791.1i 0.949017i
\(680\) 0 0
\(681\) 0 0
\(682\) −231.997 231.997i −0.0130258 0.0130258i
\(683\) −23612.1 23612.1i −1.32283 1.32283i −0.911477 0.411351i \(-0.865057\pi\)
−0.411351 0.911477i \(-0.634943\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 2016.89i 0.112253i
\(687\) 0 0
\(688\) 1835.57 1835.57i 0.101716 0.101716i
\(689\) 1119.49 0.0619000
\(690\) 0 0
\(691\) 12036.1 0.662624 0.331312 0.943521i \(-0.392509\pi\)
0.331312 + 0.943521i \(0.392509\pi\)
\(692\) −10894.0 + 10894.0i −0.598451 + 0.598451i
\(693\) 0 0
\(694\) 4712.02i 0.257732i
\(695\) 0 0
\(696\) 0 0
\(697\) −30814.2 30814.2i −1.67457 1.67457i
\(698\) 409.171 + 409.171i 0.0221882 + 0.0221882i
\(699\) 0 0
\(700\) 0 0
\(701\) 33366.3i 1.79776i −0.438200 0.898878i \(-0.644384\pi\)
0.438200 0.898878i \(-0.355616\pi\)
\(702\) 0 0
\(703\) −25810.7 + 25810.7i −1.38473 + 1.38473i
\(704\) −12583.9 −0.673684
\(705\) 0 0
\(706\) −805.875 −0.0429596
\(707\) 4514.19 4514.19i 0.240132 0.240132i
\(708\) 0 0
\(709\) 4987.22i 0.264173i 0.991238 + 0.132087i \(0.0421677\pi\)
−0.991238 + 0.132087i \(0.957832\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −637.581 637.581i −0.0335595 0.0335595i
\(713\) −3510.98 3510.98i −0.184414 0.184414i
\(714\) 0 0
\(715\) 0 0
\(716\) 867.043i 0.0452555i
\(717\) 0 0
\(718\) 1242.00 1242.00i 0.0645560 0.0645560i
\(719\) 33618.4 1.74375 0.871873 0.489732i \(-0.162905\pi\)
0.871873 + 0.489732i \(0.162905\pi\)
\(720\) 0 0
\(721\) 17403.6 0.898951
\(722\) 635.644 635.644i 0.0327649 0.0327649i
\(723\) 0 0
\(724\) 5488.61i 0.281744i
\(725\) 0 0
\(726\) 0 0
\(727\) 10057.9 + 10057.9i 0.513106 + 0.513106i 0.915477 0.402371i \(-0.131814\pi\)
−0.402371 + 0.915477i \(0.631814\pi\)
\(728\) −342.983 342.983i −0.0174613 0.0174613i
\(729\) 0 0
\(730\) 0 0
\(731\) 4151.76i 0.210066i
\(732\) 0 0
\(733\) 4209.55 4209.55i 0.212119 0.212119i −0.593048 0.805167i \(-0.702076\pi\)
0.805167 + 0.593048i \(0.202076\pi\)
\(734\) 2610.32 0.131265
\(735\) 0 0
\(736\) 13116.2 0.656890
\(737\) 13966.5 13966.5i 0.698050 0.698050i
\(738\) 0 0
\(739\) 4750.38i 0.236462i 0.992986 + 0.118231i \(0.0377223\pi\)
−0.992986 + 0.118231i \(0.962278\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1942.07 1942.07i −0.0960857 0.0960857i
\(743\) 16266.1 + 16266.1i 0.803159 + 0.803159i 0.983588 0.180429i \(-0.0577487\pi\)
−0.180429 + 0.983588i \(0.557749\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1605.32i 0.0787866i
\(747\) 0 0
\(748\) 14896.3 14896.3i 0.728159 0.728159i
\(749\) 6534.00 0.318754
\(750\) 0 0
\(751\) −32690.2 −1.58839 −0.794197 0.607660i \(-0.792108\pi\)
−0.794197 + 0.607660i \(0.792108\pi\)
\(752\) −15288.4 + 15288.4i −0.741372 + 0.741372i
\(753\) 0 0
\(754\) 142.555i 0.00688536i
\(755\) 0 0
\(756\) 0 0
\(757\) 6722.97 + 6722.97i 0.322788 + 0.322788i 0.849836 0.527048i \(-0.176701\pi\)
−0.527048 + 0.849836i \(0.676701\pi\)
\(758\) −2420.99 2420.99i −0.116008 0.116008i
\(759\) 0 0
\(760\) 0 0
\(761\) 7001.94i 0.333535i −0.985996 0.166767i \(-0.946667\pi\)
0.985996 0.166767i \(-0.0533329\pi\)
\(762\) 0 0
\(763\) 14098.4 14098.4i 0.668932 0.668932i
\(764\) 17347.5 0.821480
\(765\) 0 0
\(766\) −4898.58 −0.231061
\(767\) 1207.49 1207.49i 0.0568448 0.0568448i
\(768\) 0 0
\(769\) 25176.4i 1.18060i −0.807183 0.590301i \(-0.799009\pi\)
0.807183 0.590301i \(-0.200991\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15387.7 + 15387.7i 0.717376 + 0.717376i
\(773\) 7322.13 + 7322.13i 0.340697 + 0.340697i 0.856629 0.515932i \(-0.172554\pi\)
−0.515932 + 0.856629i \(0.672554\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 5084.17i 0.235195i
\(777\) 0 0
\(778\) −2487.83 + 2487.83i −0.114644 + 0.114644i
\(779\) −43205.9 −1.98718
\(780\) 0 0
\(781\) 17076.9 0.782405
\(782\) −4770.33 + 4770.33i −0.218142 + 0.218142i
\(783\) 0 0
\(784\) 6626.25i 0.301852i
\(785\) 0 0
\(786\) 0 0
\(787\) −16794.5 16794.5i −0.760683 0.760683i 0.215763 0.976446i \(-0.430776\pi\)
−0.976446 + 0.215763i \(0.930776\pi\)
\(788\) 21157.9 + 21157.9i 0.956495 + 0.956495i
\(789\) 0 0
\(790\) 0 0
\(791\) 32640.8i 1.46722i
\(792\) 0 0
\(793\) 660.565 660.565i 0.0295805 0.0295805i
\(794\) 1095.30 0.0489556