Properties

Label 225.4.f.c.143.3
Level $225$
Weight $4$
Character 225.143
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 143.3
Root \(2.02004 + 2.30794i\) of defining polynomial
Character \(\chi\) \(=\) 225.143
Dual form 225.4.f.c.107.3

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0.654378 0.756167i \(-0.272930\pi\)
−0.756167 + 0.654378i \(0.772930\pi\)
\(3\) 0 0
\(4\) 7.83422i 0.979278i
\(5\) 0 0
\(6\) 0 0
\(7\) −15.0557 + 15.0557i −0.812931 + 0.812931i −0.985072 0.172141i \(-0.944931\pi\)
0.172141 + 0.985072i \(0.444931\pi\)
\(8\) −4.55871 + 4.55871i −0.201468 + 0.201468i
\(9\) 0 0
\(10\) 0 0
\(11\) 27.9992i 0.767462i 0.923445 + 0.383731i \(0.125361\pi\)
−0.923445 + 0.383731i \(0.874639\pi\)
\(12\) 0 0
\(13\) −2.49862 2.49862i −0.0533071 0.0533071i 0.679951 0.733258i \(-0.262001\pi\)
−0.733258 + 0.679951i \(0.762001\pi\)
\(14\) 8.66913 0.165494
\(15\) 0 0
\(16\) −60.0489 −0.938264
\(17\) 67.9104 + 67.9104i 0.968864 + 0.968864i 0.999530 0.0306653i \(-0.00976260\pi\)
−0.0306653 + 0.999530i \(0.509763\pi\)
\(18\) 0 0
\(19\) 95.2200i 1.14974i 0.818246 + 0.574868i \(0.194946\pi\)
−0.818246 + 0.574868i \(0.805054\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 8.06104 8.06104i 0.0781191 0.0781191i
\(23\) 121.994 121.994i 1.10598 1.10598i 0.112302 0.993674i \(-0.464178\pi\)
0.993674 0.112302i \(-0.0358224\pi\)
\(24\) 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 −0.231578 + 0.972816i \(0.574389\pi\)
−0.972816 + 0.231578i \(0.925611\pi\)
\(38\) 27.4140 27.4140i 0.117030 0.117030i
\(39\) 0 0
\(40\) 0 0
\(41\) 453.748i 1.72838i 0.503166 + 0.864190i \(0.332168\pi\)
−0.503166 + 0.864190i \(0.667832\pi\)
\(42\) 0 0
\(43\) −30.5679 30.5679i −0.108409 0.108409i 0.650822 0.759230i \(-0.274424\pi\)
−0.759230 + 0.650822i \(0.774424\pi\)
\(44\) 219.352 0.751559
\(45\) 0 0
\(46\) −70.2445 −0.225152
\(47\) 254.600 + 254.600i 0.790153 + 0.790153i 0.981519 0.191365i \(-0.0612915\pi\)
−0.191365 + 0.981519i \(0.561292\pi\)
\(48\) 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 −0.935068 0.354470i \(-0.884661\pi\)
0.354470 + 0.935068i \(0.384661\pi\)
\(54\) 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 −0.0866805 0.996236i \(-0.527626\pi\)
0.996236 + 0.0866805i \(0.0276259\pi\)
\(68\) 532.025 532.025i 0.948788 0.948788i
\(69\) 0 0
\(70\) 0 0
\(71\) 609.904i 1.01947i −0.860332 0.509735i \(-0.829744\pi\)
0.860332 0.509735i \(-0.170256\pi\)
\(72\) 0 0
\(73\) 74.6843 + 74.6843i 0.119742 + 0.119742i 0.764438 0.644697i \(-0.223016\pi\)
−0.644697 + 0.764438i \(0.723016\pi\)
\(74\) 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 \(-0.906507\pi\)
0.957174 0.289513i \(-0.0934935\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 130.635 130.635i 0.175930 0.175930i
\(83\) −652.278 + 652.278i −0.862613 + 0.862613i −0.991641 0.129028i \(-0.958814\pi\)
0.129028 + 0.991641i \(0.458814\pi\)
\(84\) 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 −0.935918 0.352217i \(-0.885428\pi\)
0.352217 + 0.935918i \(0.385428\pi\)
\(98\) −31.7693 + 31.7693i −0.0327468 + 0.0327468i
\(99\) 0 0
\(100\) 0 0
\(101\) 299.833i 0.295391i −0.989033 0.147695i \(-0.952814\pi\)
0.989033 0.147695i \(-0.0471855\pi\)
\(102\) 0 0
\(103\) −577.974 577.974i −0.552907 0.552907i 0.374372 0.927279i \(-0.377858\pi\)
−0.927279 + 0.374372i \(0.877858\pi\)
\(104\) 22.7810 0.0214794
\(105\) 0 0
\(106\) 128.992 0.118197
\(107\) −216.994 216.994i −0.196053 0.196053i 0.602253 0.798305i \(-0.294270\pi\)
−0.798305 + 0.602253i \(0.794270\pi\)
\(108\) 0 0
\(109\) 936.415i 0.822865i −0.911440 0.411432i \(-0.865029\pi\)
0.911440 0.411432i \(-0.134971\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 904.077 904.077i 0.762743 0.762743i
\(113\) −1084.00 + 1084.00i −0.902428 + 0.902428i −0.995646 0.0932173i \(-0.970285\pi\)
0.0932173 + 0.995646i \(0.470285\pi\)
\(114\) 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 −0.310769 0.950486i \(-0.600586\pi\)
0.950486 + 0.310769i \(0.100586\pi\)
\(128\) 559.457 559.457i 0.386324 0.386324i
\(129\) 0 0
\(130\) 0 0
\(131\) 629.329i 0.419731i −0.977730 0.209865i \(-0.932697\pi\)
0.977730 0.209865i \(-0.0673026\pi\)
\(132\) 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 0.882494 0.470325i \(-0.155863\pi\)
−0.470325 + 0.882494i \(0.655863\pi\)
\(138\) 0 0
\(139\) 1378.35i 0.841081i 0.907274 + 0.420540i \(0.138160\pi\)
−0.907274 + 0.420540i \(0.861840\pi\)
\(140\) 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 −0.956240 0.292582i \(-0.905486\pi\)
0.292582 + 0.956240i \(0.405486\pi\)
\(158\) −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 0.725795 0.687911i \(-0.241472\pi\)
−0.687911 + 0.725795i \(0.741472\pi\)
\(164\) 3554.77 1.69256
\(165\) 0 0
\(166\) 375.585 0.175609
\(167\) 428.116 + 428.116i 0.198375 + 0.198375i 0.799303 0.600928i \(-0.205202\pi\)
−0.600928 + 0.799303i \(0.705202\pi\)
\(168\) 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 −0.332122 0.943236i \(-0.607765\pi\)
0.943236 + 0.332122i \(0.107765\pi\)
\(174\) 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 \(0.137770\pi\)
−0.907787 + 0.419431i \(0.862230\pi\)
\(192\) 0 0
\(193\) 1964.16 + 1964.16i 0.732556 + 0.732556i 0.971125 0.238569i \(-0.0766785\pi\)
−0.238569 + 0.971125i \(0.576678\pi\)
\(194\) 321.087 0.118828
\(195\) 0 0
\(196\) −864.488 −0.315047
\(197\) 2700.70 + 2700.70i 0.976735 + 0.976735i 0.999735 0.0230004i \(-0.00732189\pi\)
−0.0230004 + 0.999735i \(0.507322\pi\)
\(198\) 0 0
\(199\) 841.195i 0.299652i 0.988712 + 0.149826i \(0.0478713\pi\)
−0.988712 + 0.149826i \(0.952129\pi\)
\(200\) 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 −0.996402 0.0847496i \(-0.972991\pi\)
−0.0847496 0.996402i \(-0.527009\pi\)
\(224\) −1618.72 −0.482837
\(225\) 0 0
\(226\) 624.173 0.183714
\(227\) 1734.81 + 1734.81i 0.507239 + 0.507239i 0.913678 0.406439i \(-0.133230\pi\)
−0.406439 + 0.913678i \(0.633230\pi\)
\(228\) 0 0
\(229\) 3467.74i 1.00067i 0.865831 + 0.500337i \(0.166791\pi\)
−0.865831 + 0.500337i \(0.833209\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −451.700 + 451.700i −0.127826 + 0.127826i
\(233\) 1070.17 1070.17i 0.300899 0.300899i −0.540467 0.841365i \(-0.681752\pi\)
0.841365 + 0.540467i \(0.181752\pi\)
\(234\) 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 \(-0.905048\pi\)
0.955837 0.293897i \(-0.0949523\pi\)
\(252\) 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 0.578419 0.815740i \(-0.303670\pi\)
−0.815740 + 0.578419i \(0.803670\pi\)
\(258\) 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 −0.793697 0.608313i \(-0.791847\pi\)
0.608313 + 0.793697i \(0.291847\pi\)
\(264\) 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 −0.798694 0.601737i \(-0.794475\pi\)
0.601737 + 0.798694i \(0.294475\pi\)
\(278\) 396.830 396.830i 0.0856126 0.0856126i
\(279\) 0 0
\(280\) 0 0
\(281\) 7102.70i 1.50787i −0.656949 0.753935i \(-0.728153\pi\)
0.656949 0.753935i \(-0.271847\pi\)
\(282\) 0 0
\(283\) 4721.93 + 4721.93i 0.991837 + 0.991837i 0.999967 0.00813014i \(-0.00258793\pi\)
−0.00813014 + 0.999967i \(0.502588\pi\)
\(284\) −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 −0.468841 0.883283i \(-0.655328\pi\)
0.883283 + 0.468841i \(0.155328\pi\)
\(294\) 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 −0.00989542 0.999951i \(-0.503150\pi\)
0.999951 + 0.00989542i \(0.00314986\pi\)
\(308\) −3302.50 + 3302.50i −0.610966 + 0.610966i
\(309\) 0 0
\(310\) 0 0
\(311\) 2005.56i 0.365676i 0.983143 + 0.182838i \(0.0585283\pi\)
−0.983143 + 0.182838i \(0.941472\pi\)
\(312\) 0 0
\(313\) −5026.49 5026.49i −0.907713 0.907713i 0.0883746 0.996087i \(-0.471833\pi\)
−0.996087 + 0.0883746i \(0.971833\pi\)
\(314\) 751.742 0.135106
\(315\) 0 0
\(316\) −3185.19 −0.567028
\(317\) 3137.15 + 3137.15i 0.555836 + 0.555836i 0.928119 0.372283i \(-0.121425\pi\)
−0.372283 + 0.928119i \(0.621425\pi\)
\(318\) 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 −0.0319428 0.999490i \(-0.510169\pi\)
0.999490 + 0.0319428i \(0.0101694\pi\)
\(338\) −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 −0.948130 0.317881i \(-0.897029\pi\)
−0.317881 0.948130i \(-0.602971\pi\)
\(348\) 0 0
\(349\) 1421.22i 0.217983i 0.994043 + 0.108991i \(0.0347621\pi\)
−0.994043 + 0.108991i \(0.965238\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1505.18 + 1505.18i −0.227916 + 0.227916i
\(353\) 1399.56 1399.56i 0.211023 0.211023i −0.593679 0.804702i \(-0.702325\pi\)
0.804702 + 0.593679i \(0.202325\pi\)
\(354\) 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 −0.951730 0.306938i \(-0.900696\pi\)
0.306938 + 0.951730i \(0.400696\pi\)
\(368\) −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 0.873620 0.486609i \(-0.161766\pi\)
−0.486609 + 0.873620i \(0.661766\pi\)
\(374\) 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 \(-0.807002\pi\)
0.821749 0.569849i \(-0.192998\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 637.508 637.508i 0.0853868 0.0853868i
\(383\) 8507.38 8507.38i 1.13500 1.13500i 0.145672 0.989333i \(-0.453466\pi\)
0.989333 0.145672i \(-0.0465343\pi\)
\(384\) 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 −0.817047 0.576571i \(-0.804390\pi\)
0.576571 + 0.817047i \(0.304390\pi\)
\(398\) 242.182 242.182i 0.0305012 0.0305012i
\(399\) 0 0
\(400\) 0 0
\(401\) 13640.1i 1.69864i 0.527882 + 0.849318i \(0.322986\pi\)
−0.527882 + 0.849318i \(0.677014\pi\)
\(402\) 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 \(0.126340\pi\)
−0.922260 + 0.386569i \(0.873660\pi\)
\(410\) 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 \(-0.844713\pi\)
0.883344 0.468725i \(-0.155287\pi\)
\(432\) 0 0
\(433\) 4132.17 + 4132.17i 0.458613 + 0.458613i 0.898200 0.439587i \(-0.144875\pi\)
−0.439587 + 0.898200i \(0.644875\pi\)
\(434\) −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 \(0.193333\pi\)
−0.821149 + 0.570714i \(0.806667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −97.7038 + 97.7038i −0.0105142 + 0.0105142i
\(443\) 1465.93 1465.93i 0.157220 0.157220i −0.624114 0.781333i \(-0.714540\pi\)
0.781333 + 0.624114i \(0.214540\pi\)
\(444\) 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 −0.997570 0.0696767i \(-0.977803\pi\)
0.0696767 + 0.997570i \(0.477803\pi\)
\(458\) 998.368 998.368i 0.101857 0.101857i
\(459\) 0 0
\(460\) 0 0
\(461\) 13305.5i 1.34424i 0.740440 + 0.672122i \(0.234617\pi\)
−0.740440 + 0.672122i \(0.765383\pi\)
\(462\) 0 0
\(463\) 3124.86 + 3124.86i 0.313660 + 0.313660i 0.846326 0.532666i \(-0.178810\pi\)
−0.532666 + 0.846326i \(0.678810\pi\)
\(464\) −5949.95 −0.595301
\(465\) 0 0
\(466\) −616.210 −0.0612562
\(467\) 4255.07 + 4255.07i 0.421629 + 0.421629i 0.885764 0.464135i \(-0.153635\pi\)
−0.464135 + 0.885764i \(0.653635\pi\)
\(468\) 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 −0.538469 0.842645i \(-0.680997\pi\)
0.842645 + 0.538469i \(0.180997\pi\)
\(488\) 1205.19 1205.19i 0.111796 0.111796i
\(489\) 0 0
\(490\) 0 0
\(491\) 18791.1i 1.72715i −0.504220 0.863575i \(-0.668220\pi\)
0.504220 0.863575i \(-0.331780\pi\)
\(492\) 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 \(-0.895010\pi\)
0.946095 0.323889i \(-0.104990\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −672.947 + 672.947i −0.0598308 + 0.0598308i
\(503\) 2081.38 2081.38i 0.184501 0.184501i −0.608813 0.793314i \(-0.708354\pi\)
0.793314 + 0.608813i \(0.208354\pi\)
\(504\) 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 \(0.165824\pi\)
−0.867347 + 0.497705i \(0.834176\pi\)
\(522\) 0 0
\(523\) 5538.72 + 5538.72i 0.463081 + 0.463081i 0.899664 0.436583i \(-0.143811\pi\)
−0.436583 + 0.899664i \(0.643811\pi\)
\(524\) −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 −0.536121 0.844141i \(-0.680111\pi\)
0.844141 + 0.536121i \(0.180111\pi\)
\(548\) 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 0.590320 0.807170i \(-0.299002\pi\)
−0.807170 + 0.590320i \(0.799002\pi\)
\(558\) 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 −0.999288 0.0377198i \(-0.987991\pi\)
0.0377198 + 0.999288i \(0.487991\pi\)
\(564\) 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 −0.733995 0.679155i \(-0.762346\pi\)
0.679155 + 0.733995i \(0.262346\pi\)
\(578\) 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 0.359139 0.933284i \(-0.383071\pi\)
−0.933284 + 0.359139i \(0.883071\pi\)
\(588\) 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 −0.277758 0.960651i \(-0.589591\pi\)
0.960651 + 0.277758i \(0.0895913\pi\)
\(594\) 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 0.161565 0.986862i \(-0.448346\pi\)
0.986862 0.161565i \(-0.0516540\pi\)
\(608\) −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 0.207691 0.978195i \(-0.433405\pi\)
−0.978195 + 0.207691i \(0.933405\pi\)
\(614\) −3066.49 −0.201553
\(615\) 0 0
\(616\) 3843.43 0.251390
\(617\) −5586.69 5586.69i −0.364525 0.364525i 0.500951 0.865476i \(-0.332984\pi\)
−0.865476 + 0.500951i \(0.832984\pi\)
\(618\) 0 0
\(619\) 16137.1i 1.04783i 0.851771 + 0.523914i \(0.175529\pi\)
−0.851771 + 0.523914i \(0.824471\pi\)
\(620\) 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 \(-0.920147\pi\)
0.968698 0.248242i \(-0.0798528\pi\)
\(642\) 0 0
\(643\) −15024.4 15024.4i −0.921471 0.921471i 0.0756629 0.997133i \(-0.475893\pi\)
−0.997133 + 0.0756629i \(0.975893\pi\)
\(644\) 28778.2 1.76090
\(645\) 0 0
\(646\) 3723.40 0.226773
\(647\) −2396.69 2396.69i −0.145631 0.145631i 0.630532 0.776163i \(-0.282837\pi\)
−0.776163 + 0.630532i \(0.782837\pi\)
\(648\) 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 −0.953076 0.302732i \(-0.902101\pi\)
0.302732 + 0.953076i \(0.402101\pi\)
\(654\) 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 0.751932 0.659241i \(-0.229122\pi\)
−0.659241 + 0.751932i \(0.729122\pi\)
\(674\) −3446.61 −0.196971
\(675\) 0 0
\(676\) −17114.0 −0.973713
\(677\) −16119.8 16119.8i −0.915118 0.915118i 0.0815511 0.996669i \(-0.474013\pi\)
−0.996669 + 0.0815511i \(0.974013\pi\)
\(678\) 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 −0.411351 + 0.911477i \(0.634943\pi\)
−0.911477 + 0.411351i \(0.865057\pi\)
\(684\) 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 \(0.355616\pi\)
−0.438200 + 0.898878i \(0.644384\pi\)
\(702\) 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 \(-0.957832\pi\)
0.991238 0.132087i \(-0.0421677\pi\)
\(710\) 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 −0.402371 0.915477i \(-0.631814\pi\)
0.915477 + 0.402371i \(0.131814\pi\)
\(728\) −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 0.805167 0.593048i \(-0.202076\pi\)
−0.593048 + 0.805167i \(0.702076\pi\)
\(734\) 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 \(-0.962278\pi\)
0.992986 0.118231i \(-0.0377223\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1942.07 + 1942.07i −0.0960857 + 0.0960857i
\(743\) 16266.1 16266.1i 0.803159 0.803159i −0.180429 0.983588i \(-0.557749\pi\)
0.983588 + 0.180429i \(0.0577487\pi\)
\(744\) 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 −0.527048 0.849836i \(-0.676701\pi\)
0.849836 + 0.527048i \(0.176701\pi\)
\(758\) −2420.99 + 2420.99i −0.116008 + 0.116008i
\(759\) 0 0
\(760\) 0 0
\(761\) 7001.94i 0.333535i 0.985996 + 0.166767i \(0.0533329\pi\)
−0.985996 + 0.166767i \(0.946667\pi\)
\(762\) 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 \(0.200991\pi\)
−0.807183 + 0.590301i \(0.799009\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15387.7 15387.7i 0.717376 0.717376i
\(773\) 7322.13 7322.13i 0.340697 0.340697i −0.515932 0.856629i \(-0.672554\pi\)
0.856629 + 0.515932i \(0.172554\pi\)
\(774\) 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 −0.976446 0.215763i \(-0.930776\pi\)
0.215763 + 0.976446i \(0.430776\pi\)
\(788\) 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