Properties

Label 225.4.f.c.107.4
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: \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) Copy content Toggle raw display
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 107.4
Root \(-2.02004 + 2.30794i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.c.143.4

$q$-expansion

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

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 −0.654378 0.756167i \(-0.727070\pi\)
0.756167 + 0.654378i \(0.227070\pi\)
\(3\) 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 \(0.125361\pi\)
−0.923445 + 0.383731i \(0.874639\pi\)
\(12\) 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 −0.999530 0.0306653i \(-0.990237\pi\)
0.0306653 + 0.999530i \(0.490237\pi\)
\(18\) 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 \(-0.964178\pi\)
−0.112302 0.993674i \(-0.535822\pi\)
\(24\) 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 \(-0.602755\pi\)
−0.317235 + 0.948347i \(0.602755\pi\)
\(30\) 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 \(0.332168\pi\)
−0.503166 + 0.864190i \(0.667832\pi\)
\(42\) 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 −0.981519 0.191365i \(-0.938708\pi\)
0.191365 + 0.981519i \(0.438708\pi\)
\(48\) 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 \(-0.115339\pi\)
−0.354470 + 0.935068i \(0.615339\pi\)
\(54\) 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 \(-0.320996\pi\)
0.533182 + 0.846001i \(0.320996\pi\)
\(60\) 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 \(-0.829744\pi\)
0.860332 0.509735i \(-0.170256\pi\)
\(72\) 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 0.991641 0.129028i \(-0.0411858\pi\)
−0.129028 + 0.991641i \(0.541186\pi\)
\(84\) 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 \(-0.526542\pi\)
−0.0832873 + 0.996526i \(0.526542\pi\)
\(90\) 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 \(-0.952814\pi\)
0.989033 0.147695i \(-0.0471855\pi\)
\(102\) 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 −0.602253 0.798305i \(-0.705730\pi\)
0.798305 + 0.602253i \(0.205730\pi\)
\(108\) 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 0.995646 0.0932173i \(-0.0297151\pi\)
−0.0932173 + 0.995646i \(0.529715\pi\)
\(114\) 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 \(-0.932697\pi\)
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 \(-0.844137\pi\)
0.470325 + 0.882494i \(0.344137\pi\)
\(138\) 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 \(-0.581817\pi\)
−0.254215 + 0.967148i \(0.581817\pi\)
\(150\) 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 −0.799303 0.600928i \(-0.794798\pi\)
0.600928 + 0.799303i \(0.294798\pi\)
\(168\) 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 \(-0.392235\pi\)
−0.943236 + 0.332122i \(0.892235\pi\)
\(174\) 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 \(-0.492644\pi\)
0.0231065 + 0.999733i \(0.492644\pi\)
\(180\) 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 −0.238569 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 −0.999735 0.0230004i \(-0.992678\pi\)
0.0230004 + 0.999735i \(0.492678\pi\)
\(198\) 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 −0.913678 0.406439i \(-0.866770\pi\)
0.406439 + 0.913678i \(0.366770\pi\)
\(228\) 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 0.540467 0.841365i \(-0.318248\pi\)
−0.841365 + 0.540467i \(0.818248\pi\)
\(234\) 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 \(-0.677447\pi\)
−0.529038 + 0.848598i \(0.677447\pi\)
\(240\) 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 \(-0.696330\pi\)
0.815740 + 0.578419i \(0.196330\pi\)
\(258\) 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 \(-0.208153\pi\)
−0.608313 + 0.793697i \(0.708153\pi\)
\(264\) 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 \(-0.647920\pi\)
−0.448159 + 0.893954i \(0.647920\pi\)
\(270\) 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 \(-0.728153\pi\)
0.656949 0.753935i \(-0.271847\pi\)
\(282\) 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 0.468841 0.883283i \(-0.344672\pi\)
−0.883283 + 0.468841i \(0.844672\pi\)
\(294\) 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 \(0.0585283\pi\)
−0.983143 + 0.182838i \(0.941472\pi\)
\(312\) 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 −0.928119 0.372283i \(-0.878575\pi\)
0.372283 + 0.928119i \(0.378575\pi\)
\(318\) 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 \(-0.397029\pi\)
0.948130 0.317881i \(-0.102971\pi\)
\(348\) 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 0.593679 0.804702i \(-0.297675\pi\)
−0.804702 + 0.593679i \(0.797675\pi\)
\(354\) 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 \(-0.397288\pi\)
0.317108 + 0.948390i \(0.397288\pi\)
\(360\) 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 \(-0.953466\pi\)
−0.145672 0.989333i \(-0.546534\pi\)
\(384\) 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 \(-0.690409\pi\)
−0.563146 + 0.826357i \(0.690409\pi\)
\(390\) 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 \(0.322986\pi\)
−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 \(-0.873660\pi\)
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 \(-0.664490\pi\)
−0.494067 + 0.869424i \(0.664490\pi\)
\(420\) 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 −0.439587 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 0.624114 0.781333i \(-0.285460\pi\)
−0.781333 + 0.624114i \(0.785460\pi\)
\(444\) 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 \(-0.607334\pi\)
−0.330846 + 0.943685i \(0.607334\pi\)
\(450\) 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 \(0.234617\pi\)
−0.740440 + 0.672122i \(0.765383\pi\)
\(462\) 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 −0.885764 0.464135i \(-0.846365\pi\)
0.464135 + 0.885764i \(0.346365\pi\)
\(468\) 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 \(-0.330843\pi\)
0.506761 + 0.862087i \(0.330843\pi\)
\(480\) 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 \(-0.668220\pi\)
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 \(0.104990\pi\)
−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 0.608813 0.793314i \(-0.291646\pi\)
−0.793314 + 0.608813i \(0.791646\pi\)
\(504\) 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 \(-0.685242\pi\)
−0.549659 + 0.835389i \(0.685242\pi\)
\(510\) 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 −0.436583 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 −0.590320 0.807170i \(-0.700998\pi\)
0.807170 + 0.590320i \(0.200998\pi\)
\(558\) 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 \(-0.0120094\pi\)
−0.0377198 + 0.999288i \(0.512009\pi\)
\(564\) 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 \(-0.874800\pi\)
−0.923639 + 0.383263i \(0.874800\pi\)
\(570\) 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 −0.359139 0.933284i \(-0.616929\pi\)
0.933284 + 0.359139i \(0.116929\pi\)
\(588\) 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 \(-0.410409\pi\)
−0.960651 + 0.277758i \(0.910409\pi\)
\(594\) 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 \(-0.249434\pi\)
0.708363 + 0.705848i \(0.249434\pi\)
\(600\) 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 −0.500951 0.865476i \(-0.667016\pi\)
0.865476 + 0.500951i \(0.167016\pi\)
\(618\) 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 \(-0.920147\pi\)
0.968698 0.248242i \(-0.0798528\pi\)
\(642\) 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 −0.630532 0.776163i \(-0.717163\pi\)
0.776163 + 0.630532i \(0.217163\pi\)
\(648\) 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 \(-0.0978988\pi\)
−0.302732 + 0.953076i \(0.597899\pi\)
\(654\) 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 \(-0.284879\pi\)
0.625538 + 0.780193i \(0.284879\pi\)
\(660\) 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 −0.0815511 0.996669i \(-0.525987\pi\)
0.996669 + 0.0815511i \(0.0259874\pi\)
\(678\) 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 \(0.134943\pi\)
0.411351 + 0.911477i \(0.365057\pi\)
\(684\) 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 \(0.0421677\pi\)
−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 \(-0.837095\pi\)
−0.871873 + 0.489732i \(0.837095\pi\)
\(720\) 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 0.180429 0.983588i \(-0.442251\pi\)
−0.983588 + 0.180429i \(0.942251\pi\)
\(744\) 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 \(0.0533329\pi\)
−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 \(-0.799009\pi\)
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 0.515932 0.856629i \(-0.327446\pi\)
−0.856629 + 0.515932i \(0.827446\pi\)
\(774\) 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
\(792\)