Properties

Label 405.4.e.j.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.j.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +24.0000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +24.0000 q^{8} -10.0000 q^{10} +(-5.00000 - 8.66025i) q^{11} +(40.0000 - 69.2820i) q^{13} +(8.00000 + 13.8564i) q^{16} +7.00000 q^{17} -113.000 q^{19} +(10.0000 + 17.3205i) q^{20} +(10.0000 - 17.3205i) q^{22} +(40.5000 - 70.1481i) q^{23} +(-12.5000 - 21.6506i) q^{25} +160.000 q^{26} +(110.000 + 190.526i) q^{29} +(94.5000 - 163.679i) q^{31} +(80.0000 - 138.564i) q^{32} +(7.00000 + 12.1244i) q^{34} +170.000 q^{37} +(-113.000 - 195.722i) q^{38} +(-60.0000 + 103.923i) q^{40} +(65.0000 - 112.583i) q^{41} +(-5.00000 - 8.66025i) q^{43} -40.0000 q^{44} +162.000 q^{46} +(-80.0000 - 138.564i) q^{47} +(171.500 - 297.047i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-160.000 - 277.128i) q^{52} +631.000 q^{53} +50.0000 q^{55} +(-220.000 + 381.051i) q^{58} +(280.000 - 484.974i) q^{59} +(-114.500 - 198.320i) q^{61} +378.000 q^{62} +448.000 q^{64} +(200.000 + 346.410i) q^{65} +(-375.000 + 649.519i) q^{67} +(14.0000 - 24.2487i) q^{68} +890.000 q^{71} -890.000 q^{73} +(170.000 + 294.449i) q^{74} +(-226.000 + 391.443i) q^{76} +(13.5000 + 23.3827i) q^{79} -80.0000 q^{80} +260.000 q^{82} +(-214.500 - 371.525i) q^{83} +(-17.5000 + 30.3109i) q^{85} +(10.0000 - 17.3205i) q^{86} +(-120.000 - 207.846i) q^{88} -750.000 q^{89} +(-162.000 - 280.592i) q^{92} +(160.000 - 277.128i) q^{94} +(282.500 - 489.304i) q^{95} +(740.000 + 1281.72i) q^{97} +686.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 4 q^{4} - 5 q^{5} + 48 q^{8} + O(q^{10}) \) \( 2 q + 2 q^{2} + 4 q^{4} - 5 q^{5} + 48 q^{8} - 20 q^{10} - 10 q^{11} + 80 q^{13} + 16 q^{16} + 14 q^{17} - 226 q^{19} + 20 q^{20} + 20 q^{22} + 81 q^{23} - 25 q^{25} + 320 q^{26} + 220 q^{29} + 189 q^{31} + 160 q^{32} + 14 q^{34} + 340 q^{37} - 226 q^{38} - 120 q^{40} + 130 q^{41} - 10 q^{43} - 80 q^{44} + 324 q^{46} - 160 q^{47} + 343 q^{49} + 50 q^{50} - 320 q^{52} + 1262 q^{53} + 100 q^{55} - 440 q^{58} + 560 q^{59} - 229 q^{61} + 756 q^{62} + 896 q^{64} + 400 q^{65} - 750 q^{67} + 28 q^{68} + 1780 q^{71} - 1780 q^{73} + 340 q^{74} - 452 q^{76} + 27 q^{79} - 160 q^{80} + 520 q^{82} - 429 q^{83} - 35 q^{85} + 20 q^{86} - 240 q^{88} - 1500 q^{89} - 324 q^{92} + 320 q^{94} + 565 q^{95} + 1480 q^{97} + 1372 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0 0
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 24.0000 1.06066
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) −5.00000 8.66025i −0.137051 0.237379i 0.789328 0.613971i \(-0.210429\pi\)
−0.926379 + 0.376593i \(0.877096\pi\)
\(12\) 0 0
\(13\) 40.0000 69.2820i 0.853385 1.47811i −0.0247504 0.999694i \(-0.507879\pi\)
0.878135 0.478412i \(-0.158788\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 8.00000 + 13.8564i 0.125000 + 0.216506i
\(17\) 7.00000 0.0998676 0.0499338 0.998753i \(-0.484099\pi\)
0.0499338 + 0.998753i \(0.484099\pi\)
\(18\) 0 0
\(19\) −113.000 −1.36442 −0.682210 0.731156i \(-0.738981\pi\)
−0.682210 + 0.731156i \(0.738981\pi\)
\(20\) 10.0000 + 17.3205i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 10.0000 17.3205i 0.0969094 0.167852i
\(23\) 40.5000 70.1481i 0.367167 0.635951i −0.621955 0.783053i \(-0.713661\pi\)
0.989121 + 0.147102i \(0.0469945\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 160.000 1.20687
\(27\) 0 0
\(28\) 0 0
\(29\) 110.000 + 190.526i 0.704362 + 1.21999i 0.966921 + 0.255074i \(0.0821000\pi\)
−0.262560 + 0.964916i \(0.584567\pi\)
\(30\) 0 0
\(31\) 94.5000 163.679i 0.547506 0.948309i −0.450938 0.892555i \(-0.648910\pi\)
0.998445 0.0557538i \(-0.0177562\pi\)
\(32\) 80.0000 138.564i 0.441942 0.765466i
\(33\) 0 0
\(34\) 7.00000 + 12.1244i 0.0353085 + 0.0611562i
\(35\) 0 0
\(36\) 0 0
\(37\) 170.000 0.755347 0.377673 0.925939i \(-0.376724\pi\)
0.377673 + 0.925939i \(0.376724\pi\)
\(38\) −113.000 195.722i −0.482395 0.835533i
\(39\) 0 0
\(40\) −60.0000 + 103.923i −0.237171 + 0.410792i
\(41\) 65.0000 112.583i 0.247593 0.428843i −0.715265 0.698854i \(-0.753694\pi\)
0.962857 + 0.270011i \(0.0870272\pi\)
\(42\) 0 0
\(43\) −5.00000 8.66025i −0.0177324 0.0307134i 0.857023 0.515278i \(-0.172311\pi\)
−0.874755 + 0.484565i \(0.838978\pi\)
\(44\) −40.0000 −0.137051
\(45\) 0 0
\(46\) 162.000 0.519252
\(47\) −80.0000 138.564i −0.248281 0.430035i 0.714768 0.699362i \(-0.246532\pi\)
−0.963049 + 0.269327i \(0.913199\pi\)
\(48\) 0 0
\(49\) 171.500 297.047i 0.500000 0.866025i
\(50\) 25.0000 43.3013i 0.0707107 0.122474i
\(51\) 0 0
\(52\) −160.000 277.128i −0.426692 0.739053i
\(53\) 631.000 1.63537 0.817684 0.575667i \(-0.195258\pi\)
0.817684 + 0.575667i \(0.195258\pi\)
\(54\) 0 0
\(55\) 50.0000 0.122582
\(56\) 0 0
\(57\) 0 0
\(58\) −220.000 + 381.051i −0.498059 + 0.862663i
\(59\) 280.000 484.974i 0.617846 1.07014i −0.372032 0.928220i \(-0.621339\pi\)
0.989878 0.141920i \(-0.0453277\pi\)
\(60\) 0 0
\(61\) −114.500 198.320i −0.240332 0.416266i 0.720477 0.693479i \(-0.243923\pi\)
−0.960809 + 0.277212i \(0.910589\pi\)
\(62\) 378.000 0.774291
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) 200.000 + 346.410i 0.381645 + 0.661029i
\(66\) 0 0
\(67\) −375.000 + 649.519i −0.683784 + 1.18435i 0.290033 + 0.957017i \(0.406334\pi\)
−0.973817 + 0.227332i \(0.927000\pi\)
\(68\) 14.0000 24.2487i 0.0249669 0.0432439i
\(69\) 0 0
\(70\) 0 0
\(71\) 890.000 1.48766 0.743828 0.668371i \(-0.233008\pi\)
0.743828 + 0.668371i \(0.233008\pi\)
\(72\) 0 0
\(73\) −890.000 −1.42694 −0.713470 0.700686i \(-0.752878\pi\)
−0.713470 + 0.700686i \(0.752878\pi\)
\(74\) 170.000 + 294.449i 0.267055 + 0.462553i
\(75\) 0 0
\(76\) −226.000 + 391.443i −0.341105 + 0.590811i
\(77\) 0 0
\(78\) 0 0
\(79\) 13.5000 + 23.3827i 0.0192262 + 0.0333007i 0.875478 0.483257i \(-0.160546\pi\)
−0.856252 + 0.516558i \(0.827213\pi\)
\(80\) −80.0000 −0.111803
\(81\) 0 0
\(82\) 260.000 0.350149
\(83\) −214.500 371.525i −0.283668 0.491327i 0.688617 0.725125i \(-0.258218\pi\)
−0.972285 + 0.233798i \(0.924885\pi\)
\(84\) 0 0
\(85\) −17.5000 + 30.3109i −0.0223311 + 0.0386786i
\(86\) 10.0000 17.3205i 0.0125387 0.0217177i
\(87\) 0 0
\(88\) −120.000 207.846i −0.145364 0.251778i
\(89\) −750.000 −0.893257 −0.446628 0.894720i \(-0.647375\pi\)
−0.446628 + 0.894720i \(0.647375\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −162.000 280.592i −0.183583 0.317976i
\(93\) 0 0
\(94\) 160.000 277.128i 0.175561 0.304081i
\(95\) 282.500 489.304i 0.305094 0.528438i
\(96\) 0 0
\(97\) 740.000 + 1281.72i 0.774594 + 1.34164i 0.935022 + 0.354589i \(0.115379\pi\)
−0.160428 + 0.987047i \(0.551288\pi\)
\(98\) 686.000 0.707107
\(99\) 0 0
\(100\) −100.000 −0.100000
\(101\) 750.000 + 1299.04i 0.738889 + 1.27979i 0.952996 + 0.302983i \(0.0979826\pi\)
−0.214107 + 0.976810i \(0.568684\pi\)
\(102\) 0 0
\(103\) 230.000 398.372i 0.220025 0.381094i −0.734790 0.678294i \(-0.762719\pi\)
0.954815 + 0.297200i \(0.0960528\pi\)
\(104\) 960.000 1662.77i 0.905151 1.56777i
\(105\) 0 0
\(106\) 631.000 + 1092.92i 0.578190 + 1.00145i
\(107\) −420.000 −0.379467 −0.189733 0.981836i \(-0.560762\pi\)
−0.189733 + 0.981836i \(0.560762\pi\)
\(108\) 0 0
\(109\) −607.000 −0.533395 −0.266698 0.963780i \(-0.585932\pi\)
−0.266698 + 0.963780i \(0.585932\pi\)
\(110\) 50.0000 + 86.6025i 0.0433392 + 0.0750657i
\(111\) 0 0
\(112\) 0 0
\(113\) −1085.00 + 1879.28i −0.903259 + 1.56449i −0.0800206 + 0.996793i \(0.525499\pi\)
−0.823238 + 0.567696i \(0.807835\pi\)
\(114\) 0 0
\(115\) 202.500 + 350.740i 0.164202 + 0.284406i
\(116\) 880.000 0.704362
\(117\) 0 0
\(118\) 1120.00 0.873766
\(119\) 0 0
\(120\) 0 0
\(121\) 615.500 1066.08i 0.462434 0.800960i
\(122\) 229.000 396.640i 0.169940 0.294345i
\(123\) 0 0
\(124\) −378.000 654.715i −0.273753 0.474155i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1610.00 −1.12492 −0.562458 0.826826i \(-0.690144\pi\)
−0.562458 + 0.826826i \(0.690144\pi\)
\(128\) −192.000 332.554i −0.132583 0.229640i
\(129\) 0 0
\(130\) −400.000 + 692.820i −0.269864 + 0.467418i
\(131\) −1185.00 + 2052.48i −0.790335 + 1.36890i 0.135424 + 0.990788i \(0.456760\pi\)
−0.925759 + 0.378113i \(0.876573\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1500.00 −0.967017
\(135\) 0 0
\(136\) 168.000 0.105926
\(137\) −898.500 1556.25i −0.560321 0.970505i −0.997468 0.0711150i \(-0.977344\pi\)
0.437147 0.899390i \(-0.355989\pi\)
\(138\) 0 0
\(139\) 62.0000 107.387i 0.0378329 0.0655285i −0.846489 0.532406i \(-0.821288\pi\)
0.884322 + 0.466878i \(0.154621\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 890.000 + 1541.53i 0.525966 + 0.910999i
\(143\) −800.000 −0.467828
\(144\) 0 0
\(145\) −1100.00 −0.630000
\(146\) −890.000 1541.53i −0.504499 0.873819i
\(147\) 0 0
\(148\) 340.000 588.897i 0.188837 0.327075i
\(149\) 35.0000 60.6218i 0.0192437 0.0333311i −0.856243 0.516573i \(-0.827207\pi\)
0.875487 + 0.483242i \(0.160541\pi\)
\(150\) 0 0
\(151\) −1124.00 1946.83i −0.605760 1.04921i −0.991931 0.126780i \(-0.959536\pi\)
0.386170 0.922427i \(-0.373798\pi\)
\(152\) −2712.00 −1.44719
\(153\) 0 0
\(154\) 0 0
\(155\) 472.500 + 818.394i 0.244852 + 0.424097i
\(156\) 0 0
\(157\) −505.000 + 874.686i −0.256709 + 0.444634i −0.965358 0.260927i \(-0.915972\pi\)
0.708649 + 0.705561i \(0.249305\pi\)
\(158\) −27.0000 + 46.7654i −0.0135950 + 0.0235472i
\(159\) 0 0
\(160\) 400.000 + 692.820i 0.197642 + 0.342327i
\(161\) 0 0
\(162\) 0 0
\(163\) 590.000 0.283511 0.141756 0.989902i \(-0.454725\pi\)
0.141756 + 0.989902i \(0.454725\pi\)
\(164\) −260.000 450.333i −0.123796 0.214421i
\(165\) 0 0
\(166\) 429.000 743.050i 0.200583 0.347421i
\(167\) −1201.50 + 2081.06i −0.556736 + 0.964295i 0.441031 + 0.897492i \(0.354613\pi\)
−0.997766 + 0.0668024i \(0.978720\pi\)
\(168\) 0 0
\(169\) −2101.50 3639.90i −0.956532 1.65676i
\(170\) −70.0000 −0.0315809
\(171\) 0 0
\(172\) −40.0000 −0.0177324
\(173\) −400.500 693.686i −0.176008 0.304855i 0.764501 0.644622i \(-0.222985\pi\)
−0.940510 + 0.339767i \(0.889652\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 80.0000 138.564i 0.0342627 0.0593447i
\(177\) 0 0
\(178\) −750.000 1299.04i −0.315814 0.547006i
\(179\) −2360.00 −0.985445 −0.492723 0.870186i \(-0.663998\pi\)
−0.492723 + 0.870186i \(0.663998\pi\)
\(180\) 0 0
\(181\) 1241.00 0.509629 0.254814 0.966990i \(-0.417986\pi\)
0.254814 + 0.966990i \(0.417986\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 972.000 1683.55i 0.389439 0.674528i
\(185\) −425.000 + 736.122i −0.168901 + 0.292545i
\(186\) 0 0
\(187\) −35.0000 60.6218i −0.0136869 0.0237064i
\(188\) −640.000 −0.248281
\(189\) 0 0
\(190\) 1130.00 0.431467
\(191\) 2495.00 + 4321.47i 0.945193 + 1.63712i 0.755364 + 0.655305i \(0.227460\pi\)
0.189829 + 0.981817i \(0.439207\pi\)
\(192\) 0 0
\(193\) 1130.00 1957.22i 0.421447 0.729967i −0.574635 0.818410i \(-0.694856\pi\)
0.996081 + 0.0884432i \(0.0281892\pi\)
\(194\) −1480.00 + 2563.44i −0.547721 + 0.948680i
\(195\) 0 0
\(196\) −686.000 1188.19i −0.250000 0.433013i
\(197\) −2247.00 −0.812650 −0.406325 0.913729i \(-0.633190\pi\)
−0.406325 + 0.913729i \(0.633190\pi\)
\(198\) 0 0
\(199\) 4564.00 1.62580 0.812898 0.582406i \(-0.197889\pi\)
0.812898 + 0.582406i \(0.197889\pi\)
\(200\) −300.000 519.615i −0.106066 0.183712i
\(201\) 0 0
\(202\) −1500.00 + 2598.08i −0.522473 + 0.904951i
\(203\) 0 0
\(204\) 0 0
\(205\) 325.000 + 562.917i 0.110727 + 0.191784i
\(206\) 920.000 0.311162
\(207\) 0 0
\(208\) 1280.00 0.426692
\(209\) 565.000 + 978.609i 0.186995 + 0.323884i
\(210\) 0 0
\(211\) −2474.50 + 4285.96i −0.807354 + 1.39838i 0.107337 + 0.994223i \(0.465768\pi\)
−0.914691 + 0.404155i \(0.867566\pi\)
\(212\) 1262.00 2185.85i 0.408842 0.708135i
\(213\) 0 0
\(214\) −420.000 727.461i −0.134162 0.232375i
\(215\) 50.0000 0.0158603
\(216\) 0 0
\(217\) 0 0
\(218\) −607.000 1051.35i −0.188584 0.326636i
\(219\) 0 0
\(220\) 100.000 173.205i 0.0306454 0.0530795i
\(221\) 280.000 484.974i 0.0852255 0.147615i
\(222\) 0 0
\(223\) −1945.00 3368.84i −0.584067 1.01163i −0.994991 0.0999635i \(-0.968127\pi\)
0.410925 0.911669i \(-0.365206\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4340.00 −1.27740
\(227\) −1226.50 2124.36i −0.358615 0.621140i 0.629114 0.777313i \(-0.283418\pi\)
−0.987730 + 0.156173i \(0.950084\pi\)
\(228\) 0 0
\(229\) 3106.50 5380.62i 0.896434 1.55267i 0.0644134 0.997923i \(-0.479482\pi\)
0.832020 0.554745i \(-0.187184\pi\)
\(230\) −405.000 + 701.481i −0.116108 + 0.201105i
\(231\) 0 0
\(232\) 2640.00 + 4572.61i 0.747088 + 1.29399i
\(233\) −3450.00 −0.970030 −0.485015 0.874506i \(-0.661186\pi\)
−0.485015 + 0.874506i \(0.661186\pi\)
\(234\) 0 0
\(235\) 800.000 0.222069
\(236\) −1120.00 1939.90i −0.308923 0.535070i
\(237\) 0 0
\(238\) 0 0
\(239\) −3245.00 + 5620.50i −0.878249 + 1.52117i −0.0249888 + 0.999688i \(0.507955\pi\)
−0.853261 + 0.521485i \(0.825378\pi\)
\(240\) 0 0
\(241\) 1700.50 + 2945.35i 0.454518 + 0.787248i 0.998660 0.0517447i \(-0.0164782\pi\)
−0.544142 + 0.838993i \(0.683145\pi\)
\(242\) 2462.00 0.653981
\(243\) 0 0
\(244\) −916.000 −0.240332
\(245\) 857.500 + 1485.23i 0.223607 + 0.387298i
\(246\) 0 0
\(247\) −4520.00 + 7828.87i −1.16438 + 2.01676i
\(248\) 2268.00 3928.29i 0.580718 1.00583i
\(249\) 0 0
\(250\) 125.000 + 216.506i 0.0316228 + 0.0547723i
\(251\) −4980.00 −1.25233 −0.626165 0.779691i \(-0.715376\pi\)
−0.626165 + 0.779691i \(0.715376\pi\)
\(252\) 0 0
\(253\) −810.000 −0.201282
\(254\) −1610.00 2788.60i −0.397718 0.688868i
\(255\) 0 0
\(256\) 2176.00 3768.94i 0.531250 0.920152i
\(257\) −1678.50 + 2907.25i −0.407401 + 0.705639i −0.994598 0.103806i \(-0.966898\pi\)
0.587197 + 0.809444i \(0.300231\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1600.00 0.381645
\(261\) 0 0
\(262\) −4740.00 −1.11770
\(263\) 2270.00 + 3931.76i 0.532221 + 0.921834i 0.999292 + 0.0376145i \(0.0119759\pi\)
−0.467071 + 0.884220i \(0.654691\pi\)
\(264\) 0 0
\(265\) −1577.50 + 2732.31i −0.365679 + 0.633375i
\(266\) 0 0
\(267\) 0 0
\(268\) 1500.00 + 2598.08i 0.341892 + 0.592174i
\(269\) 8410.00 1.90620 0.953098 0.302662i \(-0.0978752\pi\)
0.953098 + 0.302662i \(0.0978752\pi\)
\(270\) 0 0
\(271\) 259.000 0.0580558 0.0290279 0.999579i \(-0.490759\pi\)
0.0290279 + 0.999579i \(0.490759\pi\)
\(272\) 56.0000 + 96.9948i 0.0124835 + 0.0216220i
\(273\) 0 0
\(274\) 1797.00 3112.50i 0.396207 0.686251i
\(275\) −125.000 + 216.506i −0.0274101 + 0.0474757i
\(276\) 0 0
\(277\) 2085.00 + 3611.33i 0.452258 + 0.783334i 0.998526 0.0542765i \(-0.0172852\pi\)
−0.546268 + 0.837611i \(0.683952\pi\)
\(278\) 248.000 0.0535038
\(279\) 0 0
\(280\) 0 0
\(281\) 870.000 + 1506.88i 0.184697 + 0.319905i 0.943474 0.331445i \(-0.107536\pi\)
−0.758777 + 0.651350i \(0.774203\pi\)
\(282\) 0 0
\(283\) 2535.00 4390.75i 0.532474 0.922272i −0.466807 0.884359i \(-0.654596\pi\)
0.999281 0.0379127i \(-0.0120709\pi\)
\(284\) 1780.00 3083.05i 0.371914 0.644174i
\(285\) 0 0
\(286\) −800.000 1385.64i −0.165402 0.286485i
\(287\) 0 0
\(288\) 0 0
\(289\) −4864.00 −0.990026
\(290\) −1100.00 1905.26i −0.222739 0.385795i
\(291\) 0 0
\(292\) −1780.00 + 3083.05i −0.356735 + 0.617883i
\(293\) 79.5000 137.698i 0.0158513 0.0274553i −0.857991 0.513665i \(-0.828287\pi\)
0.873842 + 0.486210i \(0.161621\pi\)
\(294\) 0 0
\(295\) 1400.00 + 2424.87i 0.276309 + 0.478581i
\(296\) 4080.00 0.801166
\(297\) 0 0
\(298\) 140.000 0.0272147
\(299\) −3240.00 5611.84i −0.626669 1.08542i
\(300\) 0 0
\(301\) 0 0
\(302\) 2248.00 3893.65i 0.428337 0.741902i
\(303\) 0 0
\(304\) −904.000 1565.77i −0.170552 0.295406i
\(305\) 1145.00 0.214959
\(306\) 0 0
\(307\) 6490.00 1.20653 0.603264 0.797542i \(-0.293867\pi\)
0.603264 + 0.797542i \(0.293867\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −945.000 + 1636.79i −0.173137 + 0.299882i
\(311\) 4110.00 7118.73i 0.749379 1.29796i −0.198742 0.980052i \(-0.563686\pi\)
0.948121 0.317910i \(-0.102981\pi\)
\(312\) 0 0
\(313\) 2330.00 + 4035.68i 0.420765 + 0.728786i 0.996014 0.0891919i \(-0.0284284\pi\)
−0.575250 + 0.817978i \(0.695095\pi\)
\(314\) −2020.00 −0.363042
\(315\) 0 0
\(316\) 108.000 0.0192262
\(317\) 3408.50 + 5903.70i 0.603913 + 1.04601i 0.992222 + 0.124479i \(0.0397259\pi\)
−0.388309 + 0.921529i \(0.626941\pi\)
\(318\) 0 0
\(319\) 1100.00 1905.26i 0.193066 0.334401i
\(320\) −1120.00 + 1939.90i −0.195656 + 0.338886i
\(321\) 0 0
\(322\) 0 0
\(323\) −791.000 −0.136261
\(324\) 0 0
\(325\) −2000.00 −0.341354
\(326\) 590.000 + 1021.91i 0.100236 + 0.173615i
\(327\) 0 0
\(328\) 1560.00 2702.00i 0.262612 0.454857i
\(329\) 0 0
\(330\) 0 0
\(331\) −96.0000 166.277i −0.0159415 0.0276115i 0.857945 0.513742i \(-0.171741\pi\)
−0.873886 + 0.486131i \(0.838408\pi\)
\(332\) −1716.00 −0.283668
\(333\) 0 0
\(334\) −4806.00 −0.787343
\(335\) −1875.00 3247.60i −0.305798 0.529657i
\(336\) 0 0
\(337\) −2420.00 + 4191.56i −0.391174 + 0.677534i −0.992605 0.121391i \(-0.961264\pi\)
0.601430 + 0.798925i \(0.294598\pi\)
\(338\) 4203.00 7279.81i 0.676370 1.17151i
\(339\) 0 0
\(340\) 70.0000 + 121.244i 0.0111655 + 0.0193393i
\(341\) −1890.00 −0.300144
\(342\) 0 0
\(343\) 0 0
\(344\) −120.000 207.846i −0.0188080 0.0325765i
\(345\) 0 0
\(346\) 801.000 1387.37i 0.124457 0.215565i
\(347\) 430.000 744.782i 0.0665234 0.115222i −0.830845 0.556503i \(-0.812143\pi\)
0.897369 + 0.441282i \(0.145476\pi\)
\(348\) 0 0
\(349\) −2688.50 4656.62i −0.412356 0.714221i 0.582791 0.812622i \(-0.301961\pi\)
−0.995147 + 0.0984011i \(0.968627\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1600.00 −0.242274
\(353\) 4005.00 + 6936.86i 0.603866 + 1.04593i 0.992230 + 0.124420i \(0.0397071\pi\)
−0.388364 + 0.921506i \(0.626960\pi\)
\(354\) 0 0
\(355\) −2225.00 + 3853.81i −0.332650 + 0.576167i
\(356\) −1500.00 + 2598.08i −0.223314 + 0.386791i
\(357\) 0 0
\(358\) −2360.00 4087.64i −0.348407 0.603459i
\(359\) 12930.0 1.90089 0.950445 0.310894i \(-0.100628\pi\)
0.950445 + 0.310894i \(0.100628\pi\)
\(360\) 0 0
\(361\) 5910.00 0.861642
\(362\) 1241.00 + 2149.48i 0.180181 + 0.312083i
\(363\) 0 0
\(364\) 0 0
\(365\) 2225.00 3853.81i 0.319073 0.552651i
\(366\) 0 0
\(367\) 3000.00 + 5196.15i 0.426700 + 0.739065i 0.996577 0.0826641i \(-0.0263429\pi\)
−0.569878 + 0.821729i \(0.693010\pi\)
\(368\) 1296.00 0.183583
\(369\) 0 0
\(370\) −1700.00 −0.238862
\(371\) 0 0
\(372\) 0 0
\(373\) 70.0000 121.244i 0.00971706 0.0168304i −0.861126 0.508392i \(-0.830240\pi\)
0.870843 + 0.491561i \(0.163574\pi\)
\(374\) 70.0000 121.244i 0.00967811 0.0167630i
\(375\) 0 0
\(376\) −1920.00 3325.54i −0.263342 0.456121i
\(377\) 17600.0 2.40437
\(378\) 0 0
\(379\) 6217.00 0.842601 0.421301 0.906921i \(-0.361574\pi\)
0.421301 + 0.906921i \(0.361574\pi\)
\(380\) −1130.00 1957.22i −0.152547 0.264219i
\(381\) 0 0
\(382\) −4990.00 + 8642.93i −0.668352 + 1.15762i
\(383\) −2275.50 + 3941.28i −0.303584 + 0.525823i −0.976945 0.213491i \(-0.931517\pi\)
0.673361 + 0.739314i \(0.264850\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4520.00 0.596015
\(387\) 0 0
\(388\) 5920.00 0.774594
\(389\) 1155.00 + 2000.52i 0.150542 + 0.260746i 0.931427 0.363929i \(-0.118565\pi\)
−0.780885 + 0.624675i \(0.785231\pi\)
\(390\) 0 0
\(391\) 283.500 491.036i 0.0366681 0.0635109i
\(392\) 4116.00 7129.12i 0.530330 0.918559i
\(393\) 0 0
\(394\) −2247.00 3891.92i −0.287315 0.497645i
\(395\) −135.000 −0.0171964
\(396\) 0 0
\(397\) −2900.00 −0.366617 −0.183308 0.983055i \(-0.558681\pi\)
−0.183308 + 0.983055i \(0.558681\pi\)
\(398\) 4564.00 + 7905.08i 0.574806 + 0.995593i
\(399\) 0 0
\(400\) 200.000 346.410i 0.0250000 0.0433013i
\(401\) −1125.00 + 1948.56i −0.140099 + 0.242659i −0.927534 0.373739i \(-0.878076\pi\)
0.787435 + 0.616398i \(0.211409\pi\)
\(402\) 0 0
\(403\) −7560.00 13094.3i −0.934468 1.61855i
\(404\) 6000.00 0.738889
\(405\) 0 0
\(406\) 0 0
\(407\) −850.000 1472.24i −0.103521 0.179303i
\(408\) 0 0
\(409\) 5631.50 9754.04i 0.680831 1.17923i −0.293897 0.955837i \(-0.594952\pi\)
0.974728 0.223396i \(-0.0717144\pi\)
\(410\) −650.000 + 1125.83i −0.0782956 + 0.135612i
\(411\) 0 0
\(412\) −920.000 1593.49i −0.110012 0.190547i
\(413\) 0 0
\(414\) 0 0
\(415\) 2145.00 0.253720
\(416\) −6400.00 11085.1i −0.754293 1.30647i
\(417\) 0 0
\(418\) −1130.00 + 1957.22i −0.132225 + 0.229021i
\(419\) 3455.00 5984.24i 0.402835 0.697730i −0.591232 0.806502i \(-0.701358\pi\)
0.994067 + 0.108771i \(0.0346916\pi\)
\(420\) 0 0
\(421\) 2624.50 + 4545.77i 0.303825 + 0.526240i 0.976999 0.213244i \(-0.0684029\pi\)
−0.673174 + 0.739484i \(0.735070\pi\)
\(422\) −9898.00 −1.14177
\(423\) 0 0
\(424\) 15144.0 1.73457
\(425\) −87.5000 151.554i −0.00998676 0.0172976i
\(426\) 0 0
\(427\) 0 0
\(428\) −840.000 + 1454.92i −0.0948667 + 0.164314i
\(429\) 0 0
\(430\) 50.0000 + 86.6025i 0.00560747 + 0.00971243i
\(431\) −11880.0 −1.32770 −0.663851 0.747865i \(-0.731079\pi\)
−0.663851 + 0.747865i \(0.731079\pi\)
\(432\) 0 0
\(433\) −4280.00 −0.475020 −0.237510 0.971385i \(-0.576331\pi\)
−0.237510 + 0.971385i \(0.576331\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1214.00 + 2102.71i −0.133349 + 0.230967i
\(437\) −4576.50 + 7926.73i −0.500970 + 0.867705i
\(438\) 0 0
\(439\) −3231.50 5597.12i −0.351324 0.608510i 0.635158 0.772382i \(-0.280935\pi\)
−0.986482 + 0.163872i \(0.947602\pi\)
\(440\) 1200.00 0.130018
\(441\) 0 0
\(442\) 1120.00 0.120527
\(443\) −5860.50 10150.7i −0.628534 1.08865i −0.987846 0.155436i \(-0.950322\pi\)
0.359312 0.933218i \(-0.383012\pi\)
\(444\) 0 0
\(445\) 1875.00 3247.60i 0.199738 0.345957i
\(446\) 3890.00 6737.68i 0.412997 0.715332i
\(447\) 0 0
\(448\) 0 0
\(449\) −2180.00 −0.229133 −0.114566 0.993416i \(-0.536548\pi\)
−0.114566 + 0.993416i \(0.536548\pi\)
\(450\) 0 0
\(451\) −1300.00 −0.135731
\(452\) 4340.00 + 7517.10i 0.451629 + 0.782245i
\(453\) 0 0
\(454\) 2453.00 4248.72i 0.253579 0.439212i
\(455\) 0 0
\(456\) 0 0
\(457\) 8920.00 + 15449.9i 0.913042 + 1.58143i 0.809744 + 0.586784i \(0.199606\pi\)
0.103298 + 0.994650i \(0.467060\pi\)
\(458\) 12426.0 1.26775
\(459\) 0 0
\(460\) 1620.00 0.164202
\(461\) 1125.00 + 1948.56i 0.113658 + 0.196862i 0.917243 0.398329i \(-0.130410\pi\)
−0.803584 + 0.595191i \(0.797076\pi\)
\(462\) 0 0
\(463\) −615.000 + 1065.21i −0.0617310 + 0.106921i −0.895239 0.445586i \(-0.852995\pi\)
0.833508 + 0.552507i \(0.186329\pi\)
\(464\) −1760.00 + 3048.41i −0.176090 + 0.304998i
\(465\) 0 0
\(466\) −3450.00 5975.58i −0.342957 0.594020i
\(467\) 5813.00 0.576003 0.288002 0.957630i \(-0.407009\pi\)
0.288002 + 0.957630i \(0.407009\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 800.000 + 1385.64i 0.0785133 + 0.135989i
\(471\) 0 0
\(472\) 6720.00 11639.4i 0.655324 1.13505i
\(473\) −50.0000 + 86.6025i −0.00486047 + 0.00841858i
\(474\) 0 0
\(475\) 1412.50 + 2446.52i 0.136442 + 0.236324i
\(476\) 0 0
\(477\) 0 0
\(478\) −12980.0 −1.24203
\(479\) 3375.00 + 5845.67i 0.321937 + 0.557611i 0.980888 0.194575i \(-0.0623328\pi\)
−0.658951 + 0.752186i \(0.729000\pi\)
\(480\) 0 0
\(481\) 6800.00 11777.9i 0.644601 1.11648i
\(482\) −3401.00 + 5890.70i −0.321393 + 0.556669i
\(483\) 0 0
\(484\) −2462.00 4264.31i −0.231217 0.400480i
\(485\) −7400.00 −0.692818
\(486\) 0 0
\(487\) −6610.00 −0.615047 −0.307523 0.951541i \(-0.599500\pi\)
−0.307523 + 0.951541i \(0.599500\pi\)
\(488\) −2748.00 4759.68i −0.254910 0.441517i
\(489\) 0 0
\(490\) −1715.00 + 2970.47i −0.158114 + 0.273861i
\(491\) 2495.00 4321.47i 0.229323 0.397200i −0.728284 0.685275i \(-0.759682\pi\)
0.957608 + 0.288075i \(0.0930153\pi\)
\(492\) 0 0
\(493\) 770.000 + 1333.68i 0.0703429 + 0.121837i
\(494\) −18080.0 −1.64668
\(495\) 0 0
\(496\) 3024.00 0.273753
\(497\) 0 0
\(498\) 0 0
\(499\) −741.500 + 1284.32i −0.0665212 + 0.115218i −0.897368 0.441283i \(-0.854523\pi\)
0.830847 + 0.556502i \(0.187857\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) −4980.00 8625.61i −0.442765 0.766892i
\(503\) −11641.0 −1.03190 −0.515951 0.856618i \(-0.672561\pi\)
−0.515951 + 0.856618i \(0.672561\pi\)
\(504\) 0 0
\(505\) −7500.00 −0.660882
\(506\) −810.000 1402.96i −0.0711638 0.123259i
\(507\) 0 0
\(508\) −3220.00 + 5577.20i −0.281229 + 0.487103i
\(509\) −1310.00 + 2268.99i −0.114076 + 0.197586i −0.917410 0.397943i \(-0.869724\pi\)
0.803334 + 0.595529i \(0.203057\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5632.00 0.486136
\(513\) 0 0
\(514\) −6714.00 −0.576151
\(515\) 1150.00 + 1991.86i 0.0983982 + 0.170431i
\(516\) 0 0
\(517\) −800.000 + 1385.64i −0.0680541 + 0.117873i
\(518\) 0 0
\(519\) 0 0
\(520\) 4800.00 + 8313.84i 0.404796 + 0.701127i
\(521\) −13690.0 −1.15119 −0.575595 0.817735i \(-0.695229\pi\)
−0.575595 + 0.817735i \(0.695229\pi\)
\(522\) 0 0
\(523\) −10220.0 −0.854473 −0.427237 0.904140i \(-0.640513\pi\)
−0.427237 + 0.904140i \(0.640513\pi\)
\(524\) 4740.00 + 8209.92i 0.395168 + 0.684450i
\(525\) 0 0
\(526\) −4540.00 + 7863.51i −0.376337 + 0.651835i
\(527\) 661.500 1145.75i 0.0546782 0.0947054i
\(528\) 0 0
\(529\) 2803.00 + 4854.94i 0.230377 + 0.399025i
\(530\) −6310.00 −0.517149
\(531\) 0 0
\(532\) 0 0
\(533\) −5200.00 9006.66i −0.422583 0.731936i
\(534\) 0 0
\(535\) 1050.00 1818.65i 0.0848513 0.146967i
\(536\) −9000.00 + 15588.5i −0.725263 + 1.25619i
\(537\) 0 0
\(538\) 8410.00 + 14566.5i 0.673942 + 1.16730i
\(539\) −3430.00 −0.274101
\(540\) 0 0
\(541\) −2778.00 −0.220768 −0.110384 0.993889i \(-0.535208\pi\)
−0.110384 + 0.993889i \(0.535208\pi\)
\(542\) 259.000 + 448.601i 0.0205258 + 0.0355518i
\(543\) 0 0
\(544\) 560.000 969.948i 0.0441357 0.0764452i
\(545\) 1517.50 2628.39i 0.119271 0.206583i
\(546\) 0 0
\(547\) 6415.00 + 11111.1i 0.501436 + 0.868513i 0.999999 + 0.00165916i \(0.000528127\pi\)
−0.498562 + 0.866854i \(0.666139\pi\)
\(548\) −7188.00 −0.560321
\(549\) 0 0
\(550\) −500.000 −0.0387638
\(551\) −12430.0 21529.4i −0.961045 1.66458i
\(552\) 0 0
\(553\) 0 0
\(554\) −4170.00 + 7222.65i −0.319795 + 0.553901i
\(555\) 0 0
\(556\) −248.000 429.549i −0.0189164 0.0327642i
\(557\) −4950.00 −0.376550 −0.188275 0.982116i \(-0.560290\pi\)
−0.188275 + 0.982116i \(0.560290\pi\)
\(558\) 0 0
\(559\) −800.000 −0.0605302
\(560\) 0 0
\(561\) 0 0
\(562\) −1740.00 + 3013.77i −0.130600 + 0.226207i
\(563\) −3270.00 + 5663.81i −0.244785 + 0.423980i −0.962071 0.272798i \(-0.912051\pi\)
0.717286 + 0.696779i \(0.245384\pi\)
\(564\) 0 0
\(565\) −5425.00 9396.38i −0.403949 0.699661i
\(566\) 10140.0 0.753032
\(567\) 0 0
\(568\) 21360.0 1.57790
\(569\) 7620.00 + 13198.2i 0.561418 + 0.972405i 0.997373 + 0.0724364i \(0.0230774\pi\)
−0.435955 + 0.899969i \(0.643589\pi\)
\(570\) 0 0
\(571\) 2640.50 4573.48i 0.193523 0.335191i −0.752893 0.658144i \(-0.771342\pi\)
0.946415 + 0.322952i \(0.104675\pi\)
\(572\) −1600.00 + 2771.28i −0.116957 + 0.202575i
\(573\) 0 0
\(574\) 0 0
\(575\) −2025.00 −0.146867
\(576\) 0 0
\(577\) −10510.0 −0.758296 −0.379148 0.925336i \(-0.623783\pi\)
−0.379148 + 0.925336i \(0.623783\pi\)
\(578\) −4864.00 8424.70i −0.350027 0.606265i
\(579\) 0 0
\(580\) −2200.00 + 3810.51i −0.157500 + 0.272798i
\(581\) 0 0
\(582\) 0 0
\(583\) −3155.00 5464.62i −0.224128 0.388201i
\(584\) −21360.0 −1.51350
\(585\) 0 0
\(586\) 318.000 0.0224172
\(587\) −2053.50 3556.77i −0.144390 0.250091i 0.784755 0.619806i \(-0.212789\pi\)
−0.929145 + 0.369715i \(0.879455\pi\)
\(588\) 0 0
\(589\) −10678.5 + 18495.7i −0.747029 + 1.29389i
\(590\) −2800.00 + 4849.74i −0.195380 + 0.338408i
\(591\) 0 0
\(592\) 1360.00 + 2355.59i 0.0944183 + 0.163537i
\(593\) 26129.0 1.80943 0.904713 0.426022i \(-0.140085\pi\)
0.904713 + 0.426022i \(0.140085\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −140.000 242.487i −0.00962185 0.0166655i
\(597\) 0 0
\(598\) 6480.00 11223.7i 0.443122 0.767510i
\(599\) 2180.00 3775.87i 0.148702 0.257559i −0.782046 0.623221i \(-0.785824\pi\)
0.930748 + 0.365661i \(0.119157\pi\)
\(600\) 0 0
\(601\) 8319.50 + 14409.8i 0.564658 + 0.978016i 0.997081 + 0.0763457i \(0.0243253\pi\)
−0.432423 + 0.901671i \(0.642341\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8992.00 −0.605760
\(605\) 3077.50 + 5330.39i 0.206807 + 0.358200i
\(606\) 0 0
\(607\) −245.000 + 424.352i −0.0163826 + 0.0283755i −0.874100 0.485745i \(-0.838548\pi\)
0.857718 + 0.514121i \(0.171882\pi\)
\(608\) −9040.00 + 15657.7i −0.602994 + 1.04442i
\(609\) 0 0
\(610\) 1145.00 + 1983.20i 0.0759995 + 0.131635i
\(611\) −12800.0 −0.847516
\(612\) 0 0
\(613\) 18400.0 1.21235 0.606174 0.795332i \(-0.292704\pi\)
0.606174 + 0.795332i \(0.292704\pi\)
\(614\) 6490.00 + 11241.0i 0.426572 + 0.738844i
\(615\) 0 0
\(616\) 0 0
\(617\) −3913.50 + 6778.38i −0.255351 + 0.442281i −0.964991 0.262284i \(-0.915524\pi\)
0.709640 + 0.704565i \(0.248858\pi\)
\(618\) 0 0
\(619\) 9878.00 + 17109.2i 0.641406 + 1.11095i 0.985119 + 0.171873i \(0.0549819\pi\)
−0.343713 + 0.939075i \(0.611685\pi\)
\(620\) 3780.00 0.244852
\(621\) 0 0
\(622\) 16440.0 1.05978
\(623\) 0 0
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −4660.00 + 8071.36i −0.297526 + 0.515330i
\(627\) 0 0
\(628\) 2020.00 + 3498.74i 0.128355 + 0.222317i
\(629\) 1190.00 0.0754347
\(630\) 0 0
\(631\) 9829.00 0.620105 0.310053 0.950719i \(-0.399653\pi\)
0.310053 + 0.950719i \(0.399653\pi\)
\(632\) 324.000 + 561.184i 0.0203924 + 0.0353208i
\(633\) 0 0
\(634\) −6817.00 + 11807.4i −0.427031 + 0.739639i
\(635\) 4025.00 6971.50i 0.251539 0.435678i
\(636\) 0 0
\(637\) −13720.0 23763.7i −0.853385 1.47811i
\(638\) 4400.00 0.273037
\(639\) 0 0
\(640\) 1920.00 0.118585
\(641\) 3000.00 + 5196.15i 0.184856 + 0.320180i 0.943528 0.331293i \(-0.107485\pi\)
−0.758672 + 0.651473i \(0.774151\pi\)
\(642\) 0 0
\(643\) −4140.00 + 7170.69i −0.253912 + 0.439789i −0.964600 0.263719i \(-0.915051\pi\)
0.710687 + 0.703508i \(0.248384\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −791.000 1370.05i −0.0481757 0.0834427i
\(647\) −16637.0 −1.01092 −0.505462 0.862849i \(-0.668678\pi\)
−0.505462 + 0.862849i \(0.668678\pi\)
\(648\) 0 0
\(649\) −5600.00 −0.338705
\(650\) −2000.00 3464.10i −0.120687 0.209036i
\(651\) 0 0
\(652\) 1180.00 2043.82i 0.0708779 0.122764i
\(653\) −9875.50 + 17104.9i −0.591820 + 1.02506i 0.402168 + 0.915566i \(0.368257\pi\)
−0.993987 + 0.109496i \(0.965076\pi\)
\(654\) 0 0
\(655\) −5925.00 10262.4i −0.353449 0.612191i
\(656\) 2080.00 0.123796
\(657\) 0 0
\(658\) 0 0
\(659\) −7130.00 12349.5i −0.421465 0.729999i 0.574618 0.818422i \(-0.305151\pi\)
−0.996083 + 0.0884231i \(0.971817\pi\)
\(660\) 0 0
\(661\) −11159.0 + 19328.0i −0.656634 + 1.13732i 0.324848 + 0.945766i \(0.394687\pi\)
−0.981482 + 0.191556i \(0.938646\pi\)
\(662\) 192.000 332.554i 0.0112723 0.0195243i
\(663\) 0 0
\(664\) −5148.00 8916.60i −0.300875 0.521131i
\(665\) 0 0
\(666\) 0 0
\(667\) 17820.0 1.03447
\(668\) 4806.00 + 8324.24i 0.278368 + 0.482147i
\(669\) 0 0
\(670\) 3750.00 6495.19i 0.216232 0.374524i
\(671\) −1145.00 + 1983.20i −0.0658752 + 0.114099i
\(672\) 0 0
\(673\) −10020.0 17355.1i −0.573912 0.994044i −0.996159 0.0875636i \(-0.972092\pi\)
0.422247 0.906481i \(-0.361241\pi\)
\(674\) −9680.00 −0.553204
\(675\) 0 0
\(676\) −16812.0 −0.956532
\(677\) 1155.00 + 2000.52i 0.0655691 + 0.113569i 0.896946 0.442140i \(-0.145780\pi\)
−0.831377 + 0.555708i \(0.812447\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −420.000 + 727.461i −0.0236857 + 0.0410248i
\(681\) 0 0
\(682\) −1890.00 3273.58i −0.106117 0.183800i
\(683\) −26739.0 −1.49801 −0.749004 0.662566i \(-0.769468\pi\)
−0.749004 + 0.662566i \(0.769468\pi\)
\(684\) 0 0
\(685\) 8985.00 0.501167
\(686\) 0 0
\(687\) 0 0
\(688\) 80.0000 138.564i 0.00443310 0.00767835i
\(689\) 25240.0 43717.0i 1.39560 2.41725i
\(690\) 0 0
\(691\) −2550.50 4417.60i −0.140413 0.243203i 0.787239 0.616648i \(-0.211510\pi\)
−0.927652 + 0.373445i \(0.878176\pi\)
\(692\) −3204.00 −0.176008
\(693\) 0 0
\(694\) 1720.00 0.0940783
\(695\) 310.000 + 536.936i 0.0169194 + 0.0293052i
\(696\) 0 0
\(697\) 455.000 788.083i 0.0247265 0.0428275i
\(698\) 5377.00 9313.24i 0.291579 0.505030i
\(699\) 0 0
\(700\) 0 0
\(701\) 26030.0 1.40248 0.701241 0.712925i \(-0.252630\pi\)
0.701241 + 0.712925i \(0.252630\pi\)
\(702\) 0 0
\(703\) −19210.0 −1.03061
\(704\) −2240.00 3879.79i −0.119919 0.207706i
\(705\) 0 0
\(706\) −8010.00 + 13873.7i −0.426998 + 0.739582i
\(707\) 0 0
\(708\) 0 0
\(709\) 1927.00 + 3337.66i 0.102073 + 0.176796i 0.912539 0.408990i \(-0.134119\pi\)
−0.810465 + 0.585787i \(0.800786\pi\)
\(710\) −8900.00 −0.470438
\(711\) 0 0
\(712\) −18000.0 −0.947442
\(713\) −7654.50 13258.0i −0.402052 0.696375i
\(714\) 0 0
\(715\) 2000.00 3464.10i 0.104609 0.181189i
\(716\) −4720.00 + 8175.28i −0.246361 + 0.426710i
\(717\) 0 0
\(718\) 12930.0 + 22395.4i 0.672066 + 1.16405i
\(719\) −870.000 −0.0451259 −0.0225630 0.999745i \(-0.507183\pi\)
−0.0225630 + 0.999745i \(0.507183\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5910.00 + 10236.4i 0.304636 + 0.527646i
\(723\) 0 0
\(724\) 2482.00 4298.95i 0.127407 0.220676i
\(725\) 2750.00 4763.14i 0.140872 0.243998i
\(726\) 0 0
\(727\) −17890.0 30986.4i −0.912659 1.58077i −0.810292 0.586026i \(-0.800692\pi\)
−0.102367 0.994747i \(-0.532642\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 8900.00 0.451238
\(731\) −35.0000 60.6218i −0.00177089 0.00306727i
\(732\) 0 0
\(733\) 1700.00 2944.49i 0.0856629 0.148373i −0.820011 0.572348i \(-0.806033\pi\)
0.905674 + 0.423976i \(0.139366\pi\)
\(734\) −6000.00 + 10392.3i −0.301722 + 0.522598i
\(735\) 0 0
\(736\) −6480.00 11223.7i −0.324533 0.562107i
\(737\) 7500.00 0.374852
\(738\) 0 0
\(739\) −683.000 −0.0339981 −0.0169990 0.999856i \(-0.505411\pi\)
−0.0169990 + 0.999856i \(0.505411\pi\)
\(740\) 1700.00 + 2944.49i 0.0844503 + 0.146272i
\(741\) 0 0
\(742\) 0 0
\(743\) 6700.00 11604.7i 0.330820 0.572997i −0.651853 0.758345i \(-0.726008\pi\)
0.982673 + 0.185349i \(0.0593414\pi\)
\(744\) 0 0
\(745\) 175.000 + 303.109i 0.00860605 + 0.0149061i
\(746\) 280.000 0.0137420
\(747\) 0 0
\(748\) −280.000 −0.0136869
\(749\) 0 0
\(750\) 0 0
\(751\) 11609.5 20108.2i 0.564097 0.977044i −0.433036 0.901376i \(-0.642558\pi\)
0.997133 0.0756678i \(-0.0241088\pi\)
\(752\) 1280.00 2217.03i 0.0620702 0.107509i
\(753\) 0 0
\(754\) 17600.0 + 30484.1i 0.850072 + 1.47237i
\(755\) 11240.0 0.541809
\(756\) 0 0
\(757\) 19630.0 0.942489 0.471245 0.882003i \(-0.343805\pi\)
0.471245 + 0.882003i \(0.343805\pi\)
\(758\) 6217.00 + 10768.2i 0.297904 + 0.515986i
\(759\) 0 0
\(760\) 6780.00 11743.3i 0.323601 0.560493i
\(761\) −1470.00 + 2546.11i −0.0700229 + 0.121283i −0.898911 0.438131i \(-0.855641\pi\)
0.828888 + 0.559414i \(0.188974\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19960.0 0.945193
\(765\) 0 0
\(766\) −9102.00 −0.429332
\(767\) −22400.0 38797.9i −1.05452 1.82648i
\(768\) 0 0
\(769\) 6993.50 12113.1i 0.327948 0.568023i −0.654156 0.756359i \(-0.726976\pi\)
0.982105 + 0.188337i \(0.0603096\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4520.00 7828.87i −0.210723 0.364983i
\(773\) 19839.0 0.923104 0.461552 0.887113i \(-0.347293\pi\)
0.461552 + 0.887113i \(0.347293\pi\)
\(774\) 0 0
\(775\) −4725.00 −0.219003
\(776\) 17760.0 + 30761.2i 0.821581 + 1.42302i
\(777\) 0 0
\(778\) −2310.00 + 4001.04i −0.106449 + 0.184376i
\(779\) −7345.00 + 12721.9i −0.337820 + 0.585122i
\(780\) 0 0
\(781\) −4450.00 7707.63i −0.203884 0.353138i
\(782\) 1134.00 0.0518565
\(783\) 0 0
\(784\) 5488.00 0.250000
\(785\) −2525.00 4373.43i −0.114804 0.198846i
\(786\) 0 0
\(787\) 19195.0 33246.7i 0.869413 1.50587i 0.00681497 0.999977i \(-0.497831\pi\)
0.862598 0.505890i \(-0.168836\pi\)
\(788\) −4494.00 + 7783.84i −0.203163 + 0.351888i
\(789\) 0 0