Properties

Label 405.4.b.e.244.10
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.10
Root \(0.785333i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.e.244.7

$q$-expansion

\(f(q)\) \(=\) \(q+0.785333i q^{2} +7.38325 q^{4} +(-3.61462 + 10.5799i) q^{5} -20.9136i q^{7} +12.0810i q^{8} +O(q^{10})\) \(q+0.785333i q^{2} +7.38325 q^{4} +(-3.61462 + 10.5799i) q^{5} -20.9136i q^{7} +12.0810i q^{8} +(-8.30875 - 2.83868i) q^{10} -59.3838 q^{11} -45.9320i q^{13} +16.4241 q^{14} +49.5784 q^{16} -43.0872i q^{17} -140.178 q^{19} +(-26.6877 + 78.1141i) q^{20} -46.6360i q^{22} -101.756i q^{23} +(-98.8690 - 76.4848i) q^{25} +36.0719 q^{26} -154.410i q^{28} -12.3918 q^{29} +71.9790 q^{31} +135.583i q^{32} +33.8378 q^{34} +(221.264 + 75.5948i) q^{35} +150.734i q^{37} -110.087i q^{38} +(-127.816 - 43.6682i) q^{40} +51.0821 q^{41} -34.4716i q^{43} -438.445 q^{44} +79.9121 q^{46} -117.976i q^{47} -94.3781 q^{49} +(60.0660 - 77.6451i) q^{50} -339.128i q^{52} -137.196i q^{53} +(214.650 - 628.275i) q^{55} +252.657 q^{56} -9.73173i q^{58} -496.314 q^{59} -247.700 q^{61} +56.5275i q^{62} +290.149 q^{64} +(485.956 + 166.027i) q^{65} -826.052i q^{67} -318.124i q^{68} +(-59.3671 + 173.766i) q^{70} -260.049 q^{71} -372.227i q^{73} -118.376 q^{74} -1034.97 q^{76} +1241.93i q^{77} -476.404 q^{79} +(-179.207 + 524.535i) q^{80} +40.1164i q^{82} +313.173i q^{83} +(455.859 + 155.744i) q^{85} +27.0717 q^{86} -717.414i q^{88} +817.628 q^{89} -960.603 q^{91} -751.288i q^{92} +92.6502 q^{94} +(506.692 - 1483.07i) q^{95} -941.296i q^{97} -74.1183i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} - 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} - 3 q^{5} - 10 q^{10} - 90 q^{11} + 102 q^{14} + 146 q^{16} - 4 q^{19} + 6 q^{20} - 71 q^{25} - 468 q^{26} + 516 q^{29} + 38 q^{31} - 212 q^{34} - 267 q^{35} - 44 q^{40} - 576 q^{41} + 1644 q^{44} - 290 q^{46} + 4 q^{49} - 558 q^{50} + 15 q^{55} - 2430 q^{56} + 2202 q^{59} + 20 q^{61} + 322 q^{64} - 339 q^{65} - 636 q^{70} - 2952 q^{71} + 4080 q^{74} - 396 q^{76} + 218 q^{79} + 1266 q^{80} + 704 q^{85} - 6108 q^{86} + 4074 q^{89} - 942 q^{91} + 1078 q^{94} + 1692 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.785333i 0.277657i 0.990316 + 0.138829i \(0.0443337\pi\)
−0.990316 + 0.138829i \(0.955666\pi\)
\(3\) 0 0
\(4\) 7.38325 0.922907
\(5\) −3.61462 + 10.5799i −0.323302 + 0.946296i
\(6\) 0 0
\(7\) 20.9136i 1.12923i −0.825355 0.564614i \(-0.809025\pi\)
0.825355 0.564614i \(-0.190975\pi\)
\(8\) 12.0810i 0.533909i
\(9\) 0 0
\(10\) −8.30875 2.83868i −0.262746 0.0897671i
\(11\) −59.3838 −1.62772 −0.813858 0.581064i \(-0.802637\pi\)
−0.813858 + 0.581064i \(0.802637\pi\)
\(12\) 0 0
\(13\) 45.9320i 0.979942i −0.871739 0.489971i \(-0.837007\pi\)
0.871739 0.489971i \(-0.162993\pi\)
\(14\) 16.4241 0.313538
\(15\) 0 0
\(16\) 49.5784 0.774663
\(17\) 43.0872i 0.614717i −0.951594 0.307359i \(-0.900555\pi\)
0.951594 0.307359i \(-0.0994451\pi\)
\(18\) 0 0
\(19\) −140.178 −1.69258 −0.846292 0.532719i \(-0.821170\pi\)
−0.846292 + 0.532719i \(0.821170\pi\)
\(20\) −26.6877 + 78.1141i −0.298377 + 0.873343i
\(21\) 0 0
\(22\) 46.6360i 0.451947i
\(23\) 101.756i 0.922501i −0.887270 0.461251i \(-0.847401\pi\)
0.887270 0.461251i \(-0.152599\pi\)
\(24\) 0 0
\(25\) −98.8690 76.4848i −0.790952 0.611878i
\(26\) 36.0719 0.272088
\(27\) 0 0
\(28\) 154.410i 1.04217i
\(29\) −12.3918 −0.0793486 −0.0396743 0.999213i \(-0.512632\pi\)
−0.0396743 + 0.999213i \(0.512632\pi\)
\(30\) 0 0
\(31\) 71.9790 0.417026 0.208513 0.978020i \(-0.433138\pi\)
0.208513 + 0.978020i \(0.433138\pi\)
\(32\) 135.583i 0.748999i
\(33\) 0 0
\(34\) 33.8378 0.170681
\(35\) 221.264 + 75.5948i 1.06858 + 0.365081i
\(36\) 0 0
\(37\) 150.734i 0.669742i 0.942264 + 0.334871i \(0.108693\pi\)
−0.942264 + 0.334871i \(0.891307\pi\)
\(38\) 110.087i 0.469958i
\(39\) 0 0
\(40\) −127.816 43.6682i −0.505236 0.172614i
\(41\) 51.0821 0.194577 0.0972887 0.995256i \(-0.468983\pi\)
0.0972887 + 0.995256i \(0.468983\pi\)
\(42\) 0 0
\(43\) 34.4716i 0.122253i −0.998130 0.0611264i \(-0.980531\pi\)
0.998130 0.0611264i \(-0.0194693\pi\)
\(44\) −438.445 −1.50223
\(45\) 0 0
\(46\) 79.9121 0.256139
\(47\) 117.976i 0.366139i −0.983100 0.183069i \(-0.941397\pi\)
0.983100 0.183069i \(-0.0586033\pi\)
\(48\) 0 0
\(49\) −94.3781 −0.275155
\(50\) 60.0660 77.6451i 0.169892 0.219613i
\(51\) 0 0
\(52\) 339.128i 0.904395i
\(53\) 137.196i 0.355573i −0.984069 0.177787i \(-0.943106\pi\)
0.984069 0.177787i \(-0.0568937\pi\)
\(54\) 0 0
\(55\) 214.650 628.275i 0.526244 1.54030i
\(56\) 252.657 0.602904
\(57\) 0 0
\(58\) 9.73173i 0.0220317i
\(59\) −496.314 −1.09516 −0.547581 0.836753i \(-0.684451\pi\)
−0.547581 + 0.836753i \(0.684451\pi\)
\(60\) 0 0
\(61\) −247.700 −0.519914 −0.259957 0.965620i \(-0.583708\pi\)
−0.259957 + 0.965620i \(0.583708\pi\)
\(62\) 56.5275i 0.115790i
\(63\) 0 0
\(64\) 290.149 0.566698
\(65\) 485.956 + 166.027i 0.927315 + 0.316817i
\(66\) 0 0
\(67\) 826.052i 1.50624i −0.657881 0.753121i \(-0.728547\pi\)
0.657881 0.753121i \(-0.271453\pi\)
\(68\) 318.124i 0.567326i
\(69\) 0 0
\(70\) −59.3671 + 173.766i −0.101367 + 0.296700i
\(71\) −260.049 −0.434677 −0.217339 0.976096i \(-0.569738\pi\)
−0.217339 + 0.976096i \(0.569738\pi\)
\(72\) 0 0
\(73\) 372.227i 0.596793i −0.954442 0.298396i \(-0.903548\pi\)
0.954442 0.298396i \(-0.0964518\pi\)
\(74\) −118.376 −0.185959
\(75\) 0 0
\(76\) −1034.97 −1.56210
\(77\) 1241.93i 1.83806i
\(78\) 0 0
\(79\) −476.404 −0.678476 −0.339238 0.940701i \(-0.610169\pi\)
−0.339238 + 0.940701i \(0.610169\pi\)
\(80\) −179.207 + 524.535i −0.250450 + 0.733060i
\(81\) 0 0
\(82\) 40.1164i 0.0540258i
\(83\) 313.173i 0.414160i 0.978324 + 0.207080i \(0.0663960\pi\)
−0.978324 + 0.207080i \(0.933604\pi\)
\(84\) 0 0
\(85\) 455.859 + 155.744i 0.581704 + 0.198739i
\(86\) 27.0717 0.0339444
\(87\) 0 0
\(88\) 717.414i 0.869052i
\(89\) 817.628 0.973802 0.486901 0.873457i \(-0.338127\pi\)
0.486901 + 0.873457i \(0.338127\pi\)
\(90\) 0 0
\(91\) −960.603 −1.10658
\(92\) 751.288i 0.851382i
\(93\) 0 0
\(94\) 92.6502 0.101661
\(95\) 506.692 1483.07i 0.547216 1.60169i
\(96\) 0 0
\(97\) 941.296i 0.985300i −0.870227 0.492650i \(-0.836028\pi\)
0.870227 0.492650i \(-0.163972\pi\)
\(98\) 74.1183i 0.0763987i
\(99\) 0 0
\(100\) −729.975 564.707i −0.729975 0.564707i
\(101\) −1002.87 −0.988017 −0.494008 0.869457i \(-0.664469\pi\)
−0.494008 + 0.869457i \(0.664469\pi\)
\(102\) 0 0
\(103\) 298.834i 0.285873i 0.989732 + 0.142937i \(0.0456545\pi\)
−0.989732 + 0.142937i \(0.954345\pi\)
\(104\) 554.903 0.523199
\(105\) 0 0
\(106\) 107.745 0.0987275
\(107\) 984.533i 0.889518i −0.895650 0.444759i \(-0.853289\pi\)
0.895650 0.444759i \(-0.146711\pi\)
\(108\) 0 0
\(109\) 224.770 0.197514 0.0987572 0.995112i \(-0.468513\pi\)
0.0987572 + 0.995112i \(0.468513\pi\)
\(110\) 493.405 + 168.572i 0.427675 + 0.146115i
\(111\) 0 0
\(112\) 1036.86i 0.874771i
\(113\) 137.764i 0.114688i 0.998354 + 0.0573440i \(0.0182632\pi\)
−0.998354 + 0.0573440i \(0.981737\pi\)
\(114\) 0 0
\(115\) 1076.57 + 367.809i 0.872959 + 0.298246i
\(116\) −91.4921 −0.0732313
\(117\) 0 0
\(118\) 389.772i 0.304080i
\(119\) −901.109 −0.694155
\(120\) 0 0
\(121\) 2195.43 1.64946
\(122\) 194.527i 0.144358i
\(123\) 0 0
\(124\) 531.439 0.384876
\(125\) 1166.58 769.561i 0.834734 0.550653i
\(126\) 0 0
\(127\) 2742.19i 1.91598i 0.286800 + 0.957991i \(0.407409\pi\)
−0.286800 + 0.957991i \(0.592591\pi\)
\(128\) 1312.53i 0.906347i
\(129\) 0 0
\(130\) −130.386 + 381.638i −0.0879665 + 0.257476i
\(131\) −960.401 −0.640539 −0.320270 0.947326i \(-0.603774\pi\)
−0.320270 + 0.947326i \(0.603774\pi\)
\(132\) 0 0
\(133\) 2931.63i 1.91131i
\(134\) 648.726 0.418219
\(135\) 0 0
\(136\) 520.536 0.328203
\(137\) 726.517i 0.453070i −0.974003 0.226535i \(-0.927260\pi\)
0.974003 0.226535i \(-0.0727397\pi\)
\(138\) 0 0
\(139\) −499.893 −0.305039 −0.152519 0.988300i \(-0.548739\pi\)
−0.152519 + 0.988300i \(0.548739\pi\)
\(140\) 1633.65 + 558.135i 0.986203 + 0.336936i
\(141\) 0 0
\(142\) 204.225i 0.120691i
\(143\) 2727.61i 1.59507i
\(144\) 0 0
\(145\) 44.7919 131.105i 0.0256535 0.0750872i
\(146\) 292.322 0.165704
\(147\) 0 0
\(148\) 1112.90i 0.618109i
\(149\) 19.6970 0.0108298 0.00541492 0.999985i \(-0.498276\pi\)
0.00541492 + 0.999985i \(0.498276\pi\)
\(150\) 0 0
\(151\) 655.417 0.353226 0.176613 0.984280i \(-0.443486\pi\)
0.176613 + 0.984280i \(0.443486\pi\)
\(152\) 1693.49i 0.903686i
\(153\) 0 0
\(154\) −975.326 −0.510351
\(155\) −260.177 + 761.532i −0.134825 + 0.394630i
\(156\) 0 0
\(157\) 1703.54i 0.865969i 0.901401 + 0.432984i \(0.142540\pi\)
−0.901401 + 0.432984i \(0.857460\pi\)
\(158\) 374.136i 0.188384i
\(159\) 0 0
\(160\) −1434.46 490.083i −0.708775 0.242153i
\(161\) −2128.08 −1.04171
\(162\) 0 0
\(163\) 2606.84i 1.25266i 0.779559 + 0.626329i \(0.215443\pi\)
−0.779559 + 0.626329i \(0.784557\pi\)
\(164\) 377.152 0.179577
\(165\) 0 0
\(166\) −245.945 −0.114994
\(167\) 1639.42i 0.759651i 0.925058 + 0.379826i \(0.124016\pi\)
−0.925058 + 0.379826i \(0.875984\pi\)
\(168\) 0 0
\(169\) 87.2514 0.0397139
\(170\) −122.311 + 358.001i −0.0551813 + 0.161514i
\(171\) 0 0
\(172\) 254.513i 0.112828i
\(173\) 1174.44i 0.516132i −0.966127 0.258066i \(-0.916915\pi\)
0.966127 0.258066i \(-0.0830852\pi\)
\(174\) 0 0
\(175\) −1599.57 + 2067.71i −0.690950 + 0.893165i
\(176\) −2944.15 −1.26093
\(177\) 0 0
\(178\) 642.110i 0.270383i
\(179\) −2512.58 −1.04916 −0.524578 0.851362i \(-0.675777\pi\)
−0.524578 + 0.851362i \(0.675777\pi\)
\(180\) 0 0
\(181\) 3685.91 1.51366 0.756828 0.653614i \(-0.226748\pi\)
0.756828 + 0.653614i \(0.226748\pi\)
\(182\) 754.393i 0.307249i
\(183\) 0 0
\(184\) 1229.31 0.492531
\(185\) −1594.75 544.846i −0.633774 0.216529i
\(186\) 0 0
\(187\) 2558.68i 1.00058i
\(188\) 871.044i 0.337912i
\(189\) 0 0
\(190\) 1164.71 + 397.922i 0.444720 + 0.151938i
\(191\) −2716.35 −1.02905 −0.514524 0.857476i \(-0.672031\pi\)
−0.514524 + 0.857476i \(0.672031\pi\)
\(192\) 0 0
\(193\) 1972.75i 0.735762i 0.929873 + 0.367881i \(0.119917\pi\)
−0.929873 + 0.367881i \(0.880083\pi\)
\(194\) 739.231 0.273576
\(195\) 0 0
\(196\) −696.818 −0.253942
\(197\) 3406.43i 1.23197i 0.787758 + 0.615985i \(0.211242\pi\)
−0.787758 + 0.615985i \(0.788758\pi\)
\(198\) 0 0
\(199\) 981.722 0.349711 0.174855 0.984594i \(-0.444054\pi\)
0.174855 + 0.984594i \(0.444054\pi\)
\(200\) 924.011 1194.43i 0.326687 0.422296i
\(201\) 0 0
\(202\) 787.590i 0.274330i
\(203\) 259.158i 0.0896026i
\(204\) 0 0
\(205\) −184.642 + 540.444i −0.0629073 + 0.184128i
\(206\) −234.684 −0.0793748
\(207\) 0 0
\(208\) 2277.24i 0.759125i
\(209\) 8324.31 2.75505
\(210\) 0 0
\(211\) −2017.52 −0.658254 −0.329127 0.944286i \(-0.606754\pi\)
−0.329127 + 0.944286i \(0.606754\pi\)
\(212\) 1012.96i 0.328161i
\(213\) 0 0
\(214\) 773.186 0.246981
\(215\) 364.706 + 124.602i 0.115687 + 0.0395246i
\(216\) 0 0
\(217\) 1505.34i 0.470918i
\(218\) 176.519i 0.0548413i
\(219\) 0 0
\(220\) 1584.81 4638.71i 0.485674 1.42155i
\(221\) −1979.08 −0.602387
\(222\) 0 0
\(223\) 265.712i 0.0797911i −0.999204 0.0398956i \(-0.987297\pi\)
0.999204 0.0398956i \(-0.0127025\pi\)
\(224\) 2835.53 0.845791
\(225\) 0 0
\(226\) −108.191 −0.0318440
\(227\) 5124.95i 1.49848i 0.662300 + 0.749239i \(0.269581\pi\)
−0.662300 + 0.749239i \(0.730419\pi\)
\(228\) 0 0
\(229\) −90.7643 −0.0261916 −0.0130958 0.999914i \(-0.504169\pi\)
−0.0130958 + 0.999914i \(0.504169\pi\)
\(230\) −288.852 + 845.463i −0.0828102 + 0.242383i
\(231\) 0 0
\(232\) 149.706i 0.0423649i
\(233\) 5856.17i 1.64657i −0.567629 0.823284i \(-0.692139\pi\)
0.567629 0.823284i \(-0.307861\pi\)
\(234\) 0 0
\(235\) 1248.17 + 426.438i 0.346475 + 0.118373i
\(236\) −3664.41 −1.01073
\(237\) 0 0
\(238\) 707.670i 0.192737i
\(239\) 6868.82 1.85903 0.929513 0.368790i \(-0.120228\pi\)
0.929513 + 0.368790i \(0.120228\pi\)
\(240\) 0 0
\(241\) −25.1374 −0.00671886 −0.00335943 0.999994i \(-0.501069\pi\)
−0.00335943 + 0.999994i \(0.501069\pi\)
\(242\) 1724.14i 0.457984i
\(243\) 0 0
\(244\) −1828.83 −0.479832
\(245\) 341.142 998.512i 0.0889581 0.260378i
\(246\) 0 0
\(247\) 6438.67i 1.65863i
\(248\) 869.577i 0.222654i
\(249\) 0 0
\(250\) 604.362 + 916.151i 0.152893 + 0.231770i
\(251\) −5765.12 −1.44976 −0.724882 0.688873i \(-0.758106\pi\)
−0.724882 + 0.688873i \(0.758106\pi\)
\(252\) 0 0
\(253\) 6042.63i 1.50157i
\(254\) −2153.53 −0.531986
\(255\) 0 0
\(256\) 1290.42 0.315044
\(257\) 5609.90i 1.36162i −0.732460 0.680810i \(-0.761628\pi\)
0.732460 0.680810i \(-0.238372\pi\)
\(258\) 0 0
\(259\) 3152.38 0.756291
\(260\) 3587.94 + 1225.82i 0.855825 + 0.292392i
\(261\) 0 0
\(262\) 754.235i 0.177850i
\(263\) 5803.41i 1.36066i −0.732906 0.680330i \(-0.761837\pi\)
0.732906 0.680330i \(-0.238163\pi\)
\(264\) 0 0
\(265\) 1451.53 + 495.914i 0.336478 + 0.114958i
\(266\) −2302.31 −0.530690
\(267\) 0 0
\(268\) 6098.95i 1.39012i
\(269\) 7317.07 1.65847 0.829237 0.558897i \(-0.188775\pi\)
0.829237 + 0.558897i \(0.188775\pi\)
\(270\) 0 0
\(271\) −8201.78 −1.83846 −0.919230 0.393722i \(-0.871187\pi\)
−0.919230 + 0.393722i \(0.871187\pi\)
\(272\) 2136.20i 0.476199i
\(273\) 0 0
\(274\) 570.558 0.125798
\(275\) 5871.21 + 4541.95i 1.28744 + 0.995964i
\(276\) 0 0
\(277\) 4598.40i 0.997441i 0.866763 + 0.498720i \(0.166197\pi\)
−0.866763 + 0.498720i \(0.833803\pi\)
\(278\) 392.582i 0.0846961i
\(279\) 0 0
\(280\) −913.258 + 2673.08i −0.194920 + 0.570526i
\(281\) −3811.87 −0.809243 −0.404621 0.914484i \(-0.632597\pi\)
−0.404621 + 0.914484i \(0.632597\pi\)
\(282\) 0 0
\(283\) 4099.09i 0.861009i −0.902588 0.430504i \(-0.858336\pi\)
0.902588 0.430504i \(-0.141664\pi\)
\(284\) −1920.00 −0.401167
\(285\) 0 0
\(286\) −2142.09 −0.442882
\(287\) 1068.31i 0.219722i
\(288\) 0 0
\(289\) 3056.49 0.622123
\(290\) 102.961 + 35.1765i 0.0208485 + 0.00712289i
\(291\) 0 0
\(292\) 2748.25i 0.550784i
\(293\) 573.453i 0.114340i −0.998364 0.0571698i \(-0.981792\pi\)
0.998364 0.0571698i \(-0.0182076\pi\)
\(294\) 0 0
\(295\) 1793.99 5250.96i 0.354068 1.03635i
\(296\) −1821.01 −0.357581
\(297\) 0 0
\(298\) 15.4687i 0.00300698i
\(299\) −4673.84 −0.903997
\(300\) 0 0
\(301\) −720.925 −0.138051
\(302\) 514.721i 0.0980757i
\(303\) 0 0
\(304\) −6949.82 −1.31118
\(305\) 895.342 2620.64i 0.168089 0.491992i
\(306\) 0 0
\(307\) 8610.98i 1.60083i −0.599447 0.800414i \(-0.704613\pi\)
0.599447 0.800414i \(-0.295387\pi\)
\(308\) 9169.46i 1.69636i
\(309\) 0 0
\(310\) −598.056 204.326i −0.109572 0.0374352i
\(311\) −3049.69 −0.556052 −0.278026 0.960574i \(-0.589680\pi\)
−0.278026 + 0.960574i \(0.589680\pi\)
\(312\) 0 0
\(313\) 4105.22i 0.741344i 0.928764 + 0.370672i \(0.120873\pi\)
−0.928764 + 0.370672i \(0.879127\pi\)
\(314\) −1337.84 −0.240442
\(315\) 0 0
\(316\) −3517.41 −0.626170
\(317\) 5420.67i 0.960427i 0.877152 + 0.480214i \(0.159441\pi\)
−0.877152 + 0.480214i \(0.840559\pi\)
\(318\) 0 0
\(319\) 735.874 0.129157
\(320\) −1048.78 + 3069.75i −0.183215 + 0.536264i
\(321\) 0 0
\(322\) 1671.25i 0.289239i
\(323\) 6039.90i 1.04046i
\(324\) 0 0
\(325\) −3513.10 + 4541.25i −0.599605 + 0.775087i
\(326\) −2047.23 −0.347809
\(327\) 0 0
\(328\) 617.121i 0.103887i
\(329\) −2467.29 −0.413454
\(330\) 0 0
\(331\) 5909.23 0.981272 0.490636 0.871365i \(-0.336765\pi\)
0.490636 + 0.871365i \(0.336765\pi\)
\(332\) 2312.24i 0.382231i
\(333\) 0 0
\(334\) −1287.49 −0.210923
\(335\) 8739.55 + 2985.87i 1.42535 + 0.486971i
\(336\) 0 0
\(337\) 1324.01i 0.214016i −0.994258 0.107008i \(-0.965873\pi\)
0.994258 0.107008i \(-0.0341271\pi\)
\(338\) 68.5214i 0.0110268i
\(339\) 0 0
\(340\) 3365.72 + 1149.90i 0.536859 + 0.183418i
\(341\) −4274.39 −0.678800
\(342\) 0 0
\(343\) 5199.58i 0.818515i
\(344\) 416.451 0.0652718
\(345\) 0 0
\(346\) 922.324 0.143308
\(347\) 11227.7i 1.73699i −0.495697 0.868495i \(-0.665087\pi\)
0.495697 0.868495i \(-0.334913\pi\)
\(348\) 0 0
\(349\) −1042.88 −0.159954 −0.0799772 0.996797i \(-0.525485\pi\)
−0.0799772 + 0.996797i \(0.525485\pi\)
\(350\) −1623.84 1256.20i −0.247994 0.191847i
\(351\) 0 0
\(352\) 8051.45i 1.21916i
\(353\) 11522.2i 1.73730i −0.495426 0.868650i \(-0.664988\pi\)
0.495426 0.868650i \(-0.335012\pi\)
\(354\) 0 0
\(355\) 939.978 2751.29i 0.140532 0.411333i
\(356\) 6036.75 0.898728
\(357\) 0 0
\(358\) 1973.21i 0.291306i
\(359\) 4751.13 0.698482 0.349241 0.937033i \(-0.386440\pi\)
0.349241 + 0.937033i \(0.386440\pi\)
\(360\) 0 0
\(361\) 12791.0 1.86484
\(362\) 2894.67i 0.420277i
\(363\) 0 0
\(364\) −7092.37 −1.02127
\(365\) 3938.13 + 1345.46i 0.564743 + 0.192944i
\(366\) 0 0
\(367\) 11120.8i 1.58174i −0.611981 0.790872i \(-0.709627\pi\)
0.611981 0.790872i \(-0.290373\pi\)
\(368\) 5044.89i 0.714627i
\(369\) 0 0
\(370\) 427.885 1252.41i 0.0601208 0.175972i
\(371\) −2869.27 −0.401523
\(372\) 0 0
\(373\) 9512.54i 1.32048i −0.751053 0.660242i \(-0.770454\pi\)
0.751053 0.660242i \(-0.229546\pi\)
\(374\) −2009.42 −0.277819
\(375\) 0 0
\(376\) 1425.26 0.195485
\(377\) 569.182i 0.0777570i
\(378\) 0 0
\(379\) 3029.06 0.410534 0.205267 0.978706i \(-0.434194\pi\)
0.205267 + 0.978706i \(0.434194\pi\)
\(380\) 3741.03 10949.9i 0.505029 1.47821i
\(381\) 0 0
\(382\) 2133.24i 0.285722i
\(383\) 10405.3i 1.38822i 0.719871 + 0.694108i \(0.244201\pi\)
−0.719871 + 0.694108i \(0.755799\pi\)
\(384\) 0 0
\(385\) −13139.5 4489.10i −1.73935 0.594249i
\(386\) −1549.27 −0.204289
\(387\) 0 0
\(388\) 6949.83i 0.909340i
\(389\) 9049.43 1.17950 0.589748 0.807587i \(-0.299227\pi\)
0.589748 + 0.807587i \(0.299227\pi\)
\(390\) 0 0
\(391\) −4384.37 −0.567077
\(392\) 1140.18i 0.146908i
\(393\) 0 0
\(394\) −2675.18 −0.342065
\(395\) 1722.02 5040.31i 0.219353 0.642039i
\(396\) 0 0
\(397\) 276.228i 0.0349206i 0.999848 + 0.0174603i \(0.00555807\pi\)
−0.999848 + 0.0174603i \(0.994442\pi\)
\(398\) 770.979i 0.0970997i
\(399\) 0 0
\(400\) −4901.77 3792.00i −0.612721 0.474000i
\(401\) −14902.5 −1.85585 −0.927925 0.372767i \(-0.878409\pi\)
−0.927925 + 0.372767i \(0.878409\pi\)
\(402\) 0 0
\(403\) 3306.14i 0.408662i
\(404\) −7404.47 −0.911847
\(405\) 0 0
\(406\) −203.525 −0.0248788
\(407\) 8951.13i 1.09015i
\(408\) 0 0
\(409\) 1116.83 0.135021 0.0675104 0.997719i \(-0.478494\pi\)
0.0675104 + 0.997719i \(0.478494\pi\)
\(410\) −424.428 145.006i −0.0511244 0.0174666i
\(411\) 0 0
\(412\) 2206.36i 0.263834i
\(413\) 10379.7i 1.23669i
\(414\) 0 0
\(415\) −3313.35 1132.00i −0.391918 0.133899i
\(416\) 6227.62 0.733976
\(417\) 0 0
\(418\) 6537.36i 0.764958i
\(419\) 5086.23 0.593027 0.296514 0.955029i \(-0.404176\pi\)
0.296514 + 0.955029i \(0.404176\pi\)
\(420\) 0 0
\(421\) −9640.06 −1.11598 −0.557990 0.829848i \(-0.688427\pi\)
−0.557990 + 0.829848i \(0.688427\pi\)
\(422\) 1584.42i 0.182769i
\(423\) 0 0
\(424\) 1657.47 0.189844
\(425\) −3295.52 + 4259.99i −0.376132 + 0.486212i
\(426\) 0 0
\(427\) 5180.30i 0.587101i
\(428\) 7269.06i 0.820942i
\(429\) 0 0
\(430\) −97.8540 + 286.416i −0.0109743 + 0.0321214i
\(431\) −857.490 −0.0958326 −0.0479163 0.998851i \(-0.515258\pi\)
−0.0479163 + 0.998851i \(0.515258\pi\)
\(432\) 0 0
\(433\) 2306.40i 0.255978i 0.991776 + 0.127989i \(0.0408523\pi\)
−0.991776 + 0.127989i \(0.959148\pi\)
\(434\) 1182.19 0.130754
\(435\) 0 0
\(436\) 1659.53 0.182287
\(437\) 14263.9i 1.56141i
\(438\) 0 0
\(439\) 711.237 0.0773246 0.0386623 0.999252i \(-0.487690\pi\)
0.0386623 + 0.999252i \(0.487690\pi\)
\(440\) 7590.17 + 2593.18i 0.822380 + 0.280966i
\(441\) 0 0
\(442\) 1554.24i 0.167257i
\(443\) 15639.9i 1.67737i 0.544618 + 0.838684i \(0.316675\pi\)
−0.544618 + 0.838684i \(0.683325\pi\)
\(444\) 0 0
\(445\) −2955.42 + 8650.43i −0.314832 + 0.921505i
\(446\) 208.673 0.0221546
\(447\) 0 0
\(448\) 6068.06i 0.639931i
\(449\) −8156.47 −0.857299 −0.428650 0.903471i \(-0.641011\pi\)
−0.428650 + 0.903471i \(0.641011\pi\)
\(450\) 0 0
\(451\) −3033.44 −0.316717
\(452\) 1017.15i 0.105846i
\(453\) 0 0
\(454\) −4024.79 −0.416063
\(455\) 3472.22 10163.1i 0.357759 1.04715i
\(456\) 0 0
\(457\) 14785.2i 1.51339i 0.653766 + 0.756697i \(0.273188\pi\)
−0.653766 + 0.756697i \(0.726812\pi\)
\(458\) 71.2802i 0.00727228i
\(459\) 0 0
\(460\) 7948.56 + 2715.62i 0.805660 + 0.275253i
\(461\) −8293.15 −0.837853 −0.418927 0.908020i \(-0.637594\pi\)
−0.418927 + 0.908020i \(0.637594\pi\)
\(462\) 0 0
\(463\) 14357.0i 1.44109i −0.693407 0.720546i \(-0.743891\pi\)
0.693407 0.720546i \(-0.256109\pi\)
\(464\) −614.368 −0.0614684
\(465\) 0 0
\(466\) 4599.04 0.457181
\(467\) 4815.25i 0.477138i −0.971126 0.238569i \(-0.923322\pi\)
0.971126 0.238569i \(-0.0766782\pi\)
\(468\) 0 0
\(469\) −17275.7 −1.70089
\(470\) −334.896 + 980.230i −0.0328672 + 0.0962014i
\(471\) 0 0
\(472\) 5995.96i 0.584717i
\(473\) 2047.05i 0.198993i
\(474\) 0 0
\(475\) 13859.3 + 10721.5i 1.33875 + 1.03566i
\(476\) −6653.11 −0.640641
\(477\) 0 0
\(478\) 5394.31i 0.516172i
\(479\) −11827.7 −1.12823 −0.564116 0.825695i \(-0.690783\pi\)
−0.564116 + 0.825695i \(0.690783\pi\)
\(480\) 0 0
\(481\) 6923.50 0.656308
\(482\) 19.7413i 0.00186554i
\(483\) 0 0
\(484\) 16209.4 1.52230
\(485\) 9958.83 + 3402.43i 0.932386 + 0.318549i
\(486\) 0 0
\(487\) 13087.8i 1.21779i 0.793251 + 0.608894i \(0.208387\pi\)
−0.793251 + 0.608894i \(0.791613\pi\)
\(488\) 2992.46i 0.277586i
\(489\) 0 0
\(490\) 784.164 + 267.910i 0.0722958 + 0.0246998i
\(491\) −6593.39 −0.606019 −0.303010 0.952988i \(-0.597991\pi\)
−0.303010 + 0.952988i \(0.597991\pi\)
\(492\) 0 0
\(493\) 533.930i 0.0487769i
\(494\) −5056.50 −0.460532
\(495\) 0 0
\(496\) 3568.61 0.323055
\(497\) 5438.55i 0.490850i
\(498\) 0 0
\(499\) 16184.8 1.45196 0.725982 0.687713i \(-0.241385\pi\)
0.725982 + 0.687713i \(0.241385\pi\)
\(500\) 8613.13 5681.86i 0.770382 0.508201i
\(501\) 0 0
\(502\) 4527.54i 0.402537i
\(503\) 10342.9i 0.916833i −0.888738 0.458416i \(-0.848417\pi\)
0.888738 0.458416i \(-0.151583\pi\)
\(504\) 0 0
\(505\) 3625.01 10610.3i 0.319428 0.934956i
\(506\) −4745.48 −0.416921
\(507\) 0 0
\(508\) 20246.2i 1.76827i
\(509\) −5648.61 −0.491887 −0.245943 0.969284i \(-0.579098\pi\)
−0.245943 + 0.969284i \(0.579098\pi\)
\(510\) 0 0
\(511\) −7784.60 −0.673915
\(512\) 11513.7i 0.993821i
\(513\) 0 0
\(514\) 4405.64 0.378063
\(515\) −3161.63 1080.17i −0.270521 0.0924234i
\(516\) 0 0
\(517\) 7005.84i 0.595970i
\(518\) 2475.67i 0.209990i
\(519\) 0 0
\(520\) −2005.77 + 5870.83i −0.169151 + 0.495102i
\(521\) 15511.7 1.30438 0.652188 0.758058i \(-0.273851\pi\)
0.652188 + 0.758058i \(0.273851\pi\)
\(522\) 0 0
\(523\) 613.845i 0.0513223i −0.999671 0.0256612i \(-0.991831\pi\)
0.999671 0.0256612i \(-0.00816910\pi\)
\(524\) −7090.89 −0.591158
\(525\) 0 0
\(526\) 4557.61 0.377797
\(527\) 3101.38i 0.256353i
\(528\) 0 0
\(529\) 1812.78 0.148992
\(530\) −389.457 + 1139.93i −0.0319188 + 0.0934254i
\(531\) 0 0
\(532\) 21645.0i 1.76396i
\(533\) 2346.30i 0.190675i
\(534\) 0 0
\(535\) 10416.3 + 3558.72i 0.841747 + 0.287583i
\(536\) 9979.51 0.804196
\(537\) 0 0
\(538\) 5746.34i 0.460487i
\(539\) 5604.53 0.447874
\(540\) 0 0
\(541\) −12701.1 −1.00936 −0.504678 0.863308i \(-0.668389\pi\)
−0.504678 + 0.863308i \(0.668389\pi\)
\(542\) 6441.12i 0.510461i
\(543\) 0 0
\(544\) 5841.91 0.460423
\(545\) −812.459 + 2378.05i −0.0638568 + 0.186907i
\(546\) 0 0
\(547\) 9413.79i 0.735840i −0.929857 0.367920i \(-0.880070\pi\)
0.929857 0.367920i \(-0.119930\pi\)
\(548\) 5364.06i 0.418141i
\(549\) 0 0
\(550\) −3566.95 + 4610.85i −0.276537 + 0.357468i
\(551\) 1737.07 0.134304
\(552\) 0 0
\(553\) 9963.31i 0.766154i
\(554\) −3611.27 −0.276947
\(555\) 0 0
\(556\) −3690.83 −0.281522
\(557\) 14085.5i 1.07149i −0.844379 0.535746i \(-0.820031\pi\)
0.844379 0.535746i \(-0.179969\pi\)
\(558\) 0 0
\(559\) −1583.35 −0.119801
\(560\) 10969.9 + 3747.87i 0.827792 + 0.282815i
\(561\) 0 0
\(562\) 2993.59i 0.224692i
\(563\) 8442.04i 0.631953i −0.948767 0.315977i \(-0.897668\pi\)
0.948767 0.315977i \(-0.102332\pi\)
\(564\) 0 0
\(565\) −1457.53 497.965i −0.108529 0.0370789i
\(566\) 3219.15 0.239065
\(567\) 0 0
\(568\) 3141.64i 0.232078i
\(569\) 3528.48 0.259968 0.129984 0.991516i \(-0.458507\pi\)
0.129984 + 0.991516i \(0.458507\pi\)
\(570\) 0 0
\(571\) −14738.1 −1.08016 −0.540078 0.841615i \(-0.681605\pi\)
−0.540078 + 0.841615i \(0.681605\pi\)
\(572\) 20138.7i 1.47210i
\(573\) 0 0
\(574\) 838.978 0.0610074
\(575\) −7782.76 + 10060.5i −0.564458 + 0.729654i
\(576\) 0 0
\(577\) 17485.6i 1.26159i 0.775951 + 0.630793i \(0.217270\pi\)
−0.775951 + 0.630793i \(0.782730\pi\)
\(578\) 2400.36i 0.172737i
\(579\) 0 0
\(580\) 330.710 967.979i 0.0236758 0.0692985i
\(581\) 6549.58 0.467681
\(582\) 0 0
\(583\) 8147.24i 0.578772i
\(584\) 4496.87 0.318633
\(585\) 0 0
\(586\) 450.352 0.0317472
\(587\) 12494.4i 0.878536i −0.898356 0.439268i \(-0.855238\pi\)
0.898356 0.439268i \(-0.144762\pi\)
\(588\) 0 0
\(589\) −10089.9 −0.705853
\(590\) 4123.75 + 1408.88i 0.287749 + 0.0983095i
\(591\) 0 0
\(592\) 7473.14i 0.518824i
\(593\) 4044.65i 0.280091i 0.990145 + 0.140046i \(0.0447249\pi\)
−0.990145 + 0.140046i \(0.955275\pi\)
\(594\) 0 0
\(595\) 3257.17 9533.65i 0.224422 0.656876i
\(596\) 145.428 0.00999492
\(597\) 0 0
\(598\) 3670.52i 0.251001i
\(599\) 21563.1 1.47086 0.735431 0.677600i \(-0.236980\pi\)
0.735431 + 0.677600i \(0.236980\pi\)
\(600\) 0 0
\(601\) 20115.9 1.36530 0.682648 0.730747i \(-0.260828\pi\)
0.682648 + 0.730747i \(0.260828\pi\)
\(602\) 566.166i 0.0383309i
\(603\) 0 0
\(604\) 4839.11 0.325994
\(605\) −7935.65 + 23227.5i −0.533273 + 1.56088i
\(606\) 0 0
\(607\) 17200.6i 1.15017i −0.818094 0.575084i \(-0.804969\pi\)
0.818094 0.575084i \(-0.195031\pi\)
\(608\) 19005.8i 1.26774i
\(609\) 0 0
\(610\) 2058.08 + 703.142i 0.136605 + 0.0466711i
\(611\) −5418.86 −0.358795
\(612\) 0 0
\(613\) 894.343i 0.0589269i −0.999566 0.0294634i \(-0.990620\pi\)
0.999566 0.0294634i \(-0.00937986\pi\)
\(614\) 6762.48 0.444481
\(615\) 0 0
\(616\) −15003.7 −0.981357
\(617\) 6856.71i 0.447392i 0.974659 + 0.223696i \(0.0718122\pi\)
−0.974659 + 0.223696i \(0.928188\pi\)
\(618\) 0 0
\(619\) −21165.2 −1.37431 −0.687157 0.726509i \(-0.741142\pi\)
−0.687157 + 0.726509i \(0.741142\pi\)
\(620\) −1920.95 + 5622.58i −0.124431 + 0.364207i
\(621\) 0 0
\(622\) 2395.02i 0.154392i
\(623\) 17099.5i 1.09964i
\(624\) 0 0
\(625\) 3925.15 + 15123.9i 0.251210 + 0.967933i
\(626\) −3223.96 −0.205839
\(627\) 0 0
\(628\) 12577.6i 0.799208i
\(629\) 6494.70 0.411702
\(630\) 0 0
\(631\) 14889.2 0.939352 0.469676 0.882839i \(-0.344371\pi\)
0.469676 + 0.882839i \(0.344371\pi\)
\(632\) 5755.42i 0.362244i
\(633\) 0 0
\(634\) −4257.03 −0.266669
\(635\) −29012.1 9911.97i −1.81309 0.619440i
\(636\) 0 0
\(637\) 4334.98i 0.269636i
\(638\) 577.906i 0.0358613i
\(639\) 0 0
\(640\) −13886.5 4744.31i −0.857673 0.293024i
\(641\) 22428.3 1.38200 0.691001 0.722854i \(-0.257170\pi\)
0.691001 + 0.722854i \(0.257170\pi\)
\(642\) 0 0
\(643\) 4262.51i 0.261426i −0.991420 0.130713i \(-0.958273\pi\)
0.991420 0.130713i \(-0.0417267\pi\)
\(644\) −15712.1 −0.961404
\(645\) 0 0
\(646\) −4743.33 −0.288891
\(647\) 19619.7i 1.19216i −0.802924 0.596082i \(-0.796723\pi\)
0.802924 0.596082i \(-0.203277\pi\)
\(648\) 0 0
\(649\) 29473.0 1.78261
\(650\) −3566.39 2758.95i −0.215208 0.166485i
\(651\) 0 0
\(652\) 19246.9i 1.15609i
\(653\) 4708.94i 0.282198i −0.989996 0.141099i \(-0.954936\pi\)
0.989996 0.141099i \(-0.0450635\pi\)
\(654\) 0 0
\(655\) 3471.49 10161.0i 0.207088 0.606140i
\(656\) 2532.57 0.150732
\(657\) 0 0
\(658\) 1937.65i 0.114798i
\(659\) 24138.8 1.42688 0.713441 0.700715i \(-0.247135\pi\)
0.713441 + 0.700715i \(0.247135\pi\)
\(660\) 0 0
\(661\) 31706.5 1.86572 0.932859 0.360241i \(-0.117305\pi\)
0.932859 + 0.360241i \(0.117305\pi\)
\(662\) 4640.72i 0.272457i
\(663\) 0 0
\(664\) −3783.44 −0.221123
\(665\) −31016.4 10596.7i −1.80867 0.617931i
\(666\) 0 0
\(667\) 1260.94i 0.0731991i
\(668\) 12104.2i 0.701087i
\(669\) 0 0
\(670\) −2344.90 + 6863.46i −0.135211 + 0.395759i
\(671\) 14709.4 0.846272
\(672\) 0 0
\(673\) 277.641i 0.0159023i 0.999968 + 0.00795116i \(0.00253096\pi\)
−0.999968 + 0.00795116i \(0.997469\pi\)
\(674\) 1039.79 0.0594231
\(675\) 0 0
\(676\) 644.199 0.0366522
\(677\) 8744.57i 0.496427i −0.968705 0.248213i \(-0.920157\pi\)
0.968705 0.248213i \(-0.0798434\pi\)
\(678\) 0 0
\(679\) −19685.9 −1.11263
\(680\) −1881.54 + 5507.22i −0.106109 + 0.310577i
\(681\) 0 0
\(682\) 3356.82i 0.188474i
\(683\) 34097.3i 1.91025i 0.296210 + 0.955123i \(0.404277\pi\)
−0.296210 + 0.955123i \(0.595723\pi\)
\(684\) 0 0
\(685\) 7686.49 + 2626.09i 0.428738 + 0.146478i
\(686\) 4083.40 0.227267
\(687\) 0 0
\(688\) 1709.05i 0.0947047i
\(689\) −6301.71 −0.348441
\(690\) 0 0
\(691\) −4982.20 −0.274286 −0.137143 0.990551i \(-0.543792\pi\)
−0.137143 + 0.990551i \(0.543792\pi\)
\(692\) 8671.17i 0.476341i
\(693\) 0 0
\(694\) 8817.50 0.482288
\(695\) 1806.92 5288.82i 0.0986195 0.288657i
\(696\) 0 0
\(697\) 2200.98i 0.119610i
\(698\) 819.008i 0.0444125i
\(699\) 0 0
\(700\) −11810.0 + 15266.4i −0.637682 + 0.824307i
\(701\) −16450.0 −0.886315 −0.443158 0.896444i \(-0.646142\pi\)
−0.443158 + 0.896444i \(0.646142\pi\)
\(702\) 0 0
\(703\) 21129.6i 1.13360i
\(704\) −17230.2 −0.922423
\(705\) 0 0
\(706\) 9048.79 0.482374
\(707\) 20973.7i 1.11570i
\(708\) 0 0
\(709\) 9139.71 0.484131 0.242066 0.970260i \(-0.422175\pi\)
0.242066 + 0.970260i \(0.422175\pi\)
\(710\) 2160.68 + 738.196i 0.114210 + 0.0390197i
\(711\) 0 0
\(712\) 9877.74i 0.519921i
\(713\) 7324.28i 0.384707i
\(714\) 0 0
\(715\) −28857.9 9859.30i −1.50941 0.515688i
\(716\) −18551.0 −0.968273
\(717\) 0 0
\(718\) 3731.22i 0.193938i
\(719\) 28268.2 1.46624 0.733121 0.680098i \(-0.238063\pi\)
0.733121 + 0.680098i \(0.238063\pi\)
\(720\) 0 0
\(721\) 6249.68 0.322816
\(722\) 10045.2i 0.517787i
\(723\) 0 0
\(724\) 27214.0 1.39696
\(725\) 1225.17 + 947.788i 0.0627609 + 0.0485517i
\(726\) 0 0
\(727\) 32221.9i 1.64380i −0.569632 0.821900i \(-0.692914\pi\)
0.569632 0.821900i \(-0.307086\pi\)
\(728\) 11605.0i 0.590811i
\(729\) 0 0
\(730\) −1056.63 + 3092.74i −0.0535723 + 0.156805i
\(731\) −1485.29 −0.0751509
\(732\) 0 0
\(733\) 10764.2i 0.542408i 0.962522 + 0.271204i \(0.0874218\pi\)
−0.962522 + 0.271204i \(0.912578\pi\)
\(734\) 8733.52 0.439183
\(735\) 0 0
\(736\) 13796.4 0.690953
\(737\) 49054.0i 2.45174i
\(738\) 0 0
\(739\) −21955.9 −1.09291 −0.546456 0.837488i \(-0.684023\pi\)
−0.546456 + 0.837488i \(0.684023\pi\)
\(740\) −11774.4 4022.73i −0.584914 0.199836i
\(741\) 0 0
\(742\) 2253.33i 0.111486i
\(743\) 5929.17i 0.292759i 0.989228 + 0.146380i \(0.0467621\pi\)
−0.989228 + 0.146380i \(0.953238\pi\)
\(744\) 0 0
\(745\) −71.1974 + 208.393i −0.00350130 + 0.0102482i
\(746\) 7470.51 0.366642
\(747\) 0 0
\(748\) 18891.4i 0.923446i
\(749\) −20590.1 −1.00447
\(750\) 0 0
\(751\) −14894.6 −0.723716 −0.361858 0.932233i \(-0.617857\pi\)
−0.361858 + 0.932233i \(0.617857\pi\)
\(752\) 5849.05i 0.283634i
\(753\) 0 0
\(754\) −446.998 −0.0215898
\(755\) −2369.09 + 6934.26i −0.114199 + 0.334256i
\(756\) 0 0
\(757\) 11935.5i 0.573058i −0.958072 0.286529i \(-0.907499\pi\)
0.958072 0.286529i \(-0.0925014\pi\)
\(758\) 2378.82i 0.113988i
\(759\) 0 0
\(760\) 17917.0 + 6121.33i 0.855154 + 0.292163i
\(761\) 28482.5 1.35675 0.678377 0.734714i \(-0.262683\pi\)
0.678377 + 0.734714i \(0.262683\pi\)
\(762\) 0 0
\(763\) 4700.75i 0.223039i
\(764\) −20055.5 −0.949715
\(765\) 0 0
\(766\) −8171.63 −0.385448
\(767\) 22796.7i 1.07320i
\(768\) 0 0
\(769\) −13392.3 −0.628009 −0.314005 0.949421i \(-0.601671\pi\)
−0.314005 + 0.949421i \(0.601671\pi\)
\(770\) 3525.44 10318.9i 0.164997 0.482943i
\(771\) 0 0
\(772\) 14565.3i 0.679039i
\(773\) 37031.6i 1.72307i −0.507696 0.861536i \(-0.669503\pi\)
0.507696 0.861536i \(-0.330497\pi\)
\(774\) 0 0
\(775\) −7116.49 5505.30i −0.329848 0.255169i
\(776\) 11371.8 0.526060
\(777\) 0 0
\(778\) 7106.81i 0.327496i
\(779\) −7160.60 −0.329339
\(780\) 0 0
\(781\) 15442.7 0.707531
\(782\) 3443.19i 0.157453i
\(783\) 0 0
\(784\) −4679.12 −0.213152
\(785\) −18023.3 6157.65i −0.819463 0.279969i
\(786\) 0 0
\(787\) 29263.5i 1.32545i −0.748862 0.662726i \(-0.769399\pi\)
0.748862 0.662726i \(-0.230601\pi\)
\(788\) 25150.5i 1.13699i
\(789\) 0 0
\(790\) 3958.32 + 1352.36i 0.178267 + 0.0609048i
\(791\) 2881.14 0.129509
\(792\) 0 0
\(793\) 11377.4i 0.509485i
\(794\) −216.931 −0.00969596