Properties

Label 324.5.d.e.163.4
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.4
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.e.163.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.76125 + 1.36126i) q^{2} +(12.2940 - 10.2400i) q^{4} +28.6092 q^{5} +25.6487i q^{7} +(-32.3013 + 55.2506i) q^{8} +O(q^{10})\) \(q+(-3.76125 + 1.36126i) q^{2} +(12.2940 - 10.2400i) q^{4} +28.6092 q^{5} +25.6487i q^{7} +(-32.3013 + 55.2506i) q^{8} +(-107.606 + 38.9445i) q^{10} -108.505i q^{11} -88.4493 q^{13} +(-34.9144 - 96.4710i) q^{14} +(46.2831 - 251.781i) q^{16} -504.169 q^{17} +191.405i q^{19} +(351.721 - 292.960i) q^{20} +(147.703 + 408.113i) q^{22} -960.592i q^{23} +193.489 q^{25} +(332.680 - 120.402i) q^{26} +(262.643 + 315.324i) q^{28} -793.341 q^{29} +329.584i q^{31} +(168.657 + 1010.02i) q^{32} +(1896.30 - 686.303i) q^{34} +733.789i q^{35} +209.943 q^{37} +(-260.551 - 719.921i) q^{38} +(-924.116 + 1580.68i) q^{40} -1056.40 q^{41} +3334.14i q^{43} +(-1111.09 - 1333.95i) q^{44} +(1307.61 + 3613.02i) q^{46} +1128.36i q^{47} +1743.15 q^{49} +(-727.758 + 263.387i) q^{50} +(-1087.39 + 905.724i) q^{52} -1138.62 q^{53} -3104.23i q^{55} +(-1417.10 - 828.486i) q^{56} +(2983.95 - 1079.94i) q^{58} -4662.09i q^{59} -5599.68 q^{61} +(-448.648 - 1239.65i) q^{62} +(-2009.25 - 3569.33i) q^{64} -2530.47 q^{65} -7075.70i q^{67} +(-6198.24 + 5162.71i) q^{68} +(-998.874 - 2759.96i) q^{70} -4433.42i q^{71} -1953.21 q^{73} +(-789.648 + 285.786i) q^{74} +(1959.99 + 2353.12i) q^{76} +2783.00 q^{77} -1759.65i q^{79} +(1324.12 - 7203.27i) q^{80} +(3973.38 - 1438.03i) q^{82} -3027.21i q^{83} -14423.9 q^{85} +(-4538.62 - 12540.5i) q^{86} +(5994.94 + 3504.84i) q^{88} +559.336 q^{89} -2268.61i q^{91} +(-9836.50 - 11809.5i) q^{92} +(-1535.98 - 4244.03i) q^{94} +5475.95i q^{95} -2201.78 q^{97} +(-6556.40 + 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + O(q^{10}) \) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + 14q^{10} + 2q^{13} + 252q^{14} + q^{16} + 28q^{17} - 140q^{20} + 33q^{22} + 1752q^{25} - 548q^{26} - 258q^{28} + 526q^{29} - 121q^{32} - 385q^{34} - 4q^{37} + 1395q^{38} + 2276q^{40} - 2762q^{41} - 3357q^{44} + 1788q^{46} - 3428q^{49} + 6375q^{50} - 1438q^{52} + 5044q^{53} - 7506q^{56} + 4064q^{58} + 2q^{61} + 9162q^{62} + 4513q^{64} - 2014q^{65} - 11405q^{68} - 3666q^{70} - 1708q^{73} + 14620q^{74} - 1581q^{76} - 3942q^{77} - 22760q^{80} - 4243q^{82} + 1252q^{85} + 22113q^{86} - 1995q^{88} - 6524q^{89} - 30294q^{92} - 7524q^{94} - 5638q^{97} + 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.76125 + 1.36126i −0.940312 + 0.340314i
\(3\) 0 0
\(4\) 12.2940 10.2400i 0.768373 0.640003i
\(5\) 28.6092 1.14437 0.572185 0.820125i \(-0.306096\pi\)
0.572185 + 0.820125i \(0.306096\pi\)
\(6\) 0 0
\(7\) 25.6487i 0.523442i 0.965144 + 0.261721i \(0.0842900\pi\)
−0.965144 + 0.261721i \(0.915710\pi\)
\(8\) −32.3013 + 55.2506i −0.504708 + 0.863290i
\(9\) 0 0
\(10\) −107.606 + 38.9445i −1.07606 + 0.389445i
\(11\) 108.505i 0.896732i −0.893850 0.448366i \(-0.852006\pi\)
0.893850 0.448366i \(-0.147994\pi\)
\(12\) 0 0
\(13\) −88.4493 −0.523368 −0.261684 0.965154i \(-0.584278\pi\)
−0.261684 + 0.965154i \(0.584278\pi\)
\(14\) −34.9144 96.4710i −0.178135 0.492199i
\(15\) 0 0
\(16\) 46.2831 251.781i 0.180793 0.983521i
\(17\) −504.169 −1.74453 −0.872265 0.489034i \(-0.837349\pi\)
−0.872265 + 0.489034i \(0.837349\pi\)
\(18\) 0 0
\(19\) 191.405i 0.530207i 0.964220 + 0.265104i \(0.0854062\pi\)
−0.964220 + 0.265104i \(0.914594\pi\)
\(20\) 351.721 292.960i 0.879302 0.732400i
\(21\) 0 0
\(22\) 147.703 + 408.113i 0.305170 + 0.843208i
\(23\) 960.592i 1.81586i −0.419118 0.907932i \(-0.637661\pi\)
0.419118 0.907932i \(-0.362339\pi\)
\(24\) 0 0
\(25\) 193.489 0.309582
\(26\) 332.680 120.402i 0.492129 0.178110i
\(27\) 0 0
\(28\) 262.643 + 315.324i 0.335004 + 0.402199i
\(29\) −793.341 −0.943331 −0.471665 0.881778i \(-0.656347\pi\)
−0.471665 + 0.881778i \(0.656347\pi\)
\(30\) 0 0
\(31\) 329.584i 0.342959i 0.985188 + 0.171480i \(0.0548547\pi\)
−0.985188 + 0.171480i \(0.945145\pi\)
\(32\) 168.657 + 1010.02i 0.164704 + 0.986343i
\(33\) 0 0
\(34\) 1896.30 686.303i 1.64040 0.593688i
\(35\) 733.789i 0.599011i
\(36\) 0 0
\(37\) 209.943 0.153355 0.0766775 0.997056i \(-0.475569\pi\)
0.0766775 + 0.997056i \(0.475569\pi\)
\(38\) −260.551 719.921i −0.180437 0.498560i
\(39\) 0 0
\(40\) −924.116 + 1580.68i −0.577573 + 0.987923i
\(41\) −1056.40 −0.628435 −0.314218 0.949351i \(-0.601742\pi\)
−0.314218 + 0.949351i \(0.601742\pi\)
\(42\) 0 0
\(43\) 3334.14i 1.80322i 0.432555 + 0.901608i \(0.357612\pi\)
−0.432555 + 0.901608i \(0.642388\pi\)
\(44\) −1111.09 1333.95i −0.573911 0.689024i
\(45\) 0 0
\(46\) 1307.61 + 3613.02i 0.617964 + 1.70748i
\(47\) 1128.36i 0.510799i 0.966836 + 0.255400i \(0.0822071\pi\)
−0.966836 + 0.255400i \(0.917793\pi\)
\(48\) 0 0
\(49\) 1743.15 0.726008
\(50\) −727.758 + 263.387i −0.291103 + 0.105355i
\(51\) 0 0
\(52\) −1087.39 + 905.724i −0.402142 + 0.334957i
\(53\) −1138.62 −0.405346 −0.202673 0.979247i \(-0.564963\pi\)
−0.202673 + 0.979247i \(0.564963\pi\)
\(54\) 0 0
\(55\) 3104.23i 1.02619i
\(56\) −1417.10 828.486i −0.451882 0.264185i
\(57\) 0 0
\(58\) 2983.95 1079.94i 0.887025 0.321029i
\(59\) 4662.09i 1.33930i −0.742678 0.669648i \(-0.766445\pi\)
0.742678 0.669648i \(-0.233555\pi\)
\(60\) 0 0
\(61\) −5599.68 −1.50488 −0.752442 0.658658i \(-0.771124\pi\)
−0.752442 + 0.658658i \(0.771124\pi\)
\(62\) −448.648 1239.65i −0.116714 0.322488i
\(63\) 0 0
\(64\) −2009.25 3569.33i −0.490540 0.871419i
\(65\) −2530.47 −0.598927
\(66\) 0 0
\(67\) 7075.70i 1.57623i −0.615527 0.788116i \(-0.711057\pi\)
0.615527 0.788116i \(-0.288943\pi\)
\(68\) −6198.24 + 5162.71i −1.34045 + 1.11650i
\(69\) 0 0
\(70\) −998.874 2759.96i −0.203852 0.563257i
\(71\) 4433.42i 0.879472i −0.898127 0.439736i \(-0.855072\pi\)
0.898127 0.439736i \(-0.144928\pi\)
\(72\) 0 0
\(73\) −1953.21 −0.366524 −0.183262 0.983064i \(-0.558666\pi\)
−0.183262 + 0.983064i \(0.558666\pi\)
\(74\) −789.648 + 285.786i −0.144202 + 0.0521889i
\(75\) 0 0
\(76\) 1959.99 + 2353.12i 0.339334 + 0.407397i
\(77\) 2783.00 0.469387
\(78\) 0 0
\(79\) 1759.65i 0.281950i −0.990013 0.140975i \(-0.954976\pi\)
0.990013 0.140975i \(-0.0450238\pi\)
\(80\) 1324.12 7203.27i 0.206894 1.12551i
\(81\) 0 0
\(82\) 3973.38 1438.03i 0.590925 0.213865i
\(83\) 3027.21i 0.439427i −0.975564 0.219714i \(-0.929488\pi\)
0.975564 0.219714i \(-0.0705123\pi\)
\(84\) 0 0
\(85\) −14423.9 −1.99639
\(86\) −4538.62 12540.5i −0.613659 1.69558i
\(87\) 0 0
\(88\) 5994.94 + 3504.84i 0.774140 + 0.452588i
\(89\) 559.336 0.0706144 0.0353072 0.999377i \(-0.488759\pi\)
0.0353072 + 0.999377i \(0.488759\pi\)
\(90\) 0 0
\(91\) 2268.61i 0.273953i
\(92\) −9836.50 11809.5i −1.16216 1.39526i
\(93\) 0 0
\(94\) −1535.98 4244.03i −0.173832 0.480311i
\(95\) 5475.95i 0.606753i
\(96\) 0 0
\(97\) −2201.78 −0.234007 −0.117004 0.993131i \(-0.537329\pi\)
−0.117004 + 0.993131i \(0.537329\pi\)
\(98\) −6556.40 + 2372.87i −0.682674 + 0.247071i
\(99\) 0 0
\(100\) 2378.74 1981.33i 0.237874 0.198133i
\(101\) 731.682 0.0717265 0.0358632 0.999357i \(-0.488582\pi\)
0.0358632 + 0.999357i \(0.488582\pi\)
\(102\) 0 0
\(103\) 9853.96i 0.928831i 0.885618 + 0.464415i \(0.153735\pi\)
−0.885618 + 0.464415i \(0.846265\pi\)
\(104\) 2857.03 4886.87i 0.264148 0.451819i
\(105\) 0 0
\(106\) 4282.61 1549.95i 0.381151 0.137945i
\(107\) 804.642i 0.0702806i −0.999382 0.0351403i \(-0.988812\pi\)
0.999382 0.0351403i \(-0.0111878\pi\)
\(108\) 0 0
\(109\) −17324.9 −1.45820 −0.729102 0.684405i \(-0.760062\pi\)
−0.729102 + 0.684405i \(0.760062\pi\)
\(110\) 4225.66 + 11675.8i 0.349228 + 0.964941i
\(111\) 0 0
\(112\) 6457.86 + 1187.10i 0.514816 + 0.0946348i
\(113\) −17147.9 −1.34293 −0.671465 0.741036i \(-0.734335\pi\)
−0.671465 + 0.741036i \(0.734335\pi\)
\(114\) 0 0
\(115\) 27481.8i 2.07802i
\(116\) −9753.31 + 8123.85i −0.724829 + 0.603734i
\(117\) 0 0
\(118\) 6346.30 + 17535.3i 0.455782 + 1.25936i
\(119\) 12931.3i 0.913160i
\(120\) 0 0
\(121\) 2867.76 0.195872
\(122\) 21061.8 7622.59i 1.41506 0.512133i
\(123\) 0 0
\(124\) 3374.95 + 4051.89i 0.219495 + 0.263520i
\(125\) −12345.2 −0.790094
\(126\) 0 0
\(127\) 9591.51i 0.594675i 0.954772 + 0.297337i \(0.0960986\pi\)
−0.954772 + 0.297337i \(0.903901\pi\)
\(128\) 12416.1 + 10690.0i 0.757816 + 0.652468i
\(129\) 0 0
\(130\) 9517.71 3444.61i 0.563178 0.203823i
\(131\) 4541.75i 0.264655i 0.991206 + 0.132328i \(0.0422451\pi\)
−0.991206 + 0.132328i \(0.957755\pi\)
\(132\) 0 0
\(133\) −4909.28 −0.277533
\(134\) 9631.84 + 26613.5i 0.536414 + 1.48215i
\(135\) 0 0
\(136\) 16285.3 27855.6i 0.880478 1.50604i
\(137\) 4901.64 0.261156 0.130578 0.991438i \(-0.458317\pi\)
0.130578 + 0.991438i \(0.458317\pi\)
\(138\) 0 0
\(139\) 8650.79i 0.447740i −0.974619 0.223870i \(-0.928131\pi\)
0.974619 0.223870i \(-0.0718691\pi\)
\(140\) 7514.03 + 9021.17i 0.383369 + 0.460264i
\(141\) 0 0
\(142\) 6035.02 + 16675.2i 0.299297 + 0.826978i
\(143\) 9597.15i 0.469321i
\(144\) 0 0
\(145\) −22696.9 −1.07952
\(146\) 7346.49 2658.81i 0.344647 0.124733i
\(147\) 0 0
\(148\) 2581.03 2149.83i 0.117834 0.0981476i
\(149\) 12692.9 0.571727 0.285863 0.958270i \(-0.407720\pi\)
0.285863 + 0.958270i \(0.407720\pi\)
\(150\) 0 0
\(151\) 12765.6i 0.559869i −0.960019 0.279934i \(-0.909687\pi\)
0.960019 0.279934i \(-0.0903127\pi\)
\(152\) −10575.2 6182.63i −0.457723 0.267600i
\(153\) 0 0
\(154\) −10467.5 + 3788.37i −0.441370 + 0.159739i
\(155\) 9429.14i 0.392472i
\(156\) 0 0
\(157\) −40566.0 −1.64575 −0.822873 0.568225i \(-0.807630\pi\)
−0.822873 + 0.568225i \(0.807630\pi\)
\(158\) 2395.34 + 6618.49i 0.0959517 + 0.265121i
\(159\) 0 0
\(160\) 4825.15 + 28895.8i 0.188482 + 1.12874i
\(161\) 24637.9 0.950499
\(162\) 0 0
\(163\) 6872.98i 0.258684i −0.991600 0.129342i \(-0.958713\pi\)
0.991600 0.129342i \(-0.0412865\pi\)
\(164\) −12987.3 + 10817.6i −0.482873 + 0.402200i
\(165\) 0 0
\(166\) 4120.81 + 11386.1i 0.149543 + 0.413199i
\(167\) 35109.3i 1.25889i 0.777043 + 0.629447i \(0.216719\pi\)
−0.777043 + 0.629447i \(0.783281\pi\)
\(168\) 0 0
\(169\) −20737.7 −0.726086
\(170\) 54251.8 19634.6i 1.87723 0.679398i
\(171\) 0 0
\(172\) 34141.8 + 40989.9i 1.15406 + 1.38554i
\(173\) −2983.45 −0.0996841 −0.0498420 0.998757i \(-0.515872\pi\)
−0.0498420 + 0.998757i \(0.515872\pi\)
\(174\) 0 0
\(175\) 4962.72i 0.162048i
\(176\) −27319.4 5021.92i −0.881955 0.162123i
\(177\) 0 0
\(178\) −2103.80 + 761.400i −0.0663995 + 0.0240311i
\(179\) 45199.3i 1.41067i −0.708874 0.705335i \(-0.750797\pi\)
0.708874 0.705335i \(-0.249203\pi\)
\(180\) 0 0
\(181\) 27600.9 0.842492 0.421246 0.906946i \(-0.361593\pi\)
0.421246 + 0.906946i \(0.361593\pi\)
\(182\) 3088.15 + 8532.78i 0.0932301 + 0.257601i
\(183\) 0 0
\(184\) 53073.2 + 31028.4i 1.56762 + 0.916481i
\(185\) 6006.31 0.175495
\(186\) 0 0
\(187\) 54704.7i 1.56438i
\(188\) 11554.4 + 13872.0i 0.326913 + 0.392484i
\(189\) 0 0
\(190\) −7454.16 20596.4i −0.206487 0.570537i
\(191\) 18822.7i 0.515958i 0.966151 + 0.257979i \(0.0830565\pi\)
−0.966151 + 0.257979i \(0.916943\pi\)
\(192\) 0 0
\(193\) 9454.22 0.253811 0.126906 0.991915i \(-0.459495\pi\)
0.126906 + 0.991915i \(0.459495\pi\)
\(194\) 8281.43 2997.18i 0.220040 0.0796360i
\(195\) 0 0
\(196\) 21430.2 17849.9i 0.557845 0.464647i
\(197\) 21650.0 0.557860 0.278930 0.960311i \(-0.410020\pi\)
0.278930 + 0.960311i \(0.410020\pi\)
\(198\) 0 0
\(199\) 25261.4i 0.637898i −0.947772 0.318949i \(-0.896670\pi\)
0.947772 0.318949i \(-0.103330\pi\)
\(200\) −6249.93 + 10690.4i −0.156248 + 0.267259i
\(201\) 0 0
\(202\) −2752.04 + 996.006i −0.0674453 + 0.0244095i
\(203\) 20348.1i 0.493779i
\(204\) 0 0
\(205\) −30222.8 −0.719162
\(206\) −13413.8 37063.2i −0.316094 0.873390i
\(207\) 0 0
\(208\) −4093.70 + 22269.9i −0.0946214 + 0.514744i
\(209\) 20768.3 0.475454
\(210\) 0 0
\(211\) 21562.9i 0.484331i −0.970235 0.242166i \(-0.922142\pi\)
0.970235 0.242166i \(-0.0778577\pi\)
\(212\) −13998.1 + 11659.5i −0.311456 + 0.259422i
\(213\) 0 0
\(214\) 1095.32 + 3026.46i 0.0239175 + 0.0660856i
\(215\) 95387.3i 2.06354i
\(216\) 0 0
\(217\) −8453.38 −0.179519
\(218\) 65163.3 23583.7i 1.37117 0.496247i
\(219\) 0 0
\(220\) −31787.5 38163.3i −0.656766 0.788499i
\(221\) 44593.4 0.913032
\(222\) 0 0
\(223\) 19294.4i 0.387992i 0.981002 + 0.193996i \(0.0621448\pi\)
−0.981002 + 0.193996i \(0.937855\pi\)
\(224\) −25905.5 + 4325.83i −0.516293 + 0.0862130i
\(225\) 0 0
\(226\) 64497.4 23342.7i 1.26277 0.457018i
\(227\) 64830.0i 1.25813i 0.777354 + 0.629063i \(0.216561\pi\)
−0.777354 + 0.629063i \(0.783439\pi\)
\(228\) 0 0
\(229\) 39150.9 0.746570 0.373285 0.927717i \(-0.378231\pi\)
0.373285 + 0.927717i \(0.378231\pi\)
\(230\) 37409.8 + 103366.i 0.707179 + 1.95399i
\(231\) 0 0
\(232\) 25626.0 43832.5i 0.476107 0.814368i
\(233\) 2307.53 0.0425045 0.0212522 0.999774i \(-0.493235\pi\)
0.0212522 + 0.999774i \(0.493235\pi\)
\(234\) 0 0
\(235\) 32281.4i 0.584543i
\(236\) −47740.0 57315.6i −0.857154 1.02908i
\(237\) 0 0
\(238\) 17602.8 + 48637.7i 0.310761 + 0.858655i
\(239\) 76209.8i 1.33418i −0.744976 0.667091i \(-0.767539\pi\)
0.744976 0.667091i \(-0.232461\pi\)
\(240\) 0 0
\(241\) 16314.2 0.280888 0.140444 0.990089i \(-0.455147\pi\)
0.140444 + 0.990089i \(0.455147\pi\)
\(242\) −10786.3 + 3903.75i −0.184180 + 0.0666579i
\(243\) 0 0
\(244\) −68842.2 + 57340.9i −1.15631 + 0.963130i
\(245\) 49870.1 0.830822
\(246\) 0 0
\(247\) 16929.6i 0.277494i
\(248\) −18209.7 10646.0i −0.296073 0.173094i
\(249\) 0 0
\(250\) 46433.4 16805.0i 0.742934 0.268880i
\(251\) 33833.6i 0.537033i 0.963275 + 0.268517i \(0.0865334\pi\)
−0.963275 + 0.268517i \(0.913467\pi\)
\(252\) 0 0
\(253\) −104229. −1.62834
\(254\) −13056.5 36076.0i −0.202376 0.559180i
\(255\) 0 0
\(256\) −61251.8 23306.4i −0.934628 0.355628i
\(257\) 57546.1 0.871264 0.435632 0.900125i \(-0.356525\pi\)
0.435632 + 0.900125i \(0.356525\pi\)
\(258\) 0 0
\(259\) 5384.76i 0.0802725i
\(260\) −31109.5 + 25912.1i −0.460199 + 0.383315i
\(261\) 0 0
\(262\) −6182.49 17082.6i −0.0900659 0.248859i
\(263\) 78541.9i 1.13551i −0.823199 0.567753i \(-0.807813\pi\)
0.823199 0.567753i \(-0.192187\pi\)
\(264\) 0 0
\(265\) −32574.9 −0.463865
\(266\) 18465.0 6682.78i 0.260967 0.0944483i
\(267\) 0 0
\(268\) −72455.5 86988.4i −1.00879 1.21113i
\(269\) 5376.96 0.0743074 0.0371537 0.999310i \(-0.488171\pi\)
0.0371537 + 0.999310i \(0.488171\pi\)
\(270\) 0 0
\(271\) 108113.i 1.47211i −0.676924 0.736053i \(-0.736688\pi\)
0.676924 0.736053i \(-0.263312\pi\)
\(272\) −23334.5 + 126940.i −0.315399 + 1.71578i
\(273\) 0 0
\(274\) −18436.3 + 6672.39i −0.245568 + 0.0888752i
\(275\) 20994.4i 0.277612i
\(276\) 0 0
\(277\) −43942.3 −0.572695 −0.286347 0.958126i \(-0.592441\pi\)
−0.286347 + 0.958126i \(0.592441\pi\)
\(278\) 11775.9 + 32537.8i 0.152372 + 0.421015i
\(279\) 0 0
\(280\) −40542.2 23702.3i −0.517120 0.302326i
\(281\) −50871.3 −0.644259 −0.322130 0.946696i \(-0.604399\pi\)
−0.322130 + 0.946696i \(0.604399\pi\)
\(282\) 0 0
\(283\) 26395.1i 0.329572i −0.986329 0.164786i \(-0.947307\pi\)
0.986329 0.164786i \(-0.0526933\pi\)
\(284\) −45398.4 54504.3i −0.562864 0.675762i
\(285\) 0 0
\(286\) −13064.2 36097.2i −0.159717 0.441308i
\(287\) 27095.2i 0.328950i
\(288\) 0 0
\(289\) 170665. 2.04338
\(290\) 85368.6 30896.3i 1.01508 0.367375i
\(291\) 0 0
\(292\) −24012.7 + 20000.9i −0.281627 + 0.234576i
\(293\) −130791. −1.52350 −0.761748 0.647873i \(-0.775659\pi\)
−0.761748 + 0.647873i \(0.775659\pi\)
\(294\) 0 0
\(295\) 133379.i 1.53265i
\(296\) −6781.44 + 11599.5i −0.0773995 + 0.132390i
\(297\) 0 0
\(298\) −47741.2 + 17278.3i −0.537602 + 0.194567i
\(299\) 84963.6i 0.950365i
\(300\) 0 0
\(301\) −85516.3 −0.943879
\(302\) 17377.2 + 48014.4i 0.190531 + 0.526451i
\(303\) 0 0
\(304\) 48192.2 + 8858.80i 0.521470 + 0.0958579i
\(305\) −160202. −1.72214
\(306\) 0 0
\(307\) 54227.3i 0.575362i 0.957726 + 0.287681i \(0.0928843\pi\)
−0.957726 + 0.287681i \(0.907116\pi\)
\(308\) 34214.1 28498.0i 0.360664 0.300409i
\(309\) 0 0
\(310\) −12835.5 35465.3i −0.133564 0.369046i
\(311\) 135960.i 1.40569i 0.711341 + 0.702847i \(0.248088\pi\)
−0.711341 + 0.702847i \(0.751912\pi\)
\(312\) 0 0
\(313\) 164388. 1.67796 0.838981 0.544160i \(-0.183152\pi\)
0.838981 + 0.544160i \(0.183152\pi\)
\(314\) 152579. 55220.7i 1.54751 0.560070i
\(315\) 0 0
\(316\) −18018.9 21633.1i −0.180449 0.216643i
\(317\) −120619. −1.20032 −0.600160 0.799880i \(-0.704896\pi\)
−0.600160 + 0.799880i \(0.704896\pi\)
\(318\) 0 0
\(319\) 86081.1i 0.845915i
\(320\) −57483.1 102116.i −0.561359 0.997225i
\(321\) 0 0
\(322\) −92669.2 + 33538.5i −0.893766 + 0.323468i
\(323\) 96500.4i 0.924962i
\(324\) 0 0
\(325\) −17113.9 −0.162025
\(326\) 9355.88 + 25851.0i 0.0880338 + 0.243244i
\(327\) 0 0
\(328\) 34123.1 58366.7i 0.317176 0.542522i
\(329\) −28940.8 −0.267374
\(330\) 0 0
\(331\) 115682.i 1.05587i 0.849284 + 0.527936i \(0.177034\pi\)
−0.849284 + 0.527936i \(0.822966\pi\)
\(332\) −30998.8 37216.5i −0.281235 0.337644i
\(333\) 0 0
\(334\) −47792.7 132055.i −0.428419 1.18375i
\(335\) 202430.i 1.80379i
\(336\) 0 0
\(337\) 187736. 1.65306 0.826528 0.562895i \(-0.190313\pi\)
0.826528 + 0.562895i \(0.190313\pi\)
\(338\) 77999.7 28229.4i 0.682747 0.247097i
\(339\) 0 0
\(340\) −177327. + 147701.i −1.53397 + 1.27769i
\(341\) 35761.3 0.307542
\(342\) 0 0
\(343\) 106292.i 0.903465i
\(344\) −184213. 107697.i −1.55670 0.910097i
\(345\) 0 0
\(346\) 11221.5 4061.23i 0.0937341 0.0339239i
\(347\) 135244.i 1.12320i −0.827408 0.561601i \(-0.810186\pi\)
0.827408 0.561601i \(-0.189814\pi\)
\(348\) 0 0
\(349\) 3302.89 0.0271171 0.0135585 0.999908i \(-0.495684\pi\)
0.0135585 + 0.999908i \(0.495684\pi\)
\(350\) −6755.54 18666.0i −0.0551472 0.152376i
\(351\) 0 0
\(352\) 109591. 18300.1i 0.884485 0.147695i
\(353\) −42732.8 −0.342935 −0.171467 0.985190i \(-0.554851\pi\)
−0.171467 + 0.985190i \(0.554851\pi\)
\(354\) 0 0
\(355\) 126837.i 1.00644i
\(356\) 6876.46 5727.63i 0.0542582 0.0451934i
\(357\) 0 0
\(358\) 61527.8 + 170006.i 0.480071 + 1.32647i
\(359\) 175816.i 1.36418i −0.731270 0.682088i \(-0.761072\pi\)
0.731270 0.682088i \(-0.238928\pi\)
\(360\) 0 0
\(361\) 93685.2 0.718880
\(362\) −103814. + 37571.9i −0.792205 + 0.286712i
\(363\) 0 0
\(364\) −23230.6 27890.1i −0.175331 0.210498i
\(365\) −55879.8 −0.419439
\(366\) 0 0
\(367\) 7929.69i 0.0588740i 0.999567 + 0.0294370i \(0.00937145\pi\)
−0.999567 + 0.0294370i \(0.990629\pi\)
\(368\) −241859. 44459.1i −1.78594 0.328296i
\(369\) 0 0
\(370\) −22591.2 + 8176.13i −0.165020 + 0.0597234i
\(371\) 29204.0i 0.212175i
\(372\) 0 0
\(373\) 246672. 1.77297 0.886486 0.462755i \(-0.153139\pi\)
0.886486 + 0.462755i \(0.153139\pi\)
\(374\) −74467.0 205758.i −0.532379 1.47100i
\(375\) 0 0
\(376\) −62342.3 36447.4i −0.440968 0.257805i
\(377\) 70170.4 0.493709
\(378\) 0 0
\(379\) 147423.i 1.02633i 0.858291 + 0.513163i \(0.171526\pi\)
−0.858291 + 0.513163i \(0.828474\pi\)
\(380\) 56073.9 + 67321.1i 0.388324 + 0.466212i
\(381\) 0 0
\(382\) −25622.5 70796.7i −0.175588 0.485161i
\(383\) 122362.i 0.834158i 0.908870 + 0.417079i \(0.136946\pi\)
−0.908870 + 0.417079i \(0.863054\pi\)
\(384\) 0 0
\(385\) 79619.4 0.537153
\(386\) −35559.6 + 12869.6i −0.238662 + 0.0863755i
\(387\) 0 0
\(388\) −27068.6 + 22546.3i −0.179805 + 0.149765i
\(389\) 183456. 1.21236 0.606182 0.795326i \(-0.292700\pi\)
0.606182 + 0.795326i \(0.292700\pi\)
\(390\) 0 0
\(391\) 484301.i 3.16783i
\(392\) −56305.9 + 96309.8i −0.366422 + 0.626756i
\(393\) 0 0
\(394\) −81431.0 + 29471.2i −0.524562 + 0.189848i
\(395\) 50342.3i 0.322656i
\(396\) 0 0
\(397\) 81466.1 0.516887 0.258444 0.966026i \(-0.416790\pi\)
0.258444 + 0.966026i \(0.416790\pi\)
\(398\) 34387.2 + 95014.4i 0.217086 + 0.599823i
\(399\) 0 0
\(400\) 8955.24 48716.8i 0.0559703 0.304480i
\(401\) −201168. −1.25104 −0.625518 0.780209i \(-0.715113\pi\)
−0.625518 + 0.780209i \(0.715113\pi\)
\(402\) 0 0
\(403\) 29151.4i 0.179494i
\(404\) 8995.27 7492.45i 0.0551127 0.0459051i
\(405\) 0 0
\(406\) 27699.0 + 76534.4i 0.168040 + 0.464306i
\(407\) 22779.8i 0.137518i
\(408\) 0 0
\(409\) −140640. −0.840742 −0.420371 0.907352i \(-0.638100\pi\)
−0.420371 + 0.907352i \(0.638100\pi\)
\(410\) 113675. 41141.0i 0.676237 0.244741i
\(411\) 0 0
\(412\) 100905. + 121144.i 0.594454 + 0.713688i
\(413\) 119576. 0.701044
\(414\) 0 0
\(415\) 86606.3i 0.502867i
\(416\) −14917.6 89335.1i −0.0862009 0.516221i
\(417\) 0 0
\(418\) −78114.7 + 28271.0i −0.447075 + 0.161804i
\(419\) 153693.i 0.875441i 0.899111 + 0.437720i \(0.144214\pi\)
−0.899111 + 0.437720i \(0.855786\pi\)
\(420\) 0 0
\(421\) 154412. 0.871197 0.435599 0.900141i \(-0.356537\pi\)
0.435599 + 0.900141i \(0.356537\pi\)
\(422\) 29352.6 + 81103.5i 0.164825 + 0.455422i
\(423\) 0 0
\(424\) 36778.8 62909.2i 0.204581 0.349931i
\(425\) −97550.9 −0.540074
\(426\) 0 0
\(427\) 143624.i 0.787720i
\(428\) −8239.57 9892.24i −0.0449797 0.0540017i
\(429\) 0 0
\(430\) −129847. 358775.i −0.702253 1.94038i
\(431\) 191579.i 1.03132i 0.856793 + 0.515660i \(0.172453\pi\)
−0.856793 + 0.515660i \(0.827547\pi\)
\(432\) 0 0
\(433\) −53963.8 −0.287824 −0.143912 0.989591i \(-0.545968\pi\)
−0.143912 + 0.989591i \(0.545968\pi\)
\(434\) 31795.2 11507.2i 0.168804 0.0610929i
\(435\) 0 0
\(436\) −212992. + 177408.i −1.12044 + 0.933255i
\(437\) 183862. 0.962784
\(438\) 0 0
\(439\) 16842.9i 0.0873951i −0.999045 0.0436976i \(-0.986086\pi\)
0.999045 0.0436976i \(-0.0139138\pi\)
\(440\) 171511. + 100271.i 0.885902 + 0.517928i
\(441\) 0 0
\(442\) −167727. + 60703.0i −0.858534 + 0.310718i
\(443\) 161786.i 0.824391i 0.911095 + 0.412195i \(0.135238\pi\)
−0.911095 + 0.412195i \(0.864762\pi\)
\(444\) 0 0
\(445\) 16002.2 0.0808089
\(446\) −26264.7 72571.2i −0.132039 0.364833i
\(447\) 0 0
\(448\) 91548.6 51534.6i 0.456137 0.256769i
\(449\) −127200. −0.630949 −0.315475 0.948934i \(-0.602164\pi\)
−0.315475 + 0.948934i \(0.602164\pi\)
\(450\) 0 0
\(451\) 114624.i 0.563538i
\(452\) −210815. + 175595.i −1.03187 + 0.859479i
\(453\) 0 0
\(454\) −88250.2 243842.i −0.428158 1.18303i
\(455\) 64903.1i 0.313504i
\(456\) 0 0
\(457\) −18847.9 −0.0902463 −0.0451232 0.998981i \(-0.514368\pi\)
−0.0451232 + 0.998981i \(0.514368\pi\)
\(458\) −147256. + 53294.4i −0.702009 + 0.254068i
\(459\) 0 0
\(460\) −281415. 337860.i −1.32994 1.59669i
\(461\) 58671.8 0.276075 0.138038 0.990427i \(-0.455920\pi\)
0.138038 + 0.990427i \(0.455920\pi\)
\(462\) 0 0
\(463\) 47536.3i 0.221750i −0.993834 0.110875i \(-0.964635\pi\)
0.993834 0.110875i \(-0.0353653\pi\)
\(464\) −36718.3 + 199749.i −0.170548 + 0.927786i
\(465\) 0 0
\(466\) −8679.18 + 3141.13i −0.0399675 + 0.0144649i
\(467\) 150686.i 0.690936i 0.938431 + 0.345468i \(0.112280\pi\)
−0.938431 + 0.345468i \(0.887720\pi\)
\(468\) 0 0
\(469\) 181482. 0.825066
\(470\) −43943.3 121418.i −0.198928 0.549653i
\(471\) 0 0
\(472\) 257583. + 150592.i 1.15620 + 0.675954i
\(473\) 361770. 1.61700
\(474\) 0 0
\(475\) 37034.6i 0.164142i
\(476\) −132417. 158976.i −0.584425 0.701647i
\(477\) 0 0
\(478\) 103741. + 286644.i 0.454041 + 1.25455i
\(479\) 55229.7i 0.240714i −0.992731 0.120357i \(-0.961596\pi\)
0.992731 0.120357i \(-0.0384039\pi\)
\(480\) 0 0
\(481\) −18569.3 −0.0802612
\(482\) −61361.9 + 22207.8i −0.264122 + 0.0955900i
\(483\) 0 0
\(484\) 35256.1 29366.0i 0.150502 0.125358i
\(485\) −62991.1 −0.267791
\(486\) 0 0
\(487\) 2975.59i 0.0125463i −0.999980 0.00627313i \(-0.998003\pi\)
0.999980 0.00627313i \(-0.00199681\pi\)
\(488\) 180877. 309385.i 0.759528 1.29915i
\(489\) 0 0
\(490\) −187574. + 67886.0i −0.781232 + 0.282740i
\(491\) 270712.i 1.12291i −0.827508 0.561454i \(-0.810242\pi\)
0.827508 0.561454i \(-0.189758\pi\)
\(492\) 0 0
\(493\) 399978. 1.64567
\(494\) 23045.5 + 63676.5i 0.0944350 + 0.260931i
\(495\) 0 0
\(496\) 82983.0 + 15254.1i 0.337307 + 0.0620047i
\(497\) 113711. 0.460353
\(498\) 0 0
\(499\) 261354.i 1.04961i −0.851223 0.524805i \(-0.824138\pi\)
0.851223 0.524805i \(-0.175862\pi\)
\(500\) −151772. + 126416.i −0.607086 + 0.505662i
\(501\) 0 0
\(502\) −46056.2 127257.i −0.182760 0.504979i
\(503\) 283008.i 1.11857i 0.828976 + 0.559284i \(0.188924\pi\)
−0.828976 + 0.559284i \(0.811076\pi\)
\(504\) 0 0
\(505\) 20932.9 0.0820816
\(506\) 392030. 141882.i 1.53115 0.554148i
\(507\) 0 0
\(508\) 98217.4 + 117918.i 0.380593 + 0.456932i
\(509\) 213678. 0.824755 0.412378 0.911013i \(-0.364698\pi\)
0.412378 + 0.911013i \(0.364698\pi\)
\(510\) 0 0
\(511\) 50097.1i 0.191854i
\(512\) 262109. + 4281.91i 0.999867 + 0.0163342i
\(513\) 0 0
\(514\) −216445. + 78335.0i −0.819260 + 0.296503i
\(515\) 281914.i 1.06293i
\(516\) 0 0
\(517\) 122432. 0.458050
\(518\) −7330.04 20253.4i −0.0273179 0.0754812i
\(519\) 0 0
\(520\) 81737.4 139810.i 0.302283 0.517048i
\(521\) −168525. −0.620854 −0.310427 0.950597i \(-0.600472\pi\)
−0.310427 + 0.950597i \(0.600472\pi\)
\(522\) 0 0
\(523\) 231592.i 0.846681i −0.905971 0.423340i \(-0.860857\pi\)
0.905971 0.423340i \(-0.139143\pi\)
\(524\) 46507.7 + 55836.1i 0.169380 + 0.203354i
\(525\) 0 0
\(526\) 106916. + 295415.i 0.386429 + 1.06773i
\(527\) 166166.i 0.598302i
\(528\) 0 0
\(529\) −642895. −2.29736
\(530\) 122522. 44342.8i 0.436178 0.157860i
\(531\) 0 0
\(532\) −60354.5 + 50271.2i −0.213249 + 0.177622i
\(533\) 93437.8 0.328903
\(534\) 0 0
\(535\) 23020.2i 0.0804269i
\(536\) 390937. + 228554.i 1.36074 + 0.795537i
\(537\) 0 0
\(538\) −20224.1 + 7319.42i −0.0698721 + 0.0252879i
\(539\) 189139.i 0.651035i
\(540\) 0 0
\(541\) −3552.06 −0.0121363 −0.00606815 0.999982i \(-0.501932\pi\)
−0.00606815 + 0.999982i \(0.501932\pi\)
\(542\) 147169. + 406639.i 0.500978 + 1.38424i
\(543\) 0 0
\(544\) −85031.6 509218.i −0.287331 1.72070i
\(545\) −495653. −1.66872
\(546\) 0 0
\(547\) 513025.i 1.71460i 0.514813 + 0.857302i \(0.327861\pi\)
−0.514813 + 0.857302i \(0.672139\pi\)
\(548\) 60260.6 50193.0i 0.200665 0.167141i
\(549\) 0 0
\(550\) 28578.7 + 78965.1i 0.0944752 + 0.261042i
\(551\) 151849.i 0.500161i
\(552\) 0 0
\(553\) 45132.7 0.147585
\(554\) 165278. 59816.7i 0.538512 0.194896i
\(555\) 0 0
\(556\) −88584.4 106352.i −0.286555 0.344031i
\(557\) 269383. 0.868281 0.434141 0.900845i \(-0.357052\pi\)
0.434141 + 0.900845i \(0.357052\pi\)
\(558\) 0 0
\(559\) 294903.i 0.943746i
\(560\) 184754. + 33962.0i 0.589140 + 0.108297i
\(561\) 0 0
\(562\) 191340. 69248.9i 0.605805 0.219250i
\(563\) 55932.8i 0.176461i 0.996100 + 0.0882307i \(0.0281213\pi\)
−0.996100 + 0.0882307i \(0.971879\pi\)
\(564\) 0 0
\(565\) −490588. −1.53681
\(566\) 35930.5 + 99278.4i 0.112158 + 0.309900i
\(567\) 0 0
\(568\) 244949. + 143205.i 0.759239 + 0.443877i
\(569\) −424532. −1.31125 −0.655625 0.755086i \(-0.727595\pi\)
−0.655625 + 0.755086i \(0.727595\pi\)
\(570\) 0 0
\(571\) 29210.9i 0.0895928i −0.998996 0.0447964i \(-0.985736\pi\)
0.998996 0.0447964i \(-0.0142639\pi\)
\(572\) 98275.2 + 117987.i 0.300367 + 0.360614i
\(573\) 0 0
\(574\) 36883.6 + 101912.i 0.111946 + 0.309315i
\(575\) 185863.i 0.562158i
\(576\) 0 0
\(577\) −494524. −1.48537 −0.742687 0.669639i \(-0.766449\pi\)
−0.742687 + 0.669639i \(0.766449\pi\)
\(578\) −641915. + 232319.i −1.92142 + 0.695392i
\(579\) 0 0
\(580\) −279035. + 232417.i −0.829473 + 0.690895i
\(581\) 77644.0 0.230015
\(582\) 0 0
\(583\) 123545.i 0.363486i
\(584\) 63091.1 107916.i 0.184988 0.316417i
\(585\) 0 0
\(586\) 491936. 178040.i 1.43256 0.518467i
\(587\) 240416.i 0.697729i 0.937173 + 0.348865i \(0.113433\pi\)
−0.937173 + 0.348865i \(0.886567\pi\)
\(588\) 0 0
\(589\) −63083.9 −0.181839
\(590\) 181563. + 501671.i 0.521583 + 1.44117i
\(591\) 0 0
\(592\) 9716.81 52859.8i 0.0277256 0.150828i
\(593\) 470902. 1.33912 0.669562 0.742756i \(-0.266482\pi\)
0.669562 + 0.742756i \(0.266482\pi\)
\(594\) 0 0
\(595\) 369954.i 1.04499i
\(596\) 156046. 129976.i 0.439299 0.365907i
\(597\) 0 0
\(598\) −115657. 319569.i −0.323423 0.893640i
\(599\) 10011.2i 0.0279017i 0.999903 + 0.0139509i \(0.00444084\pi\)
−0.999903 + 0.0139509i \(0.995559\pi\)
\(600\) 0 0
\(601\) 392897. 1.08775 0.543876 0.839165i \(-0.316956\pi\)
0.543876 + 0.839165i \(0.316956\pi\)
\(602\) 321648. 116410.i 0.887540 0.321215i
\(603\) 0 0
\(604\) −130720. 156939.i −0.358317 0.430188i
\(605\) 82044.4 0.224150
\(606\) 0 0
\(607\) 433505.i 1.17657i −0.808655 0.588283i \(-0.799804\pi\)
0.808655 0.588283i \(-0.200196\pi\)
\(608\) −193322. + 32281.8i −0.522966 + 0.0873273i
\(609\) 0 0
\(610\) 602561. 218077.i 1.61935 0.586070i
\(611\) 99802.2i 0.267336i
\(612\) 0 0
\(613\) 301951. 0.803555 0.401778 0.915737i \(-0.368393\pi\)
0.401778 + 0.915737i \(0.368393\pi\)
\(614\) −73817.2 203962.i −0.195804 0.541020i
\(615\) 0 0
\(616\) −89894.5 + 153762.i −0.236904 + 0.405217i
\(617\) −196747. −0.516817 −0.258409 0.966036i \(-0.583198\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(618\) 0 0
\(619\) 619149.i 1.61590i −0.589252 0.807949i \(-0.700578\pi\)
0.589252 0.807949i \(-0.299422\pi\)
\(620\) 96554.8 + 115921.i 0.251183 + 0.301565i
\(621\) 0 0
\(622\) −185077. 511380.i −0.478378 1.32179i
\(623\) 14346.2i 0.0369625i
\(624\) 0 0
\(625\) −474118. −1.21374
\(626\) −618305. + 223775.i −1.57781 + 0.571034i
\(627\) 0 0
\(628\) −498717. + 415397.i −1.26455 + 1.05328i
\(629\) −105847. −0.267532
\(630\) 0 0
\(631\) 308766.i 0.775479i 0.921769 + 0.387740i \(0.126744\pi\)
−0.921769 + 0.387740i \(0.873256\pi\)
\(632\) 97221.8 + 56839.1i 0.243405 + 0.142303i
\(633\) 0 0
\(634\) 453678. 164193.i 1.12867 0.408486i
\(635\) 274406.i 0.680528i
\(636\) 0 0
\(637\) −154180. −0.379970
\(638\) −117178. 323772.i −0.287877 0.795424i
\(639\) 0 0
\(640\) 355214. + 305834.i 0.867222 + 0.746665i
\(641\) 342401. 0.833333 0.416666 0.909059i \(-0.363198\pi\)
0.416666 + 0.909059i \(0.363198\pi\)
\(642\) 0 0
\(643\) 552948.i 1.33740i 0.743531 + 0.668702i \(0.233150\pi\)
−0.743531 + 0.668702i \(0.766850\pi\)
\(644\) 302897. 252293.i 0.730338 0.608322i
\(645\) 0 0
\(646\) 131362. + 362962.i 0.314778 + 0.869753i
\(647\) 576814.i 1.37793i 0.724794 + 0.688965i \(0.241935\pi\)
−0.724794 + 0.688965i \(0.758065\pi\)
\(648\) 0 0
\(649\) −505858. −1.20099
\(650\) 64369.7 23296.4i 0.152354 0.0551395i
\(651\) 0 0
\(652\) −70379.6 84496.1i −0.165558 0.198766i
\(653\) 573591. 1.34517 0.672583 0.740022i \(-0.265185\pi\)
0.672583 + 0.740022i \(0.265185\pi\)
\(654\) 0 0
\(655\) 129936.i 0.302864i
\(656\) −48893.4 + 265982.i −0.113617 + 0.618080i
\(657\) 0 0
\(658\) 108854. 39395.9i 0.251415 0.0909911i
\(659\) 345600.i 0.795797i 0.917429 + 0.397899i \(0.130260\pi\)
−0.917429 + 0.397899i \(0.869740\pi\)
\(660\) 0 0
\(661\) −375167. −0.858661 −0.429330 0.903148i \(-0.641250\pi\)
−0.429330 + 0.903148i \(0.641250\pi\)
\(662\) −157473. 435110.i −0.359328 0.992849i
\(663\) 0 0
\(664\) 167255. + 97783.0i 0.379353 + 0.221782i
\(665\) −140451. −0.317600
\(666\) 0 0
\(667\) 762077.i 1.71296i
\(668\) 359521. + 431632.i 0.805695 + 0.967300i
\(669\) 0 0
\(670\) 275560. + 761391.i 0.613855 + 1.69613i
\(671\) 607591.i 1.34948i
\(672\) 0 0
\(673\) −573732. −1.26672 −0.633358 0.773859i \(-0.718324\pi\)
−0.633358 + 0.773859i \(0.718324\pi\)
\(674\) −706121. + 255557.i −1.55439 + 0.562558i
\(675\) 0 0
\(676\) −254949. + 212355.i −0.557904 + 0.464697i
\(677\) 27578.5 0.0601718 0.0300859 0.999547i \(-0.490422\pi\)
0.0300859 + 0.999547i \(0.490422\pi\)
\(678\) 0 0
\(679\) 56472.6i 0.122489i
\(680\) 465911. 796928.i 1.00759 1.72346i
\(681\) 0 0
\(682\) −134507. + 48680.3i −0.289186 + 0.104661i
\(683\) 1038.30i 0.00222578i −0.999999 0.00111289i \(-0.999646\pi\)
0.999999 0.00111289i \(-0.000354244\pi\)
\(684\) 0 0
\(685\) 140232. 0.298859
\(686\) −144690. 399790.i −0.307462 0.849539i
\(687\) 0 0
\(688\) 839476. + 154314.i 1.77350 + 0.326009i
\(689\) 100710. 0.212145
\(690\) 0 0
\(691\) 334105.i 0.699724i −0.936801 0.349862i \(-0.886229\pi\)
0.936801 0.349862i \(-0.113771\pi\)
\(692\) −36678.4 + 30550.6i −0.0765945 + 0.0637981i
\(693\) 0 0
\(694\) 184101. + 508685.i 0.382241 + 1.05616i
\(695\) 247492.i 0.512380i
\(696\) 0 0
\(697\) 532604. 1.09632
\(698\) −12423.0 + 4496.08i −0.0254985 + 0.00922832i
\(699\) 0 0
\(700\) 50818.5 + 61011.5i 0.103711 + 0.124513i
\(701\) −177927. −0.362082 −0.181041 0.983476i \(-0.557947\pi\)
−0.181041 + 0.983476i \(0.557947\pi\)
\(702\) 0 0
\(703\) 40184.1i 0.0813100i
\(704\) −387289. + 218013.i −0.781429 + 0.439883i
\(705\) 0 0
\(706\) 160729. 58170.2i 0.322466 0.116706i
\(707\) 18766.7i 0.0375447i
\(708\) 0 0
\(709\) 724969. 1.44220 0.721102 0.692829i \(-0.243636\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(710\) 172657. + 477064.i 0.342506 + 0.946368i
\(711\) 0 0
\(712\) −18067.3 + 30903.7i −0.0356396 + 0.0609607i
\(713\) 316595. 0.622767
\(714\) 0 0
\(715\) 274567.i 0.537077i
\(716\) −462842. 555678.i −0.902832 1.08392i
\(717\) 0 0
\(718\) 239331. + 661289.i 0.464248 + 1.28275i
\(719\) 536436.i 1.03767i −0.854874 0.518836i \(-0.826366\pi\)
0.854874 0.518836i \(-0.173634\pi\)
\(720\) 0 0
\(721\) −252741. −0.486189
\(722\) −352373. + 127530.i −0.675972 + 0.244645i
\(723\) 0 0
\(724\) 339324. 282634.i 0.647348 0.539197i
\(725\) −153502. −0.292038
\(726\) 0 0
\(727\) 433953.i 0.821058i −0.911847 0.410529i \(-0.865344\pi\)
0.911847 0.410529i \(-0.134656\pi\)
\(728\) 125342. + 73278.9i 0.236501 + 0.138266i
\(729\) 0 0
\(730\) 210178. 76066.7i 0.394403 0.142741i
\(731\) 1.68097e6i 3.14576i
\(732\) 0 0
\(733\) −780416. −1.45251 −0.726254 0.687427i \(-0.758740\pi\)
−0.726254 + 0.687427i \(0.758740\pi\)
\(734\) −10794.3 29825.5i −0.0200357 0.0553600i
\(735\) 0 0
\(736\) 970212. 162010.i 1.79106 0.299080i
\(737\) −767746. −1.41346
\(738\) 0 0
\(739\) 215142.i 0.393947i −0.980409 0.196973i \(-0.936889\pi\)
0.980409 0.196973i \(-0.0631112\pi\)
\(740\) 73841.4 61504.9i 0.134845 0.112317i
\(741\) 0 0
\(742\) 39754.1 + 109843.i 0.0722061 + 0.199511i
\(743\) 289091.i 0.523670i −0.965113 0.261835i \(-0.915672\pi\)
0.965113 0.261835i \(-0.0843276\pi\)
\(744\) 0 0
\(745\) 363135. 0.654267
\(746\) −927794. + 335784.i −1.66715 + 0.603367i
\(747\) 0 0
\(748\) 560178. + 672537.i 1.00120 + 1.20202i
\(749\) 20638.0 0.0367878
\(750\) 0 0
\(751\) 684873.i 1.21431i 0.794583 + 0.607156i \(0.207690\pi\)
−0.794583 + 0.607156i \(0.792310\pi\)
\(752\) 284099. + 52223.8i 0.502382 + 0.0923491i
\(753\) 0 0
\(754\) −263928. + 95519.9i −0.464241 + 0.168016i
\(755\) 365213.i 0.640697i
\(756\) 0 0
\(757\) −646906. −1.12888 −0.564442 0.825472i \(-0.690909\pi\)
−0.564442 + 0.825472i \(0.690909\pi\)
\(758\) −200680. 554493.i −0.349273 0.965067i
\(759\) 0 0
\(760\) −302549. 176880.i −0.523804 0.306233i
\(761\) −766822. −1.32411 −0.662057 0.749454i \(-0.730316\pi\)
−0.662057 + 0.749454i \(0.730316\pi\)
\(762\) 0 0
\(763\) 444361.i 0.763286i
\(764\) 192745. + 231405.i 0.330214 + 0.396448i
\(765\) 0 0
\(766\) −166566. 460233.i −0.283876 0.784369i
\(767\) 412359.i 0.700946i
\(768\) 0 0
\(769\) −579735. −0.980340 −0.490170 0.871627i \(-0.663065\pi\)
−0.490170 + 0.871627i \(0.663065\pi\)
\(770\) −299468. + 108382.i −0.505091 + 0.182801i
\(771\) 0 0
\(772\) 116230. 96811.6i 0.195022 0.162440i
\(773\) 885783. 1.48241 0.741205 0.671279i \(-0.234255\pi\)
0.741205 + 0.671279i \(0.234255\pi\)
\(774\) 0 0
\(775\) 63770.7i 0.106174i
\(776\) 71120.3 121649.i 0.118105 0.202016i
\(777\) 0 0
\(778\) −690024. + 249731.i −1.14000 + 0.412584i
\(779\) 202200.i 0.333201i
\(780\) 0 0
\(781\) −481046. −0.788651
\(782\) −659257. 1.82157e6i −1.07806 2.97875i
\(783\) 0 0
\(784\) 80678.1 438892.i 0.131257 0.714045i
\(785\) −1.16056e6 −1.88334
\(786\) 0 0
\(787\) 1.05137e6i 1.69749i −0.528803 0.848744i \(-0.677359\pi\)
0.528803 0.848744i \(-0.322641\pi\)