Properties

Label 324.5.d.f.163.20
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 163.20
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.19

$q$-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 \(-0.693904\pi\)
−0.572185 + 0.820125i \(0.693904\pi\)
\(6\) 0 0
\(7\) 25.6487i 0.523442i −0.965144 0.261721i \(-0.915710\pi\)
0.965144 0.261721i \(-0.0842900\pi\)
\(8\) 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 \(-0.162651\pi\)
0.872265 + 0.489034i \(0.162651\pi\)
\(18\) 0 0
\(19\) 191.405i 0.530207i −0.964220 0.265104i \(-0.914594\pi\)
0.964220 0.265104i \(-0.0854062\pi\)
\(20\) −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 \(-0.343653\pi\)
0.471665 + 0.881778i \(0.343653\pi\)
\(30\) 0 0
\(31\) 329.584i 0.342959i −0.985188 0.171480i \(-0.945145\pi\)
0.985188 0.171480i \(-0.0548547\pi\)
\(32\) −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 \(-0.398258\pi\)
0.314218 + 0.949351i \(0.398258\pi\)
\(42\) 0 0
\(43\) 3334.14i 1.80322i −0.432555 0.901608i \(-0.642388\pi\)
0.432555 0.901608i \(-0.357612\pi\)
\(44\) 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 \(-0.435037\pi\)
0.202673 + 0.979247i \(0.435037\pi\)
\(54\) 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 \(0.288943\pi\)
−0.615527 + 0.788116i \(0.711057\pi\)
\(68\) 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 \(0.0450238\pi\)
−0.990013 + 0.140975i \(0.954976\pi\)
\(80\) −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 \(-0.511241\pi\)
−0.0353072 + 0.999377i \(0.511241\pi\)
\(90\) 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 \(-0.511418\pi\)
−0.0358632 + 0.999357i \(0.511418\pi\)
\(102\) 0 0
\(103\) 9853.96i 0.928831i −0.885618 0.464415i \(-0.846265\pi\)
0.885618 0.464415i \(-0.153735\pi\)
\(104\) −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 \(-0.265665\pi\)
0.671465 + 0.741036i \(0.265665\pi\)
\(114\) 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 \(-0.903901\pi\)
0.954772 0.297337i \(-0.0960986\pi\)
\(128\) −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 \(-0.541683\pi\)
−0.130578 + 0.991438i \(0.541683\pi\)
\(138\) 0 0
\(139\) 8650.79i 0.447740i 0.974619 + 0.223870i \(0.0718691\pi\)
−0.974619 + 0.223870i \(0.928131\pi\)
\(140\) −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 \(-0.592280\pi\)
−0.285863 + 0.958270i \(0.592280\pi\)
\(150\) 0 0
\(151\) 12765.6i 0.559869i 0.960019 + 0.279934i \(0.0903127\pi\)
−0.960019 + 0.279934i \(0.909687\pi\)
\(152\) 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 \(0.0412865\pi\)
−0.991600 + 0.129342i \(0.958713\pi\)
\(164\) 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 \(-0.484128\pi\)
0.0498420 + 0.998757i \(0.484128\pi\)
\(174\) 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 \(-0.589980\pi\)
−0.278930 + 0.960311i \(0.589980\pi\)
\(198\) 0 0
\(199\) 25261.4i 0.637898i 0.947772 + 0.318949i \(0.103330\pi\)
−0.947772 + 0.318949i \(0.896670\pi\)
\(200\) 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 \(0.0778577\pi\)
−0.970235 + 0.242166i \(0.922142\pi\)
\(212\) 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 \(-0.937855\pi\)
0.981002 0.193996i \(-0.0621448\pi\)
\(224\) 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 \(-0.506765\pi\)
−0.0212522 + 0.999774i \(0.506765\pi\)
\(234\) 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 \(-0.643475\pi\)
−0.435632 + 0.900125i \(0.643475\pi\)
\(258\) 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 \(-0.511829\pi\)
−0.0371537 + 0.999310i \(0.511829\pi\)
\(270\) 0 0
\(271\) 108113.i 1.47211i 0.676924 + 0.736053i \(0.263312\pi\)
−0.676924 + 0.736053i \(0.736688\pi\)
\(272\) 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 \(-0.395601\pi\)
0.322130 + 0.946696i \(0.395601\pi\)
\(282\) 0 0
\(283\) 26395.1i 0.329572i 0.986329 + 0.164786i \(0.0526933\pi\)
−0.986329 + 0.164786i \(0.947307\pi\)
\(284\) 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 \(-0.224341\pi\)
0.761748 + 0.647873i \(0.224341\pi\)
\(294\) 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 \(-0.907116\pi\)
0.957726 0.287681i \(-0.0928843\pi\)
\(308\) −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 \(-0.295104\pi\)
0.600160 + 0.799880i \(0.295104\pi\)
\(318\) 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 \(-0.822966\pi\)
0.849284 0.527936i \(-0.177034\pi\)
\(332\) 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 \(-0.445149\pi\)
0.171467 + 0.985190i \(0.445149\pi\)
\(354\) 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 \(-0.990629\pi\)
0.999567 0.0294370i \(-0.00937145\pi\)
\(368\) 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 \(-0.828474\pi\)
0.858291 0.513163i \(-0.171526\pi\)
\(380\) −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 \(-0.707300\pi\)
−0.606182 + 0.795326i \(0.707300\pi\)
\(390\) 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 \(-0.284887\pi\)
0.625518 + 0.780209i \(0.284887\pi\)
\(402\) 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 \(0.0139138\pi\)
−0.999045 + 0.0436976i \(0.986086\pi\)
\(440\) −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 \(-0.397836\pi\)
0.315475 + 0.948934i \(0.397836\pi\)
\(450\) 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 \(-0.544080\pi\)
−0.138038 + 0.990427i \(0.544080\pi\)
\(462\) 0 0
\(463\) 47536.3i 0.221750i 0.993834 + 0.110875i \(0.0353653\pi\)
−0.993834 + 0.110875i \(0.964635\pi\)
\(464\) 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 \(0.00199681\pi\)
−0.999980 + 0.00627313i \(0.998003\pi\)
\(488\) −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 \(0.175862\pi\)
−0.851223 + 0.524805i \(0.824138\pi\)
\(500\) 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 \(-0.635302\pi\)
−0.412378 + 0.911013i \(0.635302\pi\)
\(510\) 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 \(-0.399528\pi\)
0.310427 + 0.950597i \(0.399528\pi\)
\(522\) 0 0
\(523\) 231592.i 0.846681i 0.905971 + 0.423340i \(0.139143\pi\)
−0.905971 + 0.423340i \(0.860857\pi\)
\(524\) −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 \(-0.672139\pi\)
0.514813 0.857302i \(-0.327861\pi\)
\(548\) −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 \(-0.642948\pi\)
−0.434141 + 0.900845i \(0.642948\pi\)
\(558\) 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 \(-0.272405\pi\)
0.655625 + 0.755086i \(0.272405\pi\)
\(570\) 0 0
\(571\) 29210.9i 0.0895928i 0.998996 + 0.0447964i \(0.0142639\pi\)
−0.998996 + 0.0447964i \(0.985736\pi\)
\(572\) −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 \(-0.733518\pi\)
−0.669562 + 0.742756i \(0.733518\pi\)
\(594\) 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 \(0.200196\pi\)
−0.808655 + 0.588283i \(0.799804\pi\)
\(608\) 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 \(-0.416802\pi\)
0.258409 + 0.966036i \(0.416802\pi\)
\(618\) 0 0
\(619\) 619149.i 1.61590i 0.589252 + 0.807949i \(0.299422\pi\)
−0.589252 + 0.807949i \(0.700578\pi\)
\(620\) −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 \(-0.873256\pi\)
0.921769 0.387740i \(-0.126744\pi\)
\(632\) −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 \(-0.636802\pi\)
−0.416666 + 0.909059i \(0.636802\pi\)
\(642\) 0 0
\(643\) 552948.i 1.33740i −0.743531 0.668702i \(-0.766850\pi\)
0.743531 0.668702i \(-0.233150\pi\)
\(644\) −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 \(-0.734815\pi\)
−0.672583 + 0.740022i \(0.734815\pi\)
\(654\) 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 \(-0.509578\pi\)
−0.0300859 + 0.999547i \(0.509578\pi\)
\(678\) 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 \(0.113771\pi\)
−0.936801 + 0.349862i \(0.886229\pi\)
\(692\) 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 \(-0.442053\pi\)
0.181041 + 0.983476i \(0.442053\pi\)
\(702\) 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 \(0.134656\pi\)
−0.911847 + 0.410529i \(0.865344\pi\)
\(728\) −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 \(0.0631112\pi\)
−0.980409 + 0.196973i \(0.936889\pi\)
\(740\) −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 \(-0.792310\pi\)
0.794583 0.607156i \(-0.207690\pi\)
\(752\) −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 \(-0.269684\pi\)
0.662057 + 0.749454i \(0.269684\pi\)
\(762\) 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 \(-0.765745\pi\)
−0.741205 + 0.671279i \(0.765745\pi\)
\(774\) 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
\(787\)