Properties

Label 324.5.d.e.163.9
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 163.9
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.e.163.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +O(q^{10})\) \(q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +(14.8544 + 41.5509i) q^{10} -219.387i q^{11} -37.0701 q^{13} +(44.8790 - 16.0441i) q^{14} +(50.2175 - 251.026i) q^{16} -284.021 q^{17} -45.4901i q^{19} +(136.502 - 111.899i) q^{20} +(-826.332 + 295.412i) q^{22} +201.286i q^{23} -503.304 q^{25} +(49.9160 + 139.626i) q^{26} +(-120.862 - 147.435i) q^{28} +1228.31 q^{29} +1514.77i q^{31} +(-1013.12 + 148.868i) q^{32} +(382.443 + 1069.78i) q^{34} -131.443i q^{35} -1521.29 q^{37} +(-171.340 + 61.2538i) q^{38} +(-605.277 - 363.464i) q^{40} +2633.95 q^{41} -39.9593i q^{43} +(2225.36 + 2714.63i) q^{44} +(758.153 - 271.038i) q^{46} +2884.86i q^{47} +2259.03 q^{49} +(677.714 + 1895.72i) q^{50} +(458.694 - 376.021i) q^{52} -1415.13 q^{53} +2420.19i q^{55} +(-392.576 + 653.757i) q^{56} +(-1653.95 - 4626.47i) q^{58} +2832.86i q^{59} -5257.27 q^{61} +(5705.44 - 2039.68i) q^{62} +(1924.92 + 3615.51i) q^{64} +408.941 q^{65} -930.592i q^{67} +(3514.39 - 2880.97i) q^{68} +(-495.087 + 176.992i) q^{70} +1162.75i q^{71} -2162.87 q^{73} +(2048.47 + 5730.02i) q^{74} +(461.430 + 562.881i) q^{76} +2614.04 q^{77} +7485.40i q^{79} +(-553.978 + 2769.22i) q^{80} +(-3546.69 - 9920.88i) q^{82} +1116.31i q^{83} +3133.20 q^{85} +(-150.508 + 53.8064i) q^{86} +(7228.27 - 12037.3i) q^{88} +6739.71 q^{89} -441.696i q^{91} +(-2041.75 - 2490.66i) q^{92} +(10865.9 - 3884.55i) q^{94} +501.828i q^{95} +12046.6 q^{97} +(-3041.85 - 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + O(q^{10}) \) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + 14q^{10} + 2q^{13} + 252q^{14} + q^{16} + 28q^{17} - 140q^{20} + 33q^{22} + 1752q^{25} - 548q^{26} - 258q^{28} + 526q^{29} - 121q^{32} - 385q^{34} - 4q^{37} + 1395q^{38} + 2276q^{40} - 2762q^{41} - 3357q^{44} + 1788q^{46} - 3428q^{49} + 6375q^{50} - 1438q^{52} + 5044q^{53} - 7506q^{56} + 4064q^{58} + 2q^{61} + 9162q^{62} + 4513q^{64} - 2014q^{65} - 11405q^{68} - 3666q^{70} - 1708q^{73} + 14620q^{74} - 1581q^{76} - 3942q^{77} - 22760q^{80} - 4243q^{82} + 1252q^{85} + 22113q^{86} - 1995q^{88} - 6524q^{89} - 30294q^{92} - 7524q^{94} - 5638q^{97} + 46469q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34653 3.76654i −0.336633 0.941636i
\(3\) 0 0
\(4\) −12.3737 + 10.1435i −0.773357 + 0.633971i
\(5\) −11.0316 −0.441263 −0.220632 0.975357i \(-0.570812\pi\)
−0.220632 + 0.975357i \(0.570812\pi\)
\(6\) 0 0
\(7\) 11.9152i 0.243167i 0.992581 + 0.121583i \(0.0387972\pi\)
−0.992581 + 0.121583i \(0.961203\pi\)
\(8\) 54.8676 + 32.9476i 0.857307 + 0.514806i
\(9\) 0 0
\(10\) 14.8544 + 41.5509i 0.148544 + 0.415509i
\(11\) 219.387i 1.81312i −0.422080 0.906559i \(-0.638700\pi\)
0.422080 0.906559i \(-0.361300\pi\)
\(12\) 0 0
\(13\) −37.0701 −0.219349 −0.109675 0.993968i \(-0.534981\pi\)
−0.109675 + 0.993968i \(0.534981\pi\)
\(14\) 44.8790 16.0441i 0.228975 0.0818579i
\(15\) 0 0
\(16\) 50.2175 251.026i 0.196162 0.980571i
\(17\) −284.021 −0.982771 −0.491386 0.870942i \(-0.663509\pi\)
−0.491386 + 0.870942i \(0.663509\pi\)
\(18\) 0 0
\(19\) 45.4901i 0.126011i −0.998013 0.0630057i \(-0.979931\pi\)
0.998013 0.0630057i \(-0.0200686\pi\)
\(20\) 136.502 111.899i 0.341254 0.279748i
\(21\) 0 0
\(22\) −826.332 + 295.412i −1.70730 + 0.610354i
\(23\) 201.286i 0.380503i 0.981735 + 0.190252i \(0.0609304\pi\)
−0.981735 + 0.190252i \(0.939070\pi\)
\(24\) 0 0
\(25\) −503.304 −0.805287
\(26\) 49.9160 + 139.626i 0.0738402 + 0.206547i
\(27\) 0 0
\(28\) −120.862 147.435i −0.154161 0.188055i
\(29\) 1228.31 1.46053 0.730265 0.683164i \(-0.239397\pi\)
0.730265 + 0.683164i \(0.239397\pi\)
\(30\) 0 0
\(31\) 1514.77i 1.57624i 0.615520 + 0.788121i \(0.288946\pi\)
−0.615520 + 0.788121i \(0.711054\pi\)
\(32\) −1013.12 + 148.868i −0.989376 + 0.145379i
\(33\) 0 0
\(34\) 382.443 + 1069.78i 0.330833 + 0.925413i
\(35\) 131.443i 0.107301i
\(36\) 0 0
\(37\) −1521.29 −1.11124 −0.555622 0.831435i \(-0.687520\pi\)
−0.555622 + 0.831435i \(0.687520\pi\)
\(38\) −171.340 + 61.2538i −0.118657 + 0.0424195i
\(39\) 0 0
\(40\) −605.277 363.464i −0.378298 0.227165i
\(41\) 2633.95 1.56689 0.783447 0.621459i \(-0.213460\pi\)
0.783447 + 0.621459i \(0.213460\pi\)
\(42\) 0 0
\(43\) 39.9593i 0.0216113i −0.999942 0.0108056i \(-0.996560\pi\)
0.999942 0.0108056i \(-0.00343961\pi\)
\(44\) 2225.36 + 2714.63i 1.14946 + 1.40219i
\(45\) 0 0
\(46\) 758.153 271.038i 0.358295 0.128090i
\(47\) 2884.86i 1.30596i 0.757377 + 0.652978i \(0.226481\pi\)
−0.757377 + 0.652978i \(0.773519\pi\)
\(48\) 0 0
\(49\) 2259.03 0.940870
\(50\) 677.714 + 1895.72i 0.271086 + 0.758287i
\(51\) 0 0
\(52\) 458.694 376.021i 0.169635 0.139061i
\(53\) −1415.13 −0.503783 −0.251892 0.967755i \(-0.581053\pi\)
−0.251892 + 0.967755i \(0.581053\pi\)
\(54\) 0 0
\(55\) 2420.19i 0.800062i
\(56\) −392.576 + 653.757i −0.125184 + 0.208469i
\(57\) 0 0
\(58\) −1653.95 4626.47i −0.491662 1.37529i
\(59\) 2832.86i 0.813808i 0.913471 + 0.406904i \(0.133392\pi\)
−0.913471 + 0.406904i \(0.866608\pi\)
\(60\) 0 0
\(61\) −5257.27 −1.41287 −0.706433 0.707780i \(-0.749697\pi\)
−0.706433 + 0.707780i \(0.749697\pi\)
\(62\) 5705.44 2039.68i 1.48425 0.530614i
\(63\) 0 0
\(64\) 1924.92 + 3615.51i 0.469950 + 0.882693i
\(65\) 408.941 0.0967909
\(66\) 0 0
\(67\) 930.592i 0.207305i −0.994614 0.103653i \(-0.966947\pi\)
0.994614 0.103653i \(-0.0330530\pi\)
\(68\) 3514.39 2880.97i 0.760033 0.623048i
\(69\) 0 0
\(70\) −495.087 + 176.992i −0.101038 + 0.0361209i
\(71\) 1162.75i 0.230659i 0.993327 + 0.115329i \(0.0367923\pi\)
−0.993327 + 0.115329i \(0.963208\pi\)
\(72\) 0 0
\(73\) −2162.87 −0.405867 −0.202934 0.979192i \(-0.565048\pi\)
−0.202934 + 0.979192i \(0.565048\pi\)
\(74\) 2048.47 + 5730.02i 0.374081 + 1.04639i
\(75\) 0 0
\(76\) 461.430 + 562.881i 0.0798875 + 0.0974518i
\(77\) 2614.04 0.440890
\(78\) 0 0
\(79\) 7485.40i 1.19939i 0.800229 + 0.599695i \(0.204711\pi\)
−0.800229 + 0.599695i \(0.795289\pi\)
\(80\) −553.978 + 2769.22i −0.0865591 + 0.432690i
\(81\) 0 0
\(82\) −3546.69 9920.88i −0.527467 1.47544i
\(83\) 1116.31i 0.162043i 0.996712 + 0.0810215i \(0.0258182\pi\)
−0.996712 + 0.0810215i \(0.974182\pi\)
\(84\) 0 0
\(85\) 3133.20 0.433661
\(86\) −150.508 + 53.8064i −0.0203500 + 0.00727506i
\(87\) 0 0
\(88\) 7228.27 12037.3i 0.933403 1.55440i
\(89\) 6739.71 0.850866 0.425433 0.904990i \(-0.360122\pi\)
0.425433 + 0.904990i \(0.360122\pi\)
\(90\) 0 0
\(91\) 441.696i 0.0533385i
\(92\) −2041.75 2490.66i −0.241228 0.294265i
\(93\) 0 0
\(94\) 10865.9 3884.55i 1.22974 0.439627i
\(95\) 501.828i 0.0556042i
\(96\) 0 0
\(97\) 12046.6 1.28032 0.640161 0.768240i \(-0.278867\pi\)
0.640161 + 0.768240i \(0.278867\pi\)
\(98\) −3041.85 8508.73i −0.316727 0.885957i
\(99\) 0 0
\(100\) 6227.74 5105.28i 0.622774 0.510528i
\(101\) 9555.20 0.936692 0.468346 0.883545i \(-0.344850\pi\)
0.468346 + 0.883545i \(0.344850\pi\)
\(102\) 0 0
\(103\) 11503.4i 1.08431i 0.840279 + 0.542154i \(0.182391\pi\)
−0.840279 + 0.542154i \(0.817609\pi\)
\(104\) −2033.95 1221.37i −0.188050 0.112922i
\(105\) 0 0
\(106\) 1905.51 + 5330.14i 0.169590 + 0.474380i
\(107\) 6602.72i 0.576707i 0.957524 + 0.288353i \(0.0931078\pi\)
−0.957524 + 0.288353i \(0.906892\pi\)
\(108\) 0 0
\(109\) 12045.3 1.01383 0.506913 0.861997i \(-0.330786\pi\)
0.506913 + 0.861997i \(0.330786\pi\)
\(110\) 9115.74 3258.86i 0.753367 0.269327i
\(111\) 0 0
\(112\) 2991.02 + 598.350i 0.238442 + 0.0477001i
\(113\) −3730.69 −0.292168 −0.146084 0.989272i \(-0.546667\pi\)
−0.146084 + 0.989272i \(0.546667\pi\)
\(114\) 0 0
\(115\) 2220.50i 0.167902i
\(116\) −15198.7 + 12459.4i −1.12951 + 0.925933i
\(117\) 0 0
\(118\) 10670.1 3814.54i 0.766311 0.273954i
\(119\) 3384.16i 0.238977i
\(120\) 0 0
\(121\) −33489.7 −2.28739
\(122\) 7079.08 + 19801.7i 0.475617 + 1.33041i
\(123\) 0 0
\(124\) −15365.1 18743.3i −0.999291 1.21900i
\(125\) 12447.0 0.796607
\(126\) 0 0
\(127\) 26549.7i 1.64608i 0.567980 + 0.823042i \(0.307725\pi\)
−0.567980 + 0.823042i \(0.692275\pi\)
\(128\) 11026.0 12118.7i 0.672975 0.739665i
\(129\) 0 0
\(130\) −550.652 1540.30i −0.0325830 0.0911418i
\(131\) 1319.64i 0.0768978i −0.999261 0.0384489i \(-0.987758\pi\)
0.999261 0.0384489i \(-0.0122417\pi\)
\(132\) 0 0
\(133\) 542.022 0.0306418
\(134\) −3505.12 + 1253.07i −0.195206 + 0.0697856i
\(135\) 0 0
\(136\) −15583.6 9357.79i −0.842537 0.505936i
\(137\) −25812.9 −1.37530 −0.687648 0.726044i \(-0.741357\pi\)
−0.687648 + 0.726044i \(0.741357\pi\)
\(138\) 0 0
\(139\) 13138.0i 0.679985i 0.940428 + 0.339993i \(0.110425\pi\)
−0.940428 + 0.339993i \(0.889575\pi\)
\(140\) 1333.30 + 1626.44i 0.0680254 + 0.0829816i
\(141\) 0 0
\(142\) 4379.55 1565.68i 0.217197 0.0776472i
\(143\) 8132.70i 0.397706i
\(144\) 0 0
\(145\) −13550.2 −0.644478
\(146\) 2912.37 + 8146.54i 0.136628 + 0.382179i
\(147\) 0 0
\(148\) 18824.0 15431.3i 0.859388 0.704496i
\(149\) −25936.4 −1.16826 −0.584128 0.811662i \(-0.698563\pi\)
−0.584128 + 0.811662i \(0.698563\pi\)
\(150\) 0 0
\(151\) 28395.5i 1.24536i 0.782475 + 0.622681i \(0.213957\pi\)
−0.782475 + 0.622681i \(0.786043\pi\)
\(152\) 1498.79 2495.93i 0.0648714 0.108030i
\(153\) 0 0
\(154\) −3519.88 9845.88i −0.148418 0.415158i
\(155\) 16710.3i 0.695538i
\(156\) 0 0
\(157\) −5520.37 −0.223959 −0.111980 0.993711i \(-0.535719\pi\)
−0.111980 + 0.993711i \(0.535719\pi\)
\(158\) 28194.1 10079.3i 1.12939 0.403754i
\(159\) 0 0
\(160\) 11176.3 1642.25i 0.436575 0.0641504i
\(161\) −2398.36 −0.0925257
\(162\) 0 0
\(163\) 407.281i 0.0153292i −0.999971 0.00766459i \(-0.997560\pi\)
0.999971 0.00766459i \(-0.00243974\pi\)
\(164\) −32591.7 + 26717.5i −1.21177 + 0.993365i
\(165\) 0 0
\(166\) 4204.65 1503.15i 0.152586 0.0545490i
\(167\) 23742.9i 0.851334i −0.904880 0.425667i \(-0.860040\pi\)
0.904880 0.425667i \(-0.139960\pi\)
\(168\) 0 0
\(169\) −27186.8 −0.951886
\(170\) −4218.95 11801.3i −0.145984 0.408351i
\(171\) 0 0
\(172\) 405.328 + 494.444i 0.0137009 + 0.0167132i
\(173\) 2826.49 0.0944400 0.0472200 0.998885i \(-0.484964\pi\)
0.0472200 + 0.998885i \(0.484964\pi\)
\(174\) 0 0
\(175\) 5996.96i 0.195819i
\(176\) −55072.0 11017.1i −1.77789 0.355665i
\(177\) 0 0
\(178\) −9075.23 25385.4i −0.286429 0.801206i
\(179\) 45743.4i 1.42765i −0.700323 0.713826i \(-0.746961\pi\)
0.700323 0.713826i \(-0.253039\pi\)
\(180\) 0 0
\(181\) −24226.2 −0.739483 −0.369742 0.929135i \(-0.620554\pi\)
−0.369742 + 0.929135i \(0.620554\pi\)
\(182\) −1663.67 + 594.757i −0.0502255 + 0.0179555i
\(183\) 0 0
\(184\) −6631.89 + 11044.1i −0.195885 + 0.326208i
\(185\) 16782.3 0.490351
\(186\) 0 0
\(187\) 62310.5i 1.78188i
\(188\) −29262.6 35696.4i −0.827938 1.00997i
\(189\) 0 0
\(190\) 1890.16 675.726i 0.0523589 0.0187182i
\(191\) 22522.0i 0.617362i 0.951166 + 0.308681i \(0.0998875\pi\)
−0.951166 + 0.308681i \(0.900112\pi\)
\(192\) 0 0
\(193\) 18288.7 0.490985 0.245493 0.969398i \(-0.421050\pi\)
0.245493 + 0.969398i \(0.421050\pi\)
\(194\) −16221.1 45373.9i −0.430998 1.20560i
\(195\) 0 0
\(196\) −27952.6 + 22914.5i −0.727628 + 0.596484i
\(197\) −36300.2 −0.935356 −0.467678 0.883899i \(-0.654909\pi\)
−0.467678 + 0.883899i \(0.654909\pi\)
\(198\) 0 0
\(199\) 47336.5i 1.19533i 0.801744 + 0.597667i \(0.203906\pi\)
−0.801744 + 0.597667i \(0.796094\pi\)
\(200\) −27615.1 16582.6i −0.690378 0.414566i
\(201\) 0 0
\(202\) −12866.4 35990.1i −0.315321 0.882023i
\(203\) 14635.5i 0.355152i
\(204\) 0 0
\(205\) −29056.6 −0.691412
\(206\) 43328.2 15489.7i 1.02102 0.365014i
\(207\) 0 0
\(208\) −1861.57 + 9305.56i −0.0430280 + 0.215088i
\(209\) −9979.95 −0.228473
\(210\) 0 0
\(211\) 46490.2i 1.04423i 0.852875 + 0.522115i \(0.174857\pi\)
−0.852875 + 0.522115i \(0.825143\pi\)
\(212\) 17510.4 14354.4i 0.389604 0.319384i
\(213\) 0 0
\(214\) 24869.4 8890.76i 0.543048 0.194138i
\(215\) 440.814i 0.00953626i
\(216\) 0 0
\(217\) −18048.7 −0.383290
\(218\) −16219.3 45369.1i −0.341287 0.954656i
\(219\) 0 0
\(220\) −24549.3 29946.7i −0.507216 0.618734i
\(221\) 10528.7 0.215570
\(222\) 0 0
\(223\) 82597.9i 1.66096i −0.557048 0.830480i \(-0.688066\pi\)
0.557048 0.830480i \(-0.311934\pi\)
\(224\) −1773.79 12071.5i −0.0353514 0.240583i
\(225\) 0 0
\(226\) 5023.49 + 14051.8i 0.0983533 + 0.275116i
\(227\) 29701.6i 0.576405i −0.957569 0.288203i \(-0.906942\pi\)
0.957569 0.288203i \(-0.0930577\pi\)
\(228\) 0 0
\(229\) 45335.9 0.864512 0.432256 0.901751i \(-0.357718\pi\)
0.432256 + 0.901751i \(0.357718\pi\)
\(230\) −8363.63 + 2989.98i −0.158103 + 0.0565213i
\(231\) 0 0
\(232\) 67394.2 + 40469.7i 1.25212 + 0.751889i
\(233\) −50931.3 −0.938151 −0.469075 0.883158i \(-0.655413\pi\)
−0.469075 + 0.883158i \(0.655413\pi\)
\(234\) 0 0
\(235\) 31824.5i 0.576270i
\(236\) −28735.3 35053.1i −0.515930 0.629364i
\(237\) 0 0
\(238\) −12746.6 + 4556.87i −0.225030 + 0.0804475i
\(239\) 36888.3i 0.645792i −0.946434 0.322896i \(-0.895344\pi\)
0.946434 0.322896i \(-0.104656\pi\)
\(240\) 0 0
\(241\) 8387.27 0.144407 0.0722033 0.997390i \(-0.476997\pi\)
0.0722033 + 0.997390i \(0.476997\pi\)
\(242\) 45094.9 + 126141.i 0.770011 + 2.15389i
\(243\) 0 0
\(244\) 65052.0 53327.3i 1.09265 0.895715i
\(245\) −24920.7 −0.415171
\(246\) 0 0
\(247\) 1686.32i 0.0276405i
\(248\) −49907.9 + 83111.8i −0.811458 + 1.35132i
\(249\) 0 0
\(250\) −16760.2 46882.1i −0.268164 0.750114i
\(251\) 1475.47i 0.0234198i −0.999931 0.0117099i \(-0.996273\pi\)
0.999931 0.0117099i \(-0.00372746\pi\)
\(252\) 0 0
\(253\) 44159.6 0.689897
\(254\) 100001. 35750.0i 1.55001 0.554126i
\(255\) 0 0
\(256\) −60492.4 25211.8i −0.923041 0.384702i
\(257\) −34673.1 −0.524960 −0.262480 0.964937i \(-0.584540\pi\)
−0.262480 + 0.964937i \(0.584540\pi\)
\(258\) 0 0
\(259\) 18126.5i 0.270218i
\(260\) −5060.12 + 4148.11i −0.0748539 + 0.0613626i
\(261\) 0 0
\(262\) −4970.49 + 1776.94i −0.0724097 + 0.0258863i
\(263\) 19032.4i 0.275158i 0.990491 + 0.137579i \(0.0439321\pi\)
−0.990491 + 0.137579i \(0.956068\pi\)
\(264\) 0 0
\(265\) 15611.1 0.222301
\(266\) −729.850 2041.55i −0.0103150 0.0288534i
\(267\) 0 0
\(268\) 9439.50 + 11514.9i 0.131425 + 0.160321i
\(269\) −58724.1 −0.811544 −0.405772 0.913974i \(-0.632997\pi\)
−0.405772 + 0.913974i \(0.632997\pi\)
\(270\) 0 0
\(271\) 31474.1i 0.428563i −0.976772 0.214281i \(-0.931259\pi\)
0.976772 0.214281i \(-0.0687409\pi\)
\(272\) −14262.8 + 71296.7i −0.192782 + 0.963677i
\(273\) 0 0
\(274\) 34757.9 + 97225.5i 0.462969 + 1.29503i
\(275\) 110418.i 1.46008i
\(276\) 0 0
\(277\) 66531.5 0.867098 0.433549 0.901130i \(-0.357261\pi\)
0.433549 + 0.901130i \(0.357261\pi\)
\(278\) 49484.8 17690.7i 0.640299 0.228905i
\(279\) 0 0
\(280\) 4330.73 7211.98i 0.0552389 0.0919895i
\(281\) 123720. 1.56685 0.783424 0.621488i \(-0.213471\pi\)
0.783424 + 0.621488i \(0.213471\pi\)
\(282\) 0 0
\(283\) 54735.0i 0.683427i 0.939804 + 0.341713i \(0.111007\pi\)
−0.939804 + 0.341713i \(0.888993\pi\)
\(284\) −11794.4 14387.5i −0.146231 0.178382i
\(285\) 0 0
\(286\) 30632.2 10950.9i 0.374495 0.133881i
\(287\) 31383.9i 0.381016i
\(288\) 0 0
\(289\) −2853.15 −0.0341609
\(290\) 18245.7 + 51037.2i 0.216952 + 0.606864i
\(291\) 0 0
\(292\) 26762.7 21939.1i 0.313880 0.257308i
\(293\) 88617.9 1.03225 0.516127 0.856512i \(-0.327373\pi\)
0.516127 + 0.856512i \(0.327373\pi\)
\(294\) 0 0
\(295\) 31251.0i 0.359103i
\(296\) −83469.8 50122.9i −0.952677 0.572075i
\(297\) 0 0
\(298\) 34924.2 + 97690.7i 0.393273 + 1.10007i
\(299\) 7461.69i 0.0834632i
\(300\) 0 0
\(301\) 476.121 0.00525514
\(302\) 106953. 38235.4i 1.17268 0.419230i
\(303\) 0 0
\(304\) −11419.2 2284.40i −0.123563 0.0247186i
\(305\) 57996.0 0.623446
\(306\) 0 0
\(307\) 123447.i 1.30980i −0.755716 0.654900i \(-0.772711\pi\)
0.755716 0.654900i \(-0.227289\pi\)
\(308\) −32345.3 + 26515.6i −0.340965 + 0.279511i
\(309\) 0 0
\(310\) −62940.1 + 22500.9i −0.654943 + 0.234141i
\(311\) 60543.1i 0.625956i −0.949760 0.312978i \(-0.898673\pi\)
0.949760 0.312978i \(-0.101327\pi\)
\(312\) 0 0
\(313\) −52386.2 −0.534722 −0.267361 0.963596i \(-0.586152\pi\)
−0.267361 + 0.963596i \(0.586152\pi\)
\(314\) 7433.35 + 20792.7i 0.0753920 + 0.210888i
\(315\) 0 0
\(316\) −75928.4 92622.1i −0.760378 0.927557i
\(317\) 25997.4 0.258708 0.129354 0.991598i \(-0.458710\pi\)
0.129354 + 0.991598i \(0.458710\pi\)
\(318\) 0 0
\(319\) 269474.i 2.64811i
\(320\) −21234.9 39884.8i −0.207372 0.389500i
\(321\) 0 0
\(322\) 3229.46 + 9033.52i 0.0311472 + 0.0871255i
\(323\) 12920.1i 0.123840i
\(324\) 0 0
\(325\) 18657.5 0.176639
\(326\) −1534.04 + 548.416i −0.0144345 + 0.00516030i
\(327\) 0 0
\(328\) 144518. + 86782.1i 1.34331 + 0.806645i
\(329\) −34373.6 −0.317565
\(330\) 0 0
\(331\) 43231.1i 0.394584i 0.980345 + 0.197292i \(0.0632148\pi\)
−0.980345 + 0.197292i \(0.936785\pi\)
\(332\) −11323.4 13812.9i −0.102731 0.125317i
\(333\) 0 0
\(334\) −89428.5 + 31970.5i −0.801647 + 0.286587i
\(335\) 10265.9i 0.0914761i
\(336\) 0 0
\(337\) 11852.8 0.104366 0.0521831 0.998638i \(-0.483382\pi\)
0.0521831 + 0.998638i \(0.483382\pi\)
\(338\) 36607.9 + 102400.i 0.320436 + 0.896330i
\(339\) 0 0
\(340\) −38769.3 + 31781.7i −0.335375 + 0.274928i
\(341\) 332321. 2.85791
\(342\) 0 0
\(343\) 55525.0i 0.471955i
\(344\) 1316.56 2192.47i 0.0111256 0.0185275i
\(345\) 0 0
\(346\) −3805.96 10646.1i −0.0317916 0.0889281i
\(347\) 29124.4i 0.241879i 0.992660 + 0.120940i \(0.0385907\pi\)
−0.992660 + 0.120940i \(0.961409\pi\)
\(348\) 0 0
\(349\) 119977. 0.985023 0.492512 0.870306i \(-0.336079\pi\)
0.492512 + 0.870306i \(0.336079\pi\)
\(350\) −22587.8 + 8075.08i −0.184390 + 0.0659191i
\(351\) 0 0
\(352\) 32659.8 + 222266.i 0.263589 + 1.79385i
\(353\) −154758. −1.24195 −0.620975 0.783831i \(-0.713263\pi\)
−0.620975 + 0.783831i \(0.713263\pi\)
\(354\) 0 0
\(355\) 12827.0i 0.101781i
\(356\) −83395.3 + 68364.5i −0.658023 + 0.539424i
\(357\) 0 0
\(358\) −172294. + 61594.9i −1.34433 + 0.480594i
\(359\) 66839.6i 0.518615i 0.965795 + 0.259307i \(0.0834942\pi\)
−0.965795 + 0.259307i \(0.916506\pi\)
\(360\) 0 0
\(361\) 128252. 0.984121
\(362\) 32621.3 + 91249.1i 0.248934 + 0.696324i
\(363\) 0 0
\(364\) 4480.36 + 5465.42i 0.0338151 + 0.0412497i
\(365\) 23859.8 0.179094
\(366\) 0 0
\(367\) 94571.4i 0.702147i −0.936348 0.351073i \(-0.885817\pi\)
0.936348 0.351073i \(-0.114183\pi\)
\(368\) 50528.1 + 10108.1i 0.373110 + 0.0746403i
\(369\) 0 0
\(370\) −22597.8 63211.2i −0.165068 0.461732i
\(371\) 16861.5i 0.122503i
\(372\) 0 0
\(373\) −181061. −1.30139 −0.650694 0.759340i \(-0.725522\pi\)
−0.650694 + 0.759340i \(0.725522\pi\)
\(374\) 234695. 83903.0i 1.67788 0.599839i
\(375\) 0 0
\(376\) −95049.0 + 158285.i −0.672313 + 1.11960i
\(377\) −45533.4 −0.320366
\(378\) 0 0
\(379\) 51191.3i 0.356384i 0.983996 + 0.178192i \(0.0570248\pi\)
−0.983996 + 0.178192i \(0.942975\pi\)
\(380\) −5090.31 6209.47i −0.0352514 0.0430019i
\(381\) 0 0
\(382\) 84830.0 30326.5i 0.581330 0.207824i
\(383\) 152568.i 1.04008i −0.854143 0.520039i \(-0.825917\pi\)
0.854143 0.520039i \(-0.174083\pi\)
\(384\) 0 0
\(385\) −28836.9 −0.194548
\(386\) −24626.3 68885.2i −0.165282 0.462329i
\(387\) 0 0
\(388\) −149061. + 122195.i −0.990147 + 0.811687i
\(389\) −67896.8 −0.448694 −0.224347 0.974509i \(-0.572025\pi\)
−0.224347 + 0.974509i \(0.572025\pi\)
\(390\) 0 0
\(391\) 57169.5i 0.373947i
\(392\) 123948. + 74429.5i 0.806614 + 0.484365i
\(393\) 0 0
\(394\) 48879.4 + 136726.i 0.314871 + 0.880765i
\(395\) 82575.7i 0.529247i
\(396\) 0 0
\(397\) −126087. −0.799998 −0.399999 0.916516i \(-0.630990\pi\)
−0.399999 + 0.916516i \(0.630990\pi\)
\(398\) 178295. 63740.0i 1.12557 0.402389i
\(399\) 0 0
\(400\) −25274.7 + 126343.i −0.157967 + 0.789641i
\(401\) −70890.8 −0.440860 −0.220430 0.975403i \(-0.570746\pi\)
−0.220430 + 0.975403i \(0.570746\pi\)
\(402\) 0 0
\(403\) 56152.6i 0.345748i
\(404\) −118233. + 96923.5i −0.724398 + 0.593836i
\(405\) 0 0
\(406\) 55125.1 19707.1i 0.334424 0.119556i
\(407\) 333752.i 2.01482i
\(408\) 0 0
\(409\) 43544.2 0.260306 0.130153 0.991494i \(-0.458453\pi\)
0.130153 + 0.991494i \(0.458453\pi\)
\(410\) 39125.6 + 109443.i 0.232752 + 0.651059i
\(411\) 0 0
\(412\) −116685. 142340.i −0.687420 0.838557i
\(413\) −33754.1 −0.197891
\(414\) 0 0
\(415\) 12314.7i 0.0715036i
\(416\) 37556.5 5518.55i 0.217019 0.0318888i
\(417\) 0 0
\(418\) 13438.3 + 37589.9i 0.0769116 + 0.215139i
\(419\) 210600.i 1.19958i 0.800156 + 0.599792i \(0.204750\pi\)
−0.800156 + 0.599792i \(0.795250\pi\)
\(420\) 0 0
\(421\) 84126.0 0.474642 0.237321 0.971431i \(-0.423731\pi\)
0.237321 + 0.971431i \(0.423731\pi\)
\(422\) 175107. 62600.4i 0.983285 0.351522i
\(423\) 0 0
\(424\) −77644.7 46625.0i −0.431897 0.259350i
\(425\) 142949. 0.791413
\(426\) 0 0
\(427\) 62641.3i 0.343562i
\(428\) −66974.9 81700.1i −0.365615 0.446000i
\(429\) 0 0
\(430\) 1660.34 593.569i 0.00897969 0.00321022i
\(431\) 150083.i 0.807933i 0.914774 + 0.403967i \(0.132369\pi\)
−0.914774 + 0.403967i \(0.867631\pi\)
\(432\) 0 0
\(433\) 71221.5 0.379871 0.189935 0.981797i \(-0.439172\pi\)
0.189935 + 0.981797i \(0.439172\pi\)
\(434\) 24303.2 + 67981.3i 0.129028 + 0.360919i
\(435\) 0 0
\(436\) −149045. + 122182.i −0.784050 + 0.642736i
\(437\) 9156.53 0.0479477
\(438\) 0 0
\(439\) 109245.i 0.566858i −0.958993 0.283429i \(-0.908528\pi\)
0.958993 0.283429i \(-0.0914720\pi\)
\(440\) −79739.3 + 132790.i −0.411876 + 0.685899i
\(441\) 0 0
\(442\) −14177.2 39656.7i −0.0725680 0.202989i
\(443\) 230658.i 1.17533i −0.809103 0.587666i \(-0.800047\pi\)
0.809103 0.587666i \(-0.199953\pi\)
\(444\) 0 0
\(445\) −74349.7 −0.375456
\(446\) −311109. + 111221.i −1.56402 + 0.559133i
\(447\) 0 0
\(448\) −43079.4 + 22935.7i −0.214642 + 0.114276i
\(449\) 9751.64 0.0483710 0.0241855 0.999707i \(-0.492301\pi\)
0.0241855 + 0.999707i \(0.492301\pi\)
\(450\) 0 0
\(451\) 577854.i 2.84096i
\(452\) 46162.5 37842.4i 0.225950 0.185226i
\(453\) 0 0
\(454\) −111872. + 39994.1i −0.542764 + 0.194037i
\(455\) 4872.61i 0.0235363i
\(456\) 0 0
\(457\) 66139.1 0.316684 0.158342 0.987384i \(-0.449385\pi\)
0.158342 + 0.987384i \(0.449385\pi\)
\(458\) −61046.1 170760.i −0.291023 0.814056i
\(459\) 0 0
\(460\) 22523.8 + 27475.9i 0.106445 + 0.129848i
\(461\) 173989. 0.818692 0.409346 0.912379i \(-0.365757\pi\)
0.409346 + 0.912379i \(0.365757\pi\)
\(462\) 0 0
\(463\) 173993.i 0.811650i 0.913951 + 0.405825i \(0.133016\pi\)
−0.913951 + 0.405825i \(0.866984\pi\)
\(464\) 61682.4 308337.i 0.286500 1.43215i
\(465\) 0 0
\(466\) 68580.5 + 191835.i 0.315812 + 0.883397i
\(467\) 172090.i 0.789080i 0.918879 + 0.394540i \(0.129096\pi\)
−0.918879 + 0.394540i \(0.870904\pi\)
\(468\) 0 0
\(469\) 11088.2 0.0504097
\(470\) −119868. + 42852.7i −0.542637 + 0.193991i
\(471\) 0 0
\(472\) −93336.0 + 155433.i −0.418953 + 0.697683i
\(473\) −8766.55 −0.0391838
\(474\) 0 0
\(475\) 22895.4i 0.101475i
\(476\) 34327.3 + 41874.6i 0.151505 + 0.184815i
\(477\) 0 0
\(478\) −138941. + 49671.2i −0.608101 + 0.217395i
\(479\) 218398.i 0.951869i −0.879481 0.475935i \(-0.842110\pi\)
0.879481 0.475935i \(-0.157890\pi\)
\(480\) 0 0
\(481\) 56394.4 0.243751
\(482\) −11293.7 31591.0i −0.0486119 0.135978i
\(483\) 0 0
\(484\) 414392. 339704.i 1.76897 1.45014i
\(485\) −132893. −0.564959
\(486\) 0 0
\(487\) 392112.i 1.65330i 0.562716 + 0.826650i \(0.309757\pi\)
−0.562716 + 0.826650i \(0.690243\pi\)
\(488\) −288454. 173214.i −1.21126 0.727351i
\(489\) 0 0
\(490\) 33556.4 + 93864.8i 0.139760 + 0.390940i
\(491\) 209717.i 0.869903i 0.900454 + 0.434951i \(0.143234\pi\)
−0.900454 + 0.434951i \(0.856766\pi\)
\(492\) 0 0
\(493\) −348864. −1.43537
\(494\) 6351.60 2270.68i 0.0260273 0.00930470i
\(495\) 0 0
\(496\) 380247. + 76067.9i 1.54562 + 0.309199i
\(497\) −13854.4 −0.0560885
\(498\) 0 0
\(499\) 135886.i 0.545725i −0.962053 0.272862i \(-0.912030\pi\)
0.962053 0.272862i \(-0.0879704\pi\)
\(500\) −154015. + 126256.i −0.616061 + 0.505025i
\(501\) 0 0
\(502\) −5557.42 + 1986.76i −0.0220529 + 0.00788385i
\(503\) 232332.i 0.918275i −0.888365 0.459137i \(-0.848159\pi\)
0.888365 0.459137i \(-0.151841\pi\)
\(504\) 0 0
\(505\) −105409. −0.413328
\(506\) −59462.2 166329.i −0.232242 0.649632i
\(507\) 0 0
\(508\) −269308. 328518.i −1.04357 1.27301i
\(509\) 145319. 0.560901 0.280451 0.959868i \(-0.409516\pi\)
0.280451 + 0.959868i \(0.409516\pi\)
\(510\) 0 0
\(511\) 25770.9i 0.0986935i
\(512\) −13506.6 + 261796.i −0.0515234 + 0.998672i
\(513\) 0 0
\(514\) 46688.3 + 130598.i 0.176719 + 0.494321i
\(515\) 126901.i 0.478465i
\(516\) 0 0
\(517\) 632900. 2.36785
\(518\) −68274.1 + 24407.8i −0.254447 + 0.0909641i
\(519\) 0 0
\(520\) 22437.7 + 13473.6i 0.0829795 + 0.0498285i
\(521\) −443088. −1.63235 −0.816177 0.577803i \(-0.803910\pi\)
−0.816177 + 0.577803i \(0.803910\pi\)
\(522\) 0 0
\(523\) 73202.4i 0.267622i −0.991007 0.133811i \(-0.957278\pi\)
0.991007 0.133811i \(-0.0427215\pi\)
\(524\) 13385.8 + 16328.9i 0.0487509 + 0.0594694i
\(525\) 0 0
\(526\) 71686.3 25627.7i 0.259098 0.0926271i
\(527\) 430226.i 1.54909i
\(528\) 0 0
\(529\) 239325. 0.855217
\(530\) −21020.8 58799.9i −0.0748338 0.209327i
\(531\) 0 0
\(532\) −6706.83 + 5498.02i −0.0236970 + 0.0194260i
\(533\) −97640.6 −0.343697
\(534\) 0 0
\(535\) 72838.4i 0.254480i
\(536\) 30660.7 51059.4i 0.106722 0.177724i
\(537\) 0 0
\(538\) 79073.8 + 221187.i 0.273192 + 0.764179i
\(539\) 495602.i 1.70591i
\(540\) 0 0
\(541\) 438165. 1.49707 0.748536 0.663094i \(-0.230757\pi\)
0.748536 + 0.663094i \(0.230757\pi\)
\(542\) −118548. + 42380.8i −0.403550 + 0.144268i
\(543\) 0 0
\(544\) 287748. 42281.7i 0.972330 0.142874i
\(545\) −132878. −0.447364
\(546\) 0 0
\(547\) 312024.i 1.04283i −0.853303 0.521416i \(-0.825404\pi\)
0.853303 0.521416i \(-0.174596\pi\)
\(548\) 319402. 261834.i 1.06359 0.871898i
\(549\) 0 0
\(550\) 415896. 148682.i 1.37486 0.491510i
\(551\) 55875.7i 0.184043i
\(552\) 0 0
\(553\) −89189.8 −0.291652
\(554\) −89586.7 250594.i −0.291893 0.816490i
\(555\) 0 0
\(556\) −133266. 162566.i −0.431091 0.525871i
\(557\) −312549. −1.00741 −0.503707 0.863874i \(-0.668031\pi\)
−0.503707 + 0.863874i \(0.668031\pi\)
\(558\) 0 0
\(559\) 1481.29i 0.00474042i
\(560\) −32995.7 6600.75i −0.105216 0.0210483i
\(561\) 0 0
\(562\) −166593. 465996.i −0.527452 1.47540i
\(563\) 86349.2i 0.272422i −0.990680 0.136211i \(-0.956508\pi\)
0.990680 0.136211i \(-0.0434925\pi\)
\(564\) 0 0
\(565\) 41155.5 0.128923
\(566\) 206162. 73702.3i 0.643539 0.230064i
\(567\) 0 0
\(568\) −38309.8 + 63797.4i −0.118744 + 0.197745i
\(569\) −554958. −1.71410 −0.857049 0.515235i \(-0.827705\pi\)
−0.857049 + 0.515235i \(0.827705\pi\)
\(570\) 0 0
\(571\) 303511.i 0.930898i 0.885075 + 0.465449i \(0.154107\pi\)
−0.885075 + 0.465449i \(0.845893\pi\)
\(572\) −82494.3 100632.i −0.252134 0.307569i
\(573\) 0 0
\(574\) 118209. 42259.4i 0.358779 0.128263i
\(575\) 101308.i 0.306414i
\(576\) 0 0
\(577\) −500884. −1.50448 −0.752238 0.658892i \(-0.771026\pi\)
−0.752238 + 0.658892i \(0.771026\pi\)
\(578\) 3841.86 + 10746.5i 0.0114997 + 0.0321671i
\(579\) 0 0
\(580\) 167666. 137446.i 0.498412 0.408580i
\(581\) −13301.1 −0.0394035
\(582\) 0 0
\(583\) 310461.i 0.913418i
\(584\) −118671. 71261.2i −0.347953 0.208943i
\(585\) 0 0
\(586\) −119327. 333783.i −0.347490 0.972007i
\(587\) 575710.i 1.67081i 0.549633 + 0.835406i \(0.314767\pi\)
−0.549633 + 0.835406i \(0.685233\pi\)
\(588\) 0 0
\(589\) 68907.0 0.198624
\(590\) −117708. + 42080.4i −0.338145 + 0.120886i
\(591\) 0 0
\(592\) −76395.5 + 381885.i −0.217984 + 1.08965i
\(593\) 138143. 0.392843 0.196421 0.980520i \(-0.437068\pi\)
0.196421 + 0.980520i \(0.437068\pi\)
\(594\) 0 0
\(595\) 37332.6i 0.105452i
\(596\) 320930. 263087.i 0.903478 0.740640i
\(597\) 0 0
\(598\) −28104.8 + 10047.4i −0.0785919 + 0.0280964i
\(599\) 191294.i 0.533147i −0.963815 0.266574i \(-0.914108\pi\)
0.963815 0.266574i \(-0.0858916\pi\)
\(600\) 0 0
\(601\) −406240. −1.12469 −0.562346 0.826902i \(-0.690101\pi\)
−0.562346 + 0.826902i \(0.690101\pi\)
\(602\) −641.112 1793.33i −0.00176905 0.00494843i
\(603\) 0 0
\(604\) −288031. 351358.i −0.789524 0.963110i
\(605\) 369445. 1.00934
\(606\) 0 0
\(607\) 68666.5i 0.186366i −0.995649 0.0931831i \(-0.970296\pi\)
0.995649 0.0931831i \(-0.0297042\pi\)
\(608\) 6772.03 + 46087.0i 0.0183194 + 0.124673i
\(609\) 0 0
\(610\) −78093.4 218445.i −0.209872 0.587059i
\(611\) 106942.i 0.286461i
\(612\) 0 0
\(613\) −572114. −1.52252 −0.761258 0.648450i \(-0.775418\pi\)
−0.761258 + 0.648450i \(0.775418\pi\)
\(614\) −464970. + 166225.i −1.23335 + 0.440921i
\(615\) 0 0
\(616\) 143426. + 86126.1i 0.377978 + 0.226973i
\(617\) −20380.8 −0.0535367 −0.0267684 0.999642i \(-0.508522\pi\)
−0.0267684 + 0.999642i \(0.508522\pi\)
\(618\) 0 0
\(619\) 448721.i 1.17110i 0.810635 + 0.585552i \(0.199122\pi\)
−0.810635 + 0.585552i \(0.800878\pi\)
\(620\) 169501. + 206768.i 0.440951 + 0.537899i
\(621\) 0 0
\(622\) −228038. + 81523.2i −0.589423 + 0.210717i
\(623\) 80304.8i 0.206902i
\(624\) 0 0
\(625\) 177255. 0.453773
\(626\) 70539.6 + 197315.i 0.180005 + 0.503514i
\(627\) 0 0
\(628\) 68307.5 55996.1i 0.173200 0.141984i
\(629\) 432079. 1.09210
\(630\) 0 0
\(631\) 402529.i 1.01097i 0.862835 + 0.505486i \(0.168687\pi\)
−0.862835 + 0.505486i \(0.831313\pi\)
\(632\) −246625. + 410706.i −0.617453 + 1.02825i
\(633\) 0 0
\(634\) −35006.2 97920.2i −0.0870897 0.243609i
\(635\) 292885.i 0.726357i
\(636\) 0 0
\(637\) −83742.3 −0.206379
\(638\) −1.01499e6 + 362856.i −2.49356 + 0.891441i
\(639\) 0 0
\(640\) −121634. + 133688.i −0.296959 + 0.326387i
\(641\) −353813. −0.861108 −0.430554 0.902565i \(-0.641682\pi\)
−0.430554 + 0.902565i \(0.641682\pi\)
\(642\) 0 0
\(643\) 263141.i 0.636452i 0.948015 + 0.318226i \(0.103087\pi\)
−0.948015 + 0.318226i \(0.896913\pi\)
\(644\) 29676.6 24327.8i 0.0715554 0.0586586i
\(645\) 0 0
\(646\) 48664.3 17397.4i 0.116613 0.0416887i
\(647\) 265174.i 0.633464i 0.948515 + 0.316732i \(0.102586\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(648\) 0 0
\(649\) 621494. 1.47553
\(650\) −25122.9 70274.4i −0.0594625 0.166330i
\(651\) 0 0
\(652\) 4131.27 + 5039.58i 0.00971825 + 0.0118549i
\(653\) 5877.92 0.0137847 0.00689235 0.999976i \(-0.497806\pi\)
0.00689235 + 0.999976i \(0.497806\pi\)
\(654\) 0 0
\(655\) 14557.7i 0.0339322i
\(656\) 132270. 661190.i 0.307365 1.53645i
\(657\) 0 0
\(658\) 46285.0 + 129470.i 0.106903 + 0.299031i
\(659\) 554642.i 1.27715i −0.769560 0.638575i \(-0.779524\pi\)
0.769560 0.638575i \(-0.220476\pi\)
\(660\) 0 0
\(661\) −821227. −1.87958 −0.939789 0.341755i \(-0.888979\pi\)
−0.939789 + 0.341755i \(0.888979\pi\)
\(662\) 162832. 58212.0i 0.371555 0.132830i
\(663\) 0 0
\(664\) −36779.8 + 61249.5i −0.0834206 + 0.138921i
\(665\) −5979.36 −0.0135211
\(666\) 0 0
\(667\) 247241.i 0.555736i
\(668\) 240836. + 293787.i 0.539721 + 0.658385i
\(669\) 0 0
\(670\) 38667.0 13823.4i 0.0861372 0.0307938i
\(671\) 1.15338e6i 2.56169i
\(672\) 0 0
\(673\) 516865. 1.14116 0.570580 0.821242i \(-0.306718\pi\)
0.570580 + 0.821242i \(0.306718\pi\)
\(674\) −15960.1 44643.9i −0.0351330 0.0982749i
\(675\) 0 0
\(676\) 336402. 275770.i 0.736148 0.603468i
\(677\) 690686. 1.50697 0.753483 0.657468i \(-0.228372\pi\)
0.753483 + 0.657468i \(0.228372\pi\)
\(678\) 0 0
\(679\) 143537.i 0.311332i
\(680\) 171911. + 103231.i 0.371780 + 0.223251i
\(681\) 0 0
\(682\) −447480. 1.25170e6i −0.962066 2.69111i
\(683\) 764551.i 1.63895i 0.573117 + 0.819474i \(0.305734\pi\)
−0.573117 + 0.819474i \(0.694266\pi\)
\(684\) 0 0
\(685\) 284757. 0.606868
\(686\) 209138. 74766.2i 0.444410 0.158875i
\(687\) 0 0
\(688\) −10030.8 2006.65i −0.0211914 0.00423931i
\(689\) 52458.9 0.110505
\(690\) 0 0
\(691\) 321130.i 0.672550i 0.941764 + 0.336275i \(0.109167\pi\)
−0.941764 + 0.336275i \(0.890833\pi\)
\(692\) −34974.2 + 28670.6i −0.0730358 + 0.0598722i
\(693\) 0 0
\(694\) 109698. 39216.9i 0.227762 0.0814244i
\(695\) 144933.i 0.300053i
\(696\) 0 0
\(697\) −748096. −1.53990
\(698\) −161552. 451898.i −0.331591 0.927534i
\(699\) 0 0
\(700\) 60830.3 + 74204.6i 0.124144 + 0.151438i
\(701\) 621799. 1.26536 0.632680 0.774413i \(-0.281955\pi\)
0.632680 + 0.774413i \(0.281955\pi\)
\(702\) 0 0
\(703\) 69203.8i 0.140029i
\(704\) 793196. 422302.i 1.60043 0.852075i
\(705\) 0 0
\(706\) 208386. + 582903.i 0.418081 + 1.16946i
\(707\) 113852.i 0.227772i
\(708\) 0 0
\(709\) −524870. −1.04414 −0.522070 0.852903i \(-0.674840\pi\)
−0.522070 + 0.852903i \(0.674840\pi\)
\(710\) −48313.4 + 17271.9i −0.0958409 + 0.0342629i
\(711\) 0 0
\(712\) 369792. + 222057.i 0.729454 + 0.438031i
\(713\) −304902. −0.599765
\(714\) 0 0
\(715\) 89716.5i 0.175493i
\(716\) 463999. + 566015.i 0.905089 + 1.10408i
\(717\) 0 0
\(718\) 251754. 90001.5i 0.488346 0.174583i
\(719\) 348658.i 0.674438i 0.941426 + 0.337219i \(0.109486\pi\)
−0.941426 + 0.337219i \(0.890514\pi\)
\(720\) 0 0
\(721\) −137065. −0.263668
\(722\) −172695. 483066.i −0.331287 0.926684i
\(723\) 0 0
\(724\) 299768. 245739.i 0.571885 0.468811i
\(725\) −618211. −1.17615
\(726\) 0 0
\(727\) 604820.i 1.14435i 0.820133 + 0.572173i \(0.193899\pi\)
−0.820133 + 0.572173i \(0.806101\pi\)
\(728\) 14552.8 24234.8i 0.0274590 0.0457275i
\(729\) 0 0
\(730\) −32128.0 89869.2i −0.0602890 0.168642i
\(731\) 11349.3i 0.0212389i
\(732\) 0 0
\(733\) −475610. −0.885204 −0.442602 0.896718i \(-0.645945\pi\)
−0.442602 + 0.896718i \(0.645945\pi\)
\(734\) −356208. + 127343.i −0.661167 + 0.236365i
\(735\) 0 0
\(736\) −29965.1 203927.i −0.0553172 0.376461i
\(737\) −204160. −0.375868
\(738\) 0 0
\(739\) 844449.i 1.54627i 0.634244 + 0.773133i \(0.281312\pi\)
−0.634244 + 0.773133i \(0.718688\pi\)
\(740\) −207659. + 170231.i −0.379216 + 0.310868i
\(741\) 0 0
\(742\) −63509.5 + 22704.5i −0.115354 + 0.0412386i
\(743\) 620323.i 1.12367i −0.827248 0.561837i \(-0.810095\pi\)
0.827248 0.561837i \(-0.189905\pi\)
\(744\) 0 0
\(745\) 286120. 0.515508
\(746\) 243804. + 681974.i 0.438090 + 1.22543i
\(747\) 0 0
\(748\) −632049. 771013.i −1.12966 1.37803i
\(749\) −78672.5 −0.140236
\(750\) 0 0
\(751\) 730748.i 1.29565i 0.761789 + 0.647825i \(0.224321\pi\)
−0.761789 + 0.647825i \(0.775679\pi\)
\(752\) 724175. + 144870.i 1.28058 + 0.256179i
\(753\) 0 0
\(754\) 61312.0 + 171503.i 0.107846 + 0.301669i
\(755\) 313247.i 0.549533i
\(756\) 0 0
\(757\) −769023. −1.34198 −0.670992 0.741465i \(-0.734132\pi\)
−0.670992 + 0.741465i \(0.734132\pi\)
\(758\) 192814. 68930.6i 0.335584 0.119970i
\(759\) 0 0
\(760\) −16534.0 + 27534.1i −0.0286253 + 0.0476699i
\(761\) −275394. −0.475538 −0.237769 0.971322i \(-0.576416\pi\)
−0.237769 + 0.971322i \(0.576416\pi\)
\(762\) 0 0
\(763\) 143522.i 0.246529i
\(764\) −228452. 278680.i −0.391389 0.477441i
\(765\) 0 0
\(766\) −574654. + 205437.i −0.979375 + 0.350124i
\(767\) 105014.i 0.178508i
\(768\) 0 0
\(769\) −52842.1 −0.0893568 −0.0446784 0.999001i \(-0.514226\pi\)
−0.0446784 + 0.999001i \(0.514226\pi\)
\(770\) 38829.8 + 108616.i 0.0654914 + 0.183194i
\(771\) 0 0
\(772\) −226299. + 185512.i −0.379707 + 0.311270i
\(773\) 195309. 0.326861 0.163430 0.986555i \(-0.447744\pi\)
0.163430 + 0.986555i \(0.447744\pi\)
\(774\) 0 0
\(775\) 762389.i 1.26933i
\(776\) 660966. + 396905.i 1.09763 + 0.659117i
\(777\) 0 0
\(778\) 91425.1 + 255736.i 0.151045 + 0.422506i
\(779\) 119819.i 0.197446i
\(780\) 0 0
\(781\) 255093. 0.418211
\(782\) −215331. + 76980.4i −0.352122 + 0.125883i
\(783\) 0 0
\(784\) 113443. 567076.i 0.184563 0.922590i
\(785\) 60898.4 0.0988250
\(786\) 0 0