Properties

Label 320.3.e.b.159.15
Level $320$
Weight $3$
Character 320.159
Analytic conductor $8.719$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 320.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.71936845953\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 19 x^{14} + 301 x^{12} + 1102 x^{10} + 3238 x^{8} + 1102 x^{6} + 301 x^{4} + 19 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{34} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 159.15
Root \(-0.265804 + 0.460386i\) of defining polynomial
Character \(\chi\) \(=\) 320.159
Dual form 320.3.e.b.159.4

$q$-expansion

\(f(q)\) \(=\) \(q+5.13399i q^{3} +(2.79662 - 4.14474i) q^{5} +6.19337 q^{7} -17.3578 q^{9} +O(q^{10})\) \(q+5.13399i q^{3} +(2.79662 - 4.14474i) q^{5} +6.19337 q^{7} -17.3578 q^{9} +20.0431 q^{11} +15.8612 q^{13} +(21.2791 + 14.3578i) q^{15} +6.98882i q^{17} -10.3923 q^{19} +31.7967i q^{21} -22.3871 q^{23} +(-9.35782 - 23.1826i) q^{25} -42.9089i q^{27} -4.20563i q^{29} +20.7156i q^{31} +102.901i q^{33} +(17.3205 - 25.6699i) q^{35} -35.4786 q^{37} +81.4313i q^{39} -37.0735 q^{41} +23.8329i q^{43} +(-48.5432 + 71.9437i) q^{45} +48.7515 q^{47} -10.6422 q^{49} -35.8805 q^{51} +77.4691 q^{53} +(56.0529 - 83.0735i) q^{55} -53.3540i q^{57} +0.497984 q^{59} -60.7490i q^{61} -107.503 q^{63} +(44.3578 - 65.7407i) q^{65} +82.5209i q^{67} -114.935i q^{69} -28.7156i q^{71} -10.1706i q^{73} +(119.019 - 48.0429i) q^{75} +124.134 q^{77} -87.5782i q^{79} +64.0735 q^{81} +103.057i q^{83} +(28.9669 + 19.5451i) q^{85} +21.5917 q^{87} -49.2844 q^{89} +98.2344 q^{91} -106.354 q^{93} +(-29.0633 + 43.0735i) q^{95} -84.4911i q^{97} -347.904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 96q^{9} + O(q^{10}) \) \( 16q - 96q^{9} + 32q^{25} - 48q^{41} - 352q^{49} + 528q^{65} + 480q^{81} - 1152q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.13399i 1.71133i 0.517531 + 0.855664i \(0.326851\pi\)
−0.517531 + 0.855664i \(0.673149\pi\)
\(4\) 0 0
\(5\) 2.79662 4.14474i 0.559324 0.828949i
\(6\) 0 0
\(7\) 6.19337 0.884767 0.442383 0.896826i \(-0.354133\pi\)
0.442383 + 0.896826i \(0.354133\pi\)
\(8\) 0 0
\(9\) −17.3578 −1.92865
\(10\) 0 0
\(11\) 20.0431 1.82210 0.911049 0.412298i \(-0.135274\pi\)
0.911049 + 0.412298i \(0.135274\pi\)
\(12\) 0 0
\(13\) 15.8612 1.22009 0.610047 0.792365i \(-0.291151\pi\)
0.610047 + 0.792365i \(0.291151\pi\)
\(14\) 0 0
\(15\) 21.2791 + 14.3578i 1.41860 + 0.957188i
\(16\) 0 0
\(17\) 6.98882i 0.411107i 0.978646 + 0.205554i \(0.0658995\pi\)
−0.978646 + 0.205554i \(0.934100\pi\)
\(18\) 0 0
\(19\) −10.3923 −0.546963 −0.273482 0.961877i \(-0.588175\pi\)
−0.273482 + 0.961877i \(0.588175\pi\)
\(20\) 0 0
\(21\) 31.7967i 1.51413i
\(22\) 0 0
\(23\) −22.3871 −0.973353 −0.486676 0.873582i \(-0.661791\pi\)
−0.486676 + 0.873582i \(0.661791\pi\)
\(24\) 0 0
\(25\) −9.35782 23.1826i −0.374313 0.927303i
\(26\) 0 0
\(27\) 42.9089i 1.58922i
\(28\) 0 0
\(29\) 4.20563i 0.145022i −0.997368 0.0725109i \(-0.976899\pi\)
0.997368 0.0725109i \(-0.0231012\pi\)
\(30\) 0 0
\(31\) 20.7156i 0.668246i 0.942529 + 0.334123i \(0.108440\pi\)
−0.942529 + 0.334123i \(0.891560\pi\)
\(32\) 0 0
\(33\) 102.901i 3.11821i
\(34\) 0 0
\(35\) 17.3205 25.6699i 0.494872 0.733427i
\(36\) 0 0
\(37\) −35.4786 −0.958882 −0.479441 0.877574i \(-0.659161\pi\)
−0.479441 + 0.877574i \(0.659161\pi\)
\(38\) 0 0
\(39\) 81.4313i 2.08798i
\(40\) 0 0
\(41\) −37.0735 −0.904230 −0.452115 0.891960i \(-0.649330\pi\)
−0.452115 + 0.891960i \(0.649330\pi\)
\(42\) 0 0
\(43\) 23.8329i 0.554254i 0.960833 + 0.277127i \(0.0893822\pi\)
−0.960833 + 0.277127i \(0.910618\pi\)
\(44\) 0 0
\(45\) −48.5432 + 71.9437i −1.07874 + 1.59875i
\(46\) 0 0
\(47\) 48.7515 1.03727 0.518633 0.854997i \(-0.326441\pi\)
0.518633 + 0.854997i \(0.326441\pi\)
\(48\) 0 0
\(49\) −10.6422 −0.217187
\(50\) 0 0
\(51\) −35.8805 −0.703540
\(52\) 0 0
\(53\) 77.4691 1.46168 0.730840 0.682549i \(-0.239128\pi\)
0.730840 + 0.682549i \(0.239128\pi\)
\(54\) 0 0
\(55\) 56.0529 83.0735i 1.01914 1.51043i
\(56\) 0 0
\(57\) 53.3540i 0.936034i
\(58\) 0 0
\(59\) 0.497984 0.00844041 0.00422020 0.999991i \(-0.498657\pi\)
0.00422020 + 0.999991i \(0.498657\pi\)
\(60\) 0 0
\(61\) 60.7490i 0.995885i −0.867210 0.497943i \(-0.834089\pi\)
0.867210 0.497943i \(-0.165911\pi\)
\(62\) 0 0
\(63\) −107.503 −1.70640
\(64\) 0 0
\(65\) 44.3578 65.7407i 0.682428 1.01140i
\(66\) 0 0
\(67\) 82.5209i 1.23165i 0.787881 + 0.615827i \(0.211178\pi\)
−0.787881 + 0.615827i \(0.788822\pi\)
\(68\) 0 0
\(69\) 114.935i 1.66573i
\(70\) 0 0
\(71\) 28.7156i 0.404446i −0.979340 0.202223i \(-0.935183\pi\)
0.979340 0.202223i \(-0.0648165\pi\)
\(72\) 0 0
\(73\) 10.1706i 0.139324i −0.997571 0.0696620i \(-0.977808\pi\)
0.997571 0.0696620i \(-0.0221921\pi\)
\(74\) 0 0
\(75\) 119.019 48.0429i 1.58692 0.640572i
\(76\) 0 0
\(77\) 124.134 1.61213
\(78\) 0 0
\(79\) 87.5782i 1.10858i −0.832322 0.554292i \(-0.812989\pi\)
0.832322 0.554292i \(-0.187011\pi\)
\(80\) 0 0
\(81\) 64.0735 0.791030
\(82\) 0 0
\(83\) 103.057i 1.24165i 0.783950 + 0.620824i \(0.213202\pi\)
−0.783950 + 0.620824i \(0.786798\pi\)
\(84\) 0 0
\(85\) 28.9669 + 19.5451i 0.340787 + 0.229942i
\(86\) 0 0
\(87\) 21.5917 0.248180
\(88\) 0 0
\(89\) −49.2844 −0.553757 −0.276878 0.960905i \(-0.589300\pi\)
−0.276878 + 0.960905i \(0.589300\pi\)
\(90\) 0 0
\(91\) 98.2344 1.07950
\(92\) 0 0
\(93\) −106.354 −1.14359
\(94\) 0 0
\(95\) −29.0633 + 43.0735i −0.305930 + 0.453405i
\(96\) 0 0
\(97\) 84.4911i 0.871042i −0.900179 0.435521i \(-0.856564\pi\)
0.900179 0.435521i \(-0.143436\pi\)
\(98\) 0 0
\(99\) −347.904 −3.51418
\(100\) 0 0
\(101\) 92.7892i 0.918705i 0.888254 + 0.459353i \(0.151919\pi\)
−0.888254 + 0.459353i \(0.848081\pi\)
\(102\) 0 0
\(103\) −42.7284 −0.414839 −0.207419 0.978252i \(-0.566506\pi\)
−0.207419 + 0.978252i \(0.566506\pi\)
\(104\) 0 0
\(105\) 131.789 + 88.9233i 1.25513 + 0.846888i
\(106\) 0 0
\(107\) 29.3440i 0.274243i −0.990554 0.137121i \(-0.956215\pi\)
0.990554 0.137121i \(-0.0437851\pi\)
\(108\) 0 0
\(109\) 163.433i 1.49938i −0.661789 0.749691i \(-0.730202\pi\)
0.661789 0.749691i \(-0.269798\pi\)
\(110\) 0 0
\(111\) 182.147i 1.64096i
\(112\) 0 0
\(113\) 120.686i 1.06801i −0.845480 0.534007i \(-0.820686\pi\)
0.845480 0.534007i \(-0.179314\pi\)
\(114\) 0 0
\(115\) −62.6083 + 92.7888i −0.544420 + 0.806860i
\(116\) 0 0
\(117\) −275.316 −2.35313
\(118\) 0 0
\(119\) 43.2844i 0.363734i
\(120\) 0 0
\(121\) 280.725 2.32004
\(122\) 0 0
\(123\) 190.335i 1.54744i
\(124\) 0 0
\(125\) −122.256 26.0471i −0.978049 0.208377i
\(126\) 0 0
\(127\) −227.564 −1.79184 −0.895920 0.444215i \(-0.853483\pi\)
−0.895920 + 0.444215i \(0.853483\pi\)
\(128\) 0 0
\(129\) −122.358 −0.948510
\(130\) 0 0
\(131\) 34.1430 0.260634 0.130317 0.991472i \(-0.458401\pi\)
0.130317 + 0.991472i \(0.458401\pi\)
\(132\) 0 0
\(133\) −64.3634 −0.483935
\(134\) 0 0
\(135\) −177.847 120.000i −1.31738 0.888889i
\(136\) 0 0
\(137\) 216.598i 1.58100i 0.612459 + 0.790502i \(0.290180\pi\)
−0.612459 + 0.790502i \(0.709820\pi\)
\(138\) 0 0
\(139\) −113.076 −0.813495 −0.406748 0.913541i \(-0.633337\pi\)
−0.406748 + 0.913541i \(0.633337\pi\)
\(140\) 0 0
\(141\) 250.290i 1.77510i
\(142\) 0 0
\(143\) 317.908 2.22313
\(144\) 0 0
\(145\) −17.4313 11.7616i −0.120216 0.0811142i
\(146\) 0 0
\(147\) 54.6368i 0.371679i
\(148\) 0 0
\(149\) 171.844i 1.15331i −0.816986 0.576657i \(-0.804357\pi\)
0.816986 0.576657i \(-0.195643\pi\)
\(150\) 0 0
\(151\) 30.5687i 0.202442i 0.994864 + 0.101221i \(0.0322749\pi\)
−0.994864 + 0.101221i \(0.967725\pi\)
\(152\) 0 0
\(153\) 121.311i 0.792881i
\(154\) 0 0
\(155\) 85.8610 + 57.9338i 0.553942 + 0.373766i
\(156\) 0 0
\(157\) 265.212 1.68925 0.844626 0.535357i \(-0.179823\pi\)
0.844626 + 0.535357i \(0.179823\pi\)
\(158\) 0 0
\(159\) 397.725i 2.50142i
\(160\) 0 0
\(161\) −138.652 −0.861190
\(162\) 0 0
\(163\) 69.6617i 0.427372i −0.976902 0.213686i \(-0.931453\pi\)
0.976902 0.213686i \(-0.0685470\pi\)
\(164\) 0 0
\(165\) 426.498 + 287.775i 2.58484 + 1.74409i
\(166\) 0 0
\(167\) −101.140 −0.605627 −0.302814 0.953050i \(-0.597926\pi\)
−0.302814 + 0.953050i \(0.597926\pi\)
\(168\) 0 0
\(169\) 82.5782 0.488628
\(170\) 0 0
\(171\) 180.388 1.05490
\(172\) 0 0
\(173\) −65.5284 −0.378777 −0.189388 0.981902i \(-0.560651\pi\)
−0.189388 + 0.981902i \(0.560651\pi\)
\(174\) 0 0
\(175\) −57.9564 143.578i −0.331179 0.820447i
\(176\) 0 0
\(177\) 2.55664i 0.0144443i
\(178\) 0 0
\(179\) 47.2688 0.264072 0.132036 0.991245i \(-0.457849\pi\)
0.132036 + 0.991245i \(0.457849\pi\)
\(180\) 0 0
\(181\) 255.613i 1.41223i −0.708099 0.706113i \(-0.750447\pi\)
0.708099 0.706113i \(-0.249553\pi\)
\(182\) 0 0
\(183\) 311.885 1.70429
\(184\) 0 0
\(185\) −99.2204 + 147.050i −0.536326 + 0.794865i
\(186\) 0 0
\(187\) 140.078i 0.749078i
\(188\) 0 0
\(189\) 265.751i 1.40609i
\(190\) 0 0
\(191\) 67.7062i 0.354483i −0.984167 0.177241i \(-0.943283\pi\)
0.984167 0.177241i \(-0.0567173\pi\)
\(192\) 0 0
\(193\) 327.113i 1.69488i −0.530888 0.847442i \(-0.678142\pi\)
0.530888 0.847442i \(-0.321858\pi\)
\(194\) 0 0
\(195\) 337.512 + 227.732i 1.73083 + 1.16786i
\(196\) 0 0
\(197\) −120.542 −0.611890 −0.305945 0.952049i \(-0.598972\pi\)
−0.305945 + 0.952049i \(0.598972\pi\)
\(198\) 0 0
\(199\) 175.578i 0.882302i −0.897433 0.441151i \(-0.854570\pi\)
0.897433 0.441151i \(-0.145430\pi\)
\(200\) 0 0
\(201\) −423.661 −2.10777
\(202\) 0 0
\(203\) 26.0470i 0.128310i
\(204\) 0 0
\(205\) −103.680 + 153.660i −0.505758 + 0.749561i
\(206\) 0 0
\(207\) 388.591 1.87725
\(208\) 0 0
\(209\) −208.294 −0.996621
\(210\) 0 0
\(211\) −237.053 −1.12347 −0.561737 0.827316i \(-0.689867\pi\)
−0.561737 + 0.827316i \(0.689867\pi\)
\(212\) 0 0
\(213\) 147.426 0.692139
\(214\) 0 0
\(215\) 98.7813 + 66.6516i 0.459448 + 0.310008i
\(216\) 0 0
\(217\) 128.300i 0.591242i
\(218\) 0 0
\(219\) 52.2160 0.238429
\(220\) 0 0
\(221\) 110.851i 0.501589i
\(222\) 0 0
\(223\) 13.8074 0.0619165 0.0309582 0.999521i \(-0.490144\pi\)
0.0309582 + 0.999521i \(0.490144\pi\)
\(224\) 0 0
\(225\) 162.431 + 402.399i 0.721917 + 1.78844i
\(226\) 0 0
\(227\) 2.21412i 0.00975382i −0.999988 0.00487691i \(-0.998448\pi\)
0.999988 0.00487691i \(-0.00155238\pi\)
\(228\) 0 0
\(229\) 241.756i 1.05571i 0.849336 + 0.527853i \(0.177003\pi\)
−0.849336 + 0.527853i \(0.822997\pi\)
\(230\) 0 0
\(231\) 637.303i 2.75889i
\(232\) 0 0
\(233\) 30.5119i 0.130953i 0.997854 + 0.0654763i \(0.0208567\pi\)
−0.997854 + 0.0654763i \(0.979143\pi\)
\(234\) 0 0
\(235\) 136.339 202.062i 0.580168 0.859840i
\(236\) 0 0
\(237\) 449.625 1.89715
\(238\) 0 0
\(239\) 426.441i 1.78427i 0.451768 + 0.892135i \(0.350793\pi\)
−0.451768 + 0.892135i \(0.649207\pi\)
\(240\) 0 0
\(241\) 147.936 0.613842 0.306921 0.951735i \(-0.400701\pi\)
0.306921 + 0.951735i \(0.400701\pi\)
\(242\) 0 0
\(243\) 57.2280i 0.235506i
\(244\) 0 0
\(245\) −29.7622 + 44.1091i −0.121478 + 0.180037i
\(246\) 0 0
\(247\) −164.835 −0.667347
\(248\) 0 0
\(249\) −529.092 −2.12487
\(250\) 0 0
\(251\) 97.7364 0.389388 0.194694 0.980864i \(-0.437629\pi\)
0.194694 + 0.980864i \(0.437629\pi\)
\(252\) 0 0
\(253\) −448.707 −1.77354
\(254\) 0 0
\(255\) −100.344 + 148.716i −0.393507 + 0.583199i
\(256\) 0 0
\(257\) 354.443i 1.37915i 0.724212 + 0.689577i \(0.242204\pi\)
−0.724212 + 0.689577i \(0.757796\pi\)
\(258\) 0 0
\(259\) −219.732 −0.848387
\(260\) 0 0
\(261\) 73.0006i 0.279696i
\(262\) 0 0
\(263\) −44.6039 −0.169597 −0.0847984 0.996398i \(-0.527025\pi\)
−0.0847984 + 0.996398i \(0.527025\pi\)
\(264\) 0 0
\(265\) 216.652 321.089i 0.817553 1.21166i
\(266\) 0 0
\(267\) 253.025i 0.947660i
\(268\) 0 0
\(269\) 314.879i 1.17055i 0.810834 + 0.585277i \(0.199014\pi\)
−0.810834 + 0.585277i \(0.800986\pi\)
\(270\) 0 0
\(271\) 449.009i 1.65686i −0.560092 0.828431i \(-0.689234\pi\)
0.560092 0.828431i \(-0.310766\pi\)
\(272\) 0 0
\(273\) 504.334i 1.84738i
\(274\) 0 0
\(275\) −187.559 464.650i −0.682034 1.68964i
\(276\) 0 0
\(277\) −330.330 −1.19253 −0.596264 0.802789i \(-0.703349\pi\)
−0.596264 + 0.802789i \(0.703349\pi\)
\(278\) 0 0
\(279\) 359.578i 1.28881i
\(280\) 0 0
\(281\) 307.936 1.09586 0.547929 0.836525i \(-0.315416\pi\)
0.547929 + 0.836525i \(0.315416\pi\)
\(282\) 0 0
\(283\) 182.609i 0.645263i −0.946525 0.322631i \(-0.895433\pi\)
0.946525 0.322631i \(-0.104567\pi\)
\(284\) 0 0
\(285\) −221.139 149.211i −0.775925 0.523547i
\(286\) 0 0
\(287\) −229.610 −0.800033
\(288\) 0 0
\(289\) 240.156 0.830991
\(290\) 0 0
\(291\) 433.776 1.49064
\(292\) 0 0
\(293\) 259.373 0.885231 0.442616 0.896711i \(-0.354051\pi\)
0.442616 + 0.896711i \(0.354051\pi\)
\(294\) 0 0
\(295\) 1.39267 2.06402i 0.00472092 0.00699667i
\(296\) 0 0
\(297\) 860.027i 2.89571i
\(298\) 0 0
\(299\) −355.087 −1.18758
\(300\) 0 0
\(301\) 147.606i 0.490385i
\(302\) 0 0
\(303\) −476.379 −1.57221
\(304\) 0 0
\(305\) −251.789 169.892i −0.825538 0.557023i
\(306\) 0 0
\(307\) 209.411i 0.682119i 0.940042 + 0.341060i \(0.110786\pi\)
−0.940042 + 0.341060i \(0.889214\pi\)
\(308\) 0 0
\(309\) 219.367i 0.709926i
\(310\) 0 0
\(311\) 149.137i 0.479542i 0.970830 + 0.239771i \(0.0770723\pi\)
−0.970830 + 0.239771i \(0.922928\pi\)
\(312\) 0 0
\(313\) 296.601i 0.947606i 0.880631 + 0.473803i \(0.157119\pi\)
−0.880631 + 0.473803i \(0.842881\pi\)
\(314\) 0 0
\(315\) −300.646 + 445.574i −0.954432 + 1.41452i
\(316\) 0 0
\(317\) −23.0450 −0.0726971 −0.0363486 0.999339i \(-0.511573\pi\)
−0.0363486 + 0.999339i \(0.511573\pi\)
\(318\) 0 0
\(319\) 84.2938i 0.264244i
\(320\) 0 0
\(321\) 150.652 0.469320
\(322\) 0 0
\(323\) 72.6300i 0.224861i
\(324\) 0 0
\(325\) −148.426 367.704i −0.456696 1.13140i
\(326\) 0 0
\(327\) 839.060 2.56593
\(328\) 0 0
\(329\) 301.936 0.917739
\(330\) 0 0
\(331\) −419.665 −1.26787 −0.633935 0.773386i \(-0.718561\pi\)
−0.633935 + 0.773386i \(0.718561\pi\)
\(332\) 0 0
\(333\) 615.832 1.84934
\(334\) 0 0
\(335\) 342.028 + 230.780i 1.02098 + 0.688894i
\(336\) 0 0
\(337\) 52.0477i 0.154444i 0.997014 + 0.0772221i \(0.0246050\pi\)
−0.997014 + 0.0772221i \(0.975395\pi\)
\(338\) 0 0
\(339\) 619.598 1.82772
\(340\) 0 0
\(341\) 415.205i 1.21761i
\(342\) 0 0
\(343\) −369.386 −1.07693
\(344\) 0 0
\(345\) −476.377 321.430i −1.38080 0.931681i
\(346\) 0 0
\(347\) 329.706i 0.950163i 0.879942 + 0.475081i \(0.157581\pi\)
−0.879942 + 0.475081i \(0.842419\pi\)
\(348\) 0 0
\(349\) 517.423i 1.48259i −0.671180 0.741294i \(-0.734212\pi\)
0.671180 0.741294i \(-0.265788\pi\)
\(350\) 0 0
\(351\) 680.588i 1.93900i
\(352\) 0 0
\(353\) 44.4337i 0.125874i 0.998017 + 0.0629372i \(0.0200468\pi\)
−0.998017 + 0.0629372i \(0.979953\pi\)
\(354\) 0 0
\(355\) −119.019 80.3068i −0.335265 0.226216i
\(356\) 0 0
\(357\) −222.221 −0.622469
\(358\) 0 0
\(359\) 53.1375i 0.148015i −0.997258 0.0740076i \(-0.976421\pi\)
0.997258 0.0740076i \(-0.0235789\pi\)
\(360\) 0 0
\(361\) −253.000 −0.700831
\(362\) 0 0
\(363\) 1441.24i 3.97035i
\(364\) 0 0
\(365\) −42.1547 28.4434i −0.115492 0.0779273i
\(366\) 0 0
\(367\) −374.954 −1.02167 −0.510837 0.859678i \(-0.670664\pi\)
−0.510837 + 0.859678i \(0.670664\pi\)
\(368\) 0 0
\(369\) 643.514 1.74394
\(370\) 0 0
\(371\) 479.794 1.29325
\(372\) 0 0
\(373\) 24.6208 0.0660076 0.0330038 0.999455i \(-0.489493\pi\)
0.0330038 + 0.999455i \(0.489493\pi\)
\(374\) 0 0
\(375\) 133.725 627.661i 0.356601 1.67376i
\(376\) 0 0
\(377\) 66.7064i 0.176940i
\(378\) 0 0
\(379\) 170.472 0.449793 0.224897 0.974383i \(-0.427796\pi\)
0.224897 + 0.974383i \(0.427796\pi\)
\(380\) 0 0
\(381\) 1168.31i 3.06643i
\(382\) 0 0
\(383\) −136.084 −0.355310 −0.177655 0.984093i \(-0.556851\pi\)
−0.177655 + 0.984093i \(0.556851\pi\)
\(384\) 0 0
\(385\) 347.156 514.505i 0.901705 1.33638i
\(386\) 0 0
\(387\) 413.687i 1.06896i
\(388\) 0 0
\(389\) 60.5055i 0.155541i −0.996971 0.0777705i \(-0.975220\pi\)
0.996971 0.0777705i \(-0.0247801\pi\)
\(390\) 0 0
\(391\) 156.460i 0.400152i
\(392\) 0 0
\(393\) 175.290i 0.446030i
\(394\) 0 0
\(395\) −362.989 244.923i −0.918960 0.620058i
\(396\) 0 0
\(397\) −124.216 −0.312888 −0.156444 0.987687i \(-0.550003\pi\)
−0.156444 + 0.987687i \(0.550003\pi\)
\(398\) 0 0
\(399\) 330.441i 0.828172i
\(400\) 0 0
\(401\) 46.7156 0.116498 0.0582489 0.998302i \(-0.481448\pi\)
0.0582489 + 0.998302i \(0.481448\pi\)
\(402\) 0 0
\(403\) 328.575i 0.815323i
\(404\) 0 0
\(405\) 179.189 265.568i 0.442442 0.655724i
\(406\) 0 0
\(407\) −711.101 −1.74718
\(408\) 0 0
\(409\) 582.377 1.42390 0.711952 0.702228i \(-0.247811\pi\)
0.711952 + 0.702228i \(0.247811\pi\)
\(410\) 0 0
\(411\) −1112.01 −2.70562
\(412\) 0 0
\(413\) 3.08420 0.00746779
\(414\) 0 0
\(415\) 427.144 + 288.211i 1.02926 + 0.694484i
\(416\) 0 0
\(417\) 580.530i 1.39216i
\(418\) 0 0
\(419\) 479.296 1.14391 0.571953 0.820287i \(-0.306186\pi\)
0.571953 + 0.820287i \(0.306186\pi\)
\(420\) 0 0
\(421\) 116.905i 0.277685i −0.990314 0.138842i \(-0.955662\pi\)
0.990314 0.138842i \(-0.0443381\pi\)
\(422\) 0 0
\(423\) −846.220 −2.00052
\(424\) 0 0
\(425\) 162.019 65.4001i 0.381221 0.153883i
\(426\) 0 0
\(427\) 376.241i 0.881126i
\(428\) 0 0
\(429\) 1632.13i 3.80451i
\(430\) 0 0
\(431\) 204.460i 0.474384i 0.971463 + 0.237192i \(0.0762271\pi\)
−0.971463 + 0.237192i \(0.923773\pi\)
\(432\) 0 0
\(433\) 403.364i 0.931558i −0.884901 0.465779i \(-0.845774\pi\)
0.884901 0.465779i \(-0.154226\pi\)
\(434\) 0 0
\(435\) 60.3837 89.4919i 0.138813 0.205728i
\(436\) 0 0
\(437\) 232.654 0.532388
\(438\) 0 0
\(439\) 114.275i 0.260307i −0.991494 0.130154i \(-0.958453\pi\)
0.991494 0.130154i \(-0.0415471\pi\)
\(440\) 0 0
\(441\) 184.725 0.418878
\(442\) 0 0
\(443\) 750.268i 1.69361i −0.531906 0.846803i \(-0.678524\pi\)
0.531906 0.846803i \(-0.321476\pi\)
\(444\) 0 0
\(445\) −137.830 + 204.271i −0.309730 + 0.459036i
\(446\) 0 0
\(447\) 882.244 1.97370
\(448\) 0 0
\(449\) −554.377 −1.23469 −0.617346 0.786692i \(-0.711792\pi\)
−0.617346 + 0.786692i \(0.711792\pi\)
\(450\) 0 0
\(451\) −743.066 −1.64760
\(452\) 0 0
\(453\) −156.939 −0.346445
\(454\) 0 0
\(455\) 274.724 407.156i 0.603790 0.894849i
\(456\) 0 0
\(457\) 870.823i 1.90552i 0.303724 + 0.952760i \(0.401770\pi\)
−0.303724 + 0.952760i \(0.598230\pi\)
\(458\) 0 0
\(459\) 299.883 0.653340
\(460\) 0 0
\(461\) 37.3636i 0.0810490i −0.999179 0.0405245i \(-0.987097\pi\)
0.999179 0.0405245i \(-0.0129029\pi\)
\(462\) 0 0
\(463\) −228.189 −0.492849 −0.246424 0.969162i \(-0.579256\pi\)
−0.246424 + 0.969162i \(0.579256\pi\)
\(464\) 0 0
\(465\) −297.431 + 440.809i −0.639637 + 0.947977i
\(466\) 0 0
\(467\) 414.441i 0.887455i −0.896162 0.443727i \(-0.853656\pi\)
0.896162 0.443727i \(-0.146344\pi\)
\(468\) 0 0
\(469\) 511.082i 1.08973i
\(470\) 0 0
\(471\) 1361.60i 2.89086i
\(472\) 0 0
\(473\) 477.685i 1.00990i
\(474\) 0 0
\(475\) 97.2493 + 240.920i 0.204735 + 0.507201i
\(476\) 0 0
\(477\) −1344.69 −2.81906
\(478\) 0 0
\(479\) 871.744i 1.81992i −0.414691 0.909962i \(-0.636110\pi\)
0.414691 0.909962i \(-0.363890\pi\)
\(480\) 0 0
\(481\) −562.735 −1.16993
\(482\) 0 0
\(483\) 711.836i 1.47378i
\(484\) 0 0
\(485\) −350.194 236.290i −0.722049 0.487195i
\(486\) 0 0
\(487\) −316.431 −0.649756 −0.324878 0.945756i \(-0.605323\pi\)
−0.324878 + 0.945756i \(0.605323\pi\)
\(488\) 0 0
\(489\) 357.642 0.731375
\(490\) 0 0
\(491\) 372.142 0.757927 0.378963 0.925412i \(-0.376281\pi\)
0.378963 + 0.925412i \(0.376281\pi\)
\(492\) 0 0
\(493\) 29.3924 0.0596195
\(494\) 0 0
\(495\) −972.956 + 1441.97i −1.96557 + 2.91308i
\(496\) 0 0
\(497\) 177.847i 0.357840i
\(498\) 0 0
\(499\) 198.184 0.397163 0.198582 0.980084i \(-0.436367\pi\)
0.198582 + 0.980084i \(0.436367\pi\)
\(500\) 0 0
\(501\) 519.250i 1.03643i
\(502\) 0 0
\(503\) 638.202 1.26879 0.634395 0.773009i \(-0.281249\pi\)
0.634395 + 0.773009i \(0.281249\pi\)
\(504\) 0 0
\(505\) 384.588 + 259.496i 0.761560 + 0.513854i
\(506\) 0 0
\(507\) 423.955i 0.836204i
\(508\) 0 0
\(509\) 58.6571i 0.115240i −0.998339 0.0576199i \(-0.981649\pi\)
0.998339 0.0576199i \(-0.0183512\pi\)
\(510\) 0 0
\(511\) 62.9906i 0.123269i
\(512\) 0 0
\(513\) 445.923i 0.869245i
\(514\) 0 0
\(515\) −119.495 + 177.098i −0.232029 + 0.343880i
\(516\) 0 0
\(517\) 977.130 1.89000
\(518\) 0 0
\(519\) 336.422i 0.648212i
\(520\) 0 0
\(521\) 171.431 0.329043 0.164521 0.986374i \(-0.447392\pi\)
0.164521 + 0.986374i \(0.447392\pi\)
\(522\) 0 0
\(523\) 407.751i 0.779638i 0.920892 + 0.389819i \(0.127462\pi\)
−0.920892 + 0.389819i \(0.872538\pi\)
\(524\) 0 0
\(525\) 737.128 297.547i 1.40405 0.566757i
\(526\) 0 0
\(527\) −144.778 −0.274721
\(528\) 0 0
\(529\) −27.8174 −0.0525848
\(530\) 0 0
\(531\) −8.64391 −0.0162786
\(532\) 0 0
\(533\) −588.030 −1.10325
\(534\) 0 0
\(535\) −121.623 82.0640i −0.227333 0.153391i
\(536\) 0 0
\(537\) 242.677i 0.451913i
\(538\) 0 0
\(539\) −213.302 −0.395737
\(540\) 0 0
\(541\) 144.762i 0.267582i 0.991010 + 0.133791i \(0.0427150\pi\)
−0.991010 + 0.133791i \(0.957285\pi\)
\(542\) 0 0
\(543\) 1312.31 2.41678
\(544\) 0 0
\(545\) −677.386 457.059i −1.24291 0.838640i
\(546\) 0 0
\(547\) 570.627i 1.04319i 0.853192 + 0.521597i \(0.174663\pi\)
−0.853192 + 0.521597i \(0.825337\pi\)
\(548\) 0 0
\(549\) 1054.47i 1.92071i
\(550\) 0 0
\(551\) 43.7062i 0.0793216i
\(552\) 0 0
\(553\) 542.404i 0.980839i
\(554\) 0 0
\(555\) −754.952 509.396i −1.36027 0.917831i
\(556\) 0 0
\(557\) 824.208 1.47973 0.739864 0.672757i \(-0.234890\pi\)
0.739864 + 0.672757i \(0.234890\pi\)
\(558\) 0 0
\(559\) 378.019i 0.676241i
\(560\) 0 0
\(561\) −719.156 −1.28192
\(562\) 0 0
\(563\) 216.333i 0.384251i 0.981370 + 0.192125i \(0.0615380\pi\)
−0.981370 + 0.192125i \(0.938462\pi\)
\(564\) 0 0
\(565\) −500.211 337.512i −0.885329 0.597366i
\(566\) 0 0
\(567\) 396.831 0.699877
\(568\) 0 0
\(569\) −468.230 −0.822899 −0.411450 0.911432i \(-0.634977\pi\)
−0.411450 + 0.911432i \(0.634977\pi\)
\(570\) 0 0
\(571\) 759.434 1.33001 0.665004 0.746840i \(-0.268430\pi\)
0.665004 + 0.746840i \(0.268430\pi\)
\(572\) 0 0
\(573\) 347.603 0.606636
\(574\) 0 0
\(575\) 209.494 + 518.991i 0.364338 + 0.902592i
\(576\) 0 0
\(577\) 29.2057i 0.0506164i −0.999680 0.0253082i \(-0.991943\pi\)
0.999680 0.0253082i \(-0.00805671\pi\)
\(578\) 0 0
\(579\) 1679.39 2.90050
\(580\) 0 0
\(581\) 638.269i 1.09857i
\(582\) 0 0
\(583\) 1552.72 2.66332
\(584\) 0 0
\(585\) −769.955 + 1141.11i −1.31616 + 1.95062i
\(586\) 0 0
\(587\) 1014.74i 1.72869i 0.502900 + 0.864345i \(0.332266\pi\)
−0.502900 + 0.864345i \(0.667734\pi\)
\(588\) 0 0
\(589\) 215.283i 0.365506i
\(590\) 0 0
\(591\) 618.863i 1.04714i
\(592\) 0 0
\(593\) 835.823i 1.40948i −0.709465 0.704741i \(-0.751063\pi\)
0.709465 0.704741i \(-0.248937\pi\)
\(594\) 0 0
\(595\) 179.403 + 121.050i 0.301517 + 0.203445i
\(596\) 0 0
\(597\) 901.416 1.50991
\(598\) 0 0
\(599\) 851.616i 1.42173i 0.703329 + 0.710865i \(0.251696\pi\)
−0.703329 + 0.710865i \(0.748304\pi\)
\(600\) 0 0
\(601\) −618.377 −1.02891 −0.514456 0.857516i \(-0.672006\pi\)
−0.514456 + 0.857516i \(0.672006\pi\)
\(602\) 0 0
\(603\) 1432.38i 2.37543i
\(604\) 0 0
\(605\) 785.082 1163.53i 1.29766 1.92320i
\(606\) 0 0
\(607\) −182.393 −0.300483 −0.150241 0.988649i \(-0.548005\pi\)
−0.150241 + 0.988649i \(0.548005\pi\)
\(608\) 0 0
\(609\) 133.725 0.219581
\(610\) 0 0
\(611\) 773.258 1.26556
\(612\) 0 0
\(613\) 638.630 1.04181 0.520906 0.853614i \(-0.325594\pi\)
0.520906 + 0.853614i \(0.325594\pi\)
\(614\) 0 0
\(615\) −788.888 532.294i −1.28275 0.865518i
\(616\) 0 0
\(617\) 416.661i 0.675301i 0.941271 + 0.337651i \(0.109632\pi\)
−0.941271 + 0.337651i \(0.890368\pi\)
\(618\) 0 0
\(619\) 1090.24 1.76129 0.880646 0.473775i \(-0.157109\pi\)
0.880646 + 0.473775i \(0.157109\pi\)
\(620\) 0 0
\(621\) 960.607i 1.54687i
\(622\) 0 0
\(623\) −305.236 −0.489946
\(624\) 0 0
\(625\) −449.863 + 433.876i −0.719780 + 0.694202i
\(626\) 0 0
\(627\) 1069.38i 1.70555i
\(628\) 0 0
\(629\) 247.954i 0.394204i
\(630\) 0 0
\(631\) 574.569i 0.910569i 0.890346 + 0.455284i \(0.150462\pi\)
−0.890346 + 0.455284i \(0.849538\pi\)
\(632\) 0 0
\(633\) 1217.03i 1.92263i
\(634\) 0 0
\(635\) −636.410 + 943.194i −1.00222 + 1.48534i
\(636\) 0 0
\(637\) −168.798 −0.264989
\(638\) 0 0
\(639\) 498.441i 0.780032i
\(640\) 0 0
\(641\) 893.367 1.39371 0.696854 0.717213i \(-0.254582\pi\)
0.696854 + 0.717213i \(0.254582\pi\)
\(642\) 0 0
\(643\) 675.801i 1.05101i −0.850790 0.525506i \(-0.823876\pi\)
0.850790 0.525506i \(-0.176124\pi\)
\(644\) 0 0
\(645\) −342.188 + 507.142i −0.530525 + 0.786267i
\(646\) 0 0
\(647\) 737.921 1.14053 0.570263 0.821462i \(-0.306841\pi\)
0.570263 + 0.821462i \(0.306841\pi\)
\(648\) 0 0
\(649\) 9.98113 0.0153792
\(650\) 0 0
\(651\) −658.688 −1.01181
\(652\) 0 0
\(653\) −771.853 −1.18201 −0.591005 0.806668i \(-0.701269\pi\)
−0.591005 + 0.806668i \(0.701269\pi\)
\(654\) 0 0
\(655\) 95.4851 141.514i 0.145779 0.216052i
\(656\) 0 0
\(657\) 176.540i 0.268707i
\(658\) 0 0
\(659\) −814.838 −1.23648 −0.618238 0.785991i \(-0.712153\pi\)
−0.618238 + 0.785991i \(0.712153\pi\)
\(660\) 0 0
\(661\) 1038.13i 1.57055i −0.619146 0.785276i \(-0.712521\pi\)
0.619146 0.785276i \(-0.287479\pi\)
\(662\) 0 0
\(663\) −569.109 −0.858384
\(664\) 0 0
\(665\) −180.000 + 266.770i −0.270677 + 0.401158i
\(666\) 0 0
\(667\) 94.1519i 0.141157i
\(668\) 0 0
\(669\) 70.8869i 0.105959i
\(670\) 0 0
\(671\) 1217.60i 1.81460i
\(672\) 0 0
\(673\) 367.795i 0.546501i 0.961943 + 0.273250i \(0.0880988\pi\)
−0.961943 + 0.273250i \(0.911901\pi\)
\(674\) 0 0
\(675\) −994.739 + 401.534i −1.47369 + 0.594865i
\(676\) 0 0
\(677\) 463.978 0.685344 0.342672 0.939455i \(-0.388668\pi\)
0.342672 + 0.939455i \(0.388668\pi\)
\(678\) 0 0
\(679\) 523.284i 0.770669i
\(680\) 0 0
\(681\) 11.3673 0.0166920
\(682\) 0 0
\(683\) 632.563i 0.926154i 0.886318 + 0.463077i \(0.153255\pi\)
−0.886318 + 0.463077i \(0.846745\pi\)
\(684\) 0 0
\(685\) 897.742 + 605.742i 1.31057 + 0.884294i
\(686\) 0 0
\(687\) −1241.17 −1.80666
\(688\) 0 0
\(689\) 1228.75 1.78339
\(690\) 0 0
\(691\) −436.001 −0.630970 −0.315485 0.948930i \(-0.602167\pi\)
−0.315485 + 0.948930i \(0.602167\pi\)
\(692\) 0 0
\(693\) −2154.70 −3.10923
\(694\) 0 0
\(695\) −316.230 + 468.670i −0.455008 + 0.674346i
\(696\) 0 0
\(697\) 259.100i 0.371736i
\(698\) 0 0
\(699\) −156.648 −0.224103
\(700\) 0 0
\(701\) 364.085i 0.519380i 0.965692 + 0.259690i \(0.0836203\pi\)
−0.965692 + 0.259690i \(0.916380\pi\)
\(702\) 0 0
\(703\) 368.705 0.524474
\(704\) 0 0
\(705\) 1037.39 + 699.965i 1.47147 + 0.992858i
\(706\) 0 0
\(707\) 574.678i 0.812840i
\(708\) 0 0
\(709\) 789.593i 1.11367i 0.830622 + 0.556836i \(0.187985\pi\)
−0.830622 + 0.556836i \(0.812015\pi\)
\(710\) 0 0
\(711\) 1520.17i 2.13807i
\(712\) 0 0
\(713\) 463.763i 0.650439i
\(714\) 0 0
\(715\) 889.067 1317.65i 1.24345 1.84286i
\(716\) 0 0
\(717\) −2189.34 −3.05347
\(718\) 0 0
\(719\) 168.422i 0.234245i 0.993118 + 0.117122i \(0.0373669\pi\)
−0.993118 + 0.117122i \(0.962633\pi\)
\(720\) 0 0
\(721\) −264.633 −0.367036
\(722\) 0 0
\(723\) 759.501i 1.05049i
\(724\) 0 0
\(725\) −97.4973 + 39.3555i −0.134479 + 0.0542835i
\(726\) 0 0
\(727\) −382.568 −0.526229 −0.263114 0.964765i \(-0.584750\pi\)
−0.263114 + 0.964765i \(0.584750\pi\)
\(728\) 0 0
\(729\) 870.469 1.19406
\(730\) 0 0
\(731\) −166.564 −0.227858
\(732\) 0 0
\(733\) 74.5492 0.101704 0.0508521 0.998706i \(-0.483806\pi\)
0.0508521 + 0.998706i \(0.483806\pi\)
\(734\) 0 0
\(735\) −226.456 152.799i −0.308103 0.207889i
\(736\) 0 0
\(737\) 1653.97i 2.24420i
\(738\) 0 0
\(739\) −682.206 −0.923148 −0.461574 0.887102i \(-0.652715\pi\)
−0.461574 + 0.887102i \(0.652715\pi\)
\(740\) 0 0
\(741\) 846.259i 1.14205i
\(742\) 0 0
\(743\) 359.274 0.483545 0.241772 0.970333i \(-0.422271\pi\)
0.241772 + 0.970333i \(0.422271\pi\)
\(744\) 0 0
\(745\) −712.249 480.582i −0.956038 0.645077i
\(746\) 0 0
\(747\) 1788.84i 2.39470i
\(748\) 0 0
\(749\) 181.738i 0.242641i
\(750\) 0 0
\(751\) 532.038i 0.708439i 0.935162 + 0.354220i \(0.115253\pi\)
−0.935162 + 0.354220i \(0.884747\pi\)
\(752\) 0 0
\(753\) 501.777i 0.666371i
\(754\) 0 0
\(755\) 126.700 + 85.4892i 0.167814 + 0.113231i
\(756\) 0 0
\(757\) 444.854 0.587653 0.293827 0.955859i \(-0.405071\pi\)
0.293827 + 0.955859i \(0.405071\pi\)
\(758\) 0 0
\(759\) 2303.65i 3.03512i
\(760\) 0 0
\(761\) −244.735 −0.321596 −0.160798 0.986987i \(-0.551407\pi\)
−0.160798 + 0.986987i \(0.551407\pi\)
\(762\) 0 0
\(763\) 1012.20i 1.32660i
\(764\) 0 0
\(765\) −502.802 339.260i −0.657258 0.443477i
\(766\) 0 0
\(767\) 7.89863 0.0102981
\(768\) 0 0
\(769\) −1131.73 −1.47168 −0.735842 0.677153i \(-0.763213\pi\)
−0.735842 + 0.677153i \(0.763213\pi\)
\(770\) 0 0
\(771\) −1819.70 −2.36019
\(772\) 0 0
\(773\) 294.508 0.380994 0.190497 0.981688i \(-0.438990\pi\)
0.190497 + 0.981688i \(0.438990\pi\)
\(774\) 0 0
\(775\) 480.241 193.853i 0.619666 0.250133i
\(776\) 0 0
\(777\) 1128.10i 1.45187i
\(778\) 0 0
\(779\) 385.279 0.494581
\(780\) 0 0
\(781\) 575.550i 0.736939i
\(782\) 0 0
\(783\) −180.459 −0.230471
\(784\) 0 0
\(785\) 741.699 1099.24i 0.944839 1.40030i
\(786\) 0 0
\(787\) 1017.00i 1.29225i 0.763230 + 0.646127i \(0.223612\pi\)
−0.763230 + 0.646127i \(0.776388\pi\)
\(788\) 0 0
\(789\) 228.996i 0.290236i
\(790\) 0 0
\(791\) 747.450i 0.944943i
\(792\) 0 0
\(793\) 963.553i 1.21507i
\(794\) 0 0
\(795\) 1648.47 + 1112.29i 2.07355 + 1.39910i
\(796\) 0 0
\(797\) −1105.61 −1.38722 −0.693608 0.720353i \(-0.743980\pi\)
−0.693608 + 0.720353i \(0.743980\pi\)
\(798\) 0 0
\(799\) 340.716i 0.426428i
\(800\) 0 0