Properties

Label 160.4.c.d.129.1
Level $160$
Weight $4$
Character 160.129
Analytic conductor $9.440$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 160.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44030560092\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.359712057600.22
Defining polynomial: \( x^{8} + 17x^{6} + 82x^{4} + 96x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{22} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 129.1
Root \(1.24759i\) of defining polynomial
Character \(\chi\) \(=\) 160.129
Dual form 160.4.c.d.129.8

$q$-expansion

\(f(q)\) \(=\) \(q-8.57295i q^{3} +(-0.582576 - 11.1652i) q^{5} -22.1403i q^{7} -46.4955 q^{9} +O(q^{10})\) \(q-8.57295i q^{3} +(-0.582576 - 11.1652i) q^{5} -22.1403i q^{7} -46.4955 q^{9} +27.1347 q^{11} +70.3303i q^{13} +(-95.7183 + 4.99439i) q^{15} -73.3212i q^{17} +110.033 q^{19} -189.808 q^{21} +107.870i q^{23} +(-124.321 + 13.0091i) q^{25} +167.134i q^{27} -68.6424 q^{29} -137.167 q^{31} -232.624i q^{33} +(-247.200 + 12.8984i) q^{35} +60.3121i q^{37} +602.938 q^{39} +95.1470 q^{41} -501.479i q^{43} +(27.0871 + 519.129i) q^{45} -439.305i q^{47} -147.192 q^{49} -628.579 q^{51} +286.955i q^{53} +(-15.8080 - 302.963i) q^{55} -943.303i q^{57} +547.175 q^{59} +511.459 q^{61} +1029.42i q^{63} +(785.248 - 40.9727i) q^{65} +301.547i q^{67} +924.762 q^{69} +82.8978 q^{71} +763.267i q^{73} +(111.526 + 1065.80i) q^{75} -600.770i q^{77} -1011.45 q^{79} +177.450 q^{81} -704.554i q^{83} +(-818.642 + 42.7152i) q^{85} +588.468i q^{87} +743.212 q^{89} +1557.13 q^{91} +1175.93i q^{93} +(-64.1023 - 1228.53i) q^{95} -1136.00i q^{97} -1261.64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 32 q^{5} - 152 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 32 q^{5} - 152 q^{9} - 272 q^{21} - 408 q^{25} + 624 q^{29} - 192 q^{41} + 400 q^{45} - 2424 q^{49} + 2112 q^{61} + 2176 q^{65} + 3952 q^{69} - 1000 q^{81} - 5376 q^{85} + 80 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 8.57295i 1.64986i −0.565231 0.824932i \(-0.691213\pi\)
0.565231 0.824932i \(-0.308787\pi\)
\(4\) 0 0
\(5\) −0.582576 11.1652i −0.0521072 0.998641i
\(6\) 0 0
\(7\) 22.1403i 1.19546i −0.801696 0.597732i \(-0.796069\pi\)
0.801696 0.597732i \(-0.203931\pi\)
\(8\) 0 0
\(9\) −46.4955 −1.72205
\(10\) 0 0
\(11\) 27.1347 0.743765 0.371882 0.928280i \(-0.378712\pi\)
0.371882 + 0.928280i \(0.378712\pi\)
\(12\) 0 0
\(13\) 70.3303i 1.50047i 0.661171 + 0.750235i \(0.270060\pi\)
−0.661171 + 0.750235i \(0.729940\pi\)
\(14\) 0 0
\(15\) −95.7183 + 4.99439i −1.64762 + 0.0859698i
\(16\) 0 0
\(17\) 73.3212i 1.04606i −0.852315 0.523030i \(-0.824802\pi\)
0.852315 0.523030i \(-0.175198\pi\)
\(18\) 0 0
\(19\) 110.033 1.32859 0.664294 0.747471i \(-0.268732\pi\)
0.664294 + 0.747471i \(0.268732\pi\)
\(20\) 0 0
\(21\) −189.808 −1.97235
\(22\) 0 0
\(23\) 107.870i 0.977931i 0.872303 + 0.488965i \(0.162626\pi\)
−0.872303 + 0.488965i \(0.837374\pi\)
\(24\) 0 0
\(25\) −124.321 + 13.0091i −0.994570 + 0.104073i
\(26\) 0 0
\(27\) 167.134i 1.19129i
\(28\) 0 0
\(29\) −68.6424 −0.439537 −0.219769 0.975552i \(-0.570530\pi\)
−0.219769 + 0.975552i \(0.570530\pi\)
\(30\) 0 0
\(31\) −137.167 −0.794708 −0.397354 0.917665i \(-0.630072\pi\)
−0.397354 + 0.917665i \(0.630072\pi\)
\(32\) 0 0
\(33\) 232.624i 1.22711i
\(34\) 0 0
\(35\) −247.200 + 12.8984i −1.19384 + 0.0622922i
\(36\) 0 0
\(37\) 60.3121i 0.267980i 0.990983 + 0.133990i \(0.0427790\pi\)
−0.990983 + 0.133990i \(0.957221\pi\)
\(38\) 0 0
\(39\) 602.938 2.47557
\(40\) 0 0
\(41\) 95.1470 0.362426 0.181213 0.983444i \(-0.441998\pi\)
0.181213 + 0.983444i \(0.441998\pi\)
\(42\) 0 0
\(43\) 501.479i 1.77848i −0.457438 0.889241i \(-0.651233\pi\)
0.457438 0.889241i \(-0.348767\pi\)
\(44\) 0 0
\(45\) 27.0871 + 519.129i 0.0897313 + 1.71971i
\(46\) 0 0
\(47\) 439.305i 1.36339i −0.731637 0.681694i \(-0.761244\pi\)
0.731637 0.681694i \(-0.238756\pi\)
\(48\) 0 0
\(49\) −147.192 −0.429132
\(50\) 0 0
\(51\) −628.579 −1.72586
\(52\) 0 0
\(53\) 286.955i 0.743703i 0.928292 + 0.371851i \(0.121277\pi\)
−0.928292 + 0.371851i \(0.878723\pi\)
\(54\) 0 0
\(55\) −15.8080 302.963i −0.0387555 0.742755i
\(56\) 0 0
\(57\) 943.303i 2.19199i
\(58\) 0 0
\(59\) 547.175 1.20739 0.603696 0.797215i \(-0.293694\pi\)
0.603696 + 0.797215i \(0.293694\pi\)
\(60\) 0 0
\(61\) 511.459 1.07353 0.536767 0.843730i \(-0.319645\pi\)
0.536767 + 0.843730i \(0.319645\pi\)
\(62\) 0 0
\(63\) 1029.42i 2.05865i
\(64\) 0 0
\(65\) 785.248 40.9727i 1.49843 0.0781852i
\(66\) 0 0
\(67\) 301.547i 0.549848i 0.961466 + 0.274924i \(0.0886527\pi\)
−0.961466 + 0.274924i \(0.911347\pi\)
\(68\) 0 0
\(69\) 924.762 1.61345
\(70\) 0 0
\(71\) 82.8978 0.138566 0.0692828 0.997597i \(-0.477929\pi\)
0.0692828 + 0.997597i \(0.477929\pi\)
\(72\) 0 0
\(73\) 763.267i 1.22375i 0.790955 + 0.611874i \(0.209584\pi\)
−0.790955 + 0.611874i \(0.790416\pi\)
\(74\) 0 0
\(75\) 111.526 + 1065.80i 0.171706 + 1.64091i
\(76\) 0 0
\(77\) 600.770i 0.889144i
\(78\) 0 0
\(79\) −1011.45 −1.44047 −0.720236 0.693729i \(-0.755966\pi\)
−0.720236 + 0.693729i \(0.755966\pi\)
\(80\) 0 0
\(81\) 177.450 0.243416
\(82\) 0 0
\(83\) 704.554i 0.931745i −0.884852 0.465872i \(-0.845741\pi\)
0.884852 0.465872i \(-0.154259\pi\)
\(84\) 0 0
\(85\) −818.642 + 42.7152i −1.04464 + 0.0545072i
\(86\) 0 0
\(87\) 588.468i 0.725177i
\(88\) 0 0
\(89\) 743.212 0.885172 0.442586 0.896726i \(-0.354061\pi\)
0.442586 + 0.896726i \(0.354061\pi\)
\(90\) 0 0
\(91\) 1557.13 1.79376
\(92\) 0 0
\(93\) 1175.93i 1.31116i
\(94\) 0 0
\(95\) −64.1023 1228.53i −0.0692290 1.32678i
\(96\) 0 0
\(97\) 1136.00i 1.18911i −0.804056 0.594553i \(-0.797329\pi\)
0.804056 0.594553i \(-0.202671\pi\)
\(98\) 0 0
\(99\) −1261.64 −1.28080
\(100\) 0 0
\(101\) 291.212 0.286898 0.143449 0.989658i \(-0.454181\pi\)
0.143449 + 0.989658i \(0.454181\pi\)
\(102\) 0 0
\(103\) 200.445i 0.191751i −0.995393 0.0958757i \(-0.969435\pi\)
0.995393 0.0958757i \(-0.0305651\pi\)
\(104\) 0 0
\(105\) 110.577 + 2119.23i 0.102774 + 1.96967i
\(106\) 0 0
\(107\) 754.342i 0.681542i −0.940146 0.340771i \(-0.889312\pi\)
0.940146 0.340771i \(-0.110688\pi\)
\(108\) 0 0
\(109\) −501.680 −0.440846 −0.220423 0.975404i \(-0.570744\pi\)
−0.220423 + 0.975404i \(0.570744\pi\)
\(110\) 0 0
\(111\) 517.053 0.442130
\(112\) 0 0
\(113\) 497.248i 0.413958i −0.978345 0.206979i \(-0.933637\pi\)
0.978345 0.206979i \(-0.0663631\pi\)
\(114\) 0 0
\(115\) 1204.38 62.8423i 0.976602 0.0509572i
\(116\) 0 0
\(117\) 3270.04i 2.58389i
\(118\) 0 0
\(119\) −1623.35 −1.25053
\(120\) 0 0
\(121\) −594.709 −0.446814
\(122\) 0 0
\(123\) 815.690i 0.597954i
\(124\) 0 0
\(125\) 217.675 + 1380.49i 0.155756 + 0.987796i
\(126\) 0 0
\(127\) 915.221i 0.639470i −0.947507 0.319735i \(-0.896406\pi\)
0.947507 0.319735i \(-0.103594\pi\)
\(128\) 0 0
\(129\) −4299.15 −2.93426
\(130\) 0 0
\(131\) 607.419 0.405118 0.202559 0.979270i \(-0.435074\pi\)
0.202559 + 0.979270i \(0.435074\pi\)
\(132\) 0 0
\(133\) 2436.15i 1.58828i
\(134\) 0 0
\(135\) 1866.07 97.3679i 1.18967 0.0620748i
\(136\) 0 0
\(137\) 1418.98i 0.884900i 0.896793 + 0.442450i \(0.145891\pi\)
−0.896793 + 0.442450i \(0.854109\pi\)
\(138\) 0 0
\(139\) −3035.85 −1.85250 −0.926250 0.376910i \(-0.876987\pi\)
−0.926250 + 0.376910i \(0.876987\pi\)
\(140\) 0 0
\(141\) −3766.14 −2.24941
\(142\) 0 0
\(143\) 1908.39i 1.11600i
\(144\) 0 0
\(145\) 39.9894 + 766.403i 0.0229030 + 0.438940i
\(146\) 0 0
\(147\) 1261.87i 0.708011i
\(148\) 0 0
\(149\) 2649.26 1.45662 0.728308 0.685250i \(-0.240307\pi\)
0.728308 + 0.685250i \(0.240307\pi\)
\(150\) 0 0
\(151\) 283.297 0.152678 0.0763390 0.997082i \(-0.475677\pi\)
0.0763390 + 0.997082i \(0.475677\pi\)
\(152\) 0 0
\(153\) 3409.10i 1.80137i
\(154\) 0 0
\(155\) 79.9103 + 1531.49i 0.0414100 + 0.793629i
\(156\) 0 0
\(157\) 1414.88i 0.719235i −0.933100 0.359617i \(-0.882907\pi\)
0.933100 0.359617i \(-0.117093\pi\)
\(158\) 0 0
\(159\) 2460.05 1.22701
\(160\) 0 0
\(161\) 2388.27 1.16908
\(162\) 0 0
\(163\) 1725.68i 0.829239i 0.909995 + 0.414619i \(0.136085\pi\)
−0.909995 + 0.414619i \(0.863915\pi\)
\(164\) 0 0
\(165\) −2597.28 + 135.521i −1.22544 + 0.0639413i
\(166\) 0 0
\(167\) 1979.92i 0.917428i 0.888584 + 0.458714i \(0.151690\pi\)
−0.888584 + 0.458714i \(0.848310\pi\)
\(168\) 0 0
\(169\) −2749.35 −1.25141
\(170\) 0 0
\(171\) −5116.01 −2.28790
\(172\) 0 0
\(173\) 1468.72i 0.645460i 0.946491 + 0.322730i \(0.104601\pi\)
−0.946491 + 0.322730i \(0.895399\pi\)
\(174\) 0 0
\(175\) 288.025 + 2752.51i 0.124415 + 1.18897i
\(176\) 0 0
\(177\) 4690.90i 1.99203i
\(178\) 0 0
\(179\) 2978.59 1.24375 0.621873 0.783118i \(-0.286372\pi\)
0.621873 + 0.783118i \(0.286372\pi\)
\(180\) 0 0
\(181\) −1682.07 −0.690760 −0.345380 0.938463i \(-0.612250\pi\)
−0.345380 + 0.938463i \(0.612250\pi\)
\(182\) 0 0
\(183\) 4384.71i 1.77119i
\(184\) 0 0
\(185\) 673.394 35.1364i 0.267616 0.0139637i
\(186\) 0 0
\(187\) 1989.55i 0.778022i
\(188\) 0 0
\(189\) 3700.38 1.42414
\(190\) 0 0
\(191\) 274.334 0.103927 0.0519637 0.998649i \(-0.483452\pi\)
0.0519637 + 0.998649i \(0.483452\pi\)
\(192\) 0 0
\(193\) 2898.50i 1.08103i 0.841335 + 0.540514i \(0.181770\pi\)
−0.841335 + 0.540514i \(0.818230\pi\)
\(194\) 0 0
\(195\) −351.257 6731.90i −0.128995 2.47221i
\(196\) 0 0
\(197\) 2330.37i 0.842801i −0.906875 0.421400i \(-0.861539\pi\)
0.906875 0.421400i \(-0.138461\pi\)
\(198\) 0 0
\(199\) −1105.05 −0.393644 −0.196822 0.980439i \(-0.563062\pi\)
−0.196822 + 0.980439i \(0.563062\pi\)
\(200\) 0 0
\(201\) 2585.15 0.907175
\(202\) 0 0
\(203\) 1519.76i 0.525451i
\(204\) 0 0
\(205\) −55.4303 1062.33i −0.0188850 0.361933i
\(206\) 0 0
\(207\) 5015.45i 1.68405i
\(208\) 0 0
\(209\) 2985.70 0.988158
\(210\) 0 0
\(211\) 4749.82 1.54972 0.774860 0.632133i \(-0.217820\pi\)
0.774860 + 0.632133i \(0.217820\pi\)
\(212\) 0 0
\(213\) 710.679i 0.228615i
\(214\) 0 0
\(215\) −5599.08 + 292.149i −1.77607 + 0.0926717i
\(216\) 0 0
\(217\) 3036.92i 0.950044i
\(218\) 0 0
\(219\) 6543.45 2.01902
\(220\) 0 0
\(221\) 5156.70 1.56958
\(222\) 0 0
\(223\) 1889.71i 0.567462i −0.958904 0.283731i \(-0.908428\pi\)
0.958904 0.283731i \(-0.0915723\pi\)
\(224\) 0 0
\(225\) 5780.37 604.864i 1.71270 0.179219i
\(226\) 0 0
\(227\) 4154.11i 1.21462i 0.794466 + 0.607309i \(0.207751\pi\)
−0.794466 + 0.607309i \(0.792249\pi\)
\(228\) 0 0
\(229\) 888.642 0.256433 0.128216 0.991746i \(-0.459075\pi\)
0.128216 + 0.991746i \(0.459075\pi\)
\(230\) 0 0
\(231\) −5150.37 −1.46697
\(232\) 0 0
\(233\) 4919.38i 1.38317i −0.722294 0.691586i \(-0.756912\pi\)
0.722294 0.691586i \(-0.243088\pi\)
\(234\) 0 0
\(235\) −4904.91 + 255.929i −1.36154 + 0.0710423i
\(236\) 0 0
\(237\) 8671.13i 2.37658i
\(238\) 0 0
\(239\) 2178.00 0.589468 0.294734 0.955579i \(-0.404769\pi\)
0.294734 + 0.955579i \(0.404769\pi\)
\(240\) 0 0
\(241\) −3156.12 −0.843583 −0.421792 0.906693i \(-0.638599\pi\)
−0.421792 + 0.906693i \(0.638599\pi\)
\(242\) 0 0
\(243\) 2991.34i 0.789688i
\(244\) 0 0
\(245\) 85.7507 + 1643.43i 0.0223609 + 0.428549i
\(246\) 0 0
\(247\) 7738.62i 1.99351i
\(248\) 0 0
\(249\) −6040.10 −1.53725
\(250\) 0 0
\(251\) 2719.20 0.683801 0.341901 0.939736i \(-0.388929\pi\)
0.341901 + 0.939736i \(0.388929\pi\)
\(252\) 0 0
\(253\) 2927.01i 0.727350i
\(254\) 0 0
\(255\) 366.195 + 7018.18i 0.0899295 + 1.72351i
\(256\) 0 0
\(257\) 749.067i 0.181811i −0.995860 0.0909056i \(-0.971024\pi\)
0.995860 0.0909056i \(-0.0289762\pi\)
\(258\) 0 0
\(259\) 1335.33 0.320360
\(260\) 0 0
\(261\) 3191.56 0.756907
\(262\) 0 0
\(263\) 2546.04i 0.596942i −0.954419 0.298471i \(-0.903523\pi\)
0.954419 0.298471i \(-0.0964766\pi\)
\(264\) 0 0
\(265\) 3203.89 167.173i 0.742692 0.0387522i
\(266\) 0 0
\(267\) 6371.52i 1.46041i
\(268\) 0 0
\(269\) 7982.07 1.80920 0.904601 0.426260i \(-0.140169\pi\)
0.904601 + 0.426260i \(0.140169\pi\)
\(270\) 0 0
\(271\) 1686.58 0.378054 0.189027 0.981972i \(-0.439467\pi\)
0.189027 + 0.981972i \(0.439467\pi\)
\(272\) 0 0
\(273\) 13349.2i 2.95946i
\(274\) 0 0
\(275\) −3373.42 + 352.998i −0.739726 + 0.0774056i
\(276\) 0 0
\(277\) 1423.07i 0.308679i −0.988018 0.154339i \(-0.950675\pi\)
0.988018 0.154339i \(-0.0493249\pi\)
\(278\) 0 0
\(279\) 6377.65 1.36853
\(280\) 0 0
\(281\) 5418.67 1.15036 0.575180 0.818027i \(-0.304932\pi\)
0.575180 + 0.818027i \(0.304932\pi\)
\(282\) 0 0
\(283\) 8343.38i 1.75252i 0.481842 + 0.876258i \(0.339968\pi\)
−0.481842 + 0.876258i \(0.660032\pi\)
\(284\) 0 0
\(285\) −10532.1 + 549.545i −2.18901 + 0.114218i
\(286\) 0 0
\(287\) 2106.58i 0.433267i
\(288\) 0 0
\(289\) −463.000 −0.0942398
\(290\) 0 0
\(291\) −9738.87 −1.96186
\(292\) 0 0
\(293\) 2331.73i 0.464919i 0.972606 + 0.232459i \(0.0746772\pi\)
−0.972606 + 0.232459i \(0.925323\pi\)
\(294\) 0 0
\(295\) −318.771 6109.29i −0.0629137 1.20575i
\(296\) 0 0
\(297\) 4535.12i 0.886041i
\(298\) 0 0
\(299\) −7586.51 −1.46736
\(300\) 0 0
\(301\) −11102.9 −2.12611
\(302\) 0 0
\(303\) 2496.55i 0.473343i
\(304\) 0 0
\(305\) −297.964 5710.52i −0.0559388 1.07208i
\(306\) 0 0
\(307\) 2100.00i 0.390401i −0.980763 0.195200i \(-0.937464\pi\)
0.980763 0.195200i \(-0.0625357\pi\)
\(308\) 0 0
\(309\) −1718.40 −0.316364
\(310\) 0 0
\(311\) 8501.38 1.55006 0.775030 0.631924i \(-0.217735\pi\)
0.775030 + 0.631924i \(0.217735\pi\)
\(312\) 0 0
\(313\) 7257.73i 1.31064i 0.755350 + 0.655321i \(0.227467\pi\)
−0.755350 + 0.655321i \(0.772533\pi\)
\(314\) 0 0
\(315\) 11493.7 599.717i 2.05586 0.107271i
\(316\) 0 0
\(317\) 9639.14i 1.70785i 0.520397 + 0.853925i \(0.325784\pi\)
−0.520397 + 0.853925i \(0.674216\pi\)
\(318\) 0 0
\(319\) −1862.59 −0.326912
\(320\) 0 0
\(321\) −6466.93 −1.12445
\(322\) 0 0
\(323\) 8067.72i 1.38978i
\(324\) 0 0
\(325\) −914.933 8743.55i −0.156158 1.49232i
\(326\) 0 0
\(327\) 4300.88i 0.727337i
\(328\) 0 0
\(329\) −9726.34 −1.62988
\(330\) 0 0
\(331\) −360.466 −0.0598581 −0.0299290 0.999552i \(-0.509528\pi\)
−0.0299290 + 0.999552i \(0.509528\pi\)
\(332\) 0 0
\(333\) 2804.24i 0.461476i
\(334\) 0 0
\(335\) 3366.82 175.674i 0.549101 0.0286510i
\(336\) 0 0
\(337\) 2820.47i 0.455908i 0.973672 + 0.227954i \(0.0732036\pi\)
−0.973672 + 0.227954i \(0.926796\pi\)
\(338\) 0 0
\(339\) −4262.89 −0.682974
\(340\) 0 0
\(341\) −3721.99 −0.591076
\(342\) 0 0
\(343\) 4335.24i 0.682451i
\(344\) 0 0
\(345\) −538.744 10325.1i −0.0840725 1.61126i
\(346\) 0 0
\(347\) 8617.62i 1.33319i −0.745419 0.666597i \(-0.767750\pi\)
0.745419 0.666597i \(-0.232250\pi\)
\(348\) 0 0
\(349\) −735.067 −0.112743 −0.0563714 0.998410i \(-0.517953\pi\)
−0.0563714 + 0.998410i \(0.517953\pi\)
\(350\) 0 0
\(351\) −11754.6 −1.78750
\(352\) 0 0
\(353\) 4535.35i 0.683830i 0.939731 + 0.341915i \(0.111076\pi\)
−0.939731 + 0.341915i \(0.888924\pi\)
\(354\) 0 0
\(355\) −48.2943 925.567i −0.00722026 0.138377i
\(356\) 0 0
\(357\) 13916.9i 2.06320i
\(358\) 0 0
\(359\) −5426.44 −0.797762 −0.398881 0.917003i \(-0.630601\pi\)
−0.398881 + 0.917003i \(0.630601\pi\)
\(360\) 0 0
\(361\) 5248.15 0.765148
\(362\) 0 0
\(363\) 5098.41i 0.737182i
\(364\) 0 0
\(365\) 8521.99 444.661i 1.22209 0.0637660i
\(366\) 0 0
\(367\) 609.673i 0.0867157i 0.999060 + 0.0433579i \(0.0138056\pi\)
−0.999060 + 0.0433579i \(0.986194\pi\)
\(368\) 0 0
\(369\) −4423.90 −0.624117
\(370\) 0 0
\(371\) 6353.26 0.889069
\(372\) 0 0
\(373\) 5089.42i 0.706489i −0.935531 0.353244i \(-0.885078\pi\)
0.935531 0.353244i \(-0.114922\pi\)
\(374\) 0 0
\(375\) 11834.8 1866.12i 1.62973 0.256976i
\(376\) 0 0
\(377\) 4827.64i 0.659513i
\(378\) 0 0
\(379\) 910.876 0.123453 0.0617263 0.998093i \(-0.480339\pi\)
0.0617263 + 0.998093i \(0.480339\pi\)
\(380\) 0 0
\(381\) −7846.14 −1.05504
\(382\) 0 0
\(383\) 7686.98i 1.02555i 0.858522 + 0.512776i \(0.171383\pi\)
−0.858522 + 0.512776i \(0.828617\pi\)
\(384\) 0 0
\(385\) −6707.68 + 349.994i −0.887936 + 0.0463307i
\(386\) 0 0
\(387\) 23316.5i 3.06264i
\(388\) 0 0
\(389\) −4372.77 −0.569943 −0.284972 0.958536i \(-0.591984\pi\)
−0.284972 + 0.958536i \(0.591984\pi\)
\(390\) 0 0
\(391\) 7909.14 1.02297
\(392\) 0 0
\(393\) 5207.38i 0.668390i
\(394\) 0 0
\(395\) 589.247 + 11293.0i 0.0750589 + 1.43851i
\(396\) 0 0
\(397\) 12591.9i 1.59186i −0.605391 0.795928i \(-0.706983\pi\)
0.605391 0.795928i \(-0.293017\pi\)
\(398\) 0 0
\(399\) −20885.0 −2.62045
\(400\) 0 0
\(401\) 3614.48 0.450122 0.225061 0.974345i \(-0.427742\pi\)
0.225061 + 0.974345i \(0.427742\pi\)
\(402\) 0 0
\(403\) 9647.01i 1.19244i
\(404\) 0 0
\(405\) −103.378 1981.26i −0.0126837 0.243085i
\(406\) 0 0
\(407\) 1636.55i 0.199314i
\(408\) 0 0
\(409\) −639.314 −0.0772910 −0.0386455 0.999253i \(-0.512304\pi\)
−0.0386455 + 0.999253i \(0.512304\pi\)
\(410\) 0 0
\(411\) 12164.8 1.45997
\(412\) 0 0
\(413\) 12114.6i 1.44339i
\(414\) 0 0
\(415\) −7866.45 + 410.456i −0.930479 + 0.0485506i
\(416\) 0 0
\(417\) 26026.2i 3.05637i
\(418\) 0 0
\(419\) −11018.4 −1.28469 −0.642346 0.766415i \(-0.722039\pi\)
−0.642346 + 0.766415i \(0.722039\pi\)
\(420\) 0 0
\(421\) 16513.1 1.91164 0.955820 0.293952i \(-0.0949707\pi\)
0.955820 + 0.293952i \(0.0949707\pi\)
\(422\) 0 0
\(423\) 20425.7i 2.34783i
\(424\) 0 0
\(425\) 953.842 + 9115.38i 0.108866 + 1.04038i
\(426\) 0 0
\(427\) 11323.9i 1.28337i
\(428\) 0 0
\(429\) 16360.5 1.84124
\(430\) 0 0
\(431\) 6106.80 0.682492 0.341246 0.939974i \(-0.389151\pi\)
0.341246 + 0.939974i \(0.389151\pi\)
\(432\) 0 0
\(433\) 1757.88i 0.195100i 0.995231 + 0.0975500i \(0.0311006\pi\)
−0.995231 + 0.0975500i \(0.968899\pi\)
\(434\) 0 0
\(435\) 6570.33 342.827i 0.724192 0.0377869i
\(436\) 0 0
\(437\) 11869.2i 1.29927i
\(438\) 0 0
\(439\) −1055.02 −0.114700 −0.0573500 0.998354i \(-0.518265\pi\)
−0.0573500 + 0.998354i \(0.518265\pi\)
\(440\) 0 0
\(441\) 6843.78 0.738989
\(442\) 0 0
\(443\) 7775.51i 0.833918i −0.908925 0.416959i \(-0.863096\pi\)
0.908925 0.416959i \(-0.136904\pi\)
\(444\) 0 0
\(445\) −432.977 8298.08i −0.0461238 0.883970i
\(446\) 0 0
\(447\) 22712.0i 2.40322i
\(448\) 0 0
\(449\) 11245.1 1.18194 0.590969 0.806694i \(-0.298745\pi\)
0.590969 + 0.806694i \(0.298745\pi\)
\(450\) 0 0
\(451\) 2581.78 0.269560
\(452\) 0 0
\(453\) 2428.69i 0.251898i
\(454\) 0 0
\(455\) −907.148 17385.6i −0.0934676 1.79132i
\(456\) 0 0
\(457\) 13576.9i 1.38972i 0.719145 + 0.694860i \(0.244534\pi\)
−0.719145 + 0.694860i \(0.755466\pi\)
\(458\) 0 0
\(459\) 12254.4 1.24616
\(460\) 0 0
\(461\) −9605.08 −0.970397 −0.485199 0.874404i \(-0.661253\pi\)
−0.485199 + 0.874404i \(0.661253\pi\)
\(462\) 0 0
\(463\) 3226.71i 0.323883i −0.986800 0.161942i \(-0.948224\pi\)
0.986800 0.161942i \(-0.0517756\pi\)
\(464\) 0 0
\(465\) 13129.4 685.067i 1.30938 0.0683209i
\(466\) 0 0
\(467\) 20.6790i 0.00204906i 0.999999 + 0.00102453i \(0.000326118\pi\)
−0.999999 + 0.00102453i \(0.999674\pi\)
\(468\) 0 0
\(469\) 6676.34 0.657323
\(470\) 0 0
\(471\) −12129.7 −1.18664
\(472\) 0 0
\(473\) 13607.5i 1.32277i
\(474\) 0 0
\(475\) −13679.4 + 1431.42i −1.32137 + 0.138270i
\(476\) 0 0
\(477\) 13342.1i 1.28070i
\(478\) 0 0
\(479\) 12492.9 1.19168 0.595841 0.803102i \(-0.296819\pi\)
0.595841 + 0.803102i \(0.296819\pi\)
\(480\) 0 0
\(481\) −4241.77 −0.402096
\(482\) 0 0
\(483\) 20474.5i 1.92882i
\(484\) 0 0
\(485\) −12683.6 + 661.806i −1.18749 + 0.0619610i
\(486\) 0 0
\(487\) 4944.60i 0.460084i −0.973181 0.230042i \(-0.926114\pi\)
0.973181 0.230042i \(-0.0738864\pi\)
\(488\) 0 0
\(489\) 14794.2 1.36813
\(490\) 0 0
\(491\) −7712.73 −0.708902 −0.354451 0.935075i \(-0.615332\pi\)
−0.354451 + 0.935075i \(0.615332\pi\)
\(492\) 0 0
\(493\) 5032.95i 0.459782i
\(494\) 0 0
\(495\) 735.000 + 14086.4i 0.0667390 + 1.27906i
\(496\) 0 0
\(497\) 1835.38i 0.165650i
\(498\) 0 0
\(499\) 1492.41 0.133886 0.0669432 0.997757i \(-0.478675\pi\)
0.0669432 + 0.997757i \(0.478675\pi\)
\(500\) 0 0
\(501\) 16973.7 1.51363
\(502\) 0 0
\(503\) 3105.13i 0.275250i 0.990484 + 0.137625i \(0.0439469\pi\)
−0.990484 + 0.137625i \(0.956053\pi\)
\(504\) 0 0
\(505\) −169.653 3251.43i −0.0149494 0.286508i
\(506\) 0 0
\(507\) 23570.1i 2.06466i
\(508\) 0 0
\(509\) −15363.5 −1.33787 −0.668933 0.743322i \(-0.733249\pi\)
−0.668933 + 0.743322i \(0.733249\pi\)
\(510\) 0 0
\(511\) 16898.9 1.46295
\(512\) 0 0
\(513\) 18390.1i 1.58274i
\(514\) 0 0
\(515\) −2237.99 + 116.774i −0.191491 + 0.00999162i
\(516\) 0 0
\(517\) 11920.4i 1.01404i
\(518\) 0 0
\(519\) 12591.2 1.06492
\(520\) 0 0
\(521\) −9924.25 −0.834529 −0.417264 0.908785i \(-0.637011\pi\)
−0.417264 + 0.908785i \(0.637011\pi\)
\(522\) 0 0
\(523\) 455.146i 0.0380538i 0.999819 + 0.0190269i \(0.00605681\pi\)
−0.999819 + 0.0190269i \(0.993943\pi\)
\(524\) 0 0
\(525\) 23597.1 2469.22i 1.96164 0.205268i
\(526\) 0 0
\(527\) 10057.3i 0.831312i
\(528\) 0 0
\(529\) 531.111 0.0436517
\(530\) 0 0
\(531\) −25441.1 −2.07919
\(532\) 0 0
\(533\) 6691.72i 0.543809i
\(534\) 0 0
\(535\) −8422.34 + 439.461i −0.680616 + 0.0355132i
\(536\) 0 0
\(537\) 25535.3i 2.05201i
\(538\) 0 0
\(539\) −3994.02 −0.319174
\(540\) 0 0
\(541\) 23383.9 1.85832 0.929160 0.369678i \(-0.120532\pi\)
0.929160 + 0.369678i \(0.120532\pi\)
\(542\) 0 0
\(543\) 14420.3i 1.13966i
\(544\) 0 0
\(545\) 292.267 + 5601.34i 0.0229713 + 0.440248i
\(546\) 0 0
\(547\) 6908.03i 0.539974i 0.962864 + 0.269987i \(0.0870195\pi\)
−0.962864 + 0.269987i \(0.912981\pi\)
\(548\) 0 0
\(549\) −23780.5 −1.84868
\(550\) 0 0
\(551\) −7552.90 −0.583964
\(552\) 0 0
\(553\) 22393.8i 1.72203i
\(554\) 0 0
\(555\) −301.222 5772.97i −0.0230382 0.441530i
\(556\) 0 0
\(557\) 3221.81i 0.245085i 0.992463 + 0.122543i \(0.0391048\pi\)
−0.992463 + 0.122543i \(0.960895\pi\)
\(558\) 0 0
\(559\) 35269.1 2.66856
\(560\) 0 0
\(561\) −17056.3 −1.28363
\(562\) 0 0
\(563\) 14822.7i 1.10959i 0.831986 + 0.554796i \(0.187204\pi\)
−0.831986 + 0.554796i \(0.812796\pi\)
\(564\) 0 0
\(565\) −5551.85 + 289.685i −0.413395 + 0.0215701i
\(566\) 0 0
\(567\) 3928.79i 0.290994i
\(568\) 0 0
\(569\) −6434.10 −0.474045 −0.237022 0.971504i \(-0.576172\pi\)
−0.237022 + 0.971504i \(0.576172\pi\)
\(570\) 0 0
\(571\) −17760.3 −1.30165 −0.650827 0.759226i \(-0.725578\pi\)
−0.650827 + 0.759226i \(0.725578\pi\)
\(572\) 0 0
\(573\) 2351.85i 0.171466i
\(574\) 0 0
\(575\) −1403.29 13410.5i −0.101776 0.972620i
\(576\) 0 0
\(577\) 1341.96i 0.0968227i 0.998827 + 0.0484113i \(0.0154158\pi\)
−0.998827 + 0.0484113i \(0.984584\pi\)
\(578\) 0 0
\(579\) 24848.7 1.78355
\(580\) 0 0
\(581\) −15599.0 −1.11387
\(582\) 0 0
\(583\) 7786.42i 0.553140i
\(584\) 0 0
\(585\) −36510.5 + 1905.05i −2.58038 + 0.134639i
\(586\) 0 0
\(587\) 12957.3i 0.911082i −0.890215 0.455541i \(-0.849446\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(588\) 0 0
\(589\) −15092.8 −1.05584
\(590\) 0 0
\(591\) −19978.1 −1.39051
\(592\) 0 0
\(593\) 5966.63i 0.413187i −0.978427 0.206594i \(-0.933762\pi\)
0.978427 0.206594i \(-0.0662378\pi\)
\(594\) 0 0
\(595\) 945.726 + 18125.0i 0.0651613 + 1.24883i
\(596\) 0 0
\(597\) 9473.56i 0.649459i
\(598\) 0 0
\(599\) −10311.9 −0.703396 −0.351698 0.936114i \(-0.614396\pi\)
−0.351698 + 0.936114i \(0.614396\pi\)
\(600\) 0 0
\(601\) 2594.60 0.176100 0.0880499 0.996116i \(-0.471936\pi\)
0.0880499 + 0.996116i \(0.471936\pi\)
\(602\) 0 0
\(603\) 14020.6i 0.946868i
\(604\) 0 0
\(605\) 346.463 + 6640.02i 0.0232822 + 0.446207i
\(606\) 0 0
\(607\) 7796.08i 0.521306i 0.965432 + 0.260653i \(0.0839379\pi\)
−0.965432 + 0.260653i \(0.916062\pi\)
\(608\) 0 0
\(609\) 13028.9 0.866922
\(610\) 0 0
\(611\) 30896.5 2.04572
\(612\) 0 0
\(613\) 10443.5i 0.688106i 0.938950 + 0.344053i \(0.111800\pi\)
−0.938950 + 0.344053i \(0.888200\pi\)
\(614\) 0 0
\(615\) −9107.30 + 475.201i −0.597141 + 0.0311577i
\(616\) 0 0
\(617\) 18306.1i 1.19445i −0.802073 0.597226i \(-0.796270\pi\)
0.802073 0.597226i \(-0.203730\pi\)
\(618\) 0 0
\(619\) 149.857 0.00973066 0.00486533 0.999988i \(-0.498451\pi\)
0.00486533 + 0.999988i \(0.498451\pi\)
\(620\) 0 0
\(621\) −18028.7 −1.16500
\(622\) 0 0
\(623\) 16454.9i 1.05819i
\(624\) 0 0
\(625\) 15286.5 3234.61i 0.978338 0.207015i
\(626\) 0 0
\(627\) 25596.2i 1.63033i
\(628\) 0 0
\(629\) 4422.16 0.280323
\(630\) 0 0
\(631\) −24466.5 −1.54358 −0.771789 0.635879i \(-0.780638\pi\)
−0.771789 + 0.635879i \(0.780638\pi\)
\(632\) 0 0
\(633\) 40719.9i 2.55683i
\(634\) 0 0
\(635\) −10218.6 + 533.185i −0.638601 + 0.0333210i
\(636\) 0 0
\(637\) 10352.1i 0.643901i
\(638\) 0 0
\(639\) −3854.37 −0.238618
\(640\) 0 0
\(641\) −20274.7 −1.24930 −0.624652 0.780903i \(-0.714759\pi\)
−0.624652 + 0.780903i \(0.714759\pi\)
\(642\) 0 0
\(643\) 9167.25i 0.562241i 0.959672 + 0.281121i \(0.0907061\pi\)
−0.959672 + 0.281121i \(0.909294\pi\)
\(644\) 0 0
\(645\) 2504.58 + 48000.7i 0.152896 + 2.93027i
\(646\) 0 0
\(647\) 5459.82i 0.331758i 0.986146 + 0.165879i \(0.0530462\pi\)
−0.986146 + 0.165879i \(0.946954\pi\)
\(648\) 0 0
\(649\) 14847.4 0.898016
\(650\) 0 0
\(651\) 26035.4 1.56744
\(652\) 0 0
\(653\) 16280.5i 0.975659i −0.872939 0.487830i \(-0.837789\pi\)
0.872939 0.487830i \(-0.162211\pi\)
\(654\) 0 0
\(655\) −353.868 6781.93i −0.0211096 0.404568i
\(656\) 0 0
\(657\) 35488.4i 2.10736i
\(658\) 0 0
\(659\) 23975.9 1.41725 0.708625 0.705585i \(-0.249316\pi\)
0.708625 + 0.705585i \(0.249316\pi\)
\(660\) 0 0
\(661\) −13876.4 −0.816532 −0.408266 0.912863i \(-0.633866\pi\)
−0.408266 + 0.912863i \(0.633866\pi\)
\(662\) 0 0
\(663\) 44208.2i 2.58960i
\(664\) 0 0
\(665\) −27200.0 + 1419.24i −1.58612 + 0.0827607i
\(666\) 0 0
\(667\) 7404.44i 0.429837i
\(668\) 0 0
\(669\) −16200.3 −0.936236
\(670\) 0 0
\(671\) 13878.3 0.798458
\(672\) 0 0
\(673\) 30526.1i 1.74843i 0.485537 + 0.874216i \(0.338624\pi\)
−0.485537 + 0.874216i \(0.661376\pi\)
\(674\) 0 0
\(675\) −2174.26 20778.2i −0.123981 1.18482i
\(676\) 0 0
\(677\) 6992.09i 0.396939i −0.980107 0.198470i \(-0.936403\pi\)
0.980107 0.198470i \(-0.0635971\pi\)
\(678\) 0 0
\(679\) −25151.4 −1.42153
\(680\) 0 0
\(681\) 35613.0 2.00395
\(682\) 0 0
\(683\) 22479.2i 1.25936i 0.776854 + 0.629681i \(0.216814\pi\)
−0.776854 + 0.629681i \(0.783186\pi\)
\(684\) 0 0
\(685\) 15843.1 826.661i 0.883698 0.0461096i
\(686\) 0 0
\(687\) 7618.29i 0.423080i
\(688\) 0 0
\(689\) −20181.6 −1.11590
\(690\) 0 0
\(691\) 5536.97 0.304828 0.152414 0.988317i \(-0.451295\pi\)
0.152414 + 0.988317i \(0.451295\pi\)
\(692\) 0 0
\(693\) 27933.1i 1.53115i
\(694\) 0 0
\(695\) 1768.61 + 33895.7i 0.0965285 + 1.84998i
\(696\) 0 0
\(697\) 6976.29i 0.379119i
\(698\) 0 0
\(699\) −42173.6 −2.28205
\(700\) 0 0
\(701\) −16934.8 −0.912436 −0.456218 0.889868i \(-0.650796\pi\)
−0.456218 + 0.889868i \(0.650796\pi\)
\(702\) 0 0
\(703\) 6636.29i 0.356035i
\(704\) 0 0
\(705\) 2194.06 + 42049.5i 0.117210 + 2.24635i
\(706\) 0 0
\(707\) 6447.52i 0.342976i
\(708\) 0 0
\(709\) 4112.16 0.217821 0.108911 0.994052i \(-0.465264\pi\)
0.108911 + 0.994052i \(0.465264\pi\)
\(710\) 0 0
\(711\) 47027.9 2.48057
\(712\) 0 0
\(713\) 14796.2i 0.777169i
\(714\) 0 0
\(715\) 21307.5 1111.78i 1.11448 0.0581514i
\(716\) 0 0
\(717\) 18671.9i 0.972543i
\(718\) 0 0
\(719\) −34938.3 −1.81221 −0.906105 0.423053i \(-0.860958\pi\)
−0.906105 + 0.423053i \(0.860958\pi\)
\(720\) 0 0
\(721\) −4437.90 −0.229232
\(722\) 0 0
\(723\) 27057.3i 1.39180i
\(724\) 0 0
\(725\) 8533.71 892.976i 0.437150 0.0457438i
\(726\) 0 0
\(727\) 34679.2i 1.76916i 0.466389 + 0.884580i \(0.345555\pi\)
−0.466389 + 0.884580i \(0.654445\pi\)
\(728\) 0 0
\(729\) 30435.7 1.54629
\(730\) 0 0
\(731\) −36769.0 −1.86040
\(732\) 0 0
\(733\) 30802.4i 1.55213i 0.630652 + 0.776065i \(0.282787\pi\)
−0.630652 + 0.776065i \(0.717213\pi\)
\(734\) 0 0
\(735\) 14089.0 735.137i 0.707049 0.0368924i
\(736\) 0 0
\(737\) 8182.38i 0.408958i
\(738\) 0 0
\(739\) −16364.2 −0.814570 −0.407285 0.913301i \(-0.633524\pi\)
−0.407285 + 0.913301i \(0.633524\pi\)
\(740\) 0 0
\(741\) 66342.8 3.28902
\(742\) 0 0
\(743\) 4464.06i 0.220418i 0.993908 + 0.110209i \(0.0351520\pi\)
−0.993908 + 0.110209i \(0.964848\pi\)
\(744\) 0 0
\(745\) −1543.39 29579.4i −0.0759001 1.45464i
\(746\) 0 0
\(747\) 32758.5i 1.60451i
\(748\) 0 0
\(749\) −16701.3 −0.814758
\(750\) 0 0
\(751\) 17873.6 0.868463 0.434231 0.900801i \(-0.357020\pi\)
0.434231 + 0.900801i \(0.357020\pi\)
\(752\) 0 0
\(753\) 23311.5i 1.12818i
\(754\) 0 0
\(755\) −165.042 3163.05i −0.00795562 0.152471i
\(756\) 0 0
\(757\) 14305.3i 0.686834i −0.939183 0.343417i \(-0.888416\pi\)
0.939183 0.343417i \(-0.111584\pi\)
\(758\) 0 0
\(759\) 25093.1 1.20003
\(760\) 0 0
\(761\) 21819.9 1.03938 0.519692 0.854354i \(-0.326047\pi\)
0.519692 + 0.854354i \(0.326047\pi\)
\(762\) 0 0
\(763\) 11107.3i 0.527016i
\(764\) 0 0
\(765\) 38063.2 1986.06i 1.79892 0.0938643i
\(766\) 0 0
\(767\) 38483.0i 1.81166i
\(768\) 0 0
\(769\) 29446.6 1.38085 0.690423 0.723406i \(-0.257425\pi\)
0.690423 + 0.723406i \(0.257425\pi\)
\(770\) 0 0
\(771\) −6421.71 −0.299964
\(772\) 0 0
\(773\) 30232.4i 1.40671i 0.710840 + 0.703354i \(0.248315\pi\)
−0.710840 + 0.703354i \(0.751685\pi\)
\(774\) 0 0
\(775\) 17052.8 1784.42i 0.790393 0.0827075i
\(776\) 0 0
\(777\) 11447.7i 0.528551i
\(778\) 0 0
\(779\) 10469.3 0.481515
\(780\) 0 0
\(781\) 2249.41 0.103060
\(782\) 0 0
\(783\) 11472.5i 0.523617i
\(784\) 0 0
\(785\) −15797.4 + 824.276i −0.718258 + 0.0374773i
\(786\) 0 0
\(787\) 30871.6i 1.39829i −0.714980 0.699145i \(-0.753564\pi\)
0.714980 0.699145i \(-0.246436\pi\)
\(788\) 0 0
\(789\) −21827.1 −0.984873
\(790\) 0 0
\(791\) −11009.2 −0.494871
\(792\) 0 0
\(793\) 35971.1i 1.61081i
\(794\) 0 0
\(795\) −1433.16 27466.8i −0.0639359 1.22534i
\(796\) 0 0
\(797\) 4612.35i 0.204991i 0.994733 + 0.102496i \(0.0326828\pi\)
−0.994733 +