Properties

Label 320.6.f.d.289.9
Level 320
Weight 6
Character 320.289
Analytic conductor 51.323
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.9
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.d.289.12

$q$-expansion

\(f(q)\) \(=\) \(q-11.4004 q^{3} +(-32.3114 + 45.6177i) q^{5} +121.355i q^{7} -113.031 q^{9} +O(q^{10})\) \(q-11.4004 q^{3} +(-32.3114 + 45.6177i) q^{5} +121.355i q^{7} -113.031 q^{9} -625.005i q^{11} +924.688 q^{13} +(368.363 - 520.060i) q^{15} -1325.51i q^{17} +1135.08i q^{19} -1383.49i q^{21} -3055.36i q^{23} +(-1036.94 - 2947.94i) q^{25} +4058.90 q^{27} +8232.27i q^{29} +1985.84 q^{31} +7125.31i q^{33} +(-5535.91 - 3921.14i) q^{35} -9681.82 q^{37} -10541.8 q^{39} -15897.7 q^{41} +18727.8 q^{43} +(3652.18 - 5156.20i) q^{45} -5162.47i q^{47} +2080.07 q^{49} +15111.4i q^{51} +5659.20 q^{53} +(28511.3 + 20194.8i) q^{55} -12940.3i q^{57} +28693.0i q^{59} -2410.34i q^{61} -13716.8i q^{63} +(-29878.0 + 42182.1i) q^{65} +45886.3 q^{67} +34832.3i q^{69} +5535.02 q^{71} +58819.4i q^{73} +(11821.6 + 33607.8i) q^{75} +75847.2 q^{77} +79344.3 q^{79} -18806.6 q^{81} -102859. q^{83} +(60466.7 + 42829.1i) q^{85} -93851.2i q^{87} -95263.4 q^{89} +112215. i q^{91} -22639.3 q^{93} +(-51779.6 - 36675.9i) q^{95} +55240.6i q^{97} +70644.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2944q^{9} + O(q^{10}) \) \( 32q + 2944q^{9} - 46528q^{25} - 36768q^{41} - 113920q^{49} + 25376q^{65} + 633472q^{81} + 968704q^{89} + O(q^{100}) \)

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
\(3\) −11.4004 −0.731337 −0.365668 0.930745i \(-0.619160\pi\)
−0.365668 + 0.930745i \(0.619160\pi\)
\(4\) 0 0
\(5\) −32.3114 + 45.6177i −0.578004 + 0.816034i
\(6\) 0 0
\(7\) 121.355i 0.936076i 0.883708 + 0.468038i \(0.155039\pi\)
−0.883708 + 0.468038i \(0.844961\pi\)
\(8\) 0 0
\(9\) −113.031 −0.465147
\(10\) 0 0
\(11\) 625.005i 1.55741i −0.627393 0.778703i \(-0.715878\pi\)
0.627393 0.778703i \(-0.284122\pi\)
\(12\) 0 0
\(13\) 924.688 1.51753 0.758764 0.651366i \(-0.225804\pi\)
0.758764 + 0.651366i \(0.225804\pi\)
\(14\) 0 0
\(15\) 368.363 520.060i 0.422716 0.596795i
\(16\) 0 0
\(17\) 1325.51i 1.11240i −0.831049 0.556199i \(-0.812259\pi\)
0.831049 0.556199i \(-0.187741\pi\)
\(18\) 0 0
\(19\) 1135.08i 0.721342i 0.932693 + 0.360671i \(0.117452\pi\)
−0.932693 + 0.360671i \(0.882548\pi\)
\(20\) 0 0
\(21\) 1383.49i 0.684586i
\(22\) 0 0
\(23\) 3055.36i 1.20432i −0.798375 0.602160i \(-0.794307\pi\)
0.798375 0.602160i \(-0.205693\pi\)
\(24\) 0 0
\(25\) −1036.94 2947.94i −0.331822 0.943342i
\(26\) 0 0
\(27\) 4058.90 1.07152
\(28\) 0 0
\(29\) 8232.27i 1.81771i 0.417113 + 0.908855i \(0.363042\pi\)
−0.417113 + 0.908855i \(0.636958\pi\)
\(30\) 0 0
\(31\) 1985.84 0.371141 0.185571 0.982631i \(-0.440587\pi\)
0.185571 + 0.982631i \(0.440587\pi\)
\(32\) 0 0
\(33\) 7125.31i 1.13899i
\(34\) 0 0
\(35\) −5535.91 3921.14i −0.763869 0.541056i
\(36\) 0 0
\(37\) −9681.82 −1.16266 −0.581330 0.813668i \(-0.697468\pi\)
−0.581330 + 0.813668i \(0.697468\pi\)
\(38\) 0 0
\(39\) −10541.8 −1.10982
\(40\) 0 0
\(41\) −15897.7 −1.47698 −0.738491 0.674264i \(-0.764461\pi\)
−0.738491 + 0.674264i \(0.764461\pi\)
\(42\) 0 0
\(43\) 18727.8 1.54460 0.772299 0.635259i \(-0.219107\pi\)
0.772299 + 0.635259i \(0.219107\pi\)
\(44\) 0 0
\(45\) 3652.18 5156.20i 0.268857 0.379575i
\(46\) 0 0
\(47\) 5162.47i 0.340889i −0.985367 0.170444i \(-0.945480\pi\)
0.985367 0.170444i \(-0.0545203\pi\)
\(48\) 0 0
\(49\) 2080.07 0.123762
\(50\) 0 0
\(51\) 15111.4i 0.813538i
\(52\) 0 0
\(53\) 5659.20 0.276736 0.138368 0.990381i \(-0.455814\pi\)
0.138368 + 0.990381i \(0.455814\pi\)
\(54\) 0 0
\(55\) 28511.3 + 20194.8i 1.27090 + 0.900187i
\(56\) 0 0
\(57\) 12940.3i 0.527544i
\(58\) 0 0
\(59\) 28693.0i 1.07311i 0.843864 + 0.536557i \(0.180275\pi\)
−0.843864 + 0.536557i \(0.819725\pi\)
\(60\) 0 0
\(61\) 2410.34i 0.0829382i −0.999140 0.0414691i \(-0.986796\pi\)
0.999140 0.0414691i \(-0.0132038\pi\)
\(62\) 0 0
\(63\) 13716.8i 0.435413i
\(64\) 0 0
\(65\) −29878.0 + 42182.1i −0.877138 + 1.23835i
\(66\) 0 0
\(67\) 45886.3 1.24881 0.624405 0.781101i \(-0.285342\pi\)
0.624405 + 0.781101i \(0.285342\pi\)
\(68\) 0 0
\(69\) 34832.3i 0.880764i
\(70\) 0 0
\(71\) 5535.02 0.130309 0.0651544 0.997875i \(-0.479246\pi\)
0.0651544 + 0.997875i \(0.479246\pi\)
\(72\) 0 0
\(73\) 58819.4i 1.29185i 0.763399 + 0.645927i \(0.223529\pi\)
−0.763399 + 0.645927i \(0.776471\pi\)
\(74\) 0 0
\(75\) 11821.6 + 33607.8i 0.242674 + 0.689901i
\(76\) 0 0
\(77\) 75847.2 1.45785
\(78\) 0 0
\(79\) 79344.3 1.43037 0.715185 0.698935i \(-0.246343\pi\)
0.715185 + 0.698935i \(0.246343\pi\)
\(80\) 0 0
\(81\) −18806.6 −0.318492
\(82\) 0 0
\(83\) −102859. −1.63888 −0.819441 0.573164i \(-0.805716\pi\)
−0.819441 + 0.573164i \(0.805716\pi\)
\(84\) 0 0
\(85\) 60466.7 + 42829.1i 0.907755 + 0.642971i
\(86\) 0 0
\(87\) 93851.2i 1.32936i
\(88\) 0 0
\(89\) −95263.4 −1.27483 −0.637413 0.770522i \(-0.719996\pi\)
−0.637413 + 0.770522i \(0.719996\pi\)
\(90\) 0 0
\(91\) 112215.i 1.42052i
\(92\) 0 0
\(93\) −22639.3 −0.271429
\(94\) 0 0
\(95\) −51779.6 36675.9i −0.588639 0.416939i
\(96\) 0 0
\(97\) 55240.6i 0.596113i 0.954548 + 0.298057i \(0.0963384\pi\)
−0.954548 + 0.298057i \(0.903662\pi\)
\(98\) 0 0
\(99\) 70644.7i 0.724422i
\(100\) 0 0
\(101\) 104507.i 1.01940i 0.860353 + 0.509699i \(0.170243\pi\)
−0.860353 + 0.509699i \(0.829757\pi\)
\(102\) 0 0
\(103\) 16103.7i 0.149566i −0.997200 0.0747832i \(-0.976174\pi\)
0.997200 0.0747832i \(-0.0238265\pi\)
\(104\) 0 0
\(105\) 63111.7 + 44702.6i 0.558646 + 0.395694i
\(106\) 0 0
\(107\) 156165. 1.31863 0.659317 0.751865i \(-0.270845\pi\)
0.659317 + 0.751865i \(0.270845\pi\)
\(108\) 0 0
\(109\) 64503.2i 0.520014i −0.965607 0.260007i \(-0.916275\pi\)
0.965607 0.260007i \(-0.0837249\pi\)
\(110\) 0 0
\(111\) 110377. 0.850296
\(112\) 0 0
\(113\) 51268.0i 0.377703i 0.982006 + 0.188851i \(0.0604764\pi\)
−0.982006 + 0.188851i \(0.939524\pi\)
\(114\) 0 0
\(115\) 139378. + 98722.9i 0.982766 + 0.696103i
\(116\) 0 0
\(117\) −104518. −0.705873
\(118\) 0 0
\(119\) 160857. 1.04129
\(120\) 0 0
\(121\) −229580. −1.42551
\(122\) 0 0
\(123\) 181240. 1.08017
\(124\) 0 0
\(125\) 167983. + 47949.3i 0.961593 + 0.274478i
\(126\) 0 0
\(127\) 246962.i 1.35869i 0.733819 + 0.679345i \(0.237736\pi\)
−0.733819 + 0.679345i \(0.762264\pi\)
\(128\) 0 0
\(129\) −213504. −1.12962
\(130\) 0 0
\(131\) 24117.5i 0.122787i 0.998114 + 0.0613937i \(0.0195545\pi\)
−0.998114 + 0.0613937i \(0.980445\pi\)
\(132\) 0 0
\(133\) −137747. −0.675231
\(134\) 0 0
\(135\) −131149. + 185157.i −0.619341 + 0.874393i
\(136\) 0 0
\(137\) 132684.i 0.603974i 0.953312 + 0.301987i \(0.0976500\pi\)
−0.953312 + 0.301987i \(0.902350\pi\)
\(138\) 0 0
\(139\) 96391.0i 0.423155i −0.977361 0.211577i \(-0.932140\pi\)
0.977361 0.211577i \(-0.0678601\pi\)
\(140\) 0 0
\(141\) 58854.3i 0.249305i
\(142\) 0 0
\(143\) 577935.i 2.36341i
\(144\) 0 0
\(145\) −375537. 265996.i −1.48331 1.05064i
\(146\) 0 0
\(147\) −23713.7 −0.0905119
\(148\) 0 0
\(149\) 204014.i 0.752825i 0.926452 + 0.376413i \(0.122842\pi\)
−0.926452 + 0.376413i \(0.877158\pi\)
\(150\) 0 0
\(151\) −165135. −0.589382 −0.294691 0.955593i \(-0.595217\pi\)
−0.294691 + 0.955593i \(0.595217\pi\)
\(152\) 0 0
\(153\) 149823.i 0.517429i
\(154\) 0 0
\(155\) −64165.2 + 90589.2i −0.214521 + 0.302864i
\(156\) 0 0
\(157\) 380052. 1.23054 0.615268 0.788318i \(-0.289048\pi\)
0.615268 + 0.788318i \(0.289048\pi\)
\(158\) 0 0
\(159\) −64517.1 −0.202387
\(160\) 0 0
\(161\) 370781. 1.12734
\(162\) 0 0
\(163\) 174832. 0.515410 0.257705 0.966224i \(-0.417034\pi\)
0.257705 + 0.966224i \(0.417034\pi\)
\(164\) 0 0
\(165\) −325040. 230229.i −0.929453 0.658340i
\(166\) 0 0
\(167\) 64065.2i 0.177759i −0.996042 0.0888794i \(-0.971671\pi\)
0.996042 0.0888794i \(-0.0283286\pi\)
\(168\) 0 0
\(169\) 483754. 1.30289
\(170\) 0 0
\(171\) 128298.i 0.335530i
\(172\) 0 0
\(173\) −303497. −0.770974 −0.385487 0.922713i \(-0.625966\pi\)
−0.385487 + 0.922713i \(0.625966\pi\)
\(174\) 0 0
\(175\) 357746. 125838.i 0.883040 0.310610i
\(176\) 0 0
\(177\) 327112.i 0.784808i
\(178\) 0 0
\(179\) 95959.4i 0.223849i 0.993717 + 0.111924i \(0.0357015\pi\)
−0.993717 + 0.111924i \(0.964299\pi\)
\(180\) 0 0
\(181\) 121991.i 0.276779i −0.990378 0.138389i \(-0.955807\pi\)
0.990378 0.138389i \(-0.0441925\pi\)
\(182\) 0 0
\(183\) 27478.9i 0.0606557i
\(184\) 0 0
\(185\) 312833. 441662.i 0.672023 0.948770i
\(186\) 0 0
\(187\) −828450. −1.73246
\(188\) 0 0
\(189\) 492565.i 1.00302i
\(190\) 0 0
\(191\) 185327. 0.367582 0.183791 0.982965i \(-0.441163\pi\)
0.183791 + 0.982965i \(0.441163\pi\)
\(192\) 0 0
\(193\) 455781.i 0.880771i 0.897809 + 0.440386i \(0.145158\pi\)
−0.897809 + 0.440386i \(0.854842\pi\)
\(194\) 0 0
\(195\) 340621. 480893.i 0.641483 0.905654i
\(196\) 0 0
\(197\) 366599. 0.673017 0.336508 0.941680i \(-0.390754\pi\)
0.336508 + 0.941680i \(0.390754\pi\)
\(198\) 0 0
\(199\) −414885. −0.742669 −0.371334 0.928499i \(-0.621100\pi\)
−0.371334 + 0.928499i \(0.621100\pi\)
\(200\) 0 0
\(201\) −523123. −0.913300
\(202\) 0 0
\(203\) −999023. −1.70151
\(204\) 0 0
\(205\) 513678. 725217.i 0.853702 1.20527i
\(206\) 0 0
\(207\) 345349.i 0.560186i
\(208\) 0 0
\(209\) 709429. 1.12342
\(210\) 0 0
\(211\) 42516.6i 0.0657435i −0.999460 0.0328717i \(-0.989535\pi\)
0.999460 0.0328717i \(-0.0104653\pi\)
\(212\) 0 0
\(213\) −63101.5 −0.0952995
\(214\) 0 0
\(215\) −605122. + 854318.i −0.892784 + 1.26044i
\(216\) 0 0
\(217\) 240990.i 0.347416i
\(218\) 0 0
\(219\) 670565.i 0.944780i
\(220\) 0 0
\(221\) 1.22568e6i 1.68810i
\(222\) 0 0
\(223\) 252515.i 0.340036i 0.985441 + 0.170018i \(0.0543826\pi\)
−0.985441 + 0.170018i \(0.945617\pi\)
\(224\) 0 0
\(225\) 117206. + 333208.i 0.154346 + 0.438793i
\(226\) 0 0
\(227\) 99603.1 0.128295 0.0641473 0.997940i \(-0.479567\pi\)
0.0641473 + 0.997940i \(0.479567\pi\)
\(228\) 0 0
\(229\) 212126.i 0.267303i 0.991028 + 0.133652i \(0.0426703\pi\)
−0.991028 + 0.133652i \(0.957330\pi\)
\(230\) 0 0
\(231\) −864689. −1.06618
\(232\) 0 0
\(233\) 1.24877e6i 1.50693i −0.657487 0.753466i \(-0.728380\pi\)
0.657487 0.753466i \(-0.271620\pi\)
\(234\) 0 0
\(235\) 235500. + 166807.i 0.278177 + 0.197035i
\(236\) 0 0
\(237\) −904558. −1.04608
\(238\) 0 0
\(239\) 1.34898e6 1.52761 0.763803 0.645450i \(-0.223330\pi\)
0.763803 + 0.645450i \(0.223330\pi\)
\(240\) 0 0
\(241\) 1.34315e6 1.48964 0.744822 0.667264i \(-0.232535\pi\)
0.744822 + 0.667264i \(0.232535\pi\)
\(242\) 0 0
\(243\) −771908. −0.838591
\(244\) 0 0
\(245\) −67210.1 + 94888.1i −0.0715352 + 0.100994i
\(246\) 0 0
\(247\) 1.04959e6i 1.09466i
\(248\) 0 0
\(249\) 1.17264e6 1.19857
\(250\) 0 0
\(251\) 595167.i 0.596286i −0.954521 0.298143i \(-0.903633\pi\)
0.954521 0.298143i \(-0.0963673\pi\)
\(252\) 0 0
\(253\) −1.90961e6 −1.87562
\(254\) 0 0
\(255\) −689345. 488269.i −0.663874 0.470228i
\(256\) 0 0
\(257\) 78872.4i 0.0744890i −0.999306 0.0372445i \(-0.988142\pi\)
0.999306 0.0372445i \(-0.0118580\pi\)
\(258\) 0 0
\(259\) 1.17493e6i 1.08834i
\(260\) 0 0
\(261\) 930499.i 0.845502i
\(262\) 0 0
\(263\) 652871.i 0.582020i 0.956720 + 0.291010i \(0.0939913\pi\)
−0.956720 + 0.291010i \(0.906009\pi\)
\(264\) 0 0
\(265\) −182857. + 258159.i −0.159954 + 0.225826i
\(266\) 0 0
\(267\) 1.08604e6 0.932327
\(268\) 0 0
\(269\) 153469.i 0.129313i −0.997908 0.0646563i \(-0.979405\pi\)
0.997908 0.0646563i \(-0.0205951\pi\)
\(270\) 0 0
\(271\) −1.17390e6 −0.970972 −0.485486 0.874244i \(-0.661357\pi\)
−0.485486 + 0.874244i \(0.661357\pi\)
\(272\) 0 0
\(273\) 1.27930e6i 1.03888i
\(274\) 0 0
\(275\) −1.84248e6 + 648095.i −1.46917 + 0.516782i
\(276\) 0 0
\(277\) −719910. −0.563740 −0.281870 0.959453i \(-0.590955\pi\)
−0.281870 + 0.959453i \(0.590955\pi\)
\(278\) 0 0
\(279\) −224460. −0.172635
\(280\) 0 0
\(281\) −2785.80 −0.00210467 −0.00105234 0.999999i \(-0.500335\pi\)
−0.00105234 + 0.999999i \(0.500335\pi\)
\(282\) 0 0
\(283\) −342464. −0.254185 −0.127092 0.991891i \(-0.540564\pi\)
−0.127092 + 0.991891i \(0.540564\pi\)
\(284\) 0 0
\(285\) 590308. + 418121.i 0.430494 + 0.304923i
\(286\) 0 0
\(287\) 1.92926e6i 1.38257i
\(288\) 0 0
\(289\) −337118. −0.237431
\(290\) 0 0
\(291\) 629765.i 0.435960i
\(292\) 0 0
\(293\) 2.03747e6 1.38651 0.693255 0.720693i \(-0.256176\pi\)
0.693255 + 0.720693i \(0.256176\pi\)
\(294\) 0 0
\(295\) −1.30891e6 927112.i −0.875698 0.620265i
\(296\) 0 0
\(297\) 2.53683e6i 1.66878i
\(298\) 0 0
\(299\) 2.82525e6i 1.82759i
\(300\) 0 0
\(301\) 2.27270e6i 1.44586i
\(302\) 0 0
\(303\) 1.19143e6i 0.745523i
\(304\) 0 0
\(305\) 109954. + 77881.7i 0.0676804 + 0.0479386i
\(306\) 0 0
\(307\) −406791. −0.246335 −0.123167 0.992386i \(-0.539305\pi\)
−0.123167 + 0.992386i \(0.539305\pi\)
\(308\) 0 0
\(309\) 183589.i 0.109383i
\(310\) 0 0
\(311\) −1.64556e6 −0.964745 −0.482372 0.875966i \(-0.660225\pi\)
−0.482372 + 0.875966i \(0.660225\pi\)
\(312\) 0 0
\(313\) 2.11949e6i 1.22284i 0.791305 + 0.611422i \(0.209402\pi\)
−0.791305 + 0.611422i \(0.790598\pi\)
\(314\) 0 0
\(315\) 625728. + 443209.i 0.355311 + 0.251670i
\(316\) 0 0
\(317\) 526511. 0.294279 0.147140 0.989116i \(-0.452993\pi\)
0.147140 + 0.989116i \(0.452993\pi\)
\(318\) 0 0
\(319\) 5.14521e6 2.83091
\(320\) 0 0
\(321\) −1.78035e6 −0.964366
\(322\) 0 0
\(323\) 1.50455e6 0.802420
\(324\) 0 0
\(325\) −958849. 2.72593e6i −0.503549 1.43155i
\(326\) 0 0
\(327\) 735363.i 0.380305i
\(328\) 0 0
\(329\) 626489. 0.319098
\(330\) 0 0
\(331\) 2.72847e6i 1.36883i 0.729093 + 0.684415i \(0.239942\pi\)
−0.729093 + 0.684415i \(0.760058\pi\)
\(332\) 0 0
\(333\) 1.09434e6 0.540808
\(334\) 0 0
\(335\) −1.48265e6 + 2.09323e6i −0.721817 + 1.01907i
\(336\) 0 0
\(337\) 2.14704e6i 1.02983i −0.857241 0.514916i \(-0.827823\pi\)
0.857241 0.514916i \(-0.172177\pi\)
\(338\) 0 0
\(339\) 584476.i 0.276228i
\(340\) 0 0
\(341\) 1.24116e6i 0.578017i
\(342\) 0 0
\(343\) 2.29203e6i 1.05193i
\(344\) 0 0
\(345\) −1.58897e6 1.12548e6i −0.718733 0.509085i
\(346\) 0 0
\(347\) 917072. 0.408865 0.204432 0.978881i \(-0.434465\pi\)
0.204432 + 0.978881i \(0.434465\pi\)
\(348\) 0 0
\(349\) 3.98463e6i 1.75115i 0.483078 + 0.875577i \(0.339519\pi\)
−0.483078 + 0.875577i \(0.660481\pi\)
\(350\) 0 0
\(351\) 3.75321e6 1.62605
\(352\) 0 0
\(353\) 1.18612e6i 0.506630i 0.967384 + 0.253315i \(0.0815210\pi\)
−0.967384 + 0.253315i \(0.918479\pi\)
\(354\) 0 0
\(355\) −178844. + 252495.i −0.0753190 + 0.106336i
\(356\) 0 0
\(357\) −1.83383e6 −0.761533
\(358\) 0 0
\(359\) −265806. −0.108850 −0.0544249 0.998518i \(-0.517333\pi\)
−0.0544249 + 0.998518i \(0.517333\pi\)
\(360\) 0 0
\(361\) 1.18770e6 0.479666
\(362\) 0 0
\(363\) 2.61731e6 1.04253
\(364\) 0 0
\(365\) −2.68320e6 1.90054e6i −1.05420 0.746697i
\(366\) 0 0
\(367\) 4.89812e6i 1.89830i −0.314827 0.949149i \(-0.601947\pi\)
0.314827 0.949149i \(-0.398053\pi\)
\(368\) 0 0
\(369\) 1.79693e6 0.687013
\(370\) 0 0
\(371\) 686769.i 0.259045i
\(372\) 0 0
\(373\) 4.42717e6 1.64761 0.823804 0.566875i \(-0.191848\pi\)
0.823804 + 0.566875i \(0.191848\pi\)
\(374\) 0 0
\(375\) −1.91508e6 546642.i −0.703248 0.200736i
\(376\) 0 0
\(377\) 7.61227e6i 2.75842i
\(378\) 0 0
\(379\) 4.97522e6i 1.77916i 0.456784 + 0.889578i \(0.349001\pi\)
−0.456784 + 0.889578i \(0.650999\pi\)
\(380\) 0 0
\(381\) 2.81547e6i 0.993660i
\(382\) 0 0
\(383\) 994461.i 0.346410i 0.984886 + 0.173205i \(0.0554124\pi\)
−0.984886 + 0.173205i \(0.944588\pi\)
\(384\) 0 0
\(385\) −2.45073e6 + 3.45997e6i −0.842644 + 1.18965i
\(386\) 0 0
\(387\) −2.11681e6 −0.718465
\(388\) 0 0
\(389\) 5.89205e6i 1.97421i 0.160087 + 0.987103i \(0.448823\pi\)
−0.160087 + 0.987103i \(0.551177\pi\)
\(390\) 0 0
\(391\) −4.04990e6 −1.33968
\(392\) 0 0
\(393\) 274949.i 0.0897989i
\(394\) 0 0
\(395\) −2.56373e6 + 3.61950e6i −0.826760 + 1.16723i
\(396\) 0 0
\(397\) 1.76823e6 0.563071 0.281535 0.959551i \(-0.409156\pi\)
0.281535 + 0.959551i \(0.409156\pi\)
\(398\) 0 0
\(399\) 1.57037e6 0.493821
\(400\) 0 0
\(401\) −5.32752e6 −1.65449 −0.827245 0.561841i \(-0.810093\pi\)
−0.827245 + 0.561841i \(0.810093\pi\)
\(402\) 0 0
\(403\) 1.83628e6 0.563217
\(404\) 0 0
\(405\) 607669. 857914.i 0.184090 0.259900i
\(406\) 0 0
\(407\) 6.05119e6i 1.81073i
\(408\) 0 0
\(409\) −1.40082e6 −0.414070 −0.207035 0.978334i \(-0.566381\pi\)
−0.207035 + 0.978334i \(0.566381\pi\)
\(410\) 0 0
\(411\) 1.51266e6i 0.441709i
\(412\) 0 0
\(413\) −3.48203e6 −1.00452
\(414\) 0 0
\(415\) 3.32353e6 4.69219e6i 0.947281 1.33738i
\(416\) 0 0
\(417\) 1.09890e6i 0.309469i
\(418\) 0 0
\(419\) 461773.i 0.128497i 0.997934 + 0.0642486i \(0.0204650\pi\)
−0.997934 + 0.0642486i \(0.979535\pi\)
\(420\) 0 0
\(421\) 820398.i 0.225590i 0.993618 + 0.112795i \(0.0359803\pi\)
−0.993618 + 0.112795i \(0.964020\pi\)
\(422\) 0 0
\(423\) 583517.i 0.158563i
\(424\) 0 0
\(425\) −3.90753e6 + 1.37448e6i −1.04937 + 0.369118i
\(426\) 0 0
\(427\) 292506. 0.0776364
\(428\) 0 0
\(429\) 6.58869e6i 1.72845i
\(430\) 0 0
\(431\) 5.53969e6 1.43646 0.718229 0.695807i \(-0.244953\pi\)
0.718229 + 0.695807i \(0.244953\pi\)
\(432\) 0 0
\(433\) 360822.i 0.0924854i 0.998930 + 0.0462427i \(0.0147248\pi\)
−0.998930 + 0.0462427i \(0.985275\pi\)
\(434\) 0 0
\(435\) 4.28127e6 + 3.03247e6i 1.08480 + 0.768374i
\(436\) 0 0
\(437\) 3.46806e6 0.868727
\(438\) 0 0
\(439\) 6.40731e6 1.58677 0.793386 0.608719i \(-0.208316\pi\)
0.793386 + 0.608719i \(0.208316\pi\)
\(440\) 0 0
\(441\) −235112. −0.0575676
\(442\) 0 0
\(443\) 1.55001e6 0.375253 0.187627 0.982240i \(-0.439920\pi\)
0.187627 + 0.982240i \(0.439920\pi\)
\(444\) 0 0
\(445\) 3.07810e6 4.34569e6i 0.736855 1.04030i
\(446\) 0 0
\(447\) 2.32584e6i 0.550569i
\(448\) 0 0
\(449\) 7.15790e6 1.67560 0.837799 0.545979i \(-0.183842\pi\)
0.837799 + 0.545979i \(0.183842\pi\)
\(450\) 0 0
\(451\) 9.93615e6i 2.30026i
\(452\) 0 0
\(453\) 1.88261e6 0.431036
\(454\) 0 0
\(455\) −5.11899e6 3.62583e6i −1.15919 0.821067i
\(456\) 0 0
\(457\) 4.20570e6i 0.941994i 0.882135 + 0.470997i \(0.156106\pi\)
−0.882135 + 0.470997i \(0.843894\pi\)
\(458\) 0 0
\(459\) 5.38010e6i 1.19195i
\(460\) 0 0
\(461\) 2.81134e6i 0.616114i −0.951368 0.308057i \(-0.900321\pi\)
0.951368 0.308057i \(-0.0996788\pi\)
\(462\) 0 0
\(463\) 2.18515e6i 0.473728i −0.971543 0.236864i \(-0.923880\pi\)
0.971543 0.236864i \(-0.0761197\pi\)
\(464\) 0 0
\(465\) 731509. 1.03275e6i 0.156887 0.221495i
\(466\) 0 0
\(467\) 3.77798e6 0.801617 0.400809 0.916162i \(-0.368729\pi\)
0.400809 + 0.916162i \(0.368729\pi\)
\(468\) 0 0
\(469\) 5.56851e6i 1.16898i
\(470\) 0 0
\(471\) −4.33275e6 −0.899936
\(472\) 0 0
\(473\) 1.17050e7i 2.40557i
\(474\) 0 0
\(475\) 3.34614e6 1.17701e6i 0.680472 0.239357i
\(476\) 0 0
\(477\) −639663. −0.128723
\(478\) 0 0
\(479\) 8.16313e6 1.62562 0.812808 0.582531i \(-0.197938\pi\)
0.812808 + 0.582531i \(0.197938\pi\)
\(480\) 0 0
\(481\) −8.95266e6 −1.76437
\(482\) 0 0
\(483\) −4.22706e6 −0.824462
\(484\) 0 0
\(485\) −2.51995e6 1.78490e6i −0.486449 0.344556i
\(486\) 0 0
\(487\) 1.47312e6i 0.281459i −0.990048 0.140730i \(-0.955055\pi\)
0.990048 0.140730i \(-0.0449448\pi\)
\(488\) 0 0
\(489\) −1.99316e6 −0.376938
\(490\) 0 0
\(491\) 1.25498e6i 0.234926i 0.993077 + 0.117463i \(0.0374762\pi\)
−0.993077 + 0.117463i \(0.962524\pi\)
\(492\) 0 0
\(493\) 1.09119e7 2.02202
\(494\) 0 0
\(495\) −3.22265e6 2.28263e6i −0.591153 0.418719i
\(496\) 0 0
\(497\) 671700.i 0.121979i
\(498\) 0 0
\(499\) 8.05328e6i 1.44784i −0.689882 0.723921i \(-0.742338\pi\)
0.689882 0.723921i \(-0.257662\pi\)
\(500\) 0 0
\(501\) 730370.i 0.130002i
\(502\) 0 0
\(503\) 3.77386e6i 0.665067i 0.943091 + 0.332534i \(0.107904\pi\)
−0.943091 + 0.332534i \(0.892096\pi\)
\(504\) 0 0
\(505\) −4.76739e6 3.37679e6i −0.831863 0.589217i
\(506\) 0 0
\(507\) −5.51500e6 −0.952852
\(508\) 0 0
\(509\) 1.29923e6i 0.222276i 0.993805 + 0.111138i \(0.0354496\pi\)
−0.993805 + 0.111138i \(0.964550\pi\)
\(510\) 0 0
\(511\) −7.13800e6 −1.20927
\(512\) 0 0
\(513\) 4.60716e6i 0.772929i
\(514\) 0 0
\(515\) 734615. + 520335.i 0.122051 + 0.0864500i
\(516\) 0 0
\(517\) −3.22657e6 −0.530902
\(518\) 0 0
\(519\) 3.45999e6 0.563841
\(520\) 0 0
\(521\) 3.28934e6 0.530903 0.265451 0.964124i \(-0.414479\pi\)
0.265451 + 0.964124i \(0.414479\pi\)
\(522\) 0 0
\(523\) 2.50676e6 0.400736 0.200368 0.979721i \(-0.435786\pi\)
0.200368 + 0.979721i \(0.435786\pi\)
\(524\) 0 0
\(525\) −4.07846e6 + 1.43460e6i −0.645799 + 0.227161i
\(526\) 0 0
\(527\) 2.63224e6i 0.412857i
\(528\) 0 0
\(529\) −2.89885e6 −0.450388
\(530\) 0 0
\(531\) 3.24319e6i 0.499156i
\(532\) 0 0
\(533\) −1.47004e7 −2.24136
\(534\) 0 0
\(535\) −5.04591e6 + 7.12389e6i −0.762176 + 1.07605i
\(536\) 0 0
\(537\) 1.09398e6i 0.163709i
\(538\) 0 0
\(539\) 1.30006e6i 0.192748i
\(540\) 0 0
\(541\) 1.88877e6i 0.277451i 0.990331 + 0.138725i \(0.0443005\pi\)
−0.990331 + 0.138725i \(0.955699\pi\)
\(542\) 0 0
\(543\) 1.39075e6i 0.202418i
\(544\) 0 0
\(545\) 2.94249e6 + 2.08419e6i 0.424349 + 0.300571i
\(546\) 0 0
\(547\) 6.65871e6 0.951529 0.475764 0.879573i \(-0.342172\pi\)
0.475764 + 0.879573i \(0.342172\pi\)
\(548\) 0 0
\(549\) 272443.i 0.0385784i
\(550\) 0 0
\(551\) −9.34425e6 −1.31119
\(552\) 0 0
\(553\) 9.62880e6i 1.33893i
\(554\) 0 0
\(555\) −3.56643e6 + 5.03513e6i −0.491475 + 0.693870i
\(556\) 0 0
\(557\) −2.92957e6 −0.400098 −0.200049 0.979786i \(-0.564110\pi\)
−0.200049 + 0.979786i \(0.564110\pi\)
\(558\) 0 0
\(559\) 1.73174e7 2.34397
\(560\) 0 0
\(561\) 9.44467e6 1.26701
\(562\) 0 0
\(563\) 7.54089e6 1.00266 0.501328 0.865257i \(-0.332845\pi\)
0.501328 + 0.865257i \(0.332845\pi\)
\(564\) 0 0
\(565\) −2.33872e6 1.65654e6i −0.308218 0.218314i
\(566\) 0 0
\(567\) 2.28227e6i 0.298132i
\(568\) 0 0
\(569\) 7.78696e6 1.00829 0.504147 0.863618i \(-0.331807\pi\)
0.504147 + 0.863618i \(0.331807\pi\)
\(570\) 0 0
\(571\) 2.28912e6i 0.293817i −0.989150 0.146909i \(-0.953068\pi\)
0.989150 0.146909i \(-0.0469324\pi\)
\(572\) 0 0
\(573\) −2.11280e6 −0.268827
\(574\) 0 0
\(575\) −9.00702e6 + 3.16823e6i −1.13609 + 0.399620i
\(576\) 0 0
\(577\) 1.37541e7i 1.71986i −0.510415 0.859928i \(-0.670508\pi\)
0.510415 0.859928i \(-0.329492\pi\)
\(578\) 0 0
\(579\) 5.19609e6i 0.644140i
\(580\) 0 0
\(581\) 1.24824e7i 1.53412i
\(582\) 0 0
\(583\) 3.53703e6i 0.430990i
\(584\) 0 0
\(585\) 3.37713e6 4.76787e6i 0.407998 0.576016i
\(586\) 0 0
\(587\) −1.03428e7 −1.23892 −0.619462 0.785027i \(-0.712649\pi\)
−0.619462 + 0.785027i \(0.712649\pi\)
\(588\) 0 0
\(589\) 2.25408e6i 0.267720i
\(590\) 0 0
\(591\) −4.17938e6 −0.492202
\(592\) 0 0
\(593\) 1.02755e6i 0.119995i −0.998199 0.0599976i \(-0.980891\pi\)
0.998199 0.0599976i \(-0.0191093\pi\)
\(594\) 0 0
\(595\) −5.19751e6 + 7.33790e6i −0.601870 + 0.849727i
\(596\) 0 0
\(597\) 4.72986e6 0.543141
\(598\) 0 0
\(599\) −3.71137e6 −0.422636 −0.211318 0.977417i \(-0.567776\pi\)
−0.211318 + 0.977417i \(0.567776\pi\)
\(600\) 0 0
\(601\) −4.30716e6 −0.486412 −0.243206 0.969975i \(-0.578199\pi\)
−0.243206 + 0.969975i \(0.578199\pi\)
\(602\) 0 0
\(603\) −5.18656e6 −0.580880
\(604\) 0 0
\(605\) 7.41807e6 1.04729e7i 0.823953 1.16327i
\(606\) 0 0
\(607\) 1.70813e7i 1.88170i 0.338828 + 0.940848i \(0.389969\pi\)
−0.338828 + 0.940848i \(0.610031\pi\)
\(608\) 0 0
\(609\) 1.13893e7 1.24438
\(610\) 0 0
\(611\) 4.77367e6i 0.517308i
\(612\) 0 0
\(613\) −1.80249e6 −0.193741 −0.0968705 0.995297i \(-0.530883\pi\)
−0.0968705 + 0.995297i \(0.530883\pi\)
\(614\) 0 0
\(615\) −5.85614e6 + 8.26777e6i −0.624343 + 0.881456i
\(616\) 0 0
\(617\) 7.48312e6i 0.791353i −0.918390 0.395676i \(-0.870510\pi\)
0.918390 0.395676i \(-0.129490\pi\)
\(618\) 0 0
\(619\) 1.03953e7i 1.09047i −0.838284 0.545233i \(-0.816441\pi\)
0.838284 0.545233i \(-0.183559\pi\)
\(620\) 0 0
\(621\) 1.24014e7i 1.29045i
\(622\) 0 0
\(623\) 1.15606e7i 1.19333i
\(624\) 0 0
\(625\) −7.61512e6 + 6.11370e6i −0.779788 + 0.626043i
\(626\) 0 0
\(627\) −8.08778e6 −0.821600
\(628\) 0 0
\(629\) 1.28333e7i 1.29334i
\(630\) 0 0
\(631\) 1.37210e7 1.37187 0.685933 0.727665i \(-0.259394\pi\)
0.685933 + 0.727665i \(0.259394\pi\)
\(632\) 0 0
\(633\) 484707.i 0.0480806i
\(634\) 0 0
\(635\) −1.12658e7 7.97969e6i −1.10874 0.785329i
\(636\) 0 0
\(637\) 1.92342e6 0.187813
\(638\) 0 0
\(639\) −625627. −0.0606127
\(640\) 0 0
\(641\) 8.05003e6 0.773843 0.386921 0.922113i \(-0.373538\pi\)
0.386921 + 0.922113i \(0.373538\pi\)
\(642\) 0 0
\(643\) −1.53306e7 −1.46228 −0.731140 0.682227i \(-0.761011\pi\)
−0.731140 + 0.682227i \(0.761011\pi\)
\(644\) 0 0
\(645\) 6.89863e6 9.73958e6i 0.652926 0.921809i
\(646\) 0 0
\(647\) 2.55551e6i 0.240003i −0.992774 0.120002i \(-0.961710\pi\)
0.992774 0.120002i \(-0.0382900\pi\)
\(648\) 0 0
\(649\) 1.79333e7 1.67128
\(650\) 0 0
\(651\) 2.74739e6i 0.254078i
\(652\) 0 0
\(653\) 1.03839e7 0.952969 0.476484 0.879183i \(-0.341911\pi\)
0.476484 + 0.879183i \(0.341911\pi\)
\(654\) 0 0
\(655\) −1.10018e6 779270.i −0.100199 0.0709716i
\(656\) 0 0
\(657\) 6.64840e6i 0.600902i
\(658\) 0 0
\(659\) 1.63129e7i 1.46325i −0.681708 0.731625i \(-0.738762\pi\)
0.681708 0.731625i \(-0.261238\pi\)
\(660\) 0 0
\(661\) 9.87139e6i 0.878769i 0.898299 + 0.439385i \(0.144803\pi\)
−0.898299 + 0.439385i \(0.855197\pi\)
\(662\) 0 0
\(663\) 1.39733e7i 1.23457i
\(664\) 0 0
\(665\) 4.45079e6 6.28368e6i 0.390286 0.551011i
\(666\) 0 0
\(667\) 2.51525e7 2.18910
\(668\) 0 0
\(669\) 2.87877e6i 0.248681i
\(670\) 0 0
\(671\) −1.50648e6 −0.129168
\(672\) 0 0
\(673\) 2.67399e6i 0.227574i −0.993505 0.113787i \(-0.963702\pi\)
0.993505 0.113787i \(-0.0362981\pi\)
\(674\) 0 0
\(675\) −4.20885e6 1.19654e7i −0.355552 1.01081i
\(676\) 0 0
\(677\) −9.18547e6 −0.770247 −0.385123 0.922865i \(-0.625841\pi\)
−0.385123 + 0.922865i \(0.625841\pi\)
\(678\) 0 0
\(679\) −6.70370e6 −0.558007
\(680\) 0 0
\(681\) −1.13552e6 −0.0938265
\(682\) 0 0
\(683\) −1.63593e7 −1.34188 −0.670941 0.741511i \(-0.734109\pi\)
−0.670941 + 0.741511i \(0.734109\pi\)
\(684\) 0 0
\(685\) −6.05275e6 4.28722e6i −0.492863 0.349100i
\(686\) 0 0
\(687\) 2.41832e6i 0.195489i
\(688\) 0 0
\(689\) 5.23299e6 0.419954
\(690\) 0 0
\(691\) 1.12037e7i 0.892623i 0.894878 + 0.446311i \(0.147263\pi\)
−0.894878 + 0.446311i \(0.852737\pi\)
\(692\) 0 0
\(693\) −8.57306e6 −0.678114
\(694\) 0 0
\(695\) 4.39713e6 + 3.11453e6i 0.345309 + 0.244585i
\(696\) 0 0
\(697\) 2.10726e7i 1.64299i
\(698\) 0 0
\(699\) 1.42365e7i 1.10207i
\(700\) 0 0
\(701\) 1.26088e6i 0.0969122i 0.998825 + 0.0484561i \(0.0154301\pi\)
−0.998825 + 0.0484561i \(0.984570\pi\)
\(702\) 0 0
\(703\) 1.09896e7i 0.838676i
\(704\) 0 0
\(705\) −2.68479e6 1.90167e6i −0.203441 0.144099i
\(706\) 0 0
\(707\) −1.26825e7 −0.954234
\(708\) 0 0
\(709\) 6.78380e6i 0.506824i 0.967358 + 0.253412i \(0.0815528\pi\)
−0.967358 + 0.253412i \(0.918447\pi\)
\(710\) 0 0
\(711\) −8.96834e6 −0.665332
\(712\) 0 0
\(713\) 6.06743e6i 0.446973i
\(714\) 0 0
\(715\) 2.63640e7 + 1.86739e7i 1.92862 + 1.36606i
\(716\) 0 0
\(717\) −1.53789e7 −1.11719
\(718\) 0 0
\(719\) −1.05951e7 −0.764332 −0.382166 0.924094i \(-0.624822\pi\)
−0.382166 + 0.924094i \(0.624822\pi\)
\(720\) 0 0
\(721\) 1.95426e6 0.140005
\(722\) 0 0
\(723\) −1.53125e7 −1.08943
\(724\) 0 0
\(725\) 2.42683e7 8.53640e6i 1.71472 0.603156i
\(726\) 0 0
\(727\) 1.24737e7i 0.875307i −0.899144 0.437653i \(-0.855810\pi\)
0.899144 0.437653i \(-0.144190\pi\)
\(728\) 0 0
\(729\) 1.33701e7 0.931784
\(730\) 0 0
\(731\) 2.48239e7i 1.71821i
\(732\) 0 0
\(733\) −2.45429e7 −1.68720 −0.843599 0.536974i \(-0.819567\pi\)
−0.843599 + 0.536974i \(0.819567\pi\)
\(734\) 0 0
\(735\) 766223. 1.08176e6i 0.0523163 0.0738608i
\(736\) 0 0
\(737\) 2.86792e7i 1.94490i
\(738\) 0 0
\(739\) 1.22999e7i 0.828495i 0.910164 + 0.414247i \(0.135955\pi\)
−0.910164 + 0.414247i \(0.864045\pi\)
\(740\) 0 0
\(741\) 1.19658e7i 0.800562i
\(742\) 0 0
\(743\) 1.22075e7i 0.811249i −0.914040 0.405625i \(-0.867054\pi\)
0.914040 0.405625i \(-0.132946\pi\)
\(744\) 0 0
\(745\) −9.30664e6 6.59198e6i −0.614331 0.435136i
\(746\) 0 0
\(747\) 1.16262e7 0.762321
\(748\) 0 0
\(749\) 1.89513e7i 1.23434i
\(750\) 0 0
\(751\) −9.31871e6 −0.602915 −0.301457 0.953480i \(-0.597473\pi\)
−0.301457 + 0.953480i \(0.597473\pi\)
\(752\) 0 0
\(753\) 6.78515e6i 0.436086i
\(754\) 0 0
\(755\) 5.33575e6 7.53307e6i 0.340665 0.480955i
\(756\) 0 0
\(757\) 1.47661e7 0.936542 0.468271 0.883585i \(-0.344877\pi\)
0.468271 + 0.883585i \(0.344877\pi\)
\(758\) 0 0
\(759\) 2.17704e7 1.37171
\(760\) 0 0
\(761\) −5.04414e6 −0.315737 −0.157868 0.987460i \(-0.550462\pi\)
−0.157868 + 0.987460i \(0.550462\pi\)
\(762\) 0 0
\(763\) 7.82776e6 0.486773
\(764\) 0 0
\(765\) −6.83459e6 4.84100e6i −0.422239 0.299076i
\(766\) 0 0
\(767\) 2.65321e7i 1.62848i
\(768\) 0 0
\(769\) −3.04383e7 −1.85612 −0.928058 0.372435i \(-0.878523\pi\)
−0.928058 + 0.372435i \(0.878523\pi\)
\(770\) 0 0
\(771\) 899177.i 0.0544765i
\(772\) 0 0
\(773\) −2.30104e7 −1.38508 −0.692540 0.721380i \(-0.743508\pi\)
−0.692540 + 0.721380i \(0.743508\pi\)
\(774\) 0 0
\(775\) −2.05920e6 5.85413e6i −0.123153 0.350113i
\(776\) 0 0
\(777\) 1.33947e7i 0.795941i
\(778\) 0 0
\(779\) 1.80451e7i 1.06541i
\(780\) 0 0
\(781\) 3.45942e6i 0.202944i
\(782\) 0 0
\(783\) 3.34139e7i 1.94770i
\(784\) 0 0
\(785\) −1.22800e7 + 1.73371e7i −0.711255 + 1.00416i
\(786\) 0 0
\(787\) 5.52083e6 0.317737 0.158868 0.987300i \(-0.449215\pi\)
0.158868 + 0.987300i \(0.449215\pi\)
\(788\) 0 0
\(789\) 7.44300e6i 0.425653i
\(790\) 0 0
\(791\) −6.22160e6 −0.353558
\(792\) 0 0
\(793\) 2.22882e6i 0.125861i
\(794\) 0 0