Properties

Label 320.6.f.d.289.5
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 289.5
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.d.289.8

$q$-expansion

\(f(q)\) \(=\) \(q-19.3064 q^{3} +(-19.7709 - 52.2887i) q^{5} +226.751i q^{7} +129.737 q^{9} +O(q^{10})\) \(q-19.3064 q^{3} +(-19.7709 - 52.2887i) q^{5} +226.751i q^{7} +129.737 q^{9} -533.326i q^{11} -540.576 q^{13} +(381.706 + 1009.51i) q^{15} +300.043i q^{17} +2825.45i q^{19} -4377.74i q^{21} +1511.21i q^{23} +(-2343.22 + 2067.59i) q^{25} +2186.69 q^{27} +5353.99i q^{29} -2542.00 q^{31} +10296.6i q^{33} +(11856.5 - 4483.07i) q^{35} +2944.93 q^{37} +10436.6 q^{39} -1971.77 q^{41} +9176.59 q^{43} +(-2565.03 - 6783.81i) q^{45} -8141.80i q^{47} -34608.9 q^{49} -5792.75i q^{51} -25644.1 q^{53} +(-27886.9 + 10544.3i) q^{55} -54549.3i q^{57} -39333.8i q^{59} -11682.5i q^{61} +29418.1i q^{63} +(10687.7 + 28266.0i) q^{65} -69680.1 q^{67} -29176.1i q^{69} +74876.9 q^{71} -57405.0i q^{73} +(45239.2 - 39917.8i) q^{75} +120932. q^{77} +42125.5 q^{79} -73743.4 q^{81} -2655.02 q^{83} +(15688.9 - 5932.13i) q^{85} -103366. i q^{87} +14466.5 q^{89} -122576. i q^{91} +49076.9 q^{93} +(147739. - 55861.8i) q^{95} -97239.7i q^{97} -69192.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2944q^{9} + O(q^{10}) \) \( 32q + 2944q^{9} - 46528q^{25} - 36768q^{41} - 113920q^{49} + 25376q^{65} + 633472q^{81} + 968704q^{89} + O(q^{100}) \)

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
\(3\) −19.3064 −1.23851 −0.619253 0.785191i \(-0.712565\pi\)
−0.619253 + 0.785191i \(0.712565\pi\)
\(4\) 0 0
\(5\) −19.7709 52.2887i −0.353673 0.935369i
\(6\) 0 0
\(7\) 226.751i 1.74906i 0.484976 + 0.874528i \(0.338828\pi\)
−0.484976 + 0.874528i \(0.661172\pi\)
\(8\) 0 0
\(9\) 129.737 0.533899
\(10\) 0 0
\(11\) 533.326i 1.32896i −0.747307 0.664478i \(-0.768654\pi\)
0.747307 0.664478i \(-0.231346\pi\)
\(12\) 0 0
\(13\) −540.576 −0.887153 −0.443577 0.896236i \(-0.646291\pi\)
−0.443577 + 0.896236i \(0.646291\pi\)
\(14\) 0 0
\(15\) 381.706 + 1009.51i 0.438026 + 1.15846i
\(16\) 0 0
\(17\) 300.043i 0.251803i 0.992043 + 0.125902i \(0.0401824\pi\)
−0.992043 + 0.125902i \(0.959818\pi\)
\(18\) 0 0
\(19\) 2825.45i 1.79558i 0.440427 + 0.897788i \(0.354827\pi\)
−0.440427 + 0.897788i \(0.645173\pi\)
\(20\) 0 0
\(21\) 4377.74i 2.16622i
\(22\) 0 0
\(23\) 1511.21i 0.595671i 0.954617 + 0.297836i \(0.0962647\pi\)
−0.954617 + 0.297836i \(0.903735\pi\)
\(24\) 0 0
\(25\) −2343.22 + 2067.59i −0.749831 + 0.661630i
\(26\) 0 0
\(27\) 2186.69 0.577269
\(28\) 0 0
\(29\) 5353.99i 1.18218i 0.806607 + 0.591088i \(0.201302\pi\)
−0.806607 + 0.591088i \(0.798698\pi\)
\(30\) 0 0
\(31\) −2542.00 −0.475085 −0.237543 0.971377i \(-0.576342\pi\)
−0.237543 + 0.971377i \(0.576342\pi\)
\(32\) 0 0
\(33\) 10296.6i 1.64592i
\(34\) 0 0
\(35\) 11856.5 4483.07i 1.63601 0.618594i
\(36\) 0 0
\(37\) 2944.93 0.353648 0.176824 0.984242i \(-0.443418\pi\)
0.176824 + 0.984242i \(0.443418\pi\)
\(38\) 0 0
\(39\) 10436.6 1.09875
\(40\) 0 0
\(41\) −1971.77 −0.183188 −0.0915939 0.995796i \(-0.529196\pi\)
−0.0915939 + 0.995796i \(0.529196\pi\)
\(42\) 0 0
\(43\) 9176.59 0.756850 0.378425 0.925632i \(-0.376466\pi\)
0.378425 + 0.925632i \(0.376466\pi\)
\(44\) 0 0
\(45\) −2565.03 6783.81i −0.188826 0.499393i
\(46\) 0 0
\(47\) 8141.80i 0.537620i −0.963193 0.268810i \(-0.913370\pi\)
0.963193 0.268810i \(-0.0866304\pi\)
\(48\) 0 0
\(49\) −34608.9 −2.05919
\(50\) 0 0
\(51\) 5792.75i 0.311860i
\(52\) 0 0
\(53\) −25644.1 −1.25400 −0.627002 0.779018i \(-0.715718\pi\)
−0.627002 + 0.779018i \(0.715718\pi\)
\(54\) 0 0
\(55\) −27886.9 + 10544.3i −1.24307 + 0.470016i
\(56\) 0 0
\(57\) 54549.3i 2.22383i
\(58\) 0 0
\(59\) 39333.8i 1.47108i −0.677482 0.735539i \(-0.736929\pi\)
0.677482 0.735539i \(-0.263071\pi\)
\(60\) 0 0
\(61\) 11682.5i 0.401985i −0.979593 0.200993i \(-0.935583\pi\)
0.979593 0.200993i \(-0.0644167\pi\)
\(62\) 0 0
\(63\) 29418.1i 0.933819i
\(64\) 0 0
\(65\) 10687.7 + 28266.0i 0.313762 + 0.829816i
\(66\) 0 0
\(67\) −69680.1 −1.89636 −0.948181 0.317729i \(-0.897080\pi\)
−0.948181 + 0.317729i \(0.897080\pi\)
\(68\) 0 0
\(69\) 29176.1i 0.737743i
\(70\) 0 0
\(71\) 74876.9 1.76280 0.881398 0.472374i \(-0.156603\pi\)
0.881398 + 0.472374i \(0.156603\pi\)
\(72\) 0 0
\(73\) 57405.0i 1.26079i −0.776275 0.630394i \(-0.782893\pi\)
0.776275 0.630394i \(-0.217107\pi\)
\(74\) 0 0
\(75\) 45239.2 39917.8i 0.928670 0.819433i
\(76\) 0 0
\(77\) 120932. 2.32442
\(78\) 0 0
\(79\) 42125.5 0.759411 0.379706 0.925107i \(-0.376025\pi\)
0.379706 + 0.925107i \(0.376025\pi\)
\(80\) 0 0
\(81\) −73743.4 −1.24885
\(82\) 0 0
\(83\) −2655.02 −0.0423031 −0.0211516 0.999776i \(-0.506733\pi\)
−0.0211516 + 0.999776i \(0.506733\pi\)
\(84\) 0 0
\(85\) 15688.9 5932.13i 0.235529 0.0890560i
\(86\) 0 0
\(87\) 103366.i 1.46413i
\(88\) 0 0
\(89\) 14466.5 0.193593 0.0967964 0.995304i \(-0.469140\pi\)
0.0967964 + 0.995304i \(0.469140\pi\)
\(90\) 0 0
\(91\) 122576.i 1.55168i
\(92\) 0 0
\(93\) 49076.9 0.588396
\(94\) 0 0
\(95\) 147739. 55861.8i 1.67953 0.635047i
\(96\) 0 0
\(97\) 97239.7i 1.04934i −0.851307 0.524668i \(-0.824190\pi\)
0.851307 0.524668i \(-0.175810\pi\)
\(98\) 0 0
\(99\) 69192.3i 0.709529i
\(100\) 0 0
\(101\) 84471.8i 0.823964i −0.911192 0.411982i \(-0.864837\pi\)
0.911192 0.411982i \(-0.135163\pi\)
\(102\) 0 0
\(103\) 180020.i 1.67196i 0.548756 + 0.835982i \(0.315101\pi\)
−0.548756 + 0.835982i \(0.684899\pi\)
\(104\) 0 0
\(105\) −228907. + 86552.0i −2.02621 + 0.766133i
\(106\) 0 0
\(107\) 36894.9 0.311535 0.155768 0.987794i \(-0.450215\pi\)
0.155768 + 0.987794i \(0.450215\pi\)
\(108\) 0 0
\(109\) 126450.i 1.01942i −0.860348 0.509708i \(-0.829754\pi\)
0.860348 0.509708i \(-0.170246\pi\)
\(110\) 0 0
\(111\) −56856.1 −0.437995
\(112\) 0 0
\(113\) 155890.i 1.14848i −0.818688 0.574238i \(-0.805298\pi\)
0.818688 0.574238i \(-0.194702\pi\)
\(114\) 0 0
\(115\) 79019.5 29878.1i 0.557172 0.210673i
\(116\) 0 0
\(117\) −70133.0 −0.473650
\(118\) 0 0
\(119\) −68035.0 −0.440418
\(120\) 0 0
\(121\) −123385. −0.766126
\(122\) 0 0
\(123\) 38067.8 0.226879
\(124\) 0 0
\(125\) 154439. + 81645.8i 0.884063 + 0.467368i
\(126\) 0 0
\(127\) 145038.i 0.797943i 0.916963 + 0.398972i \(0.130633\pi\)
−0.916963 + 0.398972i \(0.869367\pi\)
\(128\) 0 0
\(129\) −177167. −0.937364
\(130\) 0 0
\(131\) 144244.i 0.734380i −0.930146 0.367190i \(-0.880320\pi\)
0.930146 0.367190i \(-0.119680\pi\)
\(132\) 0 0
\(133\) −640673. −3.14056
\(134\) 0 0
\(135\) −43232.9 114339.i −0.204165 0.539960i
\(136\) 0 0
\(137\) 317515.i 1.44532i 0.691205 + 0.722658i \(0.257080\pi\)
−0.691205 + 0.722658i \(0.742920\pi\)
\(138\) 0 0
\(139\) 188691.i 0.828351i −0.910197 0.414176i \(-0.864070\pi\)
0.910197 0.414176i \(-0.135930\pi\)
\(140\) 0 0
\(141\) 157189.i 0.665846i
\(142\) 0 0
\(143\) 288303.i 1.17899i
\(144\) 0 0
\(145\) 279953. 105853.i 1.10577 0.418104i
\(146\) 0 0
\(147\) 668173. 2.55033
\(148\) 0 0
\(149\) 332812.i 1.22810i −0.789268 0.614049i \(-0.789540\pi\)
0.789268 0.614049i \(-0.210460\pi\)
\(150\) 0 0
\(151\) −58016.7 −0.207067 −0.103533 0.994626i \(-0.533015\pi\)
−0.103533 + 0.994626i \(0.533015\pi\)
\(152\) 0 0
\(153\) 38926.8i 0.134437i
\(154\) 0 0
\(155\) 50257.7 + 132918.i 0.168025 + 0.444380i
\(156\) 0 0
\(157\) 42076.6 0.136236 0.0681179 0.997677i \(-0.478301\pi\)
0.0681179 + 0.997677i \(0.478301\pi\)
\(158\) 0 0
\(159\) 495096. 1.55309
\(160\) 0 0
\(161\) −342669. −1.04186
\(162\) 0 0
\(163\) −522575. −1.54056 −0.770282 0.637703i \(-0.779885\pi\)
−0.770282 + 0.637703i \(0.779885\pi\)
\(164\) 0 0
\(165\) 538396. 203573.i 1.53954 0.582118i
\(166\) 0 0
\(167\) 99237.7i 0.275350i −0.990477 0.137675i \(-0.956037\pi\)
0.990477 0.137675i \(-0.0439630\pi\)
\(168\) 0 0
\(169\) −79070.3 −0.212959
\(170\) 0 0
\(171\) 366567.i 0.958657i
\(172\) 0 0
\(173\) 371065. 0.942617 0.471308 0.881969i \(-0.343782\pi\)
0.471308 + 0.881969i \(0.343782\pi\)
\(174\) 0 0
\(175\) −468828. 531327.i −1.15723 1.31150i
\(176\) 0 0
\(177\) 759394.i 1.82194i
\(178\) 0 0
\(179\) 550467.i 1.28410i 0.766662 + 0.642050i \(0.221916\pi\)
−0.766662 + 0.642050i \(0.778084\pi\)
\(180\) 0 0
\(181\) 151958.i 0.344768i 0.985030 + 0.172384i \(0.0551470\pi\)
−0.985030 + 0.172384i \(0.944853\pi\)
\(182\) 0 0
\(183\) 225547.i 0.497861i
\(184\) 0 0
\(185\) −58224.0 153987.i −0.125076 0.330791i
\(186\) 0 0
\(187\) 160021. 0.334636
\(188\) 0 0
\(189\) 495834.i 1.00968i
\(190\) 0 0
\(191\) 361650. 0.717308 0.358654 0.933471i \(-0.383236\pi\)
0.358654 + 0.933471i \(0.383236\pi\)
\(192\) 0 0
\(193\) 721956.i 1.39514i −0.716518 0.697569i \(-0.754265\pi\)
0.716518 0.697569i \(-0.245735\pi\)
\(194\) 0 0
\(195\) −206341. 545716.i −0.388597 1.02773i
\(196\) 0 0
\(197\) 225516. 0.414011 0.207006 0.978340i \(-0.433628\pi\)
0.207006 + 0.978340i \(0.433628\pi\)
\(198\) 0 0
\(199\) 39098.4 0.0699884 0.0349942 0.999388i \(-0.488859\pi\)
0.0349942 + 0.999388i \(0.488859\pi\)
\(200\) 0 0
\(201\) 1.34527e6 2.34866
\(202\) 0 0
\(203\) −1.21402e6 −2.06769
\(204\) 0 0
\(205\) 38983.7 + 103101.i 0.0647886 + 0.171348i
\(206\) 0 0
\(207\) 196061.i 0.318028i
\(208\) 0 0
\(209\) 1.50689e6 2.38624
\(210\) 0 0
\(211\) 218246.i 0.337474i −0.985661 0.168737i \(-0.946031\pi\)
0.985661 0.168737i \(-0.0539688\pi\)
\(212\) 0 0
\(213\) −1.44560e6 −2.18324
\(214\) 0 0
\(215\) −181430. 479832.i −0.267678 0.707934i
\(216\) 0 0
\(217\) 576401.i 0.830951i
\(218\) 0 0
\(219\) 1.10828e6i 1.56150i
\(220\) 0 0
\(221\) 162196.i 0.223388i
\(222\) 0 0
\(223\) 169634.i 0.228429i 0.993456 + 0.114214i \(0.0364350\pi\)
−0.993456 + 0.114214i \(0.963565\pi\)
\(224\) 0 0
\(225\) −304004. + 268244.i −0.400334 + 0.353243i
\(226\) 0 0
\(227\) −1.00025e6 −1.28839 −0.644193 0.764863i \(-0.722807\pi\)
−0.644193 + 0.764863i \(0.722807\pi\)
\(228\) 0 0
\(229\) 642993.i 0.810247i 0.914262 + 0.405124i \(0.132772\pi\)
−0.914262 + 0.405124i \(0.867228\pi\)
\(230\) 0 0
\(231\) −2.33476e6 −2.87881
\(232\) 0 0
\(233\) 853190.i 1.02957i −0.857319 0.514785i \(-0.827872\pi\)
0.857319 0.514785i \(-0.172128\pi\)
\(234\) 0 0
\(235\) −425724. + 160971.i −0.502873 + 0.190142i
\(236\) 0 0
\(237\) −813292. −0.940536
\(238\) 0 0
\(239\) 138181. 0.156478 0.0782389 0.996935i \(-0.475070\pi\)
0.0782389 + 0.996935i \(0.475070\pi\)
\(240\) 0 0
\(241\) −208470. −0.231207 −0.115604 0.993295i \(-0.536880\pi\)
−0.115604 + 0.993295i \(0.536880\pi\)
\(242\) 0 0
\(243\) 892354. 0.969441
\(244\) 0 0
\(245\) 684250. + 1.80965e6i 0.728282 + 1.92611i
\(246\) 0 0
\(247\) 1.52737e6i 1.59295i
\(248\) 0 0
\(249\) 51258.9 0.0523927
\(250\) 0 0
\(251\) 537488.i 0.538499i 0.963071 + 0.269249i \(0.0867756\pi\)
−0.963071 + 0.269249i \(0.913224\pi\)
\(252\) 0 0
\(253\) 805970. 0.791621
\(254\) 0 0
\(255\) −302896. + 114528.i −0.291704 + 0.110296i
\(256\) 0 0
\(257\) 516235.i 0.487545i 0.969832 + 0.243772i \(0.0783850\pi\)
−0.969832 + 0.243772i \(0.921615\pi\)
\(258\) 0 0
\(259\) 667766.i 0.618550i
\(260\) 0 0
\(261\) 694613.i 0.631163i
\(262\) 0 0
\(263\) 43960.1i 0.0391894i −0.999808 0.0195947i \(-0.993762\pi\)
0.999808 0.0195947i \(-0.00623759\pi\)
\(264\) 0 0
\(265\) 507009. + 1.34090e6i 0.443507 + 1.17296i
\(266\) 0 0
\(267\) −279297. −0.239766
\(268\) 0 0
\(269\) 2.17299e6i 1.83095i −0.402376 0.915475i \(-0.631815\pi\)
0.402376 0.915475i \(-0.368185\pi\)
\(270\) 0 0
\(271\) 1.99442e6 1.64965 0.824826 0.565386i \(-0.191273\pi\)
0.824826 + 0.565386i \(0.191273\pi\)
\(272\) 0 0
\(273\) 2.36650e6i 1.92177i
\(274\) 0 0
\(275\) 1.10270e6 + 1.24970e6i 0.879277 + 0.996493i
\(276\) 0 0
\(277\) 2.13008e6 1.66800 0.834002 0.551761i \(-0.186044\pi\)
0.834002 + 0.551761i \(0.186044\pi\)
\(278\) 0 0
\(279\) −329793. −0.253648
\(280\) 0 0
\(281\) 541626. 0.409198 0.204599 0.978846i \(-0.434411\pi\)
0.204599 + 0.978846i \(0.434411\pi\)
\(282\) 0 0
\(283\) 1.41618e6 1.05112 0.525560 0.850757i \(-0.323856\pi\)
0.525560 + 0.850757i \(0.323856\pi\)
\(284\) 0 0
\(285\) −2.85232e6 + 1.07849e6i −2.08011 + 0.786510i
\(286\) 0 0
\(287\) 447100.i 0.320406i
\(288\) 0 0
\(289\) 1.32983e6 0.936595
\(290\) 0 0
\(291\) 1.87735e6i 1.29961i
\(292\) 0 0
\(293\) −546813. −0.372109 −0.186054 0.982539i \(-0.559570\pi\)
−0.186054 + 0.982539i \(0.559570\pi\)
\(294\) 0 0
\(295\) −2.05671e6 + 777665.i −1.37600 + 0.520281i
\(296\) 0 0
\(297\) 1.16622e6i 0.767166i
\(298\) 0 0
\(299\) 816927.i 0.528451i
\(300\) 0 0
\(301\) 2.08080e6i 1.32377i
\(302\) 0 0
\(303\) 1.63085e6i 1.02048i
\(304\) 0 0
\(305\) −610861. + 230973.i −0.376005 + 0.142171i
\(306\) 0 0
\(307\) −1.16103e6 −0.703067 −0.351533 0.936175i \(-0.614340\pi\)
−0.351533 + 0.936175i \(0.614340\pi\)
\(308\) 0 0
\(309\) 3.47554e6i 2.07074i
\(310\) 0 0
\(311\) −1.56419e6 −0.917041 −0.458521 0.888684i \(-0.651620\pi\)
−0.458521 + 0.888684i \(0.651620\pi\)
\(312\) 0 0
\(313\) 2.79472e6i 1.61242i 0.591630 + 0.806209i \(0.298485\pi\)
−0.591630 + 0.806209i \(0.701515\pi\)
\(314\) 0 0
\(315\) 1.53823e6 581622.i 0.873465 0.330267i
\(316\) 0 0
\(317\) −2.09586e6 −1.17142 −0.585712 0.810519i \(-0.699185\pi\)
−0.585712 + 0.810519i \(0.699185\pi\)
\(318\) 0 0
\(319\) 2.85542e6 1.57106
\(320\) 0 0
\(321\) −712308. −0.385838
\(322\) 0 0
\(323\) −847757. −0.452132
\(324\) 0 0
\(325\) 1.26669e6 1.11769e6i 0.665215 0.586967i
\(326\) 0 0
\(327\) 2.44129e6i 1.26255i
\(328\) 0 0
\(329\) 1.84616e6 0.940328
\(330\) 0 0
\(331\) 748106.i 0.375312i −0.982235 0.187656i \(-0.939911\pi\)
0.982235 0.187656i \(-0.0600891\pi\)
\(332\) 0 0
\(333\) 382068. 0.188812
\(334\) 0 0
\(335\) 1.37764e6 + 3.64348e6i 0.670692 + 1.77380i
\(336\) 0 0
\(337\) 1.65588e6i 0.794244i −0.917766 0.397122i \(-0.870009\pi\)
0.917766 0.397122i \(-0.129991\pi\)
\(338\) 0 0
\(339\) 3.00968e6i 1.42240i
\(340\) 0 0
\(341\) 1.35572e6i 0.631368i
\(342\) 0 0
\(343\) 4.03659e6i 1.85259i
\(344\) 0 0
\(345\) −1.52558e6 + 576839.i −0.690062 + 0.260920i
\(346\) 0 0
\(347\) −1.38459e6 −0.617301 −0.308651 0.951175i \(-0.599877\pi\)
−0.308651 + 0.951175i \(0.599877\pi\)
\(348\) 0 0
\(349\) 1.99067e6i 0.874853i −0.899254 0.437426i \(-0.855890\pi\)
0.899254 0.437426i \(-0.144110\pi\)
\(350\) 0 0
\(351\) −1.18207e6 −0.512126
\(352\) 0 0
\(353\) 2.93425e6i 1.25332i −0.779294 0.626658i \(-0.784422\pi\)
0.779294 0.626658i \(-0.215578\pi\)
\(354\) 0 0
\(355\) −1.48039e6 3.91522e6i −0.623454 1.64887i
\(356\) 0 0
\(357\) 1.31351e6 0.545460
\(358\) 0 0
\(359\) −89539.5 −0.0366673 −0.0183336 0.999832i \(-0.505836\pi\)
−0.0183336 + 0.999832i \(0.505836\pi\)
\(360\) 0 0
\(361\) −5.50708e6 −2.22410
\(362\) 0 0
\(363\) 2.38213e6 0.948853
\(364\) 0 0
\(365\) −3.00163e6 + 1.13495e6i −1.17930 + 0.445907i
\(366\) 0 0
\(367\) 52253.3i 0.0202511i 0.999949 + 0.0101256i \(0.00322312\pi\)
−0.999949 + 0.0101256i \(0.996777\pi\)
\(368\) 0 0
\(369\) −255812. −0.0978038
\(370\) 0 0
\(371\) 5.81483e6i 2.19332i
\(372\) 0 0
\(373\) 2.64065e6 0.982740 0.491370 0.870951i \(-0.336496\pi\)
0.491370 + 0.870951i \(0.336496\pi\)
\(374\) 0 0
\(375\) −2.98167e6 1.57629e6i −1.09492 0.578838i
\(376\) 0 0
\(377\) 2.89424e6i 1.04877i
\(378\) 0 0
\(379\) 848415.i 0.303396i 0.988427 + 0.151698i \(0.0484742\pi\)
−0.988427 + 0.151698i \(0.951526\pi\)
\(380\) 0 0
\(381\) 2.80016e6i 0.988258i
\(382\) 0 0
\(383\) 4.92606e6i 1.71594i −0.513698 0.857971i \(-0.671725\pi\)
0.513698 0.857971i \(-0.328275\pi\)
\(384\) 0 0
\(385\) −2.39094e6 6.32338e6i −0.822084 2.17419i
\(386\) 0 0
\(387\) 1.19055e6 0.404082
\(388\) 0 0
\(389\) 2.26748e6i 0.759749i 0.925038 + 0.379874i \(0.124033\pi\)
−0.925038 + 0.379874i \(0.875967\pi\)
\(390\) 0 0
\(391\) −453429. −0.149992
\(392\) 0 0
\(393\) 2.78484e6i 0.909535i
\(394\) 0 0
\(395\) −832860. 2.20269e6i −0.268583 0.710330i
\(396\) 0 0
\(397\) −184998. −0.0589103 −0.0294552 0.999566i \(-0.509377\pi\)
−0.0294552 + 0.999566i \(0.509377\pi\)
\(398\) 0 0
\(399\) 1.23691e7 3.88961
\(400\) 0 0
\(401\) 3.28234e6 1.01935 0.509675 0.860367i \(-0.329766\pi\)
0.509675 + 0.860367i \(0.329766\pi\)
\(402\) 0 0
\(403\) 1.37415e6 0.421473
\(404\) 0 0
\(405\) 1.45798e6 + 3.85595e6i 0.441685 + 1.16814i
\(406\) 0 0
\(407\) 1.57061e6i 0.469983i
\(408\) 0 0
\(409\) 20416.4 0.00603491 0.00301745 0.999995i \(-0.499040\pi\)
0.00301745 + 0.999995i \(0.499040\pi\)
\(410\) 0 0
\(411\) 6.13008e6i 1.79003i
\(412\) 0 0
\(413\) 8.91897e6 2.57300
\(414\) 0 0
\(415\) 52492.2 + 138828.i 0.0149615 + 0.0395690i
\(416\) 0 0
\(417\) 3.64295e6i 1.02592i
\(418\) 0 0
\(419\) 1.02946e6i 0.286468i −0.989689 0.143234i \(-0.954250\pi\)
0.989689 0.143234i \(-0.0457502\pi\)
\(420\) 0 0
\(421\) 205645.i 0.0565474i −0.999600 0.0282737i \(-0.990999\pi\)
0.999600 0.0282737i \(-0.00900100\pi\)
\(422\) 0 0
\(423\) 1.05630e6i 0.287035i
\(424\) 0 0
\(425\) −620367. 703067.i −0.166600 0.188810i
\(426\) 0 0
\(427\) 2.64901e6 0.703094
\(428\) 0 0
\(429\) 5.56610e6i 1.46018i
\(430\) 0 0
\(431\) −2.60103e6 −0.674455 −0.337227 0.941423i \(-0.609489\pi\)
−0.337227 + 0.941423i \(0.609489\pi\)
\(432\) 0 0
\(433\) 2.78929e6i 0.714948i −0.933923 0.357474i \(-0.883638\pi\)
0.933923 0.357474i \(-0.116362\pi\)
\(434\) 0 0
\(435\) −5.40489e6 + 2.04365e6i −1.36951 + 0.517825i
\(436\) 0 0
\(437\) −4.26986e6 −1.06957
\(438\) 0 0
\(439\) 3.77670e6 0.935301 0.467651 0.883913i \(-0.345101\pi\)
0.467651 + 0.883913i \(0.345101\pi\)
\(440\) 0 0
\(441\) −4.49007e6 −1.09940
\(442\) 0 0
\(443\) −2.17639e6 −0.526899 −0.263449 0.964673i \(-0.584860\pi\)
−0.263449 + 0.964673i \(0.584860\pi\)
\(444\) 0 0
\(445\) −286017. 756436.i −0.0684686 0.181081i
\(446\) 0 0
\(447\) 6.42540e6i 1.52101i
\(448\) 0 0
\(449\) −7.28951e6 −1.70641 −0.853204 0.521578i \(-0.825344\pi\)
−0.853204 + 0.521578i \(0.825344\pi\)
\(450\) 0 0
\(451\) 1.05160e6i 0.243449i
\(452\) 0 0
\(453\) 1.12009e6 0.256454
\(454\) 0 0
\(455\) −6.40935e6 + 2.42344e6i −1.45139 + 0.548787i
\(456\) 0 0
\(457\) 2.29557e6i 0.514162i −0.966390 0.257081i \(-0.917239\pi\)
0.966390 0.257081i \(-0.0827608\pi\)
\(458\) 0 0
\(459\) 656102.i 0.145358i
\(460\) 0 0
\(461\) 728492.i 0.159651i 0.996809 + 0.0798256i \(0.0254363\pi\)
−0.996809 + 0.0798256i \(0.974564\pi\)
\(462\) 0 0
\(463\) 5.59971e6i 1.21398i 0.794708 + 0.606992i \(0.207624\pi\)
−0.794708 + 0.606992i \(0.792376\pi\)
\(464\) 0 0
\(465\) −970296. 2.56617e6i −0.208100 0.550368i
\(466\) 0 0
\(467\) 4.92150e6 1.04425 0.522126 0.852868i \(-0.325139\pi\)
0.522126 + 0.852868i \(0.325139\pi\)
\(468\) 0 0
\(469\) 1.58000e7i 3.31684i
\(470\) 0 0
\(471\) −812347. −0.168729
\(472\) 0 0
\(473\) 4.89411e6i 1.00582i
\(474\) 0 0
\(475\) −5.84188e6 6.62066e6i −1.18801 1.34638i
\(476\) 0 0
\(477\) −3.32701e6 −0.669511
\(478\) 0 0
\(479\) 8.31194e6 1.65525 0.827625 0.561281i \(-0.189691\pi\)
0.827625 + 0.561281i \(0.189691\pi\)
\(480\) 0 0
\(481\) −1.59196e6 −0.313740
\(482\) 0 0
\(483\) 6.61571e6 1.29035
\(484\) 0 0
\(485\) −5.08454e6 + 1.92252e6i −0.981516 + 0.371122i
\(486\) 0 0
\(487\) 7.86871e6i 1.50342i 0.659493 + 0.751711i \(0.270771\pi\)
−0.659493 + 0.751711i \(0.729229\pi\)
\(488\) 0 0
\(489\) 1.00891e7 1.90800
\(490\) 0 0
\(491\) 8.53923e6i 1.59851i 0.600993 + 0.799254i \(0.294772\pi\)
−0.600993 + 0.799254i \(0.705228\pi\)
\(492\) 0 0
\(493\) −1.60643e6 −0.297676
\(494\) 0 0
\(495\) −3.61798e6 + 1.36800e6i −0.663671 + 0.250941i
\(496\) 0 0
\(497\) 1.69784e7i 3.08323i
\(498\) 0 0
\(499\) 6.12241e6i 1.10070i −0.834933 0.550352i \(-0.814493\pi\)
0.834933 0.550352i \(-0.185507\pi\)
\(500\) 0 0
\(501\) 1.91592e6i 0.341023i
\(502\) 0 0
\(503\) 8.42810e6i 1.48528i −0.669689 0.742642i \(-0.733572\pi\)
0.669689 0.742642i \(-0.266428\pi\)
\(504\) 0 0
\(505\) −4.41692e6 + 1.67008e6i −0.770710 + 0.291414i
\(506\) 0 0
\(507\) 1.52656e6 0.263752
\(508\) 0 0
\(509\) 1.64869e6i 0.282062i −0.990005 0.141031i \(-0.954958\pi\)
0.990005 0.141031i \(-0.0450417\pi\)
\(510\) 0 0
\(511\) 1.30166e7 2.20519
\(512\) 0 0
\(513\) 6.17840e6i 1.03653i
\(514\) 0 0
\(515\) 9.41300e6 3.55916e6i 1.56390 0.591329i
\(516\) 0 0
\(517\) −4.34223e6 −0.714474
\(518\) 0 0
\(519\) −7.16394e6 −1.16744
\(520\) 0 0
\(521\) −3.34886e6 −0.540509 −0.270255 0.962789i \(-0.587108\pi\)
−0.270255 + 0.962789i \(0.587108\pi\)
\(522\) 0 0
\(523\) 4.84532e6 0.774583 0.387292 0.921957i \(-0.373411\pi\)
0.387292 + 0.921957i \(0.373411\pi\)
\(524\) 0 0
\(525\) 9.05139e6 + 1.02580e7i 1.43323 + 1.62430i
\(526\) 0 0
\(527\) 762710.i 0.119628i
\(528\) 0 0
\(529\) 4.15257e6 0.645176
\(530\) 0 0
\(531\) 5.10307e6i 0.785407i
\(532\) 0 0
\(533\) 1.06589e6 0.162516
\(534\) 0 0
\(535\) −729446. 1.92919e6i −0.110182 0.291400i
\(536\) 0 0
\(537\) 1.06276e7i 1.59037i
\(538\) 0 0
\(539\) 1.84578e7i 2.73658i
\(540\) 0 0
\(541\) 1.00573e7i 1.47737i 0.674053 + 0.738683i \(0.264552\pi\)
−0.674053 + 0.738683i \(0.735448\pi\)
\(542\) 0 0
\(543\) 2.93376e6i 0.426998i
\(544\) 0 0
\(545\) −6.61189e6 + 2.50003e6i −0.953530 + 0.360540i
\(546\) 0 0
\(547\) 2.20875e6 0.315630 0.157815 0.987469i \(-0.449555\pi\)
0.157815 + 0.987469i \(0.449555\pi\)
\(548\) 0 0
\(549\) 1.51565e6i 0.214620i
\(550\) 0 0
\(551\) −1.51274e7 −2.12269
\(552\) 0 0
\(553\) 9.55198e6i 1.32825i
\(554\) 0 0
\(555\) 1.12410e6 + 2.97293e6i 0.154907 + 0.409687i
\(556\) 0 0
\(557\) 9.18396e6 1.25427 0.627136 0.778909i \(-0.284227\pi\)
0.627136 + 0.778909i \(0.284227\pi\)
\(558\) 0 0
\(559\) −4.96065e6 −0.671442
\(560\) 0 0
\(561\) −3.08942e6 −0.414448
\(562\) 0 0
\(563\) −1.10566e7 −1.47011 −0.735054 0.678009i \(-0.762843\pi\)
−0.735054 + 0.678009i \(0.762843\pi\)
\(564\) 0 0
\(565\) −8.15129e6 + 3.08209e6i −1.07425 + 0.406185i
\(566\) 0 0
\(567\) 1.67214e7i 2.18431i
\(568\) 0 0
\(569\) 1.00197e7 1.29740 0.648699 0.761045i \(-0.275314\pi\)
0.648699 + 0.761045i \(0.275314\pi\)
\(570\) 0 0
\(571\) 5.44283e6i 0.698609i −0.937009 0.349305i \(-0.886418\pi\)
0.937009 0.349305i \(-0.113582\pi\)
\(572\) 0 0
\(573\) −6.98217e6 −0.888390
\(574\) 0 0
\(575\) −3.12458e6 3.54111e6i −0.394114 0.446652i
\(576\) 0 0
\(577\) 1.03799e6i 0.129793i −0.997892 0.0648967i \(-0.979328\pi\)
0.997892 0.0648967i \(-0.0206718\pi\)
\(578\) 0 0
\(579\) 1.39384e7i 1.72789i
\(580\) 0 0
\(581\) 602028.i 0.0739905i
\(582\) 0 0
\(583\) 1.36767e7i 1.66652i
\(584\) 0 0
\(585\) 1.38659e6 + 3.66716e6i 0.167517 + 0.443038i
\(586\) 0 0
\(587\) −4.01891e6 −0.481407 −0.240704 0.970599i \(-0.577378\pi\)
−0.240704 + 0.970599i \(0.577378\pi\)
\(588\) 0 0
\(589\) 7.18230e6i 0.853052i
\(590\) 0 0
\(591\) −4.35391e6 −0.512755
\(592\) 0 0
\(593\) 9.73063e6i 1.13633i −0.822915 0.568165i \(-0.807654\pi\)
0.822915 0.568165i \(-0.192346\pi\)
\(594\) 0 0
\(595\) 1.34511e6 + 3.55746e6i 0.155764 + 0.411953i
\(596\) 0 0
\(597\) −754849. −0.0866811
\(598\) 0 0
\(599\) 1.50621e7 1.71522 0.857609 0.514301i \(-0.171949\pi\)
0.857609 + 0.514301i \(0.171949\pi\)
\(600\) 0 0
\(601\) 6.76656e6 0.764156 0.382078 0.924130i \(-0.375209\pi\)
0.382078 + 0.924130i \(0.375209\pi\)
\(602\) 0 0
\(603\) −9.04011e6 −1.01247
\(604\) 0 0
\(605\) 2.43944e6 + 6.45167e6i 0.270958 + 0.716611i
\(606\) 0 0
\(607\) 787439.i 0.0867451i −0.999059 0.0433726i \(-0.986190\pi\)
0.999059 0.0433726i \(-0.0138102\pi\)
\(608\) 0 0
\(609\) 2.34384e7 2.56085
\(610\) 0 0
\(611\) 4.40126e6i 0.476952i
\(612\) 0 0
\(613\) −1.14982e7 −1.23588 −0.617942 0.786224i \(-0.712033\pi\)
−0.617942 + 0.786224i \(0.712033\pi\)
\(614\) 0 0
\(615\) −752636. 1.99052e6i −0.0802411 0.212216i
\(616\) 0 0
\(617\) 1.15286e7i 1.21917i −0.792720 0.609586i \(-0.791336\pi\)
0.792720 0.609586i \(-0.208664\pi\)
\(618\) 0 0
\(619\) 1.23282e7i 1.29323i −0.762819 0.646613i \(-0.776185\pi\)
0.762819 0.646613i \(-0.223815\pi\)
\(620\) 0 0
\(621\) 3.30456e6i 0.343863i
\(622\) 0 0
\(623\) 3.28029e6i 0.338605i
\(624\) 0 0
\(625\) 1.21574e6 9.68965e6i 0.124492 0.992221i
\(626\) 0 0
\(627\) −2.90926e7 −2.95538
\(628\) 0 0
\(629\) 883606.i 0.0890497i
\(630\) 0 0
\(631\) −1.55376e7 −1.55350 −0.776749 0.629810i \(-0.783133\pi\)
−0.776749 + 0.629810i \(0.783133\pi\)
\(632\) 0 0
\(633\) 4.21355e6i 0.417964i
\(634\) 0 0
\(635\) 7.58384e6 2.86753e6i 0.746371 0.282211i
\(636\) 0 0
\(637\) 1.87087e7 1.82682
\(638\) 0 0
\(639\) 9.71434e6 0.941155
\(640\) 0 0
\(641\) 1.69129e7 1.62582 0.812910 0.582389i \(-0.197882\pi\)
0.812910 + 0.582389i \(0.197882\pi\)
\(642\) 0 0
\(643\) −451136. −0.0430309 −0.0215154 0.999769i \(-0.506849\pi\)
−0.0215154 + 0.999769i \(0.506849\pi\)
\(644\) 0 0
\(645\) 3.50275e6 + 9.26383e6i 0.331521 + 0.876782i
\(646\) 0 0
\(647\) 2.24615e6i 0.210949i −0.994422 0.105475i \(-0.966364\pi\)
0.994422 0.105475i \(-0.0336362\pi\)
\(648\) 0 0
\(649\) −2.09777e7 −1.95500
\(650\) 0 0
\(651\) 1.11282e7i 1.02914i
\(652\) 0 0
\(653\) −1.66966e7 −1.53230 −0.766151 0.642660i \(-0.777831\pi\)
−0.766151 + 0.642660i \(0.777831\pi\)
\(654\) 0 0
\(655\) −7.54236e6 + 2.85185e6i −0.686916 + 0.259730i
\(656\) 0 0
\(657\) 7.44757e6i 0.673134i
\(658\) 0 0
\(659\) 1.16732e7i 1.04708i 0.852002 + 0.523538i \(0.175388\pi\)
−0.852002 + 0.523538i \(0.824612\pi\)
\(660\) 0 0
\(661\) 699962.i 0.0623118i 0.999515 + 0.0311559i \(0.00991884\pi\)
−0.999515 + 0.0311559i \(0.990081\pi\)
\(662\) 0 0
\(663\) 3.13142e6i 0.276668i
\(664\) 0 0
\(665\) 1.26667e7 + 3.35000e7i 1.11073 + 2.93759i
\(666\) 0 0
\(667\) −8.09102e6 −0.704188
\(668\) 0 0
\(669\) 3.27502e6i 0.282910i
\(670\) 0 0
\(671\) −6.23056e6 −0.534221
\(672\) 0 0
\(673\) 7.73374e6i 0.658191i −0.944297 0.329096i \(-0.893256\pi\)
0.944297 0.329096i \(-0.106744\pi\)
\(674\) 0 0
\(675\) −5.12391e6 + 4.52119e6i −0.432854 + 0.381938i
\(676\) 0 0
\(677\) 1.12616e6 0.0944337 0.0472169 0.998885i \(-0.484965\pi\)
0.0472169 + 0.998885i \(0.484965\pi\)
\(678\) 0 0
\(679\) 2.20492e7 1.83535
\(680\) 0 0
\(681\) 1.93113e7 1.59567
\(682\) 0 0
\(683\) −1.30937e7 −1.07402 −0.537009 0.843577i \(-0.680446\pi\)
−0.537009 + 0.843577i \(0.680446\pi\)
\(684\) 0 0
\(685\) 1.66025e7 6.27757e6i 1.35190 0.511170i
\(686\) 0 0
\(687\) 1.24139e7i 1.00350i
\(688\) 0 0
\(689\) 1.38626e7 1.11249
\(690\) 0 0
\(691\) 1.11322e6i 0.0886923i −0.999016 0.0443461i \(-0.985880\pi\)
0.999016 0.0443461i \(-0.0141204\pi\)
\(692\) 0 0
\(693\) 1.56894e7 1.24100
\(694\) 0 0
\(695\) −9.86642e6 + 3.73060e6i −0.774814 + 0.292966i
\(696\) 0 0
\(697\) 591616.i 0.0461273i
\(698\) 0 0
\(699\) 1.64720e7i 1.27513i
\(700\) 0 0
\(701\) 1.36127e7i 1.04629i 0.852245 + 0.523143i \(0.175241\pi\)
−0.852245 + 0.523143i \(0.824759\pi\)
\(702\) 0 0
\(703\) 8.32077e6i 0.635002i
\(704\) 0 0
\(705\) 8.21921e6 3.10777e6i 0.622812 0.235492i
\(706\) 0 0
\(707\) 1.91540e7 1.44116
\(708\) 0 0
\(709\) 2.49344e6i 0.186288i −0.995653 0.0931438i \(-0.970308\pi\)
0.995653 0.0931438i \(-0.0296916\pi\)
\(710\) 0 0
\(711\) 5.46525e6 0.405449
\(712\) 0 0
\(713\) 3.84151e6i 0.282995i
\(714\) 0 0
\(715\) 1.50750e7 5.70002e6i 1.10279 0.416976i
\(716\) 0 0
\(717\) −2.66777e6 −0.193799
\(718\) 0 0
\(719\) −8.87181e6 −0.640015 −0.320008 0.947415i \(-0.603685\pi\)
−0.320008 + 0.947415i \(0.603685\pi\)
\(720\) 0 0
\(721\) −4.08196e7 −2.92436
\(722\) 0 0
\(723\) 4.02481e6 0.286352
\(724\) 0 0
\(725\) −1.10699e7 1.25456e7i −0.782163 0.886432i
\(726\) 0 0
\(727\) 2.19342e7i 1.53917i −0.638545 0.769585i \(-0.720463\pi\)
0.638545 0.769585i \(-0.279537\pi\)
\(728\) 0 0
\(729\) 691498. 0.0481917
\(730\) 0 0
\(731\) 2.75337e6i 0.190577i
\(732\) 0 0
\(733\) −2.46781e7 −1.69649 −0.848246 0.529602i \(-0.822341\pi\)
−0.848246 + 0.529602i \(0.822341\pi\)
\(734\) 0 0
\(735\) −1.32104e7 3.49379e7i −0.901982 2.38550i
\(736\) 0 0
\(737\) 3.71622e7i 2.52018i
\(738\) 0 0
\(739\) 1.01741e7i 0.685310i 0.939461 + 0.342655i \(0.111326\pi\)
−0.939461 + 0.342655i \(0.888674\pi\)
\(740\) 0 0
\(741\) 2.94881e7i 1.97288i
\(742\) 0 0
\(743\) 1.62520e7i 1.08003i 0.841657 + 0.540013i \(0.181581\pi\)
−0.841657 + 0.540013i \(0.818419\pi\)
\(744\) 0 0
\(745\) −1.74023e7 + 6.57999e6i −1.14872 + 0.434345i
\(746\) 0 0
\(747\) −344455. −0.0225856
\(748\) 0 0
\(749\) 8.36595e6i 0.544892i
\(750\) 0 0
\(751\) −4.07295e6 −0.263517 −0.131759 0.991282i \(-0.542062\pi\)
−0.131759 + 0.991282i \(0.542062\pi\)
\(752\) 0 0
\(753\) 1.03770e7i 0.666934i
\(754\) 0 0
\(755\) 1.14704e6 + 3.03362e6i 0.0732339 + 0.193684i
\(756\) 0 0
\(757\) −2.59518e6 −0.164599 −0.0822996 0.996608i \(-0.526226\pi\)
−0.0822996 + 0.996608i \(0.526226\pi\)
\(758\) 0 0
\(759\) −1.55604e7 −0.980428
\(760\) 0 0
\(761\) −3.27320e6 −0.204885 −0.102443 0.994739i \(-0.532666\pi\)
−0.102443 + 0.994739i \(0.532666\pi\)
\(762\) 0 0
\(763\) 2.86725e7 1.78301
\(764\) 0 0
\(765\) 2.03543e6 769619.i 0.125749 0.0475469i
\(766\) 0 0
\(767\) 2.12629e7i 1.30507i
\(768\) 0 0
\(769\) −3.06637e6 −0.186986 −0.0934930 0.995620i \(-0.529803\pi\)
−0.0934930 + 0.995620i \(0.529803\pi\)
\(770\) 0 0
\(771\) 9.96664e6i 0.603827i
\(772\) 0 0
\(773\) 8.35882e6 0.503149 0.251574 0.967838i \(-0.419052\pi\)
0.251574 + 0.967838i \(0.419052\pi\)
\(774\) 0 0
\(775\) 5.95647e6 5.25582e6i 0.356234 0.314331i
\(776\) 0 0
\(777\) 1.28922e7i 0.766078i
\(778\) 0 0
\(779\) 5.57114e6i 0.328928i
\(780\) 0 0
\(781\) 3.99338e7i 2.34268i
\(782\) 0 0
\(783\) 1.17075e7i 0.682434i
\(784\) 0 0
\(785\) −831893. 2.20013e6i −0.0481829 0.127431i
\(786\) 0 0
\(787\) 2.90786e7 1.67354 0.836771 0.547552i \(-0.184440\pi\)
0.836771 + 0.547552i \(0.184440\pi\)
\(788\) 0 0
\(789\) 848711.i 0.0485364i
\(790\) 0 0
\(791\) 3.53482e7 2.00875
\(792\) 0 0
\(793\) 6.31527e6i 0.356622i
\(794\) 0 0