Properties

Label 720.6.f.g.289.1
Level $720$
Weight $6$
Character 720.289
Analytic conductor $115.476$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(115.476350265\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 720.289
Dual form 720.6.f.g.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(55.0000 - 10.0000i) q^{5} +4.00000i q^{7} +O(q^{10})\) \(q+(55.0000 - 10.0000i) q^{5} +4.00000i q^{7} -500.000 q^{11} +288.000i q^{13} -1516.00i q^{17} -1344.00 q^{19} +4100.00i q^{23} +(2925.00 - 1100.00i) q^{25} -2646.00 q^{29} +5612.00 q^{31} +(40.0000 + 220.000i) q^{35} -7288.00i q^{37} +18986.0 q^{41} -2404.00i q^{43} +8900.00i q^{47} +16791.0 q^{49} +39804.0i q^{53} +(-27500.0 + 5000.00i) q^{55} +28300.0 q^{59} +18290.0 q^{61} +(2880.00 + 15840.0i) q^{65} -65956.0i q^{67} -28800.0 q^{71} +30808.0i q^{73} -2000.00i q^{77} +60228.0 q^{79} +2468.00i q^{83} +(-15160.0 - 83380.0i) q^{85} +22678.0 q^{89} -1152.00 q^{91} +(-73920.0 + 13440.0i) q^{95} -36968.0i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 110q^{5} + O(q^{10}) \) \( 2q + 110q^{5} - 1000q^{11} - 2688q^{19} + 5850q^{25} - 5292q^{29} + 11224q^{31} + 80q^{35} + 37972q^{41} + 33582q^{49} - 55000q^{55} + 56600q^{59} + 36580q^{61} + 5760q^{65} - 57600q^{71} + 120456q^{79} - 30320q^{85} + 45356q^{89} - 2304q^{91} - 147840q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 55.0000 10.0000i 0.983870 0.178885i
\(6\) 0 0
\(7\) 4.00000i 0.0308542i 0.999881 + 0.0154271i \(0.00491080\pi\)
−0.999881 + 0.0154271i \(0.995089\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −500.000 −1.24591 −0.622957 0.782256i \(-0.714069\pi\)
−0.622957 + 0.782256i \(0.714069\pi\)
\(12\) 0 0
\(13\) 288.000i 0.472644i 0.971675 + 0.236322i \(0.0759420\pi\)
−0.971675 + 0.236322i \(0.924058\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1516.00i 1.27226i −0.771581 0.636132i \(-0.780534\pi\)
0.771581 0.636132i \(-0.219466\pi\)
\(18\) 0 0
\(19\) −1344.00 −0.854113 −0.427056 0.904225i \(-0.640449\pi\)
−0.427056 + 0.904225i \(0.640449\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4100.00i 1.61609i 0.589124 + 0.808043i \(0.299473\pi\)
−0.589124 + 0.808043i \(0.700527\pi\)
\(24\) 0 0
\(25\) 2925.00 1100.00i 0.936000 0.352000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2646.00 −0.584245 −0.292122 0.956381i \(-0.594361\pi\)
−0.292122 + 0.956381i \(0.594361\pi\)
\(30\) 0 0
\(31\) 5612.00 1.04885 0.524425 0.851457i \(-0.324280\pi\)
0.524425 + 0.851457i \(0.324280\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 40.0000 + 220.000i 0.00551937 + 0.0303566i
\(36\) 0 0
\(37\) 7288.00i 0.875193i −0.899171 0.437597i \(-0.855830\pi\)
0.899171 0.437597i \(-0.144170\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 18986.0 1.76390 0.881950 0.471343i \(-0.156231\pi\)
0.881950 + 0.471343i \(0.156231\pi\)
\(42\) 0 0
\(43\) 2404.00i 0.198273i −0.995074 0.0991364i \(-0.968392\pi\)
0.995074 0.0991364i \(-0.0316080\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8900.00i 0.587686i 0.955854 + 0.293843i \(0.0949343\pi\)
−0.955854 + 0.293843i \(0.905066\pi\)
\(48\) 0 0
\(49\) 16791.0 0.999048
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 39804.0i 1.94642i 0.229913 + 0.973211i \(0.426156\pi\)
−0.229913 + 0.973211i \(0.573844\pi\)
\(54\) 0 0
\(55\) −27500.0 + 5000.00i −1.22582 + 0.222876i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 28300.0 1.05842 0.529208 0.848492i \(-0.322489\pi\)
0.529208 + 0.848492i \(0.322489\pi\)
\(60\) 0 0
\(61\) 18290.0 0.629345 0.314673 0.949200i \(-0.398105\pi\)
0.314673 + 0.949200i \(0.398105\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2880.00 + 15840.0i 0.0845491 + 0.465020i
\(66\) 0 0
\(67\) 65956.0i 1.79501i −0.441002 0.897506i \(-0.645377\pi\)
0.441002 0.897506i \(-0.354623\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −28800.0 −0.678026 −0.339013 0.940782i \(-0.610093\pi\)
−0.339013 + 0.940782i \(0.610093\pi\)
\(72\) 0 0
\(73\) 30808.0i 0.676638i 0.941031 + 0.338319i \(0.109858\pi\)
−0.941031 + 0.338319i \(0.890142\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2000.00i 0.0384418i
\(78\) 0 0
\(79\) 60228.0 1.08575 0.542876 0.839813i \(-0.317335\pi\)
0.542876 + 0.839813i \(0.317335\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2468.00i 0.0393233i 0.999807 + 0.0196616i \(0.00625890\pi\)
−0.999807 + 0.0196616i \(0.993741\pi\)
\(84\) 0 0
\(85\) −15160.0 83380.0i −0.227589 1.25174i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 22678.0 0.303480 0.151740 0.988420i \(-0.451512\pi\)
0.151740 + 0.988420i \(0.451512\pi\)
\(90\) 0 0
\(91\) −1152.00 −0.0145831
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −73920.0 + 13440.0i −0.840336 + 0.152788i
\(96\) 0 0
\(97\) 36968.0i 0.398930i −0.979905 0.199465i \(-0.936080\pi\)
0.979905 0.199465i \(-0.0639204\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −167918. −1.63792 −0.818962 0.573848i \(-0.805450\pi\)
−0.818962 + 0.573848i \(0.805450\pi\)
\(102\) 0 0
\(103\) 154364.i 1.43368i −0.697236 0.716841i \(-0.745587\pi\)
0.697236 0.716841i \(-0.254413\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 136788.i 1.15502i 0.816385 + 0.577509i \(0.195975\pi\)
−0.816385 + 0.577509i \(0.804025\pi\)
\(108\) 0 0
\(109\) 53810.0 0.433807 0.216904 0.976193i \(-0.430404\pi\)
0.216904 + 0.976193i \(0.430404\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 82692.0i 0.609211i 0.952479 + 0.304605i \(0.0985245\pi\)
−0.952479 + 0.304605i \(0.901475\pi\)
\(114\) 0 0
\(115\) 41000.0 + 225500.i 0.289094 + 1.59002i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 6064.00 0.0392547
\(120\) 0 0
\(121\) 88949.0 0.552303
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 149875. 89750.0i 0.857935 0.513759i
\(126\) 0 0
\(127\) 211780.i 1.16513i 0.812783 + 0.582567i \(0.197952\pi\)
−0.812783 + 0.582567i \(0.802048\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 169500. 0.862962 0.431481 0.902122i \(-0.357991\pi\)
0.431481 + 0.902122i \(0.357991\pi\)
\(132\) 0 0
\(133\) 5376.00i 0.0263530i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 252036.i 1.14726i −0.819115 0.573629i \(-0.805535\pi\)
0.819115 0.573629i \(-0.194465\pi\)
\(138\) 0 0
\(139\) 192016. 0.842947 0.421474 0.906841i \(-0.361513\pi\)
0.421474 + 0.906841i \(0.361513\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 144000.i 0.588874i
\(144\) 0 0
\(145\) −145530. + 26460.0i −0.574821 + 0.104513i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 235694. 0.869727 0.434863 0.900496i \(-0.356797\pi\)
0.434863 + 0.900496i \(0.356797\pi\)
\(150\) 0 0
\(151\) 371492. 1.32589 0.662944 0.748669i \(-0.269307\pi\)
0.662944 + 0.748669i \(0.269307\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 308660. 56120.0i 1.03193 0.187624i
\(156\) 0 0
\(157\) 264952.i 0.857863i 0.903337 + 0.428932i \(0.141110\pi\)
−0.903337 + 0.428932i \(0.858890\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −16400.0 −0.0498631
\(162\) 0 0
\(163\) 403124.i 1.18842i −0.804310 0.594210i \(-0.797465\pi\)
0.804310 0.594210i \(-0.202535\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 261900.i 0.726682i −0.931656 0.363341i \(-0.881636\pi\)
0.931656 0.363341i \(-0.118364\pi\)
\(168\) 0 0
\(169\) 288349. 0.776608
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 326228.i 0.828716i 0.910114 + 0.414358i \(0.135994\pi\)
−0.910114 + 0.414358i \(0.864006\pi\)
\(174\) 0 0
\(175\) 4400.00 + 11700.0i 0.0108607 + 0.0288796i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 109516. 0.255473 0.127736 0.991808i \(-0.459229\pi\)
0.127736 + 0.991808i \(0.459229\pi\)
\(180\) 0 0
\(181\) −53146.0 −0.120580 −0.0602898 0.998181i \(-0.519202\pi\)
−0.0602898 + 0.998181i \(0.519202\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −72880.0 400840.i −0.156559 0.861076i
\(186\) 0 0
\(187\) 758000.i 1.58513i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 232056. 0.460267 0.230133 0.973159i \(-0.426084\pi\)
0.230133 + 0.973159i \(0.426084\pi\)
\(192\) 0 0
\(193\) 1.03067e6i 1.99172i 0.0909274 + 0.995858i \(0.471017\pi\)
−0.0909274 + 0.995858i \(0.528983\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 522796.i 0.959769i 0.877332 + 0.479884i \(0.159321\pi\)
−0.877332 + 0.479884i \(0.840679\pi\)
\(198\) 0 0
\(199\) −215292. −0.385385 −0.192693 0.981259i \(-0.561722\pi\)
−0.192693 + 0.981259i \(0.561722\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10584.0i 0.0180264i
\(204\) 0 0
\(205\) 1.04423e6 189860.i 1.73545 0.315536i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 672000. 1.06415
\(210\) 0 0
\(211\) 1.03008e6 1.59281 0.796407 0.604762i \(-0.206732\pi\)
0.796407 + 0.604762i \(0.206732\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −24040.0 132220.i −0.0354681 0.195075i
\(216\) 0 0
\(217\) 22448.0i 0.0323615i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 436608. 0.601327
\(222\) 0 0
\(223\) 456020.i 0.614075i 0.951697 + 0.307038i \(0.0993378\pi\)
−0.951697 + 0.307038i \(0.900662\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 434252.i 0.559342i −0.960096 0.279671i \(-0.909775\pi\)
0.960096 0.279671i \(-0.0902253\pi\)
\(228\) 0 0
\(229\) 722710. 0.910700 0.455350 0.890313i \(-0.349514\pi\)
0.455350 + 0.890313i \(0.349514\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 565348.i 0.682223i −0.940023 0.341111i \(-0.889197\pi\)
0.940023 0.341111i \(-0.110803\pi\)
\(234\) 0 0
\(235\) 89000.0 + 489500.i 0.105128 + 0.578207i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −324904. −0.367926 −0.183963 0.982933i \(-0.558893\pi\)
−0.183963 + 0.982933i \(0.558893\pi\)
\(240\) 0 0
\(241\) 915262. 1.01509 0.507543 0.861626i \(-0.330554\pi\)
0.507543 + 0.861626i \(0.330554\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 923505. 167910.i 0.982933 0.178715i
\(246\) 0 0
\(247\) 387072.i 0.403691i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.36708e6 1.36965 0.684823 0.728709i \(-0.259879\pi\)
0.684823 + 0.728709i \(0.259879\pi\)
\(252\) 0 0
\(253\) 2.05000e6i 2.01350i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 892932.i 0.843307i −0.906757 0.421653i \(-0.861450\pi\)
0.906757 0.421653i \(-0.138550\pi\)
\(258\) 0 0
\(259\) 29152.0 0.0270034
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.86650e6i 1.66394i 0.554818 + 0.831972i \(0.312788\pi\)
−0.554818 + 0.831972i \(0.687212\pi\)
\(264\) 0 0
\(265\) 398040. + 2.18922e6i 0.348187 + 1.91503i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.37227e6 −1.15627 −0.578133 0.815943i \(-0.696218\pi\)
−0.578133 + 0.815943i \(0.696218\pi\)
\(270\) 0 0
\(271\) −458644. −0.379361 −0.189680 0.981846i \(-0.560745\pi\)
−0.189680 + 0.981846i \(0.560745\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.46250e6 + 550000.i −1.16618 + 0.438562i
\(276\) 0 0
\(277\) 985408.i 0.771643i −0.922573 0.385822i \(-0.873918\pi\)
0.922573 0.385822i \(-0.126082\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −165798. −0.125260 −0.0626302 0.998037i \(-0.519949\pi\)
−0.0626302 + 0.998037i \(0.519949\pi\)
\(282\) 0 0
\(283\) 1.66471e6i 1.23558i −0.786342 0.617792i \(-0.788028\pi\)
0.786342 0.617792i \(-0.211972\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 75944.0i 0.0544238i
\(288\) 0 0
\(289\) −878399. −0.618653
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.55104e6i 1.73600i 0.496567 + 0.867998i \(0.334594\pi\)
−0.496567 + 0.867998i \(0.665406\pi\)
\(294\) 0 0
\(295\) 1.55650e6 283000.i 1.04134 0.189335i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.18080e6 −0.763833
\(300\) 0 0
\(301\) 9616.00 0.00611756
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.00595e6 182900.i 0.619194 0.112581i
\(306\) 0 0
\(307\) 736020.i 0.445701i −0.974853 0.222851i \(-0.928464\pi\)
0.974853 0.222851i \(-0.0715362\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.71660e6 1.00639 0.503197 0.864172i \(-0.332157\pi\)
0.503197 + 0.864172i \(0.332157\pi\)
\(312\) 0 0
\(313\) 2.83851e6i 1.63768i −0.574020 0.818842i \(-0.694617\pi\)
0.574020 0.818842i \(-0.305383\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.27605e6i 0.713215i 0.934254 + 0.356607i \(0.116067\pi\)
−0.934254 + 0.356607i \(0.883933\pi\)
\(318\) 0 0
\(319\) 1.32300e6 0.727919
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.03750e6i 1.08666i
\(324\) 0 0
\(325\) 316800. + 842400.i 0.166371 + 0.442395i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −35600.0 −0.0181326
\(330\) 0 0
\(331\) −443992. −0.222744 −0.111372 0.993779i \(-0.535524\pi\)
−0.111372 + 0.993779i \(0.535524\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −659560. 3.62758e6i −0.321101 1.76606i
\(336\) 0 0
\(337\) 2.71326e6i 1.30142i 0.759328 + 0.650708i \(0.225528\pi\)
−0.759328 + 0.650708i \(0.774472\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.80600e6 −1.30678
\(342\) 0 0
\(343\) 134392.i 0.0616791i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.31051e6i 0.584273i −0.956377 0.292137i \(-0.905634\pi\)
0.956377 0.292137i \(-0.0943662\pi\)
\(348\) 0 0
\(349\) 298910. 0.131364 0.0656821 0.997841i \(-0.479078\pi\)
0.0656821 + 0.997841i \(0.479078\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 737996.i 0.315223i 0.987501 + 0.157611i \(0.0503793\pi\)
−0.987501 + 0.157611i \(0.949621\pi\)
\(354\) 0 0
\(355\) −1.58400e6 + 288000.i −0.667090 + 0.121289i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.34074e6 0.958557 0.479278 0.877663i \(-0.340898\pi\)
0.479278 + 0.877663i \(0.340898\pi\)
\(360\) 0 0
\(361\) −669763. −0.270491
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 308080. + 1.69444e6i 0.121041 + 0.665724i
\(366\) 0 0
\(367\) 127292.i 0.0493328i −0.999696 0.0246664i \(-0.992148\pi\)
0.999696 0.0246664i \(-0.00785236\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −159216. −0.0600554
\(372\) 0 0
\(373\) 4.03870e6i 1.50303i −0.659713 0.751517i \(-0.729322\pi\)
0.659713 0.751517i \(-0.270678\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 762048.i 0.276140i
\(378\) 0 0
\(379\) 1.01214e6 0.361944 0.180972 0.983488i \(-0.442076\pi\)
0.180972 + 0.983488i \(0.442076\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.37610e6i 0.827690i 0.910347 + 0.413845i \(0.135814\pi\)
−0.910347 + 0.413845i \(0.864186\pi\)
\(384\) 0 0
\(385\) −20000.0 110000.i −0.00687667 0.0378217i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.42497e6 0.477456 0.238728 0.971087i \(-0.423270\pi\)
0.238728 + 0.971087i \(0.423270\pi\)
\(390\) 0 0
\(391\) 6.21560e6 2.05609
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.31254e6 602280.i 1.06824 0.194225i
\(396\) 0 0
\(397\) 1.69345e6i 0.539257i 0.962964 + 0.269628i \(0.0869009\pi\)
−0.962964 + 0.269628i \(0.913099\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.84501e6 0.883532 0.441766 0.897130i \(-0.354352\pi\)
0.441766 + 0.897130i \(0.354352\pi\)
\(402\) 0 0
\(403\) 1.61626e6i 0.495733i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.64400e6i 1.09042i
\(408\) 0 0
\(409\) 1.89069e6 0.558873 0.279436 0.960164i \(-0.409852\pi\)
0.279436 + 0.960164i \(0.409852\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 113200.i 0.0326566i
\(414\) 0 0
\(415\) 24680.0 + 135740.i 0.00703437 + 0.0386890i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.60930e6 −1.28263 −0.641313 0.767280i \(-0.721610\pi\)
−0.641313 + 0.767280i \(0.721610\pi\)
\(420\) 0 0
\(421\) −6.04151e6 −1.66127 −0.830635 0.556817i \(-0.812022\pi\)
−0.830635 + 0.556817i \(0.812022\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.66760e6 4.43430e6i −0.447837 1.19084i
\(426\) 0 0
\(427\) 73160.0i 0.0194180i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3800.00 −0.000985350 −0.000492675 1.00000i \(-0.500157\pi\)
−0.000492675 1.00000i \(0.500157\pi\)
\(432\) 0 0
\(433\) 250736.i 0.0642683i −0.999484 0.0321342i \(-0.989770\pi\)
0.999484 0.0321342i \(-0.0102304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.51040e6i 1.38032i
\(438\) 0 0
\(439\) −3.58873e6 −0.888750 −0.444375 0.895841i \(-0.646574\pi\)
−0.444375 + 0.895841i \(0.646574\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.41479e6i 0.342517i 0.985226 + 0.171258i \(0.0547833\pi\)
−0.985226 + 0.171258i \(0.945217\pi\)
\(444\) 0 0
\(445\) 1.24729e6 226780.i 0.298585 0.0542881i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −829806. −0.194250 −0.0971249 0.995272i \(-0.530965\pi\)
−0.0971249 + 0.995272i \(0.530965\pi\)
\(450\) 0 0
\(451\) −9.49300e6 −2.19767
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −63360.0 + 11520.0i −0.0143478 + 0.00260870i
\(456\) 0 0
\(457\) 4.68198e6i 1.04867i 0.851512 + 0.524335i \(0.175686\pi\)
−0.851512 + 0.524335i \(0.824314\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 141930. 0.0311044 0.0155522 0.999879i \(-0.495049\pi\)
0.0155522 + 0.999879i \(0.495049\pi\)
\(462\) 0 0
\(463\) 727476.i 0.157713i 0.996886 + 0.0788563i \(0.0251268\pi\)
−0.996886 + 0.0788563i \(0.974873\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.47640e6i 0.949809i −0.880037 0.474905i \(-0.842483\pi\)
0.880037 0.474905i \(-0.157517\pi\)
\(468\) 0 0
\(469\) 263824. 0.0553837
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.20200e6i 0.247031i
\(474\) 0 0
\(475\) −3.93120e6 + 1.47840e6i −0.799450 + 0.300648i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.32718e6 0.264297 0.132149 0.991230i \(-0.457812\pi\)
0.132149 + 0.991230i \(0.457812\pi\)
\(480\) 0 0
\(481\) 2.09894e6 0.413655
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −369680. 2.03324e6i −0.0713628 0.392495i
\(486\) 0 0
\(487\) 4.11647e6i 0.786507i 0.919430 + 0.393253i \(0.128650\pi\)
−0.919430 + 0.393253i \(0.871350\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.12316e6 −1.14623 −0.573115 0.819475i \(-0.694265\pi\)
−0.573115 + 0.819475i \(0.694265\pi\)
\(492\) 0 0
\(493\) 4.01134e6i 0.743313i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 115200.i 0.0209200i
\(498\) 0 0
\(499\) −7.90490e6 −1.42117 −0.710584 0.703613i \(-0.751569\pi\)
−0.710584 + 0.703613i \(0.751569\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.97628e6i 0.700741i −0.936611 0.350370i \(-0.886056\pi\)
0.936611 0.350370i \(-0.113944\pi\)
\(504\) 0 0
\(505\) −9.23549e6 + 1.67918e6i −1.61150 + 0.293001i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 781914. 0.133772 0.0668859 0.997761i \(-0.478694\pi\)
0.0668859 + 0.997761i \(0.478694\pi\)
\(510\) 0 0
\(511\) −123232. −0.0208772
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.54364e6 8.49002e6i −0.256465 1.41056i
\(516\) 0 0
\(517\) 4.45000e6i 0.732207i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.82694e6 −0.940472 −0.470236 0.882541i \(-0.655831\pi\)
−0.470236 + 0.882541i \(0.655831\pi\)
\(522\) 0 0
\(523\) 9.78938e6i 1.56495i −0.622681 0.782476i \(-0.713957\pi\)
0.622681 0.782476i \(-0.286043\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.50779e6i 1.33441i
\(528\) 0 0
\(529\) −1.03737e7 −1.61173
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.46797e6i 0.833696i
\(534\) 0 0
\(535\) 1.36788e6 + 7.52334e6i 0.206616 + 1.13639i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.39550e6 −1.24473
\(540\) 0 0
\(541\) 4.76059e6 0.699307 0.349653 0.936879i \(-0.386299\pi\)
0.349653 + 0.936879i \(0.386299\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.95955e6 538100.i 0.426810 0.0776018i
\(546\) 0 0
\(547\) 1.16595e6i 0.166614i 0.996524 + 0.0833069i \(0.0265482\pi\)
−0.996524 + 0.0833069i \(0.973452\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.55622e6 0.499011
\(552\) 0 0
\(553\) 240912.i 0.0335001i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.61293e6i 0.220282i 0.993916 + 0.110141i \(0.0351302\pi\)
−0.993916 + 0.110141i \(0.964870\pi\)
\(558\) 0 0
\(559\) 692352. 0.0937125
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.40603e6i 0.452874i −0.974026 0.226437i \(-0.927292\pi\)
0.974026 0.226437i \(-0.0727077\pi\)
\(564\) 0 0
\(565\) 826920. + 4.54806e6i 0.108979 + 0.599384i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.44009e7 −1.86470 −0.932350 0.361557i \(-0.882245\pi\)
−0.932350 + 0.361557i \(0.882245\pi\)
\(570\) 0 0
\(571\) −4.74772e6 −0.609389 −0.304695 0.952450i \(-0.598554\pi\)
−0.304695 + 0.952450i \(0.598554\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.51000e6 + 1.19925e7i 0.568862 + 1.51266i
\(576\) 0 0
\(577\) 1.09094e7i 1.36415i −0.731283 0.682074i \(-0.761078\pi\)
0.731283 0.682074i \(-0.238922\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9872.00 −0.00121329
\(582\) 0 0
\(583\) 1.99020e7i 2.42508i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.53223e6i 1.02204i 0.859569 + 0.511019i \(0.170732\pi\)
−0.859569 + 0.511019i \(0.829268\pi\)
\(588\) 0 0
\(589\) −7.54253e6 −0.895836
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.63182e6i 0.540897i −0.962734 0.270449i \(-0.912828\pi\)
0.962734 0.270449i \(-0.0871721\pi\)
\(594\) 0 0
\(595\) 333520. 60640.0i 0.0386215 0.00702210i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.27598e6 −0.714684 −0.357342 0.933974i \(-0.616317\pi\)
−0.357342 + 0.933974i \(0.616317\pi\)
\(600\) 0 0
\(601\) 7.71988e6 0.871815 0.435907 0.899992i \(-0.356428\pi\)
0.435907 + 0.899992i \(0.356428\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.89220e6 889490.i 0.543395 0.0987990i
\(606\) 0 0
\(607\) 6.06160e6i 0.667753i 0.942617 + 0.333876i \(0.108357\pi\)
−0.942617 + 0.333876i \(0.891643\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.56320e6 −0.277766
\(612\) 0 0
\(613\) 3.66489e6i 0.393921i 0.980411 + 0.196961i \(0.0631071\pi\)
−0.980411 + 0.196961i \(0.936893\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.32522e6i 0.986157i 0.869985 + 0.493079i \(0.164129\pi\)
−0.869985 + 0.493079i \(0.835871\pi\)
\(618\) 0 0
\(619\) −7.40162e6 −0.776426 −0.388213 0.921570i \(-0.626907\pi\)
−0.388213 + 0.921570i \(0.626907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 90712.0i 0.00936364i
\(624\) 0 0
\(625\) 7.34562e6 6.43500e6i 0.752192 0.658944i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.10486e7 −1.11348
\(630\) 0 0
\(631\) −160052. −0.0160025 −0.00800125 0.999968i \(-0.502547\pi\)
−0.00800125 + 0.999968i \(0.502547\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.11780e6 + 1.16479e7i 0.208425 + 1.14634i
\(636\) 0 0
\(637\) 4.83581e6i 0.472194i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.69565e7 1.63002 0.815008 0.579450i \(-0.196732\pi\)
0.815008 + 0.579450i \(0.196732\pi\)
\(642\) 0 0
\(643\) 1.10128e7i 1.05044i 0.850967 + 0.525219i \(0.176016\pi\)
−0.850967 + 0.525219i \(0.823984\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.33848e6i 0.313537i 0.987635 + 0.156768i \(0.0501076\pi\)
−0.987635 + 0.156768i \(0.949892\pi\)
\(648\) 0 0
\(649\) −1.41500e7 −1.31870
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.76181e6i 0.437008i −0.975836 0.218504i \(-0.929882\pi\)
0.975836 0.218504i \(-0.0701177\pi\)
\(654\) 0 0
\(655\) 9.32250e6 1.69500e6i 0.849042 0.154371i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −798188. −0.0715965 −0.0357982 0.999359i \(-0.511397\pi\)
−0.0357982 + 0.999359i \(0.511397\pi\)
\(660\) 0 0
\(661\) −1.54048e7 −1.37136 −0.685682 0.727901i \(-0.740496\pi\)
−0.685682 + 0.727901i \(0.740496\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −53760.0 295680.i −0.00471417 0.0259279i
\(666\) 0 0
\(667\) 1.08486e7i 0.944189i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.14500e6 −0.784111
\(672\) 0 0
\(673\) 976704.i 0.0831238i 0.999136 + 0.0415619i \(0.0132334\pi\)
−0.999136 + 0.0415619i \(0.986767\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.93885e7i 1.62582i −0.582388 0.812911i \(-0.697881\pi\)
0.582388 0.812911i \(-0.302119\pi\)
\(678\) 0 0
\(679\) 147872. 0.0123087
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.25573e6i 0.431103i 0.976492 + 0.215552i \(0.0691550\pi\)
−0.976492 + 0.215552i \(0.930845\pi\)
\(684\) 0 0
\(685\) −2.52036e6 1.38620e7i −0.205228 1.12875i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.14636e7 −0.919965
\(690\) 0 0
\(691\) 5.45034e6 0.434238 0.217119 0.976145i \(-0.430334\pi\)
0.217119 + 0.976145i \(0.430334\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.05609e7 1.92016e6i 0.829350 0.150791i
\(696\) 0 0
\(697\) 2.87828e7i 2.24414i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.43961e6 0.341232 0.170616 0.985338i \(-0.445424\pi\)
0.170616 + 0.985338i \(0.445424\pi\)
\(702\) 0 0
\(703\) 9.79507e6i 0.747514i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 671672.i 0.0505369i
\(708\) 0 0
\(709\) −4.55918e6 −0.340621 −0.170310 0.985390i \(-0.554477\pi\)
−0.170310 + 0.985390i \(0.554477\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.30092e7i 1.69503i
\(714\) 0 0
\(715\) −1.44000e6 7.92000e6i −0.105341 0.579375i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.06630e7 1.49063 0.745317 0.666710i \(-0.232298\pi\)
0.745317 + 0.666710i \(0.232298\pi\)
\(720\) 0 0
\(721\) 617456. 0.0442352
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.73955e6 + 2.91060e6i −0.546853 + 0.205654i
\(726\) 0 0
\(727\) 5.48161e6i 0.384656i −0.981331 0.192328i \(-0.938396\pi\)
0.981331 0.192328i \(-0.0616037\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.64446e6 −0.252255
\(732\) 0 0
\(733\) 8.55579e6i 0.588166i 0.955780 + 0.294083i \(0.0950143\pi\)
−0.955780 + 0.294083i \(0.904986\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.29780e7i 2.23643i
\(738\) 0 0
\(739\) −5.29119e6 −0.356404 −0.178202 0.983994i \(-0.557028\pi\)
−0.178202 + 0.983994i \(0.557028\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.36432e6i 0.157121i 0.996909 + 0.0785606i \(0.0250324\pi\)
−0.996909 + 0.0785606i \(0.974968\pi\)
\(744\) 0 0
\(745\) 1.29632e7 2.35694e6i 0.855698 0.155581i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −547152. −0.0356372
\(750\) 0 0
\(751\) 8.79694e6 0.569157 0.284578 0.958653i \(-0.408146\pi\)
0.284578 + 0.958653i \(0.408146\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.04321e7 3.71492e6i 1.30450 0.237182i
\(756\) 0 0
\(757\) 2.95808e7i 1.87616i 0.346421 + 0.938079i \(0.387397\pi\)
−0.346421 + 0.938079i \(0.612603\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.26296e7 0.790549 0.395274 0.918563i \(-0.370649\pi\)
0.395274 + 0.918563i \(0.370649\pi\)
\(762\) 0 0
\(763\) 215240.i 0.0133848i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.15040e6i 0.500254i
\(768\) 0 0
\(769\) 2.32186e7 1.41586 0.707929 0.706283i \(-0.249630\pi\)
0.707929 + 0.706283i \(0.249630\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.73201e7i 1.04256i −0.853386 0.521280i \(-0.825455\pi\)
0.853386 0.521280i \(-0.174545\pi\)
\(774\) 0 0
\(775\) 1.64151e7 6.17320e6i 0.981724 0.369195i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.55172e7 −1.50657
\(780\) 0 0
\(781\) 1.44000e7 0.844763
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.64952e6 + 1.45724e7i 0.153459 + 0.844026i
\(786\) 0 0
\(787\) 556676.i 0.0320380i −0.999872 0.0160190i \(-0.994901\pi\)
0.999872 0.0160190i \(-0.00509923\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −330768. −0.0187967
\(792\) 0 0
\(793\) 5.26752e6i 0.297456i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.00562e6i 0.167606i −0.996482 0.0838028i \(-0.973293\pi\)
0.996482 0.0838028i \(-0.0267066\pi\)
\(798\) 0 0
\(799\) 1.34924e7