Properties

Label 720.6.f.a.289.2
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 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+(-55.0000 + 10.0000i) q^{5} -158.000i q^{7} +O(q^{10})\) \(q+(-55.0000 + 10.0000i) q^{5} -158.000i q^{7} -148.000 q^{11} -684.000i q^{13} -2048.00i q^{17} +2220.00 q^{19} +1246.00i q^{23} +(2925.00 - 1100.00i) q^{25} -270.000 q^{29} +2048.00 q^{31} +(1580.00 + 8690.00i) q^{35} -4372.00i q^{37} +2398.00 q^{41} +2294.00i q^{43} -10682.0i q^{47} -8157.00 q^{49} +2964.00i q^{53} +(8140.00 - 1480.00i) q^{55} +39740.0 q^{59} -42298.0 q^{61} +(6840.00 + 37620.0i) q^{65} -32098.0i q^{67} -4248.00 q^{71} -30104.0i q^{73} +23384.0i q^{77} +35280.0 q^{79} +27826.0i q^{83} +(20480.0 + 112640. i) q^{85} -85210.0 q^{89} -108072. q^{91} +(-122100. + 22200.0i) q^{95} -97232.0i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 110q^{5} + O(q^{10}) \) \( 2q - 110q^{5} - 296q^{11} + 4440q^{19} + 5850q^{25} - 540q^{29} + 4096q^{31} + 3160q^{35} + 4796q^{41} - 16314q^{49} + 16280q^{55} + 79480q^{59} - 84596q^{61} + 13680q^{65} - 8496q^{71} + 70560q^{79} + 40960q^{85} - 170420q^{89} - 216144q^{91} - 244200q^{95} + O(q^{100}) \)

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
\(7\) 158.000i 1.21874i −0.792885 0.609371i \(-0.791422\pi\)
0.792885 0.609371i \(-0.208578\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −148.000 −0.368791 −0.184395 0.982852i \(-0.559033\pi\)
−0.184395 + 0.982852i \(0.559033\pi\)
\(12\) 0 0
\(13\) 684.000i 1.12253i −0.827636 0.561265i \(-0.810315\pi\)
0.827636 0.561265i \(-0.189685\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2048.00i 1.71873i −0.511363 0.859365i \(-0.670859\pi\)
0.511363 0.859365i \(-0.329141\pi\)
\(18\) 0 0
\(19\) 2220.00 1.41081 0.705406 0.708804i \(-0.250765\pi\)
0.705406 + 0.708804i \(0.250765\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1246.00i 0.491132i 0.969380 + 0.245566i \(0.0789738\pi\)
−0.969380 + 0.245566i \(0.921026\pi\)
\(24\) 0 0
\(25\) 2925.00 1100.00i 0.936000 0.352000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −270.000 −0.0596168 −0.0298084 0.999556i \(-0.509490\pi\)
−0.0298084 + 0.999556i \(0.509490\pi\)
\(30\) 0 0
\(31\) 2048.00 0.382759 0.191380 0.981516i \(-0.438704\pi\)
0.191380 + 0.981516i \(0.438704\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1580.00 + 8690.00i 0.218015 + 1.19908i
\(36\) 0 0
\(37\) 4372.00i 0.525020i −0.964929 0.262510i \(-0.915450\pi\)
0.964929 0.262510i \(-0.0845503\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2398.00 0.222787 0.111393 0.993776i \(-0.464469\pi\)
0.111393 + 0.993776i \(0.464469\pi\)
\(42\) 0 0
\(43\) 2294.00i 0.189200i 0.995515 + 0.0946002i \(0.0301573\pi\)
−0.995515 + 0.0946002i \(0.969843\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10682.0i 0.705355i −0.935745 0.352678i \(-0.885271\pi\)
0.935745 0.352678i \(-0.114729\pi\)
\(48\) 0 0
\(49\) −8157.00 −0.485333
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2964.00i 0.144940i 0.997371 + 0.0724700i \(0.0230882\pi\)
−0.997371 + 0.0724700i \(0.976912\pi\)
\(54\) 0 0
\(55\) 8140.00 1480.00i 0.362842 0.0659713i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 39740.0 1.48627 0.743135 0.669141i \(-0.233338\pi\)
0.743135 + 0.669141i \(0.233338\pi\)
\(60\) 0 0
\(61\) −42298.0 −1.45544 −0.727722 0.685873i \(-0.759421\pi\)
−0.727722 + 0.685873i \(0.759421\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6840.00 + 37620.0i 0.200804 + 1.10442i
\(66\) 0 0
\(67\) 32098.0i 0.873556i −0.899569 0.436778i \(-0.856119\pi\)
0.899569 0.436778i \(-0.143881\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4248.00 −0.100009 −0.0500044 0.998749i \(-0.515924\pi\)
−0.0500044 + 0.998749i \(0.515924\pi\)
\(72\) 0 0
\(73\) 30104.0i 0.661176i −0.943775 0.330588i \(-0.892753\pi\)
0.943775 0.330588i \(-0.107247\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 23384.0i 0.449461i
\(78\) 0 0
\(79\) 35280.0 0.636005 0.318003 0.948090i \(-0.396988\pi\)
0.318003 + 0.948090i \(0.396988\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 27826.0i 0.443359i 0.975120 + 0.221680i \(0.0711539\pi\)
−0.975120 + 0.221680i \(0.928846\pi\)
\(84\) 0 0
\(85\) 20480.0 + 112640.i 0.307456 + 1.69101i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −85210.0 −1.14029 −0.570145 0.821544i \(-0.693113\pi\)
−0.570145 + 0.821544i \(0.693113\pi\)
\(90\) 0 0
\(91\) −108072. −1.36807
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −122100. + 22200.0i −1.38805 + 0.252374i
\(96\) 0 0
\(97\) 97232.0i 1.04925i −0.851333 0.524626i \(-0.824205\pi\)
0.851333 0.524626i \(-0.175795\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4298.00 0.0419240 0.0209620 0.999780i \(-0.493327\pi\)
0.0209620 + 0.999780i \(0.493327\pi\)
\(102\) 0 0
\(103\) 124114.i 1.15273i 0.817192 + 0.576365i \(0.195529\pi\)
−0.817192 + 0.576365i \(0.804471\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 42342.0i 0.357530i −0.983892 0.178765i \(-0.942790\pi\)
0.983892 0.178765i \(-0.0572101\pi\)
\(108\) 0 0
\(109\) 35990.0 0.290145 0.145073 0.989421i \(-0.453658\pi\)
0.145073 + 0.989421i \(0.453658\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 228816.i 1.68574i −0.538118 0.842869i \(-0.680865\pi\)
0.538118 0.842869i \(-0.319135\pi\)
\(114\) 0 0
\(115\) −12460.0 68530.0i −0.0878564 0.483210i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −323584. −2.09469
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −149875. + 89750.0i −0.857935 + 0.513759i
\(126\) 0 0
\(127\) 175238.i 0.964093i −0.876146 0.482047i \(-0.839894\pi\)
0.876146 0.482047i \(-0.160106\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 299652. 1.52559 0.762797 0.646638i \(-0.223826\pi\)
0.762797 + 0.646638i \(0.223826\pi\)
\(132\) 0 0
\(133\) 350760.i 1.71942i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 107928.i 0.491284i −0.969361 0.245642i \(-0.921001\pi\)
0.969361 0.245642i \(-0.0789988\pi\)
\(138\) 0 0
\(139\) −196460. −0.862456 −0.431228 0.902243i \(-0.641920\pi\)
−0.431228 + 0.902243i \(0.641920\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 101232.i 0.413978i
\(144\) 0 0
\(145\) 14850.0 2700.00i 0.0586552 0.0106646i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 138850. 0.512366 0.256183 0.966628i \(-0.417535\pi\)
0.256183 + 0.966628i \(0.417535\pi\)
\(150\) 0 0
\(151\) −416152. −1.48528 −0.742642 0.669688i \(-0.766428\pi\)
−0.742642 + 0.669688i \(0.766428\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −112640. + 20480.0i −0.376585 + 0.0684701i
\(156\) 0 0
\(157\) 433108.i 1.40232i 0.713004 + 0.701160i \(0.247334\pi\)
−0.713004 + 0.701160i \(0.752666\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 196868. 0.598564
\(162\) 0 0
\(163\) 149134.i 0.439651i 0.975539 + 0.219825i \(0.0705487\pi\)
−0.975539 + 0.219825i \(0.929451\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 559602.i 1.55270i −0.630301 0.776351i \(-0.717068\pi\)
0.630301 0.776351i \(-0.282932\pi\)
\(168\) 0 0
\(169\) −96563.0 −0.260072
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 343804.i 0.873365i 0.899616 + 0.436682i \(0.143847\pi\)
−0.899616 + 0.436682i \(0.856153\pi\)
\(174\) 0 0
\(175\) −173800. 462150.i −0.428997 1.14074i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −23980.0 −0.0559392 −0.0279696 0.999609i \(-0.508904\pi\)
−0.0279696 + 0.999609i \(0.508904\pi\)
\(180\) 0 0
\(181\) −651898. −1.47905 −0.739526 0.673128i \(-0.764950\pi\)
−0.739526 + 0.673128i \(0.764950\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 43720.0 + 240460.i 0.0939184 + 0.516551i
\(186\) 0 0
\(187\) 303104.i 0.633852i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 202752. 0.402144 0.201072 0.979576i \(-0.435557\pi\)
0.201072 + 0.979576i \(0.435557\pi\)
\(192\) 0 0
\(193\) 452656.i 0.874732i 0.899284 + 0.437366i \(0.144089\pi\)
−0.899284 + 0.437366i \(0.855911\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 337468.i 0.619537i −0.950812 0.309768i \(-0.899748\pi\)
0.950812 0.309768i \(-0.100252\pi\)
\(198\) 0 0
\(199\) −561000. −1.00422 −0.502112 0.864803i \(-0.667443\pi\)
−0.502112 + 0.864803i \(0.667443\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 42660.0i 0.0726576i
\(204\) 0 0
\(205\) −131890. + 23980.0i −0.219193 + 0.0398533i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −328560. −0.520294
\(210\) 0 0
\(211\) 805548. 1.24562 0.622810 0.782373i \(-0.285991\pi\)
0.622810 + 0.782373i \(0.285991\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −22940.0 126170.i −0.0338452 0.186149i
\(216\) 0 0
\(217\) 323584.i 0.466485i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.40083e6 −1.92932
\(222\) 0 0
\(223\) 1.21855e6i 1.64090i 0.571717 + 0.820451i \(0.306278\pi\)
−0.571717 + 0.820451i \(0.693722\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 564338.i 0.726900i 0.931614 + 0.363450i \(0.118401\pi\)
−0.931614 + 0.363450i \(0.881599\pi\)
\(228\) 0 0
\(229\) −560330. −0.706082 −0.353041 0.935608i \(-0.614852\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 293576.i 0.354267i −0.984187 0.177134i \(-0.943318\pi\)
0.984187 0.177134i \(-0.0566824\pi\)
\(234\) 0 0
\(235\) 106820. + 587510.i 0.126178 + 0.693978i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −584240. −0.661602 −0.330801 0.943701i \(-0.607319\pi\)
−0.330801 + 0.943701i \(0.607319\pi\)
\(240\) 0 0
\(241\) −563798. −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 448635. 81570.0i 0.477505 0.0868191i
\(246\) 0 0
\(247\) 1.51848e6i 1.58368i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.01975e6 −1.02167 −0.510833 0.859680i \(-0.670663\pi\)
−0.510833 + 0.859680i \(0.670663\pi\)
\(252\) 0 0
\(253\) 184408.i 0.181125i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 657408.i 0.620872i −0.950594 0.310436i \(-0.899525\pi\)
0.950594 0.310436i \(-0.100475\pi\)
\(258\) 0 0
\(259\) −690776. −0.639864
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 562366.i 0.501337i 0.968073 + 0.250668i \(0.0806504\pi\)
−0.968073 + 0.250668i \(0.919350\pi\)
\(264\) 0 0
\(265\) −29640.0 163020.i −0.0259277 0.142602i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 366570. 0.308870 0.154435 0.988003i \(-0.450644\pi\)
0.154435 + 0.988003i \(0.450644\pi\)
\(270\) 0 0
\(271\) −1.16075e6 −0.960099 −0.480050 0.877241i \(-0.659381\pi\)
−0.480050 + 0.877241i \(0.659381\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −432900. + 162800.i −0.345188 + 0.129814i
\(276\) 0 0
\(277\) 2.51501e6i 1.96943i −0.174172 0.984715i \(-0.555725\pi\)
0.174172 0.984715i \(-0.444275\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.08600e6 −1.57597 −0.787987 0.615692i \(-0.788876\pi\)
−0.787987 + 0.615692i \(0.788876\pi\)
\(282\) 0 0
\(283\) 2.23803e6i 1.66111i −0.556935 0.830556i \(-0.688023\pi\)
0.556935 0.830556i \(-0.311977\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 378884.i 0.271520i
\(288\) 0 0
\(289\) −2.77445e6 −1.95403
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 975756.i 0.664006i −0.943278 0.332003i \(-0.892276\pi\)
0.943278 0.332003i \(-0.107724\pi\)
\(294\) 0 0
\(295\) −2.18570e6 + 397400.i −1.46230 + 0.265872i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 852264. 0.551310
\(300\) 0 0
\(301\) 362452. 0.230587
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.32639e6 422980.i 1.43197 0.260358i
\(306\) 0 0
\(307\) 87858.0i 0.0532029i −0.999646 0.0266015i \(-0.991531\pi\)
0.999646 0.0266015i \(-0.00846850\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 599352. 0.351383 0.175692 0.984445i \(-0.443784\pi\)
0.175692 + 0.984445i \(0.443784\pi\)
\(312\) 0 0
\(313\) 2.09342e6i 1.20780i 0.797060 + 0.603900i \(0.206387\pi\)
−0.797060 + 0.603900i \(0.793613\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.41625e6i 1.35050i 0.737590 + 0.675249i \(0.235964\pi\)
−0.737590 + 0.675249i \(0.764036\pi\)
\(318\) 0 0
\(319\) 39960.0 0.0219861
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.54656e6i 2.42480i
\(324\) 0 0
\(325\) −752400. 2.00070e6i −0.395130 1.05069i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.68776e6 −0.859647
\(330\) 0 0
\(331\) 1.64095e6 0.823237 0.411618 0.911356i \(-0.364964\pi\)
0.411618 + 0.911356i \(0.364964\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 320980. + 1.76539e6i 0.156267 + 0.859466i
\(336\) 0 0
\(337\) 2.18773e6i 1.04935i 0.851304 + 0.524673i \(0.175812\pi\)
−0.851304 + 0.524673i \(0.824188\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −303104. −0.141158
\(342\) 0 0
\(343\) 1.36670e6i 0.627246i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.74502e6i 1.22383i 0.790923 + 0.611916i \(0.209601\pi\)
−0.790923 + 0.611916i \(0.790399\pi\)
\(348\) 0 0
\(349\) 2.65115e6 1.16512 0.582560 0.812788i \(-0.302051\pi\)
0.582560 + 0.812788i \(0.302051\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.05766e6i 1.30603i 0.757345 + 0.653015i \(0.226496\pi\)
−0.757345 + 0.653015i \(0.773504\pi\)
\(354\) 0 0
\(355\) 233640. 42480.0i 0.0983957 0.0178901i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.79356e6 −1.55350 −0.776749 0.629810i \(-0.783133\pi\)
−0.776749 + 0.629810i \(0.783133\pi\)
\(360\) 0 0
\(361\) 2.45230e6 0.990389
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 301040. + 1.65572e6i 0.118275 + 0.650511i
\(366\) 0 0
\(367\) 3.11060e6i 1.20553i 0.797917 + 0.602767i \(0.205935\pi\)
−0.797917 + 0.602767i \(0.794065\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 468312. 0.176645
\(372\) 0 0
\(373\) 1.41520e6i 0.526677i 0.964703 + 0.263339i \(0.0848236\pi\)
−0.964703 + 0.263339i \(0.915176\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 184680.i 0.0669216i
\(378\) 0 0
\(379\) −3.90262e6 −1.39559 −0.697796 0.716297i \(-0.745836\pi\)
−0.697796 + 0.716297i \(0.745836\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 695674.i 0.242331i −0.992632 0.121165i \(-0.961337\pi\)
0.992632 0.121165i \(-0.0386632\pi\)
\(384\) 0 0
\(385\) −233840. 1.28612e6i −0.0804020 0.442211i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 498290. 0.166958 0.0834792 0.996510i \(-0.473397\pi\)
0.0834792 + 0.996510i \(0.473397\pi\)
\(390\) 0 0
\(391\) 2.55181e6 0.844124
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.94040e6 + 352800.i −0.625747 + 0.113772i
\(396\) 0 0
\(397\) 1.09567e6i 0.348901i 0.984666 + 0.174451i \(0.0558150\pi\)
−0.984666 + 0.174451i \(0.944185\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.49160e6 0.773779 0.386890 0.922126i \(-0.373549\pi\)
0.386890 + 0.922126i \(0.373549\pi\)
\(402\) 0 0
\(403\) 1.40083e6i 0.429659i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 647056.i 0.193623i
\(408\) 0 0
\(409\) 3.63349e6 1.07403 0.537014 0.843573i \(-0.319552\pi\)
0.537014 + 0.843573i \(0.319552\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.27892e6i 1.81138i
\(414\) 0 0
\(415\) −278260. 1.53043e6i −0.0793105 0.436208i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.64378e6 1.01395 0.506976 0.861960i \(-0.330763\pi\)
0.506976 + 0.861960i \(0.330763\pi\)
\(420\) 0 0
\(421\) −1.82530e6 −0.501913 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.25280e6 5.99040e6i −0.604993 1.60873i
\(426\) 0 0
\(427\) 6.68308e6i 1.77381i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.85435e6 0.740141 0.370070 0.929004i \(-0.379334\pi\)
0.370070 + 0.929004i \(0.379334\pi\)
\(432\) 0 0
\(433\) 587776.i 0.150658i 0.997159 + 0.0753290i \(0.0240007\pi\)
−0.997159 + 0.0753290i \(0.975999\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.76612e6i 0.692895i
\(438\) 0 0
\(439\) 6.11604e6 1.51464 0.757319 0.653045i \(-0.226509\pi\)
0.757319 + 0.653045i \(0.226509\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.35771e6i 0.570795i 0.958409 + 0.285398i \(0.0921257\pi\)
−0.958409 + 0.285398i \(0.907874\pi\)
\(444\) 0 0
\(445\) 4.68655e6 852100.i 1.12190 0.203981i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.49735e6 1.28688 0.643439 0.765497i \(-0.277507\pi\)
0.643439 + 0.765497i \(0.277507\pi\)
\(450\) 0 0
\(451\) −354904. −0.0821617
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.94396e6 1.08072e6i 1.34601 0.244729i
\(456\) 0 0
\(457\) 1.16039e6i 0.259905i −0.991520 0.129952i \(-0.958518\pi\)
0.991520 0.129952i \(-0.0414824\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.30330e6 0.504775 0.252387 0.967626i \(-0.418784\pi\)
0.252387 + 0.967626i \(0.418784\pi\)
\(462\) 0 0
\(463\) 2.71343e6i 0.588257i 0.955766 + 0.294128i \(0.0950293\pi\)
−0.955766 + 0.294128i \(0.904971\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.05050e6i 0.859441i 0.902962 + 0.429721i \(0.141388\pi\)
−0.902962 + 0.429721i \(0.858612\pi\)
\(468\) 0 0
\(469\) −5.07148e6 −1.06464
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 339512.i 0.0697754i
\(474\) 0 0
\(475\) 6.49350e6 2.44200e6i 1.32052 0.496606i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.60528e6 −1.11624 −0.558121 0.829759i \(-0.688478\pi\)
−0.558121 + 0.829759i \(0.688478\pi\)
\(480\) 0 0
\(481\) −2.99045e6 −0.589350
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 972320. + 5.34776e6i 0.187696 + 1.03233i
\(486\) 0 0
\(487\) 7.13168e6i 1.36260i −0.732003 0.681301i \(-0.761414\pi\)
0.732003 0.681301i \(-0.238586\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.88145e6 1.10098 0.550492 0.834841i \(-0.314440\pi\)
0.550492 + 0.834841i \(0.314440\pi\)
\(492\) 0 0
\(493\) 552960.i 0.102465i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 671184.i 0.121885i
\(498\) 0 0
\(499\) 1.75710e6 0.315897 0.157948 0.987447i \(-0.449512\pi\)
0.157948 + 0.987447i \(0.449512\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.91411e6i 0.866015i −0.901390 0.433007i \(-0.857452\pi\)
0.901390 0.433007i \(-0.142548\pi\)
\(504\) 0 0
\(505\) −236390. + 42980.0i −0.0412478 + 0.00749960i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.75499e6 −0.984578 −0.492289 0.870432i \(-0.663840\pi\)
−0.492289 + 0.870432i \(0.663840\pi\)
\(510\) 0 0
\(511\) −4.75643e6 −0.805803
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.24114e6 6.82627e6i −0.206207 1.13414i
\(516\) 0 0
\(517\) 1.58094e6i 0.260128i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.61980e6 0.261437 0.130718 0.991420i \(-0.458272\pi\)
0.130718 + 0.991420i \(0.458272\pi\)
\(522\) 0 0
\(523\) 1.19117e7i 1.90422i 0.305751 + 0.952112i \(0.401093\pi\)
−0.305751 + 0.952112i \(0.598907\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.19430e6i 0.657860i
\(528\) 0 0
\(529\) 4.88383e6 0.758789
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.64023e6i 0.250085i
\(534\) 0 0
\(535\) 423420. + 2.32881e6i 0.0639568 + 0.351763i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.20724e6 0.178986
\(540\) 0 0
\(541\) 4.07630e6 0.598788 0.299394 0.954130i \(-0.403215\pi\)
0.299394 + 0.954130i \(0.403215\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.97945e6 + 359900.i −0.285465 + 0.0519028i
\(546\) 0 0
\(547\) 1.23680e7i 1.76739i −0.468065 0.883694i \(-0.655049\pi\)
0.468065 0.883694i \(-0.344951\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −599400. −0.0841081
\(552\) 0 0
\(553\) 5.57424e6i 0.775127i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 130308.i 0.0177964i −0.999960 0.00889822i \(-0.997168\pi\)
0.999960 0.00889822i \(-0.00283243\pi\)
\(558\) 0 0
\(559\) 1.56910e6 0.212383
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.91687e6i 0.786721i 0.919384 + 0.393361i \(0.128688\pi\)
−0.919384 + 0.393361i \(0.871312\pi\)
\(564\) 0 0
\(565\) 2.28816e6 + 1.25849e7i 0.301554 + 1.65855i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.03013e6 −1.16927 −0.584633 0.811298i \(-0.698761\pi\)
−0.584633 + 0.811298i \(0.698761\pi\)
\(570\) 0 0
\(571\) 1.07093e7 1.37459 0.687294 0.726379i \(-0.258798\pi\)
0.687294 + 0.726379i \(0.258798\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.37060e6 + 3.64455e6i 0.172879 + 0.459700i
\(576\) 0 0
\(577\) 1.22051e6i 0.152617i −0.997084 0.0763084i \(-0.975687\pi\)
0.997084 0.0763084i \(-0.0243134\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.39651e6 0.540341
\(582\) 0 0
\(583\) 438672.i 0.0534526i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.47104e7i 1.76210i −0.473026 0.881049i \(-0.656838\pi\)
0.473026 0.881049i \(-0.343162\pi\)
\(588\) 0 0
\(589\) 4.54656e6 0.540001
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.52014e6i 0.994970i 0.867472 + 0.497485i \(0.165743\pi\)
−0.867472 + 0.497485i \(0.834257\pi\)
\(594\) 0 0
\(595\) 1.77971e7 3.23584e6i 2.06090 0.374709i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.90100e6 −0.330355 −0.165177 0.986264i \(-0.552820\pi\)
−0.165177 + 0.986264i \(0.552820\pi\)
\(600\) 0 0
\(601\) 5.72760e6 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.65308e6 1.39147e6i 0.850057 0.154556i
\(606\) 0 0
\(607\) 8.79924e6i 0.969334i 0.874699 + 0.484667i \(0.161059\pi\)
−0.874699 + 0.484667i \(0.838941\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.30649e6 −0.791782
\(612\) 0 0
\(613\) 1.03408e6i 0.111149i −0.998455 0.0555744i \(-0.982301\pi\)
0.998455 0.0555744i \(-0.0176990\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.29854e7i 1.37323i −0.727020 0.686616i \(-0.759095\pi\)
0.727020 0.686616i \(-0.240905\pi\)
\(618\) 0 0
\(619\) 7.92002e6 0.830806 0.415403 0.909637i \(-0.363641\pi\)
0.415403 + 0.909637i \(0.363641\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.34632e7i 1.38972i
\(624\) 0 0
\(625\) 7.34562e6 6.43500e6i 0.752192 0.658944i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.95386e6 −0.902368
\(630\) 0 0
\(631\) −1.68218e7 −1.68189 −0.840945 0.541120i \(-0.818001\pi\)
−0.840945 + 0.541120i \(0.818001\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.75238e6 + 9.63809e6i 0.172462 + 0.948542i
\(636\) 0 0
\(637\) 5.57939e6i 0.544801i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.55154e7 1.49148 0.745741 0.666236i \(-0.232096\pi\)
0.745741 + 0.666236i \(0.232096\pi\)
\(642\) 0 0
\(643\) 1.05801e7i 1.00916i 0.863364 + 0.504582i \(0.168354\pi\)
−0.863364 + 0.504582i \(0.831646\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.37883e7i 1.29494i 0.762090 + 0.647471i \(0.224173\pi\)
−0.762090 + 0.647471i \(0.775827\pi\)
\(648\) 0 0
\(649\) −5.88152e6 −0.548123
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.58924e6i 0.145850i −0.997337 0.0729248i \(-0.976767\pi\)
0.997337 0.0729248i \(-0.0232333\pi\)
\(654\) 0 0
\(655\) −1.64809e7 + 2.99652e6i −1.50099 + 0.272907i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.12434e6 0.818442 0.409221 0.912435i \(-0.365801\pi\)
0.409221 + 0.912435i \(0.365801\pi\)
\(660\) 0 0
\(661\) 6.50310e6 0.578918 0.289459 0.957190i \(-0.406525\pi\)
0.289459 + 0.957190i \(0.406525\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.50760e6 + 1.92918e7i 0.307578 + 1.69168i
\(666\) 0 0
\(667\) 336420.i 0.0292797i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.26010e6 0.536754
\(672\) 0 0
\(673\) 2.17810e6i 0.185370i 0.995695 + 0.0926850i \(0.0295449\pi\)
−0.995695 + 0.0926850i \(0.970455\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.98419e6i 0.334094i −0.985949 0.167047i \(-0.946577\pi\)
0.985949 0.167047i \(-0.0534231\pi\)
\(678\) 0 0
\(679\) −1.53627e7 −1.27877
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.91563e6i 0.485231i 0.970122 + 0.242616i \(0.0780054\pi\)
−0.970122 + 0.242616i \(0.921995\pi\)
\(684\) 0 0
\(685\) 1.07928e6 + 5.93604e6i 0.0878836 + 0.483360i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.02738e6 0.162700
\(690\) 0 0
\(691\) 1.55471e7 1.23867 0.619335 0.785127i \(-0.287402\pi\)
0.619335 + 0.785127i \(0.287402\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.08053e7 1.96460e6i 0.848545 0.154281i
\(696\) 0 0
\(697\) 4.91110e6i 0.382910i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.27103e7 1.74553 0.872766 0.488139i \(-0.162324\pi\)
0.872766 + 0.488139i \(0.162324\pi\)
\(702\) 0 0
\(703\) 9.70584e6i 0.740704i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 679084.i 0.0510946i
\(708\) 0 0
\(709\) −6.29841e6 −0.470560 −0.235280 0.971928i \(-0.575601\pi\)
−0.235280 + 0.971928i \(0.575601\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.55181e6i 0.187985i
\(714\) 0 0
\(715\) −1.01232e6 5.56776e6i −0.0740547 0.407301i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.11911e7 −1.52873 −0.764367 0.644782i \(-0.776948\pi\)
−0.764367 + 0.644782i \(0.776948\pi\)
\(720\) 0 0
\(721\) 1.96100e7 1.40488
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −789750. + 297000.i −0.0558013 + 0.0209851i
\(726\) 0 0
\(727\) 1.35610e7i 0.951605i −0.879552 0.475803i \(-0.842158\pi\)
0.879552 0.475803i \(-0.157842\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.69811e6 0.325185
\(732\) 0 0
\(733\) 2.69413e7i 1.85208i −0.377429 0.926038i \(-0.623192\pi\)
0.377429 0.926038i \(-0.376808\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.75050e6i 0.322160i
\(738\) 0 0
\(739\) 2.77414e6 0.186860 0.0934302 0.995626i \(-0.470217\pi\)
0.0934302 + 0.995626i \(0.470217\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.85538e7i 1.23299i −0.787358 0.616497i \(-0.788551\pi\)
0.787358 0.616497i \(-0.211449\pi\)
\(744\) 0 0
\(745\) −7.63675e6 + 1.38850e6i −0.504101 + 0.0916548i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.69004e6 −0.435736
\(750\) 0 0
\(751\) 2.19285e6 0.141876 0.0709380 0.997481i \(-0.477401\pi\)
0.0709380 + 0.997481i \(0.477401\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.28884e7 4.16152e6i 1.46133 0.265696i
\(756\) 0 0
\(757\) 9.48749e6i 0.601744i −0.953665 0.300872i \(-0.902722\pi\)
0.953665 0.300872i \(-0.0972777\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.69580e6 −0.606907 −0.303453 0.952846i \(-0.598140\pi\)
−0.303453 + 0.952846i \(0.598140\pi\)
\(762\) 0 0
\(763\) 5.68642e6i 0.353612i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.71822e7i 1.66838i
\(768\) 0 0
\(769\) −9.32787e6 −0.568809 −0.284405 0.958704i \(-0.591796\pi\)
−0.284405 + 0.958704i \(0.591796\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.68080e6i 0.582723i −0.956613 0.291362i \(-0.905892\pi\)
0.956613 0.291362i \(-0.0941083\pi\)
\(774\) 0 0
\(775\) 5.99040e6 2.25280e6i 0.358263 0.134731i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.32356e6 0.314310
\(780\) 0 0
\(781\) 628704. 0.0368824
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.33108e6 2.38209e7i −0.250855 1.37970i
\(786\) 0 0
\(787\) 5.52302e6i 0.317863i 0.987290 + 0.158931i \(0.0508049\pi\)
−0.987290 + 0.158931i \(0.949195\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.61529e7 −2.05448
\(792\) 0 0
\(793\) 2.89318e7i 1.63378i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.71119e7i 0.954230i 0.878841 + 0.477115i \(0.158318\pi\)
−0.878841 + 0.477115i \(0.841682\pi\)
\(798\) 0 0
\(799\) −2.18767e7 −1.21232