Properties

Label 400.6.a.w.1.2
Level $400$
Weight $6$
Character 400.1
Self dual yes
Analytic conductor $64.154$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1535279252\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{241}) \)
Defining polynomial: \(x^{2} - x - 60\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 25)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-7.26209\) of defining polynomial
Character \(\chi\) \(=\) 400.1

$q$-expansion

\(f(q)\) \(=\) \(q+25.5242 q^{3} +131.048 q^{7} +408.483 q^{9} +O(q^{10})\) \(q+25.5242 q^{3} +131.048 q^{7} +408.483 q^{9} -290.104 q^{11} -68.3868 q^{13} +310.644 q^{17} +2133.35 q^{19} +3344.90 q^{21} +873.145 q^{23} +4223.83 q^{27} -2580.97 q^{29} +9086.30 q^{31} -7404.67 q^{33} -3990.64 q^{37} -1745.52 q^{39} +16981.8 q^{41} -18017.7 q^{43} +24864.7 q^{47} +366.670 q^{49} +7928.93 q^{51} +7652.91 q^{53} +54451.9 q^{57} +9233.69 q^{59} +3326.17 q^{61} +53531.1 q^{63} -32340.7 q^{67} +22286.3 q^{69} +35885.9 q^{71} +26513.6 q^{73} -38017.7 q^{77} -71705.7 q^{79} +8548.28 q^{81} +39630.1 q^{83} -65877.1 q^{87} -117441. q^{89} -8961.98 q^{91} +231920. q^{93} -21878.3 q^{97} -118503. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 20q^{3} + 200q^{7} + 196q^{9} + O(q^{10}) \) \( 2q + 20q^{3} + 200q^{7} + 196q^{9} + 196q^{11} + 360q^{13} - 1490q^{17} + 3180q^{19} + 2964q^{21} + 1560q^{23} + 6740q^{27} - 3920q^{29} + 1096q^{31} - 10090q^{33} - 2020q^{37} - 4112q^{39} + 27754q^{41} - 3000q^{43} + 25760q^{47} - 11686q^{49} + 17876q^{51} + 26980q^{53} + 48670q^{57} - 11960q^{59} - 24396q^{61} + 38880q^{63} - 40060q^{67} + 18492q^{69} + 87296q^{71} + 70290q^{73} - 4500q^{77} - 65480q^{79} + 46282q^{81} + 92580q^{83} - 58480q^{87} - 72810q^{89} + 20576q^{91} + 276060q^{93} + 126140q^{97} - 221792q^{99} + O(q^{100}) \)

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
\(3\) 25.5242 1.63738 0.818688 0.574238i \(-0.194702\pi\)
0.818688 + 0.574238i \(0.194702\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 131.048 1.01085 0.505425 0.862871i \(-0.331336\pi\)
0.505425 + 0.862871i \(0.331336\pi\)
\(8\) 0 0
\(9\) 408.483 1.68100
\(10\) 0 0
\(11\) −290.104 −0.722891 −0.361445 0.932393i \(-0.617717\pi\)
−0.361445 + 0.932393i \(0.617717\pi\)
\(12\) 0 0
\(13\) −68.3868 −0.112231 −0.0561156 0.998424i \(-0.517872\pi\)
−0.0561156 + 0.998424i \(0.517872\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 310.644 0.260700 0.130350 0.991468i \(-0.458390\pi\)
0.130350 + 0.991468i \(0.458390\pi\)
\(18\) 0 0
\(19\) 2133.35 1.35574 0.677871 0.735180i \(-0.262903\pi\)
0.677871 + 0.735180i \(0.262903\pi\)
\(20\) 0 0
\(21\) 3344.90 1.65514
\(22\) 0 0
\(23\) 873.145 0.344165 0.172083 0.985083i \(-0.444950\pi\)
0.172083 + 0.985083i \(0.444950\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4223.83 1.11506
\(28\) 0 0
\(29\) −2580.97 −0.569885 −0.284943 0.958545i \(-0.591975\pi\)
−0.284943 + 0.958545i \(0.591975\pi\)
\(30\) 0 0
\(31\) 9086.30 1.69818 0.849088 0.528252i \(-0.177152\pi\)
0.849088 + 0.528252i \(0.177152\pi\)
\(32\) 0 0
\(33\) −7404.67 −1.18364
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3990.64 −0.479224 −0.239612 0.970869i \(-0.577020\pi\)
−0.239612 + 0.970869i \(0.577020\pi\)
\(38\) 0 0
\(39\) −1745.52 −0.183765
\(40\) 0 0
\(41\) 16981.8 1.57770 0.788851 0.614584i \(-0.210676\pi\)
0.788851 + 0.614584i \(0.210676\pi\)
\(42\) 0 0
\(43\) −18017.7 −1.48603 −0.743017 0.669273i \(-0.766606\pi\)
−0.743017 + 0.669273i \(0.766606\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 24864.7 1.64187 0.820933 0.571024i \(-0.193454\pi\)
0.820933 + 0.571024i \(0.193454\pi\)
\(48\) 0 0
\(49\) 366.670 0.0218165
\(50\) 0 0
\(51\) 7928.93 0.426864
\(52\) 0 0
\(53\) 7652.91 0.374229 0.187114 0.982338i \(-0.440087\pi\)
0.187114 + 0.982338i \(0.440087\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 54451.9 2.21986
\(58\) 0 0
\(59\) 9233.69 0.345339 0.172669 0.984980i \(-0.444761\pi\)
0.172669 + 0.984980i \(0.444761\pi\)
\(60\) 0 0
\(61\) 3326.17 0.114451 0.0572256 0.998361i \(-0.481775\pi\)
0.0572256 + 0.998361i \(0.481775\pi\)
\(62\) 0 0
\(63\) 53531.1 1.69924
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −32340.7 −0.880161 −0.440080 0.897958i \(-0.645050\pi\)
−0.440080 + 0.897958i \(0.645050\pi\)
\(68\) 0 0
\(69\) 22286.3 0.563528
\(70\) 0 0
\(71\) 35885.9 0.844847 0.422424 0.906399i \(-0.361179\pi\)
0.422424 + 0.906399i \(0.361179\pi\)
\(72\) 0 0
\(73\) 26513.6 0.582319 0.291159 0.956675i \(-0.405959\pi\)
0.291159 + 0.956675i \(0.405959\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −38017.7 −0.730733
\(78\) 0 0
\(79\) −71705.7 −1.29266 −0.646332 0.763056i \(-0.723698\pi\)
−0.646332 + 0.763056i \(0.723698\pi\)
\(80\) 0 0
\(81\) 8548.28 0.144766
\(82\) 0 0
\(83\) 39630.1 0.631437 0.315719 0.948853i \(-0.397754\pi\)
0.315719 + 0.948853i \(0.397754\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −65877.1 −0.933117
\(88\) 0 0
\(89\) −117441. −1.57161 −0.785806 0.618473i \(-0.787752\pi\)
−0.785806 + 0.618473i \(0.787752\pi\)
\(90\) 0 0
\(91\) −8961.98 −0.113449
\(92\) 0 0
\(93\) 231920. 2.78055
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −21878.3 −0.236093 −0.118047 0.993008i \(-0.537663\pi\)
−0.118047 + 0.993008i \(0.537663\pi\)
\(98\) 0 0
\(99\) −118503. −1.21518
\(100\) 0 0
\(101\) −75072.1 −0.732276 −0.366138 0.930561i \(-0.619320\pi\)
−0.366138 + 0.930561i \(0.619320\pi\)
\(102\) 0 0
\(103\) 47928.6 0.445145 0.222573 0.974916i \(-0.428555\pi\)
0.222573 + 0.974916i \(0.428555\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 92012.3 0.776938 0.388469 0.921462i \(-0.373004\pi\)
0.388469 + 0.921462i \(0.373004\pi\)
\(108\) 0 0
\(109\) −10647.5 −0.0858387 −0.0429194 0.999079i \(-0.513666\pi\)
−0.0429194 + 0.999079i \(0.513666\pi\)
\(110\) 0 0
\(111\) −101858. −0.784670
\(112\) 0 0
\(113\) −87373.9 −0.643703 −0.321852 0.946790i \(-0.604305\pi\)
−0.321852 + 0.946790i \(0.604305\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −27934.9 −0.188661
\(118\) 0 0
\(119\) 40709.4 0.263528
\(120\) 0 0
\(121\) −76890.5 −0.477429
\(122\) 0 0
\(123\) 433447. 2.58329
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 197379. 1.08591 0.542953 0.839763i \(-0.317306\pi\)
0.542953 + 0.839763i \(0.317306\pi\)
\(128\) 0 0
\(129\) −459887. −2.43320
\(130\) 0 0
\(131\) 118490. 0.603258 0.301629 0.953425i \(-0.402470\pi\)
0.301629 + 0.953425i \(0.402470\pi\)
\(132\) 0 0
\(133\) 279571. 1.37045
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 302570. 1.37728 0.688642 0.725101i \(-0.258207\pi\)
0.688642 + 0.725101i \(0.258207\pi\)
\(138\) 0 0
\(139\) −157190. −0.690062 −0.345031 0.938591i \(-0.612132\pi\)
−0.345031 + 0.938591i \(0.612132\pi\)
\(140\) 0 0
\(141\) 634650. 2.68835
\(142\) 0 0
\(143\) 19839.3 0.0811309
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9358.95 0.0357218
\(148\) 0 0
\(149\) 526340. 1.94223 0.971115 0.238612i \(-0.0766923\pi\)
0.971115 + 0.238612i \(0.0766923\pi\)
\(150\) 0 0
\(151\) −1849.08 −0.00659954 −0.00329977 0.999995i \(-0.501050\pi\)
−0.00329977 + 0.999995i \(0.501050\pi\)
\(152\) 0 0
\(153\) 126893. 0.438237
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −343342. −1.11167 −0.555837 0.831292i \(-0.687602\pi\)
−0.555837 + 0.831292i \(0.687602\pi\)
\(158\) 0 0
\(159\) 195334. 0.612753
\(160\) 0 0
\(161\) 114424. 0.347899
\(162\) 0 0
\(163\) −267463. −0.788487 −0.394243 0.919006i \(-0.628993\pi\)
−0.394243 + 0.919006i \(0.628993\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 122968. 0.341193 0.170596 0.985341i \(-0.445431\pi\)
0.170596 + 0.985341i \(0.445431\pi\)
\(168\) 0 0
\(169\) −366616. −0.987404
\(170\) 0 0
\(171\) 871437. 2.27901
\(172\) 0 0
\(173\) −288020. −0.731657 −0.365829 0.930682i \(-0.619214\pi\)
−0.365829 + 0.930682i \(0.619214\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 235682. 0.565450
\(178\) 0 0
\(179\) −246177. −0.574268 −0.287134 0.957890i \(-0.592702\pi\)
−0.287134 + 0.957890i \(0.592702\pi\)
\(180\) 0 0
\(181\) 433120. 0.982678 0.491339 0.870968i \(-0.336508\pi\)
0.491339 + 0.870968i \(0.336508\pi\)
\(182\) 0 0
\(183\) 84897.9 0.187400
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −90119.1 −0.188457
\(188\) 0 0
\(189\) 553526. 1.12715
\(190\) 0 0
\(191\) 701011. 1.39040 0.695202 0.718814i \(-0.255315\pi\)
0.695202 + 0.718814i \(0.255315\pi\)
\(192\) 0 0
\(193\) −215730. −0.416887 −0.208443 0.978034i \(-0.566840\pi\)
−0.208443 + 0.978034i \(0.566840\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 700484. 1.28598 0.642988 0.765876i \(-0.277695\pi\)
0.642988 + 0.765876i \(0.277695\pi\)
\(198\) 0 0
\(199\) −22097.5 −0.0395558 −0.0197779 0.999804i \(-0.506296\pi\)
−0.0197779 + 0.999804i \(0.506296\pi\)
\(200\) 0 0
\(201\) −825469. −1.44115
\(202\) 0 0
\(203\) −338231. −0.576068
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 356665. 0.578542
\(208\) 0 0
\(209\) −618893. −0.980054
\(210\) 0 0
\(211\) −910782. −1.40834 −0.704172 0.710030i \(-0.748681\pi\)
−0.704172 + 0.710030i \(0.748681\pi\)
\(212\) 0 0
\(213\) 915958. 1.38333
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.19074e6 1.71660
\(218\) 0 0
\(219\) 676737. 0.953475
\(220\) 0 0
\(221\) −21243.9 −0.0292587
\(222\) 0 0
\(223\) 132745. 0.178754 0.0893768 0.995998i \(-0.471512\pi\)
0.0893768 + 0.995998i \(0.471512\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −354321. −0.456386 −0.228193 0.973616i \(-0.573282\pi\)
−0.228193 + 0.973616i \(0.573282\pi\)
\(228\) 0 0
\(229\) 366643. 0.462013 0.231007 0.972952i \(-0.425798\pi\)
0.231007 + 0.972952i \(0.425798\pi\)
\(230\) 0 0
\(231\) −970370. −1.19649
\(232\) 0 0
\(233\) −1.02388e6 −1.23555 −0.617776 0.786355i \(-0.711966\pi\)
−0.617776 + 0.786355i \(0.711966\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.83023e6 −2.11658
\(238\) 0 0
\(239\) −1.19966e6 −1.35852 −0.679258 0.733899i \(-0.737698\pi\)
−0.679258 + 0.733899i \(0.737698\pi\)
\(240\) 0 0
\(241\) −94967.5 −0.105325 −0.0526626 0.998612i \(-0.516771\pi\)
−0.0526626 + 0.998612i \(0.516771\pi\)
\(242\) 0 0
\(243\) −808203. −0.878021
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −145893. −0.152157
\(248\) 0 0
\(249\) 1.01153e6 1.03390
\(250\) 0 0
\(251\) −418053. −0.418839 −0.209419 0.977826i \(-0.567157\pi\)
−0.209419 + 0.977826i \(0.567157\pi\)
\(252\) 0 0
\(253\) −253303. −0.248794
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.04586e6 −1.93216 −0.966079 0.258246i \(-0.916856\pi\)
−0.966079 + 0.258246i \(0.916856\pi\)
\(258\) 0 0
\(259\) −522967. −0.484423
\(260\) 0 0
\(261\) −1.05428e6 −0.957978
\(262\) 0 0
\(263\) 1.64024e6 1.46224 0.731119 0.682250i \(-0.238998\pi\)
0.731119 + 0.682250i \(0.238998\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.99759e6 −2.57332
\(268\) 0 0
\(269\) −720582. −0.607160 −0.303580 0.952806i \(-0.598182\pi\)
−0.303580 + 0.952806i \(0.598182\pi\)
\(270\) 0 0
\(271\) −1.14186e6 −0.944477 −0.472238 0.881471i \(-0.656554\pi\)
−0.472238 + 0.881471i \(0.656554\pi\)
\(272\) 0 0
\(273\) −228747. −0.185759
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −377028. −0.295239 −0.147620 0.989044i \(-0.547161\pi\)
−0.147620 + 0.989044i \(0.547161\pi\)
\(278\) 0 0
\(279\) 3.71160e6 2.85464
\(280\) 0 0
\(281\) −617249. −0.466331 −0.233166 0.972437i \(-0.574908\pi\)
−0.233166 + 0.972437i \(0.574908\pi\)
\(282\) 0 0
\(283\) −1.25311e6 −0.930087 −0.465044 0.885288i \(-0.653961\pi\)
−0.465044 + 0.885288i \(0.653961\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.22544e6 1.59482
\(288\) 0 0
\(289\) −1.32336e6 −0.932036
\(290\) 0 0
\(291\) −558425. −0.386574
\(292\) 0 0
\(293\) −818972. −0.557314 −0.278657 0.960391i \(-0.589889\pi\)
−0.278657 + 0.960391i \(0.589889\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.22535e6 −0.806064
\(298\) 0 0
\(299\) −59711.6 −0.0386261
\(300\) 0 0
\(301\) −2.36119e6 −1.50216
\(302\) 0 0
\(303\) −1.91615e6 −1.19901
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −136224. −0.0824915 −0.0412458 0.999149i \(-0.513133\pi\)
−0.0412458 + 0.999149i \(0.513133\pi\)
\(308\) 0 0
\(309\) 1.22334e6 0.728871
\(310\) 0 0
\(311\) −2.62886e6 −1.54122 −0.770612 0.637304i \(-0.780050\pi\)
−0.770612 + 0.637304i \(0.780050\pi\)
\(312\) 0 0
\(313\) 218161. 0.125868 0.0629341 0.998018i \(-0.479954\pi\)
0.0629341 + 0.998018i \(0.479954\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.25865e6 0.703491 0.351745 0.936096i \(-0.385588\pi\)
0.351745 + 0.936096i \(0.385588\pi\)
\(318\) 0 0
\(319\) 748750. 0.411965
\(320\) 0 0
\(321\) 2.34854e6 1.27214
\(322\) 0 0
\(323\) 662711. 0.353442
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −271770. −0.140550
\(328\) 0 0
\(329\) 3.25847e6 1.65968
\(330\) 0 0
\(331\) 3.21863e6 1.61473 0.807366 0.590051i \(-0.200892\pi\)
0.807366 + 0.590051i \(0.200892\pi\)
\(332\) 0 0
\(333\) −1.63011e6 −0.805576
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.63574e6 0.784585 0.392293 0.919840i \(-0.371682\pi\)
0.392293 + 0.919840i \(0.371682\pi\)
\(338\) 0 0
\(339\) −2.23015e6 −1.05398
\(340\) 0 0
\(341\) −2.63597e6 −1.22760
\(342\) 0 0
\(343\) −2.15448e6 −0.988796
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.83815e6 0.819514 0.409757 0.912195i \(-0.365614\pi\)
0.409757 + 0.912195i \(0.365614\pi\)
\(348\) 0 0
\(349\) −2.53806e6 −1.11542 −0.557710 0.830036i \(-0.688320\pi\)
−0.557710 + 0.830036i \(0.688320\pi\)
\(350\) 0 0
\(351\) −288854. −0.125144
\(352\) 0 0
\(353\) −1.88471e6 −0.805023 −0.402511 0.915415i \(-0.631863\pi\)
−0.402511 + 0.915415i \(0.631863\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.03907e6 0.431495
\(358\) 0 0
\(359\) −305057. −0.124924 −0.0624619 0.998047i \(-0.519895\pi\)
−0.0624619 + 0.998047i \(0.519895\pi\)
\(360\) 0 0
\(361\) 2.07507e6 0.838039
\(362\) 0 0
\(363\) −1.96257e6 −0.781731
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 727834. 0.282077 0.141038 0.990004i \(-0.454956\pi\)
0.141038 + 0.990004i \(0.454956\pi\)
\(368\) 0 0
\(369\) 6.93680e6 2.65212
\(370\) 0 0
\(371\) 1.00290e6 0.378289
\(372\) 0 0
\(373\) −4.77676e6 −1.77771 −0.888855 0.458188i \(-0.848499\pi\)
−0.888855 + 0.458188i \(0.848499\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 176504. 0.0639590
\(378\) 0 0
\(379\) 701558. 0.250880 0.125440 0.992101i \(-0.459966\pi\)
0.125440 + 0.992101i \(0.459966\pi\)
\(380\) 0 0
\(381\) 5.03794e6 1.77804
\(382\) 0 0
\(383\) −4.01069e6 −1.39708 −0.698541 0.715570i \(-0.746167\pi\)
−0.698541 + 0.715570i \(0.746167\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7.35994e6 −2.49803
\(388\) 0 0
\(389\) −4.45952e6 −1.49422 −0.747108 0.664702i \(-0.768558\pi\)
−0.747108 + 0.664702i \(0.768558\pi\)
\(390\) 0 0
\(391\) 271237. 0.0897237
\(392\) 0 0
\(393\) 3.02436e6 0.987761
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3.36993e6 1.07311 0.536555 0.843865i \(-0.319725\pi\)
0.536555 + 0.843865i \(0.319725\pi\)
\(398\) 0 0
\(399\) 7.13583e6 2.24395
\(400\) 0 0
\(401\) −3.00679e6 −0.933775 −0.466888 0.884317i \(-0.654625\pi\)
−0.466888 + 0.884317i \(0.654625\pi\)
\(402\) 0 0
\(403\) −621383. −0.190588
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.15770e6 0.346426
\(408\) 0 0
\(409\) −998012. −0.295004 −0.147502 0.989062i \(-0.547123\pi\)
−0.147502 + 0.989062i \(0.547123\pi\)
\(410\) 0 0
\(411\) 7.72284e6 2.25513
\(412\) 0 0
\(413\) 1.21006e6 0.349085
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.01215e6 −1.12989
\(418\) 0 0
\(419\) −5.53743e6 −1.54090 −0.770448 0.637503i \(-0.779967\pi\)
−0.770448 + 0.637503i \(0.779967\pi\)
\(420\) 0 0
\(421\) 1.98635e6 0.546198 0.273099 0.961986i \(-0.411951\pi\)
0.273099 + 0.961986i \(0.411951\pi\)
\(422\) 0 0
\(423\) 1.01568e7 2.75998
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 435890. 0.115693
\(428\) 0 0
\(429\) 506382. 0.132842
\(430\) 0 0
\(431\) −116512. −0.0302118 −0.0151059 0.999886i \(-0.504809\pi\)
−0.0151059 + 0.999886i \(0.504809\pi\)
\(432\) 0 0
\(433\) 4.56166e6 1.16924 0.584619 0.811308i \(-0.301244\pi\)
0.584619 + 0.811308i \(0.301244\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.86272e6 0.466599
\(438\) 0 0
\(439\) −2.92172e6 −0.723565 −0.361782 0.932263i \(-0.617832\pi\)
−0.361782 + 0.932263i \(0.617832\pi\)
\(440\) 0 0
\(441\) 149779. 0.0366736
\(442\) 0 0
\(443\) −1.59752e6 −0.386756 −0.193378 0.981124i \(-0.561944\pi\)
−0.193378 + 0.981124i \(0.561944\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.34344e7 3.18016
\(448\) 0 0
\(449\) 3.11073e6 0.728193 0.364096 0.931361i \(-0.381378\pi\)
0.364096 + 0.931361i \(0.381378\pi\)
\(450\) 0 0
\(451\) −4.92650e6 −1.14051
\(452\) 0 0
\(453\) −47196.3 −0.0108059
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6.47145e6 −1.44948 −0.724738 0.689025i \(-0.758039\pi\)
−0.724738 + 0.689025i \(0.758039\pi\)
\(458\) 0 0
\(459\) 1.31211e6 0.290695
\(460\) 0 0
\(461\) −5.47864e6 −1.20066 −0.600330 0.799752i \(-0.704964\pi\)
−0.600330 + 0.799752i \(0.704964\pi\)
\(462\) 0 0
\(463\) 2.35489e6 0.510526 0.255263 0.966872i \(-0.417838\pi\)
0.255263 + 0.966872i \(0.417838\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.56027e6 −0.967606 −0.483803 0.875177i \(-0.660745\pi\)
−0.483803 + 0.875177i \(0.660745\pi\)
\(468\) 0 0
\(469\) −4.23819e6 −0.889710
\(470\) 0 0
\(471\) −8.76351e6 −1.82023
\(472\) 0 0
\(473\) 5.22702e6 1.07424
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.12609e6 0.629079
\(478\) 0 0
\(479\) 1.88004e6 0.374394 0.187197 0.982322i \(-0.440060\pi\)
0.187197 + 0.982322i \(0.440060\pi\)
\(480\) 0 0
\(481\) 272907. 0.0537839
\(482\) 0 0
\(483\) 2.92058e6 0.569642
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.69396e6 0.323654 0.161827 0.986819i \(-0.448261\pi\)
0.161827 + 0.986819i \(0.448261\pi\)
\(488\) 0 0
\(489\) −6.82677e6 −1.29105
\(490\) 0 0
\(491\) −1.48645e6 −0.278258 −0.139129 0.990274i \(-0.544430\pi\)
−0.139129 + 0.990274i \(0.544430\pi\)
\(492\) 0 0
\(493\) −801762. −0.148569
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.70279e6 0.854013
\(498\) 0 0
\(499\) −7.09934e6 −1.27634 −0.638170 0.769896i \(-0.720308\pi\)
−0.638170 + 0.769896i \(0.720308\pi\)
\(500\) 0 0
\(501\) 3.13865e6 0.558661
\(502\) 0 0
\(503\) 9.24224e6 1.62876 0.814381 0.580331i \(-0.197077\pi\)
0.814381 + 0.580331i \(0.197077\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.35758e6 −1.61675
\(508\) 0 0
\(509\) −8.12506e6 −1.39006 −0.695028 0.718983i \(-0.744608\pi\)
−0.695028 + 0.718983i \(0.744608\pi\)
\(510\) 0 0
\(511\) 3.47456e6 0.588637
\(512\) 0 0
\(513\) 9.01089e6 1.51173
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −7.21335e6 −1.18689
\(518\) 0 0
\(519\) −7.35148e6 −1.19800
\(520\) 0 0
\(521\) 5.06245e6 0.817084 0.408542 0.912740i \(-0.366037\pi\)
0.408542 + 0.912740i \(0.366037\pi\)
\(522\) 0 0
\(523\) −4.76222e6 −0.761299 −0.380649 0.924719i \(-0.624300\pi\)
−0.380649 + 0.924719i \(0.624300\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.82260e6 0.442714
\(528\) 0 0
\(529\) −5.67396e6 −0.881550
\(530\) 0 0
\(531\) 3.77181e6 0.580515
\(532\) 0 0
\(533\) −1.16133e6 −0.177067
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.28346e6 −0.940292
\(538\) 0 0
\(539\) −106373. −0.0157709
\(540\) 0 0
\(541\) −2.89920e6 −0.425877 −0.212939 0.977066i \(-0.568303\pi\)
−0.212939 + 0.977066i \(0.568303\pi\)
\(542\) 0 0
\(543\) 1.10550e7 1.60901
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.74434e6 −0.820866 −0.410433 0.911891i \(-0.634622\pi\)
−0.410433 + 0.911891i \(0.634622\pi\)
\(548\) 0 0
\(549\) 1.35869e6 0.192393
\(550\) 0 0
\(551\) −5.50610e6 −0.772618
\(552\) 0 0
\(553\) −9.39691e6 −1.30669
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.29174e6 0.995848 0.497924 0.867221i \(-0.334096\pi\)
0.497924 + 0.867221i \(0.334096\pi\)
\(558\) 0 0
\(559\) 1.23217e6 0.166779
\(560\) 0 0
\(561\) −2.30022e6 −0.308576
\(562\) 0 0
\(563\) 6.65348e6 0.884663 0.442331 0.896852i \(-0.354151\pi\)
0.442331 + 0.896852i \(0.354151\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.12024e6 0.146336
\(568\) 0 0
\(569\) 5.78715e6 0.749349 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(570\) 0 0
\(571\) 1.22059e7 1.56667 0.783336 0.621599i \(-0.213517\pi\)
0.783336 + 0.621599i \(0.213517\pi\)
\(572\) 0 0
\(573\) 1.78927e7 2.27662
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.02981e7 1.28771 0.643853 0.765149i \(-0.277335\pi\)
0.643853 + 0.765149i \(0.277335\pi\)
\(578\) 0 0
\(579\) −5.50634e6 −0.682601
\(580\) 0 0
\(581\) 5.19346e6 0.638288
\(582\) 0 0
\(583\) −2.22014e6 −0.270526
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.30519e7 1.56343 0.781715 0.623636i \(-0.214345\pi\)
0.781715 + 0.623636i \(0.214345\pi\)
\(588\) 0 0
\(589\) 1.93842e7 2.30229
\(590\) 0 0
\(591\) 1.78793e7 2.10563
\(592\) 0 0
\(593\) 6.43920e6 0.751961 0.375980 0.926628i \(-0.377306\pi\)
0.375980 + 0.926628i \(0.377306\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −564020. −0.0647677
\(598\) 0 0
\(599\) 1.00760e7 1.14741 0.573707 0.819061i \(-0.305505\pi\)
0.573707 + 0.819061i \(0.305505\pi\)
\(600\) 0 0
\(601\) 1.57050e6 0.177358 0.0886791 0.996060i \(-0.471735\pi\)
0.0886791 + 0.996060i \(0.471735\pi\)
\(602\) 0 0
\(603\) −1.32106e7 −1.47955
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.31039e6 0.805321 0.402660 0.915349i \(-0.368086\pi\)
0.402660 + 0.915349i \(0.368086\pi\)
\(608\) 0 0
\(609\) −8.63308e6 −0.943241
\(610\) 0 0
\(611\) −1.70041e6 −0.184269
\(612\) 0 0
\(613\) 1.31997e7 1.41878 0.709389 0.704817i \(-0.248971\pi\)
0.709389 + 0.704817i \(0.248971\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.02423e7 1.08314 0.541570 0.840655i \(-0.317830\pi\)
0.541570 + 0.840655i \(0.317830\pi\)
\(618\) 0 0
\(619\) −1.05614e7 −1.10788 −0.553942 0.832555i \(-0.686877\pi\)
−0.553942 + 0.832555i \(0.686877\pi\)
\(620\) 0 0
\(621\) 3.68802e6 0.383764
\(622\) 0 0
\(623\) −1.53905e7 −1.58866
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.57967e7 −1.60472
\(628\) 0 0
\(629\) −1.23967e6 −0.124933
\(630\) 0 0
\(631\) −1.90535e7 −1.90503 −0.952513 0.304497i \(-0.901512\pi\)
−0.952513 + 0.304497i \(0.901512\pi\)
\(632\) 0 0
\(633\) −2.32470e7 −2.30599
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −25075.4 −0.00244849
\(638\) 0 0
\(639\) 1.46588e7 1.42019
\(640\) 0 0
\(641\) 8.56937e6 0.823766 0.411883 0.911237i \(-0.364871\pi\)
0.411883 + 0.911237i \(0.364871\pi\)
\(642\) 0 0
\(643\) 1.79513e7 1.71226 0.856130 0.516761i \(-0.172862\pi\)
0.856130 + 0.516761i \(0.172862\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.05470e7 0.990534 0.495267 0.868741i \(-0.335070\pi\)
0.495267 + 0.868741i \(0.335070\pi\)
\(648\) 0 0
\(649\) −2.67873e6 −0.249642
\(650\) 0 0
\(651\) 3.03928e7 2.81072
\(652\) 0 0
\(653\) −1.00324e7 −0.920712 −0.460356 0.887734i \(-0.652278\pi\)
−0.460356 + 0.887734i \(0.652278\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.08304e7 0.978879
\(658\) 0 0
\(659\) 8.99161e6 0.806536 0.403268 0.915082i \(-0.367874\pi\)
0.403268 + 0.915082i \(0.367874\pi\)
\(660\) 0 0
\(661\) 2.39297e6 0.213027 0.106513 0.994311i \(-0.466031\pi\)
0.106513 + 0.994311i \(0.466031\pi\)
\(662\) 0 0
\(663\) −542234. −0.0479074
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.25356e6 −0.196135
\(668\) 0 0
\(669\) 3.38820e6 0.292687
\(670\) 0 0
\(671\) −964938. −0.0827357
\(672\) 0 0
\(673\) −1.53612e7 −1.30733 −0.653666 0.756783i \(-0.726770\pi\)
−0.653666 + 0.756783i \(0.726770\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.16026e7 −0.972934 −0.486467 0.873699i \(-0.661715\pi\)
−0.486467 + 0.873699i \(0.661715\pi\)
\(678\) 0 0
\(679\) −2.86711e6 −0.238655
\(680\) 0 0
\(681\) −9.04375e6 −0.747275
\(682\) 0 0
\(683\) −1.20315e7 −0.986890 −0.493445 0.869777i \(-0.664263\pi\)
−0.493445 + 0.869777i \(0.664263\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 9.35825e6 0.756490
\(688\) 0 0
\(689\) −523358. −0.0420001
\(690\) 0 0
\(691\) −5.18616e6 −0.413191 −0.206595 0.978426i \(-0.566238\pi\)
−0.206595 + 0.978426i \(0.566238\pi\)
\(692\) 0 0
\(693\) −1.55296e7 −1.22836
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 5.27530e6 0.411306
\(698\) 0 0
\(699\) −2.61338e7 −2.02306
\(700\) 0 0
\(701\) 6.00859e6 0.461825 0.230913 0.972974i \(-0.425829\pi\)
0.230913 + 0.972974i \(0.425829\pi\)
\(702\) 0 0
\(703\) −8.51342e6 −0.649704
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.83807e6 −0.740221
\(708\) 0 0
\(709\) 5.90083e6 0.440857 0.220429 0.975403i \(-0.429254\pi\)
0.220429 + 0.975403i \(0.429254\pi\)
\(710\) 0 0
\(711\) −2.92906e7 −2.17297
\(712\) 0 0
\(713\) 7.93365e6 0.584453
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.06204e7 −2.22440
\(718\) 0 0
\(719\) 1.36592e7 0.985382 0.492691 0.870204i \(-0.336013\pi\)
0.492691 + 0.870204i \(0.336013\pi\)
\(720\) 0 0
\(721\) 6.28097e6 0.449975
\(722\) 0 0
\(723\) −2.42397e6 −0.172457
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.11594e7 −0.783079 −0.391539 0.920161i \(-0.628057\pi\)
−0.391539 + 0.920161i \(0.628057\pi\)
\(728\) 0 0
\(729\) −2.27059e7 −1.58242
\(730\) 0 0
\(731\) −5.59710e6 −0.387409
\(732\) 0 0
\(733\) 1.52510e7 1.04843 0.524215 0.851586i \(-0.324359\pi\)
0.524215 + 0.851586i \(0.324359\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.38217e6 0.636260
\(738\) 0 0
\(739\) 1.11820e7 0.753196 0.376598 0.926377i \(-0.377094\pi\)
0.376598 + 0.926377i \(0.377094\pi\)
\(740\) 0 0
\(741\) −3.72379e6 −0.249138
\(742\) 0 0
\(743\) 7.71450e6 0.512667 0.256334 0.966588i \(-0.417485\pi\)
0.256334 + 0.966588i \(0.417485\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.61883e7 1.06145
\(748\) 0 0
\(749\) 1.20581e7 0.785367
\(750\) 0 0
\(751\) 2.23973e7 1.44909 0.724545 0.689228i \(-0.242050\pi\)
0.724545 + 0.689228i \(0.242050\pi\)
\(752\) 0 0
\(753\) −1.06704e7 −0.685796
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.57267e7 −1.63171 −0.815857 0.578254i \(-0.803734\pi\)
−0.815857 + 0.578254i \(0.803734\pi\)
\(758\) 0 0
\(759\) −6.46535e6 −0.407369
\(760\) 0 0
\(761\) −1.48340e7 −0.928533 −0.464267 0.885696i \(-0.653682\pi\)
−0.464267 + 0.885696i \(0.653682\pi\)
\(762\) 0 0
\(763\) −1.39534e6 −0.0867700
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −631463. −0.0387578
\(768\) 0 0
\(769\) −5.57112e6 −0.339724 −0.169862 0.985468i \(-0.554332\pi\)
−0.169862 + 0.985468i \(0.554332\pi\)
\(770\) 0 0
\(771\) −5.22188e7 −3.16367
\(772\) 0 0
\(773\) 1.58230e7 0.952447 0.476224 0.879324i \(-0.342005\pi\)
0.476224 + 0.879324i \(0.342005\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.33483e7 −0.793183
\(778\) 0 0
\(779\) 3.62281e7 2.13896
\(780\) 0 0
\(781\) −1.04107e7 −0.610732
\(782\) 0 0
\(783\) −1.09016e7 −0.635454
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.31529e7 −0.756981 −0.378491 0.925605i \(-0.623557\pi\)
−0.378491 + 0.925605i \(0.623557\pi\)
\(788\) 0 0
\(789\) 4.18658e7 2.39423
\(790\) 0 0
\(791\) −1.14502e7 −0.650687
\(792\) 0 0
\(793\) −227466. −0.0128450
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.58443e7 1.44118 0.720590 0.693361i \(-0.243871\pi\)
0.720590 + 0.693361i \(0.243871\pi\)
\(798\) 0 0
\(799\) 7.72406e6 0.428034
\(800\) 0 0
\(801\) −4.79728e7 −2.64188
\(802\) 0 0
\(803\) −7.69170e6 −0.420953
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.83923e7 −0.994149
\(808\) 0 0
\(809\) 1.78857e7 0.960804 0.480402 0.877048i \(-0.340491\pi\)
0.480402 + 0.877048i \(0.340491\pi\)
\(810\) 0 0
\(811\) 1.41608e7 0.756026 0.378013 0.925800i \(-0.376607\pi\)
0.378013 + 0.925800i \(0.376607\pi\)
\(812\) 0 0
\(813\) −2.91451e7 −1.54646
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −3.84380e7 −2.01468
\(818\) 0 0
\(819\) −3.66082e6 −0.190708
\(820\) 0 0
\(821\) −3.46248e7 −1.79279 −0.896394 0.443258i \(-0.853823\pi\)
−0.896394 + 0.443258i \(0.853823\pi\)
\(822\) 0 0
\(823\) 2.13360e7 1.09803 0.549015 0.835813i \(-0.315003\pi\)
0.549015 + 0.835813i \(0.315003\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.59813e6 −0.0812548 −0.0406274 0.999174i \(-0.512936\pi\)
−0.0406274 + 0.999174i \(0.512936\pi\)
\(828\) 0 0
\(829\) −2.53923e7 −1.28327 −0.641633 0.767012i \(-0.721743\pi\)
−0.641633 + 0.767012i \(0.721743\pi\)
\(830\) 0 0
\(831\) −9.62333e6 −0.483418
\(832\) 0 0
\(833\) 113904. 0.00568755
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.83790e7 1.89356
\(838\) 0 0
\(839\) −1.98528e7 −0.973681 −0.486841 0.873491i \(-0.661851\pi\)
−0.486841 + 0.873491i \(0.661851\pi\)
\(840\) 0 0
\(841\) −1.38498e7 −0.675231
\(842\) 0 0
\(843\) −1.57548e7 −0.763560
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00764e7 −0.482609
\(848\) 0 0
\(849\) −3.19846e7 −1.52290
\(850\) 0 0
\(851\) −3.48441e6 −0.164932
\(852\) 0 0
\(853\) −1.59794e7 −0.751948 −0.375974 0.926630i \(-0.622692\pi\)
−0.375974 + 0.926630i \(0.622692\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7.00157e6 0.325644 0.162822 0.986655i \(-0.447940\pi\)
0.162822 + 0.986655i \(0.447940\pi\)
\(858\) 0 0
\(859\) 7.28414e6 0.336818 0.168409 0.985717i \(-0.446137\pi\)
0.168409 + 0.985717i \(0.446137\pi\)
\(860\) 0 0
\(861\) 5.68026e7 2.61132
\(862\) 0 0
\(863\) 1.76361e7 0.806075 0.403037 0.915184i \(-0.367954\pi\)
0.403037 + 0.915184i \(0.367954\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −3.37776e7 −1.52609
\(868\) 0 0
\(869\) 2.08021e7 0.934455
\(870\) 0 0
\(871\) 2.21167e6 0.0987816
\(872\) 0 0
\(873\) −8.93692e6 −0.396874
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.69004e7 −1.18102 −0.590512 0.807029i \(-0.701074\pi\)
−0.590512 + 0.807029i \(0.701074\pi\)
\(878\) 0 0
\(879\) −2.09036e7 −0.912533
\(880\) 0 0
\(881\) 2.51911e7 1.09347 0.546735 0.837306i \(-0.315870\pi\)
0.546735 + 0.837306i \(0.315870\pi\)
\(882\) 0 0
\(883\) −3.22126e7 −1.39035 −0.695175 0.718840i \(-0.744673\pi\)
−0.695175 + 0.718840i \(0.744673\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.96139e6 0.382443 0.191221 0.981547i \(-0.438755\pi\)
0.191221 + 0.981547i \(0.438755\pi\)
\(888\) 0 0
\(889\) 2.58662e7 1.09769
\(890\) 0 0
\(891\) −2.47989e6 −0.104650
\(892\) 0 0
\(893\) 5.30449e7 2.22595
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.52409e6 −0.0632454
\(898\) 0 0
\(899\) −2.34514e7 −0.967765
\(900\) 0 0
\(901\) 2.37733e6 0.0975613
\(902\) 0 0
\(903\) −6.02675e7 −2.45960
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −5.81689e6 −0.234786 −0.117393 0.993086i \(-0.537454\pi\)
−0.117393 + 0.993086i \(0.537454\pi\)
\(908\) 0 0
\(909\) −3.06657e7 −1.23096
\(910\) 0 0
\(911\) 1.96435e7 0.784192 0.392096 0.919924i \(-0.371750\pi\)
0.392096 + 0.919924i \(0.371750\pi\)
\(912\) 0 0
\(913\) −1.14969e7 −0.456460
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.55279e7 0.609803
\(918\) 0 0
\(919\) 89962.4 0.00351376 0.00175688 0.999998i \(-0.499441\pi\)
0.00175688 + 0.999998i \(0.499441\pi\)
\(920\) 0 0
\(921\) −3.47702e6 −0.135070
\(922\) 0 0
\(923\) −2.45412e6 −0.0948183
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.95781e7 0.748290
\(928\) 0 0
\(929\) 3.65192e7 1.38830 0.694149 0.719832i \(-0.255781\pi\)
0.694149 + 0.719832i \(0.255781\pi\)
\(930\) 0 0
\(931\) 782234. 0.0295776
\(932\) 0 0
\(933\) −6.70994e7 −2.52357
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 3.58659e7 1.33454 0.667272 0.744814i \(-0.267462\pi\)
0.667272 + 0.744814i \(0.267462\pi\)
\(938\) 0 0
\(939\) 5.56838e6 0.206094
\(940\) 0 0
\(941\) −3.19693e7 −1.17695 −0.588476 0.808515i \(-0.700272\pi\)
−0.588476 + 0.808515i \(0.700272\pi\)
\(942\) 0 0
\(943\) 1.48276e7 0.542990
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.71846e7 1.70972 0.854861 0.518858i \(-0.173643\pi\)
0.854861 + 0.518858i \(0.173643\pi\)
\(948\) 0 0
\(949\) −1.81318e6 −0.0653544
\(950\) 0 0
\(951\) 3.21261e7 1.15188
\(952\) 0 0
\(953\) −1.65226e6 −0.0589315 −0.0294657 0.999566i \(-0.509381\pi\)
−0.0294657 + 0.999566i \(0.509381\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.91112e7 0.674541
\(958\) 0 0
\(959\) 3.96512e7 1.39223
\(960\) 0 0
\(961\) 5.39316e7 1.88380
\(962\) 0 0
\(963\) 3.75855e7 1.30603
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −3.23040e7 −1.11094 −0.555470 0.831537i \(-0.687462\pi\)
−0.555470 + 0.831537i \(0.687462\pi\)
\(968\) 0 0
\(969\) 1.69151e7 0.578717
\(970\) 0 0
\(971\) −1.15927e7 −0.394582 −0.197291 0.980345i \(-0.563214\pi\)
−0.197291 + 0.980345i \(0.563214\pi\)
\(972\) 0 0
\(973\) −2.05995e7 −0.697549
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.58947e7 −0.867909 −0.433954 0.900935i \(-0.642882\pi\)
−0.433954 + 0.900935i \(0.642882\pi\)
\(978\) 0 0
\(979\) 3.40702e7 1.13610
\(980\) 0 0
\(981\) −4.34935e6 −0.144295
\(982\) 0 0
\(983\) 3.46040e7 1.14220 0.571101 0.820880i \(-0.306517\pi\)
0.571101 + 0.820880i \(0.306517\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 8.31698e7 2.71752
\(988\) 0 0
\(989\) −1.57321e7 −0.511441
\(990\) 0 0
\(991\) 3.71464e7 1.20152 0.600762 0.799428i \(-0.294864\pi\)
0.600762 + 0.799428i \(0.294864\pi\)
\(992\) 0 0
\(993\) 8.21528e7 2.64393
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.47350e7 0.788086 0.394043 0.919092i \(-0.371076\pi\)
0.394043 + 0.919092i \(0.371076\pi\)
\(998\) 0 0
\(999\) −1.68558e7 −0.534362
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 400.6.a.w.1.2 2
4.3 odd 2 25.6.a.b.1.2 2
5.2 odd 4 400.6.c.n.49.1 4
5.3 odd 4 400.6.c.n.49.4 4
5.4 even 2 400.6.a.o.1.1 2
12.11 even 2 225.6.a.s.1.1 2
20.3 even 4 25.6.b.b.24.2 4
20.7 even 4 25.6.b.b.24.3 4
20.19 odd 2 25.6.a.d.1.1 yes 2
60.23 odd 4 225.6.b.i.199.3 4
60.47 odd 4 225.6.b.i.199.2 4
60.59 even 2 225.6.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.6.a.b.1.2 2 4.3 odd 2
25.6.a.d.1.1 yes 2 20.19 odd 2
25.6.b.b.24.2 4 20.3 even 4
25.6.b.b.24.3 4 20.7 even 4
225.6.a.l.1.2 2 60.59 even 2
225.6.a.s.1.1 2 12.11 even 2
225.6.b.i.199.2 4 60.47 odd 4
225.6.b.i.199.3 4 60.23 odd 4
400.6.a.o.1.1 2 5.4 even 2
400.6.a.w.1.2 2 1.1 even 1 trivial
400.6.c.n.49.1 4 5.2 odd 4
400.6.c.n.49.4 4 5.3 odd 4