Properties

Label 900.3.g.a.701.2
Level $900$
Weight $3$
Character 900.701
Analytic conductor $24.523$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Defining polynomial: \(x^{2} + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.2
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 900.701
Dual form 900.3.g.a.701.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{7} +O(q^{10})\) \(q-1.00000 q^{7} +4.24264i q^{11} -7.00000 q^{13} -4.24264i q^{17} -7.00000 q^{19} -29.6985i q^{23} -29.6985i q^{29} +17.0000 q^{31} -16.0000 q^{37} +50.9117i q^{41} -55.0000 q^{43} -46.6690i q^{47} -48.0000 q^{49} -84.8528i q^{53} -55.1543i q^{59} +65.0000 q^{61} -49.0000 q^{67} +50.9117i q^{71} -88.0000 q^{73} -4.24264i q^{77} -40.0000 q^{79} -156.978i q^{83} -101.823i q^{89} +7.00000 q^{91} +41.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{7} + O(q^{10}) \) \( 2q - 2q^{7} - 14q^{13} - 14q^{19} + 34q^{31} - 32q^{37} - 110q^{43} - 96q^{49} + 130q^{61} - 98q^{67} - 176q^{73} - 80q^{79} + 14q^{91} + 82q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.142857 −0.0714286 0.997446i \(-0.522756\pi\)
−0.0714286 + 0.997446i \(0.522756\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.24264i 0.385695i 0.981229 + 0.192847i \(0.0617722\pi\)
−0.981229 + 0.192847i \(0.938228\pi\)
\(12\) 0 0
\(13\) −7.00000 −0.538462 −0.269231 0.963076i \(-0.586769\pi\)
−0.269231 + 0.963076i \(0.586769\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 4.24264i − 0.249567i −0.992184 0.124784i \(-0.960176\pi\)
0.992184 0.124784i \(-0.0398236\pi\)
\(18\) 0 0
\(19\) −7.00000 −0.368421 −0.184211 0.982887i \(-0.558973\pi\)
−0.184211 + 0.982887i \(0.558973\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 29.6985i − 1.29124i −0.763659 0.645619i \(-0.776599\pi\)
0.763659 0.645619i \(-0.223401\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 29.6985i − 1.02409i −0.858960 0.512043i \(-0.828889\pi\)
0.858960 0.512043i \(-0.171111\pi\)
\(30\) 0 0
\(31\) 17.0000 0.548387 0.274194 0.961675i \(-0.411589\pi\)
0.274194 + 0.961675i \(0.411589\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −16.0000 −0.432432 −0.216216 0.976346i \(-0.569372\pi\)
−0.216216 + 0.976346i \(0.569372\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 50.9117i 1.24175i 0.783910 + 0.620874i \(0.213222\pi\)
−0.783910 + 0.620874i \(0.786778\pi\)
\(42\) 0 0
\(43\) −55.0000 −1.27907 −0.639535 0.768762i \(-0.720873\pi\)
−0.639535 + 0.768762i \(0.720873\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 46.6690i − 0.992958i −0.868049 0.496479i \(-0.834626\pi\)
0.868049 0.496479i \(-0.165374\pi\)
\(48\) 0 0
\(49\) −48.0000 −0.979592
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 84.8528i − 1.60100i −0.599335 0.800498i \(-0.704568\pi\)
0.599335 0.800498i \(-0.295432\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 55.1543i − 0.934819i −0.884041 0.467410i \(-0.845187\pi\)
0.884041 0.467410i \(-0.154813\pi\)
\(60\) 0 0
\(61\) 65.0000 1.06557 0.532787 0.846249i \(-0.321145\pi\)
0.532787 + 0.846249i \(0.321145\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −49.0000 −0.731343 −0.365672 0.930744i \(-0.619161\pi\)
−0.365672 + 0.930744i \(0.619161\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 50.9117i 0.717066i 0.933517 + 0.358533i \(0.116723\pi\)
−0.933517 + 0.358533i \(0.883277\pi\)
\(72\) 0 0
\(73\) −88.0000 −1.20548 −0.602740 0.797938i \(-0.705924\pi\)
−0.602740 + 0.797938i \(0.705924\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.24264i − 0.0550992i
\(78\) 0 0
\(79\) −40.0000 −0.506329 −0.253165 0.967423i \(-0.581471\pi\)
−0.253165 + 0.967423i \(0.581471\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 156.978i − 1.89130i −0.325190 0.945649i \(-0.605428\pi\)
0.325190 0.945649i \(-0.394572\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 101.823i − 1.14408i −0.820225 0.572041i \(-0.806152\pi\)
0.820225 0.572041i \(-0.193848\pi\)
\(90\) 0 0
\(91\) 7.00000 0.0769231
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 41.0000 0.422680 0.211340 0.977413i \(-0.432217\pi\)
0.211340 + 0.977413i \(0.432217\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 118.794i 1.17618i 0.808796 + 0.588089i \(0.200119\pi\)
−0.808796 + 0.588089i \(0.799881\pi\)
\(102\) 0 0
\(103\) −82.0000 −0.796117 −0.398058 0.917360i \(-0.630316\pi\)
−0.398058 + 0.917360i \(0.630316\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 118.794i − 1.11022i −0.831776 0.555112i \(-0.812675\pi\)
0.831776 0.555112i \(-0.187325\pi\)
\(108\) 0 0
\(109\) −49.0000 −0.449541 −0.224771 0.974412i \(-0.572163\pi\)
−0.224771 + 0.974412i \(0.572163\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 67.8823i − 0.600728i −0.953825 0.300364i \(-0.902892\pi\)
0.953825 0.300364i \(-0.0971081\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.24264i 0.0356524i
\(120\) 0 0
\(121\) 103.000 0.851240
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −160.000 −1.25984 −0.629921 0.776659i \(-0.716913\pi\)
−0.629921 + 0.776659i \(0.716913\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 16.9706i − 0.129546i −0.997900 0.0647731i \(-0.979368\pi\)
0.997900 0.0647731i \(-0.0206324\pi\)
\(132\) 0 0
\(133\) 7.00000 0.0526316
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 89.0955i 0.650332i 0.945657 + 0.325166i \(0.105420\pi\)
−0.945657 + 0.325166i \(0.894580\pi\)
\(138\) 0 0
\(139\) 8.00000 0.0575540 0.0287770 0.999586i \(-0.490839\pi\)
0.0287770 + 0.999586i \(0.490839\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 29.6985i − 0.207682i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 89.0955i − 0.597956i −0.954260 0.298978i \(-0.903354\pi\)
0.954260 0.298978i \(-0.0966457\pi\)
\(150\) 0 0
\(151\) −25.0000 −0.165563 −0.0827815 0.996568i \(-0.526380\pi\)
−0.0827815 + 0.996568i \(0.526380\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 137.000 0.872611 0.436306 0.899798i \(-0.356287\pi\)
0.436306 + 0.899798i \(0.356287\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 29.6985i 0.184463i
\(162\) 0 0
\(163\) −79.0000 −0.484663 −0.242331 0.970194i \(-0.577912\pi\)
−0.242331 + 0.970194i \(0.577912\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 118.794i − 0.711341i −0.934611 0.355670i \(-0.884253\pi\)
0.934611 0.355670i \(-0.115747\pi\)
\(168\) 0 0
\(169\) −120.000 −0.710059
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 131.522i 0.760242i 0.924937 + 0.380121i \(0.124118\pi\)
−0.924937 + 0.380121i \(0.875882\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 148.492i 0.829567i 0.909920 + 0.414783i \(0.136143\pi\)
−0.909920 + 0.414783i \(0.863857\pi\)
\(180\) 0 0
\(181\) −97.0000 −0.535912 −0.267956 0.963431i \(-0.586348\pi\)
−0.267956 + 0.963431i \(0.586348\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 18.0000 0.0962567
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 207.889i − 1.08843i −0.838947 0.544213i \(-0.816828\pi\)
0.838947 0.544213i \(-0.183172\pi\)
\(192\) 0 0
\(193\) 185.000 0.958549 0.479275 0.877665i \(-0.340900\pi\)
0.479275 + 0.877665i \(0.340900\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 258.801i 1.31371i 0.754016 + 0.656856i \(0.228114\pi\)
−0.754016 + 0.656856i \(0.771886\pi\)
\(198\) 0 0
\(199\) 311.000 1.56281 0.781407 0.624022i \(-0.214502\pi\)
0.781407 + 0.624022i \(0.214502\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 29.6985i 0.146298i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 29.6985i − 0.142098i
\(210\) 0 0
\(211\) −97.0000 −0.459716 −0.229858 0.973224i \(-0.573826\pi\)
−0.229858 + 0.973224i \(0.573826\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −17.0000 −0.0783410
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 29.6985i 0.134382i
\(222\) 0 0
\(223\) 239.000 1.07175 0.535874 0.844298i \(-0.319982\pi\)
0.535874 + 0.844298i \(0.319982\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 152.735i − 0.672842i −0.941712 0.336421i \(-0.890784\pi\)
0.941712 0.336421i \(-0.109216\pi\)
\(228\) 0 0
\(229\) 17.0000 0.0742358 0.0371179 0.999311i \(-0.488182\pi\)
0.0371179 + 0.999311i \(0.488182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 356.382i 1.52954i 0.644306 + 0.764768i \(0.277146\pi\)
−0.644306 + 0.764768i \(0.722854\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 424.264i 1.77516i 0.460650 + 0.887582i \(0.347616\pi\)
−0.460650 + 0.887582i \(0.652384\pi\)
\(240\) 0 0
\(241\) 95.0000 0.394191 0.197095 0.980384i \(-0.436849\pi\)
0.197095 + 0.980384i \(0.436849\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 49.0000 0.198381
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 237.588i − 0.946565i −0.880911 0.473283i \(-0.843069\pi\)
0.880911 0.473283i \(-0.156931\pi\)
\(252\) 0 0
\(253\) 126.000 0.498024
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 339.411i 1.32067i 0.750973 + 0.660333i \(0.229585\pi\)
−0.750973 + 0.660333i \(0.770415\pi\)
\(258\) 0 0
\(259\) 16.0000 0.0617761
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 322.441i 1.22601i 0.790079 + 0.613005i \(0.210040\pi\)
−0.790079 + 0.613005i \(0.789960\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.6985i 0.110403i 0.998475 + 0.0552016i \(0.0175802\pi\)
−0.998475 + 0.0552016i \(0.982420\pi\)
\(270\) 0 0
\(271\) −448.000 −1.65314 −0.826568 0.562836i \(-0.809710\pi\)
−0.826568 + 0.562836i \(0.809710\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 455.000 1.64260 0.821300 0.570497i \(-0.193249\pi\)
0.821300 + 0.570497i \(0.193249\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 97.5807i − 0.347262i −0.984811 0.173631i \(-0.944450\pi\)
0.984811 0.173631i \(-0.0555501\pi\)
\(282\) 0 0
\(283\) 71.0000 0.250883 0.125442 0.992101i \(-0.459965\pi\)
0.125442 + 0.992101i \(0.459965\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 50.9117i − 0.177393i
\(288\) 0 0
\(289\) 271.000 0.937716
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 394.566i 1.34664i 0.739351 + 0.673320i \(0.235132\pi\)
−0.739351 + 0.673320i \(0.764868\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 207.889i 0.695282i
\(300\) 0 0
\(301\) 55.0000 0.182724
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −559.000 −1.82085 −0.910423 0.413678i \(-0.864244\pi\)
−0.910423 + 0.413678i \(0.864244\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 564.271i − 1.81438i −0.420725 0.907188i \(-0.638224\pi\)
0.420725 0.907188i \(-0.361776\pi\)
\(312\) 0 0
\(313\) 383.000 1.22364 0.611821 0.790996i \(-0.290437\pi\)
0.611821 + 0.790996i \(0.290437\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 373.352i 1.17777i 0.808218 + 0.588884i \(0.200432\pi\)
−0.808218 + 0.588884i \(0.799568\pi\)
\(318\) 0 0
\(319\) 126.000 0.394984
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 29.6985i 0.0919458i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 46.6690i 0.141851i
\(330\) 0 0
\(331\) −40.0000 −0.120846 −0.0604230 0.998173i \(-0.519245\pi\)
−0.0604230 + 0.998173i \(0.519245\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 449.000 1.33234 0.666172 0.745798i \(-0.267932\pi\)
0.666172 + 0.745798i \(0.267932\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 72.1249i 0.211510i
\(342\) 0 0
\(343\) 97.0000 0.282799
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 292.742i − 0.843637i −0.906680 0.421819i \(-0.861392\pi\)
0.906680 0.421819i \(-0.138608\pi\)
\(348\) 0 0
\(349\) −184.000 −0.527221 −0.263610 0.964629i \(-0.584913\pi\)
−0.263610 + 0.964629i \(0.584913\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 267.286i 0.757185i 0.925563 + 0.378593i \(0.123592\pi\)
−0.925563 + 0.378593i \(0.876408\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 220.617i 0.614533i 0.951624 + 0.307266i \(0.0994143\pi\)
−0.951624 + 0.307266i \(0.900586\pi\)
\(360\) 0 0
\(361\) −312.000 −0.864266
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 263.000 0.716621 0.358311 0.933602i \(-0.383353\pi\)
0.358311 + 0.933602i \(0.383353\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 84.8528i 0.228714i
\(372\) 0 0
\(373\) 305.000 0.817694 0.408847 0.912603i \(-0.365931\pi\)
0.408847 + 0.912603i \(0.365931\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 207.889i 0.551431i
\(378\) 0 0
\(379\) 497.000 1.31135 0.655673 0.755045i \(-0.272385\pi\)
0.655673 + 0.755045i \(0.272385\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 237.588i 0.620334i 0.950682 + 0.310167i \(0.100385\pi\)
−0.950682 + 0.310167i \(0.899615\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 84.8528i 0.218131i 0.994035 + 0.109065i \(0.0347858\pi\)
−0.994035 + 0.109065i \(0.965214\pi\)
\(390\) 0 0
\(391\) −126.000 −0.322251
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −439.000 −1.10579 −0.552897 0.833250i \(-0.686478\pi\)
−0.552897 + 0.833250i \(0.686478\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 254.558i 0.634809i 0.948290 + 0.317405i \(0.102811\pi\)
−0.948290 + 0.317405i \(0.897189\pi\)
\(402\) 0 0
\(403\) −119.000 −0.295285
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 67.8823i − 0.166787i
\(408\) 0 0
\(409\) −343.000 −0.838631 −0.419315 0.907841i \(-0.637730\pi\)
−0.419315 + 0.907841i \(0.637730\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 55.1543i 0.133546i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 118.794i − 0.283518i −0.989901 0.141759i \(-0.954724\pi\)
0.989901 0.141759i \(-0.0452758\pi\)
\(420\) 0 0
\(421\) 608.000 1.44418 0.722090 0.691799i \(-0.243182\pi\)
0.722090 + 0.691799i \(0.243182\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −65.0000 −0.152225
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 445.477i − 1.03359i −0.856109 0.516795i \(-0.827125\pi\)
0.856109 0.516795i \(-0.172875\pi\)
\(432\) 0 0
\(433\) −337.000 −0.778291 −0.389145 0.921176i \(-0.627230\pi\)
−0.389145 + 0.921176i \(0.627230\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 207.889i 0.475719i
\(438\) 0 0
\(439\) 65.0000 0.148064 0.0740319 0.997256i \(-0.476413\pi\)
0.0740319 + 0.997256i \(0.476413\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 576.999i − 1.30248i −0.758871 0.651241i \(-0.774249\pi\)
0.758871 0.651241i \(-0.225751\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 237.588i − 0.529149i −0.964365 0.264574i \(-0.914769\pi\)
0.964365 0.264574i \(-0.0852315\pi\)
\(450\) 0 0
\(451\) −216.000 −0.478936
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 590.000 1.29103 0.645514 0.763748i \(-0.276643\pi\)
0.645514 + 0.763748i \(0.276643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 50.9117i − 0.110438i −0.998474 0.0552188i \(-0.982414\pi\)
0.998474 0.0552188i \(-0.0175856\pi\)
\(462\) 0 0
\(463\) −64.0000 −0.138229 −0.0691145 0.997609i \(-0.522017\pi\)
−0.0691145 + 0.997609i \(0.522017\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 343.654i − 0.735876i −0.929850 0.367938i \(-0.880064\pi\)
0.929850 0.367938i \(-0.119936\pi\)
\(468\) 0 0
\(469\) 49.0000 0.104478
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 233.345i − 0.493330i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 326.683i 0.682011i 0.940061 + 0.341006i \(0.110768\pi\)
−0.940061 + 0.341006i \(0.889232\pi\)
\(480\) 0 0
\(481\) 112.000 0.232848
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −823.000 −1.68994 −0.844969 0.534815i \(-0.820381\pi\)
−0.844969 + 0.534815i \(0.820381\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 475.176i 0.967771i 0.875131 + 0.483886i \(0.160775\pi\)
−0.875131 + 0.483886i \(0.839225\pi\)
\(492\) 0 0
\(493\) −126.000 −0.255578
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 50.9117i − 0.102438i
\(498\) 0 0
\(499\) −553.000 −1.10822 −0.554108 0.832445i \(-0.686941\pi\)
−0.554108 + 0.832445i \(0.686941\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 118.794i − 0.236171i −0.993003 0.118085i \(-0.962324\pi\)
0.993003 0.118085i \(-0.0376757\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 725.492i − 1.42533i −0.701506 0.712664i \(-0.747489\pi\)
0.701506 0.712664i \(-0.252511\pi\)
\(510\) 0 0
\(511\) 88.0000 0.172211
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 198.000 0.382979
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 649.124i 1.24592i 0.782254 + 0.622960i \(0.214070\pi\)
−0.782254 + 0.622960i \(0.785930\pi\)
\(522\) 0 0
\(523\) −775.000 −1.48184 −0.740918 0.671596i \(-0.765609\pi\)
−0.740918 + 0.671596i \(0.765609\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 72.1249i − 0.136859i
\(528\) 0 0
\(529\) −353.000 −0.667297
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 356.382i − 0.668634i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 203.647i − 0.377823i
\(540\) 0 0
\(541\) −175.000 −0.323475 −0.161738 0.986834i \(-0.551710\pi\)
−0.161738 + 0.986834i \(0.551710\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 266.000 0.486289 0.243144 0.969990i \(-0.421821\pi\)
0.243144 + 0.969990i \(0.421821\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 207.889i 0.377295i
\(552\) 0 0
\(553\) 40.0000 0.0723327
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 292.742i − 0.525569i −0.964854 0.262785i \(-0.915359\pi\)
0.964854 0.262785i \(-0.0846409\pi\)
\(558\) 0 0
\(559\) 385.000 0.688730
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 1013.99i − 1.80105i −0.434804 0.900525i \(-0.643182\pi\)
0.434804 0.900525i \(-0.356818\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 683.065i − 1.20047i −0.799825 0.600233i \(-0.795075\pi\)
0.799825 0.600233i \(-0.204925\pi\)
\(570\) 0 0
\(571\) 1001.00 1.75306 0.876532 0.481343i \(-0.159851\pi\)
0.876532 + 0.481343i \(0.159851\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1081.00 −1.87348 −0.936742 0.350021i \(-0.886174\pi\)
−0.936742 + 0.350021i \(0.886174\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 156.978i 0.270185i
\(582\) 0 0
\(583\) 360.000 0.617496
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 661.852i − 1.12752i −0.825940 0.563758i \(-0.809355\pi\)
0.825940 0.563758i \(-0.190645\pi\)
\(588\) 0 0
\(589\) −119.000 −0.202037
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 593.970i − 1.00164i −0.865553 0.500818i \(-0.833033\pi\)
0.865553 0.500818i \(-0.166967\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 665.000 1.10649 0.553245 0.833019i \(-0.313389\pi\)
0.553245 + 0.833019i \(0.313389\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 296.000 0.487644 0.243822 0.969820i \(-0.421599\pi\)
0.243822 + 0.969820i \(0.421599\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 326.683i 0.534670i
\(612\) 0 0
\(613\) −952.000 −1.55302 −0.776509 0.630106i \(-0.783011\pi\)
−0.776509 + 0.630106i \(0.783011\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 50.9117i 0.0825149i 0.999149 + 0.0412574i \(0.0131364\pi\)
−0.999149 + 0.0412574i \(0.986864\pi\)
\(618\) 0 0
\(619\) −1033.00 −1.66882 −0.834410 0.551144i \(-0.814192\pi\)
−0.834410 + 0.551144i \(0.814192\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 101.823i 0.163440i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 67.8823i 0.107921i
\(630\) 0 0
\(631\) −799.000 −1.26624 −0.633122 0.774052i \(-0.718227\pi\)
−0.633122 + 0.774052i \(0.718227\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 336.000 0.527473
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 203.647i 0.317702i 0.987303 + 0.158851i \(0.0507789\pi\)
−0.987303 + 0.158851i \(0.949221\pi\)
\(642\) 0 0
\(643\) −1000.00 −1.55521 −0.777605 0.628753i \(-0.783566\pi\)
−0.777605 + 0.628753i \(0.783566\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 33.9411i 0.0524592i 0.999656 + 0.0262296i \(0.00835010\pi\)
−0.999656 + 0.0262296i \(0.991650\pi\)
\(648\) 0 0
\(649\) 234.000 0.360555
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 462.448i − 0.708190i −0.935210 0.354095i \(-0.884789\pi\)
0.935210 0.354095i \(-0.115211\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 1238.85i − 1.87990i −0.341318 0.939948i \(-0.610873\pi\)
0.341318 0.939948i \(-0.389127\pi\)
\(660\) 0 0
\(661\) −136.000 −0.205749 −0.102874 0.994694i \(-0.532804\pi\)
−0.102874 + 0.994694i \(0.532804\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −882.000 −1.32234
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 275.772i 0.410986i
\(672\) 0 0
\(673\) −328.000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 29.6985i − 0.0438678i −0.999759 0.0219339i \(-0.993018\pi\)
0.999759 0.0219339i \(-0.00698233\pi\)
\(678\) 0 0
\(679\) −41.0000 −0.0603829
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 984.293i − 1.44113i −0.693387 0.720566i \(-0.743882\pi\)
0.693387 0.720566i \(-0.256118\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 593.970i 0.862075i
\(690\) 0 0
\(691\) 842.000 1.21852 0.609262 0.792969i \(-0.291466\pi\)
0.609262 + 0.792969i \(0.291466\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 216.000 0.309900
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 335.169i 0.478129i 0.971004 + 0.239065i \(0.0768408\pi\)
−0.971004 + 0.239065i \(0.923159\pi\)
\(702\) 0 0
\(703\) 112.000 0.159317
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 118.794i − 0.168025i
\(708\) 0 0
\(709\) −985.000 −1.38928 −0.694640 0.719357i \(-0.744436\pi\)
−0.694640 + 0.719357i \(0.744436\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 504.874i − 0.708099i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 267.286i − 0.371747i −0.982574 0.185874i \(-0.940488\pi\)
0.982574 0.185874i \(-0.0595115\pi\)
\(720\) 0 0
\(721\) 82.0000 0.113731
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 623.000 0.856946 0.428473 0.903555i \(-0.359052\pi\)
0.428473 + 0.903555i \(0.359052\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 233.345i 0.319214i
\(732\) 0 0
\(733\) 296.000 0.403820 0.201910 0.979404i \(-0.435285\pi\)
0.201910 + 0.979404i \(0.435285\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 207.889i − 0.282075i
\(738\) 0 0
\(739\) 704.000 0.952639 0.476319 0.879272i \(-0.341971\pi\)
0.476319 + 0.879272i \(0.341971\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 712.764i 0.959305i 0.877459 + 0.479653i \(0.159237\pi\)
−0.877459 + 0.479653i \(0.840763\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 118.794i 0.158603i
\(750\) 0 0
\(751\) 656.000 0.873502 0.436751 0.899582i \(-0.356129\pi\)
0.436751 + 0.899582i \(0.356129\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −937.000 −1.23778 −0.618890 0.785477i \(-0.712417\pi\)
−0.618890 + 0.785477i \(0.712417\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 475.176i − 0.624410i −0.950015 0.312205i \(-0.898932\pi\)
0.950015 0.312205i \(-0.101068\pi\)
\(762\) 0 0
\(763\) 49.0000 0.0642202
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 386.080i 0.503364i
\(768\) 0 0
\(769\) 281.000 0.365410 0.182705 0.983168i \(-0.441515\pi\)
0.182705 + 0.983168i \(0.441515\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 118.794i − 0.153679i −0.997043 0.0768395i \(-0.975517\pi\)
0.997043 0.0768395i \(-0.0244829\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 356.382i − 0.457486i
\(780\) 0 0
\(781\) −216.000 −0.276569
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 95.0000 0.120712 0.0603558 0.998177i \(-0.480776\pi\)
0.0603558 + 0.998177i \(0.480776\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 67.8823i 0.0858183i
\(792\) 0 0
\(793\) −455.000 −0.573770
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 950.352i − 1.19241i −0.802832 0.596205i \(-0.796674\pi\)
0.802832 0.596205i \(-0.203326\pi\)
\(798\) 0 0
\(799\) −198.000 −0.247810
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 373.352i − 0.464947i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 356.382i − 0.440521i −0.975441 0.220261i \(-0.929309\pi\)
0.975441 0.220261i \(-0.0706908\pi\)
\(810\) 0 0
\(811\) −1177.00 −1.45129 −0.725647 0.688067i \(-0.758460\pi\)
−0.725647 + 0.688067i \(0.758460\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 385.000 0.471236
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 564.271i 0.687297i 0.939098 + 0.343649i \(0.111663\pi\)
−0.939098 + 0.343649i \(0.888337\pi\)
\(822\) 0 0
\(823\) 641.000 0.778858 0.389429 0.921057i \(-0.372672\pi\)
0.389429 + 0.921057i \(0.372672\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 526.087i 0.636140i 0.948067 + 0.318070i \(0.103035\pi\)
−0.948067 + 0.318070i \(0.896965\pi\)
\(828\) 0 0
\(829\) 1046.00 1.26176 0.630881 0.775880i \(-0.282694\pi\)
0.630881 + 0.775880i \(0.282694\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 203.647i 0.244474i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1387.34i 1.65357i 0.562520 + 0.826784i \(0.309832\pi\)
−0.562520 + 0.826784i \(0.690168\pi\)
\(840\) 0 0
\(841\) −41.0000 −0.0487515
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −103.000 −0.121606
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 475.176i 0.558373i
\(852\) 0 0
\(853\) 335.000 0.392732 0.196366 0.980531i \(-0.437086\pi\)
0.196366 + 0.980531i \(0.437086\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 237.588i − 0.277232i −0.990346 0.138616i \(-0.955735\pi\)
0.990346 0.138616i \(-0.0442654\pi\)
\(858\) 0 0
\(859\) −1414.00 −1.64610 −0.823050 0.567969i \(-0.807729\pi\)
−0.823050 + 0.567969i \(0.807729\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1561.29i 1.80914i 0.426320 + 0.904572i \(0.359810\pi\)
−0.426320 + 0.904572i \(0.640190\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 169.706i − 0.195288i
\(870\) 0 0
\(871\) 343.000 0.393800
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 425.000 0.484607 0.242303 0.970201i \(-0.422097\pi\)
0.242303 + 0.970201i \(0.422097\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 1731.00i − 1.96481i −0.186764 0.982405i \(-0.559800\pi\)
0.186764 0.982405i \(-0.440200\pi\)
\(882\) 0 0
\(883\) −385.000 −0.436014 −0.218007 0.975947i \(-0.569955\pi\)
−0.218007 + 0.975947i \(0.569955\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1141.27i 1.28666i 0.765588 + 0.643332i \(0.222448\pi\)
−0.765588 + 0.643332i \(0.777552\pi\)
\(888\) 0 0
\(889\) 160.000 0.179978
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 326.683i 0.365827i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 504.874i − 0.561595i
\(900\) 0 0
\(901\) −360.000 −0.399556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 752.000 0.829107 0.414553 0.910025i \(-0.363938\pi\)
0.414553 + 0.910025i \(0.363938\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 1336.43i − 1.46699i −0.679693 0.733497i \(-0.737887\pi\)
0.679693 0.733497i \(-0.262113\pi\)
\(912\) 0 0
\(913\) 666.000 0.729463
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 16.9706i 0.0185066i
\(918\) 0 0
\(919\) 719.000 0.782372 0.391186 0.920312i \(-0.372065\pi\)
0.391186 + 0.920312i \(0.372065\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 356.382i − 0.386112i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1294.01i 1.39290i 0.717605 + 0.696451i \(0.245239\pi\)
−0.717605 + 0.696451i \(0.754761\pi\)
\(930\) 0 0
\(931\) 336.000 0.360902
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1471.00 −1.56990 −0.784952 0.619557i \(-0.787312\pi\)
−0.784952 + 0.619557i \(0.787312\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 895.197i − 0.951325i −0.879628 0.475663i \(-0.842208\pi\)
0.879628 0.475663i \(-0.157792\pi\)
\(942\) 0 0
\(943\) 1512.00 1.60339
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1022.48i 1.07970i 0.841761 + 0.539850i \(0.181519\pi\)
−0.841761 + 0.539850i \(0.818481\pi\)
\(948\) 0 0
\(949\) 616.000 0.649104
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 950.352i 0.997221i 0.866826 + 0.498610i \(0.166156\pi\)
−0.866826 + 0.498610i \(0.833844\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 89.0955i − 0.0929045i
\(960\) 0 0
\(961\) −672.000 −0.699272
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1016.00 1.05067 0.525336 0.850895i \(-0.323940\pi\)
0.525336 + 0.850895i \(0.323940\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1574.02i 1.62103i 0.585718 + 0.810515i \(0.300813\pi\)
−0.585718 + 0.810515i \(0.699187\pi\)
\(972\) 0 0
\(973\) −8.00000 −0.00822199
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 801.859i − 0.820736i −0.911920 0.410368i \(-0.865400\pi\)
0.911920 0.410368i \(-0.134600\pi\)
\(978\) 0 0
\(979\) 432.000 0.441267
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1866.76i 1.89905i 0.313698 + 0.949523i \(0.398432\pi\)
−0.313698 + 0.949523i \(0.601568\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1633.42i 1.65158i
\(990\) 0 0
\(991\) −1081.00 −1.09082 −0.545409 0.838170i \(-0.683626\pi\)
−0.545409 + 0.838170i \(0.683626\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 248.000 0.248746 0.124373 0.992236i \(-0.460308\pi\)
0.124373 + 0.992236i \(0.460308\pi\)
\(998\) 0 0
\(999\) 0 0
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 900.3.g.a.701.2 yes 2
3.2 odd 2 inner 900.3.g.a.701.1 2
4.3 odd 2 3600.3.l.g.1601.1 2
5.2 odd 4 900.3.b.a.449.2 4
5.3 odd 4 900.3.b.a.449.4 4
5.4 even 2 900.3.g.b.701.2 yes 2
12.11 even 2 3600.3.l.g.1601.2 2
15.2 even 4 900.3.b.a.449.1 4
15.8 even 4 900.3.b.a.449.3 4
15.14 odd 2 900.3.g.b.701.1 yes 2
20.3 even 4 3600.3.c.d.449.1 4
20.7 even 4 3600.3.c.d.449.3 4
20.19 odd 2 3600.3.l.f.1601.1 2
60.23 odd 4 3600.3.c.d.449.2 4
60.47 odd 4 3600.3.c.d.449.4 4
60.59 even 2 3600.3.l.f.1601.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
900.3.b.a.449.1 4 15.2 even 4
900.3.b.a.449.2 4 5.2 odd 4
900.3.b.a.449.3 4 15.8 even 4
900.3.b.a.449.4 4 5.3 odd 4
900.3.g.a.701.1 2 3.2 odd 2 inner
900.3.g.a.701.2 yes 2 1.1 even 1 trivial
900.3.g.b.701.1 yes 2 15.14 odd 2
900.3.g.b.701.2 yes 2 5.4 even 2
3600.3.c.d.449.1 4 20.3 even 4
3600.3.c.d.449.2 4 60.23 odd 4
3600.3.c.d.449.3 4 20.7 even 4
3600.3.c.d.449.4 4 60.47 odd 4
3600.3.l.f.1601.1 2 20.19 odd 2
3600.3.l.f.1601.2 2 60.59 even 2
3600.3.l.g.1601.1 2 4.3 odd 2
3600.3.l.g.1601.2 2 12.11 even 2