Properties

Label 2880.3.l.b.1601.2
Level $2880$
Weight $3$
Character 2880.1601
Analytic conductor $78.474$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2880.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(78.4743161358\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-5})\)
Defining polynomial: \( x^{4} - 4x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 180)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1601.2
Root \(1.58114 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2880.1601
Dual form 2880.3.l.b.1601.4

$q$-expansion

\(f(q)\) \(=\) \(q-2.23607i q^{5} +5.48683 q^{7} +O(q^{10})\) \(q-2.23607i q^{5} +5.48683 q^{7} -9.17377i q^{11} -11.4868 q^{13} +16.9706i q^{17} -26.9737 q^{19} +4.93113i q^{23} -5.00000 q^{25} +20.5247i q^{29} +20.9737 q^{31} -12.2689i q^{35} +62.4605 q^{37} -40.9377i q^{41} -1.02633 q^{43} +86.2298i q^{47} -18.8947 q^{49} +96.0920i q^{53} -20.5132 q^{55} +112.374i q^{59} +66.9210 q^{61} +25.6853i q^{65} +76.0000 q^{67} -24.0789i q^{71} -18.9210 q^{73} -50.3349i q^{77} +106.921 q^{79} -45.1804i q^{83} +37.9473 q^{85} -115.928i q^{89} -63.0263 q^{91} +60.3150i q^{95} -87.0263 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{7} - 8 q^{13} - 32 q^{19} - 20 q^{25} + 8 q^{31} + 136 q^{37} - 80 q^{43} + 228 q^{49} - 120 q^{55} + 40 q^{61} + 304 q^{67} + 152 q^{73} + 200 q^{79} - 328 q^{91} - 424 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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
\(5\) − 2.23607i − 0.447214i
\(6\) 0 0
\(7\) 5.48683 0.783833 0.391917 0.920001i \(-0.371812\pi\)
0.391917 + 0.920001i \(0.371812\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 9.17377i − 0.833979i −0.908911 0.416989i \(-0.863085\pi\)
0.908911 0.416989i \(-0.136915\pi\)
\(12\) 0 0
\(13\) −11.4868 −0.883603 −0.441801 0.897113i \(-0.645660\pi\)
−0.441801 + 0.897113i \(0.645660\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16.9706i 0.998268i 0.866525 + 0.499134i \(0.166349\pi\)
−0.866525 + 0.499134i \(0.833651\pi\)
\(18\) 0 0
\(19\) −26.9737 −1.41967 −0.709833 0.704370i \(-0.751230\pi\)
−0.709833 + 0.704370i \(0.751230\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.93113i 0.214397i 0.994238 + 0.107198i \(0.0341880\pi\)
−0.994238 + 0.107198i \(0.965812\pi\)
\(24\) 0 0
\(25\) −5.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 20.5247i 0.707749i 0.935293 + 0.353874i \(0.115136\pi\)
−0.935293 + 0.353874i \(0.884864\pi\)
\(30\) 0 0
\(31\) 20.9737 0.676570 0.338285 0.941044i \(-0.390153\pi\)
0.338285 + 0.941044i \(0.390153\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 12.2689i − 0.350541i
\(36\) 0 0
\(37\) 62.4605 1.68812 0.844061 0.536247i \(-0.180159\pi\)
0.844061 + 0.536247i \(0.180159\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 40.9377i − 0.998481i −0.866464 0.499240i \(-0.833612\pi\)
0.866464 0.499240i \(-0.166388\pi\)
\(42\) 0 0
\(43\) −1.02633 −0.0238682 −0.0119341 0.999929i \(-0.503799\pi\)
−0.0119341 + 0.999929i \(0.503799\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 86.2298i 1.83468i 0.398109 + 0.917338i \(0.369667\pi\)
−0.398109 + 0.917338i \(0.630333\pi\)
\(48\) 0 0
\(49\) −18.8947 −0.385605
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 96.0920i 1.81306i 0.422144 + 0.906529i \(0.361278\pi\)
−0.422144 + 0.906529i \(0.638722\pi\)
\(54\) 0 0
\(55\) −20.5132 −0.372967
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 112.374i 1.90465i 0.305092 + 0.952323i \(0.401313\pi\)
−0.305092 + 0.952323i \(0.598687\pi\)
\(60\) 0 0
\(61\) 66.9210 1.09707 0.548533 0.836129i \(-0.315187\pi\)
0.548533 + 0.836129i \(0.315187\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 25.6853i 0.395159i
\(66\) 0 0
\(67\) 76.0000 1.13433 0.567164 0.823605i \(-0.308040\pi\)
0.567164 + 0.823605i \(0.308040\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 24.0789i − 0.339139i −0.985518 0.169570i \(-0.945762\pi\)
0.985518 0.169570i \(-0.0542377\pi\)
\(72\) 0 0
\(73\) −18.9210 −0.259192 −0.129596 0.991567i \(-0.541368\pi\)
−0.129596 + 0.991567i \(0.541368\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 50.3349i − 0.653700i
\(78\) 0 0
\(79\) 106.921 1.35343 0.676715 0.736245i \(-0.263403\pi\)
0.676715 + 0.736245i \(0.263403\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 45.1804i − 0.544342i −0.962249 0.272171i \(-0.912258\pi\)
0.962249 0.272171i \(-0.0877416\pi\)
\(84\) 0 0
\(85\) 37.9473 0.446439
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 115.928i − 1.30256i −0.758835 0.651282i \(-0.774231\pi\)
0.758835 0.651282i \(-0.225769\pi\)
\(90\) 0 0
\(91\) −63.0263 −0.692597
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 60.3150i 0.634894i
\(96\) 0 0
\(97\) −87.0263 −0.897179 −0.448589 0.893738i \(-0.648073\pi\)
−0.448589 + 0.893738i \(0.648073\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 129.233i − 1.27953i −0.768569 0.639767i \(-0.779031\pi\)
0.768569 0.639767i \(-0.220969\pi\)
\(102\) 0 0
\(103\) 114.302 1.10973 0.554866 0.831939i \(-0.312769\pi\)
0.554866 + 0.831939i \(0.312769\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 93.3381i − 0.872319i −0.899869 0.436159i \(-0.856338\pi\)
0.899869 0.436159i \(-0.143662\pi\)
\(108\) 0 0
\(109\) −120.868 −1.10888 −0.554442 0.832222i \(-0.687068\pi\)
−0.554442 + 0.832222i \(0.687068\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 110.309i − 0.976183i −0.872793 0.488091i \(-0.837693\pi\)
0.872793 0.488091i \(-0.162307\pi\)
\(114\) 0 0
\(115\) 11.0263 0.0958812
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 93.1146i 0.782476i
\(120\) 0 0
\(121\) 36.8420 0.304479
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) 105.381 0.829776 0.414888 0.909873i \(-0.363821\pi\)
0.414888 + 0.909873i \(0.363821\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 140.584i 1.07316i 0.843850 + 0.536580i \(0.180284\pi\)
−0.843850 + 0.536580i \(0.819716\pi\)
\(132\) 0 0
\(133\) −148.000 −1.11278
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 266.951i 1.94855i 0.225365 + 0.974274i \(0.427643\pi\)
−0.225365 + 0.974274i \(0.572357\pi\)
\(138\) 0 0
\(139\) 15.8420 0.113971 0.0569856 0.998375i \(-0.481851\pi\)
0.0569856 + 0.998375i \(0.481851\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 105.378i 0.736906i
\(144\) 0 0
\(145\) 45.8947 0.316515
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 41.6262i 0.279370i 0.990196 + 0.139685i \(0.0446091\pi\)
−0.990196 + 0.139685i \(0.955391\pi\)
\(150\) 0 0
\(151\) 103.842 0.687695 0.343848 0.939025i \(-0.388270\pi\)
0.343848 + 0.939025i \(0.388270\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 46.8985i − 0.302571i
\(156\) 0 0
\(157\) 12.5132 0.0797017 0.0398509 0.999206i \(-0.487312\pi\)
0.0398509 + 0.999206i \(0.487312\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 27.0563i 0.168051i
\(162\) 0 0
\(163\) 290.868 1.78447 0.892234 0.451573i \(-0.149137\pi\)
0.892234 + 0.451573i \(0.149137\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 174.637i − 1.04573i −0.852416 0.522865i \(-0.824863\pi\)
0.852416 0.522865i \(-0.175137\pi\)
\(168\) 0 0
\(169\) −37.0527 −0.219247
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 43.5799i − 0.251907i −0.992036 0.125954i \(-0.959801\pi\)
0.992036 0.125954i \(-0.0401990\pi\)
\(174\) 0 0
\(175\) −27.4342 −0.156767
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 88.2952i 0.493270i 0.969109 + 0.246635i \(0.0793248\pi\)
−0.969109 + 0.246635i \(0.920675\pi\)
\(180\) 0 0
\(181\) 56.8683 0.314190 0.157095 0.987584i \(-0.449787\pi\)
0.157095 + 0.987584i \(0.449787\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 139.666i − 0.754951i
\(186\) 0 0
\(187\) 155.684 0.832535
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 56.6430i − 0.296560i −0.988945 0.148280i \(-0.952626\pi\)
0.988945 0.148280i \(-0.0473737\pi\)
\(192\) 0 0
\(193\) 110.000 0.569948 0.284974 0.958535i \(-0.408015\pi\)
0.284974 + 0.958535i \(0.408015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 245.049i 1.24391i 0.783055 + 0.621953i \(0.213661\pi\)
−0.783055 + 0.621953i \(0.786339\pi\)
\(198\) 0 0
\(199\) −169.895 −0.853742 −0.426871 0.904313i \(-0.640384\pi\)
−0.426871 + 0.904313i \(0.640384\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 112.616i 0.554757i
\(204\) 0 0
\(205\) −91.5395 −0.446534
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 247.450i 1.18397i
\(210\) 0 0
\(211\) 265.579 1.25867 0.629333 0.777136i \(-0.283328\pi\)
0.629333 + 0.777136i \(0.283328\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.29495i 0.0106742i
\(216\) 0 0
\(217\) 115.079 0.530318
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 194.938i − 0.882072i
\(222\) 0 0
\(223\) −187.329 −0.840040 −0.420020 0.907515i \(-0.637977\pi\)
−0.420020 + 0.907515i \(0.637977\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 421.063i 1.85490i 0.373942 + 0.927452i \(0.378006\pi\)
−0.373942 + 0.927452i \(0.621994\pi\)
\(228\) 0 0
\(229\) 102.105 0.445875 0.222937 0.974833i \(-0.428435\pi\)
0.222937 + 0.974833i \(0.428435\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 99.0694i − 0.425191i −0.977140 0.212595i \(-0.931808\pi\)
0.977140 0.212595i \(-0.0681916\pi\)
\(234\) 0 0
\(235\) 192.816 0.820492
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 77.9680i 0.326226i 0.986607 + 0.163113i \(0.0521535\pi\)
−0.986607 + 0.163113i \(0.947847\pi\)
\(240\) 0 0
\(241\) −257.947 −1.07032 −0.535160 0.844750i \(-0.679749\pi\)
−0.535160 + 0.844750i \(0.679749\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 42.2498i 0.172448i
\(246\) 0 0
\(247\) 309.842 1.25442
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 274.971i 1.09550i 0.836641 + 0.547752i \(0.184516\pi\)
−0.836641 + 0.547752i \(0.815484\pi\)
\(252\) 0 0
\(253\) 45.2370 0.178802
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 131.634i − 0.512193i −0.966651 0.256096i \(-0.917564\pi\)
0.966651 0.256096i \(-0.0824365\pi\)
\(258\) 0 0
\(259\) 342.710 1.32321
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 458.782i 1.74442i 0.489133 + 0.872209i \(0.337313\pi\)
−0.489133 + 0.872209i \(0.662687\pi\)
\(264\) 0 0
\(265\) 214.868 0.810824
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 301.916i − 1.12236i −0.827692 0.561182i \(-0.810347\pi\)
0.827692 0.561182i \(-0.189653\pi\)
\(270\) 0 0
\(271\) 475.842 1.75587 0.877937 0.478776i \(-0.158919\pi\)
0.877937 + 0.478776i \(0.158919\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 45.8688i 0.166796i
\(276\) 0 0
\(277\) −322.039 −1.16260 −0.581298 0.813691i \(-0.697455\pi\)
−0.581298 + 0.813691i \(0.697455\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 352.139i 1.25316i 0.779355 + 0.626582i \(0.215547\pi\)
−0.779355 + 0.626582i \(0.784453\pi\)
\(282\) 0 0
\(283\) 281.631 0.995164 0.497582 0.867417i \(-0.334221\pi\)
0.497582 + 0.867417i \(0.334221\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 224.618i − 0.782642i
\(288\) 0 0
\(289\) 1.00000 0.00346021
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 64.3281i 0.219550i 0.993956 + 0.109775i \(0.0350130\pi\)
−0.993956 + 0.109775i \(0.964987\pi\)
\(294\) 0 0
\(295\) 251.276 0.851784
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 56.6430i − 0.189442i
\(300\) 0 0
\(301\) −5.63132 −0.0187087
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 149.640i − 0.490623i
\(306\) 0 0
\(307\) −230.158 −0.749700 −0.374850 0.927085i \(-0.622306\pi\)
−0.374850 + 0.927085i \(0.622306\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 8.48528i − 0.0272839i −0.999907 0.0136419i \(-0.995658\pi\)
0.999907 0.0136419i \(-0.00434250\pi\)
\(312\) 0 0
\(313\) 605.579 1.93476 0.967378 0.253337i \(-0.0815282\pi\)
0.967378 + 0.253337i \(0.0815282\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 87.9601i − 0.277477i −0.990329 0.138738i \(-0.955695\pi\)
0.990329 0.138738i \(-0.0443047\pi\)
\(318\) 0 0
\(319\) 188.289 0.590248
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 457.758i − 1.41721i
\(324\) 0 0
\(325\) 57.4342 0.176721
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 473.128i 1.43808i
\(330\) 0 0
\(331\) 49.2370 0.148752 0.0743761 0.997230i \(-0.476303\pi\)
0.0743761 + 0.997230i \(0.476303\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 169.941i − 0.507287i
\(336\) 0 0
\(337\) −2.71033 −0.00804251 −0.00402125 0.999992i \(-0.501280\pi\)
−0.00402125 + 0.999992i \(0.501280\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 192.408i − 0.564245i
\(342\) 0 0
\(343\) −372.527 −1.08608
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 74.9906i 0.216111i 0.994145 + 0.108056i \(0.0344624\pi\)
−0.994145 + 0.108056i \(0.965538\pi\)
\(348\) 0 0
\(349\) 150.921 0.432438 0.216219 0.976345i \(-0.430627\pi\)
0.216219 + 0.976345i \(0.430627\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 292.407i − 0.828349i −0.910198 0.414174i \(-0.864070\pi\)
0.910198 0.414174i \(-0.135930\pi\)
\(354\) 0 0
\(355\) −53.8420 −0.151668
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 576.776i 1.60662i 0.595563 + 0.803309i \(0.296929\pi\)
−0.595563 + 0.803309i \(0.703071\pi\)
\(360\) 0 0
\(361\) 366.579 1.01545
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 42.3086i 0.115914i
\(366\) 0 0
\(367\) 243.540 0.663595 0.331798 0.943351i \(-0.392345\pi\)
0.331798 + 0.943351i \(0.392345\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 527.241i 1.42113i
\(372\) 0 0
\(373\) −115.908 −0.310746 −0.155373 0.987856i \(-0.549658\pi\)
−0.155373 + 0.987856i \(0.549658\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 235.764i − 0.625369i
\(378\) 0 0
\(379\) −30.2107 −0.0797115 −0.0398558 0.999205i \(-0.512690\pi\)
−0.0398558 + 0.999205i \(0.512690\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 651.319i 1.70057i 0.526320 + 0.850286i \(0.323571\pi\)
−0.526320 + 0.850286i \(0.676429\pi\)
\(384\) 0 0
\(385\) −112.552 −0.292344
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 205.600i 0.528536i 0.964449 + 0.264268i \(0.0851303\pi\)
−0.964449 + 0.264268i \(0.914870\pi\)
\(390\) 0 0
\(391\) −83.6840 −0.214026
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 239.083i − 0.605272i
\(396\) 0 0
\(397\) −118.355 −0.298124 −0.149062 0.988828i \(-0.547625\pi\)
−0.149062 + 0.988828i \(0.547625\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 170.971i 0.426361i 0.977013 + 0.213181i \(0.0683823\pi\)
−0.977013 + 0.213181i \(0.931618\pi\)
\(402\) 0 0
\(403\) −240.921 −0.597819
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 572.998i − 1.40786i
\(408\) 0 0
\(409\) −335.947 −0.821387 −0.410694 0.911773i \(-0.634713\pi\)
−0.410694 + 0.911773i \(0.634713\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 616.578i 1.49292i
\(414\) 0 0
\(415\) −101.026 −0.243437
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 407.535i 0.972637i 0.873781 + 0.486319i \(0.161661\pi\)
−0.873781 + 0.486319i \(0.838339\pi\)
\(420\) 0 0
\(421\) 771.210 1.83185 0.915926 0.401346i \(-0.131458\pi\)
0.915926 + 0.401346i \(0.131458\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 84.8528i − 0.199654i
\(426\) 0 0
\(427\) 367.184 0.859916
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 436.210i 1.01209i 0.862508 + 0.506044i \(0.168893\pi\)
−0.862508 + 0.506044i \(0.831107\pi\)
\(432\) 0 0
\(433\) −838.500 −1.93649 −0.968244 0.250006i \(-0.919568\pi\)
−0.968244 + 0.250006i \(0.919568\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 133.011i − 0.304372i
\(438\) 0 0
\(439\) 50.0000 0.113895 0.0569476 0.998377i \(-0.481863\pi\)
0.0569476 + 0.998377i \(0.481863\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 492.853i 1.11253i 0.831003 + 0.556267i \(0.187767\pi\)
−0.831003 + 0.556267i \(0.812233\pi\)
\(444\) 0 0
\(445\) −259.223 −0.582525
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 483.102i − 1.07595i −0.842960 0.537976i \(-0.819189\pi\)
0.842960 0.537976i \(-0.180811\pi\)
\(450\) 0 0
\(451\) −375.553 −0.832712
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 140.931i 0.309739i
\(456\) 0 0
\(457\) −546.921 −1.19676 −0.598382 0.801211i \(-0.704189\pi\)
−0.598382 + 0.801211i \(0.704189\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 130.386i 0.282834i 0.989950 + 0.141417i \(0.0451658\pi\)
−0.989950 + 0.141417i \(0.954834\pi\)
\(462\) 0 0
\(463\) 24.7765 0.0535130 0.0267565 0.999642i \(-0.491482\pi\)
0.0267565 + 0.999642i \(0.491482\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 671.491i − 1.43788i −0.695071 0.718941i \(-0.744627\pi\)
0.695071 0.718941i \(-0.255373\pi\)
\(468\) 0 0
\(469\) 416.999 0.889124
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.41535i 0.0199056i
\(474\) 0 0
\(475\) 134.868 0.283933
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) − 538.257i − 1.12371i −0.827236 0.561855i \(-0.810088\pi\)
0.827236 0.561855i \(-0.189912\pi\)
\(480\) 0 0
\(481\) −717.473 −1.49163
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 194.597i 0.401231i
\(486\) 0 0
\(487\) 608.250 1.24897 0.624486 0.781036i \(-0.285308\pi\)
0.624486 + 0.781036i \(0.285308\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 143.561i 0.292386i 0.989256 + 0.146193i \(0.0467020\pi\)
−0.989256 + 0.146193i \(0.953298\pi\)
\(492\) 0 0
\(493\) −348.316 −0.706523
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 132.117i − 0.265828i
\(498\) 0 0
\(499\) −616.605 −1.23568 −0.617841 0.786303i \(-0.711992\pi\)
−0.617841 + 0.786303i \(0.711992\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 374.729i 0.744989i 0.928034 + 0.372494i \(0.121497\pi\)
−0.928034 + 0.372494i \(0.878503\pi\)
\(504\) 0 0
\(505\) −288.974 −0.572225
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 173.036i − 0.339953i −0.985448 0.169977i \(-0.945631\pi\)
0.985448 0.169977i \(-0.0543693\pi\)
\(510\) 0 0
\(511\) −103.816 −0.203163
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 255.588i − 0.496288i
\(516\) 0 0
\(517\) 791.052 1.53008
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 455.116i − 0.873543i −0.899572 0.436772i \(-0.856122\pi\)
0.899572 0.436772i \(-0.143878\pi\)
\(522\) 0 0
\(523\) 295.395 0.564809 0.282404 0.959295i \(-0.408868\pi\)
0.282404 + 0.959295i \(0.408868\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 355.935i 0.675398i
\(528\) 0 0
\(529\) 504.684 0.954034
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 470.245i 0.882260i
\(534\) 0 0
\(535\) −208.710 −0.390113
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 173.335i 0.321587i
\(540\) 0 0
\(541\) −906.394 −1.67541 −0.837703 0.546127i \(-0.816102\pi\)
−0.837703 + 0.546127i \(0.816102\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 270.270i 0.495908i
\(546\) 0 0
\(547\) 672.921 1.23020 0.615101 0.788448i \(-0.289115\pi\)
0.615101 + 0.788448i \(0.289115\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 553.627i − 1.00477i
\(552\) 0 0
\(553\) 586.658 1.06086
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 870.336i − 1.56254i −0.624192 0.781271i \(-0.714572\pi\)
0.624192 0.781271i \(-0.285428\pi\)
\(558\) 0 0
\(559\) 11.7893 0.0210900
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 23.6320i − 0.0419751i −0.999780 0.0209875i \(-0.993319\pi\)
0.999780 0.0209875i \(-0.00668103\pi\)
\(564\) 0 0
\(565\) −246.658 −0.436562
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 295.273i − 0.518933i −0.965752 0.259466i \(-0.916453\pi\)
0.965752 0.259466i \(-0.0835467\pi\)
\(570\) 0 0
\(571\) −893.920 −1.56553 −0.782767 0.622314i \(-0.786193\pi\)
−0.782767 + 0.622314i \(0.786193\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 24.6556i − 0.0428794i
\(576\) 0 0
\(577\) −264.763 −0.458861 −0.229431 0.973325i \(-0.573686\pi\)
−0.229431 + 0.973325i \(0.573686\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 247.897i − 0.426673i
\(582\) 0 0
\(583\) 881.526 1.51205
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 791.885i − 1.34904i −0.738258 0.674519i \(-0.764351\pi\)
0.738258 0.674519i \(-0.235649\pi\)
\(588\) 0 0
\(589\) −565.737 −0.960504
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 1.82388i − 0.00307567i −0.999999 0.00153784i \(-0.999510\pi\)
0.999999 0.00153784i \(-0.000489509\pi\)
\(594\) 0 0
\(595\) 208.211 0.349934
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 758.204i 1.26578i 0.774241 + 0.632891i \(0.218132\pi\)
−0.774241 + 0.632891i \(0.781868\pi\)
\(600\) 0 0
\(601\) −283.579 −0.471845 −0.235922 0.971772i \(-0.575811\pi\)
−0.235922 + 0.971772i \(0.575811\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 82.3812i − 0.136167i
\(606\) 0 0
\(607\) 167.828 0.276488 0.138244 0.990398i \(-0.455854\pi\)
0.138244 + 0.990398i \(0.455854\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 990.507i − 1.62112i
\(612\) 0 0
\(613\) 395.698 0.645510 0.322755 0.946483i \(-0.395391\pi\)
0.322755 + 0.946483i \(0.395391\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 855.190i 1.38604i 0.720916 + 0.693022i \(0.243721\pi\)
−0.720916 + 0.693022i \(0.756279\pi\)
\(618\) 0 0
\(619\) −308.158 −0.497832 −0.248916 0.968525i \(-0.580074\pi\)
−0.248916 + 0.968525i \(0.580074\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 636.079i − 1.02099i
\(624\) 0 0
\(625\) 25.0000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1059.99i 1.68520i
\(630\) 0 0
\(631\) 344.974 0.546709 0.273355 0.961913i \(-0.411867\pi\)
0.273355 + 0.961913i \(0.411867\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 235.640i − 0.371087i
\(636\) 0 0
\(637\) 217.040 0.340722
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 202.641i 0.316133i 0.987428 + 0.158066i \(0.0505260\pi\)
−0.987428 + 0.158066i \(0.949474\pi\)
\(642\) 0 0
\(643\) −724.605 −1.12691 −0.563456 0.826146i \(-0.690529\pi\)
−0.563456 + 0.826146i \(0.690529\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 125.679i 0.194249i 0.995272 + 0.0971243i \(0.0309644\pi\)
−0.995272 + 0.0971243i \(0.969036\pi\)
\(648\) 0 0
\(649\) 1030.89 1.58843
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 551.226i − 0.844144i −0.906562 0.422072i \(-0.861303\pi\)
0.906562 0.422072i \(-0.138697\pi\)
\(654\) 0 0
\(655\) 314.355 0.479932
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 801.765i 1.21664i 0.793692 + 0.608320i \(0.208156\pi\)
−0.793692 + 0.608320i \(0.791844\pi\)
\(660\) 0 0
\(661\) 529.079 0.800422 0.400211 0.916423i \(-0.368937\pi\)
0.400211 + 0.916423i \(0.368937\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 330.938i 0.497651i
\(666\) 0 0
\(667\) −101.210 −0.151739
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) − 613.918i − 0.914929i
\(672\) 0 0
\(673\) 413.395 0.614257 0.307129 0.951668i \(-0.400632\pi\)
0.307129 + 0.951668i \(0.400632\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 359.936i − 0.531663i −0.964019 0.265832i \(-0.914353\pi\)
0.964019 0.265832i \(-0.0856465\pi\)
\(678\) 0 0
\(679\) −477.499 −0.703239
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.5484i 0.0315496i 0.999876 + 0.0157748i \(0.00502148\pi\)
−0.999876 + 0.0157748i \(0.994979\pi\)
\(684\) 0 0
\(685\) 596.921 0.871418
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 1103.79i − 1.60202i
\(690\) 0 0
\(691\) 384.921 0.557049 0.278525 0.960429i \(-0.410155\pi\)
0.278525 + 0.960429i \(0.410155\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 35.4238i − 0.0509695i
\(696\) 0 0
\(697\) 694.736 0.996752
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 439.057i 0.626330i 0.949699 + 0.313165i \(0.101389\pi\)
−0.949699 + 0.313165i \(0.898611\pi\)
\(702\) 0 0
\(703\) −1684.79 −2.39657
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 709.080i − 1.00294i
\(708\) 0 0
\(709\) 126.421 0.178309 0.0891547 0.996018i \(-0.471583\pi\)
0.0891547 + 0.996018i \(0.471583\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 103.424i 0.145054i
\(714\) 0 0
\(715\) 235.631 0.329554
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 571.715i 0.795153i 0.917569 + 0.397576i \(0.130149\pi\)
−0.917569 + 0.397576i \(0.869851\pi\)
\(720\) 0 0
\(721\) 627.159 0.869846
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 102.624i − 0.141550i
\(726\) 0 0
\(727\) −841.038 −1.15686 −0.578431 0.815731i \(-0.696335\pi\)
−0.578431 + 0.815731i \(0.696335\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 17.4175i − 0.0238269i
\(732\) 0 0
\(733\) −494.749 −0.674965 −0.337483 0.941332i \(-0.609575\pi\)
−0.337483 + 0.941332i \(0.609575\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 697.206i − 0.946006i
\(738\) 0 0
\(739\) −1263.97 −1.71038 −0.855191 0.518312i \(-0.826561\pi\)
−0.855191 + 0.518312i \(0.826561\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 956.343i − 1.28714i −0.765389 0.643568i \(-0.777453\pi\)
0.765389 0.643568i \(-0.222547\pi\)
\(744\) 0 0
\(745\) 93.0790 0.124938
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 512.131i − 0.683752i
\(750\) 0 0
\(751\) −1121.66 −1.49355 −0.746776 0.665076i \(-0.768399\pi\)
−0.746776 + 0.665076i \(0.768399\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 232.198i − 0.307547i
\(756\) 0 0
\(757\) 466.433 0.616160 0.308080 0.951360i \(-0.400313\pi\)
0.308080 + 0.951360i \(0.400313\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1223.41i 1.60763i 0.594880 + 0.803814i \(0.297199\pi\)
−0.594880 + 0.803814i \(0.702801\pi\)
\(762\) 0 0
\(763\) −663.184 −0.869180
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 1290.82i − 1.68295i
\(768\) 0 0
\(769\) −1290.63 −1.67832 −0.839162 0.543882i \(-0.816954\pi\)
−0.839162 + 0.543882i \(0.816954\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 329.455i 0.426204i 0.977030 + 0.213102i \(0.0683566\pi\)
−0.977030 + 0.213102i \(0.931643\pi\)
\(774\) 0 0
\(775\) −104.868 −0.135314
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1104.24i 1.41751i
\(780\) 0 0
\(781\) −220.894 −0.282835
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 27.9803i − 0.0356437i
\(786\) 0 0
\(787\) 1506.13 1.91376 0.956881 0.290480i \(-0.0938148\pi\)
0.956881 + 0.290480i \(0.0938148\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 605.245i − 0.765165i
\(792\) 0 0
\(793\) −768.710 −0.969370
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 250.874i 0.314773i 0.987537 + 0.157387i \(0.0503069\pi\)
−0.987537 + 0.157387i \(0.949693\pi\)
\(798\) 0 0
\(799\) −1463.37 −1.83150
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 173.577i 0.216160i
\(804\) 0 0
\(805\) 60.4997 0.0751548
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1097.02i 1.35602i 0.735053 + 0.678010i \(0.237157\pi\)
−0.735053 + 0.678010i \(0.762843\pi\)
\(810\) 0 0
\(811\) 221.473 0.273087 0.136543 0.990634i \(-0.456401\pi\)
0.136543 + 0.990634i \(0.456401\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 650.401i − 0.798038i
\(816\) 0 0
\(817\) 27.6840 0.0338849
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1003.92i 1.22281i 0.791319 + 0.611403i \(0.209395\pi\)
−0.791319 + 0.611403i \(0.790605\pi\)
\(822\) 0 0
\(823\) 335.013 0.407063 0.203531 0.979068i \(-0.434758\pi\)
0.203531 + 0.979068i \(0.434758\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 1004.72i − 1.21490i −0.794357 0.607451i \(-0.792192\pi\)
0.794357 0.607451i \(-0.207808\pi\)
\(828\) 0 0
\(829\) −676.763 −0.816361 −0.408180 0.912901i \(-0.633837\pi\)
−0.408180 + 0.912901i \(0.633837\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 320.653i − 0.384938i
\(834\) 0 0
\(835\) −390.500 −0.467664
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 621.286i − 0.740507i −0.928931 0.370254i \(-0.879271\pi\)
0.928931 0.370254i \(-0.120729\pi\)
\(840\) 0 0
\(841\) 419.736 0.499092
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 82.8523i 0.0980500i
\(846\) 0 0
\(847\) 202.146 0.238661
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 308.001i 0.361928i
\(852\) 0 0
\(853\) 544.591 0.638443 0.319221 0.947680i \(-0.396579\pi\)
0.319221 + 0.947680i \(0.396579\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 362.149i 0.422578i 0.977424 + 0.211289i \(0.0677661\pi\)
−0.977424 + 0.211289i \(0.932234\pi\)
\(858\) 0 0
\(859\) 21.6840 0.0252433 0.0126216 0.999920i \(-0.495982\pi\)
0.0126216 + 0.999920i \(0.495982\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 220.300i 0.255273i 0.991821 + 0.127636i \(0.0407390\pi\)
−0.991821 + 0.127636i \(0.959261\pi\)
\(864\) 0 0
\(865\) −97.4477 −0.112656
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 980.868i − 1.12873i
\(870\) 0 0
\(871\) −872.999 −1.00230
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 61.3447i 0.0701082i
\(876\) 0 0
\(877\) −1136.41 −1.29579 −0.647895 0.761730i \(-0.724350\pi\)
−0.647895 + 0.761730i \(0.724350\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 711.758i − 0.807898i −0.914782 0.403949i \(-0.867637\pi\)
0.914782 0.403949i \(-0.132363\pi\)
\(882\) 0 0
\(883\) 536.394 0.607468 0.303734 0.952757i \(-0.401767\pi\)
0.303734 + 0.952757i \(0.401767\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 1463.95i − 1.65045i −0.564801 0.825227i \(-0.691047\pi\)
0.564801 0.825227i \(-0.308953\pi\)
\(888\) 0 0
\(889\) 578.211 0.650406
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 2325.93i − 2.60463i
\(894\) 0 0
\(895\) 197.434 0.220597
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 430.479i 0.478842i
\(900\) 0 0
\(901\) −1630.74 −1.80992
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 127.161i − 0.140510i
\(906\) 0 0
\(907\) −855.657 −0.943392 −0.471696 0.881761i \(-0.656358\pi\)
−0.471696 + 0.881761i \(0.656358\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1581.02i 1.73547i 0.497024 + 0.867737i \(0.334426\pi\)
−0.497024 + 0.867737i \(0.665574\pi\)
\(912\) 0 0
\(913\) −414.474 −0.453969
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 771.360i 0.841178i
\(918\) 0 0
\(919\) −1489.08 −1.62033 −0.810163 0.586205i \(-0.800621\pi\)
−0.810163 + 0.586205i \(0.800621\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 276.590i 0.299664i
\(924\) 0 0
\(925\) −312.302 −0.337624
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 736.990i 0.793316i 0.917966 + 0.396658i \(0.129830\pi\)
−0.917966 + 0.396658i \(0.870170\pi\)
\(930\) 0 0
\(931\) 509.658 0.547431
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 348.120i − 0.372321i
\(936\) 0 0
\(937\) 1550.05 1.65427 0.827135 0.562003i \(-0.189969\pi\)
0.827135 + 0.562003i \(0.189969\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 628.711i 0.668131i 0.942550 + 0.334065i \(0.108421\pi\)
−0.942550 + 0.334065i \(0.891579\pi\)
\(942\) 0 0
\(943\) 201.869 0.214071
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 1498.73i − 1.58261i −0.611423 0.791304i \(-0.709402\pi\)
0.611423 0.791304i \(-0.290598\pi\)
\(948\) 0 0
\(949\) 217.342 0.229022
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 224.748i 0.235832i 0.993024 + 0.117916i \(0.0376214\pi\)
−0.993024 + 0.117916i \(0.962379\pi\)
\(954\) 0 0
\(955\) −126.658 −0.132626
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1464.72i 1.52734i
\(960\) 0 0
\(961\) −521.105 −0.542253
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 245.967i − 0.254889i
\(966\) 0 0
\(967\) 233.986 0.241972 0.120986 0.992654i \(-0.461394\pi\)
0.120986 + 0.992654i \(0.461394\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 691.940i − 0.712606i −0.934371 0.356303i \(-0.884037\pi\)
0.934371 0.356303i \(-0.115963\pi\)
\(972\) 0 0
\(973\) 86.9224 0.0893344
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 395.571i − 0.404883i −0.979294 0.202442i \(-0.935112\pi\)
0.979294 0.202442i \(-0.0648877\pi\)
\(978\) 0 0
\(979\) −1063.50 −1.08631
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.82388i 0.00185542i 1.00000 0.000927709i \(0.000295299\pi\)
−1.00000 0.000927709i \(0.999705\pi\)
\(984\) 0 0
\(985\) 547.947 0.556292
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 5.06098i − 0.00511727i
\(990\) 0 0
\(991\) 506.316 0.510914 0.255457 0.966820i \(-0.417774\pi\)
0.255457 + 0.966820i \(0.417774\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 379.896i 0.381805i
\(996\) 0 0
\(997\) 295.670 0.296560 0.148280 0.988945i \(-0.452626\pi\)
0.148280 + 0.988945i \(0.452626\pi\)
\(998\) 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 2880.3.l.b.1601.2 4
3.2 odd 2 inner 2880.3.l.b.1601.4 4
4.3 odd 2 2880.3.l.f.1601.1 4
8.3 odd 2 720.3.l.c.161.3 4
8.5 even 2 180.3.g.a.161.4 yes 4
12.11 even 2 2880.3.l.f.1601.3 4
24.5 odd 2 180.3.g.a.161.2 4
24.11 even 2 720.3.l.c.161.1 4
40.3 even 4 3600.3.c.k.449.5 8
40.13 odd 4 900.3.b.b.449.4 8
40.19 odd 2 3600.3.l.n.1601.3 4
40.27 even 4 3600.3.c.k.449.3 8
40.29 even 2 900.3.g.d.701.2 4
40.37 odd 4 900.3.b.b.449.6 8
72.5 odd 6 1620.3.o.f.1241.1 8
72.13 even 6 1620.3.o.f.1241.3 8
72.29 odd 6 1620.3.o.f.701.3 8
72.61 even 6 1620.3.o.f.701.1 8
120.29 odd 2 900.3.g.d.701.1 4
120.53 even 4 900.3.b.b.449.3 8
120.59 even 2 3600.3.l.n.1601.4 4
120.77 even 4 900.3.b.b.449.5 8
120.83 odd 4 3600.3.c.k.449.6 8
120.107 odd 4 3600.3.c.k.449.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.3.g.a.161.2 4 24.5 odd 2
180.3.g.a.161.4 yes 4 8.5 even 2
720.3.l.c.161.1 4 24.11 even 2
720.3.l.c.161.3 4 8.3 odd 2
900.3.b.b.449.3 8 120.53 even 4
900.3.b.b.449.4 8 40.13 odd 4
900.3.b.b.449.5 8 120.77 even 4
900.3.b.b.449.6 8 40.37 odd 4
900.3.g.d.701.1 4 120.29 odd 2
900.3.g.d.701.2 4 40.29 even 2
1620.3.o.f.701.1 8 72.61 even 6
1620.3.o.f.701.3 8 72.29 odd 6
1620.3.o.f.1241.1 8 72.5 odd 6
1620.3.o.f.1241.3 8 72.13 even 6
2880.3.l.b.1601.2 4 1.1 even 1 trivial
2880.3.l.b.1601.4 4 3.2 odd 2 inner
2880.3.l.f.1601.1 4 4.3 odd 2
2880.3.l.f.1601.3 4 12.11 even 2
3600.3.c.k.449.3 8 40.27 even 4
3600.3.c.k.449.4 8 120.107 odd 4
3600.3.c.k.449.5 8 40.3 even 4
3600.3.c.k.449.6 8 120.83 odd 4
3600.3.l.n.1601.3 4 40.19 odd 2
3600.3.l.n.1601.4 4 120.59 even 2