Properties

Label 5796.2.a.m.1.1
Level $5796$
Weight $2$
Character 5796.1
Self dual yes
Analytic conductor $46.281$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.2812930115\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1932)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 5796.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.697224 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+0.697224 q^{5} -1.00000 q^{7} -5.60555 q^{11} +2.30278 q^{13} +0.394449 q^{17} -0.394449 q^{19} +1.00000 q^{23} -4.51388 q^{25} +5.60555 q^{29} -3.60555 q^{31} -0.697224 q^{35} +5.60555 q^{37} -3.60555 q^{41} +4.30278 q^{43} +4.60555 q^{47} +1.00000 q^{49} -5.90833 q^{53} -3.90833 q^{55} -3.90833 q^{59} +4.90833 q^{61} +1.60555 q^{65} +13.3028 q^{67} -12.9083 q^{71} +11.0000 q^{73} +5.60555 q^{77} +13.4222 q^{79} -16.2111 q^{83} +0.275019 q^{85} +15.5139 q^{89} -2.30278 q^{91} -0.275019 q^{95} +3.78890 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 5 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 5 q^{5} - 2 q^{7} - 4 q^{11} + q^{13} + 8 q^{17} - 8 q^{19} + 2 q^{23} + 9 q^{25} + 4 q^{29} - 5 q^{35} + 4 q^{37} + 5 q^{43} + 2 q^{47} + 2 q^{49} - q^{53} + 3 q^{55} + 3 q^{59} - q^{61} - 4 q^{65} + 23 q^{67} - 15 q^{71} + 22 q^{73} + 4 q^{77} - 2 q^{79} - 18 q^{83} + 33 q^{85} + 13 q^{89} - q^{91} - 33 q^{95} + 22 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 0.697224 0.311808 0.155904 0.987772i \(-0.450171\pi\)
0.155904 + 0.987772i \(0.450171\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.60555 −1.69014 −0.845069 0.534658i \(-0.820441\pi\)
−0.845069 + 0.534658i \(0.820441\pi\)
\(12\) 0 0
\(13\) 2.30278 0.638675 0.319338 0.947641i \(-0.396540\pi\)
0.319338 + 0.947641i \(0.396540\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.394449 0.0956679 0.0478339 0.998855i \(-0.484768\pi\)
0.0478339 + 0.998855i \(0.484768\pi\)
\(18\) 0 0
\(19\) −0.394449 −0.0904927 −0.0452464 0.998976i \(-0.514407\pi\)
−0.0452464 + 0.998976i \(0.514407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.51388 −0.902776
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.60555 1.04092 0.520462 0.853885i \(-0.325760\pi\)
0.520462 + 0.853885i \(0.325760\pi\)
\(30\) 0 0
\(31\) −3.60555 −0.647576 −0.323788 0.946130i \(-0.604956\pi\)
−0.323788 + 0.946130i \(0.604956\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.697224 −0.117852
\(36\) 0 0
\(37\) 5.60555 0.921547 0.460773 0.887518i \(-0.347572\pi\)
0.460773 + 0.887518i \(0.347572\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.60555 −0.563093 −0.281546 0.959548i \(-0.590847\pi\)
−0.281546 + 0.959548i \(0.590847\pi\)
\(42\) 0 0
\(43\) 4.30278 0.656167 0.328084 0.944649i \(-0.393597\pi\)
0.328084 + 0.944649i \(0.393597\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.60555 0.671789 0.335894 0.941900i \(-0.390961\pi\)
0.335894 + 0.941900i \(0.390961\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.90833 −0.811571 −0.405786 0.913968i \(-0.633002\pi\)
−0.405786 + 0.913968i \(0.633002\pi\)
\(54\) 0 0
\(55\) −3.90833 −0.526999
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.90833 −0.508821 −0.254410 0.967096i \(-0.581881\pi\)
−0.254410 + 0.967096i \(0.581881\pi\)
\(60\) 0 0
\(61\) 4.90833 0.628447 0.314223 0.949349i \(-0.398256\pi\)
0.314223 + 0.949349i \(0.398256\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.60555 0.199144
\(66\) 0 0
\(67\) 13.3028 1.62519 0.812596 0.582827i \(-0.198053\pi\)
0.812596 + 0.582827i \(0.198053\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.9083 −1.53194 −0.765968 0.642878i \(-0.777740\pi\)
−0.765968 + 0.642878i \(0.777740\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.60555 0.638812
\(78\) 0 0
\(79\) 13.4222 1.51012 0.755058 0.655658i \(-0.227609\pi\)
0.755058 + 0.655658i \(0.227609\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −16.2111 −1.77940 −0.889700 0.456546i \(-0.849086\pi\)
−0.889700 + 0.456546i \(0.849086\pi\)
\(84\) 0 0
\(85\) 0.275019 0.0298300
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 15.5139 1.64447 0.822234 0.569150i \(-0.192728\pi\)
0.822234 + 0.569150i \(0.192728\pi\)
\(90\) 0 0
\(91\) −2.30278 −0.241396
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.275019 −0.0282164
\(96\) 0 0
\(97\) 3.78890 0.384704 0.192352 0.981326i \(-0.438388\pi\)
0.192352 + 0.981326i \(0.438388\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.5139 1.24518 0.622589 0.782549i \(-0.286081\pi\)
0.622589 + 0.782549i \(0.286081\pi\)
\(102\) 0 0
\(103\) 2.78890 0.274798 0.137399 0.990516i \(-0.456126\pi\)
0.137399 + 0.990516i \(0.456126\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.302776 −0.0292704 −0.0146352 0.999893i \(-0.504659\pi\)
−0.0146352 + 0.999893i \(0.504659\pi\)
\(108\) 0 0
\(109\) −4.51388 −0.432351 −0.216176 0.976355i \(-0.569358\pi\)
−0.216176 + 0.976355i \(0.569358\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.30278 −0.498843 −0.249422 0.968395i \(-0.580240\pi\)
−0.249422 + 0.968395i \(0.580240\pi\)
\(114\) 0 0
\(115\) 0.697224 0.0650165
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.394449 −0.0361591
\(120\) 0 0
\(121\) 20.4222 1.85656
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.63331 −0.593301
\(126\) 0 0
\(127\) 18.1194 1.60784 0.803920 0.594738i \(-0.202744\pi\)
0.803920 + 0.594738i \(0.202744\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.81665 0.595574 0.297787 0.954632i \(-0.403752\pi\)
0.297787 + 0.954632i \(0.403752\pi\)
\(132\) 0 0
\(133\) 0.394449 0.0342030
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.60555 0.478915 0.239457 0.970907i \(-0.423030\pi\)
0.239457 + 0.970907i \(0.423030\pi\)
\(138\) 0 0
\(139\) −15.1194 −1.28241 −0.641207 0.767368i \(-0.721566\pi\)
−0.641207 + 0.767368i \(0.721566\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.9083 −1.07945
\(144\) 0 0
\(145\) 3.90833 0.324569
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.3944 1.26116 0.630581 0.776123i \(-0.282817\pi\)
0.630581 + 0.776123i \(0.282817\pi\)
\(150\) 0 0
\(151\) 8.60555 0.700310 0.350155 0.936692i \(-0.386129\pi\)
0.350155 + 0.936692i \(0.386129\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.51388 −0.201920
\(156\) 0 0
\(157\) 11.8167 0.943072 0.471536 0.881847i \(-0.343700\pi\)
0.471536 + 0.881847i \(0.343700\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −9.11943 −0.714289 −0.357144 0.934049i \(-0.616250\pi\)
−0.357144 + 0.934049i \(0.616250\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.0278 1.08550 0.542750 0.839894i \(-0.317383\pi\)
0.542750 + 0.839894i \(0.317383\pi\)
\(168\) 0 0
\(169\) −7.69722 −0.592094
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.39445 0.486161 0.243080 0.970006i \(-0.421842\pi\)
0.243080 + 0.970006i \(0.421842\pi\)
\(174\) 0 0
\(175\) 4.51388 0.341217
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −24.9361 −1.86381 −0.931905 0.362702i \(-0.881854\pi\)
−0.931905 + 0.362702i \(0.881854\pi\)
\(180\) 0 0
\(181\) −19.0000 −1.41226 −0.706129 0.708083i \(-0.749560\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.90833 0.287346
\(186\) 0 0
\(187\) −2.21110 −0.161692
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.60555 0.622676 0.311338 0.950299i \(-0.399223\pi\)
0.311338 + 0.950299i \(0.399223\pi\)
\(192\) 0 0
\(193\) 21.0278 1.51361 0.756806 0.653640i \(-0.226759\pi\)
0.756806 + 0.653640i \(0.226759\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.9361 1.84787 0.923935 0.382550i \(-0.124954\pi\)
0.923935 + 0.382550i \(0.124954\pi\)
\(198\) 0 0
\(199\) −1.90833 −0.135278 −0.0676389 0.997710i \(-0.521547\pi\)
−0.0676389 + 0.997710i \(0.521547\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.60555 −0.393433
\(204\) 0 0
\(205\) −2.51388 −0.175577
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.21110 0.152945
\(210\) 0 0
\(211\) 25.6056 1.76276 0.881379 0.472409i \(-0.156615\pi\)
0.881379 + 0.472409i \(0.156615\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) 3.60555 0.244761
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.908327 0.0611007
\(222\) 0 0
\(223\) 17.7250 1.18695 0.593476 0.804852i \(-0.297755\pi\)
0.593476 + 0.804852i \(0.297755\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.9083 −0.790383 −0.395192 0.918599i \(-0.629322\pi\)
−0.395192 + 0.918599i \(0.629322\pi\)
\(228\) 0 0
\(229\) 3.11943 0.206138 0.103069 0.994674i \(-0.467134\pi\)
0.103069 + 0.994674i \(0.467134\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.11943 −0.466409 −0.233205 0.972428i \(-0.574921\pi\)
−0.233205 + 0.972428i \(0.574921\pi\)
\(234\) 0 0
\(235\) 3.21110 0.209469
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.90833 −0.382178 −0.191089 0.981573i \(-0.561202\pi\)
−0.191089 + 0.981573i \(0.561202\pi\)
\(240\) 0 0
\(241\) 8.21110 0.528924 0.264462 0.964396i \(-0.414806\pi\)
0.264462 + 0.964396i \(0.414806\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.697224 0.0445440
\(246\) 0 0
\(247\) −0.908327 −0.0577955
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.18335 −0.264050 −0.132025 0.991246i \(-0.542148\pi\)
−0.132025 + 0.991246i \(0.542148\pi\)
\(252\) 0 0
\(253\) −5.60555 −0.352418
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −25.8167 −1.61040 −0.805199 0.593004i \(-0.797942\pi\)
−0.805199 + 0.593004i \(0.797942\pi\)
\(258\) 0 0
\(259\) −5.60555 −0.348312
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.42221 0.580998 0.290499 0.956875i \(-0.406179\pi\)
0.290499 + 0.956875i \(0.406179\pi\)
\(264\) 0 0
\(265\) −4.11943 −0.253055
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.1194 −0.738935 −0.369467 0.929244i \(-0.620460\pi\)
−0.369467 + 0.929244i \(0.620460\pi\)
\(270\) 0 0
\(271\) −0.577795 −0.0350985 −0.0175493 0.999846i \(-0.505586\pi\)
−0.0175493 + 0.999846i \(0.505586\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 25.3028 1.52581
\(276\) 0 0
\(277\) 24.5416 1.47456 0.737282 0.675585i \(-0.236109\pi\)
0.737282 + 0.675585i \(0.236109\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.60555 −0.394054 −0.197027 0.980398i \(-0.563129\pi\)
−0.197027 + 0.980398i \(0.563129\pi\)
\(282\) 0 0
\(283\) 25.3028 1.50409 0.752047 0.659110i \(-0.229067\pi\)
0.752047 + 0.659110i \(0.229067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.60555 0.212829
\(288\) 0 0
\(289\) −16.8444 −0.990848
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 18.7889 1.09766 0.548830 0.835934i \(-0.315074\pi\)
0.548830 + 0.835934i \(0.315074\pi\)
\(294\) 0 0
\(295\) −2.72498 −0.158655
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.30278 0.133173
\(300\) 0 0
\(301\) −4.30278 −0.248008
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.42221 0.195955
\(306\) 0 0
\(307\) −25.6056 −1.46139 −0.730693 0.682706i \(-0.760803\pi\)
−0.730693 + 0.682706i \(0.760803\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −10.1194 −0.573820 −0.286910 0.957958i \(-0.592628\pi\)
−0.286910 + 0.957958i \(0.592628\pi\)
\(312\) 0 0
\(313\) −30.4222 −1.71956 −0.859782 0.510661i \(-0.829401\pi\)
−0.859782 + 0.510661i \(0.829401\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.6972 0.713147 0.356574 0.934267i \(-0.383945\pi\)
0.356574 + 0.934267i \(0.383945\pi\)
\(318\) 0 0
\(319\) −31.4222 −1.75931
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.155590 −0.00865725
\(324\) 0 0
\(325\) −10.3944 −0.576580
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.60555 −0.253912
\(330\) 0 0
\(331\) −2.00000 −0.109930 −0.0549650 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.27502 0.506748
\(336\) 0 0
\(337\) 16.7250 0.911068 0.455534 0.890218i \(-0.349448\pi\)
0.455534 + 0.890218i \(0.349448\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 20.2111 1.09449
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.211103 −0.0113326 −0.00566629 0.999984i \(-0.501804\pi\)
−0.00566629 + 0.999984i \(0.501804\pi\)
\(348\) 0 0
\(349\) 0.697224 0.0373216 0.0186608 0.999826i \(-0.494060\pi\)
0.0186608 + 0.999826i \(0.494060\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −15.6056 −0.830600 −0.415300 0.909685i \(-0.636323\pi\)
−0.415300 + 0.909685i \(0.636323\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.90833 −0.522941 −0.261471 0.965211i \(-0.584207\pi\)
−0.261471 + 0.965211i \(0.584207\pi\)
\(360\) 0 0
\(361\) −18.8444 −0.991811
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.66947 0.401438
\(366\) 0 0
\(367\) 25.5139 1.33181 0.665907 0.746035i \(-0.268045\pi\)
0.665907 + 0.746035i \(0.268045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.90833 0.306745
\(372\) 0 0
\(373\) 11.1833 0.579052 0.289526 0.957170i \(-0.406502\pi\)
0.289526 + 0.957170i \(0.406502\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.9083 0.664813
\(378\) 0 0
\(379\) −10.4222 −0.535353 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 26.6333 1.36090 0.680449 0.732795i \(-0.261785\pi\)
0.680449 + 0.732795i \(0.261785\pi\)
\(384\) 0 0
\(385\) 3.90833 0.199187
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.6333 0.640534 0.320267 0.947327i \(-0.396227\pi\)
0.320267 + 0.947327i \(0.396227\pi\)
\(390\) 0 0
\(391\) 0.394449 0.0199481
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.35829 0.470867
\(396\) 0 0
\(397\) −8.60555 −0.431900 −0.215950 0.976404i \(-0.569285\pi\)
−0.215950 + 0.976404i \(0.569285\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 26.6333 1.33000 0.665002 0.746842i \(-0.268431\pi\)
0.665002 + 0.746842i \(0.268431\pi\)
\(402\) 0 0
\(403\) −8.30278 −0.413591
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −31.4222 −1.55754
\(408\) 0 0
\(409\) 8.39445 0.415079 0.207539 0.978227i \(-0.433454\pi\)
0.207539 + 0.978227i \(0.433454\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.90833 0.192316
\(414\) 0 0
\(415\) −11.3028 −0.554831
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11.9083 0.581760 0.290880 0.956760i \(-0.406052\pi\)
0.290880 + 0.956760i \(0.406052\pi\)
\(420\) 0 0
\(421\) −7.09167 −0.345627 −0.172813 0.984955i \(-0.555286\pi\)
−0.172813 + 0.984955i \(0.555286\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.78049 −0.0863666
\(426\) 0 0
\(427\) −4.90833 −0.237531
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.30278 0.207257 0.103629 0.994616i \(-0.466955\pi\)
0.103629 + 0.994616i \(0.466955\pi\)
\(432\) 0 0
\(433\) 23.8167 1.14456 0.572278 0.820060i \(-0.306060\pi\)
0.572278 + 0.820060i \(0.306060\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.394449 −0.0188690
\(438\) 0 0
\(439\) −27.6056 −1.31754 −0.658771 0.752344i \(-0.728923\pi\)
−0.658771 + 0.752344i \(0.728923\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.78890 0.322550 0.161275 0.986909i \(-0.448439\pi\)
0.161275 + 0.986909i \(0.448439\pi\)
\(444\) 0 0
\(445\) 10.8167 0.512759
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.11943 0.335987 0.167993 0.985788i \(-0.446271\pi\)
0.167993 + 0.985788i \(0.446271\pi\)
\(450\) 0 0
\(451\) 20.2111 0.951704
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.60555 −0.0752694
\(456\) 0 0
\(457\) −20.6972 −0.968175 −0.484088 0.875020i \(-0.660848\pi\)
−0.484088 + 0.875020i \(0.660848\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 26.0917 1.21521 0.607605 0.794239i \(-0.292130\pi\)
0.607605 + 0.794239i \(0.292130\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.8444 1.10339 0.551694 0.834047i \(-0.313982\pi\)
0.551694 + 0.834047i \(0.313982\pi\)
\(468\) 0 0
\(469\) −13.3028 −0.614265
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24.1194 −1.10901
\(474\) 0 0
\(475\) 1.78049 0.0816946
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 27.2389 1.24458 0.622288 0.782789i \(-0.286203\pi\)
0.622288 + 0.782789i \(0.286203\pi\)
\(480\) 0 0
\(481\) 12.9083 0.588569
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.64171 0.119954
\(486\) 0 0
\(487\) 4.21110 0.190823 0.0954116 0.995438i \(-0.469583\pi\)
0.0954116 + 0.995438i \(0.469583\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −34.9083 −1.57539 −0.787695 0.616065i \(-0.788726\pi\)
−0.787695 + 0.616065i \(0.788726\pi\)
\(492\) 0 0
\(493\) 2.21110 0.0995831
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.9083 0.579018
\(498\) 0 0
\(499\) 12.8806 0.576614 0.288307 0.957538i \(-0.406908\pi\)
0.288307 + 0.957538i \(0.406908\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.1194 −0.941669 −0.470834 0.882222i \(-0.656047\pi\)
−0.470834 + 0.882222i \(0.656047\pi\)
\(504\) 0 0
\(505\) 8.72498 0.388257
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.3944 0.859644 0.429822 0.902914i \(-0.358576\pi\)
0.429822 + 0.902914i \(0.358576\pi\)
\(510\) 0 0
\(511\) −11.0000 −0.486611
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.94449 0.0856843
\(516\) 0 0
\(517\) −25.8167 −1.13542
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.78890 −0.209805 −0.104903 0.994482i \(-0.533453\pi\)
−0.104903 + 0.994482i \(0.533453\pi\)
\(522\) 0 0
\(523\) 31.2111 1.36477 0.682383 0.730995i \(-0.260944\pi\)
0.682383 + 0.730995i \(0.260944\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.42221 −0.0619522
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8.30278 −0.359633
\(534\) 0 0
\(535\) −0.211103 −0.00912676
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.60555 −0.241448
\(540\) 0 0
\(541\) 27.0278 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.14719 −0.134811
\(546\) 0 0
\(547\) −28.3305 −1.21133 −0.605663 0.795721i \(-0.707092\pi\)
−0.605663 + 0.795721i \(0.707092\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.21110 −0.0941961
\(552\) 0 0
\(553\) −13.4222 −0.570770
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.1833 −0.685710 −0.342855 0.939388i \(-0.611394\pi\)
−0.342855 + 0.939388i \(0.611394\pi\)
\(558\) 0 0
\(559\) 9.90833 0.419078
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 38.5416 1.62434 0.812168 0.583423i \(-0.198287\pi\)
0.812168 + 0.583423i \(0.198287\pi\)
\(564\) 0 0
\(565\) −3.69722 −0.155543
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14.7889 0.619983 0.309991 0.950739i \(-0.399674\pi\)
0.309991 + 0.950739i \(0.399674\pi\)
\(570\) 0 0
\(571\) −29.7889 −1.24663 −0.623313 0.781972i \(-0.714214\pi\)
−0.623313 + 0.781972i \(0.714214\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.51388 −0.188242
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.2111 0.672550
\(582\) 0 0
\(583\) 33.1194 1.37167
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 35.5139 1.46581 0.732907 0.680329i \(-0.238163\pi\)
0.732907 + 0.680329i \(0.238163\pi\)
\(588\) 0 0
\(589\) 1.42221 0.0586009
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.3944 −0.878565 −0.439282 0.898349i \(-0.644767\pi\)
−0.439282 + 0.898349i \(0.644767\pi\)
\(594\) 0 0
\(595\) −0.275019 −0.0112747
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −26.5416 −1.08446 −0.542231 0.840230i \(-0.682420\pi\)
−0.542231 + 0.840230i \(0.682420\pi\)
\(600\) 0 0
\(601\) −27.5416 −1.12345 −0.561723 0.827325i \(-0.689861\pi\)
−0.561723 + 0.827325i \(0.689861\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 14.2389 0.578892
\(606\) 0 0
\(607\) −20.5416 −0.833759 −0.416880 0.908962i \(-0.636876\pi\)
−0.416880 + 0.908962i \(0.636876\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.6056 0.429055
\(612\) 0 0
\(613\) −28.6333 −1.15649 −0.578244 0.815864i \(-0.696262\pi\)
−0.578244 + 0.815864i \(0.696262\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −20.3028 −0.817359 −0.408679 0.912678i \(-0.634011\pi\)
−0.408679 + 0.912678i \(0.634011\pi\)
\(618\) 0 0
\(619\) 40.3028 1.61991 0.809953 0.586495i \(-0.199493\pi\)
0.809953 + 0.586495i \(0.199493\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −15.5139 −0.621550
\(624\) 0 0
\(625\) 17.9445 0.717779
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.21110 0.0881624
\(630\) 0 0
\(631\) 16.3944 0.652653 0.326326 0.945257i \(-0.394189\pi\)
0.326326 + 0.945257i \(0.394189\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 12.6333 0.501338
\(636\) 0 0
\(637\) 2.30278 0.0912393
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 30.5416 1.20632 0.603161 0.797619i \(-0.293908\pi\)
0.603161 + 0.797619i \(0.293908\pi\)
\(642\) 0 0
\(643\) 19.0917 0.752902 0.376451 0.926437i \(-0.377144\pi\)
0.376451 + 0.926437i \(0.377144\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.5139 0.649228 0.324614 0.945847i \(-0.394766\pi\)
0.324614 + 0.945847i \(0.394766\pi\)
\(648\) 0 0
\(649\) 21.9083 0.859977
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17.9083 −0.700807 −0.350403 0.936599i \(-0.613956\pi\)
−0.350403 + 0.936599i \(0.613956\pi\)
\(654\) 0 0
\(655\) 4.75274 0.185705
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.1833 0.513550 0.256775 0.966471i \(-0.417340\pi\)
0.256775 + 0.966471i \(0.417340\pi\)
\(660\) 0 0
\(661\) −5.42221 −0.210899 −0.105450 0.994425i \(-0.533628\pi\)
−0.105450 + 0.994425i \(0.533628\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.275019 0.0106648
\(666\) 0 0
\(667\) 5.60555 0.217048
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −27.5139 −1.06216
\(672\) 0 0
\(673\) 5.00000 0.192736 0.0963679 0.995346i \(-0.469277\pi\)
0.0963679 + 0.995346i \(0.469277\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.1194 1.15758 0.578792 0.815475i \(-0.303524\pi\)
0.578792 + 0.815475i \(0.303524\pi\)
\(678\) 0 0
\(679\) −3.78890 −0.145405
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 30.6333 1.17215 0.586075 0.810256i \(-0.300672\pi\)
0.586075 + 0.810256i \(0.300672\pi\)
\(684\) 0 0
\(685\) 3.90833 0.149329
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −13.6056 −0.518330
\(690\) 0 0
\(691\) −3.09167 −0.117613 −0.0588064 0.998269i \(-0.518729\pi\)
−0.0588064 + 0.998269i \(0.518729\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.5416 −0.399867
\(696\) 0 0
\(697\) −1.42221 −0.0538699
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18.9361 −0.715206 −0.357603 0.933874i \(-0.616406\pi\)
−0.357603 + 0.933874i \(0.616406\pi\)
\(702\) 0 0
\(703\) −2.21110 −0.0833933
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.5139 −0.470633
\(708\) 0 0
\(709\) −20.1194 −0.755601 −0.377801 0.925887i \(-0.623319\pi\)
−0.377801 + 0.925887i \(0.623319\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.60555 −0.135029
\(714\) 0 0
\(715\) −9.00000 −0.336581
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −41.8444 −1.56053 −0.780267 0.625447i \(-0.784917\pi\)
−0.780267 + 0.625447i \(0.784917\pi\)
\(720\) 0 0
\(721\) −2.78890 −0.103864
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.3028 −0.939721
\(726\) 0 0
\(727\) −6.39445 −0.237157 −0.118578 0.992945i \(-0.537834\pi\)
−0.118578 + 0.992945i \(0.537834\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.69722 0.0627741
\(732\) 0 0
\(733\) −37.0278 −1.36765 −0.683826 0.729645i \(-0.739685\pi\)
−0.683826 + 0.729645i \(0.739685\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −74.5694 −2.74680
\(738\) 0 0
\(739\) −36.8167 −1.35432 −0.677161 0.735835i \(-0.736790\pi\)
−0.677161 + 0.735835i \(0.736790\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.4861 −1.00837 −0.504184 0.863596i \(-0.668207\pi\)
−0.504184 + 0.863596i \(0.668207\pi\)
\(744\) 0 0
\(745\) 10.7334 0.393241
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.302776 0.0110632
\(750\) 0 0
\(751\) −42.9361 −1.56676 −0.783380 0.621543i \(-0.786506\pi\)
−0.783380 + 0.621543i \(0.786506\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 20.8167 0.756594 0.378297 0.925684i \(-0.376510\pi\)
0.378297 + 0.925684i \(0.376510\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.6333 0.566707 0.283353 0.959016i \(-0.408553\pi\)
0.283353 + 0.959016i \(0.408553\pi\)
\(762\) 0 0
\(763\) 4.51388 0.163413
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.00000 −0.324971
\(768\) 0 0
\(769\) 11.8167 0.426119 0.213060 0.977039i \(-0.431657\pi\)
0.213060 + 0.977039i \(0.431657\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.21110 0.0795278 0.0397639 0.999209i \(-0.487339\pi\)
0.0397639 + 0.999209i \(0.487339\pi\)
\(774\) 0 0
\(775\) 16.2750 0.584616
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.42221 0.0509558
\(780\) 0 0
\(781\) 72.3583 2.58918
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.23886 0.294057
\(786\) 0 0
\(787\) −31.1194 −1.10929 −0.554644 0.832088i \(-0.687146\pi\)
−0.554644 + 0.832088i \(0.687146\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.30278 0.188545
\(792\) 0 0
\(793\) 11.3028 0.401373
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 49.8167 1.76460 0.882298 0.470691i \(-0.155995\pi\)
0.882298 + 0.470691i \(0.155995\pi\)
\(798\) 0 0
\(799\) 1.81665 0.0642686
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −61.6611 −2.17597
\(804\) 0 0
\(805\) −0.697224 −0.0245739
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −25.5139 −0.897020 −0.448510 0.893778i \(-0.648045\pi\)
−0.448510 + 0.893778i \(0.648045\pi\)
\(810\) 0 0
\(811\) 10.6333 0.373386 0.186693 0.982418i \(-0.440223\pi\)
0.186693 + 0.982418i \(0.440223\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −6.35829 −0.222721
\(816\) 0 0
\(817\) −1.69722 −0.0593784
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.4500 0.609008 0.304504 0.952511i \(-0.401509\pi\)
0.304504 + 0.952511i \(0.401509\pi\)
\(822\) 0 0
\(823\) −48.5139 −1.69109 −0.845544 0.533906i \(-0.820724\pi\)
−0.845544 + 0.533906i \(0.820724\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.6972 −0.789260 −0.394630 0.918840i \(-0.629127\pi\)
−0.394630 + 0.918840i \(0.629127\pi\)
\(828\) 0 0
\(829\) 1.18335 0.0410993 0.0205497 0.999789i \(-0.493458\pi\)
0.0205497 + 0.999789i \(0.493458\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.394449 0.0136668
\(834\) 0 0
\(835\) 9.78049 0.338468
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 28.5416 0.985367 0.492683 0.870209i \(-0.336016\pi\)
0.492683 + 0.870209i \(0.336016\pi\)
\(840\) 0 0
\(841\) 2.42221 0.0835243
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5.36669 −0.184620
\(846\) 0 0
\(847\) −20.4222 −0.701715
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5.60555 0.192156
\(852\) 0 0
\(853\) −2.60555 −0.0892124 −0.0446062 0.999005i \(-0.514203\pi\)
−0.0446062 + 0.999005i \(0.514203\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.02776 −0.308382 −0.154191 0.988041i \(-0.549277\pi\)
−0.154191 + 0.988041i \(0.549277\pi\)
\(858\) 0 0
\(859\) 28.0555 0.957242 0.478621 0.878022i \(-0.341137\pi\)
0.478621 + 0.878022i \(0.341137\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11.8167 0.402244 0.201122 0.979566i \(-0.435541\pi\)
0.201122 + 0.979566i \(0.435541\pi\)
\(864\) 0 0
\(865\) 4.45837 0.151589
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −75.2389 −2.55230
\(870\) 0 0
\(871\) 30.6333 1.03797
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.63331 0.224247
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.23886 0.0754291 0.0377145 0.999289i \(-0.487992\pi\)
0.0377145 + 0.999289i \(0.487992\pi\)
\(882\) 0 0
\(883\) −6.90833 −0.232484 −0.116242 0.993221i \(-0.537085\pi\)
−0.116242 + 0.993221i \(0.537085\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.51388 0.0508311 0.0254155 0.999677i \(-0.491909\pi\)
0.0254155 + 0.999677i \(0.491909\pi\)
\(888\) 0 0
\(889\) −18.1194 −0.607706
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.81665 −0.0607920
\(894\) 0 0
\(895\) −17.3860 −0.581151
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −20.2111 −0.674078
\(900\) 0 0
\(901\) −2.33053 −0.0776413
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13.2473 −0.440354
\(906\) 0 0
\(907\) −49.7250 −1.65109 −0.825545 0.564336i \(-0.809132\pi\)
−0.825545 + 0.564336i \(0.809132\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24.6056 −0.815218 −0.407609 0.913156i \(-0.633637\pi\)
−0.407609 + 0.913156i \(0.633637\pi\)
\(912\) 0 0
\(913\) 90.8722 3.00743
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −6.81665 −0.225106
\(918\) 0 0
\(919\) 8.02776 0.264811 0.132406 0.991196i \(-0.457730\pi\)
0.132406 + 0.991196i \(0.457730\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −29.7250 −0.978410
\(924\) 0 0
\(925\) −25.3028 −0.831950
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34.6972 1.13838 0.569190 0.822206i \(-0.307257\pi\)
0.569190 + 0.822206i \(0.307257\pi\)
\(930\) 0 0
\(931\) −0.394449 −0.0129275
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.54163 −0.0504168
\(936\) 0 0
\(937\) −5.97224 −0.195105 −0.0975523 0.995230i \(-0.531101\pi\)
−0.0975523 + 0.995230i \(0.531101\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 5.21110 0.169877 0.0849385 0.996386i \(-0.472931\pi\)
0.0849385 + 0.996386i \(0.472931\pi\)
\(942\) 0 0
\(943\) −3.60555 −0.117413
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18.8444 0.612361 0.306181 0.951973i \(-0.400949\pi\)
0.306181 + 0.951973i \(0.400949\pi\)
\(948\) 0 0
\(949\) 25.3305 0.822264
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −26.7250 −0.865707 −0.432854 0.901464i \(-0.642493\pi\)
−0.432854 + 0.901464i \(0.642493\pi\)
\(954\) 0 0
\(955\) 6.00000 0.194155
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.60555 −0.181013
\(960\) 0 0
\(961\) −18.0000 −0.580645
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 14.6611 0.471956
\(966\) 0 0
\(967\) −16.0555 −0.516310 −0.258155 0.966103i \(-0.583115\pi\)
−0.258155 + 0.966103i \(0.583115\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −6.06392 −0.194600 −0.0973002 0.995255i \(-0.531021\pi\)
−0.0973002 + 0.995255i \(0.531021\pi\)
\(972\) 0 0
\(973\) 15.1194 0.484707
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13.6972 0.438213 0.219107 0.975701i \(-0.429686\pi\)
0.219107 + 0.975701i \(0.429686\pi\)
\(978\) 0 0
\(979\) −86.9638 −2.77938
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.57779 −0.0822189 −0.0411094 0.999155i \(-0.513089\pi\)
−0.0411094 + 0.999155i \(0.513089\pi\)
\(984\) 0 0
\(985\) 18.0833 0.576181
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.30278 0.136820
\(990\) 0 0
\(991\) −30.9638 −0.983599 −0.491799 0.870709i \(-0.663661\pi\)
−0.491799 + 0.870709i \(0.663661\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.33053 −0.0421807
\(996\) 0 0
\(997\) −3.18335 −0.100818 −0.0504088 0.998729i \(-0.516052\pi\)
−0.0504088 + 0.998729i \(0.516052\pi\)
\(998\) 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 5796.2.a.m.1.1 2
3.2 odd 2 1932.2.a.c.1.2 2
12.11 even 2 7728.2.a.bf.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.2.a.c.1.2 2 3.2 odd 2
5796.2.a.m.1.1 2 1.1 even 1 trivial
7728.2.a.bf.1.2 2 12.11 even 2