Properties

Label 7623.2.a.bh.1.2
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 1
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.30278\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{4} +3.60555 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{4} +3.60555 q^{5} +1.00000 q^{7} -2.00000 q^{13} +4.00000 q^{16} -3.60555 q^{17} -6.00000 q^{19} -7.21110 q^{20} +7.21110 q^{23} +8.00000 q^{25} -2.00000 q^{28} -7.21110 q^{29} -2.00000 q^{31} +3.60555 q^{35} -2.00000 q^{37} -7.21110 q^{41} +5.00000 q^{43} +3.60555 q^{47} +1.00000 q^{49} +4.00000 q^{52} -10.8167 q^{59} +14.0000 q^{61} -8.00000 q^{64} -7.21110 q^{65} -15.0000 q^{67} +7.21110 q^{68} -14.4222 q^{71} -4.00000 q^{73} +12.0000 q^{76} +14.4222 q^{80} -10.8167 q^{83} -13.0000 q^{85} +10.8167 q^{89} -2.00000 q^{91} -14.4222 q^{92} -21.6333 q^{95} -8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{4} + 2q^{7} + O(q^{10}) \) \( 2q - 4q^{4} + 2q^{7} - 4q^{13} + 8q^{16} - 12q^{19} + 16q^{25} - 4q^{28} - 4q^{31} - 4q^{37} + 10q^{43} + 2q^{49} + 8q^{52} + 28q^{61} - 16q^{64} - 30q^{67} - 8q^{73} + 24q^{76} - 26q^{85} - 4q^{91} - 16q^{97} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) 3.60555 1.61245 0.806226 0.591608i \(-0.201507\pi\)
0.806226 + 0.591608i \(0.201507\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −3.60555 −0.874475 −0.437237 0.899346i \(-0.644043\pi\)
−0.437237 + 0.899346i \(0.644043\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −7.21110 −1.61245
\(21\) 0 0
\(22\) 0 0
\(23\) 7.21110 1.50362 0.751809 0.659380i \(-0.229181\pi\)
0.751809 + 0.659380i \(0.229181\pi\)
\(24\) 0 0
\(25\) 8.00000 1.60000
\(26\) 0 0
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) −7.21110 −1.33907 −0.669534 0.742781i \(-0.733506\pi\)
−0.669534 + 0.742781i \(0.733506\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.60555 0.609449
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.21110 −1.12619 −0.563093 0.826394i \(-0.690389\pi\)
−0.563093 + 0.826394i \(0.690389\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.60555 0.525924 0.262962 0.964806i \(-0.415301\pi\)
0.262962 + 0.964806i \(0.415301\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 4.00000 0.554700
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.8167 −1.40821 −0.704104 0.710097i \(-0.748651\pi\)
−0.704104 + 0.710097i \(0.748651\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −7.21110 −0.894427
\(66\) 0 0
\(67\) −15.0000 −1.83254 −0.916271 0.400559i \(-0.868816\pi\)
−0.916271 + 0.400559i \(0.868816\pi\)
\(68\) 7.21110 0.874475
\(69\) 0 0
\(70\) 0 0
\(71\) −14.4222 −1.71160 −0.855800 0.517306i \(-0.826935\pi\)
−0.855800 + 0.517306i \(0.826935\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 12.0000 1.37649
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 14.4222 1.61245
\(81\) 0 0
\(82\) 0 0
\(83\) −10.8167 −1.18728 −0.593641 0.804730i \(-0.702310\pi\)
−0.593641 + 0.804730i \(0.702310\pi\)
\(84\) 0 0
\(85\) −13.0000 −1.41005
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.8167 1.14656 0.573282 0.819358i \(-0.305670\pi\)
0.573282 + 0.819358i \(0.305670\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) −14.4222 −1.50362
\(93\) 0 0
\(94\) 0 0
\(95\) −21.6333 −2.21953
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −16.0000 −1.60000
\(101\) −10.8167 −1.07630 −0.538149 0.842850i \(-0.680876\pi\)
−0.538149 + 0.842850i \(0.680876\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.21110 0.697124 0.348562 0.937286i \(-0.386670\pi\)
0.348562 + 0.937286i \(0.386670\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.00000 0.377964
\(113\) −7.21110 −0.678363 −0.339182 0.940721i \(-0.610150\pi\)
−0.339182 + 0.940721i \(0.610150\pi\)
\(114\) 0 0
\(115\) 26.0000 2.42451
\(116\) 14.4222 1.33907
\(117\) 0 0
\(118\) 0 0
\(119\) −3.60555 −0.330520
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) 10.8167 0.967471
\(126\) 0 0
\(127\) 1.00000 0.0887357 0.0443678 0.999015i \(-0.485873\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.8167 −0.945055 −0.472528 0.881316i \(-0.656658\pi\)
−0.472528 + 0.881316i \(0.656658\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.6333 1.84826 0.924129 0.382080i \(-0.124792\pi\)
0.924129 + 0.382080i \(0.124792\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) −7.21110 −0.609449
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −26.0000 −2.15918
\(146\) 0 0
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) −14.4222 −1.18151 −0.590757 0.806850i \(-0.701171\pi\)
−0.590757 + 0.806850i \(0.701171\pi\)
\(150\) 0 0
\(151\) −9.00000 −0.732410 −0.366205 0.930534i \(-0.619343\pi\)
−0.366205 + 0.930534i \(0.619343\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.21110 −0.579210
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.21110 0.568314
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 14.4222 1.12619
\(165\) 0 0
\(166\) 0 0
\(167\) 3.60555 0.279006 0.139503 0.990222i \(-0.455450\pi\)
0.139503 + 0.990222i \(0.455450\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) 3.60555 0.274125 0.137062 0.990562i \(-0.456234\pi\)
0.137062 + 0.990562i \(0.456234\pi\)
\(174\) 0 0
\(175\) 8.00000 0.604743
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −14.4222 −1.07797 −0.538983 0.842317i \(-0.681191\pi\)
−0.538983 + 0.842317i \(0.681191\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7.21110 −0.530171
\(186\) 0 0
\(187\) 0 0
\(188\) −7.21110 −0.525924
\(189\) 0 0
\(190\) 0 0
\(191\) 14.4222 1.04355 0.521777 0.853082i \(-0.325269\pi\)
0.521777 + 0.853082i \(0.325269\pi\)
\(192\) 0 0
\(193\) −23.0000 −1.65558 −0.827788 0.561041i \(-0.810401\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.00000 −0.142857
\(197\) 21.6333 1.54131 0.770655 0.637253i \(-0.219929\pi\)
0.770655 + 0.637253i \(0.219929\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.21110 −0.506120
\(204\) 0 0
\(205\) −26.0000 −1.81592
\(206\) 0 0
\(207\) 0 0
\(208\) −8.00000 −0.554700
\(209\) 0 0
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 18.0278 1.22948
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.21110 0.485071
\(222\) 0 0
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 25.2389 1.67516 0.837581 0.546313i \(-0.183969\pi\)
0.837581 + 0.546313i \(0.183969\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 13.0000 0.848026
\(236\) 21.6333 1.40821
\(237\) 0 0
\(238\) 0 0
\(239\) −7.21110 −0.466447 −0.233224 0.972423i \(-0.574927\pi\)
−0.233224 + 0.972423i \(0.574927\pi\)
\(240\) 0 0
\(241\) 12.0000 0.772988 0.386494 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −28.0000 −1.79252
\(245\) 3.60555 0.230350
\(246\) 0 0
\(247\) 12.0000 0.763542
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 10.8167 0.674724 0.337362 0.941375i \(-0.390465\pi\)
0.337362 + 0.941375i \(0.390465\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 14.4222 0.894427
\(261\) 0 0
\(262\) 0 0
\(263\) −21.6333 −1.33397 −0.666983 0.745073i \(-0.732415\pi\)
−0.666983 + 0.745073i \(0.732415\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 30.0000 1.83254
\(269\) −21.6333 −1.31901 −0.659503 0.751702i \(-0.729233\pi\)
−0.659503 + 0.751702i \(0.729233\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −14.4222 −0.874475
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −21.0000 −1.26177 −0.630884 0.775877i \(-0.717308\pi\)
−0.630884 + 0.775877i \(0.717308\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14.4222 −0.860357 −0.430178 0.902744i \(-0.641549\pi\)
−0.430178 + 0.902744i \(0.641549\pi\)
\(282\) 0 0
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 28.8444 1.71160
\(285\) 0 0
\(286\) 0 0
\(287\) −7.21110 −0.425658
\(288\) 0 0
\(289\) −4.00000 −0.235294
\(290\) 0 0
\(291\) 0 0
\(292\) 8.00000 0.468165
\(293\) 32.4500 1.89575 0.947873 0.318647i \(-0.103228\pi\)
0.947873 + 0.318647i \(0.103228\pi\)
\(294\) 0 0
\(295\) −39.0000 −2.27067
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −14.4222 −0.834058
\(300\) 0 0
\(301\) 5.00000 0.288195
\(302\) 0 0
\(303\) 0 0
\(304\) −24.0000 −1.37649
\(305\) 50.4777 2.89035
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.0278 −1.02226 −0.511130 0.859503i \(-0.670773\pi\)
−0.511130 + 0.859503i \(0.670773\pi\)
\(312\) 0 0
\(313\) 4.00000 0.226093 0.113047 0.993590i \(-0.463939\pi\)
0.113047 + 0.993590i \(0.463939\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.6333 1.21505 0.607524 0.794301i \(-0.292163\pi\)
0.607524 + 0.794301i \(0.292163\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −28.8444 −1.61245
\(321\) 0 0
\(322\) 0 0
\(323\) 21.6333 1.20371
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.60555 0.198780
\(330\) 0 0
\(331\) −5.00000 −0.274825 −0.137412 0.990514i \(-0.543879\pi\)
−0.137412 + 0.990514i \(0.543879\pi\)
\(332\) 21.6333 1.18728
\(333\) 0 0
\(334\) 0 0
\(335\) −54.0833 −2.95488
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 26.0000 1.41005
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.8444 1.54845 0.774225 0.632911i \(-0.218140\pi\)
0.774225 + 0.632911i \(0.218140\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.6333 −1.15142 −0.575712 0.817652i \(-0.695275\pi\)
−0.575712 + 0.817652i \(0.695275\pi\)
\(354\) 0 0
\(355\) −52.0000 −2.75987
\(356\) −21.6333 −1.14656
\(357\) 0 0
\(358\) 0 0
\(359\) −14.4222 −0.761175 −0.380587 0.924745i \(-0.624278\pi\)
−0.380587 + 0.924745i \(0.624278\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) −14.4222 −0.754893
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 28.8444 1.50362
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 25.0000 1.29445 0.647225 0.762299i \(-0.275929\pi\)
0.647225 + 0.762299i \(0.275929\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.4222 0.742781
\(378\) 0 0
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 43.2666 2.21953
\(381\) 0 0
\(382\) 0 0
\(383\) 25.2389 1.28965 0.644823 0.764332i \(-0.276931\pi\)
0.644823 + 0.764332i \(0.276931\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 16.0000 0.812277
\(389\) 21.6333 1.09685 0.548426 0.836199i \(-0.315227\pi\)
0.548426 + 0.836199i \(0.315227\pi\)
\(390\) 0 0
\(391\) −26.0000 −1.31488
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 32.0000 1.60000
\(401\) 21.6333 1.08032 0.540158 0.841564i \(-0.318365\pi\)
0.540158 + 0.841564i \(0.318365\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 21.6333 1.07630
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −34.0000 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −12.0000 −0.591198
\(413\) −10.8167 −0.532253
\(414\) 0 0
\(415\) −39.0000 −1.91443
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.60555 −0.176143 −0.0880714 0.996114i \(-0.528070\pi\)
−0.0880714 + 0.996114i \(0.528070\pi\)
\(420\) 0 0
\(421\) −35.0000 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −28.8444 −1.39916
\(426\) 0 0
\(427\) 14.0000 0.677507
\(428\) −14.4222 −0.697124
\(429\) 0 0
\(430\) 0 0
\(431\) −7.21110 −0.347347 −0.173673 0.984803i \(-0.555564\pi\)
−0.173673 + 0.984803i \(0.555564\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) −43.2666 −2.06972
\(438\) 0 0
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −21.6333 −1.02783 −0.513915 0.857841i \(-0.671805\pi\)
−0.513915 + 0.857841i \(0.671805\pi\)
\(444\) 0 0
\(445\) 39.0000 1.84878
\(446\) 0 0
\(447\) 0 0
\(448\) −8.00000 −0.377964
\(449\) −21.6333 −1.02094 −0.510469 0.859896i \(-0.670528\pi\)
−0.510469 + 0.859896i \(0.670528\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 14.4222 0.678363
\(453\) 0 0
\(454\) 0 0
\(455\) −7.21110 −0.338062
\(456\) 0 0
\(457\) −29.0000 −1.35656 −0.678281 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −52.0000 −2.42451
\(461\) 32.4500 1.51135 0.755673 0.654949i \(-0.227310\pi\)
0.755673 + 0.654949i \(0.227310\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −28.8444 −1.33907
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −48.0000 −2.20239
\(476\) 7.21110 0.330520
\(477\) 0 0
\(478\) 0 0
\(479\) −25.2389 −1.15319 −0.576596 0.817029i \(-0.695619\pi\)
−0.576596 + 0.817029i \(0.695619\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −28.8444 −1.30976
\(486\) 0 0
\(487\) 5.00000 0.226572 0.113286 0.993562i \(-0.463862\pi\)
0.113286 + 0.993562i \(0.463862\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 43.2666 1.95260 0.976298 0.216433i \(-0.0694422\pi\)
0.976298 + 0.216433i \(0.0694422\pi\)
\(492\) 0 0
\(493\) 26.0000 1.17098
\(494\) 0 0
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) −14.4222 −0.646924
\(498\) 0 0
\(499\) 11.0000 0.492428 0.246214 0.969216i \(-0.420813\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) −21.6333 −0.967471
\(501\) 0 0
\(502\) 0 0
\(503\) 10.8167 0.482291 0.241145 0.970489i \(-0.422477\pi\)
0.241145 + 0.970489i \(0.422477\pi\)
\(504\) 0 0
\(505\) −39.0000 −1.73548
\(506\) 0 0
\(507\) 0 0
\(508\) −2.00000 −0.0887357
\(509\) −39.6611 −1.75795 −0.878973 0.476872i \(-0.841771\pi\)
−0.878973 + 0.476872i \(0.841771\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 21.6333 0.953277
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0278 0.789810 0.394905 0.918722i \(-0.370777\pi\)
0.394905 + 0.918722i \(0.370777\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 21.6333 0.945055
\(525\) 0 0
\(526\) 0 0
\(527\) 7.21110 0.314121
\(528\) 0 0
\(529\) 29.0000 1.26087
\(530\) 0 0
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) 14.4222 0.624695
\(534\) 0 0
\(535\) 26.0000 1.12408
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.00000 0.300954 0.150477 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −25.2389 −1.08111
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −43.2666 −1.84826
\(549\) 0 0
\(550\) 0 0
\(551\) 43.2666 1.84322
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −32.0000 −1.35710
\(557\) −36.0555 −1.52772 −0.763861 0.645381i \(-0.776698\pi\)
−0.763861 + 0.645381i \(0.776698\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 14.4222 0.609449
\(561\) 0 0
\(562\) 0 0
\(563\) 18.0278 0.759779 0.379890 0.925032i \(-0.375962\pi\)
0.379890 + 0.925032i \(0.375962\pi\)
\(564\) 0 0
\(565\) −26.0000 −1.09383
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 57.6888 2.40579
\(576\) 0 0
\(577\) −28.0000 −1.16566 −0.582828 0.812596i \(-0.698054\pi\)
−0.582828 + 0.812596i \(0.698054\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 52.0000 2.15918
\(581\) −10.8167 −0.448750
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −32.4500 −1.33935 −0.669677 0.742653i \(-0.733567\pi\)
−0.669677 + 0.742653i \(0.733567\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) 10.8167 0.444187 0.222093 0.975025i \(-0.428711\pi\)
0.222093 + 0.975025i \(0.428711\pi\)
\(594\) 0 0
\(595\) −13.0000 −0.532948
\(596\) 28.8444 1.18151
\(597\) 0 0
\(598\) 0 0
\(599\) 43.2666 1.76783 0.883913 0.467651i \(-0.154900\pi\)
0.883913 + 0.467651i \(0.154900\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 18.0000 0.732410
\(605\) 0 0
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.21110 −0.291730
\(612\) 0 0
\(613\) 11.0000 0.444286 0.222143 0.975014i \(-0.428695\pi\)
0.222143 + 0.975014i \(0.428695\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 32.0000 1.28619 0.643094 0.765787i \(-0.277650\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 14.4222 0.579210
\(621\) 0 0
\(622\) 0 0
\(623\) 10.8167 0.433360
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 7.21110 0.287525
\(630\) 0 0
\(631\) −21.0000 −0.835997 −0.417998 0.908448i \(-0.637268\pi\)
−0.417998 + 0.908448i \(0.637268\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.60555 0.143082
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) −14.4222 −0.568314
\(645\) 0 0
\(646\) 0 0
\(647\) −32.4500 −1.27574 −0.637870 0.770144i \(-0.720184\pi\)
−0.637870 + 0.770144i \(0.720184\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) −36.0555 −1.41096 −0.705481 0.708729i \(-0.749269\pi\)
−0.705481 + 0.708729i \(0.749269\pi\)
\(654\) 0 0
\(655\) −39.0000 −1.52386
\(656\) −28.8444 −1.12619
\(657\) 0 0
\(658\) 0 0
\(659\) −28.8444 −1.12362 −0.561809 0.827267i \(-0.689895\pi\)
−0.561809 + 0.827267i \(0.689895\pi\)
\(660\) 0 0
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21.6333 −0.838904
\(666\) 0 0
\(667\) −52.0000 −2.01345
\(668\) −7.21110 −0.279006
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −13.0000 −0.501113 −0.250557 0.968102i \(-0.580614\pi\)
−0.250557 + 0.968102i \(0.580614\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 18.0000 0.692308
\(677\) 18.0278 0.692863 0.346431 0.938075i \(-0.387393\pi\)
0.346431 + 0.938075i \(0.387393\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 43.2666 1.65555 0.827776 0.561059i \(-0.189606\pi\)
0.827776 + 0.561059i \(0.189606\pi\)
\(684\) 0 0
\(685\) 78.0000 2.98023
\(686\) 0 0
\(687\) 0 0
\(688\) 20.0000 0.762493
\(689\) 0 0
\(690\) 0 0
\(691\) −36.0000 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) −7.21110 −0.274125
\(693\) 0 0
\(694\) 0 0
\(695\) 57.6888 2.18826
\(696\) 0 0
\(697\) 26.0000 0.984820
\(698\) 0 0
\(699\) 0 0
\(700\) −16.0000 −0.604743
\(701\) −43.2666 −1.63416 −0.817079 0.576526i \(-0.804408\pi\)
−0.817079 + 0.576526i \(0.804408\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.8167 −0.406802
\(708\) 0 0
\(709\) −9.00000 −0.338002 −0.169001 0.985616i \(-0.554054\pi\)
−0.169001 + 0.985616i \(0.554054\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −14.4222 −0.540116
\(714\) 0 0
\(715\) 0 0
\(716\) 28.8444 1.07797
\(717\) 0 0
\(718\) 0 0
\(719\) −14.4222 −0.537857 −0.268929 0.963160i \(-0.586670\pi\)
−0.268929 + 0.963160i \(0.586670\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 0 0
\(724\) −40.0000 −1.48659
\(725\) −57.6888 −2.14251
\(726\) 0 0
\(727\) 44.0000 1.63187 0.815935 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −18.0278 −0.666781
\(732\) 0 0
\(733\) 28.0000 1.03420 0.517102 0.855924i \(-0.327011\pi\)
0.517102 + 0.855924i \(0.327011\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) 14.4222 0.530171
\(741\) 0 0
\(742\) 0 0
\(743\) −21.6333 −0.793649 −0.396825 0.917894i \(-0.629888\pi\)
−0.396825 + 0.917894i \(0.629888\pi\)
\(744\) 0 0
\(745\) −52.0000 −1.90513
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.21110 0.263488
\(750\) 0 0
\(751\) −41.0000 −1.49611 −0.748056 0.663636i \(-0.769012\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) 14.4222 0.525924
\(753\) 0 0
\(754\) 0 0
\(755\) −32.4500 −1.18098
\(756\) 0 0
\(757\) 23.0000 0.835949 0.417975 0.908459i \(-0.362740\pi\)
0.417975 + 0.908459i \(0.362740\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10.8167 −0.392103 −0.196052 0.980594i \(-0.562812\pi\)
−0.196052 + 0.980594i \(0.562812\pi\)
\(762\) 0 0
\(763\) −7.00000 −0.253417
\(764\) −28.8444 −1.04355
\(765\) 0 0
\(766\) 0 0
\(767\) 21.6333 0.781133
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 46.0000 1.65558
\(773\) 10.8167 0.389048 0.194524 0.980898i \(-0.437684\pi\)
0.194524 + 0.980898i \(0.437684\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 43.2666 1.55019
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 4.00000 0.142857
\(785\) −7.21110 −0.257375
\(786\) 0 0
\(787\) 22.0000 0.784215 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(788\) −43.2666 −1.54131
\(789\) 0 0
\(790\) 0 0
\(791\) −7.21110 −0.256397
\(792\) 0 0
\(793\) −28.0000 −0.994309
\(794\) 0 0
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) 25.2389 0.894006 0.447003 0.894532i \(-0.352491\pi\)
0.447003 + 0.894532i \(0.352491\pi\)
\(798\) 0 0
\(799\) −13.0000 −0.459907
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 26.0000 0.916380
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.6333 0.760587 0.380293 0.924866i \(-0.375823\pi\)
0.380293 + 0.924866i \(0.375823\pi\)
\(810\) 0 0
\(811\) −2.00000 −0.0702295 −0.0351147 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 14.4222 0.506120
\(813\) 0 0
\(814\) 0 0
\(815\) 14.4222 0.505188
\(816\) 0 0
\(817\) −30.0000 −1.04957
\(818\) 0 0
\(819\) 0 0
\(820\) 52.0000 1.81592
\(821\) −43.2666 −1.51002 −0.755008 0.655716i \(-0.772367\pi\)
−0.755008 + 0.655716i \(0.772367\pi\)
\(822\) 0 0
\(823\) 44.0000 1.53374 0.766872 0.641800i \(-0.221812\pi\)
0.766872 + 0.641800i \(0.221812\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.21110 0.250755 0.125377 0.992109i \(-0.459986\pi\)
0.125377 + 0.992109i \(0.459986\pi\)
\(828\) 0 0
\(829\) −20.0000 −0.694629 −0.347314 0.937749i \(-0.612906\pi\)
−0.347314 + 0.937749i \(0.612906\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 16.0000 0.554700
\(833\) −3.60555 −0.124925
\(834\) 0 0
\(835\) 13.0000 0.449884
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.8167 0.373432 0.186716 0.982414i \(-0.440216\pi\)
0.186716 + 0.982414i \(0.440216\pi\)
\(840\) 0 0
\(841\) 23.0000 0.793103
\(842\) 0 0
\(843\) 0 0
\(844\) 26.0000 0.894957
\(845\) −32.4500 −1.11631
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −14.4222 −0.494387
\(852\) 0 0
\(853\) 16.0000 0.547830 0.273915 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.2389 −0.862143 −0.431071 0.902318i \(-0.641864\pi\)
−0.431071 + 0.902318i \(0.641864\pi\)
\(858\) 0 0
\(859\) 52.0000 1.77422 0.887109 0.461561i \(-0.152710\pi\)
0.887109 + 0.461561i \(0.152710\pi\)
\(860\) −36.0555 −1.22948
\(861\) 0 0
\(862\) 0 0
\(863\) 7.21110 0.245469 0.122734 0.992440i \(-0.460834\pi\)
0.122734 + 0.992440i \(0.460834\pi\)
\(864\) 0 0
\(865\) 13.0000 0.442013
\(866\) 0 0
\(867\) 0 0
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 0 0
\(871\) 30.0000 1.01651
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.8167 0.365670
\(876\) 0 0
\(877\) −46.0000 −1.55331 −0.776655 0.629926i \(-0.783085\pi\)
−0.776655 + 0.629926i \(0.783085\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −21.6333 −0.728845 −0.364422 0.931234i \(-0.618734\pi\)
−0.364422 + 0.931234i \(0.618734\pi\)
\(882\) 0 0
\(883\) −29.0000 −0.975928 −0.487964 0.872864i \(-0.662260\pi\)
−0.487964 + 0.872864i \(0.662260\pi\)
\(884\) −14.4222 −0.485071
\(885\) 0 0
\(886\) 0 0
\(887\) 3.60555 0.121063 0.0605313 0.998166i \(-0.480721\pi\)
0.0605313 + 0.998166i \(0.480721\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 0 0
\(891\) 0 0
\(892\) −20.0000 −0.669650
\(893\) −21.6333 −0.723931
\(894\) 0 0
\(895\) −52.0000 −1.73817
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14.4222 0.481007
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 72.1110 2.39705
\(906\) 0 0
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) −50.4777 −1.67516
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 44.0000 1.45380
\(917\) −10.8167 −0.357197
\(918\) 0 0
\(919\) −12.0000 −0.395843 −0.197922 0.980218i \(-0.563419\pi\)
−0.197922 + 0.980218i \(0.563419\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 28.8444 0.949425
\(924\) 0 0
\(925\) −16.0000 −0.526077
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 10.8167 0.354883 0.177441 0.984131i \(-0.443218\pi\)
0.177441 + 0.984131i \(0.443218\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −48.0000 −1.56809 −0.784046 0.620703i \(-0.786847\pi\)
−0.784046 + 0.620703i \(0.786847\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −26.0000 −0.848026
\(941\) −7.21110 −0.235075 −0.117538 0.993068i \(-0.537500\pi\)
−0.117538 + 0.993068i \(0.537500\pi\)
\(942\) 0 0
\(943\) −52.0000 −1.69335
\(944\) −43.2666 −1.40821
\(945\) 0 0
\(946\) 0 0
\(947\) 14.4222 0.468659 0.234329 0.972157i \(-0.424711\pi\)
0.234329 + 0.972157i \(0.424711\pi\)
\(948\) 0 0
\(949\) 8.00000 0.259691
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −36.0555 −1.16795 −0.583976 0.811771i \(-0.698504\pi\)
−0.583976 + 0.811771i \(0.698504\pi\)
\(954\) 0 0
\(955\) 52.0000 1.68268
\(956\) 14.4222 0.466447
\(957\) 0 0
\(958\) 0 0
\(959\) 21.6333 0.698576
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 0 0
\(964\) −24.0000 −0.772988
\(965\) −82.9277 −2.66954
\(966\) 0 0
\(967\) 37.0000 1.18984 0.594920 0.803785i \(-0.297184\pi\)
0.594920 + 0.803785i \(0.297184\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.60555 0.115708 0.0578538 0.998325i \(-0.481574\pi\)
0.0578538 + 0.998325i \(0.481574\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 0 0
\(975\) 0 0
\(976\) 56.0000 1.79252
\(977\) −28.8444 −0.922814 −0.461407 0.887188i \(-0.652655\pi\)
−0.461407 + 0.887188i \(0.652655\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −7.21110 −0.230350
\(981\) 0 0
\(982\) 0 0
\(983\) −43.2666 −1.37999 −0.689995 0.723814i \(-0.742387\pi\)
−0.689995 + 0.723814i \(0.742387\pi\)
\(984\) 0 0
\(985\) 78.0000 2.48529
\(986\) 0 0
\(987\) 0 0
\(988\) −24.0000 −0.763542
\(989\) 36.0555 1.14650
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −7.21110 −0.228607
\(996\) 0 0
\(997\) 36.0000 1.14013 0.570066 0.821599i \(-0.306918\pi\)
0.570066 + 0.821599i \(0.306918\pi\)
\(998\) 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 7623.2.a.bh.1.2 yes 2
3.2 odd 2 inner 7623.2.a.bh.1.1 yes 2
11.10 odd 2 7623.2.a.bg.1.2 yes 2
33.32 even 2 7623.2.a.bg.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7623.2.a.bg.1.1 2 33.32 even 2
7623.2.a.bg.1.2 yes 2 11.10 odd 2
7623.2.a.bh.1.1 yes 2 3.2 odd 2 inner
7623.2.a.bh.1.2 yes 2 1.1 even 1 trivial