Properties

Label 1400.2.a.o.1.1
Level $1400$
Weight $2$
Character 1400.1
Self dual yes
Analytic conductor $11.179$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.1790562830\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 1400.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56155 q^{3} -1.00000 q^{7} +3.56155 q^{9} +O(q^{10})\) \(q-2.56155 q^{3} -1.00000 q^{7} +3.56155 q^{9} +2.12311 q^{11} -2.00000 q^{13} +2.56155 q^{17} -0.561553 q^{19} +2.56155 q^{21} -5.56155 q^{23} -1.43845 q^{27} +7.56155 q^{29} -0.876894 q^{31} -5.43845 q^{33} +11.8078 q^{37} +5.12311 q^{39} -6.56155 q^{41} -2.43845 q^{43} -8.24621 q^{47} +1.00000 q^{49} -6.56155 q^{51} -7.12311 q^{53} +1.43845 q^{57} -13.3693 q^{59} +2.87689 q^{61} -3.56155 q^{63} -16.1231 q^{67} +14.2462 q^{69} -10.6847 q^{71} -10.5616 q^{73} -2.12311 q^{77} +6.68466 q^{79} -7.00000 q^{81} +13.6847 q^{83} -19.3693 q^{87} -10.8078 q^{89} +2.00000 q^{91} +2.24621 q^{93} -6.00000 q^{97} +7.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{7} + 3q^{9} - 4q^{11} - 4q^{13} + q^{17} + 3q^{19} + q^{21} - 7q^{23} - 7q^{27} + 11q^{29} - 10q^{31} - 15q^{33} + 3q^{37} + 2q^{39} - 9q^{41} - 9q^{43} + 2q^{49} - 9q^{51} - 6q^{53} + 7q^{57} - 2q^{59} + 14q^{61} - 3q^{63} - 24q^{67} + 12q^{69} - 9q^{71} - 17q^{73} + 4q^{77} + q^{79} - 14q^{81} + 15q^{83} - 14q^{87} - q^{89} + 4q^{91} - 12q^{93} - 12q^{97} + 11q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.56155 −1.47891 −0.739457 0.673204i \(-0.764917\pi\)
−0.739457 + 0.673204i \(0.764917\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 3.56155 1.18718
\(10\) 0 0
\(11\) 2.12311 0.640140 0.320070 0.947394i \(-0.396293\pi\)
0.320070 + 0.947394i \(0.396293\pi\)
\(12\) 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
\(16\) 0 0
\(17\) 2.56155 0.621268 0.310634 0.950530i \(-0.399459\pi\)
0.310634 + 0.950530i \(0.399459\pi\)
\(18\) 0 0
\(19\) −0.561553 −0.128829 −0.0644145 0.997923i \(-0.520518\pi\)
−0.0644145 + 0.997923i \(0.520518\pi\)
\(20\) 0 0
\(21\) 2.56155 0.558977
\(22\) 0 0
\(23\) −5.56155 −1.15966 −0.579832 0.814736i \(-0.696882\pi\)
−0.579832 + 0.814736i \(0.696882\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.43845 −0.276829
\(28\) 0 0
\(29\) 7.56155 1.40415 0.702073 0.712105i \(-0.252258\pi\)
0.702073 + 0.712105i \(0.252258\pi\)
\(30\) 0 0
\(31\) −0.876894 −0.157495 −0.0787474 0.996895i \(-0.525092\pi\)
−0.0787474 + 0.996895i \(0.525092\pi\)
\(32\) 0 0
\(33\) −5.43845 −0.946712
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.8078 1.94118 0.970592 0.240730i \(-0.0773867\pi\)
0.970592 + 0.240730i \(0.0773867\pi\)
\(38\) 0 0
\(39\) 5.12311 0.820353
\(40\) 0 0
\(41\) −6.56155 −1.02474 −0.512371 0.858764i \(-0.671233\pi\)
−0.512371 + 0.858764i \(0.671233\pi\)
\(42\) 0 0
\(43\) −2.43845 −0.371860 −0.185930 0.982563i \(-0.559530\pi\)
−0.185930 + 0.982563i \(0.559530\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.24621 −1.20283 −0.601417 0.798935i \(-0.705397\pi\)
−0.601417 + 0.798935i \(0.705397\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −6.56155 −0.918801
\(52\) 0 0
\(53\) −7.12311 −0.978434 −0.489217 0.872162i \(-0.662717\pi\)
−0.489217 + 0.872162i \(0.662717\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.43845 0.190527
\(58\) 0 0
\(59\) −13.3693 −1.74054 −0.870268 0.492578i \(-0.836055\pi\)
−0.870268 + 0.492578i \(0.836055\pi\)
\(60\) 0 0
\(61\) 2.87689 0.368349 0.184174 0.982894i \(-0.441039\pi\)
0.184174 + 0.982894i \(0.441039\pi\)
\(62\) 0 0
\(63\) −3.56155 −0.448713
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −16.1231 −1.96975 −0.984875 0.173264i \(-0.944569\pi\)
−0.984875 + 0.173264i \(0.944569\pi\)
\(68\) 0 0
\(69\) 14.2462 1.71504
\(70\) 0 0
\(71\) −10.6847 −1.26804 −0.634018 0.773318i \(-0.718595\pi\)
−0.634018 + 0.773318i \(0.718595\pi\)
\(72\) 0 0
\(73\) −10.5616 −1.23614 −0.618068 0.786125i \(-0.712084\pi\)
−0.618068 + 0.786125i \(0.712084\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.12311 −0.241950
\(78\) 0 0
\(79\) 6.68466 0.752083 0.376041 0.926603i \(-0.377285\pi\)
0.376041 + 0.926603i \(0.377285\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) 13.6847 1.50209 0.751043 0.660253i \(-0.229551\pi\)
0.751043 + 0.660253i \(0.229551\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −19.3693 −2.07661
\(88\) 0 0
\(89\) −10.8078 −1.14562 −0.572810 0.819688i \(-0.694147\pi\)
−0.572810 + 0.819688i \(0.694147\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 2.24621 0.232921
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 7.56155 0.759965
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −7.12311 −0.701860 −0.350930 0.936402i \(-0.614135\pi\)
−0.350930 + 0.936402i \(0.614135\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.8078 1.23817 0.619087 0.785323i \(-0.287503\pi\)
0.619087 + 0.785323i \(0.287503\pi\)
\(108\) 0 0
\(109\) −8.93087 −0.855422 −0.427711 0.903915i \(-0.640680\pi\)
−0.427711 + 0.903915i \(0.640680\pi\)
\(110\) 0 0
\(111\) −30.2462 −2.87084
\(112\) 0 0
\(113\) −0.753789 −0.0709105 −0.0354552 0.999371i \(-0.511288\pi\)
−0.0354552 + 0.999371i \(0.511288\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −7.12311 −0.658531
\(118\) 0 0
\(119\) −2.56155 −0.234817
\(120\) 0 0
\(121\) −6.49242 −0.590220
\(122\) 0 0
\(123\) 16.8078 1.51551
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.80776 0.870298 0.435149 0.900358i \(-0.356696\pi\)
0.435149 + 0.900358i \(0.356696\pi\)
\(128\) 0 0
\(129\) 6.24621 0.549948
\(130\) 0 0
\(131\) −1.75379 −0.153229 −0.0766146 0.997061i \(-0.524411\pi\)
−0.0766146 + 0.997061i \(0.524411\pi\)
\(132\) 0 0
\(133\) 0.561553 0.0486928
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.31534 0.197813 0.0989065 0.995097i \(-0.468466\pi\)
0.0989065 + 0.995097i \(0.468466\pi\)
\(138\) 0 0
\(139\) −19.6847 −1.66963 −0.834815 0.550530i \(-0.814426\pi\)
−0.834815 + 0.550530i \(0.814426\pi\)
\(140\) 0 0
\(141\) 21.1231 1.77889
\(142\) 0 0
\(143\) −4.24621 −0.355086
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −2.56155 −0.211273
\(148\) 0 0
\(149\) 17.5616 1.43870 0.719349 0.694649i \(-0.244440\pi\)
0.719349 + 0.694649i \(0.244440\pi\)
\(150\) 0 0
\(151\) −5.56155 −0.452593 −0.226296 0.974058i \(-0.572662\pi\)
−0.226296 + 0.974058i \(0.572662\pi\)
\(152\) 0 0
\(153\) 9.12311 0.737559
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −24.4924 −1.95471 −0.977354 0.211611i \(-0.932129\pi\)
−0.977354 + 0.211611i \(0.932129\pi\)
\(158\) 0 0
\(159\) 18.2462 1.44702
\(160\) 0 0
\(161\) 5.56155 0.438312
\(162\) 0 0
\(163\) 13.9309 1.09115 0.545575 0.838062i \(-0.316311\pi\)
0.545575 + 0.838062i \(0.316311\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.6155 1.51790 0.758948 0.651152i \(-0.225714\pi\)
0.758948 + 0.651152i \(0.225714\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) −14.4924 −1.10184 −0.550919 0.834559i \(-0.685723\pi\)
−0.550919 + 0.834559i \(0.685723\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 34.2462 2.57410
\(178\) 0 0
\(179\) −8.31534 −0.621518 −0.310759 0.950489i \(-0.600583\pi\)
−0.310759 + 0.950489i \(0.600583\pi\)
\(180\) 0 0
\(181\) −2.87689 −0.213838 −0.106919 0.994268i \(-0.534099\pi\)
−0.106919 + 0.994268i \(0.534099\pi\)
\(182\) 0 0
\(183\) −7.36932 −0.544756
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.43845 0.397699
\(188\) 0 0
\(189\) 1.43845 0.104632
\(190\) 0 0
\(191\) 0.630683 0.0456346 0.0228173 0.999740i \(-0.492736\pi\)
0.0228173 + 0.999740i \(0.492736\pi\)
\(192\) 0 0
\(193\) −20.6155 −1.48394 −0.741969 0.670434i \(-0.766108\pi\)
−0.741969 + 0.670434i \(0.766108\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.56155 0.253750 0.126875 0.991919i \(-0.459505\pi\)
0.126875 + 0.991919i \(0.459505\pi\)
\(198\) 0 0
\(199\) −13.1231 −0.930272 −0.465136 0.885239i \(-0.653995\pi\)
−0.465136 + 0.885239i \(0.653995\pi\)
\(200\) 0 0
\(201\) 41.3002 2.91309
\(202\) 0 0
\(203\) −7.56155 −0.530717
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −19.8078 −1.37673
\(208\) 0 0
\(209\) −1.19224 −0.0824687
\(210\) 0 0
\(211\) 10.5616 0.727087 0.363544 0.931577i \(-0.381567\pi\)
0.363544 + 0.931577i \(0.381567\pi\)
\(212\) 0 0
\(213\) 27.3693 1.87531
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.876894 0.0595275
\(218\) 0 0
\(219\) 27.0540 1.82814
\(220\) 0 0
\(221\) −5.12311 −0.344617
\(222\) 0 0
\(223\) 0.630683 0.0422337 0.0211168 0.999777i \(-0.493278\pi\)
0.0211168 + 0.999777i \(0.493278\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.3693 0.887353 0.443676 0.896187i \(-0.353674\pi\)
0.443676 + 0.896187i \(0.353674\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 5.43845 0.357824
\(232\) 0 0
\(233\) −3.56155 −0.233325 −0.116663 0.993172i \(-0.537220\pi\)
−0.116663 + 0.993172i \(0.537220\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −17.1231 −1.11227
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) 25.0540 1.61387 0.806934 0.590641i \(-0.201125\pi\)
0.806934 + 0.590641i \(0.201125\pi\)
\(242\) 0 0
\(243\) 22.2462 1.42710
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.12311 0.0714615
\(248\) 0 0
\(249\) −35.0540 −2.22146
\(250\) 0 0
\(251\) −12.3153 −0.777337 −0.388669 0.921378i \(-0.627065\pi\)
−0.388669 + 0.921378i \(0.627065\pi\)
\(252\) 0 0
\(253\) −11.8078 −0.742348
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.24621 0.264871 0.132436 0.991192i \(-0.457720\pi\)
0.132436 + 0.991192i \(0.457720\pi\)
\(258\) 0 0
\(259\) −11.8078 −0.733699
\(260\) 0 0
\(261\) 26.9309 1.66698
\(262\) 0 0
\(263\) 10.6847 0.658844 0.329422 0.944183i \(-0.393146\pi\)
0.329422 + 0.944183i \(0.393146\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 27.6847 1.69427
\(268\) 0 0
\(269\) 11.7538 0.716641 0.358321 0.933599i \(-0.383349\pi\)
0.358321 + 0.933599i \(0.383349\pi\)
\(270\) 0 0
\(271\) 16.2462 0.986887 0.493444 0.869778i \(-0.335738\pi\)
0.493444 + 0.869778i \(0.335738\pi\)
\(272\) 0 0
\(273\) −5.12311 −0.310064
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.4924 0.630429 0.315214 0.949021i \(-0.397924\pi\)
0.315214 + 0.949021i \(0.397924\pi\)
\(278\) 0 0
\(279\) −3.12311 −0.186975
\(280\) 0 0
\(281\) 11.5616 0.689704 0.344852 0.938657i \(-0.387929\pi\)
0.344852 + 0.938657i \(0.387929\pi\)
\(282\) 0 0
\(283\) 13.6847 0.813469 0.406734 0.913547i \(-0.366667\pi\)
0.406734 + 0.913547i \(0.366667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.56155 0.387316
\(288\) 0 0
\(289\) −10.4384 −0.614026
\(290\) 0 0
\(291\) 15.3693 0.900965
\(292\) 0 0
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.05398 −0.177210
\(298\) 0 0
\(299\) 11.1231 0.643266
\(300\) 0 0
\(301\) 2.43845 0.140550
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.31534 −0.246290 −0.123145 0.992389i \(-0.539298\pi\)
−0.123145 + 0.992389i \(0.539298\pi\)
\(308\) 0 0
\(309\) 18.2462 1.03799
\(310\) 0 0
\(311\) 2.87689 0.163134 0.0815669 0.996668i \(-0.474008\pi\)
0.0815669 + 0.996668i \(0.474008\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.6847 1.16177 0.580883 0.813987i \(-0.302707\pi\)
0.580883 + 0.813987i \(0.302707\pi\)
\(318\) 0 0
\(319\) 16.0540 0.898850
\(320\) 0 0
\(321\) −32.8078 −1.83115
\(322\) 0 0
\(323\) −1.43845 −0.0800373
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 22.8769 1.26510
\(328\) 0 0
\(329\) 8.24621 0.454628
\(330\) 0 0
\(331\) 27.0000 1.48405 0.742027 0.670370i \(-0.233865\pi\)
0.742027 + 0.670370i \(0.233865\pi\)
\(332\) 0 0
\(333\) 42.0540 2.30454
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 5.68466 0.309663 0.154832 0.987941i \(-0.450517\pi\)
0.154832 + 0.987941i \(0.450517\pi\)
\(338\) 0 0
\(339\) 1.93087 0.104870
\(340\) 0 0
\(341\) −1.86174 −0.100819
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −22.6155 −1.21407 −0.607033 0.794677i \(-0.707640\pi\)
−0.607033 + 0.794677i \(0.707640\pi\)
\(348\) 0 0
\(349\) −12.8769 −0.689284 −0.344642 0.938734i \(-0.612000\pi\)
−0.344642 + 0.938734i \(0.612000\pi\)
\(350\) 0 0
\(351\) 2.87689 0.153557
\(352\) 0 0
\(353\) 11.7538 0.625591 0.312796 0.949820i \(-0.398735\pi\)
0.312796 + 0.949820i \(0.398735\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 6.56155 0.347274
\(358\) 0 0
\(359\) −14.6847 −0.775027 −0.387513 0.921864i \(-0.626666\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(360\) 0 0
\(361\) −18.6847 −0.983403
\(362\) 0 0
\(363\) 16.6307 0.872884
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.7538 −0.926740 −0.463370 0.886165i \(-0.653360\pi\)
−0.463370 + 0.886165i \(0.653360\pi\)
\(368\) 0 0
\(369\) −23.3693 −1.21656
\(370\) 0 0
\(371\) 7.12311 0.369813
\(372\) 0 0
\(373\) −14.0540 −0.727687 −0.363844 0.931460i \(-0.618536\pi\)
−0.363844 + 0.931460i \(0.618536\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.1231 −0.778880
\(378\) 0 0
\(379\) −24.8617 −1.27706 −0.638531 0.769596i \(-0.720458\pi\)
−0.638531 + 0.769596i \(0.720458\pi\)
\(380\) 0 0
\(381\) −25.1231 −1.28710
\(382\) 0 0
\(383\) 20.2462 1.03453 0.517267 0.855824i \(-0.326950\pi\)
0.517267 + 0.855824i \(0.326950\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.68466 −0.441466
\(388\) 0 0
\(389\) 2.43845 0.123634 0.0618171 0.998087i \(-0.480310\pi\)
0.0618171 + 0.998087i \(0.480310\pi\)
\(390\) 0 0
\(391\) −14.2462 −0.720462
\(392\) 0 0
\(393\) 4.49242 0.226613
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −38.4924 −1.93188 −0.965940 0.258767i \(-0.916684\pi\)
−0.965940 + 0.258767i \(0.916684\pi\)
\(398\) 0 0
\(399\) −1.43845 −0.0720124
\(400\) 0 0
\(401\) −31.4924 −1.57266 −0.786328 0.617809i \(-0.788021\pi\)
−0.786328 + 0.617809i \(0.788021\pi\)
\(402\) 0 0
\(403\) 1.75379 0.0873624
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.0691 1.24263
\(408\) 0 0
\(409\) −5.19224 −0.256740 −0.128370 0.991726i \(-0.540974\pi\)
−0.128370 + 0.991726i \(0.540974\pi\)
\(410\) 0 0
\(411\) −5.93087 −0.292548
\(412\) 0 0
\(413\) 13.3693 0.657861
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 50.4233 2.46924
\(418\) 0 0
\(419\) −18.8078 −0.918819 −0.459410 0.888224i \(-0.651939\pi\)
−0.459410 + 0.888224i \(0.651939\pi\)
\(420\) 0 0
\(421\) 5.06913 0.247054 0.123527 0.992341i \(-0.460579\pi\)
0.123527 + 0.992341i \(0.460579\pi\)
\(422\) 0 0
\(423\) −29.3693 −1.42799
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.87689 −0.139223
\(428\) 0 0
\(429\) 10.8769 0.525141
\(430\) 0 0
\(431\) −13.7538 −0.662497 −0.331248 0.943544i \(-0.607470\pi\)
−0.331248 + 0.943544i \(0.607470\pi\)
\(432\) 0 0
\(433\) 35.5464 1.70825 0.854125 0.520067i \(-0.174093\pi\)
0.854125 + 0.520067i \(0.174093\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.12311 0.149398
\(438\) 0 0
\(439\) −7.12311 −0.339967 −0.169984 0.985447i \(-0.554371\pi\)
−0.169984 + 0.985447i \(0.554371\pi\)
\(440\) 0 0
\(441\) 3.56155 0.169598
\(442\) 0 0
\(443\) −22.5616 −1.07193 −0.535966 0.844240i \(-0.680052\pi\)
−0.535966 + 0.844240i \(0.680052\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −44.9848 −2.12771
\(448\) 0 0
\(449\) 10.3693 0.489358 0.244679 0.969604i \(-0.421317\pi\)
0.244679 + 0.969604i \(0.421317\pi\)
\(450\) 0 0
\(451\) −13.9309 −0.655979
\(452\) 0 0
\(453\) 14.2462 0.669345
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −37.1080 −1.73584 −0.867918 0.496707i \(-0.834542\pi\)
−0.867918 + 0.496707i \(0.834542\pi\)
\(458\) 0 0
\(459\) −3.68466 −0.171985
\(460\) 0 0
\(461\) 6.49242 0.302382 0.151191 0.988505i \(-0.451689\pi\)
0.151191 + 0.988505i \(0.451689\pi\)
\(462\) 0 0
\(463\) 20.4924 0.952364 0.476182 0.879347i \(-0.342020\pi\)
0.476182 + 0.879347i \(0.342020\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 24.8769 1.15117 0.575583 0.817744i \(-0.304775\pi\)
0.575583 + 0.817744i \(0.304775\pi\)
\(468\) 0 0
\(469\) 16.1231 0.744496
\(470\) 0 0
\(471\) 62.7386 2.89084
\(472\) 0 0
\(473\) −5.17708 −0.238042
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −25.3693 −1.16158
\(478\) 0 0
\(479\) −40.7386 −1.86140 −0.930698 0.365789i \(-0.880799\pi\)
−0.930698 + 0.365789i \(0.880799\pi\)
\(480\) 0 0
\(481\) −23.6155 −1.07678
\(482\) 0 0
\(483\) −14.2462 −0.648225
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −35.5616 −1.61145 −0.805724 0.592291i \(-0.798223\pi\)
−0.805724 + 0.592291i \(0.798223\pi\)
\(488\) 0 0
\(489\) −35.6847 −1.61372
\(490\) 0 0
\(491\) 20.6847 0.933486 0.466743 0.884393i \(-0.345427\pi\)
0.466743 + 0.884393i \(0.345427\pi\)
\(492\) 0 0
\(493\) 19.3693 0.872350
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.6847 0.479272
\(498\) 0 0
\(499\) −16.4924 −0.738302 −0.369151 0.929369i \(-0.620352\pi\)
−0.369151 + 0.929369i \(0.620352\pi\)
\(500\) 0 0
\(501\) −50.2462 −2.24484
\(502\) 0 0
\(503\) −19.7538 −0.880778 −0.440389 0.897807i \(-0.645159\pi\)
−0.440389 + 0.897807i \(0.645159\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.0540 1.02386
\(508\) 0 0
\(509\) 26.0000 1.15243 0.576215 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(510\) 0 0
\(511\) 10.5616 0.467216
\(512\) 0 0
\(513\) 0.807764 0.0356637
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −17.5076 −0.769982
\(518\) 0 0
\(519\) 37.1231 1.62952
\(520\) 0 0
\(521\) −27.4384 −1.20210 −0.601050 0.799211i \(-0.705251\pi\)
−0.601050 + 0.799211i \(0.705251\pi\)
\(522\) 0 0
\(523\) −28.3153 −1.23814 −0.619072 0.785334i \(-0.712491\pi\)
−0.619072 + 0.785334i \(0.712491\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.24621 −0.0978465
\(528\) 0 0
\(529\) 7.93087 0.344820
\(530\) 0 0
\(531\) −47.6155 −2.06634
\(532\) 0 0
\(533\) 13.1231 0.568425
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.3002 0.919171
\(538\) 0 0
\(539\) 2.12311 0.0914486
\(540\) 0 0
\(541\) 41.4233 1.78093 0.890463 0.455055i \(-0.150380\pi\)
0.890463 + 0.455055i \(0.150380\pi\)
\(542\) 0 0
\(543\) 7.36932 0.316248
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −33.7386 −1.44256 −0.721280 0.692644i \(-0.756446\pi\)
−0.721280 + 0.692644i \(0.756446\pi\)
\(548\) 0 0
\(549\) 10.2462 0.437298
\(550\) 0 0
\(551\) −4.24621 −0.180895
\(552\) 0 0
\(553\) −6.68466 −0.284261
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.56155 −0.405136 −0.202568 0.979268i \(-0.564929\pi\)
−0.202568 + 0.979268i \(0.564929\pi\)
\(558\) 0 0
\(559\) 4.87689 0.206271
\(560\) 0 0
\(561\) −13.9309 −0.588162
\(562\) 0 0
\(563\) 7.12311 0.300203 0.150102 0.988671i \(-0.452040\pi\)
0.150102 + 0.988671i \(0.452040\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.00000 0.293972
\(568\) 0 0
\(569\) −19.9848 −0.837808 −0.418904 0.908030i \(-0.637586\pi\)
−0.418904 + 0.908030i \(0.637586\pi\)
\(570\) 0 0
\(571\) 27.3153 1.14311 0.571556 0.820563i \(-0.306340\pi\)
0.571556 + 0.820563i \(0.306340\pi\)
\(572\) 0 0
\(573\) −1.61553 −0.0674897
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 45.5464 1.89612 0.948061 0.318090i \(-0.103041\pi\)
0.948061 + 0.318090i \(0.103041\pi\)
\(578\) 0 0
\(579\) 52.8078 2.19462
\(580\) 0 0
\(581\) −13.6847 −0.567735
\(582\) 0 0
\(583\) −15.1231 −0.626335
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.17708 −0.337504 −0.168752 0.985659i \(-0.553974\pi\)
−0.168752 + 0.985659i \(0.553974\pi\)
\(588\) 0 0
\(589\) 0.492423 0.0202899
\(590\) 0 0
\(591\) −9.12311 −0.375274
\(592\) 0 0
\(593\) −12.3153 −0.505730 −0.252865 0.967502i \(-0.581373\pi\)
−0.252865 + 0.967502i \(0.581373\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 33.6155 1.37579
\(598\) 0 0
\(599\) 24.3002 0.992879 0.496439 0.868071i \(-0.334641\pi\)
0.496439 + 0.868071i \(0.334641\pi\)
\(600\) 0 0
\(601\) −4.94602 −0.201753 −0.100876 0.994899i \(-0.532165\pi\)
−0.100876 + 0.994899i \(0.532165\pi\)
\(602\) 0 0
\(603\) −57.4233 −2.33846
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 37.3693 1.51677 0.758387 0.651805i \(-0.225988\pi\)
0.758387 + 0.651805i \(0.225988\pi\)
\(608\) 0 0
\(609\) 19.3693 0.784884
\(610\) 0 0
\(611\) 16.4924 0.667212
\(612\) 0 0
\(613\) 6.68466 0.269991 0.134995 0.990846i \(-0.456898\pi\)
0.134995 + 0.990846i \(0.456898\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.8078 −0.716914 −0.358457 0.933546i \(-0.616697\pi\)
−0.358457 + 0.933546i \(0.616697\pi\)
\(618\) 0 0
\(619\) 29.3693 1.18045 0.590226 0.807238i \(-0.299039\pi\)
0.590226 + 0.807238i \(0.299039\pi\)
\(620\) 0 0
\(621\) 8.00000 0.321029
\(622\) 0 0
\(623\) 10.8078 0.433004
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.05398 0.121964
\(628\) 0 0
\(629\) 30.2462 1.20600
\(630\) 0 0
\(631\) 34.0540 1.35567 0.677834 0.735215i \(-0.262919\pi\)
0.677834 + 0.735215i \(0.262919\pi\)
\(632\) 0 0
\(633\) −27.0540 −1.07530
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) −38.0540 −1.50539
\(640\) 0 0
\(641\) −16.4384 −0.649280 −0.324640 0.945838i \(-0.605243\pi\)
−0.324640 + 0.945838i \(0.605243\pi\)
\(642\) 0 0
\(643\) −2.73863 −0.108001 −0.0540006 0.998541i \(-0.517197\pi\)
−0.0540006 + 0.998541i \(0.517197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25.3693 0.997371 0.498685 0.866783i \(-0.333816\pi\)
0.498685 + 0.866783i \(0.333816\pi\)
\(648\) 0 0
\(649\) −28.3845 −1.11419
\(650\) 0 0
\(651\) −2.24621 −0.0880360
\(652\) 0 0
\(653\) −33.8617 −1.32511 −0.662556 0.749012i \(-0.730528\pi\)
−0.662556 + 0.749012i \(0.730528\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −37.6155 −1.46752
\(658\) 0 0
\(659\) 18.5616 0.723055 0.361528 0.932361i \(-0.382255\pi\)
0.361528 + 0.932361i \(0.382255\pi\)
\(660\) 0 0
\(661\) −22.4924 −0.874854 −0.437427 0.899254i \(-0.644110\pi\)
−0.437427 + 0.899254i \(0.644110\pi\)
\(662\) 0 0
\(663\) 13.1231 0.509659
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −42.0540 −1.62834
\(668\) 0 0
\(669\) −1.61553 −0.0624599
\(670\) 0 0
\(671\) 6.10795 0.235795
\(672\) 0 0
\(673\) −46.4924 −1.79215 −0.896076 0.443901i \(-0.853594\pi\)
−0.896076 + 0.443901i \(0.853594\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.6307 −0.562303 −0.281151 0.959663i \(-0.590716\pi\)
−0.281151 + 0.959663i \(0.590716\pi\)
\(678\) 0 0
\(679\) 6.00000 0.230259
\(680\) 0 0
\(681\) −34.2462 −1.31232
\(682\) 0 0
\(683\) −34.1231 −1.30568 −0.652842 0.757494i \(-0.726424\pi\)
−0.652842 + 0.757494i \(0.726424\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 35.8617 1.36821
\(688\) 0 0
\(689\) 14.2462 0.542737
\(690\) 0 0
\(691\) −17.4384 −0.663390 −0.331695 0.943387i \(-0.607620\pi\)
−0.331695 + 0.943387i \(0.607620\pi\)
\(692\) 0 0
\(693\) −7.56155 −0.287240
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16.8078 −0.636639
\(698\) 0 0
\(699\) 9.12311 0.345068
\(700\) 0 0
\(701\) 44.1080 1.66593 0.832967 0.553322i \(-0.186640\pi\)
0.832967 + 0.553322i \(0.186640\pi\)
\(702\) 0 0
\(703\) −6.63068 −0.250081
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 37.3693 1.40343 0.701717 0.712456i \(-0.252417\pi\)
0.701717 + 0.712456i \(0.252417\pi\)
\(710\) 0 0
\(711\) 23.8078 0.892861
\(712\) 0 0
\(713\) 4.87689 0.182641
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.2462 0.382652
\(718\) 0 0
\(719\) 38.2462 1.42634 0.713171 0.700990i \(-0.247258\pi\)
0.713171 + 0.700990i \(0.247258\pi\)
\(720\) 0 0
\(721\) 7.12311 0.265278
\(722\) 0 0
\(723\) −64.1771 −2.38677
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.61553 0.0599166 0.0299583 0.999551i \(-0.490463\pi\)
0.0299583 + 0.999551i \(0.490463\pi\)
\(728\) 0 0
\(729\) −35.9848 −1.33277
\(730\) 0 0
\(731\) −6.24621 −0.231024
\(732\) 0 0
\(733\) −22.2462 −0.821683 −0.410841 0.911707i \(-0.634765\pi\)
−0.410841 + 0.911707i \(0.634765\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −34.2311 −1.26092
\(738\) 0 0
\(739\) 17.1771 0.631869 0.315935 0.948781i \(-0.397682\pi\)
0.315935 + 0.948781i \(0.397682\pi\)
\(740\) 0 0
\(741\) −2.87689 −0.105685
\(742\) 0 0
\(743\) 18.7386 0.687454 0.343727 0.939070i \(-0.388311\pi\)
0.343727 + 0.939070i \(0.388311\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 48.7386 1.78325
\(748\) 0 0
\(749\) −12.8078 −0.467986
\(750\) 0 0
\(751\) 27.3693 0.998721 0.499360 0.866394i \(-0.333568\pi\)
0.499360 + 0.866394i \(0.333568\pi\)
\(752\) 0 0
\(753\) 31.5464 1.14961
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −13.3153 −0.483954 −0.241977 0.970282i \(-0.577796\pi\)
−0.241977 + 0.970282i \(0.577796\pi\)
\(758\) 0 0
\(759\) 30.2462 1.09787
\(760\) 0 0
\(761\) 34.4233 1.24784 0.623922 0.781487i \(-0.285538\pi\)
0.623922 + 0.781487i \(0.285538\pi\)
\(762\) 0 0
\(763\) 8.93087 0.323319
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.7386 0.965476
\(768\) 0 0
\(769\) −33.3002 −1.20084 −0.600418 0.799687i \(-0.704999\pi\)
−0.600418 + 0.799687i \(0.704999\pi\)
\(770\) 0 0
\(771\) −10.8769 −0.391722
\(772\) 0 0
\(773\) 11.6155 0.417782 0.208891 0.977939i \(-0.433015\pi\)
0.208891 + 0.977939i \(0.433015\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 30.2462 1.08508
\(778\) 0 0
\(779\) 3.68466 0.132017
\(780\) 0 0
\(781\) −22.6847 −0.811721
\(782\) 0 0
\(783\) −10.8769 −0.388708
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −26.2462 −0.935576 −0.467788 0.883841i \(-0.654949\pi\)
−0.467788 + 0.883841i \(0.654949\pi\)
\(788\) 0 0
\(789\) −27.3693 −0.974373
\(790\) 0 0
\(791\) 0.753789 0.0268016
\(792\) 0 0
\(793\) −5.75379 −0.204323
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −41.6155 −1.47410 −0.737049 0.675840i \(-0.763781\pi\)
−0.737049 + 0.675840i \(0.763781\pi\)
\(798\) 0 0
\(799\) −21.1231 −0.747282
\(800\) 0 0
\(801\) −38.4924 −1.36006
\(802\) 0 0
\(803\) −22.4233 −0.791301
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −30.1080 −1.05985
\(808\) 0 0
\(809\) 49.4233 1.73763 0.868815 0.495136i \(-0.164882\pi\)
0.868815 + 0.495136i \(0.164882\pi\)
\(810\) 0 0
\(811\) 43.6155 1.53155 0.765774 0.643110i \(-0.222356\pi\)
0.765774 + 0.643110i \(0.222356\pi\)
\(812\) 0 0
\(813\) −41.6155 −1.45952
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.36932 0.0479063
\(818\) 0 0
\(819\) 7.12311 0.248901
\(820\) 0 0
\(821\) 45.8617 1.60059 0.800293 0.599609i \(-0.204677\pi\)
0.800293 + 0.599609i \(0.204677\pi\)
\(822\) 0 0
\(823\) −12.4384 −0.433577 −0.216789 0.976219i \(-0.569558\pi\)
−0.216789 + 0.976219i \(0.569558\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.24621 0.321522 0.160761 0.986993i \(-0.448605\pi\)
0.160761 + 0.986993i \(0.448605\pi\)
\(828\) 0 0
\(829\) −2.24621 −0.0780141 −0.0390071 0.999239i \(-0.512419\pi\)
−0.0390071 + 0.999239i \(0.512419\pi\)
\(830\) 0 0
\(831\) −26.8769 −0.932349
\(832\) 0 0
\(833\) 2.56155 0.0887525
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.26137 0.0435992
\(838\) 0 0
\(839\) −1.12311 −0.0387739 −0.0193870 0.999812i \(-0.506171\pi\)
−0.0193870 + 0.999812i \(0.506171\pi\)
\(840\) 0 0
\(841\) 28.1771 0.971623
\(842\) 0 0
\(843\) −29.6155 −1.02001
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 6.49242 0.223082
\(848\) 0 0
\(849\) −35.0540 −1.20305
\(850\) 0 0
\(851\) −65.6695 −2.25112
\(852\) 0 0
\(853\) −10.8769 −0.372418 −0.186209 0.982510i \(-0.559620\pi\)
−0.186209 + 0.982510i \(0.559620\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.94602 −0.168953 −0.0844765 0.996425i \(-0.526922\pi\)
−0.0844765 + 0.996425i \(0.526922\pi\)
\(858\) 0 0
\(859\) 34.1771 1.16611 0.583053 0.812434i \(-0.301858\pi\)
0.583053 + 0.812434i \(0.301858\pi\)
\(860\) 0 0
\(861\) −16.8078 −0.572807
\(862\) 0 0
\(863\) 23.8078 0.810426 0.405213 0.914222i \(-0.367197\pi\)
0.405213 + 0.914222i \(0.367197\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 26.7386 0.908092
\(868\) 0 0
\(869\) 14.1922 0.481439
\(870\) 0 0
\(871\) 32.2462 1.09262
\(872\) 0 0
\(873\) −21.3693 −0.723242
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −23.6155 −0.797440 −0.398720 0.917073i \(-0.630545\pi\)
−0.398720 + 0.917073i \(0.630545\pi\)
\(878\) 0 0
\(879\) −76.8466 −2.59197
\(880\) 0 0
\(881\) −40.7386 −1.37252 −0.686260 0.727357i \(-0.740749\pi\)
−0.686260 + 0.727357i \(0.740749\pi\)
\(882\) 0 0
\(883\) 1.49242 0.0502240 0.0251120 0.999685i \(-0.492006\pi\)
0.0251120 + 0.999685i \(0.492006\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 49.6155 1.66593 0.832963 0.553328i \(-0.186643\pi\)
0.832963 + 0.553328i \(0.186643\pi\)
\(888\) 0 0
\(889\) −9.80776 −0.328942
\(890\) 0 0
\(891\) −14.8617 −0.497887
\(892\) 0 0
\(893\) 4.63068 0.154960
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −28.4924 −0.951334
\(898\) 0 0
\(899\) −6.63068 −0.221146
\(900\) 0 0
\(901\) −18.2462 −0.607869
\(902\) 0 0
\(903\) −6.24621 −0.207861
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −39.4233 −1.30615 −0.653076 0.757292i \(-0.726522\pi\)
−0.653076 + 0.757292i \(0.726522\pi\)
\(912\) 0 0
\(913\) 29.0540 0.961546
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.75379 0.0579152
\(918\) 0 0
\(919\) 18.1922 0.600106 0.300053 0.953922i \(-0.402996\pi\)
0.300053 + 0.953922i \(0.402996\pi\)
\(920\) 0 0
\(921\) 11.0540 0.364241
\(922\) 0 0
\(923\) 21.3693 0.703380
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −25.3693 −0.833238
\(928\) 0 0
\(929\) 56.3542 1.84892 0.924460 0.381279i \(-0.124516\pi\)
0.924460 + 0.381279i \(0.124516\pi\)
\(930\) 0 0
\(931\) −0.561553 −0.0184042
\(932\) 0 0
\(933\) −7.36932 −0.241261
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −21.3002 −0.695847 −0.347923 0.937523i \(-0.613113\pi\)
−0.347923 + 0.937523i \(0.613113\pi\)
\(938\) 0 0
\(939\) 56.3542 1.83905
\(940\) 0 0
\(941\) −1.36932 −0.0446385 −0.0223192 0.999751i \(-0.507105\pi\)
−0.0223192 + 0.999751i \(0.507105\pi\)
\(942\) 0 0
\(943\) 36.4924 1.18836
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −16.4924 −0.535932 −0.267966 0.963428i \(-0.586351\pi\)
−0.267966 + 0.963428i \(0.586351\pi\)
\(948\) 0 0
\(949\) 21.1231 0.685685
\(950\) 0 0
\(951\) −52.9848 −1.71815
\(952\) 0 0
\(953\) 27.8769 0.903021 0.451511 0.892266i \(-0.350885\pi\)
0.451511 + 0.892266i \(0.350885\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −41.1231 −1.32932
\(958\) 0 0
\(959\) −2.31534 −0.0747663
\(960\) 0 0
\(961\) −30.2311 −0.975195
\(962\) 0 0
\(963\) 45.6155 1.46994
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 16.6307 0.534807 0.267403 0.963585i \(-0.413834\pi\)
0.267403 + 0.963585i \(0.413834\pi\)
\(968\) 0 0
\(969\) 3.68466 0.118368
\(970\) 0 0
\(971\) −2.31534 −0.0743028 −0.0371514 0.999310i \(-0.511828\pi\)
−0.0371514 + 0.999310i \(0.511828\pi\)
\(972\) 0 0
\(973\) 19.6847 0.631061
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 33.2462 1.06364 0.531820 0.846857i \(-0.321508\pi\)
0.531820 + 0.846857i \(0.321508\pi\)
\(978\) 0 0
\(979\) −22.9460 −0.733358
\(980\) 0 0
\(981\) −31.8078 −1.01554
\(982\) 0 0
\(983\) 62.3542 1.98879 0.994394 0.105734i \(-0.0337192\pi\)
0.994394 + 0.105734i \(0.0337192\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −21.1231 −0.672356
\(988\) 0 0
\(989\) 13.5616 0.431232
\(990\) 0 0
\(991\) −29.6695 −0.942483 −0.471241 0.882004i \(-0.656194\pi\)
−0.471241 + 0.882004i \(0.656194\pi\)
\(992\) 0 0
\(993\) −69.1619 −2.19479
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −12.2462 −0.387841 −0.193921 0.981017i \(-0.562120\pi\)
−0.193921 + 0.981017i \(0.562120\pi\)
\(998\) 0 0
\(999\) −16.9848 −0.537377
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 1400.2.a.o.1.1 2
4.3 odd 2 2800.2.a.bo.1.2 2
5.2 odd 4 1400.2.g.j.449.4 4
5.3 odd 4 1400.2.g.j.449.1 4
5.4 even 2 1400.2.a.q.1.2 yes 2
7.6 odd 2 9800.2.a.bx.1.2 2
20.3 even 4 2800.2.g.v.449.4 4
20.7 even 4 2800.2.g.v.449.1 4
20.19 odd 2 2800.2.a.bj.1.1 2
35.34 odd 2 9800.2.a.bt.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1400.2.a.o.1.1 2 1.1 even 1 trivial
1400.2.a.q.1.2 yes 2 5.4 even 2
1400.2.g.j.449.1 4 5.3 odd 4
1400.2.g.j.449.4 4 5.2 odd 4
2800.2.a.bj.1.1 2 20.19 odd 2
2800.2.a.bo.1.2 2 4.3 odd 2
2800.2.g.v.449.1 4 20.7 even 4
2800.2.g.v.449.4 4 20.3 even 4
9800.2.a.bt.1.1 2 35.34 odd 2
9800.2.a.bx.1.2 2 7.6 odd 2