Properties

Label 1900.2.a.f.1.1
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \( x^{3} - x^{2} - 4x + 3 \) Copy content Toggle raw display
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 \(-1.91223\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.91223 q^{3} -2.91223 q^{7} +5.48108 q^{9} +O(q^{10})\) \(q-2.91223 q^{3} -2.91223 q^{7} +5.48108 q^{9} +0.598988 q^{11} +2.56885 q^{13} -2.91223 q^{17} -1.00000 q^{19} +8.48108 q^{21} +1.16784 q^{23} -7.22547 q^{27} -1.40101 q^{29} +7.88209 q^{31} -1.74439 q^{33} +6.53871 q^{37} -7.48108 q^{39} +9.48108 q^{41} +0.824458 q^{43} -6.05763 q^{47} +1.48108 q^{49} +8.48108 q^{51} +0.824458 q^{53} +2.91223 q^{57} -14.1601 q^{59} -1.88209 q^{61} -15.9622 q^{63} -5.11021 q^{67} -3.40101 q^{69} -11.9622 q^{71} -1.03014 q^{73} -1.74439 q^{77} -15.3632 q^{79} +4.59899 q^{81} +15.7565 q^{83} +4.08007 q^{87} +15.4432 q^{89} -7.48108 q^{91} -22.9545 q^{93} -7.70655 q^{97} +3.28310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 2 q^{7} + q^{9} - q^{11} - q^{13} - 2 q^{17} - 3 q^{19} + 10 q^{21} - 8 q^{23} - 11 q^{27} - 7 q^{29} + 11 q^{31} - 10 q^{33} + 5 q^{37} - 7 q^{39} + 13 q^{41} - 11 q^{43} - 19 q^{47} - 11 q^{49} + 10 q^{51} - 11 q^{53} + 2 q^{57} - 6 q^{59} + 7 q^{61} - 17 q^{63} - 3 q^{67} - 13 q^{69} - 5 q^{71} - 9 q^{73} - 10 q^{77} - 18 q^{79} + 11 q^{81} - 3 q^{83} - 6 q^{87} - 7 q^{91} - 13 q^{93} + 3 q^{97}+O(q^{100}) \) 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
\(3\) −2.91223 −1.68138 −0.840688 0.541520i \(-0.817849\pi\)
−0.840688 + 0.541520i \(0.817849\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.91223 −1.10072 −0.550360 0.834928i \(-0.685509\pi\)
−0.550360 + 0.834928i \(0.685509\pi\)
\(8\) 0 0
\(9\) 5.48108 1.82703
\(10\) 0 0
\(11\) 0.598988 0.180602 0.0903009 0.995915i \(-0.471217\pi\)
0.0903009 + 0.995915i \(0.471217\pi\)
\(12\) 0 0
\(13\) 2.56885 0.712471 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.91223 −0.706319 −0.353160 0.935563i \(-0.614893\pi\)
−0.353160 + 0.935563i \(0.614893\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 8.48108 1.85072
\(22\) 0 0
\(23\) 1.16784 0.243511 0.121756 0.992560i \(-0.461148\pi\)
0.121756 + 0.992560i \(0.461148\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −7.22547 −1.39054
\(28\) 0 0
\(29\) −1.40101 −0.260161 −0.130081 0.991503i \(-0.541524\pi\)
−0.130081 + 0.991503i \(0.541524\pi\)
\(30\) 0 0
\(31\) 7.88209 1.41567 0.707833 0.706380i \(-0.249673\pi\)
0.707833 + 0.706380i \(0.249673\pi\)
\(32\) 0 0
\(33\) −1.74439 −0.303660
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.53871 1.07496 0.537479 0.843277i \(-0.319377\pi\)
0.537479 + 0.843277i \(0.319377\pi\)
\(38\) 0 0
\(39\) −7.48108 −1.19793
\(40\) 0 0
\(41\) 9.48108 1.48070 0.740348 0.672224i \(-0.234661\pi\)
0.740348 + 0.672224i \(0.234661\pi\)
\(42\) 0 0
\(43\) 0.824458 0.125729 0.0628644 0.998022i \(-0.479976\pi\)
0.0628644 + 0.998022i \(0.479976\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.05763 −0.883596 −0.441798 0.897114i \(-0.645659\pi\)
−0.441798 + 0.897114i \(0.645659\pi\)
\(48\) 0 0
\(49\) 1.48108 0.211583
\(50\) 0 0
\(51\) 8.48108 1.18759
\(52\) 0 0
\(53\) 0.824458 0.113248 0.0566240 0.998396i \(-0.481966\pi\)
0.0566240 + 0.998396i \(0.481966\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.91223 0.385734
\(58\) 0 0
\(59\) −14.1601 −1.84349 −0.921746 0.387794i \(-0.873237\pi\)
−0.921746 + 0.387794i \(0.873237\pi\)
\(60\) 0 0
\(61\) −1.88209 −0.240977 −0.120488 0.992715i \(-0.538446\pi\)
−0.120488 + 0.992715i \(0.538446\pi\)
\(62\) 0 0
\(63\) −15.9622 −2.01104
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −5.11021 −0.624311 −0.312156 0.950031i \(-0.601051\pi\)
−0.312156 + 0.950031i \(0.601051\pi\)
\(68\) 0 0
\(69\) −3.40101 −0.409434
\(70\) 0 0
\(71\) −11.9622 −1.41965 −0.709823 0.704380i \(-0.751225\pi\)
−0.709823 + 0.704380i \(0.751225\pi\)
\(72\) 0 0
\(73\) −1.03014 −0.120569 −0.0602843 0.998181i \(-0.519201\pi\)
−0.0602843 + 0.998181i \(0.519201\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.74439 −0.198792
\(78\) 0 0
\(79\) −15.3632 −1.72849 −0.864246 0.503070i \(-0.832204\pi\)
−0.864246 + 0.503070i \(0.832204\pi\)
\(80\) 0 0
\(81\) 4.59899 0.510999
\(82\) 0 0
\(83\) 15.7565 1.72950 0.864749 0.502204i \(-0.167477\pi\)
0.864749 + 0.502204i \(0.167477\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.08007 0.437429
\(88\) 0 0
\(89\) 15.4432 1.63698 0.818490 0.574521i \(-0.194812\pi\)
0.818490 + 0.574521i \(0.194812\pi\)
\(90\) 0 0
\(91\) −7.48108 −0.784230
\(92\) 0 0
\(93\) −22.9545 −2.38027
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −7.70655 −0.782481 −0.391241 0.920288i \(-0.627954\pi\)
−0.391241 + 0.920288i \(0.627954\pi\)
\(98\) 0 0
\(99\) 3.28310 0.329964
\(100\) 0 0
\(101\) 4.40101 0.437917 0.218959 0.975734i \(-0.429734\pi\)
0.218959 + 0.975734i \(0.429734\pi\)
\(102\) 0 0
\(103\) −17.3632 −1.71084 −0.855422 0.517932i \(-0.826702\pi\)
−0.855422 + 0.517932i \(0.826702\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −14.1903 −1.37183 −0.685913 0.727684i \(-0.740597\pi\)
−0.685913 + 0.727684i \(0.740597\pi\)
\(108\) 0 0
\(109\) −10.6791 −1.02287 −0.511434 0.859323i \(-0.670886\pi\)
−0.511434 + 0.859323i \(0.670886\pi\)
\(110\) 0 0
\(111\) −19.0422 −1.80741
\(112\) 0 0
\(113\) −8.25561 −0.776622 −0.388311 0.921528i \(-0.626941\pi\)
−0.388311 + 0.921528i \(0.626941\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 14.0801 1.30170
\(118\) 0 0
\(119\) 8.48108 0.777459
\(120\) 0 0
\(121\) −10.6412 −0.967383
\(122\) 0 0
\(123\) −27.6111 −2.48961
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.1300 1.07636 0.538182 0.842829i \(-0.319111\pi\)
0.538182 + 0.842829i \(0.319111\pi\)
\(128\) 0 0
\(129\) −2.40101 −0.211397
\(130\) 0 0
\(131\) 5.48108 0.478884 0.239442 0.970911i \(-0.423035\pi\)
0.239442 + 0.970911i \(0.423035\pi\)
\(132\) 0 0
\(133\) 2.91223 0.252522
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.59634 −0.648999 −0.324500 0.945886i \(-0.605196\pi\)
−0.324500 + 0.945886i \(0.605196\pi\)
\(138\) 0 0
\(139\) 7.16013 0.607315 0.303657 0.952781i \(-0.401792\pi\)
0.303657 + 0.952781i \(0.401792\pi\)
\(140\) 0 0
\(141\) 17.6412 1.48566
\(142\) 0 0
\(143\) 1.53871 0.128673
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.31324 −0.355750
\(148\) 0 0
\(149\) −18.4432 −1.51093 −0.755464 0.655190i \(-0.772589\pi\)
−0.755464 + 0.655190i \(0.772589\pi\)
\(150\) 0 0
\(151\) −9.27804 −0.755036 −0.377518 0.926002i \(-0.623222\pi\)
−0.377518 + 0.926002i \(0.623222\pi\)
\(152\) 0 0
\(153\) −15.9622 −1.29046
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 14.1903 1.13251 0.566254 0.824231i \(-0.308392\pi\)
0.566254 + 0.824231i \(0.308392\pi\)
\(158\) 0 0
\(159\) −2.40101 −0.190413
\(160\) 0 0
\(161\) −3.40101 −0.268037
\(162\) 0 0
\(163\) 25.1799 1.97224 0.986122 0.166023i \(-0.0530925\pi\)
0.986122 + 0.166023i \(0.0530925\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.0301 −0.853538 −0.426769 0.904361i \(-0.640348\pi\)
−0.426769 + 0.904361i \(0.640348\pi\)
\(168\) 0 0
\(169\) −6.40101 −0.492386
\(170\) 0 0
\(171\) −5.48108 −0.419149
\(172\) 0 0
\(173\) −15.3029 −1.16346 −0.581729 0.813383i \(-0.697623\pi\)
−0.581729 + 0.813383i \(0.697623\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 41.2376 3.09960
\(178\) 0 0
\(179\) −14.9243 −1.11550 −0.557748 0.830010i \(-0.688334\pi\)
−0.557748 + 0.830010i \(0.688334\pi\)
\(180\) 0 0
\(181\) 3.80202 0.282602 0.141301 0.989967i \(-0.454871\pi\)
0.141301 + 0.989967i \(0.454871\pi\)
\(182\) 0 0
\(183\) 5.48108 0.405173
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.74439 −0.127563
\(188\) 0 0
\(189\) 21.0422 1.53060
\(190\) 0 0
\(191\) −10.5990 −0.766916 −0.383458 0.923558i \(-0.625267\pi\)
−0.383458 + 0.923558i \(0.625267\pi\)
\(192\) 0 0
\(193\) −22.2677 −1.60286 −0.801432 0.598086i \(-0.795928\pi\)
−0.801432 + 0.598086i \(0.795928\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.1652 1.08048 0.540238 0.841513i \(-0.318334\pi\)
0.540238 + 0.841513i \(0.318334\pi\)
\(198\) 0 0
\(199\) 16.3632 1.15995 0.579977 0.814633i \(-0.303061\pi\)
0.579977 + 0.814633i \(0.303061\pi\)
\(200\) 0 0
\(201\) 14.8821 1.04970
\(202\) 0 0
\(203\) 4.08007 0.286365
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.40101 0.444901
\(208\) 0 0
\(209\) −0.598988 −0.0414329
\(210\) 0 0
\(211\) −5.80202 −0.399428 −0.199714 0.979854i \(-0.564001\pi\)
−0.199714 + 0.979854i \(0.564001\pi\)
\(212\) 0 0
\(213\) 34.8365 2.38696
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −22.9545 −1.55825
\(218\) 0 0
\(219\) 3.00000 0.202721
\(220\) 0 0
\(221\) −7.48108 −0.503232
\(222\) 0 0
\(223\) 10.1377 0.678871 0.339435 0.940629i \(-0.389764\pi\)
0.339435 + 0.940629i \(0.389764\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.5189 −0.963655 −0.481827 0.876266i \(-0.660027\pi\)
−0.481827 + 0.876266i \(0.660027\pi\)
\(228\) 0 0
\(229\) −27.2024 −1.79758 −0.898791 0.438377i \(-0.855554\pi\)
−0.898791 + 0.438377i \(0.855554\pi\)
\(230\) 0 0
\(231\) 5.08007 0.334244
\(232\) 0 0
\(233\) 1.40101 0.0917833 0.0458917 0.998946i \(-0.485387\pi\)
0.0458917 + 0.998946i \(0.485387\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 44.7411 2.90624
\(238\) 0 0
\(239\) 9.88209 0.639219 0.319610 0.947549i \(-0.396448\pi\)
0.319610 + 0.947549i \(0.396448\pi\)
\(240\) 0 0
\(241\) −3.08513 −0.198730 −0.0993652 0.995051i \(-0.531681\pi\)
−0.0993652 + 0.995051i \(0.531681\pi\)
\(242\) 0 0
\(243\) 8.28310 0.531361
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.56885 −0.163452
\(248\) 0 0
\(249\) −45.8865 −2.90794
\(250\) 0 0
\(251\) 6.08007 0.383770 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(252\) 0 0
\(253\) 0.699521 0.0439785
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.0121 −1.18594 −0.592971 0.805224i \(-0.702045\pi\)
−0.592971 + 0.805224i \(0.702045\pi\)
\(258\) 0 0
\(259\) −19.0422 −1.18323
\(260\) 0 0
\(261\) −7.67906 −0.475322
\(262\) 0 0
\(263\) 0.453585 0.0279693 0.0139846 0.999902i \(-0.495548\pi\)
0.0139846 + 0.999902i \(0.495548\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −44.9742 −2.75238
\(268\) 0 0
\(269\) 23.8442 1.45381 0.726905 0.686738i \(-0.240958\pi\)
0.726905 + 0.686738i \(0.240958\pi\)
\(270\) 0 0
\(271\) 12.7591 0.775061 0.387531 0.921857i \(-0.373328\pi\)
0.387531 + 0.921857i \(0.373328\pi\)
\(272\) 0 0
\(273\) 21.7866 1.31859
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.29783 −0.498568 −0.249284 0.968430i \(-0.580195\pi\)
−0.249284 + 0.968430i \(0.580195\pi\)
\(278\) 0 0
\(279\) 43.2024 2.58646
\(280\) 0 0
\(281\) −9.19798 −0.548705 −0.274353 0.961629i \(-0.588464\pi\)
−0.274353 + 0.961629i \(0.588464\pi\)
\(282\) 0 0
\(283\) 19.8770 1.18157 0.590783 0.806830i \(-0.298819\pi\)
0.590783 + 0.806830i \(0.298819\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −27.6111 −1.62983
\(288\) 0 0
\(289\) −8.51892 −0.501113
\(290\) 0 0
\(291\) 22.4432 1.31565
\(292\) 0 0
\(293\) 8.14540 0.475860 0.237930 0.971282i \(-0.423531\pi\)
0.237930 + 0.971282i \(0.423531\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.32797 −0.251134
\(298\) 0 0
\(299\) 3.00000 0.173494
\(300\) 0 0
\(301\) −2.40101 −0.138392
\(302\) 0 0
\(303\) −12.8168 −0.736303
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.7565 −0.613905 −0.306952 0.951725i \(-0.599309\pi\)
−0.306952 + 0.951725i \(0.599309\pi\)
\(308\) 0 0
\(309\) 50.5655 2.87657
\(310\) 0 0
\(311\) −30.8442 −1.74902 −0.874508 0.485010i \(-0.838816\pi\)
−0.874508 + 0.485010i \(0.838816\pi\)
\(312\) 0 0
\(313\) −6.53871 −0.369590 −0.184795 0.982777i \(-0.559162\pi\)
−0.184795 + 0.982777i \(0.559162\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.3055 −0.634982 −0.317491 0.948261i \(-0.602840\pi\)
−0.317491 + 0.948261i \(0.602840\pi\)
\(318\) 0 0
\(319\) −0.839190 −0.0469856
\(320\) 0 0
\(321\) 41.3253 2.30655
\(322\) 0 0
\(323\) 2.91223 0.162041
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 31.0999 1.71983
\(328\) 0 0
\(329\) 17.6412 0.972592
\(330\) 0 0
\(331\) 22.8064 1.25355 0.626777 0.779199i \(-0.284374\pi\)
0.626777 + 0.779199i \(0.284374\pi\)
\(332\) 0 0
\(333\) 35.8392 1.96398
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 17.7065 0.964537 0.482269 0.876023i \(-0.339813\pi\)
0.482269 + 0.876023i \(0.339813\pi\)
\(338\) 0 0
\(339\) 24.0422 1.30579
\(340\) 0 0
\(341\) 4.72128 0.255672
\(342\) 0 0
\(343\) 16.0724 0.867826
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.26331 −0.336232 −0.168116 0.985767i \(-0.553768\pi\)
−0.168116 + 0.985767i \(0.553768\pi\)
\(348\) 0 0
\(349\) −14.8821 −0.796620 −0.398310 0.917251i \(-0.630403\pi\)
−0.398310 + 0.917251i \(0.630403\pi\)
\(350\) 0 0
\(351\) −18.5611 −0.990721
\(352\) 0 0
\(353\) 5.45359 0.290265 0.145133 0.989412i \(-0.453639\pi\)
0.145133 + 0.989412i \(0.453639\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −24.6988 −1.30720
\(358\) 0 0
\(359\) 2.11791 0.111779 0.0558895 0.998437i \(-0.482201\pi\)
0.0558895 + 0.998437i \(0.482201\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 30.9897 1.62653
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.5414 0.915651 0.457826 0.889042i \(-0.348628\pi\)
0.457826 + 0.889042i \(0.348628\pi\)
\(368\) 0 0
\(369\) 51.9665 2.70527
\(370\) 0 0
\(371\) −2.40101 −0.124654
\(372\) 0 0
\(373\) 29.0801 1.50571 0.752854 0.658187i \(-0.228676\pi\)
0.752854 + 0.658187i \(0.228676\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.59899 −0.185357
\(378\) 0 0
\(379\) 26.2780 1.34981 0.674906 0.737904i \(-0.264184\pi\)
0.674906 + 0.737904i \(0.264184\pi\)
\(380\) 0 0
\(381\) −35.3253 −1.80977
\(382\) 0 0
\(383\) −21.6911 −1.10837 −0.554183 0.832395i \(-0.686969\pi\)
−0.554183 + 0.832395i \(0.686969\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.51892 0.229710
\(388\) 0 0
\(389\) 2.43380 0.123398 0.0616992 0.998095i \(-0.480348\pi\)
0.0616992 + 0.998095i \(0.480348\pi\)
\(390\) 0 0
\(391\) −3.40101 −0.171997
\(392\) 0 0
\(393\) −15.9622 −0.805184
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 31.2780 1.56980 0.784900 0.619622i \(-0.212714\pi\)
0.784900 + 0.619622i \(0.212714\pi\)
\(398\) 0 0
\(399\) −8.48108 −0.424585
\(400\) 0 0
\(401\) −8.95710 −0.447296 −0.223648 0.974670i \(-0.571797\pi\)
−0.223648 + 0.974670i \(0.571797\pi\)
\(402\) 0 0
\(403\) 20.2479 1.00862
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.91661 0.194139
\(408\) 0 0
\(409\) −24.6412 −1.21843 −0.609215 0.793005i \(-0.708515\pi\)
−0.609215 + 0.793005i \(0.708515\pi\)
\(410\) 0 0
\(411\) 22.1223 1.09121
\(412\) 0 0
\(413\) 41.2376 2.02917
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −20.8520 −1.02112
\(418\) 0 0
\(419\) 13.9199 0.680033 0.340017 0.940419i \(-0.389567\pi\)
0.340017 + 0.940419i \(0.389567\pi\)
\(420\) 0 0
\(421\) 4.91993 0.239783 0.119891 0.992787i \(-0.461745\pi\)
0.119891 + 0.992787i \(0.461745\pi\)
\(422\) 0 0
\(423\) −33.2024 −1.61435
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.48108 0.265248
\(428\) 0 0
\(429\) −4.48108 −0.216349
\(430\) 0 0
\(431\) 20.2875 0.977214 0.488607 0.872504i \(-0.337505\pi\)
0.488607 + 0.872504i \(0.337505\pi\)
\(432\) 0 0
\(433\) 20.9769 1.00808 0.504042 0.863679i \(-0.331845\pi\)
0.504042 + 0.863679i \(0.331845\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.16784 −0.0558653
\(438\) 0 0
\(439\) −18.7591 −0.895324 −0.447662 0.894203i \(-0.647743\pi\)
−0.447662 + 0.894203i \(0.647743\pi\)
\(440\) 0 0
\(441\) 8.11791 0.386567
\(442\) 0 0
\(443\) −40.4828 −1.92340 −0.961698 0.274110i \(-0.911617\pi\)
−0.961698 + 0.274110i \(0.911617\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 53.7109 2.54044
\(448\) 0 0
\(449\) −19.2402 −0.908001 −0.454001 0.891001i \(-0.650004\pi\)
−0.454001 + 0.891001i \(0.650004\pi\)
\(450\) 0 0
\(451\) 5.67906 0.267416
\(452\) 0 0
\(453\) 27.0198 1.26950
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.44829 0.395195 0.197597 0.980283i \(-0.436686\pi\)
0.197597 + 0.980283i \(0.436686\pi\)
\(458\) 0 0
\(459\) 21.0422 0.982167
\(460\) 0 0
\(461\) −25.2780 −1.17732 −0.588658 0.808382i \(-0.700343\pi\)
−0.588658 + 0.808382i \(0.700343\pi\)
\(462\) 0 0
\(463\) −7.15749 −0.332637 −0.166318 0.986072i \(-0.553188\pi\)
−0.166318 + 0.986072i \(0.553188\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.71690 −0.0794486 −0.0397243 0.999211i \(-0.512648\pi\)
−0.0397243 + 0.999211i \(0.512648\pi\)
\(468\) 0 0
\(469\) 14.8821 0.687191
\(470\) 0 0
\(471\) −41.3253 −1.90417
\(472\) 0 0
\(473\) 0.493841 0.0227068
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4.51892 0.206907
\(478\) 0 0
\(479\) −31.6885 −1.44788 −0.723942 0.689861i \(-0.757672\pi\)
−0.723942 + 0.689861i \(0.757672\pi\)
\(480\) 0 0
\(481\) 16.7970 0.765876
\(482\) 0 0
\(483\) 9.90453 0.450672
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.08513 −0.0491717 −0.0245859 0.999698i \(-0.507827\pi\)
−0.0245859 + 0.999698i \(0.507827\pi\)
\(488\) 0 0
\(489\) −73.3297 −3.31608
\(490\) 0 0
\(491\) −10.9149 −0.492581 −0.246291 0.969196i \(-0.579212\pi\)
−0.246291 + 0.969196i \(0.579212\pi\)
\(492\) 0 0
\(493\) 4.08007 0.183757
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 34.8365 1.56263
\(498\) 0 0
\(499\) 38.8814 1.74057 0.870286 0.492547i \(-0.163934\pi\)
0.870286 + 0.492547i \(0.163934\pi\)
\(500\) 0 0
\(501\) 32.1223 1.43512
\(502\) 0 0
\(503\) −20.3306 −0.906497 −0.453249 0.891384i \(-0.649735\pi\)
−0.453249 + 0.891384i \(0.649735\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 18.6412 0.827885
\(508\) 0 0
\(509\) 10.5189 0.466243 0.233121 0.972448i \(-0.425106\pi\)
0.233121 + 0.972448i \(0.425106\pi\)
\(510\) 0 0
\(511\) 3.00000 0.132712
\(512\) 0 0
\(513\) 7.22547 0.319012
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.62845 −0.159579
\(518\) 0 0
\(519\) 44.5655 1.95621
\(520\) 0 0
\(521\) −25.7642 −1.12875 −0.564375 0.825519i \(-0.690883\pi\)
−0.564375 + 0.825519i \(0.690883\pi\)
\(522\) 0 0
\(523\) −30.8814 −1.35035 −0.675175 0.737658i \(-0.735932\pi\)
−0.675175 + 0.737658i \(0.735932\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −22.9545 −0.999912
\(528\) 0 0
\(529\) −21.6362 −0.940702
\(530\) 0 0
\(531\) −77.6128 −3.36811
\(532\) 0 0
\(533\) 24.3555 1.05495
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 43.4630 1.87557
\(538\) 0 0
\(539\) 0.887149 0.0382122
\(540\) 0 0
\(541\) 13.3253 0.572901 0.286450 0.958095i \(-0.407525\pi\)
0.286450 + 0.958095i \(0.407525\pi\)
\(542\) 0 0
\(543\) −11.0724 −0.475161
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.8821 −1.14940 −0.574698 0.818366i \(-0.694880\pi\)
−0.574698 + 0.818366i \(0.694880\pi\)
\(548\) 0 0
\(549\) −10.3159 −0.440271
\(550\) 0 0
\(551\) 1.40101 0.0596851
\(552\) 0 0
\(553\) 44.7411 1.90258
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 27.3082 1.15708 0.578542 0.815652i \(-0.303622\pi\)
0.578542 + 0.815652i \(0.303622\pi\)
\(558\) 0 0
\(559\) 2.11791 0.0895780
\(560\) 0 0
\(561\) 5.08007 0.214481
\(562\) 0 0
\(563\) 40.3324 1.69981 0.849903 0.526939i \(-0.176660\pi\)
0.849903 + 0.526939i \(0.176660\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −13.3933 −0.562466
\(568\) 0 0
\(569\) 11.8399 0.496353 0.248176 0.968715i \(-0.420169\pi\)
0.248176 + 0.968715i \(0.420169\pi\)
\(570\) 0 0
\(571\) −1.71690 −0.0718499 −0.0359250 0.999354i \(-0.511438\pi\)
−0.0359250 + 0.999354i \(0.511438\pi\)
\(572\) 0 0
\(573\) 30.8667 1.28947
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0.0552190 0.00229880 0.00114940 0.999999i \(-0.499634\pi\)
0.00114940 + 0.999999i \(0.499634\pi\)
\(578\) 0 0
\(579\) 64.8486 2.69502
\(580\) 0 0
\(581\) −45.8865 −1.90369
\(582\) 0 0
\(583\) 0.493841 0.0204528
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.4010 0.470570 0.235285 0.971926i \(-0.424398\pi\)
0.235285 + 0.971926i \(0.424398\pi\)
\(588\) 0 0
\(589\) −7.88209 −0.324776
\(590\) 0 0
\(591\) −44.1645 −1.81669
\(592\) 0 0
\(593\) −36.8288 −1.51238 −0.756190 0.654353i \(-0.772941\pi\)
−0.756190 + 0.654353i \(0.772941\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −47.6533 −1.95032
\(598\) 0 0
\(599\) −22.7591 −0.929913 −0.464956 0.885334i \(-0.653930\pi\)
−0.464956 + 0.885334i \(0.653930\pi\)
\(600\) 0 0
\(601\) −36.5277 −1.49000 −0.744998 0.667067i \(-0.767549\pi\)
−0.744998 + 0.667067i \(0.767549\pi\)
\(602\) 0 0
\(603\) −28.0094 −1.14063
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −10.1230 −0.410879 −0.205439 0.978670i \(-0.565862\pi\)
−0.205439 + 0.978670i \(0.565862\pi\)
\(608\) 0 0
\(609\) −11.8821 −0.481487
\(610\) 0 0
\(611\) −15.5611 −0.629537
\(612\) 0 0
\(613\) −35.5930 −1.43759 −0.718794 0.695223i \(-0.755306\pi\)
−0.718794 + 0.695223i \(0.755306\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.2134 −0.531951 −0.265975 0.963980i \(-0.585694\pi\)
−0.265975 + 0.963980i \(0.585694\pi\)
\(618\) 0 0
\(619\) −23.2453 −0.934306 −0.467153 0.884177i \(-0.654720\pi\)
−0.467153 + 0.884177i \(0.654720\pi\)
\(620\) 0 0
\(621\) −8.43818 −0.338612
\(622\) 0 0
\(623\) −44.9742 −1.80186
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.74439 0.0696643
\(628\) 0 0
\(629\) −19.0422 −0.759263
\(630\) 0 0
\(631\) 3.88715 0.154745 0.0773725 0.997002i \(-0.475347\pi\)
0.0773725 + 0.997002i \(0.475347\pi\)
\(632\) 0 0
\(633\) 16.8968 0.671588
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.80467 0.150746
\(638\) 0 0
\(639\) −65.5655 −2.59373
\(640\) 0 0
\(641\) −34.1223 −1.34775 −0.673875 0.738846i \(-0.735371\pi\)
−0.673875 + 0.738846i \(0.735371\pi\)
\(642\) 0 0
\(643\) −31.9243 −1.25897 −0.629486 0.777012i \(-0.716735\pi\)
−0.629486 + 0.777012i \(0.716735\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −35.3434 −1.38949 −0.694746 0.719255i \(-0.744483\pi\)
−0.694746 + 0.719255i \(0.744483\pi\)
\(648\) 0 0
\(649\) −8.48175 −0.332938
\(650\) 0 0
\(651\) 66.8486 2.62000
\(652\) 0 0
\(653\) −27.5431 −1.07784 −0.538922 0.842356i \(-0.681168\pi\)
−0.538922 + 0.842356i \(0.681168\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.64627 −0.220282
\(658\) 0 0
\(659\) 29.6740 1.15593 0.577967 0.816060i \(-0.303846\pi\)
0.577967 + 0.816060i \(0.303846\pi\)
\(660\) 0 0
\(661\) −16.3159 −0.634614 −0.317307 0.948323i \(-0.602779\pi\)
−0.317307 + 0.948323i \(0.602779\pi\)
\(662\) 0 0
\(663\) 21.7866 0.846122
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.63615 −0.0633522
\(668\) 0 0
\(669\) −29.5233 −1.14144
\(670\) 0 0
\(671\) −1.12735 −0.0435209
\(672\) 0 0
\(673\) −13.6945 −0.527883 −0.263941 0.964539i \(-0.585023\pi\)
−0.263941 + 0.964539i \(0.585023\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.2426 −0.701121 −0.350560 0.936540i \(-0.614009\pi\)
−0.350560 + 0.936540i \(0.614009\pi\)
\(678\) 0 0
\(679\) 22.4432 0.861292
\(680\) 0 0
\(681\) 42.2824 1.62027
\(682\) 0 0
\(683\) −8.92764 −0.341607 −0.170803 0.985305i \(-0.554636\pi\)
−0.170803 + 0.985305i \(0.554636\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 79.2195 3.02241
\(688\) 0 0
\(689\) 2.11791 0.0806859
\(690\) 0 0
\(691\) 37.5284 1.42765 0.713823 0.700326i \(-0.246962\pi\)
0.713823 + 0.700326i \(0.246962\pi\)
\(692\) 0 0
\(693\) −9.56115 −0.363198
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −27.6111 −1.04584
\(698\) 0 0
\(699\) −4.08007 −0.154322
\(700\) 0 0
\(701\) −42.1746 −1.59291 −0.796457 0.604695i \(-0.793295\pi\)
−0.796457 + 0.604695i \(0.793295\pi\)
\(702\) 0 0
\(703\) −6.53871 −0.246612
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.8168 −0.482024
\(708\) 0 0
\(709\) −4.35373 −0.163508 −0.0817539 0.996653i \(-0.526052\pi\)
−0.0817539 + 0.996653i \(0.526052\pi\)
\(710\) 0 0
\(711\) −84.2067 −3.15800
\(712\) 0 0
\(713\) 9.20500 0.344730
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −28.7789 −1.07477
\(718\) 0 0
\(719\) 14.2780 0.532481 0.266241 0.963907i \(-0.414218\pi\)
0.266241 + 0.963907i \(0.414218\pi\)
\(720\) 0 0
\(721\) 50.5655 1.88316
\(722\) 0 0
\(723\) 8.98459 0.334141
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 29.7538 1.10351 0.551754 0.834007i \(-0.313959\pi\)
0.551754 + 0.834007i \(0.313959\pi\)
\(728\) 0 0
\(729\) −37.9193 −1.40442
\(730\) 0 0
\(731\) −2.40101 −0.0888046
\(732\) 0 0
\(733\) −16.4580 −0.607889 −0.303944 0.952690i \(-0.598304\pi\)
−0.303944 + 0.952690i \(0.598304\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.06095 −0.112752
\(738\) 0 0
\(739\) 11.2024 0.412085 0.206043 0.978543i \(-0.433941\pi\)
0.206043 + 0.978543i \(0.433941\pi\)
\(740\) 0 0
\(741\) 7.48108 0.274824
\(742\) 0 0
\(743\) 28.5053 1.04576 0.522878 0.852407i \(-0.324858\pi\)
0.522878 + 0.852407i \(0.324858\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 86.3625 3.15984
\(748\) 0 0
\(749\) 41.3253 1.50999
\(750\) 0 0
\(751\) −24.9716 −0.911227 −0.455613 0.890178i \(-0.650580\pi\)
−0.455613 + 0.890178i \(0.650580\pi\)
\(752\) 0 0
\(753\) −17.7065 −0.645263
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 12.8717 0.467831 0.233916 0.972257i \(-0.424846\pi\)
0.233916 + 0.972257i \(0.424846\pi\)
\(758\) 0 0
\(759\) −2.03717 −0.0739445
\(760\) 0 0
\(761\) −26.6791 −0.967115 −0.483558 0.875313i \(-0.660656\pi\)
−0.483558 + 0.875313i \(0.660656\pi\)
\(762\) 0 0
\(763\) 31.0999 1.12589
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −36.3753 −1.31343
\(768\) 0 0
\(769\) 29.7541 1.07296 0.536479 0.843913i \(-0.319754\pi\)
0.536479 + 0.843913i \(0.319754\pi\)
\(770\) 0 0
\(771\) 55.3676 1.99401
\(772\) 0 0
\(773\) −50.5655 −1.81872 −0.909358 0.416015i \(-0.863426\pi\)
−0.909358 + 0.416015i \(0.863426\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 55.4553 1.98945
\(778\) 0 0
\(779\) −9.48108 −0.339695
\(780\) 0 0
\(781\) −7.16519 −0.256391
\(782\) 0 0
\(783\) 10.1230 0.361765
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 54.8530 1.95530 0.977649 0.210242i \(-0.0674252\pi\)
0.977649 + 0.210242i \(0.0674252\pi\)
\(788\) 0 0
\(789\) −1.32094 −0.0470269
\(790\) 0 0
\(791\) 24.0422 0.854843
\(792\) 0 0
\(793\) −4.83481 −0.171689
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.3434 −1.07482 −0.537409 0.843322i \(-0.680597\pi\)
−0.537409 + 0.843322i \(0.680597\pi\)
\(798\) 0 0
\(799\) 17.6412 0.624101
\(800\) 0 0
\(801\) 84.6456 2.99081
\(802\) 0 0
\(803\) −0.617041 −0.0217749
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −69.4399 −2.44440
\(808\) 0 0
\(809\) −11.0801 −0.389554 −0.194777 0.980848i \(-0.562398\pi\)
−0.194777 + 0.980848i \(0.562398\pi\)
\(810\) 0 0
\(811\) 39.3625 1.38220 0.691102 0.722757i \(-0.257126\pi\)
0.691102 + 0.722757i \(0.257126\pi\)
\(812\) 0 0
\(813\) −37.1575 −1.30317
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.824458 −0.0288441
\(818\) 0 0
\(819\) −41.0044 −1.43281
\(820\) 0 0
\(821\) 34.8493 1.21625 0.608125 0.793842i \(-0.291922\pi\)
0.608125 + 0.793842i \(0.291922\pi\)
\(822\) 0 0
\(823\) 22.7615 0.793417 0.396709 0.917945i \(-0.370152\pi\)
0.396709 + 0.917945i \(0.370152\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −32.7615 −1.13923 −0.569615 0.821912i \(-0.692908\pi\)
−0.569615 + 0.821912i \(0.692908\pi\)
\(828\) 0 0
\(829\) 36.4905 1.26737 0.633684 0.773592i \(-0.281542\pi\)
0.633684 + 0.773592i \(0.281542\pi\)
\(830\) 0 0
\(831\) 24.1652 0.838281
\(832\) 0 0
\(833\) −4.31324 −0.149445
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −56.9518 −1.96854
\(838\) 0 0
\(839\) 47.4949 1.63971 0.819853 0.572574i \(-0.194055\pi\)
0.819853 + 0.572574i \(0.194055\pi\)
\(840\) 0 0
\(841\) −27.0372 −0.932316
\(842\) 0 0
\(843\) 26.7866 0.922580
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 30.9897 1.06482
\(848\) 0 0
\(849\) −57.8865 −1.98666
\(850\) 0 0
\(851\) 7.63615 0.261764
\(852\) 0 0
\(853\) −1.86736 −0.0639372 −0.0319686 0.999489i \(-0.510178\pi\)
−0.0319686 + 0.999489i \(0.510178\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −16.3608 −0.558873 −0.279436 0.960164i \(-0.590148\pi\)
−0.279436 + 0.960164i \(0.590148\pi\)
\(858\) 0 0
\(859\) −21.0851 −0.719415 −0.359708 0.933065i \(-0.617124\pi\)
−0.359708 + 0.933065i \(0.617124\pi\)
\(860\) 0 0
\(861\) 80.4098 2.74036
\(862\) 0 0
\(863\) −25.6868 −0.874387 −0.437194 0.899367i \(-0.644028\pi\)
−0.437194 + 0.899367i \(0.644028\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 24.8091 0.842560
\(868\) 0 0
\(869\) −9.20236 −0.312169
\(870\) 0 0
\(871\) −13.1274 −0.444803
\(872\) 0 0
\(873\) −42.2402 −1.42961
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 43.2978 1.46206 0.731032 0.682343i \(-0.239039\pi\)
0.731032 + 0.682343i \(0.239039\pi\)
\(878\) 0 0
\(879\) −23.7213 −0.800099
\(880\) 0 0
\(881\) 22.0750 0.743726 0.371863 0.928288i \(-0.378719\pi\)
0.371863 + 0.928288i \(0.378719\pi\)
\(882\) 0 0
\(883\) 0.385604 0.0129766 0.00648831 0.999979i \(-0.497935\pi\)
0.00648831 + 0.999979i \(0.497935\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 54.9210 1.84407 0.922033 0.387111i \(-0.126527\pi\)
0.922033 + 0.387111i \(0.126527\pi\)
\(888\) 0 0
\(889\) −35.3253 −1.18477
\(890\) 0 0
\(891\) 2.75474 0.0922873
\(892\) 0 0
\(893\) 6.05763 0.202711
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8.73669 −0.291710
\(898\) 0 0
\(899\) −11.0429 −0.368301
\(900\) 0 0
\(901\) −2.40101 −0.0799893
\(902\) 0 0
\(903\) 6.99230 0.232689
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −41.4727 −1.37708 −0.688539 0.725199i \(-0.741748\pi\)
−0.688539 + 0.725199i \(0.741748\pi\)
\(908\) 0 0
\(909\) 24.1223 0.800086
\(910\) 0 0
\(911\) 41.8909 1.38791 0.693953 0.720020i \(-0.255868\pi\)
0.693953 + 0.720020i \(0.255868\pi\)
\(912\) 0 0
\(913\) 9.43795 0.312350
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15.9622 −0.527117
\(918\) 0 0
\(919\) −36.0044 −1.18767 −0.593837 0.804585i \(-0.702388\pi\)
−0.593837 + 0.804585i \(0.702388\pi\)
\(920\) 0 0
\(921\) 31.3253 1.03220
\(922\) 0 0
\(923\) −30.7290 −1.01146
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −95.1689 −3.12576
\(928\) 0 0
\(929\) 59.4898 1.95180 0.975899 0.218222i \(-0.0700256\pi\)
0.975899 + 0.218222i \(0.0700256\pi\)
\(930\) 0 0
\(931\) −1.48108 −0.0485404
\(932\) 0 0
\(933\) 89.8255 2.94076
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 35.7143 1.16673 0.583367 0.812209i \(-0.301735\pi\)
0.583367 + 0.812209i \(0.301735\pi\)
\(938\) 0 0
\(939\) 19.0422 0.621420
\(940\) 0 0
\(941\) 20.2074 0.658743 0.329371 0.944200i \(-0.393163\pi\)
0.329371 + 0.944200i \(0.393163\pi\)
\(942\) 0 0
\(943\) 11.0724 0.360566
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −51.4982 −1.67347 −0.836734 0.547610i \(-0.815538\pi\)
−0.836734 + 0.547610i \(0.815538\pi\)
\(948\) 0 0
\(949\) −2.64627 −0.0859016
\(950\) 0 0
\(951\) 32.9243 1.06764
\(952\) 0 0
\(953\) −7.95272 −0.257614 −0.128807 0.991670i \(-0.541115\pi\)
−0.128807 + 0.991670i \(0.541115\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 2.44391 0.0790005
\(958\) 0 0
\(959\) 22.1223 0.714366
\(960\) 0 0
\(961\) 31.1274 1.00411
\(962\) 0 0
\(963\) −77.7780 −2.50636
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −32.5706 −1.04740 −0.523700 0.851903i \(-0.675449\pi\)
−0.523700 + 0.851903i \(0.675449\pi\)
\(968\) 0 0
\(969\) −8.48108 −0.272452
\(970\) 0 0
\(971\) 21.0378 0.675136 0.337568 0.941301i \(-0.390396\pi\)
0.337568 + 0.941301i \(0.390396\pi\)
\(972\) 0 0
\(973\) −20.8520 −0.668483
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −46.9648 −1.50254 −0.751269 0.659997i \(-0.770558\pi\)
−0.751269 + 0.659997i \(0.770558\pi\)
\(978\) 0 0
\(979\) 9.25032 0.295641
\(980\) 0 0
\(981\) −58.5327 −1.86881
\(982\) 0 0
\(983\) 18.5182 0.590640 0.295320 0.955398i \(-0.404574\pi\)
0.295320 + 0.955398i \(0.404574\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −51.3753 −1.63529
\(988\) 0 0
\(989\) 0.962834 0.0306163
\(990\) 0 0
\(991\) −5.40539 −0.171708 −0.0858540 0.996308i \(-0.527362\pi\)
−0.0858540 + 0.996308i \(0.527362\pi\)
\(992\) 0 0
\(993\) −66.4175 −2.10770
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −8.55676 −0.270995 −0.135498 0.990778i \(-0.543263\pi\)
−0.135498 + 0.990778i \(0.543263\pi\)
\(998\) 0 0
\(999\) −47.2453 −1.49477
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 1900.2.a.f.1.1 3
4.3 odd 2 7600.2.a.by.1.3 3
5.2 odd 4 1900.2.c.g.1749.6 6
5.3 odd 4 1900.2.c.g.1749.1 6
5.4 even 2 1900.2.a.h.1.3 yes 3
20.19 odd 2 7600.2.a.bj.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1900.2.a.f.1.1 3 1.1 even 1 trivial
1900.2.a.h.1.3 yes 3 5.4 even 2
1900.2.c.g.1749.1 6 5.3 odd 4
1900.2.c.g.1749.6 6 5.2 odd 4
7600.2.a.bj.1.1 3 20.19 odd 2
7600.2.a.by.1.3 3 4.3 odd 2