Properties

Label 1900.2.a.i.1.1
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $0$
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: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.321.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 1\)
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 \(0.239123\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18194 q^{3} +3.70370 q^{7} +1.76088 q^{9} +O(q^{10})\) \(q-2.18194 q^{3} +3.70370 q^{7} +1.76088 q^{9} -3.18194 q^{11} -1.94282 q^{13} +4.66019 q^{17} +1.00000 q^{19} -8.08126 q^{21} +5.23912 q^{23} +2.70370 q^{27} -1.66019 q^{29} -3.46457 q^{31} +6.94282 q^{33} -7.18194 q^{37} +4.23912 q^{39} -0.717370 q^{41} -1.36389 q^{43} +5.37756 q^{47} +6.71737 q^{49} -10.1683 q^{51} +0.0435069 q^{53} -2.18194 q^{57} -7.88564 q^{59} -4.98633 q^{61} +6.52175 q^{63} +14.5023 q^{67} -11.4315 q^{69} +4.88564 q^{71} +10.6030 q^{73} -11.7850 q^{77} +14.9097 q^{79} -11.1819 q^{81} +9.76088 q^{83} +3.62244 q^{87} +10.0813 q^{89} -7.19562 q^{91} +7.55950 q^{93} -14.6706 q^{97} -5.60301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 2 q^{7} + 5 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{3} + 2 q^{7} + 5 q^{9} - q^{11} + 3 q^{13} + 6 q^{17} + 3 q^{19} - 8 q^{21} + 16 q^{23} - q^{27} + 3 q^{29} - q^{31} + 12 q^{33} - 13 q^{37} + 13 q^{39} - 3 q^{41} + 13 q^{43} + 9 q^{47} + 21 q^{49} - 12 q^{51} - q^{53} + 2 q^{57} - 6 q^{59} - 5 q^{61} + 19 q^{63} + 19 q^{67} + 9 q^{69} - 3 q^{71} + 15 q^{73} - 10 q^{77} + 2 q^{79} - 25 q^{81} + 29 q^{83} + 18 q^{87} + 14 q^{89} - 23 q^{91} + 7 q^{93} - q^{97} + O(q^{100}) \)

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
\(3\) −2.18194 −1.25975 −0.629873 0.776698i \(-0.716893\pi\)
−0.629873 + 0.776698i \(0.716893\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.70370 1.39987 0.699933 0.714209i \(-0.253213\pi\)
0.699933 + 0.714209i \(0.253213\pi\)
\(8\) 0 0
\(9\) 1.76088 0.586959
\(10\) 0 0
\(11\) −3.18194 −0.959392 −0.479696 0.877435i \(-0.659253\pi\)
−0.479696 + 0.877435i \(0.659253\pi\)
\(12\) 0 0
\(13\) −1.94282 −0.538841 −0.269421 0.963023i \(-0.586832\pi\)
−0.269421 + 0.963023i \(0.586832\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.66019 1.13026 0.565131 0.825001i \(-0.308826\pi\)
0.565131 + 0.825001i \(0.308826\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −8.08126 −1.76347
\(22\) 0 0
\(23\) 5.23912 1.09243 0.546216 0.837644i \(-0.316068\pi\)
0.546216 + 0.837644i \(0.316068\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.70370 0.520327
\(28\) 0 0
\(29\) −1.66019 −0.308290 −0.154145 0.988048i \(-0.549262\pi\)
−0.154145 + 0.988048i \(0.549262\pi\)
\(30\) 0 0
\(31\) −3.46457 −0.622256 −0.311128 0.950368i \(-0.600707\pi\)
−0.311128 + 0.950368i \(0.600707\pi\)
\(32\) 0 0
\(33\) 6.94282 1.20859
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.18194 −1.18070 −0.590352 0.807146i \(-0.701011\pi\)
−0.590352 + 0.807146i \(0.701011\pi\)
\(38\) 0 0
\(39\) 4.23912 0.678803
\(40\) 0 0
\(41\) −0.717370 −0.112034 −0.0560172 0.998430i \(-0.517840\pi\)
−0.0560172 + 0.998430i \(0.517840\pi\)
\(42\) 0 0
\(43\) −1.36389 −0.207991 −0.103995 0.994578i \(-0.533163\pi\)
−0.103995 + 0.994578i \(0.533163\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.37756 0.784398 0.392199 0.919880i \(-0.371715\pi\)
0.392199 + 0.919880i \(0.371715\pi\)
\(48\) 0 0
\(49\) 6.71737 0.959624
\(50\) 0 0
\(51\) −10.1683 −1.42384
\(52\) 0 0
\(53\) 0.0435069 0.00597613 0.00298807 0.999996i \(-0.499049\pi\)
0.00298807 + 0.999996i \(0.499049\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.18194 −0.289005
\(58\) 0 0
\(59\) −7.88564 −1.02662 −0.513311 0.858202i \(-0.671581\pi\)
−0.513311 + 0.858202i \(0.671581\pi\)
\(60\) 0 0
\(61\) −4.98633 −0.638434 −0.319217 0.947682i \(-0.603420\pi\)
−0.319217 + 0.947682i \(0.603420\pi\)
\(62\) 0 0
\(63\) 6.52175 0.821664
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.5023 1.77174 0.885870 0.463933i \(-0.153562\pi\)
0.885870 + 0.463933i \(0.153562\pi\)
\(68\) 0 0
\(69\) −11.4315 −1.37619
\(70\) 0 0
\(71\) 4.88564 0.579819 0.289909 0.957054i \(-0.406375\pi\)
0.289909 + 0.957054i \(0.406375\pi\)
\(72\) 0 0
\(73\) 10.6030 1.24099 0.620494 0.784211i \(-0.286932\pi\)
0.620494 + 0.784211i \(0.286932\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.7850 −1.34302
\(78\) 0 0
\(79\) 14.9097 1.67747 0.838737 0.544537i \(-0.183294\pi\)
0.838737 + 0.544537i \(0.183294\pi\)
\(80\) 0 0
\(81\) −11.1819 −1.24244
\(82\) 0 0
\(83\) 9.76088 1.07140 0.535698 0.844410i \(-0.320049\pi\)
0.535698 + 0.844410i \(0.320049\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.62244 0.388366
\(88\) 0 0
\(89\) 10.0813 1.06861 0.534306 0.845291i \(-0.320573\pi\)
0.534306 + 0.845291i \(0.320573\pi\)
\(90\) 0 0
\(91\) −7.19562 −0.754306
\(92\) 0 0
\(93\) 7.55950 0.783884
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.6706 −1.48957 −0.744787 0.667303i \(-0.767449\pi\)
−0.744787 + 0.667303i \(0.767449\pi\)
\(98\) 0 0
\(99\) −5.60301 −0.563124
\(100\) 0 0
\(101\) 15.9532 1.58741 0.793703 0.608306i \(-0.208151\pi\)
0.793703 + 0.608306i \(0.208151\pi\)
\(102\) 0 0
\(103\) −10.6328 −1.04769 −0.523843 0.851815i \(-0.675502\pi\)
−0.523843 + 0.851815i \(0.675502\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.6465 1.41593 0.707966 0.706246i \(-0.249613\pi\)
0.707966 + 0.706246i \(0.249613\pi\)
\(108\) 0 0
\(109\) −3.55950 −0.340939 −0.170469 0.985363i \(-0.554528\pi\)
−0.170469 + 0.985363i \(0.554528\pi\)
\(110\) 0 0
\(111\) 15.6706 1.48739
\(112\) 0 0
\(113\) 14.8285 1.39494 0.697472 0.716612i \(-0.254308\pi\)
0.697472 + 0.716612i \(0.254308\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.42107 −0.316278
\(118\) 0 0
\(119\) 17.2599 1.58222
\(120\) 0 0
\(121\) −0.875237 −0.0795670
\(122\) 0 0
\(123\) 1.56526 0.141135
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.69002 0.682379 0.341190 0.939994i \(-0.389170\pi\)
0.341190 + 0.939994i \(0.389170\pi\)
\(128\) 0 0
\(129\) 2.97592 0.262015
\(130\) 0 0
\(131\) 19.4451 1.69893 0.849465 0.527645i \(-0.176925\pi\)
0.849465 + 0.527645i \(0.176925\pi\)
\(132\) 0 0
\(133\) 3.70370 0.321151
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.39699 0.290224 0.145112 0.989415i \(-0.453646\pi\)
0.145112 + 0.989415i \(0.453646\pi\)
\(138\) 0 0
\(139\) 10.5699 0.896528 0.448264 0.893901i \(-0.352042\pi\)
0.448264 + 0.893901i \(0.352042\pi\)
\(140\) 0 0
\(141\) −11.7335 −0.988142
\(142\) 0 0
\(143\) 6.18194 0.516960
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −14.6569 −1.20888
\(148\) 0 0
\(149\) 19.5322 1.60014 0.800068 0.599909i \(-0.204797\pi\)
0.800068 + 0.599909i \(0.204797\pi\)
\(150\) 0 0
\(151\) −1.17154 −0.0953386 −0.0476693 0.998863i \(-0.515179\pi\)
−0.0476693 + 0.998863i \(0.515179\pi\)
\(152\) 0 0
\(153\) 8.20602 0.663417
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.01040 0.399874 0.199937 0.979809i \(-0.435926\pi\)
0.199937 + 0.979809i \(0.435926\pi\)
\(158\) 0 0
\(159\) −0.0949296 −0.00752840
\(160\) 0 0
\(161\) 19.4041 1.52926
\(162\) 0 0
\(163\) −6.78495 −0.531439 −0.265719 0.964050i \(-0.585609\pi\)
−0.265719 + 0.964050i \(0.585609\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.64652 −0.436941 −0.218470 0.975844i \(-0.570107\pi\)
−0.218470 + 0.975844i \(0.570107\pi\)
\(168\) 0 0
\(169\) −9.22545 −0.709650
\(170\) 0 0
\(171\) 1.76088 0.134658
\(172\) 0 0
\(173\) 5.38796 0.409639 0.204820 0.978800i \(-0.434339\pi\)
0.204820 + 0.978800i \(0.434339\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.2060 1.29328
\(178\) 0 0
\(179\) 3.27687 0.244925 0.122462 0.992473i \(-0.460921\pi\)
0.122462 + 0.992473i \(0.460921\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 10.8799 0.804264
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −14.8285 −1.08436
\(188\) 0 0
\(189\) 10.0137 0.728388
\(190\) 0 0
\(191\) 0.225450 0.0163130 0.00815650 0.999967i \(-0.497404\pi\)
0.00815650 + 0.999967i \(0.497404\pi\)
\(192\) 0 0
\(193\) −8.12476 −0.584833 −0.292417 0.956291i \(-0.594459\pi\)
−0.292417 + 0.956291i \(0.594459\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.25280 0.302999 0.151500 0.988457i \(-0.451590\pi\)
0.151500 + 0.988457i \(0.451590\pi\)
\(198\) 0 0
\(199\) 26.1592 1.85438 0.927190 0.374592i \(-0.122217\pi\)
0.927190 + 0.374592i \(0.122217\pi\)
\(200\) 0 0
\(201\) −31.6432 −2.23194
\(202\) 0 0
\(203\) −6.14884 −0.431564
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 9.22545 0.641213
\(208\) 0 0
\(209\) −3.18194 −0.220100
\(210\) 0 0
\(211\) 4.27223 0.294112 0.147056 0.989128i \(-0.453020\pi\)
0.147056 + 0.989128i \(0.453020\pi\)
\(212\) 0 0
\(213\) −10.6602 −0.730424
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −12.8317 −0.871075
\(218\) 0 0
\(219\) −23.1352 −1.56333
\(220\) 0 0
\(221\) −9.05391 −0.609032
\(222\) 0 0
\(223\) 23.0208 1.54159 0.770794 0.637085i \(-0.219860\pi\)
0.770794 + 0.637085i \(0.219860\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.96690 0.595154 0.297577 0.954698i \(-0.403822\pi\)
0.297577 + 0.954698i \(0.403822\pi\)
\(228\) 0 0
\(229\) −8.62709 −0.570094 −0.285047 0.958514i \(-0.592009\pi\)
−0.285047 + 0.958514i \(0.592009\pi\)
\(230\) 0 0
\(231\) 25.7141 1.69186
\(232\) 0 0
\(233\) −29.0014 −1.89994 −0.949972 0.312336i \(-0.898889\pi\)
−0.949972 + 0.312336i \(0.898889\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −32.5322 −2.11319
\(238\) 0 0
\(239\) −23.7414 −1.53571 −0.767853 0.640626i \(-0.778675\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(240\) 0 0
\(241\) −6.32614 −0.407502 −0.203751 0.979023i \(-0.565313\pi\)
−0.203751 + 0.979023i \(0.565313\pi\)
\(242\) 0 0
\(243\) 16.2873 1.04483
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.94282 −0.123619
\(248\) 0 0
\(249\) −21.2977 −1.34969
\(250\) 0 0
\(251\) −21.9201 −1.38359 −0.691793 0.722096i \(-0.743179\pi\)
−0.691793 + 0.722096i \(0.743179\pi\)
\(252\) 0 0
\(253\) −16.6706 −1.04807
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.31246 0.206626 0.103313 0.994649i \(-0.467056\pi\)
0.103313 + 0.994649i \(0.467056\pi\)
\(258\) 0 0
\(259\) −26.5997 −1.65283
\(260\) 0 0
\(261\) −2.92339 −0.180953
\(262\) 0 0
\(263\) −2.33405 −0.143924 −0.0719619 0.997407i \(-0.522926\pi\)
−0.0719619 + 0.997407i \(0.522926\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −21.9967 −1.34618
\(268\) 0 0
\(269\) −24.5789 −1.49860 −0.749302 0.662228i \(-0.769611\pi\)
−0.749302 + 0.662228i \(0.769611\pi\)
\(270\) 0 0
\(271\) 16.3880 0.995498 0.497749 0.867321i \(-0.334160\pi\)
0.497749 + 0.867321i \(0.334160\pi\)
\(272\) 0 0
\(273\) 15.7004 0.950233
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.68427 0.521787 0.260894 0.965368i \(-0.415983\pi\)
0.260894 + 0.965368i \(0.415983\pi\)
\(278\) 0 0
\(279\) −6.10069 −0.365239
\(280\) 0 0
\(281\) −0.450900 −0.0268985 −0.0134492 0.999910i \(-0.504281\pi\)
−0.0134492 + 0.999910i \(0.504281\pi\)
\(282\) 0 0
\(283\) −28.6512 −1.70313 −0.851567 0.524245i \(-0.824348\pi\)
−0.851567 + 0.524245i \(0.824348\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.65692 −0.156833
\(288\) 0 0
\(289\) 4.71737 0.277492
\(290\) 0 0
\(291\) 32.0104 1.87648
\(292\) 0 0
\(293\) −20.7335 −1.21127 −0.605633 0.795744i \(-0.707080\pi\)
−0.605633 + 0.795744i \(0.707080\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.60301 −0.499197
\(298\) 0 0
\(299\) −10.1787 −0.588648
\(300\) 0 0
\(301\) −5.05142 −0.291159
\(302\) 0 0
\(303\) −34.8090 −1.99973
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 34.4933 1.96864 0.984318 0.176402i \(-0.0564459\pi\)
0.984318 + 0.176402i \(0.0564459\pi\)
\(308\) 0 0
\(309\) 23.2003 1.31982
\(310\) 0 0
\(311\) 15.5789 0.883400 0.441700 0.897163i \(-0.354376\pi\)
0.441700 + 0.897163i \(0.354376\pi\)
\(312\) 0 0
\(313\) −2.98057 −0.168472 −0.0842359 0.996446i \(-0.526845\pi\)
−0.0842359 + 0.996446i \(0.526845\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.5803 0.987409 0.493704 0.869630i \(-0.335643\pi\)
0.493704 + 0.869630i \(0.335643\pi\)
\(318\) 0 0
\(319\) 5.28263 0.295771
\(320\) 0 0
\(321\) −31.9579 −1.78371
\(322\) 0 0
\(323\) 4.66019 0.259300
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 7.76663 0.429496
\(328\) 0 0
\(329\) 19.9169 1.09805
\(330\) 0 0
\(331\) −35.2405 −1.93699 −0.968497 0.249027i \(-0.919889\pi\)
−0.968497 + 0.249027i \(0.919889\pi\)
\(332\) 0 0
\(333\) −12.6465 −0.693025
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9.74145 −0.530650 −0.265325 0.964159i \(-0.585479\pi\)
−0.265325 + 0.964159i \(0.585479\pi\)
\(338\) 0 0
\(339\) −32.3549 −1.75727
\(340\) 0 0
\(341\) 11.0241 0.596987
\(342\) 0 0
\(343\) −1.04678 −0.0565206
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.2028 1.78242 0.891209 0.453594i \(-0.149858\pi\)
0.891209 + 0.453594i \(0.149858\pi\)
\(348\) 0 0
\(349\) −14.7141 −0.787628 −0.393814 0.919190i \(-0.628845\pi\)
−0.393814 + 0.919190i \(0.628845\pi\)
\(350\) 0 0
\(351\) −5.25280 −0.280374
\(352\) 0 0
\(353\) 3.44841 0.183540 0.0917702 0.995780i \(-0.470747\pi\)
0.0917702 + 0.995780i \(0.470747\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −37.6602 −1.99319
\(358\) 0 0
\(359\) 6.55623 0.346025 0.173012 0.984920i \(-0.444650\pi\)
0.173012 + 0.984920i \(0.444650\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 1.90972 0.100234
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 32.5641 1.69983 0.849917 0.526916i \(-0.176652\pi\)
0.849917 + 0.526916i \(0.176652\pi\)
\(368\) 0 0
\(369\) −1.26320 −0.0657596
\(370\) 0 0
\(371\) 0.161136 0.00836578
\(372\) 0 0
\(373\) −15.0137 −0.777379 −0.388689 0.921369i \(-0.627072\pi\)
−0.388689 + 0.921369i \(0.627072\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.22545 0.166119
\(378\) 0 0
\(379\) 12.4807 0.641092 0.320546 0.947233i \(-0.396134\pi\)
0.320546 + 0.947233i \(0.396134\pi\)
\(380\) 0 0
\(381\) −16.7792 −0.859624
\(382\) 0 0
\(383\) 12.5354 0.640530 0.320265 0.947328i \(-0.396228\pi\)
0.320265 + 0.947328i \(0.396228\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.40164 −0.122082
\(388\) 0 0
\(389\) 37.4328 1.89792 0.948960 0.315395i \(-0.102137\pi\)
0.948960 + 0.315395i \(0.102137\pi\)
\(390\) 0 0
\(391\) 24.4153 1.23474
\(392\) 0 0
\(393\) −42.4282 −2.14022
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −3.05718 −0.153435 −0.0767177 0.997053i \(-0.524444\pi\)
−0.0767177 + 0.997053i \(0.524444\pi\)
\(398\) 0 0
\(399\) −8.08126 −0.404569
\(400\) 0 0
\(401\) 18.5458 0.926135 0.463067 0.886323i \(-0.346749\pi\)
0.463067 + 0.886323i \(0.346749\pi\)
\(402\) 0 0
\(403\) 6.73104 0.335297
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.8525 1.13276
\(408\) 0 0
\(409\) 13.9669 0.690619 0.345309 0.938489i \(-0.387774\pi\)
0.345309 + 0.938489i \(0.387774\pi\)
\(410\) 0 0
\(411\) −7.41204 −0.365609
\(412\) 0 0
\(413\) −29.2060 −1.43713
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −23.0629 −1.12940
\(418\) 0 0
\(419\) −32.7623 −1.60054 −0.800270 0.599639i \(-0.795311\pi\)
−0.800270 + 0.599639i \(0.795311\pi\)
\(420\) 0 0
\(421\) 29.5127 1.43836 0.719181 0.694823i \(-0.244517\pi\)
0.719181 + 0.694823i \(0.244517\pi\)
\(422\) 0 0
\(423\) 9.46922 0.460409
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −18.4678 −0.893722
\(428\) 0 0
\(429\) −13.4887 −0.651238
\(430\) 0 0
\(431\) −2.90507 −0.139932 −0.0699662 0.997549i \(-0.522289\pi\)
−0.0699662 + 0.997549i \(0.522289\pi\)
\(432\) 0 0
\(433\) −29.4887 −1.41713 −0.708567 0.705643i \(-0.750658\pi\)
−0.708567 + 0.705643i \(0.750658\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.23912 0.250621
\(438\) 0 0
\(439\) −30.4088 −1.45133 −0.725666 0.688047i \(-0.758468\pi\)
−0.725666 + 0.688047i \(0.758468\pi\)
\(440\) 0 0
\(441\) 11.8285 0.563260
\(442\) 0 0
\(443\) −1.80903 −0.0859496 −0.0429748 0.999076i \(-0.513684\pi\)
−0.0429748 + 0.999076i \(0.513684\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −42.6181 −2.01577
\(448\) 0 0
\(449\) −21.4257 −1.01114 −0.505571 0.862785i \(-0.668718\pi\)
−0.505571 + 0.862785i \(0.668718\pi\)
\(450\) 0 0
\(451\) 2.28263 0.107485
\(452\) 0 0
\(453\) 2.55623 0.120102
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −19.5789 −0.915864 −0.457932 0.888987i \(-0.651410\pi\)
−0.457932 + 0.888987i \(0.651410\pi\)
\(458\) 0 0
\(459\) 12.5997 0.588106
\(460\) 0 0
\(461\) 7.92666 0.369181 0.184591 0.982815i \(-0.440904\pi\)
0.184591 + 0.982815i \(0.440904\pi\)
\(462\) 0 0
\(463\) −11.0298 −0.512600 −0.256300 0.966597i \(-0.582503\pi\)
−0.256300 + 0.966597i \(0.582503\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.48400 0.161220 0.0806102 0.996746i \(-0.474313\pi\)
0.0806102 + 0.996746i \(0.474313\pi\)
\(468\) 0 0
\(469\) 53.7122 2.48020
\(470\) 0 0
\(471\) −10.9324 −0.503739
\(472\) 0 0
\(473\) 4.33981 0.199545
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.0766103 0.00350774
\(478\) 0 0
\(479\) −29.6569 −1.35506 −0.677530 0.735495i \(-0.736949\pi\)
−0.677530 + 0.735495i \(0.736949\pi\)
\(480\) 0 0
\(481\) 13.9532 0.636212
\(482\) 0 0
\(483\) −42.3387 −1.92648
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.65116 −0.210764 −0.105382 0.994432i \(-0.533607\pi\)
−0.105382 + 0.994432i \(0.533607\pi\)
\(488\) 0 0
\(489\) 14.8044 0.669477
\(490\) 0 0
\(491\) −21.6947 −0.979067 −0.489533 0.871985i \(-0.662833\pi\)
−0.489533 + 0.871985i \(0.662833\pi\)
\(492\) 0 0
\(493\) −7.73680 −0.348448
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 18.0949 0.811669
\(498\) 0 0
\(499\) 7.83886 0.350916 0.175458 0.984487i \(-0.443859\pi\)
0.175458 + 0.984487i \(0.443859\pi\)
\(500\) 0 0
\(501\) 12.3204 0.550434
\(502\) 0 0
\(503\) −32.8824 −1.46615 −0.733076 0.680146i \(-0.761916\pi\)
−0.733076 + 0.680146i \(0.761916\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 20.1294 0.893978
\(508\) 0 0
\(509\) −43.5530 −1.93045 −0.965226 0.261418i \(-0.915810\pi\)
−0.965226 + 0.261418i \(0.915810\pi\)
\(510\) 0 0
\(511\) 39.2703 1.73722
\(512\) 0 0
\(513\) 2.70370 0.119371
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −17.1111 −0.752545
\(518\) 0 0
\(519\) −11.7562 −0.516041
\(520\) 0 0
\(521\) −6.34308 −0.277895 −0.138948 0.990300i \(-0.544372\pi\)
−0.138948 + 0.990300i \(0.544372\pi\)
\(522\) 0 0
\(523\) 31.0449 1.35750 0.678749 0.734370i \(-0.262522\pi\)
0.678749 + 0.734370i \(0.262522\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.1456 −0.703312
\(528\) 0 0
\(529\) 4.44841 0.193409
\(530\) 0 0
\(531\) −13.8856 −0.602585
\(532\) 0 0
\(533\) 1.39372 0.0603687
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −7.14995 −0.308543
\(538\) 0 0
\(539\) −21.3743 −0.920656
\(540\) 0 0
\(541\) 34.3218 1.47561 0.737804 0.675015i \(-0.235863\pi\)
0.737804 + 0.675015i \(0.235863\pi\)
\(542\) 0 0
\(543\) 15.2736 0.655453
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −23.5836 −1.00836 −0.504181 0.863598i \(-0.668205\pi\)
−0.504181 + 0.863598i \(0.668205\pi\)
\(548\) 0 0
\(549\) −8.78031 −0.374734
\(550\) 0 0
\(551\) −1.66019 −0.0707265
\(552\) 0 0
\(553\) 55.2211 2.34824
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 44.8824 1.90173 0.950864 0.309610i \(-0.100199\pi\)
0.950864 + 0.309610i \(0.100199\pi\)
\(558\) 0 0
\(559\) 2.64979 0.112074
\(560\) 0 0
\(561\) 32.3549 1.36602
\(562\) 0 0
\(563\) 6.13844 0.258704 0.129352 0.991599i \(-0.458710\pi\)
0.129352 + 0.991599i \(0.458710\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −41.4145 −1.73925
\(568\) 0 0
\(569\) 42.9384 1.80007 0.900037 0.435814i \(-0.143540\pi\)
0.900037 + 0.435814i \(0.143540\pi\)
\(570\) 0 0
\(571\) −3.00576 −0.125787 −0.0628935 0.998020i \(-0.520033\pi\)
−0.0628935 + 0.998020i \(0.520033\pi\)
\(572\) 0 0
\(573\) −0.491920 −0.0205502
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −16.2028 −0.674529 −0.337265 0.941410i \(-0.609502\pi\)
−0.337265 + 0.941410i \(0.609502\pi\)
\(578\) 0 0
\(579\) 17.7278 0.736741
\(580\) 0 0
\(581\) 36.1513 1.49981
\(582\) 0 0
\(583\) −0.138436 −0.00573345
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26.4542 1.09188 0.545940 0.837824i \(-0.316173\pi\)
0.545940 + 0.837824i \(0.316173\pi\)
\(588\) 0 0
\(589\) −3.46457 −0.142755
\(590\) 0 0
\(591\) −9.27936 −0.381702
\(592\) 0 0
\(593\) 25.3710 1.04186 0.520931 0.853599i \(-0.325585\pi\)
0.520931 + 0.853599i \(0.325585\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −57.0780 −2.33605
\(598\) 0 0
\(599\) −3.26896 −0.133566 −0.0667830 0.997768i \(-0.521274\pi\)
−0.0667830 + 0.997768i \(0.521274\pi\)
\(600\) 0 0
\(601\) −27.6465 −1.12772 −0.563862 0.825869i \(-0.690685\pi\)
−0.563862 + 0.825869i \(0.690685\pi\)
\(602\) 0 0
\(603\) 25.5368 1.03994
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −31.6739 −1.28560 −0.642801 0.766033i \(-0.722228\pi\)
−0.642801 + 0.766033i \(0.722228\pi\)
\(608\) 0 0
\(609\) 13.4164 0.543661
\(610\) 0 0
\(611\) −10.4476 −0.422666
\(612\) 0 0
\(613\) −20.1970 −0.815749 −0.407874 0.913038i \(-0.633730\pi\)
−0.407874 + 0.913038i \(0.633730\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 36.4717 1.46830 0.734148 0.678990i \(-0.237582\pi\)
0.734148 + 0.678990i \(0.237582\pi\)
\(618\) 0 0
\(619\) 2.99424 0.120349 0.0601744 0.998188i \(-0.480834\pi\)
0.0601744 + 0.998188i \(0.480834\pi\)
\(620\) 0 0
\(621\) 14.1650 0.568422
\(622\) 0 0
\(623\) 37.3379 1.49591
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 6.94282 0.277270
\(628\) 0 0
\(629\) −33.4692 −1.33451
\(630\) 0 0
\(631\) 33.1683 1.32041 0.660204 0.751086i \(-0.270470\pi\)
0.660204 + 0.751086i \(0.270470\pi\)
\(632\) 0 0
\(633\) −9.32176 −0.370507
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.0506 −0.517085
\(638\) 0 0
\(639\) 8.60301 0.340330
\(640\) 0 0
\(641\) 12.0435 0.475690 0.237845 0.971303i \(-0.423559\pi\)
0.237845 + 0.971303i \(0.423559\pi\)
\(642\) 0 0
\(643\) −22.0000 −0.867595 −0.433798 0.901010i \(-0.642827\pi\)
−0.433798 + 0.901010i \(0.642827\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28.0150 −1.10139 −0.550693 0.834708i \(-0.685636\pi\)
−0.550693 + 0.834708i \(0.685636\pi\)
\(648\) 0 0
\(649\) 25.0917 0.984934
\(650\) 0 0
\(651\) 27.9981 1.09733
\(652\) 0 0
\(653\) 7.85254 0.307294 0.153647 0.988126i \(-0.450898\pi\)
0.153647 + 0.988126i \(0.450898\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 18.6706 0.728409
\(658\) 0 0
\(659\) −29.9590 −1.16704 −0.583518 0.812100i \(-0.698324\pi\)
−0.583518 + 0.812100i \(0.698324\pi\)
\(660\) 0 0
\(661\) −3.42107 −0.133064 −0.0665320 0.997784i \(-0.521193\pi\)
−0.0665320 + 0.997784i \(0.521193\pi\)
\(662\) 0 0
\(663\) 19.7551 0.767225
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.69794 −0.336786
\(668\) 0 0
\(669\) −50.2301 −1.94201
\(670\) 0 0
\(671\) 15.8662 0.612508
\(672\) 0 0
\(673\) 45.5095 1.75426 0.877130 0.480252i \(-0.159455\pi\)
0.877130 + 0.480252i \(0.159455\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.6375 −0.639431 −0.319715 0.947514i \(-0.603587\pi\)
−0.319715 + 0.947514i \(0.603587\pi\)
\(678\) 0 0
\(679\) −54.3354 −2.08520
\(680\) 0 0
\(681\) −19.5653 −0.749742
\(682\) 0 0
\(683\) −15.2463 −0.583382 −0.291691 0.956513i \(-0.594218\pi\)
−0.291691 + 0.956513i \(0.594218\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.8238 0.718173
\(688\) 0 0
\(689\) −0.0845261 −0.00322019
\(690\) 0 0
\(691\) −45.8676 −1.74489 −0.872443 0.488717i \(-0.837465\pi\)
−0.872443 + 0.488717i \(0.837465\pi\)
\(692\) 0 0
\(693\) −20.7518 −0.788298
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.34308 −0.126628
\(698\) 0 0
\(699\) 63.2794 2.39345
\(700\) 0 0
\(701\) −6.59974 −0.249269 −0.124634 0.992203i \(-0.539776\pi\)
−0.124634 + 0.992203i \(0.539776\pi\)
\(702\) 0 0
\(703\) −7.18194 −0.270872
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 59.0859 2.22215
\(708\) 0 0
\(709\) 22.0118 0.826670 0.413335 0.910579i \(-0.364364\pi\)
0.413335 + 0.910579i \(0.364364\pi\)
\(710\) 0 0
\(711\) 26.2542 0.984608
\(712\) 0 0
\(713\) −18.1513 −0.679773
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 51.8025 1.93460
\(718\) 0 0
\(719\) −22.2405 −0.829431 −0.414715 0.909951i \(-0.636119\pi\)
−0.414715 + 0.909951i \(0.636119\pi\)
\(720\) 0 0
\(721\) −39.3808 −1.46662
\(722\) 0 0
\(723\) 13.8033 0.513349
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −37.8662 −1.40438 −0.702190 0.711990i \(-0.747794\pi\)
−0.702190 + 0.711990i \(0.747794\pi\)
\(728\) 0 0
\(729\) −1.99208 −0.0737809
\(730\) 0 0
\(731\) −6.35597 −0.235084
\(732\) 0 0
\(733\) −5.02735 −0.185689 −0.0928446 0.995681i \(-0.529596\pi\)
−0.0928446 + 0.995681i \(0.529596\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −46.1456 −1.69979
\(738\) 0 0
\(739\) 31.6159 1.16301 0.581505 0.813543i \(-0.302464\pi\)
0.581505 + 0.813543i \(0.302464\pi\)
\(740\) 0 0
\(741\) 4.23912 0.155728
\(742\) 0 0
\(743\) 33.8252 1.24093 0.620463 0.784236i \(-0.286945\pi\)
0.620463 + 0.784236i \(0.286945\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 17.1877 0.628865
\(748\) 0 0
\(749\) 54.2463 1.98212
\(750\) 0 0
\(751\) −45.5368 −1.66166 −0.830831 0.556525i \(-0.812134\pi\)
−0.830831 + 0.556525i \(0.812134\pi\)
\(752\) 0 0
\(753\) 47.8285 1.74297
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 4.55950 0.165718 0.0828590 0.996561i \(-0.473595\pi\)
0.0828590 + 0.996561i \(0.473595\pi\)
\(758\) 0 0
\(759\) 36.3743 1.32030
\(760\) 0 0
\(761\) −51.4386 −1.86465 −0.932324 0.361624i \(-0.882222\pi\)
−0.932324 + 0.361624i \(0.882222\pi\)
\(762\) 0 0
\(763\) −13.1833 −0.477268
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.3204 0.553187
\(768\) 0 0
\(769\) 9.34773 0.337088 0.168544 0.985694i \(-0.446094\pi\)
0.168544 + 0.985694i \(0.446094\pi\)
\(770\) 0 0
\(771\) −7.22761 −0.260296
\(772\) 0 0
\(773\) −19.4887 −0.700958 −0.350479 0.936571i \(-0.613981\pi\)
−0.350479 + 0.936571i \(0.613981\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 58.0391 2.08214
\(778\) 0 0
\(779\) −0.717370 −0.0257024
\(780\) 0 0
\(781\) −15.5458 −0.556274
\(782\) 0 0
\(783\) −4.48865 −0.160411
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5.32941 −0.189973 −0.0949864 0.995479i \(-0.530281\pi\)
−0.0949864 + 0.995479i \(0.530281\pi\)
\(788\) 0 0
\(789\) 5.09277 0.181307
\(790\) 0 0
\(791\) 54.9201 1.95273
\(792\) 0 0
\(793\) 9.68754 0.344014
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.7220 −1.33618 −0.668091 0.744079i \(-0.732888\pi\)
−0.668091 + 0.744079i \(0.732888\pi\)
\(798\) 0 0
\(799\) 25.0604 0.886575
\(800\) 0 0
\(801\) 17.7518 0.627231
\(802\) 0 0
\(803\) −33.7382 −1.19059
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 53.6298 1.88786
\(808\) 0 0
\(809\) 31.0071 1.09015 0.545076 0.838386i \(-0.316501\pi\)
0.545076 + 0.838386i \(0.316501\pi\)
\(810\) 0 0
\(811\) 26.7738 0.940154 0.470077 0.882625i \(-0.344226\pi\)
0.470077 + 0.882625i \(0.344226\pi\)
\(812\) 0 0
\(813\) −35.7576 −1.25407
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.36389 −0.0477164
\(818\) 0 0
\(819\) −12.6706 −0.442746
\(820\) 0 0
\(821\) 24.2873 0.847632 0.423816 0.905748i \(-0.360690\pi\)
0.423816 + 0.905748i \(0.360690\pi\)
\(822\) 0 0
\(823\) −0.828460 −0.0288783 −0.0144392 0.999896i \(-0.504596\pi\)
−0.0144392 + 0.999896i \(0.504596\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 42.3387 1.47226 0.736130 0.676840i \(-0.236651\pi\)
0.736130 + 0.676840i \(0.236651\pi\)
\(828\) 0 0
\(829\) −3.20602 −0.111350 −0.0556748 0.998449i \(-0.517731\pi\)
−0.0556748 + 0.998449i \(0.517731\pi\)
\(830\) 0 0
\(831\) −18.9486 −0.657319
\(832\) 0 0
\(833\) 31.3042 1.08463
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −9.36716 −0.323776
\(838\) 0 0
\(839\) −20.2520 −0.699177 −0.349589 0.936903i \(-0.613679\pi\)
−0.349589 + 0.936903i \(0.613679\pi\)
\(840\) 0 0
\(841\) −26.2438 −0.904958
\(842\) 0 0
\(843\) 0.983839 0.0338852
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −3.24161 −0.111383
\(848\) 0 0
\(849\) 62.5152 2.14552
\(850\) 0 0
\(851\) −37.6271 −1.28984
\(852\) 0 0
\(853\) 3.10644 0.106363 0.0531813 0.998585i \(-0.483064\pi\)
0.0531813 + 0.998585i \(0.483064\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8.89467 0.303836 0.151918 0.988393i \(-0.451455\pi\)
0.151918 + 0.988393i \(0.451455\pi\)
\(858\) 0 0
\(859\) −17.9989 −0.614114 −0.307057 0.951691i \(-0.599344\pi\)
−0.307057 + 0.951691i \(0.599344\pi\)
\(860\) 0 0
\(861\) 5.79725 0.197570
\(862\) 0 0
\(863\) 43.9291 1.49537 0.747683 0.664056i \(-0.231166\pi\)
0.747683 + 0.664056i \(0.231166\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −10.2930 −0.349570
\(868\) 0 0
\(869\) −47.4419 −1.60936
\(870\) 0 0
\(871\) −28.1754 −0.954687
\(872\) 0 0
\(873\) −25.8331 −0.874318
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −4.55375 −0.153769 −0.0768845 0.997040i \(-0.524497\pi\)
−0.0768845 + 0.997040i \(0.524497\pi\)
\(878\) 0 0
\(879\) 45.2394 1.52589
\(880\) 0 0
\(881\) 2.71272 0.0913940 0.0456970 0.998955i \(-0.485449\pi\)
0.0456970 + 0.998955i \(0.485449\pi\)
\(882\) 0 0
\(883\) −9.92588 −0.334032 −0.167016 0.985954i \(-0.553413\pi\)
−0.167016 + 0.985954i \(0.553413\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −52.7018 −1.76955 −0.884777 0.466015i \(-0.845689\pi\)
−0.884777 + 0.466015i \(0.845689\pi\)
\(888\) 0 0
\(889\) 28.4815 0.955239
\(890\) 0 0
\(891\) 35.5803 1.19199
\(892\) 0 0
\(893\) 5.37756 0.179953
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 22.2093 0.741547
\(898\) 0 0
\(899\) 5.75185 0.191835
\(900\) 0 0
\(901\) 0.202750 0.00675459
\(902\) 0 0
\(903\) 11.0219 0.366786
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −37.3743 −1.24099 −0.620496 0.784209i \(-0.713069\pi\)
−0.620496 + 0.784209i \(0.713069\pi\)
\(908\) 0 0
\(909\) 28.0917 0.931742
\(910\) 0 0
\(911\) −47.6752 −1.57955 −0.789776 0.613396i \(-0.789803\pi\)
−0.789776 + 0.613396i \(0.789803\pi\)
\(912\) 0 0
\(913\) −31.0586 −1.02789
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 72.0189 2.37827
\(918\) 0 0
\(919\) −35.8605 −1.18293 −0.591464 0.806332i \(-0.701450\pi\)
−0.591464 + 0.806332i \(0.701450\pi\)
\(920\) 0 0
\(921\) −75.2624 −2.47998
\(922\) 0 0
\(923\) −9.49192 −0.312430
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −18.7231 −0.614948
\(928\) 0 0
\(929\) −55.1229 −1.80852 −0.904261 0.426979i \(-0.859578\pi\)
−0.904261 + 0.426979i \(0.859578\pi\)
\(930\) 0 0
\(931\) 6.71737 0.220153
\(932\) 0 0
\(933\) −33.9923 −1.11286
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 53.3333 1.74232 0.871161 0.490997i \(-0.163368\pi\)
0.871161 + 0.490997i \(0.163368\pi\)
\(938\) 0 0
\(939\) 6.50343 0.212232
\(940\) 0 0
\(941\) 29.7335 0.969285 0.484643 0.874712i \(-0.338950\pi\)
0.484643 + 0.874712i \(0.338950\pi\)
\(942\) 0 0
\(943\) −3.75839 −0.122390
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 39.4821 1.28300 0.641498 0.767125i \(-0.278313\pi\)
0.641498 + 0.767125i \(0.278313\pi\)
\(948\) 0 0
\(949\) −20.5997 −0.668696
\(950\) 0 0
\(951\) −38.3592 −1.24388
\(952\) 0 0
\(953\) 15.8479 0.513364 0.256682 0.966496i \(-0.417371\pi\)
0.256682 + 0.966496i \(0.417371\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −11.5264 −0.372596
\(958\) 0 0
\(959\) 12.5814 0.406275
\(960\) 0 0
\(961\) −18.9967 −0.612798
\(962\) 0 0
\(963\) 25.7907 0.831094
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 20.2150 0.650072 0.325036 0.945702i \(-0.394624\pi\)
0.325036 + 0.945702i \(0.394624\pi\)
\(968\) 0 0
\(969\) −10.1683 −0.326652
\(970\) 0 0
\(971\) −26.8903 −0.862950 −0.431475 0.902125i \(-0.642007\pi\)
−0.431475 + 0.902125i \(0.642007\pi\)
\(972\) 0 0
\(973\) 39.1477 1.25502
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18.6432 −0.596450 −0.298225 0.954496i \(-0.596395\pi\)
−0.298225 + 0.954496i \(0.596395\pi\)
\(978\) 0 0
\(979\) −32.0780 −1.02522
\(980\) 0 0
\(981\) −6.26785 −0.200117
\(982\) 0 0
\(983\) 36.7713 1.17282 0.586411 0.810014i \(-0.300540\pi\)
0.586411 + 0.810014i \(0.300540\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −43.4574 −1.38327
\(988\) 0 0
\(989\) −7.14557 −0.227216
\(990\) 0 0
\(991\) −60.0197 −1.90659 −0.953294 0.302043i \(-0.902331\pi\)
−0.953294 + 0.302043i \(0.902331\pi\)
\(992\) 0 0
\(993\) 76.8928 2.44012
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 28.8364 0.913257 0.456629 0.889657i \(-0.349057\pi\)
0.456629 + 0.889657i \(0.349057\pi\)
\(998\) 0 0
\(999\) −19.4178 −0.614352
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.i.1.1 yes 3
4.3 odd 2 7600.2.a.bl.1.3 3
5.2 odd 4 1900.2.c.f.1749.5 6
5.3 odd 4 1900.2.c.f.1749.2 6
5.4 even 2 1900.2.a.g.1.3 3
20.19 odd 2 7600.2.a.ca.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1900.2.a.g.1.3 3 5.4 even 2
1900.2.a.i.1.1 yes 3 1.1 even 1 trivial
1900.2.c.f.1749.2 6 5.3 odd 4
1900.2.c.f.1749.5 6 5.2 odd 4
7600.2.a.bl.1.3 3 4.3 odd 2
7600.2.a.ca.1.1 3 20.19 odd 2