Properties

Label 1200.4.a.bt.1.2
Level $1200$
Weight $4$
Character 1200.1
Self dual yes
Analytic conductor $70.802$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(70.8022920069\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 15)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.70156\) of defining polynomial
Character \(\chi\) \(=\) 1200.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} +22.2094 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +22.2094 q^{7} +9.00000 q^{9} +1.79063 q^{11} -58.2094 q^{13} -18.9844 q^{17} -104.837 q^{19} +66.6281 q^{21} -49.6125 q^{23} +27.0000 q^{27} -293.466 q^{29} -64.4187 q^{31} +5.37188 q^{33} +19.8844 q^{37} -174.628 q^{39} -165.581 q^{41} -247.350 q^{43} +384.544 q^{47} +150.256 q^{49} -56.9531 q^{51} -463.528 q^{53} -314.512 q^{57} +73.7906 q^{59} -137.350 q^{61} +199.884 q^{63} +173.906 q^{67} -148.837 q^{69} +594.281 q^{71} -320.231 q^{73} +39.7687 q^{77} +770.469 q^{79} +81.0000 q^{81} +173.925 q^{83} -880.397 q^{87} +1019.02 q^{89} -1292.79 q^{91} -193.256 q^{93} -384.375 q^{97} +16.1156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{3} + 6 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{3} + 6 q^{7} + 18 q^{9} + 42 q^{11} - 78 q^{13} - 102 q^{17} - 56 q^{19} + 18 q^{21} - 48 q^{23} + 54 q^{27} - 318 q^{29} - 52 q^{31} + 126 q^{33} - 306 q^{37} - 234 q^{39} - 408 q^{41} + 120 q^{43} + 180 q^{47} + 70 q^{49} - 306 q^{51} - 402 q^{53} - 168 q^{57} + 186 q^{59} + 340 q^{61} + 54 q^{63} + 732 q^{67} - 144 q^{69} + 36 q^{71} - 1332 q^{73} - 612 q^{77} - 380 q^{79} + 162 q^{81} - 984 q^{83} - 954 q^{87} + 1116 q^{89} - 972 q^{91} - 156 q^{93} + 768 q^{97} + 378 q^{99}+O(q^{100}) \) 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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 22.2094 1.19919 0.599597 0.800302i \(-0.295328\pi\)
0.599597 + 0.800302i \(0.295328\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 1.79063 0.0490813 0.0245407 0.999699i \(-0.492188\pi\)
0.0245407 + 0.999699i \(0.492188\pi\)
\(12\) 0 0
\(13\) −58.2094 −1.24188 −0.620938 0.783860i \(-0.713248\pi\)
−0.620938 + 0.783860i \(0.713248\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −18.9844 −0.270846 −0.135423 0.990788i \(-0.543239\pi\)
−0.135423 + 0.990788i \(0.543239\pi\)
\(18\) 0 0
\(19\) −104.837 −1.26586 −0.632931 0.774208i \(-0.718148\pi\)
−0.632931 + 0.774208i \(0.718148\pi\)
\(20\) 0 0
\(21\) 66.6281 0.692355
\(22\) 0 0
\(23\) −49.6125 −0.449779 −0.224890 0.974384i \(-0.572202\pi\)
−0.224890 + 0.974384i \(0.572202\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −293.466 −1.87914 −0.939572 0.342350i \(-0.888777\pi\)
−0.939572 + 0.342350i \(0.888777\pi\)
\(30\) 0 0
\(31\) −64.4187 −0.373224 −0.186612 0.982434i \(-0.559751\pi\)
−0.186612 + 0.982434i \(0.559751\pi\)
\(32\) 0 0
\(33\) 5.37188 0.0283371
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 19.8844 0.0883505 0.0441752 0.999024i \(-0.485934\pi\)
0.0441752 + 0.999024i \(0.485934\pi\)
\(38\) 0 0
\(39\) −174.628 −0.716997
\(40\) 0 0
\(41\) −165.581 −0.630718 −0.315359 0.948972i \(-0.602125\pi\)
−0.315359 + 0.948972i \(0.602125\pi\)
\(42\) 0 0
\(43\) −247.350 −0.877221 −0.438611 0.898677i \(-0.644529\pi\)
−0.438611 + 0.898677i \(0.644529\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 384.544 1.19344 0.596718 0.802451i \(-0.296471\pi\)
0.596718 + 0.802451i \(0.296471\pi\)
\(48\) 0 0
\(49\) 150.256 0.438065
\(50\) 0 0
\(51\) −56.9531 −0.156373
\(52\) 0 0
\(53\) −463.528 −1.20133 −0.600665 0.799501i \(-0.705097\pi\)
−0.600665 + 0.799501i \(0.705097\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −314.512 −0.730846
\(58\) 0 0
\(59\) 73.7906 0.162826 0.0814129 0.996680i \(-0.474057\pi\)
0.0814129 + 0.996680i \(0.474057\pi\)
\(60\) 0 0
\(61\) −137.350 −0.288293 −0.144146 0.989556i \(-0.546044\pi\)
−0.144146 + 0.989556i \(0.546044\pi\)
\(62\) 0 0
\(63\) 199.884 0.399731
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 173.906 0.317105 0.158552 0.987351i \(-0.449317\pi\)
0.158552 + 0.987351i \(0.449317\pi\)
\(68\) 0 0
\(69\) −148.837 −0.259680
\(70\) 0 0
\(71\) 594.281 0.993355 0.496677 0.867935i \(-0.334553\pi\)
0.496677 + 0.867935i \(0.334553\pi\)
\(72\) 0 0
\(73\) −320.231 −0.513428 −0.256714 0.966487i \(-0.582640\pi\)
−0.256714 + 0.966487i \(0.582640\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 39.7687 0.0588580
\(78\) 0 0
\(79\) 770.469 1.09727 0.548636 0.836061i \(-0.315147\pi\)
0.548636 + 0.836061i \(0.315147\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 173.925 0.230009 0.115004 0.993365i \(-0.463312\pi\)
0.115004 + 0.993365i \(0.463312\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −880.397 −1.08492
\(88\) 0 0
\(89\) 1019.02 1.21367 0.606834 0.794829i \(-0.292439\pi\)
0.606834 + 0.794829i \(0.292439\pi\)
\(90\) 0 0
\(91\) −1292.79 −1.48925
\(92\) 0 0
\(93\) −193.256 −0.215481
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −384.375 −0.402344 −0.201172 0.979556i \(-0.564475\pi\)
−0.201172 + 0.979556i \(0.564475\pi\)
\(98\) 0 0
\(99\) 16.1156 0.0163604
\(100\) 0 0
\(101\) 34.4906 0.0339796 0.0169898 0.999856i \(-0.494592\pi\)
0.0169898 + 0.999856i \(0.494592\pi\)
\(102\) 0 0
\(103\) −1756.30 −1.68013 −0.840066 0.542484i \(-0.817484\pi\)
−0.840066 + 0.542484i \(0.817484\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1361.74 −1.23032 −0.615159 0.788403i \(-0.710908\pi\)
−0.615159 + 0.788403i \(0.710908\pi\)
\(108\) 0 0
\(109\) 321.119 0.282180 0.141090 0.989997i \(-0.454939\pi\)
0.141090 + 0.989997i \(0.454939\pi\)
\(110\) 0 0
\(111\) 59.6531 0.0510092
\(112\) 0 0
\(113\) 1582.25 1.31721 0.658607 0.752487i \(-0.271146\pi\)
0.658607 + 0.752487i \(0.271146\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −523.884 −0.413958
\(118\) 0 0
\(119\) −421.631 −0.324797
\(120\) 0 0
\(121\) −1327.79 −0.997591
\(122\) 0 0
\(123\) −496.744 −0.364145
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1197.14 −0.836449 −0.418225 0.908344i \(-0.637348\pi\)
−0.418225 + 0.908344i \(0.637348\pi\)
\(128\) 0 0
\(129\) −742.050 −0.506464
\(130\) 0 0
\(131\) 321.647 0.214522 0.107261 0.994231i \(-0.465792\pi\)
0.107261 + 0.994231i \(0.465792\pi\)
\(132\) 0 0
\(133\) −2328.37 −1.51801
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −354.291 −0.220942 −0.110471 0.993879i \(-0.535236\pi\)
−0.110471 + 0.993879i \(0.535236\pi\)
\(138\) 0 0
\(139\) −77.2562 −0.0471424 −0.0235712 0.999722i \(-0.507504\pi\)
−0.0235712 + 0.999722i \(0.507504\pi\)
\(140\) 0 0
\(141\) 1153.63 0.689030
\(142\) 0 0
\(143\) −104.231 −0.0609529
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 450.769 0.252917
\(148\) 0 0
\(149\) −1705.38 −0.937651 −0.468826 0.883291i \(-0.655323\pi\)
−0.468826 + 0.883291i \(0.655323\pi\)
\(150\) 0 0
\(151\) −758.281 −0.408663 −0.204331 0.978902i \(-0.565502\pi\)
−0.204331 + 0.978902i \(0.565502\pi\)
\(152\) 0 0
\(153\) −170.859 −0.0902821
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1769.05 0.899273 0.449636 0.893212i \(-0.351554\pi\)
0.449636 + 0.893212i \(0.351554\pi\)
\(158\) 0 0
\(159\) −1390.58 −0.693588
\(160\) 0 0
\(161\) −1101.86 −0.539372
\(162\) 0 0
\(163\) −881.719 −0.423690 −0.211845 0.977303i \(-0.567947\pi\)
−0.211845 + 0.977303i \(0.567947\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −216.900 −0.100504 −0.0502522 0.998737i \(-0.516003\pi\)
−0.0502522 + 0.998737i \(0.516003\pi\)
\(168\) 0 0
\(169\) 1191.33 0.542254
\(170\) 0 0
\(171\) −943.537 −0.421954
\(172\) 0 0
\(173\) −4125.91 −1.81322 −0.906610 0.421970i \(-0.861339\pi\)
−0.906610 + 0.421970i \(0.861339\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 221.372 0.0940075
\(178\) 0 0
\(179\) 3213.14 1.34168 0.670842 0.741600i \(-0.265933\pi\)
0.670842 + 0.741600i \(0.265933\pi\)
\(180\) 0 0
\(181\) 3394.42 1.39395 0.696976 0.717095i \(-0.254529\pi\)
0.696976 + 0.717095i \(0.254529\pi\)
\(182\) 0 0
\(183\) −412.050 −0.166446
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −33.9939 −0.0132935
\(188\) 0 0
\(189\) 599.653 0.230785
\(190\) 0 0
\(191\) 3467.49 1.31361 0.656804 0.754062i \(-0.271908\pi\)
0.656804 + 0.754062i \(0.271908\pi\)
\(192\) 0 0
\(193\) −1792.14 −0.668401 −0.334200 0.942502i \(-0.608466\pi\)
−0.334200 + 0.942502i \(0.608466\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1678.19 −0.606935 −0.303467 0.952842i \(-0.598144\pi\)
−0.303467 + 0.952842i \(0.598144\pi\)
\(198\) 0 0
\(199\) −3108.23 −1.10722 −0.553610 0.832776i \(-0.686750\pi\)
−0.553610 + 0.832776i \(0.686750\pi\)
\(200\) 0 0
\(201\) 521.719 0.183081
\(202\) 0 0
\(203\) −6517.69 −2.25346
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −446.512 −0.149926
\(208\) 0 0
\(209\) −187.725 −0.0621301
\(210\) 0 0
\(211\) 4473.27 1.45949 0.729745 0.683719i \(-0.239639\pi\)
0.729745 + 0.683719i \(0.239639\pi\)
\(212\) 0 0
\(213\) 1782.84 0.573514
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1430.70 −0.447568
\(218\) 0 0
\(219\) −960.694 −0.296428
\(220\) 0 0
\(221\) 1105.07 0.336357
\(222\) 0 0
\(223\) −1753.42 −0.526535 −0.263268 0.964723i \(-0.584800\pi\)
−0.263268 + 0.964723i \(0.584800\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −936.900 −0.273939 −0.136970 0.990575i \(-0.543736\pi\)
−0.136970 + 0.990575i \(0.543736\pi\)
\(228\) 0 0
\(229\) −2582.06 −0.745096 −0.372548 0.928013i \(-0.621516\pi\)
−0.372548 + 0.928013i \(0.621516\pi\)
\(230\) 0 0
\(231\) 119.306 0.0339817
\(232\) 0 0
\(233\) −2295.01 −0.645284 −0.322642 0.946521i \(-0.604571\pi\)
−0.322642 + 0.946521i \(0.604571\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2311.41 0.633510
\(238\) 0 0
\(239\) 2294.01 0.620866 0.310433 0.950595i \(-0.399526\pi\)
0.310433 + 0.950595i \(0.399526\pi\)
\(240\) 0 0
\(241\) 382.287 0.102180 0.0510898 0.998694i \(-0.483731\pi\)
0.0510898 + 0.998694i \(0.483731\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6102.52 1.57204
\(248\) 0 0
\(249\) 521.775 0.132796
\(250\) 0 0
\(251\) 2259.98 0.568322 0.284161 0.958777i \(-0.408285\pi\)
0.284161 + 0.958777i \(0.408285\pi\)
\(252\) 0 0
\(253\) −88.8375 −0.0220758
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 92.7843 0.0225203 0.0112602 0.999937i \(-0.496416\pi\)
0.0112602 + 0.999937i \(0.496416\pi\)
\(258\) 0 0
\(259\) 441.619 0.105949
\(260\) 0 0
\(261\) −2641.19 −0.626382
\(262\) 0 0
\(263\) −568.312 −0.133246 −0.0666229 0.997778i \(-0.521222\pi\)
−0.0666229 + 0.997778i \(0.521222\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3057.07 0.700711
\(268\) 0 0
\(269\) 7582.41 1.71862 0.859309 0.511458i \(-0.170894\pi\)
0.859309 + 0.511458i \(0.170894\pi\)
\(270\) 0 0
\(271\) −7943.69 −1.78061 −0.890304 0.455366i \(-0.849508\pi\)
−0.890304 + 0.455366i \(0.849508\pi\)
\(272\) 0 0
\(273\) −3878.38 −0.859818
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6823.00 −1.47998 −0.739990 0.672618i \(-0.765170\pi\)
−0.739990 + 0.672618i \(0.765170\pi\)
\(278\) 0 0
\(279\) −579.769 −0.124408
\(280\) 0 0
\(281\) 3315.86 0.703942 0.351971 0.936011i \(-0.385512\pi\)
0.351971 + 0.936011i \(0.385512\pi\)
\(282\) 0 0
\(283\) 6602.76 1.38690 0.693451 0.720504i \(-0.256090\pi\)
0.693451 + 0.720504i \(0.256090\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3677.46 −0.756353
\(288\) 0 0
\(289\) −4552.59 −0.926642
\(290\) 0 0
\(291\) −1153.12 −0.232293
\(292\) 0 0
\(293\) −5814.14 −1.15927 −0.579634 0.814877i \(-0.696805\pi\)
−0.579634 + 0.814877i \(0.696805\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 48.3469 0.00944570
\(298\) 0 0
\(299\) 2887.91 0.558570
\(300\) 0 0
\(301\) −5493.49 −1.05196
\(302\) 0 0
\(303\) 103.472 0.0196181
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −8124.86 −1.51046 −0.755229 0.655462i \(-0.772474\pi\)
−0.755229 + 0.655462i \(0.772474\pi\)
\(308\) 0 0
\(309\) −5268.91 −0.970025
\(310\) 0 0
\(311\) −7336.26 −1.33762 −0.668812 0.743432i \(-0.733197\pi\)
−0.668812 + 0.743432i \(0.733197\pi\)
\(312\) 0 0
\(313\) 2202.66 0.397768 0.198884 0.980023i \(-0.436268\pi\)
0.198884 + 0.980023i \(0.436268\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10008.9 −1.77336 −0.886679 0.462386i \(-0.846993\pi\)
−0.886679 + 0.462386i \(0.846993\pi\)
\(318\) 0 0
\(319\) −525.488 −0.0922309
\(320\) 0 0
\(321\) −4085.21 −0.710325
\(322\) 0 0
\(323\) 1990.27 0.342854
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 963.356 0.162917
\(328\) 0 0
\(329\) 8540.47 1.43116
\(330\) 0 0
\(331\) 8695.94 1.44402 0.722012 0.691881i \(-0.243218\pi\)
0.722012 + 0.691881i \(0.243218\pi\)
\(332\) 0 0
\(333\) 178.959 0.0294502
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 7400.61 1.19625 0.598126 0.801402i \(-0.295912\pi\)
0.598126 + 0.801402i \(0.295912\pi\)
\(338\) 0 0
\(339\) 4746.74 0.760494
\(340\) 0 0
\(341\) −115.350 −0.0183183
\(342\) 0 0
\(343\) −4280.72 −0.673869
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7841.44 1.21311 0.606557 0.795040i \(-0.292550\pi\)
0.606557 + 0.795040i \(0.292550\pi\)
\(348\) 0 0
\(349\) −4961.26 −0.760946 −0.380473 0.924792i \(-0.624239\pi\)
−0.380473 + 0.924792i \(0.624239\pi\)
\(350\) 0 0
\(351\) −1571.65 −0.238999
\(352\) 0 0
\(353\) 12163.0 1.83392 0.916959 0.398981i \(-0.130636\pi\)
0.916959 + 0.398981i \(0.130636\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1264.89 −0.187522
\(358\) 0 0
\(359\) −5193.79 −0.763559 −0.381779 0.924253i \(-0.624689\pi\)
−0.381779 + 0.924253i \(0.624689\pi\)
\(360\) 0 0
\(361\) 4131.90 0.602406
\(362\) 0 0
\(363\) −3983.38 −0.575959
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −6086.09 −0.865644 −0.432822 0.901479i \(-0.642482\pi\)
−0.432822 + 0.901479i \(0.642482\pi\)
\(368\) 0 0
\(369\) −1490.23 −0.210239
\(370\) 0 0
\(371\) −10294.7 −1.44063
\(372\) 0 0
\(373\) 10581.9 1.46893 0.734466 0.678646i \(-0.237433\pi\)
0.734466 + 0.678646i \(0.237433\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 17082.4 2.33366
\(378\) 0 0
\(379\) −11655.2 −1.57964 −0.789822 0.613336i \(-0.789827\pi\)
−0.789822 + 0.613336i \(0.789827\pi\)
\(380\) 0 0
\(381\) −3591.42 −0.482924
\(382\) 0 0
\(383\) 6364.97 0.849177 0.424588 0.905387i \(-0.360419\pi\)
0.424588 + 0.905387i \(0.360419\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2226.15 −0.292407
\(388\) 0 0
\(389\) 6134.33 0.799545 0.399773 0.916614i \(-0.369089\pi\)
0.399773 + 0.916614i \(0.369089\pi\)
\(390\) 0 0
\(391\) 941.862 0.121821
\(392\) 0 0
\(393\) 964.941 0.123855
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9746.46 −1.23214 −0.616072 0.787690i \(-0.711277\pi\)
−0.616072 + 0.787690i \(0.711277\pi\)
\(398\) 0 0
\(399\) −6985.12 −0.876425
\(400\) 0 0
\(401\) −1306.44 −0.162695 −0.0813474 0.996686i \(-0.525922\pi\)
−0.0813474 + 0.996686i \(0.525922\pi\)
\(402\) 0 0
\(403\) 3749.77 0.463498
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 35.6055 0.00433636
\(408\) 0 0
\(409\) −3876.93 −0.468709 −0.234354 0.972151i \(-0.575298\pi\)
−0.234354 + 0.972151i \(0.575298\pi\)
\(410\) 0 0
\(411\) −1062.87 −0.127561
\(412\) 0 0
\(413\) 1638.84 0.195260
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −231.769 −0.0272177
\(418\) 0 0
\(419\) 16022.5 1.86814 0.934071 0.357088i \(-0.116230\pi\)
0.934071 + 0.357088i \(0.116230\pi\)
\(420\) 0 0
\(421\) −8119.73 −0.939980 −0.469990 0.882672i \(-0.655742\pi\)
−0.469990 + 0.882672i \(0.655742\pi\)
\(422\) 0 0
\(423\) 3460.89 0.397812
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3050.46 −0.345719
\(428\) 0 0
\(429\) −312.694 −0.0351911
\(430\) 0 0
\(431\) 5713.99 0.638592 0.319296 0.947655i \(-0.396554\pi\)
0.319296 + 0.947655i \(0.396554\pi\)
\(432\) 0 0
\(433\) −6251.34 −0.693811 −0.346906 0.937900i \(-0.612768\pi\)
−0.346906 + 0.937900i \(0.612768\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5201.25 0.569358
\(438\) 0 0
\(439\) 4230.97 0.459984 0.229992 0.973192i \(-0.426130\pi\)
0.229992 + 0.973192i \(0.426130\pi\)
\(440\) 0 0
\(441\) 1352.31 0.146022
\(442\) 0 0
\(443\) 6314.29 0.677203 0.338601 0.940930i \(-0.390046\pi\)
0.338601 + 0.940930i \(0.390046\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −5116.13 −0.541353
\(448\) 0 0
\(449\) −9349.71 −0.982717 −0.491358 0.870957i \(-0.663499\pi\)
−0.491358 + 0.870957i \(0.663499\pi\)
\(450\) 0 0
\(451\) −296.494 −0.0309565
\(452\) 0 0
\(453\) −2274.84 −0.235941
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9547.46 0.977268 0.488634 0.872489i \(-0.337495\pi\)
0.488634 + 0.872489i \(0.337495\pi\)
\(458\) 0 0
\(459\) −512.578 −0.0521244
\(460\) 0 0
\(461\) 6237.23 0.630145 0.315073 0.949068i \(-0.397971\pi\)
0.315073 + 0.949068i \(0.397971\pi\)
\(462\) 0 0
\(463\) 6469.98 0.649428 0.324714 0.945812i \(-0.394732\pi\)
0.324714 + 0.945812i \(0.394732\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7206.64 0.714097 0.357049 0.934086i \(-0.383783\pi\)
0.357049 + 0.934086i \(0.383783\pi\)
\(468\) 0 0
\(469\) 3862.35 0.380270
\(470\) 0 0
\(471\) 5307.16 0.519195
\(472\) 0 0
\(473\) −442.912 −0.0430552
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4171.75 −0.400443
\(478\) 0 0
\(479\) 10851.8 1.03514 0.517571 0.855640i \(-0.326836\pi\)
0.517571 + 0.855640i \(0.326836\pi\)
\(480\) 0 0
\(481\) −1157.46 −0.109720
\(482\) 0 0
\(483\) −3305.59 −0.311407
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12757.1 1.18702 0.593510 0.804827i \(-0.297742\pi\)
0.593510 + 0.804827i \(0.297742\pi\)
\(488\) 0 0
\(489\) −2645.16 −0.244618
\(490\) 0 0
\(491\) 7016.52 0.644911 0.322455 0.946585i \(-0.395492\pi\)
0.322455 + 0.946585i \(0.395492\pi\)
\(492\) 0 0
\(493\) 5571.26 0.508960
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13198.6 1.19122
\(498\) 0 0
\(499\) −11372.3 −1.02023 −0.510113 0.860107i \(-0.670396\pi\)
−0.510113 + 0.860107i \(0.670396\pi\)
\(500\) 0 0
\(501\) −650.700 −0.0580262
\(502\) 0 0
\(503\) −5587.37 −0.495285 −0.247643 0.968851i \(-0.579656\pi\)
−0.247643 + 0.968851i \(0.579656\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3573.99 0.313070
\(508\) 0 0
\(509\) 16256.7 1.41565 0.707825 0.706388i \(-0.249676\pi\)
0.707825 + 0.706388i \(0.249676\pi\)
\(510\) 0 0
\(511\) −7112.14 −0.615699
\(512\) 0 0
\(513\) −2830.61 −0.243615
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 688.574 0.0585754
\(518\) 0 0
\(519\) −12377.7 −1.04686
\(520\) 0 0
\(521\) 19748.4 1.66064 0.830320 0.557286i \(-0.188157\pi\)
0.830320 + 0.557286i \(0.188157\pi\)
\(522\) 0 0
\(523\) −7843.44 −0.655774 −0.327887 0.944717i \(-0.606337\pi\)
−0.327887 + 0.944717i \(0.606337\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1222.95 0.101086
\(528\) 0 0
\(529\) −9705.60 −0.797699
\(530\) 0 0
\(531\) 664.116 0.0542753
\(532\) 0 0
\(533\) 9638.38 0.783273
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9639.42 0.774622
\(538\) 0 0
\(539\) 269.053 0.0215008
\(540\) 0 0
\(541\) 7383.29 0.586751 0.293376 0.955997i \(-0.405221\pi\)
0.293376 + 0.955997i \(0.405221\pi\)
\(542\) 0 0
\(543\) 10183.3 0.804798
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3354.90 −0.262240 −0.131120 0.991367i \(-0.541857\pi\)
−0.131120 + 0.991367i \(0.541857\pi\)
\(548\) 0 0
\(549\) −1236.15 −0.0960976
\(550\) 0 0
\(551\) 30766.2 2.37874
\(552\) 0 0
\(553\) 17111.6 1.31584
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20771.8 −1.58012 −0.790061 0.613028i \(-0.789951\pi\)
−0.790061 + 0.613028i \(0.789951\pi\)
\(558\) 0 0
\(559\) 14398.1 1.08940
\(560\) 0 0
\(561\) −101.982 −0.00767500
\(562\) 0 0
\(563\) 7194.86 0.538592 0.269296 0.963057i \(-0.413209\pi\)
0.269296 + 0.963057i \(0.413209\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1798.96 0.133244
\(568\) 0 0
\(569\) 11549.5 0.850931 0.425466 0.904975i \(-0.360110\pi\)
0.425466 + 0.904975i \(0.360110\pi\)
\(570\) 0 0
\(571\) −1482.54 −0.108655 −0.0543277 0.998523i \(-0.517302\pi\)
−0.0543277 + 0.998523i \(0.517302\pi\)
\(572\) 0 0
\(573\) 10402.5 0.758412
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 15264.0 1.10130 0.550649 0.834737i \(-0.314380\pi\)
0.550649 + 0.834737i \(0.314380\pi\)
\(578\) 0 0
\(579\) −5376.43 −0.385901
\(580\) 0 0
\(581\) 3862.76 0.275825
\(582\) 0 0
\(583\) −830.006 −0.0589628
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1736.89 0.122128 0.0610639 0.998134i \(-0.480551\pi\)
0.0610639 + 0.998134i \(0.480551\pi\)
\(588\) 0 0
\(589\) 6753.50 0.472450
\(590\) 0 0
\(591\) −5034.57 −0.350414
\(592\) 0 0
\(593\) 11764.8 0.814707 0.407353 0.913271i \(-0.366452\pi\)
0.407353 + 0.913271i \(0.366452\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −9324.69 −0.639253
\(598\) 0 0
\(599\) 9451.99 0.644737 0.322369 0.946614i \(-0.395521\pi\)
0.322369 + 0.946614i \(0.395521\pi\)
\(600\) 0 0
\(601\) −3131.93 −0.212569 −0.106285 0.994336i \(-0.533895\pi\)
−0.106285 + 0.994336i \(0.533895\pi\)
\(602\) 0 0
\(603\) 1565.16 0.105702
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 22700.8 1.51795 0.758975 0.651120i \(-0.225700\pi\)
0.758975 + 0.651120i \(0.225700\pi\)
\(608\) 0 0
\(609\) −19553.1 −1.30103
\(610\) 0 0
\(611\) −22384.0 −1.48210
\(612\) 0 0
\(613\) −28911.6 −1.90494 −0.952471 0.304629i \(-0.901468\pi\)
−0.952471 + 0.304629i \(0.901468\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5566.87 0.363231 0.181616 0.983370i \(-0.441867\pi\)
0.181616 + 0.983370i \(0.441867\pi\)
\(618\) 0 0
\(619\) −4150.32 −0.269492 −0.134746 0.990880i \(-0.543022\pi\)
−0.134746 + 0.990880i \(0.543022\pi\)
\(620\) 0 0
\(621\) −1339.54 −0.0865600
\(622\) 0 0
\(623\) 22631.9 1.45542
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −563.175 −0.0358709
\(628\) 0 0
\(629\) −377.492 −0.0239294
\(630\) 0 0
\(631\) 4090.09 0.258041 0.129021 0.991642i \(-0.458817\pi\)
0.129021 + 0.991642i \(0.458817\pi\)
\(632\) 0 0
\(633\) 13419.8 0.842637
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8746.32 −0.544022
\(638\) 0 0
\(639\) 5348.53 0.331118
\(640\) 0 0
\(641\) 3909.35 0.240890 0.120445 0.992720i \(-0.461568\pi\)
0.120445 + 0.992720i \(0.461568\pi\)
\(642\) 0 0
\(643\) 30539.5 1.87303 0.936516 0.350624i \(-0.114031\pi\)
0.936516 + 0.350624i \(0.114031\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12707.7 −0.772167 −0.386083 0.922464i \(-0.626172\pi\)
−0.386083 + 0.922464i \(0.626172\pi\)
\(648\) 0 0
\(649\) 132.132 0.00799170
\(650\) 0 0
\(651\) −4292.10 −0.258403
\(652\) 0 0
\(653\) −12777.6 −0.765737 −0.382869 0.923803i \(-0.625064\pi\)
−0.382869 + 0.923803i \(0.625064\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2882.08 −0.171143
\(658\) 0 0
\(659\) −23563.5 −1.39287 −0.696435 0.717620i \(-0.745232\pi\)
−0.696435 + 0.717620i \(0.745232\pi\)
\(660\) 0 0
\(661\) −4361.31 −0.256634 −0.128317 0.991733i \(-0.540958\pi\)
−0.128317 + 0.991733i \(0.540958\pi\)
\(662\) 0 0
\(663\) 3315.21 0.194196
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 14559.6 0.845200
\(668\) 0 0
\(669\) −5260.25 −0.303995
\(670\) 0 0
\(671\) −245.943 −0.0141498
\(672\) 0 0
\(673\) 8203.52 0.469870 0.234935 0.972011i \(-0.424512\pi\)
0.234935 + 0.972011i \(0.424512\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −28057.1 −1.59279 −0.796397 0.604774i \(-0.793263\pi\)
−0.796397 + 0.604774i \(0.793263\pi\)
\(678\) 0 0
\(679\) −8536.73 −0.482488
\(680\) 0 0
\(681\) −2810.70 −0.158159
\(682\) 0 0
\(683\) −3344.62 −0.187377 −0.0936885 0.995602i \(-0.529866\pi\)
−0.0936885 + 0.995602i \(0.529866\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −7746.17 −0.430182
\(688\) 0 0
\(689\) 26981.7 1.49190
\(690\) 0 0
\(691\) −12964.8 −0.713757 −0.356879 0.934151i \(-0.616159\pi\)
−0.356879 + 0.934151i \(0.616159\pi\)
\(692\) 0 0
\(693\) 357.918 0.0196193
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3143.46 0.170828
\(698\) 0 0
\(699\) −6885.03 −0.372555
\(700\) 0 0
\(701\) −16162.1 −0.870806 −0.435403 0.900236i \(-0.643394\pi\)
−0.435403 + 0.900236i \(0.643394\pi\)
\(702\) 0 0
\(703\) −2084.63 −0.111839
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 766.014 0.0407481
\(708\) 0 0
\(709\) −14244.4 −0.754529 −0.377265 0.926105i \(-0.623135\pi\)
−0.377265 + 0.926105i \(0.623135\pi\)
\(710\) 0 0
\(711\) 6934.22 0.365757
\(712\) 0 0
\(713\) 3195.97 0.167868
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6882.02 0.358457
\(718\) 0 0
\(719\) 27638.5 1.43358 0.716790 0.697289i \(-0.245611\pi\)
0.716790 + 0.697289i \(0.245611\pi\)
\(720\) 0 0
\(721\) −39006.4 −2.01480
\(722\) 0 0
\(723\) 1146.86 0.0589934
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2525.52 −0.128840 −0.0644199 0.997923i \(-0.520520\pi\)
−0.0644199 + 0.997923i \(0.520520\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 4695.79 0.237592
\(732\) 0 0
\(733\) 8400.27 0.423289 0.211645 0.977347i \(-0.432118\pi\)
0.211645 + 0.977347i \(0.432118\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 311.401 0.0155639
\(738\) 0 0
\(739\) 19689.1 0.980074 0.490037 0.871702i \(-0.336983\pi\)
0.490037 + 0.871702i \(0.336983\pi\)
\(740\) 0 0
\(741\) 18307.6 0.907619
\(742\) 0 0
\(743\) −22526.6 −1.11227 −0.556137 0.831091i \(-0.687717\pi\)
−0.556137 + 0.831091i \(0.687717\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1565.32 0.0766696
\(748\) 0 0
\(749\) −30243.3 −1.47539
\(750\) 0 0
\(751\) −34691.1 −1.68562 −0.842808 0.538215i \(-0.819099\pi\)
−0.842808 + 0.538215i \(0.819099\pi\)
\(752\) 0 0
\(753\) 6779.95 0.328121
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −6619.98 −0.317843 −0.158922 0.987291i \(-0.550802\pi\)
−0.158922 + 0.987291i \(0.550802\pi\)
\(758\) 0 0
\(759\) −266.512 −0.0127454
\(760\) 0 0
\(761\) −29368.7 −1.39897 −0.699483 0.714649i \(-0.746586\pi\)
−0.699483 + 0.714649i \(0.746586\pi\)
\(762\) 0 0
\(763\) 7131.84 0.338388
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4295.31 −0.202209
\(768\) 0 0
\(769\) 32677.4 1.53235 0.766174 0.642633i \(-0.222158\pi\)
0.766174 + 0.642633i \(0.222158\pi\)
\(770\) 0 0
\(771\) 278.353 0.0130021
\(772\) 0 0
\(773\) 28047.5 1.30504 0.652522 0.757770i \(-0.273711\pi\)
0.652522 + 0.757770i \(0.273711\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1324.86 0.0611699
\(778\) 0 0
\(779\) 17359.1 0.798402
\(780\) 0 0
\(781\) 1064.14 0.0487552
\(782\) 0 0
\(783\) −7923.57 −0.361642
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22172.1 −1.00426 −0.502128 0.864793i \(-0.667449\pi\)
−0.502128 + 0.864793i \(0.667449\pi\)
\(788\) 0 0
\(789\) −1704.94 −0.0769295
\(790\) 0 0
\(791\) 35140.7 1.57960
\(792\) 0 0
\(793\) 7995.06 0.358024
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24170.3 1.07422 0.537112 0.843511i \(-0.319515\pi\)
0.537112 + 0.843511i \(0.319515\pi\)
\(798\) 0 0
\(799\) −7300.32 −0.323238
\(800\) 0 0
\(801\) 9171.22 0.404556
\(802\) 0 0
\(803\) −573.415 −0.0251997
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 22747.2 0.992244
\(808\) 0 0
\(809\) 15304.2 0.665102 0.332551 0.943085i \(-0.392091\pi\)
0.332551 + 0.943085i \(0.392091\pi\)
\(810\) 0 0
\(811\) 27002.2 1.16914 0.584572 0.811342i \(-0.301262\pi\)
0.584572 + 0.811342i \(0.301262\pi\)
\(812\) 0 0
\(813\) −23831.1 −1.02803
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 25931.5 1.11044
\(818\) 0 0
\(819\) −11635.1 −0.496416
\(820\) 0 0
\(821\) 25061.4 1.06535 0.532673 0.846321i \(-0.321188\pi\)
0.532673 + 0.846321i \(0.321188\pi\)
\(822\) 0 0
\(823\) −24896.4 −1.05448 −0.527238 0.849718i \(-0.676772\pi\)
−0.527238 + 0.849718i \(0.676772\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20063.2 −0.843612 −0.421806 0.906686i \(-0.638604\pi\)
−0.421806 + 0.906686i \(0.638604\pi\)
\(828\) 0 0
\(829\) −13884.2 −0.581687 −0.290844 0.956771i \(-0.593936\pi\)
−0.290844 + 0.956771i \(0.593936\pi\)
\(830\) 0 0
\(831\) −20469.0 −0.854467
\(832\) 0 0
\(833\) −2852.52 −0.118648
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1739.31 −0.0718270
\(838\) 0 0
\(839\) 13678.1 0.562838 0.281419 0.959585i \(-0.409195\pi\)
0.281419 + 0.959585i \(0.409195\pi\)
\(840\) 0 0
\(841\) 61733.1 2.53118
\(842\) 0 0
\(843\) 9947.59 0.406421
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −29489.5 −1.19630
\(848\) 0 0
\(849\) 19808.3 0.800728
\(850\) 0 0
\(851\) −986.512 −0.0397382
\(852\) 0 0
\(853\) −29802.9 −1.19629 −0.598143 0.801390i \(-0.704094\pi\)
−0.598143 + 0.801390i \(0.704094\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −22045.2 −0.878706 −0.439353 0.898314i \(-0.644792\pi\)
−0.439353 + 0.898314i \(0.644792\pi\)
\(858\) 0 0
\(859\) −33609.5 −1.33497 −0.667487 0.744622i \(-0.732630\pi\)
−0.667487 + 0.744622i \(0.732630\pi\)
\(860\) 0 0
\(861\) −11032.4 −0.436681
\(862\) 0 0
\(863\) 33775.6 1.33226 0.666128 0.745838i \(-0.267951\pi\)
0.666128 + 0.745838i \(0.267951\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −13657.8 −0.534997
\(868\) 0 0
\(869\) 1379.62 0.0538556
\(870\) 0 0
\(871\) −10123.0 −0.393805
\(872\) 0 0
\(873\) −3459.37 −0.134115
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −12637.0 −0.486570 −0.243285 0.969955i \(-0.578225\pi\)
−0.243285 + 0.969955i \(0.578225\pi\)
\(878\) 0 0
\(879\) −17442.4 −0.669304
\(880\) 0 0
\(881\) −6579.45 −0.251609 −0.125804 0.992055i \(-0.540151\pi\)
−0.125804 + 0.992055i \(0.540151\pi\)
\(882\) 0 0
\(883\) −50442.1 −1.92244 −0.961219 0.275786i \(-0.911062\pi\)
−0.961219 + 0.275786i \(0.911062\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 984.823 0.0372797 0.0186399 0.999826i \(-0.494066\pi\)
0.0186399 + 0.999826i \(0.494066\pi\)
\(888\) 0 0
\(889\) −26587.7 −1.00306
\(890\) 0 0
\(891\) 145.041 0.00545348
\(892\) 0 0
\(893\) −40314.6 −1.51072
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 8663.74 0.322490
\(898\) 0 0
\(899\) 18904.7 0.701342
\(900\) 0 0
\(901\) 8799.79 0.325376
\(902\) 0 0
\(903\) −16480.5 −0.607348
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 43679.9 1.59908 0.799541 0.600612i \(-0.205076\pi\)
0.799541 + 0.600612i \(0.205076\pi\)
\(908\) 0 0
\(909\) 310.415 0.0113265
\(910\) 0 0
\(911\) 10364.3 0.376930 0.188465 0.982080i \(-0.439649\pi\)
0.188465 + 0.982080i \(0.439649\pi\)
\(912\) 0 0
\(913\) 311.435 0.0112891
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7143.58 0.257254
\(918\) 0 0
\(919\) −11451.9 −0.411059 −0.205530 0.978651i \(-0.565892\pi\)
−0.205530 + 0.978651i \(0.565892\pi\)
\(920\) 0 0
\(921\) −24374.6 −0.872063
\(922\) 0 0
\(923\) −34592.7 −1.23362
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −15806.7 −0.560044
\(928\) 0 0
\(929\) −27701.8 −0.978326 −0.489163 0.872192i \(-0.662698\pi\)
−0.489163 + 0.872192i \(0.662698\pi\)
\(930\) 0 0
\(931\) −15752.5 −0.554529
\(932\) 0 0
\(933\) −22008.8 −0.772277
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5878.01 0.204937 0.102469 0.994736i \(-0.467326\pi\)
0.102469 + 0.994736i \(0.467326\pi\)
\(938\) 0 0
\(939\) 6607.97 0.229652
\(940\) 0 0
\(941\) −28786.0 −0.997234 −0.498617 0.866823i \(-0.666159\pi\)
−0.498617 + 0.866823i \(0.666159\pi\)
\(942\) 0 0
\(943\) 8214.90 0.283684
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1695.04 −0.0581641 −0.0290821 0.999577i \(-0.509258\pi\)
−0.0290821 + 0.999577i \(0.509258\pi\)
\(948\) 0 0
\(949\) 18640.5 0.637613
\(950\) 0 0
\(951\) −30026.6 −1.02385
\(952\) 0 0
\(953\) −31929.4 −1.08530 −0.542651 0.839958i \(-0.682580\pi\)
−0.542651 + 0.839958i \(0.682580\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −1576.46 −0.0532495
\(958\) 0 0
\(959\) −7868.57 −0.264952
\(960\) 0 0
\(961\) −25641.2 −0.860704
\(962\) 0 0
\(963\) −12255.6 −0.410106
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −10897.1 −0.362385 −0.181193 0.983448i \(-0.557996\pi\)
−0.181193 + 0.983448i \(0.557996\pi\)
\(968\) 0 0
\(969\) 5970.82 0.197947
\(970\) 0 0
\(971\) −7041.97 −0.232737 −0.116368 0.993206i \(-0.537125\pi\)
−0.116368 + 0.993206i \(0.537125\pi\)
\(972\) 0 0
\(973\) −1715.81 −0.0565328
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 37607.6 1.23150 0.615749 0.787943i \(-0.288854\pi\)
0.615749 + 0.787943i \(0.288854\pi\)
\(978\) 0 0
\(979\) 1824.69 0.0595684
\(980\) 0 0
\(981\) 2890.07 0.0940599
\(982\) 0 0
\(983\) −25297.7 −0.820826 −0.410413 0.911900i \(-0.634615\pi\)
−0.410413 + 0.911900i \(0.634615\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 25621.4 0.826281
\(988\) 0 0
\(989\) 12271.6 0.394556
\(990\) 0 0
\(991\) 41686.5 1.33624 0.668120 0.744053i \(-0.267099\pi\)
0.668120 + 0.744053i \(0.267099\pi\)
\(992\) 0 0
\(993\) 26087.8 0.833708
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −25465.9 −0.808939 −0.404470 0.914551i \(-0.632544\pi\)
−0.404470 + 0.914551i \(0.632544\pi\)
\(998\) 0 0
\(999\) 536.878 0.0170031
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 1200.4.a.bt.1.2 2
4.3 odd 2 75.4.a.c.1.2 2
5.2 odd 4 240.4.f.f.49.1 4
5.3 odd 4 240.4.f.f.49.3 4
5.4 even 2 1200.4.a.bn.1.1 2
12.11 even 2 225.4.a.o.1.1 2
15.2 even 4 720.4.f.j.289.4 4
15.8 even 4 720.4.f.j.289.3 4
20.3 even 4 15.4.b.a.4.2 4
20.7 even 4 15.4.b.a.4.3 yes 4
20.19 odd 2 75.4.a.f.1.1 2
40.3 even 4 960.4.f.q.769.4 4
40.13 odd 4 960.4.f.p.769.2 4
40.27 even 4 960.4.f.q.769.2 4
40.37 odd 4 960.4.f.p.769.4 4
60.23 odd 4 45.4.b.b.19.3 4
60.47 odd 4 45.4.b.b.19.2 4
60.59 even 2 225.4.a.i.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.b.a.4.2 4 20.3 even 4
15.4.b.a.4.3 yes 4 20.7 even 4
45.4.b.b.19.2 4 60.47 odd 4
45.4.b.b.19.3 4 60.23 odd 4
75.4.a.c.1.2 2 4.3 odd 2
75.4.a.f.1.1 2 20.19 odd 2
225.4.a.i.1.2 2 60.59 even 2
225.4.a.o.1.1 2 12.11 even 2
240.4.f.f.49.1 4 5.2 odd 4
240.4.f.f.49.3 4 5.3 odd 4
720.4.f.j.289.3 4 15.8 even 4
720.4.f.j.289.4 4 15.2 even 4
960.4.f.p.769.2 4 40.13 odd 4
960.4.f.p.769.4 4 40.37 odd 4
960.4.f.q.769.2 4 40.27 even 4
960.4.f.q.769.4 4 40.3 even 4
1200.4.a.bn.1.1 2 5.4 even 2
1200.4.a.bt.1.2 2 1.1 even 1 trivial