Properties

Label 4600.2.a.bd.1.1
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.521397.1
Defining polynomial: \(x^{5} - 9 x^{3} - 3 x^{2} + 18 x + 12\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.61696\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61696 q^{3} -3.83744 q^{7} +3.84849 q^{9} +O(q^{10})\) \(q-2.61696 q^{3} -3.83744 q^{7} +3.84849 q^{9} -0.508005 q^{11} -1.01106 q^{13} -1.44705 q^{17} -0.508005 q^{19} +10.0424 q^{21} +1.00000 q^{23} -2.22047 q^{27} +7.51040 q^{29} -0.439038 q^{31} +1.32943 q^{33} +7.02642 q^{37} +2.64590 q^{39} +5.47041 q^{41} -6.72592 q^{43} +2.64098 q^{47} +7.72592 q^{49} +3.78688 q^{51} -4.77648 q^{53} +1.32943 q^{57} +3.85345 q^{59} -9.05844 q^{61} -14.7683 q^{63} -3.45696 q^{67} -2.61696 q^{69} -2.73649 q^{71} +9.21300 q^{73} +1.94944 q^{77} +10.5504 q^{79} -5.73458 q^{81} +1.40211 q^{83} -19.6544 q^{87} +6.77086 q^{89} +3.87986 q^{91} +1.14895 q^{93} +0.313420 q^{97} -1.95506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 4 q^{7} + 3 q^{9} + O(q^{10}) \) \( 5 q - 4 q^{7} + 3 q^{9} - 4 q^{13} - 6 q^{17} + 5 q^{23} - 9 q^{27} + 12 q^{29} - 18 q^{31} - 6 q^{33} - 10 q^{37} + 9 q^{39} - 6 q^{41} - 10 q^{43} - 22 q^{47} + 15 q^{49} - 6 q^{51} - 10 q^{53} - 6 q^{57} - q^{59} + 10 q^{61} - 8 q^{67} + 8 q^{71} - 6 q^{73} - 27 q^{81} + 2 q^{83} - 39 q^{87} + 14 q^{89} - 46 q^{91} + 3 q^{93} - 6 q^{97} - 6 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.61696 −1.51090 −0.755452 0.655204i \(-0.772583\pi\)
−0.755452 + 0.655204i \(0.772583\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.83744 −1.45041 −0.725207 0.688531i \(-0.758256\pi\)
−0.725207 + 0.688531i \(0.758256\pi\)
\(8\) 0 0
\(9\) 3.84849 1.28283
\(10\) 0 0
\(11\) −0.508005 −0.153169 −0.0765847 0.997063i \(-0.524402\pi\)
−0.0765847 + 0.997063i \(0.524402\pi\)
\(12\) 0 0
\(13\) −1.01106 −0.280417 −0.140208 0.990122i \(-0.544777\pi\)
−0.140208 + 0.990122i \(0.544777\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.44705 −0.350961 −0.175481 0.984483i \(-0.556148\pi\)
−0.175481 + 0.984483i \(0.556148\pi\)
\(18\) 0 0
\(19\) −0.508005 −0.116544 −0.0582722 0.998301i \(-0.518559\pi\)
−0.0582722 + 0.998301i \(0.518559\pi\)
\(20\) 0 0
\(21\) 10.0424 2.19144
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.22047 −0.427330
\(28\) 0 0
\(29\) 7.51040 1.39465 0.697323 0.716757i \(-0.254374\pi\)
0.697323 + 0.716757i \(0.254374\pi\)
\(30\) 0 0
\(31\) −0.439038 −0.0788536 −0.0394268 0.999222i \(-0.512553\pi\)
−0.0394268 + 0.999222i \(0.512553\pi\)
\(32\) 0 0
\(33\) 1.32943 0.231424
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.02642 1.15514 0.577568 0.816343i \(-0.304002\pi\)
0.577568 + 0.816343i \(0.304002\pi\)
\(38\) 0 0
\(39\) 2.64590 0.423683
\(40\) 0 0
\(41\) 5.47041 0.854335 0.427167 0.904173i \(-0.359512\pi\)
0.427167 + 0.904173i \(0.359512\pi\)
\(42\) 0 0
\(43\) −6.72592 −1.02569 −0.512847 0.858480i \(-0.671409\pi\)
−0.512847 + 0.858480i \(0.671409\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.64098 0.385227 0.192614 0.981275i \(-0.438304\pi\)
0.192614 + 0.981275i \(0.438304\pi\)
\(48\) 0 0
\(49\) 7.72592 1.10370
\(50\) 0 0
\(51\) 3.78688 0.530269
\(52\) 0 0
\(53\) −4.77648 −0.656100 −0.328050 0.944660i \(-0.606391\pi\)
−0.328050 + 0.944660i \(0.606391\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.32943 0.176087
\(58\) 0 0
\(59\) 3.85345 0.501676 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(60\) 0 0
\(61\) −9.05844 −1.15981 −0.579907 0.814683i \(-0.696911\pi\)
−0.579907 + 0.814683i \(0.696911\pi\)
\(62\) 0 0
\(63\) −14.7683 −1.86064
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.45696 −0.422335 −0.211167 0.977450i \(-0.567727\pi\)
−0.211167 + 0.977450i \(0.567727\pi\)
\(68\) 0 0
\(69\) −2.61696 −0.315045
\(70\) 0 0
\(71\) −2.73649 −0.324762 −0.162381 0.986728i \(-0.551917\pi\)
−0.162381 + 0.986728i \(0.551917\pi\)
\(72\) 0 0
\(73\) 9.21300 1.07830 0.539150 0.842210i \(-0.318746\pi\)
0.539150 + 0.842210i \(0.318746\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.94944 0.222159
\(78\) 0 0
\(79\) 10.5504 1.18702 0.593508 0.804828i \(-0.297742\pi\)
0.593508 + 0.804828i \(0.297742\pi\)
\(80\) 0 0
\(81\) −5.73458 −0.637176
\(82\) 0 0
\(83\) 1.40211 0.153901 0.0769505 0.997035i \(-0.475482\pi\)
0.0769505 + 0.997035i \(0.475482\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −19.6544 −2.10718
\(88\) 0 0
\(89\) 6.77086 0.717710 0.358855 0.933393i \(-0.383167\pi\)
0.358855 + 0.933393i \(0.383167\pi\)
\(90\) 0 0
\(91\) 3.87986 0.406720
\(92\) 0 0
\(93\) 1.14895 0.119140
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.313420 0.0318230 0.0159115 0.999873i \(-0.494935\pi\)
0.0159115 + 0.999873i \(0.494935\pi\)
\(98\) 0 0
\(99\) −1.95506 −0.196490
\(100\) 0 0
\(101\) −4.83182 −0.480784 −0.240392 0.970676i \(-0.577276\pi\)
−0.240392 + 0.970676i \(0.577276\pi\)
\(102\) 0 0
\(103\) −8.07746 −0.795896 −0.397948 0.917408i \(-0.630278\pi\)
−0.397948 + 0.917408i \(0.630278\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.1587 1.07876 0.539378 0.842064i \(-0.318659\pi\)
0.539378 + 0.842064i \(0.318659\pi\)
\(108\) 0 0
\(109\) 17.6015 1.68592 0.842958 0.537979i \(-0.180812\pi\)
0.842958 + 0.537979i \(0.180812\pi\)
\(110\) 0 0
\(111\) −18.3879 −1.74530
\(112\) 0 0
\(113\) 4.06454 0.382360 0.191180 0.981555i \(-0.438769\pi\)
0.191180 + 0.981555i \(0.438769\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.89104 −0.359727
\(118\) 0 0
\(119\) 5.55296 0.509039
\(120\) 0 0
\(121\) −10.7419 −0.976539
\(122\) 0 0
\(123\) −14.3159 −1.29082
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −4.75246 −0.421713 −0.210856 0.977517i \(-0.567625\pi\)
−0.210856 + 0.977517i \(0.567625\pi\)
\(128\) 0 0
\(129\) 17.6015 1.54972
\(130\) 0 0
\(131\) 1.96851 0.171989 0.0859946 0.996296i \(-0.472593\pi\)
0.0859946 + 0.996296i \(0.472593\pi\)
\(132\) 0 0
\(133\) 1.94944 0.169038
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.64285 0.482101 0.241051 0.970513i \(-0.422508\pi\)
0.241051 + 0.970513i \(0.422508\pi\)
\(138\) 0 0
\(139\) −7.59724 −0.644390 −0.322195 0.946673i \(-0.604421\pi\)
−0.322195 + 0.946673i \(0.604421\pi\)
\(140\) 0 0
\(141\) −6.91136 −0.582041
\(142\) 0 0
\(143\) 0.513622 0.0429512
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −20.2184 −1.66759
\(148\) 0 0
\(149\) 10.7709 0.882384 0.441192 0.897413i \(-0.354556\pi\)
0.441192 + 0.897413i \(0.354556\pi\)
\(150\) 0 0
\(151\) −16.5333 −1.34546 −0.672729 0.739889i \(-0.734878\pi\)
−0.672729 + 0.739889i \(0.734878\pi\)
\(152\) 0 0
\(153\) −5.56896 −0.450224
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.5436 0.921281 0.460640 0.887587i \(-0.347620\pi\)
0.460640 + 0.887587i \(0.347620\pi\)
\(158\) 0 0
\(159\) 12.4999 0.991304
\(160\) 0 0
\(161\) −3.83744 −0.302432
\(162\) 0 0
\(163\) −3.32143 −0.260155 −0.130077 0.991504i \(-0.541523\pi\)
−0.130077 + 0.991504i \(0.541523\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.6742 −0.980755 −0.490378 0.871510i \(-0.663141\pi\)
−0.490378 + 0.871510i \(0.663141\pi\)
\(168\) 0 0
\(169\) −11.9778 −0.921367
\(170\) 0 0
\(171\) −1.95506 −0.149507
\(172\) 0 0
\(173\) −17.5733 −1.33607 −0.668035 0.744130i \(-0.732864\pi\)
−0.668035 + 0.744130i \(0.732864\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.0843 −0.757984
\(178\) 0 0
\(179\) −14.8952 −1.11332 −0.556659 0.830741i \(-0.687917\pi\)
−0.556659 + 0.830741i \(0.687917\pi\)
\(180\) 0 0
\(181\) −23.2868 −1.73089 −0.865446 0.501003i \(-0.832965\pi\)
−0.865446 + 0.501003i \(0.832965\pi\)
\(182\) 0 0
\(183\) 23.7056 1.75237
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.735109 0.0537565
\(188\) 0 0
\(189\) 8.52093 0.619806
\(190\) 0 0
\(191\) 6.92360 0.500974 0.250487 0.968120i \(-0.419409\pi\)
0.250487 + 0.968120i \(0.419409\pi\)
\(192\) 0 0
\(193\) 7.74318 0.557366 0.278683 0.960383i \(-0.410102\pi\)
0.278683 + 0.960383i \(0.410102\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.8908 1.70215 0.851074 0.525045i \(-0.175952\pi\)
0.851074 + 0.525045i \(0.175952\pi\)
\(198\) 0 0
\(199\) −23.9444 −1.69737 −0.848687 0.528896i \(-0.822606\pi\)
−0.848687 + 0.528896i \(0.822606\pi\)
\(200\) 0 0
\(201\) 9.04673 0.638107
\(202\) 0 0
\(203\) −28.8207 −2.02282
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.84849 0.267489
\(208\) 0 0
\(209\) 0.258070 0.0178510
\(210\) 0 0
\(211\) 14.4709 0.996220 0.498110 0.867114i \(-0.334027\pi\)
0.498110 + 0.867114i \(0.334027\pi\)
\(212\) 0 0
\(213\) 7.16129 0.490684
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.68478 0.114370
\(218\) 0 0
\(219\) −24.1101 −1.62921
\(220\) 0 0
\(221\) 1.46305 0.0984153
\(222\) 0 0
\(223\) 4.74755 0.317919 0.158960 0.987285i \(-0.449186\pi\)
0.158960 + 0.987285i \(0.449186\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.98399 −0.596288 −0.298144 0.954521i \(-0.596368\pi\)
−0.298144 + 0.954521i \(0.596368\pi\)
\(228\) 0 0
\(229\) 20.7290 1.36981 0.684906 0.728631i \(-0.259843\pi\)
0.684906 + 0.728631i \(0.259843\pi\)
\(230\) 0 0
\(231\) −5.10161 −0.335661
\(232\) 0 0
\(233\) −26.0634 −1.70747 −0.853735 0.520707i \(-0.825668\pi\)
−0.853735 + 0.520707i \(0.825668\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −27.6101 −1.79347
\(238\) 0 0
\(239\) −2.94209 −0.190308 −0.0951540 0.995463i \(-0.530334\pi\)
−0.0951540 + 0.995463i \(0.530334\pi\)
\(240\) 0 0
\(241\) −24.9413 −1.60661 −0.803306 0.595567i \(-0.796927\pi\)
−0.803306 + 0.595567i \(0.796927\pi\)
\(242\) 0 0
\(243\) 21.6686 1.39004
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.513622 0.0326810
\(248\) 0 0
\(249\) −3.66926 −0.232530
\(250\) 0 0
\(251\) 21.1908 1.33755 0.668774 0.743465i \(-0.266819\pi\)
0.668774 + 0.743465i \(0.266819\pi\)
\(252\) 0 0
\(253\) −0.508005 −0.0319380
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −26.2110 −1.63500 −0.817500 0.575929i \(-0.804640\pi\)
−0.817500 + 0.575929i \(0.804640\pi\)
\(258\) 0 0
\(259\) −26.9634 −1.67543
\(260\) 0 0
\(261\) 28.9037 1.78910
\(262\) 0 0
\(263\) 5.65276 0.348564 0.174282 0.984696i \(-0.444240\pi\)
0.174282 + 0.984696i \(0.444240\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −17.7191 −1.08439
\(268\) 0 0
\(269\) 9.65772 0.588841 0.294421 0.955676i \(-0.404873\pi\)
0.294421 + 0.955676i \(0.404873\pi\)
\(270\) 0 0
\(271\) 8.39040 0.509680 0.254840 0.966983i \(-0.417977\pi\)
0.254840 + 0.966983i \(0.417977\pi\)
\(272\) 0 0
\(273\) −10.1535 −0.614515
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −30.3317 −1.82246 −0.911229 0.411900i \(-0.864865\pi\)
−0.911229 + 0.411900i \(0.864865\pi\)
\(278\) 0 0
\(279\) −1.68964 −0.101156
\(280\) 0 0
\(281\) −25.3132 −1.51006 −0.755028 0.655692i \(-0.772377\pi\)
−0.755028 + 0.655692i \(0.772377\pi\)
\(282\) 0 0
\(283\) 12.9629 0.770566 0.385283 0.922798i \(-0.374104\pi\)
0.385283 + 0.922798i \(0.374104\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −20.9924 −1.23914
\(288\) 0 0
\(289\) −14.9060 −0.876826
\(290\) 0 0
\(291\) −0.820209 −0.0480815
\(292\) 0 0
\(293\) −25.9469 −1.51584 −0.757918 0.652350i \(-0.773783\pi\)
−0.757918 + 0.652350i \(0.773783\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.12801 0.0654539
\(298\) 0 0
\(299\) −1.01106 −0.0584709
\(300\) 0 0
\(301\) 25.8103 1.48768
\(302\) 0 0
\(303\) 12.6447 0.726419
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12.0640 −0.688531 −0.344266 0.938872i \(-0.611872\pi\)
−0.344266 + 0.938872i \(0.611872\pi\)
\(308\) 0 0
\(309\) 21.1384 1.20252
\(310\) 0 0
\(311\) −31.8125 −1.80392 −0.901959 0.431821i \(-0.857871\pi\)
−0.901959 + 0.431821i \(0.857871\pi\)
\(312\) 0 0
\(313\) 4.30122 0.243119 0.121560 0.992584i \(-0.461210\pi\)
0.121560 + 0.992584i \(0.461210\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.28317 0.352898 0.176449 0.984310i \(-0.443539\pi\)
0.176449 + 0.984310i \(0.443539\pi\)
\(318\) 0 0
\(319\) −3.81532 −0.213617
\(320\) 0 0
\(321\) −29.2020 −1.62990
\(322\) 0 0
\(323\) 0.735109 0.0409026
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −46.0624 −2.54726
\(328\) 0 0
\(329\) −10.1346 −0.558739
\(330\) 0 0
\(331\) −8.00053 −0.439749 −0.219874 0.975528i \(-0.570565\pi\)
−0.219874 + 0.975528i \(0.570565\pi\)
\(332\) 0 0
\(333\) 27.0411 1.48184
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −10.1436 −0.552554 −0.276277 0.961078i \(-0.589101\pi\)
−0.276277 + 0.961078i \(0.589101\pi\)
\(338\) 0 0
\(339\) −10.6367 −0.577709
\(340\) 0 0
\(341\) 0.223034 0.0120780
\(342\) 0 0
\(343\) −2.78567 −0.150412
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.8747 1.01325 0.506625 0.862167i \(-0.330893\pi\)
0.506625 + 0.862167i \(0.330893\pi\)
\(348\) 0 0
\(349\) 9.26611 0.496004 0.248002 0.968760i \(-0.420226\pi\)
0.248002 + 0.968760i \(0.420226\pi\)
\(350\) 0 0
\(351\) 2.24502 0.119831
\(352\) 0 0
\(353\) −8.04442 −0.428161 −0.214081 0.976816i \(-0.568676\pi\)
−0.214081 + 0.976816i \(0.568676\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −14.5319 −0.769109
\(358\) 0 0
\(359\) 20.5443 1.08429 0.542144 0.840285i \(-0.317613\pi\)
0.542144 + 0.840285i \(0.317613\pi\)
\(360\) 0 0
\(361\) −18.7419 −0.986417
\(362\) 0 0
\(363\) 28.1112 1.47546
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.64032 0.451021 0.225511 0.974241i \(-0.427595\pi\)
0.225511 + 0.974241i \(0.427595\pi\)
\(368\) 0 0
\(369\) 21.0528 1.09597
\(370\) 0 0
\(371\) 18.3294 0.951617
\(372\) 0 0
\(373\) 19.0442 0.986073 0.493037 0.870009i \(-0.335887\pi\)
0.493037 + 0.870009i \(0.335887\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.59344 −0.391082
\(378\) 0 0
\(379\) 0.926121 0.0475717 0.0237858 0.999717i \(-0.492428\pi\)
0.0237858 + 0.999717i \(0.492428\pi\)
\(380\) 0 0
\(381\) 12.4370 0.637167
\(382\) 0 0
\(383\) 9.38526 0.479564 0.239782 0.970827i \(-0.422924\pi\)
0.239782 + 0.970827i \(0.422924\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −25.8847 −1.31579
\(388\) 0 0
\(389\) 2.22865 0.112997 0.0564985 0.998403i \(-0.482006\pi\)
0.0564985 + 0.998403i \(0.482006\pi\)
\(390\) 0 0
\(391\) −1.44705 −0.0731805
\(392\) 0 0
\(393\) −5.15151 −0.259859
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0448 −0.654701 −0.327350 0.944903i \(-0.606156\pi\)
−0.327350 + 0.944903i \(0.606156\pi\)
\(398\) 0 0
\(399\) −5.10161 −0.255400
\(400\) 0 0
\(401\) −2.22221 −0.110972 −0.0554859 0.998459i \(-0.517671\pi\)
−0.0554859 + 0.998459i \(0.517671\pi\)
\(402\) 0 0
\(403\) 0.443893 0.0221119
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.56946 −0.176931
\(408\) 0 0
\(409\) −19.5232 −0.965362 −0.482681 0.875796i \(-0.660337\pi\)
−0.482681 + 0.875796i \(0.660337\pi\)
\(410\) 0 0
\(411\) −14.7671 −0.728409
\(412\) 0 0
\(413\) −14.7874 −0.727638
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 19.8817 0.973611
\(418\) 0 0
\(419\) −24.9180 −1.21732 −0.608662 0.793430i \(-0.708293\pi\)
−0.608662 + 0.793430i \(0.708293\pi\)
\(420\) 0 0
\(421\) 6.10721 0.297647 0.148824 0.988864i \(-0.452451\pi\)
0.148824 + 0.988864i \(0.452451\pi\)
\(422\) 0 0
\(423\) 10.1638 0.494181
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 34.7612 1.68221
\(428\) 0 0
\(429\) −1.34413 −0.0648952
\(430\) 0 0
\(431\) 4.44095 0.213913 0.106956 0.994264i \(-0.465889\pi\)
0.106956 + 0.994264i \(0.465889\pi\)
\(432\) 0 0
\(433\) −3.25554 −0.156451 −0.0782257 0.996936i \(-0.524925\pi\)
−0.0782257 + 0.996936i \(0.524925\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.508005 −0.0243012
\(438\) 0 0
\(439\) −26.9611 −1.28678 −0.643392 0.765537i \(-0.722473\pi\)
−0.643392 + 0.765537i \(0.722473\pi\)
\(440\) 0 0
\(441\) 29.7331 1.41586
\(442\) 0 0
\(443\) 16.0072 0.760526 0.380263 0.924878i \(-0.375833\pi\)
0.380263 + 0.924878i \(0.375833\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −28.1869 −1.33320
\(448\) 0 0
\(449\) −37.4278 −1.76633 −0.883163 0.469066i \(-0.844591\pi\)
−0.883163 + 0.469066i \(0.844591\pi\)
\(450\) 0 0
\(451\) −2.77900 −0.130858
\(452\) 0 0
\(453\) 43.2670 2.03286
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.75949 0.409752 0.204876 0.978788i \(-0.434321\pi\)
0.204876 + 0.978788i \(0.434321\pi\)
\(458\) 0 0
\(459\) 3.21314 0.149976
\(460\) 0 0
\(461\) 11.4459 0.533089 0.266545 0.963823i \(-0.414118\pi\)
0.266545 + 0.963823i \(0.414118\pi\)
\(462\) 0 0
\(463\) −8.23570 −0.382745 −0.191373 0.981517i \(-0.561294\pi\)
−0.191373 + 0.981517i \(0.561294\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.9436 1.33935 0.669675 0.742654i \(-0.266433\pi\)
0.669675 + 0.742654i \(0.266433\pi\)
\(468\) 0 0
\(469\) 13.2659 0.612561
\(470\) 0 0
\(471\) −30.2092 −1.39197
\(472\) 0 0
\(473\) 3.41680 0.157105
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −18.3823 −0.841666
\(478\) 0 0
\(479\) 31.1031 1.42114 0.710569 0.703627i \(-0.248437\pi\)
0.710569 + 0.703627i \(0.248437\pi\)
\(480\) 0 0
\(481\) −7.10410 −0.323919
\(482\) 0 0
\(483\) 10.0424 0.456946
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.90588 −0.0863635 −0.0431817 0.999067i \(-0.513749\pi\)
−0.0431817 + 0.999067i \(0.513749\pi\)
\(488\) 0 0
\(489\) 8.69206 0.393069
\(490\) 0 0
\(491\) −27.2222 −1.22852 −0.614259 0.789104i \(-0.710545\pi\)
−0.614259 + 0.789104i \(0.710545\pi\)
\(492\) 0 0
\(493\) −10.8679 −0.489467
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.5011 0.471039
\(498\) 0 0
\(499\) −9.38913 −0.420315 −0.210158 0.977668i \(-0.567398\pi\)
−0.210158 + 0.977668i \(0.567398\pi\)
\(500\) 0 0
\(501\) 33.1678 1.48183
\(502\) 0 0
\(503\) −29.5613 −1.31807 −0.659037 0.752110i \(-0.729036\pi\)
−0.659037 + 0.752110i \(0.729036\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 31.3454 1.39210
\(508\) 0 0
\(509\) 0.448890 0.0198967 0.00994835 0.999951i \(-0.496833\pi\)
0.00994835 + 0.999951i \(0.496833\pi\)
\(510\) 0 0
\(511\) −35.3543 −1.56398
\(512\) 0 0
\(513\) 1.12801 0.0498030
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.34163 −0.0590050
\(518\) 0 0
\(519\) 45.9886 2.01867
\(520\) 0 0
\(521\) 26.8712 1.17725 0.588623 0.808407i \(-0.299670\pi\)
0.588623 + 0.808407i \(0.299670\pi\)
\(522\) 0 0
\(523\) −2.90473 −0.127015 −0.0635075 0.997981i \(-0.520229\pi\)
−0.0635075 + 0.997981i \(0.520229\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.635311 0.0276746
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 14.8300 0.643566
\(532\) 0 0
\(533\) −5.53089 −0.239570
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 38.9801 1.68212
\(538\) 0 0
\(539\) −3.92481 −0.169053
\(540\) 0 0
\(541\) 34.0386 1.46343 0.731716 0.681610i \(-0.238720\pi\)
0.731716 + 0.681610i \(0.238720\pi\)
\(542\) 0 0
\(543\) 60.9406 2.61521
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23.8364 1.01917 0.509586 0.860420i \(-0.329798\pi\)
0.509586 + 0.860420i \(0.329798\pi\)
\(548\) 0 0
\(549\) −34.8613 −1.48785
\(550\) 0 0
\(551\) −3.81532 −0.162538
\(552\) 0 0
\(553\) −40.4866 −1.72167
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −40.4201 −1.71265 −0.856326 0.516435i \(-0.827259\pi\)
−0.856326 + 0.516435i \(0.827259\pi\)
\(558\) 0 0
\(559\) 6.80028 0.287621
\(560\) 0 0
\(561\) −1.92375 −0.0812209
\(562\) 0 0
\(563\) 6.54758 0.275948 0.137974 0.990436i \(-0.455941\pi\)
0.137974 + 0.990436i \(0.455941\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 22.0061 0.924169
\(568\) 0 0
\(569\) 20.4590 0.857686 0.428843 0.903379i \(-0.358921\pi\)
0.428843 + 0.903379i \(0.358921\pi\)
\(570\) 0 0
\(571\) 4.71300 0.197233 0.0986164 0.995126i \(-0.468558\pi\)
0.0986164 + 0.995126i \(0.468558\pi\)
\(572\) 0 0
\(573\) −18.1188 −0.756924
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 25.9331 1.07961 0.539805 0.841790i \(-0.318498\pi\)
0.539805 + 0.841790i \(0.318498\pi\)
\(578\) 0 0
\(579\) −20.2636 −0.842127
\(580\) 0 0
\(581\) −5.38049 −0.223220
\(582\) 0 0
\(583\) 2.42648 0.100494
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.4711 −0.432189 −0.216095 0.976372i \(-0.569332\pi\)
−0.216095 + 0.976372i \(0.569332\pi\)
\(588\) 0 0
\(589\) 0.223034 0.00918995
\(590\) 0 0
\(591\) −62.5213 −2.57178
\(592\) 0 0
\(593\) −20.8158 −0.854803 −0.427401 0.904062i \(-0.640571\pi\)
−0.427401 + 0.904062i \(0.640571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 62.6616 2.56457
\(598\) 0 0
\(599\) −14.7951 −0.604511 −0.302256 0.953227i \(-0.597740\pi\)
−0.302256 + 0.953227i \(0.597740\pi\)
\(600\) 0 0
\(601\) −33.8995 −1.38279 −0.691394 0.722477i \(-0.743003\pi\)
−0.691394 + 0.722477i \(0.743003\pi\)
\(602\) 0 0
\(603\) −13.3041 −0.541784
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −32.9350 −1.33679 −0.668394 0.743807i \(-0.733018\pi\)
−0.668394 + 0.743807i \(0.733018\pi\)
\(608\) 0 0
\(609\) 75.4227 3.05628
\(610\) 0 0
\(611\) −2.67018 −0.108024
\(612\) 0 0
\(613\) 24.8664 1.00434 0.502172 0.864768i \(-0.332535\pi\)
0.502172 + 0.864768i \(0.332535\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.1280 0.810324 0.405162 0.914245i \(-0.367215\pi\)
0.405162 + 0.914245i \(0.367215\pi\)
\(618\) 0 0
\(619\) −15.3719 −0.617847 −0.308924 0.951087i \(-0.599969\pi\)
−0.308924 + 0.951087i \(0.599969\pi\)
\(620\) 0 0
\(621\) −2.22047 −0.0891046
\(622\) 0 0
\(623\) −25.9828 −1.04098
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.675358 −0.0269712
\(628\) 0 0
\(629\) −10.1676 −0.405408
\(630\) 0 0
\(631\) −25.7115 −1.02356 −0.511779 0.859117i \(-0.671013\pi\)
−0.511779 + 0.859117i \(0.671013\pi\)
\(632\) 0 0
\(633\) −37.8699 −1.50519
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −7.81134 −0.309497
\(638\) 0 0
\(639\) −10.5314 −0.416614
\(640\) 0 0
\(641\) 2.95684 0.116788 0.0583941 0.998294i \(-0.481402\pi\)
0.0583941 + 0.998294i \(0.481402\pi\)
\(642\) 0 0
\(643\) 16.7764 0.661596 0.330798 0.943702i \(-0.392682\pi\)
0.330798 + 0.943702i \(0.392682\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.99247 0.0783322 0.0391661 0.999233i \(-0.487530\pi\)
0.0391661 + 0.999233i \(0.487530\pi\)
\(648\) 0 0
\(649\) −1.95757 −0.0768414
\(650\) 0 0
\(651\) −4.40901 −0.172803
\(652\) 0 0
\(653\) −46.4989 −1.81964 −0.909822 0.414999i \(-0.863782\pi\)
−0.909822 + 0.414999i \(0.863782\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 35.4562 1.38328
\(658\) 0 0
\(659\) −37.1468 −1.44703 −0.723517 0.690307i \(-0.757476\pi\)
−0.723517 + 0.690307i \(0.757476\pi\)
\(660\) 0 0
\(661\) −7.01756 −0.272952 −0.136476 0.990643i \(-0.543578\pi\)
−0.136476 + 0.990643i \(0.543578\pi\)
\(662\) 0 0
\(663\) −3.82874 −0.148696
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.51040 0.290804
\(668\) 0 0
\(669\) −12.4242 −0.480346
\(670\) 0 0
\(671\) 4.60174 0.177648
\(672\) 0 0
\(673\) 6.81155 0.262566 0.131283 0.991345i \(-0.458090\pi\)
0.131283 + 0.991345i \(0.458090\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −0.522812 −0.0200933 −0.0100466 0.999950i \(-0.503198\pi\)
−0.0100466 + 0.999950i \(0.503198\pi\)
\(678\) 0 0
\(679\) −1.20273 −0.0461566
\(680\) 0 0
\(681\) 23.5108 0.900934
\(682\) 0 0
\(683\) −2.93412 −0.112271 −0.0561355 0.998423i \(-0.517878\pi\)
−0.0561355 + 0.998423i \(0.517878\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −54.2471 −2.06965
\(688\) 0 0
\(689\) 4.82929 0.183981
\(690\) 0 0
\(691\) −31.8456 −1.21146 −0.605731 0.795669i \(-0.707119\pi\)
−0.605731 + 0.795669i \(0.707119\pi\)
\(692\) 0 0
\(693\) 7.50240 0.284993
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −7.91596 −0.299838
\(698\) 0 0
\(699\) 68.2070 2.57982
\(700\) 0 0
\(701\) 11.2070 0.423283 0.211642 0.977347i \(-0.432119\pi\)
0.211642 + 0.977347i \(0.432119\pi\)
\(702\) 0 0
\(703\) −3.56946 −0.134625
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.5418 0.697336
\(708\) 0 0
\(709\) 23.7300 0.891198 0.445599 0.895233i \(-0.352991\pi\)
0.445599 + 0.895233i \(0.352991\pi\)
\(710\) 0 0
\(711\) 40.6033 1.52274
\(712\) 0 0
\(713\) −0.439038 −0.0164421
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 7.69934 0.287537
\(718\) 0 0
\(719\) −27.8687 −1.03933 −0.519664 0.854371i \(-0.673943\pi\)
−0.519664 + 0.854371i \(0.673943\pi\)
\(720\) 0 0
\(721\) 30.9968 1.15438
\(722\) 0 0
\(723\) 65.2705 2.42744
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 47.5773 1.76455 0.882273 0.470739i \(-0.156013\pi\)
0.882273 + 0.470739i \(0.156013\pi\)
\(728\) 0 0
\(729\) −39.5022 −1.46304
\(730\) 0 0
\(731\) 9.73274 0.359978
\(732\) 0 0
\(733\) −15.4086 −0.569129 −0.284565 0.958657i \(-0.591849\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.75615 0.0646888
\(738\) 0 0
\(739\) 53.0212 1.95042 0.975208 0.221292i \(-0.0710275\pi\)
0.975208 + 0.221292i \(0.0710275\pi\)
\(740\) 0 0
\(741\) −1.34413 −0.0493778
\(742\) 0 0
\(743\) −15.6611 −0.574551 −0.287275 0.957848i \(-0.592750\pi\)
−0.287275 + 0.957848i \(0.592750\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.39599 0.197429
\(748\) 0 0
\(749\) −42.8209 −1.56464
\(750\) 0 0
\(751\) 34.6216 1.26336 0.631679 0.775230i \(-0.282366\pi\)
0.631679 + 0.775230i \(0.282366\pi\)
\(752\) 0 0
\(753\) −55.4554 −2.02091
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.4389 1.39709 0.698543 0.715568i \(-0.253832\pi\)
0.698543 + 0.715568i \(0.253832\pi\)
\(758\) 0 0
\(759\) 1.32943 0.0482553
\(760\) 0 0
\(761\) 42.0932 1.52588 0.762939 0.646470i \(-0.223755\pi\)
0.762939 + 0.646470i \(0.223755\pi\)
\(762\) 0 0
\(763\) −67.5446 −2.44528
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.89605 −0.140678
\(768\) 0 0
\(769\) 34.2859 1.23638 0.618191 0.786028i \(-0.287866\pi\)
0.618191 + 0.786028i \(0.287866\pi\)
\(770\) 0 0
\(771\) 68.5933 2.47033
\(772\) 0 0
\(773\) 12.7422 0.458304 0.229152 0.973391i \(-0.426405\pi\)
0.229152 + 0.973391i \(0.426405\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 70.5623 2.53141
\(778\) 0 0
\(779\) −2.77900 −0.0995679
\(780\) 0 0
\(781\) 1.39015 0.0497436
\(782\) 0 0
\(783\) −16.6766 −0.595975
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −28.5534 −1.01782 −0.508910 0.860820i \(-0.669951\pi\)
−0.508910 + 0.860820i \(0.669951\pi\)
\(788\) 0 0
\(789\) −14.7931 −0.526647
\(790\) 0 0
\(791\) −15.5974 −0.554580
\(792\) 0 0
\(793\) 9.15859 0.325231
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.39925 0.297517 0.148758 0.988874i \(-0.452472\pi\)
0.148758 + 0.988874i \(0.452472\pi\)
\(798\) 0 0
\(799\) −3.82164 −0.135200
\(800\) 0 0
\(801\) 26.0576 0.920701
\(802\) 0 0
\(803\) −4.68026 −0.165163
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −25.2739 −0.889683
\(808\) 0 0
\(809\) −28.8816 −1.01542 −0.507712 0.861527i \(-0.669509\pi\)
−0.507712 + 0.861527i \(0.669509\pi\)
\(810\) 0 0
\(811\) −46.5292 −1.63386 −0.816931 0.576736i \(-0.804326\pi\)
−0.816931 + 0.576736i \(0.804326\pi\)
\(812\) 0 0
\(813\) −21.9574 −0.770078
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 3.41680 0.119539
\(818\) 0 0
\(819\) 14.9316 0.521753
\(820\) 0 0
\(821\) −2.99065 −0.104374 −0.0521872 0.998637i \(-0.516619\pi\)
−0.0521872 + 0.998637i \(0.516619\pi\)
\(822\) 0 0
\(823\) −5.14357 −0.179294 −0.0896468 0.995974i \(-0.528574\pi\)
−0.0896468 + 0.995974i \(0.528574\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 53.4288 1.85790 0.928950 0.370205i \(-0.120713\pi\)
0.928950 + 0.370205i \(0.120713\pi\)
\(828\) 0 0
\(829\) 11.5290 0.400420 0.200210 0.979753i \(-0.435838\pi\)
0.200210 + 0.979753i \(0.435838\pi\)
\(830\) 0 0
\(831\) 79.3770 2.75356
\(832\) 0 0
\(833\) −11.1798 −0.387357
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.974874 0.0336966
\(838\) 0 0
\(839\) 12.0983 0.417678 0.208839 0.977950i \(-0.433032\pi\)
0.208839 + 0.977950i \(0.433032\pi\)
\(840\) 0 0
\(841\) 27.4061 0.945038
\(842\) 0 0
\(843\) 66.2436 2.28155
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 41.2215 1.41639
\(848\) 0 0
\(849\) −33.9235 −1.16425
\(850\) 0 0
\(851\) 7.02642 0.240862
\(852\) 0 0
\(853\) −3.10103 −0.106177 −0.0530886 0.998590i \(-0.516907\pi\)
−0.0530886 + 0.998590i \(0.516907\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.39457 −0.150116 −0.0750578 0.997179i \(-0.523914\pi\)
−0.0750578 + 0.997179i \(0.523914\pi\)
\(858\) 0 0
\(859\) −29.0453 −0.991014 −0.495507 0.868604i \(-0.665018\pi\)
−0.495507 + 0.868604i \(0.665018\pi\)
\(860\) 0 0
\(861\) 54.9362 1.87222
\(862\) 0 0
\(863\) 40.1020 1.36509 0.682543 0.730845i \(-0.260874\pi\)
0.682543 + 0.730845i \(0.260874\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 39.0086 1.32480
\(868\) 0 0
\(869\) −5.35968 −0.181815
\(870\) 0 0
\(871\) 3.49518 0.118430
\(872\) 0 0
\(873\) 1.20620 0.0408235
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.7503 −1.27474 −0.637368 0.770559i \(-0.719977\pi\)
−0.637368 + 0.770559i \(0.719977\pi\)
\(878\) 0 0
\(879\) 67.9021 2.29028
\(880\) 0 0
\(881\) −29.1541 −0.982227 −0.491113 0.871096i \(-0.663410\pi\)
−0.491113 + 0.871096i \(0.663410\pi\)
\(882\) 0 0
\(883\) 43.3971 1.46043 0.730214 0.683218i \(-0.239420\pi\)
0.730214 + 0.683218i \(0.239420\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 25.4091 0.853155 0.426578 0.904451i \(-0.359719\pi\)
0.426578 + 0.904451i \(0.359719\pi\)
\(888\) 0 0
\(889\) 18.2373 0.611658
\(890\) 0 0
\(891\) 2.91320 0.0975958
\(892\) 0 0
\(893\) −1.34163 −0.0448961
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.64590 0.0883439
\(898\) 0 0
\(899\) −3.29735 −0.109973
\(900\) 0 0
\(901\) 6.91181 0.230266
\(902\) 0 0
\(903\) −67.5446 −2.24774
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.00778 −0.0666672 −0.0333336 0.999444i \(-0.510612\pi\)
−0.0333336 + 0.999444i \(0.510612\pi\)
\(908\) 0 0
\(909\) −18.5952 −0.616765
\(910\) 0 0
\(911\) −8.45792 −0.280223 −0.140112 0.990136i \(-0.544746\pi\)
−0.140112 + 0.990136i \(0.544746\pi\)
\(912\) 0 0
\(913\) −0.712277 −0.0235729
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.55402 −0.249456
\(918\) 0 0
\(919\) 0.840028 0.0277100 0.0138550 0.999904i \(-0.495590\pi\)
0.0138550 + 0.999904i \(0.495590\pi\)
\(920\) 0 0
\(921\) 31.5711 1.04030
\(922\) 0 0
\(923\) 2.76675 0.0910686
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −31.0861 −1.02100
\(928\) 0 0
\(929\) 15.7877 0.517979 0.258989 0.965880i \(-0.416611\pi\)
0.258989 + 0.965880i \(0.416611\pi\)
\(930\) 0 0
\(931\) −3.92481 −0.128630
\(932\) 0 0
\(933\) 83.2520 2.72555
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −31.6568 −1.03418 −0.517091 0.855930i \(-0.672985\pi\)
−0.517091 + 0.855930i \(0.672985\pi\)
\(938\) 0 0
\(939\) −11.2561 −0.367330
\(940\) 0 0
\(941\) −38.3932 −1.25158 −0.625792 0.779990i \(-0.715224\pi\)
−0.625792 + 0.779990i \(0.715224\pi\)
\(942\) 0 0
\(943\) 5.47041 0.178141
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 34.3783 1.11714 0.558572 0.829456i \(-0.311349\pi\)
0.558572 + 0.829456i \(0.311349\pi\)
\(948\) 0 0
\(949\) −9.31486 −0.302373
\(950\) 0 0
\(951\) −16.4428 −0.533195
\(952\) 0 0
\(953\) −48.3782 −1.56712 −0.783562 0.621314i \(-0.786599\pi\)
−0.783562 + 0.621314i \(0.786599\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 9.98456 0.322755
\(958\) 0 0
\(959\) −21.6541 −0.699247
\(960\) 0 0
\(961\) −30.8072 −0.993782
\(962\) 0 0
\(963\) 42.9443 1.38386
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 51.3705 1.65196 0.825982 0.563697i \(-0.190621\pi\)
0.825982 + 0.563697i \(0.190621\pi\)
\(968\) 0 0
\(969\) −1.92375 −0.0617999
\(970\) 0 0
\(971\) 50.4587 1.61930 0.809649 0.586914i \(-0.199657\pi\)
0.809649 + 0.586914i \(0.199657\pi\)
\(972\) 0 0
\(973\) 29.1539 0.934633
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32.1406 −1.02827 −0.514134 0.857710i \(-0.671887\pi\)
−0.514134 + 0.857710i \(0.671887\pi\)
\(978\) 0 0
\(979\) −3.43964 −0.109931
\(980\) 0 0
\(981\) 67.7392 2.16275
\(982\) 0 0
\(983\) −24.1306 −0.769647 −0.384824 0.922990i \(-0.625738\pi\)
−0.384824 + 0.922990i \(0.625738\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 26.5219 0.844201
\(988\) 0 0
\(989\) −6.72592 −0.213872
\(990\) 0 0
\(991\) 40.1267 1.27467 0.637333 0.770588i \(-0.280038\pi\)
0.637333 + 0.770588i \(0.280038\pi\)
\(992\) 0 0
\(993\) 20.9371 0.664418
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 48.9890 1.55150 0.775749 0.631042i \(-0.217372\pi\)
0.775749 + 0.631042i \(0.217372\pi\)
\(998\) 0 0
\(999\) −15.6020 −0.493625
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 4600.2.a.bd.1.1 5
4.3 odd 2 9200.2.a.cv.1.5 5
5.2 odd 4 4600.2.e.w.4049.10 10
5.3 odd 4 4600.2.e.w.4049.1 10
5.4 even 2 4600.2.a.bf.1.5 yes 5
20.19 odd 2 9200.2.a.ct.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bd.1.1 5 1.1 even 1 trivial
4600.2.a.bf.1.5 yes 5 5.4 even 2
4600.2.e.w.4049.1 10 5.3 odd 4
4600.2.e.w.4049.10 10 5.2 odd 4
9200.2.a.ct.1.1 5 20.19 odd 2
9200.2.a.cv.1.5 5 4.3 odd 2