Properties

Label 600.4.f.a.49.1
Level $600$
Weight $4$
Character 600.49
Analytic conductor $35.401$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 600.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(35.4011460034\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 600.49
Dual form 600.4.f.a.49.2

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000i q^{3} -20.0000i q^{7} -9.00000 q^{9} +O(q^{10})\) \(q-3.00000i q^{3} -20.0000i q^{7} -9.00000 q^{9} -56.0000 q^{11} -86.0000i q^{13} +106.000i q^{17} -4.00000 q^{19} -60.0000 q^{21} +136.000i q^{23} +27.0000i q^{27} +206.000 q^{29} -152.000 q^{31} +168.000i q^{33} -282.000i q^{37} -258.000 q^{39} -246.000 q^{41} +412.000i q^{43} -40.0000i q^{47} -57.0000 q^{49} +318.000 q^{51} -126.000i q^{53} +12.0000i q^{57} -56.0000 q^{59} -2.00000 q^{61} +180.000i q^{63} +388.000i q^{67} +408.000 q^{69} -672.000 q^{71} +1170.00i q^{73} +1120.00i q^{77} -408.000 q^{79} +81.0000 q^{81} +668.000i q^{83} -618.000i q^{87} -66.0000 q^{89} -1720.00 q^{91} +456.000i q^{93} +926.000i q^{97} +504.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 18 q^{9} - 112 q^{11} - 8 q^{19} - 120 q^{21} + 412 q^{29} - 304 q^{31} - 516 q^{39} - 492 q^{41} - 114 q^{49} + 636 q^{51} - 112 q^{59} - 4 q^{61} + 816 q^{69} - 1344 q^{71} - 816 q^{79} + 162 q^{81} - 132 q^{89} - 3440 q^{91} + 1008 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) − 3.00000i − 0.577350i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 20.0000i − 1.07990i −0.841698 0.539949i \(-0.818443\pi\)
0.841698 0.539949i \(-0.181557\pi\)
\(8\) 0 0
\(9\) −9.00000 −0.333333
\(10\) 0 0
\(11\) −56.0000 −1.53497 −0.767483 0.641069i \(-0.778491\pi\)
−0.767483 + 0.641069i \(0.778491\pi\)
\(12\) 0 0
\(13\) − 86.0000i − 1.83478i −0.397992 0.917389i \(-0.630293\pi\)
0.397992 0.917389i \(-0.369707\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 106.000i 1.51228i 0.654409 + 0.756140i \(0.272917\pi\)
−0.654409 + 0.756140i \(0.727083\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) −60.0000 −0.623480
\(22\) 0 0
\(23\) 136.000i 1.23295i 0.787373 + 0.616477i \(0.211441\pi\)
−0.787373 + 0.616477i \(0.788559\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000i 0.192450i
\(28\) 0 0
\(29\) 206.000 1.31908 0.659539 0.751671i \(-0.270752\pi\)
0.659539 + 0.751671i \(0.270752\pi\)
\(30\) 0 0
\(31\) −152.000 −0.880645 −0.440323 0.897840i \(-0.645136\pi\)
−0.440323 + 0.897840i \(0.645136\pi\)
\(32\) 0 0
\(33\) 168.000i 0.886214i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 282.000i − 1.25299i −0.779427 0.626493i \(-0.784490\pi\)
0.779427 0.626493i \(-0.215510\pi\)
\(38\) 0 0
\(39\) −258.000 −1.05931
\(40\) 0 0
\(41\) −246.000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 412.000i 1.46115i 0.682833 + 0.730575i \(0.260748\pi\)
−0.682833 + 0.730575i \(0.739252\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 40.0000i − 0.124140i −0.998072 0.0620702i \(-0.980230\pi\)
0.998072 0.0620702i \(-0.0197703\pi\)
\(48\) 0 0
\(49\) −57.0000 −0.166181
\(50\) 0 0
\(51\) 318.000 0.873116
\(52\) 0 0
\(53\) − 126.000i − 0.326555i −0.986580 0.163278i \(-0.947793\pi\)
0.986580 0.163278i \(-0.0522066\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 12.0000i 0.0278849i
\(58\) 0 0
\(59\) −56.0000 −0.123569 −0.0617846 0.998090i \(-0.519679\pi\)
−0.0617846 + 0.998090i \(0.519679\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.00419793 −0.00209897 0.999998i \(-0.500668\pi\)
−0.00209897 + 0.999998i \(0.500668\pi\)
\(62\) 0 0
\(63\) 180.000i 0.359966i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 388.000i 0.707489i 0.935342 + 0.353744i \(0.115092\pi\)
−0.935342 + 0.353744i \(0.884908\pi\)
\(68\) 0 0
\(69\) 408.000 0.711847
\(70\) 0 0
\(71\) −672.000 −1.12326 −0.561632 0.827387i \(-0.689826\pi\)
−0.561632 + 0.827387i \(0.689826\pi\)
\(72\) 0 0
\(73\) 1170.00i 1.87586i 0.346818 + 0.937932i \(0.387262\pi\)
−0.346818 + 0.937932i \(0.612738\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1120.00i 1.65761i
\(78\) 0 0
\(79\) −408.000 −0.581058 −0.290529 0.956866i \(-0.593831\pi\)
−0.290529 + 0.956866i \(0.593831\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 668.000i 0.883404i 0.897162 + 0.441702i \(0.145625\pi\)
−0.897162 + 0.441702i \(0.854375\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 618.000i − 0.761570i
\(88\) 0 0
\(89\) −66.0000 −0.0786066 −0.0393033 0.999227i \(-0.512514\pi\)
−0.0393033 + 0.999227i \(0.512514\pi\)
\(90\) 0 0
\(91\) −1720.00 −1.98137
\(92\) 0 0
\(93\) 456.000i 0.508441i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 926.000i 0.969289i 0.874711 + 0.484645i \(0.161051\pi\)
−0.874711 + 0.484645i \(0.838949\pi\)
\(98\) 0 0
\(99\) 504.000 0.511656
\(100\) 0 0
\(101\) −198.000 −0.195067 −0.0975333 0.995232i \(-0.531095\pi\)
−0.0975333 + 0.995232i \(0.531095\pi\)
\(102\) 0 0
\(103\) − 1532.00i − 1.46556i −0.680467 0.732779i \(-0.738223\pi\)
0.680467 0.732779i \(-0.261777\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 444.000i 0.401150i 0.979678 + 0.200575i \(0.0642811\pi\)
−0.979678 + 0.200575i \(0.935719\pi\)
\(108\) 0 0
\(109\) −62.0000 −0.0544819 −0.0272409 0.999629i \(-0.508672\pi\)
−0.0272409 + 0.999629i \(0.508672\pi\)
\(110\) 0 0
\(111\) −846.000 −0.723412
\(112\) 0 0
\(113\) 414.000i 0.344653i 0.985040 + 0.172327i \(0.0551285\pi\)
−0.985040 + 0.172327i \(0.944872\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 774.000i 0.611593i
\(118\) 0 0
\(119\) 2120.00 1.63311
\(120\) 0 0
\(121\) 1805.00 1.35612
\(122\) 0 0
\(123\) 738.000i 0.541002i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 996.000i 0.695911i 0.937511 + 0.347956i \(0.113124\pi\)
−0.937511 + 0.347956i \(0.886876\pi\)
\(128\) 0 0
\(129\) 1236.00 0.843595
\(130\) 0 0
\(131\) −264.000 −0.176075 −0.0880374 0.996117i \(-0.528059\pi\)
−0.0880374 + 0.996117i \(0.528059\pi\)
\(132\) 0 0
\(133\) 80.0000i 0.0521570i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 2278.00i − 1.42060i −0.703897 0.710302i \(-0.748558\pi\)
0.703897 0.710302i \(-0.251442\pi\)
\(138\) 0 0
\(139\) −1812.00 −1.10570 −0.552848 0.833282i \(-0.686459\pi\)
−0.552848 + 0.833282i \(0.686459\pi\)
\(140\) 0 0
\(141\) −120.000 −0.0716725
\(142\) 0 0
\(143\) 4816.00i 2.81632i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 171.000i 0.0959445i
\(148\) 0 0
\(149\) 1534.00 0.843424 0.421712 0.906730i \(-0.361429\pi\)
0.421712 + 0.906730i \(0.361429\pi\)
\(150\) 0 0
\(151\) −3016.00 −1.62542 −0.812711 0.582668i \(-0.802009\pi\)
−0.812711 + 0.582668i \(0.802009\pi\)
\(152\) 0 0
\(153\) − 954.000i − 0.504094i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1814.00i 0.922121i 0.887369 + 0.461060i \(0.152531\pi\)
−0.887369 + 0.461060i \(0.847469\pi\)
\(158\) 0 0
\(159\) −378.000 −0.188537
\(160\) 0 0
\(161\) 2720.00 1.33147
\(162\) 0 0
\(163\) − 1844.00i − 0.886093i −0.896499 0.443047i \(-0.853898\pi\)
0.896499 0.443047i \(-0.146102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 3768.00i − 1.74597i −0.487749 0.872984i \(-0.662182\pi\)
0.487749 0.872984i \(-0.337818\pi\)
\(168\) 0 0
\(169\) −5199.00 −2.36641
\(170\) 0 0
\(171\) 36.0000 0.0160993
\(172\) 0 0
\(173\) 938.000i 0.412224i 0.978528 + 0.206112i \(0.0660812\pi\)
−0.978528 + 0.206112i \(0.933919\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 168.000i 0.0713427i
\(178\) 0 0
\(179\) −3968.00 −1.65688 −0.828442 0.560075i \(-0.810772\pi\)
−0.828442 + 0.560075i \(0.810772\pi\)
\(180\) 0 0
\(181\) −3514.00 −1.44306 −0.721529 0.692384i \(-0.756560\pi\)
−0.721529 + 0.692384i \(0.756560\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.00242368i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 5936.00i − 2.32130i
\(188\) 0 0
\(189\) 540.000 0.207827
\(190\) 0 0
\(191\) −1480.00 −0.560676 −0.280338 0.959901i \(-0.590446\pi\)
−0.280338 + 0.959901i \(0.590446\pi\)
\(192\) 0 0
\(193\) − 2774.00i − 1.03460i −0.855806 0.517298i \(-0.826938\pi\)
0.855806 0.517298i \(-0.173062\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3806.00i 1.37648i 0.725484 + 0.688239i \(0.241616\pi\)
−0.725484 + 0.688239i \(0.758384\pi\)
\(198\) 0 0
\(199\) 856.000 0.304926 0.152463 0.988309i \(-0.451280\pi\)
0.152463 + 0.988309i \(0.451280\pi\)
\(200\) 0 0
\(201\) 1164.00 0.408469
\(202\) 0 0
\(203\) − 4120.00i − 1.42447i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 1224.00i − 0.410985i
\(208\) 0 0
\(209\) 224.000 0.0741359
\(210\) 0 0
\(211\) 3020.00 0.985334 0.492667 0.870218i \(-0.336022\pi\)
0.492667 + 0.870218i \(0.336022\pi\)
\(212\) 0 0
\(213\) 2016.00i 0.648517i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3040.00i 0.951008i
\(218\) 0 0
\(219\) 3510.00 1.08303
\(220\) 0 0
\(221\) 9116.00 2.77470
\(222\) 0 0
\(223\) − 1684.00i − 0.505690i −0.967507 0.252845i \(-0.918634\pi\)
0.967507 0.252845i \(-0.0813664\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 2004.00i − 0.585948i −0.956120 0.292974i \(-0.905355\pi\)
0.956120 0.292974i \(-0.0946449\pi\)
\(228\) 0 0
\(229\) 5042.00 1.45496 0.727478 0.686131i \(-0.240693\pi\)
0.727478 + 0.686131i \(0.240693\pi\)
\(230\) 0 0
\(231\) 3360.00 0.957021
\(232\) 0 0
\(233\) − 3090.00i − 0.868810i −0.900718 0.434405i \(-0.856959\pi\)
0.900718 0.434405i \(-0.143041\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1224.00i 0.335474i
\(238\) 0 0
\(239\) −2136.00 −0.578102 −0.289051 0.957314i \(-0.593340\pi\)
−0.289051 + 0.957314i \(0.593340\pi\)
\(240\) 0 0
\(241\) 98.0000 0.0261939 0.0130970 0.999914i \(-0.495831\pi\)
0.0130970 + 0.999914i \(0.495831\pi\)
\(242\) 0 0
\(243\) − 243.000i − 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 344.000i 0.0886162i
\(248\) 0 0
\(249\) 2004.00 0.510033
\(250\) 0 0
\(251\) −5040.00 −1.26742 −0.633709 0.773571i \(-0.718468\pi\)
−0.633709 + 0.773571i \(0.718468\pi\)
\(252\) 0 0
\(253\) − 7616.00i − 1.89254i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1986.00i 0.482036i 0.970521 + 0.241018i \(0.0774813\pi\)
−0.970521 + 0.241018i \(0.922519\pi\)
\(258\) 0 0
\(259\) −5640.00 −1.35310
\(260\) 0 0
\(261\) −1854.00 −0.439692
\(262\) 0 0
\(263\) 1416.00i 0.331994i 0.986126 + 0.165997i \(0.0530841\pi\)
−0.986126 + 0.165997i \(0.946916\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 198.000i 0.0453835i
\(268\) 0 0
\(269\) 6670.00 1.51181 0.755905 0.654681i \(-0.227197\pi\)
0.755905 + 0.654681i \(0.227197\pi\)
\(270\) 0 0
\(271\) 48.0000 0.0107594 0.00537969 0.999986i \(-0.498288\pi\)
0.00537969 + 0.999986i \(0.498288\pi\)
\(272\) 0 0
\(273\) 5160.00i 1.14395i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 6938.00i − 1.50492i −0.658636 0.752462i \(-0.728866\pi\)
0.658636 0.752462i \(-0.271134\pi\)
\(278\) 0 0
\(279\) 1368.00 0.293548
\(280\) 0 0
\(281\) −1694.00 −0.359628 −0.179814 0.983701i \(-0.557550\pi\)
−0.179814 + 0.983701i \(0.557550\pi\)
\(282\) 0 0
\(283\) − 6364.00i − 1.33675i −0.743824 0.668376i \(-0.766990\pi\)
0.743824 0.668376i \(-0.233010\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4920.00i 1.01191i
\(288\) 0 0
\(289\) −6323.00 −1.28699
\(290\) 0 0
\(291\) 2778.00 0.559619
\(292\) 0 0
\(293\) − 3134.00i − 0.624881i −0.949937 0.312441i \(-0.898853\pi\)
0.949937 0.312441i \(-0.101147\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) − 1512.00i − 0.295405i
\(298\) 0 0
\(299\) 11696.0 2.26220
\(300\) 0 0
\(301\) 8240.00 1.57789
\(302\) 0 0
\(303\) 594.000i 0.112622i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 236.000i 0.0438737i 0.999759 + 0.0219369i \(0.00698328\pi\)
−0.999759 + 0.0219369i \(0.993017\pi\)
\(308\) 0 0
\(309\) −4596.00 −0.846140
\(310\) 0 0
\(311\) 3776.00 0.688480 0.344240 0.938882i \(-0.388137\pi\)
0.344240 + 0.938882i \(0.388137\pi\)
\(312\) 0 0
\(313\) − 7918.00i − 1.42988i −0.699187 0.714939i \(-0.746454\pi\)
0.699187 0.714939i \(-0.253546\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 4362.00i − 0.772853i −0.922320 0.386426i \(-0.873709\pi\)
0.922320 0.386426i \(-0.126291\pi\)
\(318\) 0 0
\(319\) −11536.0 −2.02474
\(320\) 0 0
\(321\) 1332.00 0.231604
\(322\) 0 0
\(323\) − 424.000i − 0.0730402i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 186.000i 0.0314551i
\(328\) 0 0
\(329\) −800.000 −0.134059
\(330\) 0 0
\(331\) 7980.00 1.32514 0.662569 0.749001i \(-0.269466\pi\)
0.662569 + 0.749001i \(0.269466\pi\)
\(332\) 0 0
\(333\) 2538.00i 0.417662i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8294.00i 1.34066i 0.742062 + 0.670331i \(0.233848\pi\)
−0.742062 + 0.670331i \(0.766152\pi\)
\(338\) 0 0
\(339\) 1242.00 0.198986
\(340\) 0 0
\(341\) 8512.00 1.35176
\(342\) 0 0
\(343\) − 5720.00i − 0.900440i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 964.000i 0.149136i 0.997216 + 0.0745681i \(0.0237578\pi\)
−0.997216 + 0.0745681i \(0.976242\pi\)
\(348\) 0 0
\(349\) −8670.00 −1.32978 −0.664892 0.746940i \(-0.731522\pi\)
−0.664892 + 0.746940i \(0.731522\pi\)
\(350\) 0 0
\(351\) 2322.00 0.353103
\(352\) 0 0
\(353\) − 2314.00i − 0.348900i −0.984666 0.174450i \(-0.944185\pi\)
0.984666 0.174450i \(-0.0558148\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 6360.00i − 0.942876i
\(358\) 0 0
\(359\) 1896.00 0.278738 0.139369 0.990240i \(-0.455493\pi\)
0.139369 + 0.990240i \(0.455493\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) − 5415.00i − 0.782958i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 1484.00i − 0.211074i −0.994415 0.105537i \(-0.966344\pi\)
0.994415 0.105537i \(-0.0336562\pi\)
\(368\) 0 0
\(369\) 2214.00 0.312348
\(370\) 0 0
\(371\) −2520.00 −0.352647
\(372\) 0 0
\(373\) 12370.0i 1.71714i 0.512694 + 0.858571i \(0.328648\pi\)
−0.512694 + 0.858571i \(0.671352\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 17716.0i − 2.42021i
\(378\) 0 0
\(379\) −5620.00 −0.761689 −0.380844 0.924639i \(-0.624367\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(380\) 0 0
\(381\) 2988.00 0.401784
\(382\) 0 0
\(383\) 5880.00i 0.784475i 0.919864 + 0.392238i \(0.128299\pi\)
−0.919864 + 0.392238i \(0.871701\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 3708.00i − 0.487050i
\(388\) 0 0
\(389\) −2082.00 −0.271367 −0.135683 0.990752i \(-0.543323\pi\)
−0.135683 + 0.990752i \(0.543323\pi\)
\(390\) 0 0
\(391\) −14416.0 −1.86457
\(392\) 0 0
\(393\) 792.000i 0.101657i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1742.00i 0.220223i 0.993919 + 0.110111i \(0.0351208\pi\)
−0.993919 + 0.110111i \(0.964879\pi\)
\(398\) 0 0
\(399\) 240.000 0.0301129
\(400\) 0 0
\(401\) −3270.00 −0.407222 −0.203611 0.979052i \(-0.565268\pi\)
−0.203611 + 0.979052i \(0.565268\pi\)
\(402\) 0 0
\(403\) 13072.0i 1.61579i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 15792.0i 1.92329i
\(408\) 0 0
\(409\) 6134.00 0.741581 0.370791 0.928716i \(-0.379087\pi\)
0.370791 + 0.928716i \(0.379087\pi\)
\(410\) 0 0
\(411\) −6834.00 −0.820186
\(412\) 0 0
\(413\) 1120.00i 0.133442i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5436.00i 0.638374i
\(418\) 0 0
\(419\) 10392.0 1.21165 0.605826 0.795597i \(-0.292843\pi\)
0.605826 + 0.795597i \(0.292843\pi\)
\(420\) 0 0
\(421\) −12690.0 −1.46906 −0.734528 0.678578i \(-0.762596\pi\)
−0.734528 + 0.678578i \(0.762596\pi\)
\(422\) 0 0
\(423\) 360.000i 0.0413801i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 40.0000i 0.00453334i
\(428\) 0 0
\(429\) 14448.0 1.62600
\(430\) 0 0
\(431\) −7408.00 −0.827914 −0.413957 0.910297i \(-0.635854\pi\)
−0.413957 + 0.910297i \(0.635854\pi\)
\(432\) 0 0
\(433\) − 5062.00i − 0.561811i −0.959735 0.280906i \(-0.909365\pi\)
0.959735 0.280906i \(-0.0906348\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 544.000i − 0.0595493i
\(438\) 0 0
\(439\) 7160.00 0.778424 0.389212 0.921148i \(-0.372747\pi\)
0.389212 + 0.921148i \(0.372747\pi\)
\(440\) 0 0
\(441\) 513.000 0.0553936
\(442\) 0 0
\(443\) 17100.0i 1.83396i 0.398930 + 0.916981i \(0.369382\pi\)
−0.398930 + 0.916981i \(0.630618\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 4602.00i − 0.486951i
\(448\) 0 0
\(449\) −8634.00 −0.907491 −0.453746 0.891131i \(-0.649913\pi\)
−0.453746 + 0.891131i \(0.649913\pi\)
\(450\) 0 0
\(451\) 13776.0 1.43833
\(452\) 0 0
\(453\) 9048.00i 0.938437i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 2986.00i − 0.305644i −0.988254 0.152822i \(-0.951164\pi\)
0.988254 0.152822i \(-0.0488361\pi\)
\(458\) 0 0
\(459\) −2862.00 −0.291039
\(460\) 0 0
\(461\) −2406.00 −0.243077 −0.121539 0.992587i \(-0.538783\pi\)
−0.121539 + 0.992587i \(0.538783\pi\)
\(462\) 0 0
\(463\) − 14316.0i − 1.43698i −0.695538 0.718489i \(-0.744834\pi\)
0.695538 0.718489i \(-0.255166\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 292.000i 0.0289339i 0.999895 + 0.0144670i \(0.00460514\pi\)
−0.999895 + 0.0144670i \(0.995395\pi\)
\(468\) 0 0
\(469\) 7760.00 0.764016
\(470\) 0 0
\(471\) 5442.00 0.532387
\(472\) 0 0
\(473\) − 23072.0i − 2.24282i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1134.00i 0.108852i
\(478\) 0 0
\(479\) −14056.0 −1.34078 −0.670391 0.742008i \(-0.733874\pi\)
−0.670391 + 0.742008i \(0.733874\pi\)
\(480\) 0 0
\(481\) −24252.0 −2.29895
\(482\) 0 0
\(483\) − 8160.00i − 0.768722i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11204.0i 1.04251i 0.853401 + 0.521254i \(0.174536\pi\)
−0.853401 + 0.521254i \(0.825464\pi\)
\(488\) 0 0
\(489\) −5532.00 −0.511586
\(490\) 0 0
\(491\) 4608.00 0.423536 0.211768 0.977320i \(-0.432078\pi\)
0.211768 + 0.977320i \(0.432078\pi\)
\(492\) 0 0
\(493\) 21836.0i 1.99482i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13440.0i 1.21301i
\(498\) 0 0
\(499\) −2468.00 −0.221409 −0.110704 0.993853i \(-0.535311\pi\)
−0.110704 + 0.993853i \(0.535311\pi\)
\(500\) 0 0
\(501\) −11304.0 −1.00803
\(502\) 0 0
\(503\) 12192.0i 1.08074i 0.841426 + 0.540372i \(0.181717\pi\)
−0.841426 + 0.540372i \(0.818283\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 15597.0i 1.36625i
\(508\) 0 0
\(509\) −1714.00 −0.149257 −0.0746284 0.997211i \(-0.523777\pi\)
−0.0746284 + 0.997211i \(0.523777\pi\)
\(510\) 0 0
\(511\) 23400.0 2.02574
\(512\) 0 0
\(513\) − 108.000i − 0.00929496i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2240.00i 0.190551i
\(518\) 0 0
\(519\) 2814.00 0.237998
\(520\) 0 0
\(521\) −18014.0 −1.51479 −0.757397 0.652955i \(-0.773529\pi\)
−0.757397 + 0.652955i \(0.773529\pi\)
\(522\) 0 0
\(523\) − 16748.0i − 1.40027i −0.714013 0.700133i \(-0.753124\pi\)
0.714013 0.700133i \(-0.246876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 16112.0i − 1.33178i
\(528\) 0 0
\(529\) −6329.00 −0.520178
\(530\) 0 0
\(531\) 504.000 0.0411897
\(532\) 0 0
\(533\) 21156.0i 1.71926i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11904.0i 0.956602i
\(538\) 0 0
\(539\) 3192.00 0.255082
\(540\) 0 0
\(541\) −14018.0 −1.11401 −0.557006 0.830508i \(-0.688050\pi\)
−0.557006 + 0.830508i \(0.688050\pi\)
\(542\) 0 0
\(543\) 10542.0i 0.833150i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 412.000i 0.0322045i 0.999870 + 0.0161022i \(0.00512572\pi\)
−0.999870 + 0.0161022i \(0.994874\pi\)
\(548\) 0 0
\(549\) 18.0000 0.00139931
\(550\) 0 0
\(551\) −824.000 −0.0637089
\(552\) 0 0
\(553\) 8160.00i 0.627484i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 18218.0i − 1.38586i −0.721007 0.692928i \(-0.756321\pi\)
0.721007 0.692928i \(-0.243679\pi\)
\(558\) 0 0
\(559\) 35432.0 2.68088
\(560\) 0 0
\(561\) −17808.0 −1.34020
\(562\) 0 0
\(563\) 23524.0i 1.76096i 0.474087 + 0.880478i \(0.342778\pi\)
−0.474087 + 0.880478i \(0.657222\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 1620.00i − 0.119989i
\(568\) 0 0
\(569\) −23330.0 −1.71888 −0.859442 0.511234i \(-0.829189\pi\)
−0.859442 + 0.511234i \(0.829189\pi\)
\(570\) 0 0
\(571\) −13124.0 −0.961860 −0.480930 0.876759i \(-0.659701\pi\)
−0.480930 + 0.876759i \(0.659701\pi\)
\(572\) 0 0
\(573\) 4440.00i 0.323706i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 11714.0i − 0.845165i −0.906324 0.422582i \(-0.861124\pi\)
0.906324 0.422582i \(-0.138876\pi\)
\(578\) 0 0
\(579\) −8322.00 −0.597324
\(580\) 0 0
\(581\) 13360.0 0.953987
\(582\) 0 0
\(583\) 7056.00i 0.501252i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 17628.0i 1.23950i 0.784800 + 0.619749i \(0.212766\pi\)
−0.784800 + 0.619749i \(0.787234\pi\)
\(588\) 0 0
\(589\) 608.000 0.0425335
\(590\) 0 0
\(591\) 11418.0 0.794710
\(592\) 0 0
\(593\) − 2802.00i − 0.194038i −0.995283 0.0970188i \(-0.969069\pi\)
0.995283 0.0970188i \(-0.0309307\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 2568.00i − 0.176049i
\(598\) 0 0
\(599\) 2664.00 0.181716 0.0908582 0.995864i \(-0.471039\pi\)
0.0908582 + 0.995864i \(0.471039\pi\)
\(600\) 0 0
\(601\) 23962.0 1.62634 0.813170 0.582026i \(-0.197740\pi\)
0.813170 + 0.582026i \(0.197740\pi\)
\(602\) 0 0
\(603\) − 3492.00i − 0.235830i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 11940.0i − 0.798401i −0.916864 0.399201i \(-0.869288\pi\)
0.916864 0.399201i \(-0.130712\pi\)
\(608\) 0 0
\(609\) −12360.0 −0.822418
\(610\) 0 0
\(611\) −3440.00 −0.227770
\(612\) 0 0
\(613\) 16794.0i 1.10653i 0.833005 + 0.553265i \(0.186618\pi\)
−0.833005 + 0.553265i \(0.813382\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20706.0i 1.35104i 0.737341 + 0.675520i \(0.236081\pi\)
−0.737341 + 0.675520i \(0.763919\pi\)
\(618\) 0 0
\(619\) −10724.0 −0.696339 −0.348170 0.937432i \(-0.613197\pi\)
−0.348170 + 0.937432i \(0.613197\pi\)
\(620\) 0 0
\(621\) −3672.00 −0.237282
\(622\) 0 0
\(623\) 1320.00i 0.0848871i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) − 672.000i − 0.0428024i
\(628\) 0 0
\(629\) 29892.0 1.89487
\(630\) 0 0
\(631\) −5744.00 −0.362385 −0.181193 0.983448i \(-0.557996\pi\)
−0.181193 + 0.983448i \(0.557996\pi\)
\(632\) 0 0
\(633\) − 9060.00i − 0.568883i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4902.00i 0.304905i
\(638\) 0 0
\(639\) 6048.00 0.374421
\(640\) 0 0
\(641\) 27906.0 1.71953 0.859767 0.510687i \(-0.170609\pi\)
0.859767 + 0.510687i \(0.170609\pi\)
\(642\) 0 0
\(643\) 20556.0i 1.26073i 0.776299 + 0.630365i \(0.217095\pi\)
−0.776299 + 0.630365i \(0.782905\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10224.0i 0.621247i 0.950533 + 0.310624i \(0.100538\pi\)
−0.950533 + 0.310624i \(0.899462\pi\)
\(648\) 0 0
\(649\) 3136.00 0.189675
\(650\) 0 0
\(651\) 9120.00 0.549064
\(652\) 0 0
\(653\) − 12982.0i − 0.777986i −0.921241 0.388993i \(-0.872823\pi\)
0.921241 0.388993i \(-0.127177\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 10530.0i − 0.625288i
\(658\) 0 0
\(659\) 1512.00 0.0893766 0.0446883 0.999001i \(-0.485771\pi\)
0.0446883 + 0.999001i \(0.485771\pi\)
\(660\) 0 0
\(661\) 16710.0 0.983273 0.491637 0.870800i \(-0.336399\pi\)
0.491637 + 0.870800i \(0.336399\pi\)
\(662\) 0 0
\(663\) − 27348.0i − 1.60197i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28016.0i 1.62636i
\(668\) 0 0
\(669\) −5052.00 −0.291961
\(670\) 0 0
\(671\) 112.000 0.00644368
\(672\) 0 0
\(673\) 7962.00i 0.456036i 0.973657 + 0.228018i \(0.0732246\pi\)
−0.973657 + 0.228018i \(0.926775\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 12226.0i − 0.694067i −0.937853 0.347033i \(-0.887189\pi\)
0.937853 0.347033i \(-0.112811\pi\)
\(678\) 0 0
\(679\) 18520.0 1.04673
\(680\) 0 0
\(681\) −6012.00 −0.338297
\(682\) 0 0
\(683\) − 8748.00i − 0.490092i −0.969511 0.245046i \(-0.921197\pi\)
0.969511 0.245046i \(-0.0788031\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 15126.0i − 0.840019i
\(688\) 0 0
\(689\) −10836.0 −0.599156
\(690\) 0 0
\(691\) −7324.00 −0.403210 −0.201605 0.979467i \(-0.564616\pi\)
−0.201605 + 0.979467i \(0.564616\pi\)
\(692\) 0 0
\(693\) − 10080.0i − 0.552536i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 26076.0i − 1.41707i
\(698\) 0 0
\(699\) −9270.00 −0.501607
\(700\) 0 0
\(701\) −21934.0 −1.18179 −0.590896 0.806748i \(-0.701226\pi\)
−0.590896 + 0.806748i \(0.701226\pi\)
\(702\) 0 0
\(703\) 1128.00i 0.0605168i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3960.00i 0.210652i
\(708\) 0 0
\(709\) 10690.0 0.566250 0.283125 0.959083i \(-0.408629\pi\)
0.283125 + 0.959083i \(0.408629\pi\)
\(710\) 0 0
\(711\) 3672.00 0.193686
\(712\) 0 0
\(713\) − 20672.0i − 1.08580i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6408.00i 0.333767i
\(718\) 0 0
\(719\) −13792.0 −0.715375 −0.357688 0.933841i \(-0.616435\pi\)
−0.357688 + 0.933841i \(0.616435\pi\)
\(720\) 0 0
\(721\) −30640.0 −1.58265
\(722\) 0 0
\(723\) − 294.000i − 0.0151231i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 24004.0i 1.22457i 0.790639 + 0.612283i \(0.209749\pi\)
−0.790639 + 0.612283i \(0.790251\pi\)
\(728\) 0 0
\(729\) −729.000 −0.0370370
\(730\) 0 0
\(731\) −43672.0 −2.20967
\(732\) 0 0
\(733\) 8562.00i 0.431439i 0.976455 + 0.215719i \(0.0692097\pi\)
−0.976455 + 0.215719i \(0.930790\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 21728.0i − 1.08597i
\(738\) 0 0
\(739\) 13836.0 0.688722 0.344361 0.938837i \(-0.388096\pi\)
0.344361 + 0.938837i \(0.388096\pi\)
\(740\) 0 0
\(741\) 1032.00 0.0511626
\(742\) 0 0
\(743\) − 22224.0i − 1.09733i −0.836041 0.548667i \(-0.815135\pi\)
0.836041 0.548667i \(-0.184865\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 6012.00i − 0.294468i
\(748\) 0 0
\(749\) 8880.00 0.433202
\(750\) 0 0
\(751\) 11544.0 0.560914 0.280457 0.959867i \(-0.409514\pi\)
0.280457 + 0.959867i \(0.409514\pi\)
\(752\) 0 0
\(753\) 15120.0i 0.731744i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3814.00i 0.183120i 0.995800 + 0.0915602i \(0.0291854\pi\)
−0.995800 + 0.0915602i \(0.970815\pi\)
\(758\) 0 0
\(759\) −22848.0 −1.09266
\(760\) 0 0
\(761\) −25662.0 −1.22240 −0.611200 0.791476i \(-0.709313\pi\)
−0.611200 + 0.791476i \(0.709313\pi\)
\(762\) 0 0
\(763\) 1240.00i 0.0588349i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4816.00i 0.226722i
\(768\) 0 0
\(769\) −30658.0 −1.43765 −0.718827 0.695189i \(-0.755321\pi\)
−0.718827 + 0.695189i \(0.755321\pi\)
\(770\) 0 0
\(771\) 5958.00 0.278304
\(772\) 0 0
\(773\) − 30894.0i − 1.43749i −0.695274 0.718745i \(-0.744717\pi\)
0.695274 0.718745i \(-0.255283\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16920.0i 0.781212i
\(778\) 0 0
\(779\) 984.000 0.0452573
\(780\) 0 0
\(781\) 37632.0 1.72417
\(782\) 0 0
\(783\) 5562.00i 0.253857i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 21596.0i − 0.978163i −0.872238 0.489081i \(-0.837332\pi\)
0.872238 0.489081i \(-0.162668\pi\)
\(788\) 0 0
\(789\) 4248.00 0.191677
\(790\) 0 0
\(791\) 8280.00 0.372191
\(792\) 0 0
\(793\) 172.000i 0.00770227i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8646.00i 0.384262i 0.981369 + 0.192131i \(0.0615399\pi\)
−0.981369 + 0.192131i \(0.938460\pi\)
\(798\) 0 0
\(799\) 4240.00 0.187735
\(800\) 0 0
\(801\) 594.000 0.0262022
\(802\) 0 0
\(803\) − 65520.0i − 2.87939i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) − 20010.0i − 0.872844i
\(808\) 0 0
\(809\) −24954.0 −1.08447 −0.542235 0.840227i \(-0.682422\pi\)
−0.542235 + 0.840227i \(0.682422\pi\)
\(810\) 0 0
\(811\) 40004.0 1.73210 0.866048 0.499960i \(-0.166652\pi\)
0.866048 + 0.499960i \(0.166652\pi\)
\(812\) 0 0
\(813\) − 144.000i − 0.00621193i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 1648.00i − 0.0705707i
\(818\) 0 0
\(819\) 15480.0 0.660458
\(820\) 0 0
\(821\) 16570.0 0.704381 0.352191 0.935928i \(-0.385437\pi\)
0.352191 + 0.935928i \(0.385437\pi\)
\(822\) 0 0
\(823\) − 4388.00i − 0.185852i −0.995673 0.0929259i \(-0.970378\pi\)
0.995673 0.0929259i \(-0.0296220\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 14364.0i − 0.603972i −0.953312 0.301986i \(-0.902350\pi\)
0.953312 0.301986i \(-0.0976497\pi\)
\(828\) 0 0
\(829\) 21170.0 0.886929 0.443465 0.896292i \(-0.353749\pi\)
0.443465 + 0.896292i \(0.353749\pi\)
\(830\) 0 0
\(831\) −20814.0 −0.868868
\(832\) 0 0
\(833\) − 6042.00i − 0.251312i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 4104.00i − 0.169480i
\(838\) 0 0
\(839\) −10664.0 −0.438811 −0.219405 0.975634i \(-0.570412\pi\)
−0.219405 + 0.975634i \(0.570412\pi\)
\(840\) 0 0
\(841\) 18047.0 0.739965
\(842\) 0 0
\(843\) 5082.00i 0.207632i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 36100.0i − 1.46448i
\(848\) 0 0
\(849\) −19092.0 −0.771774
\(850\) 0 0
\(851\) 38352.0 1.54488
\(852\) 0 0
\(853\) − 3190.00i − 0.128046i −0.997948 0.0640232i \(-0.979607\pi\)
0.997948 0.0640232i \(-0.0203932\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 20814.0i − 0.829630i −0.909906 0.414815i \(-0.863846\pi\)
0.909906 0.414815i \(-0.136154\pi\)
\(858\) 0 0
\(859\) 18988.0 0.754205 0.377103 0.926172i \(-0.376920\pi\)
0.377103 + 0.926172i \(0.376920\pi\)
\(860\) 0 0
\(861\) 14760.0 0.584227
\(862\) 0 0
\(863\) 11664.0i 0.460078i 0.973181 + 0.230039i \(0.0738854\pi\)
−0.973181 + 0.230039i \(0.926115\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 18969.0i 0.743046i
\(868\) 0 0
\(869\) 22848.0 0.891905
\(870\) 0 0
\(871\) 33368.0 1.29808
\(872\) 0 0
\(873\) − 8334.00i − 0.323096i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 8246.00i 0.317500i 0.987319 + 0.158750i \(0.0507464\pi\)
−0.987319 + 0.158750i \(0.949254\pi\)
\(878\) 0 0
\(879\) −9402.00 −0.360775
\(880\) 0 0
\(881\) 22890.0 0.875350 0.437675 0.899133i \(-0.355802\pi\)
0.437675 + 0.899133i \(0.355802\pi\)
\(882\) 0 0
\(883\) 33548.0i 1.27857i 0.768969 + 0.639287i \(0.220770\pi\)
−0.768969 + 0.639287i \(0.779230\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32264.0i 1.22133i 0.791889 + 0.610665i \(0.209098\pi\)
−0.791889 + 0.610665i \(0.790902\pi\)
\(888\) 0 0
\(889\) 19920.0 0.751513
\(890\) 0 0
\(891\) −4536.00 −0.170552
\(892\) 0 0
\(893\) 160.000i 0.00599574i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 35088.0i − 1.30608i
\(898\) 0 0
\(899\) −31312.0 −1.16164
\(900\) 0 0
\(901\) 13356.0 0.493843
\(902\) 0 0
\(903\) − 24720.0i − 0.910997i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 51228.0i − 1.87541i −0.347431 0.937706i \(-0.612946\pi\)
0.347431 0.937706i \(-0.387054\pi\)
\(908\) 0 0
\(909\) 1782.00 0.0650222
\(910\) 0 0
\(911\) −2144.00 −0.0779735 −0.0389868 0.999240i \(-0.512413\pi\)
−0.0389868 + 0.999240i \(0.512413\pi\)
\(912\) 0 0
\(913\) − 37408.0i − 1.35600i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5280.00i 0.190143i
\(918\) 0 0
\(919\) −33584.0 −1.20548 −0.602739 0.797939i \(-0.705924\pi\)
−0.602739 + 0.797939i \(0.705924\pi\)
\(920\) 0 0
\(921\) 708.000 0.0253305
\(922\) 0 0
\(923\) 57792.0i 2.06094i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 13788.0i 0.488519i
\(928\) 0 0
\(929\) 3590.00 0.126786 0.0633929 0.997989i \(-0.479808\pi\)
0.0633929 + 0.997989i \(0.479808\pi\)
\(930\) 0 0
\(931\) 228.000 0.00802621
\(932\) 0 0
\(933\) − 11328.0i − 0.397494i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 21686.0i 0.756084i 0.925788 + 0.378042i \(0.123403\pi\)
−0.925788 + 0.378042i \(0.876597\pi\)
\(938\) 0 0
\(939\) −23754.0 −0.825540
\(940\) 0 0
\(941\) −5174.00 −0.179243 −0.0896215 0.995976i \(-0.528566\pi\)
−0.0896215 + 0.995976i \(0.528566\pi\)
\(942\) 0 0
\(943\) − 33456.0i − 1.15533i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 35524.0i − 1.21898i −0.792793 0.609490i \(-0.791374\pi\)
0.792793 0.609490i \(-0.208626\pi\)
\(948\) 0 0
\(949\) 100620. 3.44179
\(950\) 0 0
\(951\) −13086.0 −0.446207
\(952\) 0 0
\(953\) − 16122.0i − 0.547999i −0.961730 0.273999i \(-0.911653\pi\)
0.961730 0.273999i \(-0.0883466\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 34608.0i 1.16898i
\(958\) 0 0
\(959\) −45560.0 −1.53411
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) 0 0
\(963\) − 3996.00i − 0.133717i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 19188.0i − 0.638102i −0.947738 0.319051i \(-0.896636\pi\)
0.947738 0.319051i \(-0.103364\pi\)
\(968\) 0 0
\(969\) −1272.00 −0.0421698
\(970\) 0 0
\(971\) −38464.0 −1.27123 −0.635617 0.772004i \(-0.719254\pi\)
−0.635617 + 0.772004i \(0.719254\pi\)
\(972\) 0 0
\(973\) 36240.0i 1.19404i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43930.0i 1.43853i 0.694735 + 0.719266i \(0.255522\pi\)
−0.694735 + 0.719266i \(0.744478\pi\)
\(978\) 0 0
\(979\) 3696.00 0.120659
\(980\) 0 0
\(981\) 558.000 0.0181606
\(982\) 0 0
\(983\) 17328.0i 0.562235i 0.959673 + 0.281118i \(0.0907051\pi\)
−0.959673 + 0.281118i \(0.909295\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2400.00i 0.0773990i
\(988\) 0 0
\(989\) −56032.0 −1.80153
\(990\) 0 0
\(991\) −18160.0 −0.582110 −0.291055 0.956706i \(-0.594006\pi\)
−0.291055 + 0.956706i \(0.594006\pi\)
\(992\) 0 0
\(993\) − 23940.0i − 0.765068i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 9102.00i 0.289131i 0.989495 + 0.144565i \(0.0461784\pi\)
−0.989495 + 0.144565i \(0.953822\pi\)
\(998\) 0 0
\(999\) 7614.00 0.241137
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 600.4.f.a.49.1 2
3.2 odd 2 1800.4.f.v.649.1 2
4.3 odd 2 1200.4.f.t.49.2 2
5.2 odd 4 120.4.a.b.1.1 1
5.3 odd 4 600.4.a.i.1.1 1
5.4 even 2 inner 600.4.f.a.49.2 2
15.2 even 4 360.4.a.n.1.1 1
15.8 even 4 1800.4.a.f.1.1 1
15.14 odd 2 1800.4.f.v.649.2 2
20.3 even 4 1200.4.a.p.1.1 1
20.7 even 4 240.4.a.g.1.1 1
20.19 odd 2 1200.4.f.t.49.1 2
40.27 even 4 960.4.a.k.1.1 1
40.37 odd 4 960.4.a.bj.1.1 1
60.47 odd 4 720.4.a.q.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.b.1.1 1 5.2 odd 4
240.4.a.g.1.1 1 20.7 even 4
360.4.a.n.1.1 1 15.2 even 4
600.4.a.i.1.1 1 5.3 odd 4
600.4.f.a.49.1 2 1.1 even 1 trivial
600.4.f.a.49.2 2 5.4 even 2 inner
720.4.a.q.1.1 1 60.47 odd 4
960.4.a.k.1.1 1 40.27 even 4
960.4.a.bj.1.1 1 40.37 odd 4
1200.4.a.p.1.1 1 20.3 even 4
1200.4.f.t.49.1 2 20.19 odd 2
1200.4.f.t.49.2 2 4.3 odd 2
1800.4.a.f.1.1 1 15.8 even 4
1800.4.f.v.649.1 2 3.2 odd 2
1800.4.f.v.649.2 2 15.14 odd 2