Properties

Label 2450.4.a.bx.1.1
Level $2450$
Weight $4$
Character 2450.1
Self dual yes
Analytic conductor $144.555$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(144.554679514\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 98)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 2450.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -7.07107 q^{3} +4.00000 q^{4} -14.1421 q^{6} +8.00000 q^{8} +23.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -7.07107 q^{3} +4.00000 q^{4} -14.1421 q^{6} +8.00000 q^{8} +23.0000 q^{9} -14.0000 q^{11} -28.2843 q^{12} +50.9117 q^{13} +16.0000 q^{16} +1.41421 q^{17} +46.0000 q^{18} +1.41421 q^{19} -28.0000 q^{22} -140.000 q^{23} -56.5685 q^{24} +101.823 q^{26} +28.2843 q^{27} -286.000 q^{29} +93.3381 q^{31} +32.0000 q^{32} +98.9949 q^{33} +2.82843 q^{34} +92.0000 q^{36} +38.0000 q^{37} +2.82843 q^{38} -360.000 q^{39} +125.865 q^{41} +34.0000 q^{43} -56.0000 q^{44} -280.000 q^{46} +523.259 q^{47} -113.137 q^{48} -10.0000 q^{51} +203.647 q^{52} +74.0000 q^{53} +56.5685 q^{54} -10.0000 q^{57} -572.000 q^{58} -434.164 q^{59} -14.1421 q^{61} +186.676 q^{62} +64.0000 q^{64} +197.990 q^{66} -684.000 q^{67} +5.65685 q^{68} +989.949 q^{69} +588.000 q^{71} +184.000 q^{72} -270.115 q^{73} +76.0000 q^{74} +5.65685 q^{76} -720.000 q^{78} +1220.00 q^{79} -821.000 q^{81} +251.730 q^{82} +422.850 q^{83} +68.0000 q^{86} +2022.33 q^{87} -112.000 q^{88} -618.011 q^{89} -560.000 q^{92} -660.000 q^{93} +1046.52 q^{94} -226.274 q^{96} +1483.51 q^{97} -322.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{2} + 8q^{4} + 16q^{8} + 46q^{9} + O(q^{10}) \) \( 2q + 4q^{2} + 8q^{4} + 16q^{8} + 46q^{9} - 28q^{11} + 32q^{16} + 92q^{18} - 56q^{22} - 280q^{23} - 572q^{29} + 64q^{32} + 184q^{36} + 76q^{37} - 720q^{39} + 68q^{43} - 112q^{44} - 560q^{46} - 20q^{51} + 148q^{53} - 20q^{57} - 1144q^{58} + 128q^{64} - 1368q^{67} + 1176q^{71} + 368q^{72} + 152q^{74} - 1440q^{78} + 2440q^{79} - 1642q^{81} + 136q^{86} - 224q^{88} - 1120q^{92} - 1320q^{93} - 644q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −7.07107 −1.36083 −0.680414 0.732828i \(-0.738200\pi\)
−0.680414 + 0.732828i \(0.738200\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −14.1421 −0.962250
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 23.0000 0.851852
\(10\) 0 0
\(11\) −14.0000 −0.383742 −0.191871 0.981420i \(-0.561455\pi\)
−0.191871 + 0.981420i \(0.561455\pi\)
\(12\) −28.2843 −0.680414
\(13\) 50.9117 1.08618 0.543091 0.839674i \(-0.317254\pi\)
0.543091 + 0.839674i \(0.317254\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 1.41421 0.0201763 0.0100882 0.999949i \(-0.496789\pi\)
0.0100882 + 0.999949i \(0.496789\pi\)
\(18\) 46.0000 0.602350
\(19\) 1.41421 0.0170759 0.00853797 0.999964i \(-0.497282\pi\)
0.00853797 + 0.999964i \(0.497282\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −28.0000 −0.271346
\(23\) −140.000 −1.26922 −0.634609 0.772833i \(-0.718839\pi\)
−0.634609 + 0.772833i \(0.718839\pi\)
\(24\) −56.5685 −0.481125
\(25\) 0 0
\(26\) 101.823 0.768046
\(27\) 28.2843 0.201604
\(28\) 0 0
\(29\) −286.000 −1.83134 −0.915670 0.401931i \(-0.868339\pi\)
−0.915670 + 0.401931i \(0.868339\pi\)
\(30\) 0 0
\(31\) 93.3381 0.540775 0.270387 0.962752i \(-0.412848\pi\)
0.270387 + 0.962752i \(0.412848\pi\)
\(32\) 32.0000 0.176777
\(33\) 98.9949 0.522206
\(34\) 2.82843 0.0142668
\(35\) 0 0
\(36\) 92.0000 0.425926
\(37\) 38.0000 0.168842 0.0844211 0.996430i \(-0.473096\pi\)
0.0844211 + 0.996430i \(0.473096\pi\)
\(38\) 2.82843 0.0120745
\(39\) −360.000 −1.47811
\(40\) 0 0
\(41\) 125.865 0.479434 0.239717 0.970843i \(-0.422945\pi\)
0.239717 + 0.970843i \(0.422945\pi\)
\(42\) 0 0
\(43\) 34.0000 0.120580 0.0602901 0.998181i \(-0.480797\pi\)
0.0602901 + 0.998181i \(0.480797\pi\)
\(44\) −56.0000 −0.191871
\(45\) 0 0
\(46\) −280.000 −0.897473
\(47\) 523.259 1.62394 0.811970 0.583699i \(-0.198395\pi\)
0.811970 + 0.583699i \(0.198395\pi\)
\(48\) −113.137 −0.340207
\(49\) 0 0
\(50\) 0 0
\(51\) −10.0000 −0.0274565
\(52\) 203.647 0.543091
\(53\) 74.0000 0.191786 0.0958932 0.995392i \(-0.469429\pi\)
0.0958932 + 0.995392i \(0.469429\pi\)
\(54\) 56.5685 0.142556
\(55\) 0 0
\(56\) 0 0
\(57\) −10.0000 −0.0232374
\(58\) −572.000 −1.29495
\(59\) −434.164 −0.958022 −0.479011 0.877809i \(-0.659005\pi\)
−0.479011 + 0.877809i \(0.659005\pi\)
\(60\) 0 0
\(61\) −14.1421 −0.0296839 −0.0148419 0.999890i \(-0.504725\pi\)
−0.0148419 + 0.999890i \(0.504725\pi\)
\(62\) 186.676 0.382385
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 197.990 0.369256
\(67\) −684.000 −1.24722 −0.623611 0.781735i \(-0.714335\pi\)
−0.623611 + 0.781735i \(0.714335\pi\)
\(68\) 5.65685 0.0100882
\(69\) 989.949 1.72719
\(70\) 0 0
\(71\) 588.000 0.982856 0.491428 0.870918i \(-0.336475\pi\)
0.491428 + 0.870918i \(0.336475\pi\)
\(72\) 184.000 0.301175
\(73\) −270.115 −0.433076 −0.216538 0.976274i \(-0.569477\pi\)
−0.216538 + 0.976274i \(0.569477\pi\)
\(74\) 76.0000 0.119389
\(75\) 0 0
\(76\) 5.65685 0.00853797
\(77\) 0 0
\(78\) −720.000 −1.04518
\(79\) 1220.00 1.73748 0.868739 0.495271i \(-0.164931\pi\)
0.868739 + 0.495271i \(0.164931\pi\)
\(80\) 0 0
\(81\) −821.000 −1.12620
\(82\) 251.730 0.339011
\(83\) 422.850 0.559202 0.279601 0.960116i \(-0.409798\pi\)
0.279601 + 0.960116i \(0.409798\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 68.0000 0.0852631
\(87\) 2022.33 2.49214
\(88\) −112.000 −0.135673
\(89\) −618.011 −0.736057 −0.368028 0.929815i \(-0.619967\pi\)
−0.368028 + 0.929815i \(0.619967\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −560.000 −0.634609
\(93\) −660.000 −0.735901
\(94\) 1046.52 1.14830
\(95\) 0 0
\(96\) −226.274 −0.240563
\(97\) 1483.51 1.55286 0.776431 0.630202i \(-0.217028\pi\)
0.776431 + 0.630202i \(0.217028\pi\)
\(98\) 0 0
\(99\) −322.000 −0.326891
\(100\) 0 0
\(101\) −1128.54 −1.11182 −0.555912 0.831241i \(-0.687631\pi\)
−0.555912 + 0.831241i \(0.687631\pi\)
\(102\) −20.0000 −0.0194147
\(103\) −868.327 −0.830668 −0.415334 0.909669i \(-0.636335\pi\)
−0.415334 + 0.909669i \(0.636335\pi\)
\(104\) 407.294 0.384023
\(105\) 0 0
\(106\) 148.000 0.135613
\(107\) 1684.00 1.52148 0.760740 0.649056i \(-0.224836\pi\)
0.760740 + 0.649056i \(0.224836\pi\)
\(108\) 113.137 0.100802
\(109\) −818.000 −0.718809 −0.359405 0.933182i \(-0.617020\pi\)
−0.359405 + 0.933182i \(0.617020\pi\)
\(110\) 0 0
\(111\) −268.701 −0.229765
\(112\) 0 0
\(113\) 540.000 0.449548 0.224774 0.974411i \(-0.427836\pi\)
0.224774 + 0.974411i \(0.427836\pi\)
\(114\) −20.0000 −0.0164313
\(115\) 0 0
\(116\) −1144.00 −0.915670
\(117\) 1170.97 0.925266
\(118\) −868.327 −0.677424
\(119\) 0 0
\(120\) 0 0
\(121\) −1135.00 −0.852742
\(122\) −28.2843 −0.0209897
\(123\) −890.000 −0.652428
\(124\) 373.352 0.270387
\(125\) 0 0
\(126\) 0 0
\(127\) −1720.00 −1.20177 −0.600887 0.799334i \(-0.705186\pi\)
−0.600887 + 0.799334i \(0.705186\pi\)
\(128\) 128.000 0.0883883
\(129\) −240.416 −0.164089
\(130\) 0 0
\(131\) 1735.24 1.15732 0.578659 0.815570i \(-0.303576\pi\)
0.578659 + 0.815570i \(0.303576\pi\)
\(132\) 395.980 0.261103
\(133\) 0 0
\(134\) −1368.00 −0.881919
\(135\) 0 0
\(136\) 11.3137 0.00713340
\(137\) −828.000 −0.516356 −0.258178 0.966097i \(-0.583122\pi\)
−0.258178 + 0.966097i \(0.583122\pi\)
\(138\) 1979.90 1.22131
\(139\) 425.678 0.259752 0.129876 0.991530i \(-0.458542\pi\)
0.129876 + 0.991530i \(0.458542\pi\)
\(140\) 0 0
\(141\) −3700.00 −2.20990
\(142\) 1176.00 0.694984
\(143\) −712.764 −0.416813
\(144\) 368.000 0.212963
\(145\) 0 0
\(146\) −540.230 −0.306231
\(147\) 0 0
\(148\) 152.000 0.0844211
\(149\) 2050.00 1.12713 0.563566 0.826071i \(-0.309429\pi\)
0.563566 + 0.826071i \(0.309429\pi\)
\(150\) 0 0
\(151\) −472.000 −0.254376 −0.127188 0.991879i \(-0.540595\pi\)
−0.127188 + 0.991879i \(0.540595\pi\)
\(152\) 11.3137 0.00603726
\(153\) 32.5269 0.0171872
\(154\) 0 0
\(155\) 0 0
\(156\) −1440.00 −0.739053
\(157\) −2211.83 −1.12435 −0.562176 0.827018i \(-0.690036\pi\)
−0.562176 + 0.827018i \(0.690036\pi\)
\(158\) 2440.00 1.22858
\(159\) −523.259 −0.260988
\(160\) 0 0
\(161\) 0 0
\(162\) −1642.00 −0.796344
\(163\) −3286.00 −1.57901 −0.789507 0.613741i \(-0.789664\pi\)
−0.789507 + 0.613741i \(0.789664\pi\)
\(164\) 503.460 0.239717
\(165\) 0 0
\(166\) 845.700 0.395416
\(167\) −1490.58 −0.690686 −0.345343 0.938476i \(-0.612237\pi\)
−0.345343 + 0.938476i \(0.612237\pi\)
\(168\) 0 0
\(169\) 395.000 0.179791
\(170\) 0 0
\(171\) 32.5269 0.0145462
\(172\) 136.000 0.0602901
\(173\) −2070.41 −0.909886 −0.454943 0.890521i \(-0.650340\pi\)
−0.454943 + 0.890521i \(0.650340\pi\)
\(174\) 4044.65 1.76221
\(175\) 0 0
\(176\) −224.000 −0.0959354
\(177\) 3070.00 1.30370
\(178\) −1236.02 −0.520471
\(179\) 540.000 0.225483 0.112742 0.993624i \(-0.464037\pi\)
0.112742 + 0.993624i \(0.464037\pi\)
\(180\) 0 0
\(181\) −3784.44 −1.55412 −0.777058 0.629429i \(-0.783289\pi\)
−0.777058 + 0.629429i \(0.783289\pi\)
\(182\) 0 0
\(183\) 100.000 0.0403946
\(184\) −1120.00 −0.448736
\(185\) 0 0
\(186\) −1320.00 −0.520361
\(187\) −19.7990 −0.00774249
\(188\) 2093.04 0.811970
\(189\) 0 0
\(190\) 0 0
\(191\) 1028.00 0.389442 0.194721 0.980859i \(-0.437620\pi\)
0.194721 + 0.980859i \(0.437620\pi\)
\(192\) −452.548 −0.170103
\(193\) −4592.00 −1.71264 −0.856320 0.516446i \(-0.827255\pi\)
−0.856320 + 0.516446i \(0.827255\pi\)
\(194\) 2967.02 1.09804
\(195\) 0 0
\(196\) 0 0
\(197\) −794.000 −0.287158 −0.143579 0.989639i \(-0.545861\pi\)
−0.143579 + 0.989639i \(0.545861\pi\)
\(198\) −644.000 −0.231147
\(199\) −2486.19 −0.885634 −0.442817 0.896612i \(-0.646021\pi\)
−0.442817 + 0.896612i \(0.646021\pi\)
\(200\) 0 0
\(201\) 4836.61 1.69725
\(202\) −2257.08 −0.786178
\(203\) 0 0
\(204\) −40.0000 −0.0137282
\(205\) 0 0
\(206\) −1736.65 −0.587371
\(207\) −3220.00 −1.08119
\(208\) 814.587 0.271545
\(209\) −19.7990 −0.00655275
\(210\) 0 0
\(211\) −2748.00 −0.896588 −0.448294 0.893886i \(-0.647968\pi\)
−0.448294 + 0.893886i \(0.647968\pi\)
\(212\) 296.000 0.0958932
\(213\) −4157.79 −1.33750
\(214\) 3368.00 1.07585
\(215\) 0 0
\(216\) 226.274 0.0712778
\(217\) 0 0
\(218\) −1636.00 −0.508275
\(219\) 1910.00 0.589342
\(220\) 0 0
\(221\) 72.0000 0.0219151
\(222\) −537.401 −0.162468
\(223\) −3428.05 −1.02941 −0.514707 0.857366i \(-0.672099\pi\)
−0.514707 + 0.857366i \(0.672099\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1080.00 0.317878
\(227\) 5290.57 1.54691 0.773453 0.633854i \(-0.218528\pi\)
0.773453 + 0.633854i \(0.218528\pi\)
\(228\) −40.0000 −0.0116187
\(229\) 2749.23 0.793338 0.396669 0.917962i \(-0.370166\pi\)
0.396669 + 0.917962i \(0.370166\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2288.00 −0.647477
\(233\) −72.0000 −0.0202441 −0.0101221 0.999949i \(-0.503222\pi\)
−0.0101221 + 0.999949i \(0.503222\pi\)
\(234\) 2341.94 0.654262
\(235\) 0 0
\(236\) −1736.65 −0.479011
\(237\) −8626.70 −2.36441
\(238\) 0 0
\(239\) 4308.00 1.16595 0.582974 0.812491i \(-0.301889\pi\)
0.582974 + 0.812491i \(0.301889\pi\)
\(240\) 0 0
\(241\) 1540.08 0.411640 0.205820 0.978590i \(-0.434014\pi\)
0.205820 + 0.978590i \(0.434014\pi\)
\(242\) −2270.00 −0.602980
\(243\) 5041.67 1.33096
\(244\) −56.5685 −0.0148419
\(245\) 0 0
\(246\) −1780.00 −0.461336
\(247\) 72.0000 0.0185476
\(248\) 746.705 0.191193
\(249\) −2990.00 −0.760978
\(250\) 0 0
\(251\) −931.967 −0.234363 −0.117182 0.993110i \(-0.537386\pi\)
−0.117182 + 0.993110i \(0.537386\pi\)
\(252\) 0 0
\(253\) 1960.00 0.487052
\(254\) −3440.00 −0.849783
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 937.624 0.227577 0.113789 0.993505i \(-0.463701\pi\)
0.113789 + 0.993505i \(0.463701\pi\)
\(258\) −480.833 −0.116028
\(259\) 0 0
\(260\) 0 0
\(261\) −6578.00 −1.56003
\(262\) 3470.48 0.818347
\(263\) −7140.00 −1.67404 −0.837018 0.547176i \(-0.815703\pi\)
−0.837018 + 0.547176i \(0.815703\pi\)
\(264\) 791.960 0.184628
\(265\) 0 0
\(266\) 0 0
\(267\) 4370.00 1.00165
\(268\) −2736.00 −0.623611
\(269\) −4610.34 −1.04497 −0.522485 0.852648i \(-0.674995\pi\)
−0.522485 + 0.852648i \(0.674995\pi\)
\(270\) 0 0
\(271\) 2364.57 0.530026 0.265013 0.964245i \(-0.414624\pi\)
0.265013 + 0.964245i \(0.414624\pi\)
\(272\) 22.6274 0.00504408
\(273\) 0 0
\(274\) −1656.00 −0.365119
\(275\) 0 0
\(276\) 3959.80 0.863594
\(277\) −4006.00 −0.868943 −0.434472 0.900686i \(-0.643065\pi\)
−0.434472 + 0.900686i \(0.643065\pi\)
\(278\) 851.357 0.183673
\(279\) 2146.78 0.460660
\(280\) 0 0
\(281\) −5984.00 −1.27038 −0.635188 0.772358i \(-0.719077\pi\)
−0.635188 + 0.772358i \(0.719077\pi\)
\(282\) −7400.00 −1.56264
\(283\) −4928.53 −1.03523 −0.517617 0.855613i \(-0.673181\pi\)
−0.517617 + 0.855613i \(0.673181\pi\)
\(284\) 2352.00 0.491428
\(285\) 0 0
\(286\) −1425.53 −0.294731
\(287\) 0 0
\(288\) 736.000 0.150588
\(289\) −4911.00 −0.999593
\(290\) 0 0
\(291\) −10490.0 −2.11318
\(292\) −1080.46 −0.216538
\(293\) 1971.41 0.393076 0.196538 0.980496i \(-0.437030\pi\)
0.196538 + 0.980496i \(0.437030\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 304.000 0.0596947
\(297\) −395.980 −0.0773639
\(298\) 4100.00 0.797002
\(299\) −7127.64 −1.37860
\(300\) 0 0
\(301\) 0 0
\(302\) −944.000 −0.179871
\(303\) 7980.00 1.51300
\(304\) 22.6274 0.00426898
\(305\) 0 0
\(306\) 65.0538 0.0121532
\(307\) −4767.31 −0.886270 −0.443135 0.896455i \(-0.646134\pi\)
−0.443135 + 0.896455i \(0.646134\pi\)
\(308\) 0 0
\(309\) 6140.00 1.13040
\(310\) 0 0
\(311\) 6776.91 1.23564 0.617819 0.786320i \(-0.288016\pi\)
0.617819 + 0.786320i \(0.288016\pi\)
\(312\) −2880.00 −0.522589
\(313\) −6190.01 −1.11783 −0.558914 0.829226i \(-0.688782\pi\)
−0.558914 + 0.829226i \(0.688782\pi\)
\(314\) −4423.66 −0.795037
\(315\) 0 0
\(316\) 4880.00 0.868739
\(317\) −9826.00 −1.74096 −0.870478 0.492207i \(-0.836190\pi\)
−0.870478 + 0.492207i \(0.836190\pi\)
\(318\) −1046.52 −0.184547
\(319\) 4004.00 0.702762
\(320\) 0 0
\(321\) −11907.7 −2.07047
\(322\) 0 0
\(323\) 2.00000 0.000344529 0
\(324\) −3284.00 −0.563100
\(325\) 0 0
\(326\) −6572.00 −1.11653
\(327\) 5784.13 0.978175
\(328\) 1006.92 0.169506
\(329\) 0 0
\(330\) 0 0
\(331\) −5738.00 −0.952837 −0.476418 0.879219i \(-0.658065\pi\)
−0.476418 + 0.879219i \(0.658065\pi\)
\(332\) 1691.40 0.279601
\(333\) 874.000 0.143829
\(334\) −2981.16 −0.488389
\(335\) 0 0
\(336\) 0 0
\(337\) 2254.00 0.364342 0.182171 0.983267i \(-0.441688\pi\)
0.182171 + 0.983267i \(0.441688\pi\)
\(338\) 790.000 0.127131
\(339\) −3818.38 −0.611757
\(340\) 0 0
\(341\) −1306.73 −0.207518
\(342\) 65.0538 0.0102857
\(343\) 0 0
\(344\) 272.000 0.0426316
\(345\) 0 0
\(346\) −4140.82 −0.643386
\(347\) 1986.00 0.307245 0.153623 0.988130i \(-0.450906\pi\)
0.153623 + 0.988130i \(0.450906\pi\)
\(348\) 8089.30 1.24607
\(349\) −6771.25 −1.03856 −0.519279 0.854605i \(-0.673800\pi\)
−0.519279 + 0.854605i \(0.673800\pi\)
\(350\) 0 0
\(351\) 1440.00 0.218979
\(352\) −448.000 −0.0678366
\(353\) 6993.29 1.05443 0.527217 0.849731i \(-0.323236\pi\)
0.527217 + 0.849731i \(0.323236\pi\)
\(354\) 6140.00 0.921857
\(355\) 0 0
\(356\) −2472.05 −0.368028
\(357\) 0 0
\(358\) 1080.00 0.159441
\(359\) 5944.00 0.873850 0.436925 0.899498i \(-0.356067\pi\)
0.436925 + 0.899498i \(0.356067\pi\)
\(360\) 0 0
\(361\) −6857.00 −0.999708
\(362\) −7568.87 −1.09893
\(363\) 8025.66 1.16044
\(364\) 0 0
\(365\) 0 0
\(366\) 200.000 0.0285633
\(367\) −842.871 −0.119884 −0.0599421 0.998202i \(-0.519092\pi\)
−0.0599421 + 0.998202i \(0.519092\pi\)
\(368\) −2240.00 −0.317305
\(369\) 2894.90 0.408407
\(370\) 0 0
\(371\) 0 0
\(372\) −2640.00 −0.367951
\(373\) 5726.00 0.794855 0.397428 0.917634i \(-0.369903\pi\)
0.397428 + 0.917634i \(0.369903\pi\)
\(374\) −39.5980 −0.00547477
\(375\) 0 0
\(376\) 4186.07 0.574149
\(377\) −14560.7 −1.98917
\(378\) 0 0
\(379\) 10330.0 1.40004 0.700022 0.714122i \(-0.253174\pi\)
0.700022 + 0.714122i \(0.253174\pi\)
\(380\) 0 0
\(381\) 12162.2 1.63541
\(382\) 2056.00 0.275377
\(383\) 1004.09 0.133960 0.0669800 0.997754i \(-0.478664\pi\)
0.0669800 + 0.997754i \(0.478664\pi\)
\(384\) −905.097 −0.120281
\(385\) 0 0
\(386\) −9184.00 −1.21102
\(387\) 782.000 0.102717
\(388\) 5934.04 0.776431
\(389\) 5210.00 0.679068 0.339534 0.940594i \(-0.389731\pi\)
0.339534 + 0.940594i \(0.389731\pi\)
\(390\) 0 0
\(391\) −197.990 −0.0256081
\(392\) 0 0
\(393\) −12270.0 −1.57491
\(394\) −1588.00 −0.203051
\(395\) 0 0
\(396\) −1288.00 −0.163446
\(397\) −73.5391 −0.00929678 −0.00464839 0.999989i \(-0.501480\pi\)
−0.00464839 + 0.999989i \(0.501480\pi\)
\(398\) −4972.37 −0.626238
\(399\) 0 0
\(400\) 0 0
\(401\) −498.000 −0.0620173 −0.0310086 0.999519i \(-0.509872\pi\)
−0.0310086 + 0.999519i \(0.509872\pi\)
\(402\) 9673.22 1.20014
\(403\) 4752.00 0.587380
\(404\) −4514.17 −0.555912
\(405\) 0 0
\(406\) 0 0
\(407\) −532.000 −0.0647918
\(408\) −80.0000 −0.00970733
\(409\) −3355.93 −0.405721 −0.202861 0.979208i \(-0.565024\pi\)
−0.202861 + 0.979208i \(0.565024\pi\)
\(410\) 0 0
\(411\) 5854.84 0.702672
\(412\) −3473.31 −0.415334
\(413\) 0 0
\(414\) −6440.00 −0.764514
\(415\) 0 0
\(416\) 1629.17 0.192012
\(417\) −3010.00 −0.353478
\(418\) −39.5980 −0.00463349
\(419\) −14545.2 −1.69589 −0.847946 0.530082i \(-0.822161\pi\)
−0.847946 + 0.530082i \(0.822161\pi\)
\(420\) 0 0
\(421\) 10854.0 1.25651 0.628256 0.778007i \(-0.283769\pi\)
0.628256 + 0.778007i \(0.283769\pi\)
\(422\) −5496.00 −0.633984
\(423\) 12035.0 1.38336
\(424\) 592.000 0.0678067
\(425\) 0 0
\(426\) −8315.58 −0.945753
\(427\) 0 0
\(428\) 6736.00 0.760740
\(429\) 5040.00 0.567211
\(430\) 0 0
\(431\) −5364.00 −0.599477 −0.299739 0.954021i \(-0.596900\pi\)
−0.299739 + 0.954021i \(0.596900\pi\)
\(432\) 452.548 0.0504010
\(433\) −6487.00 −0.719966 −0.359983 0.932959i \(-0.617217\pi\)
−0.359983 + 0.932959i \(0.617217\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3272.00 −0.359405
\(437\) −197.990 −0.0216731
\(438\) 3820.00 0.416728
\(439\) −13932.8 −1.51476 −0.757378 0.652977i \(-0.773520\pi\)
−0.757378 + 0.652977i \(0.773520\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 144.000 0.0154963
\(443\) −5996.00 −0.643067 −0.321533 0.946898i \(-0.604198\pi\)
−0.321533 + 0.946898i \(0.604198\pi\)
\(444\) −1074.80 −0.114883
\(445\) 0 0
\(446\) −6856.11 −0.727906
\(447\) −14495.7 −1.53383
\(448\) 0 0
\(449\) 2622.00 0.275590 0.137795 0.990461i \(-0.455999\pi\)
0.137795 + 0.990461i \(0.455999\pi\)
\(450\) 0 0
\(451\) −1762.11 −0.183979
\(452\) 2160.00 0.224774
\(453\) 3337.54 0.346162
\(454\) 10581.1 1.09383
\(455\) 0 0
\(456\) −80.0000 −0.00821567
\(457\) −11208.0 −1.14724 −0.573619 0.819122i \(-0.694461\pi\)
−0.573619 + 0.819122i \(0.694461\pi\)
\(458\) 5498.46 0.560974
\(459\) 40.0000 0.00406763
\(460\) 0 0
\(461\) −9786.36 −0.988712 −0.494356 0.869260i \(-0.664596\pi\)
−0.494356 + 0.869260i \(0.664596\pi\)
\(462\) 0 0
\(463\) −3952.00 −0.396685 −0.198342 0.980133i \(-0.563556\pi\)
−0.198342 + 0.980133i \(0.563556\pi\)
\(464\) −4576.00 −0.457835
\(465\) 0 0
\(466\) −144.000 −0.0143147
\(467\) 17506.5 1.73470 0.867352 0.497696i \(-0.165820\pi\)
0.867352 + 0.497696i \(0.165820\pi\)
\(468\) 4683.88 0.462633
\(469\) 0 0
\(470\) 0 0
\(471\) 15640.0 1.53005
\(472\) −3473.31 −0.338712
\(473\) −476.000 −0.0462717
\(474\) −17253.4 −1.67189
\(475\) 0 0
\(476\) 0 0
\(477\) 1702.00 0.163374
\(478\) 8616.00 0.824449
\(479\) −2288.20 −0.218268 −0.109134 0.994027i \(-0.534808\pi\)
−0.109134 + 0.994027i \(0.534808\pi\)
\(480\) 0 0
\(481\) 1934.64 0.183393
\(482\) 3080.16 0.291073
\(483\) 0 0
\(484\) −4540.00 −0.426371
\(485\) 0 0
\(486\) 10083.3 0.941131
\(487\) −972.000 −0.0904426 −0.0452213 0.998977i \(-0.514399\pi\)
−0.0452213 + 0.998977i \(0.514399\pi\)
\(488\) −113.137 −0.0104948
\(489\) 23235.5 2.14877
\(490\) 0 0
\(491\) −7404.00 −0.680525 −0.340263 0.940330i \(-0.610516\pi\)
−0.340263 + 0.940330i \(0.610516\pi\)
\(492\) −3560.00 −0.326214
\(493\) −404.465 −0.0369497
\(494\) 144.000 0.0131151
\(495\) 0 0
\(496\) 1493.41 0.135194
\(497\) 0 0
\(498\) −5980.00 −0.538093
\(499\) −12244.0 −1.09843 −0.549215 0.835681i \(-0.685073\pi\)
−0.549215 + 0.835681i \(0.685073\pi\)
\(500\) 0 0
\(501\) 10540.0 0.939905
\(502\) −1863.93 −0.165720
\(503\) −2415.48 −0.214117 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3920.00 0.344398
\(507\) −2793.07 −0.244664
\(508\) −6880.00 −0.600887
\(509\) 5707.77 0.497038 0.248519 0.968627i \(-0.420056\pi\)
0.248519 + 0.968627i \(0.420056\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 40.0000 0.00344258
\(514\) 1875.25 0.160921
\(515\) 0 0
\(516\) −961.665 −0.0820445
\(517\) −7325.63 −0.623173
\(518\) 0 0
\(519\) 14640.0 1.23820
\(520\) 0 0
\(521\) −1.41421 −0.000118921 0 −5.94605e−5 1.00000i \(-0.500019\pi\)
−5.94605e−5 1.00000i \(0.500019\pi\)
\(522\) −13156.0 −1.10311
\(523\) −12257.0 −1.02478 −0.512391 0.858752i \(-0.671240\pi\)
−0.512391 + 0.858752i \(0.671240\pi\)
\(524\) 6940.96 0.578659
\(525\) 0 0
\(526\) −14280.0 −1.18372
\(527\) 132.000 0.0109108
\(528\) 1583.92 0.130552
\(529\) 7433.00 0.610915
\(530\) 0 0
\(531\) −9985.76 −0.816093
\(532\) 0 0
\(533\) 6408.00 0.520753
\(534\) 8740.00 0.708271
\(535\) 0 0
\(536\) −5472.00 −0.440960
\(537\) −3818.38 −0.306844
\(538\) −9220.67 −0.738906
\(539\) 0 0
\(540\) 0 0
\(541\) 2050.00 0.162914 0.0814569 0.996677i \(-0.474043\pi\)
0.0814569 + 0.996677i \(0.474043\pi\)
\(542\) 4729.13 0.374785
\(543\) 26760.0 2.11488
\(544\) 45.2548 0.00356670
\(545\) 0 0
\(546\) 0 0
\(547\) −14554.0 −1.13763 −0.568815 0.822465i \(-0.692598\pi\)
−0.568815 + 0.822465i \(0.692598\pi\)
\(548\) −3312.00 −0.258178
\(549\) −325.269 −0.0252862
\(550\) 0 0
\(551\) −404.465 −0.0312719
\(552\) 7919.60 0.610653
\(553\) 0 0
\(554\) −8012.00 −0.614435
\(555\) 0 0
\(556\) 1702.71 0.129876
\(557\) −6954.00 −0.528995 −0.264498 0.964386i \(-0.585206\pi\)
−0.264498 + 0.964386i \(0.585206\pi\)
\(558\) 4293.55 0.325736
\(559\) 1731.00 0.130972
\(560\) 0 0
\(561\) 140.000 0.0105362
\(562\) −11968.0 −0.898291
\(563\) −1636.25 −0.122486 −0.0612429 0.998123i \(-0.519506\pi\)
−0.0612429 + 0.998123i \(0.519506\pi\)
\(564\) −14800.0 −1.10495
\(565\) 0 0
\(566\) −9857.07 −0.732020
\(567\) 0 0
\(568\) 4704.00 0.347492
\(569\) −7142.00 −0.526201 −0.263100 0.964768i \(-0.584745\pi\)
−0.263100 + 0.964768i \(0.584745\pi\)
\(570\) 0 0
\(571\) −20606.0 −1.51022 −0.755109 0.655599i \(-0.772416\pi\)
−0.755109 + 0.655599i \(0.772416\pi\)
\(572\) −2851.05 −0.208407
\(573\) −7269.06 −0.529964
\(574\) 0 0
\(575\) 0 0
\(576\) 1472.00 0.106481
\(577\) −8803.48 −0.635171 −0.317585 0.948230i \(-0.602872\pi\)
−0.317585 + 0.948230i \(0.602872\pi\)
\(578\) −9822.00 −0.706819
\(579\) 32470.3 2.33061
\(580\) 0 0
\(581\) 0 0
\(582\) −20980.0 −1.49424
\(583\) −1036.00 −0.0735965
\(584\) −2160.92 −0.153115
\(585\) 0 0
\(586\) 3942.83 0.277947
\(587\) 6503.97 0.457321 0.228661 0.973506i \(-0.426565\pi\)
0.228661 + 0.973506i \(0.426565\pi\)
\(588\) 0 0
\(589\) 132.000 0.00923424
\(590\) 0 0
\(591\) 5614.43 0.390773
\(592\) 608.000 0.0422106
\(593\) −23140.8 −1.60249 −0.801246 0.598335i \(-0.795829\pi\)
−0.801246 + 0.598335i \(0.795829\pi\)
\(594\) −791.960 −0.0547045
\(595\) 0 0
\(596\) 8200.00 0.563566
\(597\) 17580.0 1.20520
\(598\) −14255.3 −0.974818
\(599\) −11296.0 −0.770521 −0.385260 0.922808i \(-0.625888\pi\)
−0.385260 + 0.922808i \(0.625888\pi\)
\(600\) 0 0
\(601\) −8727.11 −0.592323 −0.296162 0.955138i \(-0.595707\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(602\) 0 0
\(603\) −15732.0 −1.06245
\(604\) −1888.00 −0.127188
\(605\) 0 0
\(606\) 15960.0 1.06985
\(607\) 19736.8 1.31975 0.659877 0.751374i \(-0.270608\pi\)
0.659877 + 0.751374i \(0.270608\pi\)
\(608\) 45.2548 0.00301863
\(609\) 0 0
\(610\) 0 0
\(611\) 26640.0 1.76389
\(612\) 130.108 0.00859361
\(613\) −16962.0 −1.11760 −0.558800 0.829302i \(-0.688738\pi\)
−0.558800 + 0.829302i \(0.688738\pi\)
\(614\) −9534.63 −0.626688
\(615\) 0 0
\(616\) 0 0
\(617\) 19034.0 1.24194 0.620972 0.783832i \(-0.286738\pi\)
0.620972 + 0.783832i \(0.286738\pi\)
\(618\) 12280.0 0.799311
\(619\) 18677.5 1.21278 0.606392 0.795166i \(-0.292616\pi\)
0.606392 + 0.795166i \(0.292616\pi\)
\(620\) 0 0
\(621\) −3959.80 −0.255880
\(622\) 13553.8 0.873728
\(623\) 0 0
\(624\) −5760.00 −0.369527
\(625\) 0 0
\(626\) −12380.0 −0.790424
\(627\) 140.000 0.00891716
\(628\) −8847.32 −0.562176
\(629\) 53.7401 0.00340661
\(630\) 0 0
\(631\) −14716.0 −0.928423 −0.464211 0.885724i \(-0.653662\pi\)
−0.464211 + 0.885724i \(0.653662\pi\)
\(632\) 9760.00 0.614291
\(633\) 19431.3 1.22010
\(634\) −19652.0 −1.23104
\(635\) 0 0
\(636\) −2093.04 −0.130494
\(637\) 0 0
\(638\) 8008.00 0.496928
\(639\) 13524.0 0.837248
\(640\) 0 0
\(641\) 4730.00 0.291457 0.145728 0.989325i \(-0.453447\pi\)
0.145728 + 0.989325i \(0.453447\pi\)
\(642\) −23815.4 −1.46405
\(643\) 19056.5 1.16877 0.584383 0.811478i \(-0.301337\pi\)
0.584383 + 0.811478i \(0.301337\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 0.000243619 0
\(647\) 9342.29 0.567672 0.283836 0.958873i \(-0.408393\pi\)
0.283836 + 0.958873i \(0.408393\pi\)
\(648\) −6568.00 −0.398172
\(649\) 6078.29 0.367633
\(650\) 0 0
\(651\) 0 0
\(652\) −13144.0 −0.789507
\(653\) −3774.00 −0.226169 −0.113084 0.993585i \(-0.536073\pi\)
−0.113084 + 0.993585i \(0.536073\pi\)
\(654\) 11568.3 0.691674
\(655\) 0 0
\(656\) 2013.84 0.119859
\(657\) −6212.64 −0.368917
\(658\) 0 0
\(659\) −21150.0 −1.25021 −0.625104 0.780541i \(-0.714943\pi\)
−0.625104 + 0.780541i \(0.714943\pi\)
\(660\) 0 0
\(661\) 10377.5 0.610647 0.305324 0.952249i \(-0.401235\pi\)
0.305324 + 0.952249i \(0.401235\pi\)
\(662\) −11476.0 −0.673757
\(663\) −509.117 −0.0298227
\(664\) 3382.80 0.197708
\(665\) 0 0
\(666\) 1748.00 0.101702
\(667\) 40040.0 2.32437
\(668\) −5962.32 −0.345343
\(669\) 24240.0 1.40086
\(670\) 0 0
\(671\) 197.990 0.0113909
\(672\) 0 0
\(673\) 1164.00 0.0666700 0.0333350 0.999444i \(-0.489387\pi\)
0.0333350 + 0.999444i \(0.489387\pi\)
\(674\) 4508.00 0.257629
\(675\) 0 0
\(676\) 1580.00 0.0898953
\(677\) 27152.9 1.54146 0.770732 0.637160i \(-0.219891\pi\)
0.770732 + 0.637160i \(0.219891\pi\)
\(678\) −7636.75 −0.432578
\(679\) 0 0
\(680\) 0 0
\(681\) −37410.0 −2.10507
\(682\) −2613.47 −0.146737
\(683\) 16596.0 0.929763 0.464882 0.885373i \(-0.346097\pi\)
0.464882 + 0.885373i \(0.346097\pi\)
\(684\) 130.108 0.00727309
\(685\) 0 0
\(686\) 0 0
\(687\) −19440.0 −1.07960
\(688\) 544.000 0.0301451
\(689\) 3767.46 0.208315
\(690\) 0 0
\(691\) −11298.2 −0.622000 −0.311000 0.950410i \(-0.600664\pi\)
−0.311000 + 0.950410i \(0.600664\pi\)
\(692\) −8281.63 −0.454943
\(693\) 0 0
\(694\) 3972.00 0.217255
\(695\) 0 0
\(696\) 16178.6 0.881104
\(697\) 178.000 0.00967321
\(698\) −13542.5 −0.734372
\(699\) 509.117 0.0275487
\(700\) 0 0
\(701\) −2754.00 −0.148384 −0.0741920 0.997244i \(-0.523638\pi\)
−0.0741920 + 0.997244i \(0.523638\pi\)
\(702\) 2880.00 0.154841
\(703\) 53.7401 0.00288314
\(704\) −896.000 −0.0479677
\(705\) 0 0
\(706\) 13986.6 0.745597
\(707\) 0 0
\(708\) 12280.0 0.651851
\(709\) 29434.0 1.55912 0.779561 0.626327i \(-0.215442\pi\)
0.779561 + 0.626327i \(0.215442\pi\)
\(710\) 0 0
\(711\) 28060.0 1.48007
\(712\) −4944.09 −0.260235
\(713\) −13067.3 −0.686361
\(714\) 0 0
\(715\) 0 0
\(716\) 2160.00 0.112742
\(717\) −30462.2 −1.58665
\(718\) 11888.0 0.617906
\(719\) 17669.2 0.916480 0.458240 0.888828i \(-0.348480\pi\)
0.458240 + 0.888828i \(0.348480\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −13714.0 −0.706901
\(723\) −10890.0 −0.560171
\(724\) −15137.7 −0.777058
\(725\) 0 0
\(726\) 16051.3 0.820552
\(727\) 28445.5 1.45115 0.725574 0.688144i \(-0.241574\pi\)
0.725574 + 0.688144i \(0.241574\pi\)
\(728\) 0 0
\(729\) −13483.0 −0.685007
\(730\) 0 0
\(731\) 48.0833 0.00243286
\(732\) 400.000 0.0201973
\(733\) 22341.7 1.12580 0.562900 0.826525i \(-0.309686\pi\)
0.562900 + 0.826525i \(0.309686\pi\)
\(734\) −1685.74 −0.0847710
\(735\) 0 0
\(736\) −4480.00 −0.224368
\(737\) 9576.00 0.478611
\(738\) 5789.79 0.288787
\(739\) 20670.0 1.02890 0.514451 0.857520i \(-0.327996\pi\)
0.514451 + 0.857520i \(0.327996\pi\)
\(740\) 0 0
\(741\) −509.117 −0.0252400
\(742\) 0 0
\(743\) 25400.0 1.25415 0.627076 0.778958i \(-0.284251\pi\)
0.627076 + 0.778958i \(0.284251\pi\)
\(744\) −5280.00 −0.260180
\(745\) 0 0
\(746\) 11452.0 0.562048
\(747\) 9725.55 0.476358
\(748\) −79.1960 −0.00387124
\(749\) 0 0
\(750\) 0 0
\(751\) 29180.0 1.41783 0.708917 0.705292i \(-0.249184\pi\)
0.708917 + 0.705292i \(0.249184\pi\)
\(752\) 8372.14 0.405985
\(753\) 6590.00 0.318928
\(754\) −29121.5 −1.40655
\(755\) 0 0
\(756\) 0 0
\(757\) 26206.0 1.25822 0.629110 0.777316i \(-0.283419\pi\)
0.629110 + 0.777316i \(0.283419\pi\)
\(758\) 20660.0 0.989980
\(759\) −13859.3 −0.662794
\(760\) 0 0
\(761\) −6863.18 −0.326925 −0.163463 0.986550i \(-0.552266\pi\)
−0.163463 + 0.986550i \(0.552266\pi\)
\(762\) 24324.5 1.15641
\(763\) 0 0
\(764\) 4112.00 0.194721
\(765\) 0 0
\(766\) 2008.18 0.0947240
\(767\) −22104.0 −1.04059
\(768\) −1810.19 −0.0850517
\(769\) 9058.04 0.424761 0.212380 0.977187i \(-0.431878\pi\)
0.212380 + 0.977187i \(0.431878\pi\)
\(770\) 0 0
\(771\) −6630.00 −0.309693
\(772\) −18368.0 −0.856320
\(773\) −132.936 −0.00618548 −0.00309274 0.999995i \(-0.500984\pi\)
−0.00309274 + 0.999995i \(0.500984\pi\)
\(774\) 1564.00 0.0726315
\(775\) 0 0
\(776\) 11868.1 0.549020
\(777\) 0 0
\(778\) 10420.0 0.480174
\(779\) 178.000 0.00818679
\(780\) 0 0
\(781\) −8232.00 −0.377163
\(782\) −395.980 −0.0181077
\(783\) −8089.30 −0.369206
\(784\) 0 0
\(785\) 0 0
\(786\) −24540.0 −1.11363
\(787\) −8729.94 −0.395411 −0.197706 0.980261i \(-0.563349\pi\)
−0.197706 + 0.980261i \(0.563349\pi\)
\(788\) −3176.00 −0.143579
\(789\) 50487.4 2.27807
\(790\) 0 0
\(791\) 0 0
\(792\) −2576.00 −0.115573
\(793\) −720.000 −0.0322421
\(794\) −147.078 −0.00657382
\(795\) 0 0
\(796\) −9944.75 −0.442817
\(797\) 7517.96 0.334128 0.167064 0.985946i \(-0.446571\pi\)
0.167064 + 0.985946i \(0.446571\pi\)
\(798\) 0 0
\(799\) 740.000 0.0327651
\(800\) 0 0
\(801\) −14214.3 −0.627011
\(802\) −996.000 −0.0438528
\(803\) 3781.61 0.166189
\(804\) 19346.4 0.848627
\(805\) 0 0
\(806\) 9504.00 0.415340
\(807\) 32600.0 1.42203
\(808\) −9028.34 −0.393089
\(809\) 3776.00 0.164100 0.0820501 0.996628i \(-0.473853\pi\)
0.0820501 + 0.996628i \(0.473853\pi\)
\(810\) 0 0
\(811\) 36227.9 1.56860 0.784300 0.620382i \(-0.213023\pi\)
0.784300 + 0.620382i \(0.213023\pi\)
\(812\) 0 0
\(813\) −16720.0 −0.721274
\(814\) −1064.00 −0.0458147
\(815\) 0 0
\(816\) −160.000 −0.00686412
\(817\) 48.0833 0.00205902
\(818\) −6711.86 −0.286888
\(819\) 0 0
\(820\) 0 0
\(821\) −16410.0 −0.697580 −0.348790 0.937201i \(-0.613407\pi\)
−0.348790 + 0.937201i \(0.613407\pi\)
\(822\) 11709.7 0.496864
\(823\) −22072.0 −0.934850 −0.467425 0.884033i \(-0.654818\pi\)
−0.467425 + 0.884033i \(0.654818\pi\)
\(824\) −6946.62 −0.293686
\(825\) 0 0
\(826\) 0 0
\(827\) 11628.0 0.488930 0.244465 0.969658i \(-0.421388\pi\)
0.244465 + 0.969658i \(0.421388\pi\)
\(828\) −12880.0 −0.540593
\(829\) 30906.2 1.29483 0.647417 0.762136i \(-0.275849\pi\)
0.647417 + 0.762136i \(0.275849\pi\)
\(830\) 0 0
\(831\) 28326.7 1.18248
\(832\) 3258.35 0.135773
\(833\) 0 0
\(834\) −6020.00 −0.249947
\(835\) 0 0
\(836\) −79.1960 −0.00327638
\(837\) 2640.00 0.109022
\(838\) −29090.4 −1.19918
\(839\) −17884.1 −0.735911 −0.367955 0.929843i \(-0.619942\pi\)
−0.367955 + 0.929843i \(0.619942\pi\)
\(840\) 0 0
\(841\) 57407.0 2.35381
\(842\) 21708.0 0.888488
\(843\) 42313.3 1.72876
\(844\) −10992.0 −0.448294
\(845\) 0 0
\(846\) 24069.9 0.978181
\(847\) 0 0
\(848\) 1184.00 0.0479466
\(849\) 34850.0 1.40877
\(850\) 0 0
\(851\) −5320.00 −0.214298
\(852\) −16631.2 −0.668749
\(853\) −20755.0 −0.833104 −0.416552 0.909112i \(-0.636762\pi\)
−0.416552 + 0.909112i \(0.636762\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 13472.0 0.537925
\(857\) 44919.7 1.79046 0.895231 0.445602i \(-0.147010\pi\)
0.895231 + 0.445602i \(0.147010\pi\)
\(858\) 10080.0 0.401079
\(859\) −69.2965 −0.00275246 −0.00137623 0.999999i \(-0.500438\pi\)
−0.00137623 + 0.999999i \(0.500438\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −10728.0 −0.423895
\(863\) 5452.00 0.215050 0.107525 0.994202i \(-0.465707\pi\)
0.107525 + 0.994202i \(0.465707\pi\)
\(864\) 905.097 0.0356389
\(865\) 0 0
\(866\) −12974.0 −0.509093
\(867\) 34726.0 1.36027
\(868\) 0 0
\(869\) −17080.0 −0.666743
\(870\) 0 0
\(871\) −34823.6 −1.35471
\(872\) −6544.00 −0.254137
\(873\) 34120.7 1.32281
\(874\) −395.980 −0.0153252
\(875\) 0 0
\(876\) 7640.00 0.294671
\(877\) −31106.0 −1.19769 −0.598845 0.800865i \(-0.704374\pi\)
−0.598845 + 0.800865i \(0.704374\pi\)
\(878\) −27865.7 −1.07109
\(879\) −13940.0 −0.534908
\(880\) 0 0
\(881\) −5943.94 −0.227306 −0.113653 0.993521i \(-0.536255\pi\)
−0.113653 + 0.993521i \(0.536255\pi\)
\(882\) 0 0
\(883\) −34796.0 −1.32614 −0.663068 0.748559i \(-0.730746\pi\)
−0.663068 + 0.748559i \(0.730746\pi\)
\(884\) 288.000 0.0109576
\(885\) 0 0
\(886\) −11992.0 −0.454717
\(887\) 9964.55 0.377200 0.188600 0.982054i \(-0.439605\pi\)
0.188600 + 0.982054i \(0.439605\pi\)
\(888\) −2149.60 −0.0812342
\(889\) 0 0
\(890\) 0 0
\(891\) 11494.0 0.432170
\(892\) −13712.2 −0.514707
\(893\) 740.000 0.0277303
\(894\) −28991.4 −1.08458
\(895\) 0 0
\(896\) 0 0
\(897\) 50400.0 1.87604
\(898\) 5244.00 0.194871
\(899\) −26694.7 −0.990343
\(900\) 0 0
\(901\) 104.652 0.00386954
\(902\) −3524.22 −0.130093
\(903\) 0 0
\(904\) 4320.00 0.158939
\(905\) 0 0
\(906\) 6675.09 0.244774
\(907\) 29756.0 1.08934 0.544670 0.838650i \(-0.316655\pi\)
0.544670 + 0.838650i \(0.316655\pi\)
\(908\) 21162.3 0.773453
\(909\) −25956.5 −0.947109
\(910\) 0 0
\(911\) 21440.0 0.779735 0.389868 0.920871i \(-0.372521\pi\)
0.389868 + 0.920871i \(0.372521\pi\)
\(912\) −160.000 −0.00580935
\(913\) −5919.90 −0.214589
\(914\) −22416.0 −0.811220
\(915\) 0 0
\(916\) 10996.9 0.396669
\(917\) 0 0
\(918\) 80.0000 0.00287625
\(919\) −8288.00 −0.297493 −0.148746 0.988875i \(-0.547524\pi\)
−0.148746 + 0.988875i \(0.547524\pi\)
\(920\) 0 0
\(921\) 33710.0 1.20606
\(922\) −19572.7 −0.699125
\(923\) 29936.1 1.06756
\(924\) 0 0
\(925\) 0 0
\(926\) −7904.00 −0.280498
\(927\) −19971.5 −0.707606
\(928\) −9152.00 −0.323738
\(929\) 45581.5 1.60978 0.804888 0.593427i \(-0.202226\pi\)
0.804888 + 0.593427i \(0.202226\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −288.000 −0.0101221
\(933\) −47920.0 −1.68149
\(934\) 35013.1 1.22662
\(935\) 0 0
\(936\) 9367.75 0.327131
\(937\) 11665.8 0.406731 0.203365 0.979103i \(-0.434812\pi\)
0.203365 + 0.979103i \(0.434812\pi\)
\(938\) 0 0
\(939\) 43770.0 1.52117
\(940\) 0 0
\(941\) −14.1421 −0.000489926 0 −0.000244963 1.00000i \(-0.500078\pi\)
−0.000244963 1.00000i \(0.500078\pi\)
\(942\) 31280.0 1.08191
\(943\) −17621.1 −0.608507
\(944\) −6946.62 −0.239505
\(945\) 0 0
\(946\) −952.000 −0.0327190
\(947\) −14034.0 −0.481567 −0.240783 0.970579i \(-0.577404\pi\)
−0.240783 + 0.970579i \(0.577404\pi\)
\(948\) −34506.8 −1.18220
\(949\) −13752.0 −0.470399
\(950\) 0 0
\(951\) 69480.3 2.36914
\(952\) 0 0
\(953\) 42698.0 1.45134 0.725668 0.688045i \(-0.241531\pi\)
0.725668 + 0.688045i \(0.241531\pi\)
\(954\) 3404.00 0.115523
\(955\) 0 0
\(956\) 17232.0 0.582974
\(957\) −28312.6 −0.956337
\(958\) −4576.40 −0.154339
\(959\) 0 0
\(960\) 0 0
\(961\) −21079.0 −0.707563
\(962\) 3869.29 0.129679
\(963\) 38732.0 1.29608
\(964\) 6160.31 0.205820
\(965\) 0 0
\(966\) 0 0
\(967\) 48492.0 1.61261 0.806307 0.591497i \(-0.201463\pi\)
0.806307 + 0.591497i \(0.201463\pi\)
\(968\) −9080.00 −0.301490
\(969\) −14.1421 −0.000468845 0
\(970\) 0 0
\(971\) −52669.6 −1.74073 −0.870364 0.492409i \(-0.836116\pi\)
−0.870364 + 0.492409i \(0.836116\pi\)
\(972\) 20166.7 0.665480
\(973\) 0 0
\(974\) −1944.00 −0.0639525
\(975\) 0 0
\(976\) −226.274 −0.00742096
\(977\) 55380.0 1.81347 0.906737 0.421698i \(-0.138566\pi\)
0.906737 + 0.421698i \(0.138566\pi\)
\(978\) 46471.1 1.51941
\(979\) 8652.16 0.282456
\(980\) 0 0
\(981\) −18814.0 −0.612319
\(982\) −14808.0 −0.481204
\(983\) −50535.5 −1.63971 −0.819854 0.572573i \(-0.805945\pi\)
−0.819854 + 0.572573i \(0.805945\pi\)
\(984\) −7120.00 −0.230668
\(985\) 0 0
\(986\) −808.930 −0.0261274
\(987\) 0 0
\(988\) 288.000 0.00927379
\(989\) −4760.00 −0.153043
\(990\) 0 0
\(991\) −39712.0 −1.27295 −0.636475 0.771297i \(-0.719608\pi\)
−0.636475 + 0.771297i \(0.719608\pi\)
\(992\) 2986.82 0.0955964
\(993\) 40573.8 1.29665
\(994\) 0 0
\(995\) 0 0
\(996\) −11960.0 −0.380489
\(997\) 2186.37 0.0694515 0.0347258 0.999397i \(-0.488944\pi\)
0.0347258 + 0.999397i \(0.488944\pi\)
\(998\) −24488.0 −0.776708
\(999\) 1074.80 0.0340393
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 2450.4.a.bx.1.1 2
5.4 even 2 98.4.a.g.1.2 yes 2
7.6 odd 2 inner 2450.4.a.bx.1.2 2
15.14 odd 2 882.4.a.bg.1.1 2
20.19 odd 2 784.4.a.y.1.1 2
35.4 even 6 98.4.c.h.79.1 4
35.9 even 6 98.4.c.h.67.1 4
35.19 odd 6 98.4.c.h.67.2 4
35.24 odd 6 98.4.c.h.79.2 4
35.34 odd 2 98.4.a.g.1.1 2
105.44 odd 6 882.4.g.ba.361.2 4
105.59 even 6 882.4.g.ba.667.1 4
105.74 odd 6 882.4.g.ba.667.2 4
105.89 even 6 882.4.g.ba.361.1 4
105.104 even 2 882.4.a.bg.1.2 2
140.139 even 2 784.4.a.y.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.4.a.g.1.1 2 35.34 odd 2
98.4.a.g.1.2 yes 2 5.4 even 2
98.4.c.h.67.1 4 35.9 even 6
98.4.c.h.67.2 4 35.19 odd 6
98.4.c.h.79.1 4 35.4 even 6
98.4.c.h.79.2 4 35.24 odd 6
784.4.a.y.1.1 2 20.19 odd 2
784.4.a.y.1.2 2 140.139 even 2
882.4.a.bg.1.1 2 15.14 odd 2
882.4.a.bg.1.2 2 105.104 even 2
882.4.g.ba.361.1 4 105.89 even 6
882.4.g.ba.361.2 4 105.44 odd 6
882.4.g.ba.667.1 4 105.59 even 6
882.4.g.ba.667.2 4 105.74 odd 6
2450.4.a.bx.1.1 2 1.1 even 1 trivial
2450.4.a.bx.1.2 2 7.6 odd 2 inner