Properties

Label 531.4.a.d.1.2
Level $531$
Weight $4$
Character 531.1
Self dual yes
Analytic conductor $31.330$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 531.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.3300142130\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 177)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.68175\) of defining polynomial
Character \(\chi\) \(=\) 531.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.68175 q^{2} -5.17172 q^{4} +9.78761 q^{5} +6.87552 q^{7} +22.1515 q^{8} +O(q^{10})\) \(q-1.68175 q^{2} -5.17172 q^{4} +9.78761 q^{5} +6.87552 q^{7} +22.1515 q^{8} -16.4603 q^{10} +37.8468 q^{11} -11.3334 q^{13} -11.5629 q^{14} +4.12039 q^{16} +60.3439 q^{17} -92.5767 q^{19} -50.6188 q^{20} -63.6489 q^{22} +183.718 q^{23} -29.2026 q^{25} +19.0599 q^{26} -35.5582 q^{28} -265.559 q^{29} +177.376 q^{31} -184.142 q^{32} -101.483 q^{34} +67.2949 q^{35} -70.0886 q^{37} +155.691 q^{38} +216.811 q^{40} -208.760 q^{41} +393.127 q^{43} -195.733 q^{44} -308.968 q^{46} +134.917 q^{47} -295.727 q^{49} +49.1115 q^{50} +58.6131 q^{52} +650.432 q^{53} +370.430 q^{55} +152.303 q^{56} +446.604 q^{58} +59.0000 q^{59} +22.5322 q^{61} -298.302 q^{62} +276.717 q^{64} -110.927 q^{65} -209.476 q^{67} -312.082 q^{68} -113.173 q^{70} -209.160 q^{71} +865.282 q^{73} +117.872 q^{74} +478.781 q^{76} +260.217 q^{77} +843.604 q^{79} +40.3287 q^{80} +351.082 q^{82} +845.384 q^{83} +590.623 q^{85} -661.141 q^{86} +838.365 q^{88} +974.766 q^{89} -77.9229 q^{91} -950.139 q^{92} -226.897 q^{94} -906.105 q^{95} +338.796 q^{97} +497.339 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 8q^{2} + 22q^{4} + 28q^{5} - 59q^{7} + 117q^{8} + O(q^{10}) \) \( 7q + 8q^{2} + 22q^{4} + 28q^{5} - 59q^{7} + 117q^{8} - 79q^{10} + 131q^{11} - 123q^{13} + 117q^{14} + 202q^{16} + 235q^{17} - 80q^{19} - 61q^{20} + 688q^{22} + 274q^{23} + 193q^{25} + 180q^{26} - 118q^{28} + 406q^{29} - 346q^{31} + 854q^{32} + 178q^{34} + 424q^{35} - 157q^{37} + 129q^{38} - 590q^{40} + 825q^{41} - 815q^{43} + 1690q^{44} + 1457q^{46} + 1196q^{47} + 914q^{49} - 713q^{50} + 1030q^{52} + 900q^{53} - 1044q^{55} - 2172q^{56} + 1242q^{58} + 413q^{59} + 420q^{61} - 646q^{62} + 3541q^{64} - 190q^{65} + 1316q^{67} + 611q^{68} + 4658q^{70} + 173q^{71} - 418q^{73} - 660q^{74} + 1540q^{76} + 753q^{77} + 2635q^{79} - 6155q^{80} - 125q^{82} - 457q^{83} + 1270q^{85} - 3482q^{86} + 7685q^{88} - 592q^{89} + 3179q^{91} + 3500q^{92} + 2064q^{94} + 2250q^{95} - 1906q^{97} - 2994q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.68175 −0.594588 −0.297294 0.954786i \(-0.596084\pi\)
−0.297294 + 0.954786i \(0.596084\pi\)
\(3\) 0 0
\(4\) −5.17172 −0.646465
\(5\) 9.78761 0.875431 0.437715 0.899114i \(-0.355788\pi\)
0.437715 + 0.899114i \(0.355788\pi\)
\(6\) 0 0
\(7\) 6.87552 0.371243 0.185622 0.982621i \(-0.440570\pi\)
0.185622 + 0.982621i \(0.440570\pi\)
\(8\) 22.1515 0.978969
\(9\) 0 0
\(10\) −16.4603 −0.520521
\(11\) 37.8468 1.03739 0.518693 0.854961i \(-0.326419\pi\)
0.518693 + 0.854961i \(0.326419\pi\)
\(12\) 0 0
\(13\) −11.3334 −0.241794 −0.120897 0.992665i \(-0.538577\pi\)
−0.120897 + 0.992665i \(0.538577\pi\)
\(14\) −11.5629 −0.220737
\(15\) 0 0
\(16\) 4.12039 0.0643810
\(17\) 60.3439 0.860915 0.430457 0.902611i \(-0.358352\pi\)
0.430457 + 0.902611i \(0.358352\pi\)
\(18\) 0 0
\(19\) −92.5767 −1.11782 −0.558909 0.829229i \(-0.688780\pi\)
−0.558909 + 0.829229i \(0.688780\pi\)
\(20\) −50.6188 −0.565935
\(21\) 0 0
\(22\) −63.6489 −0.616818
\(23\) 183.718 1.66556 0.832781 0.553603i \(-0.186748\pi\)
0.832781 + 0.553603i \(0.186748\pi\)
\(24\) 0 0
\(25\) −29.2026 −0.233621
\(26\) 19.0599 0.143768
\(27\) 0 0
\(28\) −35.5582 −0.239995
\(29\) −265.559 −1.70045 −0.850225 0.526419i \(-0.823534\pi\)
−0.850225 + 0.526419i \(0.823534\pi\)
\(30\) 0 0
\(31\) 177.376 1.02767 0.513833 0.857890i \(-0.328225\pi\)
0.513833 + 0.857890i \(0.328225\pi\)
\(32\) −184.142 −1.01725
\(33\) 0 0
\(34\) −101.483 −0.511890
\(35\) 67.2949 0.324998
\(36\) 0 0
\(37\) −70.0886 −0.311419 −0.155709 0.987803i \(-0.549766\pi\)
−0.155709 + 0.987803i \(0.549766\pi\)
\(38\) 155.691 0.664642
\(39\) 0 0
\(40\) 216.811 0.857019
\(41\) −208.760 −0.795190 −0.397595 0.917561i \(-0.630155\pi\)
−0.397595 + 0.917561i \(0.630155\pi\)
\(42\) 0 0
\(43\) 393.127 1.39421 0.697107 0.716967i \(-0.254470\pi\)
0.697107 + 0.716967i \(0.254470\pi\)
\(44\) −195.733 −0.670633
\(45\) 0 0
\(46\) −308.968 −0.990323
\(47\) 134.917 0.418717 0.209358 0.977839i \(-0.432862\pi\)
0.209358 + 0.977839i \(0.432862\pi\)
\(48\) 0 0
\(49\) −295.727 −0.862179
\(50\) 49.1115 0.138908
\(51\) 0 0
\(52\) 58.6131 0.156311
\(53\) 650.432 1.68573 0.842865 0.538126i \(-0.180867\pi\)
0.842865 + 0.538126i \(0.180867\pi\)
\(54\) 0 0
\(55\) 370.430 0.908160
\(56\) 152.303 0.363435
\(57\) 0 0
\(58\) 446.604 1.01107
\(59\) 59.0000 0.130189
\(60\) 0 0
\(61\) 22.5322 0.0472943 0.0236472 0.999720i \(-0.492472\pi\)
0.0236472 + 0.999720i \(0.492472\pi\)
\(62\) −298.302 −0.611038
\(63\) 0 0
\(64\) 276.717 0.540463
\(65\) −110.927 −0.211674
\(66\) 0 0
\(67\) −209.476 −0.381964 −0.190982 0.981594i \(-0.561167\pi\)
−0.190982 + 0.981594i \(0.561167\pi\)
\(68\) −312.082 −0.556551
\(69\) 0 0
\(70\) −113.173 −0.193240
\(71\) −209.160 −0.349616 −0.174808 0.984603i \(-0.555930\pi\)
−0.174808 + 0.984603i \(0.555930\pi\)
\(72\) 0 0
\(73\) 865.282 1.38731 0.693655 0.720308i \(-0.255999\pi\)
0.693655 + 0.720308i \(0.255999\pi\)
\(74\) 117.872 0.185166
\(75\) 0 0
\(76\) 478.781 0.722630
\(77\) 260.217 0.385122
\(78\) 0 0
\(79\) 843.604 1.20143 0.600715 0.799464i \(-0.294883\pi\)
0.600715 + 0.799464i \(0.294883\pi\)
\(80\) 40.3287 0.0563611
\(81\) 0 0
\(82\) 351.082 0.472811
\(83\) 845.384 1.11799 0.558994 0.829172i \(-0.311188\pi\)
0.558994 + 0.829172i \(0.311188\pi\)
\(84\) 0 0
\(85\) 590.623 0.753671
\(86\) −661.141 −0.828984
\(87\) 0 0
\(88\) 838.365 1.01557
\(89\) 974.766 1.16096 0.580478 0.814276i \(-0.302866\pi\)
0.580478 + 0.814276i \(0.302866\pi\)
\(90\) 0 0
\(91\) −77.9229 −0.0897642
\(92\) −950.139 −1.07673
\(93\) 0 0
\(94\) −226.897 −0.248964
\(95\) −906.105 −0.978573
\(96\) 0 0
\(97\) 338.796 0.354634 0.177317 0.984154i \(-0.443258\pi\)
0.177317 + 0.984154i \(0.443258\pi\)
\(98\) 497.339 0.512641
\(99\) 0 0
\(100\) 151.028 0.151028
\(101\) 683.879 0.673747 0.336874 0.941550i \(-0.390631\pi\)
0.336874 + 0.941550i \(0.390631\pi\)
\(102\) 0 0
\(103\) −1235.54 −1.18196 −0.590979 0.806687i \(-0.701258\pi\)
−0.590979 + 0.806687i \(0.701258\pi\)
\(104\) −251.052 −0.236708
\(105\) 0 0
\(106\) −1093.86 −1.00231
\(107\) −431.478 −0.389837 −0.194918 0.980819i \(-0.562444\pi\)
−0.194918 + 0.980819i \(0.562444\pi\)
\(108\) 0 0
\(109\) 427.874 0.375989 0.187995 0.982170i \(-0.439801\pi\)
0.187995 + 0.982170i \(0.439801\pi\)
\(110\) −622.971 −0.539981
\(111\) 0 0
\(112\) 28.3298 0.0239010
\(113\) 1934.70 1.61063 0.805317 0.592845i \(-0.201995\pi\)
0.805317 + 0.592845i \(0.201995\pi\)
\(114\) 0 0
\(115\) 1798.16 1.45808
\(116\) 1373.40 1.09928
\(117\) 0 0
\(118\) −99.2233 −0.0774088
\(119\) 414.896 0.319609
\(120\) 0 0
\(121\) 101.382 0.0761698
\(122\) −37.8935 −0.0281207
\(123\) 0 0
\(124\) −917.337 −0.664349
\(125\) −1509.28 −1.07995
\(126\) 0 0
\(127\) −1334.46 −0.932395 −0.466198 0.884681i \(-0.654376\pi\)
−0.466198 + 0.884681i \(0.654376\pi\)
\(128\) 1007.76 0.695896
\(129\) 0 0
\(130\) 186.551 0.125859
\(131\) 739.638 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(132\) 0 0
\(133\) −636.513 −0.414982
\(134\) 352.287 0.227111
\(135\) 0 0
\(136\) 1336.71 0.842809
\(137\) 1262.30 0.787196 0.393598 0.919283i \(-0.371230\pi\)
0.393598 + 0.919283i \(0.371230\pi\)
\(138\) 0 0
\(139\) 2630.69 1.60527 0.802634 0.596471i \(-0.203431\pi\)
0.802634 + 0.596471i \(0.203431\pi\)
\(140\) −348.030 −0.210099
\(141\) 0 0
\(142\) 351.755 0.207877
\(143\) −428.933 −0.250833
\(144\) 0 0
\(145\) −2599.19 −1.48863
\(146\) −1455.19 −0.824878
\(147\) 0 0
\(148\) 362.478 0.201321
\(149\) 434.666 0.238988 0.119494 0.992835i \(-0.461873\pi\)
0.119494 + 0.992835i \(0.461873\pi\)
\(150\) 0 0
\(151\) −1585.40 −0.854425 −0.427213 0.904151i \(-0.640504\pi\)
−0.427213 + 0.904151i \(0.640504\pi\)
\(152\) −2050.72 −1.09431
\(153\) 0 0
\(154\) −437.619 −0.228989
\(155\) 1736.09 0.899650
\(156\) 0 0
\(157\) 3744.07 1.90324 0.951622 0.307270i \(-0.0994155\pi\)
0.951622 + 0.307270i \(0.0994155\pi\)
\(158\) −1418.73 −0.714356
\(159\) 0 0
\(160\) −1802.31 −0.890531
\(161\) 1263.16 0.618328
\(162\) 0 0
\(163\) −1331.85 −0.639993 −0.319996 0.947419i \(-0.603682\pi\)
−0.319996 + 0.947419i \(0.603682\pi\)
\(164\) 1079.65 0.514062
\(165\) 0 0
\(166\) −1421.73 −0.664743
\(167\) −16.5584 −0.00767260 −0.00383630 0.999993i \(-0.501221\pi\)
−0.00383630 + 0.999993i \(0.501221\pi\)
\(168\) 0 0
\(169\) −2068.55 −0.941536
\(170\) −993.280 −0.448124
\(171\) 0 0
\(172\) −2033.14 −0.901310
\(173\) 2397.07 1.05344 0.526721 0.850038i \(-0.323421\pi\)
0.526721 + 0.850038i \(0.323421\pi\)
\(174\) 0 0
\(175\) −200.783 −0.0867302
\(176\) 155.944 0.0667880
\(177\) 0 0
\(178\) −1639.31 −0.690291
\(179\) −1223.00 −0.510680 −0.255340 0.966851i \(-0.582187\pi\)
−0.255340 + 0.966851i \(0.582187\pi\)
\(180\) 0 0
\(181\) −4266.97 −1.75227 −0.876137 0.482063i \(-0.839888\pi\)
−0.876137 + 0.482063i \(0.839888\pi\)
\(182\) 131.047 0.0533728
\(183\) 0 0
\(184\) 4069.64 1.63053
\(185\) −686.000 −0.272626
\(186\) 0 0
\(187\) 2283.83 0.893101
\(188\) −697.753 −0.270686
\(189\) 0 0
\(190\) 1523.84 0.581848
\(191\) 3080.45 1.16698 0.583491 0.812120i \(-0.301687\pi\)
0.583491 + 0.812120i \(0.301687\pi\)
\(192\) 0 0
\(193\) 3469.71 1.29407 0.647033 0.762462i \(-0.276009\pi\)
0.647033 + 0.762462i \(0.276009\pi\)
\(194\) −569.770 −0.210862
\(195\) 0 0
\(196\) 1529.42 0.557368
\(197\) 1487.74 0.538055 0.269027 0.963133i \(-0.413298\pi\)
0.269027 + 0.963133i \(0.413298\pi\)
\(198\) 0 0
\(199\) −3027.73 −1.07854 −0.539271 0.842132i \(-0.681300\pi\)
−0.539271 + 0.842132i \(0.681300\pi\)
\(200\) −646.883 −0.228708
\(201\) 0 0
\(202\) −1150.11 −0.400602
\(203\) −1825.86 −0.631280
\(204\) 0 0
\(205\) −2043.26 −0.696134
\(206\) 2077.87 0.702779
\(207\) 0 0
\(208\) −46.6980 −0.0155669
\(209\) −3503.74 −1.15961
\(210\) 0 0
\(211\) −1655.90 −0.540269 −0.270135 0.962823i \(-0.587068\pi\)
−0.270135 + 0.962823i \(0.587068\pi\)
\(212\) −3363.85 −1.08976
\(213\) 0 0
\(214\) 725.638 0.231792
\(215\) 3847.77 1.22054
\(216\) 0 0
\(217\) 1219.55 0.381514
\(218\) −719.576 −0.223559
\(219\) 0 0
\(220\) −1915.76 −0.587093
\(221\) −683.901 −0.208164
\(222\) 0 0
\(223\) −1225.20 −0.367916 −0.183958 0.982934i \(-0.558891\pi\)
−0.183958 + 0.982934i \(0.558891\pi\)
\(224\) −1266.07 −0.377647
\(225\) 0 0
\(226\) −3253.69 −0.957664
\(227\) 657.677 0.192298 0.0961488 0.995367i \(-0.469348\pi\)
0.0961488 + 0.995367i \(0.469348\pi\)
\(228\) 0 0
\(229\) 1407.97 0.406294 0.203147 0.979148i \(-0.434883\pi\)
0.203147 + 0.979148i \(0.434883\pi\)
\(230\) −3024.06 −0.866959
\(231\) 0 0
\(232\) −5882.54 −1.66469
\(233\) −6393.48 −1.79764 −0.898821 0.438315i \(-0.855575\pi\)
−0.898821 + 0.438315i \(0.855575\pi\)
\(234\) 0 0
\(235\) 1320.52 0.366558
\(236\) −305.131 −0.0841625
\(237\) 0 0
\(238\) −697.751 −0.190036
\(239\) −1941.60 −0.525489 −0.262744 0.964865i \(-0.584628\pi\)
−0.262744 + 0.964865i \(0.584628\pi\)
\(240\) 0 0
\(241\) −3701.61 −0.989385 −0.494692 0.869068i \(-0.664719\pi\)
−0.494692 + 0.869068i \(0.664719\pi\)
\(242\) −170.499 −0.0452897
\(243\) 0 0
\(244\) −116.530 −0.0305741
\(245\) −2894.46 −0.754778
\(246\) 0 0
\(247\) 1049.21 0.270282
\(248\) 3929.15 1.00605
\(249\) 0 0
\(250\) 2538.22 0.642126
\(251\) 239.067 0.0601186 0.0300593 0.999548i \(-0.490430\pi\)
0.0300593 + 0.999548i \(0.490430\pi\)
\(252\) 0 0
\(253\) 6953.15 1.72783
\(254\) 2244.23 0.554392
\(255\) 0 0
\(256\) −3908.55 −0.954235
\(257\) −6633.12 −1.60997 −0.804985 0.593295i \(-0.797827\pi\)
−0.804985 + 0.593295i \(0.797827\pi\)
\(258\) 0 0
\(259\) −481.895 −0.115612
\(260\) 573.682 0.136839
\(261\) 0 0
\(262\) −1243.89 −0.293311
\(263\) 2010.45 0.471368 0.235684 0.971830i \(-0.424267\pi\)
0.235684 + 0.971830i \(0.424267\pi\)
\(264\) 0 0
\(265\) 6366.17 1.47574
\(266\) 1070.46 0.246744
\(267\) 0 0
\(268\) 1083.35 0.246926
\(269\) −5923.22 −1.34255 −0.671273 0.741210i \(-0.734252\pi\)
−0.671273 + 0.741210i \(0.734252\pi\)
\(270\) 0 0
\(271\) −1908.94 −0.427896 −0.213948 0.976845i \(-0.568632\pi\)
−0.213948 + 0.976845i \(0.568632\pi\)
\(272\) 248.640 0.0554266
\(273\) 0 0
\(274\) −2122.88 −0.468057
\(275\) −1105.23 −0.242355
\(276\) 0 0
\(277\) 7685.54 1.66707 0.833536 0.552464i \(-0.186312\pi\)
0.833536 + 0.552464i \(0.186312\pi\)
\(278\) −4424.17 −0.954474
\(279\) 0 0
\(280\) 1490.69 0.318162
\(281\) −1223.20 −0.259680 −0.129840 0.991535i \(-0.541446\pi\)
−0.129840 + 0.991535i \(0.541446\pi\)
\(282\) 0 0
\(283\) −1543.59 −0.324229 −0.162115 0.986772i \(-0.551831\pi\)
−0.162115 + 0.986772i \(0.551831\pi\)
\(284\) 1081.72 0.226014
\(285\) 0 0
\(286\) 721.358 0.149143
\(287\) −1435.33 −0.295209
\(288\) 0 0
\(289\) −1271.61 −0.258826
\(290\) 4371.18 0.885120
\(291\) 0 0
\(292\) −4474.99 −0.896846
\(293\) 3987.52 0.795063 0.397532 0.917589i \(-0.369867\pi\)
0.397532 + 0.917589i \(0.369867\pi\)
\(294\) 0 0
\(295\) 577.469 0.113971
\(296\) −1552.57 −0.304869
\(297\) 0 0
\(298\) −731.000 −0.142100
\(299\) −2082.15 −0.402722
\(300\) 0 0
\(301\) 2702.95 0.517593
\(302\) 2666.25 0.508031
\(303\) 0 0
\(304\) −381.452 −0.0719663
\(305\) 220.537 0.0414029
\(306\) 0 0
\(307\) −895.829 −0.166540 −0.0832698 0.996527i \(-0.526536\pi\)
−0.0832698 + 0.996527i \(0.526536\pi\)
\(308\) −1345.77 −0.248968
\(309\) 0 0
\(310\) −2919.66 −0.534921
\(311\) −4166.91 −0.759754 −0.379877 0.925037i \(-0.624034\pi\)
−0.379877 + 0.925037i \(0.624034\pi\)
\(312\) 0 0
\(313\) −3619.78 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(314\) −6296.59 −1.13165
\(315\) 0 0
\(316\) −4362.88 −0.776681
\(317\) −865.480 −0.153344 −0.0766722 0.997056i \(-0.524430\pi\)
−0.0766722 + 0.997056i \(0.524430\pi\)
\(318\) 0 0
\(319\) −10050.6 −1.76402
\(320\) 2708.40 0.473138
\(321\) 0 0
\(322\) −2124.32 −0.367651
\(323\) −5586.44 −0.962347
\(324\) 0 0
\(325\) 330.965 0.0564881
\(326\) 2239.84 0.380532
\(327\) 0 0
\(328\) −4624.35 −0.778467
\(329\) 927.626 0.155446
\(330\) 0 0
\(331\) 8140.89 1.35185 0.675927 0.736968i \(-0.263743\pi\)
0.675927 + 0.736968i \(0.263743\pi\)
\(332\) −4372.09 −0.722739
\(333\) 0 0
\(334\) 27.8470 0.00456204
\(335\) −2050.27 −0.334383
\(336\) 0 0
\(337\) 7396.34 1.19556 0.597781 0.801659i \(-0.296049\pi\)
0.597781 + 0.801659i \(0.296049\pi\)
\(338\) 3478.79 0.559826
\(339\) 0 0
\(340\) −3054.53 −0.487222
\(341\) 6713.11 1.06609
\(342\) 0 0
\(343\) −4391.58 −0.691321
\(344\) 8708.36 1.36489
\(345\) 0 0
\(346\) −4031.27 −0.626365
\(347\) 1341.98 0.207612 0.103806 0.994598i \(-0.466898\pi\)
0.103806 + 0.994598i \(0.466898\pi\)
\(348\) 0 0
\(349\) 2193.32 0.336407 0.168203 0.985752i \(-0.446203\pi\)
0.168203 + 0.985752i \(0.446203\pi\)
\(350\) 337.667 0.0515688
\(351\) 0 0
\(352\) −6969.18 −1.05528
\(353\) 636.290 0.0959386 0.0479693 0.998849i \(-0.484725\pi\)
0.0479693 + 0.998849i \(0.484725\pi\)
\(354\) 0 0
\(355\) −2047.18 −0.306064
\(356\) −5041.22 −0.750516
\(357\) 0 0
\(358\) 2056.79 0.303644
\(359\) 7124.07 1.04734 0.523668 0.851922i \(-0.324563\pi\)
0.523668 + 0.851922i \(0.324563\pi\)
\(360\) 0 0
\(361\) 1711.45 0.249519
\(362\) 7175.98 1.04188
\(363\) 0 0
\(364\) 402.995 0.0580294
\(365\) 8469.04 1.21449
\(366\) 0 0
\(367\) −8714.69 −1.23952 −0.619759 0.784792i \(-0.712770\pi\)
−0.619759 + 0.784792i \(0.712770\pi\)
\(368\) 756.990 0.107231
\(369\) 0 0
\(370\) 1153.68 0.162100
\(371\) 4472.05 0.625815
\(372\) 0 0
\(373\) 9123.29 1.26645 0.633225 0.773967i \(-0.281731\pi\)
0.633225 + 0.773967i \(0.281731\pi\)
\(374\) −3840.82 −0.531027
\(375\) 0 0
\(376\) 2988.62 0.409911
\(377\) 3009.68 0.411158
\(378\) 0 0
\(379\) 8539.81 1.15742 0.578708 0.815535i \(-0.303557\pi\)
0.578708 + 0.815535i \(0.303557\pi\)
\(380\) 4686.12 0.632613
\(381\) 0 0
\(382\) −5180.54 −0.693873
\(383\) 8691.08 1.15951 0.579757 0.814790i \(-0.303148\pi\)
0.579757 + 0.814790i \(0.303148\pi\)
\(384\) 0 0
\(385\) 2546.90 0.337148
\(386\) −5835.18 −0.769437
\(387\) 0 0
\(388\) −1752.16 −0.229259
\(389\) 10079.9 1.31381 0.656904 0.753974i \(-0.271866\pi\)
0.656904 + 0.753974i \(0.271866\pi\)
\(390\) 0 0
\(391\) 11086.3 1.43391
\(392\) −6550.81 −0.844046
\(393\) 0 0
\(394\) −2502.00 −0.319921
\(395\) 8256.87 1.05177
\(396\) 0 0
\(397\) −1829.51 −0.231286 −0.115643 0.993291i \(-0.536893\pi\)
−0.115643 + 0.993291i \(0.536893\pi\)
\(398\) 5091.88 0.641288
\(399\) 0 0
\(400\) −120.326 −0.0150408
\(401\) 10919.6 1.35985 0.679926 0.733281i \(-0.262012\pi\)
0.679926 + 0.733281i \(0.262012\pi\)
\(402\) 0 0
\(403\) −2010.27 −0.248483
\(404\) −3536.83 −0.435554
\(405\) 0 0
\(406\) 3070.63 0.375352
\(407\) −2652.63 −0.323061
\(408\) 0 0
\(409\) 6441.50 0.778757 0.389378 0.921078i \(-0.372690\pi\)
0.389378 + 0.921078i \(0.372690\pi\)
\(410\) 3436.25 0.413913
\(411\) 0 0
\(412\) 6389.88 0.764094
\(413\) 405.656 0.0483317
\(414\) 0 0
\(415\) 8274.29 0.978721
\(416\) 2086.95 0.245964
\(417\) 0 0
\(418\) 5892.41 0.689491
\(419\) −6784.29 −0.791012 −0.395506 0.918463i \(-0.629431\pi\)
−0.395506 + 0.918463i \(0.629431\pi\)
\(420\) 0 0
\(421\) 827.842 0.0958350 0.0479175 0.998851i \(-0.484742\pi\)
0.0479175 + 0.998851i \(0.484742\pi\)
\(422\) 2784.81 0.321238
\(423\) 0 0
\(424\) 14408.1 1.65028
\(425\) −1762.20 −0.201128
\(426\) 0 0
\(427\) 154.921 0.0175577
\(428\) 2231.48 0.252016
\(429\) 0 0
\(430\) −6470.99 −0.725718
\(431\) −1719.44 −0.192163 −0.0960815 0.995373i \(-0.530631\pi\)
−0.0960815 + 0.995373i \(0.530631\pi\)
\(432\) 0 0
\(433\) 11944.5 1.32567 0.662836 0.748765i \(-0.269353\pi\)
0.662836 + 0.748765i \(0.269353\pi\)
\(434\) −2050.98 −0.226844
\(435\) 0 0
\(436\) −2212.84 −0.243064
\(437\) −17008.0 −1.86180
\(438\) 0 0
\(439\) 316.306 0.0343882 0.0171941 0.999852i \(-0.494527\pi\)
0.0171941 + 0.999852i \(0.494527\pi\)
\(440\) 8205.59 0.889060
\(441\) 0 0
\(442\) 1150.15 0.123772
\(443\) 9043.41 0.969899 0.484950 0.874542i \(-0.338838\pi\)
0.484950 + 0.874542i \(0.338838\pi\)
\(444\) 0 0
\(445\) 9540.63 1.01634
\(446\) 2060.47 0.218758
\(447\) 0 0
\(448\) 1902.57 0.200643
\(449\) −9058.55 −0.952114 −0.476057 0.879414i \(-0.657934\pi\)
−0.476057 + 0.879414i \(0.657934\pi\)
\(450\) 0 0
\(451\) −7900.90 −0.824920
\(452\) −10005.7 −1.04122
\(453\) 0 0
\(454\) −1106.05 −0.114338
\(455\) −762.680 −0.0785824
\(456\) 0 0
\(457\) 14344.7 1.46831 0.734155 0.678982i \(-0.237579\pi\)
0.734155 + 0.678982i \(0.237579\pi\)
\(458\) −2367.85 −0.241578
\(459\) 0 0
\(460\) −9299.59 −0.942599
\(461\) 10742.1 1.08527 0.542634 0.839969i \(-0.317427\pi\)
0.542634 + 0.839969i \(0.317427\pi\)
\(462\) 0 0
\(463\) −17574.2 −1.76402 −0.882009 0.471232i \(-0.843809\pi\)
−0.882009 + 0.471232i \(0.843809\pi\)
\(464\) −1094.21 −0.109477
\(465\) 0 0
\(466\) 10752.2 1.06886
\(467\) −8958.29 −0.887667 −0.443833 0.896109i \(-0.646382\pi\)
−0.443833 + 0.896109i \(0.646382\pi\)
\(468\) 0 0
\(469\) −1440.26 −0.141802
\(470\) −2220.78 −0.217951
\(471\) 0 0
\(472\) 1306.94 0.127451
\(473\) 14878.6 1.44634
\(474\) 0 0
\(475\) 2703.49 0.261146
\(476\) −2145.72 −0.206616
\(477\) 0 0
\(478\) 3265.29 0.312450
\(479\) −6909.71 −0.659108 −0.329554 0.944137i \(-0.606898\pi\)
−0.329554 + 0.944137i \(0.606898\pi\)
\(480\) 0 0
\(481\) 794.342 0.0752991
\(482\) 6225.19 0.588277
\(483\) 0 0
\(484\) −524.319 −0.0492411
\(485\) 3316.01 0.310458
\(486\) 0 0
\(487\) −15008.4 −1.39650 −0.698248 0.715856i \(-0.746037\pi\)
−0.698248 + 0.715856i \(0.746037\pi\)
\(488\) 499.123 0.0462997
\(489\) 0 0
\(490\) 4867.76 0.448782
\(491\) −10939.9 −1.00552 −0.502761 0.864425i \(-0.667682\pi\)
−0.502761 + 0.864425i \(0.667682\pi\)
\(492\) 0 0
\(493\) −16024.9 −1.46394
\(494\) −1764.51 −0.160706
\(495\) 0 0
\(496\) 730.857 0.0661622
\(497\) −1438.08 −0.129792
\(498\) 0 0
\(499\) −1960.94 −0.175919 −0.0879596 0.996124i \(-0.528035\pi\)
−0.0879596 + 0.996124i \(0.528035\pi\)
\(500\) 7805.55 0.698149
\(501\) 0 0
\(502\) −402.051 −0.0357458
\(503\) 7812.26 0.692508 0.346254 0.938141i \(-0.387453\pi\)
0.346254 + 0.938141i \(0.387453\pi\)
\(504\) 0 0
\(505\) 6693.54 0.589819
\(506\) −11693.5 −1.02735
\(507\) 0 0
\(508\) 6901.45 0.602761
\(509\) −11915.7 −1.03763 −0.518816 0.854886i \(-0.673627\pi\)
−0.518816 + 0.854886i \(0.673627\pi\)
\(510\) 0 0
\(511\) 5949.26 0.515029
\(512\) −1488.92 −0.128519
\(513\) 0 0
\(514\) 11155.2 0.957270
\(515\) −12093.0 −1.03472
\(516\) 0 0
\(517\) 5106.19 0.434371
\(518\) 810.428 0.0687416
\(519\) 0 0
\(520\) −2457.20 −0.207222
\(521\) −12795.0 −1.07593 −0.537963 0.842969i \(-0.680806\pi\)
−0.537963 + 0.842969i \(0.680806\pi\)
\(522\) 0 0
\(523\) −18908.5 −1.58090 −0.790452 0.612524i \(-0.790154\pi\)
−0.790452 + 0.612524i \(0.790154\pi\)
\(524\) −3825.20 −0.318902
\(525\) 0 0
\(526\) −3381.08 −0.280270
\(527\) 10703.5 0.884732
\(528\) 0 0
\(529\) 21585.4 1.77409
\(530\) −10706.3 −0.877457
\(531\) 0 0
\(532\) 3291.86 0.268271
\(533\) 2365.96 0.192272
\(534\) 0 0
\(535\) −4223.14 −0.341275
\(536\) −4640.22 −0.373931
\(537\) 0 0
\(538\) 9961.37 0.798263
\(539\) −11192.3 −0.894412
\(540\) 0 0
\(541\) −13497.9 −1.07268 −0.536340 0.844002i \(-0.680194\pi\)
−0.536340 + 0.844002i \(0.680194\pi\)
\(542\) 3210.36 0.254422
\(543\) 0 0
\(544\) −11111.8 −0.875765
\(545\) 4187.86 0.329153
\(546\) 0 0
\(547\) 7859.46 0.614344 0.307172 0.951654i \(-0.400617\pi\)
0.307172 + 0.951654i \(0.400617\pi\)
\(548\) −6528.27 −0.508894
\(549\) 0 0
\(550\) 1858.72 0.144102
\(551\) 24584.6 1.90080
\(552\) 0 0
\(553\) 5800.22 0.446022
\(554\) −12925.2 −0.991222
\(555\) 0 0
\(556\) −13605.2 −1.03775
\(557\) −20367.3 −1.54936 −0.774678 0.632356i \(-0.782088\pi\)
−0.774678 + 0.632356i \(0.782088\pi\)
\(558\) 0 0
\(559\) −4455.46 −0.337112
\(560\) 277.281 0.0209237
\(561\) 0 0
\(562\) 2057.12 0.154403
\(563\) −3392.89 −0.253985 −0.126992 0.991904i \(-0.540532\pi\)
−0.126992 + 0.991904i \(0.540532\pi\)
\(564\) 0 0
\(565\) 18936.1 1.41000
\(566\) 2595.93 0.192783
\(567\) 0 0
\(568\) −4633.21 −0.342263
\(569\) −8441.27 −0.621927 −0.310964 0.950422i \(-0.600652\pi\)
−0.310964 + 0.950422i \(0.600652\pi\)
\(570\) 0 0
\(571\) 1840.67 0.134903 0.0674514 0.997723i \(-0.478513\pi\)
0.0674514 + 0.997723i \(0.478513\pi\)
\(572\) 2218.32 0.162155
\(573\) 0 0
\(574\) 2413.87 0.175528
\(575\) −5365.06 −0.389110
\(576\) 0 0
\(577\) −14007.9 −1.01067 −0.505335 0.862923i \(-0.668631\pi\)
−0.505335 + 0.862923i \(0.668631\pi\)
\(578\) 2138.53 0.153895
\(579\) 0 0
\(580\) 13442.3 0.962344
\(581\) 5812.45 0.415045
\(582\) 0 0
\(583\) 24616.8 1.74875
\(584\) 19167.3 1.35813
\(585\) 0 0
\(586\) −6706.01 −0.472735
\(587\) 26870.9 1.88940 0.944702 0.327931i \(-0.106351\pi\)
0.944702 + 0.327931i \(0.106351\pi\)
\(588\) 0 0
\(589\) −16420.9 −1.14874
\(590\) −971.159 −0.0677661
\(591\) 0 0
\(592\) −288.792 −0.0200495
\(593\) 7529.46 0.521413 0.260707 0.965418i \(-0.416044\pi\)
0.260707 + 0.965418i \(0.416044\pi\)
\(594\) 0 0
\(595\) 4060.84 0.279795
\(596\) −2247.97 −0.154497
\(597\) 0 0
\(598\) 3501.66 0.239454
\(599\) −3363.55 −0.229434 −0.114717 0.993398i \(-0.536596\pi\)
−0.114717 + 0.993398i \(0.536596\pi\)
\(600\) 0 0
\(601\) 13338.7 0.905316 0.452658 0.891684i \(-0.350476\pi\)
0.452658 + 0.891684i \(0.350476\pi\)
\(602\) −4545.68 −0.307755
\(603\) 0 0
\(604\) 8199.25 0.552356
\(605\) 992.288 0.0666814
\(606\) 0 0
\(607\) −7189.25 −0.480729 −0.240365 0.970683i \(-0.577267\pi\)
−0.240365 + 0.970683i \(0.577267\pi\)
\(608\) 17047.2 1.13710
\(609\) 0 0
\(610\) −370.887 −0.0246177
\(611\) −1529.07 −0.101243
\(612\) 0 0
\(613\) −22156.6 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(614\) 1506.56 0.0990225
\(615\) 0 0
\(616\) 5764.20 0.377023
\(617\) 15462.4 1.00890 0.504452 0.863440i \(-0.331695\pi\)
0.504452 + 0.863440i \(0.331695\pi\)
\(618\) 0 0
\(619\) −18599.5 −1.20772 −0.603858 0.797092i \(-0.706371\pi\)
−0.603858 + 0.797092i \(0.706371\pi\)
\(620\) −8978.54 −0.581592
\(621\) 0 0
\(622\) 7007.69 0.451741
\(623\) 6702.02 0.430997
\(624\) 0 0
\(625\) −11121.9 −0.711800
\(626\) 6087.57 0.388671
\(627\) 0 0
\(628\) −19363.3 −1.23038
\(629\) −4229.42 −0.268105
\(630\) 0 0
\(631\) −14886.6 −0.939187 −0.469594 0.882883i \(-0.655600\pi\)
−0.469594 + 0.882883i \(0.655600\pi\)
\(632\) 18687.1 1.17616
\(633\) 0 0
\(634\) 1455.52 0.0911768
\(635\) −13061.2 −0.816248
\(636\) 0 0
\(637\) 3351.59 0.208469
\(638\) 16902.5 1.04887
\(639\) 0 0
\(640\) 9863.61 0.609208
\(641\) −30295.2 −1.86675 −0.933376 0.358899i \(-0.883152\pi\)
−0.933376 + 0.358899i \(0.883152\pi\)
\(642\) 0 0
\(643\) 12393.0 0.760080 0.380040 0.924970i \(-0.375910\pi\)
0.380040 + 0.924970i \(0.375910\pi\)
\(644\) −6532.70 −0.399727
\(645\) 0 0
\(646\) 9395.00 0.572200
\(647\) 18759.0 1.13986 0.569931 0.821692i \(-0.306970\pi\)
0.569931 + 0.821692i \(0.306970\pi\)
\(648\) 0 0
\(649\) 2232.96 0.135056
\(650\) −556.601 −0.0335872
\(651\) 0 0
\(652\) 6887.97 0.413733
\(653\) −17228.9 −1.03249 −0.516247 0.856440i \(-0.672671\pi\)
−0.516247 + 0.856440i \(0.672671\pi\)
\(654\) 0 0
\(655\) 7239.29 0.431851
\(656\) −860.171 −0.0511952
\(657\) 0 0
\(658\) −1560.03 −0.0924262
\(659\) −10789.4 −0.637776 −0.318888 0.947792i \(-0.603309\pi\)
−0.318888 + 0.947792i \(0.603309\pi\)
\(660\) 0 0
\(661\) 91.3456 0.00537509 0.00268754 0.999996i \(-0.499145\pi\)
0.00268754 + 0.999996i \(0.499145\pi\)
\(662\) −13690.9 −0.803797
\(663\) 0 0
\(664\) 18726.6 1.09448
\(665\) −6229.94 −0.363288
\(666\) 0 0
\(667\) −48788.0 −2.83220
\(668\) 85.6351 0.00496006
\(669\) 0 0
\(670\) 3448.05 0.198820
\(671\) 852.773 0.0490625
\(672\) 0 0
\(673\) −25294.9 −1.44881 −0.724404 0.689376i \(-0.757885\pi\)
−0.724404 + 0.689376i \(0.757885\pi\)
\(674\) −12438.8 −0.710868
\(675\) 0 0
\(676\) 10698.0 0.608670
\(677\) −1529.96 −0.0868557 −0.0434278 0.999057i \(-0.513828\pi\)
−0.0434278 + 0.999057i \(0.513828\pi\)
\(678\) 0 0
\(679\) 2329.40 0.131656
\(680\) 13083.2 0.737820
\(681\) 0 0
\(682\) −11289.8 −0.633882
\(683\) −7588.88 −0.425154 −0.212577 0.977144i \(-0.568186\pi\)
−0.212577 + 0.977144i \(0.568186\pi\)
\(684\) 0 0
\(685\) 12354.9 0.689135
\(686\) 7385.54 0.411051
\(687\) 0 0
\(688\) 1619.83 0.0897610
\(689\) −7371.60 −0.407599
\(690\) 0 0
\(691\) −7781.95 −0.428421 −0.214211 0.976787i \(-0.568718\pi\)
−0.214211 + 0.976787i \(0.568718\pi\)
\(692\) −12396.9 −0.681013
\(693\) 0 0
\(694\) −2256.87 −0.123443
\(695\) 25748.2 1.40530
\(696\) 0 0
\(697\) −12597.4 −0.684591
\(698\) −3688.62 −0.200024
\(699\) 0 0
\(700\) 1038.39 0.0560680
\(701\) −16501.9 −0.889111 −0.444555 0.895751i \(-0.646638\pi\)
−0.444555 + 0.895751i \(0.646638\pi\)
\(702\) 0 0
\(703\) 6488.57 0.348110
\(704\) 10472.9 0.560669
\(705\) 0 0
\(706\) −1070.08 −0.0570440
\(707\) 4702.02 0.250124
\(708\) 0 0
\(709\) −26435.2 −1.40027 −0.700136 0.714009i \(-0.746877\pi\)
−0.700136 + 0.714009i \(0.746877\pi\)
\(710\) 3442.84 0.181982
\(711\) 0 0
\(712\) 21592.6 1.13654
\(713\) 32587.2 1.71164
\(714\) 0 0
\(715\) −4198.23 −0.219587
\(716\) 6325.03 0.330136
\(717\) 0 0
\(718\) −11980.9 −0.622734
\(719\) 9576.02 0.496697 0.248348 0.968671i \(-0.420112\pi\)
0.248348 + 0.968671i \(0.420112\pi\)
\(720\) 0 0
\(721\) −8495.00 −0.438794
\(722\) −2878.23 −0.148361
\(723\) 0 0
\(724\) 22067.6 1.13278
\(725\) 7755.02 0.397261
\(726\) 0 0
\(727\) −11408.0 −0.581979 −0.290990 0.956726i \(-0.593985\pi\)
−0.290990 + 0.956726i \(0.593985\pi\)
\(728\) −1726.11 −0.0878764
\(729\) 0 0
\(730\) −14242.8 −0.722124
\(731\) 23722.8 1.20030
\(732\) 0 0
\(733\) −25829.0 −1.30152 −0.650762 0.759282i \(-0.725550\pi\)
−0.650762 + 0.759282i \(0.725550\pi\)
\(734\) 14655.9 0.737003
\(735\) 0 0
\(736\) −33830.2 −1.69429
\(737\) −7928.01 −0.396244
\(738\) 0 0
\(739\) 37906.8 1.88691 0.943454 0.331503i \(-0.107556\pi\)
0.943454 + 0.331503i \(0.107556\pi\)
\(740\) 3547.80 0.176243
\(741\) 0 0
\(742\) −7520.88 −0.372102
\(743\) −17868.7 −0.882286 −0.441143 0.897437i \(-0.645427\pi\)
−0.441143 + 0.897437i \(0.645427\pi\)
\(744\) 0 0
\(745\) 4254.35 0.209218
\(746\) −15343.1 −0.753017
\(747\) 0 0
\(748\) −11811.3 −0.577358
\(749\) −2966.63 −0.144724
\(750\) 0 0
\(751\) −12.6803 −0.000616125 0 −0.000308063 1.00000i \(-0.500098\pi\)
−0.000308063 1.00000i \(0.500098\pi\)
\(752\) 555.911 0.0269574
\(753\) 0 0
\(754\) −5061.54 −0.244470
\(755\) −15517.3 −0.747990
\(756\) 0 0
\(757\) 39700.2 1.90611 0.953056 0.302793i \(-0.0979192\pi\)
0.953056 + 0.302793i \(0.0979192\pi\)
\(758\) −14361.8 −0.688186
\(759\) 0 0
\(760\) −20071.6 −0.957992
\(761\) 9323.77 0.444134 0.222067 0.975031i \(-0.428720\pi\)
0.222067 + 0.975031i \(0.428720\pi\)
\(762\) 0 0
\(763\) 2941.85 0.139583
\(764\) −15931.2 −0.754412
\(765\) 0 0
\(766\) −14616.2 −0.689433
\(767\) −668.670 −0.0314789
\(768\) 0 0
\(769\) 20630.0 0.967408 0.483704 0.875232i \(-0.339291\pi\)
0.483704 + 0.875232i \(0.339291\pi\)
\(770\) −4283.25 −0.200464
\(771\) 0 0
\(772\) −17944.3 −0.836568
\(773\) −9335.33 −0.434370 −0.217185 0.976130i \(-0.569688\pi\)
−0.217185 + 0.976130i \(0.569688\pi\)
\(774\) 0 0
\(775\) −5179.84 −0.240084
\(776\) 7504.85 0.347176
\(777\) 0 0
\(778\) −16951.9 −0.781175
\(779\) 19326.3 0.888879
\(780\) 0 0
\(781\) −7916.04 −0.362686
\(782\) −18644.3 −0.852584
\(783\) 0 0
\(784\) −1218.51 −0.0555080
\(785\) 36645.5 1.66616
\(786\) 0 0
\(787\) −14965.2 −0.677831 −0.338916 0.940817i \(-0.610060\pi\)
−0.338916 + 0.940817i \(0.610060\pi\)
\(788\) −7694.15 −0.347833
\(789\) 0 0
\(790\) −13886.0 −0.625369
\(791\) 13302.1 0.597937
\(792\) 0 0
\(793\) −255.366 −0.0114355
\(794\) 3076.78 0.137520
\(795\) 0 0
\(796\) 15658.5 0.697239
\(797\) −35050.2 −1.55777 −0.778885 0.627167i \(-0.784214\pi\)
−0.778885 + 0.627167i \(0.784214\pi\)
\(798\) 0 0
\(799\) 8141.43 0.360480
\(800\) 5377.43 0.237651
\(801\) 0 0
\(802\) −18364.1 −0.808552
\(803\) 32748.2 1.43918
\(804\) 0 0
\(805\) 12363.3 0.541303
\(806\) 3380.77 0.147745
\(807\) 0 0
\(808\) 15149.0 0.659577
\(809\) 14925.1 0.648628 0.324314 0.945950i \(-0.394867\pi\)
0.324314 + 0.945950i \(0.394867\pi\)
\(810\) 0 0
\(811\) −28928.7 −1.25256 −0.626280 0.779598i \(-0.715423\pi\)
−0.626280 + 0.779598i \(0.715423\pi\)
\(812\) 9442.81 0.408100
\(813\) 0 0
\(814\) 4461.06 0.192089
\(815\) −13035.7 −0.560269
\(816\) 0 0
\(817\) −36394.4 −1.55848
\(818\) −10833.0 −0.463040
\(819\) 0 0
\(820\) 10567.2 0.450026
\(821\) 1009.83 0.0429274 0.0214637 0.999770i \(-0.493167\pi\)
0.0214637 + 0.999770i \(0.493167\pi\)
\(822\) 0 0
\(823\) 4148.74 0.175718 0.0878590 0.996133i \(-0.471998\pi\)
0.0878590 + 0.996133i \(0.471998\pi\)
\(824\) −27369.2 −1.15710
\(825\) 0 0
\(826\) −682.211 −0.0287375
\(827\) −46387.4 −1.95048 −0.975241 0.221147i \(-0.929020\pi\)
−0.975241 + 0.221147i \(0.929020\pi\)
\(828\) 0 0
\(829\) 16193.2 0.678423 0.339211 0.940710i \(-0.389840\pi\)
0.339211 + 0.940710i \(0.389840\pi\)
\(830\) −13915.3 −0.581936
\(831\) 0 0
\(832\) −3136.15 −0.130681
\(833\) −17845.3 −0.742262
\(834\) 0 0
\(835\) −162.067 −0.00671683
\(836\) 18120.3 0.749647
\(837\) 0 0
\(838\) 11409.5 0.470327
\(839\) 26644.1 1.09637 0.548186 0.836357i \(-0.315319\pi\)
0.548186 + 0.836357i \(0.315319\pi\)
\(840\) 0 0
\(841\) 46132.5 1.89153
\(842\) −1392.22 −0.0569824
\(843\) 0 0
\(844\) 8563.84 0.349265
\(845\) −20246.2 −0.824249
\(846\) 0 0
\(847\) 697.054 0.0282775
\(848\) 2680.03 0.108529
\(849\) 0 0
\(850\) 2963.58 0.119588
\(851\) −12876.6 −0.518687
\(852\) 0 0
\(853\) −28697.2 −1.15190 −0.575952 0.817484i \(-0.695368\pi\)
−0.575952 + 0.817484i \(0.695368\pi\)
\(854\) −260.538 −0.0104396
\(855\) 0 0
\(856\) −9557.89 −0.381638
\(857\) −19383.8 −0.772623 −0.386311 0.922368i \(-0.626251\pi\)
−0.386311 + 0.922368i \(0.626251\pi\)
\(858\) 0 0
\(859\) −18991.9 −0.754362 −0.377181 0.926140i \(-0.623107\pi\)
−0.377181 + 0.926140i \(0.623107\pi\)
\(860\) −19899.6 −0.789035
\(861\) 0 0
\(862\) 2891.66 0.114258
\(863\) −34623.5 −1.36570 −0.682849 0.730560i \(-0.739259\pi\)
−0.682849 + 0.730560i \(0.739259\pi\)
\(864\) 0 0
\(865\) 23461.6 0.922216
\(866\) −20087.7 −0.788229
\(867\) 0 0
\(868\) −6307.17 −0.246635
\(869\) 31927.7 1.24635
\(870\) 0 0
\(871\) 2374.08 0.0923565
\(872\) 9478.06 0.368082
\(873\) 0 0
\(874\) 28603.3 1.10700
\(875\) −10377.1 −0.400924
\(876\) 0 0
\(877\) −33705.2 −1.29777 −0.648884 0.760887i \(-0.724764\pi\)
−0.648884 + 0.760887i \(0.724764\pi\)
\(878\) −531.947 −0.0204469
\(879\) 0 0
\(880\) 1526.31 0.0584683
\(881\) 24525.5 0.937896 0.468948 0.883226i \(-0.344633\pi\)
0.468948 + 0.883226i \(0.344633\pi\)
\(882\) 0 0
\(883\) 3141.61 0.119732 0.0598662 0.998206i \(-0.480933\pi\)
0.0598662 + 0.998206i \(0.480933\pi\)
\(884\) 3536.94 0.134570
\(885\) 0 0
\(886\) −15208.8 −0.576691
\(887\) 5590.87 0.211638 0.105819 0.994385i \(-0.466254\pi\)
0.105819 + 0.994385i \(0.466254\pi\)
\(888\) 0 0
\(889\) −9175.11 −0.346145
\(890\) −16045.0 −0.604302
\(891\) 0 0
\(892\) 6336.37 0.237845
\(893\) −12490.2 −0.468050
\(894\) 0 0
\(895\) −11970.3 −0.447065
\(896\) 6928.90 0.258346
\(897\) 0 0
\(898\) 15234.2 0.566116
\(899\) −47103.7 −1.74749
\(900\) 0 0
\(901\) 39249.6 1.45127
\(902\) 13287.3 0.490488
\(903\) 0 0
\(904\) 42856.7 1.57676
\(905\) −41763.5 −1.53399
\(906\) 0 0
\(907\) −27732.8 −1.01527 −0.507637 0.861571i \(-0.669481\pi\)
−0.507637 + 0.861571i \(0.669481\pi\)
\(908\) −3401.32 −0.124314
\(909\) 0 0
\(910\) 1282.64 0.0467242
\(911\) −7724.27 −0.280918 −0.140459 0.990086i \(-0.544858\pi\)
−0.140459 + 0.990086i \(0.544858\pi\)
\(912\) 0 0
\(913\) 31995.1 1.15978
\(914\) −24124.2 −0.873040
\(915\) 0 0
\(916\) −7281.62 −0.262655
\(917\) 5085.39 0.183135
\(918\) 0 0
\(919\) 40052.6 1.43767 0.718833 0.695183i \(-0.244677\pi\)
0.718833 + 0.695183i \(0.244677\pi\)
\(920\) 39832.1 1.42742
\(921\) 0 0
\(922\) −18065.5 −0.645288
\(923\) 2370.49 0.0845349
\(924\) 0 0
\(925\) 2046.77 0.0727540
\(926\) 29555.3 1.04887
\(927\) 0 0
\(928\) 48900.5 1.72978
\(929\) −14184.7 −0.500952 −0.250476 0.968123i \(-0.580587\pi\)
−0.250476 + 0.968123i \(0.580587\pi\)
\(930\) 0 0
\(931\) 27377.5 0.963759
\(932\) 33065.3 1.16211
\(933\) 0 0
\(934\) 15065.6 0.527796
\(935\) 22353.2 0.781848
\(936\) 0 0
\(937\) −30556.2 −1.06534 −0.532672 0.846322i \(-0.678812\pi\)
−0.532672 + 0.846322i \(0.678812\pi\)
\(938\) 2422.15 0.0843135
\(939\) 0 0
\(940\) −6829.34 −0.236967
\(941\) 9474.36 0.328220 0.164110 0.986442i \(-0.447525\pi\)
0.164110 + 0.986442i \(0.447525\pi\)
\(942\) 0 0
\(943\) −38353.0 −1.32444
\(944\) 243.103 0.00838170
\(945\) 0 0
\(946\) −25022.1 −0.859976
\(947\) −55248.5 −1.89581 −0.947906 0.318549i \(-0.896804\pi\)
−0.947906 + 0.318549i \(0.896804\pi\)
\(948\) 0 0
\(949\) −9806.58 −0.335443
\(950\) −4546.59 −0.155274
\(951\) 0 0
\(952\) 9190.58 0.312887
\(953\) −6103.29 −0.207455 −0.103728 0.994606i \(-0.533077\pi\)
−0.103728 + 0.994606i \(0.533077\pi\)
\(954\) 0 0
\(955\) 30150.2 1.02161
\(956\) 10041.4 0.339710
\(957\) 0 0
\(958\) 11620.4 0.391898
\(959\) 8678.99 0.292241
\(960\) 0 0
\(961\) 1671.17 0.0560963
\(962\) −1335.88 −0.0447720
\(963\) 0 0
\(964\) 19143.7 0.639602
\(965\) 33960.1 1.13287
\(966\) 0 0
\(967\) −22070.6 −0.733965 −0.366982 0.930228i \(-0.619609\pi\)
−0.366982 + 0.930228i \(0.619609\pi\)
\(968\) 2245.77 0.0745678
\(969\) 0 0
\(970\) −5576.69 −0.184595
\(971\) 46982.7 1.55278 0.776389 0.630254i \(-0.217049\pi\)
0.776389 + 0.630254i \(0.217049\pi\)
\(972\) 0 0
\(973\) 18087.4 0.595945
\(974\) 25240.3 0.830341
\(975\) 0 0
\(976\) 92.8414 0.00304486
\(977\) 38521.7 1.26143 0.630715 0.776014i \(-0.282762\pi\)
0.630715 + 0.776014i \(0.282762\pi\)
\(978\) 0 0
\(979\) 36891.8 1.20436
\(980\) 14969.3 0.487937
\(981\) 0 0
\(982\) 18398.2 0.597872
\(983\) 17793.1 0.577327 0.288664 0.957431i \(-0.406789\pi\)
0.288664 + 0.957431i \(0.406789\pi\)
\(984\) 0 0
\(985\) 14561.4 0.471030
\(986\) 26949.8 0.870443
\(987\) 0 0
\(988\) −5426.21 −0.174727
\(989\) 72224.5 2.32215
\(990\) 0 0
\(991\) −52191.4 −1.67297 −0.836485 0.547990i \(-0.815393\pi\)
−0.836485 + 0.547990i \(0.815393\pi\)
\(992\) −32662.3 −1.04539
\(993\) 0 0
\(994\) 2418.50 0.0771731
\(995\) −29634.2 −0.944189
\(996\) 0 0
\(997\) 6732.09 0.213849 0.106924 0.994267i \(-0.465900\pi\)
0.106924 + 0.994267i \(0.465900\pi\)
\(998\) 3297.81 0.104600
\(999\) 0 0
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 531.4.a.d.1.2 7
3.2 odd 2 177.4.a.a.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.6 7 3.2 odd 2
531.4.a.d.1.2 7 1.1 even 1 trivial