Properties

Label 735.4.a.p.1.1
Level $735$
Weight $4$
Character 735.1
Self dual yes
Analytic conductor $43.366$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.3664038542\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{65}) \)
Defining polynomial: \( x^{2} - x - 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.53113\) of defining polynomial
Character \(\chi\) \(=\) 735.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-3.53113 q^{2} -3.00000 q^{3} +4.46887 q^{4} -5.00000 q^{5} +10.5934 q^{6} +12.4689 q^{8} +9.00000 q^{9} +17.6556 q^{10} -2.93774 q^{11} -13.4066 q^{12} +19.0623 q^{13} +15.0000 q^{15} -79.7802 q^{16} -122.498 q^{17} -31.7802 q^{18} -107.436 q^{19} -22.3444 q^{20} +10.3735 q^{22} +210.623 q^{23} -37.4066 q^{24} +25.0000 q^{25} -67.3113 q^{26} -27.0000 q^{27} +95.4942 q^{29} -52.9669 q^{30} +94.3074 q^{31} +181.963 q^{32} +8.81323 q^{33} +432.556 q^{34} +40.2198 q^{36} +97.1206 q^{37} +379.370 q^{38} -57.1868 q^{39} -62.3444 q^{40} +491.113 q^{41} -43.0039 q^{43} -13.1284 q^{44} -45.0000 q^{45} -743.735 q^{46} -473.494 q^{47} +239.340 q^{48} -88.2782 q^{50} +367.494 q^{51} +85.1868 q^{52} -183.677 q^{53} +95.3405 q^{54} +14.6887 q^{55} +322.307 q^{57} -337.202 q^{58} +760.615 q^{59} +67.0331 q^{60} +198.747 q^{61} -333.012 q^{62} -4.29373 q^{64} -95.3113 q^{65} -31.1206 q^{66} -309.992 q^{67} -547.428 q^{68} -631.868 q^{69} +665.693 q^{71} +112.220 q^{72} -621.288 q^{73} -342.945 q^{74} -75.0000 q^{75} -480.117 q^{76} +201.934 q^{78} -24.7626 q^{79} +398.901 q^{80} +81.0000 q^{81} -1734.18 q^{82} +406.724 q^{83} +612.490 q^{85} +151.852 q^{86} -286.483 q^{87} -36.6303 q^{88} -261.751 q^{89} +158.901 q^{90} +941.245 q^{92} -282.922 q^{93} +1671.97 q^{94} +537.179 q^{95} -545.889 q^{96} +1004.77 q^{97} -26.4397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} - 3 q^{6} + 33 q^{8} + 18 q^{9} - 5 q^{10} - 22 q^{11} - 51 q^{12} + 22 q^{13} + 30 q^{15} - 87 q^{16} - 116 q^{17} + 9 q^{18} - 102 q^{19} - 85 q^{20} - 76 q^{22} + 260 q^{23} - 99 q^{24} + 50 q^{25} - 54 q^{26} - 54 q^{27} - 196 q^{29} + 15 q^{30} - 150 q^{31} - 15 q^{32} + 66 q^{33} + 462 q^{34} + 153 q^{36} - 96 q^{37} + 404 q^{38} - 66 q^{39} - 165 q^{40} + 176 q^{41} - 344 q^{43} - 252 q^{44} - 90 q^{45} - 520 q^{46} - 560 q^{47} + 261 q^{48} + 25 q^{50} + 348 q^{51} + 122 q^{52} + 326 q^{53} - 27 q^{54} + 110 q^{55} + 306 q^{57} - 1658 q^{58} + 844 q^{59} + 255 q^{60} + 204 q^{61} - 1440 q^{62} - 839 q^{64} - 110 q^{65} + 228 q^{66} - 104 q^{67} - 466 q^{68} - 780 q^{69} + 1670 q^{71} + 297 q^{72} + 386 q^{73} - 1218 q^{74} - 150 q^{75} - 412 q^{76} + 162 q^{78} - 888 q^{79} + 435 q^{80} + 162 q^{81} - 3162 q^{82} - 928 q^{83} + 580 q^{85} - 1212 q^{86} + 588 q^{87} - 428 q^{88} - 588 q^{89} - 45 q^{90} + 1560 q^{92} + 450 q^{93} + 1280 q^{94} + 510 q^{95} + 45 q^{96} - 522 q^{97} - 198 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.53113 −1.24844 −0.624221 0.781248i \(-0.714584\pi\)
−0.624221 + 0.781248i \(0.714584\pi\)
\(3\) −3.00000 −0.577350
\(4\) 4.46887 0.558609
\(5\) −5.00000 −0.447214
\(6\) 10.5934 0.720789
\(7\) 0 0
\(8\) 12.4689 0.551051
\(9\) 9.00000 0.333333
\(10\) 17.6556 0.558320
\(11\) −2.93774 −0.0805239 −0.0402619 0.999189i \(-0.512819\pi\)
−0.0402619 + 0.999189i \(0.512819\pi\)
\(12\) −13.4066 −0.322513
\(13\) 19.0623 0.406686 0.203343 0.979108i \(-0.434819\pi\)
0.203343 + 0.979108i \(0.434819\pi\)
\(14\) 0 0
\(15\) 15.0000 0.258199
\(16\) −79.7802 −1.24656
\(17\) −122.498 −1.74766 −0.873828 0.486236i \(-0.838370\pi\)
−0.873828 + 0.486236i \(0.838370\pi\)
\(18\) −31.7802 −0.416148
\(19\) −107.436 −1.29723 −0.648617 0.761115i \(-0.724652\pi\)
−0.648617 + 0.761115i \(0.724652\pi\)
\(20\) −22.3444 −0.249817
\(21\) 0 0
\(22\) 10.3735 0.100529
\(23\) 210.623 1.90947 0.954736 0.297455i \(-0.0961379\pi\)
0.954736 + 0.297455i \(0.0961379\pi\)
\(24\) −37.4066 −0.318150
\(25\) 25.0000 0.200000
\(26\) −67.3113 −0.507724
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 95.4942 0.611477 0.305738 0.952116i \(-0.401097\pi\)
0.305738 + 0.952116i \(0.401097\pi\)
\(30\) −52.9669 −0.322346
\(31\) 94.3074 0.546391 0.273195 0.961959i \(-0.411919\pi\)
0.273195 + 0.961959i \(0.411919\pi\)
\(32\) 181.963 1.00521
\(33\) 8.81323 0.0464905
\(34\) 432.556 2.18185
\(35\) 0 0
\(36\) 40.2198 0.186203
\(37\) 97.1206 0.431528 0.215764 0.976446i \(-0.430776\pi\)
0.215764 + 0.976446i \(0.430776\pi\)
\(38\) 379.370 1.61952
\(39\) −57.1868 −0.234800
\(40\) −62.3444 −0.246438
\(41\) 491.113 1.87071 0.935353 0.353716i \(-0.115082\pi\)
0.935353 + 0.353716i \(0.115082\pi\)
\(42\) 0 0
\(43\) −43.0039 −0.152512 −0.0762562 0.997088i \(-0.524297\pi\)
−0.0762562 + 0.997088i \(0.524297\pi\)
\(44\) −13.1284 −0.0449814
\(45\) −45.0000 −0.149071
\(46\) −743.735 −2.38387
\(47\) −473.494 −1.46949 −0.734747 0.678341i \(-0.762699\pi\)
−0.734747 + 0.678341i \(0.762699\pi\)
\(48\) 239.340 0.719705
\(49\) 0 0
\(50\) −88.2782 −0.249689
\(51\) 367.494 1.00901
\(52\) 85.1868 0.227178
\(53\) −183.677 −0.476038 −0.238019 0.971261i \(-0.576498\pi\)
−0.238019 + 0.971261i \(0.576498\pi\)
\(54\) 95.3405 0.240263
\(55\) 14.6887 0.0360114
\(56\) 0 0
\(57\) 322.307 0.748959
\(58\) −337.202 −0.763394
\(59\) 760.615 1.67837 0.839183 0.543849i \(-0.183034\pi\)
0.839183 + 0.543849i \(0.183034\pi\)
\(60\) 67.0331 0.144232
\(61\) 198.747 0.417163 0.208582 0.978005i \(-0.433115\pi\)
0.208582 + 0.978005i \(0.433115\pi\)
\(62\) −333.012 −0.682137
\(63\) 0 0
\(64\) −4.29373 −0.00838618
\(65\) −95.3113 −0.181876
\(66\) −31.1206 −0.0580407
\(67\) −309.992 −0.565247 −0.282624 0.959231i \(-0.591205\pi\)
−0.282624 + 0.959231i \(0.591205\pi\)
\(68\) −547.428 −0.976256
\(69\) −631.868 −1.10243
\(70\) 0 0
\(71\) 665.693 1.11272 0.556360 0.830941i \(-0.312197\pi\)
0.556360 + 0.830941i \(0.312197\pi\)
\(72\) 112.220 0.183684
\(73\) −621.288 −0.996113 −0.498057 0.867145i \(-0.665953\pi\)
−0.498057 + 0.867145i \(0.665953\pi\)
\(74\) −342.945 −0.538738
\(75\) −75.0000 −0.115470
\(76\) −480.117 −0.724647
\(77\) 0 0
\(78\) 201.934 0.293135
\(79\) −24.7626 −0.0352659 −0.0176330 0.999845i \(-0.505613\pi\)
−0.0176330 + 0.999845i \(0.505613\pi\)
\(80\) 398.901 0.557481
\(81\) 81.0000 0.111111
\(82\) −1734.18 −2.33547
\(83\) 406.724 0.537876 0.268938 0.963157i \(-0.413327\pi\)
0.268938 + 0.963157i \(0.413327\pi\)
\(84\) 0 0
\(85\) 612.490 0.781575
\(86\) 151.852 0.190403
\(87\) −286.483 −0.353036
\(88\) −36.6303 −0.0443728
\(89\) −261.751 −0.311748 −0.155874 0.987777i \(-0.549819\pi\)
−0.155874 + 0.987777i \(0.549819\pi\)
\(90\) 158.901 0.186107
\(91\) 0 0
\(92\) 941.245 1.06665
\(93\) −282.922 −0.315459
\(94\) 1671.97 1.83458
\(95\) 537.179 0.580141
\(96\) −545.889 −0.580360
\(97\) 1004.77 1.05175 0.525873 0.850563i \(-0.323739\pi\)
0.525873 + 0.850563i \(0.323739\pi\)
\(98\) 0 0
\(99\) −26.4397 −0.0268413
\(100\) 111.722 0.111722
\(101\) 128.872 0.126962 0.0634812 0.997983i \(-0.479780\pi\)
0.0634812 + 0.997983i \(0.479780\pi\)
\(102\) −1297.67 −1.25969
\(103\) −806.008 −0.771051 −0.385526 0.922697i \(-0.625980\pi\)
−0.385526 + 0.922697i \(0.625980\pi\)
\(104\) 237.685 0.224105
\(105\) 0 0
\(106\) 648.587 0.594305
\(107\) −769.712 −0.695429 −0.347714 0.937600i \(-0.613042\pi\)
−0.347714 + 0.937600i \(0.613042\pi\)
\(108\) −120.660 −0.107504
\(109\) −780.856 −0.686169 −0.343085 0.939304i \(-0.611472\pi\)
−0.343085 + 0.939304i \(0.611472\pi\)
\(110\) −51.8677 −0.0449581
\(111\) −291.362 −0.249143
\(112\) 0 0
\(113\) −1115.65 −0.928771 −0.464386 0.885633i \(-0.653725\pi\)
−0.464386 + 0.885633i \(0.653725\pi\)
\(114\) −1138.11 −0.935032
\(115\) −1053.11 −0.853942
\(116\) 426.751 0.341576
\(117\) 171.560 0.135562
\(118\) −2685.83 −2.09534
\(119\) 0 0
\(120\) 187.033 0.142281
\(121\) −1322.37 −0.993516
\(122\) −701.802 −0.520804
\(123\) −1473.34 −1.08005
\(124\) 421.448 0.305219
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1875.98 −1.31076 −0.655381 0.755299i \(-0.727492\pi\)
−0.655381 + 0.755299i \(0.727492\pi\)
\(128\) −1440.54 −0.994744
\(129\) 129.012 0.0880530
\(130\) 336.556 0.227061
\(131\) −364.203 −0.242905 −0.121452 0.992597i \(-0.538755\pi\)
−0.121452 + 0.992597i \(0.538755\pi\)
\(132\) 39.3852 0.0259700
\(133\) 0 0
\(134\) 1094.62 0.705679
\(135\) 135.000 0.0860663
\(136\) −1527.41 −0.963048
\(137\) 1603.13 0.999743 0.499872 0.866099i \(-0.333380\pi\)
0.499872 + 0.866099i \(0.333380\pi\)
\(138\) 2231.21 1.37633
\(139\) −2431.12 −1.48349 −0.741746 0.670681i \(-0.766002\pi\)
−0.741746 + 0.670681i \(0.766002\pi\)
\(140\) 0 0
\(141\) 1420.48 0.848413
\(142\) −2350.65 −1.38917
\(143\) −56.0000 −0.0327479
\(144\) −718.021 −0.415522
\(145\) −477.471 −0.273461
\(146\) 2193.85 1.24359
\(147\) 0 0
\(148\) 434.020 0.241055
\(149\) 2341.57 1.28744 0.643722 0.765260i \(-0.277389\pi\)
0.643722 + 0.765260i \(0.277389\pi\)
\(150\) 264.835 0.144158
\(151\) −2104.07 −1.13395 −0.566976 0.823734i \(-0.691887\pi\)
−0.566976 + 0.823734i \(0.691887\pi\)
\(152\) −1339.60 −0.714843
\(153\) −1102.48 −0.582552
\(154\) 0 0
\(155\) −471.537 −0.244353
\(156\) −255.560 −0.131162
\(157\) 593.467 0.301680 0.150840 0.988558i \(-0.451802\pi\)
0.150840 + 0.988558i \(0.451802\pi\)
\(158\) 87.4399 0.0440275
\(159\) 551.031 0.274840
\(160\) −909.815 −0.449545
\(161\) 0 0
\(162\) −286.021 −0.138716
\(163\) 2178.71 1.04693 0.523465 0.852047i \(-0.324639\pi\)
0.523465 + 0.852047i \(0.324639\pi\)
\(164\) 2194.72 1.04499
\(165\) −44.0661 −0.0207912
\(166\) −1436.19 −0.671508
\(167\) −799.502 −0.370463 −0.185231 0.982695i \(-0.559303\pi\)
−0.185231 + 0.982695i \(0.559303\pi\)
\(168\) 0 0
\(169\) −1833.63 −0.834606
\(170\) −2162.78 −0.975752
\(171\) −966.922 −0.432412
\(172\) −192.179 −0.0851947
\(173\) 1444.36 0.634754 0.317377 0.948299i \(-0.397198\pi\)
0.317377 + 0.948299i \(0.397198\pi\)
\(174\) 1011.61 0.440745
\(175\) 0 0
\(176\) 234.374 0.100378
\(177\) −2281.84 −0.969005
\(178\) 924.276 0.389199
\(179\) 3343.49 1.39611 0.698056 0.716043i \(-0.254048\pi\)
0.698056 + 0.716043i \(0.254048\pi\)
\(180\) −201.099 −0.0832725
\(181\) −2251.81 −0.924729 −0.462365 0.886690i \(-0.652999\pi\)
−0.462365 + 0.886690i \(0.652999\pi\)
\(182\) 0 0
\(183\) −596.241 −0.240849
\(184\) 2626.23 1.05222
\(185\) −485.603 −0.192985
\(186\) 999.035 0.393832
\(187\) 359.868 0.140728
\(188\) −2115.98 −0.820873
\(189\) 0 0
\(190\) −1896.85 −0.724273
\(191\) −1001.93 −0.379565 −0.189782 0.981826i \(-0.560778\pi\)
−0.189782 + 0.981826i \(0.560778\pi\)
\(192\) 12.8812 0.00484177
\(193\) −4054.97 −1.51235 −0.756173 0.654372i \(-0.772933\pi\)
−0.756173 + 0.654372i \(0.772933\pi\)
\(194\) −3547.99 −1.31304
\(195\) 285.934 0.105006
\(196\) 0 0
\(197\) −5140.23 −1.85902 −0.929508 0.368802i \(-0.879768\pi\)
−0.929508 + 0.368802i \(0.879768\pi\)
\(198\) 93.3619 0.0335098
\(199\) −585.631 −0.208614 −0.104307 0.994545i \(-0.533263\pi\)
−0.104307 + 0.994545i \(0.533263\pi\)
\(200\) 311.722 0.110210
\(201\) 929.977 0.326346
\(202\) −455.062 −0.158505
\(203\) 0 0
\(204\) 1642.28 0.563642
\(205\) −2455.56 −0.836605
\(206\) 2846.12 0.962614
\(207\) 1895.60 0.636490
\(208\) −1520.79 −0.506961
\(209\) 315.619 0.104458
\(210\) 0 0
\(211\) −1055.16 −0.344266 −0.172133 0.985074i \(-0.555066\pi\)
−0.172133 + 0.985074i \(0.555066\pi\)
\(212\) −820.829 −0.265919
\(213\) −1997.08 −0.642430
\(214\) 2717.95 0.868203
\(215\) 215.019 0.0682056
\(216\) −336.660 −0.106050
\(217\) 0 0
\(218\) 2757.30 0.856643
\(219\) 1863.86 0.575106
\(220\) 65.6420 0.0201163
\(221\) −2335.09 −0.710747
\(222\) 1028.84 0.311040
\(223\) −4675.85 −1.40412 −0.702059 0.712119i \(-0.747736\pi\)
−0.702059 + 0.712119i \(0.747736\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 3939.49 1.15952
\(227\) −5443.11 −1.59151 −0.795754 0.605621i \(-0.792925\pi\)
−0.795754 + 0.605621i \(0.792925\pi\)
\(228\) 1440.35 0.418375
\(229\) 536.303 0.154759 0.0773797 0.997002i \(-0.475345\pi\)
0.0773797 + 0.997002i \(0.475345\pi\)
\(230\) 3718.68 1.06610
\(231\) 0 0
\(232\) 1190.70 0.336955
\(233\) −183.490 −0.0515916 −0.0257958 0.999667i \(-0.508212\pi\)
−0.0257958 + 0.999667i \(0.508212\pi\)
\(234\) −605.802 −0.169241
\(235\) 2367.47 0.657178
\(236\) 3399.09 0.937550
\(237\) 74.2878 0.0203608
\(238\) 0 0
\(239\) 643.218 0.174085 0.0870425 0.996205i \(-0.472258\pi\)
0.0870425 + 0.996205i \(0.472258\pi\)
\(240\) −1196.70 −0.321862
\(241\) 5755.61 1.53839 0.769194 0.639015i \(-0.220658\pi\)
0.769194 + 0.639015i \(0.220658\pi\)
\(242\) 4669.46 1.24035
\(243\) −243.000 −0.0641500
\(244\) 888.175 0.233031
\(245\) 0 0
\(246\) 5202.55 1.34838
\(247\) −2047.97 −0.527567
\(248\) 1175.91 0.301089
\(249\) −1220.17 −0.310543
\(250\) 441.391 0.111664
\(251\) 5132.27 1.29062 0.645311 0.763920i \(-0.276728\pi\)
0.645311 + 0.763920i \(0.276728\pi\)
\(252\) 0 0
\(253\) −618.755 −0.153758
\(254\) 6624.34 1.63641
\(255\) −1837.47 −0.451243
\(256\) 5121.09 1.25027
\(257\) −5041.74 −1.22372 −0.611859 0.790967i \(-0.709578\pi\)
−0.611859 + 0.790967i \(0.709578\pi\)
\(258\) −455.557 −0.109929
\(259\) 0 0
\(260\) −425.934 −0.101597
\(261\) 859.448 0.203826
\(262\) 1286.05 0.303253
\(263\) 7577.00 1.77649 0.888246 0.459367i \(-0.151924\pi\)
0.888246 + 0.459367i \(0.151924\pi\)
\(264\) 109.891 0.0256186
\(265\) 918.385 0.212890
\(266\) 0 0
\(267\) 785.253 0.179988
\(268\) −1385.32 −0.315752
\(269\) −1023.10 −0.231893 −0.115947 0.993255i \(-0.536990\pi\)
−0.115947 + 0.993255i \(0.536990\pi\)
\(270\) −476.702 −0.107449
\(271\) 2251.98 0.504790 0.252395 0.967624i \(-0.418782\pi\)
0.252395 + 0.967624i \(0.418782\pi\)
\(272\) 9772.91 2.17857
\(273\) 0 0
\(274\) −5660.87 −1.24812
\(275\) −73.4436 −0.0161048
\(276\) −2823.74 −0.615829
\(277\) −8630.72 −1.87209 −0.936047 0.351875i \(-0.885544\pi\)
−0.936047 + 0.351875i \(0.885544\pi\)
\(278\) 8584.61 1.85205
\(279\) 848.767 0.182130
\(280\) 0 0
\(281\) −7521.62 −1.59680 −0.798402 0.602124i \(-0.794321\pi\)
−0.798402 + 0.602124i \(0.794321\pi\)
\(282\) −5015.91 −1.05919
\(283\) −14.8169 −0.00311226 −0.00155613 0.999999i \(-0.500495\pi\)
−0.00155613 + 0.999999i \(0.500495\pi\)
\(284\) 2974.89 0.621576
\(285\) −1611.54 −0.334945
\(286\) 197.743 0.0408839
\(287\) 0 0
\(288\) 1637.67 0.335071
\(289\) 10092.8 2.05430
\(290\) 1686.01 0.341400
\(291\) −3014.32 −0.607226
\(292\) −2776.46 −0.556438
\(293\) −6913.39 −1.37844 −0.689222 0.724550i \(-0.742048\pi\)
−0.689222 + 0.724550i \(0.742048\pi\)
\(294\) 0 0
\(295\) −3803.07 −0.750588
\(296\) 1210.98 0.237794
\(297\) 79.3190 0.0154968
\(298\) −8268.39 −1.60730
\(299\) 4014.94 0.776555
\(300\) −335.165 −0.0645026
\(301\) 0 0
\(302\) 7429.74 1.41567
\(303\) −386.615 −0.0733018
\(304\) 8571.25 1.61709
\(305\) −993.735 −0.186561
\(306\) 3893.01 0.727283
\(307\) 7644.12 1.42108 0.710542 0.703655i \(-0.248450\pi\)
0.710542 + 0.703655i \(0.248450\pi\)
\(308\) 0 0
\(309\) 2418.02 0.445167
\(310\) 1665.06 0.305061
\(311\) −7593.99 −1.38462 −0.692308 0.721602i \(-0.743406\pi\)
−0.692308 + 0.721602i \(0.743406\pi\)
\(312\) −713.055 −0.129387
\(313\) 9127.84 1.64836 0.824179 0.566329i \(-0.191637\pi\)
0.824179 + 0.566329i \(0.191637\pi\)
\(314\) −2095.61 −0.376631
\(315\) 0 0
\(316\) −110.661 −0.0196999
\(317\) −4929.81 −0.873456 −0.436728 0.899593i \(-0.643863\pi\)
−0.436728 + 0.899593i \(0.643863\pi\)
\(318\) −1945.76 −0.343122
\(319\) −280.537 −0.0492385
\(320\) 21.4686 0.00375042
\(321\) 2309.14 0.401506
\(322\) 0 0
\(323\) 13160.7 2.26712
\(324\) 361.979 0.0620677
\(325\) 476.556 0.0813372
\(326\) −7693.30 −1.30703
\(327\) 2342.57 0.396160
\(328\) 6123.62 1.03086
\(329\) 0 0
\(330\) 155.603 0.0259566
\(331\) 1221.67 0.202867 0.101433 0.994842i \(-0.467657\pi\)
0.101433 + 0.994842i \(0.467657\pi\)
\(332\) 1817.60 0.300463
\(333\) 874.086 0.143843
\(334\) 2823.14 0.462502
\(335\) 1549.96 0.252786
\(336\) 0 0
\(337\) −8744.83 −1.41354 −0.706768 0.707446i \(-0.749847\pi\)
−0.706768 + 0.707446i \(0.749847\pi\)
\(338\) 6474.79 1.04196
\(339\) 3346.94 0.536226
\(340\) 2737.14 0.436595
\(341\) −277.051 −0.0439975
\(342\) 3414.33 0.539841
\(343\) 0 0
\(344\) −536.210 −0.0840421
\(345\) 3159.34 0.493023
\(346\) −5100.21 −0.792454
\(347\) 4589.56 0.710031 0.355015 0.934860i \(-0.384476\pi\)
0.355015 + 0.934860i \(0.384476\pi\)
\(348\) −1280.25 −0.197209
\(349\) 3989.89 0.611960 0.305980 0.952038i \(-0.401016\pi\)
0.305980 + 0.952038i \(0.401016\pi\)
\(350\) 0 0
\(351\) −514.681 −0.0782668
\(352\) −534.561 −0.0809437
\(353\) −2416.35 −0.364333 −0.182166 0.983268i \(-0.558311\pi\)
−0.182166 + 0.983268i \(0.558311\pi\)
\(354\) 8057.49 1.20975
\(355\) −3328.46 −0.497624
\(356\) −1169.73 −0.174145
\(357\) 0 0
\(358\) −11806.3 −1.74297
\(359\) −2756.24 −0.405206 −0.202603 0.979261i \(-0.564940\pi\)
−0.202603 + 0.979261i \(0.564940\pi\)
\(360\) −561.099 −0.0821459
\(361\) 4683.45 0.682818
\(362\) 7951.44 1.15447
\(363\) 3967.11 0.573607
\(364\) 0 0
\(365\) 3106.44 0.445475
\(366\) 2105.40 0.300687
\(367\) −11112.8 −1.58061 −0.790307 0.612711i \(-0.790079\pi\)
−0.790307 + 0.612711i \(0.790079\pi\)
\(368\) −16803.5 −2.38028
\(369\) 4420.02 0.623569
\(370\) 1714.73 0.240931
\(371\) 0 0
\(372\) −1264.34 −0.176218
\(373\) 6091.09 0.845535 0.422768 0.906238i \(-0.361059\pi\)
0.422768 + 0.906238i \(0.361059\pi\)
\(374\) −1270.74 −0.175691
\(375\) 375.000 0.0516398
\(376\) −5903.94 −0.809767
\(377\) 1820.33 0.248679
\(378\) 0 0
\(379\) 3984.29 0.539998 0.269999 0.962861i \(-0.412977\pi\)
0.269999 + 0.962861i \(0.412977\pi\)
\(380\) 2400.58 0.324072
\(381\) 5627.95 0.756768
\(382\) 3537.93 0.473865
\(383\) −318.475 −0.0424890 −0.0212445 0.999774i \(-0.506763\pi\)
−0.0212445 + 0.999774i \(0.506763\pi\)
\(384\) 4321.63 0.574316
\(385\) 0 0
\(386\) 14318.6 1.88808
\(387\) −387.035 −0.0508374
\(388\) 4490.21 0.587515
\(389\) 3885.46 0.506429 0.253214 0.967410i \(-0.418512\pi\)
0.253214 + 0.967410i \(0.418512\pi\)
\(390\) −1009.67 −0.131094
\(391\) −25800.9 −3.33710
\(392\) 0 0
\(393\) 1092.61 0.140241
\(394\) 18150.8 2.32088
\(395\) 123.813 0.0157714
\(396\) −118.156 −0.0149938
\(397\) −4806.04 −0.607578 −0.303789 0.952739i \(-0.598252\pi\)
−0.303789 + 0.952739i \(0.598252\pi\)
\(398\) 2067.94 0.260443
\(399\) 0 0
\(400\) −1994.50 −0.249313
\(401\) 3618.59 0.450633 0.225316 0.974286i \(-0.427658\pi\)
0.225316 + 0.974286i \(0.427658\pi\)
\(402\) −3283.87 −0.407424
\(403\) 1797.71 0.222209
\(404\) 575.911 0.0709223
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) −285.315 −0.0347483
\(408\) 4582.24 0.556016
\(409\) 2109.05 0.254978 0.127489 0.991840i \(-0.459308\pi\)
0.127489 + 0.991840i \(0.459308\pi\)
\(410\) 8670.91 1.04445
\(411\) −4809.40 −0.577202
\(412\) −3601.94 −0.430716
\(413\) 0 0
\(414\) −6693.62 −0.794622
\(415\) −2033.62 −0.240546
\(416\) 3468.63 0.408806
\(417\) 7293.37 0.856494
\(418\) −1114.49 −0.130410
\(419\) 6905.91 0.805193 0.402597 0.915377i \(-0.368108\pi\)
0.402597 + 0.915377i \(0.368108\pi\)
\(420\) 0 0
\(421\) −9647.54 −1.11685 −0.558423 0.829556i \(-0.688593\pi\)
−0.558423 + 0.829556i \(0.688593\pi\)
\(422\) 3725.91 0.429797
\(423\) −4261.45 −0.489831
\(424\) −2290.25 −0.262321
\(425\) −3062.45 −0.349531
\(426\) 7051.94 0.802037
\(427\) 0 0
\(428\) −3439.74 −0.388473
\(429\) 168.000 0.0189070
\(430\) −759.261 −0.0851508
\(431\) −13002.7 −1.45318 −0.726589 0.687073i \(-0.758895\pi\)
−0.726589 + 0.687073i \(0.758895\pi\)
\(432\) 2154.06 0.239902
\(433\) −7356.07 −0.816420 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(434\) 0 0
\(435\) 1432.41 0.157883
\(436\) −3489.55 −0.383300
\(437\) −22628.4 −2.47703
\(438\) −6581.54 −0.717987
\(439\) −6909.21 −0.751159 −0.375579 0.926790i \(-0.622556\pi\)
−0.375579 + 0.926790i \(0.622556\pi\)
\(440\) 183.152 0.0198441
\(441\) 0 0
\(442\) 8245.50 0.887327
\(443\) −14812.6 −1.58864 −0.794318 0.607502i \(-0.792172\pi\)
−0.794318 + 0.607502i \(0.792172\pi\)
\(444\) −1302.06 −0.139173
\(445\) 1308.75 0.139418
\(446\) 16511.0 1.75296
\(447\) −7024.72 −0.743306
\(448\) 0 0
\(449\) −10654.5 −1.11986 −0.559932 0.828538i \(-0.689173\pi\)
−0.559932 + 0.828538i \(0.689173\pi\)
\(450\) −794.504 −0.0832295
\(451\) −1442.76 −0.150636
\(452\) −4985.68 −0.518820
\(453\) 6312.21 0.654688
\(454\) 19220.3 1.98691
\(455\) 0 0
\(456\) 4018.81 0.412715
\(457\) −5855.16 −0.599328 −0.299664 0.954045i \(-0.596875\pi\)
−0.299664 + 0.954045i \(0.596875\pi\)
\(458\) −1893.76 −0.193208
\(459\) 3307.45 0.336336
\(460\) −4706.23 −0.477019
\(461\) −3204.74 −0.323774 −0.161887 0.986809i \(-0.551758\pi\)
−0.161887 + 0.986809i \(0.551758\pi\)
\(462\) 0 0
\(463\) 371.658 0.0373054 0.0186527 0.999826i \(-0.494062\pi\)
0.0186527 + 0.999826i \(0.494062\pi\)
\(464\) −7618.54 −0.762245
\(465\) 1414.61 0.141077
\(466\) 647.927 0.0644091
\(467\) 19752.3 1.95723 0.978614 0.205703i \(-0.0659482\pi\)
0.978614 + 0.205703i \(0.0659482\pi\)
\(468\) 766.681 0.0757262
\(469\) 0 0
\(470\) −8359.84 −0.820449
\(471\) −1780.40 −0.174175
\(472\) 9484.01 0.924866
\(473\) 126.334 0.0122809
\(474\) −262.320 −0.0254193
\(475\) −2685.90 −0.259447
\(476\) 0 0
\(477\) −1653.09 −0.158679
\(478\) −2271.28 −0.217335
\(479\) 20762.0 1.98046 0.990232 0.139433i \(-0.0445279\pi\)
0.990232 + 0.139433i \(0.0445279\pi\)
\(480\) 2729.45 0.259545
\(481\) 1851.34 0.175496
\(482\) −20323.8 −1.92059
\(483\) 0 0
\(484\) −5909.50 −0.554987
\(485\) −5023.87 −0.470355
\(486\) 858.064 0.0800876
\(487\) 17647.6 1.64207 0.821035 0.570878i \(-0.193397\pi\)
0.821035 + 0.570878i \(0.193397\pi\)
\(488\) 2478.15 0.229878
\(489\) −6536.12 −0.604445
\(490\) 0 0
\(491\) −5637.46 −0.518157 −0.259078 0.965856i \(-0.583419\pi\)
−0.259078 + 0.965856i \(0.583419\pi\)
\(492\) −6584.16 −0.603327
\(493\) −11697.9 −1.06865
\(494\) 7231.64 0.658638
\(495\) 132.198 0.0120038
\(496\) −7523.86 −0.681112
\(497\) 0 0
\(498\) 4308.58 0.387695
\(499\) −17474.1 −1.56764 −0.783818 0.620991i \(-0.786730\pi\)
−0.783818 + 0.620991i \(0.786730\pi\)
\(500\) −558.609 −0.0499635
\(501\) 2398.51 0.213887
\(502\) −18122.7 −1.61127
\(503\) −7444.81 −0.659936 −0.329968 0.943992i \(-0.607038\pi\)
−0.329968 + 0.943992i \(0.607038\pi\)
\(504\) 0 0
\(505\) −644.358 −0.0567793
\(506\) 2184.90 0.191958
\(507\) 5500.89 0.481860
\(508\) −8383.53 −0.732203
\(509\) 3384.48 0.294724 0.147362 0.989083i \(-0.452922\pi\)
0.147362 + 0.989083i \(0.452922\pi\)
\(510\) 6488.35 0.563351
\(511\) 0 0
\(512\) −6558.89 −0.566142
\(513\) 2900.77 0.249653
\(514\) 17803.0 1.52774
\(515\) 4030.04 0.344825
\(516\) 576.536 0.0491872
\(517\) 1391.00 0.118329
\(518\) 0 0
\(519\) −4333.07 −0.366476
\(520\) −1188.42 −0.100223
\(521\) −2973.12 −0.250009 −0.125005 0.992156i \(-0.539895\pi\)
−0.125005 + 0.992156i \(0.539895\pi\)
\(522\) −3034.82 −0.254465
\(523\) −2689.02 −0.224823 −0.112412 0.993662i \(-0.535858\pi\)
−0.112412 + 0.993662i \(0.535858\pi\)
\(524\) −1627.57 −0.135689
\(525\) 0 0
\(526\) −26755.3 −2.21785
\(527\) −11552.5 −0.954903
\(528\) −703.121 −0.0579534
\(529\) 32194.9 2.64608
\(530\) −3242.94 −0.265781
\(531\) 6845.53 0.559455
\(532\) 0 0
\(533\) 9361.72 0.760790
\(534\) −2772.83 −0.224704
\(535\) 3848.56 0.311005
\(536\) −3865.25 −0.311480
\(537\) −10030.5 −0.806046
\(538\) 3612.69 0.289506
\(539\) 0 0
\(540\) 603.298 0.0480774
\(541\) −14429.5 −1.14671 −0.573356 0.819306i \(-0.694359\pi\)
−0.573356 + 0.819306i \(0.694359\pi\)
\(542\) −7952.03 −0.630201
\(543\) 6755.44 0.533893
\(544\) −22290.1 −1.75677
\(545\) 3904.28 0.306864
\(546\) 0 0
\(547\) 13811.2 1.07957 0.539784 0.841804i \(-0.318506\pi\)
0.539784 + 0.841804i \(0.318506\pi\)
\(548\) 7164.19 0.558466
\(549\) 1788.72 0.139054
\(550\) 259.339 0.0201059
\(551\) −10259.5 −0.793229
\(552\) −7878.68 −0.607498
\(553\) 0 0
\(554\) 30476.2 2.33720
\(555\) 1456.81 0.111420
\(556\) −10864.4 −0.828692
\(557\) −6033.26 −0.458954 −0.229477 0.973314i \(-0.573702\pi\)
−0.229477 + 0.973314i \(0.573702\pi\)
\(558\) −2997.10 −0.227379
\(559\) −819.751 −0.0620246
\(560\) 0 0
\(561\) −1079.60 −0.0812493
\(562\) 26559.8 1.99352
\(563\) 6958.47 0.520896 0.260448 0.965488i \(-0.416130\pi\)
0.260448 + 0.965488i \(0.416130\pi\)
\(564\) 6347.95 0.473931
\(565\) 5578.23 0.415359
\(566\) 52.3202 0.00388548
\(567\) 0 0
\(568\) 8300.44 0.613166
\(569\) −13396.4 −0.987009 −0.493505 0.869743i \(-0.664284\pi\)
−0.493505 + 0.869743i \(0.664284\pi\)
\(570\) 5690.55 0.418159
\(571\) −8055.84 −0.590414 −0.295207 0.955433i \(-0.595389\pi\)
−0.295207 + 0.955433i \(0.595389\pi\)
\(572\) −250.257 −0.0182933
\(573\) 3005.78 0.219142
\(574\) 0 0
\(575\) 5265.56 0.381894
\(576\) −38.6435 −0.00279539
\(577\) 21456.9 1.54812 0.774059 0.633114i \(-0.218223\pi\)
0.774059 + 0.633114i \(0.218223\pi\)
\(578\) −35638.9 −2.56468
\(579\) 12164.9 0.873153
\(580\) −2133.76 −0.152758
\(581\) 0 0
\(582\) 10644.0 0.758087
\(583\) 539.596 0.0383324
\(584\) −7746.76 −0.548910
\(585\) −857.802 −0.0606252
\(586\) 24412.1 1.72091
\(587\) −20156.3 −1.41728 −0.708638 0.705572i \(-0.750690\pi\)
−0.708638 + 0.705572i \(0.750690\pi\)
\(588\) 0 0
\(589\) −10132.0 −0.708797
\(590\) 13429.1 0.937066
\(591\) 15420.7 1.07330
\(592\) −7748.30 −0.537928
\(593\) −599.307 −0.0415018 −0.0207509 0.999785i \(-0.506606\pi\)
−0.0207509 + 0.999785i \(0.506606\pi\)
\(594\) −280.086 −0.0193469
\(595\) 0 0
\(596\) 10464.2 0.719177
\(597\) 1756.89 0.120444
\(598\) −14177.3 −0.969485
\(599\) −5493.05 −0.374691 −0.187346 0.982294i \(-0.559988\pi\)
−0.187346 + 0.982294i \(0.559988\pi\)
\(600\) −935.165 −0.0636299
\(601\) −24292.8 −1.64879 −0.824396 0.566014i \(-0.808485\pi\)
−0.824396 + 0.566014i \(0.808485\pi\)
\(602\) 0 0
\(603\) −2789.93 −0.188416
\(604\) −9402.82 −0.633436
\(605\) 6611.85 0.444314
\(606\) 1365.19 0.0915131
\(607\) −3029.50 −0.202576 −0.101288 0.994857i \(-0.532296\pi\)
−0.101288 + 0.994857i \(0.532296\pi\)
\(608\) −19549.3 −1.30400
\(609\) 0 0
\(610\) 3509.01 0.232911
\(611\) −9025.87 −0.597623
\(612\) −4926.85 −0.325419
\(613\) −19339.6 −1.27426 −0.637129 0.770757i \(-0.719878\pi\)
−0.637129 + 0.770757i \(0.719878\pi\)
\(614\) −26992.4 −1.77414
\(615\) 7366.69 0.483014
\(616\) 0 0
\(617\) −5743.91 −0.374783 −0.187391 0.982285i \(-0.560003\pi\)
−0.187391 + 0.982285i \(0.560003\pi\)
\(618\) −8538.35 −0.555765
\(619\) 8243.35 0.535264 0.267632 0.963521i \(-0.413759\pi\)
0.267632 + 0.963521i \(0.413759\pi\)
\(620\) −2107.24 −0.136498
\(621\) −5686.81 −0.367478
\(622\) 26815.4 1.72861
\(623\) 0 0
\(624\) 4562.37 0.292694
\(625\) 625.000 0.0400000
\(626\) −32231.6 −2.05788
\(627\) −946.856 −0.0603091
\(628\) 2652.13 0.168521
\(629\) −11897.1 −0.754162
\(630\) 0 0
\(631\) −4376.56 −0.276114 −0.138057 0.990424i \(-0.544086\pi\)
−0.138057 + 0.990424i \(0.544086\pi\)
\(632\) −308.762 −0.0194334
\(633\) 3165.48 0.198762
\(634\) 17407.8 1.09046
\(635\) 9379.92 0.586190
\(636\) 2462.49 0.153528
\(637\) 0 0
\(638\) 990.613 0.0614714
\(639\) 5991.23 0.370907
\(640\) 7202.71 0.444863
\(641\) 11836.6 0.729357 0.364678 0.931133i \(-0.381179\pi\)
0.364678 + 0.931133i \(0.381179\pi\)
\(642\) −8153.86 −0.501257
\(643\) −1448.21 −0.0888209 −0.0444104 0.999013i \(-0.514141\pi\)
−0.0444104 + 0.999013i \(0.514141\pi\)
\(644\) 0 0
\(645\) −645.058 −0.0393785
\(646\) −46472.0 −2.83037
\(647\) 8732.95 0.530646 0.265323 0.964160i \(-0.414521\pi\)
0.265323 + 0.964160i \(0.414521\pi\)
\(648\) 1009.98 0.0612279
\(649\) −2234.49 −0.135149
\(650\) −1682.78 −0.101545
\(651\) 0 0
\(652\) 9736.37 0.584824
\(653\) −21978.4 −1.31712 −0.658562 0.752527i \(-0.728835\pi\)
−0.658562 + 0.752527i \(0.728835\pi\)
\(654\) −8271.91 −0.494583
\(655\) 1821.01 0.108630
\(656\) −39181.1 −2.33196
\(657\) −5591.59 −0.332038
\(658\) 0 0
\(659\) −27761.7 −1.64103 −0.820516 0.571623i \(-0.806314\pi\)
−0.820516 + 0.571623i \(0.806314\pi\)
\(660\) −196.926 −0.0116141
\(661\) 8573.72 0.504507 0.252254 0.967661i \(-0.418828\pi\)
0.252254 + 0.967661i \(0.418828\pi\)
\(662\) −4313.86 −0.253267
\(663\) 7005.27 0.410350
\(664\) 5071.39 0.296398
\(665\) 0 0
\(666\) −3086.51 −0.179579
\(667\) 20113.2 1.16760
\(668\) −3572.87 −0.206944
\(669\) 14027.6 0.810668
\(670\) −5473.11 −0.315589
\(671\) −583.868 −0.0335916
\(672\) 0 0
\(673\) 27159.2 1.55559 0.777795 0.628518i \(-0.216338\pi\)
0.777795 + 0.628518i \(0.216338\pi\)
\(674\) 30879.1 1.76472
\(675\) −675.000 −0.0384900
\(676\) −8194.26 −0.466219
\(677\) 1392.30 0.0790404 0.0395202 0.999219i \(-0.487417\pi\)
0.0395202 + 0.999219i \(0.487417\pi\)
\(678\) −11818.5 −0.669448
\(679\) 0 0
\(680\) 7637.06 0.430688
\(681\) 16329.3 0.918857
\(682\) 978.302 0.0549283
\(683\) −8675.09 −0.486007 −0.243004 0.970025i \(-0.578133\pi\)
−0.243004 + 0.970025i \(0.578133\pi\)
\(684\) −4321.05 −0.241549
\(685\) −8015.66 −0.447099
\(686\) 0 0
\(687\) −1608.91 −0.0893504
\(688\) 3430.86 0.190117
\(689\) −3501.30 −0.193598
\(690\) −11156.0 −0.615511
\(691\) 21426.0 1.17957 0.589785 0.807561i \(-0.299213\pi\)
0.589785 + 0.807561i \(0.299213\pi\)
\(692\) 6454.65 0.354579
\(693\) 0 0
\(694\) −16206.3 −0.886433
\(695\) 12155.6 0.663438
\(696\) −3572.11 −0.194541
\(697\) −60160.4 −3.26935
\(698\) −14088.8 −0.763997
\(699\) 550.470 0.0297864
\(700\) 0 0
\(701\) 24840.5 1.33839 0.669197 0.743085i \(-0.266638\pi\)
0.669197 + 0.743085i \(0.266638\pi\)
\(702\) 1817.40 0.0977116
\(703\) −10434.2 −0.559793
\(704\) 12.6139 0.000675288 0
\(705\) −7102.41 −0.379422
\(706\) 8532.45 0.454848
\(707\) 0 0
\(708\) −10197.3 −0.541295
\(709\) 12525.0 0.663450 0.331725 0.943376i \(-0.392369\pi\)
0.331725 + 0.943376i \(0.392369\pi\)
\(710\) 11753.2 0.621255
\(711\) −222.863 −0.0117553
\(712\) −3263.74 −0.171789
\(713\) 19863.3 1.04332
\(714\) 0 0
\(715\) 280.000 0.0146453
\(716\) 14941.6 0.779881
\(717\) −1929.65 −0.100508
\(718\) 9732.66 0.505877
\(719\) −28085.0 −1.45674 −0.728369 0.685185i \(-0.759721\pi\)
−0.728369 + 0.685185i \(0.759721\pi\)
\(720\) 3590.11 0.185827
\(721\) 0 0
\(722\) −16537.9 −0.852460
\(723\) −17266.8 −0.888189
\(724\) −10063.1 −0.516562
\(725\) 2387.35 0.122295
\(726\) −14008.4 −0.716115
\(727\) 14326.2 0.730851 0.365426 0.930841i \(-0.380923\pi\)
0.365426 + 0.930841i \(0.380923\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −10969.2 −0.556150
\(731\) 5267.89 0.266539
\(732\) −2664.53 −0.134541
\(733\) −6727.85 −0.339016 −0.169508 0.985529i \(-0.554218\pi\)
−0.169508 + 0.985529i \(0.554218\pi\)
\(734\) 39240.8 1.97331
\(735\) 0 0
\(736\) 38325.5 1.91943
\(737\) 910.677 0.0455159
\(738\) −15607.6 −0.778490
\(739\) −3418.51 −0.170165 −0.0850826 0.996374i \(-0.527115\pi\)
−0.0850826 + 0.996374i \(0.527115\pi\)
\(740\) −2170.10 −0.107803
\(741\) 6143.91 0.304591
\(742\) 0 0
\(743\) 8095.50 0.399724 0.199862 0.979824i \(-0.435951\pi\)
0.199862 + 0.979824i \(0.435951\pi\)
\(744\) −3527.72 −0.173834
\(745\) −11707.9 −0.575762
\(746\) −21508.4 −1.05560
\(747\) 3660.51 0.179292
\(748\) 1608.20 0.0786119
\(749\) 0 0
\(750\) −1324.17 −0.0644693
\(751\) 13446.8 0.653371 0.326686 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(752\) 37775.4 1.83182
\(753\) −15396.8 −0.745141
\(754\) −6427.84 −0.310462
\(755\) 10520.4 0.507119
\(756\) 0 0
\(757\) −2593.24 −0.124508 −0.0622541 0.998060i \(-0.519829\pi\)
−0.0622541 + 0.998060i \(0.519829\pi\)
\(758\) −14069.0 −0.674156
\(759\) 1856.26 0.0887722
\(760\) 6698.02 0.319688
\(761\) −27079.4 −1.28992 −0.644959 0.764217i \(-0.723125\pi\)
−0.644959 + 0.764217i \(0.723125\pi\)
\(762\) −19873.0 −0.944782
\(763\) 0 0
\(764\) −4477.48 −0.212028
\(765\) 5512.41 0.260525
\(766\) 1124.58 0.0530451
\(767\) 14499.0 0.682568
\(768\) −15363.3 −0.721842
\(769\) −2138.72 −0.100292 −0.0501458 0.998742i \(-0.515969\pi\)
−0.0501458 + 0.998742i \(0.515969\pi\)
\(770\) 0 0
\(771\) 15125.2 0.706513
\(772\) −18121.1 −0.844810
\(773\) −25864.0 −1.20345 −0.601724 0.798704i \(-0.705519\pi\)
−0.601724 + 0.798704i \(0.705519\pi\)
\(774\) 1366.67 0.0634676
\(775\) 2357.69 0.109278
\(776\) 12528.4 0.579566
\(777\) 0 0
\(778\) −13720.1 −0.632247
\(779\) −52763.1 −2.42675
\(780\) 1277.80 0.0586572
\(781\) −1955.63 −0.0896006
\(782\) 91106.2 4.16618
\(783\) −2578.34 −0.117679
\(784\) 0 0
\(785\) −2967.33 −0.134916
\(786\) −3858.14 −0.175083
\(787\) 32371.3 1.46621 0.733107 0.680113i \(-0.238069\pi\)
0.733107 + 0.680113i \(0.238069\pi\)
\(788\) −22971.0 −1.03846
\(789\) −22731.0 −1.02566
\(790\) −437.200 −0.0196897
\(791\) 0 0
\(792\) −329.673 −0.0147909
\(793\) 3788.57 0.169654
\(794\) 16970.8 0.758526
\(795\) −2755.16 −0.122912
\(796\) −2617.11 −0.116534
\(797\) −2024.33 −0.0899691 −0.0449845 0.998988i \(-0.514324\pi\)
−0.0449845 + 0.998988i \(0.514324\pi\)
\(798\) 0 0
\(799\) 58002.1 2.56817
\(800\) 4549.08 0.201043
\(801\) −2355.76 −0.103916
\(802\) −12777.7 −0.562589
\(803\) 1825.18 0.0802109
\(804\) 4155.95 0.182300
\(805\) 0 0
\(806\) −6347.95 −0.277416
\(807\) 3069.29 0.133884
\(808\) 1606.88 0.0699628
\(809\) 12391.7 0.538526 0.269263 0.963067i \(-0.413220\pi\)
0.269263 + 0.963067i \(0.413220\pi\)
\(810\) 1430.11 0.0620356
\(811\) −14654.5 −0.634511 −0.317256 0.948340i \(-0.602761\pi\)
−0.317256 + 0.948340i \(0.602761\pi\)
\(812\) 0 0
\(813\) −6755.94 −0.291441
\(814\) 1007.49 0.0433813
\(815\) −10893.5 −0.468201
\(816\) −29318.7 −1.25780
\(817\) 4620.16 0.197844
\(818\) −7447.33 −0.318325
\(819\) 0 0
\(820\) −10973.6 −0.467335
\(821\) 23887.9 1.01546 0.507731 0.861516i \(-0.330485\pi\)
0.507731 + 0.861516i \(0.330485\pi\)
\(822\) 16982.6 0.720604
\(823\) −4008.41 −0.169774 −0.0848871 0.996391i \(-0.527053\pi\)
−0.0848871 + 0.996391i \(0.527053\pi\)
\(824\) −10050.0 −0.424889
\(825\) 220.331 0.00929810
\(826\) 0 0
\(827\) −45110.4 −1.89679 −0.948394 0.317096i \(-0.897292\pi\)
−0.948394 + 0.317096i \(0.897292\pi\)
\(828\) 8471.21 0.355549
\(829\) −16165.4 −0.677260 −0.338630 0.940920i \(-0.609964\pi\)
−0.338630 + 0.940920i \(0.609964\pi\)
\(830\) 7180.97 0.300307
\(831\) 25892.2 1.08085
\(832\) −81.8481 −0.00341054
\(833\) 0 0
\(834\) −25753.8 −1.06928
\(835\) 3997.51 0.165676
\(836\) 1410.46 0.0583514
\(837\) −2546.30 −0.105153
\(838\) −24385.7 −1.00524
\(839\) 25244.4 1.03878 0.519388 0.854538i \(-0.326160\pi\)
0.519388 + 0.854538i \(0.326160\pi\)
\(840\) 0 0
\(841\) −15269.9 −0.626096
\(842\) 34066.7 1.39432
\(843\) 22564.9 0.921916
\(844\) −4715.37 −0.192310
\(845\) 9168.15 0.373247
\(846\) 15047.7 0.611526
\(847\) 0 0
\(848\) 14653.8 0.593412
\(849\) 44.4506 0.00179687
\(850\) 10813.9 0.436370
\(851\) 20455.8 0.823990
\(852\) −8924.68 −0.358867
\(853\) 30168.1 1.21094 0.605472 0.795867i \(-0.292984\pi\)
0.605472 + 0.795867i \(0.292984\pi\)
\(854\) 0 0
\(855\) 4834.61 0.193380
\(856\) −9597.44 −0.383217
\(857\) 13393.6 0.533857 0.266929 0.963716i \(-0.413991\pi\)
0.266929 + 0.963716i \(0.413991\pi\)
\(858\) −593.230 −0.0236043
\(859\) −19060.4 −0.757081 −0.378541 0.925585i \(-0.623574\pi\)
−0.378541 + 0.925585i \(0.623574\pi\)
\(860\) 960.894 0.0381002
\(861\) 0 0
\(862\) 45914.3 1.81421
\(863\) −9466.86 −0.373413 −0.186707 0.982416i \(-0.559781\pi\)
−0.186707 + 0.982416i \(0.559781\pi\)
\(864\) −4913.00 −0.193453
\(865\) −7221.79 −0.283871
\(866\) 25975.2 1.01925
\(867\) −30278.3 −1.18605
\(868\) 0 0
\(869\) 72.7461 0.00283975
\(870\) −5058.03 −0.197107
\(871\) −5909.15 −0.229878
\(872\) −9736.39 −0.378115
\(873\) 9042.97 0.350582
\(874\) 79903.8 3.09243
\(875\) 0 0
\(876\) 8329.37 0.321259
\(877\) 37740.6 1.45315 0.726573 0.687090i \(-0.241112\pi\)
0.726573 + 0.687090i \(0.241112\pi\)
\(878\) 24397.3 0.937778
\(879\) 20740.2 0.795845
\(880\) −1171.87 −0.0448905
\(881\) −25991.5 −0.993957 −0.496979 0.867763i \(-0.665557\pi\)
−0.496979 + 0.867763i \(0.665557\pi\)
\(882\) 0 0
\(883\) 39420.3 1.50238 0.751189 0.660087i \(-0.229481\pi\)
0.751189 + 0.660087i \(0.229481\pi\)
\(884\) −10435.2 −0.397030
\(885\) 11409.2 0.433352
\(886\) 52305.0 1.98332
\(887\) −46005.2 −1.74149 −0.870745 0.491735i \(-0.836363\pi\)
−0.870745 + 0.491735i \(0.836363\pi\)
\(888\) −3632.95 −0.137290
\(889\) 0 0
\(890\) −4621.38 −0.174055
\(891\) −237.957 −0.00894710
\(892\) −20895.8 −0.784353
\(893\) 50870.2 1.90628
\(894\) 24805.2 0.927975
\(895\) −16717.5 −0.624361
\(896\) 0 0
\(897\) −12044.8 −0.448345
\(898\) 37622.6 1.39809
\(899\) 9005.81 0.334105
\(900\) 1005.50 0.0372406
\(901\) 22500.1 0.831950
\(902\) 5094.58 0.188061
\(903\) 0 0
\(904\) −13910.8 −0.511801
\(905\) 11259.1 0.413551
\(906\) −22289.2 −0.817340
\(907\) −2838.97 −0.103932 −0.0519661 0.998649i \(-0.516549\pi\)
−0.0519661 + 0.998649i \(0.516549\pi\)
\(908\) −24324.6 −0.889030
\(909\) 1159.84 0.0423208
\(910\) 0 0
\(911\) 39890.9 1.45076 0.725382 0.688347i \(-0.241663\pi\)
0.725382 + 0.688347i \(0.241663\pi\)
\(912\) −25713.7 −0.933626
\(913\) −1194.85 −0.0433119
\(914\) 20675.3 0.748226
\(915\) 2981.21 0.107711
\(916\) 2396.67 0.0864500
\(917\) 0 0
\(918\) −11679.0 −0.419897
\(919\) −646.475 −0.0232048 −0.0116024 0.999933i \(-0.503693\pi\)
−0.0116024 + 0.999933i \(0.503693\pi\)
\(920\) −13131.1 −0.470566
\(921\) −22932.4 −0.820463
\(922\) 11316.3 0.404213
\(923\) 12689.6 0.452528
\(924\) 0 0
\(925\) 2428.02 0.0863056
\(926\) −1312.37 −0.0465737
\(927\) −7254.07 −0.257017
\(928\) 17376.4 0.614665
\(929\) −51188.2 −1.80778 −0.903892 0.427760i \(-0.859303\pi\)
−0.903892 + 0.427760i \(0.859303\pi\)
\(930\) −4995.17 −0.176127
\(931\) 0 0
\(932\) −819.993 −0.0288195
\(933\) 22782.0 0.799409
\(934\) −69747.8 −2.44349
\(935\) −1799.34 −0.0629355
\(936\) 2139.16 0.0747017
\(937\) −29786.1 −1.03849 −0.519247 0.854624i \(-0.673788\pi\)
−0.519247 + 0.854624i \(0.673788\pi\)
\(938\) 0 0
\(939\) −27383.5 −0.951680
\(940\) 10579.9 0.367105
\(941\) 44817.4 1.55261 0.776304 0.630358i \(-0.217092\pi\)
0.776304 + 0.630358i \(0.217092\pi\)
\(942\) 6286.82 0.217448
\(943\) 103439. 3.57206
\(944\) −60682.0 −2.09219
\(945\) 0 0
\(946\) −446.103 −0.0153320
\(947\) 54697.1 1.87689 0.938446 0.345425i \(-0.112265\pi\)
0.938446 + 0.345425i \(0.112265\pi\)
\(948\) 331.983 0.0113737
\(949\) −11843.2 −0.405105
\(950\) 9484.24 0.323905
\(951\) 14789.4 0.504290
\(952\) 0 0
\(953\) −7577.51 −0.257565 −0.128783 0.991673i \(-0.541107\pi\)
−0.128783 + 0.991673i \(0.541107\pi\)
\(954\) 5837.29 0.198102
\(955\) 5009.63 0.169746
\(956\) 2874.46 0.0972454
\(957\) 841.612 0.0284278
\(958\) −73313.4 −2.47249
\(959\) 0 0
\(960\) −64.4059 −0.00216530
\(961\) −20897.1 −0.701457
\(962\) −6537.32 −0.219097
\(963\) −6927.41 −0.231810
\(964\) 25721.1 0.859357
\(965\) 20274.8 0.676342
\(966\) 0 0
\(967\) 50779.0 1.68867 0.844334 0.535817i \(-0.179996\pi\)
0.844334 + 0.535817i \(0.179996\pi\)
\(968\) −16488.5 −0.547478
\(969\) −39482.0 −1.30892
\(970\) 17739.9 0.587212
\(971\) 15313.2 0.506102 0.253051 0.967453i \(-0.418566\pi\)
0.253051 + 0.967453i \(0.418566\pi\)
\(972\) −1085.94 −0.0358348
\(973\) 0 0
\(974\) −62315.9 −2.05003
\(975\) −1429.67 −0.0469601
\(976\) −15856.1 −0.520021
\(977\) 46620.4 1.52663 0.763316 0.646025i \(-0.223570\pi\)
0.763316 + 0.646025i \(0.223570\pi\)
\(978\) 23079.9 0.754615
\(979\) 768.957 0.0251031
\(980\) 0 0
\(981\) −7027.70 −0.228723
\(982\) 19906.6 0.646889
\(983\) 2824.37 0.0916414 0.0458207 0.998950i \(-0.485410\pi\)
0.0458207 + 0.998950i \(0.485410\pi\)
\(984\) −18370.9 −0.595165
\(985\) 25701.1 0.831377
\(986\) 41306.6 1.33415
\(987\) 0 0
\(988\) −9152.11 −0.294704
\(989\) −9057.59 −0.291218
\(990\) −466.810 −0.0149860
\(991\) 16951.4 0.543370 0.271685 0.962386i \(-0.412419\pi\)
0.271685 + 0.962386i \(0.412419\pi\)
\(992\) 17160.5 0.549239
\(993\) −3665.00 −0.117125
\(994\) 0 0
\(995\) 2928.15 0.0932952
\(996\) −5452.79 −0.173472
\(997\) −23847.8 −0.757540 −0.378770 0.925491i \(-0.623653\pi\)
−0.378770 + 0.925491i \(0.623653\pi\)
\(998\) 61703.4 1.95710
\(999\) −2622.26 −0.0830476
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 735.4.a.p.1.1 2
3.2 odd 2 2205.4.a.z.1.2 2
7.6 odd 2 105.4.a.f.1.1 2
21.20 even 2 315.4.a.i.1.2 2
28.27 even 2 1680.4.a.bg.1.1 2
35.13 even 4 525.4.d.h.274.3 4
35.27 even 4 525.4.d.h.274.2 4
35.34 odd 2 525.4.a.k.1.2 2
105.104 even 2 1575.4.a.w.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.f.1.1 2 7.6 odd 2
315.4.a.i.1.2 2 21.20 even 2
525.4.a.k.1.2 2 35.34 odd 2
525.4.d.h.274.2 4 35.27 even 4
525.4.d.h.274.3 4 35.13 even 4
735.4.a.p.1.1 2 1.1 even 1 trivial
1575.4.a.w.1.1 2 105.104 even 2
1680.4.a.bg.1.1 2 28.27 even 2
2205.4.a.z.1.2 2 3.2 odd 2