Properties

Label 525.4.a.i.1.2
Level $525$
Weight $4$
Character 525.1
Self dual yes
Analytic conductor $30.976$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(30.9760027530\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \(x^{2} - x - 10\)
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 1.2
Root \(-2.70156\) of defining polynomial
Character \(\chi\) \(=\) 525.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.70156 q^{2} -3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} -7.00000 q^{7} -22.2984 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.70156 q^{2} -3.00000 q^{3} -5.10469 q^{4} -5.10469 q^{6} -7.00000 q^{7} -22.2984 q^{8} +9.00000 q^{9} +37.4031 q^{11} +15.3141 q^{12} -29.0156 q^{13} -11.9109 q^{14} +2.89531 q^{16} -58.4187 q^{17} +15.3141 q^{18} -54.5969 q^{19} +21.0000 q^{21} +63.6437 q^{22} -161.675 q^{23} +66.8953 q^{24} -49.3719 q^{26} -27.0000 q^{27} +35.7328 q^{28} +137.581 q^{29} +154.659 q^{31} +183.314 q^{32} -112.209 q^{33} -99.4031 q^{34} -45.9422 q^{36} +350.125 q^{37} -92.9000 q^{38} +87.0469 q^{39} +353.769 q^{41} +35.7328 q^{42} +518.156 q^{43} -190.931 q^{44} -275.100 q^{46} +542.219 q^{47} -8.68594 q^{48} +49.0000 q^{49} +175.256 q^{51} +148.116 q^{52} -305.309 q^{53} -45.9422 q^{54} +156.089 q^{56} +163.791 q^{57} +234.103 q^{58} +14.6813 q^{59} -171.069 q^{61} +263.163 q^{62} -63.0000 q^{63} +288.758 q^{64} -190.931 q^{66} -551.956 q^{67} +298.209 q^{68} +485.025 q^{69} -120.334 q^{71} -200.686 q^{72} -284.659 q^{73} +595.759 q^{74} +278.700 q^{76} -261.822 q^{77} +148.116 q^{78} +941.612 q^{79} +81.0000 q^{81} +601.959 q^{82} -377.150 q^{83} -107.198 q^{84} +881.675 q^{86} -412.744 q^{87} -834.031 q^{88} -677.725 q^{89} +203.109 q^{91} +825.300 q^{92} -463.978 q^{93} +922.619 q^{94} -549.942 q^{96} +1225.03 q^{97} +83.3765 q^{98} +336.628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - 6q^{3} + 9q^{4} + 9q^{6} - 14q^{7} - 51q^{8} + 18q^{9} + O(q^{10}) \) \( 2q - 3q^{2} - 6q^{3} + 9q^{4} + 9q^{6} - 14q^{7} - 51q^{8} + 18q^{9} + 62q^{11} - 27q^{12} + 6q^{13} + 21q^{14} + 25q^{16} - 40q^{17} - 27q^{18} - 122q^{19} + 42q^{21} - 52q^{22} - 16q^{23} + 153q^{24} - 214q^{26} - 54q^{27} - 63q^{28} + 352q^{29} + 66q^{31} + 309q^{32} - 186q^{33} - 186q^{34} + 81q^{36} + 188q^{37} + 224q^{38} - 18q^{39} + 16q^{41} - 63q^{42} + 396q^{43} + 156q^{44} - 960q^{46} + 188q^{47} - 75q^{48} + 98q^{49} + 120q^{51} + 642q^{52} - 982q^{53} + 81q^{54} + 357q^{56} + 366q^{57} - 774q^{58} + 516q^{59} - 880q^{61} + 680q^{62} - 126q^{63} - 479q^{64} + 156q^{66} + 356q^{67} + 558q^{68} + 48q^{69} + 310q^{71} - 459q^{72} - 326q^{73} + 1358q^{74} - 672q^{76} - 434q^{77} + 642q^{78} + 1832q^{79} + 162q^{81} + 2190q^{82} + 680q^{83} + 189q^{84} + 1456q^{86} - 1056q^{87} - 1540q^{88} + 796q^{89} - 42q^{91} + 2880q^{92} - 198q^{93} + 2588q^{94} - 927q^{96} + 670q^{97} - 147q^{98} + 558q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70156 0.601593 0.300797 0.953688i \(-0.402747\pi\)
0.300797 + 0.953688i \(0.402747\pi\)
\(3\) −3.00000 −0.577350
\(4\) −5.10469 −0.638086
\(5\) 0 0
\(6\) −5.10469 −0.347330
\(7\) −7.00000 −0.377964
\(8\) −22.2984 −0.985461
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 37.4031 1.02522 0.512612 0.858620i \(-0.328678\pi\)
0.512612 + 0.858620i \(0.328678\pi\)
\(12\) 15.3141 0.368399
\(13\) −29.0156 −0.619037 −0.309519 0.950893i \(-0.600168\pi\)
−0.309519 + 0.950893i \(0.600168\pi\)
\(14\) −11.9109 −0.227381
\(15\) 0 0
\(16\) 2.89531 0.0452393
\(17\) −58.4187 −0.833449 −0.416724 0.909033i \(-0.636822\pi\)
−0.416724 + 0.909033i \(0.636822\pi\)
\(18\) 15.3141 0.200531
\(19\) −54.5969 −0.659231 −0.329615 0.944115i \(-0.606919\pi\)
−0.329615 + 0.944115i \(0.606919\pi\)
\(20\) 0 0
\(21\) 21.0000 0.218218
\(22\) 63.6437 0.616768
\(23\) −161.675 −1.46572 −0.732860 0.680379i \(-0.761815\pi\)
−0.732860 + 0.680379i \(0.761815\pi\)
\(24\) 66.8953 0.568956
\(25\) 0 0
\(26\) −49.3719 −0.372409
\(27\) −27.0000 −0.192450
\(28\) 35.7328 0.241174
\(29\) 137.581 0.880972 0.440486 0.897759i \(-0.354806\pi\)
0.440486 + 0.897759i \(0.354806\pi\)
\(30\) 0 0
\(31\) 154.659 0.896053 0.448026 0.894020i \(-0.352127\pi\)
0.448026 + 0.894020i \(0.352127\pi\)
\(32\) 183.314 1.01268
\(33\) −112.209 −0.591913
\(34\) −99.4031 −0.501397
\(35\) 0 0
\(36\) −45.9422 −0.212695
\(37\) 350.125 1.55568 0.777840 0.628462i \(-0.216315\pi\)
0.777840 + 0.628462i \(0.216315\pi\)
\(38\) −92.9000 −0.396589
\(39\) 87.0469 0.357401
\(40\) 0 0
\(41\) 353.769 1.34755 0.673773 0.738938i \(-0.264673\pi\)
0.673773 + 0.738938i \(0.264673\pi\)
\(42\) 35.7328 0.131278
\(43\) 518.156 1.83763 0.918815 0.394689i \(-0.129148\pi\)
0.918815 + 0.394689i \(0.129148\pi\)
\(44\) −190.931 −0.654181
\(45\) 0 0
\(46\) −275.100 −0.881767
\(47\) 542.219 1.68278 0.841391 0.540427i \(-0.181737\pi\)
0.841391 + 0.540427i \(0.181737\pi\)
\(48\) −8.68594 −0.0261189
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 175.256 0.481192
\(52\) 148.116 0.394999
\(53\) −305.309 −0.791273 −0.395637 0.918407i \(-0.629476\pi\)
−0.395637 + 0.918407i \(0.629476\pi\)
\(54\) −45.9422 −0.115777
\(55\) 0 0
\(56\) 156.089 0.372469
\(57\) 163.791 0.380607
\(58\) 234.103 0.529987
\(59\) 14.6813 0.0323956 0.0161978 0.999869i \(-0.494844\pi\)
0.0161978 + 0.999869i \(0.494844\pi\)
\(60\) 0 0
\(61\) −171.069 −0.359067 −0.179534 0.983752i \(-0.557459\pi\)
−0.179534 + 0.983752i \(0.557459\pi\)
\(62\) 263.163 0.539059
\(63\) −63.0000 −0.125988
\(64\) 288.758 0.563980
\(65\) 0 0
\(66\) −190.931 −0.356091
\(67\) −551.956 −1.00645 −0.503225 0.864155i \(-0.667853\pi\)
−0.503225 + 0.864155i \(0.667853\pi\)
\(68\) 298.209 0.531812
\(69\) 485.025 0.846234
\(70\) 0 0
\(71\) −120.334 −0.201142 −0.100571 0.994930i \(-0.532067\pi\)
−0.100571 + 0.994930i \(0.532067\pi\)
\(72\) −200.686 −0.328487
\(73\) −284.659 −0.456395 −0.228198 0.973615i \(-0.573283\pi\)
−0.228198 + 0.973615i \(0.573283\pi\)
\(74\) 595.759 0.935887
\(75\) 0 0
\(76\) 278.700 0.420646
\(77\) −261.822 −0.387498
\(78\) 148.116 0.215010
\(79\) 941.612 1.34101 0.670504 0.741906i \(-0.266078\pi\)
0.670504 + 0.741906i \(0.266078\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 601.959 0.810674
\(83\) −377.150 −0.498766 −0.249383 0.968405i \(-0.580228\pi\)
−0.249383 + 0.968405i \(0.580228\pi\)
\(84\) −107.198 −0.139242
\(85\) 0 0
\(86\) 881.675 1.10551
\(87\) −412.744 −0.508630
\(88\) −834.031 −1.01032
\(89\) −677.725 −0.807176 −0.403588 0.914941i \(-0.632237\pi\)
−0.403588 + 0.914941i \(0.632237\pi\)
\(90\) 0 0
\(91\) 203.109 0.233974
\(92\) 825.300 0.935255
\(93\) −463.978 −0.517336
\(94\) 922.619 1.01235
\(95\) 0 0
\(96\) −549.942 −0.584669
\(97\) 1225.03 1.28230 0.641151 0.767414i \(-0.278457\pi\)
0.641151 + 0.767414i \(0.278457\pi\)
\(98\) 83.3765 0.0859419
\(99\) 336.628 0.341741
\(100\) 0 0
\(101\) −338.144 −0.333134 −0.166567 0.986030i \(-0.553268\pi\)
−0.166567 + 0.986030i \(0.553268\pi\)
\(102\) 298.209 0.289482
\(103\) 566.700 0.542122 0.271061 0.962562i \(-0.412625\pi\)
0.271061 + 0.962562i \(0.412625\pi\)
\(104\) 647.003 0.610037
\(105\) 0 0
\(106\) −519.503 −0.476024
\(107\) 562.531 0.508242 0.254121 0.967172i \(-0.418214\pi\)
0.254121 + 0.967172i \(0.418214\pi\)
\(108\) 137.827 0.122800
\(109\) 1830.79 1.60879 0.804396 0.594094i \(-0.202489\pi\)
0.804396 + 0.594094i \(0.202489\pi\)
\(110\) 0 0
\(111\) −1050.37 −0.898173
\(112\) −20.2672 −0.0170988
\(113\) 31.8032 0.0264761 0.0132380 0.999912i \(-0.495786\pi\)
0.0132380 + 0.999912i \(0.495786\pi\)
\(114\) 278.700 0.228971
\(115\) 0 0
\(116\) −702.309 −0.562136
\(117\) −261.141 −0.206346
\(118\) 24.9811 0.0194890
\(119\) 408.931 0.315014
\(120\) 0 0
\(121\) 67.9937 0.0510847
\(122\) −291.084 −0.216012
\(123\) −1061.31 −0.778006
\(124\) −789.488 −0.571759
\(125\) 0 0
\(126\) −107.198 −0.0757936
\(127\) −2220.81 −1.55169 −0.775847 0.630921i \(-0.782677\pi\)
−0.775847 + 0.630921i \(0.782677\pi\)
\(128\) −975.173 −0.673390
\(129\) −1554.47 −1.06096
\(130\) 0 0
\(131\) 646.512 0.431191 0.215596 0.976483i \(-0.430831\pi\)
0.215596 + 0.976483i \(0.430831\pi\)
\(132\) 572.794 0.377692
\(133\) 382.178 0.249166
\(134\) −939.188 −0.605474
\(135\) 0 0
\(136\) 1302.65 0.821331
\(137\) 896.009 0.558768 0.279384 0.960179i \(-0.409870\pi\)
0.279384 + 0.960179i \(0.409870\pi\)
\(138\) 825.300 0.509088
\(139\) −2313.61 −1.41178 −0.705891 0.708320i \(-0.749453\pi\)
−0.705891 + 0.708320i \(0.749453\pi\)
\(140\) 0 0
\(141\) −1626.66 −0.971554
\(142\) −204.756 −0.121005
\(143\) −1085.27 −0.634652
\(144\) 26.0578 0.0150798
\(145\) 0 0
\(146\) −484.366 −0.274564
\(147\) −147.000 −0.0824786
\(148\) −1787.28 −0.992658
\(149\) 819.337 0.450488 0.225244 0.974302i \(-0.427682\pi\)
0.225244 + 0.974302i \(0.427682\pi\)
\(150\) 0 0
\(151\) 534.744 0.288191 0.144095 0.989564i \(-0.453973\pi\)
0.144095 + 0.989564i \(0.453973\pi\)
\(152\) 1217.43 0.649646
\(153\) −525.769 −0.277816
\(154\) −445.506 −0.233116
\(155\) 0 0
\(156\) −444.347 −0.228053
\(157\) −1564.76 −0.795423 −0.397711 0.917511i \(-0.630195\pi\)
−0.397711 + 0.917511i \(0.630195\pi\)
\(158\) 1602.21 0.806741
\(159\) 915.928 0.456842
\(160\) 0 0
\(161\) 1131.72 0.553990
\(162\) 137.827 0.0668437
\(163\) 1114.31 0.535455 0.267728 0.963495i \(-0.413727\pi\)
0.267728 + 0.963495i \(0.413727\pi\)
\(164\) −1805.88 −0.859850
\(165\) 0 0
\(166\) −641.744 −0.300054
\(167\) 1774.47 0.822231 0.411115 0.911583i \(-0.365139\pi\)
0.411115 + 0.911583i \(0.365139\pi\)
\(168\) −468.267 −0.215045
\(169\) −1355.09 −0.616793
\(170\) 0 0
\(171\) −491.372 −0.219744
\(172\) −2645.02 −1.17257
\(173\) 4215.88 1.85276 0.926380 0.376590i \(-0.122903\pi\)
0.926380 + 0.376590i \(0.122903\pi\)
\(174\) −702.309 −0.305988
\(175\) 0 0
\(176\) 108.294 0.0463804
\(177\) −44.0438 −0.0187036
\(178\) −1153.19 −0.485592
\(179\) −2430.70 −1.01497 −0.507483 0.861662i \(-0.669424\pi\)
−0.507483 + 0.861662i \(0.669424\pi\)
\(180\) 0 0
\(181\) −2700.91 −1.10916 −0.554578 0.832132i \(-0.687120\pi\)
−0.554578 + 0.832132i \(0.687120\pi\)
\(182\) 345.603 0.140757
\(183\) 513.206 0.207308
\(184\) 3605.10 1.44441
\(185\) 0 0
\(186\) −789.488 −0.311226
\(187\) −2185.04 −0.854472
\(188\) −2767.86 −1.07376
\(189\) 189.000 0.0727393
\(190\) 0 0
\(191\) 3611.10 1.36801 0.684005 0.729478i \(-0.260237\pi\)
0.684005 + 0.729478i \(0.260237\pi\)
\(192\) −866.273 −0.325614
\(193\) 4468.33 1.66651 0.833257 0.552886i \(-0.186474\pi\)
0.833257 + 0.552886i \(0.186474\pi\)
\(194\) 2084.47 0.771425
\(195\) 0 0
\(196\) −250.130 −0.0911551
\(197\) 434.422 0.157113 0.0785566 0.996910i \(-0.474969\pi\)
0.0785566 + 0.996910i \(0.474969\pi\)
\(198\) 572.794 0.205589
\(199\) −468.915 −0.167038 −0.0835189 0.996506i \(-0.526616\pi\)
−0.0835189 + 0.996506i \(0.526616\pi\)
\(200\) 0 0
\(201\) 1655.87 0.581074
\(202\) −575.372 −0.200411
\(203\) −963.069 −0.332976
\(204\) −894.628 −0.307042
\(205\) 0 0
\(206\) 964.275 0.326137
\(207\) −1455.07 −0.488573
\(208\) −84.0093 −0.0280048
\(209\) −2042.09 −0.675859
\(210\) 0 0
\(211\) 3735.51 1.21878 0.609392 0.792869i \(-0.291414\pi\)
0.609392 + 0.792869i \(0.291414\pi\)
\(212\) 1558.51 0.504900
\(213\) 361.003 0.116129
\(214\) 957.182 0.305755
\(215\) 0 0
\(216\) 602.058 0.189652
\(217\) −1082.62 −0.338676
\(218\) 3115.21 0.967838
\(219\) 853.978 0.263500
\(220\) 0 0
\(221\) 1695.06 0.515936
\(222\) −1787.28 −0.540334
\(223\) −842.806 −0.253087 −0.126544 0.991961i \(-0.540388\pi\)
−0.126544 + 0.991961i \(0.540388\pi\)
\(224\) −1283.20 −0.382756
\(225\) 0 0
\(226\) 54.1152 0.0159278
\(227\) −992.150 −0.290094 −0.145047 0.989425i \(-0.546333\pi\)
−0.145047 + 0.989425i \(0.546333\pi\)
\(228\) −836.100 −0.242860
\(229\) −6411.39 −1.85012 −0.925059 0.379825i \(-0.875984\pi\)
−0.925059 + 0.379825i \(0.875984\pi\)
\(230\) 0 0
\(231\) 785.466 0.223722
\(232\) −3067.85 −0.868164
\(233\) 2274.35 0.639476 0.319738 0.947506i \(-0.396405\pi\)
0.319738 + 0.947506i \(0.396405\pi\)
\(234\) −444.347 −0.124136
\(235\) 0 0
\(236\) −74.9433 −0.0206712
\(237\) −2824.84 −0.774232
\(238\) 695.822 0.189510
\(239\) 2863.12 0.774893 0.387447 0.921892i \(-0.373357\pi\)
0.387447 + 0.921892i \(0.373357\pi\)
\(240\) 0 0
\(241\) −5364.23 −1.43378 −0.716889 0.697187i \(-0.754435\pi\)
−0.716889 + 0.697187i \(0.754435\pi\)
\(242\) 115.696 0.0307322
\(243\) −243.000 −0.0641500
\(244\) 873.252 0.229116
\(245\) 0 0
\(246\) −1805.88 −0.468043
\(247\) 1584.16 0.408088
\(248\) −3448.66 −0.883025
\(249\) 1131.45 0.287963
\(250\) 0 0
\(251\) 5569.81 1.40065 0.700325 0.713824i \(-0.253039\pi\)
0.700325 + 0.713824i \(0.253039\pi\)
\(252\) 321.595 0.0803913
\(253\) −6047.15 −1.50269
\(254\) −3778.85 −0.933489
\(255\) 0 0
\(256\) −3969.38 −0.969087
\(257\) −2095.36 −0.508580 −0.254290 0.967128i \(-0.581842\pi\)
−0.254290 + 0.967128i \(0.581842\pi\)
\(258\) −2645.02 −0.638264
\(259\) −2450.87 −0.587992
\(260\) 0 0
\(261\) 1238.23 0.293657
\(262\) 1100.08 0.259402
\(263\) 7465.88 1.75044 0.875220 0.483724i \(-0.160716\pi\)
0.875220 + 0.483724i \(0.160716\pi\)
\(264\) 2502.09 0.583308
\(265\) 0 0
\(266\) 650.300 0.149896
\(267\) 2033.17 0.466023
\(268\) 2817.56 0.642202
\(269\) −6521.38 −1.47812 −0.739062 0.673637i \(-0.764731\pi\)
−0.739062 + 0.673637i \(0.764731\pi\)
\(270\) 0 0
\(271\) 2409.70 0.540144 0.270072 0.962840i \(-0.412952\pi\)
0.270072 + 0.962840i \(0.412952\pi\)
\(272\) −169.141 −0.0377046
\(273\) −609.328 −0.135085
\(274\) 1524.62 0.336151
\(275\) 0 0
\(276\) −2475.90 −0.539970
\(277\) 2219.83 0.481503 0.240752 0.970587i \(-0.422606\pi\)
0.240752 + 0.970587i \(0.422606\pi\)
\(278\) −3936.75 −0.849319
\(279\) 1391.93 0.298684
\(280\) 0 0
\(281\) 5838.56 1.23950 0.619749 0.784800i \(-0.287234\pi\)
0.619749 + 0.784800i \(0.287234\pi\)
\(282\) −2767.86 −0.584480
\(283\) 3645.04 0.765636 0.382818 0.923824i \(-0.374954\pi\)
0.382818 + 0.923824i \(0.374954\pi\)
\(284\) 614.269 0.128346
\(285\) 0 0
\(286\) −1846.66 −0.381802
\(287\) −2476.38 −0.509325
\(288\) 1649.83 0.337559
\(289\) −1500.25 −0.305363
\(290\) 0 0
\(291\) −3675.10 −0.740338
\(292\) 1453.10 0.291219
\(293\) −3777.91 −0.753268 −0.376634 0.926362i \(-0.622919\pi\)
−0.376634 + 0.926362i \(0.622919\pi\)
\(294\) −250.130 −0.0496186
\(295\) 0 0
\(296\) −7807.24 −1.53306
\(297\) −1009.88 −0.197304
\(298\) 1394.15 0.271011
\(299\) 4691.10 0.907336
\(300\) 0 0
\(301\) −3627.09 −0.694559
\(302\) 909.900 0.173374
\(303\) 1014.43 0.192335
\(304\) −158.075 −0.0298231
\(305\) 0 0
\(306\) −894.628 −0.167132
\(307\) 4799.64 0.892281 0.446140 0.894963i \(-0.352798\pi\)
0.446140 + 0.894963i \(0.352798\pi\)
\(308\) 1336.52 0.247257
\(309\) −1700.10 −0.312994
\(310\) 0 0
\(311\) 580.113 0.105772 0.0528861 0.998601i \(-0.483158\pi\)
0.0528861 + 0.998601i \(0.483158\pi\)
\(312\) −1941.01 −0.352205
\(313\) 6114.78 1.10424 0.552121 0.833764i \(-0.313818\pi\)
0.552121 + 0.833764i \(0.313818\pi\)
\(314\) −2662.53 −0.478521
\(315\) 0 0
\(316\) −4806.64 −0.855679
\(317\) 4300.63 0.761979 0.380989 0.924579i \(-0.375583\pi\)
0.380989 + 0.924579i \(0.375583\pi\)
\(318\) 1558.51 0.274833
\(319\) 5145.97 0.903194
\(320\) 0 0
\(321\) −1687.59 −0.293434
\(322\) 1925.70 0.333277
\(323\) 3189.48 0.549435
\(324\) −413.480 −0.0708984
\(325\) 0 0
\(326\) 1896.06 0.322126
\(327\) −5492.38 −0.928836
\(328\) −7888.49 −1.32795
\(329\) −3795.53 −0.636032
\(330\) 0 0
\(331\) −6687.54 −1.11051 −0.555257 0.831679i \(-0.687380\pi\)
−0.555257 + 0.831679i \(0.687380\pi\)
\(332\) 1925.23 0.318256
\(333\) 3151.12 0.518560
\(334\) 3019.37 0.494648
\(335\) 0 0
\(336\) 60.8016 0.00987202
\(337\) −5869.28 −0.948723 −0.474362 0.880330i \(-0.657321\pi\)
−0.474362 + 0.880330i \(0.657321\pi\)
\(338\) −2305.78 −0.371058
\(339\) −95.4097 −0.0152860
\(340\) 0 0
\(341\) 5784.74 0.918655
\(342\) −836.100 −0.132196
\(343\) −343.000 −0.0539949
\(344\) −11554.1 −1.81091
\(345\) 0 0
\(346\) 7173.58 1.11461
\(347\) −1937.22 −0.299699 −0.149850 0.988709i \(-0.547879\pi\)
−0.149850 + 0.988709i \(0.547879\pi\)
\(348\) 2106.93 0.324549
\(349\) −9748.82 −1.49525 −0.747625 0.664121i \(-0.768806\pi\)
−0.747625 + 0.664121i \(0.768806\pi\)
\(350\) 0 0
\(351\) 783.422 0.119134
\(352\) 6856.52 1.03822
\(353\) 4576.61 0.690052 0.345026 0.938593i \(-0.387870\pi\)
0.345026 + 0.938593i \(0.387870\pi\)
\(354\) −74.9433 −0.0112520
\(355\) 0 0
\(356\) 3459.57 0.515048
\(357\) −1226.79 −0.181873
\(358\) −4135.98 −0.610596
\(359\) 10849.9 1.59509 0.797546 0.603258i \(-0.206131\pi\)
0.797546 + 0.603258i \(0.206131\pi\)
\(360\) 0 0
\(361\) −3878.18 −0.565415
\(362\) −4595.77 −0.667261
\(363\) −203.981 −0.0294938
\(364\) −1036.81 −0.149296
\(365\) 0 0
\(366\) 873.252 0.124715
\(367\) −11467.7 −1.63108 −0.815541 0.578699i \(-0.803561\pi\)
−0.815541 + 0.578699i \(0.803561\pi\)
\(368\) −468.100 −0.0663081
\(369\) 3183.92 0.449182
\(370\) 0 0
\(371\) 2137.17 0.299073
\(372\) 2368.46 0.330105
\(373\) −539.982 −0.0749576 −0.0374788 0.999297i \(-0.511933\pi\)
−0.0374788 + 0.999297i \(0.511933\pi\)
\(374\) −3717.99 −0.514044
\(375\) 0 0
\(376\) −12090.6 −1.65832
\(377\) −3992.01 −0.545355
\(378\) 321.595 0.0437595
\(379\) 8577.57 1.16253 0.581267 0.813713i \(-0.302557\pi\)
0.581267 + 0.813713i \(0.302557\pi\)
\(380\) 0 0
\(381\) 6662.44 0.895871
\(382\) 6144.51 0.822985
\(383\) −8627.96 −1.15109 −0.575546 0.817770i \(-0.695210\pi\)
−0.575546 + 0.817770i \(0.695210\pi\)
\(384\) 2925.52 0.388782
\(385\) 0 0
\(386\) 7603.13 1.00256
\(387\) 4663.41 0.612543
\(388\) −6253.42 −0.818219
\(389\) 9234.06 1.20356 0.601781 0.798661i \(-0.294458\pi\)
0.601781 + 0.798661i \(0.294458\pi\)
\(390\) 0 0
\(391\) 9444.85 1.22160
\(392\) −1092.62 −0.140780
\(393\) −1939.54 −0.248948
\(394\) 739.196 0.0945182
\(395\) 0 0
\(396\) −1718.38 −0.218060
\(397\) −11618.0 −1.46874 −0.734372 0.678747i \(-0.762523\pi\)
−0.734372 + 0.678747i \(0.762523\pi\)
\(398\) −797.889 −0.100489
\(399\) −1146.53 −0.143856
\(400\) 0 0
\(401\) 11157.1 1.38942 0.694711 0.719289i \(-0.255532\pi\)
0.694711 + 0.719289i \(0.255532\pi\)
\(402\) 2817.56 0.349570
\(403\) −4487.54 −0.554690
\(404\) 1726.12 0.212568
\(405\) 0 0
\(406\) −1638.72 −0.200316
\(407\) 13095.8 1.59492
\(408\) −3907.94 −0.474196
\(409\) −7428.08 −0.898031 −0.449015 0.893524i \(-0.648225\pi\)
−0.449015 + 0.893524i \(0.648225\pi\)
\(410\) 0 0
\(411\) −2688.03 −0.322605
\(412\) −2892.83 −0.345921
\(413\) −102.769 −0.0122444
\(414\) −2475.90 −0.293922
\(415\) 0 0
\(416\) −5318.97 −0.626885
\(417\) 6940.83 0.815093
\(418\) −3474.75 −0.406592
\(419\) 9644.74 1.12453 0.562263 0.826959i \(-0.309931\pi\)
0.562263 + 0.826959i \(0.309931\pi\)
\(420\) 0 0
\(421\) 9918.18 1.14818 0.574088 0.818793i \(-0.305357\pi\)
0.574088 + 0.818793i \(0.305357\pi\)
\(422\) 6356.21 0.733212
\(423\) 4879.97 0.560927
\(424\) 6807.92 0.779769
\(425\) 0 0
\(426\) 614.269 0.0698625
\(427\) 1197.48 0.135715
\(428\) −2871.54 −0.324302
\(429\) 3255.82 0.366417
\(430\) 0 0
\(431\) −16324.1 −1.82437 −0.912185 0.409779i \(-0.865606\pi\)
−0.912185 + 0.409779i \(0.865606\pi\)
\(432\) −78.1735 −0.00870630
\(433\) 5168.75 0.573659 0.286829 0.957982i \(-0.407399\pi\)
0.286829 + 0.957982i \(0.407399\pi\)
\(434\) −1842.14 −0.203745
\(435\) 0 0
\(436\) −9345.63 −1.02655
\(437\) 8826.95 0.966248
\(438\) 1453.10 0.158520
\(439\) 18339.0 1.99378 0.996892 0.0787782i \(-0.0251019\pi\)
0.996892 + 0.0787782i \(0.0251019\pi\)
\(440\) 0 0
\(441\) 441.000 0.0476190
\(442\) 2884.24 0.310383
\(443\) 1613.28 0.173023 0.0865113 0.996251i \(-0.472428\pi\)
0.0865113 + 0.996251i \(0.472428\pi\)
\(444\) 5361.83 0.573111
\(445\) 0 0
\(446\) −1434.09 −0.152256
\(447\) −2458.01 −0.260089
\(448\) −2021.30 −0.213164
\(449\) −886.750 −0.0932034 −0.0466017 0.998914i \(-0.514839\pi\)
−0.0466017 + 0.998914i \(0.514839\pi\)
\(450\) 0 0
\(451\) 13232.1 1.38154
\(452\) −162.345 −0.0168940
\(453\) −1604.23 −0.166387
\(454\) −1688.21 −0.174518
\(455\) 0 0
\(456\) −3652.28 −0.375073
\(457\) −7391.22 −0.756557 −0.378279 0.925692i \(-0.623484\pi\)
−0.378279 + 0.925692i \(0.623484\pi\)
\(458\) −10909.4 −1.11302
\(459\) 1577.31 0.160397
\(460\) 0 0
\(461\) −7133.35 −0.720679 −0.360340 0.932821i \(-0.617339\pi\)
−0.360340 + 0.932821i \(0.617339\pi\)
\(462\) 1336.52 0.134590
\(463\) −14461.8 −1.45162 −0.725808 0.687897i \(-0.758534\pi\)
−0.725808 + 0.687897i \(0.758534\pi\)
\(464\) 398.341 0.0398546
\(465\) 0 0
\(466\) 3869.95 0.384704
\(467\) 16393.5 1.62441 0.812206 0.583370i \(-0.198266\pi\)
0.812206 + 0.583370i \(0.198266\pi\)
\(468\) 1333.04 0.131666
\(469\) 3863.69 0.380403
\(470\) 0 0
\(471\) 4694.28 0.459238
\(472\) −327.370 −0.0319246
\(473\) 19380.7 1.88398
\(474\) −4806.64 −0.465772
\(475\) 0 0
\(476\) −2087.47 −0.201006
\(477\) −2747.78 −0.263758
\(478\) 4871.77 0.466171
\(479\) −12991.4 −1.23923 −0.619617 0.784904i \(-0.712712\pi\)
−0.619617 + 0.784904i \(0.712712\pi\)
\(480\) 0 0
\(481\) −10159.1 −0.963025
\(482\) −9127.57 −0.862551
\(483\) −3395.17 −0.319846
\(484\) −347.087 −0.0325964
\(485\) 0 0
\(486\) −413.480 −0.0385922
\(487\) 12863.5 1.19692 0.598461 0.801152i \(-0.295779\pi\)
0.598461 + 0.801152i \(0.295779\pi\)
\(488\) 3814.57 0.353847
\(489\) −3342.92 −0.309145
\(490\) 0 0
\(491\) −4898.10 −0.450200 −0.225100 0.974336i \(-0.572271\pi\)
−0.225100 + 0.974336i \(0.572271\pi\)
\(492\) 5417.63 0.496435
\(493\) −8037.32 −0.734245
\(494\) 2695.55 0.245503
\(495\) 0 0
\(496\) 447.787 0.0405368
\(497\) 842.340 0.0760244
\(498\) 1925.23 0.173236
\(499\) 10308.0 0.924746 0.462373 0.886686i \(-0.346998\pi\)
0.462373 + 0.886686i \(0.346998\pi\)
\(500\) 0 0
\(501\) −5323.41 −0.474715
\(502\) 9477.37 0.842621
\(503\) 15119.6 1.34026 0.670130 0.742244i \(-0.266238\pi\)
0.670130 + 0.742244i \(0.266238\pi\)
\(504\) 1404.80 0.124156
\(505\) 0 0
\(506\) −10289.6 −0.904009
\(507\) 4065.28 0.356105
\(508\) 11336.6 0.990114
\(509\) 14183.8 1.23514 0.617571 0.786515i \(-0.288117\pi\)
0.617571 + 0.786515i \(0.288117\pi\)
\(510\) 0 0
\(511\) 1992.62 0.172501
\(512\) 1047.24 0.0903943
\(513\) 1474.12 0.126869
\(514\) −3565.39 −0.305958
\(515\) 0 0
\(516\) 7935.07 0.676981
\(517\) 20280.7 1.72523
\(518\) −4170.32 −0.353732
\(519\) −12647.6 −1.06969
\(520\) 0 0
\(521\) −7464.08 −0.627653 −0.313827 0.949480i \(-0.601611\pi\)
−0.313827 + 0.949480i \(0.601611\pi\)
\(522\) 2106.93 0.176662
\(523\) 16642.9 1.39148 0.695739 0.718295i \(-0.255077\pi\)
0.695739 + 0.718295i \(0.255077\pi\)
\(524\) −3300.24 −0.275137
\(525\) 0 0
\(526\) 12703.7 1.05305
\(527\) −9035.01 −0.746814
\(528\) −324.881 −0.0267777
\(529\) 13971.8 1.14834
\(530\) 0 0
\(531\) 132.132 0.0107985
\(532\) −1950.90 −0.158989
\(533\) −10264.8 −0.834181
\(534\) 3459.57 0.280356
\(535\) 0 0
\(536\) 12307.8 0.991818
\(537\) 7292.09 0.585991
\(538\) −11096.5 −0.889230
\(539\) 1832.75 0.146461
\(540\) 0 0
\(541\) 67.8755 0.00539408 0.00269704 0.999996i \(-0.499142\pi\)
0.00269704 + 0.999996i \(0.499142\pi\)
\(542\) 4100.26 0.324947
\(543\) 8102.74 0.640372
\(544\) −10709.0 −0.844014
\(545\) 0 0
\(546\) −1036.81 −0.0812662
\(547\) 9212.91 0.720138 0.360069 0.932926i \(-0.382753\pi\)
0.360069 + 0.932926i \(0.382753\pi\)
\(548\) −4573.85 −0.356542
\(549\) −1539.62 −0.119689
\(550\) 0 0
\(551\) −7511.51 −0.580764
\(552\) −10815.3 −0.833931
\(553\) −6591.29 −0.506854
\(554\) 3777.17 0.289669
\(555\) 0 0
\(556\) 11810.2 0.900838
\(557\) −16699.6 −1.27035 −0.635173 0.772370i \(-0.719071\pi\)
−0.635173 + 0.772370i \(0.719071\pi\)
\(558\) 2368.46 0.179686
\(559\) −15034.6 −1.13756
\(560\) 0 0
\(561\) 6555.13 0.493329
\(562\) 9934.67 0.745674
\(563\) −14772.8 −1.10586 −0.552931 0.833227i \(-0.686491\pi\)
−0.552931 + 0.833227i \(0.686491\pi\)
\(564\) 8303.57 0.619935
\(565\) 0 0
\(566\) 6202.26 0.460601
\(567\) −567.000 −0.0419961
\(568\) 2683.27 0.198217
\(569\) 5663.76 0.417289 0.208644 0.977992i \(-0.433095\pi\)
0.208644 + 0.977992i \(0.433095\pi\)
\(570\) 0 0
\(571\) 5579.58 0.408929 0.204464 0.978874i \(-0.434455\pi\)
0.204464 + 0.978874i \(0.434455\pi\)
\(572\) 5539.99 0.404962
\(573\) −10833.3 −0.789821
\(574\) −4213.72 −0.306406
\(575\) 0 0
\(576\) 2598.82 0.187993
\(577\) 2301.23 0.166034 0.0830170 0.996548i \(-0.473544\pi\)
0.0830170 + 0.996548i \(0.473544\pi\)
\(578\) −2552.77 −0.183704
\(579\) −13405.0 −0.962162
\(580\) 0 0
\(581\) 2640.05 0.188516
\(582\) −6253.42 −0.445382
\(583\) −11419.5 −0.811232
\(584\) 6347.46 0.449760
\(585\) 0 0
\(586\) −6428.34 −0.453161
\(587\) 16470.4 1.15810 0.579052 0.815291i \(-0.303423\pi\)
0.579052 + 0.815291i \(0.303423\pi\)
\(588\) 750.389 0.0526284
\(589\) −8443.92 −0.590706
\(590\) 0 0
\(591\) −1303.27 −0.0907093
\(592\) 1013.72 0.0703779
\(593\) 13570.0 0.939715 0.469858 0.882742i \(-0.344305\pi\)
0.469858 + 0.882742i \(0.344305\pi\)
\(594\) −1718.38 −0.118697
\(595\) 0 0
\(596\) −4182.46 −0.287450
\(597\) 1406.75 0.0964393
\(598\) 7982.20 0.545847
\(599\) 27814.1 1.89725 0.948625 0.316403i \(-0.102475\pi\)
0.948625 + 0.316403i \(0.102475\pi\)
\(600\) 0 0
\(601\) 20646.1 1.40128 0.700641 0.713514i \(-0.252898\pi\)
0.700641 + 0.713514i \(0.252898\pi\)
\(602\) −6171.72 −0.417842
\(603\) −4967.61 −0.335483
\(604\) −2729.70 −0.183891
\(605\) 0 0
\(606\) 1726.12 0.115707
\(607\) −3315.28 −0.221686 −0.110843 0.993838i \(-0.535355\pi\)
−0.110843 + 0.993838i \(0.535355\pi\)
\(608\) −10008.4 −0.667588
\(609\) 2889.21 0.192244
\(610\) 0 0
\(611\) −15732.8 −1.04170
\(612\) 2683.88 0.177271
\(613\) 11113.9 0.732278 0.366139 0.930560i \(-0.380680\pi\)
0.366139 + 0.930560i \(0.380680\pi\)
\(614\) 8166.89 0.536790
\(615\) 0 0
\(616\) 5838.22 0.381865
\(617\) −7871.34 −0.513595 −0.256797 0.966465i \(-0.582667\pi\)
−0.256797 + 0.966465i \(0.582667\pi\)
\(618\) −2892.83 −0.188295
\(619\) −19107.1 −1.24068 −0.620339 0.784334i \(-0.713005\pi\)
−0.620339 + 0.784334i \(0.713005\pi\)
\(620\) 0 0
\(621\) 4365.22 0.282078
\(622\) 987.098 0.0636319
\(623\) 4744.07 0.305084
\(624\) 252.028 0.0161686
\(625\) 0 0
\(626\) 10404.7 0.664305
\(627\) 6126.28 0.390208
\(628\) 7987.60 0.507548
\(629\) −20453.9 −1.29658
\(630\) 0 0
\(631\) −25769.9 −1.62580 −0.812902 0.582401i \(-0.802113\pi\)
−0.812902 + 0.582401i \(0.802113\pi\)
\(632\) −20996.5 −1.32151
\(633\) −11206.5 −0.703665
\(634\) 7317.79 0.458401
\(635\) 0 0
\(636\) −4675.53 −0.291504
\(637\) −1421.77 −0.0884339
\(638\) 8756.19 0.543355
\(639\) −1083.01 −0.0670472
\(640\) 0 0
\(641\) −1954.61 −0.120440 −0.0602202 0.998185i \(-0.519180\pi\)
−0.0602202 + 0.998185i \(0.519180\pi\)
\(642\) −2871.54 −0.176528
\(643\) 19396.5 1.18961 0.594807 0.803868i \(-0.297228\pi\)
0.594807 + 0.803868i \(0.297228\pi\)
\(644\) −5777.10 −0.353493
\(645\) 0 0
\(646\) 5427.10 0.330536
\(647\) −31264.3 −1.89973 −0.949865 0.312661i \(-0.898780\pi\)
−0.949865 + 0.312661i \(0.898780\pi\)
\(648\) −1806.17 −0.109496
\(649\) 549.126 0.0332127
\(650\) 0 0
\(651\) 3247.85 0.195535
\(652\) −5688.18 −0.341666
\(653\) −6442.75 −0.386102 −0.193051 0.981189i \(-0.561838\pi\)
−0.193051 + 0.981189i \(0.561838\pi\)
\(654\) −9345.63 −0.558781
\(655\) 0 0
\(656\) 1024.27 0.0609620
\(657\) −2561.93 −0.152132
\(658\) −6458.33 −0.382632
\(659\) −3584.70 −0.211897 −0.105949 0.994372i \(-0.533788\pi\)
−0.105949 + 0.994372i \(0.533788\pi\)
\(660\) 0 0
\(661\) 6294.43 0.370386 0.185193 0.982702i \(-0.440709\pi\)
0.185193 + 0.982702i \(0.440709\pi\)
\(662\) −11379.3 −0.668078
\(663\) −5085.17 −0.297876
\(664\) 8409.85 0.491514
\(665\) 0 0
\(666\) 5361.83 0.311962
\(667\) −22243.4 −1.29126
\(668\) −9058.11 −0.524654
\(669\) 2528.42 0.146120
\(670\) 0 0
\(671\) −6398.51 −0.368125
\(672\) 3849.60 0.220984
\(673\) 10233.9 0.586162 0.293081 0.956088i \(-0.405319\pi\)
0.293081 + 0.956088i \(0.405319\pi\)
\(674\) −9986.94 −0.570745
\(675\) 0 0
\(676\) 6917.33 0.393567
\(677\) 7100.75 0.403108 0.201554 0.979477i \(-0.435401\pi\)
0.201554 + 0.979477i \(0.435401\pi\)
\(678\) −162.345 −0.00919593
\(679\) −8575.24 −0.484665
\(680\) 0 0
\(681\) 2976.45 0.167486
\(682\) 9843.10 0.552657
\(683\) 35274.6 1.97620 0.988100 0.153813i \(-0.0491554\pi\)
0.988100 + 0.153813i \(0.0491554\pi\)
\(684\) 2508.30 0.140215
\(685\) 0 0
\(686\) −583.636 −0.0324830
\(687\) 19234.2 1.06817
\(688\) 1500.22 0.0831330
\(689\) 8858.74 0.489828
\(690\) 0 0
\(691\) 4945.12 0.272245 0.136122 0.990692i \(-0.456536\pi\)
0.136122 + 0.990692i \(0.456536\pi\)
\(692\) −21520.8 −1.18222
\(693\) −2356.40 −0.129166
\(694\) −3296.31 −0.180297
\(695\) 0 0
\(696\) 9203.54 0.501235
\(697\) −20666.7 −1.12311
\(698\) −16588.2 −0.899532
\(699\) −6823.06 −0.369201
\(700\) 0 0
\(701\) −15300.4 −0.824379 −0.412190 0.911098i \(-0.635236\pi\)
−0.412190 + 0.911098i \(0.635236\pi\)
\(702\) 1333.04 0.0716701
\(703\) −19115.7 −1.02555
\(704\) 10800.4 0.578206
\(705\) 0 0
\(706\) 7787.38 0.415130
\(707\) 2367.01 0.125913
\(708\) 224.830 0.0119345
\(709\) −28297.4 −1.49892 −0.749458 0.662052i \(-0.769686\pi\)
−0.749458 + 0.662052i \(0.769686\pi\)
\(710\) 0 0
\(711\) 8474.51 0.447003
\(712\) 15112.2 0.795441
\(713\) −25004.5 −1.31336
\(714\) −2087.47 −0.109414
\(715\) 0 0
\(716\) 12407.9 0.647635
\(717\) −8589.35 −0.447385
\(718\) 18461.9 0.959597
\(719\) 8548.96 0.443425 0.221712 0.975112i \(-0.428835\pi\)
0.221712 + 0.975112i \(0.428835\pi\)
\(720\) 0 0
\(721\) −3966.90 −0.204903
\(722\) −6598.97 −0.340150
\(723\) 16092.7 0.827792
\(724\) 13787.3 0.707737
\(725\) 0 0
\(726\) −347.087 −0.0177432
\(727\) −14345.3 −0.731827 −0.365913 0.930649i \(-0.619243\pi\)
−0.365913 + 0.930649i \(0.619243\pi\)
\(728\) −4529.02 −0.230572
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −30270.0 −1.53157
\(732\) −2619.76 −0.132280
\(733\) 22624.0 1.14002 0.570012 0.821637i \(-0.306939\pi\)
0.570012 + 0.821637i \(0.306939\pi\)
\(734\) −19512.9 −0.981248
\(735\) 0 0
\(736\) −29637.3 −1.48430
\(737\) −20644.9 −1.03184
\(738\) 5417.63 0.270225
\(739\) 14837.3 0.738566 0.369283 0.929317i \(-0.379603\pi\)
0.369283 + 0.929317i \(0.379603\pi\)
\(740\) 0 0
\(741\) −4752.49 −0.235610
\(742\) 3636.52 0.179920
\(743\) −13073.1 −0.645497 −0.322749 0.946485i \(-0.604607\pi\)
−0.322749 + 0.946485i \(0.604607\pi\)
\(744\) 10346.0 0.509815
\(745\) 0 0
\(746\) −918.813 −0.0450940
\(747\) −3394.35 −0.166255
\(748\) 11154.0 0.545226
\(749\) −3937.72 −0.192098
\(750\) 0 0
\(751\) 16213.3 0.787791 0.393895 0.919155i \(-0.371127\pi\)
0.393895 + 0.919155i \(0.371127\pi\)
\(752\) 1569.89 0.0761278
\(753\) −16709.4 −0.808665
\(754\) −6792.65 −0.328082
\(755\) 0 0
\(756\) −964.786 −0.0464139
\(757\) −19903.9 −0.955642 −0.477821 0.878457i \(-0.658573\pi\)
−0.477821 + 0.878457i \(0.658573\pi\)
\(758\) 14595.3 0.699372
\(759\) 18141.4 0.867580
\(760\) 0 0
\(761\) −30125.5 −1.43502 −0.717509 0.696549i \(-0.754718\pi\)
−0.717509 + 0.696549i \(0.754718\pi\)
\(762\) 11336.6 0.538950
\(763\) −12815.6 −0.608066
\(764\) −18433.5 −0.872907
\(765\) 0 0
\(766\) −14681.0 −0.692489
\(767\) −425.986 −0.0200541
\(768\) 11908.1 0.559503
\(769\) −36049.1 −1.69046 −0.845230 0.534402i \(-0.820537\pi\)
−0.845230 + 0.534402i \(0.820537\pi\)
\(770\) 0 0
\(771\) 6286.09 0.293629
\(772\) −22809.4 −1.06338
\(773\) 9644.77 0.448769 0.224384 0.974501i \(-0.427963\pi\)
0.224384 + 0.974501i \(0.427963\pi\)
\(774\) 7935.07 0.368502
\(775\) 0 0
\(776\) −27316.4 −1.26366
\(777\) 7352.62 0.339477
\(778\) 15712.3 0.724054
\(779\) −19314.7 −0.888344
\(780\) 0 0
\(781\) −4500.88 −0.206215
\(782\) 16071.0 0.734908
\(783\) −3714.69 −0.169543
\(784\) 141.870 0.00646275
\(785\) 0 0
\(786\) −3300.24 −0.149766
\(787\) 25218.6 1.14224 0.571122 0.820865i \(-0.306508\pi\)
0.571122 + 0.820865i \(0.306508\pi\)
\(788\) −2217.59 −0.100252
\(789\) −22397.6 −1.01062
\(790\) 0 0
\(791\) −222.623 −0.0100070
\(792\) −7506.28 −0.336773
\(793\) 4963.67 0.222276
\(794\) −19768.8 −0.883586
\(795\) 0 0
\(796\) 2393.67 0.106584
\(797\) −32042.3 −1.42409 −0.712044 0.702135i \(-0.752230\pi\)
−0.712044 + 0.702135i \(0.752230\pi\)
\(798\) −1950.90 −0.0865427
\(799\) −31675.7 −1.40251
\(800\) 0 0
\(801\) −6099.52 −0.269059
\(802\) 18984.5 0.835867
\(803\) −10647.1 −0.467908
\(804\) −8452.69 −0.370775
\(805\) 0 0
\(806\) −7635.82 −0.333698
\(807\) 19564.1 0.853396
\(808\) 7540.07 0.328291
\(809\) 3427.90 0.148972 0.0744860 0.997222i \(-0.476268\pi\)
0.0744860 + 0.997222i \(0.476268\pi\)
\(810\) 0 0
\(811\) 23094.4 0.999943 0.499972 0.866042i \(-0.333344\pi\)
0.499972 + 0.866042i \(0.333344\pi\)
\(812\) 4916.16 0.212467
\(813\) −7229.11 −0.311852
\(814\) 22283.3 0.959494
\(815\) 0 0
\(816\) 507.422 0.0217688
\(817\) −28289.7 −1.21142
\(818\) −12639.3 −0.540249
\(819\) 1827.98 0.0779914
\(820\) 0 0
\(821\) 474.741 0.0201810 0.0100905 0.999949i \(-0.496788\pi\)
0.0100905 + 0.999949i \(0.496788\pi\)
\(822\) −4573.85 −0.194077
\(823\) −24159.8 −1.02328 −0.511638 0.859201i \(-0.670961\pi\)
−0.511638 + 0.859201i \(0.670961\pi\)
\(824\) −12636.5 −0.534240
\(825\) 0 0
\(826\) −174.868 −0.00736613
\(827\) 7566.35 0.318147 0.159074 0.987267i \(-0.449149\pi\)
0.159074 + 0.987267i \(0.449149\pi\)
\(828\) 7427.70 0.311752
\(829\) −10580.9 −0.443295 −0.221648 0.975127i \(-0.571143\pi\)
−0.221648 + 0.975127i \(0.571143\pi\)
\(830\) 0 0
\(831\) −6659.48 −0.277996
\(832\) −8378.49 −0.349125
\(833\) −2862.52 −0.119064
\(834\) 11810.2 0.490354
\(835\) 0 0
\(836\) 10424.2 0.431256
\(837\) −4175.80 −0.172445
\(838\) 16411.1 0.676507
\(839\) 15315.6 0.630218 0.315109 0.949055i \(-0.397959\pi\)
0.315109 + 0.949055i \(0.397959\pi\)
\(840\) 0 0
\(841\) −5460.40 −0.223888
\(842\) 16876.4 0.690735
\(843\) −17515.7 −0.715625
\(844\) −19068.6 −0.777688
\(845\) 0 0
\(846\) 8303.57 0.337450
\(847\) −475.956 −0.0193082
\(848\) −883.966 −0.0357966
\(849\) −10935.1 −0.442040
\(850\) 0 0
\(851\) −56606.4 −2.28019
\(852\) −1842.81 −0.0741004
\(853\) −18598.2 −0.746528 −0.373264 0.927725i \(-0.621761\pi\)
−0.373264 + 0.927725i \(0.621761\pi\)
\(854\) 2037.59 0.0816450
\(855\) 0 0
\(856\) −12543.6 −0.500853
\(857\) −41775.3 −1.66513 −0.832566 0.553926i \(-0.813129\pi\)
−0.832566 + 0.553926i \(0.813129\pi\)
\(858\) 5539.99 0.220434
\(859\) 32414.7 1.28752 0.643758 0.765229i \(-0.277374\pi\)
0.643758 + 0.765229i \(0.277374\pi\)
\(860\) 0 0
\(861\) 7429.14 0.294059
\(862\) −27776.4 −1.09753
\(863\) 31299.7 1.23459 0.617297 0.786730i \(-0.288228\pi\)
0.617297 + 0.786730i \(0.288228\pi\)
\(864\) −4949.48 −0.194890
\(865\) 0 0
\(866\) 8794.94 0.345109
\(867\) 4500.75 0.176302
\(868\) 5526.41 0.216104
\(869\) 35219.2 1.37483
\(870\) 0 0
\(871\) 16015.4 0.623030
\(872\) −40823.8 −1.58540
\(873\) 11025.3 0.427434
\(874\) 15019.6 0.581288
\(875\) 0 0
\(876\) −4359.29 −0.168136
\(877\) 19973.0 0.769031 0.384515 0.923119i \(-0.374369\pi\)
0.384515 + 0.923119i \(0.374369\pi\)
\(878\) 31204.9 1.19945
\(879\) 11333.7 0.434900
\(880\) 0 0
\(881\) 17367.9 0.664176 0.332088 0.943248i \(-0.392247\pi\)
0.332088 + 0.943248i \(0.392247\pi\)
\(882\) 750.389 0.0286473
\(883\) 14364.2 0.547446 0.273723 0.961809i \(-0.411745\pi\)
0.273723 + 0.961809i \(0.411745\pi\)
\(884\) −8652.73 −0.329211
\(885\) 0 0
\(886\) 2745.09 0.104089
\(887\) 33738.1 1.27713 0.638564 0.769568i \(-0.279529\pi\)
0.638564 + 0.769568i \(0.279529\pi\)
\(888\) 23421.7 0.885114
\(889\) 15545.7 0.586485
\(890\) 0 0
\(891\) 3029.65 0.113914
\(892\) 4302.26 0.161491
\(893\) −29603.4 −1.10934
\(894\) −4182.46 −0.156468
\(895\) 0 0
\(896\) 6826.21 0.254518
\(897\) −14073.3 −0.523850
\(898\) −1508.86 −0.0560705
\(899\) 21278.2 0.789398
\(900\) 0 0
\(901\) 17835.8 0.659485
\(902\) 22515.2 0.831123
\(903\) 10881.3 0.401004
\(904\) −709.162 −0.0260911
\(905\) 0 0
\(906\) −2729.70 −0.100097
\(907\) 32998.6 1.20805 0.604024 0.796966i \(-0.293563\pi\)
0.604024 + 0.796966i \(0.293563\pi\)
\(908\) 5064.62 0.185105
\(909\) −3043.29 −0.111045
\(910\) 0 0
\(911\) 33446.3 1.21638 0.608192 0.793790i \(-0.291895\pi\)
0.608192 + 0.793790i \(0.291895\pi\)
\(912\) 474.225 0.0172184
\(913\) −14106.6 −0.511347
\(914\) −12576.6 −0.455139
\(915\) 0 0
\(916\) 32728.2 1.18053
\(917\) −4525.59 −0.162975
\(918\) 2683.88 0.0964939
\(919\) 41708.7 1.49711 0.748554 0.663074i \(-0.230748\pi\)
0.748554 + 0.663074i \(0.230748\pi\)
\(920\) 0 0
\(921\) −14398.9 −0.515158
\(922\) −12137.8 −0.433556
\(923\) 3491.58 0.124514
\(924\) −4009.56 −0.142754
\(925\) 0 0
\(926\) −24607.7 −0.873283
\(927\) 5100.30 0.180707
\(928\) 25220.6 0.892140
\(929\) 49024.6 1.73137 0.865686 0.500587i \(-0.166883\pi\)
0.865686 + 0.500587i \(0.166883\pi\)
\(930\) 0 0
\(931\) −2675.25 −0.0941758
\(932\) −11609.9 −0.408040
\(933\) −1740.34 −0.0610677
\(934\) 27894.6 0.977235
\(935\) 0 0
\(936\) 5823.03 0.203346
\(937\) 5447.58 0.189930 0.0949651 0.995481i \(-0.469726\pi\)
0.0949651 + 0.995481i \(0.469726\pi\)
\(938\) 6574.31 0.228848
\(939\) −18344.4 −0.637535
\(940\) 0 0
\(941\) 4125.75 0.142928 0.0714642 0.997443i \(-0.477233\pi\)
0.0714642 + 0.997443i \(0.477233\pi\)
\(942\) 7987.60 0.276274
\(943\) −57195.5 −1.97513
\(944\) 42.5069 0.00146555
\(945\) 0 0
\(946\) 32977.4 1.13339
\(947\) −17332.3 −0.594747 −0.297374 0.954761i \(-0.596111\pi\)
−0.297374 + 0.954761i \(0.596111\pi\)
\(948\) 14419.9 0.494026
\(949\) 8259.57 0.282526
\(950\) 0 0
\(951\) −12901.9 −0.439929
\(952\) −9118.53 −0.310434
\(953\) −56839.4 −1.93201 −0.966007 0.258517i \(-0.916766\pi\)
−0.966007 + 0.258517i \(0.916766\pi\)
\(954\) −4675.53 −0.158675
\(955\) 0 0
\(956\) −14615.3 −0.494449
\(957\) −15437.9 −0.521459
\(958\) −22105.7 −0.745515
\(959\) −6272.07 −0.211195
\(960\) 0 0
\(961\) −5871.48 −0.197089
\(962\) −17286.3 −0.579349
\(963\) 5062.78 0.169414
\(964\) 27382.7 0.914873
\(965\) 0 0
\(966\) −5777.10 −0.192417
\(967\) 13284.2 0.441769 0.220884 0.975300i \(-0.429106\pi\)
0.220884 + 0.975300i \(0.429106\pi\)
\(968\) −1516.15 −0.0503420
\(969\) −9568.44 −0.317216
\(970\) 0 0
\(971\) 12153.0 0.401658 0.200829 0.979626i \(-0.435636\pi\)
0.200829 + 0.979626i \(0.435636\pi\)
\(972\) 1240.44 0.0409332
\(973\) 16195.3 0.533604
\(974\) 21888.1 0.720060
\(975\) 0 0
\(976\) −495.298 −0.0162440
\(977\) 37999.3 1.24433 0.622163 0.782888i \(-0.286254\pi\)
0.622163 + 0.782888i \(0.286254\pi\)
\(978\) −5688.18 −0.185980
\(979\) −25349.0 −0.827537
\(980\) 0 0
\(981\) 16477.1 0.536264
\(982\) −8334.42 −0.270837
\(983\) −22375.0 −0.725993 −0.362996 0.931791i \(-0.618246\pi\)
−0.362996 + 0.931791i \(0.618246\pi\)
\(984\) 23665.5 0.766695
\(985\) 0 0
\(986\) −13676.0 −0.441717
\(987\) 11386.6 0.367213
\(988\) −8086.65 −0.260395
\(989\) −83772.9 −2.69345
\(990\) 0 0
\(991\) 18985.3 0.608564 0.304282 0.952582i \(-0.401583\pi\)
0.304282 + 0.952582i \(0.401583\pi\)
\(992\) 28351.2 0.907412
\(993\) 20062.6 0.641156
\(994\) 1433.29 0.0457358
\(995\) 0 0
\(996\) −5775.70 −0.183745
\(997\) 56476.5 1.79401 0.897006 0.442019i \(-0.145738\pi\)
0.897006 + 0.442019i \(0.145738\pi\)
\(998\) 17539.6 0.556321
\(999\) −9453.37 −0.299391
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 525.4.a.i.1.2 2
3.2 odd 2 1575.4.a.y.1.1 2
5.2 odd 4 525.4.d.j.274.3 4
5.3 odd 4 525.4.d.j.274.2 4
5.4 even 2 105.4.a.g.1.1 2
15.14 odd 2 315.4.a.g.1.2 2
20.19 odd 2 1680.4.a.y.1.1 2
35.34 odd 2 735.4.a.q.1.1 2
105.104 even 2 2205.4.a.v.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.g.1.1 2 5.4 even 2
315.4.a.g.1.2 2 15.14 odd 2
525.4.a.i.1.2 2 1.1 even 1 trivial
525.4.d.j.274.2 4 5.3 odd 4
525.4.d.j.274.3 4 5.2 odd 4
735.4.a.q.1.1 2 35.34 odd 2
1575.4.a.y.1.1 2 3.2 odd 2
1680.4.a.y.1.1 2 20.19 odd 2
2205.4.a.v.1.2 2 105.104 even 2