Properties

Label 177.4.a.b.1.4
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 41 x^{5} - 7 x^{4} + 484 x^{3} + 63 x^{2} - 1736 x - 44\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.0253269\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0253269 q^{2} -3.00000 q^{3} -7.99936 q^{4} +8.85515 q^{5} -0.0759806 q^{6} +13.8749 q^{7} -0.405214 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+0.0253269 q^{2} -3.00000 q^{3} -7.99936 q^{4} +8.85515 q^{5} -0.0759806 q^{6} +13.8749 q^{7} -0.405214 q^{8} +9.00000 q^{9} +0.224273 q^{10} -33.5949 q^{11} +23.9981 q^{12} -15.9269 q^{13} +0.351408 q^{14} -26.5655 q^{15} +63.9846 q^{16} -14.1822 q^{17} +0.227942 q^{18} -111.821 q^{19} -70.8356 q^{20} -41.6247 q^{21} -0.850854 q^{22} -188.829 q^{23} +1.21564 q^{24} -46.5862 q^{25} -0.403379 q^{26} -27.0000 q^{27} -110.990 q^{28} -56.6729 q^{29} -0.672820 q^{30} -18.4624 q^{31} +4.86224 q^{32} +100.785 q^{33} -0.359190 q^{34} +122.864 q^{35} -71.9942 q^{36} +53.8076 q^{37} -2.83209 q^{38} +47.7807 q^{39} -3.58823 q^{40} -68.8886 q^{41} -1.05422 q^{42} -344.210 q^{43} +268.738 q^{44} +79.6964 q^{45} -4.78246 q^{46} +291.289 q^{47} -191.954 q^{48} -150.487 q^{49} -1.17988 q^{50} +42.5466 q^{51} +127.405 q^{52} +636.830 q^{53} -0.683826 q^{54} -297.488 q^{55} -5.62230 q^{56} +335.464 q^{57} -1.43535 q^{58} +59.0000 q^{59} +212.507 q^{60} -489.425 q^{61} -0.467594 q^{62} +124.874 q^{63} -511.754 q^{64} -141.035 q^{65} +2.55256 q^{66} +91.2469 q^{67} +113.448 q^{68} +566.488 q^{69} +3.11177 q^{70} +179.941 q^{71} -3.64692 q^{72} -414.334 q^{73} +1.36278 q^{74} +139.759 q^{75} +894.500 q^{76} -466.126 q^{77} +1.21014 q^{78} -889.652 q^{79} +566.594 q^{80} +81.0000 q^{81} -1.74473 q^{82} +812.868 q^{83} +332.971 q^{84} -125.585 q^{85} -8.71778 q^{86} +170.019 q^{87} +13.6131 q^{88} -623.403 q^{89} +2.01846 q^{90} -220.984 q^{91} +1510.51 q^{92} +55.3871 q^{93} +7.37743 q^{94} -990.196 q^{95} -14.5867 q^{96} +1229.07 q^{97} -3.81137 q^{98} -302.354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} - 71q^{10} - 5q^{11} - 78q^{12} - 67q^{13} - 65q^{14} + 6q^{15} - 94q^{16} - 23q^{17} - 176q^{19} - 207q^{20} + 177q^{21} - 704q^{22} - 218q^{23} + 63q^{24} - 183q^{25} + 58q^{26} - 189q^{27} - 938q^{28} + 168q^{29} + 213q^{30} - 604q^{31} - 448q^{32} + 15q^{33} - 610q^{34} - 336q^{35} + 234q^{36} - 505q^{37} - 453q^{38} + 201q^{39} - 1080q^{40} - 265q^{41} + 195q^{42} - 493q^{43} + 504q^{44} - 18q^{45} + 381q^{46} - 244q^{47} + 282q^{48} + 770q^{49} + 1639q^{50} + 69q^{51} + 160q^{52} + 686q^{53} - 116q^{55} + 2190q^{56} + 528q^{57} + 1584q^{58} + 413q^{59} + 621q^{60} - 838q^{61} + 286q^{62} - 531q^{63} + 205q^{64} + 490q^{65} + 2112q^{66} - 1504q^{67} + 3047q^{68} + 654q^{69} + 1530q^{70} - 1267q^{71} - 189q^{72} - 666q^{73} + 528q^{74} + 549q^{75} - 64q^{76} + 1109q^{77} - 174q^{78} - 2741q^{79} + 1213q^{80} + 567q^{81} + 953q^{82} - 2025q^{83} + 2814q^{84} - 1274q^{85} + 4394q^{86} - 504q^{87} - 1639q^{88} + 616q^{89} - 639q^{90} - 2415q^{91} + 218q^{92} + 1812q^{93} + 900q^{94} + 2554q^{95} + 1344q^{96} - 1298q^{97} - 172q^{98} - 45q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0253269 0.00895440 0.00447720 0.999990i \(-0.498575\pi\)
0.00447720 + 0.999990i \(0.498575\pi\)
\(3\) −3.00000 −0.577350
\(4\) −7.99936 −0.999920
\(5\) 8.85515 0.792029 0.396015 0.918244i \(-0.370393\pi\)
0.396015 + 0.918244i \(0.370393\pi\)
\(6\) −0.0759806 −0.00516983
\(7\) 13.8749 0.749174 0.374587 0.927192i \(-0.377784\pi\)
0.374587 + 0.927192i \(0.377784\pi\)
\(8\) −0.405214 −0.0179081
\(9\) 9.00000 0.333333
\(10\) 0.224273 0.00709215
\(11\) −33.5949 −0.920841 −0.460420 0.887701i \(-0.652301\pi\)
−0.460420 + 0.887701i \(0.652301\pi\)
\(12\) 23.9981 0.577304
\(13\) −15.9269 −0.339794 −0.169897 0.985462i \(-0.554344\pi\)
−0.169897 + 0.985462i \(0.554344\pi\)
\(14\) 0.351408 0.00670841
\(15\) −26.5655 −0.457278
\(16\) 63.9846 0.999759
\(17\) −14.1822 −0.202334 −0.101167 0.994869i \(-0.532258\pi\)
−0.101167 + 0.994869i \(0.532258\pi\)
\(18\) 0.227942 0.00298480
\(19\) −111.821 −1.35019 −0.675095 0.737731i \(-0.735897\pi\)
−0.675095 + 0.737731i \(0.735897\pi\)
\(20\) −70.8356 −0.791966
\(21\) −41.6247 −0.432536
\(22\) −0.850854 −0.00824558
\(23\) −188.829 −1.71190 −0.855949 0.517060i \(-0.827026\pi\)
−0.855949 + 0.517060i \(0.827026\pi\)
\(24\) 1.21564 0.0103392
\(25\) −46.5862 −0.372690
\(26\) −0.403379 −0.00304266
\(27\) −27.0000 −0.192450
\(28\) −110.990 −0.749114
\(29\) −56.6729 −0.362893 −0.181446 0.983401i \(-0.558078\pi\)
−0.181446 + 0.983401i \(0.558078\pi\)
\(30\) −0.672820 −0.00409465
\(31\) −18.4624 −0.106966 −0.0534829 0.998569i \(-0.517032\pi\)
−0.0534829 + 0.998569i \(0.517032\pi\)
\(32\) 4.86224 0.0268603
\(33\) 100.785 0.531648
\(34\) −0.359190 −0.00181178
\(35\) 122.864 0.593368
\(36\) −71.9942 −0.333307
\(37\) 53.8076 0.239079 0.119539 0.992829i \(-0.461858\pi\)
0.119539 + 0.992829i \(0.461858\pi\)
\(38\) −2.83209 −0.0120901
\(39\) 47.7807 0.196180
\(40\) −3.58823 −0.0141837
\(41\) −68.8886 −0.262405 −0.131202 0.991356i \(-0.541884\pi\)
−0.131202 + 0.991356i \(0.541884\pi\)
\(42\) −1.05422 −0.00387310
\(43\) −344.210 −1.22073 −0.610367 0.792118i \(-0.708978\pi\)
−0.610367 + 0.792118i \(0.708978\pi\)
\(44\) 268.738 0.920767
\(45\) 79.6964 0.264010
\(46\) −4.78246 −0.0153290
\(47\) 291.289 0.904017 0.452009 0.892014i \(-0.350708\pi\)
0.452009 + 0.892014i \(0.350708\pi\)
\(48\) −191.954 −0.577211
\(49\) −150.487 −0.438738
\(50\) −1.17988 −0.00333721
\(51\) 42.5466 0.116818
\(52\) 127.405 0.339767
\(53\) 636.830 1.65048 0.825238 0.564785i \(-0.191041\pi\)
0.825238 + 0.564785i \(0.191041\pi\)
\(54\) −0.683826 −0.00172328
\(55\) −297.488 −0.729333
\(56\) −5.62230 −0.0134163
\(57\) 335.464 0.779532
\(58\) −1.43535 −0.00324949
\(59\) 59.0000 0.130189
\(60\) 212.507 0.457242
\(61\) −489.425 −1.02729 −0.513643 0.858004i \(-0.671704\pi\)
−0.513643 + 0.858004i \(0.671704\pi\)
\(62\) −0.467594 −0.000957814 0
\(63\) 124.874 0.249725
\(64\) −511.754 −0.999519
\(65\) −141.035 −0.269127
\(66\) 2.55256 0.00476059
\(67\) 91.2469 0.166382 0.0831909 0.996534i \(-0.473489\pi\)
0.0831909 + 0.996534i \(0.473489\pi\)
\(68\) 113.448 0.202318
\(69\) 566.488 0.988365
\(70\) 3.11177 0.00531325
\(71\) 179.941 0.300776 0.150388 0.988627i \(-0.451948\pi\)
0.150388 + 0.988627i \(0.451948\pi\)
\(72\) −3.64692 −0.00596936
\(73\) −414.334 −0.664304 −0.332152 0.943226i \(-0.607775\pi\)
−0.332152 + 0.943226i \(0.607775\pi\)
\(74\) 1.36278 0.00214081
\(75\) 139.759 0.215173
\(76\) 894.500 1.35008
\(77\) −466.126 −0.689870
\(78\) 1.21014 0.00175668
\(79\) −889.652 −1.26701 −0.633504 0.773739i \(-0.718384\pi\)
−0.633504 + 0.773739i \(0.718384\pi\)
\(80\) 566.594 0.791839
\(81\) 81.0000 0.111111
\(82\) −1.74473 −0.00234968
\(83\) 812.868 1.07499 0.537493 0.843268i \(-0.319371\pi\)
0.537493 + 0.843268i \(0.319371\pi\)
\(84\) 332.971 0.432501
\(85\) −125.585 −0.160255
\(86\) −8.71778 −0.0109310
\(87\) 170.019 0.209516
\(88\) 13.6131 0.0164905
\(89\) −623.403 −0.742479 −0.371240 0.928537i \(-0.621067\pi\)
−0.371240 + 0.928537i \(0.621067\pi\)
\(90\) 2.01846 0.00236405
\(91\) −220.984 −0.254565
\(92\) 1510.51 1.71176
\(93\) 55.3871 0.0617567
\(94\) 7.37743 0.00809493
\(95\) −990.196 −1.06939
\(96\) −14.5867 −0.0155078
\(97\) 1229.07 1.28653 0.643266 0.765643i \(-0.277579\pi\)
0.643266 + 0.765643i \(0.277579\pi\)
\(98\) −3.81137 −0.00392864
\(99\) −302.354 −0.306947
\(100\) 372.660 0.372660
\(101\) 792.722 0.780978 0.390489 0.920608i \(-0.372306\pi\)
0.390489 + 0.920608i \(0.372306\pi\)
\(102\) 1.07757 0.00104603
\(103\) 56.2822 0.0538413 0.0269206 0.999638i \(-0.491430\pi\)
0.0269206 + 0.999638i \(0.491430\pi\)
\(104\) 6.45380 0.00608507
\(105\) −368.593 −0.342581
\(106\) 16.1289 0.0147790
\(107\) −342.964 −0.309865 −0.154933 0.987925i \(-0.549516\pi\)
−0.154933 + 0.987925i \(0.549516\pi\)
\(108\) 215.983 0.192435
\(109\) 1581.04 1.38932 0.694662 0.719336i \(-0.255554\pi\)
0.694662 + 0.719336i \(0.255554\pi\)
\(110\) −7.53444 −0.00653074
\(111\) −161.423 −0.138032
\(112\) 887.780 0.748994
\(113\) −142.494 −0.118626 −0.0593128 0.998239i \(-0.518891\pi\)
−0.0593128 + 0.998239i \(0.518891\pi\)
\(114\) 8.49626 0.00698024
\(115\) −1672.11 −1.35587
\(116\) 453.346 0.362863
\(117\) −143.342 −0.113265
\(118\) 1.49429 0.00116576
\(119\) −196.776 −0.151584
\(120\) 10.7647 0.00818898
\(121\) −202.382 −0.152053
\(122\) −12.3956 −0.00919873
\(123\) 206.666 0.151500
\(124\) 147.687 0.106957
\(125\) −1519.42 −1.08721
\(126\) 3.16267 0.00223614
\(127\) −1616.84 −1.12970 −0.564848 0.825195i \(-0.691065\pi\)
−0.564848 + 0.825195i \(0.691065\pi\)
\(128\) −51.8590 −0.0358104
\(129\) 1032.63 0.704792
\(130\) −3.57198 −0.00240987
\(131\) −617.730 −0.411995 −0.205998 0.978553i \(-0.566044\pi\)
−0.205998 + 0.978553i \(0.566044\pi\)
\(132\) −806.213 −0.531605
\(133\) −1551.51 −1.01153
\(134\) 2.31100 0.00148985
\(135\) −239.089 −0.152426
\(136\) 5.74682 0.00362342
\(137\) 149.739 0.0933798 0.0466899 0.998909i \(-0.485133\pi\)
0.0466899 + 0.998909i \(0.485133\pi\)
\(138\) 14.3474 0.00885022
\(139\) −1014.64 −0.619139 −0.309569 0.950877i \(-0.600185\pi\)
−0.309569 + 0.950877i \(0.600185\pi\)
\(140\) −982.836 −0.593320
\(141\) −873.866 −0.521935
\(142\) 4.55734 0.00269327
\(143\) 535.063 0.312897
\(144\) 575.861 0.333253
\(145\) −501.847 −0.287422
\(146\) −10.4938 −0.00594844
\(147\) 451.462 0.253306
\(148\) −430.426 −0.239060
\(149\) 1456.96 0.801066 0.400533 0.916282i \(-0.368825\pi\)
0.400533 + 0.916282i \(0.368825\pi\)
\(150\) 3.53965 0.00192674
\(151\) 620.816 0.334578 0.167289 0.985908i \(-0.446499\pi\)
0.167289 + 0.985908i \(0.446499\pi\)
\(152\) 45.3116 0.0241793
\(153\) −127.640 −0.0674448
\(154\) −11.8055 −0.00617737
\(155\) −163.487 −0.0847200
\(156\) −382.215 −0.196165
\(157\) 2085.11 1.05993 0.529967 0.848018i \(-0.322204\pi\)
0.529967 + 0.848018i \(0.322204\pi\)
\(158\) −22.5321 −0.0113453
\(159\) −1910.49 −0.952903
\(160\) 43.0559 0.0212742
\(161\) −2619.99 −1.28251
\(162\) 2.05148 0.000994934 0
\(163\) −3928.28 −1.88765 −0.943823 0.330451i \(-0.892799\pi\)
−0.943823 + 0.330451i \(0.892799\pi\)
\(164\) 551.065 0.262384
\(165\) 892.464 0.421080
\(166\) 20.5874 0.00962586
\(167\) −1209.74 −0.560552 −0.280276 0.959919i \(-0.590426\pi\)
−0.280276 + 0.959919i \(0.590426\pi\)
\(168\) 16.8669 0.00774589
\(169\) −1943.33 −0.884540
\(170\) −3.18069 −0.00143499
\(171\) −1006.39 −0.450063
\(172\) 2753.46 1.22064
\(173\) 920.080 0.404349 0.202174 0.979350i \(-0.435199\pi\)
0.202174 + 0.979350i \(0.435199\pi\)
\(174\) 4.30604 0.00187609
\(175\) −646.379 −0.279210
\(176\) −2149.56 −0.920619
\(177\) −177.000 −0.0751646
\(178\) −15.7889 −0.00664846
\(179\) 4056.88 1.69400 0.846999 0.531594i \(-0.178407\pi\)
0.846999 + 0.531594i \(0.178407\pi\)
\(180\) −637.520 −0.263989
\(181\) 2038.25 0.837026 0.418513 0.908211i \(-0.362551\pi\)
0.418513 + 0.908211i \(0.362551\pi\)
\(182\) −5.59684 −0.00227948
\(183\) 1468.27 0.593104
\(184\) 76.5163 0.0306568
\(185\) 476.475 0.189357
\(186\) 1.40278 0.000552994 0
\(187\) 476.449 0.186318
\(188\) −2330.12 −0.903945
\(189\) −374.622 −0.144179
\(190\) −25.0786 −0.00957574
\(191\) −1362.37 −0.516115 −0.258057 0.966130i \(-0.583082\pi\)
−0.258057 + 0.966130i \(0.583082\pi\)
\(192\) 1535.26 0.577073
\(193\) −2837.51 −1.05828 −0.529142 0.848533i \(-0.677486\pi\)
−0.529142 + 0.848533i \(0.677486\pi\)
\(194\) 31.1286 0.0115201
\(195\) 423.106 0.155381
\(196\) 1203.80 0.438703
\(197\) 4236.08 1.53202 0.766011 0.642828i \(-0.222239\pi\)
0.766011 + 0.642828i \(0.222239\pi\)
\(198\) −7.65769 −0.00274853
\(199\) 2678.88 0.954274 0.477137 0.878829i \(-0.341675\pi\)
0.477137 + 0.878829i \(0.341675\pi\)
\(200\) 18.8774 0.00667416
\(201\) −273.741 −0.0960606
\(202\) 20.0772 0.00699319
\(203\) −786.330 −0.271870
\(204\) −340.345 −0.116808
\(205\) −610.020 −0.207832
\(206\) 1.42545 0.000482116 0
\(207\) −1699.46 −0.570633
\(208\) −1019.08 −0.339713
\(209\) 3756.63 1.24331
\(210\) −9.33531 −0.00306761
\(211\) −4807.45 −1.56852 −0.784262 0.620430i \(-0.786958\pi\)
−0.784262 + 0.620430i \(0.786958\pi\)
\(212\) −5094.23 −1.65034
\(213\) −539.823 −0.173653
\(214\) −8.68621 −0.00277466
\(215\) −3048.04 −0.966858
\(216\) 10.9408 0.00344641
\(217\) −256.163 −0.0801360
\(218\) 40.0428 0.0124406
\(219\) 1243.00 0.383536
\(220\) 2379.71 0.729274
\(221\) 225.878 0.0687521
\(222\) −4.08833 −0.00123600
\(223\) 3465.13 1.04055 0.520274 0.853999i \(-0.325830\pi\)
0.520274 + 0.853999i \(0.325830\pi\)
\(224\) 67.4631 0.0201231
\(225\) −419.276 −0.124230
\(226\) −3.60892 −0.00106222
\(227\) −759.521 −0.222076 −0.111038 0.993816i \(-0.535417\pi\)
−0.111038 + 0.993816i \(0.535417\pi\)
\(228\) −2683.50 −0.779470
\(229\) 6541.52 1.88767 0.943834 0.330419i \(-0.107190\pi\)
0.943834 + 0.330419i \(0.107190\pi\)
\(230\) −42.3494 −0.0121410
\(231\) 1398.38 0.398297
\(232\) 22.9646 0.00649871
\(233\) −6389.44 −1.79651 −0.898254 0.439477i \(-0.855164\pi\)
−0.898254 + 0.439477i \(0.855164\pi\)
\(234\) −3.63041 −0.00101422
\(235\) 2579.41 0.716008
\(236\) −471.962 −0.130178
\(237\) 2668.96 0.731508
\(238\) −4.98373 −0.00135734
\(239\) 1601.37 0.433406 0.216703 0.976238i \(-0.430470\pi\)
0.216703 + 0.976238i \(0.430470\pi\)
\(240\) −1699.78 −0.457168
\(241\) 5739.23 1.53401 0.767004 0.641642i \(-0.221746\pi\)
0.767004 + 0.641642i \(0.221746\pi\)
\(242\) −5.12570 −0.00136154
\(243\) −243.000 −0.0641500
\(244\) 3915.08 1.02720
\(245\) −1332.59 −0.347493
\(246\) 5.23420 0.00135659
\(247\) 1780.97 0.458787
\(248\) 7.48120 0.00191555
\(249\) −2438.60 −0.620643
\(250\) −38.4822 −0.00973532
\(251\) −2418.34 −0.608145 −0.304072 0.952649i \(-0.598347\pi\)
−0.304072 + 0.952649i \(0.598347\pi\)
\(252\) −998.913 −0.249705
\(253\) 6343.71 1.57639
\(254\) −40.9495 −0.0101158
\(255\) 376.756 0.0925231
\(256\) 4092.72 0.999198
\(257\) 2849.27 0.691566 0.345783 0.938314i \(-0.387613\pi\)
0.345783 + 0.938314i \(0.387613\pi\)
\(258\) 26.1533 0.00631099
\(259\) 746.575 0.179112
\(260\) 1128.19 0.269106
\(261\) −510.056 −0.120964
\(262\) −15.6452 −0.00368917
\(263\) 6916.57 1.62165 0.810825 0.585289i \(-0.199019\pi\)
0.810825 + 0.585289i \(0.199019\pi\)
\(264\) −40.8394 −0.00952079
\(265\) 5639.22 1.30723
\(266\) −39.2949 −0.00905762
\(267\) 1870.21 0.428670
\(268\) −729.916 −0.166368
\(269\) 5951.84 1.34903 0.674517 0.738260i \(-0.264352\pi\)
0.674517 + 0.738260i \(0.264352\pi\)
\(270\) −6.05538 −0.00136488
\(271\) −2810.97 −0.630089 −0.315044 0.949077i \(-0.602019\pi\)
−0.315044 + 0.949077i \(0.602019\pi\)
\(272\) −907.441 −0.202286
\(273\) 662.953 0.146973
\(274\) 3.79241 0.000836161 0
\(275\) 1565.06 0.343188
\(276\) −4531.54 −0.988285
\(277\) −2077.94 −0.450727 −0.225363 0.974275i \(-0.572357\pi\)
−0.225363 + 0.974275i \(0.572357\pi\)
\(278\) −25.6976 −0.00554402
\(279\) −166.161 −0.0356553
\(280\) −49.7863 −0.0106261
\(281\) 3252.61 0.690513 0.345257 0.938508i \(-0.387792\pi\)
0.345257 + 0.938508i \(0.387792\pi\)
\(282\) −22.1323 −0.00467361
\(283\) −2305.82 −0.484335 −0.242167 0.970234i \(-0.577858\pi\)
−0.242167 + 0.970234i \(0.577858\pi\)
\(284\) −1439.41 −0.300751
\(285\) 2970.59 0.617412
\(286\) 13.5515 0.00280180
\(287\) −955.823 −0.196587
\(288\) 43.7602 0.00895345
\(289\) −4711.87 −0.959061
\(290\) −12.7102 −0.00257369
\(291\) −3687.22 −0.742779
\(292\) 3314.41 0.664250
\(293\) −5556.39 −1.10788 −0.553939 0.832558i \(-0.686876\pi\)
−0.553939 + 0.832558i \(0.686876\pi\)
\(294\) 11.4341 0.00226820
\(295\) 522.454 0.103113
\(296\) −21.8036 −0.00428144
\(297\) 907.063 0.177216
\(298\) 36.9003 0.00717307
\(299\) 3007.47 0.581693
\(300\) −1117.98 −0.215155
\(301\) −4775.89 −0.914543
\(302\) 15.7233 0.00299595
\(303\) −2378.17 −0.450898
\(304\) −7154.85 −1.34986
\(305\) −4333.93 −0.813640
\(306\) −3.23271 −0.000603928 0
\(307\) −4370.47 −0.812494 −0.406247 0.913763i \(-0.633163\pi\)
−0.406247 + 0.913763i \(0.633163\pi\)
\(308\) 3728.71 0.689815
\(309\) −168.847 −0.0310853
\(310\) −4.14062 −0.000758617 0
\(311\) −6394.69 −1.16595 −0.582974 0.812491i \(-0.698111\pi\)
−0.582974 + 0.812491i \(0.698111\pi\)
\(312\) −19.3614 −0.00351322
\(313\) 1266.98 0.228798 0.114399 0.993435i \(-0.463506\pi\)
0.114399 + 0.993435i \(0.463506\pi\)
\(314\) 52.8093 0.00949108
\(315\) 1105.78 0.197789
\(316\) 7116.64 1.26691
\(317\) −236.906 −0.0419746 −0.0209873 0.999780i \(-0.506681\pi\)
−0.0209873 + 0.999780i \(0.506681\pi\)
\(318\) −48.3867 −0.00853268
\(319\) 1903.92 0.334166
\(320\) −4531.66 −0.791648
\(321\) 1028.89 0.178901
\(322\) −66.3561 −0.0114841
\(323\) 1585.87 0.273190
\(324\) −647.948 −0.111102
\(325\) 741.974 0.126638
\(326\) −99.4910 −0.0169027
\(327\) −4743.12 −0.802126
\(328\) 27.9146 0.00469917
\(329\) 4041.60 0.677266
\(330\) 22.6033 0.00377052
\(331\) −549.458 −0.0912415 −0.0456208 0.998959i \(-0.514527\pi\)
−0.0456208 + 0.998959i \(0.514527\pi\)
\(332\) −6502.42 −1.07490
\(333\) 484.268 0.0796929
\(334\) −30.6388 −0.00501941
\(335\) 808.005 0.131779
\(336\) −2663.34 −0.432432
\(337\) −4347.11 −0.702677 −0.351339 0.936248i \(-0.614273\pi\)
−0.351339 + 0.936248i \(0.614273\pi\)
\(338\) −49.2186 −0.00792052
\(339\) 427.481 0.0684885
\(340\) 1004.60 0.160242
\(341\) 620.241 0.0984984
\(342\) −25.4888 −0.00403005
\(343\) −6847.08 −1.07787
\(344\) 139.479 0.0218610
\(345\) 5016.34 0.782814
\(346\) 23.3027 0.00362070
\(347\) 4628.06 0.715987 0.357993 0.933724i \(-0.383461\pi\)
0.357993 + 0.933724i \(0.383461\pi\)
\(348\) −1360.04 −0.209499
\(349\) 3589.52 0.550552 0.275276 0.961365i \(-0.411231\pi\)
0.275276 + 0.961365i \(0.411231\pi\)
\(350\) −16.3708 −0.00250015
\(351\) 430.026 0.0653935
\(352\) −163.347 −0.0247341
\(353\) −6895.16 −1.03964 −0.519819 0.854276i \(-0.674001\pi\)
−0.519819 + 0.854276i \(0.674001\pi\)
\(354\) −4.48286 −0.000673054 0
\(355\) 1593.41 0.238223
\(356\) 4986.83 0.742420
\(357\) 590.329 0.0875169
\(358\) 102.748 0.0151687
\(359\) −4916.16 −0.722744 −0.361372 0.932422i \(-0.617692\pi\)
−0.361372 + 0.932422i \(0.617692\pi\)
\(360\) −32.2941 −0.00472791
\(361\) 5645.03 0.823011
\(362\) 51.6224 0.00749507
\(363\) 607.146 0.0877876
\(364\) 1767.73 0.254545
\(365\) −3669.00 −0.526148
\(366\) 37.1868 0.00531089
\(367\) 3909.42 0.556050 0.278025 0.960574i \(-0.410320\pi\)
0.278025 + 0.960574i \(0.410320\pi\)
\(368\) −12082.2 −1.71149
\(369\) −619.998 −0.0874683
\(370\) 12.0676 0.00169558
\(371\) 8835.95 1.23649
\(372\) −443.061 −0.0617518
\(373\) −12322.0 −1.71048 −0.855238 0.518236i \(-0.826589\pi\)
−0.855238 + 0.518236i \(0.826589\pi\)
\(374\) 12.0670 0.00166836
\(375\) 4558.27 0.627701
\(376\) −118.034 −0.0161892
\(377\) 902.623 0.123309
\(378\) −9.48801 −0.00129103
\(379\) −2231.61 −0.302453 −0.151227 0.988499i \(-0.548322\pi\)
−0.151227 + 0.988499i \(0.548322\pi\)
\(380\) 7920.93 1.06930
\(381\) 4850.52 0.652230
\(382\) −34.5047 −0.00462150
\(383\) 6278.86 0.837689 0.418845 0.908058i \(-0.362435\pi\)
0.418845 + 0.908058i \(0.362435\pi\)
\(384\) 155.577 0.0206752
\(385\) −4127.62 −0.546397
\(386\) −71.8653 −0.00947630
\(387\) −3097.89 −0.406912
\(388\) −9831.80 −1.28643
\(389\) 5321.38 0.693585 0.346792 0.937942i \(-0.387271\pi\)
0.346792 + 0.937942i \(0.387271\pi\)
\(390\) 10.7159 0.00139134
\(391\) 2678.01 0.346376
\(392\) 60.9795 0.00785696
\(393\) 1853.19 0.237865
\(394\) 107.287 0.0137183
\(395\) −7878.01 −1.00351
\(396\) 2418.64 0.306922
\(397\) −14422.3 −1.82326 −0.911630 0.411011i \(-0.865176\pi\)
−0.911630 + 0.411011i \(0.865176\pi\)
\(398\) 67.8476 0.00854495
\(399\) 4654.53 0.584005
\(400\) −2980.80 −0.372600
\(401\) 5306.39 0.660820 0.330410 0.943838i \(-0.392813\pi\)
0.330410 + 0.943838i \(0.392813\pi\)
\(402\) −6.93299 −0.000860165 0
\(403\) 294.048 0.0363464
\(404\) −6341.27 −0.780915
\(405\) 717.268 0.0880032
\(406\) −19.9153 −0.00243443
\(407\) −1807.66 −0.220153
\(408\) −17.2404 −0.00209198
\(409\) −8289.85 −1.00222 −0.501108 0.865385i \(-0.667074\pi\)
−0.501108 + 0.865385i \(0.667074\pi\)
\(410\) −15.4499 −0.00186101
\(411\) −449.216 −0.0539129
\(412\) −450.222 −0.0538370
\(413\) 818.619 0.0975342
\(414\) −43.0421 −0.00510967
\(415\) 7198.07 0.851420
\(416\) −77.4404 −0.00912699
\(417\) 3043.91 0.357460
\(418\) 95.1437 0.0111331
\(419\) −14094.4 −1.64333 −0.821666 0.569969i \(-0.806955\pi\)
−0.821666 + 0.569969i \(0.806955\pi\)
\(420\) 2948.51 0.342554
\(421\) 4731.09 0.547694 0.273847 0.961773i \(-0.411704\pi\)
0.273847 + 0.961773i \(0.411704\pi\)
\(422\) −121.758 −0.0140452
\(423\) 2621.60 0.301339
\(424\) −258.052 −0.0295569
\(425\) 660.695 0.0754080
\(426\) −13.6720 −0.00155496
\(427\) −6790.72 −0.769616
\(428\) 2743.49 0.309841
\(429\) −1605.19 −0.180651
\(430\) −77.1973 −0.00865763
\(431\) −5813.25 −0.649685 −0.324843 0.945768i \(-0.605311\pi\)
−0.324843 + 0.945768i \(0.605311\pi\)
\(432\) −1727.58 −0.192404
\(433\) −6041.84 −0.670559 −0.335280 0.942119i \(-0.608831\pi\)
−0.335280 + 0.942119i \(0.608831\pi\)
\(434\) −6.48782 −0.000717570 0
\(435\) 1505.54 0.165943
\(436\) −12647.3 −1.38921
\(437\) 21115.2 2.31139
\(438\) 31.4814 0.00343433
\(439\) −900.540 −0.0979053 −0.0489526 0.998801i \(-0.515588\pi\)
−0.0489526 + 0.998801i \(0.515588\pi\)
\(440\) 120.546 0.0130610
\(441\) −1354.38 −0.146246
\(442\) 5.72079 0.000615634 0
\(443\) −883.492 −0.0947538 −0.0473769 0.998877i \(-0.515086\pi\)
−0.0473769 + 0.998877i \(0.515086\pi\)
\(444\) 1291.28 0.138021
\(445\) −5520.33 −0.588065
\(446\) 87.7609 0.00931748
\(447\) −4370.88 −0.462496
\(448\) −7100.53 −0.748814
\(449\) 2759.86 0.290079 0.145040 0.989426i \(-0.453669\pi\)
0.145040 + 0.989426i \(0.453669\pi\)
\(450\) −10.6190 −0.00111240
\(451\) 2314.31 0.241633
\(452\) 1139.86 0.118616
\(453\) −1862.45 −0.193169
\(454\) −19.2363 −0.00198856
\(455\) −1956.85 −0.201623
\(456\) −135.935 −0.0139599
\(457\) 953.929 0.0976432 0.0488216 0.998808i \(-0.484453\pi\)
0.0488216 + 0.998808i \(0.484453\pi\)
\(458\) 165.676 0.0169029
\(459\) 382.919 0.0389393
\(460\) 13375.8 1.35576
\(461\) −615.985 −0.0622327 −0.0311163 0.999516i \(-0.509906\pi\)
−0.0311163 + 0.999516i \(0.509906\pi\)
\(462\) 35.4165 0.00356651
\(463\) 571.209 0.0573355 0.0286677 0.999589i \(-0.490874\pi\)
0.0286677 + 0.999589i \(0.490874\pi\)
\(464\) −3626.19 −0.362805
\(465\) 490.461 0.0489131
\(466\) −161.825 −0.0160867
\(467\) −15066.7 −1.49294 −0.746470 0.665419i \(-0.768253\pi\)
−0.746470 + 0.665419i \(0.768253\pi\)
\(468\) 1146.65 0.113256
\(469\) 1266.04 0.124649
\(470\) 65.3283 0.00641142
\(471\) −6255.32 −0.611953
\(472\) −23.9076 −0.00233143
\(473\) 11563.7 1.12410
\(474\) 67.5963 0.00655021
\(475\) 5209.34 0.503202
\(476\) 1574.08 0.151572
\(477\) 5731.47 0.550159
\(478\) 40.5577 0.00388089
\(479\) 10104.3 0.963840 0.481920 0.876215i \(-0.339940\pi\)
0.481920 + 0.876215i \(0.339940\pi\)
\(480\) −129.168 −0.0122826
\(481\) −856.988 −0.0812376
\(482\) 145.357 0.0137361
\(483\) 7859.97 0.740457
\(484\) 1618.93 0.152040
\(485\) 10883.6 1.01897
\(486\) −6.15443 −0.000574425 0
\(487\) −13243.9 −1.23232 −0.616160 0.787621i \(-0.711313\pi\)
−0.616160 + 0.787621i \(0.711313\pi\)
\(488\) 198.322 0.0183967
\(489\) 11784.8 1.08983
\(490\) −33.7503 −0.00311160
\(491\) −1801.88 −0.165616 −0.0828081 0.996566i \(-0.526389\pi\)
−0.0828081 + 0.996566i \(0.526389\pi\)
\(492\) −1653.19 −0.151487
\(493\) 803.745 0.0734257
\(494\) 45.1064 0.00410816
\(495\) −2677.39 −0.243111
\(496\) −1181.31 −0.106940
\(497\) 2496.66 0.225333
\(498\) −61.7622 −0.00555749
\(499\) 18836.7 1.68987 0.844937 0.534867i \(-0.179638\pi\)
0.844937 + 0.534867i \(0.179638\pi\)
\(500\) 12154.4 1.08712
\(501\) 3629.21 0.323635
\(502\) −61.2490 −0.00544557
\(503\) 11244.9 0.996786 0.498393 0.866951i \(-0.333924\pi\)
0.498393 + 0.866951i \(0.333924\pi\)
\(504\) −50.6007 −0.00447209
\(505\) 7019.67 0.618557
\(506\) 160.666 0.0141156
\(507\) 5830.00 0.510689
\(508\) 12933.7 1.12961
\(509\) 5157.16 0.449091 0.224545 0.974464i \(-0.427910\pi\)
0.224545 + 0.974464i \(0.427910\pi\)
\(510\) 9.54206 0.000828489 0
\(511\) −5748.85 −0.497679
\(512\) 518.528 0.0447577
\(513\) 3019.18 0.259844
\(514\) 72.1631 0.00619256
\(515\) 498.388 0.0426439
\(516\) −8260.39 −0.704735
\(517\) −9785.81 −0.832456
\(518\) 18.9084 0.00160384
\(519\) −2760.24 −0.233451
\(520\) 57.1494 0.00481955
\(521\) −20667.2 −1.73790 −0.868952 0.494896i \(-0.835206\pi\)
−0.868952 + 0.494896i \(0.835206\pi\)
\(522\) −12.9181 −0.00108316
\(523\) −22161.5 −1.85288 −0.926439 0.376445i \(-0.877146\pi\)
−0.926439 + 0.376445i \(0.877146\pi\)
\(524\) 4941.45 0.411962
\(525\) 1939.14 0.161202
\(526\) 175.175 0.0145209
\(527\) 261.837 0.0216429
\(528\) 6448.67 0.531520
\(529\) 23489.5 1.93059
\(530\) 142.824 0.0117054
\(531\) 531.000 0.0433963
\(532\) 12411.1 1.01145
\(533\) 1097.18 0.0891637
\(534\) 47.3666 0.00383849
\(535\) −3037.00 −0.245422
\(536\) −36.9745 −0.00297958
\(537\) −12170.7 −0.978031
\(538\) 150.741 0.0120798
\(539\) 5055.60 0.404008
\(540\) 1912.56 0.152414
\(541\) 3396.28 0.269903 0.134952 0.990852i \(-0.456912\pi\)
0.134952 + 0.990852i \(0.456912\pi\)
\(542\) −71.1930 −0.00564207
\(543\) −6114.74 −0.483257
\(544\) −68.9572 −0.00543477
\(545\) 14000.4 1.10038
\(546\) 16.7905 0.00131606
\(547\) 4790.05 0.374420 0.187210 0.982320i \(-0.440055\pi\)
0.187210 + 0.982320i \(0.440055\pi\)
\(548\) −1197.81 −0.0933724
\(549\) −4404.82 −0.342429
\(550\) 39.6381 0.00307304
\(551\) 6337.24 0.489974
\(552\) −229.549 −0.0176997
\(553\) −12343.8 −0.949210
\(554\) −52.6277 −0.00403599
\(555\) −1429.42 −0.109326
\(556\) 8116.44 0.619089
\(557\) 17592.3 1.33825 0.669127 0.743148i \(-0.266668\pi\)
0.669127 + 0.743148i \(0.266668\pi\)
\(558\) −4.20835 −0.000319271 0
\(559\) 5482.21 0.414799
\(560\) 7861.43 0.593225
\(561\) −1429.35 −0.107571
\(562\) 82.3784 0.00618313
\(563\) −22917.8 −1.71558 −0.857789 0.514002i \(-0.828162\pi\)
−0.857789 + 0.514002i \(0.828162\pi\)
\(564\) 6990.36 0.521893
\(565\) −1261.80 −0.0939549
\(566\) −58.3992 −0.00433693
\(567\) 1123.87 0.0832416
\(568\) −72.9146 −0.00538631
\(569\) 3650.54 0.268961 0.134480 0.990916i \(-0.457063\pi\)
0.134480 + 0.990916i \(0.457063\pi\)
\(570\) 75.2357 0.00552856
\(571\) 5473.59 0.401160 0.200580 0.979677i \(-0.435717\pi\)
0.200580 + 0.979677i \(0.435717\pi\)
\(572\) −4280.16 −0.312871
\(573\) 4087.12 0.297979
\(574\) −24.2080 −0.00176032
\(575\) 8796.85 0.638007
\(576\) −4605.78 −0.333173
\(577\) 11228.4 0.810129 0.405065 0.914288i \(-0.367249\pi\)
0.405065 + 0.914288i \(0.367249\pi\)
\(578\) −119.337 −0.00858782
\(579\) 8512.54 0.611000
\(580\) 4014.45 0.287398
\(581\) 11278.5 0.805352
\(582\) −93.3858 −0.00665115
\(583\) −21394.2 −1.51983
\(584\) 167.894 0.0118964
\(585\) −1269.32 −0.0897090
\(586\) −140.726 −0.00992038
\(587\) −21794.4 −1.53246 −0.766228 0.642569i \(-0.777869\pi\)
−0.766228 + 0.642569i \(0.777869\pi\)
\(588\) −3611.40 −0.253285
\(589\) 2064.49 0.144424
\(590\) 13.2321 0.000923319 0
\(591\) −12708.2 −0.884513
\(592\) 3442.86 0.239021
\(593\) 10553.5 0.730824 0.365412 0.930846i \(-0.380928\pi\)
0.365412 + 0.930846i \(0.380928\pi\)
\(594\) 22.9731 0.00158686
\(595\) −1742.49 −0.120059
\(596\) −11654.8 −0.801002
\(597\) −8036.63 −0.550950
\(598\) 76.1698 0.00520872
\(599\) −12542.5 −0.855544 −0.427772 0.903887i \(-0.640701\pi\)
−0.427772 + 0.903887i \(0.640701\pi\)
\(600\) −56.6321 −0.00385333
\(601\) −19080.4 −1.29502 −0.647508 0.762059i \(-0.724189\pi\)
−0.647508 + 0.762059i \(0.724189\pi\)
\(602\) −120.958 −0.00818919
\(603\) 821.222 0.0554606
\(604\) −4966.13 −0.334551
\(605\) −1792.12 −0.120430
\(606\) −60.2315 −0.00403752
\(607\) 3062.83 0.204805 0.102402 0.994743i \(-0.467347\pi\)
0.102402 + 0.994743i \(0.467347\pi\)
\(608\) −543.703 −0.0362665
\(609\) 2358.99 0.156964
\(610\) −109.765 −0.00728566
\(611\) −4639.32 −0.307180
\(612\) 1021.04 0.0674394
\(613\) −757.895 −0.0499366 −0.0249683 0.999688i \(-0.507948\pi\)
−0.0249683 + 0.999688i \(0.507948\pi\)
\(614\) −110.690 −0.00727540
\(615\) 1830.06 0.119992
\(616\) 188.881 0.0123543
\(617\) −29721.4 −1.93928 −0.969641 0.244531i \(-0.921366\pi\)
−0.969641 + 0.244531i \(0.921366\pi\)
\(618\) −4.27636 −0.000278350 0
\(619\) −16540.8 −1.07404 −0.537021 0.843569i \(-0.680450\pi\)
−0.537021 + 0.843569i \(0.680450\pi\)
\(620\) 1307.79 0.0847132
\(621\) 5098.39 0.329455
\(622\) −161.958 −0.0104404
\(623\) −8649.66 −0.556246
\(624\) 3057.23 0.196133
\(625\) −7631.44 −0.488412
\(626\) 32.0886 0.00204875
\(627\) −11269.9 −0.717825
\(628\) −16679.5 −1.05985
\(629\) −763.109 −0.0483739
\(630\) 28.0059 0.00177108
\(631\) 3442.24 0.217169 0.108584 0.994087i \(-0.465368\pi\)
0.108584 + 0.994087i \(0.465368\pi\)
\(632\) 360.499 0.0226897
\(633\) 14422.3 0.905587
\(634\) −6.00009 −0.000375858 0
\(635\) −14317.4 −0.894752
\(636\) 15282.7 0.952827
\(637\) 2396.80 0.149081
\(638\) 48.2203 0.00299226
\(639\) 1619.47 0.100259
\(640\) −459.220 −0.0283629
\(641\) −1578.29 −0.0972524 −0.0486262 0.998817i \(-0.515484\pi\)
−0.0486262 + 0.998817i \(0.515484\pi\)
\(642\) 26.0586 0.00160195
\(643\) −23885.3 −1.46492 −0.732460 0.680810i \(-0.761628\pi\)
−0.732460 + 0.680810i \(0.761628\pi\)
\(644\) 20958.2 1.28241
\(645\) 9144.11 0.558216
\(646\) 40.1652 0.00244625
\(647\) −28377.5 −1.72432 −0.862161 0.506634i \(-0.830889\pi\)
−0.862161 + 0.506634i \(0.830889\pi\)
\(648\) −32.8223 −0.00198979
\(649\) −1982.10 −0.119883
\(650\) 18.7919 0.00113397
\(651\) 768.490 0.0462665
\(652\) 31423.7 1.88749
\(653\) −3579.86 −0.214534 −0.107267 0.994230i \(-0.534210\pi\)
−0.107267 + 0.994230i \(0.534210\pi\)
\(654\) −120.129 −0.00718256
\(655\) −5470.10 −0.326312
\(656\) −4407.81 −0.262342
\(657\) −3729.01 −0.221435
\(658\) 102.361 0.00606451
\(659\) 27873.3 1.64763 0.823816 0.566857i \(-0.191841\pi\)
0.823816 + 0.566857i \(0.191841\pi\)
\(660\) −7139.14 −0.421047
\(661\) −10031.8 −0.590307 −0.295154 0.955450i \(-0.595371\pi\)
−0.295154 + 0.955450i \(0.595371\pi\)
\(662\) −13.9161 −0.000817013 0
\(663\) −677.635 −0.0396941
\(664\) −329.385 −0.0192509
\(665\) −13738.9 −0.801159
\(666\) 12.2650 0.000713602 0
\(667\) 10701.5 0.621235
\(668\) 9677.11 0.560507
\(669\) −10395.4 −0.600761
\(670\) 20.4642 0.00118000
\(671\) 16442.2 0.945966
\(672\) −202.389 −0.0116181
\(673\) −1426.11 −0.0816828 −0.0408414 0.999166i \(-0.513004\pi\)
−0.0408414 + 0.999166i \(0.513004\pi\)
\(674\) −110.099 −0.00629206
\(675\) 1257.83 0.0717242
\(676\) 15545.4 0.884469
\(677\) 17441.8 0.990165 0.495082 0.868846i \(-0.335138\pi\)
0.495082 + 0.868846i \(0.335138\pi\)
\(678\) 10.8268 0.000613273 0
\(679\) 17053.3 0.963836
\(680\) 50.8889 0.00286986
\(681\) 2278.56 0.128216
\(682\) 15.7088 0.000881994 0
\(683\) −6216.52 −0.348270 −0.174135 0.984722i \(-0.555713\pi\)
−0.174135 + 0.984722i \(0.555713\pi\)
\(684\) 8050.50 0.450027
\(685\) 1325.96 0.0739596
\(686\) −173.415 −0.00965164
\(687\) −19624.6 −1.08985
\(688\) −22024.2 −1.22044
\(689\) −10142.7 −0.560823
\(690\) 127.048 0.00700963
\(691\) 21688.1 1.19400 0.597001 0.802240i \(-0.296359\pi\)
0.597001 + 0.802240i \(0.296359\pi\)
\(692\) −7360.05 −0.404317
\(693\) −4195.13 −0.229957
\(694\) 117.214 0.00641123
\(695\) −8984.76 −0.490376
\(696\) −68.8939 −0.00375203
\(697\) 976.991 0.0530935
\(698\) 90.9113 0.00492986
\(699\) 19168.3 1.03721
\(700\) 5170.62 0.279187
\(701\) −29389.5 −1.58349 −0.791744 0.610853i \(-0.790827\pi\)
−0.791744 + 0.610853i \(0.790827\pi\)
\(702\) 10.8912 0.000585560 0
\(703\) −6016.84 −0.322802
\(704\) 17192.3 0.920398
\(705\) −7738.22 −0.413387
\(706\) −174.633 −0.00930934
\(707\) 10998.9 0.585088
\(708\) 1415.89 0.0751586
\(709\) −8186.60 −0.433645 −0.216823 0.976211i \(-0.569569\pi\)
−0.216823 + 0.976211i \(0.569569\pi\)
\(710\) 40.3560 0.00213314
\(711\) −8006.87 −0.422336
\(712\) 252.612 0.0132964
\(713\) 3486.24 0.183114
\(714\) 14.9512 0.000783661 0
\(715\) 4738.07 0.247823
\(716\) −32452.5 −1.69386
\(717\) −4804.11 −0.250227
\(718\) −124.511 −0.00647174
\(719\) −28735.1 −1.49046 −0.745229 0.666808i \(-0.767660\pi\)
−0.745229 + 0.666808i \(0.767660\pi\)
\(720\) 5099.34 0.263946
\(721\) 780.910 0.0403365
\(722\) 142.971 0.00736957
\(723\) −17217.7 −0.885660
\(724\) −16304.7 −0.836959
\(725\) 2640.17 0.135246
\(726\) 15.3771 0.000786086 0
\(727\) −12141.5 −0.619397 −0.309698 0.950835i \(-0.600228\pi\)
−0.309698 + 0.950835i \(0.600228\pi\)
\(728\) 89.5458 0.00455878
\(729\) 729.000 0.0370370
\(730\) −92.9242 −0.00471134
\(731\) 4881.66 0.246997
\(732\) −11745.3 −0.593056
\(733\) 20396.0 1.02775 0.513877 0.857864i \(-0.328209\pi\)
0.513877 + 0.857864i \(0.328209\pi\)
\(734\) 99.0135 0.00497909
\(735\) 3997.76 0.200625
\(736\) −918.134 −0.0459822
\(737\) −3065.43 −0.153211
\(738\) −15.7026 −0.000783226 0
\(739\) 15016.7 0.747492 0.373746 0.927531i \(-0.378073\pi\)
0.373746 + 0.927531i \(0.378073\pi\)
\(740\) −3811.49 −0.189342
\(741\) −5342.91 −0.264881
\(742\) 223.787 0.0110721
\(743\) 8964.84 0.442649 0.221324 0.975200i \(-0.428962\pi\)
0.221324 + 0.975200i \(0.428962\pi\)
\(744\) −22.4436 −0.00110594
\(745\) 12901.6 0.634468
\(746\) −312.077 −0.0153163
\(747\) 7315.81 0.358329
\(748\) −3811.29 −0.186303
\(749\) −4758.59 −0.232143
\(750\) 115.447 0.00562069
\(751\) 6506.21 0.316132 0.158066 0.987429i \(-0.449474\pi\)
0.158066 + 0.987429i \(0.449474\pi\)
\(752\) 18638.0 0.903800
\(753\) 7255.03 0.351113
\(754\) 22.8606 0.00110416
\(755\) 5497.42 0.264996
\(756\) 2996.74 0.144167
\(757\) −1562.84 −0.0750364 −0.0375182 0.999296i \(-0.511945\pi\)
−0.0375182 + 0.999296i \(0.511945\pi\)
\(758\) −56.5196 −0.00270829
\(759\) −19031.1 −0.910126
\(760\) 401.241 0.0191507
\(761\) −2971.60 −0.141551 −0.0707757 0.997492i \(-0.522547\pi\)
−0.0707757 + 0.997492i \(0.522547\pi\)
\(762\) 122.849 0.00584033
\(763\) 21936.8 1.04085
\(764\) 10898.1 0.516073
\(765\) −1130.27 −0.0534182
\(766\) 159.024 0.00750100
\(767\) −939.687 −0.0442375
\(768\) −12278.1 −0.576887
\(769\) 18566.0 0.870619 0.435310 0.900281i \(-0.356639\pi\)
0.435310 + 0.900281i \(0.356639\pi\)
\(770\) −104.540 −0.00489266
\(771\) −8547.81 −0.399276
\(772\) 22698.3 1.05820
\(773\) −4922.01 −0.229020 −0.114510 0.993422i \(-0.536530\pi\)
−0.114510 + 0.993422i \(0.536530\pi\)
\(774\) −78.4600 −0.00364365
\(775\) 860.092 0.0398650
\(776\) −498.038 −0.0230393
\(777\) −2239.72 −0.103410
\(778\) 134.774 0.00621064
\(779\) 7703.23 0.354296
\(780\) −3384.57 −0.155368
\(781\) −6045.10 −0.276966
\(782\) 67.8257 0.00310159
\(783\) 1530.17 0.0698387
\(784\) −9628.86 −0.438633
\(785\) 18463.9 0.839499
\(786\) 46.9355 0.00212994
\(787\) 22392.8 1.01425 0.507126 0.861872i \(-0.330708\pi\)
0.507126 + 0.861872i \(0.330708\pi\)
\(788\) −33885.9 −1.53190
\(789\) −20749.7 −0.936260
\(790\) −199.525 −0.00898581
\(791\) −1977.09 −0.0888712
\(792\) 122.518 0.00549683
\(793\) 7795.02 0.349066
\(794\) −365.272 −0.0163262
\(795\) −16917.7 −0.754727
\(796\) −21429.3 −0.954197
\(797\) −11623.6 −0.516597 −0.258298 0.966065i \(-0.583162\pi\)
−0.258298 + 0.966065i \(0.583162\pi\)
\(798\) 117.885 0.00522942
\(799\) −4131.11 −0.182914
\(800\) −226.513 −0.0100106
\(801\) −5610.63 −0.247493
\(802\) 134.394 0.00591724
\(803\) 13919.5 0.611718
\(804\) 2189.75 0.0960529
\(805\) −23200.4 −1.01578
\(806\) 7.44732 0.000325460 0
\(807\) −17855.5 −0.778865
\(808\) −321.222 −0.0139858
\(809\) −11274.6 −0.489978 −0.244989 0.969526i \(-0.578784\pi\)
−0.244989 + 0.969526i \(0.578784\pi\)
\(810\) 18.1661 0.000788016 0
\(811\) 20634.8 0.893449 0.446724 0.894672i \(-0.352590\pi\)
0.446724 + 0.894672i \(0.352590\pi\)
\(812\) 6290.14 0.271848
\(813\) 8432.90 0.363782
\(814\) −45.7824 −0.00197134
\(815\) −34785.5 −1.49507
\(816\) 2722.32 0.116790
\(817\) 38490.1 1.64822
\(818\) −209.956 −0.00897425
\(819\) −1988.86 −0.0848551
\(820\) 4879.77 0.207816
\(821\) 42062.6 1.78806 0.894029 0.448009i \(-0.147867\pi\)
0.894029 + 0.448009i \(0.147867\pi\)
\(822\) −11.3772 −0.000482758 0
\(823\) 32974.8 1.39663 0.698317 0.715789i \(-0.253933\pi\)
0.698317 + 0.715789i \(0.253933\pi\)
\(824\) −22.8063 −0.000964194 0
\(825\) −4695.18 −0.198140
\(826\) 20.7331 0.000873360 0
\(827\) 9364.19 0.393742 0.196871 0.980429i \(-0.436922\pi\)
0.196871 + 0.980429i \(0.436922\pi\)
\(828\) 13594.6 0.570587
\(829\) −18611.4 −0.779734 −0.389867 0.920871i \(-0.627479\pi\)
−0.389867 + 0.920871i \(0.627479\pi\)
\(830\) 182.305 0.00762396
\(831\) 6233.82 0.260227
\(832\) 8150.65 0.339631
\(833\) 2134.24 0.0887718
\(834\) 77.0927 0.00320084
\(835\) −10712.4 −0.443973
\(836\) −30050.6 −1.24321
\(837\) 498.484 0.0205856
\(838\) −356.967 −0.0147151
\(839\) 30534.1 1.25644 0.628221 0.778035i \(-0.283784\pi\)
0.628221 + 0.778035i \(0.283784\pi\)
\(840\) 149.359 0.00613497
\(841\) −21177.2 −0.868309
\(842\) 119.824 0.00490427
\(843\) −9757.82 −0.398668
\(844\) 38456.5 1.56840
\(845\) −17208.5 −0.700581
\(846\) 66.3969 0.00269831
\(847\) −2808.03 −0.113914
\(848\) 40747.3 1.65008
\(849\) 6917.46 0.279631
\(850\) 16.7333 0.000675233 0
\(851\) −10160.5 −0.409278
\(852\) 4318.24 0.173639
\(853\) 1881.16 0.0755098 0.0377549 0.999287i \(-0.487979\pi\)
0.0377549 + 0.999287i \(0.487979\pi\)
\(854\) −171.988 −0.00689145
\(855\) −8911.76 −0.356463
\(856\) 138.974 0.00554910
\(857\) −24782.3 −0.987803 −0.493902 0.869518i \(-0.664430\pi\)
−0.493902 + 0.869518i \(0.664430\pi\)
\(858\) −40.6544 −0.00161762
\(859\) 34731.4 1.37953 0.689767 0.724032i \(-0.257713\pi\)
0.689767 + 0.724032i \(0.257713\pi\)
\(860\) 24382.3 0.966780
\(861\) 2867.47 0.113500
\(862\) −147.231 −0.00581754
\(863\) −15140.1 −0.597190 −0.298595 0.954380i \(-0.596518\pi\)
−0.298595 + 0.954380i \(0.596518\pi\)
\(864\) −131.280 −0.00516927
\(865\) 8147.45 0.320256
\(866\) −153.021 −0.00600446
\(867\) 14135.6 0.553714
\(868\) 2049.14 0.0801295
\(869\) 29887.8 1.16671
\(870\) 38.1306 0.00148592
\(871\) −1453.28 −0.0565356
\(872\) −640.660 −0.0248801
\(873\) 11061.7 0.428844
\(874\) 534.781 0.0206971
\(875\) −21081.8 −0.814510
\(876\) −9943.23 −0.383505
\(877\) 50253.4 1.93493 0.967467 0.252996i \(-0.0814158\pi\)
0.967467 + 0.252996i \(0.0814158\pi\)
\(878\) −22.8079 −0.000876683 0
\(879\) 16669.2 0.639633
\(880\) −19034.7 −0.729157
\(881\) −6565.72 −0.251084 −0.125542 0.992088i \(-0.540067\pi\)
−0.125542 + 0.992088i \(0.540067\pi\)
\(882\) −34.3023 −0.00130955
\(883\) 35396.1 1.34901 0.674504 0.738271i \(-0.264357\pi\)
0.674504 + 0.738271i \(0.264357\pi\)
\(884\) −1806.88 −0.0687466
\(885\) −1567.36 −0.0595326
\(886\) −22.3761 −0.000848464 0
\(887\) −40472.0 −1.53204 −0.766019 0.642818i \(-0.777765\pi\)
−0.766019 + 0.642818i \(0.777765\pi\)
\(888\) 65.4107 0.00247189
\(889\) −22433.5 −0.846339
\(890\) −139.813 −0.00526577
\(891\) −2721.19 −0.102316
\(892\) −27718.8 −1.04046
\(893\) −32572.3 −1.22059
\(894\) −110.701 −0.00414137
\(895\) 35924.3 1.34170
\(896\) −719.539 −0.0268282
\(897\) −9022.40 −0.335841
\(898\) 69.8985 0.00259749
\(899\) 1046.31 0.0388171
\(900\) 3353.94 0.124220
\(901\) −9031.63 −0.333948
\(902\) 58.6142 0.00216368
\(903\) 14327.7 0.528012
\(904\) 57.7404 0.00212436
\(905\) 18049.0 0.662949
\(906\) −47.1700 −0.00172971
\(907\) 19742.8 0.722765 0.361382 0.932418i \(-0.382305\pi\)
0.361382 + 0.932418i \(0.382305\pi\)
\(908\) 6075.68 0.222058
\(909\) 7134.50 0.260326
\(910\) −49.5609 −0.00180541
\(911\) 54399.1 1.97840 0.989201 0.146568i \(-0.0468228\pi\)
0.989201 + 0.146568i \(0.0468228\pi\)
\(912\) 21464.5 0.779345
\(913\) −27308.2 −0.989891
\(914\) 24.1600 0.000874336 0
\(915\) 13001.8 0.469755
\(916\) −52328.0 −1.88752
\(917\) −8570.95 −0.308656
\(918\) 9.69814 0.000348678 0
\(919\) 14039.6 0.503943 0.251972 0.967735i \(-0.418921\pi\)
0.251972 + 0.967735i \(0.418921\pi\)
\(920\) 677.563 0.0242811
\(921\) 13111.4 0.469094
\(922\) −15.6010 −0.000557256 0
\(923\) −2865.90 −0.102202
\(924\) −11186.1 −0.398265
\(925\) −2506.69 −0.0891022
\(926\) 14.4669 0.000513405 0
\(927\) 506.540 0.0179471
\(928\) −275.557 −0.00974742
\(929\) 49759.1 1.75731 0.878656 0.477456i \(-0.158441\pi\)
0.878656 + 0.477456i \(0.158441\pi\)
\(930\) 12.4219 0.000437988 0
\(931\) 16827.7 0.592380
\(932\) 51111.4 1.79636
\(933\) 19184.1 0.673160
\(934\) −381.592 −0.0133684
\(935\) 4219.03 0.147569
\(936\) 58.0842 0.00202836
\(937\) −24113.8 −0.840728 −0.420364 0.907355i \(-0.638098\pi\)
−0.420364 + 0.907355i \(0.638098\pi\)
\(938\) 32.0649 0.00111616
\(939\) −3800.93 −0.132097
\(940\) −20633.6 −0.715950
\(941\) −7779.87 −0.269518 −0.134759 0.990878i \(-0.543026\pi\)
−0.134759 + 0.990878i \(0.543026\pi\)
\(942\) −158.428 −0.00547968
\(943\) 13008.2 0.449210
\(944\) 3775.09 0.130158
\(945\) −3317.34 −0.114194
\(946\) 292.873 0.0100657
\(947\) 42730.7 1.46627 0.733137 0.680081i \(-0.238055\pi\)
0.733137 + 0.680081i \(0.238055\pi\)
\(948\) −21349.9 −0.731449
\(949\) 6599.06 0.225727
\(950\) 131.936 0.00450587
\(951\) 710.718 0.0242341
\(952\) 79.7365 0.00271457
\(953\) −15153.9 −0.515094 −0.257547 0.966266i \(-0.582914\pi\)
−0.257547 + 0.966266i \(0.582914\pi\)
\(954\) 145.160 0.00492634
\(955\) −12064.0 −0.408778
\(956\) −12809.9 −0.433371
\(957\) −5711.76 −0.192931
\(958\) 255.912 0.00863061
\(959\) 2077.61 0.0699578
\(960\) 13595.0 0.457058
\(961\) −29450.1 −0.988558
\(962\) −21.7048 −0.000727435 0
\(963\) −3086.68 −0.103288
\(964\) −45910.1 −1.53389
\(965\) −25126.6 −0.838191
\(966\) 199.068 0.00663035
\(967\) 22252.0 0.739996 0.369998 0.929033i \(-0.379358\pi\)
0.369998 + 0.929033i \(0.379358\pi\)
\(968\) 82.0080 0.00272297
\(969\) −4757.62 −0.157726
\(970\) 275.649 0.00912427
\(971\) −35050.0 −1.15840 −0.579201 0.815184i \(-0.696636\pi\)
−0.579201 + 0.815184i \(0.696636\pi\)
\(972\) 1943.84 0.0641449
\(973\) −14078.0 −0.463843
\(974\) −335.428 −0.0110347
\(975\) −2225.92 −0.0731145
\(976\) −31315.7 −1.02704
\(977\) −28934.1 −0.947476 −0.473738 0.880666i \(-0.657096\pi\)
−0.473738 + 0.880666i \(0.657096\pi\)
\(978\) 298.473 0.00975880
\(979\) 20943.2 0.683705
\(980\) 10659.8 0.347466
\(981\) 14229.4 0.463108
\(982\) −45.6359 −0.00148299
\(983\) −18336.9 −0.594972 −0.297486 0.954726i \(-0.596148\pi\)
−0.297486 + 0.954726i \(0.596148\pi\)
\(984\) −83.7439 −0.00271307
\(985\) 37511.1 1.21341
\(986\) 20.3563 0.000657483 0
\(987\) −12124.8 −0.391020
\(988\) −14246.6 −0.458750
\(989\) 64997.1 2.08977
\(990\) −67.8100 −0.00217691
\(991\) −13126.3 −0.420758 −0.210379 0.977620i \(-0.567470\pi\)
−0.210379 + 0.977620i \(0.567470\pi\)
\(992\) −89.7684 −0.00287314
\(993\) 1648.37 0.0526783
\(994\) 63.2327 0.00201772
\(995\) 23721.9 0.755813
\(996\) 19507.3 0.620594
\(997\) −18514.9 −0.588137 −0.294069 0.955784i \(-0.595009\pi\)
−0.294069 + 0.955784i \(0.595009\pi\)
\(998\) 477.075 0.0151318
\(999\) −1452.81 −0.0460107
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 177.4.a.b.1.4 7
3.2 odd 2 531.4.a.c.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.b.1.4 7 1.1 even 1 trivial
531.4.a.c.1.4 7 3.2 odd 2