Properties

Label 177.4.a.a.1.2
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: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.58179\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.58179 q^{2} +3.00000 q^{3} +12.9928 q^{4} -12.2965 q^{5} -13.7454 q^{6} +15.3493 q^{7} -22.8759 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.58179 q^{2} +3.00000 q^{3} +12.9928 q^{4} -12.2965 q^{5} -13.7454 q^{6} +15.3493 q^{7} -22.8759 q^{8} +9.00000 q^{9} +56.3401 q^{10} -41.7826 q^{11} +38.9784 q^{12} -23.4975 q^{13} -70.3273 q^{14} -36.8896 q^{15} +0.870331 q^{16} +123.900 q^{17} -41.2361 q^{18} +106.282 q^{19} -159.766 q^{20} +46.0479 q^{21} +191.439 q^{22} -207.156 q^{23} -68.6278 q^{24} +26.2045 q^{25} +107.660 q^{26} +27.0000 q^{27} +199.430 q^{28} -53.4048 q^{29} +169.020 q^{30} -252.361 q^{31} +179.020 q^{32} -125.348 q^{33} -567.686 q^{34} -188.743 q^{35} +116.935 q^{36} -357.560 q^{37} -486.962 q^{38} -70.4924 q^{39} +281.294 q^{40} -353.220 q^{41} -210.982 q^{42} -80.6872 q^{43} -542.873 q^{44} -110.669 q^{45} +949.144 q^{46} -5.12471 q^{47} +2.61099 q^{48} -107.399 q^{49} -120.063 q^{50} +371.701 q^{51} -305.298 q^{52} -260.709 q^{53} -123.708 q^{54} +513.781 q^{55} -351.129 q^{56} +318.846 q^{57} +244.689 q^{58} -59.0000 q^{59} -479.299 q^{60} +35.7406 q^{61} +1156.26 q^{62} +138.144 q^{63} -827.193 q^{64} +288.937 q^{65} +574.318 q^{66} +635.590 q^{67} +1609.81 q^{68} -621.467 q^{69} +864.781 q^{70} -644.029 q^{71} -205.883 q^{72} -531.586 q^{73} +1638.27 q^{74} +78.6134 q^{75} +1380.90 q^{76} -641.334 q^{77} +322.981 q^{78} +594.860 q^{79} -10.7020 q^{80} +81.0000 q^{81} +1618.38 q^{82} -95.7821 q^{83} +598.291 q^{84} -1523.54 q^{85} +369.692 q^{86} -160.214 q^{87} +955.816 q^{88} +1002.86 q^{89} +507.061 q^{90} -360.670 q^{91} -2691.53 q^{92} -757.083 q^{93} +23.4803 q^{94} -1306.90 q^{95} +537.059 q^{96} -964.276 q^{97} +492.080 q^{98} -376.044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.58179 −1.61991 −0.809954 0.586494i \(-0.800508\pi\)
−0.809954 + 0.586494i \(0.800508\pi\)
\(3\) 3.00000 0.577350
\(4\) 12.9928 1.62410
\(5\) −12.2965 −1.09983 −0.549917 0.835219i \(-0.685341\pi\)
−0.549917 + 0.835219i \(0.685341\pi\)
\(6\) −13.7454 −0.935254
\(7\) 15.3493 0.828784 0.414392 0.910098i \(-0.363994\pi\)
0.414392 + 0.910098i \(0.363994\pi\)
\(8\) −22.8759 −1.01098
\(9\) 9.00000 0.333333
\(10\) 56.3401 1.78163
\(11\) −41.7826 −1.14527 −0.572633 0.819812i \(-0.694078\pi\)
−0.572633 + 0.819812i \(0.694078\pi\)
\(12\) 38.9784 0.937674
\(13\) −23.4975 −0.501310 −0.250655 0.968077i \(-0.580646\pi\)
−0.250655 + 0.968077i \(0.580646\pi\)
\(14\) −70.3273 −1.34255
\(15\) −36.8896 −0.634990
\(16\) 0.870331 0.0135989
\(17\) 123.900 1.76766 0.883832 0.467805i \(-0.154955\pi\)
0.883832 + 0.467805i \(0.154955\pi\)
\(18\) −41.2361 −0.539969
\(19\) 106.282 1.28330 0.641651 0.766996i \(-0.278250\pi\)
0.641651 + 0.766996i \(0.278250\pi\)
\(20\) −159.766 −1.78624
\(21\) 46.0479 0.478499
\(22\) 191.439 1.85523
\(23\) −207.156 −1.87804 −0.939021 0.343860i \(-0.888265\pi\)
−0.939021 + 0.343860i \(0.888265\pi\)
\(24\) −68.6278 −0.583691
\(25\) 26.2045 0.209636
\(26\) 107.660 0.812075
\(27\) 27.0000 0.192450
\(28\) 199.430 1.34603
\(29\) −53.4048 −0.341966 −0.170983 0.985274i \(-0.554694\pi\)
−0.170983 + 0.985274i \(0.554694\pi\)
\(30\) 169.020 1.02862
\(31\) −252.361 −1.46211 −0.731054 0.682319i \(-0.760971\pi\)
−0.731054 + 0.682319i \(0.760971\pi\)
\(32\) 179.020 0.988954
\(33\) −125.348 −0.661220
\(34\) −567.686 −2.86345
\(35\) −188.743 −0.911525
\(36\) 116.935 0.541366
\(37\) −357.560 −1.58872 −0.794359 0.607449i \(-0.792193\pi\)
−0.794359 + 0.607449i \(0.792193\pi\)
\(38\) −486.962 −2.07883
\(39\) −70.4924 −0.289431
\(40\) 281.294 1.11191
\(41\) −353.220 −1.34545 −0.672727 0.739891i \(-0.734877\pi\)
−0.672727 + 0.739891i \(0.734877\pi\)
\(42\) −210.982 −0.775124
\(43\) −80.6872 −0.286155 −0.143078 0.989711i \(-0.545700\pi\)
−0.143078 + 0.989711i \(0.545700\pi\)
\(44\) −542.873 −1.86003
\(45\) −110.669 −0.366611
\(46\) 949.144 3.04225
\(47\) −5.12471 −0.0159046 −0.00795229 0.999968i \(-0.502531\pi\)
−0.00795229 + 0.999968i \(0.502531\pi\)
\(48\) 2.61099 0.00785134
\(49\) −107.399 −0.313117
\(50\) −120.063 −0.339591
\(51\) 371.701 1.02056
\(52\) −305.298 −0.814176
\(53\) −260.709 −0.675681 −0.337841 0.941203i \(-0.609697\pi\)
−0.337841 + 0.941203i \(0.609697\pi\)
\(54\) −123.708 −0.311751
\(55\) 513.781 1.25960
\(56\) −351.129 −0.837887
\(57\) 318.846 0.740915
\(58\) 244.689 0.553953
\(59\) −59.0000 −0.130189
\(60\) −479.299 −1.03129
\(61\) 35.7406 0.0750182 0.0375091 0.999296i \(-0.488058\pi\)
0.0375091 + 0.999296i \(0.488058\pi\)
\(62\) 1156.26 2.36848
\(63\) 138.144 0.276261
\(64\) −827.193 −1.61561
\(65\) 288.937 0.551358
\(66\) 574.318 1.07112
\(67\) 635.590 1.15895 0.579475 0.814990i \(-0.303258\pi\)
0.579475 + 0.814990i \(0.303258\pi\)
\(68\) 1609.81 2.87086
\(69\) −621.467 −1.08429
\(70\) 864.781 1.47659
\(71\) −644.029 −1.07651 −0.538255 0.842782i \(-0.680916\pi\)
−0.538255 + 0.842782i \(0.680916\pi\)
\(72\) −205.883 −0.336994
\(73\) −531.586 −0.852293 −0.426147 0.904654i \(-0.640129\pi\)
−0.426147 + 0.904654i \(0.640129\pi\)
\(74\) 1638.27 2.57357
\(75\) 78.6134 0.121033
\(76\) 1380.90 2.08421
\(77\) −641.334 −0.949179
\(78\) 322.981 0.468852
\(79\) 594.860 0.847176 0.423588 0.905855i \(-0.360770\pi\)
0.423588 + 0.905855i \(0.360770\pi\)
\(80\) −10.7020 −0.0149566
\(81\) 81.0000 0.111111
\(82\) 1618.38 2.17951
\(83\) −95.7821 −0.126668 −0.0633340 0.997992i \(-0.520173\pi\)
−0.0633340 + 0.997992i \(0.520173\pi\)
\(84\) 598.291 0.777129
\(85\) −1523.54 −1.94414
\(86\) 369.692 0.463545
\(87\) −160.214 −0.197434
\(88\) 955.816 1.15784
\(89\) 1002.86 1.19442 0.597208 0.802086i \(-0.296277\pi\)
0.597208 + 0.802086i \(0.296277\pi\)
\(90\) 507.061 0.593877
\(91\) −360.670 −0.415477
\(92\) −2691.53 −3.05013
\(93\) −757.083 −0.844149
\(94\) 23.4803 0.0257639
\(95\) −1306.90 −1.41142
\(96\) 537.059 0.570973
\(97\) −964.276 −1.00935 −0.504677 0.863308i \(-0.668388\pi\)
−0.504677 + 0.863308i \(0.668388\pi\)
\(98\) 492.080 0.507220
\(99\) −376.044 −0.381756
\(100\) 340.469 0.340469
\(101\) 1294.85 1.27567 0.637835 0.770173i \(-0.279830\pi\)
0.637835 + 0.770173i \(0.279830\pi\)
\(102\) −1703.06 −1.65321
\(103\) 17.3037 0.0165533 0.00827663 0.999966i \(-0.497365\pi\)
0.00827663 + 0.999966i \(0.497365\pi\)
\(104\) 537.526 0.506815
\(105\) −566.229 −0.526269
\(106\) 1194.51 1.09454
\(107\) 267.634 0.241805 0.120903 0.992664i \(-0.461421\pi\)
0.120903 + 0.992664i \(0.461421\pi\)
\(108\) 350.805 0.312558
\(109\) −179.027 −0.157318 −0.0786591 0.996902i \(-0.525064\pi\)
−0.0786591 + 0.996902i \(0.525064\pi\)
\(110\) −2354.04 −2.04044
\(111\) −1072.68 −0.917246
\(112\) 13.3590 0.0112706
\(113\) −694.415 −0.578098 −0.289049 0.957314i \(-0.593339\pi\)
−0.289049 + 0.957314i \(0.593339\pi\)
\(114\) −1460.88 −1.20021
\(115\) 2547.30 2.06553
\(116\) −693.877 −0.555387
\(117\) −211.477 −0.167103
\(118\) 270.326 0.210894
\(119\) 1901.78 1.46501
\(120\) 843.883 0.641964
\(121\) 414.788 0.311636
\(122\) −163.756 −0.121523
\(123\) −1059.66 −0.776799
\(124\) −3278.87 −2.37461
\(125\) 1214.84 0.869270
\(126\) −632.945 −0.447518
\(127\) −1929.31 −1.34802 −0.674010 0.738722i \(-0.735430\pi\)
−0.674010 + 0.738722i \(0.735430\pi\)
\(128\) 2357.87 1.62819
\(129\) −242.062 −0.165212
\(130\) −1323.85 −0.893148
\(131\) 2118.62 1.41301 0.706506 0.707707i \(-0.250270\pi\)
0.706506 + 0.707707i \(0.250270\pi\)
\(132\) −1628.62 −1.07389
\(133\) 1631.35 1.06358
\(134\) −2912.14 −1.87739
\(135\) −332.006 −0.211663
\(136\) −2834.34 −1.78708
\(137\) 318.864 0.198850 0.0994249 0.995045i \(-0.468300\pi\)
0.0994249 + 0.995045i \(0.468300\pi\)
\(138\) 2847.43 1.75645
\(139\) 2310.92 1.41014 0.705070 0.709138i \(-0.250916\pi\)
0.705070 + 0.709138i \(0.250916\pi\)
\(140\) −2452.30 −1.48041
\(141\) −15.3741 −0.00918251
\(142\) 2950.81 1.74385
\(143\) 981.786 0.574133
\(144\) 7.83298 0.00453297
\(145\) 656.693 0.376106
\(146\) 2435.61 1.38064
\(147\) −322.197 −0.180778
\(148\) −4645.71 −2.58023
\(149\) −1168.54 −0.642485 −0.321243 0.946997i \(-0.604101\pi\)
−0.321243 + 0.946997i \(0.604101\pi\)
\(150\) −360.190 −0.196063
\(151\) −1537.12 −0.828402 −0.414201 0.910186i \(-0.635939\pi\)
−0.414201 + 0.910186i \(0.635939\pi\)
\(152\) −2431.30 −1.29740
\(153\) 1115.10 0.589221
\(154\) 2938.46 1.53758
\(155\) 3103.16 1.60808
\(156\) −915.893 −0.470065
\(157\) −2351.07 −1.19513 −0.597565 0.801820i \(-0.703865\pi\)
−0.597565 + 0.801820i \(0.703865\pi\)
\(158\) −2725.52 −1.37235
\(159\) −782.127 −0.390105
\(160\) −2201.32 −1.08769
\(161\) −3179.70 −1.55649
\(162\) −371.125 −0.179990
\(163\) −2755.11 −1.32391 −0.661954 0.749545i \(-0.730272\pi\)
−0.661954 + 0.749545i \(0.730272\pi\)
\(164\) −4589.31 −2.18515
\(165\) 1541.34 0.727233
\(166\) 438.853 0.205190
\(167\) −3741.97 −1.73390 −0.866952 0.498391i \(-0.833924\pi\)
−0.866952 + 0.498391i \(0.833924\pi\)
\(168\) −1053.39 −0.483754
\(169\) −1644.87 −0.748689
\(170\) 6980.56 3.14932
\(171\) 956.538 0.427768
\(172\) −1048.35 −0.464745
\(173\) 3970.75 1.74503 0.872515 0.488587i \(-0.162487\pi\)
0.872515 + 0.488587i \(0.162487\pi\)
\(174\) 734.068 0.319825
\(175\) 402.220 0.173743
\(176\) −36.3647 −0.0155744
\(177\) −177.000 −0.0751646
\(178\) −4594.90 −1.93484
\(179\) 1322.29 0.552139 0.276070 0.961138i \(-0.410968\pi\)
0.276070 + 0.961138i \(0.410968\pi\)
\(180\) −1437.90 −0.595413
\(181\) 3244.93 1.33256 0.666280 0.745701i \(-0.267885\pi\)
0.666280 + 0.745701i \(0.267885\pi\)
\(182\) 1652.51 0.673035
\(183\) 107.222 0.0433118
\(184\) 4738.88 1.89867
\(185\) 4396.75 1.74733
\(186\) 3468.79 1.36744
\(187\) −5176.89 −2.02445
\(188\) −66.5842 −0.0258306
\(189\) 414.431 0.159500
\(190\) 5987.93 2.28637
\(191\) 1496.99 0.567110 0.283555 0.958956i \(-0.408486\pi\)
0.283555 + 0.958956i \(0.408486\pi\)
\(192\) −2481.58 −0.932774
\(193\) 219.504 0.0818665 0.0409333 0.999162i \(-0.486967\pi\)
0.0409333 + 0.999162i \(0.486967\pi\)
\(194\) 4418.11 1.63506
\(195\) 866.811 0.318326
\(196\) −1395.41 −0.508533
\(197\) 740.027 0.267638 0.133819 0.991006i \(-0.457276\pi\)
0.133819 + 0.991006i \(0.457276\pi\)
\(198\) 1722.95 0.618409
\(199\) 2138.04 0.761617 0.380808 0.924654i \(-0.375646\pi\)
0.380808 + 0.924654i \(0.375646\pi\)
\(200\) −599.452 −0.211938
\(201\) 1906.77 0.669120
\(202\) −5932.74 −2.06647
\(203\) −819.726 −0.283416
\(204\) 4829.44 1.65749
\(205\) 4343.37 1.47978
\(206\) −79.2820 −0.0268147
\(207\) −1864.40 −0.626014
\(208\) −20.4506 −0.00681727
\(209\) −4440.74 −1.46972
\(210\) 2594.34 0.852508
\(211\) −510.304 −0.166497 −0.0832483 0.996529i \(-0.526529\pi\)
−0.0832483 + 0.996529i \(0.526529\pi\)
\(212\) −3387.34 −1.09737
\(213\) −1932.09 −0.621524
\(214\) −1226.24 −0.391702
\(215\) 992.172 0.314723
\(216\) −617.650 −0.194564
\(217\) −3873.56 −1.21177
\(218\) 820.264 0.254841
\(219\) −1594.76 −0.492072
\(220\) 6675.45 2.04572
\(221\) −2911.35 −0.886146
\(222\) 4914.80 1.48585
\(223\) −2449.19 −0.735469 −0.367735 0.929931i \(-0.619867\pi\)
−0.367735 + 0.929931i \(0.619867\pi\)
\(224\) 2747.83 0.819629
\(225\) 235.840 0.0698786
\(226\) 3181.66 0.936465
\(227\) −185.296 −0.0541786 −0.0270893 0.999633i \(-0.508624\pi\)
−0.0270893 + 0.999633i \(0.508624\pi\)
\(228\) 4142.70 1.20332
\(229\) 6185.66 1.78498 0.892488 0.451071i \(-0.148958\pi\)
0.892488 + 0.451071i \(0.148958\pi\)
\(230\) −11671.2 −3.34597
\(231\) −1924.00 −0.548009
\(232\) 1221.68 0.345722
\(233\) −4695.37 −1.32019 −0.660094 0.751183i \(-0.729484\pi\)
−0.660094 + 0.751183i \(0.729484\pi\)
\(234\) 968.944 0.270692
\(235\) 63.0161 0.0174924
\(236\) −766.575 −0.211440
\(237\) 1784.58 0.489117
\(238\) −8713.58 −2.37318
\(239\) −3690.23 −0.998748 −0.499374 0.866386i \(-0.666437\pi\)
−0.499374 + 0.866386i \(0.666437\pi\)
\(240\) −32.1061 −0.00863518
\(241\) −129.939 −0.0347307 −0.0173654 0.999849i \(-0.505528\pi\)
−0.0173654 + 0.999849i \(0.505528\pi\)
\(242\) −1900.47 −0.504822
\(243\) 243.000 0.0641500
\(244\) 464.370 0.121837
\(245\) 1320.63 0.344377
\(246\) 4855.13 1.25834
\(247\) −2497.36 −0.643332
\(248\) 5772.99 1.47817
\(249\) −287.346 −0.0731318
\(250\) −5566.15 −1.40814
\(251\) −921.958 −0.231846 −0.115923 0.993258i \(-0.536983\pi\)
−0.115923 + 0.993258i \(0.536983\pi\)
\(252\) 1794.87 0.448676
\(253\) 8655.51 2.15086
\(254\) 8839.69 2.18367
\(255\) −4570.63 −1.12245
\(256\) −4185.71 −1.02190
\(257\) 2067.03 0.501704 0.250852 0.968026i \(-0.419289\pi\)
0.250852 + 0.968026i \(0.419289\pi\)
\(258\) 1109.07 0.267628
\(259\) −5488.30 −1.31670
\(260\) 3754.10 0.895459
\(261\) −480.643 −0.113989
\(262\) −9707.07 −2.28895
\(263\) 4434.33 1.03967 0.519833 0.854268i \(-0.325994\pi\)
0.519833 + 0.854268i \(0.325994\pi\)
\(264\) 2867.45 0.668482
\(265\) 3205.81 0.743138
\(266\) −7474.52 −1.72290
\(267\) 3008.58 0.689596
\(268\) 8258.09 1.88225
\(269\) 2401.90 0.544410 0.272205 0.962239i \(-0.412247\pi\)
0.272205 + 0.962239i \(0.412247\pi\)
\(270\) 1521.18 0.342875
\(271\) 3740.90 0.838537 0.419268 0.907862i \(-0.362287\pi\)
0.419268 + 0.907862i \(0.362287\pi\)
\(272\) 107.834 0.0240383
\(273\) −1082.01 −0.239876
\(274\) −1460.97 −0.322118
\(275\) −1094.89 −0.240089
\(276\) −8074.59 −1.76099
\(277\) −1443.22 −0.313049 −0.156525 0.987674i \(-0.550029\pi\)
−0.156525 + 0.987674i \(0.550029\pi\)
\(278\) −10588.1 −2.28430
\(279\) −2271.25 −0.487370
\(280\) 4317.67 0.921536
\(281\) −3497.86 −0.742580 −0.371290 0.928517i \(-0.621084\pi\)
−0.371290 + 0.928517i \(0.621084\pi\)
\(282\) 70.4410 0.0148748
\(283\) −396.792 −0.0833457 −0.0416728 0.999131i \(-0.513269\pi\)
−0.0416728 + 0.999131i \(0.513269\pi\)
\(284\) −8367.74 −1.74836
\(285\) −3920.70 −0.814884
\(286\) −4498.34 −0.930043
\(287\) −5421.67 −1.11509
\(288\) 1611.18 0.329651
\(289\) 10438.3 2.12463
\(290\) −3008.83 −0.609257
\(291\) −2892.83 −0.582751
\(292\) −6906.79 −1.38421
\(293\) 9247.65 1.84387 0.921934 0.387347i \(-0.126609\pi\)
0.921934 + 0.387347i \(0.126609\pi\)
\(294\) 1476.24 0.292844
\(295\) 725.495 0.143186
\(296\) 8179.52 1.60617
\(297\) −1128.13 −0.220407
\(298\) 5353.99 1.04077
\(299\) 4867.63 0.941480
\(300\) 1021.41 0.196570
\(301\) −1238.49 −0.237161
\(302\) 7042.74 1.34193
\(303\) 3884.56 0.736508
\(304\) 92.5005 0.0174515
\(305\) −439.485 −0.0825076
\(306\) −5109.17 −0.954483
\(307\) 5013.01 0.931946 0.465973 0.884799i \(-0.345704\pi\)
0.465973 + 0.884799i \(0.345704\pi\)
\(308\) −8332.72 −1.54156
\(309\) 51.9112 0.00955703
\(310\) −14218.0 −2.60494
\(311\) −6356.34 −1.15896 −0.579478 0.814988i \(-0.696743\pi\)
−0.579478 + 0.814988i \(0.696743\pi\)
\(312\) 1612.58 0.292610
\(313\) 1664.15 0.300521 0.150261 0.988646i \(-0.451989\pi\)
0.150261 + 0.988646i \(0.451989\pi\)
\(314\) 10772.1 1.93600
\(315\) −1698.69 −0.303842
\(316\) 7728.89 1.37590
\(317\) −9467.95 −1.67752 −0.838759 0.544503i \(-0.816718\pi\)
−0.838759 + 0.544503i \(0.816718\pi\)
\(318\) 3583.54 0.631934
\(319\) 2231.39 0.391642
\(320\) 10171.6 1.77691
\(321\) 802.901 0.139606
\(322\) 14568.7 2.52137
\(323\) 13168.4 2.26845
\(324\) 1052.42 0.180455
\(325\) −615.739 −0.105092
\(326\) 12623.3 2.14461
\(327\) −537.081 −0.0908277
\(328\) 8080.23 1.36023
\(329\) −78.6606 −0.0131815
\(330\) −7062.11 −1.17805
\(331\) −5398.35 −0.896436 −0.448218 0.893924i \(-0.647941\pi\)
−0.448218 + 0.893924i \(0.647941\pi\)
\(332\) −1244.48 −0.205721
\(333\) −3218.04 −0.529572
\(334\) 17144.9 2.80876
\(335\) −7815.54 −1.27465
\(336\) 40.0769 0.00650707
\(337\) 4793.04 0.774759 0.387379 0.921920i \(-0.373380\pi\)
0.387379 + 0.921920i \(0.373380\pi\)
\(338\) 7536.44 1.21281
\(339\) −2083.25 −0.333765
\(340\) −19795.1 −3.15747
\(341\) 10544.3 1.67450
\(342\) −4382.65 −0.692944
\(343\) −6913.31 −1.08829
\(344\) 1845.79 0.289298
\(345\) 7641.89 1.19254
\(346\) −18193.1 −2.82679
\(347\) −10721.0 −1.65860 −0.829298 0.558806i \(-0.811260\pi\)
−0.829298 + 0.558806i \(0.811260\pi\)
\(348\) −2081.63 −0.320653
\(349\) 1043.92 0.160114 0.0800571 0.996790i \(-0.474490\pi\)
0.0800571 + 0.996790i \(0.474490\pi\)
\(350\) −1842.89 −0.281447
\(351\) −634.432 −0.0964771
\(352\) −7479.91 −1.13262
\(353\) −9834.72 −1.48286 −0.741429 0.671031i \(-0.765852\pi\)
−0.741429 + 0.671031i \(0.765852\pi\)
\(354\) 810.977 0.121760
\(355\) 7919.32 1.18398
\(356\) 13030.0 1.93985
\(357\) 5705.35 0.845825
\(358\) −6058.48 −0.894414
\(359\) 9944.23 1.46194 0.730970 0.682409i \(-0.239068\pi\)
0.730970 + 0.682409i \(0.239068\pi\)
\(360\) 2531.65 0.370638
\(361\) 4436.85 0.646866
\(362\) −14867.6 −2.15862
\(363\) 1244.36 0.179923
\(364\) −4686.11 −0.674777
\(365\) 6536.66 0.937382
\(366\) −491.267 −0.0701611
\(367\) 8177.88 1.16317 0.581583 0.813487i \(-0.302433\pi\)
0.581583 + 0.813487i \(0.302433\pi\)
\(368\) −180.294 −0.0255393
\(369\) −3178.98 −0.448485
\(370\) −20145.0 −2.83051
\(371\) −4001.70 −0.559994
\(372\) −9836.62 −1.37098
\(373\) −5263.36 −0.730633 −0.365317 0.930883i \(-0.619039\pi\)
−0.365317 + 0.930883i \(0.619039\pi\)
\(374\) 23719.4 3.27941
\(375\) 3644.52 0.501873
\(376\) 117.232 0.0160793
\(377\) 1254.88 0.171431
\(378\) −1898.84 −0.258375
\(379\) −1581.26 −0.214310 −0.107155 0.994242i \(-0.534174\pi\)
−0.107155 + 0.994242i \(0.534174\pi\)
\(380\) −16980.3 −2.29229
\(381\) −5787.93 −0.778280
\(382\) −6858.87 −0.918666
\(383\) 18.1202 0.00241749 0.00120875 0.999999i \(-0.499615\pi\)
0.00120875 + 0.999999i \(0.499615\pi\)
\(384\) 7073.60 0.940035
\(385\) 7886.18 1.04394
\(386\) −1005.72 −0.132616
\(387\) −726.185 −0.0953851
\(388\) −12528.6 −1.63929
\(389\) −7475.52 −0.974354 −0.487177 0.873303i \(-0.661973\pi\)
−0.487177 + 0.873303i \(0.661973\pi\)
\(390\) −3971.55 −0.515659
\(391\) −25666.7 −3.31974
\(392\) 2456.85 0.316556
\(393\) 6355.86 0.815803
\(394\) −3390.65 −0.433549
\(395\) −7314.70 −0.931754
\(396\) −4885.86 −0.620009
\(397\) −8078.60 −1.02129 −0.510647 0.859791i \(-0.670594\pi\)
−0.510647 + 0.859791i \(0.670594\pi\)
\(398\) −9796.06 −1.23375
\(399\) 4894.06 0.614059
\(400\) 22.8066 0.00285082
\(401\) 1634.60 0.203561 0.101781 0.994807i \(-0.467546\pi\)
0.101781 + 0.994807i \(0.467546\pi\)
\(402\) −8736.42 −1.08391
\(403\) 5929.84 0.732969
\(404\) 16823.7 2.07181
\(405\) −996.018 −0.122204
\(406\) 3755.81 0.459108
\(407\) 14939.8 1.81951
\(408\) −8503.01 −1.03177
\(409\) −2121.07 −0.256430 −0.128215 0.991746i \(-0.540925\pi\)
−0.128215 + 0.991746i \(0.540925\pi\)
\(410\) −19900.4 −2.39710
\(411\) 956.593 0.114806
\(412\) 224.824 0.0268841
\(413\) −905.609 −0.107899
\(414\) 8542.30 1.01408
\(415\) 1177.79 0.139314
\(416\) −4206.51 −0.495772
\(417\) 6932.75 0.814145
\(418\) 20346.5 2.38082
\(419\) −14819.7 −1.72790 −0.863950 0.503577i \(-0.832017\pi\)
−0.863950 + 0.503577i \(0.832017\pi\)
\(420\) −7356.90 −0.854714
\(421\) 5226.64 0.605061 0.302531 0.953140i \(-0.402169\pi\)
0.302531 + 0.953140i \(0.402169\pi\)
\(422\) 2338.10 0.269709
\(423\) −46.1223 −0.00530153
\(424\) 5963.96 0.683102
\(425\) 3246.75 0.370565
\(426\) 8852.42 1.00681
\(427\) 548.593 0.0621739
\(428\) 3477.31 0.392715
\(429\) 2945.36 0.331476
\(430\) −4545.92 −0.509823
\(431\) −10926.6 −1.22115 −0.610577 0.791957i \(-0.709063\pi\)
−0.610577 + 0.791957i \(0.709063\pi\)
\(432\) 23.4989 0.00261711
\(433\) 3172.98 0.352157 0.176078 0.984376i \(-0.443659\pi\)
0.176078 + 0.984376i \(0.443659\pi\)
\(434\) 17747.9 1.96296
\(435\) 1970.08 0.217145
\(436\) −2326.06 −0.255500
\(437\) −22016.9 −2.41010
\(438\) 7306.84 0.797111
\(439\) 2162.68 0.235123 0.117562 0.993066i \(-0.462492\pi\)
0.117562 + 0.993066i \(0.462492\pi\)
\(440\) −11753.2 −1.27344
\(441\) −966.591 −0.104372
\(442\) 13339.2 1.43547
\(443\) −10270.6 −1.10152 −0.550760 0.834664i \(-0.685662\pi\)
−0.550760 + 0.834664i \(0.685662\pi\)
\(444\) −13937.1 −1.48970
\(445\) −12331.7 −1.31366
\(446\) 11221.7 1.19139
\(447\) −3505.61 −0.370939
\(448\) −12696.8 −1.33899
\(449\) −3822.43 −0.401763 −0.200882 0.979616i \(-0.564381\pi\)
−0.200882 + 0.979616i \(0.564381\pi\)
\(450\) −1080.57 −0.113197
\(451\) 14758.4 1.54090
\(452\) −9022.39 −0.938889
\(453\) −4611.35 −0.478278
\(454\) 848.989 0.0877644
\(455\) 4434.98 0.456956
\(456\) −7293.89 −0.749052
\(457\) 16654.3 1.70471 0.852357 0.522961i \(-0.175173\pi\)
0.852357 + 0.522961i \(0.175173\pi\)
\(458\) −28341.4 −2.89150
\(459\) 3345.31 0.340187
\(460\) 33096.5 3.35463
\(461\) 14478.5 1.46276 0.731378 0.681972i \(-0.238878\pi\)
0.731378 + 0.681972i \(0.238878\pi\)
\(462\) 8815.37 0.887723
\(463\) −11106.8 −1.11485 −0.557425 0.830227i \(-0.688211\pi\)
−0.557425 + 0.830227i \(0.688211\pi\)
\(464\) −46.4798 −0.00465037
\(465\) 9309.49 0.928424
\(466\) 21513.2 2.13858
\(467\) 18099.7 1.79347 0.896737 0.442563i \(-0.145931\pi\)
0.896737 + 0.442563i \(0.145931\pi\)
\(468\) −2747.68 −0.271392
\(469\) 9755.86 0.960519
\(470\) −288.726 −0.0283361
\(471\) −7053.20 −0.690009
\(472\) 1349.68 0.131619
\(473\) 3371.32 0.327724
\(474\) −8176.56 −0.792325
\(475\) 2785.06 0.269026
\(476\) 24709.5 2.37932
\(477\) −2346.38 −0.225227
\(478\) 16907.8 1.61788
\(479\) −15597.9 −1.48787 −0.743933 0.668255i \(-0.767042\pi\)
−0.743933 + 0.668255i \(0.767042\pi\)
\(480\) −6603.96 −0.627975
\(481\) 8401.76 0.796439
\(482\) 595.353 0.0562606
\(483\) −9539.09 −0.898641
\(484\) 5389.25 0.506128
\(485\) 11857.2 1.11012
\(486\) −1113.37 −0.103917
\(487\) 14116.3 1.31349 0.656745 0.754113i \(-0.271933\pi\)
0.656745 + 0.754113i \(0.271933\pi\)
\(488\) −817.598 −0.0758421
\(489\) −8265.33 −0.764358
\(490\) −6050.87 −0.557858
\(491\) 14694.8 1.35064 0.675321 0.737524i \(-0.264005\pi\)
0.675321 + 0.737524i \(0.264005\pi\)
\(492\) −13767.9 −1.26160
\(493\) −6616.88 −0.604481
\(494\) 11442.4 1.04214
\(495\) 4624.03 0.419868
\(496\) −219.638 −0.0198831
\(497\) −9885.40 −0.892195
\(498\) 1316.56 0.118467
\(499\) 4395.99 0.394372 0.197186 0.980366i \(-0.436820\pi\)
0.197186 + 0.980366i \(0.436820\pi\)
\(500\) 15784.2 1.41178
\(501\) −11225.9 −1.00107
\(502\) 4224.22 0.375570
\(503\) −2345.33 −0.207899 −0.103950 0.994583i \(-0.533148\pi\)
−0.103950 + 0.994583i \(0.533148\pi\)
\(504\) −3160.16 −0.279296
\(505\) −15922.2 −1.40303
\(506\) −39657.7 −3.48419
\(507\) −4934.61 −0.432256
\(508\) −25067.1 −2.18932
\(509\) −7711.84 −0.671554 −0.335777 0.941941i \(-0.608999\pi\)
−0.335777 + 0.941941i \(0.608999\pi\)
\(510\) 20941.7 1.81826
\(511\) −8159.47 −0.706367
\(512\) 315.083 0.0271970
\(513\) 2869.61 0.246972
\(514\) −9470.70 −0.812713
\(515\) −212.776 −0.0182058
\(516\) −3145.06 −0.268320
\(517\) 214.124 0.0182150
\(518\) 25146.2 2.13294
\(519\) 11912.2 1.00749
\(520\) −6609.70 −0.557413
\(521\) 5616.57 0.472296 0.236148 0.971717i \(-0.424115\pi\)
0.236148 + 0.971717i \(0.424115\pi\)
\(522\) 2202.20 0.184651
\(523\) −14763.5 −1.23435 −0.617173 0.786828i \(-0.711722\pi\)
−0.617173 + 0.786828i \(0.711722\pi\)
\(524\) 27526.8 2.29487
\(525\) 1206.66 0.100310
\(526\) −20317.1 −1.68416
\(527\) −31267.6 −2.58452
\(528\) −109.094 −0.00899188
\(529\) 30746.5 2.52704
\(530\) −14688.4 −1.20381
\(531\) −531.000 −0.0433963
\(532\) 21195.8 1.72736
\(533\) 8299.77 0.674489
\(534\) −13784.7 −1.11708
\(535\) −3290.97 −0.265945
\(536\) −14539.7 −1.17168
\(537\) 3966.88 0.318778
\(538\) −11005.0 −0.881894
\(539\) 4487.41 0.358602
\(540\) −4313.69 −0.343762
\(541\) 15882.7 1.26220 0.631102 0.775700i \(-0.282603\pi\)
0.631102 + 0.775700i \(0.282603\pi\)
\(542\) −17140.0 −1.35835
\(543\) 9734.78 0.769354
\(544\) 22180.6 1.74814
\(545\) 2201.41 0.173024
\(546\) 4957.54 0.388577
\(547\) −3258.45 −0.254701 −0.127350 0.991858i \(-0.540647\pi\)
−0.127350 + 0.991858i \(0.540647\pi\)
\(548\) 4142.94 0.322952
\(549\) 321.665 0.0250061
\(550\) 5016.56 0.388922
\(551\) −5675.96 −0.438846
\(552\) 14216.6 1.09620
\(553\) 9130.68 0.702126
\(554\) 6612.53 0.507111
\(555\) 13190.2 1.00882
\(556\) 30025.3 2.29021
\(557\) −8065.81 −0.613572 −0.306786 0.951779i \(-0.599254\pi\)
−0.306786 + 0.951779i \(0.599254\pi\)
\(558\) 10406.4 0.789493
\(559\) 1895.94 0.143452
\(560\) −164.269 −0.0123958
\(561\) −15530.7 −1.16881
\(562\) 16026.5 1.20291
\(563\) 19540.5 1.46276 0.731379 0.681971i \(-0.238877\pi\)
0.731379 + 0.681971i \(0.238877\pi\)
\(564\) −199.753 −0.0149133
\(565\) 8538.89 0.635812
\(566\) 1818.02 0.135012
\(567\) 1243.29 0.0920871
\(568\) 14732.8 1.08833
\(569\) 13811.1 1.01756 0.508780 0.860897i \(-0.330097\pi\)
0.508780 + 0.860897i \(0.330097\pi\)
\(570\) 17963.8 1.32004
\(571\) 9120.73 0.668460 0.334230 0.942492i \(-0.391524\pi\)
0.334230 + 0.942492i \(0.391524\pi\)
\(572\) 12756.1 0.932449
\(573\) 4490.96 0.327421
\(574\) 24841.0 1.80634
\(575\) −5428.41 −0.393705
\(576\) −7444.74 −0.538537
\(577\) 19680.3 1.41993 0.709965 0.704237i \(-0.248711\pi\)
0.709965 + 0.704237i \(0.248711\pi\)
\(578\) −47826.2 −3.44171
\(579\) 658.512 0.0472657
\(580\) 8532.28 0.610834
\(581\) −1470.19 −0.104980
\(582\) 13254.3 0.944002
\(583\) 10893.1 0.773835
\(584\) 12160.5 0.861654
\(585\) 2600.43 0.183786
\(586\) −42370.8 −2.98689
\(587\) −26509.2 −1.86398 −0.931988 0.362489i \(-0.881927\pi\)
−0.931988 + 0.362489i \(0.881927\pi\)
\(588\) −4186.24 −0.293601
\(589\) −26821.4 −1.87633
\(590\) −3324.06 −0.231948
\(591\) 2220.08 0.154521
\(592\) −311.196 −0.0216048
\(593\) −1515.35 −0.104937 −0.0524686 0.998623i \(-0.516709\pi\)
−0.0524686 + 0.998623i \(0.516709\pi\)
\(594\) 5168.86 0.357038
\(595\) −23385.3 −1.61127
\(596\) −15182.6 −1.04346
\(597\) 6414.12 0.439720
\(598\) −22302.5 −1.52511
\(599\) −4721.57 −0.322067 −0.161033 0.986949i \(-0.551483\pi\)
−0.161033 + 0.986949i \(0.551483\pi\)
\(600\) −1798.36 −0.122363
\(601\) 14051.0 0.953663 0.476831 0.878995i \(-0.341785\pi\)
0.476831 + 0.878995i \(0.341785\pi\)
\(602\) 5674.51 0.384179
\(603\) 5720.31 0.386317
\(604\) −19971.4 −1.34541
\(605\) −5100.45 −0.342748
\(606\) −17798.2 −1.19307
\(607\) −8076.32 −0.540046 −0.270023 0.962854i \(-0.587031\pi\)
−0.270023 + 0.962854i \(0.587031\pi\)
\(608\) 19026.6 1.26913
\(609\) −2459.18 −0.163630
\(610\) 2013.63 0.133655
\(611\) 120.418 0.00797312
\(612\) 14488.3 0.956953
\(613\) −3386.14 −0.223107 −0.111554 0.993758i \(-0.535583\pi\)
−0.111554 + 0.993758i \(0.535583\pi\)
\(614\) −22968.6 −1.50967
\(615\) 13030.1 0.854350
\(616\) 14671.1 0.959604
\(617\) 26131.0 1.70502 0.852508 0.522714i \(-0.175080\pi\)
0.852508 + 0.522714i \(0.175080\pi\)
\(618\) −237.846 −0.0154815
\(619\) 7409.73 0.481134 0.240567 0.970633i \(-0.422667\pi\)
0.240567 + 0.970633i \(0.422667\pi\)
\(620\) 40318.7 2.61168
\(621\) −5593.20 −0.361429
\(622\) 29123.4 1.87740
\(623\) 15393.2 0.989913
\(624\) −61.3517 −0.00393595
\(625\) −18213.9 −1.16569
\(626\) −7624.77 −0.486816
\(627\) −13322.2 −0.848546
\(628\) −30546.9 −1.94101
\(629\) −44301.9 −2.80832
\(630\) 7783.03 0.492196
\(631\) −18236.5 −1.15053 −0.575264 0.817968i \(-0.695101\pi\)
−0.575264 + 0.817968i \(0.695101\pi\)
\(632\) −13608.0 −0.856481
\(633\) −1530.91 −0.0961268
\(634\) 43380.2 2.71742
\(635\) 23723.8 1.48260
\(636\) −10162.0 −0.633569
\(637\) 2523.61 0.156968
\(638\) −10223.8 −0.634424
\(639\) −5796.27 −0.358837
\(640\) −28993.6 −1.79074
\(641\) −27792.6 −1.71255 −0.856273 0.516524i \(-0.827226\pi\)
−0.856273 + 0.516524i \(0.827226\pi\)
\(642\) −3678.73 −0.226149
\(643\) −19061.5 −1.16907 −0.584534 0.811369i \(-0.698723\pi\)
−0.584534 + 0.811369i \(0.698723\pi\)
\(644\) −41313.1 −2.52790
\(645\) 2976.52 0.181706
\(646\) −60334.7 −3.67467
\(647\) −6267.83 −0.380856 −0.190428 0.981701i \(-0.560988\pi\)
−0.190428 + 0.981701i \(0.560988\pi\)
\(648\) −1852.95 −0.112331
\(649\) 2465.17 0.149101
\(650\) 2821.19 0.170240
\(651\) −11620.7 −0.699617
\(652\) −35796.6 −2.15016
\(653\) 21401.4 1.28254 0.641271 0.767314i \(-0.278407\pi\)
0.641271 + 0.767314i \(0.278407\pi\)
\(654\) 2460.79 0.147132
\(655\) −26051.7 −1.55408
\(656\) −307.418 −0.0182967
\(657\) −4784.27 −0.284098
\(658\) 360.406 0.0213527
\(659\) 17027.7 1.00653 0.503267 0.864131i \(-0.332131\pi\)
0.503267 + 0.864131i \(0.332131\pi\)
\(660\) 20026.4 1.18110
\(661\) 26007.0 1.53034 0.765170 0.643828i \(-0.222655\pi\)
0.765170 + 0.643828i \(0.222655\pi\)
\(662\) 24734.1 1.45214
\(663\) −8734.04 −0.511617
\(664\) 2191.10 0.128059
\(665\) −20060.0 −1.16976
\(666\) 14744.4 0.857858
\(667\) 11063.1 0.642227
\(668\) −48618.6 −2.81603
\(669\) −7347.56 −0.424623
\(670\) 35809.2 2.06482
\(671\) −1493.33 −0.0859159
\(672\) 8243.48 0.473213
\(673\) 11947.8 0.684329 0.342164 0.939640i \(-0.388840\pi\)
0.342164 + 0.939640i \(0.388840\pi\)
\(674\) −21960.7 −1.25504
\(675\) 707.521 0.0403444
\(676\) −21371.4 −1.21594
\(677\) −6173.05 −0.350442 −0.175221 0.984529i \(-0.556064\pi\)
−0.175221 + 0.984529i \(0.556064\pi\)
\(678\) 9544.99 0.540669
\(679\) −14801.0 −0.836537
\(680\) 34852.5 1.96549
\(681\) −555.889 −0.0312801
\(682\) −48311.8 −2.71254
\(683\) −31454.6 −1.76219 −0.881097 0.472936i \(-0.843194\pi\)
−0.881097 + 0.472936i \(0.843194\pi\)
\(684\) 12428.1 0.694737
\(685\) −3920.92 −0.218702
\(686\) 31675.3 1.76293
\(687\) 18557.0 1.03056
\(688\) −70.2246 −0.00389140
\(689\) 6126.00 0.338726
\(690\) −35013.5 −1.93180
\(691\) 5719.61 0.314883 0.157441 0.987528i \(-0.449675\pi\)
0.157441 + 0.987528i \(0.449675\pi\)
\(692\) 51591.1 2.83410
\(693\) −5772.01 −0.316393
\(694\) 49121.3 2.68677
\(695\) −28416.3 −1.55092
\(696\) 3665.05 0.199603
\(697\) −43764.1 −2.37831
\(698\) −4783.03 −0.259370
\(699\) −14086.1 −0.762211
\(700\) 5225.97 0.282176
\(701\) −1237.43 −0.0666719 −0.0333360 0.999444i \(-0.510613\pi\)
−0.0333360 + 0.999444i \(0.510613\pi\)
\(702\) 2906.83 0.156284
\(703\) −38002.2 −2.03881
\(704\) 34562.3 1.85031
\(705\) 189.048 0.0100992
\(706\) 45060.6 2.40209
\(707\) 19875.1 1.05725
\(708\) −2299.72 −0.122075
\(709\) −14978.1 −0.793393 −0.396697 0.917950i \(-0.629844\pi\)
−0.396697 + 0.917950i \(0.629844\pi\)
\(710\) −36284.7 −1.91794
\(711\) 5353.74 0.282392
\(712\) −22941.4 −1.20753
\(713\) 52278.0 2.74590
\(714\) −26140.7 −1.37016
\(715\) −12072.6 −0.631452
\(716\) 17180.3 0.896729
\(717\) −11070.7 −0.576628
\(718\) −45562.4 −2.36821
\(719\) 1416.69 0.0734822 0.0367411 0.999325i \(-0.488302\pi\)
0.0367411 + 0.999325i \(0.488302\pi\)
\(720\) −96.3184 −0.00498552
\(721\) 265.600 0.0137191
\(722\) −20328.7 −1.04786
\(723\) −389.817 −0.0200518
\(724\) 42160.7 2.16421
\(725\) −1399.44 −0.0716884
\(726\) −5701.41 −0.291459
\(727\) −15069.5 −0.768773 −0.384387 0.923172i \(-0.625587\pi\)
−0.384387 + 0.923172i \(0.625587\pi\)
\(728\) 8250.65 0.420041
\(729\) 729.000 0.0370370
\(730\) −29949.6 −1.51847
\(731\) −9997.18 −0.505826
\(732\) 1393.11 0.0703426
\(733\) 17103.5 0.861844 0.430922 0.902389i \(-0.358188\pi\)
0.430922 + 0.902389i \(0.358188\pi\)
\(734\) −37469.3 −1.88422
\(735\) 3961.90 0.198826
\(736\) −37085.0 −1.85730
\(737\) −26556.6 −1.32731
\(738\) 14565.4 0.726504
\(739\) 9749.49 0.485306 0.242653 0.970113i \(-0.421982\pi\)
0.242653 + 0.970113i \(0.421982\pi\)
\(740\) 57126.0 2.83783
\(741\) −7492.07 −0.371428
\(742\) 18334.9 0.907138
\(743\) −13906.1 −0.686630 −0.343315 0.939220i \(-0.611550\pi\)
−0.343315 + 0.939220i \(0.611550\pi\)
\(744\) 17319.0 0.853420
\(745\) 14369.0 0.706628
\(746\) 24115.6 1.18356
\(747\) −862.038 −0.0422227
\(748\) −67262.2 −3.28790
\(749\) 4107.99 0.200404
\(750\) −16698.4 −0.812988
\(751\) −11178.8 −0.543170 −0.271585 0.962415i \(-0.587548\pi\)
−0.271585 + 0.962415i \(0.587548\pi\)
\(752\) −4.46019 −0.000216285 0
\(753\) −2765.87 −0.133857
\(754\) −5749.58 −0.277702
\(755\) 18901.2 0.911105
\(756\) 5384.62 0.259043
\(757\) 4697.99 0.225563 0.112782 0.993620i \(-0.464024\pi\)
0.112782 + 0.993620i \(0.464024\pi\)
\(758\) 7244.98 0.347163
\(759\) 25966.5 1.24180
\(760\) 29896.5 1.42692
\(761\) 15776.9 0.751526 0.375763 0.926716i \(-0.377381\pi\)
0.375763 + 0.926716i \(0.377381\pi\)
\(762\) 26519.1 1.26074
\(763\) −2747.94 −0.130383
\(764\) 19450.0 0.921044
\(765\) −13711.9 −0.648046
\(766\) −83.0230 −0.00391611
\(767\) 1386.35 0.0652649
\(768\) −12557.1 −0.589995
\(769\) −25079.3 −1.17605 −0.588024 0.808843i \(-0.700094\pi\)
−0.588024 + 0.808843i \(0.700094\pi\)
\(770\) −36132.8 −1.69109
\(771\) 6201.09 0.289659
\(772\) 2851.97 0.132959
\(773\) 15991.3 0.744071 0.372036 0.928218i \(-0.378660\pi\)
0.372036 + 0.928218i \(0.378660\pi\)
\(774\) 3327.22 0.154515
\(775\) −6612.99 −0.306510
\(776\) 22058.7 1.02044
\(777\) −16464.9 −0.760199
\(778\) 34251.2 1.57836
\(779\) −37540.9 −1.72663
\(780\) 11262.3 0.516994
\(781\) 26909.2 1.23289
\(782\) 117599. 5.37768
\(783\) −1441.93 −0.0658114
\(784\) −93.4727 −0.00425805
\(785\) 28909.9 1.31445
\(786\) −29121.2 −1.32153
\(787\) 32468.4 1.47061 0.735307 0.677734i \(-0.237038\pi\)
0.735307 + 0.677734i \(0.237038\pi\)
\(788\) 9615.02 0.434671
\(789\) 13303.0 0.600252
\(790\) 33514.4 1.50935
\(791\) −10658.8 −0.479119
\(792\) 8602.35 0.385948
\(793\) −839.813 −0.0376073
\(794\) 37014.4 1.65440
\(795\) 9617.44 0.429051
\(796\) 27779.1 1.23694
\(797\) 16858.3 0.749248 0.374624 0.927177i \(-0.377772\pi\)
0.374624 + 0.927177i \(0.377772\pi\)
\(798\) −22423.6 −0.994718
\(799\) −634.953 −0.0281139
\(800\) 4691.12 0.207320
\(801\) 9025.75 0.398139
\(802\) −7489.40 −0.329751
\(803\) 22211.1 0.976103
\(804\) 24774.3 1.08672
\(805\) 39099.2 1.71188
\(806\) −27169.3 −1.18734
\(807\) 7205.70 0.314315
\(808\) −29620.9 −1.28968
\(809\) −9132.42 −0.396884 −0.198442 0.980113i \(-0.563588\pi\)
−0.198442 + 0.980113i \(0.563588\pi\)
\(810\) 4563.55 0.197959
\(811\) −10235.5 −0.443179 −0.221589 0.975140i \(-0.571124\pi\)
−0.221589 + 0.975140i \(0.571124\pi\)
\(812\) −10650.5 −0.460296
\(813\) 11222.7 0.484129
\(814\) −68451.0 −2.94743
\(815\) 33878.3 1.45608
\(816\) 323.503 0.0138785
\(817\) −8575.59 −0.367224
\(818\) 9718.28 0.415393
\(819\) −3246.03 −0.138492
\(820\) 56432.5 2.40330
\(821\) −32830.2 −1.39559 −0.697797 0.716295i \(-0.745836\pi\)
−0.697797 + 0.716295i \(0.745836\pi\)
\(822\) −4382.91 −0.185975
\(823\) 27497.4 1.16464 0.582320 0.812960i \(-0.302145\pi\)
0.582320 + 0.812960i \(0.302145\pi\)
\(824\) −395.839 −0.0167351
\(825\) −3284.68 −0.138615
\(826\) 4149.31 0.174786
\(827\) −39886.2 −1.67712 −0.838560 0.544809i \(-0.816602\pi\)
−0.838560 + 0.544809i \(0.816602\pi\)
\(828\) −24223.8 −1.01671
\(829\) −42518.9 −1.78135 −0.890676 0.454638i \(-0.849769\pi\)
−0.890676 + 0.454638i \(0.849769\pi\)
\(830\) −5396.37 −0.225676
\(831\) −4329.66 −0.180739
\(832\) 19436.9 0.809922
\(833\) −13306.8 −0.553485
\(834\) −31764.4 −1.31884
\(835\) 46013.2 1.90701
\(836\) −57697.6 −2.38698
\(837\) −6813.75 −0.281383
\(838\) 67900.8 2.79904
\(839\) 22032.0 0.906592 0.453296 0.891360i \(-0.350248\pi\)
0.453296 + 0.891360i \(0.350248\pi\)
\(840\) 12953.0 0.532049
\(841\) −21536.9 −0.883059
\(842\) −23947.4 −0.980143
\(843\) −10493.6 −0.428729
\(844\) −6630.27 −0.270407
\(845\) 20226.2 0.823434
\(846\) 211.323 0.00858798
\(847\) 6366.70 0.258279
\(848\) −226.903 −0.00918854
\(849\) −1190.38 −0.0481196
\(850\) −14875.9 −0.600282
\(851\) 74070.7 2.98368
\(852\) −25103.2 −1.00942
\(853\) −43140.4 −1.73165 −0.865825 0.500346i \(-0.833206\pi\)
−0.865825 + 0.500346i \(0.833206\pi\)
\(854\) −2513.54 −0.100716
\(855\) −11762.1 −0.470474
\(856\) −6122.37 −0.244461
\(857\) 8131.01 0.324096 0.162048 0.986783i \(-0.448190\pi\)
0.162048 + 0.986783i \(0.448190\pi\)
\(858\) −13495.0 −0.536960
\(859\) −25210.4 −1.00136 −0.500680 0.865632i \(-0.666917\pi\)
−0.500680 + 0.865632i \(0.666917\pi\)
\(860\) 12891.1 0.511142
\(861\) −16265.0 −0.643798
\(862\) 50063.6 1.97816
\(863\) 23.0095 0.000907593 0 0.000453797 1.00000i \(-0.499856\pi\)
0.000453797 1.00000i \(0.499856\pi\)
\(864\) 4833.53 0.190324
\(865\) −48826.4 −1.91924
\(866\) −14537.9 −0.570461
\(867\) 31315.0 1.22666
\(868\) −50328.4 −1.96804
\(869\) −24854.8 −0.970243
\(870\) −9026.49 −0.351755
\(871\) −14934.7 −0.580993
\(872\) 4095.41 0.159046
\(873\) −8678.48 −0.336451
\(874\) 100877. 3.90413
\(875\) 18647.0 0.720437
\(876\) −20720.4 −0.799174
\(877\) −3988.93 −0.153588 −0.0767939 0.997047i \(-0.524468\pi\)
−0.0767939 + 0.997047i \(0.524468\pi\)
\(878\) −9908.94 −0.380877
\(879\) 27742.9 1.06456
\(880\) 447.160 0.0171293
\(881\) 42436.5 1.62284 0.811420 0.584464i \(-0.198695\pi\)
0.811420 + 0.584464i \(0.198695\pi\)
\(882\) 4428.72 0.169073
\(883\) −9854.79 −0.375583 −0.187792 0.982209i \(-0.560133\pi\)
−0.187792 + 0.982209i \(0.560133\pi\)
\(884\) −37826.5 −1.43919
\(885\) 2176.48 0.0826686
\(886\) 47057.9 1.78436
\(887\) 631.042 0.0238876 0.0119438 0.999929i \(-0.496198\pi\)
0.0119438 + 0.999929i \(0.496198\pi\)
\(888\) 24538.6 0.927320
\(889\) −29613.6 −1.11722
\(890\) 56501.2 2.12801
\(891\) −3384.39 −0.127252
\(892\) −31821.8 −1.19447
\(893\) −544.664 −0.0204104
\(894\) 16062.0 0.600887
\(895\) −16259.6 −0.607262
\(896\) 36191.6 1.34942
\(897\) 14602.9 0.543564
\(898\) 17513.6 0.650819
\(899\) 13477.3 0.499992
\(900\) 3064.22 0.113490
\(901\) −32301.9 −1.19438
\(902\) −67620.1 −2.49612
\(903\) −3715.47 −0.136925
\(904\) 15885.4 0.584447
\(905\) −39901.3 −1.46560
\(906\) 21128.2 0.774766
\(907\) 18816.6 0.688858 0.344429 0.938812i \(-0.388072\pi\)
0.344429 + 0.938812i \(0.388072\pi\)
\(908\) −2407.52 −0.0879915
\(909\) 11653.7 0.425223
\(910\) −20320.2 −0.740227
\(911\) 3772.72 0.137207 0.0686036 0.997644i \(-0.478146\pi\)
0.0686036 + 0.997644i \(0.478146\pi\)
\(912\) 277.501 0.0100756
\(913\) 4002.03 0.145069
\(914\) −76306.4 −2.76148
\(915\) −1318.45 −0.0476358
\(916\) 80368.9 2.89898
\(917\) 32519.3 1.17108
\(918\) −15327.5 −0.551071
\(919\) −28498.4 −1.02293 −0.511467 0.859303i \(-0.670898\pi\)
−0.511467 + 0.859303i \(0.670898\pi\)
\(920\) −58271.7 −2.08822
\(921\) 15039.0 0.538059
\(922\) −66337.4 −2.36953
\(923\) 15133.1 0.539665
\(924\) −24998.2 −0.890021
\(925\) −9369.68 −0.333052
\(926\) 50888.9 1.80595
\(927\) 155.733 0.00551775
\(928\) −9560.51 −0.338189
\(929\) −15966.5 −0.563879 −0.281940 0.959432i \(-0.590978\pi\)
−0.281940 + 0.959432i \(0.590978\pi\)
\(930\) −42654.1 −1.50396
\(931\) −11414.6 −0.401824
\(932\) −61006.0 −2.14412
\(933\) −19069.0 −0.669123
\(934\) −82928.9 −2.90526
\(935\) 63657.7 2.22656
\(936\) 4837.74 0.168938
\(937\) 3986.01 0.138973 0.0694863 0.997583i \(-0.477864\pi\)
0.0694863 + 0.997583i \(0.477864\pi\)
\(938\) −44699.3 −1.55595
\(939\) 4992.44 0.173506
\(940\) 818.755 0.0284094
\(941\) 30284.1 1.04913 0.524566 0.851370i \(-0.324227\pi\)
0.524566 + 0.851370i \(0.324227\pi\)
\(942\) 32316.3 1.11775
\(943\) 73171.5 2.52682
\(944\) −51.3495 −0.00177043
\(945\) −5096.06 −0.175423
\(946\) −15446.7 −0.530883
\(947\) −30270.4 −1.03871 −0.519354 0.854559i \(-0.673827\pi\)
−0.519354 + 0.854559i \(0.673827\pi\)
\(948\) 23186.7 0.794375
\(949\) 12490.9 0.427263
\(950\) −12760.6 −0.435798
\(951\) −28403.9 −0.968515
\(952\) −43505.1 −1.48110
\(953\) 19399.4 0.659401 0.329700 0.944086i \(-0.393052\pi\)
0.329700 + 0.944086i \(0.393052\pi\)
\(954\) 10750.6 0.364847
\(955\) −18407.7 −0.623728
\(956\) −47946.3 −1.62207
\(957\) 6694.18 0.226115
\(958\) 71466.4 2.41020
\(959\) 4894.35 0.164804
\(960\) 30514.8 1.02590
\(961\) 33895.0 1.13776
\(962\) −38495.1 −1.29016
\(963\) 2408.70 0.0806017
\(964\) −1688.27 −0.0564062
\(965\) −2699.14 −0.0900396
\(966\) 43706.1 1.45571
\(967\) 20800.3 0.691720 0.345860 0.938286i \(-0.387587\pi\)
0.345860 + 0.938286i \(0.387587\pi\)
\(968\) −9488.65 −0.315059
\(969\) 39505.1 1.30969
\(970\) −54327.4 −1.79830
\(971\) −27717.3 −0.916055 −0.458028 0.888938i \(-0.651444\pi\)
−0.458028 + 0.888938i \(0.651444\pi\)
\(972\) 3157.25 0.104186
\(973\) 35471.0 1.16870
\(974\) −64677.8 −2.12773
\(975\) −1847.22 −0.0606752
\(976\) 31.1061 0.00102017
\(977\) −19576.1 −0.641039 −0.320519 0.947242i \(-0.603857\pi\)
−0.320519 + 0.947242i \(0.603857\pi\)
\(978\) 37870.0 1.23819
\(979\) −41902.1 −1.36792
\(980\) 17158.7 0.559302
\(981\) −1611.24 −0.0524394
\(982\) −67328.3 −2.18792
\(983\) −11769.7 −0.381888 −0.190944 0.981601i \(-0.561155\pi\)
−0.190944 + 0.981601i \(0.561155\pi\)
\(984\) 24240.7 0.785330
\(985\) −9099.76 −0.294358
\(986\) 30317.1 0.979203
\(987\) −235.982 −0.00761032
\(988\) −32447.6 −1.04483
\(989\) 16714.8 0.537412
\(990\) −21186.3 −0.680147
\(991\) 52861.1 1.69444 0.847219 0.531245i \(-0.178275\pi\)
0.847219 + 0.531245i \(0.178275\pi\)
\(992\) −45177.6 −1.44596
\(993\) −16195.1 −0.517558
\(994\) 45292.8 1.44527
\(995\) −26290.5 −0.837652
\(996\) −3733.43 −0.118773
\(997\) −38949.2 −1.23725 −0.618623 0.785688i \(-0.712309\pi\)
−0.618623 + 0.785688i \(0.712309\pi\)
\(998\) −20141.5 −0.638846
\(999\) −9654.13 −0.305749
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.a.1.2 7
3.2 odd 2 531.4.a.d.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.2 7 1.1 even 1 trivial
531.4.a.d.1.6 7 3.2 odd 2