Properties

Label 177.4.a.a.1.6
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 1.6
Root \(-2.68175\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.68175 q^{2} +3.00000 q^{3} -5.17172 q^{4} -9.78761 q^{5} +5.04525 q^{6} +6.87552 q^{7} -22.1515 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.68175 q^{2} +3.00000 q^{3} -5.17172 q^{4} -9.78761 q^{5} +5.04525 q^{6} +6.87552 q^{7} -22.1515 q^{8} +9.00000 q^{9} -16.4603 q^{10} -37.8468 q^{11} -15.5151 q^{12} -11.3334 q^{13} +11.5629 q^{14} -29.3628 q^{15} +4.12039 q^{16} -60.3439 q^{17} +15.1358 q^{18} -92.5767 q^{19} +50.6188 q^{20} +20.6266 q^{21} -63.6489 q^{22} -183.718 q^{23} -66.4546 q^{24} -29.2026 q^{25} -19.0599 q^{26} +27.0000 q^{27} -35.5582 q^{28} +265.559 q^{29} -49.3810 q^{30} +177.376 q^{31} +184.142 q^{32} -113.540 q^{33} -101.483 q^{34} -67.2949 q^{35} -46.5454 q^{36} -70.0886 q^{37} -155.691 q^{38} -34.0002 q^{39} +216.811 q^{40} +208.760 q^{41} +34.6887 q^{42} +393.127 q^{43} +195.733 q^{44} -88.0885 q^{45} -308.968 q^{46} -134.917 q^{47} +12.3612 q^{48} -295.727 q^{49} -49.1115 q^{50} -181.032 q^{51} +58.6131 q^{52} -650.432 q^{53} +45.4073 q^{54} +370.430 q^{55} -152.303 q^{56} -277.730 q^{57} +446.604 q^{58} -59.0000 q^{59} +151.856 q^{60} +22.5322 q^{61} +298.302 q^{62} +61.8797 q^{63} +276.717 q^{64} +110.927 q^{65} -190.947 q^{66} -209.476 q^{67} +312.082 q^{68} -551.155 q^{69} -113.173 q^{70} +209.160 q^{71} -199.364 q^{72} +865.282 q^{73} -117.872 q^{74} -87.6079 q^{75} +478.781 q^{76} -260.217 q^{77} -57.1798 q^{78} +843.604 q^{79} -40.3287 q^{80} +81.0000 q^{81} +351.082 q^{82} -845.384 q^{83} -106.675 q^{84} +590.623 q^{85} +661.141 q^{86} +796.677 q^{87} +838.365 q^{88} -974.766 q^{89} -148.143 q^{90} -77.9229 q^{91} +950.139 q^{92} +532.127 q^{93} -226.897 q^{94} +906.105 q^{95} +552.425 q^{96} +338.796 q^{97} -497.339 q^{98} -340.621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.68175 0.594588 0.297294 0.954786i \(-0.403916\pi\)
0.297294 + 0.954786i \(0.403916\pi\)
\(3\) 3.00000 0.577350
\(4\) −5.17172 −0.646465
\(5\) −9.78761 −0.875431 −0.437715 0.899114i \(-0.644212\pi\)
−0.437715 + 0.899114i \(0.644212\pi\)
\(6\) 5.04525 0.343286
\(7\) 6.87552 0.371243 0.185622 0.982621i \(-0.440570\pi\)
0.185622 + 0.982621i \(0.440570\pi\)
\(8\) −22.1515 −0.978969
\(9\) 9.00000 0.333333
\(10\) −16.4603 −0.520521
\(11\) −37.8468 −1.03739 −0.518693 0.854961i \(-0.673581\pi\)
−0.518693 + 0.854961i \(0.673581\pi\)
\(12\) −15.5151 −0.373237
\(13\) −11.3334 −0.241794 −0.120897 0.992665i \(-0.538577\pi\)
−0.120897 + 0.992665i \(0.538577\pi\)
\(14\) 11.5629 0.220737
\(15\) −29.3628 −0.505430
\(16\) 4.12039 0.0643810
\(17\) −60.3439 −0.860915 −0.430457 0.902611i \(-0.641648\pi\)
−0.430457 + 0.902611i \(0.641648\pi\)
\(18\) 15.1358 0.198196
\(19\) −92.5767 −1.11782 −0.558909 0.829229i \(-0.688780\pi\)
−0.558909 + 0.829229i \(0.688780\pi\)
\(20\) 50.6188 0.565935
\(21\) 20.6266 0.214337
\(22\) −63.6489 −0.616818
\(23\) −183.718 −1.66556 −0.832781 0.553603i \(-0.813252\pi\)
−0.832781 + 0.553603i \(0.813252\pi\)
\(24\) −66.4546 −0.565208
\(25\) −29.2026 −0.233621
\(26\) −19.0599 −0.143768
\(27\) 27.0000 0.192450
\(28\) −35.5582 −0.239995
\(29\) 265.559 1.70045 0.850225 0.526419i \(-0.176466\pi\)
0.850225 + 0.526419i \(0.176466\pi\)
\(30\) −49.3810 −0.300523
\(31\) 177.376 1.02767 0.513833 0.857890i \(-0.328225\pi\)
0.513833 + 0.857890i \(0.328225\pi\)
\(32\) 184.142 1.01725
\(33\) −113.540 −0.598935
\(34\) −101.483 −0.511890
\(35\) −67.2949 −0.324998
\(36\) −46.5454 −0.215488
\(37\) −70.0886 −0.311419 −0.155709 0.987803i \(-0.549766\pi\)
−0.155709 + 0.987803i \(0.549766\pi\)
\(38\) −155.691 −0.664642
\(39\) −34.0002 −0.139600
\(40\) 216.811 0.857019
\(41\) 208.760 0.795190 0.397595 0.917561i \(-0.369845\pi\)
0.397595 + 0.917561i \(0.369845\pi\)
\(42\) 34.6887 0.127442
\(43\) 393.127 1.39421 0.697107 0.716967i \(-0.254470\pi\)
0.697107 + 0.716967i \(0.254470\pi\)
\(44\) 195.733 0.670633
\(45\) −88.0885 −0.291810
\(46\) −308.968 −0.990323
\(47\) −134.917 −0.418717 −0.209358 0.977839i \(-0.567138\pi\)
−0.209358 + 0.977839i \(0.567138\pi\)
\(48\) 12.3612 0.0371704
\(49\) −295.727 −0.862179
\(50\) −49.1115 −0.138908
\(51\) −181.032 −0.497049
\(52\) 58.6131 0.156311
\(53\) −650.432 −1.68573 −0.842865 0.538126i \(-0.819133\pi\)
−0.842865 + 0.538126i \(0.819133\pi\)
\(54\) 45.4073 0.114429
\(55\) 370.430 0.908160
\(56\) −152.303 −0.363435
\(57\) −277.730 −0.645373
\(58\) 446.604 1.01107
\(59\) −59.0000 −0.130189
\(60\) 151.856 0.326743
\(61\) 22.5322 0.0472943 0.0236472 0.999720i \(-0.492472\pi\)
0.0236472 + 0.999720i \(0.492472\pi\)
\(62\) 298.302 0.611038
\(63\) 61.8797 0.123748
\(64\) 276.717 0.540463
\(65\) 110.927 0.211674
\(66\) −190.947 −0.356120
\(67\) −209.476 −0.381964 −0.190982 0.981594i \(-0.561167\pi\)
−0.190982 + 0.981594i \(0.561167\pi\)
\(68\) 312.082 0.556551
\(69\) −551.155 −0.961612
\(70\) −113.173 −0.193240
\(71\) 209.160 0.349616 0.174808 0.984603i \(-0.444070\pi\)
0.174808 + 0.984603i \(0.444070\pi\)
\(72\) −199.364 −0.326323
\(73\) 865.282 1.38731 0.693655 0.720308i \(-0.255999\pi\)
0.693655 + 0.720308i \(0.255999\pi\)
\(74\) −117.872 −0.185166
\(75\) −87.6079 −0.134881
\(76\) 478.781 0.722630
\(77\) −260.217 −0.385122
\(78\) −57.1798 −0.0830043
\(79\) 843.604 1.20143 0.600715 0.799464i \(-0.294883\pi\)
0.600715 + 0.799464i \(0.294883\pi\)
\(80\) −40.3287 −0.0563611
\(81\) 81.0000 0.111111
\(82\) 351.082 0.472811
\(83\) −845.384 −1.11799 −0.558994 0.829172i \(-0.688812\pi\)
−0.558994 + 0.829172i \(0.688812\pi\)
\(84\) −106.675 −0.138561
\(85\) 590.623 0.753671
\(86\) 661.141 0.828984
\(87\) 796.677 0.981755
\(88\) 838.365 1.01557
\(89\) −974.766 −1.16096 −0.580478 0.814276i \(-0.697134\pi\)
−0.580478 + 0.814276i \(0.697134\pi\)
\(90\) −148.143 −0.173507
\(91\) −77.9229 −0.0897642
\(92\) 950.139 1.07673
\(93\) 532.127 0.593323
\(94\) −226.897 −0.248964
\(95\) 906.105 0.978573
\(96\) 552.425 0.587309
\(97\) 338.796 0.354634 0.177317 0.984154i \(-0.443258\pi\)
0.177317 + 0.984154i \(0.443258\pi\)
\(98\) −497.339 −0.512641
\(99\) −340.621 −0.345795
\(100\) 151.028 0.151028
\(101\) −683.879 −0.673747 −0.336874 0.941550i \(-0.609369\pi\)
−0.336874 + 0.941550i \(0.609369\pi\)
\(102\) −304.450 −0.295540
\(103\) −1235.54 −1.18196 −0.590979 0.806687i \(-0.701258\pi\)
−0.590979 + 0.806687i \(0.701258\pi\)
\(104\) 251.052 0.236708
\(105\) −201.885 −0.187637
\(106\) −1093.86 −1.00231
\(107\) 431.478 0.389837 0.194918 0.980819i \(-0.437556\pi\)
0.194918 + 0.980819i \(0.437556\pi\)
\(108\) −139.636 −0.124412
\(109\) 427.874 0.375989 0.187995 0.982170i \(-0.439801\pi\)
0.187995 + 0.982170i \(0.439801\pi\)
\(110\) 622.971 0.539981
\(111\) −210.266 −0.179798
\(112\) 28.3298 0.0239010
\(113\) −1934.70 −1.61063 −0.805317 0.592845i \(-0.798005\pi\)
−0.805317 + 0.592845i \(0.798005\pi\)
\(114\) −467.073 −0.383731
\(115\) 1798.16 1.45808
\(116\) −1373.40 −1.09928
\(117\) −102.001 −0.0805979
\(118\) −99.2233 −0.0774088
\(119\) −414.896 −0.319609
\(120\) 650.432 0.494800
\(121\) 101.382 0.0761698
\(122\) 37.8935 0.0281207
\(123\) 626.280 0.459103
\(124\) −917.337 −0.664349
\(125\) 1509.28 1.07995
\(126\) 104.066 0.0735789
\(127\) −1334.46 −0.932395 −0.466198 0.884681i \(-0.654376\pi\)
−0.466198 + 0.884681i \(0.654376\pi\)
\(128\) −1007.76 −0.695896
\(129\) 1179.38 0.804950
\(130\) 186.551 0.125859
\(131\) −739.638 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(132\) 587.199 0.387190
\(133\) −636.513 −0.414982
\(134\) −352.287 −0.227111
\(135\) −264.266 −0.168477
\(136\) 1336.71 0.842809
\(137\) −1262.30 −0.787196 −0.393598 0.919283i \(-0.628770\pi\)
−0.393598 + 0.919283i \(0.628770\pi\)
\(138\) −926.905 −0.571763
\(139\) 2630.69 1.60527 0.802634 0.596471i \(-0.203431\pi\)
0.802634 + 0.596471i \(0.203431\pi\)
\(140\) 348.030 0.210099
\(141\) −404.752 −0.241746
\(142\) 351.755 0.207877
\(143\) 428.933 0.250833
\(144\) 37.0835 0.0214603
\(145\) −2599.19 −1.48863
\(146\) 1455.19 0.824878
\(147\) −887.182 −0.497779
\(148\) 362.478 0.201321
\(149\) −434.666 −0.238988 −0.119494 0.992835i \(-0.538127\pi\)
−0.119494 + 0.992835i \(0.538127\pi\)
\(150\) −147.335 −0.0801988
\(151\) −1585.40 −0.854425 −0.427213 0.904151i \(-0.640504\pi\)
−0.427213 + 0.904151i \(0.640504\pi\)
\(152\) 2050.72 1.09431
\(153\) −543.095 −0.286972
\(154\) −437.619 −0.228989
\(155\) −1736.09 −0.899650
\(156\) 175.839 0.0902462
\(157\) 3744.07 1.90324 0.951622 0.307270i \(-0.0994155\pi\)
0.951622 + 0.307270i \(0.0994155\pi\)
\(158\) 1418.73 0.714356
\(159\) −1951.29 −0.973256
\(160\) −1802.31 −0.890531
\(161\) −1263.16 −0.618328
\(162\) 136.222 0.0660654
\(163\) −1331.85 −0.639993 −0.319996 0.947419i \(-0.603682\pi\)
−0.319996 + 0.947419i \(0.603682\pi\)
\(164\) −1079.65 −0.514062
\(165\) 1111.29 0.524326
\(166\) −1421.73 −0.664743
\(167\) 16.5584 0.00767260 0.00383630 0.999993i \(-0.498779\pi\)
0.00383630 + 0.999993i \(0.498779\pi\)
\(168\) −456.910 −0.209830
\(169\) −2068.55 −0.941536
\(170\) 993.280 0.448124
\(171\) −833.191 −0.372606
\(172\) −2033.14 −0.901310
\(173\) −2397.07 −1.05344 −0.526721 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(174\) 1339.81 0.583740
\(175\) −200.783 −0.0867302
\(176\) −155.944 −0.0667880
\(177\) −177.000 −0.0751646
\(178\) −1639.31 −0.690291
\(179\) 1223.00 0.510680 0.255340 0.966851i \(-0.417813\pi\)
0.255340 + 0.966851i \(0.417813\pi\)
\(180\) 455.569 0.188645
\(181\) −4266.97 −1.75227 −0.876137 0.482063i \(-0.839888\pi\)
−0.876137 + 0.482063i \(0.839888\pi\)
\(182\) −131.047 −0.0533728
\(183\) 67.5966 0.0273054
\(184\) 4069.64 1.63053
\(185\) 686.000 0.272626
\(186\) 894.905 0.352783
\(187\) 2283.83 0.893101
\(188\) 697.753 0.270686
\(189\) 185.639 0.0714458
\(190\) 1523.84 0.581848
\(191\) −3080.45 −1.16698 −0.583491 0.812120i \(-0.698313\pi\)
−0.583491 + 0.812120i \(0.698313\pi\)
\(192\) 830.152 0.312037
\(193\) 3469.71 1.29407 0.647033 0.762462i \(-0.276009\pi\)
0.647033 + 0.762462i \(0.276009\pi\)
\(194\) 569.770 0.210862
\(195\) 332.781 0.122210
\(196\) 1529.42 0.557368
\(197\) −1487.74 −0.538055 −0.269027 0.963133i \(-0.586702\pi\)
−0.269027 + 0.963133i \(0.586702\pi\)
\(198\) −572.840 −0.205606
\(199\) −3027.73 −1.07854 −0.539271 0.842132i \(-0.681300\pi\)
−0.539271 + 0.842132i \(0.681300\pi\)
\(200\) 646.883 0.228708
\(201\) −628.429 −0.220527
\(202\) −1150.11 −0.400602
\(203\) 1825.86 0.631280
\(204\) 936.245 0.321325
\(205\) −2043.26 −0.696134
\(206\) −2077.87 −0.702779
\(207\) −1653.46 −0.555187
\(208\) −46.6980 −0.0155669
\(209\) 3503.74 1.15961
\(210\) −339.520 −0.111567
\(211\) −1655.90 −0.540269 −0.270135 0.962823i \(-0.587068\pi\)
−0.270135 + 0.962823i \(0.587068\pi\)
\(212\) 3363.85 1.08976
\(213\) 627.480 0.201851
\(214\) 725.638 0.231792
\(215\) −3847.77 −1.22054
\(216\) −598.091 −0.188403
\(217\) 1219.55 0.381514
\(218\) 719.576 0.223559
\(219\) 2595.85 0.800964
\(220\) −1915.76 −0.587093
\(221\) 683.901 0.208164
\(222\) −353.615 −0.106906
\(223\) −1225.20 −0.367916 −0.183958 0.982934i \(-0.558891\pi\)
−0.183958 + 0.982934i \(0.558891\pi\)
\(224\) 1266.07 0.377647
\(225\) −262.824 −0.0778737
\(226\) −3253.69 −0.957664
\(227\) −657.677 −0.192298 −0.0961488 0.995367i \(-0.530652\pi\)
−0.0961488 + 0.995367i \(0.530652\pi\)
\(228\) 1436.34 0.417211
\(229\) 1407.97 0.406294 0.203147 0.979148i \(-0.434883\pi\)
0.203147 + 0.979148i \(0.434883\pi\)
\(230\) 3024.06 0.866959
\(231\) −780.650 −0.222351
\(232\) −5882.54 −1.66469
\(233\) 6393.48 1.79764 0.898821 0.438315i \(-0.144425\pi\)
0.898821 + 0.438315i \(0.144425\pi\)
\(234\) −171.539 −0.0479226
\(235\) 1320.52 0.366558
\(236\) 305.131 0.0841625
\(237\) 2530.81 0.693645
\(238\) −697.751 −0.190036
\(239\) 1941.60 0.525489 0.262744 0.964865i \(-0.415372\pi\)
0.262744 + 0.964865i \(0.415372\pi\)
\(240\) −120.986 −0.0325401
\(241\) −3701.61 −0.989385 −0.494692 0.869068i \(-0.664719\pi\)
−0.494692 + 0.869068i \(0.664719\pi\)
\(242\) 170.499 0.0452897
\(243\) 243.000 0.0641500
\(244\) −116.530 −0.0305741
\(245\) 2894.46 0.754778
\(246\) 1053.25 0.272978
\(247\) 1049.21 0.270282
\(248\) −3929.15 −1.00605
\(249\) −2536.15 −0.645471
\(250\) 2538.22 0.642126
\(251\) −239.067 −0.0601186 −0.0300593 0.999548i \(-0.509570\pi\)
−0.0300593 + 0.999548i \(0.509570\pi\)
\(252\) −320.024 −0.0799985
\(253\) 6953.15 1.72783
\(254\) −2244.23 −0.554392
\(255\) 1771.87 0.435132
\(256\) −3908.55 −0.954235
\(257\) 6633.12 1.60997 0.804985 0.593295i \(-0.202173\pi\)
0.804985 + 0.593295i \(0.202173\pi\)
\(258\) 1983.42 0.478614
\(259\) −481.895 −0.115612
\(260\) −573.682 −0.136839
\(261\) 2390.03 0.566817
\(262\) −1243.89 −0.293311
\(263\) −2010.45 −0.471368 −0.235684 0.971830i \(-0.575733\pi\)
−0.235684 + 0.971830i \(0.575733\pi\)
\(264\) 2515.10 0.586339
\(265\) 6366.17 1.47574
\(266\) −1070.46 −0.246744
\(267\) −2924.30 −0.670278
\(268\) 1083.35 0.246926
\(269\) 5923.22 1.34255 0.671273 0.741210i \(-0.265748\pi\)
0.671273 + 0.741210i \(0.265748\pi\)
\(270\) −444.429 −0.100174
\(271\) −1908.94 −0.427896 −0.213948 0.976845i \(-0.568632\pi\)
−0.213948 + 0.976845i \(0.568632\pi\)
\(272\) −248.640 −0.0554266
\(273\) −233.769 −0.0518254
\(274\) −2122.88 −0.468057
\(275\) 1105.23 0.242355
\(276\) 2850.42 0.621648
\(277\) 7685.54 1.66707 0.833536 0.552464i \(-0.186312\pi\)
0.833536 + 0.552464i \(0.186312\pi\)
\(278\) 4424.17 0.954474
\(279\) 1596.38 0.342555
\(280\) 1490.69 0.318162
\(281\) 1223.20 0.259680 0.129840 0.991535i \(-0.458554\pi\)
0.129840 + 0.991535i \(0.458554\pi\)
\(282\) −680.691 −0.143740
\(283\) −1543.59 −0.324229 −0.162115 0.986772i \(-0.551831\pi\)
−0.162115 + 0.986772i \(0.551831\pi\)
\(284\) −1081.72 −0.226014
\(285\) 2718.32 0.564979
\(286\) 721.358 0.149143
\(287\) 1435.33 0.295209
\(288\) 1657.28 0.339083
\(289\) −1271.61 −0.258826
\(290\) −4371.18 −0.885120
\(291\) 1016.39 0.204748
\(292\) −4474.99 −0.896846
\(293\) −3987.52 −0.795063 −0.397532 0.917589i \(-0.630133\pi\)
−0.397532 + 0.917589i \(0.630133\pi\)
\(294\) −1492.02 −0.295974
\(295\) 577.469 0.113971
\(296\) 1552.57 0.304869
\(297\) −1021.86 −0.199645
\(298\) −731.000 −0.142100
\(299\) 2082.15 0.402722
\(300\) 453.083 0.0871959
\(301\) 2702.95 0.517593
\(302\) −2666.25 −0.508031
\(303\) −2051.64 −0.388988
\(304\) −381.452 −0.0719663
\(305\) −220.537 −0.0414029
\(306\) −913.350 −0.170630
\(307\) −895.829 −0.166540 −0.0832698 0.996527i \(-0.526536\pi\)
−0.0832698 + 0.996527i \(0.526536\pi\)
\(308\) 1345.77 0.248968
\(309\) −3706.63 −0.682404
\(310\) −2919.66 −0.534921
\(311\) 4166.91 0.759754 0.379877 0.925037i \(-0.375966\pi\)
0.379877 + 0.925037i \(0.375966\pi\)
\(312\) 753.156 0.136664
\(313\) −3619.78 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(314\) 6296.59 1.13165
\(315\) −605.654 −0.108333
\(316\) −4362.88 −0.776681
\(317\) 865.480 0.153344 0.0766722 0.997056i \(-0.475570\pi\)
0.0766722 + 0.997056i \(0.475570\pi\)
\(318\) −3281.59 −0.578687
\(319\) −10050.6 −1.76402
\(320\) −2708.40 −0.473138
\(321\) 1294.43 0.225072
\(322\) −2124.32 −0.367651
\(323\) 5586.44 0.962347
\(324\) −418.909 −0.0718294
\(325\) 330.965 0.0564881
\(326\) −2239.84 −0.380532
\(327\) 1283.62 0.217078
\(328\) −4624.35 −0.778467
\(329\) −927.626 −0.155446
\(330\) 1868.91 0.311758
\(331\) 8140.89 1.35185 0.675927 0.736968i \(-0.263743\pi\)
0.675927 + 0.736968i \(0.263743\pi\)
\(332\) 4372.09 0.722739
\(333\) −630.797 −0.103806
\(334\) 27.8470 0.00456204
\(335\) 2050.27 0.334383
\(336\) 84.9894 0.0137993
\(337\) 7396.34 1.19556 0.597781 0.801659i \(-0.296049\pi\)
0.597781 + 0.801659i \(0.296049\pi\)
\(338\) −3478.79 −0.559826
\(339\) −5804.11 −0.929900
\(340\) −3054.53 −0.487222
\(341\) −6713.11 −1.06609
\(342\) −1401.22 −0.221547
\(343\) −4391.58 −0.691321
\(344\) −8708.36 −1.36489
\(345\) 5394.49 0.841825
\(346\) −4031.27 −0.626365
\(347\) −1341.98 −0.207612 −0.103806 0.994598i \(-0.533102\pi\)
−0.103806 + 0.994598i \(0.533102\pi\)
\(348\) −4120.19 −0.634670
\(349\) 2193.32 0.336407 0.168203 0.985752i \(-0.446203\pi\)
0.168203 + 0.985752i \(0.446203\pi\)
\(350\) −337.667 −0.0515688
\(351\) −306.002 −0.0465332
\(352\) −6969.18 −1.05528
\(353\) −636.290 −0.0959386 −0.0479693 0.998849i \(-0.515275\pi\)
−0.0479693 + 0.998849i \(0.515275\pi\)
\(354\) −297.670 −0.0446920
\(355\) −2047.18 −0.306064
\(356\) 5041.22 0.750516
\(357\) −1244.69 −0.184526
\(358\) 2056.79 0.303644
\(359\) −7124.07 −1.04734 −0.523668 0.851922i \(-0.675437\pi\)
−0.523668 + 0.851922i \(0.675437\pi\)
\(360\) 1951.30 0.285673
\(361\) 1711.45 0.249519
\(362\) −7175.98 −1.04188
\(363\) 304.146 0.0439766
\(364\) 402.995 0.0580294
\(365\) −8469.04 −1.21449
\(366\) 113.681 0.0162355
\(367\) −8714.69 −1.23952 −0.619759 0.784792i \(-0.712770\pi\)
−0.619759 + 0.784792i \(0.712770\pi\)
\(368\) −756.990 −0.107231
\(369\) 1878.84 0.265063
\(370\) 1153.68 0.162100
\(371\) −4472.05 −0.625815
\(372\) −2752.01 −0.383562
\(373\) 9123.29 1.26645 0.633225 0.773967i \(-0.281731\pi\)
0.633225 + 0.773967i \(0.281731\pi\)
\(374\) 3840.82 0.531027
\(375\) 4527.83 0.623509
\(376\) 2988.62 0.409911
\(377\) −3009.68 −0.411158
\(378\) 312.198 0.0424808
\(379\) 8539.81 1.15742 0.578708 0.815535i \(-0.303557\pi\)
0.578708 + 0.815535i \(0.303557\pi\)
\(380\) −4686.12 −0.632613
\(381\) −4003.38 −0.538319
\(382\) −5180.54 −0.693873
\(383\) −8691.08 −1.15951 −0.579757 0.814790i \(-0.696852\pi\)
−0.579757 + 0.814790i \(0.696852\pi\)
\(384\) −3023.29 −0.401776
\(385\) 2546.90 0.337148
\(386\) 5835.18 0.769437
\(387\) 3538.14 0.464738
\(388\) −1752.16 −0.229259
\(389\) −10079.9 −1.31381 −0.656904 0.753974i \(-0.728134\pi\)
−0.656904 + 0.753974i \(0.728134\pi\)
\(390\) 559.654 0.0726645
\(391\) 11086.3 1.43391
\(392\) 6550.81 0.844046
\(393\) −2218.91 −0.284808
\(394\) −2502.00 −0.319921
\(395\) −8256.87 −1.05177
\(396\) 1761.60 0.223544
\(397\) −1829.51 −0.231286 −0.115643 0.993291i \(-0.536893\pi\)
−0.115643 + 0.993291i \(0.536893\pi\)
\(398\) −5091.88 −0.641288
\(399\) −1909.54 −0.239590
\(400\) −120.326 −0.0150408
\(401\) −10919.6 −1.35985 −0.679926 0.733281i \(-0.737988\pi\)
−0.679926 + 0.733281i \(0.737988\pi\)
\(402\) −1056.86 −0.131123
\(403\) −2010.27 −0.248483
\(404\) 3536.83 0.435554
\(405\) −792.797 −0.0972701
\(406\) 3070.63 0.375352
\(407\) 2652.63 0.323061
\(408\) 4010.13 0.486596
\(409\) 6441.50 0.778757 0.389378 0.921078i \(-0.372690\pi\)
0.389378 + 0.921078i \(0.372690\pi\)
\(410\) −3436.25 −0.413913
\(411\) −3786.91 −0.454488
\(412\) 6389.88 0.764094
\(413\) −405.656 −0.0483317
\(414\) −2780.71 −0.330108
\(415\) 8274.29 0.978721
\(416\) −2086.95 −0.245964
\(417\) 7892.08 0.926802
\(418\) 5892.41 0.689491
\(419\) 6784.29 0.791012 0.395506 0.918463i \(-0.370569\pi\)
0.395506 + 0.918463i \(0.370569\pi\)
\(420\) 1044.09 0.121301
\(421\) 827.842 0.0958350 0.0479175 0.998851i \(-0.484742\pi\)
0.0479175 + 0.998851i \(0.484742\pi\)
\(422\) −2784.81 −0.321238
\(423\) −1214.25 −0.139572
\(424\) 14408.1 1.65028
\(425\) 1762.20 0.201128
\(426\) 1055.26 0.120018
\(427\) 154.921 0.0175577
\(428\) −2231.48 −0.252016
\(429\) 1286.80 0.144819
\(430\) −6470.99 −0.725718
\(431\) 1719.44 0.192163 0.0960815 0.995373i \(-0.469369\pi\)
0.0960815 + 0.995373i \(0.469369\pi\)
\(432\) 111.250 0.0123901
\(433\) 11944.5 1.32567 0.662836 0.748765i \(-0.269353\pi\)
0.662836 + 0.748765i \(0.269353\pi\)
\(434\) 2050.98 0.226844
\(435\) −7797.56 −0.859459
\(436\) −2212.84 −0.243064
\(437\) 17008.0 1.86180
\(438\) 4365.56 0.476244
\(439\) 316.306 0.0343882 0.0171941 0.999852i \(-0.494527\pi\)
0.0171941 + 0.999852i \(0.494527\pi\)
\(440\) −8205.59 −0.889060
\(441\) −2661.55 −0.287393
\(442\) 1150.15 0.123772
\(443\) −9043.41 −0.969899 −0.484950 0.874542i \(-0.661162\pi\)
−0.484950 + 0.874542i \(0.661162\pi\)
\(444\) 1087.44 0.116233
\(445\) 9540.63 1.01634
\(446\) −2060.47 −0.218758
\(447\) −1304.00 −0.137980
\(448\) 1902.57 0.200643
\(449\) 9058.55 0.952114 0.476057 0.879414i \(-0.342066\pi\)
0.476057 + 0.879414i \(0.342066\pi\)
\(450\) −442.004 −0.0463028
\(451\) −7900.90 −0.824920
\(452\) 10005.7 1.04122
\(453\) −4756.21 −0.493303
\(454\) −1106.05 −0.114338
\(455\) 762.680 0.0785824
\(456\) 6152.15 0.631800
\(457\) 14344.7 1.46831 0.734155 0.678982i \(-0.237579\pi\)
0.734155 + 0.678982i \(0.237579\pi\)
\(458\) 2367.85 0.241578
\(459\) −1629.29 −0.165683
\(460\) −9299.59 −0.942599
\(461\) −10742.1 −1.08527 −0.542634 0.839969i \(-0.682573\pi\)
−0.542634 + 0.839969i \(0.682573\pi\)
\(462\) −1312.86 −0.132207
\(463\) −17574.2 −1.76402 −0.882009 0.471232i \(-0.843809\pi\)
−0.882009 + 0.471232i \(0.843809\pi\)
\(464\) 1094.21 0.109477
\(465\) −5208.26 −0.519413
\(466\) 10752.2 1.06886
\(467\) 8958.29 0.887667 0.443833 0.896109i \(-0.353618\pi\)
0.443833 + 0.896109i \(0.353618\pi\)
\(468\) 527.518 0.0521037
\(469\) −1440.26 −0.141802
\(470\) 2220.78 0.217951
\(471\) 11232.2 1.09884
\(472\) 1306.94 0.127451
\(473\) −14878.6 −1.44634
\(474\) 4256.19 0.412434
\(475\) 2703.49 0.261146
\(476\) 2145.72 0.206616
\(477\) −5853.88 −0.561910
\(478\) 3265.29 0.312450
\(479\) 6909.71 0.659108 0.329554 0.944137i \(-0.393102\pi\)
0.329554 + 0.944137i \(0.393102\pi\)
\(480\) −5406.92 −0.514148
\(481\) 794.342 0.0752991
\(482\) −6225.19 −0.588277
\(483\) −3789.47 −0.356992
\(484\) −524.319 −0.0492411
\(485\) −3316.01 −0.310458
\(486\) 408.665 0.0381429
\(487\) −15008.4 −1.39650 −0.698248 0.715856i \(-0.746037\pi\)
−0.698248 + 0.715856i \(0.746037\pi\)
\(488\) −499.123 −0.0462997
\(489\) −3995.56 −0.369500
\(490\) 4867.76 0.448782
\(491\) 10939.9 1.00552 0.502761 0.864425i \(-0.332318\pi\)
0.502761 + 0.864425i \(0.332318\pi\)
\(492\) −3238.94 −0.296794
\(493\) −16024.9 −1.46394
\(494\) 1764.51 0.160706
\(495\) 3333.87 0.302720
\(496\) 730.857 0.0661622
\(497\) 1438.08 0.129792
\(498\) −4265.18 −0.383789
\(499\) −1960.94 −0.175919 −0.0879596 0.996124i \(-0.528035\pi\)
−0.0879596 + 0.996124i \(0.528035\pi\)
\(500\) −7805.55 −0.698149
\(501\) 49.6751 0.00442978
\(502\) −402.051 −0.0357458
\(503\) −7812.26 −0.692508 −0.346254 0.938141i \(-0.612547\pi\)
−0.346254 + 0.938141i \(0.612547\pi\)
\(504\) −1370.73 −0.121145
\(505\) 6693.54 0.589819
\(506\) 11693.5 1.02735
\(507\) −6205.66 −0.543596
\(508\) 6901.45 0.602761
\(509\) 11915.7 1.03763 0.518816 0.854886i \(-0.326373\pi\)
0.518816 + 0.854886i \(0.326373\pi\)
\(510\) 2979.84 0.258725
\(511\) 5949.26 0.515029
\(512\) 1488.92 0.128519
\(513\) −2499.57 −0.215124
\(514\) 11155.2 0.957270
\(515\) 12093.0 1.03472
\(516\) −6099.42 −0.520372
\(517\) 5106.19 0.434371
\(518\) −810.428 −0.0687416
\(519\) −7191.20 −0.608205
\(520\) −2457.20 −0.207222
\(521\) 12795.0 1.07593 0.537963 0.842969i \(-0.319194\pi\)
0.537963 + 0.842969i \(0.319194\pi\)
\(522\) 4019.43 0.337023
\(523\) −18908.5 −1.58090 −0.790452 0.612524i \(-0.790154\pi\)
−0.790452 + 0.612524i \(0.790154\pi\)
\(524\) 3825.20 0.318902
\(525\) −602.350 −0.0500737
\(526\) −3381.08 −0.280270
\(527\) −10703.5 −0.884732
\(528\) −467.831 −0.0385601
\(529\) 21585.4 1.77409
\(530\) 10706.3 0.877457
\(531\) −531.000 −0.0433963
\(532\) 3291.86 0.268271
\(533\) −2365.96 −0.192272
\(534\) −4917.94 −0.398539
\(535\) −4223.14 −0.341275
\(536\) 4640.22 0.373931
\(537\) 3669.01 0.294841
\(538\) 9961.37 0.798263
\(539\) 11192.3 0.894412
\(540\) 1366.71 0.108914
\(541\) −13497.9 −1.07268 −0.536340 0.844002i \(-0.680194\pi\)
−0.536340 + 0.844002i \(0.680194\pi\)
\(542\) −3210.36 −0.254422
\(543\) −12800.9 −1.01168
\(544\) −11111.8 −0.875765
\(545\) −4187.86 −0.329153
\(546\) −393.141 −0.0308148
\(547\) 7859.46 0.614344 0.307172 0.951654i \(-0.400617\pi\)
0.307172 + 0.951654i \(0.400617\pi\)
\(548\) 6528.27 0.508894
\(549\) 202.790 0.0157648
\(550\) 1858.72 0.144102
\(551\) −24584.6 −1.90080
\(552\) 12208.9 0.941388
\(553\) 5800.22 0.446022
\(554\) 12925.2 0.991222
\(555\) 2058.00 0.157400
\(556\) −13605.2 −1.03775
\(557\) 20367.3 1.54936 0.774678 0.632356i \(-0.217912\pi\)
0.774678 + 0.632356i \(0.217912\pi\)
\(558\) 2684.72 0.203679
\(559\) −4455.46 −0.337112
\(560\) −277.281 −0.0209237
\(561\) 6851.48 0.515632
\(562\) 2057.12 0.154403
\(563\) 3392.89 0.253985 0.126992 0.991904i \(-0.459468\pi\)
0.126992 + 0.991904i \(0.459468\pi\)
\(564\) 2093.26 0.156280
\(565\) 18936.1 1.41000
\(566\) −2595.93 −0.192783
\(567\) 556.917 0.0412492
\(568\) −4633.21 −0.342263
\(569\) 8441.27 0.621927 0.310964 0.950422i \(-0.399348\pi\)
0.310964 + 0.950422i \(0.399348\pi\)
\(570\) 4571.53 0.335930
\(571\) 1840.67 0.134903 0.0674514 0.997723i \(-0.478513\pi\)
0.0674514 + 0.997723i \(0.478513\pi\)
\(572\) −2218.32 −0.162155
\(573\) −9241.34 −0.673757
\(574\) 2413.87 0.175528
\(575\) 5365.06 0.389110
\(576\) 2490.46 0.180154
\(577\) −14007.9 −1.01067 −0.505335 0.862923i \(-0.668631\pi\)
−0.505335 + 0.862923i \(0.668631\pi\)
\(578\) −2138.53 −0.153895
\(579\) 10409.1 0.747130
\(580\) 13442.3 0.962344
\(581\) −5812.45 −0.415045
\(582\) 1709.31 0.121741
\(583\) 24616.8 1.74875
\(584\) −19167.3 −1.35813
\(585\) 998.342 0.0705579
\(586\) −6706.01 −0.472735
\(587\) −26870.9 −1.88940 −0.944702 0.327931i \(-0.893649\pi\)
−0.944702 + 0.327931i \(0.893649\pi\)
\(588\) 4588.25 0.321797
\(589\) −16420.9 −1.14874
\(590\) 971.159 0.0677661
\(591\) −4463.21 −0.310646
\(592\) −288.792 −0.0200495
\(593\) −7529.46 −0.521413 −0.260707 0.965418i \(-0.583956\pi\)
−0.260707 + 0.965418i \(0.583956\pi\)
\(594\) −1718.52 −0.118707
\(595\) 4060.84 0.279795
\(596\) 2247.97 0.154497
\(597\) −9083.18 −0.622696
\(598\) 3501.66 0.239454
\(599\) 3363.55 0.229434 0.114717 0.993398i \(-0.463404\pi\)
0.114717 + 0.993398i \(0.463404\pi\)
\(600\) 1940.65 0.132045
\(601\) 13338.7 0.905316 0.452658 0.891684i \(-0.350476\pi\)
0.452658 + 0.891684i \(0.350476\pi\)
\(602\) 4545.68 0.307755
\(603\) −1885.29 −0.127321
\(604\) 8199.25 0.552356
\(605\) −992.288 −0.0666814
\(606\) −3450.34 −0.231288
\(607\) −7189.25 −0.480729 −0.240365 0.970683i \(-0.577267\pi\)
−0.240365 + 0.970683i \(0.577267\pi\)
\(608\) −17047.2 −1.13710
\(609\) 5477.57 0.364470
\(610\) −370.887 −0.0246177
\(611\) 1529.07 0.101243
\(612\) 2808.73 0.185517
\(613\) −22156.6 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(614\) −1506.56 −0.0990225
\(615\) −6129.78 −0.401913
\(616\) 5764.20 0.377023
\(617\) −15462.4 −1.00890 −0.504452 0.863440i \(-0.668305\pi\)
−0.504452 + 0.863440i \(0.668305\pi\)
\(618\) −6233.62 −0.405749
\(619\) −18599.5 −1.20772 −0.603858 0.797092i \(-0.706371\pi\)
−0.603858 + 0.797092i \(0.706371\pi\)
\(620\) 8978.54 0.581592
\(621\) −4960.39 −0.320537
\(622\) 7007.69 0.451741
\(623\) −6702.02 −0.430997
\(624\) −140.094 −0.00898757
\(625\) −11121.9 −0.711800
\(626\) −6087.57 −0.388671
\(627\) 10511.2 0.669501
\(628\) −19363.3 −1.23038
\(629\) 4229.42 0.268105
\(630\) −1018.56 −0.0644133
\(631\) −14886.6 −0.939187 −0.469594 0.882883i \(-0.655600\pi\)
−0.469594 + 0.882883i \(0.655600\pi\)
\(632\) −18687.1 −1.17616
\(633\) −4967.70 −0.311925
\(634\) 1455.52 0.0911768
\(635\) 13061.2 0.816248
\(636\) 10091.5 0.629176
\(637\) 3351.59 0.208469
\(638\) −16902.5 −1.04887
\(639\) 1882.44 0.116539
\(640\) 9863.61 0.609208
\(641\) 30295.2 1.86675 0.933376 0.358899i \(-0.116848\pi\)
0.933376 + 0.358899i \(0.116848\pi\)
\(642\) 2176.91 0.133825
\(643\) 12393.0 0.760080 0.380040 0.924970i \(-0.375910\pi\)
0.380040 + 0.924970i \(0.375910\pi\)
\(644\) 6532.70 0.399727
\(645\) −11543.3 −0.704678
\(646\) 9395.00 0.572200
\(647\) −18759.0 −1.13986 −0.569931 0.821692i \(-0.693030\pi\)
−0.569931 + 0.821692i \(0.693030\pi\)
\(648\) −1794.27 −0.108774
\(649\) 2232.96 0.135056
\(650\) 556.601 0.0335872
\(651\) 3658.65 0.220267
\(652\) 6887.97 0.413733
\(653\) 17228.9 1.03249 0.516247 0.856440i \(-0.327329\pi\)
0.516247 + 0.856440i \(0.327329\pi\)
\(654\) 2158.73 0.129072
\(655\) 7239.29 0.431851
\(656\) 860.171 0.0511952
\(657\) 7787.54 0.462437
\(658\) −1560.03 −0.0924262
\(659\) 10789.4 0.637776 0.318888 0.947792i \(-0.396691\pi\)
0.318888 + 0.947792i \(0.396691\pi\)
\(660\) −5747.28 −0.338958
\(661\) 91.3456 0.00537509 0.00268754 0.999996i \(-0.499145\pi\)
0.00268754 + 0.999996i \(0.499145\pi\)
\(662\) 13690.9 0.803797
\(663\) 2051.70 0.120183
\(664\) 18726.6 1.09448
\(665\) 6229.94 0.363288
\(666\) −1060.84 −0.0617220
\(667\) −48788.0 −2.83220
\(668\) −85.6351 −0.00496006
\(669\) −3675.59 −0.212416
\(670\) 3448.05 0.198820
\(671\) −852.773 −0.0490625
\(672\) 3798.21 0.218034
\(673\) −25294.9 −1.44881 −0.724404 0.689376i \(-0.757885\pi\)
−0.724404 + 0.689376i \(0.757885\pi\)
\(674\) 12438.8 0.710868
\(675\) −788.471 −0.0449604
\(676\) 10698.0 0.608670
\(677\) 1529.96 0.0868557 0.0434278 0.999057i \(-0.486172\pi\)
0.0434278 + 0.999057i \(0.486172\pi\)
\(678\) −9761.06 −0.552908
\(679\) 2329.40 0.131656
\(680\) −13083.2 −0.737820
\(681\) −1973.03 −0.111023
\(682\) −11289.8 −0.633882
\(683\) 7588.88 0.425154 0.212577 0.977144i \(-0.431814\pi\)
0.212577 + 0.977144i \(0.431814\pi\)
\(684\) 4309.03 0.240877
\(685\) 12354.9 0.689135
\(686\) −7385.54 −0.411051
\(687\) 4223.91 0.234574
\(688\) 1619.83 0.0897610
\(689\) 7371.60 0.407599
\(690\) 9072.18 0.500539
\(691\) −7781.95 −0.428421 −0.214211 0.976787i \(-0.568718\pi\)
−0.214211 + 0.976787i \(0.568718\pi\)
\(692\) 12396.9 0.681013
\(693\) −2341.95 −0.128374
\(694\) −2256.87 −0.123443
\(695\) −25748.2 −1.40530
\(696\) −17647.6 −0.961108
\(697\) −12597.4 −0.684591
\(698\) 3688.62 0.200024
\(699\) 19180.4 1.03787
\(700\) 1038.39 0.0560680
\(701\) 16501.9 0.889111 0.444555 0.895751i \(-0.353362\pi\)
0.444555 + 0.895751i \(0.353362\pi\)
\(702\) −514.618 −0.0276681
\(703\) 6488.57 0.348110
\(704\) −10472.9 −0.560669
\(705\) 3961.55 0.211632
\(706\) −1070.08 −0.0570440
\(707\) −4702.02 −0.250124
\(708\) 915.394 0.0485913
\(709\) −26435.2 −1.40027 −0.700136 0.714009i \(-0.746877\pi\)
−0.700136 + 0.714009i \(0.746877\pi\)
\(710\) −3442.84 −0.181982
\(711\) 7592.44 0.400476
\(712\) 21592.6 1.13654
\(713\) −32587.2 −1.71164
\(714\) −2093.25 −0.109717
\(715\) −4198.23 −0.219587
\(716\) −6325.03 −0.330136
\(717\) 5824.81 0.303391
\(718\) −11980.9 −0.622734
\(719\) −9576.02 −0.496697 −0.248348 0.968671i \(-0.579888\pi\)
−0.248348 + 0.968671i \(0.579888\pi\)
\(720\) −362.959 −0.0187870
\(721\) −8495.00 −0.438794
\(722\) 2878.23 0.148361
\(723\) −11104.8 −0.571222
\(724\) 22067.6 1.13278
\(725\) −7755.02 −0.397261
\(726\) 511.498 0.0261480
\(727\) −11408.0 −0.581979 −0.290990 0.956726i \(-0.593985\pi\)
−0.290990 + 0.956726i \(0.593985\pi\)
\(728\) 1726.11 0.0878764
\(729\) 729.000 0.0370370
\(730\) −14242.8 −0.722124
\(731\) −23722.8 −1.20030
\(732\) −349.591 −0.0176520
\(733\) −25829.0 −1.30152 −0.650762 0.759282i \(-0.725550\pi\)
−0.650762 + 0.759282i \(0.725550\pi\)
\(734\) −14655.9 −0.737003
\(735\) 8683.39 0.435771
\(736\) −33830.2 −1.69429
\(737\) 7928.01 0.396244
\(738\) 3159.74 0.157604
\(739\) 37906.8 1.88691 0.943454 0.331503i \(-0.107556\pi\)
0.943454 + 0.331503i \(0.107556\pi\)
\(740\) −3547.80 −0.176243
\(741\) 3147.63 0.156047
\(742\) −7520.88 −0.372102
\(743\) 17868.7 0.882286 0.441143 0.897437i \(-0.354573\pi\)
0.441143 + 0.897437i \(0.354573\pi\)
\(744\) −11787.4 −0.580845
\(745\) 4254.35 0.209218
\(746\) 15343.1 0.753017
\(747\) −7608.46 −0.372663
\(748\) −11811.3 −0.577358
\(749\) 2966.63 0.144724
\(750\) 7614.67 0.370731
\(751\) −12.6803 −0.000616125 0 −0.000308063 1.00000i \(-0.500098\pi\)
−0.000308063 1.00000i \(0.500098\pi\)
\(752\) −555.911 −0.0269574
\(753\) −717.201 −0.0347095
\(754\) −5061.54 −0.244470
\(755\) 15517.3 0.747990
\(756\) −960.072 −0.0461872
\(757\) 39700.2 1.90611 0.953056 0.302793i \(-0.0979192\pi\)
0.953056 + 0.302793i \(0.0979192\pi\)
\(758\) 14361.8 0.688186
\(759\) 20859.5 0.997563
\(760\) −20071.6 −0.957992
\(761\) −9323.77 −0.444134 −0.222067 0.975031i \(-0.571280\pi\)
−0.222067 + 0.975031i \(0.571280\pi\)
\(762\) −6732.69 −0.320078
\(763\) 2941.85 0.139583
\(764\) 15931.2 0.754412
\(765\) 5315.61 0.251224
\(766\) −14616.2 −0.689433
\(767\) 668.670 0.0314789
\(768\) −11725.6 −0.550928
\(769\) 20630.0 0.967408 0.483704 0.875232i \(-0.339291\pi\)
0.483704 + 0.875232i \(0.339291\pi\)
\(770\) 4283.25 0.200464
\(771\) 19899.3 0.929517
\(772\) −17944.3 −0.836568
\(773\) 9335.33 0.434370 0.217185 0.976130i \(-0.430312\pi\)
0.217185 + 0.976130i \(0.430312\pi\)
\(774\) 5950.27 0.276328
\(775\) −5179.84 −0.240084
\(776\) −7504.85 −0.347176
\(777\) −1445.69 −0.0667487
\(778\) −16951.9 −0.781175
\(779\) −19326.3 −0.888879
\(780\) −1721.05 −0.0790043
\(781\) −7916.04 −0.362686
\(782\) 18644.3 0.852584
\(783\) 7170.09 0.327252
\(784\) −1218.51 −0.0555080
\(785\) −36645.5 −1.66616
\(786\) −3731.66 −0.169343
\(787\) −14965.2 −0.677831 −0.338916 0.940817i \(-0.610060\pi\)
−0.338916 + 0.940817i \(0.610060\pi\)
\(788\) 7694.15 0.347833
\(789\) −6031.36 −0.272144
\(790\) −13886.0 −0.625369
\(791\) −13302.1 −0.597937
\(792\) 7545.29 0.338523
\(793\) −255.366 −0.0114355
\(794\) −3076.78 −0.137520
\(795\) 19098.5 0.852018
\(796\) 15658.5 0.697239
\(797\) 35050.2 1.55777 0.778885 0.627167i \(-0.215786\pi\)
0.778885 + 0.627167i \(0.215786\pi\)
\(798\) −3211.37 −0.142458
\(799\) 8141.43 0.360480
\(800\) −5377.43 −0.237651
\(801\) −8772.90 −0.386985
\(802\) −18364.1 −0.808552
\(803\) −32748.2 −1.43918
\(804\) 3250.06 0.142563
\(805\) 12363.3 0.541303
\(806\) −3380.77 −0.147745
\(807\) 17769.7 0.775120
\(808\) 15149.0 0.659577
\(809\) −14925.1 −0.648628 −0.324314 0.945950i \(-0.605133\pi\)
−0.324314 + 0.945950i \(0.605133\pi\)
\(810\) −1333.29 −0.0578357
\(811\) −28928.7 −1.25256 −0.626280 0.779598i \(-0.715423\pi\)
−0.626280 + 0.779598i \(0.715423\pi\)
\(812\) −9442.81 −0.408100
\(813\) −5726.82 −0.247046
\(814\) 4461.06 0.192089
\(815\) 13035.7 0.560269
\(816\) −745.921 −0.0320005
\(817\) −36394.4 −1.55848
\(818\) 10833.0 0.463040
\(819\) −701.307 −0.0299214
\(820\) 10567.2 0.450026
\(821\) −1009.83 −0.0429274 −0.0214637 0.999770i \(-0.506833\pi\)
−0.0214637 + 0.999770i \(0.506833\pi\)
\(822\) −6368.63 −0.270233
\(823\) 4148.74 0.175718 0.0878590 0.996133i \(-0.471998\pi\)
0.0878590 + 0.996133i \(0.471998\pi\)
\(824\) 27369.2 1.15710
\(825\) 3315.68 0.139924
\(826\) −682.211 −0.0287375
\(827\) 46387.4 1.95048 0.975241 0.221147i \(-0.0709800\pi\)
0.975241 + 0.221147i \(0.0709800\pi\)
\(828\) 8551.25 0.358909
\(829\) 16193.2 0.678423 0.339211 0.940710i \(-0.389840\pi\)
0.339211 + 0.940710i \(0.389840\pi\)
\(830\) 13915.3 0.581936
\(831\) 23056.6 0.962485
\(832\) −3136.15 −0.130681
\(833\) 17845.3 0.742262
\(834\) 13272.5 0.551066
\(835\) −162.067 −0.00671683
\(836\) −18120.3 −0.749647
\(837\) 4789.15 0.197774
\(838\) 11409.5 0.470327
\(839\) −26644.1 −1.09637 −0.548186 0.836357i \(-0.684681\pi\)
−0.548186 + 0.836357i \(0.684681\pi\)
\(840\) 4472.06 0.183691
\(841\) 46132.5 1.89153
\(842\) 1392.22 0.0569824
\(843\) 3669.60 0.149926
\(844\) 8563.84 0.349265
\(845\) 20246.2 0.824249
\(846\) −2042.07 −0.0829881
\(847\) 697.054 0.0282775
\(848\) −2680.03 −0.108529
\(849\) −4630.77 −0.187194
\(850\) 2963.58 0.119588
\(851\) 12876.6 0.518687
\(852\) −3245.15 −0.130489
\(853\) −28697.2 −1.15190 −0.575952 0.817484i \(-0.695368\pi\)
−0.575952 + 0.817484i \(0.695368\pi\)
\(854\) 260.538 0.0104396
\(855\) 8154.95 0.326191
\(856\) −9557.89 −0.381638
\(857\) 19383.8 0.772623 0.386311 0.922368i \(-0.373749\pi\)
0.386311 + 0.922368i \(0.373749\pi\)
\(858\) 2164.07 0.0861075
\(859\) −18991.9 −0.754362 −0.377181 0.926140i \(-0.623107\pi\)
−0.377181 + 0.926140i \(0.623107\pi\)
\(860\) 19899.6 0.789035
\(861\) 4306.00 0.170439
\(862\) 2891.66 0.114258
\(863\) 34623.5 1.36570 0.682849 0.730560i \(-0.260741\pi\)
0.682849 + 0.730560i \(0.260741\pi\)
\(864\) 4971.83 0.195770
\(865\) 23461.6 0.922216
\(866\) 20087.7 0.788229
\(867\) −3814.84 −0.149433
\(868\) −6307.17 −0.246635
\(869\) −31927.7 −1.24635
\(870\) −13113.6 −0.511024
\(871\) 2374.08 0.0923565
\(872\) −9478.06 −0.368082
\(873\) 3049.17 0.118211
\(874\) 28603.3 1.10700
\(875\) 10377.1 0.400924
\(876\) −13425.0 −0.517795
\(877\) −33705.2 −1.29777 −0.648884 0.760887i \(-0.724764\pi\)
−0.648884 + 0.760887i \(0.724764\pi\)
\(878\) 531.947 0.0204469
\(879\) −11962.6 −0.459030
\(880\) 1526.31 0.0584683
\(881\) −24525.5 −0.937896 −0.468948 0.883226i \(-0.655367\pi\)
−0.468948 + 0.883226i \(0.655367\pi\)
\(882\) −4476.05 −0.170880
\(883\) 3141.61 0.119732 0.0598662 0.998206i \(-0.480933\pi\)
0.0598662 + 0.998206i \(0.480933\pi\)
\(884\) −3536.94 −0.134570
\(885\) 1732.41 0.0658014
\(886\) −15208.8 −0.576691
\(887\) −5590.87 −0.211638 −0.105819 0.994385i \(-0.533746\pi\)
−0.105819 + 0.994385i \(0.533746\pi\)
\(888\) 4657.71 0.176016
\(889\) −9175.11 −0.346145
\(890\) 16045.0 0.604302
\(891\) −3065.59 −0.115265
\(892\) 6336.37 0.237845
\(893\) 12490.2 0.468050
\(894\) −2193.00 −0.0820413
\(895\) −11970.3 −0.447065
\(896\) −6928.90 −0.258346
\(897\) 6246.45 0.232512
\(898\) 15234.2 0.566116
\(899\) 47103.7 1.74749
\(900\) 1359.25 0.0503426
\(901\) 39249.6 1.45127
\(902\) −13287.3 −0.490488
\(903\) 8108.85 0.298832
\(904\) 42856.7 1.57676
\(905\) 41763.5 1.53399
\(906\) −7998.75 −0.293312
\(907\) −27732.8 −1.01527 −0.507637 0.861571i \(-0.669481\pi\)
−0.507637 + 0.861571i \(0.669481\pi\)
\(908\) 3401.32 0.124314
\(909\) −6154.91 −0.224582
\(910\) 1282.64 0.0467242
\(911\) 7724.27 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(912\) −1144.36 −0.0415498
\(913\) 31995.1 1.15978
\(914\) 24124.2 0.873040
\(915\) −661.610 −0.0239040
\(916\) −7281.62 −0.262655
\(917\) −5085.39 −0.183135
\(918\) −2740.05 −0.0985133
\(919\) 40052.6 1.43767 0.718833 0.695183i \(-0.244677\pi\)
0.718833 + 0.695183i \(0.244677\pi\)
\(920\) −39832.1 −1.42742
\(921\) −2687.49 −0.0961517
\(922\) −18065.5 −0.645288
\(923\) −2370.49 −0.0845349
\(924\) 4037.30 0.143742
\(925\) 2046.77 0.0727540
\(926\) −29555.3 −1.04887
\(927\) −11119.9 −0.393986
\(928\) 48900.5 1.72978
\(929\) 14184.7 0.500952 0.250476 0.968123i \(-0.419413\pi\)
0.250476 + 0.968123i \(0.419413\pi\)
\(930\) −8758.99 −0.308837
\(931\) 27377.5 0.963759
\(932\) −33065.3 −1.16211
\(933\) 12500.7 0.438644
\(934\) 15065.6 0.527796
\(935\) −22353.2 −0.781848
\(936\) 2259.47 0.0789028
\(937\) −30556.2 −1.06534 −0.532672 0.846322i \(-0.678812\pi\)
−0.532672 + 0.846322i \(0.678812\pi\)
\(938\) −2422.15 −0.0843135
\(939\) −10859.4 −0.377403
\(940\) −6829.34 −0.236967
\(941\) −9474.36 −0.328220 −0.164110 0.986442i \(-0.552475\pi\)
−0.164110 + 0.986442i \(0.552475\pi\)
\(942\) 18889.8 0.653357
\(943\) −38353.0 −1.32444
\(944\) −243.103 −0.00838170
\(945\) −1816.96 −0.0625458
\(946\) −25022.1 −0.859976
\(947\) 55248.5 1.89581 0.947906 0.318549i \(-0.103196\pi\)
0.947906 + 0.318549i \(0.103196\pi\)
\(948\) −13088.6 −0.448417
\(949\) −9806.58 −0.335443
\(950\) 4546.59 0.155274
\(951\) 2596.44 0.0885335
\(952\) 9190.58 0.312887
\(953\) 6103.29 0.207455 0.103728 0.994606i \(-0.466923\pi\)
0.103728 + 0.994606i \(0.466923\pi\)
\(954\) −9844.77 −0.334105
\(955\) 30150.2 1.02161
\(956\) −10041.4 −0.339710
\(957\) −30151.7 −1.01846
\(958\) 11620.4 0.391898
\(959\) −8678.99 −0.292241
\(960\) −8125.21 −0.273167
\(961\) 1671.17 0.0560963
\(962\) 1335.88 0.0447720
\(963\) 3883.30 0.129946
\(964\) 19143.7 0.639602
\(965\) −33960.1 −1.13287
\(966\) −6372.95 −0.212263
\(967\) −22070.6 −0.733965 −0.366982 0.930228i \(-0.619609\pi\)
−0.366982 + 0.930228i \(0.619609\pi\)
\(968\) −2245.77 −0.0745678
\(969\) 16759.3 0.555611
\(970\) −5576.69 −0.184595
\(971\) −46982.7 −1.55278 −0.776389 0.630254i \(-0.782951\pi\)
−0.776389 + 0.630254i \(0.782951\pi\)
\(972\) −1256.73 −0.0414707
\(973\) 18087.4 0.595945
\(974\) −25240.3 −0.830341
\(975\) 992.895 0.0326134
\(976\) 92.8414 0.00304486
\(977\) −38521.7 −1.26143 −0.630715 0.776014i \(-0.717238\pi\)
−0.630715 + 0.776014i \(0.717238\pi\)
\(978\) −6719.53 −0.219700
\(979\) 36891.8 1.20436
\(980\) −14969.3 −0.487937
\(981\) 3850.86 0.125330
\(982\) 18398.2 0.597872
\(983\) −17793.1 −0.577327 −0.288664 0.957431i \(-0.593211\pi\)
−0.288664 + 0.957431i \(0.593211\pi\)
\(984\) −13873.1 −0.449448
\(985\) 14561.4 0.471030
\(986\) −26949.8 −0.870443
\(987\) −2782.88 −0.0897466
\(988\) −5426.21 −0.174727
\(989\) −72224.5 −2.32215
\(990\) 5606.74 0.179994
\(991\) −52191.4 −1.67297 −0.836485 0.547990i \(-0.815393\pi\)
−0.836485 + 0.547990i \(0.815393\pi\)
\(992\) 32662.3 1.04539
\(993\) 24422.7 0.780494
\(994\) 2418.50 0.0771731
\(995\) 29634.2 0.944189
\(996\) 13116.3 0.417274
\(997\) 6732.09 0.213849 0.106924 0.994267i \(-0.465900\pi\)
0.106924 + 0.994267i \(0.465900\pi\)
\(998\) −3297.81 −0.104600
\(999\) −1892.39 −0.0599326
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.1.6 7
3.2 odd 2 531.4.a.d.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.6 7 1.1 even 1 trivial
531.4.a.d.1.2 7 3.2 odd 2