Properties

Label 177.2.a.d.1.3
Level $177$
Weight $2$
Character 177.1
Self dual yes
Analytic conductor $1.413$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \(x^{3} - 4 x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.11491\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.11491 q^{2} -1.00000 q^{3} +2.47283 q^{4} -0.357926 q^{5} -2.11491 q^{6} +5.11491 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.11491 q^{2} -1.00000 q^{3} +2.47283 q^{4} -0.357926 q^{5} -2.11491 q^{6} +5.11491 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.756981 q^{10} -4.58774 q^{11} -2.47283 q^{12} -2.58774 q^{13} +10.8176 q^{14} +0.357926 q^{15} -2.83076 q^{16} +2.18869 q^{17} +2.11491 q^{18} +0.527166 q^{19} -0.885092 q^{20} -5.11491 q^{21} -9.70265 q^{22} -5.70265 q^{23} -1.00000 q^{24} -4.87189 q^{25} -5.47283 q^{26} -1.00000 q^{27} +12.6483 q^{28} +2.06058 q^{29} +0.756981 q^{30} +5.83076 q^{31} -7.98680 q^{32} +4.58774 q^{33} +4.62887 q^{34} -1.83076 q^{35} +2.47283 q^{36} -7.70265 q^{37} +1.11491 q^{38} +2.58774 q^{39} -0.357926 q^{40} +2.39905 q^{41} -10.8176 q^{42} +7.15604 q^{43} -11.3447 q^{44} -0.357926 q^{45} -12.0606 q^{46} +8.77643 q^{47} +2.83076 q^{48} +19.1623 q^{49} -10.3036 q^{50} -2.18869 q^{51} -6.39905 q^{52} -8.10170 q^{53} -2.11491 q^{54} +1.64207 q^{55} +5.11491 q^{56} -0.527166 q^{57} +4.35793 q^{58} +1.00000 q^{59} +0.885092 q^{60} +9.00624 q^{61} +12.3315 q^{62} +5.11491 q^{63} -11.2298 q^{64} +0.926221 q^{65} +9.70265 q^{66} +14.4791 q^{67} +5.41226 q^{68} +5.70265 q^{69} -3.87189 q^{70} +4.12811 q^{71} +1.00000 q^{72} -11.2361 q^{73} -16.2904 q^{74} +4.87189 q^{75} +1.30359 q^{76} -23.4659 q^{77} +5.47283 q^{78} -3.87189 q^{79} +1.01320 q^{80} +1.00000 q^{81} +5.07378 q^{82} -0.737534 q^{83} -12.6483 q^{84} -0.783389 q^{85} +15.1344 q^{86} -2.06058 q^{87} -4.58774 q^{88} -8.54661 q^{89} -0.756981 q^{90} -13.2361 q^{91} -14.1017 q^{92} -5.83076 q^{93} +18.5613 q^{94} -0.188687 q^{95} +7.98680 q^{96} -4.10170 q^{97} +40.5264 q^{98} -4.58774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{3} + 2q^{4} - 2q^{5} + 9q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 3q^{3} + 2q^{4} - 2q^{5} + 9q^{7} + 3q^{8} + 3q^{9} + 5q^{10} - 2q^{11} - 2q^{12} + 4q^{13} + 8q^{14} + 2q^{15} - 4q^{16} + 3q^{17} + 7q^{19} - 9q^{20} - 9q^{21} - 11q^{22} + q^{23} - 3q^{24} - q^{25} - 11q^{26} - 3q^{27} + 9q^{28} - 11q^{29} - 5q^{30} + 13q^{31} - 4q^{32} + 2q^{33} - 7q^{34} - q^{35} + 2q^{36} - 5q^{37} - 3q^{38} - 4q^{39} - 2q^{40} - q^{41} - 8q^{42} + 6q^{43} - 15q^{44} - 2q^{45} - 19q^{46} + 11q^{47} + 4q^{48} + 14q^{49} - 21q^{50} - 3q^{51} - 11q^{52} + 2q^{53} + 4q^{55} + 9q^{56} - 7q^{57} + 14q^{58} + 3q^{59} + 9q^{60} - q^{61} - 2q^{62} + 9q^{63} - 21q^{64} + 11q^{66} + 10q^{67} + 28q^{68} - q^{69} + 2q^{70} + 26q^{71} + 3q^{72} + 7q^{73} - 19q^{74} + q^{75} - 6q^{76} - 17q^{77} + 11q^{78} + 2q^{79} + 23q^{80} + 3q^{81} + 18q^{82} - 3q^{83} - 9q^{84} - 35q^{85} + 31q^{86} + 11q^{87} - 2q^{88} - 23q^{89} + 5q^{90} + q^{91} - 16q^{92} - 13q^{93} + 4q^{94} + 3q^{95} + 4q^{96} + 14q^{97} + 51q^{98} - 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11491 1.49547 0.747733 0.664000i \(-0.231142\pi\)
0.747733 + 0.664000i \(0.231142\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.47283 1.23642
\(5\) −0.357926 −0.160070 −0.0800348 0.996792i \(-0.525503\pi\)
−0.0800348 + 0.996792i \(0.525503\pi\)
\(6\) −2.11491 −0.863407
\(7\) 5.11491 1.93325 0.966627 0.256189i \(-0.0824670\pi\)
0.966627 + 0.256189i \(0.0824670\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −0.756981 −0.239378
\(11\) −4.58774 −1.38326 −0.691628 0.722254i \(-0.743106\pi\)
−0.691628 + 0.722254i \(0.743106\pi\)
\(12\) −2.47283 −0.713846
\(13\) −2.58774 −0.717710 −0.358855 0.933393i \(-0.616833\pi\)
−0.358855 + 0.933393i \(0.616833\pi\)
\(14\) 10.8176 2.89111
\(15\) 0.357926 0.0924162
\(16\) −2.83076 −0.707690
\(17\) 2.18869 0.530834 0.265417 0.964134i \(-0.414490\pi\)
0.265417 + 0.964134i \(0.414490\pi\)
\(18\) 2.11491 0.498488
\(19\) 0.527166 0.120940 0.0604701 0.998170i \(-0.480740\pi\)
0.0604701 + 0.998170i \(0.480740\pi\)
\(20\) −0.885092 −0.197913
\(21\) −5.11491 −1.11616
\(22\) −9.70265 −2.06861
\(23\) −5.70265 −1.18908 −0.594542 0.804064i \(-0.702667\pi\)
−0.594542 + 0.804064i \(0.702667\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.87189 −0.974378
\(26\) −5.47283 −1.07331
\(27\) −1.00000 −0.192450
\(28\) 12.6483 2.39031
\(29\) 2.06058 0.382639 0.191320 0.981528i \(-0.438723\pi\)
0.191320 + 0.981528i \(0.438723\pi\)
\(30\) 0.756981 0.138205
\(31\) 5.83076 1.04724 0.523618 0.851953i \(-0.324582\pi\)
0.523618 + 0.851953i \(0.324582\pi\)
\(32\) −7.98680 −1.41188
\(33\) 4.58774 0.798623
\(34\) 4.62887 0.793845
\(35\) −1.83076 −0.309455
\(36\) 2.47283 0.412139
\(37\) −7.70265 −1.26631 −0.633154 0.774026i \(-0.718240\pi\)
−0.633154 + 0.774026i \(0.718240\pi\)
\(38\) 1.11491 0.180862
\(39\) 2.58774 0.414370
\(40\) −0.357926 −0.0565931
\(41\) 2.39905 0.374669 0.187335 0.982296i \(-0.440015\pi\)
0.187335 + 0.982296i \(0.440015\pi\)
\(42\) −10.8176 −1.66919
\(43\) 7.15604 1.09129 0.545643 0.838018i \(-0.316286\pi\)
0.545643 + 0.838018i \(0.316286\pi\)
\(44\) −11.3447 −1.71028
\(45\) −0.357926 −0.0533565
\(46\) −12.0606 −1.77823
\(47\) 8.77643 1.28017 0.640087 0.768303i \(-0.278898\pi\)
0.640087 + 0.768303i \(0.278898\pi\)
\(48\) 2.83076 0.408585
\(49\) 19.1623 2.73747
\(50\) −10.3036 −1.45715
\(51\) −2.18869 −0.306477
\(52\) −6.39905 −0.887389
\(53\) −8.10170 −1.11285 −0.556427 0.830896i \(-0.687828\pi\)
−0.556427 + 0.830896i \(0.687828\pi\)
\(54\) −2.11491 −0.287802
\(55\) 1.64207 0.221417
\(56\) 5.11491 0.683508
\(57\) −0.527166 −0.0698249
\(58\) 4.35793 0.572224
\(59\) 1.00000 0.130189
\(60\) 0.885092 0.114265
\(61\) 9.00624 1.15313 0.576566 0.817051i \(-0.304393\pi\)
0.576566 + 0.817051i \(0.304393\pi\)
\(62\) 12.3315 1.56610
\(63\) 5.11491 0.644418
\(64\) −11.2298 −1.40373
\(65\) 0.926221 0.114884
\(66\) 9.70265 1.19431
\(67\) 14.4791 1.76890 0.884450 0.466634i \(-0.154534\pi\)
0.884450 + 0.466634i \(0.154534\pi\)
\(68\) 5.41226 0.656333
\(69\) 5.70265 0.686518
\(70\) −3.87189 −0.462779
\(71\) 4.12811 0.489917 0.244958 0.969534i \(-0.421226\pi\)
0.244958 + 0.969534i \(0.421226\pi\)
\(72\) 1.00000 0.117851
\(73\) −11.2361 −1.31508 −0.657541 0.753419i \(-0.728403\pi\)
−0.657541 + 0.753419i \(0.728403\pi\)
\(74\) −16.2904 −1.89372
\(75\) 4.87189 0.562557
\(76\) 1.30359 0.149533
\(77\) −23.4659 −2.67418
\(78\) 5.47283 0.619676
\(79\) −3.87189 −0.435622 −0.217811 0.975991i \(-0.569892\pi\)
−0.217811 + 0.975991i \(0.569892\pi\)
\(80\) 1.01320 0.113280
\(81\) 1.00000 0.111111
\(82\) 5.07378 0.560305
\(83\) −0.737534 −0.0809549 −0.0404775 0.999180i \(-0.512888\pi\)
−0.0404775 + 0.999180i \(0.512888\pi\)
\(84\) −12.6483 −1.38004
\(85\) −0.783389 −0.0849704
\(86\) 15.1344 1.63198
\(87\) −2.06058 −0.220917
\(88\) −4.58774 −0.489055
\(89\) −8.54661 −0.905939 −0.452970 0.891526i \(-0.649635\pi\)
−0.452970 + 0.891526i \(0.649635\pi\)
\(90\) −0.756981 −0.0797928
\(91\) −13.2361 −1.38752
\(92\) −14.1017 −1.47020
\(93\) −5.83076 −0.604622
\(94\) 18.5613 1.91446
\(95\) −0.188687 −0.0193588
\(96\) 7.98680 0.815149
\(97\) −4.10170 −0.416465 −0.208232 0.978079i \(-0.566771\pi\)
−0.208232 + 0.978079i \(0.566771\pi\)
\(98\) 40.5264 4.09379
\(99\) −4.58774 −0.461085
\(100\) −12.0474 −1.20474
\(101\) −8.22982 −0.818897 −0.409449 0.912333i \(-0.634279\pi\)
−0.409449 + 0.912333i \(0.634279\pi\)
\(102\) −4.62887 −0.458326
\(103\) 4.79811 0.472772 0.236386 0.971659i \(-0.424037\pi\)
0.236386 + 0.971659i \(0.424037\pi\)
\(104\) −2.58774 −0.253749
\(105\) 1.83076 0.178664
\(106\) −17.1344 −1.66424
\(107\) 14.0411 1.35741 0.678704 0.734412i \(-0.262542\pi\)
0.678704 + 0.734412i \(0.262542\pi\)
\(108\) −2.47283 −0.237949
\(109\) −9.81131 −0.939753 −0.469877 0.882732i \(-0.655702\pi\)
−0.469877 + 0.882732i \(0.655702\pi\)
\(110\) 3.47283 0.331122
\(111\) 7.70265 0.731103
\(112\) −14.4791 −1.36814
\(113\) 13.2772 1.24901 0.624506 0.781020i \(-0.285300\pi\)
0.624506 + 0.781020i \(0.285300\pi\)
\(114\) −1.11491 −0.104421
\(115\) 2.04113 0.190336
\(116\) 5.09546 0.473102
\(117\) −2.58774 −0.239237
\(118\) 2.11491 0.194693
\(119\) 11.1949 1.02624
\(120\) 0.357926 0.0326741
\(121\) 10.0474 0.913397
\(122\) 19.0474 1.72447
\(123\) −2.39905 −0.216315
\(124\) 14.4185 1.29482
\(125\) 3.53341 0.316038
\(126\) 10.8176 0.963705
\(127\) −0.587741 −0.0521536 −0.0260768 0.999660i \(-0.508301\pi\)
−0.0260768 + 0.999660i \(0.508301\pi\)
\(128\) −7.77643 −0.687346
\(129\) −7.15604 −0.630054
\(130\) 1.95887 0.171804
\(131\) −8.08226 −0.706150 −0.353075 0.935595i \(-0.614864\pi\)
−0.353075 + 0.935595i \(0.614864\pi\)
\(132\) 11.3447 0.987431
\(133\) 2.69641 0.233808
\(134\) 30.6219 2.64533
\(135\) 0.357926 0.0308054
\(136\) 2.18869 0.187678
\(137\) 8.10170 0.692175 0.346088 0.938202i \(-0.387510\pi\)
0.346088 + 0.938202i \(0.387510\pi\)
\(138\) 12.0606 1.02666
\(139\) 4.96511 0.421136 0.210568 0.977579i \(-0.432469\pi\)
0.210568 + 0.977579i \(0.432469\pi\)
\(140\) −4.52717 −0.382615
\(141\) −8.77643 −0.739109
\(142\) 8.73057 0.732653
\(143\) 11.8719 0.992777
\(144\) −2.83076 −0.235897
\(145\) −0.737534 −0.0612489
\(146\) −23.7632 −1.96666
\(147\) −19.1623 −1.58048
\(148\) −19.0474 −1.56568
\(149\) −21.9325 −1.79678 −0.898389 0.439201i \(-0.855262\pi\)
−0.898389 + 0.439201i \(0.855262\pi\)
\(150\) 10.3036 0.841285
\(151\) 1.49228 0.121440 0.0607200 0.998155i \(-0.480660\pi\)
0.0607200 + 0.998155i \(0.480660\pi\)
\(152\) 0.527166 0.0427588
\(153\) 2.18869 0.176945
\(154\) −49.6282 −3.99915
\(155\) −2.08698 −0.167630
\(156\) 6.39905 0.512334
\(157\) −18.7089 −1.49313 −0.746566 0.665311i \(-0.768299\pi\)
−0.746566 + 0.665311i \(0.768299\pi\)
\(158\) −8.18869 −0.651457
\(159\) 8.10170 0.642507
\(160\) 2.85868 0.225999
\(161\) −29.1685 −2.29880
\(162\) 2.11491 0.166163
\(163\) 3.34472 0.261979 0.130989 0.991384i \(-0.458185\pi\)
0.130989 + 0.991384i \(0.458185\pi\)
\(164\) 5.93246 0.463248
\(165\) −1.64207 −0.127835
\(166\) −1.55982 −0.121065
\(167\) 16.3991 1.26900 0.634498 0.772924i \(-0.281207\pi\)
0.634498 + 0.772924i \(0.281207\pi\)
\(168\) −5.11491 −0.394624
\(169\) −6.30359 −0.484892
\(170\) −1.65679 −0.127070
\(171\) 0.527166 0.0403134
\(172\) 17.6957 1.34928
\(173\) 25.2097 1.91665 0.958327 0.285673i \(-0.0922171\pi\)
0.958327 + 0.285673i \(0.0922171\pi\)
\(174\) −4.35793 −0.330374
\(175\) −24.9193 −1.88372
\(176\) 12.9868 0.978917
\(177\) −1.00000 −0.0751646
\(178\) −18.0753 −1.35480
\(179\) −15.0738 −1.12667 −0.563334 0.826230i \(-0.690481\pi\)
−0.563334 + 0.826230i \(0.690481\pi\)
\(180\) −0.885092 −0.0659709
\(181\) 14.7764 1.09832 0.549162 0.835716i \(-0.314947\pi\)
0.549162 + 0.835716i \(0.314947\pi\)
\(182\) −27.9930 −2.07498
\(183\) −9.00624 −0.665761
\(184\) −5.70265 −0.420405
\(185\) 2.75698 0.202697
\(186\) −12.3315 −0.904191
\(187\) −10.0411 −0.734280
\(188\) 21.7026 1.58283
\(189\) −5.11491 −0.372055
\(190\) −0.399055 −0.0289505
\(191\) −19.9930 −1.44665 −0.723323 0.690510i \(-0.757386\pi\)
−0.723323 + 0.690510i \(0.757386\pi\)
\(192\) 11.2298 0.810442
\(193\) 5.28415 0.380361 0.190181 0.981749i \(-0.439093\pi\)
0.190181 + 0.981749i \(0.439093\pi\)
\(194\) −8.67472 −0.622809
\(195\) −0.926221 −0.0663281
\(196\) 47.3851 3.38465
\(197\) 6.12115 0.436114 0.218057 0.975936i \(-0.430028\pi\)
0.218057 + 0.975936i \(0.430028\pi\)
\(198\) −9.70265 −0.689537
\(199\) −18.7500 −1.32915 −0.664577 0.747220i \(-0.731388\pi\)
−0.664577 + 0.747220i \(0.731388\pi\)
\(200\) −4.87189 −0.344495
\(201\) −14.4791 −1.02128
\(202\) −17.4053 −1.22463
\(203\) 10.5397 0.739739
\(204\) −5.41226 −0.378934
\(205\) −0.858685 −0.0599732
\(206\) 10.1476 0.707014
\(207\) −5.70265 −0.396362
\(208\) 7.32528 0.507916
\(209\) −2.41850 −0.167291
\(210\) 3.87189 0.267186
\(211\) 5.32528 0.366607 0.183304 0.983056i \(-0.441321\pi\)
0.183304 + 0.983056i \(0.441321\pi\)
\(212\) −20.0342 −1.37595
\(213\) −4.12811 −0.282854
\(214\) 29.6957 2.02996
\(215\) −2.56133 −0.174682
\(216\) −1.00000 −0.0680414
\(217\) 29.8238 2.02457
\(218\) −20.7500 −1.40537
\(219\) 11.2361 0.759262
\(220\) 4.06058 0.273764
\(221\) −5.66376 −0.380985
\(222\) 16.2904 1.09334
\(223\) −11.0279 −0.738484 −0.369242 0.929333i \(-0.620383\pi\)
−0.369242 + 0.929333i \(0.620383\pi\)
\(224\) −40.8517 −2.72952
\(225\) −4.87189 −0.324793
\(226\) 28.0800 1.86786
\(227\) −11.1344 −0.739013 −0.369507 0.929228i \(-0.620473\pi\)
−0.369507 + 0.929228i \(0.620473\pi\)
\(228\) −1.30359 −0.0863326
\(229\) 25.4270 1.68026 0.840131 0.542383i \(-0.182478\pi\)
0.840131 + 0.542383i \(0.182478\pi\)
\(230\) 4.31680 0.284641
\(231\) 23.4659 1.54394
\(232\) 2.06058 0.135283
\(233\) −10.1212 −0.663059 −0.331529 0.943445i \(-0.607565\pi\)
−0.331529 + 0.943445i \(0.607565\pi\)
\(234\) −5.47283 −0.357770
\(235\) −3.14132 −0.204917
\(236\) 2.47283 0.160968
\(237\) 3.87189 0.251506
\(238\) 23.6762 1.53470
\(239\) 10.9387 0.707566 0.353783 0.935328i \(-0.384895\pi\)
0.353783 + 0.935328i \(0.384895\pi\)
\(240\) −1.01320 −0.0654020
\(241\) −10.2034 −0.657259 −0.328630 0.944459i \(-0.606587\pi\)
−0.328630 + 0.944459i \(0.606587\pi\)
\(242\) 21.2493 1.36595
\(243\) −1.00000 −0.0641500
\(244\) 22.2709 1.42575
\(245\) −6.85868 −0.438185
\(246\) −5.07378 −0.323492
\(247\) −1.36417 −0.0868000
\(248\) 5.83076 0.370254
\(249\) 0.737534 0.0467393
\(250\) 7.47283 0.472624
\(251\) 12.2104 0.770712 0.385356 0.922768i \(-0.374079\pi\)
0.385356 + 0.922768i \(0.374079\pi\)
\(252\) 12.6483 0.796769
\(253\) 26.1623 1.64481
\(254\) −1.24302 −0.0779939
\(255\) 0.783389 0.0490577
\(256\) 6.01320 0.375825
\(257\) −9.52645 −0.594244 −0.297122 0.954840i \(-0.596027\pi\)
−0.297122 + 0.954840i \(0.596027\pi\)
\(258\) −15.1344 −0.942224
\(259\) −39.3983 −2.44809
\(260\) 2.29039 0.142044
\(261\) 2.06058 0.127546
\(262\) −17.0932 −1.05602
\(263\) −16.0995 −0.992736 −0.496368 0.868112i \(-0.665333\pi\)
−0.496368 + 0.868112i \(0.665333\pi\)
\(264\) 4.58774 0.282356
\(265\) 2.89981 0.178134
\(266\) 5.70265 0.349652
\(267\) 8.54661 0.523044
\(268\) 35.8044 2.18710
\(269\) 28.3051 1.72579 0.862897 0.505381i \(-0.168648\pi\)
0.862897 + 0.505381i \(0.168648\pi\)
\(270\) 0.756981 0.0460684
\(271\) 1.38585 0.0841845 0.0420922 0.999114i \(-0.486598\pi\)
0.0420922 + 0.999114i \(0.486598\pi\)
\(272\) −6.19565 −0.375666
\(273\) 13.2361 0.801083
\(274\) 17.1344 1.03512
\(275\) 22.3510 1.34781
\(276\) 14.1017 0.848823
\(277\) −1.15604 −0.0694595 −0.0347297 0.999397i \(-0.511057\pi\)
−0.0347297 + 0.999397i \(0.511057\pi\)
\(278\) 10.5008 0.629794
\(279\) 5.83076 0.349078
\(280\) −1.83076 −0.109409
\(281\) −19.5140 −1.16411 −0.582053 0.813151i \(-0.697750\pi\)
−0.582053 + 0.813151i \(0.697750\pi\)
\(282\) −18.5613 −1.10531
\(283\) −2.04113 −0.121332 −0.0606662 0.998158i \(-0.519323\pi\)
−0.0606662 + 0.998158i \(0.519323\pi\)
\(284\) 10.2081 0.605741
\(285\) 0.188687 0.0111768
\(286\) 25.1079 1.48466
\(287\) 12.2709 0.724331
\(288\) −7.98680 −0.470626
\(289\) −12.2097 −0.718215
\(290\) −1.55982 −0.0915956
\(291\) 4.10170 0.240446
\(292\) −27.7849 −1.62599
\(293\) −2.73057 −0.159522 −0.0797609 0.996814i \(-0.525416\pi\)
−0.0797609 + 0.996814i \(0.525416\pi\)
\(294\) −40.5264 −2.36355
\(295\) −0.357926 −0.0208393
\(296\) −7.70265 −0.447707
\(297\) 4.58774 0.266208
\(298\) −46.3851 −2.68702
\(299\) 14.7570 0.853418
\(300\) 12.0474 0.695555
\(301\) 36.6025 2.10973
\(302\) 3.15604 0.181609
\(303\) 8.22982 0.472791
\(304\) −1.49228 −0.0855882
\(305\) −3.22357 −0.184581
\(306\) 4.62887 0.264615
\(307\) −28.2423 −1.61187 −0.805937 0.592002i \(-0.798338\pi\)
−0.805937 + 0.592002i \(0.798338\pi\)
\(308\) −58.0272 −3.30641
\(309\) −4.79811 −0.272955
\(310\) −4.41378 −0.250686
\(311\) 20.5272 1.16399 0.581994 0.813193i \(-0.302273\pi\)
0.581994 + 0.813193i \(0.302273\pi\)
\(312\) 2.58774 0.146502
\(313\) −6.86565 −0.388069 −0.194035 0.980995i \(-0.562157\pi\)
−0.194035 + 0.980995i \(0.562157\pi\)
\(314\) −39.5676 −2.23293
\(315\) −1.83076 −0.103152
\(316\) −9.57454 −0.538610
\(317\) 28.6002 1.60635 0.803174 0.595744i \(-0.203143\pi\)
0.803174 + 0.595744i \(0.203143\pi\)
\(318\) 17.1344 0.960847
\(319\) −9.45339 −0.529288
\(320\) 4.01945 0.224694
\(321\) −14.0411 −0.783699
\(322\) −61.6887 −3.43778
\(323\) 1.15380 0.0641992
\(324\) 2.47283 0.137380
\(325\) 12.6072 0.699321
\(326\) 7.07378 0.391780
\(327\) 9.81131 0.542567
\(328\) 2.39905 0.132466
\(329\) 44.8906 2.47490
\(330\) −3.47283 −0.191173
\(331\) 21.2966 1.17057 0.585284 0.810828i \(-0.300983\pi\)
0.585284 + 0.810828i \(0.300983\pi\)
\(332\) −1.82380 −0.100094
\(333\) −7.70265 −0.422103
\(334\) 34.6825 1.89774
\(335\) −5.18244 −0.283147
\(336\) 14.4791 0.789898
\(337\) −11.3253 −0.616927 −0.308464 0.951236i \(-0.599815\pi\)
−0.308464 + 0.951236i \(0.599815\pi\)
\(338\) −13.3315 −0.725139
\(339\) −13.2772 −0.721118
\(340\) −1.93719 −0.105059
\(341\) −26.7500 −1.44859
\(342\) 1.11491 0.0602873
\(343\) 62.2089 3.35897
\(344\) 7.15604 0.385828
\(345\) −2.04113 −0.109891
\(346\) 53.3161 2.86629
\(347\) 2.58998 0.139037 0.0695186 0.997581i \(-0.477854\pi\)
0.0695186 + 0.997581i \(0.477854\pi\)
\(348\) −5.09546 −0.273145
\(349\) −26.0319 −1.39346 −0.696729 0.717335i \(-0.745362\pi\)
−0.696729 + 0.717335i \(0.745362\pi\)
\(350\) −52.7019 −2.81704
\(351\) 2.58774 0.138123
\(352\) 36.6414 1.95299
\(353\) 13.9325 0.741550 0.370775 0.928723i \(-0.379092\pi\)
0.370775 + 0.928723i \(0.379092\pi\)
\(354\) −2.11491 −0.112406
\(355\) −1.47756 −0.0784207
\(356\) −21.1344 −1.12012
\(357\) −11.1949 −0.592499
\(358\) −31.8796 −1.68489
\(359\) −5.89134 −0.310933 −0.155466 0.987841i \(-0.549688\pi\)
−0.155466 + 0.987841i \(0.549688\pi\)
\(360\) −0.357926 −0.0188644
\(361\) −18.7221 −0.985373
\(362\) 31.2508 1.64250
\(363\) −10.0474 −0.527350
\(364\) −32.7306 −1.71555
\(365\) 4.02168 0.210504
\(366\) −19.0474 −0.995622
\(367\) −0.926221 −0.0483483 −0.0241742 0.999708i \(-0.507696\pi\)
−0.0241742 + 0.999708i \(0.507696\pi\)
\(368\) 16.1428 0.841503
\(369\) 2.39905 0.124890
\(370\) 5.83076 0.303127
\(371\) −41.4395 −2.15143
\(372\) −14.4185 −0.747564
\(373\) 10.1498 0.525536 0.262768 0.964859i \(-0.415365\pi\)
0.262768 + 0.964859i \(0.415365\pi\)
\(374\) −21.2361 −1.09809
\(375\) −3.53341 −0.182464
\(376\) 8.77643 0.452610
\(377\) −5.33224 −0.274624
\(378\) −10.8176 −0.556395
\(379\) −28.0753 −1.44213 −0.721066 0.692867i \(-0.756347\pi\)
−0.721066 + 0.692867i \(0.756347\pi\)
\(380\) −0.466591 −0.0239356
\(381\) 0.587741 0.0301109
\(382\) −42.2834 −2.16341
\(383\) 34.8176 1.77909 0.889547 0.456844i \(-0.151020\pi\)
0.889547 + 0.456844i \(0.151020\pi\)
\(384\) 7.77643 0.396839
\(385\) 8.39905 0.428055
\(386\) 11.1755 0.568817
\(387\) 7.15604 0.363762
\(388\) −10.1428 −0.514924
\(389\) 1.78267 0.0903850 0.0451925 0.998978i \(-0.485610\pi\)
0.0451925 + 0.998978i \(0.485610\pi\)
\(390\) −1.95887 −0.0991913
\(391\) −12.4813 −0.631207
\(392\) 19.1623 0.967841
\(393\) 8.08226 0.407696
\(394\) 12.9457 0.652193
\(395\) 1.38585 0.0697297
\(396\) −11.3447 −0.570094
\(397\) 0.817557 0.0410320 0.0205160 0.999790i \(-0.493469\pi\)
0.0205160 + 0.999790i \(0.493469\pi\)
\(398\) −39.6546 −1.98770
\(399\) −2.69641 −0.134989
\(400\) 13.7911 0.689557
\(401\) −5.35168 −0.267250 −0.133625 0.991032i \(-0.542662\pi\)
−0.133625 + 0.991032i \(0.542662\pi\)
\(402\) −30.6219 −1.52728
\(403\) −15.0885 −0.751612
\(404\) −20.3510 −1.01250
\(405\) −0.357926 −0.0177855
\(406\) 22.2904 1.10625
\(407\) 35.3378 1.75163
\(408\) −2.18869 −0.108356
\(409\) −38.4068 −1.89909 −0.949547 0.313624i \(-0.898457\pi\)
−0.949547 + 0.313624i \(0.898457\pi\)
\(410\) −1.81604 −0.0896878
\(411\) −8.10170 −0.399628
\(412\) 11.8649 0.584543
\(413\) 5.11491 0.251688
\(414\) −12.0606 −0.592745
\(415\) 0.263983 0.0129584
\(416\) 20.6678 1.01332
\(417\) −4.96511 −0.243143
\(418\) −5.11491 −0.250178
\(419\) 8.71585 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(420\) 4.52717 0.220903
\(421\) −0.357926 −0.0174443 −0.00872213 0.999962i \(-0.502776\pi\)
−0.00872213 + 0.999962i \(0.502776\pi\)
\(422\) 11.2625 0.548248
\(423\) 8.77643 0.426725
\(424\) −8.10170 −0.393454
\(425\) −10.6630 −0.517233
\(426\) −8.73057 −0.422998
\(427\) 46.0661 2.22929
\(428\) 34.7214 1.67832
\(429\) −11.8719 −0.573180
\(430\) −5.41698 −0.261230
\(431\) −13.2361 −0.637558 −0.318779 0.947829i \(-0.603273\pi\)
−0.318779 + 0.947829i \(0.603273\pi\)
\(432\) 2.83076 0.136195
\(433\) −27.4031 −1.31691 −0.658454 0.752621i \(-0.728789\pi\)
−0.658454 + 0.752621i \(0.728789\pi\)
\(434\) 63.0746 3.02768
\(435\) 0.737534 0.0353621
\(436\) −24.2617 −1.16193
\(437\) −3.00624 −0.143808
\(438\) 23.7632 1.13545
\(439\) 32.5955 1.55570 0.777849 0.628451i \(-0.216311\pi\)
0.777849 + 0.628451i \(0.216311\pi\)
\(440\) 1.64207 0.0782828
\(441\) 19.1623 0.912489
\(442\) −11.9783 −0.569751
\(443\) −30.8392 −1.46522 −0.732608 0.680651i \(-0.761697\pi\)
−0.732608 + 0.680651i \(0.761697\pi\)
\(444\) 19.0474 0.903948
\(445\) 3.05906 0.145013
\(446\) −23.3230 −1.10438
\(447\) 21.9325 1.03737
\(448\) −57.4395 −2.71376
\(449\) 35.0863 1.65582 0.827912 0.560859i \(-0.189529\pi\)
0.827912 + 0.560859i \(0.189529\pi\)
\(450\) −10.3036 −0.485716
\(451\) −11.0062 −0.518264
\(452\) 32.8323 1.54430
\(453\) −1.49228 −0.0701135
\(454\) −23.5481 −1.10517
\(455\) 4.73753 0.222099
\(456\) −0.527166 −0.0246868
\(457\) 10.6414 0.497782 0.248891 0.968532i \(-0.419934\pi\)
0.248891 + 0.968532i \(0.419934\pi\)
\(458\) 53.7757 2.51277
\(459\) −2.18869 −0.102159
\(460\) 5.04737 0.235335
\(461\) −28.4046 −1.32293 −0.661467 0.749975i \(-0.730066\pi\)
−0.661467 + 0.749975i \(0.730066\pi\)
\(462\) 49.6282 2.30891
\(463\) −9.58150 −0.445290 −0.222645 0.974900i \(-0.571469\pi\)
−0.222645 + 0.974900i \(0.571469\pi\)
\(464\) −5.83299 −0.270790
\(465\) 2.08698 0.0967815
\(466\) −21.4053 −0.991581
\(467\) 26.1336 1.20932 0.604660 0.796484i \(-0.293309\pi\)
0.604660 + 0.796484i \(0.293309\pi\)
\(468\) −6.39905 −0.295796
\(469\) 74.0591 3.41973
\(470\) −6.64359 −0.306446
\(471\) 18.7089 0.862060
\(472\) 1.00000 0.0460287
\(473\) −32.8300 −1.50953
\(474\) 8.18869 0.376119
\(475\) −2.56829 −0.117841
\(476\) 27.6832 1.26886
\(477\) −8.10170 −0.370952
\(478\) 23.1344 1.05814
\(479\) −18.5397 −0.847098 −0.423549 0.905873i \(-0.639216\pi\)
−0.423549 + 0.905873i \(0.639216\pi\)
\(480\) −2.85868 −0.130481
\(481\) 19.9325 0.908842
\(482\) −21.5793 −0.982909
\(483\) 29.1685 1.32721
\(484\) 24.8455 1.12934
\(485\) 1.46811 0.0666633
\(486\) −2.11491 −0.0959342
\(487\) −21.5676 −0.977320 −0.488660 0.872474i \(-0.662514\pi\)
−0.488660 + 0.872474i \(0.662514\pi\)
\(488\) 9.00624 0.407693
\(489\) −3.34472 −0.151254
\(490\) −14.5055 −0.655291
\(491\) −11.4659 −0.517448 −0.258724 0.965951i \(-0.583302\pi\)
−0.258724 + 0.965951i \(0.583302\pi\)
\(492\) −5.93246 −0.267456
\(493\) 4.50995 0.203118
\(494\) −2.88509 −0.129806
\(495\) 1.64207 0.0738057
\(496\) −16.5055 −0.741118
\(497\) 21.1149 0.947133
\(498\) 1.55982 0.0698971
\(499\) −17.4681 −0.781980 −0.390990 0.920395i \(-0.627867\pi\)
−0.390990 + 0.920395i \(0.627867\pi\)
\(500\) 8.73753 0.390754
\(501\) −16.3991 −0.732656
\(502\) 25.8238 1.15257
\(503\) 0.655277 0.0292174 0.0146087 0.999893i \(-0.495350\pi\)
0.0146087 + 0.999893i \(0.495350\pi\)
\(504\) 5.11491 0.227836
\(505\) 2.94567 0.131080
\(506\) 55.3308 2.45975
\(507\) 6.30359 0.279952
\(508\) −1.45339 −0.0644836
\(509\) −15.8168 −0.701069 −0.350535 0.936550i \(-0.614000\pi\)
−0.350535 + 0.936550i \(0.614000\pi\)
\(510\) 1.65679 0.0733641
\(511\) −57.4714 −2.54239
\(512\) 28.2702 1.24938
\(513\) −0.527166 −0.0232750
\(514\) −20.1476 −0.888671
\(515\) −1.71737 −0.0756764
\(516\) −17.6957 −0.779009
\(517\) −40.2640 −1.77081
\(518\) −83.3238 −3.66104
\(519\) −25.2097 −1.10658
\(520\) 0.926221 0.0406175
\(521\) −12.2470 −0.536552 −0.268276 0.963342i \(-0.586454\pi\)
−0.268276 + 0.963342i \(0.586454\pi\)
\(522\) 4.35793 0.190741
\(523\) −2.23678 −0.0978074 −0.0489037 0.998803i \(-0.515573\pi\)
−0.0489037 + 0.998803i \(0.515573\pi\)
\(524\) −19.9861 −0.873096
\(525\) 24.9193 1.08757
\(526\) −34.0489 −1.48460
\(527\) 12.7617 0.555909
\(528\) −12.9868 −0.565178
\(529\) 9.52021 0.413922
\(530\) 6.13284 0.266393
\(531\) 1.00000 0.0433963
\(532\) 6.66776 0.289084
\(533\) −6.20813 −0.268904
\(534\) 18.0753 0.782195
\(535\) −5.02569 −0.217280
\(536\) 14.4791 0.625401
\(537\) 15.0738 0.650482
\(538\) 59.8627 2.58086
\(539\) −87.9116 −3.78662
\(540\) 0.885092 0.0380883
\(541\) −11.0863 −0.476636 −0.238318 0.971187i \(-0.576596\pi\)
−0.238318 + 0.971187i \(0.576596\pi\)
\(542\) 2.93095 0.125895
\(543\) −14.7764 −0.634117
\(544\) −17.4806 −0.749474
\(545\) 3.51173 0.150426
\(546\) 27.9930 1.19799
\(547\) 12.1887 0.521151 0.260575 0.965454i \(-0.416088\pi\)
0.260575 + 0.965454i \(0.416088\pi\)
\(548\) 20.0342 0.855817
\(549\) 9.00624 0.384377
\(550\) 47.2702 2.01561
\(551\) 1.08627 0.0462765
\(552\) 5.70265 0.242721
\(553\) −19.8044 −0.842167
\(554\) −2.44491 −0.103874
\(555\) −2.75698 −0.117027
\(556\) 12.2779 0.520699
\(557\) −8.56829 −0.363050 −0.181525 0.983386i \(-0.558103\pi\)
−0.181525 + 0.983386i \(0.558103\pi\)
\(558\) 12.3315 0.522035
\(559\) −18.5180 −0.783227
\(560\) 5.18244 0.218998
\(561\) 10.0411 0.423937
\(562\) −41.2702 −1.74088
\(563\) 9.98055 0.420630 0.210315 0.977634i \(-0.432551\pi\)
0.210315 + 0.977634i \(0.432551\pi\)
\(564\) −21.7026 −0.913846
\(565\) −4.75226 −0.199929
\(566\) −4.31680 −0.181449
\(567\) 5.11491 0.214806
\(568\) 4.12811 0.173212
\(569\) 46.1428 1.93441 0.967204 0.254001i \(-0.0817465\pi\)
0.967204 + 0.254001i \(0.0817465\pi\)
\(570\) 0.399055 0.0167146
\(571\) −21.1824 −0.886458 −0.443229 0.896409i \(-0.646167\pi\)
−0.443229 + 0.896409i \(0.646167\pi\)
\(572\) 29.3572 1.22749
\(573\) 19.9930 0.835221
\(574\) 25.9519 1.08321
\(575\) 27.7827 1.15862
\(576\) −11.2298 −0.467909
\(577\) 40.8859 1.70210 0.851051 0.525083i \(-0.175966\pi\)
0.851051 + 0.525083i \(0.175966\pi\)
\(578\) −25.8223 −1.07407
\(579\) −5.28415 −0.219602
\(580\) −1.82380 −0.0757292
\(581\) −3.77242 −0.156506
\(582\) 8.67472 0.359579
\(583\) 37.1685 1.53936
\(584\) −11.2361 −0.464951
\(585\) 0.926221 0.0382945
\(586\) −5.77491 −0.238559
\(587\) −4.21037 −0.173780 −0.0868902 0.996218i \(-0.527693\pi\)
−0.0868902 + 0.996218i \(0.527693\pi\)
\(588\) −47.3851 −1.95413
\(589\) 3.07378 0.126653
\(590\) −0.756981 −0.0311644
\(591\) −6.12115 −0.251790
\(592\) 21.8044 0.896153
\(593\) −22.5202 −0.924794 −0.462397 0.886673i \(-0.653010\pi\)
−0.462397 + 0.886673i \(0.653010\pi\)
\(594\) 9.70265 0.398105
\(595\) −4.00696 −0.164269
\(596\) −54.2353 −2.22157
\(597\) 18.7500 0.767387
\(598\) 31.2097 1.27626
\(599\) −16.7981 −0.686352 −0.343176 0.939271i \(-0.611503\pi\)
−0.343176 + 0.939271i \(0.611503\pi\)
\(600\) 4.87189 0.198894
\(601\) −17.0955 −0.697338 −0.348669 0.937246i \(-0.613366\pi\)
−0.348669 + 0.937246i \(0.613366\pi\)
\(602\) 77.4108 3.15503
\(603\) 14.4791 0.589634
\(604\) 3.69016 0.150151
\(605\) −3.59622 −0.146207
\(606\) 17.4053 0.707042
\(607\) −7.53341 −0.305772 −0.152886 0.988244i \(-0.548857\pi\)
−0.152886 + 0.988244i \(0.548857\pi\)
\(608\) −4.21037 −0.170753
\(609\) −10.5397 −0.427088
\(610\) −6.81756 −0.276035
\(611\) −22.7111 −0.918794
\(612\) 5.41226 0.218778
\(613\) 15.1321 0.611181 0.305590 0.952163i \(-0.401146\pi\)
0.305590 + 0.952163i \(0.401146\pi\)
\(614\) −59.7299 −2.41050
\(615\) 0.858685 0.0346255
\(616\) −23.4659 −0.945467
\(617\) 15.8672 0.638788 0.319394 0.947622i \(-0.396521\pi\)
0.319394 + 0.947622i \(0.396521\pi\)
\(618\) −10.1476 −0.408195
\(619\) 11.0210 0.442970 0.221485 0.975164i \(-0.428910\pi\)
0.221485 + 0.975164i \(0.428910\pi\)
\(620\) −5.16076 −0.207261
\(621\) 5.70265 0.228839
\(622\) 43.4131 1.74071
\(623\) −43.7151 −1.75141
\(624\) −7.32528 −0.293246
\(625\) 23.0947 0.923790
\(626\) −14.5202 −0.580344
\(627\) 2.41850 0.0965857
\(628\) −46.2640 −1.84613
\(629\) −16.8587 −0.672200
\(630\) −3.87189 −0.154260
\(631\) −23.1560 −0.921827 −0.460914 0.887445i \(-0.652478\pi\)
−0.460914 + 0.887445i \(0.652478\pi\)
\(632\) −3.87189 −0.154015
\(633\) −5.32528 −0.211661
\(634\) 60.4868 2.40224
\(635\) 0.210368 0.00834821
\(636\) 20.0342 0.794406
\(637\) −49.5870 −1.96471
\(638\) −19.9930 −0.791532
\(639\) 4.12811 0.163306
\(640\) 2.78339 0.110023
\(641\) 39.5459 1.56197 0.780984 0.624550i \(-0.214718\pi\)
0.780984 + 0.624550i \(0.214718\pi\)
\(642\) −29.6957 −1.17200
\(643\) 18.6219 0.734376 0.367188 0.930147i \(-0.380320\pi\)
0.367188 + 0.930147i \(0.380320\pi\)
\(644\) −72.1289 −2.84228
\(645\) 2.56133 0.100852
\(646\) 2.44018 0.0960077
\(647\) 7.24525 0.284840 0.142420 0.989806i \(-0.454512\pi\)
0.142420 + 0.989806i \(0.454512\pi\)
\(648\) 1.00000 0.0392837
\(649\) −4.58774 −0.180085
\(650\) 26.6630 1.04581
\(651\) −29.8238 −1.16889
\(652\) 8.27094 0.323915
\(653\) 31.3183 1.22558 0.612790 0.790246i \(-0.290047\pi\)
0.612790 + 0.790246i \(0.290047\pi\)
\(654\) 20.7500 0.811390
\(655\) 2.89285 0.113033
\(656\) −6.79115 −0.265150
\(657\) −11.2361 −0.438360
\(658\) 94.9395 3.70113
\(659\) 8.13587 0.316929 0.158464 0.987365i \(-0.449346\pi\)
0.158464 + 0.987365i \(0.449346\pi\)
\(660\) −4.06058 −0.158058
\(661\) −9.47979 −0.368721 −0.184361 0.982859i \(-0.559021\pi\)
−0.184361 + 0.982859i \(0.559021\pi\)
\(662\) 45.0404 1.75055
\(663\) 5.66376 0.219962
\(664\) −0.737534 −0.0286219
\(665\) −0.965115 −0.0374255
\(666\) −16.2904 −0.631240
\(667\) −11.7507 −0.454990
\(668\) 40.5521 1.56901
\(669\) 11.0279 0.426364
\(670\) −10.9604 −0.423437
\(671\) −41.3183 −1.59508
\(672\) 40.8517 1.57589
\(673\) 11.4317 0.440660 0.220330 0.975425i \(-0.429287\pi\)
0.220330 + 0.975425i \(0.429287\pi\)
\(674\) −23.9519 −0.922593
\(675\) 4.87189 0.187519
\(676\) −15.5877 −0.599529
\(677\) −6.83700 −0.262767 −0.131384 0.991332i \(-0.541942\pi\)
−0.131384 + 0.991332i \(0.541942\pi\)
\(678\) −28.0800 −1.07841
\(679\) −20.9798 −0.805132
\(680\) −0.783389 −0.0300416
\(681\) 11.1344 0.426669
\(682\) −56.5738 −2.16632
\(683\) −34.6002 −1.32394 −0.661970 0.749530i \(-0.730280\pi\)
−0.661970 + 0.749530i \(0.730280\pi\)
\(684\) 1.30359 0.0498442
\(685\) −2.89981 −0.110796
\(686\) 131.566 5.02322
\(687\) −25.4270 −0.970100
\(688\) −20.2570 −0.772292
\(689\) 20.9651 0.798707
\(690\) −4.31680 −0.164338
\(691\) −42.8929 −1.63172 −0.815861 0.578249i \(-0.803736\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(692\) 62.3393 2.36978
\(693\) −23.4659 −0.891395
\(694\) 5.47756 0.207925
\(695\) −1.77715 −0.0674110
\(696\) −2.06058 −0.0781059
\(697\) 5.25078 0.198887
\(698\) −55.0551 −2.08387
\(699\) 10.1212 0.382817
\(700\) −61.6212 −2.32906
\(701\) 8.83228 0.333591 0.166795 0.985992i \(-0.446658\pi\)
0.166795 + 0.985992i \(0.446658\pi\)
\(702\) 5.47283 0.206559
\(703\) −4.06058 −0.153148
\(704\) 51.5195 1.94171
\(705\) 3.14132 0.118309
\(706\) 29.4659 1.10896
\(707\) −42.0947 −1.58314
\(708\) −2.47283 −0.0929348
\(709\) 22.7981 0.856201 0.428100 0.903731i \(-0.359183\pi\)
0.428100 + 0.903731i \(0.359183\pi\)
\(710\) −3.12490 −0.117276
\(711\) −3.87189 −0.145207
\(712\) −8.54661 −0.320298
\(713\) −33.2508 −1.24525
\(714\) −23.6762 −0.886061
\(715\) −4.24926 −0.158913
\(716\) −37.2750 −1.39303
\(717\) −10.9387 −0.408514
\(718\) −12.4596 −0.464989
\(719\) 21.6887 0.808853 0.404427 0.914570i \(-0.367471\pi\)
0.404427 + 0.914570i \(0.367471\pi\)
\(720\) 1.01320 0.0377599
\(721\) 24.5419 0.913988
\(722\) −39.5955 −1.47359
\(723\) 10.2034 0.379469
\(724\) 36.5397 1.35799
\(725\) −10.0389 −0.372835
\(726\) −21.2493 −0.788634
\(727\) 47.7438 1.77072 0.885359 0.464907i \(-0.153912\pi\)
0.885359 + 0.464907i \(0.153912\pi\)
\(728\) −13.2361 −0.490561
\(729\) 1.00000 0.0370370
\(730\) 8.50548 0.314802
\(731\) 15.6623 0.579292
\(732\) −22.2709 −0.823158
\(733\) 37.3983 1.38134 0.690670 0.723170i \(-0.257316\pi\)
0.690670 + 0.723170i \(0.257316\pi\)
\(734\) −1.95887 −0.0723033
\(735\) 6.85868 0.252986
\(736\) 45.5459 1.67884
\(737\) −66.4263 −2.44684
\(738\) 5.07378 0.186768
\(739\) −13.9450 −0.512973 −0.256487 0.966548i \(-0.582565\pi\)
−0.256487 + 0.966548i \(0.582565\pi\)
\(740\) 6.81756 0.250618
\(741\) 1.36417 0.0501140
\(742\) −87.6406 −3.21739
\(743\) 47.4200 1.73967 0.869836 0.493341i \(-0.164225\pi\)
0.869836 + 0.493341i \(0.164225\pi\)
\(744\) −5.83076 −0.213766
\(745\) 7.85021 0.287609
\(746\) 21.4659 0.785921
\(747\) −0.737534 −0.0269850
\(748\) −24.8300 −0.907876
\(749\) 71.8191 2.62421
\(750\) −7.47283 −0.272869
\(751\) 46.8929 1.71114 0.855572 0.517683i \(-0.173205\pi\)
0.855572 + 0.517683i \(0.173205\pi\)
\(752\) −24.8440 −0.905966
\(753\) −12.2104 −0.444971
\(754\) −11.2772 −0.410691
\(755\) −0.534127 −0.0194389
\(756\) −12.6483 −0.460015
\(757\) −21.7151 −0.789250 −0.394625 0.918842i \(-0.629125\pi\)
−0.394625 + 0.918842i \(0.629125\pi\)
\(758\) −59.3767 −2.15666
\(759\) −26.1623 −0.949631
\(760\) −0.188687 −0.00684438
\(761\) −36.6002 −1.32676 −0.663379 0.748284i \(-0.730878\pi\)
−0.663379 + 0.748284i \(0.730878\pi\)
\(762\) 1.24302 0.0450298
\(763\) −50.1840 −1.81678
\(764\) −49.4395 −1.78866
\(765\) −0.783389 −0.0283235
\(766\) 73.6359 2.66057
\(767\) −2.58774 −0.0934379
\(768\) −6.01320 −0.216983
\(769\) 11.9200 0.429845 0.214923 0.976631i \(-0.431050\pi\)
0.214923 + 0.976631i \(0.431050\pi\)
\(770\) 17.7632 0.640142
\(771\) 9.52645 0.343087
\(772\) 13.0668 0.470285
\(773\) 20.3076 0.730414 0.365207 0.930926i \(-0.380998\pi\)
0.365207 + 0.930926i \(0.380998\pi\)
\(774\) 15.1344 0.543993
\(775\) −28.4068 −1.02040
\(776\) −4.10170 −0.147243
\(777\) 39.3983 1.41341
\(778\) 3.77018 0.135168
\(779\) 1.26470 0.0453126
\(780\) −2.29039 −0.0820091
\(781\) −18.9387 −0.677680
\(782\) −26.3968 −0.943948
\(783\) −2.06058 −0.0736390
\(784\) −54.2438 −1.93728
\(785\) 6.69641 0.239005
\(786\) 17.0932 0.609695
\(787\) 18.2687 0.651209 0.325605 0.945506i \(-0.394432\pi\)
0.325605 + 0.945506i \(0.394432\pi\)
\(788\) 15.1366 0.539219
\(789\) 16.0995 0.573156
\(790\) 2.93095 0.104278
\(791\) 67.9116 2.41466
\(792\) −4.58774 −0.163018
\(793\) −23.3058 −0.827614
\(794\) 1.72906 0.0613619
\(795\) −2.89981 −0.102846
\(796\) −46.3657 −1.64339
\(797\) −21.3664 −0.756837 −0.378418 0.925635i \(-0.623532\pi\)
−0.378418 + 0.925635i \(0.623532\pi\)
\(798\) −5.70265 −0.201872
\(799\) 19.2089 0.679560
\(800\) 38.9108 1.37570
\(801\) −8.54661 −0.301980
\(802\) −11.3183 −0.399664
\(803\) 51.5481 1.81909
\(804\) −35.8044 −1.26272
\(805\) 10.4402 0.367968
\(806\) −31.9108 −1.12401
\(807\) −28.3051 −0.996387
\(808\) −8.22982 −0.289524
\(809\) −23.7460 −0.834865 −0.417433 0.908708i \(-0.637070\pi\)
−0.417433 + 0.908708i \(0.637070\pi\)
\(810\) −0.756981 −0.0265976
\(811\) 15.3664 0.539587 0.269794 0.962918i \(-0.413044\pi\)
0.269794 + 0.962918i \(0.413044\pi\)
\(812\) 26.0628 0.914625
\(813\) −1.38585 −0.0486039
\(814\) 74.7361 2.61950
\(815\) −1.19716 −0.0419348
\(816\) 6.19565 0.216891
\(817\) 3.77242 0.131980
\(818\) −81.2269 −2.84003
\(819\) −13.2361 −0.462505
\(820\) −2.12339 −0.0741518
\(821\) −29.6009 −1.03308 −0.516540 0.856263i \(-0.672780\pi\)
−0.516540 + 0.856263i \(0.672780\pi\)
\(822\) −17.1344 −0.597629
\(823\) −19.6546 −0.685115 −0.342557 0.939497i \(-0.611293\pi\)
−0.342557 + 0.939497i \(0.611293\pi\)
\(824\) 4.79811 0.167150
\(825\) −22.3510 −0.778161
\(826\) 10.8176 0.376391
\(827\) −13.1296 −0.456562 −0.228281 0.973595i \(-0.573310\pi\)
−0.228281 + 0.973595i \(0.573310\pi\)
\(828\) −14.1017 −0.490068
\(829\) −3.69569 −0.128357 −0.0641783 0.997938i \(-0.520443\pi\)
−0.0641783 + 0.997938i \(0.520443\pi\)
\(830\) 0.558300 0.0193789
\(831\) 1.15604 0.0401024
\(832\) 29.0599 1.00747
\(833\) 41.9402 1.45314
\(834\) −10.5008 −0.363612
\(835\) −5.86965 −0.203128
\(836\) −5.98055 −0.206842
\(837\) −5.83076 −0.201541
\(838\) 18.4332 0.636765
\(839\) 20.7911 0.717790 0.358895 0.933378i \(-0.383154\pi\)
0.358895 + 0.933378i \(0.383154\pi\)
\(840\) 1.83076 0.0631672
\(841\) −24.7540 −0.853587
\(842\) −0.756981 −0.0260873
\(843\) 19.5140 0.672097
\(844\) 13.1685 0.453279
\(845\) 2.25622 0.0776164
\(846\) 18.5613 0.638152
\(847\) 51.3914 1.76583
\(848\) 22.9340 0.787556
\(849\) 2.04113 0.0700513
\(850\) −22.5513 −0.773505
\(851\) 43.9255 1.50575
\(852\) −10.2081 −0.349725
\(853\) 17.5162 0.599743 0.299872 0.953980i \(-0.403056\pi\)
0.299872 + 0.953980i \(0.403056\pi\)
\(854\) 97.4255 3.33383
\(855\) −0.188687 −0.00645295
\(856\) 14.0411 0.479916
\(857\) 16.0628 0.548695 0.274348 0.961631i \(-0.411538\pi\)
0.274348 + 0.961631i \(0.411538\pi\)
\(858\) −25.1079 −0.857171
\(859\) −5.39281 −0.184000 −0.0920002 0.995759i \(-0.529326\pi\)
−0.0920002 + 0.995759i \(0.529326\pi\)
\(860\) −6.33375 −0.215979
\(861\) −12.2709 −0.418193
\(862\) −27.9930 −0.953447
\(863\) 7.55509 0.257178 0.128589 0.991698i \(-0.458955\pi\)
0.128589 + 0.991698i \(0.458955\pi\)
\(864\) 7.98680 0.271716
\(865\) −9.02320 −0.306798
\(866\) −57.9549 −1.96939
\(867\) 12.2097 0.414661
\(868\) 73.7493 2.50321
\(869\) 17.7632 0.602576
\(870\) 1.55982 0.0528827
\(871\) −37.4681 −1.26956
\(872\) −9.81131 −0.332253
\(873\) −4.10170 −0.138822
\(874\) −6.35793 −0.215060
\(875\) 18.0731 0.610981
\(876\) 27.7849 0.938765
\(877\) 21.0807 0.711846 0.355923 0.934515i \(-0.384167\pi\)
0.355923 + 0.934515i \(0.384167\pi\)
\(878\) 68.9365 2.32649
\(879\) 2.73057 0.0921000
\(880\) −4.64832 −0.156695
\(881\) 8.90677 0.300077 0.150038 0.988680i \(-0.452060\pi\)
0.150038 + 0.988680i \(0.452060\pi\)
\(882\) 40.5264 1.36460
\(883\) 7.94719 0.267444 0.133722 0.991019i \(-0.457307\pi\)
0.133722 + 0.991019i \(0.457307\pi\)
\(884\) −14.0055 −0.471057
\(885\) 0.357926 0.0120316
\(886\) −65.2221 −2.19118
\(887\) −13.1685 −0.442156 −0.221078 0.975256i \(-0.570957\pi\)
−0.221078 + 0.975256i \(0.570957\pi\)
\(888\) 7.70265 0.258484
\(889\) −3.00624 −0.100826
\(890\) 6.46963 0.216862
\(891\) −4.58774 −0.153695
\(892\) −27.2702 −0.913075
\(893\) 4.62664 0.154824
\(894\) 46.3851 1.55135
\(895\) 5.39530 0.180345
\(896\) −39.7757 −1.32881
\(897\) −14.7570 −0.492721
\(898\) 74.2042 2.47623
\(899\) 12.0147 0.400713
\(900\) −12.0474 −0.401579
\(901\) −17.7321 −0.590742
\(902\) −23.2772 −0.775046
\(903\) −36.6025 −1.21805
\(904\) 13.2772 0.441593
\(905\) −5.28887 −0.175808
\(906\) −3.15604 −0.104852
\(907\) −23.9497 −0.795236 −0.397618 0.917551i \(-0.630163\pi\)
−0.397618 + 0.917551i \(0.630163\pi\)
\(908\) −27.5334 −0.913728
\(909\) −8.22982 −0.272966
\(910\) 10.0194 0.332141
\(911\) −46.8184 −1.55116 −0.775581 0.631248i \(-0.782543\pi\)
−0.775581 + 0.631248i \(0.782543\pi\)
\(912\) 1.49228 0.0494144
\(913\) 3.38362 0.111981
\(914\) 22.5055 0.744415
\(915\) 3.22357 0.106568
\(916\) 62.8767 2.07750
\(917\) −41.3400 −1.36517
\(918\) −4.62887 −0.152775
\(919\) 30.6506 1.01107 0.505534 0.862807i \(-0.331295\pi\)
0.505534 + 0.862807i \(0.331295\pi\)
\(920\) 2.04113 0.0672940
\(921\) 28.2423 0.930615
\(922\) −60.0731 −1.97840
\(923\) −10.6825 −0.351618
\(924\) 58.0272 1.90895
\(925\) 37.5264 1.23386
\(926\) −20.2640 −0.665916
\(927\) 4.79811 0.157591
\(928\) −16.4574 −0.540240
\(929\) 7.52092 0.246753 0.123377 0.992360i \(-0.460628\pi\)
0.123377 + 0.992360i \(0.460628\pi\)
\(930\) 4.41378 0.144733
\(931\) 10.1017 0.331070
\(932\) −25.0279 −0.819817
\(933\) −20.5272 −0.672029
\(934\) 55.2702 1.80850
\(935\) 3.59398 0.117536
\(936\) −2.58774 −0.0845830
\(937\) −31.6421 −1.03370 −0.516851 0.856076i \(-0.672896\pi\)
−0.516851 + 0.856076i \(0.672896\pi\)
\(938\) 156.628 5.11409
\(939\) 6.86565 0.224052
\(940\) −7.76795 −0.253363
\(941\) −11.1824 −0.364537 −0.182269 0.983249i \(-0.558344\pi\)
−0.182269 + 0.983249i \(0.558344\pi\)
\(942\) 39.5676 1.28918
\(943\) −13.6810 −0.445514
\(944\) −2.83076 −0.0921334
\(945\) 1.83076 0.0595546
\(946\) −69.4325 −2.25745
\(947\) −30.6149 −0.994852 −0.497426 0.867506i \(-0.665721\pi\)
−0.497426 + 0.867506i \(0.665721\pi\)
\(948\) 9.57454 0.310967
\(949\) 29.0760 0.943847
\(950\) −5.43171 −0.176228
\(951\) −28.6002 −0.927426
\(952\) 11.1949 0.362830
\(953\) 3.17548 0.102864 0.0514320 0.998676i \(-0.483621\pi\)
0.0514320 + 0.998676i \(0.483621\pi\)
\(954\) −17.1344 −0.554745
\(955\) 7.15604 0.231564
\(956\) 27.0496 0.874847
\(957\) 9.45339 0.305585
\(958\) −39.2097 −1.26681
\(959\) 41.4395 1.33815
\(960\) −4.01945 −0.129727
\(961\) 2.99777 0.0967021
\(962\) 42.1553 1.35914
\(963\) 14.0411 0.452469
\(964\) −25.2313 −0.812646
\(965\) −1.89134 −0.0608842
\(966\) 61.6887 1.98480
\(967\) 40.5566 1.30421 0.652106 0.758128i \(-0.273886\pi\)
0.652106 + 0.758128i \(0.273886\pi\)
\(968\) 10.0474 0.322935
\(969\) −1.15380 −0.0370654
\(970\) 3.10491 0.0996927
\(971\) −4.23205 −0.135813 −0.0679065 0.997692i \(-0.521632\pi\)
−0.0679065 + 0.997692i \(0.521632\pi\)
\(972\) −2.47283 −0.0793162
\(973\) 25.3961 0.814162
\(974\) −45.6134 −1.46155
\(975\) −12.6072 −0.403753
\(976\) −25.4945 −0.816060
\(977\) 26.5055 0.847986 0.423993 0.905666i \(-0.360628\pi\)
0.423993 + 0.905666i \(0.360628\pi\)
\(978\) −7.07378 −0.226195
\(979\) 39.2097 1.25315
\(980\) −16.9604 −0.541780
\(981\) −9.81131 −0.313251
\(982\) −24.2493 −0.773825
\(983\) 2.27567 0.0725826 0.0362913 0.999341i \(-0.488446\pi\)
0.0362913 + 0.999341i \(0.488446\pi\)
\(984\) −2.39905 −0.0764791
\(985\) −2.19092 −0.0698086
\(986\) 9.53814 0.303756
\(987\) −44.8906 −1.42888
\(988\) −3.37336 −0.107321
\(989\) −40.8084 −1.29763
\(990\) 3.47283 0.110374
\(991\) 43.9185 1.39512 0.697559 0.716527i \(-0.254269\pi\)
0.697559 + 0.716527i \(0.254269\pi\)
\(992\) −46.5691 −1.47857
\(993\) −21.2966 −0.675828
\(994\) 44.6561 1.41640
\(995\) 6.71113 0.212757
\(996\) 1.82380 0.0577893
\(997\) 2.81532 0.0891621 0.0445811 0.999006i \(-0.485805\pi\)
0.0445811 + 0.999006i \(0.485805\pi\)
\(998\) −36.9434 −1.16942
\(999\) 7.70265 0.243701
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 177.2.a.d.1.3 3
3.2 odd 2 531.2.a.d.1.1 3
4.3 odd 2 2832.2.a.t.1.2 3
5.4 even 2 4425.2.a.w.1.1 3
7.6 odd 2 8673.2.a.s.1.3 3
12.11 even 2 8496.2.a.bl.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.a.d.1.3 3 1.1 even 1 trivial
531.2.a.d.1.1 3 3.2 odd 2
2832.2.a.t.1.2 3 4.3 odd 2
4425.2.a.w.1.1 3 5.4 even 2
8496.2.a.bl.1.2 3 12.11 even 2
8673.2.a.s.1.3 3 7.6 odd 2