Properties

Label 547.2.a.b.1.17
Level $547$
Weight $2$
Character 547.1
Self dual yes
Analytic conductor $4.368$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.36781699056\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + 4048 x^{4} + 3834 x^{3} - 1851 x^{2} - 654 x + 328\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Root \(-2.24960\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.24960 q^{2} -0.790850 q^{3} +3.06069 q^{4} -3.96974 q^{5} -1.77909 q^{6} -4.97706 q^{7} +2.38611 q^{8} -2.37456 q^{9} +O(q^{10})\) \(q+2.24960 q^{2} -0.790850 q^{3} +3.06069 q^{4} -3.96974 q^{5} -1.77909 q^{6} -4.97706 q^{7} +2.38611 q^{8} -2.37456 q^{9} -8.93031 q^{10} +6.10795 q^{11} -2.42054 q^{12} -0.944916 q^{13} -11.1964 q^{14} +3.13947 q^{15} -0.753576 q^{16} +0.884722 q^{17} -5.34179 q^{18} -2.59993 q^{19} -12.1501 q^{20} +3.93611 q^{21} +13.7404 q^{22} -2.77074 q^{23} -1.88706 q^{24} +10.7588 q^{25} -2.12568 q^{26} +4.25047 q^{27} -15.2332 q^{28} -1.93886 q^{29} +7.06254 q^{30} -3.39568 q^{31} -6.46747 q^{32} -4.83047 q^{33} +1.99027 q^{34} +19.7576 q^{35} -7.26777 q^{36} +2.71002 q^{37} -5.84880 q^{38} +0.747287 q^{39} -9.47225 q^{40} +1.37400 q^{41} +8.85466 q^{42} -10.4149 q^{43} +18.6945 q^{44} +9.42637 q^{45} -6.23305 q^{46} -2.84781 q^{47} +0.595966 q^{48} +17.7712 q^{49} +24.2030 q^{50} -0.699683 q^{51} -2.89209 q^{52} +6.58855 q^{53} +9.56184 q^{54} -24.2470 q^{55} -11.8758 q^{56} +2.05616 q^{57} -4.36165 q^{58} +0.838365 q^{59} +9.60893 q^{60} -9.71712 q^{61} -7.63890 q^{62} +11.8183 q^{63} -13.0420 q^{64} +3.75107 q^{65} -10.8666 q^{66} +13.4835 q^{67} +2.70786 q^{68} +2.19124 q^{69} +44.4467 q^{70} -7.51364 q^{71} -5.66596 q^{72} -12.4106 q^{73} +6.09645 q^{74} -8.50862 q^{75} -7.95758 q^{76} -30.3996 q^{77} +1.68110 q^{78} -0.398622 q^{79} +2.99150 q^{80} +3.76218 q^{81} +3.09095 q^{82} +4.09663 q^{83} +12.0472 q^{84} -3.51212 q^{85} -23.4292 q^{86} +1.53335 q^{87} +14.5743 q^{88} -15.7666 q^{89} +21.2055 q^{90} +4.70291 q^{91} -8.48037 q^{92} +2.68547 q^{93} -6.40641 q^{94} +10.3211 q^{95} +5.11480 q^{96} -3.97689 q^{97} +39.9779 q^{98} -14.5037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24960 1.59071 0.795353 0.606147i \(-0.207286\pi\)
0.795353 + 0.606147i \(0.207286\pi\)
\(3\) −0.790850 −0.456598 −0.228299 0.973591i \(-0.573316\pi\)
−0.228299 + 0.973591i \(0.573316\pi\)
\(4\) 3.06069 1.53034
\(5\) −3.96974 −1.77532 −0.887660 0.460499i \(-0.847671\pi\)
−0.887660 + 0.460499i \(0.847671\pi\)
\(6\) −1.77909 −0.726312
\(7\) −4.97706 −1.88115 −0.940576 0.339582i \(-0.889714\pi\)
−0.940576 + 0.339582i \(0.889714\pi\)
\(8\) 2.38611 0.843619
\(9\) −2.37456 −0.791519
\(10\) −8.93031 −2.82401
\(11\) 6.10795 1.84162 0.920808 0.390016i \(-0.127531\pi\)
0.920808 + 0.390016i \(0.127531\pi\)
\(12\) −2.42054 −0.698751
\(13\) −0.944916 −0.262073 −0.131036 0.991378i \(-0.541830\pi\)
−0.131036 + 0.991378i \(0.541830\pi\)
\(14\) −11.1964 −2.99236
\(15\) 3.13947 0.810607
\(16\) −0.753576 −0.188394
\(17\) 0.884722 0.214577 0.107288 0.994228i \(-0.465783\pi\)
0.107288 + 0.994228i \(0.465783\pi\)
\(18\) −5.34179 −1.25907
\(19\) −2.59993 −0.596466 −0.298233 0.954493i \(-0.596397\pi\)
−0.298233 + 0.954493i \(0.596397\pi\)
\(20\) −12.1501 −2.71685
\(21\) 3.93611 0.858930
\(22\) 13.7404 2.92947
\(23\) −2.77074 −0.577740 −0.288870 0.957368i \(-0.593280\pi\)
−0.288870 + 0.957368i \(0.593280\pi\)
\(24\) −1.88706 −0.385194
\(25\) 10.7588 2.15176
\(26\) −2.12568 −0.416880
\(27\) 4.25047 0.818003
\(28\) −15.2332 −2.87881
\(29\) −1.93886 −0.360037 −0.180019 0.983663i \(-0.557616\pi\)
−0.180019 + 0.983663i \(0.557616\pi\)
\(30\) 7.06254 1.28944
\(31\) −3.39568 −0.609881 −0.304941 0.952371i \(-0.598637\pi\)
−0.304941 + 0.952371i \(0.598637\pi\)
\(32\) −6.46747 −1.14330
\(33\) −4.83047 −0.840878
\(34\) 1.99027 0.341328
\(35\) 19.7576 3.33965
\(36\) −7.26777 −1.21129
\(37\) 2.71002 0.445525 0.222762 0.974873i \(-0.428493\pi\)
0.222762 + 0.974873i \(0.428493\pi\)
\(38\) −5.84880 −0.948801
\(39\) 0.747287 0.119662
\(40\) −9.47225 −1.49769
\(41\) 1.37400 0.214583 0.107291 0.994228i \(-0.465782\pi\)
0.107291 + 0.994228i \(0.465782\pi\)
\(42\) 8.85466 1.36630
\(43\) −10.4149 −1.58825 −0.794126 0.607753i \(-0.792071\pi\)
−0.794126 + 0.607753i \(0.792071\pi\)
\(44\) 18.6945 2.81830
\(45\) 9.42637 1.40520
\(46\) −6.23305 −0.919014
\(47\) −2.84781 −0.415395 −0.207698 0.978193i \(-0.566597\pi\)
−0.207698 + 0.978193i \(0.566597\pi\)
\(48\) 0.595966 0.0860202
\(49\) 17.7712 2.53874
\(50\) 24.2030 3.42282
\(51\) −0.699683 −0.0979752
\(52\) −2.89209 −0.401061
\(53\) 6.58855 0.905007 0.452503 0.891763i \(-0.350531\pi\)
0.452503 + 0.891763i \(0.350531\pi\)
\(54\) 9.56184 1.30120
\(55\) −24.2470 −3.26946
\(56\) −11.8758 −1.58698
\(57\) 2.05616 0.272345
\(58\) −4.36165 −0.572713
\(59\) 0.838365 0.109146 0.0545729 0.998510i \(-0.482620\pi\)
0.0545729 + 0.998510i \(0.482620\pi\)
\(60\) 9.60893 1.24051
\(61\) −9.71712 −1.24415 −0.622075 0.782958i \(-0.713710\pi\)
−0.622075 + 0.782958i \(0.713710\pi\)
\(62\) −7.63890 −0.970141
\(63\) 11.8183 1.48897
\(64\) −13.0420 −1.63026
\(65\) 3.75107 0.465263
\(66\) −10.8666 −1.33759
\(67\) 13.4835 1.64727 0.823633 0.567123i \(-0.191944\pi\)
0.823633 + 0.567123i \(0.191944\pi\)
\(68\) 2.70786 0.328376
\(69\) 2.19124 0.263795
\(70\) 44.4467 5.31240
\(71\) −7.51364 −0.891705 −0.445853 0.895106i \(-0.647099\pi\)
−0.445853 + 0.895106i \(0.647099\pi\)
\(72\) −5.66596 −0.667740
\(73\) −12.4106 −1.45255 −0.726274 0.687405i \(-0.758750\pi\)
−0.726274 + 0.687405i \(0.758750\pi\)
\(74\) 6.09645 0.708698
\(75\) −8.50862 −0.982491
\(76\) −7.95758 −0.912797
\(77\) −30.3996 −3.46436
\(78\) 1.68110 0.190347
\(79\) −0.398622 −0.0448485 −0.0224243 0.999749i \(-0.507138\pi\)
−0.0224243 + 0.999749i \(0.507138\pi\)
\(80\) 2.99150 0.334460
\(81\) 3.76218 0.418020
\(82\) 3.09095 0.341338
\(83\) 4.09663 0.449664 0.224832 0.974398i \(-0.427817\pi\)
0.224832 + 0.974398i \(0.427817\pi\)
\(84\) 12.0472 1.31446
\(85\) −3.51212 −0.380943
\(86\) −23.4292 −2.52644
\(87\) 1.53335 0.164392
\(88\) 14.5743 1.55362
\(89\) −15.7666 −1.67125 −0.835626 0.549298i \(-0.814895\pi\)
−0.835626 + 0.549298i \(0.814895\pi\)
\(90\) 21.2055 2.23526
\(91\) 4.70291 0.492999
\(92\) −8.48037 −0.884140
\(93\) 2.68547 0.278470
\(94\) −6.40641 −0.660771
\(95\) 10.3211 1.05892
\(96\) 5.11480 0.522027
\(97\) −3.97689 −0.403792 −0.201896 0.979407i \(-0.564710\pi\)
−0.201896 + 0.979407i \(0.564710\pi\)
\(98\) 39.9779 4.03838
\(99\) −14.5037 −1.45767
\(100\) 32.9294 3.29294
\(101\) −1.75191 −0.174321 −0.0871605 0.996194i \(-0.527779\pi\)
−0.0871605 + 0.996194i \(0.527779\pi\)
\(102\) −1.57400 −0.155850
\(103\) −9.27653 −0.914044 −0.457022 0.889455i \(-0.651084\pi\)
−0.457022 + 0.889455i \(0.651084\pi\)
\(104\) −2.25468 −0.221089
\(105\) −15.6253 −1.52488
\(106\) 14.8216 1.43960
\(107\) −8.46764 −0.818597 −0.409299 0.912400i \(-0.634227\pi\)
−0.409299 + 0.912400i \(0.634227\pi\)
\(108\) 13.0093 1.25183
\(109\) −2.68117 −0.256810 −0.128405 0.991722i \(-0.540986\pi\)
−0.128405 + 0.991722i \(0.540986\pi\)
\(110\) −54.5459 −5.20075
\(111\) −2.14322 −0.203425
\(112\) 3.75059 0.354398
\(113\) −17.8209 −1.67645 −0.838223 0.545327i \(-0.816405\pi\)
−0.838223 + 0.545327i \(0.816405\pi\)
\(114\) 4.62553 0.433220
\(115\) 10.9991 1.02567
\(116\) −5.93424 −0.550980
\(117\) 2.24376 0.207435
\(118\) 1.88598 0.173619
\(119\) −4.40332 −0.403652
\(120\) 7.49113 0.683844
\(121\) 26.3070 2.39155
\(122\) −21.8596 −1.97908
\(123\) −1.08663 −0.0979781
\(124\) −10.3931 −0.933327
\(125\) −22.8610 −2.04475
\(126\) 26.5864 2.36851
\(127\) 14.9282 1.32467 0.662333 0.749210i \(-0.269567\pi\)
0.662333 + 0.749210i \(0.269567\pi\)
\(128\) −16.4044 −1.44996
\(129\) 8.23660 0.725192
\(130\) 8.43840 0.740096
\(131\) 15.7075 1.37237 0.686185 0.727427i \(-0.259284\pi\)
0.686185 + 0.727427i \(0.259284\pi\)
\(132\) −14.7846 −1.28683
\(133\) 12.9400 1.12204
\(134\) 30.3323 2.62031
\(135\) −16.8732 −1.45222
\(136\) 2.11105 0.181021
\(137\) 2.42982 0.207593 0.103797 0.994599i \(-0.466901\pi\)
0.103797 + 0.994599i \(0.466901\pi\)
\(138\) 4.92941 0.419619
\(139\) 10.6270 0.901368 0.450684 0.892684i \(-0.351180\pi\)
0.450684 + 0.892684i \(0.351180\pi\)
\(140\) 60.4719 5.11081
\(141\) 2.25219 0.189668
\(142\) −16.9027 −1.41844
\(143\) −5.77150 −0.482637
\(144\) 1.78941 0.149117
\(145\) 7.69677 0.639182
\(146\) −27.9188 −2.31058
\(147\) −14.0543 −1.15918
\(148\) 8.29452 0.681805
\(149\) 8.49250 0.695733 0.347866 0.937544i \(-0.386906\pi\)
0.347866 + 0.937544i \(0.386906\pi\)
\(150\) −19.1410 −1.56285
\(151\) 23.1852 1.88679 0.943393 0.331677i \(-0.107615\pi\)
0.943393 + 0.331677i \(0.107615\pi\)
\(152\) −6.20374 −0.503190
\(153\) −2.10082 −0.169841
\(154\) −68.3870 −5.51078
\(155\) 13.4799 1.08274
\(156\) 2.28721 0.183123
\(157\) −10.9628 −0.874927 −0.437464 0.899236i \(-0.644123\pi\)
−0.437464 + 0.899236i \(0.644123\pi\)
\(158\) −0.896740 −0.0713408
\(159\) −5.21055 −0.413224
\(160\) 25.6742 2.02972
\(161\) 13.7902 1.08682
\(162\) 8.46339 0.664947
\(163\) −10.0906 −0.790355 −0.395178 0.918605i \(-0.629317\pi\)
−0.395178 + 0.918605i \(0.629317\pi\)
\(164\) 4.20539 0.328385
\(165\) 19.1757 1.49283
\(166\) 9.21578 0.715283
\(167\) 6.93218 0.536428 0.268214 0.963359i \(-0.413567\pi\)
0.268214 + 0.963359i \(0.413567\pi\)
\(168\) 9.39201 0.724609
\(169\) −12.1071 −0.931318
\(170\) −7.90085 −0.605967
\(171\) 6.17369 0.472114
\(172\) −31.8766 −2.43057
\(173\) −25.8915 −1.96850 −0.984249 0.176789i \(-0.943429\pi\)
−0.984249 + 0.176789i \(0.943429\pi\)
\(174\) 3.44941 0.261499
\(175\) −53.5473 −4.04780
\(176\) −4.60280 −0.346949
\(177\) −0.663021 −0.0498357
\(178\) −35.4684 −2.65847
\(179\) 0.366164 0.0273684 0.0136842 0.999906i \(-0.495644\pi\)
0.0136842 + 0.999906i \(0.495644\pi\)
\(180\) 28.8511 2.15044
\(181\) 13.7369 1.02105 0.510527 0.859862i \(-0.329450\pi\)
0.510527 + 0.859862i \(0.329450\pi\)
\(182\) 10.5796 0.784216
\(183\) 7.68479 0.568076
\(184\) −6.61131 −0.487392
\(185\) −10.7581 −0.790949
\(186\) 6.04123 0.442964
\(187\) 5.40384 0.395168
\(188\) −8.71624 −0.635697
\(189\) −21.1549 −1.53879
\(190\) 23.2182 1.68443
\(191\) 8.48775 0.614152 0.307076 0.951685i \(-0.400649\pi\)
0.307076 + 0.951685i \(0.400649\pi\)
\(192\) 10.3143 0.744371
\(193\) 16.0739 1.15703 0.578513 0.815673i \(-0.303633\pi\)
0.578513 + 0.815673i \(0.303633\pi\)
\(194\) −8.94640 −0.642314
\(195\) −2.96654 −0.212438
\(196\) 54.3919 3.88514
\(197\) −16.7983 −1.19683 −0.598415 0.801186i \(-0.704203\pi\)
−0.598415 + 0.801186i \(0.704203\pi\)
\(198\) −32.6274 −2.31873
\(199\) 8.79192 0.623243 0.311621 0.950206i \(-0.399128\pi\)
0.311621 + 0.950206i \(0.399128\pi\)
\(200\) 25.6718 1.81527
\(201\) −10.6634 −0.752138
\(202\) −3.94108 −0.277293
\(203\) 9.64983 0.677285
\(204\) −2.14151 −0.149936
\(205\) −5.45443 −0.380954
\(206\) −20.8685 −1.45397
\(207\) 6.57928 0.457292
\(208\) 0.712066 0.0493729
\(209\) −15.8803 −1.09846
\(210\) −35.1507 −2.42563
\(211\) −14.8938 −1.02533 −0.512665 0.858589i \(-0.671342\pi\)
−0.512665 + 0.858589i \(0.671342\pi\)
\(212\) 20.1655 1.38497
\(213\) 5.94217 0.407150
\(214\) −19.0488 −1.30215
\(215\) 41.3443 2.81966
\(216\) 10.1421 0.690083
\(217\) 16.9005 1.14728
\(218\) −6.03156 −0.408509
\(219\) 9.81491 0.663230
\(220\) −74.2123 −5.00339
\(221\) −0.835989 −0.0562347
\(222\) −4.82138 −0.323590
\(223\) 4.16716 0.279054 0.139527 0.990218i \(-0.455442\pi\)
0.139527 + 0.990218i \(0.455442\pi\)
\(224\) 32.1890 2.15072
\(225\) −25.5474 −1.70316
\(226\) −40.0898 −2.66673
\(227\) −22.3637 −1.48433 −0.742166 0.670216i \(-0.766201\pi\)
−0.742166 + 0.670216i \(0.766201\pi\)
\(228\) 6.29326 0.416781
\(229\) 9.45321 0.624686 0.312343 0.949969i \(-0.398886\pi\)
0.312343 + 0.949969i \(0.398886\pi\)
\(230\) 24.7436 1.63154
\(231\) 24.0416 1.58182
\(232\) −4.62634 −0.303734
\(233\) −10.2088 −0.668803 −0.334402 0.942431i \(-0.608534\pi\)
−0.334402 + 0.942431i \(0.608534\pi\)
\(234\) 5.04755 0.329969
\(235\) 11.3050 0.737460
\(236\) 2.56597 0.167030
\(237\) 0.315251 0.0204777
\(238\) −9.90569 −0.642091
\(239\) 10.1387 0.655820 0.327910 0.944709i \(-0.393656\pi\)
0.327910 + 0.944709i \(0.393656\pi\)
\(240\) −2.36583 −0.152714
\(241\) 1.70025 0.109523 0.0547613 0.998499i \(-0.482560\pi\)
0.0547613 + 0.998499i \(0.482560\pi\)
\(242\) 59.1803 3.80425
\(243\) −15.7267 −1.00887
\(244\) −29.7410 −1.90398
\(245\) −70.5468 −4.50707
\(246\) −2.44448 −0.155854
\(247\) 2.45672 0.156317
\(248\) −8.10247 −0.514507
\(249\) −3.23982 −0.205316
\(250\) −51.4281 −3.25260
\(251\) 2.42104 0.152815 0.0764074 0.997077i \(-0.475655\pi\)
0.0764074 + 0.997077i \(0.475655\pi\)
\(252\) 36.1721 2.27863
\(253\) −16.9236 −1.06397
\(254\) 33.5825 2.10715
\(255\) 2.77756 0.173937
\(256\) −10.8192 −0.676200
\(257\) 5.01711 0.312958 0.156479 0.987681i \(-0.449986\pi\)
0.156479 + 0.987681i \(0.449986\pi\)
\(258\) 18.5290 1.15357
\(259\) −13.4879 −0.838100
\(260\) 11.4808 0.712012
\(261\) 4.60393 0.284976
\(262\) 35.3355 2.18304
\(263\) −22.9041 −1.41233 −0.706164 0.708049i \(-0.749576\pi\)
−0.706164 + 0.708049i \(0.749576\pi\)
\(264\) −11.5261 −0.709380
\(265\) −26.1548 −1.60668
\(266\) 29.1099 1.78484
\(267\) 12.4690 0.763090
\(268\) 41.2686 2.52088
\(269\) −3.74942 −0.228606 −0.114303 0.993446i \(-0.536464\pi\)
−0.114303 + 0.993446i \(0.536464\pi\)
\(270\) −37.9580 −2.31005
\(271\) 10.2651 0.623562 0.311781 0.950154i \(-0.399075\pi\)
0.311781 + 0.950154i \(0.399075\pi\)
\(272\) −0.666706 −0.0404250
\(273\) −3.71930 −0.225102
\(274\) 5.46611 0.330220
\(275\) 65.7143 3.96272
\(276\) 6.70670 0.403696
\(277\) −15.9783 −0.960044 −0.480022 0.877256i \(-0.659371\pi\)
−0.480022 + 0.877256i \(0.659371\pi\)
\(278\) 23.9064 1.43381
\(279\) 8.06322 0.482732
\(280\) 47.1440 2.81739
\(281\) 29.6055 1.76612 0.883059 0.469262i \(-0.155480\pi\)
0.883059 + 0.469262i \(0.155480\pi\)
\(282\) 5.06651 0.301706
\(283\) 19.3104 1.14788 0.573941 0.818897i \(-0.305414\pi\)
0.573941 + 0.818897i \(0.305414\pi\)
\(284\) −22.9969 −1.36461
\(285\) −8.16241 −0.483500
\(286\) −12.9836 −0.767733
\(287\) −6.83849 −0.403663
\(288\) 15.3574 0.904942
\(289\) −16.2173 −0.953957
\(290\) 17.3146 1.01675
\(291\) 3.14513 0.184371
\(292\) −37.9849 −2.22290
\(293\) −8.44273 −0.493230 −0.246615 0.969114i \(-0.579318\pi\)
−0.246615 + 0.969114i \(0.579318\pi\)
\(294\) −31.6166 −1.84391
\(295\) −3.32809 −0.193769
\(296\) 6.46642 0.375853
\(297\) 25.9616 1.50645
\(298\) 19.1047 1.10671
\(299\) 2.61812 0.151410
\(300\) −26.0422 −1.50355
\(301\) 51.8354 2.98775
\(302\) 52.1574 3.00132
\(303\) 1.38549 0.0795946
\(304\) 1.95925 0.112371
\(305\) 38.5744 2.20876
\(306\) −4.72600 −0.270168
\(307\) 18.4753 1.05444 0.527219 0.849729i \(-0.323235\pi\)
0.527219 + 0.849729i \(0.323235\pi\)
\(308\) −93.0438 −5.30166
\(309\) 7.33635 0.417350
\(310\) 30.3244 1.72231
\(311\) 18.2445 1.03455 0.517276 0.855819i \(-0.326946\pi\)
0.517276 + 0.855819i \(0.326946\pi\)
\(312\) 1.78311 0.100949
\(313\) −10.9949 −0.621467 −0.310733 0.950497i \(-0.600575\pi\)
−0.310733 + 0.950497i \(0.600575\pi\)
\(314\) −24.6619 −1.39175
\(315\) −46.9156 −2.64340
\(316\) −1.22006 −0.0686336
\(317\) −10.7948 −0.606294 −0.303147 0.952944i \(-0.598037\pi\)
−0.303147 + 0.952944i \(0.598037\pi\)
\(318\) −11.7216 −0.657317
\(319\) −11.8425 −0.663050
\(320\) 51.7735 2.89423
\(321\) 6.69663 0.373770
\(322\) 31.0223 1.72881
\(323\) −2.30022 −0.127988
\(324\) 11.5149 0.639714
\(325\) −10.1662 −0.563919
\(326\) −22.6997 −1.25722
\(327\) 2.12041 0.117259
\(328\) 3.27852 0.181026
\(329\) 14.1737 0.781422
\(330\) 43.1376 2.37465
\(331\) 2.70530 0.148697 0.0743483 0.997232i \(-0.476312\pi\)
0.0743483 + 0.997232i \(0.476312\pi\)
\(332\) 12.5385 0.688140
\(333\) −6.43510 −0.352641
\(334\) 15.5946 0.853299
\(335\) −53.5258 −2.92443
\(336\) −2.96616 −0.161817
\(337\) −6.92073 −0.376996 −0.188498 0.982074i \(-0.560362\pi\)
−0.188498 + 0.982074i \(0.560362\pi\)
\(338\) −27.2362 −1.48145
\(339\) 14.0936 0.765461
\(340\) −10.7495 −0.582973
\(341\) −20.7406 −1.12317
\(342\) 13.8883 0.750994
\(343\) −53.6087 −2.89460
\(344\) −24.8511 −1.33988
\(345\) −8.69866 −0.468320
\(346\) −58.2455 −3.13130
\(347\) −17.6570 −0.947877 −0.473939 0.880558i \(-0.657168\pi\)
−0.473939 + 0.880558i \(0.657168\pi\)
\(348\) 4.69309 0.251576
\(349\) 2.79807 0.149777 0.0748886 0.997192i \(-0.476140\pi\)
0.0748886 + 0.997192i \(0.476140\pi\)
\(350\) −120.460 −6.43885
\(351\) −4.01634 −0.214376
\(352\) −39.5030 −2.10552
\(353\) 3.67373 0.195533 0.0977665 0.995209i \(-0.468830\pi\)
0.0977665 + 0.995209i \(0.468830\pi\)
\(354\) −1.49153 −0.0792739
\(355\) 29.8272 1.58306
\(356\) −48.2565 −2.55759
\(357\) 3.48237 0.184306
\(358\) 0.823721 0.0435350
\(359\) −30.6246 −1.61631 −0.808153 0.588972i \(-0.799533\pi\)
−0.808153 + 0.588972i \(0.799533\pi\)
\(360\) 22.4924 1.18545
\(361\) −12.2403 −0.644228
\(362\) 30.9024 1.62420
\(363\) −20.8049 −1.09198
\(364\) 14.3941 0.754457
\(365\) 49.2667 2.57874
\(366\) 17.2877 0.903641
\(367\) −16.2490 −0.848189 −0.424095 0.905618i \(-0.639408\pi\)
−0.424095 + 0.905618i \(0.639408\pi\)
\(368\) 2.08797 0.108843
\(369\) −3.26264 −0.169846
\(370\) −24.2013 −1.25817
\(371\) −32.7916 −1.70246
\(372\) 8.21938 0.426155
\(373\) 3.35997 0.173973 0.0869863 0.996210i \(-0.472276\pi\)
0.0869863 + 0.996210i \(0.472276\pi\)
\(374\) 12.1565 0.628596
\(375\) 18.0796 0.933629
\(376\) −6.79519 −0.350435
\(377\) 1.83206 0.0943559
\(378\) −47.5899 −2.44776
\(379\) −13.0292 −0.669265 −0.334632 0.942349i \(-0.608612\pi\)
−0.334632 + 0.942349i \(0.608612\pi\)
\(380\) 31.5895 1.62051
\(381\) −11.8060 −0.604839
\(382\) 19.0940 0.976935
\(383\) 16.4540 0.840762 0.420381 0.907348i \(-0.361896\pi\)
0.420381 + 0.907348i \(0.361896\pi\)
\(384\) 12.9734 0.662048
\(385\) 120.679 6.15035
\(386\) 36.1598 1.84049
\(387\) 24.7307 1.25713
\(388\) −12.1720 −0.617941
\(389\) −31.8937 −1.61708 −0.808538 0.588444i \(-0.799741\pi\)
−0.808538 + 0.588444i \(0.799741\pi\)
\(390\) −6.67351 −0.337926
\(391\) −2.45134 −0.123969
\(392\) 42.4040 2.14173
\(393\) −12.4223 −0.626621
\(394\) −37.7894 −1.90380
\(395\) 1.58243 0.0796205
\(396\) −44.3912 −2.23074
\(397\) 31.4614 1.57900 0.789502 0.613748i \(-0.210339\pi\)
0.789502 + 0.613748i \(0.210339\pi\)
\(398\) 19.7783 0.991395
\(399\) −10.2336 −0.512322
\(400\) −8.10759 −0.405379
\(401\) −3.09593 −0.154603 −0.0773016 0.997008i \(-0.524630\pi\)
−0.0773016 + 0.997008i \(0.524630\pi\)
\(402\) −23.9883 −1.19643
\(403\) 3.20863 0.159833
\(404\) −5.36203 −0.266771
\(405\) −14.9349 −0.742120
\(406\) 21.7082 1.07736
\(407\) 16.5527 0.820485
\(408\) −1.66952 −0.0826537
\(409\) 12.6949 0.627721 0.313860 0.949469i \(-0.398378\pi\)
0.313860 + 0.949469i \(0.398378\pi\)
\(410\) −12.2703 −0.605985
\(411\) −1.92162 −0.0947867
\(412\) −28.3925 −1.39880
\(413\) −4.17259 −0.205320
\(414\) 14.8007 0.727416
\(415\) −16.2626 −0.798298
\(416\) 6.11122 0.299627
\(417\) −8.40435 −0.411563
\(418\) −35.7242 −1.74733
\(419\) −19.0216 −0.929266 −0.464633 0.885503i \(-0.653814\pi\)
−0.464633 + 0.885503i \(0.653814\pi\)
\(420\) −47.8242 −2.33358
\(421\) −27.0312 −1.31742 −0.658710 0.752397i \(-0.728897\pi\)
−0.658710 + 0.752397i \(0.728897\pi\)
\(422\) −33.5050 −1.63100
\(423\) 6.76227 0.328793
\(424\) 15.7210 0.763481
\(425\) 9.51857 0.461719
\(426\) 13.3675 0.647656
\(427\) 48.3627 2.34044
\(428\) −25.9168 −1.25273
\(429\) 4.56439 0.220371
\(430\) 93.0080 4.48524
\(431\) 1.88408 0.0907530 0.0453765 0.998970i \(-0.485551\pi\)
0.0453765 + 0.998970i \(0.485551\pi\)
\(432\) −3.20305 −0.154107
\(433\) 15.6410 0.751660 0.375830 0.926689i \(-0.377358\pi\)
0.375830 + 0.926689i \(0.377358\pi\)
\(434\) 38.0193 1.82498
\(435\) −6.08699 −0.291849
\(436\) −8.20623 −0.393007
\(437\) 7.20375 0.344602
\(438\) 22.0796 1.05500
\(439\) 28.8504 1.37696 0.688478 0.725257i \(-0.258279\pi\)
0.688478 + 0.725257i \(0.258279\pi\)
\(440\) −57.8560 −2.75818
\(441\) −42.1986 −2.00946
\(442\) −1.88064 −0.0894528
\(443\) −28.5293 −1.35547 −0.677733 0.735308i \(-0.737038\pi\)
−0.677733 + 0.735308i \(0.737038\pi\)
\(444\) −6.55972 −0.311311
\(445\) 62.5892 2.96701
\(446\) 9.37443 0.443892
\(447\) −6.71630 −0.317670
\(448\) 64.9111 3.06676
\(449\) 0.158303 0.00747076 0.00373538 0.999993i \(-0.498811\pi\)
0.00373538 + 0.999993i \(0.498811\pi\)
\(450\) −57.4714 −2.70923
\(451\) 8.39233 0.395179
\(452\) −54.5441 −2.56554
\(453\) −18.3360 −0.861502
\(454\) −50.3094 −2.36113
\(455\) −18.6693 −0.875231
\(456\) 4.90623 0.229755
\(457\) 20.8707 0.976288 0.488144 0.872763i \(-0.337674\pi\)
0.488144 + 0.872763i \(0.337674\pi\)
\(458\) 21.2659 0.993691
\(459\) 3.76049 0.175524
\(460\) 33.6649 1.56963
\(461\) 25.4051 1.18323 0.591616 0.806220i \(-0.298490\pi\)
0.591616 + 0.806220i \(0.298490\pi\)
\(462\) 54.0838 2.51621
\(463\) 9.62944 0.447518 0.223759 0.974645i \(-0.428167\pi\)
0.223759 + 0.974645i \(0.428167\pi\)
\(464\) 1.46108 0.0678288
\(465\) −10.6606 −0.494374
\(466\) −22.9658 −1.06387
\(467\) −36.4715 −1.68770 −0.843849 0.536581i \(-0.819716\pi\)
−0.843849 + 0.536581i \(0.819716\pi\)
\(468\) 6.86743 0.317447
\(469\) −67.1080 −3.09876
\(470\) 25.4318 1.17308
\(471\) 8.66994 0.399490
\(472\) 2.00043 0.0920774
\(473\) −63.6135 −2.92495
\(474\) 0.709187 0.0325740
\(475\) −27.9722 −1.28345
\(476\) −13.4772 −0.617725
\(477\) −15.6449 −0.716330
\(478\) 22.8080 1.04322
\(479\) 19.9600 0.911996 0.455998 0.889981i \(-0.349282\pi\)
0.455998 + 0.889981i \(0.349282\pi\)
\(480\) −20.3044 −0.926766
\(481\) −2.56074 −0.116760
\(482\) 3.82487 0.174218
\(483\) −10.9060 −0.496238
\(484\) 80.5176 3.65989
\(485\) 15.7872 0.716861
\(486\) −35.3788 −1.60481
\(487\) −12.9846 −0.588390 −0.294195 0.955745i \(-0.595051\pi\)
−0.294195 + 0.955745i \(0.595051\pi\)
\(488\) −23.1862 −1.04959
\(489\) 7.98014 0.360874
\(490\) −158.702 −7.16942
\(491\) 39.2860 1.77295 0.886476 0.462774i \(-0.153146\pi\)
0.886476 + 0.462774i \(0.153146\pi\)
\(492\) −3.32583 −0.149940
\(493\) −1.71535 −0.0772556
\(494\) 5.52663 0.248655
\(495\) 57.5758 2.58784
\(496\) 2.55890 0.114898
\(497\) 37.3959 1.67743
\(498\) −7.28830 −0.326596
\(499\) 18.9542 0.848506 0.424253 0.905544i \(-0.360537\pi\)
0.424253 + 0.905544i \(0.360537\pi\)
\(500\) −69.9704 −3.12917
\(501\) −5.48231 −0.244932
\(502\) 5.44637 0.243083
\(503\) 19.9072 0.887617 0.443808 0.896122i \(-0.353627\pi\)
0.443808 + 0.896122i \(0.353627\pi\)
\(504\) 28.1998 1.25612
\(505\) 6.95460 0.309476
\(506\) −38.0712 −1.69247
\(507\) 9.57493 0.425238
\(508\) 45.6906 2.02719
\(509\) −13.6549 −0.605244 −0.302622 0.953111i \(-0.597862\pi\)
−0.302622 + 0.953111i \(0.597862\pi\)
\(510\) 6.24839 0.276683
\(511\) 61.7682 2.73246
\(512\) 8.46997 0.374323
\(513\) −11.0509 −0.487911
\(514\) 11.2865 0.497825
\(515\) 36.8254 1.62272
\(516\) 25.2096 1.10979
\(517\) −17.3943 −0.764998
\(518\) −30.3424 −1.33317
\(519\) 20.4763 0.898811
\(520\) 8.95048 0.392505
\(521\) −7.74427 −0.339283 −0.169641 0.985506i \(-0.554261\pi\)
−0.169641 + 0.985506i \(0.554261\pi\)
\(522\) 10.3570 0.453313
\(523\) 39.9635 1.74748 0.873740 0.486393i \(-0.161688\pi\)
0.873740 + 0.486393i \(0.161688\pi\)
\(524\) 48.0757 2.10020
\(525\) 42.3479 1.84821
\(526\) −51.5250 −2.24660
\(527\) −3.00423 −0.130866
\(528\) 3.64013 0.158416
\(529\) −15.3230 −0.666217
\(530\) −58.8378 −2.55575
\(531\) −1.99074 −0.0863909
\(532\) 39.6054 1.71711
\(533\) −1.29832 −0.0562363
\(534\) 28.0502 1.21385
\(535\) 33.6143 1.45327
\(536\) 32.1731 1.38966
\(537\) −0.289581 −0.0124963
\(538\) −8.43469 −0.363645
\(539\) 108.545 4.67538
\(540\) −51.6437 −2.22239
\(541\) −16.7943 −0.722042 −0.361021 0.932558i \(-0.617572\pi\)
−0.361021 + 0.932558i \(0.617572\pi\)
\(542\) 23.0924 0.991903
\(543\) −10.8638 −0.466211
\(544\) −5.72192 −0.245325
\(545\) 10.6436 0.455920
\(546\) −8.36692 −0.358071
\(547\) −1.00000 −0.0427569
\(548\) 7.43691 0.317689
\(549\) 23.0738 0.984768
\(550\) 147.831 6.30353
\(551\) 5.04091 0.214750
\(552\) 5.22856 0.222542
\(553\) 1.98397 0.0843669
\(554\) −35.9448 −1.52715
\(555\) 8.50802 0.361146
\(556\) 32.5258 1.37940
\(557\) −20.5063 −0.868882 −0.434441 0.900700i \(-0.643054\pi\)
−0.434441 + 0.900700i \(0.643054\pi\)
\(558\) 18.1390 0.767885
\(559\) 9.84118 0.416237
\(560\) −14.8889 −0.629170
\(561\) −4.27363 −0.180433
\(562\) 66.6005 2.80937
\(563\) −32.4055 −1.36573 −0.682865 0.730545i \(-0.739266\pi\)
−0.682865 + 0.730545i \(0.739266\pi\)
\(564\) 6.89324 0.290258
\(565\) 70.7442 2.97623
\(566\) 43.4405 1.82594
\(567\) −18.7246 −0.786360
\(568\) −17.9284 −0.752259
\(569\) −8.66151 −0.363110 −0.181555 0.983381i \(-0.558113\pi\)
−0.181555 + 0.983381i \(0.558113\pi\)
\(570\) −18.3621 −0.769105
\(571\) 24.3017 1.01699 0.508496 0.861064i \(-0.330202\pi\)
0.508496 + 0.861064i \(0.330202\pi\)
\(572\) −17.6647 −0.738600
\(573\) −6.71254 −0.280420
\(574\) −15.3838 −0.642109
\(575\) −29.8099 −1.24316
\(576\) 30.9691 1.29038
\(577\) 21.4414 0.892617 0.446309 0.894879i \(-0.352738\pi\)
0.446309 + 0.894879i \(0.352738\pi\)
\(578\) −36.4823 −1.51746
\(579\) −12.7121 −0.528295
\(580\) 23.5574 0.978167
\(581\) −20.3892 −0.845887
\(582\) 7.07527 0.293279
\(583\) 40.2425 1.66667
\(584\) −29.6131 −1.22540
\(585\) −8.90713 −0.368264
\(586\) −18.9927 −0.784583
\(587\) 7.24339 0.298967 0.149483 0.988764i \(-0.452239\pi\)
0.149483 + 0.988764i \(0.452239\pi\)
\(588\) −43.0159 −1.77394
\(589\) 8.82853 0.363773
\(590\) −7.48686 −0.308229
\(591\) 13.2849 0.546470
\(592\) −2.04221 −0.0839342
\(593\) −30.4235 −1.24934 −0.624672 0.780887i \(-0.714767\pi\)
−0.624672 + 0.780887i \(0.714767\pi\)
\(594\) 58.4032 2.39631
\(595\) 17.4800 0.716611
\(596\) 25.9929 1.06471
\(597\) −6.95309 −0.284571
\(598\) 5.88971 0.240848
\(599\) 33.3767 1.36373 0.681866 0.731477i \(-0.261168\pi\)
0.681866 + 0.731477i \(0.261168\pi\)
\(600\) −20.3025 −0.828847
\(601\) −15.6192 −0.637119 −0.318559 0.947903i \(-0.603199\pi\)
−0.318559 + 0.947903i \(0.603199\pi\)
\(602\) 116.609 4.75262
\(603\) −32.0172 −1.30384
\(604\) 70.9626 2.88743
\(605\) −104.432 −4.24577
\(606\) 3.11680 0.126612
\(607\) −34.4069 −1.39653 −0.698267 0.715837i \(-0.746045\pi\)
−0.698267 + 0.715837i \(0.746045\pi\)
\(608\) 16.8150 0.681938
\(609\) −7.63157 −0.309247
\(610\) 86.7769 3.51349
\(611\) 2.69094 0.108864
\(612\) −6.42996 −0.259916
\(613\) 7.54454 0.304721 0.152361 0.988325i \(-0.451312\pi\)
0.152361 + 0.988325i \(0.451312\pi\)
\(614\) 41.5619 1.67730
\(615\) 4.31363 0.173943
\(616\) −72.5370 −2.92260
\(617\) 24.6440 0.992131 0.496065 0.868285i \(-0.334778\pi\)
0.496065 + 0.868285i \(0.334778\pi\)
\(618\) 16.5038 0.663881
\(619\) −37.1366 −1.49264 −0.746322 0.665585i \(-0.768182\pi\)
−0.746322 + 0.665585i \(0.768182\pi\)
\(620\) 41.2579 1.65696
\(621\) −11.7770 −0.472593
\(622\) 41.0428 1.64567
\(623\) 78.4712 3.14388
\(624\) −0.563138 −0.0225436
\(625\) 36.9581 1.47833
\(626\) −24.7340 −0.988570
\(627\) 12.5589 0.501555
\(628\) −33.5537 −1.33894
\(629\) 2.39762 0.0955992
\(630\) −105.541 −4.20486
\(631\) −17.4883 −0.696197 −0.348099 0.937458i \(-0.613173\pi\)
−0.348099 + 0.937458i \(0.613173\pi\)
\(632\) −0.951159 −0.0378351
\(633\) 11.7788 0.468163
\(634\) −24.2838 −0.964435
\(635\) −59.2611 −2.35171
\(636\) −15.9479 −0.632374
\(637\) −16.7923 −0.665333
\(638\) −26.6408 −1.05472
\(639\) 17.8416 0.705801
\(640\) 65.1212 2.57414
\(641\) −48.0566 −1.89812 −0.949061 0.315094i \(-0.897964\pi\)
−0.949061 + 0.315094i \(0.897964\pi\)
\(642\) 15.0647 0.594557
\(643\) 11.4373 0.451044 0.225522 0.974238i \(-0.427591\pi\)
0.225522 + 0.974238i \(0.427591\pi\)
\(644\) 42.2073 1.66320
\(645\) −32.6971 −1.28745
\(646\) −5.17457 −0.203591
\(647\) −4.77121 −0.187576 −0.0937878 0.995592i \(-0.529898\pi\)
−0.0937878 + 0.995592i \(0.529898\pi\)
\(648\) 8.97700 0.352650
\(649\) 5.12069 0.201005
\(650\) −22.8698 −0.897028
\(651\) −13.3658 −0.523845
\(652\) −30.8841 −1.20951
\(653\) −23.7882 −0.930904 −0.465452 0.885073i \(-0.654108\pi\)
−0.465452 + 0.885073i \(0.654108\pi\)
\(654\) 4.77006 0.186524
\(655\) −62.3546 −2.43640
\(656\) −1.03541 −0.0404261
\(657\) 29.4696 1.14972
\(658\) 31.8851 1.24301
\(659\) 18.8698 0.735062 0.367531 0.930011i \(-0.380203\pi\)
0.367531 + 0.930011i \(0.380203\pi\)
\(660\) 58.6908 2.28454
\(661\) −31.2126 −1.21403 −0.607015 0.794691i \(-0.707633\pi\)
−0.607015 + 0.794691i \(0.707633\pi\)
\(662\) 6.08583 0.236532
\(663\) 0.661142 0.0256766
\(664\) 9.77504 0.379345
\(665\) −51.3686 −1.99199
\(666\) −14.4764 −0.560948
\(667\) 5.37208 0.208008
\(668\) 21.2172 0.820918
\(669\) −3.29560 −0.127415
\(670\) −120.411 −4.65190
\(671\) −59.3517 −2.29125
\(672\) −25.4567 −0.982013
\(673\) 47.1177 1.81625 0.908127 0.418695i \(-0.137512\pi\)
0.908127 + 0.418695i \(0.137512\pi\)
\(674\) −15.5689 −0.599690
\(675\) 45.7300 1.76015
\(676\) −37.0561 −1.42524
\(677\) −2.36717 −0.0909779 −0.0454889 0.998965i \(-0.514485\pi\)
−0.0454889 + 0.998965i \(0.514485\pi\)
\(678\) 31.7050 1.21762
\(679\) 19.7932 0.759595
\(680\) −8.38031 −0.321370
\(681\) 17.6864 0.677743
\(682\) −46.6580 −1.78663
\(683\) −5.92218 −0.226606 −0.113303 0.993560i \(-0.536143\pi\)
−0.113303 + 0.993560i \(0.536143\pi\)
\(684\) 18.8957 0.722496
\(685\) −9.64575 −0.368545
\(686\) −120.598 −4.60445
\(687\) −7.47607 −0.285230
\(688\) 7.84839 0.299217
\(689\) −6.22563 −0.237177
\(690\) −19.5685 −0.744959
\(691\) −14.5963 −0.555270 −0.277635 0.960687i \(-0.589551\pi\)
−0.277635 + 0.960687i \(0.589551\pi\)
\(692\) −79.2459 −3.01248
\(693\) 72.1857 2.74211
\(694\) −39.7211 −1.50779
\(695\) −42.1863 −1.60022
\(696\) 3.65874 0.138684
\(697\) 1.21561 0.0460445
\(698\) 6.29452 0.238251
\(699\) 8.07366 0.305374
\(700\) −163.892 −6.19452
\(701\) −0.810679 −0.0306189 −0.0153095 0.999883i \(-0.504873\pi\)
−0.0153095 + 0.999883i \(0.504873\pi\)
\(702\) −9.03514 −0.341009
\(703\) −7.04588 −0.265740
\(704\) −79.6602 −3.00231
\(705\) −8.94059 −0.336722
\(706\) 8.26441 0.311035
\(707\) 8.71934 0.327925
\(708\) −2.02930 −0.0762657
\(709\) −14.7383 −0.553508 −0.276754 0.960941i \(-0.589259\pi\)
−0.276754 + 0.960941i \(0.589259\pi\)
\(710\) 67.0992 2.51819
\(711\) 0.946551 0.0354984
\(712\) −37.6208 −1.40990
\(713\) 9.40854 0.352353
\(714\) 7.83392 0.293177
\(715\) 22.9114 0.856836
\(716\) 1.12071 0.0418830
\(717\) −8.01821 −0.299446
\(718\) −68.8931 −2.57107
\(719\) 5.18877 0.193508 0.0967542 0.995308i \(-0.469154\pi\)
0.0967542 + 0.995308i \(0.469154\pi\)
\(720\) −7.10348 −0.264731
\(721\) 46.1699 1.71946
\(722\) −27.5358 −1.02478
\(723\) −1.34464 −0.0500078
\(724\) 42.0443 1.56256
\(725\) −20.8598 −0.774715
\(726\) −46.8027 −1.73701
\(727\) −2.93624 −0.108899 −0.0544496 0.998517i \(-0.517340\pi\)
−0.0544496 + 0.998517i \(0.517340\pi\)
\(728\) 11.2217 0.415903
\(729\) 1.15094 0.0426274
\(730\) 110.830 4.10201
\(731\) −9.21427 −0.340802
\(732\) 23.5207 0.869351
\(733\) −4.53301 −0.167430 −0.0837152 0.996490i \(-0.526679\pi\)
−0.0837152 + 0.996490i \(0.526679\pi\)
\(734\) −36.5536 −1.34922
\(735\) 55.7920 2.05792
\(736\) 17.9197 0.660529
\(737\) 82.3563 3.03363
\(738\) −7.33963 −0.270176
\(739\) −33.7934 −1.24311 −0.621555 0.783371i \(-0.713499\pi\)
−0.621555 + 0.783371i \(0.713499\pi\)
\(740\) −32.9271 −1.21042
\(741\) −1.94290 −0.0713741
\(742\) −73.7679 −2.70811
\(743\) 6.05916 0.222289 0.111144 0.993804i \(-0.464548\pi\)
0.111144 + 0.993804i \(0.464548\pi\)
\(744\) 6.40784 0.234923
\(745\) −33.7130 −1.23515
\(746\) 7.55857 0.276739
\(747\) −9.72769 −0.355917
\(748\) 16.5395 0.604742
\(749\) 42.1440 1.53991
\(750\) 40.6719 1.48513
\(751\) 38.1075 1.39056 0.695280 0.718739i \(-0.255280\pi\)
0.695280 + 0.718739i \(0.255280\pi\)
\(752\) 2.14604 0.0782579
\(753\) −1.91468 −0.0697748
\(754\) 4.12140 0.150092
\(755\) −92.0392 −3.34965
\(756\) −64.7483 −2.35487
\(757\) 3.62120 0.131615 0.0658074 0.997832i \(-0.479038\pi\)
0.0658074 + 0.997832i \(0.479038\pi\)
\(758\) −29.3104 −1.06460
\(759\) 13.3840 0.485808
\(760\) 24.6272 0.893323
\(761\) 33.9368 1.23021 0.615105 0.788446i \(-0.289114\pi\)
0.615105 + 0.788446i \(0.289114\pi\)
\(762\) −26.5587 −0.962120
\(763\) 13.3444 0.483099
\(764\) 25.9783 0.939863
\(765\) 8.33972 0.301523
\(766\) 37.0150 1.33740
\(767\) −0.792185 −0.0286041
\(768\) 8.55637 0.308751
\(769\) −22.6616 −0.817199 −0.408599 0.912714i \(-0.633983\pi\)
−0.408599 + 0.912714i \(0.633983\pi\)
\(770\) 271.478 9.78340
\(771\) −3.96778 −0.142896
\(772\) 49.1972 1.77065
\(773\) −1.85144 −0.0665915 −0.0332958 0.999446i \(-0.510600\pi\)
−0.0332958 + 0.999446i \(0.510600\pi\)
\(774\) 55.6341 1.99972
\(775\) −36.5335 −1.31232
\(776\) −9.48932 −0.340647
\(777\) 10.6669 0.382674
\(778\) −71.7480 −2.57229
\(779\) −3.57231 −0.127991
\(780\) −9.07963 −0.325103
\(781\) −45.8929 −1.64218
\(782\) −5.51452 −0.197199
\(783\) −8.24106 −0.294512
\(784\) −13.3919 −0.478283
\(785\) 43.5195 1.55328
\(786\) −27.9451 −0.996769
\(787\) 1.88604 0.0672302 0.0336151 0.999435i \(-0.489298\pi\)
0.0336151 + 0.999435i \(0.489298\pi\)
\(788\) −51.4143 −1.83156
\(789\) 18.1137 0.644865
\(790\) 3.55982 0.126653
\(791\) 88.6956 3.15365
\(792\) −34.6074 −1.22972
\(793\) 9.18187 0.326058
\(794\) 70.7755 2.51173
\(795\) 20.6845 0.733605
\(796\) 26.9093 0.953775
\(797\) −12.7479 −0.451555 −0.225777 0.974179i \(-0.572492\pi\)
−0.225777 + 0.974179i \(0.572492\pi\)
\(798\) −23.0215 −0.814954
\(799\) −2.51952 −0.0891341
\(800\) −69.5824 −2.46011
\(801\) 37.4386 1.32283
\(802\) −6.96458 −0.245928
\(803\) −75.8032 −2.67504
\(804\) −32.6373 −1.15103
\(805\) −54.7433 −1.92945
\(806\) 7.21812 0.254247
\(807\) 2.96523 0.104381
\(808\) −4.18025 −0.147061
\(809\) −5.11274 −0.179754 −0.0898772 0.995953i \(-0.528647\pi\)
−0.0898772 + 0.995953i \(0.528647\pi\)
\(810\) −33.5975 −1.18049
\(811\) −16.5806 −0.582225 −0.291113 0.956689i \(-0.594025\pi\)
−0.291113 + 0.956689i \(0.594025\pi\)
\(812\) 29.5351 1.03648
\(813\) −8.11817 −0.284717
\(814\) 37.2368 1.30515
\(815\) 40.0570 1.40313
\(816\) 0.527264 0.0184579
\(817\) 27.0780 0.947338
\(818\) 28.5583 0.998519
\(819\) −11.1673 −0.390218
\(820\) −16.6943 −0.582990
\(821\) 36.7875 1.28389 0.641946 0.766750i \(-0.278127\pi\)
0.641946 + 0.766750i \(0.278127\pi\)
\(822\) −4.32288 −0.150778
\(823\) 35.7536 1.24629 0.623145 0.782106i \(-0.285854\pi\)
0.623145 + 0.782106i \(0.285854\pi\)
\(824\) −22.1349 −0.771105
\(825\) −51.9702 −1.80937
\(826\) −9.38665 −0.326603
\(827\) −43.6084 −1.51641 −0.758206 0.652015i \(-0.773924\pi\)
−0.758206 + 0.652015i \(0.773924\pi\)
\(828\) 20.1371 0.699813
\(829\) −41.5254 −1.44224 −0.721118 0.692812i \(-0.756372\pi\)
−0.721118 + 0.692812i \(0.756372\pi\)
\(830\) −36.5842 −1.26986
\(831\) 12.6365 0.438354
\(832\) 12.3236 0.427246
\(833\) 15.7225 0.544754
\(834\) −18.9064 −0.654675
\(835\) −27.5189 −0.952332
\(836\) −48.6045 −1.68102
\(837\) −14.4332 −0.498885
\(838\) −42.7909 −1.47819
\(839\) 1.67546 0.0578433 0.0289216 0.999582i \(-0.490793\pi\)
0.0289216 + 0.999582i \(0.490793\pi\)
\(840\) −37.2838 −1.28641
\(841\) −25.2408 −0.870373
\(842\) −60.8093 −2.09563
\(843\) −23.4135 −0.806405
\(844\) −45.5852 −1.56911
\(845\) 48.0622 1.65339
\(846\) 15.2124 0.523013
\(847\) −130.932 −4.49887
\(848\) −4.96497 −0.170498
\(849\) −15.2716 −0.524120
\(850\) 21.4129 0.734458
\(851\) −7.50877 −0.257397
\(852\) 18.1871 0.623080
\(853\) −16.7442 −0.573311 −0.286655 0.958034i \(-0.592543\pi\)
−0.286655 + 0.958034i \(0.592543\pi\)
\(854\) 108.797 3.72294
\(855\) −24.5079 −0.838154
\(856\) −20.2047 −0.690584
\(857\) −30.4030 −1.03855 −0.519273 0.854608i \(-0.673797\pi\)
−0.519273 + 0.854608i \(0.673797\pi\)
\(858\) 10.2680 0.350545
\(859\) 38.6690 1.31937 0.659685 0.751542i \(-0.270690\pi\)
0.659685 + 0.751542i \(0.270690\pi\)
\(860\) 126.542 4.31504
\(861\) 5.40822 0.184312
\(862\) 4.23842 0.144361
\(863\) 21.7245 0.739511 0.369756 0.929129i \(-0.379441\pi\)
0.369756 + 0.929129i \(0.379441\pi\)
\(864\) −27.4898 −0.935221
\(865\) 102.783 3.49471
\(866\) 35.1860 1.19567
\(867\) 12.8254 0.435574
\(868\) 51.7271 1.75573
\(869\) −2.43477 −0.0825938
\(870\) −13.6933 −0.464245
\(871\) −12.7407 −0.431703
\(872\) −6.39759 −0.216650
\(873\) 9.44335 0.319609
\(874\) 16.2055 0.548160
\(875\) 113.781 3.84649
\(876\) 30.0403 1.01497
\(877\) −25.2290 −0.851923 −0.425961 0.904741i \(-0.640064\pi\)
−0.425961 + 0.904741i \(0.640064\pi\)
\(878\) 64.9018 2.19033
\(879\) 6.67694 0.225208
\(880\) 18.2719 0.615947
\(881\) −8.90432 −0.299994 −0.149997 0.988686i \(-0.547926\pi\)
−0.149997 + 0.988686i \(0.547926\pi\)
\(882\) −94.9298 −3.19645
\(883\) −51.5248 −1.73395 −0.866974 0.498353i \(-0.833938\pi\)
−0.866974 + 0.498353i \(0.833938\pi\)
\(884\) −2.55870 −0.0860583
\(885\) 2.63202 0.0884744
\(886\) −64.1794 −2.15615
\(887\) 46.1037 1.54801 0.774005 0.633179i \(-0.218250\pi\)
0.774005 + 0.633179i \(0.218250\pi\)
\(888\) −5.11397 −0.171614
\(889\) −74.2987 −2.49190
\(890\) 140.800 4.71964
\(891\) 22.9792 0.769833
\(892\) 12.7544 0.427048
\(893\) 7.40411 0.247769
\(894\) −15.1090 −0.505319
\(895\) −1.45357 −0.0485876
\(896\) 81.6458 2.72759
\(897\) −2.07054 −0.0691333
\(898\) 0.356117 0.0118838
\(899\) 6.58374 0.219580
\(900\) −78.1926 −2.60642
\(901\) 5.82904 0.194193
\(902\) 18.8794 0.628614
\(903\) −40.9941 −1.36420
\(904\) −42.5226 −1.41428
\(905\) −54.5318 −1.81270
\(906\) −41.2487 −1.37040
\(907\) 14.9725 0.497152 0.248576 0.968612i \(-0.420037\pi\)
0.248576 + 0.968612i \(0.420037\pi\)
\(908\) −68.4483 −2.27154
\(909\) 4.16000 0.137978
\(910\) −41.9984 −1.39223
\(911\) 19.9974 0.662543 0.331271 0.943536i \(-0.392522\pi\)
0.331271 + 0.943536i \(0.392522\pi\)
\(912\) −1.54947 −0.0513081
\(913\) 25.0220 0.828109
\(914\) 46.9506 1.55299
\(915\) −30.5066 −1.00852
\(916\) 28.9333 0.955983
\(917\) −78.1772 −2.58164
\(918\) 8.45957 0.279208
\(919\) −42.9780 −1.41771 −0.708857 0.705353i \(-0.750789\pi\)
−0.708857 + 0.705353i \(0.750789\pi\)
\(920\) 26.2452 0.865277
\(921\) −14.6112 −0.481454
\(922\) 57.1512 1.88217
\(923\) 7.09976 0.233692
\(924\) 73.5837 2.42073
\(925\) 29.1566 0.958664
\(926\) 21.6624 0.711869
\(927\) 22.0276 0.723483
\(928\) 12.5395 0.411630
\(929\) 23.1037 0.758007 0.379003 0.925395i \(-0.376267\pi\)
0.379003 + 0.925395i \(0.376267\pi\)
\(930\) −23.9821 −0.786404
\(931\) −46.2038 −1.51427
\(932\) −31.2460 −1.02350
\(933\) −14.4287 −0.472374
\(934\) −82.0461 −2.68463
\(935\) −21.4518 −0.701550
\(936\) 5.35386 0.174996
\(937\) 0.0952572 0.00311192 0.00155596 0.999999i \(-0.499505\pi\)
0.00155596 + 0.999999i \(0.499505\pi\)
\(938\) −150.966 −4.92921
\(939\) 8.69529 0.283760
\(940\) 34.6012 1.12857
\(941\) −31.3460 −1.02185 −0.510925 0.859625i \(-0.670697\pi\)
−0.510925 + 0.859625i \(0.670697\pi\)
\(942\) 19.5039 0.635470
\(943\) −3.80700 −0.123973
\(944\) −0.631772 −0.0205624
\(945\) 83.9792 2.73184
\(946\) −143.105 −4.65273
\(947\) 46.5491 1.51264 0.756321 0.654200i \(-0.226995\pi\)
0.756321 + 0.654200i \(0.226995\pi\)
\(948\) 0.964883 0.0313379
\(949\) 11.7270 0.380673
\(950\) −62.9262 −2.04160
\(951\) 8.53703 0.276832
\(952\) −10.5068 −0.340528
\(953\) −23.5470 −0.762761 −0.381380 0.924418i \(-0.624551\pi\)
−0.381380 + 0.924418i \(0.624551\pi\)
\(954\) −35.1947 −1.13947
\(955\) −33.6942 −1.09032
\(956\) 31.0315 1.00363
\(957\) 9.36561 0.302747
\(958\) 44.9020 1.45072
\(959\) −12.0934 −0.390515
\(960\) −40.9451 −1.32150
\(961\) −19.4694 −0.628045
\(962\) −5.76064 −0.185730
\(963\) 20.1069 0.647935
\(964\) 5.20392 0.167607
\(965\) −63.8093 −2.05409
\(966\) −24.5340 −0.789368
\(967\) −23.9508 −0.770204 −0.385102 0.922874i \(-0.625834\pi\)
−0.385102 + 0.922874i \(0.625834\pi\)
\(968\) 62.7716 2.01756
\(969\) 1.81913 0.0584389
\(970\) 35.5149 1.14031
\(971\) −43.5907 −1.39889 −0.699447 0.714685i \(-0.746570\pi\)
−0.699447 + 0.714685i \(0.746570\pi\)
\(972\) −48.1346 −1.54392
\(973\) −52.8911 −1.69561
\(974\) −29.2102 −0.935954
\(975\) 8.03993 0.257484
\(976\) 7.32259 0.234390
\(977\) −17.2616 −0.552246 −0.276123 0.961122i \(-0.589050\pi\)
−0.276123 + 0.961122i \(0.589050\pi\)
\(978\) 17.9521 0.574045
\(979\) −96.3014 −3.07781
\(980\) −215.922 −6.89736
\(981\) 6.36660 0.203270
\(982\) 88.3777 2.82025
\(983\) 45.3830 1.44749 0.723747 0.690066i \(-0.242418\pi\)
0.723747 + 0.690066i \(0.242418\pi\)
\(984\) −2.59282 −0.0826561
\(985\) 66.6849 2.12476
\(986\) −3.85885 −0.122891
\(987\) −11.2093 −0.356795
\(988\) 7.51925 0.239219
\(989\) 28.8569 0.917596
\(990\) 129.522 4.11649
\(991\) 38.7136 1.22978 0.614889 0.788613i \(-0.289201\pi\)
0.614889 + 0.788613i \(0.289201\pi\)
\(992\) 21.9614 0.697276
\(993\) −2.13948 −0.0678945
\(994\) 84.1256 2.66830
\(995\) −34.9016 −1.10646
\(996\) −9.91608 −0.314203
\(997\) 58.6255 1.85669 0.928343 0.371724i \(-0.121233\pi\)
0.928343 + 0.371724i \(0.121233\pi\)
\(998\) 42.6393 1.34972
\(999\) 11.5189 0.364441
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 547.2.a.b.1.17 18
3.2 odd 2 4923.2.a.l.1.2 18
4.3 odd 2 8752.2.a.s.1.10 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.17 18 1.1 even 1 trivial
4923.2.a.l.1.2 18 3.2 odd 2
8752.2.a.s.1.10 18 4.3 odd 2