Properties

Label 547.2.a.b.1.15
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 1.15
Root \(-1.52216\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +O(q^{10})\) \(q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +1.89831 q^{10} +3.77827 q^{11} -0.819785 q^{12} -4.29029 q^{13} -1.36890 q^{14} -3.22549 q^{15} -4.53346 q^{16} -7.86362 q^{17} +5.61560 q^{18} -6.61960 q^{19} +0.395293 q^{20} +2.32595 q^{21} +5.75113 q^{22} +3.37854 q^{23} +6.62584 q^{24} -3.44470 q^{25} -6.53050 q^{26} -1.78261 q^{27} -0.285052 q^{28} -2.81309 q^{29} -4.90970 q^{30} -1.72157 q^{31} -1.77696 q^{32} -9.77196 q^{33} -11.9697 q^{34} -1.12155 q^{35} +1.16936 q^{36} -4.86769 q^{37} -10.0761 q^{38} +11.0962 q^{39} -3.19492 q^{40} +5.86463 q^{41} +3.54046 q^{42} +7.30517 q^{43} +1.19758 q^{44} +4.60091 q^{45} +5.14268 q^{46} +2.08319 q^{47} +11.7252 q^{48} -6.19123 q^{49} -5.24338 q^{50} +20.3381 q^{51} -1.35987 q^{52} +3.26386 q^{53} -2.71342 q^{54} +4.71195 q^{55} +2.30391 q^{56} +17.1206 q^{57} -4.28196 q^{58} -6.21926 q^{59} -1.02237 q^{60} +12.5220 q^{61} -2.62050 q^{62} -3.31779 q^{63} +6.36212 q^{64} -5.35050 q^{65} -14.8745 q^{66} -10.3052 q^{67} -2.49250 q^{68} -8.73812 q^{69} -1.70718 q^{70} +16.3692 q^{71} -9.45125 q^{72} -15.5143 q^{73} -7.40939 q^{74} +8.90922 q^{75} -2.09818 q^{76} -3.39786 q^{77} +16.8902 q^{78} +5.15466 q^{79} -5.65376 q^{80} -6.45724 q^{81} +8.92689 q^{82} +6.55843 q^{83} +0.737245 q^{84} -9.80686 q^{85} +11.1196 q^{86} +7.27565 q^{87} -9.67935 q^{88} -4.60031 q^{89} +7.00331 q^{90} +3.85833 q^{91} +1.07088 q^{92} +4.45258 q^{93} +3.17095 q^{94} -8.25541 q^{95} +4.59585 q^{96} +9.16155 q^{97} -9.42403 q^{98} +13.9389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52216 1.07633 0.538164 0.842840i \(-0.319118\pi\)
0.538164 + 0.842840i \(0.319118\pi\)
\(3\) −2.58636 −1.49323 −0.746617 0.665254i \(-0.768323\pi\)
−0.746617 + 0.665254i \(0.768323\pi\)
\(4\) 0.316965 0.158483
\(5\) 1.24712 0.557728 0.278864 0.960331i \(-0.410042\pi\)
0.278864 + 0.960331i \(0.410042\pi\)
\(6\) −3.93684 −1.60721
\(7\) −0.899316 −0.339909 −0.169955 0.985452i \(-0.554362\pi\)
−0.169955 + 0.985452i \(0.554362\pi\)
\(8\) −2.56184 −0.905749
\(9\) 3.68924 1.22975
\(10\) 1.89831 0.600298
\(11\) 3.77827 1.13919 0.569596 0.821925i \(-0.307100\pi\)
0.569596 + 0.821925i \(0.307100\pi\)
\(12\) −0.819785 −0.236652
\(13\) −4.29029 −1.18991 −0.594957 0.803758i \(-0.702831\pi\)
−0.594957 + 0.803758i \(0.702831\pi\)
\(14\) −1.36890 −0.365854
\(15\) −3.22549 −0.832818
\(16\) −4.53346 −1.13337
\(17\) −7.86362 −1.90721 −0.953604 0.301063i \(-0.902658\pi\)
−0.953604 + 0.301063i \(0.902658\pi\)
\(18\) 5.61560 1.32361
\(19\) −6.61960 −1.51864 −0.759320 0.650718i \(-0.774468\pi\)
−0.759320 + 0.650718i \(0.774468\pi\)
\(20\) 0.395293 0.0883902
\(21\) 2.32595 0.507564
\(22\) 5.75113 1.22614
\(23\) 3.37854 0.704475 0.352238 0.935911i \(-0.385421\pi\)
0.352238 + 0.935911i \(0.385421\pi\)
\(24\) 6.62584 1.35249
\(25\) −3.44470 −0.688940
\(26\) −6.53050 −1.28074
\(27\) −1.78261 −0.343064
\(28\) −0.285052 −0.0538697
\(29\) −2.81309 −0.522377 −0.261189 0.965288i \(-0.584114\pi\)
−0.261189 + 0.965288i \(0.584114\pi\)
\(30\) −4.90970 −0.896385
\(31\) −1.72157 −0.309202 −0.154601 0.987977i \(-0.549409\pi\)
−0.154601 + 0.987977i \(0.549409\pi\)
\(32\) −1.77696 −0.314125
\(33\) −9.77196 −1.70108
\(34\) −11.9697 −2.05278
\(35\) −1.12155 −0.189577
\(36\) 1.16936 0.194893
\(37\) −4.86769 −0.800243 −0.400122 0.916462i \(-0.631032\pi\)
−0.400122 + 0.916462i \(0.631032\pi\)
\(38\) −10.0761 −1.63456
\(39\) 11.0962 1.77682
\(40\) −3.19492 −0.505161
\(41\) 5.86463 0.915901 0.457951 0.888978i \(-0.348584\pi\)
0.457951 + 0.888978i \(0.348584\pi\)
\(42\) 3.54046 0.546305
\(43\) 7.30517 1.11403 0.557014 0.830503i \(-0.311947\pi\)
0.557014 + 0.830503i \(0.311947\pi\)
\(44\) 1.19758 0.180542
\(45\) 4.60091 0.685863
\(46\) 5.14268 0.758247
\(47\) 2.08319 0.303865 0.151932 0.988391i \(-0.451450\pi\)
0.151932 + 0.988391i \(0.451450\pi\)
\(48\) 11.7252 1.69238
\(49\) −6.19123 −0.884462
\(50\) −5.24338 −0.741525
\(51\) 20.3381 2.84791
\(52\) −1.35987 −0.188581
\(53\) 3.26386 0.448325 0.224163 0.974552i \(-0.428035\pi\)
0.224163 + 0.974552i \(0.428035\pi\)
\(54\) −2.71342 −0.369250
\(55\) 4.71195 0.635359
\(56\) 2.30391 0.307873
\(57\) 17.1206 2.26768
\(58\) −4.28196 −0.562250
\(59\) −6.21926 −0.809679 −0.404840 0.914388i \(-0.632673\pi\)
−0.404840 + 0.914388i \(0.632673\pi\)
\(60\) −1.02237 −0.131987
\(61\) 12.5220 1.60327 0.801636 0.597812i \(-0.203963\pi\)
0.801636 + 0.597812i \(0.203963\pi\)
\(62\) −2.62050 −0.332803
\(63\) −3.31779 −0.418002
\(64\) 6.36212 0.795264
\(65\) −5.35050 −0.663648
\(66\) −14.8745 −1.83092
\(67\) −10.3052 −1.25898 −0.629491 0.777008i \(-0.716737\pi\)
−0.629491 + 0.777008i \(0.716737\pi\)
\(68\) −2.49250 −0.302259
\(69\) −8.73812 −1.05195
\(70\) −1.70718 −0.204047
\(71\) 16.3692 1.94267 0.971334 0.237718i \(-0.0763994\pi\)
0.971334 + 0.237718i \(0.0763994\pi\)
\(72\) −9.45125 −1.11384
\(73\) −15.5143 −1.81581 −0.907907 0.419172i \(-0.862320\pi\)
−0.907907 + 0.419172i \(0.862320\pi\)
\(74\) −7.40939 −0.861324
\(75\) 8.90922 1.02875
\(76\) −2.09818 −0.240678
\(77\) −3.39786 −0.387222
\(78\) 16.8902 1.91244
\(79\) 5.15466 0.579945 0.289973 0.957035i \(-0.406354\pi\)
0.289973 + 0.957035i \(0.406354\pi\)
\(80\) −5.65376 −0.632109
\(81\) −6.45724 −0.717471
\(82\) 8.92689 0.985811
\(83\) 6.55843 0.719881 0.359941 0.932975i \(-0.382797\pi\)
0.359941 + 0.932975i \(0.382797\pi\)
\(84\) 0.737245 0.0804401
\(85\) −9.80686 −1.06370
\(86\) 11.1196 1.19906
\(87\) 7.27565 0.780031
\(88\) −9.67935 −1.03182
\(89\) −4.60031 −0.487632 −0.243816 0.969822i \(-0.578399\pi\)
−0.243816 + 0.969822i \(0.578399\pi\)
\(90\) 7.00331 0.738214
\(91\) 3.85833 0.404463
\(92\) 1.07088 0.111647
\(93\) 4.45258 0.461711
\(94\) 3.17095 0.327058
\(95\) −8.25541 −0.846987
\(96\) 4.59585 0.469062
\(97\) 9.16155 0.930215 0.465107 0.885254i \(-0.346016\pi\)
0.465107 + 0.885254i \(0.346016\pi\)
\(98\) −9.42403 −0.951971
\(99\) 13.9389 1.40092
\(100\) −1.09185 −0.109185
\(101\) −11.0854 −1.10304 −0.551521 0.834161i \(-0.685952\pi\)
−0.551521 + 0.834161i \(0.685952\pi\)
\(102\) 30.9578 3.06528
\(103\) −4.38943 −0.432503 −0.216252 0.976338i \(-0.569383\pi\)
−0.216252 + 0.976338i \(0.569383\pi\)
\(104\) 10.9911 1.07776
\(105\) 2.90073 0.283082
\(106\) 4.96811 0.482545
\(107\) −19.0618 −1.84277 −0.921385 0.388650i \(-0.872941\pi\)
−0.921385 + 0.388650i \(0.872941\pi\)
\(108\) −0.565027 −0.0543697
\(109\) 4.54306 0.435147 0.217573 0.976044i \(-0.430186\pi\)
0.217573 + 0.976044i \(0.430186\pi\)
\(110\) 7.17233 0.683855
\(111\) 12.5896 1.19495
\(112\) 4.07701 0.385242
\(113\) 11.6865 1.09937 0.549685 0.835372i \(-0.314748\pi\)
0.549685 + 0.835372i \(0.314748\pi\)
\(114\) 26.0603 2.44077
\(115\) 4.21344 0.392905
\(116\) −0.891651 −0.0827877
\(117\) −15.8279 −1.46329
\(118\) −9.46670 −0.871481
\(119\) 7.07188 0.648278
\(120\) 8.26320 0.754324
\(121\) 3.27535 0.297759
\(122\) 19.0604 1.72565
\(123\) −15.1680 −1.36765
\(124\) −0.545677 −0.0490032
\(125\) −10.5315 −0.941968
\(126\) −5.05020 −0.449907
\(127\) −13.7079 −1.21638 −0.608189 0.793792i \(-0.708104\pi\)
−0.608189 + 0.793792i \(0.708104\pi\)
\(128\) 13.2381 1.17009
\(129\) −18.8938 −1.66350
\(130\) −8.14430 −0.714303
\(131\) 15.4415 1.34913 0.674563 0.738217i \(-0.264332\pi\)
0.674563 + 0.738217i \(0.264332\pi\)
\(132\) −3.09737 −0.269592
\(133\) 5.95311 0.516200
\(134\) −15.6862 −1.35508
\(135\) −2.22313 −0.191336
\(136\) 20.1454 1.72745
\(137\) 0.634397 0.0542002 0.0271001 0.999633i \(-0.491373\pi\)
0.0271001 + 0.999633i \(0.491373\pi\)
\(138\) −13.3008 −1.13224
\(139\) 8.90062 0.754941 0.377470 0.926022i \(-0.376794\pi\)
0.377470 + 0.926022i \(0.376794\pi\)
\(140\) −0.355493 −0.0300446
\(141\) −5.38787 −0.453741
\(142\) 24.9165 2.09095
\(143\) −16.2099 −1.35554
\(144\) −16.7250 −1.39375
\(145\) −3.50825 −0.291344
\(146\) −23.6152 −1.95441
\(147\) 16.0127 1.32071
\(148\) −1.54289 −0.126825
\(149\) 0.864000 0.0707816 0.0353908 0.999374i \(-0.488732\pi\)
0.0353908 + 0.999374i \(0.488732\pi\)
\(150\) 13.5612 1.10727
\(151\) 9.82722 0.799728 0.399864 0.916575i \(-0.369057\pi\)
0.399864 + 0.916575i \(0.369057\pi\)
\(152\) 16.9584 1.37551
\(153\) −29.0108 −2.34538
\(154\) −5.17208 −0.416778
\(155\) −2.14699 −0.172451
\(156\) 3.51712 0.281595
\(157\) −11.4355 −0.912656 −0.456328 0.889812i \(-0.650836\pi\)
−0.456328 + 0.889812i \(0.650836\pi\)
\(158\) 7.84621 0.624211
\(159\) −8.44150 −0.669454
\(160\) −2.21608 −0.175196
\(161\) −3.03838 −0.239458
\(162\) −9.82894 −0.772234
\(163\) −19.1215 −1.49771 −0.748854 0.662735i \(-0.769396\pi\)
−0.748854 + 0.662735i \(0.769396\pi\)
\(164\) 1.85888 0.145154
\(165\) −12.1868 −0.948739
\(166\) 9.98297 0.774828
\(167\) 13.2573 1.02588 0.512942 0.858423i \(-0.328556\pi\)
0.512942 + 0.858423i \(0.328556\pi\)
\(168\) −5.95872 −0.459725
\(169\) 5.40662 0.415893
\(170\) −14.9276 −1.14489
\(171\) −24.4213 −1.86754
\(172\) 2.31549 0.176554
\(173\) −1.24666 −0.0947815 −0.0473907 0.998876i \(-0.515091\pi\)
−0.0473907 + 0.998876i \(0.515091\pi\)
\(174\) 11.0747 0.839570
\(175\) 3.09787 0.234177
\(176\) −17.1287 −1.29112
\(177\) 16.0852 1.20904
\(178\) −7.00240 −0.524852
\(179\) 0.595954 0.0445437 0.0222718 0.999752i \(-0.492910\pi\)
0.0222718 + 0.999752i \(0.492910\pi\)
\(180\) 1.45833 0.108697
\(181\) −9.48635 −0.705115 −0.352557 0.935790i \(-0.614688\pi\)
−0.352557 + 0.935790i \(0.614688\pi\)
\(182\) 5.87298 0.435335
\(183\) −32.3862 −2.39406
\(184\) −8.65531 −0.638078
\(185\) −6.07058 −0.446318
\(186\) 6.77753 0.496953
\(187\) −29.7109 −2.17268
\(188\) 0.660299 0.0481573
\(189\) 1.60313 0.116611
\(190\) −12.5660 −0.911637
\(191\) 7.23592 0.523573 0.261786 0.965126i \(-0.415688\pi\)
0.261786 + 0.965126i \(0.415688\pi\)
\(192\) −16.4547 −1.18752
\(193\) 4.36945 0.314520 0.157260 0.987557i \(-0.449734\pi\)
0.157260 + 0.987557i \(0.449734\pi\)
\(194\) 13.9453 1.00122
\(195\) 13.8383 0.990981
\(196\) −1.96241 −0.140172
\(197\) −19.5262 −1.39118 −0.695592 0.718437i \(-0.744858\pi\)
−0.695592 + 0.718437i \(0.744858\pi\)
\(198\) 21.2173 1.50785
\(199\) 0.0647319 0.00458872 0.00229436 0.999997i \(-0.499270\pi\)
0.00229436 + 0.999997i \(0.499270\pi\)
\(200\) 8.82479 0.624007
\(201\) 26.6529 1.87995
\(202\) −16.8738 −1.18723
\(203\) 2.52985 0.177561
\(204\) 6.44648 0.451344
\(205\) 7.31388 0.510824
\(206\) −6.68141 −0.465516
\(207\) 12.4643 0.866325
\(208\) 19.4499 1.34861
\(209\) −25.0106 −1.73002
\(210\) 4.41537 0.304690
\(211\) 9.65449 0.664642 0.332321 0.943166i \(-0.392168\pi\)
0.332321 + 0.943166i \(0.392168\pi\)
\(212\) 1.03453 0.0710518
\(213\) −42.3366 −2.90086
\(214\) −29.0150 −1.98343
\(215\) 9.11040 0.621324
\(216\) 4.56678 0.310730
\(217\) 1.54823 0.105101
\(218\) 6.91526 0.468361
\(219\) 40.1256 2.71143
\(220\) 1.49352 0.100693
\(221\) 33.7372 2.26941
\(222\) 19.1633 1.28616
\(223\) 12.7892 0.856429 0.428215 0.903677i \(-0.359143\pi\)
0.428215 + 0.903677i \(0.359143\pi\)
\(224\) 1.59805 0.106774
\(225\) −12.7083 −0.847221
\(226\) 17.7887 1.18328
\(227\) 4.94823 0.328426 0.164213 0.986425i \(-0.447492\pi\)
0.164213 + 0.986425i \(0.447492\pi\)
\(228\) 5.42665 0.359389
\(229\) −26.7697 −1.76899 −0.884496 0.466548i \(-0.845497\pi\)
−0.884496 + 0.466548i \(0.845497\pi\)
\(230\) 6.41352 0.422895
\(231\) 8.78808 0.578213
\(232\) 7.20670 0.473143
\(233\) −22.2664 −1.45872 −0.729361 0.684129i \(-0.760182\pi\)
−0.729361 + 0.684129i \(0.760182\pi\)
\(234\) −24.0926 −1.57498
\(235\) 2.59798 0.169474
\(236\) −1.97129 −0.128320
\(237\) −13.3318 −0.865993
\(238\) 10.7645 0.697760
\(239\) −18.3982 −1.19008 −0.595041 0.803695i \(-0.702864\pi\)
−0.595041 + 0.803695i \(0.702864\pi\)
\(240\) 14.6226 0.943887
\(241\) 21.7977 1.40411 0.702056 0.712122i \(-0.252266\pi\)
0.702056 + 0.712122i \(0.252266\pi\)
\(242\) 4.98560 0.320486
\(243\) 22.0486 1.41442
\(244\) 3.96903 0.254091
\(245\) −7.72119 −0.493289
\(246\) −23.0881 −1.47205
\(247\) 28.4000 1.80705
\(248\) 4.41038 0.280060
\(249\) −16.9624 −1.07495
\(250\) −16.0307 −1.01387
\(251\) −22.0114 −1.38935 −0.694674 0.719325i \(-0.744451\pi\)
−0.694674 + 0.719325i \(0.744451\pi\)
\(252\) −1.05162 −0.0662461
\(253\) 12.7651 0.802533
\(254\) −20.8656 −1.30922
\(255\) 25.3640 1.58836
\(256\) 7.42619 0.464137
\(257\) 9.18964 0.573234 0.286617 0.958045i \(-0.407469\pi\)
0.286617 + 0.958045i \(0.407469\pi\)
\(258\) −28.7593 −1.79048
\(259\) 4.37759 0.272010
\(260\) −1.69592 −0.105177
\(261\) −10.3781 −0.642391
\(262\) 23.5043 1.45210
\(263\) −15.6117 −0.962656 −0.481328 0.876540i \(-0.659845\pi\)
−0.481328 + 0.876540i \(0.659845\pi\)
\(264\) 25.0342 1.54075
\(265\) 4.07041 0.250043
\(266\) 9.06157 0.555600
\(267\) 11.8980 0.728148
\(268\) −3.26639 −0.199527
\(269\) −17.8631 −1.08913 −0.544566 0.838718i \(-0.683306\pi\)
−0.544566 + 0.838718i \(0.683306\pi\)
\(270\) −3.38395 −0.205941
\(271\) −16.5337 −1.00435 −0.502174 0.864767i \(-0.667466\pi\)
−0.502174 + 0.864767i \(0.667466\pi\)
\(272\) 35.6494 2.16156
\(273\) −9.97901 −0.603957
\(274\) 0.965653 0.0583372
\(275\) −13.0150 −0.784835
\(276\) −2.76968 −0.166715
\(277\) 28.3672 1.70442 0.852210 0.523199i \(-0.175262\pi\)
0.852210 + 0.523199i \(0.175262\pi\)
\(278\) 13.5482 0.812564
\(279\) −6.35126 −0.380240
\(280\) 2.87324 0.171709
\(281\) 1.04933 0.0625977 0.0312988 0.999510i \(-0.490036\pi\)
0.0312988 + 0.999510i \(0.490036\pi\)
\(282\) −8.20120 −0.488374
\(283\) −13.8367 −0.822505 −0.411253 0.911521i \(-0.634909\pi\)
−0.411253 + 0.911521i \(0.634909\pi\)
\(284\) 5.18847 0.307879
\(285\) 21.3514 1.26475
\(286\) −24.6740 −1.45901
\(287\) −5.27415 −0.311323
\(288\) −6.55562 −0.386294
\(289\) 44.8365 2.63744
\(290\) −5.34011 −0.313582
\(291\) −23.6950 −1.38903
\(292\) −4.91750 −0.287775
\(293\) 8.25156 0.482061 0.241031 0.970517i \(-0.422515\pi\)
0.241031 + 0.970517i \(0.422515\pi\)
\(294\) 24.3739 1.42152
\(295\) −7.75615 −0.451581
\(296\) 12.4703 0.724819
\(297\) −6.73520 −0.390816
\(298\) 1.31514 0.0761842
\(299\) −14.4949 −0.838264
\(300\) 2.82391 0.163039
\(301\) −6.56965 −0.378669
\(302\) 14.9586 0.860770
\(303\) 28.6709 1.64710
\(304\) 30.0097 1.72117
\(305\) 15.6163 0.894189
\(306\) −44.1590 −2.52440
\(307\) −5.46378 −0.311835 −0.155917 0.987770i \(-0.549833\pi\)
−0.155917 + 0.987770i \(0.549833\pi\)
\(308\) −1.07700 −0.0613680
\(309\) 11.3526 0.645829
\(310\) −3.26806 −0.185614
\(311\) −18.4424 −1.04577 −0.522887 0.852402i \(-0.675145\pi\)
−0.522887 + 0.852402i \(0.675145\pi\)
\(312\) −28.4268 −1.60935
\(313\) −21.9260 −1.23933 −0.619664 0.784867i \(-0.712731\pi\)
−0.619664 + 0.784867i \(0.712731\pi\)
\(314\) −17.4067 −0.982317
\(315\) −4.13767 −0.233131
\(316\) 1.63385 0.0919112
\(317\) −7.73837 −0.434630 −0.217315 0.976102i \(-0.569730\pi\)
−0.217315 + 0.976102i \(0.569730\pi\)
\(318\) −12.8493 −0.720553
\(319\) −10.6286 −0.595088
\(320\) 7.93430 0.443541
\(321\) 49.3005 2.75169
\(322\) −4.62489 −0.257735
\(323\) 52.0540 2.89636
\(324\) −2.04672 −0.113707
\(325\) 14.7788 0.819779
\(326\) −29.1059 −1.61203
\(327\) −11.7500 −0.649775
\(328\) −15.0243 −0.829577
\(329\) −1.87345 −0.103286
\(330\) −18.5502 −1.02115
\(331\) −21.2914 −1.17028 −0.585140 0.810932i \(-0.698960\pi\)
−0.585140 + 0.810932i \(0.698960\pi\)
\(332\) 2.07879 0.114089
\(333\) −17.9581 −0.984096
\(334\) 20.1798 1.10419
\(335\) −12.8518 −0.702169
\(336\) −10.5446 −0.575256
\(337\) 21.3815 1.16472 0.582362 0.812930i \(-0.302129\pi\)
0.582362 + 0.812930i \(0.302129\pi\)
\(338\) 8.22972 0.447638
\(339\) −30.2254 −1.64162
\(340\) −3.10843 −0.168578
\(341\) −6.50455 −0.352241
\(342\) −37.1730 −2.01009
\(343\) 11.8631 0.640546
\(344\) −18.7147 −1.00903
\(345\) −10.8975 −0.586699
\(346\) −1.89761 −0.102016
\(347\) −7.25286 −0.389354 −0.194677 0.980867i \(-0.562366\pi\)
−0.194677 + 0.980867i \(0.562366\pi\)
\(348\) 2.30613 0.123621
\(349\) 24.7806 1.32647 0.663236 0.748410i \(-0.269182\pi\)
0.663236 + 0.748410i \(0.269182\pi\)
\(350\) 4.71545 0.252051
\(351\) 7.64793 0.408217
\(352\) −6.71384 −0.357849
\(353\) −24.3581 −1.29645 −0.648227 0.761447i \(-0.724489\pi\)
−0.648227 + 0.761447i \(0.724489\pi\)
\(354\) 24.4843 1.30132
\(355\) 20.4143 1.08348
\(356\) −1.45814 −0.0772811
\(357\) −18.2904 −0.968030
\(358\) 0.907136 0.0479436
\(359\) 24.9267 1.31558 0.657790 0.753201i \(-0.271491\pi\)
0.657790 + 0.753201i \(0.271491\pi\)
\(360\) −11.7868 −0.621220
\(361\) 24.8191 1.30627
\(362\) −14.4397 −0.758935
\(363\) −8.47122 −0.444624
\(364\) 1.22296 0.0641003
\(365\) −19.3482 −1.01273
\(366\) −49.2970 −2.57679
\(367\) −2.52376 −0.131739 −0.0658695 0.997828i \(-0.520982\pi\)
−0.0658695 + 0.997828i \(0.520982\pi\)
\(368\) −15.3165 −0.798428
\(369\) 21.6360 1.12633
\(370\) −9.24038 −0.480384
\(371\) −2.93524 −0.152390
\(372\) 1.41131 0.0731732
\(373\) 27.2959 1.41333 0.706664 0.707549i \(-0.250199\pi\)
0.706664 + 0.707549i \(0.250199\pi\)
\(374\) −45.2247 −2.33851
\(375\) 27.2383 1.40658
\(376\) −5.33681 −0.275225
\(377\) 12.0690 0.621584
\(378\) 2.44022 0.125511
\(379\) −8.84527 −0.454351 −0.227175 0.973854i \(-0.572949\pi\)
−0.227175 + 0.973854i \(0.572949\pi\)
\(380\) −2.61668 −0.134233
\(381\) 35.4535 1.81634
\(382\) 11.0142 0.563536
\(383\) −9.56433 −0.488715 −0.244357 0.969685i \(-0.578577\pi\)
−0.244357 + 0.969685i \(0.578577\pi\)
\(384\) −34.2383 −1.74722
\(385\) −4.23753 −0.215964
\(386\) 6.65099 0.338527
\(387\) 26.9505 1.36997
\(388\) 2.90389 0.147423
\(389\) −0.0942924 −0.00478081 −0.00239041 0.999997i \(-0.500761\pi\)
−0.00239041 + 0.999997i \(0.500761\pi\)
\(390\) 21.0641 1.06662
\(391\) −26.5676 −1.34358
\(392\) 15.8610 0.801100
\(393\) −39.9371 −2.01456
\(394\) −29.7220 −1.49737
\(395\) 6.42847 0.323451
\(396\) 4.41816 0.222021
\(397\) −29.4428 −1.47769 −0.738847 0.673873i \(-0.764629\pi\)
−0.738847 + 0.673873i \(0.764629\pi\)
\(398\) 0.0985322 0.00493897
\(399\) −15.3969 −0.770807
\(400\) 15.6164 0.780821
\(401\) −28.1453 −1.40551 −0.702756 0.711431i \(-0.748047\pi\)
−0.702756 + 0.711431i \(0.748047\pi\)
\(402\) 40.5700 2.02345
\(403\) 7.38602 0.367924
\(404\) −3.51370 −0.174813
\(405\) −8.05293 −0.400153
\(406\) 3.85084 0.191114
\(407\) −18.3915 −0.911631
\(408\) −52.1031 −2.57949
\(409\) 10.4165 0.515062 0.257531 0.966270i \(-0.417091\pi\)
0.257531 + 0.966270i \(0.417091\pi\)
\(410\) 11.1329 0.549814
\(411\) −1.64078 −0.0809336
\(412\) −1.39130 −0.0685443
\(413\) 5.59308 0.275218
\(414\) 18.9726 0.932450
\(415\) 8.17913 0.401498
\(416\) 7.62367 0.373781
\(417\) −23.0202 −1.12730
\(418\) −38.0702 −1.86207
\(419\) −10.1329 −0.495026 −0.247513 0.968885i \(-0.579613\pi\)
−0.247513 + 0.968885i \(0.579613\pi\)
\(420\) 0.919431 0.0448637
\(421\) −34.9879 −1.70521 −0.852603 0.522559i \(-0.824977\pi\)
−0.852603 + 0.522559i \(0.824977\pi\)
\(422\) 14.6957 0.715373
\(423\) 7.68539 0.373676
\(424\) −8.36150 −0.406070
\(425\) 27.0878 1.31395
\(426\) −64.4430 −3.12227
\(427\) −11.2612 −0.544967
\(428\) −6.04192 −0.292047
\(429\) 41.9246 2.02414
\(430\) 13.8675 0.668749
\(431\) 5.20902 0.250910 0.125455 0.992099i \(-0.459961\pi\)
0.125455 + 0.992099i \(0.459961\pi\)
\(432\) 8.08141 0.388817
\(433\) 15.2360 0.732196 0.366098 0.930576i \(-0.380693\pi\)
0.366098 + 0.930576i \(0.380693\pi\)
\(434\) 2.35665 0.113123
\(435\) 9.07358 0.435045
\(436\) 1.43999 0.0689632
\(437\) −22.3646 −1.06984
\(438\) 61.0774 2.91839
\(439\) 1.92960 0.0920947 0.0460473 0.998939i \(-0.485337\pi\)
0.0460473 + 0.998939i \(0.485337\pi\)
\(440\) −12.0713 −0.575476
\(441\) −22.8409 −1.08766
\(442\) 51.3534 2.44263
\(443\) 12.2961 0.584204 0.292102 0.956387i \(-0.405645\pi\)
0.292102 + 0.956387i \(0.405645\pi\)
\(444\) 3.99046 0.189379
\(445\) −5.73712 −0.271966
\(446\) 19.4672 0.921799
\(447\) −2.23461 −0.105693
\(448\) −5.72155 −0.270318
\(449\) 26.8719 1.26816 0.634082 0.773266i \(-0.281378\pi\)
0.634082 + 0.773266i \(0.281378\pi\)
\(450\) −19.3441 −0.911888
\(451\) 22.1582 1.04339
\(452\) 3.70421 0.174231
\(453\) −25.4167 −1.19418
\(454\) 7.53199 0.353494
\(455\) 4.81179 0.225580
\(456\) −43.8604 −2.05395
\(457\) −0.906919 −0.0424239 −0.0212119 0.999775i \(-0.506752\pi\)
−0.0212119 + 0.999775i \(0.506752\pi\)
\(458\) −40.7477 −1.90402
\(459\) 14.0178 0.654295
\(460\) 1.33551 0.0622687
\(461\) 4.46280 0.207853 0.103927 0.994585i \(-0.466859\pi\)
0.103927 + 0.994585i \(0.466859\pi\)
\(462\) 13.3768 0.622347
\(463\) 23.4974 1.09202 0.546009 0.837779i \(-0.316146\pi\)
0.546009 + 0.837779i \(0.316146\pi\)
\(464\) 12.7530 0.592045
\(465\) 5.55289 0.257509
\(466\) −33.8930 −1.57006
\(467\) 8.31369 0.384712 0.192356 0.981325i \(-0.438387\pi\)
0.192356 + 0.981325i \(0.438387\pi\)
\(468\) −5.01690 −0.231906
\(469\) 9.26764 0.427940
\(470\) 3.95454 0.182409
\(471\) 29.5764 1.36281
\(472\) 15.9328 0.733366
\(473\) 27.6009 1.26909
\(474\) −20.2931 −0.932093
\(475\) 22.8025 1.04625
\(476\) 2.24154 0.102741
\(477\) 12.0411 0.551326
\(478\) −28.0050 −1.28092
\(479\) 21.3313 0.974651 0.487325 0.873220i \(-0.337973\pi\)
0.487325 + 0.873220i \(0.337973\pi\)
\(480\) 5.73156 0.261609
\(481\) 20.8838 0.952220
\(482\) 33.1795 1.51129
\(483\) 7.85832 0.357566
\(484\) 1.03817 0.0471896
\(485\) 11.4255 0.518806
\(486\) 33.5614 1.52238
\(487\) 15.0513 0.682038 0.341019 0.940056i \(-0.389228\pi\)
0.341019 + 0.940056i \(0.389228\pi\)
\(488\) −32.0793 −1.45216
\(489\) 49.4549 2.23643
\(490\) −11.7529 −0.530941
\(491\) −43.1675 −1.94812 −0.974060 0.226289i \(-0.927341\pi\)
−0.974060 + 0.226289i \(0.927341\pi\)
\(492\) −4.80774 −0.216750
\(493\) 22.1211 0.996282
\(494\) 43.2293 1.94498
\(495\) 17.3835 0.781330
\(496\) 7.80465 0.350439
\(497\) −14.7211 −0.660331
\(498\) −25.8195 −1.15700
\(499\) 16.8824 0.755759 0.377880 0.925855i \(-0.376653\pi\)
0.377880 + 0.925855i \(0.376653\pi\)
\(500\) −3.33813 −0.149286
\(501\) −34.2882 −1.53188
\(502\) −33.5048 −1.49539
\(503\) −13.4026 −0.597592 −0.298796 0.954317i \(-0.596585\pi\)
−0.298796 + 0.954317i \(0.596585\pi\)
\(504\) 8.49966 0.378605
\(505\) −13.8248 −0.615197
\(506\) 19.4304 0.863789
\(507\) −13.9834 −0.621026
\(508\) −4.34492 −0.192775
\(509\) −17.5986 −0.780045 −0.390022 0.920805i \(-0.627533\pi\)
−0.390022 + 0.920805i \(0.627533\pi\)
\(510\) 38.6080 1.70959
\(511\) 13.9523 0.617212
\(512\) −15.1723 −0.670527
\(513\) 11.8002 0.520991
\(514\) 13.9881 0.616988
\(515\) −5.47413 −0.241219
\(516\) −5.98867 −0.263637
\(517\) 7.87086 0.346160
\(518\) 6.66338 0.292772
\(519\) 3.22430 0.141531
\(520\) 13.7071 0.601098
\(521\) −9.08215 −0.397896 −0.198948 0.980010i \(-0.563753\pi\)
−0.198948 + 0.980010i \(0.563753\pi\)
\(522\) −15.7972 −0.691424
\(523\) 12.7052 0.555561 0.277780 0.960645i \(-0.410401\pi\)
0.277780 + 0.960645i \(0.410401\pi\)
\(524\) 4.89440 0.213813
\(525\) −8.01220 −0.349681
\(526\) −23.7634 −1.03613
\(527\) 13.5377 0.589713
\(528\) 44.3008 1.92795
\(529\) −11.5854 −0.503715
\(530\) 6.19581 0.269129
\(531\) −22.9443 −0.995700
\(532\) 1.88693 0.0818087
\(533\) −25.1610 −1.08984
\(534\) 18.1107 0.783726
\(535\) −23.7723 −1.02776
\(536\) 26.4004 1.14032
\(537\) −1.54135 −0.0665141
\(538\) −27.1905 −1.17226
\(539\) −23.3922 −1.00757
\(540\) −0.704654 −0.0303235
\(541\) 37.0432 1.59261 0.796306 0.604894i \(-0.206785\pi\)
0.796306 + 0.604894i \(0.206785\pi\)
\(542\) −25.1668 −1.08101
\(543\) 24.5351 1.05290
\(544\) 13.9733 0.599102
\(545\) 5.66573 0.242693
\(546\) −15.1896 −0.650056
\(547\) −1.00000 −0.0427569
\(548\) 0.201082 0.00858980
\(549\) 46.1965 1.97162
\(550\) −19.8109 −0.844740
\(551\) 18.6215 0.793303
\(552\) 22.3857 0.952799
\(553\) −4.63567 −0.197129
\(554\) 43.1794 1.83452
\(555\) 15.7007 0.666456
\(556\) 2.82119 0.119645
\(557\) −46.3948 −1.96581 −0.982905 0.184111i \(-0.941059\pi\)
−0.982905 + 0.184111i \(0.941059\pi\)
\(558\) −9.66763 −0.409263
\(559\) −31.3413 −1.32560
\(560\) 5.08451 0.214860
\(561\) 76.8430 3.24431
\(562\) 1.59724 0.0673757
\(563\) −25.5383 −1.07631 −0.538155 0.842846i \(-0.680878\pi\)
−0.538155 + 0.842846i \(0.680878\pi\)
\(564\) −1.70777 −0.0719100
\(565\) 14.5744 0.613149
\(566\) −21.0616 −0.885286
\(567\) 5.80710 0.243875
\(568\) −41.9354 −1.75957
\(569\) 34.7766 1.45791 0.728956 0.684560i \(-0.240006\pi\)
0.728956 + 0.684560i \(0.240006\pi\)
\(570\) 32.5003 1.36129
\(571\) −18.0804 −0.756643 −0.378322 0.925674i \(-0.623499\pi\)
−0.378322 + 0.925674i \(0.623499\pi\)
\(572\) −5.13798 −0.214830
\(573\) −18.7147 −0.781816
\(574\) −8.02809 −0.335086
\(575\) −11.6381 −0.485341
\(576\) 23.4714 0.977973
\(577\) 17.7760 0.740025 0.370012 0.929027i \(-0.379353\pi\)
0.370012 + 0.929027i \(0.379353\pi\)
\(578\) 68.2483 2.83876
\(579\) −11.3010 −0.469652
\(580\) −1.11199 −0.0461730
\(581\) −5.89810 −0.244694
\(582\) −36.0676 −1.49505
\(583\) 12.3317 0.510729
\(584\) 39.7453 1.64467
\(585\) −19.7393 −0.816118
\(586\) 12.5602 0.518856
\(587\) −12.4600 −0.514279 −0.257139 0.966374i \(-0.582780\pi\)
−0.257139 + 0.966374i \(0.582780\pi\)
\(588\) 5.07548 0.209309
\(589\) 11.3961 0.469567
\(590\) −11.8061 −0.486049
\(591\) 50.5017 2.07736
\(592\) 22.0675 0.906968
\(593\) −5.62287 −0.230904 −0.115452 0.993313i \(-0.536832\pi\)
−0.115452 + 0.993313i \(0.536832\pi\)
\(594\) −10.2520 −0.420646
\(595\) 8.81946 0.361563
\(596\) 0.273858 0.0112177
\(597\) −0.167420 −0.00685203
\(598\) −22.0636 −0.902248
\(599\) 19.3513 0.790673 0.395337 0.918536i \(-0.370628\pi\)
0.395337 + 0.918536i \(0.370628\pi\)
\(600\) −22.8240 −0.931787
\(601\) −25.3645 −1.03464 −0.517321 0.855792i \(-0.673071\pi\)
−0.517321 + 0.855792i \(0.673071\pi\)
\(602\) −10.0001 −0.407572
\(603\) −38.0184 −1.54823
\(604\) 3.11489 0.126743
\(605\) 4.08474 0.166068
\(606\) 43.6416 1.77282
\(607\) 13.9505 0.566235 0.283117 0.959085i \(-0.408631\pi\)
0.283117 + 0.959085i \(0.408631\pi\)
\(608\) 11.7628 0.477043
\(609\) −6.54310 −0.265140
\(610\) 23.7705 0.962441
\(611\) −8.93750 −0.361573
\(612\) −9.19541 −0.371702
\(613\) 25.5058 1.03017 0.515084 0.857139i \(-0.327761\pi\)
0.515084 + 0.857139i \(0.327761\pi\)
\(614\) −8.31674 −0.335636
\(615\) −18.9163 −0.762779
\(616\) 8.70479 0.350726
\(617\) 7.43879 0.299474 0.149737 0.988726i \(-0.452157\pi\)
0.149737 + 0.988726i \(0.452157\pi\)
\(618\) 17.2805 0.695124
\(619\) 10.5397 0.423626 0.211813 0.977310i \(-0.432063\pi\)
0.211813 + 0.977310i \(0.432063\pi\)
\(620\) −0.680522 −0.0273304
\(621\) −6.02264 −0.241680
\(622\) −28.0723 −1.12560
\(623\) 4.13713 0.165751
\(624\) −50.3043 −2.01379
\(625\) 4.08945 0.163578
\(626\) −33.3748 −1.33392
\(627\) 64.6864 2.58333
\(628\) −3.62467 −0.144640
\(629\) 38.2777 1.52623
\(630\) −6.29819 −0.250926
\(631\) 23.4904 0.935139 0.467570 0.883956i \(-0.345130\pi\)
0.467570 + 0.883956i \(0.345130\pi\)
\(632\) −13.2055 −0.525285
\(633\) −24.9699 −0.992466
\(634\) −11.7790 −0.467805
\(635\) −17.0953 −0.678408
\(636\) −2.67566 −0.106097
\(637\) 26.5622 1.05243
\(638\) −16.1784 −0.640510
\(639\) 60.3899 2.38899
\(640\) 16.5094 0.652592
\(641\) −12.1894 −0.481454 −0.240727 0.970593i \(-0.577386\pi\)
−0.240727 + 0.970593i \(0.577386\pi\)
\(642\) 75.0432 2.96172
\(643\) −45.5594 −1.79669 −0.898343 0.439295i \(-0.855228\pi\)
−0.898343 + 0.439295i \(0.855228\pi\)
\(644\) −0.963060 −0.0379499
\(645\) −23.5627 −0.927782
\(646\) 79.2344 3.11744
\(647\) −13.8400 −0.544107 −0.272054 0.962282i \(-0.587703\pi\)
−0.272054 + 0.962282i \(0.587703\pi\)
\(648\) 16.5424 0.649849
\(649\) −23.4981 −0.922380
\(650\) 22.4956 0.882351
\(651\) −4.00428 −0.156940
\(652\) −6.06084 −0.237361
\(653\) −37.0134 −1.44845 −0.724224 0.689565i \(-0.757802\pi\)
−0.724224 + 0.689565i \(0.757802\pi\)
\(654\) −17.8853 −0.699372
\(655\) 19.2573 0.752445
\(656\) −26.5871 −1.03805
\(657\) −57.2360 −2.23299
\(658\) −2.85168 −0.111170
\(659\) 4.58672 0.178673 0.0893366 0.996001i \(-0.471525\pi\)
0.0893366 + 0.996001i \(0.471525\pi\)
\(660\) −3.86279 −0.150359
\(661\) 33.9504 1.32052 0.660259 0.751038i \(-0.270446\pi\)
0.660259 + 0.751038i \(0.270446\pi\)
\(662\) −32.4088 −1.25961
\(663\) −87.2565 −3.38876
\(664\) −16.8017 −0.652032
\(665\) 7.42422 0.287899
\(666\) −27.3350 −1.05921
\(667\) −9.50414 −0.368002
\(668\) 4.20212 0.162585
\(669\) −33.0775 −1.27885
\(670\) −19.5625 −0.755764
\(671\) 47.3114 1.82644
\(672\) −4.13312 −0.159438
\(673\) −19.4772 −0.750792 −0.375396 0.926865i \(-0.622493\pi\)
−0.375396 + 0.926865i \(0.622493\pi\)
\(674\) 32.5460 1.25363
\(675\) 6.14057 0.236351
\(676\) 1.71371 0.0659119
\(677\) 4.07259 0.156523 0.0782613 0.996933i \(-0.475063\pi\)
0.0782613 + 0.996933i \(0.475063\pi\)
\(678\) −46.0078 −1.76692
\(679\) −8.23913 −0.316189
\(680\) 25.1236 0.963448
\(681\) −12.7979 −0.490416
\(682\) −9.90095 −0.379127
\(683\) −0.965668 −0.0369503 −0.0184751 0.999829i \(-0.505881\pi\)
−0.0184751 + 0.999829i \(0.505881\pi\)
\(684\) −7.74069 −0.295973
\(685\) 0.791168 0.0302290
\(686\) 18.0575 0.689438
\(687\) 69.2360 2.64152
\(688\) −33.1177 −1.26260
\(689\) −14.0029 −0.533468
\(690\) −16.5876 −0.631481
\(691\) −9.03055 −0.343538 −0.171769 0.985137i \(-0.554948\pi\)
−0.171769 + 0.985137i \(0.554948\pi\)
\(692\) −0.395147 −0.0150212
\(693\) −12.5355 −0.476185
\(694\) −11.0400 −0.419073
\(695\) 11.1001 0.421051
\(696\) −18.6391 −0.706512
\(697\) −46.1172 −1.74681
\(698\) 37.7199 1.42772
\(699\) 57.5889 2.17821
\(700\) 0.981918 0.0371130
\(701\) 9.28360 0.350637 0.175318 0.984512i \(-0.443905\pi\)
0.175318 + 0.984512i \(0.443905\pi\)
\(702\) 11.6414 0.439375
\(703\) 32.2221 1.21528
\(704\) 24.0378 0.905959
\(705\) −6.71931 −0.253064
\(706\) −37.0770 −1.39541
\(707\) 9.96930 0.374934
\(708\) 5.09846 0.191612
\(709\) −42.7085 −1.60395 −0.801976 0.597357i \(-0.796218\pi\)
−0.801976 + 0.597357i \(0.796218\pi\)
\(710\) 31.0738 1.16618
\(711\) 19.0168 0.713185
\(712\) 11.7853 0.441672
\(713\) −5.81639 −0.217825
\(714\) −27.8409 −1.04192
\(715\) −20.2156 −0.756022
\(716\) 0.188897 0.00705940
\(717\) 47.5844 1.77707
\(718\) 37.9424 1.41600
\(719\) 3.48301 0.129895 0.0649473 0.997889i \(-0.479312\pi\)
0.0649473 + 0.997889i \(0.479312\pi\)
\(720\) −20.8581 −0.777334
\(721\) 3.94748 0.147012
\(722\) 37.7786 1.40597
\(723\) −56.3766 −2.09667
\(724\) −3.00684 −0.111748
\(725\) 9.69024 0.359887
\(726\) −12.8945 −0.478561
\(727\) −43.5536 −1.61531 −0.807657 0.589652i \(-0.799265\pi\)
−0.807657 + 0.589652i \(0.799265\pi\)
\(728\) −9.88444 −0.366342
\(729\) −37.6537 −1.39458
\(730\) −29.4510 −1.09003
\(731\) −57.4451 −2.12468
\(732\) −10.2653 −0.379417
\(733\) 35.9769 1.32884 0.664418 0.747361i \(-0.268679\pi\)
0.664418 + 0.747361i \(0.268679\pi\)
\(734\) −3.84155 −0.141794
\(735\) 19.9697 0.736595
\(736\) −6.00353 −0.221293
\(737\) −38.9359 −1.43422
\(738\) 32.9334 1.21230
\(739\) −9.01253 −0.331531 −0.165766 0.986165i \(-0.553010\pi\)
−0.165766 + 0.986165i \(0.553010\pi\)
\(740\) −1.92416 −0.0707336
\(741\) −73.4525 −2.69835
\(742\) −4.46790 −0.164022
\(743\) −27.7846 −1.01932 −0.509658 0.860377i \(-0.670228\pi\)
−0.509658 + 0.860377i \(0.670228\pi\)
\(744\) −11.4068 −0.418194
\(745\) 1.07751 0.0394769
\(746\) 41.5487 1.52120
\(747\) 24.1956 0.885271
\(748\) −9.41733 −0.344332
\(749\) 17.1425 0.626375
\(750\) 41.4610 1.51394
\(751\) −35.3238 −1.28898 −0.644492 0.764611i \(-0.722931\pi\)
−0.644492 + 0.764611i \(0.722931\pi\)
\(752\) −9.44407 −0.344390
\(753\) 56.9293 2.07462
\(754\) 18.3709 0.669028
\(755\) 12.2557 0.446030
\(756\) 0.508137 0.0184808
\(757\) −7.21058 −0.262073 −0.131036 0.991378i \(-0.541830\pi\)
−0.131036 + 0.991378i \(0.541830\pi\)
\(758\) −13.4639 −0.489031
\(759\) −33.0150 −1.19837
\(760\) 21.1491 0.767158
\(761\) 15.5783 0.564712 0.282356 0.959310i \(-0.408884\pi\)
0.282356 + 0.959310i \(0.408884\pi\)
\(762\) 53.9658 1.95497
\(763\) −4.08565 −0.147910
\(764\) 2.29353 0.0829772
\(765\) −36.1798 −1.30808
\(766\) −14.5584 −0.526017
\(767\) 26.6825 0.963448
\(768\) −19.2068 −0.693065
\(769\) 24.1433 0.870629 0.435314 0.900279i \(-0.356637\pi\)
0.435314 + 0.900279i \(0.356637\pi\)
\(770\) −6.45019 −0.232449
\(771\) −23.7677 −0.855972
\(772\) 1.38496 0.0498460
\(773\) −23.9888 −0.862818 −0.431409 0.902156i \(-0.641983\pi\)
−0.431409 + 0.902156i \(0.641983\pi\)
\(774\) 41.0229 1.47454
\(775\) 5.93028 0.213022
\(776\) −23.4705 −0.842541
\(777\) −11.3220 −0.406175
\(778\) −0.143528 −0.00514572
\(779\) −38.8215 −1.39092
\(780\) 4.38626 0.157053
\(781\) 61.8474 2.21307
\(782\) −40.4401 −1.44613
\(783\) 5.01465 0.179209
\(784\) 28.0677 1.00242
\(785\) −14.2615 −0.509013
\(786\) −60.7906 −2.16833
\(787\) −5.35961 −0.191050 −0.0955248 0.995427i \(-0.530453\pi\)
−0.0955248 + 0.995427i \(0.530453\pi\)
\(788\) −6.18913 −0.220479
\(789\) 40.3773 1.43747
\(790\) 9.78515 0.348140
\(791\) −10.5098 −0.373686
\(792\) −35.7094 −1.26888
\(793\) −53.7229 −1.90776
\(794\) −44.8167 −1.59048
\(795\) −10.5275 −0.373373
\(796\) 0.0205178 0.000727233 0
\(797\) −19.3882 −0.686766 −0.343383 0.939195i \(-0.611573\pi\)
−0.343383 + 0.939195i \(0.611573\pi\)
\(798\) −23.4364 −0.829641
\(799\) −16.3814 −0.579533
\(800\) 6.12109 0.216413
\(801\) −16.9716 −0.599663
\(802\) −42.8417 −1.51279
\(803\) −58.6173 −2.06856
\(804\) 8.44806 0.297940
\(805\) −3.78921 −0.133552
\(806\) 11.2427 0.396007
\(807\) 46.2003 1.62633
\(808\) 28.3992 0.999079
\(809\) −35.6076 −1.25190 −0.625948 0.779865i \(-0.715288\pi\)
−0.625948 + 0.779865i \(0.715288\pi\)
\(810\) −12.2578 −0.430696
\(811\) 7.02922 0.246829 0.123415 0.992355i \(-0.460615\pi\)
0.123415 + 0.992355i \(0.460615\pi\)
\(812\) 0.801876 0.0281403
\(813\) 42.7619 1.49973
\(814\) −27.9947 −0.981214
\(815\) −23.8467 −0.835314
\(816\) −92.2021 −3.22772
\(817\) −48.3573 −1.69181
\(818\) 15.8555 0.554376
\(819\) 14.2343 0.497386
\(820\) 2.31825 0.0809567
\(821\) −11.9108 −0.415691 −0.207845 0.978162i \(-0.566645\pi\)
−0.207845 + 0.978162i \(0.566645\pi\)
\(822\) −2.49752 −0.0871111
\(823\) 38.1506 1.32985 0.664924 0.746911i \(-0.268464\pi\)
0.664924 + 0.746911i \(0.268464\pi\)
\(824\) 11.2450 0.391740
\(825\) 33.6615 1.17194
\(826\) 8.51355 0.296224
\(827\) 22.1837 0.771404 0.385702 0.922623i \(-0.373959\pi\)
0.385702 + 0.922623i \(0.373959\pi\)
\(828\) 3.95074 0.137298
\(829\) −26.7091 −0.927646 −0.463823 0.885928i \(-0.653523\pi\)
−0.463823 + 0.885928i \(0.653523\pi\)
\(830\) 12.4499 0.432143
\(831\) −73.3677 −2.54510
\(832\) −27.2953 −0.946296
\(833\) 48.6855 1.68685
\(834\) −35.0403 −1.21335
\(835\) 16.5335 0.572164
\(836\) −7.92751 −0.274179
\(837\) 3.06889 0.106076
\(838\) −15.4239 −0.532810
\(839\) −24.3713 −0.841392 −0.420696 0.907202i \(-0.638214\pi\)
−0.420696 + 0.907202i \(0.638214\pi\)
\(840\) −7.43122 −0.256402
\(841\) −21.0865 −0.727122
\(842\) −53.2571 −1.83536
\(843\) −2.71394 −0.0934730
\(844\) 3.06014 0.105334
\(845\) 6.74268 0.231955
\(846\) 11.6984 0.402198
\(847\) −2.94557 −0.101211
\(848\) −14.7966 −0.508117
\(849\) 35.7866 1.22819
\(850\) 41.2319 1.41424
\(851\) −16.4457 −0.563751
\(852\) −13.4192 −0.459736
\(853\) −21.5357 −0.737369 −0.368685 0.929555i \(-0.620192\pi\)
−0.368685 + 0.929555i \(0.620192\pi\)
\(854\) −17.1413 −0.586564
\(855\) −30.4562 −1.04158
\(856\) 48.8333 1.66909
\(857\) 10.1092 0.345325 0.172663 0.984981i \(-0.444763\pi\)
0.172663 + 0.984981i \(0.444763\pi\)
\(858\) 63.8158 2.17864
\(859\) 29.3539 1.00154 0.500771 0.865580i \(-0.333050\pi\)
0.500771 + 0.865580i \(0.333050\pi\)
\(860\) 2.88768 0.0984691
\(861\) 13.6408 0.464878
\(862\) 7.92895 0.270061
\(863\) 9.84744 0.335211 0.167605 0.985854i \(-0.446397\pi\)
0.167605 + 0.985854i \(0.446397\pi\)
\(864\) 3.16763 0.107765
\(865\) −1.55473 −0.0528622
\(866\) 23.1916 0.788083
\(867\) −115.963 −3.93832
\(868\) 0.490735 0.0166566
\(869\) 19.4757 0.660669
\(870\) 13.8114 0.468251
\(871\) 44.2124 1.49808
\(872\) −11.6386 −0.394134
\(873\) 33.7991 1.14393
\(874\) −34.0425 −1.15150
\(875\) 9.47117 0.320184
\(876\) 12.7184 0.429715
\(877\) −32.9822 −1.11373 −0.556864 0.830603i \(-0.687996\pi\)
−0.556864 + 0.830603i \(0.687996\pi\)
\(878\) 2.93715 0.0991241
\(879\) −21.3415 −0.719830
\(880\) −21.3614 −0.720094
\(881\) 34.3375 1.15686 0.578429 0.815733i \(-0.303666\pi\)
0.578429 + 0.815733i \(0.303666\pi\)
\(882\) −34.7675 −1.17068
\(883\) 12.5688 0.422974 0.211487 0.977381i \(-0.432169\pi\)
0.211487 + 0.977381i \(0.432169\pi\)
\(884\) 10.6935 0.359662
\(885\) 20.0602 0.674315
\(886\) 18.7166 0.628795
\(887\) 34.7329 1.16622 0.583109 0.812394i \(-0.301836\pi\)
0.583109 + 0.812394i \(0.301836\pi\)
\(888\) −32.2525 −1.08232
\(889\) 12.3277 0.413458
\(890\) −8.73281 −0.292724
\(891\) −24.3972 −0.817337
\(892\) 4.05374 0.135729
\(893\) −13.7899 −0.461461
\(894\) −3.40143 −0.113761
\(895\) 0.743224 0.0248432
\(896\) −11.9052 −0.397725
\(897\) 37.4891 1.25172
\(898\) 40.9033 1.36496
\(899\) 4.84292 0.161520
\(900\) −4.02809 −0.134270
\(901\) −25.6657 −0.855050
\(902\) 33.7282 1.12303
\(903\) 16.9915 0.565441
\(904\) −29.9389 −0.995754
\(905\) −11.8306 −0.393262
\(906\) −38.6882 −1.28533
\(907\) 18.5744 0.616753 0.308376 0.951264i \(-0.400214\pi\)
0.308376 + 0.951264i \(0.400214\pi\)
\(908\) 1.56842 0.0520498
\(909\) −40.8968 −1.35646
\(910\) 7.32430 0.242798
\(911\) −4.83712 −0.160261 −0.0801304 0.996784i \(-0.525534\pi\)
−0.0801304 + 0.996784i \(0.525534\pi\)
\(912\) −77.6158 −2.57012
\(913\) 24.7795 0.820083
\(914\) −1.38047 −0.0456620
\(915\) −40.3894 −1.33523
\(916\) −8.48506 −0.280354
\(917\) −13.8867 −0.458580
\(918\) 21.3373 0.704236
\(919\) 57.3488 1.89176 0.945881 0.324513i \(-0.105200\pi\)
0.945881 + 0.324513i \(0.105200\pi\)
\(920\) −10.7942 −0.355874
\(921\) 14.1313 0.465642
\(922\) 6.79309 0.223718
\(923\) −70.2287 −2.31161
\(924\) 2.78551 0.0916367
\(925\) 16.7677 0.551319
\(926\) 35.7668 1.17537
\(927\) −16.1937 −0.531869
\(928\) 4.99874 0.164092
\(929\) 46.6546 1.53069 0.765344 0.643622i \(-0.222569\pi\)
0.765344 + 0.643622i \(0.222569\pi\)
\(930\) 8.45238 0.277164
\(931\) 40.9835 1.34318
\(932\) −7.05768 −0.231182
\(933\) 47.6987 1.56159
\(934\) 12.6547 0.414076
\(935\) −37.0530 −1.21176
\(936\) 40.5487 1.32537
\(937\) 20.5835 0.672433 0.336217 0.941785i \(-0.390853\pi\)
0.336217 + 0.941785i \(0.390853\pi\)
\(938\) 14.1068 0.460604
\(939\) 56.7083 1.85061
\(940\) 0.823470 0.0268586
\(941\) 26.4195 0.861251 0.430625 0.902531i \(-0.358293\pi\)
0.430625 + 0.902531i \(0.358293\pi\)
\(942\) 45.0199 1.46683
\(943\) 19.8139 0.645230
\(944\) 28.1948 0.917663
\(945\) 1.99929 0.0650370
\(946\) 42.0130 1.36596
\(947\) 30.9279 1.00502 0.502510 0.864571i \(-0.332410\pi\)
0.502510 + 0.864571i \(0.332410\pi\)
\(948\) −4.22572 −0.137245
\(949\) 66.5610 2.16066
\(950\) 34.7090 1.12611
\(951\) 20.0142 0.649004
\(952\) −18.1171 −0.587177
\(953\) 31.9144 1.03381 0.516905 0.856043i \(-0.327084\pi\)
0.516905 + 0.856043i \(0.327084\pi\)
\(954\) 18.3285 0.593408
\(955\) 9.02404 0.292011
\(956\) −5.83160 −0.188607
\(957\) 27.4894 0.888606
\(958\) 32.4696 1.04904
\(959\) −0.570523 −0.0184232
\(960\) −20.5209 −0.662310
\(961\) −28.0362 −0.904394
\(962\) 31.7885 1.02490
\(963\) −70.3234 −2.26614
\(964\) 6.90911 0.222527
\(965\) 5.44922 0.175416
\(966\) 11.9616 0.384859
\(967\) 25.3550 0.815363 0.407682 0.913124i \(-0.366337\pi\)
0.407682 + 0.913124i \(0.366337\pi\)
\(968\) −8.39094 −0.269695
\(969\) −134.630 −4.32495
\(970\) 17.3915 0.558406
\(971\) 4.38779 0.140811 0.0704054 0.997518i \(-0.477571\pi\)
0.0704054 + 0.997518i \(0.477571\pi\)
\(972\) 6.98863 0.224160
\(973\) −8.00447 −0.256611
\(974\) 22.9104 0.734097
\(975\) −38.2232 −1.22412
\(976\) −56.7678 −1.81709
\(977\) 3.45588 0.110563 0.0552817 0.998471i \(-0.482394\pi\)
0.0552817 + 0.998471i \(0.482394\pi\)
\(978\) 75.2782 2.40713
\(979\) −17.3812 −0.555506
\(980\) −2.44735 −0.0781777
\(981\) 16.7604 0.535120
\(982\) −65.7077 −2.09682
\(983\) 56.4424 1.80023 0.900117 0.435648i \(-0.143481\pi\)
0.900117 + 0.435648i \(0.143481\pi\)
\(984\) 38.8581 1.23875
\(985\) −24.3515 −0.775902
\(986\) 33.6717 1.07233
\(987\) 4.84540 0.154231
\(988\) 9.00182 0.286386
\(989\) 24.6808 0.784805
\(990\) 26.4604 0.840968
\(991\) −55.5706 −1.76526 −0.882629 0.470069i \(-0.844229\pi\)
−0.882629 + 0.470069i \(0.844229\pi\)
\(992\) 3.05915 0.0971281
\(993\) 55.0671 1.74750
\(994\) −22.4078 −0.710733
\(995\) 0.0807282 0.00255926
\(996\) −5.37650 −0.170361
\(997\) −20.1408 −0.637866 −0.318933 0.947777i \(-0.603324\pi\)
−0.318933 + 0.947777i \(0.603324\pi\)
\(998\) 25.6977 0.813445
\(999\) 8.67721 0.274535
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.1.15 18
3.2 odd 2 4923.2.a.l.1.4 18
4.3 odd 2 8752.2.a.s.1.14 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.15 18 1.1 even 1 trivial
4923.2.a.l.1.4 18 3.2 odd 2
8752.2.a.s.1.14 18 4.3 odd 2