Properties

Label 547.2.a.b.1.5
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 1.5
Root \(1.74487\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +O(q^{10})\) \(q-1.74487 q^{2} -1.27304 q^{3} +1.04455 q^{4} -3.61409 q^{5} +2.22129 q^{6} +4.28084 q^{7} +1.66712 q^{8} -1.37936 q^{9} +6.30610 q^{10} -1.82207 q^{11} -1.32976 q^{12} +1.54763 q^{13} -7.46949 q^{14} +4.60089 q^{15} -4.99801 q^{16} +5.89804 q^{17} +2.40680 q^{18} +5.77207 q^{19} -3.77512 q^{20} -5.44969 q^{21} +3.17927 q^{22} -7.36494 q^{23} -2.12232 q^{24} +8.06166 q^{25} -2.70041 q^{26} +5.57511 q^{27} +4.47157 q^{28} -4.20778 q^{29} -8.02794 q^{30} -8.68625 q^{31} +5.38662 q^{32} +2.31958 q^{33} -10.2913 q^{34} -15.4714 q^{35} -1.44082 q^{36} -9.26711 q^{37} -10.0715 q^{38} -1.97020 q^{39} -6.02514 q^{40} +8.29157 q^{41} +9.50898 q^{42} -2.50047 q^{43} -1.90326 q^{44} +4.98514 q^{45} +12.8508 q^{46} -6.07577 q^{47} +6.36269 q^{48} +11.3256 q^{49} -14.0665 q^{50} -7.50845 q^{51} +1.61659 q^{52} -4.35174 q^{53} -9.72782 q^{54} +6.58514 q^{55} +7.13669 q^{56} -7.34809 q^{57} +7.34201 q^{58} -13.6982 q^{59} +4.80588 q^{60} -9.67314 q^{61} +15.1563 q^{62} -5.90483 q^{63} +0.597111 q^{64} -5.59329 q^{65} -4.04735 q^{66} -3.67729 q^{67} +6.16082 q^{68} +9.37589 q^{69} +26.9954 q^{70} +6.92649 q^{71} -2.29957 q^{72} +2.36768 q^{73} +16.1699 q^{74} -10.2628 q^{75} +6.02925 q^{76} -7.80001 q^{77} +3.43774 q^{78} +6.27816 q^{79} +18.0633 q^{80} -2.95927 q^{81} -14.4677 q^{82} -2.57942 q^{83} -5.69250 q^{84} -21.3161 q^{85} +4.36299 q^{86} +5.35668 q^{87} -3.03762 q^{88} +8.45581 q^{89} -8.69840 q^{90} +6.62517 q^{91} -7.69309 q^{92} +11.0580 q^{93} +10.6014 q^{94} -20.8608 q^{95} -6.85739 q^{96} -11.0935 q^{97} -19.7617 q^{98} +2.51330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74487 −1.23381 −0.616903 0.787039i \(-0.711613\pi\)
−0.616903 + 0.787039i \(0.711613\pi\)
\(3\) −1.27304 −0.734991 −0.367496 0.930025i \(-0.619785\pi\)
−0.367496 + 0.930025i \(0.619785\pi\)
\(4\) 1.04455 0.522277
\(5\) −3.61409 −1.61627 −0.808135 0.588997i \(-0.799523\pi\)
−0.808135 + 0.588997i \(0.799523\pi\)
\(6\) 2.22129 0.906837
\(7\) 4.28084 1.61801 0.809003 0.587804i \(-0.200008\pi\)
0.809003 + 0.587804i \(0.200008\pi\)
\(8\) 1.66712 0.589417
\(9\) −1.37936 −0.459788
\(10\) 6.30610 1.99416
\(11\) −1.82207 −0.549376 −0.274688 0.961533i \(-0.588575\pi\)
−0.274688 + 0.961533i \(0.588575\pi\)
\(12\) −1.32976 −0.383869
\(13\) 1.54763 0.429236 0.214618 0.976698i \(-0.431149\pi\)
0.214618 + 0.976698i \(0.431149\pi\)
\(14\) −7.46949 −1.99631
\(15\) 4.60089 1.18795
\(16\) −4.99801 −1.24950
\(17\) 5.89804 1.43048 0.715242 0.698877i \(-0.246316\pi\)
0.715242 + 0.698877i \(0.246316\pi\)
\(18\) 2.40680 0.567289
\(19\) 5.77207 1.32420 0.662102 0.749414i \(-0.269664\pi\)
0.662102 + 0.749414i \(0.269664\pi\)
\(20\) −3.77512 −0.844142
\(21\) −5.44969 −1.18922
\(22\) 3.17927 0.677824
\(23\) −7.36494 −1.53570 −0.767848 0.640632i \(-0.778673\pi\)
−0.767848 + 0.640632i \(0.778673\pi\)
\(24\) −2.12232 −0.433217
\(25\) 8.06166 1.61233
\(26\) −2.70041 −0.529594
\(27\) 5.57511 1.07293
\(28\) 4.47157 0.845048
\(29\) −4.20778 −0.781365 −0.390683 0.920525i \(-0.627761\pi\)
−0.390683 + 0.920525i \(0.627761\pi\)
\(30\) −8.02794 −1.46569
\(31\) −8.68625 −1.56010 −0.780049 0.625719i \(-0.784806\pi\)
−0.780049 + 0.625719i \(0.784806\pi\)
\(32\) 5.38662 0.952228
\(33\) 2.31958 0.403787
\(34\) −10.2913 −1.76494
\(35\) −15.4714 −2.61514
\(36\) −1.44082 −0.240137
\(37\) −9.26711 −1.52350 −0.761752 0.647869i \(-0.775660\pi\)
−0.761752 + 0.647869i \(0.775660\pi\)
\(38\) −10.0715 −1.63381
\(39\) −1.97020 −0.315485
\(40\) −6.02514 −0.952658
\(41\) 8.29157 1.29493 0.647463 0.762097i \(-0.275830\pi\)
0.647463 + 0.762097i \(0.275830\pi\)
\(42\) 9.50898 1.46727
\(43\) −2.50047 −0.381319 −0.190659 0.981656i \(-0.561063\pi\)
−0.190659 + 0.981656i \(0.561063\pi\)
\(44\) −1.90326 −0.286927
\(45\) 4.98514 0.743141
\(46\) 12.8508 1.89475
\(47\) −6.07577 −0.886242 −0.443121 0.896462i \(-0.646129\pi\)
−0.443121 + 0.896462i \(0.646129\pi\)
\(48\) 6.36269 0.918375
\(49\) 11.3256 1.61794
\(50\) −14.0665 −1.98930
\(51\) −7.50845 −1.05139
\(52\) 1.61659 0.224180
\(53\) −4.35174 −0.597757 −0.298879 0.954291i \(-0.596613\pi\)
−0.298879 + 0.954291i \(0.596613\pi\)
\(54\) −9.72782 −1.32379
\(55\) 6.58514 0.887941
\(56\) 7.13669 0.953680
\(57\) −7.34809 −0.973279
\(58\) 7.34201 0.964053
\(59\) −13.6982 −1.78336 −0.891680 0.452667i \(-0.850473\pi\)
−0.891680 + 0.452667i \(0.850473\pi\)
\(60\) 4.80588 0.620437
\(61\) −9.67314 −1.23852 −0.619259 0.785186i \(-0.712567\pi\)
−0.619259 + 0.785186i \(0.712567\pi\)
\(62\) 15.1563 1.92486
\(63\) −5.90483 −0.743939
\(64\) 0.597111 0.0746389
\(65\) −5.59329 −0.693762
\(66\) −4.04735 −0.498194
\(67\) −3.67729 −0.449253 −0.224626 0.974445i \(-0.572116\pi\)
−0.224626 + 0.974445i \(0.572116\pi\)
\(68\) 6.16082 0.747110
\(69\) 9.37589 1.12872
\(70\) 26.9954 3.22657
\(71\) 6.92649 0.822023 0.411012 0.911630i \(-0.365176\pi\)
0.411012 + 0.911630i \(0.365176\pi\)
\(72\) −2.29957 −0.271007
\(73\) 2.36768 0.277116 0.138558 0.990354i \(-0.455753\pi\)
0.138558 + 0.990354i \(0.455753\pi\)
\(74\) 16.1699 1.87971
\(75\) −10.2628 −1.18505
\(76\) 6.02925 0.691602
\(77\) −7.80001 −0.888894
\(78\) 3.43774 0.389247
\(79\) 6.27816 0.706348 0.353174 0.935558i \(-0.385102\pi\)
0.353174 + 0.935558i \(0.385102\pi\)
\(80\) 18.0633 2.01954
\(81\) −2.95927 −0.328808
\(82\) −14.4677 −1.59769
\(83\) −2.57942 −0.283128 −0.141564 0.989929i \(-0.545213\pi\)
−0.141564 + 0.989929i \(0.545213\pi\)
\(84\) −5.69250 −0.621103
\(85\) −21.3161 −2.31205
\(86\) 4.36299 0.470473
\(87\) 5.35668 0.574297
\(88\) −3.03762 −0.323812
\(89\) 8.45581 0.896314 0.448157 0.893955i \(-0.352081\pi\)
0.448157 + 0.893955i \(0.352081\pi\)
\(90\) −8.69840 −0.916892
\(91\) 6.62517 0.694507
\(92\) −7.69309 −0.802060
\(93\) 11.0580 1.14666
\(94\) 10.6014 1.09345
\(95\) −20.8608 −2.14027
\(96\) −6.85739 −0.699880
\(97\) −11.0935 −1.12637 −0.563187 0.826329i \(-0.690425\pi\)
−0.563187 + 0.826329i \(0.690425\pi\)
\(98\) −19.7617 −1.99623
\(99\) 2.51330 0.252596
\(100\) 8.42084 0.842084
\(101\) −12.1254 −1.20652 −0.603259 0.797545i \(-0.706131\pi\)
−0.603259 + 0.797545i \(0.706131\pi\)
\(102\) 13.1012 1.29722
\(103\) −10.8356 −1.06767 −0.533833 0.845590i \(-0.679249\pi\)
−0.533833 + 0.845590i \(0.679249\pi\)
\(104\) 2.58010 0.252999
\(105\) 19.6957 1.92210
\(106\) 7.59320 0.737517
\(107\) 15.7365 1.52130 0.760652 0.649160i \(-0.224879\pi\)
0.760652 + 0.649160i \(0.224879\pi\)
\(108\) 5.82351 0.560368
\(109\) −7.74111 −0.741464 −0.370732 0.928740i \(-0.620893\pi\)
−0.370732 + 0.928740i \(0.620893\pi\)
\(110\) −11.4902 −1.09555
\(111\) 11.7974 1.11976
\(112\) −21.3957 −2.02170
\(113\) −0.0433232 −0.00407550 −0.00203775 0.999998i \(-0.500649\pi\)
−0.00203775 + 0.999998i \(0.500649\pi\)
\(114\) 12.8214 1.20084
\(115\) 26.6176 2.48210
\(116\) −4.39526 −0.408089
\(117\) −2.13475 −0.197358
\(118\) 23.9016 2.20032
\(119\) 25.2486 2.31453
\(120\) 7.67026 0.700195
\(121\) −7.68004 −0.698186
\(122\) 16.8783 1.52809
\(123\) −10.5555 −0.951760
\(124\) −9.07327 −0.814803
\(125\) −11.0651 −0.989694
\(126\) 10.3031 0.917877
\(127\) 0.557420 0.0494630 0.0247315 0.999694i \(-0.492127\pi\)
0.0247315 + 0.999694i \(0.492127\pi\)
\(128\) −11.8151 −1.04432
\(129\) 3.18321 0.280266
\(130\) 9.75954 0.855968
\(131\) −4.31192 −0.376735 −0.188367 0.982099i \(-0.560320\pi\)
−0.188367 + 0.982099i \(0.560320\pi\)
\(132\) 2.42293 0.210889
\(133\) 24.7093 2.14257
\(134\) 6.41638 0.554291
\(135\) −20.1490 −1.73415
\(136\) 9.83276 0.843152
\(137\) −9.86688 −0.842985 −0.421492 0.906832i \(-0.638494\pi\)
−0.421492 + 0.906832i \(0.638494\pi\)
\(138\) −16.3597 −1.39263
\(139\) 11.3673 0.964163 0.482082 0.876126i \(-0.339881\pi\)
0.482082 + 0.876126i \(0.339881\pi\)
\(140\) −16.1607 −1.36583
\(141\) 7.73472 0.651381
\(142\) −12.0858 −1.01422
\(143\) −2.81990 −0.235812
\(144\) 6.89408 0.574506
\(145\) 15.2073 1.26290
\(146\) −4.13128 −0.341907
\(147\) −14.4180 −1.18917
\(148\) −9.68001 −0.795692
\(149\) 14.2550 1.16781 0.583907 0.811821i \(-0.301523\pi\)
0.583907 + 0.811821i \(0.301523\pi\)
\(150\) 17.9073 1.46212
\(151\) 17.5151 1.42536 0.712680 0.701489i \(-0.247481\pi\)
0.712680 + 0.701489i \(0.247481\pi\)
\(152\) 9.62276 0.780509
\(153\) −8.13554 −0.657719
\(154\) 13.6100 1.09672
\(155\) 31.3929 2.52154
\(156\) −2.05798 −0.164771
\(157\) −0.960703 −0.0766725 −0.0383362 0.999265i \(-0.512206\pi\)
−0.0383362 + 0.999265i \(0.512206\pi\)
\(158\) −10.9545 −0.871497
\(159\) 5.53995 0.439346
\(160\) −19.4677 −1.53906
\(161\) −31.5282 −2.48477
\(162\) 5.16353 0.405685
\(163\) −8.10300 −0.634676 −0.317338 0.948313i \(-0.602789\pi\)
−0.317338 + 0.948313i \(0.602789\pi\)
\(164\) 8.66100 0.676311
\(165\) −8.38317 −0.652629
\(166\) 4.50074 0.349325
\(167\) −12.7559 −0.987083 −0.493541 0.869722i \(-0.664298\pi\)
−0.493541 + 0.869722i \(0.664298\pi\)
\(168\) −9.08531 −0.700947
\(169\) −10.6048 −0.815756
\(170\) 37.1936 2.85262
\(171\) −7.96178 −0.608853
\(172\) −2.61188 −0.199154
\(173\) −6.36016 −0.483554 −0.241777 0.970332i \(-0.577730\pi\)
−0.241777 + 0.970332i \(0.577730\pi\)
\(174\) −9.34669 −0.708571
\(175\) 34.5107 2.60876
\(176\) 9.10675 0.686447
\(177\) 17.4384 1.31075
\(178\) −14.7542 −1.10588
\(179\) 15.6282 1.16811 0.584055 0.811714i \(-0.301465\pi\)
0.584055 + 0.811714i \(0.301465\pi\)
\(180\) 5.20726 0.388126
\(181\) −12.0567 −0.896164 −0.448082 0.893992i \(-0.647893\pi\)
−0.448082 + 0.893992i \(0.647893\pi\)
\(182\) −11.5600 −0.856887
\(183\) 12.3143 0.910301
\(184\) −12.2783 −0.905166
\(185\) 33.4922 2.46240
\(186\) −19.2947 −1.41475
\(187\) −10.7467 −0.785874
\(188\) −6.34648 −0.462864
\(189\) 23.8662 1.73601
\(190\) 36.3993 2.64068
\(191\) −15.1622 −1.09710 −0.548550 0.836118i \(-0.684820\pi\)
−0.548550 + 0.836118i \(0.684820\pi\)
\(192\) −0.760148 −0.0548590
\(193\) −6.95522 −0.500648 −0.250324 0.968162i \(-0.580537\pi\)
−0.250324 + 0.968162i \(0.580537\pi\)
\(194\) 19.3567 1.38973
\(195\) 7.12049 0.509909
\(196\) 11.8302 0.845015
\(197\) −14.5377 −1.03577 −0.517884 0.855451i \(-0.673280\pi\)
−0.517884 + 0.855451i \(0.673280\pi\)
\(198\) −4.38537 −0.311655
\(199\) −5.94365 −0.421334 −0.210667 0.977558i \(-0.567564\pi\)
−0.210667 + 0.977558i \(0.567564\pi\)
\(200\) 13.4398 0.950336
\(201\) 4.68135 0.330197
\(202\) 21.1571 1.48861
\(203\) −18.0128 −1.26425
\(204\) −7.84299 −0.549119
\(205\) −29.9665 −2.09295
\(206\) 18.9067 1.31729
\(207\) 10.1589 0.706094
\(208\) −7.73509 −0.536332
\(209\) −10.5171 −0.727486
\(210\) −34.3663 −2.37150
\(211\) −27.1667 −1.87024 −0.935118 0.354337i \(-0.884707\pi\)
−0.935118 + 0.354337i \(0.884707\pi\)
\(212\) −4.54563 −0.312195
\(213\) −8.81772 −0.604180
\(214\) −27.4581 −1.87699
\(215\) 9.03694 0.616314
\(216\) 9.29440 0.632404
\(217\) −37.1845 −2.52425
\(218\) 13.5072 0.914823
\(219\) −3.01415 −0.203678
\(220\) 6.87854 0.463751
\(221\) 9.12800 0.614016
\(222\) −20.5849 −1.38157
\(223\) 3.41548 0.228717 0.114359 0.993440i \(-0.463519\pi\)
0.114359 + 0.993440i \(0.463519\pi\)
\(224\) 23.0592 1.54071
\(225\) −11.1200 −0.741330
\(226\) 0.0755931 0.00502838
\(227\) −22.1539 −1.47041 −0.735204 0.677846i \(-0.762914\pi\)
−0.735204 + 0.677846i \(0.762914\pi\)
\(228\) −7.67549 −0.508321
\(229\) 1.65658 0.109470 0.0547350 0.998501i \(-0.482569\pi\)
0.0547350 + 0.998501i \(0.482569\pi\)
\(230\) −46.4441 −3.06243
\(231\) 9.92975 0.653329
\(232\) −7.01489 −0.460550
\(233\) 9.45846 0.619644 0.309822 0.950795i \(-0.399731\pi\)
0.309822 + 0.950795i \(0.399731\pi\)
\(234\) 3.72485 0.243501
\(235\) 21.9584 1.43241
\(236\) −14.3086 −0.931408
\(237\) −7.99236 −0.519160
\(238\) −44.0554 −2.85568
\(239\) −20.2498 −1.30985 −0.654926 0.755693i \(-0.727300\pi\)
−0.654926 + 0.755693i \(0.727300\pi\)
\(240\) −22.9953 −1.48434
\(241\) 12.5021 0.805328 0.402664 0.915348i \(-0.368084\pi\)
0.402664 + 0.915348i \(0.368084\pi\)
\(242\) 13.4006 0.861426
\(243\) −12.9581 −0.831260
\(244\) −10.1041 −0.646850
\(245\) −40.9318 −2.61504
\(246\) 18.4180 1.17429
\(247\) 8.93305 0.568397
\(248\) −14.4811 −0.919548
\(249\) 3.28371 0.208097
\(250\) 19.3071 1.22109
\(251\) 15.4087 0.972590 0.486295 0.873795i \(-0.338348\pi\)
0.486295 + 0.873795i \(0.338348\pi\)
\(252\) −6.16792 −0.388543
\(253\) 13.4195 0.843675
\(254\) −0.972622 −0.0610277
\(255\) 27.1362 1.69934
\(256\) 19.4216 1.21385
\(257\) −5.96426 −0.372040 −0.186020 0.982546i \(-0.559559\pi\)
−0.186020 + 0.982546i \(0.559559\pi\)
\(258\) −5.55427 −0.345794
\(259\) −39.6710 −2.46504
\(260\) −5.84250 −0.362336
\(261\) 5.80406 0.359262
\(262\) 7.52373 0.464817
\(263\) 22.1233 1.36418 0.682089 0.731269i \(-0.261072\pi\)
0.682089 + 0.731269i \(0.261072\pi\)
\(264\) 3.86702 0.237999
\(265\) 15.7276 0.966138
\(266\) −43.1144 −2.64352
\(267\) −10.7646 −0.658783
\(268\) −3.84113 −0.234635
\(269\) −8.96149 −0.546391 −0.273196 0.961958i \(-0.588081\pi\)
−0.273196 + 0.961958i \(0.588081\pi\)
\(270\) 35.1572 2.13960
\(271\) 2.25602 0.137043 0.0685217 0.997650i \(-0.478172\pi\)
0.0685217 + 0.997650i \(0.478172\pi\)
\(272\) −29.4785 −1.78740
\(273\) −8.43413 −0.510457
\(274\) 17.2164 1.04008
\(275\) −14.6889 −0.885777
\(276\) 9.79363 0.589507
\(277\) −12.2849 −0.738128 −0.369064 0.929404i \(-0.620322\pi\)
−0.369064 + 0.929404i \(0.620322\pi\)
\(278\) −19.8344 −1.18959
\(279\) 11.9815 0.717313
\(280\) −25.7927 −1.54141
\(281\) −31.3296 −1.86897 −0.934484 0.356005i \(-0.884139\pi\)
−0.934484 + 0.356005i \(0.884139\pi\)
\(282\) −13.4960 −0.803677
\(283\) 26.8312 1.59495 0.797474 0.603353i \(-0.206169\pi\)
0.797474 + 0.603353i \(0.206169\pi\)
\(284\) 7.23510 0.429324
\(285\) 26.5567 1.57308
\(286\) 4.92035 0.290946
\(287\) 35.4949 2.09520
\(288\) −7.43010 −0.437823
\(289\) 17.7869 1.04629
\(290\) −26.5347 −1.55817
\(291\) 14.1225 0.827876
\(292\) 2.47317 0.144731
\(293\) 8.91567 0.520859 0.260430 0.965493i \(-0.416136\pi\)
0.260430 + 0.965493i \(0.416136\pi\)
\(294\) 25.1574 1.46721
\(295\) 49.5067 2.88239
\(296\) −15.4494 −0.897979
\(297\) −10.1583 −0.589443
\(298\) −24.8730 −1.44086
\(299\) −11.3982 −0.659177
\(300\) −10.7201 −0.618925
\(301\) −10.7041 −0.616976
\(302\) −30.5615 −1.75862
\(303\) 15.4361 0.886780
\(304\) −28.8489 −1.65460
\(305\) 34.9596 2.00178
\(306\) 14.1954 0.811498
\(307\) −20.6821 −1.18039 −0.590195 0.807260i \(-0.700949\pi\)
−0.590195 + 0.807260i \(0.700949\pi\)
\(308\) −8.14754 −0.464249
\(309\) 13.7942 0.784725
\(310\) −54.7764 −3.11109
\(311\) 9.54165 0.541057 0.270529 0.962712i \(-0.412802\pi\)
0.270529 + 0.962712i \(0.412802\pi\)
\(312\) −3.28457 −0.185952
\(313\) −19.8618 −1.12265 −0.561327 0.827594i \(-0.689709\pi\)
−0.561327 + 0.827594i \(0.689709\pi\)
\(314\) 1.67630 0.0945989
\(315\) 21.3406 1.20241
\(316\) 6.55788 0.368910
\(317\) −12.6386 −0.709857 −0.354929 0.934893i \(-0.615495\pi\)
−0.354929 + 0.934893i \(0.615495\pi\)
\(318\) −9.66646 −0.542068
\(319\) 7.66689 0.429263
\(320\) −2.15802 −0.120637
\(321\) −20.0332 −1.11815
\(322\) 55.0124 3.06572
\(323\) 34.0439 1.89425
\(324\) −3.09112 −0.171729
\(325\) 12.4765 0.692071
\(326\) 14.1386 0.783067
\(327\) 9.85477 0.544970
\(328\) 13.8231 0.763252
\(329\) −26.0094 −1.43395
\(330\) 14.6275 0.805217
\(331\) 17.8621 0.981790 0.490895 0.871219i \(-0.336670\pi\)
0.490895 + 0.871219i \(0.336670\pi\)
\(332\) −2.69434 −0.147871
\(333\) 12.7827 0.700488
\(334\) 22.2574 1.21787
\(335\) 13.2901 0.726114
\(336\) 27.2376 1.48594
\(337\) 11.1406 0.606865 0.303432 0.952853i \(-0.401867\pi\)
0.303432 + 0.952853i \(0.401867\pi\)
\(338\) 18.5040 1.00648
\(339\) 0.0551522 0.00299546
\(340\) −22.2658 −1.20753
\(341\) 15.8270 0.857080
\(342\) 13.8922 0.751206
\(343\) 18.5172 0.999836
\(344\) −4.16860 −0.224756
\(345\) −33.8853 −1.82432
\(346\) 11.0976 0.596612
\(347\) −0.533400 −0.0286344 −0.0143172 0.999898i \(-0.504557\pi\)
−0.0143172 + 0.999898i \(0.504557\pi\)
\(348\) 5.59535 0.299942
\(349\) 26.6600 1.42708 0.713539 0.700616i \(-0.247091\pi\)
0.713539 + 0.700616i \(0.247091\pi\)
\(350\) −60.2165 −3.21871
\(351\) 8.62823 0.460541
\(352\) −9.81481 −0.523131
\(353\) −2.12890 −0.113310 −0.0566548 0.998394i \(-0.518043\pi\)
−0.0566548 + 0.998394i \(0.518043\pi\)
\(354\) −30.4277 −1.61722
\(355\) −25.0330 −1.32861
\(356\) 8.83255 0.468124
\(357\) −32.1425 −1.70116
\(358\) −27.2692 −1.44122
\(359\) 1.54866 0.0817353 0.0408677 0.999165i \(-0.486988\pi\)
0.0408677 + 0.999165i \(0.486988\pi\)
\(360\) 8.31085 0.438020
\(361\) 14.3168 0.753517
\(362\) 21.0372 1.10569
\(363\) 9.77702 0.513161
\(364\) 6.92036 0.362725
\(365\) −8.55700 −0.447894
\(366\) −21.4868 −1.12313
\(367\) 8.10473 0.423064 0.211532 0.977371i \(-0.432155\pi\)
0.211532 + 0.977371i \(0.432155\pi\)
\(368\) 36.8101 1.91886
\(369\) −11.4371 −0.595391
\(370\) −58.4394 −3.03812
\(371\) −18.6291 −0.967175
\(372\) 11.5507 0.598874
\(373\) 36.4059 1.88503 0.942514 0.334167i \(-0.108455\pi\)
0.942514 + 0.334167i \(0.108455\pi\)
\(374\) 18.7515 0.969616
\(375\) 14.0864 0.727417
\(376\) −10.1291 −0.522366
\(377\) −6.51210 −0.335390
\(378\) −41.6433 −2.14190
\(379\) −1.17841 −0.0605309 −0.0302655 0.999542i \(-0.509635\pi\)
−0.0302655 + 0.999542i \(0.509635\pi\)
\(380\) −21.7902 −1.11782
\(381\) −0.709619 −0.0363549
\(382\) 26.4560 1.35361
\(383\) 3.86230 0.197355 0.0986773 0.995119i \(-0.468539\pi\)
0.0986773 + 0.995119i \(0.468539\pi\)
\(384\) 15.0411 0.767565
\(385\) 28.1900 1.43669
\(386\) 12.1359 0.617702
\(387\) 3.44906 0.175326
\(388\) −11.5878 −0.588280
\(389\) −9.33318 −0.473211 −0.236605 0.971606i \(-0.576035\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(390\) −12.4243 −0.629129
\(391\) −43.4387 −2.19679
\(392\) 18.8812 0.953644
\(393\) 5.48926 0.276897
\(394\) 25.3663 1.27794
\(395\) −22.6898 −1.14165
\(396\) 2.62528 0.131925
\(397\) −29.7948 −1.49536 −0.747680 0.664059i \(-0.768832\pi\)
−0.747680 + 0.664059i \(0.768832\pi\)
\(398\) 10.3709 0.519844
\(399\) −31.4560 −1.57477
\(400\) −40.2923 −2.01461
\(401\) 5.34757 0.267045 0.133522 0.991046i \(-0.457371\pi\)
0.133522 + 0.991046i \(0.457371\pi\)
\(402\) −8.16833 −0.407399
\(403\) −13.4431 −0.669650
\(404\) −12.6656 −0.630137
\(405\) 10.6951 0.531442
\(406\) 31.4300 1.55984
\(407\) 16.8854 0.836977
\(408\) −12.5175 −0.619710
\(409\) −6.05618 −0.299459 −0.149729 0.988727i \(-0.547840\pi\)
−0.149729 + 0.988727i \(0.547840\pi\)
\(410\) 52.2875 2.58230
\(411\) 12.5610 0.619587
\(412\) −11.3184 −0.557617
\(413\) −58.6400 −2.88549
\(414\) −17.7260 −0.871184
\(415\) 9.32226 0.457612
\(416\) 8.33651 0.408731
\(417\) −14.4711 −0.708652
\(418\) 18.3510 0.897577
\(419\) 8.84901 0.432303 0.216151 0.976360i \(-0.430650\pi\)
0.216151 + 0.976360i \(0.430650\pi\)
\(420\) 20.5732 1.00387
\(421\) −18.4589 −0.899631 −0.449816 0.893121i \(-0.648510\pi\)
−0.449816 + 0.893121i \(0.648510\pi\)
\(422\) 47.4023 2.30751
\(423\) 8.38069 0.407483
\(424\) −7.25489 −0.352328
\(425\) 47.5480 2.30642
\(426\) 15.3857 0.745441
\(427\) −41.4092 −2.00393
\(428\) 16.4376 0.794543
\(429\) 3.58986 0.173320
\(430\) −15.7682 −0.760413
\(431\) 17.9207 0.863212 0.431606 0.902062i \(-0.357947\pi\)
0.431606 + 0.902062i \(0.357947\pi\)
\(432\) −27.8645 −1.34063
\(433\) −39.6184 −1.90394 −0.951969 0.306193i \(-0.900945\pi\)
−0.951969 + 0.306193i \(0.900945\pi\)
\(434\) 64.8819 3.11443
\(435\) −19.3595 −0.928219
\(436\) −8.08602 −0.387250
\(437\) −42.5110 −2.03358
\(438\) 5.25929 0.251299
\(439\) 14.0915 0.672553 0.336276 0.941763i \(-0.390832\pi\)
0.336276 + 0.941763i \(0.390832\pi\)
\(440\) 10.9782 0.523367
\(441\) −15.6221 −0.743910
\(442\) −15.9271 −0.757576
\(443\) −24.4089 −1.15970 −0.579850 0.814723i \(-0.696889\pi\)
−0.579850 + 0.814723i \(0.696889\pi\)
\(444\) 12.3231 0.584826
\(445\) −30.5601 −1.44869
\(446\) −5.95955 −0.282193
\(447\) −18.1472 −0.858333
\(448\) 2.55614 0.120766
\(449\) 25.2207 1.19024 0.595120 0.803637i \(-0.297105\pi\)
0.595120 + 0.803637i \(0.297105\pi\)
\(450\) 19.4028 0.914658
\(451\) −15.1079 −0.711401
\(452\) −0.0452534 −0.00212854
\(453\) −22.2975 −1.04763
\(454\) 38.6556 1.81420
\(455\) −23.9440 −1.12251
\(456\) −12.2502 −0.573667
\(457\) 33.5255 1.56826 0.784128 0.620599i \(-0.213111\pi\)
0.784128 + 0.620599i \(0.213111\pi\)
\(458\) −2.89051 −0.135065
\(459\) 32.8822 1.53481
\(460\) 27.8035 1.29635
\(461\) 8.70385 0.405379 0.202689 0.979243i \(-0.435032\pi\)
0.202689 + 0.979243i \(0.435032\pi\)
\(462\) −17.3261 −0.806082
\(463\) 16.2456 0.754997 0.377498 0.926010i \(-0.376784\pi\)
0.377498 + 0.926010i \(0.376784\pi\)
\(464\) 21.0306 0.976319
\(465\) −39.9645 −1.85331
\(466\) −16.5037 −0.764521
\(467\) 13.7642 0.636932 0.318466 0.947934i \(-0.396832\pi\)
0.318466 + 0.947934i \(0.396832\pi\)
\(468\) −2.22986 −0.103075
\(469\) −15.7419 −0.726894
\(470\) −38.3144 −1.76731
\(471\) 1.22302 0.0563536
\(472\) −22.8367 −1.05114
\(473\) 4.55605 0.209487
\(474\) 13.9456 0.640542
\(475\) 46.5325 2.13506
\(476\) 26.3735 1.20883
\(477\) 6.00263 0.274841
\(478\) 35.3332 1.61610
\(479\) 5.69599 0.260256 0.130128 0.991497i \(-0.458461\pi\)
0.130128 + 0.991497i \(0.458461\pi\)
\(480\) 24.7832 1.13119
\(481\) −14.3421 −0.653943
\(482\) −21.8144 −0.993619
\(483\) 40.1367 1.82628
\(484\) −8.02223 −0.364647
\(485\) 40.0930 1.82053
\(486\) 22.6101 1.02561
\(487\) 22.3309 1.01191 0.505954 0.862560i \(-0.331140\pi\)
0.505954 + 0.862560i \(0.331140\pi\)
\(488\) −16.1263 −0.730004
\(489\) 10.3155 0.466481
\(490\) 71.4204 3.22645
\(491\) 27.1853 1.22686 0.613429 0.789750i \(-0.289790\pi\)
0.613429 + 0.789750i \(0.289790\pi\)
\(492\) −11.0258 −0.497082
\(493\) −24.8177 −1.11773
\(494\) −15.5870 −0.701291
\(495\) −9.08330 −0.408264
\(496\) 43.4140 1.94935
\(497\) 29.6512 1.33004
\(498\) −5.72963 −0.256751
\(499\) 19.0533 0.852941 0.426470 0.904502i \(-0.359757\pi\)
0.426470 + 0.904502i \(0.359757\pi\)
\(500\) −11.5581 −0.516895
\(501\) 16.2388 0.725497
\(502\) −26.8861 −1.19999
\(503\) −8.63613 −0.385066 −0.192533 0.981290i \(-0.561670\pi\)
−0.192533 + 0.981290i \(0.561670\pi\)
\(504\) −9.84409 −0.438490
\(505\) 43.8222 1.95006
\(506\) −23.4152 −1.04093
\(507\) 13.5004 0.599574
\(508\) 0.582255 0.0258334
\(509\) 25.5400 1.13204 0.566020 0.824392i \(-0.308483\pi\)
0.566020 + 0.824392i \(0.308483\pi\)
\(510\) −47.3491 −2.09665
\(511\) 10.1356 0.448375
\(512\) −10.2578 −0.453334
\(513\) 32.1800 1.42078
\(514\) 10.4068 0.459025
\(515\) 39.1609 1.72564
\(516\) 3.32504 0.146377
\(517\) 11.0705 0.486880
\(518\) 69.2206 3.04138
\(519\) 8.09676 0.355408
\(520\) −9.32470 −0.408915
\(521\) −39.4866 −1.72994 −0.864970 0.501824i \(-0.832663\pi\)
−0.864970 + 0.501824i \(0.832663\pi\)
\(522\) −10.1273 −0.443260
\(523\) −17.3341 −0.757967 −0.378984 0.925403i \(-0.623726\pi\)
−0.378984 + 0.925403i \(0.623726\pi\)
\(524\) −4.50404 −0.196760
\(525\) −43.9336 −1.91742
\(526\) −38.6021 −1.68313
\(527\) −51.2319 −2.23169
\(528\) −11.5933 −0.504533
\(529\) 31.2424 1.35837
\(530\) −27.4425 −1.19203
\(531\) 18.8948 0.819967
\(532\) 25.8102 1.11902
\(533\) 12.8323 0.555829
\(534\) 18.7828 0.812810
\(535\) −56.8731 −2.45884
\(536\) −6.13050 −0.264797
\(537\) −19.8954 −0.858551
\(538\) 15.6366 0.674141
\(539\) −20.6361 −0.888859
\(540\) −21.0467 −0.905706
\(541\) −26.4300 −1.13632 −0.568158 0.822919i \(-0.692344\pi\)
−0.568158 + 0.822919i \(0.692344\pi\)
\(542\) −3.93645 −0.169085
\(543\) 15.3486 0.658673
\(544\) 31.7705 1.36215
\(545\) 27.9771 1.19841
\(546\) 14.7164 0.629804
\(547\) −1.00000 −0.0427569
\(548\) −10.3065 −0.440272
\(549\) 13.3428 0.569456
\(550\) 25.6302 1.09288
\(551\) −24.2876 −1.03469
\(552\) 15.6308 0.665289
\(553\) 26.8758 1.14288
\(554\) 21.4355 0.910706
\(555\) −42.6370 −1.80984
\(556\) 11.8738 0.503561
\(557\) 1.27168 0.0538829 0.0269414 0.999637i \(-0.491423\pi\)
0.0269414 + 0.999637i \(0.491423\pi\)
\(558\) −20.9061 −0.885026
\(559\) −3.86982 −0.163676
\(560\) 77.3261 3.26762
\(561\) 13.6810 0.577611
\(562\) 54.6660 2.30594
\(563\) −3.96838 −0.167247 −0.0836237 0.996497i \(-0.526649\pi\)
−0.0836237 + 0.996497i \(0.526649\pi\)
\(564\) 8.07933 0.340201
\(565\) 0.156574 0.00658711
\(566\) −46.8168 −1.96786
\(567\) −12.6682 −0.532013
\(568\) 11.5473 0.484515
\(569\) 16.1671 0.677761 0.338881 0.940829i \(-0.389952\pi\)
0.338881 + 0.940829i \(0.389952\pi\)
\(570\) −46.3378 −1.94088
\(571\) 17.9457 0.751005 0.375503 0.926821i \(-0.377470\pi\)
0.375503 + 0.926821i \(0.377470\pi\)
\(572\) −2.94554 −0.123159
\(573\) 19.3022 0.806359
\(574\) −61.9338 −2.58507
\(575\) −59.3737 −2.47605
\(576\) −0.823633 −0.0343180
\(577\) 16.6268 0.692184 0.346092 0.938200i \(-0.387508\pi\)
0.346092 + 0.938200i \(0.387508\pi\)
\(578\) −31.0357 −1.29091
\(579\) 8.85429 0.367972
\(580\) 15.8849 0.659583
\(581\) −11.0421 −0.458103
\(582\) −24.6419 −1.02144
\(583\) 7.92919 0.328394
\(584\) 3.94721 0.163337
\(585\) 7.71517 0.318983
\(586\) −15.5566 −0.642639
\(587\) 33.9183 1.39996 0.699979 0.714163i \(-0.253193\pi\)
0.699979 + 0.714163i \(0.253193\pi\)
\(588\) −15.0604 −0.621079
\(589\) −50.1377 −2.06589
\(590\) −86.3825 −3.55631
\(591\) 18.5071 0.761280
\(592\) 46.3172 1.90362
\(593\) 23.7489 0.975252 0.487626 0.873053i \(-0.337863\pi\)
0.487626 + 0.873053i \(0.337863\pi\)
\(594\) 17.7248 0.727258
\(595\) −91.2506 −3.74091
\(596\) 14.8901 0.609922
\(597\) 7.56651 0.309677
\(598\) 19.8884 0.813296
\(599\) 35.6788 1.45779 0.728897 0.684623i \(-0.240033\pi\)
0.728897 + 0.684623i \(0.240033\pi\)
\(600\) −17.1094 −0.698489
\(601\) −7.46392 −0.304460 −0.152230 0.988345i \(-0.548645\pi\)
−0.152230 + 0.988345i \(0.548645\pi\)
\(602\) 18.6773 0.761229
\(603\) 5.07232 0.206561
\(604\) 18.2955 0.744433
\(605\) 27.7564 1.12846
\(606\) −26.9339 −1.09412
\(607\) −3.18262 −0.129179 −0.0645893 0.997912i \(-0.520574\pi\)
−0.0645893 + 0.997912i \(0.520574\pi\)
\(608\) 31.0919 1.26094
\(609\) 22.9311 0.929216
\(610\) −60.9998 −2.46981
\(611\) −9.40307 −0.380407
\(612\) −8.49801 −0.343512
\(613\) −21.7245 −0.877446 −0.438723 0.898622i \(-0.644569\pi\)
−0.438723 + 0.898622i \(0.644569\pi\)
\(614\) 36.0875 1.45637
\(615\) 38.1486 1.53830
\(616\) −13.0036 −0.523929
\(617\) −6.04399 −0.243322 −0.121661 0.992572i \(-0.538822\pi\)
−0.121661 + 0.992572i \(0.538822\pi\)
\(618\) −24.0690 −0.968198
\(619\) −10.9041 −0.438272 −0.219136 0.975694i \(-0.570324\pi\)
−0.219136 + 0.975694i \(0.570324\pi\)
\(620\) 32.7916 1.31694
\(621\) −41.0604 −1.64770
\(622\) −16.6489 −0.667559
\(623\) 36.1980 1.45024
\(624\) 9.84710 0.394200
\(625\) −0.317943 −0.0127177
\(626\) 34.6561 1.38514
\(627\) 13.3888 0.534696
\(628\) −1.00351 −0.0400443
\(629\) −54.6578 −2.17935
\(630\) −37.2365 −1.48354
\(631\) −6.17161 −0.245688 −0.122844 0.992426i \(-0.539201\pi\)
−0.122844 + 0.992426i \(0.539201\pi\)
\(632\) 10.4665 0.416334
\(633\) 34.5844 1.37461
\(634\) 22.0527 0.875826
\(635\) −2.01457 −0.0799456
\(636\) 5.78678 0.229461
\(637\) 17.5279 0.694480
\(638\) −13.3777 −0.529628
\(639\) −9.55414 −0.377956
\(640\) 42.7009 1.68790
\(641\) −4.63006 −0.182876 −0.0914382 0.995811i \(-0.529146\pi\)
−0.0914382 + 0.995811i \(0.529146\pi\)
\(642\) 34.9553 1.37957
\(643\) −25.9357 −1.02281 −0.511403 0.859341i \(-0.670874\pi\)
−0.511403 + 0.859341i \(0.670874\pi\)
\(644\) −32.9329 −1.29774
\(645\) −11.5044 −0.452986
\(646\) −59.4020 −2.33714
\(647\) −18.9502 −0.745009 −0.372505 0.928030i \(-0.621501\pi\)
−0.372505 + 0.928030i \(0.621501\pi\)
\(648\) −4.93347 −0.193805
\(649\) 24.9592 0.979735
\(650\) −21.7698 −0.853882
\(651\) 47.3374 1.85530
\(652\) −8.46403 −0.331477
\(653\) −21.2753 −0.832568 −0.416284 0.909235i \(-0.636668\pi\)
−0.416284 + 0.909235i \(0.636668\pi\)
\(654\) −17.1952 −0.672387
\(655\) 15.5837 0.608905
\(656\) −41.4414 −1.61802
\(657\) −3.26588 −0.127414
\(658\) 45.3829 1.76921
\(659\) 2.22303 0.0865968 0.0432984 0.999062i \(-0.486213\pi\)
0.0432984 + 0.999062i \(0.486213\pi\)
\(660\) −8.75668 −0.340853
\(661\) −29.9111 −1.16341 −0.581704 0.813401i \(-0.697614\pi\)
−0.581704 + 0.813401i \(0.697614\pi\)
\(662\) −31.1670 −1.21134
\(663\) −11.6203 −0.451296
\(664\) −4.30021 −0.166881
\(665\) −89.3018 −3.46297
\(666\) −22.3041 −0.864267
\(667\) 30.9901 1.19994
\(668\) −13.3243 −0.515531
\(669\) −4.34805 −0.168105
\(670\) −23.1894 −0.895884
\(671\) 17.6252 0.680413
\(672\) −29.3554 −1.13241
\(673\) −2.14161 −0.0825530 −0.0412765 0.999148i \(-0.513142\pi\)
−0.0412765 + 0.999148i \(0.513142\pi\)
\(674\) −19.4388 −0.748754
\(675\) 44.9447 1.72992
\(676\) −11.0773 −0.426051
\(677\) 46.7475 1.79665 0.898326 0.439329i \(-0.144784\pi\)
0.898326 + 0.439329i \(0.144784\pi\)
\(678\) −0.0962332 −0.00369581
\(679\) −47.4895 −1.82248
\(680\) −35.5365 −1.36276
\(681\) 28.2029 1.08074
\(682\) −27.6160 −1.05747
\(683\) 43.9641 1.68224 0.841119 0.540850i \(-0.181897\pi\)
0.841119 + 0.540850i \(0.181897\pi\)
\(684\) −8.31652 −0.317990
\(685\) 35.6598 1.36249
\(686\) −32.3101 −1.23360
\(687\) −2.10890 −0.0804595
\(688\) 12.4974 0.476459
\(689\) −6.73490 −0.256579
\(690\) 59.1253 2.25086
\(691\) 14.2320 0.541412 0.270706 0.962662i \(-0.412743\pi\)
0.270706 + 0.962662i \(0.412743\pi\)
\(692\) −6.64354 −0.252549
\(693\) 10.7590 0.408702
\(694\) 0.930711 0.0353293
\(695\) −41.0825 −1.55835
\(696\) 8.93025 0.338500
\(697\) 48.9040 1.85237
\(698\) −46.5181 −1.76074
\(699\) −12.0410 −0.455433
\(700\) 36.0483 1.36250
\(701\) 25.9017 0.978293 0.489147 0.872202i \(-0.337308\pi\)
0.489147 + 0.872202i \(0.337308\pi\)
\(702\) −15.0551 −0.568218
\(703\) −53.4904 −2.01743
\(704\) −1.08798 −0.0410048
\(705\) −27.9540 −1.05281
\(706\) 3.71464 0.139802
\(707\) −51.9067 −1.95215
\(708\) 18.2154 0.684577
\(709\) 29.1752 1.09570 0.547849 0.836577i \(-0.315447\pi\)
0.547849 + 0.836577i \(0.315447\pi\)
\(710\) 43.6792 1.63925
\(711\) −8.65986 −0.324770
\(712\) 14.0969 0.528303
\(713\) 63.9738 2.39584
\(714\) 56.0843 2.09890
\(715\) 10.1914 0.381136
\(716\) 16.3246 0.610077
\(717\) 25.7789 0.962730
\(718\) −2.70221 −0.100846
\(719\) −29.1591 −1.08745 −0.543725 0.839263i \(-0.682987\pi\)
−0.543725 + 0.839263i \(0.682987\pi\)
\(720\) −24.9158 −0.928558
\(721\) −46.3856 −1.72749
\(722\) −24.9809 −0.929694
\(723\) −15.9157 −0.591910
\(724\) −12.5938 −0.468046
\(725\) −33.9217 −1.25982
\(726\) −17.0596 −0.633141
\(727\) −24.6294 −0.913456 −0.456728 0.889606i \(-0.650979\pi\)
−0.456728 + 0.889606i \(0.650979\pi\)
\(728\) 11.0450 0.409354
\(729\) 25.3740 0.939777
\(730\) 14.9308 0.552614
\(731\) −14.7479 −0.545471
\(732\) 12.8630 0.475429
\(733\) −22.1022 −0.816362 −0.408181 0.912901i \(-0.633837\pi\)
−0.408181 + 0.912901i \(0.633837\pi\)
\(734\) −14.1417 −0.521978
\(735\) 52.1079 1.92203
\(736\) −39.6721 −1.46233
\(737\) 6.70030 0.246809
\(738\) 19.9562 0.734597
\(739\) −9.16477 −0.337131 −0.168566 0.985690i \(-0.553914\pi\)
−0.168566 + 0.985690i \(0.553914\pi\)
\(740\) 34.9844 1.28605
\(741\) −11.3722 −0.417767
\(742\) 32.5053 1.19331
\(743\) 32.0802 1.17691 0.588454 0.808531i \(-0.299737\pi\)
0.588454 + 0.808531i \(0.299737\pi\)
\(744\) 18.4350 0.675860
\(745\) −51.5188 −1.88750
\(746\) −63.5234 −2.32576
\(747\) 3.55796 0.130179
\(748\) −11.2255 −0.410444
\(749\) 67.3654 2.46148
\(750\) −24.5788 −0.897491
\(751\) −19.3094 −0.704611 −0.352305 0.935885i \(-0.614602\pi\)
−0.352305 + 0.935885i \(0.614602\pi\)
\(752\) 30.3668 1.10736
\(753\) −19.6160 −0.714845
\(754\) 11.3627 0.413807
\(755\) −63.3012 −2.30377
\(756\) 24.9295 0.906678
\(757\) 9.52491 0.346189 0.173094 0.984905i \(-0.444623\pi\)
0.173094 + 0.984905i \(0.444623\pi\)
\(758\) 2.05617 0.0746834
\(759\) −17.0836 −0.620094
\(760\) −34.7775 −1.26151
\(761\) 26.1744 0.948823 0.474411 0.880303i \(-0.342661\pi\)
0.474411 + 0.880303i \(0.342661\pi\)
\(762\) 1.23819 0.0448549
\(763\) −33.1385 −1.19969
\(764\) −15.8378 −0.572991
\(765\) 29.4026 1.06305
\(766\) −6.73920 −0.243497
\(767\) −21.1999 −0.765483
\(768\) −24.7245 −0.892167
\(769\) 28.8856 1.04164 0.520820 0.853666i \(-0.325626\pi\)
0.520820 + 0.853666i \(0.325626\pi\)
\(770\) −49.1877 −1.77260
\(771\) 7.59275 0.273446
\(772\) −7.26511 −0.261477
\(773\) −4.07993 −0.146745 −0.0733725 0.997305i \(-0.523376\pi\)
−0.0733725 + 0.997305i \(0.523376\pi\)
\(774\) −6.01815 −0.216318
\(775\) −70.0256 −2.51539
\(776\) −18.4942 −0.663905
\(777\) 50.5029 1.81178
\(778\) 16.2851 0.583851
\(779\) 47.8596 1.71475
\(780\) 7.43775 0.266314
\(781\) −12.6206 −0.451600
\(782\) 75.7947 2.71041
\(783\) −23.4589 −0.838351
\(784\) −56.6055 −2.02163
\(785\) 3.47207 0.123923
\(786\) −9.57802 −0.341637
\(787\) −11.4800 −0.409219 −0.204609 0.978844i \(-0.565592\pi\)
−0.204609 + 0.978844i \(0.565592\pi\)
\(788\) −15.1854 −0.540958
\(789\) −28.1638 −1.00266
\(790\) 39.5907 1.40857
\(791\) −0.185460 −0.00659418
\(792\) 4.18998 0.148885
\(793\) −14.9705 −0.531617
\(794\) 51.9880 1.84498
\(795\) −20.0219 −0.710103
\(796\) −6.20846 −0.220053
\(797\) −22.6786 −0.803316 −0.401658 0.915790i \(-0.631566\pi\)
−0.401658 + 0.915790i \(0.631566\pi\)
\(798\) 54.8865 1.94296
\(799\) −35.8351 −1.26776
\(800\) 43.4251 1.53531
\(801\) −11.6636 −0.412114
\(802\) −9.33079 −0.329482
\(803\) −4.31408 −0.152241
\(804\) 4.88993 0.172454
\(805\) 113.946 4.01606
\(806\) 23.4565 0.826219
\(807\) 11.4084 0.401593
\(808\) −20.2145 −0.711142
\(809\) −8.43197 −0.296452 −0.148226 0.988953i \(-0.547356\pi\)
−0.148226 + 0.988953i \(0.547356\pi\)
\(810\) −18.6615 −0.655697
\(811\) −25.0503 −0.879637 −0.439818 0.898087i \(-0.644957\pi\)
−0.439818 + 0.898087i \(0.644957\pi\)
\(812\) −18.8154 −0.660291
\(813\) −2.87201 −0.100726
\(814\) −29.4627 −1.03267
\(815\) 29.2850 1.02581
\(816\) 37.5274 1.31372
\(817\) −14.4329 −0.504944
\(818\) 10.5672 0.369474
\(819\) −9.13852 −0.319326
\(820\) −31.3017 −1.09310
\(821\) 3.90486 0.136280 0.0681402 0.997676i \(-0.478293\pi\)
0.0681402 + 0.997676i \(0.478293\pi\)
\(822\) −21.9172 −0.764450
\(823\) −19.1872 −0.668825 −0.334412 0.942427i \(-0.608538\pi\)
−0.334412 + 0.942427i \(0.608538\pi\)
\(824\) −18.0643 −0.629300
\(825\) 18.6996 0.651038
\(826\) 102.319 3.56013
\(827\) −32.9961 −1.14739 −0.573694 0.819070i \(-0.694490\pi\)
−0.573694 + 0.819070i \(0.694490\pi\)
\(828\) 10.6116 0.368777
\(829\) −9.64456 −0.334969 −0.167485 0.985875i \(-0.553564\pi\)
−0.167485 + 0.985875i \(0.553564\pi\)
\(830\) −16.2661 −0.564604
\(831\) 15.6392 0.542518
\(832\) 0.924109 0.0320377
\(833\) 66.7989 2.31444
\(834\) 25.2501 0.874339
\(835\) 46.1011 1.59539
\(836\) −10.9857 −0.379950
\(837\) −48.4269 −1.67388
\(838\) −15.4403 −0.533378
\(839\) 49.6031 1.71249 0.856244 0.516572i \(-0.172792\pi\)
0.856244 + 0.516572i \(0.172792\pi\)
\(840\) 32.8351 1.13292
\(841\) −11.2946 −0.389468
\(842\) 32.2083 1.10997
\(843\) 39.8839 1.37368
\(844\) −28.3771 −0.976782
\(845\) 38.3268 1.31848
\(846\) −14.6232 −0.502755
\(847\) −32.8771 −1.12967
\(848\) 21.7501 0.746900
\(849\) −34.1572 −1.17227
\(850\) −82.9648 −2.84567
\(851\) 68.2518 2.33964
\(852\) −9.21059 −0.315550
\(853\) 17.9174 0.613480 0.306740 0.951793i \(-0.400762\pi\)
0.306740 + 0.951793i \(0.400762\pi\)
\(854\) 72.2535 2.47246
\(855\) 28.7746 0.984071
\(856\) 26.2347 0.896683
\(857\) −2.42086 −0.0826950 −0.0413475 0.999145i \(-0.513165\pi\)
−0.0413475 + 0.999145i \(0.513165\pi\)
\(858\) −6.26382 −0.213843
\(859\) −16.6676 −0.568692 −0.284346 0.958722i \(-0.591776\pi\)
−0.284346 + 0.958722i \(0.591776\pi\)
\(860\) 9.43958 0.321887
\(861\) −45.1865 −1.53995
\(862\) −31.2693 −1.06504
\(863\) 34.8647 1.18681 0.593404 0.804905i \(-0.297784\pi\)
0.593404 + 0.804905i \(0.297784\pi\)
\(864\) 30.0310 1.02168
\(865\) 22.9862 0.781554
\(866\) 69.1288 2.34909
\(867\) −22.6434 −0.769011
\(868\) −38.8412 −1.31836
\(869\) −11.4393 −0.388051
\(870\) 33.7798 1.14524
\(871\) −5.69110 −0.192836
\(872\) −12.9054 −0.437032
\(873\) 15.3020 0.517893
\(874\) 74.1760 2.50904
\(875\) −47.3680 −1.60133
\(876\) −3.14845 −0.106376
\(877\) −6.48932 −0.219129 −0.109564 0.993980i \(-0.534946\pi\)
−0.109564 + 0.993980i \(0.534946\pi\)
\(878\) −24.5879 −0.829800
\(879\) −11.3500 −0.382827
\(880\) −32.9126 −1.10949
\(881\) −57.2243 −1.92794 −0.963968 0.266020i \(-0.914291\pi\)
−0.963968 + 0.266020i \(0.914291\pi\)
\(882\) 27.2585 0.917841
\(883\) −24.1168 −0.811595 −0.405797 0.913963i \(-0.633006\pi\)
−0.405797 + 0.913963i \(0.633006\pi\)
\(884\) 9.53470 0.320687
\(885\) −63.0241 −2.11853
\(886\) 42.5902 1.43084
\(887\) 42.1176 1.41417 0.707086 0.707128i \(-0.250010\pi\)
0.707086 + 0.707128i \(0.250010\pi\)
\(888\) 19.6678 0.660007
\(889\) 2.38622 0.0800314
\(890\) 53.3232 1.78740
\(891\) 5.39201 0.180639
\(892\) 3.56765 0.119454
\(893\) −35.0698 −1.17357
\(894\) 31.6644 1.05902
\(895\) −56.4819 −1.88798
\(896\) −50.5786 −1.68971
\(897\) 14.5104 0.484489
\(898\) −44.0068 −1.46852
\(899\) 36.5499 1.21901
\(900\) −11.6154 −0.387180
\(901\) −25.6667 −0.855083
\(902\) 26.3612 0.877731
\(903\) 13.6268 0.453472
\(904\) −0.0722250 −0.00240217
\(905\) 43.5739 1.44844
\(906\) 38.9061 1.29257
\(907\) 25.8210 0.857371 0.428686 0.903454i \(-0.358977\pi\)
0.428686 + 0.903454i \(0.358977\pi\)
\(908\) −23.1410 −0.767960
\(909\) 16.7253 0.554742
\(910\) 41.7790 1.38496
\(911\) −20.3911 −0.675587 −0.337794 0.941220i \(-0.609681\pi\)
−0.337794 + 0.941220i \(0.609681\pi\)
\(912\) 36.7259 1.21612
\(913\) 4.69989 0.155544
\(914\) −58.4974 −1.93492
\(915\) −44.5051 −1.47129
\(916\) 1.73039 0.0571737
\(917\) −18.4587 −0.609559
\(918\) −57.3751 −1.89366
\(919\) −23.0410 −0.760054 −0.380027 0.924975i \(-0.624085\pi\)
−0.380027 + 0.924975i \(0.624085\pi\)
\(920\) 44.3748 1.46299
\(921\) 26.3292 0.867577
\(922\) −15.1870 −0.500159
\(923\) 10.7197 0.352842
\(924\) 10.3722 0.341219
\(925\) −74.7083 −2.45639
\(926\) −28.3464 −0.931520
\(927\) 14.9463 0.490899
\(928\) −22.6657 −0.744038
\(929\) −24.2154 −0.794483 −0.397241 0.917714i \(-0.630032\pi\)
−0.397241 + 0.917714i \(0.630032\pi\)
\(930\) 69.7327 2.28663
\(931\) 65.3722 2.14249
\(932\) 9.87987 0.323626
\(933\) −12.1469 −0.397672
\(934\) −24.0167 −0.785850
\(935\) 38.8394 1.27019
\(936\) −3.55889 −0.116326
\(937\) 28.7273 0.938479 0.469239 0.883071i \(-0.344528\pi\)
0.469239 + 0.883071i \(0.344528\pi\)
\(938\) 27.4675 0.896846
\(939\) 25.2849 0.825141
\(940\) 22.9367 0.748114
\(941\) −36.9396 −1.20420 −0.602098 0.798422i \(-0.705669\pi\)
−0.602098 + 0.798422i \(0.705669\pi\)
\(942\) −2.13400 −0.0695294
\(943\) −61.0670 −1.98861
\(944\) 68.4640 2.22831
\(945\) −86.2546 −2.80586
\(946\) −7.94969 −0.258467
\(947\) −56.3251 −1.83032 −0.915160 0.403090i \(-0.867936\pi\)
−0.915160 + 0.403090i \(0.867936\pi\)
\(948\) −8.34846 −0.271145
\(949\) 3.66430 0.118948
\(950\) −81.1929 −2.63425
\(951\) 16.0895 0.521739
\(952\) 42.0925 1.36423
\(953\) −10.9066 −0.353298 −0.176649 0.984274i \(-0.556526\pi\)
−0.176649 + 0.984274i \(0.556526\pi\)
\(954\) −10.4738 −0.339101
\(955\) 54.7977 1.77321
\(956\) −21.1520 −0.684106
\(957\) −9.76028 −0.315505
\(958\) −9.93873 −0.321106
\(959\) −42.2386 −1.36395
\(960\) 2.74725 0.0886670
\(961\) 44.4510 1.43390
\(962\) 25.0250 0.806839
\(963\) −21.7063 −0.699477
\(964\) 13.0591 0.420605
\(965\) 25.1368 0.809182
\(966\) −70.0331 −2.25328
\(967\) 16.0179 0.515100 0.257550 0.966265i \(-0.417085\pi\)
0.257550 + 0.966265i \(0.417085\pi\)
\(968\) −12.8036 −0.411523
\(969\) −43.3393 −1.39226
\(970\) −69.9568 −2.24618
\(971\) 24.3509 0.781457 0.390728 0.920506i \(-0.372223\pi\)
0.390728 + 0.920506i \(0.372223\pi\)
\(972\) −13.5354 −0.434149
\(973\) 48.6617 1.56002
\(974\) −38.9644 −1.24850
\(975\) −15.8831 −0.508666
\(976\) 48.3465 1.54753
\(977\) −9.25929 −0.296231 −0.148115 0.988970i \(-0.547321\pi\)
−0.148115 + 0.988970i \(0.547321\pi\)
\(978\) −17.9991 −0.575547
\(979\) −15.4071 −0.492413
\(980\) −42.7555 −1.36577
\(981\) 10.6778 0.340916
\(982\) −47.4348 −1.51370
\(983\) −50.2659 −1.60323 −0.801617 0.597839i \(-0.796026\pi\)
−0.801617 + 0.597839i \(0.796026\pi\)
\(984\) −17.5974 −0.560983
\(985\) 52.5405 1.67408
\(986\) 43.3035 1.37906
\(987\) 33.1111 1.05394
\(988\) 9.33106 0.296861
\(989\) 18.4159 0.585590
\(990\) 15.8491 0.503719
\(991\) −37.3702 −1.18711 −0.593553 0.804795i \(-0.702275\pi\)
−0.593553 + 0.804795i \(0.702275\pi\)
\(992\) −46.7895 −1.48557
\(993\) −22.7392 −0.721607
\(994\) −51.7374 −1.64101
\(995\) 21.4809 0.680990
\(996\) 3.43002 0.108684
\(997\) −38.1667 −1.20875 −0.604375 0.796700i \(-0.706577\pi\)
−0.604375 + 0.796700i \(0.706577\pi\)
\(998\) −33.2454 −1.05236
\(999\) −51.6652 −1.63462
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.1.5 18
3.2 odd 2 4923.2.a.l.1.14 18
4.3 odd 2 8752.2.a.s.1.12 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.5 18 1.1 even 1 trivial
4923.2.a.l.1.14 18 3.2 odd 2
8752.2.a.s.1.12 18 4.3 odd 2