Properties

Label 547.2.a.b.1.2
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 1.2
Root \(2.59964\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +O(q^{10})\) \(q-2.59964 q^{2} +2.09484 q^{3} +4.75812 q^{4} -3.02323 q^{5} -5.44583 q^{6} -0.561390 q^{7} -7.17011 q^{8} +1.38836 q^{9} +7.85930 q^{10} +4.23111 q^{11} +9.96751 q^{12} -4.87964 q^{13} +1.45941 q^{14} -6.33319 q^{15} +9.12345 q^{16} -6.39965 q^{17} -3.60924 q^{18} +6.29628 q^{19} -14.3849 q^{20} -1.17602 q^{21} -10.9994 q^{22} -9.21357 q^{23} -15.0202 q^{24} +4.13991 q^{25} +12.6853 q^{26} -3.37612 q^{27} -2.67116 q^{28} +1.14750 q^{29} +16.4640 q^{30} -7.52167 q^{31} -9.37744 q^{32} +8.86351 q^{33} +16.6368 q^{34} +1.69721 q^{35} +6.60600 q^{36} +8.74347 q^{37} -16.3680 q^{38} -10.2221 q^{39} +21.6769 q^{40} +2.81890 q^{41} +3.05723 q^{42} -1.57023 q^{43} +20.1321 q^{44} -4.19734 q^{45} +23.9520 q^{46} -4.08126 q^{47} +19.1122 q^{48} -6.68484 q^{49} -10.7623 q^{50} -13.4063 q^{51} -23.2179 q^{52} -4.00434 q^{53} +8.77670 q^{54} -12.7916 q^{55} +4.02522 q^{56} +13.1897 q^{57} -2.98307 q^{58} -12.2872 q^{59} -30.1341 q^{60} -0.473603 q^{61} +19.5536 q^{62} -0.779413 q^{63} +6.13107 q^{64} +14.7523 q^{65} -23.0419 q^{66} +1.80684 q^{67} -30.4503 q^{68} -19.3010 q^{69} -4.41213 q^{70} -1.76871 q^{71} -9.95472 q^{72} +0.611682 q^{73} -22.7298 q^{74} +8.67247 q^{75} +29.9584 q^{76} -2.37530 q^{77} +26.5737 q^{78} -2.49642 q^{79} -27.5823 q^{80} -11.2375 q^{81} -7.32811 q^{82} +8.29336 q^{83} -5.59565 q^{84} +19.3476 q^{85} +4.08204 q^{86} +2.40382 q^{87} -30.3375 q^{88} -14.8521 q^{89} +10.9116 q^{90} +2.73938 q^{91} -43.8393 q^{92} -15.7567 q^{93} +10.6098 q^{94} -19.0351 q^{95} -19.6443 q^{96} -7.36588 q^{97} +17.3782 q^{98} +5.87432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59964 −1.83822 −0.919111 0.393999i \(-0.871091\pi\)
−0.919111 + 0.393999i \(0.871091\pi\)
\(3\) 2.09484 1.20946 0.604729 0.796431i \(-0.293281\pi\)
0.604729 + 0.796431i \(0.293281\pi\)
\(4\) 4.75812 2.37906
\(5\) −3.02323 −1.35203 −0.676015 0.736888i \(-0.736294\pi\)
−0.676015 + 0.736888i \(0.736294\pi\)
\(6\) −5.44583 −2.22325
\(7\) −0.561390 −0.212185 −0.106093 0.994356i \(-0.533834\pi\)
−0.106093 + 0.994356i \(0.533834\pi\)
\(8\) −7.17011 −2.53502
\(9\) 1.38836 0.462788
\(10\) 7.85930 2.48533
\(11\) 4.23111 1.27573 0.637864 0.770149i \(-0.279818\pi\)
0.637864 + 0.770149i \(0.279818\pi\)
\(12\) 9.96751 2.87737
\(13\) −4.87964 −1.35337 −0.676684 0.736274i \(-0.736584\pi\)
−0.676684 + 0.736274i \(0.736584\pi\)
\(14\) 1.45941 0.390044
\(15\) −6.33319 −1.63522
\(16\) 9.12345 2.28086
\(17\) −6.39965 −1.55214 −0.776071 0.630645i \(-0.782790\pi\)
−0.776071 + 0.630645i \(0.782790\pi\)
\(18\) −3.60924 −0.850707
\(19\) 6.29628 1.44447 0.722233 0.691650i \(-0.243116\pi\)
0.722233 + 0.691650i \(0.243116\pi\)
\(20\) −14.3849 −3.21656
\(21\) −1.17602 −0.256629
\(22\) −10.9994 −2.34507
\(23\) −9.21357 −1.92116 −0.960581 0.277999i \(-0.910329\pi\)
−0.960581 + 0.277999i \(0.910329\pi\)
\(24\) −15.0202 −3.06599
\(25\) 4.13991 0.827983
\(26\) 12.6853 2.48779
\(27\) −3.37612 −0.649735
\(28\) −2.67116 −0.504801
\(29\) 1.14750 0.213085 0.106542 0.994308i \(-0.466022\pi\)
0.106542 + 0.994308i \(0.466022\pi\)
\(30\) 16.4640 3.00590
\(31\) −7.52167 −1.35093 −0.675466 0.737391i \(-0.736058\pi\)
−0.675466 + 0.737391i \(0.736058\pi\)
\(32\) −9.37744 −1.65771
\(33\) 8.86351 1.54294
\(34\) 16.6368 2.85318
\(35\) 1.69721 0.286881
\(36\) 6.60600 1.10100
\(37\) 8.74347 1.43742 0.718708 0.695312i \(-0.244734\pi\)
0.718708 + 0.695312i \(0.244734\pi\)
\(38\) −16.3680 −2.65525
\(39\) −10.2221 −1.63684
\(40\) 21.6769 3.42741
\(41\) 2.81890 0.440238 0.220119 0.975473i \(-0.429355\pi\)
0.220119 + 0.975473i \(0.429355\pi\)
\(42\) 3.05723 0.471741
\(43\) −1.57023 −0.239458 −0.119729 0.992807i \(-0.538203\pi\)
−0.119729 + 0.992807i \(0.538203\pi\)
\(44\) 20.1321 3.03503
\(45\) −4.19734 −0.625703
\(46\) 23.9520 3.53152
\(47\) −4.08126 −0.595313 −0.297657 0.954673i \(-0.596205\pi\)
−0.297657 + 0.954673i \(0.596205\pi\)
\(48\) 19.1122 2.75861
\(49\) −6.68484 −0.954977
\(50\) −10.7623 −1.52202
\(51\) −13.4063 −1.87725
\(52\) −23.2179 −3.21974
\(53\) −4.00434 −0.550039 −0.275019 0.961439i \(-0.588684\pi\)
−0.275019 + 0.961439i \(0.588684\pi\)
\(54\) 8.77670 1.19436
\(55\) −12.7916 −1.72482
\(56\) 4.02522 0.537893
\(57\) 13.1897 1.74702
\(58\) −2.98307 −0.391697
\(59\) −12.2872 −1.59966 −0.799828 0.600229i \(-0.795076\pi\)
−0.799828 + 0.600229i \(0.795076\pi\)
\(60\) −30.1341 −3.89029
\(61\) −0.473603 −0.0606386 −0.0303193 0.999540i \(-0.509652\pi\)
−0.0303193 + 0.999540i \(0.509652\pi\)
\(62\) 19.5536 2.48331
\(63\) −0.779413 −0.0981968
\(64\) 6.13107 0.766383
\(65\) 14.7523 1.82979
\(66\) −23.0419 −2.83626
\(67\) 1.80684 0.220740 0.110370 0.993891i \(-0.464796\pi\)
0.110370 + 0.993891i \(0.464796\pi\)
\(68\) −30.4503 −3.69264
\(69\) −19.3010 −2.32356
\(70\) −4.41213 −0.527350
\(71\) −1.76871 −0.209907 −0.104954 0.994477i \(-0.533469\pi\)
−0.104954 + 0.994477i \(0.533469\pi\)
\(72\) −9.95472 −1.17317
\(73\) 0.611682 0.0715919 0.0357960 0.999359i \(-0.488603\pi\)
0.0357960 + 0.999359i \(0.488603\pi\)
\(74\) −22.7298 −2.64229
\(75\) 8.67247 1.00141
\(76\) 29.9584 3.43647
\(77\) −2.37530 −0.270691
\(78\) 26.5737 3.00888
\(79\) −2.49642 −0.280869 −0.140434 0.990090i \(-0.544850\pi\)
−0.140434 + 0.990090i \(0.544850\pi\)
\(80\) −27.5823 −3.08379
\(81\) −11.2375 −1.24862
\(82\) −7.32811 −0.809254
\(83\) 8.29336 0.910315 0.455158 0.890411i \(-0.349583\pi\)
0.455158 + 0.890411i \(0.349583\pi\)
\(84\) −5.59565 −0.610536
\(85\) 19.3476 2.09854
\(86\) 4.08204 0.440178
\(87\) 2.40382 0.257717
\(88\) −30.3375 −3.23399
\(89\) −14.8521 −1.57432 −0.787162 0.616746i \(-0.788450\pi\)
−0.787162 + 0.616746i \(0.788450\pi\)
\(90\) 10.9116 1.15018
\(91\) 2.73938 0.287165
\(92\) −43.8393 −4.57056
\(93\) −15.7567 −1.63390
\(94\) 10.6098 1.09432
\(95\) −19.0351 −1.95296
\(96\) −19.6443 −2.00493
\(97\) −7.36588 −0.747891 −0.373946 0.927451i \(-0.621995\pi\)
−0.373946 + 0.927451i \(0.621995\pi\)
\(98\) 17.3782 1.75546
\(99\) 5.87432 0.590392
\(100\) 19.6982 1.96982
\(101\) 5.05569 0.503060 0.251530 0.967849i \(-0.419066\pi\)
0.251530 + 0.967849i \(0.419066\pi\)
\(102\) 34.8514 3.45080
\(103\) 1.90289 0.187497 0.0937486 0.995596i \(-0.470115\pi\)
0.0937486 + 0.995596i \(0.470115\pi\)
\(104\) 34.9875 3.43081
\(105\) 3.55539 0.346970
\(106\) 10.4098 1.01109
\(107\) 11.8307 1.14371 0.571856 0.820354i \(-0.306224\pi\)
0.571856 + 0.820354i \(0.306224\pi\)
\(108\) −16.0640 −1.54576
\(109\) 4.76603 0.456503 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(110\) 33.2536 3.17060
\(111\) 18.3162 1.73849
\(112\) −5.12181 −0.483965
\(113\) 12.6049 1.18577 0.592886 0.805287i \(-0.297989\pi\)
0.592886 + 0.805287i \(0.297989\pi\)
\(114\) −34.2885 −3.21141
\(115\) 27.8547 2.59747
\(116\) 5.45992 0.506941
\(117\) −6.77471 −0.626322
\(118\) 31.9423 2.94052
\(119\) 3.59270 0.329342
\(120\) 45.4096 4.14531
\(121\) 6.90230 0.627482
\(122\) 1.23120 0.111467
\(123\) 5.90514 0.532449
\(124\) −35.7890 −3.21395
\(125\) 2.60024 0.232572
\(126\) 2.02619 0.180508
\(127\) −20.3142 −1.80260 −0.901298 0.433199i \(-0.857385\pi\)
−0.901298 + 0.433199i \(0.857385\pi\)
\(128\) 2.81634 0.248931
\(129\) −3.28939 −0.289615
\(130\) −38.3505 −3.36356
\(131\) 13.5167 1.18096 0.590478 0.807054i \(-0.298939\pi\)
0.590478 + 0.807054i \(0.298939\pi\)
\(132\) 42.1736 3.67074
\(133\) −3.53467 −0.306494
\(134\) −4.69712 −0.405770
\(135\) 10.2068 0.878461
\(136\) 45.8861 3.93470
\(137\) 8.32726 0.711446 0.355723 0.934591i \(-0.384235\pi\)
0.355723 + 0.934591i \(0.384235\pi\)
\(138\) 50.1756 4.27123
\(139\) −16.6457 −1.41187 −0.705936 0.708275i \(-0.749474\pi\)
−0.705936 + 0.708275i \(0.749474\pi\)
\(140\) 8.07552 0.682506
\(141\) −8.54960 −0.720006
\(142\) 4.59801 0.385856
\(143\) −20.6463 −1.72653
\(144\) 12.6667 1.05556
\(145\) −3.46914 −0.288096
\(146\) −1.59015 −0.131602
\(147\) −14.0037 −1.15500
\(148\) 41.6024 3.41970
\(149\) 9.40634 0.770598 0.385299 0.922792i \(-0.374098\pi\)
0.385299 + 0.922792i \(0.374098\pi\)
\(150\) −22.5453 −1.84081
\(151\) −20.3010 −1.65207 −0.826035 0.563619i \(-0.809409\pi\)
−0.826035 + 0.563619i \(0.809409\pi\)
\(152\) −45.1450 −3.66174
\(153\) −8.88504 −0.718313
\(154\) 6.17492 0.497590
\(155\) 22.7397 1.82650
\(156\) −48.6378 −3.89414
\(157\) −6.07853 −0.485120 −0.242560 0.970136i \(-0.577987\pi\)
−0.242560 + 0.970136i \(0.577987\pi\)
\(158\) 6.48978 0.516299
\(159\) −8.38846 −0.665249
\(160\) 28.3502 2.24128
\(161\) 5.17240 0.407643
\(162\) 29.2135 2.29523
\(163\) 7.36070 0.576535 0.288267 0.957550i \(-0.406921\pi\)
0.288267 + 0.957550i \(0.406921\pi\)
\(164\) 13.4126 1.04735
\(165\) −26.7964 −2.08610
\(166\) −21.5597 −1.67336
\(167\) 7.50992 0.581135 0.290568 0.956854i \(-0.406156\pi\)
0.290568 + 0.956854i \(0.406156\pi\)
\(168\) 8.43221 0.650559
\(169\) 10.8108 0.831604
\(170\) −50.2967 −3.85758
\(171\) 8.74153 0.668481
\(172\) −7.47136 −0.569686
\(173\) 5.25063 0.399198 0.199599 0.979878i \(-0.436036\pi\)
0.199599 + 0.979878i \(0.436036\pi\)
\(174\) −6.24907 −0.473740
\(175\) −2.32410 −0.175686
\(176\) 38.6023 2.90976
\(177\) −25.7397 −1.93472
\(178\) 38.6102 2.89396
\(179\) −9.57025 −0.715314 −0.357657 0.933853i \(-0.616424\pi\)
−0.357657 + 0.933853i \(0.616424\pi\)
\(180\) −19.9714 −1.48858
\(181\) −1.66933 −0.124081 −0.0620403 0.998074i \(-0.519761\pi\)
−0.0620403 + 0.998074i \(0.519761\pi\)
\(182\) −7.12139 −0.527872
\(183\) −0.992123 −0.0733398
\(184\) 66.0623 4.87018
\(185\) −26.4335 −1.94343
\(186\) 40.9618 3.00346
\(187\) −27.0776 −1.98011
\(188\) −19.4191 −1.41629
\(189\) 1.89532 0.137864
\(190\) 49.4843 3.58997
\(191\) 26.7101 1.93268 0.966339 0.257272i \(-0.0828236\pi\)
0.966339 + 0.257272i \(0.0828236\pi\)
\(192\) 12.8436 0.926908
\(193\) 17.1594 1.23516 0.617582 0.786506i \(-0.288112\pi\)
0.617582 + 0.786506i \(0.288112\pi\)
\(194\) 19.1486 1.37479
\(195\) 30.9037 2.21306
\(196\) −31.8073 −2.27195
\(197\) −5.98278 −0.426255 −0.213128 0.977024i \(-0.568365\pi\)
−0.213128 + 0.977024i \(0.568365\pi\)
\(198\) −15.2711 −1.08527
\(199\) 16.0373 1.13685 0.568426 0.822734i \(-0.307552\pi\)
0.568426 + 0.822734i \(0.307552\pi\)
\(200\) −29.6836 −2.09895
\(201\) 3.78504 0.266976
\(202\) −13.1430 −0.924737
\(203\) −0.644192 −0.0452134
\(204\) −63.7885 −4.46609
\(205\) −8.52217 −0.595214
\(206\) −4.94682 −0.344661
\(207\) −12.7918 −0.889091
\(208\) −44.5191 −3.08684
\(209\) 26.6403 1.84274
\(210\) −9.24272 −0.637808
\(211\) 11.5087 0.792291 0.396146 0.918188i \(-0.370348\pi\)
0.396146 + 0.918188i \(0.370348\pi\)
\(212\) −19.0531 −1.30857
\(213\) −3.70517 −0.253874
\(214\) −30.7554 −2.10240
\(215\) 4.74718 0.323755
\(216\) 24.2072 1.64709
\(217\) 4.22259 0.286648
\(218\) −12.3900 −0.839154
\(219\) 1.28138 0.0865874
\(220\) −60.8640 −4.10345
\(221\) 31.2279 2.10062
\(222\) −47.6154 −3.19574
\(223\) 4.40148 0.294745 0.147372 0.989081i \(-0.452918\pi\)
0.147372 + 0.989081i \(0.452918\pi\)
\(224\) 5.26440 0.351742
\(225\) 5.74771 0.383180
\(226\) −32.7682 −2.17971
\(227\) 14.9252 0.990618 0.495309 0.868717i \(-0.335055\pi\)
0.495309 + 0.868717i \(0.335055\pi\)
\(228\) 62.7582 4.15626
\(229\) 4.19125 0.276966 0.138483 0.990365i \(-0.455777\pi\)
0.138483 + 0.990365i \(0.455777\pi\)
\(230\) −72.4122 −4.77472
\(231\) −4.97588 −0.327389
\(232\) −8.22766 −0.540173
\(233\) 1.32186 0.0865980 0.0432990 0.999062i \(-0.486213\pi\)
0.0432990 + 0.999062i \(0.486213\pi\)
\(234\) 17.6118 1.15132
\(235\) 12.3386 0.804881
\(236\) −58.4639 −3.80568
\(237\) −5.22960 −0.339699
\(238\) −9.33971 −0.605403
\(239\) −3.57501 −0.231248 −0.115624 0.993293i \(-0.536887\pi\)
−0.115624 + 0.993293i \(0.536887\pi\)
\(240\) −57.7805 −3.72972
\(241\) 14.5198 0.935301 0.467650 0.883914i \(-0.345101\pi\)
0.467650 + 0.883914i \(0.345101\pi\)
\(242\) −17.9435 −1.15345
\(243\) −13.4125 −0.860412
\(244\) −2.25346 −0.144263
\(245\) 20.2098 1.29116
\(246\) −15.3512 −0.978759
\(247\) −30.7235 −1.95489
\(248\) 53.9312 3.42464
\(249\) 17.3733 1.10099
\(250\) −6.75968 −0.427520
\(251\) 5.30634 0.334933 0.167467 0.985878i \(-0.446441\pi\)
0.167467 + 0.985878i \(0.446441\pi\)
\(252\) −3.70854 −0.233616
\(253\) −38.9836 −2.45088
\(254\) 52.8097 3.31357
\(255\) 40.5302 2.53810
\(256\) −19.5836 −1.22397
\(257\) −2.08054 −0.129781 −0.0648903 0.997892i \(-0.520670\pi\)
−0.0648903 + 0.997892i \(0.520670\pi\)
\(258\) 8.55123 0.532376
\(259\) −4.90849 −0.304999
\(260\) 70.1930 4.35318
\(261\) 1.59314 0.0986130
\(262\) −35.1384 −2.17086
\(263\) 16.6250 1.02514 0.512570 0.858645i \(-0.328694\pi\)
0.512570 + 0.858645i \(0.328694\pi\)
\(264\) −63.5523 −3.91137
\(265\) 12.1060 0.743668
\(266\) 9.18885 0.563405
\(267\) −31.1129 −1.90408
\(268\) 8.59714 0.525154
\(269\) −7.61200 −0.464112 −0.232056 0.972702i \(-0.574545\pi\)
−0.232056 + 0.972702i \(0.574545\pi\)
\(270\) −26.5340 −1.61481
\(271\) 4.15827 0.252597 0.126298 0.991992i \(-0.459690\pi\)
0.126298 + 0.991992i \(0.459690\pi\)
\(272\) −58.3868 −3.54022
\(273\) 5.73856 0.347314
\(274\) −21.6479 −1.30779
\(275\) 17.5164 1.05628
\(276\) −91.8363 −5.52790
\(277\) 9.42089 0.566047 0.283023 0.959113i \(-0.408663\pi\)
0.283023 + 0.959113i \(0.408663\pi\)
\(278\) 43.2729 2.59533
\(279\) −10.4428 −0.625195
\(280\) −12.1692 −0.727247
\(281\) −23.1796 −1.38278 −0.691391 0.722481i \(-0.743002\pi\)
−0.691391 + 0.722481i \(0.743002\pi\)
\(282\) 22.2259 1.32353
\(283\) −24.6282 −1.46399 −0.731997 0.681308i \(-0.761412\pi\)
−0.731997 + 0.681308i \(0.761412\pi\)
\(284\) −8.41573 −0.499382
\(285\) −39.8755 −2.36202
\(286\) 53.6729 3.17374
\(287\) −1.58250 −0.0934120
\(288\) −13.0193 −0.767170
\(289\) 23.9555 1.40915
\(290\) 9.01851 0.529585
\(291\) −15.4303 −0.904543
\(292\) 2.91045 0.170321
\(293\) 23.3449 1.36382 0.681910 0.731436i \(-0.261149\pi\)
0.681910 + 0.731436i \(0.261149\pi\)
\(294\) 36.4045 2.12315
\(295\) 37.1470 2.16278
\(296\) −62.6916 −3.64387
\(297\) −14.2848 −0.828885
\(298\) −24.4531 −1.41653
\(299\) 44.9589 2.60004
\(300\) 41.2646 2.38241
\(301\) 0.881513 0.0508096
\(302\) 52.7752 3.03687
\(303\) 10.5909 0.608430
\(304\) 57.4438 3.29463
\(305\) 1.43181 0.0819851
\(306\) 23.0979 1.32042
\(307\) −13.1646 −0.751342 −0.375671 0.926753i \(-0.622588\pi\)
−0.375671 + 0.926753i \(0.622588\pi\)
\(308\) −11.3020 −0.643989
\(309\) 3.98625 0.226770
\(310\) −59.1151 −3.35751
\(311\) −18.1219 −1.02760 −0.513800 0.857910i \(-0.671763\pi\)
−0.513800 + 0.857910i \(0.671763\pi\)
\(312\) 73.2933 4.14942
\(313\) 14.2295 0.804299 0.402150 0.915574i \(-0.368263\pi\)
0.402150 + 0.915574i \(0.368263\pi\)
\(314\) 15.8020 0.891758
\(315\) 2.35634 0.132765
\(316\) −11.8783 −0.668204
\(317\) 0.706042 0.0396553 0.0198276 0.999803i \(-0.493688\pi\)
0.0198276 + 0.999803i \(0.493688\pi\)
\(318\) 21.8070 1.22287
\(319\) 4.85518 0.271838
\(320\) −18.5356 −1.03617
\(321\) 24.7834 1.38327
\(322\) −13.4464 −0.749337
\(323\) −40.2940 −2.24202
\(324\) −53.4695 −2.97053
\(325\) −20.2013 −1.12056
\(326\) −19.1352 −1.05980
\(327\) 9.98408 0.552121
\(328\) −20.2118 −1.11601
\(329\) 2.29118 0.126317
\(330\) 69.6610 3.83471
\(331\) −1.50165 −0.0825381 −0.0412691 0.999148i \(-0.513140\pi\)
−0.0412691 + 0.999148i \(0.513140\pi\)
\(332\) 39.4608 2.16569
\(333\) 12.1391 0.665219
\(334\) −19.5231 −1.06825
\(335\) −5.46248 −0.298447
\(336\) −10.7294 −0.585336
\(337\) −10.5820 −0.576437 −0.288219 0.957565i \(-0.593063\pi\)
−0.288219 + 0.957565i \(0.593063\pi\)
\(338\) −28.1043 −1.52867
\(339\) 26.4053 1.43414
\(340\) 92.0581 4.99255
\(341\) −31.8250 −1.72342
\(342\) −22.7248 −1.22882
\(343\) 7.68253 0.414818
\(344\) 11.2587 0.607031
\(345\) 58.3513 3.14153
\(346\) −13.6497 −0.733815
\(347\) −21.9609 −1.17892 −0.589461 0.807797i \(-0.700660\pi\)
−0.589461 + 0.807797i \(0.700660\pi\)
\(348\) 11.4377 0.613123
\(349\) −13.7632 −0.736727 −0.368364 0.929682i \(-0.620082\pi\)
−0.368364 + 0.929682i \(0.620082\pi\)
\(350\) 6.04183 0.322949
\(351\) 16.4743 0.879330
\(352\) −39.6770 −2.11479
\(353\) −33.1723 −1.76558 −0.882791 0.469766i \(-0.844338\pi\)
−0.882791 + 0.469766i \(0.844338\pi\)
\(354\) 66.9140 3.55644
\(355\) 5.34722 0.283801
\(356\) −70.6682 −3.74541
\(357\) 7.52613 0.398325
\(358\) 24.8792 1.31491
\(359\) −18.0716 −0.953782 −0.476891 0.878962i \(-0.658236\pi\)
−0.476891 + 0.878962i \(0.658236\pi\)
\(360\) 30.0954 1.58617
\(361\) 20.6431 1.08648
\(362\) 4.33966 0.228087
\(363\) 14.4592 0.758913
\(364\) 13.0343 0.683182
\(365\) −1.84925 −0.0967944
\(366\) 2.57916 0.134815
\(367\) −32.7727 −1.71072 −0.855361 0.518033i \(-0.826665\pi\)
−0.855361 + 0.518033i \(0.826665\pi\)
\(368\) −84.0595 −4.38191
\(369\) 3.91365 0.203737
\(370\) 68.7175 3.57245
\(371\) 2.24800 0.116710
\(372\) −74.9723 −3.88713
\(373\) 3.25311 0.168440 0.0842199 0.996447i \(-0.473160\pi\)
0.0842199 + 0.996447i \(0.473160\pi\)
\(374\) 70.3920 3.63988
\(375\) 5.44709 0.281287
\(376\) 29.2631 1.50913
\(377\) −5.59936 −0.288382
\(378\) −4.92715 −0.253425
\(379\) −19.1603 −0.984198 −0.492099 0.870539i \(-0.663770\pi\)
−0.492099 + 0.870539i \(0.663770\pi\)
\(380\) −90.5712 −4.64620
\(381\) −42.5551 −2.18016
\(382\) −69.4367 −3.55269
\(383\) 22.6686 1.15831 0.579155 0.815217i \(-0.303383\pi\)
0.579155 + 0.815217i \(0.303383\pi\)
\(384\) 5.89978 0.301072
\(385\) 7.18108 0.365982
\(386\) −44.6084 −2.27051
\(387\) −2.18006 −0.110818
\(388\) −35.0477 −1.77928
\(389\) −39.0808 −1.98148 −0.990738 0.135788i \(-0.956643\pi\)
−0.990738 + 0.135788i \(0.956643\pi\)
\(390\) −80.3383 −4.06809
\(391\) 58.9636 2.98192
\(392\) 47.9310 2.42088
\(393\) 28.3153 1.42832
\(394\) 15.5531 0.783551
\(395\) 7.54724 0.379743
\(396\) 27.9507 1.40458
\(397\) 17.4671 0.876649 0.438324 0.898817i \(-0.355572\pi\)
0.438324 + 0.898817i \(0.355572\pi\)
\(398\) −41.6911 −2.08979
\(399\) −7.40457 −0.370692
\(400\) 37.7703 1.88851
\(401\) 7.16631 0.357868 0.178934 0.983861i \(-0.442735\pi\)
0.178934 + 0.983861i \(0.442735\pi\)
\(402\) −9.83973 −0.490761
\(403\) 36.7030 1.82831
\(404\) 24.0556 1.19681
\(405\) 33.9736 1.68816
\(406\) 1.67467 0.0831123
\(407\) 36.9946 1.83375
\(408\) 96.1242 4.75886
\(409\) −20.3350 −1.00550 −0.502750 0.864432i \(-0.667678\pi\)
−0.502750 + 0.864432i \(0.667678\pi\)
\(410\) 22.1546 1.09414
\(411\) 17.4443 0.860464
\(412\) 9.05417 0.446067
\(413\) 6.89791 0.339424
\(414\) 33.2540 1.63435
\(415\) −25.0727 −1.23077
\(416\) 45.7585 2.24350
\(417\) −34.8702 −1.70760
\(418\) −69.2550 −3.38737
\(419\) −28.3481 −1.38490 −0.692448 0.721468i \(-0.743468\pi\)
−0.692448 + 0.721468i \(0.743468\pi\)
\(420\) 16.9169 0.825462
\(421\) −2.21872 −0.108134 −0.0540670 0.998537i \(-0.517218\pi\)
−0.0540670 + 0.998537i \(0.517218\pi\)
\(422\) −29.9184 −1.45641
\(423\) −5.66628 −0.275504
\(424\) 28.7116 1.39436
\(425\) −26.4940 −1.28515
\(426\) 9.63210 0.466677
\(427\) 0.265876 0.0128666
\(428\) 56.2916 2.72096
\(429\) −43.2507 −2.08816
\(430\) −12.3409 −0.595133
\(431\) −1.89601 −0.0913274 −0.0456637 0.998957i \(-0.514540\pi\)
−0.0456637 + 0.998957i \(0.514540\pi\)
\(432\) −30.8019 −1.48196
\(433\) −33.8222 −1.62539 −0.812697 0.582687i \(-0.802001\pi\)
−0.812697 + 0.582687i \(0.802001\pi\)
\(434\) −10.9772 −0.526923
\(435\) −7.26730 −0.348440
\(436\) 22.6773 1.08605
\(437\) −58.0112 −2.77505
\(438\) −3.33112 −0.159167
\(439\) 6.31659 0.301474 0.150737 0.988574i \(-0.451835\pi\)
0.150737 + 0.988574i \(0.451835\pi\)
\(440\) 91.7173 4.37245
\(441\) −9.28099 −0.441952
\(442\) −81.1814 −3.86140
\(443\) 19.5315 0.927967 0.463984 0.885844i \(-0.346420\pi\)
0.463984 + 0.885844i \(0.346420\pi\)
\(444\) 87.1505 4.13598
\(445\) 44.9014 2.12853
\(446\) −11.4423 −0.541807
\(447\) 19.7048 0.932005
\(448\) −3.44192 −0.162615
\(449\) −15.3252 −0.723242 −0.361621 0.932325i \(-0.617777\pi\)
−0.361621 + 0.932325i \(0.617777\pi\)
\(450\) −14.9420 −0.704371
\(451\) 11.9271 0.561623
\(452\) 59.9757 2.82102
\(453\) −42.5273 −1.99811
\(454\) −38.8000 −1.82098
\(455\) −8.28176 −0.388255
\(456\) −94.5716 −4.42872
\(457\) −14.7763 −0.691207 −0.345603 0.938381i \(-0.612326\pi\)
−0.345603 + 0.938381i \(0.612326\pi\)
\(458\) −10.8957 −0.509124
\(459\) 21.6060 1.00848
\(460\) 132.536 6.17953
\(461\) −28.1311 −1.31020 −0.655098 0.755544i \(-0.727373\pi\)
−0.655098 + 0.755544i \(0.727373\pi\)
\(462\) 12.9355 0.601814
\(463\) 16.7165 0.776880 0.388440 0.921474i \(-0.373014\pi\)
0.388440 + 0.921474i \(0.373014\pi\)
\(464\) 10.4691 0.486016
\(465\) 47.6362 2.20907
\(466\) −3.43636 −0.159186
\(467\) −22.4105 −1.03703 −0.518517 0.855067i \(-0.673516\pi\)
−0.518517 + 0.855067i \(0.673516\pi\)
\(468\) −32.2349 −1.49006
\(469\) −1.01434 −0.0468379
\(470\) −32.0759 −1.47955
\(471\) −12.7336 −0.586732
\(472\) 88.1005 4.05515
\(473\) −6.64383 −0.305484
\(474\) 13.5951 0.624442
\(475\) 26.0660 1.19599
\(476\) 17.0945 0.783524
\(477\) −5.55948 −0.254551
\(478\) 9.29372 0.425085
\(479\) −15.0630 −0.688247 −0.344123 0.938924i \(-0.611824\pi\)
−0.344123 + 0.938924i \(0.611824\pi\)
\(480\) 59.3891 2.71073
\(481\) −42.6649 −1.94535
\(482\) −37.7462 −1.71929
\(483\) 10.8354 0.493026
\(484\) 32.8420 1.49282
\(485\) 22.2687 1.01117
\(486\) 34.8676 1.58163
\(487\) 39.0354 1.76886 0.884432 0.466669i \(-0.154546\pi\)
0.884432 + 0.466669i \(0.154546\pi\)
\(488\) 3.39578 0.153720
\(489\) 15.4195 0.697294
\(490\) −52.5382 −2.37343
\(491\) 21.8721 0.987075 0.493537 0.869725i \(-0.335704\pi\)
0.493537 + 0.869725i \(0.335704\pi\)
\(492\) 28.0974 1.26673
\(493\) −7.34356 −0.330737
\(494\) 79.8701 3.59353
\(495\) −17.7594 −0.798227
\(496\) −68.6236 −3.08129
\(497\) 0.992936 0.0445393
\(498\) −45.1643 −2.02386
\(499\) 20.4160 0.913947 0.456973 0.889480i \(-0.348933\pi\)
0.456973 + 0.889480i \(0.348933\pi\)
\(500\) 12.3722 0.553304
\(501\) 15.7321 0.702858
\(502\) −13.7946 −0.615681
\(503\) −17.2592 −0.769551 −0.384776 0.923010i \(-0.625721\pi\)
−0.384776 + 0.923010i \(0.625721\pi\)
\(504\) 5.58848 0.248930
\(505\) −15.2845 −0.680152
\(506\) 101.343 4.50526
\(507\) 22.6470 1.00579
\(508\) −96.6575 −4.28848
\(509\) −29.7166 −1.31717 −0.658584 0.752508i \(-0.728844\pi\)
−0.658584 + 0.752508i \(0.728844\pi\)
\(510\) −105.364 −4.66559
\(511\) −0.343392 −0.0151908
\(512\) 45.2776 2.00100
\(513\) −21.2570 −0.938520
\(514\) 5.40865 0.238566
\(515\) −5.75287 −0.253502
\(516\) −15.6513 −0.689011
\(517\) −17.2683 −0.759458
\(518\) 12.7603 0.560655
\(519\) 10.9992 0.482813
\(520\) −105.775 −4.63855
\(521\) 32.4429 1.42135 0.710675 0.703520i \(-0.248390\pi\)
0.710675 + 0.703520i \(0.248390\pi\)
\(522\) −4.14159 −0.181272
\(523\) 5.45155 0.238380 0.119190 0.992871i \(-0.461970\pi\)
0.119190 + 0.992871i \(0.461970\pi\)
\(524\) 64.3138 2.80956
\(525\) −4.86863 −0.212485
\(526\) −43.2189 −1.88443
\(527\) 48.1361 2.09684
\(528\) 80.8658 3.51923
\(529\) 61.8899 2.69087
\(530\) −31.4713 −1.36703
\(531\) −17.0591 −0.740302
\(532\) −16.8184 −0.729168
\(533\) −13.7552 −0.595803
\(534\) 80.8823 3.50012
\(535\) −35.7668 −1.54633
\(536\) −12.9552 −0.559580
\(537\) −20.0482 −0.865142
\(538\) 19.7884 0.853140
\(539\) −28.2843 −1.21829
\(540\) 48.5651 2.08991
\(541\) 31.1191 1.33792 0.668958 0.743301i \(-0.266741\pi\)
0.668958 + 0.743301i \(0.266741\pi\)
\(542\) −10.8100 −0.464329
\(543\) −3.49699 −0.150070
\(544\) 60.0123 2.57301
\(545\) −14.4088 −0.617205
\(546\) −14.9182 −0.638439
\(547\) −1.00000 −0.0427569
\(548\) 39.6221 1.69257
\(549\) −0.657533 −0.0280628
\(550\) −45.5364 −1.94168
\(551\) 7.22495 0.307793
\(552\) 138.390 5.89027
\(553\) 1.40146 0.0595963
\(554\) −24.4909 −1.04052
\(555\) −55.3740 −2.35050
\(556\) −79.2023 −3.35893
\(557\) 41.0931 1.74117 0.870585 0.492017i \(-0.163740\pi\)
0.870585 + 0.492017i \(0.163740\pi\)
\(558\) 27.1476 1.14925
\(559\) 7.66217 0.324075
\(560\) 15.4844 0.654335
\(561\) −56.7233 −2.39486
\(562\) 60.2587 2.54186
\(563\) 6.83856 0.288211 0.144105 0.989562i \(-0.453970\pi\)
0.144105 + 0.989562i \(0.453970\pi\)
\(564\) −40.6800 −1.71294
\(565\) −38.1076 −1.60320
\(566\) 64.0244 2.69115
\(567\) 6.30864 0.264938
\(568\) 12.6818 0.532118
\(569\) −27.4209 −1.14955 −0.574773 0.818313i \(-0.694909\pi\)
−0.574773 + 0.818313i \(0.694909\pi\)
\(570\) 103.662 4.34192
\(571\) −34.1032 −1.42718 −0.713588 0.700566i \(-0.752931\pi\)
−0.713588 + 0.700566i \(0.752931\pi\)
\(572\) −98.2374 −4.10751
\(573\) 55.9535 2.33749
\(574\) 4.11392 0.171712
\(575\) −38.1434 −1.59069
\(576\) 8.51215 0.354673
\(577\) −33.6417 −1.40052 −0.700260 0.713888i \(-0.746933\pi\)
−0.700260 + 0.713888i \(0.746933\pi\)
\(578\) −62.2756 −2.59032
\(579\) 35.9463 1.49388
\(580\) −16.5066 −0.685398
\(581\) −4.65581 −0.193155
\(582\) 40.1133 1.66275
\(583\) −16.9428 −0.701700
\(584\) −4.38582 −0.181487
\(585\) 20.4815 0.846806
\(586\) −60.6882 −2.50701
\(587\) −13.2895 −0.548516 −0.274258 0.961656i \(-0.588432\pi\)
−0.274258 + 0.961656i \(0.588432\pi\)
\(588\) −66.6312 −2.74782
\(589\) −47.3586 −1.95138
\(590\) −96.5688 −3.97567
\(591\) −12.5330 −0.515538
\(592\) 79.7705 3.27855
\(593\) −44.2951 −1.81898 −0.909491 0.415724i \(-0.863528\pi\)
−0.909491 + 0.415724i \(0.863528\pi\)
\(594\) 37.1352 1.52367
\(595\) −10.8615 −0.445280
\(596\) 44.7565 1.83330
\(597\) 33.5956 1.37498
\(598\) −116.877 −4.77945
\(599\) 5.59011 0.228406 0.114203 0.993457i \(-0.463569\pi\)
0.114203 + 0.993457i \(0.463569\pi\)
\(600\) −62.1825 −2.53859
\(601\) 25.4727 1.03905 0.519526 0.854454i \(-0.326108\pi\)
0.519526 + 0.854454i \(0.326108\pi\)
\(602\) −2.29161 −0.0933992
\(603\) 2.50855 0.102156
\(604\) −96.5944 −3.93037
\(605\) −20.8672 −0.848374
\(606\) −27.5325 −1.11843
\(607\) −27.4291 −1.11331 −0.556657 0.830742i \(-0.687916\pi\)
−0.556657 + 0.830742i \(0.687916\pi\)
\(608\) −59.0430 −2.39451
\(609\) −1.34948 −0.0546837
\(610\) −3.72218 −0.150707
\(611\) 19.9151 0.805678
\(612\) −42.2761 −1.70891
\(613\) 16.8113 0.679000 0.339500 0.940606i \(-0.389742\pi\)
0.339500 + 0.940606i \(0.389742\pi\)
\(614\) 34.2231 1.38113
\(615\) −17.8526 −0.719886
\(616\) 17.0312 0.686205
\(617\) 12.2317 0.492429 0.246215 0.969215i \(-0.420813\pi\)
0.246215 + 0.969215i \(0.420813\pi\)
\(618\) −10.3628 −0.416854
\(619\) −17.1538 −0.689471 −0.344736 0.938700i \(-0.612031\pi\)
−0.344736 + 0.938700i \(0.612031\pi\)
\(620\) 108.198 4.34535
\(621\) 31.1062 1.24825
\(622\) 47.1105 1.88896
\(623\) 8.33784 0.334048
\(624\) −93.2605 −3.73341
\(625\) −28.5607 −1.14243
\(626\) −36.9916 −1.47848
\(627\) 55.8071 2.22872
\(628\) −28.9224 −1.15413
\(629\) −55.9551 −2.23108
\(630\) −6.12564 −0.244051
\(631\) −6.57839 −0.261882 −0.130941 0.991390i \(-0.541800\pi\)
−0.130941 + 0.991390i \(0.541800\pi\)
\(632\) 17.8996 0.712007
\(633\) 24.1089 0.958243
\(634\) −1.83545 −0.0728952
\(635\) 61.4146 2.43716
\(636\) −39.9133 −1.58267
\(637\) 32.6196 1.29244
\(638\) −12.6217 −0.499698
\(639\) −2.45561 −0.0971426
\(640\) −8.51443 −0.336562
\(641\) 2.33872 0.0923737 0.0461868 0.998933i \(-0.485293\pi\)
0.0461868 + 0.998933i \(0.485293\pi\)
\(642\) −64.4277 −2.54276
\(643\) −17.3754 −0.685218 −0.342609 0.939478i \(-0.611311\pi\)
−0.342609 + 0.939478i \(0.611311\pi\)
\(644\) 24.6109 0.969805
\(645\) 9.94459 0.391568
\(646\) 104.750 4.12132
\(647\) 38.9519 1.53136 0.765679 0.643223i \(-0.222403\pi\)
0.765679 + 0.643223i \(0.222403\pi\)
\(648\) 80.5743 3.16526
\(649\) −51.9885 −2.04073
\(650\) 52.5160 2.05985
\(651\) 8.84566 0.346689
\(652\) 35.0231 1.37161
\(653\) −7.75059 −0.303304 −0.151652 0.988434i \(-0.548459\pi\)
−0.151652 + 0.988434i \(0.548459\pi\)
\(654\) −25.9550 −1.01492
\(655\) −40.8639 −1.59669
\(656\) 25.7180 1.00412
\(657\) 0.849237 0.0331319
\(658\) −5.95624 −0.232198
\(659\) −22.3674 −0.871309 −0.435655 0.900114i \(-0.643483\pi\)
−0.435655 + 0.900114i \(0.643483\pi\)
\(660\) −127.501 −4.96295
\(661\) 30.2526 1.17669 0.588345 0.808610i \(-0.299780\pi\)
0.588345 + 0.808610i \(0.299780\pi\)
\(662\) 3.90375 0.151723
\(663\) 65.4176 2.54061
\(664\) −59.4643 −2.30766
\(665\) 10.6861 0.414389
\(666\) −31.5573 −1.22282
\(667\) −10.5725 −0.409370
\(668\) 35.7331 1.38255
\(669\) 9.22041 0.356482
\(670\) 14.2005 0.548612
\(671\) −2.00386 −0.0773583
\(672\) 11.0281 0.425418
\(673\) 11.7416 0.452604 0.226302 0.974057i \(-0.427336\pi\)
0.226302 + 0.974057i \(0.427336\pi\)
\(674\) 27.5093 1.05962
\(675\) −13.9769 −0.537969
\(676\) 51.4393 1.97843
\(677\) −30.4285 −1.16946 −0.584732 0.811227i \(-0.698800\pi\)
−0.584732 + 0.811227i \(0.698800\pi\)
\(678\) −68.6443 −2.63627
\(679\) 4.13513 0.158692
\(680\) −138.724 −5.31984
\(681\) 31.2659 1.19811
\(682\) 82.7336 3.16803
\(683\) −11.6989 −0.447647 −0.223823 0.974630i \(-0.571854\pi\)
−0.223823 + 0.974630i \(0.571854\pi\)
\(684\) 41.5932 1.59036
\(685\) −25.1752 −0.961895
\(686\) −19.9718 −0.762527
\(687\) 8.78001 0.334978
\(688\) −14.3259 −0.546171
\(689\) 19.5397 0.744404
\(690\) −151.692 −5.77482
\(691\) 27.2076 1.03502 0.517512 0.855676i \(-0.326858\pi\)
0.517512 + 0.855676i \(0.326858\pi\)
\(692\) 24.9831 0.949716
\(693\) −3.29778 −0.125272
\(694\) 57.0903 2.16712
\(695\) 50.3239 1.90889
\(696\) −17.2357 −0.653316
\(697\) −18.0399 −0.683311
\(698\) 35.7794 1.35427
\(699\) 2.76909 0.104737
\(700\) −11.0584 −0.417967
\(701\) −21.2354 −0.802049 −0.401024 0.916067i \(-0.631346\pi\)
−0.401024 + 0.916067i \(0.631346\pi\)
\(702\) −42.8271 −1.61640
\(703\) 55.0513 2.07630
\(704\) 25.9412 0.977697
\(705\) 25.8474 0.973470
\(706\) 86.2359 3.24553
\(707\) −2.83821 −0.106742
\(708\) −122.473 −4.60281
\(709\) 16.8807 0.633967 0.316983 0.948431i \(-0.397330\pi\)
0.316983 + 0.948431i \(0.397330\pi\)
\(710\) −13.9008 −0.521689
\(711\) −3.46594 −0.129983
\(712\) 106.491 3.99094
\(713\) 69.3015 2.59536
\(714\) −19.5652 −0.732210
\(715\) 62.4184 2.33432
\(716\) −45.5364 −1.70177
\(717\) −7.48907 −0.279685
\(718\) 46.9796 1.75326
\(719\) −20.3235 −0.757941 −0.378970 0.925409i \(-0.623722\pi\)
−0.378970 + 0.925409i \(0.623722\pi\)
\(720\) −38.2942 −1.42714
\(721\) −1.06826 −0.0397842
\(722\) −53.6646 −1.99719
\(723\) 30.4166 1.13121
\(724\) −7.94288 −0.295195
\(725\) 4.75053 0.176430
\(726\) −37.5888 −1.39505
\(727\) −9.13646 −0.338853 −0.169426 0.985543i \(-0.554191\pi\)
−0.169426 + 0.985543i \(0.554191\pi\)
\(728\) −19.6416 −0.727967
\(729\) 5.61554 0.207983
\(730\) 4.80739 0.177929
\(731\) 10.0489 0.371674
\(732\) −4.72064 −0.174480
\(733\) −6.55001 −0.241930 −0.120965 0.992657i \(-0.538599\pi\)
−0.120965 + 0.992657i \(0.538599\pi\)
\(734\) 85.1972 3.14469
\(735\) 42.3364 1.56160
\(736\) 86.3997 3.18474
\(737\) 7.64493 0.281605
\(738\) −10.1741 −0.374513
\(739\) −37.2949 −1.37192 −0.685958 0.727641i \(-0.740617\pi\)
−0.685958 + 0.727641i \(0.740617\pi\)
\(740\) −125.774 −4.62353
\(741\) −64.3610 −2.36436
\(742\) −5.84398 −0.214539
\(743\) −45.7404 −1.67805 −0.839026 0.544092i \(-0.816874\pi\)
−0.839026 + 0.544092i \(0.816874\pi\)
\(744\) 112.977 4.14195
\(745\) −28.4375 −1.04187
\(746\) −8.45692 −0.309630
\(747\) 11.5142 0.421283
\(748\) −128.838 −4.71080
\(749\) −6.64161 −0.242679
\(750\) −14.1605 −0.517067
\(751\) −38.4995 −1.40487 −0.702434 0.711749i \(-0.747903\pi\)
−0.702434 + 0.711749i \(0.747903\pi\)
\(752\) −37.2352 −1.35783
\(753\) 11.1159 0.405087
\(754\) 14.5563 0.530109
\(755\) 61.3745 2.23365
\(756\) 9.01816 0.327987
\(757\) 20.5989 0.748681 0.374340 0.927291i \(-0.377869\pi\)
0.374340 + 0.927291i \(0.377869\pi\)
\(758\) 49.8098 1.80917
\(759\) −81.6646 −2.96424
\(760\) 136.484 4.95078
\(761\) 18.6360 0.675555 0.337778 0.941226i \(-0.390325\pi\)
0.337778 + 0.941226i \(0.390325\pi\)
\(762\) 110.628 4.00763
\(763\) −2.67560 −0.0968632
\(764\) 127.090 4.59795
\(765\) 26.8615 0.971180
\(766\) −58.9301 −2.12923
\(767\) 59.9571 2.16492
\(768\) −41.0245 −1.48034
\(769\) 32.6001 1.17559 0.587795 0.809010i \(-0.299996\pi\)
0.587795 + 0.809010i \(0.299996\pi\)
\(770\) −18.6682 −0.672756
\(771\) −4.35841 −0.156964
\(772\) 81.6467 2.93853
\(773\) −50.6910 −1.82323 −0.911614 0.411047i \(-0.865163\pi\)
−0.911614 + 0.411047i \(0.865163\pi\)
\(774\) 5.66736 0.203709
\(775\) −31.1391 −1.11855
\(776\) 52.8141 1.89592
\(777\) −10.2825 −0.368883
\(778\) 101.596 3.64239
\(779\) 17.7486 0.635908
\(780\) 147.043 5.26499
\(781\) −7.48361 −0.267785
\(782\) −153.284 −5.48143
\(783\) −3.87409 −0.138449
\(784\) −60.9888 −2.17817
\(785\) 18.3768 0.655896
\(786\) −73.6094 −2.62556
\(787\) 17.5394 0.625213 0.312607 0.949883i \(-0.398798\pi\)
0.312607 + 0.949883i \(0.398798\pi\)
\(788\) −28.4668 −1.01409
\(789\) 34.8267 1.23986
\(790\) −19.6201 −0.698052
\(791\) −7.07627 −0.251603
\(792\) −42.1195 −1.49665
\(793\) 2.31101 0.0820663
\(794\) −45.4081 −1.61147
\(795\) 25.3602 0.899435
\(796\) 76.3072 2.70464
\(797\) −11.2655 −0.399044 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(798\) 19.2492 0.681414
\(799\) 26.1186 0.924011
\(800\) −38.8218 −1.37256
\(801\) −20.6202 −0.728578
\(802\) −18.6298 −0.657841
\(803\) 2.58809 0.0913318
\(804\) 18.0097 0.635152
\(805\) −15.6374 −0.551145
\(806\) −95.4146 −3.36084
\(807\) −15.9459 −0.561323
\(808\) −36.2499 −1.27527
\(809\) −1.43789 −0.0505534 −0.0252767 0.999680i \(-0.508047\pi\)
−0.0252767 + 0.999680i \(0.508047\pi\)
\(810\) −88.3192 −3.10322
\(811\) −39.2119 −1.37692 −0.688458 0.725276i \(-0.741712\pi\)
−0.688458 + 0.725276i \(0.741712\pi\)
\(812\) −3.06514 −0.107565
\(813\) 8.71092 0.305505
\(814\) −96.1725 −3.37084
\(815\) −22.2531 −0.779492
\(816\) −122.311 −4.28175
\(817\) −9.88663 −0.345889
\(818\) 52.8636 1.84833
\(819\) 3.80325 0.132896
\(820\) −40.5495 −1.41605
\(821\) 9.41950 0.328743 0.164371 0.986399i \(-0.447440\pi\)
0.164371 + 0.986399i \(0.447440\pi\)
\(822\) −45.3488 −1.58172
\(823\) −28.7149 −1.00094 −0.500470 0.865754i \(-0.666839\pi\)
−0.500470 + 0.865754i \(0.666839\pi\)
\(824\) −13.6439 −0.475308
\(825\) 36.6942 1.27753
\(826\) −17.9321 −0.623936
\(827\) 32.2145 1.12021 0.560104 0.828422i \(-0.310761\pi\)
0.560104 + 0.828422i \(0.310761\pi\)
\(828\) −60.8648 −2.11520
\(829\) −41.3853 −1.43737 −0.718685 0.695335i \(-0.755256\pi\)
−0.718685 + 0.695335i \(0.755256\pi\)
\(830\) 65.1800 2.26243
\(831\) 19.7353 0.684610
\(832\) −29.9174 −1.03720
\(833\) 42.7806 1.48226
\(834\) 90.6498 3.13895
\(835\) −22.7042 −0.785711
\(836\) 126.757 4.38400
\(837\) 25.3941 0.877748
\(838\) 73.6948 2.54575
\(839\) 31.6092 1.09127 0.545635 0.838023i \(-0.316289\pi\)
0.545635 + 0.838023i \(0.316289\pi\)
\(840\) −25.4925 −0.879575
\(841\) −27.6833 −0.954595
\(842\) 5.76788 0.198774
\(843\) −48.5577 −1.67242
\(844\) 54.7597 1.88491
\(845\) −32.6837 −1.12435
\(846\) 14.7303 0.506437
\(847\) −3.87488 −0.133142
\(848\) −36.5334 −1.25456
\(849\) −51.5922 −1.77064
\(850\) 68.8748 2.36238
\(851\) −80.5585 −2.76151
\(852\) −17.6296 −0.603981
\(853\) 26.9128 0.921477 0.460739 0.887536i \(-0.347585\pi\)
0.460739 + 0.887536i \(0.347585\pi\)
\(854\) −0.691180 −0.0236517
\(855\) −26.4276 −0.903806
\(856\) −84.8270 −2.89933
\(857\) 25.4512 0.869398 0.434699 0.900576i \(-0.356855\pi\)
0.434699 + 0.900576i \(0.356855\pi\)
\(858\) 112.436 3.83851
\(859\) 33.5688 1.14535 0.572676 0.819781i \(-0.305905\pi\)
0.572676 + 0.819781i \(0.305905\pi\)
\(860\) 22.5876 0.770231
\(861\) −3.31509 −0.112978
\(862\) 4.92893 0.167880
\(863\) 21.3439 0.726554 0.363277 0.931681i \(-0.381658\pi\)
0.363277 + 0.931681i \(0.381658\pi\)
\(864\) 31.6594 1.07707
\(865\) −15.8739 −0.539728
\(866\) 87.9256 2.98783
\(867\) 50.1829 1.70430
\(868\) 20.0916 0.681953
\(869\) −10.5626 −0.358312
\(870\) 18.8924 0.640511
\(871\) −8.81671 −0.298743
\(872\) −34.1729 −1.15724
\(873\) −10.2265 −0.346115
\(874\) 150.808 5.10116
\(875\) −1.45975 −0.0493485
\(876\) 6.09694 0.205997
\(877\) −32.2943 −1.09050 −0.545251 0.838273i \(-0.683566\pi\)
−0.545251 + 0.838273i \(0.683566\pi\)
\(878\) −16.4208 −0.554176
\(879\) 48.9038 1.64948
\(880\) −116.704 −3.93408
\(881\) 16.3456 0.550698 0.275349 0.961344i \(-0.411207\pi\)
0.275349 + 0.961344i \(0.411207\pi\)
\(882\) 24.1272 0.812406
\(883\) 7.21171 0.242693 0.121347 0.992610i \(-0.461279\pi\)
0.121347 + 0.992610i \(0.461279\pi\)
\(884\) 148.586 4.99750
\(885\) 77.8171 2.61579
\(886\) −50.7747 −1.70581
\(887\) 35.6173 1.19591 0.597956 0.801529i \(-0.295980\pi\)
0.597956 + 0.801529i \(0.295980\pi\)
\(888\) −131.329 −4.40711
\(889\) 11.4042 0.382485
\(890\) −116.727 −3.91271
\(891\) −47.5473 −1.59289
\(892\) 20.9428 0.701216
\(893\) −25.6968 −0.859910
\(894\) −51.2254 −1.71323
\(895\) 28.9330 0.967125
\(896\) −1.58106 −0.0528196
\(897\) 94.1818 3.14464
\(898\) 39.8401 1.32948
\(899\) −8.63109 −0.287863
\(900\) 27.3483 0.911609
\(901\) 25.6264 0.853738
\(902\) −31.0060 −1.03239
\(903\) 1.84663 0.0614520
\(904\) −90.3786 −3.00595
\(905\) 5.04677 0.167760
\(906\) 110.556 3.67297
\(907\) −49.0472 −1.62859 −0.814293 0.580454i \(-0.802875\pi\)
−0.814293 + 0.580454i \(0.802875\pi\)
\(908\) 71.0157 2.35674
\(909\) 7.01914 0.232810
\(910\) 21.5296 0.713699
\(911\) −45.6848 −1.51361 −0.756803 0.653643i \(-0.773240\pi\)
−0.756803 + 0.653643i \(0.773240\pi\)
\(912\) 120.336 3.98471
\(913\) 35.0901 1.16131
\(914\) 38.4131 1.27059
\(915\) 2.99941 0.0991576
\(916\) 19.9425 0.658917
\(917\) −7.58811 −0.250581
\(918\) −56.1678 −1.85381
\(919\) −12.9459 −0.427045 −0.213522 0.976938i \(-0.568494\pi\)
−0.213522 + 0.976938i \(0.568494\pi\)
\(920\) −199.721 −6.58462
\(921\) −27.5777 −0.908716
\(922\) 73.1307 2.40843
\(923\) 8.63067 0.284082
\(924\) −23.6758 −0.778878
\(925\) 36.1972 1.19016
\(926\) −43.4568 −1.42808
\(927\) 2.64190 0.0867715
\(928\) −10.7606 −0.353233
\(929\) −4.49235 −0.147389 −0.0736946 0.997281i \(-0.523479\pi\)
−0.0736946 + 0.997281i \(0.523479\pi\)
\(930\) −123.837 −4.06077
\(931\) −42.0896 −1.37943
\(932\) 6.28957 0.206022
\(933\) −37.9626 −1.24284
\(934\) 58.2592 1.90630
\(935\) 81.8618 2.67717
\(936\) 48.5754 1.58774
\(937\) −1.90994 −0.0623951 −0.0311975 0.999513i \(-0.509932\pi\)
−0.0311975 + 0.999513i \(0.509932\pi\)
\(938\) 2.63692 0.0860984
\(939\) 29.8086 0.972766
\(940\) 58.7085 1.91486
\(941\) −1.34900 −0.0439761 −0.0219881 0.999758i \(-0.507000\pi\)
−0.0219881 + 0.999758i \(0.507000\pi\)
\(942\) 33.1027 1.07854
\(943\) −25.9721 −0.845768
\(944\) −112.102 −3.64860
\(945\) −5.72999 −0.186397
\(946\) 17.2716 0.561547
\(947\) −23.5579 −0.765530 −0.382765 0.923846i \(-0.625028\pi\)
−0.382765 + 0.923846i \(0.625028\pi\)
\(948\) −24.8831 −0.808164
\(949\) −2.98478 −0.0968902
\(950\) −67.7623 −2.19850
\(951\) 1.47905 0.0479614
\(952\) −25.7600 −0.834887
\(953\) 44.6075 1.44498 0.722489 0.691383i \(-0.242998\pi\)
0.722489 + 0.691383i \(0.242998\pi\)
\(954\) 14.4526 0.467922
\(955\) −80.7509 −2.61304
\(956\) −17.0103 −0.550152
\(957\) 10.1708 0.328776
\(958\) 39.1584 1.26515
\(959\) −4.67484 −0.150958
\(960\) −38.8292 −1.25321
\(961\) 25.5756 0.825019
\(962\) 110.913 3.57599
\(963\) 16.4253 0.529296
\(964\) 69.0868 2.22514
\(965\) −51.8769 −1.66998
\(966\) −28.1680 −0.906292
\(967\) −8.74032 −0.281070 −0.140535 0.990076i \(-0.544882\pi\)
−0.140535 + 0.990076i \(0.544882\pi\)
\(968\) −49.4902 −1.59068
\(969\) −84.4095 −2.71162
\(970\) −57.8906 −1.85876
\(971\) 36.7867 1.18054 0.590271 0.807205i \(-0.299021\pi\)
0.590271 + 0.807205i \(0.299021\pi\)
\(972\) −63.8182 −2.04697
\(973\) 9.34474 0.299579
\(974\) −101.478 −3.25156
\(975\) −42.3185 −1.35528
\(976\) −4.32089 −0.138308
\(977\) −17.6031 −0.563172 −0.281586 0.959536i \(-0.590860\pi\)
−0.281586 + 0.959536i \(0.590860\pi\)
\(978\) −40.0851 −1.28178
\(979\) −62.8411 −2.00841
\(980\) 96.1606 3.07174
\(981\) 6.61699 0.211264
\(982\) −56.8596 −1.81446
\(983\) −50.6464 −1.61537 −0.807684 0.589615i \(-0.799279\pi\)
−0.807684 + 0.589615i \(0.799279\pi\)
\(984\) −42.3405 −1.34977
\(985\) 18.0873 0.576309
\(986\) 19.0906 0.607969
\(987\) 4.79966 0.152775
\(988\) −146.186 −4.65080
\(989\) 14.4675 0.460039
\(990\) 46.1681 1.46732
\(991\) 4.79288 0.152251 0.0761254 0.997098i \(-0.475745\pi\)
0.0761254 + 0.997098i \(0.475745\pi\)
\(992\) 70.5341 2.23946
\(993\) −3.14572 −0.0998264
\(994\) −2.58127 −0.0818730
\(995\) −48.4844 −1.53706
\(996\) 82.6642 2.61931
\(997\) 12.0839 0.382700 0.191350 0.981522i \(-0.438714\pi\)
0.191350 + 0.981522i \(0.438714\pi\)
\(998\) −53.0743 −1.68004
\(999\) −29.5190 −0.933940
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.1.2 18
3.2 odd 2 4923.2.a.l.1.17 18
4.3 odd 2 8752.2.a.s.1.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.2 18 1.1 even 1 trivial
4923.2.a.l.1.17 18 3.2 odd 2
8752.2.a.s.1.3 18 4.3 odd 2