Properties

Label 547.2.a.b.1.4
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 1.4
Root \(1.98431\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} +O(q^{10})\) \(q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} -5.71188 q^{10} +0.368123 q^{11} -0.290844 q^{12} -2.43844 q^{13} +5.32721 q^{14} -0.432105 q^{15} -4.12111 q^{16} -3.34729 q^{17} +5.90822 q^{18} +0.377567 q^{19} +5.57710 q^{20} +0.403005 q^{21} -0.730471 q^{22} -0.915445 q^{23} -0.0186202 q^{24} +3.28588 q^{25} +4.83862 q^{26} +0.897299 q^{27} -5.20151 q^{28} -2.06894 q^{29} +0.857431 q^{30} +5.88622 q^{31} +7.92949 q^{32} -0.0552603 q^{33} +6.64207 q^{34} -7.72786 q^{35} -5.76881 q^{36} -7.95740 q^{37} -0.749211 q^{38} +0.366043 q^{39} +0.357054 q^{40} -1.24111 q^{41} -0.799687 q^{42} +5.58190 q^{43} +0.713235 q^{44} -8.57070 q^{45} +1.81653 q^{46} -12.4681 q^{47} +0.618636 q^{48} +0.207426 q^{49} -6.52020 q^{50} +0.502474 q^{51} -4.72445 q^{52} -11.7975 q^{53} -1.78052 q^{54} +1.05965 q^{55} -0.333009 q^{56} -0.0566780 q^{57} +4.10542 q^{58} -13.7347 q^{59} -0.837199 q^{60} +1.64414 q^{61} -11.6801 q^{62} +7.99350 q^{63} -7.49234 q^{64} -7.01909 q^{65} +0.109654 q^{66} +5.77093 q^{67} -6.48534 q^{68} +0.137421 q^{69} +15.3345 q^{70} -7.47759 q^{71} -0.369328 q^{72} -10.4002 q^{73} +15.7900 q^{74} -0.493255 q^{75} +0.731532 q^{76} -0.988288 q^{77} -0.726343 q^{78} +0.641853 q^{79} -11.8627 q^{80} +8.79770 q^{81} +2.46275 q^{82} +15.7053 q^{83} +0.780818 q^{84} -9.63525 q^{85} -11.0762 q^{86} +0.310576 q^{87} +0.0456624 q^{88} +4.77332 q^{89} +17.0069 q^{90} +6.54639 q^{91} -1.77367 q^{92} -0.883602 q^{93} +24.7406 q^{94} +1.08683 q^{95} -1.19032 q^{96} -15.9649 q^{97} -0.411598 q^{98} -1.09607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98431 −1.40312 −0.701560 0.712611i \(-0.747513\pi\)
−0.701560 + 0.712611i \(0.747513\pi\)
\(3\) −0.150114 −0.0866682 −0.0433341 0.999061i \(-0.513798\pi\)
−0.0433341 + 0.999061i \(0.513798\pi\)
\(4\) 1.93749 0.968745
\(5\) 2.87852 1.28731 0.643657 0.765314i \(-0.277417\pi\)
0.643657 + 0.765314i \(0.277417\pi\)
\(6\) 0.297872 0.121606
\(7\) −2.68467 −1.01471 −0.507354 0.861738i \(-0.669376\pi\)
−0.507354 + 0.861738i \(0.669376\pi\)
\(8\) 0.124041 0.0438551
\(9\) −2.97747 −0.992489
\(10\) −5.71188 −1.80625
\(11\) 0.368123 0.110993 0.0554967 0.998459i \(-0.482326\pi\)
0.0554967 + 0.998459i \(0.482326\pi\)
\(12\) −0.290844 −0.0839593
\(13\) −2.43844 −0.676301 −0.338150 0.941092i \(-0.609801\pi\)
−0.338150 + 0.941092i \(0.609801\pi\)
\(14\) 5.32721 1.42376
\(15\) −0.432105 −0.111569
\(16\) −4.12111 −1.03028
\(17\) −3.34729 −0.811838 −0.405919 0.913909i \(-0.633048\pi\)
−0.405919 + 0.913909i \(0.633048\pi\)
\(18\) 5.90822 1.39258
\(19\) 0.377567 0.0866199 0.0433099 0.999062i \(-0.486210\pi\)
0.0433099 + 0.999062i \(0.486210\pi\)
\(20\) 5.57710 1.24708
\(21\) 0.403005 0.0879429
\(22\) −0.730471 −0.155737
\(23\) −0.915445 −0.190884 −0.0954418 0.995435i \(-0.530426\pi\)
−0.0954418 + 0.995435i \(0.530426\pi\)
\(24\) −0.0186202 −0.00380084
\(25\) 3.28588 0.657175
\(26\) 4.83862 0.948931
\(27\) 0.897299 0.172685
\(28\) −5.20151 −0.982993
\(29\) −2.06894 −0.384192 −0.192096 0.981376i \(-0.561529\pi\)
−0.192096 + 0.981376i \(0.561529\pi\)
\(30\) 0.857431 0.156545
\(31\) 5.88622 1.05720 0.528598 0.848872i \(-0.322718\pi\)
0.528598 + 0.848872i \(0.322718\pi\)
\(32\) 7.92949 1.40175
\(33\) −0.0552603 −0.00961959
\(34\) 6.64207 1.13911
\(35\) −7.72786 −1.30625
\(36\) −5.76881 −0.961468
\(37\) −7.95740 −1.30819 −0.654094 0.756413i \(-0.726950\pi\)
−0.654094 + 0.756413i \(0.726950\pi\)
\(38\) −0.749211 −0.121538
\(39\) 0.366043 0.0586138
\(40\) 0.357054 0.0564553
\(41\) −1.24111 −0.193829 −0.0969145 0.995293i \(-0.530897\pi\)
−0.0969145 + 0.995293i \(0.530897\pi\)
\(42\) −0.799687 −0.123394
\(43\) 5.58190 0.851232 0.425616 0.904904i \(-0.360057\pi\)
0.425616 + 0.904904i \(0.360057\pi\)
\(44\) 0.713235 0.107524
\(45\) −8.57070 −1.27764
\(46\) 1.81653 0.267832
\(47\) −12.4681 −1.81866 −0.909329 0.416077i \(-0.863405\pi\)
−0.909329 + 0.416077i \(0.863405\pi\)
\(48\) 0.618636 0.0892924
\(49\) 0.207426 0.0296323
\(50\) −6.52020 −0.922096
\(51\) 0.502474 0.0703605
\(52\) −4.72445 −0.655163
\(53\) −11.7975 −1.62052 −0.810258 0.586074i \(-0.800673\pi\)
−0.810258 + 0.586074i \(0.800673\pi\)
\(54\) −1.78052 −0.242298
\(55\) 1.05965 0.142883
\(56\) −0.333009 −0.0445001
\(57\) −0.0566780 −0.00750719
\(58\) 4.10542 0.539068
\(59\) −13.7347 −1.78810 −0.894051 0.447964i \(-0.852149\pi\)
−0.894051 + 0.447964i \(0.852149\pi\)
\(60\) −0.837199 −0.108082
\(61\) 1.64414 0.210511 0.105255 0.994445i \(-0.466434\pi\)
0.105255 + 0.994445i \(0.466434\pi\)
\(62\) −11.6801 −1.48337
\(63\) 7.99350 1.00709
\(64\) −7.49234 −0.936543
\(65\) −7.01909 −0.870611
\(66\) 0.109654 0.0134974
\(67\) 5.77093 0.705031 0.352515 0.935806i \(-0.385326\pi\)
0.352515 + 0.935806i \(0.385326\pi\)
\(68\) −6.48534 −0.786463
\(69\) 0.137421 0.0165435
\(70\) 15.3345 1.83282
\(71\) −7.47759 −0.887426 −0.443713 0.896169i \(-0.646339\pi\)
−0.443713 + 0.896169i \(0.646339\pi\)
\(72\) −0.369328 −0.0435257
\(73\) −10.4002 −1.21725 −0.608625 0.793458i \(-0.708279\pi\)
−0.608625 + 0.793458i \(0.708279\pi\)
\(74\) 15.7900 1.83555
\(75\) −0.493255 −0.0569562
\(76\) 0.731532 0.0839125
\(77\) −0.988288 −0.112626
\(78\) −0.726343 −0.0822421
\(79\) 0.641853 0.0722141 0.0361070 0.999348i \(-0.488504\pi\)
0.0361070 + 0.999348i \(0.488504\pi\)
\(80\) −11.8627 −1.32629
\(81\) 8.79770 0.977522
\(82\) 2.46275 0.271965
\(83\) 15.7053 1.72388 0.861942 0.507006i \(-0.169248\pi\)
0.861942 + 0.507006i \(0.169248\pi\)
\(84\) 0.780818 0.0851942
\(85\) −9.63525 −1.04509
\(86\) −11.0762 −1.19438
\(87\) 0.310576 0.0332972
\(88\) 0.0456624 0.00486763
\(89\) 4.77332 0.505971 0.252986 0.967470i \(-0.418587\pi\)
0.252986 + 0.967470i \(0.418587\pi\)
\(90\) 17.0069 1.79269
\(91\) 6.54639 0.686248
\(92\) −1.77367 −0.184917
\(93\) −0.883602 −0.0916253
\(94\) 24.7406 2.55180
\(95\) 1.08683 0.111507
\(96\) −1.19032 −0.121487
\(97\) −15.9649 −1.62099 −0.810497 0.585742i \(-0.800803\pi\)
−0.810497 + 0.585742i \(0.800803\pi\)
\(98\) −0.411598 −0.0415777
\(99\) −1.09607 −0.110160
\(100\) 6.36635 0.636635
\(101\) 13.4395 1.33728 0.668642 0.743585i \(-0.266876\pi\)
0.668642 + 0.743585i \(0.266876\pi\)
\(102\) −0.997065 −0.0987242
\(103\) 8.31399 0.819202 0.409601 0.912265i \(-0.365668\pi\)
0.409601 + 0.912265i \(0.365668\pi\)
\(104\) −0.302466 −0.0296593
\(105\) 1.16006 0.113210
\(106\) 23.4100 2.27378
\(107\) 1.14891 0.111069 0.0555347 0.998457i \(-0.482314\pi\)
0.0555347 + 0.998457i \(0.482314\pi\)
\(108\) 1.73851 0.167288
\(109\) 8.92809 0.855156 0.427578 0.903978i \(-0.359367\pi\)
0.427578 + 0.903978i \(0.359367\pi\)
\(110\) −2.10268 −0.200482
\(111\) 1.19451 0.113378
\(112\) 11.0638 1.04543
\(113\) −8.71949 −0.820260 −0.410130 0.912027i \(-0.634517\pi\)
−0.410130 + 0.912027i \(0.634517\pi\)
\(114\) 0.112467 0.0105335
\(115\) −2.63513 −0.245727
\(116\) −4.00855 −0.372184
\(117\) 7.26037 0.671221
\(118\) 27.2539 2.50892
\(119\) 8.98636 0.823778
\(120\) −0.0535988 −0.00489287
\(121\) −10.8645 −0.987680
\(122\) −3.26248 −0.295371
\(123\) 0.186308 0.0167988
\(124\) 11.4045 1.02415
\(125\) −4.93414 −0.441323
\(126\) −15.8616 −1.41306
\(127\) −2.33627 −0.207310 −0.103655 0.994613i \(-0.533054\pi\)
−0.103655 + 0.994613i \(0.533054\pi\)
\(128\) −0.991843 −0.0876674
\(129\) −0.837920 −0.0737747
\(130\) 13.9281 1.22157
\(131\) −1.82810 −0.159722 −0.0798610 0.996806i \(-0.525448\pi\)
−0.0798610 + 0.996806i \(0.525448\pi\)
\(132\) −0.107066 −0.00931893
\(133\) −1.01364 −0.0878939
\(134\) −11.4513 −0.989243
\(135\) 2.58289 0.222300
\(136\) −0.415202 −0.0356032
\(137\) −13.2541 −1.13238 −0.566188 0.824276i \(-0.691582\pi\)
−0.566188 + 0.824276i \(0.691582\pi\)
\(138\) −0.272686 −0.0232125
\(139\) 11.3648 0.963953 0.481976 0.876184i \(-0.339919\pi\)
0.481976 + 0.876184i \(0.339919\pi\)
\(140\) −14.9726 −1.26542
\(141\) 1.87163 0.157620
\(142\) 14.8379 1.24516
\(143\) −0.897646 −0.0750649
\(144\) 12.2705 1.02254
\(145\) −5.95548 −0.494576
\(146\) 20.6372 1.70795
\(147\) −0.0311375 −0.00256818
\(148\) −15.4174 −1.26730
\(149\) 6.54097 0.535857 0.267929 0.963439i \(-0.413661\pi\)
0.267929 + 0.963439i \(0.413661\pi\)
\(150\) 0.978771 0.0799164
\(151\) 10.4153 0.847586 0.423793 0.905759i \(-0.360698\pi\)
0.423793 + 0.905759i \(0.360698\pi\)
\(152\) 0.0468338 0.00379872
\(153\) 9.96645 0.805740
\(154\) 1.96107 0.158028
\(155\) 16.9436 1.36094
\(156\) 0.709204 0.0567818
\(157\) 9.34946 0.746168 0.373084 0.927797i \(-0.378300\pi\)
0.373084 + 0.927797i \(0.378300\pi\)
\(158\) −1.27364 −0.101325
\(159\) 1.77097 0.140447
\(160\) 22.8252 1.80449
\(161\) 2.45766 0.193691
\(162\) −17.4574 −1.37158
\(163\) 7.10285 0.556338 0.278169 0.960532i \(-0.410272\pi\)
0.278169 + 0.960532i \(0.410272\pi\)
\(164\) −2.40464 −0.187771
\(165\) −0.159068 −0.0123834
\(166\) −31.1643 −2.41882
\(167\) −10.3824 −0.803411 −0.401705 0.915769i \(-0.631582\pi\)
−0.401705 + 0.915769i \(0.631582\pi\)
\(168\) 0.0499891 0.00385675
\(169\) −7.05402 −0.542617
\(170\) 19.1193 1.46639
\(171\) −1.12419 −0.0859692
\(172\) 10.8149 0.824626
\(173\) −4.93534 −0.375227 −0.187614 0.982243i \(-0.560075\pi\)
−0.187614 + 0.982243i \(0.560075\pi\)
\(174\) −0.616279 −0.0467200
\(175\) −8.82148 −0.666841
\(176\) −1.51708 −0.114354
\(177\) 2.06176 0.154972
\(178\) −9.47175 −0.709938
\(179\) 17.2958 1.29275 0.646375 0.763020i \(-0.276284\pi\)
0.646375 + 0.763020i \(0.276284\pi\)
\(180\) −16.6056 −1.23771
\(181\) 17.2065 1.27895 0.639476 0.768811i \(-0.279152\pi\)
0.639476 + 0.768811i \(0.279152\pi\)
\(182\) −12.9901 −0.962888
\(183\) −0.246808 −0.0182446
\(184\) −0.113553 −0.00837122
\(185\) −22.9055 −1.68405
\(186\) 1.75334 0.128561
\(187\) −1.23222 −0.0901086
\(188\) −24.1568 −1.76182
\(189\) −2.40895 −0.175225
\(190\) −2.15662 −0.156458
\(191\) −0.969679 −0.0701635 −0.0350817 0.999384i \(-0.511169\pi\)
−0.0350817 + 0.999384i \(0.511169\pi\)
\(192\) 1.12470 0.0811684
\(193\) 7.21747 0.519525 0.259763 0.965673i \(-0.416356\pi\)
0.259763 + 0.965673i \(0.416356\pi\)
\(194\) 31.6794 2.27445
\(195\) 1.05366 0.0754543
\(196\) 0.401886 0.0287062
\(197\) −7.29036 −0.519417 −0.259708 0.965687i \(-0.583626\pi\)
−0.259708 + 0.965687i \(0.583626\pi\)
\(198\) 2.17495 0.154567
\(199\) −6.97295 −0.494299 −0.247150 0.968977i \(-0.579494\pi\)
−0.247150 + 0.968977i \(0.579494\pi\)
\(200\) 0.407583 0.0288205
\(201\) −0.866295 −0.0611037
\(202\) −26.6682 −1.87637
\(203\) 5.55441 0.389843
\(204\) 0.973539 0.0681613
\(205\) −3.57256 −0.249519
\(206\) −16.4975 −1.14944
\(207\) 2.72571 0.189450
\(208\) 10.0491 0.696778
\(209\) 0.138991 0.00961423
\(210\) −2.30192 −0.158847
\(211\) 2.25378 0.155157 0.0775784 0.996986i \(-0.475281\pi\)
0.0775784 + 0.996986i \(0.475281\pi\)
\(212\) −22.8576 −1.56987
\(213\) 1.12249 0.0769116
\(214\) −2.27979 −0.155844
\(215\) 16.0676 1.09580
\(216\) 0.111302 0.00757314
\(217\) −15.8025 −1.07275
\(218\) −17.7161 −1.19989
\(219\) 1.56121 0.105497
\(220\) 2.05306 0.138417
\(221\) 8.16217 0.549047
\(222\) −2.37029 −0.159083
\(223\) −5.31003 −0.355586 −0.177793 0.984068i \(-0.556896\pi\)
−0.177793 + 0.984068i \(0.556896\pi\)
\(224\) −21.2880 −1.42237
\(225\) −9.78359 −0.652239
\(226\) 17.3022 1.15092
\(227\) −2.18872 −0.145271 −0.0726354 0.997359i \(-0.523141\pi\)
−0.0726354 + 0.997359i \(0.523141\pi\)
\(228\) −0.109813 −0.00727254
\(229\) 4.87556 0.322186 0.161093 0.986939i \(-0.448498\pi\)
0.161093 + 0.986939i \(0.448498\pi\)
\(230\) 5.22891 0.344784
\(231\) 0.148356 0.00976108
\(232\) −0.256633 −0.0168488
\(233\) −15.8464 −1.03813 −0.519066 0.854734i \(-0.673720\pi\)
−0.519066 + 0.854734i \(0.673720\pi\)
\(234\) −14.4068 −0.941803
\(235\) −35.8897 −2.34118
\(236\) −26.6108 −1.73221
\(237\) −0.0963509 −0.00625866
\(238\) −17.8317 −1.15586
\(239\) 24.8660 1.60845 0.804223 0.594328i \(-0.202582\pi\)
0.804223 + 0.594328i \(0.202582\pi\)
\(240\) 1.78075 0.114947
\(241\) 17.9529 1.15645 0.578223 0.815879i \(-0.303746\pi\)
0.578223 + 0.815879i \(0.303746\pi\)
\(242\) 21.5585 1.38583
\(243\) −4.01255 −0.257405
\(244\) 3.18550 0.203931
\(245\) 0.597081 0.0381461
\(246\) −0.369693 −0.0235707
\(247\) −0.920674 −0.0585811
\(248\) 0.730133 0.0463635
\(249\) −2.35759 −0.149406
\(250\) 9.79086 0.619228
\(251\) 1.86475 0.117702 0.0588509 0.998267i \(-0.481256\pi\)
0.0588509 + 0.998267i \(0.481256\pi\)
\(252\) 15.4873 0.975609
\(253\) −0.336997 −0.0211868
\(254\) 4.63588 0.290881
\(255\) 1.44638 0.0905760
\(256\) 16.9528 1.05955
\(257\) 2.57803 0.160813 0.0804066 0.996762i \(-0.474378\pi\)
0.0804066 + 0.996762i \(0.474378\pi\)
\(258\) 1.66269 0.103515
\(259\) 21.3630 1.32743
\(260\) −13.5994 −0.843400
\(261\) 6.16019 0.381306
\(262\) 3.62752 0.224109
\(263\) 5.06765 0.312484 0.156242 0.987719i \(-0.450062\pi\)
0.156242 + 0.987719i \(0.450062\pi\)
\(264\) −0.00685455 −0.000421868 0
\(265\) −33.9594 −2.08611
\(266\) 2.01138 0.123326
\(267\) −0.716541 −0.0438516
\(268\) 11.1811 0.682995
\(269\) −10.2521 −0.625082 −0.312541 0.949904i \(-0.601180\pi\)
−0.312541 + 0.949904i \(0.601180\pi\)
\(270\) −5.12526 −0.311914
\(271\) −26.7152 −1.62283 −0.811415 0.584470i \(-0.801302\pi\)
−0.811415 + 0.584470i \(0.801302\pi\)
\(272\) 13.7946 0.836419
\(273\) −0.982703 −0.0594759
\(274\) 26.3003 1.58886
\(275\) 1.20961 0.0729421
\(276\) 0.266251 0.0160265
\(277\) 9.61574 0.577754 0.288877 0.957366i \(-0.406718\pi\)
0.288877 + 0.957366i \(0.406718\pi\)
\(278\) −22.5514 −1.35254
\(279\) −17.5260 −1.04926
\(280\) −0.958572 −0.0572856
\(281\) 22.9906 1.37150 0.685751 0.727837i \(-0.259474\pi\)
0.685751 + 0.727837i \(0.259474\pi\)
\(282\) −3.71390 −0.221159
\(283\) 8.48049 0.504113 0.252056 0.967713i \(-0.418893\pi\)
0.252056 + 0.967713i \(0.418893\pi\)
\(284\) −14.4877 −0.859689
\(285\) −0.163149 −0.00966410
\(286\) 1.78121 0.105325
\(287\) 3.33197 0.196680
\(288\) −23.6098 −1.39122
\(289\) −5.79563 −0.340919
\(290\) 11.8175 0.693949
\(291\) 2.39656 0.140489
\(292\) −20.1503 −1.17921
\(293\) −11.3819 −0.664937 −0.332468 0.943114i \(-0.607881\pi\)
−0.332468 + 0.943114i \(0.607881\pi\)
\(294\) 0.0617865 0.00360346
\(295\) −39.5355 −2.30185
\(296\) −0.987044 −0.0573708
\(297\) 0.330317 0.0191669
\(298\) −12.9793 −0.751872
\(299\) 2.23226 0.129095
\(300\) −0.955676 −0.0551760
\(301\) −14.9855 −0.863752
\(302\) −20.6672 −1.18927
\(303\) −2.01746 −0.115900
\(304\) −1.55600 −0.0892426
\(305\) 4.73269 0.270993
\(306\) −19.7765 −1.13055
\(307\) −5.38784 −0.307500 −0.153750 0.988110i \(-0.549135\pi\)
−0.153750 + 0.988110i \(0.549135\pi\)
\(308\) −1.91480 −0.109106
\(309\) −1.24804 −0.0709987
\(310\) −33.6214 −1.90957
\(311\) −20.0317 −1.13589 −0.567947 0.823065i \(-0.692262\pi\)
−0.567947 + 0.823065i \(0.692262\pi\)
\(312\) 0.0454043 0.00257051
\(313\) 27.9448 1.57953 0.789766 0.613408i \(-0.210202\pi\)
0.789766 + 0.613408i \(0.210202\pi\)
\(314\) −18.5522 −1.04696
\(315\) 23.0094 1.29644
\(316\) 1.24358 0.0699570
\(317\) 4.64368 0.260815 0.130408 0.991460i \(-0.458371\pi\)
0.130408 + 0.991460i \(0.458371\pi\)
\(318\) −3.51416 −0.197064
\(319\) −0.761625 −0.0426428
\(320\) −21.5669 −1.20562
\(321\) −0.172467 −0.00962618
\(322\) −4.87677 −0.271772
\(323\) −1.26383 −0.0703213
\(324\) 17.0454 0.946969
\(325\) −8.01241 −0.444448
\(326\) −14.0943 −0.780609
\(327\) −1.34023 −0.0741148
\(328\) −0.153949 −0.00850039
\(329\) 33.4727 1.84541
\(330\) 0.315640 0.0173754
\(331\) 6.20064 0.340818 0.170409 0.985373i \(-0.445491\pi\)
0.170409 + 0.985373i \(0.445491\pi\)
\(332\) 30.4289 1.67000
\(333\) 23.6929 1.29836
\(334\) 20.6018 1.12728
\(335\) 16.6117 0.907596
\(336\) −1.66083 −0.0906057
\(337\) −5.35112 −0.291494 −0.145747 0.989322i \(-0.546559\pi\)
−0.145747 + 0.989322i \(0.546559\pi\)
\(338\) 13.9974 0.761357
\(339\) 1.30891 0.0710905
\(340\) −18.6682 −1.01242
\(341\) 2.16686 0.117342
\(342\) 2.23075 0.120625
\(343\) 18.2358 0.984640
\(344\) 0.692384 0.0373309
\(345\) 0.395569 0.0212967
\(346\) 9.79326 0.526489
\(347\) −23.3962 −1.25597 −0.627987 0.778224i \(-0.716121\pi\)
−0.627987 + 0.778224i \(0.716121\pi\)
\(348\) 0.601738 0.0322565
\(349\) 15.4705 0.828119 0.414060 0.910250i \(-0.364111\pi\)
0.414060 + 0.910250i \(0.364111\pi\)
\(350\) 17.5046 0.935658
\(351\) −2.18801 −0.116787
\(352\) 2.91903 0.155585
\(353\) 26.3066 1.40016 0.700079 0.714066i \(-0.253148\pi\)
0.700079 + 0.714066i \(0.253148\pi\)
\(354\) −4.09118 −0.217444
\(355\) −21.5244 −1.14240
\(356\) 9.24826 0.490157
\(357\) −1.34898 −0.0713954
\(358\) −34.3203 −1.81388
\(359\) −36.8814 −1.94652 −0.973262 0.229698i \(-0.926226\pi\)
−0.973262 + 0.229698i \(0.926226\pi\)
\(360\) −1.06312 −0.0560312
\(361\) −18.8574 −0.992497
\(362\) −34.1431 −1.79452
\(363\) 1.63091 0.0856005
\(364\) 12.6836 0.664799
\(365\) −29.9372 −1.56698
\(366\) 0.489744 0.0255993
\(367\) 20.8701 1.08941 0.544706 0.838627i \(-0.316641\pi\)
0.544706 + 0.838627i \(0.316641\pi\)
\(368\) 3.77265 0.196663
\(369\) 3.69537 0.192373
\(370\) 45.4517 2.36292
\(371\) 31.6724 1.64435
\(372\) −1.71197 −0.0887615
\(373\) −18.4400 −0.954786 −0.477393 0.878690i \(-0.658418\pi\)
−0.477393 + 0.878690i \(0.658418\pi\)
\(374\) 2.44510 0.126433
\(375\) 0.740681 0.0382486
\(376\) −1.54656 −0.0797575
\(377\) 5.04498 0.259830
\(378\) 4.78010 0.245862
\(379\) 13.2372 0.679947 0.339974 0.940435i \(-0.389582\pi\)
0.339974 + 0.940435i \(0.389582\pi\)
\(380\) 2.10573 0.108022
\(381\) 0.350706 0.0179672
\(382\) 1.92414 0.0984478
\(383\) −3.10284 −0.158548 −0.0792738 0.996853i \(-0.525260\pi\)
−0.0792738 + 0.996853i \(0.525260\pi\)
\(384\) 0.148889 0.00759797
\(385\) −2.84481 −0.144985
\(386\) −14.3217 −0.728956
\(387\) −16.6199 −0.844838
\(388\) −30.9319 −1.57033
\(389\) 0.502131 0.0254591 0.0127295 0.999919i \(-0.495948\pi\)
0.0127295 + 0.999919i \(0.495948\pi\)
\(390\) −2.09079 −0.105871
\(391\) 3.06426 0.154966
\(392\) 0.0257294 0.00129953
\(393\) 0.274423 0.0138428
\(394\) 14.4663 0.728803
\(395\) 1.84759 0.0929622
\(396\) −2.12363 −0.106717
\(397\) −6.23481 −0.312916 −0.156458 0.987685i \(-0.550008\pi\)
−0.156458 + 0.987685i \(0.550008\pi\)
\(398\) 13.8365 0.693561
\(399\) 0.152161 0.00761760
\(400\) −13.5415 −0.677074
\(401\) −12.4398 −0.621216 −0.310608 0.950538i \(-0.600533\pi\)
−0.310608 + 0.950538i \(0.600533\pi\)
\(402\) 1.71900 0.0857359
\(403\) −14.3532 −0.714983
\(404\) 26.0390 1.29549
\(405\) 25.3244 1.25838
\(406\) −11.0217 −0.546996
\(407\) −2.92931 −0.145200
\(408\) 0.0623274 0.00308567
\(409\) 20.4619 1.01178 0.505888 0.862599i \(-0.331165\pi\)
0.505888 + 0.862599i \(0.331165\pi\)
\(410\) 7.08908 0.350105
\(411\) 1.98962 0.0981409
\(412\) 16.1083 0.793597
\(413\) 36.8730 1.81440
\(414\) −5.40865 −0.265821
\(415\) 45.2081 2.21918
\(416\) −19.3356 −0.948004
\(417\) −1.70602 −0.0835440
\(418\) −0.275802 −0.0134899
\(419\) 28.1633 1.37587 0.687933 0.725774i \(-0.258518\pi\)
0.687933 + 0.725774i \(0.258518\pi\)
\(420\) 2.24760 0.109672
\(421\) 30.5281 1.48785 0.743924 0.668264i \(-0.232962\pi\)
0.743924 + 0.668264i \(0.232962\pi\)
\(422\) −4.47220 −0.217703
\(423\) 37.1233 1.80500
\(424\) −1.46338 −0.0710679
\(425\) −10.9988 −0.533520
\(426\) −2.22736 −0.107916
\(427\) −4.41397 −0.213607
\(428\) 2.22600 0.107598
\(429\) 0.134749 0.00650574
\(430\) −31.8831 −1.53754
\(431\) 25.7216 1.23897 0.619483 0.785010i \(-0.287342\pi\)
0.619483 + 0.785010i \(0.287342\pi\)
\(432\) −3.69787 −0.177914
\(433\) 23.1151 1.11084 0.555420 0.831570i \(-0.312557\pi\)
0.555420 + 0.831570i \(0.312557\pi\)
\(434\) 31.3571 1.50519
\(435\) 0.893999 0.0428640
\(436\) 17.2981 0.828428
\(437\) −0.345642 −0.0165343
\(438\) −3.09793 −0.148025
\(439\) −32.1881 −1.53626 −0.768128 0.640296i \(-0.778812\pi\)
−0.768128 + 0.640296i \(0.778812\pi\)
\(440\) 0.131440 0.00626616
\(441\) −0.617605 −0.0294098
\(442\) −16.1963 −0.770378
\(443\) −3.71749 −0.176623 −0.0883117 0.996093i \(-0.528147\pi\)
−0.0883117 + 0.996093i \(0.528147\pi\)
\(444\) 2.31436 0.109835
\(445\) 13.7401 0.651343
\(446\) 10.5367 0.498929
\(447\) −0.981889 −0.0464418
\(448\) 20.1144 0.950317
\(449\) 21.5153 1.01537 0.507686 0.861542i \(-0.330501\pi\)
0.507686 + 0.861542i \(0.330501\pi\)
\(450\) 19.4137 0.915170
\(451\) −0.456882 −0.0215137
\(452\) −16.8939 −0.794623
\(453\) −1.56348 −0.0734588
\(454\) 4.34311 0.203832
\(455\) 18.8439 0.883416
\(456\) −0.00703040 −0.000329228 0
\(457\) −33.1622 −1.55126 −0.775630 0.631187i \(-0.782568\pi\)
−0.775630 + 0.631187i \(0.782568\pi\)
\(458\) −9.67463 −0.452066
\(459\) −3.00352 −0.140192
\(460\) −5.10553 −0.238047
\(461\) −24.3478 −1.13399 −0.566994 0.823722i \(-0.691894\pi\)
−0.566994 + 0.823722i \(0.691894\pi\)
\(462\) −0.294383 −0.0136960
\(463\) 7.49196 0.348181 0.174090 0.984730i \(-0.444301\pi\)
0.174090 + 0.984730i \(0.444301\pi\)
\(464\) 8.52633 0.395825
\(465\) −2.54347 −0.117950
\(466\) 31.4442 1.45662
\(467\) −13.2796 −0.614504 −0.307252 0.951628i \(-0.599410\pi\)
−0.307252 + 0.951628i \(0.599410\pi\)
\(468\) 14.0669 0.650242
\(469\) −15.4930 −0.715401
\(470\) 71.2163 3.28496
\(471\) −1.40348 −0.0646690
\(472\) −1.70366 −0.0784174
\(473\) 2.05483 0.0944811
\(474\) 0.191190 0.00878165
\(475\) 1.24064 0.0569244
\(476\) 17.4110 0.798031
\(477\) 35.1268 1.60834
\(478\) −49.3418 −2.25684
\(479\) 12.1494 0.555122 0.277561 0.960708i \(-0.410474\pi\)
0.277561 + 0.960708i \(0.410474\pi\)
\(480\) −3.42637 −0.156392
\(481\) 19.4036 0.884729
\(482\) −35.6241 −1.62263
\(483\) −0.368929 −0.0167869
\(484\) −21.0498 −0.956810
\(485\) −45.9554 −2.08673
\(486\) 7.96215 0.361171
\(487\) −10.7245 −0.485974 −0.242987 0.970029i \(-0.578127\pi\)
−0.242987 + 0.970029i \(0.578127\pi\)
\(488\) 0.203941 0.00923196
\(489\) −1.06623 −0.0482168
\(490\) −1.18479 −0.0535235
\(491\) −28.6725 −1.29397 −0.646985 0.762503i \(-0.723970\pi\)
−0.646985 + 0.762503i \(0.723970\pi\)
\(492\) 0.360969 0.0162738
\(493\) 6.92534 0.311902
\(494\) 1.82690 0.0821963
\(495\) −3.15507 −0.141810
\(496\) −24.2578 −1.08921
\(497\) 20.0748 0.900478
\(498\) 4.67818 0.209634
\(499\) −10.6822 −0.478203 −0.239102 0.970995i \(-0.576853\pi\)
−0.239102 + 0.970995i \(0.576853\pi\)
\(500\) −9.55984 −0.427529
\(501\) 1.55853 0.0696301
\(502\) −3.70024 −0.165150
\(503\) 33.7672 1.50561 0.752803 0.658245i \(-0.228701\pi\)
0.752803 + 0.658245i \(0.228701\pi\)
\(504\) 0.991521 0.0441659
\(505\) 38.6860 1.72150
\(506\) 0.668706 0.0297276
\(507\) 1.05891 0.0470276
\(508\) −4.52650 −0.200831
\(509\) −16.5306 −0.732704 −0.366352 0.930476i \(-0.619393\pi\)
−0.366352 + 0.930476i \(0.619393\pi\)
\(510\) −2.87007 −0.127089
\(511\) 27.9210 1.23515
\(512\) −31.6560 −1.39901
\(513\) 0.338791 0.0149580
\(514\) −5.11562 −0.225640
\(515\) 23.9320 1.05457
\(516\) −1.62346 −0.0714688
\(517\) −4.58980 −0.201859
\(518\) −42.3908 −1.86254
\(519\) 0.740863 0.0325203
\(520\) −0.870655 −0.0381808
\(521\) −30.3577 −1.33000 −0.664999 0.746845i \(-0.731568\pi\)
−0.664999 + 0.746845i \(0.731568\pi\)
\(522\) −12.2237 −0.535019
\(523\) −16.6911 −0.729851 −0.364925 0.931037i \(-0.618905\pi\)
−0.364925 + 0.931037i \(0.618905\pi\)
\(524\) −3.54193 −0.154730
\(525\) 1.32422 0.0577939
\(526\) −10.0558 −0.438453
\(527\) −19.7029 −0.858272
\(528\) 0.227734 0.00991086
\(529\) −22.1620 −0.963563
\(530\) 67.3861 2.92706
\(531\) 40.8945 1.77467
\(532\) −1.96392 −0.0851467
\(533\) 3.02637 0.131087
\(534\) 1.42184 0.0615290
\(535\) 3.30716 0.142981
\(536\) 0.715831 0.0309192
\(537\) −2.59634 −0.112040
\(538\) 20.3434 0.877065
\(539\) 0.0763585 0.00328899
\(540\) 5.00433 0.215352
\(541\) −36.1017 −1.55213 −0.776067 0.630650i \(-0.782788\pi\)
−0.776067 + 0.630650i \(0.782788\pi\)
\(542\) 53.0112 2.27702
\(543\) −2.58294 −0.110844
\(544\) −26.5423 −1.13799
\(545\) 25.6997 1.10085
\(546\) 1.94999 0.0834517
\(547\) −1.00000 −0.0427569
\(548\) −25.6797 −1.09698
\(549\) −4.89537 −0.208929
\(550\) −2.40024 −0.102347
\(551\) −0.781163 −0.0332787
\(552\) 0.0170458 0.000725518 0
\(553\) −1.72316 −0.0732762
\(554\) −19.0806 −0.810658
\(555\) 3.43844 0.145953
\(556\) 22.0192 0.933824
\(557\) 2.18856 0.0927321 0.0463661 0.998925i \(-0.485236\pi\)
0.0463661 + 0.998925i \(0.485236\pi\)
\(558\) 34.7771 1.47223
\(559\) −13.6111 −0.575689
\(560\) 31.8474 1.34580
\(561\) 0.184973 0.00780955
\(562\) −45.6204 −1.92438
\(563\) −23.1881 −0.977260 −0.488630 0.872491i \(-0.662503\pi\)
−0.488630 + 0.872491i \(0.662503\pi\)
\(564\) 3.62627 0.152693
\(565\) −25.0992 −1.05593
\(566\) −16.8279 −0.707331
\(567\) −23.6189 −0.991900
\(568\) −0.927527 −0.0389182
\(569\) −7.55092 −0.316551 −0.158276 0.987395i \(-0.550593\pi\)
−0.158276 + 0.987395i \(0.550593\pi\)
\(570\) 0.323738 0.0135599
\(571\) −2.22139 −0.0929621 −0.0464810 0.998919i \(-0.514801\pi\)
−0.0464810 + 0.998919i \(0.514801\pi\)
\(572\) −1.73918 −0.0727187
\(573\) 0.145562 0.00608094
\(574\) −6.61166 −0.275965
\(575\) −3.00804 −0.125444
\(576\) 22.3082 0.929508
\(577\) 23.8362 0.992314 0.496157 0.868233i \(-0.334744\pi\)
0.496157 + 0.868233i \(0.334744\pi\)
\(578\) 11.5003 0.478351
\(579\) −1.08344 −0.0450263
\(580\) −11.5387 −0.479118
\(581\) −42.1636 −1.74924
\(582\) −4.75551 −0.197122
\(583\) −4.34295 −0.179866
\(584\) −1.29005 −0.0533827
\(585\) 20.8991 0.864072
\(586\) 22.5852 0.932986
\(587\) 29.6166 1.22241 0.611204 0.791473i \(-0.290685\pi\)
0.611204 + 0.791473i \(0.290685\pi\)
\(588\) −0.0603286 −0.00248791
\(589\) 2.22244 0.0915742
\(590\) 78.4508 3.22977
\(591\) 1.09438 0.0450169
\(592\) 32.7934 1.34780
\(593\) −40.2054 −1.65104 −0.825520 0.564373i \(-0.809118\pi\)
−0.825520 + 0.564373i \(0.809118\pi\)
\(594\) −0.655451 −0.0268935
\(595\) 25.8674 1.06046
\(596\) 12.6731 0.519109
\(597\) 1.04673 0.0428400
\(598\) −4.42949 −0.181135
\(599\) −24.9569 −1.01971 −0.509856 0.860259i \(-0.670301\pi\)
−0.509856 + 0.860259i \(0.670301\pi\)
\(600\) −0.0611839 −0.00249782
\(601\) −30.2445 −1.23370 −0.616850 0.787081i \(-0.711591\pi\)
−0.616850 + 0.787081i \(0.711591\pi\)
\(602\) 29.7360 1.21195
\(603\) −17.1827 −0.699735
\(604\) 20.1796 0.821095
\(605\) −31.2736 −1.27145
\(606\) 4.00326 0.162621
\(607\) 18.6504 0.756998 0.378499 0.925602i \(-0.376440\pi\)
0.378499 + 0.925602i \(0.376440\pi\)
\(608\) 2.99392 0.121419
\(609\) −0.833793 −0.0337870
\(610\) −9.39113 −0.380236
\(611\) 30.4027 1.22996
\(612\) 19.3099 0.780556
\(613\) 12.7148 0.513545 0.256773 0.966472i \(-0.417341\pi\)
0.256773 + 0.966472i \(0.417341\pi\)
\(614\) 10.6912 0.431460
\(615\) 0.536291 0.0216253
\(616\) −0.122588 −0.00493922
\(617\) −9.36487 −0.377016 −0.188508 0.982072i \(-0.560365\pi\)
−0.188508 + 0.982072i \(0.560365\pi\)
\(618\) 2.47651 0.0996197
\(619\) 4.28108 0.172071 0.0860355 0.996292i \(-0.472580\pi\)
0.0860355 + 0.996292i \(0.472580\pi\)
\(620\) 32.8281 1.31841
\(621\) −0.821429 −0.0329628
\(622\) 39.7492 1.59380
\(623\) −12.8148 −0.513413
\(624\) −1.50850 −0.0603885
\(625\) −30.6324 −1.22530
\(626\) −55.4511 −2.21627
\(627\) −0.0208645 −0.000833248 0
\(628\) 18.1145 0.722847
\(629\) 26.6358 1.06204
\(630\) −45.6579 −1.81905
\(631\) −39.5061 −1.57271 −0.786357 0.617772i \(-0.788035\pi\)
−0.786357 + 0.617772i \(0.788035\pi\)
\(632\) 0.0796161 0.00316696
\(633\) −0.338324 −0.0134472
\(634\) −9.21451 −0.365955
\(635\) −6.72500 −0.266873
\(636\) 3.43124 0.136057
\(637\) −0.505796 −0.0200404
\(638\) 1.51130 0.0598329
\(639\) 22.2643 0.880760
\(640\) −2.85504 −0.112855
\(641\) 18.2383 0.720369 0.360184 0.932881i \(-0.382714\pi\)
0.360184 + 0.932881i \(0.382714\pi\)
\(642\) 0.342228 0.0135067
\(643\) −36.2895 −1.43112 −0.715559 0.698552i \(-0.753828\pi\)
−0.715559 + 0.698552i \(0.753828\pi\)
\(644\) 4.76170 0.187637
\(645\) −2.41197 −0.0949712
\(646\) 2.50783 0.0986692
\(647\) −33.5029 −1.31714 −0.658568 0.752522i \(-0.728837\pi\)
−0.658568 + 0.752522i \(0.728837\pi\)
\(648\) 1.09128 0.0428694
\(649\) −5.05606 −0.198468
\(650\) 15.8991 0.623614
\(651\) 2.37218 0.0929729
\(652\) 13.7617 0.538950
\(653\) −15.9755 −0.625170 −0.312585 0.949890i \(-0.601195\pi\)
−0.312585 + 0.949890i \(0.601195\pi\)
\(654\) 2.65943 0.103992
\(655\) −5.26223 −0.205612
\(656\) 5.11476 0.199698
\(657\) 30.9662 1.20811
\(658\) −66.4202 −2.58933
\(659\) 40.3580 1.57213 0.786063 0.618147i \(-0.212116\pi\)
0.786063 + 0.618147i \(0.212116\pi\)
\(660\) −0.308193 −0.0119964
\(661\) −15.5296 −0.604032 −0.302016 0.953303i \(-0.597660\pi\)
−0.302016 + 0.953303i \(0.597660\pi\)
\(662\) −12.3040 −0.478209
\(663\) −1.22525 −0.0475849
\(664\) 1.94811 0.0756012
\(665\) −2.91779 −0.113147
\(666\) −47.0141 −1.82176
\(667\) 1.89400 0.0733360
\(668\) −20.1157 −0.778300
\(669\) 0.797108 0.0308180
\(670\) −32.9628 −1.27347
\(671\) 0.605246 0.0233653
\(672\) 3.19562 0.123274
\(673\) −43.0979 −1.66130 −0.830652 0.556792i \(-0.812032\pi\)
−0.830652 + 0.556792i \(0.812032\pi\)
\(674\) 10.6183 0.409001
\(675\) 2.94842 0.113485
\(676\) −13.6671 −0.525657
\(677\) −23.0443 −0.885663 −0.442831 0.896605i \(-0.646026\pi\)
−0.442831 + 0.896605i \(0.646026\pi\)
\(678\) −2.59729 −0.0997484
\(679\) 42.8605 1.64484
\(680\) −1.19517 −0.0458325
\(681\) 0.328557 0.0125903
\(682\) −4.29971 −0.164645
\(683\) −45.7310 −1.74985 −0.874923 0.484261i \(-0.839088\pi\)
−0.874923 + 0.484261i \(0.839088\pi\)
\(684\) −2.17811 −0.0832822
\(685\) −38.1522 −1.45772
\(686\) −36.1855 −1.38157
\(687\) −0.731888 −0.0279233
\(688\) −23.0036 −0.877006
\(689\) 28.7676 1.09596
\(690\) −0.784931 −0.0298818
\(691\) 2.00105 0.0761236 0.0380618 0.999275i \(-0.487882\pi\)
0.0380618 + 0.999275i \(0.487882\pi\)
\(692\) −9.56218 −0.363499
\(693\) 2.94259 0.111780
\(694\) 46.4253 1.76228
\(695\) 32.7139 1.24091
\(696\) 0.0385242 0.00146025
\(697\) 4.15436 0.157358
\(698\) −30.6984 −1.16195
\(699\) 2.37876 0.0899729
\(700\) −17.0915 −0.645999
\(701\) −36.9644 −1.39613 −0.698063 0.716036i \(-0.745954\pi\)
−0.698063 + 0.716036i \(0.745954\pi\)
\(702\) 4.34169 0.163867
\(703\) −3.00445 −0.113315
\(704\) −2.75811 −0.103950
\(705\) 5.38753 0.202906
\(706\) −52.2004 −1.96459
\(707\) −36.0806 −1.35695
\(708\) 3.99464 0.150128
\(709\) −16.4717 −0.618609 −0.309305 0.950963i \(-0.600096\pi\)
−0.309305 + 0.950963i \(0.600096\pi\)
\(710\) 42.7111 1.60292
\(711\) −1.91110 −0.0716717
\(712\) 0.592087 0.0221894
\(713\) −5.38851 −0.201801
\(714\) 2.67679 0.100176
\(715\) −2.58389 −0.0966321
\(716\) 33.5104 1.25234
\(717\) −3.73272 −0.139401
\(718\) 73.1841 2.73121
\(719\) 1.45386 0.0542200 0.0271100 0.999632i \(-0.491370\pi\)
0.0271100 + 0.999632i \(0.491370\pi\)
\(720\) 35.3208 1.31633
\(721\) −22.3203 −0.831250
\(722\) 37.4190 1.39259
\(723\) −2.69497 −0.100227
\(724\) 33.3375 1.23898
\(725\) −6.79828 −0.252482
\(726\) −3.23623 −0.120108
\(727\) 33.1204 1.22837 0.614184 0.789163i \(-0.289485\pi\)
0.614184 + 0.789163i \(0.289485\pi\)
\(728\) 0.812021 0.0300955
\(729\) −25.7908 −0.955213
\(730\) 59.4046 2.19866
\(731\) −18.6843 −0.691062
\(732\) −0.478188 −0.0176743
\(733\) 5.43027 0.200572 0.100286 0.994959i \(-0.468024\pi\)
0.100286 + 0.994959i \(0.468024\pi\)
\(734\) −41.4129 −1.52858
\(735\) −0.0896300 −0.00330605
\(736\) −7.25901 −0.267571
\(737\) 2.12441 0.0782537
\(738\) −7.33276 −0.269922
\(739\) −14.1862 −0.521847 −0.260924 0.965359i \(-0.584027\pi\)
−0.260924 + 0.965359i \(0.584027\pi\)
\(740\) −44.3792 −1.63141
\(741\) 0.138206 0.00507712
\(742\) −62.8479 −2.30722
\(743\) −18.3288 −0.672417 −0.336209 0.941788i \(-0.609145\pi\)
−0.336209 + 0.941788i \(0.609145\pi\)
\(744\) −0.109603 −0.00401824
\(745\) 18.8283 0.689816
\(746\) 36.5906 1.33968
\(747\) −46.7621 −1.71094
\(748\) −2.38741 −0.0872922
\(749\) −3.08444 −0.112703
\(750\) −1.46974 −0.0536674
\(751\) −4.60177 −0.167921 −0.0839605 0.996469i \(-0.526757\pi\)
−0.0839605 + 0.996469i \(0.526757\pi\)
\(752\) 51.3825 1.87373
\(753\) −0.279924 −0.0102010
\(754\) −10.0108 −0.364572
\(755\) 29.9807 1.09111
\(756\) −4.66731 −0.169748
\(757\) 31.7533 1.15409 0.577047 0.816711i \(-0.304205\pi\)
0.577047 + 0.816711i \(0.304205\pi\)
\(758\) −26.2666 −0.954048
\(759\) 0.0505878 0.00183622
\(760\) 0.134812 0.00489015
\(761\) 10.3955 0.376837 0.188418 0.982089i \(-0.439664\pi\)
0.188418 + 0.982089i \(0.439664\pi\)
\(762\) −0.695909 −0.0252101
\(763\) −23.9689 −0.867734
\(764\) −1.87874 −0.0679705
\(765\) 28.6886 1.03724
\(766\) 6.15699 0.222461
\(767\) 33.4912 1.20930
\(768\) −2.54485 −0.0918293
\(769\) 31.1538 1.12344 0.561718 0.827329i \(-0.310141\pi\)
0.561718 + 0.827329i \(0.310141\pi\)
\(770\) 5.64498 0.203431
\(771\) −0.386998 −0.0139374
\(772\) 13.9838 0.503287
\(773\) 3.74734 0.134782 0.0673912 0.997727i \(-0.478532\pi\)
0.0673912 + 0.997727i \(0.478532\pi\)
\(774\) 32.9791 1.18541
\(775\) 19.3414 0.694764
\(776\) −1.98031 −0.0710889
\(777\) −3.20687 −0.115046
\(778\) −0.996384 −0.0357221
\(779\) −0.468603 −0.0167894
\(780\) 2.04146 0.0730959
\(781\) −2.75267 −0.0984984
\(782\) −6.08045 −0.217436
\(783\) −1.85646 −0.0663444
\(784\) −0.854828 −0.0305296
\(785\) 26.9126 0.960552
\(786\) −0.544541 −0.0194231
\(787\) 50.4938 1.79991 0.899955 0.435983i \(-0.143599\pi\)
0.899955 + 0.435983i \(0.143599\pi\)
\(788\) −14.1250 −0.503182
\(789\) −0.760723 −0.0270825
\(790\) −3.66619 −0.130437
\(791\) 23.4089 0.832325
\(792\) −0.135958 −0.00483106
\(793\) −4.00913 −0.142368
\(794\) 12.3718 0.439059
\(795\) 5.09778 0.180799
\(796\) −13.5100 −0.478850
\(797\) −48.9797 −1.73495 −0.867475 0.497481i \(-0.834258\pi\)
−0.867475 + 0.497481i \(0.834258\pi\)
\(798\) −0.301936 −0.0106884
\(799\) 41.7344 1.47646
\(800\) 26.0553 0.921195
\(801\) −14.2124 −0.502171
\(802\) 24.6845 0.871641
\(803\) −3.82855 −0.135107
\(804\) −1.67844 −0.0591939
\(805\) 7.07444 0.249341
\(806\) 28.4812 1.00321
\(807\) 1.53898 0.0541747
\(808\) 1.66705 0.0586467
\(809\) −24.6489 −0.866611 −0.433305 0.901247i \(-0.642653\pi\)
−0.433305 + 0.901247i \(0.642653\pi\)
\(810\) −50.2514 −1.76565
\(811\) 31.9192 1.12083 0.560417 0.828210i \(-0.310641\pi\)
0.560417 + 0.828210i \(0.310641\pi\)
\(812\) 10.7616 0.377658
\(813\) 4.01031 0.140648
\(814\) 5.81265 0.203733
\(815\) 20.4457 0.716182
\(816\) −2.07075 −0.0724909
\(817\) 2.10754 0.0737336
\(818\) −40.6028 −1.41964
\(819\) −19.4916 −0.681093
\(820\) −6.92180 −0.241720
\(821\) 10.1931 0.355740 0.177870 0.984054i \(-0.443079\pi\)
0.177870 + 0.984054i \(0.443079\pi\)
\(822\) −3.94803 −0.137703
\(823\) 34.6165 1.20666 0.603328 0.797493i \(-0.293841\pi\)
0.603328 + 0.797493i \(0.293841\pi\)
\(824\) 1.03128 0.0359262
\(825\) −0.181579 −0.00632176
\(826\) −73.1675 −2.54582
\(827\) 37.5580 1.30602 0.653010 0.757349i \(-0.273506\pi\)
0.653010 + 0.757349i \(0.273506\pi\)
\(828\) 5.28103 0.183528
\(829\) 24.0820 0.836401 0.418200 0.908355i \(-0.362661\pi\)
0.418200 + 0.908355i \(0.362661\pi\)
\(830\) −89.7070 −3.11377
\(831\) −1.44345 −0.0500729
\(832\) 18.2696 0.633385
\(833\) −0.694317 −0.0240567
\(834\) 3.38527 0.117222
\(835\) −29.8858 −1.03424
\(836\) 0.269294 0.00931373
\(837\) 5.28170 0.182562
\(838\) −55.8847 −1.93051
\(839\) −34.4662 −1.18991 −0.594953 0.803761i \(-0.702829\pi\)
−0.594953 + 0.803761i \(0.702829\pi\)
\(840\) 0.143895 0.00496484
\(841\) −24.7195 −0.852396
\(842\) −60.5772 −2.08763
\(843\) −3.45120 −0.118866
\(844\) 4.36668 0.150307
\(845\) −20.3051 −0.698518
\(846\) −73.6642 −2.53263
\(847\) 29.1675 1.00221
\(848\) 48.6190 1.66958
\(849\) −1.27304 −0.0436905
\(850\) 21.8250 0.748592
\(851\) 7.28457 0.249712
\(852\) 2.17481 0.0745077
\(853\) 8.14117 0.278748 0.139374 0.990240i \(-0.455491\pi\)
0.139374 + 0.990240i \(0.455491\pi\)
\(854\) 8.75868 0.299716
\(855\) −3.23601 −0.110669
\(856\) 0.142512 0.00487096
\(857\) 57.4729 1.96324 0.981618 0.190854i \(-0.0611258\pi\)
0.981618 + 0.190854i \(0.0611258\pi\)
\(858\) −0.267384 −0.00912833
\(859\) 38.5381 1.31490 0.657451 0.753497i \(-0.271635\pi\)
0.657451 + 0.753497i \(0.271635\pi\)
\(860\) 31.1308 1.06155
\(861\) −0.500174 −0.0170459
\(862\) −51.0397 −1.73842
\(863\) 41.0444 1.39717 0.698584 0.715529i \(-0.253814\pi\)
0.698584 + 0.715529i \(0.253814\pi\)
\(864\) 7.11513 0.242061
\(865\) −14.2065 −0.483035
\(866\) −45.8675 −1.55864
\(867\) 0.870003 0.0295469
\(868\) −30.6172 −1.03922
\(869\) 0.236281 0.00801528
\(870\) −1.77397 −0.0601433
\(871\) −14.0720 −0.476813
\(872\) 1.10745 0.0375030
\(873\) 47.5351 1.60882
\(874\) 0.685861 0.0231996
\(875\) 13.2465 0.447814
\(876\) 3.02483 0.102200
\(877\) 9.31493 0.314543 0.157271 0.987555i \(-0.449730\pi\)
0.157271 + 0.987555i \(0.449730\pi\)
\(878\) 63.8713 2.15555
\(879\) 1.70858 0.0576288
\(880\) −4.36694 −0.147210
\(881\) −29.9630 −1.00948 −0.504739 0.863272i \(-0.668411\pi\)
−0.504739 + 0.863272i \(0.668411\pi\)
\(882\) 1.22552 0.0412654
\(883\) −45.4522 −1.52959 −0.764794 0.644275i \(-0.777159\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(884\) 15.8141 0.531886
\(885\) 5.93483 0.199497
\(886\) 7.37666 0.247824
\(887\) −31.0703 −1.04324 −0.521620 0.853178i \(-0.674672\pi\)
−0.521620 + 0.853178i \(0.674672\pi\)
\(888\) 0.148169 0.00497222
\(889\) 6.27210 0.210359
\(890\) −27.2646 −0.913912
\(891\) 3.23864 0.108498
\(892\) −10.2881 −0.344472
\(893\) −4.70754 −0.157532
\(894\) 1.94837 0.0651633
\(895\) 49.7863 1.66417
\(896\) 2.66277 0.0889568
\(897\) −0.335092 −0.0111884
\(898\) −42.6931 −1.42469
\(899\) −12.1782 −0.406167
\(900\) −18.9556 −0.631853
\(901\) 39.4898 1.31560
\(902\) 0.906596 0.0301863
\(903\) 2.24953 0.0748598
\(904\) −1.08157 −0.0359726
\(905\) 49.5293 1.64641
\(906\) 3.10243 0.103071
\(907\) 27.4635 0.911910 0.455955 0.890003i \(-0.349298\pi\)
0.455955 + 0.890003i \(0.349298\pi\)
\(908\) −4.24063 −0.140730
\(909\) −40.0158 −1.32724
\(910\) −37.3922 −1.23954
\(911\) −8.25357 −0.273453 −0.136727 0.990609i \(-0.543658\pi\)
−0.136727 + 0.990609i \(0.543658\pi\)
\(912\) 0.233577 0.00773449
\(913\) 5.78150 0.191340
\(914\) 65.8040 2.17660
\(915\) −0.710442 −0.0234865
\(916\) 9.44635 0.312116
\(917\) 4.90784 0.162071
\(918\) 5.95992 0.196707
\(919\) −40.7751 −1.34505 −0.672524 0.740075i \(-0.734790\pi\)
−0.672524 + 0.740075i \(0.734790\pi\)
\(920\) −0.326864 −0.0107764
\(921\) 0.808789 0.0266505
\(922\) 48.3135 1.59112
\(923\) 18.2336 0.600167
\(924\) 0.287437 0.00945599
\(925\) −26.1470 −0.859710
\(926\) −14.8664 −0.488539
\(927\) −24.7546 −0.813048
\(928\) −16.4056 −0.538541
\(929\) −49.6880 −1.63021 −0.815104 0.579314i \(-0.803321\pi\)
−0.815104 + 0.579314i \(0.803321\pi\)
\(930\) 5.04703 0.165499
\(931\) 0.0783174 0.00256675
\(932\) −30.7022 −1.00568
\(933\) 3.00704 0.0984459
\(934\) 26.3508 0.862223
\(935\) −3.54696 −0.115998
\(936\) 0.900583 0.0294365
\(937\) −11.8945 −0.388575 −0.194288 0.980945i \(-0.562239\pi\)
−0.194288 + 0.980945i \(0.562239\pi\)
\(938\) 30.7429 1.00379
\(939\) −4.19489 −0.136895
\(940\) −69.5358 −2.26801
\(941\) −23.3867 −0.762386 −0.381193 0.924496i \(-0.624487\pi\)
−0.381193 + 0.924496i \(0.624487\pi\)
\(942\) 2.78494 0.0907384
\(943\) 1.13617 0.0369988
\(944\) 56.6022 1.84224
\(945\) −6.93421 −0.225570
\(946\) −4.07742 −0.132568
\(947\) 3.24137 0.105330 0.0526651 0.998612i \(-0.483228\pi\)
0.0526651 + 0.998612i \(0.483228\pi\)
\(948\) −0.186679 −0.00606305
\(949\) 25.3602 0.823228
\(950\) −2.46181 −0.0798718
\(951\) −0.697080 −0.0226044
\(952\) 1.11468 0.0361269
\(953\) 55.4588 1.79649 0.898244 0.439498i \(-0.144844\pi\)
0.898244 + 0.439498i \(0.144844\pi\)
\(954\) −69.7024 −2.25670
\(955\) −2.79124 −0.0903224
\(956\) 48.1775 1.55817
\(957\) 0.114330 0.00369577
\(958\) −24.1082 −0.778902
\(959\) 35.5829 1.14903
\(960\) 3.23748 0.104489
\(961\) 3.64761 0.117665
\(962\) −38.5028 −1.24138
\(963\) −3.42084 −0.110235
\(964\) 34.7835 1.12030
\(965\) 20.7756 0.668792
\(966\) 0.732070 0.0235540
\(967\) −19.5302 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(968\) −1.34764 −0.0433148
\(969\) 0.189718 0.00609462
\(970\) 91.1898 2.92793
\(971\) −14.9189 −0.478770 −0.239385 0.970925i \(-0.576946\pi\)
−0.239385 + 0.970925i \(0.576946\pi\)
\(972\) −7.77428 −0.249360
\(973\) −30.5108 −0.978130
\(974\) 21.2808 0.681880
\(975\) 1.20277 0.0385195
\(976\) −6.77569 −0.216885
\(977\) −38.6671 −1.23707 −0.618536 0.785757i \(-0.712274\pi\)
−0.618536 + 0.785757i \(0.712274\pi\)
\(978\) 2.11574 0.0676540
\(979\) 1.75717 0.0561594
\(980\) 1.15684 0.0369538
\(981\) −26.5831 −0.848733
\(982\) 56.8951 1.81559
\(983\) −43.8743 −1.39937 −0.699687 0.714449i \(-0.746677\pi\)
−0.699687 + 0.714449i \(0.746677\pi\)
\(984\) 0.0231098 0.000736714 0
\(985\) −20.9854 −0.668652
\(986\) −13.7420 −0.437636
\(987\) −5.02470 −0.159938
\(988\) −1.78380 −0.0567501
\(989\) −5.10992 −0.162486
\(990\) 6.26064 0.198976
\(991\) 7.55457 0.239979 0.119989 0.992775i \(-0.461714\pi\)
0.119989 + 0.992775i \(0.461714\pi\)
\(992\) 46.6747 1.48192
\(993\) −0.930801 −0.0295381
\(994\) −39.8347 −1.26348
\(995\) −20.0718 −0.636318
\(996\) −4.56780 −0.144736
\(997\) −0.872251 −0.0276245 −0.0138122 0.999905i \(-0.504397\pi\)
−0.0138122 + 0.999905i \(0.504397\pi\)
\(998\) 21.1969 0.670976
\(999\) −7.14017 −0.225905
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.1.4 18
3.2 odd 2 4923.2.a.l.1.15 18
4.3 odd 2 8752.2.a.s.1.8 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.4 18 1.1 even 1 trivial
4923.2.a.l.1.15 18 3.2 odd 2
8752.2.a.s.1.8 18 4.3 odd 2