Properties

Label 5577.2.a.x.1.1
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 21 x^{4} + 13 x^{3} - 33 x^{2} - 7 x + 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.73878\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} +2.84154 q^{5} -2.73878 q^{6} -3.93129 q^{7} -9.58828 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} +2.84154 q^{5} -2.73878 q^{6} -3.93129 q^{7} -9.58828 q^{8} +1.00000 q^{9} -7.78236 q^{10} -1.00000 q^{11} +5.50093 q^{12} +10.7670 q^{14} +2.84154 q^{15} +15.2584 q^{16} +3.81818 q^{17} -2.73878 q^{18} +2.94082 q^{19} +15.6311 q^{20} -3.93129 q^{21} +2.73878 q^{22} -1.89484 q^{23} -9.58828 q^{24} +3.07435 q^{25} +1.00000 q^{27} -21.6258 q^{28} -2.09928 q^{29} -7.78236 q^{30} +6.16032 q^{31} -22.6127 q^{32} -1.00000 q^{33} -10.4572 q^{34} -11.1709 q^{35} +5.50093 q^{36} -8.34404 q^{37} -8.05426 q^{38} -27.2455 q^{40} -6.35787 q^{41} +10.7670 q^{42} -11.7275 q^{43} -5.50093 q^{44} +2.84154 q^{45} +5.18956 q^{46} -5.31137 q^{47} +15.2584 q^{48} +8.45506 q^{49} -8.41997 q^{50} +3.81818 q^{51} -2.37985 q^{53} -2.73878 q^{54} -2.84154 q^{55} +37.6943 q^{56} +2.94082 q^{57} +5.74947 q^{58} +5.38624 q^{59} +15.6311 q^{60} -2.34857 q^{61} -16.8718 q^{62} -3.93129 q^{63} +31.4147 q^{64} +2.73878 q^{66} -10.4731 q^{67} +21.0035 q^{68} -1.89484 q^{69} +30.5947 q^{70} -10.0939 q^{71} -9.58828 q^{72} +15.1079 q^{73} +22.8525 q^{74} +3.07435 q^{75} +16.1772 q^{76} +3.93129 q^{77} +1.57120 q^{79} +43.3572 q^{80} +1.00000 q^{81} +17.4128 q^{82} -10.6736 q^{83} -21.6258 q^{84} +10.8495 q^{85} +32.1190 q^{86} -2.09928 q^{87} +9.58828 q^{88} -3.23647 q^{89} -7.78236 q^{90} -10.4234 q^{92} +6.16032 q^{93} +14.5467 q^{94} +8.35645 q^{95} -22.6127 q^{96} +17.7914 q^{97} -23.1566 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{2} + 7q^{3} + 9q^{4} - 6q^{5} - 3q^{6} - 6q^{7} - 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 7q^{3} + 9q^{4} - 6q^{5} - 3q^{6} - 6q^{7} - 15q^{8} + 7q^{9} - 7q^{11} + 9q^{12} + 8q^{14} - 6q^{15} + 17q^{16} - 2q^{17} - 3q^{18} - 8q^{19} + 2q^{20} - 6q^{21} + 3q^{22} + 4q^{23} - 15q^{24} + 13q^{25} + 7q^{27} - 12q^{28} - 12q^{29} + 10q^{31} - 33q^{32} - 7q^{33} - 28q^{34} - 4q^{35} + 9q^{36} - 6q^{37} + 16q^{38} - 10q^{40} - 2q^{41} + 8q^{42} - 16q^{43} - 9q^{44} - 6q^{45} + 26q^{46} - 18q^{47} + 17q^{48} + 23q^{49} - 39q^{50} - 2q^{51} + 10q^{53} - 3q^{54} + 6q^{55} + 16q^{56} - 8q^{57} - 10q^{58} - 2q^{59} + 2q^{60} - 10q^{61} - 36q^{62} - 6q^{63} + 29q^{64} + 3q^{66} - 8q^{67} - 10q^{68} + 4q^{69} + 20q^{70} - 36q^{71} - 15q^{72} - 20q^{73} + 13q^{75} - 10q^{76} + 6q^{77} + 6q^{79} + 20q^{80} + 7q^{81} - 10q^{82} - 30q^{83} - 12q^{84} + 40q^{85} - 6q^{86} - 12q^{87} + 15q^{88} - 34q^{89} - 12q^{92} + 10q^{93} + 32q^{94} + 18q^{95} - 33q^{96} - 16q^{97} - q^{98} - 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73878 −1.93661 −0.968306 0.249768i \(-0.919646\pi\)
−0.968306 + 0.249768i \(0.919646\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.50093 2.75046
\(5\) 2.84154 1.27078 0.635388 0.772193i \(-0.280840\pi\)
0.635388 + 0.772193i \(0.280840\pi\)
\(6\) −2.73878 −1.11810
\(7\) −3.93129 −1.48589 −0.742944 0.669353i \(-0.766571\pi\)
−0.742944 + 0.669353i \(0.766571\pi\)
\(8\) −9.58828 −3.38997
\(9\) 1.00000 0.333333
\(10\) −7.78236 −2.46100
\(11\) −1.00000 −0.301511
\(12\) 5.50093 1.58798
\(13\) 0 0
\(14\) 10.7670 2.87759
\(15\) 2.84154 0.733682
\(16\) 15.2584 3.81459
\(17\) 3.81818 0.926044 0.463022 0.886347i \(-0.346765\pi\)
0.463022 + 0.886347i \(0.346765\pi\)
\(18\) −2.73878 −0.645537
\(19\) 2.94082 0.674670 0.337335 0.941385i \(-0.390474\pi\)
0.337335 + 0.941385i \(0.390474\pi\)
\(20\) 15.6311 3.49522
\(21\) −3.93129 −0.857878
\(22\) 2.73878 0.583910
\(23\) −1.89484 −0.395102 −0.197551 0.980293i \(-0.563299\pi\)
−0.197551 + 0.980293i \(0.563299\pi\)
\(24\) −9.58828 −1.95720
\(25\) 3.07435 0.614869
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −21.6258 −4.08688
\(29\) −2.09928 −0.389826 −0.194913 0.980821i \(-0.562443\pi\)
−0.194913 + 0.980821i \(0.562443\pi\)
\(30\) −7.78236 −1.42086
\(31\) 6.16032 1.10643 0.553213 0.833040i \(-0.313402\pi\)
0.553213 + 0.833040i \(0.313402\pi\)
\(32\) −22.6127 −3.99741
\(33\) −1.00000 −0.174078
\(34\) −10.4572 −1.79339
\(35\) −11.1709 −1.88823
\(36\) 5.50093 0.916821
\(37\) −8.34404 −1.37175 −0.685876 0.727719i \(-0.740581\pi\)
−0.685876 + 0.727719i \(0.740581\pi\)
\(38\) −8.05426 −1.30657
\(39\) 0 0
\(40\) −27.2455 −4.30789
\(41\) −6.35787 −0.992933 −0.496466 0.868056i \(-0.665369\pi\)
−0.496466 + 0.868056i \(0.665369\pi\)
\(42\) 10.7670 1.66138
\(43\) −11.7275 −1.78842 −0.894212 0.447643i \(-0.852264\pi\)
−0.894212 + 0.447643i \(0.852264\pi\)
\(44\) −5.50093 −0.829296
\(45\) 2.84154 0.423592
\(46\) 5.18956 0.765159
\(47\) −5.31137 −0.774743 −0.387371 0.921924i \(-0.626617\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(48\) 15.2584 2.20235
\(49\) 8.45506 1.20787
\(50\) −8.41997 −1.19076
\(51\) 3.81818 0.534652
\(52\) 0 0
\(53\) −2.37985 −0.326898 −0.163449 0.986552i \(-0.552262\pi\)
−0.163449 + 0.986552i \(0.552262\pi\)
\(54\) −2.73878 −0.372701
\(55\) −2.84154 −0.383153
\(56\) 37.6943 5.03712
\(57\) 2.94082 0.389521
\(58\) 5.74947 0.754942
\(59\) 5.38624 0.701229 0.350615 0.936520i \(-0.385973\pi\)
0.350615 + 0.936520i \(0.385973\pi\)
\(60\) 15.6311 2.01797
\(61\) −2.34857 −0.300703 −0.150352 0.988633i \(-0.548041\pi\)
−0.150352 + 0.988633i \(0.548041\pi\)
\(62\) −16.8718 −2.14272
\(63\) −3.93129 −0.495296
\(64\) 31.4147 3.92684
\(65\) 0 0
\(66\) 2.73878 0.337121
\(67\) −10.4731 −1.27949 −0.639744 0.768588i \(-0.720960\pi\)
−0.639744 + 0.768588i \(0.720960\pi\)
\(68\) 21.0035 2.54705
\(69\) −1.89484 −0.228112
\(70\) 30.5947 3.65677
\(71\) −10.0939 −1.19793 −0.598964 0.800776i \(-0.704421\pi\)
−0.598964 + 0.800776i \(0.704421\pi\)
\(72\) −9.58828 −1.12999
\(73\) 15.1079 1.76824 0.884120 0.467260i \(-0.154759\pi\)
0.884120 + 0.467260i \(0.154759\pi\)
\(74\) 22.8525 2.65655
\(75\) 3.07435 0.354995
\(76\) 16.1772 1.85566
\(77\) 3.93129 0.448012
\(78\) 0 0
\(79\) 1.57120 0.176774 0.0883872 0.996086i \(-0.471829\pi\)
0.0883872 + 0.996086i \(0.471829\pi\)
\(80\) 43.3572 4.84748
\(81\) 1.00000 0.111111
\(82\) 17.4128 1.92293
\(83\) −10.6736 −1.17157 −0.585787 0.810465i \(-0.699215\pi\)
−0.585787 + 0.810465i \(0.699215\pi\)
\(84\) −21.6258 −2.35956
\(85\) 10.8495 1.17679
\(86\) 32.1190 3.46348
\(87\) −2.09928 −0.225066
\(88\) 9.58828 1.02211
\(89\) −3.23647 −0.343065 −0.171533 0.985178i \(-0.554872\pi\)
−0.171533 + 0.985178i \(0.554872\pi\)
\(90\) −7.78236 −0.820333
\(91\) 0 0
\(92\) −10.4234 −1.08671
\(93\) 6.16032 0.638795
\(94\) 14.5467 1.50038
\(95\) 8.35645 0.857354
\(96\) −22.6127 −2.30790
\(97\) 17.7914 1.80645 0.903223 0.429172i \(-0.141195\pi\)
0.903223 + 0.429172i \(0.141195\pi\)
\(98\) −23.1566 −2.33917
\(99\) −1.00000 −0.100504
\(100\) 16.9118 1.69118
\(101\) −12.1229 −1.20627 −0.603136 0.797638i \(-0.706083\pi\)
−0.603136 + 0.797638i \(0.706083\pi\)
\(102\) −10.4572 −1.03541
\(103\) −3.40983 −0.335981 −0.167990 0.985789i \(-0.553728\pi\)
−0.167990 + 0.985789i \(0.553728\pi\)
\(104\) 0 0
\(105\) −11.1709 −1.09017
\(106\) 6.51790 0.633075
\(107\) −12.2352 −1.18282 −0.591411 0.806370i \(-0.701429\pi\)
−0.591411 + 0.806370i \(0.701429\pi\)
\(108\) 5.50093 0.529327
\(109\) 8.72763 0.835956 0.417978 0.908457i \(-0.362739\pi\)
0.417978 + 0.908457i \(0.362739\pi\)
\(110\) 7.78236 0.742019
\(111\) −8.34404 −0.791981
\(112\) −59.9850 −5.66805
\(113\) 0.0155525 0.00146305 0.000731527 1.00000i \(-0.499767\pi\)
0.000731527 1.00000i \(0.499767\pi\)
\(114\) −8.05426 −0.754351
\(115\) −5.38427 −0.502086
\(116\) −11.5480 −1.07220
\(117\) 0 0
\(118\) −14.7517 −1.35801
\(119\) −15.0104 −1.37600
\(120\) −27.2455 −2.48716
\(121\) 1.00000 0.0909091
\(122\) 6.43222 0.582346
\(123\) −6.35787 −0.573270
\(124\) 33.8875 3.04318
\(125\) −5.47182 −0.489414
\(126\) 10.7670 0.959196
\(127\) −5.91514 −0.524883 −0.262442 0.964948i \(-0.584528\pi\)
−0.262442 + 0.964948i \(0.584528\pi\)
\(128\) −40.8125 −3.60735
\(129\) −11.7275 −1.03255
\(130\) 0 0
\(131\) −1.32191 −0.115496 −0.0577481 0.998331i \(-0.518392\pi\)
−0.0577481 + 0.998331i \(0.518392\pi\)
\(132\) −5.50093 −0.478794
\(133\) −11.5612 −1.00248
\(134\) 28.6835 2.47787
\(135\) 2.84154 0.244561
\(136\) −36.6097 −3.13926
\(137\) −4.82127 −0.411909 −0.205955 0.978562i \(-0.566030\pi\)
−0.205955 + 0.978562i \(0.566030\pi\)
\(138\) 5.18956 0.441765
\(139\) 17.1877 1.45784 0.728919 0.684600i \(-0.240023\pi\)
0.728919 + 0.684600i \(0.240023\pi\)
\(140\) −61.4504 −5.19351
\(141\) −5.31137 −0.447298
\(142\) 27.6451 2.31992
\(143\) 0 0
\(144\) 15.2584 1.27153
\(145\) −5.96518 −0.495382
\(146\) −41.3771 −3.42439
\(147\) 8.45506 0.697361
\(148\) −45.8999 −3.77295
\(149\) 5.31754 0.435629 0.217815 0.975990i \(-0.430107\pi\)
0.217815 + 0.975990i \(0.430107\pi\)
\(150\) −8.41997 −0.687487
\(151\) 6.77573 0.551401 0.275700 0.961244i \(-0.411090\pi\)
0.275700 + 0.961244i \(0.411090\pi\)
\(152\) −28.1974 −2.28711
\(153\) 3.81818 0.308681
\(154\) −10.7670 −0.867626
\(155\) 17.5048 1.40602
\(156\) 0 0
\(157\) 16.2884 1.29995 0.649977 0.759954i \(-0.274779\pi\)
0.649977 + 0.759954i \(0.274779\pi\)
\(158\) −4.30319 −0.342343
\(159\) −2.37985 −0.188735
\(160\) −64.2550 −5.07981
\(161\) 7.44918 0.587077
\(162\) −2.73878 −0.215179
\(163\) −11.4032 −0.893170 −0.446585 0.894741i \(-0.647360\pi\)
−0.446585 + 0.894741i \(0.647360\pi\)
\(164\) −34.9742 −2.73103
\(165\) −2.84154 −0.221214
\(166\) 29.2325 2.26888
\(167\) 14.7302 1.13985 0.569927 0.821695i \(-0.306971\pi\)
0.569927 + 0.821695i \(0.306971\pi\)
\(168\) 37.6943 2.90818
\(169\) 0 0
\(170\) −29.7144 −2.27899
\(171\) 2.94082 0.224890
\(172\) −64.5121 −4.91900
\(173\) 0.186647 0.0141905 0.00709527 0.999975i \(-0.497741\pi\)
0.00709527 + 0.999975i \(0.497741\pi\)
\(174\) 5.74947 0.435866
\(175\) −12.0862 −0.913627
\(176\) −15.2584 −1.15014
\(177\) 5.38624 0.404855
\(178\) 8.86399 0.664384
\(179\) 10.9555 0.818856 0.409428 0.912342i \(-0.365728\pi\)
0.409428 + 0.912342i \(0.365728\pi\)
\(180\) 15.6311 1.16507
\(181\) −8.52034 −0.633312 −0.316656 0.948540i \(-0.602560\pi\)
−0.316656 + 0.948540i \(0.602560\pi\)
\(182\) 0 0
\(183\) −2.34857 −0.173611
\(184\) 18.1683 1.33938
\(185\) −23.7099 −1.74319
\(186\) −16.8718 −1.23710
\(187\) −3.81818 −0.279213
\(188\) −29.2175 −2.13090
\(189\) −3.93129 −0.285959
\(190\) −22.8865 −1.66036
\(191\) −11.8003 −0.853840 −0.426920 0.904289i \(-0.640401\pi\)
−0.426920 + 0.904289i \(0.640401\pi\)
\(192\) 31.4147 2.26716
\(193\) −10.9405 −0.787518 −0.393759 0.919214i \(-0.628826\pi\)
−0.393759 + 0.919214i \(0.628826\pi\)
\(194\) −48.7268 −3.49838
\(195\) 0 0
\(196\) 46.5107 3.32219
\(197\) −9.43307 −0.672079 −0.336039 0.941848i \(-0.609088\pi\)
−0.336039 + 0.941848i \(0.609088\pi\)
\(198\) 2.73878 0.194637
\(199\) −15.3198 −1.08599 −0.542996 0.839735i \(-0.682710\pi\)
−0.542996 + 0.839735i \(0.682710\pi\)
\(200\) −29.4777 −2.08439
\(201\) −10.4731 −0.738713
\(202\) 33.2020 2.33608
\(203\) 8.25288 0.579238
\(204\) 21.0035 1.47054
\(205\) −18.0661 −1.26179
\(206\) 9.33878 0.650664
\(207\) −1.89484 −0.131701
\(208\) 0 0
\(209\) −2.94082 −0.203421
\(210\) 30.5947 2.11124
\(211\) 2.91243 0.200500 0.100250 0.994962i \(-0.468036\pi\)
0.100250 + 0.994962i \(0.468036\pi\)
\(212\) −13.0914 −0.899122
\(213\) −10.0939 −0.691625
\(214\) 33.5096 2.29067
\(215\) −33.3241 −2.27269
\(216\) −9.58828 −0.652400
\(217\) −24.2180 −1.64403
\(218\) −23.9031 −1.61892
\(219\) 15.1079 1.02089
\(220\) −15.6311 −1.05385
\(221\) 0 0
\(222\) 22.8525 1.53376
\(223\) −10.8511 −0.726641 −0.363320 0.931664i \(-0.618357\pi\)
−0.363320 + 0.931664i \(0.618357\pi\)
\(224\) 88.8973 5.93970
\(225\) 3.07435 0.204956
\(226\) −0.0425948 −0.00283337
\(227\) −0.322636 −0.0214141 −0.0107070 0.999943i \(-0.503408\pi\)
−0.0107070 + 0.999943i \(0.503408\pi\)
\(228\) 16.1772 1.07136
\(229\) 5.94060 0.392566 0.196283 0.980547i \(-0.437113\pi\)
0.196283 + 0.980547i \(0.437113\pi\)
\(230\) 14.7463 0.972345
\(231\) 3.93129 0.258660
\(232\) 20.1285 1.32150
\(233\) −12.6202 −0.826774 −0.413387 0.910555i \(-0.635654\pi\)
−0.413387 + 0.910555i \(0.635654\pi\)
\(234\) 0 0
\(235\) −15.0925 −0.984524
\(236\) 29.6293 1.92871
\(237\) 1.57120 0.102061
\(238\) 41.1101 2.66477
\(239\) −20.7706 −1.34354 −0.671768 0.740762i \(-0.734465\pi\)
−0.671768 + 0.740762i \(0.734465\pi\)
\(240\) 43.3572 2.79870
\(241\) 18.2163 1.17341 0.586706 0.809800i \(-0.300424\pi\)
0.586706 + 0.809800i \(0.300424\pi\)
\(242\) −2.73878 −0.176056
\(243\) 1.00000 0.0641500
\(244\) −12.9193 −0.827074
\(245\) 24.0254 1.53492
\(246\) 17.4128 1.11020
\(247\) 0 0
\(248\) −59.0668 −3.75075
\(249\) −10.6736 −0.676409
\(250\) 14.9861 0.947806
\(251\) −22.6662 −1.43068 −0.715340 0.698776i \(-0.753728\pi\)
−0.715340 + 0.698776i \(0.753728\pi\)
\(252\) −21.6258 −1.36229
\(253\) 1.89484 0.119128
\(254\) 16.2003 1.01650
\(255\) 10.8495 0.679422
\(256\) 48.9471 3.05920
\(257\) 17.7333 1.10617 0.553087 0.833124i \(-0.313450\pi\)
0.553087 + 0.833124i \(0.313450\pi\)
\(258\) 32.1190 1.99964
\(259\) 32.8028 2.03827
\(260\) 0 0
\(261\) −2.09928 −0.129942
\(262\) 3.62044 0.223671
\(263\) 29.5107 1.81971 0.909853 0.414930i \(-0.136194\pi\)
0.909853 + 0.414930i \(0.136194\pi\)
\(264\) 9.58828 0.590118
\(265\) −6.76245 −0.415414
\(266\) 31.6637 1.94142
\(267\) −3.23647 −0.198069
\(268\) −57.6116 −3.51919
\(269\) −9.02091 −0.550015 −0.275007 0.961442i \(-0.588680\pi\)
−0.275007 + 0.961442i \(0.588680\pi\)
\(270\) −7.78236 −0.473619
\(271\) −4.58320 −0.278410 −0.139205 0.990264i \(-0.544455\pi\)
−0.139205 + 0.990264i \(0.544455\pi\)
\(272\) 58.2591 3.53248
\(273\) 0 0
\(274\) 13.2044 0.797708
\(275\) −3.07435 −0.185390
\(276\) −10.4234 −0.627414
\(277\) 20.9859 1.26092 0.630461 0.776221i \(-0.282866\pi\)
0.630461 + 0.776221i \(0.282866\pi\)
\(278\) −47.0732 −2.82327
\(279\) 6.16032 0.368809
\(280\) 107.110 6.40104
\(281\) −10.5360 −0.628524 −0.314262 0.949336i \(-0.601757\pi\)
−0.314262 + 0.949336i \(0.601757\pi\)
\(282\) 14.5467 0.866242
\(283\) −2.57169 −0.152871 −0.0764355 0.997075i \(-0.524354\pi\)
−0.0764355 + 0.997075i \(0.524354\pi\)
\(284\) −55.5260 −3.29486
\(285\) 8.35645 0.494993
\(286\) 0 0
\(287\) 24.9947 1.47539
\(288\) −22.6127 −1.33247
\(289\) −2.42153 −0.142443
\(290\) 16.3373 0.959362
\(291\) 17.7914 1.04295
\(292\) 83.1072 4.86348
\(293\) −5.16162 −0.301545 −0.150772 0.988568i \(-0.548176\pi\)
−0.150772 + 0.988568i \(0.548176\pi\)
\(294\) −23.1566 −1.35052
\(295\) 15.3052 0.891105
\(296\) 80.0050 4.65019
\(297\) −1.00000 −0.0580259
\(298\) −14.5636 −0.843645
\(299\) 0 0
\(300\) 16.9118 0.976401
\(301\) 46.1042 2.65740
\(302\) −18.5572 −1.06785
\(303\) −12.1229 −0.696442
\(304\) 44.8720 2.57359
\(305\) −6.67355 −0.382126
\(306\) −10.4572 −0.597796
\(307\) 30.0561 1.71539 0.857697 0.514156i \(-0.171895\pi\)
0.857697 + 0.514156i \(0.171895\pi\)
\(308\) 21.6258 1.23224
\(309\) −3.40983 −0.193978
\(310\) −47.9418 −2.72291
\(311\) −21.7462 −1.23311 −0.616557 0.787310i \(-0.711473\pi\)
−0.616557 + 0.787310i \(0.711473\pi\)
\(312\) 0 0
\(313\) −24.4361 −1.38121 −0.690606 0.723231i \(-0.742656\pi\)
−0.690606 + 0.723231i \(0.742656\pi\)
\(314\) −44.6103 −2.51751
\(315\) −11.1709 −0.629410
\(316\) 8.64309 0.486212
\(317\) −21.1040 −1.18532 −0.592658 0.805454i \(-0.701921\pi\)
−0.592658 + 0.805454i \(0.701921\pi\)
\(318\) 6.51790 0.365506
\(319\) 2.09928 0.117537
\(320\) 89.2661 4.99013
\(321\) −12.2352 −0.682903
\(322\) −20.4017 −1.13694
\(323\) 11.2286 0.624774
\(324\) 5.50093 0.305607
\(325\) 0 0
\(326\) 31.2310 1.72972
\(327\) 8.72763 0.482639
\(328\) 60.9611 3.36601
\(329\) 20.8805 1.15118
\(330\) 7.78236 0.428405
\(331\) −0.560518 −0.0308089 −0.0154044 0.999881i \(-0.504904\pi\)
−0.0154044 + 0.999881i \(0.504904\pi\)
\(332\) −58.7144 −3.22237
\(333\) −8.34404 −0.457250
\(334\) −40.3427 −2.20745
\(335\) −29.7596 −1.62594
\(336\) −59.9850 −3.27245
\(337\) −7.76850 −0.423177 −0.211589 0.977359i \(-0.567864\pi\)
−0.211589 + 0.977359i \(0.567864\pi\)
\(338\) 0 0
\(339\) 0.0155525 0.000844695 0
\(340\) 59.6823 3.23673
\(341\) −6.16032 −0.333600
\(342\) −8.05426 −0.435525
\(343\) −5.72025 −0.308864
\(344\) 112.446 6.06270
\(345\) −5.38427 −0.289879
\(346\) −0.511186 −0.0274816
\(347\) −10.1357 −0.544110 −0.272055 0.962282i \(-0.587703\pi\)
−0.272055 + 0.962282i \(0.587703\pi\)
\(348\) −11.5480 −0.619037
\(349\) 20.0030 1.07074 0.535369 0.844619i \(-0.320173\pi\)
0.535369 + 0.844619i \(0.320173\pi\)
\(350\) 33.1013 1.76934
\(351\) 0 0
\(352\) 22.6127 1.20526
\(353\) 26.7905 1.42591 0.712957 0.701208i \(-0.247355\pi\)
0.712957 + 0.701208i \(0.247355\pi\)
\(354\) −14.7517 −0.784047
\(355\) −28.6823 −1.52230
\(356\) −17.8036 −0.943589
\(357\) −15.0104 −0.794433
\(358\) −30.0049 −1.58581
\(359\) −26.7347 −1.41101 −0.705503 0.708707i \(-0.749279\pi\)
−0.705503 + 0.708707i \(0.749279\pi\)
\(360\) −27.2455 −1.43596
\(361\) −10.3516 −0.544820
\(362\) 23.3354 1.22648
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 42.9296 2.24704
\(366\) 6.43222 0.336218
\(367\) 1.89563 0.0989512 0.0494756 0.998775i \(-0.484245\pi\)
0.0494756 + 0.998775i \(0.484245\pi\)
\(368\) −28.9122 −1.50715
\(369\) −6.35787 −0.330978
\(370\) 64.9363 3.37588
\(371\) 9.35590 0.485734
\(372\) 33.8875 1.75698
\(373\) −36.7517 −1.90293 −0.951464 0.307759i \(-0.900421\pi\)
−0.951464 + 0.307759i \(0.900421\pi\)
\(374\) 10.4572 0.540726
\(375\) −5.47182 −0.282564
\(376\) 50.9269 2.62635
\(377\) 0 0
\(378\) 10.7670 0.553792
\(379\) 26.1328 1.34235 0.671176 0.741298i \(-0.265789\pi\)
0.671176 + 0.741298i \(0.265789\pi\)
\(380\) 45.9682 2.35812
\(381\) −5.91514 −0.303042
\(382\) 32.3185 1.65356
\(383\) −16.9211 −0.864629 −0.432315 0.901723i \(-0.642303\pi\)
−0.432315 + 0.901723i \(0.642303\pi\)
\(384\) −40.8125 −2.08270
\(385\) 11.1709 0.569323
\(386\) 29.9638 1.52512
\(387\) −11.7275 −0.596142
\(388\) 97.8693 4.96856
\(389\) −5.05607 −0.256353 −0.128177 0.991751i \(-0.540912\pi\)
−0.128177 + 0.991751i \(0.540912\pi\)
\(390\) 0 0
\(391\) −7.23484 −0.365882
\(392\) −81.0694 −4.09462
\(393\) −1.32191 −0.0666818
\(394\) 25.8351 1.30156
\(395\) 4.46464 0.224640
\(396\) −5.50093 −0.276432
\(397\) −15.7731 −0.791631 −0.395815 0.918330i \(-0.629538\pi\)
−0.395815 + 0.918330i \(0.629538\pi\)
\(398\) 41.9576 2.10314
\(399\) −11.5612 −0.578785
\(400\) 46.9095 2.34547
\(401\) −8.42218 −0.420584 −0.210292 0.977639i \(-0.567441\pi\)
−0.210292 + 0.977639i \(0.567441\pi\)
\(402\) 28.6835 1.43060
\(403\) 0 0
\(404\) −66.6872 −3.31781
\(405\) 2.84154 0.141197
\(406\) −22.6028 −1.12176
\(407\) 8.34404 0.413599
\(408\) −36.6097 −1.81245
\(409\) −31.3861 −1.55194 −0.775971 0.630768i \(-0.782740\pi\)
−0.775971 + 0.630768i \(0.782740\pi\)
\(410\) 49.4792 2.44361
\(411\) −4.82127 −0.237816
\(412\) −18.7572 −0.924102
\(413\) −21.1749 −1.04195
\(414\) 5.18956 0.255053
\(415\) −30.3293 −1.48881
\(416\) 0 0
\(417\) 17.1877 0.841683
\(418\) 8.05426 0.393947
\(419\) −6.62928 −0.323861 −0.161931 0.986802i \(-0.551772\pi\)
−0.161931 + 0.986802i \(0.551772\pi\)
\(420\) −61.4504 −2.99847
\(421\) 2.61327 0.127363 0.0636816 0.997970i \(-0.479716\pi\)
0.0636816 + 0.997970i \(0.479716\pi\)
\(422\) −7.97651 −0.388290
\(423\) −5.31137 −0.258248
\(424\) 22.8187 1.10817
\(425\) 11.7384 0.569396
\(426\) 27.6451 1.33941
\(427\) 9.23291 0.446812
\(428\) −67.3050 −3.25331
\(429\) 0 0
\(430\) 91.2675 4.40131
\(431\) 24.8745 1.19816 0.599081 0.800688i \(-0.295533\pi\)
0.599081 + 0.800688i \(0.295533\pi\)
\(432\) 15.2584 0.734118
\(433\) 6.55556 0.315040 0.157520 0.987516i \(-0.449650\pi\)
0.157520 + 0.987516i \(0.449650\pi\)
\(434\) 66.3278 3.18384
\(435\) −5.96518 −0.286009
\(436\) 48.0101 2.29927
\(437\) −5.57239 −0.266563
\(438\) −41.3771 −1.97707
\(439\) −38.2180 −1.82405 −0.912023 0.410138i \(-0.865480\pi\)
−0.912023 + 0.410138i \(0.865480\pi\)
\(440\) 27.2455 1.29888
\(441\) 8.45506 0.402622
\(442\) 0 0
\(443\) −12.7407 −0.605330 −0.302665 0.953097i \(-0.597876\pi\)
−0.302665 + 0.953097i \(0.597876\pi\)
\(444\) −45.8999 −2.17831
\(445\) −9.19656 −0.435959
\(446\) 29.7187 1.40722
\(447\) 5.31754 0.251511
\(448\) −123.500 −5.83484
\(449\) −25.9513 −1.22472 −0.612358 0.790581i \(-0.709779\pi\)
−0.612358 + 0.790581i \(0.709779\pi\)
\(450\) −8.41997 −0.396921
\(451\) 6.35787 0.299381
\(452\) 0.0855531 0.00402408
\(453\) 6.77573 0.318351
\(454\) 0.883629 0.0414708
\(455\) 0 0
\(456\) −28.1974 −1.32046
\(457\) −16.0372 −0.750190 −0.375095 0.926986i \(-0.622390\pi\)
−0.375095 + 0.926986i \(0.622390\pi\)
\(458\) −16.2700 −0.760247
\(459\) 3.81818 0.178217
\(460\) −29.6185 −1.38097
\(461\) −3.48566 −0.162343 −0.0811716 0.996700i \(-0.525866\pi\)
−0.0811716 + 0.996700i \(0.525866\pi\)
\(462\) −10.7670 −0.500924
\(463\) 27.0784 1.25844 0.629220 0.777227i \(-0.283374\pi\)
0.629220 + 0.777227i \(0.283374\pi\)
\(464\) −32.0315 −1.48703
\(465\) 17.5048 0.811765
\(466\) 34.5639 1.60114
\(467\) −15.6899 −0.726041 −0.363020 0.931781i \(-0.618254\pi\)
−0.363020 + 0.931781i \(0.618254\pi\)
\(468\) 0 0
\(469\) 41.1727 1.90118
\(470\) 41.3350 1.90664
\(471\) 16.2884 0.750529
\(472\) −51.6448 −2.37715
\(473\) 11.7275 0.539230
\(474\) −4.30319 −0.197652
\(475\) 9.04109 0.414834
\(476\) −82.5709 −3.78463
\(477\) −2.37985 −0.108966
\(478\) 56.8860 2.60191
\(479\) −33.0061 −1.50809 −0.754043 0.656825i \(-0.771899\pi\)
−0.754043 + 0.656825i \(0.771899\pi\)
\(480\) −64.2550 −2.93283
\(481\) 0 0
\(482\) −49.8904 −2.27244
\(483\) 7.44918 0.338949
\(484\) 5.50093 0.250042
\(485\) 50.5550 2.29559
\(486\) −2.73878 −0.124234
\(487\) −18.6684 −0.845945 −0.422973 0.906142i \(-0.639013\pi\)
−0.422973 + 0.906142i \(0.639013\pi\)
\(488\) 22.5187 1.01938
\(489\) −11.4032 −0.515672
\(490\) −65.8003 −2.97255
\(491\) −6.78238 −0.306084 −0.153042 0.988220i \(-0.548907\pi\)
−0.153042 + 0.988220i \(0.548907\pi\)
\(492\) −34.9742 −1.57676
\(493\) −8.01542 −0.360996
\(494\) 0 0
\(495\) −2.84154 −0.127718
\(496\) 93.9963 4.22056
\(497\) 39.6822 1.77999
\(498\) 29.2325 1.30994
\(499\) 0.212900 0.00953070 0.00476535 0.999989i \(-0.498483\pi\)
0.00476535 + 0.999989i \(0.498483\pi\)
\(500\) −30.1001 −1.34612
\(501\) 14.7302 0.658095
\(502\) 62.0779 2.77067
\(503\) −10.5282 −0.469430 −0.234715 0.972064i \(-0.575416\pi\)
−0.234715 + 0.972064i \(0.575416\pi\)
\(504\) 37.6943 1.67904
\(505\) −34.4477 −1.53290
\(506\) −5.18956 −0.230704
\(507\) 0 0
\(508\) −32.5387 −1.44367
\(509\) 26.1335 1.15835 0.579175 0.815204i \(-0.303375\pi\)
0.579175 + 0.815204i \(0.303375\pi\)
\(510\) −29.7144 −1.31578
\(511\) −59.3934 −2.62741
\(512\) −52.4306 −2.31713
\(513\) 2.94082 0.129840
\(514\) −48.5677 −2.14223
\(515\) −9.68917 −0.426956
\(516\) −64.5121 −2.83999
\(517\) 5.31137 0.233594
\(518\) −89.8398 −3.94734
\(519\) 0.186647 0.00819291
\(520\) 0 0
\(521\) 44.5983 1.95389 0.976944 0.213495i \(-0.0684847\pi\)
0.976944 + 0.213495i \(0.0684847\pi\)
\(522\) 5.74947 0.251647
\(523\) −35.9788 −1.57324 −0.786622 0.617435i \(-0.788172\pi\)
−0.786622 + 0.617435i \(0.788172\pi\)
\(524\) −7.27176 −0.317668
\(525\) −12.0862 −0.527483
\(526\) −80.8233 −3.52406
\(527\) 23.5212 1.02460
\(528\) −15.2584 −0.664035
\(529\) −19.4096 −0.843895
\(530\) 18.5209 0.804495
\(531\) 5.38624 0.233743
\(532\) −63.5974 −2.75730
\(533\) 0 0
\(534\) 8.86399 0.383583
\(535\) −34.7668 −1.50310
\(536\) 100.419 4.33743
\(537\) 10.9555 0.472767
\(538\) 24.7063 1.06516
\(539\) −8.45506 −0.364185
\(540\) 15.6311 0.672656
\(541\) −19.2806 −0.828937 −0.414469 0.910064i \(-0.636033\pi\)
−0.414469 + 0.910064i \(0.636033\pi\)
\(542\) 12.5524 0.539172
\(543\) −8.52034 −0.365643
\(544\) −86.3395 −3.70177
\(545\) 24.7999 1.06231
\(546\) 0 0
\(547\) −18.3680 −0.785359 −0.392679 0.919675i \(-0.628452\pi\)
−0.392679 + 0.919675i \(0.628452\pi\)
\(548\) −26.5215 −1.13294
\(549\) −2.34857 −0.100234
\(550\) 8.41997 0.359029
\(551\) −6.17360 −0.263004
\(552\) 18.1683 0.773293
\(553\) −6.17686 −0.262667
\(554\) −57.4759 −2.44192
\(555\) −23.7099 −1.00643
\(556\) 94.5481 4.00973
\(557\) 20.9920 0.889459 0.444730 0.895665i \(-0.353300\pi\)
0.444730 + 0.895665i \(0.353300\pi\)
\(558\) −16.8718 −0.714239
\(559\) 0 0
\(560\) −170.450 −7.20282
\(561\) −3.81818 −0.161204
\(562\) 28.8558 1.21721
\(563\) 3.18924 0.134411 0.0672053 0.997739i \(-0.478592\pi\)
0.0672053 + 0.997739i \(0.478592\pi\)
\(564\) −29.2175 −1.23028
\(565\) 0.0441930 0.00185921
\(566\) 7.04329 0.296052
\(567\) −3.93129 −0.165099
\(568\) 96.7834 4.06094
\(569\) 19.0570 0.798909 0.399455 0.916753i \(-0.369200\pi\)
0.399455 + 0.916753i \(0.369200\pi\)
\(570\) −22.8865 −0.958610
\(571\) 13.1418 0.549967 0.274984 0.961449i \(-0.411328\pi\)
0.274984 + 0.961449i \(0.411328\pi\)
\(572\) 0 0
\(573\) −11.8003 −0.492965
\(574\) −68.4549 −2.85725
\(575\) −5.82540 −0.242936
\(576\) 31.4147 1.30895
\(577\) −6.38825 −0.265946 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(578\) 6.63205 0.275857
\(579\) −10.9405 −0.454674
\(580\) −32.8140 −1.36253
\(581\) 41.9608 1.74083
\(582\) −48.7268 −2.01979
\(583\) 2.37985 0.0985635
\(584\) −144.858 −5.99428
\(585\) 0 0
\(586\) 14.1365 0.583975
\(587\) 8.66483 0.357636 0.178818 0.983882i \(-0.442773\pi\)
0.178818 + 0.983882i \(0.442773\pi\)
\(588\) 46.5107 1.91807
\(589\) 18.1164 0.746472
\(590\) −41.9177 −1.72572
\(591\) −9.43307 −0.388025
\(592\) −127.316 −5.23267
\(593\) −5.41552 −0.222389 −0.111194 0.993799i \(-0.535468\pi\)
−0.111194 + 0.993799i \(0.535468\pi\)
\(594\) 2.73878 0.112374
\(595\) −42.6525 −1.74858
\(596\) 29.2514 1.19818
\(597\) −15.3198 −0.626997
\(598\) 0 0
\(599\) 17.1821 0.702041 0.351021 0.936368i \(-0.385835\pi\)
0.351021 + 0.936368i \(0.385835\pi\)
\(600\) −29.4777 −1.20342
\(601\) 4.44618 0.181364 0.0906818 0.995880i \(-0.471095\pi\)
0.0906818 + 0.995880i \(0.471095\pi\)
\(602\) −126.269 −5.14635
\(603\) −10.4731 −0.426496
\(604\) 37.2728 1.51661
\(605\) 2.84154 0.115525
\(606\) 33.2020 1.34874
\(607\) 12.1499 0.493148 0.246574 0.969124i \(-0.420695\pi\)
0.246574 + 0.969124i \(0.420695\pi\)
\(608\) −66.5000 −2.69693
\(609\) 8.25288 0.334423
\(610\) 18.2774 0.740031
\(611\) 0 0
\(612\) 21.0035 0.849017
\(613\) 30.6073 1.23622 0.618108 0.786093i \(-0.287899\pi\)
0.618108 + 0.786093i \(0.287899\pi\)
\(614\) −82.3172 −3.32205
\(615\) −18.0661 −0.728497
\(616\) −37.6943 −1.51875
\(617\) −15.3414 −0.617622 −0.308811 0.951123i \(-0.599931\pi\)
−0.308811 + 0.951123i \(0.599931\pi\)
\(618\) 9.33878 0.375661
\(619\) 10.0391 0.403505 0.201752 0.979437i \(-0.435336\pi\)
0.201752 + 0.979437i \(0.435336\pi\)
\(620\) 96.2926 3.86720
\(621\) −1.89484 −0.0760374
\(622\) 59.5581 2.38806
\(623\) 12.7235 0.509757
\(624\) 0 0
\(625\) −30.9201 −1.23681
\(626\) 66.9253 2.67487
\(627\) −2.94082 −0.117445
\(628\) 89.6012 3.57548
\(629\) −31.8590 −1.27030
\(630\) 30.5947 1.21892
\(631\) −20.8523 −0.830119 −0.415059 0.909794i \(-0.636239\pi\)
−0.415059 + 0.909794i \(0.636239\pi\)
\(632\) −15.0652 −0.599260
\(633\) 2.91243 0.115759
\(634\) 57.7991 2.29550
\(635\) −16.8081 −0.667009
\(636\) −13.0914 −0.519108
\(637\) 0 0
\(638\) −5.74947 −0.227624
\(639\) −10.0939 −0.399310
\(640\) −115.970 −4.58413
\(641\) 29.3934 1.16097 0.580484 0.814272i \(-0.302863\pi\)
0.580484 + 0.814272i \(0.302863\pi\)
\(642\) 33.5096 1.32252
\(643\) 7.23812 0.285444 0.142722 0.989763i \(-0.454415\pi\)
0.142722 + 0.989763i \(0.454415\pi\)
\(644\) 40.9774 1.61474
\(645\) −33.3241 −1.31214
\(646\) −30.7526 −1.20994
\(647\) −25.4069 −0.998848 −0.499424 0.866358i \(-0.666455\pi\)
−0.499424 + 0.866358i \(0.666455\pi\)
\(648\) −9.58828 −0.376663
\(649\) −5.38624 −0.211429
\(650\) 0 0
\(651\) −24.2180 −0.949178
\(652\) −62.7284 −2.45663
\(653\) −10.1486 −0.397146 −0.198573 0.980086i \(-0.563631\pi\)
−0.198573 + 0.980086i \(0.563631\pi\)
\(654\) −23.9031 −0.934685
\(655\) −3.75627 −0.146770
\(656\) −97.0107 −3.78763
\(657\) 15.1079 0.589413
\(658\) −57.1873 −2.22939
\(659\) −18.8648 −0.734869 −0.367434 0.930049i \(-0.619764\pi\)
−0.367434 + 0.930049i \(0.619764\pi\)
\(660\) −15.6311 −0.608440
\(661\) 7.39059 0.287461 0.143730 0.989617i \(-0.454090\pi\)
0.143730 + 0.989617i \(0.454090\pi\)
\(662\) 1.53514 0.0596648
\(663\) 0 0
\(664\) 102.341 3.97160
\(665\) −32.8516 −1.27393
\(666\) 22.8525 0.885516
\(667\) 3.97780 0.154021
\(668\) 81.0296 3.13513
\(669\) −10.8511 −0.419526
\(670\) 81.5052 3.14882
\(671\) 2.34857 0.0906655
\(672\) 88.8973 3.42929
\(673\) −13.8241 −0.532879 −0.266439 0.963852i \(-0.585847\pi\)
−0.266439 + 0.963852i \(0.585847\pi\)
\(674\) 21.2762 0.819530
\(675\) 3.07435 0.118332
\(676\) 0 0
\(677\) −28.1714 −1.08272 −0.541358 0.840792i \(-0.682090\pi\)
−0.541358 + 0.840792i \(0.682090\pi\)
\(678\) −0.0425948 −0.00163585
\(679\) −69.9433 −2.68418
\(680\) −104.028 −3.98929
\(681\) −0.322636 −0.0123634
\(682\) 16.8718 0.646053
\(683\) 20.1458 0.770856 0.385428 0.922738i \(-0.374054\pi\)
0.385428 + 0.922738i \(0.374054\pi\)
\(684\) 16.1772 0.618552
\(685\) −13.6998 −0.523444
\(686\) 15.6665 0.598150
\(687\) 5.94060 0.226648
\(688\) −178.942 −6.82211
\(689\) 0 0
\(690\) 14.7463 0.561384
\(691\) 4.60090 0.175026 0.0875132 0.996163i \(-0.472108\pi\)
0.0875132 + 0.996163i \(0.472108\pi\)
\(692\) 1.02673 0.0390306
\(693\) 3.93129 0.149337
\(694\) 27.7593 1.05373
\(695\) 48.8394 1.85258
\(696\) 20.1285 0.762968
\(697\) −24.2755 −0.919499
\(698\) −54.7839 −2.07360
\(699\) −12.6202 −0.477338
\(700\) −66.4851 −2.51290
\(701\) −2.14477 −0.0810067 −0.0405033 0.999179i \(-0.512896\pi\)
−0.0405033 + 0.999179i \(0.512896\pi\)
\(702\) 0 0
\(703\) −24.5383 −0.925479
\(704\) −31.4147 −1.18399
\(705\) −15.0925 −0.568415
\(706\) −73.3733 −2.76144
\(707\) 47.6586 1.79239
\(708\) 29.6293 1.11354
\(709\) 18.0751 0.678826 0.339413 0.940637i \(-0.389772\pi\)
0.339413 + 0.940637i \(0.389772\pi\)
\(710\) 78.5546 2.94810
\(711\) 1.57120 0.0589248
\(712\) 31.0322 1.16298
\(713\) −11.6728 −0.437151
\(714\) 41.1101 1.53851
\(715\) 0 0
\(716\) 60.2657 2.25223
\(717\) −20.7706 −0.775691
\(718\) 73.2206 2.73257
\(719\) −5.67258 −0.211552 −0.105776 0.994390i \(-0.533733\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(720\) 43.3572 1.61583
\(721\) 13.4050 0.499230
\(722\) 28.3507 1.05511
\(723\) 18.2163 0.677470
\(724\) −46.8698 −1.74190
\(725\) −6.45391 −0.239692
\(726\) −2.73878 −0.101646
\(727\) 20.7279 0.768756 0.384378 0.923176i \(-0.374416\pi\)
0.384378 + 0.923176i \(0.374416\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −117.575 −4.35163
\(731\) −44.7776 −1.65616
\(732\) −12.9193 −0.477511
\(733\) −13.8875 −0.512945 −0.256473 0.966552i \(-0.582560\pi\)
−0.256473 + 0.966552i \(0.582560\pi\)
\(734\) −5.19172 −0.191630
\(735\) 24.0254 0.886189
\(736\) 42.8476 1.57938
\(737\) 10.4731 0.385780
\(738\) 17.4128 0.640975
\(739\) 2.10062 0.0772725 0.0386362 0.999253i \(-0.487699\pi\)
0.0386362 + 0.999253i \(0.487699\pi\)
\(740\) −130.427 −4.79457
\(741\) 0 0
\(742\) −25.6238 −0.940678
\(743\) −39.5255 −1.45005 −0.725025 0.688722i \(-0.758172\pi\)
−0.725025 + 0.688722i \(0.758172\pi\)
\(744\) −59.0668 −2.16550
\(745\) 15.1100 0.553587
\(746\) 100.655 3.68523
\(747\) −10.6736 −0.390525
\(748\) −21.0035 −0.767964
\(749\) 48.1002 1.75754
\(750\) 14.9861 0.547216
\(751\) −7.96076 −0.290492 −0.145246 0.989396i \(-0.546397\pi\)
−0.145246 + 0.989396i \(0.546397\pi\)
\(752\) −81.0427 −2.95532
\(753\) −22.6662 −0.826004
\(754\) 0 0
\(755\) 19.2535 0.700707
\(756\) −21.6258 −0.786521
\(757\) −21.7720 −0.791316 −0.395658 0.918398i \(-0.629484\pi\)
−0.395658 + 0.918398i \(0.629484\pi\)
\(758\) −71.5721 −2.59962
\(759\) 1.89484 0.0687784
\(760\) −80.1240 −2.90640
\(761\) 25.3978 0.920668 0.460334 0.887746i \(-0.347730\pi\)
0.460334 + 0.887746i \(0.347730\pi\)
\(762\) 16.2003 0.586874
\(763\) −34.3109 −1.24214
\(764\) −64.9126 −2.34846
\(765\) 10.8495 0.392264
\(766\) 46.3433 1.67445
\(767\) 0 0
\(768\) 48.9471 1.76623
\(769\) 17.5471 0.632763 0.316382 0.948632i \(-0.397532\pi\)
0.316382 + 0.948632i \(0.397532\pi\)
\(770\) −30.5947 −1.10256
\(771\) 17.7333 0.638649
\(772\) −60.1832 −2.16604
\(773\) −16.9181 −0.608503 −0.304251 0.952592i \(-0.598406\pi\)
−0.304251 + 0.952592i \(0.598406\pi\)
\(774\) 32.1190 1.15449
\(775\) 18.9389 0.680307
\(776\) −170.589 −6.12379
\(777\) 32.8028 1.17680
\(778\) 13.8475 0.496456
\(779\) −18.6974 −0.669902
\(780\) 0 0
\(781\) 10.0939 0.361189
\(782\) 19.8147 0.708570
\(783\) −2.09928 −0.0750221
\(784\) 129.010 4.60751
\(785\) 46.2841 1.65195
\(786\) 3.62044 0.129137
\(787\) −27.1659 −0.968361 −0.484181 0.874968i \(-0.660882\pi\)
−0.484181 + 0.874968i \(0.660882\pi\)
\(788\) −51.8907 −1.84853
\(789\) 29.5107 1.05061
\(790\) −12.2277 −0.435041
\(791\) −0.0611413 −0.00217394
\(792\) 9.58828 0.340705
\(793\) 0 0
\(794\) 43.1992 1.53308
\(795\) −6.76245 −0.239839
\(796\) −84.2731 −2.98698
\(797\) 12.3253 0.436583 0.218292 0.975884i \(-0.429952\pi\)
0.218292 + 0.975884i \(0.429952\pi\)
\(798\) 31.6637 1.12088
\(799\) −20.2797 −0.717446
\(800\) −69.5194 −2.45788
\(801\) −3.23647 −0.114355
\(802\) 23.0665 0.814507
\(803\) −15.1079 −0.533144
\(804\) −57.6116 −2.03180
\(805\) 21.1671 0.746043
\(806\) 0 0
\(807\) −9.02091 −0.317551
\(808\) 116.238 4.08923
\(809\) 51.6306 1.81523 0.907617 0.419798i \(-0.137899\pi\)
0.907617 + 0.419798i \(0.137899\pi\)
\(810\) −7.78236 −0.273444
\(811\) −22.5443 −0.791637 −0.395818 0.918329i \(-0.629539\pi\)
−0.395818 + 0.918329i \(0.629539\pi\)
\(812\) 45.3985 1.59317
\(813\) −4.58320 −0.160740
\(814\) −22.8525 −0.800980
\(815\) −32.4027 −1.13502
\(816\) 58.2591 2.03948
\(817\) −34.4884 −1.20660
\(818\) 85.9597 3.00551
\(819\) 0 0
\(820\) −99.3806 −3.47052
\(821\) 18.1907 0.634861 0.317430 0.948282i \(-0.397180\pi\)
0.317430 + 0.948282i \(0.397180\pi\)
\(822\) 13.2044 0.460557
\(823\) 44.4631 1.54989 0.774944 0.632030i \(-0.217778\pi\)
0.774944 + 0.632030i \(0.217778\pi\)
\(824\) 32.6944 1.13896
\(825\) −3.07435 −0.107035
\(826\) 57.9934 2.01785
\(827\) 6.33341 0.220234 0.110117 0.993919i \(-0.464877\pi\)
0.110117 + 0.993919i \(0.464877\pi\)
\(828\) −10.4234 −0.362238
\(829\) 7.54455 0.262033 0.131017 0.991380i \(-0.458176\pi\)
0.131017 + 0.991380i \(0.458176\pi\)
\(830\) 83.0654 2.88324
\(831\) 20.9859 0.727994
\(832\) 0 0
\(833\) 32.2829 1.11854
\(834\) −47.0732 −1.63001
\(835\) 41.8563 1.44850
\(836\) −16.1772 −0.559501
\(837\) 6.16032 0.212932
\(838\) 18.1561 0.627194
\(839\) −30.1703 −1.04159 −0.520797 0.853681i \(-0.674365\pi\)
−0.520797 + 0.853681i \(0.674365\pi\)
\(840\) 107.110 3.69564
\(841\) −24.5930 −0.848035
\(842\) −7.15719 −0.246653
\(843\) −10.5360 −0.362878
\(844\) 16.0211 0.551468
\(845\) 0 0
\(846\) 14.5467 0.500125
\(847\) −3.93129 −0.135081
\(848\) −36.3127 −1.24698
\(849\) −2.57169 −0.0882601
\(850\) −32.1489 −1.10270
\(851\) 15.8106 0.541981
\(852\) −55.5260 −1.90229
\(853\) 14.6801 0.502637 0.251319 0.967904i \(-0.419136\pi\)
0.251319 + 0.967904i \(0.419136\pi\)
\(854\) −25.2869 −0.865301
\(855\) 8.35645 0.285785
\(856\) 117.315 4.00973
\(857\) −21.1257 −0.721641 −0.360821 0.932635i \(-0.617503\pi\)
−0.360821 + 0.932635i \(0.617503\pi\)
\(858\) 0 0
\(859\) 29.4462 1.00469 0.502346 0.864667i \(-0.332470\pi\)
0.502346 + 0.864667i \(0.332470\pi\)
\(860\) −183.314 −6.25094
\(861\) 24.9947 0.851816
\(862\) −68.1258 −2.32038
\(863\) −33.8929 −1.15373 −0.576865 0.816840i \(-0.695724\pi\)
−0.576865 + 0.816840i \(0.695724\pi\)
\(864\) −22.6127 −0.769301
\(865\) 0.530366 0.0180330
\(866\) −17.9543 −0.610111
\(867\) −2.42153 −0.0822396
\(868\) −133.221 −4.52183
\(869\) −1.57120 −0.0532995
\(870\) 16.3373 0.553888
\(871\) 0 0
\(872\) −83.6830 −2.83386
\(873\) 17.7914 0.602148
\(874\) 15.2616 0.516230
\(875\) 21.5113 0.727215
\(876\) 83.1072 2.80793
\(877\) 6.62356 0.223662 0.111831 0.993727i \(-0.464329\pi\)
0.111831 + 0.993727i \(0.464329\pi\)
\(878\) 104.671 3.53247
\(879\) −5.16162 −0.174097
\(880\) −43.3572 −1.46157
\(881\) 18.7993 0.633366 0.316683 0.948531i \(-0.397431\pi\)
0.316683 + 0.948531i \(0.397431\pi\)
\(882\) −23.1566 −0.779722
\(883\) −35.0323 −1.17893 −0.589465 0.807794i \(-0.700661\pi\)
−0.589465 + 0.807794i \(0.700661\pi\)
\(884\) 0 0
\(885\) 15.3052 0.514479
\(886\) 34.8941 1.17229
\(887\) 12.8619 0.431860 0.215930 0.976409i \(-0.430722\pi\)
0.215930 + 0.976409i \(0.430722\pi\)
\(888\) 80.0050 2.68479
\(889\) 23.2541 0.779918
\(890\) 25.1874 0.844283
\(891\) −1.00000 −0.0335013
\(892\) −59.6909 −1.99860
\(893\) −15.6198 −0.522696
\(894\) −14.5636 −0.487079
\(895\) 31.1306 1.04058
\(896\) 160.446 5.36012
\(897\) 0 0
\(898\) 71.0749 2.37180
\(899\) −12.9322 −0.431314
\(900\) 16.9118 0.563725
\(901\) −9.08670 −0.302722
\(902\) −17.4128 −0.579784
\(903\) 46.1042 1.53425
\(904\) −0.149121 −0.00495971
\(905\) −24.2109 −0.804797
\(906\) −18.5572 −0.616523
\(907\) 47.0378 1.56187 0.780933 0.624615i \(-0.214744\pi\)
0.780933 + 0.624615i \(0.214744\pi\)
\(908\) −1.77480 −0.0588987
\(909\) −12.1229 −0.402091
\(910\) 0 0
\(911\) 40.3206 1.33588 0.667940 0.744215i \(-0.267176\pi\)
0.667940 + 0.744215i \(0.267176\pi\)
\(912\) 44.8720 1.48586
\(913\) 10.6736 0.353243
\(914\) 43.9225 1.45283
\(915\) −6.67355 −0.220621
\(916\) 32.6788 1.07974
\(917\) 5.19683 0.171614
\(918\) −10.4572 −0.345137
\(919\) −1.80179 −0.0594356 −0.0297178 0.999558i \(-0.509461\pi\)
−0.0297178 + 0.999558i \(0.509461\pi\)
\(920\) 51.6259 1.70205
\(921\) 30.0561 0.990383
\(922\) 9.54646 0.314396
\(923\) 0 0
\(924\) 21.6258 0.711435
\(925\) −25.6525 −0.843448
\(926\) −74.1619 −2.43711
\(927\) −3.40983 −0.111994
\(928\) 47.4705 1.55829
\(929\) −26.3015 −0.862924 −0.431462 0.902131i \(-0.642002\pi\)
−0.431462 + 0.902131i \(0.642002\pi\)
\(930\) −47.9418 −1.57207
\(931\) 24.8648 0.814910
\(932\) −69.4226 −2.27401
\(933\) −21.7462 −0.711939
\(934\) 42.9711 1.40606
\(935\) −10.8495 −0.354817
\(936\) 0 0
\(937\) 8.45280 0.276141 0.138070 0.990422i \(-0.455910\pi\)
0.138070 + 0.990422i \(0.455910\pi\)
\(938\) −112.763 −3.68184
\(939\) −24.4361 −0.797443
\(940\) −83.0226 −2.70790
\(941\) 8.34188 0.271937 0.135969 0.990713i \(-0.456585\pi\)
0.135969 + 0.990713i \(0.456585\pi\)
\(942\) −44.6103 −1.45348
\(943\) 12.0472 0.392310
\(944\) 82.1852 2.67490
\(945\) −11.1709 −0.363390
\(946\) −32.1190 −1.04428
\(947\) 21.8593 0.710330 0.355165 0.934804i \(-0.384425\pi\)
0.355165 + 0.934804i \(0.384425\pi\)
\(948\) 8.64309 0.280714
\(949\) 0 0
\(950\) −24.7616 −0.803372
\(951\) −21.1040 −0.684343
\(952\) 143.924 4.66459
\(953\) 57.6509 1.86750 0.933748 0.357932i \(-0.116518\pi\)
0.933748 + 0.357932i \(0.116518\pi\)
\(954\) 6.51790 0.211025
\(955\) −33.5310 −1.08504
\(956\) −114.257 −3.69535
\(957\) 2.09928 0.0678600
\(958\) 90.3964 2.92058
\(959\) 18.9538 0.612051
\(960\) 89.2661 2.88105
\(961\) 6.94950 0.224177
\(962\) 0 0
\(963\) −12.2352 −0.394274
\(964\) 100.206 3.22743
\(965\) −31.0880 −1.00076
\(966\) −20.4017 −0.656413
\(967\) −41.2637 −1.32695 −0.663476 0.748197i \(-0.730920\pi\)
−0.663476 + 0.748197i \(0.730920\pi\)
\(968\) −9.58828 −0.308179
\(969\) 11.2286 0.360713
\(970\) −138.459 −4.44566
\(971\) 10.2876 0.330146 0.165073 0.986281i \(-0.447214\pi\)
0.165073 + 0.986281i \(0.447214\pi\)
\(972\) 5.50093 0.176442
\(973\) −67.5697 −2.16618
\(974\) 51.1286 1.63827
\(975\) 0 0
\(976\) −35.8353 −1.14706
\(977\) 54.0502 1.72922 0.864609 0.502445i \(-0.167566\pi\)
0.864609 + 0.502445i \(0.167566\pi\)
\(978\) 31.2310 0.998657
\(979\) 3.23647 0.103438
\(980\) 132.162 4.22176
\(981\) 8.72763 0.278652
\(982\) 18.5755 0.592766
\(983\) 33.3316 1.06311 0.531557 0.847022i \(-0.321607\pi\)
0.531557 + 0.847022i \(0.321607\pi\)
\(984\) 60.9611 1.94337
\(985\) −26.8045 −0.854061
\(986\) 21.9525 0.699109
\(987\) 20.8805 0.664635
\(988\) 0 0
\(989\) 22.2217 0.706610
\(990\) 7.78236 0.247340
\(991\) 15.1783 0.482155 0.241077 0.970506i \(-0.422499\pi\)
0.241077 + 0.970506i \(0.422499\pi\)
\(992\) −139.302 −4.42283
\(993\) −0.560518 −0.0177875
\(994\) −108.681 −3.44715
\(995\) −43.5318 −1.38005
\(996\) −58.7144 −1.86044
\(997\) −23.6131 −0.747834 −0.373917 0.927462i \(-0.621986\pi\)
−0.373917 + 0.927462i \(0.621986\pi\)
\(998\) −0.583086 −0.0184573
\(999\) −8.34404 −0.263994
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 5577.2.a.x.1.1 7
13.5 odd 4 429.2.b.b.298.14 yes 14
13.8 odd 4 429.2.b.b.298.1 14
13.12 even 2 5577.2.a.y.1.7 7
39.5 even 4 1287.2.b.c.298.1 14
39.8 even 4 1287.2.b.c.298.14 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.1 14 13.8 odd 4
429.2.b.b.298.14 yes 14 13.5 odd 4
1287.2.b.c.298.1 14 39.5 even 4
1287.2.b.c.298.14 14 39.8 even 4
5577.2.a.x.1.1 7 1.1 even 1 trivial
5577.2.a.y.1.7 7 13.12 even 2