Properties

Label 4598.2.a.bt.1.3
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.7488.1
Defining polynomial: \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.05896\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.326909 q^{3} +1.00000 q^{4} +2.05896 q^{5} +0.326909 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.89313 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.326909 q^{3} +1.00000 q^{4} +2.05896 q^{5} +0.326909 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.89313 q^{9} +2.05896 q^{10} +0.326909 q^{12} -6.11792 q^{13} -1.00000 q^{14} +0.673091 q^{15} +1.00000 q^{16} +0.239314 q^{17} -2.89313 q^{18} +1.00000 q^{19} +2.05896 q^{20} -0.326909 q^{21} -7.61066 q^{23} +0.326909 q^{24} -0.760686 q^{25} -6.11792 q^{26} -1.92651 q^{27} -1.00000 q^{28} +9.90893 q^{29} +0.673091 q^{30} -3.80037 q^{31} +1.00000 q^{32} +0.239314 q^{34} -2.05896 q^{35} -2.89313 q^{36} -11.4162 q^{37} +1.00000 q^{38} -2.00000 q^{39} +2.05896 q^{40} -6.77690 q^{41} -0.326909 q^{42} +6.97136 q^{43} -5.95684 q^{45} -7.61066 q^{46} +4.21068 q^{47} +0.326909 q^{48} -6.00000 q^{49} -0.760686 q^{50} +0.0782337 q^{51} -6.11792 q^{52} -8.68414 q^{53} -1.92651 q^{54} -1.00000 q^{56} +0.326909 q^{57} +9.90893 q^{58} +13.2551 q^{59} +0.673091 q^{60} +6.50854 q^{61} -3.80037 q^{62} +2.89313 q^{63} +1.00000 q^{64} -12.5965 q^{65} -9.28891 q^{67} +0.239314 q^{68} -2.48799 q^{69} -2.05896 q^{70} -8.28416 q^{71} -2.89313 q^{72} -5.37176 q^{73} -11.4162 q^{74} -0.248675 q^{75} +1.00000 q^{76} -2.00000 q^{78} +13.2311 q^{79} +2.05896 q^{80} +8.04960 q^{81} -6.77690 q^{82} -13.6983 q^{83} -0.326909 q^{84} +0.492737 q^{85} +6.97136 q^{86} +3.23931 q^{87} -13.5486 q^{89} -5.95684 q^{90} +6.11792 q^{91} -7.61066 q^{92} -1.24237 q^{93} +4.21068 q^{94} +2.05896 q^{95} +0.326909 q^{96} +17.9789 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{12} - 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 4 q^{32} - 4 q^{34} + 2 q^{35} - 10 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 2 q^{48} - 24 q^{49} - 8 q^{50} - 4 q^{52} - 6 q^{53} - 14 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 20 q^{65} - 20 q^{67} - 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} + 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} - 34 q^{83} + 2 q^{84} + 16 q^{86} + 8 q^{87} - 2 q^{89} - 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} - 2 q^{95} - 2 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.326909 0.188741 0.0943704 0.995537i \(-0.469916\pi\)
0.0943704 + 0.995537i \(0.469916\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.05896 0.920795 0.460397 0.887713i \(-0.347707\pi\)
0.460397 + 0.887713i \(0.347707\pi\)
\(6\) 0.326909 0.133460
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.89313 −0.964377
\(10\) 2.05896 0.651100
\(11\) 0 0
\(12\) 0.326909 0.0943704
\(13\) −6.11792 −1.69681 −0.848403 0.529351i \(-0.822435\pi\)
−0.848403 + 0.529351i \(0.822435\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0.673091 0.173791
\(16\) 1.00000 0.250000
\(17\) 0.239314 0.0580421 0.0290210 0.999579i \(-0.490761\pi\)
0.0290210 + 0.999579i \(0.490761\pi\)
\(18\) −2.89313 −0.681917
\(19\) 1.00000 0.229416
\(20\) 2.05896 0.460397
\(21\) −0.326909 −0.0713373
\(22\) 0 0
\(23\) −7.61066 −1.58693 −0.793466 0.608615i \(-0.791725\pi\)
−0.793466 + 0.608615i \(0.791725\pi\)
\(24\) 0.326909 0.0667299
\(25\) −0.760686 −0.152137
\(26\) −6.11792 −1.19982
\(27\) −1.92651 −0.370758
\(28\) −1.00000 −0.188982
\(29\) 9.90893 1.84004 0.920021 0.391869i \(-0.128171\pi\)
0.920021 + 0.391869i \(0.128171\pi\)
\(30\) 0.673091 0.122889
\(31\) −3.80037 −0.682567 −0.341283 0.939960i \(-0.610862\pi\)
−0.341283 + 0.939960i \(0.610862\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.239314 0.0410420
\(35\) −2.05896 −0.348028
\(36\) −2.89313 −0.482188
\(37\) −11.4162 −1.87681 −0.938405 0.345537i \(-0.887697\pi\)
−0.938405 + 0.345537i \(0.887697\pi\)
\(38\) 1.00000 0.162221
\(39\) −2.00000 −0.320256
\(40\) 2.05896 0.325550
\(41\) −6.77690 −1.05837 −0.529187 0.848505i \(-0.677503\pi\)
−0.529187 + 0.848505i \(0.677503\pi\)
\(42\) −0.326909 −0.0504431
\(43\) 6.97136 1.06312 0.531562 0.847020i \(-0.321605\pi\)
0.531562 + 0.847020i \(0.321605\pi\)
\(44\) 0 0
\(45\) −5.95684 −0.887993
\(46\) −7.61066 −1.12213
\(47\) 4.21068 0.614191 0.307095 0.951679i \(-0.400643\pi\)
0.307095 + 0.951679i \(0.400643\pi\)
\(48\) 0.326909 0.0471852
\(49\) −6.00000 −0.857143
\(50\) −0.760686 −0.107577
\(51\) 0.0782337 0.0109549
\(52\) −6.11792 −0.848403
\(53\) −8.68414 −1.19286 −0.596429 0.802666i \(-0.703414\pi\)
−0.596429 + 0.802666i \(0.703414\pi\)
\(54\) −1.92651 −0.262165
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0.326909 0.0433001
\(58\) 9.90893 1.30111
\(59\) 13.2551 1.72567 0.862834 0.505487i \(-0.168687\pi\)
0.862834 + 0.505487i \(0.168687\pi\)
\(60\) 0.673091 0.0868957
\(61\) 6.50854 0.833333 0.416666 0.909060i \(-0.363198\pi\)
0.416666 + 0.909060i \(0.363198\pi\)
\(62\) −3.80037 −0.482648
\(63\) 2.89313 0.364500
\(64\) 1.00000 0.125000
\(65\) −12.5965 −1.56241
\(66\) 0 0
\(67\) −9.28891 −1.13482 −0.567411 0.823435i \(-0.692055\pi\)
−0.567411 + 0.823435i \(0.692055\pi\)
\(68\) 0.239314 0.0290210
\(69\) −2.48799 −0.299519
\(70\) −2.05896 −0.246093
\(71\) −8.28416 −0.983149 −0.491575 0.870835i \(-0.663579\pi\)
−0.491575 + 0.870835i \(0.663579\pi\)
\(72\) −2.89313 −0.340959
\(73\) −5.37176 −0.628717 −0.314358 0.949304i \(-0.601789\pi\)
−0.314358 + 0.949304i \(0.601789\pi\)
\(74\) −11.4162 −1.32711
\(75\) −0.248675 −0.0287145
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 13.2311 1.48861 0.744307 0.667838i \(-0.232780\pi\)
0.744307 + 0.667838i \(0.232780\pi\)
\(80\) 2.05896 0.230199
\(81\) 8.04960 0.894400
\(82\) −6.77690 −0.748383
\(83\) −13.6983 −1.50358 −0.751789 0.659404i \(-0.770809\pi\)
−0.751789 + 0.659404i \(0.770809\pi\)
\(84\) −0.326909 −0.0356686
\(85\) 0.492737 0.0534448
\(86\) 6.97136 0.751742
\(87\) 3.23931 0.347291
\(88\) 0 0
\(89\) −13.5486 −1.43615 −0.718076 0.695964i \(-0.754977\pi\)
−0.718076 + 0.695964i \(0.754977\pi\)
\(90\) −5.95684 −0.627906
\(91\) 6.11792 0.641332
\(92\) −7.61066 −0.793466
\(93\) −1.24237 −0.128828
\(94\) 4.21068 0.434298
\(95\) 2.05896 0.211245
\(96\) 0.326909 0.0333650
\(97\) 17.9789 1.82548 0.912742 0.408536i \(-0.133961\pi\)
0.912742 + 0.408536i \(0.133961\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) −0.760686 −0.0760686
\(101\) 0.755938 0.0752186 0.0376093 0.999293i \(-0.488026\pi\)
0.0376093 + 0.999293i \(0.488026\pi\)
\(102\) 0.0782337 0.00774629
\(103\) −10.2842 −1.01333 −0.506664 0.862143i \(-0.669122\pi\)
−0.506664 + 0.862143i \(0.669122\pi\)
\(104\) −6.11792 −0.599911
\(105\) −0.673091 −0.0656870
\(106\) −8.68414 −0.843478
\(107\) −19.7478 −1.90910 −0.954548 0.298056i \(-0.903662\pi\)
−0.954548 + 0.298056i \(0.903662\pi\)
\(108\) −1.92651 −0.185379
\(109\) 0.462413 0.0442912 0.0221456 0.999755i \(-0.492950\pi\)
0.0221456 + 0.999755i \(0.492950\pi\)
\(110\) 0 0
\(111\) −3.73205 −0.354231
\(112\) −1.00000 −0.0944911
\(113\) −1.12728 −0.106046 −0.0530228 0.998593i \(-0.516886\pi\)
−0.0530228 + 0.998593i \(0.516886\pi\)
\(114\) 0.326909 0.0306178
\(115\) −15.6700 −1.46124
\(116\) 9.90893 0.920021
\(117\) 17.6999 1.63636
\(118\) 13.2551 1.22023
\(119\) −0.239314 −0.0219378
\(120\) 0.673091 0.0614446
\(121\) 0 0
\(122\) 6.50854 0.589255
\(123\) −2.21543 −0.199758
\(124\) −3.80037 −0.341283
\(125\) −11.8610 −1.06088
\(126\) 2.89313 0.257741
\(127\) −1.70689 −0.151462 −0.0757311 0.997128i \(-0.524129\pi\)
−0.0757311 + 0.997128i \(0.524129\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.27900 0.200655
\(130\) −12.5965 −1.10479
\(131\) −4.75763 −0.415676 −0.207838 0.978163i \(-0.566643\pi\)
−0.207838 + 0.978163i \(0.566643\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) −9.28891 −0.802440
\(135\) −3.96662 −0.341392
\(136\) 0.239314 0.0205210
\(137\) 6.66067 0.569059 0.284530 0.958667i \(-0.408163\pi\)
0.284530 + 0.958667i \(0.408163\pi\)
\(138\) −2.48799 −0.211792
\(139\) 9.90418 0.840062 0.420031 0.907510i \(-0.362019\pi\)
0.420031 + 0.907510i \(0.362019\pi\)
\(140\) −2.05896 −0.174014
\(141\) 1.37651 0.115923
\(142\) −8.28416 −0.695192
\(143\) 0 0
\(144\) −2.89313 −0.241094
\(145\) 20.4021 1.69430
\(146\) −5.37176 −0.444570
\(147\) −1.96145 −0.161778
\(148\) −11.4162 −0.938405
\(149\) 15.6427 1.28150 0.640749 0.767751i \(-0.278624\pi\)
0.640749 + 0.767751i \(0.278624\pi\)
\(150\) −0.248675 −0.0203042
\(151\) 7.72383 0.628556 0.314278 0.949331i \(-0.398238\pi\)
0.314278 + 0.949331i \(0.398238\pi\)
\(152\) 1.00000 0.0811107
\(153\) −0.692366 −0.0559745
\(154\) 0 0
\(155\) −7.82481 −0.628504
\(156\) −2.00000 −0.160128
\(157\) −8.20132 −0.654536 −0.327268 0.944932i \(-0.606128\pi\)
−0.327268 + 0.944932i \(0.606128\pi\)
\(158\) 13.2311 1.05261
\(159\) −2.83892 −0.225141
\(160\) 2.05896 0.162775
\(161\) 7.61066 0.599804
\(162\) 8.04960 0.632436
\(163\) −3.24237 −0.253962 −0.126981 0.991905i \(-0.540529\pi\)
−0.126981 + 0.991905i \(0.540529\pi\)
\(164\) −6.77690 −0.529187
\(165\) 0 0
\(166\) −13.6983 −1.06319
\(167\) −18.8278 −1.45694 −0.728468 0.685079i \(-0.759767\pi\)
−0.728468 + 0.685079i \(0.759767\pi\)
\(168\) −0.326909 −0.0252215
\(169\) 24.4289 1.87915
\(170\) 0.492737 0.0377912
\(171\) −2.89313 −0.221243
\(172\) 6.97136 0.531562
\(173\) −5.34143 −0.406102 −0.203051 0.979168i \(-0.565086\pi\)
−0.203051 + 0.979168i \(0.565086\pi\)
\(174\) 3.23931 0.245572
\(175\) 0.760686 0.0575025
\(176\) 0 0
\(177\) 4.33321 0.325704
\(178\) −13.5486 −1.01551
\(179\) 17.7349 1.32557 0.662783 0.748811i \(-0.269375\pi\)
0.662783 + 0.748811i \(0.269375\pi\)
\(180\) −5.95684 −0.443997
\(181\) 3.94273 0.293061 0.146530 0.989206i \(-0.453189\pi\)
0.146530 + 0.989206i \(0.453189\pi\)
\(182\) 6.11792 0.453490
\(183\) 2.12770 0.157284
\(184\) −7.61066 −0.561065
\(185\) −23.5055 −1.72816
\(186\) −1.24237 −0.0910953
\(187\) 0 0
\(188\) 4.21068 0.307095
\(189\) 1.92651 0.140133
\(190\) 2.05896 0.149373
\(191\) 23.2183 1.68001 0.840007 0.542576i \(-0.182551\pi\)
0.840007 + 0.542576i \(0.182551\pi\)
\(192\) 0.326909 0.0235926
\(193\) 22.6431 1.62988 0.814942 0.579542i \(-0.196769\pi\)
0.814942 + 0.579542i \(0.196769\pi\)
\(194\) 17.9789 1.29081
\(195\) −4.11792 −0.294890
\(196\) −6.00000 −0.428571
\(197\) 11.7534 0.837397 0.418699 0.908125i \(-0.362486\pi\)
0.418699 + 0.908125i \(0.362486\pi\)
\(198\) 0 0
\(199\) −2.14012 −0.151709 −0.0758544 0.997119i \(-0.524168\pi\)
−0.0758544 + 0.997119i \(0.524168\pi\)
\(200\) −0.760686 −0.0537886
\(201\) −3.03662 −0.214187
\(202\) 0.755938 0.0531876
\(203\) −9.90893 −0.695470
\(204\) 0.0782337 0.00547745
\(205\) −13.9534 −0.974545
\(206\) −10.2842 −0.716532
\(207\) 22.0186 1.53040
\(208\) −6.11792 −0.424201
\(209\) 0 0
\(210\) −0.673091 −0.0464477
\(211\) −26.3268 −1.81241 −0.906206 0.422836i \(-0.861035\pi\)
−0.906206 + 0.422836i \(0.861035\pi\)
\(212\) −8.68414 −0.596429
\(213\) −2.70816 −0.185560
\(214\) −19.7478 −1.34994
\(215\) 14.3538 0.978918
\(216\) −1.92651 −0.131083
\(217\) 3.80037 0.257986
\(218\) 0.462413 0.0313186
\(219\) −1.75607 −0.118664
\(220\) 0 0
\(221\) −1.46410 −0.0984861
\(222\) −3.73205 −0.250479
\(223\) 6.11359 0.409396 0.204698 0.978825i \(-0.434379\pi\)
0.204698 + 0.978825i \(0.434379\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 2.20077 0.146718
\(226\) −1.12728 −0.0749855
\(227\) 5.67784 0.376851 0.188426 0.982087i \(-0.439662\pi\)
0.188426 + 0.982087i \(0.439662\pi\)
\(228\) 0.326909 0.0216500
\(229\) 1.27397 0.0841863 0.0420932 0.999114i \(-0.486597\pi\)
0.0420932 + 0.999114i \(0.486597\pi\)
\(230\) −15.6700 −1.03325
\(231\) 0 0
\(232\) 9.90893 0.650553
\(233\) −6.32512 −0.414372 −0.207186 0.978302i \(-0.566431\pi\)
−0.207186 + 0.978302i \(0.566431\pi\)
\(234\) 17.6999 1.15708
\(235\) 8.66962 0.565543
\(236\) 13.2551 0.862834
\(237\) 4.32536 0.280962
\(238\) −0.239314 −0.0155124
\(239\) −12.3145 −0.796558 −0.398279 0.917264i \(-0.630392\pi\)
−0.398279 + 0.917264i \(0.630392\pi\)
\(240\) 0.673091 0.0434479
\(241\) 10.6345 0.685031 0.342516 0.939512i \(-0.388721\pi\)
0.342516 + 0.939512i \(0.388721\pi\)
\(242\) 0 0
\(243\) 8.41103 0.539568
\(244\) 6.50854 0.416666
\(245\) −12.3538 −0.789253
\(246\) −2.21543 −0.141250
\(247\) −6.11792 −0.389274
\(248\) −3.80037 −0.241324
\(249\) −4.47808 −0.283786
\(250\) −11.8610 −0.750157
\(251\) −17.4068 −1.09871 −0.549355 0.835589i \(-0.685126\pi\)
−0.549355 + 0.835589i \(0.685126\pi\)
\(252\) 2.89313 0.182250
\(253\) 0 0
\(254\) −1.70689 −0.107100
\(255\) 0.161080 0.0100872
\(256\) 1.00000 0.0625000
\(257\) 10.1752 0.634711 0.317355 0.948307i \(-0.397205\pi\)
0.317355 + 0.948307i \(0.397205\pi\)
\(258\) 2.27900 0.141884
\(259\) 11.4162 0.709368
\(260\) −12.5965 −0.781205
\(261\) −28.6678 −1.77449
\(262\) −4.75763 −0.293927
\(263\) 1.02977 0.0634985 0.0317492 0.999496i \(-0.489892\pi\)
0.0317492 + 0.999496i \(0.489892\pi\)
\(264\) 0 0
\(265\) −17.8803 −1.09838
\(266\) −1.00000 −0.0613139
\(267\) −4.42917 −0.271061
\(268\) −9.28891 −0.567411
\(269\) 13.9055 0.847830 0.423915 0.905702i \(-0.360655\pi\)
0.423915 + 0.905702i \(0.360655\pi\)
\(270\) −3.96662 −0.241401
\(271\) 17.5690 1.06724 0.533622 0.845723i \(-0.320831\pi\)
0.533622 + 0.845723i \(0.320831\pi\)
\(272\) 0.239314 0.0145105
\(273\) 2.00000 0.121046
\(274\) 6.66067 0.402386
\(275\) 0 0
\(276\) −2.48799 −0.149759
\(277\) −22.7162 −1.36488 −0.682441 0.730941i \(-0.739081\pi\)
−0.682441 + 0.730941i \(0.739081\pi\)
\(278\) 9.90418 0.594013
\(279\) 10.9950 0.658252
\(280\) −2.05896 −0.123046
\(281\) −1.25215 −0.0746971 −0.0373485 0.999302i \(-0.511891\pi\)
−0.0373485 + 0.999302i \(0.511891\pi\)
\(282\) 1.37651 0.0819698
\(283\) 0.0103291 0.000614000 0 0.000307000 1.00000i \(-0.499902\pi\)
0.000307000 1.00000i \(0.499902\pi\)
\(284\) −8.28416 −0.491575
\(285\) 0.673091 0.0398705
\(286\) 0 0
\(287\) 6.77690 0.400028
\(288\) −2.89313 −0.170479
\(289\) −16.9427 −0.996631
\(290\) 20.4021 1.19805
\(291\) 5.87747 0.344543
\(292\) −5.37176 −0.314358
\(293\) 11.8307 0.691157 0.345578 0.938390i \(-0.387683\pi\)
0.345578 + 0.938390i \(0.387683\pi\)
\(294\) −1.96145 −0.114394
\(295\) 27.2917 1.58899
\(296\) −11.4162 −0.663553
\(297\) 0 0
\(298\) 15.6427 0.906155
\(299\) 46.5614 2.69271
\(300\) −0.248675 −0.0143573
\(301\) −6.97136 −0.401823
\(302\) 7.72383 0.444456
\(303\) 0.247123 0.0141968
\(304\) 1.00000 0.0573539
\(305\) 13.4008 0.767328
\(306\) −0.692366 −0.0395799
\(307\) −25.9451 −1.48077 −0.740384 0.672185i \(-0.765356\pi\)
−0.740384 + 0.672185i \(0.765356\pi\)
\(308\) 0 0
\(309\) −3.36198 −0.191256
\(310\) −7.82481 −0.444419
\(311\) 17.7512 1.00658 0.503289 0.864118i \(-0.332123\pi\)
0.503289 + 0.864118i \(0.332123\pi\)
\(312\) −2.00000 −0.113228
\(313\) 7.63162 0.431365 0.215682 0.976464i \(-0.430802\pi\)
0.215682 + 0.976464i \(0.430802\pi\)
\(314\) −8.20132 −0.462827
\(315\) 5.95684 0.335630
\(316\) 13.2311 0.744307
\(317\) 12.5298 0.703742 0.351871 0.936048i \(-0.385546\pi\)
0.351871 + 0.936048i \(0.385546\pi\)
\(318\) −2.83892 −0.159199
\(319\) 0 0
\(320\) 2.05896 0.115099
\(321\) −6.45574 −0.360324
\(322\) 7.61066 0.424125
\(323\) 0.239314 0.0133158
\(324\) 8.04960 0.447200
\(325\) 4.65382 0.258147
\(326\) −3.24237 −0.179578
\(327\) 0.151167 0.00835955
\(328\) −6.77690 −0.374192
\(329\) −4.21068 −0.232142
\(330\) 0 0
\(331\) −34.3093 −1.88581 −0.942905 0.333060i \(-0.891919\pi\)
−0.942905 + 0.333060i \(0.891919\pi\)
\(332\) −13.6983 −0.751789
\(333\) 33.0285 1.80995
\(334\) −18.8278 −1.03021
\(335\) −19.1255 −1.04494
\(336\) −0.326909 −0.0178343
\(337\) 1.03380 0.0563147 0.0281573 0.999604i \(-0.491036\pi\)
0.0281573 + 0.999604i \(0.491036\pi\)
\(338\) 24.4289 1.32876
\(339\) −0.368517 −0.0200151
\(340\) 0.492737 0.0267224
\(341\) 0 0
\(342\) −2.89313 −0.156443
\(343\) 13.0000 0.701934
\(344\) 6.97136 0.375871
\(345\) −5.12267 −0.275795
\(346\) −5.34143 −0.287157
\(347\) 2.59025 0.139052 0.0695258 0.997580i \(-0.477851\pi\)
0.0695258 + 0.997580i \(0.477851\pi\)
\(348\) 3.23931 0.173645
\(349\) 11.1278 0.595659 0.297830 0.954619i \(-0.403737\pi\)
0.297830 + 0.954619i \(0.403737\pi\)
\(350\) 0.760686 0.0406604
\(351\) 11.7863 0.629104
\(352\) 0 0
\(353\) −28.1896 −1.50038 −0.750191 0.661221i \(-0.770038\pi\)
−0.750191 + 0.661221i \(0.770038\pi\)
\(354\) 4.33321 0.230307
\(355\) −17.0568 −0.905279
\(356\) −13.5486 −0.718076
\(357\) −0.0782337 −0.00414057
\(358\) 17.7349 0.937317
\(359\) −22.4469 −1.18470 −0.592352 0.805679i \(-0.701800\pi\)
−0.592352 + 0.805679i \(0.701800\pi\)
\(360\) −5.95684 −0.313953
\(361\) 1.00000 0.0526316
\(362\) 3.94273 0.207225
\(363\) 0 0
\(364\) 6.11792 0.320666
\(365\) −11.0602 −0.578919
\(366\) 2.12770 0.111216
\(367\) −7.10729 −0.370997 −0.185499 0.982645i \(-0.559390\pi\)
−0.185499 + 0.982645i \(0.559390\pi\)
\(368\) −7.61066 −0.396733
\(369\) 19.6065 1.02067
\(370\) −23.5055 −1.22199
\(371\) 8.68414 0.450858
\(372\) −1.24237 −0.0644141
\(373\) 6.36546 0.329591 0.164795 0.986328i \(-0.447304\pi\)
0.164795 + 0.986328i \(0.447304\pi\)
\(374\) 0 0
\(375\) −3.87747 −0.200232
\(376\) 4.21068 0.217149
\(377\) −60.6220 −3.12219
\(378\) 1.92651 0.0990892
\(379\) 21.0623 1.08190 0.540950 0.841055i \(-0.318065\pi\)
0.540950 + 0.841055i \(0.318065\pi\)
\(380\) 2.05896 0.105622
\(381\) −0.557997 −0.0285871
\(382\) 23.2183 1.18795
\(383\) −24.8640 −1.27049 −0.635245 0.772311i \(-0.719101\pi\)
−0.635245 + 0.772311i \(0.719101\pi\)
\(384\) 0.326909 0.0166825
\(385\) 0 0
\(386\) 22.6431 1.15250
\(387\) −20.1691 −1.02525
\(388\) 17.9789 0.912742
\(389\) −11.6841 −0.592409 −0.296205 0.955124i \(-0.595721\pi\)
−0.296205 + 0.955124i \(0.595721\pi\)
\(390\) −4.11792 −0.208519
\(391\) −1.82133 −0.0921088
\(392\) −6.00000 −0.303046
\(393\) −1.55531 −0.0784549
\(394\) 11.7534 0.592129
\(395\) 27.2423 1.37071
\(396\) 0 0
\(397\) −24.7751 −1.24343 −0.621714 0.783245i \(-0.713563\pi\)
−0.621714 + 0.783245i \(0.713563\pi\)
\(398\) −2.14012 −0.107274
\(399\) −0.326909 −0.0163659
\(400\) −0.760686 −0.0380343
\(401\) −15.5124 −0.774654 −0.387327 0.921942i \(-0.626601\pi\)
−0.387327 + 0.921942i \(0.626601\pi\)
\(402\) −3.03662 −0.151453
\(403\) 23.2504 1.15818
\(404\) 0.755938 0.0376093
\(405\) 16.5738 0.823559
\(406\) −9.90893 −0.491772
\(407\) 0 0
\(408\) 0.0782337 0.00387314
\(409\) −36.1316 −1.78659 −0.893297 0.449467i \(-0.851614\pi\)
−0.893297 + 0.449467i \(0.851614\pi\)
\(410\) −13.9534 −0.689107
\(411\) 2.17743 0.107405
\(412\) −10.2842 −0.506664
\(413\) −13.2551 −0.652241
\(414\) 22.0186 1.08216
\(415\) −28.2041 −1.38449
\(416\) −6.11792 −0.299956
\(417\) 3.23776 0.158554
\(418\) 0 0
\(419\) −29.9947 −1.46534 −0.732669 0.680585i \(-0.761726\pi\)
−0.732669 + 0.680585i \(0.761726\pi\)
\(420\) −0.673091 −0.0328435
\(421\) 30.1891 1.47132 0.735662 0.677348i \(-0.236871\pi\)
0.735662 + 0.677348i \(0.236871\pi\)
\(422\) −26.3268 −1.28157
\(423\) −12.1820 −0.592311
\(424\) −8.68414 −0.421739
\(425\) −0.182043 −0.00883037
\(426\) −2.70816 −0.131211
\(427\) −6.50854 −0.314970
\(428\) −19.7478 −0.954548
\(429\) 0 0
\(430\) 14.3538 0.692200
\(431\) 6.56694 0.316318 0.158159 0.987414i \(-0.449444\pi\)
0.158159 + 0.987414i \(0.449444\pi\)
\(432\) −1.92651 −0.0926895
\(433\) 25.2584 1.21384 0.606919 0.794763i \(-0.292405\pi\)
0.606919 + 0.794763i \(0.292405\pi\)
\(434\) 3.80037 0.182424
\(435\) 6.66962 0.319784
\(436\) 0.462413 0.0221456
\(437\) −7.61066 −0.364067
\(438\) −1.75607 −0.0839084
\(439\) 27.5247 1.31368 0.656842 0.754028i \(-0.271892\pi\)
0.656842 + 0.754028i \(0.271892\pi\)
\(440\) 0 0
\(441\) 17.3588 0.826609
\(442\) −1.46410 −0.0696402
\(443\) −17.1569 −0.815148 −0.407574 0.913172i \(-0.633625\pi\)
−0.407574 + 0.913172i \(0.633625\pi\)
\(444\) −3.73205 −0.177115
\(445\) −27.8961 −1.32240
\(446\) 6.11359 0.289487
\(447\) 5.11372 0.241871
\(448\) −1.00000 −0.0472456
\(449\) −37.2186 −1.75645 −0.878226 0.478245i \(-0.841273\pi\)
−0.878226 + 0.478245i \(0.841273\pi\)
\(450\) 2.20077 0.103745
\(451\) 0 0
\(452\) −1.12728 −0.0530228
\(453\) 2.52498 0.118634
\(454\) 5.67784 0.266474
\(455\) 12.5965 0.590535
\(456\) 0.326909 0.0153089
\(457\) 1.31069 0.0613117 0.0306559 0.999530i \(-0.490240\pi\)
0.0306559 + 0.999530i \(0.490240\pi\)
\(458\) 1.27397 0.0595287
\(459\) −0.461041 −0.0215196
\(460\) −15.6700 −0.730619
\(461\) 19.3338 0.900463 0.450232 0.892912i \(-0.351341\pi\)
0.450232 + 0.892912i \(0.351341\pi\)
\(462\) 0 0
\(463\) 2.81631 0.130885 0.0654424 0.997856i \(-0.479154\pi\)
0.0654424 + 0.997856i \(0.479154\pi\)
\(464\) 9.90893 0.460010
\(465\) −2.55800 −0.118624
\(466\) −6.32512 −0.293006
\(467\) 19.0030 0.879352 0.439676 0.898156i \(-0.355093\pi\)
0.439676 + 0.898156i \(0.355093\pi\)
\(468\) 17.6999 0.818180
\(469\) 9.28891 0.428922
\(470\) 8.66962 0.399900
\(471\) −2.68108 −0.123538
\(472\) 13.2551 0.610116
\(473\) 0 0
\(474\) 4.32536 0.198670
\(475\) −0.760686 −0.0349027
\(476\) −0.239314 −0.0109689
\(477\) 25.1244 1.15037
\(478\) −12.3145 −0.563252
\(479\) 34.7289 1.58680 0.793402 0.608698i \(-0.208308\pi\)
0.793402 + 0.608698i \(0.208308\pi\)
\(480\) 0.673091 0.0307223
\(481\) 69.8433 3.18458
\(482\) 10.6345 0.484390
\(483\) 2.48799 0.113207
\(484\) 0 0
\(485\) 37.0179 1.68090
\(486\) 8.41103 0.381532
\(487\) −16.5313 −0.749104 −0.374552 0.927206i \(-0.622203\pi\)
−0.374552 + 0.927206i \(0.622203\pi\)
\(488\) 6.50854 0.294628
\(489\) −1.05996 −0.0479330
\(490\) −12.3538 −0.558086
\(491\) −27.1874 −1.22695 −0.613475 0.789714i \(-0.710229\pi\)
−0.613475 + 0.789714i \(0.710229\pi\)
\(492\) −2.21543 −0.0998792
\(493\) 2.37134 0.106800
\(494\) −6.11792 −0.275258
\(495\) 0 0
\(496\) −3.80037 −0.170642
\(497\) 8.28416 0.371596
\(498\) −4.47808 −0.200667
\(499\) −2.60980 −0.116831 −0.0584153 0.998292i \(-0.518605\pi\)
−0.0584153 + 0.998292i \(0.518605\pi\)
\(500\) −11.8610 −0.530441
\(501\) −6.15496 −0.274983
\(502\) −17.4068 −0.776905
\(503\) 11.5111 0.513253 0.256626 0.966511i \(-0.417389\pi\)
0.256626 + 0.966511i \(0.417389\pi\)
\(504\) 2.89313 0.128870
\(505\) 1.55645 0.0692609
\(506\) 0 0
\(507\) 7.98603 0.354672
\(508\) −1.70689 −0.0757311
\(509\) −20.5685 −0.911681 −0.455841 0.890061i \(-0.650661\pi\)
−0.455841 + 0.890061i \(0.650661\pi\)
\(510\) 0.161080 0.00713274
\(511\) 5.37176 0.237633
\(512\) 1.00000 0.0441942
\(513\) −1.92651 −0.0850577
\(514\) 10.1752 0.448808
\(515\) −21.1747 −0.933068
\(516\) 2.27900 0.100327
\(517\) 0 0
\(518\) 11.4162 0.501599
\(519\) −1.74616 −0.0766479
\(520\) −12.5965 −0.552395
\(521\) 14.6328 0.641073 0.320536 0.947236i \(-0.396137\pi\)
0.320536 + 0.947236i \(0.396137\pi\)
\(522\) −28.6678 −1.25476
\(523\) −21.7222 −0.949844 −0.474922 0.880028i \(-0.657524\pi\)
−0.474922 + 0.880028i \(0.657524\pi\)
\(524\) −4.75763 −0.207838
\(525\) 0.248675 0.0108531
\(526\) 1.02977 0.0449002
\(527\) −0.909481 −0.0396176
\(528\) 0 0
\(529\) 34.9221 1.51835
\(530\) −17.8803 −0.776670
\(531\) −38.3488 −1.66419
\(532\) −1.00000 −0.0433555
\(533\) 41.4605 1.79585
\(534\) −4.42917 −0.191669
\(535\) −40.6600 −1.75789
\(536\) −9.28891 −0.401220
\(537\) 5.79768 0.250188
\(538\) 13.9055 0.599507
\(539\) 0 0
\(540\) −3.96662 −0.170696
\(541\) 7.31796 0.314624 0.157312 0.987549i \(-0.449717\pi\)
0.157312 + 0.987549i \(0.449717\pi\)
\(542\) 17.5690 0.754655
\(543\) 1.28891 0.0553125
\(544\) 0.239314 0.0102605
\(545\) 0.952090 0.0407831
\(546\) 2.00000 0.0855921
\(547\) −10.1644 −0.434599 −0.217300 0.976105i \(-0.569725\pi\)
−0.217300 + 0.976105i \(0.569725\pi\)
\(548\) 6.66067 0.284530
\(549\) −18.8300 −0.803647
\(550\) 0 0
\(551\) 9.90893 0.422135
\(552\) −2.48799 −0.105896
\(553\) −13.2311 −0.562643
\(554\) −22.7162 −0.965117
\(555\) −7.68414 −0.326174
\(556\) 9.90418 0.420031
\(557\) −6.23584 −0.264221 −0.132110 0.991235i \(-0.542175\pi\)
−0.132110 + 0.991235i \(0.542175\pi\)
\(558\) 10.9950 0.465454
\(559\) −42.6502 −1.80391
\(560\) −2.05896 −0.0870069
\(561\) 0 0
\(562\) −1.25215 −0.0528188
\(563\) 12.4704 0.525565 0.262782 0.964855i \(-0.415360\pi\)
0.262782 + 0.964855i \(0.415360\pi\)
\(564\) 1.37651 0.0579614
\(565\) −2.32102 −0.0976462
\(566\) 0.0103291 0.000434164 0
\(567\) −8.04960 −0.338051
\(568\) −8.28416 −0.347596
\(569\) 6.33861 0.265728 0.132864 0.991134i \(-0.457583\pi\)
0.132864 + 0.991134i \(0.457583\pi\)
\(570\) 0.673091 0.0281927
\(571\) 21.6888 0.907646 0.453823 0.891092i \(-0.350060\pi\)
0.453823 + 0.891092i \(0.350060\pi\)
\(572\) 0 0
\(573\) 7.59025 0.317087
\(574\) 6.77690 0.282862
\(575\) 5.78932 0.241431
\(576\) −2.89313 −0.120547
\(577\) 10.1622 0.423059 0.211529 0.977372i \(-0.432156\pi\)
0.211529 + 0.977372i \(0.432156\pi\)
\(578\) −16.9427 −0.704725
\(579\) 7.40222 0.307626
\(580\) 20.4021 0.847150
\(581\) 13.6983 0.568299
\(582\) 5.87747 0.243629
\(583\) 0 0
\(584\) −5.37176 −0.222285
\(585\) 36.4435 1.50675
\(586\) 11.8307 0.488722
\(587\) −24.2773 −1.00203 −0.501016 0.865438i \(-0.667040\pi\)
−0.501016 + 0.865438i \(0.667040\pi\)
\(588\) −1.96145 −0.0808889
\(589\) −3.80037 −0.156592
\(590\) 27.2917 1.12358
\(591\) 3.84230 0.158051
\(592\) −11.4162 −0.469203
\(593\) −15.5115 −0.636979 −0.318490 0.947926i \(-0.603176\pi\)
−0.318490 + 0.947926i \(0.603176\pi\)
\(594\) 0 0
\(595\) −0.492737 −0.0202003
\(596\) 15.6427 0.640749
\(597\) −0.699623 −0.0286336
\(598\) 46.5614 1.90404
\(599\) −6.71530 −0.274380 −0.137190 0.990545i \(-0.543807\pi\)
−0.137190 + 0.990545i \(0.543807\pi\)
\(600\) −0.248675 −0.0101521
\(601\) 18.3912 0.750193 0.375096 0.926986i \(-0.377610\pi\)
0.375096 + 0.926986i \(0.377610\pi\)
\(602\) −6.97136 −0.284132
\(603\) 26.8740 1.09440
\(604\) 7.72383 0.314278
\(605\) 0 0
\(606\) 0.247123 0.0100387
\(607\) −3.35974 −0.136368 −0.0681838 0.997673i \(-0.521720\pi\)
−0.0681838 + 0.997673i \(0.521720\pi\)
\(608\) 1.00000 0.0405554
\(609\) −3.23931 −0.131264
\(610\) 13.4008 0.542583
\(611\) −25.7606 −1.04216
\(612\) −0.692366 −0.0279872
\(613\) 19.0516 0.769487 0.384743 0.923024i \(-0.374290\pi\)
0.384743 + 0.923024i \(0.374290\pi\)
\(614\) −25.9451 −1.04706
\(615\) −4.56147 −0.183936
\(616\) 0 0
\(617\) −20.5000 −0.825299 −0.412650 0.910890i \(-0.635397\pi\)
−0.412650 + 0.910890i \(0.635397\pi\)
\(618\) −3.36198 −0.135239
\(619\) −6.78351 −0.272652 −0.136326 0.990664i \(-0.543529\pi\)
−0.136326 + 0.990664i \(0.543529\pi\)
\(620\) −7.82481 −0.314252
\(621\) 14.6620 0.588367
\(622\) 17.7512 0.711758
\(623\) 13.5486 0.542815
\(624\) −2.00000 −0.0800641
\(625\) −20.6179 −0.824717
\(626\) 7.63162 0.305021
\(627\) 0 0
\(628\) −8.20132 −0.327268
\(629\) −2.73205 −0.108934
\(630\) 5.95684 0.237326
\(631\) −0.184271 −0.00733571 −0.00366786 0.999993i \(-0.501168\pi\)
−0.00366786 + 0.999993i \(0.501168\pi\)
\(632\) 13.2311 0.526304
\(633\) −8.60646 −0.342076
\(634\) 12.5298 0.497621
\(635\) −3.51442 −0.139466
\(636\) −2.83892 −0.112571
\(637\) 36.7075 1.45440
\(638\) 0 0
\(639\) 23.9672 0.948127
\(640\) 2.05896 0.0813875
\(641\) 16.9380 0.669010 0.334505 0.942394i \(-0.391431\pi\)
0.334505 + 0.942394i \(0.391431\pi\)
\(642\) −6.45574 −0.254788
\(643\) 0.934052 0.0368354 0.0184177 0.999830i \(-0.494137\pi\)
0.0184177 + 0.999830i \(0.494137\pi\)
\(644\) 7.61066 0.299902
\(645\) 4.69237 0.184762
\(646\) 0.239314 0.00941567
\(647\) 29.1175 1.14473 0.572364 0.820000i \(-0.306027\pi\)
0.572364 + 0.820000i \(0.306027\pi\)
\(648\) 8.04960 0.316218
\(649\) 0 0
\(650\) 4.65382 0.182538
\(651\) 1.24237 0.0486925
\(652\) −3.24237 −0.126981
\(653\) 2.11414 0.0827326 0.0413663 0.999144i \(-0.486829\pi\)
0.0413663 + 0.999144i \(0.486829\pi\)
\(654\) 0.151167 0.00591109
\(655\) −9.79576 −0.382752
\(656\) −6.77690 −0.264594
\(657\) 15.5412 0.606320
\(658\) −4.21068 −0.164149
\(659\) −30.7961 −1.19964 −0.599822 0.800133i \(-0.704762\pi\)
−0.599822 + 0.800133i \(0.704762\pi\)
\(660\) 0 0
\(661\) −2.31197 −0.0899251 −0.0449625 0.998989i \(-0.514317\pi\)
−0.0449625 + 0.998989i \(0.514317\pi\)
\(662\) −34.3093 −1.33347
\(663\) −0.478627 −0.0185883
\(664\) −13.6983 −0.531595
\(665\) −2.05896 −0.0798430
\(666\) 33.0285 1.27983
\(667\) −75.4134 −2.92002
\(668\) −18.8278 −0.728468
\(669\) 1.99858 0.0772697
\(670\) −19.1255 −0.738882
\(671\) 0 0
\(672\) −0.326909 −0.0126108
\(673\) 30.8157 1.18786 0.593928 0.804518i \(-0.297576\pi\)
0.593928 + 0.804518i \(0.297576\pi\)
\(674\) 1.03380 0.0398205
\(675\) 1.46547 0.0564061
\(676\) 24.4289 0.939574
\(677\) −29.4745 −1.13280 −0.566399 0.824131i \(-0.691664\pi\)
−0.566399 + 0.824131i \(0.691664\pi\)
\(678\) −0.368517 −0.0141528
\(679\) −17.9789 −0.689968
\(680\) 0.492737 0.0188956
\(681\) 1.85613 0.0711272
\(682\) 0 0
\(683\) 35.8855 1.37312 0.686559 0.727074i \(-0.259120\pi\)
0.686559 + 0.727074i \(0.259120\pi\)
\(684\) −2.89313 −0.110622
\(685\) 13.7140 0.523987
\(686\) 13.0000 0.496342
\(687\) 0.416472 0.0158894
\(688\) 6.97136 0.265781
\(689\) 53.1289 2.02405
\(690\) −5.12267 −0.195017
\(691\) 24.3791 0.927423 0.463711 0.885986i \(-0.346517\pi\)
0.463711 + 0.885986i \(0.346517\pi\)
\(692\) −5.34143 −0.203051
\(693\) 0 0
\(694\) 2.59025 0.0983244
\(695\) 20.3923 0.773524
\(696\) 3.23931 0.122786
\(697\) −1.62180 −0.0614302
\(698\) 11.1278 0.421195
\(699\) −2.06774 −0.0782090
\(700\) 0.760686 0.0287512
\(701\) −17.4077 −0.657478 −0.328739 0.944421i \(-0.606624\pi\)
−0.328739 + 0.944421i \(0.606624\pi\)
\(702\) 11.7863 0.444844
\(703\) −11.4162 −0.430570
\(704\) 0 0
\(705\) 2.83417 0.106741
\(706\) −28.1896 −1.06093
\(707\) −0.755938 −0.0284300
\(708\) 4.33321 0.162852
\(709\) 16.4309 0.617074 0.308537 0.951212i \(-0.400161\pi\)
0.308537 + 0.951212i \(0.400161\pi\)
\(710\) −17.0568 −0.640129
\(711\) −38.2793 −1.43558
\(712\) −13.5486 −0.507757
\(713\) 28.9233 1.08319
\(714\) −0.0782337 −0.00292782
\(715\) 0 0
\(716\) 17.7349 0.662783
\(717\) −4.02571 −0.150343
\(718\) −22.4469 −0.837712
\(719\) −17.2596 −0.643674 −0.321837 0.946795i \(-0.604300\pi\)
−0.321837 + 0.946795i \(0.604300\pi\)
\(720\) −5.95684 −0.221998
\(721\) 10.2842 0.383002
\(722\) 1.00000 0.0372161
\(723\) 3.47652 0.129293
\(724\) 3.94273 0.146530
\(725\) −7.53759 −0.279939
\(726\) 0 0
\(727\) −16.6519 −0.617583 −0.308792 0.951130i \(-0.599925\pi\)
−0.308792 + 0.951130i \(0.599925\pi\)
\(728\) 6.11792 0.226745
\(729\) −21.3992 −0.792561
\(730\) −11.0602 −0.409358
\(731\) 1.66834 0.0617059
\(732\) 2.12770 0.0786419
\(733\) 37.2550 1.37604 0.688022 0.725690i \(-0.258479\pi\)
0.688022 + 0.725690i \(0.258479\pi\)
\(734\) −7.10729 −0.262335
\(735\) −4.03855 −0.148964
\(736\) −7.61066 −0.280532
\(737\) 0 0
\(738\) 19.6065 0.721724
\(739\) 17.6970 0.650995 0.325498 0.945543i \(-0.394468\pi\)
0.325498 + 0.945543i \(0.394468\pi\)
\(740\) −23.5055 −0.864078
\(741\) −2.00000 −0.0734718
\(742\) 8.68414 0.318805
\(743\) −13.0381 −0.478323 −0.239161 0.970980i \(-0.576872\pi\)
−0.239161 + 0.970980i \(0.576872\pi\)
\(744\) −1.24237 −0.0455476
\(745\) 32.2076 1.18000
\(746\) 6.36546 0.233056
\(747\) 39.6308 1.45002
\(748\) 0 0
\(749\) 19.7478 0.721571
\(750\) −3.87747 −0.141585
\(751\) −28.7414 −1.04879 −0.524395 0.851475i \(-0.675709\pi\)
−0.524395 + 0.851475i \(0.675709\pi\)
\(752\) 4.21068 0.153548
\(753\) −5.69044 −0.207371
\(754\) −60.6220 −2.20772
\(755\) 15.9030 0.578771
\(756\) 1.92651 0.0700667
\(757\) −47.5277 −1.72742 −0.863711 0.503987i \(-0.831866\pi\)
−0.863711 + 0.503987i \(0.831866\pi\)
\(758\) 21.0623 0.765018
\(759\) 0 0
\(760\) 2.05896 0.0746863
\(761\) 15.3362 0.555936 0.277968 0.960590i \(-0.410339\pi\)
0.277968 + 0.960590i \(0.410339\pi\)
\(762\) −0.557997 −0.0202141
\(763\) −0.462413 −0.0167405
\(764\) 23.2183 0.840007
\(765\) −1.42555 −0.0515410
\(766\) −24.8640 −0.898372
\(767\) −81.0937 −2.92812
\(768\) 0.326909 0.0117963
\(769\) 4.81672 0.173695 0.0868477 0.996222i \(-0.472321\pi\)
0.0868477 + 0.996222i \(0.472321\pi\)
\(770\) 0 0
\(771\) 3.32636 0.119796
\(772\) 22.6431 0.814942
\(773\) 38.2891 1.37716 0.688581 0.725159i \(-0.258234\pi\)
0.688581 + 0.725159i \(0.258234\pi\)
\(774\) −20.1691 −0.724962
\(775\) 2.89089 0.103844
\(776\) 17.9789 0.645406
\(777\) 3.73205 0.133887
\(778\) −11.6841 −0.418897
\(779\) −6.77690 −0.242808
\(780\) −4.11792 −0.147445
\(781\) 0 0
\(782\) −1.82133 −0.0651308
\(783\) −19.0897 −0.682210
\(784\) −6.00000 −0.214286
\(785\) −16.8862 −0.602694
\(786\) −1.55531 −0.0554760
\(787\) −48.0759 −1.71372 −0.856861 0.515548i \(-0.827589\pi\)
−0.856861 + 0.515548i \(0.827589\pi\)
\(788\) 11.7534 0.418699
\(789\) 0.336641 0.0119847
\(790\) 27.2423 0.969237
\(791\) 1.12728 0.0400815
\(792\) 0 0
\(793\) −39.8187 −1.41400
\(794\) −24.7751 −0.879236
\(795\) −5.84522 −0.207309
\(796\) −2.14012 −0.0758544
\(797\) 12.8137 0.453883 0.226942 0.973908i \(-0.427127\pi\)
0.226942 + 0.973908i \(0.427127\pi\)
\(798\) −0.326909 −0.0115724
\(799\) 1.00767 0.0356489
\(800\) −0.760686 −0.0268943
\(801\) 39.1980 1.38499
\(802\) −15.5124 −0.547763
\(803\) 0 0
\(804\) −3.03662 −0.107093
\(805\) 15.6700 0.552296
\(806\) 23.2504 0.818959
\(807\) 4.54581 0.160020
\(808\) 0.755938 0.0265938
\(809\) 10.4695 0.368090 0.184045 0.982918i \(-0.441081\pi\)
0.184045 + 0.982918i \(0.441081\pi\)
\(810\) 16.5738 0.582344
\(811\) −37.4640 −1.31554 −0.657769 0.753220i \(-0.728500\pi\)
−0.657769 + 0.753220i \(0.728500\pi\)
\(812\) −9.90893 −0.347735
\(813\) 5.74347 0.201432
\(814\) 0 0
\(815\) −6.67592 −0.233847
\(816\) 0.0782337 0.00273873
\(817\) 6.97136 0.243897
\(818\) −36.1316 −1.26331
\(819\) −17.6999 −0.618486
\(820\) −13.9534 −0.487273
\(821\) −1.99474 −0.0696168 −0.0348084 0.999394i \(-0.511082\pi\)
−0.0348084 + 0.999394i \(0.511082\pi\)
\(822\) 2.17743 0.0759466
\(823\) −39.5721 −1.37940 −0.689698 0.724097i \(-0.742257\pi\)
−0.689698 + 0.724097i \(0.742257\pi\)
\(824\) −10.2842 −0.358266
\(825\) 0 0
\(826\) −13.2551 −0.461204
\(827\) 15.1252 0.525954 0.262977 0.964802i \(-0.415296\pi\)
0.262977 + 0.964802i \(0.415296\pi\)
\(828\) 22.0186 0.765200
\(829\) 4.54877 0.157985 0.0789927 0.996875i \(-0.474830\pi\)
0.0789927 + 0.996875i \(0.474830\pi\)
\(830\) −28.2041 −0.978980
\(831\) −7.42610 −0.257609
\(832\) −6.11792 −0.212101
\(833\) −1.43588 −0.0497504
\(834\) 3.23776 0.112115
\(835\) −38.7656 −1.34154
\(836\) 0 0
\(837\) 7.32147 0.253067
\(838\) −29.9947 −1.03615
\(839\) 22.7135 0.784157 0.392079 0.919932i \(-0.371756\pi\)
0.392079 + 0.919932i \(0.371756\pi\)
\(840\) −0.673091 −0.0232239
\(841\) 69.1869 2.38575
\(842\) 30.1891 1.04038
\(843\) −0.409339 −0.0140984
\(844\) −26.3268 −0.906206
\(845\) 50.2982 1.73031
\(846\) −12.1820 −0.418827
\(847\) 0 0
\(848\) −8.68414 −0.298215
\(849\) 0.00337666 0.000115887 0
\(850\) −0.182043 −0.00624401
\(851\) 86.8847 2.97837
\(852\) −2.70816 −0.0927802
\(853\) −8.10525 −0.277518 −0.138759 0.990326i \(-0.544311\pi\)
−0.138759 + 0.990326i \(0.544311\pi\)
\(854\) −6.50854 −0.222717
\(855\) −5.95684 −0.203720
\(856\) −19.7478 −0.674968
\(857\) −12.0630 −0.412064 −0.206032 0.978545i \(-0.566055\pi\)
−0.206032 + 0.978545i \(0.566055\pi\)
\(858\) 0 0
\(859\) 28.7979 0.982570 0.491285 0.870999i \(-0.336527\pi\)
0.491285 + 0.870999i \(0.336527\pi\)
\(860\) 14.3538 0.489459
\(861\) 2.21543 0.0755015
\(862\) 6.56694 0.223671
\(863\) −18.7423 −0.637995 −0.318997 0.947756i \(-0.603346\pi\)
−0.318997 + 0.947756i \(0.603346\pi\)
\(864\) −1.92651 −0.0655414
\(865\) −10.9978 −0.373936
\(866\) 25.2584 0.858314
\(867\) −5.53872 −0.188105
\(868\) 3.80037 0.128993
\(869\) 0 0
\(870\) 6.66962 0.226121
\(871\) 56.8288 1.92557
\(872\) 0.462413 0.0156593
\(873\) −52.0154 −1.76046
\(874\) −7.61066 −0.257434
\(875\) 11.8610 0.400976
\(876\) −1.75607 −0.0593322
\(877\) 44.6022 1.50611 0.753054 0.657959i \(-0.228580\pi\)
0.753054 + 0.657959i \(0.228580\pi\)
\(878\) 27.5247 0.928915
\(879\) 3.86756 0.130449
\(880\) 0 0
\(881\) 9.17519 0.309120 0.154560 0.987983i \(-0.450604\pi\)
0.154560 + 0.987983i \(0.450604\pi\)
\(882\) 17.3588 0.584501
\(883\) 15.1520 0.509906 0.254953 0.966953i \(-0.417940\pi\)
0.254953 + 0.966953i \(0.417940\pi\)
\(884\) −1.46410 −0.0492431
\(885\) 8.92190 0.299906
\(886\) −17.1569 −0.576397
\(887\) −4.03883 −0.135611 −0.0678053 0.997699i \(-0.521600\pi\)
−0.0678053 + 0.997699i \(0.521600\pi\)
\(888\) −3.73205 −0.125239
\(889\) 1.70689 0.0572473
\(890\) −27.8961 −0.935079
\(891\) 0 0
\(892\) 6.11359 0.204698
\(893\) 4.21068 0.140905
\(894\) 5.11372 0.171028
\(895\) 36.5154 1.22057
\(896\) −1.00000 −0.0334077
\(897\) 15.2213 0.508225
\(898\) −37.2186 −1.24200
\(899\) −37.6576 −1.25595
\(900\) 2.20077 0.0733588
\(901\) −2.07823 −0.0692360
\(902\) 0 0
\(903\) −2.27900 −0.0758403
\(904\) −1.12728 −0.0374928
\(905\) 8.11792 0.269849
\(906\) 2.52498 0.0838870
\(907\) 12.0131 0.398890 0.199445 0.979909i \(-0.436086\pi\)
0.199445 + 0.979909i \(0.436086\pi\)
\(908\) 5.67784 0.188426
\(909\) −2.18703 −0.0725391
\(910\) 12.5965 0.417571
\(911\) 21.8314 0.723307 0.361654 0.932313i \(-0.382212\pi\)
0.361654 + 0.932313i \(0.382212\pi\)
\(912\) 0.326909 0.0108250
\(913\) 0 0
\(914\) 1.31069 0.0433539
\(915\) 4.38084 0.144826
\(916\) 1.27397 0.0420932
\(917\) 4.75763 0.157111
\(918\) −0.461041 −0.0152166
\(919\) −26.5793 −0.876769 −0.438385 0.898788i \(-0.644449\pi\)
−0.438385 + 0.898788i \(0.644449\pi\)
\(920\) −15.6700 −0.516626
\(921\) −8.48169 −0.279481
\(922\) 19.3338 0.636724
\(923\) 50.6818 1.66821
\(924\) 0 0
\(925\) 8.68414 0.285533
\(926\) 2.81631 0.0925495
\(927\) 29.7534 0.977231
\(928\) 9.90893 0.325277
\(929\) 46.5896 1.52856 0.764278 0.644887i \(-0.223096\pi\)
0.764278 + 0.644887i \(0.223096\pi\)
\(930\) −2.55800 −0.0838800
\(931\) −6.00000 −0.196642
\(932\) −6.32512 −0.207186
\(933\) 5.80302 0.189982
\(934\) 19.0030 0.621796
\(935\) 0 0
\(936\) 17.6999 0.578541
\(937\) 40.0189 1.30736 0.653681 0.756770i \(-0.273224\pi\)
0.653681 + 0.756770i \(0.273224\pi\)
\(938\) 9.28891 0.303294
\(939\) 2.49484 0.0814161
\(940\) 8.66962 0.282772
\(941\) 10.7298 0.349782 0.174891 0.984588i \(-0.444043\pi\)
0.174891 + 0.984588i \(0.444043\pi\)
\(942\) −2.68108 −0.0873543
\(943\) 51.5767 1.67957
\(944\) 13.2551 0.431417
\(945\) 3.96662 0.129034
\(946\) 0 0
\(947\) 58.1190 1.88861 0.944306 0.329068i \(-0.106735\pi\)
0.944306 + 0.329068i \(0.106735\pi\)
\(948\) 4.32536 0.140481
\(949\) 32.8640 1.06681
\(950\) −0.760686 −0.0246799
\(951\) 4.09609 0.132825
\(952\) −0.239314 −0.00775620
\(953\) 31.4693 1.01939 0.509695 0.860355i \(-0.329758\pi\)
0.509695 + 0.860355i \(0.329758\pi\)
\(954\) 25.1244 0.813431
\(955\) 47.8054 1.54695
\(956\) −12.3145 −0.398279
\(957\) 0 0
\(958\) 34.7289 1.12204
\(959\) −6.66067 −0.215084
\(960\) 0.673091 0.0217239
\(961\) −16.5572 −0.534102
\(962\) 69.8433 2.25184
\(963\) 57.1331 1.84109
\(964\) 10.6345 0.342516
\(965\) 46.6212 1.50079
\(966\) 2.48799 0.0800497
\(967\) 28.9626 0.931373 0.465686 0.884950i \(-0.345807\pi\)
0.465686 + 0.884950i \(0.345807\pi\)
\(968\) 0 0
\(969\) 0.0782337 0.00251323
\(970\) 37.0179 1.18857
\(971\) −4.45629 −0.143009 −0.0715046 0.997440i \(-0.522780\pi\)
−0.0715046 + 0.997440i \(0.522780\pi\)
\(972\) 8.41103 0.269784
\(973\) −9.90418 −0.317513
\(974\) −16.5313 −0.529697
\(975\) 1.52137 0.0487229
\(976\) 6.50854 0.208333
\(977\) 4.61527 0.147656 0.0738278 0.997271i \(-0.476478\pi\)
0.0738278 + 0.997271i \(0.476478\pi\)
\(978\) −1.05996 −0.0338938
\(979\) 0 0
\(980\) −12.3538 −0.394626
\(981\) −1.33782 −0.0427134
\(982\) −27.1874 −0.867584
\(983\) 3.49665 0.111526 0.0557630 0.998444i \(-0.482241\pi\)
0.0557630 + 0.998444i \(0.482241\pi\)
\(984\) −2.21543 −0.0706252
\(985\) 24.1998 0.771071
\(986\) 2.37134 0.0755189
\(987\) −1.37651 −0.0438147
\(988\) −6.11792 −0.194637
\(989\) −53.0567 −1.68710
\(990\) 0 0
\(991\) −41.3012 −1.31198 −0.655988 0.754771i \(-0.727748\pi\)
−0.655988 + 0.754771i \(0.727748\pi\)
\(992\) −3.80037 −0.120662
\(993\) −11.2160 −0.355929
\(994\) 8.28416 0.262758
\(995\) −4.40641 −0.139693
\(996\) −4.47808 −0.141893
\(997\) −34.1333 −1.08101 −0.540506 0.841340i \(-0.681767\pi\)
−0.540506 + 0.841340i \(0.681767\pi\)
\(998\) −2.60980 −0.0826118
\(999\) 21.9935 0.695842
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 4598.2.a.bt.1.3 yes 4
11.10 odd 2 4598.2.a.bq.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bq.1.3 4 11.10 odd 2
4598.2.a.bt.1.3 yes 4 1.1 even 1 trivial