Properties

Label 4598.2.a.bq.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: \(x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 1\)
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

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

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 \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −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 \(-0.177565\pi\)
0.848403 + 0.529351i \(0.177565\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0.673091 0.173791
\(16\) 1.00000 0.250000
\(17\) −0.239314 −0.0580421 −0.0290210 0.999579i \(-0.509239\pi\)
−0.0290210 + 0.999579i \(0.509239\pi\)
\(18\) 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 \(-0.871829\pi\)
−0.920021 + 0.391869i \(0.871829\pi\)
\(30\) −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 \(-0.322497\pi\)
0.529187 + 0.848505i \(0.322497\pi\)
\(42\) −0.326909 −0.0504431
\(43\) −6.97136 −1.06312 −0.531562 0.847020i \(-0.678395\pi\)
−0.531562 + 0.847020i \(0.678395\pi\)
\(44\) 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 \(-0.636802\pi\)
−0.416666 + 0.909060i \(0.636802\pi\)
\(62\) 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 \(-0.398211\pi\)
0.314358 + 0.949304i \(0.398211\pi\)
\(74\) 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 \(-0.767220\pi\)
−0.744307 + 0.667838i \(0.767220\pi\)
\(80\) 2.05896 0.230199
\(81\) 8.04960 0.894400
\(82\) −6.77690 −0.748383
\(83\) 13.6983 1.50358 0.751789 0.659404i \(-0.229191\pi\)
0.751789 + 0.659404i \(0.229191\pi\)
\(84\) 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 \(-0.511974\pi\)
−0.0376093 + 0.999293i \(0.511974\pi\)
\(102\) 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 \(-0.0963383\pi\)
0.954548 + 0.298056i \(0.0963383\pi\)
\(108\) −1.92651 −0.185379
\(109\) −0.462413 −0.0442912 −0.0221456 0.999755i \(-0.507050\pi\)
−0.0221456 + 0.999755i \(0.507050\pi\)
\(110\) 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 \(-0.475871\pi\)
0.0757311 + 0.997128i \(0.475871\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.27900 −0.200655
\(130\) −12.5965 −1.10479
\(131\) 4.75763 0.415676 0.207838 0.978163i \(-0.433357\pi\)
0.207838 + 0.978163i \(0.433357\pi\)
\(132\) 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 \(-0.637981\pi\)
−0.420031 + 0.907510i \(0.637981\pi\)
\(140\) 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 \(-0.721376\pi\)
−0.640749 + 0.767751i \(0.721376\pi\)
\(150\) 0.248675 0.0203042
\(151\) −7.72383 −0.628556 −0.314278 0.949331i \(-0.601762\pi\)
−0.314278 + 0.949331i \(0.601762\pi\)
\(152\) 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 \(-0.240233\pi\)
0.728468 + 0.685079i \(0.240233\pi\)
\(168\) −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 \(-0.434914\pi\)
0.203051 + 0.979168i \(0.434914\pi\)
\(174\) 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 \(-0.803231\pi\)
−0.814942 + 0.579542i \(0.803231\pi\)
\(194\) −17.9789 −1.29081
\(195\) 4.11792 0.294890
\(196\) −6.00000 −0.428571
\(197\) −11.7534 −0.837397 −0.418699 0.908125i \(-0.637514\pi\)
−0.418699 + 0.908125i \(0.637514\pi\)
\(198\) 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 \(-0.138965\pi\)
0.906206 + 0.422836i \(0.138965\pi\)
\(212\) −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 \(-0.560338\pi\)
−0.188426 + 0.982087i \(0.560338\pi\)
\(228\) −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 \(-0.433569\pi\)
0.207186 + 0.978302i \(0.433569\pi\)
\(234\) 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 \(-0.369608\pi\)
0.398279 + 0.917264i \(0.369608\pi\)
\(240\) 0.673091 0.0434479
\(241\) −10.6345 −0.685031 −0.342516 0.939512i \(-0.611279\pi\)
−0.342516 + 0.939512i \(0.611279\pi\)
\(242\) 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 \(-0.510108\pi\)
−0.0317492 + 0.999496i \(0.510108\pi\)
\(264\) 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 \(-0.679169\pi\)
−0.533622 + 0.845723i \(0.679169\pi\)
\(272\) −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 \(-0.260919\pi\)
0.682441 + 0.730941i \(0.260919\pi\)
\(278\) 9.90418 0.594013
\(279\) 10.9950 0.658252
\(280\) −2.05896 −0.123046
\(281\) 1.25215 0.0746971 0.0373485 0.999302i \(-0.488109\pi\)
0.0373485 + 0.999302i \(0.488109\pi\)
\(282\) −1.37651 −0.0819698
\(283\) −0.0103291 −0.000614000 0 −0.000307000 1.00000i \(-0.500098\pi\)
−0.000307000 1.00000i \(0.500098\pi\)
\(284\) −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 \(-0.612317\pi\)
−0.345578 + 0.938390i \(0.612317\pi\)
\(294\) 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 \(-0.234644\pi\)
0.740384 + 0.672185i \(0.234644\pi\)
\(308\) 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 \(-0.508964\pi\)
−0.0281573 + 0.999604i \(0.508964\pi\)
\(338\) −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 \(-0.522149\pi\)
−0.0695258 + 0.997580i \(0.522149\pi\)
\(348\) −3.23931 −0.173645
\(349\) −11.1278 −0.595659 −0.297830 0.954619i \(-0.596263\pi\)
−0.297830 + 0.954619i \(0.596263\pi\)
\(350\) 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 \(-0.298200\pi\)
0.592352 + 0.805679i \(0.298200\pi\)
\(360\) 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 \(-0.552696\pi\)
−0.164795 + 0.986328i \(0.552696\pi\)
\(374\) 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 \(-0.148386\pi\)
0.893297 + 0.449467i \(0.148386\pi\)
\(410\) −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 \(-0.550556\pi\)
−0.158159 + 0.987414i \(0.550556\pi\)
\(432\) −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 \(-0.728108\pi\)
−0.656842 + 0.754028i \(0.728108\pi\)
\(440\) 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 \(-0.509760\pi\)
−0.0306559 + 0.999530i \(0.509760\pi\)
\(458\) −1.27397 −0.0595287
\(459\) 0.461041 0.0215196
\(460\) −15.6700 −0.730619
\(461\) −19.3338 −0.900463 −0.450232 0.892912i \(-0.648659\pi\)
−0.450232 + 0.892912i \(0.648659\pi\)
\(462\) 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 \(-0.791692\pi\)
−0.793402 + 0.608698i \(0.791692\pi\)
\(480\) −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 \(-0.289771\pi\)
0.613475 + 0.789714i \(0.289771\pi\)
\(492\) 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 \(-0.582611\pi\)
−0.256626 + 0.966511i \(0.582611\pi\)
\(504\) 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 \(-0.342476\pi\)
0.474922 + 0.880028i \(0.342476\pi\)
\(524\) 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 \(-0.550283\pi\)
−0.157312 + 0.987549i \(0.550283\pi\)
\(542\) 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 \(-0.430275\pi\)
0.217300 + 0.976105i \(0.430275\pi\)
\(548\) 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 \(-0.457825\pi\)
0.132110 + 0.991235i \(0.457825\pi\)
\(558\) −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 \(-0.584640\pi\)
−0.262782 + 0.964855i \(0.584640\pi\)
\(564\) 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 \(-0.542417\pi\)
−0.132864 + 0.991134i \(0.542417\pi\)
\(570\) 0.673091 0.0281927
\(571\) −21.6888 −0.907646 −0.453823 0.891092i \(-0.649940\pi\)
−0.453823 + 0.891092i \(0.649940\pi\)
\(572\) 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 \(-0.396824\pi\)
0.318490 + 0.947926i \(0.396824\pi\)
\(594\) 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 \(-0.622390\pi\)
−0.375096 + 0.926986i \(0.622390\pi\)
\(602\) 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 \(-0.478280\pi\)
0.0681838 + 0.997673i \(0.478280\pi\)
\(608\) 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 \(-0.625710\pi\)
−0.384743 + 0.923024i \(0.625710\pi\)
\(614\) −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 \(-0.295238\pi\)
0.599822 + 0.800133i \(0.295238\pi\)
\(660\) 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 \(-0.702424\pi\)
−0.593928 + 0.804518i \(0.702424\pi\)
\(674\) 1.03380 0.0398205
\(675\) 1.46547 0.0564061
\(676\) 24.4289 0.939574
\(677\) 29.4745 1.13280 0.566399 0.824131i \(-0.308336\pi\)
0.566399 + 0.824131i \(0.308336\pi\)
\(678\) 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 \(-0.393376\pi\)
0.328739 + 0.944421i \(0.393376\pi\)
\(702\) 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 \(-0.741521\pi\)
−0.688022 + 0.725690i \(0.741521\pi\)
\(734\) 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 \(-0.605532\pi\)
−0.325498 + 0.945543i \(0.605532\pi\)
\(740\) −23.5055 −0.864078
\(741\) −2.00000 −0.0734718
\(742\) 8.68414 0.318805
\(743\) 13.0381 0.478323 0.239161 0.970980i \(-0.423128\pi\)
0.239161 + 0.970980i \(0.423128\pi\)
\(744\) 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 \(-0.589661\pi\)
−0.277968 + 0.960590i \(0.589661\pi\)
\(762\) −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 \(-0.527679\pi\)
−0.0868477 + 0.996222i \(0.527679\pi\)
\(770\) 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 \(-0.172411\pi\)
0.856861 + 0.515548i \(0.172411\pi\)
\(788\) −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 \(-0.558919\pi\)
−0.184045 + 0.982918i \(0.558919\pi\)
\(810\) −16.5738 −0.582344
\(811\) 37.4640 1.31554 0.657769 0.753220i \(-0.271500\pi\)
0.657769 + 0.753220i \(0.271500\pi\)
\(812\) −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 \(-0.488918\pi\)
0.0348084 + 0.999394i \(0.488918\pi\)
\(822\) −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 \(-0.584704\pi\)
−0.262977 + 0.964802i \(0.584704\pi\)
\(828\) 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 \(-0.455689\pi\)
0.138759 + 0.990326i \(0.455689\pi\)
\(854\) 6.50854 0.222717
\(855\) 5.95684 0.203720
\(856\) −19.7478 −0.674968
\(857\) 12.0630 0.412064 0.206032 0.978545i \(-0.433945\pi\)
0.206032 + 0.978545i \(0.433945\pi\)
\(858\) 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 \(-0.771420\pi\)
−0.753054 + 0.657959i \(0.771420\pi\)
\(878\) 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 \(-0.478400\pi\)
0.0678053 + 0.997699i \(0.478400\pi\)
\(888\) 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 \(-0.355551\pi\)
0.438385 + 0.898788i \(0.355551\pi\)
\(920\) 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 \(-0.726776\pi\)
−0.653681 + 0.756770i \(0.726776\pi\)
\(938\) 9.28891 0.303294
\(939\) 2.49484 0.0814161
\(940\) 8.66962 0.282772
\(941\) −10.7298 −0.349782 −0.174891 0.984588i \(-0.555957\pi\)
−0.174891 + 0.984588i \(0.555957\pi\)
\(942\) 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 \(-0.670242\pi\)
−0.509695 + 0.860355i \(0.670242\pi\)
\(954\) −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 \(-0.654193\pi\)
−0.465686 + 0.884950i \(0.654193\pi\)
\(968\) 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 \(-0.318233\pi\)
0.540506 + 0.841340i \(0.318233\pi\)
\(998\) 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.bq.1.3 4
11.10 odd 2 4598.2.a.bt.1.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bq.1.3 4 1.1 even 1 trivial
4598.2.a.bt.1.3 yes 4 11.10 odd 2