Properties

Label 4598.2.a.bx.1.4
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $8$
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: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.488861\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} -0.158731 q^{6} -1.35199 q^{7} -1.00000 q^{8} -2.97480 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.158731 q^{3} +1.00000 q^{4} +3.07692 q^{5} -0.158731 q^{6} -1.35199 q^{7} -1.00000 q^{8} -2.97480 q^{9} -3.07692 q^{10} +0.158731 q^{12} +0.526746 q^{13} +1.35199 q^{14} +0.488401 q^{15} +1.00000 q^{16} -7.23593 q^{17} +2.97480 q^{18} +1.00000 q^{19} +3.07692 q^{20} -0.214602 q^{21} +2.09183 q^{23} -0.158731 q^{24} +4.46742 q^{25} -0.526746 q^{26} -0.948385 q^{27} -1.35199 q^{28} +0.277873 q^{29} -0.488401 q^{30} -1.72447 q^{31} -1.00000 q^{32} +7.23593 q^{34} -4.15995 q^{35} -2.97480 q^{36} +8.91226 q^{37} -1.00000 q^{38} +0.0836108 q^{39} -3.07692 q^{40} +8.37354 q^{41} +0.214602 q^{42} -6.30119 q^{43} -9.15323 q^{45} -2.09183 q^{46} +1.96711 q^{47} +0.158731 q^{48} -5.17213 q^{49} -4.46742 q^{50} -1.14856 q^{51} +0.526746 q^{52} -2.20703 q^{53} +0.948385 q^{54} +1.35199 q^{56} +0.158731 q^{57} -0.277873 q^{58} +8.72295 q^{59} +0.488401 q^{60} -6.38710 q^{61} +1.72447 q^{62} +4.02190 q^{63} +1.00000 q^{64} +1.62075 q^{65} -1.02001 q^{67} -7.23593 q^{68} +0.332037 q^{69} +4.15995 q^{70} -3.71385 q^{71} +2.97480 q^{72} -1.72161 q^{73} -8.91226 q^{74} +0.709116 q^{75} +1.00000 q^{76} -0.0836108 q^{78} -7.53423 q^{79} +3.07692 q^{80} +8.77388 q^{81} -8.37354 q^{82} -6.49693 q^{83} -0.214602 q^{84} -22.2643 q^{85} +6.30119 q^{86} +0.0441070 q^{87} -10.3518 q^{89} +9.15323 q^{90} -0.712155 q^{91} +2.09183 q^{92} -0.273726 q^{93} -1.96711 q^{94} +3.07692 q^{95} -0.158731 q^{96} -10.4421 q^{97} +5.17213 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9} - 2 q^{10} - 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} + 8 q^{19} + 2 q^{20} - 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} - 8 q^{28} - 14 q^{29} - 10 q^{30} - 2 q^{31} - 8 q^{32} + 4 q^{34} - 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 8 q^{41} + 14 q^{42} - 28 q^{43} - 28 q^{45} - 12 q^{46} + 6 q^{47} + 32 q^{49} + 12 q^{51} - 18 q^{52} - 24 q^{53} + 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} + 24 q^{61} + 2 q^{62} - 30 q^{63} + 8 q^{64} + 16 q^{65} - 22 q^{67} - 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} - 20 q^{72} - 16 q^{73} + 22 q^{74} + 6 q^{75} + 8 q^{76} - 4 q^{78} - 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} - 12 q^{83} - 14 q^{84} - 48 q^{85} + 28 q^{86} - 42 q^{87} - 28 q^{89} + 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} - 6 q^{94} + 2 q^{95} - 22 q^{97} - 32 q^{98}+O(q^{100}) \) 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
\(3\) 0.158731 0.0916432 0.0458216 0.998950i \(-0.485409\pi\)
0.0458216 + 0.998950i \(0.485409\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.07692 1.37604 0.688019 0.725692i \(-0.258480\pi\)
0.688019 + 0.725692i \(0.258480\pi\)
\(6\) −0.158731 −0.0648015
\(7\) −1.35199 −0.511003 −0.255502 0.966809i \(-0.582241\pi\)
−0.255502 + 0.966809i \(0.582241\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.97480 −0.991602
\(10\) −3.07692 −0.973007
\(11\) 0 0
\(12\) 0.158731 0.0458216
\(13\) 0.526746 0.146093 0.0730466 0.997329i \(-0.476728\pi\)
0.0730466 + 0.997329i \(0.476728\pi\)
\(14\) 1.35199 0.361334
\(15\) 0.488401 0.126105
\(16\) 1.00000 0.250000
\(17\) −7.23593 −1.75497 −0.877485 0.479604i \(-0.840780\pi\)
−0.877485 + 0.479604i \(0.840780\pi\)
\(18\) 2.97480 0.701168
\(19\) 1.00000 0.229416
\(20\) 3.07692 0.688019
\(21\) −0.214602 −0.0468300
\(22\) 0 0
\(23\) 2.09183 0.436176 0.218088 0.975929i \(-0.430018\pi\)
0.218088 + 0.975929i \(0.430018\pi\)
\(24\) −0.158731 −0.0324008
\(25\) 4.46742 0.893483
\(26\) −0.526746 −0.103303
\(27\) −0.948385 −0.182517
\(28\) −1.35199 −0.255502
\(29\) 0.277873 0.0515998 0.0257999 0.999667i \(-0.491787\pi\)
0.0257999 + 0.999667i \(0.491787\pi\)
\(30\) −0.488401 −0.0891694
\(31\) −1.72447 −0.309724 −0.154862 0.987936i \(-0.549493\pi\)
−0.154862 + 0.987936i \(0.549493\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 7.23593 1.24095
\(35\) −4.15995 −0.703161
\(36\) −2.97480 −0.495801
\(37\) 8.91226 1.46517 0.732584 0.680677i \(-0.238314\pi\)
0.732584 + 0.680677i \(0.238314\pi\)
\(38\) −1.00000 −0.162221
\(39\) 0.0836108 0.0133884
\(40\) −3.07692 −0.486503
\(41\) 8.37354 1.30773 0.653864 0.756612i \(-0.273147\pi\)
0.653864 + 0.756612i \(0.273147\pi\)
\(42\) 0.214602 0.0331138
\(43\) −6.30119 −0.960923 −0.480461 0.877016i \(-0.659531\pi\)
−0.480461 + 0.877016i \(0.659531\pi\)
\(44\) 0 0
\(45\) −9.15323 −1.36448
\(46\) −2.09183 −0.308423
\(47\) 1.96711 0.286933 0.143466 0.989655i \(-0.454175\pi\)
0.143466 + 0.989655i \(0.454175\pi\)
\(48\) 0.158731 0.0229108
\(49\) −5.17213 −0.738875
\(50\) −4.46742 −0.631788
\(51\) −1.14856 −0.160831
\(52\) 0.526746 0.0730466
\(53\) −2.20703 −0.303158 −0.151579 0.988445i \(-0.548436\pi\)
−0.151579 + 0.988445i \(0.548436\pi\)
\(54\) 0.948385 0.129059
\(55\) 0 0
\(56\) 1.35199 0.180667
\(57\) 0.158731 0.0210244
\(58\) −0.277873 −0.0364866
\(59\) 8.72295 1.13563 0.567816 0.823156i \(-0.307789\pi\)
0.567816 + 0.823156i \(0.307789\pi\)
\(60\) 0.488401 0.0630523
\(61\) −6.38710 −0.817785 −0.408892 0.912583i \(-0.634085\pi\)
−0.408892 + 0.912583i \(0.634085\pi\)
\(62\) 1.72447 0.219008
\(63\) 4.02190 0.506712
\(64\) 1.00000 0.125000
\(65\) 1.62075 0.201030
\(66\) 0 0
\(67\) −1.02001 −0.124614 −0.0623071 0.998057i \(-0.519846\pi\)
−0.0623071 + 0.998057i \(0.519846\pi\)
\(68\) −7.23593 −0.877485
\(69\) 0.332037 0.0399726
\(70\) 4.15995 0.497210
\(71\) −3.71385 −0.440753 −0.220376 0.975415i \(-0.570729\pi\)
−0.220376 + 0.975415i \(0.570729\pi\)
\(72\) 2.97480 0.350584
\(73\) −1.72161 −0.201499 −0.100750 0.994912i \(-0.532124\pi\)
−0.100750 + 0.994912i \(0.532124\pi\)
\(74\) −8.91226 −1.03603
\(75\) 0.709116 0.0818817
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −0.0836108 −0.00946706
\(79\) −7.53423 −0.847667 −0.423833 0.905740i \(-0.639316\pi\)
−0.423833 + 0.905740i \(0.639316\pi\)
\(80\) 3.07692 0.344010
\(81\) 8.77388 0.974875
\(82\) −8.37354 −0.924703
\(83\) −6.49693 −0.713131 −0.356565 0.934270i \(-0.616052\pi\)
−0.356565 + 0.934270i \(0.616052\pi\)
\(84\) −0.214602 −0.0234150
\(85\) −22.2643 −2.41491
\(86\) 6.30119 0.679475
\(87\) 0.0441070 0.00472877
\(88\) 0 0
\(89\) −10.3518 −1.09728 −0.548642 0.836057i \(-0.684855\pi\)
−0.548642 + 0.836057i \(0.684855\pi\)
\(90\) 9.15323 0.964835
\(91\) −0.712155 −0.0746541
\(92\) 2.09183 0.218088
\(93\) −0.273726 −0.0283841
\(94\) −1.96711 −0.202892
\(95\) 3.07692 0.315685
\(96\) −0.158731 −0.0162004
\(97\) −10.4421 −1.06023 −0.530116 0.847925i \(-0.677852\pi\)
−0.530116 + 0.847925i \(0.677852\pi\)
\(98\) 5.17213 0.522464
\(99\) 0 0
\(100\) 4.46742 0.446742
\(101\) −16.6075 −1.65251 −0.826254 0.563298i \(-0.809532\pi\)
−0.826254 + 0.563298i \(0.809532\pi\)
\(102\) 1.14856 0.113725
\(103\) −6.30847 −0.621592 −0.310796 0.950477i \(-0.600596\pi\)
−0.310796 + 0.950477i \(0.600596\pi\)
\(104\) −0.526746 −0.0516517
\(105\) −0.660313 −0.0644399
\(106\) 2.20703 0.214365
\(107\) −13.1999 −1.27608 −0.638041 0.770002i \(-0.720255\pi\)
−0.638041 + 0.770002i \(0.720255\pi\)
\(108\) −0.948385 −0.0912584
\(109\) −4.47355 −0.428488 −0.214244 0.976780i \(-0.568729\pi\)
−0.214244 + 0.976780i \(0.568729\pi\)
\(110\) 0 0
\(111\) 1.41465 0.134273
\(112\) −1.35199 −0.127751
\(113\) −12.5601 −1.18156 −0.590778 0.806834i \(-0.701179\pi\)
−0.590778 + 0.806834i \(0.701179\pi\)
\(114\) −0.158731 −0.0148665
\(115\) 6.43637 0.600195
\(116\) 0.277873 0.0257999
\(117\) −1.56697 −0.144866
\(118\) −8.72295 −0.803012
\(119\) 9.78288 0.896796
\(120\) −0.488401 −0.0445847
\(121\) 0 0
\(122\) 6.38710 0.578261
\(123\) 1.32914 0.119844
\(124\) −1.72447 −0.154862
\(125\) −1.63872 −0.146571
\(126\) −4.02190 −0.358299
\(127\) 16.4582 1.46042 0.730212 0.683220i \(-0.239421\pi\)
0.730212 + 0.683220i \(0.239421\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.00019 −0.0880621
\(130\) −1.62075 −0.142150
\(131\) −15.1571 −1.32428 −0.662140 0.749380i \(-0.730352\pi\)
−0.662140 + 0.749380i \(0.730352\pi\)
\(132\) 0 0
\(133\) −1.35199 −0.117232
\(134\) 1.02001 0.0881156
\(135\) −2.91810 −0.251150
\(136\) 7.23593 0.620475
\(137\) −5.46038 −0.466512 −0.233256 0.972415i \(-0.574938\pi\)
−0.233256 + 0.972415i \(0.574938\pi\)
\(138\) −0.332037 −0.0282649
\(139\) 9.22943 0.782830 0.391415 0.920214i \(-0.371986\pi\)
0.391415 + 0.920214i \(0.371986\pi\)
\(140\) −4.15995 −0.351580
\(141\) 0.312241 0.0262954
\(142\) 3.71385 0.311659
\(143\) 0 0
\(144\) −2.97480 −0.247900
\(145\) 0.854993 0.0710033
\(146\) 1.72161 0.142481
\(147\) −0.820976 −0.0677129
\(148\) 8.91226 0.732584
\(149\) 12.3302 1.01013 0.505065 0.863081i \(-0.331469\pi\)
0.505065 + 0.863081i \(0.331469\pi\)
\(150\) −0.709116 −0.0578991
\(151\) −3.63459 −0.295779 −0.147889 0.989004i \(-0.547248\pi\)
−0.147889 + 0.989004i \(0.547248\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 21.5255 1.74023
\(154\) 0 0
\(155\) −5.30605 −0.426192
\(156\) 0.0836108 0.00669422
\(157\) −0.871549 −0.0695572 −0.0347786 0.999395i \(-0.511073\pi\)
−0.0347786 + 0.999395i \(0.511073\pi\)
\(158\) 7.53423 0.599391
\(159\) −0.350323 −0.0277824
\(160\) −3.07692 −0.243252
\(161\) −2.82812 −0.222887
\(162\) −8.77388 −0.689341
\(163\) −7.73571 −0.605908 −0.302954 0.953005i \(-0.597973\pi\)
−0.302954 + 0.953005i \(0.597973\pi\)
\(164\) 8.37354 0.653864
\(165\) 0 0
\(166\) 6.49693 0.504259
\(167\) −21.8284 −1.68913 −0.844566 0.535451i \(-0.820142\pi\)
−0.844566 + 0.535451i \(0.820142\pi\)
\(168\) 0.214602 0.0165569
\(169\) −12.7225 −0.978657
\(170\) 22.2643 1.70760
\(171\) −2.97480 −0.227489
\(172\) −6.30119 −0.480461
\(173\) 11.0102 0.837086 0.418543 0.908197i \(-0.362541\pi\)
0.418543 + 0.908197i \(0.362541\pi\)
\(174\) −0.0441070 −0.00334375
\(175\) −6.03989 −0.456573
\(176\) 0 0
\(177\) 1.38460 0.104073
\(178\) 10.3518 0.775897
\(179\) −12.5527 −0.938233 −0.469116 0.883136i \(-0.655428\pi\)
−0.469116 + 0.883136i \(0.655428\pi\)
\(180\) −9.15323 −0.682241
\(181\) −3.45298 −0.256658 −0.128329 0.991732i \(-0.540961\pi\)
−0.128329 + 0.991732i \(0.540961\pi\)
\(182\) 0.712155 0.0527884
\(183\) −1.01383 −0.0749444
\(184\) −2.09183 −0.154211
\(185\) 27.4223 2.01613
\(186\) 0.273726 0.0200706
\(187\) 0 0
\(188\) 1.96711 0.143466
\(189\) 1.28221 0.0932667
\(190\) −3.07692 −0.223223
\(191\) 21.3218 1.54279 0.771397 0.636354i \(-0.219558\pi\)
0.771397 + 0.636354i \(0.219558\pi\)
\(192\) 0.158731 0.0114554
\(193\) −23.4522 −1.68813 −0.844063 0.536243i \(-0.819843\pi\)
−0.844063 + 0.536243i \(0.819843\pi\)
\(194\) 10.4421 0.749697
\(195\) 0.257263 0.0184230
\(196\) −5.17213 −0.369438
\(197\) 7.79605 0.555445 0.277723 0.960661i \(-0.410420\pi\)
0.277723 + 0.960661i \(0.410420\pi\)
\(198\) 0 0
\(199\) −9.48281 −0.672219 −0.336109 0.941823i \(-0.609111\pi\)
−0.336109 + 0.941823i \(0.609111\pi\)
\(200\) −4.46742 −0.315894
\(201\) −0.161907 −0.0114200
\(202\) 16.6075 1.16850
\(203\) −0.375681 −0.0263677
\(204\) −1.14856 −0.0804155
\(205\) 25.7647 1.79948
\(206\) 6.30847 0.439532
\(207\) −6.22277 −0.432513
\(208\) 0.526746 0.0365233
\(209\) 0 0
\(210\) 0.660313 0.0455659
\(211\) −15.5951 −1.07361 −0.536805 0.843707i \(-0.680369\pi\)
−0.536805 + 0.843707i \(0.680369\pi\)
\(212\) −2.20703 −0.151579
\(213\) −0.589502 −0.0403920
\(214\) 13.1999 0.902327
\(215\) −19.3882 −1.32227
\(216\) 0.948385 0.0645294
\(217\) 2.33146 0.158270
\(218\) 4.47355 0.302987
\(219\) −0.273272 −0.0184660
\(220\) 0 0
\(221\) −3.81150 −0.256389
\(222\) −1.41465 −0.0949451
\(223\) −24.4375 −1.63646 −0.818230 0.574892i \(-0.805044\pi\)
−0.818230 + 0.574892i \(0.805044\pi\)
\(224\) 1.35199 0.0903335
\(225\) −13.2897 −0.885979
\(226\) 12.5601 0.835486
\(227\) 23.2524 1.54332 0.771659 0.636037i \(-0.219427\pi\)
0.771659 + 0.636037i \(0.219427\pi\)
\(228\) 0.158731 0.0105122
\(229\) −1.94364 −0.128439 −0.0642197 0.997936i \(-0.520456\pi\)
−0.0642197 + 0.997936i \(0.520456\pi\)
\(230\) −6.43637 −0.424402
\(231\) 0 0
\(232\) −0.277873 −0.0182433
\(233\) −5.46260 −0.357867 −0.178933 0.983861i \(-0.557265\pi\)
−0.178933 + 0.983861i \(0.557265\pi\)
\(234\) 1.56697 0.102436
\(235\) 6.05264 0.394831
\(236\) 8.72295 0.567816
\(237\) −1.19591 −0.0776829
\(238\) −9.78288 −0.634130
\(239\) 16.1582 1.04519 0.522595 0.852581i \(-0.324964\pi\)
0.522595 + 0.852581i \(0.324964\pi\)
\(240\) 0.488401 0.0315262
\(241\) 17.9215 1.15442 0.577212 0.816594i \(-0.304141\pi\)
0.577212 + 0.816594i \(0.304141\pi\)
\(242\) 0 0
\(243\) 4.23784 0.271857
\(244\) −6.38710 −0.408892
\(245\) −15.9142 −1.01672
\(246\) −1.32914 −0.0847428
\(247\) 0.526746 0.0335161
\(248\) 1.72447 0.109504
\(249\) −1.03126 −0.0653536
\(250\) 1.63872 0.103641
\(251\) 26.9550 1.70139 0.850693 0.525663i \(-0.176183\pi\)
0.850693 + 0.525663i \(0.176183\pi\)
\(252\) 4.02190 0.253356
\(253\) 0 0
\(254\) −16.4582 −1.03268
\(255\) −3.53403 −0.221310
\(256\) 1.00000 0.0625000
\(257\) −22.2307 −1.38671 −0.693357 0.720594i \(-0.743869\pi\)
−0.693357 + 0.720594i \(0.743869\pi\)
\(258\) 1.00019 0.0622693
\(259\) −12.0493 −0.748706
\(260\) 1.62075 0.100515
\(261\) −0.826619 −0.0511664
\(262\) 15.1571 0.936407
\(263\) 0.840832 0.0518479 0.0259240 0.999664i \(-0.491747\pi\)
0.0259240 + 0.999664i \(0.491747\pi\)
\(264\) 0 0
\(265\) −6.79084 −0.417158
\(266\) 1.35199 0.0828957
\(267\) −1.64314 −0.100559
\(268\) −1.02001 −0.0623071
\(269\) 26.6280 1.62354 0.811770 0.583978i \(-0.198504\pi\)
0.811770 + 0.583978i \(0.198504\pi\)
\(270\) 2.91810 0.177590
\(271\) 25.3809 1.54178 0.770889 0.636970i \(-0.219812\pi\)
0.770889 + 0.636970i \(0.219812\pi\)
\(272\) −7.23593 −0.438742
\(273\) −0.113041 −0.00684154
\(274\) 5.46038 0.329874
\(275\) 0 0
\(276\) 0.332037 0.0199863
\(277\) 30.1812 1.81341 0.906706 0.421763i \(-0.138589\pi\)
0.906706 + 0.421763i \(0.138589\pi\)
\(278\) −9.22943 −0.553544
\(279\) 5.12996 0.307123
\(280\) 4.15995 0.248605
\(281\) −16.8269 −1.00381 −0.501904 0.864923i \(-0.667367\pi\)
−0.501904 + 0.864923i \(0.667367\pi\)
\(282\) −0.312241 −0.0185937
\(283\) 10.4403 0.620611 0.310305 0.950637i \(-0.399569\pi\)
0.310305 + 0.950637i \(0.399569\pi\)
\(284\) −3.71385 −0.220376
\(285\) 0.488401 0.0289304
\(286\) 0 0
\(287\) −11.3209 −0.668253
\(288\) 2.97480 0.175292
\(289\) 35.3586 2.07992
\(290\) −0.854993 −0.0502069
\(291\) −1.65748 −0.0971631
\(292\) −1.72161 −0.100750
\(293\) −13.4022 −0.782965 −0.391482 0.920186i \(-0.628038\pi\)
−0.391482 + 0.920186i \(0.628038\pi\)
\(294\) 0.820976 0.0478803
\(295\) 26.8398 1.56267
\(296\) −8.91226 −0.518015
\(297\) 0 0
\(298\) −12.3302 −0.714270
\(299\) 1.10186 0.0637223
\(300\) 0.709116 0.0409408
\(301\) 8.51914 0.491035
\(302\) 3.63459 0.209147
\(303\) −2.63612 −0.151441
\(304\) 1.00000 0.0573539
\(305\) −19.6526 −1.12530
\(306\) −21.5255 −1.23053
\(307\) 18.9800 1.08325 0.541623 0.840622i \(-0.317810\pi\)
0.541623 + 0.840622i \(0.317810\pi\)
\(308\) 0 0
\(309\) −1.00135 −0.0569646
\(310\) 5.30605 0.301363
\(311\) 12.4757 0.707430 0.353715 0.935353i \(-0.384918\pi\)
0.353715 + 0.935353i \(0.384918\pi\)
\(312\) −0.0836108 −0.00473353
\(313\) −18.2742 −1.03292 −0.516459 0.856312i \(-0.672750\pi\)
−0.516459 + 0.856312i \(0.672750\pi\)
\(314\) 0.871549 0.0491844
\(315\) 12.3751 0.697255
\(316\) −7.53423 −0.423833
\(317\) −13.1830 −0.740432 −0.370216 0.928946i \(-0.620716\pi\)
−0.370216 + 0.928946i \(0.620716\pi\)
\(318\) 0.350323 0.0196451
\(319\) 0 0
\(320\) 3.07692 0.172005
\(321\) −2.09523 −0.116944
\(322\) 2.82812 0.157605
\(323\) −7.23593 −0.402618
\(324\) 8.77388 0.487438
\(325\) 2.35319 0.130532
\(326\) 7.73571 0.428441
\(327\) −0.710090 −0.0392681
\(328\) −8.37354 −0.462352
\(329\) −2.65951 −0.146624
\(330\) 0 0
\(331\) 3.69222 0.202943 0.101471 0.994838i \(-0.467645\pi\)
0.101471 + 0.994838i \(0.467645\pi\)
\(332\) −6.49693 −0.356565
\(333\) −26.5122 −1.45286
\(334\) 21.8284 1.19440
\(335\) −3.13849 −0.171474
\(336\) −0.214602 −0.0117075
\(337\) −26.2983 −1.43256 −0.716279 0.697814i \(-0.754156\pi\)
−0.716279 + 0.697814i \(0.754156\pi\)
\(338\) 12.7225 0.692015
\(339\) −1.99368 −0.108282
\(340\) −22.2643 −1.20745
\(341\) 0 0
\(342\) 2.97480 0.160859
\(343\) 16.4566 0.888571
\(344\) 6.30119 0.339738
\(345\) 1.02165 0.0550038
\(346\) −11.0102 −0.591909
\(347\) 5.33343 0.286313 0.143157 0.989700i \(-0.454275\pi\)
0.143157 + 0.989700i \(0.454275\pi\)
\(348\) 0.0441070 0.00236439
\(349\) −19.4450 −1.04087 −0.520433 0.853903i \(-0.674229\pi\)
−0.520433 + 0.853903i \(0.674229\pi\)
\(350\) 6.03989 0.322846
\(351\) −0.499558 −0.0266644
\(352\) 0 0
\(353\) −27.8728 −1.48352 −0.741761 0.670665i \(-0.766009\pi\)
−0.741761 + 0.670665i \(0.766009\pi\)
\(354\) −1.38460 −0.0735906
\(355\) −11.4272 −0.606493
\(356\) −10.3518 −0.548642
\(357\) 1.55284 0.0821852
\(358\) 12.5527 0.663431
\(359\) −35.7338 −1.88596 −0.942978 0.332856i \(-0.891988\pi\)
−0.942978 + 0.332856i \(0.891988\pi\)
\(360\) 9.15323 0.482417
\(361\) 1.00000 0.0526316
\(362\) 3.45298 0.181485
\(363\) 0 0
\(364\) −0.712155 −0.0373270
\(365\) −5.29725 −0.277271
\(366\) 1.01383 0.0529937
\(367\) 37.8147 1.97391 0.986956 0.160991i \(-0.0514691\pi\)
0.986956 + 0.160991i \(0.0514691\pi\)
\(368\) 2.09183 0.109044
\(369\) −24.9097 −1.29675
\(370\) −27.4223 −1.42562
\(371\) 2.98387 0.154915
\(372\) −0.273726 −0.0141920
\(373\) 20.1806 1.04491 0.522456 0.852667i \(-0.325016\pi\)
0.522456 + 0.852667i \(0.325016\pi\)
\(374\) 0 0
\(375\) −0.260114 −0.0134322
\(376\) −1.96711 −0.101446
\(377\) 0.146369 0.00753837
\(378\) −1.28221 −0.0659495
\(379\) −32.7152 −1.68047 −0.840233 0.542225i \(-0.817582\pi\)
−0.840233 + 0.542225i \(0.817582\pi\)
\(380\) 3.07692 0.157842
\(381\) 2.61241 0.133838
\(382\) −21.3218 −1.09092
\(383\) −25.6817 −1.31227 −0.656136 0.754643i \(-0.727810\pi\)
−0.656136 + 0.754643i \(0.727810\pi\)
\(384\) −0.158731 −0.00810019
\(385\) 0 0
\(386\) 23.4522 1.19369
\(387\) 18.7448 0.952853
\(388\) −10.4421 −0.530116
\(389\) −4.46845 −0.226559 −0.113280 0.993563i \(-0.536136\pi\)
−0.113280 + 0.993563i \(0.536136\pi\)
\(390\) −0.257263 −0.0130270
\(391\) −15.1363 −0.765475
\(392\) 5.17213 0.261232
\(393\) −2.40589 −0.121361
\(394\) −7.79605 −0.392759
\(395\) −23.1822 −1.16642
\(396\) 0 0
\(397\) 28.8810 1.44950 0.724748 0.689014i \(-0.241956\pi\)
0.724748 + 0.689014i \(0.241956\pi\)
\(398\) 9.48281 0.475330
\(399\) −0.214602 −0.0107435
\(400\) 4.46742 0.223371
\(401\) 0.797439 0.0398222 0.0199111 0.999802i \(-0.493662\pi\)
0.0199111 + 0.999802i \(0.493662\pi\)
\(402\) 0.161907 0.00807519
\(403\) −0.908358 −0.0452485
\(404\) −16.6075 −0.826254
\(405\) 26.9965 1.34147
\(406\) 0.375681 0.0186448
\(407\) 0 0
\(408\) 1.14856 0.0568624
\(409\) −22.7240 −1.12363 −0.561814 0.827263i \(-0.689897\pi\)
−0.561814 + 0.827263i \(0.689897\pi\)
\(410\) −25.7647 −1.27243
\(411\) −0.866730 −0.0427527
\(412\) −6.30847 −0.310796
\(413\) −11.7933 −0.580311
\(414\) 6.22277 0.305833
\(415\) −19.9905 −0.981296
\(416\) −0.526746 −0.0258259
\(417\) 1.46499 0.0717410
\(418\) 0 0
\(419\) −0.427754 −0.0208971 −0.0104486 0.999945i \(-0.503326\pi\)
−0.0104486 + 0.999945i \(0.503326\pi\)
\(420\) −0.660313 −0.0322200
\(421\) −9.69726 −0.472615 −0.236308 0.971678i \(-0.575937\pi\)
−0.236308 + 0.971678i \(0.575937\pi\)
\(422\) 15.5951 0.759156
\(423\) −5.85177 −0.284523
\(424\) 2.20703 0.107183
\(425\) −32.3259 −1.56804
\(426\) 0.589502 0.0285615
\(427\) 8.63529 0.417891
\(428\) −13.1999 −0.638041
\(429\) 0 0
\(430\) 19.3882 0.934984
\(431\) 6.70352 0.322897 0.161449 0.986881i \(-0.448383\pi\)
0.161449 + 0.986881i \(0.448383\pi\)
\(432\) −0.948385 −0.0456292
\(433\) −15.3773 −0.738988 −0.369494 0.929233i \(-0.620469\pi\)
−0.369494 + 0.929233i \(0.620469\pi\)
\(434\) −2.33146 −0.111914
\(435\) 0.135714 0.00650697
\(436\) −4.47355 −0.214244
\(437\) 2.09183 0.100066
\(438\) 0.273272 0.0130575
\(439\) 2.15073 0.102649 0.0513244 0.998682i \(-0.483656\pi\)
0.0513244 + 0.998682i \(0.483656\pi\)
\(440\) 0 0
\(441\) 15.3861 0.732670
\(442\) 3.81150 0.181294
\(443\) 30.3841 1.44359 0.721797 0.692105i \(-0.243317\pi\)
0.721797 + 0.692105i \(0.243317\pi\)
\(444\) 1.41465 0.0671363
\(445\) −31.8515 −1.50991
\(446\) 24.4375 1.15715
\(447\) 1.95718 0.0925715
\(448\) −1.35199 −0.0638754
\(449\) 3.34155 0.157698 0.0788488 0.996887i \(-0.474876\pi\)
0.0788488 + 0.996887i \(0.474876\pi\)
\(450\) 13.2897 0.626482
\(451\) 0 0
\(452\) −12.5601 −0.590778
\(453\) −0.576921 −0.0271061
\(454\) −23.2524 −1.09129
\(455\) −2.19124 −0.102727
\(456\) −0.158731 −0.00743325
\(457\) −29.3880 −1.37471 −0.687356 0.726321i \(-0.741229\pi\)
−0.687356 + 0.726321i \(0.741229\pi\)
\(458\) 1.94364 0.0908204
\(459\) 6.86244 0.320311
\(460\) 6.43637 0.300097
\(461\) 1.74308 0.0811833 0.0405917 0.999176i \(-0.487076\pi\)
0.0405917 + 0.999176i \(0.487076\pi\)
\(462\) 0 0
\(463\) −31.2015 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(464\) 0.277873 0.0128999
\(465\) −0.842233 −0.0390576
\(466\) 5.46260 0.253050
\(467\) 26.0733 1.20653 0.603264 0.797542i \(-0.293867\pi\)
0.603264 + 0.797542i \(0.293867\pi\)
\(468\) −1.56697 −0.0724331
\(469\) 1.37904 0.0636783
\(470\) −6.05264 −0.279187
\(471\) −0.138342 −0.00637444
\(472\) −8.72295 −0.401506
\(473\) 0 0
\(474\) 1.19591 0.0549301
\(475\) 4.46742 0.204979
\(476\) 9.78288 0.448398
\(477\) 6.56547 0.300612
\(478\) −16.1582 −0.739061
\(479\) 29.3946 1.34307 0.671536 0.740972i \(-0.265635\pi\)
0.671536 + 0.740972i \(0.265635\pi\)
\(480\) −0.488401 −0.0222924
\(481\) 4.69450 0.214051
\(482\) −17.9215 −0.816301
\(483\) −0.448910 −0.0204261
\(484\) 0 0
\(485\) −32.1294 −1.45892
\(486\) −4.23784 −0.192232
\(487\) 43.0919 1.95268 0.976340 0.216242i \(-0.0693801\pi\)
0.976340 + 0.216242i \(0.0693801\pi\)
\(488\) 6.38710 0.289131
\(489\) −1.22790 −0.0555273
\(490\) 15.9142 0.718931
\(491\) 29.5401 1.33313 0.666563 0.745449i \(-0.267765\pi\)
0.666563 + 0.745449i \(0.267765\pi\)
\(492\) 1.32914 0.0599222
\(493\) −2.01067 −0.0905561
\(494\) −0.526746 −0.0236994
\(495\) 0 0
\(496\) −1.72447 −0.0774309
\(497\) 5.02108 0.225226
\(498\) 1.03126 0.0462120
\(499\) −27.8915 −1.24859 −0.624297 0.781187i \(-0.714615\pi\)
−0.624297 + 0.781187i \(0.714615\pi\)
\(500\) −1.63872 −0.0732856
\(501\) −3.46484 −0.154798
\(502\) −26.9550 −1.20306
\(503\) −0.0484888 −0.00216201 −0.00108100 0.999999i \(-0.500344\pi\)
−0.00108100 + 0.999999i \(0.500344\pi\)
\(504\) −4.02190 −0.179150
\(505\) −51.0999 −2.27392
\(506\) 0 0
\(507\) −2.01946 −0.0896873
\(508\) 16.4582 0.730212
\(509\) 9.75291 0.432290 0.216145 0.976361i \(-0.430652\pi\)
0.216145 + 0.976361i \(0.430652\pi\)
\(510\) 3.53403 0.156490
\(511\) 2.32759 0.102967
\(512\) −1.00000 −0.0441942
\(513\) −0.948385 −0.0418722
\(514\) 22.2307 0.980555
\(515\) −19.4106 −0.855334
\(516\) −1.00019 −0.0440310
\(517\) 0 0
\(518\) 12.0493 0.529415
\(519\) 1.74765 0.0767133
\(520\) −1.62075 −0.0710748
\(521\) −40.4077 −1.77029 −0.885147 0.465312i \(-0.845942\pi\)
−0.885147 + 0.465312i \(0.845942\pi\)
\(522\) 0.826619 0.0361801
\(523\) −22.7718 −0.995742 −0.497871 0.867251i \(-0.665885\pi\)
−0.497871 + 0.867251i \(0.665885\pi\)
\(524\) −15.1571 −0.662140
\(525\) −0.958717 −0.0418418
\(526\) −0.840832 −0.0366620
\(527\) 12.4781 0.543556
\(528\) 0 0
\(529\) −18.6243 −0.809751
\(530\) 6.79084 0.294975
\(531\) −25.9491 −1.12609
\(532\) −1.35199 −0.0586161
\(533\) 4.41073 0.191050
\(534\) 1.64314 0.0711057
\(535\) −40.6150 −1.75594
\(536\) 1.02001 0.0440578
\(537\) −1.99250 −0.0859827
\(538\) −26.6280 −1.14802
\(539\) 0 0
\(540\) −2.91810 −0.125575
\(541\) 7.41552 0.318818 0.159409 0.987213i \(-0.449041\pi\)
0.159409 + 0.987213i \(0.449041\pi\)
\(542\) −25.3809 −1.09020
\(543\) −0.548094 −0.0235210
\(544\) 7.23593 0.310238
\(545\) −13.7647 −0.589617
\(546\) 0.113041 0.00483770
\(547\) −2.41910 −0.103433 −0.0517167 0.998662i \(-0.516469\pi\)
−0.0517167 + 0.998662i \(0.516469\pi\)
\(548\) −5.46038 −0.233256
\(549\) 19.0004 0.810917
\(550\) 0 0
\(551\) 0.277873 0.0118378
\(552\) −0.332037 −0.0141324
\(553\) 10.1862 0.433161
\(554\) −30.1812 −1.28228
\(555\) 4.35276 0.184764
\(556\) 9.22943 0.391415
\(557\) −0.412176 −0.0174645 −0.00873224 0.999962i \(-0.502780\pi\)
−0.00873224 + 0.999962i \(0.502780\pi\)
\(558\) −5.12996 −0.217168
\(559\) −3.31913 −0.140384
\(560\) −4.15995 −0.175790
\(561\) 0 0
\(562\) 16.8269 0.709800
\(563\) −4.49045 −0.189250 −0.0946249 0.995513i \(-0.530165\pi\)
−0.0946249 + 0.995513i \(0.530165\pi\)
\(564\) 0.312241 0.0131477
\(565\) −38.6464 −1.62587
\(566\) −10.4403 −0.438838
\(567\) −11.8622 −0.498165
\(568\) 3.71385 0.155830
\(569\) 32.6319 1.36800 0.684000 0.729482i \(-0.260239\pi\)
0.684000 + 0.729482i \(0.260239\pi\)
\(570\) −0.488401 −0.0204569
\(571\) −18.1484 −0.759486 −0.379743 0.925092i \(-0.623988\pi\)
−0.379743 + 0.925092i \(0.623988\pi\)
\(572\) 0 0
\(573\) 3.38443 0.141387
\(574\) 11.3209 0.472527
\(575\) 9.34506 0.389716
\(576\) −2.97480 −0.123950
\(577\) −21.9198 −0.912532 −0.456266 0.889843i \(-0.650814\pi\)
−0.456266 + 0.889843i \(0.650814\pi\)
\(578\) −35.3586 −1.47072
\(579\) −3.72259 −0.154705
\(580\) 0.854993 0.0355017
\(581\) 8.78377 0.364412
\(582\) 1.65748 0.0687047
\(583\) 0 0
\(584\) 1.72161 0.0712407
\(585\) −4.82143 −0.199341
\(586\) 13.4022 0.553640
\(587\) 16.9253 0.698581 0.349291 0.937014i \(-0.386423\pi\)
0.349291 + 0.937014i \(0.386423\pi\)
\(588\) −0.820976 −0.0338565
\(589\) −1.72447 −0.0710555
\(590\) −26.8398 −1.10498
\(591\) 1.23747 0.0509028
\(592\) 8.91226 0.366292
\(593\) −9.83301 −0.403793 −0.201897 0.979407i \(-0.564710\pi\)
−0.201897 + 0.979407i \(0.564710\pi\)
\(594\) 0 0
\(595\) 30.1011 1.23403
\(596\) 12.3302 0.505065
\(597\) −1.50521 −0.0616043
\(598\) −1.10186 −0.0450585
\(599\) 43.2136 1.76566 0.882829 0.469694i \(-0.155636\pi\)
0.882829 + 0.469694i \(0.155636\pi\)
\(600\) −0.709116 −0.0289495
\(601\) 6.60416 0.269389 0.134695 0.990887i \(-0.456995\pi\)
0.134695 + 0.990887i \(0.456995\pi\)
\(602\) −8.51914 −0.347214
\(603\) 3.03433 0.123568
\(604\) −3.63459 −0.147889
\(605\) 0 0
\(606\) 2.63612 0.107085
\(607\) −19.6695 −0.798359 −0.399180 0.916873i \(-0.630705\pi\)
−0.399180 + 0.916873i \(0.630705\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −0.0596322 −0.00241642
\(610\) 19.6526 0.795710
\(611\) 1.03617 0.0419189
\(612\) 21.5255 0.870115
\(613\) 1.55586 0.0628407 0.0314203 0.999506i \(-0.489997\pi\)
0.0314203 + 0.999506i \(0.489997\pi\)
\(614\) −18.9800 −0.765970
\(615\) 4.08965 0.164911
\(616\) 0 0
\(617\) −43.2521 −1.74126 −0.870632 0.491935i \(-0.836290\pi\)
−0.870632 + 0.491935i \(0.836290\pi\)
\(618\) 1.00135 0.0402801
\(619\) 3.26969 0.131420 0.0657100 0.997839i \(-0.479069\pi\)
0.0657100 + 0.997839i \(0.479069\pi\)
\(620\) −5.30605 −0.213096
\(621\) −1.98386 −0.0796094
\(622\) −12.4757 −0.500228
\(623\) 13.9955 0.560716
\(624\) 0.0836108 0.00334711
\(625\) −27.3793 −1.09517
\(626\) 18.2742 0.730383
\(627\) 0 0
\(628\) −0.871549 −0.0347786
\(629\) −64.4885 −2.57132
\(630\) −12.3751 −0.493034
\(631\) 27.6628 1.10124 0.550620 0.834756i \(-0.314391\pi\)
0.550620 + 0.834756i \(0.314391\pi\)
\(632\) 7.53423 0.299695
\(633\) −2.47542 −0.0983890
\(634\) 13.1830 0.523565
\(635\) 50.6404 2.00960
\(636\) −0.350323 −0.0138912
\(637\) −2.72440 −0.107945
\(638\) 0 0
\(639\) 11.0480 0.437051
\(640\) −3.07692 −0.121626
\(641\) −40.1504 −1.58585 −0.792924 0.609321i \(-0.791442\pi\)
−0.792924 + 0.609321i \(0.791442\pi\)
\(642\) 2.09523 0.0826921
\(643\) −29.3892 −1.15900 −0.579499 0.814973i \(-0.696752\pi\)
−0.579499 + 0.814973i \(0.696752\pi\)
\(644\) −2.82812 −0.111444
\(645\) −3.07751 −0.121177
\(646\) 7.23593 0.284694
\(647\) 3.63135 0.142763 0.0713816 0.997449i \(-0.477259\pi\)
0.0713816 + 0.997449i \(0.477259\pi\)
\(648\) −8.77388 −0.344670
\(649\) 0 0
\(650\) −2.35319 −0.0922999
\(651\) 0.370075 0.0145044
\(652\) −7.73571 −0.302954
\(653\) −25.9076 −1.01384 −0.506921 0.861992i \(-0.669217\pi\)
−0.506921 + 0.861992i \(0.669217\pi\)
\(654\) 0.710090 0.0277667
\(655\) −46.6371 −1.82226
\(656\) 8.37354 0.326932
\(657\) 5.12145 0.199807
\(658\) 2.65951 0.103679
\(659\) 22.9664 0.894644 0.447322 0.894373i \(-0.352378\pi\)
0.447322 + 0.894373i \(0.352378\pi\)
\(660\) 0 0
\(661\) 43.4685 1.69073 0.845365 0.534189i \(-0.179383\pi\)
0.845365 + 0.534189i \(0.179383\pi\)
\(662\) −3.69222 −0.143502
\(663\) −0.605002 −0.0234963
\(664\) 6.49693 0.252130
\(665\) −4.15995 −0.161316
\(666\) 26.5122 1.02733
\(667\) 0.581263 0.0225066
\(668\) −21.8284 −0.844566
\(669\) −3.87899 −0.149970
\(670\) 3.13849 0.121250
\(671\) 0 0
\(672\) 0.214602 0.00827845
\(673\) 29.2936 1.12918 0.564592 0.825370i \(-0.309033\pi\)
0.564592 + 0.825370i \(0.309033\pi\)
\(674\) 26.2983 1.01297
\(675\) −4.23683 −0.163076
\(676\) −12.7225 −0.489328
\(677\) 38.9988 1.49884 0.749422 0.662093i \(-0.230331\pi\)
0.749422 + 0.662093i \(0.230331\pi\)
\(678\) 1.99368 0.0765667
\(679\) 14.1176 0.541782
\(680\) 22.2643 0.853798
\(681\) 3.69087 0.141435
\(682\) 0 0
\(683\) −13.6716 −0.523130 −0.261565 0.965186i \(-0.584239\pi\)
−0.261565 + 0.965186i \(0.584239\pi\)
\(684\) −2.97480 −0.113744
\(685\) −16.8011 −0.641939
\(686\) −16.4566 −0.628315
\(687\) −0.308515 −0.0117706
\(688\) −6.30119 −0.240231
\(689\) −1.16254 −0.0442894
\(690\) −1.02165 −0.0388936
\(691\) 8.06092 0.306652 0.153326 0.988176i \(-0.451002\pi\)
0.153326 + 0.988176i \(0.451002\pi\)
\(692\) 11.0102 0.418543
\(693\) 0 0
\(694\) −5.33343 −0.202454
\(695\) 28.3982 1.07720
\(696\) −0.0441070 −0.00167187
\(697\) −60.5903 −2.29502
\(698\) 19.4450 0.736003
\(699\) −0.867082 −0.0327961
\(700\) −6.03989 −0.228287
\(701\) 11.0066 0.415713 0.207857 0.978159i \(-0.433351\pi\)
0.207857 + 0.978159i \(0.433351\pi\)
\(702\) 0.499558 0.0188546
\(703\) 8.91226 0.336132
\(704\) 0 0
\(705\) 0.960740 0.0361836
\(706\) 27.8728 1.04901
\(707\) 22.4531 0.844437
\(708\) 1.38460 0.0520364
\(709\) 3.81971 0.143452 0.0717260 0.997424i \(-0.477149\pi\)
0.0717260 + 0.997424i \(0.477149\pi\)
\(710\) 11.4272 0.428855
\(711\) 22.4129 0.840548
\(712\) 10.3518 0.387948
\(713\) −3.60729 −0.135094
\(714\) −1.55284 −0.0581137
\(715\) 0 0
\(716\) −12.5527 −0.469116
\(717\) 2.56481 0.0957846
\(718\) 35.7338 1.33357
\(719\) 12.4943 0.465958 0.232979 0.972482i \(-0.425153\pi\)
0.232979 + 0.972482i \(0.425153\pi\)
\(720\) −9.15323 −0.341121
\(721\) 8.52897 0.317635
\(722\) −1.00000 −0.0372161
\(723\) 2.84469 0.105795
\(724\) −3.45298 −0.128329
\(725\) 1.24138 0.0461036
\(726\) 0 0
\(727\) 21.9023 0.812311 0.406155 0.913804i \(-0.366869\pi\)
0.406155 + 0.913804i \(0.366869\pi\)
\(728\) 0.712155 0.0263942
\(729\) −25.6490 −0.949961
\(730\) 5.29725 0.196060
\(731\) 45.5950 1.68639
\(732\) −1.01383 −0.0374722
\(733\) −27.3319 −1.00953 −0.504764 0.863257i \(-0.668421\pi\)
−0.504764 + 0.863257i \(0.668421\pi\)
\(734\) −37.8147 −1.39577
\(735\) −2.52607 −0.0931756
\(736\) −2.09183 −0.0771057
\(737\) 0 0
\(738\) 24.9097 0.916937
\(739\) 6.87044 0.252733 0.126367 0.991984i \(-0.459668\pi\)
0.126367 + 0.991984i \(0.459668\pi\)
\(740\) 27.4223 1.00806
\(741\) 0.0836108 0.00307152
\(742\) −2.98387 −0.109541
\(743\) 38.5332 1.41365 0.706824 0.707390i \(-0.250127\pi\)
0.706824 + 0.707390i \(0.250127\pi\)
\(744\) 0.273726 0.0100353
\(745\) 37.9390 1.38998
\(746\) −20.1806 −0.738864
\(747\) 19.3271 0.707141
\(748\) 0 0
\(749\) 17.8461 0.652083
\(750\) 0.260114 0.00949803
\(751\) 19.0301 0.694418 0.347209 0.937788i \(-0.387130\pi\)
0.347209 + 0.937788i \(0.387130\pi\)
\(752\) 1.96711 0.0717332
\(753\) 4.27859 0.155920
\(754\) −0.146369 −0.00533044
\(755\) −11.1833 −0.407003
\(756\) 1.28221 0.0466333
\(757\) −42.0004 −1.52653 −0.763266 0.646084i \(-0.776405\pi\)
−0.763266 + 0.646084i \(0.776405\pi\)
\(758\) 32.7152 1.18827
\(759\) 0 0
\(760\) −3.07692 −0.111612
\(761\) 21.9298 0.794955 0.397477 0.917612i \(-0.369886\pi\)
0.397477 + 0.917612i \(0.369886\pi\)
\(762\) −2.61241 −0.0946378
\(763\) 6.04819 0.218959
\(764\) 21.3218 0.771397
\(765\) 66.2321 2.39463
\(766\) 25.6817 0.927917
\(767\) 4.59478 0.165908
\(768\) 0.158731 0.00572770
\(769\) 20.9969 0.757167 0.378584 0.925567i \(-0.376411\pi\)
0.378584 + 0.925567i \(0.376411\pi\)
\(770\) 0 0
\(771\) −3.52870 −0.127083
\(772\) −23.4522 −0.844063
\(773\) 38.3380 1.37892 0.689460 0.724323i \(-0.257848\pi\)
0.689460 + 0.724323i \(0.257848\pi\)
\(774\) −18.7448 −0.673769
\(775\) −7.70392 −0.276733
\(776\) 10.4421 0.374849
\(777\) −1.91259 −0.0686138
\(778\) 4.46845 0.160202
\(779\) 8.37354 0.300013
\(780\) 0.257263 0.00921151
\(781\) 0 0
\(782\) 15.1363 0.541273
\(783\) −0.263531 −0.00941783
\(784\) −5.17213 −0.184719
\(785\) −2.68168 −0.0957134
\(786\) 2.40589 0.0858154
\(787\) −3.85555 −0.137435 −0.0687177 0.997636i \(-0.521891\pi\)
−0.0687177 + 0.997636i \(0.521891\pi\)
\(788\) 7.79605 0.277723
\(789\) 0.133466 0.00475151
\(790\) 23.1822 0.824785
\(791\) 16.9811 0.603779
\(792\) 0 0
\(793\) −3.36438 −0.119473
\(794\) −28.8810 −1.02495
\(795\) −1.07791 −0.0382297
\(796\) −9.48281 −0.336109
\(797\) 7.72685 0.273699 0.136850 0.990592i \(-0.456302\pi\)
0.136850 + 0.990592i \(0.456302\pi\)
\(798\) 0.214602 0.00759683
\(799\) −14.2339 −0.503558
\(800\) −4.46742 −0.157947
\(801\) 30.7945 1.08807
\(802\) −0.797439 −0.0281586
\(803\) 0 0
\(804\) −0.161907 −0.00571002
\(805\) −8.70190 −0.306702
\(806\) 0.908358 0.0319955
\(807\) 4.22669 0.148786
\(808\) 16.6075 0.584250
\(809\) 45.8483 1.61194 0.805970 0.591957i \(-0.201644\pi\)
0.805970 + 0.591957i \(0.201644\pi\)
\(810\) −26.9965 −0.948560
\(811\) 11.9071 0.418115 0.209058 0.977903i \(-0.432960\pi\)
0.209058 + 0.977903i \(0.432960\pi\)
\(812\) −0.375681 −0.0131838
\(813\) 4.02872 0.141293
\(814\) 0 0
\(815\) −23.8021 −0.833753
\(816\) −1.14856 −0.0402078
\(817\) −6.30119 −0.220451
\(818\) 22.7240 0.794526
\(819\) 2.11852 0.0740271
\(820\) 25.7647 0.899742
\(821\) 25.0389 0.873865 0.436932 0.899494i \(-0.356065\pi\)
0.436932 + 0.899494i \(0.356065\pi\)
\(822\) 0.866730 0.0302307
\(823\) −4.14621 −0.144528 −0.0722639 0.997386i \(-0.523022\pi\)
−0.0722639 + 0.997386i \(0.523022\pi\)
\(824\) 6.30847 0.219766
\(825\) 0 0
\(826\) 11.7933 0.410342
\(827\) 47.6070 1.65546 0.827729 0.561127i \(-0.189632\pi\)
0.827729 + 0.561127i \(0.189632\pi\)
\(828\) −6.22277 −0.216256
\(829\) 5.19254 0.180344 0.0901722 0.995926i \(-0.471258\pi\)
0.0901722 + 0.995926i \(0.471258\pi\)
\(830\) 19.9905 0.693881
\(831\) 4.79068 0.166187
\(832\) 0.526746 0.0182616
\(833\) 37.4251 1.29670
\(834\) −1.46499 −0.0507286
\(835\) −67.1642 −2.32431
\(836\) 0 0
\(837\) 1.63546 0.0565298
\(838\) 0.427754 0.0147765
\(839\) −43.4560 −1.50027 −0.750133 0.661287i \(-0.770011\pi\)
−0.750133 + 0.661287i \(0.770011\pi\)
\(840\) 0.660313 0.0227829
\(841\) −28.9228 −0.997337
\(842\) 9.69726 0.334190
\(843\) −2.67094 −0.0919922
\(844\) −15.5951 −0.536805
\(845\) −39.1462 −1.34667
\(846\) 5.85177 0.201188
\(847\) 0 0
\(848\) −2.20703 −0.0757896
\(849\) 1.65719 0.0568748
\(850\) 32.3259 1.10877
\(851\) 18.6429 0.639071
\(852\) −0.589502 −0.0201960
\(853\) 29.3178 1.00382 0.501911 0.864919i \(-0.332631\pi\)
0.501911 + 0.864919i \(0.332631\pi\)
\(854\) −8.63529 −0.295493
\(855\) −9.15323 −0.313034
\(856\) 13.1999 0.451163
\(857\) −3.67262 −0.125454 −0.0627272 0.998031i \(-0.519980\pi\)
−0.0627272 + 0.998031i \(0.519980\pi\)
\(858\) 0 0
\(859\) −19.7758 −0.674742 −0.337371 0.941372i \(-0.609538\pi\)
−0.337371 + 0.941372i \(0.609538\pi\)
\(860\) −19.3882 −0.661134
\(861\) −1.79698 −0.0612409
\(862\) −6.70352 −0.228323
\(863\) −33.2555 −1.13203 −0.566015 0.824395i \(-0.691516\pi\)
−0.566015 + 0.824395i \(0.691516\pi\)
\(864\) 0.948385 0.0322647
\(865\) 33.8773 1.15186
\(866\) 15.3773 0.522544
\(867\) 5.61250 0.190610
\(868\) 2.33146 0.0791350
\(869\) 0 0
\(870\) −0.135714 −0.00460112
\(871\) −0.537287 −0.0182053
\(872\) 4.47355 0.151494
\(873\) 31.0631 1.05133
\(874\) −2.09183 −0.0707571
\(875\) 2.21552 0.0748984
\(876\) −0.273272 −0.00923301
\(877\) 14.7200 0.497060 0.248530 0.968624i \(-0.420052\pi\)
0.248530 + 0.968624i \(0.420052\pi\)
\(878\) −2.15073 −0.0725837
\(879\) −2.12734 −0.0717534
\(880\) 0 0
\(881\) −2.16151 −0.0728230 −0.0364115 0.999337i \(-0.511593\pi\)
−0.0364115 + 0.999337i \(0.511593\pi\)
\(882\) −15.3861 −0.518076
\(883\) −11.6171 −0.390947 −0.195473 0.980709i \(-0.562624\pi\)
−0.195473 + 0.980709i \(0.562624\pi\)
\(884\) −3.81150 −0.128194
\(885\) 4.26030 0.143208
\(886\) −30.3841 −1.02077
\(887\) −22.5487 −0.757111 −0.378555 0.925579i \(-0.623579\pi\)
−0.378555 + 0.925579i \(0.623579\pi\)
\(888\) −1.41465 −0.0474725
\(889\) −22.2512 −0.746282
\(890\) 31.8515 1.06766
\(891\) 0 0
\(892\) −24.4375 −0.818230
\(893\) 1.96711 0.0658269
\(894\) −1.95718 −0.0654580
\(895\) −38.6236 −1.29104
\(896\) 1.35199 0.0451668
\(897\) 0.174899 0.00583971
\(898\) −3.34155 −0.111509
\(899\) −0.479184 −0.0159817
\(900\) −13.2897 −0.442990
\(901\) 15.9699 0.532034
\(902\) 0 0
\(903\) 1.35225 0.0450000
\(904\) 12.5601 0.417743
\(905\) −10.6245 −0.353171
\(906\) 0.576921 0.0191669
\(907\) 18.3913 0.610672 0.305336 0.952245i \(-0.401231\pi\)
0.305336 + 0.952245i \(0.401231\pi\)
\(908\) 23.2524 0.771659
\(909\) 49.4041 1.63863
\(910\) 2.19124 0.0726389
\(911\) 47.2453 1.56531 0.782654 0.622458i \(-0.213866\pi\)
0.782654 + 0.622458i \(0.213866\pi\)
\(912\) 0.158731 0.00525610
\(913\) 0 0
\(914\) 29.3880 0.972068
\(915\) −3.11947 −0.103126
\(916\) −1.94364 −0.0642197
\(917\) 20.4922 0.676712
\(918\) −6.86244 −0.226494
\(919\) 9.79492 0.323105 0.161552 0.986864i \(-0.448350\pi\)
0.161552 + 0.986864i \(0.448350\pi\)
\(920\) −6.43637 −0.212201
\(921\) 3.01271 0.0992721
\(922\) −1.74308 −0.0574053
\(923\) −1.95626 −0.0643910
\(924\) 0 0
\(925\) 39.8148 1.30910
\(926\) 31.2015 1.02535
\(927\) 18.7665 0.616371
\(928\) −0.277873 −0.00912164
\(929\) 22.9921 0.754346 0.377173 0.926143i \(-0.376896\pi\)
0.377173 + 0.926143i \(0.376896\pi\)
\(930\) 0.842233 0.0276179
\(931\) −5.17213 −0.169510
\(932\) −5.46260 −0.178933
\(933\) 1.98027 0.0648311
\(934\) −26.0733 −0.853144
\(935\) 0 0
\(936\) 1.56697 0.0512179
\(937\) −36.6455 −1.19716 −0.598578 0.801065i \(-0.704267\pi\)
−0.598578 + 0.801065i \(0.704267\pi\)
\(938\) −1.37904 −0.0450274
\(939\) −2.90067 −0.0946599
\(940\) 6.05264 0.197415
\(941\) 14.2908 0.465868 0.232934 0.972493i \(-0.425167\pi\)
0.232934 + 0.972493i \(0.425167\pi\)
\(942\) 0.138342 0.00450741
\(943\) 17.5160 0.570399
\(944\) 8.72295 0.283908
\(945\) 3.94524 0.128339
\(946\) 0 0
\(947\) 49.0452 1.59375 0.796877 0.604142i \(-0.206484\pi\)
0.796877 + 0.604142i \(0.206484\pi\)
\(948\) −1.19591 −0.0388414
\(949\) −0.906851 −0.0294376
\(950\) −4.46742 −0.144942
\(951\) −2.09255 −0.0678556
\(952\) −9.78288 −0.317065
\(953\) 9.95579 0.322500 0.161250 0.986914i \(-0.448447\pi\)
0.161250 + 0.986914i \(0.448447\pi\)
\(954\) −6.56547 −0.212565
\(955\) 65.6055 2.12294
\(956\) 16.1582 0.522595
\(957\) 0 0
\(958\) −29.3946 −0.949695
\(959\) 7.38237 0.238389
\(960\) 0.488401 0.0157631
\(961\) −28.0262 −0.904071
\(962\) −4.69450 −0.151357
\(963\) 39.2671 1.26537
\(964\) 17.9215 0.577212
\(965\) −72.1605 −2.32293
\(966\) 0.448910 0.0144434
\(967\) 12.0203 0.386546 0.193273 0.981145i \(-0.438090\pi\)
0.193273 + 0.981145i \(0.438090\pi\)
\(968\) 0 0
\(969\) −1.14856 −0.0368972
\(970\) 32.1294 1.03161
\(971\) 51.9013 1.66559 0.832796 0.553580i \(-0.186739\pi\)
0.832796 + 0.553580i \(0.186739\pi\)
\(972\) 4.23784 0.135929
\(973\) −12.4781 −0.400029
\(974\) −43.0919 −1.38075
\(975\) 0.373524 0.0119624
\(976\) −6.38710 −0.204446
\(977\) −28.7379 −0.919407 −0.459703 0.888073i \(-0.652044\pi\)
−0.459703 + 0.888073i \(0.652044\pi\)
\(978\) 1.22790 0.0392638
\(979\) 0 0
\(980\) −15.9142 −0.508361
\(981\) 13.3079 0.424890
\(982\) −29.5401 −0.942662
\(983\) 36.7856 1.17328 0.586639 0.809849i \(-0.300451\pi\)
0.586639 + 0.809849i \(0.300451\pi\)
\(984\) −1.32914 −0.0423714
\(985\) 23.9878 0.764315
\(986\) 2.01067 0.0640328
\(987\) −0.422146 −0.0134371
\(988\) 0.526746 0.0167580
\(989\) −13.1810 −0.419131
\(990\) 0 0
\(991\) −59.5095 −1.89038 −0.945191 0.326517i \(-0.894125\pi\)
−0.945191 + 0.326517i \(0.894125\pi\)
\(992\) 1.72447 0.0547519
\(993\) 0.586069 0.0185983
\(994\) −5.02108 −0.159259
\(995\) −29.1778 −0.924999
\(996\) −1.03126 −0.0326768
\(997\) 27.5241 0.871697 0.435848 0.900020i \(-0.356448\pi\)
0.435848 + 0.900020i \(0.356448\pi\)
\(998\) 27.8915 0.882889
\(999\) −8.45226 −0.267418
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.bx.1.4 8
11.7 odd 10 418.2.f.f.115.3 16
11.8 odd 10 418.2.f.f.229.3 yes 16
11.10 odd 2 4598.2.a.ca.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.f.115.3 16 11.7 odd 10
418.2.f.f.229.3 yes 16 11.8 odd 10
4598.2.a.bx.1.4 8 1.1 even 1 trivial
4598.2.a.ca.1.4 8 11.10 odd 2