Properties

Label 4598.2.a.bn.1.2
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
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 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} -1.36333 q^{6} +2.14134 q^{7} +1.00000 q^{8} -1.14134 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} -1.36333 q^{6} +2.14134 q^{7} +1.00000 q^{8} -1.14134 q^{9} +0.363328 q^{10} -1.36333 q^{12} -3.14134 q^{13} +2.14134 q^{14} -0.495336 q^{15} +1.00000 q^{16} +1.14134 q^{17} -1.14134 q^{18} -1.00000 q^{19} +0.363328 q^{20} -2.91934 q^{21} -2.14134 q^{23} -1.36333 q^{24} -4.86799 q^{25} -3.14134 q^{26} +5.64600 q^{27} +2.14134 q^{28} -1.77801 q^{29} -0.495336 q^{30} +7.00933 q^{31} +1.00000 q^{32} +1.14134 q^{34} +0.778008 q^{35} -1.14134 q^{36} -9.77801 q^{37} -1.00000 q^{38} +4.28267 q^{39} +0.363328 q^{40} -7.91934 q^{41} -2.91934 q^{42} -4.28267 q^{43} -0.414680 q^{45} -2.14134 q^{46} -7.59465 q^{47} -1.36333 q^{48} -2.41468 q^{49} -4.86799 q^{50} -1.55602 q^{51} -3.14134 q^{52} +10.7873 q^{53} +5.64600 q^{54} +2.14134 q^{56} +1.36333 q^{57} -1.77801 q^{58} -1.08066 q^{59} -0.495336 q^{60} -8.51399 q^{61} +7.00933 q^{62} -2.44398 q^{63} +1.00000 q^{64} -1.14134 q^{65} +8.56534 q^{67} +1.14134 q^{68} +2.91934 q^{69} +0.778008 q^{70} +3.50466 q^{71} -1.14134 q^{72} +11.7360 q^{73} -9.77801 q^{74} +6.63667 q^{75} -1.00000 q^{76} +4.28267 q^{78} +0.778008 q^{79} +0.363328 q^{80} -4.27334 q^{81} -7.91934 q^{82} -0.778008 q^{83} -2.91934 q^{84} +0.414680 q^{85} -4.28267 q^{86} +2.42401 q^{87} -8.20202 q^{89} -0.414680 q^{90} -6.72666 q^{91} -2.14134 q^{92} -9.55602 q^{93} -7.59465 q^{94} -0.363328 q^{95} -1.36333 q^{96} -1.86799 q^{97} -2.41468 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} - 5 q^{17} + 5 q^{18} - 3 q^{19} - q^{20} + 6 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 12 q^{30} + 3 q^{32} - 5 q^{34} - 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + 6 q^{42} + 4 q^{43} + 3 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} - 2 q^{50} + 8 q^{51} - q^{52} + 5 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} + 6 q^{61} - 20 q^{63} + 3 q^{64} + 5 q^{65} - 8 q^{67} - 5 q^{68} - 6 q^{69} - 4 q^{70} + 5 q^{72} + 10 q^{73} - 23 q^{74} + 22 q^{75} - 3 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} + 4 q^{83} + 6 q^{84} - 3 q^{85} + 4 q^{86} - 18 q^{87} + 7 q^{89} + 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} - 6 q^{94} + q^{95} - 2 q^{96} + 7 q^{97} - 3 q^{98} + O(q^{100}) \)

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
\(3\) −1.36333 −0.787118 −0.393559 0.919299i \(-0.628756\pi\)
−0.393559 + 0.919299i \(0.628756\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.363328 0.162485 0.0812427 0.996694i \(-0.474111\pi\)
0.0812427 + 0.996694i \(0.474111\pi\)
\(6\) −1.36333 −0.556576
\(7\) 2.14134 0.809349 0.404674 0.914461i \(-0.367385\pi\)
0.404674 + 0.914461i \(0.367385\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.14134 −0.380445
\(10\) 0.363328 0.114894
\(11\) 0 0
\(12\) −1.36333 −0.393559
\(13\) −3.14134 −0.871250 −0.435625 0.900128i \(-0.643473\pi\)
−0.435625 + 0.900128i \(0.643473\pi\)
\(14\) 2.14134 0.572296
\(15\) −0.495336 −0.127895
\(16\) 1.00000 0.250000
\(17\) 1.14134 0.276815 0.138407 0.990375i \(-0.455802\pi\)
0.138407 + 0.990375i \(0.455802\pi\)
\(18\) −1.14134 −0.269016
\(19\) −1.00000 −0.229416
\(20\) 0.363328 0.0812427
\(21\) −2.91934 −0.637053
\(22\) 0 0
\(23\) −2.14134 −0.446499 −0.223250 0.974761i \(-0.571667\pi\)
−0.223250 + 0.974761i \(0.571667\pi\)
\(24\) −1.36333 −0.278288
\(25\) −4.86799 −0.973599
\(26\) −3.14134 −0.616067
\(27\) 5.64600 1.08657
\(28\) 2.14134 0.404674
\(29\) −1.77801 −0.330168 −0.165084 0.986280i \(-0.552789\pi\)
−0.165084 + 0.986280i \(0.552789\pi\)
\(30\) −0.495336 −0.0904355
\(31\) 7.00933 1.25891 0.629456 0.777036i \(-0.283278\pi\)
0.629456 + 0.777036i \(0.283278\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.14134 0.195738
\(35\) 0.778008 0.131507
\(36\) −1.14134 −0.190223
\(37\) −9.77801 −1.60749 −0.803747 0.594971i \(-0.797164\pi\)
−0.803747 + 0.594971i \(0.797164\pi\)
\(38\) −1.00000 −0.162221
\(39\) 4.28267 0.685776
\(40\) 0.363328 0.0574472
\(41\) −7.91934 −1.23679 −0.618397 0.785866i \(-0.712218\pi\)
−0.618397 + 0.785866i \(0.712218\pi\)
\(42\) −2.91934 −0.450465
\(43\) −4.28267 −0.653101 −0.326551 0.945180i \(-0.605886\pi\)
−0.326551 + 0.945180i \(0.605886\pi\)
\(44\) 0 0
\(45\) −0.414680 −0.0618168
\(46\) −2.14134 −0.315723
\(47\) −7.59465 −1.10779 −0.553897 0.832585i \(-0.686860\pi\)
−0.553897 + 0.832585i \(0.686860\pi\)
\(48\) −1.36333 −0.196779
\(49\) −2.41468 −0.344954
\(50\) −4.86799 −0.688438
\(51\) −1.55602 −0.217886
\(52\) −3.14134 −0.435625
\(53\) 10.7873 1.48175 0.740877 0.671640i \(-0.234410\pi\)
0.740877 + 0.671640i \(0.234410\pi\)
\(54\) 5.64600 0.768323
\(55\) 0 0
\(56\) 2.14134 0.286148
\(57\) 1.36333 0.180577
\(58\) −1.77801 −0.233464
\(59\) −1.08066 −0.140689 −0.0703447 0.997523i \(-0.522410\pi\)
−0.0703447 + 0.997523i \(0.522410\pi\)
\(60\) −0.495336 −0.0639476
\(61\) −8.51399 −1.09011 −0.545053 0.838402i \(-0.683490\pi\)
−0.545053 + 0.838402i \(0.683490\pi\)
\(62\) 7.00933 0.890186
\(63\) −2.44398 −0.307913
\(64\) 1.00000 0.125000
\(65\) −1.14134 −0.141565
\(66\) 0 0
\(67\) 8.56534 1.04642 0.523212 0.852203i \(-0.324734\pi\)
0.523212 + 0.852203i \(0.324734\pi\)
\(68\) 1.14134 0.138407
\(69\) 2.91934 0.351448
\(70\) 0.778008 0.0929897
\(71\) 3.50466 0.415927 0.207964 0.978137i \(-0.433316\pi\)
0.207964 + 0.978137i \(0.433316\pi\)
\(72\) −1.14134 −0.134508
\(73\) 11.7360 1.37359 0.686797 0.726850i \(-0.259016\pi\)
0.686797 + 0.726850i \(0.259016\pi\)
\(74\) −9.77801 −1.13667
\(75\) 6.63667 0.766337
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 4.28267 0.484917
\(79\) 0.778008 0.0875327 0.0437664 0.999042i \(-0.486064\pi\)
0.0437664 + 0.999042i \(0.486064\pi\)
\(80\) 0.363328 0.0406213
\(81\) −4.27334 −0.474816
\(82\) −7.91934 −0.874545
\(83\) −0.778008 −0.0853975 −0.0426987 0.999088i \(-0.513596\pi\)
−0.0426987 + 0.999088i \(0.513596\pi\)
\(84\) −2.91934 −0.318527
\(85\) 0.414680 0.0449783
\(86\) −4.28267 −0.461812
\(87\) 2.42401 0.259881
\(88\) 0 0
\(89\) −8.20202 −0.869412 −0.434706 0.900572i \(-0.643148\pi\)
−0.434706 + 0.900572i \(0.643148\pi\)
\(90\) −0.414680 −0.0437111
\(91\) −6.72666 −0.705145
\(92\) −2.14134 −0.223250
\(93\) −9.55602 −0.990913
\(94\) −7.59465 −0.783328
\(95\) −0.363328 −0.0372767
\(96\) −1.36333 −0.139144
\(97\) −1.86799 −0.189666 −0.0948330 0.995493i \(-0.530232\pi\)
−0.0948330 + 0.995493i \(0.530232\pi\)
\(98\) −2.41468 −0.243919
\(99\) 0 0
\(100\) −4.86799 −0.486799
\(101\) −10.0700 −1.00200 −0.501002 0.865446i \(-0.667035\pi\)
−0.501002 + 0.865446i \(0.667035\pi\)
\(102\) −1.55602 −0.154069
\(103\) −17.3434 −1.70889 −0.854446 0.519541i \(-0.826103\pi\)
−0.854446 + 0.519541i \(0.826103\pi\)
\(104\) −3.14134 −0.308033
\(105\) −1.06068 −0.103512
\(106\) 10.7873 1.04776
\(107\) −13.6460 −1.31921 −0.659604 0.751613i \(-0.729276\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(108\) 5.64600 0.543287
\(109\) 5.33402 0.510907 0.255453 0.966821i \(-0.417775\pi\)
0.255453 + 0.966821i \(0.417775\pi\)
\(110\) 0 0
\(111\) 13.3306 1.26529
\(112\) 2.14134 0.202337
\(113\) −14.3633 −1.35119 −0.675594 0.737274i \(-0.736113\pi\)
−0.675594 + 0.737274i \(0.736113\pi\)
\(114\) 1.36333 0.127687
\(115\) −0.778008 −0.0725496
\(116\) −1.77801 −0.165084
\(117\) 3.58532 0.331463
\(118\) −1.08066 −0.0994824
\(119\) 2.44398 0.224040
\(120\) −0.495336 −0.0452178
\(121\) 0 0
\(122\) −8.51399 −0.770821
\(123\) 10.7967 0.973503
\(124\) 7.00933 0.629456
\(125\) −3.58532 −0.320681
\(126\) −2.44398 −0.217727
\(127\) −2.44398 −0.216869 −0.108434 0.994104i \(-0.534584\pi\)
−0.108434 + 0.994104i \(0.534584\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.83869 0.514068
\(130\) −1.14134 −0.100102
\(131\) −0.707999 −0.0618582 −0.0309291 0.999522i \(-0.509847\pi\)
−0.0309291 + 0.999522i \(0.509847\pi\)
\(132\) 0 0
\(133\) −2.14134 −0.185677
\(134\) 8.56534 0.739933
\(135\) 2.05135 0.176552
\(136\) 1.14134 0.0978688
\(137\) 6.28267 0.536765 0.268382 0.963312i \(-0.413511\pi\)
0.268382 + 0.963312i \(0.413511\pi\)
\(138\) 2.91934 0.248511
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0.778008 0.0657537
\(141\) 10.3540 0.871964
\(142\) 3.50466 0.294105
\(143\) 0 0
\(144\) −1.14134 −0.0951113
\(145\) −0.646000 −0.0536474
\(146\) 11.7360 0.971277
\(147\) 3.29200 0.271520
\(148\) −9.77801 −0.803747
\(149\) 11.1600 0.914262 0.457131 0.889399i \(-0.348877\pi\)
0.457131 + 0.889399i \(0.348877\pi\)
\(150\) 6.63667 0.541882
\(151\) −13.8060 −1.12352 −0.561758 0.827302i \(-0.689875\pi\)
−0.561758 + 0.827302i \(0.689875\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −1.30265 −0.105313
\(154\) 0 0
\(155\) 2.54669 0.204555
\(156\) 4.28267 0.342888
\(157\) 15.8060 1.26146 0.630728 0.776004i \(-0.282756\pi\)
0.630728 + 0.776004i \(0.282756\pi\)
\(158\) 0.778008 0.0618950
\(159\) −14.7067 −1.16632
\(160\) 0.363328 0.0287236
\(161\) −4.58532 −0.361374
\(162\) −4.27334 −0.335746
\(163\) −3.71733 −0.291164 −0.145582 0.989346i \(-0.546505\pi\)
−0.145582 + 0.989346i \(0.546505\pi\)
\(164\) −7.91934 −0.618397
\(165\) 0 0
\(166\) −0.778008 −0.0603851
\(167\) 5.27334 0.408064 0.204032 0.978964i \(-0.434595\pi\)
0.204032 + 0.978964i \(0.434595\pi\)
\(168\) −2.91934 −0.225232
\(169\) −3.13201 −0.240924
\(170\) 0.414680 0.0318045
\(171\) 1.14134 0.0872802
\(172\) −4.28267 −0.326551
\(173\) 11.4660 0.871746 0.435873 0.900008i \(-0.356440\pi\)
0.435873 + 0.900008i \(0.356440\pi\)
\(174\) 2.42401 0.183764
\(175\) −10.4240 −0.787981
\(176\) 0 0
\(177\) 1.47329 0.110739
\(178\) −8.20202 −0.614767
\(179\) −0.900687 −0.0673205 −0.0336602 0.999433i \(-0.510716\pi\)
−0.0336602 + 0.999433i \(0.510716\pi\)
\(180\) −0.414680 −0.0309084
\(181\) −16.6974 −1.24110 −0.620552 0.784165i \(-0.713091\pi\)
−0.620552 + 0.784165i \(0.713091\pi\)
\(182\) −6.72666 −0.498613
\(183\) 11.6074 0.858041
\(184\) −2.14134 −0.157861
\(185\) −3.55263 −0.261194
\(186\) −9.55602 −0.700681
\(187\) 0 0
\(188\) −7.59465 −0.553897
\(189\) 12.0900 0.879417
\(190\) −0.363328 −0.0263586
\(191\) −3.87732 −0.280553 −0.140277 0.990112i \(-0.544799\pi\)
−0.140277 + 0.990112i \(0.544799\pi\)
\(192\) −1.36333 −0.0983897
\(193\) 5.32131 0.383036 0.191518 0.981489i \(-0.438659\pi\)
0.191518 + 0.981489i \(0.438659\pi\)
\(194\) −1.86799 −0.134114
\(195\) 1.55602 0.111429
\(196\) −2.41468 −0.172477
\(197\) −14.3306 −1.02102 −0.510508 0.859873i \(-0.670543\pi\)
−0.510508 + 0.859873i \(0.670543\pi\)
\(198\) 0 0
\(199\) 5.83869 0.413894 0.206947 0.978352i \(-0.433647\pi\)
0.206947 + 0.978352i \(0.433647\pi\)
\(200\) −4.86799 −0.344219
\(201\) −11.6774 −0.823659
\(202\) −10.0700 −0.708523
\(203\) −3.80731 −0.267221
\(204\) −1.55602 −0.108943
\(205\) −2.87732 −0.200961
\(206\) −17.3434 −1.20837
\(207\) 2.44398 0.169869
\(208\) −3.14134 −0.217812
\(209\) 0 0
\(210\) −1.06068 −0.0731939
\(211\) 9.74870 0.671128 0.335564 0.942017i \(-0.391073\pi\)
0.335564 + 0.942017i \(0.391073\pi\)
\(212\) 10.7873 0.740877
\(213\) −4.77801 −0.327384
\(214\) −13.6460 −0.932821
\(215\) −1.55602 −0.106119
\(216\) 5.64600 0.384162
\(217\) 15.0093 1.01890
\(218\) 5.33402 0.361266
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) −3.58532 −0.241175
\(222\) 13.3306 0.894694
\(223\) −18.6167 −1.24667 −0.623333 0.781956i \(-0.714222\pi\)
−0.623333 + 0.781956i \(0.714222\pi\)
\(224\) 2.14134 0.143074
\(225\) 5.55602 0.370401
\(226\) −14.3633 −0.955434
\(227\) −17.9160 −1.18912 −0.594562 0.804050i \(-0.702674\pi\)
−0.594562 + 0.804050i \(0.702674\pi\)
\(228\) 1.36333 0.0902886
\(229\) −8.31198 −0.549271 −0.274635 0.961548i \(-0.588557\pi\)
−0.274635 + 0.961548i \(0.588557\pi\)
\(230\) −0.778008 −0.0513003
\(231\) 0 0
\(232\) −1.77801 −0.116732
\(233\) 7.28267 0.477104 0.238552 0.971130i \(-0.423327\pi\)
0.238552 + 0.971130i \(0.423327\pi\)
\(234\) 3.58532 0.234380
\(235\) −2.75935 −0.180000
\(236\) −1.08066 −0.0703447
\(237\) −1.06068 −0.0688986
\(238\) 2.44398 0.158420
\(239\) 11.1693 0.722483 0.361242 0.932472i \(-0.382353\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(240\) −0.495336 −0.0319738
\(241\) 6.39263 0.411786 0.205893 0.978575i \(-0.433990\pi\)
0.205893 + 0.978575i \(0.433990\pi\)
\(242\) 0 0
\(243\) −11.1120 −0.712837
\(244\) −8.51399 −0.545053
\(245\) −0.877321 −0.0560500
\(246\) 10.7967 0.688370
\(247\) 3.14134 0.199878
\(248\) 7.00933 0.445093
\(249\) 1.06068 0.0672179
\(250\) −3.58532 −0.226756
\(251\) 8.17997 0.516315 0.258158 0.966103i \(-0.416885\pi\)
0.258158 + 0.966103i \(0.416885\pi\)
\(252\) −2.44398 −0.153957
\(253\) 0 0
\(254\) −2.44398 −0.153349
\(255\) −0.565344 −0.0354032
\(256\) 1.00000 0.0625000
\(257\) −28.8773 −1.80132 −0.900659 0.434527i \(-0.856916\pi\)
−0.900659 + 0.434527i \(0.856916\pi\)
\(258\) 5.83869 0.363501
\(259\) −20.9380 −1.30102
\(260\) −1.14134 −0.0707827
\(261\) 2.02930 0.125611
\(262\) −0.707999 −0.0437403
\(263\) 0.385375 0.0237632 0.0118816 0.999929i \(-0.496218\pi\)
0.0118816 + 0.999929i \(0.496218\pi\)
\(264\) 0 0
\(265\) 3.91934 0.240763
\(266\) −2.14134 −0.131294
\(267\) 11.1820 0.684330
\(268\) 8.56534 0.523212
\(269\) 13.5140 0.823963 0.411981 0.911192i \(-0.364837\pi\)
0.411981 + 0.911192i \(0.364837\pi\)
\(270\) 2.05135 0.124841
\(271\) −9.73599 −0.591419 −0.295709 0.955278i \(-0.595556\pi\)
−0.295709 + 0.955278i \(0.595556\pi\)
\(272\) 1.14134 0.0692037
\(273\) 9.17064 0.555032
\(274\) 6.28267 0.379550
\(275\) 0 0
\(276\) 2.91934 0.175724
\(277\) −6.74870 −0.405490 −0.202745 0.979232i \(-0.564986\pi\)
−0.202745 + 0.979232i \(0.564986\pi\)
\(278\) 4.00000 0.239904
\(279\) −8.00000 −0.478947
\(280\) 0.778008 0.0464949
\(281\) −7.06068 −0.421205 −0.210602 0.977572i \(-0.567543\pi\)
−0.210602 + 0.977572i \(0.567543\pi\)
\(282\) 10.3540 0.616572
\(283\) −8.46264 −0.503052 −0.251526 0.967851i \(-0.580932\pi\)
−0.251526 + 0.967851i \(0.580932\pi\)
\(284\) 3.50466 0.207964
\(285\) 0.495336 0.0293412
\(286\) 0 0
\(287\) −16.9580 −1.00100
\(288\) −1.14134 −0.0672539
\(289\) −15.6974 −0.923374
\(290\) −0.646000 −0.0379345
\(291\) 2.54669 0.149289
\(292\) 11.7360 0.686797
\(293\) 21.7967 1.27337 0.636687 0.771122i \(-0.280304\pi\)
0.636687 + 0.771122i \(0.280304\pi\)
\(294\) 3.29200 0.191993
\(295\) −0.392633 −0.0228600
\(296\) −9.77801 −0.568335
\(297\) 0 0
\(298\) 11.1600 0.646481
\(299\) 6.72666 0.389013
\(300\) 6.63667 0.383168
\(301\) −9.17064 −0.528587
\(302\) −13.8060 −0.794446
\(303\) 13.7287 0.788695
\(304\) −1.00000 −0.0573539
\(305\) −3.09337 −0.177126
\(306\) −1.30265 −0.0744674
\(307\) −16.5526 −0.944708 −0.472354 0.881409i \(-0.656596\pi\)
−0.472354 + 0.881409i \(0.656596\pi\)
\(308\) 0 0
\(309\) 23.6447 1.34510
\(310\) 2.54669 0.144642
\(311\) −20.8480 −1.18218 −0.591091 0.806605i \(-0.701303\pi\)
−0.591091 + 0.806605i \(0.701303\pi\)
\(312\) 4.28267 0.242459
\(313\) −2.98134 −0.168515 −0.0842577 0.996444i \(-0.526852\pi\)
−0.0842577 + 0.996444i \(0.526852\pi\)
\(314\) 15.8060 0.891984
\(315\) −0.887968 −0.0500314
\(316\) 0.778008 0.0437664
\(317\) −11.9160 −0.669267 −0.334633 0.942348i \(-0.608612\pi\)
−0.334633 + 0.942348i \(0.608612\pi\)
\(318\) −14.7067 −0.824710
\(319\) 0 0
\(320\) 0.363328 0.0203107
\(321\) 18.6040 1.03837
\(322\) −4.58532 −0.255530
\(323\) −1.14134 −0.0635056
\(324\) −4.27334 −0.237408
\(325\) 15.2920 0.848248
\(326\) −3.71733 −0.205884
\(327\) −7.27203 −0.402144
\(328\) −7.91934 −0.437273
\(329\) −16.2627 −0.896591
\(330\) 0 0
\(331\) 0.0127181 0.000699049 0 0.000349525 1.00000i \(-0.499889\pi\)
0.000349525 1.00000i \(0.499889\pi\)
\(332\) −0.778008 −0.0426987
\(333\) 11.1600 0.611564
\(334\) 5.27334 0.288545
\(335\) 3.11203 0.170028
\(336\) −2.91934 −0.159263
\(337\) 28.1180 1.53168 0.765842 0.643029i \(-0.222323\pi\)
0.765842 + 0.643029i \(0.222323\pi\)
\(338\) −3.13201 −0.170359
\(339\) 19.5819 1.06354
\(340\) 0.414680 0.0224892
\(341\) 0 0
\(342\) 1.14134 0.0617164
\(343\) −20.1600 −1.08854
\(344\) −4.28267 −0.230906
\(345\) 1.06068 0.0571051
\(346\) 11.4660 0.616418
\(347\) 5.66598 0.304166 0.152083 0.988368i \(-0.451402\pi\)
0.152083 + 0.988368i \(0.451402\pi\)
\(348\) 2.42401 0.129940
\(349\) 24.3306 1.30239 0.651194 0.758911i \(-0.274268\pi\)
0.651194 + 0.758911i \(0.274268\pi\)
\(350\) −10.4240 −0.557187
\(351\) −17.7360 −0.946677
\(352\) 0 0
\(353\) 2.11203 0.112412 0.0562060 0.998419i \(-0.482100\pi\)
0.0562060 + 0.998419i \(0.482100\pi\)
\(354\) 1.47329 0.0783044
\(355\) 1.27334 0.0675821
\(356\) −8.20202 −0.434706
\(357\) −3.33195 −0.176346
\(358\) −0.900687 −0.0476028
\(359\) −34.6613 −1.82935 −0.914676 0.404188i \(-0.867554\pi\)
−0.914676 + 0.404188i \(0.867554\pi\)
\(360\) −0.414680 −0.0218555
\(361\) 1.00000 0.0526316
\(362\) −16.6974 −0.877593
\(363\) 0 0
\(364\) −6.72666 −0.352573
\(365\) 4.26401 0.223189
\(366\) 11.6074 0.606727
\(367\) −36.3400 −1.89693 −0.948465 0.316881i \(-0.897364\pi\)
−0.948465 + 0.316881i \(0.897364\pi\)
\(368\) −2.14134 −0.111625
\(369\) 9.03863 0.470532
\(370\) −3.55263 −0.184692
\(371\) 23.0993 1.19926
\(372\) −9.55602 −0.495456
\(373\) 30.1273 1.55993 0.779966 0.625822i \(-0.215236\pi\)
0.779966 + 0.625822i \(0.215236\pi\)
\(374\) 0 0
\(375\) 4.88797 0.252414
\(376\) −7.59465 −0.391664
\(377\) 5.58532 0.287659
\(378\) 12.0900 0.621842
\(379\) 3.06200 0.157284 0.0786422 0.996903i \(-0.474942\pi\)
0.0786422 + 0.996903i \(0.474942\pi\)
\(380\) −0.363328 −0.0186383
\(381\) 3.33195 0.170701
\(382\) −3.87732 −0.198381
\(383\) 33.1307 1.69290 0.846450 0.532469i \(-0.178736\pi\)
0.846450 + 0.532469i \(0.178736\pi\)
\(384\) −1.36333 −0.0695721
\(385\) 0 0
\(386\) 5.32131 0.270847
\(387\) 4.88797 0.248469
\(388\) −1.86799 −0.0948330
\(389\) −3.81664 −0.193511 −0.0967557 0.995308i \(-0.530847\pi\)
−0.0967557 + 0.995308i \(0.530847\pi\)
\(390\) 1.55602 0.0787919
\(391\) −2.44398 −0.123598
\(392\) −2.41468 −0.121960
\(393\) 0.965235 0.0486897
\(394\) −14.3306 −0.721967
\(395\) 0.282672 0.0142228
\(396\) 0 0
\(397\) −25.0573 −1.25759 −0.628795 0.777571i \(-0.716451\pi\)
−0.628795 + 0.777571i \(0.716451\pi\)
\(398\) 5.83869 0.292667
\(399\) 2.91934 0.146150
\(400\) −4.86799 −0.243400
\(401\) −31.9567 −1.59584 −0.797920 0.602764i \(-0.794066\pi\)
−0.797920 + 0.602764i \(0.794066\pi\)
\(402\) −11.6774 −0.582415
\(403\) −22.0187 −1.09683
\(404\) −10.0700 −0.501002
\(405\) −1.55263 −0.0771506
\(406\) −3.80731 −0.188954
\(407\) 0 0
\(408\) −1.55602 −0.0770343
\(409\) 27.8280 1.37601 0.688004 0.725707i \(-0.258487\pi\)
0.688004 + 0.725707i \(0.258487\pi\)
\(410\) −2.87732 −0.142101
\(411\) −8.56534 −0.422497
\(412\) −17.3434 −0.854446
\(413\) −2.31405 −0.113867
\(414\) 2.44398 0.120115
\(415\) −0.282672 −0.0138758
\(416\) −3.14134 −0.154017
\(417\) −5.45331 −0.267050
\(418\) 0 0
\(419\) −5.24065 −0.256022 −0.128011 0.991773i \(-0.540859\pi\)
−0.128011 + 0.991773i \(0.540859\pi\)
\(420\) −1.06068 −0.0517559
\(421\) −15.3340 −0.747335 −0.373667 0.927563i \(-0.621900\pi\)
−0.373667 + 0.927563i \(0.621900\pi\)
\(422\) 9.74870 0.474559
\(423\) 8.66805 0.421455
\(424\) 10.7873 0.523879
\(425\) −5.55602 −0.269506
\(426\) −4.77801 −0.231495
\(427\) −18.2313 −0.882275
\(428\) −13.6460 −0.659604
\(429\) 0 0
\(430\) −1.55602 −0.0750377
\(431\) 18.8994 0.910351 0.455175 0.890402i \(-0.349577\pi\)
0.455175 + 0.890402i \(0.349577\pi\)
\(432\) 5.64600 0.271643
\(433\) −11.1787 −0.537212 −0.268606 0.963250i \(-0.586563\pi\)
−0.268606 + 0.963250i \(0.586563\pi\)
\(434\) 15.0093 0.720471
\(435\) 0.880711 0.0422268
\(436\) 5.33402 0.255453
\(437\) 2.14134 0.102434
\(438\) −16.0000 −0.764510
\(439\) 23.4720 1.12026 0.560128 0.828406i \(-0.310752\pi\)
0.560128 + 0.828406i \(0.310752\pi\)
\(440\) 0 0
\(441\) 2.75596 0.131236
\(442\) −3.58532 −0.170536
\(443\) −29.8387 −1.41768 −0.708839 0.705370i \(-0.750781\pi\)
−0.708839 + 0.705370i \(0.750781\pi\)
\(444\) 13.3306 0.632644
\(445\) −2.98002 −0.141267
\(446\) −18.6167 −0.881526
\(447\) −15.2147 −0.719632
\(448\) 2.14134 0.101169
\(449\) −10.6133 −0.500873 −0.250436 0.968133i \(-0.580574\pi\)
−0.250436 + 0.968133i \(0.580574\pi\)
\(450\) 5.55602 0.261913
\(451\) 0 0
\(452\) −14.3633 −0.675594
\(453\) 18.8221 0.884339
\(454\) −17.9160 −0.840837
\(455\) −2.44398 −0.114576
\(456\) 1.36333 0.0638437
\(457\) −7.82936 −0.366242 −0.183121 0.983090i \(-0.558620\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(458\) −8.31198 −0.388393
\(459\) 6.44398 0.300779
\(460\) −0.778008 −0.0362748
\(461\) −2.54330 −0.118453 −0.0592266 0.998245i \(-0.518863\pi\)
−0.0592266 + 0.998245i \(0.518863\pi\)
\(462\) 0 0
\(463\) −31.6519 −1.47099 −0.735495 0.677530i \(-0.763050\pi\)
−0.735495 + 0.677530i \(0.763050\pi\)
\(464\) −1.77801 −0.0825419
\(465\) −3.47197 −0.161009
\(466\) 7.28267 0.337363
\(467\) −7.85735 −0.363595 −0.181797 0.983336i \(-0.558191\pi\)
−0.181797 + 0.983336i \(0.558191\pi\)
\(468\) 3.58532 0.165731
\(469\) 18.3413 0.846922
\(470\) −2.75935 −0.127279
\(471\) −21.5488 −0.992914
\(472\) −1.08066 −0.0497412
\(473\) 0 0
\(474\) −1.06068 −0.0487187
\(475\) 4.86799 0.223359
\(476\) 2.44398 0.112020
\(477\) −12.3120 −0.563727
\(478\) 11.1693 0.510873
\(479\) 13.9614 0.637911 0.318956 0.947770i \(-0.396668\pi\)
0.318956 + 0.947770i \(0.396668\pi\)
\(480\) −0.495336 −0.0226089
\(481\) 30.7160 1.40053
\(482\) 6.39263 0.291176
\(483\) 6.25130 0.284444
\(484\) 0 0
\(485\) −0.678694 −0.0308179
\(486\) −11.1120 −0.504052
\(487\) 1.83869 0.0833189 0.0416595 0.999132i \(-0.486736\pi\)
0.0416595 + 0.999132i \(0.486736\pi\)
\(488\) −8.51399 −0.385410
\(489\) 5.06794 0.229180
\(490\) −0.877321 −0.0396333
\(491\) 27.5747 1.24443 0.622214 0.782847i \(-0.286233\pi\)
0.622214 + 0.782847i \(0.286233\pi\)
\(492\) 10.7967 0.486751
\(493\) −2.02930 −0.0913953
\(494\) 3.14134 0.141335
\(495\) 0 0
\(496\) 7.00933 0.314728
\(497\) 7.50466 0.336630
\(498\) 1.06068 0.0475302
\(499\) 26.4113 1.18233 0.591166 0.806550i \(-0.298668\pi\)
0.591166 + 0.806550i \(0.298668\pi\)
\(500\) −3.58532 −0.160340
\(501\) −7.18930 −0.321194
\(502\) 8.17997 0.365090
\(503\) 12.5853 0.561152 0.280576 0.959832i \(-0.409475\pi\)
0.280576 + 0.959832i \(0.409475\pi\)
\(504\) −2.44398 −0.108864
\(505\) −3.65872 −0.162811
\(506\) 0 0
\(507\) 4.26995 0.189635
\(508\) −2.44398 −0.108434
\(509\) 28.8166 1.27728 0.638638 0.769508i \(-0.279498\pi\)
0.638638 + 0.769508i \(0.279498\pi\)
\(510\) −0.565344 −0.0250339
\(511\) 25.1307 1.11172
\(512\) 1.00000 0.0441942
\(513\) −5.64600 −0.249277
\(514\) −28.8773 −1.27372
\(515\) −6.30133 −0.277670
\(516\) 5.83869 0.257034
\(517\) 0 0
\(518\) −20.9380 −0.919963
\(519\) −15.6320 −0.686167
\(520\) −1.14134 −0.0500509
\(521\) 32.5840 1.42753 0.713766 0.700385i \(-0.246988\pi\)
0.713766 + 0.700385i \(0.246988\pi\)
\(522\) 2.02930 0.0888202
\(523\) 43.3820 1.89696 0.948481 0.316834i \(-0.102620\pi\)
0.948481 + 0.316834i \(0.102620\pi\)
\(524\) −0.707999 −0.0309291
\(525\) 14.2113 0.620234
\(526\) 0.385375 0.0168032
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −18.4147 −0.800638
\(530\) 3.91934 0.170245
\(531\) 1.23339 0.0535246
\(532\) −2.14134 −0.0928387
\(533\) 24.8773 1.07756
\(534\) 11.1820 0.483894
\(535\) −4.95798 −0.214352
\(536\) 8.56534 0.369967
\(537\) 1.22793 0.0529892
\(538\) 13.5140 0.582630
\(539\) 0 0
\(540\) 2.05135 0.0882761
\(541\) −28.6867 −1.23334 −0.616669 0.787223i \(-0.711518\pi\)
−0.616669 + 0.787223i \(0.711518\pi\)
\(542\) −9.73599 −0.418196
\(543\) 22.7640 0.976896
\(544\) 1.14134 0.0489344
\(545\) 1.93800 0.0830149
\(546\) 9.17064 0.392467
\(547\) −3.09931 −0.132517 −0.0662585 0.997802i \(-0.521106\pi\)
−0.0662585 + 0.997802i \(0.521106\pi\)
\(548\) 6.28267 0.268382
\(549\) 9.71733 0.414725
\(550\) 0 0
\(551\) 1.77801 0.0757457
\(552\) 2.91934 0.124256
\(553\) 1.66598 0.0708445
\(554\) −6.74870 −0.286725
\(555\) 4.84340 0.205591
\(556\) 4.00000 0.169638
\(557\) 23.9160 1.01335 0.506676 0.862137i \(-0.330874\pi\)
0.506676 + 0.862137i \(0.330874\pi\)
\(558\) −8.00000 −0.338667
\(559\) 13.4533 0.569015
\(560\) 0.778008 0.0328768
\(561\) 0 0
\(562\) −7.06068 −0.297837
\(563\) 35.7674 1.50741 0.753707 0.657210i \(-0.228264\pi\)
0.753707 + 0.657210i \(0.228264\pi\)
\(564\) 10.3540 0.435982
\(565\) −5.21860 −0.219548
\(566\) −8.46264 −0.355711
\(567\) −9.15066 −0.384292
\(568\) 3.50466 0.147052
\(569\) −9.71733 −0.407372 −0.203686 0.979036i \(-0.565292\pi\)
−0.203686 + 0.979036i \(0.565292\pi\)
\(570\) 0.495336 0.0207473
\(571\) −37.6260 −1.57460 −0.787300 0.616570i \(-0.788522\pi\)
−0.787300 + 0.616570i \(0.788522\pi\)
\(572\) 0 0
\(573\) 5.28606 0.220828
\(574\) −16.9580 −0.707812
\(575\) 10.4240 0.434711
\(576\) −1.14134 −0.0475557
\(577\) 9.60398 0.399819 0.199909 0.979814i \(-0.435935\pi\)
0.199909 + 0.979814i \(0.435935\pi\)
\(578\) −15.6974 −0.652924
\(579\) −7.25469 −0.301494
\(580\) −0.646000 −0.0268237
\(581\) −1.66598 −0.0691163
\(582\) 2.54669 0.105564
\(583\) 0 0
\(584\) 11.7360 0.485639
\(585\) 1.30265 0.0538579
\(586\) 21.7967 0.900412
\(587\) 40.8153 1.68463 0.842314 0.538987i \(-0.181193\pi\)
0.842314 + 0.538987i \(0.181193\pi\)
\(588\) 3.29200 0.135760
\(589\) −7.00933 −0.288814
\(590\) −0.392633 −0.0161644
\(591\) 19.5374 0.803660
\(592\) −9.77801 −0.401874
\(593\) 47.8853 1.96641 0.983207 0.182491i \(-0.0584162\pi\)
0.983207 + 0.182491i \(0.0584162\pi\)
\(594\) 0 0
\(595\) 0.887968 0.0364032
\(596\) 11.1600 0.457131
\(597\) −7.96005 −0.325783
\(598\) 6.72666 0.275073
\(599\) 24.9253 1.01842 0.509210 0.860642i \(-0.329938\pi\)
0.509210 + 0.860642i \(0.329938\pi\)
\(600\) 6.63667 0.270941
\(601\) 8.29332 0.338292 0.169146 0.985591i \(-0.445899\pi\)
0.169146 + 0.985591i \(0.445899\pi\)
\(602\) −9.17064 −0.373767
\(603\) −9.77594 −0.398107
\(604\) −13.8060 −0.561758
\(605\) 0 0
\(606\) 13.7287 0.557691
\(607\) 5.13795 0.208543 0.104271 0.994549i \(-0.466749\pi\)
0.104271 + 0.994549i \(0.466749\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 5.19062 0.210334
\(610\) −3.09337 −0.125247
\(611\) 23.8573 0.965165
\(612\) −1.30265 −0.0526564
\(613\) 1.63667 0.0661045 0.0330523 0.999454i \(-0.489477\pi\)
0.0330523 + 0.999454i \(0.489477\pi\)
\(614\) −16.5526 −0.668010
\(615\) 3.92273 0.158180
\(616\) 0 0
\(617\) −16.8973 −0.680260 −0.340130 0.940379i \(-0.610471\pi\)
−0.340130 + 0.940379i \(0.610471\pi\)
\(618\) 23.6447 0.951129
\(619\) −28.8480 −1.15950 −0.579750 0.814795i \(-0.696850\pi\)
−0.579750 + 0.814795i \(0.696850\pi\)
\(620\) 2.54669 0.102277
\(621\) −12.0900 −0.485154
\(622\) −20.8480 −0.835929
\(623\) −17.5633 −0.703658
\(624\) 4.28267 0.171444
\(625\) 23.0373 0.921493
\(626\) −2.98134 −0.119158
\(627\) 0 0
\(628\) 15.8060 0.630728
\(629\) −11.1600 −0.444978
\(630\) −0.887968 −0.0353775
\(631\) −2.24404 −0.0893338 −0.0446669 0.999002i \(-0.514223\pi\)
−0.0446669 + 0.999002i \(0.514223\pi\)
\(632\) 0.778008 0.0309475
\(633\) −13.2907 −0.528257
\(634\) −11.9160 −0.473243
\(635\) −0.887968 −0.0352380
\(636\) −14.7067 −0.583158
\(637\) 7.58532 0.300541
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 0.363328 0.0143618
\(641\) 43.2300 1.70748 0.853741 0.520698i \(-0.174328\pi\)
0.853741 + 0.520698i \(0.174328\pi\)
\(642\) 18.6040 0.734240
\(643\) 9.69867 0.382478 0.191239 0.981543i \(-0.438749\pi\)
0.191239 + 0.981543i \(0.438749\pi\)
\(644\) −4.58532 −0.180687
\(645\) 2.12136 0.0835285
\(646\) −1.14134 −0.0449053
\(647\) 3.59465 0.141320 0.0706601 0.997500i \(-0.477489\pi\)
0.0706601 + 0.997500i \(0.477489\pi\)
\(648\) −4.27334 −0.167873
\(649\) 0 0
\(650\) 15.2920 0.599802
\(651\) −20.4626 −0.801994
\(652\) −3.71733 −0.145582
\(653\) 18.8226 0.736584 0.368292 0.929710i \(-0.379943\pi\)
0.368292 + 0.929710i \(0.379943\pi\)
\(654\) −7.27203 −0.284359
\(655\) −0.257236 −0.0100510
\(656\) −7.91934 −0.309198
\(657\) −13.3947 −0.522577
\(658\) −16.2627 −0.633986
\(659\) 46.6613 1.81766 0.908832 0.417161i \(-0.136975\pi\)
0.908832 + 0.417161i \(0.136975\pi\)
\(660\) 0 0
\(661\) −25.4554 −0.990100 −0.495050 0.868865i \(-0.664850\pi\)
−0.495050 + 0.868865i \(0.664850\pi\)
\(662\) 0.0127181 0.000494303 0
\(663\) 4.88797 0.189833
\(664\) −0.778008 −0.0301926
\(665\) −0.778008 −0.0301699
\(666\) 11.1600 0.432441
\(667\) 3.80731 0.147420
\(668\) 5.27334 0.204032
\(669\) 25.3807 0.981273
\(670\) 3.11203 0.120228
\(671\) 0 0
\(672\) −2.91934 −0.112616
\(673\) −2.03269 −0.0783546 −0.0391773 0.999232i \(-0.512474\pi\)
−0.0391773 + 0.999232i \(0.512474\pi\)
\(674\) 28.1180 1.08306
\(675\) −27.4847 −1.05789
\(676\) −3.13201 −0.120462
\(677\) 15.1727 0.583135 0.291567 0.956550i \(-0.405823\pi\)
0.291567 + 0.956550i \(0.405823\pi\)
\(678\) 19.5819 0.752040
\(679\) −4.00000 −0.153506
\(680\) 0.414680 0.0159022
\(681\) 24.4253 0.935981
\(682\) 0 0
\(683\) 14.2241 0.544269 0.272134 0.962259i \(-0.412270\pi\)
0.272134 + 0.962259i \(0.412270\pi\)
\(684\) 1.14134 0.0436401
\(685\) 2.28267 0.0872164
\(686\) −20.1600 −0.769712
\(687\) 11.3320 0.432341
\(688\) −4.28267 −0.163275
\(689\) −33.8867 −1.29098
\(690\) 1.06068 0.0403794
\(691\) 13.1379 0.499791 0.249896 0.968273i \(-0.419604\pi\)
0.249896 + 0.968273i \(0.419604\pi\)
\(692\) 11.4660 0.435873
\(693\) 0 0
\(694\) 5.66598 0.215078
\(695\) 1.45331 0.0551273
\(696\) 2.42401 0.0918818
\(697\) −9.03863 −0.342363
\(698\) 24.3306 0.920928
\(699\) −9.92867 −0.375537
\(700\) −10.4240 −0.393990
\(701\) −25.2373 −0.953198 −0.476599 0.879121i \(-0.658131\pi\)
−0.476599 + 0.879121i \(0.658131\pi\)
\(702\) −17.7360 −0.669402
\(703\) 9.77801 0.368785
\(704\) 0 0
\(705\) 3.76190 0.141681
\(706\) 2.11203 0.0794874
\(707\) −21.5633 −0.810970
\(708\) 1.47329 0.0553696
\(709\) 23.3760 0.877906 0.438953 0.898510i \(-0.355349\pi\)
0.438953 + 0.898510i \(0.355349\pi\)
\(710\) 1.27334 0.0477877
\(711\) −0.887968 −0.0333014
\(712\) −8.20202 −0.307384
\(713\) −15.0093 −0.562104
\(714\) −3.33195 −0.124695
\(715\) 0 0
\(716\) −0.900687 −0.0336602
\(717\) −15.2275 −0.568680
\(718\) −34.6613 −1.29355
\(719\) 31.6774 1.18137 0.590683 0.806903i \(-0.298858\pi\)
0.590683 + 0.806903i \(0.298858\pi\)
\(720\) −0.414680 −0.0154542
\(721\) −37.1379 −1.38309
\(722\) 1.00000 0.0372161
\(723\) −8.71526 −0.324124
\(724\) −16.6974 −0.620552
\(725\) 8.65533 0.321451
\(726\) 0 0
\(727\) −36.5199 −1.35445 −0.677225 0.735776i \(-0.736817\pi\)
−0.677225 + 0.735776i \(0.736817\pi\)
\(728\) −6.72666 −0.249306
\(729\) 27.9694 1.03590
\(730\) 4.26401 0.157818
\(731\) −4.88797 −0.180788
\(732\) 11.6074 0.429021
\(733\) 36.1880 1.33663 0.668317 0.743877i \(-0.267015\pi\)
0.668317 + 0.743877i \(0.267015\pi\)
\(734\) −36.3400 −1.34133
\(735\) 1.19608 0.0441180
\(736\) −2.14134 −0.0789307
\(737\) 0 0
\(738\) 9.03863 0.332717
\(739\) −15.1447 −0.557108 −0.278554 0.960421i \(-0.589855\pi\)
−0.278554 + 0.960421i \(0.589855\pi\)
\(740\) −3.55263 −0.130597
\(741\) −4.28267 −0.157328
\(742\) 23.0993 0.848002
\(743\) −3.85735 −0.141512 −0.0707561 0.997494i \(-0.522541\pi\)
−0.0707561 + 0.997494i \(0.522541\pi\)
\(744\) −9.55602 −0.350341
\(745\) 4.05474 0.148554
\(746\) 30.1273 1.10304
\(747\) 0.887968 0.0324891
\(748\) 0 0
\(749\) −29.2207 −1.06770
\(750\) 4.88797 0.178483
\(751\) 15.9346 0.581462 0.290731 0.956805i \(-0.406101\pi\)
0.290731 + 0.956805i \(0.406101\pi\)
\(752\) −7.59465 −0.276948
\(753\) −11.1520 −0.406401
\(754\) 5.58532 0.203405
\(755\) −5.01611 −0.182555
\(756\) 12.0900 0.439708
\(757\) 25.7767 0.936870 0.468435 0.883498i \(-0.344818\pi\)
0.468435 + 0.883498i \(0.344818\pi\)
\(758\) 3.06200 0.111217
\(759\) 0 0
\(760\) −0.363328 −0.0131793
\(761\) −24.5747 −0.890831 −0.445416 0.895324i \(-0.646944\pi\)
−0.445416 + 0.895324i \(0.646944\pi\)
\(762\) 3.33195 0.120704
\(763\) 11.4219 0.413502
\(764\) −3.87732 −0.140277
\(765\) −0.473289 −0.0171118
\(766\) 33.1307 1.19706
\(767\) 3.39470 0.122576
\(768\) −1.36333 −0.0491949
\(769\) 51.3200 1.85065 0.925323 0.379180i \(-0.123794\pi\)
0.925323 + 0.379180i \(0.123794\pi\)
\(770\) 0 0
\(771\) 39.3693 1.41785
\(772\) 5.32131 0.191518
\(773\) 27.0153 0.971672 0.485836 0.874050i \(-0.338515\pi\)
0.485836 + 0.874050i \(0.338515\pi\)
\(774\) 4.88797 0.175694
\(775\) −34.1214 −1.22568
\(776\) −1.86799 −0.0670570
\(777\) 28.5454 1.02406
\(778\) −3.81664 −0.136833
\(779\) 7.91934 0.283740
\(780\) 1.55602 0.0557143
\(781\) 0 0
\(782\) −2.44398 −0.0873967
\(783\) −10.0386 −0.358751
\(784\) −2.41468 −0.0862386
\(785\) 5.74276 0.204968
\(786\) 0.965235 0.0344288
\(787\) −22.8794 −0.815562 −0.407781 0.913080i \(-0.633697\pi\)
−0.407781 + 0.913080i \(0.633697\pi\)
\(788\) −14.3306 −0.510508
\(789\) −0.525393 −0.0187045
\(790\) 0.282672 0.0100570
\(791\) −30.7567 −1.09358
\(792\) 0 0
\(793\) 26.7453 0.949754
\(794\) −25.0573 −0.889250
\(795\) −5.34335 −0.189509
\(796\) 5.83869 0.206947
\(797\) 41.6774 1.47629 0.738144 0.674643i \(-0.235702\pi\)
0.738144 + 0.674643i \(0.235702\pi\)
\(798\) 2.91934 0.103344
\(799\) −8.66805 −0.306653
\(800\) −4.86799 −0.172110
\(801\) 9.36126 0.330764
\(802\) −31.9567 −1.12843
\(803\) 0 0
\(804\) −11.6774 −0.411829
\(805\) −1.66598 −0.0587180
\(806\) −22.0187 −0.775574
\(807\) −18.4240 −0.648556
\(808\) −10.0700 −0.354262
\(809\) 29.7347 1.04542 0.522708 0.852512i \(-0.324922\pi\)
0.522708 + 0.852512i \(0.324922\pi\)
\(810\) −1.55263 −0.0545537
\(811\) 17.6460 0.619635 0.309817 0.950796i \(-0.399732\pi\)
0.309817 + 0.950796i \(0.399732\pi\)
\(812\) −3.80731 −0.133610
\(813\) 13.2733 0.465516
\(814\) 0 0
\(815\) −1.35061 −0.0473098
\(816\) −1.55602 −0.0544714
\(817\) 4.28267 0.149832
\(818\) 27.8280 0.972985
\(819\) 7.67738 0.268269
\(820\) −2.87732 −0.100480
\(821\) −36.9766 −1.29049 −0.645247 0.763974i \(-0.723245\pi\)
−0.645247 + 0.763974i \(0.723245\pi\)
\(822\) −8.56534 −0.298751
\(823\) −38.8094 −1.35281 −0.676405 0.736530i \(-0.736463\pi\)
−0.676405 + 0.736530i \(0.736463\pi\)
\(824\) −17.3434 −0.604184
\(825\) 0 0
\(826\) −2.31405 −0.0805160
\(827\) −29.0534 −1.01029 −0.505143 0.863036i \(-0.668560\pi\)
−0.505143 + 0.863036i \(0.668560\pi\)
\(828\) 2.44398 0.0849343
\(829\) 44.9333 1.56060 0.780299 0.625407i \(-0.215067\pi\)
0.780299 + 0.625407i \(0.215067\pi\)
\(830\) −0.282672 −0.00981170
\(831\) 9.20070 0.319169
\(832\) −3.14134 −0.108906
\(833\) −2.75596 −0.0954884
\(834\) −5.45331 −0.188833
\(835\) 1.91595 0.0663043
\(836\) 0 0
\(837\) 39.5747 1.36790
\(838\) −5.24065 −0.181035
\(839\) 10.5140 0.362983 0.181492 0.983392i \(-0.441907\pi\)
0.181492 + 0.983392i \(0.441907\pi\)
\(840\) −1.06068 −0.0365969
\(841\) −25.8387 −0.890989
\(842\) −15.3340 −0.528445
\(843\) 9.62602 0.331538
\(844\) 9.74870 0.335564
\(845\) −1.13795 −0.0391466
\(846\) 8.66805 0.298014
\(847\) 0 0
\(848\) 10.7873 0.370439
\(849\) 11.5374 0.395961
\(850\) −5.55602 −0.190570
\(851\) 20.9380 0.717745
\(852\) −4.77801 −0.163692
\(853\) −8.55733 −0.292998 −0.146499 0.989211i \(-0.546800\pi\)
−0.146499 + 0.989211i \(0.546800\pi\)
\(854\) −18.2313 −0.623863
\(855\) 0.414680 0.0141817
\(856\) −13.6460 −0.466411
\(857\) 19.5560 0.668021 0.334010 0.942569i \(-0.391598\pi\)
0.334010 + 0.942569i \(0.391598\pi\)
\(858\) 0 0
\(859\) 31.7873 1.08457 0.542285 0.840195i \(-0.317559\pi\)
0.542285 + 0.840195i \(0.317559\pi\)
\(860\) −1.55602 −0.0530597
\(861\) 23.1193 0.787903
\(862\) 18.8994 0.643715
\(863\) 28.8226 0.981132 0.490566 0.871404i \(-0.336790\pi\)
0.490566 + 0.871404i \(0.336790\pi\)
\(864\) 5.64600 0.192081
\(865\) 4.16593 0.141646
\(866\) −11.1787 −0.379866
\(867\) 21.4006 0.726804
\(868\) 15.0093 0.509450
\(869\) 0 0
\(870\) 0.880711 0.0298589
\(871\) −26.9066 −0.911696
\(872\) 5.33402 0.180633
\(873\) 2.13201 0.0721575
\(874\) 2.14134 0.0724318
\(875\) −7.67738 −0.259543
\(876\) −16.0000 −0.540590
\(877\) −11.4613 −0.387021 −0.193511 0.981098i \(-0.561987\pi\)
−0.193511 + 0.981098i \(0.561987\pi\)
\(878\) 23.4720 0.792141
\(879\) −29.7160 −1.00230
\(880\) 0 0
\(881\) −45.7826 −1.54246 −0.771228 0.636559i \(-0.780357\pi\)
−0.771228 + 0.636559i \(0.780357\pi\)
\(882\) 2.75596 0.0927980
\(883\) −39.9673 −1.34501 −0.672503 0.740094i \(-0.734781\pi\)
−0.672503 + 0.740094i \(0.734781\pi\)
\(884\) −3.58532 −0.120587
\(885\) 0.535287 0.0179935
\(886\) −29.8387 −1.00245
\(887\) 37.8833 1.27200 0.635998 0.771691i \(-0.280589\pi\)
0.635998 + 0.771691i \(0.280589\pi\)
\(888\) 13.3306 0.447347
\(889\) −5.23339 −0.175522
\(890\) −2.98002 −0.0998906
\(891\) 0 0
\(892\) −18.6167 −0.623333
\(893\) 7.59465 0.254145
\(894\) −15.2147 −0.508857
\(895\) −0.327245 −0.0109386
\(896\) 2.14134 0.0715370
\(897\) −9.17064 −0.306199
\(898\) −10.6133 −0.354171
\(899\) −12.4626 −0.415652
\(900\) 5.55602 0.185201
\(901\) 12.3120 0.410171
\(902\) 0 0
\(903\) 12.5026 0.416060
\(904\) −14.3633 −0.477717
\(905\) −6.06662 −0.201661
\(906\) 18.8221 0.625322
\(907\) 9.11797 0.302757 0.151379 0.988476i \(-0.451629\pi\)
0.151379 + 0.988476i \(0.451629\pi\)
\(908\) −17.9160 −0.594562
\(909\) 11.4933 0.381208
\(910\) −2.44398 −0.0810173
\(911\) −13.9087 −0.460816 −0.230408 0.973094i \(-0.574006\pi\)
−0.230408 + 0.973094i \(0.574006\pi\)
\(912\) 1.36333 0.0451443
\(913\) 0 0
\(914\) −7.82936 −0.258972
\(915\) 4.21728 0.139419
\(916\) −8.31198 −0.274635
\(917\) −1.51606 −0.0500648
\(918\) 6.44398 0.212683
\(919\) −35.1120 −1.15824 −0.579120 0.815243i \(-0.696604\pi\)
−0.579120 + 0.815243i \(0.696604\pi\)
\(920\) −0.778008 −0.0256502
\(921\) 22.5667 0.743597
\(922\) −2.54330 −0.0837590
\(923\) −11.0093 −0.362376
\(924\) 0 0
\(925\) 47.5993 1.56505
\(926\) −31.6519 −1.04015
\(927\) 19.7946 0.650140
\(928\) −1.77801 −0.0583660
\(929\) −2.47875 −0.0813251 −0.0406626 0.999173i \(-0.512947\pi\)
−0.0406626 + 0.999173i \(0.512947\pi\)
\(930\) −3.47197 −0.113850
\(931\) 2.41468 0.0791379
\(932\) 7.28267 0.238552
\(933\) 28.4227 0.930517
\(934\) −7.85735 −0.257100
\(935\) 0 0
\(936\) 3.58532 0.117190
\(937\) −6.41600 −0.209602 −0.104801 0.994493i \(-0.533420\pi\)
−0.104801 + 0.994493i \(0.533420\pi\)
\(938\) 18.3413 0.598864
\(939\) 4.06455 0.132642
\(940\) −2.75935 −0.0900001
\(941\) 19.2373 0.627117 0.313558 0.949569i \(-0.398479\pi\)
0.313558 + 0.949569i \(0.398479\pi\)
\(942\) −21.5488 −0.702096
\(943\) 16.9580 0.552228
\(944\) −1.08066 −0.0351724
\(945\) 4.39263 0.142892
\(946\) 0 0
\(947\) 46.2614 1.50329 0.751646 0.659566i \(-0.229260\pi\)
0.751646 + 0.659566i \(0.229260\pi\)
\(948\) −1.06068 −0.0344493
\(949\) −36.8667 −1.19674
\(950\) 4.86799 0.157939
\(951\) 16.2454 0.526792
\(952\) 2.44398 0.0792100
\(953\) −55.4541 −1.79633 −0.898167 0.439655i \(-0.855101\pi\)
−0.898167 + 0.439655i \(0.855101\pi\)
\(954\) −12.3120 −0.398615
\(955\) −1.40874 −0.0455858
\(956\) 11.1693 0.361242
\(957\) 0 0
\(958\) 13.9614 0.451071
\(959\) 13.4533 0.434430
\(960\) −0.495336 −0.0159869
\(961\) 18.1307 0.584861
\(962\) 30.7160 0.990324
\(963\) 15.5747 0.501887
\(964\) 6.39263 0.205893
\(965\) 1.93338 0.0622377
\(966\) 6.25130 0.201132
\(967\) −14.4240 −0.463845 −0.231922 0.972734i \(-0.574502\pi\)
−0.231922 + 0.972734i \(0.574502\pi\)
\(968\) 0 0
\(969\) 1.55602 0.0499864
\(970\) −0.678694 −0.0217916
\(971\) 46.3140 1.48629 0.743144 0.669131i \(-0.233334\pi\)
0.743144 + 0.669131i \(0.233334\pi\)
\(972\) −11.1120 −0.356419
\(973\) 8.56534 0.274592
\(974\) 1.83869 0.0589154
\(975\) −20.8480 −0.667671
\(976\) −8.51399 −0.272526
\(977\) 47.8680 1.53143 0.765716 0.643178i \(-0.222385\pi\)
0.765716 + 0.643178i \(0.222385\pi\)
\(978\) 5.06794 0.162055
\(979\) 0 0
\(980\) −0.877321 −0.0280250
\(981\) −6.08791 −0.194372
\(982\) 27.5747 0.879943
\(983\) −3.54198 −0.112972 −0.0564858 0.998403i \(-0.517990\pi\)
−0.0564858 + 0.998403i \(0.517990\pi\)
\(984\) 10.7967 0.344185
\(985\) −5.20672 −0.165900
\(986\) −2.02930 −0.0646262
\(987\) 22.1714 0.705723
\(988\) 3.14134 0.0999392
\(989\) 9.17064 0.291609
\(990\) 0 0
\(991\) −10.4113 −0.330726 −0.165363 0.986233i \(-0.552879\pi\)
−0.165363 + 0.986233i \(0.552879\pi\)
\(992\) 7.00933 0.222546
\(993\) −0.0173389 −0.000550234 0
\(994\) 7.50466 0.238033
\(995\) 2.12136 0.0672516
\(996\) 1.06068 0.0336089
\(997\) −10.1834 −0.322510 −0.161255 0.986913i \(-0.551554\pi\)
−0.161255 + 0.986913i \(0.551554\pi\)
\(998\) 26.4113 0.836035
\(999\) −55.2066 −1.74666
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.bn.1.2 yes 3
11.10 odd 2 4598.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bk.1.2 3 11.10 odd 2
4598.2.a.bn.1.2 yes 3 1.1 even 1 trivial