Properties

Label 4006.2.a.g.1.13
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.01040 q^{3} +1.00000 q^{4} -1.91784 q^{5} +1.01040 q^{6} +4.92355 q^{7} -1.00000 q^{8} -1.97910 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.01040 q^{3} +1.00000 q^{4} -1.91784 q^{5} +1.01040 q^{6} +4.92355 q^{7} -1.00000 q^{8} -1.97910 q^{9} +1.91784 q^{10} -0.589054 q^{11} -1.01040 q^{12} +2.74206 q^{13} -4.92355 q^{14} +1.93778 q^{15} +1.00000 q^{16} -1.63182 q^{17} +1.97910 q^{18} -1.23798 q^{19} -1.91784 q^{20} -4.97474 q^{21} +0.589054 q^{22} +1.68163 q^{23} +1.01040 q^{24} -1.32190 q^{25} -2.74206 q^{26} +5.03087 q^{27} +4.92355 q^{28} -7.46754 q^{29} -1.93778 q^{30} +1.54014 q^{31} -1.00000 q^{32} +0.595179 q^{33} +1.63182 q^{34} -9.44257 q^{35} -1.97910 q^{36} +3.02720 q^{37} +1.23798 q^{38} -2.77057 q^{39} +1.91784 q^{40} +5.29308 q^{41} +4.97474 q^{42} -9.29844 q^{43} -0.589054 q^{44} +3.79559 q^{45} -1.68163 q^{46} -3.13361 q^{47} -1.01040 q^{48} +17.2414 q^{49} +1.32190 q^{50} +1.64878 q^{51} +2.74206 q^{52} -13.2036 q^{53} -5.03087 q^{54} +1.12971 q^{55} -4.92355 q^{56} +1.25085 q^{57} +7.46754 q^{58} -10.9069 q^{59} +1.93778 q^{60} +7.96946 q^{61} -1.54014 q^{62} -9.74420 q^{63} +1.00000 q^{64} -5.25882 q^{65} -0.595179 q^{66} +2.77260 q^{67} -1.63182 q^{68} -1.69912 q^{69} +9.44257 q^{70} +2.80193 q^{71} +1.97910 q^{72} +0.952283 q^{73} -3.02720 q^{74} +1.33565 q^{75} -1.23798 q^{76} -2.90024 q^{77} +2.77057 q^{78} -9.00919 q^{79} -1.91784 q^{80} +0.854123 q^{81} -5.29308 q^{82} +3.06925 q^{83} -4.97474 q^{84} +3.12956 q^{85} +9.29844 q^{86} +7.54518 q^{87} +0.589054 q^{88} +13.9420 q^{89} -3.79559 q^{90} +13.5007 q^{91} +1.68163 q^{92} -1.55615 q^{93} +3.13361 q^{94} +2.37425 q^{95} +1.01040 q^{96} -8.87552 q^{97} -17.2414 q^{98} +1.16580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.01040 −0.583353 −0.291676 0.956517i \(-0.594213\pi\)
−0.291676 + 0.956517i \(0.594213\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.91784 −0.857682 −0.428841 0.903380i \(-0.641078\pi\)
−0.428841 + 0.903380i \(0.641078\pi\)
\(6\) 1.01040 0.412493
\(7\) 4.92355 1.86093 0.930464 0.366383i \(-0.119404\pi\)
0.930464 + 0.366383i \(0.119404\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.97910 −0.659699
\(10\) 1.91784 0.606473
\(11\) −0.589054 −0.177607 −0.0888033 0.996049i \(-0.528304\pi\)
−0.0888033 + 0.996049i \(0.528304\pi\)
\(12\) −1.01040 −0.291676
\(13\) 2.74206 0.760511 0.380255 0.924882i \(-0.375836\pi\)
0.380255 + 0.924882i \(0.375836\pi\)
\(14\) −4.92355 −1.31588
\(15\) 1.93778 0.500332
\(16\) 1.00000 0.250000
\(17\) −1.63182 −0.395774 −0.197887 0.980225i \(-0.563408\pi\)
−0.197887 + 0.980225i \(0.563408\pi\)
\(18\) 1.97910 0.466478
\(19\) −1.23798 −0.284013 −0.142006 0.989866i \(-0.545355\pi\)
−0.142006 + 0.989866i \(0.545355\pi\)
\(20\) −1.91784 −0.428841
\(21\) −4.97474 −1.08558
\(22\) 0.589054 0.125587
\(23\) 1.68163 0.350645 0.175322 0.984511i \(-0.443903\pi\)
0.175322 + 0.984511i \(0.443903\pi\)
\(24\) 1.01040 0.206246
\(25\) −1.32190 −0.264381
\(26\) −2.74206 −0.537762
\(27\) 5.03087 0.968190
\(28\) 4.92355 0.930464
\(29\) −7.46754 −1.38669 −0.693343 0.720607i \(-0.743863\pi\)
−0.693343 + 0.720607i \(0.743863\pi\)
\(30\) −1.93778 −0.353788
\(31\) 1.54014 0.276618 0.138309 0.990389i \(-0.455833\pi\)
0.138309 + 0.990389i \(0.455833\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.595179 0.103607
\(34\) 1.63182 0.279854
\(35\) −9.44257 −1.59609
\(36\) −1.97910 −0.329850
\(37\) 3.02720 0.497668 0.248834 0.968546i \(-0.419953\pi\)
0.248834 + 0.968546i \(0.419953\pi\)
\(38\) 1.23798 0.200827
\(39\) −2.77057 −0.443646
\(40\) 1.91784 0.303237
\(41\) 5.29308 0.826639 0.413320 0.910586i \(-0.364369\pi\)
0.413320 + 0.910586i \(0.364369\pi\)
\(42\) 4.97474 0.767620
\(43\) −9.29844 −1.41800 −0.708999 0.705209i \(-0.750853\pi\)
−0.708999 + 0.705209i \(0.750853\pi\)
\(44\) −0.589054 −0.0888033
\(45\) 3.79559 0.565813
\(46\) −1.68163 −0.247943
\(47\) −3.13361 −0.457083 −0.228542 0.973534i \(-0.573396\pi\)
−0.228542 + 0.973534i \(0.573396\pi\)
\(48\) −1.01040 −0.145838
\(49\) 17.2414 2.46305
\(50\) 1.32190 0.186946
\(51\) 1.64878 0.230876
\(52\) 2.74206 0.380255
\(53\) −13.2036 −1.81365 −0.906826 0.421504i \(-0.861502\pi\)
−0.906826 + 0.421504i \(0.861502\pi\)
\(54\) −5.03087 −0.684614
\(55\) 1.12971 0.152330
\(56\) −4.92355 −0.657938
\(57\) 1.25085 0.165680
\(58\) 7.46754 0.980536
\(59\) −10.9069 −1.41996 −0.709980 0.704222i \(-0.751296\pi\)
−0.709980 + 0.704222i \(0.751296\pi\)
\(60\) 1.93778 0.250166
\(61\) 7.96946 1.02038 0.510192 0.860060i \(-0.329574\pi\)
0.510192 + 0.860060i \(0.329574\pi\)
\(62\) −1.54014 −0.195598
\(63\) −9.74420 −1.22765
\(64\) 1.00000 0.125000
\(65\) −5.25882 −0.652277
\(66\) −0.595179 −0.0732614
\(67\) 2.77260 0.338727 0.169363 0.985554i \(-0.445829\pi\)
0.169363 + 0.985554i \(0.445829\pi\)
\(68\) −1.63182 −0.197887
\(69\) −1.69912 −0.204550
\(70\) 9.44257 1.12860
\(71\) 2.80193 0.332528 0.166264 0.986081i \(-0.446830\pi\)
0.166264 + 0.986081i \(0.446830\pi\)
\(72\) 1.97910 0.233239
\(73\) 0.952283 0.111456 0.0557282 0.998446i \(-0.482252\pi\)
0.0557282 + 0.998446i \(0.482252\pi\)
\(74\) −3.02720 −0.351905
\(75\) 1.33565 0.154227
\(76\) −1.23798 −0.142006
\(77\) −2.90024 −0.330513
\(78\) 2.77057 0.313705
\(79\) −9.00919 −1.01361 −0.506807 0.862060i \(-0.669174\pi\)
−0.506807 + 0.862060i \(0.669174\pi\)
\(80\) −1.91784 −0.214421
\(81\) 0.854123 0.0949026
\(82\) −5.29308 −0.584522
\(83\) 3.06925 0.336894 0.168447 0.985711i \(-0.446125\pi\)
0.168447 + 0.985711i \(0.446125\pi\)
\(84\) −4.97474 −0.542789
\(85\) 3.12956 0.339448
\(86\) 9.29844 1.00268
\(87\) 7.54518 0.808928
\(88\) 0.589054 0.0627934
\(89\) 13.9420 1.47784 0.738922 0.673791i \(-0.235335\pi\)
0.738922 + 0.673791i \(0.235335\pi\)
\(90\) −3.79559 −0.400090
\(91\) 13.5007 1.41526
\(92\) 1.68163 0.175322
\(93\) −1.55615 −0.161366
\(94\) 3.13361 0.323207
\(95\) 2.37425 0.243593
\(96\) 1.01040 0.103123
\(97\) −8.87552 −0.901173 −0.450586 0.892733i \(-0.648785\pi\)
−0.450586 + 0.892733i \(0.648785\pi\)
\(98\) −17.2414 −1.74164
\(99\) 1.16580 0.117167
\(100\) −1.32190 −0.132190
\(101\) 19.4019 1.93056 0.965282 0.261211i \(-0.0841219\pi\)
0.965282 + 0.261211i \(0.0841219\pi\)
\(102\) −1.64878 −0.163254
\(103\) 1.25490 0.123649 0.0618245 0.998087i \(-0.480308\pi\)
0.0618245 + 0.998087i \(0.480308\pi\)
\(104\) −2.74206 −0.268881
\(105\) 9.54074 0.931081
\(106\) 13.2036 1.28245
\(107\) −2.53644 −0.245207 −0.122603 0.992456i \(-0.539124\pi\)
−0.122603 + 0.992456i \(0.539124\pi\)
\(108\) 5.03087 0.484095
\(109\) 0.224723 0.0215246 0.0107623 0.999942i \(-0.496574\pi\)
0.0107623 + 0.999942i \(0.496574\pi\)
\(110\) −1.12971 −0.107714
\(111\) −3.05867 −0.290316
\(112\) 4.92355 0.465232
\(113\) −16.0607 −1.51087 −0.755434 0.655225i \(-0.772574\pi\)
−0.755434 + 0.655225i \(0.772574\pi\)
\(114\) −1.25085 −0.117153
\(115\) −3.22510 −0.300742
\(116\) −7.46754 −0.693343
\(117\) −5.42681 −0.501708
\(118\) 10.9069 1.00406
\(119\) −8.03434 −0.736506
\(120\) −1.93778 −0.176894
\(121\) −10.6530 −0.968456
\(122\) −7.96946 −0.721521
\(123\) −5.34811 −0.482223
\(124\) 1.54014 0.138309
\(125\) 12.1244 1.08444
\(126\) 9.74420 0.868082
\(127\) −9.84140 −0.873283 −0.436641 0.899636i \(-0.643832\pi\)
−0.436641 + 0.899636i \(0.643832\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.39512 0.827194
\(130\) 5.25882 0.461229
\(131\) −14.5707 −1.27305 −0.636523 0.771258i \(-0.719628\pi\)
−0.636523 + 0.771258i \(0.719628\pi\)
\(132\) 0.595179 0.0518037
\(133\) −6.09527 −0.528527
\(134\) −2.77260 −0.239516
\(135\) −9.64838 −0.830400
\(136\) 1.63182 0.139927
\(137\) 12.5220 1.06982 0.534912 0.844908i \(-0.320345\pi\)
0.534912 + 0.844908i \(0.320345\pi\)
\(138\) 1.69912 0.144639
\(139\) 11.1585 0.946455 0.473228 0.880940i \(-0.343089\pi\)
0.473228 + 0.880940i \(0.343089\pi\)
\(140\) −9.44257 −0.798043
\(141\) 3.16619 0.266641
\(142\) −2.80193 −0.235133
\(143\) −1.61522 −0.135072
\(144\) −1.97910 −0.164925
\(145\) 14.3215 1.18934
\(146\) −0.952283 −0.0788115
\(147\) −17.4206 −1.43683
\(148\) 3.02720 0.248834
\(149\) −6.36321 −0.521294 −0.260647 0.965434i \(-0.583936\pi\)
−0.260647 + 0.965434i \(0.583936\pi\)
\(150\) −1.33565 −0.109055
\(151\) −12.0980 −0.984522 −0.492261 0.870448i \(-0.663829\pi\)
−0.492261 + 0.870448i \(0.663829\pi\)
\(152\) 1.23798 0.100414
\(153\) 3.22952 0.261092
\(154\) 2.90024 0.233708
\(155\) −2.95374 −0.237250
\(156\) −2.77057 −0.221823
\(157\) −6.06828 −0.484302 −0.242151 0.970239i \(-0.577853\pi\)
−0.242151 + 0.970239i \(0.577853\pi\)
\(158\) 9.00919 0.716733
\(159\) 13.3409 1.05800
\(160\) 1.91784 0.151618
\(161\) 8.27962 0.652525
\(162\) −0.854123 −0.0671063
\(163\) 10.4152 0.815782 0.407891 0.913031i \(-0.366264\pi\)
0.407891 + 0.913031i \(0.366264\pi\)
\(164\) 5.29308 0.413320
\(165\) −1.14146 −0.0888622
\(166\) −3.06925 −0.238220
\(167\) 14.3386 1.10955 0.554776 0.832000i \(-0.312804\pi\)
0.554776 + 0.832000i \(0.312804\pi\)
\(168\) 4.97474 0.383810
\(169\) −5.48111 −0.421624
\(170\) −3.12956 −0.240026
\(171\) 2.45009 0.187363
\(172\) −9.29844 −0.708999
\(173\) 7.72458 0.587289 0.293645 0.955915i \(-0.405132\pi\)
0.293645 + 0.955915i \(0.405132\pi\)
\(174\) −7.54518 −0.571998
\(175\) −6.50847 −0.491994
\(176\) −0.589054 −0.0444016
\(177\) 11.0203 0.828338
\(178\) −13.9420 −1.04499
\(179\) −26.4956 −1.98038 −0.990188 0.139739i \(-0.955374\pi\)
−0.990188 + 0.139739i \(0.955374\pi\)
\(180\) 3.79559 0.282906
\(181\) 11.5693 0.859943 0.429971 0.902843i \(-0.358524\pi\)
0.429971 + 0.902843i \(0.358524\pi\)
\(182\) −13.5007 −1.00074
\(183\) −8.05232 −0.595245
\(184\) −1.68163 −0.123972
\(185\) −5.80567 −0.426841
\(186\) 1.55615 0.114103
\(187\) 0.961228 0.0702920
\(188\) −3.13361 −0.228542
\(189\) 24.7697 1.80173
\(190\) −2.37425 −0.172246
\(191\) 21.4697 1.55349 0.776747 0.629813i \(-0.216868\pi\)
0.776747 + 0.629813i \(0.216868\pi\)
\(192\) −1.01040 −0.0729191
\(193\) −4.65467 −0.335050 −0.167525 0.985868i \(-0.553578\pi\)
−0.167525 + 0.985868i \(0.553578\pi\)
\(194\) 8.87552 0.637225
\(195\) 5.31350 0.380507
\(196\) 17.2414 1.23153
\(197\) −19.6822 −1.40230 −0.701148 0.713016i \(-0.747329\pi\)
−0.701148 + 0.713016i \(0.747329\pi\)
\(198\) −1.16580 −0.0828495
\(199\) 12.9398 0.917280 0.458640 0.888622i \(-0.348337\pi\)
0.458640 + 0.888622i \(0.348337\pi\)
\(200\) 1.32190 0.0934728
\(201\) −2.80143 −0.197597
\(202\) −19.4019 −1.36511
\(203\) −36.7668 −2.58052
\(204\) 1.64878 0.115438
\(205\) −10.1513 −0.708994
\(206\) −1.25490 −0.0874330
\(207\) −3.32812 −0.231320
\(208\) 2.74206 0.190128
\(209\) 0.729239 0.0504425
\(210\) −9.54074 −0.658374
\(211\) −8.18019 −0.563147 −0.281574 0.959540i \(-0.590856\pi\)
−0.281574 + 0.959540i \(0.590856\pi\)
\(212\) −13.2036 −0.906826
\(213\) −2.83106 −0.193981
\(214\) 2.53644 0.173387
\(215\) 17.8329 1.21619
\(216\) −5.03087 −0.342307
\(217\) 7.58297 0.514766
\(218\) −0.224723 −0.0152202
\(219\) −0.962184 −0.0650184
\(220\) 1.12971 0.0761650
\(221\) −4.47454 −0.300990
\(222\) 3.05867 0.205285
\(223\) −2.90656 −0.194638 −0.0973190 0.995253i \(-0.531027\pi\)
−0.0973190 + 0.995253i \(0.531027\pi\)
\(224\) −4.92355 −0.328969
\(225\) 2.61618 0.174412
\(226\) 16.0607 1.06834
\(227\) −15.2841 −1.01444 −0.507220 0.861817i \(-0.669327\pi\)
−0.507220 + 0.861817i \(0.669327\pi\)
\(228\) 1.25085 0.0828398
\(229\) −27.4284 −1.81252 −0.906259 0.422724i \(-0.861074\pi\)
−0.906259 + 0.422724i \(0.861074\pi\)
\(230\) 3.22510 0.212657
\(231\) 2.93039 0.192806
\(232\) 7.46754 0.490268
\(233\) 4.80887 0.315039 0.157520 0.987516i \(-0.449650\pi\)
0.157520 + 0.987516i \(0.449650\pi\)
\(234\) 5.42681 0.354761
\(235\) 6.00974 0.392032
\(236\) −10.9069 −0.709980
\(237\) 9.10286 0.591294
\(238\) 8.03434 0.520789
\(239\) −13.9477 −0.902200 −0.451100 0.892473i \(-0.648968\pi\)
−0.451100 + 0.892473i \(0.648968\pi\)
\(240\) 1.93778 0.125083
\(241\) 2.26986 0.146214 0.0731072 0.997324i \(-0.476708\pi\)
0.0731072 + 0.997324i \(0.476708\pi\)
\(242\) 10.6530 0.684802
\(243\) −15.9556 −1.02355
\(244\) 7.96946 0.510192
\(245\) −33.0661 −2.11252
\(246\) 5.34811 0.340983
\(247\) −3.39462 −0.215995
\(248\) −1.54014 −0.0977991
\(249\) −3.10117 −0.196528
\(250\) −12.1244 −0.766813
\(251\) −23.3456 −1.47356 −0.736782 0.676130i \(-0.763656\pi\)
−0.736782 + 0.676130i \(0.763656\pi\)
\(252\) −9.74420 −0.613827
\(253\) −0.990574 −0.0622768
\(254\) 9.84140 0.617504
\(255\) −3.16209 −0.198018
\(256\) 1.00000 0.0625000
\(257\) −22.6872 −1.41519 −0.707594 0.706619i \(-0.750219\pi\)
−0.707594 + 0.706619i \(0.750219\pi\)
\(258\) −9.39512 −0.584914
\(259\) 14.9046 0.926125
\(260\) −5.25882 −0.326138
\(261\) 14.7790 0.914796
\(262\) 14.5707 0.900179
\(263\) −2.12047 −0.130754 −0.0653769 0.997861i \(-0.520825\pi\)
−0.0653769 + 0.997861i \(0.520825\pi\)
\(264\) −0.595179 −0.0366307
\(265\) 25.3223 1.55554
\(266\) 6.09527 0.373725
\(267\) −14.0869 −0.862105
\(268\) 2.77260 0.169363
\(269\) −28.4298 −1.73339 −0.866697 0.498835i \(-0.833761\pi\)
−0.866697 + 0.498835i \(0.833761\pi\)
\(270\) 9.64838 0.587181
\(271\) −16.4021 −0.996359 −0.498180 0.867074i \(-0.665998\pi\)
−0.498180 + 0.867074i \(0.665998\pi\)
\(272\) −1.63182 −0.0989434
\(273\) −13.6410 −0.825594
\(274\) −12.5220 −0.756480
\(275\) 0.778673 0.0469558
\(276\) −1.69912 −0.102275
\(277\) 3.09097 0.185719 0.0928593 0.995679i \(-0.470399\pi\)
0.0928593 + 0.995679i \(0.470399\pi\)
\(278\) −11.1585 −0.669245
\(279\) −3.04809 −0.182484
\(280\) 9.44257 0.564301
\(281\) 9.46291 0.564510 0.282255 0.959339i \(-0.408918\pi\)
0.282255 + 0.959339i \(0.408918\pi\)
\(282\) −3.16619 −0.188544
\(283\) −7.00252 −0.416256 −0.208128 0.978102i \(-0.566737\pi\)
−0.208128 + 0.978102i \(0.566737\pi\)
\(284\) 2.80193 0.166264
\(285\) −2.39893 −0.142100
\(286\) 1.61522 0.0955101
\(287\) 26.0607 1.53832
\(288\) 1.97910 0.116619
\(289\) −14.3372 −0.843363
\(290\) −14.3215 −0.840988
\(291\) 8.96780 0.525702
\(292\) 0.952283 0.0557282
\(293\) −11.8399 −0.691696 −0.345848 0.938291i \(-0.612409\pi\)
−0.345848 + 0.938291i \(0.612409\pi\)
\(294\) 17.4206 1.01599
\(295\) 20.9177 1.21787
\(296\) −3.02720 −0.175952
\(297\) −2.96345 −0.171957
\(298\) 6.36321 0.368611
\(299\) 4.61114 0.266669
\(300\) 1.33565 0.0771137
\(301\) −45.7814 −2.63879
\(302\) 12.0980 0.696162
\(303\) −19.6036 −1.12620
\(304\) −1.23798 −0.0710032
\(305\) −15.2841 −0.875166
\(306\) −3.22952 −0.184620
\(307\) −5.64301 −0.322063 −0.161032 0.986949i \(-0.551482\pi\)
−0.161032 + 0.986949i \(0.551482\pi\)
\(308\) −2.90024 −0.165257
\(309\) −1.26795 −0.0721310
\(310\) 2.95374 0.167761
\(311\) 9.93607 0.563423 0.281711 0.959499i \(-0.409098\pi\)
0.281711 + 0.959499i \(0.409098\pi\)
\(312\) 2.77057 0.156853
\(313\) −25.7823 −1.45730 −0.728651 0.684885i \(-0.759852\pi\)
−0.728651 + 0.684885i \(0.759852\pi\)
\(314\) 6.06828 0.342453
\(315\) 18.6878 1.05294
\(316\) −9.00919 −0.506807
\(317\) 5.29714 0.297517 0.148758 0.988874i \(-0.452472\pi\)
0.148758 + 0.988874i \(0.452472\pi\)
\(318\) −13.3409 −0.748119
\(319\) 4.39879 0.246285
\(320\) −1.91784 −0.107210
\(321\) 2.56281 0.143042
\(322\) −8.27962 −0.461405
\(323\) 2.02016 0.112405
\(324\) 0.854123 0.0474513
\(325\) −3.62474 −0.201064
\(326\) −10.4152 −0.576845
\(327\) −0.227060 −0.0125564
\(328\) −5.29308 −0.292261
\(329\) −15.4285 −0.850599
\(330\) 1.14146 0.0628350
\(331\) −12.5579 −0.690246 −0.345123 0.938557i \(-0.612163\pi\)
−0.345123 + 0.938557i \(0.612163\pi\)
\(332\) 3.06925 0.168447
\(333\) −5.99112 −0.328311
\(334\) −14.3386 −0.784571
\(335\) −5.31739 −0.290520
\(336\) −4.97474 −0.271395
\(337\) 24.9458 1.35888 0.679441 0.733730i \(-0.262222\pi\)
0.679441 + 0.733730i \(0.262222\pi\)
\(338\) 5.48111 0.298133
\(339\) 16.2277 0.881369
\(340\) 3.12956 0.169724
\(341\) −0.907227 −0.0491291
\(342\) −2.45009 −0.132486
\(343\) 50.4240 2.72264
\(344\) 9.29844 0.501338
\(345\) 3.25863 0.175439
\(346\) −7.72458 −0.415276
\(347\) −28.8371 −1.54806 −0.774028 0.633151i \(-0.781761\pi\)
−0.774028 + 0.633151i \(0.781761\pi\)
\(348\) 7.54518 0.404464
\(349\) 32.0778 1.71709 0.858543 0.512741i \(-0.171370\pi\)
0.858543 + 0.512741i \(0.171370\pi\)
\(350\) 6.50847 0.347892
\(351\) 13.7949 0.736319
\(352\) 0.589054 0.0313967
\(353\) −21.1127 −1.12372 −0.561859 0.827233i \(-0.689914\pi\)
−0.561859 + 0.827233i \(0.689914\pi\)
\(354\) −11.0203 −0.585723
\(355\) −5.37365 −0.285204
\(356\) 13.9420 0.738922
\(357\) 8.11787 0.429643
\(358\) 26.4956 1.40034
\(359\) 12.9014 0.680910 0.340455 0.940261i \(-0.389419\pi\)
0.340455 + 0.940261i \(0.389419\pi\)
\(360\) −3.79559 −0.200045
\(361\) −17.4674 −0.919337
\(362\) −11.5693 −0.608071
\(363\) 10.7638 0.564952
\(364\) 13.5007 0.707628
\(365\) −1.82632 −0.0955941
\(366\) 8.05232 0.420901
\(367\) −6.91139 −0.360772 −0.180386 0.983596i \(-0.557735\pi\)
−0.180386 + 0.983596i \(0.557735\pi\)
\(368\) 1.68163 0.0876612
\(369\) −10.4755 −0.545334
\(370\) 5.80567 0.301822
\(371\) −65.0086 −3.37508
\(372\) −1.55615 −0.0806828
\(373\) −13.5218 −0.700132 −0.350066 0.936725i \(-0.613841\pi\)
−0.350066 + 0.936725i \(0.613841\pi\)
\(374\) −0.961228 −0.0497039
\(375\) −12.2504 −0.632610
\(376\) 3.13361 0.161603
\(377\) −20.4764 −1.05459
\(378\) −24.7697 −1.27402
\(379\) 16.9666 0.871517 0.435759 0.900064i \(-0.356480\pi\)
0.435759 + 0.900064i \(0.356480\pi\)
\(380\) 2.37425 0.121796
\(381\) 9.94372 0.509432
\(382\) −21.4697 −1.09849
\(383\) 20.5382 1.04945 0.524727 0.851271i \(-0.324168\pi\)
0.524727 + 0.851271i \(0.324168\pi\)
\(384\) 1.01040 0.0515616
\(385\) 5.56219 0.283475
\(386\) 4.65467 0.236916
\(387\) 18.4025 0.935453
\(388\) −8.87552 −0.450586
\(389\) −10.0617 −0.510146 −0.255073 0.966922i \(-0.582100\pi\)
−0.255073 + 0.966922i \(0.582100\pi\)
\(390\) −5.31350 −0.269059
\(391\) −2.74412 −0.138776
\(392\) −17.2414 −0.870821
\(393\) 14.7222 0.742635
\(394\) 19.6822 0.991573
\(395\) 17.2782 0.869358
\(396\) 1.16580 0.0585835
\(397\) −22.9490 −1.15178 −0.575889 0.817528i \(-0.695344\pi\)
−0.575889 + 0.817528i \(0.695344\pi\)
\(398\) −12.9398 −0.648615
\(399\) 6.15864 0.308318
\(400\) −1.32190 −0.0660952
\(401\) −2.94535 −0.147084 −0.0735418 0.997292i \(-0.523430\pi\)
−0.0735418 + 0.997292i \(0.523430\pi\)
\(402\) 2.80143 0.139722
\(403\) 4.22316 0.210371
\(404\) 19.4019 0.965282
\(405\) −1.63807 −0.0813963
\(406\) 36.7668 1.82471
\(407\) −1.78318 −0.0883891
\(408\) −1.64878 −0.0816269
\(409\) −11.2664 −0.557088 −0.278544 0.960423i \(-0.589852\pi\)
−0.278544 + 0.960423i \(0.589852\pi\)
\(410\) 10.1513 0.501335
\(411\) −12.6522 −0.624085
\(412\) 1.25490 0.0618245
\(413\) −53.7008 −2.64244
\(414\) 3.32812 0.163568
\(415\) −5.88633 −0.288948
\(416\) −2.74206 −0.134441
\(417\) −11.2746 −0.552118
\(418\) −0.729239 −0.0356682
\(419\) −37.6652 −1.84007 −0.920033 0.391841i \(-0.871838\pi\)
−0.920033 + 0.391841i \(0.871838\pi\)
\(420\) 9.54074 0.465541
\(421\) −7.13465 −0.347722 −0.173861 0.984770i \(-0.555624\pi\)
−0.173861 + 0.984770i \(0.555624\pi\)
\(422\) 8.18019 0.398205
\(423\) 6.20171 0.301538
\(424\) 13.2036 0.641223
\(425\) 2.15711 0.104635
\(426\) 2.83106 0.137166
\(427\) 39.2381 1.89886
\(428\) −2.53644 −0.122603
\(429\) 1.63202 0.0787945
\(430\) −17.8329 −0.859978
\(431\) 34.1950 1.64711 0.823557 0.567233i \(-0.191986\pi\)
0.823557 + 0.567233i \(0.191986\pi\)
\(432\) 5.03087 0.242048
\(433\) −9.54238 −0.458577 −0.229289 0.973358i \(-0.573640\pi\)
−0.229289 + 0.973358i \(0.573640\pi\)
\(434\) −7.58297 −0.363994
\(435\) −14.4704 −0.693803
\(436\) 0.224723 0.0107623
\(437\) −2.08183 −0.0995876
\(438\) 0.962184 0.0459749
\(439\) −13.2757 −0.633614 −0.316807 0.948490i \(-0.602611\pi\)
−0.316807 + 0.948490i \(0.602611\pi\)
\(440\) −1.12971 −0.0538568
\(441\) −34.1224 −1.62488
\(442\) 4.47454 0.212832
\(443\) −1.32775 −0.0630835 −0.0315418 0.999502i \(-0.510042\pi\)
−0.0315418 + 0.999502i \(0.510042\pi\)
\(444\) −3.05867 −0.145158
\(445\) −26.7384 −1.26752
\(446\) 2.90656 0.137630
\(447\) 6.42936 0.304098
\(448\) 4.92355 0.232616
\(449\) −1.61845 −0.0763793 −0.0381896 0.999271i \(-0.512159\pi\)
−0.0381896 + 0.999271i \(0.512159\pi\)
\(450\) −2.61618 −0.123328
\(451\) −3.11791 −0.146817
\(452\) −16.0607 −0.755434
\(453\) 12.2238 0.574324
\(454\) 15.2841 0.717318
\(455\) −25.8921 −1.21384
\(456\) −1.25085 −0.0585766
\(457\) −3.08609 −0.144361 −0.0721807 0.997392i \(-0.522996\pi\)
−0.0721807 + 0.997392i \(0.522996\pi\)
\(458\) 27.4284 1.28164
\(459\) −8.20945 −0.383184
\(460\) −3.22510 −0.150371
\(461\) 5.52833 0.257480 0.128740 0.991678i \(-0.458907\pi\)
0.128740 + 0.991678i \(0.458907\pi\)
\(462\) −2.93039 −0.136334
\(463\) −1.80724 −0.0839896 −0.0419948 0.999118i \(-0.513371\pi\)
−0.0419948 + 0.999118i \(0.513371\pi\)
\(464\) −7.46754 −0.346672
\(465\) 2.98445 0.138401
\(466\) −4.80887 −0.222766
\(467\) −25.9918 −1.20276 −0.601378 0.798965i \(-0.705381\pi\)
−0.601378 + 0.798965i \(0.705381\pi\)
\(468\) −5.42681 −0.250854
\(469\) 13.6510 0.630347
\(470\) −6.00974 −0.277209
\(471\) 6.13137 0.282519
\(472\) 10.9069 0.502032
\(473\) 5.47729 0.251846
\(474\) −9.10286 −0.418108
\(475\) 1.63649 0.0750875
\(476\) −8.03434 −0.368253
\(477\) 26.1312 1.19647
\(478\) 13.9477 0.637952
\(479\) −13.5652 −0.619812 −0.309906 0.950767i \(-0.600298\pi\)
−0.309906 + 0.950767i \(0.600298\pi\)
\(480\) −1.93778 −0.0884470
\(481\) 8.30076 0.378482
\(482\) −2.26986 −0.103389
\(483\) −8.36570 −0.380652
\(484\) −10.6530 −0.484228
\(485\) 17.0218 0.772920
\(486\) 15.9556 0.723761
\(487\) 17.3330 0.785432 0.392716 0.919660i \(-0.371536\pi\)
0.392716 + 0.919660i \(0.371536\pi\)
\(488\) −7.96946 −0.360761
\(489\) −10.5235 −0.475889
\(490\) 33.0661 1.49378
\(491\) −6.48844 −0.292819 −0.146410 0.989224i \(-0.546772\pi\)
−0.146410 + 0.989224i \(0.546772\pi\)
\(492\) −5.34811 −0.241111
\(493\) 12.1856 0.548814
\(494\) 3.39462 0.152731
\(495\) −2.23581 −0.100492
\(496\) 1.54014 0.0691544
\(497\) 13.7955 0.618811
\(498\) 3.10117 0.138967
\(499\) 24.4381 1.09400 0.547001 0.837132i \(-0.315769\pi\)
0.547001 + 0.837132i \(0.315769\pi\)
\(500\) 12.1244 0.542219
\(501\) −14.4876 −0.647260
\(502\) 23.3456 1.04197
\(503\) 1.99699 0.0890413 0.0445206 0.999008i \(-0.485824\pi\)
0.0445206 + 0.999008i \(0.485824\pi\)
\(504\) 9.74420 0.434041
\(505\) −37.2097 −1.65581
\(506\) 0.990574 0.0440364
\(507\) 5.53809 0.245955
\(508\) −9.84140 −0.436641
\(509\) 25.4817 1.12946 0.564728 0.825277i \(-0.308981\pi\)
0.564728 + 0.825277i \(0.308981\pi\)
\(510\) 3.16209 0.140020
\(511\) 4.68862 0.207412
\(512\) −1.00000 −0.0441942
\(513\) −6.22812 −0.274978
\(514\) 22.6872 1.00069
\(515\) −2.40669 −0.106052
\(516\) 9.39512 0.413597
\(517\) 1.84586 0.0811810
\(518\) −14.9046 −0.654869
\(519\) −7.80490 −0.342597
\(520\) 5.25882 0.230615
\(521\) 43.5402 1.90753 0.953765 0.300554i \(-0.0971717\pi\)
0.953765 + 0.300554i \(0.0971717\pi\)
\(522\) −14.7790 −0.646859
\(523\) −8.51651 −0.372401 −0.186201 0.982512i \(-0.559617\pi\)
−0.186201 + 0.982512i \(0.559617\pi\)
\(524\) −14.5707 −0.636523
\(525\) 6.57613 0.287006
\(526\) 2.12047 0.0924569
\(527\) −2.51323 −0.109478
\(528\) 0.595179 0.0259018
\(529\) −20.1721 −0.877048
\(530\) −25.3223 −1.09993
\(531\) 21.5859 0.936747
\(532\) −6.09527 −0.264264
\(533\) 14.5139 0.628668
\(534\) 14.0869 0.609600
\(535\) 4.86448 0.210310
\(536\) −2.77260 −0.119758
\(537\) 26.7711 1.15526
\(538\) 28.4298 1.22569
\(539\) −10.1561 −0.437455
\(540\) −9.64838 −0.415200
\(541\) 8.66645 0.372600 0.186300 0.982493i \(-0.440350\pi\)
0.186300 + 0.982493i \(0.440350\pi\)
\(542\) 16.4021 0.704532
\(543\) −11.6896 −0.501650
\(544\) 1.63182 0.0699636
\(545\) −0.430983 −0.0184613
\(546\) 13.6410 0.583783
\(547\) −5.21352 −0.222914 −0.111457 0.993769i \(-0.535552\pi\)
−0.111457 + 0.993769i \(0.535552\pi\)
\(548\) 12.5220 0.534912
\(549\) −15.7723 −0.673147
\(550\) −0.778673 −0.0332027
\(551\) 9.24468 0.393837
\(552\) 1.69912 0.0723193
\(553\) −44.3572 −1.88626
\(554\) −3.09097 −0.131323
\(555\) 5.86603 0.248999
\(556\) 11.1585 0.473228
\(557\) 36.7210 1.55592 0.777959 0.628315i \(-0.216255\pi\)
0.777959 + 0.628315i \(0.216255\pi\)
\(558\) 3.04809 0.129036
\(559\) −25.4969 −1.07840
\(560\) −9.44257 −0.399021
\(561\) −0.971222 −0.0410050
\(562\) −9.46291 −0.399169
\(563\) 13.4193 0.565556 0.282778 0.959185i \(-0.408744\pi\)
0.282778 + 0.959185i \(0.408744\pi\)
\(564\) 3.16619 0.133320
\(565\) 30.8019 1.29584
\(566\) 7.00252 0.294338
\(567\) 4.20532 0.176607
\(568\) −2.80193 −0.117566
\(569\) 29.1981 1.22405 0.612024 0.790839i \(-0.290355\pi\)
0.612024 + 0.790839i \(0.290355\pi\)
\(570\) 2.39893 0.100480
\(571\) −14.7944 −0.619128 −0.309564 0.950879i \(-0.600183\pi\)
−0.309564 + 0.950879i \(0.600183\pi\)
\(572\) −1.61522 −0.0675358
\(573\) −21.6929 −0.906235
\(574\) −26.0607 −1.08775
\(575\) −2.22296 −0.0927038
\(576\) −1.97910 −0.0824624
\(577\) −1.18517 −0.0493393 −0.0246697 0.999696i \(-0.507853\pi\)
−0.0246697 + 0.999696i \(0.507853\pi\)
\(578\) 14.3372 0.596348
\(579\) 4.70306 0.195453
\(580\) 14.3215 0.594668
\(581\) 15.1116 0.626936
\(582\) −8.96780 −0.371727
\(583\) 7.77763 0.322117
\(584\) −0.952283 −0.0394058
\(585\) 10.4077 0.430306
\(586\) 11.8399 0.489103
\(587\) 32.0501 1.32285 0.661425 0.750012i \(-0.269952\pi\)
0.661425 + 0.750012i \(0.269952\pi\)
\(588\) −17.4206 −0.718415
\(589\) −1.90667 −0.0785629
\(590\) −20.9177 −0.861167
\(591\) 19.8868 0.818033
\(592\) 3.02720 0.124417
\(593\) 17.8899 0.734650 0.367325 0.930093i \(-0.380274\pi\)
0.367325 + 0.930093i \(0.380274\pi\)
\(594\) 2.96345 0.121592
\(595\) 15.4085 0.631689
\(596\) −6.36321 −0.260647
\(597\) −13.0744 −0.535098
\(598\) −4.61114 −0.188564
\(599\) −45.7826 −1.87063 −0.935313 0.353822i \(-0.884882\pi\)
−0.935313 + 0.353822i \(0.884882\pi\)
\(600\) −1.33565 −0.0545276
\(601\) −34.2047 −1.39524 −0.697620 0.716468i \(-0.745758\pi\)
−0.697620 + 0.716468i \(0.745758\pi\)
\(602\) 45.7814 1.86591
\(603\) −5.48725 −0.223458
\(604\) −12.0980 −0.492261
\(605\) 20.4307 0.830628
\(606\) 19.6036 0.796344
\(607\) −18.1883 −0.738239 −0.369119 0.929382i \(-0.620341\pi\)
−0.369119 + 0.929382i \(0.620341\pi\)
\(608\) 1.23798 0.0502068
\(609\) 37.1491 1.50536
\(610\) 15.2841 0.618836
\(611\) −8.59253 −0.347617
\(612\) 3.22952 0.130546
\(613\) −29.6645 −1.19814 −0.599069 0.800698i \(-0.704462\pi\)
−0.599069 + 0.800698i \(0.704462\pi\)
\(614\) 5.64301 0.227733
\(615\) 10.2568 0.413594
\(616\) 2.90024 0.116854
\(617\) 17.1785 0.691580 0.345790 0.938312i \(-0.387611\pi\)
0.345790 + 0.938312i \(0.387611\pi\)
\(618\) 1.26795 0.0510043
\(619\) −35.8224 −1.43983 −0.719913 0.694065i \(-0.755818\pi\)
−0.719913 + 0.694065i \(0.755818\pi\)
\(620\) −2.95374 −0.118625
\(621\) 8.46007 0.339491
\(622\) −9.93607 −0.398400
\(623\) 68.6439 2.75016
\(624\) −2.77057 −0.110912
\(625\) −16.6430 −0.665722
\(626\) 25.7823 1.03047
\(627\) −0.736821 −0.0294258
\(628\) −6.06828 −0.242151
\(629\) −4.93983 −0.196964
\(630\) −18.6878 −0.744539
\(631\) 14.7580 0.587508 0.293754 0.955881i \(-0.405095\pi\)
0.293754 + 0.955881i \(0.405095\pi\)
\(632\) 9.00919 0.358366
\(633\) 8.26524 0.328514
\(634\) −5.29714 −0.210376
\(635\) 18.8742 0.748999
\(636\) 13.3409 0.529000
\(637\) 47.2769 1.87318
\(638\) −4.39879 −0.174150
\(639\) −5.54530 −0.219369
\(640\) 1.91784 0.0758091
\(641\) −38.0087 −1.50125 −0.750627 0.660726i \(-0.770249\pi\)
−0.750627 + 0.660726i \(0.770249\pi\)
\(642\) −2.56281 −0.101146
\(643\) 24.2289 0.955495 0.477748 0.878497i \(-0.341453\pi\)
0.477748 + 0.878497i \(0.341453\pi\)
\(644\) 8.27962 0.326263
\(645\) −18.0183 −0.709470
\(646\) −2.02016 −0.0794821
\(647\) −31.5069 −1.23866 −0.619331 0.785130i \(-0.712596\pi\)
−0.619331 + 0.785130i \(0.712596\pi\)
\(648\) −0.854123 −0.0335531
\(649\) 6.42477 0.252194
\(650\) 3.62474 0.142174
\(651\) −7.66181 −0.300290
\(652\) 10.4152 0.407891
\(653\) 14.0442 0.549594 0.274797 0.961502i \(-0.411389\pi\)
0.274797 + 0.961502i \(0.411389\pi\)
\(654\) 0.227060 0.00887874
\(655\) 27.9442 1.09187
\(656\) 5.29308 0.206660
\(657\) −1.88466 −0.0735277
\(658\) 15.4285 0.601465
\(659\) −47.7699 −1.86085 −0.930425 0.366483i \(-0.880562\pi\)
−0.930425 + 0.366483i \(0.880562\pi\)
\(660\) −1.14146 −0.0444311
\(661\) −14.1247 −0.549389 −0.274695 0.961532i \(-0.588577\pi\)
−0.274695 + 0.961532i \(0.588577\pi\)
\(662\) 12.5579 0.488078
\(663\) 4.52106 0.175583
\(664\) −3.06925 −0.119110
\(665\) 11.6897 0.453308
\(666\) 5.99112 0.232151
\(667\) −12.5577 −0.486235
\(668\) 14.3386 0.554776
\(669\) 2.93678 0.113543
\(670\) 5.31739 0.205429
\(671\) −4.69445 −0.181227
\(672\) 4.97474 0.191905
\(673\) −45.2810 −1.74546 −0.872728 0.488207i \(-0.837651\pi\)
−0.872728 + 0.488207i \(0.837651\pi\)
\(674\) −24.9458 −0.960875
\(675\) −6.65032 −0.255971
\(676\) −5.48111 −0.210812
\(677\) −4.74458 −0.182349 −0.0911746 0.995835i \(-0.529062\pi\)
−0.0911746 + 0.995835i \(0.529062\pi\)
\(678\) −16.2277 −0.623222
\(679\) −43.6991 −1.67702
\(680\) −3.12956 −0.120013
\(681\) 15.4430 0.591777
\(682\) 0.907227 0.0347395
\(683\) 41.8833 1.60262 0.801311 0.598248i \(-0.204136\pi\)
0.801311 + 0.598248i \(0.204136\pi\)
\(684\) 2.45009 0.0936815
\(685\) −24.0151 −0.917569
\(686\) −50.4240 −1.92520
\(687\) 27.7135 1.05734
\(688\) −9.29844 −0.354500
\(689\) −36.2050 −1.37930
\(690\) −3.25863 −0.124054
\(691\) 18.4628 0.702357 0.351178 0.936309i \(-0.385781\pi\)
0.351178 + 0.936309i \(0.385781\pi\)
\(692\) 7.72458 0.293645
\(693\) 5.73986 0.218039
\(694\) 28.8371 1.09464
\(695\) −21.4003 −0.811758
\(696\) −7.54518 −0.285999
\(697\) −8.63733 −0.327162
\(698\) −32.0778 −1.21416
\(699\) −4.85886 −0.183779
\(700\) −6.50847 −0.245997
\(701\) 16.6555 0.629068 0.314534 0.949246i \(-0.398152\pi\)
0.314534 + 0.949246i \(0.398152\pi\)
\(702\) −13.7949 −0.520656
\(703\) −3.74762 −0.141344
\(704\) −0.589054 −0.0222008
\(705\) −6.07222 −0.228693
\(706\) 21.1127 0.794588
\(707\) 95.5264 3.59264
\(708\) 11.0203 0.414169
\(709\) 27.0443 1.01567 0.507835 0.861455i \(-0.330446\pi\)
0.507835 + 0.861455i \(0.330446\pi\)
\(710\) 5.37365 0.201669
\(711\) 17.8301 0.668680
\(712\) −13.9420 −0.522497
\(713\) 2.58995 0.0969946
\(714\) −8.11787 −0.303804
\(715\) 3.09773 0.115849
\(716\) −26.4956 −0.990188
\(717\) 14.0927 0.526301
\(718\) −12.9014 −0.481476
\(719\) −16.6817 −0.622124 −0.311062 0.950390i \(-0.600685\pi\)
−0.311062 + 0.950390i \(0.600685\pi\)
\(720\) 3.79559 0.141453
\(721\) 6.17857 0.230102
\(722\) 17.4674 0.650069
\(723\) −2.29346 −0.0852946
\(724\) 11.5693 0.429971
\(725\) 9.87137 0.366613
\(726\) −10.7638 −0.399481
\(727\) 25.8999 0.960574 0.480287 0.877112i \(-0.340533\pi\)
0.480287 + 0.877112i \(0.340533\pi\)
\(728\) −13.5007 −0.500368
\(729\) 13.5591 0.502190
\(730\) 1.82632 0.0675952
\(731\) 15.1733 0.561207
\(732\) −8.05232 −0.297622
\(733\) 16.0897 0.594287 0.297143 0.954833i \(-0.403966\pi\)
0.297143 + 0.954833i \(0.403966\pi\)
\(734\) 6.91139 0.255104
\(735\) 33.4099 1.23234
\(736\) −1.68163 −0.0619859
\(737\) −1.63321 −0.0601601
\(738\) 10.4755 0.385609
\(739\) −52.3111 −1.92429 −0.962147 0.272531i \(-0.912139\pi\)
−0.962147 + 0.272531i \(0.912139\pi\)
\(740\) −5.80567 −0.213421
\(741\) 3.42992 0.126001
\(742\) 65.0086 2.38654
\(743\) 33.3998 1.22532 0.612659 0.790347i \(-0.290100\pi\)
0.612659 + 0.790347i \(0.290100\pi\)
\(744\) 1.55615 0.0570514
\(745\) 12.2036 0.447105
\(746\) 13.5218 0.495068
\(747\) −6.07436 −0.222249
\(748\) 0.961228 0.0351460
\(749\) −12.4883 −0.456313
\(750\) 12.2504 0.447323
\(751\) 19.9295 0.727237 0.363619 0.931548i \(-0.381541\pi\)
0.363619 + 0.931548i \(0.381541\pi\)
\(752\) −3.13361 −0.114271
\(753\) 23.5884 0.859608
\(754\) 20.4764 0.745708
\(755\) 23.2020 0.844407
\(756\) 24.7697 0.900867
\(757\) 2.43071 0.0883457 0.0441729 0.999024i \(-0.485935\pi\)
0.0441729 + 0.999024i \(0.485935\pi\)
\(758\) −16.9666 −0.616256
\(759\) 1.00087 0.0363294
\(760\) −2.37425 −0.0861230
\(761\) −46.5808 −1.68855 −0.844276 0.535908i \(-0.819969\pi\)
−0.844276 + 0.535908i \(0.819969\pi\)
\(762\) −9.94372 −0.360223
\(763\) 1.10644 0.0400557
\(764\) 21.4697 0.776747
\(765\) −6.19370 −0.223934
\(766\) −20.5382 −0.742076
\(767\) −29.9074 −1.07989
\(768\) −1.01040 −0.0364596
\(769\) 45.7293 1.64904 0.824520 0.565833i \(-0.191445\pi\)
0.824520 + 0.565833i \(0.191445\pi\)
\(770\) −5.56219 −0.200447
\(771\) 22.9231 0.825554
\(772\) −4.65467 −0.167525
\(773\) −41.4701 −1.49158 −0.745788 0.666183i \(-0.767927\pi\)
−0.745788 + 0.666183i \(0.767927\pi\)
\(774\) −18.4025 −0.661465
\(775\) −2.03592 −0.0731324
\(776\) 8.87552 0.318613
\(777\) −15.0595 −0.540258
\(778\) 10.0617 0.360728
\(779\) −6.55273 −0.234776
\(780\) 5.31350 0.190254
\(781\) −1.65049 −0.0590592
\(782\) 2.74412 0.0981295
\(783\) −37.5682 −1.34258
\(784\) 17.2414 0.615764
\(785\) 11.6380 0.415377
\(786\) −14.7222 −0.525122
\(787\) −52.9062 −1.88590 −0.942950 0.332933i \(-0.891962\pi\)
−0.942950 + 0.332933i \(0.891962\pi\)
\(788\) −19.6822 −0.701148
\(789\) 2.14252 0.0762756
\(790\) −17.2782 −0.614729
\(791\) −79.0759 −2.81162
\(792\) −1.16580 −0.0414248
\(793\) 21.8527 0.776014
\(794\) 22.9490 0.814430
\(795\) −25.5856 −0.907428
\(796\) 12.9398 0.458640
\(797\) −7.15087 −0.253297 −0.126648 0.991948i \(-0.540422\pi\)
−0.126648 + 0.991948i \(0.540422\pi\)
\(798\) −6.15864 −0.218014
\(799\) 5.11347 0.180902
\(800\) 1.32190 0.0467364
\(801\) −27.5925 −0.974933
\(802\) 2.94535 0.104004
\(803\) −0.560946 −0.0197954
\(804\) −2.80143 −0.0987987
\(805\) −15.8789 −0.559659
\(806\) −4.22316 −0.148754
\(807\) 28.7254 1.01118
\(808\) −19.4019 −0.682557
\(809\) −15.3286 −0.538924 −0.269462 0.963011i \(-0.586846\pi\)
−0.269462 + 0.963011i \(0.586846\pi\)
\(810\) 1.63807 0.0575559
\(811\) −10.5619 −0.370878 −0.185439 0.982656i \(-0.559371\pi\)
−0.185439 + 0.982656i \(0.559371\pi\)
\(812\) −36.7668 −1.29026
\(813\) 16.5727 0.581229
\(814\) 1.78318 0.0625006
\(815\) −19.9747 −0.699682
\(816\) 1.64878 0.0577189
\(817\) 11.5113 0.402730
\(818\) 11.2664 0.393921
\(819\) −26.7192 −0.933643
\(820\) −10.1513 −0.354497
\(821\) −11.8945 −0.415122 −0.207561 0.978222i \(-0.566553\pi\)
−0.207561 + 0.978222i \(0.566553\pi\)
\(822\) 12.6522 0.441295
\(823\) 46.2657 1.61272 0.806360 0.591424i \(-0.201434\pi\)
0.806360 + 0.591424i \(0.201434\pi\)
\(824\) −1.25490 −0.0437165
\(825\) −0.786769 −0.0273918
\(826\) 53.7008 1.86849
\(827\) 50.4903 1.75572 0.877859 0.478919i \(-0.158971\pi\)
0.877859 + 0.478919i \(0.158971\pi\)
\(828\) −3.32812 −0.115660
\(829\) −54.9080 −1.90703 −0.953516 0.301342i \(-0.902565\pi\)
−0.953516 + 0.301342i \(0.902565\pi\)
\(830\) 5.88633 0.204317
\(831\) −3.12311 −0.108339
\(832\) 2.74206 0.0950638
\(833\) −28.1348 −0.974812
\(834\) 11.2746 0.390406
\(835\) −27.4990 −0.951643
\(836\) 0.729239 0.0252213
\(837\) 7.74825 0.267819
\(838\) 37.6652 1.30112
\(839\) −1.23023 −0.0424722 −0.0212361 0.999774i \(-0.506760\pi\)
−0.0212361 + 0.999774i \(0.506760\pi\)
\(840\) −9.54074 −0.329187
\(841\) 26.7641 0.922900
\(842\) 7.13465 0.245876
\(843\) −9.56129 −0.329308
\(844\) −8.18019 −0.281574
\(845\) 10.5119 0.361619
\(846\) −6.20171 −0.213219
\(847\) −52.4507 −1.80223
\(848\) −13.2036 −0.453413
\(849\) 7.07532 0.242824
\(850\) −2.15711 −0.0739881
\(851\) 5.09064 0.174505
\(852\) −2.83106 −0.0969907
\(853\) 39.3405 1.34699 0.673497 0.739190i \(-0.264791\pi\)
0.673497 + 0.739190i \(0.264791\pi\)
\(854\) −39.2381 −1.34270
\(855\) −4.69887 −0.160698
\(856\) 2.53644 0.0866937
\(857\) 11.0738 0.378273 0.189137 0.981951i \(-0.439431\pi\)
0.189137 + 0.981951i \(0.439431\pi\)
\(858\) −1.63202 −0.0557161
\(859\) −8.72568 −0.297716 −0.148858 0.988859i \(-0.547560\pi\)
−0.148858 + 0.988859i \(0.547560\pi\)
\(860\) 17.8329 0.608096
\(861\) −26.3317 −0.897382
\(862\) −34.1950 −1.16469
\(863\) 16.7026 0.568562 0.284281 0.958741i \(-0.408245\pi\)
0.284281 + 0.958741i \(0.408245\pi\)
\(864\) −5.03087 −0.171154
\(865\) −14.8145 −0.503708
\(866\) 9.54238 0.324263
\(867\) 14.4862 0.491978
\(868\) 7.58297 0.257383
\(869\) 5.30690 0.180024
\(870\) 14.4704 0.490593
\(871\) 7.60263 0.257605
\(872\) −0.224723 −0.00761009
\(873\) 17.5655 0.594503
\(874\) 2.08183 0.0704191
\(875\) 59.6950 2.01806
\(876\) −0.962184 −0.0325092
\(877\) 4.38034 0.147914 0.0739568 0.997261i \(-0.476437\pi\)
0.0739568 + 0.997261i \(0.476437\pi\)
\(878\) 13.2757 0.448032
\(879\) 11.9630 0.403503
\(880\) 1.12971 0.0380825
\(881\) 33.3166 1.12246 0.561232 0.827659i \(-0.310328\pi\)
0.561232 + 0.827659i \(0.310328\pi\)
\(882\) 34.1224 1.14896
\(883\) 37.6755 1.26788 0.633941 0.773381i \(-0.281436\pi\)
0.633941 + 0.773381i \(0.281436\pi\)
\(884\) −4.47454 −0.150495
\(885\) −21.1352 −0.710451
\(886\) 1.32775 0.0446068
\(887\) 23.2146 0.779470 0.389735 0.920927i \(-0.372567\pi\)
0.389735 + 0.920927i \(0.372567\pi\)
\(888\) 3.05867 0.102642
\(889\) −48.4546 −1.62512
\(890\) 26.7384 0.896272
\(891\) −0.503125 −0.0168553
\(892\) −2.90656 −0.0973190
\(893\) 3.87935 0.129817
\(894\) −6.42936 −0.215030
\(895\) 50.8143 1.69853
\(896\) −4.92355 −0.164484
\(897\) −4.65908 −0.155562
\(898\) 1.61845 0.0540083
\(899\) −11.5011 −0.383582
\(900\) 2.61618 0.0872059
\(901\) 21.5458 0.717796
\(902\) 3.11791 0.103815
\(903\) 46.2574 1.53935
\(904\) 16.0607 0.534172
\(905\) −22.1881 −0.737558
\(906\) −12.2238 −0.406108
\(907\) 31.3556 1.04115 0.520573 0.853817i \(-0.325718\pi\)
0.520573 + 0.853817i \(0.325718\pi\)
\(908\) −15.2841 −0.507220
\(909\) −38.3983 −1.27359
\(910\) 25.8921 0.858315
\(911\) 53.3962 1.76910 0.884548 0.466450i \(-0.154467\pi\)
0.884548 + 0.466450i \(0.154467\pi\)
\(912\) 1.25085 0.0414199
\(913\) −1.80796 −0.0598347
\(914\) 3.08609 0.102079
\(915\) 15.4430 0.510531
\(916\) −27.4284 −0.906259
\(917\) −71.7395 −2.36905
\(918\) 8.20945 0.270952
\(919\) 22.0206 0.726392 0.363196 0.931713i \(-0.381686\pi\)
0.363196 + 0.931713i \(0.381686\pi\)
\(920\) 3.22510 0.106328
\(921\) 5.70168 0.187877
\(922\) −5.52833 −0.182066
\(923\) 7.68307 0.252891
\(924\) 2.93039 0.0964029
\(925\) −4.00167 −0.131574
\(926\) 1.80724 0.0593896
\(927\) −2.48357 −0.0815712
\(928\) 7.46754 0.245134
\(929\) 41.3847 1.35779 0.678894 0.734236i \(-0.262459\pi\)
0.678894 + 0.734236i \(0.262459\pi\)
\(930\) −2.98445 −0.0978639
\(931\) −21.3445 −0.699539
\(932\) 4.80887 0.157520
\(933\) −10.0394 −0.328674
\(934\) 25.9918 0.850477
\(935\) −1.84348 −0.0602882
\(936\) 5.42681 0.177381
\(937\) 26.5907 0.868679 0.434339 0.900749i \(-0.356982\pi\)
0.434339 + 0.900749i \(0.356982\pi\)
\(938\) −13.6510 −0.445722
\(939\) 26.0504 0.850121
\(940\) 6.00974 0.196016
\(941\) 12.5119 0.407878 0.203939 0.978984i \(-0.434626\pi\)
0.203939 + 0.978984i \(0.434626\pi\)
\(942\) −6.13137 −0.199771
\(943\) 8.90102 0.289857
\(944\) −10.9069 −0.354990
\(945\) −47.5043 −1.54531
\(946\) −5.47729 −0.178082
\(947\) 10.4645 0.340050 0.170025 0.985440i \(-0.445615\pi\)
0.170025 + 0.985440i \(0.445615\pi\)
\(948\) 9.10286 0.295647
\(949\) 2.61122 0.0847637
\(950\) −1.63649 −0.0530949
\(951\) −5.35221 −0.173557
\(952\) 8.03434 0.260394
\(953\) −34.9366 −1.13171 −0.565854 0.824505i \(-0.691454\pi\)
−0.565854 + 0.824505i \(0.691454\pi\)
\(954\) −26.1312 −0.846029
\(955\) −41.1754 −1.33240
\(956\) −13.9477 −0.451100
\(957\) −4.44452 −0.143671
\(958\) 13.5652 0.438273
\(959\) 61.6526 1.99087
\(960\) 1.93778 0.0625414
\(961\) −28.6280 −0.923483
\(962\) −8.30076 −0.267627
\(963\) 5.01986 0.161763
\(964\) 2.26986 0.0731072
\(965\) 8.92689 0.287367
\(966\) 8.36570 0.269162
\(967\) 25.3003 0.813602 0.406801 0.913517i \(-0.366644\pi\)
0.406801 + 0.913517i \(0.366644\pi\)
\(968\) 10.6530 0.342401
\(969\) −2.04116 −0.0655716
\(970\) −17.0218 −0.546537
\(971\) −21.9834 −0.705482 −0.352741 0.935721i \(-0.614750\pi\)
−0.352741 + 0.935721i \(0.614750\pi\)
\(972\) −15.9556 −0.511776
\(973\) 54.9397 1.76129
\(974\) −17.3330 −0.555384
\(975\) 3.66243 0.117292
\(976\) 7.96946 0.255096
\(977\) −10.7079 −0.342577 −0.171289 0.985221i \(-0.554793\pi\)
−0.171289 + 0.985221i \(0.554793\pi\)
\(978\) 10.5235 0.336504
\(979\) −8.21257 −0.262475
\(980\) −33.0661 −1.05626
\(981\) −0.444750 −0.0141998
\(982\) 6.48844 0.207054
\(983\) −16.5144 −0.526728 −0.263364 0.964697i \(-0.584832\pi\)
−0.263364 + 0.964697i \(0.584832\pi\)
\(984\) 5.34811 0.170491
\(985\) 37.7471 1.20272
\(986\) −12.1856 −0.388070
\(987\) 15.5889 0.496200
\(988\) −3.39462 −0.107997
\(989\) −15.6366 −0.497214
\(990\) 2.23581 0.0710586
\(991\) 24.0186 0.762977 0.381488 0.924374i \(-0.375412\pi\)
0.381488 + 0.924374i \(0.375412\pi\)
\(992\) −1.54014 −0.0488995
\(993\) 12.6885 0.402657
\(994\) −13.7955 −0.437566
\(995\) −24.8165 −0.786735
\(996\) −3.10117 −0.0982642
\(997\) −2.89432 −0.0916641 −0.0458320 0.998949i \(-0.514594\pi\)
−0.0458320 + 0.998949i \(0.514594\pi\)
\(998\) −24.4381 −0.773576
\(999\) 15.2294 0.481838
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 4006.2.a.g.1.13 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.13 40 1.1 even 1 trivial