Properties

Label 4029.2.a.k.1.18
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.617959 q^{2} +1.00000 q^{3} -1.61813 q^{4} +3.16624 q^{5} +0.617959 q^{6} -0.196167 q^{7} -2.23585 q^{8} +1.00000 q^{9} +1.95660 q^{10} -1.60281 q^{11} -1.61813 q^{12} -1.04507 q^{13} -0.121223 q^{14} +3.16624 q^{15} +1.85459 q^{16} +1.00000 q^{17} +0.617959 q^{18} -1.16729 q^{19} -5.12337 q^{20} -0.196167 q^{21} -0.990470 q^{22} -0.115056 q^{23} -2.23585 q^{24} +5.02505 q^{25} -0.645810 q^{26} +1.00000 q^{27} +0.317423 q^{28} +6.34232 q^{29} +1.95660 q^{30} -1.71568 q^{31} +5.61777 q^{32} -1.60281 q^{33} +0.617959 q^{34} -0.621110 q^{35} -1.61813 q^{36} +6.10971 q^{37} -0.721338 q^{38} -1.04507 q^{39} -7.07924 q^{40} +3.43821 q^{41} -0.121223 q^{42} +12.5282 q^{43} +2.59355 q^{44} +3.16624 q^{45} -0.0711002 q^{46} -2.31797 q^{47} +1.85459 q^{48} -6.96152 q^{49} +3.10527 q^{50} +1.00000 q^{51} +1.69105 q^{52} +10.5661 q^{53} +0.617959 q^{54} -5.07487 q^{55} +0.438600 q^{56} -1.16729 q^{57} +3.91929 q^{58} +2.43259 q^{59} -5.12337 q^{60} -1.11029 q^{61} -1.06022 q^{62} -0.196167 q^{63} -0.237627 q^{64} -3.30894 q^{65} -0.990470 q^{66} +9.11603 q^{67} -1.61813 q^{68} -0.115056 q^{69} -0.383821 q^{70} +7.31632 q^{71} -2.23585 q^{72} +7.19324 q^{73} +3.77555 q^{74} +5.02505 q^{75} +1.88883 q^{76} +0.314418 q^{77} -0.645810 q^{78} +1.00000 q^{79} +5.87206 q^{80} +1.00000 q^{81} +2.12467 q^{82} +1.78493 q^{83} +0.317423 q^{84} +3.16624 q^{85} +7.74191 q^{86} +6.34232 q^{87} +3.58365 q^{88} -11.2590 q^{89} +1.95660 q^{90} +0.205008 q^{91} +0.186176 q^{92} -1.71568 q^{93} -1.43241 q^{94} -3.69592 q^{95} +5.61777 q^{96} +2.57631 q^{97} -4.30193 q^{98} -1.60281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.617959 0.436963 0.218481 0.975841i \(-0.429890\pi\)
0.218481 + 0.975841i \(0.429890\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.61813 −0.809063
\(5\) 3.16624 1.41598 0.707992 0.706221i \(-0.249601\pi\)
0.707992 + 0.706221i \(0.249601\pi\)
\(6\) 0.617959 0.252281
\(7\) −0.196167 −0.0741441 −0.0370720 0.999313i \(-0.511803\pi\)
−0.0370720 + 0.999313i \(0.511803\pi\)
\(8\) −2.23585 −0.790494
\(9\) 1.00000 0.333333
\(10\) 1.95660 0.618732
\(11\) −1.60281 −0.483265 −0.241632 0.970368i \(-0.577683\pi\)
−0.241632 + 0.970368i \(0.577683\pi\)
\(12\) −1.61813 −0.467113
\(13\) −1.04507 −0.289850 −0.144925 0.989443i \(-0.546294\pi\)
−0.144925 + 0.989443i \(0.546294\pi\)
\(14\) −0.121223 −0.0323982
\(15\) 3.16624 0.817519
\(16\) 1.85459 0.463647
\(17\) 1.00000 0.242536
\(18\) 0.617959 0.145654
\(19\) −1.16729 −0.267795 −0.133897 0.990995i \(-0.542749\pi\)
−0.133897 + 0.990995i \(0.542749\pi\)
\(20\) −5.12337 −1.14562
\(21\) −0.196167 −0.0428071
\(22\) −0.990470 −0.211169
\(23\) −0.115056 −0.0239909 −0.0119955 0.999928i \(-0.503818\pi\)
−0.0119955 + 0.999928i \(0.503818\pi\)
\(24\) −2.23585 −0.456392
\(25\) 5.02505 1.00501
\(26\) −0.645810 −0.126654
\(27\) 1.00000 0.192450
\(28\) 0.317423 0.0599872
\(29\) 6.34232 1.17774 0.588869 0.808228i \(-0.299573\pi\)
0.588869 + 0.808228i \(0.299573\pi\)
\(30\) 1.95660 0.357225
\(31\) −1.71568 −0.308146 −0.154073 0.988060i \(-0.549239\pi\)
−0.154073 + 0.988060i \(0.549239\pi\)
\(32\) 5.61777 0.993090
\(33\) −1.60281 −0.279013
\(34\) 0.617959 0.105979
\(35\) −0.621110 −0.104987
\(36\) −1.61813 −0.269688
\(37\) 6.10971 1.00443 0.502215 0.864743i \(-0.332519\pi\)
0.502215 + 0.864743i \(0.332519\pi\)
\(38\) −0.721338 −0.117016
\(39\) −1.04507 −0.167345
\(40\) −7.07924 −1.11933
\(41\) 3.43821 0.536958 0.268479 0.963286i \(-0.413479\pi\)
0.268479 + 0.963286i \(0.413479\pi\)
\(42\) −0.121223 −0.0187051
\(43\) 12.5282 1.91053 0.955265 0.295750i \(-0.0955694\pi\)
0.955265 + 0.295750i \(0.0955694\pi\)
\(44\) 2.59355 0.390992
\(45\) 3.16624 0.471995
\(46\) −0.0711002 −0.0104831
\(47\) −2.31797 −0.338111 −0.169055 0.985607i \(-0.554072\pi\)
−0.169055 + 0.985607i \(0.554072\pi\)
\(48\) 1.85459 0.267687
\(49\) −6.96152 −0.994503
\(50\) 3.10527 0.439152
\(51\) 1.00000 0.140028
\(52\) 1.69105 0.234507
\(53\) 10.5661 1.45136 0.725681 0.688031i \(-0.241525\pi\)
0.725681 + 0.688031i \(0.241525\pi\)
\(54\) 0.617959 0.0840936
\(55\) −5.07487 −0.684295
\(56\) 0.438600 0.0586104
\(57\) −1.16729 −0.154612
\(58\) 3.91929 0.514628
\(59\) 2.43259 0.316697 0.158348 0.987383i \(-0.449383\pi\)
0.158348 + 0.987383i \(0.449383\pi\)
\(60\) −5.12337 −0.661424
\(61\) −1.11029 −0.142158 −0.0710789 0.997471i \(-0.522644\pi\)
−0.0710789 + 0.997471i \(0.522644\pi\)
\(62\) −1.06022 −0.134648
\(63\) −0.196167 −0.0247147
\(64\) −0.237627 −0.0297034
\(65\) −3.30894 −0.410423
\(66\) −0.990470 −0.121918
\(67\) 9.11603 1.11370 0.556850 0.830613i \(-0.312010\pi\)
0.556850 + 0.830613i \(0.312010\pi\)
\(68\) −1.61813 −0.196227
\(69\) −0.115056 −0.0138512
\(70\) −0.383821 −0.0458753
\(71\) 7.31632 0.868288 0.434144 0.900844i \(-0.357051\pi\)
0.434144 + 0.900844i \(0.357051\pi\)
\(72\) −2.23585 −0.263498
\(73\) 7.19324 0.841905 0.420952 0.907083i \(-0.361696\pi\)
0.420952 + 0.907083i \(0.361696\pi\)
\(74\) 3.77555 0.438899
\(75\) 5.02505 0.580243
\(76\) 1.88883 0.216663
\(77\) 0.314418 0.0358312
\(78\) −0.645810 −0.0731235
\(79\) 1.00000 0.112509
\(80\) 5.87206 0.656517
\(81\) 1.00000 0.111111
\(82\) 2.12467 0.234631
\(83\) 1.78493 0.195922 0.0979609 0.995190i \(-0.468768\pi\)
0.0979609 + 0.995190i \(0.468768\pi\)
\(84\) 0.317423 0.0346337
\(85\) 3.16624 0.343427
\(86\) 7.74191 0.834831
\(87\) 6.34232 0.679968
\(88\) 3.58365 0.382018
\(89\) −11.2590 −1.19346 −0.596728 0.802443i \(-0.703533\pi\)
−0.596728 + 0.802443i \(0.703533\pi\)
\(90\) 1.95660 0.206244
\(91\) 0.205008 0.0214907
\(92\) 0.186176 0.0194102
\(93\) −1.71568 −0.177908
\(94\) −1.43241 −0.147742
\(95\) −3.69592 −0.379193
\(96\) 5.61777 0.573361
\(97\) 2.57631 0.261585 0.130792 0.991410i \(-0.458248\pi\)
0.130792 + 0.991410i \(0.458248\pi\)
\(98\) −4.30193 −0.434561
\(99\) −1.60281 −0.161088
\(100\) −8.13117 −0.813117
\(101\) −16.8118 −1.67284 −0.836421 0.548088i \(-0.815356\pi\)
−0.836421 + 0.548088i \(0.815356\pi\)
\(102\) 0.617959 0.0611870
\(103\) 11.4305 1.12628 0.563142 0.826360i \(-0.309592\pi\)
0.563142 + 0.826360i \(0.309592\pi\)
\(104\) 2.33662 0.229125
\(105\) −0.621110 −0.0606142
\(106\) 6.52940 0.634192
\(107\) 13.9546 1.34904 0.674521 0.738255i \(-0.264350\pi\)
0.674521 + 0.738255i \(0.264350\pi\)
\(108\) −1.61813 −0.155704
\(109\) −13.9968 −1.34065 −0.670324 0.742068i \(-0.733845\pi\)
−0.670324 + 0.742068i \(0.733845\pi\)
\(110\) −3.13606 −0.299012
\(111\) 6.10971 0.579908
\(112\) −0.363808 −0.0343767
\(113\) −14.0417 −1.32093 −0.660465 0.750857i \(-0.729641\pi\)
−0.660465 + 0.750857i \(0.729641\pi\)
\(114\) −0.721338 −0.0675595
\(115\) −0.364296 −0.0339708
\(116\) −10.2627 −0.952865
\(117\) −1.04507 −0.0966167
\(118\) 1.50324 0.138385
\(119\) −0.196167 −0.0179826
\(120\) −7.07924 −0.646243
\(121\) −8.43100 −0.766455
\(122\) −0.686112 −0.0621176
\(123\) 3.43821 0.310013
\(124\) 2.77619 0.249309
\(125\) 0.0793166 0.00709429
\(126\) −0.121223 −0.0107994
\(127\) 8.09640 0.718439 0.359220 0.933253i \(-0.383043\pi\)
0.359220 + 0.933253i \(0.383043\pi\)
\(128\) −11.3824 −1.00607
\(129\) 12.5282 1.10305
\(130\) −2.04479 −0.179340
\(131\) 15.2332 1.33093 0.665467 0.746427i \(-0.268232\pi\)
0.665467 + 0.746427i \(0.268232\pi\)
\(132\) 2.59355 0.225739
\(133\) 0.228984 0.0198554
\(134\) 5.63333 0.486646
\(135\) 3.16624 0.272506
\(136\) −2.23585 −0.191723
\(137\) 1.28533 0.109813 0.0549065 0.998492i \(-0.482514\pi\)
0.0549065 + 0.998492i \(0.482514\pi\)
\(138\) −0.0711002 −0.00605245
\(139\) 17.5726 1.49049 0.745246 0.666790i \(-0.232332\pi\)
0.745246 + 0.666790i \(0.232332\pi\)
\(140\) 1.00504 0.0849410
\(141\) −2.31797 −0.195208
\(142\) 4.52119 0.379409
\(143\) 1.67505 0.140074
\(144\) 1.85459 0.154549
\(145\) 20.0813 1.66766
\(146\) 4.44513 0.367881
\(147\) −6.96152 −0.574176
\(148\) −9.88628 −0.812647
\(149\) −6.01942 −0.493130 −0.246565 0.969126i \(-0.579302\pi\)
−0.246565 + 0.969126i \(0.579302\pi\)
\(150\) 3.10527 0.253545
\(151\) −3.52648 −0.286981 −0.143490 0.989652i \(-0.545833\pi\)
−0.143490 + 0.989652i \(0.545833\pi\)
\(152\) 2.60989 0.211690
\(153\) 1.00000 0.0808452
\(154\) 0.194297 0.0156569
\(155\) −5.43225 −0.436329
\(156\) 1.69105 0.135393
\(157\) 17.4114 1.38958 0.694792 0.719210i \(-0.255496\pi\)
0.694792 + 0.719210i \(0.255496\pi\)
\(158\) 0.617959 0.0491622
\(159\) 10.5661 0.837944
\(160\) 17.7872 1.40620
\(161\) 0.0225703 0.00177879
\(162\) 0.617959 0.0485514
\(163\) 2.48073 0.194306 0.0971530 0.995269i \(-0.469026\pi\)
0.0971530 + 0.995269i \(0.469026\pi\)
\(164\) −5.56346 −0.434433
\(165\) −5.07487 −0.395078
\(166\) 1.10302 0.0856106
\(167\) 11.6166 0.898919 0.449460 0.893301i \(-0.351617\pi\)
0.449460 + 0.893301i \(0.351617\pi\)
\(168\) 0.438600 0.0338387
\(169\) −11.9078 −0.915987
\(170\) 1.95660 0.150065
\(171\) −1.16729 −0.0892650
\(172\) −20.2722 −1.54574
\(173\) −23.0693 −1.75393 −0.876964 0.480556i \(-0.840435\pi\)
−0.876964 + 0.480556i \(0.840435\pi\)
\(174\) 3.91929 0.297121
\(175\) −0.985748 −0.0745155
\(176\) −2.97255 −0.224064
\(177\) 2.43259 0.182845
\(178\) −6.95763 −0.521496
\(179\) −17.6162 −1.31670 −0.658349 0.752713i \(-0.728745\pi\)
−0.658349 + 0.752713i \(0.728745\pi\)
\(180\) −5.12337 −0.381874
\(181\) −15.5593 −1.15651 −0.578257 0.815855i \(-0.696267\pi\)
−0.578257 + 0.815855i \(0.696267\pi\)
\(182\) 0.126686 0.00939062
\(183\) −1.11029 −0.0820748
\(184\) 0.257249 0.0189647
\(185\) 19.3448 1.42226
\(186\) −1.06022 −0.0777392
\(187\) −1.60281 −0.117209
\(188\) 3.75077 0.273553
\(189\) −0.196167 −0.0142690
\(190\) −2.28393 −0.165693
\(191\) 2.72217 0.196969 0.0984847 0.995139i \(-0.468600\pi\)
0.0984847 + 0.995139i \(0.468600\pi\)
\(192\) −0.237627 −0.0171493
\(193\) 18.4929 1.33115 0.665575 0.746331i \(-0.268186\pi\)
0.665575 + 0.746331i \(0.268186\pi\)
\(194\) 1.59205 0.114303
\(195\) −3.30894 −0.236958
\(196\) 11.2646 0.804616
\(197\) −2.56577 −0.182803 −0.0914017 0.995814i \(-0.529135\pi\)
−0.0914017 + 0.995814i \(0.529135\pi\)
\(198\) −0.990470 −0.0703896
\(199\) 21.8900 1.55174 0.775869 0.630894i \(-0.217312\pi\)
0.775869 + 0.630894i \(0.217312\pi\)
\(200\) −11.2353 −0.794454
\(201\) 9.11603 0.642995
\(202\) −10.3890 −0.730970
\(203\) −1.24415 −0.0873223
\(204\) −1.61813 −0.113292
\(205\) 10.8862 0.760324
\(206\) 7.06360 0.492144
\(207\) −0.115056 −0.00799698
\(208\) −1.93817 −0.134388
\(209\) 1.87094 0.129416
\(210\) −0.383821 −0.0264861
\(211\) −28.6231 −1.97049 −0.985246 0.171143i \(-0.945254\pi\)
−0.985246 + 0.171143i \(0.945254\pi\)
\(212\) −17.0973 −1.17424
\(213\) 7.31632 0.501306
\(214\) 8.62337 0.589482
\(215\) 39.6672 2.70528
\(216\) −2.23585 −0.152131
\(217\) 0.336560 0.0228472
\(218\) −8.64944 −0.585814
\(219\) 7.19324 0.486074
\(220\) 8.21178 0.553638
\(221\) −1.04507 −0.0702989
\(222\) 3.77555 0.253398
\(223\) 21.7230 1.45468 0.727338 0.686279i \(-0.240757\pi\)
0.727338 + 0.686279i \(0.240757\pi\)
\(224\) −1.10202 −0.0736317
\(225\) 5.02505 0.335003
\(226\) −8.67718 −0.577197
\(227\) −7.32807 −0.486381 −0.243191 0.969979i \(-0.578194\pi\)
−0.243191 + 0.969979i \(0.578194\pi\)
\(228\) 1.88883 0.125091
\(229\) −10.2333 −0.676236 −0.338118 0.941104i \(-0.609790\pi\)
−0.338118 + 0.941104i \(0.609790\pi\)
\(230\) −0.225120 −0.0148440
\(231\) 0.314418 0.0206872
\(232\) −14.1805 −0.930995
\(233\) −0.0697658 −0.00457051 −0.00228525 0.999997i \(-0.500727\pi\)
−0.00228525 + 0.999997i \(0.500727\pi\)
\(234\) −0.645810 −0.0422179
\(235\) −7.33924 −0.478759
\(236\) −3.93625 −0.256228
\(237\) 1.00000 0.0649570
\(238\) −0.121223 −0.00785772
\(239\) −11.6063 −0.750748 −0.375374 0.926873i \(-0.622486\pi\)
−0.375374 + 0.926873i \(0.622486\pi\)
\(240\) 5.87206 0.379040
\(241\) −23.1149 −1.48896 −0.744480 0.667644i \(-0.767303\pi\)
−0.744480 + 0.667644i \(0.767303\pi\)
\(242\) −5.21001 −0.334912
\(243\) 1.00000 0.0641500
\(244\) 1.79659 0.115015
\(245\) −22.0418 −1.40820
\(246\) 2.12467 0.135464
\(247\) 1.21990 0.0776204
\(248\) 3.83601 0.243587
\(249\) 1.78493 0.113116
\(250\) 0.0490144 0.00309994
\(251\) 27.4540 1.73288 0.866439 0.499282i \(-0.166403\pi\)
0.866439 + 0.499282i \(0.166403\pi\)
\(252\) 0.317423 0.0199957
\(253\) 0.184414 0.0115940
\(254\) 5.00324 0.313931
\(255\) 3.16624 0.198277
\(256\) −6.55859 −0.409912
\(257\) −13.3605 −0.833402 −0.416701 0.909044i \(-0.636814\pi\)
−0.416701 + 0.909044i \(0.636814\pi\)
\(258\) 7.74191 0.481990
\(259\) −1.19852 −0.0744725
\(260\) 5.35428 0.332058
\(261\) 6.34232 0.392580
\(262\) 9.41351 0.581569
\(263\) −1.22433 −0.0754957 −0.0377479 0.999287i \(-0.512018\pi\)
−0.0377479 + 0.999287i \(0.512018\pi\)
\(264\) 3.58365 0.220558
\(265\) 33.4547 2.05511
\(266\) 0.141503 0.00867608
\(267\) −11.2590 −0.689042
\(268\) −14.7509 −0.901054
\(269\) −1.59729 −0.0973883 −0.0486941 0.998814i \(-0.515506\pi\)
−0.0486941 + 0.998814i \(0.515506\pi\)
\(270\) 1.95660 0.119075
\(271\) −1.26090 −0.0765940 −0.0382970 0.999266i \(-0.512193\pi\)
−0.0382970 + 0.999266i \(0.512193\pi\)
\(272\) 1.85459 0.112451
\(273\) 0.205008 0.0124076
\(274\) 0.794280 0.0479842
\(275\) −8.05419 −0.485686
\(276\) 0.186176 0.0112065
\(277\) 18.8735 1.13400 0.567000 0.823718i \(-0.308104\pi\)
0.567000 + 0.823718i \(0.308104\pi\)
\(278\) 10.8592 0.651290
\(279\) −1.71568 −0.102715
\(280\) 1.38871 0.0829914
\(281\) 15.7499 0.939562 0.469781 0.882783i \(-0.344333\pi\)
0.469781 + 0.882783i \(0.344333\pi\)
\(282\) −1.43241 −0.0852988
\(283\) −23.4972 −1.39676 −0.698382 0.715725i \(-0.746096\pi\)
−0.698382 + 0.715725i \(0.746096\pi\)
\(284\) −11.8387 −0.702500
\(285\) −3.69592 −0.218927
\(286\) 1.03511 0.0612073
\(287\) −0.674462 −0.0398123
\(288\) 5.61777 0.331030
\(289\) 1.00000 0.0588235
\(290\) 12.4094 0.728705
\(291\) 2.57631 0.151026
\(292\) −11.6396 −0.681154
\(293\) −1.56352 −0.0913417 −0.0456708 0.998957i \(-0.514543\pi\)
−0.0456708 + 0.998957i \(0.514543\pi\)
\(294\) −4.30193 −0.250894
\(295\) 7.70217 0.448438
\(296\) −13.6604 −0.793995
\(297\) −1.60281 −0.0930044
\(298\) −3.71976 −0.215480
\(299\) 0.120242 0.00695377
\(300\) −8.13117 −0.469453
\(301\) −2.45761 −0.141655
\(302\) −2.17922 −0.125400
\(303\) −16.8118 −0.965815
\(304\) −2.16484 −0.124162
\(305\) −3.51543 −0.201293
\(306\) 0.617959 0.0353264
\(307\) −10.7601 −0.614113 −0.307057 0.951691i \(-0.599344\pi\)
−0.307057 + 0.951691i \(0.599344\pi\)
\(308\) −0.508768 −0.0289897
\(309\) 11.4305 0.650260
\(310\) −3.35691 −0.190660
\(311\) 2.34771 0.133126 0.0665632 0.997782i \(-0.478797\pi\)
0.0665632 + 0.997782i \(0.478797\pi\)
\(312\) 2.33662 0.132285
\(313\) −9.51827 −0.538004 −0.269002 0.963140i \(-0.586694\pi\)
−0.269002 + 0.963140i \(0.586694\pi\)
\(314\) 10.7596 0.607197
\(315\) −0.621110 −0.0349956
\(316\) −1.61813 −0.0910267
\(317\) −25.8917 −1.45422 −0.727110 0.686521i \(-0.759137\pi\)
−0.727110 + 0.686521i \(0.759137\pi\)
\(318\) 6.52940 0.366151
\(319\) −10.1655 −0.569160
\(320\) −0.752384 −0.0420595
\(321\) 13.9546 0.778870
\(322\) 0.0139475 0.000777263 0
\(323\) −1.16729 −0.0649498
\(324\) −1.61813 −0.0898959
\(325\) −5.25152 −0.291302
\(326\) 1.53299 0.0849045
\(327\) −13.9968 −0.774024
\(328\) −7.68733 −0.424462
\(329\) 0.454709 0.0250689
\(330\) −3.13606 −0.172634
\(331\) 12.2350 0.672499 0.336250 0.941773i \(-0.390841\pi\)
0.336250 + 0.941773i \(0.390841\pi\)
\(332\) −2.88825 −0.158513
\(333\) 6.10971 0.334810
\(334\) 7.17858 0.392794
\(335\) 28.8635 1.57698
\(336\) −0.363808 −0.0198474
\(337\) 25.4193 1.38468 0.692339 0.721573i \(-0.256580\pi\)
0.692339 + 0.721573i \(0.256580\pi\)
\(338\) −7.35855 −0.400252
\(339\) −14.0417 −0.762639
\(340\) −5.12337 −0.277854
\(341\) 2.74991 0.148916
\(342\) −0.721338 −0.0390055
\(343\) 2.73879 0.147881
\(344\) −28.0112 −1.51026
\(345\) −0.364296 −0.0196130
\(346\) −14.2559 −0.766401
\(347\) 11.3923 0.611570 0.305785 0.952101i \(-0.401081\pi\)
0.305785 + 0.952101i \(0.401081\pi\)
\(348\) −10.2627 −0.550137
\(349\) 20.4374 1.09399 0.546994 0.837136i \(-0.315772\pi\)
0.546994 + 0.837136i \(0.315772\pi\)
\(350\) −0.609152 −0.0325605
\(351\) −1.04507 −0.0557817
\(352\) −9.00420 −0.479926
\(353\) 29.5110 1.57071 0.785356 0.619044i \(-0.212480\pi\)
0.785356 + 0.619044i \(0.212480\pi\)
\(354\) 1.50324 0.0798965
\(355\) 23.1652 1.22948
\(356\) 18.2186 0.965582
\(357\) −0.196167 −0.0103822
\(358\) −10.8861 −0.575348
\(359\) −0.532636 −0.0281114 −0.0140557 0.999901i \(-0.504474\pi\)
−0.0140557 + 0.999901i \(0.504474\pi\)
\(360\) −7.07924 −0.373109
\(361\) −17.6374 −0.928286
\(362\) −9.61501 −0.505354
\(363\) −8.43100 −0.442513
\(364\) −0.331729 −0.0173873
\(365\) 22.7755 1.19212
\(366\) −0.686112 −0.0358636
\(367\) 16.1291 0.841930 0.420965 0.907077i \(-0.361692\pi\)
0.420965 + 0.907077i \(0.361692\pi\)
\(368\) −0.213382 −0.0111233
\(369\) 3.43821 0.178986
\(370\) 11.9543 0.621473
\(371\) −2.07271 −0.107610
\(372\) 2.77619 0.143939
\(373\) −14.0079 −0.725302 −0.362651 0.931925i \(-0.618128\pi\)
−0.362651 + 0.931925i \(0.618128\pi\)
\(374\) −0.990470 −0.0512160
\(375\) 0.0793166 0.00409589
\(376\) 5.18264 0.267274
\(377\) −6.62816 −0.341368
\(378\) −0.121223 −0.00623504
\(379\) −19.6415 −1.00892 −0.504458 0.863436i \(-0.668308\pi\)
−0.504458 + 0.863436i \(0.668308\pi\)
\(380\) 5.98047 0.306791
\(381\) 8.09640 0.414791
\(382\) 1.68219 0.0860684
\(383\) 18.6096 0.950906 0.475453 0.879741i \(-0.342284\pi\)
0.475453 + 0.879741i \(0.342284\pi\)
\(384\) −11.3824 −0.580854
\(385\) 0.995521 0.0507364
\(386\) 11.4279 0.581663
\(387\) 12.5282 0.636844
\(388\) −4.16880 −0.211639
\(389\) −19.0565 −0.966205 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(390\) −2.04479 −0.103542
\(391\) −0.115056 −0.00581866
\(392\) 15.5649 0.786148
\(393\) 15.2332 0.768415
\(394\) −1.58554 −0.0798783
\(395\) 3.16624 0.159311
\(396\) 2.59355 0.130331
\(397\) −28.2679 −1.41872 −0.709362 0.704844i \(-0.751017\pi\)
−0.709362 + 0.704844i \(0.751017\pi\)
\(398\) 13.5271 0.678052
\(399\) 0.228984 0.0114635
\(400\) 9.31940 0.465970
\(401\) 30.5463 1.52541 0.762704 0.646747i \(-0.223871\pi\)
0.762704 + 0.646747i \(0.223871\pi\)
\(402\) 5.63333 0.280965
\(403\) 1.79301 0.0893160
\(404\) 27.2037 1.35343
\(405\) 3.16624 0.157332
\(406\) −0.768835 −0.0381566
\(407\) −9.79269 −0.485406
\(408\) −2.23585 −0.110691
\(409\) 16.4649 0.814136 0.407068 0.913398i \(-0.366551\pi\)
0.407068 + 0.913398i \(0.366551\pi\)
\(410\) 6.72721 0.332233
\(411\) 1.28533 0.0634006
\(412\) −18.4960 −0.911235
\(413\) −0.477194 −0.0234812
\(414\) −0.0711002 −0.00349438
\(415\) 5.65152 0.277422
\(416\) −5.87095 −0.287847
\(417\) 17.5726 0.860536
\(418\) 1.15617 0.0565500
\(419\) −18.6467 −0.910952 −0.455476 0.890248i \(-0.650531\pi\)
−0.455476 + 0.890248i \(0.650531\pi\)
\(420\) 1.00504 0.0490407
\(421\) 31.5927 1.53973 0.769867 0.638204i \(-0.220322\pi\)
0.769867 + 0.638204i \(0.220322\pi\)
\(422\) −17.6879 −0.861032
\(423\) −2.31797 −0.112704
\(424\) −23.6242 −1.14729
\(425\) 5.02505 0.243751
\(426\) 4.52119 0.219052
\(427\) 0.217801 0.0105401
\(428\) −22.5803 −1.09146
\(429\) 1.67505 0.0808720
\(430\) 24.5127 1.18211
\(431\) 5.08958 0.245156 0.122578 0.992459i \(-0.460884\pi\)
0.122578 + 0.992459i \(0.460884\pi\)
\(432\) 1.85459 0.0892289
\(433\) −25.4887 −1.22491 −0.612455 0.790505i \(-0.709818\pi\)
−0.612455 + 0.790505i \(0.709818\pi\)
\(434\) 0.207980 0.00998336
\(435\) 20.0813 0.962823
\(436\) 22.6486 1.08467
\(437\) 0.134304 0.00642465
\(438\) 4.44513 0.212396
\(439\) −4.28434 −0.204480 −0.102240 0.994760i \(-0.532601\pi\)
−0.102240 + 0.994760i \(0.532601\pi\)
\(440\) 11.3467 0.540931
\(441\) −6.96152 −0.331501
\(442\) −0.645810 −0.0307180
\(443\) 28.2386 1.34166 0.670828 0.741613i \(-0.265939\pi\)
0.670828 + 0.741613i \(0.265939\pi\)
\(444\) −9.88628 −0.469182
\(445\) −35.6488 −1.68992
\(446\) 13.4239 0.635640
\(447\) −6.01942 −0.284709
\(448\) 0.0466146 0.00220233
\(449\) −8.37226 −0.395111 −0.197556 0.980292i \(-0.563300\pi\)
−0.197556 + 0.980292i \(0.563300\pi\)
\(450\) 3.10527 0.146384
\(451\) −5.51079 −0.259493
\(452\) 22.7212 1.06872
\(453\) −3.52648 −0.165689
\(454\) −4.52845 −0.212531
\(455\) 0.649103 0.0304304
\(456\) 2.60989 0.122219
\(457\) −15.6571 −0.732409 −0.366204 0.930534i \(-0.619343\pi\)
−0.366204 + 0.930534i \(0.619343\pi\)
\(458\) −6.32376 −0.295490
\(459\) 1.00000 0.0466760
\(460\) 0.589477 0.0274845
\(461\) 0.739633 0.0344482 0.0172241 0.999852i \(-0.494517\pi\)
0.0172241 + 0.999852i \(0.494517\pi\)
\(462\) 0.194297 0.00903953
\(463\) −5.41429 −0.251623 −0.125812 0.992054i \(-0.540153\pi\)
−0.125812 + 0.992054i \(0.540153\pi\)
\(464\) 11.7624 0.546055
\(465\) −5.43225 −0.251915
\(466\) −0.0431124 −0.00199714
\(467\) −9.91253 −0.458697 −0.229348 0.973344i \(-0.573660\pi\)
−0.229348 + 0.973344i \(0.573660\pi\)
\(468\) 1.69105 0.0781690
\(469\) −1.78826 −0.0825742
\(470\) −4.53535 −0.209200
\(471\) 17.4114 0.802277
\(472\) −5.43893 −0.250347
\(473\) −20.0803 −0.923293
\(474\) 0.617959 0.0283838
\(475\) −5.86570 −0.269137
\(476\) 0.317423 0.0145490
\(477\) 10.5661 0.483787
\(478\) −7.17220 −0.328049
\(479\) −5.53695 −0.252989 −0.126495 0.991967i \(-0.540373\pi\)
−0.126495 + 0.991967i \(0.540373\pi\)
\(480\) 17.7872 0.811870
\(481\) −6.38507 −0.291134
\(482\) −14.2841 −0.650621
\(483\) 0.0225703 0.00102698
\(484\) 13.6424 0.620111
\(485\) 8.15720 0.370400
\(486\) 0.617959 0.0280312
\(487\) −23.9481 −1.08519 −0.542596 0.839994i \(-0.682558\pi\)
−0.542596 + 0.839994i \(0.682558\pi\)
\(488\) 2.48244 0.112375
\(489\) 2.48073 0.112183
\(490\) −13.6209 −0.615331
\(491\) −29.3370 −1.32396 −0.661980 0.749521i \(-0.730284\pi\)
−0.661980 + 0.749521i \(0.730284\pi\)
\(492\) −5.56346 −0.250820
\(493\) 6.34232 0.285644
\(494\) 0.753848 0.0339172
\(495\) −5.07487 −0.228098
\(496\) −3.18188 −0.142871
\(497\) −1.43522 −0.0643784
\(498\) 1.10302 0.0494273
\(499\) −26.7345 −1.19680 −0.598400 0.801197i \(-0.704197\pi\)
−0.598400 + 0.801197i \(0.704197\pi\)
\(500\) −0.128344 −0.00573973
\(501\) 11.6166 0.518991
\(502\) 16.9654 0.757204
\(503\) −4.75319 −0.211934 −0.105967 0.994370i \(-0.533794\pi\)
−0.105967 + 0.994370i \(0.533794\pi\)
\(504\) 0.438600 0.0195368
\(505\) −53.2303 −2.36872
\(506\) 0.113960 0.00506614
\(507\) −11.9078 −0.528845
\(508\) −13.1010 −0.581263
\(509\) −0.0359670 −0.00159421 −0.000797104 1.00000i \(-0.500254\pi\)
−0.000797104 1.00000i \(0.500254\pi\)
\(510\) 1.95660 0.0866399
\(511\) −1.41107 −0.0624222
\(512\) 18.7118 0.826953
\(513\) −1.16729 −0.0515372
\(514\) −8.25621 −0.364166
\(515\) 36.1918 1.59480
\(516\) −20.2722 −0.892434
\(517\) 3.71526 0.163397
\(518\) −0.740637 −0.0325417
\(519\) −23.0693 −1.01263
\(520\) 7.39829 0.324437
\(521\) 30.0519 1.31660 0.658298 0.752757i \(-0.271277\pi\)
0.658298 + 0.752757i \(0.271277\pi\)
\(522\) 3.91929 0.171543
\(523\) 7.94136 0.347251 0.173626 0.984812i \(-0.444452\pi\)
0.173626 + 0.984812i \(0.444452\pi\)
\(524\) −24.6493 −1.07681
\(525\) −0.985748 −0.0430216
\(526\) −0.756589 −0.0329888
\(527\) −1.71568 −0.0747363
\(528\) −2.97255 −0.129364
\(529\) −22.9868 −0.999424
\(530\) 20.6736 0.898005
\(531\) 2.43259 0.105566
\(532\) −0.370525 −0.0160643
\(533\) −3.59317 −0.155637
\(534\) −6.95763 −0.301086
\(535\) 44.1836 1.91022
\(536\) −20.3821 −0.880373
\(537\) −17.6162 −0.760196
\(538\) −0.987057 −0.0425551
\(539\) 11.1580 0.480608
\(540\) −5.12337 −0.220475
\(541\) 36.4884 1.56876 0.784380 0.620281i \(-0.212981\pi\)
0.784380 + 0.620281i \(0.212981\pi\)
\(542\) −0.779182 −0.0334687
\(543\) −15.5593 −0.667713
\(544\) 5.61777 0.240860
\(545\) −44.3171 −1.89834
\(546\) 0.126686 0.00542168
\(547\) −26.7293 −1.14286 −0.571431 0.820650i \(-0.693611\pi\)
−0.571431 + 0.820650i \(0.693611\pi\)
\(548\) −2.07982 −0.0888457
\(549\) −1.11029 −0.0473859
\(550\) −4.97716 −0.212227
\(551\) −7.40333 −0.315392
\(552\) 0.257249 0.0109493
\(553\) −0.196167 −0.00834186
\(554\) 11.6631 0.495516
\(555\) 19.3448 0.821140
\(556\) −28.4348 −1.20590
\(557\) −4.77334 −0.202253 −0.101126 0.994874i \(-0.532245\pi\)
−0.101126 + 0.994874i \(0.532245\pi\)
\(558\) −1.06022 −0.0448827
\(559\) −13.0928 −0.553767
\(560\) −1.15190 −0.0486768
\(561\) −1.60281 −0.0676706
\(562\) 9.73281 0.410554
\(563\) 12.4910 0.526431 0.263215 0.964737i \(-0.415217\pi\)
0.263215 + 0.964737i \(0.415217\pi\)
\(564\) 3.75077 0.157936
\(565\) −44.4592 −1.87041
\(566\) −14.5203 −0.610334
\(567\) −0.196167 −0.00823823
\(568\) −16.3582 −0.686376
\(569\) 35.7826 1.50008 0.750042 0.661390i \(-0.230033\pi\)
0.750042 + 0.661390i \(0.230033\pi\)
\(570\) −2.28393 −0.0956632
\(571\) −4.08656 −0.171017 −0.0855086 0.996337i \(-0.527252\pi\)
−0.0855086 + 0.996337i \(0.527252\pi\)
\(572\) −2.71044 −0.113329
\(573\) 2.72217 0.113720
\(574\) −0.416790 −0.0173965
\(575\) −0.578165 −0.0241111
\(576\) −0.237627 −0.00990113
\(577\) 20.0692 0.835492 0.417746 0.908564i \(-0.362820\pi\)
0.417746 + 0.908564i \(0.362820\pi\)
\(578\) 0.617959 0.0257037
\(579\) 18.4929 0.768540
\(580\) −32.4940 −1.34924
\(581\) −0.350145 −0.0145264
\(582\) 1.59205 0.0659927
\(583\) −16.9354 −0.701393
\(584\) −16.0830 −0.665520
\(585\) −3.30894 −0.136808
\(586\) −0.966189 −0.0399129
\(587\) 28.7936 1.18844 0.594220 0.804303i \(-0.297461\pi\)
0.594220 + 0.804303i \(0.297461\pi\)
\(588\) 11.2646 0.464545
\(589\) 2.00270 0.0825198
\(590\) 4.75962 0.195951
\(591\) −2.56577 −0.105542
\(592\) 11.3310 0.465701
\(593\) −22.7560 −0.934475 −0.467238 0.884132i \(-0.654751\pi\)
−0.467238 + 0.884132i \(0.654751\pi\)
\(594\) −0.990470 −0.0406395
\(595\) −0.621110 −0.0254630
\(596\) 9.74019 0.398974
\(597\) 21.8900 0.895896
\(598\) 0.0743046 0.00303854
\(599\) 6.68465 0.273127 0.136564 0.990631i \(-0.456394\pi\)
0.136564 + 0.990631i \(0.456394\pi\)
\(600\) −11.2353 −0.458678
\(601\) −44.0129 −1.79532 −0.897661 0.440687i \(-0.854735\pi\)
−0.897661 + 0.440687i \(0.854735\pi\)
\(602\) −1.51870 −0.0618978
\(603\) 9.11603 0.371233
\(604\) 5.70629 0.232186
\(605\) −26.6946 −1.08529
\(606\) −10.3890 −0.422026
\(607\) −3.01812 −0.122502 −0.0612508 0.998122i \(-0.519509\pi\)
−0.0612508 + 0.998122i \(0.519509\pi\)
\(608\) −6.55757 −0.265945
\(609\) −1.24415 −0.0504156
\(610\) −2.17239 −0.0879576
\(611\) 2.42244 0.0980014
\(612\) −1.61813 −0.0654089
\(613\) −4.26320 −0.172189 −0.0860946 0.996287i \(-0.527439\pi\)
−0.0860946 + 0.996287i \(0.527439\pi\)
\(614\) −6.64932 −0.268345
\(615\) 10.8862 0.438973
\(616\) −0.702992 −0.0283244
\(617\) −48.7716 −1.96347 −0.981736 0.190250i \(-0.939070\pi\)
−0.981736 + 0.190250i \(0.939070\pi\)
\(618\) 7.06360 0.284140
\(619\) −35.7957 −1.43875 −0.719376 0.694621i \(-0.755572\pi\)
−0.719376 + 0.694621i \(0.755572\pi\)
\(620\) 8.79008 0.353018
\(621\) −0.115056 −0.00461706
\(622\) 1.45079 0.0581713
\(623\) 2.20865 0.0884877
\(624\) −1.93817 −0.0775890
\(625\) −24.8741 −0.994965
\(626\) −5.88190 −0.235088
\(627\) 1.87094 0.0747183
\(628\) −28.1739 −1.12426
\(629\) 6.10971 0.243610
\(630\) −0.383821 −0.0152918
\(631\) 0.772760 0.0307631 0.0153815 0.999882i \(-0.495104\pi\)
0.0153815 + 0.999882i \(0.495104\pi\)
\(632\) −2.23585 −0.0889375
\(633\) −28.6231 −1.13766
\(634\) −16.0000 −0.635440
\(635\) 25.6351 1.01730
\(636\) −17.0973 −0.677950
\(637\) 7.27527 0.288257
\(638\) −6.28187 −0.248702
\(639\) 7.31632 0.289429
\(640\) −36.0393 −1.42458
\(641\) 5.09923 0.201407 0.100704 0.994916i \(-0.467891\pi\)
0.100704 + 0.994916i \(0.467891\pi\)
\(642\) 8.62337 0.340337
\(643\) −8.23208 −0.324642 −0.162321 0.986738i \(-0.551898\pi\)
−0.162321 + 0.986738i \(0.551898\pi\)
\(644\) −0.0365215 −0.00143915
\(645\) 39.6672 1.56189
\(646\) −0.721338 −0.0283807
\(647\) 38.8970 1.52920 0.764599 0.644506i \(-0.222937\pi\)
0.764599 + 0.644506i \(0.222937\pi\)
\(648\) −2.23585 −0.0878326
\(649\) −3.89898 −0.153048
\(650\) −3.24523 −0.127288
\(651\) 0.336560 0.0131908
\(652\) −4.01414 −0.157206
\(653\) −6.42336 −0.251365 −0.125683 0.992070i \(-0.540112\pi\)
−0.125683 + 0.992070i \(0.540112\pi\)
\(654\) −8.64944 −0.338220
\(655\) 48.2320 1.88458
\(656\) 6.37646 0.248959
\(657\) 7.19324 0.280635
\(658\) 0.280991 0.0109542
\(659\) −3.79696 −0.147909 −0.0739543 0.997262i \(-0.523562\pi\)
−0.0739543 + 0.997262i \(0.523562\pi\)
\(660\) 8.21178 0.319643
\(661\) −17.2634 −0.671468 −0.335734 0.941957i \(-0.608984\pi\)
−0.335734 + 0.941957i \(0.608984\pi\)
\(662\) 7.56076 0.293857
\(663\) −1.04507 −0.0405871
\(664\) −3.99085 −0.154875
\(665\) 0.725017 0.0281149
\(666\) 3.77555 0.146300
\(667\) −0.729725 −0.0282551
\(668\) −18.7971 −0.727282
\(669\) 21.7230 0.839858
\(670\) 17.8365 0.689082
\(671\) 1.77958 0.0686998
\(672\) −1.10202 −0.0425113
\(673\) −12.6941 −0.489320 −0.244660 0.969609i \(-0.578676\pi\)
−0.244660 + 0.969609i \(0.578676\pi\)
\(674\) 15.7081 0.605053
\(675\) 5.02505 0.193414
\(676\) 19.2684 0.741092
\(677\) −6.23783 −0.239739 −0.119870 0.992790i \(-0.538248\pi\)
−0.119870 + 0.992790i \(0.538248\pi\)
\(678\) −8.67718 −0.333245
\(679\) −0.505386 −0.0193949
\(680\) −7.07924 −0.271476
\(681\) −7.32807 −0.280812
\(682\) 1.69933 0.0650707
\(683\) −16.4951 −0.631166 −0.315583 0.948898i \(-0.602200\pi\)
−0.315583 + 0.948898i \(0.602200\pi\)
\(684\) 1.88883 0.0722210
\(685\) 4.06965 0.155493
\(686\) 1.69246 0.0646183
\(687\) −10.2333 −0.390425
\(688\) 23.2346 0.885812
\(689\) −11.0423 −0.420677
\(690\) −0.225120 −0.00857017
\(691\) 6.37863 0.242654 0.121327 0.992613i \(-0.461285\pi\)
0.121327 + 0.992613i \(0.461285\pi\)
\(692\) 37.3291 1.41904
\(693\) 0.314418 0.0119437
\(694\) 7.03996 0.267233
\(695\) 55.6391 2.11051
\(696\) −14.1805 −0.537510
\(697\) 3.43821 0.130231
\(698\) 12.6295 0.478032
\(699\) −0.0697658 −0.00263878
\(700\) 1.59507 0.0602878
\(701\) −40.4775 −1.52882 −0.764408 0.644733i \(-0.776969\pi\)
−0.764408 + 0.644733i \(0.776969\pi\)
\(702\) −0.645810 −0.0243745
\(703\) −7.13181 −0.268981
\(704\) 0.380871 0.0143546
\(705\) −7.33924 −0.276412
\(706\) 18.2366 0.686343
\(707\) 3.29793 0.124031
\(708\) −3.93625 −0.147933
\(709\) 45.2526 1.69950 0.849749 0.527188i \(-0.176754\pi\)
0.849749 + 0.527188i \(0.176754\pi\)
\(710\) 14.3151 0.537238
\(711\) 1.00000 0.0375029
\(712\) 25.1736 0.943420
\(713\) 0.197400 0.00739270
\(714\) −0.121223 −0.00453666
\(715\) 5.30359 0.198343
\(716\) 28.5053 1.06529
\(717\) −11.6063 −0.433445
\(718\) −0.329147 −0.0122837
\(719\) −15.9816 −0.596015 −0.298007 0.954564i \(-0.596322\pi\)
−0.298007 + 0.954564i \(0.596322\pi\)
\(720\) 5.87206 0.218839
\(721\) −2.24229 −0.0835072
\(722\) −10.8992 −0.405626
\(723\) −23.1149 −0.859652
\(724\) 25.1769 0.935693
\(725\) 31.8705 1.18364
\(726\) −5.21001 −0.193362
\(727\) −12.7681 −0.473541 −0.236771 0.971566i \(-0.576089\pi\)
−0.236771 + 0.971566i \(0.576089\pi\)
\(728\) −0.458367 −0.0169882
\(729\) 1.00000 0.0370370
\(730\) 14.0743 0.520914
\(731\) 12.5282 0.463372
\(732\) 1.79659 0.0664037
\(733\) −49.2623 −1.81955 −0.909773 0.415107i \(-0.863744\pi\)
−0.909773 + 0.415107i \(0.863744\pi\)
\(734\) 9.96710 0.367892
\(735\) −22.0418 −0.813024
\(736\) −0.646360 −0.0238252
\(737\) −14.6112 −0.538212
\(738\) 2.12467 0.0782103
\(739\) −37.0887 −1.36433 −0.682165 0.731198i \(-0.738961\pi\)
−0.682165 + 0.731198i \(0.738961\pi\)
\(740\) −31.3023 −1.15070
\(741\) 1.21990 0.0448141
\(742\) −1.28085 −0.0470215
\(743\) −43.6284 −1.60057 −0.800286 0.599618i \(-0.795319\pi\)
−0.800286 + 0.599618i \(0.795319\pi\)
\(744\) 3.83601 0.140635
\(745\) −19.0589 −0.698265
\(746\) −8.65632 −0.316930
\(747\) 1.78493 0.0653073
\(748\) 2.59355 0.0948295
\(749\) −2.73743 −0.100024
\(750\) 0.0490144 0.00178975
\(751\) −46.0139 −1.67907 −0.839535 0.543305i \(-0.817173\pi\)
−0.839535 + 0.543305i \(0.817173\pi\)
\(752\) −4.29888 −0.156764
\(753\) 27.4540 1.00048
\(754\) −4.09593 −0.149165
\(755\) −11.1657 −0.406360
\(756\) 0.317423 0.0115446
\(757\) 9.17048 0.333307 0.166653 0.986016i \(-0.446704\pi\)
0.166653 + 0.986016i \(0.446704\pi\)
\(758\) −12.1376 −0.440859
\(759\) 0.184414 0.00669379
\(760\) 8.26354 0.299750
\(761\) 23.7141 0.859636 0.429818 0.902916i \(-0.358578\pi\)
0.429818 + 0.902916i \(0.358578\pi\)
\(762\) 5.00324 0.181248
\(763\) 2.74570 0.0994011
\(764\) −4.40482 −0.159361
\(765\) 3.16624 0.114476
\(766\) 11.5000 0.415511
\(767\) −2.54223 −0.0917946
\(768\) −6.55859 −0.236663
\(769\) −24.5122 −0.883932 −0.441966 0.897032i \(-0.645719\pi\)
−0.441966 + 0.897032i \(0.645719\pi\)
\(770\) 0.615191 0.0221699
\(771\) −13.3605 −0.481165
\(772\) −29.9239 −1.07698
\(773\) 3.47380 0.124944 0.0624720 0.998047i \(-0.480102\pi\)
0.0624720 + 0.998047i \(0.480102\pi\)
\(774\) 7.74191 0.278277
\(775\) −8.62139 −0.309689
\(776\) −5.76025 −0.206781
\(777\) −1.19852 −0.0429967
\(778\) −11.7762 −0.422196
\(779\) −4.01339 −0.143795
\(780\) 5.35428 0.191714
\(781\) −11.7267 −0.419613
\(782\) −0.0711002 −0.00254254
\(783\) 6.34232 0.226656
\(784\) −12.9107 −0.461098
\(785\) 55.1287 1.96763
\(786\) 9.41351 0.335769
\(787\) 9.55063 0.340443 0.170222 0.985406i \(-0.445552\pi\)
0.170222 + 0.985406i \(0.445552\pi\)
\(788\) 4.15174 0.147899
\(789\) −1.22433 −0.0435875
\(790\) 1.95660 0.0696128
\(791\) 2.75451 0.0979391
\(792\) 3.58365 0.127339
\(793\) 1.16033 0.0412044
\(794\) −17.4684 −0.619930
\(795\) 33.4547 1.18652
\(796\) −35.4207 −1.25545
\(797\) 8.61101 0.305018 0.152509 0.988302i \(-0.451265\pi\)
0.152509 + 0.988302i \(0.451265\pi\)
\(798\) 0.141503 0.00500914
\(799\) −2.31797 −0.0820039
\(800\) 28.2296 0.998066
\(801\) −11.2590 −0.397819
\(802\) 18.8763 0.666547
\(803\) −11.5294 −0.406863
\(804\) −14.7509 −0.520224
\(805\) 0.0714628 0.00251873
\(806\) 1.10800 0.0390278
\(807\) −1.59729 −0.0562271
\(808\) 37.5888 1.32237
\(809\) 50.6875 1.78208 0.891039 0.453927i \(-0.149977\pi\)
0.891039 + 0.453927i \(0.149977\pi\)
\(810\) 1.95660 0.0687480
\(811\) −40.5563 −1.42412 −0.712062 0.702116i \(-0.752239\pi\)
−0.712062 + 0.702116i \(0.752239\pi\)
\(812\) 2.01320 0.0706493
\(813\) −1.26090 −0.0442216
\(814\) −6.05148 −0.212104
\(815\) 7.85459 0.275134
\(816\) 1.85459 0.0649236
\(817\) −14.6240 −0.511631
\(818\) 10.1746 0.355747
\(819\) 0.205008 0.00716355
\(820\) −17.6152 −0.615150
\(821\) 37.6706 1.31471 0.657356 0.753580i \(-0.271675\pi\)
0.657356 + 0.753580i \(0.271675\pi\)
\(822\) 0.794280 0.0277037
\(823\) −19.2670 −0.671606 −0.335803 0.941932i \(-0.609008\pi\)
−0.335803 + 0.941932i \(0.609008\pi\)
\(824\) −25.5570 −0.890320
\(825\) −8.05419 −0.280411
\(826\) −0.294886 −0.0102604
\(827\) 37.2925 1.29679 0.648393 0.761306i \(-0.275441\pi\)
0.648393 + 0.761306i \(0.275441\pi\)
\(828\) 0.186176 0.00647006
\(829\) −24.0886 −0.836631 −0.418316 0.908302i \(-0.637379\pi\)
−0.418316 + 0.908302i \(0.637379\pi\)
\(830\) 3.49241 0.121223
\(831\) 18.8735 0.654715
\(832\) 0.248337 0.00860953
\(833\) −6.96152 −0.241202
\(834\) 10.8592 0.376022
\(835\) 36.7809 1.27285
\(836\) −3.02743 −0.104706
\(837\) −1.71568 −0.0593026
\(838\) −11.5229 −0.398052
\(839\) −17.7381 −0.612388 −0.306194 0.951969i \(-0.599056\pi\)
−0.306194 + 0.951969i \(0.599056\pi\)
\(840\) 1.38871 0.0479151
\(841\) 11.2250 0.387068
\(842\) 19.5230 0.672807
\(843\) 15.7499 0.542456
\(844\) 46.3157 1.59425
\(845\) −37.7030 −1.29702
\(846\) −1.43241 −0.0492473
\(847\) 1.65388 0.0568281
\(848\) 19.5957 0.672920
\(849\) −23.4972 −0.806422
\(850\) 3.10527 0.106510
\(851\) −0.702961 −0.0240972
\(852\) −11.8387 −0.405588
\(853\) −4.87180 −0.166807 −0.0834037 0.996516i \(-0.526579\pi\)
−0.0834037 + 0.996516i \(0.526579\pi\)
\(854\) 0.134592 0.00460565
\(855\) −3.69592 −0.126398
\(856\) −31.2005 −1.06641
\(857\) 42.5821 1.45458 0.727289 0.686331i \(-0.240780\pi\)
0.727289 + 0.686331i \(0.240780\pi\)
\(858\) 1.03511 0.0353380
\(859\) 37.0814 1.26520 0.632600 0.774479i \(-0.281988\pi\)
0.632600 + 0.774479i \(0.281988\pi\)
\(860\) −64.1866 −2.18874
\(861\) −0.674462 −0.0229856
\(862\) 3.14515 0.107124
\(863\) 9.01460 0.306861 0.153430 0.988159i \(-0.450968\pi\)
0.153430 + 0.988159i \(0.450968\pi\)
\(864\) 5.61777 0.191120
\(865\) −73.0429 −2.48353
\(866\) −15.7510 −0.535240
\(867\) 1.00000 0.0339618
\(868\) −0.544596 −0.0184848
\(869\) −1.60281 −0.0543716
\(870\) 12.4094 0.420718
\(871\) −9.52688 −0.322806
\(872\) 31.2948 1.05977
\(873\) 2.57631 0.0871949
\(874\) 0.0829946 0.00280733
\(875\) −0.0155593 −0.000526000 0
\(876\) −11.6396 −0.393265
\(877\) −56.1196 −1.89503 −0.947513 0.319718i \(-0.896412\pi\)
−0.947513 + 0.319718i \(0.896412\pi\)
\(878\) −2.64754 −0.0893503
\(879\) −1.56352 −0.0527361
\(880\) −9.41179 −0.317271
\(881\) −16.2482 −0.547415 −0.273707 0.961813i \(-0.588250\pi\)
−0.273707 + 0.961813i \(0.588250\pi\)
\(882\) −4.30193 −0.144854
\(883\) −45.5590 −1.53318 −0.766591 0.642136i \(-0.778049\pi\)
−0.766591 + 0.642136i \(0.778049\pi\)
\(884\) 1.69105 0.0568763
\(885\) 7.70217 0.258906
\(886\) 17.4503 0.586254
\(887\) 27.7332 0.931188 0.465594 0.884998i \(-0.345841\pi\)
0.465594 + 0.884998i \(0.345841\pi\)
\(888\) −13.6604 −0.458413
\(889\) −1.58824 −0.0532680
\(890\) −22.0295 −0.738430
\(891\) −1.60281 −0.0536961
\(892\) −35.1505 −1.17693
\(893\) 2.70575 0.0905443
\(894\) −3.71976 −0.124407
\(895\) −55.7771 −1.86442
\(896\) 2.23284 0.0745941
\(897\) 0.120242 0.00401476
\(898\) −5.17371 −0.172649
\(899\) −10.8814 −0.362915
\(900\) −8.13117 −0.271039
\(901\) 10.5661 0.352007
\(902\) −3.40544 −0.113389
\(903\) −2.45761 −0.0817843
\(904\) 31.3951 1.04419
\(905\) −49.2644 −1.63760
\(906\) −2.17922 −0.0723998
\(907\) −38.9730 −1.29408 −0.647038 0.762458i \(-0.723993\pi\)
−0.647038 + 0.762458i \(0.723993\pi\)
\(908\) 11.8577 0.393513
\(909\) −16.8118 −0.557614
\(910\) 0.401119 0.0132970
\(911\) −11.6704 −0.386657 −0.193328 0.981134i \(-0.561928\pi\)
−0.193328 + 0.981134i \(0.561928\pi\)
\(912\) −2.16484 −0.0716852
\(913\) −2.86091 −0.0946822
\(914\) −9.67545 −0.320035
\(915\) −3.51543 −0.116217
\(916\) 16.5588 0.547118
\(917\) −2.98825 −0.0986808
\(918\) 0.617959 0.0203957
\(919\) −35.4366 −1.16895 −0.584473 0.811413i \(-0.698699\pi\)
−0.584473 + 0.811413i \(0.698699\pi\)
\(920\) 0.814513 0.0268537
\(921\) −10.7601 −0.354558
\(922\) 0.457063 0.0150526
\(923\) −7.64606 −0.251673
\(924\) −0.508768 −0.0167372
\(925\) 30.7016 1.00946
\(926\) −3.34581 −0.109950
\(927\) 11.4305 0.375428
\(928\) 35.6297 1.16960
\(929\) −1.07006 −0.0351076 −0.0175538 0.999846i \(-0.505588\pi\)
−0.0175538 + 0.999846i \(0.505588\pi\)
\(930\) −3.35691 −0.110077
\(931\) 8.12612 0.266323
\(932\) 0.112890 0.00369783
\(933\) 2.34771 0.0768605
\(934\) −6.12553 −0.200434
\(935\) −5.07487 −0.165966
\(936\) 2.33662 0.0763749
\(937\) 34.7158 1.13412 0.567058 0.823678i \(-0.308081\pi\)
0.567058 + 0.823678i \(0.308081\pi\)
\(938\) −1.10507 −0.0360819
\(939\) −9.51827 −0.310617
\(940\) 11.8758 0.387347
\(941\) 26.9717 0.879253 0.439627 0.898181i \(-0.355111\pi\)
0.439627 + 0.898181i \(0.355111\pi\)
\(942\) 10.7596 0.350565
\(943\) −0.395588 −0.0128821
\(944\) 4.51146 0.146836
\(945\) −0.621110 −0.0202047
\(946\) −12.4088 −0.403445
\(947\) 3.65450 0.118755 0.0593776 0.998236i \(-0.481088\pi\)
0.0593776 + 0.998236i \(0.481088\pi\)
\(948\) −1.61813 −0.0525543
\(949\) −7.51743 −0.244026
\(950\) −3.62476 −0.117603
\(951\) −25.8917 −0.839594
\(952\) 0.438600 0.0142151
\(953\) −18.3292 −0.593742 −0.296871 0.954918i \(-0.595943\pi\)
−0.296871 + 0.954918i \(0.595943\pi\)
\(954\) 6.52940 0.211397
\(955\) 8.61904 0.278906
\(956\) 18.7804 0.607403
\(957\) −10.1655 −0.328605
\(958\) −3.42160 −0.110547
\(959\) −0.252139 −0.00814198
\(960\) −0.752384 −0.0242831
\(961\) −28.0564 −0.905046
\(962\) −3.94571 −0.127215
\(963\) 13.9546 0.449681
\(964\) 37.4028 1.20466
\(965\) 58.5530 1.88489
\(966\) 0.0139475 0.000448753 0
\(967\) 15.2000 0.488798 0.244399 0.969675i \(-0.421409\pi\)
0.244399 + 0.969675i \(0.421409\pi\)
\(968\) 18.8505 0.605878
\(969\) −1.16729 −0.0374988
\(970\) 5.04082 0.161851
\(971\) 21.3639 0.685599 0.342800 0.939409i \(-0.388625\pi\)
0.342800 + 0.939409i \(0.388625\pi\)
\(972\) −1.61813 −0.0519014
\(973\) −3.44717 −0.110511
\(974\) −14.7989 −0.474189
\(975\) −5.25152 −0.168183
\(976\) −2.05913 −0.0659110
\(977\) 0.662290 0.0211885 0.0105943 0.999944i \(-0.496628\pi\)
0.0105943 + 0.999944i \(0.496628\pi\)
\(978\) 1.53299 0.0490196
\(979\) 18.0461 0.576756
\(980\) 35.6664 1.13932
\(981\) −13.9968 −0.446883
\(982\) −18.1291 −0.578522
\(983\) −51.8503 −1.65377 −0.826883 0.562373i \(-0.809888\pi\)
−0.826883 + 0.562373i \(0.809888\pi\)
\(984\) −7.68733 −0.245063
\(985\) −8.12382 −0.258847
\(986\) 3.91929 0.124816
\(987\) 0.454709 0.0144735
\(988\) −1.97395 −0.0627998
\(989\) −1.44145 −0.0458354
\(990\) −3.13606 −0.0996706
\(991\) 34.0048 1.08020 0.540099 0.841601i \(-0.318387\pi\)
0.540099 + 0.841601i \(0.318387\pi\)
\(992\) −9.63830 −0.306016
\(993\) 12.2350 0.388268
\(994\) −0.886906 −0.0281310
\(995\) 69.3088 2.19724
\(996\) −2.88825 −0.0915176
\(997\) −10.8324 −0.343064 −0.171532 0.985179i \(-0.554872\pi\)
−0.171532 + 0.985179i \(0.554872\pi\)
\(998\) −16.5208 −0.522957
\(999\) 6.10971 0.193303
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 4029.2.a.k.1.18 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.18 31 1.1 even 1 trivial