Properties

Label 4023.2.a.e.1.4
Level $4023$
Weight $2$
Character 4023.1
Self dual yes
Analytic conductor $32.124$
Analytic rank $1$
Dimension $25$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4023,2,Mod(1,4023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4023.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.1238167332\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 4023.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.45057 q^{2} +4.00528 q^{4} -3.55507 q^{5} -0.769224 q^{7} -4.91408 q^{8} +O(q^{10})\) \(q-2.45057 q^{2} +4.00528 q^{4} -3.55507 q^{5} -0.769224 q^{7} -4.91408 q^{8} +8.71195 q^{10} -5.40475 q^{11} -2.95178 q^{13} +1.88504 q^{14} +4.03173 q^{16} +8.13105 q^{17} -2.72141 q^{19} -14.2391 q^{20} +13.2447 q^{22} -6.87800 q^{23} +7.63854 q^{25} +7.23354 q^{26} -3.08096 q^{28} +1.15735 q^{29} +10.1050 q^{31} -0.0518563 q^{32} -19.9257 q^{34} +2.73465 q^{35} +8.27148 q^{37} +6.66901 q^{38} +17.4699 q^{40} -3.54033 q^{41} +4.30894 q^{43} -21.6476 q^{44} +16.8550 q^{46} -5.42366 q^{47} -6.40829 q^{49} -18.7188 q^{50} -11.8227 q^{52} +10.4404 q^{53} +19.2143 q^{55} +3.78003 q^{56} -2.83617 q^{58} +1.20453 q^{59} +8.45572 q^{61} -24.7630 q^{62} -7.93638 q^{64} +10.4938 q^{65} +12.6559 q^{67} +32.5671 q^{68} -6.70144 q^{70} +1.70667 q^{71} -15.0915 q^{73} -20.2698 q^{74} -10.9000 q^{76} +4.15746 q^{77} -6.79249 q^{79} -14.3331 q^{80} +8.67581 q^{82} +9.19144 q^{83} -28.9065 q^{85} -10.5594 q^{86} +26.5594 q^{88} +5.62099 q^{89} +2.27058 q^{91} -27.5483 q^{92} +13.2910 q^{94} +9.67482 q^{95} -1.92333 q^{97} +15.7040 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 7 q^{2} + 27 q^{4} - 12 q^{5} - 2 q^{7} - 21 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 7 q^{2} + 27 q^{4} - 12 q^{5} - 2 q^{7} - 21 q^{8} - 4 q^{10} - 12 q^{11} - 10 q^{14} + 35 q^{16} - 26 q^{17} - 30 q^{20} + 8 q^{22} - 26 q^{23} + 27 q^{25} - 16 q^{26} + 4 q^{28} - 20 q^{29} - 6 q^{31} - 49 q^{32} - 14 q^{34} - 16 q^{35} - 2 q^{37} - 27 q^{38} + 2 q^{40} - 35 q^{41} + 4 q^{43} - 22 q^{44} + 6 q^{46} - 38 q^{47} + 19 q^{49} - 22 q^{50} + 4 q^{52} - 36 q^{53} + 10 q^{55} - 79 q^{56} - 22 q^{58} - 15 q^{59} + 10 q^{61} + 14 q^{62} + 41 q^{64} - 80 q^{65} - 6 q^{67} - 33 q^{68} + 8 q^{70} - 26 q^{71} - 6 q^{73} - 75 q^{74} - 10 q^{76} - 47 q^{77} - 6 q^{79} - 66 q^{80} + 12 q^{82} - 40 q^{83} - 12 q^{85} - 4 q^{86} + 12 q^{88} - 30 q^{89} - 158 q^{92} + 18 q^{94} - 22 q^{95} - 20 q^{97} - 35 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45057 −1.73281 −0.866407 0.499339i \(-0.833576\pi\)
−0.866407 + 0.499339i \(0.833576\pi\)
\(3\) 0 0
\(4\) 4.00528 2.00264
\(5\) −3.55507 −1.58988 −0.794938 0.606690i \(-0.792497\pi\)
−0.794938 + 0.606690i \(0.792497\pi\)
\(6\) 0 0
\(7\) −0.769224 −0.290739 −0.145370 0.989377i \(-0.546437\pi\)
−0.145370 + 0.989377i \(0.546437\pi\)
\(8\) −4.91408 −1.73739
\(9\) 0 0
\(10\) 8.71195 2.75496
\(11\) −5.40475 −1.62959 −0.814797 0.579746i \(-0.803152\pi\)
−0.814797 + 0.579746i \(0.803152\pi\)
\(12\) 0 0
\(13\) −2.95178 −0.818677 −0.409338 0.912383i \(-0.634240\pi\)
−0.409338 + 0.912383i \(0.634240\pi\)
\(14\) 1.88504 0.503797
\(15\) 0 0
\(16\) 4.03173 1.00793
\(17\) 8.13105 1.97207 0.986034 0.166542i \(-0.0532603\pi\)
0.986034 + 0.166542i \(0.0532603\pi\)
\(18\) 0 0
\(19\) −2.72141 −0.624335 −0.312168 0.950027i \(-0.601055\pi\)
−0.312168 + 0.950027i \(0.601055\pi\)
\(20\) −14.2391 −3.18395
\(21\) 0 0
\(22\) 13.2447 2.82378
\(23\) −6.87800 −1.43416 −0.717081 0.696990i \(-0.754522\pi\)
−0.717081 + 0.696990i \(0.754522\pi\)
\(24\) 0 0
\(25\) 7.63854 1.52771
\(26\) 7.23354 1.41861
\(27\) 0 0
\(28\) −3.08096 −0.582247
\(29\) 1.15735 0.214915 0.107457 0.994210i \(-0.465729\pi\)
0.107457 + 0.994210i \(0.465729\pi\)
\(30\) 0 0
\(31\) 10.1050 1.81492 0.907458 0.420143i \(-0.138020\pi\)
0.907458 + 0.420143i \(0.138020\pi\)
\(32\) −0.0518563 −0.00916699
\(33\) 0 0
\(34\) −19.9257 −3.41723
\(35\) 2.73465 0.462240
\(36\) 0 0
\(37\) 8.27148 1.35982 0.679911 0.733294i \(-0.262018\pi\)
0.679911 + 0.733294i \(0.262018\pi\)
\(38\) 6.66901 1.08186
\(39\) 0 0
\(40\) 17.4699 2.76224
\(41\) −3.54033 −0.552906 −0.276453 0.961027i \(-0.589159\pi\)
−0.276453 + 0.961027i \(0.589159\pi\)
\(42\) 0 0
\(43\) 4.30894 0.657107 0.328554 0.944485i \(-0.393439\pi\)
0.328554 + 0.944485i \(0.393439\pi\)
\(44\) −21.6476 −3.26349
\(45\) 0 0
\(46\) 16.8550 2.48513
\(47\) −5.42366 −0.791122 −0.395561 0.918440i \(-0.629450\pi\)
−0.395561 + 0.918440i \(0.629450\pi\)
\(48\) 0 0
\(49\) −6.40829 −0.915471
\(50\) −18.7188 −2.64723
\(51\) 0 0
\(52\) −11.8227 −1.63952
\(53\) 10.4404 1.43410 0.717052 0.697019i \(-0.245491\pi\)
0.717052 + 0.697019i \(0.245491\pi\)
\(54\) 0 0
\(55\) 19.2143 2.59085
\(56\) 3.78003 0.505128
\(57\) 0 0
\(58\) −2.83617 −0.372407
\(59\) 1.20453 0.156817 0.0784084 0.996921i \(-0.475016\pi\)
0.0784084 + 0.996921i \(0.475016\pi\)
\(60\) 0 0
\(61\) 8.45572 1.08264 0.541322 0.840815i \(-0.317924\pi\)
0.541322 + 0.840815i \(0.317924\pi\)
\(62\) −24.7630 −3.14491
\(63\) 0 0
\(64\) −7.93638 −0.992047
\(65\) 10.4938 1.30160
\(66\) 0 0
\(67\) 12.6559 1.54616 0.773080 0.634308i \(-0.218715\pi\)
0.773080 + 0.634308i \(0.218715\pi\)
\(68\) 32.5671 3.94935
\(69\) 0 0
\(70\) −6.70144 −0.800975
\(71\) 1.70667 0.202544 0.101272 0.994859i \(-0.467709\pi\)
0.101272 + 0.994859i \(0.467709\pi\)
\(72\) 0 0
\(73\) −15.0915 −1.76633 −0.883165 0.469062i \(-0.844592\pi\)
−0.883165 + 0.469062i \(0.844592\pi\)
\(74\) −20.2698 −2.35632
\(75\) 0 0
\(76\) −10.9000 −1.25032
\(77\) 4.15746 0.473787
\(78\) 0 0
\(79\) −6.79249 −0.764215 −0.382107 0.924118i \(-0.624802\pi\)
−0.382107 + 0.924118i \(0.624802\pi\)
\(80\) −14.3331 −1.60249
\(81\) 0 0
\(82\) 8.67581 0.958083
\(83\) 9.19144 1.00889 0.504446 0.863443i \(-0.331697\pi\)
0.504446 + 0.863443i \(0.331697\pi\)
\(84\) 0 0
\(85\) −28.9065 −3.13535
\(86\) −10.5594 −1.13864
\(87\) 0 0
\(88\) 26.5594 2.83124
\(89\) 5.62099 0.595824 0.297912 0.954593i \(-0.403710\pi\)
0.297912 + 0.954593i \(0.403710\pi\)
\(90\) 0 0
\(91\) 2.27058 0.238021
\(92\) −27.5483 −2.87211
\(93\) 0 0
\(94\) 13.2910 1.37087
\(95\) 9.67482 0.992616
\(96\) 0 0
\(97\) −1.92333 −0.195285 −0.0976423 0.995222i \(-0.531130\pi\)
−0.0976423 + 0.995222i \(0.531130\pi\)
\(98\) 15.7040 1.58634
\(99\) 0 0
\(100\) 30.5945 3.05945
\(101\) 14.7860 1.47126 0.735629 0.677384i \(-0.236887\pi\)
0.735629 + 0.677384i \(0.236887\pi\)
\(102\) 0 0
\(103\) −14.5561 −1.43425 −0.717127 0.696942i \(-0.754543\pi\)
−0.717127 + 0.696942i \(0.754543\pi\)
\(104\) 14.5053 1.42236
\(105\) 0 0
\(106\) −25.5850 −2.48504
\(107\) 11.3547 1.09770 0.548849 0.835921i \(-0.315066\pi\)
0.548849 + 0.835921i \(0.315066\pi\)
\(108\) 0 0
\(109\) −19.8487 −1.90116 −0.950579 0.310482i \(-0.899509\pi\)
−0.950579 + 0.310482i \(0.899509\pi\)
\(110\) −47.0859 −4.48947
\(111\) 0 0
\(112\) −3.10130 −0.293045
\(113\) −15.8171 −1.48795 −0.743974 0.668208i \(-0.767062\pi\)
−0.743974 + 0.668208i \(0.767062\pi\)
\(114\) 0 0
\(115\) 24.4518 2.28014
\(116\) 4.63552 0.430397
\(117\) 0 0
\(118\) −2.95179 −0.271734
\(119\) −6.25459 −0.573358
\(120\) 0 0
\(121\) 18.2113 1.65558
\(122\) −20.7213 −1.87602
\(123\) 0 0
\(124\) 40.4735 3.63463
\(125\) −9.38020 −0.838990
\(126\) 0 0
\(127\) 5.52807 0.490537 0.245269 0.969455i \(-0.421124\pi\)
0.245269 + 0.969455i \(0.421124\pi\)
\(128\) 19.5523 1.72820
\(129\) 0 0
\(130\) −25.7158 −2.25542
\(131\) 13.6262 1.19052 0.595261 0.803532i \(-0.297049\pi\)
0.595261 + 0.803532i \(0.297049\pi\)
\(132\) 0 0
\(133\) 2.09338 0.181519
\(134\) −31.0141 −2.67921
\(135\) 0 0
\(136\) −39.9566 −3.42625
\(137\) −20.0632 −1.71411 −0.857056 0.515224i \(-0.827709\pi\)
−0.857056 + 0.515224i \(0.827709\pi\)
\(138\) 0 0
\(139\) −8.32109 −0.705786 −0.352893 0.935664i \(-0.614802\pi\)
−0.352893 + 0.935664i \(0.614802\pi\)
\(140\) 10.9530 0.925700
\(141\) 0 0
\(142\) −4.18231 −0.350972
\(143\) 15.9536 1.33411
\(144\) 0 0
\(145\) −4.11447 −0.341688
\(146\) 36.9828 3.06072
\(147\) 0 0
\(148\) 33.1296 2.72324
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) 14.7367 1.19926 0.599628 0.800279i \(-0.295315\pi\)
0.599628 + 0.800279i \(0.295315\pi\)
\(152\) 13.3733 1.08471
\(153\) 0 0
\(154\) −10.1881 −0.820984
\(155\) −35.9241 −2.88549
\(156\) 0 0
\(157\) 1.87623 0.149740 0.0748698 0.997193i \(-0.476146\pi\)
0.0748698 + 0.997193i \(0.476146\pi\)
\(158\) 16.6455 1.32424
\(159\) 0 0
\(160\) 0.184353 0.0145744
\(161\) 5.29072 0.416967
\(162\) 0 0
\(163\) −5.04253 −0.394961 −0.197481 0.980307i \(-0.563276\pi\)
−0.197481 + 0.980307i \(0.563276\pi\)
\(164\) −14.1800 −1.10727
\(165\) 0 0
\(166\) −22.5243 −1.74822
\(167\) 1.79823 0.139152 0.0695758 0.997577i \(-0.477835\pi\)
0.0695758 + 0.997577i \(0.477835\pi\)
\(168\) 0 0
\(169\) −4.28699 −0.329768
\(170\) 70.8372 5.43297
\(171\) 0 0
\(172\) 17.2585 1.31595
\(173\) −18.7212 −1.42334 −0.711672 0.702512i \(-0.752062\pi\)
−0.711672 + 0.702512i \(0.752062\pi\)
\(174\) 0 0
\(175\) −5.87575 −0.444165
\(176\) −21.7905 −1.64252
\(177\) 0 0
\(178\) −13.7746 −1.03245
\(179\) 25.1725 1.88148 0.940739 0.339132i \(-0.110133\pi\)
0.940739 + 0.339132i \(0.110133\pi\)
\(180\) 0 0
\(181\) −6.30690 −0.468788 −0.234394 0.972142i \(-0.575311\pi\)
−0.234394 + 0.972142i \(0.575311\pi\)
\(182\) −5.56421 −0.412447
\(183\) 0 0
\(184\) 33.7991 2.49170
\(185\) −29.4057 −2.16195
\(186\) 0 0
\(187\) −43.9463 −3.21367
\(188\) −21.7233 −1.58433
\(189\) 0 0
\(190\) −23.7088 −1.72002
\(191\) 14.8960 1.07784 0.538919 0.842358i \(-0.318833\pi\)
0.538919 + 0.842358i \(0.318833\pi\)
\(192\) 0 0
\(193\) −6.81837 −0.490797 −0.245399 0.969422i \(-0.578919\pi\)
−0.245399 + 0.969422i \(0.578919\pi\)
\(194\) 4.71325 0.338392
\(195\) 0 0
\(196\) −25.6670 −1.83336
\(197\) −11.7563 −0.837602 −0.418801 0.908078i \(-0.637550\pi\)
−0.418801 + 0.908078i \(0.637550\pi\)
\(198\) 0 0
\(199\) −0.198511 −0.0140721 −0.00703605 0.999975i \(-0.502240\pi\)
−0.00703605 + 0.999975i \(0.502240\pi\)
\(200\) −37.5364 −2.65423
\(201\) 0 0
\(202\) −36.2340 −2.54942
\(203\) −0.890262 −0.0624841
\(204\) 0 0
\(205\) 12.5861 0.879053
\(206\) 35.6707 2.48530
\(207\) 0 0
\(208\) −11.9008 −0.825171
\(209\) 14.7086 1.01741
\(210\) 0 0
\(211\) 5.37754 0.370205 0.185103 0.982719i \(-0.440738\pi\)
0.185103 + 0.982719i \(0.440738\pi\)
\(212\) 41.8169 2.87200
\(213\) 0 0
\(214\) −27.8254 −1.90211
\(215\) −15.3186 −1.04472
\(216\) 0 0
\(217\) −7.77302 −0.527667
\(218\) 48.6405 3.29435
\(219\) 0 0
\(220\) 76.9587 5.18855
\(221\) −24.0011 −1.61449
\(222\) 0 0
\(223\) 3.96264 0.265358 0.132679 0.991159i \(-0.457642\pi\)
0.132679 + 0.991159i \(0.457642\pi\)
\(224\) 0.0398891 0.00266520
\(225\) 0 0
\(226\) 38.7609 2.57834
\(227\) −12.0773 −0.801601 −0.400800 0.916165i \(-0.631268\pi\)
−0.400800 + 0.916165i \(0.631268\pi\)
\(228\) 0 0
\(229\) 17.4497 1.15311 0.576553 0.817060i \(-0.304397\pi\)
0.576553 + 0.817060i \(0.304397\pi\)
\(230\) −59.9208 −3.95106
\(231\) 0 0
\(232\) −5.68732 −0.373391
\(233\) −15.6470 −1.02507 −0.512535 0.858666i \(-0.671294\pi\)
−0.512535 + 0.858666i \(0.671294\pi\)
\(234\) 0 0
\(235\) 19.2815 1.25779
\(236\) 4.82449 0.314048
\(237\) 0 0
\(238\) 15.3273 0.993522
\(239\) 3.10356 0.200753 0.100376 0.994950i \(-0.467995\pi\)
0.100376 + 0.994950i \(0.467995\pi\)
\(240\) 0 0
\(241\) −2.98984 −0.192593 −0.0962963 0.995353i \(-0.530700\pi\)
−0.0962963 + 0.995353i \(0.530700\pi\)
\(242\) −44.6281 −2.86881
\(243\) 0 0
\(244\) 33.8676 2.16815
\(245\) 22.7820 1.45549
\(246\) 0 0
\(247\) 8.03302 0.511129
\(248\) −49.6569 −3.15322
\(249\) 0 0
\(250\) 22.9868 1.45381
\(251\) 21.5048 1.35737 0.678687 0.734428i \(-0.262549\pi\)
0.678687 + 0.734428i \(0.262549\pi\)
\(252\) 0 0
\(253\) 37.1739 2.33710
\(254\) −13.5469 −0.850009
\(255\) 0 0
\(256\) −32.0416 −2.00260
\(257\) −13.1601 −0.820903 −0.410451 0.911882i \(-0.634629\pi\)
−0.410451 + 0.911882i \(0.634629\pi\)
\(258\) 0 0
\(259\) −6.36262 −0.395354
\(260\) 42.0306 2.60663
\(261\) 0 0
\(262\) −33.3918 −2.06295
\(263\) −0.748397 −0.0461481 −0.0230741 0.999734i \(-0.507345\pi\)
−0.0230741 + 0.999734i \(0.507345\pi\)
\(264\) 0 0
\(265\) −37.1165 −2.28005
\(266\) −5.12996 −0.314538
\(267\) 0 0
\(268\) 50.6903 3.09641
\(269\) 6.62100 0.403689 0.201845 0.979418i \(-0.435306\pi\)
0.201845 + 0.979418i \(0.435306\pi\)
\(270\) 0 0
\(271\) 22.1504 1.34554 0.672772 0.739850i \(-0.265104\pi\)
0.672772 + 0.739850i \(0.265104\pi\)
\(272\) 32.7822 1.98771
\(273\) 0 0
\(274\) 49.1661 2.97023
\(275\) −41.2844 −2.48954
\(276\) 0 0
\(277\) 0.328464 0.0197355 0.00986774 0.999951i \(-0.496859\pi\)
0.00986774 + 0.999951i \(0.496859\pi\)
\(278\) 20.3914 1.22299
\(279\) 0 0
\(280\) −13.4383 −0.803091
\(281\) −0.887497 −0.0529436 −0.0264718 0.999650i \(-0.508427\pi\)
−0.0264718 + 0.999650i \(0.508427\pi\)
\(282\) 0 0
\(283\) −4.06911 −0.241883 −0.120942 0.992660i \(-0.538591\pi\)
−0.120942 + 0.992660i \(0.538591\pi\)
\(284\) 6.83569 0.405624
\(285\) 0 0
\(286\) −39.0955 −2.31177
\(287\) 2.72330 0.160752
\(288\) 0 0
\(289\) 49.1139 2.88905
\(290\) 10.0828 0.592081
\(291\) 0 0
\(292\) −60.4459 −3.53733
\(293\) 5.78935 0.338218 0.169109 0.985597i \(-0.445911\pi\)
0.169109 + 0.985597i \(0.445911\pi\)
\(294\) 0 0
\(295\) −4.28220 −0.249319
\(296\) −40.6467 −2.36254
\(297\) 0 0
\(298\) 2.45057 0.141958
\(299\) 20.3023 1.17412
\(300\) 0 0
\(301\) −3.31454 −0.191047
\(302\) −36.1133 −2.07809
\(303\) 0 0
\(304\) −10.9720 −0.629287
\(305\) −30.0607 −1.72127
\(306\) 0 0
\(307\) −11.3621 −0.648468 −0.324234 0.945977i \(-0.605106\pi\)
−0.324234 + 0.945977i \(0.605106\pi\)
\(308\) 16.6518 0.948825
\(309\) 0 0
\(310\) 88.0344 5.00002
\(311\) 17.5258 0.993797 0.496898 0.867809i \(-0.334472\pi\)
0.496898 + 0.867809i \(0.334472\pi\)
\(312\) 0 0
\(313\) −32.2326 −1.82189 −0.910947 0.412523i \(-0.864648\pi\)
−0.910947 + 0.412523i \(0.864648\pi\)
\(314\) −4.59783 −0.259471
\(315\) 0 0
\(316\) −27.2058 −1.53045
\(317\) −8.78252 −0.493275 −0.246638 0.969108i \(-0.579326\pi\)
−0.246638 + 0.969108i \(0.579326\pi\)
\(318\) 0 0
\(319\) −6.25520 −0.350224
\(320\) 28.2144 1.57723
\(321\) 0 0
\(322\) −12.9653 −0.722526
\(323\) −22.1279 −1.23123
\(324\) 0 0
\(325\) −22.5473 −1.25070
\(326\) 12.3571 0.684394
\(327\) 0 0
\(328\) 17.3975 0.960614
\(329\) 4.17201 0.230010
\(330\) 0 0
\(331\) −21.0169 −1.15519 −0.577597 0.816322i \(-0.696009\pi\)
−0.577597 + 0.816322i \(0.696009\pi\)
\(332\) 36.8143 2.02045
\(333\) 0 0
\(334\) −4.40669 −0.241124
\(335\) −44.9925 −2.45820
\(336\) 0 0
\(337\) 9.84346 0.536207 0.268104 0.963390i \(-0.413603\pi\)
0.268104 + 0.963390i \(0.413603\pi\)
\(338\) 10.5056 0.571427
\(339\) 0 0
\(340\) −115.779 −6.27897
\(341\) −54.6151 −2.95758
\(342\) 0 0
\(343\) 10.3140 0.556902
\(344\) −21.1745 −1.14165
\(345\) 0 0
\(346\) 45.8775 2.46639
\(347\) 12.0386 0.646264 0.323132 0.946354i \(-0.395264\pi\)
0.323132 + 0.946354i \(0.395264\pi\)
\(348\) 0 0
\(349\) −3.84312 −0.205717 −0.102859 0.994696i \(-0.532799\pi\)
−0.102859 + 0.994696i \(0.532799\pi\)
\(350\) 14.3989 0.769654
\(351\) 0 0
\(352\) 0.280271 0.0149385
\(353\) 17.6205 0.937847 0.468924 0.883239i \(-0.344642\pi\)
0.468924 + 0.883239i \(0.344642\pi\)
\(354\) 0 0
\(355\) −6.06733 −0.322021
\(356\) 22.5137 1.19322
\(357\) 0 0
\(358\) −61.6868 −3.26025
\(359\) 12.2734 0.647764 0.323882 0.946098i \(-0.395012\pi\)
0.323882 + 0.946098i \(0.395012\pi\)
\(360\) 0 0
\(361\) −11.5939 −0.610206
\(362\) 15.4555 0.812323
\(363\) 0 0
\(364\) 9.09432 0.476672
\(365\) 53.6515 2.80825
\(366\) 0 0
\(367\) 12.2785 0.640933 0.320467 0.947260i \(-0.396160\pi\)
0.320467 + 0.947260i \(0.396160\pi\)
\(368\) −27.7302 −1.44554
\(369\) 0 0
\(370\) 72.0607 3.74626
\(371\) −8.03103 −0.416950
\(372\) 0 0
\(373\) 20.6351 1.06845 0.534224 0.845343i \(-0.320604\pi\)
0.534224 + 0.845343i \(0.320604\pi\)
\(374\) 107.693 5.56869
\(375\) 0 0
\(376\) 26.6523 1.37449
\(377\) −3.41625 −0.175946
\(378\) 0 0
\(379\) −18.8103 −0.966218 −0.483109 0.875560i \(-0.660493\pi\)
−0.483109 + 0.875560i \(0.660493\pi\)
\(380\) 38.7504 1.98785
\(381\) 0 0
\(382\) −36.5037 −1.86769
\(383\) −13.9324 −0.711912 −0.355956 0.934503i \(-0.615845\pi\)
−0.355956 + 0.934503i \(0.615845\pi\)
\(384\) 0 0
\(385\) −14.7801 −0.753263
\(386\) 16.7089 0.850460
\(387\) 0 0
\(388\) −7.70348 −0.391085
\(389\) −15.8509 −0.803675 −0.401837 0.915711i \(-0.631628\pi\)
−0.401837 + 0.915711i \(0.631628\pi\)
\(390\) 0 0
\(391\) −55.9253 −2.82827
\(392\) 31.4909 1.59053
\(393\) 0 0
\(394\) 28.8096 1.45141
\(395\) 24.1478 1.21501
\(396\) 0 0
\(397\) −21.1846 −1.06322 −0.531612 0.846988i \(-0.678414\pi\)
−0.531612 + 0.846988i \(0.678414\pi\)
\(398\) 0.486466 0.0243843
\(399\) 0 0
\(400\) 30.7965 1.53983
\(401\) −3.09415 −0.154515 −0.0772573 0.997011i \(-0.524616\pi\)
−0.0772573 + 0.997011i \(0.524616\pi\)
\(402\) 0 0
\(403\) −29.8278 −1.48583
\(404\) 59.2220 2.94640
\(405\) 0 0
\(406\) 2.18165 0.108273
\(407\) −44.7053 −2.21596
\(408\) 0 0
\(409\) −25.6766 −1.26963 −0.634813 0.772666i \(-0.718923\pi\)
−0.634813 + 0.772666i \(0.718923\pi\)
\(410\) −30.8431 −1.52323
\(411\) 0 0
\(412\) −58.3013 −2.87230
\(413\) −0.926555 −0.0455928
\(414\) 0 0
\(415\) −32.6762 −1.60401
\(416\) 0.153069 0.00750481
\(417\) 0 0
\(418\) −36.0443 −1.76299
\(419\) −8.28859 −0.404924 −0.202462 0.979290i \(-0.564894\pi\)
−0.202462 + 0.979290i \(0.564894\pi\)
\(420\) 0 0
\(421\) −0.936357 −0.0456352 −0.0228176 0.999740i \(-0.507264\pi\)
−0.0228176 + 0.999740i \(0.507264\pi\)
\(422\) −13.1780 −0.641496
\(423\) 0 0
\(424\) −51.3052 −2.49160
\(425\) 62.1093 3.01274
\(426\) 0 0
\(427\) −6.50434 −0.314767
\(428\) 45.4787 2.19830
\(429\) 0 0
\(430\) 37.5393 1.81030
\(431\) −35.1809 −1.69460 −0.847302 0.531111i \(-0.821775\pi\)
−0.847302 + 0.531111i \(0.821775\pi\)
\(432\) 0 0
\(433\) −9.46548 −0.454882 −0.227441 0.973792i \(-0.573036\pi\)
−0.227441 + 0.973792i \(0.573036\pi\)
\(434\) 19.0483 0.914349
\(435\) 0 0
\(436\) −79.4996 −3.80734
\(437\) 18.7179 0.895397
\(438\) 0 0
\(439\) −8.92330 −0.425886 −0.212943 0.977065i \(-0.568305\pi\)
−0.212943 + 0.977065i \(0.568305\pi\)
\(440\) −94.4206 −4.50133
\(441\) 0 0
\(442\) 58.8163 2.79760
\(443\) 13.2830 0.631094 0.315547 0.948910i \(-0.397812\pi\)
0.315547 + 0.948910i \(0.397812\pi\)
\(444\) 0 0
\(445\) −19.9830 −0.947286
\(446\) −9.71071 −0.459816
\(447\) 0 0
\(448\) 6.10485 0.288427
\(449\) −36.6142 −1.72793 −0.863967 0.503549i \(-0.832027\pi\)
−0.863967 + 0.503549i \(0.832027\pi\)
\(450\) 0 0
\(451\) 19.1346 0.901013
\(452\) −63.3520 −2.97983
\(453\) 0 0
\(454\) 29.5963 1.38902
\(455\) −8.07208 −0.378425
\(456\) 0 0
\(457\) −20.5846 −0.962906 −0.481453 0.876472i \(-0.659891\pi\)
−0.481453 + 0.876472i \(0.659891\pi\)
\(458\) −42.7616 −1.99812
\(459\) 0 0
\(460\) 97.9363 4.56630
\(461\) −15.5222 −0.722939 −0.361470 0.932384i \(-0.617725\pi\)
−0.361470 + 0.932384i \(0.617725\pi\)
\(462\) 0 0
\(463\) 5.29274 0.245975 0.122987 0.992408i \(-0.460753\pi\)
0.122987 + 0.992408i \(0.460753\pi\)
\(464\) 4.66612 0.216619
\(465\) 0 0
\(466\) 38.3441 1.77625
\(467\) −12.4477 −0.576009 −0.288004 0.957629i \(-0.592992\pi\)
−0.288004 + 0.957629i \(0.592992\pi\)
\(468\) 0 0
\(469\) −9.73520 −0.449530
\(470\) −47.2506 −2.17951
\(471\) 0 0
\(472\) −5.91917 −0.272452
\(473\) −23.2888 −1.07082
\(474\) 0 0
\(475\) −20.7876 −0.953802
\(476\) −25.0514 −1.14823
\(477\) 0 0
\(478\) −7.60549 −0.347867
\(479\) −20.8201 −0.951296 −0.475648 0.879636i \(-0.657786\pi\)
−0.475648 + 0.879636i \(0.657786\pi\)
\(480\) 0 0
\(481\) −24.4156 −1.11326
\(482\) 7.32681 0.333727
\(483\) 0 0
\(484\) 72.9416 3.31553
\(485\) 6.83758 0.310478
\(486\) 0 0
\(487\) −8.55472 −0.387652 −0.193826 0.981036i \(-0.562090\pi\)
−0.193826 + 0.981036i \(0.562090\pi\)
\(488\) −41.5521 −1.88098
\(489\) 0 0
\(490\) −55.8287 −2.52208
\(491\) 20.2650 0.914545 0.457273 0.889327i \(-0.348826\pi\)
0.457273 + 0.889327i \(0.348826\pi\)
\(492\) 0 0
\(493\) 9.41048 0.423826
\(494\) −19.6855 −0.885691
\(495\) 0 0
\(496\) 40.7407 1.82931
\(497\) −1.31281 −0.0588876
\(498\) 0 0
\(499\) 18.4215 0.824659 0.412330 0.911035i \(-0.364715\pi\)
0.412330 + 0.911035i \(0.364715\pi\)
\(500\) −37.5704 −1.68020
\(501\) 0 0
\(502\) −52.6991 −2.35207
\(503\) −9.73021 −0.433849 −0.216924 0.976188i \(-0.569603\pi\)
−0.216924 + 0.976188i \(0.569603\pi\)
\(504\) 0 0
\(505\) −52.5652 −2.33912
\(506\) −91.0971 −4.04976
\(507\) 0 0
\(508\) 22.1415 0.982370
\(509\) −29.0199 −1.28629 −0.643143 0.765746i \(-0.722370\pi\)
−0.643143 + 0.765746i \(0.722370\pi\)
\(510\) 0 0
\(511\) 11.6088 0.513542
\(512\) 39.4154 1.74193
\(513\) 0 0
\(514\) 32.2497 1.42247
\(515\) 51.7480 2.28029
\(516\) 0 0
\(517\) 29.3135 1.28921
\(518\) 15.5920 0.685074
\(519\) 0 0
\(520\) −51.5674 −2.26138
\(521\) −5.01993 −0.219927 −0.109964 0.993936i \(-0.535073\pi\)
−0.109964 + 0.993936i \(0.535073\pi\)
\(522\) 0 0
\(523\) −6.63827 −0.290271 −0.145136 0.989412i \(-0.546362\pi\)
−0.145136 + 0.989412i \(0.546362\pi\)
\(524\) 54.5766 2.38419
\(525\) 0 0
\(526\) 1.83400 0.0799661
\(527\) 82.1644 3.57914
\(528\) 0 0
\(529\) 24.3069 1.05682
\(530\) 90.9565 3.95090
\(531\) 0 0
\(532\) 8.38456 0.363517
\(533\) 10.4503 0.452652
\(534\) 0 0
\(535\) −40.3667 −1.74521
\(536\) −62.1920 −2.68629
\(537\) 0 0
\(538\) −16.2252 −0.699518
\(539\) 34.6352 1.49185
\(540\) 0 0
\(541\) −29.2243 −1.25645 −0.628225 0.778032i \(-0.716218\pi\)
−0.628225 + 0.778032i \(0.716218\pi\)
\(542\) −54.2812 −2.33158
\(543\) 0 0
\(544\) −0.421646 −0.0180779
\(545\) 70.5635 3.02261
\(546\) 0 0
\(547\) 6.35081 0.271541 0.135770 0.990740i \(-0.456649\pi\)
0.135770 + 0.990740i \(0.456649\pi\)
\(548\) −80.3586 −3.43275
\(549\) 0 0
\(550\) 101.170 4.31391
\(551\) −3.14963 −0.134179
\(552\) 0 0
\(553\) 5.22494 0.222187
\(554\) −0.804923 −0.0341979
\(555\) 0 0
\(556\) −33.3283 −1.41344
\(557\) −25.0987 −1.06346 −0.531732 0.846913i \(-0.678459\pi\)
−0.531732 + 0.846913i \(0.678459\pi\)
\(558\) 0 0
\(559\) −12.7191 −0.537959
\(560\) 11.0253 0.465906
\(561\) 0 0
\(562\) 2.17487 0.0917414
\(563\) −15.2362 −0.642130 −0.321065 0.947057i \(-0.604041\pi\)
−0.321065 + 0.947057i \(0.604041\pi\)
\(564\) 0 0
\(565\) 56.2310 2.36565
\(566\) 9.97162 0.419139
\(567\) 0 0
\(568\) −8.38671 −0.351899
\(569\) 13.8321 0.579870 0.289935 0.957046i \(-0.406366\pi\)
0.289935 + 0.957046i \(0.406366\pi\)
\(570\) 0 0
\(571\) −22.2430 −0.930840 −0.465420 0.885090i \(-0.654097\pi\)
−0.465420 + 0.885090i \(0.654097\pi\)
\(572\) 63.8989 2.67175
\(573\) 0 0
\(574\) −6.67364 −0.278552
\(575\) −52.5379 −2.19098
\(576\) 0 0
\(577\) 40.4322 1.68322 0.841608 0.540089i \(-0.181609\pi\)
0.841608 + 0.540089i \(0.181609\pi\)
\(578\) −120.357 −5.00619
\(579\) 0 0
\(580\) −16.4796 −0.684278
\(581\) −7.07027 −0.293324
\(582\) 0 0
\(583\) −56.4280 −2.33701
\(584\) 74.1611 3.06881
\(585\) 0 0
\(586\) −14.1872 −0.586068
\(587\) −39.6873 −1.63807 −0.819036 0.573743i \(-0.805491\pi\)
−0.819036 + 0.573743i \(0.805491\pi\)
\(588\) 0 0
\(589\) −27.4999 −1.13312
\(590\) 10.4938 0.432024
\(591\) 0 0
\(592\) 33.3484 1.37061
\(593\) −38.0520 −1.56261 −0.781304 0.624151i \(-0.785445\pi\)
−0.781304 + 0.624151i \(0.785445\pi\)
\(594\) 0 0
\(595\) 22.2355 0.911568
\(596\) −4.00528 −0.164063
\(597\) 0 0
\(598\) −49.7523 −2.03452
\(599\) −10.5177 −0.429743 −0.214872 0.976642i \(-0.568933\pi\)
−0.214872 + 0.976642i \(0.568933\pi\)
\(600\) 0 0
\(601\) 14.9676 0.610540 0.305270 0.952266i \(-0.401253\pi\)
0.305270 + 0.952266i \(0.401253\pi\)
\(602\) 8.12251 0.331049
\(603\) 0 0
\(604\) 59.0247 2.40168
\(605\) −64.7427 −2.63216
\(606\) 0 0
\(607\) 30.6282 1.24316 0.621580 0.783350i \(-0.286491\pi\)
0.621580 + 0.783350i \(0.286491\pi\)
\(608\) 0.141123 0.00572328
\(609\) 0 0
\(610\) 73.6658 2.98264
\(611\) 16.0095 0.647673
\(612\) 0 0
\(613\) 21.9824 0.887862 0.443931 0.896061i \(-0.353583\pi\)
0.443931 + 0.896061i \(0.353583\pi\)
\(614\) 27.8435 1.12367
\(615\) 0 0
\(616\) −20.4301 −0.823153
\(617\) 3.65187 0.147019 0.0735093 0.997295i \(-0.476580\pi\)
0.0735093 + 0.997295i \(0.476580\pi\)
\(618\) 0 0
\(619\) −15.8678 −0.637782 −0.318891 0.947791i \(-0.603310\pi\)
−0.318891 + 0.947791i \(0.603310\pi\)
\(620\) −143.886 −5.77861
\(621\) 0 0
\(622\) −42.9482 −1.72206
\(623\) −4.32380 −0.173229
\(624\) 0 0
\(625\) −4.84541 −0.193817
\(626\) 78.9882 3.15700
\(627\) 0 0
\(628\) 7.51484 0.299875
\(629\) 67.2558 2.68166
\(630\) 0 0
\(631\) −2.03977 −0.0812020 −0.0406010 0.999175i \(-0.512927\pi\)
−0.0406010 + 0.999175i \(0.512927\pi\)
\(632\) 33.3789 1.32774
\(633\) 0 0
\(634\) 21.5222 0.854754
\(635\) −19.6527 −0.779894
\(636\) 0 0
\(637\) 18.9159 0.749475
\(638\) 15.3288 0.606872
\(639\) 0 0
\(640\) −69.5100 −2.74762
\(641\) 33.3829 1.31854 0.659272 0.751905i \(-0.270865\pi\)
0.659272 + 0.751905i \(0.270865\pi\)
\(642\) 0 0
\(643\) 10.9368 0.431304 0.215652 0.976470i \(-0.430812\pi\)
0.215652 + 0.976470i \(0.430812\pi\)
\(644\) 21.1908 0.835036
\(645\) 0 0
\(646\) 54.2260 2.13349
\(647\) −9.42459 −0.370519 −0.185259 0.982690i \(-0.559313\pi\)
−0.185259 + 0.982690i \(0.559313\pi\)
\(648\) 0 0
\(649\) −6.51020 −0.255548
\(650\) 55.2537 2.16723
\(651\) 0 0
\(652\) −20.1967 −0.790966
\(653\) 24.9058 0.974639 0.487319 0.873224i \(-0.337975\pi\)
0.487319 + 0.873224i \(0.337975\pi\)
\(654\) 0 0
\(655\) −48.4420 −1.89278
\(656\) −14.2736 −0.557292
\(657\) 0 0
\(658\) −10.2238 −0.398565
\(659\) −20.4389 −0.796186 −0.398093 0.917345i \(-0.630328\pi\)
−0.398093 + 0.917345i \(0.630328\pi\)
\(660\) 0 0
\(661\) 25.7587 1.00190 0.500949 0.865477i \(-0.332984\pi\)
0.500949 + 0.865477i \(0.332984\pi\)
\(662\) 51.5034 2.00173
\(663\) 0 0
\(664\) −45.1675 −1.75284
\(665\) −7.44210 −0.288592
\(666\) 0 0
\(667\) −7.96026 −0.308222
\(668\) 7.20244 0.278671
\(669\) 0 0
\(670\) 110.257 4.25961
\(671\) −45.7011 −1.76427
\(672\) 0 0
\(673\) −17.9606 −0.692331 −0.346165 0.938174i \(-0.612516\pi\)
−0.346165 + 0.938174i \(0.612516\pi\)
\(674\) −24.1221 −0.929147
\(675\) 0 0
\(676\) −17.1706 −0.660408
\(677\) −38.1634 −1.46674 −0.733370 0.679830i \(-0.762054\pi\)
−0.733370 + 0.679830i \(0.762054\pi\)
\(678\) 0 0
\(679\) 1.47947 0.0567769
\(680\) 142.049 5.44732
\(681\) 0 0
\(682\) 133.838 5.12493
\(683\) 16.8777 0.645809 0.322904 0.946432i \(-0.395341\pi\)
0.322904 + 0.946432i \(0.395341\pi\)
\(684\) 0 0
\(685\) 71.3260 2.72523
\(686\) −25.2751 −0.965008
\(687\) 0 0
\(688\) 17.3725 0.662319
\(689\) −30.8179 −1.17407
\(690\) 0 0
\(691\) 15.0219 0.571460 0.285730 0.958310i \(-0.407764\pi\)
0.285730 + 0.958310i \(0.407764\pi\)
\(692\) −74.9836 −2.85045
\(693\) 0 0
\(694\) −29.5013 −1.11985
\(695\) 29.5821 1.12211
\(696\) 0 0
\(697\) −28.7866 −1.09037
\(698\) 9.41783 0.356470
\(699\) 0 0
\(700\) −23.5340 −0.889503
\(701\) −2.67425 −0.101005 −0.0505026 0.998724i \(-0.516082\pi\)
−0.0505026 + 0.998724i \(0.516082\pi\)
\(702\) 0 0
\(703\) −22.5101 −0.848985
\(704\) 42.8942 1.61663
\(705\) 0 0
\(706\) −43.1803 −1.62511
\(707\) −11.3737 −0.427753
\(708\) 0 0
\(709\) −5.79666 −0.217698 −0.108849 0.994058i \(-0.534716\pi\)
−0.108849 + 0.994058i \(0.534716\pi\)
\(710\) 14.8684 0.558001
\(711\) 0 0
\(712\) −27.6220 −1.03518
\(713\) −69.5023 −2.60288
\(714\) 0 0
\(715\) −56.7164 −2.12107
\(716\) 100.823 3.76793
\(717\) 0 0
\(718\) −30.0767 −1.12245
\(719\) −42.0447 −1.56800 −0.784001 0.620759i \(-0.786824\pi\)
−0.784001 + 0.620759i \(0.786824\pi\)
\(720\) 0 0
\(721\) 11.1969 0.416994
\(722\) 28.4117 1.05737
\(723\) 0 0
\(724\) −25.2609 −0.938815
\(725\) 8.84047 0.328327
\(726\) 0 0
\(727\) −0.698186 −0.0258943 −0.0129471 0.999916i \(-0.504121\pi\)
−0.0129471 + 0.999916i \(0.504121\pi\)
\(728\) −11.1578 −0.413536
\(729\) 0 0
\(730\) −131.477 −4.86617
\(731\) 35.0362 1.29586
\(732\) 0 0
\(733\) 1.02102 0.0377122 0.0188561 0.999822i \(-0.493998\pi\)
0.0188561 + 0.999822i \(0.493998\pi\)
\(734\) −30.0893 −1.11062
\(735\) 0 0
\(736\) 0.356668 0.0131470
\(737\) −68.4018 −2.51961
\(738\) 0 0
\(739\) 36.1575 1.33008 0.665038 0.746809i \(-0.268415\pi\)
0.665038 + 0.746809i \(0.268415\pi\)
\(740\) −117.778 −4.32961
\(741\) 0 0
\(742\) 19.6806 0.722497
\(743\) −29.8813 −1.09624 −0.548119 0.836400i \(-0.684656\pi\)
−0.548119 + 0.836400i \(0.684656\pi\)
\(744\) 0 0
\(745\) 3.55507 0.130248
\(746\) −50.5678 −1.85142
\(747\) 0 0
\(748\) −176.017 −6.43583
\(749\) −8.73429 −0.319144
\(750\) 0 0
\(751\) −11.9178 −0.434886 −0.217443 0.976073i \(-0.569772\pi\)
−0.217443 + 0.976073i \(0.569772\pi\)
\(752\) −21.8667 −0.797397
\(753\) 0 0
\(754\) 8.37175 0.304881
\(755\) −52.3901 −1.90667
\(756\) 0 0
\(757\) 29.5267 1.07317 0.536584 0.843847i \(-0.319714\pi\)
0.536584 + 0.843847i \(0.319714\pi\)
\(758\) 46.0958 1.67428
\(759\) 0 0
\(760\) −47.5429 −1.72456
\(761\) 14.5195 0.526330 0.263165 0.964751i \(-0.415234\pi\)
0.263165 + 0.964751i \(0.415234\pi\)
\(762\) 0 0
\(763\) 15.2681 0.552741
\(764\) 59.6627 2.15852
\(765\) 0 0
\(766\) 34.1423 1.23361
\(767\) −3.55552 −0.128382
\(768\) 0 0
\(769\) −8.09009 −0.291736 −0.145868 0.989304i \(-0.546598\pi\)
−0.145868 + 0.989304i \(0.546598\pi\)
\(770\) 36.2196 1.30526
\(771\) 0 0
\(772\) −27.3095 −0.982891
\(773\) 6.22601 0.223934 0.111967 0.993712i \(-0.464285\pi\)
0.111967 + 0.993712i \(0.464285\pi\)
\(774\) 0 0
\(775\) 77.1876 2.77266
\(776\) 9.45140 0.339286
\(777\) 0 0
\(778\) 38.8438 1.39262
\(779\) 9.63470 0.345199
\(780\) 0 0
\(781\) −9.22412 −0.330065
\(782\) 137.049 4.90086
\(783\) 0 0
\(784\) −25.8365 −0.922732
\(785\) −6.67014 −0.238067
\(786\) 0 0
\(787\) −35.0116 −1.24803 −0.624015 0.781412i \(-0.714500\pi\)
−0.624015 + 0.781412i \(0.714500\pi\)
\(788\) −47.0873 −1.67742
\(789\) 0 0
\(790\) −59.1758 −2.10538
\(791\) 12.1669 0.432605
\(792\) 0 0
\(793\) −24.9594 −0.886336
\(794\) 51.9143 1.84237
\(795\) 0 0
\(796\) −0.795094 −0.0281814
\(797\) −5.85535 −0.207407 −0.103704 0.994608i \(-0.533069\pi\)
−0.103704 + 0.994608i \(0.533069\pi\)
\(798\) 0 0
\(799\) −44.1000 −1.56015
\(800\) −0.396107 −0.0140045
\(801\) 0 0
\(802\) 7.58243 0.267745
\(803\) 81.5660 2.87840
\(804\) 0 0
\(805\) −18.8089 −0.662926
\(806\) 73.0951 2.57466
\(807\) 0 0
\(808\) −72.6595 −2.55615
\(809\) −0.611876 −0.0215124 −0.0107562 0.999942i \(-0.503424\pi\)
−0.0107562 + 0.999942i \(0.503424\pi\)
\(810\) 0 0
\(811\) 36.9200 1.29644 0.648218 0.761455i \(-0.275514\pi\)
0.648218 + 0.761455i \(0.275514\pi\)
\(812\) −3.56575 −0.125133
\(813\) 0 0
\(814\) 109.553 3.83984
\(815\) 17.9265 0.627940
\(816\) 0 0
\(817\) −11.7264 −0.410255
\(818\) 62.9222 2.20002
\(819\) 0 0
\(820\) 50.4110 1.76043
\(821\) 13.9623 0.487287 0.243643 0.969865i \(-0.421657\pi\)
0.243643 + 0.969865i \(0.421657\pi\)
\(822\) 0 0
\(823\) 28.7876 1.00347 0.501736 0.865021i \(-0.332695\pi\)
0.501736 + 0.865021i \(0.332695\pi\)
\(824\) 71.5299 2.49186
\(825\) 0 0
\(826\) 2.27059 0.0790038
\(827\) 2.83164 0.0984657 0.0492329 0.998787i \(-0.484322\pi\)
0.0492329 + 0.998787i \(0.484322\pi\)
\(828\) 0 0
\(829\) 29.3145 1.01813 0.509067 0.860727i \(-0.329990\pi\)
0.509067 + 0.860727i \(0.329990\pi\)
\(830\) 80.0753 2.77946
\(831\) 0 0
\(832\) 23.4265 0.812166
\(833\) −52.1061 −1.80537
\(834\) 0 0
\(835\) −6.39285 −0.221234
\(836\) 58.9120 2.03751
\(837\) 0 0
\(838\) 20.3118 0.701658
\(839\) 32.5092 1.12234 0.561172 0.827699i \(-0.310351\pi\)
0.561172 + 0.827699i \(0.310351\pi\)
\(840\) 0 0
\(841\) −27.6605 −0.953812
\(842\) 2.29461 0.0790773
\(843\) 0 0
\(844\) 21.5386 0.741388
\(845\) 15.2405 0.524291
\(846\) 0 0
\(847\) −14.0086 −0.481341
\(848\) 42.0930 1.44548
\(849\) 0 0
\(850\) −152.203 −5.22052
\(851\) −56.8912 −1.95021
\(852\) 0 0
\(853\) 46.2459 1.58343 0.791714 0.610892i \(-0.209189\pi\)
0.791714 + 0.610892i \(0.209189\pi\)
\(854\) 15.9393 0.545433
\(855\) 0 0
\(856\) −55.7978 −1.90713
\(857\) −22.3375 −0.763033 −0.381517 0.924362i \(-0.624598\pi\)
−0.381517 + 0.924362i \(0.624598\pi\)
\(858\) 0 0
\(859\) −35.5297 −1.21226 −0.606130 0.795366i \(-0.707279\pi\)
−0.606130 + 0.795366i \(0.707279\pi\)
\(860\) −61.3553 −2.09220
\(861\) 0 0
\(862\) 86.2132 2.93643
\(863\) −28.6114 −0.973942 −0.486971 0.873418i \(-0.661898\pi\)
−0.486971 + 0.873418i \(0.661898\pi\)
\(864\) 0 0
\(865\) 66.5551 2.26294
\(866\) 23.1958 0.788226
\(867\) 0 0
\(868\) −31.1332 −1.05673
\(869\) 36.7117 1.24536
\(870\) 0 0
\(871\) −37.3574 −1.26581
\(872\) 97.5380 3.30305
\(873\) 0 0
\(874\) −45.8694 −1.55156
\(875\) 7.21547 0.243927
\(876\) 0 0
\(877\) 19.8532 0.670397 0.335198 0.942148i \(-0.391197\pi\)
0.335198 + 0.942148i \(0.391197\pi\)
\(878\) 21.8672 0.737981
\(879\) 0 0
\(880\) 77.4668 2.61140
\(881\) 44.3326 1.49360 0.746802 0.665046i \(-0.231588\pi\)
0.746802 + 0.665046i \(0.231588\pi\)
\(882\) 0 0
\(883\) 9.88079 0.332515 0.166258 0.986082i \(-0.446832\pi\)
0.166258 + 0.986082i \(0.446832\pi\)
\(884\) −96.1311 −3.23324
\(885\) 0 0
\(886\) −32.5509 −1.09357
\(887\) 19.3506 0.649731 0.324865 0.945760i \(-0.394681\pi\)
0.324865 + 0.945760i \(0.394681\pi\)
\(888\) 0 0
\(889\) −4.25232 −0.142618
\(890\) 48.9698 1.64147
\(891\) 0 0
\(892\) 15.8715 0.531417
\(893\) 14.7600 0.493925
\(894\) 0 0
\(895\) −89.4899 −2.99132
\(896\) −15.0401 −0.502455
\(897\) 0 0
\(898\) 89.7257 2.99419
\(899\) 11.6951 0.390052
\(900\) 0 0
\(901\) 84.8917 2.82815
\(902\) −46.8906 −1.56129
\(903\) 0 0
\(904\) 77.7266 2.58515
\(905\) 22.4215 0.745316
\(906\) 0 0
\(907\) 16.0706 0.533616 0.266808 0.963750i \(-0.414031\pi\)
0.266808 + 0.963750i \(0.414031\pi\)
\(908\) −48.3731 −1.60532
\(909\) 0 0
\(910\) 19.7812 0.655740
\(911\) 27.6907 0.917435 0.458717 0.888582i \(-0.348309\pi\)
0.458717 + 0.888582i \(0.348309\pi\)
\(912\) 0 0
\(913\) −49.6775 −1.64408
\(914\) 50.4439 1.66854
\(915\) 0 0
\(916\) 69.8909 2.30926
\(917\) −10.4816 −0.346132
\(918\) 0 0
\(919\) −42.9872 −1.41802 −0.709008 0.705201i \(-0.750857\pi\)
−0.709008 + 0.705201i \(0.750857\pi\)
\(920\) −120.158 −3.96149
\(921\) 0 0
\(922\) 38.0381 1.25272
\(923\) −5.03771 −0.165818
\(924\) 0 0
\(925\) 63.1820 2.07741
\(926\) −12.9702 −0.426228
\(927\) 0 0
\(928\) −0.0600160 −0.00197012
\(929\) 53.8096 1.76544 0.882718 0.469903i \(-0.155711\pi\)
0.882718 + 0.469903i \(0.155711\pi\)
\(930\) 0 0
\(931\) 17.4396 0.571560
\(932\) −62.6707 −2.05285
\(933\) 0 0
\(934\) 30.5038 0.998116
\(935\) 156.232 5.10934
\(936\) 0 0
\(937\) 26.0611 0.851380 0.425690 0.904869i \(-0.360031\pi\)
0.425690 + 0.904869i \(0.360031\pi\)
\(938\) 23.8568 0.778951
\(939\) 0 0
\(940\) 77.2279 2.51890
\(941\) 26.0807 0.850206 0.425103 0.905145i \(-0.360238\pi\)
0.425103 + 0.905145i \(0.360238\pi\)
\(942\) 0 0
\(943\) 24.3504 0.792957
\(944\) 4.85635 0.158061
\(945\) 0 0
\(946\) 57.0707 1.85553
\(947\) 52.1098 1.69334 0.846671 0.532117i \(-0.178603\pi\)
0.846671 + 0.532117i \(0.178603\pi\)
\(948\) 0 0
\(949\) 44.5469 1.44605
\(950\) 50.9415 1.65276
\(951\) 0 0
\(952\) 30.7356 0.996146
\(953\) −17.8589 −0.578506 −0.289253 0.957253i \(-0.593407\pi\)
−0.289253 + 0.957253i \(0.593407\pi\)
\(954\) 0 0
\(955\) −52.9564 −1.71363
\(956\) 12.4306 0.402036
\(957\) 0 0
\(958\) 51.0211 1.64842
\(959\) 15.4331 0.498359
\(960\) 0 0
\(961\) 71.1115 2.29392
\(962\) 59.8321 1.92906
\(963\) 0 0
\(964\) −11.9752 −0.385694
\(965\) 24.2398 0.780307
\(966\) 0 0
\(967\) 15.4449 0.496676 0.248338 0.968673i \(-0.420116\pi\)
0.248338 + 0.968673i \(0.420116\pi\)
\(968\) −89.4921 −2.87638
\(969\) 0 0
\(970\) −16.7559 −0.538001
\(971\) 7.46873 0.239683 0.119841 0.992793i \(-0.461761\pi\)
0.119841 + 0.992793i \(0.461761\pi\)
\(972\) 0 0
\(973\) 6.40078 0.205200
\(974\) 20.9639 0.671728
\(975\) 0 0
\(976\) 34.0912 1.09123
\(977\) −54.8743 −1.75558 −0.877792 0.479042i \(-0.840984\pi\)
−0.877792 + 0.479042i \(0.840984\pi\)
\(978\) 0 0
\(979\) −30.3801 −0.970951
\(980\) 91.2482 2.91482
\(981\) 0 0
\(982\) −49.6607 −1.58474
\(983\) −14.0687 −0.448721 −0.224361 0.974506i \(-0.572029\pi\)
−0.224361 + 0.974506i \(0.572029\pi\)
\(984\) 0 0
\(985\) 41.7945 1.33168
\(986\) −23.0610 −0.734412
\(987\) 0 0
\(988\) 32.1745 1.02361
\(989\) −29.6369 −0.942398
\(990\) 0 0
\(991\) 22.7375 0.722280 0.361140 0.932512i \(-0.382388\pi\)
0.361140 + 0.932512i \(0.382388\pi\)
\(992\) −0.524009 −0.0166373
\(993\) 0 0
\(994\) 3.21713 0.102041
\(995\) 0.705722 0.0223729
\(996\) 0 0
\(997\) −1.23102 −0.0389867 −0.0194933 0.999810i \(-0.506205\pi\)
−0.0194933 + 0.999810i \(0.506205\pi\)
\(998\) −45.1431 −1.42898
\(999\) 0 0
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 4023.2.a.e.1.4 25
3.2 odd 2 4023.2.a.f.1.22 yes 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4023.2.a.e.1.4 25 1.1 even 1 trivial
4023.2.a.f.1.22 yes 25 3.2 odd 2