Properties

Label 575.4.a.j.1.2
Level $575$
Weight $4$
Character 575.1
Self dual yes
Analytic conductor $33.926$
Analytic rank $1$
Dimension $5$
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] = [575,4,Mod(1,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 575.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: \(33.9260982533\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 27x^{3} + 7x^{2} + 168x + 92 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.41740\) of defining polynomial
Character \(\chi\) \(=\) 575.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.41740 q^{2} -7.84147 q^{3} +11.5134 q^{4} +34.6389 q^{6} +8.97260 q^{7} -15.5200 q^{8} +34.4886 q^{9} +O(q^{10})\) \(q-4.41740 q^{2} -7.84147 q^{3} +11.5134 q^{4} +34.6389 q^{6} +8.97260 q^{7} -15.5200 q^{8} +34.4886 q^{9} -28.9011 q^{11} -90.2818 q^{12} -16.0879 q^{13} -39.6355 q^{14} -23.5490 q^{16} -25.1771 q^{17} -152.350 q^{18} -35.6298 q^{19} -70.3583 q^{21} +127.668 q^{22} +23.0000 q^{23} +121.700 q^{24} +71.0668 q^{26} -58.7218 q^{27} +103.305 q^{28} +138.272 q^{29} +40.1277 q^{31} +228.186 q^{32} +226.627 q^{33} +111.217 q^{34} +397.081 q^{36} -379.745 q^{37} +157.391 q^{38} +126.153 q^{39} +412.514 q^{41} +310.801 q^{42} +402.095 q^{43} -332.750 q^{44} -101.600 q^{46} -110.070 q^{47} +184.659 q^{48} -262.492 q^{49} +197.426 q^{51} -185.227 q^{52} +421.300 q^{53} +259.397 q^{54} -139.255 q^{56} +279.390 q^{57} -610.802 q^{58} +755.913 q^{59} -307.032 q^{61} -177.260 q^{62} +309.453 q^{63} -819.594 q^{64} -1001.10 q^{66} -319.974 q^{67} -289.874 q^{68} -180.354 q^{69} -554.138 q^{71} -535.264 q^{72} +705.131 q^{73} +1677.48 q^{74} -410.219 q^{76} -259.318 q^{77} -557.268 q^{78} +1170.51 q^{79} -470.728 q^{81} -1822.24 q^{82} +455.978 q^{83} -810.063 q^{84} -1776.21 q^{86} -1084.26 q^{87} +448.546 q^{88} -1495.57 q^{89} -144.351 q^{91} +264.808 q^{92} -314.660 q^{93} +486.222 q^{94} -1789.31 q^{96} -1041.24 q^{97} +1159.53 q^{98} -996.760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9} + 23 q^{11} - 47 q^{12} - 132 q^{13} + 93 q^{14} + 282 q^{16} - 23 q^{17} + 15 q^{18} - 161 q^{19} - 60 q^{21} - 193 q^{22} + 115 q^{23} + 105 q^{24} - 257 q^{26} - 577 q^{27} - 17 q^{28} + 401 q^{29} + 32 q^{31} - 670 q^{32} - 189 q^{33} - 663 q^{34} - 659 q^{36} + 38 q^{37} + 875 q^{38} + 335 q^{39} - 12 q^{41} + 798 q^{42} + 566 q^{43} + 47 q^{44} - 138 q^{46} - 919 q^{47} + 773 q^{48} - 738 q^{49} - 993 q^{51} + 305 q^{52} - 1156 q^{53} - 8 q^{54} + 343 q^{56} - 114 q^{57} + 1042 q^{58} + 1324 q^{59} - 1673 q^{61} - 565 q^{62} - 270 q^{63} + 2466 q^{64} - 2781 q^{66} - 558 q^{67} + 2267 q^{68} - 92 q^{69} - 108 q^{71} + 789 q^{72} - 1173 q^{73} + 1458 q^{74} - 3477 q^{76} - 2608 q^{77} - 704 q^{78} + 656 q^{79} - 319 q^{81} - 3505 q^{82} + 82 q^{83} - 718 q^{84} + 112 q^{86} - 2389 q^{87} - 2397 q^{88} + 570 q^{89} - 1589 q^{91} + 506 q^{92} - 911 q^{93} - 948 q^{94} - 5991 q^{96} - 633 q^{97} + 2555 q^{98} + 2021 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.41740 −1.56179 −0.780893 0.624665i \(-0.785235\pi\)
−0.780893 + 0.624665i \(0.785235\pi\)
\(3\) −7.84147 −1.50909 −0.754546 0.656248i \(-0.772143\pi\)
−0.754546 + 0.656248i \(0.772143\pi\)
\(4\) 11.5134 1.43917
\(5\) 0 0
\(6\) 34.6389 2.35688
\(7\) 8.97260 0.484475 0.242237 0.970217i \(-0.422119\pi\)
0.242237 + 0.970217i \(0.422119\pi\)
\(8\) −15.5200 −0.685894
\(9\) 34.4886 1.27736
\(10\) 0 0
\(11\) −28.9011 −0.792183 −0.396092 0.918211i \(-0.629634\pi\)
−0.396092 + 0.918211i \(0.629634\pi\)
\(12\) −90.2818 −2.17184
\(13\) −16.0879 −0.343230 −0.171615 0.985164i \(-0.554898\pi\)
−0.171615 + 0.985164i \(0.554898\pi\)
\(14\) −39.6355 −0.756646
\(15\) 0 0
\(16\) −23.5490 −0.367954
\(17\) −25.1771 −0.359197 −0.179599 0.983740i \(-0.557480\pi\)
−0.179599 + 0.983740i \(0.557480\pi\)
\(18\) −152.350 −1.99496
\(19\) −35.6298 −0.430212 −0.215106 0.976591i \(-0.569010\pi\)
−0.215106 + 0.976591i \(0.569010\pi\)
\(20\) 0 0
\(21\) −70.3583 −0.731117
\(22\) 127.668 1.23722
\(23\) 23.0000 0.208514
\(24\) 121.700 1.03508
\(25\) 0 0
\(26\) 71.0668 0.536051
\(27\) −58.7218 −0.418556
\(28\) 103.305 0.697243
\(29\) 138.272 0.885395 0.442698 0.896671i \(-0.354022\pi\)
0.442698 + 0.896671i \(0.354022\pi\)
\(30\) 0 0
\(31\) 40.1277 0.232489 0.116244 0.993221i \(-0.462914\pi\)
0.116244 + 0.993221i \(0.462914\pi\)
\(32\) 228.186 1.26056
\(33\) 226.627 1.19548
\(34\) 111.217 0.560989
\(35\) 0 0
\(36\) 397.081 1.83834
\(37\) −379.745 −1.68729 −0.843645 0.536902i \(-0.819595\pi\)
−0.843645 + 0.536902i \(0.819595\pi\)
\(38\) 157.391 0.671899
\(39\) 126.153 0.517965
\(40\) 0 0
\(41\) 412.514 1.57132 0.785658 0.618662i \(-0.212325\pi\)
0.785658 + 0.618662i \(0.212325\pi\)
\(42\) 310.801 1.14185
\(43\) 402.095 1.42602 0.713011 0.701153i \(-0.247331\pi\)
0.713011 + 0.701153i \(0.247331\pi\)
\(44\) −332.750 −1.14009
\(45\) 0 0
\(46\) −101.600 −0.325655
\(47\) −110.070 −0.341603 −0.170801 0.985305i \(-0.554636\pi\)
−0.170801 + 0.985305i \(0.554636\pi\)
\(48\) 184.659 0.555276
\(49\) −262.492 −0.765284
\(50\) 0 0
\(51\) 197.426 0.542061
\(52\) −185.227 −0.493967
\(53\) 421.300 1.09189 0.545943 0.837822i \(-0.316171\pi\)
0.545943 + 0.837822i \(0.316171\pi\)
\(54\) 259.397 0.653695
\(55\) 0 0
\(56\) −139.255 −0.332298
\(57\) 279.390 0.649229
\(58\) −610.802 −1.38280
\(59\) 755.913 1.66799 0.833996 0.551770i \(-0.186048\pi\)
0.833996 + 0.551770i \(0.186048\pi\)
\(60\) 0 0
\(61\) −307.032 −0.644450 −0.322225 0.946663i \(-0.604431\pi\)
−0.322225 + 0.946663i \(0.604431\pi\)
\(62\) −177.260 −0.363098
\(63\) 309.453 0.618847
\(64\) −819.594 −1.60077
\(65\) 0 0
\(66\) −1001.10 −1.86708
\(67\) −319.974 −0.583448 −0.291724 0.956502i \(-0.594229\pi\)
−0.291724 + 0.956502i \(0.594229\pi\)
\(68\) −289.874 −0.516947
\(69\) −180.354 −0.314667
\(70\) 0 0
\(71\) −554.138 −0.926254 −0.463127 0.886292i \(-0.653273\pi\)
−0.463127 + 0.886292i \(0.653273\pi\)
\(72\) −535.264 −0.876131
\(73\) 705.131 1.13054 0.565269 0.824907i \(-0.308772\pi\)
0.565269 + 0.824907i \(0.308772\pi\)
\(74\) 1677.48 2.63518
\(75\) 0 0
\(76\) −410.219 −0.619149
\(77\) −259.318 −0.383793
\(78\) −557.268 −0.808950
\(79\) 1170.51 1.66699 0.833495 0.552526i \(-0.186336\pi\)
0.833495 + 0.552526i \(0.186336\pi\)
\(80\) 0 0
\(81\) −470.728 −0.645717
\(82\) −1822.24 −2.45406
\(83\) 455.978 0.603014 0.301507 0.953464i \(-0.402510\pi\)
0.301507 + 0.953464i \(0.402510\pi\)
\(84\) −810.063 −1.05220
\(85\) 0 0
\(86\) −1776.21 −2.22714
\(87\) −1084.26 −1.33614
\(88\) 448.546 0.543354
\(89\) −1495.57 −1.78124 −0.890621 0.454746i \(-0.849730\pi\)
−0.890621 + 0.454746i \(0.849730\pi\)
\(90\) 0 0
\(91\) −144.351 −0.166286
\(92\) 264.808 0.300088
\(93\) −314.660 −0.350847
\(94\) 486.222 0.533510
\(95\) 0 0
\(96\) −1789.31 −1.90230
\(97\) −1041.24 −1.08992 −0.544958 0.838463i \(-0.683455\pi\)
−0.544958 + 0.838463i \(0.683455\pi\)
\(98\) 1159.53 1.19521
\(99\) −996.760 −1.01190
\(100\) 0 0
\(101\) 1450.22 1.42873 0.714367 0.699771i \(-0.246715\pi\)
0.714367 + 0.699771i \(0.246715\pi\)
\(102\) −872.108 −0.846584
\(103\) −220.283 −0.210729 −0.105365 0.994434i \(-0.533601\pi\)
−0.105365 + 0.994434i \(0.533601\pi\)
\(104\) 249.685 0.235419
\(105\) 0 0
\(106\) −1861.05 −1.70529
\(107\) −59.2679 −0.0535481 −0.0267741 0.999642i \(-0.508523\pi\)
−0.0267741 + 0.999642i \(0.508523\pi\)
\(108\) −676.087 −0.602375
\(109\) 1966.29 1.72786 0.863930 0.503612i \(-0.167996\pi\)
0.863930 + 0.503612i \(0.167996\pi\)
\(110\) 0 0
\(111\) 2977.76 2.54627
\(112\) −211.296 −0.178264
\(113\) −1819.68 −1.51488 −0.757439 0.652905i \(-0.773550\pi\)
−0.757439 + 0.652905i \(0.773550\pi\)
\(114\) −1234.17 −1.01396
\(115\) 0 0
\(116\) 1591.98 1.27424
\(117\) −554.851 −0.438427
\(118\) −3339.17 −2.60505
\(119\) −225.904 −0.174022
\(120\) 0 0
\(121\) −495.725 −0.372445
\(122\) 1356.28 1.00649
\(123\) −3234.72 −2.37126
\(124\) 462.006 0.334592
\(125\) 0 0
\(126\) −1366.97 −0.966506
\(127\) −834.517 −0.583082 −0.291541 0.956558i \(-0.594168\pi\)
−0.291541 + 0.956558i \(0.594168\pi\)
\(128\) 1794.98 1.23950
\(129\) −3153.02 −2.15200
\(130\) 0 0
\(131\) 510.293 0.340340 0.170170 0.985415i \(-0.445568\pi\)
0.170170 + 0.985415i \(0.445568\pi\)
\(132\) 2609.25 1.72050
\(133\) −319.692 −0.208427
\(134\) 1413.45 0.911221
\(135\) 0 0
\(136\) 390.750 0.246371
\(137\) −11.2339 −0.00700567 −0.00350284 0.999994i \(-0.501115\pi\)
−0.00350284 + 0.999994i \(0.501115\pi\)
\(138\) 796.694 0.491443
\(139\) −1656.81 −1.01100 −0.505501 0.862826i \(-0.668692\pi\)
−0.505501 + 0.862826i \(0.668692\pi\)
\(140\) 0 0
\(141\) 863.109 0.515510
\(142\) 2447.85 1.44661
\(143\) 464.959 0.271901
\(144\) −812.174 −0.470008
\(145\) 0 0
\(146\) −3114.84 −1.76566
\(147\) 2058.33 1.15488
\(148\) −4372.15 −2.42830
\(149\) −510.206 −0.280522 −0.140261 0.990115i \(-0.544794\pi\)
−0.140261 + 0.990115i \(0.544794\pi\)
\(150\) 0 0
\(151\) −2337.38 −1.25969 −0.629846 0.776720i \(-0.716882\pi\)
−0.629846 + 0.776720i \(0.716882\pi\)
\(152\) 552.974 0.295080
\(153\) −868.325 −0.458823
\(154\) 1145.51 0.599402
\(155\) 0 0
\(156\) 1452.45 0.745442
\(157\) −146.592 −0.0745178 −0.0372589 0.999306i \(-0.511863\pi\)
−0.0372589 + 0.999306i \(0.511863\pi\)
\(158\) −5170.59 −2.60348
\(159\) −3303.61 −1.64776
\(160\) 0 0
\(161\) 206.370 0.101020
\(162\) 2079.39 1.00847
\(163\) 3278.19 1.57526 0.787630 0.616149i \(-0.211308\pi\)
0.787630 + 0.616149i \(0.211308\pi\)
\(164\) 4749.44 2.26139
\(165\) 0 0
\(166\) −2014.24 −0.941778
\(167\) 1555.42 0.720732 0.360366 0.932811i \(-0.382652\pi\)
0.360366 + 0.932811i \(0.382652\pi\)
\(168\) 1091.96 0.501469
\(169\) −1938.18 −0.882193
\(170\) 0 0
\(171\) −1228.82 −0.549534
\(172\) 4629.48 2.05229
\(173\) 472.392 0.207603 0.103801 0.994598i \(-0.466899\pi\)
0.103801 + 0.994598i \(0.466899\pi\)
\(174\) 4789.58 2.08677
\(175\) 0 0
\(176\) 680.594 0.291487
\(177\) −5927.47 −2.51715
\(178\) 6606.54 2.78192
\(179\) 2429.45 1.01444 0.507222 0.861815i \(-0.330672\pi\)
0.507222 + 0.861815i \(0.330672\pi\)
\(180\) 0 0
\(181\) −982.359 −0.403415 −0.201708 0.979446i \(-0.564649\pi\)
−0.201708 + 0.979446i \(0.564649\pi\)
\(182\) 637.653 0.259703
\(183\) 2407.58 0.972533
\(184\) −356.960 −0.143019
\(185\) 0 0
\(186\) 1389.98 0.547947
\(187\) 727.648 0.284550
\(188\) −1267.28 −0.491626
\(189\) −526.887 −0.202780
\(190\) 0 0
\(191\) 1361.14 0.515649 0.257824 0.966192i \(-0.416994\pi\)
0.257824 + 0.966192i \(0.416994\pi\)
\(192\) 6426.82 2.41571
\(193\) 1456.29 0.543142 0.271571 0.962418i \(-0.412457\pi\)
0.271571 + 0.962418i \(0.412457\pi\)
\(194\) 4599.57 1.70222
\(195\) 0 0
\(196\) −3022.18 −1.10138
\(197\) −1071.99 −0.387695 −0.193847 0.981032i \(-0.562097\pi\)
−0.193847 + 0.981032i \(0.562097\pi\)
\(198\) 4403.08 1.58037
\(199\) −2879.31 −1.02567 −0.512836 0.858486i \(-0.671405\pi\)
−0.512836 + 0.858486i \(0.671405\pi\)
\(200\) 0 0
\(201\) 2509.07 0.880477
\(202\) −6406.19 −2.23138
\(203\) 1240.66 0.428952
\(204\) 2273.04 0.780120
\(205\) 0 0
\(206\) 973.077 0.329114
\(207\) 793.238 0.266347
\(208\) 378.855 0.126293
\(209\) 1029.74 0.340807
\(210\) 0 0
\(211\) −4746.47 −1.54863 −0.774313 0.632802i \(-0.781905\pi\)
−0.774313 + 0.632802i \(0.781905\pi\)
\(212\) 4850.59 1.57141
\(213\) 4345.25 1.39780
\(214\) 261.810 0.0836306
\(215\) 0 0
\(216\) 911.363 0.287085
\(217\) 360.050 0.112635
\(218\) −8685.90 −2.69855
\(219\) −5529.26 −1.70609
\(220\) 0 0
\(221\) 405.048 0.123287
\(222\) −13153.9 −3.97673
\(223\) −4874.04 −1.46363 −0.731815 0.681503i \(-0.761327\pi\)
−0.731815 + 0.681503i \(0.761327\pi\)
\(224\) 2047.42 0.610709
\(225\) 0 0
\(226\) 8038.26 2.36592
\(227\) 2742.09 0.801757 0.400879 0.916131i \(-0.368705\pi\)
0.400879 + 0.916131i \(0.368705\pi\)
\(228\) 3216.72 0.934353
\(229\) 1528.38 0.441041 0.220520 0.975382i \(-0.429224\pi\)
0.220520 + 0.975382i \(0.429224\pi\)
\(230\) 0 0
\(231\) 2033.44 0.579179
\(232\) −2145.98 −0.607287
\(233\) −5552.78 −1.56126 −0.780632 0.624991i \(-0.785103\pi\)
−0.780632 + 0.624991i \(0.785103\pi\)
\(234\) 2450.99 0.684729
\(235\) 0 0
\(236\) 8703.12 2.40053
\(237\) −9178.49 −2.51564
\(238\) 997.909 0.271785
\(239\) 2779.63 0.752299 0.376149 0.926559i \(-0.377248\pi\)
0.376149 + 0.926559i \(0.377248\pi\)
\(240\) 0 0
\(241\) −5568.82 −1.48846 −0.744231 0.667922i \(-0.767184\pi\)
−0.744231 + 0.667922i \(0.767184\pi\)
\(242\) 2189.81 0.581680
\(243\) 5276.68 1.39300
\(244\) −3534.98 −0.927475
\(245\) 0 0
\(246\) 14289.0 3.70340
\(247\) 573.209 0.147662
\(248\) −622.783 −0.159463
\(249\) −3575.54 −0.910003
\(250\) 0 0
\(251\) −387.065 −0.0973360 −0.0486680 0.998815i \(-0.515498\pi\)
−0.0486680 + 0.998815i \(0.515498\pi\)
\(252\) 3562.85 0.890628
\(253\) −664.726 −0.165182
\(254\) 3686.39 0.910649
\(255\) 0 0
\(256\) −1372.41 −0.335061
\(257\) −1476.07 −0.358267 −0.179133 0.983825i \(-0.557329\pi\)
−0.179133 + 0.983825i \(0.557329\pi\)
\(258\) 13928.1 3.36096
\(259\) −3407.30 −0.817449
\(260\) 0 0
\(261\) 4768.81 1.13097
\(262\) −2254.17 −0.531537
\(263\) −203.984 −0.0478259 −0.0239130 0.999714i \(-0.507612\pi\)
−0.0239130 + 0.999714i \(0.507612\pi\)
\(264\) −3517.26 −0.819971
\(265\) 0 0
\(266\) 1412.20 0.325518
\(267\) 11727.5 2.68806
\(268\) −3683.98 −0.839683
\(269\) −6973.71 −1.58065 −0.790324 0.612689i \(-0.790088\pi\)
−0.790324 + 0.612689i \(0.790088\pi\)
\(270\) 0 0
\(271\) −2164.97 −0.485287 −0.242643 0.970116i \(-0.578015\pi\)
−0.242643 + 0.970116i \(0.578015\pi\)
\(272\) 592.898 0.132168
\(273\) 1131.92 0.250941
\(274\) 49.6246 0.0109414
\(275\) 0 0
\(276\) −2076.48 −0.452861
\(277\) −1194.00 −0.258992 −0.129496 0.991580i \(-0.541336\pi\)
−0.129496 + 0.991580i \(0.541336\pi\)
\(278\) 7318.81 1.57897
\(279\) 1383.95 0.296971
\(280\) 0 0
\(281\) 6485.98 1.37694 0.688472 0.725263i \(-0.258282\pi\)
0.688472 + 0.725263i \(0.258282\pi\)
\(282\) −3812.69 −0.805116
\(283\) 3214.41 0.675182 0.337591 0.941293i \(-0.390388\pi\)
0.337591 + 0.941293i \(0.390388\pi\)
\(284\) −6380.00 −1.33304
\(285\) 0 0
\(286\) −2053.91 −0.424651
\(287\) 3701.33 0.761263
\(288\) 7869.81 1.61018
\(289\) −4279.11 −0.870977
\(290\) 0 0
\(291\) 8164.85 1.64478
\(292\) 8118.44 1.62704
\(293\) −5585.47 −1.11367 −0.556837 0.830622i \(-0.687985\pi\)
−0.556837 + 0.830622i \(0.687985\pi\)
\(294\) −9092.44 −1.80368
\(295\) 0 0
\(296\) 5893.65 1.15730
\(297\) 1697.13 0.331573
\(298\) 2253.78 0.438115
\(299\) −370.022 −0.0715684
\(300\) 0 0
\(301\) 3607.84 0.690872
\(302\) 10325.1 1.96737
\(303\) −11371.8 −2.15609
\(304\) 839.047 0.158298
\(305\) 0 0
\(306\) 3835.73 0.716583
\(307\) −2849.51 −0.529740 −0.264870 0.964284i \(-0.585329\pi\)
−0.264870 + 0.964284i \(0.585329\pi\)
\(308\) −2985.63 −0.552344
\(309\) 1727.34 0.318010
\(310\) 0 0
\(311\) −6617.84 −1.20664 −0.603318 0.797501i \(-0.706155\pi\)
−0.603318 + 0.797501i \(0.706155\pi\)
\(312\) −1957.90 −0.355269
\(313\) 6271.26 1.13250 0.566250 0.824233i \(-0.308394\pi\)
0.566250 + 0.824233i \(0.308394\pi\)
\(314\) 647.554 0.116381
\(315\) 0 0
\(316\) 13476.5 2.39909
\(317\) −5650.73 −1.00119 −0.500594 0.865682i \(-0.666885\pi\)
−0.500594 + 0.865682i \(0.666885\pi\)
\(318\) 14593.3 2.57344
\(319\) −3996.22 −0.701395
\(320\) 0 0
\(321\) 464.748 0.0808090
\(322\) −911.617 −0.157772
\(323\) 897.055 0.154531
\(324\) −5419.67 −0.929299
\(325\) 0 0
\(326\) −14481.0 −2.46022
\(327\) −15418.6 −2.60750
\(328\) −6402.23 −1.07776
\(329\) −987.612 −0.165498
\(330\) 0 0
\(331\) −6391.40 −1.06134 −0.530669 0.847579i \(-0.678059\pi\)
−0.530669 + 0.847579i \(0.678059\pi\)
\(332\) 5249.86 0.867841
\(333\) −13096.9 −2.15527
\(334\) −6870.92 −1.12563
\(335\) 0 0
\(336\) 1656.87 0.269017
\(337\) −4153.87 −0.671441 −0.335721 0.941962i \(-0.608980\pi\)
−0.335721 + 0.941962i \(0.608980\pi\)
\(338\) 8561.70 1.37780
\(339\) 14269.0 2.28609
\(340\) 0 0
\(341\) −1159.74 −0.184174
\(342\) 5428.19 0.858254
\(343\) −5432.84 −0.855236
\(344\) −6240.52 −0.978100
\(345\) 0 0
\(346\) −2086.74 −0.324231
\(347\) 3071.86 0.475234 0.237617 0.971359i \(-0.423634\pi\)
0.237617 + 0.971359i \(0.423634\pi\)
\(348\) −12483.4 −1.92294
\(349\) −8358.91 −1.28207 −0.641035 0.767512i \(-0.721495\pi\)
−0.641035 + 0.767512i \(0.721495\pi\)
\(350\) 0 0
\(351\) 944.712 0.143661
\(352\) −6594.82 −0.998594
\(353\) −8018.12 −1.20896 −0.604478 0.796622i \(-0.706618\pi\)
−0.604478 + 0.796622i \(0.706618\pi\)
\(354\) 26184.0 3.93125
\(355\) 0 0
\(356\) −17219.1 −2.56352
\(357\) 1771.42 0.262615
\(358\) −10731.8 −1.58434
\(359\) 2138.46 0.314384 0.157192 0.987568i \(-0.449756\pi\)
0.157192 + 0.987568i \(0.449756\pi\)
\(360\) 0 0
\(361\) −5589.52 −0.814918
\(362\) 4339.47 0.630048
\(363\) 3887.21 0.562054
\(364\) −1661.96 −0.239315
\(365\) 0 0
\(366\) −10635.2 −1.51889
\(367\) 4509.96 0.641467 0.320733 0.947170i \(-0.396071\pi\)
0.320733 + 0.947170i \(0.396071\pi\)
\(368\) −541.628 −0.0767237
\(369\) 14227.1 2.00713
\(370\) 0 0
\(371\) 3780.15 0.528991
\(372\) −3622.80 −0.504929
\(373\) 3362.09 0.466709 0.233355 0.972392i \(-0.425030\pi\)
0.233355 + 0.972392i \(0.425030\pi\)
\(374\) −3214.31 −0.444406
\(375\) 0 0
\(376\) 1708.29 0.234303
\(377\) −2224.51 −0.303894
\(378\) 2327.47 0.316699
\(379\) 2107.16 0.285587 0.142793 0.989753i \(-0.454392\pi\)
0.142793 + 0.989753i \(0.454392\pi\)
\(380\) 0 0
\(381\) 6543.84 0.879924
\(382\) −6012.71 −0.805333
\(383\) −1373.05 −0.183184 −0.0915919 0.995797i \(-0.529196\pi\)
−0.0915919 + 0.995797i \(0.529196\pi\)
\(384\) −14075.3 −1.87052
\(385\) 0 0
\(386\) −6433.03 −0.848271
\(387\) 13867.7 1.82154
\(388\) −11988.2 −1.56858
\(389\) 7008.05 0.913425 0.456713 0.889614i \(-0.349027\pi\)
0.456713 + 0.889614i \(0.349027\pi\)
\(390\) 0 0
\(391\) −579.074 −0.0748978
\(392\) 4073.89 0.524904
\(393\) −4001.44 −0.513604
\(394\) 4735.39 0.605496
\(395\) 0 0
\(396\) −11476.1 −1.45630
\(397\) −2402.53 −0.303727 −0.151864 0.988401i \(-0.548527\pi\)
−0.151864 + 0.988401i \(0.548527\pi\)
\(398\) 12719.0 1.60188
\(399\) 2506.85 0.314535
\(400\) 0 0
\(401\) −11902.0 −1.48218 −0.741091 0.671404i \(-0.765691\pi\)
−0.741091 + 0.671404i \(0.765691\pi\)
\(402\) −11083.5 −1.37512
\(403\) −645.572 −0.0797971
\(404\) 16696.9 2.05620
\(405\) 0 0
\(406\) −5480.48 −0.669930
\(407\) 10975.1 1.33664
\(408\) −3064.05 −0.371797
\(409\) 5277.96 0.638089 0.319044 0.947740i \(-0.396638\pi\)
0.319044 + 0.947740i \(0.396638\pi\)
\(410\) 0 0
\(411\) 88.0903 0.0105722
\(412\) −2536.20 −0.303276
\(413\) 6782.51 0.808100
\(414\) −3504.05 −0.415977
\(415\) 0 0
\(416\) −3671.03 −0.432662
\(417\) 12991.9 1.52569
\(418\) −4548.77 −0.532267
\(419\) −11196.4 −1.30545 −0.652723 0.757597i \(-0.726373\pi\)
−0.652723 + 0.757597i \(0.726373\pi\)
\(420\) 0 0
\(421\) 5176.82 0.599293 0.299647 0.954050i \(-0.403131\pi\)
0.299647 + 0.954050i \(0.403131\pi\)
\(422\) 20967.0 2.41862
\(423\) −3796.16 −0.436349
\(424\) −6538.58 −0.748918
\(425\) 0 0
\(426\) −19194.7 −2.18307
\(427\) −2754.88 −0.312220
\(428\) −682.375 −0.0770650
\(429\) −3645.96 −0.410324
\(430\) 0 0
\(431\) 9348.93 1.04483 0.522415 0.852691i \(-0.325031\pi\)
0.522415 + 0.852691i \(0.325031\pi\)
\(432\) 1382.84 0.154009
\(433\) −4320.91 −0.479560 −0.239780 0.970827i \(-0.577075\pi\)
−0.239780 + 0.970827i \(0.577075\pi\)
\(434\) −1590.48 −0.175912
\(435\) 0 0
\(436\) 22638.7 2.48669
\(437\) −819.484 −0.0897054
\(438\) 24424.9 2.66454
\(439\) −7016.03 −0.762772 −0.381386 0.924416i \(-0.624553\pi\)
−0.381386 + 0.924416i \(0.624553\pi\)
\(440\) 0 0
\(441\) −9053.00 −0.977541
\(442\) −1789.26 −0.192548
\(443\) −12343.6 −1.32384 −0.661921 0.749574i \(-0.730259\pi\)
−0.661921 + 0.749574i \(0.730259\pi\)
\(444\) 34284.1 3.66453
\(445\) 0 0
\(446\) 21530.5 2.28588
\(447\) 4000.77 0.423333
\(448\) −7353.88 −0.775532
\(449\) 18146.9 1.90737 0.953683 0.300815i \(-0.0972587\pi\)
0.953683 + 0.300815i \(0.0972587\pi\)
\(450\) 0 0
\(451\) −11922.1 −1.24477
\(452\) −20950.7 −2.18017
\(453\) 18328.5 1.90099
\(454\) −12112.9 −1.25217
\(455\) 0 0
\(456\) −4336.13 −0.445302
\(457\) −5233.82 −0.535728 −0.267864 0.963457i \(-0.586318\pi\)
−0.267864 + 0.963457i \(0.586318\pi\)
\(458\) −6751.47 −0.688811
\(459\) 1478.45 0.150344
\(460\) 0 0
\(461\) −2335.01 −0.235905 −0.117952 0.993019i \(-0.537633\pi\)
−0.117952 + 0.993019i \(0.537633\pi\)
\(462\) −8982.49 −0.904553
\(463\) −13644.1 −1.36954 −0.684769 0.728760i \(-0.740097\pi\)
−0.684769 + 0.728760i \(0.740097\pi\)
\(464\) −3256.17 −0.325784
\(465\) 0 0
\(466\) 24528.8 2.43836
\(467\) 5246.31 0.519851 0.259925 0.965629i \(-0.416302\pi\)
0.259925 + 0.965629i \(0.416302\pi\)
\(468\) −6388.21 −0.630972
\(469\) −2871.00 −0.282666
\(470\) 0 0
\(471\) 1149.50 0.112454
\(472\) −11731.8 −1.14407
\(473\) −11621.0 −1.12967
\(474\) 40545.0 3.92889
\(475\) 0 0
\(476\) −2600.92 −0.250448
\(477\) 14530.0 1.39473
\(478\) −12278.7 −1.17493
\(479\) 12278.3 1.17121 0.585603 0.810598i \(-0.300858\pi\)
0.585603 + 0.810598i \(0.300858\pi\)
\(480\) 0 0
\(481\) 6109.31 0.579128
\(482\) 24599.7 2.32466
\(483\) −1618.24 −0.152448
\(484\) −5707.47 −0.536013
\(485\) 0 0
\(486\) −23309.2 −2.17557
\(487\) 8945.24 0.832336 0.416168 0.909288i \(-0.363373\pi\)
0.416168 + 0.909288i \(0.363373\pi\)
\(488\) 4765.14 0.442024
\(489\) −25705.8 −2.37721
\(490\) 0 0
\(491\) −7792.94 −0.716274 −0.358137 0.933669i \(-0.616588\pi\)
−0.358137 + 0.933669i \(0.616588\pi\)
\(492\) −37242.6 −3.41265
\(493\) −3481.29 −0.318031
\(494\) −2532.09 −0.230616
\(495\) 0 0
\(496\) −944.970 −0.0855451
\(497\) −4972.06 −0.448747
\(498\) 15794.6 1.42123
\(499\) −8577.71 −0.769521 −0.384761 0.923016i \(-0.625716\pi\)
−0.384761 + 0.923016i \(0.625716\pi\)
\(500\) 0 0
\(501\) −12196.8 −1.08765
\(502\) 1709.82 0.152018
\(503\) −7784.99 −0.690091 −0.345045 0.938586i \(-0.612136\pi\)
−0.345045 + 0.938586i \(0.612136\pi\)
\(504\) −4802.71 −0.424464
\(505\) 0 0
\(506\) 2936.36 0.257978
\(507\) 15198.2 1.33131
\(508\) −9608.12 −0.839156
\(509\) −11390.4 −0.991891 −0.495946 0.868354i \(-0.665178\pi\)
−0.495946 + 0.868354i \(0.665178\pi\)
\(510\) 0 0
\(511\) 6326.85 0.547717
\(512\) −8297.40 −0.716205
\(513\) 2092.24 0.180068
\(514\) 6520.37 0.559535
\(515\) 0 0
\(516\) −36301.9 −3.09710
\(517\) 3181.14 0.270612
\(518\) 15051.4 1.27668
\(519\) −3704.24 −0.313292
\(520\) 0 0
\(521\) −12824.5 −1.07841 −0.539206 0.842174i \(-0.681276\pi\)
−0.539206 + 0.842174i \(0.681276\pi\)
\(522\) −21065.7 −1.76632
\(523\) −13087.4 −1.09421 −0.547107 0.837063i \(-0.684271\pi\)
−0.547107 + 0.837063i \(0.684271\pi\)
\(524\) 5875.20 0.489808
\(525\) 0 0
\(526\) 901.080 0.0746938
\(527\) −1010.30 −0.0835093
\(528\) −5336.86 −0.439880
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) 26070.4 2.13062
\(532\) −3680.73 −0.299962
\(533\) −6636.50 −0.539322
\(534\) −51805.0 −4.19817
\(535\) 0 0
\(536\) 4966.00 0.400184
\(537\) −19050.4 −1.53089
\(538\) 30805.6 2.46863
\(539\) 7586.33 0.606245
\(540\) 0 0
\(541\) 15464.3 1.22895 0.614473 0.788938i \(-0.289369\pi\)
0.614473 + 0.788938i \(0.289369\pi\)
\(542\) 9563.54 0.757914
\(543\) 7703.14 0.608791
\(544\) −5745.06 −0.452789
\(545\) 0 0
\(546\) −5000.14 −0.391916
\(547\) −6981.32 −0.545703 −0.272852 0.962056i \(-0.587967\pi\)
−0.272852 + 0.962056i \(0.587967\pi\)
\(548\) −129.340 −0.0100824
\(549\) −10589.1 −0.823192
\(550\) 0 0
\(551\) −4926.60 −0.380908
\(552\) 2799.09 0.215828
\(553\) 10502.5 0.807615
\(554\) 5274.38 0.404489
\(555\) 0 0
\(556\) −19075.5 −1.45501
\(557\) −24964.8 −1.89909 −0.949543 0.313637i \(-0.898453\pi\)
−0.949543 + 0.313637i \(0.898453\pi\)
\(558\) −6113.45 −0.463805
\(559\) −6468.88 −0.489454
\(560\) 0 0
\(561\) −5705.83 −0.429412
\(562\) −28651.2 −2.15049
\(563\) 10820.3 0.809986 0.404993 0.914320i \(-0.367274\pi\)
0.404993 + 0.914320i \(0.367274\pi\)
\(564\) 9937.31 0.741908
\(565\) 0 0
\(566\) −14199.3 −1.05449
\(567\) −4223.65 −0.312834
\(568\) 8600.23 0.635312
\(569\) 8438.73 0.621740 0.310870 0.950453i \(-0.399380\pi\)
0.310870 + 0.950453i \(0.399380\pi\)
\(570\) 0 0
\(571\) 23107.6 1.69356 0.846781 0.531942i \(-0.178538\pi\)
0.846781 + 0.531942i \(0.178538\pi\)
\(572\) 5353.26 0.391313
\(573\) −10673.4 −0.778161
\(574\) −16350.2 −1.18893
\(575\) 0 0
\(576\) −28266.7 −2.04475
\(577\) −24848.7 −1.79283 −0.896416 0.443215i \(-0.853838\pi\)
−0.896416 + 0.443215i \(0.853838\pi\)
\(578\) 18902.5 1.36028
\(579\) −11419.5 −0.819651
\(580\) 0 0
\(581\) 4091.31 0.292145
\(582\) −36067.4 −2.56880
\(583\) −12176.0 −0.864974
\(584\) −10943.6 −0.775430
\(585\) 0 0
\(586\) 24673.2 1.73932
\(587\) −8663.94 −0.609198 −0.304599 0.952481i \(-0.598522\pi\)
−0.304599 + 0.952481i \(0.598522\pi\)
\(588\) 23698.3 1.66208
\(589\) −1429.74 −0.100019
\(590\) 0 0
\(591\) 8405.94 0.585066
\(592\) 8942.64 0.620845
\(593\) 24678.9 1.70901 0.854503 0.519446i \(-0.173862\pi\)
0.854503 + 0.519446i \(0.173862\pi\)
\(594\) −7496.88 −0.517846
\(595\) 0 0
\(596\) −5874.20 −0.403719
\(597\) 22578.0 1.54783
\(598\) 1634.54 0.111774
\(599\) 19698.4 1.34367 0.671833 0.740702i \(-0.265507\pi\)
0.671833 + 0.740702i \(0.265507\pi\)
\(600\) 0 0
\(601\) −18449.1 −1.25217 −0.626086 0.779754i \(-0.715344\pi\)
−0.626086 + 0.779754i \(0.715344\pi\)
\(602\) −15937.3 −1.07899
\(603\) −11035.5 −0.745272
\(604\) −26911.2 −1.81291
\(605\) 0 0
\(606\) 50233.9 3.36735
\(607\) 11321.0 0.757012 0.378506 0.925599i \(-0.376438\pi\)
0.378506 + 0.925599i \(0.376438\pi\)
\(608\) −8130.20 −0.542308
\(609\) −9728.59 −0.647327
\(610\) 0 0
\(611\) 1770.80 0.117248
\(612\) −9997.36 −0.660326
\(613\) −712.219 −0.0469270 −0.0234635 0.999725i \(-0.507469\pi\)
−0.0234635 + 0.999725i \(0.507469\pi\)
\(614\) 12587.4 0.827341
\(615\) 0 0
\(616\) 4024.62 0.263241
\(617\) −3234.25 −0.211031 −0.105515 0.994418i \(-0.533649\pi\)
−0.105515 + 0.994418i \(0.533649\pi\)
\(618\) −7630.36 −0.496663
\(619\) 26905.1 1.74703 0.873513 0.486801i \(-0.161836\pi\)
0.873513 + 0.486801i \(0.161836\pi\)
\(620\) 0 0
\(621\) −1350.60 −0.0872750
\(622\) 29233.6 1.88451
\(623\) −13419.2 −0.862967
\(624\) −2970.78 −0.190587
\(625\) 0 0
\(626\) −27702.6 −1.76872
\(627\) −8074.68 −0.514309
\(628\) −1687.77 −0.107244
\(629\) 9560.90 0.606070
\(630\) 0 0
\(631\) 16199.5 1.02202 0.511008 0.859576i \(-0.329272\pi\)
0.511008 + 0.859576i \(0.329272\pi\)
\(632\) −18166.3 −1.14338
\(633\) 37219.3 2.33702
\(634\) 24961.5 1.56364
\(635\) 0 0
\(636\) −38035.7 −2.37141
\(637\) 4222.96 0.262668
\(638\) 17652.9 1.09543
\(639\) −19111.5 −1.18316
\(640\) 0 0
\(641\) 19943.5 1.22889 0.614446 0.788959i \(-0.289380\pi\)
0.614446 + 0.788959i \(0.289380\pi\)
\(642\) −2052.97 −0.126206
\(643\) 27691.0 1.69833 0.849164 0.528129i \(-0.177106\pi\)
0.849164 + 0.528129i \(0.177106\pi\)
\(644\) 2376.01 0.145385
\(645\) 0 0
\(646\) −3962.65 −0.241344
\(647\) 23560.3 1.43161 0.715805 0.698300i \(-0.246060\pi\)
0.715805 + 0.698300i \(0.246060\pi\)
\(648\) 7305.70 0.442893
\(649\) −21846.7 −1.32136
\(650\) 0 0
\(651\) −2823.32 −0.169976
\(652\) 37743.0 2.26707
\(653\) −5571.58 −0.333894 −0.166947 0.985966i \(-0.553391\pi\)
−0.166947 + 0.985966i \(0.553391\pi\)
\(654\) 68110.2 4.07235
\(655\) 0 0
\(656\) −9714.32 −0.578171
\(657\) 24319.0 1.44410
\(658\) 4362.68 0.258472
\(659\) 10177.4 0.601602 0.300801 0.953687i \(-0.402746\pi\)
0.300801 + 0.953687i \(0.402746\pi\)
\(660\) 0 0
\(661\) −27413.8 −1.61312 −0.806561 0.591151i \(-0.798674\pi\)
−0.806561 + 0.591151i \(0.798674\pi\)
\(662\) 28233.3 1.65758
\(663\) −3176.17 −0.186052
\(664\) −7076.79 −0.413604
\(665\) 0 0
\(666\) 57854.1 3.36607
\(667\) 3180.25 0.184618
\(668\) 17908.2 1.03726
\(669\) 38219.6 2.20875
\(670\) 0 0
\(671\) 8873.57 0.510522
\(672\) −16054.8 −0.921616
\(673\) −12767.5 −0.731277 −0.365639 0.930757i \(-0.619149\pi\)
−0.365639 + 0.930757i \(0.619149\pi\)
\(674\) 18349.3 1.04865
\(675\) 0 0
\(676\) −22315.0 −1.26963
\(677\) −17036.9 −0.967180 −0.483590 0.875295i \(-0.660667\pi\)
−0.483590 + 0.875295i \(0.660667\pi\)
\(678\) −63031.7 −3.57038
\(679\) −9342.63 −0.528037
\(680\) 0 0
\(681\) −21502.0 −1.20993
\(682\) 5123.02 0.287640
\(683\) 510.213 0.0285838 0.0142919 0.999898i \(-0.495451\pi\)
0.0142919 + 0.999898i \(0.495451\pi\)
\(684\) −14147.9 −0.790875
\(685\) 0 0
\(686\) 23999.0 1.33569
\(687\) −11984.8 −0.665570
\(688\) −9468.96 −0.524710
\(689\) −6777.84 −0.374768
\(690\) 0 0
\(691\) 22793.1 1.25483 0.627416 0.778684i \(-0.284112\pi\)
0.627416 + 0.778684i \(0.284112\pi\)
\(692\) 5438.83 0.298776
\(693\) −8943.53 −0.490240
\(694\) −13569.6 −0.742213
\(695\) 0 0
\(696\) 16827.7 0.916452
\(697\) −10385.9 −0.564412
\(698\) 36924.6 2.00232
\(699\) 43541.9 2.35609
\(700\) 0 0
\(701\) 26324.3 1.41834 0.709168 0.705039i \(-0.249071\pi\)
0.709168 + 0.705039i \(0.249071\pi\)
\(702\) −4173.17 −0.224368
\(703\) 13530.2 0.725892
\(704\) 23687.2 1.26810
\(705\) 0 0
\(706\) 35419.2 1.88813
\(707\) 13012.2 0.692185
\(708\) −68245.2 −3.62262
\(709\) −10961.3 −0.580620 −0.290310 0.956933i \(-0.593758\pi\)
−0.290310 + 0.956933i \(0.593758\pi\)
\(710\) 0 0
\(711\) 40369.2 2.12934
\(712\) 23211.3 1.22174
\(713\) 922.938 0.0484773
\(714\) −7825.07 −0.410148
\(715\) 0 0
\(716\) 27971.2 1.45996
\(717\) −21796.4 −1.13529
\(718\) −9446.44 −0.491000
\(719\) −1304.68 −0.0676723 −0.0338362 0.999427i \(-0.510772\pi\)
−0.0338362 + 0.999427i \(0.510772\pi\)
\(720\) 0 0
\(721\) −1976.51 −0.102093
\(722\) 24691.1 1.27273
\(723\) 43667.7 2.24622
\(724\) −11310.3 −0.580585
\(725\) 0 0
\(726\) −17171.3 −0.877808
\(727\) −1583.59 −0.0807869 −0.0403934 0.999184i \(-0.512861\pi\)
−0.0403934 + 0.999184i \(0.512861\pi\)
\(728\) 2240.32 0.114055
\(729\) −28667.3 −1.45645
\(730\) 0 0
\(731\) −10123.6 −0.512223
\(732\) 27719.4 1.39964
\(733\) 34351.2 1.73095 0.865477 0.500948i \(-0.167015\pi\)
0.865477 + 0.500948i \(0.167015\pi\)
\(734\) −19922.3 −1.00183
\(735\) 0 0
\(736\) 5248.27 0.262845
\(737\) 9247.61 0.462198
\(738\) −62846.5 −3.13471
\(739\) 14996.6 0.746494 0.373247 0.927732i \(-0.378244\pi\)
0.373247 + 0.927732i \(0.378244\pi\)
\(740\) 0 0
\(741\) −4494.80 −0.222835
\(742\) −16698.4 −0.826171
\(743\) 32781.7 1.61863 0.809317 0.587372i \(-0.199838\pi\)
0.809317 + 0.587372i \(0.199838\pi\)
\(744\) 4883.53 0.240644
\(745\) 0 0
\(746\) −14851.7 −0.728899
\(747\) 15726.1 0.770263
\(748\) 8377.69 0.409517
\(749\) −531.787 −0.0259427
\(750\) 0 0
\(751\) −24044.4 −1.16830 −0.584149 0.811647i \(-0.698571\pi\)
−0.584149 + 0.811647i \(0.698571\pi\)
\(752\) 2592.04 0.125694
\(753\) 3035.16 0.146889
\(754\) 9826.54 0.474617
\(755\) 0 0
\(756\) −6066.26 −0.291835
\(757\) 21680.9 1.04096 0.520479 0.853874i \(-0.325753\pi\)
0.520479 + 0.853874i \(0.325753\pi\)
\(758\) −9308.15 −0.446025
\(759\) 5212.43 0.249274
\(760\) 0 0
\(761\) −10299.1 −0.490594 −0.245297 0.969448i \(-0.578885\pi\)
−0.245297 + 0.969448i \(0.578885\pi\)
\(762\) −28906.7 −1.37425
\(763\) 17642.8 0.837105
\(764\) 15671.4 0.742108
\(765\) 0 0
\(766\) 6065.29 0.286094
\(767\) −12161.1 −0.572505
\(768\) 10761.7 0.505637
\(769\) 28377.9 1.33073 0.665365 0.746518i \(-0.268276\pi\)
0.665365 + 0.746518i \(0.268276\pi\)
\(770\) 0 0
\(771\) 11574.5 0.540657
\(772\) 16766.9 0.781675
\(773\) −35409.5 −1.64759 −0.823797 0.566885i \(-0.808148\pi\)
−0.823797 + 0.566885i \(0.808148\pi\)
\(774\) −61259.2 −2.84485
\(775\) 0 0
\(776\) 16160.1 0.747568
\(777\) 26718.2 1.23361
\(778\) −30957.3 −1.42657
\(779\) −14697.8 −0.675999
\(780\) 0 0
\(781\) 16015.2 0.733763
\(782\) 2558.00 0.116974
\(783\) −8119.58 −0.370588
\(784\) 6181.45 0.281589
\(785\) 0 0
\(786\) 17676.0 0.802138
\(787\) −6117.56 −0.277087 −0.138544 0.990356i \(-0.544242\pi\)
−0.138544 + 0.990356i \(0.544242\pi\)
\(788\) −12342.2 −0.557960
\(789\) 1599.54 0.0721737
\(790\) 0 0
\(791\) −16327.3 −0.733921
\(792\) 15469.7 0.694057
\(793\) 4939.51 0.221194
\(794\) 10612.9 0.474357
\(795\) 0 0
\(796\) −33150.6 −1.47612
\(797\) −4099.46 −0.182196 −0.0910980 0.995842i \(-0.529038\pi\)
−0.0910980 + 0.995842i \(0.529038\pi\)
\(798\) −11073.8 −0.491236
\(799\) 2771.24 0.122703
\(800\) 0 0
\(801\) −51580.3 −2.27528
\(802\) 52575.6 2.31485
\(803\) −20379.1 −0.895594
\(804\) 28887.8 1.26716
\(805\) 0 0
\(806\) 2851.75 0.124626
\(807\) 54684.1 2.38534
\(808\) −22507.4 −0.979960
\(809\) 21358.6 0.928216 0.464108 0.885779i \(-0.346375\pi\)
0.464108 + 0.885779i \(0.346375\pi\)
\(810\) 0 0
\(811\) 13967.7 0.604776 0.302388 0.953185i \(-0.402216\pi\)
0.302388 + 0.953185i \(0.402216\pi\)
\(812\) 14284.2 0.617336
\(813\) 16976.6 0.732342
\(814\) −48481.2 −2.08755
\(815\) 0 0
\(816\) −4649.19 −0.199454
\(817\) −14326.6 −0.613492
\(818\) −23314.8 −0.996557
\(819\) −4978.45 −0.212407
\(820\) 0 0
\(821\) −22387.6 −0.951684 −0.475842 0.879531i \(-0.657857\pi\)
−0.475842 + 0.879531i \(0.657857\pi\)
\(822\) −389.130 −0.0165115
\(823\) 22615.7 0.957877 0.478939 0.877848i \(-0.341022\pi\)
0.478939 + 0.877848i \(0.341022\pi\)
\(824\) 3418.80 0.144538
\(825\) 0 0
\(826\) −29961.0 −1.26208
\(827\) −10878.0 −0.457394 −0.228697 0.973498i \(-0.573446\pi\)
−0.228697 + 0.973498i \(0.573446\pi\)
\(828\) 9132.86 0.383320
\(829\) 27382.3 1.14720 0.573600 0.819136i \(-0.305547\pi\)
0.573600 + 0.819136i \(0.305547\pi\)
\(830\) 0 0
\(831\) 9362.74 0.390842
\(832\) 13185.6 0.549432
\(833\) 6608.81 0.274888
\(834\) −57390.2 −2.38281
\(835\) 0 0
\(836\) 11855.8 0.490480
\(837\) −2356.37 −0.0973096
\(838\) 49459.1 2.03883
\(839\) −31799.7 −1.30852 −0.654260 0.756270i \(-0.727020\pi\)
−0.654260 + 0.756270i \(0.727020\pi\)
\(840\) 0 0
\(841\) −5269.87 −0.216076
\(842\) −22868.0 −0.935968
\(843\) −50859.6 −2.07793
\(844\) −54647.9 −2.22874
\(845\) 0 0
\(846\) 16769.1 0.681483
\(847\) −4447.94 −0.180440
\(848\) −9921.21 −0.401764
\(849\) −25205.7 −1.01891
\(850\) 0 0
\(851\) −8734.14 −0.351824
\(852\) 50028.6 2.01168
\(853\) −32016.4 −1.28514 −0.642568 0.766229i \(-0.722131\pi\)
−0.642568 + 0.766229i \(0.722131\pi\)
\(854\) 12169.4 0.487620
\(855\) 0 0
\(856\) 919.839 0.0367283
\(857\) −25280.1 −1.00764 −0.503822 0.863807i \(-0.668073\pi\)
−0.503822 + 0.863807i \(0.668073\pi\)
\(858\) 16105.7 0.640837
\(859\) −22313.5 −0.886296 −0.443148 0.896448i \(-0.646138\pi\)
−0.443148 + 0.896448i \(0.646138\pi\)
\(860\) 0 0
\(861\) −29023.8 −1.14881
\(862\) −41297.9 −1.63180
\(863\) 1478.28 0.0583096 0.0291548 0.999575i \(-0.490718\pi\)
0.0291548 + 0.999575i \(0.490718\pi\)
\(864\) −13399.5 −0.527615
\(865\) 0 0
\(866\) 19087.2 0.748970
\(867\) 33554.5 1.31438
\(868\) 4145.39 0.162101
\(869\) −33829.0 −1.32056
\(870\) 0 0
\(871\) 5147.72 0.200257
\(872\) −30516.9 −1.18513
\(873\) −35910.9 −1.39221
\(874\) 3619.99 0.140101
\(875\) 0 0
\(876\) −63660.5 −2.45535
\(877\) −32974.6 −1.26964 −0.634819 0.772661i \(-0.718925\pi\)
−0.634819 + 0.772661i \(0.718925\pi\)
\(878\) 30992.6 1.19129
\(879\) 43798.3 1.68064
\(880\) 0 0
\(881\) −32000.7 −1.22376 −0.611879 0.790951i \(-0.709586\pi\)
−0.611879 + 0.790951i \(0.709586\pi\)
\(882\) 39990.7 1.52671
\(883\) 44218.6 1.68525 0.842623 0.538503i \(-0.181010\pi\)
0.842623 + 0.538503i \(0.181010\pi\)
\(884\) 4663.47 0.177432
\(885\) 0 0
\(886\) 54526.6 2.06756
\(887\) −27374.8 −1.03625 −0.518126 0.855304i \(-0.673370\pi\)
−0.518126 + 0.855304i \(0.673370\pi\)
\(888\) −46214.9 −1.74647
\(889\) −7487.79 −0.282489
\(890\) 0 0
\(891\) 13604.6 0.511526
\(892\) −56116.7 −2.10642
\(893\) 3921.76 0.146962
\(894\) −17673.0 −0.661155
\(895\) 0 0
\(896\) 16105.7 0.600505
\(897\) 2901.52 0.108003
\(898\) −80162.2 −2.97889
\(899\) 5548.54 0.205844
\(900\) 0 0
\(901\) −10607.1 −0.392203
\(902\) 52664.8 1.94406
\(903\) −28290.8 −1.04259
\(904\) 28241.5 1.03905
\(905\) 0 0
\(906\) −80964.3 −2.96894
\(907\) −7835.16 −0.286838 −0.143419 0.989662i \(-0.545810\pi\)
−0.143419 + 0.989662i \(0.545810\pi\)
\(908\) 31570.7 1.15387
\(909\) 50016.0 1.82500
\(910\) 0 0
\(911\) −36528.6 −1.32848 −0.664241 0.747519i \(-0.731245\pi\)
−0.664241 + 0.747519i \(0.731245\pi\)
\(912\) −6579.36 −0.238886
\(913\) −13178.3 −0.477698
\(914\) 23119.8 0.836692
\(915\) 0 0
\(916\) 17596.8 0.634734
\(917\) 4578.65 0.164886
\(918\) −6530.89 −0.234805
\(919\) −15741.5 −0.565030 −0.282515 0.959263i \(-0.591169\pi\)
−0.282515 + 0.959263i \(0.591169\pi\)
\(920\) 0 0
\(921\) 22344.4 0.799427
\(922\) 10314.7 0.368433
\(923\) 8914.93 0.317918
\(924\) 23411.7 0.833538
\(925\) 0 0
\(926\) 60271.5 2.13892
\(927\) −7597.26 −0.269177
\(928\) 31551.7 1.11609
\(929\) 47428.9 1.67502 0.837510 0.546422i \(-0.184011\pi\)
0.837510 + 0.546422i \(0.184011\pi\)
\(930\) 0 0
\(931\) 9352.54 0.329234
\(932\) −63931.3 −2.24693
\(933\) 51893.6 1.82092
\(934\) −23175.0 −0.811895
\(935\) 0 0
\(936\) 8611.29 0.300714
\(937\) 34978.0 1.21951 0.609756 0.792589i \(-0.291267\pi\)
0.609756 + 0.792589i \(0.291267\pi\)
\(938\) 12682.3 0.441464
\(939\) −49175.9 −1.70905
\(940\) 0 0
\(941\) 45144.0 1.56392 0.781962 0.623326i \(-0.214219\pi\)
0.781962 + 0.623326i \(0.214219\pi\)
\(942\) −5077.78 −0.175629
\(943\) 9487.83 0.327642
\(944\) −17801.0 −0.613744
\(945\) 0 0
\(946\) 51334.6 1.76430
\(947\) −26123.6 −0.896413 −0.448207 0.893930i \(-0.647937\pi\)
−0.448207 + 0.893930i \(0.647937\pi\)
\(948\) −105675. −3.62044
\(949\) −11344.1 −0.388035
\(950\) 0 0
\(951\) 44310.0 1.51088
\(952\) 3506.04 0.119361
\(953\) 22143.5 0.752673 0.376336 0.926483i \(-0.377184\pi\)
0.376336 + 0.926483i \(0.377184\pi\)
\(954\) −64185.0 −2.17827
\(955\) 0 0
\(956\) 32003.0 1.08269
\(957\) 31336.2 1.05847
\(958\) −54237.9 −1.82917
\(959\) −100.797 −0.00339407
\(960\) 0 0
\(961\) −28180.8 −0.945949
\(962\) −26987.3 −0.904474
\(963\) −2044.07 −0.0684000
\(964\) −64116.0 −2.14215
\(965\) 0 0
\(966\) 7148.42 0.238092
\(967\) −44869.8 −1.49216 −0.746078 0.665858i \(-0.768066\pi\)
−0.746078 + 0.665858i \(0.768066\pi\)
\(968\) 7693.65 0.255458
\(969\) −7034.23 −0.233201
\(970\) 0 0
\(971\) −25048.3 −0.827845 −0.413923 0.910312i \(-0.635842\pi\)
−0.413923 + 0.910312i \(0.635842\pi\)
\(972\) 60752.5 2.00477
\(973\) −14865.9 −0.489805
\(974\) −39514.7 −1.29993
\(975\) 0 0
\(976\) 7230.31 0.237128
\(977\) −37320.7 −1.22210 −0.611052 0.791590i \(-0.709253\pi\)
−0.611052 + 0.791590i \(0.709253\pi\)
\(978\) 113553. 3.71269
\(979\) 43223.8 1.41107
\(980\) 0 0
\(981\) 67814.7 2.20709
\(982\) 34424.5 1.11867
\(983\) 17189.4 0.557737 0.278869 0.960329i \(-0.410041\pi\)
0.278869 + 0.960329i \(0.410041\pi\)
\(984\) 50202.9 1.62643
\(985\) 0 0
\(986\) 15378.2 0.496697
\(987\) 7744.33 0.249752
\(988\) 6599.58 0.212511
\(989\) 9248.19 0.297346
\(990\) 0 0
\(991\) −57797.1 −1.85266 −0.926330 0.376712i \(-0.877055\pi\)
−0.926330 + 0.376712i \(0.877055\pi\)
\(992\) 9156.57 0.293066
\(993\) 50117.9 1.60166
\(994\) 21963.5 0.700846
\(995\) 0 0
\(996\) −41166.6 −1.30965
\(997\) −46801.0 −1.48666 −0.743331 0.668923i \(-0.766755\pi\)
−0.743331 + 0.668923i \(0.766755\pi\)
\(998\) 37891.2 1.20183
\(999\) 22299.3 0.706226
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 575.4.a.j.1.2 5
5.2 odd 4 575.4.b.i.24.2 10
5.3 odd 4 575.4.b.i.24.9 10
5.4 even 2 115.4.a.e.1.4 5
15.14 odd 2 1035.4.a.k.1.2 5
20.19 odd 2 1840.4.a.n.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.4 5 5.4 even 2
575.4.a.j.1.2 5 1.1 even 1 trivial
575.4.b.i.24.2 10 5.2 odd 4
575.4.b.i.24.9 10 5.3 odd 4
1035.4.a.k.1.2 5 15.14 odd 2
1840.4.a.n.1.2 5 20.19 odd 2