Properties

Label 1035.4.a.k.1.2
Level $1035$
Weight $4$
Character 1035.1
Self dual yes
Analytic conductor $61.067$
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] = [1035,4,Mod(1,1035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1035.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1035.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: \(61.0669768559\)
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: \(\Z[a_1, \ldots, a_{7}]\)
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 \(\chi\) \(=\) 1035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.41740 q^{2} +11.5134 q^{4} +5.00000 q^{5} -8.97260 q^{7} -15.5200 q^{8} +O(q^{10})\) \(q-4.41740 q^{2} +11.5134 q^{4} +5.00000 q^{5} -8.97260 q^{7} -15.5200 q^{8} -22.0870 q^{10} +28.9011 q^{11} +16.0879 q^{13} +39.6355 q^{14} -23.5490 q^{16} -25.1771 q^{17} -35.6298 q^{19} +57.5669 q^{20} -127.668 q^{22} +23.0000 q^{23} +25.0000 q^{25} -71.0668 q^{26} -103.305 q^{28} -138.272 q^{29} +40.1277 q^{31} +228.186 q^{32} +111.217 q^{34} -44.8630 q^{35} +379.745 q^{37} +157.391 q^{38} -77.6001 q^{40} -412.514 q^{41} -402.095 q^{43} +332.750 q^{44} -101.600 q^{46} -110.070 q^{47} -262.492 q^{49} -110.435 q^{50} +185.227 q^{52} +421.300 q^{53} +144.506 q^{55} +139.255 q^{56} +610.802 q^{58} -755.913 q^{59} -307.032 q^{61} -177.260 q^{62} -819.594 q^{64} +80.4396 q^{65} +319.974 q^{67} -289.874 q^{68} +198.178 q^{70} +554.138 q^{71} -705.131 q^{73} -1677.48 q^{74} -410.219 q^{76} -259.318 q^{77} +1170.51 q^{79} -117.745 q^{80} +1822.24 q^{82} +455.978 q^{83} -125.886 q^{85} +1776.21 q^{86} -448.546 q^{88} +1495.57 q^{89} -144.351 q^{91} +264.808 q^{92} +486.222 q^{94} -178.149 q^{95} +1041.24 q^{97} +1159.53 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8} - 30 q^{10} - 23 q^{11} + 132 q^{13} - 93 q^{14} + 282 q^{16} - 23 q^{17} - 161 q^{19} + 110 q^{20} + 193 q^{22} + 115 q^{23} + 125 q^{25} + 257 q^{26} + 17 q^{28} - 401 q^{29} + 32 q^{31} - 670 q^{32} - 663 q^{34} - 15 q^{35} - 38 q^{37} + 875 q^{38} - 690 q^{40} + 12 q^{41} - 566 q^{43} - 47 q^{44} - 138 q^{46} - 919 q^{47} - 738 q^{49} - 150 q^{50} - 305 q^{52} - 1156 q^{53} - 115 q^{55} - 343 q^{56} - 1042 q^{58} - 1324 q^{59} - 1673 q^{61} - 565 q^{62} + 2466 q^{64} + 660 q^{65} + 558 q^{67} + 2267 q^{68} - 465 q^{70} + 108 q^{71} + 1173 q^{73} - 1458 q^{74} - 3477 q^{76} - 2608 q^{77} + 656 q^{79} + 1410 q^{80} + 3505 q^{82} + 82 q^{83} - 115 q^{85} - 112 q^{86} + 2397 q^{88} - 570 q^{89} - 1589 q^{91} + 506 q^{92} - 948 q^{94} - 805 q^{95} + 633 q^{97} + 2555 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.41740 −1.56179 −0.780893 0.624665i \(-0.785235\pi\)
−0.780893 + 0.624665i \(0.785235\pi\)
\(3\) 0 0
\(4\) 11.5134 1.43917
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −8.97260 −0.484475 −0.242237 0.970217i \(-0.577881\pi\)
−0.242237 + 0.970217i \(0.577881\pi\)
\(8\) −15.5200 −0.685894
\(9\) 0 0
\(10\) −22.0870 −0.698452
\(11\) 28.9011 0.792183 0.396092 0.918211i \(-0.370366\pi\)
0.396092 + 0.918211i \(0.370366\pi\)
\(12\) 0 0
\(13\) 16.0879 0.343230 0.171615 0.985164i \(-0.445102\pi\)
0.171615 + 0.985164i \(0.445102\pi\)
\(14\) 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 \(0.557480\pi\)
\(18\) 0 0
\(19\) −35.6298 −0.430212 −0.215106 0.976591i \(-0.569010\pi\)
−0.215106 + 0.976591i \(0.569010\pi\)
\(20\) 57.5669 0.643618
\(21\) 0 0
\(22\) −127.668 −1.23722
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −71.0668 −0.536051
\(27\) 0 0
\(28\) −103.305 −0.697243
\(29\) −138.272 −0.885395 −0.442698 0.896671i \(-0.645978\pi\)
−0.442698 + 0.896671i \(0.645978\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 111.217 0.560989
\(35\) −44.8630 −0.216664
\(36\) 0 0
\(37\) 379.745 1.68729 0.843645 0.536902i \(-0.180405\pi\)
0.843645 + 0.536902i \(0.180405\pi\)
\(38\) 157.391 0.671899
\(39\) 0 0
\(40\) −77.6001 −0.306741
\(41\) −412.514 −1.57132 −0.785658 0.618662i \(-0.787675\pi\)
−0.785658 + 0.618662i \(0.787675\pi\)
\(42\) 0 0
\(43\) −402.095 −1.42602 −0.713011 0.701153i \(-0.752669\pi\)
−0.713011 + 0.701153i \(0.752669\pi\)
\(44\) 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 \(0.554636\pi\)
\(48\) 0 0
\(49\) −262.492 −0.765284
\(50\) −110.435 −0.312357
\(51\) 0 0
\(52\) 185.227 0.493967
\(53\) 421.300 1.09189 0.545943 0.837822i \(-0.316171\pi\)
0.545943 + 0.837822i \(0.316171\pi\)
\(54\) 0 0
\(55\) 144.506 0.354275
\(56\) 139.255 0.332298
\(57\) 0 0
\(58\) 610.802 1.38280
\(59\) −755.913 −1.66799 −0.833996 0.551770i \(-0.813952\pi\)
−0.833996 + 0.551770i \(0.813952\pi\)
\(60\) 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
\(63\) 0 0
\(64\) −819.594 −1.60077
\(65\) 80.4396 0.153497
\(66\) 0 0
\(67\) 319.974 0.583448 0.291724 0.956502i \(-0.405771\pi\)
0.291724 + 0.956502i \(0.405771\pi\)
\(68\) −289.874 −0.516947
\(69\) 0 0
\(70\) 198.178 0.338382
\(71\) 554.138 0.926254 0.463127 0.886292i \(-0.346727\pi\)
0.463127 + 0.886292i \(0.346727\pi\)
\(72\) 0 0
\(73\) −705.131 −1.13054 −0.565269 0.824907i \(-0.691228\pi\)
−0.565269 + 0.824907i \(0.691228\pi\)
\(74\) −1677.48 −2.63518
\(75\) 0 0
\(76\) −410.219 −0.619149
\(77\) −259.318 −0.383793
\(78\) 0 0
\(79\) 1170.51 1.66699 0.833495 0.552526i \(-0.186336\pi\)
0.833495 + 0.552526i \(0.186336\pi\)
\(80\) −117.745 −0.164554
\(81\) 0 0
\(82\) 1822.24 2.45406
\(83\) 455.978 0.603014 0.301507 0.953464i \(-0.402510\pi\)
0.301507 + 0.953464i \(0.402510\pi\)
\(84\) 0 0
\(85\) −125.886 −0.160638
\(86\) 1776.21 2.22714
\(87\) 0 0
\(88\) −448.546 −0.543354
\(89\) 1495.57 1.78124 0.890621 0.454746i \(-0.150270\pi\)
0.890621 + 0.454746i \(0.150270\pi\)
\(90\) 0 0
\(91\) −144.351 −0.166286
\(92\) 264.808 0.300088
\(93\) 0 0
\(94\) 486.222 0.533510
\(95\) −178.149 −0.192397
\(96\) 0 0
\(97\) 1041.24 1.08992 0.544958 0.838463i \(-0.316545\pi\)
0.544958 + 0.838463i \(0.316545\pi\)
\(98\) 1159.53 1.19521
\(99\) 0 0
\(100\) 287.835 0.287835
\(101\) −1450.22 −1.42873 −0.714367 0.699771i \(-0.753285\pi\)
−0.714367 + 0.699771i \(0.753285\pi\)
\(102\) 0 0
\(103\) 220.283 0.210729 0.105365 0.994434i \(-0.466399\pi\)
0.105365 + 0.994434i \(0.466399\pi\)
\(104\) −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 \(0.508523\pi\)
\(108\) 0 0
\(109\) 1966.29 1.72786 0.863930 0.503612i \(-0.167996\pi\)
0.863930 + 0.503612i \(0.167996\pi\)
\(110\) −638.339 −0.553302
\(111\) 0 0
\(112\) 211.296 0.178264
\(113\) −1819.68 −1.51488 −0.757439 0.652905i \(-0.773550\pi\)
−0.757439 + 0.652905i \(0.773550\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) −1591.98 −1.27424
\(117\) 0 0
\(118\) 3339.17 2.60505
\(119\) 225.904 0.174022
\(120\) 0 0
\(121\) −495.725 −0.372445
\(122\) 1356.28 1.00649
\(123\) 0 0
\(124\) 462.006 0.334592
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 834.517 0.583082 0.291541 0.956558i \(-0.405832\pi\)
0.291541 + 0.956558i \(0.405832\pi\)
\(128\) 1794.98 1.23950
\(129\) 0 0
\(130\) −355.334 −0.239729
\(131\) −510.293 −0.340340 −0.170170 0.985415i \(-0.554432\pi\)
−0.170170 + 0.985415i \(0.554432\pi\)
\(132\) 0 0
\(133\) 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 \(0.501115\pi\)
\(138\) 0 0
\(139\) −1656.81 −1.01100 −0.505501 0.862826i \(-0.668692\pi\)
−0.505501 + 0.862826i \(0.668692\pi\)
\(140\) −516.525 −0.311817
\(141\) 0 0
\(142\) −2447.85 −1.44661
\(143\) 464.959 0.271901
\(144\) 0 0
\(145\) −691.360 −0.395961
\(146\) 3114.84 1.76566
\(147\) 0 0
\(148\) 4372.15 2.42830
\(149\) 510.206 0.280522 0.140261 0.990115i \(-0.455206\pi\)
0.140261 + 0.990115i \(0.455206\pi\)
\(150\) 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
\(153\) 0 0
\(154\) 1145.51 0.599402
\(155\) 200.639 0.103972
\(156\) 0 0
\(157\) 146.592 0.0745178 0.0372589 0.999306i \(-0.488137\pi\)
0.0372589 + 0.999306i \(0.488137\pi\)
\(158\) −5170.59 −2.60348
\(159\) 0 0
\(160\) 1140.93 0.563739
\(161\) −206.370 −0.101020
\(162\) 0 0
\(163\) −3278.19 −1.57526 −0.787630 0.616149i \(-0.788692\pi\)
−0.787630 + 0.616149i \(0.788692\pi\)
\(164\) −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 \(0.382652\pi\)
\(168\) 0 0
\(169\) −1938.18 −0.882193
\(170\) 556.087 0.250882
\(171\) 0 0
\(172\) −4629.48 −2.05229
\(173\) 472.392 0.207603 0.103801 0.994598i \(-0.466899\pi\)
0.103801 + 0.994598i \(0.466899\pi\)
\(174\) 0 0
\(175\) −224.315 −0.0968950
\(176\) −680.594 −0.291487
\(177\) 0 0
\(178\) −6606.54 −2.78192
\(179\) −2429.45 −1.01444 −0.507222 0.861815i \(-0.669328\pi\)
−0.507222 + 0.861815i \(0.669328\pi\)
\(180\) 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
\(183\) 0 0
\(184\) −356.960 −0.143019
\(185\) 1898.73 0.754579
\(186\) 0 0
\(187\) −727.648 −0.284550
\(188\) −1267.28 −0.491626
\(189\) 0 0
\(190\) 786.954 0.300482
\(191\) −1361.14 −0.515649 −0.257824 0.966192i \(-0.583006\pi\)
−0.257824 + 0.966192i \(0.583006\pi\)
\(192\) 0 0
\(193\) −1456.29 −0.543142 −0.271571 0.962418i \(-0.587543\pi\)
−0.271571 + 0.962418i \(0.587543\pi\)
\(194\) −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 \(0.562097\pi\)
\(198\) 0 0
\(199\) −2879.31 −1.02567 −0.512836 0.858486i \(-0.671405\pi\)
−0.512836 + 0.858486i \(0.671405\pi\)
\(200\) −388.000 −0.137179
\(201\) 0 0
\(202\) 6406.19 2.23138
\(203\) 1240.66 0.428952
\(204\) 0 0
\(205\) −2062.57 −0.702713
\(206\) −973.077 −0.329114
\(207\) 0 0
\(208\) −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
\(213\) 0 0
\(214\) 261.810 0.0836306
\(215\) −2010.48 −0.637737
\(216\) 0 0
\(217\) −360.050 −0.112635
\(218\) −8685.90 −2.69855
\(219\) 0 0
\(220\) 1663.75 0.509863
\(221\) −405.048 −0.123287
\(222\) 0 0
\(223\) 4874.04 1.46363 0.731815 0.681503i \(-0.238673\pi\)
0.731815 + 0.681503i \(0.238673\pi\)
\(224\) −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 \(0.368705\pi\)
\(228\) 0 0
\(229\) 1528.38 0.441041 0.220520 0.975382i \(-0.429224\pi\)
0.220520 + 0.975382i \(0.429224\pi\)
\(230\) −508.001 −0.145637
\(231\) 0 0
\(232\) 2145.98 0.607287
\(233\) −5552.78 −1.56126 −0.780632 0.624991i \(-0.785103\pi\)
−0.780632 + 0.624991i \(0.785103\pi\)
\(234\) 0 0
\(235\) −550.349 −0.152769
\(236\) −8703.12 −2.40053
\(237\) 0 0
\(238\) −997.909 −0.271785
\(239\) −2779.63 −0.752299 −0.376149 0.926559i \(-0.622752\pi\)
−0.376149 + 0.926559i \(0.622752\pi\)
\(240\) 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
\(243\) 0 0
\(244\) −3534.98 −0.927475
\(245\) −1312.46 −0.342245
\(246\) 0 0
\(247\) −573.209 −0.147662
\(248\) −622.783 −0.159463
\(249\) 0 0
\(250\) −552.174 −0.139690
\(251\) 387.065 0.0973360 0.0486680 0.998815i \(-0.484502\pi\)
0.0486680 + 0.998815i \(0.484502\pi\)
\(252\) 0 0
\(253\) 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 \(0.557329\pi\)
\(258\) 0 0
\(259\) −3407.30 −0.817449
\(260\) 926.133 0.220909
\(261\) 0 0
\(262\) 2254.17 0.531537
\(263\) −203.984 −0.0478259 −0.0239130 0.999714i \(-0.507612\pi\)
−0.0239130 + 0.999714i \(0.507612\pi\)
\(264\) 0 0
\(265\) 2106.50 0.488306
\(266\) −1412.20 −0.325518
\(267\) 0 0
\(268\) 3683.98 0.839683
\(269\) 6973.71 1.58065 0.790324 0.612689i \(-0.209912\pi\)
0.790324 + 0.612689i \(0.209912\pi\)
\(270\) 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
\(273\) 0 0
\(274\) 49.6246 0.0109414
\(275\) 722.528 0.158437
\(276\) 0 0
\(277\) 1194.00 0.258992 0.129496 0.991580i \(-0.458664\pi\)
0.129496 + 0.991580i \(0.458664\pi\)
\(278\) 7318.81 1.57897
\(279\) 0 0
\(280\) 696.274 0.148608
\(281\) −6485.98 −1.37694 −0.688472 0.725263i \(-0.741718\pi\)
−0.688472 + 0.725263i \(0.741718\pi\)
\(282\) 0 0
\(283\) −3214.41 −0.675182 −0.337591 0.941293i \(-0.609612\pi\)
−0.337591 + 0.941293i \(0.609612\pi\)
\(284\) 6380.00 1.33304
\(285\) 0 0
\(286\) −2053.91 −0.424651
\(287\) 3701.33 0.761263
\(288\) 0 0
\(289\) −4279.11 −0.870977
\(290\) 3054.01 0.618406
\(291\) 0 0
\(292\) −8118.44 −1.62704
\(293\) −5585.47 −1.11367 −0.556837 0.830622i \(-0.687985\pi\)
−0.556837 + 0.830622i \(0.687985\pi\)
\(294\) 0 0
\(295\) −3779.57 −0.745949
\(296\) −5893.65 −1.15730
\(297\) 0 0
\(298\) −2253.78 −0.438115
\(299\) 370.022 0.0715684
\(300\) 0 0
\(301\) 3607.84 0.690872
\(302\) 10325.1 1.96737
\(303\) 0 0
\(304\) 839.047 0.158298
\(305\) −1535.16 −0.288207
\(306\) 0 0
\(307\) 2849.51 0.529740 0.264870 0.964284i \(-0.414671\pi\)
0.264870 + 0.964284i \(0.414671\pi\)
\(308\) −2985.63 −0.552344
\(309\) 0 0
\(310\) −886.300 −0.162382
\(311\) 6617.84 1.20664 0.603318 0.797501i \(-0.293845\pi\)
0.603318 + 0.797501i \(0.293845\pi\)
\(312\) 0 0
\(313\) −6271.26 −1.13250 −0.566250 0.824233i \(-0.691606\pi\)
−0.566250 + 0.824233i \(0.691606\pi\)
\(314\) −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 \(0.666885\pi\)
\(318\) 0 0
\(319\) −3996.22 −0.701395
\(320\) −4097.97 −0.715885
\(321\) 0 0
\(322\) 911.617 0.157772
\(323\) 897.055 0.154531
\(324\) 0 0
\(325\) 402.198 0.0686460
\(326\) 14481.0 2.46022
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) −6870.92 −1.12563
\(335\) 1599.87 0.260926
\(336\) 0 0
\(337\) 4153.87 0.671441 0.335721 0.941962i \(-0.391020\pi\)
0.335721 + 0.941962i \(0.391020\pi\)
\(338\) 8561.70 1.37780
\(339\) 0 0
\(340\) −1449.37 −0.231186
\(341\) 1159.74 0.184174
\(342\) 0 0
\(343\) 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 \(0.423634\pi\)
\(348\) 0 0
\(349\) −8358.91 −1.28207 −0.641035 0.767512i \(-0.721495\pi\)
−0.641035 + 0.767512i \(0.721495\pi\)
\(350\) 990.888 0.151329
\(351\) 0 0
\(352\) 6594.82 0.998594
\(353\) −8018.12 −1.20896 −0.604478 0.796622i \(-0.706618\pi\)
−0.604478 + 0.796622i \(0.706618\pi\)
\(354\) 0 0
\(355\) 2770.69 0.414234
\(356\) 17219.1 2.56352
\(357\) 0 0
\(358\) 10731.8 1.58434
\(359\) −2138.46 −0.314384 −0.157192 0.987568i \(-0.550244\pi\)
−0.157192 + 0.987568i \(0.550244\pi\)
\(360\) 0 0
\(361\) −5589.52 −0.814918
\(362\) 4339.47 0.630048
\(363\) 0 0
\(364\) −1661.96 −0.239315
\(365\) −3525.65 −0.505592
\(366\) 0 0
\(367\) −4509.96 −0.641467 −0.320733 0.947170i \(-0.603929\pi\)
−0.320733 + 0.947170i \(0.603929\pi\)
\(368\) −541.628 −0.0767237
\(369\) 0 0
\(370\) −8387.42 −1.17849
\(371\) −3780.15 −0.528991
\(372\) 0 0
\(373\) −3362.09 −0.466709 −0.233355 0.972392i \(-0.574970\pi\)
−0.233355 + 0.972392i \(0.574970\pi\)
\(374\) 3214.31 0.444406
\(375\) 0 0
\(376\) 1708.29 0.234303
\(377\) −2224.51 −0.303894
\(378\) 0 0
\(379\) 2107.16 0.285587 0.142793 0.989753i \(-0.454392\pi\)
0.142793 + 0.989753i \(0.454392\pi\)
\(380\) −2051.10 −0.276892
\(381\) 0 0
\(382\) 6012.71 0.805333
\(383\) −1373.05 −0.183184 −0.0915919 0.995797i \(-0.529196\pi\)
−0.0915919 + 0.995797i \(0.529196\pi\)
\(384\) 0 0
\(385\) −1296.59 −0.171637
\(386\) 6433.03 0.848271
\(387\) 0 0
\(388\) 11988.2 1.56858
\(389\) −7008.05 −0.913425 −0.456713 0.889614i \(-0.650973\pi\)
−0.456713 + 0.889614i \(0.650973\pi\)
\(390\) 0 0
\(391\) −579.074 −0.0748978
\(392\) 4073.89 0.524904
\(393\) 0 0
\(394\) 4735.39 0.605496
\(395\) 5852.53 0.745501
\(396\) 0 0
\(397\) 2402.53 0.303727 0.151864 0.988401i \(-0.451473\pi\)
0.151864 + 0.988401i \(0.451473\pi\)
\(398\) 12719.0 1.60188
\(399\) 0 0
\(400\) −588.726 −0.0735908
\(401\) 11902.0 1.48218 0.741091 0.671404i \(-0.234309\pi\)
0.741091 + 0.671404i \(0.234309\pi\)
\(402\) 0 0
\(403\) 645.572 0.0797971
\(404\) −16696.9 −2.05620
\(405\) 0 0
\(406\) −5480.48 −0.669930
\(407\) 10975.1 1.33664
\(408\) 0 0
\(409\) 5277.96 0.638089 0.319044 0.947740i \(-0.396638\pi\)
0.319044 + 0.947740i \(0.396638\pi\)
\(410\) 9111.20 1.09749
\(411\) 0 0
\(412\) 2536.20 0.303276
\(413\) 6782.51 0.808100
\(414\) 0 0
\(415\) 2279.89 0.269676
\(416\) 3671.03 0.432662
\(417\) 0 0
\(418\) 4548.77 0.532267
\(419\) 11196.4 1.30545 0.652723 0.757597i \(-0.273627\pi\)
0.652723 + 0.757597i \(0.273627\pi\)
\(420\) 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
\(423\) 0 0
\(424\) −6538.58 −0.748918
\(425\) −629.428 −0.0718394
\(426\) 0 0
\(427\) 2754.88 0.312220
\(428\) −682.375 −0.0770650
\(429\) 0 0
\(430\) 8881.07 0.996008
\(431\) −9348.93 −1.04483 −0.522415 0.852691i \(-0.674969\pi\)
−0.522415 + 0.852691i \(0.674969\pi\)
\(432\) 0 0
\(433\) 4320.91 0.479560 0.239780 0.970827i \(-0.422925\pi\)
0.239780 + 0.970827i \(0.422925\pi\)
\(434\) 1590.48 0.175912
\(435\) 0 0
\(436\) 22638.7 2.48669
\(437\) −819.484 −0.0897054
\(438\) 0 0
\(439\) −7016.03 −0.762772 −0.381386 0.924416i \(-0.624553\pi\)
−0.381386 + 0.924416i \(0.624553\pi\)
\(440\) −2242.73 −0.242995
\(441\) 0 0
\(442\) 1789.26 0.192548
\(443\) −12343.6 −1.32384 −0.661921 0.749574i \(-0.730259\pi\)
−0.661921 + 0.749574i \(0.730259\pi\)
\(444\) 0 0
\(445\) 7477.87 0.796596
\(446\) −21530.5 −2.28588
\(447\) 0 0
\(448\) 7353.88 0.775532
\(449\) −18146.9 −1.90737 −0.953683 0.300815i \(-0.902741\pi\)
−0.953683 + 0.300815i \(0.902741\pi\)
\(450\) 0 0
\(451\) −11922.1 −1.24477
\(452\) −20950.7 −2.18017
\(453\) 0 0
\(454\) −12112.9 −1.25217
\(455\) −721.753 −0.0743655
\(456\) 0 0
\(457\) 5233.82 0.535728 0.267864 0.963457i \(-0.413682\pi\)
0.267864 + 0.963457i \(0.413682\pi\)
\(458\) −6751.47 −0.688811
\(459\) 0 0
\(460\) 1324.04 0.134204
\(461\) 2335.01 0.235905 0.117952 0.993019i \(-0.462367\pi\)
0.117952 + 0.993019i \(0.462367\pi\)
\(462\) 0 0
\(463\) 13644.1 1.36954 0.684769 0.728760i \(-0.259903\pi\)
0.684769 + 0.728760i \(0.259903\pi\)
\(464\) 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 \(0.416302\pi\)
\(468\) 0 0
\(469\) −2871.00 −0.282666
\(470\) 2431.11 0.238593
\(471\) 0 0
\(472\) 11731.8 1.14407
\(473\) −11621.0 −1.12967
\(474\) 0 0
\(475\) −890.744 −0.0860424
\(476\) 2600.92 0.250448
\(477\) 0 0
\(478\) 12278.7 1.17493
\(479\) −12278.3 −1.17121 −0.585603 0.810598i \(-0.699142\pi\)
−0.585603 + 0.810598i \(0.699142\pi\)
\(480\) 0 0
\(481\) 6109.31 0.579128
\(482\) 24599.7 2.32466
\(483\) 0 0
\(484\) −5707.47 −0.536013
\(485\) 5206.20 0.487426
\(486\) 0 0
\(487\) −8945.24 −0.832336 −0.416168 0.909288i \(-0.636627\pi\)
−0.416168 + 0.909288i \(0.636627\pi\)
\(488\) 4765.14 0.442024
\(489\) 0 0
\(490\) 5797.67 0.534514
\(491\) 7792.94 0.716274 0.358137 0.933669i \(-0.383412\pi\)
0.358137 + 0.933669i \(0.383412\pi\)
\(492\) 0 0
\(493\) 3481.29 0.318031
\(494\) 2532.09 0.230616
\(495\) 0 0
\(496\) −944.970 −0.0855451
\(497\) −4972.06 −0.448747
\(498\) 0 0
\(499\) −8577.71 −0.769521 −0.384761 0.923016i \(-0.625716\pi\)
−0.384761 + 0.923016i \(0.625716\pi\)
\(500\) 1439.17 0.128724
\(501\) 0 0
\(502\) −1709.82 −0.152018
\(503\) −7784.99 −0.690091 −0.345045 0.938586i \(-0.612136\pi\)
−0.345045 + 0.938586i \(0.612136\pi\)
\(504\) 0 0
\(505\) −7251.09 −0.638949
\(506\) −2936.36 −0.257978
\(507\) 0 0
\(508\) 9608.12 0.839156
\(509\) 11390.4 0.991891 0.495946 0.868354i \(-0.334822\pi\)
0.495946 + 0.868354i \(0.334822\pi\)
\(510\) 0 0
\(511\) 6326.85 0.547717
\(512\) −8297.40 −0.716205
\(513\) 0 0
\(514\) 6520.37 0.559535
\(515\) 1101.42 0.0942411
\(516\) 0 0
\(517\) −3181.14 −0.270612
\(518\) 15051.4 1.27668
\(519\) 0 0
\(520\) −1248.42 −0.105283
\(521\) 12824.5 1.07841 0.539206 0.842174i \(-0.318724\pi\)
0.539206 + 0.842174i \(0.318724\pi\)
\(522\) 0 0
\(523\) 13087.4 1.09421 0.547107 0.837063i \(-0.315729\pi\)
0.547107 + 0.837063i \(0.315729\pi\)
\(524\) −5875.20 −0.489808
\(525\) 0 0
\(526\) 901.080 0.0746938
\(527\) −1010.30 −0.0835093
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) −9305.24 −0.762630
\(531\) 0 0
\(532\) 3680.73 0.299962
\(533\) −6636.50 −0.539322
\(534\) 0 0
\(535\) −296.340 −0.0239474
\(536\) −4966.00 −0.400184
\(537\) 0 0
\(538\) −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
\(543\) 0 0
\(544\) −5745.06 −0.452789
\(545\) 9831.47 0.772722
\(546\) 0 0
\(547\) 6981.32 0.545703 0.272852 0.962056i \(-0.412033\pi\)
0.272852 + 0.962056i \(0.412033\pi\)
\(548\) −129.340 −0.0100824
\(549\) 0 0
\(550\) −3191.69 −0.247444
\(551\) 4926.60 0.380908
\(552\) 0 0
\(553\) −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 \(0.898453\pi\)
\(558\) 0 0
\(559\) −6468.88 −0.489454
\(560\) 1056.48 0.0797222
\(561\) 0 0
\(562\) 28651.2 2.15049
\(563\) 10820.3 0.809986 0.404993 0.914320i \(-0.367274\pi\)
0.404993 + 0.914320i \(0.367274\pi\)
\(564\) 0 0
\(565\) −9098.41 −0.677474
\(566\) 14199.3 1.05449
\(567\) 0 0
\(568\) −8600.23 −0.635312
\(569\) −8438.73 −0.621740 −0.310870 0.950453i \(-0.600620\pi\)
−0.310870 + 0.950453i \(0.600620\pi\)
\(570\) 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
\(573\) 0 0
\(574\) −16350.2 −1.18893
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) 24848.7 1.79283 0.896416 0.443215i \(-0.146162\pi\)
0.896416 + 0.443215i \(0.146162\pi\)
\(578\) 18902.5 1.36028
\(579\) 0 0
\(580\) −7959.89 −0.569856
\(581\) −4091.31 −0.292145
\(582\) 0 0
\(583\) 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 \(0.598522\pi\)
\(588\) 0 0
\(589\) −1429.74 −0.100019
\(590\) 16695.8 1.16501
\(591\) 0 0
\(592\) −8942.64 −0.620845
\(593\) 24678.9 1.70901 0.854503 0.519446i \(-0.173862\pi\)
0.854503 + 0.519446i \(0.173862\pi\)
\(594\) 0 0
\(595\) 1129.52 0.0778250
\(596\) 5874.20 0.403719
\(597\) 0 0
\(598\) −1634.54 −0.111774
\(599\) −19698.4 −1.34367 −0.671833 0.740702i \(-0.734493\pi\)
−0.671833 + 0.740702i \(0.734493\pi\)
\(600\) 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
\(603\) 0 0
\(604\) −26911.2 −1.81291
\(605\) −2478.62 −0.166563
\(606\) 0 0
\(607\) −11321.0 −0.757012 −0.378506 0.925599i \(-0.623562\pi\)
−0.378506 + 0.925599i \(0.623562\pi\)
\(608\) −8130.20 −0.542308
\(609\) 0 0
\(610\) 6781.41 0.450117
\(611\) −1770.80 −0.117248
\(612\) 0 0
\(613\) 712.219 0.0469270 0.0234635 0.999725i \(-0.492531\pi\)
0.0234635 + 0.999725i \(0.492531\pi\)
\(614\) −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 \(0.533649\pi\)
\(618\) 0 0
\(619\) 26905.1 1.74703 0.873513 0.486801i \(-0.161836\pi\)
0.873513 + 0.486801i \(0.161836\pi\)
\(620\) 2310.03 0.149634
\(621\) 0 0
\(622\) −29233.6 −1.88451
\(623\) −13419.2 −0.862967
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 27702.6 1.76872
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 24961.5 1.56364
\(635\) 4172.59 0.260762
\(636\) 0 0
\(637\) −4222.96 −0.262668
\(638\) 17652.9 1.09543
\(639\) 0 0
\(640\) 8974.92 0.554320
\(641\) −19943.5 −1.22889 −0.614446 0.788959i \(-0.710620\pi\)
−0.614446 + 0.788959i \(0.710620\pi\)
\(642\) 0 0
\(643\) −27691.0 −1.69833 −0.849164 0.528129i \(-0.822894\pi\)
−0.849164 + 0.528129i \(0.822894\pi\)
\(644\) −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 \(0.246060\pi\)
\(648\) 0 0
\(649\) −21846.7 −1.32136
\(650\) −1776.67 −0.107210
\(651\) 0 0
\(652\) −37743.0 −2.26707
\(653\) −5571.58 −0.333894 −0.166947 0.985966i \(-0.553391\pi\)
−0.166947 + 0.985966i \(0.553391\pi\)
\(654\) 0 0
\(655\) −2551.46 −0.152205
\(656\) 9714.32 0.578171
\(657\) 0 0
\(658\) −4362.68 −0.258472
\(659\) −10177.4 −0.601602 −0.300801 0.953687i \(-0.597254\pi\)
−0.300801 + 0.953687i \(0.597254\pi\)
\(660\) 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
\(663\) 0 0
\(664\) −7076.79 −0.413604
\(665\) 1598.46 0.0932113
\(666\) 0 0
\(667\) −3180.25 −0.184618
\(668\) 17908.2 1.03726
\(669\) 0 0
\(670\) −7067.26 −0.407511
\(671\) −8873.57 −0.510522
\(672\) 0 0
\(673\) 12767.5 0.731277 0.365639 0.930757i \(-0.380851\pi\)
0.365639 + 0.930757i \(0.380851\pi\)
\(674\) −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 \(0.660667\pi\)
\(678\) 0 0
\(679\) −9342.63 −0.528037
\(680\) 1953.75 0.110181
\(681\) 0 0
\(682\) −5123.02 −0.287640
\(683\) 510.213 0.0285838 0.0142919 0.999898i \(-0.495451\pi\)
0.0142919 + 0.999898i \(0.495451\pi\)
\(684\) 0 0
\(685\) −56.1695 −0.00313303
\(686\) −23999.0 −1.33569
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) −13569.6 −0.742213
\(695\) −8284.07 −0.452134
\(696\) 0 0
\(697\) 10385.9 0.564412
\(698\) 36924.6 2.00232
\(699\) 0 0
\(700\) −2582.62 −0.139449
\(701\) −26324.3 −1.41834 −0.709168 0.705039i \(-0.750929\pi\)
−0.709168 + 0.705039i \(0.750929\pi\)
\(702\) 0 0
\(703\) −13530.2 −0.725892
\(704\) −23687.2 −1.26810
\(705\) 0 0
\(706\) 35419.2 1.88813
\(707\) 13012.2 0.692185
\(708\) 0 0
\(709\) −10961.3 −0.580620 −0.290310 0.956933i \(-0.593758\pi\)
−0.290310 + 0.956933i \(0.593758\pi\)
\(710\) −12239.2 −0.646944
\(711\) 0 0
\(712\) −23211.3 −1.22174
\(713\) 922.938 0.0484773
\(714\) 0 0
\(715\) 2324.80 0.121598
\(716\) −27971.2 −1.45996
\(717\) 0 0
\(718\) 9446.44 0.491000
\(719\) 1304.68 0.0676723 0.0338362 0.999427i \(-0.489228\pi\)
0.0338362 + 0.999427i \(0.489228\pi\)
\(720\) 0 0
\(721\) −1976.51 −0.102093
\(722\) 24691.1 1.27273
\(723\) 0 0
\(724\) −11310.3 −0.580585
\(725\) −3456.80 −0.177079
\(726\) 0 0
\(727\) 1583.59 0.0807869 0.0403934 0.999184i \(-0.487139\pi\)
0.0403934 + 0.999184i \(0.487139\pi\)
\(728\) 2240.32 0.114055
\(729\) 0 0
\(730\) 15574.2 0.789626
\(731\) 10123.6 0.512223
\(732\) 0 0
\(733\) −34351.2 −1.73095 −0.865477 0.500948i \(-0.832985\pi\)
−0.865477 + 0.500948i \(0.832985\pi\)
\(734\) 19922.3 1.00183
\(735\) 0 0
\(736\) 5248.27 0.262845
\(737\) 9247.61 0.462198
\(738\) 0 0
\(739\) 14996.6 0.746494 0.373247 0.927732i \(-0.378244\pi\)
0.373247 + 0.927732i \(0.378244\pi\)
\(740\) 21860.8 1.08597
\(741\) 0 0
\(742\) 16698.4 0.826171
\(743\) 32781.7 1.61863 0.809317 0.587372i \(-0.199838\pi\)
0.809317 + 0.587372i \(0.199838\pi\)
\(744\) 0 0
\(745\) 2551.03 0.125453
\(746\) 14851.7 0.728899
\(747\) 0 0
\(748\) −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
\(753\) 0 0
\(754\) 9826.54 0.474617
\(755\) −11686.9 −0.563351
\(756\) 0 0
\(757\) −21680.9 −1.04096 −0.520479 0.853874i \(-0.674247\pi\)
−0.520479 + 0.853874i \(0.674247\pi\)
\(758\) −9308.15 −0.446025
\(759\) 0 0
\(760\) 2764.87 0.131964
\(761\) 10299.1 0.490594 0.245297 0.969448i \(-0.421115\pi\)
0.245297 + 0.969448i \(0.421115\pi\)
\(762\) 0 0
\(763\) −17642.8 −0.837105
\(764\) −15671.4 −0.742108
\(765\) 0 0
\(766\) 6065.29 0.286094
\(767\) −12161.1 −0.572505
\(768\) 0 0
\(769\) 28377.9 1.33073 0.665365 0.746518i \(-0.268276\pi\)
0.665365 + 0.746518i \(0.268276\pi\)
\(770\) 5727.56 0.268061
\(771\) 0 0
\(772\) −16766.9 −0.781675
\(773\) −35409.5 −1.64759 −0.823797 0.566885i \(-0.808148\pi\)
−0.823797 + 0.566885i \(0.808148\pi\)
\(774\) 0 0
\(775\) 1003.19 0.0464978
\(776\) −16160.1 −0.747568
\(777\) 0 0
\(778\) 30957.3 1.42657
\(779\) 14697.8 0.675999
\(780\) 0 0
\(781\) 16015.2 0.733763
\(782\) 2558.00 0.116974
\(783\) 0 0
\(784\) 6181.45 0.281589
\(785\) 732.959 0.0333254
\(786\) 0 0
\(787\) 6117.56 0.277087 0.138544 0.990356i \(-0.455758\pi\)
0.138544 + 0.990356i \(0.455758\pi\)
\(788\) −12342.2 −0.557960
\(789\) 0 0
\(790\) −25853.0 −1.16431
\(791\) 16327.3 0.733921
\(792\) 0 0
\(793\) −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 \(0.529038\pi\)
\(798\) 0 0
\(799\) 2771.24 0.122703
\(800\) 5704.64 0.252112
\(801\) 0 0
\(802\) −52575.6 −2.31485
\(803\) −20379.1 −0.895594
\(804\) 0 0
\(805\) −1031.85 −0.0451775
\(806\) −2851.75 −0.124626
\(807\) 0 0
\(808\) 22507.4 0.979960
\(809\) −21358.6 −0.928216 −0.464108 0.885779i \(-0.653625\pi\)
−0.464108 + 0.885779i \(0.653625\pi\)
\(810\) 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
\(813\) 0 0
\(814\) −48481.2 −2.08755
\(815\) −16390.9 −0.704478
\(816\) 0 0
\(817\) 14326.6 0.613492
\(818\) −23314.8 −0.996557
\(819\) 0 0
\(820\) −23747.2 −1.01133
\(821\) 22387.6 0.951684 0.475842 0.879531i \(-0.342143\pi\)
0.475842 + 0.879531i \(0.342143\pi\)
\(822\) 0 0
\(823\) −22615.7 −0.957877 −0.478939 0.877848i \(-0.658978\pi\)
−0.478939 + 0.877848i \(0.658978\pi\)
\(824\) −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 \(0.573446\pi\)
\(828\) 0 0
\(829\) 27382.3 1.14720 0.573600 0.819136i \(-0.305547\pi\)
0.573600 + 0.819136i \(0.305547\pi\)
\(830\) −10071.2 −0.421176
\(831\) 0 0
\(832\) −13185.6 −0.549432
\(833\) 6608.81 0.274888
\(834\) 0 0
\(835\) 7777.12 0.322321
\(836\) −11855.8 −0.490480
\(837\) 0 0
\(838\) −49459.1 −2.03883
\(839\) 31799.7 1.30852 0.654260 0.756270i \(-0.272980\pi\)
0.654260 + 0.756270i \(0.272980\pi\)
\(840\) 0 0
\(841\) −5269.87 −0.216076
\(842\) −22868.0 −0.935968
\(843\) 0 0
\(844\) −54647.9 −2.22874
\(845\) −9690.89 −0.394529
\(846\) 0 0
\(847\) 4447.94 0.180440
\(848\) −9921.21 −0.401764
\(849\) 0 0
\(850\) 2780.43 0.112198
\(851\) 8734.14 0.351824
\(852\) 0 0
\(853\) 32016.4 1.28514 0.642568 0.766229i \(-0.277869\pi\)
0.642568 + 0.766229i \(0.277869\pi\)
\(854\) −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 \(0.668073\pi\)
\(858\) 0 0
\(859\) −22313.5 −0.886296 −0.443148 0.896448i \(-0.646138\pi\)
−0.443148 + 0.896448i \(0.646138\pi\)
\(860\) −23147.4 −0.917813
\(861\) 0 0
\(862\) 41297.9 1.63180
\(863\) 1478.28 0.0583096 0.0291548 0.999575i \(-0.490718\pi\)
0.0291548 + 0.999575i \(0.490718\pi\)
\(864\) 0 0
\(865\) 2361.96 0.0928428
\(866\) −19087.2 −0.748970
\(867\) 0 0
\(868\) −4145.39 −0.162101
\(869\) 33829.0 1.32056
\(870\) 0 0
\(871\) 5147.72 0.200257
\(872\) −30516.9 −1.18513
\(873\) 0 0
\(874\) 3619.99 0.140101
\(875\) −1121.57 −0.0433327
\(876\) 0 0
\(877\) 32974.6 1.26964 0.634819 0.772661i \(-0.281075\pi\)
0.634819 + 0.772661i \(0.281075\pi\)
\(878\) 30992.6 1.19129
\(879\) 0 0
\(880\) −3402.97 −0.130357
\(881\) 32000.7 1.22376 0.611879 0.790951i \(-0.290414\pi\)
0.611879 + 0.790951i \(0.290414\pi\)
\(882\) 0 0
\(883\) −44218.6 −1.68525 −0.842623 0.538503i \(-0.818990\pi\)
−0.842623 + 0.538503i \(0.818990\pi\)
\(884\) −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 \(0.673370\pi\)
\(888\) 0 0
\(889\) −7487.79 −0.282489
\(890\) −33032.7 −1.24411
\(891\) 0 0
\(892\) 56116.7 2.10642
\(893\) 3921.76 0.146962
\(894\) 0 0
\(895\) −12147.2 −0.453673
\(896\) −16105.7 −0.600505
\(897\) 0 0
\(898\) 80162.2 2.97889
\(899\) −5548.54 −0.205844
\(900\) 0 0
\(901\) −10607.1 −0.392203
\(902\) 52664.8 1.94406
\(903\) 0 0
\(904\) 28241.5 1.03905
\(905\) −4911.80 −0.180413
\(906\) 0 0
\(907\) 7835.16 0.286838 0.143419 0.989662i \(-0.454190\pi\)
0.143419 + 0.989662i \(0.454190\pi\)
\(908\) 31570.7 1.15387
\(909\) 0 0
\(910\) 3188.27 0.116143
\(911\) 36528.6 1.32848 0.664241 0.747519i \(-0.268755\pi\)
0.664241 + 0.747519i \(0.268755\pi\)
\(912\) 0 0
\(913\) 13178.3 0.477698
\(914\) −23119.8 −0.836692
\(915\) 0 0
\(916\) 17596.8 0.634734
\(917\) 4578.65 0.164886
\(918\) 0 0
\(919\) −15741.5 −0.565030 −0.282515 0.959263i \(-0.591169\pi\)
−0.282515 + 0.959263i \(0.591169\pi\)
\(920\) −1784.80 −0.0639600
\(921\) 0 0
\(922\) −10314.7 −0.368433
\(923\) 8914.93 0.317918
\(924\) 0 0
\(925\) 9493.63 0.337458
\(926\) −60271.5 −2.13892
\(927\) 0 0
\(928\) −31551.7 −1.11609
\(929\) −47428.9 −1.67502 −0.837510 0.546422i \(-0.815989\pi\)
−0.837510 + 0.546422i \(0.815989\pi\)
\(930\) 0 0
\(931\) 9352.54 0.329234
\(932\) −63931.3 −2.24693
\(933\) 0 0
\(934\) −23175.0 −0.811895
\(935\) −3638.24 −0.127255
\(936\) 0 0
\(937\) −34978.0 −1.21951 −0.609756 0.792589i \(-0.708733\pi\)
−0.609756 + 0.792589i \(0.708733\pi\)
\(938\) 12682.3 0.441464
\(939\) 0 0
\(940\) −6336.38 −0.219862
\(941\) −45144.0 −1.56392 −0.781962 0.623326i \(-0.785781\pi\)
−0.781962 + 0.623326i \(0.785781\pi\)
\(942\) 0 0
\(943\) −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 \(0.647937\pi\)
\(948\) 0 0
\(949\) −11344.1 −0.388035
\(950\) 3934.77 0.134380
\(951\) 0 0
\(952\) −3506.04 −0.119361
\(953\) 22143.5 0.752673 0.376336 0.926483i \(-0.377184\pi\)
0.376336 + 0.926483i \(0.377184\pi\)
\(954\) 0 0
\(955\) −6805.72 −0.230605
\(956\) −32003.0 −1.08269
\(957\) 0 0
\(958\) 54237.9 1.82917
\(959\) 100.797 0.00339407
\(960\) 0 0
\(961\) −28180.8 −0.945949
\(962\) −26987.3 −0.904474
\(963\) 0 0
\(964\) −64116.0 −2.14215
\(965\) −7281.47 −0.242900
\(966\) 0 0
\(967\) 44869.8 1.49216 0.746078 0.665858i \(-0.231934\pi\)
0.746078 + 0.665858i \(0.231934\pi\)
\(968\) 7693.65 0.255458
\(969\) 0 0
\(970\) −22997.9 −0.761254
\(971\) 25048.3 0.827845 0.413923 0.910312i \(-0.364158\pi\)
0.413923 + 0.910312i \(0.364158\pi\)
\(972\) 0 0
\(973\) 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 \(0.709253\pi\)
\(978\) 0 0
\(979\) 43223.8 1.41107
\(980\) −15110.9 −0.492551
\(981\) 0 0
\(982\) −34424.5 −1.11867
\(983\) 17189.4 0.557737 0.278869 0.960329i \(-0.410041\pi\)
0.278869 + 0.960329i \(0.410041\pi\)
\(984\) 0 0
\(985\) −5359.93 −0.173382
\(986\) −15378.2 −0.496697
\(987\) 0 0
\(988\) −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
\(993\) 0 0
\(994\) 21963.5 0.700846
\(995\) −14396.5 −0.458695
\(996\) 0 0
\(997\) 46801.0 1.48666 0.743331 0.668923i \(-0.233245\pi\)
0.743331 + 0.668923i \(0.233245\pi\)
\(998\) 37891.2 1.20183
\(999\) 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 1035.4.a.k.1.2 5
3.2 odd 2 115.4.a.e.1.4 5
12.11 even 2 1840.4.a.n.1.2 5
15.2 even 4 575.4.b.i.24.9 10
15.8 even 4 575.4.b.i.24.2 10
15.14 odd 2 575.4.a.j.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.4 5 3.2 odd 2
575.4.a.j.1.2 5 15.14 odd 2
575.4.b.i.24.2 10 15.8 even 4
575.4.b.i.24.9 10 15.2 even 4
1035.4.a.k.1.2 5 1.1 even 1 trivial
1840.4.a.n.1.2 5 12.11 even 2