Properties

Label 1840.4.a.n.1.5
Level $1840$
Weight $4$
Character 1840.1
Self dual yes
Analytic conductor $108.564$
Analytic rank $0$
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] = [1840,4,Mod(1,1840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.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: \(108.563514411\)
Analytic rank: \(0\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.595043\) of defining polynomial
Character \(\chi\) \(=\) 1840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.11323 q^{3} -5.00000 q^{5} -13.7888 q^{7} +23.5981 q^{9} +O(q^{10})\) \(q+7.11323 q^{3} -5.00000 q^{5} -13.7888 q^{7} +23.5981 q^{9} -24.2317 q^{11} +3.05016 q^{13} -35.5662 q^{15} +63.1126 q^{17} +2.07770 q^{19} -98.0832 q^{21} +23.0000 q^{23} +25.0000 q^{25} -24.1987 q^{27} -8.16397 q^{29} +156.989 q^{31} -172.366 q^{33} +68.9442 q^{35} +302.801 q^{37} +21.6965 q^{39} -42.7514 q^{41} -215.265 q^{43} -117.990 q^{45} -247.096 q^{47} -152.868 q^{49} +448.935 q^{51} +600.400 q^{53} +121.159 q^{55} +14.7792 q^{57} -92.2014 q^{59} +532.635 q^{61} -325.390 q^{63} -15.2508 q^{65} -30.3010 q^{67} +163.604 q^{69} +736.349 q^{71} +349.936 q^{73} +177.831 q^{75} +334.127 q^{77} -301.545 q^{79} -809.279 q^{81} -139.488 q^{83} -315.563 q^{85} -58.0722 q^{87} +859.551 q^{89} -42.0581 q^{91} +1116.70 q^{93} -10.3885 q^{95} -927.475 q^{97} -571.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 4 q^{3} - 25 q^{5} + 3 q^{7} + 77 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 4 q^{3} - 25 q^{5} + 3 q^{7} + 77 q^{9} - 23 q^{11} + 132 q^{13} + 20 q^{15} + 23 q^{17} + 161 q^{19} - 60 q^{21} + 115 q^{23} + 125 q^{25} - 577 q^{27} + 401 q^{29} - 32 q^{31} + 189 q^{33} - 15 q^{35} - 38 q^{37} - 335 q^{39} - 12 q^{41} + 566 q^{43} - 385 q^{45} - 919 q^{47} - 738 q^{49} + 993 q^{51} + 1156 q^{53} + 115 q^{55} + 114 q^{57} - 1324 q^{59} - 1673 q^{61} - 270 q^{63} - 660 q^{65} - 558 q^{67} - 92 q^{69} + 108 q^{71} + 1173 q^{73} - 100 q^{75} + 2608 q^{77} - 656 q^{79} - 319 q^{81} + 82 q^{83} - 115 q^{85} - 2389 q^{87} + 570 q^{89} + 1589 q^{91} + 911 q^{93} - 805 q^{95} + 633 q^{97} - 2021 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 7.11323 1.36894 0.684471 0.729040i \(-0.260033\pi\)
0.684471 + 0.729040i \(0.260033\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −13.7888 −0.744527 −0.372263 0.928127i \(-0.621418\pi\)
−0.372263 + 0.928127i \(0.621418\pi\)
\(8\) 0 0
\(9\) 23.5981 0.874003
\(10\) 0 0
\(11\) −24.2317 −0.664195 −0.332098 0.943245i \(-0.607756\pi\)
−0.332098 + 0.943245i \(0.607756\pi\)
\(12\) 0 0
\(13\) 3.05016 0.0650739 0.0325370 0.999471i \(-0.489641\pi\)
0.0325370 + 0.999471i \(0.489641\pi\)
\(14\) 0 0
\(15\) −35.5662 −0.612210
\(16\) 0 0
\(17\) 63.1126 0.900415 0.450208 0.892924i \(-0.351350\pi\)
0.450208 + 0.892924i \(0.351350\pi\)
\(18\) 0 0
\(19\) 2.07770 0.0250872 0.0125436 0.999921i \(-0.496007\pi\)
0.0125436 + 0.999921i \(0.496007\pi\)
\(20\) 0 0
\(21\) −98.0832 −1.01921
\(22\) 0 0
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −24.1987 −0.172483
\(28\) 0 0
\(29\) −8.16397 −0.0522762 −0.0261381 0.999658i \(-0.508321\pi\)
−0.0261381 + 0.999658i \(0.508321\pi\)
\(30\) 0 0
\(31\) 156.989 0.909553 0.454776 0.890606i \(-0.349719\pi\)
0.454776 + 0.890606i \(0.349719\pi\)
\(32\) 0 0
\(33\) −172.366 −0.909245
\(34\) 0 0
\(35\) 68.9442 0.332963
\(36\) 0 0
\(37\) 302.801 1.34541 0.672706 0.739910i \(-0.265132\pi\)
0.672706 + 0.739910i \(0.265132\pi\)
\(38\) 0 0
\(39\) 21.6965 0.0890824
\(40\) 0 0
\(41\) −42.7514 −0.162845 −0.0814225 0.996680i \(-0.525946\pi\)
−0.0814225 + 0.996680i \(0.525946\pi\)
\(42\) 0 0
\(43\) −215.265 −0.763434 −0.381717 0.924279i \(-0.624667\pi\)
−0.381717 + 0.924279i \(0.624667\pi\)
\(44\) 0 0
\(45\) −117.990 −0.390866
\(46\) 0 0
\(47\) −247.096 −0.766866 −0.383433 0.923569i \(-0.625258\pi\)
−0.383433 + 0.923569i \(0.625258\pi\)
\(48\) 0 0
\(49\) −152.868 −0.445680
\(50\) 0 0
\(51\) 448.935 1.23262
\(52\) 0 0
\(53\) 600.400 1.55606 0.778031 0.628225i \(-0.216218\pi\)
0.778031 + 0.628225i \(0.216218\pi\)
\(54\) 0 0
\(55\) 121.159 0.297037
\(56\) 0 0
\(57\) 14.7792 0.0343430
\(58\) 0 0
\(59\) −92.2014 −0.203451 −0.101725 0.994813i \(-0.532436\pi\)
−0.101725 + 0.994813i \(0.532436\pi\)
\(60\) 0 0
\(61\) 532.635 1.11798 0.558991 0.829174i \(-0.311189\pi\)
0.558991 + 0.829174i \(0.311189\pi\)
\(62\) 0 0
\(63\) −325.390 −0.650719
\(64\) 0 0
\(65\) −15.2508 −0.0291019
\(66\) 0 0
\(67\) −30.3010 −0.0552515 −0.0276258 0.999618i \(-0.508795\pi\)
−0.0276258 + 0.999618i \(0.508795\pi\)
\(68\) 0 0
\(69\) 163.604 0.285444
\(70\) 0 0
\(71\) 736.349 1.23083 0.615413 0.788205i \(-0.288989\pi\)
0.615413 + 0.788205i \(0.288989\pi\)
\(72\) 0 0
\(73\) 349.936 0.561053 0.280527 0.959846i \(-0.409491\pi\)
0.280527 + 0.959846i \(0.409491\pi\)
\(74\) 0 0
\(75\) 177.831 0.273788
\(76\) 0 0
\(77\) 334.127 0.494511
\(78\) 0 0
\(79\) −301.545 −0.429449 −0.214725 0.976675i \(-0.568885\pi\)
−0.214725 + 0.976675i \(0.568885\pi\)
\(80\) 0 0
\(81\) −809.279 −1.11012
\(82\) 0 0
\(83\) −139.488 −0.184468 −0.0922340 0.995737i \(-0.529401\pi\)
−0.0922340 + 0.995737i \(0.529401\pi\)
\(84\) 0 0
\(85\) −315.563 −0.402678
\(86\) 0 0
\(87\) −58.0722 −0.0715631
\(88\) 0 0
\(89\) 859.551 1.02373 0.511866 0.859065i \(-0.328954\pi\)
0.511866 + 0.859065i \(0.328954\pi\)
\(90\) 0 0
\(91\) −42.0581 −0.0484493
\(92\) 0 0
\(93\) 1116.70 1.24513
\(94\) 0 0
\(95\) −10.3885 −0.0112193
\(96\) 0 0
\(97\) −927.475 −0.970833 −0.485417 0.874283i \(-0.661332\pi\)
−0.485417 + 0.874283i \(0.661332\pi\)
\(98\) 0 0
\(99\) −571.823 −0.580508
\(100\) 0 0
\(101\) 1713.34 1.68796 0.843979 0.536376i \(-0.180207\pi\)
0.843979 + 0.536376i \(0.180207\pi\)
\(102\) 0 0
\(103\) 930.516 0.890160 0.445080 0.895491i \(-0.353175\pi\)
0.445080 + 0.895491i \(0.353175\pi\)
\(104\) 0 0
\(105\) 490.416 0.455806
\(106\) 0 0
\(107\) −1514.91 −1.36871 −0.684355 0.729149i \(-0.739916\pi\)
−0.684355 + 0.729149i \(0.739916\pi\)
\(108\) 0 0
\(109\) 1748.76 1.53670 0.768352 0.640027i \(-0.221077\pi\)
0.768352 + 0.640027i \(0.221077\pi\)
\(110\) 0 0
\(111\) 2153.90 1.84179
\(112\) 0 0
\(113\) 2026.23 1.68683 0.843416 0.537261i \(-0.180541\pi\)
0.843416 + 0.537261i \(0.180541\pi\)
\(114\) 0 0
\(115\) −115.000 −0.0932505
\(116\) 0 0
\(117\) 71.9778 0.0568748
\(118\) 0 0
\(119\) −870.249 −0.670383
\(120\) 0 0
\(121\) −743.822 −0.558845
\(122\) 0 0
\(123\) −304.100 −0.222925
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 2126.49 1.48579 0.742897 0.669406i \(-0.233451\pi\)
0.742897 + 0.669406i \(0.233451\pi\)
\(128\) 0 0
\(129\) −1531.23 −1.04510
\(130\) 0 0
\(131\) 1494.23 0.996576 0.498288 0.867012i \(-0.333962\pi\)
0.498288 + 0.867012i \(0.333962\pi\)
\(132\) 0 0
\(133\) −28.6491 −0.0186781
\(134\) 0 0
\(135\) 120.993 0.0771367
\(136\) 0 0
\(137\) 2265.31 1.41269 0.706346 0.707867i \(-0.250342\pi\)
0.706346 + 0.707867i \(0.250342\pi\)
\(138\) 0 0
\(139\) 2918.66 1.78099 0.890496 0.454991i \(-0.150358\pi\)
0.890496 + 0.454991i \(0.150358\pi\)
\(140\) 0 0
\(141\) −1757.65 −1.04980
\(142\) 0 0
\(143\) −73.9106 −0.0432218
\(144\) 0 0
\(145\) 40.8198 0.0233786
\(146\) 0 0
\(147\) −1087.39 −0.610110
\(148\) 0 0
\(149\) −549.400 −0.302071 −0.151036 0.988528i \(-0.548261\pi\)
−0.151036 + 0.988528i \(0.548261\pi\)
\(150\) 0 0
\(151\) −335.721 −0.180931 −0.0904654 0.995900i \(-0.528835\pi\)
−0.0904654 + 0.995900i \(0.528835\pi\)
\(152\) 0 0
\(153\) 1489.34 0.786965
\(154\) 0 0
\(155\) −784.947 −0.406764
\(156\) 0 0
\(157\) −1593.69 −0.810130 −0.405065 0.914288i \(-0.632751\pi\)
−0.405065 + 0.914288i \(0.632751\pi\)
\(158\) 0 0
\(159\) 4270.79 2.13016
\(160\) 0 0
\(161\) −317.143 −0.155245
\(162\) 0 0
\(163\) 2767.63 1.32992 0.664962 0.746877i \(-0.268448\pi\)
0.664962 + 0.746877i \(0.268448\pi\)
\(164\) 0 0
\(165\) 861.830 0.406627
\(166\) 0 0
\(167\) −282.867 −0.131071 −0.0655357 0.997850i \(-0.520876\pi\)
−0.0655357 + 0.997850i \(0.520876\pi\)
\(168\) 0 0
\(169\) −2187.70 −0.995765
\(170\) 0 0
\(171\) 49.0297 0.0219263
\(172\) 0 0
\(173\) −2331.63 −1.02468 −0.512342 0.858782i \(-0.671222\pi\)
−0.512342 + 0.858782i \(0.671222\pi\)
\(174\) 0 0
\(175\) −344.721 −0.148905
\(176\) 0 0
\(177\) −655.850 −0.278512
\(178\) 0 0
\(179\) −109.140 −0.0455726 −0.0227863 0.999740i \(-0.507254\pi\)
−0.0227863 + 0.999740i \(0.507254\pi\)
\(180\) 0 0
\(181\) 1476.85 0.606483 0.303242 0.952914i \(-0.401931\pi\)
0.303242 + 0.952914i \(0.401931\pi\)
\(182\) 0 0
\(183\) 3788.76 1.53045
\(184\) 0 0
\(185\) −1514.01 −0.601686
\(186\) 0 0
\(187\) −1529.33 −0.598051
\(188\) 0 0
\(189\) 333.672 0.128418
\(190\) 0 0
\(191\) −2032.16 −0.769853 −0.384926 0.922947i \(-0.625773\pi\)
−0.384926 + 0.922947i \(0.625773\pi\)
\(192\) 0 0
\(193\) 3883.64 1.44845 0.724224 0.689565i \(-0.242198\pi\)
0.724224 + 0.689565i \(0.242198\pi\)
\(194\) 0 0
\(195\) −108.482 −0.0398389
\(196\) 0 0
\(197\) 3580.64 1.29498 0.647488 0.762076i \(-0.275820\pi\)
0.647488 + 0.762076i \(0.275820\pi\)
\(198\) 0 0
\(199\) 2831.17 1.00853 0.504263 0.863550i \(-0.331764\pi\)
0.504263 + 0.863550i \(0.331764\pi\)
\(200\) 0 0
\(201\) −215.538 −0.0756362
\(202\) 0 0
\(203\) 112.572 0.0389211
\(204\) 0 0
\(205\) 213.757 0.0728265
\(206\) 0 0
\(207\) 542.756 0.182242
\(208\) 0 0
\(209\) −50.3463 −0.0166628
\(210\) 0 0
\(211\) −2903.80 −0.947421 −0.473711 0.880681i \(-0.657086\pi\)
−0.473711 + 0.880681i \(0.657086\pi\)
\(212\) 0 0
\(213\) 5237.82 1.68493
\(214\) 0 0
\(215\) 1076.33 0.341418
\(216\) 0 0
\(217\) −2164.70 −0.677186
\(218\) 0 0
\(219\) 2489.17 0.768049
\(220\) 0 0
\(221\) 192.503 0.0585935
\(222\) 0 0
\(223\) −454.760 −0.136560 −0.0682802 0.997666i \(-0.521751\pi\)
−0.0682802 + 0.997666i \(0.521751\pi\)
\(224\) 0 0
\(225\) 589.952 0.174801
\(226\) 0 0
\(227\) 2103.24 0.614966 0.307483 0.951554i \(-0.400513\pi\)
0.307483 + 0.951554i \(0.400513\pi\)
\(228\) 0 0
\(229\) −4647.97 −1.34125 −0.670625 0.741796i \(-0.733974\pi\)
−0.670625 + 0.741796i \(0.733974\pi\)
\(230\) 0 0
\(231\) 2376.73 0.676957
\(232\) 0 0
\(233\) 131.118 0.0368661 0.0184331 0.999830i \(-0.494132\pi\)
0.0184331 + 0.999830i \(0.494132\pi\)
\(234\) 0 0
\(235\) 1235.48 0.342953
\(236\) 0 0
\(237\) −2144.96 −0.587891
\(238\) 0 0
\(239\) −3467.77 −0.938541 −0.469271 0.883054i \(-0.655483\pi\)
−0.469271 + 0.883054i \(0.655483\pi\)
\(240\) 0 0
\(241\) 5818.91 1.55531 0.777653 0.628694i \(-0.216410\pi\)
0.777653 + 0.628694i \(0.216410\pi\)
\(242\) 0 0
\(243\) −5103.22 −1.34721
\(244\) 0 0
\(245\) 764.341 0.199314
\(246\) 0 0
\(247\) 6.33731 0.00163252
\(248\) 0 0
\(249\) −992.213 −0.252526
\(250\) 0 0
\(251\) −4633.30 −1.16515 −0.582573 0.812779i \(-0.697954\pi\)
−0.582573 + 0.812779i \(0.697954\pi\)
\(252\) 0 0
\(253\) −557.330 −0.138494
\(254\) 0 0
\(255\) −2244.67 −0.551243
\(256\) 0 0
\(257\) −5262.78 −1.27737 −0.638683 0.769470i \(-0.720520\pi\)
−0.638683 + 0.769470i \(0.720520\pi\)
\(258\) 0 0
\(259\) −4175.28 −1.00170
\(260\) 0 0
\(261\) −192.654 −0.0456896
\(262\) 0 0
\(263\) −1890.26 −0.443189 −0.221594 0.975139i \(-0.571126\pi\)
−0.221594 + 0.975139i \(0.571126\pi\)
\(264\) 0 0
\(265\) −3002.00 −0.695892
\(266\) 0 0
\(267\) 6114.18 1.40143
\(268\) 0 0
\(269\) 7472.17 1.69363 0.846815 0.531888i \(-0.178517\pi\)
0.846815 + 0.531888i \(0.178517\pi\)
\(270\) 0 0
\(271\) −1634.38 −0.366352 −0.183176 0.983080i \(-0.558638\pi\)
−0.183176 + 0.983080i \(0.558638\pi\)
\(272\) 0 0
\(273\) −299.169 −0.0663243
\(274\) 0 0
\(275\) −605.794 −0.132839
\(276\) 0 0
\(277\) −590.262 −0.128034 −0.0640170 0.997949i \(-0.520391\pi\)
−0.0640170 + 0.997949i \(0.520391\pi\)
\(278\) 0 0
\(279\) 3704.65 0.794952
\(280\) 0 0
\(281\) 2501.14 0.530980 0.265490 0.964114i \(-0.414466\pi\)
0.265490 + 0.964114i \(0.414466\pi\)
\(282\) 0 0
\(283\) 803.901 0.168859 0.0844293 0.996429i \(-0.473093\pi\)
0.0844293 + 0.996429i \(0.473093\pi\)
\(284\) 0 0
\(285\) −73.8959 −0.0153586
\(286\) 0 0
\(287\) 589.491 0.121242
\(288\) 0 0
\(289\) −929.797 −0.189252
\(290\) 0 0
\(291\) −6597.35 −1.32901
\(292\) 0 0
\(293\) −6332.54 −1.26263 −0.631316 0.775526i \(-0.717485\pi\)
−0.631316 + 0.775526i \(0.717485\pi\)
\(294\) 0 0
\(295\) 461.007 0.0909860
\(296\) 0 0
\(297\) 586.376 0.114562
\(298\) 0 0
\(299\) 70.1536 0.0135688
\(300\) 0 0
\(301\) 2968.26 0.568397
\(302\) 0 0
\(303\) 12187.4 2.31072
\(304\) 0 0
\(305\) −2663.17 −0.499977
\(306\) 0 0
\(307\) −7317.73 −1.36041 −0.680203 0.733024i \(-0.738108\pi\)
−0.680203 + 0.733024i \(0.738108\pi\)
\(308\) 0 0
\(309\) 6618.97 1.21858
\(310\) 0 0
\(311\) −2838.86 −0.517611 −0.258805 0.965930i \(-0.583329\pi\)
−0.258805 + 0.965930i \(0.583329\pi\)
\(312\) 0 0
\(313\) 160.132 0.0289175 0.0144588 0.999895i \(-0.495397\pi\)
0.0144588 + 0.999895i \(0.495397\pi\)
\(314\) 0 0
\(315\) 1626.95 0.291010
\(316\) 0 0
\(317\) −3330.78 −0.590142 −0.295071 0.955475i \(-0.595343\pi\)
−0.295071 + 0.955475i \(0.595343\pi\)
\(318\) 0 0
\(319\) 197.827 0.0347216
\(320\) 0 0
\(321\) −10775.9 −1.87369
\(322\) 0 0
\(323\) 131.129 0.0225889
\(324\) 0 0
\(325\) 76.2539 0.0130148
\(326\) 0 0
\(327\) 12439.3 2.10366
\(328\) 0 0
\(329\) 3407.17 0.570953
\(330\) 0 0
\(331\) −7337.39 −1.21843 −0.609214 0.793006i \(-0.708515\pi\)
−0.609214 + 0.793006i \(0.708515\pi\)
\(332\) 0 0
\(333\) 7145.53 1.17589
\(334\) 0 0
\(335\) 151.505 0.0247092
\(336\) 0 0
\(337\) −7160.54 −1.15745 −0.578723 0.815524i \(-0.696449\pi\)
−0.578723 + 0.815524i \(0.696449\pi\)
\(338\) 0 0
\(339\) 14413.1 2.30918
\(340\) 0 0
\(341\) −3804.13 −0.604121
\(342\) 0 0
\(343\) 6837.44 1.07635
\(344\) 0 0
\(345\) −818.022 −0.127655
\(346\) 0 0
\(347\) −6740.51 −1.04279 −0.521397 0.853314i \(-0.674589\pi\)
−0.521397 + 0.853314i \(0.674589\pi\)
\(348\) 0 0
\(349\) −10173.9 −1.56045 −0.780224 0.625501i \(-0.784895\pi\)
−0.780224 + 0.625501i \(0.784895\pi\)
\(350\) 0 0
\(351\) −73.8097 −0.0112241
\(352\) 0 0
\(353\) −2552.87 −0.384917 −0.192458 0.981305i \(-0.561646\pi\)
−0.192458 + 0.981305i \(0.561646\pi\)
\(354\) 0 0
\(355\) −3681.75 −0.550442
\(356\) 0 0
\(357\) −6190.28 −0.917716
\(358\) 0 0
\(359\) 6677.47 0.981681 0.490841 0.871249i \(-0.336690\pi\)
0.490841 + 0.871249i \(0.336690\pi\)
\(360\) 0 0
\(361\) −6854.68 −0.999371
\(362\) 0 0
\(363\) −5290.98 −0.765026
\(364\) 0 0
\(365\) −1749.68 −0.250911
\(366\) 0 0
\(367\) −11722.8 −1.66738 −0.833688 0.552236i \(-0.813775\pi\)
−0.833688 + 0.552236i \(0.813775\pi\)
\(368\) 0 0
\(369\) −1008.85 −0.142327
\(370\) 0 0
\(371\) −8278.82 −1.15853
\(372\) 0 0
\(373\) 8070.71 1.12034 0.560168 0.828379i \(-0.310736\pi\)
0.560168 + 0.828379i \(0.310736\pi\)
\(374\) 0 0
\(375\) −889.154 −0.122442
\(376\) 0 0
\(377\) −24.9014 −0.00340182
\(378\) 0 0
\(379\) 6693.10 0.907128 0.453564 0.891224i \(-0.350152\pi\)
0.453564 + 0.891224i \(0.350152\pi\)
\(380\) 0 0
\(381\) 15126.2 2.03397
\(382\) 0 0
\(383\) 2502.49 0.333867 0.166934 0.985968i \(-0.446613\pi\)
0.166934 + 0.985968i \(0.446613\pi\)
\(384\) 0 0
\(385\) −1670.64 −0.221152
\(386\) 0 0
\(387\) −5079.85 −0.667243
\(388\) 0 0
\(389\) 5487.69 0.715262 0.357631 0.933863i \(-0.383585\pi\)
0.357631 + 0.933863i \(0.383585\pi\)
\(390\) 0 0
\(391\) 1451.59 0.187750
\(392\) 0 0
\(393\) 10628.8 1.36426
\(394\) 0 0
\(395\) 1507.73 0.192056
\(396\) 0 0
\(397\) 7760.91 0.981130 0.490565 0.871405i \(-0.336790\pi\)
0.490565 + 0.871405i \(0.336790\pi\)
\(398\) 0 0
\(399\) −203.787 −0.0255693
\(400\) 0 0
\(401\) 14485.8 1.80395 0.901977 0.431785i \(-0.142116\pi\)
0.901977 + 0.431785i \(0.142116\pi\)
\(402\) 0 0
\(403\) 478.842 0.0591882
\(404\) 0 0
\(405\) 4046.39 0.496462
\(406\) 0 0
\(407\) −7337.41 −0.893616
\(408\) 0 0
\(409\) 6664.83 0.805758 0.402879 0.915253i \(-0.368010\pi\)
0.402879 + 0.915253i \(0.368010\pi\)
\(410\) 0 0
\(411\) 16113.7 1.93389
\(412\) 0 0
\(413\) 1271.35 0.151475
\(414\) 0 0
\(415\) 697.442 0.0824966
\(416\) 0 0
\(417\) 20761.1 2.43807
\(418\) 0 0
\(419\) 8437.43 0.983760 0.491880 0.870663i \(-0.336310\pi\)
0.491880 + 0.870663i \(0.336310\pi\)
\(420\) 0 0
\(421\) 13893.2 1.60834 0.804171 0.594397i \(-0.202609\pi\)
0.804171 + 0.594397i \(0.202609\pi\)
\(422\) 0 0
\(423\) −5831.00 −0.670243
\(424\) 0 0
\(425\) 1577.82 0.180083
\(426\) 0 0
\(427\) −7344.41 −0.832368
\(428\) 0 0
\(429\) −525.743 −0.0591681
\(430\) 0 0
\(431\) 10611.5 1.18594 0.592969 0.805225i \(-0.297956\pi\)
0.592969 + 0.805225i \(0.297956\pi\)
\(432\) 0 0
\(433\) −7569.77 −0.840139 −0.420069 0.907492i \(-0.637994\pi\)
−0.420069 + 0.907492i \(0.637994\pi\)
\(434\) 0 0
\(435\) 290.361 0.0320040
\(436\) 0 0
\(437\) 47.7871 0.00523105
\(438\) 0 0
\(439\) 11794.9 1.28232 0.641162 0.767406i \(-0.278453\pi\)
0.641162 + 0.767406i \(0.278453\pi\)
\(440\) 0 0
\(441\) −3607.39 −0.389525
\(442\) 0 0
\(443\) −11424.0 −1.22521 −0.612606 0.790388i \(-0.709879\pi\)
−0.612606 + 0.790388i \(0.709879\pi\)
\(444\) 0 0
\(445\) −4297.75 −0.457827
\(446\) 0 0
\(447\) −3908.01 −0.413518
\(448\) 0 0
\(449\) 8862.74 0.931533 0.465767 0.884908i \(-0.345779\pi\)
0.465767 + 0.884908i \(0.345779\pi\)
\(450\) 0 0
\(451\) 1035.94 0.108161
\(452\) 0 0
\(453\) −2388.06 −0.247684
\(454\) 0 0
\(455\) 210.290 0.0216672
\(456\) 0 0
\(457\) 5187.22 0.530958 0.265479 0.964117i \(-0.414470\pi\)
0.265479 + 0.964117i \(0.414470\pi\)
\(458\) 0 0
\(459\) −1527.24 −0.155306
\(460\) 0 0
\(461\) −16816.7 −1.69898 −0.849491 0.527603i \(-0.823091\pi\)
−0.849491 + 0.527603i \(0.823091\pi\)
\(462\) 0 0
\(463\) −6351.26 −0.637512 −0.318756 0.947837i \(-0.603265\pi\)
−0.318756 + 0.947837i \(0.603265\pi\)
\(464\) 0 0
\(465\) −5583.51 −0.556837
\(466\) 0 0
\(467\) −1057.02 −0.104739 −0.0523693 0.998628i \(-0.516677\pi\)
−0.0523693 + 0.998628i \(0.516677\pi\)
\(468\) 0 0
\(469\) 417.815 0.0411363
\(470\) 0 0
\(471\) −11336.3 −1.10902
\(472\) 0 0
\(473\) 5216.25 0.507069
\(474\) 0 0
\(475\) 51.9425 0.00501745
\(476\) 0 0
\(477\) 14168.3 1.36000
\(478\) 0 0
\(479\) 10138.2 0.967073 0.483537 0.875324i \(-0.339352\pi\)
0.483537 + 0.875324i \(0.339352\pi\)
\(480\) 0 0
\(481\) 923.591 0.0875512
\(482\) 0 0
\(483\) −2255.91 −0.212521
\(484\) 0 0
\(485\) 4637.38 0.434170
\(486\) 0 0
\(487\) 8874.74 0.825776 0.412888 0.910782i \(-0.364520\pi\)
0.412888 + 0.910782i \(0.364520\pi\)
\(488\) 0 0
\(489\) 19686.8 1.82059
\(490\) 0 0
\(491\) 21452.2 1.97174 0.985869 0.167521i \(-0.0535761\pi\)
0.985869 + 0.167521i \(0.0535761\pi\)
\(492\) 0 0
\(493\) −515.249 −0.0470703
\(494\) 0 0
\(495\) 2859.11 0.259611
\(496\) 0 0
\(497\) −10153.4 −0.916382
\(498\) 0 0
\(499\) −9696.91 −0.869926 −0.434963 0.900448i \(-0.643239\pi\)
−0.434963 + 0.900448i \(0.643239\pi\)
\(500\) 0 0
\(501\) −2012.10 −0.179429
\(502\) 0 0
\(503\) 8892.32 0.788249 0.394124 0.919057i \(-0.371048\pi\)
0.394124 + 0.919057i \(0.371048\pi\)
\(504\) 0 0
\(505\) −8566.71 −0.754878
\(506\) 0 0
\(507\) −15561.6 −1.36315
\(508\) 0 0
\(509\) −1084.94 −0.0944778 −0.0472389 0.998884i \(-0.515042\pi\)
−0.0472389 + 0.998884i \(0.515042\pi\)
\(510\) 0 0
\(511\) −4825.20 −0.417719
\(512\) 0 0
\(513\) −50.2776 −0.00432712
\(514\) 0 0
\(515\) −4652.58 −0.398091
\(516\) 0 0
\(517\) 5987.58 0.509349
\(518\) 0 0
\(519\) −16585.4 −1.40273
\(520\) 0 0
\(521\) 4578.35 0.384993 0.192496 0.981298i \(-0.438342\pi\)
0.192496 + 0.981298i \(0.438342\pi\)
\(522\) 0 0
\(523\) −7298.28 −0.610194 −0.305097 0.952321i \(-0.598689\pi\)
−0.305097 + 0.952321i \(0.598689\pi\)
\(524\) 0 0
\(525\) −2452.08 −0.203843
\(526\) 0 0
\(527\) 9908.02 0.818975
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −2175.77 −0.177817
\(532\) 0 0
\(533\) −130.398 −0.0105970
\(534\) 0 0
\(535\) 7574.56 0.612106
\(536\) 0 0
\(537\) −776.338 −0.0623863
\(538\) 0 0
\(539\) 3704.26 0.296018
\(540\) 0 0
\(541\) −14971.5 −1.18979 −0.594895 0.803803i \(-0.702806\pi\)
−0.594895 + 0.803803i \(0.702806\pi\)
\(542\) 0 0
\(543\) 10505.2 0.830241
\(544\) 0 0
\(545\) −8743.80 −0.687235
\(546\) 0 0
\(547\) 19510.9 1.52509 0.762547 0.646932i \(-0.223948\pi\)
0.762547 + 0.646932i \(0.223948\pi\)
\(548\) 0 0
\(549\) 12569.2 0.977119
\(550\) 0 0
\(551\) −16.9623 −0.00131147
\(552\) 0 0
\(553\) 4157.96 0.319737
\(554\) 0 0
\(555\) −10769.5 −0.823674
\(556\) 0 0
\(557\) −13098.1 −0.996378 −0.498189 0.867068i \(-0.666001\pi\)
−0.498189 + 0.867068i \(0.666001\pi\)
\(558\) 0 0
\(559\) −656.592 −0.0496796
\(560\) 0 0
\(561\) −10878.5 −0.818698
\(562\) 0 0
\(563\) 4086.19 0.305883 0.152942 0.988235i \(-0.451125\pi\)
0.152942 + 0.988235i \(0.451125\pi\)
\(564\) 0 0
\(565\) −10131.2 −0.754374
\(566\) 0 0
\(567\) 11159.0 0.826516
\(568\) 0 0
\(569\) −5021.20 −0.369946 −0.184973 0.982744i \(-0.559220\pi\)
−0.184973 + 0.982744i \(0.559220\pi\)
\(570\) 0 0
\(571\) 8277.56 0.606664 0.303332 0.952885i \(-0.401901\pi\)
0.303332 + 0.952885i \(0.401901\pi\)
\(572\) 0 0
\(573\) −14455.2 −1.05388
\(574\) 0 0
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −19548.4 −1.41042 −0.705210 0.708998i \(-0.749147\pi\)
−0.705210 + 0.708998i \(0.749147\pi\)
\(578\) 0 0
\(579\) 27625.2 1.98284
\(580\) 0 0
\(581\) 1923.38 0.137341
\(582\) 0 0
\(583\) −14548.7 −1.03353
\(584\) 0 0
\(585\) −359.889 −0.0254352
\(586\) 0 0
\(587\) 17479.7 1.22907 0.614536 0.788889i \(-0.289343\pi\)
0.614536 + 0.788889i \(0.289343\pi\)
\(588\) 0 0
\(589\) 326.177 0.0228182
\(590\) 0 0
\(591\) 25469.9 1.77275
\(592\) 0 0
\(593\) 513.405 0.0355531 0.0177766 0.999842i \(-0.494341\pi\)
0.0177766 + 0.999842i \(0.494341\pi\)
\(594\) 0 0
\(595\) 4351.25 0.299805
\(596\) 0 0
\(597\) 20138.8 1.38061
\(598\) 0 0
\(599\) −13706.8 −0.934964 −0.467482 0.884003i \(-0.654839\pi\)
−0.467482 + 0.884003i \(0.654839\pi\)
\(600\) 0 0
\(601\) −24403.7 −1.65632 −0.828159 0.560493i \(-0.810612\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(602\) 0 0
\(603\) −715.045 −0.0482900
\(604\) 0 0
\(605\) 3719.11 0.249923
\(606\) 0 0
\(607\) −16304.7 −1.09026 −0.545129 0.838352i \(-0.683519\pi\)
−0.545129 + 0.838352i \(0.683519\pi\)
\(608\) 0 0
\(609\) 800.748 0.0532807
\(610\) 0 0
\(611\) −753.683 −0.0499030
\(612\) 0 0
\(613\) 7754.74 0.510948 0.255474 0.966816i \(-0.417769\pi\)
0.255474 + 0.966816i \(0.417769\pi\)
\(614\) 0 0
\(615\) 1520.50 0.0996952
\(616\) 0 0
\(617\) −1574.90 −0.102760 −0.0513801 0.998679i \(-0.516362\pi\)
−0.0513801 + 0.998679i \(0.516362\pi\)
\(618\) 0 0
\(619\) 9160.25 0.594800 0.297400 0.954753i \(-0.403880\pi\)
0.297400 + 0.954753i \(0.403880\pi\)
\(620\) 0 0
\(621\) −556.570 −0.0359652
\(622\) 0 0
\(623\) −11852.2 −0.762196
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −358.125 −0.0228104
\(628\) 0 0
\(629\) 19110.6 1.21143
\(630\) 0 0
\(631\) −11663.9 −0.735871 −0.367935 0.929851i \(-0.619935\pi\)
−0.367935 + 0.929851i \(0.619935\pi\)
\(632\) 0 0
\(633\) −20655.4 −1.29697
\(634\) 0 0
\(635\) −10632.5 −0.664467
\(636\) 0 0
\(637\) −466.272 −0.0290021
\(638\) 0 0
\(639\) 17376.4 1.07574
\(640\) 0 0
\(641\) −27074.5 −1.66830 −0.834148 0.551541i \(-0.814040\pi\)
−0.834148 + 0.551541i \(0.814040\pi\)
\(642\) 0 0
\(643\) 4463.82 0.273773 0.136886 0.990587i \(-0.456290\pi\)
0.136886 + 0.990587i \(0.456290\pi\)
\(644\) 0 0
\(645\) 7656.16 0.467381
\(646\) 0 0
\(647\) 11755.0 0.714277 0.357139 0.934051i \(-0.383752\pi\)
0.357139 + 0.934051i \(0.383752\pi\)
\(648\) 0 0
\(649\) 2234.20 0.135131
\(650\) 0 0
\(651\) −15398.0 −0.927029
\(652\) 0 0
\(653\) −1236.64 −0.0741094 −0.0370547 0.999313i \(-0.511798\pi\)
−0.0370547 + 0.999313i \(0.511798\pi\)
\(654\) 0 0
\(655\) −7471.15 −0.445682
\(656\) 0 0
\(657\) 8257.81 0.490362
\(658\) 0 0
\(659\) −23646.9 −1.39780 −0.698901 0.715218i \(-0.746327\pi\)
−0.698901 + 0.715218i \(0.746327\pi\)
\(660\) 0 0
\(661\) 10150.5 0.597290 0.298645 0.954364i \(-0.403465\pi\)
0.298645 + 0.954364i \(0.403465\pi\)
\(662\) 0 0
\(663\) 1369.32 0.0802112
\(664\) 0 0
\(665\) 143.245 0.00835311
\(666\) 0 0
\(667\) −187.771 −0.0109003
\(668\) 0 0
\(669\) −3234.81 −0.186943
\(670\) 0 0
\(671\) −12906.7 −0.742558
\(672\) 0 0
\(673\) 13941.8 0.798540 0.399270 0.916833i \(-0.369264\pi\)
0.399270 + 0.916833i \(0.369264\pi\)
\(674\) 0 0
\(675\) −604.967 −0.0344966
\(676\) 0 0
\(677\) −13370.4 −0.759035 −0.379518 0.925185i \(-0.623910\pi\)
−0.379518 + 0.925185i \(0.623910\pi\)
\(678\) 0 0
\(679\) 12788.8 0.722812
\(680\) 0 0
\(681\) 14960.9 0.841852
\(682\) 0 0
\(683\) −15659.3 −0.877288 −0.438644 0.898661i \(-0.644541\pi\)
−0.438644 + 0.898661i \(0.644541\pi\)
\(684\) 0 0
\(685\) −11326.6 −0.631775
\(686\) 0 0
\(687\) −33062.1 −1.83609
\(688\) 0 0
\(689\) 1831.31 0.101259
\(690\) 0 0
\(691\) 9631.82 0.530263 0.265131 0.964212i \(-0.414585\pi\)
0.265131 + 0.964212i \(0.414585\pi\)
\(692\) 0 0
\(693\) 7884.77 0.432204
\(694\) 0 0
\(695\) −14593.3 −0.796484
\(696\) 0 0
\(697\) −2698.15 −0.146628
\(698\) 0 0
\(699\) 932.671 0.0504676
\(700\) 0 0
\(701\) 21140.9 1.13906 0.569530 0.821971i \(-0.307125\pi\)
0.569530 + 0.821971i \(0.307125\pi\)
\(702\) 0 0
\(703\) 629.131 0.0337527
\(704\) 0 0
\(705\) 8788.27 0.469483
\(706\) 0 0
\(707\) −23625.0 −1.25673
\(708\) 0 0
\(709\) −15917.4 −0.843144 −0.421572 0.906795i \(-0.638522\pi\)
−0.421572 + 0.906795i \(0.638522\pi\)
\(710\) 0 0
\(711\) −7115.89 −0.375340
\(712\) 0 0
\(713\) 3610.76 0.189655
\(714\) 0 0
\(715\) 369.553 0.0193294
\(716\) 0 0
\(717\) −24667.1 −1.28481
\(718\) 0 0
\(719\) −3323.34 −0.172378 −0.0861889 0.996279i \(-0.527469\pi\)
−0.0861889 + 0.996279i \(0.527469\pi\)
\(720\) 0 0
\(721\) −12830.7 −0.662748
\(722\) 0 0
\(723\) 41391.2 2.12912
\(724\) 0 0
\(725\) −204.099 −0.0104552
\(726\) 0 0
\(727\) 9877.52 0.503902 0.251951 0.967740i \(-0.418928\pi\)
0.251951 + 0.967740i \(0.418928\pi\)
\(728\) 0 0
\(729\) −14449.9 −0.734130
\(730\) 0 0
\(731\) −13586.0 −0.687407
\(732\) 0 0
\(733\) 28951.5 1.45886 0.729432 0.684053i \(-0.239784\pi\)
0.729432 + 0.684053i \(0.239784\pi\)
\(734\) 0 0
\(735\) 5436.93 0.272849
\(736\) 0 0
\(737\) 734.246 0.0366978
\(738\) 0 0
\(739\) 31009.5 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(740\) 0 0
\(741\) 45.0788 0.00223483
\(742\) 0 0
\(743\) 13761.0 0.679465 0.339733 0.940522i \(-0.389663\pi\)
0.339733 + 0.940522i \(0.389663\pi\)
\(744\) 0 0
\(745\) 2747.00 0.135090
\(746\) 0 0
\(747\) −3291.66 −0.161226
\(748\) 0 0
\(749\) 20888.9 1.01904
\(750\) 0 0
\(751\) −32197.4 −1.56445 −0.782223 0.622998i \(-0.785914\pi\)
−0.782223 + 0.622998i \(0.785914\pi\)
\(752\) 0 0
\(753\) −32957.8 −1.59502
\(754\) 0 0
\(755\) 1678.60 0.0809148
\(756\) 0 0
\(757\) 26139.9 1.25505 0.627524 0.778597i \(-0.284068\pi\)
0.627524 + 0.778597i \(0.284068\pi\)
\(758\) 0 0
\(759\) −3964.42 −0.189591
\(760\) 0 0
\(761\) −24004.0 −1.14342 −0.571712 0.820454i \(-0.693721\pi\)
−0.571712 + 0.820454i \(0.693721\pi\)
\(762\) 0 0
\(763\) −24113.3 −1.14412
\(764\) 0 0
\(765\) −7446.68 −0.351942
\(766\) 0 0
\(767\) −281.229 −0.0132393
\(768\) 0 0
\(769\) −33733.4 −1.58187 −0.790934 0.611902i \(-0.790405\pi\)
−0.790934 + 0.611902i \(0.790405\pi\)
\(770\) 0 0
\(771\) −37435.3 −1.74864
\(772\) 0 0
\(773\) 40247.1 1.87269 0.936344 0.351083i \(-0.114186\pi\)
0.936344 + 0.351083i \(0.114186\pi\)
\(774\) 0 0
\(775\) 3924.74 0.181911
\(776\) 0 0
\(777\) −29699.7 −1.37126
\(778\) 0 0
\(779\) −88.8246 −0.00408533
\(780\) 0 0
\(781\) −17843.0 −0.817508
\(782\) 0 0
\(783\) 197.557 0.00901676
\(784\) 0 0
\(785\) 7968.45 0.362301
\(786\) 0 0
\(787\) 16327.3 0.739522 0.369761 0.929127i \(-0.379440\pi\)
0.369761 + 0.929127i \(0.379440\pi\)
\(788\) 0 0
\(789\) −13445.9 −0.606700
\(790\) 0 0
\(791\) −27939.4 −1.25589
\(792\) 0 0
\(793\) 1624.62 0.0727515
\(794\) 0 0
\(795\) −21353.9 −0.952636
\(796\) 0 0
\(797\) −29358.8 −1.30482 −0.652410 0.757866i \(-0.726242\pi\)
−0.652410 + 0.757866i \(0.726242\pi\)
\(798\) 0 0
\(799\) −15594.9 −0.690498
\(800\) 0 0
\(801\) 20283.7 0.894745
\(802\) 0 0
\(803\) −8479.56 −0.372649
\(804\) 0 0
\(805\) 1585.72 0.0694275
\(806\) 0 0
\(807\) 53151.3 2.31848
\(808\) 0 0
\(809\) −2426.36 −0.105447 −0.0527234 0.998609i \(-0.516790\pi\)
−0.0527234 + 0.998609i \(0.516790\pi\)
\(810\) 0 0
\(811\) 31170.9 1.34964 0.674819 0.737983i \(-0.264222\pi\)
0.674819 + 0.737983i \(0.264222\pi\)
\(812\) 0 0
\(813\) −11625.7 −0.501515
\(814\) 0 0
\(815\) −13838.2 −0.594760
\(816\) 0 0
\(817\) −447.257 −0.0191524
\(818\) 0 0
\(819\) −992.490 −0.0423448
\(820\) 0 0
\(821\) −6679.93 −0.283960 −0.141980 0.989870i \(-0.545347\pi\)
−0.141980 + 0.989870i \(0.545347\pi\)
\(822\) 0 0
\(823\) −29299.3 −1.24096 −0.620480 0.784222i \(-0.713062\pi\)
−0.620480 + 0.784222i \(0.713062\pi\)
\(824\) 0 0
\(825\) −4309.15 −0.181849
\(826\) 0 0
\(827\) −39806.7 −1.67378 −0.836889 0.547372i \(-0.815628\pi\)
−0.836889 + 0.547372i \(0.815628\pi\)
\(828\) 0 0
\(829\) −17854.1 −0.748007 −0.374004 0.927427i \(-0.622015\pi\)
−0.374004 + 0.927427i \(0.622015\pi\)
\(830\) 0 0
\(831\) −4198.67 −0.175271
\(832\) 0 0
\(833\) −9647.91 −0.401297
\(834\) 0 0
\(835\) 1414.34 0.0586169
\(836\) 0 0
\(837\) −3798.94 −0.156882
\(838\) 0 0
\(839\) 6656.92 0.273924 0.136962 0.990576i \(-0.456266\pi\)
0.136962 + 0.990576i \(0.456266\pi\)
\(840\) 0 0
\(841\) −24322.3 −0.997267
\(842\) 0 0
\(843\) 17791.2 0.726881
\(844\) 0 0
\(845\) 10938.5 0.445320
\(846\) 0 0
\(847\) 10256.4 0.416075
\(848\) 0 0
\(849\) 5718.34 0.231158
\(850\) 0 0
\(851\) 6964.43 0.280538
\(852\) 0 0
\(853\) −30008.7 −1.20455 −0.602273 0.798290i \(-0.705738\pi\)
−0.602273 + 0.798290i \(0.705738\pi\)
\(854\) 0 0
\(855\) −245.149 −0.00980574
\(856\) 0 0
\(857\) 24281.5 0.967843 0.483922 0.875111i \(-0.339212\pi\)
0.483922 + 0.875111i \(0.339212\pi\)
\(858\) 0 0
\(859\) −30635.5 −1.21685 −0.608423 0.793613i \(-0.708198\pi\)
−0.608423 + 0.793613i \(0.708198\pi\)
\(860\) 0 0
\(861\) 4193.19 0.165974
\(862\) 0 0
\(863\) 26572.1 1.04812 0.524058 0.851683i \(-0.324418\pi\)
0.524058 + 0.851683i \(0.324418\pi\)
\(864\) 0 0
\(865\) 11658.1 0.458253
\(866\) 0 0
\(867\) −6613.87 −0.259076
\(868\) 0 0
\(869\) 7306.97 0.285238
\(870\) 0 0
\(871\) −92.4227 −0.00359543
\(872\) 0 0
\(873\) −21886.6 −0.848511
\(874\) 0 0
\(875\) 1723.60 0.0665925
\(876\) 0 0
\(877\) −37158.4 −1.43073 −0.715366 0.698750i \(-0.753740\pi\)
−0.715366 + 0.698750i \(0.753740\pi\)
\(878\) 0 0
\(879\) −45044.9 −1.72847
\(880\) 0 0
\(881\) −3353.12 −0.128229 −0.0641143 0.997943i \(-0.520422\pi\)
−0.0641143 + 0.997943i \(0.520422\pi\)
\(882\) 0 0
\(883\) −16292.5 −0.620936 −0.310468 0.950584i \(-0.600486\pi\)
−0.310468 + 0.950584i \(0.600486\pi\)
\(884\) 0 0
\(885\) 3279.25 0.124555
\(886\) 0 0
\(887\) 5949.82 0.225226 0.112613 0.993639i \(-0.464078\pi\)
0.112613 + 0.993639i \(0.464078\pi\)
\(888\) 0 0
\(889\) −29321.9 −1.10621
\(890\) 0 0
\(891\) 19610.2 0.737338
\(892\) 0 0
\(893\) −513.393 −0.0192386
\(894\) 0 0
\(895\) 545.700 0.0203807
\(896\) 0 0
\(897\) 499.019 0.0185750
\(898\) 0 0
\(899\) −1281.66 −0.0475480
\(900\) 0 0
\(901\) 37892.8 1.40110
\(902\) 0 0
\(903\) 21113.9 0.778102
\(904\) 0 0
\(905\) −7384.26 −0.271228
\(906\) 0 0
\(907\) 44105.2 1.61465 0.807326 0.590106i \(-0.200914\pi\)
0.807326 + 0.590106i \(0.200914\pi\)
\(908\) 0 0
\(909\) 40431.6 1.47528
\(910\) 0 0
\(911\) −4385.18 −0.159481 −0.0797407 0.996816i \(-0.525409\pi\)
−0.0797407 + 0.996816i \(0.525409\pi\)
\(912\) 0 0
\(913\) 3380.05 0.122523
\(914\) 0 0
\(915\) −18943.8 −0.684439
\(916\) 0 0
\(917\) −20603.7 −0.741978
\(918\) 0 0
\(919\) −30027.0 −1.07780 −0.538901 0.842369i \(-0.681160\pi\)
−0.538901 + 0.842369i \(0.681160\pi\)
\(920\) 0 0
\(921\) −52052.7 −1.86232
\(922\) 0 0
\(923\) 2245.98 0.0800946
\(924\) 0 0
\(925\) 7570.03 0.269082
\(926\) 0 0
\(927\) 21958.4 0.778002
\(928\) 0 0
\(929\) −5457.52 −0.192740 −0.0963700 0.995346i \(-0.530723\pi\)
−0.0963700 + 0.995346i \(0.530723\pi\)
\(930\) 0 0
\(931\) −317.614 −0.0111809
\(932\) 0 0
\(933\) −20193.5 −0.708579
\(934\) 0 0
\(935\) 7646.65 0.267457
\(936\) 0 0
\(937\) 3039.15 0.105960 0.0529802 0.998596i \(-0.483128\pi\)
0.0529802 + 0.998596i \(0.483128\pi\)
\(938\) 0 0
\(939\) 1139.05 0.0395864
\(940\) 0 0
\(941\) 25791.0 0.893479 0.446740 0.894664i \(-0.352585\pi\)
0.446740 + 0.894664i \(0.352585\pi\)
\(942\) 0 0
\(943\) −983.282 −0.0339555
\(944\) 0 0
\(945\) −1668.36 −0.0574304
\(946\) 0 0
\(947\) −18339.3 −0.629299 −0.314650 0.949208i \(-0.601887\pi\)
−0.314650 + 0.949208i \(0.601887\pi\)
\(948\) 0 0
\(949\) 1067.36 0.0365099
\(950\) 0 0
\(951\) −23692.6 −0.807871
\(952\) 0 0
\(953\) 12658.7 0.430278 0.215139 0.976583i \(-0.430979\pi\)
0.215139 + 0.976583i \(0.430979\pi\)
\(954\) 0 0
\(955\) 10160.8 0.344289
\(956\) 0 0
\(957\) 1407.19 0.0475319
\(958\) 0 0
\(959\) −31236.0 −1.05179
\(960\) 0 0
\(961\) −5145.31 −0.172714
\(962\) 0 0
\(963\) −35749.0 −1.19626
\(964\) 0 0
\(965\) −19418.2 −0.647765
\(966\) 0 0
\(967\) −50470.3 −1.67840 −0.839201 0.543822i \(-0.816977\pi\)
−0.839201 + 0.543822i \(0.816977\pi\)
\(968\) 0 0
\(969\) 932.752 0.0309229
\(970\) 0 0
\(971\) −30778.2 −1.01722 −0.508610 0.860997i \(-0.669840\pi\)
−0.508610 + 0.860997i \(0.669840\pi\)
\(972\) 0 0
\(973\) −40245.0 −1.32600
\(974\) 0 0
\(975\) 542.412 0.0178165
\(976\) 0 0
\(977\) −23575.5 −0.772004 −0.386002 0.922498i \(-0.626144\pi\)
−0.386002 + 0.922498i \(0.626144\pi\)
\(978\) 0 0
\(979\) −20828.4 −0.679958
\(980\) 0 0
\(981\) 41267.4 1.34308
\(982\) 0 0
\(983\) 44798.3 1.45355 0.726777 0.686874i \(-0.241018\pi\)
0.726777 + 0.686874i \(0.241018\pi\)
\(984\) 0 0
\(985\) −17903.2 −0.579131
\(986\) 0 0
\(987\) 24236.0 0.781601
\(988\) 0 0
\(989\) −4951.10 −0.159187
\(990\) 0 0
\(991\) 12153.5 0.389574 0.194787 0.980846i \(-0.437598\pi\)
0.194787 + 0.980846i \(0.437598\pi\)
\(992\) 0 0
\(993\) −52192.6 −1.66796
\(994\) 0 0
\(995\) −14155.9 −0.451026
\(996\) 0 0
\(997\) 36538.1 1.16065 0.580327 0.814383i \(-0.302925\pi\)
0.580327 + 0.814383i \(0.302925\pi\)
\(998\) 0 0
\(999\) −7327.40 −0.232061
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 1840.4.a.n.1.5 5
4.3 odd 2 115.4.a.e.1.3 5
12.11 even 2 1035.4.a.k.1.3 5
20.3 even 4 575.4.b.i.24.5 10
20.7 even 4 575.4.b.i.24.6 10
20.19 odd 2 575.4.a.j.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.3 5 4.3 odd 2
575.4.a.j.1.3 5 20.19 odd 2
575.4.b.i.24.5 10 20.3 even 4
575.4.b.i.24.6 10 20.7 even 4
1035.4.a.k.1.3 5 12.11 even 2
1840.4.a.n.1.5 5 1.1 even 1 trivial