Properties

Label 1305.4.a.m.1.5
Level $1305$
Weight $4$
Character 1305.1
Self dual yes
Analytic conductor $76.997$
Analytic rank $1$
Dimension $7$
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] = [1305,4,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, 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("1305.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1305.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: \(76.9974925575\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 435)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.26184\) of defining polynomial
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.26184 q^{2} -6.40776 q^{4} +5.00000 q^{5} -13.4311 q^{7} -18.1803 q^{8} +6.30920 q^{10} +1.30869 q^{11} +85.6641 q^{13} -16.9479 q^{14} +28.3214 q^{16} -67.9685 q^{17} -63.3429 q^{19} -32.0388 q^{20} +1.65136 q^{22} +139.990 q^{23} +25.0000 q^{25} +108.094 q^{26} +86.0634 q^{28} +29.0000 q^{29} -170.385 q^{31} +181.179 q^{32} -85.7654 q^{34} -67.1557 q^{35} -405.970 q^{37} -79.9286 q^{38} -90.9015 q^{40} +447.863 q^{41} +407.779 q^{43} -8.38576 q^{44} +176.645 q^{46} +178.857 q^{47} -162.605 q^{49} +31.5460 q^{50} -548.915 q^{52} -93.3357 q^{53} +6.54344 q^{55} +244.182 q^{56} +36.5934 q^{58} -279.796 q^{59} -793.549 q^{61} -214.999 q^{62} +2.04805 q^{64} +428.321 q^{65} +460.471 q^{67} +435.526 q^{68} -84.7397 q^{70} -803.153 q^{71} -150.833 q^{73} -512.269 q^{74} +405.886 q^{76} -17.5772 q^{77} -313.814 q^{79} +141.607 q^{80} +565.132 q^{82} -250.514 q^{83} -339.842 q^{85} +514.552 q^{86} -23.7923 q^{88} +97.2972 q^{89} -1150.57 q^{91} -897.024 q^{92} +225.689 q^{94} -316.714 q^{95} -1342.23 q^{97} -205.181 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} + 15 q^{4} + 35 q^{5} - 37 q^{7} + 36 q^{8} + 5 q^{10} + 11 q^{11} - 133 q^{13} + 75 q^{14} - 53 q^{16} - 21 q^{17} - 170 q^{19} + 75 q^{20} - 369 q^{22} + 68 q^{23} + 175 q^{25} - 181 q^{26}+ \cdots - 1068 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26184 0.446128 0.223064 0.974804i \(-0.428394\pi\)
0.223064 + 0.974804i \(0.428394\pi\)
\(3\) 0 0
\(4\) −6.40776 −0.800970
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −13.4311 −0.725213 −0.362606 0.931942i \(-0.618113\pi\)
−0.362606 + 0.931942i \(0.618113\pi\)
\(8\) −18.1803 −0.803463
\(9\) 0 0
\(10\) 6.30920 0.199514
\(11\) 1.30869 0.0358713 0.0179357 0.999839i \(-0.494291\pi\)
0.0179357 + 0.999839i \(0.494291\pi\)
\(12\) 0 0
\(13\) 85.6641 1.82761 0.913806 0.406151i \(-0.133129\pi\)
0.913806 + 0.406151i \(0.133129\pi\)
\(14\) −16.9479 −0.323538
\(15\) 0 0
\(16\) 28.3214 0.442523
\(17\) −67.9685 −0.969693 −0.484846 0.874599i \(-0.661124\pi\)
−0.484846 + 0.874599i \(0.661124\pi\)
\(18\) 0 0
\(19\) −63.3429 −0.764834 −0.382417 0.923990i \(-0.624908\pi\)
−0.382417 + 0.923990i \(0.624908\pi\)
\(20\) −32.0388 −0.358205
\(21\) 0 0
\(22\) 1.65136 0.0160032
\(23\) 139.990 1.26913 0.634565 0.772870i \(-0.281179\pi\)
0.634565 + 0.772870i \(0.281179\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 108.094 0.815349
\(27\) 0 0
\(28\) 86.0634 0.580874
\(29\) 29.0000 0.185695
\(30\) 0 0
\(31\) −170.385 −0.987164 −0.493582 0.869699i \(-0.664313\pi\)
−0.493582 + 0.869699i \(0.664313\pi\)
\(32\) 181.179 1.00088
\(33\) 0 0
\(34\) −85.7654 −0.432607
\(35\) −67.1557 −0.324325
\(36\) 0 0
\(37\) −405.970 −1.80381 −0.901905 0.431934i \(-0.857831\pi\)
−0.901905 + 0.431934i \(0.857831\pi\)
\(38\) −79.9286 −0.341214
\(39\) 0 0
\(40\) −90.9015 −0.359320
\(41\) 447.863 1.70596 0.852982 0.521940i \(-0.174792\pi\)
0.852982 + 0.521940i \(0.174792\pi\)
\(42\) 0 0
\(43\) 407.779 1.44618 0.723090 0.690754i \(-0.242721\pi\)
0.723090 + 0.690754i \(0.242721\pi\)
\(44\) −8.38576 −0.0287318
\(45\) 0 0
\(46\) 176.645 0.566194
\(47\) 178.857 0.555086 0.277543 0.960713i \(-0.410480\pi\)
0.277543 + 0.960713i \(0.410480\pi\)
\(48\) 0 0
\(49\) −162.605 −0.474066
\(50\) 31.5460 0.0892256
\(51\) 0 0
\(52\) −548.915 −1.46386
\(53\) −93.3357 −0.241899 −0.120949 0.992659i \(-0.538594\pi\)
−0.120949 + 0.992659i \(0.538594\pi\)
\(54\) 0 0
\(55\) 6.54344 0.0160421
\(56\) 244.182 0.582682
\(57\) 0 0
\(58\) 36.5934 0.0828439
\(59\) −279.796 −0.617396 −0.308698 0.951160i \(-0.599893\pi\)
−0.308698 + 0.951160i \(0.599893\pi\)
\(60\) 0 0
\(61\) −793.549 −1.66563 −0.832816 0.553550i \(-0.813273\pi\)
−0.832816 + 0.553550i \(0.813273\pi\)
\(62\) −214.999 −0.440402
\(63\) 0 0
\(64\) 2.04805 0.00400010
\(65\) 428.321 0.817333
\(66\) 0 0
\(67\) 460.471 0.839635 0.419818 0.907609i \(-0.362094\pi\)
0.419818 + 0.907609i \(0.362094\pi\)
\(68\) 435.526 0.776695
\(69\) 0 0
\(70\) −84.7397 −0.144690
\(71\) −803.153 −1.34249 −0.671244 0.741236i \(-0.734240\pi\)
−0.671244 + 0.741236i \(0.734240\pi\)
\(72\) 0 0
\(73\) −150.833 −0.241832 −0.120916 0.992663i \(-0.538583\pi\)
−0.120916 + 0.992663i \(0.538583\pi\)
\(74\) −512.269 −0.804730
\(75\) 0 0
\(76\) 405.886 0.612609
\(77\) −17.5772 −0.0260143
\(78\) 0 0
\(79\) −313.814 −0.446922 −0.223461 0.974713i \(-0.571735\pi\)
−0.223461 + 0.974713i \(0.571735\pi\)
\(80\) 141.607 0.197902
\(81\) 0 0
\(82\) 565.132 0.761078
\(83\) −250.514 −0.331295 −0.165648 0.986185i \(-0.552971\pi\)
−0.165648 + 0.986185i \(0.552971\pi\)
\(84\) 0 0
\(85\) −339.842 −0.433660
\(86\) 514.552 0.645181
\(87\) 0 0
\(88\) −23.7923 −0.0288213
\(89\) 97.2972 0.115882 0.0579409 0.998320i \(-0.481547\pi\)
0.0579409 + 0.998320i \(0.481547\pi\)
\(90\) 0 0
\(91\) −1150.57 −1.32541
\(92\) −897.024 −1.01653
\(93\) 0 0
\(94\) 225.689 0.247639
\(95\) −316.714 −0.342044
\(96\) 0 0
\(97\) −1342.23 −1.40497 −0.702487 0.711697i \(-0.747927\pi\)
−0.702487 + 0.711697i \(0.747927\pi\)
\(98\) −205.181 −0.211494
\(99\) 0 0
\(100\) −160.194 −0.160194
\(101\) −73.7087 −0.0726167 −0.0363084 0.999341i \(-0.511560\pi\)
−0.0363084 + 0.999341i \(0.511560\pi\)
\(102\) 0 0
\(103\) −1307.09 −1.25040 −0.625199 0.780465i \(-0.714982\pi\)
−0.625199 + 0.780465i \(0.714982\pi\)
\(104\) −1557.40 −1.46842
\(105\) 0 0
\(106\) −117.775 −0.107918
\(107\) −845.454 −0.763861 −0.381930 0.924191i \(-0.624741\pi\)
−0.381930 + 0.924191i \(0.624741\pi\)
\(108\) 0 0
\(109\) −1502.99 −1.32074 −0.660370 0.750941i \(-0.729600\pi\)
−0.660370 + 0.750941i \(0.729600\pi\)
\(110\) 8.25678 0.00715685
\(111\) 0 0
\(112\) −380.389 −0.320923
\(113\) 317.218 0.264083 0.132042 0.991244i \(-0.457847\pi\)
0.132042 + 0.991244i \(0.457847\pi\)
\(114\) 0 0
\(115\) 699.951 0.567572
\(116\) −185.825 −0.148736
\(117\) 0 0
\(118\) −353.058 −0.275438
\(119\) 912.893 0.703234
\(120\) 0 0
\(121\) −1329.29 −0.998713
\(122\) −1001.33 −0.743085
\(123\) 0 0
\(124\) 1091.79 0.790689
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1936.01 −1.35270 −0.676349 0.736581i \(-0.736439\pi\)
−0.676349 + 0.736581i \(0.736439\pi\)
\(128\) −1446.85 −0.999100
\(129\) 0 0
\(130\) 540.472 0.364635
\(131\) 1234.54 0.823379 0.411689 0.911324i \(-0.364939\pi\)
0.411689 + 0.911324i \(0.364939\pi\)
\(132\) 0 0
\(133\) 850.767 0.554668
\(134\) 581.042 0.374585
\(135\) 0 0
\(136\) 1235.69 0.779112
\(137\) 886.190 0.552645 0.276322 0.961065i \(-0.410884\pi\)
0.276322 + 0.961065i \(0.410884\pi\)
\(138\) 0 0
\(139\) 1582.12 0.965421 0.482711 0.875780i \(-0.339652\pi\)
0.482711 + 0.875780i \(0.339652\pi\)
\(140\) 430.317 0.259775
\(141\) 0 0
\(142\) −1013.45 −0.598922
\(143\) 112.108 0.0655588
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) −190.328 −0.107888
\(147\) 0 0
\(148\) 2601.36 1.44480
\(149\) 1649.57 0.906969 0.453485 0.891264i \(-0.350181\pi\)
0.453485 + 0.891264i \(0.350181\pi\)
\(150\) 0 0
\(151\) 343.852 0.185313 0.0926565 0.995698i \(-0.470464\pi\)
0.0926565 + 0.995698i \(0.470464\pi\)
\(152\) 1151.59 0.614516
\(153\) 0 0
\(154\) −22.1796 −0.0116057
\(155\) −851.926 −0.441473
\(156\) 0 0
\(157\) 2493.83 1.26770 0.633851 0.773455i \(-0.281473\pi\)
0.633851 + 0.773455i \(0.281473\pi\)
\(158\) −395.983 −0.199384
\(159\) 0 0
\(160\) 905.897 0.447609
\(161\) −1880.23 −0.920389
\(162\) 0 0
\(163\) −1915.12 −0.920270 −0.460135 0.887849i \(-0.652199\pi\)
−0.460135 + 0.887849i \(0.652199\pi\)
\(164\) −2869.80 −1.36643
\(165\) 0 0
\(166\) −316.109 −0.147800
\(167\) −99.5806 −0.0461424 −0.0230712 0.999734i \(-0.507344\pi\)
−0.0230712 + 0.999734i \(0.507344\pi\)
\(168\) 0 0
\(169\) 5141.34 2.34016
\(170\) −428.827 −0.193468
\(171\) 0 0
\(172\) −2612.95 −1.15835
\(173\) −2139.30 −0.940160 −0.470080 0.882624i \(-0.655775\pi\)
−0.470080 + 0.882624i \(0.655775\pi\)
\(174\) 0 0
\(175\) −335.778 −0.145043
\(176\) 37.0640 0.0158739
\(177\) 0 0
\(178\) 122.773 0.0516981
\(179\) −1863.54 −0.778142 −0.389071 0.921208i \(-0.627204\pi\)
−0.389071 + 0.921208i \(0.627204\pi\)
\(180\) 0 0
\(181\) −3008.76 −1.23558 −0.617788 0.786345i \(-0.711971\pi\)
−0.617788 + 0.786345i \(0.711971\pi\)
\(182\) −1451.83 −0.591301
\(183\) 0 0
\(184\) −2545.06 −1.01970
\(185\) −2029.85 −0.806689
\(186\) 0 0
\(187\) −88.9496 −0.0347842
\(188\) −1146.07 −0.444607
\(189\) 0 0
\(190\) −399.643 −0.152596
\(191\) −5175.24 −1.96056 −0.980280 0.197611i \(-0.936682\pi\)
−0.980280 + 0.197611i \(0.936682\pi\)
\(192\) 0 0
\(193\) −3407.89 −1.27101 −0.635505 0.772097i \(-0.719208\pi\)
−0.635505 + 0.772097i \(0.719208\pi\)
\(194\) −1693.68 −0.626798
\(195\) 0 0
\(196\) 1041.93 0.379713
\(197\) 2662.23 0.962823 0.481412 0.876495i \(-0.340124\pi\)
0.481412 + 0.876495i \(0.340124\pi\)
\(198\) 0 0
\(199\) 1124.12 0.400437 0.200218 0.979751i \(-0.435835\pi\)
0.200218 + 0.979751i \(0.435835\pi\)
\(200\) −454.507 −0.160693
\(201\) 0 0
\(202\) −93.0086 −0.0323964
\(203\) −389.503 −0.134669
\(204\) 0 0
\(205\) 2239.32 0.762930
\(206\) −1649.33 −0.557837
\(207\) 0 0
\(208\) 2426.13 0.808759
\(209\) −82.8961 −0.0274356
\(210\) 0 0
\(211\) 109.248 0.0356442 0.0178221 0.999841i \(-0.494327\pi\)
0.0178221 + 0.999841i \(0.494327\pi\)
\(212\) 598.072 0.193754
\(213\) 0 0
\(214\) −1066.83 −0.340780
\(215\) 2038.89 0.646751
\(216\) 0 0
\(217\) 2288.47 0.715904
\(218\) −1896.54 −0.589219
\(219\) 0 0
\(220\) −41.9288 −0.0128493
\(221\) −5822.46 −1.77222
\(222\) 0 0
\(223\) −4655.65 −1.39805 −0.699026 0.715097i \(-0.746383\pi\)
−0.699026 + 0.715097i \(0.746383\pi\)
\(224\) −2433.45 −0.725854
\(225\) 0 0
\(226\) 400.279 0.117815
\(227\) −3715.56 −1.08639 −0.543195 0.839606i \(-0.682786\pi\)
−0.543195 + 0.839606i \(0.682786\pi\)
\(228\) 0 0
\(229\) 2437.74 0.703451 0.351726 0.936103i \(-0.385595\pi\)
0.351726 + 0.936103i \(0.385595\pi\)
\(230\) 883.227 0.253210
\(231\) 0 0
\(232\) −527.228 −0.149199
\(233\) 2704.29 0.760360 0.380180 0.924912i \(-0.375862\pi\)
0.380180 + 0.924912i \(0.375862\pi\)
\(234\) 0 0
\(235\) 894.287 0.248242
\(236\) 1792.87 0.494516
\(237\) 0 0
\(238\) 1151.93 0.313732
\(239\) −6018.67 −1.62893 −0.814467 0.580210i \(-0.802970\pi\)
−0.814467 + 0.580210i \(0.802970\pi\)
\(240\) 0 0
\(241\) −1244.90 −0.332743 −0.166372 0.986063i \(-0.553205\pi\)
−0.166372 + 0.986063i \(0.553205\pi\)
\(242\) −1677.35 −0.445554
\(243\) 0 0
\(244\) 5084.87 1.33412
\(245\) −813.024 −0.212009
\(246\) 0 0
\(247\) −5426.21 −1.39782
\(248\) 3097.65 0.793150
\(249\) 0 0
\(250\) 157.730 0.0399029
\(251\) −2477.48 −0.623016 −0.311508 0.950244i \(-0.600834\pi\)
−0.311508 + 0.950244i \(0.600834\pi\)
\(252\) 0 0
\(253\) 183.204 0.0455254
\(254\) −2442.93 −0.603477
\(255\) 0 0
\(256\) −1842.08 −0.449727
\(257\) 4778.08 1.15972 0.579860 0.814716i \(-0.303107\pi\)
0.579860 + 0.814716i \(0.303107\pi\)
\(258\) 0 0
\(259\) 5452.63 1.30815
\(260\) −2744.58 −0.654659
\(261\) 0 0
\(262\) 1557.80 0.367332
\(263\) 1571.56 0.368467 0.184233 0.982883i \(-0.441020\pi\)
0.184233 + 0.982883i \(0.441020\pi\)
\(264\) 0 0
\(265\) −466.678 −0.108180
\(266\) 1073.53 0.247453
\(267\) 0 0
\(268\) −2950.59 −0.672522
\(269\) −4946.58 −1.12118 −0.560591 0.828093i \(-0.689426\pi\)
−0.560591 + 0.828093i \(0.689426\pi\)
\(270\) 0 0
\(271\) −914.942 −0.205088 −0.102544 0.994728i \(-0.532698\pi\)
−0.102544 + 0.994728i \(0.532698\pi\)
\(272\) −1924.97 −0.429111
\(273\) 0 0
\(274\) 1118.23 0.246550
\(275\) 32.7172 0.00717426
\(276\) 0 0
\(277\) −2441.56 −0.529599 −0.264799 0.964304i \(-0.585306\pi\)
−0.264799 + 0.964304i \(0.585306\pi\)
\(278\) 1996.38 0.430701
\(279\) 0 0
\(280\) 1220.91 0.260583
\(281\) 5311.04 1.12751 0.563755 0.825942i \(-0.309356\pi\)
0.563755 + 0.825942i \(0.309356\pi\)
\(282\) 0 0
\(283\) 669.167 0.140558 0.0702789 0.997527i \(-0.477611\pi\)
0.0702789 + 0.997527i \(0.477611\pi\)
\(284\) 5146.41 1.07529
\(285\) 0 0
\(286\) 141.462 0.0292476
\(287\) −6015.31 −1.23719
\(288\) 0 0
\(289\) −293.286 −0.0596960
\(290\) 182.967 0.0370489
\(291\) 0 0
\(292\) 966.504 0.193700
\(293\) 7468.02 1.48903 0.744516 0.667604i \(-0.232680\pi\)
0.744516 + 0.667604i \(0.232680\pi\)
\(294\) 0 0
\(295\) −1398.98 −0.276108
\(296\) 7380.65 1.44930
\(297\) 0 0
\(298\) 2081.50 0.404624
\(299\) 11992.1 2.31948
\(300\) 0 0
\(301\) −5476.93 −1.04879
\(302\) 433.886 0.0826733
\(303\) 0 0
\(304\) −1793.96 −0.338456
\(305\) −3967.74 −0.744893
\(306\) 0 0
\(307\) −9927.63 −1.84560 −0.922801 0.385278i \(-0.874106\pi\)
−0.922801 + 0.385278i \(0.874106\pi\)
\(308\) 112.630 0.0208367
\(309\) 0 0
\(310\) −1075.00 −0.196954
\(311\) −3131.42 −0.570953 −0.285477 0.958386i \(-0.592152\pi\)
−0.285477 + 0.958386i \(0.592152\pi\)
\(312\) 0 0
\(313\) 8434.75 1.52320 0.761598 0.648050i \(-0.224415\pi\)
0.761598 + 0.648050i \(0.224415\pi\)
\(314\) 3146.82 0.565558
\(315\) 0 0
\(316\) 2010.84 0.357971
\(317\) 9162.80 1.62345 0.811725 0.584039i \(-0.198529\pi\)
0.811725 + 0.584039i \(0.198529\pi\)
\(318\) 0 0
\(319\) 37.9520 0.00666114
\(320\) 10.2403 0.00178890
\(321\) 0 0
\(322\) −2372.55 −0.410611
\(323\) 4305.32 0.741654
\(324\) 0 0
\(325\) 2141.60 0.365522
\(326\) −2416.58 −0.410558
\(327\) 0 0
\(328\) −8142.29 −1.37068
\(329\) −2402.26 −0.402555
\(330\) 0 0
\(331\) 5194.87 0.862647 0.431323 0.902197i \(-0.358047\pi\)
0.431323 + 0.902197i \(0.358047\pi\)
\(332\) 1605.23 0.265357
\(333\) 0 0
\(334\) −125.655 −0.0205854
\(335\) 2302.36 0.375496
\(336\) 0 0
\(337\) −3217.15 −0.520027 −0.260014 0.965605i \(-0.583727\pi\)
−0.260014 + 0.965605i \(0.583727\pi\)
\(338\) 6487.55 1.04401
\(339\) 0 0
\(340\) 2177.63 0.347348
\(341\) −222.981 −0.0354109
\(342\) 0 0
\(343\) 6790.84 1.06901
\(344\) −7413.54 −1.16195
\(345\) 0 0
\(346\) −2699.45 −0.419432
\(347\) 609.761 0.0943334 0.0471667 0.998887i \(-0.484981\pi\)
0.0471667 + 0.998887i \(0.484981\pi\)
\(348\) 0 0
\(349\) 4406.40 0.675843 0.337921 0.941174i \(-0.390276\pi\)
0.337921 + 0.941174i \(0.390276\pi\)
\(350\) −423.699 −0.0647075
\(351\) 0 0
\(352\) 237.108 0.0359031
\(353\) −2480.09 −0.373943 −0.186971 0.982365i \(-0.559867\pi\)
−0.186971 + 0.982365i \(0.559867\pi\)
\(354\) 0 0
\(355\) −4015.76 −0.600379
\(356\) −623.457 −0.0928178
\(357\) 0 0
\(358\) −2351.49 −0.347151
\(359\) −6578.82 −0.967177 −0.483589 0.875295i \(-0.660667\pi\)
−0.483589 + 0.875295i \(0.660667\pi\)
\(360\) 0 0
\(361\) −2846.68 −0.415028
\(362\) −3796.57 −0.551225
\(363\) 0 0
\(364\) 7372.55 1.06161
\(365\) −754.167 −0.108150
\(366\) 0 0
\(367\) −731.114 −0.103989 −0.0519943 0.998647i \(-0.516558\pi\)
−0.0519943 + 0.998647i \(0.516558\pi\)
\(368\) 3964.72 0.561618
\(369\) 0 0
\(370\) −2561.34 −0.359886
\(371\) 1253.60 0.175428
\(372\) 0 0
\(373\) −1673.03 −0.232242 −0.116121 0.993235i \(-0.537046\pi\)
−0.116121 + 0.993235i \(0.537046\pi\)
\(374\) −112.240 −0.0155182
\(375\) 0 0
\(376\) −3251.68 −0.445991
\(377\) 2484.26 0.339379
\(378\) 0 0
\(379\) 3760.44 0.509659 0.254830 0.966986i \(-0.417981\pi\)
0.254830 + 0.966986i \(0.417981\pi\)
\(380\) 2029.43 0.273967
\(381\) 0 0
\(382\) −6530.33 −0.874661
\(383\) 12540.8 1.67312 0.836562 0.547872i \(-0.184562\pi\)
0.836562 + 0.547872i \(0.184562\pi\)
\(384\) 0 0
\(385\) −87.8859 −0.0116340
\(386\) −4300.21 −0.567033
\(387\) 0 0
\(388\) 8600.66 1.12534
\(389\) −5779.21 −0.753259 −0.376629 0.926364i \(-0.622917\pi\)
−0.376629 + 0.926364i \(0.622917\pi\)
\(390\) 0 0
\(391\) −9514.92 −1.23067
\(392\) 2956.20 0.380895
\(393\) 0 0
\(394\) 3359.31 0.429542
\(395\) −1569.07 −0.199869
\(396\) 0 0
\(397\) 14394.6 1.81976 0.909881 0.414869i \(-0.136173\pi\)
0.909881 + 0.414869i \(0.136173\pi\)
\(398\) 1418.46 0.178646
\(399\) 0 0
\(400\) 708.036 0.0885045
\(401\) −8620.31 −1.07351 −0.536756 0.843738i \(-0.680350\pi\)
−0.536756 + 0.843738i \(0.680350\pi\)
\(402\) 0 0
\(403\) −14595.9 −1.80415
\(404\) 472.308 0.0581638
\(405\) 0 0
\(406\) −491.490 −0.0600795
\(407\) −531.288 −0.0647051
\(408\) 0 0
\(409\) −14058.0 −1.69957 −0.849783 0.527133i \(-0.823267\pi\)
−0.849783 + 0.527133i \(0.823267\pi\)
\(410\) 2825.66 0.340365
\(411\) 0 0
\(412\) 8375.49 1.00153
\(413\) 3757.98 0.447744
\(414\) 0 0
\(415\) −1252.57 −0.148160
\(416\) 15520.6 1.82923
\(417\) 0 0
\(418\) −104.602 −0.0122398
\(419\) 308.722 0.0359954 0.0179977 0.999838i \(-0.494271\pi\)
0.0179977 + 0.999838i \(0.494271\pi\)
\(420\) 0 0
\(421\) 7341.48 0.849886 0.424943 0.905220i \(-0.360294\pi\)
0.424943 + 0.905220i \(0.360294\pi\)
\(422\) 137.853 0.0159019
\(423\) 0 0
\(424\) 1696.87 0.194357
\(425\) −1699.21 −0.193939
\(426\) 0 0
\(427\) 10658.3 1.20794
\(428\) 5417.47 0.611830
\(429\) 0 0
\(430\) 2572.76 0.288534
\(431\) 16660.8 1.86201 0.931003 0.365013i \(-0.118935\pi\)
0.931003 + 0.365013i \(0.118935\pi\)
\(432\) 0 0
\(433\) 10091.5 1.12001 0.560006 0.828488i \(-0.310799\pi\)
0.560006 + 0.828488i \(0.310799\pi\)
\(434\) 2887.68 0.319385
\(435\) 0 0
\(436\) 9630.82 1.05787
\(437\) −8867.38 −0.970674
\(438\) 0 0
\(439\) 5149.74 0.559871 0.279936 0.960019i \(-0.409687\pi\)
0.279936 + 0.960019i \(0.409687\pi\)
\(440\) −118.962 −0.0128893
\(441\) 0 0
\(442\) −7347.02 −0.790638
\(443\) −15820.5 −1.69674 −0.848371 0.529402i \(-0.822416\pi\)
−0.848371 + 0.529402i \(0.822416\pi\)
\(444\) 0 0
\(445\) 486.486 0.0518239
\(446\) −5874.69 −0.623710
\(447\) 0 0
\(448\) −27.5076 −0.00290092
\(449\) 13903.0 1.46130 0.730651 0.682751i \(-0.239217\pi\)
0.730651 + 0.682751i \(0.239217\pi\)
\(450\) 0 0
\(451\) 586.114 0.0611952
\(452\) −2032.66 −0.211523
\(453\) 0 0
\(454\) −4688.45 −0.484669
\(455\) −5752.83 −0.592740
\(456\) 0 0
\(457\) 4315.24 0.441704 0.220852 0.975307i \(-0.429116\pi\)
0.220852 + 0.975307i \(0.429116\pi\)
\(458\) 3076.04 0.313829
\(459\) 0 0
\(460\) −4485.12 −0.454608
\(461\) −5936.08 −0.599720 −0.299860 0.953983i \(-0.596940\pi\)
−0.299860 + 0.953983i \(0.596940\pi\)
\(462\) 0 0
\(463\) −12894.4 −1.29428 −0.647141 0.762370i \(-0.724036\pi\)
−0.647141 + 0.762370i \(0.724036\pi\)
\(464\) 821.322 0.0821744
\(465\) 0 0
\(466\) 3412.38 0.339218
\(467\) −12653.8 −1.25385 −0.626924 0.779081i \(-0.715686\pi\)
−0.626924 + 0.779081i \(0.715686\pi\)
\(468\) 0 0
\(469\) −6184.65 −0.608914
\(470\) 1128.45 0.110748
\(471\) 0 0
\(472\) 5086.78 0.496055
\(473\) 533.656 0.0518764
\(474\) 0 0
\(475\) −1583.57 −0.152967
\(476\) −5849.60 −0.563269
\(477\) 0 0
\(478\) −7594.60 −0.726713
\(479\) −8991.57 −0.857694 −0.428847 0.903377i \(-0.641080\pi\)
−0.428847 + 0.903377i \(0.641080\pi\)
\(480\) 0 0
\(481\) −34777.0 −3.29667
\(482\) −1570.87 −0.148446
\(483\) 0 0
\(484\) 8517.75 0.799939
\(485\) −6711.13 −0.628323
\(486\) 0 0
\(487\) 7671.39 0.713806 0.356903 0.934141i \(-0.383833\pi\)
0.356903 + 0.934141i \(0.383833\pi\)
\(488\) 14426.9 1.33827
\(489\) 0 0
\(490\) −1025.91 −0.0945831
\(491\) −10322.9 −0.948809 −0.474405 0.880307i \(-0.657337\pi\)
−0.474405 + 0.880307i \(0.657337\pi\)
\(492\) 0 0
\(493\) −1971.09 −0.180067
\(494\) −6847.01 −0.623607
\(495\) 0 0
\(496\) −4825.56 −0.436843
\(497\) 10787.3 0.973590
\(498\) 0 0
\(499\) −4385.18 −0.393402 −0.196701 0.980464i \(-0.563023\pi\)
−0.196701 + 0.980464i \(0.563023\pi\)
\(500\) −800.970 −0.0716409
\(501\) 0 0
\(502\) −3126.18 −0.277945
\(503\) −8327.07 −0.738143 −0.369071 0.929401i \(-0.620324\pi\)
−0.369071 + 0.929401i \(0.620324\pi\)
\(504\) 0 0
\(505\) −368.544 −0.0324752
\(506\) 231.174 0.0203101
\(507\) 0 0
\(508\) 12405.5 1.08347
\(509\) 20580.8 1.79220 0.896098 0.443856i \(-0.146390\pi\)
0.896098 + 0.443856i \(0.146390\pi\)
\(510\) 0 0
\(511\) 2025.86 0.175379
\(512\) 9250.40 0.798465
\(513\) 0 0
\(514\) 6029.17 0.517384
\(515\) −6535.43 −0.559195
\(516\) 0 0
\(517\) 234.069 0.0199117
\(518\) 6880.35 0.583601
\(519\) 0 0
\(520\) −7786.99 −0.656697
\(521\) 15109.3 1.27054 0.635270 0.772290i \(-0.280889\pi\)
0.635270 + 0.772290i \(0.280889\pi\)
\(522\) 0 0
\(523\) −507.100 −0.0423976 −0.0211988 0.999775i \(-0.506748\pi\)
−0.0211988 + 0.999775i \(0.506748\pi\)
\(524\) −7910.66 −0.659502
\(525\) 0 0
\(526\) 1983.06 0.164383
\(527\) 11580.8 0.957246
\(528\) 0 0
\(529\) 7430.26 0.610690
\(530\) −588.874 −0.0482623
\(531\) 0 0
\(532\) −5451.51 −0.444272
\(533\) 38365.8 3.11784
\(534\) 0 0
\(535\) −4227.27 −0.341609
\(536\) −8371.51 −0.674616
\(537\) 0 0
\(538\) −6241.79 −0.500191
\(539\) −212.799 −0.0170054
\(540\) 0 0
\(541\) 8249.02 0.655551 0.327776 0.944756i \(-0.393701\pi\)
0.327776 + 0.944756i \(0.393701\pi\)
\(542\) −1154.51 −0.0914954
\(543\) 0 0
\(544\) −12314.5 −0.970551
\(545\) −7514.96 −0.590653
\(546\) 0 0
\(547\) −19432.6 −1.51897 −0.759486 0.650524i \(-0.774550\pi\)
−0.759486 + 0.650524i \(0.774550\pi\)
\(548\) −5678.49 −0.442652
\(549\) 0 0
\(550\) 41.2839 0.00320064
\(551\) −1836.94 −0.142026
\(552\) 0 0
\(553\) 4214.87 0.324113
\(554\) −3080.85 −0.236269
\(555\) 0 0
\(556\) −10137.8 −0.773273
\(557\) −18807.6 −1.43071 −0.715354 0.698762i \(-0.753735\pi\)
−0.715354 + 0.698762i \(0.753735\pi\)
\(558\) 0 0
\(559\) 34932.0 2.64305
\(560\) −1901.94 −0.143521
\(561\) 0 0
\(562\) 6701.69 0.503013
\(563\) −7337.15 −0.549243 −0.274622 0.961552i \(-0.588553\pi\)
−0.274622 + 0.961552i \(0.588553\pi\)
\(564\) 0 0
\(565\) 1586.09 0.118102
\(566\) 844.382 0.0627068
\(567\) 0 0
\(568\) 14601.6 1.07864
\(569\) −5459.12 −0.402211 −0.201106 0.979570i \(-0.564453\pi\)
−0.201106 + 0.979570i \(0.564453\pi\)
\(570\) 0 0
\(571\) 5306.93 0.388946 0.194473 0.980908i \(-0.437700\pi\)
0.194473 + 0.980908i \(0.437700\pi\)
\(572\) −718.359 −0.0525107
\(573\) 0 0
\(574\) −7590.36 −0.551944
\(575\) 3499.76 0.253826
\(576\) 0 0
\(577\) 16127.1 1.16357 0.581785 0.813343i \(-0.302355\pi\)
0.581785 + 0.813343i \(0.302355\pi\)
\(578\) −370.081 −0.0266320
\(579\) 0 0
\(580\) −929.125 −0.0665169
\(581\) 3364.69 0.240260
\(582\) 0 0
\(583\) −122.147 −0.00867723
\(584\) 2742.19 0.194303
\(585\) 0 0
\(586\) 9423.45 0.664299
\(587\) −9109.13 −0.640501 −0.320250 0.947333i \(-0.603767\pi\)
−0.320250 + 0.947333i \(0.603767\pi\)
\(588\) 0 0
\(589\) 10792.7 0.755017
\(590\) −1765.29 −0.123180
\(591\) 0 0
\(592\) −11497.6 −0.798227
\(593\) −28352.1 −1.96337 −0.981687 0.190500i \(-0.938989\pi\)
−0.981687 + 0.190500i \(0.938989\pi\)
\(594\) 0 0
\(595\) 4564.47 0.314496
\(596\) −10570.1 −0.726455
\(597\) 0 0
\(598\) 15132.2 1.03478
\(599\) 15496.1 1.05702 0.528508 0.848928i \(-0.322752\pi\)
0.528508 + 0.848928i \(0.322752\pi\)
\(600\) 0 0
\(601\) 7637.92 0.518398 0.259199 0.965824i \(-0.416541\pi\)
0.259199 + 0.965824i \(0.416541\pi\)
\(602\) −6911.01 −0.467894
\(603\) 0 0
\(604\) −2203.32 −0.148430
\(605\) −6646.44 −0.446638
\(606\) 0 0
\(607\) −12012.8 −0.803268 −0.401634 0.915800i \(-0.631558\pi\)
−0.401634 + 0.915800i \(0.631558\pi\)
\(608\) −11476.4 −0.765511
\(609\) 0 0
\(610\) −5006.66 −0.332318
\(611\) 15321.7 1.01448
\(612\) 0 0
\(613\) −6113.47 −0.402807 −0.201404 0.979508i \(-0.564550\pi\)
−0.201404 + 0.979508i \(0.564550\pi\)
\(614\) −12527.1 −0.823374
\(615\) 0 0
\(616\) 319.558 0.0209016
\(617\) 28775.9 1.87759 0.938797 0.344472i \(-0.111942\pi\)
0.938797 + 0.344472i \(0.111942\pi\)
\(618\) 0 0
\(619\) −7092.81 −0.460556 −0.230278 0.973125i \(-0.573964\pi\)
−0.230278 + 0.973125i \(0.573964\pi\)
\(620\) 5458.94 0.353607
\(621\) 0 0
\(622\) −3951.35 −0.254718
\(623\) −1306.81 −0.0840390
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 10643.3 0.679540
\(627\) 0 0
\(628\) −15979.9 −1.01539
\(629\) 27593.1 1.74914
\(630\) 0 0
\(631\) −2283.67 −0.144075 −0.0720377 0.997402i \(-0.522950\pi\)
−0.0720377 + 0.997402i \(0.522950\pi\)
\(632\) 5705.23 0.359085
\(633\) 0 0
\(634\) 11562.0 0.724267
\(635\) −9680.03 −0.604945
\(636\) 0 0
\(637\) −13929.4 −0.866409
\(638\) 47.8893 0.00297172
\(639\) 0 0
\(640\) −7234.26 −0.446811
\(641\) 17599.2 1.08444 0.542220 0.840236i \(-0.317584\pi\)
0.542220 + 0.840236i \(0.317584\pi\)
\(642\) 0 0
\(643\) 9248.80 0.567242 0.283621 0.958936i \(-0.408464\pi\)
0.283621 + 0.958936i \(0.408464\pi\)
\(644\) 12048.0 0.737204
\(645\) 0 0
\(646\) 5432.63 0.330873
\(647\) 12201.5 0.741409 0.370704 0.928751i \(-0.379116\pi\)
0.370704 + 0.928751i \(0.379116\pi\)
\(648\) 0 0
\(649\) −366.166 −0.0221468
\(650\) 2702.36 0.163070
\(651\) 0 0
\(652\) 12271.6 0.737108
\(653\) −9769.75 −0.585482 −0.292741 0.956192i \(-0.594567\pi\)
−0.292741 + 0.956192i \(0.594567\pi\)
\(654\) 0 0
\(655\) 6172.72 0.368226
\(656\) 12684.1 0.754927
\(657\) 0 0
\(658\) −3031.26 −0.179591
\(659\) 15386.3 0.909506 0.454753 0.890618i \(-0.349728\pi\)
0.454753 + 0.890618i \(0.349728\pi\)
\(660\) 0 0
\(661\) 16886.7 0.993671 0.496835 0.867845i \(-0.334495\pi\)
0.496835 + 0.867845i \(0.334495\pi\)
\(662\) 6555.10 0.384851
\(663\) 0 0
\(664\) 4554.42 0.266183
\(665\) 4253.83 0.248055
\(666\) 0 0
\(667\) 4059.72 0.235671
\(668\) 638.089 0.0369587
\(669\) 0 0
\(670\) 2905.21 0.167519
\(671\) −1038.51 −0.0597484
\(672\) 0 0
\(673\) 26462.8 1.51570 0.757851 0.652428i \(-0.226249\pi\)
0.757851 + 0.652428i \(0.226249\pi\)
\(674\) −4059.53 −0.231999
\(675\) 0 0
\(676\) −32944.5 −1.87440
\(677\) −28533.1 −1.61982 −0.809908 0.586556i \(-0.800483\pi\)
−0.809908 + 0.586556i \(0.800483\pi\)
\(678\) 0 0
\(679\) 18027.6 1.01890
\(680\) 6178.43 0.348430
\(681\) 0 0
\(682\) −281.367 −0.0157978
\(683\) −27990.7 −1.56813 −0.784066 0.620677i \(-0.786858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(684\) 0 0
\(685\) 4430.95 0.247150
\(686\) 8568.96 0.476916
\(687\) 0 0
\(688\) 11548.9 0.639967
\(689\) −7995.52 −0.442097
\(690\) 0 0
\(691\) 9248.47 0.509158 0.254579 0.967052i \(-0.418063\pi\)
0.254579 + 0.967052i \(0.418063\pi\)
\(692\) 13708.1 0.753040
\(693\) 0 0
\(694\) 769.421 0.0420848
\(695\) 7910.59 0.431749
\(696\) 0 0
\(697\) −30440.6 −1.65426
\(698\) 5560.17 0.301512
\(699\) 0 0
\(700\) 2151.59 0.116175
\(701\) −16805.6 −0.905474 −0.452737 0.891644i \(-0.649552\pi\)
−0.452737 + 0.891644i \(0.649552\pi\)
\(702\) 0 0
\(703\) 25715.3 1.37962
\(704\) 2.68026 0.000143489 0
\(705\) 0 0
\(706\) −3129.48 −0.166826
\(707\) 989.991 0.0526626
\(708\) 0 0
\(709\) 28586.0 1.51421 0.757103 0.653296i \(-0.226614\pi\)
0.757103 + 0.653296i \(0.226614\pi\)
\(710\) −5067.25 −0.267846
\(711\) 0 0
\(712\) −1768.89 −0.0931067
\(713\) −23852.3 −1.25284
\(714\) 0 0
\(715\) 560.538 0.0293188
\(716\) 11941.1 0.623268
\(717\) 0 0
\(718\) −8301.42 −0.431485
\(719\) 37753.6 1.95824 0.979119 0.203289i \(-0.0651633\pi\)
0.979119 + 0.203289i \(0.0651633\pi\)
\(720\) 0 0
\(721\) 17555.6 0.906805
\(722\) −3592.05 −0.185156
\(723\) 0 0
\(724\) 19279.4 0.989659
\(725\) 725.000 0.0371391
\(726\) 0 0
\(727\) −10769.6 −0.549412 −0.274706 0.961528i \(-0.588581\pi\)
−0.274706 + 0.961528i \(0.588581\pi\)
\(728\) 20917.6 1.06492
\(729\) 0 0
\(730\) −951.638 −0.0482489
\(731\) −27716.1 −1.40235
\(732\) 0 0
\(733\) −29083.9 −1.46554 −0.732768 0.680479i \(-0.761772\pi\)
−0.732768 + 0.680479i \(0.761772\pi\)
\(734\) −922.549 −0.0463923
\(735\) 0 0
\(736\) 25363.4 1.27025
\(737\) 602.614 0.0301188
\(738\) 0 0
\(739\) 5594.45 0.278478 0.139239 0.990259i \(-0.455534\pi\)
0.139239 + 0.990259i \(0.455534\pi\)
\(740\) 13006.8 0.646133
\(741\) 0 0
\(742\) 1581.85 0.0782634
\(743\) −8984.59 −0.443624 −0.221812 0.975089i \(-0.571197\pi\)
−0.221812 + 0.975089i \(0.571197\pi\)
\(744\) 0 0
\(745\) 8247.87 0.405609
\(746\) −2111.10 −0.103610
\(747\) 0 0
\(748\) 569.967 0.0278611
\(749\) 11355.4 0.553962
\(750\) 0 0
\(751\) 4621.64 0.224562 0.112281 0.993676i \(-0.464184\pi\)
0.112281 + 0.993676i \(0.464184\pi\)
\(752\) 5065.50 0.245638
\(753\) 0 0
\(754\) 3134.74 0.151406
\(755\) 1719.26 0.0828745
\(756\) 0 0
\(757\) −5554.76 −0.266699 −0.133349 0.991069i \(-0.542573\pi\)
−0.133349 + 0.991069i \(0.542573\pi\)
\(758\) 4745.07 0.227373
\(759\) 0 0
\(760\) 5757.96 0.274820
\(761\) −28686.9 −1.36649 −0.683245 0.730189i \(-0.739432\pi\)
−0.683245 + 0.730189i \(0.739432\pi\)
\(762\) 0 0
\(763\) 20186.9 0.957817
\(764\) 33161.7 1.57035
\(765\) 0 0
\(766\) 15824.5 0.746427
\(767\) −23968.5 −1.12836
\(768\) 0 0
\(769\) 26311.7 1.23384 0.616921 0.787025i \(-0.288380\pi\)
0.616921 + 0.787025i \(0.288380\pi\)
\(770\) −110.898 −0.00519024
\(771\) 0 0
\(772\) 21836.9 1.01804
\(773\) 25176.4 1.17145 0.585727 0.810508i \(-0.300809\pi\)
0.585727 + 0.810508i \(0.300809\pi\)
\(774\) 0 0
\(775\) −4259.63 −0.197433
\(776\) 24402.1 1.12884
\(777\) 0 0
\(778\) −7292.44 −0.336050
\(779\) −28369.0 −1.30478
\(780\) 0 0
\(781\) −1051.08 −0.0481568
\(782\) −12006.3 −0.549034
\(783\) 0 0
\(784\) −4605.20 −0.209785
\(785\) 12469.2 0.566934
\(786\) 0 0
\(787\) −27651.8 −1.25245 −0.626226 0.779641i \(-0.715401\pi\)
−0.626226 + 0.779641i \(0.715401\pi\)
\(788\) −17058.9 −0.771192
\(789\) 0 0
\(790\) −1979.91 −0.0891673
\(791\) −4260.60 −0.191516
\(792\) 0 0
\(793\) −67978.7 −3.04413
\(794\) 18163.7 0.811847
\(795\) 0 0
\(796\) −7203.11 −0.320738
\(797\) 35053.5 1.55792 0.778958 0.627076i \(-0.215748\pi\)
0.778958 + 0.627076i \(0.215748\pi\)
\(798\) 0 0
\(799\) −12156.7 −0.538262
\(800\) 4529.49 0.200177
\(801\) 0 0
\(802\) −10877.5 −0.478923
\(803\) −197.394 −0.00867482
\(804\) 0 0
\(805\) −9401.13 −0.411610
\(806\) −18417.7 −0.804883
\(807\) 0 0
\(808\) 1340.05 0.0583449
\(809\) 23824.8 1.03540 0.517699 0.855563i \(-0.326789\pi\)
0.517699 + 0.855563i \(0.326789\pi\)
\(810\) 0 0
\(811\) 19361.6 0.838322 0.419161 0.907912i \(-0.362324\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(812\) 2495.84 0.107866
\(813\) 0 0
\(814\) −670.401 −0.0288667
\(815\) −9575.61 −0.411557
\(816\) 0 0
\(817\) −25829.9 −1.10609
\(818\) −17738.9 −0.758224
\(819\) 0 0
\(820\) −14349.0 −0.611084
\(821\) 14914.6 0.634012 0.317006 0.948424i \(-0.397322\pi\)
0.317006 + 0.948424i \(0.397322\pi\)
\(822\) 0 0
\(823\) 7639.98 0.323588 0.161794 0.986825i \(-0.448272\pi\)
0.161794 + 0.986825i \(0.448272\pi\)
\(824\) 23763.2 1.00465
\(825\) 0 0
\(826\) 4741.97 0.199751
\(827\) −12462.1 −0.524003 −0.262001 0.965068i \(-0.584382\pi\)
−0.262001 + 0.965068i \(0.584382\pi\)
\(828\) 0 0
\(829\) −26986.5 −1.13062 −0.565309 0.824880i \(-0.691243\pi\)
−0.565309 + 0.824880i \(0.691243\pi\)
\(830\) −1580.54 −0.0660982
\(831\) 0 0
\(832\) 175.444 0.00731063
\(833\) 11052.0 0.459699
\(834\) 0 0
\(835\) −497.903 −0.0206355
\(836\) 531.178 0.0219751
\(837\) 0 0
\(838\) 389.558 0.0160585
\(839\) −23448.1 −0.964860 −0.482430 0.875935i \(-0.660246\pi\)
−0.482430 + 0.875935i \(0.660246\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) 9263.78 0.379158
\(843\) 0 0
\(844\) −700.034 −0.0285499
\(845\) 25706.7 1.04655
\(846\) 0 0
\(847\) 17853.8 0.724280
\(848\) −2643.40 −0.107046
\(849\) 0 0
\(850\) −2144.13 −0.0865214
\(851\) −56831.8 −2.28927
\(852\) 0 0
\(853\) −30230.4 −1.21344 −0.606722 0.794914i \(-0.707516\pi\)
−0.606722 + 0.794914i \(0.707516\pi\)
\(854\) 13449.0 0.538895
\(855\) 0 0
\(856\) 15370.6 0.613734
\(857\) −32088.1 −1.27900 −0.639502 0.768789i \(-0.720860\pi\)
−0.639502 + 0.768789i \(0.720860\pi\)
\(858\) 0 0
\(859\) −43201.3 −1.71596 −0.857980 0.513683i \(-0.828281\pi\)
−0.857980 + 0.513683i \(0.828281\pi\)
\(860\) −13064.7 −0.518028
\(861\) 0 0
\(862\) 21023.3 0.830692
\(863\) 15650.5 0.617323 0.308662 0.951172i \(-0.400119\pi\)
0.308662 + 0.951172i \(0.400119\pi\)
\(864\) 0 0
\(865\) −10696.5 −0.420452
\(866\) 12733.8 0.499669
\(867\) 0 0
\(868\) −14663.9 −0.573418
\(869\) −410.685 −0.0160317
\(870\) 0 0
\(871\) 39445.9 1.53453
\(872\) 27324.9 1.06117
\(873\) 0 0
\(874\) −11189.2 −0.433045
\(875\) −1678.89 −0.0648650
\(876\) 0 0
\(877\) −37921.1 −1.46010 −0.730049 0.683395i \(-0.760503\pi\)
−0.730049 + 0.683395i \(0.760503\pi\)
\(878\) 6498.14 0.249774
\(879\) 0 0
\(880\) 185.320 0.00709901
\(881\) −19844.4 −0.758881 −0.379441 0.925216i \(-0.623884\pi\)
−0.379441 + 0.925216i \(0.623884\pi\)
\(882\) 0 0
\(883\) 33386.5 1.27242 0.636210 0.771516i \(-0.280501\pi\)
0.636210 + 0.771516i \(0.280501\pi\)
\(884\) 37308.9 1.41950
\(885\) 0 0
\(886\) −19963.0 −0.756964
\(887\) 25988.8 0.983788 0.491894 0.870655i \(-0.336305\pi\)
0.491894 + 0.870655i \(0.336305\pi\)
\(888\) 0 0
\(889\) 26002.7 0.980994
\(890\) 613.867 0.0231201
\(891\) 0 0
\(892\) 29832.3 1.11980
\(893\) −11329.3 −0.424549
\(894\) 0 0
\(895\) −9317.69 −0.347996
\(896\) 19432.9 0.724560
\(897\) 0 0
\(898\) 17543.4 0.651928
\(899\) −4941.17 −0.183312
\(900\) 0 0
\(901\) 6343.88 0.234568
\(902\) 739.582 0.0273009
\(903\) 0 0
\(904\) −5767.12 −0.212181
\(905\) −15043.8 −0.552566
\(906\) 0 0
\(907\) −26383.8 −0.965887 −0.482943 0.875652i \(-0.660432\pi\)
−0.482943 + 0.875652i \(0.660432\pi\)
\(908\) 23808.4 0.870166
\(909\) 0 0
\(910\) −7259.15 −0.264438
\(911\) 23448.5 0.852779 0.426390 0.904540i \(-0.359785\pi\)
0.426390 + 0.904540i \(0.359785\pi\)
\(912\) 0 0
\(913\) −327.845 −0.0118840
\(914\) 5445.15 0.197056
\(915\) 0 0
\(916\) −15620.4 −0.563443
\(917\) −16581.3 −0.597125
\(918\) 0 0
\(919\) −1649.45 −0.0592060 −0.0296030 0.999562i \(-0.509424\pi\)
−0.0296030 + 0.999562i \(0.509424\pi\)
\(920\) −12725.3 −0.456023
\(921\) 0 0
\(922\) −7490.39 −0.267552
\(923\) −68801.4 −2.45355
\(924\) 0 0
\(925\) −10149.2 −0.360762
\(926\) −16270.7 −0.577415
\(927\) 0 0
\(928\) 5254.20 0.185860
\(929\) −48039.5 −1.69658 −0.848291 0.529531i \(-0.822368\pi\)
−0.848291 + 0.529531i \(0.822368\pi\)
\(930\) 0 0
\(931\) 10299.9 0.362582
\(932\) −17328.4 −0.609026
\(933\) 0 0
\(934\) −15967.0 −0.559376
\(935\) −444.748 −0.0155559
\(936\) 0 0
\(937\) −28647.5 −0.998796 −0.499398 0.866373i \(-0.666445\pi\)
−0.499398 + 0.866373i \(0.666445\pi\)
\(938\) −7804.04 −0.271654
\(939\) 0 0
\(940\) −5730.37 −0.198834
\(941\) −9541.12 −0.330533 −0.165267 0.986249i \(-0.552848\pi\)
−0.165267 + 0.986249i \(0.552848\pi\)
\(942\) 0 0
\(943\) 62696.5 2.16509
\(944\) −7924.24 −0.273212
\(945\) 0 0
\(946\) 673.388 0.0231435
\(947\) −44596.6 −1.53030 −0.765151 0.643851i \(-0.777336\pi\)
−0.765151 + 0.643851i \(0.777336\pi\)
\(948\) 0 0
\(949\) −12921.0 −0.441974
\(950\) −1998.22 −0.0682428
\(951\) 0 0
\(952\) −16596.7 −0.565022
\(953\) −437.931 −0.0148856 −0.00744279 0.999972i \(-0.502369\pi\)
−0.00744279 + 0.999972i \(0.502369\pi\)
\(954\) 0 0
\(955\) −25876.2 −0.876790
\(956\) 38566.2 1.30473
\(957\) 0 0
\(958\) −11345.9 −0.382641
\(959\) −11902.5 −0.400785
\(960\) 0 0
\(961\) −759.861 −0.0255064
\(962\) −43883.1 −1.47073
\(963\) 0 0
\(964\) 7977.02 0.266517
\(965\) −17039.4 −0.568413
\(966\) 0 0
\(967\) −37762.6 −1.25580 −0.627902 0.778292i \(-0.716086\pi\)
−0.627902 + 0.778292i \(0.716086\pi\)
\(968\) 24166.8 0.802429
\(969\) 0 0
\(970\) −8468.38 −0.280313
\(971\) −16153.0 −0.533858 −0.266929 0.963716i \(-0.586009\pi\)
−0.266929 + 0.963716i \(0.586009\pi\)
\(972\) 0 0
\(973\) −21249.6 −0.700136
\(974\) 9680.07 0.318449
\(975\) 0 0
\(976\) −22474.4 −0.737079
\(977\) −33700.3 −1.10355 −0.551775 0.833993i \(-0.686049\pi\)
−0.551775 + 0.833993i \(0.686049\pi\)
\(978\) 0 0
\(979\) 127.332 0.00415683
\(980\) 5209.66 0.169813
\(981\) 0 0
\(982\) −13025.8 −0.423290
\(983\) 7637.13 0.247799 0.123900 0.992295i \(-0.460460\pi\)
0.123900 + 0.992295i \(0.460460\pi\)
\(984\) 0 0
\(985\) 13311.2 0.430588
\(986\) −2487.20 −0.0803331
\(987\) 0 0
\(988\) 34769.9 1.11961
\(989\) 57085.1 1.83539
\(990\) 0 0
\(991\) 9339.90 0.299386 0.149693 0.988733i \(-0.452171\pi\)
0.149693 + 0.988733i \(0.452171\pi\)
\(992\) −30870.3 −0.988038
\(993\) 0 0
\(994\) 13611.8 0.434346
\(995\) 5620.61 0.179081
\(996\) 0 0
\(997\) −11144.7 −0.354017 −0.177009 0.984209i \(-0.556642\pi\)
−0.177009 + 0.984209i \(0.556642\pi\)
\(998\) −5533.39 −0.175508
\(999\) 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 1305.4.a.m.1.5 7
3.2 odd 2 435.4.a.j.1.3 7
15.14 odd 2 2175.4.a.m.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.j.1.3 7 3.2 odd 2
1305.4.a.m.1.5 7 1.1 even 1 trivial
2175.4.a.m.1.5 7 15.14 odd 2