Properties

Label 1617.4.a.be.1.5
Level $1617$
Weight $4$
Character 1617.1
Self dual yes
Analytic conductor $95.406$
Analytic rank $1$
Dimension $16$
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] = [1617,4,Mod(1,1617)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1617, 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("1617.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1617.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: \(95.4060884793\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199850 x^{9} + \cdots + 5479424 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4}\cdot 7^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.57449\) of defining polynomial
Character \(\chi\) \(=\) 1617.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57449 q^{2} -3.00000 q^{3} -1.37200 q^{4} -19.4253 q^{5} +7.72347 q^{6} +24.1281 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.57449 q^{2} -3.00000 q^{3} -1.37200 q^{4} -19.4253 q^{5} +7.72347 q^{6} +24.1281 q^{8} +9.00000 q^{9} +50.0102 q^{10} +11.0000 q^{11} +4.11600 q^{12} -44.6769 q^{13} +58.2759 q^{15} -51.1416 q^{16} -118.325 q^{17} -23.1704 q^{18} -50.3203 q^{19} +26.6515 q^{20} -28.3194 q^{22} +4.82954 q^{23} -72.3844 q^{24} +252.342 q^{25} +115.020 q^{26} -27.0000 q^{27} +62.5502 q^{29} -150.031 q^{30} -117.111 q^{31} -61.3614 q^{32} -33.0000 q^{33} +304.626 q^{34} -12.3480 q^{36} -351.826 q^{37} +129.549 q^{38} +134.031 q^{39} -468.696 q^{40} +177.291 q^{41} +551.166 q^{43} -15.0920 q^{44} -174.828 q^{45} -12.4336 q^{46} -76.4356 q^{47} +153.425 q^{48} -649.652 q^{50} +354.975 q^{51} +61.2968 q^{52} +82.6813 q^{53} +69.5112 q^{54} -213.678 q^{55} +150.961 q^{57} -161.035 q^{58} +508.741 q^{59} -79.9546 q^{60} -341.813 q^{61} +301.500 q^{62} +567.107 q^{64} +867.863 q^{65} +84.9582 q^{66} +367.341 q^{67} +162.342 q^{68} -14.4886 q^{69} +169.049 q^{71} +217.153 q^{72} +784.694 q^{73} +905.772 q^{74} -757.027 q^{75} +69.0395 q^{76} -345.061 q^{78} +284.773 q^{79} +993.441 q^{80} +81.0000 q^{81} -456.434 q^{82} +672.268 q^{83} +2298.50 q^{85} -1418.97 q^{86} -187.650 q^{87} +265.409 q^{88} +72.9697 q^{89} +450.092 q^{90} -6.62613 q^{92} +351.332 q^{93} +196.783 q^{94} +977.487 q^{95} +184.084 q^{96} -1148.94 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 48 q^{3} + 72 q^{4} - 40 q^{5} - 12 q^{6} + 66 q^{8} + 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} - 48 q^{3} + 72 q^{4} - 40 q^{5} - 12 q^{6} + 66 q^{8} + 144 q^{9} - 178 q^{10} + 176 q^{11} - 216 q^{12} - 104 q^{13} + 120 q^{15} + 220 q^{16} - 180 q^{17} + 36 q^{18} - 152 q^{19} - 298 q^{20} + 44 q^{22} + 4 q^{23} - 198 q^{24} + 588 q^{25} - 406 q^{26} - 432 q^{27} + 412 q^{29} + 534 q^{30} - 628 q^{31} + 592 q^{32} - 528 q^{33} + 88 q^{34} + 648 q^{36} + 148 q^{37} - 446 q^{38} + 312 q^{39} - 1376 q^{40} - 596 q^{41} - 260 q^{43} + 792 q^{44} - 360 q^{45} - 148 q^{46} - 2220 q^{47} - 660 q^{48} + 82 q^{50} + 540 q^{51} - 1046 q^{52} + 168 q^{53} - 108 q^{54} - 440 q^{55} + 456 q^{57} + 538 q^{58} + 48 q^{59} + 894 q^{60} - 1504 q^{61} - 1276 q^{62} + 630 q^{64} + 1224 q^{65} - 132 q^{66} + 116 q^{67} - 356 q^{68} - 12 q^{69} + 320 q^{71} + 594 q^{72} - 652 q^{73} + 1062 q^{74} - 1764 q^{75} + 594 q^{76} + 1218 q^{78} + 1136 q^{79} - 1970 q^{80} + 1296 q^{81} + 416 q^{82} - 3300 q^{83} - 1148 q^{85} + 1864 q^{86} - 1236 q^{87} + 726 q^{88} - 2416 q^{89} - 1602 q^{90} - 1064 q^{92} + 1884 q^{93} - 914 q^{94} + 1120 q^{95} - 1776 q^{96} - 3616 q^{97} + 1584 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57449 −0.910220 −0.455110 0.890435i \(-0.650400\pi\)
−0.455110 + 0.890435i \(0.650400\pi\)
\(3\) −3.00000 −0.577350
\(4\) −1.37200 −0.171500
\(5\) −19.4253 −1.73745 −0.868726 0.495293i \(-0.835061\pi\)
−0.868726 + 0.495293i \(0.835061\pi\)
\(6\) 7.72347 0.525516
\(7\) 0 0
\(8\) 24.1281 1.06632
\(9\) 9.00000 0.333333
\(10\) 50.0102 1.58146
\(11\) 11.0000 0.301511
\(12\) 4.11600 0.0990156
\(13\) −44.6769 −0.953166 −0.476583 0.879130i \(-0.658125\pi\)
−0.476583 + 0.879130i \(0.658125\pi\)
\(14\) 0 0
\(15\) 58.2759 1.00312
\(16\) −51.1416 −0.799088
\(17\) −118.325 −1.68812 −0.844059 0.536251i \(-0.819840\pi\)
−0.844059 + 0.536251i \(0.819840\pi\)
\(18\) −23.1704 −0.303407
\(19\) −50.3203 −0.607593 −0.303797 0.952737i \(-0.598254\pi\)
−0.303797 + 0.952737i \(0.598254\pi\)
\(20\) 26.6515 0.297973
\(21\) 0 0
\(22\) −28.3194 −0.274442
\(23\) 4.82954 0.0437838 0.0218919 0.999760i \(-0.493031\pi\)
0.0218919 + 0.999760i \(0.493031\pi\)
\(24\) −72.3844 −0.615642
\(25\) 252.342 2.01874
\(26\) 115.020 0.867590
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 62.5502 0.400527 0.200263 0.979742i \(-0.435820\pi\)
0.200263 + 0.979742i \(0.435820\pi\)
\(30\) −150.031 −0.913058
\(31\) −117.111 −0.678506 −0.339253 0.940695i \(-0.610174\pi\)
−0.339253 + 0.940695i \(0.610174\pi\)
\(32\) −61.3614 −0.338977
\(33\) −33.0000 −0.174078
\(34\) 304.626 1.53656
\(35\) 0 0
\(36\) −12.3480 −0.0571667
\(37\) −351.826 −1.56324 −0.781619 0.623756i \(-0.785606\pi\)
−0.781619 + 0.623756i \(0.785606\pi\)
\(38\) 129.549 0.553043
\(39\) 134.031 0.550311
\(40\) −468.696 −1.85268
\(41\) 177.291 0.675322 0.337661 0.941268i \(-0.390364\pi\)
0.337661 + 0.941268i \(0.390364\pi\)
\(42\) 0 0
\(43\) 551.166 1.95470 0.977349 0.211635i \(-0.0678788\pi\)
0.977349 + 0.211635i \(0.0678788\pi\)
\(44\) −15.0920 −0.0517092
\(45\) −174.828 −0.579150
\(46\) −12.4336 −0.0398529
\(47\) −76.4356 −0.237219 −0.118609 0.992941i \(-0.537844\pi\)
−0.118609 + 0.992941i \(0.537844\pi\)
\(48\) 153.425 0.461353
\(49\) 0 0
\(50\) −649.652 −1.83749
\(51\) 354.975 0.974635
\(52\) 61.2968 0.163468
\(53\) 82.6813 0.214286 0.107143 0.994244i \(-0.465830\pi\)
0.107143 + 0.994244i \(0.465830\pi\)
\(54\) 69.5112 0.175172
\(55\) −213.678 −0.523861
\(56\) 0 0
\(57\) 150.961 0.350794
\(58\) −161.035 −0.364567
\(59\) 508.741 1.12258 0.561291 0.827618i \(-0.310305\pi\)
0.561291 + 0.827618i \(0.310305\pi\)
\(60\) −79.9546 −0.172035
\(61\) −341.813 −0.717454 −0.358727 0.933442i \(-0.616789\pi\)
−0.358727 + 0.933442i \(0.616789\pi\)
\(62\) 301.500 0.617589
\(63\) 0 0
\(64\) 567.107 1.10763
\(65\) 867.863 1.65608
\(66\) 84.9582 0.158449
\(67\) 367.341 0.669818 0.334909 0.942250i \(-0.391294\pi\)
0.334909 + 0.942250i \(0.391294\pi\)
\(68\) 162.342 0.289512
\(69\) −14.4886 −0.0252786
\(70\) 0 0
\(71\) 169.049 0.282570 0.141285 0.989969i \(-0.454877\pi\)
0.141285 + 0.989969i \(0.454877\pi\)
\(72\) 217.153 0.355441
\(73\) 784.694 1.25810 0.629051 0.777364i \(-0.283444\pi\)
0.629051 + 0.777364i \(0.283444\pi\)
\(74\) 905.772 1.42289
\(75\) −757.027 −1.16552
\(76\) 69.0395 0.104202
\(77\) 0 0
\(78\) −345.061 −0.500903
\(79\) 284.773 0.405562 0.202781 0.979224i \(-0.435002\pi\)
0.202781 + 0.979224i \(0.435002\pi\)
\(80\) 993.441 1.38838
\(81\) 81.0000 0.111111
\(82\) −456.434 −0.614691
\(83\) 672.268 0.889048 0.444524 0.895767i \(-0.353373\pi\)
0.444524 + 0.895767i \(0.353373\pi\)
\(84\) 0 0
\(85\) 2298.50 2.93302
\(86\) −1418.97 −1.77920
\(87\) −187.650 −0.231244
\(88\) 265.409 0.321508
\(89\) 72.9697 0.0869076 0.0434538 0.999055i \(-0.486164\pi\)
0.0434538 + 0.999055i \(0.486164\pi\)
\(90\) 450.092 0.527154
\(91\) 0 0
\(92\) −6.62613 −0.00750893
\(93\) 351.332 0.391736
\(94\) 196.783 0.215921
\(95\) 977.487 1.05566
\(96\) 184.084 0.195709
\(97\) −1148.94 −1.20265 −0.601327 0.799003i \(-0.705361\pi\)
−0.601327 + 0.799003i \(0.705361\pi\)
\(98\) 0 0
\(99\) 99.0000 0.100504
\(100\) −346.214 −0.346214
\(101\) 1935.81 1.90713 0.953566 0.301185i \(-0.0973823\pi\)
0.953566 + 0.301185i \(0.0973823\pi\)
\(102\) −913.879 −0.887132
\(103\) 1448.66 1.38583 0.692916 0.721018i \(-0.256326\pi\)
0.692916 + 0.721018i \(0.256326\pi\)
\(104\) −1077.97 −1.01638
\(105\) 0 0
\(106\) −212.862 −0.195047
\(107\) −416.455 −0.376263 −0.188132 0.982144i \(-0.560243\pi\)
−0.188132 + 0.982144i \(0.560243\pi\)
\(108\) 37.0440 0.0330052
\(109\) −1625.27 −1.42819 −0.714093 0.700050i \(-0.753161\pi\)
−0.714093 + 0.700050i \(0.753161\pi\)
\(110\) 550.113 0.476829
\(111\) 1055.48 0.902536
\(112\) 0 0
\(113\) 1460.39 1.21577 0.607883 0.794026i \(-0.292019\pi\)
0.607883 + 0.794026i \(0.292019\pi\)
\(114\) −388.647 −0.319300
\(115\) −93.8152 −0.0760723
\(116\) −85.8189 −0.0686904
\(117\) −402.093 −0.317722
\(118\) −1309.75 −1.02180
\(119\) 0 0
\(120\) 1406.09 1.06965
\(121\) 121.000 0.0909091
\(122\) 879.995 0.653041
\(123\) −531.873 −0.389897
\(124\) 160.676 0.116364
\(125\) −2473.66 −1.77001
\(126\) 0 0
\(127\) −1467.60 −1.02542 −0.512712 0.858561i \(-0.671359\pi\)
−0.512712 + 0.858561i \(0.671359\pi\)
\(128\) −969.121 −0.669211
\(129\) −1653.50 −1.12855
\(130\) −2234.30 −1.50740
\(131\) 2157.31 1.43882 0.719409 0.694586i \(-0.244413\pi\)
0.719409 + 0.694586i \(0.244413\pi\)
\(132\) 45.2760 0.0298543
\(133\) 0 0
\(134\) −945.715 −0.609682
\(135\) 524.483 0.334373
\(136\) −2854.96 −1.80008
\(137\) −1665.68 −1.03875 −0.519374 0.854547i \(-0.673835\pi\)
−0.519374 + 0.854547i \(0.673835\pi\)
\(138\) 37.3008 0.0230091
\(139\) −742.747 −0.453230 −0.226615 0.973984i \(-0.572766\pi\)
−0.226615 + 0.973984i \(0.572766\pi\)
\(140\) 0 0
\(141\) 229.307 0.136958
\(142\) −435.216 −0.257201
\(143\) −491.446 −0.287390
\(144\) −460.274 −0.266363
\(145\) −1215.06 −0.695896
\(146\) −2020.19 −1.14515
\(147\) 0 0
\(148\) 482.705 0.268095
\(149\) −2256.74 −1.24080 −0.620400 0.784286i \(-0.713030\pi\)
−0.620400 + 0.784286i \(0.713030\pi\)
\(150\) 1948.96 1.06088
\(151\) 296.331 0.159703 0.0798513 0.996807i \(-0.474555\pi\)
0.0798513 + 0.996807i \(0.474555\pi\)
\(152\) −1214.13 −0.647890
\(153\) −1064.92 −0.562706
\(154\) 0 0
\(155\) 2274.91 1.17887
\(156\) −183.890 −0.0943783
\(157\) −1192.25 −0.606061 −0.303031 0.952981i \(-0.597998\pi\)
−0.303031 + 0.952981i \(0.597998\pi\)
\(158\) −733.145 −0.369151
\(159\) −248.044 −0.123718
\(160\) 1191.96 0.588956
\(161\) 0 0
\(162\) −208.534 −0.101136
\(163\) −2475.80 −1.18969 −0.594845 0.803840i \(-0.702787\pi\)
−0.594845 + 0.803840i \(0.702787\pi\)
\(164\) −243.243 −0.115818
\(165\) 641.035 0.302451
\(166\) −1730.75 −0.809229
\(167\) −803.008 −0.372087 −0.186044 0.982541i \(-0.559567\pi\)
−0.186044 + 0.982541i \(0.559567\pi\)
\(168\) 0 0
\(169\) −200.971 −0.0914750
\(170\) −5917.45 −2.66969
\(171\) −452.883 −0.202531
\(172\) −756.200 −0.335231
\(173\) 465.795 0.204704 0.102352 0.994748i \(-0.467363\pi\)
0.102352 + 0.994748i \(0.467363\pi\)
\(174\) 483.104 0.210483
\(175\) 0 0
\(176\) −562.558 −0.240934
\(177\) −1526.22 −0.648123
\(178\) −187.860 −0.0791050
\(179\) 3929.78 1.64092 0.820462 0.571701i \(-0.193716\pi\)
0.820462 + 0.571701i \(0.193716\pi\)
\(180\) 239.864 0.0993244
\(181\) 3368.29 1.38322 0.691611 0.722270i \(-0.256901\pi\)
0.691611 + 0.722270i \(0.256901\pi\)
\(182\) 0 0
\(183\) 1025.44 0.414223
\(184\) 116.528 0.0466877
\(185\) 6834.32 2.71605
\(186\) −904.500 −0.356565
\(187\) −1301.57 −0.508987
\(188\) 104.870 0.0406830
\(189\) 0 0
\(190\) −2516.53 −0.960886
\(191\) 4496.14 1.70330 0.851648 0.524115i \(-0.175604\pi\)
0.851648 + 0.524115i \(0.175604\pi\)
\(192\) −1701.32 −0.639491
\(193\) −4084.31 −1.52329 −0.761645 0.647995i \(-0.775608\pi\)
−0.761645 + 0.647995i \(0.775608\pi\)
\(194\) 2957.94 1.09468
\(195\) −2603.59 −0.956138
\(196\) 0 0
\(197\) 92.5824 0.0334834 0.0167417 0.999860i \(-0.494671\pi\)
0.0167417 + 0.999860i \(0.494671\pi\)
\(198\) −254.875 −0.0914805
\(199\) 4821.73 1.71760 0.858802 0.512307i \(-0.171209\pi\)
0.858802 + 0.512307i \(0.171209\pi\)
\(200\) 6088.54 2.15263
\(201\) −1102.02 −0.386720
\(202\) −4983.72 −1.73591
\(203\) 0 0
\(204\) −487.025 −0.167150
\(205\) −3443.93 −1.17334
\(206\) −3729.56 −1.26141
\(207\) 43.4658 0.0145946
\(208\) 2284.85 0.761663
\(209\) −553.523 −0.183196
\(210\) 0 0
\(211\) 2979.20 0.972020 0.486010 0.873953i \(-0.338452\pi\)
0.486010 + 0.873953i \(0.338452\pi\)
\(212\) −113.439 −0.0367500
\(213\) −507.148 −0.163142
\(214\) 1072.16 0.342482
\(215\) −10706.6 −3.39619
\(216\) −651.459 −0.205214
\(217\) 0 0
\(218\) 4184.23 1.29996
\(219\) −2354.08 −0.726366
\(220\) 293.167 0.0898423
\(221\) 5286.39 1.60906
\(222\) −2717.32 −0.821506
\(223\) −5933.66 −1.78183 −0.890913 0.454174i \(-0.849934\pi\)
−0.890913 + 0.454174i \(0.849934\pi\)
\(224\) 0 0
\(225\) 2271.08 0.672912
\(226\) −3759.75 −1.10661
\(227\) 3455.84 1.01045 0.505225 0.862988i \(-0.331410\pi\)
0.505225 + 0.862988i \(0.331410\pi\)
\(228\) −207.118 −0.0601612
\(229\) −2069.80 −0.597277 −0.298638 0.954366i \(-0.596532\pi\)
−0.298638 + 0.954366i \(0.596532\pi\)
\(230\) 241.526 0.0692425
\(231\) 0 0
\(232\) 1509.22 0.427091
\(233\) −2204.18 −0.619744 −0.309872 0.950778i \(-0.600286\pi\)
−0.309872 + 0.950778i \(0.600286\pi\)
\(234\) 1035.18 0.289197
\(235\) 1484.78 0.412156
\(236\) −697.992 −0.192523
\(237\) −854.318 −0.234152
\(238\) 0 0
\(239\) 3207.60 0.868126 0.434063 0.900882i \(-0.357079\pi\)
0.434063 + 0.900882i \(0.357079\pi\)
\(240\) −2980.32 −0.801579
\(241\) −1736.50 −0.464141 −0.232071 0.972699i \(-0.574550\pi\)
−0.232071 + 0.972699i \(0.574550\pi\)
\(242\) −311.513 −0.0827472
\(243\) −243.000 −0.0641500
\(244\) 468.968 0.123044
\(245\) 0 0
\(246\) 1369.30 0.354892
\(247\) 2248.16 0.579137
\(248\) −2825.66 −0.723506
\(249\) −2016.80 −0.513292
\(250\) 6368.41 1.61110
\(251\) 1607.90 0.404343 0.202171 0.979350i \(-0.435200\pi\)
0.202171 + 0.979350i \(0.435200\pi\)
\(252\) 0 0
\(253\) 53.1249 0.0132013
\(254\) 3778.33 0.933361
\(255\) −6895.49 −1.69338
\(256\) −2041.87 −0.498503
\(257\) −131.803 −0.0319908 −0.0159954 0.999872i \(-0.505092\pi\)
−0.0159954 + 0.999872i \(0.505092\pi\)
\(258\) 4256.91 1.02722
\(259\) 0 0
\(260\) −1190.71 −0.284018
\(261\) 562.951 0.133509
\(262\) −5553.98 −1.30964
\(263\) −1654.80 −0.387982 −0.193991 0.981003i \(-0.562143\pi\)
−0.193991 + 0.981003i \(0.562143\pi\)
\(264\) −796.228 −0.185623
\(265\) −1606.11 −0.372311
\(266\) 0 0
\(267\) −218.909 −0.0501761
\(268\) −503.992 −0.114874
\(269\) −7394.48 −1.67602 −0.838011 0.545654i \(-0.816281\pi\)
−0.838011 + 0.545654i \(0.816281\pi\)
\(270\) −1350.28 −0.304353
\(271\) −3399.20 −0.761943 −0.380972 0.924587i \(-0.624410\pi\)
−0.380972 + 0.924587i \(0.624410\pi\)
\(272\) 6051.32 1.34895
\(273\) 0 0
\(274\) 4288.27 0.945489
\(275\) 2775.76 0.608672
\(276\) 19.8784 0.00433528
\(277\) 923.339 0.200282 0.100141 0.994973i \(-0.468071\pi\)
0.100141 + 0.994973i \(0.468071\pi\)
\(278\) 1912.19 0.412539
\(279\) −1054.00 −0.226169
\(280\) 0 0
\(281\) −5825.29 −1.23668 −0.618341 0.785910i \(-0.712195\pi\)
−0.618341 + 0.785910i \(0.712195\pi\)
\(282\) −590.348 −0.124662
\(283\) 2510.21 0.527268 0.263634 0.964623i \(-0.415079\pi\)
0.263634 + 0.964623i \(0.415079\pi\)
\(284\) −231.936 −0.0484608
\(285\) −2932.46 −0.609488
\(286\) 1265.22 0.261588
\(287\) 0 0
\(288\) −552.253 −0.112992
\(289\) 9087.77 1.84974
\(290\) 3128.15 0.633418
\(291\) 3446.83 0.694353
\(292\) −1076.60 −0.215765
\(293\) 1134.41 0.226187 0.113093 0.993584i \(-0.463924\pi\)
0.113093 + 0.993584i \(0.463924\pi\)
\(294\) 0 0
\(295\) −9882.44 −1.95043
\(296\) −8488.90 −1.66692
\(297\) −297.000 −0.0580259
\(298\) 5809.95 1.12940
\(299\) −215.769 −0.0417332
\(300\) 1038.64 0.199887
\(301\) 0 0
\(302\) −762.902 −0.145364
\(303\) −5807.43 −1.10108
\(304\) 2573.46 0.485520
\(305\) 6639.83 1.24654
\(306\) 2741.64 0.512186
\(307\) −785.699 −0.146066 −0.0730329 0.997330i \(-0.523268\pi\)
−0.0730329 + 0.997330i \(0.523268\pi\)
\(308\) 0 0
\(309\) −4345.98 −0.800110
\(310\) −5856.73 −1.07303
\(311\) −9477.59 −1.72805 −0.864027 0.503446i \(-0.832065\pi\)
−0.864027 + 0.503446i \(0.832065\pi\)
\(312\) 3233.91 0.586808
\(313\) 7517.48 1.35755 0.678775 0.734346i \(-0.262511\pi\)
0.678775 + 0.734346i \(0.262511\pi\)
\(314\) 3069.43 0.551649
\(315\) 0 0
\(316\) −390.708 −0.0695540
\(317\) 3803.77 0.673946 0.336973 0.941514i \(-0.390597\pi\)
0.336973 + 0.941514i \(0.390597\pi\)
\(318\) 638.587 0.112611
\(319\) 688.052 0.120763
\(320\) −11016.2 −1.92446
\(321\) 1249.36 0.217236
\(322\) 0 0
\(323\) 5954.14 1.02569
\(324\) −111.132 −0.0190556
\(325\) −11273.9 −1.92419
\(326\) 6373.92 1.08288
\(327\) 4875.80 0.824564
\(328\) 4277.70 0.720111
\(329\) 0 0
\(330\) −1650.34 −0.275297
\(331\) −7452.78 −1.23759 −0.618795 0.785553i \(-0.712379\pi\)
−0.618795 + 0.785553i \(0.712379\pi\)
\(332\) −922.352 −0.152472
\(333\) −3166.43 −0.521079
\(334\) 2067.33 0.338681
\(335\) −7135.70 −1.16378
\(336\) 0 0
\(337\) 4398.08 0.710917 0.355458 0.934692i \(-0.384325\pi\)
0.355458 + 0.934692i \(0.384325\pi\)
\(338\) 517.397 0.0832624
\(339\) −4381.16 −0.701923
\(340\) −3153.54 −0.503013
\(341\) −1288.22 −0.204577
\(342\) 1165.94 0.184348
\(343\) 0 0
\(344\) 13298.6 2.08434
\(345\) 281.445 0.0439203
\(346\) −1199.19 −0.186325
\(347\) 7126.59 1.10252 0.551262 0.834332i \(-0.314147\pi\)
0.551262 + 0.834332i \(0.314147\pi\)
\(348\) 257.457 0.0396584
\(349\) −995.094 −0.152625 −0.0763125 0.997084i \(-0.524315\pi\)
−0.0763125 + 0.997084i \(0.524315\pi\)
\(350\) 0 0
\(351\) 1206.28 0.183437
\(352\) −674.976 −0.102205
\(353\) 4744.61 0.715383 0.357691 0.933840i \(-0.383564\pi\)
0.357691 + 0.933840i \(0.383564\pi\)
\(354\) 3929.24 0.589935
\(355\) −3283.84 −0.490952
\(356\) −100.115 −0.0149047
\(357\) 0 0
\(358\) −10117.2 −1.49360
\(359\) 13107.5 1.92698 0.963492 0.267736i \(-0.0862755\pi\)
0.963492 + 0.267736i \(0.0862755\pi\)
\(360\) −4218.26 −0.617561
\(361\) −4326.87 −0.630831
\(362\) −8671.64 −1.25904
\(363\) −363.000 −0.0524864
\(364\) 0 0
\(365\) −15242.9 −2.18589
\(366\) −2639.99 −0.377034
\(367\) 1275.97 0.181485 0.0907425 0.995874i \(-0.471076\pi\)
0.0907425 + 0.995874i \(0.471076\pi\)
\(368\) −246.990 −0.0349871
\(369\) 1595.62 0.225107
\(370\) −17594.9 −2.47220
\(371\) 0 0
\(372\) −482.027 −0.0671827
\(373\) −12300.8 −1.70753 −0.853765 0.520658i \(-0.825687\pi\)
−0.853765 + 0.520658i \(0.825687\pi\)
\(374\) 3350.89 0.463290
\(375\) 7420.98 1.02191
\(376\) −1844.25 −0.252952
\(377\) −2794.55 −0.381768
\(378\) 0 0
\(379\) 12999.5 1.76185 0.880924 0.473258i \(-0.156922\pi\)
0.880924 + 0.473258i \(0.156922\pi\)
\(380\) −1341.11 −0.181046
\(381\) 4402.81 0.592029
\(382\) −11575.3 −1.55037
\(383\) 1281.20 0.170930 0.0854652 0.996341i \(-0.472762\pi\)
0.0854652 + 0.996341i \(0.472762\pi\)
\(384\) 2907.36 0.386369
\(385\) 0 0
\(386\) 10515.0 1.38653
\(387\) 4960.49 0.651566
\(388\) 1576.35 0.206255
\(389\) −13294.3 −1.73277 −0.866385 0.499377i \(-0.833562\pi\)
−0.866385 + 0.499377i \(0.833562\pi\)
\(390\) 6702.91 0.870295
\(391\) −571.454 −0.0739122
\(392\) 0 0
\(393\) −6471.94 −0.830702
\(394\) −238.353 −0.0304772
\(395\) −5531.80 −0.704645
\(396\) −135.828 −0.0172364
\(397\) −446.084 −0.0563937 −0.0281969 0.999602i \(-0.508977\pi\)
−0.0281969 + 0.999602i \(0.508977\pi\)
\(398\) −12413.5 −1.56340
\(399\) 0 0
\(400\) −12905.2 −1.61315
\(401\) 10327.6 1.28613 0.643064 0.765812i \(-0.277663\pi\)
0.643064 + 0.765812i \(0.277663\pi\)
\(402\) 2837.15 0.352000
\(403\) 5232.14 0.646729
\(404\) −2655.93 −0.327073
\(405\) −1573.45 −0.193050
\(406\) 0 0
\(407\) −3870.08 −0.471334
\(408\) 8564.87 1.03928
\(409\) −13775.0 −1.66536 −0.832679 0.553757i \(-0.813194\pi\)
−0.832679 + 0.553757i \(0.813194\pi\)
\(410\) 8866.37 1.06800
\(411\) 4997.03 0.599721
\(412\) −1987.56 −0.237670
\(413\) 0 0
\(414\) −111.902 −0.0132843
\(415\) −13059.0 −1.54468
\(416\) 2741.44 0.323101
\(417\) 2228.24 0.261672
\(418\) 1425.04 0.166749
\(419\) −6325.15 −0.737479 −0.368739 0.929533i \(-0.620211\pi\)
−0.368739 + 0.929533i \(0.620211\pi\)
\(420\) 0 0
\(421\) −3647.05 −0.422201 −0.211100 0.977464i \(-0.567705\pi\)
−0.211100 + 0.977464i \(0.567705\pi\)
\(422\) −7669.91 −0.884752
\(423\) −687.920 −0.0790729
\(424\) 1994.94 0.228498
\(425\) −29858.4 −3.40787
\(426\) 1305.65 0.148495
\(427\) 0 0
\(428\) 571.376 0.0645292
\(429\) 1474.34 0.165925
\(430\) 27563.9 3.09128
\(431\) −6112.16 −0.683091 −0.341546 0.939865i \(-0.610950\pi\)
−0.341546 + 0.939865i \(0.610950\pi\)
\(432\) 1380.82 0.153784
\(433\) −15967.1 −1.77213 −0.886064 0.463563i \(-0.846571\pi\)
−0.886064 + 0.463563i \(0.846571\pi\)
\(434\) 0 0
\(435\) 3645.17 0.401776
\(436\) 2229.87 0.244934
\(437\) −243.024 −0.0266027
\(438\) 6060.56 0.661152
\(439\) 2995.02 0.325613 0.162807 0.986658i \(-0.447945\pi\)
0.162807 + 0.986658i \(0.447945\pi\)
\(440\) −5155.66 −0.558605
\(441\) 0 0
\(442\) −13609.8 −1.46459
\(443\) 11034.6 1.18346 0.591728 0.806138i \(-0.298446\pi\)
0.591728 + 0.806138i \(0.298446\pi\)
\(444\) −1448.12 −0.154785
\(445\) −1417.46 −0.150998
\(446\) 15276.1 1.62185
\(447\) 6770.21 0.716376
\(448\) 0 0
\(449\) 9877.03 1.03814 0.519071 0.854731i \(-0.326278\pi\)
0.519071 + 0.854731i \(0.326278\pi\)
\(450\) −5846.87 −0.612498
\(451\) 1950.20 0.203617
\(452\) −2003.65 −0.208504
\(453\) −888.994 −0.0922043
\(454\) −8897.02 −0.919731
\(455\) 0 0
\(456\) 3642.40 0.374060
\(457\) −12760.0 −1.30610 −0.653048 0.757316i \(-0.726510\pi\)
−0.653048 + 0.757316i \(0.726510\pi\)
\(458\) 5328.69 0.543653
\(459\) 3194.77 0.324878
\(460\) 128.714 0.0130464
\(461\) −13591.3 −1.37312 −0.686561 0.727072i \(-0.740881\pi\)
−0.686561 + 0.727072i \(0.740881\pi\)
\(462\) 0 0
\(463\) 12510.8 1.25578 0.627891 0.778301i \(-0.283918\pi\)
0.627891 + 0.778301i \(0.283918\pi\)
\(464\) −3198.92 −0.320056
\(465\) −6824.72 −0.680621
\(466\) 5674.63 0.564103
\(467\) 6070.03 0.601472 0.300736 0.953707i \(-0.402768\pi\)
0.300736 + 0.953707i \(0.402768\pi\)
\(468\) 551.671 0.0544893
\(469\) 0 0
\(470\) −3822.56 −0.375152
\(471\) 3576.74 0.349910
\(472\) 12275.0 1.19704
\(473\) 6062.82 0.589363
\(474\) 2199.43 0.213129
\(475\) −12697.9 −1.22657
\(476\) 0 0
\(477\) 744.132 0.0714286
\(478\) −8257.93 −0.790186
\(479\) −10528.7 −1.00432 −0.502158 0.864776i \(-0.667461\pi\)
−0.502158 + 0.864776i \(0.667461\pi\)
\(480\) −3575.89 −0.340034
\(481\) 15718.5 1.49002
\(482\) 4470.61 0.422470
\(483\) 0 0
\(484\) −166.012 −0.0155909
\(485\) 22318.6 2.08955
\(486\) 625.601 0.0583906
\(487\) 7370.50 0.685809 0.342905 0.939370i \(-0.388589\pi\)
0.342905 + 0.939370i \(0.388589\pi\)
\(488\) −8247.32 −0.765038
\(489\) 7427.40 0.686868
\(490\) 0 0
\(491\) −10997.7 −1.01083 −0.505414 0.862877i \(-0.668660\pi\)
−0.505414 + 0.862877i \(0.668660\pi\)
\(492\) 729.730 0.0668674
\(493\) −7401.24 −0.676136
\(494\) −5787.86 −0.527142
\(495\) −1923.10 −0.174620
\(496\) 5989.22 0.542186
\(497\) 0 0
\(498\) 5192.24 0.467209
\(499\) 10048.6 0.901474 0.450737 0.892657i \(-0.351161\pi\)
0.450737 + 0.892657i \(0.351161\pi\)
\(500\) 3393.86 0.303556
\(501\) 2409.02 0.214825
\(502\) −4139.53 −0.368041
\(503\) −6366.49 −0.564350 −0.282175 0.959363i \(-0.591056\pi\)
−0.282175 + 0.959363i \(0.591056\pi\)
\(504\) 0 0
\(505\) −37603.7 −3.31355
\(506\) −136.770 −0.0120161
\(507\) 602.912 0.0528131
\(508\) 2013.55 0.175860
\(509\) −3841.31 −0.334505 −0.167253 0.985914i \(-0.553490\pi\)
−0.167253 + 0.985914i \(0.553490\pi\)
\(510\) 17752.4 1.54135
\(511\) 0 0
\(512\) 13009.7 1.12296
\(513\) 1358.65 0.116931
\(514\) 339.325 0.0291187
\(515\) −28140.6 −2.40782
\(516\) 2268.60 0.193546
\(517\) −840.792 −0.0715241
\(518\) 0 0
\(519\) −1397.39 −0.118186
\(520\) 20939.9 1.76591
\(521\) 10660.6 0.896452 0.448226 0.893920i \(-0.352056\pi\)
0.448226 + 0.893920i \(0.352056\pi\)
\(522\) −1449.31 −0.121522
\(523\) 22153.1 1.85218 0.926088 0.377307i \(-0.123150\pi\)
0.926088 + 0.377307i \(0.123150\pi\)
\(524\) −2959.83 −0.246758
\(525\) 0 0
\(526\) 4260.26 0.353149
\(527\) 13857.1 1.14540
\(528\) 1687.67 0.139103
\(529\) −12143.7 −0.998083
\(530\) 4134.91 0.338885
\(531\) 4578.66 0.374194
\(532\) 0 0
\(533\) −7920.82 −0.643694
\(534\) 563.580 0.0456713
\(535\) 8089.75 0.653739
\(536\) 8863.24 0.714242
\(537\) −11789.3 −0.947388
\(538\) 19037.0 1.52555
\(539\) 0 0
\(540\) −719.591 −0.0573449
\(541\) 2036.94 0.161876 0.0809381 0.996719i \(-0.474208\pi\)
0.0809381 + 0.996719i \(0.474208\pi\)
\(542\) 8751.20 0.693536
\(543\) −10104.9 −0.798604
\(544\) 7260.58 0.572233
\(545\) 31571.3 2.48141
\(546\) 0 0
\(547\) 6302.96 0.492678 0.246339 0.969184i \(-0.420772\pi\)
0.246339 + 0.969184i \(0.420772\pi\)
\(548\) 2285.31 0.178145
\(549\) −3076.32 −0.239151
\(550\) −7146.18 −0.554025
\(551\) −3147.54 −0.243357
\(552\) −349.583 −0.0269551
\(553\) 0 0
\(554\) −2377.13 −0.182300
\(555\) −20503.0 −1.56811
\(556\) 1019.05 0.0777290
\(557\) 4946.75 0.376302 0.188151 0.982140i \(-0.439751\pi\)
0.188151 + 0.982140i \(0.439751\pi\)
\(558\) 2713.50 0.205863
\(559\) −24624.4 −1.86315
\(560\) 0 0
\(561\) 3904.72 0.293863
\(562\) 14997.1 1.12565
\(563\) 15465.3 1.15770 0.578850 0.815434i \(-0.303502\pi\)
0.578850 + 0.815434i \(0.303502\pi\)
\(564\) −314.609 −0.0234884
\(565\) −28368.4 −2.11234
\(566\) −6462.52 −0.479930
\(567\) 0 0
\(568\) 4078.85 0.301311
\(569\) −17074.3 −1.25798 −0.628990 0.777413i \(-0.716532\pi\)
−0.628990 + 0.777413i \(0.716532\pi\)
\(570\) 7549.59 0.554768
\(571\) −21514.1 −1.57677 −0.788385 0.615182i \(-0.789083\pi\)
−0.788385 + 0.615182i \(0.789083\pi\)
\(572\) 674.265 0.0492875
\(573\) −13488.4 −0.983398
\(574\) 0 0
\(575\) 1218.70 0.0883880
\(576\) 5103.97 0.369210
\(577\) −18284.5 −1.31923 −0.659613 0.751606i \(-0.729280\pi\)
−0.659613 + 0.751606i \(0.729280\pi\)
\(578\) −23396.4 −1.68367
\(579\) 12252.9 0.879472
\(580\) 1667.06 0.119346
\(581\) 0 0
\(582\) −8873.82 −0.632013
\(583\) 909.494 0.0646096
\(584\) 18933.2 1.34154
\(585\) 7810.77 0.552026
\(586\) −2920.52 −0.205880
\(587\) 20553.7 1.44521 0.722607 0.691259i \(-0.242944\pi\)
0.722607 + 0.691259i \(0.242944\pi\)
\(588\) 0 0
\(589\) 5893.04 0.412255
\(590\) 25442.2 1.77532
\(591\) −277.747 −0.0193316
\(592\) 17992.9 1.24916
\(593\) −8831.26 −0.611562 −0.305781 0.952102i \(-0.598918\pi\)
−0.305781 + 0.952102i \(0.598918\pi\)
\(594\) 764.624 0.0528163
\(595\) 0 0
\(596\) 3096.24 0.212797
\(597\) −14465.2 −0.991660
\(598\) 555.495 0.0379864
\(599\) 602.040 0.0410663 0.0205331 0.999789i \(-0.493464\pi\)
0.0205331 + 0.999789i \(0.493464\pi\)
\(600\) −18265.6 −1.24282
\(601\) 2057.59 0.139652 0.0698261 0.997559i \(-0.477756\pi\)
0.0698261 + 0.997559i \(0.477756\pi\)
\(602\) 0 0
\(603\) 3306.07 0.223273
\(604\) −406.567 −0.0273890
\(605\) −2350.46 −0.157950
\(606\) 14951.2 1.00223
\(607\) 4029.28 0.269429 0.134715 0.990884i \(-0.456988\pi\)
0.134715 + 0.990884i \(0.456988\pi\)
\(608\) 3087.72 0.205960
\(609\) 0 0
\(610\) −17094.2 −1.13463
\(611\) 3414.91 0.226109
\(612\) 1461.08 0.0965041
\(613\) −3976.70 −0.262018 −0.131009 0.991381i \(-0.541822\pi\)
−0.131009 + 0.991381i \(0.541822\pi\)
\(614\) 2022.77 0.132952
\(615\) 10331.8 0.677428
\(616\) 0 0
\(617\) −5943.74 −0.387822 −0.193911 0.981019i \(-0.562117\pi\)
−0.193911 + 0.981019i \(0.562117\pi\)
\(618\) 11188.7 0.728276
\(619\) 28.0366 0.00182049 0.000910247 1.00000i \(-0.499710\pi\)
0.000910247 1.00000i \(0.499710\pi\)
\(620\) −3121.18 −0.202176
\(621\) −130.397 −0.00842620
\(622\) 24400.0 1.57291
\(623\) 0 0
\(624\) −6854.55 −0.439746
\(625\) 16508.8 1.05656
\(626\) −19353.7 −1.23567
\(627\) 1660.57 0.105768
\(628\) 1635.76 0.103940
\(629\) 41629.7 2.63893
\(630\) 0 0
\(631\) −4982.71 −0.314356 −0.157178 0.987570i \(-0.550240\pi\)
−0.157178 + 0.987570i \(0.550240\pi\)
\(632\) 6871.03 0.432460
\(633\) −8937.59 −0.561196
\(634\) −9792.76 −0.613439
\(635\) 28508.7 1.78162
\(636\) 340.316 0.0212176
\(637\) 0 0
\(638\) −1771.38 −0.109921
\(639\) 1521.45 0.0941900
\(640\) 18825.5 1.16272
\(641\) 12267.1 0.755886 0.377943 0.925829i \(-0.376632\pi\)
0.377943 + 0.925829i \(0.376632\pi\)
\(642\) −3216.47 −0.197732
\(643\) 1359.44 0.0833766 0.0416883 0.999131i \(-0.486726\pi\)
0.0416883 + 0.999131i \(0.486726\pi\)
\(644\) 0 0
\(645\) 32119.7 1.96079
\(646\) −15328.9 −0.933602
\(647\) −20317.4 −1.23456 −0.617278 0.786745i \(-0.711765\pi\)
−0.617278 + 0.786745i \(0.711765\pi\)
\(648\) 1954.38 0.118480
\(649\) 5596.15 0.338471
\(650\) 29024.5 1.75144
\(651\) 0 0
\(652\) 3396.80 0.204032
\(653\) −12544.8 −0.751788 −0.375894 0.926663i \(-0.622664\pi\)
−0.375894 + 0.926663i \(0.622664\pi\)
\(654\) −12552.7 −0.750535
\(655\) −41906.4 −2.49988
\(656\) −9066.95 −0.539642
\(657\) 7062.24 0.419367
\(658\) 0 0
\(659\) −6513.21 −0.385005 −0.192503 0.981296i \(-0.561660\pi\)
−0.192503 + 0.981296i \(0.561660\pi\)
\(660\) −879.500 −0.0518705
\(661\) 7407.93 0.435908 0.217954 0.975959i \(-0.430062\pi\)
0.217954 + 0.975959i \(0.430062\pi\)
\(662\) 19187.1 1.12648
\(663\) −15859.2 −0.928989
\(664\) 16220.6 0.948012
\(665\) 0 0
\(666\) 8151.95 0.474297
\(667\) 302.088 0.0175366
\(668\) 1101.73 0.0638130
\(669\) 17801.0 1.02874
\(670\) 18370.8 1.05929
\(671\) −3759.95 −0.216321
\(672\) 0 0
\(673\) −5228.21 −0.299454 −0.149727 0.988727i \(-0.547840\pi\)
−0.149727 + 0.988727i \(0.547840\pi\)
\(674\) −11322.8 −0.647090
\(675\) −6813.24 −0.388506
\(676\) 275.732 0.0156880
\(677\) 30564.0 1.73511 0.867555 0.497341i \(-0.165690\pi\)
0.867555 + 0.497341i \(0.165690\pi\)
\(678\) 11279.3 0.638904
\(679\) 0 0
\(680\) 55458.4 3.12755
\(681\) −10367.5 −0.583383
\(682\) 3316.50 0.186210
\(683\) −3525.50 −0.197510 −0.0987552 0.995112i \(-0.531486\pi\)
−0.0987552 + 0.995112i \(0.531486\pi\)
\(684\) 621.355 0.0347341
\(685\) 32356.3 1.80477
\(686\) 0 0
\(687\) 6209.41 0.344838
\(688\) −28187.5 −1.56197
\(689\) −3693.95 −0.204250
\(690\) −724.579 −0.0399772
\(691\) 32210.6 1.77330 0.886649 0.462443i \(-0.153027\pi\)
0.886649 + 0.462443i \(0.153027\pi\)
\(692\) −639.071 −0.0351067
\(693\) 0 0
\(694\) −18347.3 −1.00354
\(695\) 14428.1 0.787465
\(696\) −4527.65 −0.246581
\(697\) −20977.9 −1.14002
\(698\) 2561.86 0.138922
\(699\) 6612.53 0.357809
\(700\) 0 0
\(701\) −17157.6 −0.924442 −0.462221 0.886765i \(-0.652947\pi\)
−0.462221 + 0.886765i \(0.652947\pi\)
\(702\) −3105.55 −0.166968
\(703\) 17704.0 0.949813
\(704\) 6238.18 0.333963
\(705\) −4454.35 −0.237958
\(706\) −12215.0 −0.651156
\(707\) 0 0
\(708\) 2093.98 0.111153
\(709\) −12558.9 −0.665244 −0.332622 0.943060i \(-0.607933\pi\)
−0.332622 + 0.943060i \(0.607933\pi\)
\(710\) 8454.20 0.446874
\(711\) 2562.95 0.135187
\(712\) 1760.62 0.0926715
\(713\) −565.590 −0.0297076
\(714\) 0 0
\(715\) 9546.49 0.499327
\(716\) −5391.66 −0.281419
\(717\) −9622.79 −0.501213
\(718\) −33745.1 −1.75398
\(719\) −7118.76 −0.369242 −0.184621 0.982810i \(-0.559106\pi\)
−0.184621 + 0.982810i \(0.559106\pi\)
\(720\) 8940.97 0.462792
\(721\) 0 0
\(722\) 11139.5 0.574194
\(723\) 5209.51 0.267972
\(724\) −4621.30 −0.237223
\(725\) 15784.0 0.808558
\(726\) 934.540 0.0477741
\(727\) −24046.2 −1.22672 −0.613358 0.789805i \(-0.710182\pi\)
−0.613358 + 0.789805i \(0.710182\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 39242.7 1.98964
\(731\) −65216.6 −3.29976
\(732\) −1406.90 −0.0710392
\(733\) 3537.80 0.178270 0.0891348 0.996020i \(-0.471590\pi\)
0.0891348 + 0.996020i \(0.471590\pi\)
\(734\) −3284.97 −0.165191
\(735\) 0 0
\(736\) −296.347 −0.0148417
\(737\) 4040.75 0.201958
\(738\) −4107.91 −0.204897
\(739\) 14950.5 0.744198 0.372099 0.928193i \(-0.378638\pi\)
0.372099 + 0.928193i \(0.378638\pi\)
\(740\) −9376.69 −0.465803
\(741\) −6744.47 −0.334365
\(742\) 0 0
\(743\) −5551.81 −0.274127 −0.137063 0.990562i \(-0.543766\pi\)
−0.137063 + 0.990562i \(0.543766\pi\)
\(744\) 8476.98 0.417716
\(745\) 43837.8 2.15583
\(746\) 31668.2 1.55423
\(747\) 6050.41 0.296349
\(748\) 1785.76 0.0872912
\(749\) 0 0
\(750\) −19105.2 −0.930166
\(751\) 29436.1 1.43028 0.715138 0.698983i \(-0.246364\pi\)
0.715138 + 0.698983i \(0.246364\pi\)
\(752\) 3909.04 0.189559
\(753\) −4823.71 −0.233447
\(754\) 7194.54 0.347493
\(755\) −5756.32 −0.277475
\(756\) 0 0
\(757\) −22285.6 −1.06999 −0.534996 0.844854i \(-0.679687\pi\)
−0.534996 + 0.844854i \(0.679687\pi\)
\(758\) −33467.1 −1.60367
\(759\) −159.375 −0.00762178
\(760\) 23584.9 1.12568
\(761\) −6522.03 −0.310675 −0.155337 0.987861i \(-0.549646\pi\)
−0.155337 + 0.987861i \(0.549646\pi\)
\(762\) −11335.0 −0.538876
\(763\) 0 0
\(764\) −6168.71 −0.292115
\(765\) 20686.5 0.977674
\(766\) −3298.44 −0.155584
\(767\) −22729.0 −1.07001
\(768\) 6125.60 0.287811
\(769\) 35853.8 1.68130 0.840651 0.541578i \(-0.182173\pi\)
0.840651 + 0.541578i \(0.182173\pi\)
\(770\) 0 0
\(771\) 395.409 0.0184699
\(772\) 5603.67 0.261244
\(773\) 20452.0 0.951627 0.475813 0.879546i \(-0.342154\pi\)
0.475813 + 0.879546i \(0.342154\pi\)
\(774\) −12770.7 −0.593068
\(775\) −29551.9 −1.36973
\(776\) −27721.8 −1.28242
\(777\) 0 0
\(778\) 34226.0 1.57720
\(779\) −8921.34 −0.410321
\(780\) 3572.13 0.163978
\(781\) 1859.54 0.0851981
\(782\) 1471.20 0.0672764
\(783\) −1688.85 −0.0770814
\(784\) 0 0
\(785\) 23159.7 1.05300
\(786\) 16661.9 0.756122
\(787\) −42335.7 −1.91754 −0.958770 0.284183i \(-0.908278\pi\)
−0.958770 + 0.284183i \(0.908278\pi\)
\(788\) −127.023 −0.00574240
\(789\) 4964.40 0.224002
\(790\) 14241.6 0.641382
\(791\) 0 0
\(792\) 2388.68 0.107169
\(793\) 15271.2 0.683853
\(794\) 1148.44 0.0513307
\(795\) 4818.33 0.214954
\(796\) −6615.42 −0.294569
\(797\) 43295.8 1.92424 0.962118 0.272635i \(-0.0878951\pi\)
0.962118 + 0.272635i \(0.0878951\pi\)
\(798\) 0 0
\(799\) 9044.23 0.400453
\(800\) −15484.1 −0.684306
\(801\) 656.728 0.0289692
\(802\) −26588.4 −1.17066
\(803\) 8631.63 0.379332
\(804\) 1511.98 0.0663225
\(805\) 0 0
\(806\) −13470.1 −0.588665
\(807\) 22183.5 0.967651
\(808\) 46707.5 2.03362
\(809\) 41114.4 1.78678 0.893391 0.449279i \(-0.148319\pi\)
0.893391 + 0.449279i \(0.148319\pi\)
\(810\) 4050.83 0.175718
\(811\) −17135.7 −0.741944 −0.370972 0.928644i \(-0.620975\pi\)
−0.370972 + 0.928644i \(0.620975\pi\)
\(812\) 0 0
\(813\) 10197.6 0.439908
\(814\) 9963.49 0.429017
\(815\) 48093.1 2.06703
\(816\) −18154.0 −0.778819
\(817\) −27734.8 −1.18766
\(818\) 35463.7 1.51584
\(819\) 0 0
\(820\) 4725.08 0.201228
\(821\) 31142.2 1.32384 0.661919 0.749575i \(-0.269742\pi\)
0.661919 + 0.749575i \(0.269742\pi\)
\(822\) −12864.8 −0.545878
\(823\) −41642.4 −1.76374 −0.881872 0.471488i \(-0.843717\pi\)
−0.881872 + 0.471488i \(0.843717\pi\)
\(824\) 34953.4 1.47774
\(825\) −8327.29 −0.351417
\(826\) 0 0
\(827\) 6851.51 0.288090 0.144045 0.989571i \(-0.453989\pi\)
0.144045 + 0.989571i \(0.453989\pi\)
\(828\) −59.6351 −0.00250298
\(829\) −26867.4 −1.12563 −0.562813 0.826584i \(-0.690281\pi\)
−0.562813 + 0.826584i \(0.690281\pi\)
\(830\) 33620.3 1.40600
\(831\) −2770.02 −0.115633
\(832\) −25336.6 −1.05576
\(833\) 0 0
\(834\) −5736.58 −0.238179
\(835\) 15598.7 0.646484
\(836\) 759.434 0.0314182
\(837\) 3161.99 0.130579
\(838\) 16284.0 0.671268
\(839\) 22864.3 0.940840 0.470420 0.882443i \(-0.344102\pi\)
0.470420 + 0.882443i \(0.344102\pi\)
\(840\) 0 0
\(841\) −20476.5 −0.839578
\(842\) 9389.30 0.384295
\(843\) 17475.9 0.713998
\(844\) −4087.46 −0.166702
\(845\) 3903.91 0.158933
\(846\) 1771.04 0.0719737
\(847\) 0 0
\(848\) −4228.46 −0.171233
\(849\) −7530.64 −0.304418
\(850\) 76870.0 3.10191
\(851\) −1699.16 −0.0684445
\(852\) 695.808 0.0279789
\(853\) −15718.2 −0.630927 −0.315463 0.948938i \(-0.602160\pi\)
−0.315463 + 0.948938i \(0.602160\pi\)
\(854\) 0 0
\(855\) 8797.38 0.351888
\(856\) −10048.3 −0.401218
\(857\) 2143.86 0.0854526 0.0427263 0.999087i \(-0.486396\pi\)
0.0427263 + 0.999087i \(0.486396\pi\)
\(858\) −3795.67 −0.151028
\(859\) 42640.8 1.69370 0.846848 0.531836i \(-0.178498\pi\)
0.846848 + 0.531836i \(0.178498\pi\)
\(860\) 14689.4 0.582447
\(861\) 0 0
\(862\) 15735.7 0.621763
\(863\) 19484.3 0.768543 0.384271 0.923220i \(-0.374453\pi\)
0.384271 + 0.923220i \(0.374453\pi\)
\(864\) 1656.76 0.0652362
\(865\) −9048.21 −0.355663
\(866\) 41107.2 1.61303
\(867\) −27263.3 −1.06795
\(868\) 0 0
\(869\) 3132.50 0.122282
\(870\) −9384.45 −0.365704
\(871\) −16411.7 −0.638448
\(872\) −39214.7 −1.52291
\(873\) −10340.5 −0.400885
\(874\) 625.662 0.0242143
\(875\) 0 0
\(876\) 3229.80 0.124572
\(877\) 4048.32 0.155875 0.0779373 0.996958i \(-0.475167\pi\)
0.0779373 + 0.996958i \(0.475167\pi\)
\(878\) −7710.64 −0.296380
\(879\) −3403.22 −0.130589
\(880\) 10927.9 0.418611
\(881\) 2567.71 0.0981933 0.0490966 0.998794i \(-0.484366\pi\)
0.0490966 + 0.998794i \(0.484366\pi\)
\(882\) 0 0
\(883\) −19974.2 −0.761250 −0.380625 0.924729i \(-0.624291\pi\)
−0.380625 + 0.924729i \(0.624291\pi\)
\(884\) −7252.93 −0.275953
\(885\) 29647.3 1.12608
\(886\) −28408.5 −1.07720
\(887\) −3266.08 −0.123635 −0.0618175 0.998087i \(-0.519690\pi\)
−0.0618175 + 0.998087i \(0.519690\pi\)
\(888\) 25466.7 0.962394
\(889\) 0 0
\(890\) 3649.23 0.137441
\(891\) 891.000 0.0335013
\(892\) 8140.98 0.305583
\(893\) 3846.26 0.144132
\(894\) −17429.8 −0.652059
\(895\) −76337.1 −2.85103
\(896\) 0 0
\(897\) 647.307 0.0240947
\(898\) −25428.3 −0.944938
\(899\) −7325.29 −0.271760
\(900\) −3115.92 −0.115405
\(901\) −9783.25 −0.361740
\(902\) −5020.77 −0.185336
\(903\) 0 0
\(904\) 35236.4 1.29640
\(905\) −65430.1 −2.40328
\(906\) 2288.71 0.0839262
\(907\) −41233.2 −1.50951 −0.754755 0.656007i \(-0.772244\pi\)
−0.754755 + 0.656007i \(0.772244\pi\)
\(908\) −4741.41 −0.173292
\(909\) 17422.3 0.635710
\(910\) 0 0
\(911\) −8501.69 −0.309191 −0.154596 0.987978i \(-0.549408\pi\)
−0.154596 + 0.987978i \(0.549408\pi\)
\(912\) −7720.38 −0.280315
\(913\) 7394.95 0.268058
\(914\) 32850.4 1.18884
\(915\) −19919.5 −0.719692
\(916\) 2839.77 0.102433
\(917\) 0 0
\(918\) −8224.91 −0.295711
\(919\) 13561.7 0.486790 0.243395 0.969927i \(-0.421739\pi\)
0.243395 + 0.969927i \(0.421739\pi\)
\(920\) −2263.58 −0.0811176
\(921\) 2357.10 0.0843311
\(922\) 34990.6 1.24984
\(923\) −7552.61 −0.269336
\(924\) 0 0
\(925\) −88780.5 −3.15577
\(926\) −32209.0 −1.14304
\(927\) 13037.9 0.461944
\(928\) −3838.17 −0.135769
\(929\) −12572.1 −0.444002 −0.222001 0.975046i \(-0.571259\pi\)
−0.222001 + 0.975046i \(0.571259\pi\)
\(930\) 17570.2 0.619515
\(931\) 0 0
\(932\) 3024.13 0.106286
\(933\) 28432.8 0.997692
\(934\) −15627.2 −0.547472
\(935\) 25283.5 0.884339
\(936\) −9701.74 −0.338794
\(937\) −29502.5 −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(938\) 0 0
\(939\) −22552.4 −0.783782
\(940\) −2037.12 −0.0706848
\(941\) 35244.5 1.22098 0.610488 0.792026i \(-0.290973\pi\)
0.610488 + 0.792026i \(0.290973\pi\)
\(942\) −9208.28 −0.318495
\(943\) 856.233 0.0295682
\(944\) −26017.8 −0.897042
\(945\) 0 0
\(946\) −15608.7 −0.536450
\(947\) −56745.3 −1.94717 −0.973587 0.228317i \(-0.926678\pi\)
−0.973587 + 0.228317i \(0.926678\pi\)
\(948\) 1172.13 0.0401570
\(949\) −35057.7 −1.19918
\(950\) 32690.7 1.11645
\(951\) −11411.3 −0.389103
\(952\) 0 0
\(953\) −41686.3 −1.41695 −0.708474 0.705737i \(-0.750616\pi\)
−0.708474 + 0.705737i \(0.750616\pi\)
\(954\) −1915.76 −0.0650157
\(955\) −87338.9 −2.95939
\(956\) −4400.82 −0.148884
\(957\) −2064.16 −0.0697227
\(958\) 27106.0 0.914149
\(959\) 0 0
\(960\) 33048.7 1.11108
\(961\) −16076.1 −0.539630
\(962\) −40467.1 −1.35625
\(963\) −3748.09 −0.125421
\(964\) 2382.48 0.0796002
\(965\) 79338.9 2.64664
\(966\) 0 0
\(967\) −10010.2 −0.332892 −0.166446 0.986051i \(-0.553229\pi\)
−0.166446 + 0.986051i \(0.553229\pi\)
\(968\) 2919.50 0.0969384
\(969\) −17862.4 −0.592181
\(970\) −57458.9 −1.90195
\(971\) −6719.55 −0.222081 −0.111041 0.993816i \(-0.535418\pi\)
−0.111041 + 0.993816i \(0.535418\pi\)
\(972\) 333.396 0.0110017
\(973\) 0 0
\(974\) −18975.3 −0.624237
\(975\) 33821.6 1.11093
\(976\) 17480.9 0.573309
\(977\) −27634.5 −0.904921 −0.452460 0.891785i \(-0.649454\pi\)
−0.452460 + 0.891785i \(0.649454\pi\)
\(978\) −19121.8 −0.625201
\(979\) 802.667 0.0262036
\(980\) 0 0
\(981\) −14627.4 −0.476062
\(982\) 28313.3 0.920076
\(983\) −43634.5 −1.41579 −0.707897 0.706316i \(-0.750356\pi\)
−0.707897 + 0.706316i \(0.750356\pi\)
\(984\) −12833.1 −0.415756
\(985\) −1798.44 −0.0581758
\(986\) 19054.4 0.615432
\(987\) 0 0
\(988\) −3084.47 −0.0993220
\(989\) 2661.87 0.0855841
\(990\) 4951.01 0.158943
\(991\) 37765.3 1.21055 0.605275 0.796016i \(-0.293063\pi\)
0.605275 + 0.796016i \(0.293063\pi\)
\(992\) 7186.07 0.229998
\(993\) 22358.4 0.714523
\(994\) 0 0
\(995\) −93663.5 −2.98425
\(996\) 2767.06 0.0880297
\(997\) 5085.69 0.161550 0.0807750 0.996732i \(-0.474260\pi\)
0.0807750 + 0.996732i \(0.474260\pi\)
\(998\) −25869.9 −0.820540
\(999\) 9499.30 0.300845
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 1617.4.a.be.1.5 16
7.6 odd 2 1617.4.a.bf.1.5 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1617.4.a.be.1.5 16 1.1 even 1 trivial
1617.4.a.bf.1.5 yes 16 7.6 odd 2