Properties

Label 1617.4.a.be.1.10
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 1.10
Root \(2.10744\) 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)
 
\(f(q)\) \(=\) \(q+2.10744 q^{2} -3.00000 q^{3} -3.55870 q^{4} +5.76870 q^{5} -6.32232 q^{6} -24.3593 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.10744 q^{2} -3.00000 q^{3} -3.55870 q^{4} +5.76870 q^{5} -6.32232 q^{6} -24.3593 q^{8} +9.00000 q^{9} +12.1572 q^{10} +11.0000 q^{11} +10.6761 q^{12} +85.4190 q^{13} -17.3061 q^{15} -22.8661 q^{16} -110.608 q^{17} +18.9670 q^{18} +4.28227 q^{19} -20.5291 q^{20} +23.1818 q^{22} -147.988 q^{23} +73.0778 q^{24} -91.7221 q^{25} +180.015 q^{26} -27.0000 q^{27} +147.890 q^{29} -36.4716 q^{30} -118.914 q^{31} +146.685 q^{32} -33.0000 q^{33} -233.099 q^{34} -32.0283 q^{36} +64.0827 q^{37} +9.02463 q^{38} -256.257 q^{39} -140.521 q^{40} +489.539 q^{41} +429.270 q^{43} -39.1456 q^{44} +51.9183 q^{45} -311.875 q^{46} -286.373 q^{47} +68.5984 q^{48} -193.299 q^{50} +331.823 q^{51} -303.980 q^{52} +114.286 q^{53} -56.9009 q^{54} +63.4557 q^{55} -12.8468 q^{57} +311.670 q^{58} +647.693 q^{59} +61.5872 q^{60} -611.859 q^{61} -250.604 q^{62} +492.059 q^{64} +492.757 q^{65} -69.5455 q^{66} -565.387 q^{67} +393.619 q^{68} +443.963 q^{69} +268.228 q^{71} -219.233 q^{72} -1093.38 q^{73} +135.050 q^{74} +275.166 q^{75} -15.2393 q^{76} -540.046 q^{78} +740.094 q^{79} -131.908 q^{80} +81.0000 q^{81} +1031.67 q^{82} -1048.69 q^{83} -638.063 q^{85} +904.661 q^{86} -443.671 q^{87} -267.952 q^{88} +408.591 q^{89} +109.415 q^{90} +526.643 q^{92} +356.742 q^{93} -603.514 q^{94} +24.7031 q^{95} -440.055 q^{96} -672.978 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 48 q^{3} + 72 q^{4} - 40 q^{5} - 12 q^{6} + 66 q^{8} + 144 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.10744 0.745093 0.372546 0.928014i \(-0.378485\pi\)
0.372546 + 0.928014i \(0.378485\pi\)
\(3\) −3.00000 −0.577350
\(4\) −3.55870 −0.444837
\(5\) 5.76870 0.515968 0.257984 0.966149i \(-0.416942\pi\)
0.257984 + 0.966149i \(0.416942\pi\)
\(6\) −6.32232 −0.430179
\(7\) 0 0
\(8\) −24.3593 −1.07654
\(9\) 9.00000 0.333333
\(10\) 12.1572 0.384444
\(11\) 11.0000 0.301511
\(12\) 10.6761 0.256827
\(13\) 85.4190 1.82238 0.911191 0.411985i \(-0.135164\pi\)
0.911191 + 0.411985i \(0.135164\pi\)
\(14\) 0 0
\(15\) −17.3061 −0.297894
\(16\) −22.8661 −0.357283
\(17\) −110.608 −1.57802 −0.789009 0.614381i \(-0.789406\pi\)
−0.789009 + 0.614381i \(0.789406\pi\)
\(18\) 18.9670 0.248364
\(19\) 4.28227 0.0517063 0.0258532 0.999666i \(-0.491770\pi\)
0.0258532 + 0.999666i \(0.491770\pi\)
\(20\) −20.5291 −0.229522
\(21\) 0 0
\(22\) 23.1818 0.224654
\(23\) −147.988 −1.34163 −0.670817 0.741623i \(-0.734056\pi\)
−0.670817 + 0.741623i \(0.734056\pi\)
\(24\) 73.0778 0.621539
\(25\) −91.7221 −0.733777
\(26\) 180.015 1.35784
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 147.890 0.946985 0.473493 0.880798i \(-0.342993\pi\)
0.473493 + 0.880798i \(0.342993\pi\)
\(30\) −36.4716 −0.221959
\(31\) −118.914 −0.688954 −0.344477 0.938795i \(-0.611944\pi\)
−0.344477 + 0.938795i \(0.611944\pi\)
\(32\) 146.685 0.810328
\(33\) −33.0000 −0.174078
\(34\) −233.099 −1.17577
\(35\) 0 0
\(36\) −32.0283 −0.148279
\(37\) 64.0827 0.284733 0.142367 0.989814i \(-0.454529\pi\)
0.142367 + 0.989814i \(0.454529\pi\)
\(38\) 9.02463 0.0385260
\(39\) −256.257 −1.05215
\(40\) −140.521 −0.555459
\(41\) 489.539 1.86471 0.932356 0.361541i \(-0.117749\pi\)
0.932356 + 0.361541i \(0.117749\pi\)
\(42\) 0 0
\(43\) 429.270 1.52240 0.761198 0.648519i \(-0.224611\pi\)
0.761198 + 0.648519i \(0.224611\pi\)
\(44\) −39.1456 −0.134123
\(45\) 51.9183 0.171989
\(46\) −311.875 −0.999641
\(47\) −286.373 −0.888762 −0.444381 0.895838i \(-0.646576\pi\)
−0.444381 + 0.895838i \(0.646576\pi\)
\(48\) 68.5984 0.206278
\(49\) 0 0
\(50\) −193.299 −0.546732
\(51\) 331.823 0.911070
\(52\) −303.980 −0.810663
\(53\) 114.286 0.296197 0.148098 0.988973i \(-0.452685\pi\)
0.148098 + 0.988973i \(0.452685\pi\)
\(54\) −56.9009 −0.143393
\(55\) 63.4557 0.155570
\(56\) 0 0
\(57\) −12.8468 −0.0298526
\(58\) 311.670 0.705592
\(59\) 647.693 1.42919 0.714597 0.699537i \(-0.246610\pi\)
0.714597 + 0.699537i \(0.246610\pi\)
\(60\) 61.5872 0.132514
\(61\) −611.859 −1.28427 −0.642135 0.766592i \(-0.721951\pi\)
−0.642135 + 0.766592i \(0.721951\pi\)
\(62\) −250.604 −0.513334
\(63\) 0 0
\(64\) 492.059 0.961053
\(65\) 492.757 0.940291
\(66\) −69.5455 −0.129704
\(67\) −565.387 −1.03094 −0.515470 0.856908i \(-0.672383\pi\)
−0.515470 + 0.856908i \(0.672383\pi\)
\(68\) 393.619 0.701961
\(69\) 443.963 0.774592
\(70\) 0 0
\(71\) 268.228 0.448349 0.224174 0.974549i \(-0.428031\pi\)
0.224174 + 0.974549i \(0.428031\pi\)
\(72\) −219.233 −0.358846
\(73\) −1093.38 −1.75301 −0.876507 0.481389i \(-0.840132\pi\)
−0.876507 + 0.481389i \(0.840132\pi\)
\(74\) 135.050 0.212153
\(75\) 275.166 0.423646
\(76\) −15.2393 −0.0230009
\(77\) 0 0
\(78\) −540.046 −0.783951
\(79\) 740.094 1.05401 0.527007 0.849861i \(-0.323314\pi\)
0.527007 + 0.849861i \(0.323314\pi\)
\(80\) −131.908 −0.184347
\(81\) 81.0000 0.111111
\(82\) 1031.67 1.38938
\(83\) −1048.69 −1.38685 −0.693425 0.720529i \(-0.743899\pi\)
−0.693425 + 0.720529i \(0.743899\pi\)
\(84\) 0 0
\(85\) −638.063 −0.814208
\(86\) 904.661 1.13433
\(87\) −443.671 −0.546742
\(88\) −267.952 −0.324588
\(89\) 408.591 0.486636 0.243318 0.969947i \(-0.421764\pi\)
0.243318 + 0.969947i \(0.421764\pi\)
\(90\) 109.415 0.128148
\(91\) 0 0
\(92\) 526.643 0.596808
\(93\) 356.742 0.397768
\(94\) −603.514 −0.662210
\(95\) 24.7031 0.0266788
\(96\) −440.055 −0.467843
\(97\) −672.978 −0.704438 −0.352219 0.935918i \(-0.614573\pi\)
−0.352219 + 0.935918i \(0.614573\pi\)
\(98\) 0 0
\(99\) 99.0000 0.100504
\(100\) 326.411 0.326411
\(101\) −945.302 −0.931298 −0.465649 0.884970i \(-0.654179\pi\)
−0.465649 + 0.884970i \(0.654179\pi\)
\(102\) 699.298 0.678831
\(103\) −1330.06 −1.27238 −0.636189 0.771533i \(-0.719490\pi\)
−0.636189 + 0.771533i \(0.719490\pi\)
\(104\) −2080.74 −1.96186
\(105\) 0 0
\(106\) 240.851 0.220694
\(107\) −1206.01 −1.08962 −0.544812 0.838558i \(-0.683399\pi\)
−0.544812 + 0.838558i \(0.683399\pi\)
\(108\) 96.0848 0.0856089
\(109\) −342.191 −0.300697 −0.150348 0.988633i \(-0.548040\pi\)
−0.150348 + 0.988633i \(0.548040\pi\)
\(110\) 133.729 0.115914
\(111\) −192.248 −0.164391
\(112\) 0 0
\(113\) −195.766 −0.162974 −0.0814872 0.996674i \(-0.525967\pi\)
−0.0814872 + 0.996674i \(0.525967\pi\)
\(114\) −27.0739 −0.0222430
\(115\) −853.697 −0.692240
\(116\) −526.297 −0.421254
\(117\) 768.771 0.607460
\(118\) 1364.97 1.06488
\(119\) 0 0
\(120\) 421.564 0.320695
\(121\) 121.000 0.0909091
\(122\) −1289.46 −0.956900
\(123\) −1468.62 −1.07659
\(124\) 423.178 0.306472
\(125\) −1250.21 −0.894574
\(126\) 0 0
\(127\) −1834.77 −1.28197 −0.640984 0.767554i \(-0.721474\pi\)
−0.640984 + 0.767554i \(0.721474\pi\)
\(128\) −136.496 −0.0942549
\(129\) −1287.81 −0.878956
\(130\) 1038.46 0.700604
\(131\) −2457.12 −1.63877 −0.819387 0.573241i \(-0.805686\pi\)
−0.819387 + 0.573241i \(0.805686\pi\)
\(132\) 117.437 0.0774362
\(133\) 0 0
\(134\) −1191.52 −0.768146
\(135\) −155.755 −0.0992982
\(136\) 2694.32 1.69880
\(137\) −2482.17 −1.54793 −0.773965 0.633229i \(-0.781729\pi\)
−0.773965 + 0.633229i \(0.781729\pi\)
\(138\) 935.626 0.577143
\(139\) −2407.17 −1.46887 −0.734437 0.678676i \(-0.762554\pi\)
−0.734437 + 0.678676i \(0.762554\pi\)
\(140\) 0 0
\(141\) 859.119 0.513127
\(142\) 565.274 0.334062
\(143\) 939.609 0.549469
\(144\) −205.795 −0.119094
\(145\) 853.136 0.488614
\(146\) −2304.23 −1.30616
\(147\) 0 0
\(148\) −228.051 −0.126660
\(149\) 479.527 0.263653 0.131827 0.991273i \(-0.457916\pi\)
0.131827 + 0.991273i \(0.457916\pi\)
\(150\) 579.896 0.315656
\(151\) −1689.99 −0.910790 −0.455395 0.890290i \(-0.650502\pi\)
−0.455395 + 0.890290i \(0.650502\pi\)
\(152\) −104.313 −0.0556638
\(153\) −995.470 −0.526006
\(154\) 0 0
\(155\) −685.979 −0.355478
\(156\) 911.940 0.468036
\(157\) 616.721 0.313501 0.156751 0.987638i \(-0.449898\pi\)
0.156751 + 0.987638i \(0.449898\pi\)
\(158\) 1559.70 0.785338
\(159\) −342.859 −0.171009
\(160\) 846.183 0.418104
\(161\) 0 0
\(162\) 170.703 0.0827881
\(163\) −1537.73 −0.738924 −0.369462 0.929246i \(-0.620458\pi\)
−0.369462 + 0.929246i \(0.620458\pi\)
\(164\) −1742.12 −0.829493
\(165\) −190.367 −0.0898186
\(166\) −2210.05 −1.03333
\(167\) −1269.76 −0.588364 −0.294182 0.955749i \(-0.595047\pi\)
−0.294182 + 0.955749i \(0.595047\pi\)
\(168\) 0 0
\(169\) 5099.40 2.32107
\(170\) −1344.68 −0.606660
\(171\) 38.5404 0.0172354
\(172\) −1527.64 −0.677218
\(173\) −3662.80 −1.60970 −0.804848 0.593481i \(-0.797753\pi\)
−0.804848 + 0.593481i \(0.797753\pi\)
\(174\) −935.011 −0.407374
\(175\) 0 0
\(176\) −251.527 −0.107725
\(177\) −1943.08 −0.825145
\(178\) 861.082 0.362589
\(179\) 3824.53 1.59698 0.798488 0.602010i \(-0.205633\pi\)
0.798488 + 0.602010i \(0.205633\pi\)
\(180\) −184.761 −0.0765073
\(181\) 3440.55 1.41290 0.706449 0.707764i \(-0.250296\pi\)
0.706449 + 0.707764i \(0.250296\pi\)
\(182\) 0 0
\(183\) 1835.58 0.741474
\(184\) 3604.87 1.44432
\(185\) 369.674 0.146913
\(186\) 751.812 0.296374
\(187\) −1216.69 −0.475791
\(188\) 1019.11 0.395354
\(189\) 0 0
\(190\) 52.0604 0.0198782
\(191\) 3216.00 1.21833 0.609167 0.793042i \(-0.291504\pi\)
0.609167 + 0.793042i \(0.291504\pi\)
\(192\) −1476.18 −0.554864
\(193\) 4943.91 1.84389 0.921944 0.387323i \(-0.126600\pi\)
0.921944 + 0.387323i \(0.126600\pi\)
\(194\) −1418.26 −0.524872
\(195\) −1478.27 −0.542877
\(196\) 0 0
\(197\) 3137.73 1.13479 0.567396 0.823445i \(-0.307951\pi\)
0.567396 + 0.823445i \(0.307951\pi\)
\(198\) 208.637 0.0748846
\(199\) −3334.84 −1.18794 −0.593971 0.804487i \(-0.702440\pi\)
−0.593971 + 0.804487i \(0.702440\pi\)
\(200\) 2234.28 0.789938
\(201\) 1696.16 0.595213
\(202\) −1992.17 −0.693903
\(203\) 0 0
\(204\) −1180.86 −0.405277
\(205\) 2824.01 0.962133
\(206\) −2803.03 −0.948039
\(207\) −1331.89 −0.447211
\(208\) −1953.20 −0.651106
\(209\) 47.1050 0.0155900
\(210\) 0 0
\(211\) −4319.61 −1.40936 −0.704679 0.709527i \(-0.748909\pi\)
−0.704679 + 0.709527i \(0.748909\pi\)
\(212\) −406.710 −0.131759
\(213\) −804.683 −0.258854
\(214\) −2541.60 −0.811870
\(215\) 2476.33 0.785509
\(216\) 657.700 0.207180
\(217\) 0 0
\(218\) −721.147 −0.224047
\(219\) 3280.13 1.01210
\(220\) −225.820 −0.0692034
\(221\) −9448.00 −2.87575
\(222\) −405.151 −0.122486
\(223\) −3600.93 −1.08133 −0.540663 0.841239i \(-0.681827\pi\)
−0.540663 + 0.841239i \(0.681827\pi\)
\(224\) 0 0
\(225\) −825.499 −0.244592
\(226\) −412.565 −0.121431
\(227\) 5607.44 1.63955 0.819777 0.572683i \(-0.194098\pi\)
0.819777 + 0.572683i \(0.194098\pi\)
\(228\) 45.7179 0.0132796
\(229\) −1065.22 −0.307387 −0.153694 0.988119i \(-0.549117\pi\)
−0.153694 + 0.988119i \(0.549117\pi\)
\(230\) −1799.12 −0.515783
\(231\) 0 0
\(232\) −3602.50 −1.01947
\(233\) −302.118 −0.0849460 −0.0424730 0.999098i \(-0.513524\pi\)
−0.0424730 + 0.999098i \(0.513524\pi\)
\(234\) 1620.14 0.452614
\(235\) −1652.00 −0.458573
\(236\) −2304.94 −0.635758
\(237\) −2220.28 −0.608535
\(238\) 0 0
\(239\) −1334.68 −0.361226 −0.180613 0.983554i \(-0.557808\pi\)
−0.180613 + 0.983554i \(0.557808\pi\)
\(240\) 395.724 0.106433
\(241\) −68.8153 −0.0183933 −0.00919664 0.999958i \(-0.502927\pi\)
−0.00919664 + 0.999958i \(0.502927\pi\)
\(242\) 255.000 0.0677357
\(243\) −243.000 −0.0641500
\(244\) 2177.42 0.571291
\(245\) 0 0
\(246\) −3095.02 −0.802161
\(247\) 365.787 0.0942286
\(248\) 2896.66 0.741685
\(249\) 3146.07 0.800699
\(250\) −2634.73 −0.666540
\(251\) −1498.07 −0.376723 −0.188361 0.982100i \(-0.560318\pi\)
−0.188361 + 0.982100i \(0.560318\pi\)
\(252\) 0 0
\(253\) −1627.86 −0.404518
\(254\) −3866.68 −0.955185
\(255\) 1914.19 0.470083
\(256\) −4224.13 −1.03128
\(257\) 4779.99 1.16019 0.580093 0.814550i \(-0.303016\pi\)
0.580093 + 0.814550i \(0.303016\pi\)
\(258\) −2713.98 −0.654904
\(259\) 0 0
\(260\) −1753.57 −0.418276
\(261\) 1331.01 0.315662
\(262\) −5178.23 −1.22104
\(263\) −2849.38 −0.668062 −0.334031 0.942562i \(-0.608409\pi\)
−0.334031 + 0.942562i \(0.608409\pi\)
\(264\) 803.856 0.187401
\(265\) 659.283 0.152828
\(266\) 0 0
\(267\) −1225.77 −0.280959
\(268\) 2012.04 0.458600
\(269\) 1180.42 0.267552 0.133776 0.991012i \(-0.457290\pi\)
0.133776 + 0.991012i \(0.457290\pi\)
\(270\) −328.244 −0.0739863
\(271\) 152.391 0.0341591 0.0170795 0.999854i \(-0.494563\pi\)
0.0170795 + 0.999854i \(0.494563\pi\)
\(272\) 2529.17 0.563800
\(273\) 0 0
\(274\) −5231.03 −1.15335
\(275\) −1008.94 −0.221242
\(276\) −1579.93 −0.344567
\(277\) −4234.89 −0.918591 −0.459295 0.888284i \(-0.651898\pi\)
−0.459295 + 0.888284i \(0.651898\pi\)
\(278\) −5072.97 −1.09445
\(279\) −1070.23 −0.229651
\(280\) 0 0
\(281\) −5822.22 −1.23603 −0.618015 0.786167i \(-0.712063\pi\)
−0.618015 + 0.786167i \(0.712063\pi\)
\(282\) 1810.54 0.382327
\(283\) 6315.63 1.32659 0.663295 0.748358i \(-0.269157\pi\)
0.663295 + 0.748358i \(0.269157\pi\)
\(284\) −954.541 −0.199442
\(285\) −74.1094 −0.0154030
\(286\) 1980.17 0.409405
\(287\) 0 0
\(288\) 1320.17 0.270109
\(289\) 7321.07 1.49014
\(290\) 1797.93 0.364063
\(291\) 2018.93 0.406708
\(292\) 3890.99 0.779805
\(293\) −6922.09 −1.38018 −0.690090 0.723723i \(-0.742429\pi\)
−0.690090 + 0.723723i \(0.742429\pi\)
\(294\) 0 0
\(295\) 3736.35 0.737419
\(296\) −1561.01 −0.306526
\(297\) −297.000 −0.0580259
\(298\) 1010.57 0.196446
\(299\) −12641.0 −2.44497
\(300\) −979.233 −0.188453
\(301\) 0 0
\(302\) −3561.55 −0.678623
\(303\) 2835.91 0.537685
\(304\) −97.9189 −0.0184738
\(305\) −3529.63 −0.662643
\(306\) −2097.89 −0.391923
\(307\) −3612.36 −0.671557 −0.335779 0.941941i \(-0.608999\pi\)
−0.335779 + 0.941941i \(0.608999\pi\)
\(308\) 0 0
\(309\) 3990.19 0.734608
\(310\) −1445.66 −0.264864
\(311\) 6285.33 1.14601 0.573003 0.819553i \(-0.305778\pi\)
0.573003 + 0.819553i \(0.305778\pi\)
\(312\) 6242.23 1.13268
\(313\) −5706.28 −1.03047 −0.515236 0.857048i \(-0.672296\pi\)
−0.515236 + 0.857048i \(0.672296\pi\)
\(314\) 1299.70 0.233588
\(315\) 0 0
\(316\) −2633.77 −0.468864
\(317\) 2362.98 0.418670 0.209335 0.977844i \(-0.432870\pi\)
0.209335 + 0.977844i \(0.432870\pi\)
\(318\) −722.554 −0.127418
\(319\) 1626.80 0.285527
\(320\) 2838.54 0.495873
\(321\) 3618.04 0.629094
\(322\) 0 0
\(323\) −473.652 −0.0815935
\(324\) −288.254 −0.0494263
\(325\) −7834.81 −1.33722
\(326\) −3240.68 −0.550567
\(327\) 1026.57 0.173607
\(328\) −11924.8 −2.00743
\(329\) 0 0
\(330\) −401.187 −0.0669232
\(331\) 4854.17 0.806071 0.403036 0.915184i \(-0.367955\pi\)
0.403036 + 0.915184i \(0.367955\pi\)
\(332\) 3731.97 0.616922
\(333\) 576.744 0.0949111
\(334\) −2675.94 −0.438386
\(335\) −3261.55 −0.531932
\(336\) 0 0
\(337\) −3193.93 −0.516274 −0.258137 0.966108i \(-0.583109\pi\)
−0.258137 + 0.966108i \(0.583109\pi\)
\(338\) 10746.7 1.72942
\(339\) 587.297 0.0940933
\(340\) 2270.67 0.362190
\(341\) −1308.05 −0.207727
\(342\) 81.2216 0.0128420
\(343\) 0 0
\(344\) −10456.7 −1.63892
\(345\) 2561.09 0.399665
\(346\) −7719.13 −1.19937
\(347\) −4587.79 −0.709757 −0.354879 0.934912i \(-0.615478\pi\)
−0.354879 + 0.934912i \(0.615478\pi\)
\(348\) 1578.89 0.243211
\(349\) 8739.42 1.34043 0.670215 0.742167i \(-0.266202\pi\)
0.670215 + 0.742167i \(0.266202\pi\)
\(350\) 0 0
\(351\) −2306.31 −0.350717
\(352\) 1613.54 0.244323
\(353\) 928.149 0.139944 0.0699722 0.997549i \(-0.477709\pi\)
0.0699722 + 0.997549i \(0.477709\pi\)
\(354\) −4094.92 −0.614810
\(355\) 1547.33 0.231334
\(356\) −1454.05 −0.216474
\(357\) 0 0
\(358\) 8059.97 1.18990
\(359\) −3416.87 −0.502327 −0.251164 0.967945i \(-0.580813\pi\)
−0.251164 + 0.967945i \(0.580813\pi\)
\(360\) −1264.69 −0.185153
\(361\) −6840.66 −0.997326
\(362\) 7250.76 1.05274
\(363\) −363.000 −0.0524864
\(364\) 0 0
\(365\) −6307.36 −0.904500
\(366\) 3868.37 0.552467
\(367\) −1698.00 −0.241511 −0.120756 0.992682i \(-0.538532\pi\)
−0.120756 + 0.992682i \(0.538532\pi\)
\(368\) 3383.91 0.479343
\(369\) 4405.85 0.621571
\(370\) 779.066 0.109464
\(371\) 0 0
\(372\) −1269.54 −0.176942
\(373\) −9514.36 −1.32074 −0.660369 0.750942i \(-0.729600\pi\)
−0.660369 + 0.750942i \(0.729600\pi\)
\(374\) −2564.09 −0.354508
\(375\) 3750.62 0.516483
\(376\) 6975.84 0.956786
\(377\) 12632.7 1.72577
\(378\) 0 0
\(379\) 6451.06 0.874324 0.437162 0.899383i \(-0.355984\pi\)
0.437162 + 0.899383i \(0.355984\pi\)
\(380\) −87.9109 −0.0118677
\(381\) 5504.32 0.740145
\(382\) 6777.53 0.907772
\(383\) −1223.41 −0.163220 −0.0816102 0.996664i \(-0.526006\pi\)
−0.0816102 + 0.996664i \(0.526006\pi\)
\(384\) 409.487 0.0544181
\(385\) 0 0
\(386\) 10419.0 1.37387
\(387\) 3863.43 0.507466
\(388\) 2394.92 0.313360
\(389\) −1788.28 −0.233084 −0.116542 0.993186i \(-0.537181\pi\)
−0.116542 + 0.993186i \(0.537181\pi\)
\(390\) −3115.37 −0.404494
\(391\) 16368.6 2.11712
\(392\) 0 0
\(393\) 7371.35 0.946147
\(394\) 6612.58 0.845525
\(395\) 4269.38 0.543838
\(396\) −352.311 −0.0447078
\(397\) −12559.0 −1.58770 −0.793848 0.608116i \(-0.791926\pi\)
−0.793848 + 0.608116i \(0.791926\pi\)
\(398\) −7027.97 −0.885126
\(399\) 0 0
\(400\) 2097.33 0.262166
\(401\) 12763.6 1.58949 0.794744 0.606945i \(-0.207605\pi\)
0.794744 + 0.606945i \(0.207605\pi\)
\(402\) 3574.56 0.443489
\(403\) −10157.5 −1.25554
\(404\) 3364.04 0.414276
\(405\) 467.265 0.0573298
\(406\) 0 0
\(407\) 704.910 0.0858503
\(408\) −8082.97 −0.980800
\(409\) −50.6926 −0.00612858 −0.00306429 0.999995i \(-0.500975\pi\)
−0.00306429 + 0.999995i \(0.500975\pi\)
\(410\) 5951.43 0.716878
\(411\) 7446.52 0.893698
\(412\) 4733.29 0.566001
\(413\) 0 0
\(414\) −2806.88 −0.333214
\(415\) −6049.58 −0.715571
\(416\) 12529.7 1.47673
\(417\) 7221.51 0.848055
\(418\) 99.2709 0.0116160
\(419\) −8082.90 −0.942423 −0.471212 0.882020i \(-0.656183\pi\)
−0.471212 + 0.882020i \(0.656183\pi\)
\(420\) 0 0
\(421\) −7170.45 −0.830087 −0.415043 0.909802i \(-0.636234\pi\)
−0.415043 + 0.909802i \(0.636234\pi\)
\(422\) −9103.32 −1.05010
\(423\) −2577.36 −0.296254
\(424\) −2783.93 −0.318867
\(425\) 10145.2 1.15791
\(426\) −1695.82 −0.192871
\(427\) 0 0
\(428\) 4291.83 0.484705
\(429\) −2818.83 −0.317236
\(430\) 5218.72 0.585277
\(431\) 12951.9 1.44750 0.723749 0.690064i \(-0.242417\pi\)
0.723749 + 0.690064i \(0.242417\pi\)
\(432\) 617.385 0.0687592
\(433\) −1540.46 −0.170970 −0.0854848 0.996339i \(-0.527244\pi\)
−0.0854848 + 0.996339i \(0.527244\pi\)
\(434\) 0 0
\(435\) −2559.41 −0.282102
\(436\) 1217.75 0.133761
\(437\) −633.723 −0.0693709
\(438\) 6912.68 0.754111
\(439\) 8172.01 0.888449 0.444224 0.895916i \(-0.353479\pi\)
0.444224 + 0.895916i \(0.353479\pi\)
\(440\) −1545.73 −0.167477
\(441\) 0 0
\(442\) −19911.1 −2.14270
\(443\) 897.352 0.0962403 0.0481202 0.998842i \(-0.484677\pi\)
0.0481202 + 0.998842i \(0.484677\pi\)
\(444\) 684.152 0.0731271
\(445\) 2357.04 0.251089
\(446\) −7588.74 −0.805688
\(447\) −1438.58 −0.152220
\(448\) 0 0
\(449\) 5939.17 0.624247 0.312123 0.950042i \(-0.398960\pi\)
0.312123 + 0.950042i \(0.398960\pi\)
\(450\) −1739.69 −0.182244
\(451\) 5384.93 0.562232
\(452\) 696.671 0.0724970
\(453\) 5069.96 0.525845
\(454\) 11817.3 1.22162
\(455\) 0 0
\(456\) 312.939 0.0321375
\(457\) 15502.6 1.58683 0.793415 0.608681i \(-0.208301\pi\)
0.793415 + 0.608681i \(0.208301\pi\)
\(458\) −2244.88 −0.229032
\(459\) 2986.41 0.303690
\(460\) 3038.05 0.307934
\(461\) −14900.7 −1.50541 −0.752704 0.658360i \(-0.771251\pi\)
−0.752704 + 0.658360i \(0.771251\pi\)
\(462\) 0 0
\(463\) −10739.0 −1.07794 −0.538968 0.842326i \(-0.681186\pi\)
−0.538968 + 0.842326i \(0.681186\pi\)
\(464\) −3381.68 −0.338342
\(465\) 2057.94 0.205236
\(466\) −636.696 −0.0632926
\(467\) 6481.13 0.642208 0.321104 0.947044i \(-0.395946\pi\)
0.321104 + 0.947044i \(0.395946\pi\)
\(468\) −2735.82 −0.270221
\(469\) 0 0
\(470\) −3481.49 −0.341679
\(471\) −1850.16 −0.181000
\(472\) −15777.3 −1.53858
\(473\) 4721.97 0.459020
\(474\) −4679.11 −0.453415
\(475\) −392.779 −0.0379409
\(476\) 0 0
\(477\) 1028.58 0.0987322
\(478\) −2812.75 −0.269147
\(479\) −7621.65 −0.727019 −0.363510 0.931590i \(-0.618422\pi\)
−0.363510 + 0.931590i \(0.618422\pi\)
\(480\) −2538.55 −0.241392
\(481\) 5473.88 0.518893
\(482\) −145.024 −0.0137047
\(483\) 0 0
\(484\) −430.602 −0.0404397
\(485\) −3882.21 −0.363468
\(486\) −512.108 −0.0477977
\(487\) −13860.0 −1.28964 −0.644821 0.764334i \(-0.723068\pi\)
−0.644821 + 0.764334i \(0.723068\pi\)
\(488\) 14904.4 1.38256
\(489\) 4613.20 0.426618
\(490\) 0 0
\(491\) 7830.43 0.719720 0.359860 0.933006i \(-0.382824\pi\)
0.359860 + 0.933006i \(0.382824\pi\)
\(492\) 5226.36 0.478908
\(493\) −16357.8 −1.49436
\(494\) 770.874 0.0702090
\(495\) 571.101 0.0518568
\(496\) 2719.10 0.246152
\(497\) 0 0
\(498\) 6630.15 0.596595
\(499\) −15359.5 −1.37793 −0.688964 0.724796i \(-0.741934\pi\)
−0.688964 + 0.724796i \(0.741934\pi\)
\(500\) 4449.10 0.397940
\(501\) 3809.27 0.339692
\(502\) −3157.09 −0.280693
\(503\) −13468.3 −1.19388 −0.596941 0.802285i \(-0.703617\pi\)
−0.596941 + 0.802285i \(0.703617\pi\)
\(504\) 0 0
\(505\) −5453.17 −0.480520
\(506\) −3430.63 −0.301403
\(507\) −15298.2 −1.34007
\(508\) 6529.40 0.570267
\(509\) −8766.51 −0.763396 −0.381698 0.924287i \(-0.624661\pi\)
−0.381698 + 0.924287i \(0.624661\pi\)
\(510\) 4034.04 0.350255
\(511\) 0 0
\(512\) −7810.13 −0.674145
\(513\) −115.621 −0.00995088
\(514\) 10073.6 0.864446
\(515\) −7672.73 −0.656507
\(516\) 4582.92 0.390992
\(517\) −3150.10 −0.267972
\(518\) 0 0
\(519\) 10988.4 0.929358
\(520\) −12003.2 −1.01226
\(521\) 12751.3 1.07226 0.536128 0.844137i \(-0.319887\pi\)
0.536128 + 0.844137i \(0.319887\pi\)
\(522\) 2805.03 0.235197
\(523\) 7852.32 0.656516 0.328258 0.944588i \(-0.393538\pi\)
0.328258 + 0.944588i \(0.393538\pi\)
\(524\) 8744.14 0.728987
\(525\) 0 0
\(526\) −6004.90 −0.497768
\(527\) 13152.8 1.08718
\(528\) 754.582 0.0621950
\(529\) 9733.36 0.799980
\(530\) 1389.40 0.113871
\(531\) 5829.23 0.476398
\(532\) 0 0
\(533\) 41815.9 3.39822
\(534\) −2583.25 −0.209341
\(535\) −6957.13 −0.562211
\(536\) 13772.4 1.10985
\(537\) −11473.6 −0.922015
\(538\) 2487.66 0.199351
\(539\) 0 0
\(540\) 554.284 0.0441715
\(541\) 17756.0 1.41108 0.705538 0.708673i \(-0.250706\pi\)
0.705538 + 0.708673i \(0.250706\pi\)
\(542\) 321.155 0.0254517
\(543\) −10321.7 −0.815736
\(544\) −16224.5 −1.27871
\(545\) −1974.00 −0.155150
\(546\) 0 0
\(547\) −9567.03 −0.747819 −0.373909 0.927465i \(-0.621983\pi\)
−0.373909 + 0.927465i \(0.621983\pi\)
\(548\) 8833.30 0.688576
\(549\) −5506.73 −0.428090
\(550\) −2126.29 −0.164846
\(551\) 633.307 0.0489651
\(552\) −10814.6 −0.833878
\(553\) 0 0
\(554\) −8924.77 −0.684435
\(555\) −1109.02 −0.0848205
\(556\) 8566.39 0.653410
\(557\) −2398.56 −0.182460 −0.0912300 0.995830i \(-0.529080\pi\)
−0.0912300 + 0.995830i \(0.529080\pi\)
\(558\) −2255.44 −0.171111
\(559\) 36667.8 2.77439
\(560\) 0 0
\(561\) 3650.06 0.274698
\(562\) −12270.0 −0.920956
\(563\) −8589.23 −0.642971 −0.321486 0.946914i \(-0.604182\pi\)
−0.321486 + 0.946914i \(0.604182\pi\)
\(564\) −3057.34 −0.228258
\(565\) −1129.31 −0.0840896
\(566\) 13309.8 0.988433
\(567\) 0 0
\(568\) −6533.83 −0.482664
\(569\) −15503.5 −1.14225 −0.571124 0.820864i \(-0.693493\pi\)
−0.571124 + 0.820864i \(0.693493\pi\)
\(570\) −156.181 −0.0114767
\(571\) −3997.92 −0.293008 −0.146504 0.989210i \(-0.546802\pi\)
−0.146504 + 0.989210i \(0.546802\pi\)
\(572\) −3343.78 −0.244424
\(573\) −9648.01 −0.703405
\(574\) 0 0
\(575\) 13573.7 0.984459
\(576\) 4428.53 0.320351
\(577\) −2211.13 −0.159533 −0.0797663 0.996814i \(-0.525417\pi\)
−0.0797663 + 0.996814i \(0.525417\pi\)
\(578\) 15428.7 1.11029
\(579\) −14831.7 −1.06457
\(580\) −3036.05 −0.217354
\(581\) 0 0
\(582\) 4254.78 0.303035
\(583\) 1257.15 0.0893066
\(584\) 26633.8 1.88718
\(585\) 4434.81 0.313430
\(586\) −14587.9 −1.02836
\(587\) 4858.47 0.341619 0.170810 0.985304i \(-0.445362\pi\)
0.170810 + 0.985304i \(0.445362\pi\)
\(588\) 0 0
\(589\) −509.221 −0.0356233
\(590\) 7874.13 0.549445
\(591\) −9413.19 −0.655173
\(592\) −1465.32 −0.101730
\(593\) 14415.7 0.998281 0.499141 0.866521i \(-0.333649\pi\)
0.499141 + 0.866521i \(0.333649\pi\)
\(594\) −625.910 −0.0432347
\(595\) 0 0
\(596\) −1706.49 −0.117283
\(597\) 10004.5 0.685858
\(598\) −26640.1 −1.82173
\(599\) −16321.2 −1.11330 −0.556648 0.830748i \(-0.687913\pi\)
−0.556648 + 0.830748i \(0.687913\pi\)
\(600\) −6702.85 −0.456071
\(601\) 5726.01 0.388634 0.194317 0.980939i \(-0.437751\pi\)
0.194317 + 0.980939i \(0.437751\pi\)
\(602\) 0 0
\(603\) −5088.48 −0.343647
\(604\) 6014.15 0.405153
\(605\) 698.013 0.0469062
\(606\) 5976.50 0.400625
\(607\) 11825.4 0.790740 0.395370 0.918522i \(-0.370616\pi\)
0.395370 + 0.918522i \(0.370616\pi\)
\(608\) 628.145 0.0418991
\(609\) 0 0
\(610\) −7438.49 −0.493730
\(611\) −24461.7 −1.61966
\(612\) 3542.57 0.233987
\(613\) 21445.0 1.41298 0.706488 0.707725i \(-0.250278\pi\)
0.706488 + 0.707725i \(0.250278\pi\)
\(614\) −7612.82 −0.500372
\(615\) −8472.02 −0.555488
\(616\) 0 0
\(617\) 6816.87 0.444792 0.222396 0.974956i \(-0.428612\pi\)
0.222396 + 0.974956i \(0.428612\pi\)
\(618\) 8409.08 0.547351
\(619\) −768.817 −0.0499214 −0.0249607 0.999688i \(-0.507946\pi\)
−0.0249607 + 0.999688i \(0.507946\pi\)
\(620\) 2441.19 0.158130
\(621\) 3995.67 0.258197
\(622\) 13245.9 0.853881
\(623\) 0 0
\(624\) 5859.60 0.375916
\(625\) 4253.20 0.272205
\(626\) −12025.6 −0.767797
\(627\) −141.315 −0.00900091
\(628\) −2194.72 −0.139457
\(629\) −7088.04 −0.449314
\(630\) 0 0
\(631\) 14314.5 0.903092 0.451546 0.892248i \(-0.350873\pi\)
0.451546 + 0.892248i \(0.350873\pi\)
\(632\) −18028.1 −1.13468
\(633\) 12958.8 0.813693
\(634\) 4979.85 0.311948
\(635\) −10584.3 −0.661455
\(636\) 1220.13 0.0760712
\(637\) 0 0
\(638\) 3428.37 0.212744
\(639\) 2414.05 0.149450
\(640\) −787.402 −0.0486325
\(641\) 5745.30 0.354018 0.177009 0.984209i \(-0.443358\pi\)
0.177009 + 0.984209i \(0.443358\pi\)
\(642\) 7624.80 0.468734
\(643\) 754.948 0.0463021 0.0231510 0.999732i \(-0.492630\pi\)
0.0231510 + 0.999732i \(0.492630\pi\)
\(644\) 0 0
\(645\) −7428.99 −0.453514
\(646\) −998.194 −0.0607947
\(647\) 17460.5 1.06097 0.530483 0.847696i \(-0.322011\pi\)
0.530483 + 0.847696i \(0.322011\pi\)
\(648\) −1973.10 −0.119615
\(649\) 7124.62 0.430918
\(650\) −16511.4 −0.996354
\(651\) 0 0
\(652\) 5472.33 0.328701
\(653\) −7577.92 −0.454130 −0.227065 0.973880i \(-0.572913\pi\)
−0.227065 + 0.973880i \(0.572913\pi\)
\(654\) 2163.44 0.129354
\(655\) −14174.4 −0.845556
\(656\) −11193.9 −0.666230
\(657\) −9840.39 −0.584338
\(658\) 0 0
\(659\) −5011.73 −0.296251 −0.148125 0.988969i \(-0.547324\pi\)
−0.148125 + 0.988969i \(0.547324\pi\)
\(660\) 677.459 0.0399546
\(661\) −10691.2 −0.629109 −0.314555 0.949239i \(-0.601855\pi\)
−0.314555 + 0.949239i \(0.601855\pi\)
\(662\) 10229.9 0.600598
\(663\) 28344.0 1.66032
\(664\) 25545.3 1.49300
\(665\) 0 0
\(666\) 1215.45 0.0707175
\(667\) −21886.0 −1.27051
\(668\) 4518.68 0.261726
\(669\) 10802.8 0.624304
\(670\) −6873.51 −0.396339
\(671\) −6730.45 −0.387222
\(672\) 0 0
\(673\) 27560.7 1.57858 0.789292 0.614018i \(-0.210448\pi\)
0.789292 + 0.614018i \(0.210448\pi\)
\(674\) −6731.01 −0.384672
\(675\) 2476.50 0.141215
\(676\) −18147.2 −1.03250
\(677\) 1643.64 0.0933093 0.0466546 0.998911i \(-0.485144\pi\)
0.0466546 + 0.998911i \(0.485144\pi\)
\(678\) 1237.69 0.0701082
\(679\) 0 0
\(680\) 15542.7 0.876525
\(681\) −16822.3 −0.946596
\(682\) −2756.64 −0.154776
\(683\) 5412.07 0.303202 0.151601 0.988442i \(-0.451557\pi\)
0.151601 + 0.988442i \(0.451557\pi\)
\(684\) −137.154 −0.00766696
\(685\) −14318.9 −0.798683
\(686\) 0 0
\(687\) 3195.66 0.177470
\(688\) −9815.74 −0.543927
\(689\) 9762.21 0.539783
\(690\) 5397.35 0.297788
\(691\) −8125.61 −0.447341 −0.223671 0.974665i \(-0.571804\pi\)
−0.223671 + 0.974665i \(0.571804\pi\)
\(692\) 13034.8 0.716052
\(693\) 0 0
\(694\) −9668.50 −0.528835
\(695\) −13886.3 −0.757893
\(696\) 10807.5 0.588588
\(697\) −54146.8 −2.94255
\(698\) 18417.8 0.998745
\(699\) 906.354 0.0490436
\(700\) 0 0
\(701\) 21532.4 1.16015 0.580076 0.814563i \(-0.303023\pi\)
0.580076 + 0.814563i \(0.303023\pi\)
\(702\) −4860.42 −0.261317
\(703\) 274.419 0.0147225
\(704\) 5412.65 0.289768
\(705\) 4956.00 0.264757
\(706\) 1956.02 0.104272
\(707\) 0 0
\(708\) 6914.82 0.367055
\(709\) −19128.1 −1.01322 −0.506608 0.862177i \(-0.669101\pi\)
−0.506608 + 0.862177i \(0.669101\pi\)
\(710\) 3260.90 0.172365
\(711\) 6660.84 0.351338
\(712\) −9952.98 −0.523882
\(713\) 17597.8 0.924324
\(714\) 0 0
\(715\) 5420.32 0.283508
\(716\) −13610.3 −0.710394
\(717\) 4004.03 0.208554
\(718\) −7200.85 −0.374280
\(719\) −14299.8 −0.741714 −0.370857 0.928690i \(-0.620936\pi\)
−0.370857 + 0.928690i \(0.620936\pi\)
\(720\) −1187.17 −0.0614489
\(721\) 0 0
\(722\) −14416.3 −0.743101
\(723\) 206.446 0.0106194
\(724\) −12243.9 −0.628509
\(725\) −13564.8 −0.694876
\(726\) −765.001 −0.0391072
\(727\) 19873.8 1.01387 0.506933 0.861986i \(-0.330779\pi\)
0.506933 + 0.861986i \(0.330779\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −13292.4 −0.673936
\(731\) −47480.6 −2.40237
\(732\) −6532.26 −0.329835
\(733\) 11510.9 0.580036 0.290018 0.957021i \(-0.406339\pi\)
0.290018 + 0.957021i \(0.406339\pi\)
\(734\) −3578.42 −0.179948
\(735\) 0 0
\(736\) −21707.6 −1.08716
\(737\) −6219.25 −0.310840
\(738\) 9285.07 0.463128
\(739\) −35163.8 −1.75037 −0.875183 0.483791i \(-0.839259\pi\)
−0.875183 + 0.483791i \(0.839259\pi\)
\(740\) −1315.56 −0.0653525
\(741\) −1097.36 −0.0544029
\(742\) 0 0
\(743\) 18247.9 0.901010 0.450505 0.892774i \(-0.351244\pi\)
0.450505 + 0.892774i \(0.351244\pi\)
\(744\) −8689.97 −0.428212
\(745\) 2766.25 0.136037
\(746\) −20050.9 −0.984072
\(747\) −9438.20 −0.462284
\(748\) 4329.81 0.211649
\(749\) 0 0
\(750\) 7904.20 0.384827
\(751\) −26563.0 −1.29068 −0.645339 0.763896i \(-0.723284\pi\)
−0.645339 + 0.763896i \(0.723284\pi\)
\(752\) 6548.24 0.317540
\(753\) 4494.21 0.217501
\(754\) 26622.6 1.28586
\(755\) −9749.03 −0.469939
\(756\) 0 0
\(757\) 34226.7 1.64332 0.821659 0.569979i \(-0.193049\pi\)
0.821659 + 0.569979i \(0.193049\pi\)
\(758\) 13595.2 0.651452
\(759\) 4883.59 0.233548
\(760\) −601.750 −0.0287207
\(761\) −5117.70 −0.243780 −0.121890 0.992544i \(-0.538895\pi\)
−0.121890 + 0.992544i \(0.538895\pi\)
\(762\) 11600.0 0.551476
\(763\) 0 0
\(764\) −11444.8 −0.541960
\(765\) −5742.57 −0.271403
\(766\) −2578.27 −0.121614
\(767\) 55325.2 2.60454
\(768\) 12672.4 0.595411
\(769\) −23149.5 −1.08555 −0.542777 0.839877i \(-0.682627\pi\)
−0.542777 + 0.839877i \(0.682627\pi\)
\(770\) 0 0
\(771\) −14340.0 −0.669834
\(772\) −17593.9 −0.820230
\(773\) −16245.4 −0.755893 −0.377946 0.925828i \(-0.623370\pi\)
−0.377946 + 0.925828i \(0.623370\pi\)
\(774\) 8141.95 0.378109
\(775\) 10907.0 0.505538
\(776\) 16393.2 0.758354
\(777\) 0 0
\(778\) −3768.70 −0.173669
\(779\) 2096.34 0.0964174
\(780\) 5260.71 0.241492
\(781\) 2950.51 0.135182
\(782\) 34495.8 1.57745
\(783\) −3993.04 −0.182247
\(784\) 0 0
\(785\) 3557.68 0.161757
\(786\) 15534.7 0.704967
\(787\) −33701.7 −1.52648 −0.763238 0.646118i \(-0.776391\pi\)
−0.763238 + 0.646118i \(0.776391\pi\)
\(788\) −11166.2 −0.504797
\(789\) 8548.14 0.385706
\(790\) 8997.46 0.405209
\(791\) 0 0
\(792\) −2411.57 −0.108196
\(793\) −52264.3 −2.34043
\(794\) −26467.2 −1.18298
\(795\) −1977.85 −0.0882353
\(796\) 11867.7 0.528440
\(797\) 3774.95 0.167774 0.0838868 0.996475i \(-0.473267\pi\)
0.0838868 + 0.996475i \(0.473267\pi\)
\(798\) 0 0
\(799\) 31675.1 1.40248
\(800\) −13454.3 −0.594600
\(801\) 3677.32 0.162212
\(802\) 26898.6 1.18432
\(803\) −12027.1 −0.528554
\(804\) −6036.12 −0.264773
\(805\) 0 0
\(806\) −21406.3 −0.935491
\(807\) −3541.26 −0.154471
\(808\) 23026.9 1.00258
\(809\) 28880.9 1.25513 0.627565 0.778564i \(-0.284052\pi\)
0.627565 + 0.778564i \(0.284052\pi\)
\(810\) 984.733 0.0427160
\(811\) 18559.7 0.803599 0.401800 0.915728i \(-0.368385\pi\)
0.401800 + 0.915728i \(0.368385\pi\)
\(812\) 0 0
\(813\) −457.174 −0.0197217
\(814\) 1485.55 0.0639664
\(815\) −8870.73 −0.381261
\(816\) −7587.51 −0.325510
\(817\) 1838.25 0.0787175
\(818\) −106.832 −0.00456636
\(819\) 0 0
\(820\) −10049.8 −0.427992
\(821\) 13617.9 0.578888 0.289444 0.957195i \(-0.406530\pi\)
0.289444 + 0.957195i \(0.406530\pi\)
\(822\) 15693.1 0.665888
\(823\) −16112.7 −0.682447 −0.341224 0.939982i \(-0.610841\pi\)
−0.341224 + 0.939982i \(0.610841\pi\)
\(824\) 32399.3 1.36976
\(825\) 3026.83 0.127734
\(826\) 0 0
\(827\) −6525.44 −0.274380 −0.137190 0.990545i \(-0.543807\pi\)
−0.137190 + 0.990545i \(0.543807\pi\)
\(828\) 4739.79 0.198936
\(829\) 30051.5 1.25903 0.629513 0.776990i \(-0.283254\pi\)
0.629513 + 0.776990i \(0.283254\pi\)
\(830\) −12749.1 −0.533167
\(831\) 12704.7 0.530349
\(832\) 42031.2 1.75140
\(833\) 0 0
\(834\) 15218.9 0.631880
\(835\) −7324.85 −0.303577
\(836\) −167.632 −0.00693502
\(837\) 3210.68 0.132589
\(838\) −17034.2 −0.702193
\(839\) −4000.67 −0.164623 −0.0823115 0.996607i \(-0.526230\pi\)
−0.0823115 + 0.996607i \(0.526230\pi\)
\(840\) 0 0
\(841\) −2517.40 −0.103219
\(842\) −15111.3 −0.618492
\(843\) 17466.6 0.713622
\(844\) 15372.2 0.626934
\(845\) 29416.9 1.19760
\(846\) −5431.63 −0.220737
\(847\) 0 0
\(848\) −2613.28 −0.105826
\(849\) −18946.9 −0.765908
\(850\) 21380.3 0.862753
\(851\) −9483.45 −0.382008
\(852\) 2863.62 0.115148
\(853\) −9701.56 −0.389420 −0.194710 0.980861i \(-0.562377\pi\)
−0.194710 + 0.980861i \(0.562377\pi\)
\(854\) 0 0
\(855\) 222.328 0.00889294
\(856\) 29377.6 1.17302
\(857\) 39092.4 1.55819 0.779096 0.626905i \(-0.215679\pi\)
0.779096 + 0.626905i \(0.215679\pi\)
\(858\) −5940.51 −0.236370
\(859\) 4035.63 0.160296 0.0801478 0.996783i \(-0.474461\pi\)
0.0801478 + 0.996783i \(0.474461\pi\)
\(860\) −8812.51 −0.349423
\(861\) 0 0
\(862\) 27295.4 1.07852
\(863\) 21186.3 0.835677 0.417839 0.908521i \(-0.362788\pi\)
0.417839 + 0.908521i \(0.362788\pi\)
\(864\) −3960.50 −0.155948
\(865\) −21129.6 −0.830552
\(866\) −3246.43 −0.127388
\(867\) −21963.2 −0.860335
\(868\) 0 0
\(869\) 8141.03 0.317797
\(870\) −5393.80 −0.210192
\(871\) −48294.7 −1.87877
\(872\) 8335.52 0.323711
\(873\) −6056.80 −0.234813
\(874\) −1335.53 −0.0516878
\(875\) 0 0
\(876\) −11673.0 −0.450221
\(877\) −4894.79 −0.188467 −0.0942334 0.995550i \(-0.530040\pi\)
−0.0942334 + 0.995550i \(0.530040\pi\)
\(878\) 17222.0 0.661977
\(879\) 20766.3 0.796847
\(880\) −1450.99 −0.0555827
\(881\) 3971.38 0.151872 0.0759360 0.997113i \(-0.475806\pi\)
0.0759360 + 0.997113i \(0.475806\pi\)
\(882\) 0 0
\(883\) −25172.6 −0.959372 −0.479686 0.877440i \(-0.659250\pi\)
−0.479686 + 0.877440i \(0.659250\pi\)
\(884\) 33622.6 1.27924
\(885\) −11209.0 −0.425749
\(886\) 1891.12 0.0717080
\(887\) −10432.4 −0.394910 −0.197455 0.980312i \(-0.563268\pi\)
−0.197455 + 0.980312i \(0.563268\pi\)
\(888\) 4683.02 0.176973
\(889\) 0 0
\(890\) 4967.32 0.187084
\(891\) 891.000 0.0335013
\(892\) 12814.6 0.481014
\(893\) −1226.33 −0.0459546
\(894\) −3031.72 −0.113418
\(895\) 22062.6 0.823989
\(896\) 0 0
\(897\) 37922.9 1.41160
\(898\) 12516.4 0.465122
\(899\) −17586.2 −0.652429
\(900\) 2937.70 0.108804
\(901\) −12640.9 −0.467404
\(902\) 11348.4 0.418915
\(903\) 0 0
\(904\) 4768.71 0.175448
\(905\) 19847.5 0.729010
\(906\) 10684.6 0.391803
\(907\) 30122.0 1.10274 0.551370 0.834261i \(-0.314105\pi\)
0.551370 + 0.834261i \(0.314105\pi\)
\(908\) −19955.2 −0.729334
\(909\) −8507.72 −0.310433
\(910\) 0 0
\(911\) 1905.80 0.0693105 0.0346552 0.999399i \(-0.488967\pi\)
0.0346552 + 0.999399i \(0.488967\pi\)
\(912\) 293.757 0.0106658
\(913\) −11535.6 −0.418151
\(914\) 32670.8 1.18234
\(915\) 10588.9 0.382577
\(916\) 3790.79 0.136737
\(917\) 0 0
\(918\) 6293.68 0.226277
\(919\) 21121.7 0.758149 0.379075 0.925366i \(-0.376242\pi\)
0.379075 + 0.925366i \(0.376242\pi\)
\(920\) 20795.4 0.745223
\(921\) 10837.1 0.387724
\(922\) −31402.2 −1.12167
\(923\) 22911.7 0.817063
\(924\) 0 0
\(925\) −5877.80 −0.208931
\(926\) −22631.8 −0.803162
\(927\) −11970.6 −0.424126
\(928\) 21693.3 0.767369
\(929\) 3893.68 0.137511 0.0687555 0.997634i \(-0.478097\pi\)
0.0687555 + 0.997634i \(0.478097\pi\)
\(930\) 4336.98 0.152920
\(931\) 0 0
\(932\) 1075.15 0.0377871
\(933\) −18856.0 −0.661647
\(934\) 13658.6 0.478504
\(935\) −7018.69 −0.245493
\(936\) −18726.7 −0.653954
\(937\) −15347.1 −0.535076 −0.267538 0.963547i \(-0.586210\pi\)
−0.267538 + 0.963547i \(0.586210\pi\)
\(938\) 0 0
\(939\) 17118.8 0.594943
\(940\) 5878.97 0.203990
\(941\) 14752.2 0.511059 0.255530 0.966801i \(-0.417750\pi\)
0.255530 + 0.966801i \(0.417750\pi\)
\(942\) −3899.11 −0.134862
\(943\) −72445.8 −2.50176
\(944\) −14810.2 −0.510627
\(945\) 0 0
\(946\) 9951.27 0.342012
\(947\) 32652.6 1.12045 0.560225 0.828341i \(-0.310715\pi\)
0.560225 + 0.828341i \(0.310715\pi\)
\(948\) 7901.30 0.270699
\(949\) −93395.1 −3.19466
\(950\) −827.757 −0.0282695
\(951\) −7088.95 −0.241719
\(952\) 0 0
\(953\) 6951.66 0.236292 0.118146 0.992996i \(-0.462305\pi\)
0.118146 + 0.992996i \(0.462305\pi\)
\(954\) 2167.66 0.0735646
\(955\) 18552.2 0.628622
\(956\) 4749.70 0.160687
\(957\) −4880.39 −0.164849
\(958\) −16062.2 −0.541697
\(959\) 0 0
\(960\) −8515.63 −0.286292
\(961\) −15650.5 −0.525343
\(962\) 11535.9 0.386623
\(963\) −10854.1 −0.363208
\(964\) 244.893 0.00818201
\(965\) 28519.9 0.951388
\(966\) 0 0
\(967\) 20176.9 0.670990 0.335495 0.942042i \(-0.391097\pi\)
0.335495 + 0.942042i \(0.391097\pi\)
\(968\) −2947.47 −0.0978670
\(969\) 1420.96 0.0471080
\(970\) −8181.52 −0.270817
\(971\) 47848.1 1.58138 0.790690 0.612217i \(-0.209722\pi\)
0.790690 + 0.612217i \(0.209722\pi\)
\(972\) 864.763 0.0285363
\(973\) 0 0
\(974\) −29209.1 −0.960902
\(975\) 23504.4 0.772045
\(976\) 13990.8 0.458848
\(977\) −1445.48 −0.0473338 −0.0236669 0.999720i \(-0.507534\pi\)
−0.0236669 + 0.999720i \(0.507534\pi\)
\(978\) 9722.04 0.317870
\(979\) 4494.50 0.146726
\(980\) 0 0
\(981\) −3079.72 −0.100232
\(982\) 16502.2 0.536258
\(983\) −45902.2 −1.48937 −0.744687 0.667414i \(-0.767401\pi\)
−0.744687 + 0.667414i \(0.767401\pi\)
\(984\) 35774.5 1.15899
\(985\) 18100.6 0.585517
\(986\) −34473.2 −1.11344
\(987\) 0 0
\(988\) −1301.72 −0.0419164
\(989\) −63526.7 −2.04250
\(990\) 1203.56 0.0386381
\(991\) 33011.4 1.05817 0.529083 0.848570i \(-0.322536\pi\)
0.529083 + 0.848570i \(0.322536\pi\)
\(992\) −17442.9 −0.558279
\(993\) −14562.5 −0.465385
\(994\) 0 0
\(995\) −19237.7 −0.612940
\(996\) −11195.9 −0.356180
\(997\) 37302.2 1.18493 0.592463 0.805597i \(-0.298155\pi\)
0.592463 + 0.805597i \(0.298155\pi\)
\(998\) −32369.2 −1.02668
\(999\) −1730.23 −0.0547969
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.1.10 16
7.6 odd 2 1617.4.a.bf.1.10 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1617.4.a.be.1.10 16 1.1 even 1 trivial
1617.4.a.bf.1.10 yes 16 7.6 odd 2