Properties

Label 1617.4.a.be.1.15
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 1.15
Root \(5.23364\) 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)
 
\(f(q)\) \(=\) \(q+5.23364 q^{2} -3.00000 q^{3} +19.3910 q^{4} -10.0477 q^{5} -15.7009 q^{6} +59.6162 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.23364 q^{2} -3.00000 q^{3} +19.3910 q^{4} -10.0477 q^{5} -15.7009 q^{6} +59.6162 q^{8} +9.00000 q^{9} -52.5859 q^{10} +11.0000 q^{11} -58.1729 q^{12} -14.5278 q^{13} +30.1430 q^{15} +156.882 q^{16} -83.6725 q^{17} +47.1027 q^{18} -31.1140 q^{19} -194.834 q^{20} +57.5700 q^{22} +64.0037 q^{23} -178.849 q^{24} -24.0443 q^{25} -76.0331 q^{26} -27.0000 q^{27} -245.493 q^{29} +157.758 q^{30} +126.423 q^{31} +344.134 q^{32} -33.0000 q^{33} -437.912 q^{34} +174.519 q^{36} -237.016 q^{37} -162.839 q^{38} +43.5833 q^{39} -599.004 q^{40} +325.514 q^{41} -164.169 q^{43} +213.301 q^{44} -90.4290 q^{45} +334.972 q^{46} -74.3576 q^{47} -470.646 q^{48} -125.839 q^{50} +251.018 q^{51} -281.707 q^{52} -255.640 q^{53} -141.308 q^{54} -110.524 q^{55} +93.3419 q^{57} -1284.82 q^{58} -50.3681 q^{59} +584.502 q^{60} -68.5090 q^{61} +661.654 q^{62} +546.017 q^{64} +145.970 q^{65} -172.710 q^{66} +633.216 q^{67} -1622.49 q^{68} -192.011 q^{69} +451.839 q^{71} +536.546 q^{72} -1132.91 q^{73} -1240.46 q^{74} +72.1329 q^{75} -603.330 q^{76} +228.099 q^{78} -814.108 q^{79} -1576.30 q^{80} +81.0000 q^{81} +1703.62 q^{82} -265.403 q^{83} +840.714 q^{85} -859.200 q^{86} +736.479 q^{87} +655.779 q^{88} -1144.84 q^{89} -473.273 q^{90} +1241.09 q^{92} -379.270 q^{93} -389.161 q^{94} +312.623 q^{95} -1032.40 q^{96} -1087.06 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 48 q^{3} + 72 q^{4} - 40 q^{5} - 12 q^{6} + 66 q^{8} + 144 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.23364 1.85037 0.925185 0.379516i \(-0.123909\pi\)
0.925185 + 0.379516i \(0.123909\pi\)
\(3\) −3.00000 −0.577350
\(4\) 19.3910 2.42387
\(5\) −10.0477 −0.898691 −0.449346 0.893358i \(-0.648343\pi\)
−0.449346 + 0.893358i \(0.648343\pi\)
\(6\) −15.7009 −1.06831
\(7\) 0 0
\(8\) 59.6162 2.63469
\(9\) 9.00000 0.333333
\(10\) −52.5859 −1.66291
\(11\) 11.0000 0.301511
\(12\) −58.1729 −1.39942
\(13\) −14.5278 −0.309944 −0.154972 0.987919i \(-0.549529\pi\)
−0.154972 + 0.987919i \(0.549529\pi\)
\(14\) 0 0
\(15\) 30.1430 0.518860
\(16\) 156.882 2.45128
\(17\) −83.6725 −1.19374 −0.596870 0.802338i \(-0.703589\pi\)
−0.596870 + 0.802338i \(0.703589\pi\)
\(18\) 47.1027 0.616790
\(19\) −31.1140 −0.375686 −0.187843 0.982199i \(-0.560150\pi\)
−0.187843 + 0.982199i \(0.560150\pi\)
\(20\) −194.834 −2.17831
\(21\) 0 0
\(22\) 57.5700 0.557908
\(23\) 64.0037 0.580247 0.290124 0.956989i \(-0.406304\pi\)
0.290124 + 0.956989i \(0.406304\pi\)
\(24\) −178.849 −1.52114
\(25\) −24.0443 −0.192354
\(26\) −76.0331 −0.573512
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −245.493 −1.57196 −0.785981 0.618251i \(-0.787842\pi\)
−0.785981 + 0.618251i \(0.787842\pi\)
\(30\) 157.758 0.960083
\(31\) 126.423 0.732461 0.366231 0.930524i \(-0.380648\pi\)
0.366231 + 0.930524i \(0.380648\pi\)
\(32\) 344.134 1.90109
\(33\) −33.0000 −0.174078
\(34\) −437.912 −2.20886
\(35\) 0 0
\(36\) 174.519 0.807957
\(37\) −237.016 −1.05311 −0.526557 0.850140i \(-0.676517\pi\)
−0.526557 + 0.850140i \(0.676517\pi\)
\(38\) −162.839 −0.695158
\(39\) 43.5833 0.178946
\(40\) −599.004 −2.36777
\(41\) 325.514 1.23992 0.619959 0.784634i \(-0.287149\pi\)
0.619959 + 0.784634i \(0.287149\pi\)
\(42\) 0 0
\(43\) −164.169 −0.582221 −0.291110 0.956689i \(-0.594025\pi\)
−0.291110 + 0.956689i \(0.594025\pi\)
\(44\) 213.301 0.730825
\(45\) −90.4290 −0.299564
\(46\) 334.972 1.07367
\(47\) −74.3576 −0.230770 −0.115385 0.993321i \(-0.536810\pi\)
−0.115385 + 0.993321i \(0.536810\pi\)
\(48\) −470.646 −1.41525
\(49\) 0 0
\(50\) −125.839 −0.355927
\(51\) 251.018 0.689206
\(52\) −281.707 −0.751265
\(53\) −255.640 −0.662545 −0.331273 0.943535i \(-0.607478\pi\)
−0.331273 + 0.943535i \(0.607478\pi\)
\(54\) −141.308 −0.356104
\(55\) −110.524 −0.270966
\(56\) 0 0
\(57\) 93.3419 0.216902
\(58\) −1284.82 −2.90871
\(59\) −50.3681 −0.111142 −0.0555709 0.998455i \(-0.517698\pi\)
−0.0555709 + 0.998455i \(0.517698\pi\)
\(60\) 584.502 1.25765
\(61\) −68.5090 −0.143798 −0.0718990 0.997412i \(-0.522906\pi\)
−0.0718990 + 0.997412i \(0.522906\pi\)
\(62\) 661.654 1.35532
\(63\) 0 0
\(64\) 546.017 1.06644
\(65\) 145.970 0.278544
\(66\) −172.710 −0.322108
\(67\) 633.216 1.15462 0.577311 0.816525i \(-0.304102\pi\)
0.577311 + 0.816525i \(0.304102\pi\)
\(68\) −1622.49 −2.89347
\(69\) −192.011 −0.335006
\(70\) 0 0
\(71\) 451.839 0.755260 0.377630 0.925957i \(-0.376739\pi\)
0.377630 + 0.925957i \(0.376739\pi\)
\(72\) 536.546 0.878230
\(73\) −1132.91 −1.81639 −0.908195 0.418546i \(-0.862540\pi\)
−0.908195 + 0.418546i \(0.862540\pi\)
\(74\) −1240.46 −1.94865
\(75\) 72.1329 0.111056
\(76\) −603.330 −0.910614
\(77\) 0 0
\(78\) 228.099 0.331117
\(79\) −814.108 −1.15942 −0.579711 0.814822i \(-0.696834\pi\)
−0.579711 + 0.814822i \(0.696834\pi\)
\(80\) −1576.30 −2.20295
\(81\) 81.0000 0.111111
\(82\) 1703.62 2.29431
\(83\) −265.403 −0.350986 −0.175493 0.984481i \(-0.556152\pi\)
−0.175493 + 0.984481i \(0.556152\pi\)
\(84\) 0 0
\(85\) 840.714 1.07280
\(86\) −859.200 −1.07732
\(87\) 736.479 0.907573
\(88\) 655.779 0.794389
\(89\) −1144.84 −1.36351 −0.681755 0.731580i \(-0.738783\pi\)
−0.681755 + 0.731580i \(0.738783\pi\)
\(90\) −473.273 −0.554304
\(91\) 0 0
\(92\) 1241.09 1.40645
\(93\) −379.270 −0.422887
\(94\) −389.161 −0.427009
\(95\) 312.623 0.337626
\(96\) −1032.40 −1.09759
\(97\) −1087.06 −1.13787 −0.568937 0.822381i \(-0.692645\pi\)
−0.568937 + 0.822381i \(0.692645\pi\)
\(98\) 0 0
\(99\) 99.0000 0.100504
\(100\) −466.242 −0.466242
\(101\) −1440.70 −1.41935 −0.709676 0.704528i \(-0.751159\pi\)
−0.709676 + 0.704528i \(0.751159\pi\)
\(102\) 1313.74 1.27529
\(103\) 823.835 0.788105 0.394053 0.919088i \(-0.371073\pi\)
0.394053 + 0.919088i \(0.371073\pi\)
\(104\) −866.090 −0.816607
\(105\) 0 0
\(106\) −1337.93 −1.22595
\(107\) −1905.26 −1.72139 −0.860693 0.509125i \(-0.829969\pi\)
−0.860693 + 0.509125i \(0.829969\pi\)
\(108\) −523.556 −0.466474
\(109\) 206.963 0.181867 0.0909333 0.995857i \(-0.471015\pi\)
0.0909333 + 0.995857i \(0.471015\pi\)
\(110\) −578.445 −0.501387
\(111\) 711.048 0.608016
\(112\) 0 0
\(113\) −898.382 −0.747899 −0.373950 0.927449i \(-0.621997\pi\)
−0.373950 + 0.927449i \(0.621997\pi\)
\(114\) 488.518 0.401350
\(115\) −643.088 −0.521463
\(116\) −4760.35 −3.81023
\(117\) −130.750 −0.103315
\(118\) −263.608 −0.205654
\(119\) 0 0
\(120\) 1797.01 1.36703
\(121\) 121.000 0.0909091
\(122\) −358.551 −0.266079
\(123\) −976.541 −0.715867
\(124\) 2451.47 1.77539
\(125\) 1497.55 1.07156
\(126\) 0 0
\(127\) 1163.37 0.812853 0.406426 0.913683i \(-0.366775\pi\)
0.406426 + 0.913683i \(0.366775\pi\)
\(128\) 104.583 0.0722178
\(129\) 492.506 0.336145
\(130\) 763.955 0.515410
\(131\) 2504.26 1.67021 0.835106 0.550089i \(-0.185406\pi\)
0.835106 + 0.550089i \(0.185406\pi\)
\(132\) −639.902 −0.421942
\(133\) 0 0
\(134\) 3314.02 2.13648
\(135\) 271.287 0.172953
\(136\) −4988.24 −3.14513
\(137\) −1118.29 −0.697389 −0.348695 0.937236i \(-0.613375\pi\)
−0.348695 + 0.937236i \(0.613375\pi\)
\(138\) −1004.92 −0.619885
\(139\) 84.4969 0.0515607 0.0257803 0.999668i \(-0.491793\pi\)
0.0257803 + 0.999668i \(0.491793\pi\)
\(140\) 0 0
\(141\) 223.073 0.133235
\(142\) 2364.76 1.39751
\(143\) −159.805 −0.0934517
\(144\) 1411.94 0.817094
\(145\) 2466.63 1.41271
\(146\) −5929.22 −3.36100
\(147\) 0 0
\(148\) −4595.97 −2.55261
\(149\) 3303.28 1.81621 0.908106 0.418741i \(-0.137529\pi\)
0.908106 + 0.418741i \(0.137529\pi\)
\(150\) 377.517 0.205494
\(151\) −2874.86 −1.54936 −0.774679 0.632355i \(-0.782089\pi\)
−0.774679 + 0.632355i \(0.782089\pi\)
\(152\) −1854.90 −0.989816
\(153\) −753.053 −0.397913
\(154\) 0 0
\(155\) −1270.26 −0.658256
\(156\) 845.122 0.433743
\(157\) −1555.82 −0.790879 −0.395440 0.918492i \(-0.629408\pi\)
−0.395440 + 0.918492i \(0.629408\pi\)
\(158\) −4260.75 −2.14536
\(159\) 766.921 0.382521
\(160\) −3457.75 −1.70849
\(161\) 0 0
\(162\) 423.925 0.205597
\(163\) 2868.89 1.37858 0.689291 0.724484i \(-0.257922\pi\)
0.689291 + 0.724484i \(0.257922\pi\)
\(164\) 6312.02 3.00540
\(165\) 331.573 0.156442
\(166\) −1389.03 −0.649454
\(167\) 1582.18 0.733130 0.366565 0.930392i \(-0.380534\pi\)
0.366565 + 0.930392i \(0.380534\pi\)
\(168\) 0 0
\(169\) −1985.94 −0.903935
\(170\) 4399.99 1.98508
\(171\) −280.026 −0.125229
\(172\) −3183.39 −1.41123
\(173\) −1386.47 −0.609313 −0.304657 0.952462i \(-0.598542\pi\)
−0.304657 + 0.952462i \(0.598542\pi\)
\(174\) 3854.46 1.67935
\(175\) 0 0
\(176\) 1725.70 0.739089
\(177\) 151.104 0.0641678
\(178\) −5991.66 −2.52300
\(179\) −3403.02 −1.42097 −0.710485 0.703712i \(-0.751525\pi\)
−0.710485 + 0.703712i \(0.751525\pi\)
\(180\) −1753.51 −0.726104
\(181\) 1988.34 0.816530 0.408265 0.912864i \(-0.366134\pi\)
0.408265 + 0.912864i \(0.366134\pi\)
\(182\) 0 0
\(183\) 205.527 0.0830218
\(184\) 3815.66 1.52877
\(185\) 2381.46 0.946424
\(186\) −1984.96 −0.782497
\(187\) −920.398 −0.359926
\(188\) −1441.87 −0.559356
\(189\) 0 0
\(190\) 1636.16 0.624733
\(191\) 2011.73 0.762115 0.381057 0.924551i \(-0.375560\pi\)
0.381057 + 0.924551i \(0.375560\pi\)
\(192\) −1638.05 −0.615709
\(193\) −4722.68 −1.76138 −0.880688 0.473696i \(-0.842919\pi\)
−0.880688 + 0.473696i \(0.842919\pi\)
\(194\) −5689.25 −2.10549
\(195\) −437.911 −0.160818
\(196\) 0 0
\(197\) 635.116 0.229696 0.114848 0.993383i \(-0.463362\pi\)
0.114848 + 0.993383i \(0.463362\pi\)
\(198\) 518.130 0.185969
\(199\) −1392.81 −0.496148 −0.248074 0.968741i \(-0.579798\pi\)
−0.248074 + 0.968741i \(0.579798\pi\)
\(200\) −1433.43 −0.506794
\(201\) −1899.65 −0.666621
\(202\) −7540.08 −2.62633
\(203\) 0 0
\(204\) 4867.47 1.67055
\(205\) −3270.65 −1.11430
\(206\) 4311.65 1.45829
\(207\) 576.033 0.193416
\(208\) −2279.14 −0.759761
\(209\) −342.254 −0.113274
\(210\) 0 0
\(211\) 3894.55 1.27067 0.635337 0.772235i \(-0.280861\pi\)
0.635337 + 0.772235i \(0.280861\pi\)
\(212\) −4957.12 −1.60593
\(213\) −1355.52 −0.436049
\(214\) −9971.43 −3.18520
\(215\) 1649.51 0.523237
\(216\) −1609.64 −0.507046
\(217\) 0 0
\(218\) 1083.17 0.336521
\(219\) 3398.72 1.04869
\(220\) −2143.18 −0.656786
\(221\) 1215.57 0.369993
\(222\) 3721.37 1.12505
\(223\) −3954.10 −1.18738 −0.593691 0.804693i \(-0.702330\pi\)
−0.593691 + 0.804693i \(0.702330\pi\)
\(224\) 0 0
\(225\) −216.399 −0.0641181
\(226\) −4701.80 −1.38389
\(227\) 6399.19 1.87105 0.935527 0.353255i \(-0.114925\pi\)
0.935527 + 0.353255i \(0.114925\pi\)
\(228\) 1809.99 0.525743
\(229\) 3850.88 1.11124 0.555618 0.831437i \(-0.312482\pi\)
0.555618 + 0.831437i \(0.312482\pi\)
\(230\) −3365.69 −0.964900
\(231\) 0 0
\(232\) −14635.4 −4.14163
\(233\) −1802.37 −0.506768 −0.253384 0.967366i \(-0.581544\pi\)
−0.253384 + 0.967366i \(0.581544\pi\)
\(234\) −684.297 −0.191171
\(235\) 747.121 0.207391
\(236\) −976.686 −0.269393
\(237\) 2442.32 0.669392
\(238\) 0 0
\(239\) 2587.11 0.700193 0.350097 0.936714i \(-0.386149\pi\)
0.350097 + 0.936714i \(0.386149\pi\)
\(240\) 4728.90 1.27187
\(241\) −1154.38 −0.308547 −0.154274 0.988028i \(-0.549304\pi\)
−0.154274 + 0.988028i \(0.549304\pi\)
\(242\) 633.270 0.168216
\(243\) −243.000 −0.0641500
\(244\) −1328.46 −0.348548
\(245\) 0 0
\(246\) −5110.86 −1.32462
\(247\) 452.016 0.116442
\(248\) 7536.88 1.92981
\(249\) 796.210 0.202642
\(250\) 7837.63 1.98278
\(251\) 4893.14 1.23049 0.615243 0.788337i \(-0.289058\pi\)
0.615243 + 0.788337i \(0.289058\pi\)
\(252\) 0 0
\(253\) 704.041 0.174951
\(254\) 6088.65 1.50408
\(255\) −2522.14 −0.619383
\(256\) −3820.79 −0.932809
\(257\) −2680.92 −0.650706 −0.325353 0.945593i \(-0.605483\pi\)
−0.325353 + 0.945593i \(0.605483\pi\)
\(258\) 2577.60 0.621993
\(259\) 0 0
\(260\) 2830.50 0.675155
\(261\) −2209.44 −0.523987
\(262\) 13106.4 3.09051
\(263\) 5906.73 1.38488 0.692442 0.721474i \(-0.256535\pi\)
0.692442 + 0.721474i \(0.256535\pi\)
\(264\) −1967.34 −0.458641
\(265\) 2568.59 0.595424
\(266\) 0 0
\(267\) 3434.51 0.787223
\(268\) 12278.7 2.79865
\(269\) 3181.21 0.721047 0.360523 0.932750i \(-0.382598\pi\)
0.360523 + 0.932750i \(0.382598\pi\)
\(270\) 1419.82 0.320028
\(271\) 2254.85 0.505434 0.252717 0.967540i \(-0.418676\pi\)
0.252717 + 0.967540i \(0.418676\pi\)
\(272\) −13126.7 −2.92619
\(273\) 0 0
\(274\) −5852.75 −1.29043
\(275\) −264.487 −0.0579970
\(276\) −3723.28 −0.812012
\(277\) −983.703 −0.213375 −0.106688 0.994293i \(-0.534024\pi\)
−0.106688 + 0.994293i \(0.534024\pi\)
\(278\) 442.226 0.0954063
\(279\) 1137.81 0.244154
\(280\) 0 0
\(281\) 7467.02 1.58521 0.792607 0.609733i \(-0.208723\pi\)
0.792607 + 0.609733i \(0.208723\pi\)
\(282\) 1167.48 0.246534
\(283\) 4340.50 0.911716 0.455858 0.890052i \(-0.349332\pi\)
0.455858 + 0.890052i \(0.349332\pi\)
\(284\) 8761.60 1.83065
\(285\) −937.869 −0.194928
\(286\) −836.364 −0.172920
\(287\) 0 0
\(288\) 3097.21 0.633697
\(289\) 2088.09 0.425013
\(290\) 12909.5 2.61403
\(291\) 3261.17 0.656952
\(292\) −21968.1 −4.40270
\(293\) 4550.78 0.907369 0.453685 0.891162i \(-0.350109\pi\)
0.453685 + 0.891162i \(0.350109\pi\)
\(294\) 0 0
\(295\) 506.082 0.0998822
\(296\) −14130.0 −2.77463
\(297\) −297.000 −0.0580259
\(298\) 17288.2 3.36066
\(299\) −929.830 −0.179844
\(300\) 1398.73 0.269185
\(301\) 0 0
\(302\) −15046.0 −2.86689
\(303\) 4322.09 0.819464
\(304\) −4881.22 −0.920912
\(305\) 688.355 0.129230
\(306\) −3941.21 −0.736287
\(307\) 9500.37 1.76617 0.883086 0.469212i \(-0.155462\pi\)
0.883086 + 0.469212i \(0.155462\pi\)
\(308\) 0 0
\(309\) −2471.50 −0.455013
\(310\) −6648.08 −1.21802
\(311\) −5141.73 −0.937494 −0.468747 0.883333i \(-0.655294\pi\)
−0.468747 + 0.883333i \(0.655294\pi\)
\(312\) 2598.27 0.471468
\(313\) 2108.59 0.380782 0.190391 0.981708i \(-0.439024\pi\)
0.190391 + 0.981708i \(0.439024\pi\)
\(314\) −8142.61 −1.46342
\(315\) 0 0
\(316\) −15786.3 −2.81029
\(317\) −2837.60 −0.502763 −0.251381 0.967888i \(-0.580885\pi\)
−0.251381 + 0.967888i \(0.580885\pi\)
\(318\) 4013.79 0.707805
\(319\) −2700.42 −0.473964
\(320\) −5486.20 −0.958399
\(321\) 5715.77 0.993842
\(322\) 0 0
\(323\) 2603.38 0.448471
\(324\) 1570.67 0.269319
\(325\) 349.310 0.0596191
\(326\) 15014.7 2.55089
\(327\) −620.889 −0.105001
\(328\) 19405.9 3.26680
\(329\) 0 0
\(330\) 1735.33 0.289476
\(331\) 1969.45 0.327042 0.163521 0.986540i \(-0.447715\pi\)
0.163521 + 0.986540i \(0.447715\pi\)
\(332\) −5146.43 −0.850744
\(333\) −2133.15 −0.351038
\(334\) 8280.56 1.35656
\(335\) −6362.34 −1.03765
\(336\) 0 0
\(337\) 5269.67 0.851802 0.425901 0.904770i \(-0.359957\pi\)
0.425901 + 0.904770i \(0.359957\pi\)
\(338\) −10393.7 −1.67261
\(339\) 2695.14 0.431800
\(340\) 16302.3 2.60034
\(341\) 1390.66 0.220845
\(342\) −1465.55 −0.231719
\(343\) 0 0
\(344\) −9787.12 −1.53397
\(345\) 1929.26 0.301067
\(346\) −7256.27 −1.12746
\(347\) −3270.34 −0.505939 −0.252969 0.967474i \(-0.581407\pi\)
−0.252969 + 0.967474i \(0.581407\pi\)
\(348\) 14281.0 2.19984
\(349\) −8167.05 −1.25264 −0.626321 0.779565i \(-0.715440\pi\)
−0.626321 + 0.779565i \(0.715440\pi\)
\(350\) 0 0
\(351\) 392.250 0.0596488
\(352\) 3785.47 0.573200
\(353\) 10063.6 1.51736 0.758682 0.651461i \(-0.225844\pi\)
0.758682 + 0.651461i \(0.225844\pi\)
\(354\) 790.825 0.118734
\(355\) −4539.93 −0.678745
\(356\) −22199.5 −3.30497
\(357\) 0 0
\(358\) −17810.2 −2.62932
\(359\) 9119.05 1.34063 0.670313 0.742078i \(-0.266160\pi\)
0.670313 + 0.742078i \(0.266160\pi\)
\(360\) −5391.04 −0.789258
\(361\) −5890.92 −0.858860
\(362\) 10406.2 1.51088
\(363\) −363.000 −0.0524864
\(364\) 0 0
\(365\) 11383.1 1.63237
\(366\) 1075.65 0.153621
\(367\) −7969.48 −1.13352 −0.566762 0.823881i \(-0.691804\pi\)
−0.566762 + 0.823881i \(0.691804\pi\)
\(368\) 10041.0 1.42235
\(369\) 2929.62 0.413306
\(370\) 12463.7 1.75124
\(371\) 0 0
\(372\) −7354.41 −1.02502
\(373\) 2154.63 0.299096 0.149548 0.988754i \(-0.452218\pi\)
0.149548 + 0.988754i \(0.452218\pi\)
\(374\) −4817.03 −0.665996
\(375\) −4492.64 −0.618664
\(376\) −4432.92 −0.608006
\(377\) 3566.46 0.487221
\(378\) 0 0
\(379\) 1307.69 0.177234 0.0886170 0.996066i \(-0.471755\pi\)
0.0886170 + 0.996066i \(0.471755\pi\)
\(380\) 6062.06 0.818361
\(381\) −3490.11 −0.469301
\(382\) 10528.7 1.41019
\(383\) −5684.39 −0.758378 −0.379189 0.925319i \(-0.623797\pi\)
−0.379189 + 0.925319i \(0.623797\pi\)
\(384\) −313.748 −0.0416950
\(385\) 0 0
\(386\) −24716.8 −3.25920
\(387\) −1477.52 −0.194074
\(388\) −21079.1 −2.75806
\(389\) −7272.79 −0.947930 −0.473965 0.880544i \(-0.657178\pi\)
−0.473965 + 0.880544i \(0.657178\pi\)
\(390\) −2291.87 −0.297572
\(391\) −5355.35 −0.692664
\(392\) 0 0
\(393\) −7512.77 −0.964298
\(394\) 3323.97 0.425023
\(395\) 8179.89 1.04196
\(396\) 1919.71 0.243608
\(397\) 1554.55 0.196525 0.0982626 0.995161i \(-0.468671\pi\)
0.0982626 + 0.995161i \(0.468671\pi\)
\(398\) −7289.44 −0.918057
\(399\) 0 0
\(400\) −3772.12 −0.471515
\(401\) −3230.51 −0.402304 −0.201152 0.979560i \(-0.564468\pi\)
−0.201152 + 0.979560i \(0.564468\pi\)
\(402\) −9942.07 −1.23350
\(403\) −1836.65 −0.227022
\(404\) −27936.5 −3.44033
\(405\) −813.861 −0.0998546
\(406\) 0 0
\(407\) −2607.18 −0.317526
\(408\) 14964.7 1.81584
\(409\) −4687.04 −0.566648 −0.283324 0.959024i \(-0.591437\pi\)
−0.283324 + 0.959024i \(0.591437\pi\)
\(410\) −17117.4 −2.06188
\(411\) 3354.88 0.402638
\(412\) 15975.0 1.91027
\(413\) 0 0
\(414\) 3014.75 0.357891
\(415\) 2666.69 0.315428
\(416\) −4999.50 −0.589232
\(417\) −253.491 −0.0297686
\(418\) −1791.23 −0.209598
\(419\) 7317.66 0.853201 0.426600 0.904440i \(-0.359711\pi\)
0.426600 + 0.904440i \(0.359711\pi\)
\(420\) 0 0
\(421\) 10791.9 1.24932 0.624659 0.780898i \(-0.285238\pi\)
0.624659 + 0.780898i \(0.285238\pi\)
\(422\) 20382.7 2.35122
\(423\) −669.218 −0.0769232
\(424\) −15240.3 −1.74560
\(425\) 2011.85 0.229621
\(426\) −7094.29 −0.806853
\(427\) 0 0
\(428\) −36944.8 −4.17242
\(429\) 479.416 0.0539544
\(430\) 8632.96 0.968182
\(431\) −3977.69 −0.444545 −0.222272 0.974985i \(-0.571347\pi\)
−0.222272 + 0.974985i \(0.571347\pi\)
\(432\) −4235.82 −0.471749
\(433\) −10522.9 −1.16789 −0.583947 0.811792i \(-0.698493\pi\)
−0.583947 + 0.811792i \(0.698493\pi\)
\(434\) 0 0
\(435\) −7399.90 −0.815627
\(436\) 4013.22 0.440821
\(437\) −1991.41 −0.217991
\(438\) 17787.7 1.94047
\(439\) 5949.96 0.646871 0.323435 0.946250i \(-0.395162\pi\)
0.323435 + 0.946250i \(0.395162\pi\)
\(440\) −6589.05 −0.713910
\(441\) 0 0
\(442\) 6361.88 0.684624
\(443\) −16472.8 −1.76670 −0.883351 0.468713i \(-0.844718\pi\)
−0.883351 + 0.468713i \(0.844718\pi\)
\(444\) 13787.9 1.47375
\(445\) 11502.9 1.22537
\(446\) −20694.3 −2.19710
\(447\) −9909.85 −1.04859
\(448\) 0 0
\(449\) −6258.94 −0.657857 −0.328928 0.944355i \(-0.606687\pi\)
−0.328928 + 0.944355i \(0.606687\pi\)
\(450\) −1132.55 −0.118642
\(451\) 3580.65 0.373850
\(452\) −17420.5 −1.81281
\(453\) 8624.59 0.894522
\(454\) 33491.1 3.46214
\(455\) 0 0
\(456\) 5564.69 0.571471
\(457\) 6449.06 0.660119 0.330060 0.943960i \(-0.392931\pi\)
0.330060 + 0.943960i \(0.392931\pi\)
\(458\) 20154.1 2.05620
\(459\) 2259.16 0.229735
\(460\) −12470.1 −1.26396
\(461\) −11548.7 −1.16676 −0.583381 0.812199i \(-0.698270\pi\)
−0.583381 + 0.812199i \(0.698270\pi\)
\(462\) 0 0
\(463\) −3072.97 −0.308451 −0.154226 0.988036i \(-0.549288\pi\)
−0.154226 + 0.988036i \(0.549288\pi\)
\(464\) −38513.4 −3.85332
\(465\) 3810.78 0.380044
\(466\) −9432.93 −0.937708
\(467\) −2235.77 −0.221539 −0.110770 0.993846i \(-0.535332\pi\)
−0.110770 + 0.993846i \(0.535332\pi\)
\(468\) −2535.37 −0.250422
\(469\) 0 0
\(470\) 3910.16 0.383749
\(471\) 4667.46 0.456614
\(472\) −3002.76 −0.292824
\(473\) −1805.86 −0.175546
\(474\) 12782.2 1.23862
\(475\) 748.113 0.0722648
\(476\) 0 0
\(477\) −2300.76 −0.220848
\(478\) 13540.0 1.29562
\(479\) −1588.59 −0.151533 −0.0757665 0.997126i \(-0.524140\pi\)
−0.0757665 + 0.997126i \(0.524140\pi\)
\(480\) 10373.2 0.986399
\(481\) 3443.31 0.326407
\(482\) −6041.59 −0.570927
\(483\) 0 0
\(484\) 2346.31 0.220352
\(485\) 10922.4 1.02260
\(486\) −1271.77 −0.118701
\(487\) −10503.4 −0.977323 −0.488661 0.872473i \(-0.662515\pi\)
−0.488661 + 0.872473i \(0.662515\pi\)
\(488\) −4084.25 −0.378863
\(489\) −8606.68 −0.795925
\(490\) 0 0
\(491\) 10864.4 0.998586 0.499293 0.866433i \(-0.333593\pi\)
0.499293 + 0.866433i \(0.333593\pi\)
\(492\) −18936.1 −1.73517
\(493\) 20541.0 1.87651
\(494\) 2365.69 0.215460
\(495\) −994.720 −0.0903219
\(496\) 19833.5 1.79547
\(497\) 0 0
\(498\) 4167.08 0.374962
\(499\) 19429.0 1.74300 0.871502 0.490391i \(-0.163146\pi\)
0.871502 + 0.490391i \(0.163146\pi\)
\(500\) 29038.9 2.59732
\(501\) −4746.54 −0.423273
\(502\) 25608.9 2.27686
\(503\) 11111.2 0.984941 0.492470 0.870329i \(-0.336094\pi\)
0.492470 + 0.870329i \(0.336094\pi\)
\(504\) 0 0
\(505\) 14475.6 1.27556
\(506\) 3684.69 0.323725
\(507\) 5957.83 0.521887
\(508\) 22558.9 1.97025
\(509\) 16094.5 1.40152 0.700762 0.713395i \(-0.252843\pi\)
0.700762 + 0.713395i \(0.252843\pi\)
\(510\) −13200.0 −1.14609
\(511\) 0 0
\(512\) −20833.3 −1.79826
\(513\) 840.077 0.0723008
\(514\) −14031.0 −1.20405
\(515\) −8277.62 −0.708263
\(516\) 9550.17 0.814773
\(517\) −817.934 −0.0695797
\(518\) 0 0
\(519\) 4159.40 0.351787
\(520\) 8702.19 0.733878
\(521\) 1867.78 0.157061 0.0785304 0.996912i \(-0.474977\pi\)
0.0785304 + 0.996912i \(0.474977\pi\)
\(522\) −11563.4 −0.969571
\(523\) −16673.9 −1.39407 −0.697036 0.717037i \(-0.745498\pi\)
−0.697036 + 0.717037i \(0.745498\pi\)
\(524\) 48560.0 4.04838
\(525\) 0 0
\(526\) 30913.7 2.56255
\(527\) −10578.2 −0.874367
\(528\) −5177.11 −0.426713
\(529\) −8070.53 −0.663313
\(530\) 13443.1 1.10175
\(531\) −453.313 −0.0370473
\(532\) 0 0
\(533\) −4728.98 −0.384306
\(534\) 17975.0 1.45665
\(535\) 19143.4 1.54699
\(536\) 37749.9 3.04207
\(537\) 10209.1 0.820398
\(538\) 16649.3 1.33420
\(539\) 0 0
\(540\) 5260.52 0.419216
\(541\) −21055.3 −1.67327 −0.836633 0.547763i \(-0.815479\pi\)
−0.836633 + 0.547763i \(0.815479\pi\)
\(542\) 11801.1 0.935241
\(543\) −5965.01 −0.471424
\(544\) −28794.6 −2.26941
\(545\) −2079.50 −0.163442
\(546\) 0 0
\(547\) 11378.8 0.889441 0.444720 0.895669i \(-0.353303\pi\)
0.444720 + 0.895669i \(0.353303\pi\)
\(548\) −21684.8 −1.69038
\(549\) −616.581 −0.0479326
\(550\) −1384.23 −0.107316
\(551\) 7638.26 0.590564
\(552\) −11447.0 −0.882637
\(553\) 0 0
\(554\) −5148.34 −0.394823
\(555\) −7144.38 −0.546418
\(556\) 1638.48 0.124976
\(557\) −21552.1 −1.63948 −0.819740 0.572735i \(-0.805882\pi\)
−0.819740 + 0.572735i \(0.805882\pi\)
\(558\) 5954.88 0.451775
\(559\) 2385.00 0.180456
\(560\) 0 0
\(561\) 2761.19 0.207803
\(562\) 39079.7 2.93323
\(563\) −3834.25 −0.287024 −0.143512 0.989649i \(-0.545840\pi\)
−0.143512 + 0.989649i \(0.545840\pi\)
\(564\) 4325.60 0.322944
\(565\) 9026.64 0.672131
\(566\) 22716.6 1.68701
\(567\) 0 0
\(568\) 26936.9 1.98988
\(569\) 5242.80 0.386274 0.193137 0.981172i \(-0.438134\pi\)
0.193137 + 0.981172i \(0.438134\pi\)
\(570\) −4908.47 −0.360689
\(571\) 16660.4 1.22104 0.610521 0.792000i \(-0.290960\pi\)
0.610521 + 0.792000i \(0.290960\pi\)
\(572\) −3098.78 −0.226515
\(573\) −6035.20 −0.440007
\(574\) 0 0
\(575\) −1538.92 −0.111613
\(576\) 4914.15 0.355480
\(577\) 6285.45 0.453495 0.226748 0.973954i \(-0.427191\pi\)
0.226748 + 0.973954i \(0.427191\pi\)
\(578\) 10928.3 0.786432
\(579\) 14168.0 1.01693
\(580\) 47830.4 3.42422
\(581\) 0 0
\(582\) 17067.8 1.21560
\(583\) −2812.04 −0.199765
\(584\) −67539.6 −4.78563
\(585\) 1313.73 0.0928481
\(586\) 23817.1 1.67897
\(587\) −20940.0 −1.47238 −0.736188 0.676777i \(-0.763376\pi\)
−0.736188 + 0.676777i \(0.763376\pi\)
\(588\) 0 0
\(589\) −3933.53 −0.275175
\(590\) 2648.65 0.184819
\(591\) −1905.35 −0.132615
\(592\) −37183.6 −2.58148
\(593\) 21728.9 1.50472 0.752361 0.658751i \(-0.228915\pi\)
0.752361 + 0.658751i \(0.228915\pi\)
\(594\) −1554.39 −0.107369
\(595\) 0 0
\(596\) 64053.9 4.40226
\(597\) 4178.42 0.286451
\(598\) −4866.40 −0.332779
\(599\) −12091.3 −0.824767 −0.412383 0.911010i \(-0.635304\pi\)
−0.412383 + 0.911010i \(0.635304\pi\)
\(600\) 4300.29 0.292598
\(601\) −21744.9 −1.47586 −0.737932 0.674875i \(-0.764197\pi\)
−0.737932 + 0.674875i \(0.764197\pi\)
\(602\) 0 0
\(603\) 5698.94 0.384874
\(604\) −55746.4 −3.75545
\(605\) −1215.77 −0.0816992
\(606\) 22620.2 1.51631
\(607\) −7953.37 −0.531824 −0.265912 0.963997i \(-0.585673\pi\)
−0.265912 + 0.963997i \(0.585673\pi\)
\(608\) −10707.4 −0.714213
\(609\) 0 0
\(610\) 3602.60 0.239123
\(611\) 1080.25 0.0715257
\(612\) −14602.4 −0.964490
\(613\) 2989.80 0.196993 0.0984965 0.995137i \(-0.468597\pi\)
0.0984965 + 0.995137i \(0.468597\pi\)
\(614\) 49721.5 3.26807
\(615\) 9811.96 0.643344
\(616\) 0 0
\(617\) 19646.3 1.28190 0.640950 0.767583i \(-0.278541\pi\)
0.640950 + 0.767583i \(0.278541\pi\)
\(618\) −12935.0 −0.841942
\(619\) −16688.2 −1.08361 −0.541807 0.840503i \(-0.682260\pi\)
−0.541807 + 0.840503i \(0.682260\pi\)
\(620\) −24631.6 −1.59553
\(621\) −1728.10 −0.111669
\(622\) −26909.9 −1.73471
\(623\) 0 0
\(624\) 6837.43 0.438648
\(625\) −12041.3 −0.770646
\(626\) 11035.6 0.704588
\(627\) 1026.76 0.0653985
\(628\) −30168.9 −1.91699
\(629\) 19831.7 1.25714
\(630\) 0 0
\(631\) 1146.71 0.0723453 0.0361727 0.999346i \(-0.488483\pi\)
0.0361727 + 0.999346i \(0.488483\pi\)
\(632\) −48534.0 −3.05472
\(633\) −11683.7 −0.733623
\(634\) −14851.0 −0.930297
\(635\) −11689.2 −0.730504
\(636\) 14871.3 0.927181
\(637\) 0 0
\(638\) −14133.0 −0.877010
\(639\) 4066.55 0.251753
\(640\) −1050.81 −0.0649015
\(641\) −15024.4 −0.925782 −0.462891 0.886415i \(-0.653188\pi\)
−0.462891 + 0.886415i \(0.653188\pi\)
\(642\) 29914.3 1.83898
\(643\) −1972.58 −0.120981 −0.0604907 0.998169i \(-0.519267\pi\)
−0.0604907 + 0.998169i \(0.519267\pi\)
\(644\) 0 0
\(645\) −4948.54 −0.302091
\(646\) 13625.2 0.829838
\(647\) −25518.9 −1.55062 −0.775312 0.631579i \(-0.782407\pi\)
−0.775312 + 0.631579i \(0.782407\pi\)
\(648\) 4828.92 0.292743
\(649\) −554.049 −0.0335105
\(650\) 1828.16 0.110317
\(651\) 0 0
\(652\) 55630.6 3.34151
\(653\) 14086.7 0.844191 0.422095 0.906551i \(-0.361295\pi\)
0.422095 + 0.906551i \(0.361295\pi\)
\(654\) −3249.51 −0.194290
\(655\) −25161.9 −1.50101
\(656\) 51067.2 3.03939
\(657\) −10196.1 −0.605464
\(658\) 0 0
\(659\) 21036.5 1.24350 0.621749 0.783217i \(-0.286423\pi\)
0.621749 + 0.783217i \(0.286423\pi\)
\(660\) 6429.53 0.379195
\(661\) −10417.3 −0.612988 −0.306494 0.951873i \(-0.599156\pi\)
−0.306494 + 0.951873i \(0.599156\pi\)
\(662\) 10307.4 0.605149
\(663\) −3646.72 −0.213615
\(664\) −15822.4 −0.924739
\(665\) 0 0
\(666\) −11164.1 −0.649550
\(667\) −15712.5 −0.912127
\(668\) 30680.0 1.77701
\(669\) 11862.3 0.685536
\(670\) −33298.2 −1.92003
\(671\) −753.598 −0.0433567
\(672\) 0 0
\(673\) −32223.2 −1.84564 −0.922818 0.385236i \(-0.874120\pi\)
−0.922818 + 0.385236i \(0.874120\pi\)
\(674\) 27579.5 1.57615
\(675\) 649.196 0.0370186
\(676\) −38509.4 −2.19102
\(677\) 10313.1 0.585470 0.292735 0.956194i \(-0.405435\pi\)
0.292735 + 0.956194i \(0.405435\pi\)
\(678\) 14105.4 0.798990
\(679\) 0 0
\(680\) 50120.2 2.82650
\(681\) −19197.6 −1.08025
\(682\) 7278.19 0.408646
\(683\) 6019.58 0.337237 0.168618 0.985681i \(-0.446069\pi\)
0.168618 + 0.985681i \(0.446069\pi\)
\(684\) −5429.97 −0.303538
\(685\) 11236.3 0.626738
\(686\) 0 0
\(687\) −11552.6 −0.641573
\(688\) −25755.1 −1.42719
\(689\) 3713.88 0.205352
\(690\) 10097.1 0.557085
\(691\) 26018.3 1.43239 0.716197 0.697898i \(-0.245881\pi\)
0.716197 + 0.697898i \(0.245881\pi\)
\(692\) −26885.0 −1.47690
\(693\) 0 0
\(694\) −17115.8 −0.936175
\(695\) −848.997 −0.0463371
\(696\) 43906.1 2.39117
\(697\) −27236.5 −1.48014
\(698\) −42743.4 −2.31785
\(699\) 5407.10 0.292582
\(700\) 0 0
\(701\) 24350.1 1.31197 0.655986 0.754773i \(-0.272253\pi\)
0.655986 + 0.754773i \(0.272253\pi\)
\(702\) 2052.89 0.110372
\(703\) 7374.51 0.395640
\(704\) 6006.19 0.321544
\(705\) −2241.36 −0.119737
\(706\) 52669.1 2.80769
\(707\) 0 0
\(708\) 2930.06 0.155534
\(709\) 3334.65 0.176637 0.0883183 0.996092i \(-0.471851\pi\)
0.0883183 + 0.996092i \(0.471851\pi\)
\(710\) −23760.4 −1.25593
\(711\) −7326.97 −0.386474
\(712\) −68250.8 −3.59243
\(713\) 8091.56 0.425009
\(714\) 0 0
\(715\) 1605.67 0.0839842
\(716\) −65987.9 −3.44425
\(717\) −7761.33 −0.404257
\(718\) 47725.8 2.48066
\(719\) −36433.9 −1.88978 −0.944891 0.327385i \(-0.893833\pi\)
−0.944891 + 0.327385i \(0.893833\pi\)
\(720\) −14186.7 −0.734315
\(721\) 0 0
\(722\) −30831.0 −1.58921
\(723\) 3463.13 0.178140
\(724\) 38555.8 1.97916
\(725\) 5902.70 0.302374
\(726\) −1899.81 −0.0971193
\(727\) −27236.6 −1.38948 −0.694739 0.719262i \(-0.744480\pi\)
−0.694739 + 0.719262i \(0.744480\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 59574.8 3.02050
\(731\) 13736.4 0.695020
\(732\) 3985.37 0.201234
\(733\) 8953.75 0.451179 0.225590 0.974222i \(-0.427569\pi\)
0.225590 + 0.974222i \(0.427569\pi\)
\(734\) −41709.4 −2.09744
\(735\) 0 0
\(736\) 22025.8 1.10310
\(737\) 6965.37 0.348131
\(738\) 15332.6 0.764770
\(739\) −29366.2 −1.46178 −0.730888 0.682498i \(-0.760894\pi\)
−0.730888 + 0.682498i \(0.760894\pi\)
\(740\) 46178.8 2.29401
\(741\) −1356.05 −0.0672277
\(742\) 0 0
\(743\) 9178.79 0.453213 0.226607 0.973986i \(-0.427237\pi\)
0.226607 + 0.973986i \(0.427237\pi\)
\(744\) −22610.6 −1.11418
\(745\) −33190.3 −1.63221
\(746\) 11276.6 0.553438
\(747\) −2388.63 −0.116995
\(748\) −17847.4 −0.872414
\(749\) 0 0
\(750\) −23512.9 −1.14476
\(751\) 35382.8 1.71922 0.859611 0.510949i \(-0.170706\pi\)
0.859611 + 0.510949i \(0.170706\pi\)
\(752\) −11665.4 −0.565681
\(753\) −14679.4 −0.710422
\(754\) 18665.6 0.901539
\(755\) 28885.7 1.39239
\(756\) 0 0
\(757\) −10160.7 −0.487841 −0.243920 0.969795i \(-0.578434\pi\)
−0.243920 + 0.969795i \(0.578434\pi\)
\(758\) 6843.99 0.327949
\(759\) −2112.12 −0.101008
\(760\) 18637.4 0.889539
\(761\) −13747.6 −0.654863 −0.327431 0.944875i \(-0.606183\pi\)
−0.327431 + 0.944875i \(0.606183\pi\)
\(762\) −18266.0 −0.868381
\(763\) 0 0
\(764\) 39009.5 1.84727
\(765\) 7566.43 0.357601
\(766\) −29750.0 −1.40328
\(767\) 731.736 0.0344478
\(768\) 11462.4 0.538558
\(769\) −19309.5 −0.905483 −0.452742 0.891642i \(-0.649554\pi\)
−0.452742 + 0.891642i \(0.649554\pi\)
\(770\) 0 0
\(771\) 8042.77 0.375685
\(772\) −91577.3 −4.26935
\(773\) 19830.5 0.922709 0.461355 0.887216i \(-0.347364\pi\)
0.461355 + 0.887216i \(0.347364\pi\)
\(774\) −7732.80 −0.359108
\(775\) −3039.76 −0.140892
\(776\) −64806.1 −2.99794
\(777\) 0 0
\(778\) −38063.1 −1.75402
\(779\) −10128.0 −0.465820
\(780\) −8491.51 −0.389801
\(781\) 4970.23 0.227719
\(782\) −28028.0 −1.28169
\(783\) 6628.31 0.302524
\(784\) 0 0
\(785\) 15632.4 0.710756
\(786\) −39319.1 −1.78431
\(787\) 35276.3 1.59780 0.798898 0.601467i \(-0.205417\pi\)
0.798898 + 0.601467i \(0.205417\pi\)
\(788\) 12315.5 0.556754
\(789\) −17720.2 −0.799563
\(790\) 42810.6 1.92802
\(791\) 0 0
\(792\) 5902.01 0.264796
\(793\) 995.282 0.0445693
\(794\) 8135.94 0.363645
\(795\) −7705.77 −0.343768
\(796\) −27007.9 −1.20260
\(797\) −36635.1 −1.62821 −0.814105 0.580718i \(-0.802772\pi\)
−0.814105 + 0.580718i \(0.802772\pi\)
\(798\) 0 0
\(799\) 6221.69 0.275479
\(800\) −8274.46 −0.365683
\(801\) −10303.5 −0.454503
\(802\) −16907.3 −0.744411
\(803\) −12462.0 −0.547662
\(804\) −36836.0 −1.61580
\(805\) 0 0
\(806\) −9612.35 −0.420075
\(807\) −9543.62 −0.416296
\(808\) −85888.9 −3.73955
\(809\) 39216.1 1.70428 0.852142 0.523310i \(-0.175303\pi\)
0.852142 + 0.523310i \(0.175303\pi\)
\(810\) −4259.46 −0.184768
\(811\) 5610.73 0.242934 0.121467 0.992595i \(-0.461240\pi\)
0.121467 + 0.992595i \(0.461240\pi\)
\(812\) 0 0
\(813\) −6764.56 −0.291813
\(814\) −13645.0 −0.587540
\(815\) −28825.7 −1.23892
\(816\) 39380.2 1.68944
\(817\) 5107.94 0.218732
\(818\) −24530.3 −1.04851
\(819\) 0 0
\(820\) −63421.1 −2.70093
\(821\) −21971.3 −0.933986 −0.466993 0.884261i \(-0.654663\pi\)
−0.466993 + 0.884261i \(0.654663\pi\)
\(822\) 17558.2 0.745029
\(823\) −772.530 −0.0327202 −0.0163601 0.999866i \(-0.505208\pi\)
−0.0163601 + 0.999866i \(0.505208\pi\)
\(824\) 49113.9 2.07641
\(825\) 793.461 0.0334846
\(826\) 0 0
\(827\) −10138.2 −0.426286 −0.213143 0.977021i \(-0.568370\pi\)
−0.213143 + 0.977021i \(0.568370\pi\)
\(828\) 11169.8 0.468815
\(829\) −15443.6 −0.647018 −0.323509 0.946225i \(-0.604863\pi\)
−0.323509 + 0.946225i \(0.604863\pi\)
\(830\) 13956.5 0.583658
\(831\) 2951.11 0.123192
\(832\) −7932.40 −0.330537
\(833\) 0 0
\(834\) −1326.68 −0.0550829
\(835\) −15897.2 −0.658858
\(836\) −6636.63 −0.274561
\(837\) −3413.43 −0.140962
\(838\) 38298.0 1.57874
\(839\) 9019.03 0.371122 0.185561 0.982633i \(-0.440590\pi\)
0.185561 + 0.982633i \(0.440590\pi\)
\(840\) 0 0
\(841\) 35877.8 1.47106
\(842\) 56480.7 2.31170
\(843\) −22401.1 −0.915224
\(844\) 75519.2 3.07995
\(845\) 19954.1 0.812358
\(846\) −3502.45 −0.142336
\(847\) 0 0
\(848\) −40105.4 −1.62409
\(849\) −13021.5 −0.526380
\(850\) 10529.3 0.424884
\(851\) −15169.9 −0.611067
\(852\) −26284.8 −1.05693
\(853\) −4895.50 −0.196505 −0.0982524 0.995162i \(-0.531325\pi\)
−0.0982524 + 0.995162i \(0.531325\pi\)
\(854\) 0 0
\(855\) 2813.61 0.112542
\(856\) −113584. −4.53532
\(857\) −2488.43 −0.0991871 −0.0495935 0.998769i \(-0.515793\pi\)
−0.0495935 + 0.998769i \(0.515793\pi\)
\(858\) 2509.09 0.0998356
\(859\) −28121.0 −1.11697 −0.558485 0.829514i \(-0.688617\pi\)
−0.558485 + 0.829514i \(0.688617\pi\)
\(860\) 31985.7 1.26826
\(861\) 0 0
\(862\) −20817.8 −0.822572
\(863\) 39797.7 1.56979 0.784896 0.619628i \(-0.212716\pi\)
0.784896 + 0.619628i \(0.212716\pi\)
\(864\) −9291.62 −0.365865
\(865\) 13930.8 0.547584
\(866\) −55073.1 −2.16104
\(867\) −6264.27 −0.245382
\(868\) 0 0
\(869\) −8955.19 −0.349579
\(870\) −38728.4 −1.50921
\(871\) −9199.21 −0.357868
\(872\) 12338.4 0.479162
\(873\) −9783.50 −0.379291
\(874\) −10422.3 −0.403364
\(875\) 0 0
\(876\) 65904.4 2.54190
\(877\) 3644.85 0.140340 0.0701698 0.997535i \(-0.477646\pi\)
0.0701698 + 0.997535i \(0.477646\pi\)
\(878\) 31140.0 1.19695
\(879\) −13652.3 −0.523870
\(880\) −17339.3 −0.664213
\(881\) −45259.0 −1.73078 −0.865389 0.501102i \(-0.832928\pi\)
−0.865389 + 0.501102i \(0.832928\pi\)
\(882\) 0 0
\(883\) −25598.4 −0.975600 −0.487800 0.872955i \(-0.662200\pi\)
−0.487800 + 0.872955i \(0.662200\pi\)
\(884\) 23571.2 0.896815
\(885\) −1518.25 −0.0576670
\(886\) −86212.9 −3.26905
\(887\) 4570.17 0.173000 0.0865002 0.996252i \(-0.472432\pi\)
0.0865002 + 0.996252i \(0.472432\pi\)
\(888\) 42390.0 1.60193
\(889\) 0 0
\(890\) 60202.2 2.26740
\(891\) 891.000 0.0335013
\(892\) −76673.9 −2.87806
\(893\) 2313.56 0.0866969
\(894\) −51864.6 −1.94028
\(895\) 34192.4 1.27701
\(896\) 0 0
\(897\) 2789.49 0.103833
\(898\) −32757.0 −1.21728
\(899\) −31036.0 −1.15140
\(900\) −4196.18 −0.155414
\(901\) 21390.1 0.790906
\(902\) 18739.8 0.691760
\(903\) 0 0
\(904\) −53558.1 −1.97048
\(905\) −19978.2 −0.733808
\(906\) 45138.0 1.65520
\(907\) −640.152 −0.0234354 −0.0117177 0.999931i \(-0.503730\pi\)
−0.0117177 + 0.999931i \(0.503730\pi\)
\(908\) 124087. 4.53520
\(909\) −12966.3 −0.473118
\(910\) 0 0
\(911\) 52835.8 1.92155 0.960773 0.277337i \(-0.0894519\pi\)
0.960773 + 0.277337i \(0.0894519\pi\)
\(912\) 14643.7 0.531689
\(913\) −2919.44 −0.105826
\(914\) 33752.1 1.22147
\(915\) −2065.07 −0.0746109
\(916\) 74672.3 2.69350
\(917\) 0 0
\(918\) 11823.6 0.425095
\(919\) −21898.7 −0.786042 −0.393021 0.919530i \(-0.628570\pi\)
−0.393021 + 0.919530i \(0.628570\pi\)
\(920\) −38338.5 −1.37389
\(921\) −28501.1 −1.01970
\(922\) −60441.8 −2.15894
\(923\) −6564.21 −0.234088
\(924\) 0 0
\(925\) 5698.88 0.202571
\(926\) −16082.8 −0.570749
\(927\) 7414.51 0.262702
\(928\) −84482.5 −2.98844
\(929\) −17869.1 −0.631071 −0.315535 0.948914i \(-0.602184\pi\)
−0.315535 + 0.948914i \(0.602184\pi\)
\(930\) 19944.2 0.703223
\(931\) 0 0
\(932\) −34949.6 −1.22834
\(933\) 15425.2 0.541262
\(934\) −11701.2 −0.409930
\(935\) 9247.85 0.323462
\(936\) −7794.81 −0.272202
\(937\) 31017.7 1.08143 0.540717 0.841205i \(-0.318153\pi\)
0.540717 + 0.841205i \(0.318153\pi\)
\(938\) 0 0
\(939\) −6325.78 −0.219845
\(940\) 14487.4 0.502688
\(941\) 14359.3 0.497449 0.248725 0.968574i \(-0.419989\pi\)
0.248725 + 0.968574i \(0.419989\pi\)
\(942\) 24427.8 0.844906
\(943\) 20834.1 0.719460
\(944\) −7901.85 −0.272440
\(945\) 0 0
\(946\) −9451.19 −0.324825
\(947\) −6138.31 −0.210632 −0.105316 0.994439i \(-0.533585\pi\)
−0.105316 + 0.994439i \(0.533585\pi\)
\(948\) 47359.0 1.62252
\(949\) 16458.6 0.562980
\(950\) 3915.35 0.133717
\(951\) 8512.81 0.290270
\(952\) 0 0
\(953\) 11197.1 0.380598 0.190299 0.981726i \(-0.439054\pi\)
0.190299 + 0.981726i \(0.439054\pi\)
\(954\) −12041.4 −0.408652
\(955\) −20213.2 −0.684906
\(956\) 50166.6 1.69718
\(957\) 8101.27 0.273643
\(958\) −8314.09 −0.280392
\(959\) 0 0
\(960\) 16458.6 0.553332
\(961\) −13808.2 −0.463501
\(962\) 18021.1 0.603973
\(963\) −17147.3 −0.573795
\(964\) −22384.5 −0.747879
\(965\) 47451.9 1.58293
\(966\) 0 0
\(967\) 35801.6 1.19059 0.595295 0.803507i \(-0.297035\pi\)
0.595295 + 0.803507i \(0.297035\pi\)
\(968\) 7213.56 0.239517
\(969\) −7810.15 −0.258925
\(970\) 57163.8 1.89218
\(971\) −36961.7 −1.22158 −0.610791 0.791791i \(-0.709149\pi\)
−0.610791 + 0.791791i \(0.709149\pi\)
\(972\) −4712.01 −0.155491
\(973\) 0 0
\(974\) −54971.2 −1.80841
\(975\) −1047.93 −0.0344211
\(976\) −10747.8 −0.352489
\(977\) 14892.0 0.487652 0.243826 0.969819i \(-0.421597\pi\)
0.243826 + 0.969819i \(0.421597\pi\)
\(978\) −45044.2 −1.47276
\(979\) −12593.2 −0.411114
\(980\) 0 0
\(981\) 1862.67 0.0606222
\(982\) 56860.6 1.84775
\(983\) 28822.0 0.935178 0.467589 0.883946i \(-0.345123\pi\)
0.467589 + 0.883946i \(0.345123\pi\)
\(984\) −58217.7 −1.88609
\(985\) −6381.44 −0.206426
\(986\) 107504. 3.47224
\(987\) 0 0
\(988\) 8765.03 0.282240
\(989\) −10507.4 −0.337832
\(990\) −5206.00 −0.167129
\(991\) 58476.0 1.87442 0.937211 0.348764i \(-0.113399\pi\)
0.937211 + 0.348764i \(0.113399\pi\)
\(992\) 43506.6 1.39247
\(993\) −5908.36 −0.188818
\(994\) 0 0
\(995\) 13994.5 0.445883
\(996\) 15439.3 0.491177
\(997\) 35710.4 1.13436 0.567181 0.823593i \(-0.308034\pi\)
0.567181 + 0.823593i \(0.308034\pi\)
\(998\) 101684. 3.22520
\(999\) 6399.44 0.202672
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.1.15 16
7.6 odd 2 1617.4.a.bf.1.15 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1617.4.a.be.1.15 16 1.1 even 1 trivial
1617.4.a.bf.1.15 yes 16 7.6 odd 2