Properties

Label 1859.4.a.e.1.8
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $0$
Dimension $11$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + 68209 x^{3} - 90926 x^{2} - 1672 x + 16256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(3.58491\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.58491 q^{2} -2.54183 q^{3} -1.31822 q^{4} +20.1048 q^{5} -6.57040 q^{6} +29.2165 q^{7} -24.0868 q^{8} -20.5391 q^{9} +O(q^{10})\) \(q+2.58491 q^{2} -2.54183 q^{3} -1.31822 q^{4} +20.1048 q^{5} -6.57040 q^{6} +29.2165 q^{7} -24.0868 q^{8} -20.5391 q^{9} +51.9693 q^{10} -11.0000 q^{11} +3.35069 q^{12} +75.5221 q^{14} -51.1030 q^{15} -51.7165 q^{16} -127.832 q^{17} -53.0918 q^{18} +14.1385 q^{19} -26.5026 q^{20} -74.2633 q^{21} -28.4341 q^{22} +93.3531 q^{23} +61.2245 q^{24} +279.205 q^{25} +120.836 q^{27} -38.5137 q^{28} -83.3385 q^{29} -132.097 q^{30} +211.118 q^{31} +59.0115 q^{32} +27.9601 q^{33} -330.435 q^{34} +587.393 q^{35} +27.0751 q^{36} -125.862 q^{37} +36.5469 q^{38} -484.261 q^{40} +250.303 q^{41} -191.964 q^{42} +367.915 q^{43} +14.5004 q^{44} -412.936 q^{45} +241.310 q^{46} +477.490 q^{47} +131.455 q^{48} +510.603 q^{49} +721.720 q^{50} +324.927 q^{51} -297.083 q^{53} +312.351 q^{54} -221.153 q^{55} -703.732 q^{56} -35.9377 q^{57} -215.423 q^{58} +578.993 q^{59} +67.3650 q^{60} -305.672 q^{61} +545.722 q^{62} -600.081 q^{63} +566.272 q^{64} +72.2745 q^{66} +330.902 q^{67} +168.511 q^{68} -237.287 q^{69} +1518.36 q^{70} +123.873 q^{71} +494.721 q^{72} +432.090 q^{73} -325.343 q^{74} -709.690 q^{75} -18.6377 q^{76} -321.381 q^{77} +269.398 q^{79} -1039.75 q^{80} +247.411 q^{81} +647.011 q^{82} -425.366 q^{83} +97.8953 q^{84} -2570.04 q^{85} +951.028 q^{86} +211.832 q^{87} +264.955 q^{88} +317.243 q^{89} -1067.40 q^{90} -123.060 q^{92} -536.626 q^{93} +1234.27 q^{94} +284.253 q^{95} -149.997 q^{96} -1562.33 q^{97} +1319.87 q^{98} +225.930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58491 0.913905 0.456953 0.889491i \(-0.348941\pi\)
0.456953 + 0.889491i \(0.348941\pi\)
\(3\) −2.54183 −0.489175 −0.244587 0.969627i \(-0.578653\pi\)
−0.244587 + 0.969627i \(0.578653\pi\)
\(4\) −1.31822 −0.164777
\(5\) 20.1048 1.79823 0.899116 0.437710i \(-0.144210\pi\)
0.899116 + 0.437710i \(0.144210\pi\)
\(6\) −6.57040 −0.447059
\(7\) 29.2165 1.57754 0.788771 0.614687i \(-0.210718\pi\)
0.788771 + 0.614687i \(0.210718\pi\)
\(8\) −24.0868 −1.06450
\(9\) −20.5391 −0.760708
\(10\) 51.9693 1.64341
\(11\) −11.0000 −0.301511
\(12\) 3.35069 0.0806050
\(13\) 0 0
\(14\) 75.5221 1.44172
\(15\) −51.1030 −0.879650
\(16\) −51.7165 −0.808071
\(17\) −127.832 −1.82376 −0.911878 0.410462i \(-0.865367\pi\)
−0.911878 + 0.410462i \(0.865367\pi\)
\(18\) −53.0918 −0.695215
\(19\) 14.1385 0.170716 0.0853580 0.996350i \(-0.472797\pi\)
0.0853580 + 0.996350i \(0.472797\pi\)
\(20\) −26.5026 −0.296308
\(21\) −74.2633 −0.771694
\(22\) −28.4341 −0.275553
\(23\) 93.3531 0.846324 0.423162 0.906054i \(-0.360920\pi\)
0.423162 + 0.906054i \(0.360920\pi\)
\(24\) 61.2245 0.520725
\(25\) 279.205 2.23364
\(26\) 0 0
\(27\) 120.836 0.861294
\(28\) −38.5137 −0.259943
\(29\) −83.3385 −0.533641 −0.266820 0.963746i \(-0.585973\pi\)
−0.266820 + 0.963746i \(0.585973\pi\)
\(30\) −132.097 −0.803917
\(31\) 211.118 1.22316 0.611579 0.791183i \(-0.290534\pi\)
0.611579 + 0.791183i \(0.290534\pi\)
\(32\) 59.0115 0.325996
\(33\) 27.9601 0.147492
\(34\) −330.435 −1.66674
\(35\) 587.393 2.83679
\(36\) 27.0751 0.125347
\(37\) −125.862 −0.559233 −0.279616 0.960112i \(-0.590207\pi\)
−0.279616 + 0.960112i \(0.590207\pi\)
\(38\) 36.5469 0.156018
\(39\) 0 0
\(40\) −484.261 −1.91421
\(41\) 250.303 0.953432 0.476716 0.879057i \(-0.341827\pi\)
0.476716 + 0.879057i \(0.341827\pi\)
\(42\) −191.964 −0.705255
\(43\) 367.915 1.30480 0.652401 0.757874i \(-0.273762\pi\)
0.652401 + 0.757874i \(0.273762\pi\)
\(44\) 14.5004 0.0496823
\(45\) −412.936 −1.36793
\(46\) 241.310 0.773460
\(47\) 477.490 1.48190 0.740948 0.671563i \(-0.234377\pi\)
0.740948 + 0.671563i \(0.234377\pi\)
\(48\) 131.455 0.395288
\(49\) 510.603 1.48864
\(50\) 721.720 2.04133
\(51\) 324.927 0.892135
\(52\) 0 0
\(53\) −297.083 −0.769953 −0.384976 0.922926i \(-0.625790\pi\)
−0.384976 + 0.922926i \(0.625790\pi\)
\(54\) 312.351 0.787141
\(55\) −221.153 −0.542187
\(56\) −703.732 −1.67929
\(57\) −35.9377 −0.0835100
\(58\) −215.423 −0.487697
\(59\) 578.993 1.27760 0.638800 0.769373i \(-0.279431\pi\)
0.638800 + 0.769373i \(0.279431\pi\)
\(60\) 67.3650 0.144946
\(61\) −305.672 −0.641595 −0.320798 0.947148i \(-0.603951\pi\)
−0.320798 + 0.947148i \(0.603951\pi\)
\(62\) 545.722 1.11785
\(63\) −600.081 −1.20005
\(64\) 566.272 1.10600
\(65\) 0 0
\(66\) 72.2745 0.134793
\(67\) 330.902 0.603374 0.301687 0.953407i \(-0.402450\pi\)
0.301687 + 0.953407i \(0.402450\pi\)
\(68\) 168.511 0.300514
\(69\) −237.287 −0.414001
\(70\) 1518.36 2.59255
\(71\) 123.873 0.207056 0.103528 0.994627i \(-0.466987\pi\)
0.103528 + 0.994627i \(0.466987\pi\)
\(72\) 494.721 0.809771
\(73\) 432.090 0.692771 0.346385 0.938092i \(-0.387409\pi\)
0.346385 + 0.938092i \(0.387409\pi\)
\(74\) −325.343 −0.511086
\(75\) −709.690 −1.09264
\(76\) −18.6377 −0.0281301
\(77\) −321.381 −0.475647
\(78\) 0 0
\(79\) 269.398 0.383666 0.191833 0.981428i \(-0.438557\pi\)
0.191833 + 0.981428i \(0.438557\pi\)
\(80\) −1039.75 −1.45310
\(81\) 247.411 0.339385
\(82\) 647.011 0.871346
\(83\) −425.366 −0.562530 −0.281265 0.959630i \(-0.590754\pi\)
−0.281265 + 0.959630i \(0.590754\pi\)
\(84\) 97.8953 0.127158
\(85\) −2570.04 −3.27954
\(86\) 951.028 1.19246
\(87\) 211.832 0.261044
\(88\) 264.955 0.320958
\(89\) 317.243 0.377840 0.188920 0.981993i \(-0.439501\pi\)
0.188920 + 0.981993i \(0.439501\pi\)
\(90\) −1067.40 −1.25016
\(91\) 0 0
\(92\) −123.060 −0.139455
\(93\) −536.626 −0.598339
\(94\) 1234.27 1.35431
\(95\) 284.253 0.306987
\(96\) −149.997 −0.159469
\(97\) −1562.33 −1.63536 −0.817682 0.575671i \(-0.804741\pi\)
−0.817682 + 0.575671i \(0.804741\pi\)
\(98\) 1319.87 1.36047
\(99\) 225.930 0.229362
\(100\) −368.053 −0.368053
\(101\) 572.371 0.563891 0.281946 0.959430i \(-0.409020\pi\)
0.281946 + 0.959430i \(0.409020\pi\)
\(102\) 839.909 0.815327
\(103\) 64.9567 0.0621395 0.0310698 0.999517i \(-0.490109\pi\)
0.0310698 + 0.999517i \(0.490109\pi\)
\(104\) 0 0
\(105\) −1493.05 −1.38768
\(106\) −767.934 −0.703664
\(107\) −324.100 −0.292822 −0.146411 0.989224i \(-0.546772\pi\)
−0.146411 + 0.989224i \(0.546772\pi\)
\(108\) −159.289 −0.141922
\(109\) −49.2595 −0.0432862 −0.0216431 0.999766i \(-0.506890\pi\)
−0.0216431 + 0.999766i \(0.506890\pi\)
\(110\) −571.662 −0.495508
\(111\) 319.920 0.273563
\(112\) −1510.98 −1.27477
\(113\) −462.767 −0.385252 −0.192626 0.981272i \(-0.561700\pi\)
−0.192626 + 0.981272i \(0.561700\pi\)
\(114\) −92.8959 −0.0763202
\(115\) 1876.85 1.52189
\(116\) 109.858 0.0879319
\(117\) 0 0
\(118\) 1496.65 1.16761
\(119\) −3734.81 −2.87705
\(120\) 1230.91 0.936384
\(121\) 121.000 0.0909091
\(122\) −790.136 −0.586357
\(123\) −636.226 −0.466395
\(124\) −278.300 −0.201549
\(125\) 3100.26 2.21837
\(126\) −1551.16 −1.09673
\(127\) 1618.54 1.13088 0.565441 0.824789i \(-0.308706\pi\)
0.565441 + 0.824789i \(0.308706\pi\)
\(128\) 991.672 0.684783
\(129\) −935.175 −0.638276
\(130\) 0 0
\(131\) 1858.13 1.23928 0.619641 0.784885i \(-0.287278\pi\)
0.619641 + 0.784885i \(0.287278\pi\)
\(132\) −36.8575 −0.0243033
\(133\) 413.079 0.269312
\(134\) 855.352 0.551427
\(135\) 2429.39 1.54881
\(136\) 3079.07 1.94138
\(137\) −1987.30 −1.23932 −0.619660 0.784871i \(-0.712729\pi\)
−0.619660 + 0.784871i \(0.712729\pi\)
\(138\) −613.367 −0.378357
\(139\) 322.673 0.196898 0.0984488 0.995142i \(-0.468612\pi\)
0.0984488 + 0.995142i \(0.468612\pi\)
\(140\) −774.313 −0.467438
\(141\) −1213.70 −0.724906
\(142\) 320.200 0.189230
\(143\) 0 0
\(144\) 1062.21 0.614706
\(145\) −1675.51 −0.959610
\(146\) 1116.91 0.633127
\(147\) −1297.86 −0.728205
\(148\) 165.914 0.0921489
\(149\) 2965.54 1.63051 0.815257 0.579100i \(-0.196596\pi\)
0.815257 + 0.579100i \(0.196596\pi\)
\(150\) −1834.49 −0.998569
\(151\) 1914.70 1.03190 0.515948 0.856620i \(-0.327440\pi\)
0.515948 + 0.856620i \(0.327440\pi\)
\(152\) −340.552 −0.181726
\(153\) 2625.56 1.38735
\(154\) −830.743 −0.434696
\(155\) 4244.50 2.19952
\(156\) 0 0
\(157\) −16.2680 −0.00826960 −0.00413480 0.999991i \(-0.501316\pi\)
−0.00413480 + 0.999991i \(0.501316\pi\)
\(158\) 696.370 0.350634
\(159\) 755.134 0.376641
\(160\) 1186.42 0.586216
\(161\) 2727.45 1.33511
\(162\) 639.537 0.310165
\(163\) 1584.56 0.761424 0.380712 0.924694i \(-0.375679\pi\)
0.380712 + 0.924694i \(0.375679\pi\)
\(164\) −329.954 −0.157104
\(165\) 562.133 0.265224
\(166\) −1099.53 −0.514099
\(167\) 600.706 0.278347 0.139174 0.990268i \(-0.455555\pi\)
0.139174 + 0.990268i \(0.455555\pi\)
\(168\) 1788.76 0.821465
\(169\) 0 0
\(170\) −6643.35 −2.99718
\(171\) −290.393 −0.129865
\(172\) −484.992 −0.215002
\(173\) 1707.02 0.750185 0.375093 0.926987i \(-0.377611\pi\)
0.375093 + 0.926987i \(0.377611\pi\)
\(174\) 547.568 0.238569
\(175\) 8157.38 3.52366
\(176\) 568.882 0.243643
\(177\) −1471.70 −0.624970
\(178\) 820.047 0.345310
\(179\) −4568.66 −1.90770 −0.953849 0.300287i \(-0.902917\pi\)
−0.953849 + 0.300287i \(0.902917\pi\)
\(180\) 544.340 0.225404
\(181\) 1562.07 0.641477 0.320739 0.947168i \(-0.396069\pi\)
0.320739 + 0.947168i \(0.396069\pi\)
\(182\) 0 0
\(183\) 776.966 0.313852
\(184\) −2248.58 −0.900909
\(185\) −2530.44 −1.00563
\(186\) −1387.13 −0.546825
\(187\) 1406.15 0.549883
\(188\) −629.436 −0.244183
\(189\) 3530.41 1.35873
\(190\) 734.770 0.280557
\(191\) −3288.63 −1.24585 −0.622923 0.782283i \(-0.714055\pi\)
−0.622923 + 0.782283i \(0.714055\pi\)
\(192\) −1439.37 −0.541028
\(193\) −2159.36 −0.805358 −0.402679 0.915341i \(-0.631921\pi\)
−0.402679 + 0.915341i \(0.631921\pi\)
\(194\) −4038.48 −1.49457
\(195\) 0 0
\(196\) −673.087 −0.245294
\(197\) −5369.47 −1.94192 −0.970961 0.239237i \(-0.923103\pi\)
−0.970961 + 0.239237i \(0.923103\pi\)
\(198\) 584.010 0.209615
\(199\) 46.8723 0.0166969 0.00834846 0.999965i \(-0.497343\pi\)
0.00834846 + 0.999965i \(0.497343\pi\)
\(200\) −6725.15 −2.37770
\(201\) −841.095 −0.295155
\(202\) 1479.53 0.515343
\(203\) −2434.86 −0.841840
\(204\) −428.325 −0.147004
\(205\) 5032.30 1.71449
\(206\) 167.907 0.0567896
\(207\) −1917.39 −0.643806
\(208\) 0 0
\(209\) −155.524 −0.0514728
\(210\) −3859.41 −1.26821
\(211\) 2336.92 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(212\) 391.620 0.126871
\(213\) −314.863 −0.101287
\(214\) −837.770 −0.267611
\(215\) 7396.87 2.34634
\(216\) −2910.56 −0.916844
\(217\) 6168.13 1.92958
\(218\) −127.331 −0.0395595
\(219\) −1098.30 −0.338886
\(220\) 291.529 0.0893402
\(221\) 0 0
\(222\) 826.965 0.250010
\(223\) 1803.10 0.541454 0.270727 0.962656i \(-0.412736\pi\)
0.270727 + 0.962656i \(0.412736\pi\)
\(224\) 1724.11 0.514272
\(225\) −5734.62 −1.69915
\(226\) −1196.21 −0.352084
\(227\) −2123.99 −0.621031 −0.310516 0.950568i \(-0.600502\pi\)
−0.310516 + 0.950568i \(0.600502\pi\)
\(228\) 47.3738 0.0137606
\(229\) 5138.84 1.48290 0.741450 0.671008i \(-0.234139\pi\)
0.741450 + 0.671008i \(0.234139\pi\)
\(230\) 4851.49 1.39086
\(231\) 816.896 0.232674
\(232\) 2007.36 0.568058
\(233\) 3454.75 0.971366 0.485683 0.874135i \(-0.338571\pi\)
0.485683 + 0.874135i \(0.338571\pi\)
\(234\) 0 0
\(235\) 9599.86 2.66479
\(236\) −763.239 −0.210520
\(237\) −684.762 −0.187680
\(238\) −9654.15 −2.62935
\(239\) 5868.90 1.58840 0.794200 0.607656i \(-0.207890\pi\)
0.794200 + 0.607656i \(0.207890\pi\)
\(240\) 2642.87 0.710820
\(241\) −7025.67 −1.87786 −0.938928 0.344114i \(-0.888179\pi\)
−0.938928 + 0.344114i \(0.888179\pi\)
\(242\) 312.775 0.0830823
\(243\) −3891.45 −1.02731
\(244\) 402.943 0.105720
\(245\) 10265.6 2.67692
\(246\) −1644.59 −0.426241
\(247\) 0 0
\(248\) −5085.16 −1.30205
\(249\) 1081.21 0.275175
\(250\) 8013.91 2.02738
\(251\) −6384.82 −1.60560 −0.802801 0.596247i \(-0.796658\pi\)
−0.802801 + 0.596247i \(0.796658\pi\)
\(252\) 791.038 0.197741
\(253\) −1026.88 −0.255176
\(254\) 4183.78 1.03352
\(255\) 6532.61 1.60427
\(256\) −1966.79 −0.480173
\(257\) 71.1715 0.0172745 0.00863726 0.999963i \(-0.497251\pi\)
0.00863726 + 0.999963i \(0.497251\pi\)
\(258\) −2417.35 −0.583324
\(259\) −3677.25 −0.882213
\(260\) 0 0
\(261\) 1711.70 0.405945
\(262\) 4803.12 1.13259
\(263\) −795.011 −0.186397 −0.0931986 0.995648i \(-0.529709\pi\)
−0.0931986 + 0.995648i \(0.529709\pi\)
\(264\) −673.469 −0.157004
\(265\) −5972.81 −1.38455
\(266\) 1067.77 0.246125
\(267\) −806.378 −0.184830
\(268\) −436.201 −0.0994224
\(269\) 1886.71 0.427638 0.213819 0.976873i \(-0.431410\pi\)
0.213819 + 0.976873i \(0.431410\pi\)
\(270\) 6279.77 1.41546
\(271\) 1280.68 0.287070 0.143535 0.989645i \(-0.454153\pi\)
0.143535 + 0.989645i \(0.454153\pi\)
\(272\) 6611.04 1.47372
\(273\) 0 0
\(274\) −5137.01 −1.13262
\(275\) −3071.25 −0.673467
\(276\) 312.797 0.0682179
\(277\) −369.108 −0.0800634 −0.0400317 0.999198i \(-0.512746\pi\)
−0.0400317 + 0.999198i \(0.512746\pi\)
\(278\) 834.082 0.179946
\(279\) −4336.18 −0.930467
\(280\) −14148.4 −3.01975
\(281\) 1026.86 0.217997 0.108999 0.994042i \(-0.465236\pi\)
0.108999 + 0.994042i \(0.465236\pi\)
\(282\) −3137.30 −0.662495
\(283\) 1815.31 0.381303 0.190652 0.981658i \(-0.438940\pi\)
0.190652 + 0.981658i \(0.438940\pi\)
\(284\) −163.291 −0.0341182
\(285\) −722.522 −0.150170
\(286\) 0 0
\(287\) 7312.96 1.50408
\(288\) −1212.04 −0.247988
\(289\) 11428.1 2.32608
\(290\) −4331.04 −0.876992
\(291\) 3971.16 0.799979
\(292\) −569.589 −0.114153
\(293\) 6464.43 1.28893 0.644464 0.764635i \(-0.277081\pi\)
0.644464 + 0.764635i \(0.277081\pi\)
\(294\) −3354.87 −0.665510
\(295\) 11640.6 2.29742
\(296\) 3031.62 0.595301
\(297\) −1329.20 −0.259690
\(298\) 7665.67 1.49013
\(299\) 0 0
\(300\) 935.527 0.180042
\(301\) 10749.2 2.05838
\(302\) 4949.34 0.943054
\(303\) −1454.87 −0.275841
\(304\) −731.196 −0.137951
\(305\) −6145.49 −1.15374
\(306\) 6786.84 1.26790
\(307\) 9616.30 1.78772 0.893862 0.448342i \(-0.147985\pi\)
0.893862 + 0.448342i \(0.147985\pi\)
\(308\) 423.651 0.0783758
\(309\) −165.109 −0.0303971
\(310\) 10971.7 2.01016
\(311\) −4420.02 −0.805904 −0.402952 0.915221i \(-0.632016\pi\)
−0.402952 + 0.915221i \(0.632016\pi\)
\(312\) 0 0
\(313\) 4656.56 0.840909 0.420454 0.907314i \(-0.361871\pi\)
0.420454 + 0.907314i \(0.361871\pi\)
\(314\) −42.0514 −0.00755763
\(315\) −12064.5 −2.15797
\(316\) −355.125 −0.0632195
\(317\) −5986.49 −1.06068 −0.530339 0.847786i \(-0.677935\pi\)
−0.530339 + 0.847786i \(0.677935\pi\)
\(318\) 1951.96 0.344215
\(319\) 916.724 0.160899
\(320\) 11384.8 1.98885
\(321\) 823.806 0.143241
\(322\) 7050.22 1.22017
\(323\) −1807.36 −0.311344
\(324\) −326.142 −0.0559229
\(325\) 0 0
\(326\) 4095.95 0.695870
\(327\) 125.209 0.0211745
\(328\) −6028.99 −1.01492
\(329\) 13950.6 2.33775
\(330\) 1453.07 0.242390
\(331\) −3685.65 −0.612028 −0.306014 0.952027i \(-0.598996\pi\)
−0.306014 + 0.952027i \(0.598996\pi\)
\(332\) 560.725 0.0926922
\(333\) 2585.10 0.425413
\(334\) 1552.77 0.254383
\(335\) 6652.72 1.08501
\(336\) 3840.64 0.623583
\(337\) −8580.79 −1.38702 −0.693509 0.720447i \(-0.743936\pi\)
−0.693509 + 0.720447i \(0.743936\pi\)
\(338\) 0 0
\(339\) 1176.27 0.188456
\(340\) 3387.88 0.540393
\(341\) −2322.30 −0.368796
\(342\) −750.641 −0.118684
\(343\) 4896.77 0.770848
\(344\) −8861.88 −1.38896
\(345\) −4770.63 −0.744469
\(346\) 4412.49 0.685598
\(347\) 194.543 0.0300968 0.0150484 0.999887i \(-0.495210\pi\)
0.0150484 + 0.999887i \(0.495210\pi\)
\(348\) −279.241 −0.0430141
\(349\) 10043.2 1.54040 0.770200 0.637802i \(-0.220156\pi\)
0.770200 + 0.637802i \(0.220156\pi\)
\(350\) 21086.1 3.22029
\(351\) 0 0
\(352\) −649.127 −0.0982914
\(353\) −9089.71 −1.37053 −0.685264 0.728295i \(-0.740313\pi\)
−0.685264 + 0.728295i \(0.740313\pi\)
\(354\) −3804.22 −0.571163
\(355\) 2490.44 0.372335
\(356\) −418.196 −0.0622594
\(357\) 9493.23 1.40738
\(358\) −11809.6 −1.74345
\(359\) −8571.96 −1.26020 −0.630098 0.776515i \(-0.716985\pi\)
−0.630098 + 0.776515i \(0.716985\pi\)
\(360\) 9946.30 1.45616
\(361\) −6659.10 −0.970856
\(362\) 4037.80 0.586249
\(363\) −307.561 −0.0444704
\(364\) 0 0
\(365\) 8687.10 1.24576
\(366\) 2008.39 0.286831
\(367\) −4128.93 −0.587271 −0.293636 0.955917i \(-0.594865\pi\)
−0.293636 + 0.955917i \(0.594865\pi\)
\(368\) −4827.90 −0.683890
\(369\) −5140.99 −0.725283
\(370\) −6540.97 −0.919051
\(371\) −8679.72 −1.21463
\(372\) 707.390 0.0985927
\(373\) −12786.4 −1.77495 −0.887474 0.460857i \(-0.847542\pi\)
−0.887474 + 0.460857i \(0.847542\pi\)
\(374\) 3634.79 0.502541
\(375\) −7880.33 −1.08517
\(376\) −11501.2 −1.57747
\(377\) 0 0
\(378\) 9125.81 1.24175
\(379\) 7006.18 0.949561 0.474780 0.880104i \(-0.342527\pi\)
0.474780 + 0.880104i \(0.342527\pi\)
\(380\) −374.708 −0.0505845
\(381\) −4114.04 −0.553199
\(382\) −8500.82 −1.13859
\(383\) 5394.86 0.719750 0.359875 0.933000i \(-0.382819\pi\)
0.359875 + 0.933000i \(0.382819\pi\)
\(384\) −2520.66 −0.334979
\(385\) −6461.32 −0.855323
\(386\) −5581.76 −0.736021
\(387\) −7556.64 −0.992573
\(388\) 2059.49 0.269471
\(389\) 7762.65 1.01178 0.505889 0.862598i \(-0.331164\pi\)
0.505889 + 0.862598i \(0.331164\pi\)
\(390\) 0 0
\(391\) −11933.5 −1.54349
\(392\) −12298.8 −1.58465
\(393\) −4723.06 −0.606226
\(394\) −13879.6 −1.77473
\(395\) 5416.20 0.689920
\(396\) −297.826 −0.0377937
\(397\) 1736.65 0.219547 0.109773 0.993957i \(-0.464988\pi\)
0.109773 + 0.993957i \(0.464988\pi\)
\(398\) 121.161 0.0152594
\(399\) −1049.97 −0.131740
\(400\) −14439.5 −1.80494
\(401\) 8665.93 1.07919 0.539596 0.841924i \(-0.318577\pi\)
0.539596 + 0.841924i \(0.318577\pi\)
\(402\) −2174.16 −0.269744
\(403\) 0 0
\(404\) −754.510 −0.0929165
\(405\) 4974.17 0.610292
\(406\) −6293.90 −0.769362
\(407\) 1384.48 0.168615
\(408\) −7826.45 −0.949675
\(409\) −12146.8 −1.46851 −0.734257 0.678871i \(-0.762469\pi\)
−0.734257 + 0.678871i \(0.762469\pi\)
\(410\) 13008.1 1.56688
\(411\) 5051.38 0.606244
\(412\) −85.6271 −0.0102392
\(413\) 16916.1 2.01547
\(414\) −4956.29 −0.588377
\(415\) −8551.91 −1.01156
\(416\) 0 0
\(417\) −820.179 −0.0963174
\(418\) −402.016 −0.0470413
\(419\) −5363.15 −0.625315 −0.312658 0.949866i \(-0.601219\pi\)
−0.312658 + 0.949866i \(0.601219\pi\)
\(420\) 1968.17 0.228659
\(421\) 9460.90 1.09524 0.547620 0.836727i \(-0.315534\pi\)
0.547620 + 0.836727i \(0.315534\pi\)
\(422\) 6040.73 0.696820
\(423\) −9807.22 −1.12729
\(424\) 7155.78 0.819611
\(425\) −35691.3 −4.07361
\(426\) −813.894 −0.0925664
\(427\) −8930.67 −1.01214
\(428\) 427.235 0.0482504
\(429\) 0 0
\(430\) 19120.3 2.14433
\(431\) 1127.27 0.125983 0.0629915 0.998014i \(-0.479936\pi\)
0.0629915 + 0.998014i \(0.479936\pi\)
\(432\) −6249.23 −0.695987
\(433\) 13819.1 1.53373 0.766865 0.641809i \(-0.221816\pi\)
0.766865 + 0.641809i \(0.221816\pi\)
\(434\) 15944.1 1.76346
\(435\) 4258.85 0.469417
\(436\) 64.9348 0.00713260
\(437\) 1319.88 0.144481
\(438\) −2839.00 −0.309710
\(439\) 548.517 0.0596339 0.0298170 0.999555i \(-0.490508\pi\)
0.0298170 + 0.999555i \(0.490508\pi\)
\(440\) 5326.87 0.577156
\(441\) −10487.3 −1.13242
\(442\) 0 0
\(443\) 7693.16 0.825086 0.412543 0.910938i \(-0.364641\pi\)
0.412543 + 0.910938i \(0.364641\pi\)
\(444\) −421.724 −0.0450769
\(445\) 6378.13 0.679443
\(446\) 4660.85 0.494838
\(447\) −7537.89 −0.797606
\(448\) 16544.5 1.74476
\(449\) 2843.93 0.298916 0.149458 0.988768i \(-0.452247\pi\)
0.149458 + 0.988768i \(0.452247\pi\)
\(450\) −14823.5 −1.55286
\(451\) −2753.33 −0.287471
\(452\) 610.029 0.0634808
\(453\) −4866.84 −0.504777
\(454\) −5490.33 −0.567564
\(455\) 0 0
\(456\) 865.625 0.0888960
\(457\) −3002.57 −0.307340 −0.153670 0.988122i \(-0.549109\pi\)
−0.153670 + 0.988122i \(0.549109\pi\)
\(458\) 13283.5 1.35523
\(459\) −15446.7 −1.57079
\(460\) −2474.10 −0.250773
\(461\) 5826.46 0.588645 0.294322 0.955706i \(-0.404906\pi\)
0.294322 + 0.955706i \(0.404906\pi\)
\(462\) 2111.61 0.212642
\(463\) −8250.98 −0.828197 −0.414099 0.910232i \(-0.635903\pi\)
−0.414099 + 0.910232i \(0.635903\pi\)
\(464\) 4309.98 0.431219
\(465\) −10788.8 −1.07595
\(466\) 8930.24 0.887737
\(467\) −14425.6 −1.42942 −0.714709 0.699422i \(-0.753441\pi\)
−0.714709 + 0.699422i \(0.753441\pi\)
\(468\) 0 0
\(469\) 9667.78 0.951848
\(470\) 24814.8 2.43537
\(471\) 41.3505 0.00404528
\(472\) −13946.1 −1.36000
\(473\) −4047.06 −0.393412
\(474\) −1770.05 −0.171521
\(475\) 3947.55 0.381318
\(476\) 4923.29 0.474073
\(477\) 6101.82 0.585709
\(478\) 15170.6 1.45165
\(479\) −17012.9 −1.62284 −0.811419 0.584465i \(-0.801305\pi\)
−0.811419 + 0.584465i \(0.801305\pi\)
\(480\) −3015.67 −0.286762
\(481\) 0 0
\(482\) −18160.8 −1.71618
\(483\) −6932.70 −0.653103
\(484\) −159.505 −0.0149798
\(485\) −31410.3 −2.94076
\(486\) −10059.1 −0.938866
\(487\) 8912.81 0.829318 0.414659 0.909977i \(-0.363901\pi\)
0.414659 + 0.909977i \(0.363901\pi\)
\(488\) 7362.66 0.682976
\(489\) −4027.67 −0.372470
\(490\) 26535.7 2.44645
\(491\) 16340.6 1.50192 0.750959 0.660349i \(-0.229592\pi\)
0.750959 + 0.660349i \(0.229592\pi\)
\(492\) 838.685 0.0768513
\(493\) 10653.3 0.973230
\(494\) 0 0
\(495\) 4542.29 0.412446
\(496\) −10918.3 −0.988399
\(497\) 3619.13 0.326640
\(498\) 2794.83 0.251484
\(499\) 1245.47 0.111733 0.0558665 0.998438i \(-0.482208\pi\)
0.0558665 + 0.998438i \(0.482208\pi\)
\(500\) −4086.83 −0.365537
\(501\) −1526.89 −0.136160
\(502\) −16504.2 −1.46737
\(503\) 2095.58 0.185760 0.0928801 0.995677i \(-0.470393\pi\)
0.0928801 + 0.995677i \(0.470393\pi\)
\(504\) 14454.0 1.27745
\(505\) 11507.4 1.01401
\(506\) −2654.41 −0.233207
\(507\) 0 0
\(508\) −2133.59 −0.186344
\(509\) −17414.0 −1.51643 −0.758216 0.652004i \(-0.773929\pi\)
−0.758216 + 0.652004i \(0.773929\pi\)
\(510\) 16886.2 1.46615
\(511\) 12624.1 1.09288
\(512\) −13017.4 −1.12362
\(513\) 1708.45 0.147037
\(514\) 183.972 0.0157873
\(515\) 1305.94 0.111741
\(516\) 1232.77 0.105173
\(517\) −5252.39 −0.446808
\(518\) −9505.38 −0.806259
\(519\) −4338.94 −0.366972
\(520\) 0 0
\(521\) −14865.5 −1.25004 −0.625020 0.780609i \(-0.714909\pi\)
−0.625020 + 0.780609i \(0.714909\pi\)
\(522\) 4424.60 0.370995
\(523\) −4969.64 −0.415501 −0.207751 0.978182i \(-0.566614\pi\)
−0.207751 + 0.978182i \(0.566614\pi\)
\(524\) −2449.43 −0.204206
\(525\) −20734.7 −1.72369
\(526\) −2055.04 −0.170349
\(527\) −26987.7 −2.23074
\(528\) −1446.00 −0.119184
\(529\) −3452.21 −0.283735
\(530\) −15439.2 −1.26535
\(531\) −11892.0 −0.971881
\(532\) −544.528 −0.0443765
\(533\) 0 0
\(534\) −2084.42 −0.168917
\(535\) −6515.98 −0.526561
\(536\) −7970.36 −0.642289
\(537\) 11612.8 0.933198
\(538\) 4876.97 0.390820
\(539\) −5616.63 −0.448842
\(540\) −3202.47 −0.255208
\(541\) −3278.56 −0.260548 −0.130274 0.991478i \(-0.541586\pi\)
−0.130274 + 0.991478i \(0.541586\pi\)
\(542\) 3310.46 0.262355
\(543\) −3970.50 −0.313795
\(544\) −7543.57 −0.594537
\(545\) −990.354 −0.0778387
\(546\) 0 0
\(547\) −1923.63 −0.150363 −0.0751813 0.997170i \(-0.523954\pi\)
−0.0751813 + 0.997170i \(0.523954\pi\)
\(548\) 2619.70 0.204212
\(549\) 6278.23 0.488067
\(550\) −7938.92 −0.615485
\(551\) −1178.29 −0.0911010
\(552\) 5715.49 0.440702
\(553\) 7870.85 0.605249
\(554\) −954.113 −0.0731703
\(555\) 6431.94 0.491929
\(556\) −425.354 −0.0324443
\(557\) −4445.39 −0.338163 −0.169082 0.985602i \(-0.554080\pi\)
−0.169082 + 0.985602i \(0.554080\pi\)
\(558\) −11208.6 −0.850358
\(559\) 0 0
\(560\) −30377.9 −2.29232
\(561\) −3574.20 −0.268989
\(562\) 2654.34 0.199229
\(563\) 7326.15 0.548420 0.274210 0.961670i \(-0.411584\pi\)
0.274210 + 0.961670i \(0.411584\pi\)
\(564\) 1599.92 0.119448
\(565\) −9303.86 −0.692772
\(566\) 4692.41 0.348475
\(567\) 7228.49 0.535393
\(568\) −2983.70 −0.220410
\(569\) 20265.7 1.49311 0.746557 0.665322i \(-0.231706\pi\)
0.746557 + 0.665322i \(0.231706\pi\)
\(570\) −1867.66 −0.137241
\(571\) 10664.6 0.781612 0.390806 0.920473i \(-0.372196\pi\)
0.390806 + 0.920473i \(0.372196\pi\)
\(572\) 0 0
\(573\) 8359.12 0.609437
\(574\) 18903.4 1.37459
\(575\) 26064.6 1.89038
\(576\) −11630.7 −0.841343
\(577\) −23415.6 −1.68943 −0.844717 0.535214i \(-0.820231\pi\)
−0.844717 + 0.535214i \(0.820231\pi\)
\(578\) 29540.5 2.12582
\(579\) 5488.72 0.393961
\(580\) 2208.69 0.158122
\(581\) −12427.7 −0.887414
\(582\) 10265.1 0.731105
\(583\) 3267.91 0.232149
\(584\) −10407.7 −0.737452
\(585\) 0 0
\(586\) 16710.0 1.17796
\(587\) −24346.6 −1.71191 −0.855954 0.517052i \(-0.827030\pi\)
−0.855954 + 0.517052i \(0.827030\pi\)
\(588\) 1710.87 0.119992
\(589\) 2984.90 0.208813
\(590\) 30089.8 2.09963
\(591\) 13648.3 0.949940
\(592\) 6509.16 0.451900
\(593\) −25082.6 −1.73696 −0.868480 0.495725i \(-0.834903\pi\)
−0.868480 + 0.495725i \(0.834903\pi\)
\(594\) −3435.86 −0.237332
\(595\) −75087.7 −5.17360
\(596\) −3909.23 −0.268672
\(597\) −119.141 −0.00816771
\(598\) 0 0
\(599\) −26412.5 −1.80165 −0.900823 0.434186i \(-0.857036\pi\)
−0.900823 + 0.434186i \(0.857036\pi\)
\(600\) 17094.2 1.16311
\(601\) −2941.50 −0.199645 −0.0998223 0.995005i \(-0.531827\pi\)
−0.0998223 + 0.995005i \(0.531827\pi\)
\(602\) 27785.7 1.88116
\(603\) −6796.43 −0.458991
\(604\) −2524.00 −0.170033
\(605\) 2432.69 0.163476
\(606\) −3760.71 −0.252093
\(607\) 28694.7 1.91875 0.959377 0.282128i \(-0.0910404\pi\)
0.959377 + 0.282128i \(0.0910404\pi\)
\(608\) 834.337 0.0556527
\(609\) 6188.99 0.411807
\(610\) −15885.6 −1.05441
\(611\) 0 0
\(612\) −3461.06 −0.228603
\(613\) −2153.88 −0.141916 −0.0709578 0.997479i \(-0.522606\pi\)
−0.0709578 + 0.997479i \(0.522606\pi\)
\(614\) 24857.3 1.63381
\(615\) −12791.2 −0.838686
\(616\) 7741.05 0.506324
\(617\) −2450.26 −0.159877 −0.0799383 0.996800i \(-0.525472\pi\)
−0.0799383 + 0.996800i \(0.525472\pi\)
\(618\) −426.792 −0.0277801
\(619\) −15715.2 −1.02043 −0.510216 0.860046i \(-0.670435\pi\)
−0.510216 + 0.860046i \(0.670435\pi\)
\(620\) −5595.18 −0.362432
\(621\) 11280.4 0.728934
\(622\) −11425.4 −0.736520
\(623\) 9268.73 0.596058
\(624\) 0 0
\(625\) 27429.7 1.75550
\(626\) 12036.8 0.768511
\(627\) 395.315 0.0251792
\(628\) 21.4448 0.00136264
\(629\) 16089.2 1.01990
\(630\) −31185.8 −1.97218
\(631\) 8790.00 0.554555 0.277278 0.960790i \(-0.410568\pi\)
0.277278 + 0.960790i \(0.410568\pi\)
\(632\) −6488.93 −0.408411
\(633\) −5940.04 −0.372978
\(634\) −15474.6 −0.969358
\(635\) 32540.4 2.03359
\(636\) −995.432 −0.0620620
\(637\) 0 0
\(638\) 2369.65 0.147046
\(639\) −2544.24 −0.157509
\(640\) 19937.4 1.23140
\(641\) 15059.9 0.927973 0.463987 0.885842i \(-0.346419\pi\)
0.463987 + 0.885842i \(0.346419\pi\)
\(642\) 2129.47 0.130909
\(643\) −4383.40 −0.268841 −0.134420 0.990924i \(-0.542917\pi\)
−0.134420 + 0.990924i \(0.542917\pi\)
\(644\) −3595.38 −0.219996
\(645\) −18801.6 −1.14777
\(646\) −4671.87 −0.284539
\(647\) −7536.76 −0.457961 −0.228980 0.973431i \(-0.573539\pi\)
−0.228980 + 0.973431i \(0.573539\pi\)
\(648\) −5959.35 −0.361273
\(649\) −6368.92 −0.385211
\(650\) 0 0
\(651\) −15678.3 −0.943904
\(652\) −2088.80 −0.125466
\(653\) −13190.7 −0.790493 −0.395247 0.918575i \(-0.629341\pi\)
−0.395247 + 0.918575i \(0.629341\pi\)
\(654\) 323.655 0.0193515
\(655\) 37357.5 2.22852
\(656\) −12944.8 −0.770441
\(657\) −8874.74 −0.526996
\(658\) 36061.1 2.13648
\(659\) 7596.99 0.449069 0.224535 0.974466i \(-0.427914\pi\)
0.224535 + 0.974466i \(0.427914\pi\)
\(660\) −741.015 −0.0437030
\(661\) 1252.96 0.0737285 0.0368642 0.999320i \(-0.488263\pi\)
0.0368642 + 0.999320i \(0.488263\pi\)
\(662\) −9527.08 −0.559336
\(663\) 0 0
\(664\) 10245.7 0.598811
\(665\) 8304.88 0.484285
\(666\) 6682.25 0.388787
\(667\) −7779.91 −0.451633
\(668\) −791.862 −0.0458653
\(669\) −4583.16 −0.264866
\(670\) 17196.7 0.991593
\(671\) 3362.39 0.193448
\(672\) −4382.39 −0.251569
\(673\) 6436.84 0.368680 0.184340 0.982862i \(-0.440985\pi\)
0.184340 + 0.982862i \(0.440985\pi\)
\(674\) −22180.6 −1.26760
\(675\) 33738.0 1.92382
\(676\) 0 0
\(677\) −19087.6 −1.08360 −0.541798 0.840509i \(-0.682256\pi\)
−0.541798 + 0.840509i \(0.682256\pi\)
\(678\) 3040.57 0.172231
\(679\) −45645.7 −2.57985
\(680\) 61904.1 3.49105
\(681\) 5398.81 0.303793
\(682\) −6002.94 −0.337045
\(683\) 22989.3 1.28794 0.643970 0.765051i \(-0.277286\pi\)
0.643970 + 0.765051i \(0.277286\pi\)
\(684\) 382.802 0.0213988
\(685\) −39954.4 −2.22858
\(686\) 12657.7 0.704482
\(687\) −13062.0 −0.725397
\(688\) −19027.3 −1.05437
\(689\) 0 0
\(690\) −12331.7 −0.680374
\(691\) 22256.4 1.22529 0.612644 0.790359i \(-0.290106\pi\)
0.612644 + 0.790359i \(0.290106\pi\)
\(692\) −2250.22 −0.123614
\(693\) 6600.89 0.361828
\(694\) 502.876 0.0275056
\(695\) 6487.29 0.354068
\(696\) −5102.36 −0.277880
\(697\) −31996.7 −1.73883
\(698\) 25960.8 1.40778
\(699\) −8781.38 −0.475168
\(700\) −10753.2 −0.580619
\(701\) 26090.6 1.40575 0.702874 0.711315i \(-0.251900\pi\)
0.702874 + 0.711315i \(0.251900\pi\)
\(702\) 0 0
\(703\) −1779.51 −0.0954700
\(704\) −6228.99 −0.333472
\(705\) −24401.2 −1.30355
\(706\) −23496.1 −1.25253
\(707\) 16722.7 0.889562
\(708\) 1940.02 0.102981
\(709\) −15288.9 −0.809855 −0.404927 0.914349i \(-0.632703\pi\)
−0.404927 + 0.914349i \(0.632703\pi\)
\(710\) 6437.58 0.340279
\(711\) −5533.19 −0.291858
\(712\) −7641.37 −0.402209
\(713\) 19708.5 1.03519
\(714\) 24539.2 1.28621
\(715\) 0 0
\(716\) 6022.50 0.314345
\(717\) −14917.7 −0.777006
\(718\) −22157.8 −1.15170
\(719\) 7202.62 0.373592 0.186796 0.982399i \(-0.440190\pi\)
0.186796 + 0.982399i \(0.440190\pi\)
\(720\) 21355.6 1.10538
\(721\) 1897.81 0.0980277
\(722\) −17213.2 −0.887270
\(723\) 17858.0 0.918600
\(724\) −2059.14 −0.105701
\(725\) −23268.5 −1.19196
\(726\) −795.019 −0.0406418
\(727\) −8345.29 −0.425736 −0.212868 0.977081i \(-0.568280\pi\)
−0.212868 + 0.977081i \(0.568280\pi\)
\(728\) 0 0
\(729\) 3211.30 0.163151
\(730\) 22455.4 1.13851
\(731\) −47031.3 −2.37964
\(732\) −1024.21 −0.0517158
\(733\) 6942.80 0.349847 0.174924 0.984582i \(-0.444032\pi\)
0.174924 + 0.984582i \(0.444032\pi\)
\(734\) −10672.9 −0.536710
\(735\) −26093.4 −1.30948
\(736\) 5508.91 0.275898
\(737\) −3639.92 −0.181924
\(738\) −13289.0 −0.662840
\(739\) −18054.1 −0.898686 −0.449343 0.893359i \(-0.648342\pi\)
−0.449343 + 0.893359i \(0.648342\pi\)
\(740\) 3335.67 0.165705
\(741\) 0 0
\(742\) −22436.3 −1.11006
\(743\) 27215.4 1.34379 0.671895 0.740647i \(-0.265481\pi\)
0.671895 + 0.740647i \(0.265481\pi\)
\(744\) 12925.6 0.636929
\(745\) 59621.7 2.93204
\(746\) −33051.8 −1.62213
\(747\) 8736.64 0.427921
\(748\) −1853.62 −0.0906083
\(749\) −9469.06 −0.461938
\(750\) −20370.0 −0.991742
\(751\) 30044.8 1.45985 0.729927 0.683525i \(-0.239554\pi\)
0.729927 + 0.683525i \(0.239554\pi\)
\(752\) −24694.1 −1.19748
\(753\) 16229.1 0.785420
\(754\) 0 0
\(755\) 38494.8 1.85559
\(756\) −4653.85 −0.223888
\(757\) −32140.6 −1.54316 −0.771578 0.636135i \(-0.780532\pi\)
−0.771578 + 0.636135i \(0.780532\pi\)
\(758\) 18110.4 0.867808
\(759\) 2610.16 0.124826
\(760\) −6846.75 −0.326786
\(761\) 5510.25 0.262479 0.131240 0.991351i \(-0.458104\pi\)
0.131240 + 0.991351i \(0.458104\pi\)
\(762\) −10634.4 −0.505571
\(763\) −1439.19 −0.0682859
\(764\) 4335.13 0.205287
\(765\) 52786.4 2.49477
\(766\) 13945.2 0.657784
\(767\) 0 0
\(768\) 4999.24 0.234889
\(769\) 4317.43 0.202459 0.101229 0.994863i \(-0.467722\pi\)
0.101229 + 0.994863i \(0.467722\pi\)
\(770\) −16702.0 −0.781684
\(771\) −180.906 −0.00845026
\(772\) 2846.51 0.132705
\(773\) 11644.8 0.541831 0.270916 0.962603i \(-0.412674\pi\)
0.270916 + 0.962603i \(0.412674\pi\)
\(774\) −19533.3 −0.907117
\(775\) 58945.2 2.73209
\(776\) 37631.4 1.74084
\(777\) 9346.93 0.431556
\(778\) 20065.8 0.924670
\(779\) 3538.91 0.162766
\(780\) 0 0
\(781\) −1362.60 −0.0624298
\(782\) −30847.1 −1.41060
\(783\) −10070.3 −0.459621
\(784\) −26406.6 −1.20293
\(785\) −327.066 −0.0148707
\(786\) −12208.7 −0.554033
\(787\) −36525.7 −1.65438 −0.827191 0.561921i \(-0.810063\pi\)
−0.827191 + 0.561921i \(0.810063\pi\)
\(788\) 7078.14 0.319985
\(789\) 2020.78 0.0911809
\(790\) 14000.4 0.630522
\(791\) −13520.4 −0.607751
\(792\) −5441.94 −0.244155
\(793\) 0 0
\(794\) 4489.09 0.200645
\(795\) 15181.8 0.677289
\(796\) −61.7879 −0.00275127
\(797\) −5661.21 −0.251607 −0.125803 0.992055i \(-0.540151\pi\)
−0.125803 + 0.992055i \(0.540151\pi\)
\(798\) −2714.09 −0.120398
\(799\) −61038.6 −2.70261
\(800\) 16476.3 0.728157
\(801\) −6515.90 −0.287426
\(802\) 22400.7 0.986279
\(803\) −4752.99 −0.208878
\(804\) 1108.75 0.0486349
\(805\) 54834.9 2.40084
\(806\) 0 0
\(807\) −4795.68 −0.209190
\(808\) −13786.6 −0.600260
\(809\) 13730.7 0.596719 0.298359 0.954454i \(-0.403561\pi\)
0.298359 + 0.954454i \(0.403561\pi\)
\(810\) 12857.8 0.557749
\(811\) −12954.7 −0.560913 −0.280456 0.959867i \(-0.590486\pi\)
−0.280456 + 0.959867i \(0.590486\pi\)
\(812\) 3209.68 0.138716
\(813\) −3255.28 −0.140428
\(814\) 3578.77 0.154098
\(815\) 31857.3 1.36922
\(816\) −16804.1 −0.720909
\(817\) 5201.78 0.222750
\(818\) −31398.5 −1.34208
\(819\) 0 0
\(820\) −6633.67 −0.282509
\(821\) −12151.3 −0.516546 −0.258273 0.966072i \(-0.583153\pi\)
−0.258273 + 0.966072i \(0.583153\pi\)
\(822\) 13057.4 0.554050
\(823\) −7267.59 −0.307815 −0.153908 0.988085i \(-0.549186\pi\)
−0.153908 + 0.988085i \(0.549186\pi\)
\(824\) −1564.60 −0.0661473
\(825\) 7806.59 0.329443
\(826\) 43726.8 1.84195
\(827\) 16200.3 0.681183 0.340591 0.940211i \(-0.389373\pi\)
0.340591 + 0.940211i \(0.389373\pi\)
\(828\) 2527.54 0.106085
\(829\) 327.283 0.0137117 0.00685585 0.999976i \(-0.497818\pi\)
0.00685585 + 0.999976i \(0.497818\pi\)
\(830\) −22106.0 −0.924469
\(831\) 938.209 0.0391650
\(832\) 0 0
\(833\) −65271.5 −2.71491
\(834\) −2120.09 −0.0880249
\(835\) 12077.1 0.500533
\(836\) 205.015 0.00848156
\(837\) 25510.7 1.05350
\(838\) −13863.3 −0.571479
\(839\) 20762.4 0.854346 0.427173 0.904170i \(-0.359510\pi\)
0.427173 + 0.904170i \(0.359510\pi\)
\(840\) 35962.8 1.47718
\(841\) −17443.7 −0.715228
\(842\) 24455.6 1.00095
\(843\) −2610.10 −0.106639
\(844\) −3080.57 −0.125637
\(845\) 0 0
\(846\) −25350.8 −1.03024
\(847\) 3535.19 0.143413
\(848\) 15364.1 0.622176
\(849\) −4614.19 −0.186524
\(850\) −92259.0 −3.72289
\(851\) −11749.6 −0.473292
\(852\) 415.058 0.0166898
\(853\) −5761.34 −0.231260 −0.115630 0.993292i \(-0.536889\pi\)
−0.115630 + 0.993292i \(0.536889\pi\)
\(854\) −23085.0 −0.925003
\(855\) −5838.31 −0.233527
\(856\) 7806.53 0.311707
\(857\) −29258.6 −1.16623 −0.583113 0.812391i \(-0.698166\pi\)
−0.583113 + 0.812391i \(0.698166\pi\)
\(858\) 0 0
\(859\) −24016.1 −0.953923 −0.476961 0.878924i \(-0.658262\pi\)
−0.476961 + 0.878924i \(0.658262\pi\)
\(860\) −9750.69 −0.386623
\(861\) −18588.3 −0.735758
\(862\) 2913.89 0.115136
\(863\) −6376.10 −0.251500 −0.125750 0.992062i \(-0.540134\pi\)
−0.125750 + 0.992062i \(0.540134\pi\)
\(864\) 7130.73 0.280778
\(865\) 34319.3 1.34901
\(866\) 35721.3 1.40168
\(867\) −29048.1 −1.13786
\(868\) −8130.95 −0.317952
\(869\) −2963.37 −0.115680
\(870\) 11008.8 0.429003
\(871\) 0 0
\(872\) 1186.50 0.0460780
\(873\) 32088.8 1.24403
\(874\) 3411.77 0.132042
\(875\) 90578.8 3.49957
\(876\) 1447.80 0.0558408
\(877\) 22771.4 0.876780 0.438390 0.898785i \(-0.355549\pi\)
0.438390 + 0.898785i \(0.355549\pi\)
\(878\) 1417.87 0.0544998
\(879\) −16431.5 −0.630511
\(880\) 11437.3 0.438126
\(881\) 32496.4 1.24272 0.621358 0.783527i \(-0.286581\pi\)
0.621358 + 0.783527i \(0.286581\pi\)
\(882\) −27108.9 −1.03492
\(883\) 23978.0 0.913843 0.456922 0.889507i \(-0.348952\pi\)
0.456922 + 0.889507i \(0.348952\pi\)
\(884\) 0 0
\(885\) −29588.3 −1.12384
\(886\) 19886.2 0.754050
\(887\) 20034.6 0.758396 0.379198 0.925315i \(-0.376200\pi\)
0.379198 + 0.925315i \(0.376200\pi\)
\(888\) −7705.84 −0.291206
\(889\) 47288.0 1.78401
\(890\) 16486.9 0.620947
\(891\) −2721.52 −0.102328
\(892\) −2376.88 −0.0892194
\(893\) 6751.01 0.252983
\(894\) −19484.8 −0.728936
\(895\) −91852.3 −3.43048
\(896\) 28973.2 1.08027
\(897\) 0 0
\(898\) 7351.32 0.273181
\(899\) −17594.3 −0.652727
\(900\) 7559.49 0.279981
\(901\) 37976.7 1.40421
\(902\) −7117.12 −0.262721
\(903\) −27322.5 −1.00691
\(904\) 11146.6 0.410099
\(905\) 31405.1 1.15353
\(906\) −12580.4 −0.461318
\(907\) 9988.69 0.365677 0.182838 0.983143i \(-0.441471\pi\)
0.182838 + 0.983143i \(0.441471\pi\)
\(908\) 2799.88 0.102332
\(909\) −11756.0 −0.428957
\(910\) 0 0
\(911\) 44710.0 1.62602 0.813012 0.582246i \(-0.197826\pi\)
0.813012 + 0.582246i \(0.197826\pi\)
\(912\) 1858.58 0.0674820
\(913\) 4679.02 0.169609
\(914\) −7761.39 −0.280879
\(915\) 15620.8 0.564379
\(916\) −6774.12 −0.244348
\(917\) 54288.2 1.95502
\(918\) −39928.5 −1.43555
\(919\) −8616.15 −0.309272 −0.154636 0.987972i \(-0.549420\pi\)
−0.154636 + 0.987972i \(0.549420\pi\)
\(920\) −45207.3 −1.62004
\(921\) −24443.0 −0.874510
\(922\) 15060.9 0.537966
\(923\) 0 0
\(924\) −1076.85 −0.0383395
\(925\) −35141.3 −1.24912
\(926\) −21328.1 −0.756894
\(927\) −1334.15 −0.0472700
\(928\) −4917.94 −0.173965
\(929\) 38673.1 1.36579 0.682897 0.730515i \(-0.260720\pi\)
0.682897 + 0.730515i \(0.260720\pi\)
\(930\) −27888.1 −0.983318
\(931\) 7219.18 0.254134
\(932\) −4554.12 −0.160059
\(933\) 11234.9 0.394228
\(934\) −37289.0 −1.30635
\(935\) 28270.5 0.988817
\(936\) 0 0
\(937\) −25983.5 −0.905917 −0.452959 0.891532i \(-0.649631\pi\)
−0.452959 + 0.891532i \(0.649631\pi\)
\(938\) 24990.4 0.869899
\(939\) −11836.2 −0.411351
\(940\) −12654.7 −0.439097
\(941\) −29657.7 −1.02743 −0.513716 0.857960i \(-0.671731\pi\)
−0.513716 + 0.857960i \(0.671731\pi\)
\(942\) 106.887 0.00369700
\(943\) 23366.5 0.806913
\(944\) −29943.5 −1.03239
\(945\) 70978.3 2.44331
\(946\) −10461.3 −0.359542
\(947\) 43620.2 1.49680 0.748399 0.663249i \(-0.230823\pi\)
0.748399 + 0.663249i \(0.230823\pi\)
\(948\) 902.667 0.0309254
\(949\) 0 0
\(950\) 10204.1 0.348488
\(951\) 15216.6 0.518857
\(952\) 89959.5 3.06261
\(953\) 42069.1 1.42996 0.714980 0.699145i \(-0.246436\pi\)
0.714980 + 0.699145i \(0.246436\pi\)
\(954\) 15772.7 0.535282
\(955\) −66117.3 −2.24032
\(956\) −7736.50 −0.261733
\(957\) −2330.15 −0.0787076
\(958\) −43976.9 −1.48312
\(959\) −58062.0 −1.95508
\(960\) −28938.2 −0.972893
\(961\) 14779.8 0.496118
\(962\) 0 0
\(963\) 6656.72 0.222752
\(964\) 9261.37 0.309428
\(965\) −43413.6 −1.44822
\(966\) −17920.4 −0.596874
\(967\) −7071.73 −0.235172 −0.117586 0.993063i \(-0.537516\pi\)
−0.117586 + 0.993063i \(0.537516\pi\)
\(968\) −2914.50 −0.0967724
\(969\) 4594.00 0.152302
\(970\) −81193.0 −2.68758
\(971\) −25984.5 −0.858787 −0.429394 0.903117i \(-0.641273\pi\)
−0.429394 + 0.903117i \(0.641273\pi\)
\(972\) 5129.79 0.169278
\(973\) 9427.37 0.310614
\(974\) 23038.8 0.757918
\(975\) 0 0
\(976\) 15808.3 0.518454
\(977\) 56338.0 1.84484 0.922421 0.386186i \(-0.126208\pi\)
0.922421 + 0.386186i \(0.126208\pi\)
\(978\) −10411.2 −0.340402
\(979\) −3489.68 −0.113923
\(980\) −13532.3 −0.441096
\(981\) 1011.75 0.0329282
\(982\) 42239.1 1.37261
\(983\) −37200.9 −1.20704 −0.603522 0.797346i \(-0.706237\pi\)
−0.603522 + 0.797346i \(0.706237\pi\)
\(984\) 15324.6 0.496476
\(985\) −107952. −3.49203
\(986\) 27538.0 0.889440
\(987\) −35460.0 −1.14357
\(988\) 0 0
\(989\) 34346.0 1.10428
\(990\) 11741.4 0.376937
\(991\) −26813.7 −0.859501 −0.429751 0.902948i \(-0.641399\pi\)
−0.429751 + 0.902948i \(0.641399\pi\)
\(992\) 12458.4 0.398745
\(993\) 9368.27 0.299389
\(994\) 9355.13 0.298518
\(995\) 942.359 0.0300249
\(996\) −1425.27 −0.0453427
\(997\) −18893.6 −0.600165 −0.300083 0.953913i \(-0.597014\pi\)
−0.300083 + 0.953913i \(0.597014\pi\)
\(998\) 3219.43 0.102113
\(999\) −15208.7 −0.481664
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 1859.4.a.e.1.8 11
13.12 even 2 143.4.a.d.1.4 11
39.38 odd 2 1287.4.a.m.1.8 11
52.51 odd 2 2288.4.a.u.1.7 11
143.142 odd 2 1573.4.a.f.1.8 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.a.d.1.4 11 13.12 even 2
1287.4.a.m.1.8 11 39.38 odd 2
1573.4.a.f.1.8 11 143.142 odd 2
1859.4.a.e.1.8 11 1.1 even 1 trivial
2288.4.a.u.1.7 11 52.51 odd 2