Properties

Label 289.4.a.i.1.3
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,4,Mod(1,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.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: \(17.0515519917\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.73276\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.73276 q^{2} -3.65511 q^{3} +5.93351 q^{4} -14.5154 q^{5} +13.6437 q^{6} +12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} +O(q^{10})\) \(q-3.73276 q^{2} -3.65511 q^{3} +5.93351 q^{4} -14.5154 q^{5} +13.6437 q^{6} +12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} +54.1823 q^{10} -20.2490 q^{11} -21.6876 q^{12} -90.7856 q^{13} -48.4118 q^{14} +53.0552 q^{15} -76.2615 q^{16} +50.9155 q^{18} -127.359 q^{19} -86.1270 q^{20} -47.4047 q^{21} +75.5848 q^{22} -69.5078 q^{23} -28.1945 q^{24} +85.6954 q^{25} +338.881 q^{26} +148.544 q^{27} +76.9542 q^{28} -43.9568 q^{29} -198.042 q^{30} -218.817 q^{31} +222.956 q^{32} +74.0124 q^{33} -188.256 q^{35} -80.9340 q^{36} -41.5125 q^{37} +475.399 q^{38} +331.832 q^{39} -111.967 q^{40} +440.141 q^{41} +176.951 q^{42} -310.790 q^{43} -120.148 q^{44} +197.992 q^{45} +259.456 q^{46} +84.3763 q^{47} +278.744 q^{48} -174.794 q^{49} -319.880 q^{50} -538.677 q^{52} +47.6186 q^{53} -554.480 q^{54} +293.922 q^{55} +100.043 q^{56} +465.510 q^{57} +164.080 q^{58} -1.73428 q^{59} +314.804 q^{60} +159.400 q^{61} +816.792 q^{62} -176.905 q^{63} -222.151 q^{64} +1317.78 q^{65} -276.271 q^{66} +141.756 q^{67} +254.059 q^{69} +702.714 q^{70} +447.302 q^{71} -105.216 q^{72} +757.081 q^{73} +154.956 q^{74} -313.226 q^{75} -755.684 q^{76} -262.618 q^{77} -1238.65 q^{78} +529.801 q^{79} +1106.96 q^{80} -174.662 q^{81} -1642.94 q^{82} -762.097 q^{83} -281.276 q^{84} +1160.11 q^{86} +160.667 q^{87} -156.195 q^{88} -397.434 q^{89} -739.056 q^{90} -1177.44 q^{91} -412.425 q^{92} +799.801 q^{93} -314.957 q^{94} +1848.66 q^{95} -814.930 q^{96} -427.919 q^{97} +652.464 q^{98} +276.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9} + 60 q^{10} + 162 q^{11} + 216 q^{12} - 72 q^{13} + 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} + 129 q^{20} + 246 q^{21} + 456 q^{22} + 282 q^{23} + 72 q^{24} + 444 q^{25} + 528 q^{26} + 1092 q^{27} + 120 q^{28} + 648 q^{29} - 1890 q^{30} + 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} - 30 q^{37} - 60 q^{38} + 1758 q^{39} - 450 q^{40} + 318 q^{41} + 804 q^{42} + 486 q^{43} + 2448 q^{44} + 486 q^{45} + 1617 q^{46} - 888 q^{47} + 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} + 933 q^{54} + 972 q^{55} + 2661 q^{56} - 156 q^{57} + 201 q^{58} - 792 q^{59} + 1458 q^{60} + 1212 q^{61} + 2817 q^{62} + 2112 q^{63} - 1857 q^{64} + 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} + 2802 q^{71} + 1455 q^{72} + 726 q^{73} + 270 q^{74} - 264 q^{75} + 675 q^{76} - 1008 q^{77} - 3090 q^{78} - 444 q^{79} - 1143 q^{80} + 2520 q^{81} - 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} - 3750 q^{88} - 906 q^{89} - 7755 q^{90} + 2280 q^{91} + 87 q^{92} + 132 q^{93} + 735 q^{94} + 966 q^{95} - 5046 q^{96} - 3246 q^{97} + 1911 q^{98} - 282 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.73276 −1.31973 −0.659865 0.751384i \(-0.729387\pi\)
−0.659865 + 0.751384i \(0.729387\pi\)
\(3\) −3.65511 −0.703426 −0.351713 0.936108i \(-0.614401\pi\)
−0.351713 + 0.936108i \(0.614401\pi\)
\(4\) 5.93351 0.741689
\(5\) −14.5154 −1.29829 −0.649146 0.760664i \(-0.724874\pi\)
−0.649146 + 0.760664i \(0.724874\pi\)
\(6\) 13.6437 0.928333
\(7\) 12.9694 0.700284 0.350142 0.936697i \(-0.386133\pi\)
0.350142 + 0.936697i \(0.386133\pi\)
\(8\) 7.71372 0.340901
\(9\) −13.6402 −0.505191
\(10\) 54.1823 1.71340
\(11\) −20.2490 −0.555028 −0.277514 0.960722i \(-0.589511\pi\)
−0.277514 + 0.960722i \(0.589511\pi\)
\(12\) −21.6876 −0.521723
\(13\) −90.7856 −1.93688 −0.968438 0.249253i \(-0.919815\pi\)
−0.968438 + 0.249253i \(0.919815\pi\)
\(14\) −48.4118 −0.924186
\(15\) 53.0552 0.913253
\(16\) −76.2615 −1.19159
\(17\) 0 0
\(18\) 50.9155 0.666716
\(19\) −127.359 −1.53779 −0.768897 0.639373i \(-0.779194\pi\)
−0.768897 + 0.639373i \(0.779194\pi\)
\(20\) −86.1270 −0.962929
\(21\) −47.4047 −0.492598
\(22\) 75.5848 0.732488
\(23\) −69.5078 −0.630147 −0.315073 0.949067i \(-0.602029\pi\)
−0.315073 + 0.949067i \(0.602029\pi\)
\(24\) −28.1945 −0.239799
\(25\) 85.6954 0.685563
\(26\) 338.881 2.55616
\(27\) 148.544 1.05879
\(28\) 76.9542 0.519392
\(29\) −43.9568 −0.281468 −0.140734 0.990047i \(-0.544946\pi\)
−0.140734 + 0.990047i \(0.544946\pi\)
\(30\) −198.042 −1.20525
\(31\) −218.817 −1.26776 −0.633882 0.773430i \(-0.718540\pi\)
−0.633882 + 0.773430i \(0.718540\pi\)
\(32\) 222.956 1.23167
\(33\) 74.0124 0.390422
\(34\) 0 0
\(35\) −188.256 −0.909173
\(36\) −80.9340 −0.374695
\(37\) −41.5125 −0.184449 −0.0922245 0.995738i \(-0.529398\pi\)
−0.0922245 + 0.995738i \(0.529398\pi\)
\(38\) 475.399 2.02947
\(39\) 331.832 1.36245
\(40\) −111.967 −0.442590
\(41\) 440.141 1.67655 0.838274 0.545249i \(-0.183565\pi\)
0.838274 + 0.545249i \(0.183565\pi\)
\(42\) 176.951 0.650097
\(43\) −310.790 −1.10221 −0.551106 0.834435i \(-0.685794\pi\)
−0.551106 + 0.834435i \(0.685794\pi\)
\(44\) −120.148 −0.411658
\(45\) 197.992 0.655886
\(46\) 259.456 0.831624
\(47\) 84.3763 0.261863 0.130931 0.991391i \(-0.458203\pi\)
0.130931 + 0.991391i \(0.458203\pi\)
\(48\) 278.744 0.838194
\(49\) −174.794 −0.509603
\(50\) −319.880 −0.904759
\(51\) 0 0
\(52\) −538.677 −1.43656
\(53\) 47.6186 0.123414 0.0617068 0.998094i \(-0.480346\pi\)
0.0617068 + 0.998094i \(0.480346\pi\)
\(54\) −554.480 −1.39732
\(55\) 293.922 0.720589
\(56\) 100.043 0.238728
\(57\) 465.510 1.08172
\(58\) 164.080 0.371462
\(59\) −1.73428 −0.00382685 −0.00191342 0.999998i \(-0.500609\pi\)
−0.00191342 + 0.999998i \(0.500609\pi\)
\(60\) 314.804 0.677350
\(61\) 159.400 0.334575 0.167287 0.985908i \(-0.446499\pi\)
0.167287 + 0.985908i \(0.446499\pi\)
\(62\) 816.792 1.67311
\(63\) −176.905 −0.353777
\(64\) −222.151 −0.433888
\(65\) 1317.78 2.51463
\(66\) −276.271 −0.515251
\(67\) 141.756 0.258482 0.129241 0.991613i \(-0.458746\pi\)
0.129241 + 0.991613i \(0.458746\pi\)
\(68\) 0 0
\(69\) 254.059 0.443262
\(70\) 702.714 1.19986
\(71\) 447.302 0.747675 0.373838 0.927494i \(-0.378042\pi\)
0.373838 + 0.927494i \(0.378042\pi\)
\(72\) −105.216 −0.172220
\(73\) 757.081 1.21383 0.606916 0.794766i \(-0.292407\pi\)
0.606916 + 0.794766i \(0.292407\pi\)
\(74\) 154.956 0.243423
\(75\) −313.226 −0.482243
\(76\) −755.684 −1.14056
\(77\) −262.618 −0.388677
\(78\) −1238.65 −1.79807
\(79\) 529.801 0.754523 0.377261 0.926107i \(-0.376866\pi\)
0.377261 + 0.926107i \(0.376866\pi\)
\(80\) 1106.96 1.54703
\(81\) −174.662 −0.239591
\(82\) −1642.94 −2.21259
\(83\) −762.097 −1.00784 −0.503922 0.863749i \(-0.668110\pi\)
−0.503922 + 0.863749i \(0.668110\pi\)
\(84\) −281.276 −0.365354
\(85\) 0 0
\(86\) 1160.11 1.45462
\(87\) 160.667 0.197992
\(88\) −156.195 −0.189210
\(89\) −397.434 −0.473348 −0.236674 0.971589i \(-0.576057\pi\)
−0.236674 + 0.971589i \(0.576057\pi\)
\(90\) −739.056 −0.865593
\(91\) −1177.44 −1.35636
\(92\) −412.425 −0.467373
\(93\) 799.801 0.891779
\(94\) −314.957 −0.345588
\(95\) 1848.66 1.99651
\(96\) −814.930 −0.866391
\(97\) −427.919 −0.447924 −0.223962 0.974598i \(-0.571899\pi\)
−0.223962 + 0.974598i \(0.571899\pi\)
\(98\) 652.464 0.672538
\(99\) 276.200 0.280395
\(100\) 508.474 0.508474
\(101\) 1591.35 1.56778 0.783889 0.620901i \(-0.213233\pi\)
0.783889 + 0.620901i \(0.213233\pi\)
\(102\) 0 0
\(103\) −1094.59 −1.04712 −0.523558 0.851990i \(-0.675396\pi\)
−0.523558 + 0.851990i \(0.675396\pi\)
\(104\) −700.295 −0.660284
\(105\) 688.096 0.639536
\(106\) −177.749 −0.162873
\(107\) −1321.45 −1.19392 −0.596960 0.802271i \(-0.703625\pi\)
−0.596960 + 0.802271i \(0.703625\pi\)
\(108\) 881.389 0.785293
\(109\) −1324.25 −1.16367 −0.581835 0.813307i \(-0.697665\pi\)
−0.581835 + 0.813307i \(0.697665\pi\)
\(110\) −1097.14 −0.950983
\(111\) 151.733 0.129746
\(112\) −989.069 −0.834449
\(113\) −1621.26 −1.34969 −0.674847 0.737958i \(-0.735790\pi\)
−0.674847 + 0.737958i \(0.735790\pi\)
\(114\) −1737.64 −1.42758
\(115\) 1008.93 0.818115
\(116\) −260.818 −0.208762
\(117\) 1238.33 0.978493
\(118\) 6.47365 0.00505041
\(119\) 0 0
\(120\) 409.253 0.311329
\(121\) −920.977 −0.691944
\(122\) −595.001 −0.441548
\(123\) −1608.76 −1.17933
\(124\) −1298.35 −0.940287
\(125\) 570.520 0.408231
\(126\) 660.345 0.466890
\(127\) 423.287 0.295753 0.147876 0.989006i \(-0.452756\pi\)
0.147876 + 0.989006i \(0.452756\pi\)
\(128\) −954.415 −0.659056
\(129\) 1135.97 0.775325
\(130\) −4918.98 −3.31864
\(131\) −792.977 −0.528876 −0.264438 0.964403i \(-0.585186\pi\)
−0.264438 + 0.964403i \(0.585186\pi\)
\(132\) 439.153 0.289571
\(133\) −1651.77 −1.07689
\(134\) −529.143 −0.341127
\(135\) −2156.17 −1.37462
\(136\) 0 0
\(137\) 809.512 0.504827 0.252414 0.967619i \(-0.418776\pi\)
0.252414 + 0.967619i \(0.418776\pi\)
\(138\) −948.341 −0.584986
\(139\) 2842.04 1.73424 0.867119 0.498102i \(-0.165969\pi\)
0.867119 + 0.498102i \(0.165969\pi\)
\(140\) −1117.02 −0.674323
\(141\) −308.405 −0.184201
\(142\) −1669.67 −0.986730
\(143\) 1838.32 1.07502
\(144\) 1040.22 0.601979
\(145\) 638.048 0.365428
\(146\) −2826.00 −1.60193
\(147\) 638.891 0.358468
\(148\) −246.315 −0.136804
\(149\) −1010.84 −0.555782 −0.277891 0.960613i \(-0.589635\pi\)
−0.277891 + 0.960613i \(0.589635\pi\)
\(150\) 1169.20 0.636431
\(151\) 1340.29 0.722327 0.361163 0.932503i \(-0.382380\pi\)
0.361163 + 0.932503i \(0.382380\pi\)
\(152\) −982.409 −0.524236
\(153\) 0 0
\(154\) 980.292 0.512949
\(155\) 3176.21 1.64593
\(156\) 1968.93 1.01051
\(157\) −947.372 −0.481583 −0.240792 0.970577i \(-0.577407\pi\)
−0.240792 + 0.970577i \(0.577407\pi\)
\(158\) −1977.62 −0.995766
\(159\) −174.051 −0.0868123
\(160\) −3236.29 −1.59907
\(161\) −901.477 −0.441282
\(162\) 651.970 0.316195
\(163\) 966.144 0.464259 0.232129 0.972685i \(-0.425431\pi\)
0.232129 + 0.972685i \(0.425431\pi\)
\(164\) 2611.58 1.24348
\(165\) −1074.32 −0.506881
\(166\) 2844.73 1.33008
\(167\) 1193.13 0.552857 0.276429 0.961034i \(-0.410849\pi\)
0.276429 + 0.961034i \(0.410849\pi\)
\(168\) −365.667 −0.167927
\(169\) 6045.03 2.75149
\(170\) 0 0
\(171\) 1737.19 0.776880
\(172\) −1844.08 −0.817498
\(173\) −8.50924 −0.00373957 −0.00186978 0.999998i \(-0.500595\pi\)
−0.00186978 + 0.999998i \(0.500595\pi\)
\(174\) −599.731 −0.261296
\(175\) 1111.42 0.480089
\(176\) 1544.22 0.661364
\(177\) 6.33899 0.00269191
\(178\) 1483.53 0.624691
\(179\) −909.300 −0.379689 −0.189844 0.981814i \(-0.560798\pi\)
−0.189844 + 0.981814i \(0.560798\pi\)
\(180\) 1174.79 0.486463
\(181\) 2448.71 1.00559 0.502793 0.864407i \(-0.332306\pi\)
0.502793 + 0.864407i \(0.332306\pi\)
\(182\) 4395.10 1.79003
\(183\) −582.624 −0.235349
\(184\) −536.164 −0.214818
\(185\) 602.568 0.239469
\(186\) −2985.47 −1.17691
\(187\) 0 0
\(188\) 500.648 0.194221
\(189\) 1926.54 0.741454
\(190\) −6900.59 −2.63485
\(191\) 845.418 0.320274 0.160137 0.987095i \(-0.448806\pi\)
0.160137 + 0.987095i \(0.448806\pi\)
\(192\) 811.986 0.305208
\(193\) −7.70682 −0.00287435 −0.00143717 0.999999i \(-0.500457\pi\)
−0.00143717 + 0.999999i \(0.500457\pi\)
\(194\) 1597.32 0.591139
\(195\) −4816.65 −1.76886
\(196\) −1037.14 −0.377967
\(197\) −5024.07 −1.81701 −0.908503 0.417879i \(-0.862773\pi\)
−0.908503 + 0.417879i \(0.862773\pi\)
\(198\) −1030.99 −0.370046
\(199\) 1210.87 0.431339 0.215669 0.976466i \(-0.430807\pi\)
0.215669 + 0.976466i \(0.430807\pi\)
\(200\) 661.030 0.233709
\(201\) −518.135 −0.181823
\(202\) −5940.15 −2.06905
\(203\) −570.095 −0.197107
\(204\) 0 0
\(205\) −6388.80 −2.17665
\(206\) 4085.84 1.38191
\(207\) 948.098 0.318345
\(208\) 6923.45 2.30796
\(209\) 2578.89 0.853519
\(210\) −2568.50 −0.844016
\(211\) −3047.09 −0.994172 −0.497086 0.867701i \(-0.665597\pi\)
−0.497086 + 0.867701i \(0.665597\pi\)
\(212\) 282.545 0.0915344
\(213\) −1634.94 −0.525934
\(214\) 4932.66 1.57565
\(215\) 4511.23 1.43099
\(216\) 1145.83 0.360943
\(217\) −2837.93 −0.887795
\(218\) 4943.10 1.53573
\(219\) −2767.22 −0.853841
\(220\) 1743.99 0.534453
\(221\) 0 0
\(222\) −566.382 −0.171230
\(223\) −2883.35 −0.865846 −0.432923 0.901431i \(-0.642518\pi\)
−0.432923 + 0.901431i \(0.642518\pi\)
\(224\) 2891.62 0.862520
\(225\) −1168.90 −0.346340
\(226\) 6051.78 1.78123
\(227\) 5402.18 1.57954 0.789770 0.613403i \(-0.210200\pi\)
0.789770 + 0.613403i \(0.210200\pi\)
\(228\) 2762.11 0.802303
\(229\) −1524.25 −0.439849 −0.219925 0.975517i \(-0.570581\pi\)
−0.219925 + 0.975517i \(0.570581\pi\)
\(230\) −3766.10 −1.07969
\(231\) 959.899 0.273406
\(232\) −339.070 −0.0959528
\(233\) −1685.79 −0.473989 −0.236995 0.971511i \(-0.576162\pi\)
−0.236995 + 0.971511i \(0.576162\pi\)
\(234\) −4622.39 −1.29135
\(235\) −1224.75 −0.339975
\(236\) −10.2904 −0.00283833
\(237\) −1936.48 −0.530751
\(238\) 0 0
\(239\) −4887.91 −1.32290 −0.661449 0.749990i \(-0.730058\pi\)
−0.661449 + 0.749990i \(0.730058\pi\)
\(240\) −4046.07 −1.08822
\(241\) −3416.56 −0.913195 −0.456597 0.889673i \(-0.650932\pi\)
−0.456597 + 0.889673i \(0.650932\pi\)
\(242\) 3437.79 0.913179
\(243\) −3372.29 −0.890257
\(244\) 945.800 0.248150
\(245\) 2537.19 0.661614
\(246\) 6005.13 1.55640
\(247\) 11562.3 2.97852
\(248\) −1687.89 −0.432183
\(249\) 2785.55 0.708944
\(250\) −2129.62 −0.538755
\(251\) 2357.42 0.592825 0.296413 0.955060i \(-0.404210\pi\)
0.296413 + 0.955060i \(0.404210\pi\)
\(252\) −1049.67 −0.262392
\(253\) 1407.47 0.349749
\(254\) −1580.03 −0.390314
\(255\) 0 0
\(256\) 5339.81 1.30366
\(257\) 2033.64 0.493598 0.246799 0.969067i \(-0.420621\pi\)
0.246799 + 0.969067i \(0.420621\pi\)
\(258\) −4240.32 −1.02322
\(259\) −538.393 −0.129167
\(260\) 7819.09 1.86507
\(261\) 599.578 0.142195
\(262\) 2960.00 0.697974
\(263\) 5377.07 1.26070 0.630351 0.776310i \(-0.282911\pi\)
0.630351 + 0.776310i \(0.282911\pi\)
\(264\) 570.911 0.133095
\(265\) −691.200 −0.160227
\(266\) 6165.66 1.42121
\(267\) 1452.67 0.332965
\(268\) 841.113 0.191713
\(269\) 3012.15 0.682728 0.341364 0.939931i \(-0.389111\pi\)
0.341364 + 0.939931i \(0.389111\pi\)
\(270\) 8048.48 1.81413
\(271\) −1340.23 −0.300417 −0.150209 0.988654i \(-0.547995\pi\)
−0.150209 + 0.988654i \(0.547995\pi\)
\(272\) 0 0
\(273\) 4303.67 0.954102
\(274\) −3021.72 −0.666236
\(275\) −1735.25 −0.380507
\(276\) 1507.46 0.328762
\(277\) −4917.83 −1.06673 −0.533365 0.845885i \(-0.679073\pi\)
−0.533365 + 0.845885i \(0.679073\pi\)
\(278\) −10608.7 −2.28873
\(279\) 2984.70 0.640463
\(280\) −1452.15 −0.309938
\(281\) −697.896 −0.148160 −0.0740801 0.997252i \(-0.523602\pi\)
−0.0740801 + 0.997252i \(0.523602\pi\)
\(282\) 1151.20 0.243096
\(283\) −5379.29 −1.12991 −0.564957 0.825121i \(-0.691107\pi\)
−0.564957 + 0.825121i \(0.691107\pi\)
\(284\) 2654.07 0.554542
\(285\) −6757.04 −1.40439
\(286\) −6862.01 −1.41874
\(287\) 5708.38 1.17406
\(288\) −3041.16 −0.622230
\(289\) 0 0
\(290\) −2381.68 −0.482266
\(291\) 1564.09 0.315081
\(292\) 4492.15 0.900285
\(293\) 2876.89 0.573616 0.286808 0.957988i \(-0.407406\pi\)
0.286808 + 0.957988i \(0.407406\pi\)
\(294\) −2384.83 −0.473081
\(295\) 25.1737 0.00496837
\(296\) −320.216 −0.0628789
\(297\) −3007.88 −0.587659
\(298\) 3773.24 0.733482
\(299\) 6310.31 1.22052
\(300\) −1858.53 −0.357674
\(301\) −4030.78 −0.771861
\(302\) −5002.99 −0.953276
\(303\) −5816.58 −1.10282
\(304\) 9712.57 1.83241
\(305\) −2313.74 −0.434376
\(306\) 0 0
\(307\) −3765.61 −0.700048 −0.350024 0.936741i \(-0.613827\pi\)
−0.350024 + 0.936741i \(0.613827\pi\)
\(308\) −1558.25 −0.288277
\(309\) 4000.84 0.736570
\(310\) −11856.0 −2.17218
\(311\) 1043.69 0.190297 0.0951483 0.995463i \(-0.469667\pi\)
0.0951483 + 0.995463i \(0.469667\pi\)
\(312\) 2559.66 0.464461
\(313\) 801.837 0.144800 0.0724002 0.997376i \(-0.476934\pi\)
0.0724002 + 0.997376i \(0.476934\pi\)
\(314\) 3536.31 0.635560
\(315\) 2567.84 0.459306
\(316\) 3143.58 0.559621
\(317\) −806.122 −0.142827 −0.0714137 0.997447i \(-0.522751\pi\)
−0.0714137 + 0.997447i \(0.522751\pi\)
\(318\) 649.692 0.114569
\(319\) 890.082 0.156223
\(320\) 3224.60 0.563314
\(321\) 4830.05 0.839836
\(322\) 3365.00 0.582373
\(323\) 0 0
\(324\) −1036.36 −0.177702
\(325\) −7779.91 −1.32785
\(326\) −3606.38 −0.612697
\(327\) 4840.27 0.818556
\(328\) 3395.12 0.571538
\(329\) 1094.31 0.183378
\(330\) 4010.17 0.668947
\(331\) 2607.01 0.432913 0.216457 0.976292i \(-0.430550\pi\)
0.216457 + 0.976292i \(0.430550\pi\)
\(332\) −4521.91 −0.747506
\(333\) 566.237 0.0931820
\(334\) −4453.67 −0.729623
\(335\) −2057.64 −0.335585
\(336\) 3615.16 0.586973
\(337\) −1067.31 −0.172523 −0.0862614 0.996273i \(-0.527492\pi\)
−0.0862614 + 0.996273i \(0.527492\pi\)
\(338\) −22564.6 −3.63123
\(339\) 5925.89 0.949410
\(340\) 0 0
\(341\) 4430.83 0.703645
\(342\) −6484.53 −1.02527
\(343\) −6715.49 −1.05715
\(344\) −2397.35 −0.375745
\(345\) −3687.75 −0.575484
\(346\) 31.7630 0.00493522
\(347\) −11380.2 −1.76058 −0.880288 0.474439i \(-0.842651\pi\)
−0.880288 + 0.474439i \(0.842651\pi\)
\(348\) 953.319 0.146848
\(349\) −2447.03 −0.375320 −0.187660 0.982234i \(-0.560090\pi\)
−0.187660 + 0.982234i \(0.560090\pi\)
\(350\) −4148.67 −0.633588
\(351\) −13485.7 −2.05075
\(352\) −4514.65 −0.683613
\(353\) 5229.05 0.788426 0.394213 0.919019i \(-0.371017\pi\)
0.394213 + 0.919019i \(0.371017\pi\)
\(354\) −23.6619 −0.00355259
\(355\) −6492.74 −0.970701
\(356\) −2358.18 −0.351077
\(357\) 0 0
\(358\) 3394.20 0.501087
\(359\) 9108.24 1.33904 0.669519 0.742795i \(-0.266500\pi\)
0.669519 + 0.742795i \(0.266500\pi\)
\(360\) 1527.25 0.223592
\(361\) 9361.22 1.36481
\(362\) −9140.44 −1.32710
\(363\) 3366.27 0.486731
\(364\) −6986.34 −1.00600
\(365\) −10989.3 −1.57591
\(366\) 2174.80 0.310597
\(367\) −1155.57 −0.164360 −0.0821801 0.996617i \(-0.526188\pi\)
−0.0821801 + 0.996617i \(0.526188\pi\)
\(368\) 5300.77 0.750875
\(369\) −6003.59 −0.846977
\(370\) −2249.24 −0.316034
\(371\) 617.586 0.0864245
\(372\) 4745.62 0.661422
\(373\) −9949.97 −1.38121 −0.690603 0.723234i \(-0.742655\pi\)
−0.690603 + 0.723234i \(0.742655\pi\)
\(374\) 0 0
\(375\) −2085.31 −0.287160
\(376\) 650.855 0.0892694
\(377\) 3990.64 0.545169
\(378\) −7191.30 −0.978520
\(379\) 1443.78 0.195678 0.0978388 0.995202i \(-0.468807\pi\)
0.0978388 + 0.995202i \(0.468807\pi\)
\(380\) 10969.0 1.48079
\(381\) −1547.16 −0.208040
\(382\) −3155.74 −0.422675
\(383\) −8249.59 −1.10061 −0.550306 0.834963i \(-0.685489\pi\)
−0.550306 + 0.834963i \(0.685489\pi\)
\(384\) 3488.49 0.463598
\(385\) 3812.00 0.504617
\(386\) 28.7677 0.00379336
\(387\) 4239.23 0.556827
\(388\) −2539.06 −0.332220
\(389\) −9396.96 −1.22479 −0.612397 0.790551i \(-0.709794\pi\)
−0.612397 + 0.790551i \(0.709794\pi\)
\(390\) 17979.4 2.33442
\(391\) 0 0
\(392\) −1348.31 −0.173724
\(393\) 2898.42 0.372025
\(394\) 18753.6 2.39796
\(395\) −7690.25 −0.979591
\(396\) 1638.83 0.207966
\(397\) −11970.7 −1.51333 −0.756667 0.653800i \(-0.773174\pi\)
−0.756667 + 0.653800i \(0.773174\pi\)
\(398\) −4519.90 −0.569251
\(399\) 6037.40 0.757514
\(400\) −6535.26 −0.816908
\(401\) −10710.9 −1.33386 −0.666928 0.745122i \(-0.732391\pi\)
−0.666928 + 0.745122i \(0.732391\pi\)
\(402\) 1934.08 0.239958
\(403\) 19865.4 2.45550
\(404\) 9442.31 1.16280
\(405\) 2535.27 0.311059
\(406\) 2128.03 0.260129
\(407\) 840.587 0.102374
\(408\) 0 0
\(409\) −1220.58 −0.147565 −0.0737824 0.997274i \(-0.523507\pi\)
−0.0737824 + 0.997274i \(0.523507\pi\)
\(410\) 23847.9 2.87259
\(411\) −2958.86 −0.355109
\(412\) −6494.75 −0.776634
\(413\) −22.4926 −0.00267988
\(414\) −3539.02 −0.420129
\(415\) 11062.1 1.30848
\(416\) −20241.2 −2.38560
\(417\) −10388.0 −1.21991
\(418\) −9626.37 −1.12641
\(419\) 10940.2 1.27557 0.637784 0.770215i \(-0.279851\pi\)
0.637784 + 0.770215i \(0.279851\pi\)
\(420\) 4082.82 0.474337
\(421\) −2304.87 −0.266823 −0.133411 0.991061i \(-0.542593\pi\)
−0.133411 + 0.991061i \(0.542593\pi\)
\(422\) 11374.1 1.31204
\(423\) −1150.91 −0.132291
\(424\) 367.316 0.0420718
\(425\) 0 0
\(426\) 6102.83 0.694092
\(427\) 2067.32 0.234297
\(428\) −7840.84 −0.885518
\(429\) −6719.26 −0.756198
\(430\) −16839.4 −1.88852
\(431\) 5741.54 0.641671 0.320835 0.947135i \(-0.396036\pi\)
0.320835 + 0.947135i \(0.396036\pi\)
\(432\) −11328.2 −1.26164
\(433\) 4553.54 0.505379 0.252690 0.967547i \(-0.418685\pi\)
0.252690 + 0.967547i \(0.418685\pi\)
\(434\) 10593.3 1.17165
\(435\) −2332.14 −0.257051
\(436\) −7857.44 −0.863080
\(437\) 8852.42 0.969036
\(438\) 10329.4 1.12684
\(439\) 10786.4 1.17268 0.586340 0.810065i \(-0.300568\pi\)
0.586340 + 0.810065i \(0.300568\pi\)
\(440\) 2267.23 0.245650
\(441\) 2384.22 0.257447
\(442\) 0 0
\(443\) 13133.5 1.40856 0.704280 0.709922i \(-0.251270\pi\)
0.704280 + 0.709922i \(0.251270\pi\)
\(444\) 900.307 0.0962313
\(445\) 5768.90 0.614544
\(446\) 10762.9 1.14268
\(447\) 3694.74 0.390952
\(448\) −2881.17 −0.303845
\(449\) −714.661 −0.0751157 −0.0375578 0.999294i \(-0.511958\pi\)
−0.0375578 + 0.999294i \(0.511958\pi\)
\(450\) 4363.22 0.457076
\(451\) −8912.42 −0.930531
\(452\) −9619.77 −1.00105
\(453\) −4898.91 −0.508104
\(454\) −20165.1 −2.08457
\(455\) 17090.9 1.76096
\(456\) 3590.81 0.368761
\(457\) −976.357 −0.0999388 −0.0499694 0.998751i \(-0.515912\pi\)
−0.0499694 + 0.998751i \(0.515912\pi\)
\(458\) 5689.67 0.580482
\(459\) 0 0
\(460\) 5986.50 0.606787
\(461\) −17713.0 −1.78953 −0.894767 0.446533i \(-0.852659\pi\)
−0.894767 + 0.446533i \(0.852659\pi\)
\(462\) −3583.08 −0.360822
\(463\) −13597.7 −1.36488 −0.682441 0.730941i \(-0.739082\pi\)
−0.682441 + 0.730941i \(0.739082\pi\)
\(464\) 3352.21 0.335393
\(465\) −11609.4 −1.15779
\(466\) 6292.63 0.625538
\(467\) 9115.78 0.903272 0.451636 0.892202i \(-0.350841\pi\)
0.451636 + 0.892202i \(0.350841\pi\)
\(468\) 7347.64 0.725737
\(469\) 1838.50 0.181011
\(470\) 4571.71 0.448675
\(471\) 3462.75 0.338758
\(472\) −13.3777 −0.00130458
\(473\) 6293.20 0.611758
\(474\) 7228.43 0.700448
\(475\) −10914.0 −1.05425
\(476\) 0 0
\(477\) −649.525 −0.0623474
\(478\) 18245.4 1.74587
\(479\) 11483.2 1.09537 0.547683 0.836686i \(-0.315510\pi\)
0.547683 + 0.836686i \(0.315510\pi\)
\(480\) 11829.0 1.12483
\(481\) 3768.74 0.357255
\(482\) 12753.2 1.20517
\(483\) 3295.00 0.310409
\(484\) −5464.63 −0.513207
\(485\) 6211.40 0.581536
\(486\) 12588.0 1.17490
\(487\) −4117.57 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(488\) 1229.57 0.114057
\(489\) −3531.36 −0.326572
\(490\) −9470.74 −0.873152
\(491\) −11870.1 −1.09102 −0.545509 0.838105i \(-0.683664\pi\)
−0.545509 + 0.838105i \(0.683664\pi\)
\(492\) −9545.61 −0.874694
\(493\) 0 0
\(494\) −43159.4 −3.93084
\(495\) −4009.14 −0.364035
\(496\) 16687.3 1.51065
\(497\) 5801.25 0.523585
\(498\) −10397.8 −0.935615
\(499\) 16770.4 1.50450 0.752252 0.658875i \(-0.228967\pi\)
0.752252 + 0.658875i \(0.228967\pi\)
\(500\) 3385.19 0.302780
\(501\) −4361.02 −0.388895
\(502\) −8799.69 −0.782369
\(503\) −14451.7 −1.28105 −0.640525 0.767938i \(-0.721283\pi\)
−0.640525 + 0.767938i \(0.721283\pi\)
\(504\) −1364.60 −0.120603
\(505\) −23099.1 −2.03544
\(506\) −5253.73 −0.461575
\(507\) −22095.2 −1.93547
\(508\) 2511.57 0.219357
\(509\) 22279.2 1.94010 0.970049 0.242910i \(-0.0781019\pi\)
0.970049 + 0.242910i \(0.0781019\pi\)
\(510\) 0 0
\(511\) 9818.92 0.850026
\(512\) −12296.9 −1.06143
\(513\) −18918.4 −1.62820
\(514\) −7591.08 −0.651417
\(515\) 15888.3 1.35946
\(516\) 6740.31 0.575049
\(517\) −1708.54 −0.145341
\(518\) 2009.69 0.170465
\(519\) 31.1022 0.00263051
\(520\) 10165.0 0.857242
\(521\) −16004.3 −1.34580 −0.672898 0.739735i \(-0.734951\pi\)
−0.672898 + 0.739735i \(0.734951\pi\)
\(522\) −2238.08 −0.187659
\(523\) −22158.6 −1.85264 −0.926319 0.376739i \(-0.877045\pi\)
−0.926319 + 0.376739i \(0.877045\pi\)
\(524\) −4705.14 −0.392261
\(525\) −4062.37 −0.337707
\(526\) −20071.3 −1.66379
\(527\) 0 0
\(528\) −5644.30 −0.465221
\(529\) −7335.66 −0.602915
\(530\) 2580.09 0.211456
\(531\) 23.6559 0.00193329
\(532\) −9800.79 −0.798718
\(533\) −39958.5 −3.24727
\(534\) −5422.46 −0.439424
\(535\) 19181.3 1.55006
\(536\) 1093.47 0.0881169
\(537\) 3323.59 0.267083
\(538\) −11243.6 −0.901017
\(539\) 3539.40 0.282844
\(540\) −12793.7 −1.01954
\(541\) 3099.41 0.246310 0.123155 0.992387i \(-0.460699\pi\)
0.123155 + 0.992387i \(0.460699\pi\)
\(542\) 5002.75 0.396470
\(543\) −8950.30 −0.707355
\(544\) 0 0
\(545\) 19221.9 1.51078
\(546\) −16064.6 −1.25916
\(547\) −21795.9 −1.70370 −0.851852 0.523783i \(-0.824520\pi\)
−0.851852 + 0.523783i \(0.824520\pi\)
\(548\) 4803.25 0.374424
\(549\) −2174.24 −0.169024
\(550\) 6477.27 0.502167
\(551\) 5598.28 0.432839
\(552\) 1959.74 0.151109
\(553\) 6871.22 0.528380
\(554\) 18357.1 1.40780
\(555\) −2202.45 −0.168449
\(556\) 16863.3 1.28626
\(557\) 12689.7 0.965315 0.482658 0.875809i \(-0.339672\pi\)
0.482658 + 0.875809i \(0.339672\pi\)
\(558\) −11141.2 −0.845239
\(559\) 28215.3 2.13485
\(560\) 14356.7 1.08336
\(561\) 0 0
\(562\) 2605.08 0.195532
\(563\) −10849.0 −0.812129 −0.406065 0.913844i \(-0.633099\pi\)
−0.406065 + 0.913844i \(0.633099\pi\)
\(564\) −1829.92 −0.136620
\(565\) 23533.2 1.75230
\(566\) 20079.6 1.49118
\(567\) −2265.26 −0.167781
\(568\) 3450.36 0.254884
\(569\) −5582.88 −0.411329 −0.205665 0.978623i \(-0.565936\pi\)
−0.205665 + 0.978623i \(0.565936\pi\)
\(570\) 25222.4 1.85342
\(571\) 20899.4 1.53172 0.765859 0.643008i \(-0.222314\pi\)
0.765859 + 0.643008i \(0.222314\pi\)
\(572\) 10907.7 0.797331
\(573\) −3090.10 −0.225289
\(574\) −21308.0 −1.54944
\(575\) −5956.50 −0.432006
\(576\) 3030.17 0.219196
\(577\) −7924.36 −0.571742 −0.285871 0.958268i \(-0.592283\pi\)
−0.285871 + 0.958268i \(0.592283\pi\)
\(578\) 0 0
\(579\) 28.1693 0.00202189
\(580\) 3785.86 0.271034
\(581\) −9883.97 −0.705776
\(582\) −5838.38 −0.415823
\(583\) −964.230 −0.0684980
\(584\) 5839.91 0.413797
\(585\) −17974.8 −1.27037
\(586\) −10738.7 −0.757019
\(587\) 1139.92 0.0801529 0.0400764 0.999197i \(-0.487240\pi\)
0.0400764 + 0.999197i \(0.487240\pi\)
\(588\) 3790.86 0.265872
\(589\) 27868.2 1.94956
\(590\) −93.9673 −0.00655690
\(591\) 18363.5 1.27813
\(592\) 3165.81 0.219787
\(593\) 2645.81 0.183222 0.0916109 0.995795i \(-0.470798\pi\)
0.0916109 + 0.995795i \(0.470798\pi\)
\(594\) 11227.7 0.775552
\(595\) 0 0
\(596\) −5997.84 −0.412217
\(597\) −4425.87 −0.303415
\(598\) −23554.9 −1.61075
\(599\) −21822.7 −1.48856 −0.744282 0.667865i \(-0.767208\pi\)
−0.744282 + 0.667865i \(0.767208\pi\)
\(600\) −2416.14 −0.164397
\(601\) 10909.3 0.740434 0.370217 0.928945i \(-0.379283\pi\)
0.370217 + 0.928945i \(0.379283\pi\)
\(602\) 15045.9 1.01865
\(603\) −1933.58 −0.130583
\(604\) 7952.63 0.535741
\(605\) 13368.3 0.898345
\(606\) 21711.9 1.45542
\(607\) 15308.1 1.02362 0.511808 0.859100i \(-0.328976\pi\)
0.511808 + 0.859100i \(0.328976\pi\)
\(608\) −28395.4 −1.89406
\(609\) 2083.76 0.138651
\(610\) 8636.65 0.573259
\(611\) −7660.16 −0.507196
\(612\) 0 0
\(613\) 24096.7 1.58769 0.793847 0.608118i \(-0.208075\pi\)
0.793847 + 0.608118i \(0.208075\pi\)
\(614\) 14056.1 0.923875
\(615\) 23351.8 1.53111
\(616\) −2025.76 −0.132501
\(617\) 7030.91 0.458758 0.229379 0.973337i \(-0.426330\pi\)
0.229379 + 0.973337i \(0.426330\pi\)
\(618\) −14934.2 −0.972073
\(619\) 19270.2 1.25127 0.625635 0.780116i \(-0.284840\pi\)
0.625635 + 0.780116i \(0.284840\pi\)
\(620\) 18846.0 1.22077
\(621\) −10325.0 −0.667194
\(622\) −3895.85 −0.251140
\(623\) −5154.50 −0.331478
\(624\) −25306.0 −1.62348
\(625\) −18993.2 −1.21557
\(626\) −2993.07 −0.191097
\(627\) −9426.12 −0.600388
\(628\) −5621.24 −0.357185
\(629\) 0 0
\(630\) −9585.14 −0.606160
\(631\) −1474.23 −0.0930079 −0.0465040 0.998918i \(-0.514808\pi\)
−0.0465040 + 0.998918i \(0.514808\pi\)
\(632\) 4086.74 0.257218
\(633\) 11137.5 0.699327
\(634\) 3009.06 0.188494
\(635\) −6144.15 −0.383974
\(636\) −1032.73 −0.0643877
\(637\) 15868.8 0.987038
\(638\) −3322.46 −0.206172
\(639\) −6101.27 −0.377719
\(640\) 13853.7 0.855648
\(641\) 18747.7 1.15521 0.577604 0.816317i \(-0.303988\pi\)
0.577604 + 0.816317i \(0.303988\pi\)
\(642\) −18029.4 −1.10836
\(643\) −2324.44 −0.142561 −0.0712807 0.997456i \(-0.522709\pi\)
−0.0712807 + 0.997456i \(0.522709\pi\)
\(644\) −5348.92 −0.327294
\(645\) −16489.1 −1.00660
\(646\) 0 0
\(647\) −11883.3 −0.722071 −0.361036 0.932552i \(-0.617577\pi\)
−0.361036 + 0.932552i \(0.617577\pi\)
\(648\) −1347.29 −0.0816768
\(649\) 35.1175 0.00212401
\(650\) 29040.5 1.75241
\(651\) 10373.0 0.624498
\(652\) 5732.62 0.344336
\(653\) −873.094 −0.0523228 −0.0261614 0.999658i \(-0.508328\pi\)
−0.0261614 + 0.999658i \(0.508328\pi\)
\(654\) −18067.6 −1.08027
\(655\) 11510.3 0.686636
\(656\) −33565.8 −1.99775
\(657\) −10326.7 −0.613217
\(658\) −4084.81 −0.242010
\(659\) −965.182 −0.0570534 −0.0285267 0.999593i \(-0.509082\pi\)
−0.0285267 + 0.999593i \(0.509082\pi\)
\(660\) −6374.47 −0.375948
\(661\) 10564.2 0.621631 0.310815 0.950470i \(-0.399398\pi\)
0.310815 + 0.950470i \(0.399398\pi\)
\(662\) −9731.35 −0.571329
\(663\) 0 0
\(664\) −5878.60 −0.343575
\(665\) 23976.0 1.39812
\(666\) −2113.63 −0.122975
\(667\) 3055.34 0.177366
\(668\) 7079.45 0.410048
\(669\) 10539.0 0.609059
\(670\) 7680.69 0.442882
\(671\) −3227.69 −0.185698
\(672\) −10569.2 −0.606719
\(673\) −24755.2 −1.41789 −0.708947 0.705262i \(-0.750829\pi\)
−0.708947 + 0.705262i \(0.750829\pi\)
\(674\) 3984.02 0.227684
\(675\) 12729.6 0.725868
\(676\) 35868.2 2.04075
\(677\) 34038.8 1.93238 0.966188 0.257840i \(-0.0830107\pi\)
0.966188 + 0.257840i \(0.0830107\pi\)
\(678\) −22119.9 −1.25297
\(679\) −5549.87 −0.313674
\(680\) 0 0
\(681\) −19745.6 −1.11109
\(682\) −16539.2 −0.928622
\(683\) −23062.1 −1.29202 −0.646008 0.763330i \(-0.723563\pi\)
−0.646008 + 0.763330i \(0.723563\pi\)
\(684\) 10307.6 0.576203
\(685\) −11750.4 −0.655413
\(686\) 25067.3 1.39515
\(687\) 5571.31 0.309401
\(688\) 23701.4 1.31338
\(689\) −4323.08 −0.239037
\(690\) 13765.5 0.759484
\(691\) 14331.9 0.789018 0.394509 0.918892i \(-0.370915\pi\)
0.394509 + 0.918892i \(0.370915\pi\)
\(692\) −50.4896 −0.00277360
\(693\) 3582.16 0.196356
\(694\) 42479.5 2.32349
\(695\) −41253.3 −2.25155
\(696\) 1239.34 0.0674958
\(697\) 0 0
\(698\) 9134.19 0.495321
\(699\) 6161.73 0.333417
\(700\) 6594.62 0.356076
\(701\) 28211.9 1.52004 0.760020 0.649900i \(-0.225189\pi\)
0.760020 + 0.649900i \(0.225189\pi\)
\(702\) 50338.9 2.70644
\(703\) 5286.97 0.283644
\(704\) 4498.34 0.240820
\(705\) 4476.61 0.239147
\(706\) −19518.8 −1.04051
\(707\) 20639.0 1.09789
\(708\) 37.6124 0.00199656
\(709\) −5397.14 −0.285887 −0.142943 0.989731i \(-0.545657\pi\)
−0.142943 + 0.989731i \(0.545657\pi\)
\(710\) 24235.8 1.28106
\(711\) −7226.57 −0.381178
\(712\) −3065.70 −0.161365
\(713\) 15209.5 0.798878
\(714\) 0 0
\(715\) −26683.9 −1.39569
\(716\) −5395.34 −0.281611
\(717\) 17865.9 0.930562
\(718\) −33998.9 −1.76717
\(719\) −17858.0 −0.926276 −0.463138 0.886286i \(-0.653277\pi\)
−0.463138 + 0.886286i \(0.653277\pi\)
\(720\) −15099.2 −0.781545
\(721\) −14196.2 −0.733279
\(722\) −34943.2 −1.80118
\(723\) 12487.9 0.642366
\(724\) 14529.4 0.745831
\(725\) −3766.89 −0.192964
\(726\) −12565.5 −0.642354
\(727\) 27634.4 1.40977 0.704885 0.709322i \(-0.250999\pi\)
0.704885 + 0.709322i \(0.250999\pi\)
\(728\) −9082.43 −0.462386
\(729\) 17042.0 0.865821
\(730\) 41020.4 2.07977
\(731\) 0 0
\(732\) −3457.00 −0.174555
\(733\) 16773.4 0.845209 0.422605 0.906314i \(-0.361116\pi\)
0.422605 + 0.906314i \(0.361116\pi\)
\(734\) 4313.46 0.216911
\(735\) −9273.72 −0.465396
\(736\) −15497.2 −0.776134
\(737\) −2870.43 −0.143465
\(738\) 22410.0 1.11778
\(739\) −26618.2 −1.32499 −0.662495 0.749067i \(-0.730502\pi\)
−0.662495 + 0.749067i \(0.730502\pi\)
\(740\) 3575.34 0.177611
\(741\) −42261.6 −2.09517
\(742\) −2305.30 −0.114057
\(743\) 3231.55 0.159561 0.0797806 0.996812i \(-0.474578\pi\)
0.0797806 + 0.996812i \(0.474578\pi\)
\(744\) 6169.44 0.304009
\(745\) 14672.7 0.721567
\(746\) 37140.9 1.82282
\(747\) 10395.1 0.509154
\(748\) 0 0
\(749\) −17138.5 −0.836083
\(750\) 7783.98 0.378974
\(751\) −6094.29 −0.296117 −0.148058 0.988979i \(-0.547302\pi\)
−0.148058 + 0.988979i \(0.547302\pi\)
\(752\) −6434.67 −0.312032
\(753\) −8616.63 −0.417009
\(754\) −14896.1 −0.719476
\(755\) −19454.8 −0.937791
\(756\) 11431.1 0.549928
\(757\) −4282.74 −0.205626 −0.102813 0.994701i \(-0.532784\pi\)
−0.102813 + 0.994701i \(0.532784\pi\)
\(758\) −5389.27 −0.258242
\(759\) −5144.44 −0.246023
\(760\) 14260.0 0.680612
\(761\) −35191.9 −1.67636 −0.838178 0.545397i \(-0.816379\pi\)
−0.838178 + 0.545397i \(0.816379\pi\)
\(762\) 5775.18 0.274557
\(763\) −17174.7 −0.814899
\(764\) 5016.29 0.237543
\(765\) 0 0
\(766\) 30793.8 1.45251
\(767\) 157.448 0.00741213
\(768\) −19517.6 −0.917032
\(769\) 23142.5 1.08523 0.542614 0.839982i \(-0.317434\pi\)
0.542614 + 0.839982i \(0.317434\pi\)
\(770\) −14229.3 −0.665958
\(771\) −7433.17 −0.347210
\(772\) −45.7285 −0.00213187
\(773\) −4345.19 −0.202181 −0.101090 0.994877i \(-0.532233\pi\)
−0.101090 + 0.994877i \(0.532233\pi\)
\(774\) −15824.0 −0.734862
\(775\) −18751.6 −0.869133
\(776\) −3300.85 −0.152698
\(777\) 1967.89 0.0908592
\(778\) 35076.6 1.61640
\(779\) −56055.7 −2.57818
\(780\) −28579.6 −1.31194
\(781\) −9057.42 −0.414981
\(782\) 0 0
\(783\) −6529.53 −0.298016
\(784\) 13330.0 0.607236
\(785\) 13751.4 0.625236
\(786\) −10819.1 −0.490973
\(787\) 15543.2 0.704010 0.352005 0.935998i \(-0.385500\pi\)
0.352005 + 0.935998i \(0.385500\pi\)
\(788\) −29810.3 −1.34765
\(789\) −19653.8 −0.886811
\(790\) 28705.9 1.29280
\(791\) −21026.8 −0.945169
\(792\) 2130.53 0.0955872
\(793\) −14471.2 −0.648030
\(794\) 44683.9 1.99719
\(795\) 2526.41 0.112708
\(796\) 7184.72 0.319919
\(797\) 15559.4 0.691519 0.345759 0.938323i \(-0.387621\pi\)
0.345759 + 0.938323i \(0.387621\pi\)
\(798\) −22536.2 −0.999714
\(799\) 0 0
\(800\) 19106.3 0.844389
\(801\) 5421.07 0.239131
\(802\) 39981.2 1.76033
\(803\) −15330.2 −0.673711
\(804\) −3074.36 −0.134856
\(805\) 13085.3 0.572913
\(806\) −74153.0 −3.24060
\(807\) −11009.7 −0.480249
\(808\) 12275.3 0.534458
\(809\) 9433.22 0.409956 0.204978 0.978767i \(-0.434288\pi\)
0.204978 + 0.978767i \(0.434288\pi\)
\(810\) −9463.57 −0.410514
\(811\) −12596.0 −0.545381 −0.272691 0.962102i \(-0.587914\pi\)
−0.272691 + 0.962102i \(0.587914\pi\)
\(812\) −3382.66 −0.146192
\(813\) 4898.68 0.211321
\(814\) −3137.71 −0.135107
\(815\) −14023.9 −0.602744
\(816\) 0 0
\(817\) 39581.8 1.69497
\(818\) 4556.15 0.194746
\(819\) 16060.4 0.685223
\(820\) −37908.0 −1.61440
\(821\) −24332.2 −1.03435 −0.517175 0.855880i \(-0.673016\pi\)
−0.517175 + 0.855880i \(0.673016\pi\)
\(822\) 11044.7 0.468648
\(823\) 40516.8 1.71607 0.858035 0.513591i \(-0.171685\pi\)
0.858035 + 0.513591i \(0.171685\pi\)
\(824\) −8443.35 −0.356964
\(825\) 6342.53 0.267659
\(826\) 83.9596 0.00353672
\(827\) 3544.77 0.149049 0.0745247 0.997219i \(-0.476256\pi\)
0.0745247 + 0.997219i \(0.476256\pi\)
\(828\) 5625.55 0.236113
\(829\) −25265.7 −1.05852 −0.529260 0.848460i \(-0.677530\pi\)
−0.529260 + 0.848460i \(0.677530\pi\)
\(830\) −41292.2 −1.72684
\(831\) 17975.2 0.750366
\(832\) 20168.1 0.840388
\(833\) 0 0
\(834\) 38775.9 1.60995
\(835\) −17318.7 −0.717771
\(836\) 15301.9 0.633045
\(837\) −32504.0 −1.34230
\(838\) −40837.1 −1.68341
\(839\) 32421.0 1.33408 0.667042 0.745021i \(-0.267560\pi\)
0.667042 + 0.745021i \(0.267560\pi\)
\(840\) 5307.78 0.218019
\(841\) −22456.8 −0.920776
\(842\) 8603.51 0.352134
\(843\) 2550.89 0.104220
\(844\) −18079.9 −0.737366
\(845\) −87745.7 −3.57224
\(846\) 4296.06 0.174588
\(847\) −11944.6 −0.484557
\(848\) −3631.47 −0.147058
\(849\) 19661.9 0.794811
\(850\) 0 0
\(851\) 2885.44 0.116230
\(852\) −9700.91 −0.390080
\(853\) −31041.4 −1.24600 −0.623000 0.782222i \(-0.714087\pi\)
−0.623000 + 0.782222i \(0.714087\pi\)
\(854\) −7716.83 −0.309209
\(855\) −25216.0 −1.00862
\(856\) −10193.3 −0.407009
\(857\) 6852.25 0.273125 0.136563 0.990631i \(-0.456394\pi\)
0.136563 + 0.990631i \(0.456394\pi\)
\(858\) 25081.4 0.997978
\(859\) 31049.1 1.23327 0.616636 0.787248i \(-0.288495\pi\)
0.616636 + 0.787248i \(0.288495\pi\)
\(860\) 26767.4 1.06135
\(861\) −20864.8 −0.825864
\(862\) −21431.8 −0.846833
\(863\) 31789.3 1.25391 0.626953 0.779057i \(-0.284302\pi\)
0.626953 + 0.779057i \(0.284302\pi\)
\(864\) 33118.9 1.30408
\(865\) 123.515 0.00485505
\(866\) −16997.3 −0.666964
\(867\) 0 0
\(868\) −16838.9 −0.658467
\(869\) −10728.0 −0.418781
\(870\) 8705.31 0.339239
\(871\) −12869.4 −0.500648
\(872\) −10214.9 −0.396697
\(873\) 5836.89 0.226287
\(874\) −33044.0 −1.27887
\(875\) 7399.32 0.285877
\(876\) −16419.3 −0.633284
\(877\) 34579.2 1.33142 0.665711 0.746210i \(-0.268128\pi\)
0.665711 + 0.746210i \(0.268128\pi\)
\(878\) −40263.0 −1.54762
\(879\) −10515.3 −0.403497
\(880\) −22414.9 −0.858644
\(881\) 14088.5 0.538765 0.269383 0.963033i \(-0.413180\pi\)
0.269383 + 0.963033i \(0.413180\pi\)
\(882\) −8899.71 −0.339761
\(883\) 4779.77 0.182165 0.0910827 0.995843i \(-0.470967\pi\)
0.0910827 + 0.995843i \(0.470967\pi\)
\(884\) 0 0
\(885\) −92.0126 −0.00349488
\(886\) −49024.3 −1.85892
\(887\) 14254.5 0.539594 0.269797 0.962917i \(-0.413043\pi\)
0.269797 + 0.962917i \(0.413043\pi\)
\(888\) 1170.42 0.0442307
\(889\) 5489.79 0.207111
\(890\) −21533.9 −0.811032
\(891\) 3536.73 0.132980
\(892\) −17108.4 −0.642188
\(893\) −10746.1 −0.402691
\(894\) −13791.6 −0.515951
\(895\) 13198.8 0.492947
\(896\) −12378.2 −0.461526
\(897\) −23064.9 −0.858544
\(898\) 2667.66 0.0991325
\(899\) 9618.49 0.356835
\(900\) −6935.67 −0.256877
\(901\) 0 0
\(902\) 33268.0 1.22805
\(903\) 14732.9 0.542947
\(904\) −12506.0 −0.460113
\(905\) −35543.8 −1.30554
\(906\) 18286.5 0.670560
\(907\) 36585.5 1.33936 0.669680 0.742650i \(-0.266431\pi\)
0.669680 + 0.742650i \(0.266431\pi\)
\(908\) 32053.9 1.17153
\(909\) −21706.3 −0.792028
\(910\) −63796.3 −2.32399
\(911\) 19721.3 0.717230 0.358615 0.933486i \(-0.383249\pi\)
0.358615 + 0.933486i \(0.383249\pi\)
\(912\) −35500.5 −1.28897
\(913\) 15431.7 0.559382
\(914\) 3644.51 0.131892
\(915\) 8456.99 0.305551
\(916\) −9044.16 −0.326231
\(917\) −10284.5 −0.370363
\(918\) 0 0
\(919\) −28189.0 −1.01183 −0.505913 0.862585i \(-0.668844\pi\)
−0.505913 + 0.862585i \(0.668844\pi\)
\(920\) 7782.60 0.278897
\(921\) 13763.7 0.492432
\(922\) 66118.3 2.36170
\(923\) −40608.5 −1.44815
\(924\) 5695.57 0.202782
\(925\) −3557.43 −0.126451
\(926\) 50757.1 1.80128
\(927\) 14930.4 0.528994
\(928\) −9800.45 −0.346676
\(929\) −30866.1 −1.09008 −0.545040 0.838410i \(-0.683485\pi\)
−0.545040 + 0.838410i \(0.683485\pi\)
\(930\) 43335.1 1.52797
\(931\) 22261.5 0.783664
\(932\) −10002.6 −0.351552
\(933\) −3814.80 −0.133860
\(934\) −34027.0 −1.19208
\(935\) 0 0
\(936\) 9552.13 0.333570
\(937\) 13990.7 0.487785 0.243893 0.969802i \(-0.421576\pi\)
0.243893 + 0.969802i \(0.421576\pi\)
\(938\) −6862.68 −0.238885
\(939\) −2930.80 −0.101856
\(940\) −7267.08 −0.252155
\(941\) −4495.60 −0.155741 −0.0778706 0.996963i \(-0.524812\pi\)
−0.0778706 + 0.996963i \(0.524812\pi\)
\(942\) −12925.6 −0.447070
\(943\) −30593.2 −1.05647
\(944\) 132.259 0.00456002
\(945\) −27964.3 −0.962624
\(946\) −23491.0 −0.807356
\(947\) 29959.5 1.02804 0.514019 0.857779i \(-0.328156\pi\)
0.514019 + 0.857779i \(0.328156\pi\)
\(948\) −11490.1 −0.393652
\(949\) −68732.1 −2.35104
\(950\) 40739.5 1.39133
\(951\) 2946.47 0.100469
\(952\) 0 0
\(953\) −44526.8 −1.51350 −0.756750 0.653704i \(-0.773214\pi\)
−0.756750 + 0.653704i \(0.773214\pi\)
\(954\) 2424.52 0.0822818
\(955\) −12271.5 −0.415809
\(956\) −29002.5 −0.981178
\(957\) −3253.35 −0.109891
\(958\) −42864.0 −1.44559
\(959\) 10498.9 0.353522
\(960\) −11786.3 −0.396250
\(961\) 18089.9 0.607227
\(962\) −14067.8 −0.471480
\(963\) 18024.8 0.603158
\(964\) −20272.2 −0.677306
\(965\) 111.867 0.00373174
\(966\) −12299.4 −0.409656
\(967\) 31696.1 1.05406 0.527031 0.849846i \(-0.323305\pi\)
0.527031 + 0.849846i \(0.323305\pi\)
\(968\) −7104.16 −0.235885
\(969\) 0 0
\(970\) −23185.7 −0.767471
\(971\) −47645.1 −1.57467 −0.787335 0.616525i \(-0.788540\pi\)
−0.787335 + 0.616525i \(0.788540\pi\)
\(972\) −20009.5 −0.660293
\(973\) 36859.7 1.21446
\(974\) 15369.9 0.505629
\(975\) 28436.4 0.934046
\(976\) −12156.1 −0.398675
\(977\) 47682.5 1.56141 0.780706 0.624898i \(-0.214860\pi\)
0.780706 + 0.624898i \(0.214860\pi\)
\(978\) 13181.7 0.430987
\(979\) 8047.66 0.262721
\(980\) 15054.5 0.490711
\(981\) 18063.0 0.587875
\(982\) 44308.2 1.43985
\(983\) 42569.9 1.38125 0.690626 0.723212i \(-0.257335\pi\)
0.690626 + 0.723212i \(0.257335\pi\)
\(984\) −12409.6 −0.402035
\(985\) 72926.1 2.35900
\(986\) 0 0
\(987\) −3999.84 −0.128993
\(988\) 68605.2 2.20913
\(989\) 21602.4 0.694555
\(990\) 14965.2 0.480428
\(991\) 36264.9 1.16245 0.581227 0.813742i \(-0.302573\pi\)
0.581227 + 0.813742i \(0.302573\pi\)
\(992\) −48786.7 −1.56147
\(993\) −9528.92 −0.304523
\(994\) −21654.7 −0.690991
\(995\) −17576.2 −0.560004
\(996\) 16528.1 0.525816
\(997\) 37027.1 1.17619 0.588094 0.808792i \(-0.299878\pi\)
0.588094 + 0.808792i \(0.299878\pi\)
\(998\) −62600.0 −1.98554
\(999\) −6166.44 −0.195293
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 289.4.a.i.1.3 yes 12
17.4 even 4 289.4.b.f.288.20 24
17.13 even 4 289.4.b.f.288.19 24
17.16 even 2 289.4.a.h.1.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.3 12 17.16 even 2
289.4.a.i.1.3 yes 12 1.1 even 1 trivial
289.4.b.f.288.19 24 17.13 even 4
289.4.b.f.288.20 24 17.4 even 4