Properties

Label 289.4.a.i.1.9
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $0$
Dimension $12$
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] = [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 1.9
Root \(-3.25752\) 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)
 
\(f(q)\) \(=\) \(q+3.25752 q^{2} -6.51757 q^{3} +2.61146 q^{4} +19.1073 q^{5} -21.2311 q^{6} +22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} +O(q^{10})\) \(q+3.25752 q^{2} -6.51757 q^{3} +2.61146 q^{4} +19.1073 q^{5} -21.2311 q^{6} +22.0995 q^{7} -17.5533 q^{8} +15.4787 q^{9} +62.2426 q^{10} -8.25972 q^{11} -17.0204 q^{12} -0.398269 q^{13} +71.9898 q^{14} -124.533 q^{15} -78.0720 q^{16} +50.4221 q^{18} +103.371 q^{19} +49.8980 q^{20} -144.035 q^{21} -26.9062 q^{22} +138.311 q^{23} +114.405 q^{24} +240.090 q^{25} -1.29737 q^{26} +75.0910 q^{27} +57.7120 q^{28} +222.296 q^{29} -405.670 q^{30} +49.1520 q^{31} -113.895 q^{32} +53.8333 q^{33} +422.263 q^{35} +40.4219 q^{36} +61.3077 q^{37} +336.734 q^{38} +2.59575 q^{39} -335.397 q^{40} -387.391 q^{41} -469.198 q^{42} -20.3847 q^{43} -21.5699 q^{44} +295.756 q^{45} +450.553 q^{46} +44.1322 q^{47} +508.839 q^{48} +145.389 q^{49} +782.100 q^{50} -1.04006 q^{52} +59.6456 q^{53} +244.611 q^{54} -157.821 q^{55} -387.920 q^{56} -673.728 q^{57} +724.134 q^{58} +238.069 q^{59} -325.214 q^{60} -595.816 q^{61} +160.114 q^{62} +342.071 q^{63} +253.561 q^{64} -7.60987 q^{65} +175.363 q^{66} -408.815 q^{67} -901.454 q^{69} +1375.53 q^{70} +1037.38 q^{71} -271.702 q^{72} +22.3789 q^{73} +199.711 q^{74} -1564.80 q^{75} +269.949 q^{76} -182.536 q^{77} +8.45571 q^{78} -682.688 q^{79} -1491.75 q^{80} -907.335 q^{81} -1261.93 q^{82} -312.352 q^{83} -376.142 q^{84} -66.4037 q^{86} -1448.83 q^{87} +144.985 q^{88} -904.392 q^{89} +963.433 q^{90} -8.80157 q^{91} +361.195 q^{92} -320.351 q^{93} +143.762 q^{94} +1975.15 q^{95} +742.317 q^{96} +1006.72 q^{97} +473.610 q^{98} -127.849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 18 q^{3} + 48 q^{4} + 30 q^{5} - 9 q^{6} + 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.25752 1.15171 0.575854 0.817552i \(-0.304670\pi\)
0.575854 + 0.817552i \(0.304670\pi\)
\(3\) −6.51757 −1.25431 −0.627153 0.778896i \(-0.715780\pi\)
−0.627153 + 0.778896i \(0.715780\pi\)
\(4\) 2.61146 0.326432
\(5\) 19.1073 1.70901 0.854506 0.519441i \(-0.173860\pi\)
0.854506 + 0.519441i \(0.173860\pi\)
\(6\) −21.2311 −1.44460
\(7\) 22.0995 1.19326 0.596631 0.802515i \(-0.296505\pi\)
0.596631 + 0.802515i \(0.296505\pi\)
\(8\) −17.5533 −0.775753
\(9\) 15.4787 0.573284
\(10\) 62.2426 1.96828
\(11\) −8.25972 −0.226400 −0.113200 0.993572i \(-0.536110\pi\)
−0.113200 + 0.993572i \(0.536110\pi\)
\(12\) −17.0204 −0.409446
\(13\) −0.398269 −0.00849693 −0.00424846 0.999991i \(-0.501352\pi\)
−0.00424846 + 0.999991i \(0.501352\pi\)
\(14\) 71.9898 1.37429
\(15\) −124.533 −2.14362
\(16\) −78.0720 −1.21987
\(17\) 0 0
\(18\) 50.4221 0.660256
\(19\) 103.371 1.24816 0.624078 0.781362i \(-0.285475\pi\)
0.624078 + 0.781362i \(0.285475\pi\)
\(20\) 49.8980 0.557877
\(21\) −144.035 −1.49672
\(22\) −26.9062 −0.260747
\(23\) 138.311 1.25391 0.626955 0.779056i \(-0.284301\pi\)
0.626955 + 0.779056i \(0.284301\pi\)
\(24\) 114.405 0.973032
\(25\) 240.090 1.92072
\(26\) −1.29737 −0.00978598
\(27\) 75.0910 0.535233
\(28\) 57.7120 0.389520
\(29\) 222.296 1.42342 0.711712 0.702471i \(-0.247920\pi\)
0.711712 + 0.702471i \(0.247920\pi\)
\(30\) −405.670 −2.46883
\(31\) 49.1520 0.284773 0.142386 0.989811i \(-0.454522\pi\)
0.142386 + 0.989811i \(0.454522\pi\)
\(32\) −113.895 −0.629186
\(33\) 53.8333 0.283975
\(34\) 0 0
\(35\) 422.263 2.03930
\(36\) 40.4219 0.187138
\(37\) 61.3077 0.272403 0.136202 0.990681i \(-0.456510\pi\)
0.136202 + 0.990681i \(0.456510\pi\)
\(38\) 336.734 1.43751
\(39\) 2.59575 0.0106577
\(40\) −335.397 −1.32577
\(41\) −387.391 −1.47562 −0.737808 0.675011i \(-0.764139\pi\)
−0.737808 + 0.675011i \(0.764139\pi\)
\(42\) −469.198 −1.72378
\(43\) −20.3847 −0.0722939 −0.0361470 0.999346i \(-0.511508\pi\)
−0.0361470 + 0.999346i \(0.511508\pi\)
\(44\) −21.5699 −0.0739043
\(45\) 295.756 0.979749
\(46\) 450.553 1.44414
\(47\) 44.1322 0.136965 0.0684824 0.997652i \(-0.478184\pi\)
0.0684824 + 0.997652i \(0.478184\pi\)
\(48\) 508.839 1.53010
\(49\) 145.389 0.423876
\(50\) 782.100 2.21211
\(51\) 0 0
\(52\) −1.04006 −0.00277367
\(53\) 59.6456 0.154584 0.0772920 0.997009i \(-0.475373\pi\)
0.0772920 + 0.997009i \(0.475373\pi\)
\(54\) 244.611 0.616432
\(55\) −157.821 −0.386920
\(56\) −387.920 −0.925678
\(57\) −673.728 −1.56557
\(58\) 724.134 1.63937
\(59\) 238.069 0.525321 0.262660 0.964888i \(-0.415400\pi\)
0.262660 + 0.964888i \(0.415400\pi\)
\(60\) −325.214 −0.699749
\(61\) −595.816 −1.25060 −0.625298 0.780386i \(-0.715023\pi\)
−0.625298 + 0.780386i \(0.715023\pi\)
\(62\) 160.114 0.327975
\(63\) 342.071 0.684078
\(64\) 253.561 0.495235
\(65\) −7.60987 −0.0145214
\(66\) 175.363 0.327056
\(67\) −408.815 −0.745442 −0.372721 0.927943i \(-0.621575\pi\)
−0.372721 + 0.927943i \(0.621575\pi\)
\(68\) 0 0
\(69\) −901.454 −1.57279
\(70\) 1375.53 2.34868
\(71\) 1037.38 1.73400 0.866999 0.498309i \(-0.166046\pi\)
0.866999 + 0.498309i \(0.166046\pi\)
\(72\) −271.702 −0.444727
\(73\) 22.3789 0.0358802 0.0179401 0.999839i \(-0.494289\pi\)
0.0179401 + 0.999839i \(0.494289\pi\)
\(74\) 199.711 0.313729
\(75\) −1564.80 −2.40917
\(76\) 269.949 0.407438
\(77\) −182.536 −0.270155
\(78\) 8.45571 0.0122746
\(79\) −682.688 −0.972259 −0.486129 0.873887i \(-0.661592\pi\)
−0.486129 + 0.873887i \(0.661592\pi\)
\(80\) −1491.75 −2.08478
\(81\) −907.335 −1.24463
\(82\) −1261.93 −1.69948
\(83\) −312.352 −0.413073 −0.206536 0.978439i \(-0.566219\pi\)
−0.206536 + 0.978439i \(0.566219\pi\)
\(84\) −376.142 −0.488577
\(85\) 0 0
\(86\) −66.4037 −0.0832616
\(87\) −1448.83 −1.78541
\(88\) 144.985 0.175630
\(89\) −904.392 −1.07714 −0.538570 0.842581i \(-0.681035\pi\)
−0.538570 + 0.842581i \(0.681035\pi\)
\(90\) 963.433 1.12839
\(91\) −8.80157 −0.0101391
\(92\) 361.195 0.409317
\(93\) −320.351 −0.357192
\(94\) 143.762 0.157744
\(95\) 1975.15 2.13311
\(96\) 742.317 0.789192
\(97\) 1006.72 1.05378 0.526891 0.849933i \(-0.323358\pi\)
0.526891 + 0.849933i \(0.323358\pi\)
\(98\) 473.610 0.488182
\(99\) −127.849 −0.129791
\(100\) 626.986 0.626986
\(101\) −1124.60 −1.10794 −0.553968 0.832538i \(-0.686887\pi\)
−0.553968 + 0.832538i \(0.686887\pi\)
\(102\) 0 0
\(103\) −396.677 −0.379473 −0.189736 0.981835i \(-0.560763\pi\)
−0.189736 + 0.981835i \(0.560763\pi\)
\(104\) 6.99094 0.00659152
\(105\) −2752.13 −2.55791
\(106\) 194.297 0.178036
\(107\) −288.906 −0.261024 −0.130512 0.991447i \(-0.541662\pi\)
−0.130512 + 0.991447i \(0.541662\pi\)
\(108\) 196.097 0.174717
\(109\) 1379.15 1.21191 0.605955 0.795499i \(-0.292791\pi\)
0.605955 + 0.795499i \(0.292791\pi\)
\(110\) −514.106 −0.445619
\(111\) −399.577 −0.341677
\(112\) −1725.35 −1.45563
\(113\) −1364.42 −1.13587 −0.567937 0.823072i \(-0.692258\pi\)
−0.567937 + 0.823072i \(0.692258\pi\)
\(114\) −2194.68 −1.80308
\(115\) 2642.76 2.14295
\(116\) 580.517 0.464652
\(117\) −6.16468 −0.00487115
\(118\) 775.515 0.605016
\(119\) 0 0
\(120\) 2185.97 1.66292
\(121\) −1262.78 −0.948743
\(122\) −1940.88 −1.44032
\(123\) 2524.84 1.85087
\(124\) 128.358 0.0929591
\(125\) 2199.07 1.57353
\(126\) 1114.31 0.787859
\(127\) 1003.33 0.701032 0.350516 0.936557i \(-0.386006\pi\)
0.350516 + 0.936557i \(0.386006\pi\)
\(128\) 1737.14 1.19955
\(129\) 132.859 0.0906787
\(130\) −24.7893 −0.0167244
\(131\) −218.014 −0.145404 −0.0727022 0.997354i \(-0.523162\pi\)
−0.0727022 + 0.997354i \(0.523162\pi\)
\(132\) 140.583 0.0926986
\(133\) 2284.45 1.48938
\(134\) −1331.72 −0.858532
\(135\) 1434.79 0.914719
\(136\) 0 0
\(137\) −1625.34 −1.01359 −0.506797 0.862066i \(-0.669171\pi\)
−0.506797 + 0.862066i \(0.669171\pi\)
\(138\) −2936.51 −1.81139
\(139\) 1034.35 0.631166 0.315583 0.948898i \(-0.397800\pi\)
0.315583 + 0.948898i \(0.397800\pi\)
\(140\) 1102.72 0.665694
\(141\) −287.635 −0.171796
\(142\) 3379.28 1.99706
\(143\) 3.28959 0.00192370
\(144\) −1208.45 −0.699334
\(145\) 4247.48 2.43265
\(146\) 72.8999 0.0413236
\(147\) −947.585 −0.531670
\(148\) 160.103 0.0889213
\(149\) −650.200 −0.357493 −0.178747 0.983895i \(-0.557204\pi\)
−0.178747 + 0.983895i \(0.557204\pi\)
\(150\) −5097.39 −2.77467
\(151\) 1023.67 0.551689 0.275845 0.961202i \(-0.411042\pi\)
0.275845 + 0.961202i \(0.411042\pi\)
\(152\) −1814.50 −0.968261
\(153\) 0 0
\(154\) −594.615 −0.311139
\(155\) 939.164 0.486680
\(156\) 6.77869 0.00347903
\(157\) 671.612 0.341404 0.170702 0.985323i \(-0.445396\pi\)
0.170702 + 0.985323i \(0.445396\pi\)
\(158\) −2223.87 −1.11976
\(159\) −388.744 −0.193896
\(160\) −2176.23 −1.07529
\(161\) 3056.62 1.49624
\(162\) −2955.66 −1.43345
\(163\) −1893.45 −0.909857 −0.454929 0.890528i \(-0.650335\pi\)
−0.454929 + 0.890528i \(0.650335\pi\)
\(164\) −1011.65 −0.481689
\(165\) 1028.61 0.485316
\(166\) −1017.49 −0.475739
\(167\) 290.246 0.134491 0.0672453 0.997736i \(-0.478579\pi\)
0.0672453 + 0.997736i \(0.478579\pi\)
\(168\) 2528.29 1.16108
\(169\) −2196.84 −0.999928
\(170\) 0 0
\(171\) 1600.05 0.715547
\(172\) −53.2339 −0.0235991
\(173\) −3665.86 −1.61104 −0.805521 0.592567i \(-0.798114\pi\)
−0.805521 + 0.592567i \(0.798114\pi\)
\(174\) −4719.59 −2.05627
\(175\) 5305.89 2.29193
\(176\) 644.852 0.276179
\(177\) −1551.63 −0.658913
\(178\) −2946.08 −1.24055
\(179\) −3628.67 −1.51519 −0.757597 0.652723i \(-0.773627\pi\)
−0.757597 + 0.652723i \(0.773627\pi\)
\(180\) 772.355 0.319822
\(181\) 3827.78 1.57191 0.785957 0.618281i \(-0.212171\pi\)
0.785957 + 0.618281i \(0.212171\pi\)
\(182\) −28.6713 −0.0116773
\(183\) 3883.27 1.56863
\(184\) −2427.82 −0.972725
\(185\) 1171.43 0.465541
\(186\) −1043.55 −0.411382
\(187\) 0 0
\(188\) 115.249 0.0447097
\(189\) 1659.48 0.638673
\(190\) 6434.08 2.45672
\(191\) −877.247 −0.332332 −0.166166 0.986098i \(-0.553139\pi\)
−0.166166 + 0.986098i \(0.553139\pi\)
\(192\) −1652.60 −0.621177
\(193\) −4769.70 −1.77891 −0.889457 0.457018i \(-0.848917\pi\)
−0.889457 + 0.457018i \(0.848917\pi\)
\(194\) 3279.41 1.21365
\(195\) 49.5978 0.0182142
\(196\) 379.679 0.138367
\(197\) 1492.97 0.539949 0.269974 0.962867i \(-0.412985\pi\)
0.269974 + 0.962867i \(0.412985\pi\)
\(198\) −416.473 −0.149482
\(199\) −3091.28 −1.10118 −0.550591 0.834775i \(-0.685598\pi\)
−0.550591 + 0.834775i \(0.685598\pi\)
\(200\) −4214.38 −1.49001
\(201\) 2664.48 0.935013
\(202\) −3663.40 −1.27602
\(203\) 4912.63 1.69852
\(204\) 0 0
\(205\) −7402.00 −2.52185
\(206\) −1292.18 −0.437042
\(207\) 2140.88 0.718846
\(208\) 31.0937 0.0103652
\(209\) −853.816 −0.282582
\(210\) −8965.12 −2.94596
\(211\) −2776.38 −0.905848 −0.452924 0.891549i \(-0.649619\pi\)
−0.452924 + 0.891549i \(0.649619\pi\)
\(212\) 155.762 0.0504612
\(213\) −6761.17 −2.17497
\(214\) −941.118 −0.300624
\(215\) −389.498 −0.123551
\(216\) −1318.10 −0.415209
\(217\) 1086.24 0.339809
\(218\) 4492.60 1.39577
\(219\) −145.856 −0.0450048
\(220\) −412.144 −0.126303
\(221\) 0 0
\(222\) −1301.63 −0.393513
\(223\) 4641.22 1.39372 0.696859 0.717209i \(-0.254581\pi\)
0.696859 + 0.717209i \(0.254581\pi\)
\(224\) −2517.02 −0.750784
\(225\) 3716.28 1.10112
\(226\) −4444.63 −1.30820
\(227\) 1712.30 0.500658 0.250329 0.968161i \(-0.419461\pi\)
0.250329 + 0.968161i \(0.419461\pi\)
\(228\) −1759.41 −0.511052
\(229\) −6028.18 −1.73954 −0.869768 0.493461i \(-0.835731\pi\)
−0.869768 + 0.493461i \(0.835731\pi\)
\(230\) 8608.86 2.46805
\(231\) 1189.69 0.338857
\(232\) −3902.02 −1.10423
\(233\) 2663.60 0.748919 0.374459 0.927243i \(-0.377828\pi\)
0.374459 + 0.927243i \(0.377828\pi\)
\(234\) −20.0816 −0.00561015
\(235\) 843.249 0.234075
\(236\) 621.707 0.171482
\(237\) 4449.47 1.21951
\(238\) 0 0
\(239\) 6020.73 1.62949 0.814747 0.579817i \(-0.196876\pi\)
0.814747 + 0.579817i \(0.196876\pi\)
\(240\) 9722.56 2.61495
\(241\) 6080.97 1.62535 0.812676 0.582716i \(-0.198010\pi\)
0.812676 + 0.582716i \(0.198010\pi\)
\(242\) −4113.53 −1.09268
\(243\) 3886.16 1.02591
\(244\) −1555.95 −0.408235
\(245\) 2778.01 0.724409
\(246\) 8224.74 2.13167
\(247\) −41.1695 −0.0106055
\(248\) −862.780 −0.220914
\(249\) 2035.77 0.518120
\(250\) 7163.52 1.81224
\(251\) −3296.82 −0.829058 −0.414529 0.910036i \(-0.636054\pi\)
−0.414529 + 0.910036i \(0.636054\pi\)
\(252\) 893.305 0.223305
\(253\) −1142.41 −0.283885
\(254\) 3268.37 0.807384
\(255\) 0 0
\(256\) 3630.28 0.886300
\(257\) −1243.37 −0.301786 −0.150893 0.988550i \(-0.548215\pi\)
−0.150893 + 0.988550i \(0.548215\pi\)
\(258\) 432.790 0.104435
\(259\) 1354.87 0.325049
\(260\) −19.8729 −0.00474024
\(261\) 3440.84 0.816026
\(262\) −710.186 −0.167463
\(263\) 4523.81 1.06065 0.530324 0.847795i \(-0.322070\pi\)
0.530324 + 0.847795i \(0.322070\pi\)
\(264\) −944.951 −0.220294
\(265\) 1139.67 0.264186
\(266\) 7441.66 1.71533
\(267\) 5894.44 1.35106
\(268\) −1067.60 −0.243337
\(269\) −2155.56 −0.488576 −0.244288 0.969703i \(-0.578554\pi\)
−0.244288 + 0.969703i \(0.578554\pi\)
\(270\) 4673.86 1.05349
\(271\) −5433.12 −1.21785 −0.608927 0.793226i \(-0.708400\pi\)
−0.608927 + 0.793226i \(0.708400\pi\)
\(272\) 0 0
\(273\) 57.3648 0.0127175
\(274\) −5294.59 −1.16736
\(275\) −1983.08 −0.434851
\(276\) −2354.11 −0.513408
\(277\) −3349.75 −0.726595 −0.363297 0.931673i \(-0.618349\pi\)
−0.363297 + 0.931673i \(0.618349\pi\)
\(278\) 3369.40 0.726919
\(279\) 760.807 0.163256
\(280\) −7412.11 −1.58199
\(281\) −2668.18 −0.566441 −0.283221 0.959055i \(-0.591403\pi\)
−0.283221 + 0.959055i \(0.591403\pi\)
\(282\) −936.977 −0.197859
\(283\) 5452.65 1.14532 0.572662 0.819792i \(-0.305911\pi\)
0.572662 + 0.819792i \(0.305911\pi\)
\(284\) 2709.07 0.566033
\(285\) −12873.1 −2.67558
\(286\) 10.7159 0.00221555
\(287\) −8561.15 −1.76080
\(288\) −1762.94 −0.360702
\(289\) 0 0
\(290\) 13836.3 2.80170
\(291\) −6561.36 −1.32177
\(292\) 58.4417 0.0117125
\(293\) 6341.24 1.26437 0.632183 0.774819i \(-0.282159\pi\)
0.632183 + 0.774819i \(0.282159\pi\)
\(294\) −3086.78 −0.612329
\(295\) 4548.86 0.897780
\(296\) −1076.15 −0.211318
\(297\) −620.231 −0.121177
\(298\) −2118.04 −0.411728
\(299\) −55.0852 −0.0106544
\(300\) −4086.42 −0.786433
\(301\) −450.493 −0.0862657
\(302\) 3334.63 0.635385
\(303\) 7329.63 1.38969
\(304\) −8070.38 −1.52259
\(305\) −11384.5 −2.13729
\(306\) 0 0
\(307\) 820.602 0.152555 0.0762773 0.997087i \(-0.475697\pi\)
0.0762773 + 0.997087i \(0.475697\pi\)
\(308\) −476.685 −0.0881872
\(309\) 2585.37 0.475975
\(310\) 3059.35 0.560514
\(311\) 7492.46 1.36610 0.683052 0.730369i \(-0.260652\pi\)
0.683052 + 0.730369i \(0.260652\pi\)
\(312\) −45.5639 −0.00826779
\(313\) 1217.76 0.219910 0.109955 0.993937i \(-0.464929\pi\)
0.109955 + 0.993937i \(0.464929\pi\)
\(314\) 2187.79 0.393198
\(315\) 6536.07 1.16910
\(316\) −1782.81 −0.317377
\(317\) −5682.18 −1.00676 −0.503380 0.864065i \(-0.667910\pi\)
−0.503380 + 0.864065i \(0.667910\pi\)
\(318\) −1266.34 −0.223311
\(319\) −1836.10 −0.322263
\(320\) 4844.87 0.846363
\(321\) 1882.96 0.327404
\(322\) 9957.00 1.72324
\(323\) 0 0
\(324\) −2369.47 −0.406287
\(325\) −95.6206 −0.0163202
\(326\) −6167.97 −1.04789
\(327\) −8988.68 −1.52011
\(328\) 6799.98 1.14471
\(329\) 975.301 0.163435
\(330\) 3350.72 0.558943
\(331\) 7387.94 1.22682 0.613411 0.789764i \(-0.289797\pi\)
0.613411 + 0.789764i \(0.289797\pi\)
\(332\) −815.693 −0.134840
\(333\) 948.962 0.156165
\(334\) 945.483 0.154894
\(335\) −7811.36 −1.27397
\(336\) 11245.1 1.82581
\(337\) −5104.29 −0.825069 −0.412534 0.910942i \(-0.635356\pi\)
−0.412534 + 0.910942i \(0.635356\pi\)
\(338\) −7156.26 −1.15163
\(339\) 8892.69 1.42473
\(340\) 0 0
\(341\) −405.982 −0.0644725
\(342\) 5212.19 0.824102
\(343\) −4367.10 −0.687467
\(344\) 357.819 0.0560823
\(345\) −17224.4 −2.68791
\(346\) −11941.6 −1.85545
\(347\) 8986.15 1.39021 0.695103 0.718910i \(-0.255359\pi\)
0.695103 + 0.718910i \(0.255359\pi\)
\(348\) −3783.55 −0.582816
\(349\) 1924.65 0.295198 0.147599 0.989047i \(-0.452845\pi\)
0.147599 + 0.989047i \(0.452845\pi\)
\(350\) 17284.0 2.63963
\(351\) −29.9065 −0.00454783
\(352\) 940.739 0.142448
\(353\) 4574.33 0.689709 0.344854 0.938656i \(-0.387928\pi\)
0.344854 + 0.938656i \(0.387928\pi\)
\(354\) −5054.47 −0.758876
\(355\) 19821.5 2.96343
\(356\) −2361.78 −0.351613
\(357\) 0 0
\(358\) −11820.5 −1.74506
\(359\) 9358.89 1.37589 0.687943 0.725765i \(-0.258514\pi\)
0.687943 + 0.725765i \(0.258514\pi\)
\(360\) −5191.50 −0.760044
\(361\) 3826.58 0.557892
\(362\) 12469.1 1.81039
\(363\) 8230.23 1.19001
\(364\) −22.9849 −0.00330972
\(365\) 427.602 0.0613198
\(366\) 12649.8 1.80661
\(367\) −1596.51 −0.227077 −0.113539 0.993534i \(-0.536219\pi\)
−0.113539 + 0.993534i \(0.536219\pi\)
\(368\) −10798.2 −1.52961
\(369\) −5996.29 −0.845947
\(370\) 3815.95 0.536167
\(371\) 1318.14 0.184459
\(372\) −836.585 −0.116599
\(373\) −10884.6 −1.51094 −0.755471 0.655182i \(-0.772592\pi\)
−0.755471 + 0.655182i \(0.772592\pi\)
\(374\) 0 0
\(375\) −14332.6 −1.97368
\(376\) −774.666 −0.106251
\(377\) −88.5336 −0.0120947
\(378\) 5405.79 0.735565
\(379\) −1561.47 −0.211629 −0.105814 0.994386i \(-0.533745\pi\)
−0.105814 + 0.994386i \(0.533745\pi\)
\(380\) 5158.01 0.696317
\(381\) −6539.26 −0.879308
\(382\) −2857.65 −0.382749
\(383\) −4409.48 −0.588287 −0.294143 0.955761i \(-0.595034\pi\)
−0.294143 + 0.955761i \(0.595034\pi\)
\(384\) −11321.9 −1.50461
\(385\) −3487.78 −0.461697
\(386\) −15537.4 −2.04879
\(387\) −315.528 −0.0414450
\(388\) 2629.01 0.343989
\(389\) −8017.21 −1.04496 −0.522479 0.852652i \(-0.674993\pi\)
−0.522479 + 0.852652i \(0.674993\pi\)
\(390\) 161.566 0.0209775
\(391\) 0 0
\(392\) −2552.06 −0.328823
\(393\) 1420.92 0.182382
\(394\) 4863.39 0.621864
\(395\) −13044.4 −1.66160
\(396\) −333.874 −0.0423681
\(397\) −9437.12 −1.19304 −0.596519 0.802599i \(-0.703450\pi\)
−0.596519 + 0.802599i \(0.703450\pi\)
\(398\) −10069.9 −1.26824
\(399\) −14889.1 −1.86814
\(400\) −18744.3 −2.34304
\(401\) 4509.28 0.561553 0.280777 0.959773i \(-0.409408\pi\)
0.280777 + 0.959773i \(0.409408\pi\)
\(402\) 8679.59 1.07686
\(403\) −19.5757 −0.00241969
\(404\) −2936.84 −0.361666
\(405\) −17336.8 −2.12709
\(406\) 16003.0 1.95620
\(407\) −506.384 −0.0616721
\(408\) 0 0
\(409\) 12446.9 1.50480 0.752398 0.658709i \(-0.228897\pi\)
0.752398 + 0.658709i \(0.228897\pi\)
\(410\) −24112.2 −2.90443
\(411\) 10593.3 1.27136
\(412\) −1035.91 −0.123872
\(413\) 5261.21 0.626846
\(414\) 6973.95 0.827901
\(415\) −5968.21 −0.705946
\(416\) 45.3608 0.00534615
\(417\) −6741.41 −0.791675
\(418\) −2781.33 −0.325452
\(419\) 1648.22 0.192173 0.0960867 0.995373i \(-0.469367\pi\)
0.0960867 + 0.995373i \(0.469367\pi\)
\(420\) −7187.07 −0.834984
\(421\) 14395.5 1.66649 0.833247 0.552901i \(-0.186479\pi\)
0.833247 + 0.552901i \(0.186479\pi\)
\(422\) −9044.13 −1.04327
\(423\) 683.108 0.0785197
\(424\) −1046.98 −0.119919
\(425\) 0 0
\(426\) −22024.7 −2.50493
\(427\) −13167.3 −1.49229
\(428\) −754.466 −0.0852068
\(429\) −21.4401 −0.00241291
\(430\) −1268.80 −0.142295
\(431\) −5351.92 −0.598127 −0.299064 0.954233i \(-0.596674\pi\)
−0.299064 + 0.954233i \(0.596674\pi\)
\(432\) −5862.50 −0.652916
\(433\) 15578.0 1.72894 0.864472 0.502680i \(-0.167653\pi\)
0.864472 + 0.502680i \(0.167653\pi\)
\(434\) 3538.44 0.391361
\(435\) −27683.2 −3.05129
\(436\) 3601.58 0.395607
\(437\) 14297.4 1.56507
\(438\) −475.130 −0.0518324
\(439\) −16584.8 −1.80307 −0.901535 0.432707i \(-0.857558\pi\)
−0.901535 + 0.432707i \(0.857558\pi\)
\(440\) 2770.28 0.300155
\(441\) 2250.44 0.243001
\(442\) 0 0
\(443\) 5163.31 0.553761 0.276881 0.960904i \(-0.410699\pi\)
0.276881 + 0.960904i \(0.410699\pi\)
\(444\) −1043.48 −0.111535
\(445\) −17280.5 −1.84084
\(446\) 15118.9 1.60516
\(447\) 4237.72 0.448406
\(448\) 5603.57 0.590946
\(449\) 10771.9 1.13220 0.566099 0.824337i \(-0.308452\pi\)
0.566099 + 0.824337i \(0.308452\pi\)
\(450\) 12105.9 1.26817
\(451\) 3199.74 0.334079
\(452\) −3563.13 −0.370786
\(453\) −6671.84 −0.691987
\(454\) 5577.86 0.576612
\(455\) −168.175 −0.0173278
\(456\) 11826.1 1.21450
\(457\) 5024.59 0.514312 0.257156 0.966370i \(-0.417215\pi\)
0.257156 + 0.966370i \(0.417215\pi\)
\(458\) −19636.9 −2.00344
\(459\) 0 0
\(460\) 6901.47 0.699527
\(461\) −2366.96 −0.239133 −0.119567 0.992826i \(-0.538151\pi\)
−0.119567 + 0.992826i \(0.538151\pi\)
\(462\) 3875.44 0.390264
\(463\) −17712.9 −1.77795 −0.888974 0.457958i \(-0.848581\pi\)
−0.888974 + 0.457958i \(0.848581\pi\)
\(464\) −17355.1 −1.73640
\(465\) −6121.06 −0.610446
\(466\) 8676.73 0.862536
\(467\) −19592.7 −1.94141 −0.970707 0.240267i \(-0.922765\pi\)
−0.970707 + 0.240267i \(0.922765\pi\)
\(468\) −16.0988 −0.00159010
\(469\) −9034.61 −0.889509
\(470\) 2746.90 0.269586
\(471\) −4377.27 −0.428225
\(472\) −4178.89 −0.407519
\(473\) 168.372 0.0163673
\(474\) 14494.2 1.40452
\(475\) 24818.4 2.39736
\(476\) 0 0
\(477\) 923.234 0.0886205
\(478\) 19612.7 1.87670
\(479\) −4060.41 −0.387317 −0.193659 0.981069i \(-0.562035\pi\)
−0.193659 + 0.981069i \(0.562035\pi\)
\(480\) 14183.7 1.34874
\(481\) −24.4170 −0.00231459
\(482\) 19808.9 1.87193
\(483\) −19921.7 −1.87675
\(484\) −3297.69 −0.309701
\(485\) 19235.7 1.80093
\(486\) 12659.2 1.18155
\(487\) −7256.96 −0.675244 −0.337622 0.941282i \(-0.609623\pi\)
−0.337622 + 0.941282i \(0.609623\pi\)
\(488\) 10458.5 0.970155
\(489\) 12340.7 1.14124
\(490\) 9049.42 0.834308
\(491\) −769.855 −0.0707598 −0.0353799 0.999374i \(-0.511264\pi\)
−0.0353799 + 0.999374i \(0.511264\pi\)
\(492\) 6593.53 0.604185
\(493\) 0 0
\(494\) −134.111 −0.0122144
\(495\) −2442.86 −0.221815
\(496\) −3837.39 −0.347387
\(497\) 22925.5 2.06912
\(498\) 6631.58 0.596723
\(499\) 1432.66 0.128526 0.0642630 0.997933i \(-0.479530\pi\)
0.0642630 + 0.997933i \(0.479530\pi\)
\(500\) 5742.78 0.513650
\(501\) −1891.70 −0.168692
\(502\) −10739.5 −0.954833
\(503\) 16206.3 1.43659 0.718295 0.695739i \(-0.244923\pi\)
0.718295 + 0.695739i \(0.244923\pi\)
\(504\) −6004.48 −0.530676
\(505\) −21488.0 −1.89348
\(506\) −3721.44 −0.326953
\(507\) 14318.1 1.25422
\(508\) 2620.15 0.228839
\(509\) 15009.4 1.30703 0.653517 0.756912i \(-0.273293\pi\)
0.653517 + 0.756912i \(0.273293\pi\)
\(510\) 0 0
\(511\) 494.564 0.0428145
\(512\) −2071.37 −0.178794
\(513\) 7762.24 0.668053
\(514\) −4050.29 −0.347570
\(515\) −7579.44 −0.648524
\(516\) 346.955 0.0296005
\(517\) −364.520 −0.0310088
\(518\) 4413.53 0.374361
\(519\) 23892.5 2.02074
\(520\) 133.578 0.0112650
\(521\) 19626.5 1.65039 0.825196 0.564846i \(-0.191064\pi\)
0.825196 + 0.564846i \(0.191064\pi\)
\(522\) 11208.6 0.939824
\(523\) −9267.41 −0.774829 −0.387414 0.921906i \(-0.626632\pi\)
−0.387414 + 0.921906i \(0.626632\pi\)
\(524\) −569.335 −0.0474647
\(525\) −34581.5 −2.87478
\(526\) 14736.4 1.22156
\(527\) 0 0
\(528\) −4202.87 −0.346414
\(529\) 6963.04 0.572289
\(530\) 3712.50 0.304265
\(531\) 3684.99 0.301158
\(532\) 5965.76 0.486181
\(533\) 154.286 0.0125382
\(534\) 19201.3 1.55603
\(535\) −5520.22 −0.446094
\(536\) 7176.04 0.578280
\(537\) 23650.1 1.90052
\(538\) −7021.79 −0.562697
\(539\) −1200.88 −0.0959655
\(540\) 3746.90 0.298594
\(541\) −907.733 −0.0721377 −0.0360689 0.999349i \(-0.511484\pi\)
−0.0360689 + 0.999349i \(0.511484\pi\)
\(542\) −17698.5 −1.40261
\(543\) −24947.8 −1.97166
\(544\) 0 0
\(545\) 26351.8 2.07117
\(546\) 186.867 0.0146468
\(547\) −11197.7 −0.875281 −0.437640 0.899150i \(-0.644186\pi\)
−0.437640 + 0.899150i \(0.644186\pi\)
\(548\) −4244.51 −0.330870
\(549\) −9222.44 −0.716947
\(550\) −6459.92 −0.500822
\(551\) 22979.0 1.77665
\(552\) 15823.5 1.22009
\(553\) −15087.1 −1.16016
\(554\) −10911.9 −0.836825
\(555\) −7634.85 −0.583931
\(556\) 2701.15 0.206033
\(557\) −3207.25 −0.243978 −0.121989 0.992531i \(-0.538927\pi\)
−0.121989 + 0.992531i \(0.538927\pi\)
\(558\) 2478.35 0.188023
\(559\) 8.11861 0.000614276 0
\(560\) −32966.9 −2.48769
\(561\) 0 0
\(562\) −8691.64 −0.652375
\(563\) −6522.79 −0.488282 −0.244141 0.969740i \(-0.578506\pi\)
−0.244141 + 0.969740i \(0.578506\pi\)
\(564\) −751.146 −0.0560797
\(565\) −26070.4 −1.94122
\(566\) 17762.2 1.31908
\(567\) −20051.7 −1.48517
\(568\) −18209.4 −1.34516
\(569\) −3040.50 −0.224015 −0.112007 0.993707i \(-0.535728\pi\)
−0.112007 + 0.993707i \(0.535728\pi\)
\(570\) −41934.6 −3.08148
\(571\) 17273.2 1.26596 0.632979 0.774169i \(-0.281832\pi\)
0.632979 + 0.774169i \(0.281832\pi\)
\(572\) 8.59064 0.000627959 0
\(573\) 5717.51 0.416846
\(574\) −27888.2 −2.02793
\(575\) 33207.2 2.40841
\(576\) 3924.78 0.283910
\(577\) −5804.29 −0.418779 −0.209390 0.977832i \(-0.567148\pi\)
−0.209390 + 0.977832i \(0.567148\pi\)
\(578\) 0 0
\(579\) 31086.8 2.23130
\(580\) 11092.1 0.794096
\(581\) −6902.83 −0.492904
\(582\) −21373.8 −1.52229
\(583\) −492.656 −0.0349978
\(584\) −392.824 −0.0278342
\(585\) −117.791 −0.00832486
\(586\) 20656.8 1.45618
\(587\) 12862.4 0.904407 0.452204 0.891915i \(-0.350638\pi\)
0.452204 + 0.891915i \(0.350638\pi\)
\(588\) −2474.58 −0.173554
\(589\) 5080.89 0.355441
\(590\) 14818.0 1.03398
\(591\) −9730.55 −0.677261
\(592\) −4786.41 −0.332298
\(593\) 1319.33 0.0913631 0.0456816 0.998956i \(-0.485454\pi\)
0.0456816 + 0.998956i \(0.485454\pi\)
\(594\) −2020.42 −0.139560
\(595\) 0 0
\(596\) −1697.97 −0.116697
\(597\) 20147.6 1.38122
\(598\) −179.441 −0.0122707
\(599\) −16269.3 −1.10976 −0.554881 0.831930i \(-0.687236\pi\)
−0.554881 + 0.831930i \(0.687236\pi\)
\(600\) 27467.5 1.86893
\(601\) −7427.38 −0.504108 −0.252054 0.967713i \(-0.581106\pi\)
−0.252054 + 0.967713i \(0.581106\pi\)
\(602\) −1467.49 −0.0993529
\(603\) −6327.90 −0.427350
\(604\) 2673.27 0.180089
\(605\) −24128.3 −1.62141
\(606\) 23876.4 1.60052
\(607\) −7212.10 −0.482257 −0.241129 0.970493i \(-0.577518\pi\)
−0.241129 + 0.970493i \(0.577518\pi\)
\(608\) −11773.4 −0.785322
\(609\) −32018.4 −2.13046
\(610\) −37085.1 −2.46153
\(611\) −17.5765 −0.00116378
\(612\) 0 0
\(613\) −15446.5 −1.01775 −0.508873 0.860842i \(-0.669938\pi\)
−0.508873 + 0.860842i \(0.669938\pi\)
\(614\) 2673.13 0.175698
\(615\) 48243.1 3.16317
\(616\) 3204.11 0.209573
\(617\) −8746.54 −0.570701 −0.285350 0.958423i \(-0.592110\pi\)
−0.285350 + 0.958423i \(0.592110\pi\)
\(618\) 8421.89 0.548185
\(619\) 4740.09 0.307787 0.153894 0.988087i \(-0.450819\pi\)
0.153894 + 0.988087i \(0.450819\pi\)
\(620\) 2452.59 0.158868
\(621\) 10385.9 0.671133
\(622\) 24406.9 1.57335
\(623\) −19986.7 −1.28531
\(624\) −202.655 −0.0130011
\(625\) 12007.1 0.768453
\(626\) 3966.89 0.253273
\(627\) 5564.80 0.354445
\(628\) 1753.89 0.111445
\(629\) 0 0
\(630\) 21291.4 1.34646
\(631\) −17055.1 −1.07600 −0.537998 0.842946i \(-0.680819\pi\)
−0.537998 + 0.842946i \(0.680819\pi\)
\(632\) 11983.4 0.754233
\(633\) 18095.2 1.13621
\(634\) −18509.8 −1.15949
\(635\) 19170.9 1.19807
\(636\) −1015.19 −0.0632938
\(637\) −57.9042 −0.00360164
\(638\) −5981.14 −0.371153
\(639\) 16057.2 0.994074
\(640\) 33192.1 2.05005
\(641\) 16050.5 0.989012 0.494506 0.869174i \(-0.335349\pi\)
0.494506 + 0.869174i \(0.335349\pi\)
\(642\) 6133.80 0.377074
\(643\) 14821.5 0.909027 0.454514 0.890740i \(-0.349813\pi\)
0.454514 + 0.890740i \(0.349813\pi\)
\(644\) 7982.23 0.488422
\(645\) 2538.58 0.154971
\(646\) 0 0
\(647\) −30527.0 −1.85493 −0.927465 0.373910i \(-0.878017\pi\)
−0.927465 + 0.373910i \(0.878017\pi\)
\(648\) 15926.7 0.965526
\(649\) −1966.38 −0.118933
\(650\) −311.486 −0.0187962
\(651\) −7079.62 −0.426224
\(652\) −4944.68 −0.297007
\(653\) −20173.6 −1.20897 −0.604483 0.796618i \(-0.706620\pi\)
−0.604483 + 0.796618i \(0.706620\pi\)
\(654\) −29280.8 −1.75072
\(655\) −4165.67 −0.248498
\(656\) 30244.3 1.80007
\(657\) 346.396 0.0205696
\(658\) 3177.07 0.188229
\(659\) −21503.0 −1.27107 −0.635537 0.772071i \(-0.719221\pi\)
−0.635537 + 0.772071i \(0.719221\pi\)
\(660\) 2686.17 0.158423
\(661\) −1772.12 −0.104278 −0.0521389 0.998640i \(-0.516604\pi\)
−0.0521389 + 0.998640i \(0.516604\pi\)
\(662\) 24066.4 1.41294
\(663\) 0 0
\(664\) 5482.80 0.320443
\(665\) 43649.8 2.54536
\(666\) 3091.26 0.179856
\(667\) 30746.0 1.78485
\(668\) 757.966 0.0439021
\(669\) −30249.4 −1.74815
\(670\) −25445.7 −1.46724
\(671\) 4921.27 0.283135
\(672\) 16404.9 0.941713
\(673\) −33449.4 −1.91587 −0.957936 0.286983i \(-0.907348\pi\)
−0.957936 + 0.286983i \(0.907348\pi\)
\(674\) −16627.3 −0.950239
\(675\) 18028.6 1.02803
\(676\) −5736.96 −0.326409
\(677\) 805.765 0.0457431 0.0228716 0.999738i \(-0.492719\pi\)
0.0228716 + 0.999738i \(0.492719\pi\)
\(678\) 28968.2 1.64088
\(679\) 22248.0 1.25744
\(680\) 0 0
\(681\) −11160.0 −0.627978
\(682\) −1322.49 −0.0742536
\(683\) −993.802 −0.0556761 −0.0278380 0.999612i \(-0.508862\pi\)
−0.0278380 + 0.999612i \(0.508862\pi\)
\(684\) 4178.46 0.233578
\(685\) −31056.0 −1.73224
\(686\) −14225.9 −0.791762
\(687\) 39289.1 2.18191
\(688\) 1591.47 0.0881895
\(689\) −23.7550 −0.00131349
\(690\) −56108.8 −3.09569
\(691\) −33450.1 −1.84154 −0.920768 0.390111i \(-0.872437\pi\)
−0.920768 + 0.390111i \(0.872437\pi\)
\(692\) −9573.25 −0.525896
\(693\) −2825.41 −0.154875
\(694\) 29272.6 1.60111
\(695\) 19763.6 1.07867
\(696\) 25431.7 1.38504
\(697\) 0 0
\(698\) 6269.59 0.339982
\(699\) −17360.2 −0.939373
\(700\) 13856.1 0.748159
\(701\) −18290.5 −0.985481 −0.492740 0.870176i \(-0.664005\pi\)
−0.492740 + 0.870176i \(0.664005\pi\)
\(702\) −97.4210 −0.00523778
\(703\) 6337.44 0.340002
\(704\) −2094.34 −0.112121
\(705\) −5495.93 −0.293601
\(706\) 14901.0 0.794343
\(707\) −24853.1 −1.32206
\(708\) −4052.02 −0.215091
\(709\) −6780.00 −0.359137 −0.179569 0.983745i \(-0.557470\pi\)
−0.179569 + 0.983745i \(0.557470\pi\)
\(710\) 64569.0 3.41300
\(711\) −10567.1 −0.557380
\(712\) 15875.1 0.835595
\(713\) 6798.28 0.357079
\(714\) 0 0
\(715\) 62.8554 0.00328763
\(716\) −9476.13 −0.494608
\(717\) −39240.5 −2.04388
\(718\) 30486.8 1.58462
\(719\) 24591.0 1.27551 0.637754 0.770240i \(-0.279864\pi\)
0.637754 + 0.770240i \(0.279864\pi\)
\(720\) −23090.3 −1.19517
\(721\) −8766.37 −0.452811
\(722\) 12465.2 0.642528
\(723\) −39633.1 −2.03869
\(724\) 9996.08 0.513124
\(725\) 53371.1 2.73400
\(726\) 26810.2 1.37055
\(727\) −9819.79 −0.500957 −0.250479 0.968122i \(-0.580588\pi\)
−0.250479 + 0.968122i \(0.580588\pi\)
\(728\) 154.497 0.00786542
\(729\) −830.242 −0.0421806
\(730\) 1392.92 0.0706225
\(731\) 0 0
\(732\) 10141.0 0.512052
\(733\) −10751.8 −0.541783 −0.270892 0.962610i \(-0.587318\pi\)
−0.270892 + 0.962610i \(0.587318\pi\)
\(734\) −5200.68 −0.261527
\(735\) −18105.8 −0.908631
\(736\) −15753.0 −0.788942
\(737\) 3376.69 0.168768
\(738\) −19533.1 −0.974284
\(739\) −1809.70 −0.0900823 −0.0450412 0.998985i \(-0.514342\pi\)
−0.0450412 + 0.998985i \(0.514342\pi\)
\(740\) 3059.13 0.151968
\(741\) 268.325 0.0133025
\(742\) 4293.87 0.212443
\(743\) 895.790 0.0442306 0.0221153 0.999755i \(-0.492960\pi\)
0.0221153 + 0.999755i \(0.492960\pi\)
\(744\) 5623.22 0.277093
\(745\) −12423.6 −0.610960
\(746\) −35456.7 −1.74016
\(747\) −4834.79 −0.236808
\(748\) 0 0
\(749\) −6384.69 −0.311470
\(750\) −46688.7 −2.27311
\(751\) 11683.1 0.567672 0.283836 0.958873i \(-0.408393\pi\)
0.283836 + 0.958873i \(0.408393\pi\)
\(752\) −3445.49 −0.167080
\(753\) 21487.2 1.03989
\(754\) −288.400 −0.0139296
\(755\) 19559.6 0.942844
\(756\) 4333.66 0.208484
\(757\) −12621.2 −0.605976 −0.302988 0.952994i \(-0.597984\pi\)
−0.302988 + 0.952994i \(0.597984\pi\)
\(758\) −5086.53 −0.243735
\(759\) 7445.75 0.356079
\(760\) −34670.3 −1.65477
\(761\) −5759.46 −0.274350 −0.137175 0.990547i \(-0.543802\pi\)
−0.137175 + 0.990547i \(0.543802\pi\)
\(762\) −21301.8 −1.01271
\(763\) 30478.5 1.44613
\(764\) −2290.89 −0.108484
\(765\) 0 0
\(766\) −14364.0 −0.677535
\(767\) −94.8156 −0.00446361
\(768\) −23660.6 −1.11169
\(769\) 3245.56 0.152195 0.0760975 0.997100i \(-0.475754\pi\)
0.0760975 + 0.997100i \(0.475754\pi\)
\(770\) −11361.5 −0.531741
\(771\) 8103.72 0.378532
\(772\) −12455.9 −0.580695
\(773\) −2500.27 −0.116337 −0.0581684 0.998307i \(-0.518526\pi\)
−0.0581684 + 0.998307i \(0.518526\pi\)
\(774\) −1027.84 −0.0477325
\(775\) 11800.9 0.546970
\(776\) −17671.2 −0.817475
\(777\) −8830.47 −0.407711
\(778\) −26116.2 −1.20349
\(779\) −40045.0 −1.84180
\(780\) 129.523 0.00594571
\(781\) −8568.44 −0.392577
\(782\) 0 0
\(783\) 16692.4 0.761863
\(784\) −11350.8 −0.517075
\(785\) 12832.7 0.583464
\(786\) 4628.68 0.210050
\(787\) −15270.8 −0.691671 −0.345835 0.938295i \(-0.612404\pi\)
−0.345835 + 0.938295i \(0.612404\pi\)
\(788\) 3898.84 0.176257
\(789\) −29484.2 −1.33038
\(790\) −42492.3 −1.91368
\(791\) −30153.0 −1.35540
\(792\) 2244.18 0.100686
\(793\) 237.295 0.0106262
\(794\) −30741.7 −1.37403
\(795\) −7427.86 −0.331370
\(796\) −8072.76 −0.359462
\(797\) 6885.20 0.306006 0.153003 0.988226i \(-0.451106\pi\)
0.153003 + 0.988226i \(0.451106\pi\)
\(798\) −48501.5 −2.15155
\(799\) 0 0
\(800\) −27345.1 −1.20849
\(801\) −13998.8 −0.617507
\(802\) 14689.1 0.646746
\(803\) −184.844 −0.00812328
\(804\) 6958.17 0.305219
\(805\) 58403.8 2.55710
\(806\) −63.7684 −0.00278678
\(807\) 14049.0 0.612824
\(808\) 19740.4 0.859485
\(809\) 13606.4 0.591318 0.295659 0.955294i \(-0.404461\pi\)
0.295659 + 0.955294i \(0.404461\pi\)
\(810\) −56474.9 −2.44978
\(811\) 12718.7 0.550694 0.275347 0.961345i \(-0.411207\pi\)
0.275347 + 0.961345i \(0.411207\pi\)
\(812\) 12829.1 0.554452
\(813\) 35410.7 1.52756
\(814\) −1649.56 −0.0710283
\(815\) −36178.9 −1.55496
\(816\) 0 0
\(817\) −2107.19 −0.0902341
\(818\) 40546.2 1.73309
\(819\) −136.237 −0.00581257
\(820\) −19330.0 −0.823212
\(821\) 29119.6 1.23786 0.618929 0.785447i \(-0.287567\pi\)
0.618929 + 0.785447i \(0.287567\pi\)
\(822\) 34507.8 1.46423
\(823\) −6284.88 −0.266193 −0.133097 0.991103i \(-0.542492\pi\)
−0.133097 + 0.991103i \(0.542492\pi\)
\(824\) 6962.98 0.294377
\(825\) 12924.8 0.545437
\(826\) 17138.5 0.721944
\(827\) 5383.60 0.226368 0.113184 0.993574i \(-0.463895\pi\)
0.113184 + 0.993574i \(0.463895\pi\)
\(828\) 5590.81 0.234655
\(829\) 25382.6 1.06342 0.531709 0.846927i \(-0.321550\pi\)
0.531709 + 0.846927i \(0.321550\pi\)
\(830\) −19441.6 −0.813045
\(831\) 21832.2 0.911372
\(832\) −100.985 −0.00420798
\(833\) 0 0
\(834\) −21960.3 −0.911779
\(835\) 5545.83 0.229846
\(836\) −2229.71 −0.0922440
\(837\) 3690.88 0.152420
\(838\) 5369.10 0.221328
\(839\) 2499.44 0.102849 0.0514246 0.998677i \(-0.483624\pi\)
0.0514246 + 0.998677i \(0.483624\pi\)
\(840\) 48308.9 1.98431
\(841\) 25026.4 1.02614
\(842\) 46893.7 1.91932
\(843\) 17390.0 0.710491
\(844\) −7250.41 −0.295698
\(845\) −41975.8 −1.70889
\(846\) 2225.24 0.0904318
\(847\) −27906.8 −1.13210
\(848\) −4656.65 −0.188573
\(849\) −35538.0 −1.43659
\(850\) 0 0
\(851\) 8479.55 0.341569
\(852\) −17656.5 −0.709979
\(853\) −38293.9 −1.53711 −0.768557 0.639781i \(-0.779025\pi\)
−0.768557 + 0.639781i \(0.779025\pi\)
\(854\) −42892.6 −1.71868
\(855\) 30572.6 1.22288
\(856\) 5071.25 0.202490
\(857\) 426.303 0.0169921 0.00849606 0.999964i \(-0.497296\pi\)
0.00849606 + 0.999964i \(0.497296\pi\)
\(858\) −69.8418 −0.00277897
\(859\) 30976.1 1.23037 0.615186 0.788382i \(-0.289081\pi\)
0.615186 + 0.788382i \(0.289081\pi\)
\(860\) −1017.16 −0.0403311
\(861\) 55797.9 2.20858
\(862\) −17434.0 −0.688868
\(863\) 38201.4 1.50682 0.753412 0.657549i \(-0.228407\pi\)
0.753412 + 0.657549i \(0.228407\pi\)
\(864\) −8552.48 −0.336761
\(865\) −70044.8 −2.75329
\(866\) 50745.8 1.99124
\(867\) 0 0
\(868\) 2836.66 0.110925
\(869\) 5638.81 0.220119
\(870\) −90178.8 −3.51419
\(871\) 162.818 0.00633397
\(872\) −24208.6 −0.940144
\(873\) 15582.7 0.604116
\(874\) 46574.1 1.80251
\(875\) 48598.4 1.87763
\(876\) −380.898 −0.0146910
\(877\) 13461.8 0.518327 0.259163 0.965833i \(-0.416553\pi\)
0.259163 + 0.965833i \(0.416553\pi\)
\(878\) −54025.2 −2.07661
\(879\) −41329.5 −1.58590
\(880\) 12321.4 0.471994
\(881\) −13867.4 −0.530310 −0.265155 0.964206i \(-0.585423\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(882\) 7330.85 0.279867
\(883\) −330.794 −0.0126072 −0.00630358 0.999980i \(-0.502007\pi\)
−0.00630358 + 0.999980i \(0.502007\pi\)
\(884\) 0 0
\(885\) −29647.5 −1.12609
\(886\) 16819.6 0.637772
\(887\) 42906.5 1.62419 0.812097 0.583523i \(-0.198326\pi\)
0.812097 + 0.583523i \(0.198326\pi\)
\(888\) 7013.90 0.265057
\(889\) 22173.1 0.836515
\(890\) −56291.7 −2.12012
\(891\) 7494.33 0.281784
\(892\) 12120.4 0.454954
\(893\) 4561.99 0.170953
\(894\) 13804.5 0.516433
\(895\) −69334.3 −2.58948
\(896\) 38389.9 1.43138
\(897\) 359.021 0.0133639
\(898\) 35089.7 1.30396
\(899\) 10926.3 0.405353
\(900\) 9704.91 0.359441
\(901\) 0 0
\(902\) 10423.2 0.384762
\(903\) 2936.12 0.108204
\(904\) 23950.1 0.881158
\(905\) 73138.6 2.68642
\(906\) −21733.7 −0.796968
\(907\) 6908.93 0.252930 0.126465 0.991971i \(-0.459637\pi\)
0.126465 + 0.991971i \(0.459637\pi\)
\(908\) 4471.60 0.163431
\(909\) −17407.2 −0.635162
\(910\) −547.833 −0.0199566
\(911\) −33032.6 −1.20134 −0.600669 0.799497i \(-0.705099\pi\)
−0.600669 + 0.799497i \(0.705099\pi\)
\(912\) 52599.2 1.90980
\(913\) 2579.94 0.0935196
\(914\) 16367.7 0.592337
\(915\) 74198.9 2.68081
\(916\) −15742.4 −0.567841
\(917\) −4818.01 −0.173506
\(918\) 0 0
\(919\) 8167.05 0.293151 0.146576 0.989199i \(-0.453175\pi\)
0.146576 + 0.989199i \(0.453175\pi\)
\(920\) −46389.2 −1.66240
\(921\) −5348.33 −0.191350
\(922\) −7710.44 −0.275412
\(923\) −413.155 −0.0147337
\(924\) 3106.83 0.110614
\(925\) 14719.4 0.523211
\(926\) −57700.3 −2.04768
\(927\) −6140.03 −0.217546
\(928\) −25318.3 −0.895599
\(929\) −1864.03 −0.0658308 −0.0329154 0.999458i \(-0.510479\pi\)
−0.0329154 + 0.999458i \(0.510479\pi\)
\(930\) −19939.5 −0.703056
\(931\) 15029.1 0.529063
\(932\) 6955.87 0.244471
\(933\) −48832.6 −1.71351
\(934\) −63823.6 −2.23594
\(935\) 0 0
\(936\) 108.210 0.00377881
\(937\) −44071.0 −1.53654 −0.768270 0.640126i \(-0.778882\pi\)
−0.768270 + 0.640126i \(0.778882\pi\)
\(938\) −29430.5 −1.02445
\(939\) −7936.84 −0.275835
\(940\) 2202.11 0.0764095
\(941\) 33030.1 1.14426 0.572131 0.820162i \(-0.306117\pi\)
0.572131 + 0.820162i \(0.306117\pi\)
\(942\) −14259.1 −0.493191
\(943\) −53580.5 −1.85029
\(944\) −18586.5 −0.640825
\(945\) 31708.2 1.09150
\(946\) 548.476 0.0188504
\(947\) −9340.37 −0.320508 −0.160254 0.987076i \(-0.551231\pi\)
−0.160254 + 0.987076i \(0.551231\pi\)
\(948\) 11619.6 0.398088
\(949\) −8.91285 −0.000304872 0
\(950\) 80846.5 2.76106
\(951\) 37034.0 1.26278
\(952\) 0 0
\(953\) 21211.2 0.720984 0.360492 0.932762i \(-0.382609\pi\)
0.360492 + 0.932762i \(0.382609\pi\)
\(954\) 3007.46 0.102065
\(955\) −16761.9 −0.567959
\(956\) 15722.9 0.531919
\(957\) 11966.9 0.404217
\(958\) −13226.9 −0.446077
\(959\) −35919.3 −1.20948
\(960\) −31576.7 −1.06160
\(961\) −27375.1 −0.918904
\(962\) −79.5389 −0.00266574
\(963\) −4471.88 −0.149641
\(964\) 15880.2 0.530567
\(965\) −91136.3 −3.04019
\(966\) −64895.4 −2.16147
\(967\) 21688.1 0.721242 0.360621 0.932712i \(-0.382565\pi\)
0.360621 + 0.932712i \(0.382565\pi\)
\(968\) 22165.9 0.735991
\(969\) 0 0
\(970\) 62660.8 2.07414
\(971\) −22478.6 −0.742918 −0.371459 0.928449i \(-0.621142\pi\)
−0.371459 + 0.928449i \(0.621142\pi\)
\(972\) 10148.5 0.334892
\(973\) 22858.5 0.753146
\(974\) −23639.7 −0.777685
\(975\) 623.214 0.0204706
\(976\) 46516.5 1.52557
\(977\) 21731.7 0.711626 0.355813 0.934557i \(-0.384204\pi\)
0.355813 + 0.934557i \(0.384204\pi\)
\(978\) 40200.2 1.31438
\(979\) 7470.03 0.243864
\(980\) 7254.65 0.236471
\(981\) 21347.3 0.694769
\(982\) −2507.82 −0.0814947
\(983\) 34128.8 1.10737 0.553683 0.832728i \(-0.313222\pi\)
0.553683 + 0.832728i \(0.313222\pi\)
\(984\) −44319.3 −1.43582
\(985\) 28526.7 0.922779
\(986\) 0 0
\(987\) −6356.59 −0.204998
\(988\) −107.513 −0.00346197
\(989\) −2819.44 −0.0906501
\(990\) −7957.68 −0.255466
\(991\) 39750.8 1.27419 0.637097 0.770784i \(-0.280135\pi\)
0.637097 + 0.770784i \(0.280135\pi\)
\(992\) −5598.16 −0.179175
\(993\) −48151.4 −1.53881
\(994\) 74680.5 2.38302
\(995\) −59066.2 −1.88193
\(996\) 5316.34 0.169131
\(997\) 54112.0 1.71890 0.859450 0.511219i \(-0.170806\pi\)
0.859450 + 0.511219i \(0.170806\pi\)
\(998\) 4666.91 0.148024
\(999\) 4603.66 0.145799
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.1.9 yes 12
17.4 even 4 289.4.b.f.288.8 24
17.13 even 4 289.4.b.f.288.7 24
17.16 even 2 289.4.a.h.1.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.9 12 17.16 even 2
289.4.a.i.1.9 yes 12 1.1 even 1 trivial
289.4.b.f.288.7 24 17.13 even 4
289.4.b.f.288.8 24 17.4 even 4