Properties

Label 289.4.a.h.1.10
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $1$
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: \(1\)
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 1.10
Root \(-4.28857\) 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)
 
\(f(q)\) \(=\) \(q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +O(q^{10})\) \(q+4.28857 q^{2} -2.85039 q^{3} +10.3918 q^{4} +6.36629 q^{5} -12.2241 q^{6} -29.4308 q^{7} +10.2575 q^{8} -18.8753 q^{9} +27.3023 q^{10} -61.3595 q^{11} -29.6207 q^{12} +18.5582 q^{13} -126.216 q^{14} -18.1464 q^{15} -39.1446 q^{16} -80.9480 q^{18} +115.793 q^{19} +66.1574 q^{20} +83.8892 q^{21} -263.144 q^{22} +7.38352 q^{23} -29.2379 q^{24} -84.4703 q^{25} +79.5883 q^{26} +130.762 q^{27} -305.840 q^{28} -164.974 q^{29} -77.8221 q^{30} +127.132 q^{31} -249.934 q^{32} +174.898 q^{33} -187.365 q^{35} -196.149 q^{36} +158.120 q^{37} +496.588 q^{38} -52.8982 q^{39} +65.3022 q^{40} +31.3736 q^{41} +359.764 q^{42} +157.708 q^{43} -637.637 q^{44} -120.166 q^{45} +31.6647 q^{46} -460.704 q^{47} +111.577 q^{48} +523.171 q^{49} -362.257 q^{50} +192.854 q^{52} -166.846 q^{53} +560.783 q^{54} -390.632 q^{55} -301.886 q^{56} -330.056 q^{57} -707.502 q^{58} -343.136 q^{59} -188.574 q^{60} -112.359 q^{61} +545.216 q^{62} +555.515 q^{63} -758.704 q^{64} +118.147 q^{65} +750.063 q^{66} -984.209 q^{67} -21.0459 q^{69} -803.528 q^{70} -524.337 q^{71} -193.613 q^{72} +852.636 q^{73} +678.106 q^{74} +240.773 q^{75} +1203.30 q^{76} +1805.86 q^{77} -226.858 q^{78} -201.021 q^{79} -249.206 q^{80} +136.909 q^{81} +134.548 q^{82} -22.5351 q^{83} +871.761 q^{84} +676.342 q^{86} +470.240 q^{87} -629.395 q^{88} +502.230 q^{89} -515.338 q^{90} -546.184 q^{91} +76.7282 q^{92} -362.377 q^{93} -1975.76 q^{94} +737.175 q^{95} +712.410 q^{96} +680.691 q^{97} +2243.65 q^{98} +1158.18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.28857 1.51624 0.758119 0.652116i \(-0.226119\pi\)
0.758119 + 0.652116i \(0.226119\pi\)
\(3\) −2.85039 −0.548557 −0.274279 0.961650i \(-0.588439\pi\)
−0.274279 + 0.961650i \(0.588439\pi\)
\(4\) 10.3918 1.29898
\(5\) 6.36629 0.569418 0.284709 0.958614i \(-0.408103\pi\)
0.284709 + 0.958614i \(0.408103\pi\)
\(6\) −12.2241 −0.831744
\(7\) −29.4308 −1.58911 −0.794556 0.607190i \(-0.792297\pi\)
−0.794556 + 0.607190i \(0.792297\pi\)
\(8\) 10.2575 0.453322
\(9\) −18.8753 −0.699085
\(10\) 27.3023 0.863374
\(11\) −61.3595 −1.68187 −0.840935 0.541136i \(-0.817995\pi\)
−0.840935 + 0.541136i \(0.817995\pi\)
\(12\) −29.6207 −0.712564
\(13\) 18.5582 0.395933 0.197967 0.980209i \(-0.436566\pi\)
0.197967 + 0.980209i \(0.436566\pi\)
\(14\) −126.216 −2.40947
\(15\) −18.1464 −0.312359
\(16\) −39.1446 −0.611634
\(17\) 0 0
\(18\) −80.9480 −1.05998
\(19\) 115.793 1.39815 0.699075 0.715049i \(-0.253596\pi\)
0.699075 + 0.715049i \(0.253596\pi\)
\(20\) 66.1574 0.739662
\(21\) 83.8892 0.871720
\(22\) −263.144 −2.55012
\(23\) 7.38352 0.0669378 0.0334689 0.999440i \(-0.489345\pi\)
0.0334689 + 0.999440i \(0.489345\pi\)
\(24\) −29.2379 −0.248673
\(25\) −84.4703 −0.675763
\(26\) 79.5883 0.600329
\(27\) 130.762 0.932046
\(28\) −305.840 −2.06422
\(29\) −164.974 −1.05638 −0.528188 0.849127i \(-0.677128\pi\)
−0.528188 + 0.849127i \(0.677128\pi\)
\(30\) −77.8221 −0.473610
\(31\) 127.132 0.736570 0.368285 0.929713i \(-0.379945\pi\)
0.368285 + 0.929713i \(0.379945\pi\)
\(32\) −249.934 −1.38070
\(33\) 174.898 0.922603
\(34\) 0 0
\(35\) −187.365 −0.904870
\(36\) −196.149 −0.908096
\(37\) 158.120 0.702559 0.351280 0.936271i \(-0.385747\pi\)
0.351280 + 0.936271i \(0.385747\pi\)
\(38\) 496.588 2.11993
\(39\) −52.8982 −0.217192
\(40\) 65.3022 0.258130
\(41\) 31.3736 0.119506 0.0597528 0.998213i \(-0.480969\pi\)
0.0597528 + 0.998213i \(0.480969\pi\)
\(42\) 359.764 1.32173
\(43\) 157.708 0.559309 0.279654 0.960101i \(-0.409780\pi\)
0.279654 + 0.960101i \(0.409780\pi\)
\(44\) −637.637 −2.18471
\(45\) −120.166 −0.398072
\(46\) 31.6647 0.101494
\(47\) −460.704 −1.42980 −0.714900 0.699227i \(-0.753528\pi\)
−0.714900 + 0.699227i \(0.753528\pi\)
\(48\) 111.577 0.335517
\(49\) 523.171 1.52528
\(50\) −362.257 −1.02462
\(51\) 0 0
\(52\) 192.854 0.514308
\(53\) −166.846 −0.432417 −0.216208 0.976347i \(-0.569369\pi\)
−0.216208 + 0.976347i \(0.569369\pi\)
\(54\) 560.783 1.41320
\(55\) −390.632 −0.957688
\(56\) −301.886 −0.720379
\(57\) −330.056 −0.766965
\(58\) −707.502 −1.60172
\(59\) −343.136 −0.757161 −0.378581 0.925568i \(-0.623588\pi\)
−0.378581 + 0.925568i \(0.623588\pi\)
\(60\) −188.574 −0.405747
\(61\) −112.359 −0.235837 −0.117918 0.993023i \(-0.537622\pi\)
−0.117918 + 0.993023i \(0.537622\pi\)
\(62\) 545.216 1.11682
\(63\) 555.515 1.11092
\(64\) −758.704 −1.48184
\(65\) 118.147 0.225452
\(66\) 750.063 1.39889
\(67\) −984.209 −1.79463 −0.897316 0.441390i \(-0.854486\pi\)
−0.897316 + 0.441390i \(0.854486\pi\)
\(68\) 0 0
\(69\) −21.0459 −0.0367192
\(70\) −803.528 −1.37200
\(71\) −524.337 −0.876442 −0.438221 0.898867i \(-0.644391\pi\)
−0.438221 + 0.898867i \(0.644391\pi\)
\(72\) −193.613 −0.316910
\(73\) 852.636 1.36703 0.683517 0.729934i \(-0.260449\pi\)
0.683517 + 0.729934i \(0.260449\pi\)
\(74\) 678.106 1.06525
\(75\) 240.773 0.370695
\(76\) 1203.30 1.81616
\(77\) 1805.86 2.67268
\(78\) −226.858 −0.329315
\(79\) −201.021 −0.286286 −0.143143 0.989702i \(-0.545721\pi\)
−0.143143 + 0.989702i \(0.545721\pi\)
\(80\) −249.206 −0.348276
\(81\) 136.909 0.187804
\(82\) 134.548 0.181199
\(83\) −22.5351 −0.0298017 −0.0149009 0.999889i \(-0.504743\pi\)
−0.0149009 + 0.999889i \(0.504743\pi\)
\(84\) 871.761 1.13234
\(85\) 0 0
\(86\) 676.342 0.848045
\(87\) 470.240 0.579483
\(88\) −629.395 −0.762428
\(89\) 502.230 0.598161 0.299080 0.954228i \(-0.403320\pi\)
0.299080 + 0.954228i \(0.403320\pi\)
\(90\) −515.338 −0.603572
\(91\) −546.184 −0.629182
\(92\) 76.7282 0.0869507
\(93\) −362.377 −0.404051
\(94\) −1975.76 −2.16792
\(95\) 737.175 0.796132
\(96\) 712.410 0.757396
\(97\) 680.691 0.712512 0.356256 0.934388i \(-0.384053\pi\)
0.356256 + 0.934388i \(0.384053\pi\)
\(98\) 2243.65 2.31269
\(99\) 1158.18 1.17577
\(100\) −877.801 −0.877801
\(101\) 1921.92 1.89345 0.946724 0.322045i \(-0.104370\pi\)
0.946724 + 0.322045i \(0.104370\pi\)
\(102\) 0 0
\(103\) −1123.80 −1.07506 −0.537529 0.843245i \(-0.680642\pi\)
−0.537529 + 0.843245i \(0.680642\pi\)
\(104\) 190.361 0.179485
\(105\) 534.063 0.496373
\(106\) −715.532 −0.655647
\(107\) −122.786 −0.110937 −0.0554683 0.998460i \(-0.517665\pi\)
−0.0554683 + 0.998460i \(0.517665\pi\)
\(108\) 1358.86 1.21071
\(109\) 791.497 0.695520 0.347760 0.937584i \(-0.386942\pi\)
0.347760 + 0.937584i \(0.386942\pi\)
\(110\) −1675.25 −1.45208
\(111\) −450.702 −0.385394
\(112\) 1152.06 0.971956
\(113\) −73.7910 −0.0614307 −0.0307154 0.999528i \(-0.509779\pi\)
−0.0307154 + 0.999528i \(0.509779\pi\)
\(114\) −1415.47 −1.16290
\(115\) 47.0056 0.0381156
\(116\) −1714.38 −1.37221
\(117\) −350.292 −0.276791
\(118\) −1471.56 −1.14804
\(119\) 0 0
\(120\) −186.137 −0.141599
\(121\) 2433.98 1.82869
\(122\) −481.857 −0.357585
\(123\) −89.4269 −0.0655557
\(124\) 1321.14 0.956788
\(125\) −1333.55 −0.954210
\(126\) 2382.36 1.68443
\(127\) −1475.81 −1.03115 −0.515577 0.856843i \(-0.672423\pi\)
−0.515577 + 0.856843i \(0.672423\pi\)
\(128\) −1254.28 −0.866122
\(129\) −449.529 −0.306813
\(130\) 506.682 0.341838
\(131\) −1029.79 −0.686821 −0.343410 0.939185i \(-0.611582\pi\)
−0.343410 + 0.939185i \(0.611582\pi\)
\(132\) 1817.51 1.19844
\(133\) −3407.89 −2.22182
\(134\) −4220.85 −2.72109
\(135\) 832.471 0.530724
\(136\) 0 0
\(137\) −1018.26 −0.635008 −0.317504 0.948257i \(-0.602845\pi\)
−0.317504 + 0.948257i \(0.602845\pi\)
\(138\) −90.2567 −0.0556751
\(139\) −1506.59 −0.919332 −0.459666 0.888092i \(-0.652031\pi\)
−0.459666 + 0.888092i \(0.652031\pi\)
\(140\) −1947.06 −1.17541
\(141\) 1313.18 0.784327
\(142\) −2248.66 −1.32890
\(143\) −1138.72 −0.665908
\(144\) 738.865 0.427584
\(145\) −1050.27 −0.601520
\(146\) 3656.59 2.07275
\(147\) −1491.24 −0.836704
\(148\) 1643.15 0.912609
\(149\) −424.614 −0.233462 −0.116731 0.993164i \(-0.537241\pi\)
−0.116731 + 0.993164i \(0.537241\pi\)
\(150\) 1032.57 0.562061
\(151\) 1566.83 0.844418 0.422209 0.906499i \(-0.361255\pi\)
0.422209 + 0.906499i \(0.361255\pi\)
\(152\) 1187.75 0.633811
\(153\) 0 0
\(154\) 7744.54 4.05242
\(155\) 809.362 0.419416
\(156\) −549.709 −0.282128
\(157\) −762.291 −0.387500 −0.193750 0.981051i \(-0.562065\pi\)
−0.193750 + 0.981051i \(0.562065\pi\)
\(158\) −862.092 −0.434078
\(159\) 475.577 0.237206
\(160\) −1591.15 −0.786199
\(161\) −217.303 −0.106372
\(162\) 587.145 0.284756
\(163\) −2253.74 −1.08299 −0.541493 0.840705i \(-0.682141\pi\)
−0.541493 + 0.840705i \(0.682141\pi\)
\(164\) 326.029 0.155235
\(165\) 1113.45 0.525347
\(166\) −96.6432 −0.0451865
\(167\) 1995.81 0.924792 0.462396 0.886673i \(-0.346990\pi\)
0.462396 + 0.886673i \(0.346990\pi\)
\(168\) 860.493 0.395169
\(169\) −1852.59 −0.843237
\(170\) 0 0
\(171\) −2185.63 −0.977425
\(172\) 1638.88 0.726529
\(173\) −1853.93 −0.814749 −0.407375 0.913261i \(-0.633556\pi\)
−0.407375 + 0.913261i \(0.633556\pi\)
\(174\) 2016.66 0.878634
\(175\) 2486.03 1.07386
\(176\) 2401.89 1.02869
\(177\) 978.071 0.415346
\(178\) 2153.85 0.906954
\(179\) −1623.39 −0.677865 −0.338933 0.940811i \(-0.610066\pi\)
−0.338933 + 0.940811i \(0.610066\pi\)
\(180\) −1248.74 −0.517086
\(181\) 759.107 0.311735 0.155867 0.987778i \(-0.450183\pi\)
0.155867 + 0.987778i \(0.450183\pi\)
\(182\) −2342.35 −0.953990
\(183\) 320.266 0.129370
\(184\) 75.7364 0.0303444
\(185\) 1006.64 0.400050
\(186\) −1554.08 −0.612637
\(187\) 0 0
\(188\) −4787.55 −1.85728
\(189\) −3848.44 −1.48113
\(190\) 3161.42 1.20713
\(191\) −1878.32 −0.711572 −0.355786 0.934567i \(-0.615787\pi\)
−0.355786 + 0.934567i \(0.615787\pi\)
\(192\) 2162.60 0.812876
\(193\) 497.364 0.185498 0.0927489 0.995690i \(-0.470435\pi\)
0.0927489 + 0.995690i \(0.470435\pi\)
\(194\) 2919.19 1.08034
\(195\) −336.765 −0.123673
\(196\) 5436.70 1.98130
\(197\) −1052.05 −0.380486 −0.190243 0.981737i \(-0.560928\pi\)
−0.190243 + 0.981737i \(0.560928\pi\)
\(198\) 4966.92 1.78275
\(199\) 1783.55 0.635338 0.317669 0.948202i \(-0.397100\pi\)
0.317669 + 0.948202i \(0.397100\pi\)
\(200\) −866.454 −0.306338
\(201\) 2805.38 0.984458
\(202\) 8242.29 2.87092
\(203\) 4855.31 1.67870
\(204\) 0 0
\(205\) 199.733 0.0680487
\(206\) −4819.48 −1.63004
\(207\) −139.366 −0.0467952
\(208\) −726.455 −0.242166
\(209\) −7105.02 −2.35151
\(210\) 2290.37 0.752620
\(211\) −3756.09 −1.22550 −0.612748 0.790278i \(-0.709936\pi\)
−0.612748 + 0.790278i \(0.709936\pi\)
\(212\) −1733.84 −0.561700
\(213\) 1494.57 0.480779
\(214\) −526.578 −0.168206
\(215\) 1004.02 0.318481
\(216\) 1341.30 0.422517
\(217\) −3741.61 −1.17049
\(218\) 3394.39 1.05457
\(219\) −2430.34 −0.749897
\(220\) −4059.38 −1.24402
\(221\) 0 0
\(222\) −1932.87 −0.584349
\(223\) −3356.40 −1.00790 −0.503949 0.863733i \(-0.668120\pi\)
−0.503949 + 0.863733i \(0.668120\pi\)
\(224\) 7355.76 2.19410
\(225\) 1594.40 0.472415
\(226\) −316.458 −0.0931436
\(227\) −1988.64 −0.581457 −0.290728 0.956806i \(-0.593898\pi\)
−0.290728 + 0.956806i \(0.593898\pi\)
\(228\) −3429.89 −0.996271
\(229\) 5203.50 1.50156 0.750779 0.660554i \(-0.229678\pi\)
0.750779 + 0.660554i \(0.229678\pi\)
\(230\) 201.587 0.0577924
\(231\) −5147.39 −1.46612
\(232\) −1692.22 −0.478878
\(233\) 5702.70 1.60342 0.801709 0.597714i \(-0.203924\pi\)
0.801709 + 0.597714i \(0.203924\pi\)
\(234\) −1502.25 −0.419681
\(235\) −2932.98 −0.814154
\(236\) −3565.81 −0.983536
\(237\) 572.988 0.157045
\(238\) 0 0
\(239\) 1418.04 0.383787 0.191894 0.981416i \(-0.438537\pi\)
0.191894 + 0.981416i \(0.438537\pi\)
\(240\) 710.334 0.191049
\(241\) −6215.71 −1.66137 −0.830683 0.556746i \(-0.812050\pi\)
−0.830683 + 0.556746i \(0.812050\pi\)
\(242\) 10438.3 2.77273
\(243\) −3920.83 −1.03507
\(244\) −1167.61 −0.306347
\(245\) 3330.66 0.868523
\(246\) −383.514 −0.0993981
\(247\) 2148.92 0.553573
\(248\) 1304.06 0.333903
\(249\) 64.2337 0.0163480
\(250\) −5719.02 −1.44681
\(251\) 1547.45 0.389139 0.194570 0.980889i \(-0.437669\pi\)
0.194570 + 0.980889i \(0.437669\pi\)
\(252\) 5772.81 1.44307
\(253\) −453.049 −0.112581
\(254\) −6329.10 −1.56348
\(255\) 0 0
\(256\) 690.569 0.168596
\(257\) 7251.45 1.76005 0.880025 0.474928i \(-0.157526\pi\)
0.880025 + 0.474928i \(0.157526\pi\)
\(258\) −1927.84 −0.465201
\(259\) −4653.58 −1.11645
\(260\) 1227.76 0.292857
\(261\) 3113.93 0.738496
\(262\) −4416.34 −1.04138
\(263\) 4635.13 1.08675 0.543373 0.839491i \(-0.317147\pi\)
0.543373 + 0.839491i \(0.317147\pi\)
\(264\) 1794.02 0.418236
\(265\) −1062.19 −0.246226
\(266\) −14615.0 −3.36880
\(267\) −1431.55 −0.328126
\(268\) −10227.7 −2.33119
\(269\) −7116.95 −1.61311 −0.806557 0.591156i \(-0.798672\pi\)
−0.806557 + 0.591156i \(0.798672\pi\)
\(270\) 3570.11 0.804704
\(271\) 163.713 0.0366970 0.0183485 0.999832i \(-0.494159\pi\)
0.0183485 + 0.999832i \(0.494159\pi\)
\(272\) 0 0
\(273\) 1556.83 0.345143
\(274\) −4366.89 −0.962823
\(275\) 5183.05 1.13655
\(276\) −218.705 −0.0476975
\(277\) 4174.84 0.905567 0.452784 0.891620i \(-0.350431\pi\)
0.452784 + 0.891620i \(0.350431\pi\)
\(278\) −6461.11 −1.39393
\(279\) −2399.66 −0.514925
\(280\) −1921.90 −0.410197
\(281\) −6920.09 −1.46910 −0.734551 0.678553i \(-0.762607\pi\)
−0.734551 + 0.678553i \(0.762607\pi\)
\(282\) 5631.68 1.18923
\(283\) −6292.91 −1.32182 −0.660909 0.750466i \(-0.729829\pi\)
−0.660909 + 0.750466i \(0.729829\pi\)
\(284\) −5448.82 −1.13848
\(285\) −2101.23 −0.436724
\(286\) −4883.50 −1.00968
\(287\) −923.350 −0.189908
\(288\) 4717.58 0.965230
\(289\) 0 0
\(290\) −4504.17 −0.912048
\(291\) −1940.23 −0.390854
\(292\) 8860.45 1.77575
\(293\) 2292.96 0.457189 0.228595 0.973522i \(-0.426587\pi\)
0.228595 + 0.973522i \(0.426587\pi\)
\(294\) −6395.29 −1.26864
\(295\) −2184.50 −0.431142
\(296\) 1621.91 0.318485
\(297\) −8023.51 −1.56758
\(298\) −1820.99 −0.353983
\(299\) 137.025 0.0265029
\(300\) 2502.07 0.481524
\(301\) −4641.47 −0.888804
\(302\) 6719.47 1.28034
\(303\) −5478.22 −1.03867
\(304\) −4532.69 −0.855156
\(305\) −715.308 −0.134290
\(306\) 0 0
\(307\) 2300.11 0.427604 0.213802 0.976877i \(-0.431415\pi\)
0.213802 + 0.976877i \(0.431415\pi\)
\(308\) 18766.1 3.47176
\(309\) 3203.26 0.589731
\(310\) 3471.01 0.635935
\(311\) −5775.22 −1.05300 −0.526499 0.850175i \(-0.676496\pi\)
−0.526499 + 0.850175i \(0.676496\pi\)
\(312\) −542.603 −0.0984579
\(313\) −2799.69 −0.505585 −0.252792 0.967521i \(-0.581349\pi\)
−0.252792 + 0.967521i \(0.581349\pi\)
\(314\) −3269.14 −0.587542
\(315\) 3536.57 0.632581
\(316\) −2088.97 −0.371880
\(317\) −5140.47 −0.910781 −0.455390 0.890292i \(-0.650500\pi\)
−0.455390 + 0.890292i \(0.650500\pi\)
\(318\) 2039.54 0.359660
\(319\) 10122.7 1.77669
\(320\) −4830.13 −0.843789
\(321\) 349.989 0.0608550
\(322\) −931.917 −0.161285
\(323\) 0 0
\(324\) 1422.74 0.243954
\(325\) −1567.62 −0.267557
\(326\) −9665.33 −1.64206
\(327\) −2256.07 −0.381533
\(328\) 321.815 0.0541745
\(329\) 13558.9 2.27211
\(330\) 4775.12 0.796551
\(331\) 459.510 0.0763050 0.0381525 0.999272i \(-0.487853\pi\)
0.0381525 + 0.999272i \(0.487853\pi\)
\(332\) −234.180 −0.0387118
\(333\) −2984.55 −0.491148
\(334\) 8559.16 1.40221
\(335\) −6265.76 −1.02190
\(336\) −3283.81 −0.533174
\(337\) 6233.46 1.00759 0.503796 0.863823i \(-0.331937\pi\)
0.503796 + 0.863823i \(0.331937\pi\)
\(338\) −7944.97 −1.27855
\(339\) 210.333 0.0336983
\(340\) 0 0
\(341\) −7800.78 −1.23882
\(342\) −9373.24 −1.48201
\(343\) −5302.57 −0.834729
\(344\) 1617.69 0.253547
\(345\) −133.984 −0.0209086
\(346\) −7950.70 −1.23535
\(347\) 6370.01 0.985476 0.492738 0.870178i \(-0.335996\pi\)
0.492738 + 0.870178i \(0.335996\pi\)
\(348\) 4886.65 0.752735
\(349\) −6494.79 −0.996155 −0.498078 0.867132i \(-0.665961\pi\)
−0.498078 + 0.867132i \(0.665961\pi\)
\(350\) 10661.5 1.62823
\(351\) 2426.72 0.369028
\(352\) 15335.8 2.32217
\(353\) 502.630 0.0757856 0.0378928 0.999282i \(-0.487935\pi\)
0.0378928 + 0.999282i \(0.487935\pi\)
\(354\) 4194.53 0.629764
\(355\) −3338.09 −0.499062
\(356\) 5219.09 0.776998
\(357\) 0 0
\(358\) −6962.02 −1.02781
\(359\) −974.431 −0.143255 −0.0716275 0.997431i \(-0.522819\pi\)
−0.0716275 + 0.997431i \(0.522819\pi\)
\(360\) −1232.60 −0.180455
\(361\) 6549.11 0.954821
\(362\) 3255.48 0.472664
\(363\) −6937.80 −1.00314
\(364\) −5675.84 −0.817294
\(365\) 5428.13 0.778415
\(366\) 1373.48 0.196156
\(367\) 4693.11 0.667515 0.333758 0.942659i \(-0.391683\pi\)
0.333758 + 0.942659i \(0.391683\pi\)
\(368\) −289.025 −0.0409415
\(369\) −592.186 −0.0835446
\(370\) 4317.02 0.606571
\(371\) 4910.42 0.687159
\(372\) −3765.76 −0.524853
\(373\) 8651.16 1.20091 0.600456 0.799658i \(-0.294986\pi\)
0.600456 + 0.799658i \(0.294986\pi\)
\(374\) 0 0
\(375\) 3801.13 0.523439
\(376\) −4725.67 −0.648159
\(377\) −3061.63 −0.418254
\(378\) −16504.3 −2.24574
\(379\) 3490.01 0.473007 0.236503 0.971631i \(-0.423999\pi\)
0.236503 + 0.971631i \(0.423999\pi\)
\(380\) 7660.59 1.03416
\(381\) 4206.62 0.565648
\(382\) −8055.29 −1.07891
\(383\) 3928.41 0.524105 0.262052 0.965054i \(-0.415601\pi\)
0.262052 + 0.965054i \(0.415601\pi\)
\(384\) 3575.18 0.475118
\(385\) 11496.6 1.52187
\(386\) 2132.98 0.281259
\(387\) −2976.79 −0.391004
\(388\) 7073.62 0.925537
\(389\) 6961.15 0.907312 0.453656 0.891177i \(-0.350120\pi\)
0.453656 + 0.891177i \(0.350120\pi\)
\(390\) −1444.24 −0.187518
\(391\) 0 0
\(392\) 5366.43 0.691443
\(393\) 2935.31 0.376761
\(394\) −4511.81 −0.576908
\(395\) −1279.76 −0.163017
\(396\) 12035.6 1.52730
\(397\) 5331.94 0.674062 0.337031 0.941494i \(-0.390577\pi\)
0.337031 + 0.941494i \(0.390577\pi\)
\(398\) 7648.86 0.963323
\(399\) 9713.81 1.21879
\(400\) 3306.56 0.413320
\(401\) 546.021 0.0679975 0.0339988 0.999422i \(-0.489176\pi\)
0.0339988 + 0.999422i \(0.489176\pi\)
\(402\) 12031.1 1.49267
\(403\) 2359.35 0.291632
\(404\) 19972.3 2.45955
\(405\) 871.604 0.106939
\(406\) 20822.3 2.54531
\(407\) −9702.13 −1.18161
\(408\) 0 0
\(409\) 15964.6 1.93007 0.965037 0.262114i \(-0.0844196\pi\)
0.965037 + 0.262114i \(0.0844196\pi\)
\(410\) 856.571 0.103178
\(411\) 2902.44 0.348338
\(412\) −11678.3 −1.39648
\(413\) 10098.8 1.20321
\(414\) −597.681 −0.0709527
\(415\) −143.465 −0.0169697
\(416\) −4638.34 −0.546667
\(417\) 4294.36 0.504306
\(418\) −30470.4 −3.56544
\(419\) 7643.91 0.891240 0.445620 0.895222i \(-0.352983\pi\)
0.445620 + 0.895222i \(0.352983\pi\)
\(420\) 5549.89 0.644778
\(421\) −7524.14 −0.871031 −0.435516 0.900181i \(-0.643434\pi\)
−0.435516 + 0.900181i \(0.643434\pi\)
\(422\) −16108.2 −1.85814
\(423\) 8695.92 0.999551
\(424\) −1711.43 −0.196024
\(425\) 0 0
\(426\) 6409.55 0.728975
\(427\) 3306.80 0.374771
\(428\) −1275.97 −0.144104
\(429\) 3245.80 0.365289
\(430\) 4305.79 0.482892
\(431\) −12222.4 −1.36597 −0.682986 0.730431i \(-0.739319\pi\)
−0.682986 + 0.730431i \(0.739319\pi\)
\(432\) −5118.64 −0.570071
\(433\) −15420.3 −1.71144 −0.855719 0.517440i \(-0.826885\pi\)
−0.855719 + 0.517440i \(0.826885\pi\)
\(434\) −16046.1 −1.77475
\(435\) 2993.68 0.329968
\(436\) 8225.10 0.903465
\(437\) 854.963 0.0935890
\(438\) −10422.7 −1.13702
\(439\) 17832.7 1.93874 0.969369 0.245607i \(-0.0789874\pi\)
0.969369 + 0.245607i \(0.0789874\pi\)
\(440\) −4006.91 −0.434141
\(441\) −9875.00 −1.06630
\(442\) 0 0
\(443\) 241.629 0.0259145 0.0129573 0.999916i \(-0.495875\pi\)
0.0129573 + 0.999916i \(0.495875\pi\)
\(444\) −4683.62 −0.500618
\(445\) 3197.35 0.340604
\(446\) −14394.2 −1.52821
\(447\) 1210.32 0.128067
\(448\) 22329.2 2.35482
\(449\) −14481.4 −1.52209 −0.761046 0.648698i \(-0.775314\pi\)
−0.761046 + 0.648698i \(0.775314\pi\)
\(450\) 6837.70 0.716294
\(451\) −1925.07 −0.200993
\(452\) −766.823 −0.0797971
\(453\) −4466.08 −0.463211
\(454\) −8528.42 −0.881627
\(455\) −3477.16 −0.358268
\(456\) −3385.55 −0.347682
\(457\) −1814.51 −0.185731 −0.0928654 0.995679i \(-0.529603\pi\)
−0.0928654 + 0.995679i \(0.529603\pi\)
\(458\) 22315.6 2.27672
\(459\) 0 0
\(460\) 488.474 0.0495114
\(461\) −13434.1 −1.35724 −0.678621 0.734489i \(-0.737422\pi\)
−0.678621 + 0.734489i \(0.737422\pi\)
\(462\) −22075.0 −2.22299
\(463\) −16593.9 −1.66562 −0.832810 0.553559i \(-0.813269\pi\)
−0.832810 + 0.553559i \(0.813269\pi\)
\(464\) 6457.84 0.646116
\(465\) −2307.00 −0.230074
\(466\) 24456.4 2.43116
\(467\) −3944.12 −0.390818 −0.195409 0.980722i \(-0.562603\pi\)
−0.195409 + 0.980722i \(0.562603\pi\)
\(468\) −3640.17 −0.359545
\(469\) 28966.0 2.85187
\(470\) −12578.3 −1.23445
\(471\) 2172.83 0.212566
\(472\) −3519.72 −0.343238
\(473\) −9676.89 −0.940685
\(474\) 2457.30 0.238117
\(475\) −9781.11 −0.944817
\(476\) 0 0
\(477\) 3149.27 0.302296
\(478\) 6081.35 0.581913
\(479\) 11162.8 1.06480 0.532401 0.846492i \(-0.321290\pi\)
0.532401 + 0.846492i \(0.321290\pi\)
\(480\) 4535.41 0.431275
\(481\) 2934.42 0.278166
\(482\) −26656.5 −2.51903
\(483\) 619.397 0.0583510
\(484\) 25293.5 2.37543
\(485\) 4333.48 0.405717
\(486\) −16814.7 −1.56941
\(487\) 9984.01 0.928991 0.464496 0.885575i \(-0.346236\pi\)
0.464496 + 0.885575i \(0.346236\pi\)
\(488\) −1152.52 −0.106910
\(489\) 6424.04 0.594080
\(490\) 14283.8 1.31689
\(491\) −19639.7 −1.80514 −0.902572 0.430540i \(-0.858323\pi\)
−0.902572 + 0.430540i \(0.858323\pi\)
\(492\) −929.309 −0.0851554
\(493\) 0 0
\(494\) 9215.80 0.839349
\(495\) 7373.30 0.669505
\(496\) −4976.55 −0.450511
\(497\) 15431.7 1.39277
\(498\) 275.470 0.0247874
\(499\) 5764.32 0.517127 0.258564 0.965994i \(-0.416751\pi\)
0.258564 + 0.965994i \(0.416751\pi\)
\(500\) −13858.0 −1.23950
\(501\) −5688.83 −0.507302
\(502\) 6636.33 0.590027
\(503\) −1747.34 −0.154890 −0.0774452 0.996997i \(-0.524676\pi\)
−0.0774452 + 0.996997i \(0.524676\pi\)
\(504\) 5698.19 0.503606
\(505\) 12235.5 1.07816
\(506\) −1942.93 −0.170699
\(507\) 5280.61 0.462564
\(508\) −15336.3 −1.33945
\(509\) −9110.89 −0.793385 −0.396693 0.917952i \(-0.629842\pi\)
−0.396693 + 0.917952i \(0.629842\pi\)
\(510\) 0 0
\(511\) −25093.8 −2.17237
\(512\) 12995.8 1.12175
\(513\) 15141.4 1.30314
\(514\) 31098.3 2.66865
\(515\) −7154.42 −0.612158
\(516\) −4671.43 −0.398543
\(517\) 28268.5 2.40474
\(518\) −19957.2 −1.69280
\(519\) 5284.42 0.446937
\(520\) 1211.89 0.102202
\(521\) −9231.61 −0.776285 −0.388142 0.921599i \(-0.626883\pi\)
−0.388142 + 0.921599i \(0.626883\pi\)
\(522\) 13354.3 1.11974
\(523\) 14927.5 1.24806 0.624028 0.781402i \(-0.285495\pi\)
0.624028 + 0.781402i \(0.285495\pi\)
\(524\) −10701.4 −0.892165
\(525\) −7086.14 −0.589076
\(526\) 19878.1 1.64777
\(527\) 0 0
\(528\) −6846.32 −0.564295
\(529\) −12112.5 −0.995519
\(530\) −4555.28 −0.373338
\(531\) 6476.79 0.529320
\(532\) −35414.2 −2.88609
\(533\) 582.239 0.0473162
\(534\) −6139.31 −0.497516
\(535\) −781.694 −0.0631693
\(536\) −10095.5 −0.813545
\(537\) 4627.29 0.371848
\(538\) −30521.5 −2.44587
\(539\) −32101.5 −2.56532
\(540\) 8650.90 0.689399
\(541\) −9005.10 −0.715637 −0.357818 0.933791i \(-0.616479\pi\)
−0.357818 + 0.933791i \(0.616479\pi\)
\(542\) 702.096 0.0556413
\(543\) −2163.75 −0.171004
\(544\) 0 0
\(545\) 5038.90 0.396042
\(546\) 6676.59 0.523318
\(547\) 6774.33 0.529524 0.264762 0.964314i \(-0.414707\pi\)
0.264762 + 0.964314i \(0.414707\pi\)
\(548\) −10581.6 −0.824861
\(549\) 2120.80 0.164870
\(550\) 22227.9 1.72327
\(551\) −19102.9 −1.47697
\(552\) −215.878 −0.0166456
\(553\) 5916.20 0.454941
\(554\) 17904.1 1.37306
\(555\) −2869.30 −0.219450
\(556\) −15656.2 −1.19419
\(557\) −8558.56 −0.651055 −0.325528 0.945533i \(-0.605542\pi\)
−0.325528 + 0.945533i \(0.605542\pi\)
\(558\) −10291.1 −0.780748
\(559\) 2926.79 0.221449
\(560\) 7334.32 0.553450
\(561\) 0 0
\(562\) −29677.3 −2.22751
\(563\) 13915.1 1.04165 0.520827 0.853662i \(-0.325624\pi\)
0.520827 + 0.853662i \(0.325624\pi\)
\(564\) 13646.4 1.01882
\(565\) −469.775 −0.0349798
\(566\) −26987.6 −2.00419
\(567\) −4029.35 −0.298442
\(568\) −5378.39 −0.397310
\(569\) −12378.8 −0.912031 −0.456015 0.889972i \(-0.650724\pi\)
−0.456015 + 0.889972i \(0.650724\pi\)
\(570\) −9011.29 −0.662178
\(571\) 785.845 0.0575947 0.0287974 0.999585i \(-0.490832\pi\)
0.0287974 + 0.999585i \(0.490832\pi\)
\(572\) −11833.4 −0.865000
\(573\) 5353.93 0.390338
\(574\) −3959.85 −0.287946
\(575\) −623.688 −0.0452341
\(576\) 14320.8 1.03593
\(577\) 19662.8 1.41867 0.709334 0.704873i \(-0.248996\pi\)
0.709334 + 0.704873i \(0.248996\pi\)
\(578\) 0 0
\(579\) −1417.68 −0.101756
\(580\) −10914.2 −0.781361
\(581\) 663.224 0.0473583
\(582\) −8320.82 −0.592627
\(583\) 10237.6 0.727269
\(584\) 8745.92 0.619707
\(585\) −2230.06 −0.157610
\(586\) 9833.54 0.693208
\(587\) −10024.7 −0.704875 −0.352438 0.935835i \(-0.614647\pi\)
−0.352438 + 0.935835i \(0.614647\pi\)
\(588\) −15496.7 −1.08686
\(589\) 14721.1 1.02983
\(590\) −9368.40 −0.653713
\(591\) 2998.76 0.208719
\(592\) −6189.52 −0.429709
\(593\) 770.054 0.0533260 0.0266630 0.999644i \(-0.491512\pi\)
0.0266630 + 0.999644i \(0.491512\pi\)
\(594\) −34409.4 −2.37682
\(595\) 0 0
\(596\) −4412.52 −0.303261
\(597\) −5083.80 −0.348519
\(598\) 587.641 0.0401847
\(599\) 20011.7 1.36503 0.682517 0.730870i \(-0.260885\pi\)
0.682517 + 0.730870i \(0.260885\pi\)
\(600\) 2469.73 0.168044
\(601\) −16303.2 −1.10652 −0.553261 0.833008i \(-0.686617\pi\)
−0.553261 + 0.833008i \(0.686617\pi\)
\(602\) −19905.3 −1.34764
\(603\) 18577.2 1.25460
\(604\) 16282.2 1.09688
\(605\) 15495.5 1.04129
\(606\) −23493.7 −1.57486
\(607\) −26777.6 −1.79056 −0.895279 0.445506i \(-0.853024\pi\)
−0.895279 + 0.445506i \(0.853024\pi\)
\(608\) −28940.7 −1.93043
\(609\) −13839.5 −0.920864
\(610\) −3067.65 −0.203615
\(611\) −8549.85 −0.566105
\(612\) 0 0
\(613\) 1385.13 0.0912639 0.0456320 0.998958i \(-0.485470\pi\)
0.0456320 + 0.998958i \(0.485470\pi\)
\(614\) 9864.19 0.648349
\(615\) −569.318 −0.0373286
\(616\) 18523.6 1.21158
\(617\) 818.646 0.0534156 0.0267078 0.999643i \(-0.491498\pi\)
0.0267078 + 0.999643i \(0.491498\pi\)
\(618\) 13737.4 0.894173
\(619\) 9468.86 0.614839 0.307420 0.951574i \(-0.400534\pi\)
0.307420 + 0.951574i \(0.400534\pi\)
\(620\) 8410.75 0.544813
\(621\) 965.486 0.0623891
\(622\) −24767.4 −1.59660
\(623\) −14781.0 −0.950545
\(624\) 2070.68 0.132842
\(625\) 2069.03 0.132418
\(626\) −12006.7 −0.766587
\(627\) 20252.1 1.28994
\(628\) −7921.60 −0.503354
\(629\) 0 0
\(630\) 15166.8 0.959143
\(631\) 11291.5 0.712374 0.356187 0.934415i \(-0.384077\pi\)
0.356187 + 0.934415i \(0.384077\pi\)
\(632\) −2061.97 −0.129780
\(633\) 10706.3 0.672255
\(634\) −22045.3 −1.38096
\(635\) −9395.41 −0.587158
\(636\) 4942.11 0.308125
\(637\) 9709.13 0.603909
\(638\) 43412.0 2.69388
\(639\) 9897.02 0.612707
\(640\) −7985.10 −0.493186
\(641\) 27604.9 1.70098 0.850489 0.525993i \(-0.176306\pi\)
0.850489 + 0.525993i \(0.176306\pi\)
\(642\) 1500.95 0.0922707
\(643\) 30899.1 1.89509 0.947544 0.319625i \(-0.103557\pi\)
0.947544 + 0.319625i \(0.103557\pi\)
\(644\) −2258.17 −0.138175
\(645\) −2861.84 −0.174705
\(646\) 0 0
\(647\) 26023.7 1.58129 0.790647 0.612272i \(-0.209744\pi\)
0.790647 + 0.612272i \(0.209744\pi\)
\(648\) 1404.35 0.0851357
\(649\) 21054.7 1.27345
\(650\) −6722.85 −0.405680
\(651\) 10665.0 0.642082
\(652\) −23420.5 −1.40677
\(653\) −18446.4 −1.10546 −0.552728 0.833362i \(-0.686413\pi\)
−0.552728 + 0.833362i \(0.686413\pi\)
\(654\) −9675.33 −0.578494
\(655\) −6555.97 −0.391088
\(656\) −1228.11 −0.0730938
\(657\) −16093.8 −0.955673
\(658\) 58148.2 3.44506
\(659\) −987.581 −0.0583774 −0.0291887 0.999574i \(-0.509292\pi\)
−0.0291887 + 0.999574i \(0.509292\pi\)
\(660\) 11570.8 0.682414
\(661\) 4126.78 0.242834 0.121417 0.992602i \(-0.461256\pi\)
0.121417 + 0.992602i \(0.461256\pi\)
\(662\) 1970.64 0.115697
\(663\) 0 0
\(664\) −231.153 −0.0135098
\(665\) −21695.6 −1.26514
\(666\) −12799.5 −0.744698
\(667\) −1218.09 −0.0707115
\(668\) 20740.1 1.20128
\(669\) 9567.05 0.552890
\(670\) −26871.2 −1.54944
\(671\) 6894.26 0.396647
\(672\) −20966.8 −1.20359
\(673\) −7788.28 −0.446086 −0.223043 0.974809i \(-0.571599\pi\)
−0.223043 + 0.974809i \(0.571599\pi\)
\(674\) 26732.6 1.52775
\(675\) −11045.5 −0.629842
\(676\) −19251.8 −1.09535
\(677\) −849.049 −0.0482003 −0.0241001 0.999710i \(-0.507672\pi\)
−0.0241001 + 0.999710i \(0.507672\pi\)
\(678\) 902.027 0.0510946
\(679\) −20033.3 −1.13226
\(680\) 0 0
\(681\) 5668.39 0.318962
\(682\) −33454.2 −1.87834
\(683\) −18449.2 −1.03359 −0.516793 0.856110i \(-0.672874\pi\)
−0.516793 + 0.856110i \(0.672874\pi\)
\(684\) −22712.7 −1.26965
\(685\) −6482.56 −0.361585
\(686\) −22740.4 −1.26565
\(687\) −14832.0 −0.823691
\(688\) −6173.42 −0.342092
\(689\) −3096.37 −0.171208
\(690\) −574.601 −0.0317024
\(691\) 33194.1 1.82744 0.913722 0.406339i \(-0.133195\pi\)
0.913722 + 0.406339i \(0.133195\pi\)
\(692\) −19265.7 −1.05834
\(693\) −34086.1 −1.86843
\(694\) 27318.2 1.49422
\(695\) −9591.38 −0.523484
\(696\) 4823.49 0.262692
\(697\) 0 0
\(698\) −27853.4 −1.51041
\(699\) −16254.9 −0.879567
\(700\) 25834.4 1.39492
\(701\) −1102.73 −0.0594146 −0.0297073 0.999559i \(-0.509458\pi\)
−0.0297073 + 0.999559i \(0.509458\pi\)
\(702\) 10407.2 0.559534
\(703\) 18309.2 0.982282
\(704\) 46553.7 2.49227
\(705\) 8360.12 0.446610
\(706\) 2155.57 0.114909
\(707\) −56563.7 −3.00890
\(708\) 10163.9 0.539526
\(709\) 5881.49 0.311543 0.155771 0.987793i \(-0.450214\pi\)
0.155771 + 0.987793i \(0.450214\pi\)
\(710\) −14315.6 −0.756697
\(711\) 3794.33 0.200138
\(712\) 5151.63 0.271159
\(713\) 938.685 0.0493044
\(714\) 0 0
\(715\) −7249.45 −0.379180
\(716\) −16870.0 −0.880532
\(717\) −4041.95 −0.210529
\(718\) −4178.92 −0.217209
\(719\) −13392.6 −0.694661 −0.347330 0.937743i \(-0.612912\pi\)
−0.347330 + 0.937743i \(0.612912\pi\)
\(720\) 4703.83 0.243474
\(721\) 33074.2 1.70839
\(722\) 28086.3 1.44774
\(723\) 17717.2 0.911355
\(724\) 7888.51 0.404937
\(725\) 13935.4 0.713859
\(726\) −29753.2 −1.52100
\(727\) 30483.7 1.55513 0.777564 0.628804i \(-0.216455\pi\)
0.777564 + 0.628804i \(0.216455\pi\)
\(728\) −5602.48 −0.285222
\(729\) 7479.33 0.379989
\(730\) 23278.9 1.18026
\(731\) 0 0
\(732\) 3328.14 0.168049
\(733\) 23656.0 1.19203 0.596013 0.802975i \(-0.296751\pi\)
0.596013 + 0.802975i \(0.296751\pi\)
\(734\) 20126.7 1.01211
\(735\) −9493.67 −0.476434
\(736\) −1845.39 −0.0924214
\(737\) 60390.5 3.01834
\(738\) −2539.63 −0.126674
\(739\) −27884.4 −1.38801 −0.694007 0.719968i \(-0.744157\pi\)
−0.694007 + 0.719968i \(0.744157\pi\)
\(740\) 10460.8 0.519656
\(741\) −6125.26 −0.303667
\(742\) 21058.7 1.04190
\(743\) 3391.10 0.167439 0.0837196 0.996489i \(-0.473320\pi\)
0.0837196 + 0.996489i \(0.473320\pi\)
\(744\) −3717.08 −0.183165
\(745\) −2703.22 −0.132937
\(746\) 37101.1 1.82087
\(747\) 425.356 0.0208339
\(748\) 0 0
\(749\) 3613.70 0.176291
\(750\) 16301.4 0.793658
\(751\) −19843.5 −0.964181 −0.482091 0.876121i \(-0.660122\pi\)
−0.482091 + 0.876121i \(0.660122\pi\)
\(752\) 18034.1 0.874514
\(753\) −4410.82 −0.213465
\(754\) −13130.0 −0.634173
\(755\) 9974.92 0.480827
\(756\) −39992.3 −1.92395
\(757\) −23915.1 −1.14823 −0.574114 0.818775i \(-0.694653\pi\)
−0.574114 + 0.818775i \(0.694653\pi\)
\(758\) 14967.1 0.717191
\(759\) 1291.36 0.0617570
\(760\) 7561.57 0.360904
\(761\) 17162.3 0.817520 0.408760 0.912642i \(-0.365961\pi\)
0.408760 + 0.912642i \(0.365961\pi\)
\(762\) 18040.4 0.857656
\(763\) −23294.4 −1.10526
\(764\) −19519.1 −0.924317
\(765\) 0 0
\(766\) 16847.2 0.794668
\(767\) −6368.00 −0.299785
\(768\) −1968.39 −0.0924845
\(769\) −18387.3 −0.862240 −0.431120 0.902295i \(-0.641881\pi\)
−0.431120 + 0.902295i \(0.641881\pi\)
\(770\) 49304.0 2.30752
\(771\) −20669.4 −0.965488
\(772\) 5168.52 0.240957
\(773\) 4428.78 0.206070 0.103035 0.994678i \(-0.467145\pi\)
0.103035 + 0.994678i \(0.467145\pi\)
\(774\) −12766.2 −0.592855
\(775\) −10738.9 −0.497746
\(776\) 6982.18 0.322997
\(777\) 13264.5 0.612435
\(778\) 29853.4 1.37570
\(779\) 3632.86 0.167087
\(780\) −3499.61 −0.160649
\(781\) 32173.1 1.47406
\(782\) 0 0
\(783\) −21572.4 −0.984591
\(784\) −20479.3 −0.932913
\(785\) −4852.97 −0.220650
\(786\) 12588.3 0.571259
\(787\) −17665.8 −0.800151 −0.400075 0.916482i \(-0.631016\pi\)
−0.400075 + 0.916482i \(0.631016\pi\)
\(788\) −10932.8 −0.494243
\(789\) −13211.9 −0.596143
\(790\) −5488.33 −0.247172
\(791\) 2171.73 0.0976203
\(792\) 11880.0 0.533002
\(793\) −2085.18 −0.0933756
\(794\) 22866.4 1.02204
\(795\) 3027.66 0.135069
\(796\) 18534.3 0.825290
\(797\) 12688.4 0.563921 0.281960 0.959426i \(-0.409015\pi\)
0.281960 + 0.959426i \(0.409015\pi\)
\(798\) 41658.3 1.84798
\(799\) 0 0
\(800\) 21112.0 0.933029
\(801\) −9479.74 −0.418165
\(802\) 2341.65 0.103100
\(803\) −52317.3 −2.29918
\(804\) 29153.0 1.27879
\(805\) −1383.41 −0.0605700
\(806\) 10118.3 0.442184
\(807\) 20286.1 0.884886
\(808\) 19714.1 0.858342
\(809\) 28633.8 1.24439 0.622194 0.782863i \(-0.286242\pi\)
0.622194 + 0.782863i \(0.286242\pi\)
\(810\) 3737.94 0.162145
\(811\) 2305.93 0.0998425 0.0499213 0.998753i \(-0.484103\pi\)
0.0499213 + 0.998753i \(0.484103\pi\)
\(812\) 50455.6 2.18060
\(813\) −466.646 −0.0201304
\(814\) −41608.3 −1.79161
\(815\) −14348.0 −0.616672
\(816\) 0 0
\(817\) 18261.6 0.781997
\(818\) 68465.4 2.92645
\(819\) 10309.4 0.439852
\(820\) 2075.60 0.0883938
\(821\) −28803.5 −1.22442 −0.612210 0.790695i \(-0.709719\pi\)
−0.612210 + 0.790695i \(0.709719\pi\)
\(822\) 12447.3 0.528164
\(823\) −14597.0 −0.618248 −0.309124 0.951022i \(-0.600036\pi\)
−0.309124 + 0.951022i \(0.600036\pi\)
\(824\) −11527.3 −0.487347
\(825\) −14773.7 −0.623460
\(826\) 43309.3 1.82436
\(827\) −32943.4 −1.38519 −0.692596 0.721326i \(-0.743533\pi\)
−0.692596 + 0.721326i \(0.743533\pi\)
\(828\) −1448.27 −0.0607859
\(829\) −35091.9 −1.47020 −0.735098 0.677961i \(-0.762864\pi\)
−0.735098 + 0.677961i \(0.762864\pi\)
\(830\) −615.259 −0.0257300
\(831\) −11899.9 −0.496756
\(832\) −14080.2 −0.586711
\(833\) 0 0
\(834\) 18416.7 0.764648
\(835\) 12705.9 0.526594
\(836\) −73834.1 −3.05455
\(837\) 16624.1 0.686517
\(838\) 32781.5 1.35133
\(839\) −19365.1 −0.796848 −0.398424 0.917201i \(-0.630443\pi\)
−0.398424 + 0.917201i \(0.630443\pi\)
\(840\) 5478.15 0.225017
\(841\) 2827.42 0.115930
\(842\) −32267.8 −1.32069
\(843\) 19724.9 0.805887
\(844\) −39032.6 −1.59189
\(845\) −11794.1 −0.480155
\(846\) 37293.0 1.51556
\(847\) −71634.1 −2.90599
\(848\) 6531.13 0.264481
\(849\) 17937.2 0.725094
\(850\) 0 0
\(851\) 1167.48 0.0470278
\(852\) 15531.3 0.624521
\(853\) −37350.6 −1.49925 −0.749625 0.661863i \(-0.769766\pi\)
−0.749625 + 0.661863i \(0.769766\pi\)
\(854\) 14181.4 0.568242
\(855\) −13914.4 −0.556564
\(856\) −1259.48 −0.0502899
\(857\) 14189.2 0.565569 0.282785 0.959183i \(-0.408742\pi\)
0.282785 + 0.959183i \(0.408742\pi\)
\(858\) 13919.9 0.553865
\(859\) 24014.5 0.953859 0.476930 0.878942i \(-0.341750\pi\)
0.476930 + 0.878942i \(0.341750\pi\)
\(860\) 10433.6 0.413699
\(861\) 2631.90 0.104175
\(862\) −52416.8 −2.07114
\(863\) −8498.07 −0.335200 −0.167600 0.985855i \(-0.553602\pi\)
−0.167600 + 0.985855i \(0.553602\pi\)
\(864\) −32682.0 −1.28688
\(865\) −11802.7 −0.463933
\(866\) −66131.1 −2.59495
\(867\) 0 0
\(868\) −38882.1 −1.52044
\(869\) 12334.5 0.481497
\(870\) 12838.6 0.500310
\(871\) −18265.2 −0.710554
\(872\) 8118.78 0.315294
\(873\) −12848.2 −0.498106
\(874\) 3666.57 0.141903
\(875\) 39247.4 1.51635
\(876\) −25255.7 −0.974100
\(877\) 16013.2 0.616566 0.308283 0.951295i \(-0.400246\pi\)
0.308283 + 0.951295i \(0.400246\pi\)
\(878\) 76476.6 2.93959
\(879\) −6535.84 −0.250794
\(880\) 15291.1 0.585755
\(881\) −16824.6 −0.643399 −0.321699 0.946842i \(-0.604254\pi\)
−0.321699 + 0.946842i \(0.604254\pi\)
\(882\) −42349.6 −1.61676
\(883\) 11327.3 0.431703 0.215851 0.976426i \(-0.430747\pi\)
0.215851 + 0.976426i \(0.430747\pi\)
\(884\) 0 0
\(885\) 6226.69 0.236506
\(886\) 1036.24 0.0392926
\(887\) −11077.4 −0.419327 −0.209663 0.977774i \(-0.567237\pi\)
−0.209663 + 0.977774i \(0.567237\pi\)
\(888\) −4623.08 −0.174708
\(889\) 43434.1 1.63862
\(890\) 13712.0 0.516436
\(891\) −8400.68 −0.315862
\(892\) −34879.2 −1.30924
\(893\) −53346.5 −1.99907
\(894\) 5190.52 0.194180
\(895\) −10335.0 −0.385989
\(896\) 36914.4 1.37637
\(897\) −390.575 −0.0145384
\(898\) −62104.5 −2.30785
\(899\) −20973.5 −0.778095
\(900\) 16568.7 0.613657
\(901\) 0 0
\(902\) −8255.78 −0.304753
\(903\) 13230.0 0.487560
\(904\) −756.911 −0.0278479
\(905\) 4832.70 0.177508
\(906\) −19153.1 −0.702339
\(907\) 1761.65 0.0644924 0.0322462 0.999480i \(-0.489734\pi\)
0.0322462 + 0.999480i \(0.489734\pi\)
\(908\) −20665.6 −0.755299
\(909\) −36276.8 −1.32368
\(910\) −14912.1 −0.543220
\(911\) −44996.2 −1.63643 −0.818217 0.574909i \(-0.805037\pi\)
−0.818217 + 0.574909i \(0.805037\pi\)
\(912\) 12919.9 0.469102
\(913\) 1382.74 0.0501227
\(914\) −7781.63 −0.281612
\(915\) 2038.90 0.0736657
\(916\) 54073.8 1.95049
\(917\) 30307.6 1.09144
\(918\) 0 0
\(919\) 34461.8 1.23699 0.618493 0.785790i \(-0.287743\pi\)
0.618493 + 0.785790i \(0.287743\pi\)
\(920\) 482.160 0.0172786
\(921\) −6556.21 −0.234565
\(922\) −57613.1 −2.05790
\(923\) −9730.78 −0.347012
\(924\) −53490.8 −1.90446
\(925\) −13356.4 −0.474763
\(926\) −71163.9 −2.52548
\(927\) 21212.0 0.751557
\(928\) 41232.7 1.45854
\(929\) −37878.7 −1.33774 −0.668870 0.743379i \(-0.733222\pi\)
−0.668870 + 0.743379i \(0.733222\pi\)
\(930\) −9893.71 −0.348847
\(931\) 60579.8 2.13257
\(932\) 59261.5 2.08281
\(933\) 16461.6 0.577630
\(934\) −16914.6 −0.592573
\(935\) 0 0
\(936\) −3593.12 −0.125475
\(937\) −599.505 −0.0209018 −0.0104509 0.999945i \(-0.503327\pi\)
−0.0104509 + 0.999945i \(0.503327\pi\)
\(938\) 124223. 4.32412
\(939\) 7980.22 0.277342
\(940\) −30479.0 −1.05757
\(941\) 10118.0 0.350519 0.175260 0.984522i \(-0.443924\pi\)
0.175260 + 0.984522i \(0.443924\pi\)
\(942\) 9318.32 0.322301
\(943\) 231.647 0.00799945
\(944\) 13431.9 0.463106
\(945\) −24500.3 −0.843380
\(946\) −41500.0 −1.42630
\(947\) 39320.2 1.34924 0.674622 0.738163i \(-0.264307\pi\)
0.674622 + 0.738163i \(0.264307\pi\)
\(948\) 5954.39 0.203997
\(949\) 15823.4 0.541254
\(950\) −41947.0 −1.43257
\(951\) 14652.3 0.499616
\(952\) 0 0
\(953\) −41203.8 −1.40055 −0.700274 0.713874i \(-0.746939\pi\)
−0.700274 + 0.713874i \(0.746939\pi\)
\(954\) 13505.9 0.458353
\(955\) −11957.9 −0.405182
\(956\) 14736.0 0.498531
\(957\) −28853.7 −0.974615
\(958\) 47872.3 1.61449
\(959\) 29968.3 1.00910
\(960\) 13767.7 0.462867
\(961\) −13628.3 −0.457465
\(962\) 12584.5 0.421766
\(963\) 2317.63 0.0775540
\(964\) −64592.6 −2.15808
\(965\) 3166.37 0.105626
\(966\) 2656.33 0.0884740
\(967\) 9403.83 0.312727 0.156363 0.987700i \(-0.450023\pi\)
0.156363 + 0.987700i \(0.450023\pi\)
\(968\) 24966.6 0.828984
\(969\) 0 0
\(970\) 18584.4 0.615164
\(971\) −44819.8 −1.48129 −0.740646 0.671895i \(-0.765481\pi\)
−0.740646 + 0.671895i \(0.765481\pi\)
\(972\) −40744.6 −1.34453
\(973\) 44340.1 1.46092
\(974\) 42817.1 1.40857
\(975\) 4468.33 0.146770
\(976\) 4398.23 0.144246
\(977\) 13700.4 0.448632 0.224316 0.974516i \(-0.427985\pi\)
0.224316 + 0.974516i \(0.427985\pi\)
\(978\) 27549.9 0.900766
\(979\) −30816.6 −1.00603
\(980\) 34611.6 1.12819
\(981\) −14939.7 −0.486227
\(982\) −84226.0 −2.73703
\(983\) 34126.9 1.10730 0.553652 0.832748i \(-0.313234\pi\)
0.553652 + 0.832748i \(0.313234\pi\)
\(984\) −917.297 −0.0297178
\(985\) −6697.69 −0.216656
\(986\) 0 0
\(987\) −38648.1 −1.24638
\(988\) 22331.2 0.719080
\(989\) 1164.44 0.0374389
\(990\) 31620.9 1.01513
\(991\) 38645.7 1.23877 0.619386 0.785087i \(-0.287382\pi\)
0.619386 + 0.785087i \(0.287382\pi\)
\(992\) −31774.8 −1.01699
\(993\) −1309.78 −0.0418577
\(994\) 66179.7 2.11176
\(995\) 11354.6 0.361773
\(996\) 667.505 0.0212356
\(997\) 13993.3 0.444505 0.222252 0.974989i \(-0.428659\pi\)
0.222252 + 0.974989i \(0.428659\pi\)
\(998\) 24720.7 0.784088
\(999\) 20676.1 0.654817
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.h.1.10 12
17.4 even 4 289.4.b.f.288.6 24
17.13 even 4 289.4.b.f.288.5 24
17.16 even 2 289.4.a.i.1.10 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.10 12 1.1 even 1 trivial
289.4.a.i.1.10 yes 12 17.16 even 2
289.4.b.f.288.5 24 17.13 even 4
289.4.b.f.288.6 24 17.4 even 4