Properties

Label 6007.2.a.c.1.12
Level $6007$
Weight $2$
Character 6007.1
Self dual yes
Analytic conductor $47.966$
Analytic rank $0$
Dimension $261$
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] = [6007,2,Mod(1,6007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6007, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6007.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: \(47.9661364942\)
Analytic rank: \(0\)
Dimension: \(261\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.53967 q^{2} +2.55882 q^{3} +4.44992 q^{4} +2.30710 q^{5} -6.49855 q^{6} -1.02038 q^{7} -6.22199 q^{8} +3.54756 q^{9} +O(q^{10})\) \(q-2.53967 q^{2} +2.55882 q^{3} +4.44992 q^{4} +2.30710 q^{5} -6.49855 q^{6} -1.02038 q^{7} -6.22199 q^{8} +3.54756 q^{9} -5.85928 q^{10} -5.18117 q^{11} +11.3865 q^{12} +3.30137 q^{13} +2.59144 q^{14} +5.90346 q^{15} +6.90195 q^{16} +2.75231 q^{17} -9.00962 q^{18} +1.75773 q^{19} +10.2664 q^{20} -2.61098 q^{21} +13.1585 q^{22} -1.22522 q^{23} -15.9209 q^{24} +0.322725 q^{25} -8.38440 q^{26} +1.40110 q^{27} -4.54063 q^{28} +1.71453 q^{29} -14.9928 q^{30} +1.16098 q^{31} -5.08469 q^{32} -13.2577 q^{33} -6.98997 q^{34} -2.35413 q^{35} +15.7863 q^{36} +4.45544 q^{37} -4.46406 q^{38} +8.44762 q^{39} -14.3548 q^{40} +11.7238 q^{41} +6.63102 q^{42} +7.10289 q^{43} -23.0558 q^{44} +8.18458 q^{45} +3.11165 q^{46} +10.7693 q^{47} +17.6608 q^{48} -5.95882 q^{49} -0.819616 q^{50} +7.04268 q^{51} +14.6909 q^{52} +11.0554 q^{53} -3.55833 q^{54} -11.9535 q^{55} +6.34882 q^{56} +4.49772 q^{57} -4.35434 q^{58} +7.40508 q^{59} +26.2699 q^{60} -1.02359 q^{61} -2.94851 q^{62} -3.61987 q^{63} -0.890461 q^{64} +7.61661 q^{65} +33.6701 q^{66} -15.2186 q^{67} +12.2476 q^{68} -3.13511 q^{69} +5.97872 q^{70} +2.13498 q^{71} -22.0728 q^{72} -10.9239 q^{73} -11.3153 q^{74} +0.825796 q^{75} +7.82178 q^{76} +5.28678 q^{77} -21.4542 q^{78} -5.83197 q^{79} +15.9235 q^{80} -7.05751 q^{81} -29.7747 q^{82} -16.7163 q^{83} -11.6186 q^{84} +6.34987 q^{85} -18.0390 q^{86} +4.38717 q^{87} +32.2372 q^{88} -6.28305 q^{89} -20.7861 q^{90} -3.36867 q^{91} -5.45212 q^{92} +2.97074 q^{93} -27.3506 q^{94} +4.05527 q^{95} -13.0108 q^{96} -10.4758 q^{97} +15.1334 q^{98} -18.3805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53967 −1.79582 −0.897909 0.440182i \(-0.854914\pi\)
−0.897909 + 0.440182i \(0.854914\pi\)
\(3\) 2.55882 1.47734 0.738668 0.674070i \(-0.235455\pi\)
0.738668 + 0.674070i \(0.235455\pi\)
\(4\) 4.44992 2.22496
\(5\) 2.30710 1.03177 0.515884 0.856658i \(-0.327464\pi\)
0.515884 + 0.856658i \(0.327464\pi\)
\(6\) −6.49855 −2.65302
\(7\) −1.02038 −0.385669 −0.192834 0.981231i \(-0.561768\pi\)
−0.192834 + 0.981231i \(0.561768\pi\)
\(8\) −6.22199 −2.19980
\(9\) 3.54756 1.18252
\(10\) −5.85928 −1.85287
\(11\) −5.18117 −1.56218 −0.781090 0.624418i \(-0.785336\pi\)
−0.781090 + 0.624418i \(0.785336\pi\)
\(12\) 11.3865 3.28701
\(13\) 3.30137 0.915636 0.457818 0.889046i \(-0.348631\pi\)
0.457818 + 0.889046i \(0.348631\pi\)
\(14\) 2.59144 0.692591
\(15\) 5.90346 1.52427
\(16\) 6.90195 1.72549
\(17\) 2.75231 0.667534 0.333767 0.942656i \(-0.391680\pi\)
0.333767 + 0.942656i \(0.391680\pi\)
\(18\) −9.00962 −2.12359
\(19\) 1.75773 0.403252 0.201626 0.979463i \(-0.435377\pi\)
0.201626 + 0.979463i \(0.435377\pi\)
\(20\) 10.2664 2.29564
\(21\) −2.61098 −0.569762
\(22\) 13.1585 2.80539
\(23\) −1.22522 −0.255476 −0.127738 0.991808i \(-0.540772\pi\)
−0.127738 + 0.991808i \(0.540772\pi\)
\(24\) −15.9209 −3.24985
\(25\) 0.322725 0.0645451
\(26\) −8.38440 −1.64432
\(27\) 1.40110 0.269642
\(28\) −4.54063 −0.858098
\(29\) 1.71453 0.318380 0.159190 0.987248i \(-0.449112\pi\)
0.159190 + 0.987248i \(0.449112\pi\)
\(30\) −14.9928 −2.73731
\(31\) 1.16098 0.208519 0.104259 0.994550i \(-0.466753\pi\)
0.104259 + 0.994550i \(0.466753\pi\)
\(32\) −5.08469 −0.898855
\(33\) −13.2577 −2.30786
\(34\) −6.98997 −1.19877
\(35\) −2.35413 −0.397921
\(36\) 15.7863 2.63106
\(37\) 4.45544 0.732470 0.366235 0.930522i \(-0.380647\pi\)
0.366235 + 0.930522i \(0.380647\pi\)
\(38\) −4.46406 −0.724167
\(39\) 8.44762 1.35270
\(40\) −14.3548 −2.26969
\(41\) 11.7238 1.83096 0.915478 0.402369i \(-0.131813\pi\)
0.915478 + 0.402369i \(0.131813\pi\)
\(42\) 6.63102 1.02319
\(43\) 7.10289 1.08318 0.541590 0.840643i \(-0.317822\pi\)
0.541590 + 0.840643i \(0.317822\pi\)
\(44\) −23.0558 −3.47579
\(45\) 8.18458 1.22009
\(46\) 3.11165 0.458788
\(47\) 10.7693 1.57087 0.785435 0.618944i \(-0.212439\pi\)
0.785435 + 0.618944i \(0.212439\pi\)
\(48\) 17.6608 2.54912
\(49\) −5.95882 −0.851259
\(50\) −0.819616 −0.115911
\(51\) 7.04268 0.986172
\(52\) 14.6909 2.03725
\(53\) 11.0554 1.51858 0.759288 0.650755i \(-0.225547\pi\)
0.759288 + 0.650755i \(0.225547\pi\)
\(54\) −3.55833 −0.484227
\(55\) −11.9535 −1.61181
\(56\) 6.34882 0.848396
\(57\) 4.49772 0.595738
\(58\) −4.35434 −0.571752
\(59\) 7.40508 0.964060 0.482030 0.876155i \(-0.339900\pi\)
0.482030 + 0.876155i \(0.339900\pi\)
\(60\) 26.2699 3.39143
\(61\) −1.02359 −0.131057 −0.0655284 0.997851i \(-0.520873\pi\)
−0.0655284 + 0.997851i \(0.520873\pi\)
\(62\) −2.94851 −0.374461
\(63\) −3.61987 −0.456061
\(64\) −0.890461 −0.111308
\(65\) 7.61661 0.944724
\(66\) 33.6701 4.14450
\(67\) −15.2186 −1.85925 −0.929625 0.368507i \(-0.879869\pi\)
−0.929625 + 0.368507i \(0.879869\pi\)
\(68\) 12.2476 1.48524
\(69\) −3.13511 −0.377423
\(70\) 5.97872 0.714593
\(71\) 2.13498 0.253376 0.126688 0.991943i \(-0.459565\pi\)
0.126688 + 0.991943i \(0.459565\pi\)
\(72\) −22.0728 −2.60131
\(73\) −10.9239 −1.27855 −0.639274 0.768979i \(-0.720765\pi\)
−0.639274 + 0.768979i \(0.720765\pi\)
\(74\) −11.3153 −1.31538
\(75\) 0.825796 0.0953547
\(76\) 7.82178 0.897219
\(77\) 5.28678 0.602485
\(78\) −21.4542 −2.42921
\(79\) −5.83197 −0.656148 −0.328074 0.944652i \(-0.606399\pi\)
−0.328074 + 0.944652i \(0.606399\pi\)
\(80\) 15.9235 1.78030
\(81\) −7.05751 −0.784168
\(82\) −29.7747 −3.28806
\(83\) −16.7163 −1.83485 −0.917426 0.397907i \(-0.869737\pi\)
−0.917426 + 0.397907i \(0.869737\pi\)
\(84\) −11.6186 −1.26770
\(85\) 6.34987 0.688740
\(86\) −18.0390 −1.94519
\(87\) 4.38717 0.470354
\(88\) 32.2372 3.43649
\(89\) −6.28305 −0.666002 −0.333001 0.942927i \(-0.608061\pi\)
−0.333001 + 0.942927i \(0.608061\pi\)
\(90\) −20.7861 −2.19105
\(91\) −3.36867 −0.353133
\(92\) −5.45212 −0.568423
\(93\) 2.97074 0.308052
\(94\) −27.3506 −2.82100
\(95\) 4.05527 0.416062
\(96\) −13.0108 −1.32791
\(97\) −10.4758 −1.06365 −0.531827 0.846853i \(-0.678494\pi\)
−0.531827 + 0.846853i \(0.678494\pi\)
\(98\) 15.1334 1.52871
\(99\) −18.3805 −1.84731
\(100\) 1.43610 0.143610
\(101\) 13.5733 1.35059 0.675296 0.737547i \(-0.264016\pi\)
0.675296 + 0.737547i \(0.264016\pi\)
\(102\) −17.8861 −1.77098
\(103\) 5.59633 0.551423 0.275711 0.961240i \(-0.411087\pi\)
0.275711 + 0.961240i \(0.411087\pi\)
\(104\) −20.5411 −2.01422
\(105\) −6.02380 −0.587862
\(106\) −28.0771 −2.72709
\(107\) 5.01637 0.484951 0.242475 0.970158i \(-0.422041\pi\)
0.242475 + 0.970158i \(0.422041\pi\)
\(108\) 6.23478 0.599942
\(109\) 12.5933 1.20622 0.603110 0.797658i \(-0.293928\pi\)
0.603110 + 0.797658i \(0.293928\pi\)
\(110\) 30.3579 2.89451
\(111\) 11.4007 1.08210
\(112\) −7.04264 −0.665467
\(113\) 7.45181 0.701008 0.350504 0.936561i \(-0.386010\pi\)
0.350504 + 0.936561i \(0.386010\pi\)
\(114\) −11.4227 −1.06984
\(115\) −2.82671 −0.263592
\(116\) 7.62952 0.708383
\(117\) 11.7118 1.08276
\(118\) −18.8065 −1.73128
\(119\) −2.80842 −0.257447
\(120\) −36.7312 −3.35309
\(121\) 15.8445 1.44041
\(122\) 2.59957 0.235354
\(123\) 29.9992 2.70493
\(124\) 5.16628 0.463945
\(125\) −10.7910 −0.965172
\(126\) 9.19327 0.819002
\(127\) −12.7484 −1.13124 −0.565618 0.824668i \(-0.691362\pi\)
−0.565618 + 0.824668i \(0.691362\pi\)
\(128\) 12.4309 1.09874
\(129\) 18.1750 1.60022
\(130\) −19.3437 −1.69655
\(131\) 12.8701 1.12447 0.562233 0.826979i \(-0.309942\pi\)
0.562233 + 0.826979i \(0.309942\pi\)
\(132\) −58.9956 −5.13491
\(133\) −1.79356 −0.155522
\(134\) 38.6503 3.33887
\(135\) 3.23248 0.278207
\(136\) −17.1249 −1.46844
\(137\) −13.1482 −1.12332 −0.561661 0.827367i \(-0.689838\pi\)
−0.561661 + 0.827367i \(0.689838\pi\)
\(138\) 7.96215 0.677783
\(139\) 10.1850 0.863877 0.431939 0.901903i \(-0.357830\pi\)
0.431939 + 0.901903i \(0.357830\pi\)
\(140\) −10.4757 −0.885358
\(141\) 27.5568 2.32070
\(142\) −5.42214 −0.455016
\(143\) −17.1050 −1.43039
\(144\) 24.4850 2.04042
\(145\) 3.95560 0.328494
\(146\) 27.7431 2.29604
\(147\) −15.2475 −1.25760
\(148\) 19.8264 1.62972
\(149\) 2.42024 0.198274 0.0991370 0.995074i \(-0.468392\pi\)
0.0991370 + 0.995074i \(0.468392\pi\)
\(150\) −2.09725 −0.171240
\(151\) 18.0697 1.47049 0.735245 0.677802i \(-0.237067\pi\)
0.735245 + 0.677802i \(0.237067\pi\)
\(152\) −10.9366 −0.887075
\(153\) 9.76399 0.789372
\(154\) −13.4267 −1.08195
\(155\) 2.67851 0.215143
\(156\) 37.5912 3.00971
\(157\) 9.96183 0.795040 0.397520 0.917593i \(-0.369871\pi\)
0.397520 + 0.917593i \(0.369871\pi\)
\(158\) 14.8113 1.17832
\(159\) 28.2888 2.24345
\(160\) −11.7309 −0.927410
\(161\) 1.25019 0.0985290
\(162\) 17.9237 1.40822
\(163\) 13.4563 1.05398 0.526988 0.849873i \(-0.323321\pi\)
0.526988 + 0.849873i \(0.323321\pi\)
\(164\) 52.1701 4.07380
\(165\) −30.5868 −2.38118
\(166\) 42.4539 3.29506
\(167\) −2.92638 −0.226450 −0.113225 0.993569i \(-0.536118\pi\)
−0.113225 + 0.993569i \(0.536118\pi\)
\(168\) 16.2455 1.25337
\(169\) −2.10093 −0.161610
\(170\) −16.1266 −1.23685
\(171\) 6.23566 0.476853
\(172\) 31.6073 2.41003
\(173\) 5.81056 0.441769 0.220884 0.975300i \(-0.429106\pi\)
0.220884 + 0.975300i \(0.429106\pi\)
\(174\) −11.1420 −0.844670
\(175\) −0.329304 −0.0248930
\(176\) −35.7601 −2.69552
\(177\) 18.9483 1.42424
\(178\) 15.9569 1.19602
\(179\) −2.72686 −0.203815 −0.101908 0.994794i \(-0.532495\pi\)
−0.101908 + 0.994794i \(0.532495\pi\)
\(180\) 36.4207 2.71464
\(181\) 5.80475 0.431464 0.215732 0.976453i \(-0.430786\pi\)
0.215732 + 0.976453i \(0.430786\pi\)
\(182\) 8.55531 0.634162
\(183\) −2.61917 −0.193615
\(184\) 7.62329 0.561997
\(185\) 10.2792 0.755739
\(186\) −7.54471 −0.553205
\(187\) −14.2602 −1.04281
\(188\) 47.9227 3.49512
\(189\) −1.42966 −0.103992
\(190\) −10.2991 −0.747172
\(191\) −7.44099 −0.538411 −0.269206 0.963083i \(-0.586761\pi\)
−0.269206 + 0.963083i \(0.586761\pi\)
\(192\) −2.27853 −0.164439
\(193\) −15.5409 −1.11866 −0.559328 0.828946i \(-0.688941\pi\)
−0.559328 + 0.828946i \(0.688941\pi\)
\(194\) 26.6050 1.91013
\(195\) 19.4895 1.39567
\(196\) −26.5163 −1.89402
\(197\) −14.3071 −1.01934 −0.509668 0.860371i \(-0.670232\pi\)
−0.509668 + 0.860371i \(0.670232\pi\)
\(198\) 46.6804 3.31743
\(199\) −4.98745 −0.353551 −0.176776 0.984251i \(-0.556567\pi\)
−0.176776 + 0.984251i \(0.556567\pi\)
\(200\) −2.00799 −0.141987
\(201\) −38.9417 −2.74674
\(202\) −34.4716 −2.42542
\(203\) −1.74948 −0.122789
\(204\) 31.3393 2.19419
\(205\) 27.0481 1.88912
\(206\) −14.2128 −0.990255
\(207\) −4.34653 −0.302105
\(208\) 22.7859 1.57992
\(209\) −9.10712 −0.629952
\(210\) 15.2985 1.05569
\(211\) 8.96046 0.616864 0.308432 0.951246i \(-0.400196\pi\)
0.308432 + 0.951246i \(0.400196\pi\)
\(212\) 49.1957 3.37877
\(213\) 5.46303 0.374321
\(214\) −12.7399 −0.870883
\(215\) 16.3871 1.11759
\(216\) −8.71761 −0.593159
\(217\) −1.18465 −0.0804191
\(218\) −31.9828 −2.16615
\(219\) −27.9523 −1.88884
\(220\) −53.1921 −3.58621
\(221\) 9.08642 0.611219
\(222\) −28.9539 −1.94326
\(223\) −3.40434 −0.227971 −0.113986 0.993482i \(-0.536362\pi\)
−0.113986 + 0.993482i \(0.536362\pi\)
\(224\) 5.18834 0.346660
\(225\) 1.14489 0.0763258
\(226\) −18.9251 −1.25888
\(227\) 25.6341 1.70139 0.850696 0.525657i \(-0.176181\pi\)
0.850696 + 0.525657i \(0.176181\pi\)
\(228\) 20.0145 1.32549
\(229\) 17.3574 1.14701 0.573504 0.819203i \(-0.305584\pi\)
0.573504 + 0.819203i \(0.305584\pi\)
\(230\) 7.17890 0.473362
\(231\) 13.5279 0.890072
\(232\) −10.6678 −0.700374
\(233\) 8.05580 0.527753 0.263876 0.964556i \(-0.414999\pi\)
0.263876 + 0.964556i \(0.414999\pi\)
\(234\) −29.7441 −1.94443
\(235\) 24.8460 1.62077
\(236\) 32.9520 2.14499
\(237\) −14.9230 −0.969350
\(238\) 7.13245 0.462328
\(239\) 20.8865 1.35103 0.675516 0.737345i \(-0.263921\pi\)
0.675516 + 0.737345i \(0.263921\pi\)
\(240\) 40.7454 2.63010
\(241\) 6.79573 0.437752 0.218876 0.975753i \(-0.429761\pi\)
0.218876 + 0.975753i \(0.429761\pi\)
\(242\) −40.2398 −2.58671
\(243\) −22.2622 −1.42812
\(244\) −4.55488 −0.291596
\(245\) −13.7476 −0.878302
\(246\) −76.1880 −4.85757
\(247\) 5.80294 0.369232
\(248\) −7.22361 −0.458700
\(249\) −42.7740 −2.71069
\(250\) 27.4055 1.73327
\(251\) 0.344721 0.0217586 0.0108793 0.999941i \(-0.496537\pi\)
0.0108793 + 0.999941i \(0.496537\pi\)
\(252\) −16.1081 −1.01472
\(253\) 6.34806 0.399099
\(254\) 32.3767 2.03149
\(255\) 16.2482 1.01750
\(256\) −29.7893 −1.86183
\(257\) 5.64934 0.352396 0.176198 0.984355i \(-0.443620\pi\)
0.176198 + 0.984355i \(0.443620\pi\)
\(258\) −46.1585 −2.87370
\(259\) −4.54626 −0.282491
\(260\) 33.8933 2.10197
\(261\) 6.08239 0.376490
\(262\) −32.6858 −2.01934
\(263\) 23.0457 1.42106 0.710529 0.703668i \(-0.248456\pi\)
0.710529 + 0.703668i \(0.248456\pi\)
\(264\) 82.4891 5.07685
\(265\) 25.5060 1.56682
\(266\) 4.55506 0.279289
\(267\) −16.0772 −0.983907
\(268\) −67.7216 −4.13676
\(269\) 25.9750 1.58373 0.791863 0.610699i \(-0.209111\pi\)
0.791863 + 0.610699i \(0.209111\pi\)
\(270\) −8.20943 −0.499610
\(271\) −2.54862 −0.154818 −0.0774089 0.996999i \(-0.524665\pi\)
−0.0774089 + 0.996999i \(0.524665\pi\)
\(272\) 18.9963 1.15182
\(273\) −8.61982 −0.521695
\(274\) 33.3920 2.01728
\(275\) −1.67209 −0.100831
\(276\) −13.9510 −0.839752
\(277\) 8.58487 0.515815 0.257907 0.966170i \(-0.416967\pi\)
0.257907 + 0.966170i \(0.416967\pi\)
\(278\) −25.8664 −1.55137
\(279\) 4.11865 0.246577
\(280\) 14.6474 0.875348
\(281\) −3.84255 −0.229228 −0.114614 0.993410i \(-0.536563\pi\)
−0.114614 + 0.993410i \(0.536563\pi\)
\(282\) −69.9852 −4.16756
\(283\) 10.5341 0.626188 0.313094 0.949722i \(-0.398635\pi\)
0.313094 + 0.949722i \(0.398635\pi\)
\(284\) 9.50049 0.563751
\(285\) 10.3767 0.614664
\(286\) 43.4410 2.56872
\(287\) −11.9628 −0.706143
\(288\) −18.0382 −1.06291
\(289\) −9.42477 −0.554398
\(290\) −10.0459 −0.589916
\(291\) −26.8056 −1.57137
\(292\) −48.6105 −2.84472
\(293\) 23.5698 1.37696 0.688482 0.725253i \(-0.258277\pi\)
0.688482 + 0.725253i \(0.258277\pi\)
\(294\) 38.7237 2.25841
\(295\) 17.0843 0.994686
\(296\) −27.7217 −1.61129
\(297\) −7.25933 −0.421229
\(298\) −6.14662 −0.356064
\(299\) −4.04490 −0.233923
\(300\) 3.67473 0.212160
\(301\) −7.24768 −0.417749
\(302\) −45.8910 −2.64073
\(303\) 34.7316 1.99528
\(304\) 12.1318 0.695806
\(305\) −2.36152 −0.135220
\(306\) −24.7973 −1.41757
\(307\) 0.981817 0.0560353 0.0280176 0.999607i \(-0.491081\pi\)
0.0280176 + 0.999607i \(0.491081\pi\)
\(308\) 23.5258 1.34050
\(309\) 14.3200 0.814636
\(310\) −6.80252 −0.386357
\(311\) −18.3664 −1.04146 −0.520732 0.853720i \(-0.674341\pi\)
−0.520732 + 0.853720i \(0.674341\pi\)
\(312\) −52.5610 −2.97568
\(313\) 15.9350 0.900698 0.450349 0.892853i \(-0.351300\pi\)
0.450349 + 0.892853i \(0.351300\pi\)
\(314\) −25.2997 −1.42775
\(315\) −8.35141 −0.470549
\(316\) −25.9518 −1.45990
\(317\) 25.4270 1.42812 0.714061 0.700084i \(-0.246854\pi\)
0.714061 + 0.700084i \(0.246854\pi\)
\(318\) −71.8441 −4.02882
\(319\) −8.88326 −0.497367
\(320\) −2.05439 −0.114844
\(321\) 12.8360 0.716435
\(322\) −3.17508 −0.176940
\(323\) 4.83784 0.269184
\(324\) −31.4054 −1.74474
\(325\) 1.06544 0.0590998
\(326\) −34.1744 −1.89275
\(327\) 32.2240 1.78199
\(328\) −72.9455 −4.02774
\(329\) −10.9889 −0.605836
\(330\) 77.6804 4.27617
\(331\) −6.81250 −0.374449 −0.187224 0.982317i \(-0.559949\pi\)
−0.187224 + 0.982317i \(0.559949\pi\)
\(332\) −74.3862 −4.08247
\(333\) 15.8059 0.866160
\(334\) 7.43205 0.406664
\(335\) −35.1109 −1.91831
\(336\) −18.0208 −0.983117
\(337\) 21.2560 1.15789 0.578945 0.815367i \(-0.303465\pi\)
0.578945 + 0.815367i \(0.303465\pi\)
\(338\) 5.33566 0.290222
\(339\) 19.0678 1.03562
\(340\) 28.2564 1.53242
\(341\) −6.01524 −0.325744
\(342\) −15.8365 −0.856341
\(343\) 13.2230 0.713973
\(344\) −44.1941 −2.38279
\(345\) −7.23303 −0.389413
\(346\) −14.7569 −0.793336
\(347\) −0.120187 −0.00645199 −0.00322599 0.999995i \(-0.501027\pi\)
−0.00322599 + 0.999995i \(0.501027\pi\)
\(348\) 19.5226 1.04652
\(349\) −9.34700 −0.500333 −0.250167 0.968203i \(-0.580485\pi\)
−0.250167 + 0.968203i \(0.580485\pi\)
\(350\) 0.836323 0.0447033
\(351\) 4.62555 0.246894
\(352\) 26.3446 1.40417
\(353\) −30.3926 −1.61763 −0.808817 0.588061i \(-0.799892\pi\)
−0.808817 + 0.588061i \(0.799892\pi\)
\(354\) −48.1223 −2.55767
\(355\) 4.92562 0.261425
\(356\) −27.9591 −1.48183
\(357\) −7.18623 −0.380336
\(358\) 6.92533 0.366015
\(359\) −21.1123 −1.11426 −0.557131 0.830425i \(-0.688098\pi\)
−0.557131 + 0.830425i \(0.688098\pi\)
\(360\) −50.9243 −2.68395
\(361\) −15.9104 −0.837388
\(362\) −14.7421 −0.774830
\(363\) 40.5432 2.12797
\(364\) −14.9903 −0.785706
\(365\) −25.2026 −1.31916
\(366\) 6.65183 0.347697
\(367\) −6.16946 −0.322043 −0.161022 0.986951i \(-0.551479\pi\)
−0.161022 + 0.986951i \(0.551479\pi\)
\(368\) −8.45639 −0.440820
\(369\) 41.5910 2.16514
\(370\) −26.1057 −1.35717
\(371\) −11.2808 −0.585668
\(372\) 13.2196 0.685403
\(373\) 22.3248 1.15594 0.577968 0.816059i \(-0.303846\pi\)
0.577968 + 0.816059i \(0.303846\pi\)
\(374\) 36.2162 1.87269
\(375\) −27.6121 −1.42588
\(376\) −67.0067 −3.45561
\(377\) 5.66030 0.291520
\(378\) 3.63086 0.186751
\(379\) −20.8606 −1.07154 −0.535768 0.844365i \(-0.679978\pi\)
−0.535768 + 0.844365i \(0.679978\pi\)
\(380\) 18.0456 0.925722
\(381\) −32.6208 −1.67121
\(382\) 18.8977 0.966888
\(383\) 6.76595 0.345724 0.172862 0.984946i \(-0.444699\pi\)
0.172862 + 0.984946i \(0.444699\pi\)
\(384\) 31.8083 1.62321
\(385\) 12.1972 0.621624
\(386\) 39.4687 2.00890
\(387\) 25.1979 1.28088
\(388\) −46.6163 −2.36659
\(389\) 14.2493 0.722468 0.361234 0.932475i \(-0.382356\pi\)
0.361234 + 0.932475i \(0.382356\pi\)
\(390\) −49.4970 −2.50638
\(391\) −3.37219 −0.170539
\(392\) 37.0757 1.87260
\(393\) 32.9323 1.66121
\(394\) 36.3352 1.83054
\(395\) −13.4550 −0.676992
\(396\) −81.7917 −4.11019
\(397\) −15.7114 −0.788534 −0.394267 0.918996i \(-0.629002\pi\)
−0.394267 + 0.918996i \(0.629002\pi\)
\(398\) 12.6665 0.634913
\(399\) −4.58941 −0.229758
\(400\) 2.22743 0.111372
\(401\) 20.7408 1.03575 0.517873 0.855458i \(-0.326724\pi\)
0.517873 + 0.855458i \(0.326724\pi\)
\(402\) 98.8990 4.93264
\(403\) 3.83284 0.190927
\(404\) 60.4000 3.00501
\(405\) −16.2824 −0.809079
\(406\) 4.44310 0.220507
\(407\) −23.0844 −1.14425
\(408\) −43.8194 −2.16938
\(409\) 4.75593 0.235166 0.117583 0.993063i \(-0.462485\pi\)
0.117583 + 0.993063i \(0.462485\pi\)
\(410\) −68.6932 −3.39252
\(411\) −33.6438 −1.65952
\(412\) 24.9032 1.22689
\(413\) −7.55603 −0.371808
\(414\) 11.0388 0.542525
\(415\) −38.5662 −1.89314
\(416\) −16.7865 −0.823024
\(417\) 26.0615 1.27624
\(418\) 23.1291 1.13128
\(419\) 19.8817 0.971286 0.485643 0.874157i \(-0.338585\pi\)
0.485643 + 0.874157i \(0.338585\pi\)
\(420\) −26.8054 −1.30797
\(421\) 9.94035 0.484463 0.242232 0.970218i \(-0.422121\pi\)
0.242232 + 0.970218i \(0.422121\pi\)
\(422\) −22.7566 −1.10777
\(423\) 38.2049 1.85758
\(424\) −68.7866 −3.34057
\(425\) 0.888242 0.0430861
\(426\) −13.8743 −0.672211
\(427\) 1.04445 0.0505445
\(428\) 22.3224 1.07900
\(429\) −43.7685 −2.11316
\(430\) −41.6178 −2.00699
\(431\) −27.1220 −1.30642 −0.653211 0.757176i \(-0.726578\pi\)
−0.653211 + 0.757176i \(0.726578\pi\)
\(432\) 9.67031 0.465263
\(433\) 26.0933 1.25396 0.626982 0.779034i \(-0.284290\pi\)
0.626982 + 0.779034i \(0.284290\pi\)
\(434\) 3.00861 0.144418
\(435\) 10.1217 0.485296
\(436\) 56.0392 2.68379
\(437\) −2.15361 −0.103021
\(438\) 70.9896 3.39202
\(439\) −22.8457 −1.09037 −0.545183 0.838317i \(-0.683540\pi\)
−0.545183 + 0.838317i \(0.683540\pi\)
\(440\) 74.3744 3.54566
\(441\) −21.1392 −1.00663
\(442\) −23.0765 −1.09764
\(443\) −27.1714 −1.29095 −0.645477 0.763780i \(-0.723341\pi\)
−0.645477 + 0.763780i \(0.723341\pi\)
\(444\) 50.7321 2.40764
\(445\) −14.4956 −0.687159
\(446\) 8.64589 0.409395
\(447\) 6.19297 0.292917
\(448\) 0.908613 0.0429279
\(449\) 21.2661 1.00361 0.501804 0.864981i \(-0.332670\pi\)
0.501804 + 0.864981i \(0.332670\pi\)
\(450\) −2.90763 −0.137067
\(451\) −60.7432 −2.86028
\(452\) 33.1600 1.55971
\(453\) 46.2370 2.17241
\(454\) −65.1021 −3.05539
\(455\) −7.77187 −0.364351
\(456\) −27.9848 −1.31051
\(457\) −24.9142 −1.16544 −0.582720 0.812673i \(-0.698011\pi\)
−0.582720 + 0.812673i \(0.698011\pi\)
\(458\) −44.0820 −2.05982
\(459\) 3.85626 0.179995
\(460\) −12.5786 −0.586481
\(461\) 28.8723 1.34472 0.672359 0.740225i \(-0.265281\pi\)
0.672359 + 0.740225i \(0.265281\pi\)
\(462\) −34.3564 −1.59841
\(463\) 10.9407 0.508457 0.254228 0.967144i \(-0.418178\pi\)
0.254228 + 0.967144i \(0.418178\pi\)
\(464\) 11.8336 0.549361
\(465\) 6.85381 0.317838
\(466\) −20.4591 −0.947748
\(467\) 22.0729 1.02141 0.510705 0.859756i \(-0.329384\pi\)
0.510705 + 0.859756i \(0.329384\pi\)
\(468\) 52.1166 2.40909
\(469\) 15.5288 0.717055
\(470\) −63.1006 −2.91061
\(471\) 25.4905 1.17454
\(472\) −46.0743 −2.12074
\(473\) −36.8013 −1.69212
\(474\) 37.8994 1.74078
\(475\) 0.567266 0.0260279
\(476\) −12.4972 −0.572810
\(477\) 39.2197 1.79575
\(478\) −53.0447 −2.42621
\(479\) −22.7668 −1.04024 −0.520121 0.854093i \(-0.674113\pi\)
−0.520121 + 0.854093i \(0.674113\pi\)
\(480\) −30.0173 −1.37009
\(481\) 14.7091 0.670676
\(482\) −17.2589 −0.786122
\(483\) 3.19902 0.145560
\(484\) 70.5068 3.20485
\(485\) −24.1687 −1.09744
\(486\) 56.5386 2.56464
\(487\) −37.4386 −1.69650 −0.848252 0.529594i \(-0.822344\pi\)
−0.848252 + 0.529594i \(0.822344\pi\)
\(488\) 6.36874 0.288299
\(489\) 34.4321 1.55707
\(490\) 34.9144 1.57727
\(491\) −28.8888 −1.30373 −0.651867 0.758333i \(-0.726014\pi\)
−0.651867 + 0.758333i \(0.726014\pi\)
\(492\) 133.494 6.01837
\(493\) 4.71892 0.212530
\(494\) −14.7375 −0.663073
\(495\) −42.4057 −1.90599
\(496\) 8.01304 0.359796
\(497\) −2.17850 −0.0977191
\(498\) 108.632 4.86791
\(499\) 36.1214 1.61702 0.808509 0.588484i \(-0.200275\pi\)
0.808509 + 0.588484i \(0.200275\pi\)
\(500\) −48.0189 −2.14747
\(501\) −7.48809 −0.334543
\(502\) −0.875477 −0.0390744
\(503\) −16.4678 −0.734265 −0.367133 0.930169i \(-0.619660\pi\)
−0.367133 + 0.930169i \(0.619660\pi\)
\(504\) 22.5228 1.00324
\(505\) 31.3150 1.39350
\(506\) −16.1220 −0.716709
\(507\) −5.37590 −0.238752
\(508\) −56.7293 −2.51695
\(509\) −9.46445 −0.419504 −0.209752 0.977755i \(-0.567266\pi\)
−0.209752 + 0.977755i \(0.567266\pi\)
\(510\) −41.2650 −1.82724
\(511\) 11.1466 0.493096
\(512\) 50.7934 2.24477
\(513\) 2.46276 0.108733
\(514\) −14.3475 −0.632839
\(515\) 12.9113 0.568940
\(516\) 80.8774 3.56043
\(517\) −55.7978 −2.45398
\(518\) 11.5460 0.507302
\(519\) 14.8682 0.652641
\(520\) −47.3904 −2.07821
\(521\) 14.5936 0.639355 0.319678 0.947526i \(-0.396425\pi\)
0.319678 + 0.947526i \(0.396425\pi\)
\(522\) −15.4473 −0.676108
\(523\) −7.93496 −0.346972 −0.173486 0.984836i \(-0.555503\pi\)
−0.173486 + 0.984836i \(0.555503\pi\)
\(524\) 57.2709 2.50189
\(525\) −0.842629 −0.0367754
\(526\) −58.5284 −2.55196
\(527\) 3.19539 0.139193
\(528\) −91.5038 −3.98219
\(529\) −21.4988 −0.934732
\(530\) −64.7767 −2.81372
\(531\) 26.2700 1.14002
\(532\) −7.98122 −0.346030
\(533\) 38.7048 1.67649
\(534\) 40.8307 1.76692
\(535\) 11.5733 0.500357
\(536\) 94.6900 4.08999
\(537\) −6.97755 −0.301104
\(538\) −65.9680 −2.84408
\(539\) 30.8736 1.32982
\(540\) 14.3843 0.619000
\(541\) −37.1944 −1.59911 −0.799557 0.600590i \(-0.794932\pi\)
−0.799557 + 0.600590i \(0.794932\pi\)
\(542\) 6.47266 0.278025
\(543\) 14.8533 0.637416
\(544\) −13.9947 −0.600016
\(545\) 29.0541 1.24454
\(546\) 21.8915 0.936869
\(547\) 36.3923 1.55602 0.778010 0.628251i \(-0.216229\pi\)
0.778010 + 0.628251i \(0.216229\pi\)
\(548\) −58.5082 −2.49935
\(549\) −3.63123 −0.154977
\(550\) 4.24657 0.181074
\(551\) 3.01369 0.128387
\(552\) 19.5066 0.830257
\(553\) 5.95085 0.253056
\(554\) −21.8027 −0.926309
\(555\) 26.3025 1.11648
\(556\) 45.3223 1.92209
\(557\) −28.1065 −1.19091 −0.595455 0.803388i \(-0.703028\pi\)
−0.595455 + 0.803388i \(0.703028\pi\)
\(558\) −10.4600 −0.442807
\(559\) 23.4493 0.991800
\(560\) −16.2481 −0.686607
\(561\) −36.4893 −1.54058
\(562\) 9.75882 0.411651
\(563\) 2.93732 0.123793 0.0618966 0.998083i \(-0.480285\pi\)
0.0618966 + 0.998083i \(0.480285\pi\)
\(564\) 122.626 5.16347
\(565\) 17.1921 0.723277
\(566\) −26.7531 −1.12452
\(567\) 7.20137 0.302429
\(568\) −13.2838 −0.557377
\(569\) 10.0156 0.419874 0.209937 0.977715i \(-0.432674\pi\)
0.209937 + 0.977715i \(0.432674\pi\)
\(570\) −26.3534 −1.10382
\(571\) 19.7007 0.824447 0.412224 0.911083i \(-0.364752\pi\)
0.412224 + 0.911083i \(0.364752\pi\)
\(572\) −76.1158 −3.18256
\(573\) −19.0402 −0.795414
\(574\) 30.3816 1.26810
\(575\) −0.395409 −0.0164897
\(576\) −3.15896 −0.131623
\(577\) −10.4580 −0.435372 −0.217686 0.976019i \(-0.569851\pi\)
−0.217686 + 0.976019i \(0.569851\pi\)
\(578\) 23.9358 0.995598
\(579\) −39.7663 −1.65263
\(580\) 17.6021 0.730887
\(581\) 17.0570 0.707645
\(582\) 68.0774 2.82190
\(583\) −57.2799 −2.37229
\(584\) 67.9684 2.81255
\(585\) 27.0204 1.11715
\(586\) −59.8596 −2.47278
\(587\) −2.33653 −0.0964388 −0.0482194 0.998837i \(-0.515355\pi\)
−0.0482194 + 0.998837i \(0.515355\pi\)
\(588\) −67.8503 −2.79810
\(589\) 2.04070 0.0840855
\(590\) −43.3884 −1.78627
\(591\) −36.6092 −1.50590
\(592\) 30.7512 1.26387
\(593\) 37.4259 1.53690 0.768449 0.639911i \(-0.221029\pi\)
0.768449 + 0.639911i \(0.221029\pi\)
\(594\) 18.4363 0.756450
\(595\) −6.47931 −0.265626
\(596\) 10.7699 0.441152
\(597\) −12.7620 −0.522313
\(598\) 10.2727 0.420083
\(599\) −10.6432 −0.434869 −0.217434 0.976075i \(-0.569769\pi\)
−0.217434 + 0.976075i \(0.569769\pi\)
\(600\) −5.13809 −0.209762
\(601\) 23.1478 0.944217 0.472108 0.881541i \(-0.343493\pi\)
0.472108 + 0.881541i \(0.343493\pi\)
\(602\) 18.4067 0.750201
\(603\) −53.9889 −2.19860
\(604\) 80.4086 3.27178
\(605\) 36.5549 1.48617
\(606\) −88.2067 −3.58315
\(607\) −31.5986 −1.28255 −0.641273 0.767313i \(-0.721593\pi\)
−0.641273 + 0.767313i \(0.721593\pi\)
\(608\) −8.93754 −0.362465
\(609\) −4.47660 −0.181401
\(610\) 5.99748 0.242831
\(611\) 35.5536 1.43835
\(612\) 43.4490 1.75632
\(613\) 41.8023 1.68838 0.844190 0.536045i \(-0.180082\pi\)
0.844190 + 0.536045i \(0.180082\pi\)
\(614\) −2.49349 −0.100629
\(615\) 69.2112 2.79086
\(616\) −32.8943 −1.32535
\(617\) −43.4379 −1.74874 −0.874372 0.485256i \(-0.838727\pi\)
−0.874372 + 0.485256i \(0.838727\pi\)
\(618\) −36.3681 −1.46294
\(619\) −43.6686 −1.75519 −0.877594 0.479405i \(-0.840852\pi\)
−0.877594 + 0.479405i \(0.840852\pi\)
\(620\) 11.9191 0.478684
\(621\) −1.71665 −0.0688869
\(622\) 46.6446 1.87028
\(623\) 6.41112 0.256856
\(624\) 58.3050 2.33407
\(625\) −26.5095 −1.06038
\(626\) −40.4696 −1.61749
\(627\) −23.3035 −0.930651
\(628\) 44.3293 1.76893
\(629\) 12.2628 0.488949
\(630\) 21.2098 0.845020
\(631\) −24.9021 −0.991336 −0.495668 0.868512i \(-0.665077\pi\)
−0.495668 + 0.868512i \(0.665077\pi\)
\(632\) 36.2864 1.44340
\(633\) 22.9282 0.911315
\(634\) −64.5761 −2.56465
\(635\) −29.4118 −1.16717
\(636\) 125.883 4.99158
\(637\) −19.6723 −0.779444
\(638\) 22.5605 0.893181
\(639\) 7.57396 0.299621
\(640\) 28.6793 1.13365
\(641\) −48.4140 −1.91224 −0.956119 0.292978i \(-0.905354\pi\)
−0.956119 + 0.292978i \(0.905354\pi\)
\(642\) −32.5992 −1.28659
\(643\) −49.5208 −1.95291 −0.976456 0.215718i \(-0.930791\pi\)
−0.976456 + 0.215718i \(0.930791\pi\)
\(644\) 5.56326 0.219223
\(645\) 41.9316 1.65106
\(646\) −12.2865 −0.483406
\(647\) 44.5616 1.75190 0.875948 0.482406i \(-0.160237\pi\)
0.875948 + 0.482406i \(0.160237\pi\)
\(648\) 43.9117 1.72502
\(649\) −38.3670 −1.50604
\(650\) −2.70586 −0.106132
\(651\) −3.03130 −0.118806
\(652\) 59.8793 2.34505
\(653\) 23.0276 0.901141 0.450571 0.892741i \(-0.351221\pi\)
0.450571 + 0.892741i \(0.351221\pi\)
\(654\) −81.8383 −3.20013
\(655\) 29.6927 1.16019
\(656\) 80.9173 3.15929
\(657\) −38.7532 −1.51191
\(658\) 27.9081 1.08797
\(659\) −22.2955 −0.868510 −0.434255 0.900790i \(-0.642988\pi\)
−0.434255 + 0.900790i \(0.642988\pi\)
\(660\) −136.109 −5.29803
\(661\) 46.4407 1.80634 0.903168 0.429288i \(-0.141236\pi\)
0.903168 + 0.429288i \(0.141236\pi\)
\(662\) 17.3015 0.672441
\(663\) 23.2505 0.902975
\(664\) 104.009 4.03631
\(665\) −4.13794 −0.160462
\(666\) −40.1418 −1.55546
\(667\) −2.10067 −0.0813384
\(668\) −13.0222 −0.503843
\(669\) −8.71109 −0.336790
\(670\) 89.1701 3.44494
\(671\) 5.30337 0.204734
\(672\) 13.2760 0.512134
\(673\) 5.74251 0.221357 0.110679 0.993856i \(-0.464698\pi\)
0.110679 + 0.993856i \(0.464698\pi\)
\(674\) −53.9833 −2.07936
\(675\) 0.452170 0.0174040
\(676\) −9.34896 −0.359575
\(677\) −3.41592 −0.131285 −0.0656423 0.997843i \(-0.520910\pi\)
−0.0656423 + 0.997843i \(0.520910\pi\)
\(678\) −48.4260 −1.85979
\(679\) 10.6893 0.410218
\(680\) −39.5088 −1.51509
\(681\) 65.5929 2.51353
\(682\) 15.2767 0.584976
\(683\) −32.6551 −1.24951 −0.624756 0.780820i \(-0.714802\pi\)
−0.624756 + 0.780820i \(0.714802\pi\)
\(684\) 27.7482 1.06098
\(685\) −30.3342 −1.15901
\(686\) −33.5820 −1.28217
\(687\) 44.4144 1.69451
\(688\) 49.0238 1.86901
\(689\) 36.4980 1.39046
\(690\) 18.3695 0.699315
\(691\) −13.1401 −0.499873 −0.249936 0.968262i \(-0.580410\pi\)
−0.249936 + 0.968262i \(0.580410\pi\)
\(692\) 25.8565 0.982918
\(693\) 18.7552 0.712449
\(694\) 0.305236 0.0115866
\(695\) 23.4978 0.891321
\(696\) −27.2969 −1.03469
\(697\) 32.2677 1.22223
\(698\) 23.7383 0.898507
\(699\) 20.6133 0.779668
\(700\) −1.46538 −0.0553860
\(701\) −21.7553 −0.821686 −0.410843 0.911706i \(-0.634766\pi\)
−0.410843 + 0.911706i \(0.634766\pi\)
\(702\) −11.7474 −0.443376
\(703\) 7.83148 0.295370
\(704\) 4.61363 0.173883
\(705\) 63.5764 2.39443
\(706\) 77.1871 2.90497
\(707\) −13.8500 −0.520881
\(708\) 84.3183 3.16888
\(709\) 9.15783 0.343930 0.171965 0.985103i \(-0.444988\pi\)
0.171965 + 0.985103i \(0.444988\pi\)
\(710\) −12.5094 −0.469471
\(711\) −20.6892 −0.775907
\(712\) 39.0930 1.46507
\(713\) −1.42246 −0.0532714
\(714\) 18.2507 0.683014
\(715\) −39.4629 −1.47583
\(716\) −12.1343 −0.453481
\(717\) 53.4447 1.99593
\(718\) 53.6181 2.00101
\(719\) −27.5086 −1.02590 −0.512948 0.858419i \(-0.671447\pi\)
−0.512948 + 0.858419i \(0.671447\pi\)
\(720\) 56.4895 2.10524
\(721\) −5.71041 −0.212667
\(722\) 40.4071 1.50380
\(723\) 17.3890 0.646706
\(724\) 25.8307 0.959989
\(725\) 0.553322 0.0205499
\(726\) −102.966 −3.82144
\(727\) −3.14110 −0.116497 −0.0582485 0.998302i \(-0.518552\pi\)
−0.0582485 + 0.998302i \(0.518552\pi\)
\(728\) 20.9598 0.776823
\(729\) −35.7924 −1.32564
\(730\) 64.0062 2.36898
\(731\) 19.5494 0.723060
\(732\) −11.6551 −0.430785
\(733\) 19.5963 0.723807 0.361903 0.932216i \(-0.382127\pi\)
0.361903 + 0.932216i \(0.382127\pi\)
\(734\) 15.6684 0.578331
\(735\) −35.1776 −1.29755
\(736\) 6.22986 0.229636
\(737\) 78.8502 2.90449
\(738\) −105.627 −3.88819
\(739\) 30.4179 1.11894 0.559470 0.828851i \(-0.311005\pi\)
0.559470 + 0.828851i \(0.311005\pi\)
\(740\) 45.7415 1.68149
\(741\) 14.8487 0.545480
\(742\) 28.6494 1.05175
\(743\) 20.0776 0.736575 0.368288 0.929712i \(-0.379944\pi\)
0.368288 + 0.929712i \(0.379944\pi\)
\(744\) −18.4839 −0.677654
\(745\) 5.58375 0.204573
\(746\) −56.6977 −2.07585
\(747\) −59.3020 −2.16975
\(748\) −63.4568 −2.32021
\(749\) −5.11862 −0.187030
\(750\) 70.1256 2.56063
\(751\) −6.34154 −0.231406 −0.115703 0.993284i \(-0.536912\pi\)
−0.115703 + 0.993284i \(0.536912\pi\)
\(752\) 74.3295 2.71052
\(753\) 0.882078 0.0321447
\(754\) −14.3753 −0.523517
\(755\) 41.6886 1.51720
\(756\) −6.36187 −0.231379
\(757\) −17.4100 −0.632776 −0.316388 0.948630i \(-0.602470\pi\)
−0.316388 + 0.948630i \(0.602470\pi\)
\(758\) 52.9790 1.92428
\(759\) 16.2435 0.589603
\(760\) −25.2319 −0.915256
\(761\) −38.5466 −1.39731 −0.698656 0.715458i \(-0.746218\pi\)
−0.698656 + 0.715458i \(0.746218\pi\)
\(762\) 82.8460 3.00119
\(763\) −12.8500 −0.465202
\(764\) −33.1118 −1.19794
\(765\) 22.5265 0.814449
\(766\) −17.1833 −0.620857
\(767\) 24.4470 0.882728
\(768\) −76.2256 −2.75055
\(769\) −47.3557 −1.70769 −0.853845 0.520527i \(-0.825735\pi\)
−0.853845 + 0.520527i \(0.825735\pi\)
\(770\) −30.9767 −1.11632
\(771\) 14.4556 0.520607
\(772\) −69.1556 −2.48896
\(773\) 52.2686 1.87997 0.939986 0.341213i \(-0.110838\pi\)
0.939986 + 0.341213i \(0.110838\pi\)
\(774\) −63.9943 −2.30023
\(775\) 0.374678 0.0134588
\(776\) 65.1801 2.33983
\(777\) −11.6331 −0.417334
\(778\) −36.1885 −1.29742
\(779\) 20.6074 0.738336
\(780\) 86.7269 3.10532
\(781\) −11.0617 −0.395818
\(782\) 8.56424 0.306257
\(783\) 2.40222 0.0858485
\(784\) −41.1274 −1.46884
\(785\) 22.9830 0.820297
\(786\) −83.6371 −2.98324
\(787\) 26.1883 0.933511 0.466756 0.884386i \(-0.345423\pi\)
0.466756 + 0.884386i \(0.345423\pi\)
\(788\) −63.6653 −2.26798
\(789\) 58.9697 2.09938
\(790\) 34.1711 1.21575
\(791\) −7.60371 −0.270357
\(792\) 114.363 4.06372
\(793\) −3.37924 −0.120000
\(794\) 39.9018 1.41606
\(795\) 65.2651 2.31472
\(796\) −22.1938 −0.786637
\(797\) −11.0850 −0.392650 −0.196325 0.980539i \(-0.562901\pi\)
−0.196325 + 0.980539i \(0.562901\pi\)
\(798\) 11.6556 0.412603
\(799\) 29.6406 1.04861
\(800\) −1.64096 −0.0580167
\(801\) −22.2895 −0.787559
\(802\) −52.6747 −1.86001
\(803\) 56.5986 1.99732
\(804\) −173.287 −6.11138
\(805\) 2.88433 0.101659
\(806\) −9.73414 −0.342870
\(807\) 66.4654 2.33969
\(808\) −84.4528 −2.97104
\(809\) 17.3132 0.608698 0.304349 0.952561i \(-0.401561\pi\)
0.304349 + 0.952561i \(0.401561\pi\)
\(810\) 41.3519 1.45296
\(811\) −22.9372 −0.805435 −0.402717 0.915324i \(-0.631934\pi\)
−0.402717 + 0.915324i \(0.631934\pi\)
\(812\) −7.78504 −0.273201
\(813\) −6.52147 −0.228718
\(814\) 58.6267 2.05487
\(815\) 31.0450 1.08746
\(816\) 48.6082 1.70163
\(817\) 12.4850 0.436795
\(818\) −12.0785 −0.422315
\(819\) −11.9505 −0.417586
\(820\) 120.362 4.20322
\(821\) 23.9003 0.834128 0.417064 0.908877i \(-0.363059\pi\)
0.417064 + 0.908877i \(0.363059\pi\)
\(822\) 85.4440 2.98020
\(823\) −34.0190 −1.18583 −0.592913 0.805266i \(-0.702022\pi\)
−0.592913 + 0.805266i \(0.702022\pi\)
\(824\) −34.8203 −1.21302
\(825\) −4.27859 −0.148961
\(826\) 19.1898 0.667699
\(827\) −12.0353 −0.418509 −0.209254 0.977861i \(-0.567104\pi\)
−0.209254 + 0.977861i \(0.567104\pi\)
\(828\) −19.3417 −0.672171
\(829\) −18.0819 −0.628012 −0.314006 0.949421i \(-0.601671\pi\)
−0.314006 + 0.949421i \(0.601671\pi\)
\(830\) 97.9454 3.39974
\(831\) 21.9671 0.762031
\(832\) −2.93975 −0.101917
\(833\) −16.4005 −0.568245
\(834\) −66.1876 −2.29189
\(835\) −6.75147 −0.233644
\(836\) −40.5259 −1.40162
\(837\) 1.62665 0.0562253
\(838\) −50.4930 −1.74425
\(839\) 41.2960 1.42570 0.712848 0.701318i \(-0.247405\pi\)
0.712848 + 0.701318i \(0.247405\pi\)
\(840\) 37.4800 1.29318
\(841\) −26.0604 −0.898634
\(842\) −25.2452 −0.870007
\(843\) −9.83240 −0.338646
\(844\) 39.8733 1.37250
\(845\) −4.84706 −0.166744
\(846\) −97.0277 −3.33588
\(847\) −16.1675 −0.555521
\(848\) 76.3038 2.62028
\(849\) 26.9549 0.925089
\(850\) −2.25584 −0.0773747
\(851\) −5.45889 −0.187128
\(852\) 24.3100 0.832848
\(853\) 3.23885 0.110896 0.0554480 0.998462i \(-0.482341\pi\)
0.0554480 + 0.998462i \(0.482341\pi\)
\(854\) −2.65256 −0.0907688
\(855\) 14.3863 0.492002
\(856\) −31.2118 −1.06680
\(857\) −18.3234 −0.625916 −0.312958 0.949767i \(-0.601320\pi\)
−0.312958 + 0.949767i \(0.601320\pi\)
\(858\) 111.158 3.79486
\(859\) −33.9225 −1.15742 −0.578711 0.815533i \(-0.696444\pi\)
−0.578711 + 0.815533i \(0.696444\pi\)
\(860\) 72.9213 2.48660
\(861\) −30.6107 −1.04321
\(862\) 68.8809 2.34609
\(863\) −51.0173 −1.73665 −0.868325 0.495995i \(-0.834803\pi\)
−0.868325 + 0.495995i \(0.834803\pi\)
\(864\) −7.12415 −0.242369
\(865\) 13.4056 0.455803
\(866\) −66.2684 −2.25189
\(867\) −24.1163 −0.819032
\(868\) −5.27159 −0.178929
\(869\) 30.2164 1.02502
\(870\) −25.7057 −0.871503
\(871\) −50.2424 −1.70240
\(872\) −78.3554 −2.65345
\(873\) −37.1634 −1.25779
\(874\) 5.46945 0.185007
\(875\) 11.0109 0.372237
\(876\) −124.386 −4.20260
\(877\) −11.6024 −0.391785 −0.195893 0.980625i \(-0.562760\pi\)
−0.195893 + 0.980625i \(0.562760\pi\)
\(878\) 58.0206 1.95810
\(879\) 60.3110 2.03424
\(880\) −82.5024 −2.78115
\(881\) −25.3671 −0.854638 −0.427319 0.904101i \(-0.640542\pi\)
−0.427319 + 0.904101i \(0.640542\pi\)
\(882\) 53.6867 1.80772
\(883\) −43.4063 −1.46074 −0.730369 0.683053i \(-0.760652\pi\)
−0.730369 + 0.683053i \(0.760652\pi\)
\(884\) 40.4338 1.35994
\(885\) 43.7156 1.46948
\(886\) 69.0065 2.31832
\(887\) 16.8270 0.564996 0.282498 0.959268i \(-0.408837\pi\)
0.282498 + 0.959268i \(0.408837\pi\)
\(888\) −70.9348 −2.38042
\(889\) 13.0082 0.436282
\(890\) 36.8141 1.23401
\(891\) 36.5662 1.22501
\(892\) −15.1490 −0.507227
\(893\) 18.9297 0.633457
\(894\) −15.7281 −0.526026
\(895\) −6.29115 −0.210290
\(896\) −12.6843 −0.423751
\(897\) −10.3502 −0.345582
\(898\) −54.0088 −1.80230
\(899\) 1.99054 0.0663881
\(900\) 5.09465 0.169822
\(901\) 30.4279 1.01370
\(902\) 154.268 5.13655
\(903\) −18.5455 −0.617155
\(904\) −46.3651 −1.54208
\(905\) 13.3922 0.445170
\(906\) −117.427 −3.90124
\(907\) −38.1979 −1.26834 −0.634170 0.773193i \(-0.718658\pi\)
−0.634170 + 0.773193i \(0.718658\pi\)
\(908\) 114.070 3.78553
\(909\) 48.1520 1.59710
\(910\) 19.7380 0.654308
\(911\) 28.1937 0.934099 0.467049 0.884231i \(-0.345317\pi\)
0.467049 + 0.884231i \(0.345317\pi\)
\(912\) 31.0431 1.02794
\(913\) 86.6099 2.86637
\(914\) 63.2739 2.09292
\(915\) −6.04270 −0.199766
\(916\) 77.2389 2.55204
\(917\) −13.1324 −0.433672
\(918\) −9.79363 −0.323238
\(919\) −51.2018 −1.68899 −0.844496 0.535561i \(-0.820100\pi\)
−0.844496 + 0.535561i \(0.820100\pi\)
\(920\) 17.5877 0.579850
\(921\) 2.51229 0.0827829
\(922\) −73.3262 −2.41487
\(923\) 7.04837 0.232000
\(924\) 60.1982 1.98037
\(925\) 1.43788 0.0472773
\(926\) −27.7857 −0.913096
\(927\) 19.8533 0.652068
\(928\) −8.71785 −0.286177
\(929\) −28.4086 −0.932056 −0.466028 0.884770i \(-0.654315\pi\)
−0.466028 + 0.884770i \(0.654315\pi\)
\(930\) −17.4064 −0.570779
\(931\) −10.4740 −0.343272
\(932\) 35.8477 1.17423
\(933\) −46.9964 −1.53859
\(934\) −56.0578 −1.83427
\(935\) −32.8998 −1.07594
\(936\) −72.8707 −2.38185
\(937\) 14.7153 0.480728 0.240364 0.970683i \(-0.422733\pi\)
0.240364 + 0.970683i \(0.422733\pi\)
\(938\) −39.4381 −1.28770
\(939\) 40.7747 1.33063
\(940\) 110.563 3.60616
\(941\) 18.2326 0.594365 0.297183 0.954821i \(-0.403953\pi\)
0.297183 + 0.954821i \(0.403953\pi\)
\(942\) −64.7375 −2.10926
\(943\) −14.3643 −0.467765
\(944\) 51.1095 1.66347
\(945\) −3.29837 −0.107296
\(946\) 93.4630 3.03875
\(947\) −40.5452 −1.31754 −0.658771 0.752343i \(-0.728924\pi\)
−0.658771 + 0.752343i \(0.728924\pi\)
\(948\) −66.4059 −2.15676
\(949\) −36.0639 −1.17068
\(950\) −1.44067 −0.0467414
\(951\) 65.0631 2.10981
\(952\) 17.4739 0.566334
\(953\) 1.49813 0.0485291 0.0242645 0.999706i \(-0.492276\pi\)
0.0242645 + 0.999706i \(0.492276\pi\)
\(954\) −99.6050 −3.22483
\(955\) −17.1671 −0.555516
\(956\) 92.9430 3.00599
\(957\) −22.7307 −0.734778
\(958\) 57.8201 1.86808
\(959\) 13.4162 0.433231
\(960\) −5.25680 −0.169663
\(961\) −29.6521 −0.956520
\(962\) −37.3562 −1.20441
\(963\) 17.7959 0.573463
\(964\) 30.2405 0.973980
\(965\) −35.8544 −1.15419
\(966\) −8.12445 −0.261400
\(967\) −25.7047 −0.826607 −0.413303 0.910593i \(-0.635625\pi\)
−0.413303 + 0.910593i \(0.635625\pi\)
\(968\) −98.5843 −3.16862
\(969\) 12.3792 0.397676
\(970\) 61.3805 1.97081
\(971\) 41.8327 1.34247 0.671237 0.741243i \(-0.265763\pi\)
0.671237 + 0.741243i \(0.265763\pi\)
\(972\) −99.0650 −3.17751
\(973\) −10.3926 −0.333171
\(974\) 95.0816 3.04661
\(975\) 2.72626 0.0873102
\(976\) −7.06474 −0.226137
\(977\) −19.4714 −0.622945 −0.311472 0.950255i \(-0.600822\pi\)
−0.311472 + 0.950255i \(0.600822\pi\)
\(978\) −87.4462 −2.79622
\(979\) 32.5535 1.04041
\(980\) −61.1757 −1.95419
\(981\) 44.6755 1.42638
\(982\) 73.3680 2.34127
\(983\) 28.5364 0.910170 0.455085 0.890448i \(-0.349609\pi\)
0.455085 + 0.890448i \(0.349609\pi\)
\(984\) −186.654 −5.95033
\(985\) −33.0079 −1.05172
\(986\) −11.9845 −0.381664
\(987\) −28.1185 −0.895023
\(988\) 25.8226 0.821527
\(989\) −8.70259 −0.276726
\(990\) 107.696 3.42282
\(991\) 21.2895 0.676284 0.338142 0.941095i \(-0.390202\pi\)
0.338142 + 0.941095i \(0.390202\pi\)
\(992\) −5.90324 −0.187428
\(993\) −17.4319 −0.553186
\(994\) 5.53267 0.175486
\(995\) −11.5066 −0.364783
\(996\) −190.341 −6.03118
\(997\) 24.2323 0.767445 0.383722 0.923448i \(-0.374642\pi\)
0.383722 + 0.923448i \(0.374642\pi\)
\(998\) −91.7365 −2.90387
\(999\) 6.24251 0.197504
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 6007.2.a.c.1.12 261
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6007.2.a.c.1.12 261 1.1 even 1 trivial