Properties

Label 4006.2.a.h.1.1
Level $4006$
Weight $2$
Character 4006.1
Self dual yes
Analytic conductor $31.988$
Analytic rank $0$
Dimension $42$
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] = [4006,2,Mod(1,4006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4006, 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("4006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4006.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: \(31.9880710497\)
Analytic rank: \(0\)
Dimension: \(42\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.21265 q^{3} +1.00000 q^{4} +3.26318 q^{5} +3.21265 q^{6} -3.74888 q^{7} -1.00000 q^{8} +7.32111 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.21265 q^{3} +1.00000 q^{4} +3.26318 q^{5} +3.21265 q^{6} -3.74888 q^{7} -1.00000 q^{8} +7.32111 q^{9} -3.26318 q^{10} +2.74731 q^{11} -3.21265 q^{12} +1.96912 q^{13} +3.74888 q^{14} -10.4834 q^{15} +1.00000 q^{16} +2.78943 q^{17} -7.32111 q^{18} +5.90910 q^{19} +3.26318 q^{20} +12.0438 q^{21} -2.74731 q^{22} +0.836221 q^{23} +3.21265 q^{24} +5.64833 q^{25} -1.96912 q^{26} -13.8822 q^{27} -3.74888 q^{28} +3.74478 q^{29} +10.4834 q^{30} +6.96260 q^{31} -1.00000 q^{32} -8.82615 q^{33} -2.78943 q^{34} -12.2333 q^{35} +7.32111 q^{36} -9.58970 q^{37} -5.90910 q^{38} -6.32609 q^{39} -3.26318 q^{40} +11.2749 q^{41} -12.0438 q^{42} +6.25743 q^{43} +2.74731 q^{44} +23.8901 q^{45} -0.836221 q^{46} -7.60552 q^{47} -3.21265 q^{48} +7.05412 q^{49} -5.64833 q^{50} -8.96145 q^{51} +1.96912 q^{52} +13.6811 q^{53} +13.8822 q^{54} +8.96497 q^{55} +3.74888 q^{56} -18.9839 q^{57} -3.74478 q^{58} -3.51087 q^{59} -10.4834 q^{60} +5.81031 q^{61} -6.96260 q^{62} -27.4460 q^{63} +1.00000 q^{64} +6.42559 q^{65} +8.82615 q^{66} -0.257564 q^{67} +2.78943 q^{68} -2.68648 q^{69} +12.2333 q^{70} -4.76765 q^{71} -7.32111 q^{72} +11.5717 q^{73} +9.58970 q^{74} -18.1461 q^{75} +5.90910 q^{76} -10.2994 q^{77} +6.32609 q^{78} -7.34390 q^{79} +3.26318 q^{80} +22.6353 q^{81} -11.2749 q^{82} -11.0188 q^{83} +12.0438 q^{84} +9.10240 q^{85} -6.25743 q^{86} -12.0307 q^{87} -2.74731 q^{88} -11.4928 q^{89} -23.8901 q^{90} -7.38200 q^{91} +0.836221 q^{92} -22.3684 q^{93} +7.60552 q^{94} +19.2825 q^{95} +3.21265 q^{96} -9.25349 q^{97} -7.05412 q^{98} +20.1134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.21265 −1.85482 −0.927412 0.374043i \(-0.877971\pi\)
−0.927412 + 0.374043i \(0.877971\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.26318 1.45934 0.729669 0.683801i \(-0.239674\pi\)
0.729669 + 0.683801i \(0.239674\pi\)
\(6\) 3.21265 1.31156
\(7\) −3.74888 −1.41694 −0.708472 0.705739i \(-0.750615\pi\)
−0.708472 + 0.705739i \(0.750615\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.32111 2.44037
\(10\) −3.26318 −1.03191
\(11\) 2.74731 0.828346 0.414173 0.910198i \(-0.364071\pi\)
0.414173 + 0.910198i \(0.364071\pi\)
\(12\) −3.21265 −0.927412
\(13\) 1.96912 0.546136 0.273068 0.961995i \(-0.411962\pi\)
0.273068 + 0.961995i \(0.411962\pi\)
\(14\) 3.74888 1.00193
\(15\) −10.4834 −2.70681
\(16\) 1.00000 0.250000
\(17\) 2.78943 0.676536 0.338268 0.941050i \(-0.390159\pi\)
0.338268 + 0.941050i \(0.390159\pi\)
\(18\) −7.32111 −1.72560
\(19\) 5.90910 1.35564 0.677821 0.735227i \(-0.262925\pi\)
0.677821 + 0.735227i \(0.262925\pi\)
\(20\) 3.26318 0.729669
\(21\) 12.0438 2.62818
\(22\) −2.74731 −0.585729
\(23\) 0.836221 0.174364 0.0871821 0.996192i \(-0.472214\pi\)
0.0871821 + 0.996192i \(0.472214\pi\)
\(24\) 3.21265 0.655779
\(25\) 5.64833 1.12967
\(26\) −1.96912 −0.386176
\(27\) −13.8822 −2.67163
\(28\) −3.74888 −0.708472
\(29\) 3.74478 0.695388 0.347694 0.937608i \(-0.386965\pi\)
0.347694 + 0.937608i \(0.386965\pi\)
\(30\) 10.4834 1.91401
\(31\) 6.96260 1.25052 0.625260 0.780417i \(-0.284993\pi\)
0.625260 + 0.780417i \(0.284993\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.82615 −1.53644
\(34\) −2.78943 −0.478383
\(35\) −12.2333 −2.06780
\(36\) 7.32111 1.22018
\(37\) −9.58970 −1.57654 −0.788268 0.615331i \(-0.789022\pi\)
−0.788268 + 0.615331i \(0.789022\pi\)
\(38\) −5.90910 −0.958583
\(39\) −6.32609 −1.01299
\(40\) −3.26318 −0.515954
\(41\) 11.2749 1.76085 0.880423 0.474189i \(-0.157259\pi\)
0.880423 + 0.474189i \(0.157259\pi\)
\(42\) −12.0438 −1.85840
\(43\) 6.25743 0.954249 0.477124 0.878836i \(-0.341679\pi\)
0.477124 + 0.878836i \(0.341679\pi\)
\(44\) 2.74731 0.414173
\(45\) 23.8901 3.56132
\(46\) −0.836221 −0.123294
\(47\) −7.60552 −1.10938 −0.554690 0.832057i \(-0.687163\pi\)
−0.554690 + 0.832057i \(0.687163\pi\)
\(48\) −3.21265 −0.463706
\(49\) 7.05412 1.00773
\(50\) −5.64833 −0.798794
\(51\) −8.96145 −1.25485
\(52\) 1.96912 0.273068
\(53\) 13.6811 1.87925 0.939624 0.342207i \(-0.111175\pi\)
0.939624 + 0.342207i \(0.111175\pi\)
\(54\) 13.8822 1.88913
\(55\) 8.96497 1.20884
\(56\) 3.74888 0.500965
\(57\) −18.9839 −2.51447
\(58\) −3.74478 −0.491714
\(59\) −3.51087 −0.457076 −0.228538 0.973535i \(-0.573395\pi\)
−0.228538 + 0.973535i \(0.573395\pi\)
\(60\) −10.4834 −1.35341
\(61\) 5.81031 0.743934 0.371967 0.928246i \(-0.378684\pi\)
0.371967 + 0.928246i \(0.378684\pi\)
\(62\) −6.96260 −0.884251
\(63\) −27.4460 −3.45787
\(64\) 1.00000 0.125000
\(65\) 6.42559 0.796996
\(66\) 8.82615 1.08642
\(67\) −0.257564 −0.0314664 −0.0157332 0.999876i \(-0.505008\pi\)
−0.0157332 + 0.999876i \(0.505008\pi\)
\(68\) 2.78943 0.338268
\(69\) −2.68648 −0.323415
\(70\) 12.2333 1.46216
\(71\) −4.76765 −0.565815 −0.282908 0.959147i \(-0.591299\pi\)
−0.282908 + 0.959147i \(0.591299\pi\)
\(72\) −7.32111 −0.862801
\(73\) 11.5717 1.35437 0.677185 0.735813i \(-0.263200\pi\)
0.677185 + 0.735813i \(0.263200\pi\)
\(74\) 9.58970 1.11478
\(75\) −18.1461 −2.09533
\(76\) 5.90910 0.677821
\(77\) −10.2994 −1.17372
\(78\) 6.32609 0.716289
\(79\) −7.34390 −0.826253 −0.413127 0.910674i \(-0.635563\pi\)
−0.413127 + 0.910674i \(0.635563\pi\)
\(80\) 3.26318 0.364834
\(81\) 22.6353 2.51503
\(82\) −11.2749 −1.24511
\(83\) −11.0188 −1.20947 −0.604734 0.796428i \(-0.706721\pi\)
−0.604734 + 0.796428i \(0.706721\pi\)
\(84\) 12.0438 1.31409
\(85\) 9.10240 0.987294
\(86\) −6.25743 −0.674756
\(87\) −12.0307 −1.28982
\(88\) −2.74731 −0.292865
\(89\) −11.4928 −1.21823 −0.609116 0.793081i \(-0.708475\pi\)
−0.609116 + 0.793081i \(0.708475\pi\)
\(90\) −23.8901 −2.51823
\(91\) −7.38200 −0.773844
\(92\) 0.836221 0.0871821
\(93\) −22.3684 −2.31949
\(94\) 7.60552 0.784450
\(95\) 19.2825 1.97834
\(96\) 3.21265 0.327889
\(97\) −9.25349 −0.939549 −0.469775 0.882786i \(-0.655665\pi\)
−0.469775 + 0.882786i \(0.655665\pi\)
\(98\) −7.05412 −0.712573
\(99\) 20.1134 2.02147
\(100\) 5.64833 0.564833
\(101\) −0.874535 −0.0870195 −0.0435097 0.999053i \(-0.513854\pi\)
−0.0435097 + 0.999053i \(0.513854\pi\)
\(102\) 8.96145 0.887316
\(103\) 6.62031 0.652318 0.326159 0.945315i \(-0.394245\pi\)
0.326159 + 0.945315i \(0.394245\pi\)
\(104\) −1.96912 −0.193088
\(105\) 39.3012 3.83540
\(106\) −13.6811 −1.32883
\(107\) 13.7276 1.32710 0.663550 0.748132i \(-0.269049\pi\)
0.663550 + 0.748132i \(0.269049\pi\)
\(108\) −13.8822 −1.33581
\(109\) −8.01601 −0.767794 −0.383897 0.923376i \(-0.625418\pi\)
−0.383897 + 0.923376i \(0.625418\pi\)
\(110\) −8.96497 −0.854776
\(111\) 30.8083 2.92420
\(112\) −3.74888 −0.354236
\(113\) 9.74825 0.917039 0.458519 0.888684i \(-0.348380\pi\)
0.458519 + 0.888684i \(0.348380\pi\)
\(114\) 18.9839 1.77800
\(115\) 2.72874 0.254456
\(116\) 3.74478 0.347694
\(117\) 14.4161 1.33277
\(118\) 3.51087 0.323202
\(119\) −10.4572 −0.958613
\(120\) 10.4834 0.957003
\(121\) −3.45227 −0.313843
\(122\) −5.81031 −0.526041
\(123\) −36.2223 −3.26606
\(124\) 6.96260 0.625260
\(125\) 2.11561 0.189226
\(126\) 27.4460 2.44508
\(127\) 18.4658 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −20.1029 −1.76996
\(130\) −6.42559 −0.563561
\(131\) −15.5116 −1.35525 −0.677627 0.735406i \(-0.736991\pi\)
−0.677627 + 0.735406i \(0.736991\pi\)
\(132\) −8.82615 −0.768218
\(133\) −22.1525 −1.92087
\(134\) 0.257564 0.0222501
\(135\) −45.3001 −3.89881
\(136\) −2.78943 −0.239191
\(137\) −18.8452 −1.61005 −0.805025 0.593241i \(-0.797848\pi\)
−0.805025 + 0.593241i \(0.797848\pi\)
\(138\) 2.68648 0.228689
\(139\) 0.0766866 0.00650448 0.00325224 0.999995i \(-0.498965\pi\)
0.00325224 + 0.999995i \(0.498965\pi\)
\(140\) −12.2333 −1.03390
\(141\) 24.4339 2.05770
\(142\) 4.76765 0.400092
\(143\) 5.40979 0.452389
\(144\) 7.32111 0.610092
\(145\) 12.2199 1.01481
\(146\) −11.5717 −0.957684
\(147\) −22.6624 −1.86916
\(148\) −9.58970 −0.788268
\(149\) −12.4778 −1.02222 −0.511110 0.859515i \(-0.670766\pi\)
−0.511110 + 0.859515i \(0.670766\pi\)
\(150\) 18.1461 1.48162
\(151\) 12.8308 1.04415 0.522076 0.852899i \(-0.325158\pi\)
0.522076 + 0.852899i \(0.325158\pi\)
\(152\) −5.90910 −0.479292
\(153\) 20.4217 1.65100
\(154\) 10.2994 0.829946
\(155\) 22.7202 1.82493
\(156\) −6.32609 −0.506493
\(157\) −6.42567 −0.512824 −0.256412 0.966568i \(-0.582540\pi\)
−0.256412 + 0.966568i \(0.582540\pi\)
\(158\) 7.34390 0.584249
\(159\) −43.9527 −3.48567
\(160\) −3.26318 −0.257977
\(161\) −3.13490 −0.247064
\(162\) −22.6353 −1.77839
\(163\) 4.69912 0.368063 0.184032 0.982920i \(-0.441085\pi\)
0.184032 + 0.982920i \(0.441085\pi\)
\(164\) 11.2749 0.880423
\(165\) −28.8013 −2.24218
\(166\) 11.0188 0.855223
\(167\) −8.48757 −0.656788 −0.328394 0.944541i \(-0.606507\pi\)
−0.328394 + 0.944541i \(0.606507\pi\)
\(168\) −12.0438 −0.929202
\(169\) −9.12256 −0.701736
\(170\) −9.10240 −0.698122
\(171\) 43.2612 3.30826
\(172\) 6.25743 0.477124
\(173\) −13.6661 −1.03901 −0.519505 0.854467i \(-0.673884\pi\)
−0.519505 + 0.854467i \(0.673884\pi\)
\(174\) 12.0307 0.912042
\(175\) −21.1749 −1.60067
\(176\) 2.74731 0.207087
\(177\) 11.2792 0.847795
\(178\) 11.4928 0.861419
\(179\) 5.71596 0.427231 0.213616 0.976918i \(-0.431476\pi\)
0.213616 + 0.976918i \(0.431476\pi\)
\(180\) 23.8901 1.78066
\(181\) −7.17041 −0.532972 −0.266486 0.963839i \(-0.585863\pi\)
−0.266486 + 0.963839i \(0.585863\pi\)
\(182\) 7.38200 0.547190
\(183\) −18.6665 −1.37987
\(184\) −0.836221 −0.0616471
\(185\) −31.2929 −2.30070
\(186\) 22.3684 1.64013
\(187\) 7.66343 0.560406
\(188\) −7.60552 −0.554690
\(189\) 52.0427 3.78555
\(190\) −19.2825 −1.39890
\(191\) −5.12685 −0.370965 −0.185483 0.982648i \(-0.559385\pi\)
−0.185483 + 0.982648i \(0.559385\pi\)
\(192\) −3.21265 −0.231853
\(193\) 15.2315 1.09639 0.548193 0.836352i \(-0.315316\pi\)
0.548193 + 0.836352i \(0.315316\pi\)
\(194\) 9.25349 0.664362
\(195\) −20.6432 −1.47829
\(196\) 7.05412 0.503865
\(197\) −24.6358 −1.75523 −0.877616 0.479365i \(-0.840867\pi\)
−0.877616 + 0.479365i \(0.840867\pi\)
\(198\) −20.1134 −1.42940
\(199\) −11.8668 −0.841215 −0.420608 0.907243i \(-0.638183\pi\)
−0.420608 + 0.907243i \(0.638183\pi\)
\(200\) −5.64833 −0.399397
\(201\) 0.827461 0.0583646
\(202\) 0.874535 0.0615321
\(203\) −14.0387 −0.985326
\(204\) −8.96145 −0.627427
\(205\) 36.7921 2.56967
\(206\) −6.62031 −0.461259
\(207\) 6.12206 0.425513
\(208\) 1.96912 0.136534
\(209\) 16.2342 1.12294
\(210\) −39.3012 −2.71204
\(211\) 15.7996 1.08769 0.543843 0.839187i \(-0.316969\pi\)
0.543843 + 0.839187i \(0.316969\pi\)
\(212\) 13.6811 0.939624
\(213\) 15.3168 1.04949
\(214\) −13.7276 −0.938401
\(215\) 20.4191 1.39257
\(216\) 13.8822 0.944563
\(217\) −26.1020 −1.77192
\(218\) 8.01601 0.542913
\(219\) −37.1759 −2.51212
\(220\) 8.96497 0.604418
\(221\) 5.49272 0.369480
\(222\) −30.8083 −2.06772
\(223\) 5.02473 0.336481 0.168241 0.985746i \(-0.446191\pi\)
0.168241 + 0.985746i \(0.446191\pi\)
\(224\) 3.74888 0.250483
\(225\) 41.3520 2.75680
\(226\) −9.74825 −0.648444
\(227\) 13.3338 0.884994 0.442497 0.896770i \(-0.354093\pi\)
0.442497 + 0.896770i \(0.354093\pi\)
\(228\) −18.9839 −1.25724
\(229\) 28.5085 1.88389 0.941947 0.335760i \(-0.108993\pi\)
0.941947 + 0.335760i \(0.108993\pi\)
\(230\) −2.72874 −0.179928
\(231\) 33.0882 2.17704
\(232\) −3.74478 −0.245857
\(233\) 17.7156 1.16059 0.580294 0.814407i \(-0.302938\pi\)
0.580294 + 0.814407i \(0.302938\pi\)
\(234\) −14.4161 −0.942413
\(235\) −24.8182 −1.61896
\(236\) −3.51087 −0.228538
\(237\) 23.5934 1.53255
\(238\) 10.4572 0.677842
\(239\) 18.9752 1.22740 0.613701 0.789538i \(-0.289680\pi\)
0.613701 + 0.789538i \(0.289680\pi\)
\(240\) −10.4834 −0.676703
\(241\) −16.4613 −1.06037 −0.530183 0.847883i \(-0.677877\pi\)
−0.530183 + 0.847883i \(0.677877\pi\)
\(242\) 3.45227 0.221920
\(243\) −31.0726 −1.99331
\(244\) 5.81031 0.371967
\(245\) 23.0188 1.47062
\(246\) 36.2223 2.30945
\(247\) 11.6357 0.740364
\(248\) −6.96260 −0.442125
\(249\) 35.3994 2.24335
\(250\) −2.11561 −0.133803
\(251\) −23.6762 −1.49443 −0.747214 0.664584i \(-0.768609\pi\)
−0.747214 + 0.664584i \(0.768609\pi\)
\(252\) −27.4460 −1.72893
\(253\) 2.29736 0.144434
\(254\) −18.4658 −1.15865
\(255\) −29.2428 −1.83126
\(256\) 1.00000 0.0625000
\(257\) 27.8689 1.73841 0.869207 0.494449i \(-0.164630\pi\)
0.869207 + 0.494449i \(0.164630\pi\)
\(258\) 20.1029 1.25155
\(259\) 35.9507 2.23386
\(260\) 6.42559 0.398498
\(261\) 27.4159 1.69700
\(262\) 15.5116 0.958309
\(263\) −16.3752 −1.00974 −0.504868 0.863196i \(-0.668459\pi\)
−0.504868 + 0.863196i \(0.668459\pi\)
\(264\) 8.82615 0.543212
\(265\) 44.6440 2.74246
\(266\) 22.1525 1.35826
\(267\) 36.9222 2.25960
\(268\) −0.257564 −0.0157332
\(269\) 12.7426 0.776931 0.388465 0.921463i \(-0.373005\pi\)
0.388465 + 0.921463i \(0.373005\pi\)
\(270\) 45.3001 2.75687
\(271\) 20.2797 1.23190 0.615951 0.787784i \(-0.288772\pi\)
0.615951 + 0.787784i \(0.288772\pi\)
\(272\) 2.78943 0.169134
\(273\) 23.7158 1.43534
\(274\) 18.8452 1.13848
\(275\) 15.5177 0.935754
\(276\) −2.68648 −0.161707
\(277\) −5.78606 −0.347651 −0.173825 0.984776i \(-0.555613\pi\)
−0.173825 + 0.984776i \(0.555613\pi\)
\(278\) −0.0766866 −0.00459936
\(279\) 50.9739 3.05173
\(280\) 12.2333 0.731078
\(281\) 16.5039 0.984540 0.492270 0.870443i \(-0.336167\pi\)
0.492270 + 0.870443i \(0.336167\pi\)
\(282\) −24.4339 −1.45502
\(283\) −1.55336 −0.0923378 −0.0461689 0.998934i \(-0.514701\pi\)
−0.0461689 + 0.998934i \(0.514701\pi\)
\(284\) −4.76765 −0.282908
\(285\) −61.9477 −3.66947
\(286\) −5.40979 −0.319888
\(287\) −42.2683 −2.49502
\(288\) −7.32111 −0.431400
\(289\) −9.21909 −0.542300
\(290\) −12.2199 −0.717576
\(291\) 29.7282 1.74270
\(292\) 11.5717 0.677185
\(293\) 26.8358 1.56776 0.783881 0.620911i \(-0.213237\pi\)
0.783881 + 0.620911i \(0.213237\pi\)
\(294\) 22.6624 1.32170
\(295\) −11.4566 −0.667028
\(296\) 9.58970 0.557390
\(297\) −38.1387 −2.21303
\(298\) 12.4778 0.722819
\(299\) 1.64662 0.0952265
\(300\) −18.1461 −1.04766
\(301\) −23.4584 −1.35212
\(302\) −12.8308 −0.738327
\(303\) 2.80957 0.161406
\(304\) 5.90910 0.338910
\(305\) 18.9601 1.08565
\(306\) −20.4217 −1.16743
\(307\) −6.60978 −0.377240 −0.188620 0.982050i \(-0.560401\pi\)
−0.188620 + 0.982050i \(0.560401\pi\)
\(308\) −10.2994 −0.586860
\(309\) −21.2687 −1.20994
\(310\) −22.7202 −1.29042
\(311\) 9.25864 0.525009 0.262505 0.964931i \(-0.415451\pi\)
0.262505 + 0.964931i \(0.415451\pi\)
\(312\) 6.32609 0.358144
\(313\) 23.6357 1.33597 0.667983 0.744176i \(-0.267158\pi\)
0.667983 + 0.744176i \(0.267158\pi\)
\(314\) 6.42567 0.362621
\(315\) −89.5610 −5.04619
\(316\) −7.34390 −0.413127
\(317\) 26.1017 1.46602 0.733010 0.680218i \(-0.238115\pi\)
0.733010 + 0.680218i \(0.238115\pi\)
\(318\) 43.9527 2.46474
\(319\) 10.2881 0.576022
\(320\) 3.26318 0.182417
\(321\) −44.1020 −2.46153
\(322\) 3.13490 0.174701
\(323\) 16.4830 0.917140
\(324\) 22.6353 1.25752
\(325\) 11.1222 0.616951
\(326\) −4.69912 −0.260260
\(327\) 25.7526 1.42412
\(328\) −11.2749 −0.622553
\(329\) 28.5122 1.57193
\(330\) 28.8013 1.58546
\(331\) −29.3754 −1.61462 −0.807309 0.590129i \(-0.799077\pi\)
−0.807309 + 0.590129i \(0.799077\pi\)
\(332\) −11.0188 −0.604734
\(333\) −70.2072 −3.84733
\(334\) 8.48757 0.464419
\(335\) −0.840476 −0.0459201
\(336\) 12.0438 0.657045
\(337\) −25.5751 −1.39316 −0.696582 0.717477i \(-0.745297\pi\)
−0.696582 + 0.717477i \(0.745297\pi\)
\(338\) 9.12256 0.496202
\(339\) −31.3177 −1.70094
\(340\) 9.10240 0.493647
\(341\) 19.1284 1.03586
\(342\) −43.2612 −2.33930
\(343\) −0.202877 −0.0109544
\(344\) −6.25743 −0.337378
\(345\) −8.76648 −0.471971
\(346\) 13.6661 0.734692
\(347\) 14.6545 0.786695 0.393347 0.919390i \(-0.371317\pi\)
0.393347 + 0.919390i \(0.371317\pi\)
\(348\) −12.0307 −0.644911
\(349\) −12.8791 −0.689402 −0.344701 0.938713i \(-0.612020\pi\)
−0.344701 + 0.938713i \(0.612020\pi\)
\(350\) 21.1749 1.13185
\(351\) −27.3357 −1.45907
\(352\) −2.74731 −0.146432
\(353\) −0.410032 −0.0218238 −0.0109119 0.999940i \(-0.503473\pi\)
−0.0109119 + 0.999940i \(0.503473\pi\)
\(354\) −11.2792 −0.599482
\(355\) −15.5577 −0.825715
\(356\) −11.4928 −0.609116
\(357\) 33.5954 1.77806
\(358\) −5.71596 −0.302098
\(359\) 15.6921 0.828195 0.414097 0.910233i \(-0.364097\pi\)
0.414097 + 0.910233i \(0.364097\pi\)
\(360\) −23.8901 −1.25912
\(361\) 15.9175 0.837763
\(362\) 7.17041 0.376868
\(363\) 11.0909 0.582122
\(364\) −7.38200 −0.386922
\(365\) 37.7606 1.97648
\(366\) 18.6665 0.975712
\(367\) 29.7225 1.55150 0.775750 0.631040i \(-0.217372\pi\)
0.775750 + 0.631040i \(0.217372\pi\)
\(368\) 0.836221 0.0435911
\(369\) 82.5449 4.29711
\(370\) 31.2929 1.62684
\(371\) −51.2890 −2.66279
\(372\) −22.3684 −1.15975
\(373\) −0.737493 −0.0381859 −0.0190930 0.999818i \(-0.506078\pi\)
−0.0190930 + 0.999818i \(0.506078\pi\)
\(374\) −7.66343 −0.396267
\(375\) −6.79670 −0.350980
\(376\) 7.60552 0.392225
\(377\) 7.37392 0.379776
\(378\) −52.0427 −2.67679
\(379\) 17.5835 0.903203 0.451602 0.892220i \(-0.350853\pi\)
0.451602 + 0.892220i \(0.350853\pi\)
\(380\) 19.2825 0.989169
\(381\) −59.3242 −3.03927
\(382\) 5.12685 0.262312
\(383\) 13.0037 0.664456 0.332228 0.943199i \(-0.392200\pi\)
0.332228 + 0.943199i \(0.392200\pi\)
\(384\) 3.21265 0.163945
\(385\) −33.6086 −1.71285
\(386\) −15.2315 −0.775262
\(387\) 45.8113 2.32872
\(388\) −9.25349 −0.469775
\(389\) −13.8361 −0.701521 −0.350760 0.936465i \(-0.614077\pi\)
−0.350760 + 0.936465i \(0.614077\pi\)
\(390\) 20.6432 1.04531
\(391\) 2.33258 0.117964
\(392\) −7.05412 −0.356287
\(393\) 49.8332 2.51375
\(394\) 24.6358 1.24114
\(395\) −23.9645 −1.20578
\(396\) 20.1134 1.01074
\(397\) 29.0131 1.45613 0.728064 0.685509i \(-0.240420\pi\)
0.728064 + 0.685509i \(0.240420\pi\)
\(398\) 11.8668 0.594829
\(399\) 71.1683 3.56287
\(400\) 5.64833 0.282416
\(401\) 35.9816 1.79684 0.898419 0.439140i \(-0.144717\pi\)
0.898419 + 0.439140i \(0.144717\pi\)
\(402\) −0.827461 −0.0412700
\(403\) 13.7102 0.682953
\(404\) −0.874535 −0.0435097
\(405\) 73.8629 3.67028
\(406\) 14.0387 0.696731
\(407\) −26.3459 −1.30592
\(408\) 8.96145 0.443658
\(409\) −22.3444 −1.10486 −0.552429 0.833560i \(-0.686299\pi\)
−0.552429 + 0.833560i \(0.686299\pi\)
\(410\) −36.7921 −1.81703
\(411\) 60.5428 2.98636
\(412\) 6.62031 0.326159
\(413\) 13.1618 0.647651
\(414\) −6.12206 −0.300883
\(415\) −35.9562 −1.76502
\(416\) −1.96912 −0.0965441
\(417\) −0.246367 −0.0120647
\(418\) −16.2342 −0.794039
\(419\) −33.6052 −1.64172 −0.820860 0.571130i \(-0.806505\pi\)
−0.820860 + 0.571130i \(0.806505\pi\)
\(420\) 39.3012 1.91770
\(421\) −15.3383 −0.747543 −0.373772 0.927521i \(-0.621936\pi\)
−0.373772 + 0.927521i \(0.621936\pi\)
\(422\) −15.7996 −0.769111
\(423\) −55.6808 −2.70729
\(424\) −13.6811 −0.664415
\(425\) 15.7556 0.764259
\(426\) −15.3168 −0.742100
\(427\) −21.7822 −1.05411
\(428\) 13.7276 0.663550
\(429\) −17.3798 −0.839102
\(430\) −20.4191 −0.984696
\(431\) 6.03095 0.290500 0.145250 0.989395i \(-0.453601\pi\)
0.145250 + 0.989395i \(0.453601\pi\)
\(432\) −13.8822 −0.667907
\(433\) −16.2591 −0.781361 −0.390680 0.920526i \(-0.627760\pi\)
−0.390680 + 0.920526i \(0.627760\pi\)
\(434\) 26.1020 1.25293
\(435\) −39.2582 −1.88229
\(436\) −8.01601 −0.383897
\(437\) 4.94132 0.236375
\(438\) 37.1759 1.77633
\(439\) −1.63102 −0.0778444 −0.0389222 0.999242i \(-0.512392\pi\)
−0.0389222 + 0.999242i \(0.512392\pi\)
\(440\) −8.96497 −0.427388
\(441\) 51.6439 2.45924
\(442\) −5.49272 −0.261262
\(443\) −24.4638 −1.16231 −0.581154 0.813794i \(-0.697399\pi\)
−0.581154 + 0.813794i \(0.697399\pi\)
\(444\) 30.8083 1.46210
\(445\) −37.5029 −1.77781
\(446\) −5.02473 −0.237928
\(447\) 40.0868 1.89604
\(448\) −3.74888 −0.177118
\(449\) 16.6981 0.788033 0.394016 0.919103i \(-0.371085\pi\)
0.394016 + 0.919103i \(0.371085\pi\)
\(450\) −41.3520 −1.94935
\(451\) 30.9757 1.45859
\(452\) 9.74825 0.458519
\(453\) −41.2207 −1.93672
\(454\) −13.3338 −0.625785
\(455\) −24.0888 −1.12930
\(456\) 18.9839 0.889001
\(457\) −16.7108 −0.781699 −0.390849 0.920455i \(-0.627819\pi\)
−0.390849 + 0.920455i \(0.627819\pi\)
\(458\) −28.5085 −1.33211
\(459\) −38.7234 −1.80745
\(460\) 2.72874 0.127228
\(461\) −11.0991 −0.516937 −0.258469 0.966020i \(-0.583218\pi\)
−0.258469 + 0.966020i \(0.583218\pi\)
\(462\) −33.0882 −1.53940
\(463\) 27.1051 1.25968 0.629840 0.776725i \(-0.283120\pi\)
0.629840 + 0.776725i \(0.283120\pi\)
\(464\) 3.74478 0.173847
\(465\) −72.9920 −3.38492
\(466\) −17.7156 −0.820660
\(467\) 30.8905 1.42944 0.714722 0.699409i \(-0.246553\pi\)
0.714722 + 0.699409i \(0.246553\pi\)
\(468\) 14.4161 0.666386
\(469\) 0.965576 0.0445862
\(470\) 24.8182 1.14478
\(471\) 20.6434 0.951198
\(472\) 3.51087 0.161601
\(473\) 17.1911 0.790448
\(474\) −23.5934 −1.08368
\(475\) 33.3765 1.53142
\(476\) −10.4572 −0.479307
\(477\) 100.161 4.58606
\(478\) −18.9752 −0.867905
\(479\) 0.270250 0.0123480 0.00617401 0.999981i \(-0.498035\pi\)
0.00617401 + 0.999981i \(0.498035\pi\)
\(480\) 10.4834 0.478501
\(481\) −18.8833 −0.861003
\(482\) 16.4613 0.749792
\(483\) 10.0713 0.458261
\(484\) −3.45227 −0.156921
\(485\) −30.1958 −1.37112
\(486\) 31.0726 1.40948
\(487\) 32.3472 1.46579 0.732895 0.680342i \(-0.238169\pi\)
0.732895 + 0.680342i \(0.238169\pi\)
\(488\) −5.81031 −0.263020
\(489\) −15.0966 −0.682692
\(490\) −23.0188 −1.03988
\(491\) 2.07595 0.0936863 0.0468432 0.998902i \(-0.485084\pi\)
0.0468432 + 0.998902i \(0.485084\pi\)
\(492\) −36.2223 −1.63303
\(493\) 10.4458 0.470455
\(494\) −11.6357 −0.523517
\(495\) 65.6335 2.95001
\(496\) 6.96260 0.312630
\(497\) 17.8733 0.801729
\(498\) −35.3994 −1.58629
\(499\) 10.1670 0.455139 0.227570 0.973762i \(-0.426922\pi\)
0.227570 + 0.973762i \(0.426922\pi\)
\(500\) 2.11561 0.0946128
\(501\) 27.2676 1.21823
\(502\) 23.6762 1.05672
\(503\) −13.3630 −0.595827 −0.297914 0.954593i \(-0.596291\pi\)
−0.297914 + 0.954593i \(0.596291\pi\)
\(504\) 27.4460 1.22254
\(505\) −2.85376 −0.126991
\(506\) −2.29736 −0.102130
\(507\) 29.3076 1.30160
\(508\) 18.4658 0.819288
\(509\) 4.72767 0.209550 0.104775 0.994496i \(-0.466588\pi\)
0.104775 + 0.994496i \(0.466588\pi\)
\(510\) 29.2428 1.29489
\(511\) −43.3811 −1.91907
\(512\) −1.00000 −0.0441942
\(513\) −82.0313 −3.62177
\(514\) −27.8689 −1.22924
\(515\) 21.6032 0.951953
\(516\) −20.1029 −0.884981
\(517\) −20.8948 −0.918950
\(518\) −35.9507 −1.57958
\(519\) 43.9042 1.92718
\(520\) −6.42559 −0.281781
\(521\) −26.9765 −1.18186 −0.590931 0.806722i \(-0.701240\pi\)
−0.590931 + 0.806722i \(0.701240\pi\)
\(522\) −27.4159 −1.19996
\(523\) −0.542034 −0.0237015 −0.0118507 0.999930i \(-0.503772\pi\)
−0.0118507 + 0.999930i \(0.503772\pi\)
\(524\) −15.5116 −0.677627
\(525\) 68.0275 2.96896
\(526\) 16.3752 0.713992
\(527\) 19.4217 0.846021
\(528\) −8.82615 −0.384109
\(529\) −22.3007 −0.969597
\(530\) −44.6440 −1.93921
\(531\) −25.7034 −1.11543
\(532\) −22.1525 −0.960434
\(533\) 22.2017 0.961661
\(534\) −36.9222 −1.59778
\(535\) 44.7957 1.93669
\(536\) 0.257564 0.0111251
\(537\) −18.3634 −0.792438
\(538\) −12.7426 −0.549373
\(539\) 19.3799 0.834750
\(540\) −45.3001 −1.94940
\(541\) 21.2539 0.913776 0.456888 0.889524i \(-0.348964\pi\)
0.456888 + 0.889524i \(0.348964\pi\)
\(542\) −20.2797 −0.871087
\(543\) 23.0360 0.988570
\(544\) −2.78943 −0.119596
\(545\) −26.1577 −1.12047
\(546\) −23.7158 −1.01494
\(547\) −22.9263 −0.980256 −0.490128 0.871650i \(-0.663050\pi\)
−0.490128 + 0.871650i \(0.663050\pi\)
\(548\) −18.8452 −0.805025
\(549\) 42.5379 1.81547
\(550\) −15.5177 −0.661678
\(551\) 22.1283 0.942697
\(552\) 2.68648 0.114344
\(553\) 27.5314 1.17076
\(554\) 5.78606 0.245826
\(555\) 100.533 4.26739
\(556\) 0.0766866 0.00325224
\(557\) 16.9861 0.719724 0.359862 0.933006i \(-0.382824\pi\)
0.359862 + 0.933006i \(0.382824\pi\)
\(558\) −50.9739 −2.15790
\(559\) 12.3216 0.521149
\(560\) −12.2333 −0.516950
\(561\) −24.6199 −1.03945
\(562\) −16.5039 −0.696175
\(563\) −32.0473 −1.35063 −0.675316 0.737529i \(-0.735993\pi\)
−0.675316 + 0.737529i \(0.735993\pi\)
\(564\) 24.4339 1.02885
\(565\) 31.8103 1.33827
\(566\) 1.55336 0.0652926
\(567\) −84.8570 −3.56366
\(568\) 4.76765 0.200046
\(569\) 5.74945 0.241030 0.120515 0.992712i \(-0.461545\pi\)
0.120515 + 0.992712i \(0.461545\pi\)
\(570\) 61.9477 2.59470
\(571\) −15.9260 −0.666482 −0.333241 0.942842i \(-0.608142\pi\)
−0.333241 + 0.942842i \(0.608142\pi\)
\(572\) 5.40979 0.226195
\(573\) 16.4707 0.688075
\(574\) 42.2683 1.76425
\(575\) 4.72325 0.196973
\(576\) 7.32111 0.305046
\(577\) −5.43332 −0.226192 −0.113096 0.993584i \(-0.536077\pi\)
−0.113096 + 0.993584i \(0.536077\pi\)
\(578\) 9.21909 0.383464
\(579\) −48.9334 −2.03360
\(580\) 12.2199 0.507403
\(581\) 41.3081 1.71375
\(582\) −29.7282 −1.23227
\(583\) 37.5864 1.55667
\(584\) −11.5717 −0.478842
\(585\) 47.0424 1.94496
\(586\) −26.8358 −1.10858
\(587\) 21.7465 0.897572 0.448786 0.893639i \(-0.351856\pi\)
0.448786 + 0.893639i \(0.351856\pi\)
\(588\) −22.6624 −0.934581
\(589\) 41.1427 1.69526
\(590\) 11.4566 0.471660
\(591\) 79.1463 3.25564
\(592\) −9.58970 −0.394134
\(593\) −20.1947 −0.829298 −0.414649 0.909981i \(-0.636096\pi\)
−0.414649 + 0.909981i \(0.636096\pi\)
\(594\) 38.1387 1.56485
\(595\) −34.1238 −1.39894
\(596\) −12.4778 −0.511110
\(597\) 38.1239 1.56031
\(598\) −1.64662 −0.0673353
\(599\) 29.3853 1.20065 0.600326 0.799756i \(-0.295038\pi\)
0.600326 + 0.799756i \(0.295038\pi\)
\(600\) 18.1461 0.740811
\(601\) −16.5934 −0.676860 −0.338430 0.940992i \(-0.609896\pi\)
−0.338430 + 0.940992i \(0.609896\pi\)
\(602\) 23.4584 0.956091
\(603\) −1.88565 −0.0767896
\(604\) 12.8308 0.522076
\(605\) −11.2654 −0.458002
\(606\) −2.80957 −0.114131
\(607\) −32.9796 −1.33860 −0.669300 0.742992i \(-0.733406\pi\)
−0.669300 + 0.742992i \(0.733406\pi\)
\(608\) −5.90910 −0.239646
\(609\) 45.1015 1.82761
\(610\) −18.9601 −0.767671
\(611\) −14.9762 −0.605872
\(612\) 20.4217 0.825498
\(613\) −8.22018 −0.332010 −0.166005 0.986125i \(-0.553087\pi\)
−0.166005 + 0.986125i \(0.553087\pi\)
\(614\) 6.60978 0.266749
\(615\) −118.200 −4.76628
\(616\) 10.2994 0.414973
\(617\) −19.8560 −0.799371 −0.399686 0.916652i \(-0.630881\pi\)
−0.399686 + 0.916652i \(0.630881\pi\)
\(618\) 21.2687 0.855553
\(619\) −32.0121 −1.28668 −0.643338 0.765582i \(-0.722451\pi\)
−0.643338 + 0.765582i \(0.722451\pi\)
\(620\) 22.7202 0.912465
\(621\) −11.6086 −0.465836
\(622\) −9.25864 −0.371238
\(623\) 43.0850 1.72617
\(624\) −6.32609 −0.253246
\(625\) −21.3380 −0.853522
\(626\) −23.6357 −0.944671
\(627\) −52.1546 −2.08286
\(628\) −6.42567 −0.256412
\(629\) −26.7498 −1.06658
\(630\) 89.5610 3.56820
\(631\) −16.4771 −0.655942 −0.327971 0.944688i \(-0.606365\pi\)
−0.327971 + 0.944688i \(0.606365\pi\)
\(632\) 7.34390 0.292125
\(633\) −50.7584 −2.01747
\(634\) −26.1017 −1.03663
\(635\) 60.2572 2.39124
\(636\) −43.9527 −1.74284
\(637\) 13.8904 0.550358
\(638\) −10.2881 −0.407309
\(639\) −34.9044 −1.38080
\(640\) −3.26318 −0.128988
\(641\) −4.88036 −0.192762 −0.0963812 0.995344i \(-0.530727\pi\)
−0.0963812 + 0.995344i \(0.530727\pi\)
\(642\) 44.1020 1.74057
\(643\) −2.80335 −0.110553 −0.0552766 0.998471i \(-0.517604\pi\)
−0.0552766 + 0.998471i \(0.517604\pi\)
\(644\) −3.13490 −0.123532
\(645\) −65.5994 −2.58297
\(646\) −16.4830 −0.648516
\(647\) −34.3332 −1.34978 −0.674888 0.737920i \(-0.735808\pi\)
−0.674888 + 0.737920i \(0.735808\pi\)
\(648\) −22.6353 −0.889197
\(649\) −9.64545 −0.378617
\(650\) −11.1222 −0.436250
\(651\) 83.8564 3.28659
\(652\) 4.69912 0.184032
\(653\) 39.6810 1.55284 0.776418 0.630218i \(-0.217035\pi\)
0.776418 + 0.630218i \(0.217035\pi\)
\(654\) −25.7526 −1.00701
\(655\) −50.6170 −1.97777
\(656\) 11.2749 0.440212
\(657\) 84.7179 3.30516
\(658\) −28.5122 −1.11152
\(659\) −23.2122 −0.904218 −0.452109 0.891963i \(-0.649328\pi\)
−0.452109 + 0.891963i \(0.649328\pi\)
\(660\) −28.8013 −1.12109
\(661\) 21.6905 0.843664 0.421832 0.906674i \(-0.361387\pi\)
0.421832 + 0.906674i \(0.361387\pi\)
\(662\) 29.3754 1.14171
\(663\) −17.6462 −0.685321
\(664\) 11.0188 0.427611
\(665\) −72.2876 −2.80319
\(666\) 70.2072 2.72047
\(667\) 3.13146 0.121251
\(668\) −8.48757 −0.328394
\(669\) −16.1427 −0.624113
\(670\) 0.840476 0.0324704
\(671\) 15.9627 0.616235
\(672\) −12.0438 −0.464601
\(673\) −28.9665 −1.11658 −0.558288 0.829648i \(-0.688541\pi\)
−0.558288 + 0.829648i \(0.688541\pi\)
\(674\) 25.5751 0.985116
\(675\) −78.4112 −3.01805
\(676\) −9.12256 −0.350868
\(677\) 26.2490 1.00883 0.504416 0.863461i \(-0.331708\pi\)
0.504416 + 0.863461i \(0.331708\pi\)
\(678\) 31.3177 1.20275
\(679\) 34.6902 1.33129
\(680\) −9.10240 −0.349061
\(681\) −42.8367 −1.64151
\(682\) −19.1284 −0.732466
\(683\) 31.6103 1.20953 0.604766 0.796403i \(-0.293266\pi\)
0.604766 + 0.796403i \(0.293266\pi\)
\(684\) 43.2612 1.65413
\(685\) −61.4951 −2.34961
\(686\) 0.202877 0.00774590
\(687\) −91.5878 −3.49429
\(688\) 6.25743 0.238562
\(689\) 26.9398 1.02633
\(690\) 8.76648 0.333734
\(691\) −30.5337 −1.16156 −0.580778 0.814062i \(-0.697252\pi\)
−0.580778 + 0.814062i \(0.697252\pi\)
\(692\) −13.6661 −0.519505
\(693\) −75.4027 −2.86431
\(694\) −14.6545 −0.556277
\(695\) 0.250242 0.00949222
\(696\) 12.0307 0.456021
\(697\) 31.4506 1.19128
\(698\) 12.8791 0.487481
\(699\) −56.9140 −2.15269
\(700\) −21.1749 −0.800336
\(701\) 22.9239 0.865823 0.432912 0.901436i \(-0.357486\pi\)
0.432912 + 0.901436i \(0.357486\pi\)
\(702\) 27.3357 1.03172
\(703\) −56.6665 −2.13722
\(704\) 2.74731 0.103543
\(705\) 79.7320 3.00288
\(706\) 0.410032 0.0154318
\(707\) 3.27853 0.123302
\(708\) 11.2792 0.423898
\(709\) −10.6309 −0.399252 −0.199626 0.979872i \(-0.563973\pi\)
−0.199626 + 0.979872i \(0.563973\pi\)
\(710\) 15.5577 0.583869
\(711\) −53.7655 −2.01636
\(712\) 11.4928 0.430710
\(713\) 5.82227 0.218046
\(714\) −33.5954 −1.25728
\(715\) 17.6531 0.660189
\(716\) 5.71596 0.213616
\(717\) −60.9606 −2.27661
\(718\) −15.6921 −0.585622
\(719\) 29.6106 1.10429 0.552144 0.833749i \(-0.313810\pi\)
0.552144 + 0.833749i \(0.313810\pi\)
\(720\) 23.8901 0.890330
\(721\) −24.8188 −0.924299
\(722\) −15.9175 −0.592388
\(723\) 52.8844 1.96679
\(724\) −7.17041 −0.266486
\(725\) 21.1517 0.785556
\(726\) −11.0909 −0.411623
\(727\) −9.68963 −0.359369 −0.179684 0.983724i \(-0.557508\pi\)
−0.179684 + 0.983724i \(0.557508\pi\)
\(728\) 7.38200 0.273595
\(729\) 31.9195 1.18220
\(730\) −37.7606 −1.39758
\(731\) 17.4546 0.645583
\(732\) −18.6665 −0.689933
\(733\) 2.86524 0.105830 0.0529151 0.998599i \(-0.483149\pi\)
0.0529151 + 0.998599i \(0.483149\pi\)
\(734\) −29.7225 −1.09708
\(735\) −73.9514 −2.72774
\(736\) −0.836221 −0.0308235
\(737\) −0.707608 −0.0260651
\(738\) −82.5449 −3.03852
\(739\) −45.2734 −1.66541 −0.832705 0.553717i \(-0.813209\pi\)
−0.832705 + 0.553717i \(0.813209\pi\)
\(740\) −31.2929 −1.15035
\(741\) −37.3815 −1.37324
\(742\) 51.2890 1.88288
\(743\) −27.5709 −1.01148 −0.505739 0.862687i \(-0.668780\pi\)
−0.505739 + 0.862687i \(0.668780\pi\)
\(744\) 22.3684 0.820064
\(745\) −40.7173 −1.49176
\(746\) 0.737493 0.0270015
\(747\) −80.6696 −2.95155
\(748\) 7.66343 0.280203
\(749\) −51.4632 −1.88043
\(750\) 6.79670 0.248180
\(751\) 21.5914 0.787882 0.393941 0.919136i \(-0.371111\pi\)
0.393941 + 0.919136i \(0.371111\pi\)
\(752\) −7.60552 −0.277345
\(753\) 76.0632 2.77190
\(754\) −7.37392 −0.268542
\(755\) 41.8690 1.52377
\(756\) 52.0427 1.89277
\(757\) 33.9685 1.23461 0.617303 0.786726i \(-0.288225\pi\)
0.617303 + 0.786726i \(0.288225\pi\)
\(758\) −17.5835 −0.638661
\(759\) −7.38062 −0.267899
\(760\) −19.2825 −0.699448
\(761\) 46.4643 1.68433 0.842165 0.539220i \(-0.181281\pi\)
0.842165 + 0.539220i \(0.181281\pi\)
\(762\) 59.3242 2.14909
\(763\) 30.0511 1.08792
\(764\) −5.12685 −0.185483
\(765\) 66.6396 2.40936
\(766\) −13.0037 −0.469841
\(767\) −6.91332 −0.249626
\(768\) −3.21265 −0.115926
\(769\) −10.0527 −0.362511 −0.181256 0.983436i \(-0.558016\pi\)
−0.181256 + 0.983436i \(0.558016\pi\)
\(770\) 33.6086 1.21117
\(771\) −89.5329 −3.22445
\(772\) 15.2315 0.548193
\(773\) 13.5930 0.488907 0.244453 0.969661i \(-0.421392\pi\)
0.244453 + 0.969661i \(0.421392\pi\)
\(774\) −45.8113 −1.64665
\(775\) 39.3270 1.41267
\(776\) 9.25349 0.332181
\(777\) −115.497 −4.14342
\(778\) 13.8361 0.496050
\(779\) 66.6246 2.38708
\(780\) −20.6432 −0.739144
\(781\) −13.0982 −0.468691
\(782\) −2.33258 −0.0834129
\(783\) −51.9857 −1.85782
\(784\) 7.05412 0.251933
\(785\) −20.9681 −0.748383
\(786\) −49.8332 −1.77749
\(787\) −16.0621 −0.572553 −0.286277 0.958147i \(-0.592418\pi\)
−0.286277 + 0.958147i \(0.592418\pi\)
\(788\) −24.6358 −0.877616
\(789\) 52.6077 1.87288
\(790\) 23.9645 0.852617
\(791\) −36.5451 −1.29939
\(792\) −20.1134 −0.714698
\(793\) 11.4412 0.406289
\(794\) −29.0131 −1.02964
\(795\) −143.425 −5.08677
\(796\) −11.8668 −0.420608
\(797\) 1.00246 0.0355088 0.0177544 0.999842i \(-0.494348\pi\)
0.0177544 + 0.999842i \(0.494348\pi\)
\(798\) −71.1683 −2.51933
\(799\) −21.2151 −0.750535
\(800\) −5.64833 −0.199699
\(801\) −84.1398 −2.97293
\(802\) −35.9816 −1.27056
\(803\) 31.7912 1.12189
\(804\) 0.827461 0.0291823
\(805\) −10.2297 −0.360550
\(806\) −13.7102 −0.482921
\(807\) −40.9375 −1.44107
\(808\) 0.874535 0.0307660
\(809\) −34.3337 −1.20711 −0.603555 0.797322i \(-0.706249\pi\)
−0.603555 + 0.797322i \(0.706249\pi\)
\(810\) −73.8629 −2.59528
\(811\) 50.4335 1.77096 0.885479 0.464679i \(-0.153830\pi\)
0.885479 + 0.464679i \(0.153830\pi\)
\(812\) −14.0387 −0.492663
\(813\) −65.1515 −2.28496
\(814\) 26.3459 0.923424
\(815\) 15.3340 0.537128
\(816\) −8.96145 −0.313713
\(817\) 36.9758 1.29362
\(818\) 22.3444 0.781252
\(819\) −54.0444 −1.88846
\(820\) 36.7921 1.28483
\(821\) −1.52327 −0.0531625 −0.0265812 0.999647i \(-0.508462\pi\)
−0.0265812 + 0.999647i \(0.508462\pi\)
\(822\) −60.5428 −2.11167
\(823\) −29.4844 −1.02776 −0.513881 0.857862i \(-0.671793\pi\)
−0.513881 + 0.857862i \(0.671793\pi\)
\(824\) −6.62031 −0.230629
\(825\) −49.8530 −1.73566
\(826\) −13.1618 −0.457959
\(827\) 22.0399 0.766404 0.383202 0.923665i \(-0.374821\pi\)
0.383202 + 0.923665i \(0.374821\pi\)
\(828\) 6.12206 0.212756
\(829\) −39.3626 −1.36712 −0.683559 0.729895i \(-0.739569\pi\)
−0.683559 + 0.729895i \(0.739569\pi\)
\(830\) 35.9562 1.24806
\(831\) 18.5886 0.644831
\(832\) 1.96912 0.0682670
\(833\) 19.6770 0.681766
\(834\) 0.246367 0.00853100
\(835\) −27.6964 −0.958475
\(836\) 16.2342 0.561470
\(837\) −96.6561 −3.34092
\(838\) 33.6052 1.16087
\(839\) 36.6796 1.26632 0.633160 0.774021i \(-0.281758\pi\)
0.633160 + 0.774021i \(0.281758\pi\)
\(840\) −39.3012 −1.35602
\(841\) −14.9766 −0.516435
\(842\) 15.3383 0.528593
\(843\) −53.0212 −1.82615
\(844\) 15.7996 0.543843
\(845\) −29.7685 −1.02407
\(846\) 55.6808 1.91435
\(847\) 12.9421 0.444697
\(848\) 13.6811 0.469812
\(849\) 4.99040 0.171270
\(850\) −15.7556 −0.540413
\(851\) −8.01911 −0.274892
\(852\) 15.3168 0.524744
\(853\) 22.7441 0.778743 0.389371 0.921081i \(-0.372692\pi\)
0.389371 + 0.921081i \(0.372692\pi\)
\(854\) 21.7822 0.745370
\(855\) 141.169 4.82787
\(856\) −13.7276 −0.469200
\(857\) −35.3073 −1.20608 −0.603038 0.797713i \(-0.706043\pi\)
−0.603038 + 0.797713i \(0.706043\pi\)
\(858\) 17.3798 0.593335
\(859\) 18.9037 0.644987 0.322493 0.946572i \(-0.395479\pi\)
0.322493 + 0.946572i \(0.395479\pi\)
\(860\) 20.4191 0.696285
\(861\) 135.793 4.62782
\(862\) −6.03095 −0.205415
\(863\) −8.22936 −0.280131 −0.140065 0.990142i \(-0.544731\pi\)
−0.140065 + 0.990142i \(0.544731\pi\)
\(864\) 13.8822 0.472282
\(865\) −44.5948 −1.51627
\(866\) 16.2591 0.552506
\(867\) 29.6177 1.00587
\(868\) −26.1020 −0.885958
\(869\) −20.1760 −0.684424
\(870\) 39.2582 1.33098
\(871\) −0.507174 −0.0171849
\(872\) 8.01601 0.271456
\(873\) −67.7458 −2.29285
\(874\) −4.94132 −0.167143
\(875\) −7.93116 −0.268122
\(876\) −37.1759 −1.25606
\(877\) 3.72004 0.125617 0.0628084 0.998026i \(-0.479994\pi\)
0.0628084 + 0.998026i \(0.479994\pi\)
\(878\) 1.63102 0.0550443
\(879\) −86.2139 −2.90792
\(880\) 8.96497 0.302209
\(881\) −8.46897 −0.285327 −0.142663 0.989771i \(-0.545567\pi\)
−0.142663 + 0.989771i \(0.545567\pi\)
\(882\) −51.6439 −1.73894
\(883\) −32.5328 −1.09481 −0.547407 0.836866i \(-0.684385\pi\)
−0.547407 + 0.836866i \(0.684385\pi\)
\(884\) 5.49272 0.184740
\(885\) 36.8060 1.23722
\(886\) 24.4638 0.821876
\(887\) 39.4037 1.32305 0.661524 0.749924i \(-0.269910\pi\)
0.661524 + 0.749924i \(0.269910\pi\)
\(888\) −30.8083 −1.03386
\(889\) −69.2262 −2.32177
\(890\) 37.5029 1.25710
\(891\) 62.1862 2.08332
\(892\) 5.02473 0.168241
\(893\) −44.9418 −1.50392
\(894\) −40.0868 −1.34070
\(895\) 18.6522 0.623474
\(896\) 3.74888 0.125241
\(897\) −5.29001 −0.176628
\(898\) −16.6981 −0.557223
\(899\) 26.0734 0.869596
\(900\) 41.3520 1.37840
\(901\) 38.1625 1.27138
\(902\) −30.9757 −1.03138
\(903\) 75.3635 2.50794
\(904\) −9.74825 −0.324222
\(905\) −23.3983 −0.777787
\(906\) 41.2207 1.36947
\(907\) −10.2299 −0.339677 −0.169839 0.985472i \(-0.554325\pi\)
−0.169839 + 0.985472i \(0.554325\pi\)
\(908\) 13.3338 0.442497
\(909\) −6.40256 −0.212360
\(910\) 24.0888 0.798535
\(911\) −17.3354 −0.574348 −0.287174 0.957878i \(-0.592716\pi\)
−0.287174 + 0.957878i \(0.592716\pi\)
\(912\) −18.9839 −0.628619
\(913\) −30.2720 −1.00186
\(914\) 16.7108 0.552745
\(915\) −60.9120 −2.01369
\(916\) 28.5085 0.941947
\(917\) 58.1511 1.92032
\(918\) 38.7234 1.27806
\(919\) −36.0779 −1.19010 −0.595050 0.803689i \(-0.702868\pi\)
−0.595050 + 0.803689i \(0.702868\pi\)
\(920\) −2.72874 −0.0899638
\(921\) 21.2349 0.699714
\(922\) 11.0991 0.365530
\(923\) −9.38807 −0.309012
\(924\) 33.0882 1.08852
\(925\) −54.1658 −1.78096
\(926\) −27.1051 −0.890728
\(927\) 48.4680 1.59190
\(928\) −3.74478 −0.122928
\(929\) 20.5507 0.674246 0.337123 0.941461i \(-0.390546\pi\)
0.337123 + 0.941461i \(0.390546\pi\)
\(930\) 72.9920 2.39350
\(931\) 41.6835 1.36612
\(932\) 17.7156 0.580294
\(933\) −29.7448 −0.973800
\(934\) −30.8905 −1.01077
\(935\) 25.0071 0.817821
\(936\) −14.4161 −0.471206
\(937\) −17.6871 −0.577812 −0.288906 0.957357i \(-0.593291\pi\)
−0.288906 + 0.957357i \(0.593291\pi\)
\(938\) −0.965576 −0.0315272
\(939\) −75.9330 −2.47798
\(940\) −24.8182 −0.809479
\(941\) 8.13342 0.265142 0.132571 0.991174i \(-0.457677\pi\)
0.132571 + 0.991174i \(0.457677\pi\)
\(942\) −20.6434 −0.672598
\(943\) 9.42833 0.307029
\(944\) −3.51087 −0.114269
\(945\) 169.825 5.52439
\(946\) −17.1911 −0.558931
\(947\) −50.5671 −1.64321 −0.821605 0.570057i \(-0.806921\pi\)
−0.821605 + 0.570057i \(0.806921\pi\)
\(948\) 23.5934 0.766277
\(949\) 22.7861 0.739669
\(950\) −33.3765 −1.08288
\(951\) −83.8557 −2.71921
\(952\) 10.4572 0.338921
\(953\) −26.8991 −0.871347 −0.435674 0.900105i \(-0.643490\pi\)
−0.435674 + 0.900105i \(0.643490\pi\)
\(954\) −100.161 −3.24283
\(955\) −16.7298 −0.541364
\(956\) 18.9752 0.613701
\(957\) −33.0520 −1.06842
\(958\) −0.270250 −0.00873137
\(959\) 70.6483 2.28135
\(960\) −10.4834 −0.338352
\(961\) 17.4778 0.563799
\(962\) 18.8833 0.608821
\(963\) 100.501 3.23861
\(964\) −16.4613 −0.530183
\(965\) 49.7030 1.60000
\(966\) −10.0713 −0.324039
\(967\) 20.9466 0.673596 0.336798 0.941577i \(-0.390656\pi\)
0.336798 + 0.941577i \(0.390656\pi\)
\(968\) 3.45227 0.110960
\(969\) −52.9541 −1.70113
\(970\) 30.1958 0.969528
\(971\) 47.4120 1.52152 0.760762 0.649031i \(-0.224826\pi\)
0.760762 + 0.649031i \(0.224826\pi\)
\(972\) −31.0726 −0.996654
\(973\) −0.287489 −0.00921648
\(974\) −32.3472 −1.03647
\(975\) −35.7318 −1.14433
\(976\) 5.81031 0.185983
\(977\) −2.69646 −0.0862675 −0.0431338 0.999069i \(-0.513734\pi\)
−0.0431338 + 0.999069i \(0.513734\pi\)
\(978\) 15.0966 0.482736
\(979\) −31.5742 −1.00912
\(980\) 23.0188 0.735310
\(981\) −58.6861 −1.87370
\(982\) −2.07595 −0.0662462
\(983\) 19.7251 0.629132 0.314566 0.949236i \(-0.398141\pi\)
0.314566 + 0.949236i \(0.398141\pi\)
\(984\) 36.2223 1.15473
\(985\) −80.3911 −2.56147
\(986\) −10.4458 −0.332662
\(987\) −91.5997 −2.91565
\(988\) 11.6357 0.370182
\(989\) 5.23260 0.166387
\(990\) −65.6335 −2.08597
\(991\) −10.3904 −0.330063 −0.165031 0.986288i \(-0.552773\pi\)
−0.165031 + 0.986288i \(0.552773\pi\)
\(992\) −6.96260 −0.221063
\(993\) 94.3728 2.99483
\(994\) −17.8733 −0.566908
\(995\) −38.7235 −1.22762
\(996\) 35.3994 1.12167
\(997\) 57.0048 1.80536 0.902680 0.430312i \(-0.141596\pi\)
0.902680 + 0.430312i \(0.141596\pi\)
\(998\) −10.1670 −0.321832
\(999\) 133.126 4.21192
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 4006.2.a.h.1.1 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.h.1.1 42 1.1 even 1 trivial