Properties

Label 1441.2.a.f.1.2
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} +O(q^{10})\) \(q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} -7.00252 q^{10} -1.00000 q^{11} -0.203744 q^{12} -3.12098 q^{13} -7.98834 q^{14} -0.130632 q^{15} +6.14343 q^{16} +1.69371 q^{17} +7.54717 q^{18} -6.80748 q^{19} +12.0665 q^{20} -0.149023 q^{21} +2.51757 q^{22} +5.59709 q^{23} +0.276464 q^{24} +2.73650 q^{25} +7.85729 q^{26} +0.281689 q^{27} +13.7652 q^{28} +0.262203 q^{29} +0.328876 q^{30} +10.5568 q^{31} -3.69347 q^{32} +0.0469654 q^{33} -4.26405 q^{34} +8.82564 q^{35} -13.0050 q^{36} +0.913895 q^{37} +17.1383 q^{38} +0.146578 q^{39} -16.3731 q^{40} +10.1347 q^{41} +0.375175 q^{42} +0.898928 q^{43} -4.33818 q^{44} -8.33823 q^{45} -14.0911 q^{46} -1.97251 q^{47} -0.288529 q^{48} +3.06811 q^{49} -6.88934 q^{50} -0.0795459 q^{51} -13.5394 q^{52} +12.2703 q^{53} -0.709173 q^{54} -2.78146 q^{55} -18.6781 q^{56} +0.319716 q^{57} -0.660116 q^{58} +1.45566 q^{59} -0.566706 q^{60} +9.70235 q^{61} -26.5774 q^{62} -9.51209 q^{63} -2.98828 q^{64} -8.68086 q^{65} -0.118239 q^{66} -5.64376 q^{67} +7.34763 q^{68} -0.262870 q^{69} -22.2192 q^{70} +15.3259 q^{71} +17.6466 q^{72} +5.38902 q^{73} -2.30080 q^{74} -0.128521 q^{75} -29.5320 q^{76} -3.17303 q^{77} -0.369021 q^{78} -12.5453 q^{79} +17.0877 q^{80} +8.98015 q^{81} -25.5149 q^{82} -7.57893 q^{83} -0.646487 q^{84} +4.71099 q^{85} -2.26312 q^{86} -0.0123145 q^{87} +5.88653 q^{88} +14.1630 q^{89} +20.9921 q^{90} -9.90295 q^{91} +24.2812 q^{92} -0.495803 q^{93} +4.96594 q^{94} -18.9347 q^{95} +0.173465 q^{96} -10.3501 q^{97} -7.72420 q^{98} +2.99779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} + O(q^{10}) \) \( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51757 −1.78019 −0.890097 0.455772i \(-0.849363\pi\)
−0.890097 + 0.455772i \(0.849363\pi\)
\(3\) −0.0469654 −0.0271155 −0.0135577 0.999908i \(-0.504316\pi\)
−0.0135577 + 0.999908i \(0.504316\pi\)
\(4\) 4.33818 2.16909
\(5\) 2.78146 1.24391 0.621953 0.783055i \(-0.286340\pi\)
0.621953 + 0.783055i \(0.286340\pi\)
\(6\) 0.118239 0.0482708
\(7\) 3.17303 1.19929 0.599646 0.800265i \(-0.295308\pi\)
0.599646 + 0.800265i \(0.295308\pi\)
\(8\) −5.88653 −2.08120
\(9\) −2.99779 −0.999265
\(10\) −7.00252 −2.21439
\(11\) −1.00000 −0.301511
\(12\) −0.203744 −0.0588159
\(13\) −3.12098 −0.865603 −0.432802 0.901489i \(-0.642475\pi\)
−0.432802 + 0.901489i \(0.642475\pi\)
\(14\) −7.98834 −2.13497
\(15\) −0.130632 −0.0337291
\(16\) 6.14343 1.53586
\(17\) 1.69371 0.410786 0.205393 0.978680i \(-0.434153\pi\)
0.205393 + 0.978680i \(0.434153\pi\)
\(18\) 7.54717 1.77888
\(19\) −6.80748 −1.56174 −0.780871 0.624692i \(-0.785225\pi\)
−0.780871 + 0.624692i \(0.785225\pi\)
\(20\) 12.0665 2.69814
\(21\) −0.149023 −0.0325194
\(22\) 2.51757 0.536749
\(23\) 5.59709 1.16707 0.583537 0.812087i \(-0.301668\pi\)
0.583537 + 0.812087i \(0.301668\pi\)
\(24\) 0.276464 0.0564329
\(25\) 2.73650 0.547300
\(26\) 7.85729 1.54094
\(27\) 0.281689 0.0542111
\(28\) 13.7652 2.60137
\(29\) 0.262203 0.0486899 0.0243450 0.999704i \(-0.492250\pi\)
0.0243450 + 0.999704i \(0.492250\pi\)
\(30\) 0.328876 0.0600443
\(31\) 10.5568 1.89605 0.948026 0.318193i \(-0.103076\pi\)
0.948026 + 0.318193i \(0.103076\pi\)
\(32\) −3.69347 −0.652919
\(33\) 0.0469654 0.00817563
\(34\) −4.26405 −0.731278
\(35\) 8.82564 1.49181
\(36\) −13.0050 −2.16749
\(37\) 0.913895 0.150243 0.0751217 0.997174i \(-0.476065\pi\)
0.0751217 + 0.997174i \(0.476065\pi\)
\(38\) 17.1383 2.78020
\(39\) 0.146578 0.0234713
\(40\) −16.3731 −2.58882
\(41\) 10.1347 1.58278 0.791389 0.611313i \(-0.209359\pi\)
0.791389 + 0.611313i \(0.209359\pi\)
\(42\) 0.375175 0.0578908
\(43\) 0.898928 0.137085 0.0685426 0.997648i \(-0.478165\pi\)
0.0685426 + 0.997648i \(0.478165\pi\)
\(44\) −4.33818 −0.654005
\(45\) −8.33823 −1.24299
\(46\) −14.0911 −2.07762
\(47\) −1.97251 −0.287720 −0.143860 0.989598i \(-0.545952\pi\)
−0.143860 + 0.989598i \(0.545952\pi\)
\(48\) −0.288529 −0.0416455
\(49\) 3.06811 0.438302
\(50\) −6.88934 −0.974299
\(51\) −0.0795459 −0.0111387
\(52\) −13.5394 −1.87757
\(53\) 12.2703 1.68546 0.842729 0.538339i \(-0.180948\pi\)
0.842729 + 0.538339i \(0.180948\pi\)
\(54\) −0.709173 −0.0965062
\(55\) −2.78146 −0.375051
\(56\) −18.6781 −2.49597
\(57\) 0.319716 0.0423474
\(58\) −0.660116 −0.0866775
\(59\) 1.45566 0.189510 0.0947552 0.995501i \(-0.469793\pi\)
0.0947552 + 0.995501i \(0.469793\pi\)
\(60\) −0.566706 −0.0731614
\(61\) 9.70235 1.24226 0.621129 0.783708i \(-0.286674\pi\)
0.621129 + 0.783708i \(0.286674\pi\)
\(62\) −26.5774 −3.37534
\(63\) −9.51209 −1.19841
\(64\) −2.98828 −0.373535
\(65\) −8.68086 −1.07673
\(66\) −0.118239 −0.0145542
\(67\) −5.64376 −0.689495 −0.344747 0.938696i \(-0.612035\pi\)
−0.344747 + 0.938696i \(0.612035\pi\)
\(68\) 7.34763 0.891031
\(69\) −0.262870 −0.0316458
\(70\) −22.2192 −2.65570
\(71\) 15.3259 1.81885 0.909423 0.415873i \(-0.136524\pi\)
0.909423 + 0.415873i \(0.136524\pi\)
\(72\) 17.6466 2.07967
\(73\) 5.38902 0.630737 0.315369 0.948969i \(-0.397872\pi\)
0.315369 + 0.948969i \(0.397872\pi\)
\(74\) −2.30080 −0.267462
\(75\) −0.128521 −0.0148403
\(76\) −29.5320 −3.38756
\(77\) −3.17303 −0.361600
\(78\) −0.369021 −0.0417834
\(79\) −12.5453 −1.41146 −0.705729 0.708482i \(-0.749380\pi\)
−0.705729 + 0.708482i \(0.749380\pi\)
\(80\) 17.0877 1.91046
\(81\) 8.98015 0.997795
\(82\) −25.5149 −2.81765
\(83\) −7.57893 −0.831896 −0.415948 0.909388i \(-0.636550\pi\)
−0.415948 + 0.909388i \(0.636550\pi\)
\(84\) −0.646487 −0.0705375
\(85\) 4.71099 0.510979
\(86\) −2.26312 −0.244038
\(87\) −0.0123145 −0.00132025
\(88\) 5.88653 0.627507
\(89\) 14.1630 1.50128 0.750638 0.660713i \(-0.229746\pi\)
0.750638 + 0.660713i \(0.229746\pi\)
\(90\) 20.9921 2.21276
\(91\) −9.90295 −1.03811
\(92\) 24.2812 2.53149
\(93\) −0.495803 −0.0514124
\(94\) 4.96594 0.512198
\(95\) −18.9347 −1.94266
\(96\) 0.173465 0.0177042
\(97\) −10.3501 −1.05090 −0.525448 0.850826i \(-0.676102\pi\)
−0.525448 + 0.850826i \(0.676102\pi\)
\(98\) −7.72420 −0.780263
\(99\) 2.99779 0.301290
\(100\) 11.8714 1.18714
\(101\) −6.20029 −0.616952 −0.308476 0.951232i \(-0.599819\pi\)
−0.308476 + 0.951232i \(0.599819\pi\)
\(102\) 0.200263 0.0198290
\(103\) 11.8866 1.17122 0.585610 0.810593i \(-0.300855\pi\)
0.585610 + 0.810593i \(0.300855\pi\)
\(104\) 18.3717 1.80150
\(105\) −0.414500 −0.0404511
\(106\) −30.8914 −3.00044
\(107\) 6.41451 0.620114 0.310057 0.950718i \(-0.399652\pi\)
0.310057 + 0.950718i \(0.399652\pi\)
\(108\) 1.22202 0.117589
\(109\) 1.99114 0.190716 0.0953581 0.995443i \(-0.469600\pi\)
0.0953581 + 0.995443i \(0.469600\pi\)
\(110\) 7.00252 0.667664
\(111\) −0.0429215 −0.00407393
\(112\) 19.4933 1.84194
\(113\) 6.84780 0.644187 0.322093 0.946708i \(-0.395613\pi\)
0.322093 + 0.946708i \(0.395613\pi\)
\(114\) −0.804909 −0.0753866
\(115\) 15.5681 1.45173
\(116\) 1.13748 0.105613
\(117\) 9.35605 0.864967
\(118\) −3.66472 −0.337365
\(119\) 5.37420 0.492652
\(120\) 0.768971 0.0701971
\(121\) 1.00000 0.0909091
\(122\) −24.4264 −2.21146
\(123\) −0.475981 −0.0429178
\(124\) 45.7971 4.11270
\(125\) −6.29583 −0.563116
\(126\) 23.9474 2.13340
\(127\) 4.64596 0.412263 0.206131 0.978524i \(-0.433913\pi\)
0.206131 + 0.978524i \(0.433913\pi\)
\(128\) 14.9102 1.31788
\(129\) −0.0422185 −0.00371714
\(130\) 21.8547 1.91678
\(131\) 1.00000 0.0873704
\(132\) 0.203744 0.0177337
\(133\) −21.6003 −1.87299
\(134\) 14.2086 1.22743
\(135\) 0.783505 0.0674334
\(136\) −9.97010 −0.854929
\(137\) 9.13518 0.780471 0.390235 0.920715i \(-0.372394\pi\)
0.390235 + 0.920715i \(0.372394\pi\)
\(138\) 0.661794 0.0563356
\(139\) 11.2144 0.951196 0.475598 0.879663i \(-0.342232\pi\)
0.475598 + 0.879663i \(0.342232\pi\)
\(140\) 38.2872 3.23586
\(141\) 0.0926398 0.00780168
\(142\) −38.5840 −3.23790
\(143\) 3.12098 0.260989
\(144\) −18.4167 −1.53473
\(145\) 0.729307 0.0605656
\(146\) −13.5673 −1.12283
\(147\) −0.144095 −0.0118848
\(148\) 3.96464 0.325891
\(149\) −16.5694 −1.35742 −0.678709 0.734408i \(-0.737460\pi\)
−0.678709 + 0.734408i \(0.737460\pi\)
\(150\) 0.323561 0.0264186
\(151\) 23.7768 1.93493 0.967466 0.253003i \(-0.0814181\pi\)
0.967466 + 0.253003i \(0.0814181\pi\)
\(152\) 40.0725 3.25031
\(153\) −5.07740 −0.410484
\(154\) 7.98834 0.643718
\(155\) 29.3632 2.35851
\(156\) 0.635881 0.0509113
\(157\) −13.4537 −1.07372 −0.536862 0.843670i \(-0.680390\pi\)
−0.536862 + 0.843670i \(0.680390\pi\)
\(158\) 31.5837 2.51267
\(159\) −0.576280 −0.0457020
\(160\) −10.2732 −0.812169
\(161\) 17.7597 1.39966
\(162\) −22.6082 −1.77627
\(163\) −15.4810 −1.21257 −0.606284 0.795248i \(-0.707341\pi\)
−0.606284 + 0.795248i \(0.707341\pi\)
\(164\) 43.9662 3.43318
\(165\) 0.130632 0.0101697
\(166\) 19.0805 1.48094
\(167\) −3.14428 −0.243312 −0.121656 0.992572i \(-0.538820\pi\)
−0.121656 + 0.992572i \(0.538820\pi\)
\(168\) 0.877227 0.0676795
\(169\) −3.25950 −0.250731
\(170\) −11.8603 −0.909641
\(171\) 20.4074 1.56059
\(172\) 3.89971 0.297350
\(173\) −17.3185 −1.31670 −0.658350 0.752712i \(-0.728745\pi\)
−0.658350 + 0.752712i \(0.728745\pi\)
\(174\) 0.0310026 0.00235030
\(175\) 8.68299 0.656372
\(176\) −6.14343 −0.463078
\(177\) −0.0683655 −0.00513867
\(178\) −35.6564 −2.67256
\(179\) 21.3593 1.59647 0.798236 0.602345i \(-0.205767\pi\)
0.798236 + 0.602345i \(0.205767\pi\)
\(180\) −36.1727 −2.69616
\(181\) −0.488126 −0.0362821 −0.0181411 0.999835i \(-0.505775\pi\)
−0.0181411 + 0.999835i \(0.505775\pi\)
\(182\) 24.9314 1.84804
\(183\) −0.455675 −0.0336845
\(184\) −32.9475 −2.42892
\(185\) 2.54196 0.186889
\(186\) 1.24822 0.0915240
\(187\) −1.69371 −0.123857
\(188\) −8.55710 −0.624091
\(189\) 0.893807 0.0650149
\(190\) 47.6695 3.45831
\(191\) −19.4681 −1.40867 −0.704333 0.709870i \(-0.748754\pi\)
−0.704333 + 0.709870i \(0.748754\pi\)
\(192\) 0.140346 0.0101286
\(193\) −7.99295 −0.575345 −0.287673 0.957729i \(-0.592881\pi\)
−0.287673 + 0.957729i \(0.592881\pi\)
\(194\) 26.0572 1.87080
\(195\) 0.407700 0.0291960
\(196\) 13.3100 0.950716
\(197\) −17.5728 −1.25201 −0.626007 0.779818i \(-0.715312\pi\)
−0.626007 + 0.779818i \(0.715312\pi\)
\(198\) −7.54717 −0.536354
\(199\) 5.69208 0.403501 0.201750 0.979437i \(-0.435337\pi\)
0.201750 + 0.979437i \(0.435337\pi\)
\(200\) −16.1085 −1.13904
\(201\) 0.265061 0.0186960
\(202\) 15.6097 1.09829
\(203\) 0.831978 0.0583934
\(204\) −0.345084 −0.0241607
\(205\) 28.1893 1.96882
\(206\) −29.9253 −2.08500
\(207\) −16.7789 −1.16622
\(208\) −19.1735 −1.32944
\(209\) 6.80748 0.470883
\(210\) 1.04353 0.0720107
\(211\) −21.1186 −1.45386 −0.726931 0.686711i \(-0.759054\pi\)
−0.726931 + 0.686711i \(0.759054\pi\)
\(212\) 53.2308 3.65591
\(213\) −0.719786 −0.0493189
\(214\) −16.1490 −1.10392
\(215\) 2.50033 0.170521
\(216\) −1.65817 −0.112824
\(217\) 33.4969 2.27392
\(218\) −5.01283 −0.339512
\(219\) −0.253098 −0.0171028
\(220\) −12.0665 −0.813520
\(221\) −5.28604 −0.355578
\(222\) 0.108058 0.00725237
\(223\) 12.3442 0.826631 0.413316 0.910588i \(-0.364371\pi\)
0.413316 + 0.910588i \(0.364371\pi\)
\(224\) −11.7195 −0.783041
\(225\) −8.20346 −0.546897
\(226\) −17.2398 −1.14678
\(227\) −23.1762 −1.53826 −0.769130 0.639092i \(-0.779310\pi\)
−0.769130 + 0.639092i \(0.779310\pi\)
\(228\) 1.38698 0.0918553
\(229\) 6.82842 0.451235 0.225617 0.974216i \(-0.427560\pi\)
0.225617 + 0.974216i \(0.427560\pi\)
\(230\) −39.1937 −2.58436
\(231\) 0.149023 0.00980497
\(232\) −1.54347 −0.101334
\(233\) 18.0665 1.18358 0.591788 0.806094i \(-0.298422\pi\)
0.591788 + 0.806094i \(0.298422\pi\)
\(234\) −23.5545 −1.53981
\(235\) −5.48645 −0.357897
\(236\) 6.31490 0.411065
\(237\) 0.589196 0.0382724
\(238\) −13.5299 −0.877016
\(239\) 19.1342 1.23769 0.618844 0.785514i \(-0.287601\pi\)
0.618844 + 0.785514i \(0.287601\pi\)
\(240\) −0.802530 −0.0518031
\(241\) −12.5772 −0.810170 −0.405085 0.914279i \(-0.632758\pi\)
−0.405085 + 0.914279i \(0.632758\pi\)
\(242\) −2.51757 −0.161836
\(243\) −1.26682 −0.0812667
\(244\) 42.0905 2.69457
\(245\) 8.53383 0.545206
\(246\) 1.19832 0.0764020
\(247\) 21.2460 1.35185
\(248\) −62.1428 −3.94607
\(249\) 0.355948 0.0225573
\(250\) 15.8502 1.00246
\(251\) 16.0840 1.01522 0.507608 0.861588i \(-0.330530\pi\)
0.507608 + 0.861588i \(0.330530\pi\)
\(252\) −41.2651 −2.59946
\(253\) −5.59709 −0.351886
\(254\) −11.6966 −0.733907
\(255\) −0.221254 −0.0138554
\(256\) −31.5609 −1.97255
\(257\) 4.01075 0.250184 0.125092 0.992145i \(-0.460077\pi\)
0.125092 + 0.992145i \(0.460077\pi\)
\(258\) 0.106288 0.00661722
\(259\) 2.89982 0.180186
\(260\) −37.6591 −2.33552
\(261\) −0.786031 −0.0486541
\(262\) −2.51757 −0.155536
\(263\) −6.30380 −0.388709 −0.194355 0.980931i \(-0.562261\pi\)
−0.194355 + 0.980931i \(0.562261\pi\)
\(264\) −0.276464 −0.0170152
\(265\) 34.1293 2.09655
\(266\) 54.3804 3.33428
\(267\) −0.665172 −0.0407079
\(268\) −24.4836 −1.49558
\(269\) 19.0933 1.16414 0.582068 0.813140i \(-0.302244\pi\)
0.582068 + 0.813140i \(0.302244\pi\)
\(270\) −1.97253 −0.120044
\(271\) 8.63112 0.524303 0.262152 0.965027i \(-0.415568\pi\)
0.262152 + 0.965027i \(0.415568\pi\)
\(272\) 10.4052 0.630908
\(273\) 0.465096 0.0281489
\(274\) −22.9985 −1.38939
\(275\) −2.73650 −0.165017
\(276\) −1.14038 −0.0686425
\(277\) −18.8542 −1.13284 −0.566421 0.824116i \(-0.691672\pi\)
−0.566421 + 0.824116i \(0.691672\pi\)
\(278\) −28.2332 −1.69331
\(279\) −31.6470 −1.89466
\(280\) −51.9524 −3.10475
\(281\) −14.4103 −0.859648 −0.429824 0.902913i \(-0.641424\pi\)
−0.429824 + 0.902913i \(0.641424\pi\)
\(282\) −0.233228 −0.0138885
\(283\) 5.11684 0.304164 0.152082 0.988368i \(-0.451402\pi\)
0.152082 + 0.988368i \(0.451402\pi\)
\(284\) 66.4863 3.94524
\(285\) 0.889276 0.0526762
\(286\) −7.85729 −0.464611
\(287\) 32.1578 1.89821
\(288\) 11.0723 0.652439
\(289\) −14.1313 −0.831255
\(290\) −1.83608 −0.107819
\(291\) 0.486098 0.0284956
\(292\) 23.3785 1.36813
\(293\) −10.4467 −0.610301 −0.305150 0.952304i \(-0.598707\pi\)
−0.305150 + 0.952304i \(0.598707\pi\)
\(294\) 0.362770 0.0211572
\(295\) 4.04885 0.235733
\(296\) −5.37968 −0.312687
\(297\) −0.281689 −0.0163452
\(298\) 41.7147 2.41647
\(299\) −17.4684 −1.01022
\(300\) −0.557546 −0.0321899
\(301\) 2.85233 0.164405
\(302\) −59.8599 −3.44455
\(303\) 0.291199 0.0167290
\(304\) −41.8213 −2.39861
\(305\) 26.9867 1.54525
\(306\) 12.7827 0.730741
\(307\) −4.07876 −0.232787 −0.116394 0.993203i \(-0.537133\pi\)
−0.116394 + 0.993203i \(0.537133\pi\)
\(308\) −13.7652 −0.784343
\(309\) −0.558258 −0.0317582
\(310\) −73.9240 −4.19860
\(311\) 14.8682 0.843101 0.421550 0.906805i \(-0.361486\pi\)
0.421550 + 0.906805i \(0.361486\pi\)
\(312\) −0.862836 −0.0488485
\(313\) −26.6883 −1.50851 −0.754257 0.656579i \(-0.772003\pi\)
−0.754257 + 0.656579i \(0.772003\pi\)
\(314\) 33.8707 1.91144
\(315\) −26.4575 −1.49071
\(316\) −54.4238 −3.06158
\(317\) −30.9599 −1.73888 −0.869440 0.494038i \(-0.835520\pi\)
−0.869440 + 0.494038i \(0.835520\pi\)
\(318\) 1.45083 0.0813584
\(319\) −0.262203 −0.0146806
\(320\) −8.31178 −0.464642
\(321\) −0.301260 −0.0168147
\(322\) −44.7114 −2.49167
\(323\) −11.5299 −0.641542
\(324\) 38.9575 2.16431
\(325\) −8.54055 −0.473745
\(326\) 38.9747 2.15861
\(327\) −0.0935145 −0.00517136
\(328\) −59.6584 −3.29408
\(329\) −6.25884 −0.345061
\(330\) −0.328876 −0.0181040
\(331\) −5.60072 −0.307843 −0.153922 0.988083i \(-0.549190\pi\)
−0.153922 + 0.988083i \(0.549190\pi\)
\(332\) −32.8787 −1.80446
\(333\) −2.73967 −0.150133
\(334\) 7.91597 0.433142
\(335\) −15.6979 −0.857666
\(336\) −0.915510 −0.0499452
\(337\) −4.10055 −0.223371 −0.111686 0.993744i \(-0.535625\pi\)
−0.111686 + 0.993744i \(0.535625\pi\)
\(338\) 8.20603 0.446349
\(339\) −0.321610 −0.0174674
\(340\) 20.4371 1.10836
\(341\) −10.5568 −0.571681
\(342\) −51.3772 −2.77816
\(343\) −12.4760 −0.673640
\(344\) −5.29157 −0.285302
\(345\) −0.731160 −0.0393644
\(346\) 43.6006 2.34398
\(347\) 24.4725 1.31375 0.656876 0.753999i \(-0.271878\pi\)
0.656876 + 0.753999i \(0.271878\pi\)
\(348\) −0.0534224 −0.00286374
\(349\) −3.40810 −0.182432 −0.0912158 0.995831i \(-0.529075\pi\)
−0.0912158 + 0.995831i \(0.529075\pi\)
\(350\) −21.8601 −1.16847
\(351\) −0.879145 −0.0469253
\(352\) 3.69347 0.196862
\(353\) 16.2358 0.864142 0.432071 0.901839i \(-0.357783\pi\)
0.432071 + 0.901839i \(0.357783\pi\)
\(354\) 0.172115 0.00914782
\(355\) 42.6282 2.26247
\(356\) 61.4417 3.25640
\(357\) −0.252402 −0.0133585
\(358\) −53.7737 −2.84203
\(359\) 18.3031 0.966000 0.483000 0.875620i \(-0.339547\pi\)
0.483000 + 0.875620i \(0.339547\pi\)
\(360\) 49.0833 2.58692
\(361\) 27.3418 1.43904
\(362\) 1.22889 0.0645892
\(363\) −0.0469654 −0.00246504
\(364\) −42.9608 −2.25176
\(365\) 14.9893 0.784577
\(366\) 1.14720 0.0599649
\(367\) −34.9177 −1.82269 −0.911343 0.411647i \(-0.864954\pi\)
−0.911343 + 0.411647i \(0.864954\pi\)
\(368\) 34.3853 1.79246
\(369\) −30.3818 −1.58161
\(370\) −6.39957 −0.332698
\(371\) 38.9341 2.02136
\(372\) −2.15088 −0.111518
\(373\) 10.6459 0.551226 0.275613 0.961269i \(-0.411119\pi\)
0.275613 + 0.961269i \(0.411119\pi\)
\(374\) 4.26405 0.220489
\(375\) 0.295686 0.0152692
\(376\) 11.6113 0.598805
\(377\) −0.818330 −0.0421462
\(378\) −2.25023 −0.115739
\(379\) 32.8449 1.68713 0.843563 0.537030i \(-0.180454\pi\)
0.843563 + 0.537030i \(0.180454\pi\)
\(380\) −82.1421 −4.21380
\(381\) −0.218200 −0.0111787
\(382\) 49.0125 2.50770
\(383\) −0.133606 −0.00682695 −0.00341348 0.999994i \(-0.501087\pi\)
−0.00341348 + 0.999994i \(0.501087\pi\)
\(384\) −0.700262 −0.0357351
\(385\) −8.82564 −0.449796
\(386\) 20.1228 1.02423
\(387\) −2.69480 −0.136985
\(388\) −44.9007 −2.27949
\(389\) −19.0392 −0.965325 −0.482662 0.875807i \(-0.660330\pi\)
−0.482662 + 0.875807i \(0.660330\pi\)
\(390\) −1.02642 −0.0519746
\(391\) 9.47987 0.479417
\(392\) −18.0606 −0.912196
\(393\) −0.0469654 −0.00236909
\(394\) 44.2409 2.22883
\(395\) −34.8942 −1.75572
\(396\) 13.0050 0.653524
\(397\) 2.09184 0.104986 0.0524931 0.998621i \(-0.483283\pi\)
0.0524931 + 0.998621i \(0.483283\pi\)
\(398\) −14.3302 −0.718309
\(399\) 1.01447 0.0507869
\(400\) 16.8115 0.840574
\(401\) −17.6116 −0.879484 −0.439742 0.898124i \(-0.644930\pi\)
−0.439742 + 0.898124i \(0.644930\pi\)
\(402\) −0.667312 −0.0332825
\(403\) −32.9474 −1.64123
\(404\) −26.8980 −1.33822
\(405\) 24.9779 1.24116
\(406\) −2.09457 −0.103952
\(407\) −0.913895 −0.0453001
\(408\) 0.468250 0.0231818
\(409\) 3.15487 0.155999 0.0779993 0.996953i \(-0.475147\pi\)
0.0779993 + 0.996953i \(0.475147\pi\)
\(410\) −70.9686 −3.50489
\(411\) −0.429037 −0.0211629
\(412\) 51.5661 2.54048
\(413\) 4.61884 0.227278
\(414\) 42.2422 2.07609
\(415\) −21.0805 −1.03480
\(416\) 11.5272 0.565169
\(417\) −0.526691 −0.0257921
\(418\) −17.1383 −0.838263
\(419\) −14.2135 −0.694377 −0.347188 0.937795i \(-0.612864\pi\)
−0.347188 + 0.937795i \(0.612864\pi\)
\(420\) −1.79817 −0.0877419
\(421\) 9.56690 0.466262 0.233131 0.972445i \(-0.425103\pi\)
0.233131 + 0.972445i \(0.425103\pi\)
\(422\) 53.1675 2.58815
\(423\) 5.91318 0.287509
\(424\) −72.2296 −3.50778
\(425\) 4.63484 0.224823
\(426\) 1.81211 0.0877972
\(427\) 30.7858 1.48983
\(428\) 27.8273 1.34508
\(429\) −0.146578 −0.00707685
\(430\) −6.29477 −0.303561
\(431\) 9.69154 0.466825 0.233413 0.972378i \(-0.425011\pi\)
0.233413 + 0.972378i \(0.425011\pi\)
\(432\) 1.73054 0.0832604
\(433\) −15.2339 −0.732096 −0.366048 0.930596i \(-0.619289\pi\)
−0.366048 + 0.930596i \(0.619289\pi\)
\(434\) −84.3310 −4.04802
\(435\) −0.0342522 −0.00164227
\(436\) 8.63790 0.413680
\(437\) −38.1021 −1.82267
\(438\) 0.637192 0.0304462
\(439\) 13.9271 0.664707 0.332353 0.943155i \(-0.392157\pi\)
0.332353 + 0.943155i \(0.392157\pi\)
\(440\) 16.3731 0.780559
\(441\) −9.19758 −0.437980
\(442\) 13.3080 0.632997
\(443\) 1.05271 0.0500156 0.0250078 0.999687i \(-0.492039\pi\)
0.0250078 + 0.999687i \(0.492039\pi\)
\(444\) −0.186201 −0.00883671
\(445\) 39.3938 1.86745
\(446\) −31.0775 −1.47156
\(447\) 0.778188 0.0368070
\(448\) −9.48191 −0.447978
\(449\) −8.25735 −0.389689 −0.194844 0.980834i \(-0.562420\pi\)
−0.194844 + 0.980834i \(0.562420\pi\)
\(450\) 20.6528 0.973583
\(451\) −10.1347 −0.477225
\(452\) 29.7070 1.39730
\(453\) −1.11669 −0.0524666
\(454\) 58.3479 2.73840
\(455\) −27.5446 −1.29131
\(456\) −1.88202 −0.0881336
\(457\) −3.69263 −0.172734 −0.0863669 0.996263i \(-0.527526\pi\)
−0.0863669 + 0.996263i \(0.527526\pi\)
\(458\) −17.1911 −0.803285
\(459\) 0.477100 0.0222691
\(460\) 67.5370 3.14893
\(461\) −21.4826 −1.00054 −0.500271 0.865869i \(-0.666766\pi\)
−0.500271 + 0.865869i \(0.666766\pi\)
\(462\) −0.375175 −0.0174547
\(463\) −2.57128 −0.119497 −0.0597487 0.998213i \(-0.519030\pi\)
−0.0597487 + 0.998213i \(0.519030\pi\)
\(464\) 1.61083 0.0747808
\(465\) −1.37905 −0.0639521
\(466\) −45.4838 −2.10699
\(467\) −36.7782 −1.70189 −0.850947 0.525252i \(-0.823971\pi\)
−0.850947 + 0.525252i \(0.823971\pi\)
\(468\) 40.5882 1.87619
\(469\) −17.9078 −0.826906
\(470\) 13.8126 0.637125
\(471\) 0.631859 0.0291145
\(472\) −8.56877 −0.394410
\(473\) −0.898928 −0.0413328
\(474\) −1.48334 −0.0681322
\(475\) −18.6287 −0.854741
\(476\) 23.3142 1.06861
\(477\) −36.7839 −1.68422
\(478\) −48.1717 −2.20332
\(479\) −3.31533 −0.151482 −0.0757408 0.997128i \(-0.524132\pi\)
−0.0757408 + 0.997128i \(0.524132\pi\)
\(480\) 0.482486 0.0220224
\(481\) −2.85225 −0.130051
\(482\) 31.6641 1.44226
\(483\) −0.834093 −0.0379525
\(484\) 4.33818 0.197190
\(485\) −28.7884 −1.30721
\(486\) 3.18932 0.144671
\(487\) 0.602575 0.0273053 0.0136526 0.999907i \(-0.495654\pi\)
0.0136526 + 0.999907i \(0.495654\pi\)
\(488\) −57.1132 −2.58539
\(489\) 0.727073 0.0328794
\(490\) −21.4845 −0.970572
\(491\) 23.3629 1.05435 0.527176 0.849756i \(-0.323251\pi\)
0.527176 + 0.849756i \(0.323251\pi\)
\(492\) −2.06489 −0.0930925
\(493\) 0.444097 0.0200011
\(494\) −53.4883 −2.40655
\(495\) 8.33823 0.374776
\(496\) 64.8548 2.91206
\(497\) 48.6294 2.18133
\(498\) −0.896124 −0.0401563
\(499\) 11.5641 0.517682 0.258841 0.965920i \(-0.416659\pi\)
0.258841 + 0.965920i \(0.416659\pi\)
\(500\) −27.3124 −1.22145
\(501\) 0.147673 0.00659752
\(502\) −40.4928 −1.80728
\(503\) −17.6659 −0.787686 −0.393843 0.919178i \(-0.628855\pi\)
−0.393843 + 0.919178i \(0.628855\pi\)
\(504\) 55.9932 2.49414
\(505\) −17.2458 −0.767430
\(506\) 14.0911 0.626425
\(507\) 0.153084 0.00679869
\(508\) 20.1550 0.894234
\(509\) −9.18213 −0.406991 −0.203495 0.979076i \(-0.565230\pi\)
−0.203495 + 0.979076i \(0.565230\pi\)
\(510\) 0.557022 0.0246654
\(511\) 17.0995 0.756439
\(512\) 49.6365 2.19364
\(513\) −1.91759 −0.0846637
\(514\) −10.0974 −0.445376
\(515\) 33.0620 1.45689
\(516\) −0.183152 −0.00806280
\(517\) 1.97251 0.0867509
\(518\) −7.30050 −0.320766
\(519\) 0.813370 0.0357030
\(520\) 51.1002 2.24089
\(521\) 42.6659 1.86923 0.934614 0.355665i \(-0.115746\pi\)
0.934614 + 0.355665i \(0.115746\pi\)
\(522\) 1.97889 0.0866137
\(523\) 31.9428 1.39676 0.698380 0.715727i \(-0.253904\pi\)
0.698380 + 0.715727i \(0.253904\pi\)
\(524\) 4.33818 0.189514
\(525\) −0.407800 −0.0177979
\(526\) 15.8703 0.691978
\(527\) 17.8801 0.778871
\(528\) 0.288529 0.0125566
\(529\) 8.32742 0.362062
\(530\) −85.9231 −3.73226
\(531\) −4.36376 −0.189371
\(532\) −93.7061 −4.06267
\(533\) −31.6302 −1.37006
\(534\) 1.67462 0.0724679
\(535\) 17.8417 0.771363
\(536\) 33.2222 1.43498
\(537\) −1.00315 −0.0432891
\(538\) −48.0687 −2.07239
\(539\) −3.06811 −0.132153
\(540\) 3.39899 0.146269
\(541\) −11.6887 −0.502536 −0.251268 0.967918i \(-0.580848\pi\)
−0.251268 + 0.967918i \(0.580848\pi\)
\(542\) −21.7295 −0.933361
\(543\) 0.0229250 0.000983807 0
\(544\) −6.25567 −0.268210
\(545\) 5.53826 0.237233
\(546\) −1.17091 −0.0501105
\(547\) 29.3344 1.25425 0.627124 0.778919i \(-0.284232\pi\)
0.627124 + 0.778919i \(0.284232\pi\)
\(548\) 39.6300 1.69291
\(549\) −29.0857 −1.24135
\(550\) 6.88934 0.293762
\(551\) −1.78494 −0.0760411
\(552\) 1.54739 0.0658613
\(553\) −39.8066 −1.69275
\(554\) 47.4670 2.01668
\(555\) −0.119384 −0.00506758
\(556\) 48.6502 2.06323
\(557\) 41.4876 1.75789 0.878943 0.476927i \(-0.158249\pi\)
0.878943 + 0.476927i \(0.158249\pi\)
\(558\) 79.6737 3.37286
\(559\) −2.80554 −0.118661
\(560\) 54.2197 2.29120
\(561\) 0.0795459 0.00335843
\(562\) 36.2791 1.53034
\(563\) 7.01042 0.295454 0.147727 0.989028i \(-0.452804\pi\)
0.147727 + 0.989028i \(0.452804\pi\)
\(564\) 0.401888 0.0169225
\(565\) 19.0469 0.801307
\(566\) −12.8820 −0.541471
\(567\) 28.4943 1.19665
\(568\) −90.2162 −3.78539
\(569\) 37.1479 1.55732 0.778660 0.627446i \(-0.215900\pi\)
0.778660 + 0.627446i \(0.215900\pi\)
\(570\) −2.23882 −0.0937738
\(571\) 34.1911 1.43085 0.715426 0.698689i \(-0.246233\pi\)
0.715426 + 0.698689i \(0.246233\pi\)
\(572\) 13.5394 0.566109
\(573\) 0.914330 0.0381967
\(574\) −80.9595 −3.37919
\(575\) 15.3164 0.638739
\(576\) 8.95825 0.373261
\(577\) −5.88069 −0.244816 −0.122408 0.992480i \(-0.539062\pi\)
−0.122408 + 0.992480i \(0.539062\pi\)
\(578\) 35.5767 1.47979
\(579\) 0.375392 0.0156008
\(580\) 3.16386 0.131372
\(581\) −24.0482 −0.997686
\(582\) −1.22379 −0.0507276
\(583\) −12.2703 −0.508184
\(584\) −31.7227 −1.31269
\(585\) 26.0234 1.07594
\(586\) 26.3002 1.08645
\(587\) −2.00019 −0.0825568 −0.0412784 0.999148i \(-0.513143\pi\)
−0.0412784 + 0.999148i \(0.513143\pi\)
\(588\) −0.625111 −0.0257791
\(589\) −71.8650 −2.96114
\(590\) −10.1933 −0.419650
\(591\) 0.825316 0.0339490
\(592\) 5.61445 0.230752
\(593\) −14.1828 −0.582420 −0.291210 0.956659i \(-0.594058\pi\)
−0.291210 + 0.956659i \(0.594058\pi\)
\(594\) 0.709173 0.0290977
\(595\) 14.9481 0.612813
\(596\) −71.8809 −2.94436
\(597\) −0.267331 −0.0109411
\(598\) 43.9780 1.79839
\(599\) −43.1297 −1.76223 −0.881115 0.472902i \(-0.843206\pi\)
−0.881115 + 0.472902i \(0.843206\pi\)
\(600\) 0.756542 0.0308857
\(601\) 9.49573 0.387339 0.193669 0.981067i \(-0.437961\pi\)
0.193669 + 0.981067i \(0.437961\pi\)
\(602\) −7.18094 −0.292673
\(603\) 16.9188 0.688988
\(604\) 103.148 4.19704
\(605\) 2.78146 0.113082
\(606\) −0.733116 −0.0297808
\(607\) 22.6942 0.921130 0.460565 0.887626i \(-0.347647\pi\)
0.460565 + 0.887626i \(0.347647\pi\)
\(608\) 25.1432 1.01969
\(609\) −0.0390742 −0.00158337
\(610\) −67.9409 −2.75085
\(611\) 6.15616 0.249052
\(612\) −22.0267 −0.890376
\(613\) 29.4704 1.19030 0.595149 0.803615i \(-0.297093\pi\)
0.595149 + 0.803615i \(0.297093\pi\)
\(614\) 10.2686 0.414406
\(615\) −1.32392 −0.0533856
\(616\) 18.6781 0.752564
\(617\) −19.1427 −0.770656 −0.385328 0.922780i \(-0.625912\pi\)
−0.385328 + 0.922780i \(0.625912\pi\)
\(618\) 1.40546 0.0565357
\(619\) −14.8539 −0.597028 −0.298514 0.954405i \(-0.596491\pi\)
−0.298514 + 0.954405i \(0.596491\pi\)
\(620\) 127.383 5.11581
\(621\) 1.57664 0.0632683
\(622\) −37.4319 −1.50088
\(623\) 44.9397 1.80047
\(624\) 0.900492 0.0360485
\(625\) −31.1941 −1.24776
\(626\) 67.1899 2.68545
\(627\) −0.319716 −0.0127682
\(628\) −58.3646 −2.32900
\(629\) 1.54788 0.0617179
\(630\) 66.6086 2.65375
\(631\) −27.4090 −1.09114 −0.545568 0.838066i \(-0.683686\pi\)
−0.545568 + 0.838066i \(0.683686\pi\)
\(632\) 73.8484 2.93753
\(633\) 0.991842 0.0394222
\(634\) 77.9438 3.09554
\(635\) 12.9225 0.512816
\(636\) −2.50001 −0.0991317
\(637\) −9.57552 −0.379396
\(638\) 0.660116 0.0261342
\(639\) −45.9438 −1.81751
\(640\) 41.4719 1.63932
\(641\) −21.8080 −0.861363 −0.430681 0.902504i \(-0.641727\pi\)
−0.430681 + 0.902504i \(0.641727\pi\)
\(642\) 0.758444 0.0299334
\(643\) 40.5113 1.59761 0.798805 0.601590i \(-0.205466\pi\)
0.798805 + 0.601590i \(0.205466\pi\)
\(644\) 77.0449 3.03599
\(645\) −0.117429 −0.00462376
\(646\) 29.0274 1.14207
\(647\) −34.6135 −1.36080 −0.680399 0.732842i \(-0.738193\pi\)
−0.680399 + 0.732842i \(0.738193\pi\)
\(648\) −52.8620 −2.07661
\(649\) −1.45566 −0.0571395
\(650\) 21.5015 0.843357
\(651\) −1.57320 −0.0616585
\(652\) −67.1595 −2.63017
\(653\) 48.9394 1.91514 0.957572 0.288193i \(-0.0930544\pi\)
0.957572 + 0.288193i \(0.0930544\pi\)
\(654\) 0.235430 0.00920603
\(655\) 2.78146 0.108680
\(656\) 62.2619 2.43092
\(657\) −16.1552 −0.630274
\(658\) 15.7571 0.614275
\(659\) −2.97733 −0.115980 −0.0579901 0.998317i \(-0.518469\pi\)
−0.0579901 + 0.998317i \(0.518469\pi\)
\(660\) 0.566706 0.0220590
\(661\) −37.6502 −1.46442 −0.732211 0.681078i \(-0.761512\pi\)
−0.732211 + 0.681078i \(0.761512\pi\)
\(662\) 14.1002 0.548021
\(663\) 0.248261 0.00964166
\(664\) 44.6136 1.73134
\(665\) −60.0804 −2.32982
\(666\) 6.89732 0.267266
\(667\) 1.46757 0.0568247
\(668\) −13.6405 −0.527765
\(669\) −0.579752 −0.0224145
\(670\) 39.5205 1.52681
\(671\) −9.70235 −0.374555
\(672\) 0.550410 0.0212325
\(673\) 6.34901 0.244736 0.122368 0.992485i \(-0.460951\pi\)
0.122368 + 0.992485i \(0.460951\pi\)
\(674\) 10.3234 0.397644
\(675\) 0.770841 0.0296697
\(676\) −14.1403 −0.543857
\(677\) 10.1630 0.390595 0.195298 0.980744i \(-0.437433\pi\)
0.195298 + 0.980744i \(0.437433\pi\)
\(678\) 0.809676 0.0310954
\(679\) −32.8412 −1.26033
\(680\) −27.7314 −1.06345
\(681\) 1.08848 0.0417107
\(682\) 26.5774 1.01770
\(683\) 38.2914 1.46518 0.732590 0.680670i \(-0.238311\pi\)
0.732590 + 0.680670i \(0.238311\pi\)
\(684\) 88.5310 3.38507
\(685\) 25.4091 0.970832
\(686\) 31.4092 1.19921
\(687\) −0.320700 −0.0122355
\(688\) 5.52250 0.210543
\(689\) −38.2954 −1.45894
\(690\) 1.84075 0.0700762
\(691\) 31.7251 1.20688 0.603439 0.797409i \(-0.293797\pi\)
0.603439 + 0.797409i \(0.293797\pi\)
\(692\) −75.1307 −2.85604
\(693\) 9.51209 0.361334
\(694\) −61.6112 −2.33873
\(695\) 31.1925 1.18320
\(696\) 0.0724896 0.00274771
\(697\) 17.1653 0.650182
\(698\) 8.58015 0.324764
\(699\) −0.848501 −0.0320932
\(700\) 37.6684 1.42373
\(701\) 20.0397 0.756890 0.378445 0.925624i \(-0.376459\pi\)
0.378445 + 0.925624i \(0.376459\pi\)
\(702\) 2.21331 0.0835361
\(703\) −6.22132 −0.234642
\(704\) 2.98828 0.112625
\(705\) 0.257674 0.00970455
\(706\) −40.8747 −1.53834
\(707\) −19.6737 −0.739906
\(708\) −0.296582 −0.0111462
\(709\) −34.0422 −1.27848 −0.639240 0.769007i \(-0.720751\pi\)
−0.639240 + 0.769007i \(0.720751\pi\)
\(710\) −107.320 −4.02764
\(711\) 37.6083 1.41042
\(712\) −83.3711 −3.12446
\(713\) 59.0872 2.21283
\(714\) 0.635440 0.0237807
\(715\) 8.68086 0.324646
\(716\) 92.6606 3.46289
\(717\) −0.898645 −0.0335605
\(718\) −46.0794 −1.71967
\(719\) 30.1973 1.12617 0.563085 0.826399i \(-0.309614\pi\)
0.563085 + 0.826399i \(0.309614\pi\)
\(720\) −51.2253 −1.90906
\(721\) 37.7165 1.40463
\(722\) −68.8349 −2.56177
\(723\) 0.590694 0.0219682
\(724\) −2.11758 −0.0786991
\(725\) 0.717519 0.0266480
\(726\) 0.118239 0.00438826
\(727\) −25.3434 −0.939935 −0.469967 0.882684i \(-0.655734\pi\)
−0.469967 + 0.882684i \(0.655734\pi\)
\(728\) 58.2941 2.16052
\(729\) −26.8810 −0.995591
\(730\) −37.7367 −1.39670
\(731\) 1.52253 0.0563127
\(732\) −1.97680 −0.0730646
\(733\) −11.5879 −0.428008 −0.214004 0.976833i \(-0.568651\pi\)
−0.214004 + 0.976833i \(0.568651\pi\)
\(734\) 87.9078 3.24474
\(735\) −0.400795 −0.0147835
\(736\) −20.6727 −0.762005
\(737\) 5.64376 0.207890
\(738\) 76.4884 2.81558
\(739\) −4.40898 −0.162187 −0.0810935 0.996706i \(-0.525841\pi\)
−0.0810935 + 0.996706i \(0.525841\pi\)
\(740\) 11.0275 0.405378
\(741\) −0.997826 −0.0366561
\(742\) −98.0194 −3.59840
\(743\) −14.3363 −0.525948 −0.262974 0.964803i \(-0.584703\pi\)
−0.262974 + 0.964803i \(0.584703\pi\)
\(744\) 2.91856 0.107000
\(745\) −46.0870 −1.68850
\(746\) −26.8019 −0.981288
\(747\) 22.7201 0.831284
\(748\) −7.34763 −0.268656
\(749\) 20.3534 0.743698
\(750\) −0.744412 −0.0271821
\(751\) −13.4353 −0.490260 −0.245130 0.969490i \(-0.578831\pi\)
−0.245130 + 0.969490i \(0.578831\pi\)
\(752\) −12.1180 −0.441897
\(753\) −0.755394 −0.0275281
\(754\) 2.06021 0.0750283
\(755\) 66.1342 2.40687
\(756\) 3.87749 0.141023
\(757\) −42.3422 −1.53895 −0.769476 0.638676i \(-0.779483\pi\)
−0.769476 + 0.638676i \(0.779483\pi\)
\(758\) −82.6893 −3.00341
\(759\) 0.262870 0.00954156
\(760\) 111.460 4.04307
\(761\) −13.4199 −0.486470 −0.243235 0.969967i \(-0.578209\pi\)
−0.243235 + 0.969967i \(0.578209\pi\)
\(762\) 0.549334 0.0199003
\(763\) 6.31793 0.228724
\(764\) −84.4563 −3.05552
\(765\) −14.1226 −0.510603
\(766\) 0.336363 0.0121533
\(767\) −4.54307 −0.164041
\(768\) 1.48227 0.0534868
\(769\) −18.3032 −0.660029 −0.330015 0.943976i \(-0.607054\pi\)
−0.330015 + 0.943976i \(0.607054\pi\)
\(770\) 22.2192 0.800725
\(771\) −0.188367 −0.00678386
\(772\) −34.6748 −1.24797
\(773\) −31.3248 −1.12667 −0.563336 0.826228i \(-0.690483\pi\)
−0.563336 + 0.826228i \(0.690483\pi\)
\(774\) 6.78436 0.243859
\(775\) 28.8886 1.03771
\(776\) 60.9264 2.18713
\(777\) −0.136191 −0.00488583
\(778\) 47.9325 1.71846
\(779\) −68.9919 −2.47189
\(780\) 1.76868 0.0633288
\(781\) −15.3259 −0.548403
\(782\) −23.8663 −0.853456
\(783\) 0.0738597 0.00263953
\(784\) 18.8487 0.673169
\(785\) −37.4209 −1.33561
\(786\) 0.118239 0.00421744
\(787\) −6.47761 −0.230902 −0.115451 0.993313i \(-0.536831\pi\)
−0.115451 + 0.993313i \(0.536831\pi\)
\(788\) −76.2341 −2.71573
\(789\) 0.296061 0.0105400
\(790\) 87.8488 3.12552
\(791\) 21.7283 0.772568
\(792\) −17.6466 −0.627045
\(793\) −30.2808 −1.07530
\(794\) −5.26635 −0.186896
\(795\) −1.60290 −0.0568490
\(796\) 24.6932 0.875229
\(797\) −19.8653 −0.703665 −0.351832 0.936063i \(-0.614441\pi\)
−0.351832 + 0.936063i \(0.614441\pi\)
\(798\) −2.55400 −0.0904106
\(799\) −3.34087 −0.118191
\(800\) −10.1072 −0.357342
\(801\) −42.4578 −1.50017
\(802\) 44.3386 1.56565
\(803\) −5.38902 −0.190174
\(804\) 1.14988 0.0405533
\(805\) 49.3979 1.74105
\(806\) 82.9476 2.92170
\(807\) −0.896723 −0.0315661
\(808\) 36.4982 1.28400
\(809\) −37.7871 −1.32852 −0.664262 0.747500i \(-0.731254\pi\)
−0.664262 + 0.747500i \(0.731254\pi\)
\(810\) −62.8837 −2.20951
\(811\) 2.96881 0.104249 0.0521244 0.998641i \(-0.483401\pi\)
0.0521244 + 0.998641i \(0.483401\pi\)
\(812\) 3.60927 0.126661
\(813\) −0.405364 −0.0142167
\(814\) 2.30080 0.0806429
\(815\) −43.0598 −1.50832
\(816\) −0.488685 −0.0171074
\(817\) −6.11944 −0.214092
\(818\) −7.94263 −0.277708
\(819\) 29.6870 1.03735
\(820\) 122.290 4.27055
\(821\) 10.0762 0.351663 0.175832 0.984420i \(-0.443739\pi\)
0.175832 + 0.984420i \(0.443739\pi\)
\(822\) 1.08013 0.0376740
\(823\) −43.3488 −1.51104 −0.755521 0.655124i \(-0.772616\pi\)
−0.755521 + 0.655124i \(0.772616\pi\)
\(824\) −69.9708 −2.43755
\(825\) 0.128521 0.00447452
\(826\) −11.6283 −0.404599
\(827\) −24.7676 −0.861252 −0.430626 0.902530i \(-0.641707\pi\)
−0.430626 + 0.902530i \(0.641707\pi\)
\(828\) −72.7900 −2.52963
\(829\) 10.6074 0.368410 0.184205 0.982888i \(-0.441029\pi\)
0.184205 + 0.982888i \(0.441029\pi\)
\(830\) 53.0716 1.84214
\(831\) 0.885498 0.0307176
\(832\) 9.32636 0.323333
\(833\) 5.19651 0.180048
\(834\) 1.32598 0.0459150
\(835\) −8.74569 −0.302657
\(836\) 29.5320 1.02139
\(837\) 2.97372 0.102787
\(838\) 35.7836 1.23612
\(839\) −52.5107 −1.81287 −0.906435 0.422346i \(-0.861207\pi\)
−0.906435 + 0.422346i \(0.861207\pi\)
\(840\) 2.43997 0.0841869
\(841\) −28.9312 −0.997629
\(842\) −24.0854 −0.830037
\(843\) 0.676787 0.0233098
\(844\) −91.6160 −3.15355
\(845\) −9.06616 −0.311885
\(846\) −14.8869 −0.511821
\(847\) 3.17303 0.109027
\(848\) 75.3818 2.58862
\(849\) −0.240314 −0.00824756
\(850\) −11.6686 −0.400228
\(851\) 5.11515 0.175345
\(852\) −3.12256 −0.106977
\(853\) 3.69806 0.126619 0.0633096 0.997994i \(-0.479834\pi\)
0.0633096 + 0.997994i \(0.479834\pi\)
\(854\) −77.5056 −2.65219
\(855\) 56.7623 1.94123
\(856\) −37.7592 −1.29058
\(857\) 3.04834 0.104129 0.0520646 0.998644i \(-0.483420\pi\)
0.0520646 + 0.998644i \(0.483420\pi\)
\(858\) 0.369021 0.0125982
\(859\) 4.23867 0.144621 0.0723107 0.997382i \(-0.476963\pi\)
0.0723107 + 0.997382i \(0.476963\pi\)
\(860\) 10.8469 0.369875
\(861\) −1.51030 −0.0514710
\(862\) −24.3992 −0.831039
\(863\) 0.242492 0.00825452 0.00412726 0.999991i \(-0.498686\pi\)
0.00412726 + 0.999991i \(0.498686\pi\)
\(864\) −1.04041 −0.0353954
\(865\) −48.1706 −1.63785
\(866\) 38.3526 1.30327
\(867\) 0.663684 0.0225399
\(868\) 145.316 4.93233
\(869\) 12.5453 0.425570
\(870\) 0.0862324 0.00292355
\(871\) 17.6140 0.596829
\(872\) −11.7209 −0.396919
\(873\) 31.0275 1.05012
\(874\) 95.9248 3.24470
\(875\) −19.9769 −0.675341
\(876\) −1.09798 −0.0370974
\(877\) −20.3217 −0.686214 −0.343107 0.939296i \(-0.611479\pi\)
−0.343107 + 0.939296i \(0.611479\pi\)
\(878\) −35.0626 −1.18331
\(879\) 0.490632 0.0165486
\(880\) −17.0877 −0.576026
\(881\) −39.6208 −1.33486 −0.667430 0.744673i \(-0.732606\pi\)
−0.667430 + 0.744673i \(0.732606\pi\)
\(882\) 23.1556 0.779689
\(883\) 19.8870 0.669252 0.334626 0.942351i \(-0.391390\pi\)
0.334626 + 0.942351i \(0.391390\pi\)
\(884\) −22.9318 −0.771279
\(885\) −0.190156 −0.00639201
\(886\) −2.65027 −0.0890375
\(887\) 31.2209 1.04830 0.524148 0.851627i \(-0.324384\pi\)
0.524148 + 0.851627i \(0.324384\pi\)
\(888\) 0.252659 0.00847867
\(889\) 14.7418 0.494423
\(890\) −99.1768 −3.32441
\(891\) −8.98015 −0.300846
\(892\) 53.5515 1.79304
\(893\) 13.4278 0.449345
\(894\) −1.95915 −0.0655236
\(895\) 59.4100 1.98586
\(896\) 47.3104 1.58053
\(897\) 0.820410 0.0273927
\(898\) 20.7885 0.693721
\(899\) 2.76802 0.0923186
\(900\) −35.5881 −1.18627
\(901\) 20.7824 0.692362
\(902\) 25.5149 0.849553
\(903\) −0.133961 −0.00445793
\(904\) −40.3098 −1.34068
\(905\) −1.35770 −0.0451315
\(906\) 2.81135 0.0934007
\(907\) −38.7326 −1.28609 −0.643047 0.765827i \(-0.722330\pi\)
−0.643047 + 0.765827i \(0.722330\pi\)
\(908\) −100.543 −3.33662
\(909\) 18.5872 0.616499
\(910\) 69.3456 2.29879
\(911\) −38.9977 −1.29205 −0.646026 0.763316i \(-0.723570\pi\)
−0.646026 + 0.763316i \(0.723570\pi\)
\(912\) 1.96415 0.0650396
\(913\) 7.57893 0.250826
\(914\) 9.29646 0.307500
\(915\) −1.26744 −0.0419003
\(916\) 29.6229 0.978769
\(917\) 3.17303 0.104783
\(918\) −1.20113 −0.0396434
\(919\) −22.5952 −0.745347 −0.372673 0.927963i \(-0.621559\pi\)
−0.372673 + 0.927963i \(0.621559\pi\)
\(920\) −91.6419 −3.02134
\(921\) 0.191561 0.00631214
\(922\) 54.0839 1.78116
\(923\) −47.8317 −1.57440
\(924\) 0.646487 0.0212678
\(925\) 2.50087 0.0822282
\(926\) 6.47338 0.212729
\(927\) −35.6335 −1.17036
\(928\) −0.968439 −0.0317906
\(929\) 52.9403 1.73691 0.868457 0.495765i \(-0.165112\pi\)
0.868457 + 0.495765i \(0.165112\pi\)
\(930\) 3.47187 0.113847
\(931\) −20.8861 −0.684515
\(932\) 78.3757 2.56728
\(933\) −0.698293 −0.0228611
\(934\) 92.5919 3.02970
\(935\) −4.71099 −0.154066
\(936\) −55.0747 −1.80017
\(937\) 38.0513 1.24308 0.621541 0.783381i \(-0.286507\pi\)
0.621541 + 0.783381i \(0.286507\pi\)
\(938\) 45.0842 1.47205
\(939\) 1.25343 0.0409041
\(940\) −23.8012 −0.776310
\(941\) 19.4908 0.635381 0.317691 0.948194i \(-0.397093\pi\)
0.317691 + 0.948194i \(0.397093\pi\)
\(942\) −1.59075 −0.0518295
\(943\) 56.7249 1.84722
\(944\) 8.94272 0.291061
\(945\) 2.48609 0.0808724
\(946\) 2.26312 0.0735803
\(947\) −1.69513 −0.0550845 −0.0275422 0.999621i \(-0.508768\pi\)
−0.0275422 + 0.999621i \(0.508768\pi\)
\(948\) 2.55604 0.0830162
\(949\) −16.8190 −0.545968
\(950\) 46.8990 1.52161
\(951\) 1.45404 0.0471506
\(952\) −31.6354 −1.02531
\(953\) −38.7305 −1.25460 −0.627302 0.778776i \(-0.715841\pi\)
−0.627302 + 0.778776i \(0.715841\pi\)
\(954\) 92.6061 2.99823
\(955\) −54.1498 −1.75225
\(956\) 83.0075 2.68465
\(957\) 0.0123145 0.000398071 0
\(958\) 8.34660 0.269666
\(959\) 28.9862 0.936013
\(960\) 0.390366 0.0125990
\(961\) 80.4454 2.59501
\(962\) 7.18074 0.231516
\(963\) −19.2294 −0.619658
\(964\) −54.5622 −1.75733
\(965\) −22.2320 −0.715675
\(966\) 2.09989 0.0675629
\(967\) 13.1156 0.421768 0.210884 0.977511i \(-0.432366\pi\)
0.210884 + 0.977511i \(0.432366\pi\)
\(968\) −5.88653 −0.189200
\(969\) 0.541507 0.0173957
\(970\) 72.4770 2.32710
\(971\) −2.65520 −0.0852094 −0.0426047 0.999092i \(-0.513566\pi\)
−0.0426047 + 0.999092i \(0.513566\pi\)
\(972\) −5.49570 −0.176275
\(973\) 35.5837 1.14076
\(974\) −1.51703 −0.0486086
\(975\) 0.401111 0.0128458
\(976\) 59.6057 1.90793
\(977\) −19.2988 −0.617424 −0.308712 0.951155i \(-0.599898\pi\)
−0.308712 + 0.951155i \(0.599898\pi\)
\(978\) −1.83046 −0.0585317
\(979\) −14.1630 −0.452652
\(980\) 37.0213 1.18260
\(981\) −5.96901 −0.190576
\(982\) −58.8178 −1.87695
\(983\) −44.8887 −1.43173 −0.715864 0.698239i \(-0.753967\pi\)
−0.715864 + 0.698239i \(0.753967\pi\)
\(984\) 2.80188 0.0893207
\(985\) −48.8781 −1.55739
\(986\) −1.11805 −0.0356059
\(987\) 0.293949 0.00935649
\(988\) 92.1689 2.93228
\(989\) 5.03138 0.159989
\(990\) −20.9921 −0.667173
\(991\) −34.3843 −1.09225 −0.546126 0.837703i \(-0.683898\pi\)
−0.546126 + 0.837703i \(0.683898\pi\)
\(992\) −38.9911 −1.23797
\(993\) 0.263040 0.00834733
\(994\) −122.428 −3.88319
\(995\) 15.8323 0.501916
\(996\) 1.54416 0.0489287
\(997\) −40.1054 −1.27015 −0.635076 0.772450i \(-0.719031\pi\)
−0.635076 + 0.772450i \(0.719031\pi\)
\(998\) −29.1136 −0.921574
\(999\) 0.257434 0.00814485
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 1441.2.a.f.1.2 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.f.1.2 31 1.1 even 1 trivial