Properties

Label 1859.2.a.t.1.13
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} +0.0164567 q^{5} +2.33656 q^{6} +0.793722 q^{7} -2.63725 q^{8} +6.06060 q^{9} +O(q^{10})\) \(q+0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} +0.0164567 q^{5} +2.33656 q^{6} +0.793722 q^{7} -2.63725 q^{8} +6.06060 q^{9} +0.0127744 q^{10} +1.00000 q^{11} -4.20643 q^{12} +0.616122 q^{14} +0.0495361 q^{15} +0.747743 q^{16} +3.12834 q^{17} +4.70450 q^{18} +1.22596 q^{19} -0.0229974 q^{20} +2.38917 q^{21} +0.776244 q^{22} +4.26925 q^{23} -7.93833 q^{24} -4.99973 q^{25} +9.21265 q^{27} -1.10918 q^{28} +8.01948 q^{29} +0.0384521 q^{30} +2.49364 q^{31} +5.85492 q^{32} +3.01008 q^{33} +2.42836 q^{34} +0.0130621 q^{35} -8.46935 q^{36} -8.88674 q^{37} +0.951641 q^{38} -0.0434004 q^{40} -8.43142 q^{41} +1.85458 q^{42} +11.8954 q^{43} -1.39745 q^{44} +0.0997375 q^{45} +3.31398 q^{46} +12.2753 q^{47} +2.25077 q^{48} -6.37001 q^{49} -3.88101 q^{50} +9.41657 q^{51} +4.56675 q^{53} +7.15126 q^{54} +0.0164567 q^{55} -2.09324 q^{56} +3.69023 q^{57} +6.22507 q^{58} +0.265214 q^{59} -0.0692239 q^{60} -4.49240 q^{61} +1.93567 q^{62} +4.81043 q^{63} +3.04936 q^{64} +2.33656 q^{66} +5.31411 q^{67} -4.37169 q^{68} +12.8508 q^{69} +0.0101393 q^{70} -13.1162 q^{71} -15.9833 q^{72} -11.5434 q^{73} -6.89828 q^{74} -15.0496 q^{75} -1.71321 q^{76} +0.793722 q^{77} -9.35606 q^{79} +0.0123054 q^{80} +9.54904 q^{81} -6.54484 q^{82} -4.81647 q^{83} -3.33873 q^{84} +0.0514822 q^{85} +9.23375 q^{86} +24.1393 q^{87} -2.63725 q^{88} -1.66164 q^{89} +0.0774207 q^{90} -5.96605 q^{92} +7.50605 q^{93} +9.52863 q^{94} +0.0201752 q^{95} +17.6238 q^{96} +8.35282 q^{97} -4.94468 q^{98} +6.06060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.776244 0.548887 0.274444 0.961603i \(-0.411506\pi\)
0.274444 + 0.961603i \(0.411506\pi\)
\(3\) 3.01008 1.73787 0.868936 0.494925i \(-0.164804\pi\)
0.868936 + 0.494925i \(0.164804\pi\)
\(4\) −1.39745 −0.698723
\(5\) 0.0164567 0.00735967 0.00367983 0.999993i \(-0.498829\pi\)
0.00367983 + 0.999993i \(0.498829\pi\)
\(6\) 2.33656 0.953896
\(7\) 0.793722 0.299999 0.149999 0.988686i \(-0.452073\pi\)
0.149999 + 0.988686i \(0.452073\pi\)
\(8\) −2.63725 −0.932407
\(9\) 6.06060 2.02020
\(10\) 0.0127744 0.00403963
\(11\) 1.00000 0.301511
\(12\) −4.20643 −1.21429
\(13\) 0 0
\(14\) 0.616122 0.164665
\(15\) 0.0495361 0.0127902
\(16\) 0.747743 0.186936
\(17\) 3.12834 0.758734 0.379367 0.925246i \(-0.376142\pi\)
0.379367 + 0.925246i \(0.376142\pi\)
\(18\) 4.70450 1.10886
\(19\) 1.22596 0.281254 0.140627 0.990063i \(-0.455088\pi\)
0.140627 + 0.990063i \(0.455088\pi\)
\(20\) −0.0229974 −0.00514237
\(21\) 2.38917 0.521359
\(22\) 0.776244 0.165496
\(23\) 4.26925 0.890201 0.445100 0.895481i \(-0.353168\pi\)
0.445100 + 0.895481i \(0.353168\pi\)
\(24\) −7.93833 −1.62040
\(25\) −4.99973 −0.999946
\(26\) 0 0
\(27\) 9.21265 1.77298
\(28\) −1.10918 −0.209616
\(29\) 8.01948 1.48918 0.744590 0.667522i \(-0.232645\pi\)
0.744590 + 0.667522i \(0.232645\pi\)
\(30\) 0.0384521 0.00702036
\(31\) 2.49364 0.447870 0.223935 0.974604i \(-0.428110\pi\)
0.223935 + 0.974604i \(0.428110\pi\)
\(32\) 5.85492 1.03501
\(33\) 3.01008 0.523988
\(34\) 2.42836 0.416460
\(35\) 0.0130621 0.00220789
\(36\) −8.46935 −1.41156
\(37\) −8.88674 −1.46097 −0.730486 0.682928i \(-0.760706\pi\)
−0.730486 + 0.682928i \(0.760706\pi\)
\(38\) 0.951641 0.154377
\(39\) 0 0
\(40\) −0.0434004 −0.00686221
\(41\) −8.43142 −1.31677 −0.658384 0.752683i \(-0.728760\pi\)
−0.658384 + 0.752683i \(0.728760\pi\)
\(42\) 1.85458 0.286167
\(43\) 11.8954 1.81404 0.907018 0.421092i \(-0.138353\pi\)
0.907018 + 0.421092i \(0.138353\pi\)
\(44\) −1.39745 −0.210673
\(45\) 0.0997375 0.0148680
\(46\) 3.31398 0.488620
\(47\) 12.2753 1.79054 0.895268 0.445528i \(-0.146984\pi\)
0.895268 + 0.445528i \(0.146984\pi\)
\(48\) 2.25077 0.324871
\(49\) −6.37001 −0.910001
\(50\) −3.88101 −0.548858
\(51\) 9.41657 1.31858
\(52\) 0 0
\(53\) 4.56675 0.627292 0.313646 0.949540i \(-0.398450\pi\)
0.313646 + 0.949540i \(0.398450\pi\)
\(54\) 7.15126 0.973164
\(55\) 0.0164567 0.00221902
\(56\) −2.09324 −0.279721
\(57\) 3.69023 0.488783
\(58\) 6.22507 0.817392
\(59\) 0.265214 0.0345279 0.0172639 0.999851i \(-0.494504\pi\)
0.0172639 + 0.999851i \(0.494504\pi\)
\(60\) −0.0692239 −0.00893677
\(61\) −4.49240 −0.575192 −0.287596 0.957752i \(-0.592856\pi\)
−0.287596 + 0.957752i \(0.592856\pi\)
\(62\) 1.93567 0.245830
\(63\) 4.81043 0.606057
\(64\) 3.04936 0.381170
\(65\) 0 0
\(66\) 2.33656 0.287610
\(67\) 5.31411 0.649221 0.324611 0.945848i \(-0.394767\pi\)
0.324611 + 0.945848i \(0.394767\pi\)
\(68\) −4.37169 −0.530145
\(69\) 12.8508 1.54706
\(70\) 0.0101393 0.00121188
\(71\) −13.1162 −1.55661 −0.778304 0.627888i \(-0.783920\pi\)
−0.778304 + 0.627888i \(0.783920\pi\)
\(72\) −15.9833 −1.88365
\(73\) −11.5434 −1.35106 −0.675529 0.737333i \(-0.736085\pi\)
−0.675529 + 0.737333i \(0.736085\pi\)
\(74\) −6.89828 −0.801909
\(75\) −15.0496 −1.73778
\(76\) −1.71321 −0.196518
\(77\) 0.793722 0.0904530
\(78\) 0 0
\(79\) −9.35606 −1.05264 −0.526320 0.850287i \(-0.676428\pi\)
−0.526320 + 0.850287i \(0.676428\pi\)
\(80\) 0.0123054 0.00137579
\(81\) 9.54904 1.06100
\(82\) −6.54484 −0.722757
\(83\) −4.81647 −0.528677 −0.264338 0.964430i \(-0.585154\pi\)
−0.264338 + 0.964430i \(0.585154\pi\)
\(84\) −3.33873 −0.364285
\(85\) 0.0514822 0.00558403
\(86\) 9.23375 0.995701
\(87\) 24.1393 2.58800
\(88\) −2.63725 −0.281131
\(89\) −1.66164 −0.176134 −0.0880668 0.996115i \(-0.528069\pi\)
−0.0880668 + 0.996115i \(0.528069\pi\)
\(90\) 0.0774207 0.00816085
\(91\) 0 0
\(92\) −5.96605 −0.622003
\(93\) 7.50605 0.778341
\(94\) 9.52863 0.982803
\(95\) 0.0201752 0.00206993
\(96\) 17.6238 1.79872
\(97\) 8.35282 0.848101 0.424050 0.905639i \(-0.360608\pi\)
0.424050 + 0.905639i \(0.360608\pi\)
\(98\) −4.94468 −0.499488
\(99\) 6.06060 0.609113
\(100\) 6.98685 0.698685
\(101\) 5.67235 0.564420 0.282210 0.959353i \(-0.408933\pi\)
0.282210 + 0.959353i \(0.408933\pi\)
\(102\) 7.30955 0.723754
\(103\) 16.9225 1.66743 0.833714 0.552197i \(-0.186210\pi\)
0.833714 + 0.552197i \(0.186210\pi\)
\(104\) 0 0
\(105\) 0.0393178 0.00383703
\(106\) 3.54491 0.344312
\(107\) 4.36032 0.421528 0.210764 0.977537i \(-0.432405\pi\)
0.210764 + 0.977537i \(0.432405\pi\)
\(108\) −12.8742 −1.23882
\(109\) −17.4935 −1.67557 −0.837787 0.545997i \(-0.816151\pi\)
−0.837787 + 0.545997i \(0.816151\pi\)
\(110\) 0.0127744 0.00121799
\(111\) −26.7498 −2.53898
\(112\) 0.593500 0.0560805
\(113\) 1.17709 0.110731 0.0553655 0.998466i \(-0.482368\pi\)
0.0553655 + 0.998466i \(0.482368\pi\)
\(114\) 2.86452 0.268287
\(115\) 0.0702579 0.00655158
\(116\) −11.2068 −1.04052
\(117\) 0 0
\(118\) 0.205870 0.0189519
\(119\) 2.48303 0.227619
\(120\) −0.130639 −0.0119256
\(121\) 1.00000 0.0909091
\(122\) −3.48720 −0.315716
\(123\) −25.3793 −2.28837
\(124\) −3.48472 −0.312937
\(125\) −0.164563 −0.0147189
\(126\) 3.73406 0.332657
\(127\) −0.134766 −0.0119585 −0.00597926 0.999982i \(-0.501903\pi\)
−0.00597926 + 0.999982i \(0.501903\pi\)
\(128\) −9.34280 −0.825795
\(129\) 35.8062 3.15256
\(130\) 0 0
\(131\) −21.2414 −1.85587 −0.927933 0.372746i \(-0.878416\pi\)
−0.927933 + 0.372746i \(0.878416\pi\)
\(132\) −4.20643 −0.366122
\(133\) 0.973068 0.0843757
\(134\) 4.12504 0.356349
\(135\) 0.151610 0.0130485
\(136\) −8.25021 −0.707450
\(137\) 10.7421 0.917763 0.458882 0.888497i \(-0.348250\pi\)
0.458882 + 0.888497i \(0.348250\pi\)
\(138\) 9.97536 0.849159
\(139\) −13.7985 −1.17037 −0.585186 0.810899i \(-0.698979\pi\)
−0.585186 + 0.810899i \(0.698979\pi\)
\(140\) −0.0182535 −0.00154270
\(141\) 36.9497 3.11172
\(142\) −10.1814 −0.854402
\(143\) 0 0
\(144\) 4.53177 0.377648
\(145\) 0.131974 0.0109599
\(146\) −8.96053 −0.741579
\(147\) −19.1742 −1.58146
\(148\) 12.4187 1.02081
\(149\) −12.7827 −1.04720 −0.523600 0.851964i \(-0.675411\pi\)
−0.523600 + 0.851964i \(0.675411\pi\)
\(150\) −11.6822 −0.953844
\(151\) 8.66190 0.704895 0.352448 0.935832i \(-0.385349\pi\)
0.352448 + 0.935832i \(0.385349\pi\)
\(152\) −3.23315 −0.262243
\(153\) 18.9596 1.53279
\(154\) 0.616122 0.0496485
\(155\) 0.0410371 0.00329618
\(156\) 0 0
\(157\) −5.07034 −0.404657 −0.202328 0.979318i \(-0.564851\pi\)
−0.202328 + 0.979318i \(0.564851\pi\)
\(158\) −7.26259 −0.577780
\(159\) 13.7463 1.09015
\(160\) 0.0963528 0.00761736
\(161\) 3.38860 0.267059
\(162\) 7.41239 0.582372
\(163\) 18.7754 1.47060 0.735300 0.677741i \(-0.237041\pi\)
0.735300 + 0.677741i \(0.237041\pi\)
\(164\) 11.7825 0.920055
\(165\) 0.0495361 0.00385638
\(166\) −3.73876 −0.290184
\(167\) −15.4424 −1.19497 −0.597483 0.801882i \(-0.703832\pi\)
−0.597483 + 0.801882i \(0.703832\pi\)
\(168\) −6.30082 −0.486119
\(169\) 0 0
\(170\) 0.0399628 0.00306500
\(171\) 7.43003 0.568188
\(172\) −16.6232 −1.26751
\(173\) −7.64125 −0.580953 −0.290477 0.956882i \(-0.593814\pi\)
−0.290477 + 0.956882i \(0.593814\pi\)
\(174\) 18.7380 1.42052
\(175\) −3.96839 −0.299982
\(176\) 0.747743 0.0563633
\(177\) 0.798315 0.0600050
\(178\) −1.28984 −0.0966776
\(179\) −21.6699 −1.61968 −0.809841 0.586649i \(-0.800447\pi\)
−0.809841 + 0.586649i \(0.800447\pi\)
\(180\) −0.139378 −0.0103886
\(181\) −11.9637 −0.889252 −0.444626 0.895716i \(-0.646663\pi\)
−0.444626 + 0.895716i \(0.646663\pi\)
\(182\) 0 0
\(183\) −13.5225 −0.999611
\(184\) −11.2591 −0.830030
\(185\) −0.146247 −0.0107523
\(186\) 5.82653 0.427222
\(187\) 3.12834 0.228767
\(188\) −17.1541 −1.25109
\(189\) 7.31228 0.531890
\(190\) 0.0156609 0.00113616
\(191\) −11.5803 −0.837924 −0.418962 0.908004i \(-0.637606\pi\)
−0.418962 + 0.908004i \(0.637606\pi\)
\(192\) 9.17884 0.662425
\(193\) −23.4115 −1.68519 −0.842597 0.538545i \(-0.818974\pi\)
−0.842597 + 0.538545i \(0.818974\pi\)
\(194\) 6.48383 0.465512
\(195\) 0 0
\(196\) 8.90173 0.635838
\(197\) 6.57290 0.468300 0.234150 0.972200i \(-0.424769\pi\)
0.234150 + 0.972200i \(0.424769\pi\)
\(198\) 4.70450 0.334334
\(199\) 19.8590 1.40777 0.703884 0.710315i \(-0.251448\pi\)
0.703884 + 0.710315i \(0.251448\pi\)
\(200\) 13.1855 0.932357
\(201\) 15.9959 1.12826
\(202\) 4.40313 0.309803
\(203\) 6.36523 0.446752
\(204\) −13.1591 −0.921324
\(205\) −0.138754 −0.00969097
\(206\) 13.1360 0.915230
\(207\) 25.8742 1.79838
\(208\) 0 0
\(209\) 1.22596 0.0848012
\(210\) 0.0305202 0.00210610
\(211\) 7.79372 0.536542 0.268271 0.963343i \(-0.413548\pi\)
0.268271 + 0.963343i \(0.413548\pi\)
\(212\) −6.38179 −0.438303
\(213\) −39.4809 −2.70518
\(214\) 3.38467 0.231372
\(215\) 0.195760 0.0133507
\(216\) −24.2960 −1.65314
\(217\) 1.97925 0.134360
\(218\) −13.5792 −0.919702
\(219\) −34.7467 −2.34797
\(220\) −0.0229974 −0.00155048
\(221\) 0 0
\(222\) −20.7644 −1.39361
\(223\) 4.38266 0.293485 0.146742 0.989175i \(-0.453121\pi\)
0.146742 + 0.989175i \(0.453121\pi\)
\(224\) 4.64718 0.310503
\(225\) −30.3013 −2.02009
\(226\) 0.913707 0.0607789
\(227\) 21.0447 1.39679 0.698393 0.715714i \(-0.253899\pi\)
0.698393 + 0.715714i \(0.253899\pi\)
\(228\) −5.15689 −0.341524
\(229\) −12.8810 −0.851197 −0.425599 0.904912i \(-0.639936\pi\)
−0.425599 + 0.904912i \(0.639936\pi\)
\(230\) 0.0545373 0.00359608
\(231\) 2.38917 0.157196
\(232\) −21.1493 −1.38852
\(233\) −13.8170 −0.905185 −0.452592 0.891717i \(-0.649501\pi\)
−0.452592 + 0.891717i \(0.649501\pi\)
\(234\) 0 0
\(235\) 0.202011 0.0131778
\(236\) −0.370621 −0.0241254
\(237\) −28.1625 −1.82935
\(238\) 1.92744 0.124937
\(239\) 3.95240 0.255659 0.127830 0.991796i \(-0.459199\pi\)
0.127830 + 0.991796i \(0.459199\pi\)
\(240\) 0.0370403 0.00239094
\(241\) 5.51486 0.355243 0.177622 0.984099i \(-0.443160\pi\)
0.177622 + 0.984099i \(0.443160\pi\)
\(242\) 0.776244 0.0498989
\(243\) 1.10546 0.0709152
\(244\) 6.27788 0.401900
\(245\) −0.104829 −0.00669730
\(246\) −19.7005 −1.25606
\(247\) 0 0
\(248\) −6.57633 −0.417598
\(249\) −14.4980 −0.918772
\(250\) −0.127741 −0.00807904
\(251\) −6.96137 −0.439398 −0.219699 0.975568i \(-0.570508\pi\)
−0.219699 + 0.975568i \(0.570508\pi\)
\(252\) −6.72231 −0.423466
\(253\) 4.26925 0.268406
\(254\) −0.104611 −0.00656388
\(255\) 0.154966 0.00970433
\(256\) −13.3510 −0.834439
\(257\) 13.5802 0.847108 0.423554 0.905871i \(-0.360782\pi\)
0.423554 + 0.905871i \(0.360782\pi\)
\(258\) 27.7944 1.73040
\(259\) −7.05360 −0.438289
\(260\) 0 0
\(261\) 48.6028 3.00844
\(262\) −16.4885 −1.01866
\(263\) −10.5992 −0.653575 −0.326788 0.945098i \(-0.605966\pi\)
−0.326788 + 0.945098i \(0.605966\pi\)
\(264\) −7.93833 −0.488570
\(265\) 0.0751537 0.00461666
\(266\) 0.755338 0.0463128
\(267\) −5.00168 −0.306098
\(268\) −7.42617 −0.453626
\(269\) 0.00954813 0.000582160 0 0.000291080 1.00000i \(-0.499907\pi\)
0.000291080 1.00000i \(0.499907\pi\)
\(270\) 0.117686 0.00716216
\(271\) −3.75212 −0.227925 −0.113963 0.993485i \(-0.536354\pi\)
−0.113963 + 0.993485i \(0.536354\pi\)
\(272\) 2.33920 0.141835
\(273\) 0 0
\(274\) 8.33852 0.503749
\(275\) −4.99973 −0.301495
\(276\) −17.9583 −1.08096
\(277\) 13.1876 0.792368 0.396184 0.918171i \(-0.370334\pi\)
0.396184 + 0.918171i \(0.370334\pi\)
\(278\) −10.7110 −0.642403
\(279\) 15.1129 0.904787
\(280\) −0.0344478 −0.00205865
\(281\) −24.7282 −1.47516 −0.737579 0.675261i \(-0.764031\pi\)
−0.737579 + 0.675261i \(0.764031\pi\)
\(282\) 28.6820 1.70799
\(283\) −23.1300 −1.37493 −0.687467 0.726216i \(-0.741277\pi\)
−0.687467 + 0.726216i \(0.741277\pi\)
\(284\) 18.3292 1.08764
\(285\) 0.0607291 0.00359728
\(286\) 0 0
\(287\) −6.69220 −0.395028
\(288\) 35.4843 2.09093
\(289\) −7.21348 −0.424322
\(290\) 0.102444 0.00601573
\(291\) 25.1427 1.47389
\(292\) 16.1313 0.944015
\(293\) 10.9621 0.640411 0.320206 0.947348i \(-0.396248\pi\)
0.320206 + 0.947348i \(0.396248\pi\)
\(294\) −14.8839 −0.868046
\(295\) 0.00436454 0.000254114 0
\(296\) 23.4365 1.36222
\(297\) 9.21265 0.534572
\(298\) −9.92249 −0.574795
\(299\) 0 0
\(300\) 21.0310 1.21422
\(301\) 9.44166 0.544208
\(302\) 6.72375 0.386908
\(303\) 17.0742 0.980889
\(304\) 0.916701 0.0525764
\(305\) −0.0739301 −0.00423322
\(306\) 14.7173 0.841331
\(307\) −19.6256 −1.12009 −0.560046 0.828462i \(-0.689216\pi\)
−0.560046 + 0.828462i \(0.689216\pi\)
\(308\) −1.10918 −0.0632015
\(309\) 50.9382 2.89777
\(310\) 0.0318548 0.00180923
\(311\) 14.9752 0.849167 0.424583 0.905389i \(-0.360421\pi\)
0.424583 + 0.905389i \(0.360421\pi\)
\(312\) 0 0
\(313\) 11.5917 0.655201 0.327600 0.944816i \(-0.393760\pi\)
0.327600 + 0.944816i \(0.393760\pi\)
\(314\) −3.93582 −0.222111
\(315\) 0.0791638 0.00446038
\(316\) 13.0746 0.735503
\(317\) 5.55127 0.311791 0.155895 0.987774i \(-0.450174\pi\)
0.155895 + 0.987774i \(0.450174\pi\)
\(318\) 10.6705 0.598371
\(319\) 8.01948 0.449004
\(320\) 0.0501825 0.00280529
\(321\) 13.1249 0.732562
\(322\) 2.63038 0.146585
\(323\) 3.83521 0.213397
\(324\) −13.3443 −0.741348
\(325\) 0 0
\(326\) 14.5743 0.807194
\(327\) −52.6569 −2.91193
\(328\) 22.2357 1.22776
\(329\) 9.74317 0.537158
\(330\) 0.0384521 0.00211672
\(331\) 7.04341 0.387141 0.193570 0.981086i \(-0.437993\pi\)
0.193570 + 0.981086i \(0.437993\pi\)
\(332\) 6.73076 0.369398
\(333\) −53.8590 −2.95145
\(334\) −11.9870 −0.655901
\(335\) 0.0874527 0.00477805
\(336\) 1.78648 0.0974607
\(337\) −16.3751 −0.892009 −0.446004 0.895031i \(-0.647153\pi\)
−0.446004 + 0.895031i \(0.647153\pi\)
\(338\) 0 0
\(339\) 3.54313 0.192436
\(340\) −0.0719436 −0.00390169
\(341\) 2.49364 0.135038
\(342\) 5.76751 0.311871
\(343\) −10.6121 −0.572997
\(344\) −31.3712 −1.69142
\(345\) 0.211482 0.0113858
\(346\) −5.93147 −0.318878
\(347\) 11.2716 0.605091 0.302545 0.953135i \(-0.402164\pi\)
0.302545 + 0.953135i \(0.402164\pi\)
\(348\) −33.7333 −1.80830
\(349\) 22.7506 1.21781 0.608907 0.793242i \(-0.291608\pi\)
0.608907 + 0.793242i \(0.291608\pi\)
\(350\) −3.08044 −0.164657
\(351\) 0 0
\(352\) 5.85492 0.312069
\(353\) 3.24835 0.172892 0.0864462 0.996257i \(-0.472449\pi\)
0.0864462 + 0.996257i \(0.472449\pi\)
\(354\) 0.619687 0.0329360
\(355\) −0.215850 −0.0114561
\(356\) 2.32205 0.123069
\(357\) 7.47413 0.395573
\(358\) −16.8211 −0.889023
\(359\) 31.4679 1.66081 0.830405 0.557160i \(-0.188109\pi\)
0.830405 + 0.557160i \(0.188109\pi\)
\(360\) −0.263032 −0.0138630
\(361\) −17.4970 −0.920896
\(362\) −9.28672 −0.488099
\(363\) 3.01008 0.157988
\(364\) 0 0
\(365\) −0.189967 −0.00994334
\(366\) −10.4967 −0.548674
\(367\) 23.1155 1.20662 0.603310 0.797507i \(-0.293848\pi\)
0.603310 + 0.797507i \(0.293848\pi\)
\(368\) 3.19231 0.166410
\(369\) −51.0995 −2.66013
\(370\) −0.113523 −0.00590178
\(371\) 3.62473 0.188187
\(372\) −10.4893 −0.543845
\(373\) −7.74228 −0.400880 −0.200440 0.979706i \(-0.564237\pi\)
−0.200440 + 0.979706i \(0.564237\pi\)
\(374\) 2.42836 0.125567
\(375\) −0.495347 −0.0255796
\(376\) −32.3730 −1.66951
\(377\) 0 0
\(378\) 5.67611 0.291948
\(379\) −10.4868 −0.538670 −0.269335 0.963047i \(-0.586804\pi\)
−0.269335 + 0.963047i \(0.586804\pi\)
\(380\) −0.0281938 −0.00144631
\(381\) −0.405656 −0.0207824
\(382\) −8.98917 −0.459926
\(383\) 9.84176 0.502891 0.251445 0.967872i \(-0.419094\pi\)
0.251445 + 0.967872i \(0.419094\pi\)
\(384\) −28.1226 −1.43513
\(385\) 0.0130621 0.000665704 0
\(386\) −18.1730 −0.924981
\(387\) 72.0934 3.66471
\(388\) −11.6726 −0.592587
\(389\) −24.0364 −1.21869 −0.609347 0.792904i \(-0.708568\pi\)
−0.609347 + 0.792904i \(0.708568\pi\)
\(390\) 0 0
\(391\) 13.3557 0.675426
\(392\) 16.7993 0.848492
\(393\) −63.9383 −3.22526
\(394\) 5.10218 0.257044
\(395\) −0.153970 −0.00774707
\(396\) −8.46935 −0.425601
\(397\) 10.7120 0.537619 0.268809 0.963193i \(-0.413370\pi\)
0.268809 + 0.963193i \(0.413370\pi\)
\(398\) 15.4154 0.772706
\(399\) 2.92901 0.146634
\(400\) −3.73851 −0.186926
\(401\) 10.8191 0.540281 0.270140 0.962821i \(-0.412930\pi\)
0.270140 + 0.962821i \(0.412930\pi\)
\(402\) 12.4167 0.619290
\(403\) 0 0
\(404\) −7.92679 −0.394373
\(405\) 0.157146 0.00780864
\(406\) 4.94097 0.245216
\(407\) −8.88674 −0.440499
\(408\) −24.8338 −1.22946
\(409\) 29.7938 1.47321 0.736604 0.676324i \(-0.236428\pi\)
0.736604 + 0.676324i \(0.236428\pi\)
\(410\) −0.107707 −0.00531925
\(411\) 32.3347 1.59495
\(412\) −23.6483 −1.16507
\(413\) 0.210506 0.0103583
\(414\) 20.0847 0.987110
\(415\) −0.0792634 −0.00389088
\(416\) 0 0
\(417\) −41.5346 −2.03396
\(418\) 0.951641 0.0465463
\(419\) 0.335538 0.0163921 0.00819605 0.999966i \(-0.497391\pi\)
0.00819605 + 0.999966i \(0.497391\pi\)
\(420\) −0.0549445 −0.00268102
\(421\) 34.9448 1.70311 0.851554 0.524267i \(-0.175661\pi\)
0.851554 + 0.524267i \(0.175661\pi\)
\(422\) 6.04983 0.294501
\(423\) 74.3956 3.61724
\(424\) −12.0437 −0.584891
\(425\) −15.6409 −0.758693
\(426\) −30.6468 −1.48484
\(427\) −3.56571 −0.172557
\(428\) −6.09331 −0.294531
\(429\) 0 0
\(430\) 0.151957 0.00732803
\(431\) 15.8744 0.764641 0.382320 0.924030i \(-0.375125\pi\)
0.382320 + 0.924030i \(0.375125\pi\)
\(432\) 6.88870 0.331433
\(433\) −9.59664 −0.461185 −0.230593 0.973050i \(-0.574066\pi\)
−0.230593 + 0.973050i \(0.574066\pi\)
\(434\) 1.53638 0.0737488
\(435\) 0.397253 0.0190468
\(436\) 24.4462 1.17076
\(437\) 5.23392 0.250372
\(438\) −26.9719 −1.28877
\(439\) 7.77923 0.371283 0.185641 0.982618i \(-0.440564\pi\)
0.185641 + 0.982618i \(0.440564\pi\)
\(440\) −0.0434004 −0.00206903
\(441\) −38.6060 −1.83838
\(442\) 0 0
\(443\) −23.0476 −1.09503 −0.547513 0.836797i \(-0.684425\pi\)
−0.547513 + 0.836797i \(0.684425\pi\)
\(444\) 37.3814 1.77404
\(445\) −0.0273452 −0.00129629
\(446\) 3.40201 0.161090
\(447\) −38.4770 −1.81990
\(448\) 2.42035 0.114351
\(449\) 29.1978 1.37793 0.688964 0.724796i \(-0.258066\pi\)
0.688964 + 0.724796i \(0.258066\pi\)
\(450\) −23.5212 −1.10880
\(451\) −8.43142 −0.397020
\(452\) −1.64491 −0.0773703
\(453\) 26.0730 1.22502
\(454\) 16.3358 0.766679
\(455\) 0 0
\(456\) −9.73204 −0.455745
\(457\) −31.1916 −1.45908 −0.729541 0.683937i \(-0.760266\pi\)
−0.729541 + 0.683937i \(0.760266\pi\)
\(458\) −9.99876 −0.467211
\(459\) 28.8203 1.34522
\(460\) −0.0981816 −0.00457774
\(461\) −37.6692 −1.75443 −0.877215 0.480097i \(-0.840601\pi\)
−0.877215 + 0.480097i \(0.840601\pi\)
\(462\) 1.85458 0.0862827
\(463\) −0.988906 −0.0459584 −0.0229792 0.999736i \(-0.507315\pi\)
−0.0229792 + 0.999736i \(0.507315\pi\)
\(464\) 5.99651 0.278381
\(465\) 0.123525 0.00572833
\(466\) −10.7254 −0.496845
\(467\) 11.5156 0.532878 0.266439 0.963852i \(-0.414153\pi\)
0.266439 + 0.963852i \(0.414153\pi\)
\(468\) 0 0
\(469\) 4.21792 0.194765
\(470\) 0.156810 0.00723310
\(471\) −15.2621 −0.703242
\(472\) −0.699434 −0.0321940
\(473\) 11.8954 0.546952
\(474\) −21.8610 −1.00411
\(475\) −6.12945 −0.281238
\(476\) −3.46990 −0.159043
\(477\) 27.6772 1.26725
\(478\) 3.06803 0.140328
\(479\) −9.11697 −0.416565 −0.208283 0.978069i \(-0.566787\pi\)
−0.208283 + 0.978069i \(0.566787\pi\)
\(480\) 0.290030 0.0132380
\(481\) 0 0
\(482\) 4.28088 0.194989
\(483\) 10.2000 0.464114
\(484\) −1.39745 −0.0635202
\(485\) 0.137460 0.00624174
\(486\) 0.858106 0.0389245
\(487\) 18.6189 0.843704 0.421852 0.906665i \(-0.361380\pi\)
0.421852 + 0.906665i \(0.361380\pi\)
\(488\) 11.8476 0.536314
\(489\) 56.5154 2.55572
\(490\) −0.0813732 −0.00367607
\(491\) −25.0177 −1.12903 −0.564517 0.825421i \(-0.690938\pi\)
−0.564517 + 0.825421i \(0.690938\pi\)
\(492\) 35.4662 1.59894
\(493\) 25.0877 1.12989
\(494\) 0 0
\(495\) 0.0997375 0.00448287
\(496\) 1.86460 0.0837230
\(497\) −10.4106 −0.466980
\(498\) −11.2540 −0.504303
\(499\) 6.05960 0.271265 0.135632 0.990759i \(-0.456693\pi\)
0.135632 + 0.990759i \(0.456693\pi\)
\(500\) 0.229967 0.0102845
\(501\) −46.4828 −2.07670
\(502\) −5.40372 −0.241180
\(503\) 11.7680 0.524707 0.262354 0.964972i \(-0.415501\pi\)
0.262354 + 0.964972i \(0.415501\pi\)
\(504\) −12.6863 −0.565092
\(505\) 0.0933482 0.00415394
\(506\) 3.31398 0.147324
\(507\) 0 0
\(508\) 0.188328 0.00835568
\(509\) −2.42538 −0.107503 −0.0537515 0.998554i \(-0.517118\pi\)
−0.0537515 + 0.998554i \(0.517118\pi\)
\(510\) 0.120291 0.00532659
\(511\) −9.16228 −0.405316
\(512\) 8.32195 0.367782
\(513\) 11.2943 0.498656
\(514\) 10.5415 0.464967
\(515\) 0.278489 0.0122717
\(516\) −50.0372 −2.20277
\(517\) 12.2753 0.539867
\(518\) −5.47531 −0.240571
\(519\) −23.0008 −1.00962
\(520\) 0 0
\(521\) −25.3612 −1.11109 −0.555547 0.831485i \(-0.687491\pi\)
−0.555547 + 0.831485i \(0.687491\pi\)
\(522\) 37.7276 1.65129
\(523\) 8.65849 0.378609 0.189305 0.981918i \(-0.439377\pi\)
0.189305 + 0.981918i \(0.439377\pi\)
\(524\) 29.6836 1.29674
\(525\) −11.9452 −0.521331
\(526\) −8.22757 −0.358739
\(527\) 7.80095 0.339815
\(528\) 2.25077 0.0979522
\(529\) −4.77347 −0.207542
\(530\) 0.0583376 0.00253403
\(531\) 1.60735 0.0697531
\(532\) −1.35981 −0.0589552
\(533\) 0 0
\(534\) −3.88252 −0.168013
\(535\) 0.0717566 0.00310231
\(536\) −14.0146 −0.605339
\(537\) −65.2281 −2.81480
\(538\) 0.00741168 0.000319540 0
\(539\) −6.37001 −0.274376
\(540\) −0.211867 −0.00911729
\(541\) 29.9184 1.28629 0.643146 0.765744i \(-0.277629\pi\)
0.643146 + 0.765744i \(0.277629\pi\)
\(542\) −2.91256 −0.125105
\(543\) −36.0116 −1.54541
\(544\) 18.3162 0.785301
\(545\) −0.287886 −0.0123317
\(546\) 0 0
\(547\) 34.8749 1.49114 0.745572 0.666425i \(-0.232176\pi\)
0.745572 + 0.666425i \(0.232176\pi\)
\(548\) −15.0116 −0.641262
\(549\) −27.2266 −1.16200
\(550\) −3.88101 −0.165487
\(551\) 9.83153 0.418837
\(552\) −33.8907 −1.44249
\(553\) −7.42611 −0.315790
\(554\) 10.2368 0.434921
\(555\) −0.440214 −0.0186861
\(556\) 19.2826 0.817766
\(557\) 29.4325 1.24710 0.623548 0.781785i \(-0.285691\pi\)
0.623548 + 0.781785i \(0.285691\pi\)
\(558\) 11.7313 0.496626
\(559\) 0 0
\(560\) 0.00976706 0.000412734 0
\(561\) 9.41657 0.397568
\(562\) −19.1951 −0.809696
\(563\) −31.9030 −1.34455 −0.672276 0.740301i \(-0.734683\pi\)
−0.672276 + 0.740301i \(0.734683\pi\)
\(564\) −51.6351 −2.17423
\(565\) 0.0193710 0.000814943 0
\(566\) −17.9545 −0.754684
\(567\) 7.57928 0.318300
\(568\) 34.5907 1.45139
\(569\) 1.00569 0.0421605 0.0210803 0.999778i \(-0.493289\pi\)
0.0210803 + 0.999778i \(0.493289\pi\)
\(570\) 0.0471406 0.00197450
\(571\) −24.9551 −1.04434 −0.522170 0.852841i \(-0.674877\pi\)
−0.522170 + 0.852841i \(0.674877\pi\)
\(572\) 0 0
\(573\) −34.8578 −1.45620
\(574\) −5.19478 −0.216826
\(575\) −21.3451 −0.890153
\(576\) 18.4810 0.770040
\(577\) −37.2141 −1.54924 −0.774621 0.632426i \(-0.782059\pi\)
−0.774621 + 0.632426i \(0.782059\pi\)
\(578\) −5.59942 −0.232905
\(579\) −70.4704 −2.92865
\(580\) −0.184427 −0.00765791
\(581\) −3.82294 −0.158602
\(582\) 19.5169 0.809000
\(583\) 4.56675 0.189136
\(584\) 30.4429 1.25974
\(585\) 0 0
\(586\) 8.50924 0.351514
\(587\) −2.81457 −0.116170 −0.0580849 0.998312i \(-0.518499\pi\)
−0.0580849 + 0.998312i \(0.518499\pi\)
\(588\) 26.7950 1.10501
\(589\) 3.05709 0.125965
\(590\) 0.00338795 0.000139480 0
\(591\) 19.7850 0.813845
\(592\) −6.64500 −0.273108
\(593\) −12.7265 −0.522614 −0.261307 0.965256i \(-0.584154\pi\)
−0.261307 + 0.965256i \(0.584154\pi\)
\(594\) 7.15126 0.293420
\(595\) 0.0408626 0.00167520
\(596\) 17.8631 0.731702
\(597\) 59.7772 2.44652
\(598\) 0 0
\(599\) −30.9274 −1.26366 −0.631830 0.775107i \(-0.717696\pi\)
−0.631830 + 0.775107i \(0.717696\pi\)
\(600\) 39.6895 1.62032
\(601\) −9.40485 −0.383632 −0.191816 0.981431i \(-0.561438\pi\)
−0.191816 + 0.981431i \(0.561438\pi\)
\(602\) 7.32903 0.298709
\(603\) 32.2067 1.31156
\(604\) −12.1045 −0.492526
\(605\) 0.0164567 0.000669061 0
\(606\) 13.2538 0.538398
\(607\) 37.6487 1.52811 0.764056 0.645150i \(-0.223205\pi\)
0.764056 + 0.645150i \(0.223205\pi\)
\(608\) 7.17788 0.291102
\(609\) 19.1599 0.776397
\(610\) −0.0573878 −0.00232356
\(611\) 0 0
\(612\) −26.4950 −1.07100
\(613\) −8.20597 −0.331436 −0.165718 0.986173i \(-0.552994\pi\)
−0.165718 + 0.986173i \(0.552994\pi\)
\(614\) −15.2342 −0.614804
\(615\) −0.417660 −0.0168417
\(616\) −2.09324 −0.0843390
\(617\) 19.7324 0.794396 0.397198 0.917733i \(-0.369983\pi\)
0.397198 + 0.917733i \(0.369983\pi\)
\(618\) 39.5405 1.59055
\(619\) −36.5226 −1.46797 −0.733983 0.679168i \(-0.762341\pi\)
−0.733983 + 0.679168i \(0.762341\pi\)
\(620\) −0.0573470 −0.00230311
\(621\) 39.3311 1.57830
\(622\) 11.6244 0.466097
\(623\) −1.31888 −0.0528399
\(624\) 0 0
\(625\) 24.9959 0.999838
\(626\) 8.99798 0.359631
\(627\) 3.69023 0.147374
\(628\) 7.08552 0.282743
\(629\) −27.8008 −1.10849
\(630\) 0.0614504 0.00244824
\(631\) −5.64926 −0.224894 −0.112447 0.993658i \(-0.535869\pi\)
−0.112447 + 0.993658i \(0.535869\pi\)
\(632\) 24.6742 0.981489
\(633\) 23.4597 0.932441
\(634\) 4.30914 0.171138
\(635\) −0.00221780 −8.80107e−5 0
\(636\) −19.2097 −0.761714
\(637\) 0 0
\(638\) 6.22507 0.246453
\(639\) −79.4921 −3.14466
\(640\) −0.153752 −0.00607757
\(641\) −22.5700 −0.891461 −0.445730 0.895167i \(-0.647056\pi\)
−0.445730 + 0.895167i \(0.647056\pi\)
\(642\) 10.1881 0.402094
\(643\) −27.0779 −1.06785 −0.533924 0.845532i \(-0.679283\pi\)
−0.533924 + 0.845532i \(0.679283\pi\)
\(644\) −4.73538 −0.186600
\(645\) 0.589253 0.0232018
\(646\) 2.97706 0.117131
\(647\) 1.96650 0.0773110 0.0386555 0.999253i \(-0.487693\pi\)
0.0386555 + 0.999253i \(0.487693\pi\)
\(648\) −25.1832 −0.989289
\(649\) 0.265214 0.0104105
\(650\) 0 0
\(651\) 5.95771 0.233501
\(652\) −26.2376 −1.02754
\(653\) −7.55567 −0.295676 −0.147838 0.989012i \(-0.547231\pi\)
−0.147838 + 0.989012i \(0.547231\pi\)
\(654\) −40.8746 −1.59832
\(655\) −0.349563 −0.0136586
\(656\) −6.30454 −0.246151
\(657\) −69.9602 −2.72941
\(658\) 7.56308 0.294839
\(659\) 12.1726 0.474178 0.237089 0.971488i \(-0.423807\pi\)
0.237089 + 0.971488i \(0.423807\pi\)
\(660\) −0.0692239 −0.00269454
\(661\) −12.8925 −0.501459 −0.250729 0.968057i \(-0.580670\pi\)
−0.250729 + 0.968057i \(0.580670\pi\)
\(662\) 5.46740 0.212497
\(663\) 0 0
\(664\) 12.7022 0.492942
\(665\) 0.0160135 0.000620977 0
\(666\) −41.8077 −1.62002
\(667\) 34.2372 1.32567
\(668\) 21.5798 0.834949
\(669\) 13.1922 0.510039
\(670\) 0.0678847 0.00262261
\(671\) −4.49240 −0.173427
\(672\) 13.9884 0.539614
\(673\) −13.8175 −0.532625 −0.266312 0.963887i \(-0.585805\pi\)
−0.266312 + 0.963887i \(0.585805\pi\)
\(674\) −12.7111 −0.489612
\(675\) −46.0607 −1.77288
\(676\) 0 0
\(677\) −28.9663 −1.11326 −0.556632 0.830759i \(-0.687907\pi\)
−0.556632 + 0.830759i \(0.687907\pi\)
\(678\) 2.75033 0.105626
\(679\) 6.62982 0.254429
\(680\) −0.135771 −0.00520659
\(681\) 63.3463 2.42744
\(682\) 1.93567 0.0741206
\(683\) −15.3612 −0.587782 −0.293891 0.955839i \(-0.594950\pi\)
−0.293891 + 0.955839i \(0.594950\pi\)
\(684\) −10.3831 −0.397006
\(685\) 0.176780 0.00675443
\(686\) −8.23755 −0.314511
\(687\) −38.7727 −1.47927
\(688\) 8.89473 0.339108
\(689\) 0 0
\(690\) 0.164162 0.00624953
\(691\) 21.8394 0.830811 0.415406 0.909636i \(-0.363640\pi\)
0.415406 + 0.909636i \(0.363640\pi\)
\(692\) 10.6782 0.405925
\(693\) 4.81043 0.182733
\(694\) 8.74950 0.332127
\(695\) −0.227078 −0.00861355
\(696\) −63.6613 −2.41307
\(697\) −26.3764 −0.999076
\(698\) 17.6600 0.668443
\(699\) −41.5905 −1.57310
\(700\) 5.54561 0.209604
\(701\) 9.49260 0.358531 0.179265 0.983801i \(-0.442628\pi\)
0.179265 + 0.983801i \(0.442628\pi\)
\(702\) 0 0
\(703\) −10.8948 −0.410904
\(704\) 3.04936 0.114927
\(705\) 0.608070 0.0229012
\(706\) 2.52152 0.0948985
\(707\) 4.50226 0.169325
\(708\) −1.11560 −0.0419269
\(709\) 47.6774 1.79056 0.895281 0.445501i \(-0.146974\pi\)
0.895281 + 0.445501i \(0.146974\pi\)
\(710\) −0.167552 −0.00628812
\(711\) −56.7033 −2.12654
\(712\) 4.38216 0.164228
\(713\) 10.6460 0.398695
\(714\) 5.80175 0.217125
\(715\) 0 0
\(716\) 30.2825 1.13171
\(717\) 11.8970 0.444303
\(718\) 24.4267 0.911598
\(719\) −46.3833 −1.72981 −0.864903 0.501938i \(-0.832620\pi\)
−0.864903 + 0.501938i \(0.832620\pi\)
\(720\) 0.0745781 0.00277936
\(721\) 13.4318 0.500226
\(722\) −13.5820 −0.505468
\(723\) 16.6002 0.617367
\(724\) 16.7186 0.621340
\(725\) −40.0952 −1.48910
\(726\) 2.33656 0.0867178
\(727\) 40.9805 1.51988 0.759942 0.649991i \(-0.225228\pi\)
0.759942 + 0.649991i \(0.225228\pi\)
\(728\) 0 0
\(729\) −25.3196 −0.937763
\(730\) −0.147461 −0.00545777
\(731\) 37.2130 1.37637
\(732\) 18.8969 0.698450
\(733\) −35.5052 −1.31141 −0.655707 0.755015i \(-0.727629\pi\)
−0.655707 + 0.755015i \(0.727629\pi\)
\(734\) 17.9433 0.662298
\(735\) −0.315545 −0.0116391
\(736\) 24.9962 0.921371
\(737\) 5.31411 0.195748
\(738\) −39.6657 −1.46011
\(739\) −38.0716 −1.40049 −0.700243 0.713905i \(-0.746925\pi\)
−0.700243 + 0.713905i \(0.746925\pi\)
\(740\) 0.204372 0.00751285
\(741\) 0 0
\(742\) 2.81367 0.103293
\(743\) −11.3244 −0.415451 −0.207726 0.978187i \(-0.566606\pi\)
−0.207726 + 0.978187i \(0.566606\pi\)
\(744\) −19.7953 −0.725731
\(745\) −0.210361 −0.00770704
\(746\) −6.00990 −0.220038
\(747\) −29.1907 −1.06803
\(748\) −4.37169 −0.159845
\(749\) 3.46088 0.126458
\(750\) −0.384510 −0.0140403
\(751\) 1.05097 0.0383506 0.0191753 0.999816i \(-0.493896\pi\)
0.0191753 + 0.999816i \(0.493896\pi\)
\(752\) 9.17877 0.334715
\(753\) −20.9543 −0.763617
\(754\) 0 0
\(755\) 0.142546 0.00518780
\(756\) −10.2185 −0.371644
\(757\) 35.2725 1.28200 0.641001 0.767540i \(-0.278520\pi\)
0.641001 + 0.767540i \(0.278520\pi\)
\(758\) −8.14031 −0.295669
\(759\) 12.8508 0.466455
\(760\) −0.0532070 −0.00193002
\(761\) 3.55303 0.128797 0.0643986 0.997924i \(-0.479487\pi\)
0.0643986 + 0.997924i \(0.479487\pi\)
\(762\) −0.314888 −0.0114072
\(763\) −13.8850 −0.502670
\(764\) 16.1829 0.585476
\(765\) 0.312013 0.0112809
\(766\) 7.63961 0.276030
\(767\) 0 0
\(768\) −40.1877 −1.45015
\(769\) −6.79345 −0.244978 −0.122489 0.992470i \(-0.539088\pi\)
−0.122489 + 0.992470i \(0.539088\pi\)
\(770\) 0.0101393 0.000365396 0
\(771\) 40.8774 1.47216
\(772\) 32.7162 1.17748
\(773\) 47.9248 1.72373 0.861867 0.507135i \(-0.169295\pi\)
0.861867 + 0.507135i \(0.169295\pi\)
\(774\) 55.9621 2.01151
\(775\) −12.4675 −0.447846
\(776\) −22.0285 −0.790776
\(777\) −21.2319 −0.761691
\(778\) −18.6581 −0.668926
\(779\) −10.3366 −0.370346
\(780\) 0 0
\(781\) −13.1162 −0.469335
\(782\) 10.3673 0.370733
\(783\) 73.8806 2.64028
\(784\) −4.76313 −0.170112
\(785\) −0.0834411 −0.00297814
\(786\) −49.6317 −1.77030
\(787\) 48.8325 1.74069 0.870345 0.492442i \(-0.163896\pi\)
0.870345 + 0.492442i \(0.163896\pi\)
\(788\) −9.18527 −0.327212
\(789\) −31.9045 −1.13583
\(790\) −0.119518 −0.00425227
\(791\) 0.934279 0.0332191
\(792\) −15.9833 −0.567941
\(793\) 0 0
\(794\) 8.31511 0.295092
\(795\) 0.226219 0.00802316
\(796\) −27.7519 −0.983639
\(797\) −0.103318 −0.00365971 −0.00182986 0.999998i \(-0.500582\pi\)
−0.00182986 + 0.999998i \(0.500582\pi\)
\(798\) 2.27363 0.0804856
\(799\) 38.4013 1.35854
\(800\) −29.2730 −1.03496
\(801\) −10.0705 −0.355825
\(802\) 8.39827 0.296553
\(803\) −11.5434 −0.407359
\(804\) −22.3534 −0.788343
\(805\) 0.0557652 0.00196547
\(806\) 0 0
\(807\) 0.0287407 0.00101172
\(808\) −14.9594 −0.526269
\(809\) 26.3906 0.927844 0.463922 0.885876i \(-0.346442\pi\)
0.463922 + 0.885876i \(0.346442\pi\)
\(810\) 0.121984 0.00428606
\(811\) 34.1395 1.19880 0.599399 0.800450i \(-0.295406\pi\)
0.599399 + 0.800450i \(0.295406\pi\)
\(812\) −8.89506 −0.312155
\(813\) −11.2942 −0.396105
\(814\) −6.89828 −0.241785
\(815\) 0.308981 0.0108231
\(816\) 7.04118 0.246490
\(817\) 14.5833 0.510204
\(818\) 23.1272 0.808625
\(819\) 0 0
\(820\) 0.193900 0.00677130
\(821\) −10.4146 −0.363472 −0.181736 0.983347i \(-0.558172\pi\)
−0.181736 + 0.983347i \(0.558172\pi\)
\(822\) 25.0996 0.875451
\(823\) 42.5770 1.48414 0.742070 0.670322i \(-0.233844\pi\)
0.742070 + 0.670322i \(0.233844\pi\)
\(824\) −44.6289 −1.55472
\(825\) −15.0496 −0.523960
\(826\) 0.163404 0.00568555
\(827\) 26.2465 0.912680 0.456340 0.889805i \(-0.349160\pi\)
0.456340 + 0.889805i \(0.349160\pi\)
\(828\) −36.1578 −1.25657
\(829\) 28.8072 1.00051 0.500257 0.865877i \(-0.333239\pi\)
0.500257 + 0.865877i \(0.333239\pi\)
\(830\) −0.0615277 −0.00213566
\(831\) 39.6959 1.37703
\(832\) 0 0
\(833\) −19.9276 −0.690449
\(834\) −32.2410 −1.11641
\(835\) −0.254130 −0.00879455
\(836\) −1.71321 −0.0592525
\(837\) 22.9730 0.794063
\(838\) 0.260459 0.00899741
\(839\) 23.6632 0.816944 0.408472 0.912771i \(-0.366062\pi\)
0.408472 + 0.912771i \(0.366062\pi\)
\(840\) −0.103691 −0.00357767
\(841\) 35.3120 1.21766
\(842\) 27.1257 0.934814
\(843\) −74.4338 −2.56364
\(844\) −10.8913 −0.374894
\(845\) 0 0
\(846\) 57.7492 1.98546
\(847\) 0.793722 0.0272726
\(848\) 3.41476 0.117263
\(849\) −69.6231 −2.38946
\(850\) −12.1411 −0.416437
\(851\) −37.9398 −1.30056
\(852\) 55.1724 1.89017
\(853\) −46.2856 −1.58479 −0.792394 0.610009i \(-0.791166\pi\)
−0.792394 + 0.610009i \(0.791166\pi\)
\(854\) −2.76786 −0.0947143
\(855\) 0.122274 0.00418168
\(856\) −11.4992 −0.393036
\(857\) 4.37312 0.149383 0.0746915 0.997207i \(-0.476203\pi\)
0.0746915 + 0.997207i \(0.476203\pi\)
\(858\) 0 0
\(859\) 36.8769 1.25822 0.629112 0.777315i \(-0.283419\pi\)
0.629112 + 0.777315i \(0.283419\pi\)
\(860\) −0.273563 −0.00932843
\(861\) −20.1441 −0.686509
\(862\) 12.3224 0.419702
\(863\) 8.80418 0.299698 0.149849 0.988709i \(-0.452121\pi\)
0.149849 + 0.988709i \(0.452121\pi\)
\(864\) 53.9394 1.83505
\(865\) −0.125750 −0.00427562
\(866\) −7.44934 −0.253139
\(867\) −21.7132 −0.737418
\(868\) −2.76590 −0.0938807
\(869\) −9.35606 −0.317383
\(870\) 0.308366 0.0104546
\(871\) 0 0
\(872\) 46.1347 1.56232
\(873\) 50.6231 1.71333
\(874\) 4.06280 0.137426
\(875\) −0.130617 −0.00441566
\(876\) 48.5567 1.64058
\(877\) 0.0731659 0.00247064 0.00123532 0.999999i \(-0.499607\pi\)
0.00123532 + 0.999999i \(0.499607\pi\)
\(878\) 6.03858 0.203792
\(879\) 32.9967 1.11295
\(880\) 0.0123054 0.000414815 0
\(881\) 22.5405 0.759407 0.379704 0.925108i \(-0.376026\pi\)
0.379704 + 0.925108i \(0.376026\pi\)
\(882\) −29.9677 −1.00907
\(883\) −35.3920 −1.19104 −0.595518 0.803342i \(-0.703053\pi\)
−0.595518 + 0.803342i \(0.703053\pi\)
\(884\) 0 0
\(885\) 0.0131376 0.000441617 0
\(886\) −17.8906 −0.601046
\(887\) 25.3897 0.852502 0.426251 0.904605i \(-0.359834\pi\)
0.426251 + 0.904605i \(0.359834\pi\)
\(888\) 70.5459 2.36737
\(889\) −0.106966 −0.00358754
\(890\) −0.0212265 −0.000711515 0
\(891\) 9.54904 0.319905
\(892\) −6.12453 −0.205064
\(893\) 15.0490 0.503595
\(894\) −29.8675 −0.998919
\(895\) −0.356615 −0.0119203
\(896\) −7.41558 −0.247737
\(897\) 0 0
\(898\) 22.6646 0.756327
\(899\) 19.9977 0.666959
\(900\) 42.3445 1.41148
\(901\) 14.2864 0.475948
\(902\) −6.54484 −0.217919
\(903\) 28.4202 0.945764
\(904\) −3.10427 −0.103246
\(905\) −0.196882 −0.00654460
\(906\) 20.2390 0.672397
\(907\) 16.0891 0.534228 0.267114 0.963665i \(-0.413930\pi\)
0.267114 + 0.963665i \(0.413930\pi\)
\(908\) −29.4088 −0.975966
\(909\) 34.3778 1.14024
\(910\) 0 0
\(911\) −10.6061 −0.351396 −0.175698 0.984444i \(-0.556218\pi\)
−0.175698 + 0.984444i \(0.556218\pi\)
\(912\) 2.75934 0.0913710
\(913\) −4.81647 −0.159402
\(914\) −24.2123 −0.800872
\(915\) −0.222536 −0.00735680
\(916\) 18.0004 0.594751
\(917\) −16.8597 −0.556757
\(918\) 22.3716 0.738373
\(919\) −0.0784038 −0.00258630 −0.00129315 0.999999i \(-0.500412\pi\)
−0.00129315 + 0.999999i \(0.500412\pi\)
\(920\) −0.185287 −0.00610874
\(921\) −59.0746 −1.94657
\(922\) −29.2405 −0.962985
\(923\) 0 0
\(924\) −3.33873 −0.109836
\(925\) 44.4313 1.46089
\(926\) −0.767632 −0.0252260
\(927\) 102.561 3.36853
\(928\) 46.9534 1.54132
\(929\) −5.70834 −0.187284 −0.0936422 0.995606i \(-0.529851\pi\)
−0.0936422 + 0.995606i \(0.529851\pi\)
\(930\) 0.0958855 0.00314421
\(931\) −7.80935 −0.255941
\(932\) 19.3086 0.632473
\(933\) 45.0766 1.47574
\(934\) 8.93891 0.292490
\(935\) 0.0514822 0.00168365
\(936\) 0 0
\(937\) 55.6681 1.81860 0.909299 0.416143i \(-0.136619\pi\)
0.909299 + 0.416143i \(0.136619\pi\)
\(938\) 3.27414 0.106904
\(939\) 34.8919 1.13865
\(940\) −0.282299 −0.00920759
\(941\) 17.4945 0.570303 0.285151 0.958482i \(-0.407956\pi\)
0.285151 + 0.958482i \(0.407956\pi\)
\(942\) −11.8471 −0.386001
\(943\) −35.9959 −1.17219
\(944\) 0.198312 0.00645450
\(945\) 0.120336 0.00391453
\(946\) 9.23375 0.300215
\(947\) 38.2431 1.24273 0.621367 0.783520i \(-0.286578\pi\)
0.621367 + 0.783520i \(0.286578\pi\)
\(948\) 39.3556 1.27821
\(949\) 0 0
\(950\) −4.75795 −0.154368
\(951\) 16.7098 0.541852
\(952\) −6.54837 −0.212234
\(953\) −55.0966 −1.78476 −0.892378 0.451289i \(-0.850964\pi\)
−0.892378 + 0.451289i \(0.850964\pi\)
\(954\) 21.4843 0.695580
\(955\) −0.190574 −0.00616684
\(956\) −5.52326 −0.178635
\(957\) 24.1393 0.780312
\(958\) −7.07700 −0.228647
\(959\) 8.52627 0.275328
\(960\) 0.151053 0.00487523
\(961\) −24.7818 −0.799412
\(962\) 0 0
\(963\) 26.4262 0.851571
\(964\) −7.70671 −0.248216
\(965\) −0.385276 −0.0124025
\(966\) 7.91766 0.254747
\(967\) 25.7894 0.829330 0.414665 0.909974i \(-0.363899\pi\)
0.414665 + 0.909974i \(0.363899\pi\)
\(968\) −2.63725 −0.0847643
\(969\) 11.5443 0.370856
\(970\) 0.106703 0.00342601
\(971\) 42.9387 1.37797 0.688985 0.724776i \(-0.258057\pi\)
0.688985 + 0.724776i \(0.258057\pi\)
\(972\) −1.54482 −0.0495501
\(973\) −10.9522 −0.351110
\(974\) 14.4528 0.463099
\(975\) 0 0
\(976\) −3.35916 −0.107524
\(977\) 42.1485 1.34845 0.674225 0.738526i \(-0.264478\pi\)
0.674225 + 0.738526i \(0.264478\pi\)
\(978\) 43.8698 1.40280
\(979\) −1.66164 −0.0531063
\(980\) 0.146493 0.00467956
\(981\) −106.021 −3.38499
\(982\) −19.4199 −0.619713
\(983\) −51.7672 −1.65112 −0.825559 0.564316i \(-0.809140\pi\)
−0.825559 + 0.564316i \(0.809140\pi\)
\(984\) 66.9314 2.13370
\(985\) 0.108168 0.00344653
\(986\) 19.4741 0.620183
\(987\) 29.3277 0.933512
\(988\) 0 0
\(989\) 50.7846 1.61486
\(990\) 0.0774207 0.00246059
\(991\) 33.1031 1.05155 0.525777 0.850622i \(-0.323775\pi\)
0.525777 + 0.850622i \(0.323775\pi\)
\(992\) 14.6001 0.463552
\(993\) 21.2012 0.672801
\(994\) −8.08118 −0.256319
\(995\) 0.326814 0.0103607
\(996\) 20.2601 0.641967
\(997\) −10.4149 −0.329842 −0.164921 0.986307i \(-0.552737\pi\)
−0.164921 + 0.986307i \(0.552737\pi\)
\(998\) 4.70373 0.148894
\(999\) −81.8704 −2.59027
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 1859.2.a.t.1.13 yes 21
13.12 even 2 1859.2.a.s.1.9 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.9 21 13.12 even 2
1859.2.a.t.1.13 yes 21 1.1 even 1 trivial