Properties

Label 1859.2.a.t.1.3
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 1.3
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} +2.33476 q^{5} -8.39034 q^{6} +0.266736 q^{7} -8.58980 q^{8} +6.77612 q^{9} +O(q^{10})\) \(q-2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} +2.33476 q^{5} -8.39034 q^{6} +0.266736 q^{7} -8.58980 q^{8} +6.77612 q^{9} -6.26526 q^{10} +1.00000 q^{11} +16.2619 q^{12} -0.715776 q^{14} +7.30005 q^{15} +12.6484 q^{16} -1.53629 q^{17} -18.1835 q^{18} +7.55923 q^{19} +12.1431 q^{20} +0.833996 q^{21} -2.68347 q^{22} -3.95510 q^{23} -26.8575 q^{24} +0.451118 q^{25} +11.8067 q^{27} +1.38729 q^{28} +1.08736 q^{29} -19.5895 q^{30} -3.25139 q^{31} -16.7621 q^{32} +3.12668 q^{33} +4.12259 q^{34} +0.622764 q^{35} +35.2426 q^{36} +3.44806 q^{37} -20.2850 q^{38} -20.0551 q^{40} -6.30467 q^{41} -2.23800 q^{42} +2.45816 q^{43} +5.20101 q^{44} +15.8206 q^{45} +10.6134 q^{46} -6.48085 q^{47} +39.5476 q^{48} -6.92885 q^{49} -1.21056 q^{50} -4.80349 q^{51} +5.06393 q^{53} -31.6829 q^{54} +2.33476 q^{55} -2.29120 q^{56} +23.6353 q^{57} -2.91791 q^{58} +10.8892 q^{59} +37.9676 q^{60} +9.66466 q^{61} +8.72501 q^{62} +1.80743 q^{63} +19.6837 q^{64} -8.39034 q^{66} +6.41989 q^{67} -7.99026 q^{68} -12.3663 q^{69} -1.67117 q^{70} +13.0818 q^{71} -58.2055 q^{72} -1.49954 q^{73} -9.25276 q^{74} +1.41050 q^{75} +39.3156 q^{76} +0.266736 q^{77} -3.63953 q^{79} +29.5311 q^{80} +16.5874 q^{81} +16.9184 q^{82} -9.17706 q^{83} +4.33762 q^{84} -3.58688 q^{85} -6.59640 q^{86} +3.39984 q^{87} -8.58980 q^{88} -8.10322 q^{89} -42.4542 q^{90} -20.5705 q^{92} -10.1661 q^{93} +17.3912 q^{94} +17.6490 q^{95} -52.4097 q^{96} -12.7243 q^{97} +18.5934 q^{98} +6.77612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68347 −1.89750 −0.948750 0.316029i \(-0.897650\pi\)
−0.948750 + 0.316029i \(0.897650\pi\)
\(3\) 3.12668 1.80519 0.902594 0.430492i \(-0.141660\pi\)
0.902594 + 0.430492i \(0.141660\pi\)
\(4\) 5.20101 2.60050
\(5\) 2.33476 1.04414 0.522069 0.852903i \(-0.325160\pi\)
0.522069 + 0.852903i \(0.325160\pi\)
\(6\) −8.39034 −3.42534
\(7\) 0.266736 0.100817 0.0504083 0.998729i \(-0.483948\pi\)
0.0504083 + 0.998729i \(0.483948\pi\)
\(8\) −8.58980 −3.03695
\(9\) 6.77612 2.25871
\(10\) −6.26526 −1.98125
\(11\) 1.00000 0.301511
\(12\) 16.2619 4.69440
\(13\) 0 0
\(14\) −0.715776 −0.191299
\(15\) 7.30005 1.88487
\(16\) 12.6484 3.16211
\(17\) −1.53629 −0.372605 −0.186303 0.982492i \(-0.559650\pi\)
−0.186303 + 0.982492i \(0.559650\pi\)
\(18\) −18.1835 −4.28589
\(19\) 7.55923 1.73421 0.867103 0.498129i \(-0.165979\pi\)
0.867103 + 0.498129i \(0.165979\pi\)
\(20\) 12.1431 2.71528
\(21\) 0.833996 0.181993
\(22\) −2.68347 −0.572118
\(23\) −3.95510 −0.824696 −0.412348 0.911026i \(-0.635291\pi\)
−0.412348 + 0.911026i \(0.635291\pi\)
\(24\) −26.8575 −5.48227
\(25\) 0.451118 0.0902236
\(26\) 0 0
\(27\) 11.8067 2.27220
\(28\) 1.38729 0.262174
\(29\) 1.08736 0.201919 0.100959 0.994891i \(-0.467809\pi\)
0.100959 + 0.994891i \(0.467809\pi\)
\(30\) −19.5895 −3.57653
\(31\) −3.25139 −0.583967 −0.291984 0.956423i \(-0.594315\pi\)
−0.291984 + 0.956423i \(0.594315\pi\)
\(32\) −16.7621 −2.96315
\(33\) 3.12668 0.544285
\(34\) 4.12259 0.707018
\(35\) 0.622764 0.105266
\(36\) 35.2426 5.87377
\(37\) 3.44806 0.566857 0.283429 0.958993i \(-0.408528\pi\)
0.283429 + 0.958993i \(0.408528\pi\)
\(38\) −20.2850 −3.29066
\(39\) 0 0
\(40\) −20.0551 −3.17100
\(41\) −6.30467 −0.984624 −0.492312 0.870419i \(-0.663848\pi\)
−0.492312 + 0.870419i \(0.663848\pi\)
\(42\) −2.23800 −0.345331
\(43\) 2.45816 0.374866 0.187433 0.982277i \(-0.439983\pi\)
0.187433 + 0.982277i \(0.439983\pi\)
\(44\) 5.20101 0.784081
\(45\) 15.8206 2.35840
\(46\) 10.6134 1.56486
\(47\) −6.48085 −0.945329 −0.472664 0.881243i \(-0.656708\pi\)
−0.472664 + 0.881243i \(0.656708\pi\)
\(48\) 39.5476 5.70821
\(49\) −6.92885 −0.989836
\(50\) −1.21056 −0.171199
\(51\) −4.80349 −0.672623
\(52\) 0 0
\(53\) 5.06393 0.695584 0.347792 0.937572i \(-0.386932\pi\)
0.347792 + 0.937572i \(0.386932\pi\)
\(54\) −31.6829 −4.31150
\(55\) 2.33476 0.314819
\(56\) −2.29120 −0.306175
\(57\) 23.6353 3.13057
\(58\) −2.91791 −0.383140
\(59\) 10.8892 1.41766 0.708828 0.705381i \(-0.249224\pi\)
0.708828 + 0.705381i \(0.249224\pi\)
\(60\) 37.9676 4.90160
\(61\) 9.66466 1.23743 0.618716 0.785614i \(-0.287653\pi\)
0.618716 + 0.785614i \(0.287653\pi\)
\(62\) 8.72501 1.10808
\(63\) 1.80743 0.227715
\(64\) 19.6837 2.46047
\(65\) 0 0
\(66\) −8.39034 −1.03278
\(67\) 6.41989 0.784314 0.392157 0.919898i \(-0.371729\pi\)
0.392157 + 0.919898i \(0.371729\pi\)
\(68\) −7.99026 −0.968961
\(69\) −12.3663 −1.48873
\(70\) −1.67117 −0.199743
\(71\) 13.0818 1.55252 0.776262 0.630411i \(-0.217114\pi\)
0.776262 + 0.630411i \(0.217114\pi\)
\(72\) −58.2055 −6.85958
\(73\) −1.49954 −0.175508 −0.0877540 0.996142i \(-0.527969\pi\)
−0.0877540 + 0.996142i \(0.527969\pi\)
\(74\) −9.25276 −1.07561
\(75\) 1.41050 0.162871
\(76\) 39.3156 4.50981
\(77\) 0.266736 0.0303973
\(78\) 0 0
\(79\) −3.63953 −0.409479 −0.204739 0.978817i \(-0.565635\pi\)
−0.204739 + 0.978817i \(0.565635\pi\)
\(80\) 29.5311 3.30168
\(81\) 16.5874 1.84304
\(82\) 16.9184 1.86832
\(83\) −9.17706 −1.00731 −0.503657 0.863904i \(-0.668012\pi\)
−0.503657 + 0.863904i \(0.668012\pi\)
\(84\) 4.33762 0.473273
\(85\) −3.58688 −0.389051
\(86\) −6.59640 −0.711308
\(87\) 3.39984 0.364501
\(88\) −8.58980 −0.915676
\(89\) −8.10322 −0.858939 −0.429470 0.903081i \(-0.641299\pi\)
−0.429470 + 0.903081i \(0.641299\pi\)
\(90\) −42.4542 −4.47506
\(91\) 0 0
\(92\) −20.5705 −2.14462
\(93\) −10.1661 −1.05417
\(94\) 17.3912 1.79376
\(95\) 17.6490 1.81075
\(96\) −52.4097 −5.34905
\(97\) −12.7243 −1.29195 −0.645977 0.763357i \(-0.723550\pi\)
−0.645977 + 0.763357i \(0.723550\pi\)
\(98\) 18.5934 1.87821
\(99\) 6.77612 0.681025
\(100\) 2.34627 0.234627
\(101\) 12.5430 1.24807 0.624037 0.781395i \(-0.285492\pi\)
0.624037 + 0.781395i \(0.285492\pi\)
\(102\) 12.8900 1.27630
\(103\) −4.78743 −0.471719 −0.235860 0.971787i \(-0.575791\pi\)
−0.235860 + 0.971787i \(0.575791\pi\)
\(104\) 0 0
\(105\) 1.94718 0.190026
\(106\) −13.5889 −1.31987
\(107\) −20.0718 −1.94041 −0.970206 0.242283i \(-0.922104\pi\)
−0.970206 + 0.242283i \(0.922104\pi\)
\(108\) 61.4067 5.90886
\(109\) −5.37319 −0.514658 −0.257329 0.966324i \(-0.582842\pi\)
−0.257329 + 0.966324i \(0.582842\pi\)
\(110\) −6.26526 −0.597369
\(111\) 10.7810 1.02328
\(112\) 3.37379 0.318793
\(113\) −15.1793 −1.42795 −0.713976 0.700170i \(-0.753108\pi\)
−0.713976 + 0.700170i \(0.753108\pi\)
\(114\) −63.4245 −5.94025
\(115\) −9.23423 −0.861096
\(116\) 5.65539 0.525090
\(117\) 0 0
\(118\) −29.2209 −2.69000
\(119\) −0.409783 −0.0375648
\(120\) −62.7060 −5.72425
\(121\) 1.00000 0.0909091
\(122\) −25.9348 −2.34803
\(123\) −19.7127 −1.77743
\(124\) −16.9105 −1.51861
\(125\) −10.6206 −0.949932
\(126\) −4.85018 −0.432089
\(127\) 21.0600 1.86877 0.934387 0.356260i \(-0.115948\pi\)
0.934387 + 0.356260i \(0.115948\pi\)
\(128\) −19.2964 −1.70558
\(129\) 7.68588 0.676704
\(130\) 0 0
\(131\) 3.77616 0.329925 0.164962 0.986300i \(-0.447250\pi\)
0.164962 + 0.986300i \(0.447250\pi\)
\(132\) 16.2619 1.41541
\(133\) 2.01632 0.174837
\(134\) −17.2276 −1.48824
\(135\) 27.5658 2.37249
\(136\) 13.1964 1.13158
\(137\) 2.81943 0.240880 0.120440 0.992721i \(-0.461569\pi\)
0.120440 + 0.992721i \(0.461569\pi\)
\(138\) 33.1847 2.82487
\(139\) −1.84271 −0.156296 −0.0781482 0.996942i \(-0.524901\pi\)
−0.0781482 + 0.996942i \(0.524901\pi\)
\(140\) 3.23900 0.273745
\(141\) −20.2635 −1.70650
\(142\) −35.1046 −2.94591
\(143\) 0 0
\(144\) 85.7074 7.14228
\(145\) 2.53874 0.210831
\(146\) 4.02397 0.333026
\(147\) −21.6643 −1.78684
\(148\) 17.9334 1.47411
\(149\) −5.43166 −0.444979 −0.222490 0.974935i \(-0.571418\pi\)
−0.222490 + 0.974935i \(0.571418\pi\)
\(150\) −3.78504 −0.309047
\(151\) 6.87113 0.559165 0.279582 0.960122i \(-0.409804\pi\)
0.279582 + 0.960122i \(0.409804\pi\)
\(152\) −64.9323 −5.26670
\(153\) −10.4101 −0.841606
\(154\) −0.715776 −0.0576789
\(155\) −7.59123 −0.609742
\(156\) 0 0
\(157\) 5.36679 0.428317 0.214158 0.976799i \(-0.431299\pi\)
0.214158 + 0.976799i \(0.431299\pi\)
\(158\) 9.76656 0.776985
\(159\) 15.8333 1.25566
\(160\) −39.1356 −3.09394
\(161\) −1.05497 −0.0831430
\(162\) −44.5118 −3.49718
\(163\) −4.34355 −0.340213 −0.170106 0.985426i \(-0.554411\pi\)
−0.170106 + 0.985426i \(0.554411\pi\)
\(164\) −32.7906 −2.56052
\(165\) 7.30005 0.568308
\(166\) 24.6264 1.91138
\(167\) −16.6380 −1.28749 −0.643745 0.765240i \(-0.722620\pi\)
−0.643745 + 0.765240i \(0.722620\pi\)
\(168\) −7.16386 −0.552704
\(169\) 0 0
\(170\) 9.62527 0.738224
\(171\) 51.2222 3.91706
\(172\) 12.7849 0.974840
\(173\) −2.66992 −0.202990 −0.101495 0.994836i \(-0.532363\pi\)
−0.101495 + 0.994836i \(0.532363\pi\)
\(174\) −9.12336 −0.691640
\(175\) 0.120329 0.00909604
\(176\) 12.6484 0.953413
\(177\) 34.0471 2.55914
\(178\) 21.7447 1.62984
\(179\) −22.7448 −1.70002 −0.850011 0.526764i \(-0.823405\pi\)
−0.850011 + 0.526764i \(0.823405\pi\)
\(180\) 82.2832 6.13302
\(181\) 20.4550 1.52041 0.760203 0.649685i \(-0.225099\pi\)
0.760203 + 0.649685i \(0.225099\pi\)
\(182\) 0 0
\(183\) 30.2183 2.23380
\(184\) 33.9735 2.50456
\(185\) 8.05040 0.591877
\(186\) 27.2803 2.00029
\(187\) −1.53629 −0.112345
\(188\) −33.7069 −2.45833
\(189\) 3.14927 0.229075
\(190\) −47.3606 −3.43590
\(191\) −7.69998 −0.557151 −0.278575 0.960414i \(-0.589862\pi\)
−0.278575 + 0.960414i \(0.589862\pi\)
\(192\) 61.5447 4.44161
\(193\) 7.54943 0.543420 0.271710 0.962379i \(-0.412411\pi\)
0.271710 + 0.962379i \(0.412411\pi\)
\(194\) 34.1452 2.45148
\(195\) 0 0
\(196\) −36.0370 −2.57407
\(197\) −18.8155 −1.34055 −0.670275 0.742113i \(-0.733824\pi\)
−0.670275 + 0.742113i \(0.733824\pi\)
\(198\) −18.1835 −1.29224
\(199\) 9.03481 0.640461 0.320230 0.947340i \(-0.396240\pi\)
0.320230 + 0.947340i \(0.396240\pi\)
\(200\) −3.87501 −0.274005
\(201\) 20.0729 1.41584
\(202\) −33.6587 −2.36822
\(203\) 0.290039 0.0203567
\(204\) −24.9830 −1.74916
\(205\) −14.7199 −1.02808
\(206\) 12.8469 0.895087
\(207\) −26.8002 −1.86275
\(208\) 0 0
\(209\) 7.55923 0.522883
\(210\) −5.22521 −0.360573
\(211\) −11.2951 −0.777585 −0.388793 0.921325i \(-0.627108\pi\)
−0.388793 + 0.921325i \(0.627108\pi\)
\(212\) 26.3375 1.80887
\(213\) 40.9026 2.80260
\(214\) 53.8620 3.68193
\(215\) 5.73922 0.391412
\(216\) −101.417 −6.90057
\(217\) −0.867262 −0.0588736
\(218\) 14.4188 0.976563
\(219\) −4.68858 −0.316825
\(220\) 12.1431 0.818689
\(221\) 0 0
\(222\) −28.9304 −1.94168
\(223\) 25.9591 1.73835 0.869176 0.494503i \(-0.164650\pi\)
0.869176 + 0.494503i \(0.164650\pi\)
\(224\) −4.47105 −0.298735
\(225\) 3.05683 0.203789
\(226\) 40.7333 2.70954
\(227\) −10.0343 −0.665999 −0.332999 0.942927i \(-0.608061\pi\)
−0.332999 + 0.942927i \(0.608061\pi\)
\(228\) 122.927 8.14105
\(229\) −2.98115 −0.197000 −0.0985001 0.995137i \(-0.531404\pi\)
−0.0985001 + 0.995137i \(0.531404\pi\)
\(230\) 24.7798 1.63393
\(231\) 0.833996 0.0548729
\(232\) −9.34024 −0.613217
\(233\) −3.75063 −0.245712 −0.122856 0.992425i \(-0.539205\pi\)
−0.122856 + 0.992425i \(0.539205\pi\)
\(234\) 0 0
\(235\) −15.1312 −0.987053
\(236\) 56.6349 3.68662
\(237\) −11.3796 −0.739186
\(238\) 1.09964 0.0712791
\(239\) 8.17311 0.528675 0.264337 0.964430i \(-0.414847\pi\)
0.264337 + 0.964430i \(0.414847\pi\)
\(240\) 92.3343 5.96016
\(241\) 4.62614 0.297996 0.148998 0.988838i \(-0.452395\pi\)
0.148998 + 0.988838i \(0.452395\pi\)
\(242\) −2.68347 −0.172500
\(243\) 16.4434 1.05484
\(244\) 50.2660 3.21795
\(245\) −16.1772 −1.03353
\(246\) 52.8984 3.37268
\(247\) 0 0
\(248\) 27.9288 1.77348
\(249\) −28.6937 −1.81839
\(250\) 28.4999 1.80249
\(251\) −12.9557 −0.817758 −0.408879 0.912589i \(-0.634080\pi\)
−0.408879 + 0.912589i \(0.634080\pi\)
\(252\) 9.40046 0.592173
\(253\) −3.95510 −0.248655
\(254\) −56.5139 −3.54600
\(255\) −11.2150 −0.702311
\(256\) 12.4139 0.775871
\(257\) −0.638721 −0.0398423 −0.0199211 0.999802i \(-0.506342\pi\)
−0.0199211 + 0.999802i \(0.506342\pi\)
\(258\) −20.6248 −1.28405
\(259\) 0.919719 0.0571486
\(260\) 0 0
\(261\) 7.36811 0.456074
\(262\) −10.1332 −0.626032
\(263\) 14.5476 0.897046 0.448523 0.893771i \(-0.351950\pi\)
0.448523 + 0.893771i \(0.351950\pi\)
\(264\) −26.8575 −1.65297
\(265\) 11.8231 0.726285
\(266\) −5.41072 −0.331752
\(267\) −25.3362 −1.55055
\(268\) 33.3899 2.03961
\(269\) −14.9672 −0.912564 −0.456282 0.889835i \(-0.650819\pi\)
−0.456282 + 0.889835i \(0.650819\pi\)
\(270\) −73.9721 −4.50180
\(271\) −21.3675 −1.29799 −0.648993 0.760795i \(-0.724809\pi\)
−0.648993 + 0.760795i \(0.724809\pi\)
\(272\) −19.4317 −1.17822
\(273\) 0 0
\(274\) −7.56586 −0.457070
\(275\) 0.451118 0.0272035
\(276\) −64.3174 −3.87145
\(277\) 23.9016 1.43611 0.718055 0.695986i \(-0.245032\pi\)
0.718055 + 0.695986i \(0.245032\pi\)
\(278\) 4.94485 0.296572
\(279\) −22.0318 −1.31901
\(280\) −5.34942 −0.319689
\(281\) 19.5972 1.16907 0.584535 0.811368i \(-0.301277\pi\)
0.584535 + 0.811368i \(0.301277\pi\)
\(282\) 54.3765 3.23808
\(283\) −1.39789 −0.0830957 −0.0415479 0.999137i \(-0.513229\pi\)
−0.0415479 + 0.999137i \(0.513229\pi\)
\(284\) 68.0385 4.03734
\(285\) 55.1828 3.26875
\(286\) 0 0
\(287\) −1.68168 −0.0992664
\(288\) −113.582 −6.69289
\(289\) −14.6398 −0.861165
\(290\) −6.81263 −0.400051
\(291\) −39.7847 −2.33222
\(292\) −7.79912 −0.456409
\(293\) 20.0795 1.17306 0.586529 0.809928i \(-0.300494\pi\)
0.586529 + 0.809928i \(0.300494\pi\)
\(294\) 58.1355 3.39053
\(295\) 25.4238 1.48023
\(296\) −29.6181 −1.72152
\(297\) 11.8067 0.685094
\(298\) 14.5757 0.844347
\(299\) 0 0
\(300\) 7.33603 0.423546
\(301\) 0.655679 0.0377927
\(302\) −18.4385 −1.06101
\(303\) 39.2179 2.25301
\(304\) 95.6125 5.48375
\(305\) 22.5647 1.29205
\(306\) 27.9351 1.59695
\(307\) 4.32372 0.246768 0.123384 0.992359i \(-0.460625\pi\)
0.123384 + 0.992359i \(0.460625\pi\)
\(308\) 1.38729 0.0790483
\(309\) −14.9687 −0.851542
\(310\) 20.3708 1.15699
\(311\) −25.3775 −1.43902 −0.719512 0.694480i \(-0.755634\pi\)
−0.719512 + 0.694480i \(0.755634\pi\)
\(312\) 0 0
\(313\) 21.1230 1.19394 0.596972 0.802262i \(-0.296370\pi\)
0.596972 + 0.802262i \(0.296370\pi\)
\(314\) −14.4016 −0.812731
\(315\) 4.21992 0.237766
\(316\) −18.9292 −1.06485
\(317\) 21.0836 1.18417 0.592087 0.805874i \(-0.298304\pi\)
0.592087 + 0.805874i \(0.298304\pi\)
\(318\) −42.4881 −2.38261
\(319\) 1.08736 0.0608807
\(320\) 45.9568 2.56907
\(321\) −62.7580 −3.50281
\(322\) 2.83097 0.157764
\(323\) −11.6132 −0.646175
\(324\) 86.2712 4.79284
\(325\) 0 0
\(326\) 11.6558 0.645553
\(327\) −16.8002 −0.929055
\(328\) 54.1559 2.99026
\(329\) −1.72867 −0.0953048
\(330\) −19.5895 −1.07836
\(331\) −28.2148 −1.55083 −0.775413 0.631454i \(-0.782458\pi\)
−0.775413 + 0.631454i \(0.782458\pi\)
\(332\) −47.7300 −2.61952
\(333\) 23.3644 1.28036
\(334\) 44.6477 2.44301
\(335\) 14.9889 0.818932
\(336\) 10.5488 0.575482
\(337\) −7.49761 −0.408421 −0.204211 0.978927i \(-0.565463\pi\)
−0.204211 + 0.978927i \(0.565463\pi\)
\(338\) 0 0
\(339\) −47.4609 −2.57772
\(340\) −18.6554 −1.01173
\(341\) −3.25139 −0.176073
\(342\) −137.453 −7.43262
\(343\) −3.71532 −0.200608
\(344\) −21.1151 −1.13845
\(345\) −28.8725 −1.55444
\(346\) 7.16464 0.385174
\(347\) 22.1568 1.18944 0.594720 0.803933i \(-0.297263\pi\)
0.594720 + 0.803933i \(0.297263\pi\)
\(348\) 17.6826 0.947886
\(349\) −32.7247 −1.75171 −0.875856 0.482573i \(-0.839702\pi\)
−0.875856 + 0.482573i \(0.839702\pi\)
\(350\) −0.322900 −0.0172597
\(351\) 0 0
\(352\) −16.7621 −0.893424
\(353\) −8.19679 −0.436271 −0.218135 0.975919i \(-0.569997\pi\)
−0.218135 + 0.975919i \(0.569997\pi\)
\(354\) −91.3644 −4.85596
\(355\) 30.5429 1.62105
\(356\) −42.1449 −2.23367
\(357\) −1.28126 −0.0678115
\(358\) 61.0348 3.22579
\(359\) 15.1960 0.802017 0.401008 0.916074i \(-0.368660\pi\)
0.401008 + 0.916074i \(0.368660\pi\)
\(360\) −135.896 −7.16235
\(361\) 38.1420 2.00747
\(362\) −54.8903 −2.88497
\(363\) 3.12668 0.164108
\(364\) 0 0
\(365\) −3.50107 −0.183254
\(366\) −81.0898 −4.23863
\(367\) 11.8602 0.619099 0.309549 0.950883i \(-0.399822\pi\)
0.309549 + 0.950883i \(0.399822\pi\)
\(368\) −50.0259 −2.60778
\(369\) −42.7212 −2.22398
\(370\) −21.6030 −1.12309
\(371\) 1.35073 0.0701264
\(372\) −52.8737 −2.74137
\(373\) −31.4345 −1.62762 −0.813810 0.581132i \(-0.802610\pi\)
−0.813810 + 0.581132i \(0.802610\pi\)
\(374\) 4.12259 0.213174
\(375\) −33.2071 −1.71481
\(376\) 55.6692 2.87092
\(377\) 0 0
\(378\) −8.45096 −0.434670
\(379\) −27.8846 −1.43233 −0.716167 0.697929i \(-0.754105\pi\)
−0.716167 + 0.697929i \(0.754105\pi\)
\(380\) 91.7926 4.70886
\(381\) 65.8479 3.37349
\(382\) 20.6626 1.05719
\(383\) −20.0951 −1.02681 −0.513406 0.858146i \(-0.671617\pi\)
−0.513406 + 0.858146i \(0.671617\pi\)
\(384\) −60.3338 −3.07889
\(385\) 0.622764 0.0317390
\(386\) −20.2587 −1.03114
\(387\) 16.6568 0.846712
\(388\) −66.1790 −3.35973
\(389\) −1.80049 −0.0912883 −0.0456441 0.998958i \(-0.514534\pi\)
−0.0456441 + 0.998958i \(0.514534\pi\)
\(390\) 0 0
\(391\) 6.07619 0.307286
\(392\) 59.5174 3.00609
\(393\) 11.8068 0.595576
\(394\) 50.4908 2.54369
\(395\) −8.49743 −0.427552
\(396\) 35.2426 1.77101
\(397\) −4.76541 −0.239169 −0.119584 0.992824i \(-0.538156\pi\)
−0.119584 + 0.992824i \(0.538156\pi\)
\(398\) −24.2446 −1.21527
\(399\) 6.30437 0.315613
\(400\) 5.70594 0.285297
\(401\) 29.3417 1.46526 0.732628 0.680629i \(-0.238294\pi\)
0.732628 + 0.680629i \(0.238294\pi\)
\(402\) −53.8651 −2.68655
\(403\) 0 0
\(404\) 65.2361 3.24562
\(405\) 38.7277 1.92439
\(406\) −0.778310 −0.0386269
\(407\) 3.44806 0.170914
\(408\) 41.2610 2.04272
\(409\) 12.2591 0.606172 0.303086 0.952963i \(-0.401983\pi\)
0.303086 + 0.952963i \(0.401983\pi\)
\(410\) 39.5004 1.95079
\(411\) 8.81546 0.434834
\(412\) −24.8994 −1.22671
\(413\) 2.90454 0.142923
\(414\) 71.9176 3.53456
\(415\) −21.4263 −1.05177
\(416\) 0 0
\(417\) −5.76155 −0.282144
\(418\) −20.2850 −0.992170
\(419\) 36.1583 1.76645 0.883224 0.468951i \(-0.155368\pi\)
0.883224 + 0.468951i \(0.155368\pi\)
\(420\) 10.1273 0.494162
\(421\) 1.38467 0.0674849 0.0337424 0.999431i \(-0.489257\pi\)
0.0337424 + 0.999431i \(0.489257\pi\)
\(422\) 30.3100 1.47547
\(423\) −43.9150 −2.13522
\(424\) −43.4981 −2.11245
\(425\) −0.693049 −0.0336178
\(426\) −109.761 −5.31792
\(427\) 2.57791 0.124754
\(428\) −104.393 −5.04604
\(429\) 0 0
\(430\) −15.4010 −0.742704
\(431\) −0.0306402 −0.00147589 −0.000737943 1.00000i \(-0.500235\pi\)
−0.000737943 1.00000i \(0.500235\pi\)
\(432\) 149.336 7.18495
\(433\) 13.5388 0.650631 0.325315 0.945606i \(-0.394530\pi\)
0.325315 + 0.945606i \(0.394530\pi\)
\(434\) 2.32727 0.111713
\(435\) 7.93782 0.380589
\(436\) −27.9460 −1.33837
\(437\) −29.8975 −1.43019
\(438\) 12.5817 0.601175
\(439\) 15.5973 0.744417 0.372208 0.928149i \(-0.378601\pi\)
0.372208 + 0.928149i \(0.378601\pi\)
\(440\) −20.0551 −0.956092
\(441\) −46.9507 −2.23575
\(442\) 0 0
\(443\) 16.3311 0.775914 0.387957 0.921677i \(-0.373181\pi\)
0.387957 + 0.921677i \(0.373181\pi\)
\(444\) 56.0719 2.66105
\(445\) −18.9191 −0.896851
\(446\) −69.6605 −3.29852
\(447\) −16.9831 −0.803271
\(448\) 5.25035 0.248056
\(449\) −2.94124 −0.138806 −0.0694029 0.997589i \(-0.522109\pi\)
−0.0694029 + 0.997589i \(0.522109\pi\)
\(450\) −8.20291 −0.386689
\(451\) −6.30467 −0.296875
\(452\) −78.9479 −3.71340
\(453\) 21.4838 1.00940
\(454\) 26.9267 1.26373
\(455\) 0 0
\(456\) −203.022 −9.50739
\(457\) −25.6418 −1.19947 −0.599735 0.800199i \(-0.704727\pi\)
−0.599735 + 0.800199i \(0.704727\pi\)
\(458\) 7.99983 0.373808
\(459\) −18.1385 −0.846634
\(460\) −48.0273 −2.23928
\(461\) 25.4408 1.18490 0.592449 0.805608i \(-0.298161\pi\)
0.592449 + 0.805608i \(0.298161\pi\)
\(462\) −2.23800 −0.104121
\(463\) −10.6067 −0.492934 −0.246467 0.969151i \(-0.579270\pi\)
−0.246467 + 0.969151i \(0.579270\pi\)
\(464\) 13.7535 0.638489
\(465\) −23.7353 −1.10070
\(466\) 10.0647 0.466238
\(467\) −5.17505 −0.239473 −0.119736 0.992806i \(-0.538205\pi\)
−0.119736 + 0.992806i \(0.538205\pi\)
\(468\) 0 0
\(469\) 1.71241 0.0790719
\(470\) 40.6042 1.87293
\(471\) 16.7802 0.773193
\(472\) −93.5363 −4.30536
\(473\) 2.45816 0.113026
\(474\) 30.5369 1.40261
\(475\) 3.41011 0.156466
\(476\) −2.13129 −0.0976873
\(477\) 34.3138 1.57112
\(478\) −21.9323 −1.00316
\(479\) 17.9210 0.818829 0.409415 0.912348i \(-0.365733\pi\)
0.409415 + 0.912348i \(0.365733\pi\)
\(480\) −122.364 −5.58514
\(481\) 0 0
\(482\) −12.4141 −0.565447
\(483\) −3.29854 −0.150089
\(484\) 5.20101 0.236409
\(485\) −29.7081 −1.34898
\(486\) −44.1253 −2.00156
\(487\) 6.46395 0.292910 0.146455 0.989217i \(-0.453214\pi\)
0.146455 + 0.989217i \(0.453214\pi\)
\(488\) −83.0175 −3.75803
\(489\) −13.5809 −0.614148
\(490\) 43.4111 1.96111
\(491\) 16.7077 0.754007 0.377004 0.926212i \(-0.376954\pi\)
0.377004 + 0.926212i \(0.376954\pi\)
\(492\) −102.526 −4.62222
\(493\) −1.67051 −0.0752359
\(494\) 0 0
\(495\) 15.8206 0.711084
\(496\) −41.1251 −1.84657
\(497\) 3.48938 0.156520
\(498\) 76.9987 3.45040
\(499\) −18.7254 −0.838264 −0.419132 0.907925i \(-0.637665\pi\)
−0.419132 + 0.907925i \(0.637665\pi\)
\(500\) −55.2376 −2.47030
\(501\) −52.0218 −2.32416
\(502\) 34.7663 1.55169
\(503\) −38.7263 −1.72672 −0.863359 0.504590i \(-0.831644\pi\)
−0.863359 + 0.504590i \(0.831644\pi\)
\(504\) −15.5255 −0.691559
\(505\) 29.2849 1.30316
\(506\) 10.6134 0.471823
\(507\) 0 0
\(508\) 109.533 4.85975
\(509\) 10.4846 0.464721 0.232360 0.972630i \(-0.425355\pi\)
0.232360 + 0.972630i \(0.425355\pi\)
\(510\) 30.0951 1.33263
\(511\) −0.399981 −0.0176941
\(512\) 5.28047 0.233366
\(513\) 89.2496 3.94046
\(514\) 1.71399 0.0756007
\(515\) −11.1775 −0.492540
\(516\) 39.9743 1.75977
\(517\) −6.48085 −0.285027
\(518\) −2.46804 −0.108439
\(519\) −8.34797 −0.366435
\(520\) 0 0
\(521\) −8.86293 −0.388292 −0.194146 0.980973i \(-0.562194\pi\)
−0.194146 + 0.980973i \(0.562194\pi\)
\(522\) −19.7721 −0.865401
\(523\) −38.3068 −1.67504 −0.837520 0.546407i \(-0.815995\pi\)
−0.837520 + 0.546407i \(0.815995\pi\)
\(524\) 19.6398 0.857970
\(525\) 0.376231 0.0164201
\(526\) −39.0382 −1.70214
\(527\) 4.99508 0.217589
\(528\) 39.5476 1.72109
\(529\) −7.35715 −0.319876
\(530\) −31.7268 −1.37813
\(531\) 73.7867 3.20207
\(532\) 10.4869 0.454663
\(533\) 0 0
\(534\) 67.9888 2.94216
\(535\) −46.8628 −2.02606
\(536\) −55.1456 −2.38193
\(537\) −71.1155 −3.06886
\(538\) 40.1639 1.73159
\(539\) −6.92885 −0.298447
\(540\) 143.370 6.16967
\(541\) −18.3574 −0.789245 −0.394623 0.918843i \(-0.629125\pi\)
−0.394623 + 0.918843i \(0.629125\pi\)
\(542\) 57.3391 2.46293
\(543\) 63.9561 2.74462
\(544\) 25.7515 1.10409
\(545\) −12.5451 −0.537374
\(546\) 0 0
\(547\) −1.64398 −0.0702916 −0.0351458 0.999382i \(-0.511190\pi\)
−0.0351458 + 0.999382i \(0.511190\pi\)
\(548\) 14.6639 0.626410
\(549\) 65.4889 2.79500
\(550\) −1.21056 −0.0516185
\(551\) 8.21964 0.350168
\(552\) 106.224 4.52121
\(553\) −0.970791 −0.0412822
\(554\) −64.1393 −2.72502
\(555\) 25.1710 1.06845
\(556\) −9.58393 −0.406449
\(557\) 7.76685 0.329092 0.164546 0.986369i \(-0.447384\pi\)
0.164546 + 0.986369i \(0.447384\pi\)
\(558\) 59.1217 2.50282
\(559\) 0 0
\(560\) 7.87700 0.332864
\(561\) −4.80349 −0.202803
\(562\) −52.5885 −2.21831
\(563\) −45.9808 −1.93786 −0.968930 0.247333i \(-0.920446\pi\)
−0.968930 + 0.247333i \(0.920446\pi\)
\(564\) −105.391 −4.43775
\(565\) −35.4402 −1.49098
\(566\) 3.75119 0.157674
\(567\) 4.42445 0.185809
\(568\) −112.370 −4.71494
\(569\) 29.8201 1.25012 0.625061 0.780576i \(-0.285074\pi\)
0.625061 + 0.780576i \(0.285074\pi\)
\(570\) −148.081 −6.20244
\(571\) 27.3401 1.14415 0.572075 0.820202i \(-0.306139\pi\)
0.572075 + 0.820202i \(0.306139\pi\)
\(572\) 0 0
\(573\) −24.0753 −1.00576
\(574\) 4.51273 0.188358
\(575\) −1.78422 −0.0744071
\(576\) 133.379 5.55747
\(577\) −40.3312 −1.67901 −0.839504 0.543353i \(-0.817154\pi\)
−0.839504 + 0.543353i \(0.817154\pi\)
\(578\) 39.2855 1.63406
\(579\) 23.6046 0.980975
\(580\) 13.2040 0.548266
\(581\) −2.44785 −0.101554
\(582\) 106.761 4.42538
\(583\) 5.06393 0.209726
\(584\) 12.8807 0.533009
\(585\) 0 0
\(586\) −53.8827 −2.22588
\(587\) 6.46283 0.266750 0.133375 0.991066i \(-0.457419\pi\)
0.133375 + 0.991066i \(0.457419\pi\)
\(588\) −112.676 −4.64668
\(589\) −24.5780 −1.01272
\(590\) −68.2239 −2.80873
\(591\) −58.8300 −2.41994
\(592\) 43.6126 1.79247
\(593\) 18.4337 0.756983 0.378492 0.925605i \(-0.376443\pi\)
0.378492 + 0.925605i \(0.376443\pi\)
\(594\) −31.6829 −1.29997
\(595\) −0.956747 −0.0392228
\(596\) −28.2501 −1.15717
\(597\) 28.2490 1.15615
\(598\) 0 0
\(599\) −9.81967 −0.401221 −0.200610 0.979671i \(-0.564293\pi\)
−0.200610 + 0.979671i \(0.564293\pi\)
\(600\) −12.1159 −0.494631
\(601\) 15.7357 0.641872 0.320936 0.947101i \(-0.396003\pi\)
0.320936 + 0.947101i \(0.396003\pi\)
\(602\) −1.75949 −0.0717116
\(603\) 43.5019 1.77153
\(604\) 35.7368 1.45411
\(605\) 2.33476 0.0949216
\(606\) −105.240 −4.27508
\(607\) 20.9871 0.851839 0.425919 0.904761i \(-0.359951\pi\)
0.425919 + 0.904761i \(0.359951\pi\)
\(608\) −126.709 −5.13872
\(609\) 0.906858 0.0367477
\(610\) −60.5516 −2.45166
\(611\) 0 0
\(612\) −54.1429 −2.18860
\(613\) −1.66482 −0.0672413 −0.0336206 0.999435i \(-0.510704\pi\)
−0.0336206 + 0.999435i \(0.510704\pi\)
\(614\) −11.6026 −0.468241
\(615\) −46.0244 −1.85588
\(616\) −2.29120 −0.0923153
\(617\) −10.5682 −0.425462 −0.212731 0.977111i \(-0.568236\pi\)
−0.212731 + 0.977111i \(0.568236\pi\)
\(618\) 40.1682 1.61580
\(619\) 28.5798 1.14872 0.574359 0.818603i \(-0.305251\pi\)
0.574359 + 0.818603i \(0.305251\pi\)
\(620\) −39.4820 −1.58564
\(621\) −46.6967 −1.87388
\(622\) 68.0996 2.73055
\(623\) −2.16142 −0.0865953
\(624\) 0 0
\(625\) −27.0521 −1.08208
\(626\) −56.6830 −2.26551
\(627\) 23.6353 0.943902
\(628\) 27.9127 1.11384
\(629\) −5.29722 −0.211214
\(630\) −11.3240 −0.451160
\(631\) 22.7451 0.905469 0.452735 0.891645i \(-0.350448\pi\)
0.452735 + 0.891645i \(0.350448\pi\)
\(632\) 31.2628 1.24357
\(633\) −35.3161 −1.40369
\(634\) −56.5772 −2.24697
\(635\) 49.1701 1.95126
\(636\) 82.3489 3.26535
\(637\) 0 0
\(638\) −2.91791 −0.115521
\(639\) 88.6437 3.50669
\(640\) −45.0526 −1.78086
\(641\) −10.4900 −0.414329 −0.207165 0.978306i \(-0.566424\pi\)
−0.207165 + 0.978306i \(0.566424\pi\)
\(642\) 168.409 6.64658
\(643\) 35.6282 1.40504 0.702520 0.711664i \(-0.252058\pi\)
0.702520 + 0.711664i \(0.252058\pi\)
\(644\) −5.48689 −0.216214
\(645\) 17.9447 0.706572
\(646\) 31.1636 1.22612
\(647\) 4.37246 0.171899 0.0859495 0.996299i \(-0.472608\pi\)
0.0859495 + 0.996299i \(0.472608\pi\)
\(648\) −142.482 −5.59724
\(649\) 10.8892 0.427440
\(650\) 0 0
\(651\) −2.71165 −0.106278
\(652\) −22.5908 −0.884724
\(653\) −23.0934 −0.903716 −0.451858 0.892090i \(-0.649239\pi\)
−0.451858 + 0.892090i \(0.649239\pi\)
\(654\) 45.0829 1.76288
\(655\) 8.81644 0.344487
\(656\) −79.7443 −3.11349
\(657\) −10.1611 −0.396421
\(658\) 4.63884 0.180841
\(659\) 30.0102 1.16903 0.584516 0.811383i \(-0.301285\pi\)
0.584516 + 0.811383i \(0.301285\pi\)
\(660\) 37.9676 1.47789
\(661\) −35.0403 −1.36291 −0.681455 0.731860i \(-0.738653\pi\)
−0.681455 + 0.731860i \(0.738653\pi\)
\(662\) 75.7136 2.94269
\(663\) 0 0
\(664\) 78.8291 3.05916
\(665\) 4.70762 0.182554
\(666\) −62.6977 −2.42949
\(667\) −4.30064 −0.166521
\(668\) −86.5346 −3.34812
\(669\) 81.1659 3.13805
\(670\) −40.2223 −1.55392
\(671\) 9.66466 0.373100
\(672\) −13.9795 −0.539273
\(673\) −12.4420 −0.479606 −0.239803 0.970822i \(-0.577083\pi\)
−0.239803 + 0.970822i \(0.577083\pi\)
\(674\) 20.1196 0.774978
\(675\) 5.32622 0.205006
\(676\) 0 0
\(677\) 29.5713 1.13652 0.568259 0.822849i \(-0.307617\pi\)
0.568259 + 0.822849i \(0.307617\pi\)
\(678\) 127.360 4.89123
\(679\) −3.39401 −0.130250
\(680\) 30.8105 1.18153
\(681\) −31.3740 −1.20225
\(682\) 8.72501 0.334098
\(683\) 13.5278 0.517628 0.258814 0.965927i \(-0.416668\pi\)
0.258814 + 0.965927i \(0.416668\pi\)
\(684\) 266.407 10.1863
\(685\) 6.58271 0.251512
\(686\) 9.96994 0.380654
\(687\) −9.32111 −0.355622
\(688\) 31.0919 1.18537
\(689\) 0 0
\(690\) 77.4784 2.94955
\(691\) 5.92854 0.225532 0.112766 0.993622i \(-0.464029\pi\)
0.112766 + 0.993622i \(0.464029\pi\)
\(692\) −13.8863 −0.527876
\(693\) 1.80743 0.0686586
\(694\) −59.4571 −2.25696
\(695\) −4.30229 −0.163195
\(696\) −29.2039 −1.10697
\(697\) 9.68581 0.366876
\(698\) 87.8156 3.32387
\(699\) −11.7270 −0.443556
\(700\) 0.625833 0.0236543
\(701\) 0.404230 0.0152675 0.00763377 0.999971i \(-0.497570\pi\)
0.00763377 + 0.999971i \(0.497570\pi\)
\(702\) 0 0
\(703\) 26.0647 0.983047
\(704\) 19.6837 0.741858
\(705\) −47.3105 −1.78182
\(706\) 21.9958 0.827824
\(707\) 3.34566 0.125826
\(708\) 177.079 6.65505
\(709\) 22.1763 0.832849 0.416425 0.909170i \(-0.363283\pi\)
0.416425 + 0.909170i \(0.363283\pi\)
\(710\) −81.9609 −3.07594
\(711\) −24.6619 −0.924892
\(712\) 69.6050 2.60856
\(713\) 12.8596 0.481596
\(714\) 3.43822 0.128672
\(715\) 0 0
\(716\) −118.296 −4.42091
\(717\) 25.5547 0.954358
\(718\) −40.7781 −1.52183
\(719\) 8.69164 0.324144 0.162072 0.986779i \(-0.448182\pi\)
0.162072 + 0.986779i \(0.448182\pi\)
\(720\) 200.106 7.45752
\(721\) −1.27698 −0.0475571
\(722\) −102.353 −3.80918
\(723\) 14.4645 0.537939
\(724\) 106.386 3.95382
\(725\) 0.490530 0.0182178
\(726\) −8.39034 −0.311395
\(727\) −24.2296 −0.898627 −0.449314 0.893374i \(-0.648331\pi\)
−0.449314 + 0.893374i \(0.648331\pi\)
\(728\) 0 0
\(729\) 1.65092 0.0611451
\(730\) 9.39502 0.347725
\(731\) −3.77645 −0.139677
\(732\) 157.165 5.80900
\(733\) 6.69006 0.247103 0.123552 0.992338i \(-0.460572\pi\)
0.123552 + 0.992338i \(0.460572\pi\)
\(734\) −31.8266 −1.17474
\(735\) −50.5810 −1.86571
\(736\) 66.2959 2.44370
\(737\) 6.41989 0.236480
\(738\) 114.641 4.21999
\(739\) −32.0479 −1.17890 −0.589450 0.807805i \(-0.700655\pi\)
−0.589450 + 0.807805i \(0.700655\pi\)
\(740\) 41.8702 1.53918
\(741\) 0 0
\(742\) −3.62464 −0.133065
\(743\) −27.7046 −1.01638 −0.508191 0.861244i \(-0.669686\pi\)
−0.508191 + 0.861244i \(0.669686\pi\)
\(744\) 87.3244 3.20147
\(745\) −12.6816 −0.464619
\(746\) 84.3536 3.08841
\(747\) −62.1848 −2.27522
\(748\) −7.99026 −0.292153
\(749\) −5.35385 −0.195626
\(750\) 89.1102 3.25384
\(751\) 30.0879 1.09792 0.548961 0.835848i \(-0.315023\pi\)
0.548961 + 0.835848i \(0.315023\pi\)
\(752\) −81.9727 −2.98924
\(753\) −40.5084 −1.47621
\(754\) 0 0
\(755\) 16.0425 0.583845
\(756\) 16.3794 0.595711
\(757\) −18.0765 −0.657003 −0.328502 0.944503i \(-0.606544\pi\)
−0.328502 + 0.944503i \(0.606544\pi\)
\(758\) 74.8274 2.71785
\(759\) −12.3663 −0.448870
\(760\) −151.601 −5.49916
\(761\) 28.5069 1.03337 0.516687 0.856174i \(-0.327165\pi\)
0.516687 + 0.856174i \(0.327165\pi\)
\(762\) −176.701 −6.40119
\(763\) −1.43322 −0.0518861
\(764\) −40.0476 −1.44887
\(765\) −24.3051 −0.878752
\(766\) 53.9246 1.94838
\(767\) 0 0
\(768\) 38.8144 1.40059
\(769\) 15.3331 0.552927 0.276464 0.961024i \(-0.410837\pi\)
0.276464 + 0.961024i \(0.410837\pi\)
\(770\) −1.67117 −0.0602247
\(771\) −1.99707 −0.0719228
\(772\) 39.2646 1.41316
\(773\) 22.6186 0.813536 0.406768 0.913532i \(-0.366656\pi\)
0.406768 + 0.913532i \(0.366656\pi\)
\(774\) −44.6980 −1.60664
\(775\) −1.46676 −0.0526877
\(776\) 109.299 3.92360
\(777\) 2.87567 0.103164
\(778\) 4.83155 0.173219
\(779\) −47.6585 −1.70754
\(780\) 0 0
\(781\) 13.0818 0.468103
\(782\) −16.3053 −0.583075
\(783\) 12.8382 0.458799
\(784\) −87.6392 −3.12997
\(785\) 12.5302 0.447222
\(786\) −31.6833 −1.13011
\(787\) −13.6903 −0.488008 −0.244004 0.969774i \(-0.578461\pi\)
−0.244004 + 0.969774i \(0.578461\pi\)
\(788\) −97.8596 −3.48610
\(789\) 45.4858 1.61934
\(790\) 22.8026 0.811280
\(791\) −4.04887 −0.143961
\(792\) −58.2055 −2.06824
\(793\) 0 0
\(794\) 12.7878 0.453823
\(795\) 36.9669 1.31108
\(796\) 46.9901 1.66552
\(797\) 33.7231 1.19453 0.597266 0.802043i \(-0.296254\pi\)
0.597266 + 0.802043i \(0.296254\pi\)
\(798\) −16.9176 −0.598876
\(799\) 9.95647 0.352234
\(800\) −7.56170 −0.267346
\(801\) −54.9083 −1.94009
\(802\) −78.7376 −2.78032
\(803\) −1.49954 −0.0529176
\(804\) 104.399 3.68188
\(805\) −2.46310 −0.0868128
\(806\) 0 0
\(807\) −46.7975 −1.64735
\(808\) −107.742 −3.79034
\(809\) −5.96962 −0.209881 −0.104940 0.994479i \(-0.533465\pi\)
−0.104940 + 0.994479i \(0.533465\pi\)
\(810\) −103.924 −3.65153
\(811\) −34.4025 −1.20803 −0.604017 0.796971i \(-0.706434\pi\)
−0.604017 + 0.796971i \(0.706434\pi\)
\(812\) 1.50849 0.0529377
\(813\) −66.8094 −2.34311
\(814\) −9.25276 −0.324309
\(815\) −10.1411 −0.355229
\(816\) −60.7567 −2.12691
\(817\) 18.5818 0.650095
\(818\) −32.8968 −1.15021
\(819\) 0 0
\(820\) −76.5583 −2.67353
\(821\) −43.5132 −1.51862 −0.759311 0.650728i \(-0.774464\pi\)
−0.759311 + 0.650728i \(0.774464\pi\)
\(822\) −23.6560 −0.825098
\(823\) −51.6931 −1.80191 −0.900953 0.433916i \(-0.857132\pi\)
−0.900953 + 0.433916i \(0.857132\pi\)
\(824\) 41.1231 1.43259
\(825\) 1.41050 0.0491074
\(826\) −7.79425 −0.271197
\(827\) −48.9877 −1.70347 −0.851734 0.523974i \(-0.824449\pi\)
−0.851734 + 0.523974i \(0.824449\pi\)
\(828\) −139.388 −4.84408
\(829\) 41.8011 1.45181 0.725906 0.687794i \(-0.241421\pi\)
0.725906 + 0.687794i \(0.241421\pi\)
\(830\) 57.4967 1.99574
\(831\) 74.7327 2.59245
\(832\) 0 0
\(833\) 10.6447 0.368818
\(834\) 15.4609 0.535369
\(835\) −38.8459 −1.34432
\(836\) 39.3156 1.35976
\(837\) −38.3882 −1.32689
\(838\) −97.0297 −3.35183
\(839\) 30.6863 1.05941 0.529705 0.848182i \(-0.322303\pi\)
0.529705 + 0.848182i \(0.322303\pi\)
\(840\) −16.7259 −0.577099
\(841\) −27.8176 −0.959229
\(842\) −3.71573 −0.128052
\(843\) 61.2741 2.11039
\(844\) −58.7458 −2.02211
\(845\) 0 0
\(846\) 117.844 4.05158
\(847\) 0.266736 0.00916514
\(848\) 64.0508 2.19951
\(849\) −4.37074 −0.150003
\(850\) 1.85978 0.0637898
\(851\) −13.6374 −0.467485
\(852\) 212.734 7.28816
\(853\) −41.4726 −1.42000 −0.709998 0.704204i \(-0.751304\pi\)
−0.709998 + 0.704204i \(0.751304\pi\)
\(854\) −6.91774 −0.236720
\(855\) 119.592 4.08995
\(856\) 172.412 5.89294
\(857\) −24.1190 −0.823890 −0.411945 0.911209i \(-0.635150\pi\)
−0.411945 + 0.911209i \(0.635150\pi\)
\(858\) 0 0
\(859\) −47.9287 −1.63531 −0.817653 0.575712i \(-0.804725\pi\)
−0.817653 + 0.575712i \(0.804725\pi\)
\(860\) 29.8497 1.01787
\(861\) −5.25807 −0.179195
\(862\) 0.0822220 0.00280049
\(863\) −32.9887 −1.12295 −0.561474 0.827495i \(-0.689765\pi\)
−0.561474 + 0.827495i \(0.689765\pi\)
\(864\) −197.905 −6.73288
\(865\) −6.23363 −0.211950
\(866\) −36.3308 −1.23457
\(867\) −45.7740 −1.55457
\(868\) −4.51063 −0.153101
\(869\) −3.63953 −0.123462
\(870\) −21.3009 −0.722168
\(871\) 0 0
\(872\) 46.1546 1.56299
\(873\) −86.2211 −2.91814
\(874\) 80.2291 2.71379
\(875\) −2.83288 −0.0957688
\(876\) −24.3853 −0.823904
\(877\) −8.41464 −0.284142 −0.142071 0.989856i \(-0.545376\pi\)
−0.142071 + 0.989856i \(0.545376\pi\)
\(878\) −41.8548 −1.41253
\(879\) 62.7822 2.11759
\(880\) 29.5311 0.995494
\(881\) −20.8178 −0.701369 −0.350684 0.936494i \(-0.614051\pi\)
−0.350684 + 0.936494i \(0.614051\pi\)
\(882\) 125.991 4.24233
\(883\) 42.2995 1.42349 0.711746 0.702437i \(-0.247905\pi\)
0.711746 + 0.702437i \(0.247905\pi\)
\(884\) 0 0
\(885\) 79.4919 2.67209
\(886\) −43.8240 −1.47230
\(887\) −34.4350 −1.15622 −0.578108 0.815961i \(-0.696209\pi\)
−0.578108 + 0.815961i \(0.696209\pi\)
\(888\) −92.6063 −3.10766
\(889\) 5.61745 0.188403
\(890\) 50.7688 1.70177
\(891\) 16.5874 0.555699
\(892\) 135.014 4.52059
\(893\) −48.9902 −1.63940
\(894\) 45.5735 1.52421
\(895\) −53.1036 −1.77506
\(896\) −5.14705 −0.171951
\(897\) 0 0
\(898\) 7.89273 0.263384
\(899\) −3.53545 −0.117914
\(900\) 15.8986 0.529953
\(901\) −7.77966 −0.259178
\(902\) 16.9184 0.563321
\(903\) 2.05010 0.0682230
\(904\) 130.388 4.33663
\(905\) 47.7575 1.58751
\(906\) −57.6512 −1.91533
\(907\) −8.62987 −0.286550 −0.143275 0.989683i \(-0.545763\pi\)
−0.143275 + 0.989683i \(0.545763\pi\)
\(908\) −52.1884 −1.73193
\(909\) 84.9927 2.81903
\(910\) 0 0
\(911\) 43.0264 1.42553 0.712763 0.701405i \(-0.247443\pi\)
0.712763 + 0.701405i \(0.247443\pi\)
\(912\) 298.950 9.89921
\(913\) −9.17706 −0.303716
\(914\) 68.8088 2.27599
\(915\) 70.5525 2.33239
\(916\) −15.5050 −0.512300
\(917\) 1.00724 0.0332619
\(918\) 48.6742 1.60649
\(919\) −39.5049 −1.30315 −0.651574 0.758585i \(-0.725891\pi\)
−0.651574 + 0.758585i \(0.725891\pi\)
\(920\) 79.3202 2.61511
\(921\) 13.5189 0.445462
\(922\) −68.2697 −2.24834
\(923\) 0 0
\(924\) 4.33762 0.142697
\(925\) 1.55548 0.0511439
\(926\) 28.4627 0.935341
\(927\) −32.4402 −1.06548
\(928\) −18.2265 −0.598315
\(929\) 23.8514 0.782539 0.391269 0.920276i \(-0.372036\pi\)
0.391269 + 0.920276i \(0.372036\pi\)
\(930\) 63.6930 2.08858
\(931\) −52.3768 −1.71658
\(932\) −19.5070 −0.638974
\(933\) −79.3472 −2.59771
\(934\) 13.8871 0.454399
\(935\) −3.58688 −0.117303
\(936\) 0 0
\(937\) −21.8554 −0.713985 −0.356993 0.934107i \(-0.616198\pi\)
−0.356993 + 0.934107i \(0.616198\pi\)
\(938\) −4.59521 −0.150039
\(939\) 66.0449 2.15529
\(940\) −78.6977 −2.56683
\(941\) −14.3904 −0.469112 −0.234556 0.972103i \(-0.575364\pi\)
−0.234556 + 0.972103i \(0.575364\pi\)
\(942\) −45.0292 −1.46713
\(943\) 24.9356 0.812016
\(944\) 137.732 4.48279
\(945\) 7.35279 0.239186
\(946\) −6.59640 −0.214467
\(947\) −18.5363 −0.602349 −0.301175 0.953569i \(-0.597379\pi\)
−0.301175 + 0.953569i \(0.597379\pi\)
\(948\) −59.1855 −1.92226
\(949\) 0 0
\(950\) −9.15091 −0.296895
\(951\) 65.9216 2.13766
\(952\) 3.51996 0.114082
\(953\) 15.7252 0.509388 0.254694 0.967022i \(-0.418025\pi\)
0.254694 + 0.967022i \(0.418025\pi\)
\(954\) −92.0799 −2.98120
\(955\) −17.9776 −0.581742
\(956\) 42.5084 1.37482
\(957\) 3.39984 0.109901
\(958\) −48.0903 −1.55373
\(959\) 0.752043 0.0242847
\(960\) 143.692 4.63765
\(961\) −20.4284 −0.658982
\(962\) 0 0
\(963\) −136.009 −4.38282
\(964\) 24.0606 0.774939
\(965\) 17.6261 0.567405
\(966\) 8.85153 0.284793
\(967\) 40.7288 1.30975 0.654874 0.755738i \(-0.272722\pi\)
0.654874 + 0.755738i \(0.272722\pi\)
\(968\) −8.58980 −0.276087
\(969\) −36.3107 −1.16647
\(970\) 79.7209 2.55968
\(971\) 51.9398 1.66683 0.833414 0.552649i \(-0.186383\pi\)
0.833414 + 0.552649i \(0.186383\pi\)
\(972\) 85.5221 2.74312
\(973\) −0.491516 −0.0157573
\(974\) −17.3458 −0.555796
\(975\) 0 0
\(976\) 122.243 3.91290
\(977\) 6.50233 0.208028 0.104014 0.994576i \(-0.466831\pi\)
0.104014 + 0.994576i \(0.466831\pi\)
\(978\) 36.4438 1.16535
\(979\) −8.10322 −0.258980
\(980\) −84.1379 −2.68769
\(981\) −36.4093 −1.16246
\(982\) −44.8345 −1.43073
\(983\) −10.4399 −0.332981 −0.166491 0.986043i \(-0.553244\pi\)
−0.166491 + 0.986043i \(0.553244\pi\)
\(984\) 169.328 5.39798
\(985\) −43.9298 −1.39972
\(986\) 4.48276 0.142760
\(987\) −5.40500 −0.172043
\(988\) 0 0
\(989\) −9.72228 −0.309151
\(990\) −42.4542 −1.34928
\(991\) −25.3194 −0.804296 −0.402148 0.915575i \(-0.631736\pi\)
−0.402148 + 0.915575i \(0.631736\pi\)
\(992\) 54.5002 1.73038
\(993\) −88.2186 −2.79953
\(994\) −9.36364 −0.296997
\(995\) 21.0941 0.668729
\(996\) −149.236 −4.72873
\(997\) −21.2428 −0.672766 −0.336383 0.941725i \(-0.609204\pi\)
−0.336383 + 0.941725i \(0.609204\pi\)
\(998\) 50.2490 1.59060
\(999\) 40.7102 1.28801
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.1.3 yes 21
13.12 even 2 1859.2.a.s.1.19 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.19 21 13.12 even 2
1859.2.a.t.1.3 yes 21 1.1 even 1 trivial