Properties

Label 3549.2.a.bf.1.3
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.36450\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +4.53093 q^{10} +1.11378 q^{11} +0.138150 q^{12} +1.36450 q^{14} +3.32059 q^{15} -3.70462 q^{16} +0.665810 q^{17} -1.36450 q^{18} +3.22931 q^{19} +0.458738 q^{20} +1.00000 q^{21} -1.51975 q^{22} +5.07298 q^{23} -2.91750 q^{24} +6.02631 q^{25} -1.00000 q^{27} +0.138150 q^{28} -0.615375 q^{29} -4.53093 q^{30} -8.84343 q^{31} -0.780060 q^{32} -1.11378 q^{33} -0.908495 q^{34} +3.32059 q^{35} -0.138150 q^{36} -3.79560 q^{37} -4.40639 q^{38} -9.68781 q^{40} +0.916015 q^{41} -1.36450 q^{42} +8.09576 q^{43} -0.153868 q^{44} -3.32059 q^{45} -6.92207 q^{46} -13.0955 q^{47} +3.70462 q^{48} +1.00000 q^{49} -8.22287 q^{50} -0.665810 q^{51} +3.52862 q^{53} +1.36450 q^{54} -3.69841 q^{55} -2.91750 q^{56} -3.22931 q^{57} +0.839676 q^{58} +5.48952 q^{59} -0.458738 q^{60} -14.1106 q^{61} +12.0668 q^{62} -1.00000 q^{63} +8.47362 q^{64} +1.51975 q^{66} -3.47625 q^{67} -0.0919813 q^{68} -5.07298 q^{69} -4.53093 q^{70} +4.77075 q^{71} +2.91750 q^{72} -7.86139 q^{73} +5.17908 q^{74} -6.02631 q^{75} -0.446128 q^{76} -1.11378 q^{77} -11.8320 q^{79} +12.3015 q^{80} +1.00000 q^{81} -1.24990 q^{82} -16.4426 q^{83} -0.138150 q^{84} -2.21088 q^{85} -11.0466 q^{86} +0.615375 q^{87} +3.24946 q^{88} +16.1871 q^{89} +4.53093 q^{90} -0.700830 q^{92} +8.84343 q^{93} +17.8688 q^{94} -10.7232 q^{95} +0.780060 q^{96} -1.42122 q^{97} -1.36450 q^{98} +1.11378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36450 −0.964845 −0.482422 0.875939i \(-0.660243\pi\)
−0.482422 + 0.875939i \(0.660243\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.138150 −0.0690748
\(5\) −3.32059 −1.48501 −0.742506 0.669839i \(-0.766363\pi\)
−0.742506 + 0.669839i \(0.766363\pi\)
\(6\) 1.36450 0.557053
\(7\) −1.00000 −0.377964
\(8\) 2.91750 1.03149
\(9\) 1.00000 0.333333
\(10\) 4.53093 1.43281
\(11\) 1.11378 0.335818 0.167909 0.985803i \(-0.446299\pi\)
0.167909 + 0.985803i \(0.446299\pi\)
\(12\) 0.138150 0.0398803
\(13\) 0 0
\(14\) 1.36450 0.364677
\(15\) 3.32059 0.857372
\(16\) −3.70462 −0.926154
\(17\) 0.665810 0.161483 0.0807413 0.996735i \(-0.474271\pi\)
0.0807413 + 0.996735i \(0.474271\pi\)
\(18\) −1.36450 −0.321615
\(19\) 3.22931 0.740855 0.370428 0.928861i \(-0.379211\pi\)
0.370428 + 0.928861i \(0.379211\pi\)
\(20\) 0.458738 0.102577
\(21\) 1.00000 0.218218
\(22\) −1.51975 −0.324012
\(23\) 5.07298 1.05779 0.528895 0.848687i \(-0.322606\pi\)
0.528895 + 0.848687i \(0.322606\pi\)
\(24\) −2.91750 −0.595532
\(25\) 6.02631 1.20526
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0.138150 0.0261078
\(29\) −0.615375 −0.114272 −0.0571361 0.998366i \(-0.518197\pi\)
−0.0571361 + 0.998366i \(0.518197\pi\)
\(30\) −4.53093 −0.827231
\(31\) −8.84343 −1.58833 −0.794163 0.607704i \(-0.792091\pi\)
−0.794163 + 0.607704i \(0.792091\pi\)
\(32\) −0.780060 −0.137896
\(33\) −1.11378 −0.193885
\(34\) −0.908495 −0.155806
\(35\) 3.32059 0.561282
\(36\) −0.138150 −0.0230249
\(37\) −3.79560 −0.623992 −0.311996 0.950083i \(-0.600998\pi\)
−0.311996 + 0.950083i \(0.600998\pi\)
\(38\) −4.40639 −0.714810
\(39\) 0 0
\(40\) −9.68781 −1.53178
\(41\) 0.916015 0.143058 0.0715288 0.997439i \(-0.477212\pi\)
0.0715288 + 0.997439i \(0.477212\pi\)
\(42\) −1.36450 −0.210546
\(43\) 8.09576 1.23459 0.617296 0.786731i \(-0.288228\pi\)
0.617296 + 0.786731i \(0.288228\pi\)
\(44\) −0.153868 −0.0231965
\(45\) −3.32059 −0.495004
\(46\) −6.92207 −1.02060
\(47\) −13.0955 −1.91018 −0.955090 0.296316i \(-0.904242\pi\)
−0.955090 + 0.296316i \(0.904242\pi\)
\(48\) 3.70462 0.534715
\(49\) 1.00000 0.142857
\(50\) −8.22287 −1.16289
\(51\) −0.665810 −0.0932320
\(52\) 0 0
\(53\) 3.52862 0.484694 0.242347 0.970190i \(-0.422083\pi\)
0.242347 + 0.970190i \(0.422083\pi\)
\(54\) 1.36450 0.185684
\(55\) −3.69841 −0.498694
\(56\) −2.91750 −0.389867
\(57\) −3.22931 −0.427733
\(58\) 0.839676 0.110255
\(59\) 5.48952 0.714674 0.357337 0.933975i \(-0.383685\pi\)
0.357337 + 0.933975i \(0.383685\pi\)
\(60\) −0.458738 −0.0592228
\(61\) −14.1106 −1.80667 −0.903336 0.428934i \(-0.858889\pi\)
−0.903336 + 0.428934i \(0.858889\pi\)
\(62\) 12.0668 1.53249
\(63\) −1.00000 −0.125988
\(64\) 8.47362 1.05920
\(65\) 0 0
\(66\) 1.51975 0.187069
\(67\) −3.47625 −0.424691 −0.212345 0.977195i \(-0.568110\pi\)
−0.212345 + 0.977195i \(0.568110\pi\)
\(68\) −0.0919813 −0.0111544
\(69\) −5.07298 −0.610716
\(70\) −4.53093 −0.541550
\(71\) 4.77075 0.566184 0.283092 0.959093i \(-0.408640\pi\)
0.283092 + 0.959093i \(0.408640\pi\)
\(72\) 2.91750 0.343830
\(73\) −7.86139 −0.920106 −0.460053 0.887892i \(-0.652170\pi\)
−0.460053 + 0.887892i \(0.652170\pi\)
\(74\) 5.17908 0.602056
\(75\) −6.02631 −0.695858
\(76\) −0.446128 −0.0511744
\(77\) −1.11378 −0.126927
\(78\) 0 0
\(79\) −11.8320 −1.33120 −0.665601 0.746307i \(-0.731825\pi\)
−0.665601 + 0.746307i \(0.731825\pi\)
\(80\) 12.3015 1.37535
\(81\) 1.00000 0.111111
\(82\) −1.24990 −0.138028
\(83\) −16.4426 −1.80481 −0.902406 0.430887i \(-0.858201\pi\)
−0.902406 + 0.430887i \(0.858201\pi\)
\(84\) −0.138150 −0.0150733
\(85\) −2.21088 −0.239804
\(86\) −11.0466 −1.19119
\(87\) 0.615375 0.0659751
\(88\) 3.24946 0.346393
\(89\) 16.1871 1.71583 0.857913 0.513796i \(-0.171761\pi\)
0.857913 + 0.513796i \(0.171761\pi\)
\(90\) 4.53093 0.477602
\(91\) 0 0
\(92\) −0.700830 −0.0730666
\(93\) 8.84343 0.917021
\(94\) 17.8688 1.84303
\(95\) −10.7232 −1.10018
\(96\) 0.780060 0.0796145
\(97\) −1.42122 −0.144303 −0.0721516 0.997394i \(-0.522987\pi\)
−0.0721516 + 0.997394i \(0.522987\pi\)
\(98\) −1.36450 −0.137835
\(99\) 1.11378 0.111939
\(100\) −0.832531 −0.0832531
\(101\) −0.720751 −0.0717174 −0.0358587 0.999357i \(-0.511417\pi\)
−0.0358587 + 0.999357i \(0.511417\pi\)
\(102\) 0.908495 0.0899544
\(103\) 14.9632 1.47437 0.737186 0.675690i \(-0.236154\pi\)
0.737186 + 0.675690i \(0.236154\pi\)
\(104\) 0 0
\(105\) −3.32059 −0.324056
\(106\) −4.81479 −0.467654
\(107\) 11.6187 1.12323 0.561613 0.827400i \(-0.310181\pi\)
0.561613 + 0.827400i \(0.310181\pi\)
\(108\) 0.138150 0.0132934
\(109\) −4.94550 −0.473693 −0.236846 0.971547i \(-0.576114\pi\)
−0.236846 + 0.971547i \(0.576114\pi\)
\(110\) 5.04647 0.481162
\(111\) 3.79560 0.360262
\(112\) 3.70462 0.350053
\(113\) 16.2144 1.52532 0.762661 0.646798i \(-0.223892\pi\)
0.762661 + 0.646798i \(0.223892\pi\)
\(114\) 4.40639 0.412696
\(115\) −16.8453 −1.57083
\(116\) 0.0850137 0.00789332
\(117\) 0 0
\(118\) −7.49043 −0.689550
\(119\) −0.665810 −0.0610347
\(120\) 9.68781 0.884372
\(121\) −9.75949 −0.887226
\(122\) 19.2538 1.74316
\(123\) −0.916015 −0.0825943
\(124\) 1.22172 0.109713
\(125\) −3.40794 −0.304815
\(126\) 1.36450 0.121559
\(127\) −11.4819 −1.01886 −0.509429 0.860513i \(-0.670143\pi\)
−0.509429 + 0.860513i \(0.670143\pi\)
\(128\) −10.0021 −0.884070
\(129\) −8.09576 −0.712792
\(130\) 0 0
\(131\) −18.3232 −1.60090 −0.800451 0.599398i \(-0.795407\pi\)
−0.800451 + 0.599398i \(0.795407\pi\)
\(132\) 0.153868 0.0133925
\(133\) −3.22931 −0.280017
\(134\) 4.74332 0.409761
\(135\) 3.32059 0.285791
\(136\) 1.94250 0.166568
\(137\) −13.5829 −1.16047 −0.580233 0.814451i \(-0.697038\pi\)
−0.580233 + 0.814451i \(0.697038\pi\)
\(138\) 6.92207 0.589246
\(139\) −0.226772 −0.0192345 −0.00961726 0.999954i \(-0.503061\pi\)
−0.00961726 + 0.999954i \(0.503061\pi\)
\(140\) −0.458738 −0.0387704
\(141\) 13.0955 1.10284
\(142\) −6.50967 −0.546279
\(143\) 0 0
\(144\) −3.70462 −0.308718
\(145\) 2.04341 0.169696
\(146\) 10.7268 0.887759
\(147\) −1.00000 −0.0824786
\(148\) 0.524360 0.0431021
\(149\) 7.17188 0.587543 0.293772 0.955876i \(-0.405089\pi\)
0.293772 + 0.955876i \(0.405089\pi\)
\(150\) 8.22287 0.671395
\(151\) −7.19280 −0.585342 −0.292671 0.956213i \(-0.594544\pi\)
−0.292671 + 0.956213i \(0.594544\pi\)
\(152\) 9.42151 0.764186
\(153\) 0.665810 0.0538275
\(154\) 1.51975 0.122465
\(155\) 29.3654 2.35868
\(156\) 0 0
\(157\) 7.18613 0.573515 0.286758 0.958003i \(-0.407423\pi\)
0.286758 + 0.958003i \(0.407423\pi\)
\(158\) 16.1447 1.28440
\(159\) −3.52862 −0.279838
\(160\) 2.59026 0.204778
\(161\) −5.07298 −0.399807
\(162\) −1.36450 −0.107205
\(163\) −22.1597 −1.73568 −0.867839 0.496845i \(-0.834492\pi\)
−0.867839 + 0.496845i \(0.834492\pi\)
\(164\) −0.126547 −0.00988167
\(165\) 3.69841 0.287921
\(166\) 22.4359 1.74136
\(167\) 14.9897 1.15994 0.579969 0.814638i \(-0.303064\pi\)
0.579969 + 0.814638i \(0.303064\pi\)
\(168\) 2.91750 0.225090
\(169\) 0 0
\(170\) 3.01674 0.231373
\(171\) 3.22931 0.246952
\(172\) −1.11843 −0.0852791
\(173\) 0.425335 0.0323376 0.0161688 0.999869i \(-0.494853\pi\)
0.0161688 + 0.999869i \(0.494853\pi\)
\(174\) −0.839676 −0.0636557
\(175\) −6.02631 −0.455546
\(176\) −4.12614 −0.311019
\(177\) −5.48952 −0.412617
\(178\) −22.0872 −1.65550
\(179\) 13.7825 1.03015 0.515076 0.857145i \(-0.327764\pi\)
0.515076 + 0.857145i \(0.327764\pi\)
\(180\) 0.458738 0.0341923
\(181\) 21.8738 1.62587 0.812933 0.582357i \(-0.197870\pi\)
0.812933 + 0.582357i \(0.197870\pi\)
\(182\) 0 0
\(183\) 14.1106 1.04308
\(184\) 14.8004 1.09110
\(185\) 12.6036 0.926636
\(186\) −12.0668 −0.884783
\(187\) 0.741567 0.0542287
\(188\) 1.80914 0.131945
\(189\) 1.00000 0.0727393
\(190\) 14.6318 1.06150
\(191\) 10.8936 0.788231 0.394115 0.919061i \(-0.371051\pi\)
0.394115 + 0.919061i \(0.371051\pi\)
\(192\) −8.47362 −0.611531
\(193\) 17.0935 1.23042 0.615208 0.788365i \(-0.289072\pi\)
0.615208 + 0.788365i \(0.289072\pi\)
\(194\) 1.93925 0.139230
\(195\) 0 0
\(196\) −0.138150 −0.00986782
\(197\) 4.58665 0.326785 0.163393 0.986561i \(-0.447756\pi\)
0.163393 + 0.986561i \(0.447756\pi\)
\(198\) −1.51975 −0.108004
\(199\) 6.08803 0.431569 0.215785 0.976441i \(-0.430769\pi\)
0.215785 + 0.976441i \(0.430769\pi\)
\(200\) 17.5817 1.24322
\(201\) 3.47625 0.245195
\(202\) 0.983462 0.0691961
\(203\) 0.615375 0.0431908
\(204\) 0.0919813 0.00643998
\(205\) −3.04171 −0.212442
\(206\) −20.4173 −1.42254
\(207\) 5.07298 0.352597
\(208\) 0 0
\(209\) 3.59675 0.248793
\(210\) 4.53093 0.312664
\(211\) 10.3803 0.714606 0.357303 0.933988i \(-0.383696\pi\)
0.357303 + 0.933988i \(0.383696\pi\)
\(212\) −0.487478 −0.0334801
\(213\) −4.77075 −0.326886
\(214\) −15.8537 −1.08374
\(215\) −26.8827 −1.83338
\(216\) −2.91750 −0.198511
\(217\) 8.84343 0.600331
\(218\) 6.74811 0.457040
\(219\) 7.86139 0.531223
\(220\) 0.510934 0.0344471
\(221\) 0 0
\(222\) −5.17908 −0.347597
\(223\) −12.7655 −0.854840 −0.427420 0.904053i \(-0.640577\pi\)
−0.427420 + 0.904053i \(0.640577\pi\)
\(224\) 0.780060 0.0521199
\(225\) 6.02631 0.401754
\(226\) −22.1245 −1.47170
\(227\) 13.3301 0.884747 0.442374 0.896831i \(-0.354136\pi\)
0.442374 + 0.896831i \(0.354136\pi\)
\(228\) 0.446128 0.0295456
\(229\) −9.63903 −0.636965 −0.318482 0.947929i \(-0.603173\pi\)
−0.318482 + 0.947929i \(0.603173\pi\)
\(230\) 22.9853 1.51561
\(231\) 1.11378 0.0732815
\(232\) −1.79535 −0.117871
\(233\) −22.0553 −1.44489 −0.722444 0.691429i \(-0.756981\pi\)
−0.722444 + 0.691429i \(0.756981\pi\)
\(234\) 0 0
\(235\) 43.4849 2.83664
\(236\) −0.758374 −0.0493659
\(237\) 11.8320 0.768570
\(238\) 0.908495 0.0588890
\(239\) 23.6972 1.53285 0.766424 0.642335i \(-0.222034\pi\)
0.766424 + 0.642335i \(0.222034\pi\)
\(240\) −12.3015 −0.794059
\(241\) 17.5586 1.13105 0.565525 0.824731i \(-0.308673\pi\)
0.565525 + 0.824731i \(0.308673\pi\)
\(242\) 13.3168 0.856036
\(243\) −1.00000 −0.0641500
\(244\) 1.94937 0.124795
\(245\) −3.32059 −0.212145
\(246\) 1.24990 0.0796907
\(247\) 0 0
\(248\) −25.8007 −1.63834
\(249\) 16.4426 1.04201
\(250\) 4.65012 0.294099
\(251\) 30.2065 1.90662 0.953310 0.301994i \(-0.0976522\pi\)
0.953310 + 0.301994i \(0.0976522\pi\)
\(252\) 0.138150 0.00870260
\(253\) 5.65020 0.355225
\(254\) 15.6671 0.983039
\(255\) 2.21088 0.138451
\(256\) −3.29940 −0.206213
\(257\) −4.98163 −0.310746 −0.155373 0.987856i \(-0.549658\pi\)
−0.155373 + 0.987856i \(0.549658\pi\)
\(258\) 11.0466 0.687733
\(259\) 3.79560 0.235847
\(260\) 0 0
\(261\) −0.615375 −0.0380907
\(262\) 25.0019 1.54462
\(263\) −12.5614 −0.774571 −0.387286 0.921960i \(-0.626587\pi\)
−0.387286 + 0.921960i \(0.626587\pi\)
\(264\) −3.24946 −0.199990
\(265\) −11.7171 −0.719776
\(266\) 4.40639 0.270173
\(267\) −16.1871 −0.990632
\(268\) 0.480242 0.0293354
\(269\) −1.45811 −0.0889028 −0.0444514 0.999012i \(-0.514154\pi\)
−0.0444514 + 0.999012i \(0.514154\pi\)
\(270\) −4.53093 −0.275744
\(271\) −15.5702 −0.945820 −0.472910 0.881111i \(-0.656797\pi\)
−0.472910 + 0.881111i \(0.656797\pi\)
\(272\) −2.46657 −0.149558
\(273\) 0 0
\(274\) 18.5338 1.11967
\(275\) 6.71199 0.404748
\(276\) 0.700830 0.0421850
\(277\) −18.0174 −1.08256 −0.541280 0.840842i \(-0.682060\pi\)
−0.541280 + 0.840842i \(0.682060\pi\)
\(278\) 0.309429 0.0185583
\(279\) −8.84343 −0.529442
\(280\) 9.68781 0.578957
\(281\) 25.8821 1.54400 0.771999 0.635624i \(-0.219257\pi\)
0.771999 + 0.635624i \(0.219257\pi\)
\(282\) −17.8688 −1.06407
\(283\) 9.98839 0.593748 0.296874 0.954917i \(-0.404056\pi\)
0.296874 + 0.954917i \(0.404056\pi\)
\(284\) −0.659077 −0.0391090
\(285\) 10.7232 0.635189
\(286\) 0 0
\(287\) −0.916015 −0.0540707
\(288\) −0.780060 −0.0459655
\(289\) −16.5567 −0.973923
\(290\) −2.78822 −0.163730
\(291\) 1.42122 0.0833135
\(292\) 1.08605 0.0635561
\(293\) −3.60381 −0.210537 −0.105268 0.994444i \(-0.533570\pi\)
−0.105268 + 0.994444i \(0.533570\pi\)
\(294\) 1.36450 0.0795790
\(295\) −18.2284 −1.06130
\(296\) −11.0736 −0.643642
\(297\) −1.11378 −0.0646282
\(298\) −9.78600 −0.566888
\(299\) 0 0
\(300\) 0.832531 0.0480662
\(301\) −8.09576 −0.466632
\(302\) 9.81455 0.564764
\(303\) 0.720751 0.0414061
\(304\) −11.9634 −0.686146
\(305\) 46.8553 2.68293
\(306\) −0.908495 −0.0519352
\(307\) 17.4426 0.995500 0.497750 0.867321i \(-0.334160\pi\)
0.497750 + 0.867321i \(0.334160\pi\)
\(308\) 0.153868 0.00876747
\(309\) −14.9632 −0.851229
\(310\) −40.0690 −2.27576
\(311\) −22.3025 −1.26466 −0.632330 0.774699i \(-0.717901\pi\)
−0.632330 + 0.774699i \(0.717901\pi\)
\(312\) 0 0
\(313\) 0.792995 0.0448227 0.0224114 0.999749i \(-0.492866\pi\)
0.0224114 + 0.999749i \(0.492866\pi\)
\(314\) −9.80545 −0.553353
\(315\) 3.32059 0.187094
\(316\) 1.63458 0.0919525
\(317\) 8.48350 0.476481 0.238240 0.971206i \(-0.423429\pi\)
0.238240 + 0.971206i \(0.423429\pi\)
\(318\) 4.81479 0.270000
\(319\) −0.685393 −0.0383747
\(320\) −28.1374 −1.57293
\(321\) −11.6187 −0.648495
\(322\) 6.92207 0.385752
\(323\) 2.15011 0.119635
\(324\) −0.138150 −0.00767497
\(325\) 0 0
\(326\) 30.2368 1.67466
\(327\) 4.94550 0.273487
\(328\) 2.67247 0.147563
\(329\) 13.0955 0.721980
\(330\) −5.04647 −0.277799
\(331\) 33.5170 1.84226 0.921130 0.389256i \(-0.127268\pi\)
0.921130 + 0.389256i \(0.127268\pi\)
\(332\) 2.27154 0.124667
\(333\) −3.79560 −0.207997
\(334\) −20.4534 −1.11916
\(335\) 11.5432 0.630671
\(336\) −3.70462 −0.202103
\(337\) −19.4227 −1.05802 −0.529012 0.848614i \(-0.677437\pi\)
−0.529012 + 0.848614i \(0.677437\pi\)
\(338\) 0 0
\(339\) −16.2144 −0.880645
\(340\) 0.305432 0.0165644
\(341\) −9.84965 −0.533389
\(342\) −4.40639 −0.238270
\(343\) −1.00000 −0.0539949
\(344\) 23.6194 1.27347
\(345\) 16.8453 0.906920
\(346\) −0.580368 −0.0312008
\(347\) −11.1748 −0.599896 −0.299948 0.953956i \(-0.596969\pi\)
−0.299948 + 0.953956i \(0.596969\pi\)
\(348\) −0.0850137 −0.00455721
\(349\) −36.8109 −1.97044 −0.985222 0.171281i \(-0.945209\pi\)
−0.985222 + 0.171281i \(0.945209\pi\)
\(350\) 8.22287 0.439531
\(351\) 0 0
\(352\) −0.868817 −0.0463081
\(353\) −17.5115 −0.932041 −0.466021 0.884774i \(-0.654313\pi\)
−0.466021 + 0.884774i \(0.654313\pi\)
\(354\) 7.49043 0.398112
\(355\) −15.8417 −0.840790
\(356\) −2.23623 −0.118520
\(357\) 0.665810 0.0352384
\(358\) −18.8062 −0.993936
\(359\) −8.15731 −0.430527 −0.215263 0.976556i \(-0.569061\pi\)
−0.215263 + 0.976556i \(0.569061\pi\)
\(360\) −9.68781 −0.510592
\(361\) −8.57154 −0.451133
\(362\) −29.8467 −1.56871
\(363\) 9.75949 0.512240
\(364\) 0 0
\(365\) 26.1044 1.36637
\(366\) −19.2538 −1.00641
\(367\) 15.8536 0.827552 0.413776 0.910379i \(-0.364210\pi\)
0.413776 + 0.910379i \(0.364210\pi\)
\(368\) −18.7935 −0.979677
\(369\) 0.916015 0.0476859
\(370\) −17.1976 −0.894060
\(371\) −3.52862 −0.183197
\(372\) −1.22172 −0.0633430
\(373\) 11.3075 0.585482 0.292741 0.956192i \(-0.405433\pi\)
0.292741 + 0.956192i \(0.405433\pi\)
\(374\) −1.01187 −0.0523223
\(375\) 3.40794 0.175985
\(376\) −38.2062 −1.97033
\(377\) 0 0
\(378\) −1.36450 −0.0701821
\(379\) −14.8591 −0.763262 −0.381631 0.924315i \(-0.624638\pi\)
−0.381631 + 0.924315i \(0.624638\pi\)
\(380\) 1.48141 0.0759946
\(381\) 11.4819 0.588238
\(382\) −14.8642 −0.760520
\(383\) −19.5528 −0.999101 −0.499551 0.866285i \(-0.666502\pi\)
−0.499551 + 0.866285i \(0.666502\pi\)
\(384\) 10.0021 0.510418
\(385\) 3.69841 0.188489
\(386\) −23.3240 −1.18716
\(387\) 8.09576 0.411531
\(388\) 0.196341 0.00996771
\(389\) 15.4987 0.785815 0.392907 0.919578i \(-0.371469\pi\)
0.392907 + 0.919578i \(0.371469\pi\)
\(390\) 0 0
\(391\) 3.37764 0.170815
\(392\) 2.91750 0.147356
\(393\) 18.3232 0.924281
\(394\) −6.25847 −0.315297
\(395\) 39.2892 1.97685
\(396\) −0.153868 −0.00773218
\(397\) 23.2126 1.16501 0.582503 0.812828i \(-0.302073\pi\)
0.582503 + 0.812828i \(0.302073\pi\)
\(398\) −8.30710 −0.416397
\(399\) 3.22931 0.161668
\(400\) −22.3251 −1.11626
\(401\) 39.2538 1.96024 0.980121 0.198403i \(-0.0635754\pi\)
0.980121 + 0.198403i \(0.0635754\pi\)
\(402\) −4.74332 −0.236576
\(403\) 0 0
\(404\) 0.0995714 0.00495386
\(405\) −3.32059 −0.165001
\(406\) −0.839676 −0.0416724
\(407\) −4.22747 −0.209548
\(408\) −1.94250 −0.0961680
\(409\) 19.5916 0.968743 0.484371 0.874862i \(-0.339048\pi\)
0.484371 + 0.874862i \(0.339048\pi\)
\(410\) 4.15040 0.204974
\(411\) 13.5829 0.669995
\(412\) −2.06716 −0.101842
\(413\) −5.48952 −0.270121
\(414\) −6.92207 −0.340201
\(415\) 54.5992 2.68017
\(416\) 0 0
\(417\) 0.226772 0.0111051
\(418\) −4.90775 −0.240046
\(419\) 8.42940 0.411803 0.205902 0.978573i \(-0.433987\pi\)
0.205902 + 0.978573i \(0.433987\pi\)
\(420\) 0.458738 0.0223841
\(421\) −2.84921 −0.138862 −0.0694309 0.997587i \(-0.522118\pi\)
−0.0694309 + 0.997587i \(0.522118\pi\)
\(422\) −14.1638 −0.689484
\(423\) −13.0955 −0.636727
\(424\) 10.2948 0.499957
\(425\) 4.01237 0.194629
\(426\) 6.50967 0.315394
\(427\) 14.1106 0.682858
\(428\) −1.60512 −0.0775865
\(429\) 0 0
\(430\) 36.6813 1.76893
\(431\) −35.8018 −1.72451 −0.862257 0.506472i \(-0.830950\pi\)
−0.862257 + 0.506472i \(0.830950\pi\)
\(432\) 3.70462 0.178238
\(433\) 8.92560 0.428937 0.214468 0.976731i \(-0.431198\pi\)
0.214468 + 0.976731i \(0.431198\pi\)
\(434\) −12.0668 −0.579226
\(435\) −2.04341 −0.0979738
\(436\) 0.683218 0.0327202
\(437\) 16.3823 0.783670
\(438\) −10.7268 −0.512548
\(439\) −4.92169 −0.234899 −0.117450 0.993079i \(-0.537472\pi\)
−0.117450 + 0.993079i \(0.537472\pi\)
\(440\) −10.7901 −0.514398
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −4.96252 −0.235776 −0.117888 0.993027i \(-0.537612\pi\)
−0.117888 + 0.993027i \(0.537612\pi\)
\(444\) −0.524360 −0.0248850
\(445\) −53.7506 −2.54802
\(446\) 17.4185 0.824788
\(447\) −7.17188 −0.339218
\(448\) −8.47362 −0.400341
\(449\) 17.9792 0.848492 0.424246 0.905547i \(-0.360539\pi\)
0.424246 + 0.905547i \(0.360539\pi\)
\(450\) −8.22287 −0.387630
\(451\) 1.02024 0.0480413
\(452\) −2.24001 −0.105361
\(453\) 7.19280 0.337947
\(454\) −18.1888 −0.853644
\(455\) 0 0
\(456\) −9.42151 −0.441203
\(457\) 27.8074 1.30078 0.650389 0.759602i \(-0.274606\pi\)
0.650389 + 0.759602i \(0.274606\pi\)
\(458\) 13.1524 0.614572
\(459\) −0.665810 −0.0310773
\(460\) 2.32717 0.108505
\(461\) −16.5862 −0.772496 −0.386248 0.922395i \(-0.626229\pi\)
−0.386248 + 0.922395i \(0.626229\pi\)
\(462\) −1.51975 −0.0707053
\(463\) 42.4947 1.97490 0.987449 0.157940i \(-0.0504853\pi\)
0.987449 + 0.157940i \(0.0504853\pi\)
\(464\) 2.27973 0.105834
\(465\) −29.3654 −1.36179
\(466\) 30.0943 1.39409
\(467\) −1.30217 −0.0602575 −0.0301287 0.999546i \(-0.509592\pi\)
−0.0301287 + 0.999546i \(0.509592\pi\)
\(468\) 0 0
\(469\) 3.47625 0.160518
\(470\) −59.3349 −2.73692
\(471\) −7.18613 −0.331119
\(472\) 16.0157 0.737180
\(473\) 9.01691 0.414598
\(474\) −16.1447 −0.741551
\(475\) 19.4608 0.892924
\(476\) 0.0919813 0.00421595
\(477\) 3.52862 0.161565
\(478\) −32.3348 −1.47896
\(479\) 8.28495 0.378549 0.189274 0.981924i \(-0.439386\pi\)
0.189274 + 0.981924i \(0.439386\pi\)
\(480\) −2.59026 −0.118229
\(481\) 0 0
\(482\) −23.9587 −1.09129
\(483\) 5.07298 0.230829
\(484\) 1.34827 0.0612849
\(485\) 4.71929 0.214292
\(486\) 1.36450 0.0618948
\(487\) 43.5629 1.97402 0.987011 0.160651i \(-0.0513595\pi\)
0.987011 + 0.160651i \(0.0513595\pi\)
\(488\) −41.1675 −1.86357
\(489\) 22.1597 1.00209
\(490\) 4.53093 0.204687
\(491\) 41.8051 1.88664 0.943318 0.331890i \(-0.107686\pi\)
0.943318 + 0.331890i \(0.107686\pi\)
\(492\) 0.126547 0.00570518
\(493\) −0.409722 −0.0184530
\(494\) 0 0
\(495\) −3.69841 −0.166231
\(496\) 32.7615 1.47103
\(497\) −4.77075 −0.213997
\(498\) −22.4359 −1.00538
\(499\) 6.28962 0.281562 0.140781 0.990041i \(-0.455039\pi\)
0.140781 + 0.990041i \(0.455039\pi\)
\(500\) 0.470805 0.0210550
\(501\) −14.9897 −0.669691
\(502\) −41.2167 −1.83959
\(503\) 18.5950 0.829109 0.414554 0.910025i \(-0.363937\pi\)
0.414554 + 0.910025i \(0.363937\pi\)
\(504\) −2.91750 −0.129956
\(505\) 2.39332 0.106501
\(506\) −7.70968 −0.342737
\(507\) 0 0
\(508\) 1.58622 0.0703773
\(509\) 2.87537 0.127448 0.0637242 0.997968i \(-0.479702\pi\)
0.0637242 + 0.997968i \(0.479702\pi\)
\(510\) −3.01674 −0.133583
\(511\) 7.86139 0.347767
\(512\) 24.5062 1.08303
\(513\) −3.22931 −0.142578
\(514\) 6.79742 0.299821
\(515\) −49.6868 −2.18946
\(516\) 1.11843 0.0492359
\(517\) −14.5856 −0.641473
\(518\) −5.17908 −0.227556
\(519\) −0.425335 −0.0186701
\(520\) 0 0
\(521\) 18.3937 0.805843 0.402922 0.915234i \(-0.367995\pi\)
0.402922 + 0.915234i \(0.367995\pi\)
\(522\) 0.839676 0.0367516
\(523\) 2.24583 0.0982031 0.0491016 0.998794i \(-0.484364\pi\)
0.0491016 + 0.998794i \(0.484364\pi\)
\(524\) 2.53134 0.110582
\(525\) 6.02631 0.263010
\(526\) 17.1400 0.747341
\(527\) −5.88804 −0.256487
\(528\) 4.12614 0.179567
\(529\) 2.73517 0.118920
\(530\) 15.9879 0.694472
\(531\) 5.48952 0.238225
\(532\) 0.446128 0.0193421
\(533\) 0 0
\(534\) 22.0872 0.955806
\(535\) −38.5810 −1.66800
\(536\) −10.1419 −0.438065
\(537\) −13.7825 −0.594758
\(538\) 1.98959 0.0857774
\(539\) 1.11378 0.0479740
\(540\) −0.458738 −0.0197409
\(541\) 22.4028 0.963170 0.481585 0.876399i \(-0.340061\pi\)
0.481585 + 0.876399i \(0.340061\pi\)
\(542\) 21.2454 0.912570
\(543\) −21.8738 −0.938694
\(544\) −0.519371 −0.0222679
\(545\) 16.4220 0.703440
\(546\) 0 0
\(547\) −22.5948 −0.966084 −0.483042 0.875597i \(-0.660468\pi\)
−0.483042 + 0.875597i \(0.660468\pi\)
\(548\) 1.87647 0.0801589
\(549\) −14.1106 −0.602224
\(550\) −9.15849 −0.390519
\(551\) −1.98724 −0.0846591
\(552\) −14.8004 −0.629948
\(553\) 11.8320 0.503147
\(554\) 24.5847 1.04450
\(555\) −12.6036 −0.534994
\(556\) 0.0313284 0.00132862
\(557\) 18.0550 0.765014 0.382507 0.923953i \(-0.375061\pi\)
0.382507 + 0.923953i \(0.375061\pi\)
\(558\) 12.0668 0.510829
\(559\) 0 0
\(560\) −12.3015 −0.519833
\(561\) −0.741567 −0.0313090
\(562\) −35.3161 −1.48972
\(563\) 11.9664 0.504322 0.252161 0.967685i \(-0.418859\pi\)
0.252161 + 0.967685i \(0.418859\pi\)
\(564\) −1.80914 −0.0761786
\(565\) −53.8413 −2.26512
\(566\) −13.6291 −0.572875
\(567\) −1.00000 −0.0419961
\(568\) 13.9186 0.584013
\(569\) 35.7491 1.49868 0.749339 0.662186i \(-0.230371\pi\)
0.749339 + 0.662186i \(0.230371\pi\)
\(570\) −14.6318 −0.612858
\(571\) 18.4132 0.770570 0.385285 0.922798i \(-0.374103\pi\)
0.385285 + 0.922798i \(0.374103\pi\)
\(572\) 0 0
\(573\) −10.8936 −0.455085
\(574\) 1.24990 0.0521698
\(575\) 30.5714 1.27491
\(576\) 8.47362 0.353068
\(577\) −27.4531 −1.14289 −0.571444 0.820641i \(-0.693617\pi\)
−0.571444 + 0.820641i \(0.693617\pi\)
\(578\) 22.5916 0.939685
\(579\) −17.0935 −0.710381
\(580\) −0.282295 −0.0117217
\(581\) 16.4426 0.682155
\(582\) −1.93925 −0.0803846
\(583\) 3.93012 0.162769
\(584\) −22.9356 −0.949081
\(585\) 0 0
\(586\) 4.91738 0.203135
\(587\) −23.5141 −0.970531 −0.485265 0.874367i \(-0.661277\pi\)
−0.485265 + 0.874367i \(0.661277\pi\)
\(588\) 0.138150 0.00569719
\(589\) −28.5582 −1.17672
\(590\) 24.8726 1.02399
\(591\) −4.58665 −0.188670
\(592\) 14.0612 0.577913
\(593\) 31.0493 1.27504 0.637520 0.770433i \(-0.279960\pi\)
0.637520 + 0.770433i \(0.279960\pi\)
\(594\) 1.51975 0.0623562
\(595\) 2.21088 0.0906372
\(596\) −0.990792 −0.0405844
\(597\) −6.08803 −0.249167
\(598\) 0 0
\(599\) −23.3733 −0.955007 −0.477503 0.878630i \(-0.658458\pi\)
−0.477503 + 0.878630i \(0.658458\pi\)
\(600\) −17.5817 −0.717771
\(601\) −25.5738 −1.04318 −0.521588 0.853197i \(-0.674660\pi\)
−0.521588 + 0.853197i \(0.674660\pi\)
\(602\) 11.0466 0.450227
\(603\) −3.47625 −0.141564
\(604\) 0.993682 0.0404323
\(605\) 32.4072 1.31754
\(606\) −0.983462 −0.0399504
\(607\) −31.2846 −1.26980 −0.634902 0.772593i \(-0.718959\pi\)
−0.634902 + 0.772593i \(0.718959\pi\)
\(608\) −2.51906 −0.102161
\(609\) −0.615375 −0.0249362
\(610\) −63.9339 −2.58861
\(611\) 0 0
\(612\) −0.0919813 −0.00371812
\(613\) −8.72726 −0.352491 −0.176245 0.984346i \(-0.556395\pi\)
−0.176245 + 0.984346i \(0.556395\pi\)
\(614\) −23.8003 −0.960502
\(615\) 3.04171 0.122654
\(616\) −3.24946 −0.130924
\(617\) −19.2871 −0.776470 −0.388235 0.921560i \(-0.626915\pi\)
−0.388235 + 0.921560i \(0.626915\pi\)
\(618\) 20.4173 0.821304
\(619\) 42.3279 1.70130 0.850650 0.525732i \(-0.176209\pi\)
0.850650 + 0.525732i \(0.176209\pi\)
\(620\) −4.05681 −0.162926
\(621\) −5.07298 −0.203572
\(622\) 30.4317 1.22020
\(623\) −16.1871 −0.648521
\(624\) 0 0
\(625\) −18.8152 −0.752607
\(626\) −1.08204 −0.0432470
\(627\) −3.59675 −0.143640
\(628\) −0.992760 −0.0396154
\(629\) −2.52714 −0.100764
\(630\) −4.53093 −0.180517
\(631\) 15.0098 0.597531 0.298766 0.954326i \(-0.403425\pi\)
0.298766 + 0.954326i \(0.403425\pi\)
\(632\) −34.5198 −1.37312
\(633\) −10.3803 −0.412578
\(634\) −11.5757 −0.459730
\(635\) 38.1268 1.51302
\(636\) 0.487478 0.0193297
\(637\) 0 0
\(638\) 0.935217 0.0370256
\(639\) 4.77075 0.188728
\(640\) 33.2129 1.31285
\(641\) 24.5344 0.969050 0.484525 0.874777i \(-0.338992\pi\)
0.484525 + 0.874777i \(0.338992\pi\)
\(642\) 15.8537 0.625697
\(643\) −29.4303 −1.16062 −0.580309 0.814396i \(-0.697068\pi\)
−0.580309 + 0.814396i \(0.697068\pi\)
\(644\) 0.700830 0.0276166
\(645\) 26.8827 1.05850
\(646\) −2.93381 −0.115429
\(647\) −8.01884 −0.315253 −0.157627 0.987499i \(-0.550384\pi\)
−0.157627 + 0.987499i \(0.550384\pi\)
\(648\) 2.91750 0.114610
\(649\) 6.11413 0.240000
\(650\) 0 0
\(651\) −8.84343 −0.346601
\(652\) 3.06135 0.119892
\(653\) 5.06783 0.198320 0.0991598 0.995072i \(-0.468385\pi\)
0.0991598 + 0.995072i \(0.468385\pi\)
\(654\) −6.74811 −0.263872
\(655\) 60.8437 2.37736
\(656\) −3.39348 −0.132493
\(657\) −7.86139 −0.306702
\(658\) −17.8688 −0.696599
\(659\) −16.9404 −0.659904 −0.329952 0.943998i \(-0.607033\pi\)
−0.329952 + 0.943998i \(0.607033\pi\)
\(660\) −0.510934 −0.0198881
\(661\) 36.7741 1.43035 0.715174 0.698947i \(-0.246348\pi\)
0.715174 + 0.698947i \(0.246348\pi\)
\(662\) −45.7338 −1.77749
\(663\) 0 0
\(664\) −47.9713 −1.86165
\(665\) 10.7232 0.415829
\(666\) 5.17908 0.200685
\(667\) −3.12179 −0.120876
\(668\) −2.07082 −0.0801225
\(669\) 12.7655 0.493542
\(670\) −15.7506 −0.608500
\(671\) −15.7161 −0.606713
\(672\) −0.780060 −0.0300915
\(673\) −45.5657 −1.75643 −0.878214 0.478268i \(-0.841265\pi\)
−0.878214 + 0.478268i \(0.841265\pi\)
\(674\) 26.5023 1.02083
\(675\) −6.02631 −0.231953
\(676\) 0 0
\(677\) 11.9937 0.460956 0.230478 0.973077i \(-0.425971\pi\)
0.230478 + 0.973077i \(0.425971\pi\)
\(678\) 22.1245 0.849686
\(679\) 1.42122 0.0545415
\(680\) −6.45023 −0.247355
\(681\) −13.3301 −0.510809
\(682\) 13.4398 0.514637
\(683\) −23.9577 −0.916716 −0.458358 0.888768i \(-0.651562\pi\)
−0.458358 + 0.888768i \(0.651562\pi\)
\(684\) −0.446128 −0.0170581
\(685\) 45.1032 1.72331
\(686\) 1.36450 0.0520967
\(687\) 9.63903 0.367752
\(688\) −29.9917 −1.14342
\(689\) 0 0
\(690\) −22.9853 −0.875037
\(691\) 23.9462 0.910958 0.455479 0.890247i \(-0.349468\pi\)
0.455479 + 0.890247i \(0.349468\pi\)
\(692\) −0.0587598 −0.00223371
\(693\) −1.11378 −0.0423091
\(694\) 15.2480 0.578806
\(695\) 0.753015 0.0285635
\(696\) 1.79535 0.0680527
\(697\) 0.609892 0.0231013
\(698\) 50.2284 1.90117
\(699\) 22.0553 0.834207
\(700\) 0.832531 0.0314667
\(701\) −20.6807 −0.781099 −0.390550 0.920582i \(-0.627715\pi\)
−0.390550 + 0.920582i \(0.627715\pi\)
\(702\) 0 0
\(703\) −12.2572 −0.462288
\(704\) 9.43777 0.355699
\(705\) −43.4849 −1.63773
\(706\) 23.8943 0.899275
\(707\) 0.720751 0.0271066
\(708\) 0.758374 0.0285014
\(709\) 16.0902 0.604281 0.302141 0.953263i \(-0.402299\pi\)
0.302141 + 0.953263i \(0.402299\pi\)
\(710\) 21.6159 0.811231
\(711\) −11.8320 −0.443734
\(712\) 47.2257 1.76986
\(713\) −44.8626 −1.68012
\(714\) −0.908495 −0.0339996
\(715\) 0 0
\(716\) −1.90404 −0.0711575
\(717\) −23.6972 −0.884990
\(718\) 11.1306 0.415391
\(719\) −8.10172 −0.302143 −0.151072 0.988523i \(-0.548272\pi\)
−0.151072 + 0.988523i \(0.548272\pi\)
\(720\) 12.3015 0.458450
\(721\) −14.9632 −0.557260
\(722\) 11.6958 0.435274
\(723\) −17.5586 −0.653012
\(724\) −3.02185 −0.112306
\(725\) −3.70843 −0.137728
\(726\) −13.3168 −0.494232
\(727\) −8.37621 −0.310657 −0.155328 0.987863i \(-0.549644\pi\)
−0.155328 + 0.987863i \(0.549644\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −35.6194 −1.31833
\(731\) 5.39023 0.199365
\(732\) −1.94937 −0.0720506
\(733\) −13.7644 −0.508399 −0.254199 0.967152i \(-0.581812\pi\)
−0.254199 + 0.967152i \(0.581812\pi\)
\(734\) −21.6322 −0.798460
\(735\) 3.32059 0.122482
\(736\) −3.95723 −0.145865
\(737\) −3.87178 −0.142619
\(738\) −1.24990 −0.0460094
\(739\) 39.2848 1.44511 0.722557 0.691311i \(-0.242967\pi\)
0.722557 + 0.691311i \(0.242967\pi\)
\(740\) −1.74118 −0.0640072
\(741\) 0 0
\(742\) 4.81479 0.176757
\(743\) −3.96163 −0.145338 −0.0726690 0.997356i \(-0.523152\pi\)
−0.0726690 + 0.997356i \(0.523152\pi\)
\(744\) 25.8007 0.945899
\(745\) −23.8149 −0.872509
\(746\) −15.4291 −0.564899
\(747\) −16.4426 −0.601604
\(748\) −0.102447 −0.00374584
\(749\) −11.6187 −0.424539
\(750\) −4.65012 −0.169798
\(751\) −12.3197 −0.449553 −0.224776 0.974410i \(-0.572165\pi\)
−0.224776 + 0.974410i \(0.572165\pi\)
\(752\) 48.5139 1.76912
\(753\) −30.2065 −1.10079
\(754\) 0 0
\(755\) 23.8843 0.869239
\(756\) −0.138150 −0.00502445
\(757\) 27.1281 0.985988 0.492994 0.870033i \(-0.335902\pi\)
0.492994 + 0.870033i \(0.335902\pi\)
\(758\) 20.2752 0.736430
\(759\) −5.65020 −0.205089
\(760\) −31.2850 −1.13482
\(761\) −8.01574 −0.290570 −0.145285 0.989390i \(-0.546410\pi\)
−0.145285 + 0.989390i \(0.546410\pi\)
\(762\) −15.6671 −0.567558
\(763\) 4.94550 0.179039
\(764\) −1.50494 −0.0544468
\(765\) −2.21088 −0.0799345
\(766\) 26.6797 0.963978
\(767\) 0 0
\(768\) 3.29940 0.119057
\(769\) 31.3627 1.13097 0.565484 0.824759i \(-0.308689\pi\)
0.565484 + 0.824759i \(0.308689\pi\)
\(770\) −5.04647 −0.181862
\(771\) 4.98163 0.179409
\(772\) −2.36146 −0.0849907
\(773\) −4.00669 −0.144111 −0.0720553 0.997401i \(-0.522956\pi\)
−0.0720553 + 0.997401i \(0.522956\pi\)
\(774\) −11.0466 −0.397063
\(775\) −53.2932 −1.91435
\(776\) −4.14641 −0.148847
\(777\) −3.79560 −0.136166
\(778\) −21.1479 −0.758189
\(779\) 2.95810 0.105985
\(780\) 0 0
\(781\) 5.31357 0.190135
\(782\) −4.60878 −0.164810
\(783\) 0.615375 0.0219917
\(784\) −3.70462 −0.132308
\(785\) −23.8622 −0.851677
\(786\) −25.0019 −0.891788
\(787\) 10.2148 0.364117 0.182058 0.983288i \(-0.441724\pi\)
0.182058 + 0.983288i \(0.441724\pi\)
\(788\) −0.633644 −0.0225726
\(789\) 12.5614 0.447199
\(790\) −53.6099 −1.90736
\(791\) −16.2144 −0.576518
\(792\) 3.24946 0.115464
\(793\) 0 0
\(794\) −31.6735 −1.12405
\(795\) 11.7171 0.415563
\(796\) −0.841059 −0.0298105
\(797\) −15.5770 −0.551767 −0.275884 0.961191i \(-0.588970\pi\)
−0.275884 + 0.961191i \(0.588970\pi\)
\(798\) −4.40639 −0.155984
\(799\) −8.71913 −0.308461
\(800\) −4.70088 −0.166201
\(801\) 16.1871 0.571942
\(802\) −53.5617 −1.89133
\(803\) −8.75587 −0.308988
\(804\) −0.480242 −0.0169368
\(805\) 16.8453 0.593718
\(806\) 0 0
\(807\) 1.45811 0.0513281
\(808\) −2.10279 −0.0739758
\(809\) −30.9360 −1.08765 −0.543826 0.839198i \(-0.683025\pi\)
−0.543826 + 0.839198i \(0.683025\pi\)
\(810\) 4.53093 0.159201
\(811\) 14.2471 0.500284 0.250142 0.968209i \(-0.419523\pi\)
0.250142 + 0.968209i \(0.419523\pi\)
\(812\) −0.0850137 −0.00298340
\(813\) 15.5702 0.546070
\(814\) 5.76837 0.202181
\(815\) 73.5831 2.57750
\(816\) 2.46657 0.0863472
\(817\) 26.1437 0.914654
\(818\) −26.7327 −0.934686
\(819\) 0 0
\(820\) 0.420211 0.0146744
\(821\) −8.23270 −0.287323 −0.143662 0.989627i \(-0.545888\pi\)
−0.143662 + 0.989627i \(0.545888\pi\)
\(822\) −18.5338 −0.646441
\(823\) −7.03818 −0.245336 −0.122668 0.992448i \(-0.539145\pi\)
−0.122668 + 0.992448i \(0.539145\pi\)
\(824\) 43.6552 1.52080
\(825\) −6.71199 −0.233682
\(826\) 7.49043 0.260625
\(827\) 43.3827 1.50856 0.754282 0.656550i \(-0.227985\pi\)
0.754282 + 0.656550i \(0.227985\pi\)
\(828\) −0.700830 −0.0243555
\(829\) 32.7843 1.13865 0.569323 0.822114i \(-0.307206\pi\)
0.569323 + 0.822114i \(0.307206\pi\)
\(830\) −74.5004 −2.58594
\(831\) 18.0174 0.625016
\(832\) 0 0
\(833\) 0.665810 0.0230689
\(834\) −0.309429 −0.0107147
\(835\) −49.7747 −1.72252
\(836\) −0.496889 −0.0171853
\(837\) 8.84343 0.305674
\(838\) −11.5019 −0.397326
\(839\) 26.5096 0.915212 0.457606 0.889155i \(-0.348707\pi\)
0.457606 + 0.889155i \(0.348707\pi\)
\(840\) −9.68781 −0.334261
\(841\) −28.6213 −0.986942
\(842\) 3.88773 0.133980
\(843\) −25.8821 −0.891427
\(844\) −1.43403 −0.0493613
\(845\) 0 0
\(846\) 17.8688 0.614342
\(847\) 9.75949 0.335340
\(848\) −13.0722 −0.448901
\(849\) −9.98839 −0.342801
\(850\) −5.47487 −0.187786
\(851\) −19.2550 −0.660053
\(852\) 0.659077 0.0225796
\(853\) −23.0901 −0.790589 −0.395295 0.918554i \(-0.629357\pi\)
−0.395295 + 0.918554i \(0.629357\pi\)
\(854\) −19.2538 −0.658851
\(855\) −10.7232 −0.366726
\(856\) 33.8976 1.15860
\(857\) 0.861504 0.0294284 0.0147142 0.999892i \(-0.495316\pi\)
0.0147142 + 0.999892i \(0.495316\pi\)
\(858\) 0 0
\(859\) −18.6223 −0.635386 −0.317693 0.948194i \(-0.602908\pi\)
−0.317693 + 0.948194i \(0.602908\pi\)
\(860\) 3.71383 0.126641
\(861\) 0.916015 0.0312177
\(862\) 48.8515 1.66389
\(863\) −22.5310 −0.766965 −0.383482 0.923548i \(-0.625275\pi\)
−0.383482 + 0.923548i \(0.625275\pi\)
\(864\) 0.780060 0.0265382
\(865\) −1.41236 −0.0480218
\(866\) −12.1789 −0.413858
\(867\) 16.5567 0.562295
\(868\) −1.22172 −0.0414677
\(869\) −13.1783 −0.447042
\(870\) 2.78822 0.0945295
\(871\) 0 0
\(872\) −14.4285 −0.488610
\(873\) −1.42122 −0.0481011
\(874\) −22.3535 −0.756119
\(875\) 3.40794 0.115209
\(876\) −1.08605 −0.0366941
\(877\) −46.8180 −1.58093 −0.790466 0.612506i \(-0.790161\pi\)
−0.790466 + 0.612506i \(0.790161\pi\)
\(878\) 6.71563 0.226641
\(879\) 3.60381 0.121553
\(880\) 13.7012 0.461867
\(881\) −12.3276 −0.415326 −0.207663 0.978200i \(-0.566586\pi\)
−0.207663 + 0.978200i \(0.566586\pi\)
\(882\) −1.36450 −0.0459450
\(883\) −20.2249 −0.680622 −0.340311 0.940313i \(-0.610532\pi\)
−0.340311 + 0.940313i \(0.610532\pi\)
\(884\) 0 0
\(885\) 18.2284 0.612742
\(886\) 6.77134 0.227488
\(887\) −41.4430 −1.39152 −0.695760 0.718274i \(-0.744932\pi\)
−0.695760 + 0.718274i \(0.744932\pi\)
\(888\) 11.0736 0.371607
\(889\) 11.4819 0.385092
\(890\) 73.3425 2.45844
\(891\) 1.11378 0.0373131
\(892\) 1.76355 0.0590479
\(893\) −42.2896 −1.41517
\(894\) 9.78600 0.327293
\(895\) −45.7660 −1.52979
\(896\) 10.0021 0.334147
\(897\) 0 0
\(898\) −24.5326 −0.818663
\(899\) 5.44202 0.181502
\(900\) −0.832531 −0.0277510
\(901\) 2.34939 0.0782696
\(902\) −1.39212 −0.0463524
\(903\) 8.09576 0.269410
\(904\) 47.3055 1.57336
\(905\) −72.6338 −2.41443
\(906\) −9.81455 −0.326067
\(907\) 18.4094 0.611275 0.305638 0.952148i \(-0.401130\pi\)
0.305638 + 0.952148i \(0.401130\pi\)
\(908\) −1.84154 −0.0611137
\(909\) −0.720751 −0.0239058
\(910\) 0 0
\(911\) 36.7759 1.21844 0.609220 0.793001i \(-0.291483\pi\)
0.609220 + 0.793001i \(0.291483\pi\)
\(912\) 11.9634 0.396147
\(913\) −18.3135 −0.606088
\(914\) −37.9432 −1.25505
\(915\) −46.8553 −1.54899
\(916\) 1.33163 0.0439982
\(917\) 18.3232 0.605084
\(918\) 0.908495 0.0299848
\(919\) 55.6734 1.83649 0.918247 0.396008i \(-0.129605\pi\)
0.918247 + 0.396008i \(0.129605\pi\)
\(920\) −49.1461 −1.62030
\(921\) −17.4426 −0.574752
\(922\) 22.6318 0.745339
\(923\) 0 0
\(924\) −0.153868 −0.00506190
\(925\) −22.8734 −0.752074
\(926\) −57.9839 −1.90547
\(927\) 14.9632 0.491457
\(928\) 0.480029 0.0157577
\(929\) −34.2055 −1.12224 −0.561122 0.827733i \(-0.689630\pi\)
−0.561122 + 0.827733i \(0.689630\pi\)
\(930\) 40.0690 1.31391
\(931\) 3.22931 0.105836
\(932\) 3.04692 0.0998053
\(933\) 22.3025 0.730152
\(934\) 1.77681 0.0581391
\(935\) −2.46244 −0.0805303
\(936\) 0 0
\(937\) −50.2091 −1.64026 −0.820130 0.572177i \(-0.806099\pi\)
−0.820130 + 0.572177i \(0.806099\pi\)
\(938\) −4.74332 −0.154875
\(939\) −0.792995 −0.0258784
\(940\) −6.00741 −0.195940
\(941\) 3.12662 0.101925 0.0509625 0.998701i \(-0.483771\pi\)
0.0509625 + 0.998701i \(0.483771\pi\)
\(942\) 9.80545 0.319479
\(943\) 4.64693 0.151325
\(944\) −20.3366 −0.661898
\(945\) −3.32059 −0.108019
\(946\) −12.3035 −0.400023
\(947\) −2.54412 −0.0826729 −0.0413364 0.999145i \(-0.513162\pi\)
−0.0413364 + 0.999145i \(0.513162\pi\)
\(948\) −1.63458 −0.0530888
\(949\) 0 0
\(950\) −26.5542 −0.861533
\(951\) −8.48350 −0.275096
\(952\) −1.94250 −0.0629567
\(953\) 42.2175 1.36756 0.683780 0.729688i \(-0.260335\pi\)
0.683780 + 0.729688i \(0.260335\pi\)
\(954\) −4.81479 −0.155885
\(955\) −36.1730 −1.17053
\(956\) −3.27376 −0.105881
\(957\) 0.685393 0.0221556
\(958\) −11.3048 −0.365241
\(959\) 13.5829 0.438615
\(960\) 28.1374 0.908131
\(961\) 47.2062 1.52278
\(962\) 0 0
\(963\) 11.6187 0.374409
\(964\) −2.42572 −0.0781270
\(965\) −56.7604 −1.82718
\(966\) −6.92207 −0.222714
\(967\) 38.3214 1.23233 0.616166 0.787616i \(-0.288685\pi\)
0.616166 + 0.787616i \(0.288685\pi\)
\(968\) −28.4733 −0.915166
\(969\) −2.15011 −0.0690714
\(970\) −6.43946 −0.206759
\(971\) 8.66075 0.277937 0.138968 0.990297i \(-0.455621\pi\)
0.138968 + 0.990297i \(0.455621\pi\)
\(972\) 0.138150 0.00443115
\(973\) 0.226772 0.00726997
\(974\) −59.4414 −1.90463
\(975\) 0 0
\(976\) 52.2742 1.67326
\(977\) −11.2083 −0.358585 −0.179292 0.983796i \(-0.557381\pi\)
−0.179292 + 0.983796i \(0.557381\pi\)
\(978\) −30.2368 −0.966865
\(979\) 18.0289 0.576205
\(980\) 0.458738 0.0146538
\(981\) −4.94550 −0.157898
\(982\) −57.0429 −1.82031
\(983\) 24.8347 0.792102 0.396051 0.918228i \(-0.370380\pi\)
0.396051 + 0.918228i \(0.370380\pi\)
\(984\) −2.67247 −0.0851953
\(985\) −15.2304 −0.485280
\(986\) 0.559065 0.0178042
\(987\) −13.0955 −0.416835
\(988\) 0 0
\(989\) 41.0697 1.30594
\(990\) 5.04647 0.160387
\(991\) 22.6526 0.719585 0.359793 0.933032i \(-0.382847\pi\)
0.359793 + 0.933032i \(0.382847\pi\)
\(992\) 6.89840 0.219025
\(993\) −33.5170 −1.06363
\(994\) 6.50967 0.206474
\(995\) −20.2159 −0.640886
\(996\) −2.27154 −0.0719765
\(997\) 39.1382 1.23952 0.619760 0.784791i \(-0.287230\pi\)
0.619760 + 0.784791i \(0.287230\pi\)
\(998\) −8.58217 −0.271664
\(999\) 3.79560 0.120087
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 3549.2.a.bf.1.3 yes 9
13.12 even 2 3549.2.a.be.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.7 9 13.12 even 2
3549.2.a.bf.1.3 yes 9 1.1 even 1 trivial