Properties

Label 4029.2.a.l.1.13
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +3.78923 q^{10} -3.26684 q^{11} +1.26424 q^{12} +2.70187 q^{13} -0.00850689 q^{14} +4.41756 q^{15} +0.126774 q^{16} -1.00000 q^{17} -0.857766 q^{18} -4.27554 q^{19} +5.58484 q^{20} -0.00991750 q^{21} +2.80218 q^{22} -8.57091 q^{23} -2.79995 q^{24} +14.5148 q^{25} -2.31757 q^{26} -1.00000 q^{27} -0.0125381 q^{28} +2.58015 q^{29} -3.78923 q^{30} -3.29810 q^{31} -5.70865 q^{32} +3.26684 q^{33} +0.857766 q^{34} -0.0438111 q^{35} -1.26424 q^{36} -5.23127 q^{37} +3.66741 q^{38} -2.70187 q^{39} -12.3689 q^{40} -10.5143 q^{41} +0.00850689 q^{42} +1.43416 q^{43} +4.13006 q^{44} -4.41756 q^{45} +7.35183 q^{46} -1.69597 q^{47} -0.126774 q^{48} -6.99990 q^{49} -12.4503 q^{50} +1.00000 q^{51} -3.41581 q^{52} -4.25127 q^{53} +0.857766 q^{54} +14.4314 q^{55} +0.0277685 q^{56} +4.27554 q^{57} -2.21316 q^{58} +0.575912 q^{59} -5.58484 q^{60} -3.22241 q^{61} +2.82900 q^{62} +0.00991750 q^{63} +4.64313 q^{64} -11.9357 q^{65} -2.80218 q^{66} -7.36295 q^{67} +1.26424 q^{68} +8.57091 q^{69} +0.0375797 q^{70} -15.6371 q^{71} +2.79995 q^{72} -6.91670 q^{73} +4.48720 q^{74} -14.5148 q^{75} +5.40530 q^{76} -0.0323988 q^{77} +2.31757 q^{78} +1.00000 q^{79} -0.560033 q^{80} +1.00000 q^{81} +9.01881 q^{82} +0.651310 q^{83} +0.0125381 q^{84} +4.41756 q^{85} -1.23017 q^{86} -2.58015 q^{87} -9.14698 q^{88} -7.54867 q^{89} +3.78923 q^{90} +0.0267958 q^{91} +10.8357 q^{92} +3.29810 q^{93} +1.45475 q^{94} +18.8875 q^{95} +5.70865 q^{96} -11.4421 q^{97} +6.00428 q^{98} -3.26684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.857766 −0.606532 −0.303266 0.952906i \(-0.598077\pi\)
−0.303266 + 0.952906i \(0.598077\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.26424 −0.632119
\(5\) −4.41756 −1.97559 −0.987796 0.155754i \(-0.950219\pi\)
−0.987796 + 0.155754i \(0.950219\pi\)
\(6\) 0.857766 0.350181
\(7\) 0.00991750 0.00374846 0.00187423 0.999998i \(-0.499403\pi\)
0.00187423 + 0.999998i \(0.499403\pi\)
\(8\) 2.79995 0.989932
\(9\) 1.00000 0.333333
\(10\) 3.78923 1.19826
\(11\) −3.26684 −0.984988 −0.492494 0.870316i \(-0.663915\pi\)
−0.492494 + 0.870316i \(0.663915\pi\)
\(12\) 1.26424 0.364954
\(13\) 2.70187 0.749365 0.374682 0.927153i \(-0.377752\pi\)
0.374682 + 0.927153i \(0.377752\pi\)
\(14\) −0.00850689 −0.00227356
\(15\) 4.41756 1.14061
\(16\) 0.126774 0.0316936
\(17\) −1.00000 −0.242536
\(18\) −0.857766 −0.202177
\(19\) −4.27554 −0.980877 −0.490438 0.871476i \(-0.663163\pi\)
−0.490438 + 0.871476i \(0.663163\pi\)
\(20\) 5.58484 1.24881
\(21\) −0.00991750 −0.00216418
\(22\) 2.80218 0.597427
\(23\) −8.57091 −1.78716 −0.893579 0.448907i \(-0.851814\pi\)
−0.893579 + 0.448907i \(0.851814\pi\)
\(24\) −2.79995 −0.571538
\(25\) 14.5148 2.90296
\(26\) −2.31757 −0.454514
\(27\) −1.00000 −0.192450
\(28\) −0.0125381 −0.00236947
\(29\) 2.58015 0.479121 0.239561 0.970881i \(-0.422997\pi\)
0.239561 + 0.970881i \(0.422997\pi\)
\(30\) −3.78923 −0.691815
\(31\) −3.29810 −0.592356 −0.296178 0.955133i \(-0.595712\pi\)
−0.296178 + 0.955133i \(0.595712\pi\)
\(32\) −5.70865 −1.00916
\(33\) 3.26684 0.568683
\(34\) 0.857766 0.147106
\(35\) −0.0438111 −0.00740543
\(36\) −1.26424 −0.210706
\(37\) −5.23127 −0.860015 −0.430008 0.902825i \(-0.641489\pi\)
−0.430008 + 0.902825i \(0.641489\pi\)
\(38\) 3.66741 0.594933
\(39\) −2.70187 −0.432646
\(40\) −12.3689 −1.95570
\(41\) −10.5143 −1.64206 −0.821030 0.570886i \(-0.806600\pi\)
−0.821030 + 0.570886i \(0.806600\pi\)
\(42\) 0.00850689 0.00131264
\(43\) 1.43416 0.218707 0.109353 0.994003i \(-0.465122\pi\)
0.109353 + 0.994003i \(0.465122\pi\)
\(44\) 4.13006 0.622630
\(45\) −4.41756 −0.658531
\(46\) 7.35183 1.08397
\(47\) −1.69597 −0.247383 −0.123692 0.992321i \(-0.539473\pi\)
−0.123692 + 0.992321i \(0.539473\pi\)
\(48\) −0.126774 −0.0182983
\(49\) −6.99990 −0.999986
\(50\) −12.4503 −1.76074
\(51\) 1.00000 0.140028
\(52\) −3.41581 −0.473688
\(53\) −4.25127 −0.583957 −0.291978 0.956425i \(-0.594314\pi\)
−0.291978 + 0.956425i \(0.594314\pi\)
\(54\) 0.857766 0.116727
\(55\) 14.4314 1.94593
\(56\) 0.0277685 0.00371072
\(57\) 4.27554 0.566309
\(58\) −2.21316 −0.290602
\(59\) 0.575912 0.0749773 0.0374887 0.999297i \(-0.488064\pi\)
0.0374887 + 0.999297i \(0.488064\pi\)
\(60\) −5.58484 −0.721000
\(61\) −3.22241 −0.412587 −0.206294 0.978490i \(-0.566140\pi\)
−0.206294 + 0.978490i \(0.566140\pi\)
\(62\) 2.82900 0.359283
\(63\) 0.00991750 0.00124949
\(64\) 4.64313 0.580391
\(65\) −11.9357 −1.48044
\(66\) −2.80218 −0.344925
\(67\) −7.36295 −0.899528 −0.449764 0.893147i \(-0.648492\pi\)
−0.449764 + 0.893147i \(0.648492\pi\)
\(68\) 1.26424 0.153311
\(69\) 8.57091 1.03182
\(70\) 0.0375797 0.00449163
\(71\) −15.6371 −1.85578 −0.927889 0.372857i \(-0.878378\pi\)
−0.927889 + 0.372857i \(0.878378\pi\)
\(72\) 2.79995 0.329977
\(73\) −6.91670 −0.809538 −0.404769 0.914419i \(-0.632648\pi\)
−0.404769 + 0.914419i \(0.632648\pi\)
\(74\) 4.48720 0.521627
\(75\) −14.5148 −1.67603
\(76\) 5.40530 0.620031
\(77\) −0.0323988 −0.00369219
\(78\) 2.31757 0.262414
\(79\) 1.00000 0.112509
\(80\) −0.560033 −0.0626136
\(81\) 1.00000 0.111111
\(82\) 9.01881 0.995961
\(83\) 0.651310 0.0714906 0.0357453 0.999361i \(-0.488619\pi\)
0.0357453 + 0.999361i \(0.488619\pi\)
\(84\) 0.0125381 0.00136802
\(85\) 4.41756 0.479151
\(86\) −1.23017 −0.132653
\(87\) −2.58015 −0.276621
\(88\) −9.14698 −0.975072
\(89\) −7.54867 −0.800157 −0.400079 0.916481i \(-0.631017\pi\)
−0.400079 + 0.916481i \(0.631017\pi\)
\(90\) 3.78923 0.399420
\(91\) 0.0267958 0.00280896
\(92\) 10.8357 1.12970
\(93\) 3.29810 0.341997
\(94\) 1.45475 0.150046
\(95\) 18.8875 1.93781
\(96\) 5.70865 0.582636
\(97\) −11.4421 −1.16177 −0.580886 0.813985i \(-0.697294\pi\)
−0.580886 + 0.813985i \(0.697294\pi\)
\(98\) 6.00428 0.606523
\(99\) −3.26684 −0.328329
\(100\) −18.3502 −1.83502
\(101\) −12.3316 −1.22704 −0.613521 0.789679i \(-0.710247\pi\)
−0.613521 + 0.789679i \(0.710247\pi\)
\(102\) −0.857766 −0.0849315
\(103\) 13.9114 1.37073 0.685364 0.728201i \(-0.259643\pi\)
0.685364 + 0.728201i \(0.259643\pi\)
\(104\) 7.56511 0.741820
\(105\) 0.0438111 0.00427553
\(106\) 3.64659 0.354188
\(107\) −0.872179 −0.0843167 −0.0421584 0.999111i \(-0.513423\pi\)
−0.0421584 + 0.999111i \(0.513423\pi\)
\(108\) 1.26424 0.121651
\(109\) −12.5345 −1.20059 −0.600295 0.799779i \(-0.704950\pi\)
−0.600295 + 0.799779i \(0.704950\pi\)
\(110\) −12.3788 −1.18027
\(111\) 5.23127 0.496530
\(112\) 0.00125728 0.000118802 0
\(113\) 6.28218 0.590977 0.295489 0.955346i \(-0.404518\pi\)
0.295489 + 0.955346i \(0.404518\pi\)
\(114\) −3.66741 −0.343485
\(115\) 37.8625 3.53069
\(116\) −3.26192 −0.302862
\(117\) 2.70187 0.249788
\(118\) −0.493997 −0.0454761
\(119\) −0.00991750 −0.000909135 0
\(120\) 12.3689 1.12913
\(121\) −0.327777 −0.0297979
\(122\) 2.76407 0.250247
\(123\) 10.5143 0.948043
\(124\) 4.16958 0.374440
\(125\) −42.0322 −3.75948
\(126\) −0.00850689 −0.000757854 0
\(127\) −12.2427 −1.08637 −0.543184 0.839614i \(-0.682781\pi\)
−0.543184 + 0.839614i \(0.682781\pi\)
\(128\) 7.43457 0.657130
\(129\) −1.43416 −0.126271
\(130\) 10.2380 0.897933
\(131\) 11.7426 1.02596 0.512978 0.858402i \(-0.328542\pi\)
0.512978 + 0.858402i \(0.328542\pi\)
\(132\) −4.13006 −0.359476
\(133\) −0.0424027 −0.00367678
\(134\) 6.31569 0.545592
\(135\) 4.41756 0.380203
\(136\) −2.79995 −0.240094
\(137\) −4.44600 −0.379848 −0.189924 0.981799i \(-0.560824\pi\)
−0.189924 + 0.981799i \(0.560824\pi\)
\(138\) −7.35183 −0.625829
\(139\) 9.97488 0.846058 0.423029 0.906116i \(-0.360967\pi\)
0.423029 + 0.906116i \(0.360967\pi\)
\(140\) 0.0553877 0.00468111
\(141\) 1.69597 0.142827
\(142\) 13.4129 1.12559
\(143\) −8.82658 −0.738115
\(144\) 0.126774 0.0105645
\(145\) −11.3980 −0.946548
\(146\) 5.93290 0.491011
\(147\) 6.99990 0.577342
\(148\) 6.61357 0.543632
\(149\) −11.3655 −0.931098 −0.465549 0.885022i \(-0.654143\pi\)
−0.465549 + 0.885022i \(0.654143\pi\)
\(150\) 12.4503 1.01656
\(151\) −0.599460 −0.0487834 −0.0243917 0.999702i \(-0.507765\pi\)
−0.0243917 + 0.999702i \(0.507765\pi\)
\(152\) −11.9713 −0.971002
\(153\) −1.00000 −0.0808452
\(154\) 0.0277906 0.00223943
\(155\) 14.5696 1.17025
\(156\) 3.41581 0.273484
\(157\) 16.2588 1.29759 0.648796 0.760962i \(-0.275273\pi\)
0.648796 + 0.760962i \(0.275273\pi\)
\(158\) −0.857766 −0.0682402
\(159\) 4.25127 0.337148
\(160\) 25.2183 1.99368
\(161\) −0.0850019 −0.00669909
\(162\) −0.857766 −0.0673924
\(163\) −10.9405 −0.856923 −0.428461 0.903560i \(-0.640944\pi\)
−0.428461 + 0.903560i \(0.640944\pi\)
\(164\) 13.2926 1.03798
\(165\) −14.4314 −1.12349
\(166\) −0.558671 −0.0433613
\(167\) 10.1964 0.789021 0.394511 0.918891i \(-0.370914\pi\)
0.394511 + 0.918891i \(0.370914\pi\)
\(168\) −0.0277685 −0.00214239
\(169\) −5.69988 −0.438453
\(170\) −3.78923 −0.290621
\(171\) −4.27554 −0.326959
\(172\) −1.81312 −0.138249
\(173\) −15.1014 −1.14814 −0.574071 0.818806i \(-0.694637\pi\)
−0.574071 + 0.818806i \(0.694637\pi\)
\(174\) 2.21316 0.167779
\(175\) 0.143951 0.0108816
\(176\) −0.414151 −0.0312178
\(177\) −0.575912 −0.0432882
\(178\) 6.47499 0.485321
\(179\) 12.1907 0.911178 0.455589 0.890190i \(-0.349429\pi\)
0.455589 + 0.890190i \(0.349429\pi\)
\(180\) 5.58484 0.416270
\(181\) −12.8454 −0.954791 −0.477396 0.878688i \(-0.658419\pi\)
−0.477396 + 0.878688i \(0.658419\pi\)
\(182\) −0.0229845 −0.00170373
\(183\) 3.22241 0.238207
\(184\) −23.9981 −1.76916
\(185\) 23.1094 1.69904
\(186\) −2.82900 −0.207432
\(187\) 3.26684 0.238895
\(188\) 2.14412 0.156376
\(189\) −0.00991750 −0.000721392 0
\(190\) −16.2010 −1.17534
\(191\) 6.07241 0.439384 0.219692 0.975569i \(-0.429495\pi\)
0.219692 + 0.975569i \(0.429495\pi\)
\(192\) −4.64313 −0.335089
\(193\) −3.69134 −0.265709 −0.132854 0.991136i \(-0.542414\pi\)
−0.132854 + 0.991136i \(0.542414\pi\)
\(194\) 9.81467 0.704652
\(195\) 11.9357 0.854732
\(196\) 8.84954 0.632110
\(197\) 23.9789 1.70842 0.854211 0.519926i \(-0.174040\pi\)
0.854211 + 0.519926i \(0.174040\pi\)
\(198\) 2.80218 0.199142
\(199\) −5.53090 −0.392075 −0.196038 0.980596i \(-0.562807\pi\)
−0.196038 + 0.980596i \(0.562807\pi\)
\(200\) 40.6408 2.87374
\(201\) 7.36295 0.519343
\(202\) 10.5776 0.744240
\(203\) 0.0255886 0.00179597
\(204\) −1.26424 −0.0885144
\(205\) 46.4476 3.24404
\(206\) −11.9327 −0.831390
\(207\) −8.57091 −0.595719
\(208\) 0.342528 0.0237500
\(209\) 13.9675 0.966152
\(210\) −0.0375797 −0.00259324
\(211\) 21.4352 1.47566 0.737830 0.674986i \(-0.235850\pi\)
0.737830 + 0.674986i \(0.235850\pi\)
\(212\) 5.37462 0.369130
\(213\) 15.6371 1.07143
\(214\) 0.748125 0.0511408
\(215\) −6.33547 −0.432076
\(216\) −2.79995 −0.190513
\(217\) −0.0327089 −0.00222043
\(218\) 10.7517 0.728196
\(219\) 6.91670 0.467387
\(220\) −18.2448 −1.23006
\(221\) −2.70187 −0.181748
\(222\) −4.48720 −0.301161
\(223\) 26.2867 1.76029 0.880145 0.474706i \(-0.157446\pi\)
0.880145 + 0.474706i \(0.157446\pi\)
\(224\) −0.0566155 −0.00378278
\(225\) 14.5148 0.967654
\(226\) −5.38863 −0.358447
\(227\) −0.621313 −0.0412380 −0.0206190 0.999787i \(-0.506564\pi\)
−0.0206190 + 0.999787i \(0.506564\pi\)
\(228\) −5.40530 −0.357975
\(229\) 6.55118 0.432914 0.216457 0.976292i \(-0.430550\pi\)
0.216457 + 0.976292i \(0.430550\pi\)
\(230\) −32.4771 −2.14148
\(231\) 0.0323988 0.00213169
\(232\) 7.22429 0.474298
\(233\) −24.9995 −1.63777 −0.818885 0.573958i \(-0.805407\pi\)
−0.818885 + 0.573958i \(0.805407\pi\)
\(234\) −2.31757 −0.151505
\(235\) 7.49206 0.488728
\(236\) −0.728090 −0.0473946
\(237\) −1.00000 −0.0649570
\(238\) 0.00850689 0.000551420 0
\(239\) −17.5256 −1.13364 −0.566819 0.823842i \(-0.691826\pi\)
−0.566819 + 0.823842i \(0.691826\pi\)
\(240\) 0.560033 0.0361500
\(241\) 18.4610 1.18918 0.594588 0.804030i \(-0.297315\pi\)
0.594588 + 0.804030i \(0.297315\pi\)
\(242\) 0.281156 0.0180734
\(243\) −1.00000 −0.0641500
\(244\) 4.07389 0.260804
\(245\) 30.9225 1.97556
\(246\) −9.01881 −0.575019
\(247\) −11.5520 −0.735034
\(248\) −9.23452 −0.586393
\(249\) −0.651310 −0.0412751
\(250\) 36.0538 2.28024
\(251\) 29.5254 1.86363 0.931814 0.362935i \(-0.118225\pi\)
0.931814 + 0.362935i \(0.118225\pi\)
\(252\) −0.0125381 −0.000789825 0
\(253\) 27.9998 1.76033
\(254\) 10.5014 0.658917
\(255\) −4.41756 −0.276638
\(256\) −15.6634 −0.978961
\(257\) −10.8979 −0.679792 −0.339896 0.940463i \(-0.610392\pi\)
−0.339896 + 0.940463i \(0.610392\pi\)
\(258\) 1.23017 0.0765871
\(259\) −0.0518811 −0.00322373
\(260\) 15.0895 0.935814
\(261\) 2.58015 0.159707
\(262\) −10.0724 −0.622275
\(263\) −19.4022 −1.19639 −0.598196 0.801350i \(-0.704116\pi\)
−0.598196 + 0.801350i \(0.704116\pi\)
\(264\) 9.14698 0.562958
\(265\) 18.7802 1.15366
\(266\) 0.0363716 0.00223008
\(267\) 7.54867 0.461971
\(268\) 9.30853 0.568609
\(269\) 10.6240 0.647756 0.323878 0.946099i \(-0.395013\pi\)
0.323878 + 0.946099i \(0.395013\pi\)
\(270\) −3.78923 −0.230605
\(271\) −11.1895 −0.679715 −0.339857 0.940477i \(-0.610379\pi\)
−0.339857 + 0.940477i \(0.610379\pi\)
\(272\) −0.126774 −0.00768682
\(273\) −0.0267958 −0.00162176
\(274\) 3.81363 0.230390
\(275\) −47.4175 −2.85938
\(276\) −10.8357 −0.652230
\(277\) 23.7002 1.42401 0.712003 0.702176i \(-0.247788\pi\)
0.712003 + 0.702176i \(0.247788\pi\)
\(278\) −8.55611 −0.513161
\(279\) −3.29810 −0.197452
\(280\) −0.122669 −0.00733087
\(281\) −4.90376 −0.292534 −0.146267 0.989245i \(-0.546726\pi\)
−0.146267 + 0.989245i \(0.546726\pi\)
\(282\) −1.45475 −0.0866290
\(283\) 12.2940 0.730803 0.365402 0.930850i \(-0.380932\pi\)
0.365402 + 0.930850i \(0.380932\pi\)
\(284\) 19.7690 1.17307
\(285\) −18.8875 −1.11880
\(286\) 7.57113 0.447691
\(287\) −0.104276 −0.00615520
\(288\) −5.70865 −0.336385
\(289\) 1.00000 0.0588235
\(290\) 9.77677 0.574112
\(291\) 11.4421 0.670750
\(292\) 8.74435 0.511724
\(293\) −1.55549 −0.0908726 −0.0454363 0.998967i \(-0.514468\pi\)
−0.0454363 + 0.998967i \(0.514468\pi\)
\(294\) −6.00428 −0.350176
\(295\) −2.54412 −0.148125
\(296\) −14.6473 −0.851357
\(297\) 3.26684 0.189561
\(298\) 9.74894 0.564741
\(299\) −23.1575 −1.33923
\(300\) 18.3502 1.05945
\(301\) 0.0142232 0.000819814 0
\(302\) 0.514196 0.0295887
\(303\) 12.3316 0.708433
\(304\) −0.542029 −0.0310875
\(305\) 14.2352 0.815104
\(306\) 0.857766 0.0490352
\(307\) −24.0461 −1.37238 −0.686191 0.727422i \(-0.740718\pi\)
−0.686191 + 0.727422i \(0.740718\pi\)
\(308\) 0.0409599 0.00233390
\(309\) −13.9114 −0.791390
\(310\) −12.4973 −0.709797
\(311\) −23.4847 −1.33170 −0.665848 0.746088i \(-0.731930\pi\)
−0.665848 + 0.746088i \(0.731930\pi\)
\(312\) −7.56511 −0.428290
\(313\) −21.3568 −1.20716 −0.603578 0.797304i \(-0.706259\pi\)
−0.603578 + 0.797304i \(0.706259\pi\)
\(314\) −13.9462 −0.787031
\(315\) −0.0438111 −0.00246848
\(316\) −1.26424 −0.0711190
\(317\) −0.835900 −0.0469488 −0.0234744 0.999724i \(-0.507473\pi\)
−0.0234744 + 0.999724i \(0.507473\pi\)
\(318\) −3.64659 −0.204491
\(319\) −8.42892 −0.471929
\(320\) −20.5113 −1.14662
\(321\) 0.872179 0.0486803
\(322\) 0.0729117 0.00406321
\(323\) 4.27554 0.237898
\(324\) −1.26424 −0.0702355
\(325\) 39.2172 2.17538
\(326\) 9.38435 0.519751
\(327\) 12.5345 0.693161
\(328\) −29.4396 −1.62553
\(329\) −0.0168198 −0.000927307 0
\(330\) 12.3788 0.681430
\(331\) −15.9837 −0.878544 −0.439272 0.898354i \(-0.644764\pi\)
−0.439272 + 0.898354i \(0.644764\pi\)
\(332\) −0.823411 −0.0451906
\(333\) −5.23127 −0.286672
\(334\) −8.74612 −0.478567
\(335\) 32.5263 1.77710
\(336\) −0.00125728 −6.85904e−5 0
\(337\) 3.24657 0.176852 0.0884259 0.996083i \(-0.471816\pi\)
0.0884259 + 0.996083i \(0.471816\pi\)
\(338\) 4.88916 0.265935
\(339\) −6.28218 −0.341201
\(340\) −5.58484 −0.302881
\(341\) 10.7744 0.583464
\(342\) 3.66741 0.198311
\(343\) −0.138844 −0.00749687
\(344\) 4.01557 0.216505
\(345\) −37.8625 −2.03845
\(346\) 12.9535 0.696384
\(347\) 13.9015 0.746274 0.373137 0.927776i \(-0.378282\pi\)
0.373137 + 0.927776i \(0.378282\pi\)
\(348\) 3.26192 0.174857
\(349\) 9.91279 0.530620 0.265310 0.964163i \(-0.414526\pi\)
0.265310 + 0.964163i \(0.414526\pi\)
\(350\) −0.123476 −0.00660007
\(351\) −2.70187 −0.144215
\(352\) 18.6492 0.994006
\(353\) −26.0400 −1.38597 −0.692985 0.720952i \(-0.743705\pi\)
−0.692985 + 0.720952i \(0.743705\pi\)
\(354\) 0.493997 0.0262557
\(355\) 69.0776 3.66626
\(356\) 9.54332 0.505795
\(357\) 0.00991750 0.000524890 0
\(358\) −10.4568 −0.552659
\(359\) 22.3216 1.17809 0.589044 0.808101i \(-0.299504\pi\)
0.589044 + 0.808101i \(0.299504\pi\)
\(360\) −12.3689 −0.651901
\(361\) −0.719734 −0.0378807
\(362\) 11.0183 0.579111
\(363\) 0.327777 0.0172038
\(364\) −0.0338763 −0.00177560
\(365\) 30.5549 1.59932
\(366\) −2.76407 −0.144480
\(367\) 4.93974 0.257852 0.128926 0.991654i \(-0.458847\pi\)
0.128926 + 0.991654i \(0.458847\pi\)
\(368\) −1.08657 −0.0566414
\(369\) −10.5143 −0.547353
\(370\) −19.8225 −1.03052
\(371\) −0.0421619 −0.00218894
\(372\) −4.16958 −0.216183
\(373\) −6.95263 −0.359993 −0.179997 0.983667i \(-0.557609\pi\)
−0.179997 + 0.983667i \(0.557609\pi\)
\(374\) −2.80218 −0.144897
\(375\) 42.0322 2.17054
\(376\) −4.74865 −0.244893
\(377\) 6.97123 0.359037
\(378\) 0.00850689 0.000437547 0
\(379\) −33.1311 −1.70183 −0.850915 0.525303i \(-0.823952\pi\)
−0.850915 + 0.525303i \(0.823952\pi\)
\(380\) −23.8782 −1.22493
\(381\) 12.2427 0.627215
\(382\) −5.20871 −0.266501
\(383\) 6.90333 0.352744 0.176372 0.984324i \(-0.443564\pi\)
0.176372 + 0.984324i \(0.443564\pi\)
\(384\) −7.43457 −0.379394
\(385\) 0.143124 0.00729426
\(386\) 3.16631 0.161161
\(387\) 1.43416 0.0729023
\(388\) 14.4656 0.734379
\(389\) −34.4429 −1.74633 −0.873163 0.487428i \(-0.837935\pi\)
−0.873163 + 0.487428i \(0.837935\pi\)
\(390\) −10.2380 −0.518422
\(391\) 8.57091 0.433449
\(392\) −19.5994 −0.989918
\(393\) −11.7426 −0.592335
\(394\) −20.5682 −1.03621
\(395\) −4.41756 −0.222271
\(396\) 4.13006 0.207543
\(397\) −8.38591 −0.420877 −0.210438 0.977607i \(-0.567489\pi\)
−0.210438 + 0.977607i \(0.567489\pi\)
\(398\) 4.74422 0.237806
\(399\) 0.0424027 0.00212279
\(400\) 1.84011 0.0920053
\(401\) −25.0140 −1.24914 −0.624571 0.780968i \(-0.714726\pi\)
−0.624571 + 0.780968i \(0.714726\pi\)
\(402\) −6.31569 −0.314998
\(403\) −8.91105 −0.443891
\(404\) 15.5901 0.775636
\(405\) −4.41756 −0.219510
\(406\) −0.0219490 −0.00108931
\(407\) 17.0897 0.847105
\(408\) 2.79995 0.138618
\(409\) −2.21531 −0.109540 −0.0547699 0.998499i \(-0.517443\pi\)
−0.0547699 + 0.998499i \(0.517443\pi\)
\(410\) −39.8411 −1.96761
\(411\) 4.44600 0.219305
\(412\) −17.5873 −0.866463
\(413\) 0.00571160 0.000281050 0
\(414\) 7.35183 0.361323
\(415\) −2.87720 −0.141236
\(416\) −15.4240 −0.756225
\(417\) −9.97488 −0.488472
\(418\) −11.9808 −0.586002
\(419\) 24.0544 1.17514 0.587568 0.809175i \(-0.300086\pi\)
0.587568 + 0.809175i \(0.300086\pi\)
\(420\) −0.0553877 −0.00270264
\(421\) −8.23853 −0.401521 −0.200761 0.979640i \(-0.564341\pi\)
−0.200761 + 0.979640i \(0.564341\pi\)
\(422\) −18.3864 −0.895035
\(423\) −1.69597 −0.0824611
\(424\) −11.9033 −0.578078
\(425\) −14.5148 −0.704072
\(426\) −13.4129 −0.649859
\(427\) −0.0319582 −0.00154657
\(428\) 1.10264 0.0532982
\(429\) 8.82658 0.426151
\(430\) 5.43435 0.262068
\(431\) −2.57171 −0.123875 −0.0619375 0.998080i \(-0.519728\pi\)
−0.0619375 + 0.998080i \(0.519728\pi\)
\(432\) −0.126774 −0.00609943
\(433\) 7.05674 0.339125 0.169563 0.985519i \(-0.445765\pi\)
0.169563 + 0.985519i \(0.445765\pi\)
\(434\) 0.0280566 0.00134676
\(435\) 11.3980 0.546490
\(436\) 15.8466 0.758916
\(437\) 36.6453 1.75298
\(438\) −5.93290 −0.283485
\(439\) −15.8385 −0.755928 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(440\) 40.4073 1.92634
\(441\) −6.99990 −0.333329
\(442\) 2.31757 0.110236
\(443\) −18.4791 −0.877969 −0.438984 0.898495i \(-0.644662\pi\)
−0.438984 + 0.898495i \(0.644662\pi\)
\(444\) −6.61357 −0.313866
\(445\) 33.3467 1.58078
\(446\) −22.5478 −1.06767
\(447\) 11.3655 0.537570
\(448\) 0.0460482 0.00217557
\(449\) 20.1196 0.949505 0.474752 0.880119i \(-0.342538\pi\)
0.474752 + 0.880119i \(0.342538\pi\)
\(450\) −12.4503 −0.586913
\(451\) 34.3485 1.61741
\(452\) −7.94217 −0.373568
\(453\) 0.599460 0.0281651
\(454\) 0.532941 0.0250121
\(455\) −0.118372 −0.00554937
\(456\) 11.9713 0.560608
\(457\) 7.98977 0.373746 0.186873 0.982384i \(-0.440165\pi\)
0.186873 + 0.982384i \(0.440165\pi\)
\(458\) −5.61938 −0.262576
\(459\) 1.00000 0.0466760
\(460\) −47.8672 −2.23182
\(461\) 2.18374 0.101707 0.0508534 0.998706i \(-0.483806\pi\)
0.0508534 + 0.998706i \(0.483806\pi\)
\(462\) −0.0277906 −0.00129294
\(463\) −14.6319 −0.680002 −0.340001 0.940425i \(-0.610427\pi\)
−0.340001 + 0.940425i \(0.610427\pi\)
\(464\) 0.327096 0.0151851
\(465\) −14.5696 −0.675647
\(466\) 21.4437 0.993359
\(467\) 31.2841 1.44765 0.723827 0.689982i \(-0.242381\pi\)
0.723827 + 0.689982i \(0.242381\pi\)
\(468\) −3.41581 −0.157896
\(469\) −0.0730221 −0.00337185
\(470\) −6.42644 −0.296429
\(471\) −16.2588 −0.749166
\(472\) 1.61252 0.0742225
\(473\) −4.68516 −0.215424
\(474\) 0.857766 0.0393985
\(475\) −62.0587 −2.84745
\(476\) 0.0125381 0.000574682 0
\(477\) −4.25127 −0.194652
\(478\) 15.0329 0.687588
\(479\) −18.7553 −0.856953 −0.428477 0.903553i \(-0.640950\pi\)
−0.428477 + 0.903553i \(0.640950\pi\)
\(480\) −25.2183 −1.15105
\(481\) −14.1342 −0.644465
\(482\) −15.8352 −0.721273
\(483\) 0.0850019 0.00386772
\(484\) 0.414388 0.0188358
\(485\) 50.5463 2.29519
\(486\) 0.857766 0.0389090
\(487\) 30.8510 1.39799 0.698997 0.715125i \(-0.253630\pi\)
0.698997 + 0.715125i \(0.253630\pi\)
\(488\) −9.02259 −0.408433
\(489\) 10.9405 0.494744
\(490\) −26.5242 −1.19824
\(491\) −2.19111 −0.0988832 −0.0494416 0.998777i \(-0.515744\pi\)
−0.0494416 + 0.998777i \(0.515744\pi\)
\(492\) −13.2926 −0.599276
\(493\) −2.58015 −0.116204
\(494\) 9.90888 0.445822
\(495\) 14.4314 0.648645
\(496\) −0.418114 −0.0187739
\(497\) −0.155080 −0.00695631
\(498\) 0.558671 0.0250347
\(499\) −37.8977 −1.69653 −0.848267 0.529569i \(-0.822354\pi\)
−0.848267 + 0.529569i \(0.822354\pi\)
\(500\) 53.1388 2.37644
\(501\) −10.1964 −0.455542
\(502\) −25.3259 −1.13035
\(503\) 15.0939 0.673002 0.336501 0.941683i \(-0.390756\pi\)
0.336501 + 0.941683i \(0.390756\pi\)
\(504\) 0.0277685 0.00123691
\(505\) 54.4756 2.42413
\(506\) −24.0172 −1.06770
\(507\) 5.69988 0.253141
\(508\) 15.4777 0.686714
\(509\) −40.5887 −1.79906 −0.899531 0.436857i \(-0.856092\pi\)
−0.899531 + 0.436857i \(0.856092\pi\)
\(510\) 3.78923 0.167790
\(511\) −0.0685963 −0.00303452
\(512\) −1.43363 −0.0633582
\(513\) 4.27554 0.188770
\(514\) 9.34784 0.412315
\(515\) −61.4543 −2.70800
\(516\) 1.81312 0.0798180
\(517\) 5.54047 0.243670
\(518\) 0.0445018 0.00195530
\(519\) 15.1014 0.662880
\(520\) −33.4193 −1.46553
\(521\) 1.49204 0.0653673 0.0326836 0.999466i \(-0.489595\pi\)
0.0326836 + 0.999466i \(0.489595\pi\)
\(522\) −2.21316 −0.0968675
\(523\) −21.3629 −0.934135 −0.467068 0.884222i \(-0.654690\pi\)
−0.467068 + 0.884222i \(0.654690\pi\)
\(524\) −14.8454 −0.648526
\(525\) −0.143951 −0.00628252
\(526\) 16.6426 0.725650
\(527\) 3.29810 0.143668
\(528\) 0.414151 0.0180236
\(529\) 50.4604 2.19393
\(530\) −16.1090 −0.699732
\(531\) 0.575912 0.0249924
\(532\) 0.0536071 0.00232416
\(533\) −28.4083 −1.23050
\(534\) −6.47499 −0.280200
\(535\) 3.85290 0.166575
\(536\) −20.6159 −0.890472
\(537\) −12.1907 −0.526069
\(538\) −9.11290 −0.392885
\(539\) 22.8675 0.984975
\(540\) −5.58484 −0.240333
\(541\) −2.34046 −0.100624 −0.0503121 0.998734i \(-0.516022\pi\)
−0.0503121 + 0.998734i \(0.516022\pi\)
\(542\) 9.59798 0.412269
\(543\) 12.8454 0.551249
\(544\) 5.70865 0.244756
\(545\) 55.3720 2.37188
\(546\) 0.0229845 0.000983647 0
\(547\) 23.2535 0.994247 0.497124 0.867680i \(-0.334390\pi\)
0.497124 + 0.867680i \(0.334390\pi\)
\(548\) 5.62081 0.240109
\(549\) −3.22241 −0.137529
\(550\) 40.6731 1.73431
\(551\) −11.0315 −0.469959
\(552\) 23.9981 1.02143
\(553\) 0.00991750 0.000421735 0
\(554\) −20.3292 −0.863706
\(555\) −23.1094 −0.980941
\(556\) −12.6106 −0.534809
\(557\) −37.6487 −1.59523 −0.797613 0.603170i \(-0.793904\pi\)
−0.797613 + 0.603170i \(0.793904\pi\)
\(558\) 2.82900 0.119761
\(559\) 3.87491 0.163891
\(560\) −0.00555412 −0.000234704 0
\(561\) −3.26684 −0.137926
\(562\) 4.20628 0.177431
\(563\) 28.2094 1.18888 0.594442 0.804138i \(-0.297373\pi\)
0.594442 + 0.804138i \(0.297373\pi\)
\(564\) −2.14412 −0.0902835
\(565\) −27.7519 −1.16753
\(566\) −10.5454 −0.443255
\(567\) 0.00991750 0.000416496 0
\(568\) −43.7830 −1.83709
\(569\) 18.3588 0.769643 0.384821 0.922991i \(-0.374263\pi\)
0.384821 + 0.922991i \(0.374263\pi\)
\(570\) 16.2010 0.678586
\(571\) −33.4017 −1.39782 −0.698909 0.715211i \(-0.746331\pi\)
−0.698909 + 0.715211i \(0.746331\pi\)
\(572\) 11.1589 0.466577
\(573\) −6.07241 −0.253679
\(574\) 0.0894440 0.00373332
\(575\) −124.405 −5.18805
\(576\) 4.64313 0.193464
\(577\) −34.2634 −1.42640 −0.713202 0.700958i \(-0.752756\pi\)
−0.713202 + 0.700958i \(0.752756\pi\)
\(578\) −0.857766 −0.0356783
\(579\) 3.69134 0.153407
\(580\) 14.4097 0.598331
\(581\) 0.00645937 0.000267980 0
\(582\) −9.81467 −0.406831
\(583\) 13.8882 0.575191
\(584\) −19.3664 −0.801388
\(585\) −11.9357 −0.493480
\(586\) 1.33425 0.0551172
\(587\) 45.0220 1.85826 0.929128 0.369758i \(-0.120559\pi\)
0.929128 + 0.369758i \(0.120559\pi\)
\(588\) −8.84954 −0.364949
\(589\) 14.1012 0.581029
\(590\) 2.18226 0.0898423
\(591\) −23.9789 −0.986358
\(592\) −0.663190 −0.0272570
\(593\) −6.50436 −0.267102 −0.133551 0.991042i \(-0.542638\pi\)
−0.133551 + 0.991042i \(0.542638\pi\)
\(594\) −2.80218 −0.114975
\(595\) 0.0438111 0.00179608
\(596\) 14.3687 0.588565
\(597\) 5.53090 0.226365
\(598\) 19.8637 0.812287
\(599\) −17.2141 −0.703349 −0.351674 0.936122i \(-0.614388\pi\)
−0.351674 + 0.936122i \(0.614388\pi\)
\(600\) −40.6408 −1.65915
\(601\) 30.1513 1.22990 0.614948 0.788568i \(-0.289177\pi\)
0.614948 + 0.788568i \(0.289177\pi\)
\(602\) −0.0122002 −0.000497244 0
\(603\) −7.36295 −0.299843
\(604\) 0.757860 0.0308369
\(605\) 1.44797 0.0588685
\(606\) −10.5776 −0.429687
\(607\) 0.868578 0.0352545 0.0176272 0.999845i \(-0.494389\pi\)
0.0176272 + 0.999845i \(0.494389\pi\)
\(608\) 24.4076 0.989857
\(609\) −0.0255886 −0.00103690
\(610\) −12.2104 −0.494387
\(611\) −4.58231 −0.185380
\(612\) 1.26424 0.0511038
\(613\) −2.99176 −0.120836 −0.0604180 0.998173i \(-0.519243\pi\)
−0.0604180 + 0.998173i \(0.519243\pi\)
\(614\) 20.6259 0.832393
\(615\) −46.4476 −1.87295
\(616\) −0.0907152 −0.00365502
\(617\) −34.1943 −1.37661 −0.688306 0.725420i \(-0.741645\pi\)
−0.688306 + 0.725420i \(0.741645\pi\)
\(618\) 11.9327 0.480003
\(619\) 26.9489 1.08317 0.541585 0.840646i \(-0.317825\pi\)
0.541585 + 0.840646i \(0.317825\pi\)
\(620\) −18.4194 −0.739740
\(621\) 8.57091 0.343939
\(622\) 20.1444 0.807716
\(623\) −0.0748639 −0.00299936
\(624\) −0.342528 −0.0137121
\(625\) 113.106 4.52423
\(626\) 18.3191 0.732179
\(627\) −13.9675 −0.557808
\(628\) −20.5550 −0.820233
\(629\) 5.23127 0.208584
\(630\) 0.0375797 0.00149721
\(631\) 21.9961 0.875651 0.437826 0.899060i \(-0.355749\pi\)
0.437826 + 0.899060i \(0.355749\pi\)
\(632\) 2.79995 0.111376
\(633\) −21.4352 −0.851973
\(634\) 0.717006 0.0284760
\(635\) 54.0830 2.14622
\(636\) −5.37462 −0.213117
\(637\) −18.9128 −0.749354
\(638\) 7.23004 0.286240
\(639\) −15.6371 −0.618592
\(640\) −32.8427 −1.29822
\(641\) 15.1640 0.598940 0.299470 0.954106i \(-0.403190\pi\)
0.299470 + 0.954106i \(0.403190\pi\)
\(642\) −0.748125 −0.0295261
\(643\) −3.34319 −0.131842 −0.0659212 0.997825i \(-0.520999\pi\)
−0.0659212 + 0.997825i \(0.520999\pi\)
\(644\) 0.107463 0.00423462
\(645\) 6.33547 0.249459
\(646\) −3.66741 −0.144292
\(647\) −11.0469 −0.434297 −0.217149 0.976139i \(-0.569676\pi\)
−0.217149 + 0.976139i \(0.569676\pi\)
\(648\) 2.79995 0.109992
\(649\) −1.88141 −0.0738518
\(650\) −33.6392 −1.31944
\(651\) 0.0327089 0.00128196
\(652\) 13.8313 0.541677
\(653\) −19.2944 −0.755048 −0.377524 0.926000i \(-0.623225\pi\)
−0.377524 + 0.926000i \(0.623225\pi\)
\(654\) −10.7517 −0.420424
\(655\) −51.8736 −2.02687
\(656\) −1.33294 −0.0520427
\(657\) −6.91670 −0.269846
\(658\) 0.0144275 0.000562441 0
\(659\) 5.68747 0.221552 0.110776 0.993845i \(-0.464666\pi\)
0.110776 + 0.993845i \(0.464666\pi\)
\(660\) 18.2448 0.710177
\(661\) −16.5678 −0.644411 −0.322205 0.946670i \(-0.604424\pi\)
−0.322205 + 0.946670i \(0.604424\pi\)
\(662\) 13.7103 0.532865
\(663\) 2.70187 0.104932
\(664\) 1.82364 0.0707708
\(665\) 0.187316 0.00726381
\(666\) 4.48720 0.173876
\(667\) −22.1142 −0.856265
\(668\) −12.8907 −0.498755
\(669\) −26.2867 −1.01630
\(670\) −27.8999 −1.07787
\(671\) 10.5271 0.406394
\(672\) 0.0566155 0.00218399
\(673\) 32.5610 1.25513 0.627567 0.778563i \(-0.284051\pi\)
0.627567 + 0.778563i \(0.284051\pi\)
\(674\) −2.78479 −0.107266
\(675\) −14.5148 −0.558676
\(676\) 7.20601 0.277154
\(677\) 11.0341 0.424074 0.212037 0.977262i \(-0.431990\pi\)
0.212037 + 0.977262i \(0.431990\pi\)
\(678\) 5.38863 0.206949
\(679\) −0.113477 −0.00435486
\(680\) 12.3689 0.474327
\(681\) 0.621313 0.0238088
\(682\) −9.24187 −0.353890
\(683\) 37.3675 1.42983 0.714913 0.699213i \(-0.246466\pi\)
0.714913 + 0.699213i \(0.246466\pi\)
\(684\) 5.40530 0.206677
\(685\) 19.6405 0.750424
\(686\) 0.119096 0.00454709
\(687\) −6.55118 −0.249943
\(688\) 0.181814 0.00693160
\(689\) −11.4864 −0.437597
\(690\) 32.4771 1.23638
\(691\) 18.7953 0.715008 0.357504 0.933912i \(-0.383628\pi\)
0.357504 + 0.933912i \(0.383628\pi\)
\(692\) 19.0918 0.725762
\(693\) −0.0323988 −0.00123073
\(694\) −11.9243 −0.452639
\(695\) −44.0646 −1.67147
\(696\) −7.22429 −0.273836
\(697\) 10.5143 0.398258
\(698\) −8.50285 −0.321838
\(699\) 24.9995 0.945567
\(700\) −0.181988 −0.00687850
\(701\) −16.1476 −0.609888 −0.304944 0.952370i \(-0.598638\pi\)
−0.304944 + 0.952370i \(0.598638\pi\)
\(702\) 2.31757 0.0874712
\(703\) 22.3665 0.843569
\(704\) −15.1684 −0.571679
\(705\) −7.49206 −0.282167
\(706\) 22.3362 0.840635
\(707\) −0.122299 −0.00459952
\(708\) 0.728090 0.0273633
\(709\) 29.4719 1.10684 0.553420 0.832902i \(-0.313322\pi\)
0.553420 + 0.832902i \(0.313322\pi\)
\(710\) −59.2524 −2.22370
\(711\) 1.00000 0.0375029
\(712\) −21.1359 −0.792102
\(713\) 28.2677 1.05863
\(714\) −0.00850689 −0.000318362 0
\(715\) 38.9919 1.45821
\(716\) −15.4120 −0.575973
\(717\) 17.5256 0.654506
\(718\) −19.1467 −0.714548
\(719\) −31.4919 −1.17445 −0.587224 0.809424i \(-0.699779\pi\)
−0.587224 + 0.809424i \(0.699779\pi\)
\(720\) −0.560033 −0.0208712
\(721\) 0.137966 0.00513812
\(722\) 0.617363 0.0229759
\(723\) −18.4610 −0.686571
\(724\) 16.2396 0.603542
\(725\) 37.4504 1.39087
\(726\) −0.281156 −0.0104347
\(727\) −4.27714 −0.158630 −0.0793152 0.996850i \(-0.525273\pi\)
−0.0793152 + 0.996850i \(0.525273\pi\)
\(728\) 0.0750270 0.00278068
\(729\) 1.00000 0.0370370
\(730\) −26.2089 −0.970036
\(731\) −1.43416 −0.0530442
\(732\) −4.07389 −0.150575
\(733\) 8.09488 0.298991 0.149496 0.988762i \(-0.452235\pi\)
0.149496 + 0.988762i \(0.452235\pi\)
\(734\) −4.23714 −0.156396
\(735\) −30.9225 −1.14059
\(736\) 48.9283 1.80352
\(737\) 24.0536 0.886025
\(738\) 9.01881 0.331987
\(739\) 19.8278 0.729376 0.364688 0.931130i \(-0.381176\pi\)
0.364688 + 0.931130i \(0.381176\pi\)
\(740\) −29.2158 −1.07399
\(741\) 11.5520 0.424372
\(742\) 0.0361651 0.00132766
\(743\) −6.79768 −0.249383 −0.124691 0.992196i \(-0.539794\pi\)
−0.124691 + 0.992196i \(0.539794\pi\)
\(744\) 9.23452 0.338554
\(745\) 50.2078 1.83947
\(746\) 5.96373 0.218348
\(747\) 0.651310 0.0238302
\(748\) −4.13006 −0.151010
\(749\) −0.00864983 −0.000316058 0
\(750\) −36.0538 −1.31650
\(751\) 3.60740 0.131636 0.0658179 0.997832i \(-0.479034\pi\)
0.0658179 + 0.997832i \(0.479034\pi\)
\(752\) −0.215006 −0.00784046
\(753\) −29.5254 −1.07597
\(754\) −5.97968 −0.217767
\(755\) 2.64815 0.0963760
\(756\) 0.0125381 0.000456005 0
\(757\) 34.9771 1.27126 0.635631 0.771993i \(-0.280740\pi\)
0.635631 + 0.771993i \(0.280740\pi\)
\(758\) 28.4187 1.03221
\(759\) −27.9998 −1.01633
\(760\) 52.8840 1.91830
\(761\) −34.2736 −1.24242 −0.621209 0.783645i \(-0.713358\pi\)
−0.621209 + 0.783645i \(0.713358\pi\)
\(762\) −10.5014 −0.380426
\(763\) −0.124311 −0.00450036
\(764\) −7.67697 −0.277743
\(765\) 4.41756 0.159717
\(766\) −5.92144 −0.213950
\(767\) 1.55604 0.0561854
\(768\) 15.6634 0.565204
\(769\) 49.2191 1.77489 0.887443 0.460917i \(-0.152479\pi\)
0.887443 + 0.460917i \(0.152479\pi\)
\(770\) −0.122767 −0.00442420
\(771\) 10.8979 0.392478
\(772\) 4.66674 0.167960
\(773\) −11.2742 −0.405504 −0.202752 0.979230i \(-0.564989\pi\)
−0.202752 + 0.979230i \(0.564989\pi\)
\(774\) −1.23017 −0.0442176
\(775\) −47.8713 −1.71959
\(776\) −32.0374 −1.15008
\(777\) 0.0518811 0.00186122
\(778\) 29.5440 1.05920
\(779\) 44.9544 1.61066
\(780\) −15.0895 −0.540292
\(781\) 51.0837 1.82792
\(782\) −7.35183 −0.262901
\(783\) −2.58015 −0.0922070
\(784\) −0.887407 −0.0316931
\(785\) −71.8242 −2.56351
\(786\) 10.0724 0.359270
\(787\) 33.2404 1.18489 0.592447 0.805610i \(-0.298162\pi\)
0.592447 + 0.805610i \(0.298162\pi\)
\(788\) −30.3150 −1.07993
\(789\) 19.4022 0.690738
\(790\) 3.78923 0.134815
\(791\) 0.0623035 0.00221526
\(792\) −9.14698 −0.325024
\(793\) −8.70654 −0.309178
\(794\) 7.19314 0.255275
\(795\) −18.7802 −0.666066
\(796\) 6.99238 0.247838
\(797\) 41.8772 1.48337 0.741683 0.670750i \(-0.234028\pi\)
0.741683 + 0.670750i \(0.234028\pi\)
\(798\) −0.0363716 −0.00128754
\(799\) 1.69597 0.0599993
\(800\) −82.8599 −2.92954
\(801\) −7.54867 −0.266719
\(802\) 21.4562 0.757644
\(803\) 22.5957 0.797385
\(804\) −9.30853 −0.328286
\(805\) 0.375501 0.0132347
\(806\) 7.64359 0.269234
\(807\) −10.6240 −0.373982
\(808\) −34.5279 −1.21469
\(809\) −17.9758 −0.631997 −0.315998 0.948760i \(-0.602339\pi\)
−0.315998 + 0.948760i \(0.602339\pi\)
\(810\) 3.78923 0.133140
\(811\) 36.5068 1.28193 0.640963 0.767572i \(-0.278535\pi\)
0.640963 + 0.767572i \(0.278535\pi\)
\(812\) −0.0323501 −0.00113527
\(813\) 11.1895 0.392433
\(814\) −14.6590 −0.513796
\(815\) 48.3301 1.69293
\(816\) 0.126774 0.00443799
\(817\) −6.13180 −0.214525
\(818\) 1.90021 0.0664394
\(819\) 0.0267958 0.000936322 0
\(820\) −58.7208 −2.05062
\(821\) 52.0985 1.81825 0.909125 0.416524i \(-0.136752\pi\)
0.909125 + 0.416524i \(0.136752\pi\)
\(822\) −3.81363 −0.133016
\(823\) −46.9992 −1.63829 −0.819144 0.573587i \(-0.805551\pi\)
−0.819144 + 0.573587i \(0.805551\pi\)
\(824\) 38.9512 1.35693
\(825\) 47.4175 1.65087
\(826\) −0.00489922 −0.000170466 0
\(827\) −12.3299 −0.428751 −0.214376 0.976751i \(-0.568772\pi\)
−0.214376 + 0.976751i \(0.568772\pi\)
\(828\) 10.8357 0.376565
\(829\) 19.5307 0.678329 0.339165 0.940727i \(-0.389856\pi\)
0.339165 + 0.940727i \(0.389856\pi\)
\(830\) 2.46796 0.0856643
\(831\) −23.7002 −0.822151
\(832\) 12.5451 0.434925
\(833\) 6.99990 0.242532
\(834\) 8.55611 0.296274
\(835\) −45.0432 −1.55878
\(836\) −17.6582 −0.610723
\(837\) 3.29810 0.113999
\(838\) −20.6331 −0.712757
\(839\) 9.68676 0.334424 0.167212 0.985921i \(-0.446524\pi\)
0.167212 + 0.985921i \(0.446524\pi\)
\(840\) 0.122669 0.00423248
\(841\) −22.3428 −0.770443
\(842\) 7.06672 0.243535
\(843\) 4.90376 0.168894
\(844\) −27.0992 −0.932793
\(845\) 25.1796 0.866203
\(846\) 1.45475 0.0500153
\(847\) −0.00325073 −0.000111696 0
\(848\) −0.538952 −0.0185077
\(849\) −12.2940 −0.421929
\(850\) 12.4503 0.427042
\(851\) 44.8367 1.53698
\(852\) −19.7690 −0.677274
\(853\) 37.1292 1.27128 0.635640 0.771986i \(-0.280736\pi\)
0.635640 + 0.771986i \(0.280736\pi\)
\(854\) 0.0274127 0.000938042 0
\(855\) 18.8875 0.645937
\(856\) −2.44206 −0.0834678
\(857\) −6.38603 −0.218143 −0.109071 0.994034i \(-0.534788\pi\)
−0.109071 + 0.994034i \(0.534788\pi\)
\(858\) −7.57113 −0.258474
\(859\) −42.3549 −1.44513 −0.722565 0.691303i \(-0.757037\pi\)
−0.722565 + 0.691303i \(0.757037\pi\)
\(860\) 8.00955 0.273123
\(861\) 0.104276 0.00355370
\(862\) 2.20593 0.0751341
\(863\) 20.2052 0.687792 0.343896 0.939008i \(-0.388253\pi\)
0.343896 + 0.939008i \(0.388253\pi\)
\(864\) 5.70865 0.194212
\(865\) 66.7115 2.26826
\(866\) −6.05303 −0.205690
\(867\) −1.00000 −0.0339618
\(868\) 0.0413518 0.00140357
\(869\) −3.26684 −0.110820
\(870\) −9.77677 −0.331464
\(871\) −19.8938 −0.674075
\(872\) −35.0961 −1.18850
\(873\) −11.4421 −0.387257
\(874\) −31.4331 −1.06324
\(875\) −0.416855 −0.0140923
\(876\) −8.74435 −0.295444
\(877\) −44.1906 −1.49221 −0.746105 0.665829i \(-0.768078\pi\)
−0.746105 + 0.665829i \(0.768078\pi\)
\(878\) 13.5857 0.458495
\(879\) 1.55549 0.0524653
\(880\) 1.82954 0.0616736
\(881\) 8.73368 0.294245 0.147123 0.989118i \(-0.452999\pi\)
0.147123 + 0.989118i \(0.452999\pi\)
\(882\) 6.00428 0.202174
\(883\) −36.5034 −1.22844 −0.614219 0.789135i \(-0.710529\pi\)
−0.614219 + 0.789135i \(0.710529\pi\)
\(884\) 3.41581 0.114886
\(885\) 2.54412 0.0855198
\(886\) 15.8507 0.532516
\(887\) −0.247086 −0.00829633 −0.00414816 0.999991i \(-0.501320\pi\)
−0.00414816 + 0.999991i \(0.501320\pi\)
\(888\) 14.6473 0.491531
\(889\) −0.121417 −0.00407221
\(890\) −28.6036 −0.958796
\(891\) −3.26684 −0.109443
\(892\) −33.2327 −1.11271
\(893\) 7.25121 0.242653
\(894\) −9.74894 −0.326053
\(895\) −53.8533 −1.80012
\(896\) 0.0737323 0.00246322
\(897\) 23.1575 0.773206
\(898\) −17.2579 −0.575905
\(899\) −8.50959 −0.283811
\(900\) −18.3502 −0.611673
\(901\) 4.25127 0.141630
\(902\) −29.4630 −0.981010
\(903\) −0.0142232 −0.000473320 0
\(904\) 17.5898 0.585028
\(905\) 56.7453 1.88628
\(906\) −0.514196 −0.0170830
\(907\) −6.74409 −0.223934 −0.111967 0.993712i \(-0.535715\pi\)
−0.111967 + 0.993712i \(0.535715\pi\)
\(908\) 0.785487 0.0260673
\(909\) −12.3316 −0.409014
\(910\) 0.101535 0.00336587
\(911\) −29.3567 −0.972630 −0.486315 0.873784i \(-0.661659\pi\)
−0.486315 + 0.873784i \(0.661659\pi\)
\(912\) 0.542029 0.0179484
\(913\) −2.12772 −0.0704174
\(914\) −6.85335 −0.226689
\(915\) −14.2352 −0.470601
\(916\) −8.28225 −0.273653
\(917\) 0.116457 0.00384575
\(918\) −0.857766 −0.0283105
\(919\) 32.1337 1.05999 0.529996 0.848000i \(-0.322193\pi\)
0.529996 + 0.848000i \(0.322193\pi\)
\(920\) 106.013 3.49515
\(921\) 24.0461 0.792345
\(922\) −1.87314 −0.0616885
\(923\) −42.2493 −1.39065
\(924\) −0.0409599 −0.00134748
\(925\) −75.9309 −2.49659
\(926\) 12.5507 0.412443
\(927\) 13.9114 0.456909
\(928\) −14.7291 −0.483508
\(929\) 6.48527 0.212775 0.106387 0.994325i \(-0.466072\pi\)
0.106387 + 0.994325i \(0.466072\pi\)
\(930\) 12.4973 0.409801
\(931\) 29.9284 0.980863
\(932\) 31.6053 1.03527
\(933\) 23.4847 0.768855
\(934\) −26.8344 −0.878048
\(935\) −14.4314 −0.471959
\(936\) 7.56511 0.247273
\(937\) −8.72439 −0.285013 −0.142507 0.989794i \(-0.545516\pi\)
−0.142507 + 0.989794i \(0.545516\pi\)
\(938\) 0.0626358 0.00204513
\(939\) 21.3568 0.696952
\(940\) −9.47175 −0.308935
\(941\) 34.5477 1.12622 0.563112 0.826381i \(-0.309604\pi\)
0.563112 + 0.826381i \(0.309604\pi\)
\(942\) 13.9462 0.454393
\(943\) 90.1172 2.93462
\(944\) 0.0730108 0.00237630
\(945\) 0.0438111 0.00142518
\(946\) 4.01877 0.130661
\(947\) −20.9258 −0.679996 −0.339998 0.940426i \(-0.610426\pi\)
−0.339998 + 0.940426i \(0.610426\pi\)
\(948\) 1.26424 0.0410605
\(949\) −18.6880 −0.606639
\(950\) 53.2318 1.72707
\(951\) 0.835900 0.0271059
\(952\) −0.0277685 −0.000899982 0
\(953\) −7.28422 −0.235959 −0.117979 0.993016i \(-0.537642\pi\)
−0.117979 + 0.993016i \(0.537642\pi\)
\(954\) 3.64659 0.118063
\(955\) −26.8252 −0.868044
\(956\) 22.1566 0.716594
\(957\) 8.42892 0.272468
\(958\) 16.0877 0.519769
\(959\) −0.0440932 −0.00142384
\(960\) 20.5113 0.661999
\(961\) −20.1225 −0.649114
\(962\) 12.1238 0.390889
\(963\) −0.872179 −0.0281056
\(964\) −23.3391 −0.751701
\(965\) 16.3067 0.524932
\(966\) −0.0729117 −0.00234590
\(967\) −39.6715 −1.27575 −0.637874 0.770140i \(-0.720186\pi\)
−0.637874 + 0.770140i \(0.720186\pi\)
\(968\) −0.917760 −0.0294979
\(969\) −4.27554 −0.137350
\(970\) −43.3569 −1.39210
\(971\) 27.4482 0.880856 0.440428 0.897788i \(-0.354827\pi\)
0.440428 + 0.897788i \(0.354827\pi\)
\(972\) 1.26424 0.0405505
\(973\) 0.0989258 0.00317142
\(974\) −26.4629 −0.847928
\(975\) −39.2172 −1.25596
\(976\) −0.408519 −0.0130764
\(977\) −2.02254 −0.0647069 −0.0323534 0.999476i \(-0.510300\pi\)
−0.0323534 + 0.999476i \(0.510300\pi\)
\(978\) −9.38435 −0.300078
\(979\) 24.6603 0.788146
\(980\) −39.0934 −1.24879
\(981\) −12.5345 −0.400197
\(982\) 1.87946 0.0599758
\(983\) −5.48224 −0.174856 −0.0874282 0.996171i \(-0.527865\pi\)
−0.0874282 + 0.996171i \(0.527865\pi\)
\(984\) 29.4396 0.938499
\(985\) −105.928 −3.37515
\(986\) 2.21316 0.0704814
\(987\) 0.0168198 0.000535381 0
\(988\) 14.6044 0.464629
\(989\) −12.2920 −0.390864
\(990\) −12.3788 −0.393424
\(991\) 41.8540 1.32954 0.664769 0.747049i \(-0.268530\pi\)
0.664769 + 0.747049i \(0.268530\pi\)
\(992\) 18.8277 0.597780
\(993\) 15.9837 0.507227
\(994\) 0.133023 0.00421922
\(995\) 24.4331 0.774581
\(996\) 0.823411 0.0260908
\(997\) −38.2656 −1.21188 −0.605941 0.795509i \(-0.707203\pi\)
−0.605941 + 0.795509i \(0.707203\pi\)
\(998\) 32.5073 1.02900
\(999\) 5.23127 0.165510
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 4029.2.a.l.1.13 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.13 32 1.1 even 1 trivial