Properties

Label 4029.2.a.l.1.1
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 1.1
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.77670 q^{2} -1.00000 q^{3} +5.71004 q^{4} -0.322981 q^{5} +2.77670 q^{6} -2.70395 q^{7} -10.3017 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.77670 q^{2} -1.00000 q^{3} +5.71004 q^{4} -0.322981 q^{5} +2.77670 q^{6} -2.70395 q^{7} -10.3017 q^{8} +1.00000 q^{9} +0.896820 q^{10} -4.20627 q^{11} -5.71004 q^{12} -3.21667 q^{13} +7.50806 q^{14} +0.322981 q^{15} +17.1845 q^{16} -1.00000 q^{17} -2.77670 q^{18} +1.38003 q^{19} -1.84424 q^{20} +2.70395 q^{21} +11.6795 q^{22} -4.75086 q^{23} +10.3017 q^{24} -4.89568 q^{25} +8.93172 q^{26} -1.00000 q^{27} -15.4397 q^{28} +1.17961 q^{29} -0.896820 q^{30} +1.07662 q^{31} -27.1129 q^{32} +4.20627 q^{33} +2.77670 q^{34} +0.873325 q^{35} +5.71004 q^{36} -5.29347 q^{37} -3.83191 q^{38} +3.21667 q^{39} +3.32724 q^{40} -7.96803 q^{41} -7.50806 q^{42} +11.0562 q^{43} -24.0180 q^{44} -0.322981 q^{45} +13.1917 q^{46} -10.9703 q^{47} -17.1845 q^{48} +0.311361 q^{49} +13.5938 q^{50} +1.00000 q^{51} -18.3673 q^{52} -3.46843 q^{53} +2.77670 q^{54} +1.35855 q^{55} +27.8552 q^{56} -1.38003 q^{57} -3.27541 q^{58} -9.56511 q^{59} +1.84424 q^{60} -12.7275 q^{61} -2.98944 q^{62} -2.70395 q^{63} +40.9152 q^{64} +1.03892 q^{65} -11.6795 q^{66} -6.97214 q^{67} -5.71004 q^{68} +4.75086 q^{69} -2.42496 q^{70} -5.38554 q^{71} -10.3017 q^{72} -8.17791 q^{73} +14.6984 q^{74} +4.89568 q^{75} +7.88001 q^{76} +11.3736 q^{77} -8.93172 q^{78} +1.00000 q^{79} -5.55027 q^{80} +1.00000 q^{81} +22.1248 q^{82} +6.37240 q^{83} +15.4397 q^{84} +0.322981 q^{85} -30.6996 q^{86} -1.17961 q^{87} +43.3316 q^{88} +12.3288 q^{89} +0.896820 q^{90} +8.69772 q^{91} -27.1276 q^{92} -1.07662 q^{93} +30.4612 q^{94} -0.445722 q^{95} +27.1129 q^{96} +6.91187 q^{97} -0.864554 q^{98} -4.20627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77670 −1.96342 −0.981711 0.190380i \(-0.939028\pi\)
−0.981711 + 0.190380i \(0.939028\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.71004 2.85502
\(5\) −0.322981 −0.144441 −0.0722207 0.997389i \(-0.523009\pi\)
−0.0722207 + 0.997389i \(0.523009\pi\)
\(6\) 2.77670 1.13358
\(7\) −2.70395 −1.02200 −0.510999 0.859581i \(-0.670724\pi\)
−0.510999 + 0.859581i \(0.670724\pi\)
\(8\) −10.3017 −3.64219
\(9\) 1.00000 0.333333
\(10\) 0.896820 0.283599
\(11\) −4.20627 −1.26824 −0.634120 0.773235i \(-0.718637\pi\)
−0.634120 + 0.773235i \(0.718637\pi\)
\(12\) −5.71004 −1.64835
\(13\) −3.21667 −0.892144 −0.446072 0.894997i \(-0.647177\pi\)
−0.446072 + 0.894997i \(0.647177\pi\)
\(14\) 7.50806 2.00661
\(15\) 0.322981 0.0833933
\(16\) 17.1845 4.29613
\(17\) −1.00000 −0.242536
\(18\) −2.77670 −0.654474
\(19\) 1.38003 0.316600 0.158300 0.987391i \(-0.449399\pi\)
0.158300 + 0.987391i \(0.449399\pi\)
\(20\) −1.84424 −0.412384
\(21\) 2.70395 0.590051
\(22\) 11.6795 2.49009
\(23\) −4.75086 −0.990623 −0.495312 0.868715i \(-0.664946\pi\)
−0.495312 + 0.868715i \(0.664946\pi\)
\(24\) 10.3017 2.10282
\(25\) −4.89568 −0.979137
\(26\) 8.93172 1.75165
\(27\) −1.00000 −0.192450
\(28\) −15.4397 −2.91783
\(29\) 1.17961 0.219047 0.109524 0.993984i \(-0.465067\pi\)
0.109524 + 0.993984i \(0.465067\pi\)
\(30\) −0.896820 −0.163736
\(31\) 1.07662 0.193366 0.0966831 0.995315i \(-0.469177\pi\)
0.0966831 + 0.995315i \(0.469177\pi\)
\(32\) −27.1129 −4.79292
\(33\) 4.20627 0.732218
\(34\) 2.77670 0.476200
\(35\) 0.873325 0.147619
\(36\) 5.71004 0.951674
\(37\) −5.29347 −0.870242 −0.435121 0.900372i \(-0.643294\pi\)
−0.435121 + 0.900372i \(0.643294\pi\)
\(38\) −3.83191 −0.621618
\(39\) 3.21667 0.515079
\(40\) 3.32724 0.526083
\(41\) −7.96803 −1.24440 −0.622198 0.782860i \(-0.713760\pi\)
−0.622198 + 0.782860i \(0.713760\pi\)
\(42\) −7.50806 −1.15852
\(43\) 11.0562 1.68605 0.843024 0.537877i \(-0.180773\pi\)
0.843024 + 0.537877i \(0.180773\pi\)
\(44\) −24.0180 −3.62085
\(45\) −0.322981 −0.0481472
\(46\) 13.1917 1.94501
\(47\) −10.9703 −1.60018 −0.800090 0.599879i \(-0.795215\pi\)
−0.800090 + 0.599879i \(0.795215\pi\)
\(48\) −17.1845 −2.48037
\(49\) 0.311361 0.0444801
\(50\) 13.5938 1.92246
\(51\) 1.00000 0.140028
\(52\) −18.3673 −2.54709
\(53\) −3.46843 −0.476426 −0.238213 0.971213i \(-0.576562\pi\)
−0.238213 + 0.971213i \(0.576562\pi\)
\(54\) 2.77670 0.377861
\(55\) 1.35855 0.183186
\(56\) 27.8552 3.72231
\(57\) −1.38003 −0.182789
\(58\) −3.27541 −0.430082
\(59\) −9.56511 −1.24527 −0.622636 0.782512i \(-0.713938\pi\)
−0.622636 + 0.782512i \(0.713938\pi\)
\(60\) 1.84424 0.238090
\(61\) −12.7275 −1.62958 −0.814792 0.579753i \(-0.803149\pi\)
−0.814792 + 0.579753i \(0.803149\pi\)
\(62\) −2.98944 −0.379659
\(63\) −2.70395 −0.340666
\(64\) 40.9152 5.11440
\(65\) 1.03892 0.128863
\(66\) −11.6795 −1.43765
\(67\) −6.97214 −0.851782 −0.425891 0.904774i \(-0.640039\pi\)
−0.425891 + 0.904774i \(0.640039\pi\)
\(68\) −5.71004 −0.692445
\(69\) 4.75086 0.571937
\(70\) −2.42496 −0.289838
\(71\) −5.38554 −0.639147 −0.319573 0.947562i \(-0.603540\pi\)
−0.319573 + 0.947562i \(0.603540\pi\)
\(72\) −10.3017 −1.21406
\(73\) −8.17791 −0.957152 −0.478576 0.878046i \(-0.658847\pi\)
−0.478576 + 0.878046i \(0.658847\pi\)
\(74\) 14.6984 1.70865
\(75\) 4.89568 0.565305
\(76\) 7.88001 0.903899
\(77\) 11.3736 1.29614
\(78\) −8.93172 −1.01132
\(79\) 1.00000 0.112509
\(80\) −5.55027 −0.620539
\(81\) 1.00000 0.111111
\(82\) 22.1248 2.44328
\(83\) 6.37240 0.699462 0.349731 0.936850i \(-0.386273\pi\)
0.349731 + 0.936850i \(0.386273\pi\)
\(84\) 15.4397 1.68461
\(85\) 0.322981 0.0350322
\(86\) −30.6996 −3.31042
\(87\) −1.17961 −0.126467
\(88\) 43.3316 4.61917
\(89\) 12.3288 1.30685 0.653426 0.756991i \(-0.273331\pi\)
0.653426 + 0.756991i \(0.273331\pi\)
\(90\) 0.896820 0.0945331
\(91\) 8.69772 0.911769
\(92\) −27.1276 −2.82825
\(93\) −1.07662 −0.111640
\(94\) 30.4612 3.14183
\(95\) −0.445722 −0.0457301
\(96\) 27.1129 2.76720
\(97\) 6.91187 0.701794 0.350897 0.936414i \(-0.385877\pi\)
0.350897 + 0.936414i \(0.385877\pi\)
\(98\) −0.864554 −0.0873332
\(99\) −4.20627 −0.422746
\(100\) −27.9546 −2.79546
\(101\) −0.0359402 −0.00357618 −0.00178809 0.999998i \(-0.500569\pi\)
−0.00178809 + 0.999998i \(0.500569\pi\)
\(102\) −2.77670 −0.274934
\(103\) 4.41580 0.435102 0.217551 0.976049i \(-0.430193\pi\)
0.217551 + 0.976049i \(0.430193\pi\)
\(104\) 33.1371 3.24936
\(105\) −0.873325 −0.0852278
\(106\) 9.63078 0.935424
\(107\) −10.2768 −0.993494 −0.496747 0.867895i \(-0.665472\pi\)
−0.496747 + 0.867895i \(0.665472\pi\)
\(108\) −5.71004 −0.549449
\(109\) 9.01915 0.863878 0.431939 0.901903i \(-0.357830\pi\)
0.431939 + 0.901903i \(0.357830\pi\)
\(110\) −3.77227 −0.359672
\(111\) 5.29347 0.502434
\(112\) −46.4661 −4.39064
\(113\) −11.7906 −1.10916 −0.554582 0.832129i \(-0.687122\pi\)
−0.554582 + 0.832129i \(0.687122\pi\)
\(114\) 3.83191 0.358891
\(115\) 1.53444 0.143087
\(116\) 6.73561 0.625385
\(117\) −3.21667 −0.297381
\(118\) 26.5594 2.44499
\(119\) 2.70395 0.247871
\(120\) −3.32724 −0.303734
\(121\) 6.69274 0.608431
\(122\) 35.3403 3.19956
\(123\) 7.96803 0.718453
\(124\) 6.14753 0.552065
\(125\) 3.19612 0.285869
\(126\) 7.50806 0.668871
\(127\) 5.14488 0.456534 0.228267 0.973599i \(-0.426694\pi\)
0.228267 + 0.973599i \(0.426694\pi\)
\(128\) −59.3833 −5.24879
\(129\) −11.0562 −0.973440
\(130\) −2.88477 −0.253011
\(131\) 14.5680 1.27281 0.636406 0.771354i \(-0.280420\pi\)
0.636406 + 0.771354i \(0.280420\pi\)
\(132\) 24.0180 2.09050
\(133\) −3.73152 −0.323564
\(134\) 19.3595 1.67241
\(135\) 0.322981 0.0277978
\(136\) 10.3017 0.883361
\(137\) −15.2209 −1.30041 −0.650205 0.759759i \(-0.725317\pi\)
−0.650205 + 0.759759i \(0.725317\pi\)
\(138\) −13.1917 −1.12295
\(139\) −12.7423 −1.08079 −0.540396 0.841411i \(-0.681725\pi\)
−0.540396 + 0.841411i \(0.681725\pi\)
\(140\) 4.98673 0.421455
\(141\) 10.9703 0.923865
\(142\) 14.9540 1.25491
\(143\) 13.5302 1.13145
\(144\) 17.1845 1.43204
\(145\) −0.380990 −0.0316395
\(146\) 22.7076 1.87929
\(147\) −0.311361 −0.0256806
\(148\) −30.2260 −2.48456
\(149\) −8.30491 −0.680365 −0.340182 0.940360i \(-0.610489\pi\)
−0.340182 + 0.940360i \(0.610489\pi\)
\(150\) −13.5938 −1.10993
\(151\) 14.8951 1.21215 0.606074 0.795408i \(-0.292744\pi\)
0.606074 + 0.795408i \(0.292744\pi\)
\(152\) −14.2166 −1.15312
\(153\) −1.00000 −0.0808452
\(154\) −31.5809 −2.54487
\(155\) −0.347727 −0.0279301
\(156\) 18.3673 1.47056
\(157\) −7.55980 −0.603338 −0.301669 0.953413i \(-0.597544\pi\)
−0.301669 + 0.953413i \(0.597544\pi\)
\(158\) −2.77670 −0.220902
\(159\) 3.46843 0.275064
\(160\) 8.75694 0.692297
\(161\) 12.8461 1.01242
\(162\) −2.77670 −0.218158
\(163\) −6.29159 −0.492796 −0.246398 0.969169i \(-0.579247\pi\)
−0.246398 + 0.969169i \(0.579247\pi\)
\(164\) −45.4978 −3.55278
\(165\) −1.35855 −0.105763
\(166\) −17.6942 −1.37334
\(167\) −7.31128 −0.565764 −0.282882 0.959155i \(-0.591290\pi\)
−0.282882 + 0.959155i \(0.591290\pi\)
\(168\) −27.8552 −2.14908
\(169\) −2.65304 −0.204080
\(170\) −0.896820 −0.0687830
\(171\) 1.38003 0.105533
\(172\) 63.1311 4.81370
\(173\) −14.7177 −1.11897 −0.559483 0.828842i \(-0.689000\pi\)
−0.559483 + 0.828842i \(0.689000\pi\)
\(174\) 3.27541 0.248308
\(175\) 13.2377 1.00068
\(176\) −72.2828 −5.44852
\(177\) 9.56511 0.718958
\(178\) −34.2334 −2.56590
\(179\) −14.0508 −1.05021 −0.525103 0.851038i \(-0.675973\pi\)
−0.525103 + 0.851038i \(0.675973\pi\)
\(180\) −1.84424 −0.137461
\(181\) −10.5713 −0.785759 −0.392880 0.919590i \(-0.628521\pi\)
−0.392880 + 0.919590i \(0.628521\pi\)
\(182\) −24.1509 −1.79019
\(183\) 12.7275 0.940841
\(184\) 48.9418 3.60804
\(185\) 1.70969 0.125699
\(186\) 2.98944 0.219196
\(187\) 4.20627 0.307593
\(188\) −62.6408 −4.56855
\(189\) 2.70395 0.196684
\(190\) 1.23763 0.0897874
\(191\) −2.37252 −0.171670 −0.0858348 0.996309i \(-0.527356\pi\)
−0.0858348 + 0.996309i \(0.527356\pi\)
\(192\) −40.9152 −2.95280
\(193\) −22.6178 −1.62806 −0.814031 0.580821i \(-0.802732\pi\)
−0.814031 + 0.580821i \(0.802732\pi\)
\(194\) −19.1922 −1.37792
\(195\) −1.03892 −0.0743988
\(196\) 1.77788 0.126992
\(197\) 14.8804 1.06019 0.530094 0.847939i \(-0.322157\pi\)
0.530094 + 0.847939i \(0.322157\pi\)
\(198\) 11.6795 0.830029
\(199\) −2.02098 −0.143263 −0.0716316 0.997431i \(-0.522821\pi\)
−0.0716316 + 0.997431i \(0.522821\pi\)
\(200\) 50.4337 3.56620
\(201\) 6.97214 0.491777
\(202\) 0.0997951 0.00702156
\(203\) −3.18960 −0.223866
\(204\) 5.71004 0.399783
\(205\) 2.57352 0.179743
\(206\) −12.2613 −0.854289
\(207\) −4.75086 −0.330208
\(208\) −55.2769 −3.83277
\(209\) −5.80476 −0.401524
\(210\) 2.42496 0.167338
\(211\) −9.24121 −0.636191 −0.318096 0.948059i \(-0.603043\pi\)
−0.318096 + 0.948059i \(0.603043\pi\)
\(212\) −19.8049 −1.36021
\(213\) 5.38554 0.369011
\(214\) 28.5355 1.95065
\(215\) −3.57093 −0.243535
\(216\) 10.3017 0.700940
\(217\) −2.91112 −0.197620
\(218\) −25.0435 −1.69616
\(219\) 8.17791 0.552612
\(220\) 7.75736 0.523001
\(221\) 3.21667 0.216377
\(222\) −14.6984 −0.986490
\(223\) 8.34638 0.558915 0.279457 0.960158i \(-0.409845\pi\)
0.279457 + 0.960158i \(0.409845\pi\)
\(224\) 73.3119 4.89836
\(225\) −4.89568 −0.326379
\(226\) 32.7388 2.17775
\(227\) −18.3929 −1.22078 −0.610389 0.792102i \(-0.708987\pi\)
−0.610389 + 0.792102i \(0.708987\pi\)
\(228\) −7.88001 −0.521866
\(229\) −15.0245 −0.992845 −0.496422 0.868081i \(-0.665353\pi\)
−0.496422 + 0.868081i \(0.665353\pi\)
\(230\) −4.26067 −0.280940
\(231\) −11.3736 −0.748326
\(232\) −12.1519 −0.797812
\(233\) 21.0029 1.37594 0.687972 0.725737i \(-0.258501\pi\)
0.687972 + 0.725737i \(0.258501\pi\)
\(234\) 8.93172 0.583885
\(235\) 3.54319 0.231132
\(236\) −54.6172 −3.55528
\(237\) −1.00000 −0.0649570
\(238\) −7.50806 −0.486675
\(239\) −18.4947 −1.19632 −0.598160 0.801377i \(-0.704101\pi\)
−0.598160 + 0.801377i \(0.704101\pi\)
\(240\) 5.55027 0.358269
\(241\) 17.6246 1.13530 0.567651 0.823269i \(-0.307852\pi\)
0.567651 + 0.823269i \(0.307852\pi\)
\(242\) −18.5837 −1.19461
\(243\) −1.00000 −0.0641500
\(244\) −72.6744 −4.65250
\(245\) −0.100564 −0.00642477
\(246\) −22.1248 −1.41063
\(247\) −4.43909 −0.282452
\(248\) −11.0910 −0.704276
\(249\) −6.37240 −0.403834
\(250\) −8.87465 −0.561282
\(251\) 14.9045 0.940762 0.470381 0.882463i \(-0.344117\pi\)
0.470381 + 0.882463i \(0.344117\pi\)
\(252\) −15.4397 −0.972609
\(253\) 19.9834 1.25635
\(254\) −14.2858 −0.896369
\(255\) −0.322981 −0.0202259
\(256\) 83.0590 5.19119
\(257\) 10.3361 0.644749 0.322375 0.946612i \(-0.395519\pi\)
0.322375 + 0.946612i \(0.395519\pi\)
\(258\) 30.6996 1.91127
\(259\) 14.3133 0.889385
\(260\) 5.93230 0.367905
\(261\) 1.17961 0.0730158
\(262\) −40.4509 −2.49906
\(263\) 27.3781 1.68821 0.844104 0.536180i \(-0.180133\pi\)
0.844104 + 0.536180i \(0.180133\pi\)
\(264\) −43.3316 −2.66688
\(265\) 1.12024 0.0688156
\(266\) 10.3613 0.635293
\(267\) −12.3288 −0.754511
\(268\) −39.8112 −2.43186
\(269\) 8.86101 0.540265 0.270133 0.962823i \(-0.412932\pi\)
0.270133 + 0.962823i \(0.412932\pi\)
\(270\) −0.896820 −0.0545787
\(271\) 10.2725 0.624007 0.312004 0.950081i \(-0.399000\pi\)
0.312004 + 0.950081i \(0.399000\pi\)
\(272\) −17.1845 −1.04196
\(273\) −8.69772 −0.526410
\(274\) 42.2638 2.55325
\(275\) 20.5926 1.24178
\(276\) 27.1276 1.63289
\(277\) −16.9199 −1.01662 −0.508310 0.861174i \(-0.669730\pi\)
−0.508310 + 0.861174i \(0.669730\pi\)
\(278\) 35.3816 2.12205
\(279\) 1.07662 0.0644554
\(280\) −8.99671 −0.537656
\(281\) 29.1419 1.73846 0.869231 0.494406i \(-0.164614\pi\)
0.869231 + 0.494406i \(0.164614\pi\)
\(282\) −30.4612 −1.81394
\(283\) 0.580483 0.0345061 0.0172531 0.999851i \(-0.494508\pi\)
0.0172531 + 0.999851i \(0.494508\pi\)
\(284\) −30.7517 −1.82478
\(285\) 0.445722 0.0264023
\(286\) −37.5692 −2.22152
\(287\) 21.5452 1.27177
\(288\) −27.1129 −1.59764
\(289\) 1.00000 0.0588235
\(290\) 1.05789 0.0621217
\(291\) −6.91187 −0.405181
\(292\) −46.6962 −2.73269
\(293\) −20.3726 −1.19018 −0.595089 0.803660i \(-0.702883\pi\)
−0.595089 + 0.803660i \(0.702883\pi\)
\(294\) 0.864554 0.0504218
\(295\) 3.08935 0.179869
\(296\) 54.5316 3.16959
\(297\) 4.20627 0.244073
\(298\) 23.0602 1.33584
\(299\) 15.2820 0.883778
\(300\) 27.9546 1.61396
\(301\) −29.8953 −1.72314
\(302\) −41.3592 −2.37996
\(303\) 0.0359402 0.00206471
\(304\) 23.7151 1.36015
\(305\) 4.11073 0.235380
\(306\) 2.77670 0.158733
\(307\) 12.8136 0.731313 0.365656 0.930750i \(-0.380845\pi\)
0.365656 + 0.930750i \(0.380845\pi\)
\(308\) 64.9436 3.70050
\(309\) −4.41580 −0.251206
\(310\) 0.965532 0.0548385
\(311\) 30.6229 1.73646 0.868232 0.496159i \(-0.165257\pi\)
0.868232 + 0.496159i \(0.165257\pi\)
\(312\) −33.1371 −1.87602
\(313\) −11.3555 −0.641852 −0.320926 0.947104i \(-0.603994\pi\)
−0.320926 + 0.947104i \(0.603994\pi\)
\(314\) 20.9913 1.18461
\(315\) 0.873325 0.0492063
\(316\) 5.71004 0.321215
\(317\) 7.81235 0.438785 0.219393 0.975637i \(-0.429592\pi\)
0.219393 + 0.975637i \(0.429592\pi\)
\(318\) −9.63078 −0.540067
\(319\) −4.96175 −0.277805
\(320\) −13.2148 −0.738731
\(321\) 10.2768 0.573594
\(322\) −35.6697 −1.98780
\(323\) −1.38003 −0.0767867
\(324\) 5.71004 0.317225
\(325\) 15.7478 0.873531
\(326\) 17.4698 0.967565
\(327\) −9.01915 −0.498760
\(328\) 82.0840 4.53233
\(329\) 29.6631 1.63538
\(330\) 3.77227 0.207657
\(331\) 32.6427 1.79421 0.897104 0.441820i \(-0.145667\pi\)
0.897104 + 0.441820i \(0.145667\pi\)
\(332\) 36.3867 1.99698
\(333\) −5.29347 −0.290081
\(334\) 20.3012 1.11083
\(335\) 2.25187 0.123033
\(336\) 46.4661 2.53494
\(337\) 0.144926 0.00789460 0.00394730 0.999992i \(-0.498744\pi\)
0.00394730 + 0.999992i \(0.498744\pi\)
\(338\) 7.36668 0.400694
\(339\) 11.7906 0.640376
\(340\) 1.84424 0.100018
\(341\) −4.52855 −0.245235
\(342\) −3.83191 −0.207206
\(343\) 18.0858 0.976540
\(344\) −113.897 −6.14090
\(345\) −1.53444 −0.0826114
\(346\) 40.8666 2.19700
\(347\) 15.4928 0.831694 0.415847 0.909434i \(-0.363485\pi\)
0.415847 + 0.909434i \(0.363485\pi\)
\(348\) −6.73561 −0.361066
\(349\) −36.9254 −1.97657 −0.988285 0.152621i \(-0.951229\pi\)
−0.988285 + 0.152621i \(0.951229\pi\)
\(350\) −36.7571 −1.96475
\(351\) 3.21667 0.171693
\(352\) 114.044 6.07857
\(353\) 19.1010 1.01664 0.508322 0.861167i \(-0.330266\pi\)
0.508322 + 0.861167i \(0.330266\pi\)
\(354\) −26.5594 −1.41162
\(355\) 1.73943 0.0923193
\(356\) 70.3981 3.73109
\(357\) −2.70395 −0.143108
\(358\) 39.0148 2.06200
\(359\) −35.3630 −1.86639 −0.933195 0.359371i \(-0.882991\pi\)
−0.933195 + 0.359371i \(0.882991\pi\)
\(360\) 3.32724 0.175361
\(361\) −17.0955 −0.899765
\(362\) 29.3533 1.54278
\(363\) −6.69274 −0.351278
\(364\) 49.6644 2.60312
\(365\) 2.64131 0.138252
\(366\) −35.3403 −1.84727
\(367\) −29.7272 −1.55174 −0.775872 0.630890i \(-0.782690\pi\)
−0.775872 + 0.630890i \(0.782690\pi\)
\(368\) −81.6413 −4.25585
\(369\) −7.96803 −0.414799
\(370\) −4.74729 −0.246800
\(371\) 9.37847 0.486906
\(372\) −6.14753 −0.318735
\(373\) −8.59073 −0.444811 −0.222405 0.974954i \(-0.571391\pi\)
−0.222405 + 0.974954i \(0.571391\pi\)
\(374\) −11.6795 −0.603935
\(375\) −3.19612 −0.165047
\(376\) 113.012 5.82816
\(377\) −3.79440 −0.195422
\(378\) −7.50806 −0.386173
\(379\) −11.0870 −0.569501 −0.284750 0.958602i \(-0.591911\pi\)
−0.284750 + 0.958602i \(0.591911\pi\)
\(380\) −2.54509 −0.130560
\(381\) −5.14488 −0.263580
\(382\) 6.58777 0.337060
\(383\) −22.3446 −1.14176 −0.570878 0.821035i \(-0.693397\pi\)
−0.570878 + 0.821035i \(0.693397\pi\)
\(384\) 59.3833 3.03039
\(385\) −3.67345 −0.187216
\(386\) 62.8027 3.19657
\(387\) 11.0562 0.562016
\(388\) 39.4671 2.00364
\(389\) −8.28320 −0.419975 −0.209987 0.977704i \(-0.567342\pi\)
−0.209987 + 0.977704i \(0.567342\pi\)
\(390\) 2.88477 0.146076
\(391\) 4.75086 0.240261
\(392\) −3.20754 −0.162005
\(393\) −14.5680 −0.734858
\(394\) −41.3185 −2.08159
\(395\) −0.322981 −0.0162509
\(396\) −24.0180 −1.20695
\(397\) −10.7858 −0.541324 −0.270662 0.962674i \(-0.587243\pi\)
−0.270662 + 0.962674i \(0.587243\pi\)
\(398\) 5.61164 0.281286
\(399\) 3.73152 0.186810
\(400\) −84.1300 −4.20650
\(401\) −15.5146 −0.774761 −0.387381 0.921920i \(-0.626620\pi\)
−0.387381 + 0.921920i \(0.626620\pi\)
\(402\) −19.3595 −0.965565
\(403\) −3.46312 −0.172510
\(404\) −0.205220 −0.0102101
\(405\) −0.322981 −0.0160491
\(406\) 8.85655 0.439543
\(407\) 22.2658 1.10367
\(408\) −10.3017 −0.510009
\(409\) 10.1806 0.503398 0.251699 0.967806i \(-0.419011\pi\)
0.251699 + 0.967806i \(0.419011\pi\)
\(410\) −7.14589 −0.352910
\(411\) 15.2209 0.750792
\(412\) 25.2144 1.24223
\(413\) 25.8636 1.27267
\(414\) 13.1917 0.648337
\(415\) −2.05816 −0.101031
\(416\) 87.2131 4.27598
\(417\) 12.7423 0.623995
\(418\) 16.1181 0.788361
\(419\) 22.9032 1.11889 0.559447 0.828866i \(-0.311013\pi\)
0.559447 + 0.828866i \(0.311013\pi\)
\(420\) −4.98673 −0.243327
\(421\) −31.4457 −1.53257 −0.766284 0.642502i \(-0.777896\pi\)
−0.766284 + 0.642502i \(0.777896\pi\)
\(422\) 25.6600 1.24911
\(423\) −10.9703 −0.533394
\(424\) 35.7306 1.73523
\(425\) 4.89568 0.237476
\(426\) −14.9540 −0.724525
\(427\) 34.4145 1.66543
\(428\) −58.6809 −2.83645
\(429\) −13.5302 −0.653244
\(430\) 9.91538 0.478162
\(431\) 13.7981 0.664631 0.332315 0.943168i \(-0.392170\pi\)
0.332315 + 0.943168i \(0.392170\pi\)
\(432\) −17.1845 −0.826791
\(433\) 29.9389 1.43877 0.719385 0.694612i \(-0.244424\pi\)
0.719385 + 0.694612i \(0.244424\pi\)
\(434\) 8.08330 0.388011
\(435\) 0.380990 0.0182671
\(436\) 51.4998 2.46639
\(437\) −6.55631 −0.313631
\(438\) −22.7076 −1.08501
\(439\) 23.9078 1.14106 0.570528 0.821278i \(-0.306738\pi\)
0.570528 + 0.821278i \(0.306738\pi\)
\(440\) −13.9953 −0.667200
\(441\) 0.311361 0.0148267
\(442\) −8.93172 −0.424838
\(443\) 21.6491 1.02858 0.514291 0.857616i \(-0.328055\pi\)
0.514291 + 0.857616i \(0.328055\pi\)
\(444\) 30.2260 1.43446
\(445\) −3.98197 −0.188764
\(446\) −23.1754 −1.09739
\(447\) 8.30491 0.392809
\(448\) −110.633 −5.22690
\(449\) −25.7595 −1.21566 −0.607832 0.794065i \(-0.707961\pi\)
−0.607832 + 0.794065i \(0.707961\pi\)
\(450\) 13.5938 0.640819
\(451\) 33.5157 1.57819
\(452\) −67.3247 −3.16669
\(453\) −14.8951 −0.699834
\(454\) 51.0714 2.39690
\(455\) −2.80920 −0.131697
\(456\) 14.2166 0.665752
\(457\) 6.57430 0.307533 0.153767 0.988107i \(-0.450860\pi\)
0.153767 + 0.988107i \(0.450860\pi\)
\(458\) 41.7184 1.94937
\(459\) 1.00000 0.0466760
\(460\) 8.76171 0.408517
\(461\) −30.7661 −1.43292 −0.716460 0.697629i \(-0.754239\pi\)
−0.716460 + 0.697629i \(0.754239\pi\)
\(462\) 31.5809 1.46928
\(463\) 27.3687 1.27193 0.635966 0.771717i \(-0.280602\pi\)
0.635966 + 0.771717i \(0.280602\pi\)
\(464\) 20.2710 0.941056
\(465\) 0.347727 0.0161254
\(466\) −58.3186 −2.70156
\(467\) 2.36036 0.109225 0.0546123 0.998508i \(-0.482608\pi\)
0.0546123 + 0.998508i \(0.482608\pi\)
\(468\) −18.3673 −0.849030
\(469\) 18.8523 0.870520
\(470\) −9.83837 −0.453810
\(471\) 7.55980 0.348337
\(472\) 98.5366 4.53552
\(473\) −46.5052 −2.13831
\(474\) 2.77670 0.127538
\(475\) −6.75617 −0.309994
\(476\) 15.4397 0.707677
\(477\) −3.46843 −0.158809
\(478\) 51.3541 2.34888
\(479\) −17.6438 −0.806167 −0.403083 0.915163i \(-0.632062\pi\)
−0.403083 + 0.915163i \(0.632062\pi\)
\(480\) −8.75694 −0.399698
\(481\) 17.0274 0.776381
\(482\) −48.9383 −2.22908
\(483\) −12.8461 −0.584518
\(484\) 38.2159 1.73709
\(485\) −2.23240 −0.101368
\(486\) 2.77670 0.125954
\(487\) −5.71845 −0.259128 −0.129564 0.991571i \(-0.541358\pi\)
−0.129564 + 0.991571i \(0.541358\pi\)
\(488\) 131.114 5.93526
\(489\) 6.29159 0.284516
\(490\) 0.279235 0.0126145
\(491\) 10.3947 0.469107 0.234554 0.972103i \(-0.424637\pi\)
0.234554 + 0.972103i \(0.424637\pi\)
\(492\) 45.4978 2.05120
\(493\) −1.17961 −0.0531268
\(494\) 12.3260 0.554573
\(495\) 1.35855 0.0610621
\(496\) 18.5012 0.830726
\(497\) 14.5623 0.653207
\(498\) 17.6942 0.792897
\(499\) 20.1594 0.902461 0.451230 0.892407i \(-0.350985\pi\)
0.451230 + 0.892407i \(0.350985\pi\)
\(500\) 18.2500 0.816164
\(501\) 7.31128 0.326644
\(502\) −41.3852 −1.84711
\(503\) 32.1849 1.43505 0.717527 0.696531i \(-0.245274\pi\)
0.717527 + 0.696531i \(0.245274\pi\)
\(504\) 27.8552 1.24077
\(505\) 0.0116080 0.000516549 0
\(506\) −55.4879 −2.46674
\(507\) 2.65304 0.117825
\(508\) 29.3775 1.30342
\(509\) 41.3316 1.83199 0.915995 0.401189i \(-0.131403\pi\)
0.915995 + 0.401189i \(0.131403\pi\)
\(510\) 0.896820 0.0397119
\(511\) 22.1127 0.978207
\(512\) −111.863 −4.94370
\(513\) −1.38003 −0.0609296
\(514\) −28.7003 −1.26591
\(515\) −1.42622 −0.0628468
\(516\) −63.1311 −2.77919
\(517\) 46.1440 2.02941
\(518\) −39.7437 −1.74624
\(519\) 14.7177 0.646036
\(520\) −10.7026 −0.469342
\(521\) 5.84865 0.256234 0.128117 0.991759i \(-0.459107\pi\)
0.128117 + 0.991759i \(0.459107\pi\)
\(522\) −3.27541 −0.143361
\(523\) 29.2824 1.28043 0.640216 0.768195i \(-0.278845\pi\)
0.640216 + 0.768195i \(0.278845\pi\)
\(524\) 83.1839 3.63391
\(525\) −13.2377 −0.577740
\(526\) −76.0208 −3.31466
\(527\) −1.07662 −0.0468982
\(528\) 72.2828 3.14571
\(529\) −0.429303 −0.0186653
\(530\) −3.11056 −0.135114
\(531\) −9.56511 −0.415091
\(532\) −21.3072 −0.923783
\(533\) 25.6305 1.11018
\(534\) 34.2334 1.48142
\(535\) 3.31921 0.143502
\(536\) 71.8247 3.10235
\(537\) 14.0508 0.606337
\(538\) −24.6043 −1.06077
\(539\) −1.30967 −0.0564114
\(540\) 1.84424 0.0793633
\(541\) 13.5506 0.582587 0.291293 0.956634i \(-0.405914\pi\)
0.291293 + 0.956634i \(0.405914\pi\)
\(542\) −28.5235 −1.22519
\(543\) 10.5713 0.453658
\(544\) 27.1129 1.16245
\(545\) −2.91301 −0.124780
\(546\) 24.1509 1.03356
\(547\) −17.3102 −0.740130 −0.370065 0.929006i \(-0.620665\pi\)
−0.370065 + 0.929006i \(0.620665\pi\)
\(548\) −86.9120 −3.71270
\(549\) −12.7275 −0.543195
\(550\) −57.1794 −2.43814
\(551\) 1.62789 0.0693503
\(552\) −48.9418 −2.08310
\(553\) −2.70395 −0.114984
\(554\) 46.9815 1.99605
\(555\) −1.70969 −0.0725723
\(556\) −72.7593 −3.08568
\(557\) 19.5984 0.830410 0.415205 0.909728i \(-0.363710\pi\)
0.415205 + 0.909728i \(0.363710\pi\)
\(558\) −2.98944 −0.126553
\(559\) −35.5640 −1.50420
\(560\) 15.0077 0.634190
\(561\) −4.20627 −0.177589
\(562\) −80.9183 −3.41333
\(563\) 13.2572 0.558724 0.279362 0.960186i \(-0.409877\pi\)
0.279362 + 0.960186i \(0.409877\pi\)
\(564\) 62.6408 2.63765
\(565\) 3.80813 0.160209
\(566\) −1.61183 −0.0677501
\(567\) −2.70395 −0.113555
\(568\) 55.4801 2.32789
\(569\) 17.7645 0.744727 0.372363 0.928087i \(-0.378548\pi\)
0.372363 + 0.928087i \(0.378548\pi\)
\(570\) −1.23763 −0.0518388
\(571\) −19.2876 −0.807161 −0.403581 0.914944i \(-0.632234\pi\)
−0.403581 + 0.914944i \(0.632234\pi\)
\(572\) 77.2580 3.23032
\(573\) 2.37252 0.0991135
\(574\) −59.8244 −2.49702
\(575\) 23.2587 0.969956
\(576\) 40.9152 1.70480
\(577\) −10.8820 −0.453023 −0.226512 0.974008i \(-0.572732\pi\)
−0.226512 + 0.974008i \(0.572732\pi\)
\(578\) −2.77670 −0.115495
\(579\) 22.6178 0.939962
\(580\) −2.17547 −0.0903316
\(581\) −17.2307 −0.714849
\(582\) 19.1922 0.795540
\(583\) 14.5892 0.604222
\(584\) 84.2461 3.48613
\(585\) 1.03892 0.0429542
\(586\) 56.5684 2.33682
\(587\) −26.6493 −1.09994 −0.549968 0.835186i \(-0.685360\pi\)
−0.549968 + 0.835186i \(0.685360\pi\)
\(588\) −1.77788 −0.0733187
\(589\) 1.48576 0.0612196
\(590\) −8.57819 −0.353158
\(591\) −14.8804 −0.612099
\(592\) −90.9658 −3.73867
\(593\) −22.8892 −0.939947 −0.469974 0.882680i \(-0.655737\pi\)
−0.469974 + 0.882680i \(0.655737\pi\)
\(594\) −11.6795 −0.479218
\(595\) −0.873325 −0.0358028
\(596\) −47.4214 −1.94246
\(597\) 2.02098 0.0827131
\(598\) −42.4334 −1.73523
\(599\) −27.0471 −1.10511 −0.552557 0.833475i \(-0.686348\pi\)
−0.552557 + 0.833475i \(0.686348\pi\)
\(600\) −50.4337 −2.05895
\(601\) −21.8731 −0.892221 −0.446111 0.894978i \(-0.647191\pi\)
−0.446111 + 0.894978i \(0.647191\pi\)
\(602\) 83.0102 3.38324
\(603\) −6.97214 −0.283927
\(604\) 85.0518 3.46071
\(605\) −2.16163 −0.0878827
\(606\) −0.0997951 −0.00405390
\(607\) 15.0848 0.612272 0.306136 0.951988i \(-0.400964\pi\)
0.306136 + 0.951988i \(0.400964\pi\)
\(608\) −37.4164 −1.51744
\(609\) 3.18960 0.129249
\(610\) −11.4142 −0.462149
\(611\) 35.2878 1.42759
\(612\) −5.71004 −0.230815
\(613\) −5.33957 −0.215663 −0.107832 0.994169i \(-0.534391\pi\)
−0.107832 + 0.994169i \(0.534391\pi\)
\(614\) −35.5796 −1.43587
\(615\) −2.57352 −0.103774
\(616\) −117.167 −4.72078
\(617\) −23.6745 −0.953100 −0.476550 0.879147i \(-0.658113\pi\)
−0.476550 + 0.879147i \(0.658113\pi\)
\(618\) 12.2613 0.493224
\(619\) 0.369405 0.0148477 0.00742383 0.999972i \(-0.497637\pi\)
0.00742383 + 0.999972i \(0.497637\pi\)
\(620\) −1.98554 −0.0797410
\(621\) 4.75086 0.190646
\(622\) −85.0304 −3.40941
\(623\) −33.3365 −1.33560
\(624\) 55.2769 2.21285
\(625\) 23.4461 0.937845
\(626\) 31.5309 1.26023
\(627\) 5.80476 0.231820
\(628\) −43.1668 −1.72254
\(629\) 5.29347 0.211065
\(630\) −2.42496 −0.0966127
\(631\) 7.20624 0.286876 0.143438 0.989659i \(-0.454184\pi\)
0.143438 + 0.989659i \(0.454184\pi\)
\(632\) −10.3017 −0.409778
\(633\) 9.24121 0.367305
\(634\) −21.6925 −0.861520
\(635\) −1.66170 −0.0659425
\(636\) 19.8049 0.785315
\(637\) −1.00154 −0.0396826
\(638\) 13.7773 0.545447
\(639\) −5.38554 −0.213049
\(640\) 19.1797 0.758143
\(641\) −24.4041 −0.963905 −0.481953 0.876197i \(-0.660072\pi\)
−0.481953 + 0.876197i \(0.660072\pi\)
\(642\) −28.5355 −1.12621
\(643\) −4.48266 −0.176779 −0.0883895 0.996086i \(-0.528172\pi\)
−0.0883895 + 0.996086i \(0.528172\pi\)
\(644\) 73.3519 2.89047
\(645\) 3.57093 0.140605
\(646\) 3.83191 0.150765
\(647\) 22.9291 0.901434 0.450717 0.892667i \(-0.351168\pi\)
0.450717 + 0.892667i \(0.351168\pi\)
\(648\) −10.3017 −0.404688
\(649\) 40.2335 1.57930
\(650\) −43.7269 −1.71511
\(651\) 2.91112 0.114096
\(652\) −35.9253 −1.40694
\(653\) 13.0680 0.511392 0.255696 0.966757i \(-0.417695\pi\)
0.255696 + 0.966757i \(0.417695\pi\)
\(654\) 25.0435 0.979277
\(655\) −4.70518 −0.183847
\(656\) −136.927 −5.34609
\(657\) −8.17791 −0.319051
\(658\) −82.3655 −3.21094
\(659\) 31.0634 1.21006 0.605030 0.796203i \(-0.293161\pi\)
0.605030 + 0.796203i \(0.293161\pi\)
\(660\) −7.75736 −0.301955
\(661\) −19.4967 −0.758335 −0.379168 0.925328i \(-0.623790\pi\)
−0.379168 + 0.925328i \(0.623790\pi\)
\(662\) −90.6390 −3.52278
\(663\) −3.21667 −0.124925
\(664\) −65.6464 −2.54757
\(665\) 1.20521 0.0467361
\(666\) 14.6984 0.569550
\(667\) −5.60415 −0.216994
\(668\) −41.7477 −1.61527
\(669\) −8.34638 −0.322690
\(670\) −6.25276 −0.241565
\(671\) 53.5352 2.06670
\(672\) −73.3119 −2.82807
\(673\) 10.5377 0.406197 0.203098 0.979158i \(-0.434899\pi\)
0.203098 + 0.979158i \(0.434899\pi\)
\(674\) −0.402415 −0.0155004
\(675\) 4.89568 0.188435
\(676\) −15.1490 −0.582652
\(677\) 43.3226 1.66502 0.832511 0.554009i \(-0.186903\pi\)
0.832511 + 0.554009i \(0.186903\pi\)
\(678\) −32.7388 −1.25733
\(679\) −18.6894 −0.717232
\(680\) −3.32724 −0.127594
\(681\) 18.3929 0.704816
\(682\) 12.5744 0.481499
\(683\) 5.60647 0.214526 0.107263 0.994231i \(-0.465791\pi\)
0.107263 + 0.994231i \(0.465791\pi\)
\(684\) 7.88001 0.301300
\(685\) 4.91606 0.187833
\(686\) −50.2187 −1.91736
\(687\) 15.0245 0.573219
\(688\) 189.995 7.24348
\(689\) 11.1568 0.425040
\(690\) 4.26067 0.162201
\(691\) −34.5728 −1.31521 −0.657607 0.753362i \(-0.728431\pi\)
−0.657607 + 0.753362i \(0.728431\pi\)
\(692\) −84.0388 −3.19467
\(693\) 11.3736 0.432046
\(694\) −43.0187 −1.63297
\(695\) 4.11553 0.156111
\(696\) 12.1519 0.460617
\(697\) 7.96803 0.301811
\(698\) 102.531 3.88084
\(699\) −21.0029 −0.794401
\(700\) 75.5878 2.85695
\(701\) 43.3848 1.63862 0.819311 0.573349i \(-0.194356\pi\)
0.819311 + 0.573349i \(0.194356\pi\)
\(702\) −8.93172 −0.337106
\(703\) −7.30513 −0.275518
\(704\) −172.100 −6.48628
\(705\) −3.54319 −0.133444
\(706\) −53.0377 −1.99610
\(707\) 0.0971806 0.00365485
\(708\) 54.6172 2.05264
\(709\) 1.24770 0.0468585 0.0234292 0.999725i \(-0.492542\pi\)
0.0234292 + 0.999725i \(0.492542\pi\)
\(710\) −4.82986 −0.181262
\(711\) 1.00000 0.0375029
\(712\) −127.007 −4.75980
\(713\) −5.11486 −0.191553
\(714\) 7.50806 0.280982
\(715\) −4.37000 −0.163429
\(716\) −80.2307 −2.99836
\(717\) 18.4947 0.690696
\(718\) 98.1924 3.66451
\(719\) 45.3627 1.69174 0.845872 0.533385i \(-0.179080\pi\)
0.845872 + 0.533385i \(0.179080\pi\)
\(720\) −5.55027 −0.206846
\(721\) −11.9401 −0.444673
\(722\) 47.4691 1.76662
\(723\) −17.6246 −0.655467
\(724\) −60.3627 −2.24336
\(725\) −5.77498 −0.214477
\(726\) 18.5837 0.689707
\(727\) −30.4879 −1.13073 −0.565366 0.824840i \(-0.691265\pi\)
−0.565366 + 0.824840i \(0.691265\pi\)
\(728\) −89.6011 −3.32084
\(729\) 1.00000 0.0370370
\(730\) −7.33411 −0.271448
\(731\) −11.0562 −0.408927
\(732\) 72.6744 2.68612
\(733\) 8.39289 0.309998 0.154999 0.987915i \(-0.450462\pi\)
0.154999 + 0.987915i \(0.450462\pi\)
\(734\) 82.5433 3.04673
\(735\) 0.100564 0.00370934
\(736\) 128.810 4.74798
\(737\) 29.3267 1.08026
\(738\) 22.1248 0.814425
\(739\) 4.34300 0.159760 0.0798800 0.996804i \(-0.474546\pi\)
0.0798800 + 0.996804i \(0.474546\pi\)
\(740\) 9.76241 0.358873
\(741\) 4.43909 0.163074
\(742\) −26.0412 −0.956002
\(743\) −21.1018 −0.774151 −0.387075 0.922048i \(-0.626515\pi\)
−0.387075 + 0.922048i \(0.626515\pi\)
\(744\) 11.0910 0.406614
\(745\) 2.68233 0.0982729
\(746\) 23.8538 0.873351
\(747\) 6.37240 0.233154
\(748\) 24.0180 0.878186
\(749\) 27.7879 1.01535
\(750\) 8.87465 0.324056
\(751\) −47.8747 −1.74697 −0.873487 0.486848i \(-0.838146\pi\)
−0.873487 + 0.486848i \(0.838146\pi\)
\(752\) −188.519 −6.87459
\(753\) −14.9045 −0.543149
\(754\) 10.5359 0.383695
\(755\) −4.81084 −0.175084
\(756\) 15.4397 0.561536
\(757\) 14.1261 0.513422 0.256711 0.966488i \(-0.417361\pi\)
0.256711 + 0.966488i \(0.417361\pi\)
\(758\) 30.7852 1.11817
\(759\) −19.9834 −0.725353
\(760\) 4.59168 0.166558
\(761\) −44.8273 −1.62499 −0.812493 0.582970i \(-0.801890\pi\)
−0.812493 + 0.582970i \(0.801890\pi\)
\(762\) 14.2858 0.517519
\(763\) −24.3874 −0.882882
\(764\) −13.5472 −0.490121
\(765\) 0.322981 0.0116774
\(766\) 62.0442 2.24175
\(767\) 30.7678 1.11096
\(768\) −83.0590 −2.99713
\(769\) −45.5633 −1.64305 −0.821527 0.570169i \(-0.806878\pi\)
−0.821527 + 0.570169i \(0.806878\pi\)
\(770\) 10.2000 0.367584
\(771\) −10.3361 −0.372246
\(772\) −129.148 −4.64816
\(773\) 12.0215 0.432385 0.216193 0.976351i \(-0.430636\pi\)
0.216193 + 0.976351i \(0.430636\pi\)
\(774\) −30.6996 −1.10347
\(775\) −5.27078 −0.189332
\(776\) −71.2038 −2.55607
\(777\) −14.3133 −0.513487
\(778\) 22.9999 0.824587
\(779\) −10.9961 −0.393975
\(780\) −5.93230 −0.212410
\(781\) 22.6531 0.810591
\(782\) −13.1917 −0.471734
\(783\) −1.17961 −0.0421557
\(784\) 5.35059 0.191092
\(785\) 2.44167 0.0871470
\(786\) 40.4509 1.44284
\(787\) −0.683217 −0.0243541 −0.0121770 0.999926i \(-0.503876\pi\)
−0.0121770 + 0.999926i \(0.503876\pi\)
\(788\) 84.9680 3.02686
\(789\) −27.3781 −0.974687
\(790\) 0.896820 0.0319074
\(791\) 31.8811 1.13356
\(792\) 43.3316 1.53972
\(793\) 40.9401 1.45382
\(794\) 29.9489 1.06285
\(795\) −1.12024 −0.0397307
\(796\) −11.5399 −0.409020
\(797\) 29.2407 1.03576 0.517879 0.855454i \(-0.326722\pi\)
0.517879 + 0.855454i \(0.326722\pi\)
\(798\) −10.3613 −0.366786
\(799\) 10.9703 0.388101
\(800\) 132.736 4.69293
\(801\) 12.3288 0.435617
\(802\) 43.0793 1.52118
\(803\) 34.3985 1.21390
\(804\) 39.8112 1.40403
\(805\) −4.14905 −0.146235
\(806\) 9.61604 0.338711
\(807\) −8.86101 −0.311922
\(808\) 0.370244 0.0130251
\(809\) 5.21190 0.183241 0.0916203 0.995794i \(-0.470795\pi\)
0.0916203 + 0.995794i \(0.470795\pi\)
\(810\) 0.896820 0.0315110
\(811\) 46.6702 1.63881 0.819406 0.573214i \(-0.194304\pi\)
0.819406 + 0.573214i \(0.194304\pi\)
\(812\) −18.2128 −0.639143
\(813\) −10.2725 −0.360271
\(814\) −61.8254 −2.16698
\(815\) 2.03206 0.0711801
\(816\) 17.1845 0.601579
\(817\) 15.2578 0.533802
\(818\) −28.2684 −0.988381
\(819\) 8.69772 0.303923
\(820\) 14.6949 0.513169
\(821\) −8.32703 −0.290615 −0.145308 0.989387i \(-0.546417\pi\)
−0.145308 + 0.989387i \(0.546417\pi\)
\(822\) −42.2638 −1.47412
\(823\) 8.52116 0.297029 0.148514 0.988910i \(-0.452551\pi\)
0.148514 + 0.988910i \(0.452551\pi\)
\(824\) −45.4901 −1.58472
\(825\) −20.5926 −0.716942
\(826\) −71.8154 −2.49878
\(827\) −1.12600 −0.0391549 −0.0195774 0.999808i \(-0.506232\pi\)
−0.0195774 + 0.999808i \(0.506232\pi\)
\(828\) −27.1276 −0.942751
\(829\) −4.45797 −0.154832 −0.0774159 0.996999i \(-0.524667\pi\)
−0.0774159 + 0.996999i \(0.524667\pi\)
\(830\) 5.71490 0.198367
\(831\) 16.9199 0.586946
\(832\) −131.611 −4.56278
\(833\) −0.311361 −0.0107880
\(834\) −35.3816 −1.22516
\(835\) 2.36140 0.0817197
\(836\) −33.1455 −1.14636
\(837\) −1.07662 −0.0372133
\(838\) −63.5953 −2.19686
\(839\) 9.49170 0.327690 0.163845 0.986486i \(-0.447610\pi\)
0.163845 + 0.986486i \(0.447610\pi\)
\(840\) 8.99671 0.310416
\(841\) −27.6085 −0.952018
\(842\) 87.3150 3.00908
\(843\) −29.1419 −1.00370
\(844\) −52.7677 −1.81634
\(845\) 0.856880 0.0294776
\(846\) 30.4612 1.04728
\(847\) −18.0969 −0.621816
\(848\) −59.6033 −2.04679
\(849\) −0.580483 −0.0199221
\(850\) −13.5938 −0.466264
\(851\) 25.1486 0.862082
\(852\) 30.7517 1.05354
\(853\) −33.7937 −1.15708 −0.578538 0.815656i \(-0.696376\pi\)
−0.578538 + 0.815656i \(0.696376\pi\)
\(854\) −95.5585 −3.26995
\(855\) −0.445722 −0.0152434
\(856\) 105.868 3.61850
\(857\) 41.5764 1.42022 0.710112 0.704089i \(-0.248644\pi\)
0.710112 + 0.704089i \(0.248644\pi\)
\(858\) 37.5692 1.28259
\(859\) −15.3064 −0.522246 −0.261123 0.965306i \(-0.584093\pi\)
−0.261123 + 0.965306i \(0.584093\pi\)
\(860\) −20.3901 −0.695298
\(861\) −21.5452 −0.734258
\(862\) −38.3131 −1.30495
\(863\) −20.6599 −0.703271 −0.351636 0.936137i \(-0.614374\pi\)
−0.351636 + 0.936137i \(0.614374\pi\)
\(864\) 27.1129 0.922399
\(865\) 4.75354 0.161625
\(866\) −83.1311 −2.82491
\(867\) −1.00000 −0.0339618
\(868\) −16.6226 −0.564209
\(869\) −4.20627 −0.142688
\(870\) −1.05789 −0.0358660
\(871\) 22.4271 0.759912
\(872\) −92.9123 −3.14641
\(873\) 6.91187 0.233931
\(874\) 18.2049 0.615789
\(875\) −8.64215 −0.292158
\(876\) 46.6962 1.57772
\(877\) −21.9803 −0.742222 −0.371111 0.928589i \(-0.621023\pi\)
−0.371111 + 0.928589i \(0.621023\pi\)
\(878\) −66.3847 −2.24037
\(879\) 20.3726 0.687149
\(880\) 23.3460 0.786993
\(881\) −22.1315 −0.745629 −0.372814 0.927906i \(-0.621607\pi\)
−0.372814 + 0.927906i \(0.621607\pi\)
\(882\) −0.864554 −0.0291111
\(883\) 55.3958 1.86422 0.932109 0.362179i \(-0.117967\pi\)
0.932109 + 0.362179i \(0.117967\pi\)
\(884\) 18.3673 0.617760
\(885\) −3.08935 −0.103847
\(886\) −60.1131 −2.01954
\(887\) 40.3376 1.35441 0.677203 0.735797i \(-0.263192\pi\)
0.677203 + 0.735797i \(0.263192\pi\)
\(888\) −54.5316 −1.82996
\(889\) −13.9115 −0.466577
\(890\) 11.0567 0.370622
\(891\) −4.20627 −0.140915
\(892\) 47.6582 1.59571
\(893\) −15.1393 −0.506616
\(894\) −23.0602 −0.771249
\(895\) 4.53814 0.151693
\(896\) 160.570 5.36425
\(897\) −15.2820 −0.510250
\(898\) 71.5263 2.38686
\(899\) 1.26998 0.0423564
\(900\) −27.9546 −0.931819
\(901\) 3.46843 0.115550
\(902\) −93.0630 −3.09866
\(903\) 29.8953 0.994854
\(904\) 121.463 4.03978
\(905\) 3.41433 0.113496
\(906\) 41.3592 1.37407
\(907\) −15.7630 −0.523403 −0.261701 0.965149i \(-0.584284\pi\)
−0.261701 + 0.965149i \(0.584284\pi\)
\(908\) −105.024 −3.48535
\(909\) −0.0359402 −0.00119206
\(910\) 7.80029 0.258577
\(911\) −5.54103 −0.183582 −0.0917912 0.995778i \(-0.529259\pi\)
−0.0917912 + 0.995778i \(0.529259\pi\)
\(912\) −23.7151 −0.785285
\(913\) −26.8041 −0.887085
\(914\) −18.2549 −0.603817
\(915\) −4.11073 −0.135896
\(916\) −85.7904 −2.83459
\(917\) −39.3912 −1.30081
\(918\) −2.77670 −0.0916446
\(919\) −56.7047 −1.87052 −0.935258 0.353967i \(-0.884832\pi\)
−0.935258 + 0.353967i \(0.884832\pi\)
\(920\) −15.8073 −0.521150
\(921\) −12.8136 −0.422223
\(922\) 85.4281 2.81342
\(923\) 17.3235 0.570210
\(924\) −64.9436 −2.13649
\(925\) 25.9152 0.852086
\(926\) −75.9946 −2.49734
\(927\) 4.41580 0.145034
\(928\) −31.9825 −1.04988
\(929\) −53.0109 −1.73923 −0.869616 0.493729i \(-0.835633\pi\)
−0.869616 + 0.493729i \(0.835633\pi\)
\(930\) −0.965532 −0.0316610
\(931\) 0.429686 0.0140824
\(932\) 119.927 3.92835
\(933\) −30.6229 −1.00255
\(934\) −6.55401 −0.214454
\(935\) −1.35855 −0.0444292
\(936\) 33.1371 1.08312
\(937\) 25.1532 0.821719 0.410859 0.911699i \(-0.365229\pi\)
0.410859 + 0.911699i \(0.365229\pi\)
\(938\) −52.3472 −1.70920
\(939\) 11.3555 0.370574
\(940\) 20.2318 0.659888
\(941\) −7.94751 −0.259081 −0.129541 0.991574i \(-0.541350\pi\)
−0.129541 + 0.991574i \(0.541350\pi\)
\(942\) −20.9913 −0.683932
\(943\) 37.8550 1.23273
\(944\) −164.372 −5.34985
\(945\) −0.873325 −0.0284093
\(946\) 129.131 4.19841
\(947\) 41.4271 1.34620 0.673099 0.739552i \(-0.264963\pi\)
0.673099 + 0.739552i \(0.264963\pi\)
\(948\) −5.71004 −0.185454
\(949\) 26.3056 0.853917
\(950\) 18.7598 0.608649
\(951\) −7.81235 −0.253333
\(952\) −27.8552 −0.902793
\(953\) −12.4697 −0.403934 −0.201967 0.979392i \(-0.564733\pi\)
−0.201967 + 0.979392i \(0.564733\pi\)
\(954\) 9.63078 0.311808
\(955\) 0.766279 0.0247962
\(956\) −105.605 −3.41552
\(957\) 4.96175 0.160391
\(958\) 48.9916 1.58285
\(959\) 41.1566 1.32902
\(960\) 13.2148 0.426506
\(961\) −29.8409 −0.962610
\(962\) −47.2798 −1.52436
\(963\) −10.2768 −0.331165
\(964\) 100.637 3.24131
\(965\) 7.30511 0.235160
\(966\) 35.6697 1.14766
\(967\) −24.6704 −0.793346 −0.396673 0.917960i \(-0.629835\pi\)
−0.396673 + 0.917960i \(0.629835\pi\)
\(968\) −68.9464 −2.21602
\(969\) 1.38003 0.0443328
\(970\) 6.19870 0.199028
\(971\) −34.5670 −1.10931 −0.554655 0.832081i \(-0.687150\pi\)
−0.554655 + 0.832081i \(0.687150\pi\)
\(972\) −5.71004 −0.183150
\(973\) 34.4547 1.10457
\(974\) 15.8784 0.508776
\(975\) −15.7478 −0.504333
\(976\) −218.715 −7.00091
\(977\) −34.2804 −1.09673 −0.548364 0.836240i \(-0.684749\pi\)
−0.548364 + 0.836240i \(0.684749\pi\)
\(978\) −17.4698 −0.558624
\(979\) −51.8584 −1.65740
\(980\) −0.574223 −0.0183429
\(981\) 9.01915 0.287959
\(982\) −28.8630 −0.921055
\(983\) −61.0530 −1.94729 −0.973643 0.228076i \(-0.926757\pi\)
−0.973643 + 0.228076i \(0.926757\pi\)
\(984\) −82.0840 −2.61674
\(985\) −4.80610 −0.153135
\(986\) 3.27541 0.104310
\(987\) −29.6631 −0.944188
\(988\) −25.3474 −0.806407
\(989\) −52.5263 −1.67024
\(990\) −3.77227 −0.119891
\(991\) −56.8013 −1.80435 −0.902177 0.431367i \(-0.858031\pi\)
−0.902177 + 0.431367i \(0.858031\pi\)
\(992\) −29.1902 −0.926789
\(993\) −32.6427 −1.03589
\(994\) −40.4350 −1.28252
\(995\) 0.652737 0.0206932
\(996\) −36.3867 −1.15296
\(997\) −36.5206 −1.15662 −0.578310 0.815817i \(-0.696288\pi\)
−0.578310 + 0.815817i \(0.696288\pi\)
\(998\) −55.9767 −1.77191
\(999\) 5.29347 0.167478
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.1.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.1 32 1.1 even 1 trivial