Properties

Label 4026.2.a.u.1.3
Level 4026
Weight 2
Character 4026.1
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.9176805.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.689091\) of \(x^{5} - x^{4} - 12 x^{3} + 7 x^{2} + 30 x - 20\)
Character \(\chi\) \(=\) 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.689091 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.15959 q^{13} -4.91945 q^{14} -0.689091 q^{15} +1.00000 q^{16} +1.70520 q^{17} -1.00000 q^{18} -3.32636 q^{19} -0.689091 q^{20} +4.91945 q^{21} +1.00000 q^{22} -0.135207 q^{23} -1.00000 q^{24} -4.52515 q^{25} -2.15959 q^{26} +1.00000 q^{27} +4.91945 q^{28} +4.83606 q^{29} +0.689091 q^{30} +2.55388 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.70520 q^{34} -3.38995 q^{35} +1.00000 q^{36} +7.89072 q^{37} +3.32636 q^{38} +2.15959 q^{39} +0.689091 q^{40} -7.38995 q^{41} -4.91945 q^{42} +3.02873 q^{43} -1.00000 q^{44} -0.689091 q^{45} +0.135207 q^{46} +10.3738 q^{47} +1.00000 q^{48} +17.2010 q^{49} +4.52515 q^{50} +1.70520 q^{51} +2.15959 q^{52} -1.60571 q^{53} -1.00000 q^{54} +0.689091 q^{55} -4.91945 q^{56} -3.32636 q^{57} -4.83606 q^{58} -1.90614 q^{59} -0.689091 q^{60} -1.00000 q^{61} -2.55388 q^{62} +4.91945 q^{63} +1.00000 q^{64} -1.48815 q^{65} +1.00000 q^{66} +12.0862 q^{67} +1.70520 q^{68} -0.135207 q^{69} +3.38995 q^{70} -9.93207 q^{71} -1.00000 q^{72} -1.42566 q^{73} -7.89072 q^{74} -4.52515 q^{75} -3.32636 q^{76} -4.91945 q^{77} -2.15959 q^{78} +0.110825 q^{79} -0.689091 q^{80} +1.00000 q^{81} +7.38995 q^{82} +14.1106 q^{83} +4.91945 q^{84} -1.17504 q^{85} -3.02873 q^{86} +4.83606 q^{87} +1.00000 q^{88} +3.25345 q^{89} +0.689091 q^{90} +10.6240 q^{91} -0.135207 q^{92} +2.55388 q^{93} -10.3738 q^{94} +2.29216 q^{95} -1.00000 q^{96} -6.01545 q^{97} -17.2010 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + q^{10} - 5q^{11} + 5q^{12} + 2q^{13} + 3q^{14} - q^{15} + 5q^{16} + 6q^{17} - 5q^{18} + 7q^{19} - q^{20} - 3q^{21} + 5q^{22} - 12q^{23} - 5q^{24} - 2q^{26} + 5q^{27} - 3q^{28} + 4q^{29} + q^{30} - q^{31} - 5q^{32} - 5q^{33} - 6q^{34} + 17q^{35} + 5q^{36} + 3q^{37} - 7q^{38} + 2q^{39} + q^{40} - 3q^{41} + 3q^{42} + 24q^{43} - 5q^{44} - q^{45} + 12q^{46} + 18q^{47} + 5q^{48} + 26q^{49} + 6q^{51} + 2q^{52} - 13q^{53} - 5q^{54} + q^{55} + 3q^{56} + 7q^{57} - 4q^{58} - 16q^{59} - q^{60} - 5q^{61} + q^{62} - 3q^{63} + 5q^{64} + 4q^{65} + 5q^{66} + 18q^{67} + 6q^{68} - 12q^{69} - 17q^{70} - 31q^{71} - 5q^{72} + 8q^{73} - 3q^{74} + 7q^{76} + 3q^{77} - 2q^{78} + 32q^{79} - q^{80} + 5q^{81} + 3q^{82} + 8q^{83} - 3q^{84} + 29q^{85} - 24q^{86} + 4q^{87} + 5q^{88} + q^{89} + q^{90} - 3q^{91} - 12q^{92} - q^{93} - 18q^{94} + 33q^{95} - 5q^{96} - 4q^{97} - 26q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −0.689091 −0.308171 −0.154085 0.988058i \(-0.549243\pi\)
−0.154085 + 0.988058i \(0.549243\pi\)
\(6\) −1.00000 −0.408248
\(7\) 4.91945 1.85938 0.929688 0.368347i \(-0.120076\pi\)
0.929688 + 0.368347i \(0.120076\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.689091 0.217910
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 2.15959 0.598962 0.299481 0.954102i \(-0.403186\pi\)
0.299481 + 0.954102i \(0.403186\pi\)
\(14\) −4.91945 −1.31478
\(15\) −0.689091 −0.177922
\(16\) 1.00000 0.250000
\(17\) 1.70520 0.413572 0.206786 0.978386i \(-0.433700\pi\)
0.206786 + 0.978386i \(0.433700\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.32636 −0.763119 −0.381560 0.924344i \(-0.624613\pi\)
−0.381560 + 0.924344i \(0.624613\pi\)
\(20\) −0.689091 −0.154085
\(21\) 4.91945 1.07351
\(22\) 1.00000 0.213201
\(23\) −0.135207 −0.0281927 −0.0140963 0.999901i \(-0.504487\pi\)
−0.0140963 + 0.999901i \(0.504487\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.52515 −0.905031
\(26\) −2.15959 −0.423530
\(27\) 1.00000 0.192450
\(28\) 4.91945 0.929688
\(29\) 4.83606 0.898034 0.449017 0.893523i \(-0.351774\pi\)
0.449017 + 0.893523i \(0.351774\pi\)
\(30\) 0.689091 0.125810
\(31\) 2.55388 0.458691 0.229346 0.973345i \(-0.426341\pi\)
0.229346 + 0.973345i \(0.426341\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −1.70520 −0.292440
\(35\) −3.38995 −0.573006
\(36\) 1.00000 0.166667
\(37\) 7.89072 1.29723 0.648613 0.761118i \(-0.275349\pi\)
0.648613 + 0.761118i \(0.275349\pi\)
\(38\) 3.32636 0.539607
\(39\) 2.15959 0.345811
\(40\) 0.689091 0.108955
\(41\) −7.38995 −1.15412 −0.577058 0.816703i \(-0.695799\pi\)
−0.577058 + 0.816703i \(0.695799\pi\)
\(42\) −4.91945 −0.759087
\(43\) 3.02873 0.461877 0.230938 0.972968i \(-0.425820\pi\)
0.230938 + 0.972968i \(0.425820\pi\)
\(44\) −1.00000 −0.150756
\(45\) −0.689091 −0.102724
\(46\) 0.135207 0.0199352
\(47\) 10.3738 1.51318 0.756590 0.653890i \(-0.226864\pi\)
0.756590 + 0.653890i \(0.226864\pi\)
\(48\) 1.00000 0.144338
\(49\) 17.2010 2.45728
\(50\) 4.52515 0.639953
\(51\) 1.70520 0.238776
\(52\) 2.15959 0.299481
\(53\) −1.60571 −0.220561 −0.110280 0.993901i \(-0.535175\pi\)
−0.110280 + 0.993901i \(0.535175\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0.689091 0.0929170
\(56\) −4.91945 −0.657389
\(57\) −3.32636 −0.440587
\(58\) −4.83606 −0.635006
\(59\) −1.90614 −0.248158 −0.124079 0.992272i \(-0.539598\pi\)
−0.124079 + 0.992272i \(0.539598\pi\)
\(60\) −0.689091 −0.0889612
\(61\) −1.00000 −0.128037
\(62\) −2.55388 −0.324344
\(63\) 4.91945 0.619792
\(64\) 1.00000 0.125000
\(65\) −1.48815 −0.184583
\(66\) 1.00000 0.123091
\(67\) 12.0862 1.47657 0.738283 0.674491i \(-0.235637\pi\)
0.738283 + 0.674491i \(0.235637\pi\)
\(68\) 1.70520 0.206786
\(69\) −0.135207 −0.0162770
\(70\) 3.38995 0.405176
\(71\) −9.93207 −1.17872 −0.589360 0.807871i \(-0.700620\pi\)
−0.589360 + 0.807871i \(0.700620\pi\)
\(72\) −1.00000 −0.117851
\(73\) −1.42566 −0.166861 −0.0834303 0.996514i \(-0.526588\pi\)
−0.0834303 + 0.996514i \(0.526588\pi\)
\(74\) −7.89072 −0.917277
\(75\) −4.52515 −0.522520
\(76\) −3.32636 −0.381560
\(77\) −4.91945 −0.560623
\(78\) −2.15959 −0.244525
\(79\) 0.110825 0.0124688 0.00623438 0.999981i \(-0.498016\pi\)
0.00623438 + 0.999981i \(0.498016\pi\)
\(80\) −0.689091 −0.0770427
\(81\) 1.00000 0.111111
\(82\) 7.38995 0.816083
\(83\) 14.1106 1.54884 0.774420 0.632672i \(-0.218042\pi\)
0.774420 + 0.632672i \(0.218042\pi\)
\(84\) 4.91945 0.536756
\(85\) −1.17504 −0.127451
\(86\) −3.02873 −0.326596
\(87\) 4.83606 0.518480
\(88\) 1.00000 0.106600
\(89\) 3.25345 0.344865 0.172432 0.985021i \(-0.444837\pi\)
0.172432 + 0.985021i \(0.444837\pi\)
\(90\) 0.689091 0.0726366
\(91\) 10.6240 1.11370
\(92\) −0.135207 −0.0140963
\(93\) 2.55388 0.264825
\(94\) −10.3738 −1.06998
\(95\) 2.29216 0.235171
\(96\) −1.00000 −0.102062
\(97\) −6.01545 −0.610776 −0.305388 0.952228i \(-0.598786\pi\)
−0.305388 + 0.952228i \(0.598786\pi\)
\(98\) −17.2010 −1.73756
\(99\) −1.00000 −0.100504
\(100\) −4.52515 −0.452515
\(101\) −8.20881 −0.816807 −0.408403 0.912802i \(-0.633914\pi\)
−0.408403 + 0.912802i \(0.633914\pi\)
\(102\) −1.70520 −0.168840
\(103\) −0.150657 −0.0148447 −0.00742236 0.999972i \(-0.502363\pi\)
−0.00742236 + 0.999972i \(0.502363\pi\)
\(104\) −2.15959 −0.211765
\(105\) −3.38995 −0.330825
\(106\) 1.60571 0.155960
\(107\) −20.2746 −1.96002 −0.980008 0.198958i \(-0.936244\pi\)
−0.980008 + 0.198958i \(0.936244\pi\)
\(108\) 1.00000 0.0962250
\(109\) 11.4418 1.09592 0.547961 0.836504i \(-0.315404\pi\)
0.547961 + 0.836504i \(0.315404\pi\)
\(110\) −0.689091 −0.0657022
\(111\) 7.89072 0.748954
\(112\) 4.91945 0.464844
\(113\) −0.451754 −0.0424974 −0.0212487 0.999774i \(-0.506764\pi\)
−0.0212487 + 0.999774i \(0.506764\pi\)
\(114\) 3.32636 0.311542
\(115\) 0.0931701 0.00868816
\(116\) 4.83606 0.449017
\(117\) 2.15959 0.199654
\(118\) 1.90614 0.175474
\(119\) 8.38866 0.768987
\(120\) 0.689091 0.0629051
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) −7.38995 −0.666329
\(124\) 2.55388 0.229346
\(125\) 6.56370 0.587075
\(126\) −4.91945 −0.438259
\(127\) 21.0873 1.87120 0.935598 0.353067i \(-0.114861\pi\)
0.935598 + 0.353067i \(0.114861\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.02873 0.266665
\(130\) 1.48815 0.130520
\(131\) −10.7653 −0.940571 −0.470285 0.882514i \(-0.655849\pi\)
−0.470285 + 0.882514i \(0.655849\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −16.3638 −1.41893
\(134\) −12.0862 −1.04409
\(135\) −0.689091 −0.0593075
\(136\) −1.70520 −0.146220
\(137\) −16.8515 −1.43972 −0.719861 0.694118i \(-0.755794\pi\)
−0.719861 + 0.694118i \(0.755794\pi\)
\(138\) 0.135207 0.0115096
\(139\) −10.7997 −0.916018 −0.458009 0.888948i \(-0.651437\pi\)
−0.458009 + 0.888948i \(0.651437\pi\)
\(140\) −3.38995 −0.286503
\(141\) 10.3738 0.873634
\(142\) 9.93207 0.833480
\(143\) −2.15959 −0.180594
\(144\) 1.00000 0.0833333
\(145\) −3.33249 −0.276748
\(146\) 1.42566 0.117988
\(147\) 17.2010 1.41871
\(148\) 7.89072 0.648613
\(149\) 5.50795 0.451229 0.225614 0.974217i \(-0.427561\pi\)
0.225614 + 0.974217i \(0.427561\pi\)
\(150\) 4.52515 0.369477
\(151\) 7.12038 0.579449 0.289724 0.957110i \(-0.406436\pi\)
0.289724 + 0.957110i \(0.406436\pi\)
\(152\) 3.32636 0.269803
\(153\) 1.70520 0.137857
\(154\) 4.91945 0.396420
\(155\) −1.75986 −0.141355
\(156\) 2.15959 0.172906
\(157\) 16.7836 1.33948 0.669738 0.742598i \(-0.266407\pi\)
0.669738 + 0.742598i \(0.266407\pi\)
\(158\) −0.110825 −0.00881675
\(159\) −1.60571 −0.127341
\(160\) 0.689091 0.0544774
\(161\) −0.665145 −0.0524208
\(162\) −1.00000 −0.0785674
\(163\) 3.13171 0.245295 0.122647 0.992450i \(-0.460862\pi\)
0.122647 + 0.992450i \(0.460862\pi\)
\(164\) −7.38995 −0.577058
\(165\) 0.689091 0.0536457
\(166\) −14.1106 −1.09519
\(167\) −10.1883 −0.788398 −0.394199 0.919025i \(-0.628978\pi\)
−0.394199 + 0.919025i \(0.628978\pi\)
\(168\) −4.91945 −0.379544
\(169\) −8.33617 −0.641244
\(170\) 1.17504 0.0901214
\(171\) −3.32636 −0.254373
\(172\) 3.02873 0.230938
\(173\) 23.8598 1.81403 0.907014 0.421101i \(-0.138356\pi\)
0.907014 + 0.421101i \(0.138356\pi\)
\(174\) −4.83606 −0.366621
\(175\) −22.2613 −1.68279
\(176\) −1.00000 −0.0753778
\(177\) −1.90614 −0.143274
\(178\) −3.25345 −0.243856
\(179\) −13.4202 −1.00307 −0.501537 0.865136i \(-0.667232\pi\)
−0.501537 + 0.865136i \(0.667232\pi\)
\(180\) −0.689091 −0.0513618
\(181\) 2.21639 0.164743 0.0823714 0.996602i \(-0.473751\pi\)
0.0823714 + 0.996602i \(0.473751\pi\)
\(182\) −10.6240 −0.787502
\(183\) −1.00000 −0.0739221
\(184\) 0.135207 0.00996761
\(185\) −5.43742 −0.399767
\(186\) −2.55388 −0.187260
\(187\) −1.70520 −0.124697
\(188\) 10.3738 0.756590
\(189\) 4.91945 0.357837
\(190\) −2.29216 −0.166291
\(191\) −8.20752 −0.593875 −0.296938 0.954897i \(-0.595965\pi\)
−0.296938 + 0.954897i \(0.595965\pi\)
\(192\) 1.00000 0.0721688
\(193\) 10.2032 0.734440 0.367220 0.930134i \(-0.380310\pi\)
0.367220 + 0.930134i \(0.380310\pi\)
\(194\) 6.01545 0.431884
\(195\) −1.48815 −0.106569
\(196\) 17.2010 1.22864
\(197\) 0.297629 0.0212052 0.0106026 0.999944i \(-0.496625\pi\)
0.0106026 + 0.999944i \(0.496625\pi\)
\(198\) 1.00000 0.0710669
\(199\) −23.4585 −1.66293 −0.831466 0.555576i \(-0.812498\pi\)
−0.831466 + 0.555576i \(0.812498\pi\)
\(200\) 4.52515 0.319977
\(201\) 12.0862 0.852496
\(202\) 8.20881 0.577570
\(203\) 23.7908 1.66978
\(204\) 1.70520 0.119388
\(205\) 5.09234 0.355665
\(206\) 0.150657 0.0104968
\(207\) −0.135207 −0.00939756
\(208\) 2.15959 0.149741
\(209\) 3.32636 0.230089
\(210\) 3.38995 0.233929
\(211\) −18.8108 −1.29499 −0.647494 0.762070i \(-0.724183\pi\)
−0.647494 + 0.762070i \(0.724183\pi\)
\(212\) −1.60571 −0.110280
\(213\) −9.93207 −0.680534
\(214\) 20.2746 1.38594
\(215\) −2.08707 −0.142337
\(216\) −1.00000 −0.0680414
\(217\) 12.5637 0.852879
\(218\) −11.4418 −0.774934
\(219\) −1.42566 −0.0963370
\(220\) 0.689091 0.0464585
\(221\) 3.68254 0.247714
\(222\) −7.89072 −0.529590
\(223\) 27.5578 1.84541 0.922705 0.385508i \(-0.125974\pi\)
0.922705 + 0.385508i \(0.125974\pi\)
\(224\) −4.91945 −0.328694
\(225\) −4.52515 −0.301677
\(226\) 0.451754 0.0300502
\(227\) 25.8110 1.71314 0.856570 0.516031i \(-0.172591\pi\)
0.856570 + 0.516031i \(0.172591\pi\)
\(228\) −3.32636 −0.220294
\(229\) 6.33420 0.418576 0.209288 0.977854i \(-0.432885\pi\)
0.209288 + 0.977854i \(0.432885\pi\)
\(230\) −0.0931701 −0.00614345
\(231\) −4.91945 −0.323676
\(232\) −4.83606 −0.317503
\(233\) 17.3954 1.13961 0.569806 0.821779i \(-0.307018\pi\)
0.569806 + 0.821779i \(0.307018\pi\)
\(234\) −2.15959 −0.141177
\(235\) −7.14851 −0.466318
\(236\) −1.90614 −0.124079
\(237\) 0.110825 0.00719885
\(238\) −8.38866 −0.543756
\(239\) 8.57417 0.554617 0.277309 0.960781i \(-0.410558\pi\)
0.277309 + 0.960781i \(0.410558\pi\)
\(240\) −0.689091 −0.0444806
\(241\) −21.1128 −1.35999 −0.679997 0.733215i \(-0.738019\pi\)
−0.679997 + 0.733215i \(0.738019\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −11.8530 −0.757262
\(246\) 7.38995 0.471166
\(247\) −7.18357 −0.457080
\(248\) −2.55388 −0.162172
\(249\) 14.1106 0.894223
\(250\) −6.56370 −0.415125
\(251\) 1.83060 0.115546 0.0577731 0.998330i \(-0.481600\pi\)
0.0577731 + 0.998330i \(0.481600\pi\)
\(252\) 4.91945 0.309896
\(253\) 0.135207 0.00850041
\(254\) −21.0873 −1.32314
\(255\) −1.17504 −0.0735838
\(256\) 1.00000 0.0625000
\(257\) 14.2530 0.889077 0.444538 0.895760i \(-0.353368\pi\)
0.444538 + 0.895760i \(0.353368\pi\)
\(258\) −3.02873 −0.188560
\(259\) 38.8180 2.41203
\(260\) −1.48815 −0.0922914
\(261\) 4.83606 0.299345
\(262\) 10.7653 0.665084
\(263\) 30.0013 1.84996 0.924981 0.380013i \(-0.124081\pi\)
0.924981 + 0.380013i \(0.124081\pi\)
\(264\) 1.00000 0.0615457
\(265\) 1.10648 0.0679704
\(266\) 16.3638 1.00333
\(267\) 3.25345 0.199108
\(268\) 12.0862 0.738283
\(269\) 22.6897 1.38342 0.691708 0.722177i \(-0.256858\pi\)
0.691708 + 0.722177i \(0.256858\pi\)
\(270\) 0.689091 0.0419367
\(271\) 5.92225 0.359751 0.179876 0.983689i \(-0.442430\pi\)
0.179876 + 0.983689i \(0.442430\pi\)
\(272\) 1.70520 0.103393
\(273\) 10.6240 0.642993
\(274\) 16.8515 1.01804
\(275\) 4.52515 0.272877
\(276\) −0.135207 −0.00813852
\(277\) −2.44262 −0.146763 −0.0733815 0.997304i \(-0.523379\pi\)
−0.0733815 + 0.997304i \(0.523379\pi\)
\(278\) 10.7997 0.647722
\(279\) 2.55388 0.152897
\(280\) 3.38995 0.202588
\(281\) 1.08055 0.0644604 0.0322302 0.999480i \(-0.489739\pi\)
0.0322302 + 0.999480i \(0.489739\pi\)
\(282\) −10.3738 −0.617753
\(283\) −21.3543 −1.26938 −0.634690 0.772767i \(-0.718872\pi\)
−0.634690 + 0.772767i \(0.718872\pi\)
\(284\) −9.93207 −0.589360
\(285\) 2.29216 0.135776
\(286\) 2.15959 0.127699
\(287\) −36.3545 −2.14594
\(288\) −1.00000 −0.0589256
\(289\) −14.0923 −0.828958
\(290\) 3.33249 0.195690
\(291\) −6.01545 −0.352632
\(292\) −1.42566 −0.0834303
\(293\) −27.8023 −1.62423 −0.812115 0.583498i \(-0.801684\pi\)
−0.812115 + 0.583498i \(0.801684\pi\)
\(294\) −17.2010 −1.00318
\(295\) 1.31350 0.0764752
\(296\) −7.89072 −0.458639
\(297\) −1.00000 −0.0580259
\(298\) −5.50795 −0.319067
\(299\) −0.291992 −0.0168863
\(300\) −4.52515 −0.261260
\(301\) 14.8997 0.858803
\(302\) −7.12038 −0.409732
\(303\) −8.20881 −0.471584
\(304\) −3.32636 −0.190780
\(305\) 0.689091 0.0394572
\(306\) −1.70520 −0.0974800
\(307\) −31.9388 −1.82285 −0.911423 0.411470i \(-0.865015\pi\)
−0.911423 + 0.411470i \(0.865015\pi\)
\(308\) −4.91945 −0.280312
\(309\) −0.150657 −0.00857060
\(310\) 1.75986 0.0999532
\(311\) 14.0050 0.794151 0.397075 0.917786i \(-0.370025\pi\)
0.397075 + 0.917786i \(0.370025\pi\)
\(312\) −2.15959 −0.122263
\(313\) 6.21229 0.351140 0.175570 0.984467i \(-0.443823\pi\)
0.175570 + 0.984467i \(0.443823\pi\)
\(314\) −16.7836 −0.947152
\(315\) −3.38995 −0.191002
\(316\) 0.110825 0.00623438
\(317\) −0.166142 −0.00933145 −0.00466573 0.999989i \(-0.501485\pi\)
−0.00466573 + 0.999989i \(0.501485\pi\)
\(318\) 1.60571 0.0900435
\(319\) −4.83606 −0.270768
\(320\) −0.689091 −0.0385214
\(321\) −20.2746 −1.13162
\(322\) 0.665145 0.0370671
\(323\) −5.67212 −0.315605
\(324\) 1.00000 0.0555556
\(325\) −9.77248 −0.542079
\(326\) −3.13171 −0.173450
\(327\) 11.4418 0.632731
\(328\) 7.38995 0.408042
\(329\) 51.0335 2.81357
\(330\) −0.689091 −0.0379332
\(331\) −29.9118 −1.64410 −0.822051 0.569414i \(-0.807170\pi\)
−0.822051 + 0.569414i \(0.807170\pi\)
\(332\) 14.1106 0.774420
\(333\) 7.89072 0.432409
\(334\) 10.1883 0.557482
\(335\) −8.32850 −0.455035
\(336\) 4.91945 0.268378
\(337\) 8.19725 0.446533 0.223266 0.974757i \(-0.428328\pi\)
0.223266 + 0.974757i \(0.428328\pi\)
\(338\) 8.33617 0.453428
\(339\) −0.451754 −0.0245359
\(340\) −1.17504 −0.0637255
\(341\) −2.55388 −0.138301
\(342\) 3.32636 0.179869
\(343\) 50.1831 2.70963
\(344\) −3.02873 −0.163298
\(345\) 0.0931701 0.00501611
\(346\) −23.8598 −1.28271
\(347\) 26.4965 1.42240 0.711202 0.702988i \(-0.248151\pi\)
0.711202 + 0.702988i \(0.248151\pi\)
\(348\) 4.83606 0.259240
\(349\) 14.7589 0.790028 0.395014 0.918675i \(-0.370740\pi\)
0.395014 + 0.918675i \(0.370740\pi\)
\(350\) 22.2613 1.18991
\(351\) 2.15959 0.115270
\(352\) 1.00000 0.0533002
\(353\) −23.3634 −1.24351 −0.621753 0.783213i \(-0.713579\pi\)
−0.621753 + 0.783213i \(0.713579\pi\)
\(354\) 1.90614 0.101310
\(355\) 6.84410 0.363247
\(356\) 3.25345 0.172432
\(357\) 8.38866 0.443975
\(358\) 13.4202 0.709281
\(359\) −16.5426 −0.873083 −0.436541 0.899684i \(-0.643797\pi\)
−0.436541 + 0.899684i \(0.643797\pi\)
\(360\) 0.689091 0.0363183
\(361\) −7.93533 −0.417649
\(362\) −2.21639 −0.116491
\(363\) 1.00000 0.0524864
\(364\) 10.6240 0.556848
\(365\) 0.982407 0.0514215
\(366\) 1.00000 0.0522708
\(367\) −18.8578 −0.984371 −0.492185 0.870490i \(-0.663802\pi\)
−0.492185 + 0.870490i \(0.663802\pi\)
\(368\) −0.135207 −0.00704817
\(369\) −7.38995 −0.384705
\(370\) 5.43742 0.282678
\(371\) −7.89919 −0.410105
\(372\) 2.55388 0.132413
\(373\) 17.7078 0.916877 0.458439 0.888726i \(-0.348409\pi\)
0.458439 + 0.888726i \(0.348409\pi\)
\(374\) 1.70520 0.0881739
\(375\) 6.56370 0.338948
\(376\) −10.3738 −0.534990
\(377\) 10.4439 0.537889
\(378\) −4.91945 −0.253029
\(379\) −18.2613 −0.938019 −0.469010 0.883193i \(-0.655389\pi\)
−0.469010 + 0.883193i \(0.655389\pi\)
\(380\) 2.29216 0.117586
\(381\) 21.0873 1.08034
\(382\) 8.20752 0.419933
\(383\) 24.7651 1.26544 0.632719 0.774382i \(-0.281939\pi\)
0.632719 + 0.774382i \(0.281939\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 3.38995 0.172768
\(386\) −10.2032 −0.519328
\(387\) 3.02873 0.153959
\(388\) −6.01545 −0.305388
\(389\) 11.5147 0.583819 0.291909 0.956446i \(-0.405709\pi\)
0.291909 + 0.956446i \(0.405709\pi\)
\(390\) 1.48815 0.0753556
\(391\) −0.230556 −0.0116597
\(392\) −17.2010 −0.868780
\(393\) −10.7653 −0.543039
\(394\) −0.297629 −0.0149944
\(395\) −0.0763684 −0.00384251
\(396\) −1.00000 −0.0502519
\(397\) 0.602648 0.0302461 0.0151230 0.999886i \(-0.495186\pi\)
0.0151230 + 0.999886i \(0.495186\pi\)
\(398\) 23.4585 1.17587
\(399\) −16.3638 −0.819217
\(400\) −4.52515 −0.226258
\(401\) −19.3012 −0.963854 −0.481927 0.876212i \(-0.660063\pi\)
−0.481927 + 0.876212i \(0.660063\pi\)
\(402\) −12.0862 −0.602806
\(403\) 5.51534 0.274739
\(404\) −8.20881 −0.408403
\(405\) −0.689091 −0.0342412
\(406\) −23.7908 −1.18072
\(407\) −7.89072 −0.391128
\(408\) −1.70520 −0.0844201
\(409\) 19.9815 0.988023 0.494011 0.869455i \(-0.335530\pi\)
0.494011 + 0.869455i \(0.335530\pi\)
\(410\) −5.09234 −0.251493
\(411\) −16.8515 −0.831224
\(412\) −0.150657 −0.00742236
\(413\) −9.37716 −0.461420
\(414\) 0.135207 0.00664508
\(415\) −9.72349 −0.477307
\(416\) −2.15959 −0.105883
\(417\) −10.7997 −0.528863
\(418\) −3.32636 −0.162698
\(419\) 7.15349 0.349471 0.174735 0.984615i \(-0.444093\pi\)
0.174735 + 0.984615i \(0.444093\pi\)
\(420\) −3.38995 −0.165412
\(421\) 18.9743 0.924751 0.462375 0.886684i \(-0.346997\pi\)
0.462375 + 0.886684i \(0.346997\pi\)
\(422\) 18.8108 0.915695
\(423\) 10.3738 0.504393
\(424\) 1.60571 0.0779800
\(425\) −7.71631 −0.374296
\(426\) 9.93207 0.481210
\(427\) −4.91945 −0.238069
\(428\) −20.2746 −0.980008
\(429\) −2.15959 −0.104266
\(430\) 2.08707 0.100647
\(431\) 2.07792 0.100090 0.0500449 0.998747i \(-0.484064\pi\)
0.0500449 + 0.998747i \(0.484064\pi\)
\(432\) 1.00000 0.0481125
\(433\) −0.261229 −0.0125539 −0.00627694 0.999980i \(-0.501998\pi\)
−0.00627694 + 0.999980i \(0.501998\pi\)
\(434\) −12.5637 −0.603077
\(435\) −3.33249 −0.159781
\(436\) 11.4418 0.547961
\(437\) 0.449748 0.0215144
\(438\) 1.42566 0.0681205
\(439\) −3.23121 −0.154217 −0.0771086 0.997023i \(-0.524569\pi\)
−0.0771086 + 0.997023i \(0.524569\pi\)
\(440\) −0.689091 −0.0328511
\(441\) 17.2010 0.819094
\(442\) −3.68254 −0.175161
\(443\) −27.5554 −1.30920 −0.654599 0.755976i \(-0.727162\pi\)
−0.654599 + 0.755976i \(0.727162\pi\)
\(444\) 7.89072 0.374477
\(445\) −2.24192 −0.106277
\(446\) −27.5578 −1.30490
\(447\) 5.50795 0.260517
\(448\) 4.91945 0.232422
\(449\) 0.671436 0.0316870 0.0158435 0.999874i \(-0.494957\pi\)
0.0158435 + 0.999874i \(0.494957\pi\)
\(450\) 4.52515 0.213318
\(451\) 7.38995 0.347979
\(452\) −0.451754 −0.0212487
\(453\) 7.12038 0.334545
\(454\) −25.8110 −1.21137
\(455\) −7.32089 −0.343209
\(456\) 3.32636 0.155771
\(457\) 11.7230 0.548380 0.274190 0.961675i \(-0.411590\pi\)
0.274190 + 0.961675i \(0.411590\pi\)
\(458\) −6.33420 −0.295978
\(459\) 1.70520 0.0795921
\(460\) 0.0931701 0.00434408
\(461\) 2.33180 0.108603 0.0543013 0.998525i \(-0.482707\pi\)
0.0543013 + 0.998525i \(0.482707\pi\)
\(462\) 4.91945 0.228873
\(463\) −2.70741 −0.125824 −0.0629120 0.998019i \(-0.520039\pi\)
−0.0629120 + 0.998019i \(0.520039\pi\)
\(464\) 4.83606 0.224509
\(465\) −1.75986 −0.0816115
\(466\) −17.3954 −0.805827
\(467\) 5.81429 0.269053 0.134527 0.990910i \(-0.457049\pi\)
0.134527 + 0.990910i \(0.457049\pi\)
\(468\) 2.15959 0.0998271
\(469\) 59.4575 2.74549
\(470\) 7.14851 0.329736
\(471\) 16.7836 0.773346
\(472\) 1.90614 0.0877372
\(473\) −3.02873 −0.139261
\(474\) −0.110825 −0.00509035
\(475\) 15.0523 0.690646
\(476\) 8.38866 0.384493
\(477\) −1.60571 −0.0735202
\(478\) −8.57417 −0.392173
\(479\) 34.4070 1.57209 0.786047 0.618166i \(-0.212124\pi\)
0.786047 + 0.618166i \(0.212124\pi\)
\(480\) 0.689091 0.0314526
\(481\) 17.0407 0.776990
\(482\) 21.1128 0.961660
\(483\) −0.665145 −0.0302652
\(484\) 1.00000 0.0454545
\(485\) 4.14519 0.188223
\(486\) −1.00000 −0.0453609
\(487\) −18.4235 −0.834848 −0.417424 0.908712i \(-0.637067\pi\)
−0.417424 + 0.908712i \(0.637067\pi\)
\(488\) 1.00000 0.0452679
\(489\) 3.13171 0.141621
\(490\) 11.8530 0.535465
\(491\) 14.3565 0.647898 0.323949 0.946075i \(-0.394989\pi\)
0.323949 + 0.946075i \(0.394989\pi\)
\(492\) −7.38995 −0.333165
\(493\) 8.24647 0.371402
\(494\) 7.18357 0.323204
\(495\) 0.689091 0.0309723
\(496\) 2.55388 0.114673
\(497\) −48.8603 −2.19168
\(498\) −14.1106 −0.632311
\(499\) −3.64007 −0.162952 −0.0814760 0.996675i \(-0.525963\pi\)
−0.0814760 + 0.996675i \(0.525963\pi\)
\(500\) 6.56370 0.293537
\(501\) −10.1883 −0.455182
\(502\) −1.83060 −0.0817036
\(503\) 13.6647 0.609280 0.304640 0.952467i \(-0.401464\pi\)
0.304640 + 0.952467i \(0.401464\pi\)
\(504\) −4.91945 −0.219130
\(505\) 5.65661 0.251716
\(506\) −0.135207 −0.00601070
\(507\) −8.33617 −0.370222
\(508\) 21.0873 0.935598
\(509\) −29.1894 −1.29380 −0.646900 0.762575i \(-0.723935\pi\)
−0.646900 + 0.762575i \(0.723935\pi\)
\(510\) 1.17504 0.0520316
\(511\) −7.01344 −0.310257
\(512\) −1.00000 −0.0441942
\(513\) −3.32636 −0.146862
\(514\) −14.2530 −0.628672
\(515\) 0.103817 0.00457471
\(516\) 3.02873 0.133332
\(517\) −10.3738 −0.456241
\(518\) −38.8180 −1.70556
\(519\) 23.8598 1.04733
\(520\) 1.48815 0.0652599
\(521\) −31.1413 −1.36433 −0.682163 0.731200i \(-0.738961\pi\)
−0.682163 + 0.731200i \(0.738961\pi\)
\(522\) −4.83606 −0.211669
\(523\) 4.32422 0.189085 0.0945424 0.995521i \(-0.469861\pi\)
0.0945424 + 0.995521i \(0.469861\pi\)
\(524\) −10.7653 −0.470285
\(525\) −22.2613 −0.971561
\(526\) −30.0013 −1.30812
\(527\) 4.35489 0.189702
\(528\) −1.00000 −0.0435194
\(529\) −22.9817 −0.999205
\(530\) −1.10648 −0.0480623
\(531\) −1.90614 −0.0827194
\(532\) −16.3638 −0.709463
\(533\) −15.9593 −0.691272
\(534\) −3.25345 −0.140791
\(535\) 13.9710 0.604020
\(536\) −12.0862 −0.522045
\(537\) −13.4202 −0.579125
\(538\) −22.6897 −0.978223
\(539\) −17.2010 −0.740898
\(540\) −0.689091 −0.0296537
\(541\) 1.36227 0.0585685 0.0292843 0.999571i \(-0.490677\pi\)
0.0292843 + 0.999571i \(0.490677\pi\)
\(542\) −5.92225 −0.254383
\(543\) 2.21639 0.0951143
\(544\) −1.70520 −0.0731100
\(545\) −7.88442 −0.337731
\(546\) −10.6240 −0.454665
\(547\) 6.82934 0.292001 0.146001 0.989284i \(-0.453360\pi\)
0.146001 + 0.989284i \(0.453360\pi\)
\(548\) −16.8515 −0.719861
\(549\) −1.00000 −0.0426790
\(550\) −4.52515 −0.192953
\(551\) −16.0865 −0.685307
\(552\) 0.135207 0.00575480
\(553\) 0.545197 0.0231841
\(554\) 2.44262 0.103777
\(555\) −5.43742 −0.230806
\(556\) −10.7997 −0.458009
\(557\) 21.0429 0.891617 0.445809 0.895128i \(-0.352916\pi\)
0.445809 + 0.895128i \(0.352916\pi\)
\(558\) −2.55388 −0.108115
\(559\) 6.54081 0.276647
\(560\) −3.38995 −0.143251
\(561\) −1.70520 −0.0719937
\(562\) −1.08055 −0.0455804
\(563\) −32.1944 −1.35683 −0.678417 0.734677i \(-0.737334\pi\)
−0.678417 + 0.734677i \(0.737334\pi\)
\(564\) 10.3738 0.436817
\(565\) 0.311299 0.0130965
\(566\) 21.3543 0.897587
\(567\) 4.91945 0.206597
\(568\) 9.93207 0.416740
\(569\) −6.11670 −0.256425 −0.128213 0.991747i \(-0.540924\pi\)
−0.128213 + 0.991747i \(0.540924\pi\)
\(570\) −2.29216 −0.0960082
\(571\) 35.3475 1.47925 0.739623 0.673022i \(-0.235004\pi\)
0.739623 + 0.673022i \(0.235004\pi\)
\(572\) −2.15959 −0.0902970
\(573\) −8.20752 −0.342874
\(574\) 36.3545 1.51741
\(575\) 0.611834 0.0255152
\(576\) 1.00000 0.0416667
\(577\) −8.46446 −0.352380 −0.176190 0.984356i \(-0.556377\pi\)
−0.176190 + 0.984356i \(0.556377\pi\)
\(578\) 14.0923 0.586162
\(579\) 10.2032 0.424029
\(580\) −3.33249 −0.138374
\(581\) 69.4164 2.87988
\(582\) 6.01545 0.249348
\(583\) 1.60571 0.0665016
\(584\) 1.42566 0.0589941
\(585\) −1.48815 −0.0615276
\(586\) 27.8023 1.14850
\(587\) −17.8062 −0.734941 −0.367471 0.930035i \(-0.619776\pi\)
−0.367471 + 0.930035i \(0.619776\pi\)
\(588\) 17.2010 0.709356
\(589\) −8.49513 −0.350036
\(590\) −1.31350 −0.0540761
\(591\) 0.297629 0.0122428
\(592\) 7.89072 0.324307
\(593\) −14.8308 −0.609029 −0.304514 0.952508i \(-0.598494\pi\)
−0.304514 + 0.952508i \(0.598494\pi\)
\(594\) 1.00000 0.0410305
\(595\) −5.78055 −0.236979
\(596\) 5.50795 0.225614
\(597\) −23.4585 −0.960094
\(598\) 0.291992 0.0119405
\(599\) −22.6525 −0.925558 −0.462779 0.886474i \(-0.653148\pi\)
−0.462779 + 0.886474i \(0.653148\pi\)
\(600\) 4.52515 0.184739
\(601\) 41.7118 1.70146 0.850729 0.525604i \(-0.176161\pi\)
0.850729 + 0.525604i \(0.176161\pi\)
\(602\) −14.8997 −0.607266
\(603\) 12.0862 0.492189
\(604\) 7.12038 0.289724
\(605\) −0.689091 −0.0280155
\(606\) 8.20881 0.333460
\(607\) 16.9020 0.686033 0.343016 0.939329i \(-0.388551\pi\)
0.343016 + 0.939329i \(0.388551\pi\)
\(608\) 3.32636 0.134902
\(609\) 23.7908 0.964050
\(610\) −0.689091 −0.0279005
\(611\) 22.4032 0.906338
\(612\) 1.70520 0.0689287
\(613\) 9.28221 0.374905 0.187452 0.982274i \(-0.439977\pi\)
0.187452 + 0.982274i \(0.439977\pi\)
\(614\) 31.9388 1.28895
\(615\) 5.09234 0.205343
\(616\) 4.91945 0.198210
\(617\) 1.75491 0.0706500 0.0353250 0.999376i \(-0.488753\pi\)
0.0353250 + 0.999376i \(0.488753\pi\)
\(618\) 0.150657 0.00606033
\(619\) 18.0534 0.725626 0.362813 0.931862i \(-0.381816\pi\)
0.362813 + 0.931862i \(0.381816\pi\)
\(620\) −1.75986 −0.0706776
\(621\) −0.135207 −0.00542568
\(622\) −14.0050 −0.561549
\(623\) 16.0052 0.641234
\(624\) 2.15959 0.0864528
\(625\) 18.1028 0.724111
\(626\) −6.21229 −0.248293
\(627\) 3.32636 0.132842
\(628\) 16.7836 0.669738
\(629\) 13.4553 0.536497
\(630\) 3.38995 0.135059
\(631\) −44.0205 −1.75243 −0.876214 0.481923i \(-0.839939\pi\)
−0.876214 + 0.481923i \(0.839939\pi\)
\(632\) −0.110825 −0.00440838
\(633\) −18.8108 −0.747662
\(634\) 0.166142 0.00659833
\(635\) −14.5311 −0.576648
\(636\) −1.60571 −0.0636704
\(637\) 37.1470 1.47182
\(638\) 4.83606 0.191462
\(639\) −9.93207 −0.392906
\(640\) 0.689091 0.0272387
\(641\) −35.6691 −1.40884 −0.704422 0.709781i \(-0.748794\pi\)
−0.704422 + 0.709781i \(0.748794\pi\)
\(642\) 20.2746 0.800173
\(643\) 33.6105 1.32547 0.662735 0.748854i \(-0.269396\pi\)
0.662735 + 0.748854i \(0.269396\pi\)
\(644\) −0.665145 −0.0262104
\(645\) −2.08707 −0.0821783
\(646\) 5.67212 0.223166
\(647\) −31.4010 −1.23450 −0.617251 0.786767i \(-0.711754\pi\)
−0.617251 + 0.786767i \(0.711754\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.90614 0.0748226
\(650\) 9.77248 0.383308
\(651\) 12.5637 0.492410
\(652\) 3.13171 0.122647
\(653\) 50.2918 1.96807 0.984034 0.177978i \(-0.0569556\pi\)
0.984034 + 0.177978i \(0.0569556\pi\)
\(654\) −11.4418 −0.447409
\(655\) 7.41829 0.289856
\(656\) −7.38995 −0.288529
\(657\) −1.42566 −0.0556202
\(658\) −51.0335 −1.98949
\(659\) −8.34616 −0.325120 −0.162560 0.986699i \(-0.551975\pi\)
−0.162560 + 0.986699i \(0.551975\pi\)
\(660\) 0.689091 0.0268228
\(661\) −40.5254 −1.57625 −0.788127 0.615513i \(-0.788949\pi\)
−0.788127 + 0.615513i \(0.788949\pi\)
\(662\) 29.9118 1.16256
\(663\) 3.68254 0.143018
\(664\) −14.1106 −0.547597
\(665\) 11.2762 0.437271
\(666\) −7.89072 −0.305759
\(667\) −0.653871 −0.0253180
\(668\) −10.1883 −0.394199
\(669\) 27.5578 1.06545
\(670\) 8.32850 0.321758
\(671\) 1.00000 0.0386046
\(672\) −4.91945 −0.189772
\(673\) −25.2843 −0.974640 −0.487320 0.873223i \(-0.662025\pi\)
−0.487320 + 0.873223i \(0.662025\pi\)
\(674\) −8.19725 −0.315746
\(675\) −4.52515 −0.174173
\(676\) −8.33617 −0.320622
\(677\) 49.1342 1.88838 0.944190 0.329402i \(-0.106847\pi\)
0.944190 + 0.329402i \(0.106847\pi\)
\(678\) 0.451754 0.0173495
\(679\) −29.5927 −1.13566
\(680\) 1.17504 0.0450607
\(681\) 25.8110 0.989081
\(682\) 2.55388 0.0977933
\(683\) 45.0460 1.72364 0.861818 0.507218i \(-0.169326\pi\)
0.861818 + 0.507218i \(0.169326\pi\)
\(684\) −3.32636 −0.127187
\(685\) 11.6122 0.443680
\(686\) −50.1831 −1.91600
\(687\) 6.33420 0.241665
\(688\) 3.02873 0.115469
\(689\) −3.46767 −0.132108
\(690\) −0.0931701 −0.00354693
\(691\) 20.0217 0.761663 0.380832 0.924644i \(-0.375638\pi\)
0.380832 + 0.924644i \(0.375638\pi\)
\(692\) 23.8598 0.907014
\(693\) −4.91945 −0.186874
\(694\) −26.4965 −1.00579
\(695\) 7.44197 0.282290
\(696\) −4.83606 −0.183310
\(697\) −12.6014 −0.477310
\(698\) −14.7589 −0.558634
\(699\) 17.3954 0.657955
\(700\) −22.2613 −0.841396
\(701\) −1.73762 −0.0656289 −0.0328145 0.999461i \(-0.510447\pi\)
−0.0328145 + 0.999461i \(0.510447\pi\)
\(702\) −2.15959 −0.0815085
\(703\) −26.2474 −0.989938
\(704\) −1.00000 −0.0376889
\(705\) −7.14851 −0.269229
\(706\) 23.3634 0.879292
\(707\) −40.3828 −1.51875
\(708\) −1.90614 −0.0716371
\(709\) −43.0523 −1.61686 −0.808431 0.588591i \(-0.799683\pi\)
−0.808431 + 0.588591i \(0.799683\pi\)
\(710\) −6.84410 −0.256854
\(711\) 0.110825 0.00415626
\(712\) −3.25345 −0.121928
\(713\) −0.345304 −0.0129317
\(714\) −8.38866 −0.313938
\(715\) 1.48815 0.0556538
\(716\) −13.4202 −0.501537
\(717\) 8.57417 0.320208
\(718\) 16.5426 0.617363
\(719\) 5.15587 0.192281 0.0961407 0.995368i \(-0.469350\pi\)
0.0961407 + 0.995368i \(0.469350\pi\)
\(720\) −0.689091 −0.0256809
\(721\) −0.741151 −0.0276019
\(722\) 7.93533 0.295323
\(723\) −21.1128 −0.785192
\(724\) 2.21639 0.0823714
\(725\) −21.8839 −0.812749
\(726\) −1.00000 −0.0371135
\(727\) −8.87678 −0.329222 −0.164611 0.986359i \(-0.552637\pi\)
−0.164611 + 0.986359i \(0.552637\pi\)
\(728\) −10.6240 −0.393751
\(729\) 1.00000 0.0370370
\(730\) −0.982407 −0.0363605
\(731\) 5.16460 0.191020
\(732\) −1.00000 −0.0369611
\(733\) −18.6538 −0.688994 −0.344497 0.938787i \(-0.611951\pi\)
−0.344497 + 0.938787i \(0.611951\pi\)
\(734\) 18.8578 0.696055
\(735\) −11.8530 −0.437206
\(736\) 0.135207 0.00498381
\(737\) −12.0862 −0.445202
\(738\) 7.38995 0.272028
\(739\) −9.78121 −0.359808 −0.179904 0.983684i \(-0.557579\pi\)
−0.179904 + 0.983684i \(0.557579\pi\)
\(740\) −5.43742 −0.199884
\(741\) −7.18357 −0.263895
\(742\) 7.89919 0.289988
\(743\) −14.7455 −0.540959 −0.270480 0.962726i \(-0.587182\pi\)
−0.270480 + 0.962726i \(0.587182\pi\)
\(744\) −2.55388 −0.0936299
\(745\) −3.79548 −0.139056
\(746\) −17.7078 −0.648330
\(747\) 14.1106 0.516280
\(748\) −1.70520 −0.0623484
\(749\) −99.7397 −3.64441
\(750\) −6.56370 −0.239672
\(751\) −28.8023 −1.05101 −0.525506 0.850790i \(-0.676124\pi\)
−0.525506 + 0.850790i \(0.676124\pi\)
\(752\) 10.3738 0.378295
\(753\) 1.83060 0.0667107
\(754\) −10.4439 −0.380345
\(755\) −4.90659 −0.178569
\(756\) 4.91945 0.178919
\(757\) −11.5289 −0.419023 −0.209512 0.977806i \(-0.567187\pi\)
−0.209512 + 0.977806i \(0.567187\pi\)
\(758\) 18.2613 0.663280
\(759\) 0.135207 0.00490771
\(760\) −2.29216 −0.0831455
\(761\) −7.56742 −0.274319 −0.137159 0.990549i \(-0.543797\pi\)
−0.137159 + 0.990549i \(0.543797\pi\)
\(762\) −21.0873 −0.763913
\(763\) 56.2872 2.03773
\(764\) −8.20752 −0.296938
\(765\) −1.17504 −0.0424837
\(766\) −24.7651 −0.894799
\(767\) −4.11648 −0.148638
\(768\) 1.00000 0.0360844
\(769\) −45.7037 −1.64812 −0.824060 0.566503i \(-0.808296\pi\)
−0.824060 + 0.566503i \(0.808296\pi\)
\(770\) −3.38995 −0.122165
\(771\) 14.2530 0.513309
\(772\) 10.2032 0.367220
\(773\) −6.87501 −0.247277 −0.123639 0.992327i \(-0.539456\pi\)
−0.123639 + 0.992327i \(0.539456\pi\)
\(774\) −3.02873 −0.108865
\(775\) −11.5567 −0.415129
\(776\) 6.01545 0.215942
\(777\) 38.8180 1.39259
\(778\) −11.5147 −0.412822
\(779\) 24.5816 0.880728
\(780\) −1.48815 −0.0532844
\(781\) 9.93207 0.355397
\(782\) 0.230556 0.00824466
\(783\) 4.83606 0.172827
\(784\) 17.2010 0.614320
\(785\) −11.5654 −0.412787
\(786\) 10.7653 0.383986
\(787\) 25.0305 0.892240 0.446120 0.894973i \(-0.352805\pi\)
0.446120 + 0.894973i \(0.352805\pi\)
\(788\) 0.297629 0.0106026
\(789\) 30.0013 1.06808
\(790\) 0.0763684 0.00271707
\(791\) −2.22238 −0.0790187
\(792\) 1.00000 0.0355335
\(793\) −2.15959 −0.0766893
\(794\) −0.602648 −0.0213872
\(795\) 1.10648 0.0392427
\(796\) −23.4585 −0.831466
\(797\) −14.6273 −0.518124 −0.259062 0.965861i \(-0.583413\pi\)
−0.259062 + 0.965861i \(0.583413\pi\)
\(798\) 16.3638 0.579274
\(799\) 17.6895 0.625809
\(800\) 4.52515 0.159988
\(801\) 3.25345 0.114955
\(802\) 19.3012 0.681547
\(803\) 1.42566 0.0503103
\(804\) 12.0862 0.426248
\(805\) 0.458345 0.0161546
\(806\) −5.51534 −0.194270
\(807\) 22.6897 0.798716
\(808\) 8.20881 0.288785
\(809\) −28.0719 −0.986955 −0.493477 0.869759i \(-0.664274\pi\)
−0.493477 + 0.869759i \(0.664274\pi\)
\(810\) 0.689091 0.0242122
\(811\) 38.1920 1.34110 0.670552 0.741863i \(-0.266057\pi\)
0.670552 + 0.741863i \(0.266057\pi\)
\(812\) 23.7908 0.834892
\(813\) 5.92225 0.207702
\(814\) 7.89072 0.276570
\(815\) −2.15803 −0.0755927
\(816\) 1.70520 0.0596940
\(817\) −10.0746 −0.352467
\(818\) −19.9815 −0.698637
\(819\) 10.6240 0.371232
\(820\) 5.09234 0.177832
\(821\) −17.7797 −0.620517 −0.310259 0.950652i \(-0.600416\pi\)
−0.310259 + 0.950652i \(0.600416\pi\)
\(822\) 16.8515 0.587764
\(823\) −29.3850 −1.02430 −0.512148 0.858897i \(-0.671150\pi\)
−0.512148 + 0.858897i \(0.671150\pi\)
\(824\) 0.150657 0.00524840
\(825\) 4.52515 0.157546
\(826\) 9.37716 0.326273
\(827\) 16.7562 0.582669 0.291335 0.956621i \(-0.405901\pi\)
0.291335 + 0.956621i \(0.405901\pi\)
\(828\) −0.135207 −0.00469878
\(829\) −36.0749 −1.25293 −0.626466 0.779449i \(-0.715499\pi\)
−0.626466 + 0.779449i \(0.715499\pi\)
\(830\) 9.72349 0.337507
\(831\) −2.44262 −0.0847336
\(832\) 2.15959 0.0748703
\(833\) 29.3311 1.01626
\(834\) 10.7997 0.373963
\(835\) 7.02070 0.242961
\(836\) 3.32636 0.115045
\(837\) 2.55388 0.0882751
\(838\) −7.15349 −0.247113
\(839\) −37.8008 −1.30503 −0.652514 0.757777i \(-0.726286\pi\)
−0.652514 + 0.757777i \(0.726286\pi\)
\(840\) 3.38995 0.116964
\(841\) −5.61250 −0.193534
\(842\) −18.9743 −0.653898
\(843\) 1.08055 0.0372162
\(844\) −18.8108 −0.647494
\(845\) 5.74438 0.197613
\(846\) −10.3738 −0.356660
\(847\) 4.91945 0.169034
\(848\) −1.60571 −0.0551402
\(849\) −21.3543 −0.732876
\(850\) 7.71631 0.264667
\(851\) −1.06688 −0.0365723
\(852\) −9.93207 −0.340267
\(853\) −25.8469 −0.884982 −0.442491 0.896773i \(-0.645905\pi\)
−0.442491 + 0.896773i \(0.645905\pi\)
\(854\) 4.91945 0.168340
\(855\) 2.29216 0.0783903
\(856\) 20.2746 0.692970
\(857\) −14.6922 −0.501875 −0.250938 0.968003i \(-0.580739\pi\)
−0.250938 + 0.968003i \(0.580739\pi\)
\(858\) 2.15959 0.0737272
\(859\) −7.58960 −0.258954 −0.129477 0.991582i \(-0.541330\pi\)
−0.129477 + 0.991582i \(0.541330\pi\)
\(860\) −2.08707 −0.0711685
\(861\) −36.3545 −1.23896
\(862\) −2.07792 −0.0707742
\(863\) 37.4827 1.27593 0.637963 0.770067i \(-0.279777\pi\)
0.637963 + 0.770067i \(0.279777\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −16.4416 −0.559030
\(866\) 0.261229 0.00887693
\(867\) −14.0923 −0.478599
\(868\) 12.5637 0.426440
\(869\) −0.110825 −0.00375948
\(870\) 3.33249 0.112982
\(871\) 26.1013 0.884408
\(872\) −11.4418 −0.387467
\(873\) −6.01545 −0.203592
\(874\) −0.449748 −0.0152130
\(875\) 32.2898 1.09159
\(876\) −1.42566 −0.0481685
\(877\) −2.09692 −0.0708079 −0.0354039 0.999373i \(-0.511272\pi\)
−0.0354039 + 0.999373i \(0.511272\pi\)
\(878\) 3.23121 0.109048
\(879\) −27.8023 −0.937749
\(880\) 0.689091 0.0232292
\(881\) 39.5733 1.33326 0.666629 0.745389i \(-0.267736\pi\)
0.666629 + 0.745389i \(0.267736\pi\)
\(882\) −17.2010 −0.579187
\(883\) 49.5629 1.66792 0.833962 0.551822i \(-0.186067\pi\)
0.833962 + 0.551822i \(0.186067\pi\)
\(884\) 3.68254 0.123857
\(885\) 1.31350 0.0441529
\(886\) 27.5554 0.925743
\(887\) 2.72368 0.0914521 0.0457261 0.998954i \(-0.485440\pi\)
0.0457261 + 0.998954i \(0.485440\pi\)
\(888\) −7.89072 −0.264795
\(889\) 103.738 3.47926
\(890\) 2.24192 0.0751494
\(891\) −1.00000 −0.0335013
\(892\) 27.5578 0.922705
\(893\) −34.5071 −1.15474
\(894\) −5.50795 −0.184213
\(895\) 9.24775 0.309118
\(896\) −4.91945 −0.164347
\(897\) −0.291992 −0.00974934
\(898\) −0.671436 −0.0224061
\(899\) 12.3507 0.411920
\(900\) −4.52515 −0.150838
\(901\) −2.73805 −0.0912178
\(902\) −7.38995 −0.246058
\(903\) 14.8997 0.495830
\(904\) 0.451754 0.0150251
\(905\) −1.52729 −0.0507689
\(906\) −7.12038 −0.236559
\(907\) 36.4446 1.21012 0.605061 0.796179i \(-0.293149\pi\)
0.605061 + 0.796179i \(0.293149\pi\)
\(908\) 25.8110 0.856570
\(909\) −8.20881 −0.272269
\(910\) 7.32089 0.242685
\(911\) −8.92886 −0.295826 −0.147913 0.989000i \(-0.547256\pi\)
−0.147913 + 0.989000i \(0.547256\pi\)
\(912\) −3.32636 −0.110147
\(913\) −14.1106 −0.466993
\(914\) −11.7230 −0.387763
\(915\) 0.689091 0.0227806
\(916\) 6.33420 0.209288
\(917\) −52.9594 −1.74887
\(918\) −1.70520 −0.0562801
\(919\) −36.3192 −1.19806 −0.599030 0.800727i \(-0.704447\pi\)
−0.599030 + 0.800727i \(0.704447\pi\)
\(920\) −0.0931701 −0.00307173
\(921\) −31.9388 −1.05242
\(922\) −2.33180 −0.0767937
\(923\) −21.4492 −0.706009
\(924\) −4.91945 −0.161838
\(925\) −35.7067 −1.17403
\(926\) 2.70741 0.0889709
\(927\) −0.150657 −0.00494824
\(928\) −4.83606 −0.158752
\(929\) 16.2375 0.532736 0.266368 0.963871i \(-0.414176\pi\)
0.266368 + 0.963871i \(0.414176\pi\)
\(930\) 1.75986 0.0577080
\(931\) −57.2166 −1.87520
\(932\) 17.3954 0.569806
\(933\) 14.0050 0.458503
\(934\) −5.81429 −0.190249
\(935\) 1.17504 0.0384279
\(936\) −2.15959 −0.0705884
\(937\) −52.9033 −1.72828 −0.864138 0.503254i \(-0.832136\pi\)
−0.864138 + 0.503254i \(0.832136\pi\)
\(938\) −59.4575 −1.94136
\(939\) 6.21229 0.202731
\(940\) −7.14851 −0.233159
\(941\) −12.3309 −0.401977 −0.200989 0.979594i \(-0.564415\pi\)
−0.200989 + 0.979594i \(0.564415\pi\)
\(942\) −16.7836 −0.546839
\(943\) 0.999175 0.0325376
\(944\) −1.90614 −0.0620396
\(945\) −3.38995 −0.110275
\(946\) 3.02873 0.0984725
\(947\) 15.7603 0.512141 0.256070 0.966658i \(-0.417572\pi\)
0.256070 + 0.966658i \(0.417572\pi\)
\(948\) 0.110825 0.00359942
\(949\) −3.07883 −0.0999432
\(950\) −15.0523 −0.488361
\(951\) −0.166142 −0.00538752
\(952\) −8.38866 −0.271878
\(953\) −8.16087 −0.264357 −0.132178 0.991226i \(-0.542197\pi\)
−0.132178 + 0.991226i \(0.542197\pi\)
\(954\) 1.60571 0.0519867
\(955\) 5.65573 0.183015
\(956\) 8.57417 0.277309
\(957\) −4.83606 −0.156328
\(958\) −34.4070 −1.11164
\(959\) −82.9001 −2.67698
\(960\) −0.689091 −0.0222403
\(961\) −24.4777 −0.789603
\(962\) −17.0407 −0.549415
\(963\) −20.2746 −0.653339
\(964\) −21.1128 −0.679997
\(965\) −7.03091 −0.226333
\(966\) 0.665145 0.0214007
\(967\) −20.9588 −0.673990 −0.336995 0.941506i \(-0.609411\pi\)
−0.336995 + 0.941506i \(0.609411\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −5.67212 −0.182215
\(970\) −4.14519 −0.133094
\(971\) 17.2349 0.553095 0.276547 0.961000i \(-0.410810\pi\)
0.276547 + 0.961000i \(0.410810\pi\)
\(972\) 1.00000 0.0320750
\(973\) −53.1285 −1.70322
\(974\) 18.4235 0.590326
\(975\) −9.77248 −0.312970
\(976\) −1.00000 −0.0320092
\(977\) 25.4526 0.814301 0.407151 0.913361i \(-0.366522\pi\)
0.407151 + 0.913361i \(0.366522\pi\)
\(978\) −3.13171 −0.100141
\(979\) −3.25345 −0.103981
\(980\) −11.8530 −0.378631
\(981\) 11.4418 0.365308
\(982\) −14.3565 −0.458133
\(983\) −17.1080 −0.545660 −0.272830 0.962062i \(-0.587960\pi\)
−0.272830 + 0.962062i \(0.587960\pi\)
\(984\) 7.38995 0.235583
\(985\) −0.205094 −0.00653483
\(986\) −8.24647 −0.262621
\(987\) 51.0335 1.62442
\(988\) −7.18357 −0.228540
\(989\) −0.409506 −0.0130215
\(990\) −0.689091 −0.0219007
\(991\) 18.4409 0.585796 0.292898 0.956144i \(-0.405380\pi\)
0.292898 + 0.956144i \(0.405380\pi\)
\(992\) −2.55388 −0.0810859
\(993\) −29.9118 −0.949222
\(994\) 48.8603 1.54975
\(995\) 16.1651 0.512467
\(996\) 14.1106 0.447111
\(997\) −37.2711 −1.18039 −0.590193 0.807262i \(-0.700948\pi\)
−0.590193 + 0.807262i \(0.700948\pi\)
\(998\) 3.64007 0.115225
\(999\) 7.89072 0.249651
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 4026.2.a.u.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.u.1.3 5 1.1 even 1 trivial