Properties

Label 4027.2.a.c.1.18
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +O(q^{10})\) \(q-2.36345 q^{2} +0.649215 q^{3} +3.58591 q^{4} -0.526324 q^{5} -1.53439 q^{6} +1.65204 q^{7} -3.74822 q^{8} -2.57852 q^{9} +1.24394 q^{10} -0.633045 q^{11} +2.32803 q^{12} -4.08101 q^{13} -3.90453 q^{14} -0.341697 q^{15} +1.68692 q^{16} -1.27562 q^{17} +6.09421 q^{18} -0.310985 q^{19} -1.88735 q^{20} +1.07253 q^{21} +1.49617 q^{22} -3.61411 q^{23} -2.43340 q^{24} -4.72298 q^{25} +9.64527 q^{26} -3.62166 q^{27} +5.92408 q^{28} -2.51840 q^{29} +0.807585 q^{30} -1.97607 q^{31} +3.50948 q^{32} -0.410983 q^{33} +3.01487 q^{34} -0.869510 q^{35} -9.24633 q^{36} +4.86204 q^{37} +0.734997 q^{38} -2.64945 q^{39} +1.97278 q^{40} +2.89719 q^{41} -2.53488 q^{42} -10.7661 q^{43} -2.27004 q^{44} +1.35714 q^{45} +8.54177 q^{46} +8.11626 q^{47} +1.09517 q^{48} -4.27075 q^{49} +11.1625 q^{50} -0.828153 q^{51} -14.6341 q^{52} +5.26987 q^{53} +8.55962 q^{54} +0.333187 q^{55} -6.19222 q^{56} -0.201896 q^{57} +5.95212 q^{58} +5.54935 q^{59} -1.22530 q^{60} +4.30300 q^{61} +4.67035 q^{62} -4.25983 q^{63} -11.6683 q^{64} +2.14793 q^{65} +0.971338 q^{66} -3.11613 q^{67} -4.57426 q^{68} -2.34633 q^{69} +2.05504 q^{70} +6.57046 q^{71} +9.66485 q^{72} +0.973762 q^{73} -11.4912 q^{74} -3.06623 q^{75} -1.11516 q^{76} -1.04582 q^{77} +6.26186 q^{78} +4.86469 q^{79} -0.887864 q^{80} +5.38432 q^{81} -6.84738 q^{82} +12.8455 q^{83} +3.84600 q^{84} +0.671389 q^{85} +25.4451 q^{86} -1.63498 q^{87} +2.37279 q^{88} +15.0161 q^{89} -3.20753 q^{90} -6.74200 q^{91} -12.9599 q^{92} -1.28290 q^{93} -19.1824 q^{94} +0.163679 q^{95} +2.27841 q^{96} +11.4793 q^{97} +10.0937 q^{98} +1.63232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36345 −1.67121 −0.835607 0.549328i \(-0.814884\pi\)
−0.835607 + 0.549328i \(0.814884\pi\)
\(3\) 0.649215 0.374825 0.187412 0.982281i \(-0.439990\pi\)
0.187412 + 0.982281i \(0.439990\pi\)
\(4\) 3.58591 1.79295
\(5\) −0.526324 −0.235379 −0.117690 0.993050i \(-0.537549\pi\)
−0.117690 + 0.993050i \(0.537549\pi\)
\(6\) −1.53439 −0.626412
\(7\) 1.65204 0.624414 0.312207 0.950014i \(-0.398932\pi\)
0.312207 + 0.950014i \(0.398932\pi\)
\(8\) −3.74822 −1.32519
\(9\) −2.57852 −0.859506
\(10\) 1.24394 0.393369
\(11\) −0.633045 −0.190870 −0.0954352 0.995436i \(-0.530424\pi\)
−0.0954352 + 0.995436i \(0.530424\pi\)
\(12\) 2.32803 0.672043
\(13\) −4.08101 −1.13187 −0.565934 0.824450i \(-0.691484\pi\)
−0.565934 + 0.824450i \(0.691484\pi\)
\(14\) −3.90453 −1.04353
\(15\) −0.341697 −0.0882259
\(16\) 1.68692 0.421729
\(17\) −1.27562 −0.309383 −0.154692 0.987963i \(-0.549438\pi\)
−0.154692 + 0.987963i \(0.549438\pi\)
\(18\) 6.09421 1.43642
\(19\) −0.310985 −0.0713448 −0.0356724 0.999364i \(-0.511357\pi\)
−0.0356724 + 0.999364i \(0.511357\pi\)
\(20\) −1.88735 −0.422024
\(21\) 1.07253 0.234046
\(22\) 1.49617 0.318985
\(23\) −3.61411 −0.753593 −0.376797 0.926296i \(-0.622974\pi\)
−0.376797 + 0.926296i \(0.622974\pi\)
\(24\) −2.43340 −0.496716
\(25\) −4.72298 −0.944597
\(26\) 9.64527 1.89159
\(27\) −3.62166 −0.696989
\(28\) 5.92408 1.11955
\(29\) −2.51840 −0.467655 −0.233828 0.972278i \(-0.575125\pi\)
−0.233828 + 0.972278i \(0.575125\pi\)
\(30\) 0.807585 0.147444
\(31\) −1.97607 −0.354913 −0.177456 0.984129i \(-0.556787\pi\)
−0.177456 + 0.984129i \(0.556787\pi\)
\(32\) 3.50948 0.620395
\(33\) −0.410983 −0.0715429
\(34\) 3.01487 0.517046
\(35\) −0.869510 −0.146974
\(36\) −9.24633 −1.54106
\(37\) 4.86204 0.799314 0.399657 0.916665i \(-0.369129\pi\)
0.399657 + 0.916665i \(0.369129\pi\)
\(38\) 0.734997 0.119232
\(39\) −2.64945 −0.424252
\(40\) 1.97278 0.311923
\(41\) 2.89719 0.452465 0.226233 0.974073i \(-0.427359\pi\)
0.226233 + 0.974073i \(0.427359\pi\)
\(42\) −2.53488 −0.391140
\(43\) −10.7661 −1.64181 −0.820905 0.571064i \(-0.806531\pi\)
−0.820905 + 0.571064i \(0.806531\pi\)
\(44\) −2.27004 −0.342222
\(45\) 1.35714 0.202310
\(46\) 8.54177 1.25942
\(47\) 8.11626 1.18388 0.591939 0.805983i \(-0.298363\pi\)
0.591939 + 0.805983i \(0.298363\pi\)
\(48\) 1.09517 0.158075
\(49\) −4.27075 −0.610107
\(50\) 11.1625 1.57862
\(51\) −0.828153 −0.115965
\(52\) −14.6341 −2.02939
\(53\) 5.26987 0.723873 0.361936 0.932203i \(-0.382116\pi\)
0.361936 + 0.932203i \(0.382116\pi\)
\(54\) 8.55962 1.16482
\(55\) 0.333187 0.0449269
\(56\) −6.19222 −0.827470
\(57\) −0.201896 −0.0267418
\(58\) 5.95212 0.781552
\(59\) 5.54935 0.722464 0.361232 0.932476i \(-0.382356\pi\)
0.361232 + 0.932476i \(0.382356\pi\)
\(60\) −1.22530 −0.158185
\(61\) 4.30300 0.550942 0.275471 0.961309i \(-0.411166\pi\)
0.275471 + 0.961309i \(0.411166\pi\)
\(62\) 4.67035 0.593135
\(63\) −4.25983 −0.536688
\(64\) −11.6683 −1.45854
\(65\) 2.14793 0.266418
\(66\) 0.971338 0.119563
\(67\) −3.11613 −0.380695 −0.190348 0.981717i \(-0.560962\pi\)
−0.190348 + 0.981717i \(0.560962\pi\)
\(68\) −4.57426 −0.554710
\(69\) −2.34633 −0.282465
\(70\) 2.05504 0.245625
\(71\) 6.57046 0.779771 0.389885 0.920863i \(-0.372515\pi\)
0.389885 + 0.920863i \(0.372515\pi\)
\(72\) 9.66485 1.13901
\(73\) 0.973762 0.113970 0.0569851 0.998375i \(-0.481851\pi\)
0.0569851 + 0.998375i \(0.481851\pi\)
\(74\) −11.4912 −1.33582
\(75\) −3.06623 −0.354058
\(76\) −1.11516 −0.127918
\(77\) −1.04582 −0.119182
\(78\) 6.26186 0.709016
\(79\) 4.86469 0.547320 0.273660 0.961826i \(-0.411766\pi\)
0.273660 + 0.961826i \(0.411766\pi\)
\(80\) −0.887864 −0.0992663
\(81\) 5.38432 0.598258
\(82\) −6.84738 −0.756166
\(83\) 12.8455 1.40997 0.704986 0.709221i \(-0.250953\pi\)
0.704986 + 0.709221i \(0.250953\pi\)
\(84\) 3.84600 0.419633
\(85\) 0.671389 0.0728224
\(86\) 25.4451 2.74382
\(87\) −1.63498 −0.175289
\(88\) 2.37279 0.252940
\(89\) 15.0161 1.59170 0.795851 0.605492i \(-0.207024\pi\)
0.795851 + 0.605492i \(0.207024\pi\)
\(90\) −3.20753 −0.338103
\(91\) −6.74200 −0.706754
\(92\) −12.9599 −1.35116
\(93\) −1.28290 −0.133030
\(94\) −19.1824 −1.97851
\(95\) 0.163679 0.0167931
\(96\) 2.27841 0.232539
\(97\) 11.4793 1.16555 0.582774 0.812635i \(-0.301967\pi\)
0.582774 + 0.812635i \(0.301967\pi\)
\(98\) 10.0937 1.01962
\(99\) 1.63232 0.164054
\(100\) −16.9362 −1.69362
\(101\) 5.98989 0.596016 0.298008 0.954563i \(-0.403678\pi\)
0.298008 + 0.954563i \(0.403678\pi\)
\(102\) 1.95730 0.193801
\(103\) −4.94804 −0.487545 −0.243772 0.969832i \(-0.578385\pi\)
−0.243772 + 0.969832i \(0.578385\pi\)
\(104\) 15.2965 1.49995
\(105\) −0.564499 −0.0550895
\(106\) −12.4551 −1.20975
\(107\) 8.12729 0.785695 0.392847 0.919604i \(-0.371490\pi\)
0.392847 + 0.919604i \(0.371490\pi\)
\(108\) −12.9869 −1.24967
\(109\) −7.64157 −0.731930 −0.365965 0.930629i \(-0.619261\pi\)
−0.365965 + 0.930629i \(0.619261\pi\)
\(110\) −0.787471 −0.0750824
\(111\) 3.15651 0.299603
\(112\) 2.78686 0.263334
\(113\) 7.67191 0.721712 0.360856 0.932621i \(-0.382485\pi\)
0.360856 + 0.932621i \(0.382485\pi\)
\(114\) 0.477172 0.0446912
\(115\) 1.90219 0.177380
\(116\) −9.03075 −0.838484
\(117\) 10.5230 0.972848
\(118\) −13.1156 −1.20739
\(119\) −2.10738 −0.193183
\(120\) 1.28076 0.116916
\(121\) −10.5993 −0.963569
\(122\) −10.1699 −0.920742
\(123\) 1.88090 0.169595
\(124\) −7.08601 −0.636342
\(125\) 5.11744 0.457717
\(126\) 10.0679 0.896920
\(127\) 14.5359 1.28985 0.644927 0.764244i \(-0.276888\pi\)
0.644927 + 0.764244i \(0.276888\pi\)
\(128\) 20.5586 1.81714
\(129\) −6.98950 −0.615391
\(130\) −5.07653 −0.445241
\(131\) −4.14418 −0.362078 −0.181039 0.983476i \(-0.557946\pi\)
−0.181039 + 0.983476i \(0.557946\pi\)
\(132\) −1.47375 −0.128273
\(133\) −0.513760 −0.0445487
\(134\) 7.36482 0.636223
\(135\) 1.90617 0.164057
\(136\) 4.78130 0.409993
\(137\) −10.3901 −0.887686 −0.443843 0.896105i \(-0.646385\pi\)
−0.443843 + 0.896105i \(0.646385\pi\)
\(138\) 5.54545 0.472060
\(139\) 14.5831 1.23692 0.618459 0.785817i \(-0.287757\pi\)
0.618459 + 0.785817i \(0.287757\pi\)
\(140\) −3.11798 −0.263517
\(141\) 5.26920 0.443747
\(142\) −15.5290 −1.30316
\(143\) 2.58346 0.216040
\(144\) −4.34975 −0.362479
\(145\) 1.32549 0.110076
\(146\) −2.30144 −0.190468
\(147\) −2.77264 −0.228683
\(148\) 17.4348 1.43313
\(149\) −0.869103 −0.0711997 −0.0355998 0.999366i \(-0.511334\pi\)
−0.0355998 + 0.999366i \(0.511334\pi\)
\(150\) 7.24690 0.591707
\(151\) 8.95417 0.728680 0.364340 0.931266i \(-0.381295\pi\)
0.364340 + 0.931266i \(0.381295\pi\)
\(152\) 1.16564 0.0945457
\(153\) 3.28921 0.265917
\(154\) 2.47174 0.199179
\(155\) 1.04005 0.0835390
\(156\) −9.50069 −0.760664
\(157\) −13.5009 −1.07749 −0.538744 0.842470i \(-0.681101\pi\)
−0.538744 + 0.842470i \(0.681101\pi\)
\(158\) −11.4975 −0.914689
\(159\) 3.42128 0.271325
\(160\) −1.84712 −0.146028
\(161\) −5.97066 −0.470554
\(162\) −12.7256 −0.999817
\(163\) 17.3353 1.35781 0.678903 0.734228i \(-0.262456\pi\)
0.678903 + 0.734228i \(0.262456\pi\)
\(164\) 10.3891 0.811250
\(165\) 0.216310 0.0168397
\(166\) −30.3596 −2.35636
\(167\) −4.66788 −0.361212 −0.180606 0.983556i \(-0.557806\pi\)
−0.180606 + 0.983556i \(0.557806\pi\)
\(168\) −4.02008 −0.310156
\(169\) 3.65463 0.281126
\(170\) −1.58680 −0.121702
\(171\) 0.801880 0.0613213
\(172\) −38.6061 −2.94369
\(173\) −9.99524 −0.759924 −0.379962 0.925002i \(-0.624063\pi\)
−0.379962 + 0.925002i \(0.624063\pi\)
\(174\) 3.86421 0.292945
\(175\) −7.80257 −0.589819
\(176\) −1.06790 −0.0804956
\(177\) 3.60273 0.270797
\(178\) −35.4898 −2.66007
\(179\) 16.4105 1.22658 0.613291 0.789857i \(-0.289845\pi\)
0.613291 + 0.789857i \(0.289845\pi\)
\(180\) 4.86656 0.362732
\(181\) 8.86149 0.658670 0.329335 0.944213i \(-0.393176\pi\)
0.329335 + 0.944213i \(0.393176\pi\)
\(182\) 15.9344 1.18114
\(183\) 2.79357 0.206507
\(184\) 13.5465 0.998658
\(185\) −2.55900 −0.188142
\(186\) 3.03206 0.222322
\(187\) 0.807526 0.0590521
\(188\) 29.1042 2.12264
\(189\) −5.98314 −0.435209
\(190\) −0.386846 −0.0280648
\(191\) −11.6906 −0.845900 −0.422950 0.906153i \(-0.639005\pi\)
−0.422950 + 0.906153i \(0.639005\pi\)
\(192\) −7.57526 −0.546697
\(193\) 9.31426 0.670455 0.335227 0.942137i \(-0.391187\pi\)
0.335227 + 0.942137i \(0.391187\pi\)
\(194\) −27.1308 −1.94788
\(195\) 1.39447 0.0998601
\(196\) −15.3145 −1.09389
\(197\) −15.1413 −1.07877 −0.539385 0.842059i \(-0.681343\pi\)
−0.539385 + 0.842059i \(0.681343\pi\)
\(198\) −3.85791 −0.274170
\(199\) −19.1608 −1.35827 −0.679136 0.734012i \(-0.737646\pi\)
−0.679136 + 0.734012i \(0.737646\pi\)
\(200\) 17.7028 1.25177
\(201\) −2.02304 −0.142694
\(202\) −14.1568 −0.996070
\(203\) −4.16051 −0.292010
\(204\) −2.96968 −0.207919
\(205\) −1.52486 −0.106501
\(206\) 11.6945 0.814791
\(207\) 9.31904 0.647718
\(208\) −6.88432 −0.477342
\(209\) 0.196867 0.0136176
\(210\) 1.33417 0.0920662
\(211\) 12.8339 0.883522 0.441761 0.897133i \(-0.354354\pi\)
0.441761 + 0.897133i \(0.354354\pi\)
\(212\) 18.8973 1.29787
\(213\) 4.26565 0.292277
\(214\) −19.2085 −1.31306
\(215\) 5.66644 0.386448
\(216\) 13.5748 0.923646
\(217\) −3.26456 −0.221612
\(218\) 18.0605 1.22321
\(219\) 0.632181 0.0427188
\(220\) 1.19478 0.0805518
\(221\) 5.20582 0.350181
\(222\) −7.46026 −0.500700
\(223\) 21.8682 1.46441 0.732203 0.681087i \(-0.238492\pi\)
0.732203 + 0.681087i \(0.238492\pi\)
\(224\) 5.79782 0.387383
\(225\) 12.1783 0.811887
\(226\) −18.1322 −1.20614
\(227\) 3.50310 0.232509 0.116254 0.993219i \(-0.462911\pi\)
0.116254 + 0.993219i \(0.462911\pi\)
\(228\) −0.723980 −0.0479468
\(229\) −17.5497 −1.15972 −0.579860 0.814716i \(-0.696893\pi\)
−0.579860 + 0.814716i \(0.696893\pi\)
\(230\) −4.49573 −0.296440
\(231\) −0.678961 −0.0446724
\(232\) 9.43951 0.619734
\(233\) −3.93239 −0.257620 −0.128810 0.991669i \(-0.541116\pi\)
−0.128810 + 0.991669i \(0.541116\pi\)
\(234\) −24.8705 −1.62584
\(235\) −4.27178 −0.278660
\(236\) 19.8995 1.29535
\(237\) 3.15823 0.205149
\(238\) 4.98070 0.322851
\(239\) −23.6035 −1.52678 −0.763392 0.645936i \(-0.776467\pi\)
−0.763392 + 0.645936i \(0.776467\pi\)
\(240\) −0.576415 −0.0372074
\(241\) 3.80978 0.245410 0.122705 0.992443i \(-0.460843\pi\)
0.122705 + 0.992443i \(0.460843\pi\)
\(242\) 25.0508 1.61033
\(243\) 14.3606 0.921231
\(244\) 15.4301 0.987814
\(245\) 2.24780 0.143607
\(246\) −4.44542 −0.283430
\(247\) 1.26913 0.0807529
\(248\) 7.40674 0.470329
\(249\) 8.33947 0.528492
\(250\) −12.0948 −0.764943
\(251\) 15.0718 0.951322 0.475661 0.879629i \(-0.342209\pi\)
0.475661 + 0.879629i \(0.342209\pi\)
\(252\) −15.2753 −0.962256
\(253\) 2.28789 0.143839
\(254\) −34.3549 −2.15562
\(255\) 0.435876 0.0272956
\(256\) −25.2526 −1.57829
\(257\) −31.1104 −1.94061 −0.970306 0.241882i \(-0.922235\pi\)
−0.970306 + 0.241882i \(0.922235\pi\)
\(258\) 16.5193 1.02845
\(259\) 8.03230 0.499103
\(260\) 7.70228 0.477675
\(261\) 6.49375 0.401953
\(262\) 9.79456 0.605110
\(263\) −8.72424 −0.537960 −0.268980 0.963146i \(-0.586686\pi\)
−0.268980 + 0.963146i \(0.586686\pi\)
\(264\) 1.54045 0.0948083
\(265\) −2.77366 −0.170384
\(266\) 1.21425 0.0744503
\(267\) 9.74867 0.596609
\(268\) −11.1741 −0.682569
\(269\) −31.0441 −1.89279 −0.946396 0.323010i \(-0.895305\pi\)
−0.946396 + 0.323010i \(0.895305\pi\)
\(270\) −4.50513 −0.274174
\(271\) 8.71066 0.529135 0.264567 0.964367i \(-0.414771\pi\)
0.264567 + 0.964367i \(0.414771\pi\)
\(272\) −2.15187 −0.130476
\(273\) −4.37701 −0.264909
\(274\) 24.5565 1.48351
\(275\) 2.98986 0.180296
\(276\) −8.41373 −0.506447
\(277\) 30.9394 1.85897 0.929484 0.368861i \(-0.120252\pi\)
0.929484 + 0.368861i \(0.120252\pi\)
\(278\) −34.4663 −2.06715
\(279\) 5.09534 0.305050
\(280\) 3.25911 0.194769
\(281\) 32.1693 1.91906 0.959530 0.281607i \(-0.0908673\pi\)
0.959530 + 0.281607i \(0.0908673\pi\)
\(282\) −12.4535 −0.741595
\(283\) −11.3371 −0.673919 −0.336960 0.941519i \(-0.609399\pi\)
−0.336960 + 0.941519i \(0.609399\pi\)
\(284\) 23.5611 1.39809
\(285\) 0.106263 0.00629445
\(286\) −6.10589 −0.361049
\(287\) 4.78629 0.282526
\(288\) −9.04927 −0.533234
\(289\) −15.3728 −0.904282
\(290\) −3.13274 −0.183961
\(291\) 7.45254 0.436876
\(292\) 3.49182 0.204343
\(293\) 5.05427 0.295274 0.147637 0.989042i \(-0.452833\pi\)
0.147637 + 0.989042i \(0.452833\pi\)
\(294\) 6.55300 0.382179
\(295\) −2.92076 −0.170053
\(296\) −18.2240 −1.05925
\(297\) 2.29268 0.133035
\(298\) 2.05408 0.118990
\(299\) 14.7492 0.852968
\(300\) −10.9952 −0.634810
\(301\) −17.7860 −1.02517
\(302\) −21.1628 −1.21778
\(303\) 3.88873 0.223402
\(304\) −0.524605 −0.0300882
\(305\) −2.26477 −0.129680
\(306\) −7.77390 −0.444404
\(307\) −18.1759 −1.03735 −0.518677 0.854970i \(-0.673575\pi\)
−0.518677 + 0.854970i \(0.673575\pi\)
\(308\) −3.75021 −0.213688
\(309\) −3.21234 −0.182744
\(310\) −2.45812 −0.139612
\(311\) 5.07837 0.287968 0.143984 0.989580i \(-0.454009\pi\)
0.143984 + 0.989580i \(0.454009\pi\)
\(312\) 9.93073 0.562217
\(313\) −27.1417 −1.53414 −0.767071 0.641563i \(-0.778286\pi\)
−0.767071 + 0.641563i \(0.778286\pi\)
\(314\) 31.9087 1.80071
\(315\) 2.24205 0.126325
\(316\) 17.4443 0.981320
\(317\) 19.0628 1.07067 0.535337 0.844638i \(-0.320185\pi\)
0.535337 + 0.844638i \(0.320185\pi\)
\(318\) −8.08604 −0.453442
\(319\) 1.59426 0.0892615
\(320\) 6.14132 0.343310
\(321\) 5.27636 0.294498
\(322\) 14.1114 0.786396
\(323\) 0.396698 0.0220729
\(324\) 19.3077 1.07265
\(325\) 19.2745 1.06916
\(326\) −40.9712 −2.26918
\(327\) −4.96103 −0.274345
\(328\) −10.8593 −0.599605
\(329\) 13.4084 0.739230
\(330\) −0.511238 −0.0281427
\(331\) −9.27026 −0.509540 −0.254770 0.967002i \(-0.582000\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(332\) 46.0626 2.52802
\(333\) −12.5369 −0.687015
\(334\) 11.0323 0.603662
\(335\) 1.64009 0.0896077
\(336\) 1.80927 0.0987039
\(337\) −19.9624 −1.08742 −0.543710 0.839273i \(-0.682981\pi\)
−0.543710 + 0.839273i \(0.682981\pi\)
\(338\) −8.63755 −0.469821
\(339\) 4.98072 0.270516
\(340\) 2.40754 0.130567
\(341\) 1.25094 0.0677423
\(342\) −1.89521 −0.102481
\(343\) −18.6198 −1.00537
\(344\) 40.3536 2.17572
\(345\) 1.23493 0.0664864
\(346\) 23.6233 1.27000
\(347\) 23.2231 1.24668 0.623340 0.781951i \(-0.285775\pi\)
0.623340 + 0.781951i \(0.285775\pi\)
\(348\) −5.86290 −0.314285
\(349\) −19.9715 −1.06905 −0.534524 0.845153i \(-0.679509\pi\)
−0.534524 + 0.845153i \(0.679509\pi\)
\(350\) 18.4410 0.985714
\(351\) 14.7800 0.788899
\(352\) −2.22166 −0.118415
\(353\) 6.19470 0.329711 0.164855 0.986318i \(-0.447284\pi\)
0.164855 + 0.986318i \(0.447284\pi\)
\(354\) −8.51487 −0.452560
\(355\) −3.45819 −0.183542
\(356\) 53.8463 2.85385
\(357\) −1.36814 −0.0724099
\(358\) −38.7855 −2.04988
\(359\) 27.9578 1.47556 0.737778 0.675044i \(-0.235875\pi\)
0.737778 + 0.675044i \(0.235875\pi\)
\(360\) −5.08684 −0.268100
\(361\) −18.9033 −0.994910
\(362\) −20.9437 −1.10078
\(363\) −6.88120 −0.361169
\(364\) −24.1762 −1.26718
\(365\) −0.512514 −0.0268262
\(366\) −6.60247 −0.345117
\(367\) 7.43665 0.388190 0.194095 0.980983i \(-0.437823\pi\)
0.194095 + 0.980983i \(0.437823\pi\)
\(368\) −6.09670 −0.317812
\(369\) −7.47047 −0.388897
\(370\) 6.04809 0.314425
\(371\) 8.70606 0.451996
\(372\) −4.60034 −0.238517
\(373\) 6.51575 0.337373 0.168686 0.985670i \(-0.446048\pi\)
0.168686 + 0.985670i \(0.446048\pi\)
\(374\) −1.90855 −0.0986887
\(375\) 3.32232 0.171564
\(376\) −30.4215 −1.56887
\(377\) 10.2776 0.529324
\(378\) 14.1409 0.727328
\(379\) 9.91005 0.509045 0.254523 0.967067i \(-0.418082\pi\)
0.254523 + 0.967067i \(0.418082\pi\)
\(380\) 0.586936 0.0301092
\(381\) 9.43694 0.483469
\(382\) 27.6301 1.41368
\(383\) −0.632507 −0.0323196 −0.0161598 0.999869i \(-0.505144\pi\)
−0.0161598 + 0.999869i \(0.505144\pi\)
\(384\) 13.3469 0.681109
\(385\) 0.550439 0.0280530
\(386\) −22.0138 −1.12047
\(387\) 27.7605 1.41115
\(388\) 41.1637 2.08977
\(389\) −6.18092 −0.313385 −0.156693 0.987647i \(-0.550083\pi\)
−0.156693 + 0.987647i \(0.550083\pi\)
\(390\) −3.29576 −0.166887
\(391\) 4.61023 0.233149
\(392\) 16.0077 0.808511
\(393\) −2.69046 −0.135716
\(394\) 35.7857 1.80286
\(395\) −2.56040 −0.128828
\(396\) 5.85335 0.294142
\(397\) 15.1784 0.761782 0.380891 0.924620i \(-0.375617\pi\)
0.380891 + 0.924620i \(0.375617\pi\)
\(398\) 45.2856 2.26996
\(399\) −0.333541 −0.0166979
\(400\) −7.96728 −0.398364
\(401\) 33.4282 1.66932 0.834662 0.550762i \(-0.185663\pi\)
0.834662 + 0.550762i \(0.185663\pi\)
\(402\) 4.78135 0.238472
\(403\) 8.06436 0.401715
\(404\) 21.4792 1.06863
\(405\) −2.83390 −0.140817
\(406\) 9.83316 0.488012
\(407\) −3.07789 −0.152565
\(408\) 3.10410 0.153676
\(409\) 0.408352 0.0201917 0.0100959 0.999949i \(-0.496786\pi\)
0.0100959 + 0.999949i \(0.496786\pi\)
\(410\) 3.60394 0.177986
\(411\) −6.74541 −0.332726
\(412\) −17.7432 −0.874145
\(413\) 9.16778 0.451117
\(414\) −22.0251 −1.08248
\(415\) −6.76087 −0.331878
\(416\) −14.3222 −0.702205
\(417\) 9.46754 0.463627
\(418\) −0.465287 −0.0227579
\(419\) −24.8485 −1.21393 −0.606964 0.794729i \(-0.707613\pi\)
−0.606964 + 0.794729i \(0.707613\pi\)
\(420\) −2.02424 −0.0987728
\(421\) −6.48342 −0.315983 −0.157991 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(422\) −30.3323 −1.47655
\(423\) −20.9279 −1.01755
\(424\) −19.7526 −0.959272
\(425\) 6.02474 0.292243
\(426\) −10.0817 −0.488458
\(427\) 7.10874 0.344016
\(428\) 29.1437 1.40871
\(429\) 1.67722 0.0809771
\(430\) −13.3924 −0.645837
\(431\) 3.48121 0.167684 0.0838421 0.996479i \(-0.473281\pi\)
0.0838421 + 0.996479i \(0.473281\pi\)
\(432\) −6.10944 −0.293941
\(433\) 16.8220 0.808413 0.404206 0.914668i \(-0.367548\pi\)
0.404206 + 0.914668i \(0.367548\pi\)
\(434\) 7.71562 0.370362
\(435\) 0.860531 0.0412593
\(436\) −27.4020 −1.31232
\(437\) 1.12393 0.0537649
\(438\) −1.49413 −0.0713923
\(439\) −28.9313 −1.38082 −0.690408 0.723420i \(-0.742569\pi\)
−0.690408 + 0.723420i \(0.742569\pi\)
\(440\) −1.24886 −0.0595369
\(441\) 11.0122 0.524391
\(442\) −12.3037 −0.585228
\(443\) 14.6616 0.696592 0.348296 0.937385i \(-0.386760\pi\)
0.348296 + 0.937385i \(0.386760\pi\)
\(444\) 11.3189 0.537173
\(445\) −7.90332 −0.374653
\(446\) −51.6845 −2.44733
\(447\) −0.564235 −0.0266874
\(448\) −19.2766 −0.910734
\(449\) 22.4037 1.05730 0.528649 0.848841i \(-0.322699\pi\)
0.528649 + 0.848841i \(0.322699\pi\)
\(450\) −28.7828 −1.35684
\(451\) −1.83405 −0.0863622
\(452\) 27.5108 1.29400
\(453\) 5.81318 0.273127
\(454\) −8.27941 −0.388572
\(455\) 3.54848 0.166355
\(456\) 0.756750 0.0354381
\(457\) 32.9272 1.54027 0.770135 0.637881i \(-0.220189\pi\)
0.770135 + 0.637881i \(0.220189\pi\)
\(458\) 41.4780 1.93814
\(459\) 4.61987 0.215637
\(460\) 6.82108 0.318034
\(461\) 12.2143 0.568876 0.284438 0.958695i \(-0.408193\pi\)
0.284438 + 0.958695i \(0.408193\pi\)
\(462\) 1.60469 0.0746571
\(463\) 40.6005 1.88686 0.943432 0.331567i \(-0.107577\pi\)
0.943432 + 0.331567i \(0.107577\pi\)
\(464\) −4.24833 −0.197224
\(465\) 0.675218 0.0313125
\(466\) 9.29402 0.430537
\(467\) 31.2808 1.44750 0.723751 0.690061i \(-0.242416\pi\)
0.723751 + 0.690061i \(0.242416\pi\)
\(468\) 37.7344 1.74427
\(469\) −5.14798 −0.237711
\(470\) 10.0961 0.465700
\(471\) −8.76498 −0.403869
\(472\) −20.8002 −0.957406
\(473\) 6.81541 0.313373
\(474\) −7.46433 −0.342848
\(475\) 1.46878 0.0673920
\(476\) −7.55687 −0.346369
\(477\) −13.5885 −0.622173
\(478\) 55.7857 2.55158
\(479\) 20.1463 0.920509 0.460255 0.887787i \(-0.347758\pi\)
0.460255 + 0.887787i \(0.347758\pi\)
\(480\) −1.19918 −0.0547349
\(481\) −19.8420 −0.904718
\(482\) −9.00423 −0.410132
\(483\) −3.87624 −0.176375
\(484\) −38.0079 −1.72763
\(485\) −6.04183 −0.274345
\(486\) −33.9405 −1.53957
\(487\) −6.32709 −0.286708 −0.143354 0.989671i \(-0.545789\pi\)
−0.143354 + 0.989671i \(0.545789\pi\)
\(488\) −16.1286 −0.730106
\(489\) 11.2543 0.508939
\(490\) −5.31256 −0.239997
\(491\) −38.6544 −1.74445 −0.872223 0.489108i \(-0.837322\pi\)
−0.872223 + 0.489108i \(0.837322\pi\)
\(492\) 6.74474 0.304076
\(493\) 3.21252 0.144685
\(494\) −2.99953 −0.134955
\(495\) −0.859128 −0.0386150
\(496\) −3.33347 −0.149677
\(497\) 10.8547 0.486900
\(498\) −19.7099 −0.883224
\(499\) 38.0515 1.70342 0.851709 0.524014i \(-0.175566\pi\)
0.851709 + 0.524014i \(0.175566\pi\)
\(500\) 18.3507 0.820666
\(501\) −3.03046 −0.135391
\(502\) −35.6214 −1.58986
\(503\) 25.1828 1.12285 0.561423 0.827529i \(-0.310254\pi\)
0.561423 + 0.827529i \(0.310254\pi\)
\(504\) 15.9668 0.711216
\(505\) −3.15262 −0.140290
\(506\) −5.40733 −0.240385
\(507\) 2.37264 0.105373
\(508\) 52.1244 2.31265
\(509\) 17.0270 0.754709 0.377355 0.926069i \(-0.376834\pi\)
0.377355 + 0.926069i \(0.376834\pi\)
\(510\) −1.03017 −0.0456168
\(511\) 1.60870 0.0711646
\(512\) 18.5661 0.820512
\(513\) 1.12628 0.0497265
\(514\) 73.5279 3.24318
\(515\) 2.60427 0.114758
\(516\) −25.0637 −1.10337
\(517\) −5.13796 −0.225967
\(518\) −18.9839 −0.834107
\(519\) −6.48906 −0.284838
\(520\) −8.05091 −0.353056
\(521\) 21.3881 0.937029 0.468515 0.883456i \(-0.344789\pi\)
0.468515 + 0.883456i \(0.344789\pi\)
\(522\) −15.3477 −0.671749
\(523\) 1.55238 0.0678810 0.0339405 0.999424i \(-0.489194\pi\)
0.0339405 + 0.999424i \(0.489194\pi\)
\(524\) −14.8606 −0.649190
\(525\) −5.06555 −0.221079
\(526\) 20.6193 0.899045
\(527\) 2.52072 0.109804
\(528\) −0.693294 −0.0301717
\(529\) −9.93824 −0.432097
\(530\) 6.55541 0.284749
\(531\) −14.3091 −0.620963
\(532\) −1.84230 −0.0798737
\(533\) −11.8235 −0.512131
\(534\) −23.0405 −0.997061
\(535\) −4.27759 −0.184936
\(536\) 11.6799 0.504496
\(537\) 10.6540 0.459753
\(538\) 73.3712 3.16326
\(539\) 2.70358 0.116451
\(540\) 6.83533 0.294146
\(541\) 0.480736 0.0206684 0.0103342 0.999947i \(-0.496710\pi\)
0.0103342 + 0.999947i \(0.496710\pi\)
\(542\) −20.5872 −0.884297
\(543\) 5.75302 0.246886
\(544\) −4.47677 −0.191940
\(545\) 4.02194 0.172281
\(546\) 10.3449 0.442719
\(547\) 16.5777 0.708810 0.354405 0.935092i \(-0.384683\pi\)
0.354405 + 0.935092i \(0.384683\pi\)
\(548\) −37.2579 −1.59158
\(549\) −11.0954 −0.473538
\(550\) −7.06640 −0.301312
\(551\) 0.783184 0.0333648
\(552\) 8.79457 0.374322
\(553\) 8.03668 0.341754
\(554\) −73.1238 −3.10673
\(555\) −1.66134 −0.0705202
\(556\) 52.2935 2.21774
\(557\) −25.3169 −1.07271 −0.536356 0.843992i \(-0.680200\pi\)
−0.536356 + 0.843992i \(0.680200\pi\)
\(558\) −12.0426 −0.509803
\(559\) 43.9364 1.85831
\(560\) −1.46679 −0.0619832
\(561\) 0.524258 0.0221342
\(562\) −76.0306 −3.20716
\(563\) −24.4573 −1.03075 −0.515376 0.856964i \(-0.672348\pi\)
−0.515376 + 0.856964i \(0.672348\pi\)
\(564\) 18.8949 0.795617
\(565\) −4.03791 −0.169876
\(566\) 26.7946 1.12626
\(567\) 8.89513 0.373560
\(568\) −24.6275 −1.03335
\(569\) −22.3472 −0.936841 −0.468421 0.883506i \(-0.655177\pi\)
−0.468421 + 0.883506i \(0.655177\pi\)
\(570\) −0.251147 −0.0105194
\(571\) 25.1290 1.05162 0.525808 0.850603i \(-0.323763\pi\)
0.525808 + 0.850603i \(0.323763\pi\)
\(572\) 9.26406 0.387350
\(573\) −7.58970 −0.317064
\(574\) −11.3122 −0.472161
\(575\) 17.0694 0.711842
\(576\) 30.0870 1.25363
\(577\) 5.14159 0.214047 0.107024 0.994256i \(-0.465868\pi\)
0.107024 + 0.994256i \(0.465868\pi\)
\(578\) 36.3329 1.51125
\(579\) 6.04696 0.251303
\(580\) 4.75310 0.197362
\(581\) 21.2213 0.880406
\(582\) −17.6137 −0.730113
\(583\) −3.33607 −0.138166
\(584\) −3.64987 −0.151033
\(585\) −5.53848 −0.228988
\(586\) −11.9455 −0.493465
\(587\) 27.8853 1.15095 0.575474 0.817820i \(-0.304817\pi\)
0.575474 + 0.817820i \(0.304817\pi\)
\(588\) −9.94242 −0.410019
\(589\) 0.614528 0.0253212
\(590\) 6.90307 0.284195
\(591\) −9.82995 −0.404350
\(592\) 8.20185 0.337094
\(593\) −47.1304 −1.93541 −0.967706 0.252080i \(-0.918885\pi\)
−0.967706 + 0.252080i \(0.918885\pi\)
\(594\) −5.41863 −0.222329
\(595\) 1.10916 0.0454713
\(596\) −3.11652 −0.127658
\(597\) −12.4395 −0.509114
\(598\) −34.8590 −1.42549
\(599\) 13.1755 0.538337 0.269169 0.963093i \(-0.413251\pi\)
0.269169 + 0.963093i \(0.413251\pi\)
\(600\) 11.4929 0.469196
\(601\) −11.7942 −0.481096 −0.240548 0.970637i \(-0.577327\pi\)
−0.240548 + 0.970637i \(0.577327\pi\)
\(602\) 42.0364 1.71328
\(603\) 8.03499 0.327210
\(604\) 32.1088 1.30649
\(605\) 5.57864 0.226804
\(606\) −9.19082 −0.373352
\(607\) 28.4747 1.15575 0.577877 0.816124i \(-0.303881\pi\)
0.577877 + 0.816124i \(0.303881\pi\)
\(608\) −1.09140 −0.0442619
\(609\) −2.70107 −0.109453
\(610\) 5.35267 0.216723
\(611\) −33.1225 −1.33999
\(612\) 11.7948 0.476777
\(613\) 25.2323 1.01912 0.509562 0.860434i \(-0.329808\pi\)
0.509562 + 0.860434i \(0.329808\pi\)
\(614\) 42.9579 1.73364
\(615\) −0.989963 −0.0399192
\(616\) 3.91995 0.157939
\(617\) 32.1226 1.29321 0.646603 0.762827i \(-0.276189\pi\)
0.646603 + 0.762827i \(0.276189\pi\)
\(618\) 7.59222 0.305404
\(619\) −10.0797 −0.405138 −0.202569 0.979268i \(-0.564929\pi\)
−0.202569 + 0.979268i \(0.564929\pi\)
\(620\) 3.72953 0.149782
\(621\) 13.0891 0.525246
\(622\) −12.0025 −0.481256
\(623\) 24.8072 0.993881
\(624\) −4.46941 −0.178920
\(625\) 20.9215 0.836860
\(626\) 64.1482 2.56388
\(627\) 0.127809 0.00510421
\(628\) −48.4129 −1.93188
\(629\) −6.20211 −0.247295
\(630\) −5.29897 −0.211116
\(631\) −16.1451 −0.642726 −0.321363 0.946956i \(-0.604141\pi\)
−0.321363 + 0.946956i \(0.604141\pi\)
\(632\) −18.2339 −0.725306
\(633\) 8.33196 0.331166
\(634\) −45.0541 −1.78933
\(635\) −7.65059 −0.303605
\(636\) 12.2684 0.486474
\(637\) 17.4290 0.690561
\(638\) −3.76796 −0.149175
\(639\) −16.9421 −0.670218
\(640\) −10.8205 −0.427717
\(641\) 11.1707 0.441217 0.220608 0.975362i \(-0.429196\pi\)
0.220608 + 0.975362i \(0.429196\pi\)
\(642\) −12.4704 −0.492169
\(643\) −41.0142 −1.61744 −0.808722 0.588191i \(-0.799840\pi\)
−0.808722 + 0.588191i \(0.799840\pi\)
\(644\) −21.4102 −0.843682
\(645\) 3.67874 0.144850
\(646\) −0.937578 −0.0368885
\(647\) −2.94961 −0.115961 −0.0579806 0.998318i \(-0.518466\pi\)
−0.0579806 + 0.998318i \(0.518466\pi\)
\(648\) −20.1816 −0.792808
\(649\) −3.51299 −0.137897
\(650\) −45.5545 −1.78679
\(651\) −2.11940 −0.0830658
\(652\) 62.1628 2.43448
\(653\) 18.7782 0.734847 0.367424 0.930054i \(-0.380240\pi\)
0.367424 + 0.930054i \(0.380240\pi\)
\(654\) 11.7252 0.458490
\(655\) 2.18118 0.0852256
\(656\) 4.88732 0.190818
\(657\) −2.51086 −0.0979581
\(658\) −31.6901 −1.23541
\(659\) 33.6369 1.31031 0.655153 0.755496i \(-0.272604\pi\)
0.655153 + 0.755496i \(0.272604\pi\)
\(660\) 0.775667 0.0301928
\(661\) −13.3413 −0.518915 −0.259457 0.965755i \(-0.583544\pi\)
−0.259457 + 0.965755i \(0.583544\pi\)
\(662\) 21.9098 0.851549
\(663\) 3.37970 0.131257
\(664\) −48.1476 −1.86849
\(665\) 0.270404 0.0104858
\(666\) 29.6303 1.14815
\(667\) 9.10177 0.352422
\(668\) −16.7386 −0.647636
\(669\) 14.1972 0.548895
\(670\) −3.87628 −0.149754
\(671\) −2.72399 −0.105159
\(672\) 3.76403 0.145201
\(673\) −0.197926 −0.00762950 −0.00381475 0.999993i \(-0.501214\pi\)
−0.00381475 + 0.999993i \(0.501214\pi\)
\(674\) 47.1801 1.81731
\(675\) 17.1050 0.658373
\(676\) 13.1052 0.504045
\(677\) 10.9735 0.421745 0.210872 0.977514i \(-0.432370\pi\)
0.210872 + 0.977514i \(0.432370\pi\)
\(678\) −11.7717 −0.452089
\(679\) 18.9643 0.727784
\(680\) −2.51651 −0.0965039
\(681\) 2.27427 0.0871501
\(682\) −2.95654 −0.113212
\(683\) 30.6641 1.17333 0.586664 0.809830i \(-0.300441\pi\)
0.586664 + 0.809830i \(0.300441\pi\)
\(684\) 2.87547 0.109946
\(685\) 5.46855 0.208943
\(686\) 44.0069 1.68019
\(687\) −11.3936 −0.434691
\(688\) −18.1615 −0.692400
\(689\) −21.5064 −0.819328
\(690\) −2.91870 −0.111113
\(691\) 18.6644 0.710026 0.355013 0.934861i \(-0.384476\pi\)
0.355013 + 0.934861i \(0.384476\pi\)
\(692\) −35.8420 −1.36251
\(693\) 2.69666 0.102438
\(694\) −54.8866 −2.08347
\(695\) −7.67540 −0.291145
\(696\) 6.12828 0.232292
\(697\) −3.69572 −0.139985
\(698\) 47.2016 1.78661
\(699\) −2.55297 −0.0965622
\(700\) −27.9793 −1.05752
\(701\) −14.2851 −0.539541 −0.269770 0.962925i \(-0.586948\pi\)
−0.269770 + 0.962925i \(0.586948\pi\)
\(702\) −34.9319 −1.31842
\(703\) −1.51202 −0.0570269
\(704\) 7.38659 0.278392
\(705\) −2.77330 −0.104449
\(706\) −14.6409 −0.551017
\(707\) 9.89556 0.372161
\(708\) 12.9190 0.485527
\(709\) 16.7757 0.630024 0.315012 0.949088i \(-0.397992\pi\)
0.315012 + 0.949088i \(0.397992\pi\)
\(710\) 8.17327 0.306737
\(711\) −12.5437 −0.470425
\(712\) −56.2836 −2.10932
\(713\) 7.14173 0.267460
\(714\) 3.23354 0.121012
\(715\) −1.35974 −0.0508513
\(716\) 58.8467 2.19920
\(717\) −15.3238 −0.572276
\(718\) −66.0769 −2.46597
\(719\) −17.9755 −0.670373 −0.335187 0.942152i \(-0.608799\pi\)
−0.335187 + 0.942152i \(0.608799\pi\)
\(720\) 2.28938 0.0853200
\(721\) −8.17437 −0.304430
\(722\) 44.6770 1.66271
\(723\) 2.47337 0.0919855
\(724\) 31.7765 1.18096
\(725\) 11.8944 0.441746
\(726\) 16.2634 0.603591
\(727\) 12.5687 0.466146 0.233073 0.972459i \(-0.425122\pi\)
0.233073 + 0.972459i \(0.425122\pi\)
\(728\) 25.2705 0.936587
\(729\) −6.82987 −0.252958
\(730\) 1.21130 0.0448323
\(731\) 13.7334 0.507949
\(732\) 10.0175 0.370257
\(733\) −15.9789 −0.590194 −0.295097 0.955467i \(-0.595352\pi\)
−0.295097 + 0.955467i \(0.595352\pi\)
\(734\) −17.5762 −0.648748
\(735\) 1.45930 0.0538273
\(736\) −12.6837 −0.467526
\(737\) 1.97265 0.0726635
\(738\) 17.6561 0.649930
\(739\) −39.0078 −1.43493 −0.717463 0.696596i \(-0.754697\pi\)
−0.717463 + 0.696596i \(0.754697\pi\)
\(740\) −9.17635 −0.337329
\(741\) 0.823939 0.0302682
\(742\) −20.5764 −0.755382
\(743\) 26.5753 0.974952 0.487476 0.873136i \(-0.337918\pi\)
0.487476 + 0.873136i \(0.337918\pi\)
\(744\) 4.80857 0.176291
\(745\) 0.457429 0.0167589
\(746\) −15.3997 −0.563821
\(747\) −33.1223 −1.21188
\(748\) 2.89571 0.105878
\(749\) 13.4266 0.490599
\(750\) −7.85214 −0.286720
\(751\) −23.4259 −0.854822 −0.427411 0.904057i \(-0.640574\pi\)
−0.427411 + 0.904057i \(0.640574\pi\)
\(752\) 13.6915 0.499276
\(753\) 9.78483 0.356579
\(754\) −24.2907 −0.884614
\(755\) −4.71279 −0.171516
\(756\) −21.4550 −0.780310
\(757\) 40.0411 1.45532 0.727659 0.685939i \(-0.240608\pi\)
0.727659 + 0.685939i \(0.240608\pi\)
\(758\) −23.4219 −0.850723
\(759\) 1.48534 0.0539143
\(760\) −0.613503 −0.0222541
\(761\) −16.7667 −0.607792 −0.303896 0.952705i \(-0.598287\pi\)
−0.303896 + 0.952705i \(0.598287\pi\)
\(762\) −22.3038 −0.807980
\(763\) −12.6242 −0.457027
\(764\) −41.9213 −1.51666
\(765\) −1.73119 −0.0625913
\(766\) 1.49490 0.0540129
\(767\) −22.6470 −0.817734
\(768\) −16.3944 −0.591580
\(769\) 30.6719 1.10606 0.553028 0.833163i \(-0.313472\pi\)
0.553028 + 0.833163i \(0.313472\pi\)
\(770\) −1.30094 −0.0468825
\(771\) −20.1973 −0.727389
\(772\) 33.4001 1.20209
\(773\) −16.3817 −0.589210 −0.294605 0.955619i \(-0.595188\pi\)
−0.294605 + 0.955619i \(0.595188\pi\)
\(774\) −65.6107 −2.35833
\(775\) 9.33295 0.335249
\(776\) −43.0269 −1.54458
\(777\) 5.21469 0.187076
\(778\) 14.6083 0.523733
\(779\) −0.900982 −0.0322810
\(780\) 5.00044 0.179044
\(781\) −4.15940 −0.148835
\(782\) −10.8961 −0.389642
\(783\) 9.12079 0.325951
\(784\) −7.20441 −0.257300
\(785\) 7.10583 0.253618
\(786\) 6.35878 0.226810
\(787\) −30.2666 −1.07889 −0.539444 0.842022i \(-0.681365\pi\)
−0.539444 + 0.842022i \(0.681365\pi\)
\(788\) −54.2952 −1.93419
\(789\) −5.66391 −0.201640
\(790\) 6.05139 0.215299
\(791\) 12.6743 0.450647
\(792\) −6.11829 −0.217404
\(793\) −17.5606 −0.623594
\(794\) −35.8734 −1.27310
\(795\) −1.80070 −0.0638643
\(796\) −68.7088 −2.43532
\(797\) 31.5290 1.11681 0.558406 0.829567i \(-0.311413\pi\)
0.558406 + 0.829567i \(0.311413\pi\)
\(798\) 0.788308 0.0279058
\(799\) −10.3533 −0.366272
\(800\) −16.5752 −0.586023
\(801\) −38.7193 −1.36808
\(802\) −79.0059 −2.78980
\(803\) −0.616435 −0.0217535
\(804\) −7.25442 −0.255844
\(805\) 3.14250 0.110759
\(806\) −19.0597 −0.671351
\(807\) −20.1543 −0.709465
\(808\) −22.4514 −0.789838
\(809\) 10.0219 0.352352 0.176176 0.984359i \(-0.443627\pi\)
0.176176 + 0.984359i \(0.443627\pi\)
\(810\) 6.69778 0.235336
\(811\) −28.8994 −1.01479 −0.507397 0.861712i \(-0.669392\pi\)
−0.507397 + 0.861712i \(0.669392\pi\)
\(812\) −14.9192 −0.523561
\(813\) 5.65509 0.198333
\(814\) 7.27445 0.254969
\(815\) −9.12398 −0.319599
\(816\) −1.39702 −0.0489057
\(817\) 3.34808 0.117135
\(818\) −0.965121 −0.0337447
\(819\) 17.3844 0.607460
\(820\) −5.46801 −0.190951
\(821\) −48.9801 −1.70942 −0.854709 0.519107i \(-0.826265\pi\)
−0.854709 + 0.519107i \(0.826265\pi\)
\(822\) 15.9424 0.556057
\(823\) −2.10161 −0.0732576 −0.0366288 0.999329i \(-0.511662\pi\)
−0.0366288 + 0.999329i \(0.511662\pi\)
\(824\) 18.5463 0.646092
\(825\) 1.94106 0.0675792
\(826\) −21.6676 −0.753912
\(827\) 8.59211 0.298777 0.149388 0.988779i \(-0.452269\pi\)
0.149388 + 0.988779i \(0.452269\pi\)
\(828\) 33.4172 1.16133
\(829\) 6.46277 0.224461 0.112231 0.993682i \(-0.464200\pi\)
0.112231 + 0.993682i \(0.464200\pi\)
\(830\) 15.9790 0.554639
\(831\) 20.0863 0.696787
\(832\) 47.6186 1.65088
\(833\) 5.44786 0.188757
\(834\) −22.3761 −0.774820
\(835\) 2.45682 0.0850217
\(836\) 0.705948 0.0244157
\(837\) 7.15666 0.247370
\(838\) 58.7282 2.02873
\(839\) −28.6908 −0.990515 −0.495257 0.868746i \(-0.664926\pi\)
−0.495257 + 0.868746i \(0.664926\pi\)
\(840\) 2.11586 0.0730043
\(841\) −22.6577 −0.781298
\(842\) 15.3233 0.528074
\(843\) 20.8848 0.719311
\(844\) 46.0212 1.58411
\(845\) −1.92352 −0.0661711
\(846\) 49.4622 1.70054
\(847\) −17.5104 −0.601665
\(848\) 8.88984 0.305278
\(849\) −7.36020 −0.252601
\(850\) −14.2392 −0.488400
\(851\) −17.5719 −0.602358
\(852\) 15.2962 0.524040
\(853\) 23.8723 0.817371 0.408686 0.912675i \(-0.365987\pi\)
0.408686 + 0.912675i \(0.365987\pi\)
\(854\) −16.8012 −0.574924
\(855\) −0.422048 −0.0144337
\(856\) −30.4629 −1.04120
\(857\) −37.1228 −1.26809 −0.634045 0.773296i \(-0.718607\pi\)
−0.634045 + 0.773296i \(0.718607\pi\)
\(858\) −3.96404 −0.135330
\(859\) −20.2360 −0.690442 −0.345221 0.938521i \(-0.612196\pi\)
−0.345221 + 0.938521i \(0.612196\pi\)
\(860\) 20.3193 0.692883
\(861\) 3.10733 0.105898
\(862\) −8.22769 −0.280236
\(863\) −31.4426 −1.07032 −0.535159 0.844751i \(-0.679748\pi\)
−0.535159 + 0.844751i \(0.679748\pi\)
\(864\) −12.7102 −0.432408
\(865\) 5.26073 0.178870
\(866\) −39.7579 −1.35103
\(867\) −9.98025 −0.338947
\(868\) −11.7064 −0.397341
\(869\) −3.07957 −0.104467
\(870\) −2.03382 −0.0689531
\(871\) 12.7169 0.430897
\(872\) 28.6423 0.969950
\(873\) −29.5996 −1.00180
\(874\) −2.65636 −0.0898527
\(875\) 8.45423 0.285805
\(876\) 2.26694 0.0765929
\(877\) −42.6242 −1.43932 −0.719659 0.694328i \(-0.755702\pi\)
−0.719659 + 0.694328i \(0.755702\pi\)
\(878\) 68.3778 2.30764
\(879\) 3.28131 0.110676
\(880\) 0.562059 0.0189470
\(881\) −26.2582 −0.884661 −0.442330 0.896852i \(-0.645848\pi\)
−0.442330 + 0.896852i \(0.645848\pi\)
\(882\) −26.0269 −0.876370
\(883\) −30.4910 −1.02610 −0.513052 0.858357i \(-0.671485\pi\)
−0.513052 + 0.858357i \(0.671485\pi\)
\(884\) 18.6676 0.627859
\(885\) −1.89620 −0.0637401
\(886\) −34.6519 −1.16415
\(887\) −19.5268 −0.655644 −0.327822 0.944739i \(-0.606315\pi\)
−0.327822 + 0.944739i \(0.606315\pi\)
\(888\) −11.8313 −0.397032
\(889\) 24.0140 0.805402
\(890\) 18.6791 0.626126
\(891\) −3.40852 −0.114190
\(892\) 78.4175 2.62561
\(893\) −2.52403 −0.0844635
\(894\) 1.33354 0.0446003
\(895\) −8.63726 −0.288712
\(896\) 33.9637 1.13465
\(897\) 9.57541 0.319713
\(898\) −52.9502 −1.76697
\(899\) 4.97654 0.165977
\(900\) 43.6703 1.45568
\(901\) −6.72236 −0.223954
\(902\) 4.33470 0.144330
\(903\) −11.5470 −0.384259
\(904\) −28.7560 −0.956410
\(905\) −4.66401 −0.155037
\(906\) −13.7392 −0.456454
\(907\) 24.1460 0.801756 0.400878 0.916131i \(-0.368705\pi\)
0.400878 + 0.916131i \(0.368705\pi\)
\(908\) 12.5618 0.416878
\(909\) −15.4450 −0.512280
\(910\) −8.38665 −0.278015
\(911\) −28.5199 −0.944907 −0.472453 0.881356i \(-0.656631\pi\)
−0.472453 + 0.881356i \(0.656631\pi\)
\(912\) −0.340582 −0.0112778
\(913\) −8.13176 −0.269122
\(914\) −77.8219 −2.57412
\(915\) −1.47032 −0.0486074
\(916\) −62.9317 −2.07932
\(917\) −6.84636 −0.226087
\(918\) −10.9188 −0.360375
\(919\) −38.8303 −1.28089 −0.640446 0.768003i \(-0.721251\pi\)
−0.640446 + 0.768003i \(0.721251\pi\)
\(920\) −7.12982 −0.235063
\(921\) −11.8001 −0.388826
\(922\) −28.8679 −0.950712
\(923\) −26.8141 −0.882598
\(924\) −2.43469 −0.0800955
\(925\) −22.9633 −0.755029
\(926\) −95.9572 −3.15335
\(927\) 12.7586 0.419048
\(928\) −8.83829 −0.290131
\(929\) −13.3814 −0.439029 −0.219514 0.975609i \(-0.570447\pi\)
−0.219514 + 0.975609i \(0.570447\pi\)
\(930\) −1.59585 −0.0523299
\(931\) 1.32814 0.0435280
\(932\) −14.1012 −0.461900
\(933\) 3.29696 0.107938
\(934\) −73.9307 −2.41909
\(935\) −0.425020 −0.0138996
\(936\) −39.4423 −1.28921
\(937\) 33.2360 1.08577 0.542887 0.839806i \(-0.317331\pi\)
0.542887 + 0.839806i \(0.317331\pi\)
\(938\) 12.1670 0.397267
\(939\) −17.6208 −0.575034
\(940\) −15.3182 −0.499625
\(941\) 16.6981 0.544344 0.272172 0.962249i \(-0.412258\pi\)
0.272172 + 0.962249i \(0.412258\pi\)
\(942\) 20.7156 0.674951
\(943\) −10.4708 −0.340975
\(944\) 9.36130 0.304684
\(945\) 3.14907 0.102439
\(946\) −16.1079 −0.523713
\(947\) −41.6671 −1.35400 −0.676999 0.735984i \(-0.736720\pi\)
−0.676999 + 0.735984i \(0.736720\pi\)
\(948\) 11.3251 0.367823
\(949\) −3.97393 −0.128999
\(950\) −3.47138 −0.112626
\(951\) 12.3759 0.401315
\(952\) 7.89892 0.256006
\(953\) −0.601559 −0.0194864 −0.00974321 0.999953i \(-0.503101\pi\)
−0.00974321 + 0.999953i \(0.503101\pi\)
\(954\) 32.1157 1.03978
\(955\) 6.15302 0.199107
\(956\) −84.6400 −2.73745
\(957\) 1.03502 0.0334574
\(958\) −47.6149 −1.53837
\(959\) −17.1649 −0.554283
\(960\) 3.98704 0.128681
\(961\) −27.0951 −0.874037
\(962\) 46.8957 1.51198
\(963\) −20.9564 −0.675310
\(964\) 13.6615 0.440008
\(965\) −4.90231 −0.157811
\(966\) 9.16132 0.294761
\(967\) 42.4904 1.36640 0.683199 0.730232i \(-0.260588\pi\)
0.683199 + 0.730232i \(0.260588\pi\)
\(968\) 39.7283 1.27692
\(969\) 0.257543 0.00827346
\(970\) 14.2796 0.458490
\(971\) −53.6985 −1.72327 −0.861633 0.507531i \(-0.830558\pi\)
−0.861633 + 0.507531i \(0.830558\pi\)
\(972\) 51.4957 1.65172
\(973\) 24.0918 0.772349
\(974\) 14.9538 0.479150
\(975\) 12.5133 0.400747
\(976\) 7.25880 0.232349
\(977\) 52.4695 1.67865 0.839324 0.543632i \(-0.182951\pi\)
0.839324 + 0.543632i \(0.182951\pi\)
\(978\) −26.5991 −0.850546
\(979\) −9.50587 −0.303809
\(980\) 8.06039 0.257480
\(981\) 19.7039 0.629099
\(982\) 91.3577 2.91534
\(983\) 21.0306 0.670772 0.335386 0.942081i \(-0.391133\pi\)
0.335386 + 0.942081i \(0.391133\pi\)
\(984\) −7.05003 −0.224747
\(985\) 7.96921 0.253920
\(986\) −7.59265 −0.241799
\(987\) 8.70495 0.277082
\(988\) 4.55099 0.144786
\(989\) 38.9097 1.23726
\(990\) 2.03051 0.0645338
\(991\) −13.7116 −0.435563 −0.217782 0.975998i \(-0.569882\pi\)
−0.217782 + 0.975998i \(0.569882\pi\)
\(992\) −6.93499 −0.220186
\(993\) −6.01840 −0.190988
\(994\) −25.6546 −0.813713
\(995\) 10.0848 0.319709
\(996\) 29.9046 0.947562
\(997\) 23.1884 0.734385 0.367192 0.930145i \(-0.380319\pi\)
0.367192 + 0.930145i \(0.380319\pi\)
\(998\) −89.9329 −2.84678
\(999\) −17.6086 −0.557113
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 4027.2.a.c.1.18 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.18 174 1.1 even 1 trivial