Properties

Label 4027.2.a.c.1.15
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 1.15
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41774 q^{2} -1.12112 q^{3} +3.84547 q^{4} +1.14031 q^{5} +2.71058 q^{6} +1.36358 q^{7} -4.46187 q^{8} -1.74309 q^{9} +O(q^{10})\) \(q-2.41774 q^{2} -1.12112 q^{3} +3.84547 q^{4} +1.14031 q^{5} +2.71058 q^{6} +1.36358 q^{7} -4.46187 q^{8} -1.74309 q^{9} -2.75699 q^{10} +0.0870099 q^{11} -4.31124 q^{12} +6.43997 q^{13} -3.29679 q^{14} -1.27843 q^{15} +3.09671 q^{16} +2.91130 q^{17} +4.21433 q^{18} +3.65638 q^{19} +4.38505 q^{20} -1.52874 q^{21} -0.210367 q^{22} -0.109143 q^{23} +5.00230 q^{24} -3.69968 q^{25} -15.5702 q^{26} +5.31758 q^{27} +5.24362 q^{28} +6.93773 q^{29} +3.09092 q^{30} +4.75193 q^{31} +1.43670 q^{32} -0.0975486 q^{33} -7.03877 q^{34} +1.55491 q^{35} -6.70299 q^{36} -8.84338 q^{37} -8.84018 q^{38} -7.21998 q^{39} -5.08794 q^{40} +8.26020 q^{41} +3.69610 q^{42} -4.98099 q^{43} +0.334594 q^{44} -1.98767 q^{45} +0.263881 q^{46} +5.18867 q^{47} -3.47179 q^{48} -5.14064 q^{49} +8.94487 q^{50} -3.26392 q^{51} +24.7647 q^{52} +4.14206 q^{53} -12.8565 q^{54} +0.0992186 q^{55} -6.08413 q^{56} -4.09924 q^{57} -16.7736 q^{58} +11.6476 q^{59} -4.91617 q^{60} +3.54812 q^{61} -11.4889 q^{62} -2.37684 q^{63} -9.66699 q^{64} +7.34359 q^{65} +0.235847 q^{66} +1.69075 q^{67} +11.1953 q^{68} +0.122363 q^{69} -3.75938 q^{70} +7.48161 q^{71} +7.77743 q^{72} -10.0462 q^{73} +21.3810 q^{74} +4.14779 q^{75} +14.0605 q^{76} +0.118645 q^{77} +17.4561 q^{78} -12.0541 q^{79} +3.53123 q^{80} -0.732387 q^{81} -19.9710 q^{82} -2.74298 q^{83} -5.87873 q^{84} +3.31980 q^{85} +12.0427 q^{86} -7.77804 q^{87} -0.388227 q^{88} +2.53675 q^{89} +4.80567 q^{90} +8.78142 q^{91} -0.419708 q^{92} -5.32749 q^{93} -12.5449 q^{94} +4.16942 q^{95} -1.61071 q^{96} +2.88915 q^{97} +12.4287 q^{98} -0.151666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41774 −1.70960 −0.854801 0.518957i \(-0.826321\pi\)
−0.854801 + 0.518957i \(0.826321\pi\)
\(3\) −1.12112 −0.647280 −0.323640 0.946180i \(-0.604907\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(4\) 3.84547 1.92274
\(5\) 1.14031 0.509964 0.254982 0.966946i \(-0.417930\pi\)
0.254982 + 0.966946i \(0.417930\pi\)
\(6\) 2.71058 1.10659
\(7\) 1.36358 0.515385 0.257693 0.966227i \(-0.417038\pi\)
0.257693 + 0.966227i \(0.417038\pi\)
\(8\) −4.46187 −1.57751
\(9\) −1.74309 −0.581029
\(10\) −2.75699 −0.871836
\(11\) 0.0870099 0.0262345 0.0131172 0.999914i \(-0.495825\pi\)
0.0131172 + 0.999914i \(0.495825\pi\)
\(12\) −4.31124 −1.24455
\(13\) 6.43997 1.78613 0.893063 0.449932i \(-0.148552\pi\)
0.893063 + 0.449932i \(0.148552\pi\)
\(14\) −3.29679 −0.881104
\(15\) −1.27843 −0.330090
\(16\) 3.09671 0.774178
\(17\) 2.91130 0.706094 0.353047 0.935606i \(-0.385146\pi\)
0.353047 + 0.935606i \(0.385146\pi\)
\(18\) 4.21433 0.993328
\(19\) 3.65638 0.838831 0.419415 0.907794i \(-0.362235\pi\)
0.419415 + 0.907794i \(0.362235\pi\)
\(20\) 4.38505 0.980527
\(21\) −1.52874 −0.333599
\(22\) −0.210367 −0.0448505
\(23\) −0.109143 −0.0227580 −0.0113790 0.999935i \(-0.503622\pi\)
−0.0113790 + 0.999935i \(0.503622\pi\)
\(24\) 5.00230 1.02109
\(25\) −3.69968 −0.739936
\(26\) −15.5702 −3.05356
\(27\) 5.31758 1.02337
\(28\) 5.24362 0.990950
\(29\) 6.93773 1.28830 0.644152 0.764897i \(-0.277210\pi\)
0.644152 + 0.764897i \(0.277210\pi\)
\(30\) 3.09092 0.564321
\(31\) 4.75193 0.853472 0.426736 0.904376i \(-0.359663\pi\)
0.426736 + 0.904376i \(0.359663\pi\)
\(32\) 1.43670 0.253975
\(33\) −0.0975486 −0.0169810
\(34\) −7.03877 −1.20714
\(35\) 1.55491 0.262828
\(36\) −6.70299 −1.11717
\(37\) −8.84338 −1.45384 −0.726921 0.686721i \(-0.759049\pi\)
−0.726921 + 0.686721i \(0.759049\pi\)
\(38\) −8.84018 −1.43407
\(39\) −7.21998 −1.15612
\(40\) −5.08794 −0.804474
\(41\) 8.26020 1.29003 0.645014 0.764171i \(-0.276852\pi\)
0.645014 + 0.764171i \(0.276852\pi\)
\(42\) 3.69610 0.570320
\(43\) −4.98099 −0.759594 −0.379797 0.925070i \(-0.624006\pi\)
−0.379797 + 0.925070i \(0.624006\pi\)
\(44\) 0.334594 0.0504419
\(45\) −1.98767 −0.296304
\(46\) 0.263881 0.0389071
\(47\) 5.18867 0.756846 0.378423 0.925633i \(-0.376466\pi\)
0.378423 + 0.925633i \(0.376466\pi\)
\(48\) −3.47179 −0.501110
\(49\) −5.14064 −0.734378
\(50\) 8.94487 1.26500
\(51\) −3.26392 −0.457040
\(52\) 24.7647 3.43425
\(53\) 4.14206 0.568956 0.284478 0.958683i \(-0.408180\pi\)
0.284478 + 0.958683i \(0.408180\pi\)
\(54\) −12.8565 −1.74955
\(55\) 0.0992186 0.0133786
\(56\) −6.08413 −0.813026
\(57\) −4.09924 −0.542958
\(58\) −16.7736 −2.20249
\(59\) 11.6476 1.51639 0.758197 0.652026i \(-0.226081\pi\)
0.758197 + 0.652026i \(0.226081\pi\)
\(60\) −4.91617 −0.634675
\(61\) 3.54812 0.454291 0.227145 0.973861i \(-0.427061\pi\)
0.227145 + 0.973861i \(0.427061\pi\)
\(62\) −11.4889 −1.45910
\(63\) −2.37684 −0.299454
\(64\) −9.66699 −1.20837
\(65\) 7.34359 0.910860
\(66\) 0.235847 0.0290308
\(67\) 1.69075 0.206558 0.103279 0.994652i \(-0.467067\pi\)
0.103279 + 0.994652i \(0.467067\pi\)
\(68\) 11.1953 1.35763
\(69\) 0.122363 0.0147308
\(70\) −3.75938 −0.449331
\(71\) 7.48161 0.887904 0.443952 0.896051i \(-0.353576\pi\)
0.443952 + 0.896051i \(0.353576\pi\)
\(72\) 7.77743 0.916579
\(73\) −10.0462 −1.17582 −0.587910 0.808926i \(-0.700049\pi\)
−0.587910 + 0.808926i \(0.700049\pi\)
\(74\) 21.3810 2.48549
\(75\) 4.14779 0.478946
\(76\) 14.0605 1.61285
\(77\) 0.118645 0.0135209
\(78\) 17.4561 1.97651
\(79\) −12.0541 −1.35620 −0.678099 0.734971i \(-0.737196\pi\)
−0.678099 + 0.734971i \(0.737196\pi\)
\(80\) 3.53123 0.394803
\(81\) −0.732387 −0.0813764
\(82\) −19.9710 −2.20543
\(83\) −2.74298 −0.301081 −0.150540 0.988604i \(-0.548101\pi\)
−0.150540 + 0.988604i \(0.548101\pi\)
\(84\) −5.87873 −0.641422
\(85\) 3.31980 0.360083
\(86\) 12.0427 1.29860
\(87\) −7.77804 −0.833893
\(88\) −0.388227 −0.0413851
\(89\) 2.53675 0.268895 0.134447 0.990921i \(-0.457074\pi\)
0.134447 + 0.990921i \(0.457074\pi\)
\(90\) 4.80567 0.506562
\(91\) 8.78142 0.920543
\(92\) −0.419708 −0.0437576
\(93\) −5.32749 −0.552435
\(94\) −12.5449 −1.29390
\(95\) 4.16942 0.427774
\(96\) −1.61071 −0.164393
\(97\) 2.88915 0.293348 0.146674 0.989185i \(-0.453143\pi\)
0.146674 + 0.989185i \(0.453143\pi\)
\(98\) 12.4287 1.25549
\(99\) −0.151666 −0.0152430
\(100\) −14.2270 −1.42270
\(101\) 7.17439 0.713879 0.356939 0.934128i \(-0.383820\pi\)
0.356939 + 0.934128i \(0.383820\pi\)
\(102\) 7.89132 0.781357
\(103\) 19.0756 1.87957 0.939785 0.341766i \(-0.111025\pi\)
0.939785 + 0.341766i \(0.111025\pi\)
\(104\) −28.7343 −2.81763
\(105\) −1.74325 −0.170123
\(106\) −10.0144 −0.972688
\(107\) 5.73582 0.554503 0.277251 0.960797i \(-0.410577\pi\)
0.277251 + 0.960797i \(0.410577\pi\)
\(108\) 20.4486 1.96767
\(109\) 11.2233 1.07499 0.537496 0.843266i \(-0.319370\pi\)
0.537496 + 0.843266i \(0.319370\pi\)
\(110\) −0.239885 −0.0228721
\(111\) 9.91450 0.941043
\(112\) 4.22262 0.399000
\(113\) 6.04302 0.568480 0.284240 0.958753i \(-0.408259\pi\)
0.284240 + 0.958753i \(0.408259\pi\)
\(114\) 9.91091 0.928242
\(115\) −0.124458 −0.0116058
\(116\) 26.6789 2.47707
\(117\) −11.2254 −1.03779
\(118\) −28.1610 −2.59243
\(119\) 3.96980 0.363911
\(120\) 5.70420 0.520720
\(121\) −10.9924 −0.999312
\(122\) −8.57845 −0.776656
\(123\) −9.26069 −0.835008
\(124\) 18.2734 1.64100
\(125\) −9.92038 −0.887305
\(126\) 5.74659 0.511947
\(127\) −10.9045 −0.967622 −0.483811 0.875173i \(-0.660748\pi\)
−0.483811 + 0.875173i \(0.660748\pi\)
\(128\) 20.4989 1.81186
\(129\) 5.58430 0.491670
\(130\) −17.7549 −1.55721
\(131\) −16.4200 −1.43462 −0.717312 0.696752i \(-0.754628\pi\)
−0.717312 + 0.696752i \(0.754628\pi\)
\(132\) −0.375120 −0.0326500
\(133\) 4.98577 0.432321
\(134\) −4.08780 −0.353132
\(135\) 6.06371 0.521881
\(136\) −12.9899 −1.11387
\(137\) 2.08476 0.178113 0.0890565 0.996027i \(-0.471615\pi\)
0.0890565 + 0.996027i \(0.471615\pi\)
\(138\) −0.295842 −0.0251838
\(139\) −11.5106 −0.976320 −0.488160 0.872754i \(-0.662332\pi\)
−0.488160 + 0.872754i \(0.662332\pi\)
\(140\) 5.97937 0.505349
\(141\) −5.81713 −0.489891
\(142\) −18.0886 −1.51796
\(143\) 0.560341 0.0468580
\(144\) −5.39784 −0.449820
\(145\) 7.91120 0.656989
\(146\) 24.2892 2.01018
\(147\) 5.76329 0.475348
\(148\) −34.0070 −2.79535
\(149\) −6.63520 −0.543577 −0.271789 0.962357i \(-0.587615\pi\)
−0.271789 + 0.962357i \(0.587615\pi\)
\(150\) −10.0283 −0.818806
\(151\) −8.84094 −0.719465 −0.359733 0.933055i \(-0.617132\pi\)
−0.359733 + 0.933055i \(0.617132\pi\)
\(152\) −16.3143 −1.32326
\(153\) −5.07465 −0.410261
\(154\) −0.286853 −0.0231153
\(155\) 5.41870 0.435241
\(156\) −27.7642 −2.22292
\(157\) 14.0256 1.11936 0.559682 0.828707i \(-0.310923\pi\)
0.559682 + 0.828707i \(0.310923\pi\)
\(158\) 29.1438 2.31856
\(159\) −4.64375 −0.368274
\(160\) 1.63829 0.129518
\(161\) −0.148826 −0.0117291
\(162\) 1.77072 0.139121
\(163\) −3.79103 −0.296937 −0.148468 0.988917i \(-0.547434\pi\)
−0.148468 + 0.988917i \(0.547434\pi\)
\(164\) 31.7644 2.48038
\(165\) −0.111236 −0.00865972
\(166\) 6.63181 0.514728
\(167\) −10.9434 −0.846828 −0.423414 0.905936i \(-0.639168\pi\)
−0.423414 + 0.905936i \(0.639168\pi\)
\(168\) 6.82105 0.526255
\(169\) 28.4732 2.19024
\(170\) −8.02642 −0.615598
\(171\) −6.37339 −0.487385
\(172\) −19.1543 −1.46050
\(173\) −19.6040 −1.49047 −0.745233 0.666804i \(-0.767662\pi\)
−0.745233 + 0.666804i \(0.767662\pi\)
\(174\) 18.8053 1.42562
\(175\) −5.04482 −0.381352
\(176\) 0.269444 0.0203101
\(177\) −13.0584 −0.981531
\(178\) −6.13320 −0.459703
\(179\) −20.8510 −1.55848 −0.779240 0.626726i \(-0.784395\pi\)
−0.779240 + 0.626726i \(0.784395\pi\)
\(180\) −7.64352 −0.569714
\(181\) −18.2169 −1.35405 −0.677027 0.735958i \(-0.736732\pi\)
−0.677027 + 0.735958i \(0.736732\pi\)
\(182\) −21.2312 −1.57376
\(183\) −3.97788 −0.294053
\(184\) 0.486984 0.0359010
\(185\) −10.0842 −0.741408
\(186\) 12.8805 0.944444
\(187\) 0.253312 0.0185240
\(188\) 19.9529 1.45522
\(189\) 7.25095 0.527429
\(190\) −10.0806 −0.731322
\(191\) −12.0557 −0.872320 −0.436160 0.899869i \(-0.643662\pi\)
−0.436160 + 0.899869i \(0.643662\pi\)
\(192\) 10.8379 0.782156
\(193\) 21.6413 1.55778 0.778888 0.627163i \(-0.215784\pi\)
0.778888 + 0.627163i \(0.215784\pi\)
\(194\) −6.98521 −0.501509
\(195\) −8.23305 −0.589581
\(196\) −19.7682 −1.41201
\(197\) 19.3181 1.37636 0.688179 0.725541i \(-0.258410\pi\)
0.688179 + 0.725541i \(0.258410\pi\)
\(198\) 0.366688 0.0260594
\(199\) −4.89929 −0.347301 −0.173651 0.984807i \(-0.555556\pi\)
−0.173651 + 0.984807i \(0.555556\pi\)
\(200\) 16.5075 1.16726
\(201\) −1.89554 −0.133701
\(202\) −17.3458 −1.22045
\(203\) 9.46016 0.663973
\(204\) −12.5513 −0.878768
\(205\) 9.41923 0.657868
\(206\) −46.1198 −3.21332
\(207\) 0.190247 0.0132231
\(208\) 19.9427 1.38278
\(209\) 0.318141 0.0220063
\(210\) 4.21472 0.290843
\(211\) −17.0224 −1.17187 −0.585934 0.810359i \(-0.699272\pi\)
−0.585934 + 0.810359i \(0.699272\pi\)
\(212\) 15.9282 1.09395
\(213\) −8.38779 −0.574722
\(214\) −13.8677 −0.947978
\(215\) −5.67990 −0.387366
\(216\) −23.7264 −1.61437
\(217\) 6.47965 0.439867
\(218\) −27.1349 −1.83781
\(219\) 11.2630 0.761085
\(220\) 0.381542 0.0257236
\(221\) 18.7487 1.26117
\(222\) −23.9707 −1.60881
\(223\) 0.795044 0.0532401 0.0266201 0.999646i \(-0.491526\pi\)
0.0266201 + 0.999646i \(0.491526\pi\)
\(224\) 1.95906 0.130895
\(225\) 6.44887 0.429924
\(226\) −14.6105 −0.971874
\(227\) −6.10083 −0.404926 −0.202463 0.979290i \(-0.564895\pi\)
−0.202463 + 0.979290i \(0.564895\pi\)
\(228\) −15.7635 −1.04397
\(229\) −10.9860 −0.725972 −0.362986 0.931795i \(-0.618243\pi\)
−0.362986 + 0.931795i \(0.618243\pi\)
\(230\) 0.300907 0.0198412
\(231\) −0.133015 −0.00875178
\(232\) −30.9553 −2.03231
\(233\) −13.8203 −0.905401 −0.452700 0.891663i \(-0.649539\pi\)
−0.452700 + 0.891663i \(0.649539\pi\)
\(234\) 27.1402 1.77421
\(235\) 5.91672 0.385964
\(236\) 44.7907 2.91562
\(237\) 13.5142 0.877839
\(238\) −9.59794 −0.622142
\(239\) 9.16542 0.592862 0.296431 0.955054i \(-0.404204\pi\)
0.296431 + 0.955054i \(0.404204\pi\)
\(240\) −3.95893 −0.255548
\(241\) 8.76857 0.564833 0.282417 0.959292i \(-0.408864\pi\)
0.282417 + 0.959292i \(0.408864\pi\)
\(242\) 26.5768 1.70842
\(243\) −15.1316 −0.970695
\(244\) 13.6442 0.873481
\(245\) −5.86195 −0.374506
\(246\) 22.3900 1.42753
\(247\) 23.5470 1.49826
\(248\) −21.2025 −1.34636
\(249\) 3.07521 0.194884
\(250\) 23.9849 1.51694
\(251\) −20.4788 −1.29261 −0.646304 0.763080i \(-0.723686\pi\)
−0.646304 + 0.763080i \(0.723686\pi\)
\(252\) −9.14008 −0.575771
\(253\) −0.00949656 −0.000597044 0
\(254\) 26.3644 1.65425
\(255\) −3.72190 −0.233074
\(256\) −30.2270 −1.88919
\(257\) 22.3861 1.39641 0.698204 0.715899i \(-0.253983\pi\)
0.698204 + 0.715899i \(0.253983\pi\)
\(258\) −13.5014 −0.840559
\(259\) −12.0587 −0.749289
\(260\) 28.2396 1.75134
\(261\) −12.0931 −0.748542
\(262\) 39.6994 2.45264
\(263\) 15.1711 0.935492 0.467746 0.883863i \(-0.345066\pi\)
0.467746 + 0.883863i \(0.345066\pi\)
\(264\) 0.435250 0.0267878
\(265\) 4.72325 0.290147
\(266\) −12.0543 −0.739097
\(267\) −2.84400 −0.174050
\(268\) 6.50174 0.397157
\(269\) −9.22904 −0.562705 −0.281352 0.959605i \(-0.590783\pi\)
−0.281352 + 0.959605i \(0.590783\pi\)
\(270\) −14.6605 −0.892209
\(271\) 11.4607 0.696191 0.348095 0.937459i \(-0.386829\pi\)
0.348095 + 0.937459i \(0.386829\pi\)
\(272\) 9.01546 0.546643
\(273\) −9.84504 −0.595849
\(274\) −5.04041 −0.304502
\(275\) −0.321909 −0.0194118
\(276\) 0.470544 0.0283234
\(277\) 16.4137 0.986205 0.493103 0.869971i \(-0.335863\pi\)
0.493103 + 0.869971i \(0.335863\pi\)
\(278\) 27.8298 1.66912
\(279\) −8.28303 −0.495892
\(280\) −6.93782 −0.414614
\(281\) 8.91042 0.531551 0.265776 0.964035i \(-0.414372\pi\)
0.265776 + 0.964035i \(0.414372\pi\)
\(282\) 14.0643 0.837518
\(283\) 9.10448 0.541205 0.270602 0.962691i \(-0.412777\pi\)
0.270602 + 0.962691i \(0.412777\pi\)
\(284\) 28.7703 1.70720
\(285\) −4.67443 −0.276889
\(286\) −1.35476 −0.0801085
\(287\) 11.2635 0.664861
\(288\) −2.50429 −0.147567
\(289\) −8.52433 −0.501431
\(290\) −19.1272 −1.12319
\(291\) −3.23908 −0.189878
\(292\) −38.6324 −2.26079
\(293\) −33.1169 −1.93471 −0.967356 0.253422i \(-0.918444\pi\)
−0.967356 + 0.253422i \(0.918444\pi\)
\(294\) −13.9341 −0.812655
\(295\) 13.2820 0.773306
\(296\) 39.4580 2.29345
\(297\) 0.462682 0.0268475
\(298\) 16.0422 0.929300
\(299\) −0.702880 −0.0406486
\(300\) 15.9502 0.920886
\(301\) −6.79199 −0.391484
\(302\) 21.3751 1.23000
\(303\) −8.04336 −0.462079
\(304\) 11.3228 0.649404
\(305\) 4.04598 0.231672
\(306\) 12.2692 0.701383
\(307\) 12.5643 0.717083 0.358542 0.933514i \(-0.383274\pi\)
0.358542 + 0.933514i \(0.383274\pi\)
\(308\) 0.456246 0.0259970
\(309\) −21.3860 −1.21661
\(310\) −13.1010 −0.744088
\(311\) 18.4434 1.04583 0.522913 0.852386i \(-0.324845\pi\)
0.522913 + 0.852386i \(0.324845\pi\)
\(312\) 32.2147 1.82380
\(313\) 20.7952 1.17541 0.587707 0.809074i \(-0.300031\pi\)
0.587707 + 0.809074i \(0.300031\pi\)
\(314\) −33.9102 −1.91367
\(315\) −2.71035 −0.152711
\(316\) −46.3539 −2.60761
\(317\) −1.02881 −0.0577839 −0.0288920 0.999583i \(-0.509198\pi\)
−0.0288920 + 0.999583i \(0.509198\pi\)
\(318\) 11.2274 0.629601
\(319\) 0.603651 0.0337980
\(320\) −11.0234 −0.616228
\(321\) −6.43055 −0.358918
\(322\) 0.359823 0.0200521
\(323\) 10.6448 0.592294
\(324\) −2.81638 −0.156465
\(325\) −23.8258 −1.32162
\(326\) 9.16573 0.507643
\(327\) −12.5826 −0.695821
\(328\) −36.8560 −2.03503
\(329\) 7.07518 0.390067
\(330\) 0.268940 0.0148047
\(331\) −17.1569 −0.943028 −0.471514 0.881859i \(-0.656292\pi\)
−0.471514 + 0.881859i \(0.656292\pi\)
\(332\) −10.5480 −0.578899
\(333\) 15.4148 0.844724
\(334\) 26.4584 1.44774
\(335\) 1.92799 0.105337
\(336\) −4.73407 −0.258265
\(337\) 8.10201 0.441344 0.220672 0.975348i \(-0.429175\pi\)
0.220672 + 0.975348i \(0.429175\pi\)
\(338\) −68.8407 −3.74444
\(339\) −6.77496 −0.367966
\(340\) 12.7662 0.692344
\(341\) 0.413465 0.0223904
\(342\) 15.4092 0.833234
\(343\) −16.5548 −0.893873
\(344\) 22.2246 1.19827
\(345\) 0.139532 0.00751217
\(346\) 47.3975 2.54810
\(347\) 21.7315 1.16661 0.583305 0.812253i \(-0.301759\pi\)
0.583305 + 0.812253i \(0.301759\pi\)
\(348\) −29.9102 −1.60336
\(349\) −2.97203 −0.159089 −0.0795445 0.996831i \(-0.525347\pi\)
−0.0795445 + 0.996831i \(0.525347\pi\)
\(350\) 12.1971 0.651961
\(351\) 34.2450 1.82786
\(352\) 0.125007 0.00666290
\(353\) 12.4442 0.662339 0.331170 0.943571i \(-0.392557\pi\)
0.331170 + 0.943571i \(0.392557\pi\)
\(354\) 31.5719 1.67803
\(355\) 8.53139 0.452799
\(356\) 9.75500 0.517014
\(357\) −4.45062 −0.235552
\(358\) 50.4124 2.66438
\(359\) 0.846392 0.0446709 0.0223354 0.999751i \(-0.492890\pi\)
0.0223354 + 0.999751i \(0.492890\pi\)
\(360\) 8.86872 0.467423
\(361\) −5.63090 −0.296363
\(362\) 44.0438 2.31489
\(363\) 12.3238 0.646834
\(364\) 33.7687 1.76996
\(365\) −11.4559 −0.599627
\(366\) 9.61748 0.502714
\(367\) −9.12744 −0.476448 −0.238224 0.971210i \(-0.576565\pi\)
−0.238224 + 0.971210i \(0.576565\pi\)
\(368\) −0.337986 −0.0176187
\(369\) −14.3983 −0.749543
\(370\) 24.3811 1.26751
\(371\) 5.64804 0.293232
\(372\) −20.4867 −1.06219
\(373\) 32.8144 1.69907 0.849534 0.527534i \(-0.176883\pi\)
0.849534 + 0.527534i \(0.176883\pi\)
\(374\) −0.612443 −0.0316687
\(375\) 11.1219 0.574335
\(376\) −23.1512 −1.19393
\(377\) 44.6788 2.30107
\(378\) −17.5309 −0.901693
\(379\) 30.2612 1.55441 0.777206 0.629247i \(-0.216636\pi\)
0.777206 + 0.629247i \(0.216636\pi\)
\(380\) 16.0334 0.822496
\(381\) 12.2253 0.626322
\(382\) 29.1476 1.49132
\(383\) 16.6575 0.851156 0.425578 0.904922i \(-0.360071\pi\)
0.425578 + 0.904922i \(0.360071\pi\)
\(384\) −22.9817 −1.17278
\(385\) 0.135293 0.00689516
\(386\) −52.3231 −2.66318
\(387\) 8.68230 0.441346
\(388\) 11.1101 0.564032
\(389\) 33.2405 1.68536 0.842680 0.538414i \(-0.180976\pi\)
0.842680 + 0.538414i \(0.180976\pi\)
\(390\) 19.9054 1.00795
\(391\) −0.317750 −0.0160693
\(392\) 22.9369 1.15849
\(393\) 18.4088 0.928603
\(394\) −46.7062 −2.35302
\(395\) −13.7455 −0.691612
\(396\) −0.583226 −0.0293082
\(397\) 30.8250 1.54706 0.773531 0.633758i \(-0.218489\pi\)
0.773531 + 0.633758i \(0.218489\pi\)
\(398\) 11.8452 0.593746
\(399\) −5.58965 −0.279833
\(400\) −11.4569 −0.572843
\(401\) 35.2234 1.75897 0.879486 0.475925i \(-0.157887\pi\)
0.879486 + 0.475925i \(0.157887\pi\)
\(402\) 4.58292 0.228575
\(403\) 30.6023 1.52441
\(404\) 27.5889 1.37260
\(405\) −0.835152 −0.0414991
\(406\) −22.8722 −1.13513
\(407\) −0.769461 −0.0381408
\(408\) 14.5632 0.720986
\(409\) −7.12867 −0.352490 −0.176245 0.984346i \(-0.556395\pi\)
−0.176245 + 0.984346i \(0.556395\pi\)
\(410\) −22.7733 −1.12469
\(411\) −2.33727 −0.115289
\(412\) 73.3545 3.61392
\(413\) 15.8825 0.781527
\(414\) −0.459967 −0.0226061
\(415\) −3.12786 −0.153541
\(416\) 9.25230 0.453631
\(417\) 12.9048 0.631952
\(418\) −0.769182 −0.0376219
\(419\) −17.4140 −0.850728 −0.425364 0.905022i \(-0.639854\pi\)
−0.425364 + 0.905022i \(0.639854\pi\)
\(420\) −6.70360 −0.327102
\(421\) 2.64487 0.128903 0.0644516 0.997921i \(-0.479470\pi\)
0.0644516 + 0.997921i \(0.479470\pi\)
\(422\) 41.1557 2.00343
\(423\) −9.04431 −0.439749
\(424\) −18.4814 −0.897534
\(425\) −10.7709 −0.522465
\(426\) 20.2795 0.982545
\(427\) 4.83816 0.234135
\(428\) 22.0569 1.06616
\(429\) −0.628210 −0.0303303
\(430\) 13.7325 0.662241
\(431\) 5.47008 0.263484 0.131742 0.991284i \(-0.457943\pi\)
0.131742 + 0.991284i \(0.457943\pi\)
\(432\) 16.4670 0.792269
\(433\) 29.0482 1.39597 0.697984 0.716114i \(-0.254081\pi\)
0.697984 + 0.716114i \(0.254081\pi\)
\(434\) −15.6661 −0.751998
\(435\) −8.86941 −0.425256
\(436\) 43.1587 2.06693
\(437\) −0.399070 −0.0190901
\(438\) −27.2311 −1.30115
\(439\) 16.5909 0.791840 0.395920 0.918285i \(-0.370426\pi\)
0.395920 + 0.918285i \(0.370426\pi\)
\(440\) −0.442701 −0.0211049
\(441\) 8.96059 0.426695
\(442\) −45.3295 −2.15610
\(443\) 12.2823 0.583549 0.291774 0.956487i \(-0.405754\pi\)
0.291774 + 0.956487i \(0.405754\pi\)
\(444\) 38.1259 1.80938
\(445\) 2.89269 0.137127
\(446\) −1.92221 −0.0910194
\(447\) 7.43887 0.351846
\(448\) −13.1817 −0.622778
\(449\) 10.3039 0.486271 0.243136 0.969992i \(-0.421824\pi\)
0.243136 + 0.969992i \(0.421824\pi\)
\(450\) −15.5917 −0.734999
\(451\) 0.718719 0.0338432
\(452\) 23.2383 1.09304
\(453\) 9.91177 0.465695
\(454\) 14.7502 0.692263
\(455\) 10.0136 0.469444
\(456\) 18.2903 0.856522
\(457\) −20.7743 −0.971780 −0.485890 0.874020i \(-0.661504\pi\)
−0.485890 + 0.874020i \(0.661504\pi\)
\(458\) 26.5612 1.24112
\(459\) 15.4811 0.722594
\(460\) −0.478600 −0.0223148
\(461\) −3.64989 −0.169993 −0.0849963 0.996381i \(-0.527088\pi\)
−0.0849963 + 0.996381i \(0.527088\pi\)
\(462\) 0.321597 0.0149620
\(463\) −2.20595 −0.102519 −0.0512595 0.998685i \(-0.516324\pi\)
−0.0512595 + 0.998685i \(0.516324\pi\)
\(464\) 21.4842 0.997377
\(465\) −6.07502 −0.281722
\(466\) 33.4140 1.54787
\(467\) −2.58229 −0.119494 −0.0597471 0.998214i \(-0.519029\pi\)
−0.0597471 + 0.998214i \(0.519029\pi\)
\(468\) −43.1670 −1.99540
\(469\) 2.30548 0.106457
\(470\) −14.3051 −0.659845
\(471\) −15.7244 −0.724542
\(472\) −51.9703 −2.39213
\(473\) −0.433395 −0.0199275
\(474\) −32.6738 −1.50076
\(475\) −13.5274 −0.620681
\(476\) 15.2657 0.699704
\(477\) −7.21997 −0.330580
\(478\) −22.1596 −1.01356
\(479\) −13.8358 −0.632176 −0.316088 0.948730i \(-0.602369\pi\)
−0.316088 + 0.948730i \(0.602369\pi\)
\(480\) −1.83672 −0.0838345
\(481\) −56.9510 −2.59674
\(482\) −21.2001 −0.965639
\(483\) 0.166852 0.00759203
\(484\) −42.2711 −1.92141
\(485\) 3.29454 0.149597
\(486\) 36.5844 1.65950
\(487\) −3.79210 −0.171836 −0.0859181 0.996302i \(-0.527382\pi\)
−0.0859181 + 0.996302i \(0.527382\pi\)
\(488\) −15.8313 −0.716649
\(489\) 4.25021 0.192201
\(490\) 14.1727 0.640257
\(491\) 11.2189 0.506300 0.253150 0.967427i \(-0.418533\pi\)
0.253150 + 0.967427i \(0.418533\pi\)
\(492\) −35.6117 −1.60550
\(493\) 20.1978 0.909664
\(494\) −56.9304 −2.56142
\(495\) −0.172947 −0.00777338
\(496\) 14.7154 0.660740
\(497\) 10.2018 0.457613
\(498\) −7.43506 −0.333173
\(499\) −38.5875 −1.72742 −0.863708 0.503993i \(-0.831864\pi\)
−0.863708 + 0.503993i \(0.831864\pi\)
\(500\) −38.1485 −1.70605
\(501\) 12.2689 0.548135
\(502\) 49.5124 2.20984
\(503\) −32.4265 −1.44583 −0.722914 0.690938i \(-0.757198\pi\)
−0.722914 + 0.690938i \(0.757198\pi\)
\(504\) 10.6052 0.472392
\(505\) 8.18106 0.364053
\(506\) 0.0229602 0.00102071
\(507\) −31.9219 −1.41770
\(508\) −41.9331 −1.86048
\(509\) −0.971433 −0.0430580 −0.0215290 0.999768i \(-0.506853\pi\)
−0.0215290 + 0.999768i \(0.506853\pi\)
\(510\) 8.99859 0.398464
\(511\) −13.6988 −0.606001
\(512\) 32.0833 1.41790
\(513\) 19.4431 0.858433
\(514\) −54.1238 −2.38730
\(515\) 21.7521 0.958514
\(516\) 21.4743 0.945351
\(517\) 0.451466 0.0198554
\(518\) 29.1547 1.28099
\(519\) 21.9785 0.964749
\(520\) −32.7662 −1.43689
\(521\) −39.6649 −1.73775 −0.868876 0.495030i \(-0.835157\pi\)
−0.868876 + 0.495030i \(0.835157\pi\)
\(522\) 29.2379 1.27971
\(523\) −19.7760 −0.864742 −0.432371 0.901696i \(-0.642323\pi\)
−0.432371 + 0.901696i \(0.642323\pi\)
\(524\) −63.1427 −2.75840
\(525\) 5.65585 0.246842
\(526\) −36.6799 −1.59932
\(527\) 13.8343 0.602632
\(528\) −0.302080 −0.0131463
\(529\) −22.9881 −0.999482
\(530\) −11.4196 −0.496036
\(531\) −20.3028 −0.881068
\(532\) 19.1726 0.831240
\(533\) 53.1954 2.30415
\(534\) 6.87607 0.297557
\(535\) 6.54064 0.282777
\(536\) −7.54392 −0.325848
\(537\) 23.3765 1.00877
\(538\) 22.3134 0.962000
\(539\) −0.447287 −0.0192660
\(540\) 23.3178 1.00344
\(541\) 26.1412 1.12390 0.561948 0.827172i \(-0.310052\pi\)
0.561948 + 0.827172i \(0.310052\pi\)
\(542\) −27.7091 −1.19021
\(543\) 20.4234 0.876452
\(544\) 4.18267 0.179330
\(545\) 12.7980 0.548208
\(546\) 23.8028 1.01866
\(547\) −24.2586 −1.03722 −0.518612 0.855010i \(-0.673551\pi\)
−0.518612 + 0.855010i \(0.673551\pi\)
\(548\) 8.01688 0.342464
\(549\) −6.18469 −0.263956
\(550\) 0.778292 0.0331865
\(551\) 25.3670 1.08067
\(552\) −0.545969 −0.0232380
\(553\) −16.4368 −0.698965
\(554\) −39.6841 −1.68602
\(555\) 11.3056 0.479898
\(556\) −44.2639 −1.87721
\(557\) 7.12398 0.301853 0.150926 0.988545i \(-0.451774\pi\)
0.150926 + 0.988545i \(0.451774\pi\)
\(558\) 20.0262 0.847778
\(559\) −32.0774 −1.35673
\(560\) 4.81512 0.203476
\(561\) −0.283993 −0.0119902
\(562\) −21.5431 −0.908741
\(563\) 2.07416 0.0874155 0.0437077 0.999044i \(-0.486083\pi\)
0.0437077 + 0.999044i \(0.486083\pi\)
\(564\) −22.3696 −0.941931
\(565\) 6.89095 0.289904
\(566\) −22.0123 −0.925244
\(567\) −0.998670 −0.0419402
\(568\) −33.3820 −1.40068
\(569\) 30.8822 1.29465 0.647325 0.762214i \(-0.275888\pi\)
0.647325 + 0.762214i \(0.275888\pi\)
\(570\) 11.3016 0.473370
\(571\) 24.1494 1.01062 0.505311 0.862937i \(-0.331378\pi\)
0.505311 + 0.862937i \(0.331378\pi\)
\(572\) 2.15477 0.0900956
\(573\) 13.5159 0.564635
\(574\) −27.2321 −1.13665
\(575\) 0.403796 0.0168395
\(576\) 16.8504 0.702100
\(577\) 20.9884 0.873759 0.436879 0.899520i \(-0.356084\pi\)
0.436879 + 0.899520i \(0.356084\pi\)
\(578\) 20.6096 0.857247
\(579\) −24.2625 −1.00832
\(580\) 30.4223 1.26322
\(581\) −3.74027 −0.155173
\(582\) 7.83127 0.324616
\(583\) 0.360400 0.0149262
\(584\) 44.8250 1.85487
\(585\) −12.8005 −0.529236
\(586\) 80.0682 3.30759
\(587\) 36.8633 1.52151 0.760755 0.649039i \(-0.224829\pi\)
0.760755 + 0.649039i \(0.224829\pi\)
\(588\) 22.1626 0.913969
\(589\) 17.3749 0.715919
\(590\) −32.1124 −1.32205
\(591\) −21.6579 −0.890889
\(592\) −27.3854 −1.12553
\(593\) −14.3409 −0.588910 −0.294455 0.955665i \(-0.595138\pi\)
−0.294455 + 0.955665i \(0.595138\pi\)
\(594\) −1.11864 −0.0458985
\(595\) 4.52682 0.185581
\(596\) −25.5155 −1.04516
\(597\) 5.49269 0.224801
\(598\) 1.69938 0.0694929
\(599\) 2.81822 0.115149 0.0575746 0.998341i \(-0.481663\pi\)
0.0575746 + 0.998341i \(0.481663\pi\)
\(600\) −18.5069 −0.755542
\(601\) −36.6676 −1.49570 −0.747851 0.663867i \(-0.768914\pi\)
−0.747851 + 0.663867i \(0.768914\pi\)
\(602\) 16.4213 0.669281
\(603\) −2.94713 −0.120016
\(604\) −33.9976 −1.38334
\(605\) −12.5348 −0.509613
\(606\) 19.4468 0.789971
\(607\) −18.6646 −0.757573 −0.378786 0.925484i \(-0.623658\pi\)
−0.378786 + 0.925484i \(0.623658\pi\)
\(608\) 5.25312 0.213042
\(609\) −10.6060 −0.429776
\(610\) −9.78213 −0.396067
\(611\) 33.4149 1.35182
\(612\) −19.5144 −0.788824
\(613\) 24.1854 0.976839 0.488420 0.872609i \(-0.337574\pi\)
0.488420 + 0.872609i \(0.337574\pi\)
\(614\) −30.3773 −1.22593
\(615\) −10.5601 −0.425825
\(616\) −0.529379 −0.0213293
\(617\) −2.83779 −0.114245 −0.0571225 0.998367i \(-0.518193\pi\)
−0.0571225 + 0.998367i \(0.518193\pi\)
\(618\) 51.7058 2.07991
\(619\) 11.4424 0.459910 0.229955 0.973201i \(-0.426142\pi\)
0.229955 + 0.973201i \(0.426142\pi\)
\(620\) 20.8375 0.836853
\(621\) −0.580379 −0.0232898
\(622\) −44.5913 −1.78795
\(623\) 3.45907 0.138585
\(624\) −22.3582 −0.895045
\(625\) 7.18606 0.287442
\(626\) −50.2774 −2.00949
\(627\) −0.356675 −0.0142442
\(628\) 53.9350 2.15224
\(629\) −25.7457 −1.02655
\(630\) 6.55292 0.261075
\(631\) 15.8419 0.630655 0.315327 0.948983i \(-0.397886\pi\)
0.315327 + 0.948983i \(0.397886\pi\)
\(632\) 53.7841 2.13942
\(633\) 19.0841 0.758527
\(634\) 2.48740 0.0987875
\(635\) −12.4346 −0.493453
\(636\) −17.8574 −0.708093
\(637\) −33.1056 −1.31169
\(638\) −1.45947 −0.0577810
\(639\) −13.0411 −0.515898
\(640\) 23.3752 0.923985
\(641\) −15.5611 −0.614626 −0.307313 0.951608i \(-0.599430\pi\)
−0.307313 + 0.951608i \(0.599430\pi\)
\(642\) 15.5474 0.613607
\(643\) −15.0313 −0.592778 −0.296389 0.955067i \(-0.595782\pi\)
−0.296389 + 0.955067i \(0.595782\pi\)
\(644\) −0.572306 −0.0225520
\(645\) 6.36786 0.250734
\(646\) −25.7364 −1.01259
\(647\) −1.26205 −0.0496163 −0.0248082 0.999692i \(-0.507897\pi\)
−0.0248082 + 0.999692i \(0.507897\pi\)
\(648\) 3.26782 0.128372
\(649\) 1.01346 0.0397818
\(650\) 57.6047 2.25944
\(651\) −7.26447 −0.284717
\(652\) −14.5783 −0.570931
\(653\) −42.9048 −1.67899 −0.839496 0.543365i \(-0.817150\pi\)
−0.839496 + 0.543365i \(0.817150\pi\)
\(654\) 30.4215 1.18958
\(655\) −18.7240 −0.731607
\(656\) 25.5795 0.998711
\(657\) 17.5114 0.683186
\(658\) −17.1060 −0.666860
\(659\) 29.4462 1.14706 0.573530 0.819185i \(-0.305574\pi\)
0.573530 + 0.819185i \(0.305574\pi\)
\(660\) −0.427755 −0.0166504
\(661\) −4.19473 −0.163156 −0.0815780 0.996667i \(-0.525996\pi\)
−0.0815780 + 0.996667i \(0.525996\pi\)
\(662\) 41.4809 1.61220
\(663\) −21.0195 −0.816331
\(664\) 12.2388 0.474958
\(665\) 5.68535 0.220468
\(666\) −37.2689 −1.44414
\(667\) −0.757208 −0.0293192
\(668\) −42.0827 −1.62823
\(669\) −0.891341 −0.0344612
\(670\) −4.66138 −0.180085
\(671\) 0.308722 0.0119181
\(672\) −2.19634 −0.0847257
\(673\) 44.3742 1.71050 0.855250 0.518216i \(-0.173404\pi\)
0.855250 + 0.518216i \(0.173404\pi\)
\(674\) −19.5886 −0.754523
\(675\) −19.6733 −0.757227
\(676\) 109.493 4.21126
\(677\) 22.3922 0.860603 0.430302 0.902685i \(-0.358407\pi\)
0.430302 + 0.902685i \(0.358407\pi\)
\(678\) 16.3801 0.629074
\(679\) 3.93959 0.151188
\(680\) −14.8125 −0.568035
\(681\) 6.83977 0.262101
\(682\) −0.999651 −0.0382786
\(683\) 35.1837 1.34627 0.673133 0.739522i \(-0.264948\pi\)
0.673133 + 0.739522i \(0.264948\pi\)
\(684\) −24.5087 −0.937113
\(685\) 2.37728 0.0908313
\(686\) 40.0251 1.52817
\(687\) 12.3166 0.469907
\(688\) −15.4247 −0.588061
\(689\) 26.6747 1.01623
\(690\) −0.337353 −0.0128428
\(691\) 4.56256 0.173568 0.0867839 0.996227i \(-0.472341\pi\)
0.0867839 + 0.996227i \(0.472341\pi\)
\(692\) −75.3867 −2.86577
\(693\) −0.206809 −0.00785601
\(694\) −52.5412 −1.99444
\(695\) −13.1258 −0.497889
\(696\) 34.7046 1.31548
\(697\) 24.0479 0.910881
\(698\) 7.18560 0.271979
\(699\) 15.4943 0.586047
\(700\) −19.3997 −0.733240
\(701\) −40.8926 −1.54449 −0.772245 0.635325i \(-0.780866\pi\)
−0.772245 + 0.635325i \(0.780866\pi\)
\(702\) −82.7956 −3.12492
\(703\) −32.3347 −1.21953
\(704\) −0.841124 −0.0317010
\(705\) −6.63336 −0.249827
\(706\) −30.0869 −1.13234
\(707\) 9.78287 0.367923
\(708\) −50.2158 −1.88722
\(709\) −50.6931 −1.90382 −0.951910 0.306378i \(-0.900883\pi\)
−0.951910 + 0.306378i \(0.900883\pi\)
\(710\) −20.6267 −0.774106
\(711\) 21.0114 0.787990
\(712\) −11.3187 −0.424185
\(713\) −0.518643 −0.0194233
\(714\) 10.7605 0.402700
\(715\) 0.638965 0.0238959
\(716\) −80.1821 −2.99655
\(717\) −10.2756 −0.383747
\(718\) −2.04636 −0.0763694
\(719\) 46.2645 1.72537 0.862687 0.505739i \(-0.168780\pi\)
0.862687 + 0.505739i \(0.168780\pi\)
\(720\) −6.15524 −0.229392
\(721\) 26.0111 0.968703
\(722\) 13.6140 0.506662
\(723\) −9.83063 −0.365605
\(724\) −70.0527 −2.60349
\(725\) −25.6674 −0.953263
\(726\) −29.7959 −1.10583
\(727\) −42.6200 −1.58069 −0.790344 0.612663i \(-0.790098\pi\)
−0.790344 + 0.612663i \(0.790098\pi\)
\(728\) −39.1816 −1.45217
\(729\) 19.1616 0.709687
\(730\) 27.6973 1.02512
\(731\) −14.5012 −0.536345
\(732\) −15.2968 −0.565387
\(733\) 18.7431 0.692294 0.346147 0.938180i \(-0.387490\pi\)
0.346147 + 0.938180i \(0.387490\pi\)
\(734\) 22.0678 0.814537
\(735\) 6.57196 0.242410
\(736\) −0.156806 −0.00577996
\(737\) 0.147112 0.00541894
\(738\) 34.8113 1.28142
\(739\) 1.78903 0.0658106 0.0329053 0.999458i \(-0.489524\pi\)
0.0329053 + 0.999458i \(0.489524\pi\)
\(740\) −38.7786 −1.42553
\(741\) −26.3990 −0.969791
\(742\) −13.6555 −0.501309
\(743\) −6.38946 −0.234407 −0.117203 0.993108i \(-0.537393\pi\)
−0.117203 + 0.993108i \(0.537393\pi\)
\(744\) 23.7706 0.871473
\(745\) −7.56622 −0.277205
\(746\) −79.3368 −2.90473
\(747\) 4.78125 0.174937
\(748\) 0.974104 0.0356168
\(749\) 7.82126 0.285783
\(750\) −26.8900 −0.981884
\(751\) 13.7345 0.501180 0.250590 0.968093i \(-0.419375\pi\)
0.250590 + 0.968093i \(0.419375\pi\)
\(752\) 16.0678 0.585934
\(753\) 22.9592 0.836679
\(754\) −108.022 −3.93392
\(755\) −10.0815 −0.366902
\(756\) 27.8833 1.01411
\(757\) 49.9638 1.81597 0.907983 0.419007i \(-0.137622\pi\)
0.907983 + 0.419007i \(0.137622\pi\)
\(758\) −73.1636 −2.65742
\(759\) 0.0106468 0.000386454 0
\(760\) −18.6034 −0.674818
\(761\) 26.7674 0.970318 0.485159 0.874426i \(-0.338762\pi\)
0.485159 + 0.874426i \(0.338762\pi\)
\(762\) −29.5577 −1.07076
\(763\) 15.3038 0.554035
\(764\) −46.3599 −1.67724
\(765\) −5.78670 −0.209219
\(766\) −40.2734 −1.45514
\(767\) 75.0104 2.70847
\(768\) 33.8882 1.22283
\(769\) 50.7200 1.82901 0.914505 0.404575i \(-0.132580\pi\)
0.914505 + 0.404575i \(0.132580\pi\)
\(770\) −0.327103 −0.0117880
\(771\) −25.0976 −0.903867
\(772\) 83.2211 2.99519
\(773\) 6.03803 0.217173 0.108587 0.994087i \(-0.465368\pi\)
0.108587 + 0.994087i \(0.465368\pi\)
\(774\) −20.9916 −0.754526
\(775\) −17.5806 −0.631515
\(776\) −12.8910 −0.462760
\(777\) 13.5192 0.485000
\(778\) −80.3669 −2.88129
\(779\) 30.2024 1.08211
\(780\) −31.6600 −1.13361
\(781\) 0.650974 0.0232937
\(782\) 0.768236 0.0274721
\(783\) 36.8919 1.31841
\(784\) −15.9191 −0.568539
\(785\) 15.9936 0.570836
\(786\) −44.5078 −1.58754
\(787\) 20.6142 0.734817 0.367408 0.930060i \(-0.380245\pi\)
0.367408 + 0.930060i \(0.380245\pi\)
\(788\) 74.2872 2.64637
\(789\) −17.0087 −0.605525
\(790\) 33.2331 1.18238
\(791\) 8.24016 0.292986
\(792\) 0.676713 0.0240460
\(793\) 22.8498 0.811420
\(794\) −74.5269 −2.64486
\(795\) −5.29534 −0.187806
\(796\) −18.8401 −0.667768
\(797\) 42.8669 1.51842 0.759212 0.650843i \(-0.225584\pi\)
0.759212 + 0.650843i \(0.225584\pi\)
\(798\) 13.5143 0.478402
\(799\) 15.1058 0.534405
\(800\) −5.31533 −0.187925
\(801\) −4.42178 −0.156236
\(802\) −85.1610 −3.00714
\(803\) −0.874120 −0.0308470
\(804\) −7.28924 −0.257072
\(805\) −0.169709 −0.00598144
\(806\) −73.9884 −2.60613
\(807\) 10.3469 0.364227
\(808\) −32.0112 −1.12615
\(809\) −9.34123 −0.328420 −0.164210 0.986425i \(-0.552508\pi\)
−0.164210 + 0.986425i \(0.552508\pi\)
\(810\) 2.01918 0.0709468
\(811\) 17.9739 0.631150 0.315575 0.948901i \(-0.397803\pi\)
0.315575 + 0.948901i \(0.397803\pi\)
\(812\) 36.3788 1.27665
\(813\) −12.8489 −0.450630
\(814\) 1.86036 0.0652055
\(815\) −4.32297 −0.151427
\(816\) −10.1074 −0.353831
\(817\) −18.2124 −0.637171
\(818\) 17.2353 0.602617
\(819\) −15.3068 −0.534862
\(820\) 36.2214 1.26491
\(821\) −7.10180 −0.247854 −0.123927 0.992291i \(-0.539549\pi\)
−0.123927 + 0.992291i \(0.539549\pi\)
\(822\) 5.65091 0.197098
\(823\) 0.388681 0.0135486 0.00677428 0.999977i \(-0.497844\pi\)
0.00677428 + 0.999977i \(0.497844\pi\)
\(824\) −85.1127 −2.96504
\(825\) 0.360899 0.0125649
\(826\) −38.3998 −1.33610
\(827\) −15.0709 −0.524068 −0.262034 0.965059i \(-0.584393\pi\)
−0.262034 + 0.965059i \(0.584393\pi\)
\(828\) 0.731588 0.0254244
\(829\) 27.4237 0.952463 0.476232 0.879320i \(-0.342002\pi\)
0.476232 + 0.879320i \(0.342002\pi\)
\(830\) 7.56235 0.262493
\(831\) −18.4018 −0.638351
\(832\) −62.2551 −2.15831
\(833\) −14.9660 −0.518540
\(834\) −31.2005 −1.08039
\(835\) −12.4790 −0.431852
\(836\) 1.22340 0.0423123
\(837\) 25.2688 0.873416
\(838\) 42.1025 1.45441
\(839\) 21.2984 0.735304 0.367652 0.929963i \(-0.380162\pi\)
0.367652 + 0.929963i \(0.380162\pi\)
\(840\) 7.77814 0.268371
\(841\) 19.1321 0.659728
\(842\) −6.39461 −0.220373
\(843\) −9.98967 −0.344062
\(844\) −65.4591 −2.25319
\(845\) 32.4684 1.11695
\(846\) 21.8668 0.751796
\(847\) −14.9891 −0.515031
\(848\) 12.8268 0.440473
\(849\) −10.2072 −0.350311
\(850\) 26.0412 0.893206
\(851\) 0.965197 0.0330865
\(852\) −32.2550 −1.10504
\(853\) −20.7052 −0.708933 −0.354467 0.935069i \(-0.615338\pi\)
−0.354467 + 0.935069i \(0.615338\pi\)
\(854\) −11.6974 −0.400277
\(855\) −7.26767 −0.248549
\(856\) −25.5925 −0.874734
\(857\) −15.8628 −0.541861 −0.270931 0.962599i \(-0.587331\pi\)
−0.270931 + 0.962599i \(0.587331\pi\)
\(858\) 1.51885 0.0518526
\(859\) −34.3885 −1.17332 −0.586660 0.809833i \(-0.699558\pi\)
−0.586660 + 0.809833i \(0.699558\pi\)
\(860\) −21.8419 −0.744802
\(861\) −12.6277 −0.430351
\(862\) −13.2252 −0.450453
\(863\) −38.0561 −1.29545 −0.647723 0.761876i \(-0.724278\pi\)
−0.647723 + 0.761876i \(0.724278\pi\)
\(864\) 7.63976 0.259910
\(865\) −22.3548 −0.760085
\(866\) −70.2310 −2.38655
\(867\) 9.55680 0.324566
\(868\) 24.9173 0.845749
\(869\) −1.04883 −0.0355791
\(870\) 21.4439 0.727018
\(871\) 10.8884 0.368939
\(872\) −50.0767 −1.69581
\(873\) −5.03603 −0.170444
\(874\) 0.964848 0.0326365
\(875\) −13.5272 −0.457304
\(876\) 43.3117 1.46337
\(877\) −14.5169 −0.490202 −0.245101 0.969498i \(-0.578821\pi\)
−0.245101 + 0.969498i \(0.578821\pi\)
\(878\) −40.1125 −1.35373
\(879\) 37.1281 1.25230
\(880\) 0.307252 0.0103574
\(881\) 26.5788 0.895463 0.447732 0.894168i \(-0.352232\pi\)
0.447732 + 0.894168i \(0.352232\pi\)
\(882\) −21.6644 −0.729478
\(883\) −24.1050 −0.811198 −0.405599 0.914051i \(-0.632937\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(884\) 72.0975 2.42490
\(885\) −14.8907 −0.500546
\(886\) −29.6954 −0.997635
\(887\) −30.6039 −1.02758 −0.513789 0.857917i \(-0.671758\pi\)
−0.513789 + 0.857917i \(0.671758\pi\)
\(888\) −44.2372 −1.48450
\(889\) −14.8692 −0.498698
\(890\) −6.99378 −0.234432
\(891\) −0.0637249 −0.00213487
\(892\) 3.05732 0.102367
\(893\) 18.9718 0.634866
\(894\) −17.9853 −0.601517
\(895\) −23.7767 −0.794769
\(896\) 27.9519 0.933808
\(897\) 0.788014 0.0263110
\(898\) −24.9122 −0.831330
\(899\) 32.9676 1.09953
\(900\) 24.7989 0.826631
\(901\) 12.0588 0.401736
\(902\) −1.73768 −0.0578583
\(903\) 7.61464 0.253400
\(904\) −26.9632 −0.896783
\(905\) −20.7730 −0.690520
\(906\) −23.9641 −0.796153
\(907\) 17.9419 0.595751 0.297875 0.954605i \(-0.403722\pi\)
0.297875 + 0.954605i \(0.403722\pi\)
\(908\) −23.4606 −0.778567
\(909\) −12.5056 −0.414784
\(910\) −24.2103 −0.802562
\(911\) −26.2901 −0.871031 −0.435515 0.900181i \(-0.643434\pi\)
−0.435515 + 0.900181i \(0.643434\pi\)
\(912\) −12.6942 −0.420346
\(913\) −0.238666 −0.00789870
\(914\) 50.2268 1.66136
\(915\) −4.53603 −0.149957
\(916\) −42.2462 −1.39585
\(917\) −22.3900 −0.739384
\(918\) −37.4292 −1.23535
\(919\) −20.4143 −0.673407 −0.336703 0.941611i \(-0.609312\pi\)
−0.336703 + 0.941611i \(0.609312\pi\)
\(920\) 0.555316 0.0183082
\(921\) −14.0861 −0.464153
\(922\) 8.82450 0.290619
\(923\) 48.1813 1.58591
\(924\) −0.511507 −0.0168274
\(925\) 32.7177 1.07575
\(926\) 5.33341 0.175267
\(927\) −33.2503 −1.09208
\(928\) 9.96744 0.327197
\(929\) −11.6955 −0.383716 −0.191858 0.981423i \(-0.561451\pi\)
−0.191858 + 0.981423i \(0.561451\pi\)
\(930\) 14.6878 0.481633
\(931\) −18.7961 −0.616019
\(932\) −53.1457 −1.74085
\(933\) −20.6772 −0.676942
\(934\) 6.24331 0.204287
\(935\) 0.288855 0.00944658
\(936\) 50.0864 1.63713
\(937\) 52.6629 1.72042 0.860211 0.509938i \(-0.170332\pi\)
0.860211 + 0.509938i \(0.170332\pi\)
\(938\) −5.57405 −0.181999
\(939\) −23.3139 −0.760821
\(940\) 22.7526 0.742108
\(941\) 3.60812 0.117621 0.0588107 0.998269i \(-0.481269\pi\)
0.0588107 + 0.998269i \(0.481269\pi\)
\(942\) 38.0175 1.23868
\(943\) −0.901547 −0.0293584
\(944\) 36.0694 1.17396
\(945\) 8.26837 0.268970
\(946\) 1.04784 0.0340681
\(947\) 51.9572 1.68838 0.844191 0.536042i \(-0.180081\pi\)
0.844191 + 0.536042i \(0.180081\pi\)
\(948\) 51.9683 1.68785
\(949\) −64.6973 −2.10016
\(950\) 32.7058 1.06112
\(951\) 1.15342 0.0374024
\(952\) −17.7127 −0.574073
\(953\) −11.5914 −0.375481 −0.187740 0.982219i \(-0.560116\pi\)
−0.187740 + 0.982219i \(0.560116\pi\)
\(954\) 17.4560 0.565160
\(955\) −13.7473 −0.444852
\(956\) 35.2454 1.13992
\(957\) −0.676766 −0.0218767
\(958\) 33.4515 1.08077
\(959\) 2.84274 0.0917969
\(960\) 12.3586 0.398872
\(961\) −8.41913 −0.271585
\(962\) 137.693 4.43940
\(963\) −9.99803 −0.322182
\(964\) 33.7193 1.08602
\(965\) 24.6779 0.794410
\(966\) −0.403405 −0.0129793
\(967\) −49.3372 −1.58658 −0.793289 0.608846i \(-0.791633\pi\)
−0.793289 + 0.608846i \(0.791633\pi\)
\(968\) 49.0468 1.57642
\(969\) −11.9341 −0.383380
\(970\) −7.96534 −0.255752
\(971\) −22.8586 −0.733568 −0.366784 0.930306i \(-0.619541\pi\)
−0.366784 + 0.930306i \(0.619541\pi\)
\(972\) −58.1883 −1.86639
\(973\) −15.6957 −0.503181
\(974\) 9.16831 0.293771
\(975\) 26.7116 0.855457
\(976\) 10.9875 0.351702
\(977\) 14.6817 0.469709 0.234854 0.972031i \(-0.424539\pi\)
0.234854 + 0.972031i \(0.424539\pi\)
\(978\) −10.2759 −0.328587
\(979\) 0.220722 0.00705431
\(980\) −22.5420 −0.720077
\(981\) −19.5631 −0.624602
\(982\) −27.1243 −0.865571
\(983\) 35.0352 1.11745 0.558725 0.829353i \(-0.311291\pi\)
0.558725 + 0.829353i \(0.311291\pi\)
\(984\) 41.3200 1.31723
\(985\) 22.0287 0.701894
\(986\) −48.8331 −1.55516
\(987\) −7.93214 −0.252483
\(988\) 90.5492 2.88075
\(989\) 0.543643 0.0172868
\(990\) 0.418140 0.0132894
\(991\) −35.7011 −1.13408 −0.567041 0.823689i \(-0.691912\pi\)
−0.567041 + 0.823689i \(0.691912\pi\)
\(992\) 6.82710 0.216761
\(993\) 19.2350 0.610403
\(994\) −24.6653 −0.782335
\(995\) −5.58673 −0.177111
\(996\) 11.8256 0.374710
\(997\) −11.7568 −0.372342 −0.186171 0.982517i \(-0.559608\pi\)
−0.186171 + 0.982517i \(0.559608\pi\)
\(998\) 93.2947 2.95319
\(999\) −47.0253 −1.48782
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.1.15 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.15 174 1.1 even 1 trivial