Properties

Label 4027.2.a.c.1.1
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.1
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +O(q^{10})\) \(q-2.80755 q^{2} +0.290452 q^{3} +5.88232 q^{4} -1.66261 q^{5} -0.815457 q^{6} +1.40907 q^{7} -10.8998 q^{8} -2.91564 q^{9} +4.66785 q^{10} +5.00402 q^{11} +1.70853 q^{12} -2.19562 q^{13} -3.95603 q^{14} -0.482908 q^{15} +18.8371 q^{16} +5.06094 q^{17} +8.18579 q^{18} -5.60124 q^{19} -9.78000 q^{20} +0.409267 q^{21} -14.0490 q^{22} +7.70577 q^{23} -3.16587 q^{24} -2.23573 q^{25} +6.16430 q^{26} -1.71821 q^{27} +8.28860 q^{28} +7.58080 q^{29} +1.35579 q^{30} +0.908551 q^{31} -31.0863 q^{32} +1.45343 q^{33} -14.2088 q^{34} -2.34273 q^{35} -17.1507 q^{36} +5.36885 q^{37} +15.7258 q^{38} -0.637721 q^{39} +18.1221 q^{40} +5.06071 q^{41} -1.14904 q^{42} +0.206506 q^{43} +29.4353 q^{44} +4.84756 q^{45} -21.6343 q^{46} +2.86237 q^{47} +5.47126 q^{48} -5.01452 q^{49} +6.27693 q^{50} +1.46996 q^{51} -12.9153 q^{52} -10.5431 q^{53} +4.82395 q^{54} -8.31973 q^{55} -15.3586 q^{56} -1.62689 q^{57} -21.2834 q^{58} +3.61724 q^{59} -2.84062 q^{60} -10.8258 q^{61} -2.55080 q^{62} -4.10834 q^{63} +49.6022 q^{64} +3.65045 q^{65} -4.08057 q^{66} -2.76545 q^{67} +29.7701 q^{68} +2.23815 q^{69} +6.57733 q^{70} -15.8989 q^{71} +31.7799 q^{72} -2.31996 q^{73} -15.0733 q^{74} -0.649373 q^{75} -32.9483 q^{76} +7.05102 q^{77} +1.79043 q^{78} -8.14656 q^{79} -31.3187 q^{80} +8.24786 q^{81} -14.2082 q^{82} +10.8437 q^{83} +2.40744 q^{84} -8.41437 q^{85} -0.579776 q^{86} +2.20186 q^{87} -54.5429 q^{88} -0.357211 q^{89} -13.6098 q^{90} -3.09378 q^{91} +45.3278 q^{92} +0.263890 q^{93} -8.03625 q^{94} +9.31268 q^{95} -9.02908 q^{96} +13.5102 q^{97} +14.0785 q^{98} -14.5899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80755 −1.98524 −0.992618 0.121284i \(-0.961299\pi\)
−0.992618 + 0.121284i \(0.961299\pi\)
\(3\) 0.290452 0.167692 0.0838462 0.996479i \(-0.473280\pi\)
0.0838462 + 0.996479i \(0.473280\pi\)
\(4\) 5.88232 2.94116
\(5\) −1.66261 −0.743541 −0.371771 0.928325i \(-0.621249\pi\)
−0.371771 + 0.928325i \(0.621249\pi\)
\(6\) −0.815457 −0.332909
\(7\) 1.40907 0.532578 0.266289 0.963893i \(-0.414202\pi\)
0.266289 + 0.963893i \(0.414202\pi\)
\(8\) −10.8998 −3.85366
\(9\) −2.91564 −0.971879
\(10\) 4.66785 1.47610
\(11\) 5.00402 1.50877 0.754385 0.656432i \(-0.227935\pi\)
0.754385 + 0.656432i \(0.227935\pi\)
\(12\) 1.70853 0.493210
\(13\) −2.19562 −0.608955 −0.304477 0.952520i \(-0.598482\pi\)
−0.304477 + 0.952520i \(0.598482\pi\)
\(14\) −3.95603 −1.05729
\(15\) −0.482908 −0.124686
\(16\) 18.8371 4.70927
\(17\) 5.06094 1.22746 0.613729 0.789516i \(-0.289669\pi\)
0.613729 + 0.789516i \(0.289669\pi\)
\(18\) 8.18579 1.92941
\(19\) −5.60124 −1.28501 −0.642507 0.766280i \(-0.722106\pi\)
−0.642507 + 0.766280i \(0.722106\pi\)
\(20\) −9.78000 −2.18687
\(21\) 0.409267 0.0893093
\(22\) −14.0490 −2.99526
\(23\) 7.70577 1.60676 0.803382 0.595464i \(-0.203032\pi\)
0.803382 + 0.595464i \(0.203032\pi\)
\(24\) −3.16587 −0.646230
\(25\) −2.23573 −0.447147
\(26\) 6.16430 1.20892
\(27\) −1.71821 −0.330669
\(28\) 8.28860 1.56640
\(29\) 7.58080 1.40772 0.703859 0.710339i \(-0.251458\pi\)
0.703859 + 0.710339i \(0.251458\pi\)
\(30\) 1.35579 0.247531
\(31\) 0.908551 0.163181 0.0815903 0.996666i \(-0.474000\pi\)
0.0815903 + 0.996666i \(0.474000\pi\)
\(32\) −31.0863 −5.49534
\(33\) 1.45343 0.253009
\(34\) −14.2088 −2.43679
\(35\) −2.34273 −0.395994
\(36\) −17.1507 −2.85845
\(37\) 5.36885 0.882633 0.441317 0.897351i \(-0.354512\pi\)
0.441317 + 0.897351i \(0.354512\pi\)
\(38\) 15.7258 2.55105
\(39\) −0.637721 −0.102117
\(40\) 18.1221 2.86536
\(41\) 5.06071 0.790350 0.395175 0.918606i \(-0.370684\pi\)
0.395175 + 0.918606i \(0.370684\pi\)
\(42\) −1.14904 −0.177300
\(43\) 0.206506 0.0314919 0.0157459 0.999876i \(-0.494988\pi\)
0.0157459 + 0.999876i \(0.494988\pi\)
\(44\) 29.4353 4.43754
\(45\) 4.84756 0.722632
\(46\) −21.6343 −3.18981
\(47\) 2.86237 0.417520 0.208760 0.977967i \(-0.433057\pi\)
0.208760 + 0.977967i \(0.433057\pi\)
\(48\) 5.47126 0.789708
\(49\) −5.01452 −0.716360
\(50\) 6.27693 0.887691
\(51\) 1.46996 0.205835
\(52\) −12.9153 −1.79103
\(53\) −10.5431 −1.44821 −0.724105 0.689689i \(-0.757747\pi\)
−0.724105 + 0.689689i \(0.757747\pi\)
\(54\) 4.82395 0.656456
\(55\) −8.31973 −1.12183
\(56\) −15.3586 −2.05238
\(57\) −1.62689 −0.215487
\(58\) −21.2834 −2.79465
\(59\) 3.61724 0.470925 0.235462 0.971883i \(-0.424340\pi\)
0.235462 + 0.971883i \(0.424340\pi\)
\(60\) −2.84062 −0.366722
\(61\) −10.8258 −1.38610 −0.693048 0.720891i \(-0.743733\pi\)
−0.693048 + 0.720891i \(0.743733\pi\)
\(62\) −2.55080 −0.323952
\(63\) −4.10834 −0.517602
\(64\) 49.6022 6.20028
\(65\) 3.65045 0.452783
\(66\) −4.08057 −0.502283
\(67\) −2.76545 −0.337853 −0.168927 0.985629i \(-0.554030\pi\)
−0.168927 + 0.985629i \(0.554030\pi\)
\(68\) 29.7701 3.61015
\(69\) 2.23815 0.269442
\(70\) 6.57733 0.786141
\(71\) −15.8989 −1.88685 −0.943426 0.331584i \(-0.892417\pi\)
−0.943426 + 0.331584i \(0.892417\pi\)
\(72\) 31.7799 3.74529
\(73\) −2.31996 −0.271531 −0.135765 0.990741i \(-0.543349\pi\)
−0.135765 + 0.990741i \(0.543349\pi\)
\(74\) −15.0733 −1.75224
\(75\) −0.649373 −0.0749831
\(76\) −32.9483 −3.77943
\(77\) 7.05102 0.803538
\(78\) 1.79043 0.202726
\(79\) −8.14656 −0.916559 −0.458280 0.888808i \(-0.651534\pi\)
−0.458280 + 0.888808i \(0.651534\pi\)
\(80\) −31.3187 −3.50153
\(81\) 8.24786 0.916429
\(82\) −14.2082 −1.56903
\(83\) 10.8437 1.19025 0.595126 0.803632i \(-0.297102\pi\)
0.595126 + 0.803632i \(0.297102\pi\)
\(84\) 2.40744 0.262673
\(85\) −8.41437 −0.912666
\(86\) −0.579776 −0.0625188
\(87\) 2.20186 0.236064
\(88\) −54.5429 −5.81429
\(89\) −0.357211 −0.0378643 −0.0189321 0.999821i \(-0.506027\pi\)
−0.0189321 + 0.999821i \(0.506027\pi\)
\(90\) −13.6098 −1.43460
\(91\) −3.09378 −0.324316
\(92\) 45.3278 4.72575
\(93\) 0.263890 0.0273641
\(94\) −8.03625 −0.828876
\(95\) 9.31268 0.955460
\(96\) −9.02908 −0.921527
\(97\) 13.5102 1.37175 0.685877 0.727717i \(-0.259419\pi\)
0.685877 + 0.727717i \(0.259419\pi\)
\(98\) 14.0785 1.42214
\(99\) −14.5899 −1.46634
\(100\) −13.1513 −1.31513
\(101\) 5.13891 0.511340 0.255670 0.966764i \(-0.417704\pi\)
0.255670 + 0.966764i \(0.417704\pi\)
\(102\) −4.12698 −0.408632
\(103\) 19.6082 1.93205 0.966027 0.258440i \(-0.0832083\pi\)
0.966027 + 0.258440i \(0.0832083\pi\)
\(104\) 23.9318 2.34670
\(105\) −0.680450 −0.0664051
\(106\) 29.6003 2.87504
\(107\) 18.5474 1.79304 0.896522 0.442998i \(-0.146085\pi\)
0.896522 + 0.442998i \(0.146085\pi\)
\(108\) −10.1070 −0.972551
\(109\) −2.74994 −0.263397 −0.131698 0.991290i \(-0.542043\pi\)
−0.131698 + 0.991290i \(0.542043\pi\)
\(110\) 23.3580 2.22710
\(111\) 1.55939 0.148011
\(112\) 26.5427 2.50805
\(113\) −8.43829 −0.793807 −0.396904 0.917860i \(-0.629915\pi\)
−0.396904 + 0.917860i \(0.629915\pi\)
\(114\) 4.56757 0.427792
\(115\) −12.8117 −1.19470
\(116\) 44.5927 4.14033
\(117\) 6.40162 0.591830
\(118\) −10.1556 −0.934896
\(119\) 7.13122 0.653718
\(120\) 5.26360 0.480498
\(121\) 14.0403 1.27639
\(122\) 30.3938 2.75173
\(123\) 1.46989 0.132536
\(124\) 5.34439 0.479940
\(125\) 12.0302 1.07601
\(126\) 11.5343 1.02756
\(127\) 18.0162 1.59868 0.799338 0.600881i \(-0.205184\pi\)
0.799338 + 0.600881i \(0.205184\pi\)
\(128\) −77.0880 −6.81368
\(129\) 0.0599800 0.00528095
\(130\) −10.2488 −0.898881
\(131\) −15.7423 −1.37541 −0.687707 0.725989i \(-0.741383\pi\)
−0.687707 + 0.725989i \(0.741383\pi\)
\(132\) 8.54953 0.744141
\(133\) −7.89254 −0.684370
\(134\) 7.76412 0.670718
\(135\) 2.85671 0.245866
\(136\) −55.1633 −4.73021
\(137\) −15.3060 −1.30768 −0.653838 0.756634i \(-0.726842\pi\)
−0.653838 + 0.756634i \(0.726842\pi\)
\(138\) −6.28373 −0.534906
\(139\) 0.292016 0.0247685 0.0123842 0.999923i \(-0.496058\pi\)
0.0123842 + 0.999923i \(0.496058\pi\)
\(140\) −13.7807 −1.16468
\(141\) 0.831382 0.0700150
\(142\) 44.6369 3.74585
\(143\) −10.9869 −0.918773
\(144\) −54.9221 −4.57684
\(145\) −12.6039 −1.04670
\(146\) 6.51340 0.539053
\(147\) −1.45648 −0.120128
\(148\) 31.5813 2.59597
\(149\) 4.78511 0.392011 0.196006 0.980603i \(-0.437203\pi\)
0.196006 + 0.980603i \(0.437203\pi\)
\(150\) 1.82314 0.148859
\(151\) −12.0578 −0.981253 −0.490626 0.871370i \(-0.663232\pi\)
−0.490626 + 0.871370i \(0.663232\pi\)
\(152\) 61.0524 4.95201
\(153\) −14.7559 −1.19294
\(154\) −19.7961 −1.59521
\(155\) −1.51056 −0.121331
\(156\) −3.75128 −0.300343
\(157\) 3.43334 0.274010 0.137005 0.990570i \(-0.456252\pi\)
0.137005 + 0.990570i \(0.456252\pi\)
\(158\) 22.8718 1.81959
\(159\) −3.06227 −0.242854
\(160\) 51.6844 4.08601
\(161\) 10.8580 0.855728
\(162\) −23.1562 −1.81933
\(163\) 6.02508 0.471921 0.235960 0.971763i \(-0.424176\pi\)
0.235960 + 0.971763i \(0.424176\pi\)
\(164\) 29.7687 2.32455
\(165\) −2.41648 −0.188123
\(166\) −30.4443 −2.36293
\(167\) −2.20960 −0.170984 −0.0854921 0.996339i \(-0.527246\pi\)
−0.0854921 + 0.996339i \(0.527246\pi\)
\(168\) −4.46092 −0.344168
\(169\) −8.17927 −0.629174
\(170\) 23.6237 1.81186
\(171\) 16.3312 1.24888
\(172\) 1.21474 0.0926227
\(173\) −0.679197 −0.0516384 −0.0258192 0.999667i \(-0.508219\pi\)
−0.0258192 + 0.999667i \(0.508219\pi\)
\(174\) −6.18181 −0.468642
\(175\) −3.15030 −0.238141
\(176\) 94.2611 7.10520
\(177\) 1.05063 0.0789705
\(178\) 1.00289 0.0751695
\(179\) −8.70775 −0.650848 −0.325424 0.945568i \(-0.605507\pi\)
−0.325424 + 0.945568i \(0.605507\pi\)
\(180\) 28.5149 2.12538
\(181\) −11.0795 −0.823530 −0.411765 0.911290i \(-0.635088\pi\)
−0.411765 + 0.911290i \(0.635088\pi\)
\(182\) 8.68592 0.643844
\(183\) −3.14436 −0.232438
\(184\) −83.9914 −6.19193
\(185\) −8.92630 −0.656274
\(186\) −0.740884 −0.0543242
\(187\) 25.3251 1.85195
\(188\) 16.8374 1.22799
\(189\) −2.42107 −0.176107
\(190\) −26.1458 −1.89681
\(191\) 13.1574 0.952038 0.476019 0.879435i \(-0.342079\pi\)
0.476019 + 0.879435i \(0.342079\pi\)
\(192\) 14.4071 1.03974
\(193\) −6.31372 −0.454472 −0.227236 0.973840i \(-0.572969\pi\)
−0.227236 + 0.973840i \(0.572969\pi\)
\(194\) −37.9306 −2.72326
\(195\) 1.06028 0.0759282
\(196\) −29.4970 −2.10693
\(197\) 1.77553 0.126501 0.0632507 0.997998i \(-0.479853\pi\)
0.0632507 + 0.997998i \(0.479853\pi\)
\(198\) 40.9619 2.91104
\(199\) 24.7746 1.75623 0.878113 0.478453i \(-0.158802\pi\)
0.878113 + 0.478453i \(0.158802\pi\)
\(200\) 24.3690 1.72315
\(201\) −0.803229 −0.0566554
\(202\) −14.4277 −1.01513
\(203\) 10.6819 0.749720
\(204\) 8.64677 0.605395
\(205\) −8.41398 −0.587658
\(206\) −55.0510 −3.83558
\(207\) −22.4672 −1.56158
\(208\) −41.3590 −2.86773
\(209\) −28.0288 −1.93879
\(210\) 1.91040 0.131830
\(211\) 25.4241 1.75027 0.875134 0.483881i \(-0.160773\pi\)
0.875134 + 0.483881i \(0.160773\pi\)
\(212\) −62.0181 −4.25942
\(213\) −4.61786 −0.316411
\(214\) −52.0727 −3.55962
\(215\) −0.343339 −0.0234155
\(216\) 18.7281 1.27429
\(217\) 1.28021 0.0869064
\(218\) 7.72059 0.522905
\(219\) −0.673837 −0.0455337
\(220\) −48.9393 −3.29949
\(221\) −11.1119 −0.747467
\(222\) −4.37807 −0.293837
\(223\) −24.4876 −1.63981 −0.819904 0.572501i \(-0.805973\pi\)
−0.819904 + 0.572501i \(0.805973\pi\)
\(224\) −43.8028 −2.92670
\(225\) 6.51859 0.434573
\(226\) 23.6909 1.57589
\(227\) 11.5881 0.769129 0.384565 0.923098i \(-0.374352\pi\)
0.384565 + 0.923098i \(0.374352\pi\)
\(228\) −9.56990 −0.633782
\(229\) −5.28279 −0.349097 −0.174548 0.984649i \(-0.555847\pi\)
−0.174548 + 0.984649i \(0.555847\pi\)
\(230\) 35.9694 2.37175
\(231\) 2.04798 0.134747
\(232\) −82.6292 −5.42487
\(233\) 3.55731 0.233047 0.116524 0.993188i \(-0.462825\pi\)
0.116524 + 0.993188i \(0.462825\pi\)
\(234\) −17.9729 −1.17492
\(235\) −4.75901 −0.310443
\(236\) 21.2778 1.38506
\(237\) −2.36618 −0.153700
\(238\) −20.0212 −1.29778
\(239\) 18.4006 1.19024 0.595119 0.803637i \(-0.297105\pi\)
0.595119 + 0.803637i \(0.297105\pi\)
\(240\) −9.09656 −0.587180
\(241\) −4.82317 −0.310688 −0.155344 0.987860i \(-0.549649\pi\)
−0.155344 + 0.987860i \(0.549649\pi\)
\(242\) −39.4187 −2.53393
\(243\) 7.55023 0.484347
\(244\) −63.6806 −4.07673
\(245\) 8.33719 0.532643
\(246\) −4.12679 −0.263115
\(247\) 12.2982 0.782515
\(248\) −9.90302 −0.628842
\(249\) 3.14958 0.199596
\(250\) −33.7753 −2.13614
\(251\) 31.6058 1.99494 0.997471 0.0710690i \(-0.0226410\pi\)
0.997471 + 0.0710690i \(0.0226410\pi\)
\(252\) −24.1666 −1.52235
\(253\) 38.5599 2.42424
\(254\) −50.5813 −3.17375
\(255\) −2.44397 −0.153047
\(256\) 117.224 7.32648
\(257\) 7.42330 0.463053 0.231526 0.972829i \(-0.425628\pi\)
0.231526 + 0.972829i \(0.425628\pi\)
\(258\) −0.168397 −0.0104839
\(259\) 7.56508 0.470071
\(260\) 21.4731 1.33171
\(261\) −22.1029 −1.36813
\(262\) 44.1973 2.73052
\(263\) −4.85061 −0.299101 −0.149551 0.988754i \(-0.547783\pi\)
−0.149551 + 0.988754i \(0.547783\pi\)
\(264\) −15.8421 −0.975012
\(265\) 17.5291 1.07680
\(266\) 22.1587 1.35864
\(267\) −0.103752 −0.00634955
\(268\) −16.2672 −0.993680
\(269\) −1.95709 −0.119326 −0.0596630 0.998219i \(-0.519003\pi\)
−0.0596630 + 0.998219i \(0.519003\pi\)
\(270\) −8.02034 −0.488102
\(271\) 0.367832 0.0223442 0.0111721 0.999938i \(-0.496444\pi\)
0.0111721 + 0.999938i \(0.496444\pi\)
\(272\) 95.3333 5.78043
\(273\) −0.898593 −0.0543853
\(274\) 42.9722 2.59605
\(275\) −11.1877 −0.674641
\(276\) 13.1655 0.792473
\(277\) −1.54673 −0.0929337 −0.0464668 0.998920i \(-0.514796\pi\)
−0.0464668 + 0.998920i \(0.514796\pi\)
\(278\) −0.819849 −0.0491713
\(279\) −2.64900 −0.158592
\(280\) 25.5353 1.52603
\(281\) −7.57221 −0.451720 −0.225860 0.974160i \(-0.572519\pi\)
−0.225860 + 0.974160i \(0.572519\pi\)
\(282\) −2.33414 −0.138996
\(283\) −15.2704 −0.907732 −0.453866 0.891070i \(-0.649955\pi\)
−0.453866 + 0.891070i \(0.649955\pi\)
\(284\) −93.5224 −5.54953
\(285\) 2.70488 0.160223
\(286\) 30.8463 1.82398
\(287\) 7.13089 0.420923
\(288\) 90.6365 5.34081
\(289\) 8.61314 0.506655
\(290\) 35.3860 2.07794
\(291\) 3.92407 0.230033
\(292\) −13.6468 −0.798616
\(293\) 9.61255 0.561571 0.280786 0.959770i \(-0.409405\pi\)
0.280786 + 0.959770i \(0.409405\pi\)
\(294\) 4.08913 0.238483
\(295\) −6.01405 −0.350152
\(296\) −58.5194 −3.40137
\(297\) −8.59795 −0.498904
\(298\) −13.4344 −0.778235
\(299\) −16.9189 −0.978447
\(300\) −3.81982 −0.220537
\(301\) 0.290981 0.0167719
\(302\) 33.8529 1.94802
\(303\) 1.49260 0.0857479
\(304\) −105.511 −6.05147
\(305\) 17.9990 1.03062
\(306\) 41.4278 2.36827
\(307\) 15.6057 0.890665 0.445332 0.895365i \(-0.353086\pi\)
0.445332 + 0.895365i \(0.353086\pi\)
\(308\) 41.4764 2.36333
\(309\) 5.69524 0.323991
\(310\) 4.24098 0.240871
\(311\) −21.0678 −1.19465 −0.597323 0.802001i \(-0.703769\pi\)
−0.597323 + 0.802001i \(0.703769\pi\)
\(312\) 6.95103 0.393525
\(313\) 6.10679 0.345176 0.172588 0.984994i \(-0.444787\pi\)
0.172588 + 0.984994i \(0.444787\pi\)
\(314\) −9.63926 −0.543975
\(315\) 6.83055 0.384858
\(316\) −47.9207 −2.69575
\(317\) 16.4428 0.923519 0.461759 0.887005i \(-0.347218\pi\)
0.461759 + 0.887005i \(0.347218\pi\)
\(318\) 8.59747 0.482122
\(319\) 37.9345 2.12392
\(320\) −82.4691 −4.61016
\(321\) 5.38712 0.300680
\(322\) −30.4843 −1.69882
\(323\) −28.3476 −1.57730
\(324\) 48.5165 2.69536
\(325\) 4.90881 0.272292
\(326\) −16.9157 −0.936874
\(327\) −0.798726 −0.0441696
\(328\) −55.1607 −3.04574
\(329\) 4.03328 0.222362
\(330\) 6.78438 0.373468
\(331\) 6.63027 0.364433 0.182216 0.983258i \(-0.441673\pi\)
0.182216 + 0.983258i \(0.441673\pi\)
\(332\) 63.7862 3.50072
\(333\) −15.6536 −0.857813
\(334\) 6.20356 0.339444
\(335\) 4.59785 0.251208
\(336\) 7.70938 0.420581
\(337\) 21.5382 1.17326 0.586629 0.809856i \(-0.300455\pi\)
0.586629 + 0.809856i \(0.300455\pi\)
\(338\) 22.9637 1.24906
\(339\) −2.45092 −0.133115
\(340\) −49.4960 −2.68430
\(341\) 4.54641 0.246202
\(342\) −45.8506 −2.47932
\(343\) −16.9293 −0.914096
\(344\) −2.25088 −0.121359
\(345\) −3.72118 −0.200341
\(346\) 1.90688 0.102514
\(347\) 8.11244 0.435499 0.217749 0.976005i \(-0.430128\pi\)
0.217749 + 0.976005i \(0.430128\pi\)
\(348\) 12.9520 0.694301
\(349\) 15.5147 0.830483 0.415241 0.909711i \(-0.363697\pi\)
0.415241 + 0.909711i \(0.363697\pi\)
\(350\) 8.84462 0.472765
\(351\) 3.77253 0.201362
\(352\) −155.557 −8.29121
\(353\) −11.6399 −0.619529 −0.309765 0.950813i \(-0.600250\pi\)
−0.309765 + 0.950813i \(0.600250\pi\)
\(354\) −2.94970 −0.156775
\(355\) 26.4336 1.40295
\(356\) −2.10123 −0.111365
\(357\) 2.07127 0.109623
\(358\) 24.4474 1.29209
\(359\) 3.13624 0.165524 0.0827622 0.996569i \(-0.473626\pi\)
0.0827622 + 0.996569i \(0.473626\pi\)
\(360\) −52.8375 −2.78478
\(361\) 12.3739 0.651260
\(362\) 31.1061 1.63490
\(363\) 4.07802 0.214040
\(364\) −18.1986 −0.953865
\(365\) 3.85719 0.201894
\(366\) 8.82794 0.461444
\(367\) −36.1143 −1.88515 −0.942575 0.333996i \(-0.891603\pi\)
−0.942575 + 0.333996i \(0.891603\pi\)
\(368\) 145.154 7.56668
\(369\) −14.7552 −0.768125
\(370\) 25.0610 1.30286
\(371\) −14.8560 −0.771285
\(372\) 1.55229 0.0804823
\(373\) 6.46461 0.334725 0.167362 0.985895i \(-0.446475\pi\)
0.167362 + 0.985895i \(0.446475\pi\)
\(374\) −71.1014 −3.67656
\(375\) 3.49419 0.180439
\(376\) −31.1993 −1.60898
\(377\) −16.6445 −0.857237
\(378\) 6.79728 0.349614
\(379\) −12.4570 −0.639874 −0.319937 0.947439i \(-0.603662\pi\)
−0.319937 + 0.947439i \(0.603662\pi\)
\(380\) 54.7802 2.81016
\(381\) 5.23283 0.268086
\(382\) −36.9401 −1.89002
\(383\) 13.5091 0.690284 0.345142 0.938550i \(-0.387831\pi\)
0.345142 + 0.938550i \(0.387831\pi\)
\(384\) −22.3903 −1.14260
\(385\) −11.7231 −0.597464
\(386\) 17.7261 0.902233
\(387\) −0.602097 −0.0306063
\(388\) 79.4714 4.03455
\(389\) −2.52078 −0.127809 −0.0639044 0.997956i \(-0.520355\pi\)
−0.0639044 + 0.997956i \(0.520355\pi\)
\(390\) −2.97679 −0.150735
\(391\) 38.9985 1.97224
\(392\) 54.6573 2.76061
\(393\) −4.57239 −0.230646
\(394\) −4.98489 −0.251135
\(395\) 13.5445 0.681499
\(396\) −85.8226 −4.31275
\(397\) −0.514060 −0.0257999 −0.0129000 0.999917i \(-0.504106\pi\)
−0.0129000 + 0.999917i \(0.504106\pi\)
\(398\) −69.5559 −3.48652
\(399\) −2.29240 −0.114764
\(400\) −42.1146 −2.10573
\(401\) −6.37958 −0.318581 −0.159291 0.987232i \(-0.550921\pi\)
−0.159291 + 0.987232i \(0.550921\pi\)
\(402\) 2.25510 0.112474
\(403\) −1.99483 −0.0993695
\(404\) 30.2287 1.50393
\(405\) −13.7130 −0.681402
\(406\) −29.9899 −1.48837
\(407\) 26.8659 1.33169
\(408\) −16.0223 −0.793220
\(409\) −9.71668 −0.480459 −0.240229 0.970716i \(-0.577223\pi\)
−0.240229 + 0.970716i \(0.577223\pi\)
\(410\) 23.6226 1.16664
\(411\) −4.44564 −0.219287
\(412\) 115.342 5.68248
\(413\) 5.09694 0.250804
\(414\) 63.0778 3.10011
\(415\) −18.0289 −0.885002
\(416\) 68.2537 3.34641
\(417\) 0.0848165 0.00415348
\(418\) 78.6921 3.84896
\(419\) 35.0639 1.71298 0.856492 0.516161i \(-0.172639\pi\)
0.856492 + 0.516161i \(0.172639\pi\)
\(420\) −4.00263 −0.195308
\(421\) −24.0135 −1.17035 −0.585173 0.810909i \(-0.698973\pi\)
−0.585173 + 0.810909i \(0.698973\pi\)
\(422\) −71.3794 −3.47469
\(423\) −8.34565 −0.405779
\(424\) 114.918 5.58091
\(425\) −11.3149 −0.548854
\(426\) 12.9649 0.628150
\(427\) −15.2542 −0.738205
\(428\) 109.102 5.27363
\(429\) −3.19117 −0.154071
\(430\) 0.963940 0.0464853
\(431\) 24.5461 1.18235 0.591173 0.806545i \(-0.298665\pi\)
0.591173 + 0.806545i \(0.298665\pi\)
\(432\) −32.3660 −1.55721
\(433\) 26.0384 1.25133 0.625663 0.780093i \(-0.284828\pi\)
0.625663 + 0.780093i \(0.284828\pi\)
\(434\) −3.59425 −0.172530
\(435\) −3.66082 −0.175523
\(436\) −16.1760 −0.774692
\(437\) −43.1619 −2.06471
\(438\) 1.89183 0.0903950
\(439\) 28.6554 1.36765 0.683824 0.729647i \(-0.260316\pi\)
0.683824 + 0.729647i \(0.260316\pi\)
\(440\) 90.6834 4.32316
\(441\) 14.6205 0.696216
\(442\) 31.1972 1.48390
\(443\) 32.5266 1.54538 0.772692 0.634781i \(-0.218910\pi\)
0.772692 + 0.634781i \(0.218910\pi\)
\(444\) 9.17284 0.435324
\(445\) 0.593902 0.0281536
\(446\) 68.7500 3.25541
\(447\) 1.38984 0.0657373
\(448\) 69.8930 3.30213
\(449\) 4.01359 0.189413 0.0947065 0.995505i \(-0.469809\pi\)
0.0947065 + 0.995505i \(0.469809\pi\)
\(450\) −18.3012 −0.862729
\(451\) 25.3239 1.19246
\(452\) −49.6367 −2.33471
\(453\) −3.50222 −0.164549
\(454\) −32.5341 −1.52690
\(455\) 5.14374 0.241142
\(456\) 17.7328 0.830414
\(457\) −11.8745 −0.555465 −0.277732 0.960659i \(-0.589583\pi\)
−0.277732 + 0.960659i \(0.589583\pi\)
\(458\) 14.8317 0.693039
\(459\) −8.69575 −0.405883
\(460\) −75.3624 −3.51379
\(461\) 40.0771 1.86657 0.933287 0.359131i \(-0.116927\pi\)
0.933287 + 0.359131i \(0.116927\pi\)
\(462\) −5.74980 −0.267505
\(463\) 42.3281 1.96715 0.983577 0.180490i \(-0.0577684\pi\)
0.983577 + 0.180490i \(0.0577684\pi\)
\(464\) 142.800 6.62932
\(465\) −0.438746 −0.0203464
\(466\) −9.98732 −0.462654
\(467\) 25.3699 1.17398 0.586989 0.809595i \(-0.300313\pi\)
0.586989 + 0.809595i \(0.300313\pi\)
\(468\) 37.6564 1.74067
\(469\) −3.89671 −0.179933
\(470\) 13.3611 0.616303
\(471\) 0.997220 0.0459495
\(472\) −39.4272 −1.81478
\(473\) 1.03336 0.0475140
\(474\) 6.64317 0.305131
\(475\) 12.5229 0.574589
\(476\) 41.9481 1.92269
\(477\) 30.7400 1.40749
\(478\) −51.6607 −2.36290
\(479\) 7.21392 0.329612 0.164806 0.986326i \(-0.447300\pi\)
0.164806 + 0.986326i \(0.447300\pi\)
\(480\) 15.0118 0.685193
\(481\) −11.7879 −0.537484
\(482\) 13.5413 0.616788
\(483\) 3.15372 0.143499
\(484\) 82.5893 3.75406
\(485\) −22.4622 −1.01996
\(486\) −21.1976 −0.961543
\(487\) 28.8318 1.30649 0.653247 0.757145i \(-0.273406\pi\)
0.653247 + 0.757145i \(0.273406\pi\)
\(488\) 117.999 5.34155
\(489\) 1.75000 0.0791375
\(490\) −23.4071 −1.05742
\(491\) 30.3436 1.36939 0.684694 0.728831i \(-0.259936\pi\)
0.684694 + 0.728831i \(0.259936\pi\)
\(492\) 8.64638 0.389809
\(493\) 38.3660 1.72792
\(494\) −34.5277 −1.55348
\(495\) 24.2573 1.09029
\(496\) 17.1144 0.768460
\(497\) −22.4026 −1.00490
\(498\) −8.84259 −0.396246
\(499\) 7.16663 0.320822 0.160411 0.987050i \(-0.448718\pi\)
0.160411 + 0.987050i \(0.448718\pi\)
\(500\) 70.7655 3.16473
\(501\) −0.641783 −0.0286727
\(502\) −88.7349 −3.96043
\(503\) −10.6338 −0.474139 −0.237069 0.971493i \(-0.576187\pi\)
−0.237069 + 0.971493i \(0.576187\pi\)
\(504\) 44.7800 1.99466
\(505\) −8.54399 −0.380203
\(506\) −108.259 −4.81268
\(507\) −2.37568 −0.105508
\(508\) 105.977 4.70197
\(509\) −32.8438 −1.45578 −0.727888 0.685696i \(-0.759498\pi\)
−0.727888 + 0.685696i \(0.759498\pi\)
\(510\) 6.86155 0.303835
\(511\) −3.26899 −0.144611
\(512\) −174.935 −7.73110
\(513\) 9.62410 0.424914
\(514\) −20.8413 −0.919268
\(515\) −32.6008 −1.43656
\(516\) 0.352822 0.0155321
\(517\) 14.3234 0.629942
\(518\) −21.2393 −0.933202
\(519\) −0.197274 −0.00865937
\(520\) −39.7892 −1.74487
\(521\) −44.2710 −1.93955 −0.969775 0.244003i \(-0.921539\pi\)
−0.969775 + 0.244003i \(0.921539\pi\)
\(522\) 62.0548 2.71607
\(523\) 2.26456 0.0990222 0.0495111 0.998774i \(-0.484234\pi\)
0.0495111 + 0.998774i \(0.484234\pi\)
\(524\) −92.6014 −4.04531
\(525\) −0.915011 −0.0399344
\(526\) 13.6183 0.593787
\(527\) 4.59812 0.200297
\(528\) 27.3783 1.19149
\(529\) 36.3789 1.58169
\(530\) −49.2138 −2.13771
\(531\) −10.5466 −0.457682
\(532\) −46.4265 −2.01284
\(533\) −11.1114 −0.481287
\(534\) 0.291290 0.0126053
\(535\) −30.8371 −1.33320
\(536\) 30.1428 1.30197
\(537\) −2.52918 −0.109142
\(538\) 5.49462 0.236890
\(539\) −25.0928 −1.08082
\(540\) 16.8041 0.723132
\(541\) −10.1558 −0.436630 −0.218315 0.975878i \(-0.570056\pi\)
−0.218315 + 0.975878i \(0.570056\pi\)
\(542\) −1.03270 −0.0443585
\(543\) −3.21805 −0.138100
\(544\) −157.326 −6.74530
\(545\) 4.57208 0.195846
\(546\) 2.52284 0.107968
\(547\) 19.4594 0.832026 0.416013 0.909359i \(-0.363427\pi\)
0.416013 + 0.909359i \(0.363427\pi\)
\(548\) −90.0346 −3.84609
\(549\) 31.5640 1.34712
\(550\) 31.4099 1.33932
\(551\) −42.4619 −1.80894
\(552\) −24.3954 −1.03834
\(553\) −11.4791 −0.488139
\(554\) 4.34250 0.184495
\(555\) −2.59266 −0.110052
\(556\) 1.71773 0.0728481
\(557\) 16.9120 0.716582 0.358291 0.933610i \(-0.383359\pi\)
0.358291 + 0.933610i \(0.383359\pi\)
\(558\) 7.43721 0.314842
\(559\) −0.453408 −0.0191771
\(560\) −44.1302 −1.86484
\(561\) 7.35571 0.310558
\(562\) 21.2593 0.896771
\(563\) 19.8360 0.835988 0.417994 0.908450i \(-0.362733\pi\)
0.417994 + 0.908450i \(0.362733\pi\)
\(564\) 4.89045 0.205925
\(565\) 14.0296 0.590228
\(566\) 42.8724 1.80206
\(567\) 11.6218 0.488070
\(568\) 173.295 7.27129
\(569\) 8.35503 0.350261 0.175130 0.984545i \(-0.443965\pi\)
0.175130 + 0.984545i \(0.443965\pi\)
\(570\) −7.59409 −0.318081
\(571\) 44.4734 1.86116 0.930578 0.366094i \(-0.119305\pi\)
0.930578 + 0.366094i \(0.119305\pi\)
\(572\) −64.6286 −2.70226
\(573\) 3.82160 0.159649
\(574\) −20.0203 −0.835632
\(575\) −17.2280 −0.718459
\(576\) −144.622 −6.02592
\(577\) 8.60731 0.358327 0.179163 0.983819i \(-0.442661\pi\)
0.179163 + 0.983819i \(0.442661\pi\)
\(578\) −24.1818 −1.00583
\(579\) −1.83383 −0.0762114
\(580\) −74.1402 −3.07850
\(581\) 15.2796 0.633903
\(582\) −11.0170 −0.456669
\(583\) −52.7581 −2.18502
\(584\) 25.2871 1.04639
\(585\) −10.6434 −0.440050
\(586\) −26.9877 −1.11485
\(587\) −19.5518 −0.806990 −0.403495 0.914982i \(-0.632205\pi\)
−0.403495 + 0.914982i \(0.632205\pi\)
\(588\) −8.56747 −0.353316
\(589\) −5.08901 −0.209689
\(590\) 16.8847 0.695134
\(591\) 0.515706 0.0212133
\(592\) 101.133 4.15656
\(593\) 33.0068 1.35542 0.677712 0.735327i \(-0.262971\pi\)
0.677712 + 0.735327i \(0.262971\pi\)
\(594\) 24.1392 0.990442
\(595\) −11.8564 −0.486066
\(596\) 28.1475 1.15297
\(597\) 7.19583 0.294506
\(598\) 47.5007 1.94245
\(599\) 18.4843 0.755246 0.377623 0.925959i \(-0.376741\pi\)
0.377623 + 0.925959i \(0.376741\pi\)
\(600\) 7.07803 0.288959
\(601\) −15.4958 −0.632087 −0.316044 0.948745i \(-0.602355\pi\)
−0.316044 + 0.948745i \(0.602355\pi\)
\(602\) −0.816944 −0.0332962
\(603\) 8.06304 0.328352
\(604\) −70.9281 −2.88602
\(605\) −23.3435 −0.949047
\(606\) −4.19056 −0.170230
\(607\) −7.09367 −0.287923 −0.143962 0.989583i \(-0.545984\pi\)
−0.143962 + 0.989583i \(0.545984\pi\)
\(608\) 174.122 7.06159
\(609\) 3.10257 0.125722
\(610\) −50.5331 −2.04602
\(611\) −6.28468 −0.254251
\(612\) −86.7988 −3.50863
\(613\) 21.0160 0.848829 0.424415 0.905468i \(-0.360480\pi\)
0.424415 + 0.905468i \(0.360480\pi\)
\(614\) −43.8138 −1.76818
\(615\) −2.44385 −0.0985457
\(616\) −76.8547 −3.09656
\(617\) −6.54321 −0.263420 −0.131710 0.991288i \(-0.542047\pi\)
−0.131710 + 0.991288i \(0.542047\pi\)
\(618\) −15.9897 −0.643198
\(619\) 13.3357 0.536007 0.268004 0.963418i \(-0.413636\pi\)
0.268004 + 0.963418i \(0.413636\pi\)
\(620\) −8.88562 −0.356855
\(621\) −13.2401 −0.531307
\(622\) 59.1489 2.37165
\(623\) −0.503335 −0.0201657
\(624\) −12.0128 −0.480896
\(625\) −8.82283 −0.352913
\(626\) −17.1451 −0.685256
\(627\) −8.14100 −0.325120
\(628\) 20.1960 0.805908
\(629\) 27.1714 1.08340
\(630\) −19.1771 −0.764034
\(631\) 6.95539 0.276890 0.138445 0.990370i \(-0.455790\pi\)
0.138445 + 0.990370i \(0.455790\pi\)
\(632\) 88.7958 3.53211
\(633\) 7.38448 0.293507
\(634\) −46.1639 −1.83340
\(635\) −29.9538 −1.18868
\(636\) −18.0133 −0.714272
\(637\) 11.0100 0.436231
\(638\) −106.503 −4.21649
\(639\) 46.3554 1.83379
\(640\) 128.167 5.06625
\(641\) 27.2974 1.07818 0.539091 0.842247i \(-0.318768\pi\)
0.539091 + 0.842247i \(0.318768\pi\)
\(642\) −15.1246 −0.596921
\(643\) 17.3998 0.686182 0.343091 0.939302i \(-0.388526\pi\)
0.343091 + 0.939302i \(0.388526\pi\)
\(644\) 63.8701 2.51683
\(645\) −0.0997233 −0.00392660
\(646\) 79.5871 3.13131
\(647\) 44.8747 1.76421 0.882104 0.471055i \(-0.156127\pi\)
0.882104 + 0.471055i \(0.156127\pi\)
\(648\) −89.9000 −3.53161
\(649\) 18.1008 0.710517
\(650\) −13.7817 −0.540564
\(651\) 0.371839 0.0145735
\(652\) 35.4415 1.38799
\(653\) −24.4236 −0.955770 −0.477885 0.878422i \(-0.658596\pi\)
−0.477885 + 0.878422i \(0.658596\pi\)
\(654\) 2.24246 0.0876871
\(655\) 26.1733 1.02268
\(656\) 95.3289 3.72197
\(657\) 6.76416 0.263895
\(658\) −11.3236 −0.441441
\(659\) −48.5875 −1.89270 −0.946351 0.323142i \(-0.895261\pi\)
−0.946351 + 0.323142i \(0.895261\pi\)
\(660\) −14.2145 −0.553299
\(661\) −40.9706 −1.59357 −0.796785 0.604263i \(-0.793468\pi\)
−0.796785 + 0.604263i \(0.793468\pi\)
\(662\) −18.6148 −0.723485
\(663\) −3.22747 −0.125344
\(664\) −118.194 −4.58683
\(665\) 13.1222 0.508857
\(666\) 43.9483 1.70296
\(667\) 58.4159 2.26187
\(668\) −12.9976 −0.502892
\(669\) −7.11245 −0.274983
\(670\) −12.9087 −0.498706
\(671\) −54.1724 −2.09130
\(672\) −12.7226 −0.490785
\(673\) −22.9087 −0.883066 −0.441533 0.897245i \(-0.645565\pi\)
−0.441533 + 0.897245i \(0.645565\pi\)
\(674\) −60.4694 −2.32919
\(675\) 3.84145 0.147858
\(676\) −48.1131 −1.85050
\(677\) 8.96214 0.344443 0.172222 0.985058i \(-0.444906\pi\)
0.172222 + 0.985058i \(0.444906\pi\)
\(678\) 6.88106 0.264266
\(679\) 19.0368 0.730567
\(680\) 91.7149 3.51711
\(681\) 3.36578 0.128977
\(682\) −12.7643 −0.488769
\(683\) −30.5765 −1.16998 −0.584989 0.811042i \(-0.698901\pi\)
−0.584989 + 0.811042i \(0.698901\pi\)
\(684\) 96.0654 3.67315
\(685\) 25.4478 0.972311
\(686\) 47.5298 1.81470
\(687\) −1.53440 −0.0585408
\(688\) 3.88997 0.148304
\(689\) 23.1487 0.881894
\(690\) 10.4474 0.397725
\(691\) −9.81338 −0.373319 −0.186659 0.982425i \(-0.559766\pi\)
−0.186659 + 0.982425i \(0.559766\pi\)
\(692\) −3.99526 −0.151877
\(693\) −20.5582 −0.780942
\(694\) −22.7761 −0.864568
\(695\) −0.485508 −0.0184164
\(696\) −23.9998 −0.909710
\(697\) 25.6120 0.970122
\(698\) −43.5583 −1.64870
\(699\) 1.03323 0.0390803
\(700\) −18.5311 −0.700410
\(701\) −16.0568 −0.606457 −0.303229 0.952918i \(-0.598065\pi\)
−0.303229 + 0.952918i \(0.598065\pi\)
\(702\) −10.5915 −0.399752
\(703\) −30.0722 −1.13420
\(704\) 248.211 9.35480
\(705\) −1.38226 −0.0520590
\(706\) 32.6796 1.22991
\(707\) 7.24108 0.272329
\(708\) 6.18017 0.232265
\(709\) −41.9871 −1.57686 −0.788430 0.615125i \(-0.789106\pi\)
−0.788430 + 0.615125i \(0.789106\pi\)
\(710\) −74.2137 −2.78519
\(711\) 23.7524 0.890785
\(712\) 3.89353 0.145916
\(713\) 7.00108 0.262193
\(714\) −5.81520 −0.217628
\(715\) 18.2669 0.683145
\(716\) −51.2218 −1.91425
\(717\) 5.34450 0.199594
\(718\) −8.80514 −0.328605
\(719\) 29.0418 1.08308 0.541539 0.840676i \(-0.317842\pi\)
0.541539 + 0.840676i \(0.317842\pi\)
\(720\) 91.3139 3.40307
\(721\) 27.6293 1.02897
\(722\) −34.7404 −1.29290
\(723\) −1.40090 −0.0520999
\(724\) −65.1730 −2.42213
\(725\) −16.9486 −0.629457
\(726\) −11.4492 −0.424921
\(727\) 52.6711 1.95346 0.976732 0.214463i \(-0.0688000\pi\)
0.976732 + 0.214463i \(0.0688000\pi\)
\(728\) 33.7216 1.24980
\(729\) −22.5506 −0.835207
\(730\) −10.8292 −0.400808
\(731\) 1.04512 0.0386550
\(732\) −18.4961 −0.683637
\(733\) 27.4870 1.01526 0.507628 0.861576i \(-0.330522\pi\)
0.507628 + 0.861576i \(0.330522\pi\)
\(734\) 101.393 3.74247
\(735\) 2.42155 0.0893203
\(736\) −239.544 −8.82972
\(737\) −13.8384 −0.509743
\(738\) 41.4259 1.52491
\(739\) −20.8534 −0.767103 −0.383552 0.923519i \(-0.625299\pi\)
−0.383552 + 0.923519i \(0.625299\pi\)
\(740\) −52.5073 −1.93021
\(741\) 3.57203 0.131222
\(742\) 41.7089 1.53118
\(743\) −27.7996 −1.01987 −0.509935 0.860213i \(-0.670330\pi\)
−0.509935 + 0.860213i \(0.670330\pi\)
\(744\) −2.87635 −0.105452
\(745\) −7.95576 −0.291476
\(746\) −18.1497 −0.664508
\(747\) −31.6164 −1.15678
\(748\) 148.970 5.44689
\(749\) 26.1346 0.954937
\(750\) −9.81010 −0.358214
\(751\) 29.4418 1.07435 0.537174 0.843472i \(-0.319492\pi\)
0.537174 + 0.843472i \(0.319492\pi\)
\(752\) 53.9187 1.96621
\(753\) 9.17997 0.334537
\(754\) 46.7303 1.70182
\(755\) 20.0475 0.729602
\(756\) −14.2415 −0.517959
\(757\) −3.97422 −0.144446 −0.0722228 0.997389i \(-0.523009\pi\)
−0.0722228 + 0.997389i \(0.523009\pi\)
\(758\) 34.9737 1.27030
\(759\) 11.1998 0.406526
\(760\) −101.506 −3.68202
\(761\) −13.9392 −0.505296 −0.252648 0.967558i \(-0.581301\pi\)
−0.252648 + 0.967558i \(0.581301\pi\)
\(762\) −14.6914 −0.532214
\(763\) −3.87486 −0.140279
\(764\) 77.3962 2.80010
\(765\) 24.5332 0.887001
\(766\) −37.9275 −1.37038
\(767\) −7.94207 −0.286772
\(768\) 34.0478 1.22859
\(769\) −30.6344 −1.10471 −0.552353 0.833610i \(-0.686270\pi\)
−0.552353 + 0.833610i \(0.686270\pi\)
\(770\) 32.9131 1.18611
\(771\) 2.15611 0.0776504
\(772\) −37.1393 −1.33667
\(773\) −2.23805 −0.0804972 −0.0402486 0.999190i \(-0.512815\pi\)
−0.0402486 + 0.999190i \(0.512815\pi\)
\(774\) 1.69042 0.0607607
\(775\) −2.03128 −0.0729656
\(776\) −147.259 −5.28628
\(777\) 2.19729 0.0788274
\(778\) 7.07721 0.253730
\(779\) −28.3463 −1.01561
\(780\) 6.23691 0.223317
\(781\) −79.5585 −2.84683
\(782\) −109.490 −3.91536
\(783\) −13.0254 −0.465489
\(784\) −94.4589 −3.37353
\(785\) −5.70830 −0.203738
\(786\) 12.8372 0.457887
\(787\) −20.2256 −0.720966 −0.360483 0.932766i \(-0.617388\pi\)
−0.360483 + 0.932766i \(0.617388\pi\)
\(788\) 10.4442 0.372061
\(789\) −1.40887 −0.0501570
\(790\) −38.0269 −1.35294
\(791\) −11.8901 −0.422764
\(792\) 159.027 5.65079
\(793\) 23.7692 0.844070
\(794\) 1.44325 0.0512189
\(795\) 5.09136 0.180572
\(796\) 145.732 5.16535
\(797\) 53.7971 1.90559 0.952796 0.303610i \(-0.0981921\pi\)
0.952796 + 0.303610i \(0.0981921\pi\)
\(798\) 6.43603 0.227833
\(799\) 14.4863 0.512489
\(800\) 69.5008 2.45722
\(801\) 1.04150 0.0367995
\(802\) 17.9110 0.632459
\(803\) −11.6091 −0.409678
\(804\) −4.72485 −0.166633
\(805\) −18.0526 −0.636269
\(806\) 5.60058 0.197272
\(807\) −0.568440 −0.0200100
\(808\) −56.0131 −1.97053
\(809\) 2.17674 0.0765300 0.0382650 0.999268i \(-0.487817\pi\)
0.0382650 + 0.999268i \(0.487817\pi\)
\(810\) 38.4998 1.35274
\(811\) −15.4304 −0.541834 −0.270917 0.962603i \(-0.587327\pi\)
−0.270917 + 0.962603i \(0.587327\pi\)
\(812\) 62.8342 2.20505
\(813\) 0.106837 0.00374695
\(814\) −75.4272 −2.64372
\(815\) −10.0174 −0.350893
\(816\) 27.6897 0.969334
\(817\) −1.15669 −0.0404675
\(818\) 27.2800 0.953824
\(819\) 9.02033 0.315196
\(820\) −49.4937 −1.72840
\(821\) 22.8193 0.796400 0.398200 0.917299i \(-0.369635\pi\)
0.398200 + 0.917299i \(0.369635\pi\)
\(822\) 12.4814 0.435337
\(823\) −15.3082 −0.533612 −0.266806 0.963750i \(-0.585968\pi\)
−0.266806 + 0.963750i \(0.585968\pi\)
\(824\) −213.726 −7.44549
\(825\) −3.24948 −0.113132
\(826\) −14.3099 −0.497905
\(827\) −1.94467 −0.0676229 −0.0338115 0.999428i \(-0.510765\pi\)
−0.0338115 + 0.999428i \(0.510765\pi\)
\(828\) −132.160 −4.59286
\(829\) −36.5917 −1.27088 −0.635442 0.772149i \(-0.719182\pi\)
−0.635442 + 0.772149i \(0.719182\pi\)
\(830\) 50.6169 1.75694
\(831\) −0.449249 −0.0155843
\(832\) −108.908 −3.77569
\(833\) −25.3782 −0.879303
\(834\) −0.238126 −0.00824564
\(835\) 3.67370 0.127134
\(836\) −164.874 −5.70229
\(837\) −1.56108 −0.0539588
\(838\) −98.4435 −3.40068
\(839\) −50.6297 −1.74793 −0.873966 0.485987i \(-0.838460\pi\)
−0.873966 + 0.485987i \(0.838460\pi\)
\(840\) 7.41677 0.255903
\(841\) 28.4685 0.981672
\(842\) 67.4190 2.32341
\(843\) −2.19936 −0.0757500
\(844\) 149.553 5.14782
\(845\) 13.5989 0.467817
\(846\) 23.4308 0.805567
\(847\) 19.7837 0.679776
\(848\) −198.602 −6.82001
\(849\) −4.43532 −0.152220
\(850\) 31.7672 1.08960
\(851\) 41.3711 1.41818
\(852\) −27.1637 −0.930615
\(853\) 52.5281 1.79853 0.899264 0.437406i \(-0.144103\pi\)
0.899264 + 0.437406i \(0.144103\pi\)
\(854\) 42.8270 1.46551
\(855\) −27.1524 −0.928592
\(856\) −202.163 −6.90979
\(857\) 2.57822 0.0880704 0.0440352 0.999030i \(-0.485979\pi\)
0.0440352 + 0.999030i \(0.485979\pi\)
\(858\) 8.95936 0.305868
\(859\) 57.8361 1.97334 0.986671 0.162731i \(-0.0520301\pi\)
0.986671 + 0.162731i \(0.0520301\pi\)
\(860\) −2.01963 −0.0688688
\(861\) 2.07118 0.0705856
\(862\) −68.9144 −2.34723
\(863\) −49.9739 −1.70113 −0.850565 0.525870i \(-0.823740\pi\)
−0.850565 + 0.525870i \(0.823740\pi\)
\(864\) 53.4128 1.81714
\(865\) 1.12924 0.0383953
\(866\) −73.1041 −2.48418
\(867\) 2.50170 0.0849622
\(868\) 7.53061 0.255606
\(869\) −40.7656 −1.38288
\(870\) 10.2779 0.348455
\(871\) 6.07186 0.205737
\(872\) 29.9738 1.01504
\(873\) −39.3909 −1.33318
\(874\) 121.179 4.09894
\(875\) 16.9514 0.573061
\(876\) −3.96372 −0.133922
\(877\) 30.9147 1.04391 0.521957 0.852972i \(-0.325202\pi\)
0.521957 + 0.852972i \(0.325202\pi\)
\(878\) −80.4514 −2.71510
\(879\) 2.79198 0.0941713
\(880\) −156.719 −5.28301
\(881\) 32.9767 1.11101 0.555506 0.831512i \(-0.312524\pi\)
0.555506 + 0.831512i \(0.312524\pi\)
\(882\) −41.0478 −1.38215
\(883\) −34.2919 −1.15401 −0.577007 0.816739i \(-0.695780\pi\)
−0.577007 + 0.816739i \(0.695780\pi\)
\(884\) −65.3637 −2.19842
\(885\) −1.74679 −0.0587178
\(886\) −91.3199 −3.06795
\(887\) −13.1511 −0.441571 −0.220786 0.975322i \(-0.570862\pi\)
−0.220786 + 0.975322i \(0.570862\pi\)
\(888\) −16.9971 −0.570384
\(889\) 25.3860 0.851420
\(890\) −1.66741 −0.0558916
\(891\) 41.2725 1.38268
\(892\) −144.044 −4.82294
\(893\) −16.0329 −0.536519
\(894\) −3.90205 −0.130504
\(895\) 14.4776 0.483932
\(896\) −108.622 −3.62882
\(897\) −4.91413 −0.164078
\(898\) −11.2683 −0.376030
\(899\) 6.88754 0.229712
\(900\) 38.3444 1.27815
\(901\) −53.3582 −1.77762
\(902\) −71.0981 −2.36731
\(903\) 0.0845161 0.00281252
\(904\) 91.9756 3.05906
\(905\) 18.4208 0.612329
\(906\) 9.83265 0.326668
\(907\) −0.576523 −0.0191431 −0.00957156 0.999954i \(-0.503047\pi\)
−0.00957156 + 0.999954i \(0.503047\pi\)
\(908\) 68.1650 2.26213
\(909\) −14.9832 −0.496961
\(910\) −14.4413 −0.478724
\(911\) 45.3247 1.50167 0.750837 0.660487i \(-0.229650\pi\)
0.750837 + 0.660487i \(0.229650\pi\)
\(912\) −30.6458 −1.01479
\(913\) 54.2622 1.79582
\(914\) 33.3382 1.10273
\(915\) 5.22784 0.172827
\(916\) −31.0751 −1.02675
\(917\) −22.1820 −0.732515
\(918\) 24.4137 0.805773
\(919\) 4.30281 0.141937 0.0709683 0.997479i \(-0.477391\pi\)
0.0709683 + 0.997479i \(0.477391\pi\)
\(920\) 139.645 4.60395
\(921\) 4.53271 0.149358
\(922\) −112.518 −3.70559
\(923\) 34.9079 1.14901
\(924\) 12.0469 0.396313
\(925\) −12.0033 −0.394667
\(926\) −118.838 −3.90526
\(927\) −57.1705 −1.87772
\(928\) −235.659 −7.73589
\(929\) 47.2490 1.55019 0.775095 0.631844i \(-0.217702\pi\)
0.775095 + 0.631844i \(0.217702\pi\)
\(930\) 1.23180 0.0403923
\(931\) 28.0876 0.920533
\(932\) 20.9253 0.685430
\(933\) −6.11918 −0.200333
\(934\) −71.2271 −2.33062
\(935\) −42.1057 −1.37700
\(936\) −69.7764 −2.28071
\(937\) 4.10334 0.134050 0.0670251 0.997751i \(-0.478649\pi\)
0.0670251 + 0.997751i \(0.478649\pi\)
\(938\) 10.9402 0.357210
\(939\) 1.77373 0.0578835
\(940\) −27.9940 −0.913064
\(941\) 37.1625 1.21146 0.605732 0.795669i \(-0.292880\pi\)
0.605732 + 0.795669i \(0.292880\pi\)
\(942\) −2.79974 −0.0912205
\(943\) 38.9967 1.26991
\(944\) 68.1382 2.21771
\(945\) 4.02530 0.130943
\(946\) −2.90121 −0.0943265
\(947\) 9.05037 0.294098 0.147049 0.989129i \(-0.453023\pi\)
0.147049 + 0.989129i \(0.453023\pi\)
\(948\) −13.9186 −0.452056
\(949\) 5.09375 0.165350
\(950\) −35.1586 −1.14070
\(951\) 4.77583 0.154867
\(952\) −77.7289 −2.51921
\(953\) −10.6271 −0.344247 −0.172123 0.985075i \(-0.555063\pi\)
−0.172123 + 0.985075i \(0.555063\pi\)
\(954\) −86.3039 −2.79419
\(955\) −21.8756 −0.707879
\(956\) 108.239 3.50068
\(957\) 11.0181 0.356166
\(958\) −20.2534 −0.654358
\(959\) −21.5672 −0.696440
\(960\) −23.9533 −0.773089
\(961\) −30.1745 −0.973372
\(962\) 33.0952 1.06703
\(963\) −54.0775 −1.74262
\(964\) −28.3714 −0.913782
\(965\) 10.4972 0.337918
\(966\) −8.85421 −0.284879
\(967\) −2.04280 −0.0656921 −0.0328461 0.999460i \(-0.510457\pi\)
−0.0328461 + 0.999460i \(0.510457\pi\)
\(968\) −153.036 −4.91877
\(969\) −8.23360 −0.264501
\(970\) 63.0637 2.02485
\(971\) −15.7845 −0.506550 −0.253275 0.967394i \(-0.581508\pi\)
−0.253275 + 0.967394i \(0.581508\pi\)
\(972\) 44.4129 1.42454
\(973\) 0.411471 0.0131911
\(974\) −80.9467 −2.59370
\(975\) 1.42577 0.0456613
\(976\) −203.926 −6.52750
\(977\) −43.2492 −1.38367 −0.691833 0.722058i \(-0.743196\pi\)
−0.691833 + 0.722058i \(0.743196\pi\)
\(978\) −4.91319 −0.157107
\(979\) −1.78749 −0.0571285
\(980\) 49.0420 1.56659
\(981\) 8.01784 0.255990
\(982\) −85.1911 −2.71856
\(983\) −36.8090 −1.17402 −0.587012 0.809578i \(-0.699696\pi\)
−0.587012 + 0.809578i \(0.699696\pi\)
\(984\) −16.0215 −0.510748
\(985\) −2.95201 −0.0940590
\(986\) −107.714 −3.43032
\(987\) 1.17147 0.0372884
\(988\) 72.3419 2.30150
\(989\) 1.59129 0.0506000
\(990\) −68.1036 −2.16447
\(991\) −20.1774 −0.640955 −0.320477 0.947256i \(-0.603843\pi\)
−0.320477 + 0.947256i \(0.603843\pi\)
\(992\) −28.2435 −0.896732
\(993\) 1.92577 0.0611126
\(994\) 62.8965 1.99496
\(995\) −41.1905 −1.30583
\(996\) 18.5268 0.587045
\(997\) 39.1053 1.23848 0.619239 0.785203i \(-0.287441\pi\)
0.619239 + 0.785203i \(0.287441\pi\)
\(998\) −20.1206 −0.636908
\(999\) −9.22480 −0.291860
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.1.1 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.1 174 1.1 even 1 trivial