Properties

Label 4027.2.a.c.1.6
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 1.6
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61961 q^{2} +0.347361 q^{3} +4.86233 q^{4} +3.06529 q^{5} -0.909948 q^{6} -2.40365 q^{7} -7.49819 q^{8} -2.87934 q^{9} +O(q^{10})\) \(q-2.61961 q^{2} +0.347361 q^{3} +4.86233 q^{4} +3.06529 q^{5} -0.909948 q^{6} -2.40365 q^{7} -7.49819 q^{8} -2.87934 q^{9} -8.02984 q^{10} -5.26667 q^{11} +1.68898 q^{12} -3.23857 q^{13} +6.29663 q^{14} +1.06476 q^{15} +9.91762 q^{16} -1.08454 q^{17} +7.54274 q^{18} +0.530031 q^{19} +14.9044 q^{20} -0.834935 q^{21} +13.7966 q^{22} -6.75304 q^{23} -2.60458 q^{24} +4.39598 q^{25} +8.48378 q^{26} -2.04225 q^{27} -11.6874 q^{28} +8.35102 q^{29} -2.78925 q^{30} -8.45447 q^{31} -10.9839 q^{32} -1.82944 q^{33} +2.84107 q^{34} -7.36789 q^{35} -14.0003 q^{36} +2.82376 q^{37} -1.38847 q^{38} -1.12495 q^{39} -22.9841 q^{40} +3.29115 q^{41} +2.18720 q^{42} +8.64744 q^{43} -25.6083 q^{44} -8.82600 q^{45} +17.6903 q^{46} -8.21305 q^{47} +3.44499 q^{48} -1.22245 q^{49} -11.5157 q^{50} -0.376728 q^{51} -15.7470 q^{52} +13.8081 q^{53} +5.34990 q^{54} -16.1439 q^{55} +18.0230 q^{56} +0.184112 q^{57} -21.8764 q^{58} -4.99471 q^{59} +5.17722 q^{60} -15.3035 q^{61} +22.1474 q^{62} +6.92094 q^{63} +8.93821 q^{64} -9.92715 q^{65} +4.79240 q^{66} +8.93521 q^{67} -5.27341 q^{68} -2.34574 q^{69} +19.3010 q^{70} +1.95526 q^{71} +21.5898 q^{72} -0.967541 q^{73} -7.39715 q^{74} +1.52699 q^{75} +2.57719 q^{76} +12.6593 q^{77} +2.94693 q^{78} -5.71184 q^{79} +30.4004 q^{80} +7.92862 q^{81} -8.62151 q^{82} +15.6220 q^{83} -4.05973 q^{84} -3.32443 q^{85} -22.6529 q^{86} +2.90082 q^{87} +39.4905 q^{88} -3.10127 q^{89} +23.1207 q^{90} +7.78441 q^{91} -32.8356 q^{92} -2.93675 q^{93} +21.5150 q^{94} +1.62470 q^{95} -3.81537 q^{96} +9.74823 q^{97} +3.20232 q^{98} +15.1645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61961 −1.85234 −0.926170 0.377105i \(-0.876920\pi\)
−0.926170 + 0.377105i \(0.876920\pi\)
\(3\) 0.347361 0.200549 0.100274 0.994960i \(-0.468028\pi\)
0.100274 + 0.994960i \(0.468028\pi\)
\(4\) 4.86233 2.43117
\(5\) 3.06529 1.37084 0.685419 0.728149i \(-0.259619\pi\)
0.685419 + 0.728149i \(0.259619\pi\)
\(6\) −0.909948 −0.371485
\(7\) −2.40365 −0.908496 −0.454248 0.890875i \(-0.650092\pi\)
−0.454248 + 0.890875i \(0.650092\pi\)
\(8\) −7.49819 −2.65101
\(9\) −2.87934 −0.959780
\(10\) −8.02984 −2.53926
\(11\) −5.26667 −1.58796 −0.793981 0.607943i \(-0.791995\pi\)
−0.793981 + 0.607943i \(0.791995\pi\)
\(12\) 1.68898 0.487568
\(13\) −3.23857 −0.898218 −0.449109 0.893477i \(-0.648259\pi\)
−0.449109 + 0.893477i \(0.648259\pi\)
\(14\) 6.29663 1.68284
\(15\) 1.06476 0.274920
\(16\) 9.91762 2.47941
\(17\) −1.08454 −0.263040 −0.131520 0.991314i \(-0.541986\pi\)
−0.131520 + 0.991314i \(0.541986\pi\)
\(18\) 7.54274 1.77784
\(19\) 0.530031 0.121597 0.0607987 0.998150i \(-0.480635\pi\)
0.0607987 + 0.998150i \(0.480635\pi\)
\(20\) 14.9044 3.33274
\(21\) −0.834935 −0.182198
\(22\) 13.7966 2.94145
\(23\) −6.75304 −1.40811 −0.704054 0.710147i \(-0.748629\pi\)
−0.704054 + 0.710147i \(0.748629\pi\)
\(24\) −2.60458 −0.531657
\(25\) 4.39598 0.879196
\(26\) 8.48378 1.66381
\(27\) −2.04225 −0.393032
\(28\) −11.6874 −2.20871
\(29\) 8.35102 1.55075 0.775373 0.631504i \(-0.217562\pi\)
0.775373 + 0.631504i \(0.217562\pi\)
\(30\) −2.78925 −0.509245
\(31\) −8.45447 −1.51847 −0.759233 0.650818i \(-0.774426\pi\)
−0.759233 + 0.650818i \(0.774426\pi\)
\(32\) −10.9839 −1.94170
\(33\) −1.82944 −0.318464
\(34\) 2.84107 0.487240
\(35\) −7.36789 −1.24540
\(36\) −14.0003 −2.33339
\(37\) 2.82376 0.464224 0.232112 0.972689i \(-0.425436\pi\)
0.232112 + 0.972689i \(0.425436\pi\)
\(38\) −1.38847 −0.225240
\(39\) −1.12495 −0.180137
\(40\) −22.9841 −3.63410
\(41\) 3.29115 0.513991 0.256996 0.966413i \(-0.417267\pi\)
0.256996 + 0.966413i \(0.417267\pi\)
\(42\) 2.18720 0.337492
\(43\) 8.64744 1.31872 0.659361 0.751826i \(-0.270827\pi\)
0.659361 + 0.751826i \(0.270827\pi\)
\(44\) −25.6083 −3.86060
\(45\) −8.82600 −1.31570
\(46\) 17.6903 2.60829
\(47\) −8.21305 −1.19800 −0.598998 0.800750i \(-0.704434\pi\)
−0.598998 + 0.800750i \(0.704434\pi\)
\(48\) 3.44499 0.497242
\(49\) −1.22245 −0.174635
\(50\) −11.5157 −1.62857
\(51\) −0.376728 −0.0527524
\(52\) −15.7470 −2.18372
\(53\) 13.8081 1.89668 0.948341 0.317253i \(-0.102760\pi\)
0.948341 + 0.317253i \(0.102760\pi\)
\(54\) 5.34990 0.728029
\(55\) −16.1439 −2.17684
\(56\) 18.0230 2.40843
\(57\) 0.184112 0.0243862
\(58\) −21.8764 −2.87251
\(59\) −4.99471 −0.650255 −0.325128 0.945670i \(-0.605407\pi\)
−0.325128 + 0.945670i \(0.605407\pi\)
\(60\) 5.17722 0.668376
\(61\) −15.3035 −1.95942 −0.979708 0.200432i \(-0.935765\pi\)
−0.979708 + 0.200432i \(0.935765\pi\)
\(62\) 22.1474 2.81272
\(63\) 6.92094 0.871956
\(64\) 8.93821 1.11728
\(65\) −9.92715 −1.23131
\(66\) 4.79240 0.589904
\(67\) 8.93521 1.09161 0.545805 0.837912i \(-0.316224\pi\)
0.545805 + 0.837912i \(0.316224\pi\)
\(68\) −5.27341 −0.639495
\(69\) −2.34574 −0.282394
\(70\) 19.3010 2.30691
\(71\) 1.95526 0.232047 0.116024 0.993246i \(-0.462985\pi\)
0.116024 + 0.993246i \(0.462985\pi\)
\(72\) 21.5898 2.54439
\(73\) −0.967541 −0.113242 −0.0566210 0.998396i \(-0.518033\pi\)
−0.0566210 + 0.998396i \(0.518033\pi\)
\(74\) −7.39715 −0.859901
\(75\) 1.52699 0.176322
\(76\) 2.57719 0.295624
\(77\) 12.6593 1.44266
\(78\) 2.94693 0.333675
\(79\) −5.71184 −0.642632 −0.321316 0.946972i \(-0.604125\pi\)
−0.321316 + 0.946972i \(0.604125\pi\)
\(80\) 30.4004 3.39886
\(81\) 7.92862 0.880958
\(82\) −8.62151 −0.952087
\(83\) 15.6220 1.71474 0.857369 0.514702i \(-0.172097\pi\)
0.857369 + 0.514702i \(0.172097\pi\)
\(84\) −4.05973 −0.442953
\(85\) −3.32443 −0.360586
\(86\) −22.6529 −2.44272
\(87\) 2.90082 0.311000
\(88\) 39.4905 4.20970
\(89\) −3.10127 −0.328734 −0.164367 0.986399i \(-0.552558\pi\)
−0.164367 + 0.986399i \(0.552558\pi\)
\(90\) 23.1207 2.43713
\(91\) 7.78441 0.816028
\(92\) −32.8356 −3.42334
\(93\) −2.93675 −0.304527
\(94\) 21.5150 2.21910
\(95\) 1.62470 0.166690
\(96\) −3.81537 −0.389405
\(97\) 9.74823 0.989783 0.494892 0.868955i \(-0.335208\pi\)
0.494892 + 0.868955i \(0.335208\pi\)
\(98\) 3.20232 0.323484
\(99\) 15.1645 1.52409
\(100\) 21.3747 2.13747
\(101\) 11.5866 1.15291 0.576454 0.817130i \(-0.304436\pi\)
0.576454 + 0.817130i \(0.304436\pi\)
\(102\) 0.986878 0.0977155
\(103\) 20.0076 1.97141 0.985706 0.168477i \(-0.0538850\pi\)
0.985706 + 0.168477i \(0.0538850\pi\)
\(104\) 24.2834 2.38119
\(105\) −2.55932 −0.249764
\(106\) −36.1717 −3.51330
\(107\) −1.14492 −0.110684 −0.0553419 0.998467i \(-0.517625\pi\)
−0.0553419 + 0.998467i \(0.517625\pi\)
\(108\) −9.93011 −0.955526
\(109\) 20.4815 1.96177 0.980886 0.194585i \(-0.0623359\pi\)
0.980886 + 0.194585i \(0.0623359\pi\)
\(110\) 42.2906 4.03225
\(111\) 0.980865 0.0930996
\(112\) −23.8385 −2.25253
\(113\) 12.0780 1.13620 0.568101 0.822959i \(-0.307678\pi\)
0.568101 + 0.822959i \(0.307678\pi\)
\(114\) −0.482301 −0.0451716
\(115\) −20.7000 −1.93029
\(116\) 40.6054 3.77012
\(117\) 9.32495 0.862092
\(118\) 13.0842 1.20449
\(119\) 2.60687 0.238971
\(120\) −7.98377 −0.728815
\(121\) 16.7379 1.52162
\(122\) 40.0892 3.62950
\(123\) 1.14322 0.103080
\(124\) −41.1084 −3.69165
\(125\) −1.85149 −0.165602
\(126\) −18.1301 −1.61516
\(127\) −1.66730 −0.147949 −0.0739745 0.997260i \(-0.523568\pi\)
−0.0739745 + 0.997260i \(0.523568\pi\)
\(128\) −1.44681 −0.127881
\(129\) 3.00378 0.264468
\(130\) 26.0052 2.28081
\(131\) −5.87353 −0.513173 −0.256586 0.966521i \(-0.582598\pi\)
−0.256586 + 0.966521i \(0.582598\pi\)
\(132\) −8.89533 −0.774239
\(133\) −1.27401 −0.110471
\(134\) −23.4067 −2.02203
\(135\) −6.26009 −0.538783
\(136\) 8.13210 0.697322
\(137\) −11.2484 −0.961013 −0.480506 0.876991i \(-0.659547\pi\)
−0.480506 + 0.876991i \(0.659547\pi\)
\(138\) 6.14492 0.523090
\(139\) −10.8800 −0.922833 −0.461416 0.887184i \(-0.652659\pi\)
−0.461416 + 0.887184i \(0.652659\pi\)
\(140\) −35.8251 −3.02778
\(141\) −2.85289 −0.240257
\(142\) −5.12202 −0.429831
\(143\) 17.0565 1.42634
\(144\) −28.5562 −2.37968
\(145\) 25.5983 2.12582
\(146\) 2.53458 0.209763
\(147\) −0.424630 −0.0350229
\(148\) 13.7301 1.12861
\(149\) 13.7210 1.12407 0.562036 0.827113i \(-0.310018\pi\)
0.562036 + 0.827113i \(0.310018\pi\)
\(150\) −4.00012 −0.326608
\(151\) 7.63597 0.621406 0.310703 0.950507i \(-0.399436\pi\)
0.310703 + 0.950507i \(0.399436\pi\)
\(152\) −3.97427 −0.322356
\(153\) 3.12277 0.252461
\(154\) −33.1623 −2.67229
\(155\) −25.9154 −2.08157
\(156\) −5.46990 −0.437942
\(157\) −6.32759 −0.504996 −0.252498 0.967597i \(-0.581252\pi\)
−0.252498 + 0.967597i \(0.581252\pi\)
\(158\) 14.9628 1.19037
\(159\) 4.79638 0.380377
\(160\) −33.6688 −2.66175
\(161\) 16.2320 1.27926
\(162\) −20.7699 −1.63183
\(163\) −19.6986 −1.54292 −0.771458 0.636280i \(-0.780472\pi\)
−0.771458 + 0.636280i \(0.780472\pi\)
\(164\) 16.0027 1.24960
\(165\) −5.60775 −0.436562
\(166\) −40.9235 −3.17628
\(167\) 5.21277 0.403376 0.201688 0.979450i \(-0.435357\pi\)
0.201688 + 0.979450i \(0.435357\pi\)
\(168\) 6.26050 0.483008
\(169\) −2.51165 −0.193204
\(170\) 8.70871 0.667927
\(171\) −1.52614 −0.116707
\(172\) 42.0468 3.20604
\(173\) 21.1628 1.60898 0.804488 0.593969i \(-0.202440\pi\)
0.804488 + 0.593969i \(0.202440\pi\)
\(174\) −7.59899 −0.576078
\(175\) −10.5664 −0.798746
\(176\) −52.2329 −3.93720
\(177\) −1.73497 −0.130408
\(178\) 8.12411 0.608928
\(179\) −7.31645 −0.546857 −0.273429 0.961892i \(-0.588158\pi\)
−0.273429 + 0.961892i \(0.588158\pi\)
\(180\) −42.9150 −3.19869
\(181\) −14.5776 −1.08354 −0.541771 0.840526i \(-0.682246\pi\)
−0.541771 + 0.840526i \(0.682246\pi\)
\(182\) −20.3921 −1.51156
\(183\) −5.31584 −0.392958
\(184\) 50.6356 3.73290
\(185\) 8.65565 0.636376
\(186\) 7.69313 0.564087
\(187\) 5.71193 0.417698
\(188\) −39.9346 −2.91253
\(189\) 4.90887 0.357068
\(190\) −4.25606 −0.308767
\(191\) −3.18751 −0.230640 −0.115320 0.993328i \(-0.536789\pi\)
−0.115320 + 0.993328i \(0.536789\pi\)
\(192\) 3.10478 0.224068
\(193\) 9.57637 0.689322 0.344661 0.938727i \(-0.387994\pi\)
0.344661 + 0.938727i \(0.387994\pi\)
\(194\) −25.5365 −1.83342
\(195\) −3.44830 −0.246938
\(196\) −5.94394 −0.424567
\(197\) −20.1648 −1.43668 −0.718342 0.695690i \(-0.755099\pi\)
−0.718342 + 0.695690i \(0.755099\pi\)
\(198\) −39.7251 −2.82314
\(199\) −3.45675 −0.245043 −0.122521 0.992466i \(-0.539098\pi\)
−0.122521 + 0.992466i \(0.539098\pi\)
\(200\) −32.9619 −2.33076
\(201\) 3.10374 0.218921
\(202\) −30.3523 −2.13558
\(203\) −20.0730 −1.40885
\(204\) −1.83178 −0.128250
\(205\) 10.0883 0.704599
\(206\) −52.4121 −3.65173
\(207\) 19.4443 1.35147
\(208\) −32.1189 −2.22705
\(209\) −2.79150 −0.193092
\(210\) 6.70440 0.462647
\(211\) 8.35438 0.575139 0.287569 0.957760i \(-0.407153\pi\)
0.287569 + 0.957760i \(0.407153\pi\)
\(212\) 67.1394 4.61115
\(213\) 0.679182 0.0465368
\(214\) 2.99925 0.205024
\(215\) 26.5069 1.80776
\(216\) 15.3132 1.04193
\(217\) 20.3216 1.37952
\(218\) −53.6534 −3.63387
\(219\) −0.336086 −0.0227106
\(220\) −78.4969 −5.29226
\(221\) 3.51237 0.236268
\(222\) −2.56948 −0.172452
\(223\) −0.525797 −0.0352100 −0.0176050 0.999845i \(-0.505604\pi\)
−0.0176050 + 0.999845i \(0.505604\pi\)
\(224\) 26.4015 1.76402
\(225\) −12.6575 −0.843835
\(226\) −31.6396 −2.10463
\(227\) −6.09842 −0.404767 −0.202383 0.979306i \(-0.564869\pi\)
−0.202383 + 0.979306i \(0.564869\pi\)
\(228\) 0.895214 0.0592870
\(229\) −1.48962 −0.0984369 −0.0492185 0.998788i \(-0.515673\pi\)
−0.0492185 + 0.998788i \(0.515673\pi\)
\(230\) 54.2259 3.57555
\(231\) 4.39733 0.289323
\(232\) −62.6175 −4.11104
\(233\) −2.55413 −0.167327 −0.0836633 0.996494i \(-0.526662\pi\)
−0.0836633 + 0.996494i \(0.526662\pi\)
\(234\) −24.4277 −1.59689
\(235\) −25.1754 −1.64226
\(236\) −24.2859 −1.58088
\(237\) −1.98407 −0.128879
\(238\) −6.82896 −0.442656
\(239\) 25.7873 1.66804 0.834020 0.551734i \(-0.186034\pi\)
0.834020 + 0.551734i \(0.186034\pi\)
\(240\) 10.5599 0.681638
\(241\) −1.15712 −0.0745367 −0.0372683 0.999305i \(-0.511866\pi\)
−0.0372683 + 0.999305i \(0.511866\pi\)
\(242\) −43.8466 −2.81857
\(243\) 8.88085 0.569707
\(244\) −74.4108 −4.76367
\(245\) −3.74714 −0.239396
\(246\) −2.99478 −0.190940
\(247\) −1.71654 −0.109221
\(248\) 63.3932 4.02547
\(249\) 5.42647 0.343889
\(250\) 4.85017 0.306751
\(251\) 13.2403 0.835721 0.417861 0.908511i \(-0.362780\pi\)
0.417861 + 0.908511i \(0.362780\pi\)
\(252\) 33.6519 2.11987
\(253\) 35.5661 2.23602
\(254\) 4.36767 0.274052
\(255\) −1.15478 −0.0723150
\(256\) −14.0863 −0.880397
\(257\) −20.5888 −1.28430 −0.642148 0.766581i \(-0.721956\pi\)
−0.642148 + 0.766581i \(0.721956\pi\)
\(258\) −7.86873 −0.489886
\(259\) −6.78736 −0.421746
\(260\) −48.2691 −2.99352
\(261\) −24.0454 −1.48837
\(262\) 15.3863 0.950571
\(263\) 19.9625 1.23094 0.615470 0.788160i \(-0.288966\pi\)
0.615470 + 0.788160i \(0.288966\pi\)
\(264\) 13.7175 0.844251
\(265\) 42.3256 2.60004
\(266\) 3.33741 0.204630
\(267\) −1.07726 −0.0659273
\(268\) 43.4460 2.65389
\(269\) 18.1424 1.10616 0.553081 0.833128i \(-0.313452\pi\)
0.553081 + 0.833128i \(0.313452\pi\)
\(270\) 16.3990 0.998009
\(271\) −19.2515 −1.16945 −0.584723 0.811233i \(-0.698797\pi\)
−0.584723 + 0.811233i \(0.698797\pi\)
\(272\) −10.7561 −0.652183
\(273\) 2.70400 0.163653
\(274\) 29.4663 1.78012
\(275\) −23.1522 −1.39613
\(276\) −11.4058 −0.686548
\(277\) 12.1497 0.730002 0.365001 0.931007i \(-0.381069\pi\)
0.365001 + 0.931007i \(0.381069\pi\)
\(278\) 28.5014 1.70940
\(279\) 24.3433 1.45739
\(280\) 55.2458 3.30157
\(281\) 13.5051 0.805644 0.402822 0.915278i \(-0.368029\pi\)
0.402822 + 0.915278i \(0.368029\pi\)
\(282\) 7.47345 0.445038
\(283\) −1.74148 −0.103520 −0.0517601 0.998660i \(-0.516483\pi\)
−0.0517601 + 0.998660i \(0.516483\pi\)
\(284\) 9.50715 0.564146
\(285\) 0.564356 0.0334296
\(286\) −44.6813 −2.64206
\(287\) −7.91079 −0.466959
\(288\) 31.6264 1.86360
\(289\) −15.8238 −0.930810
\(290\) −67.0574 −3.93774
\(291\) 3.38615 0.198500
\(292\) −4.70451 −0.275310
\(293\) 14.3713 0.839578 0.419789 0.907622i \(-0.362104\pi\)
0.419789 + 0.907622i \(0.362104\pi\)
\(294\) 1.11236 0.0648743
\(295\) −15.3102 −0.891395
\(296\) −21.1731 −1.23066
\(297\) 10.7559 0.624119
\(298\) −35.9437 −2.08216
\(299\) 21.8702 1.26479
\(300\) 7.42474 0.428668
\(301\) −20.7855 −1.19805
\(302\) −20.0032 −1.15106
\(303\) 4.02472 0.231214
\(304\) 5.25665 0.301489
\(305\) −46.9097 −2.68604
\(306\) −8.18042 −0.467643
\(307\) −21.6167 −1.23373 −0.616865 0.787069i \(-0.711598\pi\)
−0.616865 + 0.787069i \(0.711598\pi\)
\(308\) 61.5536 3.50734
\(309\) 6.94987 0.395364
\(310\) 67.8880 3.85578
\(311\) 7.56380 0.428904 0.214452 0.976735i \(-0.431204\pi\)
0.214452 + 0.976735i \(0.431204\pi\)
\(312\) 8.43511 0.477544
\(313\) 32.4616 1.83484 0.917419 0.397922i \(-0.130269\pi\)
0.917419 + 0.397922i \(0.130269\pi\)
\(314\) 16.5758 0.935425
\(315\) 21.2147 1.19531
\(316\) −27.7729 −1.56235
\(317\) 9.96783 0.559849 0.279925 0.960022i \(-0.409691\pi\)
0.279925 + 0.960022i \(0.409691\pi\)
\(318\) −12.5646 −0.704589
\(319\) −43.9821 −2.46252
\(320\) 27.3982 1.53160
\(321\) −0.397701 −0.0221975
\(322\) −42.5214 −2.36963
\(323\) −0.574841 −0.0319850
\(324\) 38.5516 2.14176
\(325\) −14.2367 −0.789710
\(326\) 51.6027 2.85801
\(327\) 7.11447 0.393431
\(328\) −24.6777 −1.36260
\(329\) 19.7413 1.08838
\(330\) 14.6901 0.808663
\(331\) −16.5064 −0.907274 −0.453637 0.891187i \(-0.649874\pi\)
−0.453637 + 0.891187i \(0.649874\pi\)
\(332\) 75.9594 4.16881
\(333\) −8.13058 −0.445553
\(334\) −13.6554 −0.747190
\(335\) 27.3890 1.49642
\(336\) −8.28057 −0.451742
\(337\) 34.1719 1.86146 0.930730 0.365707i \(-0.119173\pi\)
0.930730 + 0.365707i \(0.119173\pi\)
\(338\) 6.57953 0.357879
\(339\) 4.19542 0.227864
\(340\) −16.1645 −0.876644
\(341\) 44.5269 2.41127
\(342\) 3.99788 0.216181
\(343\) 19.7639 1.06715
\(344\) −64.8401 −3.49595
\(345\) −7.19037 −0.387117
\(346\) −55.4381 −2.98037
\(347\) 2.97617 0.159769 0.0798845 0.996804i \(-0.474545\pi\)
0.0798845 + 0.996804i \(0.474545\pi\)
\(348\) 14.1047 0.756093
\(349\) −36.5319 −1.95551 −0.977753 0.209757i \(-0.932733\pi\)
−0.977753 + 0.209757i \(0.932733\pi\)
\(350\) 27.6799 1.47955
\(351\) 6.61398 0.353028
\(352\) 57.8486 3.08334
\(353\) 3.93091 0.209221 0.104611 0.994513i \(-0.466640\pi\)
0.104611 + 0.994513i \(0.466640\pi\)
\(354\) 4.54492 0.241560
\(355\) 5.99345 0.318099
\(356\) −15.0794 −0.799208
\(357\) 0.905523 0.0479254
\(358\) 19.1662 1.01297
\(359\) −13.4515 −0.709943 −0.354971 0.934877i \(-0.615509\pi\)
−0.354971 + 0.934877i \(0.615509\pi\)
\(360\) 66.1790 3.48794
\(361\) −18.7191 −0.985214
\(362\) 38.1875 2.00709
\(363\) 5.81408 0.305160
\(364\) 37.8504 1.98390
\(365\) −2.96579 −0.155237
\(366\) 13.9254 0.727893
\(367\) 32.0335 1.67214 0.836068 0.548625i \(-0.184849\pi\)
0.836068 + 0.548625i \(0.184849\pi\)
\(368\) −66.9741 −3.49127
\(369\) −9.47634 −0.493319
\(370\) −22.6744 −1.17879
\(371\) −33.1898 −1.72313
\(372\) −14.2795 −0.740355
\(373\) −33.3827 −1.72849 −0.864246 0.503070i \(-0.832204\pi\)
−0.864246 + 0.503070i \(0.832204\pi\)
\(374\) −14.9630 −0.773719
\(375\) −0.643134 −0.0332113
\(376\) 61.5830 3.17590
\(377\) −27.0454 −1.39291
\(378\) −12.8593 −0.661411
\(379\) 0.880105 0.0452080 0.0226040 0.999744i \(-0.492804\pi\)
0.0226040 + 0.999744i \(0.492804\pi\)
\(380\) 7.89982 0.405252
\(381\) −0.579155 −0.0296710
\(382\) 8.35001 0.427224
\(383\) 0.233986 0.0119561 0.00597806 0.999982i \(-0.498097\pi\)
0.00597806 + 0.999982i \(0.498097\pi\)
\(384\) −0.502566 −0.0256464
\(385\) 38.8043 1.97765
\(386\) −25.0863 −1.27686
\(387\) −24.8989 −1.26568
\(388\) 47.3992 2.40633
\(389\) −8.86110 −0.449276 −0.224638 0.974442i \(-0.572120\pi\)
−0.224638 + 0.974442i \(0.572120\pi\)
\(390\) 9.03320 0.457414
\(391\) 7.32397 0.370389
\(392\) 9.16612 0.462959
\(393\) −2.04023 −0.102916
\(394\) 52.8239 2.66123
\(395\) −17.5084 −0.880944
\(396\) 73.7351 3.70533
\(397\) −27.1195 −1.36109 −0.680543 0.732708i \(-0.738256\pi\)
−0.680543 + 0.732708i \(0.738256\pi\)
\(398\) 9.05533 0.453903
\(399\) −0.442542 −0.0221548
\(400\) 43.5977 2.17988
\(401\) 31.5321 1.57464 0.787320 0.616544i \(-0.211468\pi\)
0.787320 + 0.616544i \(0.211468\pi\)
\(402\) −8.13058 −0.405516
\(403\) 27.3804 1.36391
\(404\) 56.3378 2.80291
\(405\) 24.3035 1.20765
\(406\) 52.5832 2.60966
\(407\) −14.8719 −0.737170
\(408\) 2.82477 0.139847
\(409\) −17.4006 −0.860403 −0.430201 0.902733i \(-0.641557\pi\)
−0.430201 + 0.902733i \(0.641557\pi\)
\(410\) −26.4274 −1.30516
\(411\) −3.90724 −0.192730
\(412\) 97.2838 4.79283
\(413\) 12.0055 0.590754
\(414\) −50.9364 −2.50339
\(415\) 47.8859 2.35063
\(416\) 35.5721 1.74407
\(417\) −3.77930 −0.185073
\(418\) 7.31263 0.357672
\(419\) 30.6717 1.49841 0.749204 0.662339i \(-0.230436\pi\)
0.749204 + 0.662339i \(0.230436\pi\)
\(420\) −12.4442 −0.607217
\(421\) −38.8655 −1.89419 −0.947095 0.320953i \(-0.895997\pi\)
−0.947095 + 0.320953i \(0.895997\pi\)
\(422\) −21.8852 −1.06535
\(423\) 23.6482 1.14981
\(424\) −103.535 −5.02812
\(425\) −4.76763 −0.231264
\(426\) −1.77919 −0.0862020
\(427\) 36.7844 1.78012
\(428\) −5.56700 −0.269091
\(429\) 5.92476 0.286050
\(430\) −69.4376 −3.34858
\(431\) −2.51248 −0.121022 −0.0605111 0.998168i \(-0.519273\pi\)
−0.0605111 + 0.998168i \(0.519273\pi\)
\(432\) −20.2543 −0.974485
\(433\) −8.18697 −0.393441 −0.196720 0.980460i \(-0.563029\pi\)
−0.196720 + 0.980460i \(0.563029\pi\)
\(434\) −53.2346 −2.55534
\(435\) 8.89183 0.426331
\(436\) 99.5879 4.76939
\(437\) −3.57932 −0.171222
\(438\) 0.880412 0.0420677
\(439\) 22.0424 1.05203 0.526014 0.850476i \(-0.323686\pi\)
0.526014 + 0.850476i \(0.323686\pi\)
\(440\) 121.050 5.77082
\(441\) 3.51984 0.167611
\(442\) −9.20102 −0.437648
\(443\) −10.0943 −0.479595 −0.239797 0.970823i \(-0.577081\pi\)
−0.239797 + 0.970823i \(0.577081\pi\)
\(444\) 4.76929 0.226341
\(445\) −9.50629 −0.450641
\(446\) 1.37738 0.0652209
\(447\) 4.76615 0.225431
\(448\) −21.4844 −1.01504
\(449\) −30.4818 −1.43853 −0.719263 0.694738i \(-0.755520\pi\)
−0.719263 + 0.694738i \(0.755520\pi\)
\(450\) 33.1577 1.56307
\(451\) −17.3334 −0.816199
\(452\) 58.7272 2.76230
\(453\) 2.65244 0.124622
\(454\) 15.9755 0.749766
\(455\) 23.8614 1.11864
\(456\) −1.38051 −0.0646481
\(457\) −13.5412 −0.633430 −0.316715 0.948521i \(-0.602580\pi\)
−0.316715 + 0.948521i \(0.602580\pi\)
\(458\) 3.90222 0.182339
\(459\) 2.21491 0.103383
\(460\) −100.650 −4.69285
\(461\) 10.6284 0.495012 0.247506 0.968886i \(-0.420389\pi\)
0.247506 + 0.968886i \(0.420389\pi\)
\(462\) −11.5193 −0.535925
\(463\) −14.1718 −0.658622 −0.329311 0.944222i \(-0.606816\pi\)
−0.329311 + 0.944222i \(0.606816\pi\)
\(464\) 82.8222 3.84493
\(465\) −9.00198 −0.417457
\(466\) 6.69081 0.309946
\(467\) −23.1860 −1.07292 −0.536460 0.843926i \(-0.680239\pi\)
−0.536460 + 0.843926i \(0.680239\pi\)
\(468\) 45.3410 2.09589
\(469\) −21.4772 −0.991723
\(470\) 65.9495 3.04202
\(471\) −2.19796 −0.101276
\(472\) 37.4512 1.72383
\(473\) −45.5433 −2.09408
\(474\) 5.19748 0.238728
\(475\) 2.33001 0.106908
\(476\) 12.6755 0.580978
\(477\) −39.7581 −1.82040
\(478\) −67.5525 −3.08978
\(479\) 17.4123 0.795590 0.397795 0.917474i \(-0.369775\pi\)
0.397795 + 0.917474i \(0.369775\pi\)
\(480\) −11.6952 −0.533811
\(481\) −9.14497 −0.416975
\(482\) 3.03120 0.138067
\(483\) 5.63836 0.256554
\(484\) 81.3851 3.69932
\(485\) 29.8811 1.35683
\(486\) −23.2643 −1.05529
\(487\) −32.5992 −1.47721 −0.738605 0.674138i \(-0.764515\pi\)
−0.738605 + 0.674138i \(0.764515\pi\)
\(488\) 114.749 5.19443
\(489\) −6.84253 −0.309430
\(490\) 9.81604 0.443444
\(491\) 37.5041 1.69254 0.846269 0.532757i \(-0.178844\pi\)
0.846269 + 0.532757i \(0.178844\pi\)
\(492\) 5.55870 0.250606
\(493\) −9.05703 −0.407908
\(494\) 4.49667 0.202315
\(495\) 46.4837 2.08929
\(496\) −83.8482 −3.76490
\(497\) −4.69978 −0.210814
\(498\) −14.2152 −0.636999
\(499\) 12.0544 0.539627 0.269814 0.962913i \(-0.413038\pi\)
0.269814 + 0.962913i \(0.413038\pi\)
\(500\) −9.00255 −0.402606
\(501\) 1.81071 0.0808966
\(502\) −34.6844 −1.54804
\(503\) −5.70335 −0.254300 −0.127150 0.991884i \(-0.540583\pi\)
−0.127150 + 0.991884i \(0.540583\pi\)
\(504\) −51.8945 −2.31156
\(505\) 35.5162 1.58045
\(506\) −93.1691 −4.14187
\(507\) −0.872448 −0.0387468
\(508\) −8.10698 −0.359689
\(509\) 21.5555 0.955432 0.477716 0.878514i \(-0.341465\pi\)
0.477716 + 0.878514i \(0.341465\pi\)
\(510\) 3.02506 0.133952
\(511\) 2.32563 0.102880
\(512\) 39.7943 1.75868
\(513\) −1.08246 −0.0477916
\(514\) 53.9346 2.37895
\(515\) 61.3291 2.70248
\(516\) 14.6054 0.642967
\(517\) 43.2555 1.90237
\(518\) 17.7802 0.781217
\(519\) 7.35112 0.322678
\(520\) 74.4356 3.26422
\(521\) 1.16743 0.0511460 0.0255730 0.999673i \(-0.491859\pi\)
0.0255730 + 0.999673i \(0.491859\pi\)
\(522\) 62.9895 2.75698
\(523\) −20.7155 −0.905824 −0.452912 0.891555i \(-0.649615\pi\)
−0.452912 + 0.891555i \(0.649615\pi\)
\(524\) −28.5591 −1.24761
\(525\) −3.67036 −0.160188
\(526\) −52.2939 −2.28012
\(527\) 9.16923 0.399418
\(528\) −18.1437 −0.789601
\(529\) 22.6036 0.982766
\(530\) −110.876 −4.81617
\(531\) 14.3815 0.624102
\(532\) −6.19467 −0.268573
\(533\) −10.6586 −0.461676
\(534\) 2.82200 0.122120
\(535\) −3.50952 −0.151730
\(536\) −66.9979 −2.89387
\(537\) −2.54145 −0.109672
\(538\) −47.5259 −2.04899
\(539\) 6.43822 0.277314
\(540\) −30.4386 −1.30987
\(541\) 0.555716 0.0238921 0.0119461 0.999929i \(-0.496197\pi\)
0.0119461 + 0.999929i \(0.496197\pi\)
\(542\) 50.4313 2.16621
\(543\) −5.06367 −0.217303
\(544\) 11.9125 0.510744
\(545\) 62.7817 2.68927
\(546\) −7.08341 −0.303142
\(547\) −21.6852 −0.927190 −0.463595 0.886047i \(-0.653441\pi\)
−0.463595 + 0.886047i \(0.653441\pi\)
\(548\) −54.6933 −2.33638
\(549\) 44.0640 1.88061
\(550\) 60.6497 2.58611
\(551\) 4.42630 0.188567
\(552\) 17.5888 0.748630
\(553\) 13.7293 0.583829
\(554\) −31.8273 −1.35221
\(555\) 3.00663 0.127624
\(556\) −52.9024 −2.24356
\(557\) −21.6755 −0.918420 −0.459210 0.888328i \(-0.651867\pi\)
−0.459210 + 0.888328i \(0.651867\pi\)
\(558\) −63.7698 −2.69959
\(559\) −28.0054 −1.18450
\(560\) −73.0720 −3.08785
\(561\) 1.98410 0.0837688
\(562\) −35.3779 −1.49233
\(563\) −0.747473 −0.0315022 −0.0157511 0.999876i \(-0.505014\pi\)
−0.0157511 + 0.999876i \(0.505014\pi\)
\(564\) −13.8717 −0.584105
\(565\) 37.0225 1.55755
\(566\) 4.56199 0.191755
\(567\) −19.0577 −0.800347
\(568\) −14.6609 −0.615159
\(569\) −14.7619 −0.618850 −0.309425 0.950924i \(-0.600137\pi\)
−0.309425 + 0.950924i \(0.600137\pi\)
\(570\) −1.47839 −0.0619229
\(571\) −1.92429 −0.0805289 −0.0402644 0.999189i \(-0.512820\pi\)
−0.0402644 + 0.999189i \(0.512820\pi\)
\(572\) 82.9344 3.46766
\(573\) −1.10722 −0.0462546
\(574\) 20.7231 0.864967
\(575\) −29.6863 −1.23800
\(576\) −25.7362 −1.07234
\(577\) 37.0975 1.54439 0.772194 0.635386i \(-0.219159\pi\)
0.772194 + 0.635386i \(0.219159\pi\)
\(578\) 41.4520 1.72418
\(579\) 3.32646 0.138243
\(580\) 124.467 5.16822
\(581\) −37.5499 −1.55783
\(582\) −8.87039 −0.367689
\(583\) −72.7225 −3.01186
\(584\) 7.25480 0.300206
\(585\) 28.5837 1.18179
\(586\) −37.6470 −1.55518
\(587\) 12.5276 0.517070 0.258535 0.966002i \(-0.416760\pi\)
0.258535 + 0.966002i \(0.416760\pi\)
\(588\) −2.06469 −0.0851464
\(589\) −4.48113 −0.184642
\(590\) 40.1067 1.65117
\(591\) −7.00447 −0.288125
\(592\) 28.0050 1.15100
\(593\) 22.2827 0.915039 0.457520 0.889200i \(-0.348738\pi\)
0.457520 + 0.889200i \(0.348738\pi\)
\(594\) −28.1762 −1.15608
\(595\) 7.99079 0.327590
\(596\) 66.7163 2.73281
\(597\) −1.20074 −0.0491430
\(598\) −57.2914 −2.34282
\(599\) 5.58545 0.228215 0.114108 0.993468i \(-0.463599\pi\)
0.114108 + 0.993468i \(0.463599\pi\)
\(600\) −11.4497 −0.467431
\(601\) 10.0302 0.409142 0.204571 0.978852i \(-0.434420\pi\)
0.204571 + 0.978852i \(0.434420\pi\)
\(602\) 54.4497 2.21921
\(603\) −25.7275 −1.04771
\(604\) 37.1286 1.51074
\(605\) 51.3063 2.08590
\(606\) −10.5432 −0.428288
\(607\) −3.93795 −0.159836 −0.0799182 0.996801i \(-0.525466\pi\)
−0.0799182 + 0.996801i \(0.525466\pi\)
\(608\) −5.82180 −0.236105
\(609\) −6.97256 −0.282542
\(610\) 122.885 4.97546
\(611\) 26.5986 1.07606
\(612\) 15.1839 0.613774
\(613\) 5.60233 0.226276 0.113138 0.993579i \(-0.463910\pi\)
0.113138 + 0.993579i \(0.463910\pi\)
\(614\) 56.6272 2.28529
\(615\) 3.50429 0.141306
\(616\) −94.9215 −3.82450
\(617\) −28.2994 −1.13929 −0.569645 0.821891i \(-0.692919\pi\)
−0.569645 + 0.821891i \(0.692919\pi\)
\(618\) −18.2059 −0.732349
\(619\) −42.5156 −1.70885 −0.854424 0.519577i \(-0.826090\pi\)
−0.854424 + 0.519577i \(0.826090\pi\)
\(620\) −126.009 −5.06065
\(621\) 13.7914 0.553431
\(622\) −19.8142 −0.794476
\(623\) 7.45439 0.298654
\(624\) −11.1569 −0.446632
\(625\) −27.6553 −1.10621
\(626\) −85.0366 −3.39875
\(627\) −0.969658 −0.0387244
\(628\) −30.7668 −1.22773
\(629\) −3.06249 −0.122110
\(630\) −55.5741 −2.21412
\(631\) −33.9475 −1.35143 −0.675714 0.737164i \(-0.736165\pi\)
−0.675714 + 0.737164i \(0.736165\pi\)
\(632\) 42.8284 1.70362
\(633\) 2.90198 0.115343
\(634\) −26.1118 −1.03703
\(635\) −5.11076 −0.202814
\(636\) 23.3216 0.924761
\(637\) 3.95898 0.156860
\(638\) 115.216 4.56143
\(639\) −5.62987 −0.222714
\(640\) −4.43489 −0.175304
\(641\) −22.5851 −0.892059 −0.446030 0.895018i \(-0.647162\pi\)
−0.446030 + 0.895018i \(0.647162\pi\)
\(642\) 1.04182 0.0411174
\(643\) −18.4075 −0.725920 −0.362960 0.931805i \(-0.618234\pi\)
−0.362960 + 0.931805i \(0.618234\pi\)
\(644\) 78.9253 3.11009
\(645\) 9.20746 0.362543
\(646\) 1.50586 0.0592472
\(647\) 40.3752 1.58731 0.793656 0.608367i \(-0.208175\pi\)
0.793656 + 0.608367i \(0.208175\pi\)
\(648\) −59.4503 −2.33543
\(649\) 26.3055 1.03258
\(650\) 37.2946 1.46281
\(651\) 7.05893 0.276661
\(652\) −95.7813 −3.75109
\(653\) 7.44790 0.291459 0.145729 0.989324i \(-0.453447\pi\)
0.145729 + 0.989324i \(0.453447\pi\)
\(654\) −18.6371 −0.728768
\(655\) −18.0041 −0.703477
\(656\) 32.6404 1.27439
\(657\) 2.78588 0.108687
\(658\) −51.7145 −2.01604
\(659\) 38.7845 1.51083 0.755414 0.655247i \(-0.227436\pi\)
0.755414 + 0.655247i \(0.227436\pi\)
\(660\) −27.2667 −1.06136
\(661\) −15.6365 −0.608189 −0.304094 0.952642i \(-0.598354\pi\)
−0.304094 + 0.952642i \(0.598354\pi\)
\(662\) 43.2403 1.68058
\(663\) 1.22006 0.0473832
\(664\) −117.137 −4.54579
\(665\) −3.90521 −0.151438
\(666\) 21.2989 0.825316
\(667\) −56.3948 −2.18362
\(668\) 25.3462 0.980674
\(669\) −0.182641 −0.00706132
\(670\) −71.7483 −2.77188
\(671\) 80.5987 3.11148
\(672\) 9.17084 0.353773
\(673\) 49.2859 1.89983 0.949916 0.312505i \(-0.101168\pi\)
0.949916 + 0.312505i \(0.101168\pi\)
\(674\) −89.5168 −3.44806
\(675\) −8.97771 −0.345552
\(676\) −12.2125 −0.469711
\(677\) 0.758392 0.0291474 0.0145737 0.999894i \(-0.495361\pi\)
0.0145737 + 0.999894i \(0.495361\pi\)
\(678\) −10.9903 −0.422082
\(679\) −23.4314 −0.899214
\(680\) 24.9272 0.955915
\(681\) −2.11835 −0.0811755
\(682\) −116.643 −4.46649
\(683\) 24.0650 0.920823 0.460411 0.887706i \(-0.347702\pi\)
0.460411 + 0.887706i \(0.347702\pi\)
\(684\) −7.42060 −0.283734
\(685\) −34.4795 −1.31739
\(686\) −51.7737 −1.97673
\(687\) −0.517436 −0.0197414
\(688\) 85.7621 3.26965
\(689\) −44.7184 −1.70363
\(690\) 18.8359 0.717072
\(691\) 28.1699 1.07163 0.535817 0.844334i \(-0.320004\pi\)
0.535817 + 0.844334i \(0.320004\pi\)
\(692\) 102.901 3.91169
\(693\) −36.4503 −1.38463
\(694\) −7.79638 −0.295947
\(695\) −33.3504 −1.26505
\(696\) −21.7509 −0.824464
\(697\) −3.56939 −0.135200
\(698\) 95.6991 3.62227
\(699\) −0.887204 −0.0335572
\(700\) −51.3775 −1.94189
\(701\) −8.73916 −0.330074 −0.165037 0.986287i \(-0.552774\pi\)
−0.165037 + 0.986287i \(0.552774\pi\)
\(702\) −17.3260 −0.653929
\(703\) 1.49668 0.0564485
\(704\) −47.0746 −1.77419
\(705\) −8.74493 −0.329353
\(706\) −10.2974 −0.387549
\(707\) −27.8501 −1.04741
\(708\) −8.43598 −0.317044
\(709\) 23.7809 0.893109 0.446554 0.894757i \(-0.352651\pi\)
0.446554 + 0.894757i \(0.352651\pi\)
\(710\) −15.7005 −0.589228
\(711\) 16.4463 0.616785
\(712\) 23.2539 0.871478
\(713\) 57.0934 2.13816
\(714\) −2.37211 −0.0887741
\(715\) 52.2831 1.95528
\(716\) −35.5750 −1.32950
\(717\) 8.95749 0.334523
\(718\) 35.2376 1.31506
\(719\) −14.1369 −0.527216 −0.263608 0.964630i \(-0.584912\pi\)
−0.263608 + 0.964630i \(0.584912\pi\)
\(720\) −87.5330 −3.26216
\(721\) −48.0914 −1.79102
\(722\) 49.0366 1.82495
\(723\) −0.401938 −0.0149482
\(724\) −70.8810 −2.63427
\(725\) 36.7109 1.36341
\(726\) −15.2306 −0.565260
\(727\) 8.26912 0.306685 0.153342 0.988173i \(-0.450996\pi\)
0.153342 + 0.988173i \(0.450996\pi\)
\(728\) −58.3689 −2.16330
\(729\) −20.7010 −0.766704
\(730\) 7.76920 0.287551
\(731\) −9.37852 −0.346877
\(732\) −25.8474 −0.955348
\(733\) 7.18909 0.265535 0.132767 0.991147i \(-0.457614\pi\)
0.132767 + 0.991147i \(0.457614\pi\)
\(734\) −83.9152 −3.09737
\(735\) −1.30161 −0.0480107
\(736\) 74.1747 2.73412
\(737\) −47.0588 −1.73343
\(738\) 24.8243 0.913794
\(739\) −13.9348 −0.512601 −0.256300 0.966597i \(-0.582504\pi\)
−0.256300 + 0.966597i \(0.582504\pi\)
\(740\) 42.0867 1.54714
\(741\) −0.596260 −0.0219042
\(742\) 86.9442 3.19182
\(743\) −39.1786 −1.43732 −0.718661 0.695360i \(-0.755245\pi\)
−0.718661 + 0.695360i \(0.755245\pi\)
\(744\) 22.0203 0.807303
\(745\) 42.0589 1.54092
\(746\) 87.4496 3.20176
\(747\) −44.9811 −1.64577
\(748\) 27.7733 1.01549
\(749\) 2.75200 0.100556
\(750\) 1.68476 0.0615186
\(751\) −19.2815 −0.703593 −0.351796 0.936077i \(-0.614429\pi\)
−0.351796 + 0.936077i \(0.614429\pi\)
\(752\) −81.4540 −2.97032
\(753\) 4.59917 0.167603
\(754\) 70.8482 2.58014
\(755\) 23.4064 0.851847
\(756\) 23.8686 0.868091
\(757\) −22.0016 −0.799661 −0.399830 0.916589i \(-0.630931\pi\)
−0.399830 + 0.916589i \(0.630931\pi\)
\(758\) −2.30553 −0.0837406
\(759\) 12.3543 0.448431
\(760\) −12.1823 −0.441898
\(761\) 6.03626 0.218814 0.109407 0.993997i \(-0.465105\pi\)
0.109407 + 0.993997i \(0.465105\pi\)
\(762\) 1.51716 0.0549608
\(763\) −49.2304 −1.78226
\(764\) −15.4987 −0.560724
\(765\) 9.57218 0.346083
\(766\) −0.612951 −0.0221468
\(767\) 16.1757 0.584071
\(768\) −4.89304 −0.176563
\(769\) 52.9429 1.90917 0.954585 0.297940i \(-0.0962996\pi\)
0.954585 + 0.297940i \(0.0962996\pi\)
\(770\) −101.652 −3.66328
\(771\) −7.15175 −0.257564
\(772\) 46.5635 1.67586
\(773\) 9.25702 0.332952 0.166476 0.986046i \(-0.446761\pi\)
0.166476 + 0.986046i \(0.446761\pi\)
\(774\) 65.2254 2.34448
\(775\) −37.1657 −1.33503
\(776\) −73.0941 −2.62392
\(777\) −2.35766 −0.0845806
\(778\) 23.2126 0.832212
\(779\) 1.74441 0.0625000
\(780\) −16.7668 −0.600348
\(781\) −10.2977 −0.368482
\(782\) −19.1859 −0.686086
\(783\) −17.0549 −0.609492
\(784\) −12.1237 −0.432991
\(785\) −19.3959 −0.692268
\(786\) 5.34461 0.190636
\(787\) 52.3457 1.86592 0.932961 0.359977i \(-0.117216\pi\)
0.932961 + 0.359977i \(0.117216\pi\)
\(788\) −98.0481 −3.49282
\(789\) 6.93419 0.246864
\(790\) 45.8652 1.63181
\(791\) −29.0313 −1.03223
\(792\) −113.707 −4.04039
\(793\) 49.5616 1.75998
\(794\) 71.0423 2.52120
\(795\) 14.7023 0.521436
\(796\) −16.8079 −0.595740
\(797\) −7.57678 −0.268383 −0.134192 0.990955i \(-0.542844\pi\)
−0.134192 + 0.990955i \(0.542844\pi\)
\(798\) 1.15928 0.0410382
\(799\) 8.90741 0.315121
\(800\) −48.2850 −1.70713
\(801\) 8.92962 0.315513
\(802\) −82.6018 −2.91677
\(803\) 5.09572 0.179824
\(804\) 15.0914 0.532234
\(805\) 49.7557 1.75366
\(806\) −71.7259 −2.52644
\(807\) 6.30196 0.221839
\(808\) −86.8783 −3.05637
\(809\) 5.66209 0.199069 0.0995343 0.995034i \(-0.468265\pi\)
0.0995343 + 0.995034i \(0.468265\pi\)
\(810\) −63.6656 −2.23698
\(811\) 1.92817 0.0677072 0.0338536 0.999427i \(-0.489222\pi\)
0.0338536 + 0.999427i \(0.489222\pi\)
\(812\) −97.6014 −3.42514
\(813\) −6.68722 −0.234531
\(814\) 38.9584 1.36549
\(815\) −60.3820 −2.11509
\(816\) −3.73624 −0.130795
\(817\) 4.58341 0.160353
\(818\) 45.5826 1.59376
\(819\) −22.4140 −0.783207
\(820\) 49.0528 1.71300
\(821\) −21.0029 −0.733005 −0.366503 0.930417i \(-0.619445\pi\)
−0.366503 + 0.930417i \(0.619445\pi\)
\(822\) 10.2354 0.357002
\(823\) −14.5339 −0.506620 −0.253310 0.967385i \(-0.581519\pi\)
−0.253310 + 0.967385i \(0.581519\pi\)
\(824\) −150.021 −5.22623
\(825\) −8.04217 −0.279992
\(826\) −31.4498 −1.09428
\(827\) 42.2572 1.46943 0.734714 0.678377i \(-0.237316\pi\)
0.734714 + 0.678377i \(0.237316\pi\)
\(828\) 94.5448 3.28566
\(829\) 14.6924 0.510289 0.255145 0.966903i \(-0.417877\pi\)
0.255145 + 0.966903i \(0.417877\pi\)
\(830\) −125.442 −4.35416
\(831\) 4.22032 0.146401
\(832\) −28.9470 −1.00356
\(833\) 1.32579 0.0459360
\(834\) 9.90027 0.342818
\(835\) 15.9786 0.552963
\(836\) −13.5732 −0.469439
\(837\) 17.2662 0.596806
\(838\) −80.3476 −2.77556
\(839\) −17.4480 −0.602371 −0.301186 0.953566i \(-0.597382\pi\)
−0.301186 + 0.953566i \(0.597382\pi\)
\(840\) 19.1902 0.662126
\(841\) 40.7395 1.40481
\(842\) 101.812 3.50869
\(843\) 4.69113 0.161571
\(844\) 40.6218 1.39826
\(845\) −7.69892 −0.264851
\(846\) −61.9489 −2.12985
\(847\) −40.2320 −1.38239
\(848\) 136.943 4.70264
\(849\) −0.604921 −0.0207609
\(850\) 12.4893 0.428380
\(851\) −19.0690 −0.653677
\(852\) 3.30241 0.113139
\(853\) 39.5495 1.35415 0.677074 0.735914i \(-0.263247\pi\)
0.677074 + 0.735914i \(0.263247\pi\)
\(854\) −96.3606 −3.29739
\(855\) −4.67805 −0.159986
\(856\) 8.58484 0.293424
\(857\) −7.14600 −0.244103 −0.122051 0.992524i \(-0.538947\pi\)
−0.122051 + 0.992524i \(0.538947\pi\)
\(858\) −15.5205 −0.529862
\(859\) 29.8927 1.01992 0.509962 0.860197i \(-0.329659\pi\)
0.509962 + 0.860197i \(0.329659\pi\)
\(860\) 128.885 4.39496
\(861\) −2.74790 −0.0936481
\(862\) 6.58172 0.224174
\(863\) 53.9154 1.83530 0.917650 0.397390i \(-0.130084\pi\)
0.917650 + 0.397390i \(0.130084\pi\)
\(864\) 22.4319 0.763148
\(865\) 64.8700 2.20565
\(866\) 21.4466 0.728787
\(867\) −5.49656 −0.186673
\(868\) 98.8105 3.35385
\(869\) 30.0824 1.02048
\(870\) −23.2931 −0.789710
\(871\) −28.9373 −0.980504
\(872\) −153.574 −5.20067
\(873\) −28.0685 −0.949974
\(874\) 9.37641 0.317162
\(875\) 4.45034 0.150449
\(876\) −1.63416 −0.0552132
\(877\) 41.5953 1.40457 0.702287 0.711894i \(-0.252162\pi\)
0.702287 + 0.711894i \(0.252162\pi\)
\(878\) −57.7425 −1.94871
\(879\) 4.99201 0.168376
\(880\) −160.109 −5.39727
\(881\) 37.5685 1.26572 0.632858 0.774268i \(-0.281882\pi\)
0.632858 + 0.774268i \(0.281882\pi\)
\(882\) −9.22058 −0.310473
\(883\) 35.4714 1.19371 0.596854 0.802350i \(-0.296417\pi\)
0.596854 + 0.802350i \(0.296417\pi\)
\(884\) 17.0783 0.574406
\(885\) −5.31817 −0.178768
\(886\) 26.4431 0.888373
\(887\) −11.7456 −0.394378 −0.197189 0.980365i \(-0.563181\pi\)
−0.197189 + 0.980365i \(0.563181\pi\)
\(888\) −7.35471 −0.246808
\(889\) 4.00762 0.134411
\(890\) 24.9027 0.834742
\(891\) −41.7575 −1.39893
\(892\) −2.55660 −0.0856014
\(893\) −4.35317 −0.145673
\(894\) −12.4854 −0.417576
\(895\) −22.4270 −0.749652
\(896\) 3.47763 0.116180
\(897\) 7.59686 0.253652
\(898\) 79.8504 2.66464
\(899\) −70.6034 −2.35476
\(900\) −61.5451 −2.05150
\(901\) −14.9754 −0.498904
\(902\) 45.4067 1.51188
\(903\) −7.22006 −0.240268
\(904\) −90.5630 −3.01208
\(905\) −44.6844 −1.48536
\(906\) −6.94833 −0.230843
\(907\) 21.0298 0.698284 0.349142 0.937070i \(-0.386473\pi\)
0.349142 + 0.937070i \(0.386473\pi\)
\(908\) −29.6526 −0.984055
\(909\) −33.3617 −1.10654
\(910\) −62.5076 −2.07211
\(911\) 3.38392 0.112114 0.0560571 0.998428i \(-0.482147\pi\)
0.0560571 + 0.998428i \(0.482147\pi\)
\(912\) 1.82595 0.0604633
\(913\) −82.2760 −2.72294
\(914\) 35.4726 1.17333
\(915\) −16.2946 −0.538682
\(916\) −7.24303 −0.239317
\(917\) 14.1179 0.466215
\(918\) −5.80219 −0.191501
\(919\) −7.27860 −0.240099 −0.120049 0.992768i \(-0.538305\pi\)
−0.120049 + 0.992768i \(0.538305\pi\)
\(920\) 155.213 5.11721
\(921\) −7.50879 −0.247423
\(922\) −27.8421 −0.916931
\(923\) −6.33227 −0.208429
\(924\) 21.3813 0.703393
\(925\) 12.4132 0.408144
\(926\) 37.1247 1.21999
\(927\) −57.6088 −1.89212
\(928\) −91.7266 −3.01107
\(929\) 16.6585 0.546546 0.273273 0.961936i \(-0.411894\pi\)
0.273273 + 0.961936i \(0.411894\pi\)
\(930\) 23.5816 0.773272
\(931\) −0.647934 −0.0212352
\(932\) −12.4190 −0.406799
\(933\) 2.62737 0.0860161
\(934\) 60.7381 1.98741
\(935\) 17.5087 0.572596
\(936\) −69.9202 −2.28541
\(937\) 5.26000 0.171837 0.0859183 0.996302i \(-0.472618\pi\)
0.0859183 + 0.996302i \(0.472618\pi\)
\(938\) 56.2617 1.83701
\(939\) 11.2759 0.367975
\(940\) −122.411 −3.99261
\(941\) −42.9123 −1.39890 −0.699451 0.714681i \(-0.746572\pi\)
−0.699451 + 0.714681i \(0.746572\pi\)
\(942\) 5.75778 0.187598
\(943\) −22.2253 −0.723755
\(944\) −49.5356 −1.61225
\(945\) 15.0471 0.489482
\(946\) 119.305 3.87895
\(947\) 57.0141 1.85271 0.926355 0.376651i \(-0.122924\pi\)
0.926355 + 0.376651i \(0.122924\pi\)
\(948\) −9.64720 −0.313327
\(949\) 3.13345 0.101716
\(950\) −6.10370 −0.198030
\(951\) 3.46243 0.112277
\(952\) −19.5468 −0.633514
\(953\) −9.80633 −0.317658 −0.158829 0.987306i \(-0.550772\pi\)
−0.158829 + 0.987306i \(0.550772\pi\)
\(954\) 104.151 3.37200
\(955\) −9.77063 −0.316170
\(956\) 125.386 4.05528
\(957\) −15.2777 −0.493856
\(958\) −45.6135 −1.47370
\(959\) 27.0372 0.873076
\(960\) 9.51705 0.307162
\(961\) 40.4780 1.30574
\(962\) 23.9562 0.772379
\(963\) 3.29662 0.106232
\(964\) −5.62631 −0.181211
\(965\) 29.3543 0.944949
\(966\) −14.7703 −0.475226
\(967\) −16.3832 −0.526849 −0.263424 0.964680i \(-0.584852\pi\)
−0.263424 + 0.964680i \(0.584852\pi\)
\(968\) −125.504 −4.03384
\(969\) −0.199677 −0.00641456
\(970\) −78.2768 −2.51332
\(971\) 7.53526 0.241818 0.120909 0.992664i \(-0.461419\pi\)
0.120909 + 0.992664i \(0.461419\pi\)
\(972\) 43.1817 1.38505
\(973\) 26.1519 0.838390
\(974\) 85.3970 2.73630
\(975\) −4.94527 −0.158376
\(976\) −151.775 −4.85818
\(977\) 3.79906 0.121543 0.0607714 0.998152i \(-0.480644\pi\)
0.0607714 + 0.998152i \(0.480644\pi\)
\(978\) 17.9247 0.573170
\(979\) 16.3334 0.522018
\(980\) −18.2199 −0.582012
\(981\) −58.9732 −1.88287
\(982\) −98.2460 −3.13516
\(983\) −45.2032 −1.44176 −0.720879 0.693061i \(-0.756261\pi\)
−0.720879 + 0.693061i \(0.756261\pi\)
\(984\) −8.57205 −0.273267
\(985\) −61.8110 −1.96946
\(986\) 23.7259 0.755585
\(987\) 6.85737 0.218272
\(988\) −8.34641 −0.265535
\(989\) −58.3966 −1.85690
\(990\) −121.769 −3.87007
\(991\) 42.1534 1.33905 0.669524 0.742791i \(-0.266498\pi\)
0.669524 + 0.742791i \(0.266498\pi\)
\(992\) 92.8629 2.94840
\(993\) −5.73368 −0.181953
\(994\) 12.3116 0.390499
\(995\) −10.5959 −0.335914
\(996\) 26.3853 0.836051
\(997\) 57.6681 1.82637 0.913184 0.407547i \(-0.133616\pi\)
0.913184 + 0.407547i \(0.133616\pi\)
\(998\) −31.5777 −0.999574
\(999\) −5.76684 −0.182455
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.1.6 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.6 174 1.1 even 1 trivial