Properties

Label 4027.2.a.c.1.3
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 1.3
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.70396 q^{2} -2.87178 q^{3} +5.31140 q^{4} +4.01870 q^{5} +7.76519 q^{6} +2.72741 q^{7} -8.95389 q^{8} +5.24714 q^{9} +O(q^{10})\) \(q-2.70396 q^{2} -2.87178 q^{3} +5.31140 q^{4} +4.01870 q^{5} +7.76519 q^{6} +2.72741 q^{7} -8.95389 q^{8} +5.24714 q^{9} -10.8664 q^{10} +4.57600 q^{11} -15.2532 q^{12} +5.43681 q^{13} -7.37481 q^{14} -11.5409 q^{15} +13.5882 q^{16} +6.82901 q^{17} -14.1881 q^{18} -8.08441 q^{19} +21.3449 q^{20} -7.83254 q^{21} -12.3733 q^{22} -5.44872 q^{23} +25.7136 q^{24} +11.1500 q^{25} -14.7009 q^{26} -6.45330 q^{27} +14.4864 q^{28} -1.32551 q^{29} +31.2060 q^{30} -3.22161 q^{31} -18.8341 q^{32} -13.1413 q^{33} -18.4654 q^{34} +10.9607 q^{35} +27.8697 q^{36} -1.86013 q^{37} +21.8599 q^{38} -15.6133 q^{39} -35.9830 q^{40} -5.02372 q^{41} +21.1789 q^{42} +4.95146 q^{43} +24.3050 q^{44} +21.0867 q^{45} +14.7331 q^{46} -2.17330 q^{47} -39.0222 q^{48} +0.438777 q^{49} -30.1491 q^{50} -19.6114 q^{51} +28.8770 q^{52} +5.21740 q^{53} +17.4495 q^{54} +18.3896 q^{55} -24.4209 q^{56} +23.2167 q^{57} +3.58413 q^{58} +1.93179 q^{59} -61.2981 q^{60} -9.27188 q^{61} +8.71109 q^{62} +14.3111 q^{63} +23.7502 q^{64} +21.8489 q^{65} +35.5335 q^{66} +8.18887 q^{67} +36.2716 q^{68} +15.6475 q^{69} -29.6372 q^{70} +5.07002 q^{71} -46.9823 q^{72} +15.7961 q^{73} +5.02970 q^{74} -32.0204 q^{75} -42.9395 q^{76} +12.4806 q^{77} +42.2178 q^{78} -1.61459 q^{79} +54.6068 q^{80} +2.79107 q^{81} +13.5839 q^{82} +7.53318 q^{83} -41.6017 q^{84} +27.4438 q^{85} -13.3886 q^{86} +3.80658 q^{87} -40.9730 q^{88} -0.120148 q^{89} -57.0176 q^{90} +14.8284 q^{91} -28.9403 q^{92} +9.25176 q^{93} +5.87651 q^{94} -32.4888 q^{95} +54.0873 q^{96} +2.97007 q^{97} -1.18644 q^{98} +24.0109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70396 −1.91199 −0.955994 0.293386i \(-0.905218\pi\)
−0.955994 + 0.293386i \(0.905218\pi\)
\(3\) −2.87178 −1.65803 −0.829013 0.559230i \(-0.811097\pi\)
−0.829013 + 0.559230i \(0.811097\pi\)
\(4\) 5.31140 2.65570
\(5\) 4.01870 1.79722 0.898610 0.438749i \(-0.144578\pi\)
0.898610 + 0.438749i \(0.144578\pi\)
\(6\) 7.76519 3.17012
\(7\) 2.72741 1.03086 0.515432 0.856930i \(-0.327631\pi\)
0.515432 + 0.856930i \(0.327631\pi\)
\(8\) −8.95389 −3.16568
\(9\) 5.24714 1.74905
\(10\) −10.8664 −3.43626
\(11\) 4.57600 1.37972 0.689858 0.723945i \(-0.257673\pi\)
0.689858 + 0.723945i \(0.257673\pi\)
\(12\) −15.2532 −4.40322
\(13\) 5.43681 1.50790 0.753949 0.656933i \(-0.228146\pi\)
0.753949 + 0.656933i \(0.228146\pi\)
\(14\) −7.37481 −1.97100
\(15\) −11.5409 −2.97983
\(16\) 13.5882 3.39704
\(17\) 6.82901 1.65628 0.828139 0.560522i \(-0.189400\pi\)
0.828139 + 0.560522i \(0.189400\pi\)
\(18\) −14.1881 −3.34416
\(19\) −8.08441 −1.85469 −0.927345 0.374207i \(-0.877915\pi\)
−0.927345 + 0.374207i \(0.877915\pi\)
\(20\) 21.3449 4.77287
\(21\) −7.83254 −1.70920
\(22\) −12.3733 −2.63800
\(23\) −5.44872 −1.13614 −0.568068 0.822981i \(-0.692309\pi\)
−0.568068 + 0.822981i \(0.692309\pi\)
\(24\) 25.7136 5.24877
\(25\) 11.1500 2.23000
\(26\) −14.7009 −2.88308
\(27\) −6.45330 −1.24194
\(28\) 14.4864 2.73767
\(29\) −1.32551 −0.246141 −0.123070 0.992398i \(-0.539274\pi\)
−0.123070 + 0.992398i \(0.539274\pi\)
\(30\) 31.2060 5.69741
\(31\) −3.22161 −0.578618 −0.289309 0.957236i \(-0.593425\pi\)
−0.289309 + 0.957236i \(0.593425\pi\)
\(32\) −18.8341 −3.32942
\(33\) −13.1413 −2.28760
\(34\) −18.4654 −3.16679
\(35\) 10.9607 1.85269
\(36\) 27.8697 4.64494
\(37\) −1.86013 −0.305803 −0.152901 0.988241i \(-0.548862\pi\)
−0.152901 + 0.988241i \(0.548862\pi\)
\(38\) 21.8599 3.54615
\(39\) −15.6133 −2.50013
\(40\) −35.9830 −5.68942
\(41\) −5.02372 −0.784573 −0.392286 0.919843i \(-0.628316\pi\)
−0.392286 + 0.919843i \(0.628316\pi\)
\(42\) 21.1789 3.26797
\(43\) 4.95146 0.755091 0.377545 0.925991i \(-0.376768\pi\)
0.377545 + 0.925991i \(0.376768\pi\)
\(44\) 24.3050 3.66411
\(45\) 21.0867 3.14342
\(46\) 14.7331 2.17228
\(47\) −2.17330 −0.317008 −0.158504 0.987358i \(-0.550667\pi\)
−0.158504 + 0.987358i \(0.550667\pi\)
\(48\) −39.0222 −5.63238
\(49\) 0.438777 0.0626824
\(50\) −30.1491 −4.26373
\(51\) −19.6114 −2.74615
\(52\) 28.8770 4.00453
\(53\) 5.21740 0.716665 0.358332 0.933594i \(-0.383345\pi\)
0.358332 + 0.933594i \(0.383345\pi\)
\(54\) 17.4495 2.37457
\(55\) 18.3896 2.47965
\(56\) −24.4209 −3.26339
\(57\) 23.2167 3.07512
\(58\) 3.58413 0.470619
\(59\) 1.93179 0.251498 0.125749 0.992062i \(-0.459867\pi\)
0.125749 + 0.992062i \(0.459867\pi\)
\(60\) −61.2981 −7.91355
\(61\) −9.27188 −1.18714 −0.593571 0.804782i \(-0.702282\pi\)
−0.593571 + 0.804782i \(0.702282\pi\)
\(62\) 8.71109 1.10631
\(63\) 14.3111 1.80303
\(64\) 23.7502 2.96878
\(65\) 21.8489 2.71002
\(66\) 35.5335 4.37387
\(67\) 8.18887 1.00043 0.500215 0.865901i \(-0.333254\pi\)
0.500215 + 0.865901i \(0.333254\pi\)
\(68\) 36.2716 4.39858
\(69\) 15.6475 1.88374
\(70\) −29.6372 −3.54232
\(71\) 5.07002 0.601700 0.300850 0.953671i \(-0.402730\pi\)
0.300850 + 0.953671i \(0.402730\pi\)
\(72\) −46.9823 −5.53692
\(73\) 15.7961 1.84879 0.924397 0.381431i \(-0.124569\pi\)
0.924397 + 0.381431i \(0.124569\pi\)
\(74\) 5.02970 0.584691
\(75\) −32.0204 −3.69739
\(76\) −42.9395 −4.92550
\(77\) 12.4806 1.42230
\(78\) 42.2178 4.78023
\(79\) −1.61459 −0.181656 −0.0908278 0.995867i \(-0.528951\pi\)
−0.0908278 + 0.995867i \(0.528951\pi\)
\(80\) 54.6068 6.10522
\(81\) 2.79107 0.310119
\(82\) 13.5839 1.50009
\(83\) 7.53318 0.826874 0.413437 0.910533i \(-0.364328\pi\)
0.413437 + 0.910533i \(0.364328\pi\)
\(84\) −41.6017 −4.53912
\(85\) 27.4438 2.97670
\(86\) −13.3886 −1.44372
\(87\) 3.80658 0.408108
\(88\) −40.9730 −4.36774
\(89\) −0.120148 −0.0127357 −0.00636785 0.999980i \(-0.502027\pi\)
−0.00636785 + 0.999980i \(0.502027\pi\)
\(90\) −57.0176 −6.01019
\(91\) 14.8284 1.55444
\(92\) −28.9403 −3.01724
\(93\) 9.25176 0.959362
\(94\) 5.87651 0.606115
\(95\) −32.4888 −3.33329
\(96\) 54.0873 5.52026
\(97\) 2.97007 0.301565 0.150783 0.988567i \(-0.451821\pi\)
0.150783 + 0.988567i \(0.451821\pi\)
\(98\) −1.18644 −0.119848
\(99\) 24.0109 2.41319
\(100\) 59.2220 5.92220
\(101\) 13.8826 1.38137 0.690687 0.723154i \(-0.257308\pi\)
0.690687 + 0.723154i \(0.257308\pi\)
\(102\) 53.0286 5.25061
\(103\) −4.40923 −0.434454 −0.217227 0.976121i \(-0.569701\pi\)
−0.217227 + 0.976121i \(0.569701\pi\)
\(104\) −48.6806 −4.77352
\(105\) −31.4767 −3.07181
\(106\) −14.1076 −1.37025
\(107\) −2.01074 −0.194385 −0.0971926 0.995266i \(-0.530986\pi\)
−0.0971926 + 0.995266i \(0.530986\pi\)
\(108\) −34.2761 −3.29822
\(109\) −9.86599 −0.944990 −0.472495 0.881333i \(-0.656647\pi\)
−0.472495 + 0.881333i \(0.656647\pi\)
\(110\) −49.7247 −4.74107
\(111\) 5.34188 0.507029
\(112\) 37.0605 3.50189
\(113\) 17.9805 1.69146 0.845731 0.533609i \(-0.179165\pi\)
0.845731 + 0.533609i \(0.179165\pi\)
\(114\) −62.7769 −5.87960
\(115\) −21.8968 −2.04189
\(116\) −7.04031 −0.653676
\(117\) 28.5277 2.63739
\(118\) −5.22348 −0.480861
\(119\) 18.6255 1.70740
\(120\) 103.335 9.43320
\(121\) 9.93979 0.903617
\(122\) 25.0708 2.26980
\(123\) 14.4270 1.30084
\(124\) −17.1112 −1.53663
\(125\) 24.7150 2.21058
\(126\) −38.6967 −3.44737
\(127\) −14.4982 −1.28650 −0.643252 0.765655i \(-0.722415\pi\)
−0.643252 + 0.765655i \(0.722415\pi\)
\(128\) −26.5515 −2.34684
\(129\) −14.2195 −1.25196
\(130\) −59.0786 −5.18154
\(131\) −12.7793 −1.11654 −0.558268 0.829661i \(-0.688534\pi\)
−0.558268 + 0.829661i \(0.688534\pi\)
\(132\) −69.7986 −6.07519
\(133\) −22.0495 −1.91194
\(134\) −22.1424 −1.91281
\(135\) −25.9339 −2.23204
\(136\) −61.1462 −5.24324
\(137\) 1.06488 0.0909788 0.0454894 0.998965i \(-0.485515\pi\)
0.0454894 + 0.998965i \(0.485515\pi\)
\(138\) −42.3103 −3.60170
\(139\) 4.30502 0.365147 0.182573 0.983192i \(-0.441557\pi\)
0.182573 + 0.983192i \(0.441557\pi\)
\(140\) 58.2165 4.92019
\(141\) 6.24124 0.525607
\(142\) −13.7091 −1.15044
\(143\) 24.8788 2.08047
\(144\) 71.2990 5.94158
\(145\) −5.32683 −0.442369
\(146\) −42.7120 −3.53487
\(147\) −1.26007 −0.103929
\(148\) −9.87987 −0.812120
\(149\) −8.08791 −0.662587 −0.331294 0.943528i \(-0.607485\pi\)
−0.331294 + 0.943528i \(0.607485\pi\)
\(150\) 86.5817 7.06937
\(151\) −9.41429 −0.766124 −0.383062 0.923723i \(-0.625130\pi\)
−0.383062 + 0.923723i \(0.625130\pi\)
\(152\) 72.3869 5.87135
\(153\) 35.8328 2.89691
\(154\) −33.7472 −2.71942
\(155\) −12.9467 −1.03990
\(156\) −82.9286 −6.63960
\(157\) −20.3766 −1.62623 −0.813117 0.582101i \(-0.802231\pi\)
−0.813117 + 0.582101i \(0.802231\pi\)
\(158\) 4.36579 0.347323
\(159\) −14.9832 −1.18825
\(160\) −75.6885 −5.98370
\(161\) −14.8609 −1.17120
\(162\) −7.54694 −0.592944
\(163\) −13.5987 −1.06514 −0.532568 0.846387i \(-0.678773\pi\)
−0.532568 + 0.846387i \(0.678773\pi\)
\(164\) −26.6830 −2.08359
\(165\) −52.8110 −4.11133
\(166\) −20.3694 −1.58097
\(167\) 19.8281 1.53434 0.767172 0.641441i \(-0.221663\pi\)
0.767172 + 0.641441i \(0.221663\pi\)
\(168\) 70.1317 5.41078
\(169\) 16.5589 1.27376
\(170\) −74.2069 −5.69141
\(171\) −42.4200 −3.24394
\(172\) 26.2992 2.00529
\(173\) −0.231793 −0.0176229 −0.00881146 0.999961i \(-0.502805\pi\)
−0.00881146 + 0.999961i \(0.502805\pi\)
\(174\) −10.2928 −0.780298
\(175\) 30.4106 2.29883
\(176\) 62.1794 4.68695
\(177\) −5.54768 −0.416989
\(178\) 0.324877 0.0243505
\(179\) 13.1518 0.983015 0.491507 0.870873i \(-0.336446\pi\)
0.491507 + 0.870873i \(0.336446\pi\)
\(180\) 112.000 8.34798
\(181\) 15.9785 1.18767 0.593835 0.804587i \(-0.297613\pi\)
0.593835 + 0.804587i \(0.297613\pi\)
\(182\) −40.0954 −2.97207
\(183\) 26.6268 1.96831
\(184\) 48.7872 3.59664
\(185\) −7.47529 −0.549595
\(186\) −25.0164 −1.83429
\(187\) 31.2496 2.28519
\(188\) −11.5432 −0.841878
\(189\) −17.6008 −1.28027
\(190\) 87.8485 6.37320
\(191\) 2.93484 0.212358 0.106179 0.994347i \(-0.466138\pi\)
0.106179 + 0.994347i \(0.466138\pi\)
\(192\) −68.2055 −4.92231
\(193\) 10.9834 0.790601 0.395300 0.918552i \(-0.370641\pi\)
0.395300 + 0.918552i \(0.370641\pi\)
\(194\) −8.03096 −0.576589
\(195\) −62.7454 −4.49329
\(196\) 2.33052 0.166466
\(197\) −5.67595 −0.404394 −0.202197 0.979345i \(-0.564808\pi\)
−0.202197 + 0.979345i \(0.564808\pi\)
\(198\) −64.9246 −4.61399
\(199\) 7.66377 0.543270 0.271635 0.962400i \(-0.412436\pi\)
0.271635 + 0.962400i \(0.412436\pi\)
\(200\) −99.8357 −7.05945
\(201\) −23.5167 −1.65874
\(202\) −37.5381 −2.64117
\(203\) −3.61521 −0.253738
\(204\) −104.164 −7.29295
\(205\) −20.1888 −1.41005
\(206\) 11.9224 0.830672
\(207\) −28.5902 −1.98716
\(208\) 73.8762 5.12239
\(209\) −36.9943 −2.55895
\(210\) 85.1116 5.87326
\(211\) 26.1521 1.80038 0.900192 0.435493i \(-0.143426\pi\)
0.900192 + 0.435493i \(0.143426\pi\)
\(212\) 27.7117 1.90325
\(213\) −14.5600 −0.997634
\(214\) 5.43695 0.371662
\(215\) 19.8985 1.35706
\(216\) 57.7822 3.93158
\(217\) −8.78665 −0.596476
\(218\) 26.6772 1.80681
\(219\) −45.3630 −3.06535
\(220\) 97.6745 6.58521
\(221\) 37.1280 2.49750
\(222\) −14.4442 −0.969433
\(223\) −24.0467 −1.61029 −0.805144 0.593080i \(-0.797912\pi\)
−0.805144 + 0.593080i \(0.797912\pi\)
\(224\) −51.3682 −3.43218
\(225\) 58.5056 3.90037
\(226\) −48.6185 −3.23406
\(227\) 16.5296 1.09711 0.548554 0.836115i \(-0.315179\pi\)
0.548554 + 0.836115i \(0.315179\pi\)
\(228\) 123.313 8.16660
\(229\) −23.2228 −1.53461 −0.767303 0.641285i \(-0.778402\pi\)
−0.767303 + 0.641285i \(0.778402\pi\)
\(230\) 59.2081 3.90406
\(231\) −35.8417 −2.35821
\(232\) 11.8685 0.779203
\(233\) −0.649628 −0.0425585 −0.0212793 0.999774i \(-0.506774\pi\)
−0.0212793 + 0.999774i \(0.506774\pi\)
\(234\) −77.1377 −5.04265
\(235\) −8.73384 −0.569733
\(236\) 10.2605 0.667902
\(237\) 4.63675 0.301189
\(238\) −50.3627 −3.26453
\(239\) −4.97748 −0.321966 −0.160983 0.986957i \(-0.551467\pi\)
−0.160983 + 0.986957i \(0.551467\pi\)
\(240\) −156.819 −10.1226
\(241\) 6.95071 0.447735 0.223867 0.974620i \(-0.428132\pi\)
0.223867 + 0.974620i \(0.428132\pi\)
\(242\) −26.8768 −1.72771
\(243\) 11.3446 0.727754
\(244\) −49.2466 −3.15269
\(245\) 1.76332 0.112654
\(246\) −39.0101 −2.48719
\(247\) −43.9534 −2.79669
\(248\) 28.8459 1.83172
\(249\) −21.6337 −1.37098
\(250\) −66.8283 −4.22659
\(251\) 14.9223 0.941889 0.470945 0.882163i \(-0.343913\pi\)
0.470945 + 0.882163i \(0.343913\pi\)
\(252\) 76.0121 4.78831
\(253\) −24.9334 −1.56755
\(254\) 39.2024 2.45978
\(255\) −78.8126 −4.93544
\(256\) 24.2938 1.51836
\(257\) 13.8187 0.861986 0.430993 0.902355i \(-0.358163\pi\)
0.430993 + 0.902355i \(0.358163\pi\)
\(258\) 38.4490 2.39373
\(259\) −5.07333 −0.315241
\(260\) 116.048 7.19701
\(261\) −6.95514 −0.430512
\(262\) 34.5548 2.13480
\(263\) −1.12663 −0.0694711 −0.0347355 0.999397i \(-0.511059\pi\)
−0.0347355 + 0.999397i \(0.511059\pi\)
\(264\) 117.666 7.24182
\(265\) 20.9672 1.28800
\(266\) 59.6210 3.65560
\(267\) 0.345040 0.0211161
\(268\) 43.4944 2.65684
\(269\) −6.21363 −0.378851 −0.189426 0.981895i \(-0.560663\pi\)
−0.189426 + 0.981895i \(0.560663\pi\)
\(270\) 70.1243 4.26763
\(271\) 10.3105 0.626320 0.313160 0.949700i \(-0.398612\pi\)
0.313160 + 0.949700i \(0.398612\pi\)
\(272\) 92.7937 5.62644
\(273\) −42.5840 −2.57730
\(274\) −2.87939 −0.173950
\(275\) 51.0224 3.07676
\(276\) 83.1104 5.00266
\(277\) −26.2346 −1.57629 −0.788144 0.615491i \(-0.788958\pi\)
−0.788144 + 0.615491i \(0.788958\pi\)
\(278\) −11.6406 −0.698157
\(279\) −16.9042 −1.01203
\(280\) −98.1406 −5.86502
\(281\) 3.57700 0.213386 0.106693 0.994292i \(-0.465974\pi\)
0.106693 + 0.994292i \(0.465974\pi\)
\(282\) −16.8761 −1.00495
\(283\) 5.10775 0.303624 0.151812 0.988409i \(-0.451489\pi\)
0.151812 + 0.988409i \(0.451489\pi\)
\(284\) 26.9289 1.59794
\(285\) 93.3009 5.52667
\(286\) −67.2714 −3.97784
\(287\) −13.7017 −0.808789
\(288\) −98.8249 −5.82332
\(289\) 29.6354 1.74326
\(290\) 14.4035 0.845805
\(291\) −8.52941 −0.500003
\(292\) 83.8994 4.90984
\(293\) 15.6237 0.912748 0.456374 0.889788i \(-0.349148\pi\)
0.456374 + 0.889788i \(0.349148\pi\)
\(294\) 3.40719 0.198711
\(295\) 7.76329 0.451996
\(296\) 16.6554 0.968073
\(297\) −29.5303 −1.71352
\(298\) 21.8694 1.26686
\(299\) −29.6236 −1.71318
\(300\) −170.073 −9.81916
\(301\) 13.5047 0.778397
\(302\) 25.4559 1.46482
\(303\) −39.8679 −2.29035
\(304\) −109.852 −6.30046
\(305\) −37.2609 −2.13355
\(306\) −96.8904 −5.53886
\(307\) −18.0522 −1.03029 −0.515145 0.857103i \(-0.672262\pi\)
−0.515145 + 0.857103i \(0.672262\pi\)
\(308\) 66.2897 3.77720
\(309\) 12.6624 0.720336
\(310\) 35.0073 1.98828
\(311\) 29.1986 1.65570 0.827850 0.560950i \(-0.189564\pi\)
0.827850 + 0.560950i \(0.189564\pi\)
\(312\) 139.800 7.91462
\(313\) −27.9124 −1.57770 −0.788850 0.614586i \(-0.789323\pi\)
−0.788850 + 0.614586i \(0.789323\pi\)
\(314\) 55.0976 3.10934
\(315\) 57.5122 3.24044
\(316\) −8.57573 −0.482423
\(317\) −4.53841 −0.254902 −0.127451 0.991845i \(-0.540680\pi\)
−0.127451 + 0.991845i \(0.540680\pi\)
\(318\) 40.5141 2.27192
\(319\) −6.06553 −0.339605
\(320\) 95.4451 5.33554
\(321\) 5.77440 0.322296
\(322\) 40.1833 2.23933
\(323\) −55.2085 −3.07188
\(324\) 14.8245 0.823583
\(325\) 60.6203 3.36261
\(326\) 36.7705 2.03653
\(327\) 28.3330 1.56682
\(328\) 44.9818 2.48370
\(329\) −5.92748 −0.326792
\(330\) 142.799 7.86081
\(331\) −0.478223 −0.0262855 −0.0131427 0.999914i \(-0.504184\pi\)
−0.0131427 + 0.999914i \(0.504184\pi\)
\(332\) 40.0117 2.19593
\(333\) −9.76034 −0.534863
\(334\) −53.6144 −2.93365
\(335\) 32.9087 1.79799
\(336\) −106.430 −5.80622
\(337\) −15.4444 −0.841308 −0.420654 0.907221i \(-0.638199\pi\)
−0.420654 + 0.907221i \(0.638199\pi\)
\(338\) −44.7745 −2.43541
\(339\) −51.6361 −2.80449
\(340\) 145.765 7.90521
\(341\) −14.7421 −0.798328
\(342\) 114.702 6.20238
\(343\) −17.8952 −0.966248
\(344\) −44.3348 −2.39037
\(345\) 62.8829 3.38550
\(346\) 0.626760 0.0336948
\(347\) 17.5745 0.943448 0.471724 0.881746i \(-0.343632\pi\)
0.471724 + 0.881746i \(0.343632\pi\)
\(348\) 20.2182 1.08381
\(349\) 5.75155 0.307873 0.153937 0.988081i \(-0.450805\pi\)
0.153937 + 0.988081i \(0.450805\pi\)
\(350\) −82.2291 −4.39533
\(351\) −35.0854 −1.87272
\(352\) −86.1847 −4.59366
\(353\) −11.2594 −0.599279 −0.299639 0.954053i \(-0.596866\pi\)
−0.299639 + 0.954053i \(0.596866\pi\)
\(354\) 15.0007 0.797279
\(355\) 20.3749 1.08139
\(356\) −0.638156 −0.0338222
\(357\) −53.4885 −2.83091
\(358\) −35.5620 −1.87951
\(359\) 28.8258 1.52137 0.760684 0.649122i \(-0.224864\pi\)
0.760684 + 0.649122i \(0.224864\pi\)
\(360\) −188.808 −9.95106
\(361\) 46.3576 2.43988
\(362\) −43.2051 −2.27081
\(363\) −28.5449 −1.49822
\(364\) 78.7596 4.12812
\(365\) 63.4799 3.32269
\(366\) −71.9979 −3.76339
\(367\) 19.9097 1.03928 0.519638 0.854386i \(-0.326067\pi\)
0.519638 + 0.854386i \(0.326067\pi\)
\(368\) −74.0381 −3.85950
\(369\) −26.3602 −1.37226
\(370\) 20.2129 1.05082
\(371\) 14.2300 0.738785
\(372\) 49.1398 2.54778
\(373\) 21.2372 1.09962 0.549811 0.835289i \(-0.314700\pi\)
0.549811 + 0.835289i \(0.314700\pi\)
\(374\) −84.4976 −4.36927
\(375\) −70.9761 −3.66519
\(376\) 19.4595 1.00354
\(377\) −7.20654 −0.371156
\(378\) 47.5919 2.44786
\(379\) 18.1696 0.933312 0.466656 0.884439i \(-0.345459\pi\)
0.466656 + 0.884439i \(0.345459\pi\)
\(380\) −172.561 −8.85220
\(381\) 41.6356 2.13305
\(382\) −7.93570 −0.406026
\(383\) −1.77047 −0.0904670 −0.0452335 0.998976i \(-0.514403\pi\)
−0.0452335 + 0.998976i \(0.514403\pi\)
\(384\) 76.2502 3.89113
\(385\) 50.1560 2.55619
\(386\) −29.6986 −1.51162
\(387\) 25.9810 1.32069
\(388\) 15.7752 0.800867
\(389\) −4.89394 −0.248132 −0.124066 0.992274i \(-0.539594\pi\)
−0.124066 + 0.992274i \(0.539594\pi\)
\(390\) 169.661 8.59112
\(391\) −37.2094 −1.88176
\(392\) −3.92876 −0.198432
\(393\) 36.6995 1.85124
\(394\) 15.3475 0.773198
\(395\) −6.48856 −0.326475
\(396\) 127.532 6.40870
\(397\) −11.9353 −0.599015 −0.299508 0.954094i \(-0.596822\pi\)
−0.299508 + 0.954094i \(0.596822\pi\)
\(398\) −20.7225 −1.03873
\(399\) 63.3214 3.17004
\(400\) 151.508 7.57539
\(401\) −1.00471 −0.0501729 −0.0250865 0.999685i \(-0.507986\pi\)
−0.0250865 + 0.999685i \(0.507986\pi\)
\(402\) 63.5881 3.17149
\(403\) −17.5152 −0.872497
\(404\) 73.7362 3.66851
\(405\) 11.2165 0.557352
\(406\) 9.77539 0.485144
\(407\) −8.51194 −0.421921
\(408\) 175.599 8.69343
\(409\) −33.4937 −1.65615 −0.828077 0.560614i \(-0.810565\pi\)
−0.828077 + 0.560614i \(0.810565\pi\)
\(410\) 54.5898 2.69600
\(411\) −3.05810 −0.150845
\(412\) −23.4192 −1.15378
\(413\) 5.26879 0.259260
\(414\) 77.3068 3.79942
\(415\) 30.2736 1.48607
\(416\) −102.397 −5.02043
\(417\) −12.3631 −0.605423
\(418\) 100.031 4.89268
\(419\) −15.0406 −0.734779 −0.367390 0.930067i \(-0.619748\pi\)
−0.367390 + 0.930067i \(0.619748\pi\)
\(420\) −167.185 −8.15780
\(421\) 39.3021 1.91547 0.957733 0.287660i \(-0.0928773\pi\)
0.957733 + 0.287660i \(0.0928773\pi\)
\(422\) −70.7142 −3.44231
\(423\) −11.4036 −0.554462
\(424\) −46.7160 −2.26873
\(425\) 76.1434 3.69350
\(426\) 39.3696 1.90746
\(427\) −25.2882 −1.22378
\(428\) −10.6798 −0.516229
\(429\) −71.4466 −3.44948
\(430\) −53.8046 −2.59469
\(431\) 10.8570 0.522963 0.261481 0.965209i \(-0.415789\pi\)
0.261481 + 0.965209i \(0.415789\pi\)
\(432\) −87.6885 −4.21892
\(433\) −4.89839 −0.235402 −0.117701 0.993049i \(-0.537552\pi\)
−0.117701 + 0.993049i \(0.537552\pi\)
\(434\) 23.7587 1.14046
\(435\) 15.2975 0.733459
\(436\) −52.4022 −2.50961
\(437\) 44.0497 2.10718
\(438\) 122.660 5.86091
\(439\) 17.2744 0.824461 0.412230 0.911080i \(-0.364750\pi\)
0.412230 + 0.911080i \(0.364750\pi\)
\(440\) −164.658 −7.84978
\(441\) 2.30233 0.109635
\(442\) −100.393 −4.77519
\(443\) 5.20307 0.247205 0.123603 0.992332i \(-0.460555\pi\)
0.123603 + 0.992332i \(0.460555\pi\)
\(444\) 28.3728 1.34652
\(445\) −0.482841 −0.0228889
\(446\) 65.0214 3.07885
\(447\) 23.2267 1.09859
\(448\) 64.7766 3.06041
\(449\) −25.6502 −1.21051 −0.605255 0.796032i \(-0.706929\pi\)
−0.605255 + 0.796032i \(0.706929\pi\)
\(450\) −158.197 −7.45746
\(451\) −22.9885 −1.08249
\(452\) 95.5015 4.49201
\(453\) 27.0358 1.27025
\(454\) −44.6953 −2.09766
\(455\) 59.5910 2.79367
\(456\) −207.879 −9.73485
\(457\) −14.2242 −0.665378 −0.332689 0.943037i \(-0.607956\pi\)
−0.332689 + 0.943037i \(0.607956\pi\)
\(458\) 62.7935 2.93415
\(459\) −44.0697 −2.05700
\(460\) −116.303 −5.42264
\(461\) 1.56522 0.0728995 0.0364498 0.999335i \(-0.488395\pi\)
0.0364498 + 0.999335i \(0.488395\pi\)
\(462\) 96.9145 4.50887
\(463\) −14.1087 −0.655685 −0.327843 0.944732i \(-0.606322\pi\)
−0.327843 + 0.944732i \(0.606322\pi\)
\(464\) −18.0112 −0.836151
\(465\) 37.1801 1.72418
\(466\) 1.75657 0.0813714
\(467\) −31.5819 −1.46144 −0.730718 0.682680i \(-0.760814\pi\)
−0.730718 + 0.682680i \(0.760814\pi\)
\(468\) 151.522 7.00410
\(469\) 22.3344 1.03131
\(470\) 23.6159 1.08932
\(471\) 58.5173 2.69634
\(472\) −17.2970 −0.796160
\(473\) 22.6579 1.04181
\(474\) −12.5376 −0.575871
\(475\) −90.1410 −4.13595
\(476\) 98.9276 4.53434
\(477\) 27.3764 1.25348
\(478\) 13.4589 0.615596
\(479\) −21.1609 −0.966866 −0.483433 0.875381i \(-0.660610\pi\)
−0.483433 + 0.875381i \(0.660610\pi\)
\(480\) 217.361 9.92113
\(481\) −10.1131 −0.461120
\(482\) −18.7944 −0.856063
\(483\) 42.6773 1.94188
\(484\) 52.7942 2.39974
\(485\) 11.9358 0.541979
\(486\) −30.6752 −1.39146
\(487\) −0.625986 −0.0283661 −0.0141831 0.999899i \(-0.504515\pi\)
−0.0141831 + 0.999899i \(0.504515\pi\)
\(488\) 83.0193 3.75811
\(489\) 39.0527 1.76602
\(490\) −4.76793 −0.215393
\(491\) −26.9012 −1.21404 −0.607018 0.794688i \(-0.707634\pi\)
−0.607018 + 0.794688i \(0.707634\pi\)
\(492\) 76.6277 3.45464
\(493\) −9.05192 −0.407678
\(494\) 118.848 5.34723
\(495\) 96.4928 4.33703
\(496\) −43.7757 −1.96559
\(497\) 13.8280 0.620272
\(498\) 58.4965 2.62129
\(499\) −12.2138 −0.546766 −0.273383 0.961905i \(-0.588143\pi\)
−0.273383 + 0.961905i \(0.588143\pi\)
\(500\) 131.271 5.87062
\(501\) −56.9420 −2.54398
\(502\) −40.3494 −1.80088
\(503\) 20.6919 0.922608 0.461304 0.887242i \(-0.347382\pi\)
0.461304 + 0.887242i \(0.347382\pi\)
\(504\) −128.140 −5.70782
\(505\) 55.7902 2.48263
\(506\) 67.4188 2.99713
\(507\) −47.5535 −2.11192
\(508\) −77.0055 −3.41657
\(509\) 19.5747 0.867633 0.433817 0.901001i \(-0.357167\pi\)
0.433817 + 0.901001i \(0.357167\pi\)
\(510\) 213.106 9.43650
\(511\) 43.0825 1.90586
\(512\) −12.5864 −0.556245
\(513\) 52.1711 2.30341
\(514\) −37.3652 −1.64811
\(515\) −17.7194 −0.780810
\(516\) −75.5256 −3.32483
\(517\) −9.94501 −0.437381
\(518\) 13.7181 0.602738
\(519\) 0.665660 0.0292192
\(520\) −195.633 −8.57906
\(521\) −3.67724 −0.161103 −0.0805514 0.996750i \(-0.525668\pi\)
−0.0805514 + 0.996750i \(0.525668\pi\)
\(522\) 18.8064 0.823134
\(523\) 37.9982 1.66155 0.830773 0.556612i \(-0.187899\pi\)
0.830773 + 0.556612i \(0.187899\pi\)
\(524\) −67.8761 −2.96518
\(525\) −87.3327 −3.81151
\(526\) 3.04637 0.132828
\(527\) −22.0004 −0.958352
\(528\) −178.566 −7.77108
\(529\) 6.68855 0.290807
\(530\) −56.6944 −2.46265
\(531\) 10.1364 0.439881
\(532\) −117.114 −5.07752
\(533\) −27.3130 −1.18306
\(534\) −0.932975 −0.0403738
\(535\) −8.08056 −0.349353
\(536\) −73.3223 −3.16704
\(537\) −37.7692 −1.62986
\(538\) 16.8014 0.724359
\(539\) 2.00784 0.0864840
\(540\) −137.745 −5.92762
\(541\) −4.32495 −0.185944 −0.0929720 0.995669i \(-0.529637\pi\)
−0.0929720 + 0.995669i \(0.529637\pi\)
\(542\) −27.8793 −1.19752
\(543\) −45.8867 −1.96919
\(544\) −128.618 −5.51445
\(545\) −39.6485 −1.69835
\(546\) 115.145 4.92777
\(547\) −37.6310 −1.60898 −0.804492 0.593963i \(-0.797563\pi\)
−0.804492 + 0.593963i \(0.797563\pi\)
\(548\) 5.65600 0.241612
\(549\) −48.6509 −2.07637
\(550\) −137.962 −5.88274
\(551\) 10.7160 0.456515
\(552\) −140.106 −5.96332
\(553\) −4.40365 −0.187262
\(554\) 70.9374 3.01384
\(555\) 21.4674 0.911242
\(556\) 22.8657 0.969721
\(557\) −5.30569 −0.224809 −0.112405 0.993663i \(-0.535855\pi\)
−0.112405 + 0.993663i \(0.535855\pi\)
\(558\) 45.7083 1.93499
\(559\) 26.9201 1.13860
\(560\) 148.935 6.29366
\(561\) −89.7420 −3.78891
\(562\) −9.67208 −0.407992
\(563\) −20.2966 −0.855401 −0.427700 0.903921i \(-0.640676\pi\)
−0.427700 + 0.903921i \(0.640676\pi\)
\(564\) 33.1497 1.39585
\(565\) 72.2583 3.03993
\(566\) −13.8112 −0.580526
\(567\) 7.61240 0.319691
\(568\) −45.3964 −1.90479
\(569\) −13.6659 −0.572903 −0.286452 0.958095i \(-0.592476\pi\)
−0.286452 + 0.958095i \(0.592476\pi\)
\(570\) −252.282 −10.5669
\(571\) 1.14698 0.0479998 0.0239999 0.999712i \(-0.492360\pi\)
0.0239999 + 0.999712i \(0.492360\pi\)
\(572\) 132.141 5.52511
\(573\) −8.42823 −0.352095
\(574\) 37.0490 1.54639
\(575\) −60.7532 −2.53358
\(576\) 124.621 5.19253
\(577\) 2.66694 0.111026 0.0555131 0.998458i \(-0.482321\pi\)
0.0555131 + 0.998458i \(0.482321\pi\)
\(578\) −80.1329 −3.33309
\(579\) −31.5419 −1.31084
\(580\) −28.2929 −1.17480
\(581\) 20.5461 0.852395
\(582\) 23.0632 0.955999
\(583\) 23.8748 0.988794
\(584\) −141.437 −5.85269
\(585\) 114.644 4.73996
\(586\) −42.2460 −1.74516
\(587\) 38.6425 1.59494 0.797472 0.603355i \(-0.206170\pi\)
0.797472 + 0.603355i \(0.206170\pi\)
\(588\) −6.69275 −0.276004
\(589\) 26.0448 1.07316
\(590\) −20.9916 −0.864212
\(591\) 16.3001 0.670496
\(592\) −25.2757 −1.03882
\(593\) −43.2092 −1.77439 −0.887195 0.461394i \(-0.847349\pi\)
−0.887195 + 0.461394i \(0.847349\pi\)
\(594\) 79.8488 3.27624
\(595\) 74.8505 3.06857
\(596\) −42.9581 −1.75963
\(597\) −22.0087 −0.900756
\(598\) 80.1011 3.27558
\(599\) 6.56723 0.268330 0.134165 0.990959i \(-0.457165\pi\)
0.134165 + 0.990959i \(0.457165\pi\)
\(600\) 286.707 11.7048
\(601\) −3.91932 −0.159873 −0.0799363 0.996800i \(-0.525472\pi\)
−0.0799363 + 0.996800i \(0.525472\pi\)
\(602\) −36.5161 −1.48829
\(603\) 42.9682 1.74980
\(604\) −50.0031 −2.03460
\(605\) 39.9451 1.62400
\(606\) 107.801 4.37913
\(607\) 16.5146 0.670306 0.335153 0.942164i \(-0.391212\pi\)
0.335153 + 0.942164i \(0.391212\pi\)
\(608\) 152.262 6.17505
\(609\) 10.3821 0.420704
\(610\) 100.752 4.07933
\(611\) −11.8158 −0.478016
\(612\) 190.322 7.69332
\(613\) 40.0283 1.61673 0.808363 0.588684i \(-0.200354\pi\)
0.808363 + 0.588684i \(0.200354\pi\)
\(614\) 48.8123 1.96990
\(615\) 57.9780 2.33790
\(616\) −111.750 −4.50255
\(617\) −39.4857 −1.58963 −0.794817 0.606849i \(-0.792433\pi\)
−0.794817 + 0.606849i \(0.792433\pi\)
\(618\) −34.2385 −1.37727
\(619\) −36.9335 −1.48448 −0.742241 0.670132i \(-0.766237\pi\)
−0.742241 + 0.670132i \(0.766237\pi\)
\(620\) −68.7650 −2.76167
\(621\) 35.1623 1.41101
\(622\) −78.9518 −3.16568
\(623\) −0.327694 −0.0131288
\(624\) −212.156 −8.49305
\(625\) 43.5723 1.74289
\(626\) 75.4739 3.01654
\(627\) 106.240 4.24280
\(628\) −108.228 −4.31879
\(629\) −12.7028 −0.506494
\(630\) −155.511 −6.19569
\(631\) −17.7414 −0.706272 −0.353136 0.935572i \(-0.614885\pi\)
−0.353136 + 0.935572i \(0.614885\pi\)
\(632\) 14.4569 0.575063
\(633\) −75.1031 −2.98508
\(634\) 12.2717 0.487370
\(635\) −58.2638 −2.31213
\(636\) −79.5820 −3.15563
\(637\) 2.38555 0.0945188
\(638\) 16.4010 0.649320
\(639\) 26.6031 1.05240
\(640\) −106.703 −4.21779
\(641\) −17.1894 −0.678939 −0.339470 0.940617i \(-0.610248\pi\)
−0.339470 + 0.940617i \(0.610248\pi\)
\(642\) −15.6137 −0.616225
\(643\) 12.7239 0.501780 0.250890 0.968016i \(-0.419277\pi\)
0.250890 + 0.968016i \(0.419277\pi\)
\(644\) −78.9322 −3.11036
\(645\) −57.1441 −2.25005
\(646\) 149.282 5.87341
\(647\) 12.5551 0.493592 0.246796 0.969068i \(-0.420622\pi\)
0.246796 + 0.969068i \(0.420622\pi\)
\(648\) −24.9909 −0.981737
\(649\) 8.83987 0.346995
\(650\) −163.915 −6.42927
\(651\) 25.2334 0.988973
\(652\) −72.2284 −2.82868
\(653\) 31.6712 1.23939 0.619694 0.784844i \(-0.287257\pi\)
0.619694 + 0.784844i \(0.287257\pi\)
\(654\) −76.6112 −2.99574
\(655\) −51.3564 −2.00666
\(656\) −68.2631 −2.66523
\(657\) 82.8844 3.23363
\(658\) 16.0277 0.624823
\(659\) −32.4815 −1.26530 −0.632649 0.774439i \(-0.718032\pi\)
−0.632649 + 0.774439i \(0.718032\pi\)
\(660\) −280.500 −10.9184
\(661\) −39.9953 −1.55564 −0.777819 0.628489i \(-0.783674\pi\)
−0.777819 + 0.628489i \(0.783674\pi\)
\(662\) 1.29309 0.0502576
\(663\) −106.624 −4.14092
\(664\) −67.4512 −2.61762
\(665\) −88.6105 −3.43617
\(666\) 26.3916 1.02265
\(667\) 7.22233 0.279650
\(668\) 105.315 4.07476
\(669\) 69.0570 2.66990
\(670\) −88.9837 −3.43774
\(671\) −42.4281 −1.63792
\(672\) 147.518 5.69065
\(673\) −7.72283 −0.297693 −0.148847 0.988860i \(-0.547556\pi\)
−0.148847 + 0.988860i \(0.547556\pi\)
\(674\) 41.7610 1.60857
\(675\) −71.9543 −2.76952
\(676\) 87.9507 3.38272
\(677\) 44.9890 1.72907 0.864535 0.502573i \(-0.167613\pi\)
0.864535 + 0.502573i \(0.167613\pi\)
\(678\) 139.622 5.36215
\(679\) 8.10061 0.310873
\(680\) −245.729 −9.42326
\(681\) −47.4694 −1.81903
\(682\) 39.8620 1.52639
\(683\) 3.39207 0.129794 0.0648970 0.997892i \(-0.479328\pi\)
0.0648970 + 0.997892i \(0.479328\pi\)
\(684\) −225.310 −8.61493
\(685\) 4.27944 0.163509
\(686\) 48.3878 1.84745
\(687\) 66.6909 2.54441
\(688\) 67.2812 2.56507
\(689\) 28.3660 1.08066
\(690\) −170.033 −6.47304
\(691\) 43.8858 1.66949 0.834747 0.550633i \(-0.185614\pi\)
0.834747 + 0.550633i \(0.185614\pi\)
\(692\) −1.23115 −0.0468012
\(693\) 65.4877 2.48767
\(694\) −47.5207 −1.80386
\(695\) 17.3006 0.656249
\(696\) −34.0837 −1.29194
\(697\) −34.3070 −1.29947
\(698\) −15.5520 −0.588650
\(699\) 1.86559 0.0705631
\(700\) 161.523 6.10499
\(701\) −13.1266 −0.495784 −0.247892 0.968788i \(-0.579738\pi\)
−0.247892 + 0.968788i \(0.579738\pi\)
\(702\) 94.8694 3.58062
\(703\) 15.0380 0.567169
\(704\) 108.681 4.09607
\(705\) 25.0817 0.944631
\(706\) 30.4450 1.14581
\(707\) 37.8637 1.42401
\(708\) −29.4660 −1.10740
\(709\) −37.0765 −1.39244 −0.696218 0.717830i \(-0.745135\pi\)
−0.696218 + 0.717830i \(0.745135\pi\)
\(710\) −55.0929 −2.06760
\(711\) −8.47198 −0.317724
\(712\) 1.07580 0.0403171
\(713\) 17.5536 0.657389
\(714\) 144.631 5.41267
\(715\) 99.9807 3.73907
\(716\) 69.8547 2.61059
\(717\) 14.2942 0.533828
\(718\) −77.9439 −2.90884
\(719\) −38.1163 −1.42150 −0.710750 0.703445i \(-0.751644\pi\)
−0.710750 + 0.703445i \(0.751644\pi\)
\(720\) 286.530 10.6783
\(721\) −12.0258 −0.447864
\(722\) −125.349 −4.66501
\(723\) −19.9609 −0.742355
\(724\) 84.8679 3.15409
\(725\) −14.7794 −0.548894
\(726\) 77.1843 2.86458
\(727\) −11.9317 −0.442521 −0.221261 0.975215i \(-0.571017\pi\)
−0.221261 + 0.975215i \(0.571017\pi\)
\(728\) −132.772 −4.92086
\(729\) −40.9523 −1.51675
\(730\) −171.647 −6.35294
\(731\) 33.8136 1.25064
\(732\) 141.426 5.22724
\(733\) −8.32447 −0.307471 −0.153736 0.988112i \(-0.549130\pi\)
−0.153736 + 0.988112i \(0.549130\pi\)
\(734\) −53.8350 −1.98708
\(735\) −5.06386 −0.186783
\(736\) 102.621 3.78268
\(737\) 37.4723 1.38031
\(738\) 71.2768 2.62374
\(739\) −26.0581 −0.958561 −0.479280 0.877662i \(-0.659102\pi\)
−0.479280 + 0.877662i \(0.659102\pi\)
\(740\) −39.7043 −1.45956
\(741\) 126.225 4.63697
\(742\) −38.4773 −1.41255
\(743\) −49.1846 −1.80441 −0.902205 0.431308i \(-0.858052\pi\)
−0.902205 + 0.431308i \(0.858052\pi\)
\(744\) −82.8392 −3.03703
\(745\) −32.5029 −1.19081
\(746\) −57.4246 −2.10246
\(747\) 39.5277 1.44624
\(748\) 165.979 6.06879
\(749\) −5.48411 −0.200385
\(750\) 191.916 7.00780
\(751\) −7.18157 −0.262059 −0.131030 0.991378i \(-0.541828\pi\)
−0.131030 + 0.991378i \(0.541828\pi\)
\(752\) −29.5311 −1.07689
\(753\) −42.8537 −1.56168
\(754\) 19.4862 0.709645
\(755\) −37.8333 −1.37689
\(756\) −93.4850 −3.40002
\(757\) 14.3749 0.522463 0.261231 0.965276i \(-0.415871\pi\)
0.261231 + 0.965276i \(0.415871\pi\)
\(758\) −49.1300 −1.78448
\(759\) 71.6032 2.59903
\(760\) 290.901 10.5521
\(761\) 33.2258 1.20443 0.602216 0.798333i \(-0.294284\pi\)
0.602216 + 0.798333i \(0.294284\pi\)
\(762\) −112.581 −4.07838
\(763\) −26.9086 −0.974157
\(764\) 15.5881 0.563958
\(765\) 144.001 5.20638
\(766\) 4.78729 0.172972
\(767\) 10.5028 0.379233
\(768\) −69.7665 −2.51748
\(769\) 53.3505 1.92387 0.961934 0.273281i \(-0.0881090\pi\)
0.961934 + 0.273281i \(0.0881090\pi\)
\(770\) −135.620 −4.88740
\(771\) −39.6843 −1.42919
\(772\) 58.3371 2.09960
\(773\) 35.1031 1.26257 0.631285 0.775551i \(-0.282528\pi\)
0.631285 + 0.775551i \(0.282528\pi\)
\(774\) −70.2516 −2.52514
\(775\) −35.9209 −1.29032
\(776\) −26.5937 −0.954658
\(777\) 14.5695 0.522678
\(778\) 13.2330 0.474426
\(779\) 40.6138 1.45514
\(780\) −333.266 −11.9328
\(781\) 23.2004 0.830176
\(782\) 100.613 3.59790
\(783\) 8.55392 0.305692
\(784\) 5.96217 0.212935
\(785\) −81.8877 −2.92270
\(786\) −99.2339 −3.53956
\(787\) −20.8528 −0.743320 −0.371660 0.928369i \(-0.621211\pi\)
−0.371660 + 0.928369i \(0.621211\pi\)
\(788\) −30.1472 −1.07395
\(789\) 3.23544 0.115185
\(790\) 17.5448 0.624216
\(791\) 49.0402 1.74367
\(792\) −214.991 −7.63938
\(793\) −50.4094 −1.79009
\(794\) 32.2725 1.14531
\(795\) −60.2132 −2.13554
\(796\) 40.7053 1.44276
\(797\) 21.8333 0.773374 0.386687 0.922211i \(-0.373619\pi\)
0.386687 + 0.922211i \(0.373619\pi\)
\(798\) −171.219 −6.06107
\(799\) −14.8415 −0.525053
\(800\) −209.999 −7.42460
\(801\) −0.630436 −0.0222754
\(802\) 2.71670 0.0959301
\(803\) 72.2830 2.55081
\(804\) −124.906 −4.40511
\(805\) −59.7216 −2.10491
\(806\) 47.3605 1.66820
\(807\) 17.8442 0.628145
\(808\) −124.304 −4.37298
\(809\) −11.1369 −0.391553 −0.195777 0.980649i \(-0.562723\pi\)
−0.195777 + 0.980649i \(0.562723\pi\)
\(810\) −30.3289 −1.06565
\(811\) −31.8167 −1.11724 −0.558618 0.829425i \(-0.688668\pi\)
−0.558618 + 0.829425i \(0.688668\pi\)
\(812\) −19.2018 −0.673852
\(813\) −29.6096 −1.03845
\(814\) 23.0159 0.806708
\(815\) −54.6494 −1.91428
\(816\) −266.483 −9.32878
\(817\) −40.0296 −1.40046
\(818\) 90.5655 3.16655
\(819\) 77.8068 2.71879
\(820\) −107.231 −3.74467
\(821\) 33.3206 1.16290 0.581449 0.813583i \(-0.302486\pi\)
0.581449 + 0.813583i \(0.302486\pi\)
\(822\) 8.26899 0.288414
\(823\) 14.2339 0.496163 0.248082 0.968739i \(-0.420200\pi\)
0.248082 + 0.968739i \(0.420200\pi\)
\(824\) 39.4798 1.37534
\(825\) −146.525 −5.10135
\(826\) −14.2466 −0.495702
\(827\) 18.1594 0.631465 0.315732 0.948848i \(-0.397750\pi\)
0.315732 + 0.948848i \(0.397750\pi\)
\(828\) −151.854 −5.27729
\(829\) −35.3910 −1.22918 −0.614590 0.788847i \(-0.710678\pi\)
−0.614590 + 0.788847i \(0.710678\pi\)
\(830\) −81.8587 −2.84136
\(831\) 75.3402 2.61352
\(832\) 129.125 4.47661
\(833\) 2.99641 0.103820
\(834\) 33.4293 1.15756
\(835\) 79.6833 2.75755
\(836\) −196.491 −6.79579
\(837\) 20.7900 0.718608
\(838\) 40.6690 1.40489
\(839\) −11.7781 −0.406625 −0.203312 0.979114i \(-0.565171\pi\)
−0.203312 + 0.979114i \(0.565171\pi\)
\(840\) 281.838 9.72435
\(841\) −27.2430 −0.939415
\(842\) −106.271 −3.66235
\(843\) −10.2724 −0.353800
\(844\) 138.904 4.78128
\(845\) 66.5452 2.28922
\(846\) 30.8349 1.06012
\(847\) 27.1099 0.931507
\(848\) 70.8948 2.43454
\(849\) −14.6684 −0.503417
\(850\) −205.889 −7.06192
\(851\) 10.1353 0.347434
\(852\) −77.3339 −2.64942
\(853\) −6.09246 −0.208602 −0.104301 0.994546i \(-0.533261\pi\)
−0.104301 + 0.994546i \(0.533261\pi\)
\(854\) 68.3784 2.33986
\(855\) −170.474 −5.83007
\(856\) 18.0039 0.615361
\(857\) 51.3768 1.75500 0.877500 0.479577i \(-0.159210\pi\)
0.877500 + 0.479577i \(0.159210\pi\)
\(858\) 193.189 6.59536
\(859\) −21.0021 −0.716583 −0.358291 0.933610i \(-0.616641\pi\)
−0.358291 + 0.933610i \(0.616641\pi\)
\(860\) 105.689 3.60395
\(861\) 39.3485 1.34099
\(862\) −29.3569 −0.999898
\(863\) −23.8838 −0.813015 −0.406508 0.913647i \(-0.633254\pi\)
−0.406508 + 0.913647i \(0.633254\pi\)
\(864\) 121.542 4.13494
\(865\) −0.931509 −0.0316723
\(866\) 13.2451 0.450085
\(867\) −85.1064 −2.89037
\(868\) −46.6694 −1.58406
\(869\) −7.38837 −0.250633
\(870\) −41.3639 −1.40237
\(871\) 44.5213 1.50855
\(872\) 88.3389 2.99153
\(873\) 15.5844 0.527452
\(874\) −119.109 −4.02891
\(875\) 67.4079 2.27880
\(876\) −240.941 −8.14064
\(877\) −19.9052 −0.672151 −0.336076 0.941835i \(-0.609100\pi\)
−0.336076 + 0.941835i \(0.609100\pi\)
\(878\) −46.7092 −1.57636
\(879\) −44.8680 −1.51336
\(880\) 249.881 8.42348
\(881\) −41.7856 −1.40779 −0.703897 0.710302i \(-0.748558\pi\)
−0.703897 + 0.710302i \(0.748558\pi\)
\(882\) −6.22540 −0.209620
\(883\) 44.7678 1.50656 0.753279 0.657701i \(-0.228471\pi\)
0.753279 + 0.657701i \(0.228471\pi\)
\(884\) 197.202 6.63261
\(885\) −22.2945 −0.749421
\(886\) −14.0689 −0.472654
\(887\) −0.759985 −0.0255178 −0.0127589 0.999919i \(-0.504061\pi\)
−0.0127589 + 0.999919i \(0.504061\pi\)
\(888\) −47.8306 −1.60509
\(889\) −39.5424 −1.32621
\(890\) 1.30558 0.0437632
\(891\) 12.7719 0.427876
\(892\) −127.722 −4.27644
\(893\) 17.5698 0.587951
\(894\) −62.8041 −2.10048
\(895\) 52.8534 1.76669
\(896\) −72.4169 −2.41928
\(897\) 85.0727 2.84049
\(898\) 69.3572 2.31448
\(899\) 4.27027 0.142421
\(900\) 310.746 10.3582
\(901\) 35.6297 1.18700
\(902\) 62.1601 2.06970
\(903\) −38.7825 −1.29060
\(904\) −160.995 −5.35462
\(905\) 64.2127 2.13450
\(906\) −73.1038 −2.42871
\(907\) −2.38709 −0.0792619 −0.0396310 0.999214i \(-0.512618\pi\)
−0.0396310 + 0.999214i \(0.512618\pi\)
\(908\) 87.7952 2.91359
\(909\) 72.8441 2.41609
\(910\) −161.132 −5.34146
\(911\) 28.8785 0.956789 0.478394 0.878145i \(-0.341219\pi\)
0.478394 + 0.878145i \(0.341219\pi\)
\(912\) 315.472 10.4463
\(913\) 34.4718 1.14085
\(914\) 38.4615 1.27219
\(915\) 107.005 3.53749
\(916\) −123.346 −4.07545
\(917\) −34.8545 −1.15100
\(918\) 119.163 3.93295
\(919\) 4.67755 0.154298 0.0771491 0.997020i \(-0.475418\pi\)
0.0771491 + 0.997020i \(0.475418\pi\)
\(920\) 196.061 6.46396
\(921\) 51.8419 1.70825
\(922\) −4.23229 −0.139383
\(923\) 27.5647 0.907303
\(924\) −190.370 −6.26270
\(925\) −20.7404 −0.681939
\(926\) 38.1493 1.25366
\(927\) −23.1359 −0.759881
\(928\) 24.9647 0.819507
\(929\) 9.46111 0.310409 0.155204 0.987882i \(-0.450396\pi\)
0.155204 + 0.987882i \(0.450396\pi\)
\(930\) −100.533 −3.29662
\(931\) −3.54725 −0.116257
\(932\) −3.45043 −0.113023
\(933\) −83.8520 −2.74519
\(934\) 85.3962 2.79425
\(935\) 125.583 4.10700
\(936\) −255.434 −8.34911
\(937\) −20.1876 −0.659500 −0.329750 0.944068i \(-0.606965\pi\)
−0.329750 + 0.944068i \(0.606965\pi\)
\(938\) −60.3914 −1.97185
\(939\) 80.1583 2.61587
\(940\) −46.3889 −1.51304
\(941\) −21.2345 −0.692226 −0.346113 0.938193i \(-0.612499\pi\)
−0.346113 + 0.938193i \(0.612499\pi\)
\(942\) −158.228 −5.15536
\(943\) 27.3728 0.891382
\(944\) 26.2495 0.854347
\(945\) −70.7325 −2.30093
\(946\) −61.2660 −1.99193
\(947\) −50.8375 −1.65200 −0.825999 0.563672i \(-0.809388\pi\)
−0.825999 + 0.563672i \(0.809388\pi\)
\(948\) 24.6276 0.799869
\(949\) 85.8804 2.78779
\(950\) 243.738 7.90790
\(951\) 13.0333 0.422635
\(952\) −166.771 −5.40508
\(953\) 45.3000 1.46741 0.733706 0.679467i \(-0.237789\pi\)
0.733706 + 0.679467i \(0.237789\pi\)
\(954\) −74.0248 −2.39664
\(955\) 11.7943 0.381653
\(956\) −26.4374 −0.855046
\(957\) 17.4189 0.563073
\(958\) 57.2182 1.84864
\(959\) 2.90437 0.0937868
\(960\) −274.098 −8.84646
\(961\) −20.6213 −0.665202
\(962\) 27.3455 0.881655
\(963\) −10.5506 −0.339989
\(964\) 36.9180 1.18905
\(965\) 44.1389 1.42088
\(966\) −115.398 −3.71286
\(967\) 15.8230 0.508832 0.254416 0.967095i \(-0.418117\pi\)
0.254416 + 0.967095i \(0.418117\pi\)
\(968\) −88.9998 −2.86056
\(969\) 158.547 5.09326
\(970\) −32.2741 −1.03626
\(971\) 4.24996 0.136388 0.0681939 0.997672i \(-0.478276\pi\)
0.0681939 + 0.997672i \(0.478276\pi\)
\(972\) 60.2555 1.93270
\(973\) 11.7416 0.376417
\(974\) 1.69264 0.0542357
\(975\) −174.088 −5.57529
\(976\) −125.988 −4.03277
\(977\) −39.3404 −1.25861 −0.629306 0.777158i \(-0.716661\pi\)
−0.629306 + 0.777158i \(0.716661\pi\)
\(978\) −105.597 −3.37661
\(979\) −0.549799 −0.0175717
\(980\) 9.36567 0.299175
\(981\) −51.7682 −1.65283
\(982\) 72.7398 2.32122
\(983\) 22.8761 0.729634 0.364817 0.931079i \(-0.381132\pi\)
0.364817 + 0.931079i \(0.381132\pi\)
\(984\) −129.178 −4.11805
\(985\) −22.8100 −0.726786
\(986\) 24.4760 0.779476
\(987\) 17.0224 0.541830
\(988\) −233.454 −7.42715
\(989\) −26.9791 −0.857886
\(990\) −260.913 −8.29235
\(991\) 8.38581 0.266384 0.133192 0.991090i \(-0.457477\pi\)
0.133192 + 0.991090i \(0.457477\pi\)
\(992\) 60.6759 1.92646
\(993\) 1.37335 0.0435820
\(994\) −37.3904 −1.18595
\(995\) 30.7984 0.976376
\(996\) −114.905 −3.64090
\(997\) 10.5907 0.335411 0.167706 0.985837i \(-0.446364\pi\)
0.167706 + 0.985837i \(0.446364\pi\)
\(998\) 33.0257 1.04541
\(999\) 12.0040 0.379788
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.1.3 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.3 174 1.1 even 1 trivial