Properties

Label 4027.2.a.c.1.4
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 1.4
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} +O(q^{10})\) \(q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} -6.33447 q^{10} +0.0220541 q^{11} -2.52708 q^{12} -4.40501 q^{13} -3.53539 q^{14} -1.16960 q^{15} +12.0305 q^{16} +1.88399 q^{17} +7.36020 q^{18} +2.05105 q^{19} +12.1649 q^{20} -0.652774 q^{21} -0.0588757 q^{22} +3.94541 q^{23} +4.11453 q^{24} +0.630226 q^{25} +11.7596 q^{26} +2.83773 q^{27} +6.78948 q^{28} -8.40013 q^{29} +3.12236 q^{30} -5.95042 q^{31} -15.4220 q^{32} -0.0108708 q^{33} -5.02952 q^{34} +3.14234 q^{35} -14.1348 q^{36} -6.74280 q^{37} -5.47550 q^{38} +2.17130 q^{39} -19.8066 q^{40} -1.19570 q^{41} +1.74265 q^{42} +9.27473 q^{43} +0.113067 q^{44} -6.54192 q^{45} -10.5327 q^{46} +3.38827 q^{47} -5.93002 q^{48} -5.24620 q^{49} -1.68246 q^{50} -0.928651 q^{51} -22.5836 q^{52} -8.44209 q^{53} -7.57564 q^{54} +0.0523301 q^{55} -11.0545 q^{56} -1.01100 q^{57} +22.4250 q^{58} +8.17842 q^{59} -5.99629 q^{60} +7.87505 q^{61} +15.8853 q^{62} -3.65117 q^{63} +17.1098 q^{64} -10.4523 q^{65} +0.0290208 q^{66} +11.0828 q^{67} +9.65887 q^{68} -1.94475 q^{69} -8.38881 q^{70} +12.4430 q^{71} +23.0139 q^{72} +8.53257 q^{73} +18.0006 q^{74} -0.310649 q^{75} +10.5153 q^{76} +0.0292065 q^{77} -5.79652 q^{78} +2.13340 q^{79} +28.5461 q^{80} +6.87234 q^{81} +3.19206 q^{82} -9.19652 q^{83} -3.34664 q^{84} +4.47036 q^{85} -24.7599 q^{86} +4.14056 q^{87} -0.184093 q^{88} +16.1600 q^{89} +17.4643 q^{90} -5.83360 q^{91} +20.2273 q^{92} +2.93306 q^{93} -9.04535 q^{94} +4.86675 q^{95} +7.60177 q^{96} -10.1958 q^{97} +14.0053 q^{98} -0.0608039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66961 −1.88770 −0.943849 0.330378i \(-0.892824\pi\)
−0.943849 + 0.330378i \(0.892824\pi\)
\(3\) −0.492916 −0.284585 −0.142293 0.989825i \(-0.545447\pi\)
−0.142293 + 0.989825i \(0.545447\pi\)
\(4\) 5.12680 2.56340
\(5\) 2.37281 1.06115 0.530576 0.847637i \(-0.321976\pi\)
0.530576 + 0.847637i \(0.321976\pi\)
\(6\) 1.31589 0.537211
\(7\) 1.32431 0.500543 0.250271 0.968176i \(-0.419480\pi\)
0.250271 + 0.968176i \(0.419480\pi\)
\(8\) −8.34733 −2.95123
\(9\) −2.75703 −0.919011
\(10\) −6.33447 −2.00314
\(11\) 0.0220541 0.00664956 0.00332478 0.999994i \(-0.498942\pi\)
0.00332478 + 0.999994i \(0.498942\pi\)
\(12\) −2.52708 −0.729506
\(13\) −4.40501 −1.22173 −0.610865 0.791735i \(-0.709178\pi\)
−0.610865 + 0.791735i \(0.709178\pi\)
\(14\) −3.53539 −0.944873
\(15\) −1.16960 −0.301988
\(16\) 12.0305 3.00762
\(17\) 1.88399 0.456936 0.228468 0.973551i \(-0.426628\pi\)
0.228468 + 0.973551i \(0.426628\pi\)
\(18\) 7.36020 1.73482
\(19\) 2.05105 0.470543 0.235271 0.971930i \(-0.424402\pi\)
0.235271 + 0.971930i \(0.424402\pi\)
\(20\) 12.1649 2.72016
\(21\) −0.652774 −0.142447
\(22\) −0.0588757 −0.0125524
\(23\) 3.94541 0.822674 0.411337 0.911483i \(-0.365062\pi\)
0.411337 + 0.911483i \(0.365062\pi\)
\(24\) 4.11453 0.839876
\(25\) 0.630226 0.126045
\(26\) 11.7596 2.30626
\(27\) 2.83773 0.546122
\(28\) 6.78948 1.28309
\(29\) −8.40013 −1.55986 −0.779932 0.625864i \(-0.784747\pi\)
−0.779932 + 0.625864i \(0.784747\pi\)
\(30\) 3.12236 0.570063
\(31\) −5.95042 −1.06873 −0.534364 0.845255i \(-0.679449\pi\)
−0.534364 + 0.845255i \(0.679449\pi\)
\(32\) −15.4220 −2.72626
\(33\) −0.0108708 −0.00189237
\(34\) −5.02952 −0.862556
\(35\) 3.14234 0.531152
\(36\) −14.1348 −2.35579
\(37\) −6.74280 −1.10851 −0.554255 0.832347i \(-0.686997\pi\)
−0.554255 + 0.832347i \(0.686997\pi\)
\(38\) −5.47550 −0.888243
\(39\) 2.17130 0.347686
\(40\) −19.8066 −3.13170
\(41\) −1.19570 −0.186738 −0.0933688 0.995632i \(-0.529764\pi\)
−0.0933688 + 0.995632i \(0.529764\pi\)
\(42\) 1.74265 0.268897
\(43\) 9.27473 1.41438 0.707192 0.707022i \(-0.249962\pi\)
0.707192 + 0.707022i \(0.249962\pi\)
\(44\) 0.113067 0.0170455
\(45\) −6.54192 −0.975211
\(46\) −10.5327 −1.55296
\(47\) 3.38827 0.494230 0.247115 0.968986i \(-0.420517\pi\)
0.247115 + 0.968986i \(0.420517\pi\)
\(48\) −5.93002 −0.855925
\(49\) −5.24620 −0.749457
\(50\) −1.68246 −0.237935
\(51\) −0.928651 −0.130037
\(52\) −22.5836 −3.13178
\(53\) −8.44209 −1.15961 −0.579805 0.814755i \(-0.696871\pi\)
−0.579805 + 0.814755i \(0.696871\pi\)
\(54\) −7.57564 −1.03091
\(55\) 0.0523301 0.00705620
\(56\) −11.0545 −1.47722
\(57\) −1.01100 −0.133910
\(58\) 22.4250 2.94455
\(59\) 8.17842 1.06474 0.532370 0.846512i \(-0.321302\pi\)
0.532370 + 0.846512i \(0.321302\pi\)
\(60\) −5.99629 −0.774117
\(61\) 7.87505 1.00830 0.504148 0.863617i \(-0.331806\pi\)
0.504148 + 0.863617i \(0.331806\pi\)
\(62\) 15.8853 2.01743
\(63\) −3.65117 −0.460004
\(64\) 17.1098 2.13872
\(65\) −10.4523 −1.29644
\(66\) 0.0290208 0.00357221
\(67\) 11.0828 1.35398 0.676992 0.735990i \(-0.263283\pi\)
0.676992 + 0.735990i \(0.263283\pi\)
\(68\) 9.65887 1.17131
\(69\) −1.94475 −0.234121
\(70\) −8.38881 −1.00265
\(71\) 12.4430 1.47671 0.738355 0.674413i \(-0.235603\pi\)
0.738355 + 0.674413i \(0.235603\pi\)
\(72\) 23.0139 2.71221
\(73\) 8.53257 0.998661 0.499331 0.866412i \(-0.333579\pi\)
0.499331 + 0.866412i \(0.333579\pi\)
\(74\) 18.0006 2.09253
\(75\) −0.310649 −0.0358706
\(76\) 10.5153 1.20619
\(77\) 0.0292065 0.00332839
\(78\) −5.79652 −0.656326
\(79\) 2.13340 0.240027 0.120013 0.992772i \(-0.461706\pi\)
0.120013 + 0.992772i \(0.461706\pi\)
\(80\) 28.5461 3.19155
\(81\) 6.87234 0.763593
\(82\) 3.19206 0.352504
\(83\) −9.19652 −1.00945 −0.504725 0.863280i \(-0.668406\pi\)
−0.504725 + 0.863280i \(0.668406\pi\)
\(84\) −3.34664 −0.365149
\(85\) 4.47036 0.484879
\(86\) −24.7599 −2.66993
\(87\) 4.14056 0.443914
\(88\) −0.184093 −0.0196244
\(89\) 16.1600 1.71296 0.856479 0.516182i \(-0.172647\pi\)
0.856479 + 0.516182i \(0.172647\pi\)
\(90\) 17.4643 1.84090
\(91\) −5.83360 −0.611528
\(92\) 20.2273 2.10884
\(93\) 2.93306 0.304144
\(94\) −9.04535 −0.932956
\(95\) 4.86675 0.499318
\(96\) 7.60177 0.775852
\(97\) −10.1958 −1.03522 −0.517612 0.855616i \(-0.673179\pi\)
−0.517612 + 0.855616i \(0.673179\pi\)
\(98\) 14.0053 1.41475
\(99\) −0.0608039 −0.00611102
\(100\) 3.23104 0.323104
\(101\) 9.17371 0.912818 0.456409 0.889770i \(-0.349135\pi\)
0.456409 + 0.889770i \(0.349135\pi\)
\(102\) 2.47913 0.245471
\(103\) −10.2688 −1.01182 −0.505908 0.862588i \(-0.668842\pi\)
−0.505908 + 0.862588i \(0.668842\pi\)
\(104\) 36.7701 3.60560
\(105\) −1.54891 −0.151158
\(106\) 22.5371 2.18899
\(107\) 14.2555 1.37813 0.689065 0.724700i \(-0.258022\pi\)
0.689065 + 0.724700i \(0.258022\pi\)
\(108\) 14.5485 1.39993
\(109\) 10.0984 0.967255 0.483627 0.875274i \(-0.339319\pi\)
0.483627 + 0.875274i \(0.339319\pi\)
\(110\) −0.139701 −0.0133200
\(111\) 3.32363 0.315465
\(112\) 15.9321 1.50544
\(113\) −0.296080 −0.0278528 −0.0139264 0.999903i \(-0.504433\pi\)
−0.0139264 + 0.999903i \(0.504433\pi\)
\(114\) 2.69896 0.252781
\(115\) 9.36170 0.872983
\(116\) −43.0658 −3.99856
\(117\) 12.1448 1.12278
\(118\) −21.8332 −2.00991
\(119\) 2.49500 0.228716
\(120\) 9.76301 0.891237
\(121\) −10.9995 −0.999956
\(122\) −21.0233 −1.90336
\(123\) 0.589382 0.0531428
\(124\) −30.5066 −2.73958
\(125\) −10.3686 −0.927400
\(126\) 9.74719 0.868349
\(127\) 7.28789 0.646695 0.323348 0.946280i \(-0.395192\pi\)
0.323348 + 0.946280i \(0.395192\pi\)
\(128\) −14.8323 −1.31100
\(129\) −4.57166 −0.402513
\(130\) 27.9034 2.44729
\(131\) 20.0345 1.75042 0.875212 0.483739i \(-0.160722\pi\)
0.875212 + 0.483739i \(0.160722\pi\)
\(132\) −0.0557325 −0.00485089
\(133\) 2.71623 0.235527
\(134\) −29.5868 −2.55591
\(135\) 6.73340 0.579519
\(136\) −15.7263 −1.34852
\(137\) 20.2975 1.73413 0.867066 0.498193i \(-0.166003\pi\)
0.867066 + 0.498193i \(0.166003\pi\)
\(138\) 5.19173 0.441949
\(139\) −13.9576 −1.18387 −0.591933 0.805987i \(-0.701635\pi\)
−0.591933 + 0.805987i \(0.701635\pi\)
\(140\) 16.1101 1.36156
\(141\) −1.67013 −0.140651
\(142\) −33.2178 −2.78758
\(143\) −0.0971485 −0.00812396
\(144\) −33.1685 −2.76404
\(145\) −19.9319 −1.65525
\(146\) −22.7786 −1.88517
\(147\) 2.58594 0.213284
\(148\) −34.5690 −2.84155
\(149\) −15.9273 −1.30482 −0.652409 0.757867i \(-0.726242\pi\)
−0.652409 + 0.757867i \(0.726242\pi\)
\(150\) 0.829310 0.0677128
\(151\) −10.0185 −0.815296 −0.407648 0.913139i \(-0.633651\pi\)
−0.407648 + 0.913139i \(0.633651\pi\)
\(152\) −17.1208 −1.38868
\(153\) −5.19424 −0.419929
\(154\) −0.0779698 −0.00628299
\(155\) −14.1192 −1.13408
\(156\) 11.1318 0.891259
\(157\) −2.64432 −0.211040 −0.105520 0.994417i \(-0.533651\pi\)
−0.105520 + 0.994417i \(0.533651\pi\)
\(158\) −5.69535 −0.453098
\(159\) 4.16124 0.330008
\(160\) −36.5935 −2.89297
\(161\) 5.22495 0.411783
\(162\) −18.3464 −1.44143
\(163\) 20.5807 1.61201 0.806003 0.591911i \(-0.201626\pi\)
0.806003 + 0.591911i \(0.201626\pi\)
\(164\) −6.13014 −0.478683
\(165\) −0.0257944 −0.00200809
\(166\) 24.5511 1.90554
\(167\) 24.7481 1.91507 0.957534 0.288320i \(-0.0930965\pi\)
0.957534 + 0.288320i \(0.0930965\pi\)
\(168\) 5.44892 0.420394
\(169\) 6.40411 0.492624
\(170\) −11.9341 −0.915304
\(171\) −5.65481 −0.432434
\(172\) 47.5497 3.62563
\(173\) 18.9480 1.44059 0.720294 0.693668i \(-0.244007\pi\)
0.720294 + 0.693668i \(0.244007\pi\)
\(174\) −11.0537 −0.837976
\(175\) 0.834615 0.0630910
\(176\) 0.265322 0.0199994
\(177\) −4.03127 −0.303009
\(178\) −43.1409 −3.23355
\(179\) −23.0060 −1.71955 −0.859775 0.510672i \(-0.829397\pi\)
−0.859775 + 0.510672i \(0.829397\pi\)
\(180\) −33.5391 −2.49986
\(181\) 15.1869 1.12884 0.564418 0.825489i \(-0.309101\pi\)
0.564418 + 0.825489i \(0.309101\pi\)
\(182\) 15.5734 1.15438
\(183\) −3.88174 −0.286946
\(184\) −32.9336 −2.42790
\(185\) −15.9994 −1.17630
\(186\) −7.83011 −0.574132
\(187\) 0.0415498 0.00303842
\(188\) 17.3710 1.26691
\(189\) 3.75804 0.273357
\(190\) −12.9923 −0.942561
\(191\) 12.0887 0.874709 0.437354 0.899289i \(-0.355916\pi\)
0.437354 + 0.899289i \(0.355916\pi\)
\(192\) −8.43368 −0.608649
\(193\) −12.5731 −0.905033 −0.452517 0.891756i \(-0.649474\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(194\) 27.2187 1.95419
\(195\) 5.15208 0.368948
\(196\) −26.8962 −1.92116
\(197\) 22.3065 1.58927 0.794635 0.607088i \(-0.207662\pi\)
0.794635 + 0.607088i \(0.207662\pi\)
\(198\) 0.162322 0.0115358
\(199\) −6.79573 −0.481737 −0.240868 0.970558i \(-0.577432\pi\)
−0.240868 + 0.970558i \(0.577432\pi\)
\(200\) −5.26071 −0.371988
\(201\) −5.46291 −0.385324
\(202\) −24.4902 −1.72312
\(203\) −11.1244 −0.780779
\(204\) −4.76101 −0.333337
\(205\) −2.83718 −0.198157
\(206\) 27.4137 1.91000
\(207\) −10.8776 −0.756047
\(208\) −52.9945 −3.67450
\(209\) 0.0452340 0.00312890
\(210\) 4.13498 0.285341
\(211\) −4.85204 −0.334028 −0.167014 0.985954i \(-0.553413\pi\)
−0.167014 + 0.985954i \(0.553413\pi\)
\(212\) −43.2809 −2.97255
\(213\) −6.13334 −0.420250
\(214\) −38.0565 −2.60149
\(215\) 22.0072 1.50088
\(216\) −23.6875 −1.61173
\(217\) −7.88021 −0.534944
\(218\) −26.9589 −1.82588
\(219\) −4.20584 −0.284204
\(220\) 0.268286 0.0180879
\(221\) −8.29901 −0.558252
\(222\) −8.87280 −0.595503
\(223\) 10.7977 0.723070 0.361535 0.932359i \(-0.382253\pi\)
0.361535 + 0.932359i \(0.382253\pi\)
\(224\) −20.4236 −1.36461
\(225\) −1.73755 −0.115837
\(226\) 0.790416 0.0525777
\(227\) −19.5689 −1.29884 −0.649418 0.760432i \(-0.724987\pi\)
−0.649418 + 0.760432i \(0.724987\pi\)
\(228\) −5.18317 −0.343264
\(229\) 0.850754 0.0562194 0.0281097 0.999605i \(-0.491051\pi\)
0.0281097 + 0.999605i \(0.491051\pi\)
\(230\) −24.9921 −1.64793
\(231\) −0.0143963 −0.000947210 0
\(232\) 70.1187 4.60352
\(233\) 25.9394 1.69935 0.849673 0.527309i \(-0.176799\pi\)
0.849673 + 0.527309i \(0.176799\pi\)
\(234\) −32.4217 −2.11948
\(235\) 8.03972 0.524453
\(236\) 41.9291 2.72935
\(237\) −1.05159 −0.0683081
\(238\) −6.66066 −0.431746
\(239\) 5.87878 0.380267 0.190133 0.981758i \(-0.439108\pi\)
0.190133 + 0.981758i \(0.439108\pi\)
\(240\) −14.0708 −0.908268
\(241\) 14.2429 0.917469 0.458734 0.888573i \(-0.348303\pi\)
0.458734 + 0.888573i \(0.348303\pi\)
\(242\) 29.3644 1.88761
\(243\) −11.9007 −0.763429
\(244\) 40.3738 2.58467
\(245\) −12.4482 −0.795288
\(246\) −1.57342 −0.100317
\(247\) −9.03489 −0.574876
\(248\) 49.6702 3.15406
\(249\) 4.53311 0.287274
\(250\) 27.6802 1.75065
\(251\) −10.9668 −0.692219 −0.346110 0.938194i \(-0.612497\pi\)
−0.346110 + 0.938194i \(0.612497\pi\)
\(252\) −18.7188 −1.17918
\(253\) 0.0870123 0.00547042
\(254\) −19.4558 −1.22077
\(255\) −2.20351 −0.137989
\(256\) 5.37689 0.336056
\(257\) 21.3539 1.33202 0.666008 0.745944i \(-0.268002\pi\)
0.666008 + 0.745944i \(0.268002\pi\)
\(258\) 12.2045 0.759822
\(259\) −8.92957 −0.554856
\(260\) −53.5866 −3.32330
\(261\) 23.1594 1.43353
\(262\) −53.4843 −3.30427
\(263\) 9.63154 0.593906 0.296953 0.954892i \(-0.404029\pi\)
0.296953 + 0.954892i \(0.404029\pi\)
\(264\) 0.0907423 0.00558480
\(265\) −20.0315 −1.23052
\(266\) −7.25126 −0.444603
\(267\) −7.96553 −0.487482
\(268\) 56.8195 3.47081
\(269\) −2.12980 −0.129856 −0.0649282 0.997890i \(-0.520682\pi\)
−0.0649282 + 0.997890i \(0.520682\pi\)
\(270\) −17.9755 −1.09396
\(271\) 1.52317 0.0925262 0.0462631 0.998929i \(-0.485269\pi\)
0.0462631 + 0.998929i \(0.485269\pi\)
\(272\) 22.6654 1.37429
\(273\) 2.87548 0.174032
\(274\) −54.1864 −3.27352
\(275\) 0.0138991 0.000838145 0
\(276\) −9.97037 −0.600146
\(277\) −11.6260 −0.698536 −0.349268 0.937023i \(-0.613570\pi\)
−0.349268 + 0.937023i \(0.613570\pi\)
\(278\) 37.2613 2.23478
\(279\) 16.4055 0.982172
\(280\) −26.2301 −1.56755
\(281\) −24.5100 −1.46215 −0.731073 0.682300i \(-0.760980\pi\)
−0.731073 + 0.682300i \(0.760980\pi\)
\(282\) 4.45860 0.265506
\(283\) −6.50918 −0.386931 −0.193465 0.981107i \(-0.561973\pi\)
−0.193465 + 0.981107i \(0.561973\pi\)
\(284\) 63.7927 3.78540
\(285\) −2.39890 −0.142099
\(286\) 0.259348 0.0153356
\(287\) −1.58348 −0.0934701
\(288\) 42.5191 2.50546
\(289\) −13.4506 −0.791210
\(290\) 53.2104 3.12462
\(291\) 5.02566 0.294609
\(292\) 43.7448 2.55997
\(293\) 11.4226 0.667314 0.333657 0.942695i \(-0.391717\pi\)
0.333657 + 0.942695i \(0.391717\pi\)
\(294\) −6.90343 −0.402616
\(295\) 19.4058 1.12985
\(296\) 56.2844 3.27146
\(297\) 0.0625836 0.00363147
\(298\) 42.5197 2.46310
\(299\) −17.3796 −1.00509
\(300\) −1.59263 −0.0919507
\(301\) 12.2826 0.707959
\(302\) 26.7455 1.53903
\(303\) −4.52187 −0.259775
\(304\) 24.6751 1.41522
\(305\) 18.6860 1.06996
\(306\) 13.8666 0.792699
\(307\) −3.66332 −0.209077 −0.104538 0.994521i \(-0.533336\pi\)
−0.104538 + 0.994521i \(0.533336\pi\)
\(308\) 0.149736 0.00853199
\(309\) 5.06166 0.287948
\(310\) 37.6928 2.14081
\(311\) −18.6634 −1.05830 −0.529152 0.848527i \(-0.677490\pi\)
−0.529152 + 0.848527i \(0.677490\pi\)
\(312\) −18.1246 −1.02610
\(313\) 21.5401 1.21752 0.608759 0.793355i \(-0.291667\pi\)
0.608759 + 0.793355i \(0.291667\pi\)
\(314\) 7.05930 0.398380
\(315\) −8.66353 −0.488135
\(316\) 10.9375 0.615285
\(317\) 17.0387 0.956991 0.478495 0.878090i \(-0.341182\pi\)
0.478495 + 0.878090i \(0.341182\pi\)
\(318\) −11.1089 −0.622955
\(319\) −0.185257 −0.0103724
\(320\) 40.5982 2.26951
\(321\) −7.02676 −0.392195
\(322\) −13.9486 −0.777323
\(323\) 3.86417 0.215008
\(324\) 35.2331 1.95739
\(325\) −2.77615 −0.153993
\(326\) −54.9424 −3.04298
\(327\) −4.97768 −0.275266
\(328\) 9.98094 0.551105
\(329\) 4.48712 0.247383
\(330\) 0.0688608 0.00379066
\(331\) −27.5665 −1.51519 −0.757595 0.652725i \(-0.773626\pi\)
−0.757595 + 0.652725i \(0.773626\pi\)
\(332\) −47.1488 −2.58762
\(333\) 18.5901 1.01873
\(334\) −66.0678 −3.61507
\(335\) 26.2975 1.43678
\(336\) −7.85320 −0.428427
\(337\) 8.06440 0.439296 0.219648 0.975579i \(-0.429509\pi\)
0.219648 + 0.975579i \(0.429509\pi\)
\(338\) −17.0965 −0.929925
\(339\) 0.145942 0.00792650
\(340\) 22.9187 1.24294
\(341\) −0.131231 −0.00710656
\(342\) 15.0961 0.816305
\(343\) −16.2178 −0.875678
\(344\) −77.4193 −4.17417
\(345\) −4.61453 −0.248438
\(346\) −50.5837 −2.71940
\(347\) 20.8078 1.11702 0.558511 0.829497i \(-0.311373\pi\)
0.558511 + 0.829497i \(0.311373\pi\)
\(348\) 21.2278 1.13793
\(349\) 1.36090 0.0728471 0.0364236 0.999336i \(-0.488403\pi\)
0.0364236 + 0.999336i \(0.488403\pi\)
\(350\) −2.22810 −0.119097
\(351\) −12.5002 −0.667214
\(352\) −0.340119 −0.0181284
\(353\) 4.77241 0.254010 0.127005 0.991902i \(-0.459464\pi\)
0.127005 + 0.991902i \(0.459464\pi\)
\(354\) 10.7619 0.571989
\(355\) 29.5248 1.56701
\(356\) 82.8492 4.39100
\(357\) −1.22982 −0.0650891
\(358\) 61.4170 3.24599
\(359\) −27.8749 −1.47118 −0.735591 0.677426i \(-0.763096\pi\)
−0.735591 + 0.677426i \(0.763096\pi\)
\(360\) 54.6076 2.87807
\(361\) −14.7932 −0.778589
\(362\) −40.5431 −2.13090
\(363\) 5.42184 0.284573
\(364\) −29.9077 −1.56759
\(365\) 20.2462 1.05973
\(366\) 10.3627 0.541668
\(367\) −7.67869 −0.400825 −0.200412 0.979712i \(-0.564228\pi\)
−0.200412 + 0.979712i \(0.564228\pi\)
\(368\) 47.4652 2.47429
\(369\) 3.29660 0.171614
\(370\) 42.7121 2.22049
\(371\) −11.1800 −0.580435
\(372\) 15.0372 0.779643
\(373\) 1.29300 0.0669492 0.0334746 0.999440i \(-0.489343\pi\)
0.0334746 + 0.999440i \(0.489343\pi\)
\(374\) −0.110922 −0.00573562
\(375\) 5.11087 0.263924
\(376\) −28.2830 −1.45859
\(377\) 37.0026 1.90573
\(378\) −10.0325 −0.516016
\(379\) −16.1562 −0.829889 −0.414944 0.909847i \(-0.636199\pi\)
−0.414944 + 0.909847i \(0.636199\pi\)
\(380\) 24.9509 1.27995
\(381\) −3.59232 −0.184040
\(382\) −32.2721 −1.65119
\(383\) 6.91868 0.353528 0.176764 0.984253i \(-0.443437\pi\)
0.176764 + 0.984253i \(0.443437\pi\)
\(384\) 7.31108 0.373092
\(385\) 0.0693014 0.00353193
\(386\) 33.5653 1.70843
\(387\) −25.5708 −1.29983
\(388\) −52.2717 −2.65369
\(389\) 28.0120 1.42027 0.710133 0.704067i \(-0.248635\pi\)
0.710133 + 0.704067i \(0.248635\pi\)
\(390\) −13.7540 −0.696463
\(391\) 7.43312 0.375909
\(392\) 43.7918 2.21182
\(393\) −9.87534 −0.498145
\(394\) −59.5495 −3.00006
\(395\) 5.06216 0.254705
\(396\) −0.311729 −0.0156650
\(397\) 8.03898 0.403465 0.201732 0.979441i \(-0.435343\pi\)
0.201732 + 0.979441i \(0.435343\pi\)
\(398\) 18.1419 0.909373
\(399\) −1.33887 −0.0670275
\(400\) 7.58193 0.379097
\(401\) −27.1278 −1.35470 −0.677349 0.735662i \(-0.736871\pi\)
−0.677349 + 0.735662i \(0.736871\pi\)
\(402\) 14.5838 0.727375
\(403\) 26.2117 1.30570
\(404\) 47.0318 2.33992
\(405\) 16.3067 0.810289
\(406\) 29.6977 1.47387
\(407\) −0.148706 −0.00737110
\(408\) 7.75176 0.383769
\(409\) −38.9578 −1.92634 −0.963169 0.268896i \(-0.913341\pi\)
−0.963169 + 0.268896i \(0.913341\pi\)
\(410\) 7.57415 0.374061
\(411\) −10.0050 −0.493508
\(412\) −52.6461 −2.59369
\(413\) 10.8308 0.532947
\(414\) 29.0390 1.42719
\(415\) −21.8216 −1.07118
\(416\) 67.9342 3.33075
\(417\) 6.87992 0.336911
\(418\) −0.120757 −0.00590642
\(419\) −0.585367 −0.0285970 −0.0142985 0.999898i \(-0.504552\pi\)
−0.0142985 + 0.999898i \(0.504552\pi\)
\(420\) −7.94095 −0.387479
\(421\) 13.8168 0.673389 0.336695 0.941614i \(-0.390691\pi\)
0.336695 + 0.941614i \(0.390691\pi\)
\(422\) 12.9531 0.630545
\(423\) −9.34157 −0.454203
\(424\) 70.4690 3.42228
\(425\) 1.18734 0.0575946
\(426\) 16.3736 0.793304
\(427\) 10.4290 0.504695
\(428\) 73.0850 3.53270
\(429\) 0.0478860 0.00231196
\(430\) −58.7505 −2.83320
\(431\) −6.20793 −0.299026 −0.149513 0.988760i \(-0.547771\pi\)
−0.149513 + 0.988760i \(0.547771\pi\)
\(432\) 34.1394 1.64253
\(433\) −31.4001 −1.50899 −0.754495 0.656306i \(-0.772118\pi\)
−0.754495 + 0.656306i \(0.772118\pi\)
\(434\) 21.0371 1.00981
\(435\) 9.82476 0.471061
\(436\) 51.7727 2.47946
\(437\) 8.09222 0.387103
\(438\) 11.2279 0.536492
\(439\) 23.4294 1.11822 0.559111 0.829093i \(-0.311142\pi\)
0.559111 + 0.829093i \(0.311142\pi\)
\(440\) −0.436817 −0.0208244
\(441\) 14.4639 0.688759
\(442\) 22.1551 1.05381
\(443\) −18.1083 −0.860349 −0.430175 0.902746i \(-0.641548\pi\)
−0.430175 + 0.902746i \(0.641548\pi\)
\(444\) 17.0396 0.808664
\(445\) 38.3446 1.81771
\(446\) −28.8257 −1.36494
\(447\) 7.85084 0.371332
\(448\) 22.6587 1.07052
\(449\) −5.18463 −0.244678 −0.122339 0.992488i \(-0.539039\pi\)
−0.122339 + 0.992488i \(0.539039\pi\)
\(450\) 4.63859 0.218665
\(451\) −0.0263702 −0.00124172
\(452\) −1.51794 −0.0713980
\(453\) 4.93829 0.232021
\(454\) 52.2414 2.45181
\(455\) −13.8420 −0.648925
\(456\) 8.43911 0.395198
\(457\) 33.6054 1.57200 0.785998 0.618229i \(-0.212150\pi\)
0.785998 + 0.618229i \(0.212150\pi\)
\(458\) −2.27118 −0.106125
\(459\) 5.34628 0.249543
\(460\) 47.9956 2.23781
\(461\) 10.0720 0.469100 0.234550 0.972104i \(-0.424638\pi\)
0.234550 + 0.972104i \(0.424638\pi\)
\(462\) 0.0384326 0.00178805
\(463\) −2.62919 −0.122189 −0.0610945 0.998132i \(-0.519459\pi\)
−0.0610945 + 0.998132i \(0.519459\pi\)
\(464\) −101.058 −4.69149
\(465\) 6.95959 0.322743
\(466\) −69.2480 −3.20785
\(467\) −21.1690 −0.979584 −0.489792 0.871839i \(-0.662927\pi\)
−0.489792 + 0.871839i \(0.662927\pi\)
\(468\) 62.2638 2.87814
\(469\) 14.6771 0.677727
\(470\) −21.4629 −0.990009
\(471\) 1.30343 0.0600589
\(472\) −68.2680 −3.14229
\(473\) 0.204546 0.00940502
\(474\) 2.80733 0.128945
\(475\) 1.29262 0.0593097
\(476\) 12.7913 0.586290
\(477\) 23.2751 1.06570
\(478\) −15.6940 −0.717829
\(479\) 22.3250 1.02005 0.510027 0.860159i \(-0.329635\pi\)
0.510027 + 0.860159i \(0.329635\pi\)
\(480\) 18.0375 0.823298
\(481\) 29.7021 1.35430
\(482\) −38.0231 −1.73190
\(483\) −2.57546 −0.117187
\(484\) −56.3923 −2.56329
\(485\) −24.1926 −1.09853
\(486\) 31.7702 1.44112
\(487\) −12.3971 −0.561765 −0.280882 0.959742i \(-0.590627\pi\)
−0.280882 + 0.959742i \(0.590627\pi\)
\(488\) −65.7357 −2.97571
\(489\) −10.1446 −0.458753
\(490\) 33.2319 1.50126
\(491\) 21.6477 0.976948 0.488474 0.872578i \(-0.337554\pi\)
0.488474 + 0.872578i \(0.337554\pi\)
\(492\) 3.02164 0.136226
\(493\) −15.8258 −0.712758
\(494\) 24.1196 1.08519
\(495\) −0.144276 −0.00648472
\(496\) −71.5865 −3.21433
\(497\) 16.4784 0.739156
\(498\) −12.1016 −0.542287
\(499\) 36.3551 1.62748 0.813739 0.581230i \(-0.197428\pi\)
0.813739 + 0.581230i \(0.197428\pi\)
\(500\) −53.1580 −2.37730
\(501\) −12.1988 −0.545000
\(502\) 29.2771 1.30670
\(503\) 5.55810 0.247823 0.123912 0.992293i \(-0.460456\pi\)
0.123912 + 0.992293i \(0.460456\pi\)
\(504\) 30.4775 1.35758
\(505\) 21.7675 0.968640
\(506\) −0.232289 −0.0103265
\(507\) −3.15669 −0.140194
\(508\) 37.3636 1.65774
\(509\) 4.79382 0.212483 0.106241 0.994340i \(-0.466118\pi\)
0.106241 + 0.994340i \(0.466118\pi\)
\(510\) 5.88251 0.260482
\(511\) 11.2998 0.499873
\(512\) 15.3104 0.676632
\(513\) 5.82033 0.256974
\(514\) −57.0064 −2.51444
\(515\) −24.3659 −1.07369
\(516\) −23.4380 −1.03180
\(517\) 0.0747252 0.00328641
\(518\) 23.8384 1.04740
\(519\) −9.33977 −0.409970
\(520\) 87.2484 3.82610
\(521\) 7.89807 0.346021 0.173010 0.984920i \(-0.444651\pi\)
0.173010 + 0.984920i \(0.444651\pi\)
\(522\) −61.8266 −2.70608
\(523\) −7.69827 −0.336622 −0.168311 0.985734i \(-0.553831\pi\)
−0.168311 + 0.985734i \(0.553831\pi\)
\(524\) 102.713 4.48704
\(525\) −0.411395 −0.0179548
\(526\) −25.7124 −1.12112
\(527\) −11.2106 −0.488340
\(528\) −0.130781 −0.00569152
\(529\) −7.43377 −0.323207
\(530\) 53.4762 2.32286
\(531\) −22.5482 −0.978507
\(532\) 13.9256 0.603750
\(533\) 5.26709 0.228143
\(534\) 21.2648 0.920219
\(535\) 33.8255 1.46241
\(536\) −92.5122 −3.99592
\(537\) 11.3400 0.489359
\(538\) 5.68573 0.245129
\(539\) −0.115700 −0.00498356
\(540\) 34.5208 1.48554
\(541\) −9.72119 −0.417947 −0.208973 0.977921i \(-0.567012\pi\)
−0.208973 + 0.977921i \(0.567012\pi\)
\(542\) −4.06627 −0.174661
\(543\) −7.48588 −0.321250
\(544\) −29.0550 −1.24572
\(545\) 23.9617 1.02641
\(546\) −7.67640 −0.328519
\(547\) 44.4771 1.90170 0.950851 0.309649i \(-0.100212\pi\)
0.950851 + 0.309649i \(0.100212\pi\)
\(548\) 104.061 4.44528
\(549\) −21.7118 −0.926636
\(550\) −0.0371050 −0.00158216
\(551\) −17.2291 −0.733983
\(552\) 16.2335 0.690944
\(553\) 2.82529 0.120144
\(554\) 31.0367 1.31862
\(555\) 7.88635 0.334757
\(556\) −71.5578 −3.03473
\(557\) 13.1352 0.556558 0.278279 0.960500i \(-0.410236\pi\)
0.278279 + 0.960500i \(0.410236\pi\)
\(558\) −43.7963 −1.85404
\(559\) −40.8553 −1.72799
\(560\) 37.8039 1.59751
\(561\) −0.0204805 −0.000864689 0
\(562\) 65.4321 2.76009
\(563\) 25.1592 1.06033 0.530167 0.847893i \(-0.322129\pi\)
0.530167 + 0.847893i \(0.322129\pi\)
\(564\) −8.56244 −0.360544
\(565\) −0.702541 −0.0295561
\(566\) 17.3770 0.730408
\(567\) 9.10111 0.382211
\(568\) −103.866 −4.35811
\(569\) −13.6901 −0.573919 −0.286960 0.957943i \(-0.592645\pi\)
−0.286960 + 0.957943i \(0.592645\pi\)
\(570\) 6.40412 0.268239
\(571\) 35.9345 1.50381 0.751907 0.659269i \(-0.229134\pi\)
0.751907 + 0.659269i \(0.229134\pi\)
\(572\) −0.498061 −0.0208250
\(573\) −5.95872 −0.248929
\(574\) 4.22728 0.176443
\(575\) 2.48650 0.103694
\(576\) −47.1722 −1.96551
\(577\) −24.9740 −1.03968 −0.519840 0.854264i \(-0.674008\pi\)
−0.519840 + 0.854264i \(0.674008\pi\)
\(578\) 35.9077 1.49356
\(579\) 6.19749 0.257559
\(580\) −102.187 −4.24308
\(581\) −12.1791 −0.505273
\(582\) −13.4165 −0.556133
\(583\) −0.186183 −0.00771090
\(584\) −71.2242 −2.94728
\(585\) 28.8172 1.19144
\(586\) −30.4938 −1.25969
\(587\) −11.5977 −0.478689 −0.239344 0.970935i \(-0.576933\pi\)
−0.239344 + 0.970935i \(0.576933\pi\)
\(588\) 13.2576 0.546733
\(589\) −12.2046 −0.502882
\(590\) −51.8059 −2.13282
\(591\) −10.9952 −0.452283
\(592\) −81.1192 −3.33398
\(593\) 1.85002 0.0759711 0.0379856 0.999278i \(-0.487906\pi\)
0.0379856 + 0.999278i \(0.487906\pi\)
\(594\) −0.167074 −0.00685512
\(595\) 5.92015 0.242702
\(596\) −81.6563 −3.34477
\(597\) 3.34973 0.137095
\(598\) 46.3966 1.89730
\(599\) 20.0959 0.821098 0.410549 0.911839i \(-0.365337\pi\)
0.410549 + 0.911839i \(0.365337\pi\)
\(600\) 2.59309 0.105862
\(601\) 43.0798 1.75726 0.878631 0.477501i \(-0.158457\pi\)
0.878631 + 0.477501i \(0.158457\pi\)
\(602\) −32.7898 −1.33641
\(603\) −30.5558 −1.24433
\(604\) −51.3630 −2.08993
\(605\) −26.0998 −1.06111
\(606\) 12.0716 0.490376
\(607\) 9.31075 0.377912 0.188956 0.981986i \(-0.439490\pi\)
0.188956 + 0.981986i \(0.439490\pi\)
\(608\) −31.6313 −1.28282
\(609\) 5.48339 0.222198
\(610\) −49.8843 −2.01975
\(611\) −14.9254 −0.603815
\(612\) −26.6298 −1.07645
\(613\) 23.7679 0.959978 0.479989 0.877274i \(-0.340641\pi\)
0.479989 + 0.877274i \(0.340641\pi\)
\(614\) 9.77962 0.394673
\(615\) 1.39849 0.0563926
\(616\) −0.243796 −0.00982283
\(617\) −30.2247 −1.21680 −0.608400 0.793630i \(-0.708188\pi\)
−0.608400 + 0.793630i \(0.708188\pi\)
\(618\) −13.5126 −0.543558
\(619\) 19.0637 0.766234 0.383117 0.923700i \(-0.374851\pi\)
0.383117 + 0.923700i \(0.374851\pi\)
\(620\) −72.3864 −2.90711
\(621\) 11.1960 0.449281
\(622\) 49.8240 1.99776
\(623\) 21.4009 0.857408
\(624\) 26.1218 1.04571
\(625\) −27.7539 −1.11016
\(626\) −57.5036 −2.29831
\(627\) −0.0222966 −0.000890439 0
\(628\) −13.5569 −0.540980
\(629\) −12.7034 −0.506518
\(630\) 23.1282 0.921451
\(631\) 36.3233 1.44601 0.723005 0.690843i \(-0.242761\pi\)
0.723005 + 0.690843i \(0.242761\pi\)
\(632\) −17.8082 −0.708374
\(633\) 2.39165 0.0950596
\(634\) −45.4867 −1.80651
\(635\) 17.2928 0.686243
\(636\) 21.3339 0.845943
\(637\) 23.1096 0.915634
\(638\) 0.494564 0.0195800
\(639\) −34.3057 −1.35711
\(640\) −35.1942 −1.39117
\(641\) −23.0023 −0.908537 −0.454269 0.890865i \(-0.650099\pi\)
−0.454269 + 0.890865i \(0.650099\pi\)
\(642\) 18.7587 0.740346
\(643\) 39.3735 1.55274 0.776369 0.630279i \(-0.217059\pi\)
0.776369 + 0.630279i \(0.217059\pi\)
\(644\) 26.7873 1.05557
\(645\) −10.8477 −0.427127
\(646\) −10.3158 −0.405870
\(647\) 11.3424 0.445915 0.222958 0.974828i \(-0.428429\pi\)
0.222958 + 0.974828i \(0.428429\pi\)
\(648\) −57.3657 −2.25354
\(649\) 0.180368 0.00708004
\(650\) 7.41124 0.290693
\(651\) 3.88428 0.152237
\(652\) 105.513 4.13222
\(653\) 33.8088 1.32304 0.661519 0.749928i \(-0.269912\pi\)
0.661519 + 0.749928i \(0.269912\pi\)
\(654\) 13.2885 0.519620
\(655\) 47.5381 1.85747
\(656\) −14.3849 −0.561637
\(657\) −23.5246 −0.917781
\(658\) −11.9789 −0.466984
\(659\) 38.8880 1.51486 0.757430 0.652916i \(-0.226455\pi\)
0.757430 + 0.652916i \(0.226455\pi\)
\(660\) −0.132243 −0.00514754
\(661\) 48.7096 1.89458 0.947292 0.320371i \(-0.103808\pi\)
0.947292 + 0.320371i \(0.103808\pi\)
\(662\) 73.5917 2.86022
\(663\) 4.09072 0.158870
\(664\) 76.7665 2.97912
\(665\) 6.44509 0.249930
\(666\) −49.6283 −1.92306
\(667\) −33.1419 −1.28326
\(668\) 126.879 4.90909
\(669\) −5.32238 −0.205775
\(670\) −70.2039 −2.71221
\(671\) 0.173677 0.00670473
\(672\) 10.0671 0.388347
\(673\) 11.3809 0.438702 0.219351 0.975646i \(-0.429606\pi\)
0.219351 + 0.975646i \(0.429606\pi\)
\(674\) −21.5288 −0.829258
\(675\) 1.78841 0.0688361
\(676\) 32.8326 1.26279
\(677\) −24.3824 −0.937093 −0.468546 0.883439i \(-0.655222\pi\)
−0.468546 + 0.883439i \(0.655222\pi\)
\(678\) −0.389609 −0.0149628
\(679\) −13.5024 −0.518173
\(680\) −37.3156 −1.43099
\(681\) 9.64584 0.369630
\(682\) 0.350335 0.0134150
\(683\) 14.6937 0.562240 0.281120 0.959673i \(-0.409294\pi\)
0.281120 + 0.959673i \(0.409294\pi\)
\(684\) −28.9911 −1.10850
\(685\) 48.1621 1.84018
\(686\) 43.2951 1.65301
\(687\) −0.419350 −0.0159992
\(688\) 111.580 4.25393
\(689\) 37.1875 1.41673
\(690\) 12.3190 0.468976
\(691\) 5.65759 0.215225 0.107612 0.994193i \(-0.465679\pi\)
0.107612 + 0.994193i \(0.465679\pi\)
\(692\) 97.1426 3.69281
\(693\) −0.0805232 −0.00305882
\(694\) −55.5487 −2.10860
\(695\) −33.1187 −1.25626
\(696\) −34.5626 −1.31009
\(697\) −2.25270 −0.0853271
\(698\) −3.63306 −0.137513
\(699\) −12.7859 −0.483609
\(700\) 4.27891 0.161728
\(701\) −25.4597 −0.961600 −0.480800 0.876830i \(-0.659654\pi\)
−0.480800 + 0.876830i \(0.659654\pi\)
\(702\) 33.3708 1.25950
\(703\) −13.8298 −0.521601
\(704\) 0.377340 0.0142216
\(705\) −3.96291 −0.149252
\(706\) −12.7405 −0.479494
\(707\) 12.1488 0.456905
\(708\) −20.6675 −0.776734
\(709\) 43.0961 1.61851 0.809254 0.587459i \(-0.199872\pi\)
0.809254 + 0.587459i \(0.199872\pi\)
\(710\) −78.8196 −2.95805
\(711\) −5.88187 −0.220587
\(712\) −134.893 −5.05533
\(713\) −23.4768 −0.879214
\(714\) 3.28314 0.122869
\(715\) −0.230515 −0.00862077
\(716\) −117.947 −4.40790
\(717\) −2.89775 −0.108218
\(718\) 74.4151 2.77715
\(719\) −14.5383 −0.542186 −0.271093 0.962553i \(-0.587385\pi\)
−0.271093 + 0.962553i \(0.587385\pi\)
\(720\) −78.7025 −2.93307
\(721\) −13.5991 −0.506457
\(722\) 39.4920 1.46974
\(723\) −7.02058 −0.261098
\(724\) 77.8603 2.89366
\(725\) −5.29398 −0.196613
\(726\) −14.4742 −0.537187
\(727\) −19.3707 −0.718420 −0.359210 0.933257i \(-0.616954\pi\)
−0.359210 + 0.933257i \(0.616954\pi\)
\(728\) 48.6950 1.80476
\(729\) −14.7510 −0.546332
\(730\) −54.0493 −2.00045
\(731\) 17.4735 0.646282
\(732\) −19.9009 −0.735559
\(733\) 11.1626 0.412301 0.206150 0.978520i \(-0.433906\pi\)
0.206150 + 0.978520i \(0.433906\pi\)
\(734\) 20.4991 0.756635
\(735\) 6.13593 0.226327
\(736\) −60.8462 −2.24282
\(737\) 0.244422 0.00900340
\(738\) −8.80062 −0.323955
\(739\) −4.41772 −0.162509 −0.0812543 0.996693i \(-0.525893\pi\)
−0.0812543 + 0.996693i \(0.525893\pi\)
\(740\) −82.0257 −3.01532
\(741\) 4.45344 0.163601
\(742\) 29.8461 1.09568
\(743\) 30.8234 1.13080 0.565400 0.824817i \(-0.308722\pi\)
0.565400 + 0.824817i \(0.308722\pi\)
\(744\) −24.4832 −0.897598
\(745\) −37.7925 −1.38461
\(746\) −3.45181 −0.126380
\(747\) 25.3551 0.927696
\(748\) 0.213017 0.00778869
\(749\) 18.8787 0.689813
\(750\) −13.6440 −0.498209
\(751\) 15.9352 0.581483 0.290742 0.956802i \(-0.406098\pi\)
0.290742 + 0.956802i \(0.406098\pi\)
\(752\) 40.7626 1.48646
\(753\) 5.40572 0.196995
\(754\) −98.7825 −3.59745
\(755\) −23.7720 −0.865153
\(756\) 19.2667 0.700725
\(757\) −30.7460 −1.11748 −0.558741 0.829342i \(-0.688716\pi\)
−0.558741 + 0.829342i \(0.688716\pi\)
\(758\) 43.1307 1.56658
\(759\) −0.0428898 −0.00155680
\(760\) −40.6244 −1.47360
\(761\) 0.105709 0.00383195 0.00191598 0.999998i \(-0.499390\pi\)
0.00191598 + 0.999998i \(0.499390\pi\)
\(762\) 9.59007 0.347412
\(763\) 13.3735 0.484152
\(764\) 61.9765 2.24223
\(765\) −12.3249 −0.445609
\(766\) −18.4701 −0.667354
\(767\) −36.0260 −1.30082
\(768\) −2.65035 −0.0956364
\(769\) −44.3309 −1.59861 −0.799306 0.600924i \(-0.794800\pi\)
−0.799306 + 0.600924i \(0.794800\pi\)
\(770\) −0.185008 −0.00666721
\(771\) −10.5257 −0.379072
\(772\) −64.4599 −2.31996
\(773\) −1.75128 −0.0629892 −0.0314946 0.999504i \(-0.510027\pi\)
−0.0314946 + 0.999504i \(0.510027\pi\)
\(774\) 68.2639 2.45369
\(775\) −3.75011 −0.134708
\(776\) 85.1075 3.05518
\(777\) 4.40153 0.157904
\(778\) −74.7811 −2.68103
\(779\) −2.45245 −0.0878681
\(780\) 26.4137 0.945762
\(781\) 0.274418 0.00981946
\(782\) −19.8435 −0.709603
\(783\) −23.8373 −0.851877
\(784\) −63.1144 −2.25409
\(785\) −6.27448 −0.223946
\(786\) 26.3633 0.940347
\(787\) −25.1571 −0.896754 −0.448377 0.893845i \(-0.647998\pi\)
−0.448377 + 0.893845i \(0.647998\pi\)
\(788\) 114.361 4.07393
\(789\) −4.74754 −0.169017
\(790\) −13.5140 −0.480806
\(791\) −0.392102 −0.0139415
\(792\) 0.507550 0.0180350
\(793\) −34.6897 −1.23187
\(794\) −21.4609 −0.761620
\(795\) 9.87384 0.350189
\(796\) −34.8404 −1.23488
\(797\) 16.2960 0.577235 0.288617 0.957445i \(-0.406804\pi\)
0.288617 + 0.957445i \(0.406804\pi\)
\(798\) 3.57426 0.126528
\(799\) 6.38348 0.225831
\(800\) −9.71937 −0.343631
\(801\) −44.5537 −1.57423
\(802\) 72.4206 2.55726
\(803\) 0.188178 0.00664065
\(804\) −28.0073 −0.987740
\(805\) 12.3978 0.436965
\(806\) −69.9749 −2.46476
\(807\) 1.04981 0.0369552
\(808\) −76.5760 −2.69394
\(809\) −21.8305 −0.767518 −0.383759 0.923433i \(-0.625371\pi\)
−0.383759 + 0.923433i \(0.625371\pi\)
\(810\) −43.5326 −1.52958
\(811\) −49.5710 −1.74067 −0.870337 0.492456i \(-0.836099\pi\)
−0.870337 + 0.492456i \(0.836099\pi\)
\(812\) −57.0325 −2.00145
\(813\) −0.750797 −0.0263316
\(814\) 0.396987 0.0139144
\(815\) 48.8341 1.71058
\(816\) −11.1721 −0.391103
\(817\) 19.0229 0.665528
\(818\) 104.002 3.63634
\(819\) 16.0834 0.562001
\(820\) −14.5457 −0.507956
\(821\) −28.7693 −1.00405 −0.502027 0.864852i \(-0.667412\pi\)
−0.502027 + 0.864852i \(0.667412\pi\)
\(822\) 26.7093 0.931595
\(823\) 28.2424 0.984468 0.492234 0.870463i \(-0.336180\pi\)
0.492234 + 0.870463i \(0.336180\pi\)
\(824\) 85.7171 2.98610
\(825\) −0.00685107 −0.000238524 0
\(826\) −28.9139 −1.00604
\(827\) −22.4252 −0.779801 −0.389901 0.920857i \(-0.627491\pi\)
−0.389901 + 0.920857i \(0.627491\pi\)
\(828\) −55.7674 −1.93805
\(829\) −44.5840 −1.54847 −0.774233 0.632901i \(-0.781864\pi\)
−0.774233 + 0.632901i \(0.781864\pi\)
\(830\) 58.2551 2.02206
\(831\) 5.73062 0.198793
\(832\) −75.3687 −2.61294
\(833\) −9.88381 −0.342454
\(834\) −18.3667 −0.635986
\(835\) 58.7226 2.03218
\(836\) 0.231906 0.00802063
\(837\) −16.8857 −0.583656
\(838\) 1.56270 0.0539826
\(839\) −8.59628 −0.296777 −0.148388 0.988929i \(-0.547409\pi\)
−0.148388 + 0.988929i \(0.547409\pi\)
\(840\) 12.9293 0.446102
\(841\) 41.5621 1.43318
\(842\) −36.8854 −1.27116
\(843\) 12.0814 0.416105
\(844\) −24.8755 −0.856249
\(845\) 15.1957 0.522749
\(846\) 24.9383 0.857397
\(847\) −14.5668 −0.500521
\(848\) −101.563 −3.48767
\(849\) 3.20848 0.110115
\(850\) −3.16974 −0.108721
\(851\) −26.6031 −0.911942
\(852\) −31.4444 −1.07727
\(853\) 3.97518 0.136108 0.0680538 0.997682i \(-0.478321\pi\)
0.0680538 + 0.997682i \(0.478321\pi\)
\(854\) −27.8414 −0.952712
\(855\) −13.4178 −0.458879
\(856\) −118.995 −4.06717
\(857\) −35.9946 −1.22955 −0.614776 0.788701i \(-0.710754\pi\)
−0.614776 + 0.788701i \(0.710754\pi\)
\(858\) −0.127837 −0.00436428
\(859\) −40.1751 −1.37076 −0.685379 0.728186i \(-0.740363\pi\)
−0.685379 + 0.728186i \(0.740363\pi\)
\(860\) 112.826 3.84735
\(861\) 0.780525 0.0266002
\(862\) 16.5727 0.564470
\(863\) −22.6578 −0.771282 −0.385641 0.922649i \(-0.626020\pi\)
−0.385641 + 0.922649i \(0.626020\pi\)
\(864\) −43.7636 −1.48887
\(865\) 44.9600 1.52868
\(866\) 83.8258 2.84852
\(867\) 6.63000 0.225167
\(868\) −40.4003 −1.37127
\(869\) 0.0470503 0.00159607
\(870\) −26.2282 −0.889220
\(871\) −48.8200 −1.65420
\(872\) −84.2950 −2.85459
\(873\) 28.1101 0.951382
\(874\) −21.6031 −0.730734
\(875\) −13.7313 −0.464203
\(876\) −21.5625 −0.728529
\(877\) 12.1004 0.408602 0.204301 0.978908i \(-0.434508\pi\)
0.204301 + 0.978908i \(0.434508\pi\)
\(878\) −62.5472 −2.11087
\(879\) −5.63037 −0.189908
\(880\) 0.629558 0.0212224
\(881\) −14.9641 −0.504153 −0.252077 0.967707i \(-0.581113\pi\)
−0.252077 + 0.967707i \(0.581113\pi\)
\(882\) −38.6131 −1.30017
\(883\) 4.27924 0.144008 0.0720039 0.997404i \(-0.477061\pi\)
0.0720039 + 0.997404i \(0.477061\pi\)
\(884\) −42.5474 −1.43102
\(885\) −9.56544 −0.321539
\(886\) 48.3419 1.62408
\(887\) 14.5774 0.489462 0.244731 0.969591i \(-0.421300\pi\)
0.244731 + 0.969591i \(0.421300\pi\)
\(888\) −27.7435 −0.931010
\(889\) 9.65143 0.323699
\(890\) −102.365 −3.43129
\(891\) 0.151563 0.00507755
\(892\) 55.3578 1.85352
\(893\) 6.94951 0.232556
\(894\) −20.9587 −0.700962
\(895\) −54.5889 −1.82471
\(896\) −19.6426 −0.656213
\(897\) 8.56666 0.286032
\(898\) 13.8409 0.461878
\(899\) 49.9843 1.66707
\(900\) −8.90810 −0.296937
\(901\) −15.9049 −0.529868
\(902\) 0.0703980 0.00234400
\(903\) −6.05431 −0.201475
\(904\) 2.47148 0.0822001
\(905\) 36.0357 1.19787
\(906\) −13.1833 −0.437986
\(907\) 4.14976 0.137791 0.0688953 0.997624i \(-0.478053\pi\)
0.0688953 + 0.997624i \(0.478053\pi\)
\(908\) −100.326 −3.32944
\(909\) −25.2922 −0.838890
\(910\) 36.9528 1.22497
\(911\) 16.3301 0.541041 0.270520 0.962714i \(-0.412804\pi\)
0.270520 + 0.962714i \(0.412804\pi\)
\(912\) −12.1628 −0.402750
\(913\) −0.202821 −0.00671239
\(914\) −89.7133 −2.96745
\(915\) −9.21063 −0.304494
\(916\) 4.36165 0.144113
\(917\) 26.5319 0.876162
\(918\) −14.2725 −0.471061
\(919\) 25.3757 0.837067 0.418533 0.908201i \(-0.362544\pi\)
0.418533 + 0.908201i \(0.362544\pi\)
\(920\) −78.1452 −2.57637
\(921\) 1.80571 0.0595001
\(922\) −26.8883 −0.885520
\(923\) −54.8114 −1.80414
\(924\) −0.0738072 −0.00242808
\(925\) −4.24949 −0.139722
\(926\) 7.01891 0.230656
\(927\) 28.3114 0.929870
\(928\) 129.547 4.25259
\(929\) 30.1512 0.989228 0.494614 0.869113i \(-0.335309\pi\)
0.494614 + 0.869113i \(0.335309\pi\)
\(930\) −18.5794 −0.609241
\(931\) −10.7602 −0.352652
\(932\) 132.986 4.35611
\(933\) 9.19949 0.301178
\(934\) 56.5129 1.84916
\(935\) 0.0985897 0.00322423
\(936\) −101.376 −3.31359
\(937\) 7.63452 0.249409 0.124704 0.992194i \(-0.460202\pi\)
0.124704 + 0.992194i \(0.460202\pi\)
\(938\) −39.1822 −1.27934
\(939\) −10.6175 −0.346488
\(940\) 41.2180 1.34438
\(941\) 35.0964 1.14411 0.572055 0.820215i \(-0.306146\pi\)
0.572055 + 0.820215i \(0.306146\pi\)
\(942\) −3.47964 −0.113373
\(943\) −4.71754 −0.153624
\(944\) 98.3904 3.20234
\(945\) 8.91712 0.290074
\(946\) −0.546057 −0.0177538
\(947\) −7.54860 −0.245297 −0.122648 0.992450i \(-0.539139\pi\)
−0.122648 + 0.992450i \(0.539139\pi\)
\(948\) −5.39129 −0.175101
\(949\) −37.5860 −1.22009
\(950\) −3.45080 −0.111959
\(951\) −8.39867 −0.272345
\(952\) −20.8266 −0.674993
\(953\) 43.1692 1.39839 0.699194 0.714932i \(-0.253542\pi\)
0.699194 + 0.714932i \(0.253542\pi\)
\(954\) −62.1355 −2.01171
\(955\) 28.6842 0.928200
\(956\) 30.1394 0.974776
\(957\) 0.0913162 0.00295183
\(958\) −59.5989 −1.92555
\(959\) 26.8802 0.868007
\(960\) −20.0115 −0.645869
\(961\) 4.40752 0.142178
\(962\) −79.2929 −2.55651
\(963\) −39.3028 −1.26652
\(964\) 73.0208 2.35184
\(965\) −29.8336 −0.960378
\(966\) 6.87547 0.221214
\(967\) −53.3958 −1.71709 −0.858547 0.512735i \(-0.828632\pi\)
−0.858547 + 0.512735i \(0.828632\pi\)
\(968\) 91.8166 2.95110
\(969\) −1.90471 −0.0611881
\(970\) 64.5848 2.07369
\(971\) −59.1605 −1.89855 −0.949276 0.314445i \(-0.898182\pi\)
−0.949276 + 0.314445i \(0.898182\pi\)
\(972\) −61.0125 −1.95698
\(973\) −18.4842 −0.592576
\(974\) 33.0953 1.06044
\(975\) 1.36841 0.0438242
\(976\) 94.7407 3.03258
\(977\) 54.9861 1.75916 0.879580 0.475750i \(-0.157823\pi\)
0.879580 + 0.475750i \(0.157823\pi\)
\(978\) 27.0820 0.865987
\(979\) 0.356394 0.0113904
\(980\) −63.8196 −2.03864
\(981\) −27.8417 −0.888918
\(982\) −57.7909 −1.84418
\(983\) 8.21767 0.262103 0.131051 0.991376i \(-0.458165\pi\)
0.131051 + 0.991376i \(0.458165\pi\)
\(984\) −4.91977 −0.156836
\(985\) 52.9290 1.68646
\(986\) 42.2486 1.34547
\(987\) −2.21178 −0.0704016
\(988\) −46.3201 −1.47364
\(989\) 36.5926 1.16358
\(990\) 0.385160 0.0122412
\(991\) −11.8354 −0.375964 −0.187982 0.982173i \(-0.560195\pi\)
−0.187982 + 0.982173i \(0.560195\pi\)
\(992\) 91.7676 2.91362
\(993\) 13.5880 0.431201
\(994\) −43.9908 −1.39530
\(995\) −16.1250 −0.511196
\(996\) 23.2404 0.736400
\(997\) 21.6250 0.684872 0.342436 0.939541i \(-0.388748\pi\)
0.342436 + 0.939541i \(0.388748\pi\)
\(998\) −97.0539 −3.07219
\(999\) −19.1343 −0.605382
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.1.4 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.4 174 1.1 even 1 trivial