Properties

Label 4027.2.a.c.1.8
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 1.8
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54479 q^{2} +0.596838 q^{3} +4.47598 q^{4} +4.06364 q^{5} -1.51883 q^{6} -0.751735 q^{7} -6.30086 q^{8} -2.64378 q^{9} +O(q^{10})\) \(q-2.54479 q^{2} +0.596838 q^{3} +4.47598 q^{4} +4.06364 q^{5} -1.51883 q^{6} -0.751735 q^{7} -6.30086 q^{8} -2.64378 q^{9} -10.3411 q^{10} +1.59169 q^{11} +2.67143 q^{12} +0.889782 q^{13} +1.91301 q^{14} +2.42533 q^{15} +7.08244 q^{16} +6.61510 q^{17} +6.72789 q^{18} +4.89661 q^{19} +18.1888 q^{20} -0.448664 q^{21} -4.05052 q^{22} +3.07346 q^{23} -3.76059 q^{24} +11.5132 q^{25} -2.26431 q^{26} -3.36842 q^{27} -3.36475 q^{28} +4.87557 q^{29} -6.17198 q^{30} +8.96241 q^{31} -5.42164 q^{32} +0.949981 q^{33} -16.8341 q^{34} -3.05478 q^{35} -11.8335 q^{36} +8.64979 q^{37} -12.4609 q^{38} +0.531056 q^{39} -25.6044 q^{40} -7.20078 q^{41} +1.14176 q^{42} -2.22059 q^{43} +7.12437 q^{44} -10.7434 q^{45} -7.82132 q^{46} -2.58487 q^{47} +4.22707 q^{48} -6.43489 q^{49} -29.2986 q^{50} +3.94814 q^{51} +3.98265 q^{52} -0.647148 q^{53} +8.57195 q^{54} +6.46805 q^{55} +4.73658 q^{56} +2.92248 q^{57} -12.4073 q^{58} -10.6319 q^{59} +10.8557 q^{60} +9.23648 q^{61} -22.8075 q^{62} +1.98743 q^{63} -0.367927 q^{64} +3.61575 q^{65} -2.41751 q^{66} -6.56328 q^{67} +29.6090 q^{68} +1.83436 q^{69} +7.77379 q^{70} -14.7856 q^{71} +16.6581 q^{72} -7.61205 q^{73} -22.0119 q^{74} +6.87149 q^{75} +21.9171 q^{76} -1.19653 q^{77} -1.35143 q^{78} +1.24194 q^{79} +28.7805 q^{80} +5.92095 q^{81} +18.3245 q^{82} -0.207324 q^{83} -2.00821 q^{84} +26.8814 q^{85} +5.65095 q^{86} +2.90993 q^{87} -10.0290 q^{88} +16.3645 q^{89} +27.3397 q^{90} -0.668881 q^{91} +13.7567 q^{92} +5.34911 q^{93} +6.57797 q^{94} +19.8981 q^{95} -3.23584 q^{96} -8.12779 q^{97} +16.3755 q^{98} -4.20809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54479 −1.79944 −0.899721 0.436466i \(-0.856230\pi\)
−0.899721 + 0.436466i \(0.856230\pi\)
\(3\) 0.596838 0.344584 0.172292 0.985046i \(-0.444883\pi\)
0.172292 + 0.985046i \(0.444883\pi\)
\(4\) 4.47598 2.23799
\(5\) 4.06364 1.81731 0.908657 0.417543i \(-0.137109\pi\)
0.908657 + 0.417543i \(0.137109\pi\)
\(6\) −1.51883 −0.620060
\(7\) −0.751735 −0.284129 −0.142065 0.989857i \(-0.545374\pi\)
−0.142065 + 0.989857i \(0.545374\pi\)
\(8\) −6.30086 −2.22769
\(9\) −2.64378 −0.881262
\(10\) −10.3411 −3.27015
\(11\) 1.59169 0.479913 0.239956 0.970784i \(-0.422867\pi\)
0.239956 + 0.970784i \(0.422867\pi\)
\(12\) 2.67143 0.771177
\(13\) 0.889782 0.246781 0.123391 0.992358i \(-0.460623\pi\)
0.123391 + 0.992358i \(0.460623\pi\)
\(14\) 1.91301 0.511274
\(15\) 2.42533 0.626219
\(16\) 7.08244 1.77061
\(17\) 6.61510 1.60440 0.802198 0.597058i \(-0.203664\pi\)
0.802198 + 0.597058i \(0.203664\pi\)
\(18\) 6.72789 1.58578
\(19\) 4.89661 1.12336 0.561680 0.827355i \(-0.310155\pi\)
0.561680 + 0.827355i \(0.310155\pi\)
\(20\) 18.1888 4.06713
\(21\) −0.448664 −0.0979065
\(22\) −4.05052 −0.863575
\(23\) 3.07346 0.640860 0.320430 0.947272i \(-0.396173\pi\)
0.320430 + 0.947272i \(0.396173\pi\)
\(24\) −3.76059 −0.767628
\(25\) 11.5132 2.30263
\(26\) −2.26431 −0.444068
\(27\) −3.36842 −0.648254
\(28\) −3.36475 −0.635879
\(29\) 4.87557 0.905371 0.452686 0.891670i \(-0.350466\pi\)
0.452686 + 0.891670i \(0.350466\pi\)
\(30\) −6.17198 −1.12684
\(31\) 8.96241 1.60970 0.804848 0.593481i \(-0.202247\pi\)
0.804848 + 0.593481i \(0.202247\pi\)
\(32\) −5.42164 −0.958420
\(33\) 0.949981 0.165370
\(34\) −16.8341 −2.88702
\(35\) −3.05478 −0.516352
\(36\) −11.8335 −1.97225
\(37\) 8.64979 1.42202 0.711008 0.703184i \(-0.248239\pi\)
0.711008 + 0.703184i \(0.248239\pi\)
\(38\) −12.4609 −2.02142
\(39\) 0.531056 0.0850370
\(40\) −25.6044 −4.04842
\(41\) −7.20078 −1.12457 −0.562287 0.826942i \(-0.690078\pi\)
−0.562287 + 0.826942i \(0.690078\pi\)
\(42\) 1.14176 0.176177
\(43\) −2.22059 −0.338637 −0.169318 0.985561i \(-0.554157\pi\)
−0.169318 + 0.985561i \(0.554157\pi\)
\(44\) 7.12437 1.07404
\(45\) −10.7434 −1.60153
\(46\) −7.82132 −1.15319
\(47\) −2.58487 −0.377043 −0.188521 0.982069i \(-0.560369\pi\)
−0.188521 + 0.982069i \(0.560369\pi\)
\(48\) 4.22707 0.610125
\(49\) −6.43489 −0.919271
\(50\) −29.2986 −4.14345
\(51\) 3.94814 0.552850
\(52\) 3.98265 0.552294
\(53\) −0.647148 −0.0888926 −0.0444463 0.999012i \(-0.514152\pi\)
−0.0444463 + 0.999012i \(0.514152\pi\)
\(54\) 8.57195 1.16649
\(55\) 6.46805 0.872152
\(56\) 4.73658 0.632952
\(57\) 2.92248 0.387092
\(58\) −12.4073 −1.62916
\(59\) −10.6319 −1.38416 −0.692078 0.721823i \(-0.743305\pi\)
−0.692078 + 0.721823i \(0.743305\pi\)
\(60\) 10.8557 1.40147
\(61\) 9.23648 1.18261 0.591305 0.806448i \(-0.298613\pi\)
0.591305 + 0.806448i \(0.298613\pi\)
\(62\) −22.8075 −2.89655
\(63\) 1.98743 0.250392
\(64\) −0.367927 −0.0459908
\(65\) 3.61575 0.448479
\(66\) −2.41751 −0.297574
\(67\) −6.56328 −0.801832 −0.400916 0.916115i \(-0.631308\pi\)
−0.400916 + 0.916115i \(0.631308\pi\)
\(68\) 29.6090 3.59062
\(69\) 1.83436 0.220830
\(70\) 7.77379 0.929146
\(71\) −14.7856 −1.75473 −0.877364 0.479825i \(-0.840700\pi\)
−0.877364 + 0.479825i \(0.840700\pi\)
\(72\) 16.6581 1.96318
\(73\) −7.61205 −0.890923 −0.445462 0.895301i \(-0.646960\pi\)
−0.445462 + 0.895301i \(0.646960\pi\)
\(74\) −22.0119 −2.55884
\(75\) 6.87149 0.793452
\(76\) 21.9171 2.51407
\(77\) −1.19653 −0.136357
\(78\) −1.35143 −0.153019
\(79\) 1.24194 0.139730 0.0698648 0.997556i \(-0.477743\pi\)
0.0698648 + 0.997556i \(0.477743\pi\)
\(80\) 28.7805 3.21776
\(81\) 5.92095 0.657883
\(82\) 18.3245 2.02360
\(83\) −0.207324 −0.0227568 −0.0113784 0.999935i \(-0.503622\pi\)
−0.0113784 + 0.999935i \(0.503622\pi\)
\(84\) −2.00821 −0.219114
\(85\) 26.8814 2.91569
\(86\) 5.65095 0.609357
\(87\) 2.90993 0.311977
\(88\) −10.0290 −1.06910
\(89\) 16.3645 1.73463 0.867317 0.497755i \(-0.165842\pi\)
0.867317 + 0.497755i \(0.165842\pi\)
\(90\) 27.3397 2.88186
\(91\) −0.668881 −0.0701177
\(92\) 13.7567 1.43424
\(93\) 5.34911 0.554676
\(94\) 6.57797 0.678466
\(95\) 19.8981 2.04150
\(96\) −3.23584 −0.330257
\(97\) −8.12779 −0.825252 −0.412626 0.910901i \(-0.635388\pi\)
−0.412626 + 0.910901i \(0.635388\pi\)
\(98\) 16.3755 1.65417
\(99\) −4.20809 −0.422928
\(100\) 51.5327 5.15327
\(101\) −16.5090 −1.64271 −0.821355 0.570417i \(-0.806782\pi\)
−0.821355 + 0.570417i \(0.806782\pi\)
\(102\) −10.0472 −0.994822
\(103\) −12.6195 −1.24343 −0.621716 0.783242i \(-0.713564\pi\)
−0.621716 + 0.783242i \(0.713564\pi\)
\(104\) −5.60640 −0.549752
\(105\) −1.82321 −0.177927
\(106\) 1.64686 0.159957
\(107\) −5.88071 −0.568509 −0.284255 0.958749i \(-0.591746\pi\)
−0.284255 + 0.958749i \(0.591746\pi\)
\(108\) −15.0770 −1.45079
\(109\) −10.5666 −1.01210 −0.506049 0.862505i \(-0.668894\pi\)
−0.506049 + 0.862505i \(0.668894\pi\)
\(110\) −16.4599 −1.56939
\(111\) 5.16252 0.490005
\(112\) −5.32412 −0.503082
\(113\) 15.3333 1.44243 0.721216 0.692710i \(-0.243584\pi\)
0.721216 + 0.692710i \(0.243584\pi\)
\(114\) −7.43712 −0.696550
\(115\) 12.4894 1.16464
\(116\) 21.8230 2.02621
\(117\) −2.35239 −0.217479
\(118\) 27.0560 2.49071
\(119\) −4.97280 −0.455856
\(120\) −15.2817 −1.39502
\(121\) −8.46652 −0.769684
\(122\) −23.5049 −2.12804
\(123\) −4.29770 −0.387511
\(124\) 40.1156 3.60249
\(125\) 26.4672 2.36729
\(126\) −5.05759 −0.450566
\(127\) 5.59628 0.496590 0.248295 0.968685i \(-0.420130\pi\)
0.248295 + 0.968685i \(0.420130\pi\)
\(128\) 11.7796 1.04118
\(129\) −1.32533 −0.116689
\(130\) −9.20135 −0.807012
\(131\) 19.3051 1.68669 0.843347 0.537369i \(-0.180582\pi\)
0.843347 + 0.537369i \(0.180582\pi\)
\(132\) 4.25210 0.370097
\(133\) −3.68096 −0.319179
\(134\) 16.7022 1.44285
\(135\) −13.6881 −1.17808
\(136\) −41.6808 −3.57410
\(137\) 3.80008 0.324662 0.162331 0.986736i \(-0.448099\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(138\) −4.66806 −0.397371
\(139\) 9.54205 0.809346 0.404673 0.914461i \(-0.367385\pi\)
0.404673 + 0.914461i \(0.367385\pi\)
\(140\) −13.6731 −1.15559
\(141\) −1.54275 −0.129923
\(142\) 37.6263 3.15753
\(143\) 1.41626 0.118433
\(144\) −18.7245 −1.56037
\(145\) 19.8126 1.64534
\(146\) 19.3711 1.60316
\(147\) −3.84059 −0.316766
\(148\) 38.7163 3.18246
\(149\) −0.583891 −0.0478342 −0.0239171 0.999714i \(-0.507614\pi\)
−0.0239171 + 0.999714i \(0.507614\pi\)
\(150\) −17.4865 −1.42777
\(151\) 3.52011 0.286463 0.143231 0.989689i \(-0.454251\pi\)
0.143231 + 0.989689i \(0.454251\pi\)
\(152\) −30.8529 −2.50250
\(153\) −17.4889 −1.41389
\(154\) 3.04492 0.245367
\(155\) 36.4200 2.92533
\(156\) 2.37700 0.190312
\(157\) −7.64180 −0.609882 −0.304941 0.952371i \(-0.598637\pi\)
−0.304941 + 0.952371i \(0.598637\pi\)
\(158\) −3.16049 −0.251435
\(159\) −0.386242 −0.0306310
\(160\) −22.0316 −1.74175
\(161\) −2.31043 −0.182087
\(162\) −15.0676 −1.18382
\(163\) −9.88999 −0.774644 −0.387322 0.921945i \(-0.626600\pi\)
−0.387322 + 0.921945i \(0.626600\pi\)
\(164\) −32.2306 −2.51678
\(165\) 3.86038 0.300530
\(166\) 0.527597 0.0409494
\(167\) 3.14610 0.243452 0.121726 0.992564i \(-0.461157\pi\)
0.121726 + 0.992564i \(0.461157\pi\)
\(168\) 2.82697 0.218106
\(169\) −12.2083 −0.939099
\(170\) −68.4076 −5.24662
\(171\) −12.9456 −0.989974
\(172\) −9.93932 −0.757866
\(173\) −1.05704 −0.0803649 −0.0401824 0.999192i \(-0.512794\pi\)
−0.0401824 + 0.999192i \(0.512794\pi\)
\(174\) −7.40517 −0.561384
\(175\) −8.65485 −0.654245
\(176\) 11.2731 0.849739
\(177\) −6.34552 −0.476959
\(178\) −41.6443 −3.12137
\(179\) −5.90938 −0.441688 −0.220844 0.975309i \(-0.570881\pi\)
−0.220844 + 0.975309i \(0.570881\pi\)
\(180\) −48.0872 −3.58421
\(181\) −15.6026 −1.15973 −0.579865 0.814712i \(-0.696895\pi\)
−0.579865 + 0.814712i \(0.696895\pi\)
\(182\) 1.70216 0.126173
\(183\) 5.51268 0.407509
\(184\) −19.3654 −1.42764
\(185\) 35.1496 2.58425
\(186\) −13.6124 −0.998108
\(187\) 10.5292 0.769970
\(188\) −11.5698 −0.843818
\(189\) 2.53216 0.184188
\(190\) −50.6365 −3.67356
\(191\) 2.15350 0.155822 0.0779109 0.996960i \(-0.475175\pi\)
0.0779109 + 0.996960i \(0.475175\pi\)
\(192\) −0.219592 −0.0158477
\(193\) 25.4873 1.83461 0.917307 0.398181i \(-0.130358\pi\)
0.917307 + 0.398181i \(0.130358\pi\)
\(194\) 20.6836 1.48499
\(195\) 2.15802 0.154539
\(196\) −28.8025 −2.05732
\(197\) 10.0064 0.712924 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(198\) 10.7087 0.761035
\(199\) −18.0972 −1.28288 −0.641438 0.767175i \(-0.721662\pi\)
−0.641438 + 0.767175i \(0.721662\pi\)
\(200\) −72.5429 −5.12956
\(201\) −3.91721 −0.276299
\(202\) 42.0121 2.95596
\(203\) −3.66514 −0.257242
\(204\) 17.6718 1.23727
\(205\) −29.2614 −2.04370
\(206\) 32.1140 2.23748
\(207\) −8.12556 −0.564765
\(208\) 6.30183 0.436953
\(209\) 7.79389 0.539114
\(210\) 4.63969 0.320169
\(211\) −14.6750 −1.01027 −0.505135 0.863040i \(-0.668557\pi\)
−0.505135 + 0.863040i \(0.668557\pi\)
\(212\) −2.89662 −0.198941
\(213\) −8.82461 −0.604652
\(214\) 14.9652 1.02300
\(215\) −9.02368 −0.615410
\(216\) 21.2240 1.44411
\(217\) −6.73736 −0.457362
\(218\) 26.8898 1.82121
\(219\) −4.54316 −0.306998
\(220\) 28.9509 1.95187
\(221\) 5.88599 0.395935
\(222\) −13.1376 −0.881735
\(223\) −17.2178 −1.15299 −0.576493 0.817102i \(-0.695579\pi\)
−0.576493 + 0.817102i \(0.695579\pi\)
\(224\) 4.07564 0.272315
\(225\) −30.4383 −2.02922
\(226\) −39.0200 −2.59557
\(227\) 14.2320 0.944614 0.472307 0.881434i \(-0.343421\pi\)
0.472307 + 0.881434i \(0.343421\pi\)
\(228\) 13.0810 0.866309
\(229\) 26.9662 1.78197 0.890987 0.454029i \(-0.150014\pi\)
0.890987 + 0.454029i \(0.150014\pi\)
\(230\) −31.7830 −2.09571
\(231\) −0.714134 −0.0469866
\(232\) −30.7203 −2.01689
\(233\) −8.57031 −0.561460 −0.280730 0.959787i \(-0.590576\pi\)
−0.280730 + 0.959787i \(0.590576\pi\)
\(234\) 5.98636 0.391340
\(235\) −10.5040 −0.685205
\(236\) −47.5882 −3.09773
\(237\) 0.741239 0.0481486
\(238\) 12.6548 0.820286
\(239\) −11.0017 −0.711643 −0.355822 0.934554i \(-0.615799\pi\)
−0.355822 + 0.934554i \(0.615799\pi\)
\(240\) 17.1773 1.10879
\(241\) −0.868425 −0.0559402 −0.0279701 0.999609i \(-0.508904\pi\)
−0.0279701 + 0.999609i \(0.508904\pi\)
\(242\) 21.5456 1.38500
\(243\) 13.6391 0.874950
\(244\) 41.3423 2.64667
\(245\) −26.1491 −1.67060
\(246\) 10.9368 0.697303
\(247\) 4.35692 0.277224
\(248\) −56.4709 −3.58591
\(249\) −0.123739 −0.00784162
\(250\) −67.3535 −4.25981
\(251\) 25.5662 1.61373 0.806863 0.590738i \(-0.201163\pi\)
0.806863 + 0.590738i \(0.201163\pi\)
\(252\) 8.89568 0.560375
\(253\) 4.89199 0.307557
\(254\) −14.2414 −0.893584
\(255\) 16.0438 1.00470
\(256\) −29.2408 −1.82755
\(257\) 15.7501 0.982466 0.491233 0.871028i \(-0.336546\pi\)
0.491233 + 0.871028i \(0.336546\pi\)
\(258\) 3.37270 0.209975
\(259\) −6.50235 −0.404036
\(260\) 16.1840 1.00369
\(261\) −12.8900 −0.797869
\(262\) −49.1275 −3.03511
\(263\) 19.8859 1.22622 0.613110 0.789998i \(-0.289918\pi\)
0.613110 + 0.789998i \(0.289918\pi\)
\(264\) −5.98570 −0.368394
\(265\) −2.62977 −0.161546
\(266\) 9.36728 0.574345
\(267\) 9.76696 0.597728
\(268\) −29.3771 −1.79449
\(269\) −16.8977 −1.03027 −0.515134 0.857109i \(-0.672258\pi\)
−0.515134 + 0.857109i \(0.672258\pi\)
\(270\) 34.8333 2.11989
\(271\) −16.1903 −0.983490 −0.491745 0.870739i \(-0.663641\pi\)
−0.491745 + 0.870739i \(0.663641\pi\)
\(272\) 46.8510 2.84076
\(273\) −0.399213 −0.0241615
\(274\) −9.67041 −0.584211
\(275\) 18.3254 1.10506
\(276\) 8.21054 0.494216
\(277\) 21.1958 1.27353 0.636765 0.771058i \(-0.280272\pi\)
0.636765 + 0.771058i \(0.280272\pi\)
\(278\) −24.2826 −1.45637
\(279\) −23.6947 −1.41856
\(280\) 19.2478 1.15027
\(281\) 25.8399 1.54148 0.770741 0.637149i \(-0.219886\pi\)
0.770741 + 0.637149i \(0.219886\pi\)
\(282\) 3.92598 0.233789
\(283\) 30.3561 1.80448 0.902241 0.431233i \(-0.141921\pi\)
0.902241 + 0.431233i \(0.141921\pi\)
\(284\) −66.1801 −3.92707
\(285\) 11.8759 0.703469
\(286\) −3.60408 −0.213114
\(287\) 5.41308 0.319524
\(288\) 14.3336 0.844618
\(289\) 26.7595 1.57409
\(290\) −50.4189 −2.96070
\(291\) −4.85097 −0.284369
\(292\) −34.0714 −1.99388
\(293\) 13.3191 0.778109 0.389054 0.921215i \(-0.372802\pi\)
0.389054 + 0.921215i \(0.372802\pi\)
\(294\) 9.77351 0.570003
\(295\) −43.2042 −2.51545
\(296\) −54.5011 −3.16781
\(297\) −5.36149 −0.311105
\(298\) 1.48588 0.0860748
\(299\) 2.73471 0.158152
\(300\) 30.7567 1.77574
\(301\) 1.66930 0.0962166
\(302\) −8.95796 −0.515473
\(303\) −9.85322 −0.566052
\(304\) 34.6800 1.98903
\(305\) 37.5337 2.14917
\(306\) 44.5056 2.54422
\(307\) 11.3473 0.647625 0.323812 0.946121i \(-0.395035\pi\)
0.323812 + 0.946121i \(0.395035\pi\)
\(308\) −5.35564 −0.305166
\(309\) −7.53177 −0.428468
\(310\) −92.6814 −5.26395
\(311\) 28.8444 1.63562 0.817809 0.575490i \(-0.195188\pi\)
0.817809 + 0.575490i \(0.195188\pi\)
\(312\) −3.34611 −0.189436
\(313\) −7.27211 −0.411044 −0.205522 0.978652i \(-0.565889\pi\)
−0.205522 + 0.978652i \(0.565889\pi\)
\(314\) 19.4468 1.09745
\(315\) 8.07618 0.455041
\(316\) 5.55892 0.312713
\(317\) 2.30266 0.129330 0.0646651 0.997907i \(-0.479402\pi\)
0.0646651 + 0.997907i \(0.479402\pi\)
\(318\) 0.982907 0.0551187
\(319\) 7.76040 0.434499
\(320\) −1.49512 −0.0835798
\(321\) −3.50983 −0.195899
\(322\) 5.87956 0.327655
\(323\) 32.3915 1.80231
\(324\) 26.5021 1.47234
\(325\) 10.2442 0.568246
\(326\) 25.1680 1.39393
\(327\) −6.30655 −0.348753
\(328\) 45.3712 2.50520
\(329\) 1.94314 0.107129
\(330\) −9.82387 −0.540786
\(331\) −13.9717 −0.767952 −0.383976 0.923343i \(-0.625446\pi\)
−0.383976 + 0.923343i \(0.625446\pi\)
\(332\) −0.927978 −0.0509294
\(333\) −22.8682 −1.25317
\(334\) −8.00617 −0.438078
\(335\) −26.6708 −1.45718
\(336\) −3.17764 −0.173354
\(337\) −7.20428 −0.392442 −0.196221 0.980560i \(-0.562867\pi\)
−0.196221 + 0.980560i \(0.562867\pi\)
\(338\) 31.0676 1.68985
\(339\) 9.15147 0.497040
\(340\) 120.320 6.52529
\(341\) 14.2654 0.772514
\(342\) 32.9439 1.78140
\(343\) 10.0995 0.545321
\(344\) 13.9916 0.754379
\(345\) 7.45416 0.401318
\(346\) 2.68994 0.144612
\(347\) −11.8618 −0.636774 −0.318387 0.947961i \(-0.603141\pi\)
−0.318387 + 0.947961i \(0.603141\pi\)
\(348\) 13.0248 0.698201
\(349\) −9.42552 −0.504536 −0.252268 0.967657i \(-0.581177\pi\)
−0.252268 + 0.967657i \(0.581177\pi\)
\(350\) 22.0248 1.17728
\(351\) −2.99716 −0.159977
\(352\) −8.62957 −0.459958
\(353\) −21.1243 −1.12433 −0.562167 0.827024i \(-0.690032\pi\)
−0.562167 + 0.827024i \(0.690032\pi\)
\(354\) 16.1481 0.858259
\(355\) −60.0834 −3.18889
\(356\) 73.2472 3.88210
\(357\) −2.96796 −0.157081
\(358\) 15.0382 0.794791
\(359\) 26.8636 1.41780 0.708902 0.705307i \(-0.249191\pi\)
0.708902 + 0.705307i \(0.249191\pi\)
\(360\) 67.6926 3.56771
\(361\) 4.97680 0.261937
\(362\) 39.7054 2.08687
\(363\) −5.05314 −0.265221
\(364\) −2.99390 −0.156923
\(365\) −30.9326 −1.61909
\(366\) −14.0286 −0.733289
\(367\) −0.0496759 −0.00259306 −0.00129653 0.999999i \(-0.500413\pi\)
−0.00129653 + 0.999999i \(0.500413\pi\)
\(368\) 21.7676 1.13471
\(369\) 19.0373 0.991043
\(370\) −89.4486 −4.65021
\(371\) 0.486484 0.0252570
\(372\) 23.9425 1.24136
\(373\) 29.7032 1.53797 0.768986 0.639265i \(-0.220761\pi\)
0.768986 + 0.639265i \(0.220761\pi\)
\(374\) −26.7946 −1.38552
\(375\) 15.7966 0.815733
\(376\) 16.2869 0.839935
\(377\) 4.33820 0.223429
\(378\) −6.44384 −0.331435
\(379\) 7.27050 0.373461 0.186730 0.982411i \(-0.440211\pi\)
0.186730 + 0.982411i \(0.440211\pi\)
\(380\) 89.0633 4.56885
\(381\) 3.34007 0.171117
\(382\) −5.48022 −0.280392
\(383\) 14.1152 0.721252 0.360626 0.932711i \(-0.382563\pi\)
0.360626 + 0.932711i \(0.382563\pi\)
\(384\) 7.03050 0.358774
\(385\) −4.86226 −0.247804
\(386\) −64.8599 −3.30128
\(387\) 5.87076 0.298428
\(388\) −36.3798 −1.84691
\(389\) 28.4979 1.44490 0.722451 0.691423i \(-0.243016\pi\)
0.722451 + 0.691423i \(0.243016\pi\)
\(390\) −5.49172 −0.278084
\(391\) 20.3312 1.02819
\(392\) 40.5454 2.04785
\(393\) 11.5220 0.581209
\(394\) −25.4642 −1.28287
\(395\) 5.04681 0.253933
\(396\) −18.8353 −0.946510
\(397\) 11.0392 0.554041 0.277021 0.960864i \(-0.410653\pi\)
0.277021 + 0.960864i \(0.410653\pi\)
\(398\) 46.0536 2.30846
\(399\) −2.19693 −0.109984
\(400\) 81.5413 4.07707
\(401\) −31.4484 −1.57046 −0.785230 0.619204i \(-0.787455\pi\)
−0.785230 + 0.619204i \(0.787455\pi\)
\(402\) 9.96850 0.497184
\(403\) 7.97459 0.397243
\(404\) −73.8941 −3.67637
\(405\) 24.0606 1.19558
\(406\) 9.32703 0.462893
\(407\) 13.7678 0.682443
\(408\) −24.8767 −1.23158
\(409\) −23.4429 −1.15917 −0.579587 0.814910i \(-0.696786\pi\)
−0.579587 + 0.814910i \(0.696786\pi\)
\(410\) 74.4642 3.67753
\(411\) 2.26803 0.111874
\(412\) −56.4845 −2.78279
\(413\) 7.99238 0.393279
\(414\) 20.6779 1.01626
\(415\) −0.842489 −0.0413562
\(416\) −4.82408 −0.236520
\(417\) 5.69506 0.278888
\(418\) −19.8338 −0.970105
\(419\) 17.4406 0.852030 0.426015 0.904716i \(-0.359917\pi\)
0.426015 + 0.904716i \(0.359917\pi\)
\(420\) −8.16065 −0.398199
\(421\) −29.7259 −1.44875 −0.724375 0.689406i \(-0.757872\pi\)
−0.724375 + 0.689406i \(0.757872\pi\)
\(422\) 37.3449 1.81792
\(423\) 6.83385 0.332273
\(424\) 4.07759 0.198025
\(425\) 76.1607 3.69434
\(426\) 22.4568 1.08804
\(427\) −6.94339 −0.336014
\(428\) −26.3219 −1.27232
\(429\) 0.845276 0.0408103
\(430\) 22.9634 1.10739
\(431\) −27.5179 −1.32549 −0.662745 0.748845i \(-0.730609\pi\)
−0.662745 + 0.748845i \(0.730609\pi\)
\(432\) −23.8567 −1.14780
\(433\) −10.0841 −0.484613 −0.242306 0.970200i \(-0.577904\pi\)
−0.242306 + 0.970200i \(0.577904\pi\)
\(434\) 17.1452 0.822996
\(435\) 11.8249 0.566960
\(436\) −47.2959 −2.26506
\(437\) 15.0495 0.719916
\(438\) 11.5614 0.552426
\(439\) −27.8354 −1.32851 −0.664256 0.747505i \(-0.731252\pi\)
−0.664256 + 0.747505i \(0.731252\pi\)
\(440\) −40.7543 −1.94289
\(441\) 17.0125 0.810118
\(442\) −14.9786 −0.712462
\(443\) −37.2220 −1.76847 −0.884235 0.467043i \(-0.845319\pi\)
−0.884235 + 0.467043i \(0.845319\pi\)
\(444\) 23.1073 1.09663
\(445\) 66.4995 3.15238
\(446\) 43.8157 2.07473
\(447\) −0.348488 −0.0164829
\(448\) 0.276583 0.0130673
\(449\) 11.0794 0.522867 0.261434 0.965221i \(-0.415805\pi\)
0.261434 + 0.965221i \(0.415805\pi\)
\(450\) 77.4593 3.65147
\(451\) −11.4614 −0.539697
\(452\) 68.6314 3.22815
\(453\) 2.10094 0.0987106
\(454\) −36.2176 −1.69978
\(455\) −2.71809 −0.127426
\(456\) −18.4142 −0.862322
\(457\) 15.9552 0.746352 0.373176 0.927761i \(-0.378269\pi\)
0.373176 + 0.927761i \(0.378269\pi\)
\(458\) −68.6233 −3.20656
\(459\) −22.2824 −1.04006
\(460\) 55.9024 2.60646
\(461\) −3.50016 −0.163019 −0.0815093 0.996673i \(-0.525974\pi\)
−0.0815093 + 0.996673i \(0.525974\pi\)
\(462\) 1.81733 0.0845496
\(463\) 33.6980 1.56608 0.783040 0.621971i \(-0.213668\pi\)
0.783040 + 0.621971i \(0.213668\pi\)
\(464\) 34.5310 1.60306
\(465\) 21.7368 1.00802
\(466\) 21.8097 1.01031
\(467\) 4.40699 0.203931 0.101966 0.994788i \(-0.467487\pi\)
0.101966 + 0.994788i \(0.467487\pi\)
\(468\) −10.5293 −0.486715
\(469\) 4.93385 0.227824
\(470\) 26.7305 1.23299
\(471\) −4.56092 −0.210156
\(472\) 66.9902 3.08347
\(473\) −3.53449 −0.162516
\(474\) −1.88630 −0.0866407
\(475\) 56.3755 2.58668
\(476\) −22.2582 −1.02020
\(477\) 1.71092 0.0783376
\(478\) 27.9972 1.28056
\(479\) −17.4431 −0.796997 −0.398499 0.917169i \(-0.630469\pi\)
−0.398499 + 0.917169i \(0.630469\pi\)
\(480\) −13.1493 −0.600180
\(481\) 7.69643 0.350927
\(482\) 2.20996 0.100661
\(483\) −1.37895 −0.0627444
\(484\) −37.8960 −1.72255
\(485\) −33.0284 −1.49974
\(486\) −34.7088 −1.57442
\(487\) −16.6629 −0.755068 −0.377534 0.925996i \(-0.623228\pi\)
−0.377534 + 0.925996i \(0.623228\pi\)
\(488\) −58.1978 −2.63449
\(489\) −5.90272 −0.266930
\(490\) 66.5441 3.00615
\(491\) −6.65911 −0.300522 −0.150261 0.988646i \(-0.548011\pi\)
−0.150261 + 0.988646i \(0.548011\pi\)
\(492\) −19.2364 −0.867245
\(493\) 32.2524 1.45257
\(494\) −11.0875 −0.498848
\(495\) −17.1001 −0.768594
\(496\) 63.4758 2.85015
\(497\) 11.1149 0.498570
\(498\) 0.314890 0.0141105
\(499\) 0.409460 0.0183300 0.00916498 0.999958i \(-0.497083\pi\)
0.00916498 + 0.999958i \(0.497083\pi\)
\(500\) 118.466 5.29798
\(501\) 1.87771 0.0838899
\(502\) −65.0608 −2.90381
\(503\) −32.9937 −1.47112 −0.735558 0.677462i \(-0.763080\pi\)
−0.735558 + 0.677462i \(0.763080\pi\)
\(504\) −12.5225 −0.557797
\(505\) −67.0868 −2.98532
\(506\) −12.4491 −0.553430
\(507\) −7.28637 −0.323599
\(508\) 25.0488 1.11136
\(509\) 3.71307 0.164579 0.0822895 0.996608i \(-0.473777\pi\)
0.0822895 + 0.996608i \(0.473777\pi\)
\(510\) −40.8282 −1.80790
\(511\) 5.72225 0.253137
\(512\) 50.8526 2.24739
\(513\) −16.4939 −0.728222
\(514\) −40.0808 −1.76789
\(515\) −51.2810 −2.25971
\(516\) −5.93216 −0.261149
\(517\) −4.11432 −0.180947
\(518\) 16.5471 0.727040
\(519\) −0.630879 −0.0276925
\(520\) −22.7824 −0.999073
\(521\) 15.1139 0.662154 0.331077 0.943604i \(-0.392588\pi\)
0.331077 + 0.943604i \(0.392588\pi\)
\(522\) 32.8023 1.43572
\(523\) −24.4498 −1.06912 −0.534558 0.845132i \(-0.679522\pi\)
−0.534558 + 0.845132i \(0.679522\pi\)
\(524\) 86.4093 3.77481
\(525\) −5.16554 −0.225443
\(526\) −50.6056 −2.20651
\(527\) 59.2872 2.58259
\(528\) 6.72819 0.292807
\(529\) −13.5539 −0.589299
\(530\) 6.69224 0.290692
\(531\) 28.1085 1.21980
\(532\) −16.4759 −0.714320
\(533\) −6.40713 −0.277524
\(534\) −24.8549 −1.07558
\(535\) −23.8971 −1.03316
\(536\) 41.3543 1.78623
\(537\) −3.52694 −0.152199
\(538\) 43.0011 1.85391
\(539\) −10.2424 −0.441170
\(540\) −61.2675 −2.63653
\(541\) −25.5179 −1.09710 −0.548550 0.836118i \(-0.684820\pi\)
−0.548550 + 0.836118i \(0.684820\pi\)
\(542\) 41.2010 1.76973
\(543\) −9.31221 −0.399625
\(544\) −35.8647 −1.53768
\(545\) −42.9389 −1.83930
\(546\) 1.01592 0.0434772
\(547\) −30.7848 −1.31626 −0.658132 0.752903i \(-0.728653\pi\)
−0.658132 + 0.752903i \(0.728653\pi\)
\(548\) 17.0091 0.726591
\(549\) −24.4193 −1.04219
\(550\) −46.6344 −1.98850
\(551\) 23.8738 1.01706
\(552\) −11.5580 −0.491942
\(553\) −0.933613 −0.0397013
\(554\) −53.9388 −2.29164
\(555\) 20.9786 0.890493
\(556\) 42.7100 1.81131
\(557\) −18.8415 −0.798341 −0.399171 0.916877i \(-0.630702\pi\)
−0.399171 + 0.916877i \(0.630702\pi\)
\(558\) 60.2981 2.55262
\(559\) −1.97584 −0.0835692
\(560\) −21.6353 −0.914259
\(561\) 6.28421 0.265320
\(562\) −65.7573 −2.77381
\(563\) 30.5558 1.28777 0.643886 0.765121i \(-0.277321\pi\)
0.643886 + 0.765121i \(0.277321\pi\)
\(564\) −6.90532 −0.290766
\(565\) 62.3088 2.62135
\(566\) −77.2500 −3.24706
\(567\) −4.45099 −0.186924
\(568\) 93.1621 3.90900
\(569\) −36.8104 −1.54317 −0.771586 0.636125i \(-0.780536\pi\)
−0.771586 + 0.636125i \(0.780536\pi\)
\(570\) −30.2218 −1.26585
\(571\) −10.2175 −0.427591 −0.213795 0.976878i \(-0.568583\pi\)
−0.213795 + 0.976878i \(0.568583\pi\)
\(572\) 6.33914 0.265053
\(573\) 1.28529 0.0536938
\(574\) −13.7752 −0.574965
\(575\) 35.3852 1.47567
\(576\) 0.972719 0.0405299
\(577\) 14.4440 0.601314 0.300657 0.953732i \(-0.402794\pi\)
0.300657 + 0.953732i \(0.402794\pi\)
\(578\) −68.0974 −2.83248
\(579\) 15.2118 0.632180
\(580\) 88.6807 3.68226
\(581\) 0.155853 0.00646586
\(582\) 12.3447 0.511706
\(583\) −1.03006 −0.0426607
\(584\) 47.9625 1.98470
\(585\) −9.55927 −0.395227
\(586\) −33.8943 −1.40016
\(587\) 38.3102 1.58123 0.790616 0.612312i \(-0.209760\pi\)
0.790616 + 0.612312i \(0.209760\pi\)
\(588\) −17.1904 −0.708920
\(589\) 43.8854 1.80827
\(590\) 109.946 4.52640
\(591\) 5.97218 0.245663
\(592\) 61.2616 2.51784
\(593\) 37.2269 1.52873 0.764363 0.644787i \(-0.223054\pi\)
0.764363 + 0.644787i \(0.223054\pi\)
\(594\) 13.6439 0.559815
\(595\) −20.2077 −0.828434
\(596\) −2.61348 −0.107052
\(597\) −10.8011 −0.442059
\(598\) −6.95927 −0.284586
\(599\) −27.4364 −1.12102 −0.560511 0.828147i \(-0.689395\pi\)
−0.560511 + 0.828147i \(0.689395\pi\)
\(600\) −43.2963 −1.76757
\(601\) 17.9505 0.732216 0.366108 0.930572i \(-0.380690\pi\)
0.366108 + 0.930572i \(0.380690\pi\)
\(602\) −4.24802 −0.173136
\(603\) 17.3519 0.706624
\(604\) 15.7560 0.641101
\(605\) −34.4049 −1.39876
\(606\) 25.0744 1.01858
\(607\) −15.7500 −0.639272 −0.319636 0.947540i \(-0.603561\pi\)
−0.319636 + 0.947540i \(0.603561\pi\)
\(608\) −26.5477 −1.07665
\(609\) −2.18749 −0.0886417
\(610\) −95.5156 −3.86731
\(611\) −2.29997 −0.0930470
\(612\) −78.2799 −3.16428
\(613\) −1.84663 −0.0745845 −0.0372923 0.999304i \(-0.511873\pi\)
−0.0372923 + 0.999304i \(0.511873\pi\)
\(614\) −28.8766 −1.16536
\(615\) −17.4643 −0.704229
\(616\) 7.53917 0.303762
\(617\) −14.1576 −0.569962 −0.284981 0.958533i \(-0.591987\pi\)
−0.284981 + 0.958533i \(0.591987\pi\)
\(618\) 19.1668 0.771003
\(619\) 5.43999 0.218652 0.109326 0.994006i \(-0.465131\pi\)
0.109326 + 0.994006i \(0.465131\pi\)
\(620\) 163.015 6.54685
\(621\) −10.3527 −0.415440
\(622\) −73.4032 −2.94320
\(623\) −12.3018 −0.492860
\(624\) 3.76117 0.150567
\(625\) 49.9871 1.99949
\(626\) 18.5060 0.739650
\(627\) 4.65169 0.185770
\(628\) −34.2046 −1.36491
\(629\) 57.2192 2.28148
\(630\) −20.5522 −0.818821
\(631\) −25.5739 −1.01808 −0.509039 0.860743i \(-0.669999\pi\)
−0.509039 + 0.860743i \(0.669999\pi\)
\(632\) −7.82532 −0.311274
\(633\) −8.75860 −0.348123
\(634\) −5.85980 −0.232722
\(635\) 22.7413 0.902460
\(636\) −1.72881 −0.0685519
\(637\) −5.72565 −0.226859
\(638\) −19.7486 −0.781856
\(639\) 39.0900 1.54638
\(640\) 47.8680 1.89215
\(641\) −17.4812 −0.690467 −0.345234 0.938517i \(-0.612200\pi\)
−0.345234 + 0.938517i \(0.612200\pi\)
\(642\) 8.93179 0.352510
\(643\) 5.57208 0.219741 0.109871 0.993946i \(-0.464956\pi\)
0.109871 + 0.993946i \(0.464956\pi\)
\(644\) −10.3414 −0.407509
\(645\) −5.38567 −0.212061
\(646\) −82.4299 −3.24316
\(647\) −39.3096 −1.54542 −0.772709 0.634760i \(-0.781099\pi\)
−0.772709 + 0.634760i \(0.781099\pi\)
\(648\) −37.3071 −1.46556
\(649\) −16.9227 −0.664274
\(650\) −26.0694 −1.02253
\(651\) −4.02111 −0.157600
\(652\) −44.2674 −1.73365
\(653\) −24.1760 −0.946081 −0.473040 0.881041i \(-0.656843\pi\)
−0.473040 + 0.881041i \(0.656843\pi\)
\(654\) 16.0489 0.627561
\(655\) 78.4490 3.06525
\(656\) −50.9991 −1.99118
\(657\) 20.1246 0.785136
\(658\) −4.94489 −0.192772
\(659\) −7.82605 −0.304859 −0.152430 0.988314i \(-0.548710\pi\)
−0.152430 + 0.988314i \(0.548710\pi\)
\(660\) 17.2790 0.672584
\(661\) −24.2306 −0.942462 −0.471231 0.882010i \(-0.656190\pi\)
−0.471231 + 0.882010i \(0.656190\pi\)
\(662\) 35.5550 1.38189
\(663\) 3.51298 0.136433
\(664\) 1.30632 0.0506950
\(665\) −14.9581 −0.580049
\(666\) 58.1948 2.25500
\(667\) 14.9849 0.580216
\(668\) 14.0819 0.544844
\(669\) −10.2762 −0.397301
\(670\) 67.8717 2.62211
\(671\) 14.7016 0.567549
\(672\) 2.43250 0.0938355
\(673\) 32.4551 1.25105 0.625526 0.780204i \(-0.284885\pi\)
0.625526 + 0.780204i \(0.284885\pi\)
\(674\) 18.3334 0.706177
\(675\) −38.7812 −1.49269
\(676\) −54.6441 −2.10169
\(677\) 37.8082 1.45309 0.726543 0.687121i \(-0.241126\pi\)
0.726543 + 0.687121i \(0.241126\pi\)
\(678\) −23.2886 −0.894394
\(679\) 6.10995 0.234478
\(680\) −169.376 −6.49527
\(681\) 8.49422 0.325499
\(682\) −36.3025 −1.39009
\(683\) −36.8369 −1.40952 −0.704762 0.709444i \(-0.748946\pi\)
−0.704762 + 0.709444i \(0.748946\pi\)
\(684\) −57.9442 −2.21555
\(685\) 15.4421 0.590014
\(686\) −25.7011 −0.981273
\(687\) 16.0944 0.614041
\(688\) −15.7272 −0.599594
\(689\) −0.575820 −0.0219370
\(690\) −18.9693 −0.722149
\(691\) −47.2915 −1.79905 −0.899527 0.436864i \(-0.856089\pi\)
−0.899527 + 0.436864i \(0.856089\pi\)
\(692\) −4.73127 −0.179856
\(693\) 3.16337 0.120166
\(694\) 30.1858 1.14584
\(695\) 38.7754 1.47084
\(696\) −18.3350 −0.694988
\(697\) −47.6339 −1.80426
\(698\) 23.9860 0.907884
\(699\) −5.11509 −0.193470
\(700\) −38.7390 −1.46420
\(701\) 6.17292 0.233148 0.116574 0.993182i \(-0.462809\pi\)
0.116574 + 0.993182i \(0.462809\pi\)
\(702\) 7.62717 0.287869
\(703\) 42.3546 1.59744
\(704\) −0.585625 −0.0220716
\(705\) −6.26918 −0.236111
\(706\) 53.7570 2.02317
\(707\) 12.4104 0.466742
\(708\) −28.4024 −1.06743
\(709\) 48.6056 1.82542 0.912711 0.408607i \(-0.133985\pi\)
0.912711 + 0.408607i \(0.133985\pi\)
\(710\) 152.900 5.73823
\(711\) −3.28343 −0.123138
\(712\) −103.111 −3.86423
\(713\) 27.5456 1.03159
\(714\) 7.55284 0.282658
\(715\) 5.75516 0.215231
\(716\) −26.4503 −0.988493
\(717\) −6.56626 −0.245221
\(718\) −68.3623 −2.55126
\(719\) −52.0520 −1.94121 −0.970605 0.240676i \(-0.922631\pi\)
−0.970605 + 0.240676i \(0.922631\pi\)
\(720\) −76.0894 −2.83569
\(721\) 9.48650 0.353296
\(722\) −12.6649 −0.471340
\(723\) −0.518309 −0.0192761
\(724\) −69.8369 −2.59547
\(725\) 56.1333 2.08474
\(726\) 12.8592 0.477250
\(727\) 47.1599 1.74906 0.874531 0.484969i \(-0.161169\pi\)
0.874531 + 0.484969i \(0.161169\pi\)
\(728\) 4.21453 0.156201
\(729\) −9.62251 −0.356389
\(730\) 78.7172 2.91345
\(731\) −14.6894 −0.543308
\(732\) 24.6747 0.912001
\(733\) −14.4317 −0.533047 −0.266523 0.963828i \(-0.585875\pi\)
−0.266523 + 0.963828i \(0.585875\pi\)
\(734\) 0.126415 0.00466606
\(735\) −15.6068 −0.575664
\(736\) −16.6632 −0.614213
\(737\) −10.4467 −0.384809
\(738\) −48.4461 −1.78332
\(739\) 15.0399 0.553251 0.276626 0.960978i \(-0.410784\pi\)
0.276626 + 0.960978i \(0.410784\pi\)
\(740\) 157.329 5.78353
\(741\) 2.60037 0.0955271
\(742\) −1.23800 −0.0454485
\(743\) 30.6441 1.12422 0.562112 0.827061i \(-0.309989\pi\)
0.562112 + 0.827061i \(0.309989\pi\)
\(744\) −33.7040 −1.23565
\(745\) −2.37272 −0.0869298
\(746\) −75.5885 −2.76749
\(747\) 0.548120 0.0200546
\(748\) 47.1284 1.72319
\(749\) 4.42073 0.161530
\(750\) −40.1991 −1.46786
\(751\) −6.00695 −0.219197 −0.109598 0.993976i \(-0.534956\pi\)
−0.109598 + 0.993976i \(0.534956\pi\)
\(752\) −18.3072 −0.667596
\(753\) 15.2589 0.556065
\(754\) −11.0398 −0.402047
\(755\) 14.3045 0.520593
\(756\) 11.3339 0.412211
\(757\) −5.08382 −0.184774 −0.0923872 0.995723i \(-0.529450\pi\)
−0.0923872 + 0.995723i \(0.529450\pi\)
\(758\) −18.5019 −0.672021
\(759\) 2.91972 0.105979
\(760\) −125.375 −4.54783
\(761\) 3.62296 0.131332 0.0656660 0.997842i \(-0.479083\pi\)
0.0656660 + 0.997842i \(0.479083\pi\)
\(762\) −8.49980 −0.307915
\(763\) 7.94329 0.287566
\(764\) 9.63903 0.348728
\(765\) −71.0685 −2.56949
\(766\) −35.9202 −1.29785
\(767\) −9.46008 −0.341584
\(768\) −17.4520 −0.629744
\(769\) 13.2246 0.476891 0.238446 0.971156i \(-0.423362\pi\)
0.238446 + 0.971156i \(0.423362\pi\)
\(770\) 12.3735 0.445909
\(771\) 9.40027 0.338543
\(772\) 114.081 4.10585
\(773\) 19.8487 0.713908 0.356954 0.934122i \(-0.383815\pi\)
0.356954 + 0.934122i \(0.383815\pi\)
\(774\) −14.9399 −0.537003
\(775\) 103.186 3.70654
\(776\) 51.2121 1.83841
\(777\) −3.88085 −0.139225
\(778\) −72.5213 −2.60002
\(779\) −35.2594 −1.26330
\(780\) 9.65925 0.345857
\(781\) −23.5341 −0.842116
\(782\) −51.7388 −1.85017
\(783\) −16.4230 −0.586910
\(784\) −45.5748 −1.62767
\(785\) −31.0535 −1.10835
\(786\) −29.3212 −1.04585
\(787\) −42.7482 −1.52381 −0.761904 0.647690i \(-0.775735\pi\)
−0.761904 + 0.647690i \(0.775735\pi\)
\(788\) 44.7883 1.59552
\(789\) 11.8687 0.422536
\(790\) −12.8431 −0.456937
\(791\) −11.5266 −0.409837
\(792\) 26.5146 0.942154
\(793\) 8.21845 0.291846
\(794\) −28.0925 −0.996965
\(795\) −1.56955 −0.0556662
\(796\) −81.0027 −2.87106
\(797\) −26.2040 −0.928192 −0.464096 0.885785i \(-0.653621\pi\)
−0.464096 + 0.885785i \(0.653621\pi\)
\(798\) 5.59075 0.197910
\(799\) −17.0992 −0.604926
\(800\) −62.4202 −2.20689
\(801\) −43.2642 −1.52867
\(802\) 80.0298 2.82595
\(803\) −12.1160 −0.427565
\(804\) −17.5334 −0.618354
\(805\) −9.38874 −0.330909
\(806\) −20.2937 −0.714815
\(807\) −10.0852 −0.355015
\(808\) 104.021 3.65945
\(809\) 38.1138 1.34001 0.670005 0.742357i \(-0.266292\pi\)
0.670005 + 0.742357i \(0.266292\pi\)
\(810\) −61.2293 −2.15138
\(811\) −10.3856 −0.364689 −0.182345 0.983235i \(-0.558369\pi\)
−0.182345 + 0.983235i \(0.558369\pi\)
\(812\) −16.4051 −0.575706
\(813\) −9.66298 −0.338895
\(814\) −35.0362 −1.22802
\(815\) −40.1894 −1.40777
\(816\) 27.9625 0.978883
\(817\) −10.8734 −0.380411
\(818\) 59.6573 2.08587
\(819\) 1.76838 0.0617921
\(820\) −130.973 −4.57379
\(821\) 0.0281231 0.000981503 0 0.000490751 1.00000i \(-0.499844\pi\)
0.000490751 1.00000i \(0.499844\pi\)
\(822\) −5.77167 −0.201310
\(823\) −47.7297 −1.66375 −0.831876 0.554962i \(-0.812733\pi\)
−0.831876 + 0.554962i \(0.812733\pi\)
\(824\) 79.5135 2.76999
\(825\) 10.9373 0.380787
\(826\) −20.3390 −0.707683
\(827\) −19.1070 −0.664414 −0.332207 0.943206i \(-0.607793\pi\)
−0.332207 + 0.943206i \(0.607793\pi\)
\(828\) −36.3698 −1.26394
\(829\) −36.9455 −1.28317 −0.641585 0.767052i \(-0.721723\pi\)
−0.641585 + 0.767052i \(0.721723\pi\)
\(830\) 2.14396 0.0744180
\(831\) 12.6504 0.438838
\(832\) −0.327374 −0.0113497
\(833\) −42.5674 −1.47487
\(834\) −14.4927 −0.501843
\(835\) 12.7846 0.442429
\(836\) 34.8853 1.20653
\(837\) −30.1892 −1.04349
\(838\) −44.3828 −1.53318
\(839\) −10.7769 −0.372059 −0.186029 0.982544i \(-0.559562\pi\)
−0.186029 + 0.982544i \(0.559562\pi\)
\(840\) 11.4878 0.396367
\(841\) −5.22879 −0.180303
\(842\) 75.6462 2.60694
\(843\) 15.4223 0.531171
\(844\) −65.6851 −2.26097
\(845\) −49.6101 −1.70664
\(846\) −17.3907 −0.597906
\(847\) 6.36458 0.218690
\(848\) −4.58339 −0.157394
\(849\) 18.1177 0.621796
\(850\) −193.813 −6.64774
\(851\) 26.5847 0.911313
\(852\) −39.4988 −1.35321
\(853\) −13.4397 −0.460167 −0.230084 0.973171i \(-0.573900\pi\)
−0.230084 + 0.973171i \(0.573900\pi\)
\(854\) 17.6695 0.604638
\(855\) −52.6062 −1.79909
\(856\) 37.0535 1.26646
\(857\) 34.9765 1.19478 0.597388 0.801952i \(-0.296205\pi\)
0.597388 + 0.801952i \(0.296205\pi\)
\(858\) −2.15105 −0.0734358
\(859\) 49.8304 1.70019 0.850096 0.526627i \(-0.176544\pi\)
0.850096 + 0.526627i \(0.176544\pi\)
\(860\) −40.3898 −1.37728
\(861\) 3.23073 0.110103
\(862\) 70.0274 2.38514
\(863\) 40.0338 1.36277 0.681383 0.731927i \(-0.261379\pi\)
0.681383 + 0.731927i \(0.261379\pi\)
\(864\) 18.2624 0.621299
\(865\) −4.29541 −0.146048
\(866\) 25.6621 0.872033
\(867\) 15.9711 0.542406
\(868\) −30.1563 −1.02357
\(869\) 1.97679 0.0670580
\(870\) −30.0919 −1.02021
\(871\) −5.83989 −0.197877
\(872\) 66.5787 2.25464
\(873\) 21.4881 0.727263
\(874\) −38.2979 −1.29545
\(875\) −19.8963 −0.672618
\(876\) −20.3351 −0.687059
\(877\) 30.1705 1.01879 0.509393 0.860534i \(-0.329870\pi\)
0.509393 + 0.860534i \(0.329870\pi\)
\(878\) 70.8355 2.39058
\(879\) 7.94933 0.268124
\(880\) 45.8096 1.54424
\(881\) 46.5443 1.56812 0.784058 0.620687i \(-0.213146\pi\)
0.784058 + 0.620687i \(0.213146\pi\)
\(882\) −43.2933 −1.45776
\(883\) −7.16157 −0.241006 −0.120503 0.992713i \(-0.538451\pi\)
−0.120503 + 0.992713i \(0.538451\pi\)
\(884\) 26.3456 0.886098
\(885\) −25.7859 −0.866784
\(886\) 94.7223 3.18226
\(887\) 40.3578 1.35508 0.677541 0.735485i \(-0.263046\pi\)
0.677541 + 0.735485i \(0.263046\pi\)
\(888\) −32.5283 −1.09158
\(889\) −4.20692 −0.141096
\(890\) −169.228 −5.67252
\(891\) 9.42432 0.315727
\(892\) −77.0664 −2.58037
\(893\) −12.6571 −0.423554
\(894\) 0.886831 0.0296601
\(895\) −24.0136 −0.802686
\(896\) −8.85512 −0.295829
\(897\) 1.63218 0.0544968
\(898\) −28.1947 −0.940869
\(899\) 43.6969 1.45737
\(900\) −136.241 −4.54138
\(901\) −4.28094 −0.142619
\(902\) 29.1669 0.971153
\(903\) 0.996299 0.0331548
\(904\) −96.6128 −3.21329
\(905\) −63.4033 −2.10760
\(906\) −5.34645 −0.177624
\(907\) 6.22170 0.206588 0.103294 0.994651i \(-0.467062\pi\)
0.103294 + 0.994651i \(0.467062\pi\)
\(908\) 63.7023 2.11404
\(909\) 43.6463 1.44766
\(910\) 6.91698 0.229296
\(911\) −15.9935 −0.529890 −0.264945 0.964264i \(-0.585354\pi\)
−0.264945 + 0.964264i \(0.585354\pi\)
\(912\) 20.6983 0.685390
\(913\) −0.329995 −0.0109213
\(914\) −40.6026 −1.34302
\(915\) 22.4015 0.740572
\(916\) 120.700 3.98804
\(917\) −14.5123 −0.479239
\(918\) 56.7043 1.87152
\(919\) 6.37731 0.210368 0.105184 0.994453i \(-0.466457\pi\)
0.105184 + 0.994453i \(0.466457\pi\)
\(920\) −78.6941 −2.59447
\(921\) 6.77250 0.223161
\(922\) 8.90718 0.293342
\(923\) −13.1560 −0.433034
\(924\) −3.19645 −0.105156
\(925\) 99.5864 3.27438
\(926\) −85.7546 −2.81807
\(927\) 33.3631 1.09579
\(928\) −26.4336 −0.867725
\(929\) 36.3215 1.19167 0.595835 0.803107i \(-0.296821\pi\)
0.595835 + 0.803107i \(0.296821\pi\)
\(930\) −55.3158 −1.81388
\(931\) −31.5092 −1.03267
\(932\) −38.3605 −1.25654
\(933\) 17.2155 0.563609
\(934\) −11.2149 −0.366963
\(935\) 42.7868 1.39928
\(936\) 14.8221 0.484476
\(937\) −12.6650 −0.413748 −0.206874 0.978368i \(-0.566329\pi\)
−0.206874 + 0.978368i \(0.566329\pi\)
\(938\) −12.5556 −0.409956
\(939\) −4.34027 −0.141639
\(940\) −47.0157 −1.53348
\(941\) 15.8726 0.517431 0.258715 0.965954i \(-0.416701\pi\)
0.258715 + 0.965954i \(0.416701\pi\)
\(942\) 11.6066 0.378164
\(943\) −22.1313 −0.720694
\(944\) −75.2999 −2.45080
\(945\) 10.2898 0.334727
\(946\) 8.99456 0.292438
\(947\) 24.0174 0.780462 0.390231 0.920717i \(-0.372395\pi\)
0.390231 + 0.920717i \(0.372395\pi\)
\(948\) 3.31777 0.107756
\(949\) −6.77307 −0.219863
\(950\) −143.464 −4.65459
\(951\) 1.37431 0.0445652
\(952\) 31.3329 1.01551
\(953\) −47.1370 −1.52692 −0.763459 0.645856i \(-0.776500\pi\)
−0.763459 + 0.645856i \(0.776500\pi\)
\(954\) −4.35394 −0.140964
\(955\) 8.75105 0.283177
\(956\) −49.2436 −1.59265
\(957\) 4.63170 0.149722
\(958\) 44.3892 1.43415
\(959\) −2.85665 −0.0922461
\(960\) −0.892345 −0.0288003
\(961\) 49.3248 1.59112
\(962\) −19.5858 −0.631472
\(963\) 15.5473 0.501005
\(964\) −3.88705 −0.125194
\(965\) 103.571 3.33407
\(966\) 3.50914 0.112905
\(967\) −39.0783 −1.25667 −0.628336 0.777942i \(-0.716264\pi\)
−0.628336 + 0.777942i \(0.716264\pi\)
\(968\) 53.3464 1.71462
\(969\) 19.3325 0.621049
\(970\) 84.0505 2.69870
\(971\) −39.9791 −1.28299 −0.641496 0.767127i \(-0.721686\pi\)
−0.641496 + 0.767127i \(0.721686\pi\)
\(972\) 61.0484 1.95813
\(973\) −7.17310 −0.229959
\(974\) 42.4037 1.35870
\(975\) 6.11413 0.195809
\(976\) 65.4168 2.09394
\(977\) 19.1459 0.612532 0.306266 0.951946i \(-0.400920\pi\)
0.306266 + 0.951946i \(0.400920\pi\)
\(978\) 15.0212 0.480325
\(979\) 26.0472 0.832473
\(980\) −117.043 −3.73880
\(981\) 27.9358 0.891922
\(982\) 16.9461 0.540771
\(983\) 0.0268941 0.000857788 0 0.000428894 1.00000i \(-0.499863\pi\)
0.000428894 1.00000i \(0.499863\pi\)
\(984\) 27.0792 0.863254
\(985\) 40.6623 1.29561
\(986\) −82.0757 −2.61382
\(987\) 1.15974 0.0369149
\(988\) 19.5015 0.620425
\(989\) −6.82489 −0.217019
\(990\) 43.5164 1.38304
\(991\) 5.07781 0.161302 0.0806510 0.996742i \(-0.474300\pi\)
0.0806510 + 0.996742i \(0.474300\pi\)
\(992\) −48.5910 −1.54276
\(993\) −8.33882 −0.264624
\(994\) −28.2851 −0.897147
\(995\) −73.5404 −2.33139
\(996\) −0.553852 −0.0175495
\(997\) 12.7721 0.404495 0.202247 0.979334i \(-0.435175\pi\)
0.202247 + 0.979334i \(0.435175\pi\)
\(998\) −1.04199 −0.0329837
\(999\) −29.1362 −0.921827
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.1.8 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.8 174 1.1 even 1 trivial