Properties

Label 4006.2.a.g.1.10
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.84543 q^{3} +1.00000 q^{4} +2.20410 q^{5} +1.84543 q^{6} -0.412853 q^{7} -1.00000 q^{8} +0.405623 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.84543 q^{3} +1.00000 q^{4} +2.20410 q^{5} +1.84543 q^{6} -0.412853 q^{7} -1.00000 q^{8} +0.405623 q^{9} -2.20410 q^{10} +0.613987 q^{11} -1.84543 q^{12} +3.23787 q^{13} +0.412853 q^{14} -4.06752 q^{15} +1.00000 q^{16} -2.81009 q^{17} -0.405623 q^{18} -1.83735 q^{19} +2.20410 q^{20} +0.761893 q^{21} -0.613987 q^{22} +2.84700 q^{23} +1.84543 q^{24} -0.141945 q^{25} -3.23787 q^{26} +4.78775 q^{27} -0.412853 q^{28} -7.99940 q^{29} +4.06752 q^{30} +1.84300 q^{31} -1.00000 q^{32} -1.13307 q^{33} +2.81009 q^{34} -0.909969 q^{35} +0.405623 q^{36} -5.43376 q^{37} +1.83735 q^{38} -5.97528 q^{39} -2.20410 q^{40} +9.53639 q^{41} -0.761893 q^{42} +2.50374 q^{43} +0.613987 q^{44} +0.894034 q^{45} -2.84700 q^{46} -3.96547 q^{47} -1.84543 q^{48} -6.82955 q^{49} +0.141945 q^{50} +5.18584 q^{51} +3.23787 q^{52} -5.16802 q^{53} -4.78775 q^{54} +1.35329 q^{55} +0.412853 q^{56} +3.39071 q^{57} +7.99940 q^{58} -2.37561 q^{59} -4.06752 q^{60} -0.510931 q^{61} -1.84300 q^{62} -0.167463 q^{63} +1.00000 q^{64} +7.13660 q^{65} +1.13307 q^{66} +2.29164 q^{67} -2.81009 q^{68} -5.25394 q^{69} +0.909969 q^{70} -4.88690 q^{71} -0.405623 q^{72} -14.2025 q^{73} +5.43376 q^{74} +0.261949 q^{75} -1.83735 q^{76} -0.253486 q^{77} +5.97528 q^{78} +7.76859 q^{79} +2.20410 q^{80} -10.0523 q^{81} -9.53639 q^{82} -0.852265 q^{83} +0.761893 q^{84} -6.19373 q^{85} -2.50374 q^{86} +14.7624 q^{87} -0.613987 q^{88} -0.595183 q^{89} -0.894034 q^{90} -1.33677 q^{91} +2.84700 q^{92} -3.40114 q^{93} +3.96547 q^{94} -4.04971 q^{95} +1.84543 q^{96} +18.9285 q^{97} +6.82955 q^{98} +0.249048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.84543 −1.06546 −0.532731 0.846285i \(-0.678834\pi\)
−0.532731 + 0.846285i \(0.678834\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.20410 0.985703 0.492852 0.870113i \(-0.335955\pi\)
0.492852 + 0.870113i \(0.335955\pi\)
\(6\) 1.84543 0.753395
\(7\) −0.412853 −0.156044 −0.0780219 0.996952i \(-0.524860\pi\)
−0.0780219 + 0.996952i \(0.524860\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.405623 0.135208
\(10\) −2.20410 −0.696998
\(11\) 0.613987 0.185124 0.0925620 0.995707i \(-0.470494\pi\)
0.0925620 + 0.995707i \(0.470494\pi\)
\(12\) −1.84543 −0.532731
\(13\) 3.23787 0.898024 0.449012 0.893526i \(-0.351776\pi\)
0.449012 + 0.893526i \(0.351776\pi\)
\(14\) 0.412853 0.110340
\(15\) −4.06752 −1.05023
\(16\) 1.00000 0.250000
\(17\) −2.81009 −0.681548 −0.340774 0.940145i \(-0.610689\pi\)
−0.340774 + 0.940145i \(0.610689\pi\)
\(18\) −0.405623 −0.0956064
\(19\) −1.83735 −0.421518 −0.210759 0.977538i \(-0.567594\pi\)
−0.210759 + 0.977538i \(0.567594\pi\)
\(20\) 2.20410 0.492852
\(21\) 0.761893 0.166259
\(22\) −0.613987 −0.130903
\(23\) 2.84700 0.593640 0.296820 0.954933i \(-0.404074\pi\)
0.296820 + 0.954933i \(0.404074\pi\)
\(24\) 1.84543 0.376697
\(25\) −0.141945 −0.0283889
\(26\) −3.23787 −0.634999
\(27\) 4.78775 0.921403
\(28\) −0.412853 −0.0780219
\(29\) −7.99940 −1.48545 −0.742726 0.669596i \(-0.766467\pi\)
−0.742726 + 0.669596i \(0.766467\pi\)
\(30\) 4.06752 0.742624
\(31\) 1.84300 0.331013 0.165507 0.986209i \(-0.447074\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.13307 −0.197243
\(34\) 2.81009 0.481927
\(35\) −0.909969 −0.153813
\(36\) 0.405623 0.0676039
\(37\) −5.43376 −0.893304 −0.446652 0.894708i \(-0.647384\pi\)
−0.446652 + 0.894708i \(0.647384\pi\)
\(38\) 1.83735 0.298058
\(39\) −5.97528 −0.956810
\(40\) −2.20410 −0.348499
\(41\) 9.53639 1.48933 0.744667 0.667436i \(-0.232608\pi\)
0.744667 + 0.667436i \(0.232608\pi\)
\(42\) −0.761893 −0.117563
\(43\) 2.50374 0.381817 0.190909 0.981608i \(-0.438857\pi\)
0.190909 + 0.981608i \(0.438857\pi\)
\(44\) 0.613987 0.0925620
\(45\) 0.894034 0.133275
\(46\) −2.84700 −0.419767
\(47\) −3.96547 −0.578423 −0.289211 0.957265i \(-0.593393\pi\)
−0.289211 + 0.957265i \(0.593393\pi\)
\(48\) −1.84543 −0.266365
\(49\) −6.82955 −0.975650
\(50\) 0.141945 0.0200740
\(51\) 5.18584 0.726163
\(52\) 3.23787 0.449012
\(53\) −5.16802 −0.709882 −0.354941 0.934889i \(-0.615499\pi\)
−0.354941 + 0.934889i \(0.615499\pi\)
\(54\) −4.78775 −0.651530
\(55\) 1.35329 0.182477
\(56\) 0.412853 0.0551698
\(57\) 3.39071 0.449111
\(58\) 7.99940 1.05037
\(59\) −2.37561 −0.309278 −0.154639 0.987971i \(-0.549421\pi\)
−0.154639 + 0.987971i \(0.549421\pi\)
\(60\) −4.06752 −0.525114
\(61\) −0.510931 −0.0654180 −0.0327090 0.999465i \(-0.510413\pi\)
−0.0327090 + 0.999465i \(0.510413\pi\)
\(62\) −1.84300 −0.234062
\(63\) −0.167463 −0.0210983
\(64\) 1.00000 0.125000
\(65\) 7.13660 0.885186
\(66\) 1.13307 0.139472
\(67\) 2.29164 0.279969 0.139984 0.990154i \(-0.455295\pi\)
0.139984 + 0.990154i \(0.455295\pi\)
\(68\) −2.81009 −0.340774
\(69\) −5.25394 −0.632500
\(70\) 0.909969 0.108762
\(71\) −4.88690 −0.579968 −0.289984 0.957031i \(-0.593650\pi\)
−0.289984 + 0.957031i \(0.593650\pi\)
\(72\) −0.405623 −0.0478032
\(73\) −14.2025 −1.66227 −0.831137 0.556068i \(-0.812310\pi\)
−0.831137 + 0.556068i \(0.812310\pi\)
\(74\) 5.43376 0.631662
\(75\) 0.261949 0.0302473
\(76\) −1.83735 −0.210759
\(77\) −0.253486 −0.0288875
\(78\) 5.97528 0.676567
\(79\) 7.76859 0.874035 0.437017 0.899453i \(-0.356035\pi\)
0.437017 + 0.899453i \(0.356035\pi\)
\(80\) 2.20410 0.246426
\(81\) −10.0523 −1.11693
\(82\) −9.53639 −1.05312
\(83\) −0.852265 −0.0935482 −0.0467741 0.998905i \(-0.514894\pi\)
−0.0467741 + 0.998905i \(0.514894\pi\)
\(84\) 0.761893 0.0831293
\(85\) −6.19373 −0.671804
\(86\) −2.50374 −0.269986
\(87\) 14.7624 1.58269
\(88\) −0.613987 −0.0654513
\(89\) −0.595183 −0.0630893 −0.0315447 0.999502i \(-0.510043\pi\)
−0.0315447 + 0.999502i \(0.510043\pi\)
\(90\) −0.894034 −0.0942395
\(91\) −1.33677 −0.140131
\(92\) 2.84700 0.296820
\(93\) −3.40114 −0.352682
\(94\) 3.96547 0.409007
\(95\) −4.04971 −0.415492
\(96\) 1.84543 0.188349
\(97\) 18.9285 1.92190 0.960948 0.276729i \(-0.0892504\pi\)
0.960948 + 0.276729i \(0.0892504\pi\)
\(98\) 6.82955 0.689889
\(99\) 0.249048 0.0250302
\(100\) −0.141945 −0.0141945
\(101\) −7.69750 −0.765930 −0.382965 0.923763i \(-0.625097\pi\)
−0.382965 + 0.923763i \(0.625097\pi\)
\(102\) −5.18584 −0.513475
\(103\) −16.1656 −1.59284 −0.796421 0.604742i \(-0.793276\pi\)
−0.796421 + 0.604742i \(0.793276\pi\)
\(104\) −3.23787 −0.317500
\(105\) 1.67929 0.163882
\(106\) 5.16802 0.501962
\(107\) 2.94855 0.285047 0.142523 0.989791i \(-0.454478\pi\)
0.142523 + 0.989791i \(0.454478\pi\)
\(108\) 4.78775 0.460701
\(109\) 12.5956 1.20644 0.603219 0.797575i \(-0.293884\pi\)
0.603219 + 0.797575i \(0.293884\pi\)
\(110\) −1.35329 −0.129031
\(111\) 10.0276 0.951781
\(112\) −0.412853 −0.0390109
\(113\) 2.86920 0.269911 0.134956 0.990852i \(-0.456911\pi\)
0.134956 + 0.990852i \(0.456911\pi\)
\(114\) −3.39071 −0.317569
\(115\) 6.27506 0.585153
\(116\) −7.99940 −0.742726
\(117\) 1.31336 0.121420
\(118\) 2.37561 0.218692
\(119\) 1.16016 0.106351
\(120\) 4.06752 0.371312
\(121\) −10.6230 −0.965729
\(122\) 0.510931 0.0462575
\(123\) −17.5988 −1.58683
\(124\) 1.84300 0.165507
\(125\) −11.3334 −1.01369
\(126\) 0.167463 0.0149188
\(127\) −3.05903 −0.271445 −0.135722 0.990747i \(-0.543336\pi\)
−0.135722 + 0.990747i \(0.543336\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.62049 −0.406812
\(130\) −7.13660 −0.625921
\(131\) −11.1186 −0.971435 −0.485718 0.874116i \(-0.661442\pi\)
−0.485718 + 0.874116i \(0.661442\pi\)
\(132\) −1.13307 −0.0986213
\(133\) 0.758557 0.0657752
\(134\) −2.29164 −0.197968
\(135\) 10.5527 0.908230
\(136\) 2.81009 0.240963
\(137\) 13.2197 1.12943 0.564716 0.825286i \(-0.308986\pi\)
0.564716 + 0.825286i \(0.308986\pi\)
\(138\) 5.25394 0.447245
\(139\) 22.7215 1.92721 0.963605 0.267329i \(-0.0861410\pi\)
0.963605 + 0.267329i \(0.0861410\pi\)
\(140\) −0.909969 −0.0769064
\(141\) 7.31800 0.616287
\(142\) 4.88690 0.410099
\(143\) 1.98801 0.166246
\(144\) 0.405623 0.0338020
\(145\) −17.6315 −1.46421
\(146\) 14.2025 1.17541
\(147\) 12.6035 1.03952
\(148\) −5.43376 −0.446652
\(149\) −11.3141 −0.926886 −0.463443 0.886127i \(-0.653386\pi\)
−0.463443 + 0.886127i \(0.653386\pi\)
\(150\) −0.261949 −0.0213881
\(151\) 4.74613 0.386234 0.193117 0.981176i \(-0.438140\pi\)
0.193117 + 0.981176i \(0.438140\pi\)
\(152\) 1.83735 0.149029
\(153\) −1.13984 −0.0921506
\(154\) 0.253486 0.0204265
\(155\) 4.06216 0.326281
\(156\) −5.97528 −0.478405
\(157\) 2.51669 0.200854 0.100427 0.994944i \(-0.467979\pi\)
0.100427 + 0.994944i \(0.467979\pi\)
\(158\) −7.76859 −0.618036
\(159\) 9.53723 0.756351
\(160\) −2.20410 −0.174249
\(161\) −1.17539 −0.0926338
\(162\) 10.0523 0.789786
\(163\) 9.39573 0.735931 0.367965 0.929840i \(-0.380055\pi\)
0.367965 + 0.929840i \(0.380055\pi\)
\(164\) 9.53639 0.744667
\(165\) −2.49740 −0.194423
\(166\) 0.852265 0.0661486
\(167\) 22.1687 1.71546 0.857732 0.514098i \(-0.171873\pi\)
0.857732 + 0.514098i \(0.171873\pi\)
\(168\) −0.761893 −0.0587813
\(169\) −2.51618 −0.193552
\(170\) 6.19373 0.475037
\(171\) −0.745274 −0.0569925
\(172\) 2.50374 0.190909
\(173\) −24.2226 −1.84161 −0.920805 0.390024i \(-0.872467\pi\)
−0.920805 + 0.390024i \(0.872467\pi\)
\(174\) −14.7624 −1.11913
\(175\) 0.0586023 0.00442992
\(176\) 0.613987 0.0462810
\(177\) 4.38402 0.329523
\(178\) 0.595183 0.0446109
\(179\) 15.9452 1.19180 0.595901 0.803058i \(-0.296795\pi\)
0.595901 + 0.803058i \(0.296795\pi\)
\(180\) 0.894034 0.0666374
\(181\) −4.41586 −0.328228 −0.164114 0.986441i \(-0.552477\pi\)
−0.164114 + 0.986441i \(0.552477\pi\)
\(182\) 1.33677 0.0990877
\(183\) 0.942890 0.0697004
\(184\) −2.84700 −0.209883
\(185\) −11.9765 −0.880533
\(186\) 3.40114 0.249384
\(187\) −1.72536 −0.126171
\(188\) −3.96547 −0.289211
\(189\) −1.97664 −0.143779
\(190\) 4.04971 0.293797
\(191\) −18.9795 −1.37331 −0.686655 0.726984i \(-0.740922\pi\)
−0.686655 + 0.726984i \(0.740922\pi\)
\(192\) −1.84543 −0.133183
\(193\) −7.63259 −0.549406 −0.274703 0.961529i \(-0.588579\pi\)
−0.274703 + 0.961529i \(0.588579\pi\)
\(194\) −18.9285 −1.35899
\(195\) −13.1701 −0.943131
\(196\) −6.82955 −0.487825
\(197\) −0.382685 −0.0272652 −0.0136326 0.999907i \(-0.504340\pi\)
−0.0136326 + 0.999907i \(0.504340\pi\)
\(198\) −0.249048 −0.0176990
\(199\) −6.58628 −0.466889 −0.233445 0.972370i \(-0.575000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(200\) 0.141945 0.0100370
\(201\) −4.22908 −0.298296
\(202\) 7.69750 0.541594
\(203\) 3.30258 0.231795
\(204\) 5.18584 0.363081
\(205\) 21.0191 1.46804
\(206\) 16.1656 1.12631
\(207\) 1.15481 0.0802647
\(208\) 3.23787 0.224506
\(209\) −1.12811 −0.0780331
\(210\) −1.67929 −0.115882
\(211\) −24.2030 −1.66620 −0.833101 0.553121i \(-0.813437\pi\)
−0.833101 + 0.553121i \(0.813437\pi\)
\(212\) −5.16802 −0.354941
\(213\) 9.01844 0.617934
\(214\) −2.94855 −0.201559
\(215\) 5.51850 0.376359
\(216\) −4.78775 −0.325765
\(217\) −0.760889 −0.0516525
\(218\) −12.5956 −0.853081
\(219\) 26.2097 1.77109
\(220\) 1.35329 0.0912387
\(221\) −9.09873 −0.612047
\(222\) −10.0276 −0.673011
\(223\) −5.06650 −0.339278 −0.169639 0.985506i \(-0.554260\pi\)
−0.169639 + 0.985506i \(0.554260\pi\)
\(224\) 0.412853 0.0275849
\(225\) −0.0575761 −0.00383841
\(226\) −2.86920 −0.190856
\(227\) 25.1159 1.66700 0.833502 0.552517i \(-0.186332\pi\)
0.833502 + 0.552517i \(0.186332\pi\)
\(228\) 3.39071 0.224555
\(229\) −0.667287 −0.0440955 −0.0220478 0.999757i \(-0.507019\pi\)
−0.0220478 + 0.999757i \(0.507019\pi\)
\(230\) −6.27506 −0.413765
\(231\) 0.467792 0.0307785
\(232\) 7.99940 0.525187
\(233\) −16.6357 −1.08984 −0.544919 0.838488i \(-0.683440\pi\)
−0.544919 + 0.838488i \(0.683440\pi\)
\(234\) −1.31336 −0.0858568
\(235\) −8.74028 −0.570153
\(236\) −2.37561 −0.154639
\(237\) −14.3364 −0.931250
\(238\) −1.16016 −0.0752017
\(239\) −27.9364 −1.80706 −0.903528 0.428529i \(-0.859032\pi\)
−0.903528 + 0.428529i \(0.859032\pi\)
\(240\) −4.06752 −0.262557
\(241\) −0.274279 −0.0176679 −0.00883393 0.999961i \(-0.502812\pi\)
−0.00883393 + 0.999961i \(0.502812\pi\)
\(242\) 10.6230 0.682874
\(243\) 4.18768 0.268640
\(244\) −0.510931 −0.0327090
\(245\) −15.0530 −0.961702
\(246\) 17.5988 1.12206
\(247\) −5.94912 −0.378533
\(248\) −1.84300 −0.117031
\(249\) 1.57280 0.0996720
\(250\) 11.3334 0.716785
\(251\) 19.9593 1.25982 0.629909 0.776669i \(-0.283092\pi\)
0.629909 + 0.776669i \(0.283092\pi\)
\(252\) −0.167463 −0.0105492
\(253\) 1.74802 0.109897
\(254\) 3.05903 0.191941
\(255\) 11.4301 0.715781
\(256\) 1.00000 0.0625000
\(257\) −5.23270 −0.326407 −0.163204 0.986592i \(-0.552183\pi\)
−0.163204 + 0.986592i \(0.552183\pi\)
\(258\) 4.62049 0.287659
\(259\) 2.24334 0.139395
\(260\) 7.13660 0.442593
\(261\) −3.24475 −0.200845
\(262\) 11.1186 0.686909
\(263\) 3.60326 0.222186 0.111093 0.993810i \(-0.464565\pi\)
0.111093 + 0.993810i \(0.464565\pi\)
\(264\) 1.13307 0.0697358
\(265\) −11.3908 −0.699733
\(266\) −0.758557 −0.0465101
\(267\) 1.09837 0.0672192
\(268\) 2.29164 0.139984
\(269\) −13.8660 −0.845425 −0.422713 0.906264i \(-0.638922\pi\)
−0.422713 + 0.906264i \(0.638922\pi\)
\(270\) −10.5527 −0.642215
\(271\) −13.3486 −0.810869 −0.405435 0.914124i \(-0.632880\pi\)
−0.405435 + 0.914124i \(0.632880\pi\)
\(272\) −2.81009 −0.170387
\(273\) 2.46691 0.149304
\(274\) −13.2197 −0.798629
\(275\) −0.0871522 −0.00525548
\(276\) −5.25394 −0.316250
\(277\) −11.7832 −0.707983 −0.353991 0.935249i \(-0.615176\pi\)
−0.353991 + 0.935249i \(0.615176\pi\)
\(278\) −22.7215 −1.36274
\(279\) 0.747565 0.0447555
\(280\) 0.909969 0.0543811
\(281\) −18.2700 −1.08990 −0.544950 0.838469i \(-0.683451\pi\)
−0.544950 + 0.838469i \(0.683451\pi\)
\(282\) −7.31800 −0.435781
\(283\) −8.99799 −0.534875 −0.267437 0.963575i \(-0.586177\pi\)
−0.267437 + 0.963575i \(0.586177\pi\)
\(284\) −4.88690 −0.289984
\(285\) 7.47347 0.442690
\(286\) −1.98801 −0.117554
\(287\) −3.93713 −0.232401
\(288\) −0.405623 −0.0239016
\(289\) −9.10338 −0.535493
\(290\) 17.6315 1.03536
\(291\) −34.9312 −2.04771
\(292\) −14.2025 −0.831137
\(293\) −1.74780 −0.102108 −0.0510538 0.998696i \(-0.516258\pi\)
−0.0510538 + 0.998696i \(0.516258\pi\)
\(294\) −12.6035 −0.735050
\(295\) −5.23607 −0.304856
\(296\) 5.43376 0.315831
\(297\) 2.93962 0.170574
\(298\) 11.3141 0.655408
\(299\) 9.21821 0.533103
\(300\) 0.261949 0.0151237
\(301\) −1.03368 −0.0595802
\(302\) −4.74613 −0.273109
\(303\) 14.2052 0.816069
\(304\) −1.83735 −0.105379
\(305\) −1.12614 −0.0644828
\(306\) 1.13984 0.0651603
\(307\) 10.6186 0.606036 0.303018 0.952985i \(-0.402006\pi\)
0.303018 + 0.952985i \(0.402006\pi\)
\(308\) −0.253486 −0.0144437
\(309\) 29.8325 1.69711
\(310\) −4.06216 −0.230715
\(311\) 1.41206 0.0800704 0.0400352 0.999198i \(-0.487253\pi\)
0.0400352 + 0.999198i \(0.487253\pi\)
\(312\) 5.97528 0.338284
\(313\) 9.09314 0.513975 0.256987 0.966415i \(-0.417270\pi\)
0.256987 + 0.966415i \(0.417270\pi\)
\(314\) −2.51669 −0.142025
\(315\) −0.369105 −0.0207967
\(316\) 7.76859 0.437017
\(317\) −13.0336 −0.732043 −0.366021 0.930606i \(-0.619280\pi\)
−0.366021 + 0.930606i \(0.619280\pi\)
\(318\) −9.53723 −0.534821
\(319\) −4.91153 −0.274993
\(320\) 2.20410 0.123213
\(321\) −5.44135 −0.303706
\(322\) 1.17539 0.0655020
\(323\) 5.16313 0.287285
\(324\) −10.0523 −0.558463
\(325\) −0.459599 −0.0254940
\(326\) −9.39573 −0.520381
\(327\) −23.2443 −1.28541
\(328\) −9.53639 −0.526559
\(329\) 1.63715 0.0902592
\(330\) 2.49740 0.137478
\(331\) −9.12214 −0.501398 −0.250699 0.968065i \(-0.580660\pi\)
−0.250699 + 0.968065i \(0.580660\pi\)
\(332\) −0.852265 −0.0467741
\(333\) −2.20406 −0.120782
\(334\) −22.1687 −1.21302
\(335\) 5.05101 0.275966
\(336\) 0.761893 0.0415646
\(337\) −18.3422 −0.999162 −0.499581 0.866267i \(-0.666513\pi\)
−0.499581 + 0.866267i \(0.666513\pi\)
\(338\) 2.51618 0.136862
\(339\) −5.29491 −0.287580
\(340\) −6.19373 −0.335902
\(341\) 1.13158 0.0612785
\(342\) 0.745274 0.0402998
\(343\) 5.70957 0.308288
\(344\) −2.50374 −0.134993
\(345\) −11.5802 −0.623457
\(346\) 24.2226 1.30221
\(347\) 0.913014 0.0490132 0.0245066 0.999700i \(-0.492199\pi\)
0.0245066 + 0.999700i \(0.492199\pi\)
\(348\) 14.7624 0.791346
\(349\) −5.21867 −0.279349 −0.139675 0.990197i \(-0.544606\pi\)
−0.139675 + 0.990197i \(0.544606\pi\)
\(350\) −0.0586023 −0.00313242
\(351\) 15.5021 0.827442
\(352\) −0.613987 −0.0327256
\(353\) −3.76915 −0.200612 −0.100306 0.994957i \(-0.531982\pi\)
−0.100306 + 0.994957i \(0.531982\pi\)
\(354\) −4.38402 −0.233008
\(355\) −10.7712 −0.571677
\(356\) −0.595183 −0.0315447
\(357\) −2.14099 −0.113313
\(358\) −15.9452 −0.842731
\(359\) −11.4785 −0.605814 −0.302907 0.953020i \(-0.597957\pi\)
−0.302907 + 0.953020i \(0.597957\pi\)
\(360\) −0.894034 −0.0471198
\(361\) −15.6241 −0.822323
\(362\) 4.41586 0.232093
\(363\) 19.6041 1.02895
\(364\) −1.33677 −0.0700656
\(365\) −31.3037 −1.63851
\(366\) −0.942890 −0.0492856
\(367\) 6.38986 0.333548 0.166774 0.985995i \(-0.446665\pi\)
0.166774 + 0.985995i \(0.446665\pi\)
\(368\) 2.84700 0.148410
\(369\) 3.86818 0.201370
\(370\) 11.9765 0.622631
\(371\) 2.13363 0.110773
\(372\) −3.40114 −0.176341
\(373\) −18.3615 −0.950722 −0.475361 0.879791i \(-0.657682\pi\)
−0.475361 + 0.879791i \(0.657682\pi\)
\(374\) 1.72536 0.0892163
\(375\) 20.9150 1.08004
\(376\) 3.96547 0.204503
\(377\) −25.9011 −1.33397
\(378\) 1.97664 0.101667
\(379\) −25.4177 −1.30562 −0.652811 0.757521i \(-0.726410\pi\)
−0.652811 + 0.757521i \(0.726410\pi\)
\(380\) −4.04971 −0.207746
\(381\) 5.64523 0.289214
\(382\) 18.9795 0.971076
\(383\) −15.1616 −0.774720 −0.387360 0.921929i \(-0.626613\pi\)
−0.387360 + 0.921929i \(0.626613\pi\)
\(384\) 1.84543 0.0941744
\(385\) −0.558709 −0.0284745
\(386\) 7.63259 0.388488
\(387\) 1.01558 0.0516247
\(388\) 18.9285 0.960948
\(389\) −9.82325 −0.498059 −0.249029 0.968496i \(-0.580112\pi\)
−0.249029 + 0.968496i \(0.580112\pi\)
\(390\) 13.1701 0.666894
\(391\) −8.00032 −0.404594
\(392\) 6.82955 0.344944
\(393\) 20.5186 1.03503
\(394\) 0.382685 0.0192794
\(395\) 17.1228 0.861539
\(396\) 0.249048 0.0125151
\(397\) 36.4114 1.82743 0.913717 0.406351i \(-0.133199\pi\)
0.913717 + 0.406351i \(0.133199\pi\)
\(398\) 6.58628 0.330141
\(399\) −1.39987 −0.0700810
\(400\) −0.141945 −0.00709724
\(401\) −10.6699 −0.532831 −0.266416 0.963858i \(-0.585839\pi\)
−0.266416 + 0.963858i \(0.585839\pi\)
\(402\) 4.22908 0.210927
\(403\) 5.96741 0.297258
\(404\) −7.69750 −0.382965
\(405\) −22.1564 −1.10096
\(406\) −3.30258 −0.163904
\(407\) −3.33626 −0.165372
\(408\) −5.18584 −0.256737
\(409\) −16.5533 −0.818508 −0.409254 0.912421i \(-0.634211\pi\)
−0.409254 + 0.912421i \(0.634211\pi\)
\(410\) −21.0191 −1.03806
\(411\) −24.3960 −1.20337
\(412\) −16.1656 −0.796421
\(413\) 0.980776 0.0482608
\(414\) −1.15481 −0.0567557
\(415\) −1.87848 −0.0922108
\(416\) −3.23787 −0.158750
\(417\) −41.9310 −2.05337
\(418\) 1.12811 0.0551777
\(419\) −6.43215 −0.314231 −0.157115 0.987580i \(-0.550219\pi\)
−0.157115 + 0.987580i \(0.550219\pi\)
\(420\) 1.67929 0.0819408
\(421\) −16.0600 −0.782716 −0.391358 0.920239i \(-0.627995\pi\)
−0.391358 + 0.920239i \(0.627995\pi\)
\(422\) 24.2030 1.17818
\(423\) −1.60849 −0.0782072
\(424\) 5.16802 0.250981
\(425\) 0.398878 0.0193484
\(426\) −9.01844 −0.436945
\(427\) 0.210939 0.0102081
\(428\) 2.94855 0.142523
\(429\) −3.66874 −0.177129
\(430\) −5.51850 −0.266126
\(431\) −24.4450 −1.17747 −0.588737 0.808324i \(-0.700375\pi\)
−0.588737 + 0.808324i \(0.700375\pi\)
\(432\) 4.78775 0.230351
\(433\) −30.4313 −1.46243 −0.731217 0.682145i \(-0.761047\pi\)
−0.731217 + 0.682145i \(0.761047\pi\)
\(434\) 0.760889 0.0365238
\(435\) 32.5377 1.56006
\(436\) 12.5956 0.603219
\(437\) −5.23094 −0.250230
\(438\) −26.2097 −1.25235
\(439\) 36.6648 1.74992 0.874959 0.484197i \(-0.160888\pi\)
0.874959 + 0.484197i \(0.160888\pi\)
\(440\) −1.35329 −0.0645155
\(441\) −2.77023 −0.131916
\(442\) 9.09873 0.432782
\(443\) −5.55022 −0.263699 −0.131850 0.991270i \(-0.542092\pi\)
−0.131850 + 0.991270i \(0.542092\pi\)
\(444\) 10.0276 0.475891
\(445\) −1.31184 −0.0621873
\(446\) 5.06650 0.239906
\(447\) 20.8794 0.987562
\(448\) −0.412853 −0.0195055
\(449\) 7.83897 0.369944 0.184972 0.982744i \(-0.440781\pi\)
0.184972 + 0.982744i \(0.440781\pi\)
\(450\) 0.0575761 0.00271416
\(451\) 5.85522 0.275712
\(452\) 2.86920 0.134956
\(453\) −8.75866 −0.411518
\(454\) −25.1159 −1.17875
\(455\) −2.94636 −0.138128
\(456\) −3.39071 −0.158785
\(457\) 8.73163 0.408448 0.204224 0.978924i \(-0.434533\pi\)
0.204224 + 0.978924i \(0.434533\pi\)
\(458\) 0.667287 0.0311803
\(459\) −13.4540 −0.627980
\(460\) 6.27506 0.292576
\(461\) −8.15337 −0.379740 −0.189870 0.981809i \(-0.560807\pi\)
−0.189870 + 0.981809i \(0.560807\pi\)
\(462\) −0.467792 −0.0217637
\(463\) 16.1925 0.752530 0.376265 0.926512i \(-0.377208\pi\)
0.376265 + 0.926512i \(0.377208\pi\)
\(464\) −7.99940 −0.371363
\(465\) −7.49645 −0.347639
\(466\) 16.6357 0.770632
\(467\) −12.3093 −0.569605 −0.284803 0.958586i \(-0.591928\pi\)
−0.284803 + 0.958586i \(0.591928\pi\)
\(468\) 1.31336 0.0607100
\(469\) −0.946112 −0.0436874
\(470\) 8.74028 0.403159
\(471\) −4.64438 −0.214002
\(472\) 2.37561 0.109346
\(473\) 1.53727 0.0706836
\(474\) 14.3364 0.658493
\(475\) 0.260803 0.0119664
\(476\) 1.16016 0.0531756
\(477\) −2.09627 −0.0959815
\(478\) 27.9364 1.27778
\(479\) −25.6898 −1.17380 −0.586898 0.809661i \(-0.699651\pi\)
−0.586898 + 0.809661i \(0.699651\pi\)
\(480\) 4.06752 0.185656
\(481\) −17.5938 −0.802209
\(482\) 0.274279 0.0124931
\(483\) 2.16911 0.0986977
\(484\) −10.6230 −0.482865
\(485\) 41.7203 1.89442
\(486\) −4.18768 −0.189957
\(487\) −21.3897 −0.969260 −0.484630 0.874719i \(-0.661046\pi\)
−0.484630 + 0.874719i \(0.661046\pi\)
\(488\) 0.510931 0.0231288
\(489\) −17.3392 −0.784105
\(490\) 15.0530 0.680026
\(491\) −34.6435 −1.56344 −0.781719 0.623630i \(-0.785657\pi\)
−0.781719 + 0.623630i \(0.785657\pi\)
\(492\) −17.5988 −0.793414
\(493\) 22.4791 1.01241
\(494\) 5.94912 0.267663
\(495\) 0.548926 0.0246724
\(496\) 1.84300 0.0827533
\(497\) 2.01757 0.0905004
\(498\) −1.57280 −0.0704787
\(499\) 21.0611 0.942824 0.471412 0.881913i \(-0.343745\pi\)
0.471412 + 0.881913i \(0.343745\pi\)
\(500\) −11.3334 −0.506843
\(501\) −40.9108 −1.82776
\(502\) −19.9593 −0.890825
\(503\) 3.71254 0.165534 0.0827670 0.996569i \(-0.473624\pi\)
0.0827670 + 0.996569i \(0.473624\pi\)
\(504\) 0.167463 0.00745939
\(505\) −16.9661 −0.754980
\(506\) −1.74802 −0.0777089
\(507\) 4.64344 0.206222
\(508\) −3.05903 −0.135722
\(509\) −43.4530 −1.92602 −0.963010 0.269467i \(-0.913153\pi\)
−0.963010 + 0.269467i \(0.913153\pi\)
\(510\) −11.4301 −0.506134
\(511\) 5.86353 0.259388
\(512\) −1.00000 −0.0441942
\(513\) −8.79679 −0.388388
\(514\) 5.23270 0.230805
\(515\) −35.6306 −1.57007
\(516\) −4.62049 −0.203406
\(517\) −2.43474 −0.107080
\(518\) −2.24334 −0.0985668
\(519\) 44.7012 1.96216
\(520\) −7.13660 −0.312960
\(521\) −20.7774 −0.910275 −0.455137 0.890421i \(-0.650410\pi\)
−0.455137 + 0.890421i \(0.650410\pi\)
\(522\) 3.24475 0.142019
\(523\) −17.7885 −0.777837 −0.388919 0.921272i \(-0.627151\pi\)
−0.388919 + 0.921272i \(0.627151\pi\)
\(524\) −11.1186 −0.485718
\(525\) −0.108147 −0.00471991
\(526\) −3.60326 −0.157109
\(527\) −5.17901 −0.225601
\(528\) −1.13307 −0.0493106
\(529\) −14.8946 −0.647592
\(530\) 11.3908 0.494786
\(531\) −0.963602 −0.0418167
\(532\) 0.758557 0.0328876
\(533\) 30.8776 1.33746
\(534\) −1.09837 −0.0475312
\(535\) 6.49889 0.280972
\(536\) −2.29164 −0.0989839
\(537\) −29.4258 −1.26982
\(538\) 13.8660 0.597806
\(539\) −4.19326 −0.180616
\(540\) 10.5527 0.454115
\(541\) −11.5310 −0.495754 −0.247877 0.968791i \(-0.579733\pi\)
−0.247877 + 0.968791i \(0.579733\pi\)
\(542\) 13.3486 0.573371
\(543\) 8.14918 0.349715
\(544\) 2.81009 0.120482
\(545\) 27.7619 1.18919
\(546\) −2.46691 −0.105574
\(547\) −23.0159 −0.984090 −0.492045 0.870570i \(-0.663751\pi\)
−0.492045 + 0.870570i \(0.663751\pi\)
\(548\) 13.2197 0.564716
\(549\) −0.207246 −0.00884503
\(550\) 0.0871522 0.00371618
\(551\) 14.6977 0.626144
\(552\) 5.25394 0.223623
\(553\) −3.20729 −0.136388
\(554\) 11.7832 0.500619
\(555\) 22.1019 0.938174
\(556\) 22.7215 0.963605
\(557\) 32.0812 1.35932 0.679662 0.733525i \(-0.262126\pi\)
0.679662 + 0.733525i \(0.262126\pi\)
\(558\) −0.747565 −0.0316469
\(559\) 8.10681 0.342881
\(560\) −0.909969 −0.0384532
\(561\) 3.18404 0.134430
\(562\) 18.2700 0.770675
\(563\) −18.7645 −0.790830 −0.395415 0.918503i \(-0.629399\pi\)
−0.395415 + 0.918503i \(0.629399\pi\)
\(564\) 7.31800 0.308143
\(565\) 6.32399 0.266052
\(566\) 8.99799 0.378214
\(567\) 4.15014 0.174289
\(568\) 4.88690 0.205050
\(569\) 25.7723 1.08043 0.540217 0.841526i \(-0.318342\pi\)
0.540217 + 0.841526i \(0.318342\pi\)
\(570\) −7.47347 −0.313029
\(571\) 14.2617 0.596834 0.298417 0.954436i \(-0.403541\pi\)
0.298417 + 0.954436i \(0.403541\pi\)
\(572\) 1.98801 0.0831230
\(573\) 35.0254 1.46321
\(574\) 3.93713 0.164332
\(575\) −0.404116 −0.0168528
\(576\) 0.405623 0.0169010
\(577\) 47.4999 1.97744 0.988722 0.149759i \(-0.0478499\pi\)
0.988722 + 0.149759i \(0.0478499\pi\)
\(578\) 9.10338 0.378651
\(579\) 14.0854 0.585370
\(580\) −17.6315 −0.732107
\(581\) 0.351860 0.0145976
\(582\) 34.9312 1.44795
\(583\) −3.17310 −0.131416
\(584\) 14.2025 0.587703
\(585\) 2.89477 0.119684
\(586\) 1.74780 0.0722009
\(587\) −33.6147 −1.38743 −0.693713 0.720252i \(-0.744026\pi\)
−0.693713 + 0.720252i \(0.744026\pi\)
\(588\) 12.6035 0.519759
\(589\) −3.38625 −0.139528
\(590\) 5.23607 0.215566
\(591\) 0.706220 0.0290500
\(592\) −5.43376 −0.223326
\(593\) 2.49764 0.102566 0.0512829 0.998684i \(-0.483669\pi\)
0.0512829 + 0.998684i \(0.483669\pi\)
\(594\) −2.93962 −0.120614
\(595\) 2.55710 0.104831
\(596\) −11.3141 −0.463443
\(597\) 12.1545 0.497452
\(598\) −9.21821 −0.376961
\(599\) −35.0900 −1.43374 −0.716869 0.697208i \(-0.754426\pi\)
−0.716869 + 0.697208i \(0.754426\pi\)
\(600\) −0.261949 −0.0106940
\(601\) 5.21478 0.212715 0.106358 0.994328i \(-0.466081\pi\)
0.106358 + 0.994328i \(0.466081\pi\)
\(602\) 1.03368 0.0421296
\(603\) 0.929544 0.0378540
\(604\) 4.74613 0.193117
\(605\) −23.4142 −0.951922
\(606\) −14.2052 −0.577048
\(607\) −9.49355 −0.385331 −0.192666 0.981264i \(-0.561713\pi\)
−0.192666 + 0.981264i \(0.561713\pi\)
\(608\) 1.83735 0.0745145
\(609\) −6.09469 −0.246969
\(610\) 1.12614 0.0455962
\(611\) −12.8397 −0.519438
\(612\) −1.13984 −0.0460753
\(613\) 44.2857 1.78868 0.894342 0.447384i \(-0.147644\pi\)
0.894342 + 0.447384i \(0.147644\pi\)
\(614\) −10.6186 −0.428532
\(615\) −38.7894 −1.56414
\(616\) 0.253486 0.0102133
\(617\) 27.0135 1.08752 0.543762 0.839239i \(-0.316999\pi\)
0.543762 + 0.839239i \(0.316999\pi\)
\(618\) −29.8325 −1.20004
\(619\) 18.6219 0.748478 0.374239 0.927332i \(-0.377904\pi\)
0.374239 + 0.927332i \(0.377904\pi\)
\(620\) 4.06216 0.163140
\(621\) 13.6307 0.546981
\(622\) −1.41206 −0.0566183
\(623\) 0.245723 0.00984469
\(624\) −5.97528 −0.239203
\(625\) −24.2701 −0.970805
\(626\) −9.09314 −0.363435
\(627\) 2.08185 0.0831413
\(628\) 2.51669 0.100427
\(629\) 15.2694 0.608830
\(630\) 0.369105 0.0147055
\(631\) 18.3472 0.730392 0.365196 0.930931i \(-0.381002\pi\)
0.365196 + 0.930931i \(0.381002\pi\)
\(632\) −7.76859 −0.309018
\(633\) 44.6650 1.77527
\(634\) 13.0336 0.517632
\(635\) −6.74241 −0.267564
\(636\) 9.53723 0.378176
\(637\) −22.1132 −0.876158
\(638\) 4.91153 0.194449
\(639\) −1.98224 −0.0784162
\(640\) −2.20410 −0.0871247
\(641\) 45.8976 1.81285 0.906423 0.422370i \(-0.138802\pi\)
0.906423 + 0.422370i \(0.138802\pi\)
\(642\) 5.44135 0.214753
\(643\) 32.4911 1.28132 0.640662 0.767823i \(-0.278660\pi\)
0.640662 + 0.767823i \(0.278660\pi\)
\(644\) −1.17539 −0.0463169
\(645\) −10.1840 −0.400996
\(646\) −5.16313 −0.203141
\(647\) 29.0330 1.14140 0.570702 0.821157i \(-0.306671\pi\)
0.570702 + 0.821157i \(0.306671\pi\)
\(648\) 10.0523 0.394893
\(649\) −1.45859 −0.0572547
\(650\) 0.459599 0.0180270
\(651\) 1.40417 0.0550338
\(652\) 9.39573 0.367965
\(653\) −11.9431 −0.467370 −0.233685 0.972312i \(-0.575078\pi\)
−0.233685 + 0.972312i \(0.575078\pi\)
\(654\) 23.2443 0.908925
\(655\) −24.5065 −0.957547
\(656\) 9.53639 0.372333
\(657\) −5.76086 −0.224752
\(658\) −1.63715 −0.0638229
\(659\) −50.6701 −1.97383 −0.986913 0.161252i \(-0.948447\pi\)
−0.986913 + 0.161252i \(0.948447\pi\)
\(660\) −2.49740 −0.0972113
\(661\) 41.4676 1.61290 0.806452 0.591300i \(-0.201385\pi\)
0.806452 + 0.591300i \(0.201385\pi\)
\(662\) 9.12214 0.354542
\(663\) 16.7911 0.652112
\(664\) 0.852265 0.0330743
\(665\) 1.67194 0.0648349
\(666\) 2.20406 0.0854056
\(667\) −22.7743 −0.881823
\(668\) 22.1687 0.857732
\(669\) 9.34989 0.361488
\(670\) −5.05101 −0.195138
\(671\) −0.313705 −0.0121105
\(672\) −0.761893 −0.0293906
\(673\) 50.6323 1.95173 0.975866 0.218370i \(-0.0700739\pi\)
0.975866 + 0.218370i \(0.0700739\pi\)
\(674\) 18.3422 0.706514
\(675\) −0.679596 −0.0261576
\(676\) −2.51618 −0.0967760
\(677\) 21.7723 0.836777 0.418389 0.908268i \(-0.362595\pi\)
0.418389 + 0.908268i \(0.362595\pi\)
\(678\) 5.29491 0.203350
\(679\) −7.81468 −0.299900
\(680\) 6.19373 0.237519
\(681\) −46.3498 −1.77613
\(682\) −1.13158 −0.0433304
\(683\) −15.0009 −0.573993 −0.286996 0.957932i \(-0.592657\pi\)
−0.286996 + 0.957932i \(0.592657\pi\)
\(684\) −0.745274 −0.0284963
\(685\) 29.1374 1.11328
\(686\) −5.70957 −0.217992
\(687\) 1.23143 0.0469821
\(688\) 2.50374 0.0954544
\(689\) −16.7334 −0.637491
\(690\) 11.5802 0.440851
\(691\) 32.2190 1.22567 0.612834 0.790212i \(-0.290030\pi\)
0.612834 + 0.790212i \(0.290030\pi\)
\(692\) −24.2226 −0.920805
\(693\) −0.102820 −0.00390581
\(694\) −0.913014 −0.0346575
\(695\) 50.0804 1.89966
\(696\) −14.7624 −0.559566
\(697\) −26.7981 −1.01505
\(698\) 5.21867 0.197530
\(699\) 30.7000 1.16118
\(700\) 0.0586023 0.00221496
\(701\) 16.3853 0.618866 0.309433 0.950921i \(-0.399861\pi\)
0.309433 + 0.950921i \(0.399861\pi\)
\(702\) −15.5021 −0.585090
\(703\) 9.98374 0.376544
\(704\) 0.613987 0.0231405
\(705\) 16.1296 0.607476
\(706\) 3.76915 0.141854
\(707\) 3.17794 0.119519
\(708\) 4.38402 0.164762
\(709\) −41.6952 −1.56590 −0.782948 0.622087i \(-0.786285\pi\)
−0.782948 + 0.622087i \(0.786285\pi\)
\(710\) 10.7712 0.404236
\(711\) 3.15112 0.118176
\(712\) 0.595183 0.0223054
\(713\) 5.24702 0.196502
\(714\) 2.14099 0.0801245
\(715\) 4.38178 0.163869
\(716\) 15.9452 0.595901
\(717\) 51.5548 1.92535
\(718\) 11.4785 0.428375
\(719\) 22.0954 0.824020 0.412010 0.911179i \(-0.364827\pi\)
0.412010 + 0.911179i \(0.364827\pi\)
\(720\) 0.894034 0.0333187
\(721\) 6.67401 0.248553
\(722\) 15.6241 0.581470
\(723\) 0.506163 0.0188244
\(724\) −4.41586 −0.164114
\(725\) 1.13547 0.0421704
\(726\) −19.6041 −0.727575
\(727\) 21.3401 0.791461 0.395731 0.918367i \(-0.370491\pi\)
0.395731 + 0.918367i \(0.370491\pi\)
\(728\) 1.33677 0.0495438
\(729\) 22.4289 0.830702
\(730\) 31.3037 1.15860
\(731\) −7.03576 −0.260227
\(732\) 0.942890 0.0348502
\(733\) −5.99421 −0.221401 −0.110701 0.993854i \(-0.535309\pi\)
−0.110701 + 0.993854i \(0.535309\pi\)
\(734\) −6.38986 −0.235854
\(735\) 27.7793 1.02466
\(736\) −2.84700 −0.104942
\(737\) 1.40704 0.0518290
\(738\) −3.86818 −0.142390
\(739\) 41.3870 1.52244 0.761222 0.648491i \(-0.224600\pi\)
0.761222 + 0.648491i \(0.224600\pi\)
\(740\) −11.9765 −0.440267
\(741\) 10.9787 0.403313
\(742\) −2.13363 −0.0783280
\(743\) 47.4907 1.74226 0.871132 0.491049i \(-0.163387\pi\)
0.871132 + 0.491049i \(0.163387\pi\)
\(744\) 3.40114 0.124692
\(745\) −24.9374 −0.913635
\(746\) 18.3615 0.672262
\(747\) −0.345698 −0.0126484
\(748\) −1.72536 −0.0630855
\(749\) −1.21732 −0.0444798
\(750\) −20.9150 −0.763706
\(751\) 28.1302 1.02649 0.513243 0.858244i \(-0.328444\pi\)
0.513243 + 0.858244i \(0.328444\pi\)
\(752\) −3.96547 −0.144606
\(753\) −36.8335 −1.34229
\(754\) 25.9011 0.943261
\(755\) 10.4609 0.380712
\(756\) −1.97664 −0.0718896
\(757\) 34.7473 1.26291 0.631456 0.775411i \(-0.282457\pi\)
0.631456 + 0.775411i \(0.282457\pi\)
\(758\) 25.4177 0.923214
\(759\) −3.22585 −0.117091
\(760\) 4.04971 0.146898
\(761\) −1.33558 −0.0484147 −0.0242073 0.999707i \(-0.507706\pi\)
−0.0242073 + 0.999707i \(0.507706\pi\)
\(762\) −5.64523 −0.204505
\(763\) −5.20013 −0.188257
\(764\) −18.9795 −0.686655
\(765\) −2.51232 −0.0908331
\(766\) 15.1616 0.547810
\(767\) −7.69191 −0.277739
\(768\) −1.84543 −0.0665913
\(769\) 6.44597 0.232448 0.116224 0.993223i \(-0.462921\pi\)
0.116224 + 0.993223i \(0.462921\pi\)
\(770\) 0.558709 0.0201345
\(771\) 9.65660 0.347774
\(772\) −7.63259 −0.274703
\(773\) −25.7459 −0.926015 −0.463007 0.886354i \(-0.653230\pi\)
−0.463007 + 0.886354i \(0.653230\pi\)
\(774\) −1.01558 −0.0365042
\(775\) −0.261604 −0.00939711
\(776\) −18.9285 −0.679493
\(777\) −4.13994 −0.148520
\(778\) 9.82325 0.352181
\(779\) −17.5217 −0.627781
\(780\) −13.1701 −0.471566
\(781\) −3.00049 −0.107366
\(782\) 8.00032 0.286091
\(783\) −38.2991 −1.36870
\(784\) −6.82955 −0.243913
\(785\) 5.54704 0.197982
\(786\) −20.5186 −0.731874
\(787\) 36.8579 1.31384 0.656921 0.753959i \(-0.271858\pi\)
0.656921 + 0.753959i \(0.271858\pi\)
\(788\) −0.382685 −0.0136326
\(789\) −6.64957 −0.236731
\(790\) −17.1228 −0.609200
\(791\) −1.18456 −0.0421180
\(792\) −0.249048 −0.00884952
\(793\) −1.65433 −0.0587470
\(794\) −36.4114 −1.29219
\(795\) 21.0210 0.745538
\(796\) −6.58628 −0.233445
\(797\) 0.518161 0.0183542 0.00917710 0.999958i \(-0.497079\pi\)
0.00917710 + 0.999958i \(0.497079\pi\)
\(798\) 1.39987 0.0495547
\(799\) 11.1433 0.394223
\(800\) 0.141945 0.00501850
\(801\) −0.241420 −0.00853017
\(802\) 10.6699 0.376769
\(803\) −8.72014 −0.307727
\(804\) −4.22908 −0.149148
\(805\) −2.59068 −0.0913094
\(806\) −5.96741 −0.210193
\(807\) 25.5888 0.900768
\(808\) 7.69750 0.270797
\(809\) −48.5150 −1.70570 −0.852848 0.522159i \(-0.825127\pi\)
−0.852848 + 0.522159i \(0.825127\pi\)
\(810\) 22.1564 0.778495
\(811\) −0.254281 −0.00892901 −0.00446451 0.999990i \(-0.501421\pi\)
−0.00446451 + 0.999990i \(0.501421\pi\)
\(812\) 3.30258 0.115898
\(813\) 24.6339 0.863950
\(814\) 3.33626 0.116936
\(815\) 20.7091 0.725409
\(816\) 5.18584 0.181541
\(817\) −4.60026 −0.160943
\(818\) 16.5533 0.578773
\(819\) −0.542223 −0.0189468
\(820\) 21.0191 0.734021
\(821\) −43.7270 −1.52608 −0.763042 0.646349i \(-0.776295\pi\)
−0.763042 + 0.646349i \(0.776295\pi\)
\(822\) 24.3960 0.850908
\(823\) 0.692475 0.0241382 0.0120691 0.999927i \(-0.496158\pi\)
0.0120691 + 0.999927i \(0.496158\pi\)
\(824\) 16.1656 0.563155
\(825\) 0.160834 0.00559951
\(826\) −0.980776 −0.0341256
\(827\) 19.0452 0.662266 0.331133 0.943584i \(-0.392569\pi\)
0.331133 + 0.943584i \(0.392569\pi\)
\(828\) 1.15481 0.0401324
\(829\) 20.2584 0.703605 0.351802 0.936074i \(-0.385569\pi\)
0.351802 + 0.936074i \(0.385569\pi\)
\(830\) 1.87848 0.0652029
\(831\) 21.7451 0.754328
\(832\) 3.23787 0.112253
\(833\) 19.1917 0.664952
\(834\) 41.9310 1.45195
\(835\) 48.8620 1.69094
\(836\) −1.12811 −0.0390166
\(837\) 8.82383 0.304996
\(838\) 6.43215 0.222195
\(839\) −22.4422 −0.774791 −0.387396 0.921914i \(-0.626625\pi\)
−0.387396 + 0.921914i \(0.626625\pi\)
\(840\) −1.67929 −0.0579409
\(841\) 34.9904 1.20657
\(842\) 16.0600 0.553463
\(843\) 33.7161 1.16125
\(844\) −24.2030 −0.833101
\(845\) −5.54590 −0.190785
\(846\) 1.60849 0.0553009
\(847\) 4.38575 0.150696
\(848\) −5.16802 −0.177470
\(849\) 16.6052 0.569889
\(850\) −0.398878 −0.0136814
\(851\) −15.4699 −0.530301
\(852\) 9.01844 0.308967
\(853\) −41.2889 −1.41371 −0.706853 0.707361i \(-0.749886\pi\)
−0.706853 + 0.707361i \(0.749886\pi\)
\(854\) −0.210939 −0.00721820
\(855\) −1.64266 −0.0561777
\(856\) −2.94855 −0.100779
\(857\) −20.6128 −0.704121 −0.352061 0.935977i \(-0.614519\pi\)
−0.352061 + 0.935977i \(0.614519\pi\)
\(858\) 3.66874 0.125249
\(859\) −15.7362 −0.536913 −0.268457 0.963292i \(-0.586514\pi\)
−0.268457 + 0.963292i \(0.586514\pi\)
\(860\) 5.51850 0.188179
\(861\) 7.26570 0.247614
\(862\) 24.4450 0.832600
\(863\) −13.8156 −0.470290 −0.235145 0.971960i \(-0.575556\pi\)
−0.235145 + 0.971960i \(0.575556\pi\)
\(864\) −4.78775 −0.162883
\(865\) −53.3890 −1.81528
\(866\) 30.4313 1.03410
\(867\) 16.7997 0.570547
\(868\) −0.760889 −0.0258263
\(869\) 4.76982 0.161805
\(870\) −32.5377 −1.10313
\(871\) 7.42005 0.251419
\(872\) −12.5956 −0.426540
\(873\) 7.67784 0.259855
\(874\) 5.23094 0.176939
\(875\) 4.67901 0.158179
\(876\) 26.2097 0.885544
\(877\) 3.06597 0.103530 0.0517652 0.998659i \(-0.483515\pi\)
0.0517652 + 0.998659i \(0.483515\pi\)
\(878\) −36.6648 −1.23738
\(879\) 3.22545 0.108792
\(880\) 1.35329 0.0456194
\(881\) 31.8096 1.07169 0.535846 0.844316i \(-0.319993\pi\)
0.535846 + 0.844316i \(0.319993\pi\)
\(882\) 2.77023 0.0932784
\(883\) 26.2768 0.884283 0.442142 0.896945i \(-0.354219\pi\)
0.442142 + 0.896945i \(0.354219\pi\)
\(884\) −9.09873 −0.306023
\(885\) 9.66282 0.324812
\(886\) 5.55022 0.186463
\(887\) 39.1572 1.31477 0.657384 0.753555i \(-0.271663\pi\)
0.657384 + 0.753555i \(0.271663\pi\)
\(888\) −10.0276 −0.336505
\(889\) 1.26293 0.0423573
\(890\) 1.31184 0.0439731
\(891\) −6.17201 −0.206770
\(892\) −5.06650 −0.169639
\(893\) 7.28596 0.243815
\(894\) −20.8794 −0.698311
\(895\) 35.1448 1.17476
\(896\) 0.412853 0.0137924
\(897\) −17.0116 −0.568001
\(898\) −7.83897 −0.261590
\(899\) −14.7429 −0.491704
\(900\) −0.0575761 −0.00191920
\(901\) 14.5226 0.483818
\(902\) −5.85522 −0.194958
\(903\) 1.90758 0.0634804
\(904\) −2.86920 −0.0954280
\(905\) −9.73300 −0.323536
\(906\) 8.75866 0.290987
\(907\) 20.4882 0.680300 0.340150 0.940371i \(-0.389522\pi\)
0.340150 + 0.940371i \(0.389522\pi\)
\(908\) 25.1159 0.833502
\(909\) −3.12229 −0.103560
\(910\) 2.94636 0.0976710
\(911\) −31.0033 −1.02719 −0.513593 0.858034i \(-0.671686\pi\)
−0.513593 + 0.858034i \(0.671686\pi\)
\(912\) 3.39071 0.112278
\(913\) −0.523279 −0.0173180
\(914\) −8.73163 −0.288817
\(915\) 2.07822 0.0687039
\(916\) −0.667287 −0.0220478
\(917\) 4.59034 0.151586
\(918\) 13.4540 0.444049
\(919\) −34.8888 −1.15088 −0.575438 0.817845i \(-0.695169\pi\)
−0.575438 + 0.817845i \(0.695169\pi\)
\(920\) −6.27506 −0.206883
\(921\) −19.5959 −0.645708
\(922\) 8.15337 0.268517
\(923\) −15.8232 −0.520826
\(924\) 0.467792 0.0153892
\(925\) 0.771293 0.0253600
\(926\) −16.1925 −0.532119
\(927\) −6.55714 −0.215365
\(928\) 7.99940 0.262593
\(929\) 7.13875 0.234215 0.117107 0.993119i \(-0.462638\pi\)
0.117107 + 0.993119i \(0.462638\pi\)
\(930\) 7.49645 0.245818
\(931\) 12.5483 0.411254
\(932\) −16.6357 −0.544919
\(933\) −2.60586 −0.0853119
\(934\) 12.3093 0.402772
\(935\) −3.80287 −0.124367
\(936\) −1.31336 −0.0429284
\(937\) 2.34410 0.0765786 0.0382893 0.999267i \(-0.487809\pi\)
0.0382893 + 0.999267i \(0.487809\pi\)
\(938\) 0.946112 0.0308917
\(939\) −16.7808 −0.547620
\(940\) −8.74028 −0.285077
\(941\) 8.60755 0.280598 0.140299 0.990109i \(-0.455194\pi\)
0.140299 + 0.990109i \(0.455194\pi\)
\(942\) 4.64438 0.151322
\(943\) 27.1501 0.884128
\(944\) −2.37561 −0.0773194
\(945\) −4.35670 −0.141724
\(946\) −1.53727 −0.0499809
\(947\) −32.8694 −1.06811 −0.534056 0.845449i \(-0.679333\pi\)
−0.534056 + 0.845449i \(0.679333\pi\)
\(948\) −14.3364 −0.465625
\(949\) −45.9858 −1.49276
\(950\) −0.260803 −0.00846156
\(951\) 24.0527 0.779963
\(952\) −1.16016 −0.0376008
\(953\) −33.8799 −1.09748 −0.548738 0.835994i \(-0.684892\pi\)
−0.548738 + 0.835994i \(0.684892\pi\)
\(954\) 2.09627 0.0678692
\(955\) −41.8327 −1.35368
\(956\) −27.9364 −0.903528
\(957\) 9.06390 0.292994
\(958\) 25.6898 0.829999
\(959\) −5.45777 −0.176241
\(960\) −4.06752 −0.131279
\(961\) −27.6033 −0.890430
\(962\) 17.5938 0.567248
\(963\) 1.19600 0.0385406
\(964\) −0.274279 −0.00883393
\(965\) −16.8230 −0.541551
\(966\) −2.16911 −0.0697898
\(967\) −36.7770 −1.18267 −0.591335 0.806426i \(-0.701399\pi\)
−0.591335 + 0.806426i \(0.701399\pi\)
\(968\) 10.6230 0.341437
\(969\) −9.52822 −0.306091
\(970\) −41.7203 −1.33956
\(971\) −37.7181 −1.21043 −0.605216 0.796061i \(-0.706913\pi\)
−0.605216 + 0.796061i \(0.706913\pi\)
\(972\) 4.18768 0.134320
\(973\) −9.38063 −0.300729
\(974\) 21.3897 0.685370
\(975\) 0.848159 0.0271628
\(976\) −0.510931 −0.0163545
\(977\) −53.3857 −1.70796 −0.853979 0.520307i \(-0.825818\pi\)
−0.853979 + 0.520307i \(0.825818\pi\)
\(978\) 17.3392 0.554446
\(979\) −0.365435 −0.0116794
\(980\) −15.0530 −0.480851
\(981\) 5.10906 0.163120
\(982\) 34.6435 1.10552
\(983\) 2.82782 0.0901936 0.0450968 0.998983i \(-0.485640\pi\)
0.0450968 + 0.998983i \(0.485640\pi\)
\(984\) 17.5988 0.561028
\(985\) −0.843476 −0.0268754
\(986\) −22.4791 −0.715879
\(987\) −3.02126 −0.0961677
\(988\) −5.94912 −0.189267
\(989\) 7.12815 0.226662
\(990\) −0.548926 −0.0174460
\(991\) 22.1476 0.703542 0.351771 0.936086i \(-0.385580\pi\)
0.351771 + 0.936086i \(0.385580\pi\)
\(992\) −1.84300 −0.0585154
\(993\) 16.8343 0.534220
\(994\) −2.01757 −0.0639935
\(995\) −14.5168 −0.460214
\(996\) 1.57280 0.0498360
\(997\) 43.6744 1.38318 0.691591 0.722289i \(-0.256910\pi\)
0.691591 + 0.722289i \(0.256910\pi\)
\(998\) −21.0611 −0.666677
\(999\) −26.0155 −0.823093
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 4006.2.a.g.1.10 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.10 40 1.1 even 1 trivial