Properties

Label 5290.2.a.q.1.3
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1509.1
Defining polynomial: \( x^{3} - x^{2} - 7x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.47735\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +1.00000 q^{10} +4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} +2.13727 q^{14} +2.47735 q^{15} +1.00000 q^{16} +1.52265 q^{17} +3.13727 q^{18} +5.09198 q^{19} +1.00000 q^{20} +5.29478 q^{21} +4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} +2.13727 q^{28} -7.22925 q^{29} +2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} +11.0920 q^{33} +1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} -11.9094 q^{37} +5.09198 q^{38} +0.340078 q^{39} +1.00000 q^{40} +4.47735 q^{41} +5.29478 q^{42} -7.22925 q^{43} +4.47735 q^{44} +3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} +3.77213 q^{51} +0.137275 q^{52} +1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} +2.13727 q^{56} +12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} +2.47735 q^{60} +9.15751 q^{61} -2.81743 q^{62} +6.70522 q^{63} +1.00000 q^{64} +0.137275 q^{65} +11.0920 q^{66} +2.95470 q^{67} +1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} -11.9094 q^{74} +2.47735 q^{75} +5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} +4.68016 q^{79} +1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} -16.1840 q^{83} +5.29478 q^{84} +1.52265 q^{85} -7.22925 q^{86} -17.9094 q^{87} +4.47735 q^{88} +4.27455 q^{89} +3.13727 q^{90} +0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} -19.4321 q^{97} -2.43206 q^{98} +14.0467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 2.47735 1.43030 0.715150 0.698971i \(-0.246358\pi\)
0.715150 + 0.698971i \(0.246358\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.47735 1.01137
\(7\) 2.13727 0.807814 0.403907 0.914800i \(-0.367652\pi\)
0.403907 + 0.914800i \(0.367652\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.13727 1.04576
\(10\) 1.00000 0.316228
\(11\) 4.47735 1.34997 0.674986 0.737830i \(-0.264150\pi\)
0.674986 + 0.737830i \(0.264150\pi\)
\(12\) 2.47735 0.715150
\(13\) 0.137275 0.0380731 0.0190366 0.999819i \(-0.493940\pi\)
0.0190366 + 0.999819i \(0.493940\pi\)
\(14\) 2.13727 0.571211
\(15\) 2.47735 0.639650
\(16\) 1.00000 0.250000
\(17\) 1.52265 0.369296 0.184648 0.982805i \(-0.440885\pi\)
0.184648 + 0.982805i \(0.440885\pi\)
\(18\) 3.13727 0.739463
\(19\) 5.09198 1.16818 0.584090 0.811689i \(-0.301451\pi\)
0.584090 + 0.811689i \(0.301451\pi\)
\(20\) 1.00000 0.223607
\(21\) 5.29478 1.15542
\(22\) 4.47735 0.954575
\(23\) 0 0
\(24\) 2.47735 0.505687
\(25\) 1.00000 0.200000
\(26\) 0.137275 0.0269218
\(27\) 0.340078 0.0654480
\(28\) 2.13727 0.403907
\(29\) −7.22925 −1.34244 −0.671219 0.741259i \(-0.734229\pi\)
−0.671219 + 0.741259i \(0.734229\pi\)
\(30\) 2.47735 0.452301
\(31\) −2.81743 −0.506025 −0.253013 0.967463i \(-0.581421\pi\)
−0.253013 + 0.967463i \(0.581421\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.0920 1.93087
\(34\) 1.52265 0.261132
\(35\) 2.13727 0.361265
\(36\) 3.13727 0.522879
\(37\) −11.9094 −1.95789 −0.978947 0.204113i \(-0.934569\pi\)
−0.978947 + 0.204113i \(0.934569\pi\)
\(38\) 5.09198 0.826028
\(39\) 0.340078 0.0544560
\(40\) 1.00000 0.158114
\(41\) 4.47735 0.699245 0.349622 0.936891i \(-0.386310\pi\)
0.349622 + 0.936891i \(0.386310\pi\)
\(42\) 5.29478 0.817003
\(43\) −7.22925 −1.10245 −0.551225 0.834356i \(-0.685840\pi\)
−0.551225 + 0.834356i \(0.685840\pi\)
\(44\) 4.47735 0.674986
\(45\) 3.13727 0.467677
\(46\) 0 0
\(47\) −4.68016 −0.682671 −0.341335 0.939942i \(-0.610879\pi\)
−0.341335 + 0.939942i \(0.610879\pi\)
\(48\) 2.47735 0.357575
\(49\) −2.43206 −0.347437
\(50\) 1.00000 0.141421
\(51\) 3.77213 0.528205
\(52\) 0.137275 0.0190366
\(53\) 1.72545 0.237009 0.118504 0.992954i \(-0.462190\pi\)
0.118504 + 0.992954i \(0.462190\pi\)
\(54\) 0.340078 0.0462787
\(55\) 4.47735 0.603726
\(56\) 2.13727 0.285605
\(57\) 12.6146 1.67085
\(58\) −7.22925 −0.949248
\(59\) −13.2293 −1.72230 −0.861151 0.508349i \(-0.830256\pi\)
−0.861151 + 0.508349i \(0.830256\pi\)
\(60\) 2.47735 0.319825
\(61\) 9.15751 1.17250 0.586249 0.810131i \(-0.300604\pi\)
0.586249 + 0.810131i \(0.300604\pi\)
\(62\) −2.81743 −0.357814
\(63\) 6.70522 0.844778
\(64\) 1.00000 0.125000
\(65\) 0.137275 0.0170268
\(66\) 11.0920 1.36533
\(67\) 2.95470 0.360975 0.180487 0.983577i \(-0.442233\pi\)
0.180487 + 0.983577i \(0.442233\pi\)
\(68\) 1.52265 0.184648
\(69\) 0 0
\(70\) 2.13727 0.255453
\(71\) −1.52265 −0.180705 −0.0903525 0.995910i \(-0.528799\pi\)
−0.0903525 + 0.995910i \(0.528799\pi\)
\(72\) 3.13727 0.369731
\(73\) −15.2293 −1.78245 −0.891225 0.453562i \(-0.850153\pi\)
−0.891225 + 0.453562i \(0.850153\pi\)
\(74\) −11.9094 −1.38444
\(75\) 2.47735 0.286060
\(76\) 5.09198 0.584090
\(77\) 9.56933 1.09053
\(78\) 0.340078 0.0385062
\(79\) 4.68016 0.526559 0.263279 0.964720i \(-0.415196\pi\)
0.263279 + 0.964720i \(0.415196\pi\)
\(80\) 1.00000 0.111803
\(81\) −8.56933 −0.952148
\(82\) 4.47735 0.494441
\(83\) −16.1840 −1.77642 −0.888210 0.459437i \(-0.848051\pi\)
−0.888210 + 0.459437i \(0.848051\pi\)
\(84\) 5.29478 0.577708
\(85\) 1.52265 0.165154
\(86\) −7.22925 −0.779551
\(87\) −17.9094 −1.92009
\(88\) 4.47735 0.477287
\(89\) 4.27455 0.453101 0.226551 0.973999i \(-0.427255\pi\)
0.226551 + 0.973999i \(0.427255\pi\)
\(90\) 3.13727 0.330698
\(91\) 0.293394 0.0307560
\(92\) 0 0
\(93\) −6.97977 −0.723768
\(94\) −4.68016 −0.482721
\(95\) 5.09198 0.522426
\(96\) 2.47735 0.252844
\(97\) −19.4321 −1.97303 −0.986513 0.163682i \(-0.947663\pi\)
−0.986513 + 0.163682i \(0.947663\pi\)
\(98\) −2.43206 −0.245675
\(99\) 14.0467 1.41174
\(100\) 1.00000 0.100000
\(101\) −11.9094 −1.18503 −0.592515 0.805559i \(-0.701865\pi\)
−0.592515 + 0.805559i \(0.701865\pi\)
\(102\) 3.77213 0.373497
\(103\) 12.1122 1.19345 0.596726 0.802445i \(-0.296468\pi\)
0.596726 + 0.802445i \(0.296468\pi\)
\(104\) 0.137275 0.0134609
\(105\) 5.29478 0.516718
\(106\) 1.72545 0.167591
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0.340078 0.0327240
\(109\) 6.90802 0.661668 0.330834 0.943689i \(-0.392670\pi\)
0.330834 + 0.943689i \(0.392670\pi\)
\(110\) 4.47735 0.426899
\(111\) −29.5038 −2.80038
\(112\) 2.13727 0.201953
\(113\) 13.2293 1.24450 0.622252 0.782817i \(-0.286218\pi\)
0.622252 + 0.782817i \(0.286218\pi\)
\(114\) 12.6146 1.18147
\(115\) 0 0
\(116\) −7.22925 −0.671219
\(117\) 0.430668 0.0398153
\(118\) −13.2293 −1.21785
\(119\) 3.25432 0.298323
\(120\) 2.47735 0.226150
\(121\) 9.04668 0.822426
\(122\) 9.15751 0.829082
\(123\) 11.0920 1.00013
\(124\) −2.81743 −0.253013
\(125\) 1.00000 0.0894427
\(126\) 6.70522 0.597348
\(127\) 20.0934 1.78300 0.891499 0.453023i \(-0.149654\pi\)
0.891499 + 0.453023i \(0.149654\pi\)
\(128\) 1.00000 0.0883883
\(129\) −17.9094 −1.57684
\(130\) 0.137275 0.0120398
\(131\) 5.90941 0.516307 0.258154 0.966104i \(-0.416886\pi\)
0.258154 + 0.966104i \(0.416886\pi\)
\(132\) 11.0920 0.965433
\(133\) 10.8830 0.943672
\(134\) 2.95470 0.255248
\(135\) 0.340078 0.0292692
\(136\) 1.52265 0.130566
\(137\) −12.3212 −1.05267 −0.526337 0.850276i \(-0.676435\pi\)
−0.526337 + 0.850276i \(0.676435\pi\)
\(138\) 0 0
\(139\) 16.9547 1.43808 0.719040 0.694969i \(-0.244582\pi\)
0.719040 + 0.694969i \(0.244582\pi\)
\(140\) 2.13727 0.180633
\(141\) −11.5944 −0.976424
\(142\) −1.52265 −0.127778
\(143\) 0.614627 0.0513977
\(144\) 3.13727 0.261440
\(145\) −7.22925 −0.600357
\(146\) −15.2293 −1.26038
\(147\) −6.02506 −0.496939
\(148\) −11.9094 −0.978947
\(149\) 17.0920 1.40023 0.700115 0.714030i \(-0.253132\pi\)
0.700115 + 0.714030i \(0.253132\pi\)
\(150\) 2.47735 0.202275
\(151\) 18.4774 1.50367 0.751833 0.659354i \(-0.229170\pi\)
0.751833 + 0.659354i \(0.229170\pi\)
\(152\) 5.09198 0.413014
\(153\) 4.77696 0.386195
\(154\) 9.56933 0.771119
\(155\) −2.81743 −0.226301
\(156\) 0.340078 0.0272280
\(157\) −14.9547 −1.19352 −0.596758 0.802422i \(-0.703545\pi\)
−0.596758 + 0.802422i \(0.703545\pi\)
\(158\) 4.68016 0.372333
\(159\) 4.27455 0.338994
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −8.56933 −0.673270
\(163\) −11.3665 −0.890295 −0.445148 0.895457i \(-0.646849\pi\)
−0.445148 + 0.895457i \(0.646849\pi\)
\(164\) 4.47735 0.349622
\(165\) 11.0920 0.863509
\(166\) −16.1840 −1.25612
\(167\) 10.1840 0.788058 0.394029 0.919098i \(-0.371081\pi\)
0.394029 + 0.919098i \(0.371081\pi\)
\(168\) 5.29478 0.408501
\(169\) −12.9812 −0.998550
\(170\) 1.52265 0.116782
\(171\) 15.9749 1.22163
\(172\) −7.22925 −0.551225
\(173\) 4.47735 0.340407 0.170203 0.985409i \(-0.445558\pi\)
0.170203 + 0.985409i \(0.445558\pi\)
\(174\) −17.9094 −1.35771
\(175\) 2.13727 0.161563
\(176\) 4.47735 0.337493
\(177\) −32.7735 −2.46341
\(178\) 4.27455 0.320391
\(179\) −7.72545 −0.577427 −0.288714 0.957415i \(-0.593228\pi\)
−0.288714 + 0.957415i \(0.593228\pi\)
\(180\) 3.13727 0.233839
\(181\) 9.36653 0.696209 0.348104 0.937456i \(-0.386826\pi\)
0.348104 + 0.937456i \(0.386826\pi\)
\(182\) 0.293394 0.0217478
\(183\) 22.6864 1.67702
\(184\) 0 0
\(185\) −11.9094 −0.875597
\(186\) −6.97977 −0.511781
\(187\) 6.81743 0.498540
\(188\) −4.68016 −0.341335
\(189\) 0.726839 0.0528698
\(190\) 5.09198 0.369411
\(191\) 16.2745 1.17759 0.588793 0.808284i \(-0.299604\pi\)
0.588793 + 0.808284i \(0.299604\pi\)
\(192\) 2.47735 0.178788
\(193\) −6.95470 −0.500611 −0.250305 0.968167i \(-0.580531\pi\)
−0.250305 + 0.968167i \(0.580531\pi\)
\(194\) −19.4321 −1.39514
\(195\) 0.340078 0.0243535
\(196\) −2.43206 −0.173718
\(197\) 1.43206 0.102030 0.0510149 0.998698i \(-0.483754\pi\)
0.0510149 + 0.998698i \(0.483754\pi\)
\(198\) 14.0467 0.998254
\(199\) −5.90941 −0.418907 −0.209453 0.977819i \(-0.567168\pi\)
−0.209453 + 0.977819i \(0.567168\pi\)
\(200\) 1.00000 0.0707107
\(201\) 7.31984 0.516302
\(202\) −11.9094 −0.837943
\(203\) −15.4509 −1.08444
\(204\) 3.77213 0.264102
\(205\) 4.47735 0.312712
\(206\) 12.1122 0.843898
\(207\) 0 0
\(208\) 0.137275 0.00951828
\(209\) 22.7986 1.57701
\(210\) 5.29478 0.365375
\(211\) 17.6349 1.21403 0.607017 0.794689i \(-0.292366\pi\)
0.607017 + 0.794689i \(0.292366\pi\)
\(212\) 1.72545 0.118504
\(213\) −3.77213 −0.258462
\(214\) 6.00000 0.410152
\(215\) −7.22925 −0.493031
\(216\) 0.340078 0.0231394
\(217\) −6.02162 −0.408774
\(218\) 6.90802 0.467870
\(219\) −37.7282 −2.54944
\(220\) 4.47735 0.301863
\(221\) 0.209021 0.0140603
\(222\) −29.5038 −1.98017
\(223\) 13.5038 0.904282 0.452141 0.891947i \(-0.350660\pi\)
0.452141 + 0.891947i \(0.350660\pi\)
\(224\) 2.13727 0.142803
\(225\) 3.13727 0.209152
\(226\) 13.2293 0.879997
\(227\) −19.6349 −1.30321 −0.651606 0.758558i \(-0.725904\pi\)
−0.651606 + 0.758558i \(0.725904\pi\)
\(228\) 12.6146 0.835424
\(229\) 0.0905906 0.00598640 0.00299320 0.999996i \(-0.499047\pi\)
0.00299320 + 0.999996i \(0.499047\pi\)
\(230\) 0 0
\(231\) 23.7066 1.55978
\(232\) −7.22925 −0.474624
\(233\) −2.95470 −0.193569 −0.0967846 0.995305i \(-0.530856\pi\)
−0.0967846 + 0.995305i \(0.530856\pi\)
\(234\) 0.430668 0.0281537
\(235\) −4.68016 −0.305300
\(236\) −13.2293 −0.861151
\(237\) 11.5944 0.753137
\(238\) 3.25432 0.210946
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 2.47735 0.159912
\(241\) 5.90941 0.380659 0.190329 0.981720i \(-0.439044\pi\)
0.190329 + 0.981720i \(0.439044\pi\)
\(242\) 9.04668 0.581543
\(243\) −22.2495 −1.42731
\(244\) 9.15751 0.586249
\(245\) −2.43206 −0.155378
\(246\) 11.0920 0.707199
\(247\) 0.699000 0.0444763
\(248\) −2.81743 −0.178907
\(249\) −40.0934 −2.54081
\(250\) 1.00000 0.0632456
\(251\) −19.5505 −1.23402 −0.617008 0.786957i \(-0.711655\pi\)
−0.617008 + 0.786957i \(0.711655\pi\)
\(252\) 6.70522 0.422389
\(253\) 0 0
\(254\) 20.0934 1.26077
\(255\) 3.77213 0.236220
\(256\) 1.00000 0.0625000
\(257\) 29.4132 1.83475 0.917373 0.398029i \(-0.130306\pi\)
0.917373 + 0.398029i \(0.130306\pi\)
\(258\) −17.9094 −1.11499
\(259\) −25.4537 −1.58161
\(260\) 0.137275 0.00851341
\(261\) −22.6802 −1.40387
\(262\) 5.90941 0.365085
\(263\) 5.79720 0.357470 0.178735 0.983897i \(-0.442799\pi\)
0.178735 + 0.983897i \(0.442799\pi\)
\(264\) 11.0920 0.682664
\(265\) 1.72545 0.105994
\(266\) 10.8830 0.667277
\(267\) 10.5896 0.648071
\(268\) 2.95470 0.180487
\(269\) 8.86411 0.540455 0.270227 0.962797i \(-0.412901\pi\)
0.270227 + 0.962797i \(0.412901\pi\)
\(270\) 0.340078 0.0206965
\(271\) 21.0014 1.27574 0.637872 0.770143i \(-0.279815\pi\)
0.637872 + 0.770143i \(0.279815\pi\)
\(272\) 1.52265 0.0923241
\(273\) 0.726839 0.0439903
\(274\) −12.3212 −0.744353
\(275\) 4.47735 0.269995
\(276\) 0 0
\(277\) −22.3679 −1.34396 −0.671979 0.740570i \(-0.734555\pi\)
−0.671979 + 0.740570i \(0.734555\pi\)
\(278\) 16.9547 1.01688
\(279\) −8.83905 −0.529180
\(280\) 2.13727 0.127727
\(281\) −10.5896 −0.631720 −0.315860 0.948806i \(-0.602293\pi\)
−0.315860 + 0.948806i \(0.602293\pi\)
\(282\) −11.5944 −0.690436
\(283\) −7.22925 −0.429735 −0.214867 0.976643i \(-0.568932\pi\)
−0.214867 + 0.976643i \(0.568932\pi\)
\(284\) −1.52265 −0.0903525
\(285\) 12.6146 0.747226
\(286\) 0.614627 0.0363437
\(287\) 9.56933 0.564860
\(288\) 3.13727 0.184866
\(289\) −14.6815 −0.863620
\(290\) −7.22925 −0.424516
\(291\) −48.1401 −2.82202
\(292\) −15.2293 −0.891225
\(293\) 17.8188 1.04099 0.520493 0.853866i \(-0.325748\pi\)
0.520493 + 0.853866i \(0.325748\pi\)
\(294\) −6.02506 −0.351389
\(295\) −13.2293 −0.770237
\(296\) −11.9094 −0.692220
\(297\) 1.52265 0.0883530
\(298\) 17.0920 0.990112
\(299\) 0 0
\(300\) 2.47735 0.143030
\(301\) −15.4509 −0.890575
\(302\) 18.4774 1.06325
\(303\) −29.5038 −1.69495
\(304\) 5.09198 0.292045
\(305\) 9.15751 0.524357
\(306\) 4.77696 0.273081
\(307\) 17.3415 0.989730 0.494865 0.868970i \(-0.335218\pi\)
0.494865 + 0.868970i \(0.335218\pi\)
\(308\) 9.56933 0.545263
\(309\) 30.0062 1.70699
\(310\) −2.81743 −0.160019
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0.340078 0.0192531
\(313\) 12.3212 0.696437 0.348219 0.937413i \(-0.386787\pi\)
0.348219 + 0.937413i \(0.386787\pi\)
\(314\) −14.9547 −0.843943
\(315\) 6.70522 0.377796
\(316\) 4.68016 0.263279
\(317\) −21.7721 −1.22284 −0.611422 0.791304i \(-0.709402\pi\)
−0.611422 + 0.791304i \(0.709402\pi\)
\(318\) 4.27455 0.239705
\(319\) −32.3679 −1.81226
\(320\) 1.00000 0.0559017
\(321\) 14.8641 0.829634
\(322\) 0 0
\(323\) 7.75329 0.431405
\(324\) −8.56933 −0.476074
\(325\) 0.137275 0.00761463
\(326\) −11.3665 −0.629534
\(327\) 17.1136 0.946384
\(328\) 4.47735 0.247220
\(329\) −10.0028 −0.551471
\(330\) 11.0920 0.610593
\(331\) −0.274549 −0.0150906 −0.00754530 0.999972i \(-0.502402\pi\)
−0.00754530 + 0.999972i \(0.502402\pi\)
\(332\) −16.1840 −0.888210
\(333\) −37.3631 −2.04748
\(334\) 10.1840 0.557241
\(335\) 2.95470 0.161433
\(336\) 5.29478 0.288854
\(337\) 20.0467 1.09201 0.546006 0.837781i \(-0.316147\pi\)
0.546006 + 0.837781i \(0.316147\pi\)
\(338\) −12.9812 −0.706082
\(339\) 32.7735 1.78001
\(340\) 1.52265 0.0825772
\(341\) −12.6146 −0.683120
\(342\) 15.9749 0.863826
\(343\) −20.1589 −1.08848
\(344\) −7.22925 −0.389775
\(345\) 0 0
\(346\) 4.47735 0.240704
\(347\) 1.11704 0.0599659 0.0299830 0.999550i \(-0.490455\pi\)
0.0299830 + 0.999550i \(0.490455\pi\)
\(348\) −17.9094 −0.960045
\(349\) −28.7331 −1.53805 −0.769023 0.639222i \(-0.779257\pi\)
−0.769023 + 0.639222i \(0.779257\pi\)
\(350\) 2.13727 0.114242
\(351\) 0.0466840 0.00249181
\(352\) 4.47735 0.238644
\(353\) −6.82365 −0.363186 −0.181593 0.983374i \(-0.558125\pi\)
−0.181593 + 0.983374i \(0.558125\pi\)
\(354\) −32.7735 −1.74189
\(355\) −1.52265 −0.0808137
\(356\) 4.27455 0.226551
\(357\) 8.06209 0.426691
\(358\) −7.72545 −0.408303
\(359\) 22.5896 1.19223 0.596116 0.802898i \(-0.296710\pi\)
0.596116 + 0.802898i \(0.296710\pi\)
\(360\) 3.13727 0.165349
\(361\) 6.92825 0.364645
\(362\) 9.36653 0.492294
\(363\) 22.4118 1.17632
\(364\) 0.293394 0.0153780
\(365\) −15.2293 −0.797136
\(366\) 22.6864 1.18584
\(367\) 32.3679 1.68959 0.844796 0.535089i \(-0.179722\pi\)
0.844796 + 0.535089i \(0.179722\pi\)
\(368\) 0 0
\(369\) 14.0467 0.731241
\(370\) −11.9094 −0.619141
\(371\) 3.68776 0.191459
\(372\) −6.97977 −0.361884
\(373\) −13.7255 −0.710677 −0.355338 0.934738i \(-0.615634\pi\)
−0.355338 + 0.934738i \(0.615634\pi\)
\(374\) 6.81743 0.352521
\(375\) 2.47735 0.127930
\(376\) −4.68016 −0.241361
\(377\) −0.992393 −0.0511109
\(378\) 0.726839 0.0373846
\(379\) −28.4774 −1.46278 −0.731392 0.681958i \(-0.761129\pi\)
−0.731392 + 0.681958i \(0.761129\pi\)
\(380\) 5.09198 0.261213
\(381\) 49.7784 2.55022
\(382\) 16.2745 0.832678
\(383\) 9.36031 0.478290 0.239145 0.970984i \(-0.423133\pi\)
0.239145 + 0.970984i \(0.423133\pi\)
\(384\) 2.47735 0.126422
\(385\) 9.56933 0.487698
\(386\) −6.95470 −0.353985
\(387\) −22.6802 −1.15290
\(388\) −19.4321 −0.986513
\(389\) 30.1122 1.52675 0.763375 0.645956i \(-0.223541\pi\)
0.763375 + 0.645956i \(0.223541\pi\)
\(390\) 0.340078 0.0172205
\(391\) 0 0
\(392\) −2.43206 −0.122837
\(393\) 14.6397 0.738475
\(394\) 1.43206 0.0721460
\(395\) 4.68016 0.235484
\(396\) 14.0467 0.705872
\(397\) 12.8830 0.646577 0.323289 0.946300i \(-0.395212\pi\)
0.323289 + 0.946300i \(0.395212\pi\)
\(398\) −5.90941 −0.296212
\(399\) 26.9609 1.34973
\(400\) 1.00000 0.0500000
\(401\) −22.0028 −1.09877 −0.549383 0.835571i \(-0.685137\pi\)
−0.549383 + 0.835571i \(0.685137\pi\)
\(402\) 7.31984 0.365081
\(403\) −0.386762 −0.0192660
\(404\) −11.9094 −0.592515
\(405\) −8.56933 −0.425814
\(406\) −15.4509 −0.766815
\(407\) −53.3226 −2.64310
\(408\) 3.77213 0.186748
\(409\) −13.7721 −0.680988 −0.340494 0.940247i \(-0.610594\pi\)
−0.340494 + 0.940247i \(0.610594\pi\)
\(410\) 4.47735 0.221121
\(411\) −30.5240 −1.50564
\(412\) 12.1122 0.596726
\(413\) −28.2745 −1.39130
\(414\) 0 0
\(415\) −16.1840 −0.794439
\(416\) 0.137275 0.00673044
\(417\) 42.0028 2.05688
\(418\) 22.7986 1.11512
\(419\) 1.31984 0.0644786 0.0322393 0.999480i \(-0.489736\pi\)
0.0322393 + 0.999480i \(0.489736\pi\)
\(420\) 5.29478 0.258359
\(421\) −25.4599 −1.24084 −0.620420 0.784270i \(-0.713038\pi\)
−0.620420 + 0.784270i \(0.713038\pi\)
\(422\) 17.6349 0.858452
\(423\) −14.6829 −0.713909
\(424\) 1.72545 0.0837953
\(425\) 1.52265 0.0738593
\(426\) −3.77213 −0.182761
\(427\) 19.5721 0.947161
\(428\) 6.00000 0.290021
\(429\) 1.52265 0.0735141
\(430\) −7.22925 −0.348626
\(431\) 29.9094 1.44069 0.720343 0.693618i \(-0.243985\pi\)
0.720343 + 0.693618i \(0.243985\pi\)
\(432\) 0.340078 0.0163620
\(433\) −3.77213 −0.181277 −0.0906386 0.995884i \(-0.528891\pi\)
−0.0906386 + 0.995884i \(0.528891\pi\)
\(434\) −6.02162 −0.289047
\(435\) −17.9094 −0.858690
\(436\) 6.90802 0.330834
\(437\) 0 0
\(438\) −37.7282 −1.80272
\(439\) 1.99378 0.0951580 0.0475790 0.998867i \(-0.484849\pi\)
0.0475790 + 0.998867i \(0.484849\pi\)
\(440\) 4.47735 0.213449
\(441\) −7.63003 −0.363335
\(442\) 0.209021 0.00994211
\(443\) 12.7268 0.604670 0.302335 0.953202i \(-0.402234\pi\)
0.302335 + 0.953202i \(0.402234\pi\)
\(444\) −29.5038 −1.40019
\(445\) 4.27455 0.202633
\(446\) 13.5038 0.639424
\(447\) 42.3429 2.00275
\(448\) 2.13727 0.100977
\(449\) −35.4070 −1.67096 −0.835480 0.549521i \(-0.814810\pi\)
−0.835480 + 0.549521i \(0.814810\pi\)
\(450\) 3.13727 0.147893
\(451\) 20.0467 0.943961
\(452\) 13.2293 0.622252
\(453\) 45.7749 2.15069
\(454\) −19.6349 −0.921510
\(455\) 0.293394 0.0137545
\(456\) 12.6146 0.590734
\(457\) 7.31984 0.342408 0.171204 0.985236i \(-0.445234\pi\)
0.171204 + 0.985236i \(0.445234\pi\)
\(458\) 0.0905906 0.00423302
\(459\) 0.517818 0.0241697
\(460\) 0 0
\(461\) 22.2745 1.03743 0.518715 0.854947i \(-0.326411\pi\)
0.518715 + 0.854947i \(0.326411\pi\)
\(462\) 23.7066 1.10293
\(463\) 8.82365 0.410070 0.205035 0.978755i \(-0.434269\pi\)
0.205035 + 0.978755i \(0.434269\pi\)
\(464\) −7.22925 −0.335610
\(465\) −6.97977 −0.323679
\(466\) −2.95470 −0.136874
\(467\) −16.1840 −0.748904 −0.374452 0.927246i \(-0.622169\pi\)
−0.374452 + 0.927246i \(0.622169\pi\)
\(468\) 0.430668 0.0199076
\(469\) 6.31502 0.291600
\(470\) −4.68016 −0.215879
\(471\) −37.0481 −1.70709
\(472\) −13.2293 −0.608926
\(473\) −32.3679 −1.48828
\(474\) 11.5944 0.532548
\(475\) 5.09198 0.233636
\(476\) 3.25432 0.149161
\(477\) 5.41321 0.247854
\(478\) 12.0000 0.548867
\(479\) −10.3651 −0.473595 −0.236798 0.971559i \(-0.576098\pi\)
−0.236798 + 0.971559i \(0.576098\pi\)
\(480\) 2.47735 0.113075
\(481\) −1.63486 −0.0745432
\(482\) 5.90941 0.269166
\(483\) 0 0
\(484\) 9.04668 0.411213
\(485\) −19.4321 −0.882364
\(486\) −22.2495 −1.00926
\(487\) −8.27455 −0.374956 −0.187478 0.982269i \(-0.560031\pi\)
−0.187478 + 0.982269i \(0.560031\pi\)
\(488\) 9.15751 0.414541
\(489\) −28.1589 −1.27339
\(490\) −2.43206 −0.109869
\(491\) −16.2745 −0.734460 −0.367230 0.930130i \(-0.619694\pi\)
−0.367230 + 0.930130i \(0.619694\pi\)
\(492\) 11.0920 0.500065
\(493\) −11.0076 −0.495758
\(494\) 0.699000 0.0314495
\(495\) 14.0467 0.631351
\(496\) −2.81743 −0.126506
\(497\) −3.25432 −0.145976
\(498\) −40.0934 −1.79663
\(499\) 23.1387 1.03583 0.517914 0.855432i \(-0.326709\pi\)
0.517914 + 0.855432i \(0.326709\pi\)
\(500\) 1.00000 0.0447214
\(501\) 25.2293 1.12716
\(502\) −19.5505 −0.872581
\(503\) −25.1324 −1.12060 −0.560300 0.828290i \(-0.689314\pi\)
−0.560300 + 0.828290i \(0.689314\pi\)
\(504\) 6.70522 0.298674
\(505\) −11.9094 −0.529962
\(506\) 0 0
\(507\) −32.1589 −1.42823
\(508\) 20.0934 0.891499
\(509\) −23.3226 −1.03376 −0.516879 0.856059i \(-0.672906\pi\)
−0.516879 + 0.856059i \(0.672906\pi\)
\(510\) 3.77213 0.167033
\(511\) −32.5491 −1.43989
\(512\) 1.00000 0.0441942
\(513\) 1.73167 0.0764550
\(514\) 29.4132 1.29736
\(515\) 12.1122 0.533728
\(516\) −17.9094 −0.788418
\(517\) −20.9547 −0.921587
\(518\) −25.4537 −1.11837
\(519\) 11.0920 0.486884
\(520\) 0.137275 0.00601989
\(521\) 40.4990 1.77429 0.887146 0.461489i \(-0.152684\pi\)
0.887146 + 0.461489i \(0.152684\pi\)
\(522\) −22.6802 −0.992683
\(523\) 1.72545 0.0754487 0.0377243 0.999288i \(-0.487989\pi\)
0.0377243 + 0.999288i \(0.487989\pi\)
\(524\) 5.90941 0.258154
\(525\) 5.29478 0.231083
\(526\) 5.79720 0.252770
\(527\) −4.28995 −0.186873
\(528\) 11.0920 0.482716
\(529\) 0 0
\(530\) 1.72545 0.0749488
\(531\) −41.5038 −1.80111
\(532\) 10.8830 0.471836
\(533\) 0.614627 0.0266225
\(534\) 10.5896 0.458255
\(535\) 6.00000 0.259403
\(536\) 2.95470 0.127624
\(537\) −19.1387 −0.825894
\(538\) 8.86411 0.382159
\(539\) −10.8892 −0.469030
\(540\) 0.340078 0.0146346
\(541\) 9.31984 0.400691 0.200346 0.979725i \(-0.435793\pi\)
0.200346 + 0.979725i \(0.435793\pi\)
\(542\) 21.0014 0.902087
\(543\) 23.2042 0.995787
\(544\) 1.52265 0.0652830
\(545\) 6.90802 0.295907
\(546\) 0.726839 0.0311059
\(547\) −22.5429 −0.963864 −0.481932 0.876209i \(-0.660065\pi\)
−0.481932 + 0.876209i \(0.660065\pi\)
\(548\) −12.3212 −0.526337
\(549\) 28.7296 1.22615
\(550\) 4.47735 0.190915
\(551\) −36.8112 −1.56821
\(552\) 0 0
\(553\) 10.0028 0.425361
\(554\) −22.3679 −0.950322
\(555\) −29.5038 −1.25237
\(556\) 16.9547 0.719040
\(557\) −20.2773 −0.859178 −0.429589 0.903025i \(-0.641342\pi\)
−0.429589 + 0.903025i \(0.641342\pi\)
\(558\) −8.83905 −0.374187
\(559\) −0.992393 −0.0419738
\(560\) 2.13727 0.0903163
\(561\) 16.8892 0.713062
\(562\) −10.5896 −0.446694
\(563\) 23.7282 1.00003 0.500013 0.866018i \(-0.333329\pi\)
0.500013 + 0.866018i \(0.333329\pi\)
\(564\) −11.5944 −0.488212
\(565\) 13.2293 0.556559
\(566\) −7.22925 −0.303868
\(567\) −18.3150 −0.769158
\(568\) −1.52265 −0.0638889
\(569\) −35.4132 −1.48460 −0.742300 0.670068i \(-0.766265\pi\)
−0.742300 + 0.670068i \(0.766265\pi\)
\(570\) 12.6146 0.528369
\(571\) 36.8453 1.54193 0.770963 0.636880i \(-0.219775\pi\)
0.770963 + 0.636880i \(0.219775\pi\)
\(572\) 0.614627 0.0256988
\(573\) 40.3178 1.68430
\(574\) 9.56933 0.399416
\(575\) 0 0
\(576\) 3.13727 0.130720
\(577\) 15.6349 0.650888 0.325444 0.945561i \(-0.394486\pi\)
0.325444 + 0.945561i \(0.394486\pi\)
\(578\) −14.6815 −0.610672
\(579\) −17.2293 −0.716023
\(580\) −7.22925 −0.300178
\(581\) −34.5896 −1.43502
\(582\) −48.1401 −1.99547
\(583\) 7.72545 0.319955
\(584\) −15.2293 −0.630191
\(585\) 0.430668 0.0178059
\(586\) 17.8188 0.736089
\(587\) 19.0265 0.785306 0.392653 0.919687i \(-0.371557\pi\)
0.392653 + 0.919687i \(0.371557\pi\)
\(588\) −6.02506 −0.248469
\(589\) −14.3463 −0.591129
\(590\) −13.2293 −0.544640
\(591\) 3.54771 0.145933
\(592\) −11.9094 −0.489474
\(593\) 32.4585 1.33291 0.666456 0.745545i \(-0.267811\pi\)
0.666456 + 0.745545i \(0.267811\pi\)
\(594\) 1.52265 0.0624750
\(595\) 3.25432 0.133414
\(596\) 17.0920 0.700115
\(597\) −14.6397 −0.599163
\(598\) 0 0
\(599\) −28.3868 −1.15985 −0.579926 0.814669i \(-0.696918\pi\)
−0.579926 + 0.814669i \(0.696918\pi\)
\(600\) 2.47735 0.101137
\(601\) −16.4118 −0.669452 −0.334726 0.942315i \(-0.608644\pi\)
−0.334726 + 0.942315i \(0.608644\pi\)
\(602\) −15.4509 −0.629732
\(603\) 9.26972 0.377492
\(604\) 18.4774 0.751833
\(605\) 9.04668 0.367800
\(606\) −29.5038 −1.19851
\(607\) −38.1840 −1.54984 −0.774920 0.632060i \(-0.782210\pi\)
−0.774920 + 0.632060i \(0.782210\pi\)
\(608\) 5.09198 0.206507
\(609\) −38.2773 −1.55108
\(610\) 9.15751 0.370777
\(611\) −0.642467 −0.0259914
\(612\) 4.77696 0.193097
\(613\) −7.22925 −0.291987 −0.145993 0.989286i \(-0.546638\pi\)
−0.145993 + 0.989286i \(0.546638\pi\)
\(614\) 17.3415 0.699845
\(615\) 11.0920 0.447272
\(616\) 9.56933 0.385559
\(617\) 15.9812 0.643377 0.321689 0.946846i \(-0.395750\pi\)
0.321689 + 0.946846i \(0.395750\pi\)
\(618\) 30.0062 1.20703
\(619\) −47.0014 −1.88915 −0.944573 0.328302i \(-0.893523\pi\)
−0.944573 + 0.328302i \(0.893523\pi\)
\(620\) −2.81743 −0.113151
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 9.13589 0.366022
\(624\) 0.340078 0.0136140
\(625\) 1.00000 0.0400000
\(626\) 12.3212 0.492456
\(627\) 56.4801 2.25560
\(628\) −14.9547 −0.596758
\(629\) −18.1338 −0.723043
\(630\) 6.70522 0.267142
\(631\) 5.50380 0.219103 0.109551 0.993981i \(-0.465059\pi\)
0.109551 + 0.993981i \(0.465059\pi\)
\(632\) 4.68016 0.186167
\(633\) 43.6878 1.73643
\(634\) −21.7721 −0.864682
\(635\) 20.0934 0.797381
\(636\) 4.27455 0.169497
\(637\) −0.333860 −0.0132280
\(638\) −32.3679 −1.28146
\(639\) −4.77696 −0.188974
\(640\) 1.00000 0.0395285
\(641\) −26.0529 −1.02903 −0.514514 0.857482i \(-0.672028\pi\)
−0.514514 + 0.857482i \(0.672028\pi\)
\(642\) 14.8641 0.586640
\(643\) −2.14349 −0.0845311 −0.0422655 0.999106i \(-0.513458\pi\)
−0.0422655 + 0.999106i \(0.513458\pi\)
\(644\) 0 0
\(645\) −17.9094 −0.705182
\(646\) 7.75329 0.305049
\(647\) 3.85651 0.151615 0.0758075 0.997122i \(-0.475847\pi\)
0.0758075 + 0.997122i \(0.475847\pi\)
\(648\) −8.56933 −0.336635
\(649\) −59.2320 −2.32506
\(650\) 0.137275 0.00538436
\(651\) −14.9177 −0.584670
\(652\) −11.3665 −0.445148
\(653\) 5.67877 0.222227 0.111114 0.993808i \(-0.464558\pi\)
0.111114 + 0.993808i \(0.464558\pi\)
\(654\) 17.1136 0.669195
\(655\) 5.90941 0.230900
\(656\) 4.47735 0.174811
\(657\) −47.7784 −1.86401
\(658\) −10.0028 −0.389949
\(659\) 30.2369 1.17786 0.588930 0.808184i \(-0.299549\pi\)
0.588930 + 0.808184i \(0.299549\pi\)
\(660\) 11.0920 0.431755
\(661\) 20.1651 0.784332 0.392166 0.919894i \(-0.371726\pi\)
0.392166 + 0.919894i \(0.371726\pi\)
\(662\) −0.274549 −0.0106707
\(663\) 0.517818 0.0201104
\(664\) −16.1840 −0.628059
\(665\) 10.8830 0.422023
\(666\) −37.3631 −1.44779
\(667\) 0 0
\(668\) 10.1840 0.394029
\(669\) 33.4537 1.29339
\(670\) 2.95470 0.114150
\(671\) 41.0014 1.58284
\(672\) 5.29478 0.204251
\(673\) 22.2244 0.856689 0.428344 0.903616i \(-0.359097\pi\)
0.428344 + 0.903616i \(0.359097\pi\)
\(674\) 20.0467 0.772169
\(675\) 0.340078 0.0130896
\(676\) −12.9812 −0.499275
\(677\) 8.04047 0.309020 0.154510 0.987991i \(-0.450620\pi\)
0.154510 + 0.987991i \(0.450620\pi\)
\(678\) 32.7735 1.25866
\(679\) −41.5316 −1.59384
\(680\) 1.52265 0.0583909
\(681\) −48.6425 −1.86398
\(682\) −12.6146 −0.483039
\(683\) 2.72406 0.104233 0.0521167 0.998641i \(-0.483403\pi\)
0.0521167 + 0.998641i \(0.483403\pi\)
\(684\) 15.9749 0.610817
\(685\) −12.3212 −0.470770
\(686\) −20.1589 −0.769670
\(687\) 0.224425 0.00856234
\(688\) −7.22925 −0.275613
\(689\) 0.236861 0.00902367
\(690\) 0 0
\(691\) 26.9952 1.02694 0.513472 0.858106i \(-0.328359\pi\)
0.513472 + 0.858106i \(0.328359\pi\)
\(692\) 4.47735 0.170203
\(693\) 30.0216 1.14043
\(694\) 1.11704 0.0424023
\(695\) 16.9547 0.643129
\(696\) −17.9094 −0.678854
\(697\) 6.81743 0.258229
\(698\) −28.7331 −1.08756
\(699\) −7.31984 −0.276862
\(700\) 2.13727 0.0807814
\(701\) 2.63347 0.0994648 0.0497324 0.998763i \(-0.484163\pi\)
0.0497324 + 0.998763i \(0.484163\pi\)
\(702\) 0.0466840 0.00176198
\(703\) −60.6425 −2.28717
\(704\) 4.47735 0.168747
\(705\) −11.5944 −0.436670
\(706\) −6.82365 −0.256811
\(707\) −25.4537 −0.957284
\(708\) −32.7735 −1.23170
\(709\) 43.7595 1.64342 0.821711 0.569904i \(-0.193020\pi\)
0.821711 + 0.569904i \(0.193020\pi\)
\(710\) −1.52265 −0.0571439
\(711\) 14.6829 0.550653
\(712\) 4.27455 0.160196
\(713\) 0 0
\(714\) 8.06209 0.301716
\(715\) 0.614627 0.0229857
\(716\) −7.72545 −0.288714
\(717\) 29.7282 1.11022
\(718\) 22.5896 0.843035
\(719\) −32.4523 −1.21027 −0.605133 0.796124i \(-0.706880\pi\)
−0.605133 + 0.796124i \(0.706880\pi\)
\(720\) 3.13727 0.116919
\(721\) 25.8871 0.964087
\(722\) 6.92825 0.257843
\(723\) 14.6397 0.544456
\(724\) 9.36653 0.348104
\(725\) −7.22925 −0.268488
\(726\) 22.4118 0.831781
\(727\) 41.2104 1.52841 0.764205 0.644974i \(-0.223132\pi\)
0.764205 + 0.644974i \(0.223132\pi\)
\(728\) 0.293394 0.0108739
\(729\) −29.4118 −1.08933
\(730\) −15.2293 −0.563660
\(731\) −11.0076 −0.407131
\(732\) 22.6864 0.838512
\(733\) 37.5443 1.38673 0.693365 0.720587i \(-0.256128\pi\)
0.693365 + 0.720587i \(0.256128\pi\)
\(734\) 32.3679 1.19472
\(735\) −6.02506 −0.222238
\(736\) 0 0
\(737\) 13.2293 0.487306
\(738\) 14.0467 0.517066
\(739\) 14.4962 0.533251 0.266626 0.963800i \(-0.414091\pi\)
0.266626 + 0.963800i \(0.414091\pi\)
\(740\) −11.9094 −0.437799
\(741\) 1.73167 0.0636144
\(742\) 3.68776 0.135382
\(743\) 34.5052 1.26587 0.632936 0.774204i \(-0.281849\pi\)
0.632936 + 0.774204i \(0.281849\pi\)
\(744\) −6.97977 −0.255891
\(745\) 17.0920 0.626202
\(746\) −13.7255 −0.502524
\(747\) −50.7735 −1.85771
\(748\) 6.81743 0.249270
\(749\) 12.8236 0.468566
\(750\) 2.47735 0.0904601
\(751\) 22.1840 0.809504 0.404752 0.914426i \(-0.367358\pi\)
0.404752 + 0.914426i \(0.367358\pi\)
\(752\) −4.68016 −0.170668
\(753\) −48.4334 −1.76501
\(754\) −0.992393 −0.0361408
\(755\) 18.4774 0.672460
\(756\) 0.726839 0.0264349
\(757\) −1.72545 −0.0627126 −0.0313563 0.999508i \(-0.509983\pi\)
−0.0313563 + 0.999508i \(0.509983\pi\)
\(758\) −28.4774 −1.03434
\(759\) 0 0
\(760\) 5.09198 0.184706
\(761\) −39.6815 −1.43845 −0.719227 0.694775i \(-0.755504\pi\)
−0.719227 + 0.694775i \(0.755504\pi\)
\(762\) 49.7784 1.80328
\(763\) 14.7643 0.534505
\(764\) 16.2745 0.588793
\(765\) 4.77696 0.172711
\(766\) 9.36031 0.338202
\(767\) −1.81604 −0.0655735
\(768\) 2.47735 0.0893938
\(769\) −5.90941 −0.213099 −0.106549 0.994307i \(-0.533980\pi\)
−0.106549 + 0.994307i \(0.533980\pi\)
\(770\) 9.56933 0.344855
\(771\) 72.8669 2.62424
\(772\) −6.95470 −0.250305
\(773\) −12.3150 −0.442940 −0.221470 0.975167i \(-0.571086\pi\)
−0.221470 + 0.975167i \(0.571086\pi\)
\(774\) −22.6802 −0.815221
\(775\) −2.81743 −0.101205
\(776\) −19.4321 −0.697570
\(777\) −63.0577 −2.26218
\(778\) 30.1122 1.07958
\(779\) 22.7986 0.816844
\(780\) 0.340078 0.0121767
\(781\) −6.81743 −0.243947
\(782\) 0 0
\(783\) −2.45851 −0.0878599
\(784\) −2.43206 −0.0868592
\(785\) −14.9547 −0.533756
\(786\) 14.6397 0.522180
\(787\) −9.85651 −0.351347 −0.175673 0.984449i \(-0.556210\pi\)
−0.175673 + 0.984449i \(0.556210\pi\)
\(788\) 1.43206 0.0510149
\(789\) 14.3617 0.511290
\(790\) 4.68016 0.166512
\(791\) 28.2745 1.00533
\(792\) 14.0467 0.499127
\(793\) 1.25709 0.0446407
\(794\) 12.8830 0.457199
\(795\) 4.27455 0.151603
\(796\) −5.90941 −0.209453
\(797\) 19.8160 0.701920 0.350960 0.936390i \(-0.385855\pi\)
0.350960 + 0.936390i \(0.385855\pi\)
\(798\) 26.9609 0.954406
\(799\) −7.12623 −0.252108
\(800\) 1.00000 0.0353553
\(801\) 13.4104 0.473834
\(802\) −22.0028 −0.776945
\(803\) −68.1867 −2.40626
\(804\) 7.31984 0.258151
\(805\) 0 0
\(806\) −0.386762 −0.0136231
\(807\) 21.9595 0.773012
\(808\) −11.9094 −0.418972
\(809\) −7.11704 −0.250222 −0.125111 0.992143i \(-0.539929\pi\)
−0.125111 + 0.992143i \(0.539929\pi\)
\(810\) −8.56933 −0.301096
\(811\) −35.5066 −1.24680 −0.623402 0.781901i \(-0.714250\pi\)
−0.623402 + 0.781901i \(0.714250\pi\)
\(812\) −15.4509 −0.542220
\(813\) 52.0278 1.82470
\(814\) −53.3226 −1.86896
\(815\) −11.3665 −0.398152
\(816\) 3.77213 0.132051
\(817\) −36.8112 −1.28786
\(818\) −13.7721 −0.481531
\(819\) 0.920456 0.0321634
\(820\) 4.47735 0.156356
\(821\) 36.3150 1.26740 0.633701 0.773578i \(-0.281535\pi\)
0.633701 + 0.773578i \(0.281535\pi\)
\(822\) −30.5240 −1.06465
\(823\) 18.0405 0.628851 0.314426 0.949282i \(-0.398188\pi\)
0.314426 + 0.949282i \(0.398188\pi\)
\(824\) 12.1122 0.421949
\(825\) 11.0920 0.386173
\(826\) −28.2745 −0.983797
\(827\) −52.0028 −1.80831 −0.904157 0.427201i \(-0.859500\pi\)
−0.904157 + 0.427201i \(0.859500\pi\)
\(828\) 0 0
\(829\) −9.00761 −0.312847 −0.156424 0.987690i \(-0.549996\pi\)
−0.156424 + 0.987690i \(0.549996\pi\)
\(830\) −16.1840 −0.561753
\(831\) −55.4132 −1.92226
\(832\) 0.137275 0.00475914
\(833\) −3.70317 −0.128307
\(834\) 42.0028 1.45444
\(835\) 10.1840 0.352430
\(836\) 22.7986 0.788506
\(837\) −0.958145 −0.0331183
\(838\) 1.31984 0.0455933
\(839\) 49.8717 1.72176 0.860882 0.508805i \(-0.169913\pi\)
0.860882 + 0.508805i \(0.169913\pi\)
\(840\) 5.29478 0.182687
\(841\) 23.2621 0.802142
\(842\) −25.4599 −0.877406
\(843\) −26.2341 −0.903550
\(844\) 17.6349 0.607017
\(845\) −12.9812 −0.446565
\(846\) −14.6829 −0.504810
\(847\) 19.3352 0.664367
\(848\) 1.72545 0.0592522
\(849\) −17.9094 −0.614649
\(850\) 1.52265 0.0522264
\(851\) 0 0
\(852\) −3.77213 −0.129231
\(853\) −14.5958 −0.499750 −0.249875 0.968278i \(-0.580390\pi\)
−0.249875 + 0.968278i \(0.580390\pi\)
\(854\) 19.5721 0.669744
\(855\) 15.9749 0.546331
\(856\) 6.00000 0.205076
\(857\) 37.1387 1.26863 0.634316 0.773074i \(-0.281282\pi\)
0.634316 + 0.773074i \(0.281282\pi\)
\(858\) 1.52265 0.0519823
\(859\) −14.0028 −0.477769 −0.238884 0.971048i \(-0.576782\pi\)
−0.238884 + 0.971048i \(0.576782\pi\)
\(860\) −7.22925 −0.246516
\(861\) 23.7066 0.807919
\(862\) 29.9094 1.01872
\(863\) −12.1812 −0.414652 −0.207326 0.978272i \(-0.566476\pi\)
−0.207326 + 0.978272i \(0.566476\pi\)
\(864\) 0.340078 0.0115697
\(865\) 4.47735 0.152235
\(866\) −3.77213 −0.128182
\(867\) −36.3714 −1.23524
\(868\) −6.02162 −0.204387
\(869\) 20.9547 0.710840
\(870\) −17.9094 −0.607186
\(871\) 0.405606 0.0137434
\(872\) 6.90802 0.233935
\(873\) −60.9637 −2.06331
\(874\) 0 0
\(875\) 2.13727 0.0722531
\(876\) −37.7282 −1.27472
\(877\) 28.4397 0.960339 0.480170 0.877176i \(-0.340575\pi\)
0.480170 + 0.877176i \(0.340575\pi\)
\(878\) 1.99378 0.0672869
\(879\) 44.1435 1.48892
\(880\) 4.47735 0.150932
\(881\) 35.0076 1.17944 0.589718 0.807609i \(-0.299239\pi\)
0.589718 + 0.807609i \(0.299239\pi\)
\(882\) −7.63003 −0.256917
\(883\) 12.4647 0.419471 0.209736 0.977758i \(-0.432740\pi\)
0.209736 + 0.977758i \(0.432740\pi\)
\(884\) 0.209021 0.00703013
\(885\) −32.7735 −1.10167
\(886\) 12.7268 0.427567
\(887\) 1.04807 0.0351908 0.0175954 0.999845i \(-0.494399\pi\)
0.0175954 + 0.999845i \(0.494399\pi\)
\(888\) −29.5038 −0.990083
\(889\) 42.9450 1.44033
\(890\) 4.27455 0.143283
\(891\) −38.3679 −1.28537
\(892\) 13.5038 0.452141
\(893\) −23.8313 −0.797483
\(894\) 42.3429 1.41616
\(895\) −7.72545 −0.258233
\(896\) 2.13727 0.0714013
\(897\) 0 0
\(898\) −35.4070 −1.18155
\(899\) 20.3679 0.679308
\(900\) 3.13727 0.104576
\(901\) 2.62725 0.0875265
\(902\) 20.0467 0.667482
\(903\) −38.2773 −1.27379
\(904\) 13.2293 0.439998
\(905\) 9.36653 0.311354
\(906\) 45.7749 1.52077
\(907\) 22.9170 0.760947 0.380474 0.924792i \(-0.375761\pi\)
0.380474 + 0.924792i \(0.375761\pi\)
\(908\) −19.6349 −0.651606
\(909\) −37.3631 −1.23926
\(910\) 0.293394 0.00972590
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 12.6146 0.417712
\(913\) −72.4613 −2.39812
\(914\) 7.31984 0.242119
\(915\) 22.6864 0.749988
\(916\) 0.0905906 0.00299320
\(917\) 12.6300 0.417080
\(918\) 0.517818 0.0170906
\(919\) −47.2320 −1.55804 −0.779020 0.626998i \(-0.784283\pi\)
−0.779020 + 0.626998i \(0.784283\pi\)
\(920\) 0 0
\(921\) 42.9609 1.41561
\(922\) 22.2745 0.733573
\(923\) −0.209021 −0.00688001
\(924\) 23.7066 0.779890
\(925\) −11.9094 −0.391579
\(926\) 8.82365 0.289963
\(927\) 37.9993 1.24806
\(928\) −7.22925 −0.237312
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) −6.97977 −0.228876
\(931\) −12.3840 −0.405869
\(932\) −2.95470 −0.0967846
\(933\) 29.7282 0.973258
\(934\) −16.1840 −0.529555
\(935\) 6.81743 0.222954
\(936\) 0.430668 0.0140768
\(937\) −38.9609 −1.27280 −0.636399 0.771360i \(-0.719577\pi\)
−0.636399 + 0.771360i \(0.719577\pi\)
\(938\) 6.31502 0.206193
\(939\) 30.5240 0.996114
\(940\) −4.68016 −0.152650
\(941\) −3.65370 −0.119107 −0.0595537 0.998225i \(-0.518968\pi\)
−0.0595537 + 0.998225i \(0.518968\pi\)
\(942\) −37.0481 −1.20709
\(943\) 0 0
\(944\) −13.2293 −0.430576
\(945\) 0.726839 0.0236441
\(946\) −32.3679 −1.05237
\(947\) −43.4599 −1.41226 −0.706128 0.708084i \(-0.749560\pi\)
−0.706128 + 0.708084i \(0.749560\pi\)
\(948\) 11.5944 0.376568
\(949\) −2.09059 −0.0678634
\(950\) 5.09198 0.165206
\(951\) −53.9372 −1.74904
\(952\) 3.25432 0.105473
\(953\) 10.2962 0.333526 0.166763 0.985997i \(-0.446669\pi\)
0.166763 + 0.985997i \(0.446669\pi\)
\(954\) 5.41321 0.175259
\(955\) 16.2745 0.526632
\(956\) 12.0000 0.388108
\(957\) −80.1867 −2.59207
\(958\) −10.3651 −0.334882
\(959\) −26.3339 −0.850365
\(960\) 2.47735 0.0799562
\(961\) −23.0621 −0.743938
\(962\) −1.63486 −0.0527100
\(963\) 18.8236 0.606584
\(964\) 5.90941 0.190329
\(965\) −6.95470 −0.223880
\(966\) 0 0
\(967\) −24.6802 −0.793660 −0.396830 0.917892i \(-0.629890\pi\)
−0.396830 + 0.917892i \(0.629890\pi\)
\(968\) 9.04668 0.290771
\(969\) 19.2076 0.617038
\(970\) −19.4321 −0.623926
\(971\) 57.9812 1.86070 0.930352 0.366668i \(-0.119501\pi\)
0.930352 + 0.366668i \(0.119501\pi\)
\(972\) −22.2495 −0.713653
\(973\) 36.2369 1.16170
\(974\) −8.27455 −0.265134
\(975\) 0.340078 0.0108912
\(976\) 9.15751 0.293125
\(977\) 13.1324 0.420144 0.210072 0.977686i \(-0.432630\pi\)
0.210072 + 0.977686i \(0.432630\pi\)
\(978\) −28.1589 −0.900422
\(979\) 19.1387 0.611674
\(980\) −2.43206 −0.0776892
\(981\) 21.6724 0.691945
\(982\) −16.2745 −0.519342
\(983\) 30.2028 0.963320 0.481660 0.876358i \(-0.340034\pi\)
0.481660 + 0.876358i \(0.340034\pi\)
\(984\) 11.0920 0.353599
\(985\) 1.43206 0.0456291
\(986\) −11.0076 −0.350554
\(987\) −24.7804 −0.788769
\(988\) 0.699000 0.0222381
\(989\) 0 0
\(990\) 14.0467 0.446433
\(991\) −24.5679 −0.780426 −0.390213 0.920725i \(-0.627599\pi\)
−0.390213 + 0.920725i \(0.627599\pi\)
\(992\) −2.81743 −0.0894535
\(993\) −0.680155 −0.0215841
\(994\) −3.25432 −0.103221
\(995\) −5.90941 −0.187341
\(996\) −40.0934 −1.27041
\(997\) −21.8188 −0.691009 −0.345504 0.938417i \(-0.612292\pi\)
−0.345504 + 0.938417i \(0.612292\pi\)
\(998\) 23.1387 0.732442
\(999\) −4.05012 −0.128140
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 5290.2.a.q.1.3 yes 3
23.22 odd 2 5290.2.a.p.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.3 3 23.22 odd 2
5290.2.a.q.1.3 yes 3 1.1 even 1 trivial