Properties

Label 5290.2.a.p.1.3
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.1509.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 4\)
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

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

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 \(-0.632348\pi\)
−0.403907 + 0.914800i \(0.632348\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.13727 1.04576
\(10\) −1.00000 −0.316228
\(11\) −4.47735 −1.34997 −0.674986 0.737830i \(-0.735850\pi\)
−0.674986 + 0.737830i \(0.735850\pi\)
\(12\) 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 \(-0.559115\pi\)
−0.184648 + 0.982805i \(0.559115\pi\)
\(18\) 3.13727 0.739463
\(19\) −5.09198 −1.16818 −0.584090 0.811689i \(-0.698549\pi\)
−0.584090 + 0.811689i \(0.698549\pi\)
\(20\) −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 \(-0.0654309\pi\)
0.978947 + 0.204113i \(0.0654309\pi\)
\(38\) −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 \(-0.314160\pi\)
0.551225 + 0.834356i \(0.314160\pi\)
\(44\) −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 \(-0.537810\pi\)
−0.118504 + 0.992954i \(0.537810\pi\)
\(54\) 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 \(-0.699396\pi\)
−0.586249 + 0.810131i \(0.699396\pi\)
\(62\) −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 \(-0.557767\pi\)
−0.180487 + 0.983577i \(0.557767\pi\)
\(68\) −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 \(-0.584804\pi\)
−0.263279 + 0.964720i \(0.584804\pi\)
\(80\) −1.00000 −0.111803
\(81\) −8.56933 −0.952148
\(82\) 4.47735 0.494441
\(83\) 16.1840 1.77642 0.888210 0.459437i \(-0.151949\pi\)
0.888210 + 0.459437i \(0.151949\pi\)
\(84\) −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 \(-0.572745\pi\)
−0.226551 + 0.973999i \(0.572745\pi\)
\(90\) −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 \(-0.0523370\pi\)
0.986513 + 0.163682i \(0.0523370\pi\)
\(98\) −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 \(-0.703532\pi\)
−0.596726 + 0.802445i \(0.703532\pi\)
\(104\) 0.137275 0.0134609
\(105\) 5.29478 0.516718
\(106\) −1.72545 −0.167591
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0.340078 0.0327240
\(109\) −6.90802 −0.661668 −0.330834 0.943689i \(-0.607330\pi\)
−0.330834 + 0.943689i \(0.607330\pi\)
\(110\) 4.47735 0.426899
\(111\) 29.5038 2.80038
\(112\) −2.13727 −0.201953
\(113\) −13.2293 −1.24450 −0.622252 0.782817i \(-0.713782\pi\)
−0.622252 + 0.782817i \(0.713782\pi\)
\(114\) −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 \(-0.323565\pi\)
0.526337 + 0.850276i \(0.323565\pi\)
\(138\) 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 \(-0.746868\pi\)
−0.700115 + 0.714030i \(0.746868\pi\)
\(150\) 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 \(-0.296455\pi\)
0.596758 + 0.802422i \(0.296455\pi\)
\(158\) −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 \(-0.613174\pi\)
−0.348104 + 0.937456i \(0.613174\pi\)
\(182\) −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 \(-0.700396\pi\)
−0.588793 + 0.808284i \(0.700396\pi\)
\(192\) 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 \(-0.432832\pi\)
0.209453 + 0.977819i \(0.432832\pi\)
\(200\) 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 \(-0.274096\pi\)
0.651606 + 0.758558i \(0.274096\pi\)
\(228\) −12.6146 −0.835424
\(229\) −0.0905906 −0.00598640 −0.00299320 0.999996i \(-0.500953\pi\)
−0.00299320 + 0.999996i \(0.500953\pi\)
\(230\) 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 \(-0.560956\pi\)
−0.190329 + 0.981720i \(0.560956\pi\)
\(242\) 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 \(-0.288345\pi\)
0.617008 + 0.786957i \(0.288345\pi\)
\(252\) −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 \(-0.557201\pi\)
−0.178735 + 0.983897i \(0.557201\pi\)
\(264\) −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 \(-0.397707\pi\)
0.315860 + 0.948806i \(0.397707\pi\)
\(282\) −11.5944 −0.690436
\(283\) 7.22925 0.429735 0.214867 0.976643i \(-0.431068\pi\)
0.214867 + 0.976643i \(0.431068\pi\)
\(284\) −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 \(-0.674252\pi\)
−0.520493 + 0.853866i \(0.674252\pi\)
\(294\) −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 \(-0.613213\pi\)
−0.348219 + 0.937413i \(0.613213\pi\)
\(314\) 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 \(-0.683853\pi\)
−0.546006 + 0.837781i \(0.683853\pi\)
\(338\) −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 \(-0.703290\pi\)
−0.596116 + 0.802898i \(0.703290\pi\)
\(360\) −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 \(-0.820278\pi\)
−0.844796 + 0.535089i \(0.820278\pi\)
\(368\) 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 \(-0.384366\pi\)
0.355338 + 0.934738i \(0.384366\pi\)
\(374\) 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 \(-0.238871\pi\)
0.731392 + 0.681958i \(0.238871\pi\)
\(380\) 5.09198 0.261213
\(381\) 49.7784 2.55022
\(382\) −16.2745 −0.832678
\(383\) −9.36031 −0.478290 −0.239145 0.970984i \(-0.576867\pi\)
−0.239145 + 0.970984i \(0.576867\pi\)
\(384\) 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 \(-0.776459\pi\)
−0.763375 + 0.645956i \(0.776459\pi\)
\(390\) −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 \(-0.314863\pi\)
0.549383 + 0.835571i \(0.314863\pi\)
\(402\) −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 \(-0.510264\pi\)
−0.0322393 + 0.999480i \(0.510264\pi\)
\(420\) 5.29478 0.258359
\(421\) 25.4599 1.24084 0.620420 0.784270i \(-0.286962\pi\)
0.620420 + 0.784270i \(0.286962\pi\)
\(422\) 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 \(-0.756015\pi\)
−0.720343 + 0.693618i \(0.756015\pi\)
\(432\) 0.340078 0.0163620
\(433\) 3.77213 0.181277 0.0906386 0.995884i \(-0.471109\pi\)
0.0906386 + 0.995884i \(0.471109\pi\)
\(434\) 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 \(-0.554766\pi\)
−0.171204 + 0.985236i \(0.554766\pi\)
\(458\) −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 \(-0.377831\pi\)
0.374452 + 0.927246i \(0.377831\pi\)
\(468\) 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 \(-0.423902\pi\)
0.236798 + 0.971559i \(0.423902\pi\)
\(480\) −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 \(-0.310686\pi\)
0.560300 + 0.828290i \(0.310686\pi\)
\(504\) −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 \(-0.847316\pi\)
−0.887146 + 0.461489i \(0.847316\pi\)
\(522\) −22.6802 −0.992683
\(523\) −1.72545 −0.0754487 −0.0377243 0.999288i \(-0.512011\pi\)
−0.0377243 + 0.999288i \(0.512011\pi\)
\(524\) 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 \(-0.358658\pi\)
0.429589 + 0.903025i \(0.358658\pi\)
\(558\) −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 \(-0.666671\pi\)
−0.500013 + 0.866018i \(0.666671\pi\)
\(564\) −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 \(-0.233735\pi\)
0.742300 + 0.670068i \(0.233735\pi\)
\(570\) 12.6146 0.528369
\(571\) −36.8453 −1.54193 −0.770963 0.636880i \(-0.780225\pi\)
−0.770963 + 0.636880i \(0.780225\pi\)
\(572\) −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 \(-0.453362\pi\)
0.145993 + 0.989286i \(0.453362\pi\)
\(614\) 17.3415 0.699845
\(615\) −11.0920 −0.447272
\(616\) 9.56933 0.385559
\(617\) −15.9812 −0.643377 −0.321689 0.946846i \(-0.604250\pi\)
−0.321689 + 0.946846i \(0.604250\pi\)
\(618\) −30.0062 −1.20703
\(619\) 47.0014 1.88915 0.944573 0.328302i \(-0.106477\pi\)
0.944573 + 0.328302i \(0.106477\pi\)
\(620\) 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 \(-0.534941\pi\)
−0.109551 + 0.993981i \(0.534941\pi\)
\(632\) −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 \(-0.327972\pi\)
0.514514 + 0.857482i \(0.327972\pi\)
\(642\) −14.8641 −0.586640
\(643\) 2.14349 0.0845311 0.0422655 0.999106i \(-0.486542\pi\)
0.0422655 + 0.999106i \(0.486542\pi\)
\(644\) 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 \(-0.700451\pi\)
−0.588930 + 0.808184i \(0.700451\pi\)
\(660\) 11.0920 0.431755
\(661\) −20.1651 −0.784332 −0.392166 0.919894i \(-0.628274\pi\)
−0.392166 + 0.919894i \(0.628274\pi\)
\(662\) −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 \(-0.549380\pi\)
−0.154510 + 0.987991i \(0.549380\pi\)
\(678\) −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 \(-0.515837\pi\)
−0.0497324 + 0.998763i \(0.515837\pi\)
\(702\) 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 \(-0.806980\pi\)
−0.821711 + 0.569904i \(0.806980\pi\)
\(710\) 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 \(-0.776868\pi\)
−0.764205 + 0.644974i \(0.776868\pi\)
\(728\) −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 \(-0.743872\pi\)
−0.693365 + 0.720587i \(0.743872\pi\)
\(734\) −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 \(-0.718151\pi\)
−0.632936 + 0.774204i \(0.718151\pi\)
\(744\) −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 \(-0.632642\pi\)
−0.404752 + 0.914426i \(0.632642\pi\)
\(752\) −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 \(-0.490017\pi\)
0.0313563 + 0.999508i \(0.490017\pi\)
\(758\) 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 \(-0.466020\pi\)
0.106549 + 0.994307i \(0.466020\pi\)
\(770\) −9.56933 −0.344855
\(771\) 72.8669 2.62424
\(772\) −6.95470 −0.250305
\(773\) 12.3150 0.442940 0.221470 0.975167i \(-0.428914\pi\)
0.221470 + 0.975167i \(0.428914\pi\)
\(774\) 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 \(-0.443790\pi\)
0.175673 + 0.984449i \(0.443790\pi\)
\(788\) 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 \(-0.614145\pi\)
−0.350960 + 0.936390i \(0.614145\pi\)
\(798\) 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 \(-0.140500\pi\)
0.904157 + 0.427201i \(0.140500\pi\)
\(828\) 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 \(-0.830087\pi\)
−0.860882 + 0.508805i \(0.830087\pi\)
\(840\) 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 \(-0.700761\pi\)
−0.589718 + 0.807609i \(0.700761\pi\)
\(882\) −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 \(-0.624239\pi\)
−0.380474 + 0.924792i \(0.624239\pi\)
\(908\) 19.6349 0.651606
\(909\) −37.3631 −1.23926
\(910\) 0.293394 0.00972590
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −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 \(-0.215717\pi\)
0.779020 + 0.626998i \(0.215717\pi\)
\(920\) 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 \(-0.280423\pi\)
0.636399 + 0.771360i \(0.280423\pi\)
\(938\) 6.31502 0.206193
\(939\) −30.5240 −0.996114
\(940\) 4.68016 0.152650
\(941\) 3.65370 0.119107 0.0595537 0.998225i \(-0.481032\pi\)
0.0595537 + 0.998225i \(0.481032\pi\)
\(942\) 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 \(-0.553331\pi\)
−0.166763 + 0.985997i \(0.553331\pi\)
\(954\) −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 \(-0.880499\pi\)
−0.930352 + 0.366668i \(0.880499\pi\)
\(972\) −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 \(-0.567370\pi\)
−0.210072 + 0.977686i \(0.567370\pi\)
\(978\) −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 \(-0.659966\pi\)
−0.481660 + 0.876358i \(0.659966\pi\)
\(984\) 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.p.1.3 3
23.22 odd 2 5290.2.a.q.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.3 3 1.1 even 1 trivial
5290.2.a.q.1.3 yes 3 23.22 odd 2