Properties

Label 5070.2.a.bw.1.3
Level $5070$
Weight $2$
Character 5070.1
Self dual yes
Analytic conductor $40.484$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5070.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.4841538248\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 5070.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.69202 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.69202 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.04892 q^{11} +1.00000 q^{12} +3.69202 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.85086 q^{17} +1.00000 q^{18} +0.911854 q^{19} -1.00000 q^{20} +3.69202 q^{21} -3.04892 q^{22} -0.356896 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +3.69202 q^{28} +10.5036 q^{29} -1.00000 q^{30} +2.06100 q^{31} +1.00000 q^{32} -3.04892 q^{33} -6.85086 q^{34} -3.69202 q^{35} +1.00000 q^{36} -0.899772 q^{37} +0.911854 q^{38} -1.00000 q^{40} +10.2959 q^{41} +3.69202 q^{42} +9.43296 q^{43} -3.04892 q^{44} -1.00000 q^{45} -0.356896 q^{46} +11.5918 q^{47} +1.00000 q^{48} +6.63102 q^{49} +1.00000 q^{50} -6.85086 q^{51} -3.40581 q^{53} +1.00000 q^{54} +3.04892 q^{55} +3.69202 q^{56} +0.911854 q^{57} +10.5036 q^{58} +8.54288 q^{59} -1.00000 q^{60} +1.55496 q^{61} +2.06100 q^{62} +3.69202 q^{63} +1.00000 q^{64} -3.04892 q^{66} +1.14914 q^{67} -6.85086 q^{68} -0.356896 q^{69} -3.69202 q^{70} -4.13706 q^{71} +1.00000 q^{72} +11.1685 q^{73} -0.899772 q^{74} +1.00000 q^{75} +0.911854 q^{76} -11.2567 q^{77} +9.62565 q^{79} -1.00000 q^{80} +1.00000 q^{81} +10.2959 q^{82} -9.86054 q^{83} +3.69202 q^{84} +6.85086 q^{85} +9.43296 q^{86} +10.5036 q^{87} -3.04892 q^{88} -6.41119 q^{89} -1.00000 q^{90} -0.356896 q^{92} +2.06100 q^{93} +11.5918 q^{94} -0.911854 q^{95} +1.00000 q^{96} +6.97823 q^{97} +6.63102 q^{98} -3.04892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 3q^{3} + 3q^{4} - 3q^{5} + 3q^{6} + 6q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 3q^{3} + 3q^{4} - 3q^{5} + 3q^{6} + 6q^{7} + 3q^{8} + 3q^{9} - 3q^{10} + 3q^{12} + 6q^{14} - 3q^{15} + 3q^{16} - 7q^{17} + 3q^{18} - q^{19} - 3q^{20} + 6q^{21} + 3q^{23} + 3q^{24} + 3q^{25} + 3q^{27} + 6q^{28} - 3q^{30} + 16q^{31} + 3q^{32} - 7q^{34} - 6q^{35} + 3q^{36} + 20q^{37} - q^{38} - 3q^{40} + 17q^{41} + 6q^{42} + 9q^{43} - 3q^{45} + 3q^{46} + 7q^{47} + 3q^{48} + 5q^{49} + 3q^{50} - 7q^{51} + 3q^{53} + 3q^{54} + 6q^{56} - q^{57} + 7q^{59} - 3q^{60} + 5q^{61} + 16q^{62} + 6q^{63} + 3q^{64} + 17q^{67} - 7q^{68} + 3q^{69} - 6q^{70} - 7q^{71} + 3q^{72} + 3q^{73} + 20q^{74} + 3q^{75} - q^{76} - 7q^{77} + 17q^{79} - 3q^{80} + 3q^{81} + 17q^{82} + 6q^{83} + 6q^{84} + 7q^{85} + 9q^{86} - 3q^{89} - 3q^{90} + 3q^{92} + 16q^{93} + 7q^{94} + q^{95} + 3q^{96} + 24q^{97} + 5q^{98} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 3.69202 1.39545 0.697726 0.716364i \(-0.254195\pi\)
0.697726 + 0.716364i \(0.254195\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −3.04892 −0.919283 −0.459642 0.888105i \(-0.652022\pi\)
−0.459642 + 0.888105i \(0.652022\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 3.69202 0.986734
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −6.85086 −1.66158 −0.830788 0.556589i \(-0.812110\pi\)
−0.830788 + 0.556589i \(0.812110\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.911854 0.209194 0.104597 0.994515i \(-0.466645\pi\)
0.104597 + 0.994515i \(0.466645\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.69202 0.805665
\(22\) −3.04892 −0.650031
\(23\) −0.356896 −0.0744179 −0.0372090 0.999308i \(-0.511847\pi\)
−0.0372090 + 0.999308i \(0.511847\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 3.69202 0.697726
\(29\) 10.5036 1.95048 0.975239 0.221153i \(-0.0709819\pi\)
0.975239 + 0.221153i \(0.0709819\pi\)
\(30\) −1.00000 −0.182574
\(31\) 2.06100 0.370166 0.185083 0.982723i \(-0.440745\pi\)
0.185083 + 0.982723i \(0.440745\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.04892 −0.530748
\(34\) −6.85086 −1.17491
\(35\) −3.69202 −0.624066
\(36\) 1.00000 0.166667
\(37\) −0.899772 −0.147922 −0.0739608 0.997261i \(-0.523564\pi\)
−0.0739608 + 0.997261i \(0.523564\pi\)
\(38\) 0.911854 0.147922
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 10.2959 1.60795 0.803974 0.594664i \(-0.202715\pi\)
0.803974 + 0.594664i \(0.202715\pi\)
\(42\) 3.69202 0.569691
\(43\) 9.43296 1.43851 0.719256 0.694745i \(-0.244483\pi\)
0.719256 + 0.694745i \(0.244483\pi\)
\(44\) −3.04892 −0.459642
\(45\) −1.00000 −0.149071
\(46\) −0.356896 −0.0526214
\(47\) 11.5918 1.69084 0.845418 0.534105i \(-0.179351\pi\)
0.845418 + 0.534105i \(0.179351\pi\)
\(48\) 1.00000 0.144338
\(49\) 6.63102 0.947289
\(50\) 1.00000 0.141421
\(51\) −6.85086 −0.959312
\(52\) 0 0
\(53\) −3.40581 −0.467824 −0.233912 0.972258i \(-0.575153\pi\)
−0.233912 + 0.972258i \(0.575153\pi\)
\(54\) 1.00000 0.136083
\(55\) 3.04892 0.411116
\(56\) 3.69202 0.493367
\(57\) 0.911854 0.120778
\(58\) 10.5036 1.37920
\(59\) 8.54288 1.11219 0.556094 0.831119i \(-0.312299\pi\)
0.556094 + 0.831119i \(0.312299\pi\)
\(60\) −1.00000 −0.129099
\(61\) 1.55496 0.199092 0.0995460 0.995033i \(-0.468261\pi\)
0.0995460 + 0.995033i \(0.468261\pi\)
\(62\) 2.06100 0.261747
\(63\) 3.69202 0.465151
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.04892 −0.375296
\(67\) 1.14914 0.140390 0.0701952 0.997533i \(-0.477638\pi\)
0.0701952 + 0.997533i \(0.477638\pi\)
\(68\) −6.85086 −0.830788
\(69\) −0.356896 −0.0429652
\(70\) −3.69202 −0.441281
\(71\) −4.13706 −0.490979 −0.245490 0.969399i \(-0.578949\pi\)
−0.245490 + 0.969399i \(0.578949\pi\)
\(72\) 1.00000 0.117851
\(73\) 11.1685 1.30718 0.653588 0.756850i \(-0.273263\pi\)
0.653588 + 0.756850i \(0.273263\pi\)
\(74\) −0.899772 −0.104596
\(75\) 1.00000 0.115470
\(76\) 0.911854 0.104597
\(77\) −11.2567 −1.28282
\(78\) 0 0
\(79\) 9.62565 1.08297 0.541485 0.840710i \(-0.317862\pi\)
0.541485 + 0.840710i \(0.317862\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 10.2959 1.13699
\(83\) −9.86054 −1.08234 −0.541168 0.840915i \(-0.682018\pi\)
−0.541168 + 0.840915i \(0.682018\pi\)
\(84\) 3.69202 0.402833
\(85\) 6.85086 0.743080
\(86\) 9.43296 1.01718
\(87\) 10.5036 1.12611
\(88\) −3.04892 −0.325016
\(89\) −6.41119 −0.679585 −0.339792 0.940500i \(-0.610357\pi\)
−0.339792 + 0.940500i \(0.610357\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −0.356896 −0.0372090
\(93\) 2.06100 0.213716
\(94\) 11.5918 1.19560
\(95\) −0.911854 −0.0935542
\(96\) 1.00000 0.102062
\(97\) 6.97823 0.708532 0.354266 0.935145i \(-0.384731\pi\)
0.354266 + 0.935145i \(0.384731\pi\)
\(98\) 6.63102 0.669834
\(99\) −3.04892 −0.306428
\(100\) 1.00000 0.100000
\(101\) −4.09783 −0.407750 −0.203875 0.978997i \(-0.565354\pi\)
−0.203875 + 0.978997i \(0.565354\pi\)
\(102\) −6.85086 −0.678336
\(103\) −16.9215 −1.66733 −0.833665 0.552271i \(-0.813761\pi\)
−0.833665 + 0.552271i \(0.813761\pi\)
\(104\) 0 0
\(105\) −3.69202 −0.360304
\(106\) −3.40581 −0.330802
\(107\) −12.7192 −1.22961 −0.614804 0.788680i \(-0.710765\pi\)
−0.614804 + 0.788680i \(0.710765\pi\)
\(108\) 1.00000 0.0962250
\(109\) 19.9922 1.91491 0.957454 0.288585i \(-0.0931849\pi\)
0.957454 + 0.288585i \(0.0931849\pi\)
\(110\) 3.04892 0.290703
\(111\) −0.899772 −0.0854026
\(112\) 3.69202 0.348863
\(113\) −4.49934 −0.423262 −0.211631 0.977350i \(-0.567877\pi\)
−0.211631 + 0.977350i \(0.567877\pi\)
\(114\) 0.911854 0.0854030
\(115\) 0.356896 0.0332807
\(116\) 10.5036 0.975239
\(117\) 0 0
\(118\) 8.54288 0.786436
\(119\) −25.2935 −2.31865
\(120\) −1.00000 −0.0912871
\(121\) −1.70410 −0.154918
\(122\) 1.55496 0.140779
\(123\) 10.2959 0.928350
\(124\) 2.06100 0.185083
\(125\) −1.00000 −0.0894427
\(126\) 3.69202 0.328911
\(127\) −7.08815 −0.628971 −0.314486 0.949262i \(-0.601832\pi\)
−0.314486 + 0.949262i \(0.601832\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.43296 0.830526
\(130\) 0 0
\(131\) 19.7506 1.72562 0.862810 0.505528i \(-0.168702\pi\)
0.862810 + 0.505528i \(0.168702\pi\)
\(132\) −3.04892 −0.265374
\(133\) 3.36658 0.291920
\(134\) 1.14914 0.0992710
\(135\) −1.00000 −0.0860663
\(136\) −6.85086 −0.587456
\(137\) −7.94331 −0.678643 −0.339322 0.940670i \(-0.610197\pi\)
−0.339322 + 0.940670i \(0.610197\pi\)
\(138\) −0.356896 −0.0303810
\(139\) −1.71379 −0.145362 −0.0726810 0.997355i \(-0.523155\pi\)
−0.0726810 + 0.997355i \(0.523155\pi\)
\(140\) −3.69202 −0.312033
\(141\) 11.5918 0.976205
\(142\) −4.13706 −0.347175
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −10.5036 −0.872280
\(146\) 11.1685 0.924313
\(147\) 6.63102 0.546918
\(148\) −0.899772 −0.0739608
\(149\) −6.91185 −0.566241 −0.283121 0.959084i \(-0.591370\pi\)
−0.283121 + 0.959084i \(0.591370\pi\)
\(150\) 1.00000 0.0816497
\(151\) 5.43296 0.442128 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(152\) 0.911854 0.0739611
\(153\) −6.85086 −0.553859
\(154\) −11.2567 −0.907088
\(155\) −2.06100 −0.165543
\(156\) 0 0
\(157\) −9.13706 −0.729217 −0.364609 0.931161i \(-0.618797\pi\)
−0.364609 + 0.931161i \(0.618797\pi\)
\(158\) 9.62565 0.765775
\(159\) −3.40581 −0.270099
\(160\) −1.00000 −0.0790569
\(161\) −1.31767 −0.103847
\(162\) 1.00000 0.0785674
\(163\) 14.3773 1.12612 0.563060 0.826416i \(-0.309624\pi\)
0.563060 + 0.826416i \(0.309624\pi\)
\(164\) 10.2959 0.803974
\(165\) 3.04892 0.237358
\(166\) −9.86054 −0.765327
\(167\) −3.00538 −0.232563 −0.116282 0.993216i \(-0.537097\pi\)
−0.116282 + 0.993216i \(0.537097\pi\)
\(168\) 3.69202 0.284846
\(169\) 0 0
\(170\) 6.85086 0.525437
\(171\) 0.911854 0.0697312
\(172\) 9.43296 0.719256
\(173\) 6.89546 0.524252 0.262126 0.965034i \(-0.415576\pi\)
0.262126 + 0.965034i \(0.415576\pi\)
\(174\) 10.5036 0.796279
\(175\) 3.69202 0.279091
\(176\) −3.04892 −0.229821
\(177\) 8.54288 0.642122
\(178\) −6.41119 −0.480539
\(179\) −25.6461 −1.91688 −0.958439 0.285296i \(-0.907908\pi\)
−0.958439 + 0.285296i \(0.907908\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −25.8092 −1.91839 −0.959193 0.282753i \(-0.908752\pi\)
−0.959193 + 0.282753i \(0.908752\pi\)
\(182\) 0 0
\(183\) 1.55496 0.114946
\(184\) −0.356896 −0.0263107
\(185\) 0.899772 0.0661526
\(186\) 2.06100 0.151120
\(187\) 20.8877 1.52746
\(188\) 11.5918 0.845418
\(189\) 3.69202 0.268555
\(190\) −0.911854 −0.0661528
\(191\) −14.5700 −1.05425 −0.527125 0.849788i \(-0.676730\pi\)
−0.527125 + 0.849788i \(0.676730\pi\)
\(192\) 1.00000 0.0721688
\(193\) 8.32544 0.599278 0.299639 0.954053i \(-0.403134\pi\)
0.299639 + 0.954053i \(0.403134\pi\)
\(194\) 6.97823 0.501008
\(195\) 0 0
\(196\) 6.63102 0.473644
\(197\) −26.8810 −1.91519 −0.957595 0.288116i \(-0.906971\pi\)
−0.957595 + 0.288116i \(0.906971\pi\)
\(198\) −3.04892 −0.216677
\(199\) −18.7047 −1.32594 −0.662970 0.748646i \(-0.730704\pi\)
−0.662970 + 0.748646i \(0.730704\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.14914 0.0810544
\(202\) −4.09783 −0.288323
\(203\) 38.7797 2.72180
\(204\) −6.85086 −0.479656
\(205\) −10.2959 −0.719097
\(206\) −16.9215 −1.17898
\(207\) −0.356896 −0.0248060
\(208\) 0 0
\(209\) −2.78017 −0.192308
\(210\) −3.69202 −0.254774
\(211\) 2.93362 0.201959 0.100980 0.994889i \(-0.467802\pi\)
0.100980 + 0.994889i \(0.467802\pi\)
\(212\) −3.40581 −0.233912
\(213\) −4.13706 −0.283467
\(214\) −12.7192 −0.869464
\(215\) −9.43296 −0.643323
\(216\) 1.00000 0.0680414
\(217\) 7.60925 0.516550
\(218\) 19.9922 1.35404
\(219\) 11.1685 0.754699
\(220\) 3.04892 0.205558
\(221\) 0 0
\(222\) −0.899772 −0.0603888
\(223\) −18.1444 −1.21504 −0.607518 0.794306i \(-0.707835\pi\)
−0.607518 + 0.794306i \(0.707835\pi\)
\(224\) 3.69202 0.246684
\(225\) 1.00000 0.0666667
\(226\) −4.49934 −0.299291
\(227\) 12.3056 0.816750 0.408375 0.912814i \(-0.366096\pi\)
0.408375 + 0.912814i \(0.366096\pi\)
\(228\) 0.911854 0.0603890
\(229\) 4.64848 0.307180 0.153590 0.988135i \(-0.450916\pi\)
0.153590 + 0.988135i \(0.450916\pi\)
\(230\) 0.356896 0.0235330
\(231\) −11.2567 −0.740634
\(232\) 10.5036 0.689598
\(233\) 0.658170 0.0431181 0.0215591 0.999768i \(-0.493137\pi\)
0.0215591 + 0.999768i \(0.493137\pi\)
\(234\) 0 0
\(235\) −11.5918 −0.756165
\(236\) 8.54288 0.556094
\(237\) 9.62565 0.625253
\(238\) −25.2935 −1.63953
\(239\) −18.7748 −1.21444 −0.607220 0.794534i \(-0.707715\pi\)
−0.607220 + 0.794534i \(0.707715\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 18.0271 1.16123 0.580615 0.814178i \(-0.302812\pi\)
0.580615 + 0.814178i \(0.302812\pi\)
\(242\) −1.70410 −0.109544
\(243\) 1.00000 0.0641500
\(244\) 1.55496 0.0995460
\(245\) −6.63102 −0.423640
\(246\) 10.2959 0.656442
\(247\) 0 0
\(248\) 2.06100 0.130874
\(249\) −9.86054 −0.624887
\(250\) −1.00000 −0.0632456
\(251\) −2.18060 −0.137638 −0.0688192 0.997629i \(-0.521923\pi\)
−0.0688192 + 0.997629i \(0.521923\pi\)
\(252\) 3.69202 0.232575
\(253\) 1.08815 0.0684112
\(254\) −7.08815 −0.444750
\(255\) 6.85086 0.429017
\(256\) 1.00000 0.0625000
\(257\) −9.58748 −0.598051 −0.299025 0.954245i \(-0.596662\pi\)
−0.299025 + 0.954245i \(0.596662\pi\)
\(258\) 9.43296 0.587270
\(259\) −3.32198 −0.206418
\(260\) 0 0
\(261\) 10.5036 0.650159
\(262\) 19.7506 1.22020
\(263\) −1.41789 −0.0874311 −0.0437156 0.999044i \(-0.513920\pi\)
−0.0437156 + 0.999044i \(0.513920\pi\)
\(264\) −3.04892 −0.187648
\(265\) 3.40581 0.209217
\(266\) 3.36658 0.206419
\(267\) −6.41119 −0.392358
\(268\) 1.14914 0.0701952
\(269\) −4.14675 −0.252832 −0.126416 0.991977i \(-0.540347\pi\)
−0.126416 + 0.991977i \(0.540347\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 6.40044 0.388799 0.194399 0.980922i \(-0.437724\pi\)
0.194399 + 0.980922i \(0.437724\pi\)
\(272\) −6.85086 −0.415394
\(273\) 0 0
\(274\) −7.94331 −0.479873
\(275\) −3.04892 −0.183857
\(276\) −0.356896 −0.0214826
\(277\) 10.3394 0.621237 0.310618 0.950535i \(-0.399464\pi\)
0.310618 + 0.950535i \(0.399464\pi\)
\(278\) −1.71379 −0.102786
\(279\) 2.06100 0.123389
\(280\) −3.69202 −0.220640
\(281\) 5.08144 0.303133 0.151567 0.988447i \(-0.451568\pi\)
0.151567 + 0.988447i \(0.451568\pi\)
\(282\) 11.5918 0.690281
\(283\) 24.5284 1.45806 0.729031 0.684481i \(-0.239971\pi\)
0.729031 + 0.684481i \(0.239971\pi\)
\(284\) −4.13706 −0.245490
\(285\) −0.911854 −0.0540136
\(286\) 0 0
\(287\) 38.0127 2.24382
\(288\) 1.00000 0.0589256
\(289\) 29.9342 1.76084
\(290\) −10.5036 −0.616795
\(291\) 6.97823 0.409071
\(292\) 11.1685 0.653588
\(293\) 15.8538 0.926191 0.463096 0.886308i \(-0.346739\pi\)
0.463096 + 0.886308i \(0.346739\pi\)
\(294\) 6.63102 0.386729
\(295\) −8.54288 −0.497386
\(296\) −0.899772 −0.0522982
\(297\) −3.04892 −0.176916
\(298\) −6.91185 −0.400393
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 34.8267 2.00738
\(302\) 5.43296 0.312632
\(303\) −4.09783 −0.235414
\(304\) 0.911854 0.0522984
\(305\) −1.55496 −0.0890366
\(306\) −6.85086 −0.391637
\(307\) −14.2121 −0.811125 −0.405563 0.914067i \(-0.632924\pi\)
−0.405563 + 0.914067i \(0.632924\pi\)
\(308\) −11.2567 −0.641408
\(309\) −16.9215 −0.962633
\(310\) −2.06100 −0.117057
\(311\) 15.0127 0.851291 0.425645 0.904890i \(-0.360047\pi\)
0.425645 + 0.904890i \(0.360047\pi\)
\(312\) 0 0
\(313\) −13.4993 −0.763028 −0.381514 0.924363i \(-0.624597\pi\)
−0.381514 + 0.924363i \(0.624597\pi\)
\(314\) −9.13706 −0.515634
\(315\) −3.69202 −0.208022
\(316\) 9.62565 0.541485
\(317\) 33.9463 1.90661 0.953307 0.302003i \(-0.0976552\pi\)
0.953307 + 0.302003i \(0.0976552\pi\)
\(318\) −3.40581 −0.190989
\(319\) −32.0248 −1.79304
\(320\) −1.00000 −0.0559017
\(321\) −12.7192 −0.709915
\(322\) −1.31767 −0.0734307
\(323\) −6.24698 −0.347591
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.3773 0.796287
\(327\) 19.9922 1.10557
\(328\) 10.2959 0.568496
\(329\) 42.7972 2.35948
\(330\) 3.04892 0.167837
\(331\) −6.84415 −0.376189 −0.188094 0.982151i \(-0.560231\pi\)
−0.188094 + 0.982151i \(0.560231\pi\)
\(332\) −9.86054 −0.541168
\(333\) −0.899772 −0.0493072
\(334\) −3.00538 −0.164447
\(335\) −1.14914 −0.0627845
\(336\) 3.69202 0.201416
\(337\) 27.7332 1.51072 0.755361 0.655309i \(-0.227462\pi\)
0.755361 + 0.655309i \(0.227462\pi\)
\(338\) 0 0
\(339\) −4.49934 −0.244370
\(340\) 6.85086 0.371540
\(341\) −6.28382 −0.340288
\(342\) 0.911854 0.0493074
\(343\) −1.36227 −0.0735558
\(344\) 9.43296 0.508591
\(345\) 0.356896 0.0192146
\(346\) 6.89546 0.370702
\(347\) −10.4862 −0.562928 −0.281464 0.959572i \(-0.590820\pi\)
−0.281464 + 0.959572i \(0.590820\pi\)
\(348\) 10.5036 0.563055
\(349\) −8.13467 −0.435439 −0.217719 0.976011i \(-0.569862\pi\)
−0.217719 + 0.976011i \(0.569862\pi\)
\(350\) 3.69202 0.197347
\(351\) 0 0
\(352\) −3.04892 −0.162508
\(353\) −25.8649 −1.37665 −0.688324 0.725404i \(-0.741653\pi\)
−0.688324 + 0.725404i \(0.741653\pi\)
\(354\) 8.54288 0.454049
\(355\) 4.13706 0.219573
\(356\) −6.41119 −0.339792
\(357\) −25.2935 −1.33867
\(358\) −25.6461 −1.35544
\(359\) −30.2959 −1.59896 −0.799478 0.600695i \(-0.794891\pi\)
−0.799478 + 0.600695i \(0.794891\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.1685 −0.956238
\(362\) −25.8092 −1.35650
\(363\) −1.70410 −0.0894422
\(364\) 0 0
\(365\) −11.1685 −0.584587
\(366\) 1.55496 0.0812790
\(367\) −3.41013 −0.178007 −0.0890035 0.996031i \(-0.528368\pi\)
−0.0890035 + 0.996031i \(0.528368\pi\)
\(368\) −0.356896 −0.0186045
\(369\) 10.2959 0.535983
\(370\) 0.899772 0.0467769
\(371\) −12.5743 −0.652827
\(372\) 2.06100 0.106858
\(373\) 3.35988 0.173968 0.0869840 0.996210i \(-0.472277\pi\)
0.0869840 + 0.996210i \(0.472277\pi\)
\(374\) 20.8877 1.08008
\(375\) −1.00000 −0.0516398
\(376\) 11.5918 0.597801
\(377\) 0 0
\(378\) 3.69202 0.189897
\(379\) −31.4916 −1.61761 −0.808807 0.588075i \(-0.799886\pi\)
−0.808807 + 0.588075i \(0.799886\pi\)
\(380\) −0.911854 −0.0467771
\(381\) −7.08815 −0.363137
\(382\) −14.5700 −0.745467
\(383\) 21.8485 1.11640 0.558202 0.829705i \(-0.311491\pi\)
0.558202 + 0.829705i \(0.311491\pi\)
\(384\) 1.00000 0.0510310
\(385\) 11.2567 0.573693
\(386\) 8.32544 0.423754
\(387\) 9.43296 0.479504
\(388\) 6.97823 0.354266
\(389\) −11.3787 −0.576921 −0.288461 0.957492i \(-0.593143\pi\)
−0.288461 + 0.957492i \(0.593143\pi\)
\(390\) 0 0
\(391\) 2.44504 0.123651
\(392\) 6.63102 0.334917
\(393\) 19.7506 0.996287
\(394\) −26.8810 −1.35424
\(395\) −9.62565 −0.484319
\(396\) −3.04892 −0.153214
\(397\) 22.0476 1.10654 0.553268 0.833003i \(-0.313380\pi\)
0.553268 + 0.833003i \(0.313380\pi\)
\(398\) −18.7047 −0.937582
\(399\) 3.36658 0.168540
\(400\) 1.00000 0.0500000
\(401\) 10.2459 0.511657 0.255828 0.966722i \(-0.417652\pi\)
0.255828 + 0.966722i \(0.417652\pi\)
\(402\) 1.14914 0.0573141
\(403\) 0 0
\(404\) −4.09783 −0.203875
\(405\) −1.00000 −0.0496904
\(406\) 38.7797 1.92460
\(407\) 2.74333 0.135982
\(408\) −6.85086 −0.339168
\(409\) 22.8189 1.12832 0.564162 0.825664i \(-0.309200\pi\)
0.564162 + 0.825664i \(0.309200\pi\)
\(410\) −10.2959 −0.508478
\(411\) −7.94331 −0.391815
\(412\) −16.9215 −0.833665
\(413\) 31.5405 1.55201
\(414\) −0.356896 −0.0175405
\(415\) 9.86054 0.484035
\(416\) 0 0
\(417\) −1.71379 −0.0839247
\(418\) −2.78017 −0.135982
\(419\) −28.5773 −1.39609 −0.698047 0.716052i \(-0.745947\pi\)
−0.698047 + 0.716052i \(0.745947\pi\)
\(420\) −3.69202 −0.180152
\(421\) 32.3937 1.57877 0.789387 0.613896i \(-0.210399\pi\)
0.789387 + 0.613896i \(0.210399\pi\)
\(422\) 2.93362 0.142807
\(423\) 11.5918 0.563612
\(424\) −3.40581 −0.165401
\(425\) −6.85086 −0.332315
\(426\) −4.13706 −0.200441
\(427\) 5.74094 0.277824
\(428\) −12.7192 −0.614804
\(429\) 0 0
\(430\) −9.43296 −0.454898
\(431\) −14.6455 −0.705449 −0.352724 0.935727i \(-0.614745\pi\)
−0.352724 + 0.935727i \(0.614745\pi\)
\(432\) 1.00000 0.0481125
\(433\) −35.8485 −1.72277 −0.861384 0.507955i \(-0.830402\pi\)
−0.861384 + 0.507955i \(0.830402\pi\)
\(434\) 7.60925 0.365256
\(435\) −10.5036 −0.503611
\(436\) 19.9922 0.957454
\(437\) −0.325437 −0.0155678
\(438\) 11.1685 0.533653
\(439\) 2.55927 0.122147 0.0610736 0.998133i \(-0.480548\pi\)
0.0610736 + 0.998133i \(0.480548\pi\)
\(440\) 3.04892 0.145351
\(441\) 6.63102 0.315763
\(442\) 0 0
\(443\) 23.2857 1.10634 0.553169 0.833069i \(-0.313418\pi\)
0.553169 + 0.833069i \(0.313418\pi\)
\(444\) −0.899772 −0.0427013
\(445\) 6.41119 0.303920
\(446\) −18.1444 −0.859160
\(447\) −6.91185 −0.326919
\(448\) 3.69202 0.174432
\(449\) −27.3327 −1.28991 −0.644956 0.764220i \(-0.723124\pi\)
−0.644956 + 0.764220i \(0.723124\pi\)
\(450\) 1.00000 0.0471405
\(451\) −31.3913 −1.47816
\(452\) −4.49934 −0.211631
\(453\) 5.43296 0.255263
\(454\) 12.3056 0.577530
\(455\) 0 0
\(456\) 0.911854 0.0427015
\(457\) −7.74094 −0.362106 −0.181053 0.983473i \(-0.557951\pi\)
−0.181053 + 0.983473i \(0.557951\pi\)
\(458\) 4.64848 0.217209
\(459\) −6.85086 −0.319771
\(460\) 0.356896 0.0166404
\(461\) 17.1511 0.798805 0.399402 0.916776i \(-0.369218\pi\)
0.399402 + 0.916776i \(0.369218\pi\)
\(462\) −11.2567 −0.523708
\(463\) −34.2747 −1.59288 −0.796441 0.604717i \(-0.793286\pi\)
−0.796441 + 0.604717i \(0.793286\pi\)
\(464\) 10.5036 0.487620
\(465\) −2.06100 −0.0955765
\(466\) 0.658170 0.0304891
\(467\) 20.9474 0.969328 0.484664 0.874700i \(-0.338942\pi\)
0.484664 + 0.874700i \(0.338942\pi\)
\(468\) 0 0
\(469\) 4.24267 0.195908
\(470\) −11.5918 −0.534690
\(471\) −9.13706 −0.421014
\(472\) 8.54288 0.393218
\(473\) −28.7603 −1.32240
\(474\) 9.62565 0.442121
\(475\) 0.911854 0.0418387
\(476\) −25.2935 −1.15933
\(477\) −3.40581 −0.155941
\(478\) −18.7748 −0.858739
\(479\) 15.8310 0.723337 0.361669 0.932307i \(-0.382207\pi\)
0.361669 + 0.932307i \(0.382207\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0 0
\(482\) 18.0271 0.821114
\(483\) −1.31767 −0.0599559
\(484\) −1.70410 −0.0774592
\(485\) −6.97823 −0.316865
\(486\) 1.00000 0.0453609
\(487\) 33.7060 1.52737 0.763683 0.645592i \(-0.223389\pi\)
0.763683 + 0.645592i \(0.223389\pi\)
\(488\) 1.55496 0.0703896
\(489\) 14.3773 0.650166
\(490\) −6.63102 −0.299559
\(491\) 3.98925 0.180032 0.0900161 0.995940i \(-0.471308\pi\)
0.0900161 + 0.995940i \(0.471308\pi\)
\(492\) 10.2959 0.464175
\(493\) −71.9590 −3.24087
\(494\) 0 0
\(495\) 3.04892 0.137039
\(496\) 2.06100 0.0925416
\(497\) −15.2741 −0.685138
\(498\) −9.86054 −0.441862
\(499\) 20.4698 0.916354 0.458177 0.888861i \(-0.348503\pi\)
0.458177 + 0.888861i \(0.348503\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −3.00538 −0.134270
\(502\) −2.18060 −0.0973251
\(503\) 22.5351 1.00479 0.502395 0.864638i \(-0.332452\pi\)
0.502395 + 0.864638i \(0.332452\pi\)
\(504\) 3.69202 0.164456
\(505\) 4.09783 0.182351
\(506\) 1.08815 0.0483740
\(507\) 0 0
\(508\) −7.08815 −0.314486
\(509\) −10.9718 −0.486316 −0.243158 0.969987i \(-0.578183\pi\)
−0.243158 + 0.969987i \(0.578183\pi\)
\(510\) 6.85086 0.303361
\(511\) 41.2344 1.82410
\(512\) 1.00000 0.0441942
\(513\) 0.911854 0.0402593
\(514\) −9.58748 −0.422886
\(515\) 16.9215 0.745652
\(516\) 9.43296 0.415263
\(517\) −35.3424 −1.55436
\(518\) −3.32198 −0.145959
\(519\) 6.89546 0.302677
\(520\) 0 0
\(521\) 15.9691 0.699620 0.349810 0.936821i \(-0.386246\pi\)
0.349810 + 0.936821i \(0.386246\pi\)
\(522\) 10.5036 0.459732
\(523\) −24.7681 −1.08303 −0.541516 0.840690i \(-0.682150\pi\)
−0.541516 + 0.840690i \(0.682150\pi\)
\(524\) 19.7506 0.862810
\(525\) 3.69202 0.161133
\(526\) −1.41789 −0.0618232
\(527\) −14.1196 −0.615060
\(528\) −3.04892 −0.132687
\(529\) −22.8726 −0.994462
\(530\) 3.40581 0.147939
\(531\) 8.54288 0.370729
\(532\) 3.36658 0.145960
\(533\) 0 0
\(534\) −6.41119 −0.277439
\(535\) 12.7192 0.549898
\(536\) 1.14914 0.0496355
\(537\) −25.6461 −1.10671
\(538\) −4.14675 −0.178779
\(539\) −20.2174 −0.870827
\(540\) −1.00000 −0.0430331
\(541\) 0.460107 0.0197816 0.00989078 0.999951i \(-0.496852\pi\)
0.00989078 + 0.999951i \(0.496852\pi\)
\(542\) 6.40044 0.274922
\(543\) −25.8092 −1.10758
\(544\) −6.85086 −0.293728
\(545\) −19.9922 −0.856373
\(546\) 0 0
\(547\) −8.70410 −0.372161 −0.186080 0.982535i \(-0.559578\pi\)
−0.186080 + 0.982535i \(0.559578\pi\)
\(548\) −7.94331 −0.339322
\(549\) 1.55496 0.0663640
\(550\) −3.04892 −0.130006
\(551\) 9.57779 0.408028
\(552\) −0.356896 −0.0151905
\(553\) 35.5381 1.51123
\(554\) 10.3394 0.439281
\(555\) 0.899772 0.0381932
\(556\) −1.71379 −0.0726810
\(557\) −36.7415 −1.55679 −0.778394 0.627776i \(-0.783966\pi\)
−0.778394 + 0.627776i \(0.783966\pi\)
\(558\) 2.06100 0.0872490
\(559\) 0 0
\(560\) −3.69202 −0.156016
\(561\) 20.8877 0.881879
\(562\) 5.08144 0.214348
\(563\) −27.7713 −1.17042 −0.585211 0.810881i \(-0.698988\pi\)
−0.585211 + 0.810881i \(0.698988\pi\)
\(564\) 11.5918 0.488103
\(565\) 4.49934 0.189288
\(566\) 24.5284 1.03101
\(567\) 3.69202 0.155050
\(568\) −4.13706 −0.173587
\(569\) 38.4379 1.61140 0.805700 0.592324i \(-0.201790\pi\)
0.805700 + 0.592324i \(0.201790\pi\)
\(570\) −0.911854 −0.0381934
\(571\) 10.8086 0.452328 0.226164 0.974089i \(-0.427382\pi\)
0.226164 + 0.974089i \(0.427382\pi\)
\(572\) 0 0
\(573\) −14.5700 −0.608671
\(574\) 38.0127 1.58662
\(575\) −0.356896 −0.0148836
\(576\) 1.00000 0.0416667
\(577\) 35.5991 1.48201 0.741005 0.671500i \(-0.234350\pi\)
0.741005 + 0.671500i \(0.234350\pi\)
\(578\) 29.9342 1.24510
\(579\) 8.32544 0.345993
\(580\) −10.5036 −0.436140
\(581\) −36.4053 −1.51035
\(582\) 6.97823 0.289257
\(583\) 10.3840 0.430063
\(584\) 11.1685 0.462157
\(585\) 0 0
\(586\) 15.8538 0.654916
\(587\) 11.4741 0.473587 0.236794 0.971560i \(-0.423903\pi\)
0.236794 + 0.971560i \(0.423903\pi\)
\(588\) 6.63102 0.273459
\(589\) 1.87933 0.0774364
\(590\) −8.54288 −0.351705
\(591\) −26.8810 −1.10574
\(592\) −0.899772 −0.0369804
\(593\) 15.5147 0.637111 0.318555 0.947904i \(-0.396802\pi\)
0.318555 + 0.947904i \(0.396802\pi\)
\(594\) −3.04892 −0.125099
\(595\) 25.2935 1.03693
\(596\) −6.91185 −0.283121
\(597\) −18.7047 −0.765532
\(598\) 0 0
\(599\) −14.2034 −0.580337 −0.290168 0.956976i \(-0.593711\pi\)
−0.290168 + 0.956976i \(0.593711\pi\)
\(600\) 1.00000 0.0408248
\(601\) −39.5579 −1.61360 −0.806801 0.590823i \(-0.798803\pi\)
−0.806801 + 0.590823i \(0.798803\pi\)
\(602\) 34.8267 1.41943
\(603\) 1.14914 0.0467968
\(604\) 5.43296 0.221064
\(605\) 1.70410 0.0692816
\(606\) −4.09783 −0.166463
\(607\) 4.77346 0.193749 0.0968744 0.995297i \(-0.469115\pi\)
0.0968744 + 0.995297i \(0.469115\pi\)
\(608\) 0.911854 0.0369806
\(609\) 38.7797 1.57143
\(610\) −1.55496 −0.0629584
\(611\) 0 0
\(612\) −6.85086 −0.276929
\(613\) 5.43429 0.219489 0.109744 0.993960i \(-0.464997\pi\)
0.109744 + 0.993960i \(0.464997\pi\)
\(614\) −14.2121 −0.573552
\(615\) −10.2959 −0.415171
\(616\) −11.2567 −0.453544
\(617\) −20.6692 −0.832110 −0.416055 0.909339i \(-0.636588\pi\)
−0.416055 + 0.909339i \(0.636588\pi\)
\(618\) −16.9215 −0.680684
\(619\) 24.4077 0.981030 0.490515 0.871433i \(-0.336809\pi\)
0.490515 + 0.871433i \(0.336809\pi\)
\(620\) −2.06100 −0.0827717
\(621\) −0.356896 −0.0143217
\(622\) 15.0127 0.601953
\(623\) −23.6703 −0.948329
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −13.4993 −0.539542
\(627\) −2.78017 −0.111029
\(628\) −9.13706 −0.364609
\(629\) 6.16421 0.245783
\(630\) −3.69202 −0.147094
\(631\) −32.0538 −1.27604 −0.638021 0.770019i \(-0.720247\pi\)
−0.638021 + 0.770019i \(0.720247\pi\)
\(632\) 9.62565 0.382888
\(633\) 2.93362 0.116601
\(634\) 33.9463 1.34818
\(635\) 7.08815 0.281284
\(636\) −3.40581 −0.135049
\(637\) 0 0
\(638\) −32.0248 −1.26787
\(639\) −4.13706 −0.163660
\(640\) −1.00000 −0.0395285
\(641\) 18.5327 0.731998 0.365999 0.930615i \(-0.380727\pi\)
0.365999 + 0.930615i \(0.380727\pi\)
\(642\) −12.7192 −0.501986
\(643\) −22.3454 −0.881217 −0.440608 0.897699i \(-0.645237\pi\)
−0.440608 + 0.897699i \(0.645237\pi\)
\(644\) −1.31767 −0.0519234
\(645\) −9.43296 −0.371422
\(646\) −6.24698 −0.245784
\(647\) 7.86964 0.309388 0.154694 0.987962i \(-0.450561\pi\)
0.154694 + 0.987962i \(0.450561\pi\)
\(648\) 1.00000 0.0392837
\(649\) −26.0465 −1.02242
\(650\) 0 0
\(651\) 7.60925 0.298230
\(652\) 14.3773 0.563060
\(653\) −47.2271 −1.84814 −0.924070 0.382223i \(-0.875159\pi\)
−0.924070 + 0.382223i \(0.875159\pi\)
\(654\) 19.9922 0.781758
\(655\) −19.7506 −0.771721
\(656\) 10.2959 0.401987
\(657\) 11.1685 0.435726
\(658\) 42.7972 1.66841
\(659\) −46.6276 −1.81635 −0.908176 0.418588i \(-0.862525\pi\)
−0.908176 + 0.418588i \(0.862525\pi\)
\(660\) 3.04892 0.118679
\(661\) −39.9415 −1.55354 −0.776772 0.629781i \(-0.783144\pi\)
−0.776772 + 0.629781i \(0.783144\pi\)
\(662\) −6.84415 −0.266005
\(663\) 0 0
\(664\) −9.86054 −0.382663
\(665\) −3.36658 −0.130551
\(666\) −0.899772 −0.0348655
\(667\) −3.74871 −0.145151
\(668\) −3.00538 −0.116282
\(669\) −18.1444 −0.701501
\(670\) −1.14914 −0.0443953
\(671\) −4.74094 −0.183022
\(672\) 3.69202 0.142423
\(673\) −35.3612 −1.36307 −0.681537 0.731783i \(-0.738688\pi\)
−0.681537 + 0.731783i \(0.738688\pi\)
\(674\) 27.7332 1.06824
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 19.1715 0.736821 0.368410 0.929663i \(-0.379902\pi\)
0.368410 + 0.929663i \(0.379902\pi\)
\(678\) −4.49934 −0.172796
\(679\) 25.7638 0.988723
\(680\) 6.85086 0.262718
\(681\) 12.3056 0.471551
\(682\) −6.28382 −0.240620
\(683\) −1.13946 −0.0436001 −0.0218000 0.999762i \(-0.506940\pi\)
−0.0218000 + 0.999762i \(0.506940\pi\)
\(684\) 0.911854 0.0348656
\(685\) 7.94331 0.303498
\(686\) −1.36227 −0.0520118
\(687\) 4.64848 0.177351
\(688\) 9.43296 0.359628
\(689\) 0 0
\(690\) 0.356896 0.0135868
\(691\) 11.9071 0.452966 0.226483 0.974015i \(-0.427277\pi\)
0.226483 + 0.974015i \(0.427277\pi\)
\(692\) 6.89546 0.262126
\(693\) −11.2567 −0.427605
\(694\) −10.4862 −0.398050
\(695\) 1.71379 0.0650078
\(696\) 10.5036 0.398140
\(697\) −70.5357 −2.67173
\(698\) −8.13467 −0.307902
\(699\) 0.658170 0.0248943
\(700\) 3.69202 0.139545
\(701\) 38.0575 1.43741 0.718707 0.695313i \(-0.244734\pi\)
0.718707 + 0.695313i \(0.244734\pi\)
\(702\) 0 0
\(703\) −0.820461 −0.0309443
\(704\) −3.04892 −0.114910
\(705\) −11.5918 −0.436572
\(706\) −25.8649 −0.973437
\(707\) −15.1293 −0.568996
\(708\) 8.54288 0.321061
\(709\) −26.1215 −0.981014 −0.490507 0.871437i \(-0.663188\pi\)
−0.490507 + 0.871437i \(0.663188\pi\)
\(710\) 4.13706 0.155261
\(711\) 9.62565 0.360990
\(712\) −6.41119 −0.240270
\(713\) −0.735562 −0.0275470
\(714\) −25.2935 −0.946586
\(715\) 0 0
\(716\) −25.6461 −0.958439
\(717\) −18.7748 −0.701157
\(718\) −30.2959 −1.13063
\(719\) 21.3739 0.797111 0.398556 0.917144i \(-0.369512\pi\)
0.398556 + 0.917144i \(0.369512\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −62.4747 −2.32668
\(722\) −18.1685 −0.676162
\(723\) 18.0271 0.670437
\(724\) −25.8092 −0.959193
\(725\) 10.5036 0.390096
\(726\) −1.70410 −0.0632452
\(727\) −17.9124 −0.664336 −0.332168 0.943220i \(-0.607780\pi\)
−0.332168 + 0.943220i \(0.607780\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −11.1685 −0.413366
\(731\) −64.6238 −2.39020
\(732\) 1.55496 0.0574729
\(733\) −27.5386 −1.01716 −0.508580 0.861015i \(-0.669829\pi\)
−0.508580 + 0.861015i \(0.669829\pi\)
\(734\) −3.41013 −0.125870
\(735\) −6.63102 −0.244589
\(736\) −0.356896 −0.0131554
\(737\) −3.50365 −0.129059
\(738\) 10.2959 0.378997
\(739\) 7.99090 0.293950 0.146975 0.989140i \(-0.453046\pi\)
0.146975 + 0.989140i \(0.453046\pi\)
\(740\) 0.899772 0.0330763
\(741\) 0 0
\(742\) −12.5743 −0.461618
\(743\) −19.8398 −0.727853 −0.363927 0.931428i \(-0.618564\pi\)
−0.363927 + 0.931428i \(0.618564\pi\)
\(744\) 2.06100 0.0755599
\(745\) 6.91185 0.253231
\(746\) 3.35988 0.123014
\(747\) −9.86054 −0.360778
\(748\) 20.8877 0.763730
\(749\) −46.9594 −1.71586
\(750\) −1.00000 −0.0365148
\(751\) −25.7525 −0.939724 −0.469862 0.882740i \(-0.655696\pi\)
−0.469862 + 0.882740i \(0.655696\pi\)
\(752\) 11.5918 0.422709
\(753\) −2.18060 −0.0794656
\(754\) 0 0
\(755\) −5.43296 −0.197726
\(756\) 3.69202 0.134278
\(757\) −51.5096 −1.87215 −0.936074 0.351802i \(-0.885569\pi\)
−0.936074 + 0.351802i \(0.885569\pi\)
\(758\) −31.4916 −1.14383
\(759\) 1.08815 0.0394972
\(760\) −0.911854 −0.0330764
\(761\) 31.4765 1.14102 0.570511 0.821290i \(-0.306745\pi\)
0.570511 + 0.821290i \(0.306745\pi\)
\(762\) −7.08815 −0.256776
\(763\) 73.8117 2.67216
\(764\) −14.5700 −0.527125
\(765\) 6.85086 0.247693
\(766\) 21.8485 0.789417
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 47.1584 1.70057 0.850287 0.526319i \(-0.176428\pi\)
0.850287 + 0.526319i \(0.176428\pi\)
\(770\) 11.2567 0.405662
\(771\) −9.58748 −0.345285
\(772\) 8.32544 0.299639
\(773\) 3.71917 0.133769 0.0668846 0.997761i \(-0.478694\pi\)
0.0668846 + 0.997761i \(0.478694\pi\)
\(774\) 9.43296 0.339061
\(775\) 2.06100 0.0740333
\(776\) 6.97823 0.250504
\(777\) −3.32198 −0.119175
\(778\) −11.3787 −0.407945
\(779\) 9.38835 0.336373
\(780\) 0 0
\(781\) 12.6136 0.451349
\(782\) 2.44504 0.0874345
\(783\) 10.5036 0.375370
\(784\) 6.63102 0.236822
\(785\) 9.13706 0.326116
\(786\) 19.7506 0.704482
\(787\) −47.2282 −1.68350 −0.841752 0.539865i \(-0.818475\pi\)
−0.841752 + 0.539865i \(0.818475\pi\)
\(788\) −26.8810 −0.957595
\(789\) −1.41789 −0.0504784
\(790\) −9.62565 −0.342465
\(791\) −16.6116 −0.590642
\(792\) −3.04892 −0.108339
\(793\) 0 0
\(794\) 22.0476 0.782440
\(795\) 3.40581 0.120792
\(796\) −18.7047 −0.662970
\(797\) 34.4359 1.21978 0.609892 0.792485i \(-0.291213\pi\)
0.609892 + 0.792485i \(0.291213\pi\)
\(798\) 3.36658 0.119176
\(799\) −79.4137 −2.80945
\(800\) 1.00000 0.0353553
\(801\) −6.41119 −0.226528
\(802\) 10.2459 0.361796
\(803\) −34.0519 −1.20167
\(804\) 1.14914 0.0405272
\(805\) 1.31767 0.0464417
\(806\) 0 0
\(807\) −4.14675 −0.145973
\(808\) −4.09783 −0.144161
\(809\) −32.3846 −1.13858 −0.569292 0.822136i \(-0.692782\pi\)
−0.569292 + 0.822136i \(0.692782\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 37.8297 1.32838 0.664190 0.747564i \(-0.268777\pi\)
0.664190 + 0.747564i \(0.268777\pi\)
\(812\) 38.7797 1.36090
\(813\) 6.40044 0.224473
\(814\) 2.74333 0.0961537
\(815\) −14.3773 −0.503616
\(816\) −6.85086 −0.239828
\(817\) 8.60148 0.300928
\(818\) 22.8189 0.797845
\(819\) 0 0
\(820\) −10.2959 −0.359548
\(821\) 43.2820 1.51055 0.755276 0.655406i \(-0.227503\pi\)
0.755276 + 0.655406i \(0.227503\pi\)
\(822\) −7.94331 −0.277055
\(823\) −26.7399 −0.932093 −0.466047 0.884760i \(-0.654322\pi\)
−0.466047 + 0.884760i \(0.654322\pi\)
\(824\) −16.9215 −0.589490
\(825\) −3.04892 −0.106150
\(826\) 31.5405 1.09743
\(827\) 21.4437 0.745671 0.372835 0.927897i \(-0.378386\pi\)
0.372835 + 0.927897i \(0.378386\pi\)
\(828\) −0.356896 −0.0124030
\(829\) 22.4547 0.779885 0.389943 0.920839i \(-0.372495\pi\)
0.389943 + 0.920839i \(0.372495\pi\)
\(830\) 9.86054 0.342264
\(831\) 10.3394 0.358671
\(832\) 0 0
\(833\) −45.4282 −1.57399
\(834\) −1.71379 −0.0593438
\(835\) 3.00538 0.104005
\(836\) −2.78017 −0.0961541
\(837\) 2.06100 0.0712385
\(838\) −28.5773 −0.987187
\(839\) 24.4034 0.842500 0.421250 0.906945i \(-0.361592\pi\)
0.421250 + 0.906945i \(0.361592\pi\)
\(840\) −3.69202 −0.127387
\(841\) 81.3266 2.80437
\(842\) 32.3937 1.11636
\(843\) 5.08144 0.175014
\(844\) 2.93362 0.100980
\(845\) 0 0
\(846\) 11.5918 0.398534
\(847\) −6.29159 −0.216181
\(848\) −3.40581 −0.116956
\(849\) 24.5284 0.841813
\(850\) −6.85086 −0.234982
\(851\) 0.321125 0.0110080
\(852\) −4.13706 −0.141733
\(853\) −7.96184 −0.272608 −0.136304 0.990667i \(-0.543522\pi\)
−0.136304 + 0.990667i \(0.543522\pi\)
\(854\) 5.74094 0.196451
\(855\) −0.911854 −0.0311847
\(856\) −12.7192 −0.434732
\(857\) −8.12737 −0.277626 −0.138813 0.990319i \(-0.544329\pi\)
−0.138813 + 0.990319i \(0.544329\pi\)
\(858\) 0 0
\(859\) 17.1666 0.585717 0.292858 0.956156i \(-0.405394\pi\)
0.292858 + 0.956156i \(0.405394\pi\)
\(860\) −9.43296 −0.321661
\(861\) 38.0127 1.29547
\(862\) −14.6455 −0.498828
\(863\) −46.2857 −1.57558 −0.787792 0.615941i \(-0.788776\pi\)
−0.787792 + 0.615941i \(0.788776\pi\)
\(864\) 1.00000 0.0340207
\(865\) −6.89546 −0.234453
\(866\) −35.8485 −1.21818
\(867\) 29.9342 1.01662
\(868\) 7.60925 0.258275
\(869\) −29.3478 −0.995556
\(870\) −10.5036 −0.356107
\(871\) 0 0
\(872\) 19.9922 0.677022
\(873\) 6.97823 0.236177
\(874\) −0.325437 −0.0110081
\(875\) −3.69202 −0.124813
\(876\) 11.1685 0.377349
\(877\) 2.72156 0.0919006 0.0459503 0.998944i \(-0.485368\pi\)
0.0459503 + 0.998944i \(0.485368\pi\)
\(878\) 2.55927 0.0863712
\(879\) 15.8538 0.534737
\(880\) 3.04892 0.102779
\(881\) −16.7241 −0.563448 −0.281724 0.959495i \(-0.590906\pi\)
−0.281724 + 0.959495i \(0.590906\pi\)
\(882\) 6.63102 0.223278
\(883\) −2.88364 −0.0970423 −0.0485211 0.998822i \(-0.515451\pi\)
−0.0485211 + 0.998822i \(0.515451\pi\)
\(884\) 0 0
\(885\) −8.54288 −0.287166
\(886\) 23.2857 0.782300
\(887\) 55.8866 1.87649 0.938245 0.345973i \(-0.112451\pi\)
0.938245 + 0.345973i \(0.112451\pi\)
\(888\) −0.899772 −0.0301944
\(889\) −26.1696 −0.877700
\(890\) 6.41119 0.214904
\(891\) −3.04892 −0.102143
\(892\) −18.1444 −0.607518
\(893\) 10.5700 0.353712
\(894\) −6.91185 −0.231167
\(895\) 25.6461 0.857254
\(896\) 3.69202 0.123342
\(897\) 0 0
\(898\) −27.3327 −0.912105
\(899\) 21.6480 0.722001
\(900\) 1.00000 0.0333333
\(901\) 23.3327 0.777326
\(902\) −31.3913 −1.04522
\(903\) 34.8267 1.15896
\(904\) −4.49934 −0.149646
\(905\) 25.8092 0.857928
\(906\) 5.43296 0.180498
\(907\) 49.5381 1.64489 0.822443 0.568848i \(-0.192611\pi\)
0.822443 + 0.568848i \(0.192611\pi\)
\(908\) 12.3056 0.408375
\(909\) −4.09783 −0.135917
\(910\) 0 0
\(911\) 37.0603 1.22786 0.613931 0.789360i \(-0.289587\pi\)
0.613931 + 0.789360i \(0.289587\pi\)
\(912\) 0.911854 0.0301945
\(913\) 30.0640 0.994973
\(914\) −7.74094 −0.256047
\(915\) −1.55496 −0.0514053
\(916\) 4.64848 0.153590
\(917\) 72.9197 2.40802
\(918\) −6.85086 −0.226112
\(919\) 53.6228 1.76885 0.884426 0.466680i \(-0.154550\pi\)
0.884426 + 0.466680i \(0.154550\pi\)
\(920\) 0.356896 0.0117665
\(921\) −14.2121 −0.468303
\(922\) 17.1511 0.564840
\(923\) 0 0
\(924\) −11.2567 −0.370317
\(925\) −0.899772 −0.0295843
\(926\) −34.2747 −1.12634
\(927\) −16.9215 −0.555776
\(928\) 10.5036 0.344799
\(929\) −10.6726 −0.350158 −0.175079 0.984554i \(-0.556018\pi\)
−0.175079 + 0.984554i \(0.556018\pi\)
\(930\) −2.06100 −0.0675828
\(931\) 6.04652 0.198167
\(932\) 0.658170 0.0215591
\(933\) 15.0127 0.491493
\(934\) 20.9474 0.685419
\(935\) −20.8877 −0.683101
\(936\) 0 0
\(937\) 17.0538 0.557124 0.278562 0.960418i \(-0.410142\pi\)
0.278562 + 0.960418i \(0.410142\pi\)
\(938\) 4.24267 0.138528
\(939\) −13.4993 −0.440534
\(940\) −11.5918 −0.378083
\(941\) −46.7706 −1.52468 −0.762339 0.647178i \(-0.775949\pi\)
−0.762339 + 0.647178i \(0.775949\pi\)
\(942\) −9.13706 −0.297702
\(943\) −3.67456 −0.119660
\(944\) 8.54288 0.278047
\(945\) −3.69202 −0.120101
\(946\) −28.7603 −0.935079
\(947\) −30.0398 −0.976163 −0.488081 0.872798i \(-0.662303\pi\)
−0.488081 + 0.872798i \(0.662303\pi\)
\(948\) 9.62565 0.312626
\(949\) 0 0
\(950\) 0.911854 0.0295845
\(951\) 33.9463 1.10078
\(952\) −25.2935 −0.819767
\(953\) −29.4252 −0.953175 −0.476588 0.879127i \(-0.658127\pi\)
−0.476588 + 0.879127i \(0.658127\pi\)
\(954\) −3.40581 −0.110267
\(955\) 14.5700 0.471475
\(956\) −18.7748 −0.607220
\(957\) −32.0248 −1.03521
\(958\) 15.8310 0.511477
\(959\) −29.3269 −0.947014
\(960\) −1.00000 −0.0322749
\(961\) −26.7523 −0.862977
\(962\) 0 0
\(963\) −12.7192 −0.409869
\(964\) 18.0271 0.580615
\(965\) −8.32544 −0.268005
\(966\) −1.31767 −0.0423952
\(967\) 12.7023 0.408478 0.204239 0.978921i \(-0.434528\pi\)
0.204239 + 0.978921i \(0.434528\pi\)
\(968\) −1.70410 −0.0547719
\(969\) −6.24698 −0.200682
\(970\) −6.97823 −0.224057
\(971\) 22.9105 0.735234 0.367617 0.929977i \(-0.380174\pi\)
0.367617 + 0.929977i \(0.380174\pi\)
\(972\) 1.00000 0.0320750
\(973\) −6.32736 −0.202846
\(974\) 33.7060 1.08001
\(975\) 0 0
\(976\) 1.55496 0.0497730
\(977\) −25.1390 −0.804267 −0.402134 0.915581i \(-0.631731\pi\)
−0.402134 + 0.915581i \(0.631731\pi\)
\(978\) 14.3773 0.459737
\(979\) 19.5472 0.624731
\(980\) −6.63102 −0.211820
\(981\) 19.9922 0.638303
\(982\) 3.98925 0.127302
\(983\) −50.3895 −1.60718 −0.803588 0.595186i \(-0.797079\pi\)
−0.803588 + 0.595186i \(0.797079\pi\)
\(984\) 10.2959 0.328221
\(985\) 26.8810 0.856499
\(986\) −71.9590 −2.29164
\(987\) 42.7972 1.36225
\(988\) 0 0
\(989\) −3.36658 −0.107051
\(990\) 3.04892 0.0969010
\(991\) 23.3375 0.741341 0.370670 0.928764i \(-0.379128\pi\)
0.370670 + 0.928764i \(0.379128\pi\)
\(992\) 2.06100 0.0654368
\(993\) −6.84415 −0.217193
\(994\) −15.2741 −0.484466
\(995\) 18.7047 0.592979
\(996\) −9.86054 −0.312443
\(997\) 22.8127 0.722485 0.361243 0.932472i \(-0.382353\pi\)
0.361243 + 0.932472i \(0.382353\pi\)
\(998\) 20.4698 0.647960
\(999\) −0.899772 −0.0284675
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 5070.2.a.bw.1.3 yes 3
13.5 odd 4 5070.2.b.z.1351.3 6
13.8 odd 4 5070.2.b.z.1351.4 6
13.12 even 2 5070.2.a.bp.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5070.2.a.bp.1.1 3 13.12 even 2
5070.2.a.bw.1.3 yes 3 1.1 even 1 trivial
5070.2.b.z.1351.3 6 13.5 odd 4
5070.2.b.z.1351.4 6 13.8 odd 4