Properties

Label 8470.2.a.cz.1.1
Level $8470$
Weight $2$
Character 8470.1
Self dual yes
Analytic conductor $67.633$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8470.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.6332905120\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.10784448.1
Defining polynomial: \(x^{6} - 11 x^{4} - 4 x^{3} + 31 x^{2} + 22 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.0816388\) of defining polynomial
Character \(\chi\) \(=\) 8470.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} -1.00000 q^{10} -1.34292 q^{12} -4.31157 q^{13} +1.00000 q^{14} -1.34292 q^{15} +1.00000 q^{16} +2.63565 q^{17} +1.19656 q^{18} -1.56877 q^{19} +1.00000 q^{20} +1.34292 q^{21} +5.45794 q^{23} +1.34292 q^{24} +1.00000 q^{25} +4.31157 q^{26} +5.63565 q^{27} -1.00000 q^{28} -2.83920 q^{29} +1.34292 q^{30} +1.14637 q^{31} -1.00000 q^{32} -2.63565 q^{34} -1.00000 q^{35} -1.19656 q^{36} -0.839198 q^{37} +1.56877 q^{38} +5.79011 q^{39} -1.00000 q^{40} -3.47854 q^{41} -1.34292 q^{42} +2.01075 q^{43} -1.19656 q^{45} -5.45794 q^{46} -8.39442 q^{47} -1.34292 q^{48} +1.00000 q^{49} -1.00000 q^{50} -3.53948 q^{51} -4.31157 q^{52} +1.40604 q^{53} -5.63565 q^{54} +1.00000 q^{56} +2.10674 q^{57} +2.83920 q^{58} +2.32408 q^{59} -1.34292 q^{60} +5.24387 q^{61} -1.14637 q^{62} +1.19656 q^{63} +1.00000 q^{64} -4.31157 q^{65} -1.60636 q^{67} +2.63565 q^{68} -7.32959 q^{69} +1.00000 q^{70} -13.8057 q^{71} +1.19656 q^{72} +1.14830 q^{73} +0.839198 q^{74} -1.34292 q^{75} -1.56877 q^{76} -5.79011 q^{78} -9.65408 q^{79} +1.00000 q^{80} -3.97858 q^{81} +3.47854 q^{82} +2.51880 q^{83} +1.34292 q^{84} +2.63565 q^{85} -2.01075 q^{86} +3.81282 q^{87} +2.19326 q^{89} +1.19656 q^{90} +4.31157 q^{91} +5.45794 q^{92} -1.53948 q^{93} +8.39442 q^{94} -1.56877 q^{95} +1.34292 q^{96} -7.56372 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9} + O(q^{10}) \) \( 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{12} + 6 q^{14} + 4 q^{15} + 6 q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{23} - 4 q^{24} + 6 q^{25} + 16 q^{27} - 6 q^{28} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 6 q^{32} + 2 q^{34} - 6 q^{35} + 2 q^{36} + 4 q^{37} - 6 q^{40} - 12 q^{41} + 4 q^{42} + 6 q^{43} + 2 q^{45} - 4 q^{46} + 16 q^{47} + 4 q^{48} + 6 q^{49} - 6 q^{50} + 12 q^{53} - 16 q^{54} + 6 q^{56} - 8 q^{57} + 8 q^{58} + 22 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} - 2 q^{63} + 6 q^{64} + 20 q^{67} - 2 q^{68} + 12 q^{69} + 6 q^{70} + 14 q^{71} - 2 q^{72} - 18 q^{73} - 4 q^{74} + 4 q^{75} - 32 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 16 q^{83} - 4 q^{84} - 2 q^{85} - 6 q^{86} + 4 q^{87} + 4 q^{89} - 2 q^{90} + 4 q^{92} + 12 q^{93} - 16 q^{94} - 4 q^{96} + 4 q^{97} - 6 q^{98} + O(q^{100}) \)

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
\(3\) −1.34292 −0.775337 −0.387669 0.921799i \(-0.626719\pi\)
−0.387669 + 0.921799i \(0.626719\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.34292 0.548246
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −1.19656 −0.398853
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −1.34292 −0.387669
\(13\) −4.31157 −1.19582 −0.597908 0.801565i \(-0.704001\pi\)
−0.597908 + 0.801565i \(0.704001\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.34292 −0.346741
\(16\) 1.00000 0.250000
\(17\) 2.63565 0.639240 0.319620 0.947546i \(-0.396445\pi\)
0.319620 + 0.947546i \(0.396445\pi\)
\(18\) 1.19656 0.282031
\(19\) −1.56877 −0.359901 −0.179951 0.983676i \(-0.557594\pi\)
−0.179951 + 0.983676i \(0.557594\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.34292 0.293050
\(22\) 0 0
\(23\) 5.45794 1.13806 0.569030 0.822317i \(-0.307319\pi\)
0.569030 + 0.822317i \(0.307319\pi\)
\(24\) 1.34292 0.274123
\(25\) 1.00000 0.200000
\(26\) 4.31157 0.845569
\(27\) 5.63565 1.08458
\(28\) −1.00000 −0.188982
\(29\) −2.83920 −0.527226 −0.263613 0.964629i \(-0.584914\pi\)
−0.263613 + 0.964629i \(0.584914\pi\)
\(30\) 1.34292 0.245183
\(31\) 1.14637 0.205893 0.102947 0.994687i \(-0.467173\pi\)
0.102947 + 0.994687i \(0.467173\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −2.63565 −0.452011
\(35\) −1.00000 −0.169031
\(36\) −1.19656 −0.199426
\(37\) −0.839198 −0.137963 −0.0689816 0.997618i \(-0.521975\pi\)
−0.0689816 + 0.997618i \(0.521975\pi\)
\(38\) 1.56877 0.254489
\(39\) 5.79011 0.927160
\(40\) −1.00000 −0.158114
\(41\) −3.47854 −0.543256 −0.271628 0.962402i \(-0.587562\pi\)
−0.271628 + 0.962402i \(0.587562\pi\)
\(42\) −1.34292 −0.207218
\(43\) 2.01075 0.306637 0.153318 0.988177i \(-0.451004\pi\)
0.153318 + 0.988177i \(0.451004\pi\)
\(44\) 0 0
\(45\) −1.19656 −0.178372
\(46\) −5.45794 −0.804729
\(47\) −8.39442 −1.22445 −0.612226 0.790683i \(-0.709726\pi\)
−0.612226 + 0.790683i \(0.709726\pi\)
\(48\) −1.34292 −0.193834
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) −3.53948 −0.495626
\(52\) −4.31157 −0.597908
\(53\) 1.40604 0.193134 0.0965672 0.995326i \(-0.469214\pi\)
0.0965672 + 0.995326i \(0.469214\pi\)
\(54\) −5.63565 −0.766915
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 2.10674 0.279045
\(58\) 2.83920 0.372805
\(59\) 2.32408 0.302569 0.151285 0.988490i \(-0.451659\pi\)
0.151285 + 0.988490i \(0.451659\pi\)
\(60\) −1.34292 −0.173371
\(61\) 5.24387 0.671409 0.335704 0.941967i \(-0.391026\pi\)
0.335704 + 0.941967i \(0.391026\pi\)
\(62\) −1.14637 −0.145589
\(63\) 1.19656 0.150752
\(64\) 1.00000 0.125000
\(65\) −4.31157 −0.534785
\(66\) 0 0
\(67\) −1.60636 −0.196248 −0.0981241 0.995174i \(-0.531284\pi\)
−0.0981241 + 0.995174i \(0.531284\pi\)
\(68\) 2.63565 0.319620
\(69\) −7.32959 −0.882379
\(70\) 1.00000 0.119523
\(71\) −13.8057 −1.63844 −0.819220 0.573480i \(-0.805593\pi\)
−0.819220 + 0.573480i \(0.805593\pi\)
\(72\) 1.19656 0.141016
\(73\) 1.14830 0.134398 0.0671990 0.997740i \(-0.478594\pi\)
0.0671990 + 0.997740i \(0.478594\pi\)
\(74\) 0.839198 0.0975548
\(75\) −1.34292 −0.155067
\(76\) −1.56877 −0.179951
\(77\) 0 0
\(78\) −5.79011 −0.655601
\(79\) −9.65408 −1.08617 −0.543084 0.839678i \(-0.682744\pi\)
−0.543084 + 0.839678i \(0.682744\pi\)
\(80\) 1.00000 0.111803
\(81\) −3.97858 −0.442064
\(82\) 3.47854 0.384140
\(83\) 2.51880 0.276475 0.138237 0.990399i \(-0.455856\pi\)
0.138237 + 0.990399i \(0.455856\pi\)
\(84\) 1.34292 0.146525
\(85\) 2.63565 0.285877
\(86\) −2.01075 −0.216825
\(87\) 3.81282 0.408778
\(88\) 0 0
\(89\) 2.19326 0.232485 0.116242 0.993221i \(-0.462915\pi\)
0.116242 + 0.993221i \(0.462915\pi\)
\(90\) 1.19656 0.126128
\(91\) 4.31157 0.451976
\(92\) 5.45794 0.569030
\(93\) −1.53948 −0.159637
\(94\) 8.39442 0.865818
\(95\) −1.56877 −0.160953
\(96\) 1.34292 0.137062
\(97\) −7.56372 −0.767979 −0.383990 0.923337i \(-0.625450\pi\)
−0.383990 + 0.923337i \(0.625450\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −17.6449 −1.75574 −0.877868 0.478902i \(-0.841035\pi\)
−0.877868 + 0.478902i \(0.841035\pi\)
\(102\) 3.53948 0.350461
\(103\) 10.1528 1.00039 0.500194 0.865913i \(-0.333262\pi\)
0.500194 + 0.865913i \(0.333262\pi\)
\(104\) 4.31157 0.422785
\(105\) 1.34292 0.131056
\(106\) −1.40604 −0.136567
\(107\) −15.4232 −1.49102 −0.745508 0.666497i \(-0.767793\pi\)
−0.745508 + 0.666497i \(0.767793\pi\)
\(108\) 5.63565 0.542291
\(109\) −8.49656 −0.813823 −0.406911 0.913468i \(-0.633394\pi\)
−0.406911 + 0.913468i \(0.633394\pi\)
\(110\) 0 0
\(111\) 1.12698 0.106968
\(112\) −1.00000 −0.0944911
\(113\) 2.72299 0.256158 0.128079 0.991764i \(-0.459119\pi\)
0.128079 + 0.991764i \(0.459119\pi\)
\(114\) −2.10674 −0.197314
\(115\) 5.45794 0.508956
\(116\) −2.83920 −0.263613
\(117\) 5.15905 0.476954
\(118\) −2.32408 −0.213949
\(119\) −2.63565 −0.241610
\(120\) 1.34292 0.122592
\(121\) 0 0
\(122\) −5.24387 −0.474758
\(123\) 4.67141 0.421207
\(124\) 1.14637 0.102947
\(125\) 1.00000 0.0894427
\(126\) −1.19656 −0.106598
\(127\) 9.21928 0.818079 0.409040 0.912517i \(-0.365864\pi\)
0.409040 + 0.912517i \(0.365864\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.70028 −0.237747
\(130\) 4.31157 0.378150
\(131\) −17.5357 −1.53210 −0.766052 0.642779i \(-0.777781\pi\)
−0.766052 + 0.642779i \(0.777781\pi\)
\(132\) 0 0
\(133\) 1.56877 0.136030
\(134\) 1.60636 0.138768
\(135\) 5.63565 0.485040
\(136\) −2.63565 −0.226005
\(137\) 9.12927 0.779966 0.389983 0.920822i \(-0.372481\pi\)
0.389983 + 0.920822i \(0.372481\pi\)
\(138\) 7.32959 0.623936
\(139\) −0.657844 −0.0557976 −0.0278988 0.999611i \(-0.508882\pi\)
−0.0278988 + 0.999611i \(0.508882\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 11.2731 0.949363
\(142\) 13.8057 1.15855
\(143\) 0 0
\(144\) −1.19656 −0.0997131
\(145\) −2.83920 −0.235783
\(146\) −1.14830 −0.0950337
\(147\) −1.34292 −0.110762
\(148\) −0.839198 −0.0689816
\(149\) 20.5982 1.68747 0.843737 0.536757i \(-0.180351\pi\)
0.843737 + 0.536757i \(0.180351\pi\)
\(150\) 1.34292 0.109649
\(151\) 4.29219 0.349293 0.174647 0.984631i \(-0.444122\pi\)
0.174647 + 0.984631i \(0.444122\pi\)
\(152\) 1.56877 0.127244
\(153\) −3.15371 −0.254962
\(154\) 0 0
\(155\) 1.14637 0.0920783
\(156\) 5.79011 0.463580
\(157\) 10.9039 0.870226 0.435113 0.900376i \(-0.356708\pi\)
0.435113 + 0.900376i \(0.356708\pi\)
\(158\) 9.65408 0.768037
\(159\) −1.88820 −0.149744
\(160\) −1.00000 −0.0790569
\(161\) −5.45794 −0.430146
\(162\) 3.97858 0.312587
\(163\) 12.3525 0.967526 0.483763 0.875199i \(-0.339270\pi\)
0.483763 + 0.875199i \(0.339270\pi\)
\(164\) −3.47854 −0.271628
\(165\) 0 0
\(166\) −2.51880 −0.195497
\(167\) 6.93334 0.536518 0.268259 0.963347i \(-0.413552\pi\)
0.268259 + 0.963347i \(0.413552\pi\)
\(168\) −1.34292 −0.103609
\(169\) 5.58967 0.429975
\(170\) −2.63565 −0.202145
\(171\) 1.87713 0.143548
\(172\) 2.01075 0.153318
\(173\) 11.5843 0.880741 0.440370 0.897816i \(-0.354847\pi\)
0.440370 + 0.897816i \(0.354847\pi\)
\(174\) −3.81282 −0.289049
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) −3.12106 −0.234593
\(178\) −2.19326 −0.164392
\(179\) 20.4825 1.53093 0.765466 0.643476i \(-0.222508\pi\)
0.765466 + 0.643476i \(0.222508\pi\)
\(180\) −1.19656 −0.0891861
\(181\) −8.01175 −0.595509 −0.297754 0.954642i \(-0.596238\pi\)
−0.297754 + 0.954642i \(0.596238\pi\)
\(182\) −4.31157 −0.319595
\(183\) −7.04211 −0.520568
\(184\) −5.45794 −0.402365
\(185\) −0.839198 −0.0616990
\(186\) 1.53948 0.112880
\(187\) 0 0
\(188\) −8.39442 −0.612226
\(189\) −5.63565 −0.409934
\(190\) 1.56877 0.113811
\(191\) 7.72371 0.558868 0.279434 0.960165i \(-0.409853\pi\)
0.279434 + 0.960165i \(0.409853\pi\)
\(192\) −1.34292 −0.0969171
\(193\) 16.3855 1.17945 0.589727 0.807603i \(-0.299235\pi\)
0.589727 + 0.807603i \(0.299235\pi\)
\(194\) 7.56372 0.543043
\(195\) 5.79011 0.414639
\(196\) 1.00000 0.0714286
\(197\) −5.51971 −0.393263 −0.196631 0.980477i \(-0.563000\pi\)
−0.196631 + 0.980477i \(0.563000\pi\)
\(198\) 0 0
\(199\) 4.27443 0.303006 0.151503 0.988457i \(-0.451589\pi\)
0.151503 + 0.988457i \(0.451589\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.15722 0.152159
\(202\) 17.6449 1.24149
\(203\) 2.83920 0.199273
\(204\) −3.53948 −0.247813
\(205\) −3.47854 −0.242952
\(206\) −10.1528 −0.707381
\(207\) −6.53074 −0.453918
\(208\) −4.31157 −0.298954
\(209\) 0 0
\(210\) −1.34292 −0.0926705
\(211\) 19.6106 1.35005 0.675026 0.737794i \(-0.264132\pi\)
0.675026 + 0.737794i \(0.264132\pi\)
\(212\) 1.40604 0.0965672
\(213\) 18.5400 1.27034
\(214\) 15.4232 1.05431
\(215\) 2.01075 0.137132
\(216\) −5.63565 −0.383458
\(217\) −1.14637 −0.0778204
\(218\) 8.49656 0.575459
\(219\) −1.54207 −0.104204
\(220\) 0 0
\(221\) −11.3638 −0.764413
\(222\) −1.12698 −0.0756378
\(223\) 4.01943 0.269161 0.134580 0.990903i \(-0.457031\pi\)
0.134580 + 0.990903i \(0.457031\pi\)
\(224\) 1.00000 0.0668153
\(225\) −1.19656 −0.0797705
\(226\) −2.72299 −0.181131
\(227\) −20.4787 −1.35922 −0.679610 0.733574i \(-0.737851\pi\)
−0.679610 + 0.733574i \(0.737851\pi\)
\(228\) 2.10674 0.139522
\(229\) 8.74872 0.578132 0.289066 0.957309i \(-0.406655\pi\)
0.289066 + 0.957309i \(0.406655\pi\)
\(230\) −5.45794 −0.359886
\(231\) 0 0
\(232\) 2.83920 0.186402
\(233\) −14.1462 −0.926748 −0.463374 0.886163i \(-0.653361\pi\)
−0.463374 + 0.886163i \(0.653361\pi\)
\(234\) −5.15905 −0.337257
\(235\) −8.39442 −0.547591
\(236\) 2.32408 0.151285
\(237\) 12.9647 0.842147
\(238\) 2.63565 0.170844
\(239\) −2.12134 −0.137218 −0.0686091 0.997644i \(-0.521856\pi\)
−0.0686091 + 0.997644i \(0.521856\pi\)
\(240\) −1.34292 −0.0866853
\(241\) −17.4357 −1.12313 −0.561566 0.827432i \(-0.689801\pi\)
−0.561566 + 0.827432i \(0.689801\pi\)
\(242\) 0 0
\(243\) −11.5640 −0.741833
\(244\) 5.24387 0.335704
\(245\) 1.00000 0.0638877
\(246\) −4.67141 −0.297838
\(247\) 6.76388 0.430376
\(248\) −1.14637 −0.0727943
\(249\) −3.38256 −0.214361
\(250\) −1.00000 −0.0632456
\(251\) 0.936840 0.0591328 0.0295664 0.999563i \(-0.490587\pi\)
0.0295664 + 0.999563i \(0.490587\pi\)
\(252\) 1.19656 0.0753760
\(253\) 0 0
\(254\) −9.21928 −0.578469
\(255\) −3.53948 −0.221651
\(256\) 1.00000 0.0625000
\(257\) 13.7242 0.856095 0.428047 0.903756i \(-0.359202\pi\)
0.428047 + 0.903756i \(0.359202\pi\)
\(258\) 2.70028 0.168112
\(259\) 0.839198 0.0521452
\(260\) −4.31157 −0.267392
\(261\) 3.39726 0.210285
\(262\) 17.5357 1.08336
\(263\) 18.9341 1.16753 0.583763 0.811924i \(-0.301580\pi\)
0.583763 + 0.811924i \(0.301580\pi\)
\(264\) 0 0
\(265\) 1.40604 0.0863723
\(266\) −1.56877 −0.0961877
\(267\) −2.94538 −0.180254
\(268\) −1.60636 −0.0981241
\(269\) 12.9639 0.790422 0.395211 0.918590i \(-0.370672\pi\)
0.395211 + 0.918590i \(0.370672\pi\)
\(270\) −5.63565 −0.342975
\(271\) −23.5085 −1.42804 −0.714020 0.700125i \(-0.753127\pi\)
−0.714020 + 0.700125i \(0.753127\pi\)
\(272\) 2.63565 0.159810
\(273\) −5.79011 −0.350434
\(274\) −9.12927 −0.551519
\(275\) 0 0
\(276\) −7.32959 −0.441190
\(277\) −2.44560 −0.146942 −0.0734710 0.997297i \(-0.523408\pi\)
−0.0734710 + 0.997297i \(0.523408\pi\)
\(278\) 0.657844 0.0394549
\(279\) −1.37169 −0.0821211
\(280\) 1.00000 0.0597614
\(281\) 18.0116 1.07448 0.537242 0.843428i \(-0.319466\pi\)
0.537242 + 0.843428i \(0.319466\pi\)
\(282\) −11.2731 −0.671301
\(283\) 9.78930 0.581914 0.290957 0.956736i \(-0.406026\pi\)
0.290957 + 0.956736i \(0.406026\pi\)
\(284\) −13.8057 −0.819220
\(285\) 2.10674 0.124793
\(286\) 0 0
\(287\) 3.47854 0.205332
\(288\) 1.19656 0.0705078
\(289\) −10.0533 −0.591372
\(290\) 2.83920 0.166723
\(291\) 10.1575 0.595443
\(292\) 1.14830 0.0671990
\(293\) 8.44836 0.493558 0.246779 0.969072i \(-0.420628\pi\)
0.246779 + 0.969072i \(0.420628\pi\)
\(294\) 1.34292 0.0783209
\(295\) 2.32408 0.135313
\(296\) 0.839198 0.0487774
\(297\) 0 0
\(298\) −20.5982 −1.19322
\(299\) −23.5323 −1.36091
\(300\) −1.34292 −0.0775337
\(301\) −2.01075 −0.115898
\(302\) −4.29219 −0.246988
\(303\) 23.6958 1.36129
\(304\) −1.56877 −0.0899753
\(305\) 5.24387 0.300263
\(306\) 3.15371 0.180286
\(307\) 9.34689 0.533455 0.266728 0.963772i \(-0.414058\pi\)
0.266728 + 0.963772i \(0.414058\pi\)
\(308\) 0 0
\(309\) −13.6345 −0.775638
\(310\) −1.14637 −0.0651092
\(311\) −27.6729 −1.56919 −0.784593 0.620011i \(-0.787128\pi\)
−0.784593 + 0.620011i \(0.787128\pi\)
\(312\) −5.79011 −0.327801
\(313\) 5.34524 0.302131 0.151065 0.988524i \(-0.451730\pi\)
0.151065 + 0.988524i \(0.451730\pi\)
\(314\) −10.9039 −0.615343
\(315\) 1.19656 0.0674184
\(316\) −9.65408 −0.543084
\(317\) 7.13917 0.400976 0.200488 0.979696i \(-0.435747\pi\)
0.200488 + 0.979696i \(0.435747\pi\)
\(318\) 1.88820 0.105885
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 20.7122 1.15604
\(322\) 5.45794 0.304159
\(323\) −4.13474 −0.230063
\(324\) −3.97858 −0.221032
\(325\) −4.31157 −0.239163
\(326\) −12.3525 −0.684144
\(327\) 11.4102 0.630987
\(328\) 3.47854 0.192070
\(329\) 8.39442 0.462799
\(330\) 0 0
\(331\) 5.83207 0.320559 0.160280 0.987072i \(-0.448760\pi\)
0.160280 + 0.987072i \(0.448760\pi\)
\(332\) 2.51880 0.138237
\(333\) 1.00415 0.0550270
\(334\) −6.93334 −0.379375
\(335\) −1.60636 −0.0877649
\(336\) 1.34292 0.0732625
\(337\) −22.2848 −1.21393 −0.606964 0.794729i \(-0.707613\pi\)
−0.606964 + 0.794729i \(0.707613\pi\)
\(338\) −5.58967 −0.304038
\(339\) −3.65677 −0.198609
\(340\) 2.63565 0.142938
\(341\) 0 0
\(342\) −1.87713 −0.101503
\(343\) −1.00000 −0.0539949
\(344\) −2.01075 −0.108412
\(345\) −7.32959 −0.394612
\(346\) −11.5843 −0.622778
\(347\) −16.6253 −0.892495 −0.446248 0.894910i \(-0.647240\pi\)
−0.446248 + 0.894910i \(0.647240\pi\)
\(348\) 3.81282 0.204389
\(349\) −3.23934 −0.173398 −0.0866989 0.996235i \(-0.527632\pi\)
−0.0866989 + 0.996235i \(0.527632\pi\)
\(350\) 1.00000 0.0534522
\(351\) −24.2985 −1.29696
\(352\) 0 0
\(353\) −24.6580 −1.31241 −0.656205 0.754582i \(-0.727839\pi\)
−0.656205 + 0.754582i \(0.727839\pi\)
\(354\) 3.12106 0.165882
\(355\) −13.8057 −0.732732
\(356\) 2.19326 0.116242
\(357\) 3.53948 0.187329
\(358\) −20.4825 −1.08253
\(359\) −20.7493 −1.09511 −0.547554 0.836771i \(-0.684441\pi\)
−0.547554 + 0.836771i \(0.684441\pi\)
\(360\) 1.19656 0.0630641
\(361\) −16.5390 −0.870471
\(362\) 8.01175 0.421088
\(363\) 0 0
\(364\) 4.31157 0.225988
\(365\) 1.14830 0.0601046
\(366\) 7.04211 0.368097
\(367\) 2.12160 0.110746 0.0553732 0.998466i \(-0.482365\pi\)
0.0553732 + 0.998466i \(0.482365\pi\)
\(368\) 5.45794 0.284515
\(369\) 4.16227 0.216679
\(370\) 0.839198 0.0436278
\(371\) −1.40604 −0.0729979
\(372\) −1.53948 −0.0798184
\(373\) 7.19996 0.372800 0.186400 0.982474i \(-0.440318\pi\)
0.186400 + 0.982474i \(0.440318\pi\)
\(374\) 0 0
\(375\) −1.34292 −0.0693482
\(376\) 8.39442 0.432909
\(377\) 12.2414 0.630465
\(378\) 5.63565 0.289867
\(379\) −23.1300 −1.18811 −0.594055 0.804424i \(-0.702474\pi\)
−0.594055 + 0.804424i \(0.702474\pi\)
\(380\) −1.56877 −0.0804764
\(381\) −12.3808 −0.634287
\(382\) −7.72371 −0.395180
\(383\) 31.4479 1.60691 0.803455 0.595365i \(-0.202993\pi\)
0.803455 + 0.595365i \(0.202993\pi\)
\(384\) 1.34292 0.0685308
\(385\) 0 0
\(386\) −16.3855 −0.834000
\(387\) −2.40598 −0.122303
\(388\) −7.56372 −0.383990
\(389\) 17.5618 0.890420 0.445210 0.895426i \(-0.353129\pi\)
0.445210 + 0.895426i \(0.353129\pi\)
\(390\) −5.79011 −0.293194
\(391\) 14.3852 0.727493
\(392\) −1.00000 −0.0505076
\(393\) 23.5491 1.18790
\(394\) 5.51971 0.278079
\(395\) −9.65408 −0.485749
\(396\) 0 0
\(397\) 32.7839 1.64538 0.822689 0.568492i \(-0.192473\pi\)
0.822689 + 0.568492i \(0.192473\pi\)
\(398\) −4.27443 −0.214258
\(399\) −2.10674 −0.105469
\(400\) 1.00000 0.0500000
\(401\) 9.25146 0.461996 0.230998 0.972954i \(-0.425801\pi\)
0.230998 + 0.972954i \(0.425801\pi\)
\(402\) −2.15722 −0.107592
\(403\) −4.94264 −0.246210
\(404\) −17.6449 −0.877868
\(405\) −3.97858 −0.197697
\(406\) −2.83920 −0.140907
\(407\) 0 0
\(408\) 3.53948 0.175230
\(409\) 0.0174947 0.000865057 0 0.000432529 1.00000i \(-0.499862\pi\)
0.000432529 1.00000i \(0.499862\pi\)
\(410\) 3.47854 0.171793
\(411\) −12.2599 −0.604737
\(412\) 10.1528 0.500194
\(413\) −2.32408 −0.114360
\(414\) 6.53074 0.320968
\(415\) 2.51880 0.123643
\(416\) 4.31157 0.211392
\(417\) 0.883434 0.0432620
\(418\) 0 0
\(419\) 32.4579 1.58567 0.792837 0.609433i \(-0.208603\pi\)
0.792837 + 0.609433i \(0.208603\pi\)
\(420\) 1.34292 0.0655279
\(421\) 9.15329 0.446104 0.223052 0.974807i \(-0.428398\pi\)
0.223052 + 0.974807i \(0.428398\pi\)
\(422\) −19.6106 −0.954631
\(423\) 10.0444 0.488376
\(424\) −1.40604 −0.0682833
\(425\) 2.63565 0.127848
\(426\) −18.5400 −0.898268
\(427\) −5.24387 −0.253769
\(428\) −15.4232 −0.745508
\(429\) 0 0
\(430\) −2.01075 −0.0969670
\(431\) 26.0024 1.25249 0.626247 0.779625i \(-0.284590\pi\)
0.626247 + 0.779625i \(0.284590\pi\)
\(432\) 5.63565 0.271146
\(433\) 23.6006 1.13417 0.567085 0.823659i \(-0.308071\pi\)
0.567085 + 0.823659i \(0.308071\pi\)
\(434\) 1.14637 0.0550273
\(435\) 3.81282 0.182811
\(436\) −8.49656 −0.406911
\(437\) −8.56227 −0.409589
\(438\) 1.54207 0.0736832
\(439\) −31.7894 −1.51722 −0.758612 0.651543i \(-0.774122\pi\)
−0.758612 + 0.651543i \(0.774122\pi\)
\(440\) 0 0
\(441\) −1.19656 −0.0569789
\(442\) 11.3638 0.540522
\(443\) 36.1071 1.71550 0.857750 0.514067i \(-0.171862\pi\)
0.857750 + 0.514067i \(0.171862\pi\)
\(444\) 1.12698 0.0534840
\(445\) 2.19326 0.103970
\(446\) −4.01943 −0.190326
\(447\) −27.6619 −1.30836
\(448\) −1.00000 −0.0472456
\(449\) −4.52269 −0.213439 −0.106719 0.994289i \(-0.534035\pi\)
−0.106719 + 0.994289i \(0.534035\pi\)
\(450\) 1.19656 0.0564063
\(451\) 0 0
\(452\) 2.72299 0.128079
\(453\) −5.76408 −0.270820
\(454\) 20.4787 0.961114
\(455\) 4.31157 0.202130
\(456\) −2.10674 −0.0986572
\(457\) 15.1593 0.709120 0.354560 0.935033i \(-0.384631\pi\)
0.354560 + 0.935033i \(0.384631\pi\)
\(458\) −8.74872 −0.408801
\(459\) 14.8536 0.693308
\(460\) 5.45794 0.254478
\(461\) 27.6126 1.28605 0.643024 0.765846i \(-0.277680\pi\)
0.643024 + 0.765846i \(0.277680\pi\)
\(462\) 0 0
\(463\) 13.3557 0.620692 0.310346 0.950624i \(-0.399555\pi\)
0.310346 + 0.950624i \(0.399555\pi\)
\(464\) −2.83920 −0.131806
\(465\) −1.53948 −0.0713917
\(466\) 14.1462 0.655310
\(467\) 26.3287 1.21835 0.609173 0.793038i \(-0.291502\pi\)
0.609173 + 0.793038i \(0.291502\pi\)
\(468\) 5.15905 0.238477
\(469\) 1.60636 0.0741749
\(470\) 8.39442 0.387206
\(471\) −14.6431 −0.674719
\(472\) −2.32408 −0.106974
\(473\) 0 0
\(474\) −12.9647 −0.595488
\(475\) −1.56877 −0.0719803
\(476\) −2.63565 −0.120805
\(477\) −1.68241 −0.0770322
\(478\) 2.12134 0.0970279
\(479\) −8.18258 −0.373872 −0.186936 0.982372i \(-0.559856\pi\)
−0.186936 + 0.982372i \(0.559856\pi\)
\(480\) 1.34292 0.0612958
\(481\) 3.61826 0.164979
\(482\) 17.4357 0.794174
\(483\) 7.32959 0.333508
\(484\) 0 0
\(485\) −7.56372 −0.343451
\(486\) 11.5640 0.524555
\(487\) −9.09993 −0.412357 −0.206179 0.978514i \(-0.566103\pi\)
−0.206179 + 0.978514i \(0.566103\pi\)
\(488\) −5.24387 −0.237379
\(489\) −16.5885 −0.750159
\(490\) −1.00000 −0.0451754
\(491\) 3.80239 0.171600 0.0857998 0.996312i \(-0.472655\pi\)
0.0857998 + 0.996312i \(0.472655\pi\)
\(492\) 4.67141 0.210603
\(493\) −7.48314 −0.337024
\(494\) −6.76388 −0.304321
\(495\) 0 0
\(496\) 1.14637 0.0514733
\(497\) 13.8057 0.619272
\(498\) 3.38256 0.151576
\(499\) −22.9856 −1.02898 −0.514488 0.857497i \(-0.672018\pi\)
−0.514488 + 0.857497i \(0.672018\pi\)
\(500\) 1.00000 0.0447214
\(501\) −9.31094 −0.415982
\(502\) −0.936840 −0.0418132
\(503\) −13.4287 −0.598756 −0.299378 0.954135i \(-0.596779\pi\)
−0.299378 + 0.954135i \(0.596779\pi\)
\(504\) −1.19656 −0.0532989
\(505\) −17.6449 −0.785189
\(506\) 0 0
\(507\) −7.50650 −0.333375
\(508\) 9.21928 0.409040
\(509\) 36.9453 1.63757 0.818785 0.574100i \(-0.194648\pi\)
0.818785 + 0.574100i \(0.194648\pi\)
\(510\) 3.53948 0.156731
\(511\) −1.14830 −0.0507977
\(512\) −1.00000 −0.0441942
\(513\) −8.84106 −0.390342
\(514\) −13.7242 −0.605350
\(515\) 10.1528 0.447387
\(516\) −2.70028 −0.118873
\(517\) 0 0
\(518\) −0.839198 −0.0368722
\(519\) −15.5569 −0.682871
\(520\) 4.31157 0.189075
\(521\) 12.8367 0.562388 0.281194 0.959651i \(-0.409270\pi\)
0.281194 + 0.959651i \(0.409270\pi\)
\(522\) −3.39726 −0.148694
\(523\) 8.66972 0.379100 0.189550 0.981871i \(-0.439297\pi\)
0.189550 + 0.981871i \(0.439297\pi\)
\(524\) −17.5357 −0.766052
\(525\) 1.34292 0.0586100
\(526\) −18.9341 −0.825565
\(527\) 3.02142 0.131615
\(528\) 0 0
\(529\) 6.78911 0.295179
\(530\) −1.40604 −0.0610745
\(531\) −2.78090 −0.120681
\(532\) 1.56877 0.0680149
\(533\) 14.9980 0.649634
\(534\) 2.94538 0.127459
\(535\) −15.4232 −0.666803
\(536\) 1.60636 0.0693842
\(537\) −27.5064 −1.18699
\(538\) −12.9639 −0.558913
\(539\) 0 0
\(540\) 5.63565 0.242520
\(541\) 38.6634 1.66227 0.831136 0.556070i \(-0.187691\pi\)
0.831136 + 0.556070i \(0.187691\pi\)
\(542\) 23.5085 1.00978
\(543\) 10.7592 0.461720
\(544\) −2.63565 −0.113003
\(545\) −8.49656 −0.363953
\(546\) 5.79011 0.247794
\(547\) 6.20768 0.265421 0.132711 0.991155i \(-0.457632\pi\)
0.132711 + 0.991155i \(0.457632\pi\)
\(548\) 9.12927 0.389983
\(549\) −6.27459 −0.267793
\(550\) 0 0
\(551\) 4.45406 0.189749
\(552\) 7.32959 0.311968
\(553\) 9.65408 0.410533
\(554\) 2.44560 0.103904
\(555\) 1.12698 0.0478376
\(556\) −0.657844 −0.0278988
\(557\) 36.9739 1.56663 0.783317 0.621623i \(-0.213526\pi\)
0.783317 + 0.621623i \(0.213526\pi\)
\(558\) 1.37169 0.0580684
\(559\) −8.66950 −0.366681
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) −18.0116 −0.759776
\(563\) −26.0483 −1.09780 −0.548901 0.835887i \(-0.684954\pi\)
−0.548901 + 0.835887i \(0.684954\pi\)
\(564\) 11.2731 0.474681
\(565\) 2.72299 0.114557
\(566\) −9.78930 −0.411475
\(567\) 3.97858 0.167085
\(568\) 13.8057 0.579276
\(569\) 18.6278 0.780920 0.390460 0.920620i \(-0.372316\pi\)
0.390460 + 0.920620i \(0.372316\pi\)
\(570\) −2.10674 −0.0882417
\(571\) −34.4156 −1.44025 −0.720123 0.693846i \(-0.755915\pi\)
−0.720123 + 0.693846i \(0.755915\pi\)
\(572\) 0 0
\(573\) −10.3724 −0.433311
\(574\) −3.47854 −0.145191
\(575\) 5.45794 0.227612
\(576\) −1.19656 −0.0498566
\(577\) 24.5630 1.02257 0.511285 0.859411i \(-0.329170\pi\)
0.511285 + 0.859411i \(0.329170\pi\)
\(578\) 10.0533 0.418163
\(579\) −22.0045 −0.914474
\(580\) −2.83920 −0.117891
\(581\) −2.51880 −0.104498
\(582\) −10.1575 −0.421042
\(583\) 0 0
\(584\) −1.14830 −0.0475169
\(585\) 5.15905 0.213300
\(586\) −8.44836 −0.348999
\(587\) 18.3415 0.757037 0.378518 0.925594i \(-0.376434\pi\)
0.378518 + 0.925594i \(0.376434\pi\)
\(588\) −1.34292 −0.0553812
\(589\) −1.79839 −0.0741013
\(590\) −2.32408 −0.0956809
\(591\) 7.41254 0.304911
\(592\) −0.839198 −0.0344908
\(593\) 10.9987 0.451664 0.225832 0.974166i \(-0.427490\pi\)
0.225832 + 0.974166i \(0.427490\pi\)
\(594\) 0 0
\(595\) −2.63565 −0.108051
\(596\) 20.5982 0.843737
\(597\) −5.74023 −0.234932
\(598\) 23.5323 0.962308
\(599\) 4.76034 0.194502 0.0972511 0.995260i \(-0.468995\pi\)
0.0972511 + 0.995260i \(0.468995\pi\)
\(600\) 1.34292 0.0548246
\(601\) 16.5137 0.673608 0.336804 0.941575i \(-0.390654\pi\)
0.336804 + 0.941575i \(0.390654\pi\)
\(602\) 2.01075 0.0819521
\(603\) 1.92210 0.0782741
\(604\) 4.29219 0.174647
\(605\) 0 0
\(606\) −23.6958 −0.962576
\(607\) −3.14655 −0.127714 −0.0638572 0.997959i \(-0.520340\pi\)
−0.0638572 + 0.997959i \(0.520340\pi\)
\(608\) 1.56877 0.0636222
\(609\) −3.81282 −0.154503
\(610\) −5.24387 −0.212318
\(611\) 36.1932 1.46422
\(612\) −3.15371 −0.127481
\(613\) 45.9924 1.85761 0.928807 0.370564i \(-0.120836\pi\)
0.928807 + 0.370564i \(0.120836\pi\)
\(614\) −9.34689 −0.377210
\(615\) 4.67141 0.188369
\(616\) 0 0
\(617\) 45.5056 1.83198 0.915992 0.401196i \(-0.131405\pi\)
0.915992 + 0.401196i \(0.131405\pi\)
\(618\) 13.6345 0.548459
\(619\) −22.5870 −0.907849 −0.453925 0.891040i \(-0.649976\pi\)
−0.453925 + 0.891040i \(0.649976\pi\)
\(620\) 1.14637 0.0460391
\(621\) 30.7591 1.23432
\(622\) 27.6729 1.10958
\(623\) −2.19326 −0.0878710
\(624\) 5.79011 0.231790
\(625\) 1.00000 0.0400000
\(626\) −5.34524 −0.213639
\(627\) 0 0
\(628\) 10.9039 0.435113
\(629\) −2.21184 −0.0881916
\(630\) −1.19656 −0.0476720
\(631\) 14.8009 0.589213 0.294606 0.955619i \(-0.404811\pi\)
0.294606 + 0.955619i \(0.404811\pi\)
\(632\) 9.65408 0.384019
\(633\) −26.3356 −1.04675
\(634\) −7.13917 −0.283533
\(635\) 9.21928 0.365856
\(636\) −1.88820 −0.0748721
\(637\) −4.31157 −0.170831
\(638\) 0 0
\(639\) 16.5194 0.653496
\(640\) −1.00000 −0.0395285
\(641\) −34.5333 −1.36398 −0.681992 0.731360i \(-0.738886\pi\)
−0.681992 + 0.731360i \(0.738886\pi\)
\(642\) −20.7122 −0.817444
\(643\) −16.2144 −0.639434 −0.319717 0.947513i \(-0.603588\pi\)
−0.319717 + 0.947513i \(0.603588\pi\)
\(644\) −5.45794 −0.215073
\(645\) −2.70028 −0.106324
\(646\) 4.13474 0.162679
\(647\) −43.3962 −1.70608 −0.853041 0.521844i \(-0.825244\pi\)
−0.853041 + 0.521844i \(0.825244\pi\)
\(648\) 3.97858 0.156293
\(649\) 0 0
\(650\) 4.31157 0.169114
\(651\) 1.53948 0.0603370
\(652\) 12.3525 0.483763
\(653\) 7.75135 0.303334 0.151667 0.988432i \(-0.451536\pi\)
0.151667 + 0.988432i \(0.451536\pi\)
\(654\) −11.4102 −0.446175
\(655\) −17.5357 −0.685178
\(656\) −3.47854 −0.135814
\(657\) −1.37400 −0.0536050
\(658\) −8.39442 −0.327248
\(659\) −6.80255 −0.264990 −0.132495 0.991184i \(-0.542299\pi\)
−0.132495 + 0.991184i \(0.542299\pi\)
\(660\) 0 0
\(661\) −17.3537 −0.674980 −0.337490 0.941329i \(-0.609578\pi\)
−0.337490 + 0.941329i \(0.609578\pi\)
\(662\) −5.83207 −0.226670
\(663\) 15.2607 0.592678
\(664\) −2.51880 −0.0977486
\(665\) 1.56877 0.0608344
\(666\) −1.00415 −0.0389100
\(667\) −15.4962 −0.600014
\(668\) 6.93334 0.268259
\(669\) −5.39779 −0.208690
\(670\) 1.60636 0.0620592
\(671\) 0 0
\(672\) −1.34292 −0.0518044
\(673\) 47.8170 1.84321 0.921605 0.388130i \(-0.126879\pi\)
0.921605 + 0.388130i \(0.126879\pi\)
\(674\) 22.2848 0.858377
\(675\) 5.63565 0.216916
\(676\) 5.58967 0.214987
\(677\) 7.12176 0.273711 0.136856 0.990591i \(-0.456300\pi\)
0.136856 + 0.990591i \(0.456300\pi\)
\(678\) 3.65677 0.140437
\(679\) 7.56372 0.290269
\(680\) −2.63565 −0.101073
\(681\) 27.5013 1.05385
\(682\) 0 0
\(683\) 17.8302 0.682252 0.341126 0.940018i \(-0.389192\pi\)
0.341126 + 0.940018i \(0.389192\pi\)
\(684\) 1.87713 0.0717738
\(685\) 9.12927 0.348812
\(686\) 1.00000 0.0381802
\(687\) −11.7489 −0.448247
\(688\) 2.01075 0.0766591
\(689\) −6.06225 −0.230953
\(690\) 7.32959 0.279033
\(691\) −15.7399 −0.598772 −0.299386 0.954132i \(-0.596782\pi\)
−0.299386 + 0.954132i \(0.596782\pi\)
\(692\) 11.5843 0.440370
\(693\) 0 0
\(694\) 16.6253 0.631089
\(695\) −0.657844 −0.0249535
\(696\) −3.81282 −0.144525
\(697\) −9.16822 −0.347271
\(698\) 3.23934 0.122611
\(699\) 18.9973 0.718542
\(700\) −1.00000 −0.0377964
\(701\) 19.1512 0.723329 0.361665 0.932308i \(-0.382209\pi\)
0.361665 + 0.932308i \(0.382209\pi\)
\(702\) 24.2985 0.917089
\(703\) 1.31651 0.0496532
\(704\) 0 0
\(705\) 11.2731 0.424568
\(706\) 24.6580 0.928014
\(707\) 17.6449 0.663606
\(708\) −3.12106 −0.117297
\(709\) 6.08007 0.228342 0.114171 0.993461i \(-0.463579\pi\)
0.114171 + 0.993461i \(0.463579\pi\)
\(710\) 13.8057 0.518120
\(711\) 11.5517 0.433221
\(712\) −2.19326 −0.0821958
\(713\) 6.25679 0.234319
\(714\) −3.53948 −0.132462
\(715\) 0 0
\(716\) 20.4825 0.765466
\(717\) 2.84880 0.106390
\(718\) 20.7493 0.774358
\(719\) 27.3905 1.02149 0.510746 0.859732i \(-0.329369\pi\)
0.510746 + 0.859732i \(0.329369\pi\)
\(720\) −1.19656 −0.0445931
\(721\) −10.1528 −0.378111
\(722\) 16.5390 0.615516
\(723\) 23.4148 0.870805
\(724\) −8.01175 −0.297754
\(725\) −2.83920 −0.105445
\(726\) 0 0
\(727\) 28.3641 1.05197 0.525984 0.850495i \(-0.323697\pi\)
0.525984 + 0.850495i \(0.323697\pi\)
\(728\) −4.31157 −0.159798
\(729\) 27.4653 1.01724
\(730\) −1.14830 −0.0425004
\(731\) 5.29964 0.196014
\(732\) −7.04211 −0.260284
\(733\) 48.3933 1.78745 0.893724 0.448618i \(-0.148084\pi\)
0.893724 + 0.448618i \(0.148084\pi\)
\(734\) −2.12160 −0.0783096
\(735\) −1.34292 −0.0495345
\(736\) −5.45794 −0.201182
\(737\) 0 0
\(738\) −4.16227 −0.153215
\(739\) −6.07467 −0.223460 −0.111730 0.993739i \(-0.535639\pi\)
−0.111730 + 0.993739i \(0.535639\pi\)
\(740\) −0.839198 −0.0308495
\(741\) −9.08337 −0.333686
\(742\) 1.40604 0.0516173
\(743\) −32.1862 −1.18080 −0.590398 0.807112i \(-0.701029\pi\)
−0.590398 + 0.807112i \(0.701029\pi\)
\(744\) 1.53948 0.0564401
\(745\) 20.5982 0.754661
\(746\) −7.19996 −0.263609
\(747\) −3.01389 −0.110273
\(748\) 0 0
\(749\) 15.4232 0.563551
\(750\) 1.34292 0.0490366
\(751\) −24.5881 −0.897234 −0.448617 0.893724i \(-0.648083\pi\)
−0.448617 + 0.893724i \(0.648083\pi\)
\(752\) −8.39442 −0.306113
\(753\) −1.25810 −0.0458479
\(754\) −12.2414 −0.445806
\(755\) 4.29219 0.156209
\(756\) −5.63565 −0.204967
\(757\) −25.5181 −0.927470 −0.463735 0.885974i \(-0.653491\pi\)
−0.463735 + 0.885974i \(0.653491\pi\)
\(758\) 23.1300 0.840121
\(759\) 0 0
\(760\) 1.56877 0.0569054
\(761\) 13.0436 0.472830 0.236415 0.971652i \(-0.424028\pi\)
0.236415 + 0.971652i \(0.424028\pi\)
\(762\) 12.3808 0.448509
\(763\) 8.49656 0.307596
\(764\) 7.72371 0.279434
\(765\) −3.15371 −0.114023
\(766\) −31.4479 −1.13626
\(767\) −10.0204 −0.361817
\(768\) −1.34292 −0.0484586
\(769\) 48.0699 1.73344 0.866722 0.498792i \(-0.166223\pi\)
0.866722 + 0.498792i \(0.166223\pi\)
\(770\) 0 0
\(771\) −18.4306 −0.663762
\(772\) 16.3855 0.589727
\(773\) −40.5127 −1.45714 −0.728570 0.684972i \(-0.759815\pi\)
−0.728570 + 0.684972i \(0.759815\pi\)
\(774\) 2.40598 0.0864811
\(775\) 1.14637 0.0411787
\(776\) 7.56372 0.271522
\(777\) −1.12698 −0.0404301
\(778\) −17.5618 −0.629622
\(779\) 5.45704 0.195519
\(780\) 5.79011 0.207319
\(781\) 0 0
\(782\) −14.3852 −0.514415
\(783\) −16.0007 −0.571820
\(784\) 1.00000 0.0357143
\(785\) 10.9039 0.389177
\(786\) −23.5491 −0.839970
\(787\) −36.3703 −1.29646 −0.648231 0.761444i \(-0.724491\pi\)
−0.648231 + 0.761444i \(0.724491\pi\)
\(788\) −5.51971 −0.196631
\(789\) −25.4270 −0.905226
\(790\) 9.65408 0.343477
\(791\) −2.72299 −0.0968185
\(792\) 0 0
\(793\) −22.6093 −0.802881
\(794\) −32.7839 −1.16346
\(795\) −1.88820 −0.0669677
\(796\) 4.27443 0.151503
\(797\) 30.7299 1.08851 0.544254 0.838920i \(-0.316813\pi\)
0.544254 + 0.838920i \(0.316813\pi\)
\(798\) 2.10674 0.0745779
\(799\) −22.1248 −0.782719
\(800\) −1.00000 −0.0353553
\(801\) −2.62436 −0.0927272
\(802\) −9.25146 −0.326680
\(803\) 0 0
\(804\) 2.15722 0.0760793
\(805\) −5.45794 −0.192367
\(806\) 4.94264 0.174097
\(807\) −17.4095 −0.612843
\(808\) 17.6449 0.620747
\(809\) 45.6988 1.60668 0.803342 0.595517i \(-0.203053\pi\)
0.803342 + 0.595517i \(0.203053\pi\)
\(810\) 3.97858 0.139793
\(811\) 9.43169 0.331191 0.165596 0.986194i \(-0.447045\pi\)
0.165596 + 0.986194i \(0.447045\pi\)
\(812\) 2.83920 0.0996363
\(813\) 31.5701 1.10721
\(814\) 0 0
\(815\) 12.3525 0.432691
\(816\) −3.53948 −0.123907
\(817\) −3.15441 −0.110359
\(818\) −0.0174947 −0.000611688 0
\(819\) −5.15905 −0.180272
\(820\) −3.47854 −0.121476
\(821\) 12.2170 0.426376 0.213188 0.977011i \(-0.431615\pi\)
0.213188 + 0.977011i \(0.431615\pi\)
\(822\) 12.2599 0.427613
\(823\) 8.03161 0.279964 0.139982 0.990154i \(-0.455295\pi\)
0.139982 + 0.990154i \(0.455295\pi\)
\(824\) −10.1528 −0.353691
\(825\) 0 0
\(826\) 2.32408 0.0808651
\(827\) −9.90168 −0.344315 −0.172158 0.985069i \(-0.555074\pi\)
−0.172158 + 0.985069i \(0.555074\pi\)
\(828\) −6.53074 −0.226959
\(829\) −20.2243 −0.702420 −0.351210 0.936297i \(-0.614230\pi\)
−0.351210 + 0.936297i \(0.614230\pi\)
\(830\) −2.51880 −0.0874290
\(831\) 3.28426 0.113930
\(832\) −4.31157 −0.149477
\(833\) 2.63565 0.0913200
\(834\) −0.883434 −0.0305908
\(835\) 6.93334 0.239938
\(836\) 0 0
\(837\) 6.46052 0.223308
\(838\) −32.4579 −1.12124
\(839\) 35.7528 1.23432 0.617162 0.786836i \(-0.288282\pi\)
0.617162 + 0.786836i \(0.288282\pi\)
\(840\) −1.34292 −0.0463352
\(841\) −20.9390 −0.722033
\(842\) −9.15329 −0.315443
\(843\) −24.1883 −0.833088
\(844\) 19.6106 0.675026
\(845\) 5.58967 0.192291
\(846\) −10.0444 −0.345334
\(847\) 0 0
\(848\) 1.40604 0.0482836
\(849\) −13.1463 −0.451179
\(850\) −2.63565 −0.0904022
\(851\) −4.58029 −0.157010
\(852\) 18.5400 0.635171
\(853\) −23.0500 −0.789218 −0.394609 0.918849i \(-0.629120\pi\)
−0.394609 + 0.918849i \(0.629120\pi\)
\(854\) 5.24387 0.179442
\(855\) 1.87713 0.0641964
\(856\) 15.4232 0.527154
\(857\) −27.3702 −0.934948 −0.467474 0.884007i \(-0.654836\pi\)
−0.467474 + 0.884007i \(0.654836\pi\)
\(858\) 0 0
\(859\) 43.4968 1.48409 0.742045 0.670350i \(-0.233856\pi\)
0.742045 + 0.670350i \(0.233856\pi\)
\(860\) 2.01075 0.0685660
\(861\) −4.67141 −0.159201
\(862\) −26.0024 −0.885647
\(863\) −17.9594 −0.611345 −0.305672 0.952137i \(-0.598881\pi\)
−0.305672 + 0.952137i \(0.598881\pi\)
\(864\) −5.63565 −0.191729
\(865\) 11.5843 0.393879
\(866\) −23.6006 −0.801980
\(867\) 13.5008 0.458513
\(868\) −1.14637 −0.0389102
\(869\) 0 0
\(870\) −3.81282 −0.129267
\(871\) 6.92595 0.234677
\(872\) 8.49656 0.287730
\(873\) 9.05042 0.306310
\(874\) 8.56227 0.289623
\(875\) −1.00000 −0.0338062
\(876\) −1.54207 −0.0521019
\(877\) −32.8608 −1.10963 −0.554816 0.831973i \(-0.687211\pi\)
−0.554816 + 0.831973i \(0.687211\pi\)
\(878\) 31.7894 1.07284
\(879\) −11.3455 −0.382674
\(880\) 0 0
\(881\) −24.9270 −0.839812 −0.419906 0.907568i \(-0.637937\pi\)
−0.419906 + 0.907568i \(0.637937\pi\)
\(882\) 1.19656 0.0402902
\(883\) −18.1957 −0.612334 −0.306167 0.951978i \(-0.599047\pi\)
−0.306167 + 0.951978i \(0.599047\pi\)
\(884\) −11.3638 −0.382207
\(885\) −3.12106 −0.104913
\(886\) −36.1071 −1.21304
\(887\) 38.9219 1.30687 0.653434 0.756983i \(-0.273328\pi\)
0.653434 + 0.756983i \(0.273328\pi\)
\(888\) −1.12698 −0.0378189
\(889\) −9.21928 −0.309205
\(890\) −2.19326 −0.0735182
\(891\) 0 0
\(892\) 4.01943 0.134580
\(893\) 13.1689 0.440682
\(894\) 27.6619 0.925151
\(895\) 20.4825 0.684654
\(896\) 1.00000 0.0334077
\(897\) 31.6021 1.05516
\(898\) 4.52269 0.150924
\(899\) −3.25476 −0.108552
\(900\) −1.19656 −0.0398853
\(901\) 3.70583 0.123459
\(902\) 0 0
\(903\) 2.70028 0.0898598
\(904\) −2.72299 −0.0905655
\(905\) −8.01175 −0.266320
\(906\) 5.76408 0.191499
\(907\) −47.4377 −1.57514 −0.787572 0.616223i \(-0.788662\pi\)
−0.787572 + 0.616223i \(0.788662\pi\)
\(908\) −20.4787 −0.679610
\(909\) 21.1132 0.700280
\(910\) −4.31157 −0.142927
\(911\) −10.2118 −0.338333 −0.169167 0.985587i \(-0.554108\pi\)
−0.169167 + 0.985587i \(0.554108\pi\)
\(912\) 2.10674 0.0697612
\(913\) 0 0
\(914\) −15.1593 −0.501423
\(915\) −7.04211 −0.232805
\(916\) 8.74872 0.289066
\(917\) 17.5357 0.579081
\(918\) −14.8536 −0.490243
\(919\) 33.7533 1.11342 0.556710 0.830707i \(-0.312064\pi\)
0.556710 + 0.830707i \(0.312064\pi\)
\(920\) −5.45794 −0.179943
\(921\) −12.5522 −0.413608
\(922\) −27.6126 −0.909373
\(923\) 59.5244 1.95927
\(924\) 0 0
\(925\) −0.839198 −0.0275927
\(926\) −13.3557 −0.438895
\(927\) −12.1484 −0.399007
\(928\) 2.83920 0.0932012
\(929\) 41.2273 1.35262 0.676312 0.736615i \(-0.263577\pi\)
0.676312 + 0.736615i \(0.263577\pi\)
\(930\) 1.53948 0.0504816
\(931\) −1.56877 −0.0514145
\(932\) −14.1462 −0.463374
\(933\) 37.1626 1.21665
\(934\) −26.3287 −0.861500
\(935\) 0 0
\(936\) −5.15905 −0.168629
\(937\) 32.2808 1.05457 0.527283 0.849690i \(-0.323211\pi\)
0.527283 + 0.849690i \(0.323211\pi\)
\(938\) −1.60636 −0.0524496
\(939\) −7.17825 −0.234253
\(940\) −8.39442 −0.273796
\(941\) 47.3632 1.54400 0.771998 0.635625i \(-0.219257\pi\)
0.771998 + 0.635625i \(0.219257\pi\)
\(942\) 14.6431 0.477098
\(943\) −18.9857 −0.618258
\(944\) 2.32408 0.0756424
\(945\) −5.63565 −0.183328
\(946\) 0 0
\(947\) 25.4907 0.828335 0.414167 0.910201i \(-0.364073\pi\)
0.414167 + 0.910201i \(0.364073\pi\)
\(948\) 12.9647 0.421073
\(949\) −4.95097 −0.160715
\(950\) 1.56877 0.0508977
\(951\) −9.58736 −0.310891
\(952\) 2.63565 0.0854220
\(953\) 39.8135 1.28969 0.644843 0.764315i \(-0.276923\pi\)
0.644843 + 0.764315i \(0.276923\pi\)
\(954\) 1.68241 0.0544700
\(955\) 7.72371 0.249934
\(956\) −2.12134 −0.0686091
\(957\) 0 0
\(958\) 8.18258 0.264367
\(959\) −9.12927 −0.294800
\(960\) −1.34292 −0.0433427
\(961\) −29.6858 −0.957608
\(962\) −3.61826 −0.116657
\(963\) 18.4547 0.594695
\(964\) −17.4357 −0.561566
\(965\) 16.3855 0.527468
\(966\) −7.32959 −0.235826
\(967\) −29.9522 −0.963198 −0.481599 0.876392i \(-0.659944\pi\)
−0.481599 + 0.876392i \(0.659944\pi\)
\(968\) 0 0
\(969\) 5.55264 0.178377
\(970\) 7.56372 0.242856
\(971\) 8.45499 0.271333 0.135667 0.990755i \(-0.456682\pi\)
0.135667 + 0.990755i \(0.456682\pi\)
\(972\) −11.5640 −0.370917
\(973\) 0.657844 0.0210895
\(974\) 9.09993 0.291581
\(975\) 5.79011 0.185432
\(976\) 5.24387 0.167852
\(977\) −4.10946 −0.131473 −0.0657366 0.997837i \(-0.520940\pi\)
−0.0657366 + 0.997837i \(0.520940\pi\)
\(978\) 16.5885 0.530442
\(979\) 0 0
\(980\) 1.00000 0.0319438
\(981\) 10.1666 0.324595
\(982\) −3.80239 −0.121339
\(983\) 20.8447 0.664842 0.332421 0.943131i \(-0.392135\pi\)
0.332421 + 0.943131i \(0.392135\pi\)
\(984\) −4.67141 −0.148919
\(985\) −5.51971 −0.175873
\(986\) 7.48314 0.238312
\(987\) −11.2731 −0.358825
\(988\) 6.76388 0.215188
\(989\) 10.9746 0.348971
\(990\) 0 0
\(991\) 29.5690 0.939290 0.469645 0.882855i \(-0.344382\pi\)
0.469645 + 0.882855i \(0.344382\pi\)
\(992\) −1.14637 −0.0363971
\(993\) −7.83202 −0.248542
\(994\) −13.8057 −0.437891
\(995\) 4.27443 0.135508
\(996\) −3.38256 −0.107181
\(997\) −57.0730 −1.80752 −0.903760 0.428040i \(-0.859204\pi\)
−0.903760 + 0.428040i \(0.859204\pi\)
\(998\) 22.9856 0.727596
\(999\) −4.72943 −0.149632
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 8470.2.a.cz.1.1 6
11.10 odd 2 8470.2.a.df.1.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8470.2.a.cz.1.1 6 1.1 even 1 trivial
8470.2.a.df.1.2 yes 6 11.10 odd 2