Properties

Label 8470.2.a.cj.1.3
Level $8470$
Weight $2$
Character 8470.1
Self dual yes
Analytic conductor $67.633$
Analytic rank $0$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.733.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 8\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.17819\) of defining polynomial
Character \(\chi\) \(=\) 8470.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.43366 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.43366 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.79005 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.43366 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.43366 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.79005 q^{9} -1.00000 q^{10} +3.43366 q^{12} +5.79005 q^{13} -1.00000 q^{14} +3.43366 q^{15} +1.00000 q^{16} -2.43366 q^{17} -8.79005 q^{18} -8.22372 q^{19} +1.00000 q^{20} +3.43366 q^{21} +0.566335 q^{23} -3.43366 q^{24} +1.00000 q^{25} -5.79005 q^{26} +19.8811 q^{27} +1.00000 q^{28} -2.00000 q^{29} -3.43366 q^{30} -9.22372 q^{31} -1.00000 q^{32} +2.43366 q^{34} +1.00000 q^{35} +8.79005 q^{36} +8.86733 q^{37} +8.22372 q^{38} +19.8811 q^{39} -1.00000 q^{40} +6.35639 q^{41} -3.43366 q^{42} -0.433665 q^{43} +8.79005 q^{45} -0.566335 q^{46} -5.22372 q^{47} +3.43366 q^{48} +1.00000 q^{49} -1.00000 q^{50} -8.35639 q^{51} +5.79005 q^{52} -5.30099 q^{53} -19.8811 q^{54} -1.00000 q^{56} -28.2375 q^{57} +2.00000 q^{58} +7.51094 q^{59} +3.43366 q^{60} -0.0772765 q^{61} +9.22372 q^{62} +8.79005 q^{63} +1.00000 q^{64} +5.79005 q^{65} +3.56634 q^{67} -2.43366 q^{68} +1.94461 q^{69} -1.00000 q^{70} +15.6574 q^{71} -8.79005 q^{72} +0.433665 q^{73} -8.86733 q^{74} +3.43366 q^{75} -8.22372 q^{76} -19.8811 q^{78} +10.2237 q^{79} +1.00000 q^{80} +41.8949 q^{81} -6.35639 q^{82} +1.43366 q^{83} +3.43366 q^{84} -2.43366 q^{85} +0.433665 q^{86} -6.86733 q^{87} +9.22372 q^{89} -8.79005 q^{90} +5.79005 q^{91} +0.566335 q^{92} -31.6712 q^{93} +5.22372 q^{94} -8.22372 q^{95} -3.43366 q^{96} -4.94461 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} + 2q^{3} + 3q^{4} + 3q^{5} - 2q^{6} + 3q^{7} - 3q^{8} + 13q^{9} + O(q^{10}) \) \( 3q - 3q^{2} + 2q^{3} + 3q^{4} + 3q^{5} - 2q^{6} + 3q^{7} - 3q^{8} + 13q^{9} - 3q^{10} + 2q^{12} + 4q^{13} - 3q^{14} + 2q^{15} + 3q^{16} + q^{17} - 13q^{18} - 3q^{19} + 3q^{20} + 2q^{21} + 10q^{23} - 2q^{24} + 3q^{25} - 4q^{26} + 8q^{27} + 3q^{28} - 6q^{29} - 2q^{30} - 6q^{31} - 3q^{32} - q^{34} + 3q^{35} + 13q^{36} + 10q^{37} + 3q^{38} + 8q^{39} - 3q^{40} + 14q^{41} - 2q^{42} + 7q^{43} + 13q^{45} - 10q^{46} + 6q^{47} + 2q^{48} + 3q^{49} - 3q^{50} - 20q^{51} + 4q^{52} + 9q^{53} - 8q^{54} - 3q^{56} - 28q^{57} + 6q^{58} + 11q^{59} + 2q^{60} + 3q^{61} + 6q^{62} + 13q^{63} + 3q^{64} + 4q^{65} + 19q^{67} + q^{68} - 14q^{69} - 3q^{70} + 17q^{71} - 13q^{72} - 7q^{73} - 10q^{74} + 2q^{75} - 3q^{76} - 8q^{78} + 9q^{79} + 3q^{80} + 39q^{81} - 14q^{82} - 4q^{83} + 2q^{84} + q^{85} - 7q^{86} - 4q^{87} + 6q^{89} - 13q^{90} + 4q^{91} + 10q^{92} - 30q^{93} - 6q^{94} - 3q^{95} - 2q^{96} + 5q^{97} - 3q^{98} + O(q^{100}) \)

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
\(3\) 3.43366 1.98243 0.991214 0.132271i \(-0.0422269\pi\)
0.991214 + 0.132271i \(0.0422269\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.43366 −1.40179
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 8.79005 2.93002
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 3.43366 0.991214
\(13\) 5.79005 1.60587 0.802936 0.596065i \(-0.203270\pi\)
0.802936 + 0.596065i \(0.203270\pi\)
\(14\) −1.00000 −0.267261
\(15\) 3.43366 0.886568
\(16\) 1.00000 0.250000
\(17\) −2.43366 −0.590250 −0.295125 0.955459i \(-0.595361\pi\)
−0.295125 + 0.955459i \(0.595361\pi\)
\(18\) −8.79005 −2.07184
\(19\) −8.22372 −1.88665 −0.943325 0.331870i \(-0.892320\pi\)
−0.943325 + 0.331870i \(0.892320\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.43366 0.749287
\(22\) 0 0
\(23\) 0.566335 0.118089 0.0590445 0.998255i \(-0.481195\pi\)
0.0590445 + 0.998255i \(0.481195\pi\)
\(24\) −3.43366 −0.700894
\(25\) 1.00000 0.200000
\(26\) −5.79005 −1.13552
\(27\) 19.8811 3.82612
\(28\) 1.00000 0.188982
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −3.43366 −0.626899
\(31\) −9.22372 −1.65663 −0.828314 0.560264i \(-0.810700\pi\)
−0.828314 + 0.560264i \(0.810700\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.43366 0.417370
\(35\) 1.00000 0.169031
\(36\) 8.79005 1.46501
\(37\) 8.86733 1.45778 0.728890 0.684631i \(-0.240037\pi\)
0.728890 + 0.684631i \(0.240037\pi\)
\(38\) 8.22372 1.33406
\(39\) 19.8811 3.18352
\(40\) −1.00000 −0.158114
\(41\) 6.35639 0.992701 0.496351 0.868122i \(-0.334673\pi\)
0.496351 + 0.868122i \(0.334673\pi\)
\(42\) −3.43366 −0.529826
\(43\) −0.433665 −0.0661332 −0.0330666 0.999453i \(-0.510527\pi\)
−0.0330666 + 0.999453i \(0.510527\pi\)
\(44\) 0 0
\(45\) 8.79005 1.31034
\(46\) −0.566335 −0.0835016
\(47\) −5.22372 −0.761957 −0.380979 0.924584i \(-0.624413\pi\)
−0.380979 + 0.924584i \(0.624413\pi\)
\(48\) 3.43366 0.495607
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) −8.35639 −1.17013
\(52\) 5.79005 0.802936
\(53\) −5.30099 −0.728148 −0.364074 0.931370i \(-0.618614\pi\)
−0.364074 + 0.931370i \(0.618614\pi\)
\(54\) −19.8811 −2.70547
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −28.2375 −3.74015
\(58\) 2.00000 0.262613
\(59\) 7.51094 0.977841 0.488921 0.872328i \(-0.337391\pi\)
0.488921 + 0.872328i \(0.337391\pi\)
\(60\) 3.43366 0.443284
\(61\) −0.0772765 −0.00989424 −0.00494712 0.999988i \(-0.501575\pi\)
−0.00494712 + 0.999988i \(0.501575\pi\)
\(62\) 9.22372 1.17141
\(63\) 8.79005 1.10744
\(64\) 1.00000 0.125000
\(65\) 5.79005 0.718168
\(66\) 0 0
\(67\) 3.56634 0.435697 0.217849 0.975983i \(-0.430096\pi\)
0.217849 + 0.975983i \(0.430096\pi\)
\(68\) −2.43366 −0.295125
\(69\) 1.94461 0.234103
\(70\) −1.00000 −0.119523
\(71\) 15.6574 1.85819 0.929095 0.369842i \(-0.120588\pi\)
0.929095 + 0.369842i \(0.120588\pi\)
\(72\) −8.79005 −1.03592
\(73\) 0.433665 0.0507566 0.0253783 0.999678i \(-0.491921\pi\)
0.0253783 + 0.999678i \(0.491921\pi\)
\(74\) −8.86733 −1.03081
\(75\) 3.43366 0.396485
\(76\) −8.22372 −0.943325
\(77\) 0 0
\(78\) −19.8811 −2.25109
\(79\) 10.2237 1.15026 0.575129 0.818063i \(-0.304952\pi\)
0.575129 + 0.818063i \(0.304952\pi\)
\(80\) 1.00000 0.111803
\(81\) 41.8949 4.65499
\(82\) −6.35639 −0.701946
\(83\) 1.43366 0.157365 0.0786826 0.996900i \(-0.474929\pi\)
0.0786826 + 0.996900i \(0.474929\pi\)
\(84\) 3.43366 0.374644
\(85\) −2.43366 −0.263968
\(86\) 0.433665 0.0467633
\(87\) −6.86733 −0.736255
\(88\) 0 0
\(89\) 9.22372 0.977712 0.488856 0.872364i \(-0.337414\pi\)
0.488856 + 0.872364i \(0.337414\pi\)
\(90\) −8.79005 −0.926553
\(91\) 5.79005 0.606962
\(92\) 0.566335 0.0590445
\(93\) −31.6712 −3.28415
\(94\) 5.22372 0.538785
\(95\) −8.22372 −0.843736
\(96\) −3.43366 −0.350447
\(97\) −4.94461 −0.502049 −0.251024 0.967981i \(-0.580767\pi\)
−0.251024 + 0.967981i \(0.580767\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 12.6574 1.25946 0.629728 0.776815i \(-0.283166\pi\)
0.629728 + 0.776815i \(0.283166\pi\)
\(102\) 8.35639 0.827406
\(103\) −4.01377 −0.395489 −0.197744 0.980254i \(-0.563362\pi\)
−0.197744 + 0.980254i \(0.563362\pi\)
\(104\) −5.79005 −0.567761
\(105\) 3.43366 0.335091
\(106\) 5.30099 0.514878
\(107\) 10.7901 1.04311 0.521557 0.853217i \(-0.325351\pi\)
0.521557 + 0.853217i \(0.325351\pi\)
\(108\) 19.8811 1.91306
\(109\) 17.9365 1.71800 0.859002 0.511972i \(-0.171085\pi\)
0.859002 + 0.511972i \(0.171085\pi\)
\(110\) 0 0
\(111\) 30.4474 2.88994
\(112\) 1.00000 0.0944911
\(113\) −8.50283 −0.799879 −0.399939 0.916542i \(-0.630969\pi\)
−0.399939 + 0.916542i \(0.630969\pi\)
\(114\) 28.2375 2.64468
\(115\) 0.566335 0.0528110
\(116\) −2.00000 −0.185695
\(117\) 50.8949 4.70523
\(118\) −7.51094 −0.691438
\(119\) −2.43366 −0.223094
\(120\) −3.43366 −0.313449
\(121\) 0 0
\(122\) 0.0772765 0.00699628
\(123\) 21.8257 1.96796
\(124\) −9.22372 −0.828314
\(125\) 1.00000 0.0894427
\(126\) −8.79005 −0.783080
\(127\) −9.27911 −0.823388 −0.411694 0.911322i \(-0.635063\pi\)
−0.411694 + 0.911322i \(0.635063\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.48906 −0.131104
\(130\) −5.79005 −0.507821
\(131\) 12.3010 1.07474 0.537371 0.843346i \(-0.319417\pi\)
0.537371 + 0.843346i \(0.319417\pi\)
\(132\) 0 0
\(133\) −8.22372 −0.713087
\(134\) −3.56634 −0.308084
\(135\) 19.8811 1.71109
\(136\) 2.43366 0.208685
\(137\) 15.3702 1.31316 0.656581 0.754256i \(-0.272002\pi\)
0.656581 + 0.754256i \(0.272002\pi\)
\(138\) −1.94461 −0.165536
\(139\) −9.09105 −0.771093 −0.385546 0.922689i \(-0.625987\pi\)
−0.385546 + 0.922689i \(0.625987\pi\)
\(140\) 1.00000 0.0845154
\(141\) −17.9365 −1.51053
\(142\) −15.6574 −1.31394
\(143\) 0 0
\(144\) 8.79005 0.732504
\(145\) −2.00000 −0.166091
\(146\) −0.433665 −0.0358903
\(147\) 3.43366 0.283204
\(148\) 8.86733 0.728890
\(149\) −6.44743 −0.528194 −0.264097 0.964496i \(-0.585074\pi\)
−0.264097 + 0.964496i \(0.585074\pi\)
\(150\) −3.43366 −0.280358
\(151\) −10.5663 −0.859876 −0.429938 0.902858i \(-0.641465\pi\)
−0.429938 + 0.902858i \(0.641465\pi\)
\(152\) 8.22372 0.667032
\(153\) −21.3920 −1.72944
\(154\) 0 0
\(155\) −9.22372 −0.740867
\(156\) 19.8811 1.59176
\(157\) 12.5028 0.997834 0.498917 0.866650i \(-0.333731\pi\)
0.498917 + 0.866650i \(0.333731\pi\)
\(158\) −10.2237 −0.813355
\(159\) −18.2018 −1.44350
\(160\) −1.00000 −0.0790569
\(161\) 0.566335 0.0446335
\(162\) −41.8949 −3.29157
\(163\) −14.5247 −1.13766 −0.568832 0.822454i \(-0.692604\pi\)
−0.568832 + 0.822454i \(0.692604\pi\)
\(164\) 6.35639 0.496351
\(165\) 0 0
\(166\) −1.43366 −0.111274
\(167\) 9.30099 0.719733 0.359866 0.933004i \(-0.382822\pi\)
0.359866 + 0.933004i \(0.382822\pi\)
\(168\) −3.43366 −0.264913
\(169\) 20.5247 1.57882
\(170\) 2.43366 0.186654
\(171\) −72.2869 −5.52792
\(172\) −0.433665 −0.0330666
\(173\) −7.58011 −0.576305 −0.288152 0.957585i \(-0.593041\pi\)
−0.288152 + 0.957585i \(0.593041\pi\)
\(174\) 6.86733 0.520611
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 25.7901 1.93850
\(178\) −9.22372 −0.691347
\(179\) −20.0910 −1.50168 −0.750838 0.660487i \(-0.770350\pi\)
−0.750838 + 0.660487i \(0.770350\pi\)
\(180\) 8.79005 0.655172
\(181\) −15.7128 −1.16792 −0.583961 0.811782i \(-0.698498\pi\)
−0.583961 + 0.811782i \(0.698498\pi\)
\(182\) −5.79005 −0.429187
\(183\) −0.265341 −0.0196146
\(184\) −0.566335 −0.0417508
\(185\) 8.86733 0.651939
\(186\) 31.6712 2.32224
\(187\) 0 0
\(188\) −5.22372 −0.380979
\(189\) 19.8811 1.44614
\(190\) 8.22372 0.596611
\(191\) −3.99189 −0.288843 −0.144421 0.989516i \(-0.546132\pi\)
−0.144421 + 0.989516i \(0.546132\pi\)
\(192\) 3.43366 0.247803
\(193\) −4.50283 −0.324121 −0.162060 0.986781i \(-0.551814\pi\)
−0.162060 + 0.986781i \(0.551814\pi\)
\(194\) 4.94461 0.355002
\(195\) 19.8811 1.42372
\(196\) 1.00000 0.0714286
\(197\) −10.5247 −0.749855 −0.374927 0.927054i \(-0.622332\pi\)
−0.374927 + 0.927054i \(0.622332\pi\)
\(198\) 0 0
\(199\) −11.4256 −0.809936 −0.404968 0.914331i \(-0.632717\pi\)
−0.404968 + 0.914331i \(0.632717\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.2456 0.863738
\(202\) −12.6574 −0.890570
\(203\) −2.00000 −0.140372
\(204\) −8.35639 −0.585064
\(205\) 6.35639 0.443949
\(206\) 4.01377 0.279653
\(207\) 4.97812 0.346003
\(208\) 5.79005 0.401468
\(209\) 0 0
\(210\) −3.43366 −0.236945
\(211\) −1.84545 −0.127046 −0.0635229 0.997980i \(-0.520234\pi\)
−0.0635229 + 0.997980i \(0.520234\pi\)
\(212\) −5.30099 −0.364074
\(213\) 53.7622 3.68373
\(214\) −10.7901 −0.737593
\(215\) −0.433665 −0.0295757
\(216\) −19.8811 −1.35274
\(217\) −9.22372 −0.626147
\(218\) −17.9365 −1.21481
\(219\) 1.48906 0.100621
\(220\) 0 0
\(221\) −14.0910 −0.947866
\(222\) −30.4474 −2.04350
\(223\) −13.1464 −0.880351 −0.440175 0.897912i \(-0.645084\pi\)
−0.440175 + 0.897912i \(0.645084\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 8.79005 0.586004
\(226\) 8.50283 0.565600
\(227\) 7.28722 0.483670 0.241835 0.970317i \(-0.422251\pi\)
0.241835 + 0.970317i \(0.422251\pi\)
\(228\) −28.2375 −1.87007
\(229\) −2.52471 −0.166838 −0.0834188 0.996515i \(-0.526584\pi\)
−0.0834188 + 0.996515i \(0.526584\pi\)
\(230\) −0.566335 −0.0373430
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −21.5247 −1.41013 −0.705065 0.709142i \(-0.749082\pi\)
−0.705065 + 0.709142i \(0.749082\pi\)
\(234\) −50.8949 −3.32710
\(235\) −5.22372 −0.340758
\(236\) 7.51094 0.488921
\(237\) 35.1048 2.28030
\(238\) 2.43366 0.157751
\(239\) −15.2791 −0.988324 −0.494162 0.869370i \(-0.664525\pi\)
−0.494162 + 0.869370i \(0.664525\pi\)
\(240\) 3.43366 0.221642
\(241\) 6.15455 0.396450 0.198225 0.980157i \(-0.436482\pi\)
0.198225 + 0.980157i \(0.436482\pi\)
\(242\) 0 0
\(243\) 84.2096 5.40205
\(244\) −0.0772765 −0.00494712
\(245\) 1.00000 0.0638877
\(246\) −21.8257 −1.39156
\(247\) −47.6158 −3.02972
\(248\) 9.22372 0.585707
\(249\) 4.92272 0.311965
\(250\) −1.00000 −0.0632456
\(251\) −2.79005 −0.176107 −0.0880533 0.996116i \(-0.528065\pi\)
−0.0880533 + 0.996116i \(0.528065\pi\)
\(252\) 8.79005 0.553721
\(253\) 0 0
\(254\) 9.27911 0.582223
\(255\) −8.35639 −0.523297
\(256\) 1.00000 0.0625000
\(257\) 3.72089 0.232103 0.116051 0.993243i \(-0.462976\pi\)
0.116051 + 0.993243i \(0.462976\pi\)
\(258\) 1.48906 0.0927048
\(259\) 8.86733 0.550989
\(260\) 5.79005 0.359084
\(261\) −17.5801 −1.08818
\(262\) −12.3010 −0.759958
\(263\) −21.8811 −1.34925 −0.674623 0.738162i \(-0.735694\pi\)
−0.674623 + 0.738162i \(0.735694\pi\)
\(264\) 0 0
\(265\) −5.30099 −0.325637
\(266\) 8.22372 0.504228
\(267\) 31.6712 1.93824
\(268\) 3.56634 0.217849
\(269\) −4.02188 −0.245218 −0.122609 0.992455i \(-0.539126\pi\)
−0.122609 + 0.992455i \(0.539126\pi\)
\(270\) −19.8811 −1.20993
\(271\) 18.6020 1.12999 0.564995 0.825094i \(-0.308878\pi\)
0.564995 + 0.825094i \(0.308878\pi\)
\(272\) −2.43366 −0.147563
\(273\) 19.8811 1.20326
\(274\) −15.3702 −0.928545
\(275\) 0 0
\(276\) 1.94461 0.117052
\(277\) −29.6712 −1.78277 −0.891383 0.453250i \(-0.850264\pi\)
−0.891383 + 0.453250i \(0.850264\pi\)
\(278\) 9.09105 0.545245
\(279\) −81.0770 −4.85395
\(280\) −1.00000 −0.0597614
\(281\) 18.3148 1.09257 0.546284 0.837600i \(-0.316042\pi\)
0.546284 + 0.837600i \(0.316042\pi\)
\(282\) 17.9365 1.06810
\(283\) −17.0138 −1.01136 −0.505682 0.862720i \(-0.668759\pi\)
−0.505682 + 0.862720i \(0.668759\pi\)
\(284\) 15.6574 0.929095
\(285\) −28.2375 −1.67264
\(286\) 0 0
\(287\) 6.35639 0.375206
\(288\) −8.79005 −0.517959
\(289\) −11.0773 −0.651604
\(290\) 2.00000 0.117444
\(291\) −16.9781 −0.995275
\(292\) 0.433665 0.0253783
\(293\) 22.9503 1.34077 0.670384 0.742014i \(-0.266129\pi\)
0.670384 + 0.742014i \(0.266129\pi\)
\(294\) −3.43366 −0.200255
\(295\) 7.51094 0.437304
\(296\) −8.86733 −0.515403
\(297\) 0 0
\(298\) 6.44743 0.373490
\(299\) 3.27911 0.189636
\(300\) 3.43366 0.198243
\(301\) −0.433665 −0.0249960
\(302\) 10.5663 0.608024
\(303\) 43.4612 2.49678
\(304\) −8.22372 −0.471663
\(305\) −0.0772765 −0.00442484
\(306\) 21.3920 1.22290
\(307\) −7.13267 −0.407083 −0.203542 0.979066i \(-0.565245\pi\)
−0.203542 + 0.979066i \(0.565245\pi\)
\(308\) 0 0
\(309\) −13.7819 −0.784027
\(310\) 9.22372 0.523872
\(311\) −18.2456 −1.03461 −0.517307 0.855800i \(-0.673065\pi\)
−0.517307 + 0.855800i \(0.673065\pi\)
\(312\) −19.8811 −1.12555
\(313\) −27.0219 −1.52737 −0.763684 0.645591i \(-0.776611\pi\)
−0.763684 + 0.645591i \(0.776611\pi\)
\(314\) −12.5028 −0.705575
\(315\) 8.79005 0.495263
\(316\) 10.2237 0.575129
\(317\) 8.01377 0.450098 0.225049 0.974347i \(-0.427746\pi\)
0.225049 + 0.974347i \(0.427746\pi\)
\(318\) 18.2018 1.02071
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 37.0494 2.06790
\(322\) −0.566335 −0.0315606
\(323\) 20.0138 1.11360
\(324\) 41.8949 2.32749
\(325\) 5.79005 0.321174
\(326\) 14.5247 0.804449
\(327\) 61.5879 3.40582
\(328\) −6.35639 −0.350973
\(329\) −5.22372 −0.287993
\(330\) 0 0
\(331\) −12.6493 −0.695267 −0.347633 0.937631i \(-0.613015\pi\)
−0.347633 + 0.937631i \(0.613015\pi\)
\(332\) 1.43366 0.0786826
\(333\) 77.9443 4.27132
\(334\) −9.30099 −0.508928
\(335\) 3.56634 0.194850
\(336\) 3.43366 0.187322
\(337\) 14.8119 0.806858 0.403429 0.915011i \(-0.367818\pi\)
0.403429 + 0.915011i \(0.367818\pi\)
\(338\) −20.5247 −1.11640
\(339\) −29.1959 −1.58570
\(340\) −2.43366 −0.131984
\(341\) 0 0
\(342\) 72.2869 3.90883
\(343\) 1.00000 0.0539949
\(344\) 0.433665 0.0233816
\(345\) 1.94461 0.104694
\(346\) 7.58011 0.407509
\(347\) 26.6793 1.43222 0.716109 0.697988i \(-0.245921\pi\)
0.716109 + 0.697988i \(0.245921\pi\)
\(348\) −6.86733 −0.368127
\(349\) −0.475289 −0.0254416 −0.0127208 0.999919i \(-0.504049\pi\)
−0.0127208 + 0.999919i \(0.504049\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 115.113 6.14426
\(352\) 0 0
\(353\) −10.0138 −0.532979 −0.266490 0.963838i \(-0.585864\pi\)
−0.266490 + 0.963838i \(0.585864\pi\)
\(354\) −25.7901 −1.37073
\(355\) 15.6574 0.831008
\(356\) 9.22372 0.488856
\(357\) −8.35639 −0.442267
\(358\) 20.0910 1.06184
\(359\) −7.47529 −0.394531 −0.197265 0.980350i \(-0.563206\pi\)
−0.197265 + 0.980350i \(0.563206\pi\)
\(360\) −8.79005 −0.463276
\(361\) 48.6295 2.55945
\(362\) 15.7128 0.825845
\(363\) 0 0
\(364\) 5.79005 0.303481
\(365\) 0.433665 0.0226990
\(366\) 0.265341 0.0138696
\(367\) 30.1683 1.57477 0.787387 0.616459i \(-0.211433\pi\)
0.787387 + 0.616459i \(0.211433\pi\)
\(368\) 0.566335 0.0295223
\(369\) 55.8730 2.90863
\(370\) −8.86733 −0.460990
\(371\) −5.30099 −0.275214
\(372\) −31.6712 −1.64207
\(373\) −13.2099 −0.683985 −0.341993 0.939703i \(-0.611102\pi\)
−0.341993 + 0.939703i \(0.611102\pi\)
\(374\) 0 0
\(375\) 3.43366 0.177314
\(376\) 5.22372 0.269393
\(377\) −11.5801 −0.596406
\(378\) −19.8811 −1.02257
\(379\) 19.1602 0.984194 0.492097 0.870540i \(-0.336231\pi\)
0.492097 + 0.870540i \(0.336231\pi\)
\(380\) −8.22372 −0.421868
\(381\) −31.8614 −1.63231
\(382\) 3.99189 0.204243
\(383\) 6.58822 0.336642 0.168321 0.985732i \(-0.446165\pi\)
0.168321 + 0.985732i \(0.446165\pi\)
\(384\) −3.43366 −0.175223
\(385\) 0 0
\(386\) 4.50283 0.229188
\(387\) −3.81193 −0.193772
\(388\) −4.94461 −0.251024
\(389\) −25.1129 −1.27328 −0.636638 0.771163i \(-0.719675\pi\)
−0.636638 + 0.771163i \(0.719675\pi\)
\(390\) −19.8811 −1.00672
\(391\) −1.37827 −0.0697021
\(392\) −1.00000 −0.0505076
\(393\) 42.2375 2.13060
\(394\) 10.5247 0.530227
\(395\) 10.2237 0.514411
\(396\) 0 0
\(397\) −11.5801 −0.581189 −0.290594 0.956846i \(-0.593853\pi\)
−0.290594 + 0.956846i \(0.593853\pi\)
\(398\) 11.4256 0.572711
\(399\) −28.2375 −1.41364
\(400\) 1.00000 0.0500000
\(401\) −31.7347 −1.58475 −0.792377 0.610032i \(-0.791156\pi\)
−0.792377 + 0.610032i \(0.791156\pi\)
\(402\) −12.2456 −0.610755
\(403\) −53.4058 −2.66033
\(404\) 12.6574 0.629728
\(405\) 41.8949 2.08177
\(406\) 2.00000 0.0992583
\(407\) 0 0
\(408\) 8.35639 0.413703
\(409\) −2.15455 −0.106536 −0.0532679 0.998580i \(-0.516964\pi\)
−0.0532679 + 0.998580i \(0.516964\pi\)
\(410\) −6.35639 −0.313920
\(411\) 52.7760 2.60325
\(412\) −4.01377 −0.197744
\(413\) 7.51094 0.369589
\(414\) −4.97812 −0.244661
\(415\) 1.43366 0.0703758
\(416\) −5.79005 −0.283881
\(417\) −31.2156 −1.52863
\(418\) 0 0
\(419\) −13.5385 −0.661398 −0.330699 0.943736i \(-0.607285\pi\)
−0.330699 + 0.943736i \(0.607285\pi\)
\(420\) 3.43366 0.167546
\(421\) −1.42555 −0.0694772 −0.0347386 0.999396i \(-0.511060\pi\)
−0.0347386 + 0.999396i \(0.511060\pi\)
\(422\) 1.84545 0.0898350
\(423\) −45.9168 −2.23255
\(424\) 5.30099 0.257439
\(425\) −2.43366 −0.118050
\(426\) −53.7622 −2.60479
\(427\) −0.0772765 −0.00373967
\(428\) 10.7901 0.521557
\(429\) 0 0
\(430\) 0.433665 0.0209132
\(431\) 30.1129 1.45049 0.725244 0.688492i \(-0.241727\pi\)
0.725244 + 0.688492i \(0.241727\pi\)
\(432\) 19.8811 0.956530
\(433\) 29.2513 1.40573 0.702863 0.711325i \(-0.251905\pi\)
0.702863 + 0.711325i \(0.251905\pi\)
\(434\) 9.22372 0.442753
\(435\) −6.86733 −0.329263
\(436\) 17.9365 0.859002
\(437\) −4.65738 −0.222793
\(438\) −1.48906 −0.0711500
\(439\) −33.0692 −1.57831 −0.789153 0.614197i \(-0.789480\pi\)
−0.789153 + 0.614197i \(0.789480\pi\)
\(440\) 0 0
\(441\) 8.79005 0.418574
\(442\) 14.0910 0.670243
\(443\) −28.1821 −1.33897 −0.669486 0.742825i \(-0.733486\pi\)
−0.669486 + 0.742825i \(0.733486\pi\)
\(444\) 30.4474 1.44497
\(445\) 9.22372 0.437246
\(446\) 13.1464 0.622502
\(447\) −22.1383 −1.04711
\(448\) 1.00000 0.0472456
\(449\) −0.734659 −0.0346707 −0.0173353 0.999850i \(-0.505518\pi\)
−0.0173353 + 0.999850i \(0.505518\pi\)
\(450\) −8.79005 −0.414367
\(451\) 0 0
\(452\) −8.50283 −0.399939
\(453\) −36.2813 −1.70464
\(454\) −7.28722 −0.342006
\(455\) 5.79005 0.271442
\(456\) 28.2375 1.32234
\(457\) −5.21561 −0.243976 −0.121988 0.992532i \(-0.538927\pi\)
−0.121988 + 0.992532i \(0.538927\pi\)
\(458\) 2.52471 0.117972
\(459\) −48.3839 −2.25837
\(460\) 0.566335 0.0264055
\(461\) 24.9446 1.16179 0.580893 0.813980i \(-0.302703\pi\)
0.580893 + 0.813980i \(0.302703\pi\)
\(462\) 0 0
\(463\) −15.6158 −0.725726 −0.362863 0.931843i \(-0.618201\pi\)
−0.362863 + 0.931843i \(0.618201\pi\)
\(464\) −2.00000 −0.0928477
\(465\) −31.6712 −1.46871
\(466\) 21.5247 0.997113
\(467\) −36.9030 −1.70767 −0.853833 0.520547i \(-0.825728\pi\)
−0.853833 + 0.520547i \(0.825728\pi\)
\(468\) 50.8949 2.35262
\(469\) 3.56634 0.164678
\(470\) 5.22372 0.240952
\(471\) 42.9305 1.97813
\(472\) −7.51094 −0.345719
\(473\) 0 0
\(474\) −35.1048 −1.61242
\(475\) −8.22372 −0.377330
\(476\) −2.43366 −0.111547
\(477\) −46.5960 −2.13349
\(478\) 15.2791 0.698850
\(479\) −16.0910 −0.735219 −0.367609 0.929980i \(-0.619824\pi\)
−0.367609 + 0.929980i \(0.619824\pi\)
\(480\) −3.43366 −0.156725
\(481\) 51.3423 2.34101
\(482\) −6.15455 −0.280332
\(483\) 1.94461 0.0884826
\(484\) 0 0
\(485\) −4.94461 −0.224523
\(486\) −84.2096 −3.81983
\(487\) −38.6376 −1.75084 −0.875419 0.483364i \(-0.839415\pi\)
−0.875419 + 0.483364i \(0.839415\pi\)
\(488\) 0.0772765 0.00349814
\(489\) −49.8730 −2.25533
\(490\) −1.00000 −0.0451754
\(491\) −39.5604 −1.78533 −0.892667 0.450717i \(-0.851169\pi\)
−0.892667 + 0.450717i \(0.851169\pi\)
\(492\) 21.8257 0.983979
\(493\) 4.86733 0.219213
\(494\) 47.6158 2.14233
\(495\) 0 0
\(496\) −9.22372 −0.414157
\(497\) 15.6574 0.702330
\(498\) −4.92272 −0.220593
\(499\) −42.4474 −1.90021 −0.950104 0.311933i \(-0.899024\pi\)
−0.950104 + 0.311933i \(0.899024\pi\)
\(500\) 1.00000 0.0447214
\(501\) 31.9365 1.42682
\(502\) 2.79005 0.124526
\(503\) 18.4337 0.821916 0.410958 0.911654i \(-0.365194\pi\)
0.410958 + 0.911654i \(0.365194\pi\)
\(504\) −8.79005 −0.391540
\(505\) 12.6574 0.563246
\(506\) 0 0
\(507\) 70.4750 3.12990
\(508\) −9.27911 −0.411694
\(509\) 27.2929 1.20974 0.604868 0.796326i \(-0.293226\pi\)
0.604868 + 0.796326i \(0.293226\pi\)
\(510\) 8.35639 0.370027
\(511\) 0.433665 0.0191842
\(512\) −1.00000 −0.0441942
\(513\) −163.497 −7.21855
\(514\) −3.72089 −0.164121
\(515\) −4.01377 −0.176868
\(516\) −1.48906 −0.0655522
\(517\) 0 0
\(518\) −8.86733 −0.389608
\(519\) −26.0275 −1.14248
\(520\) −5.79005 −0.253911
\(521\) 7.55257 0.330884 0.165442 0.986220i \(-0.447095\pi\)
0.165442 + 0.986220i \(0.447095\pi\)
\(522\) 17.5801 0.769460
\(523\) −33.9086 −1.48272 −0.741361 0.671107i \(-0.765819\pi\)
−0.741361 + 0.671107i \(0.765819\pi\)
\(524\) 12.3010 0.537371
\(525\) 3.43366 0.149857
\(526\) 21.8811 0.954061
\(527\) 22.4474 0.977826
\(528\) 0 0
\(529\) −22.6793 −0.986055
\(530\) 5.30099 0.230260
\(531\) 66.0216 2.86509
\(532\) −8.22372 −0.356543
\(533\) 36.8038 1.59415
\(534\) −31.6712 −1.37054
\(535\) 10.7901 0.466495
\(536\) −3.56634 −0.154042
\(537\) −68.9859 −2.97696
\(538\) 4.02188 0.173396
\(539\) 0 0
\(540\) 19.8811 0.855546
\(541\) 11.0219 0.473868 0.236934 0.971526i \(-0.423858\pi\)
0.236934 + 0.971526i \(0.423858\pi\)
\(542\) −18.6020 −0.799024
\(543\) −53.9524 −2.31532
\(544\) 2.43366 0.104343
\(545\) 17.9365 0.768315
\(546\) −19.8811 −0.850833
\(547\) −27.5663 −1.17865 −0.589326 0.807896i \(-0.700607\pi\)
−0.589326 + 0.807896i \(0.700607\pi\)
\(548\) 15.3702 0.656581
\(549\) −0.679264 −0.0289903
\(550\) 0 0
\(551\) 16.4474 0.700684
\(552\) −1.94461 −0.0827679
\(553\) 10.2237 0.434757
\(554\) 29.6712 1.26061
\(555\) 30.4474 1.29242
\(556\) −9.09105 −0.385546
\(557\) 16.5385 0.700758 0.350379 0.936608i \(-0.386053\pi\)
0.350379 + 0.936608i \(0.386053\pi\)
\(558\) 81.0770 3.43226
\(559\) −2.51094 −0.106201
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) −18.3148 −0.772562
\(563\) −22.5939 −0.952218 −0.476109 0.879386i \(-0.657953\pi\)
−0.476109 + 0.879386i \(0.657953\pi\)
\(564\) −17.9365 −0.755263
\(565\) −8.50283 −0.357717
\(566\) 17.0138 0.715142
\(567\) 41.8949 1.75942
\(568\) −15.6574 −0.656969
\(569\) 15.1383 0.634632 0.317316 0.948320i \(-0.397218\pi\)
0.317316 + 0.948320i \(0.397218\pi\)
\(570\) 28.2375 1.18274
\(571\) −10.2929 −0.430744 −0.215372 0.976532i \(-0.569096\pi\)
−0.215372 + 0.976532i \(0.569096\pi\)
\(572\) 0 0
\(573\) −13.7068 −0.572610
\(574\) −6.35639 −0.265311
\(575\) 0.566335 0.0236178
\(576\) 8.79005 0.366252
\(577\) −7.00811 −0.291752 −0.145876 0.989303i \(-0.546600\pi\)
−0.145876 + 0.989303i \(0.546600\pi\)
\(578\) 11.0773 0.460754
\(579\) −15.4612 −0.642546
\(580\) −2.00000 −0.0830455
\(581\) 1.43366 0.0594784
\(582\) 16.9781 0.703766
\(583\) 0 0
\(584\) −0.433665 −0.0179452
\(585\) 50.8949 2.10424
\(586\) −22.9503 −0.948067
\(587\) 26.1740 1.08032 0.540158 0.841564i \(-0.318365\pi\)
0.540158 + 0.841564i \(0.318365\pi\)
\(588\) 3.43366 0.141602
\(589\) 75.8532 3.12548
\(590\) −7.51094 −0.309221
\(591\) −36.1383 −1.48653
\(592\) 8.86733 0.364445
\(593\) 32.2156 1.32294 0.661468 0.749973i \(-0.269934\pi\)
0.661468 + 0.749973i \(0.269934\pi\)
\(594\) 0 0
\(595\) −2.43366 −0.0997705
\(596\) −6.44743 −0.264097
\(597\) −39.2315 −1.60564
\(598\) −3.27911 −0.134093
\(599\) 10.4891 0.428571 0.214286 0.976771i \(-0.431258\pi\)
0.214286 + 0.976771i \(0.431258\pi\)
\(600\) −3.43366 −0.140179
\(601\) 19.0692 0.777847 0.388924 0.921270i \(-0.372847\pi\)
0.388924 + 0.921270i \(0.372847\pi\)
\(602\) 0.433665 0.0176749
\(603\) 31.3483 1.27660
\(604\) −10.5663 −0.429938
\(605\) 0 0
\(606\) −43.4612 −1.76549
\(607\) 37.3758 1.51704 0.758519 0.651651i \(-0.225923\pi\)
0.758519 + 0.651651i \(0.225923\pi\)
\(608\) 8.22372 0.333516
\(609\) −6.86733 −0.278278
\(610\) 0.0772765 0.00312883
\(611\) −30.2456 −1.22361
\(612\) −21.3920 −0.864722
\(613\) −23.3285 −0.942231 −0.471115 0.882072i \(-0.656148\pi\)
−0.471115 + 0.882072i \(0.656148\pi\)
\(614\) 7.13267 0.287851
\(615\) 21.8257 0.880097
\(616\) 0 0
\(617\) 18.8949 0.760679 0.380339 0.924847i \(-0.375807\pi\)
0.380339 + 0.924847i \(0.375807\pi\)
\(618\) 13.7819 0.554391
\(619\) −32.1902 −1.29383 −0.646917 0.762561i \(-0.723942\pi\)
−0.646917 + 0.762561i \(0.723942\pi\)
\(620\) −9.22372 −0.370433
\(621\) 11.2594 0.451823
\(622\) 18.2456 0.731582
\(623\) 9.22372 0.369540
\(624\) 19.8811 0.795881
\(625\) 1.00000 0.0400000
\(626\) 27.0219 1.08001
\(627\) 0 0
\(628\) 12.5028 0.498917
\(629\) −21.5801 −0.860455
\(630\) −8.79005 −0.350204
\(631\) −11.8119 −0.470226 −0.235113 0.971968i \(-0.575546\pi\)
−0.235113 + 0.971968i \(0.575546\pi\)
\(632\) −10.2237 −0.406678
\(633\) −6.33665 −0.251859
\(634\) −8.01377 −0.318267
\(635\) −9.27911 −0.368230
\(636\) −18.2018 −0.721750
\(637\) 5.79005 0.229410
\(638\) 0 0
\(639\) 137.629 5.44453
\(640\) −1.00000 −0.0395285
\(641\) −25.7403 −1.01668 −0.508341 0.861156i \(-0.669741\pi\)
−0.508341 + 0.861156i \(0.669741\pi\)
\(642\) −37.0494 −1.46222
\(643\) 26.0438 1.02707 0.513533 0.858070i \(-0.328336\pi\)
0.513533 + 0.858070i \(0.328336\pi\)
\(644\) 0.566335 0.0223167
\(645\) −1.48906 −0.0586316
\(646\) −20.0138 −0.787431
\(647\) 3.11890 0.122617 0.0613083 0.998119i \(-0.480473\pi\)
0.0613083 + 0.998119i \(0.480473\pi\)
\(648\) −41.8949 −1.64579
\(649\) 0 0
\(650\) −5.79005 −0.227105
\(651\) −31.6712 −1.24129
\(652\) −14.5247 −0.568832
\(653\) −8.27911 −0.323987 −0.161993 0.986792i \(-0.551792\pi\)
−0.161993 + 0.986792i \(0.551792\pi\)
\(654\) −61.5879 −2.40828
\(655\) 12.3010 0.480640
\(656\) 6.35639 0.248175
\(657\) 3.81193 0.148718
\(658\) 5.22372 0.203642
\(659\) 13.9527 0.543521 0.271760 0.962365i \(-0.412394\pi\)
0.271760 + 0.962365i \(0.412394\pi\)
\(660\) 0 0
\(661\) −6.51905 −0.253562 −0.126781 0.991931i \(-0.540465\pi\)
−0.126781 + 0.991931i \(0.540465\pi\)
\(662\) 12.6493 0.491628
\(663\) −48.3839 −1.87908
\(664\) −1.43366 −0.0556370
\(665\) −8.22372 −0.318902
\(666\) −77.9443 −3.02028
\(667\) −1.13267 −0.0438572
\(668\) 9.30099 0.359866
\(669\) −45.1405 −1.74523
\(670\) −3.56634 −0.137780
\(671\) 0 0
\(672\) −3.43366 −0.132456
\(673\) −10.6574 −0.410812 −0.205406 0.978677i \(-0.565851\pi\)
−0.205406 + 0.978677i \(0.565851\pi\)
\(674\) −14.8119 −0.570534
\(675\) 19.8811 0.765224
\(676\) 20.5247 0.789412
\(677\) 37.4139 1.43793 0.718967 0.695044i \(-0.244615\pi\)
0.718967 + 0.695044i \(0.244615\pi\)
\(678\) 29.1959 1.12126
\(679\) −4.94461 −0.189757
\(680\) 2.43366 0.0933268
\(681\) 25.0219 0.958841
\(682\) 0 0
\(683\) −19.2099 −0.735048 −0.367524 0.930014i \(-0.619794\pi\)
−0.367524 + 0.930014i \(0.619794\pi\)
\(684\) −72.2869 −2.76396
\(685\) 15.3702 0.587264
\(686\) −1.00000 −0.0381802
\(687\) −8.66901 −0.330743
\(688\) −0.433665 −0.0165333
\(689\) −30.6930 −1.16931
\(690\) −1.94461 −0.0740299
\(691\) 14.1048 0.536573 0.268286 0.963339i \(-0.413543\pi\)
0.268286 + 0.963339i \(0.413543\pi\)
\(692\) −7.58011 −0.288152
\(693\) 0 0
\(694\) −26.6793 −1.01273
\(695\) −9.09105 −0.344843
\(696\) 6.86733 0.260305
\(697\) −15.4693 −0.585942
\(698\) 0.475289 0.0179899
\(699\) −73.9086 −2.79548
\(700\) 1.00000 0.0377964
\(701\) 2.77628 0.104859 0.0524294 0.998625i \(-0.483304\pi\)
0.0524294 + 0.998625i \(0.483304\pi\)
\(702\) −115.113 −4.34465
\(703\) −72.9224 −2.75032
\(704\) 0 0
\(705\) −17.9365 −0.675527
\(706\) 10.0138 0.376873
\(707\) 12.6574 0.476030
\(708\) 25.7901 0.969250
\(709\) −1.17644 −0.0441819 −0.0220910 0.999756i \(-0.507032\pi\)
−0.0220910 + 0.999756i \(0.507032\pi\)
\(710\) −15.6574 −0.587611
\(711\) 89.8670 3.37028
\(712\) −9.22372 −0.345673
\(713\) −5.22372 −0.195630
\(714\) 8.35639 0.312730
\(715\) 0 0
\(716\) −20.0910 −0.750838
\(717\) −52.4633 −1.95928
\(718\) 7.47529 0.278975
\(719\) 8.74032 0.325959 0.162979 0.986629i \(-0.447890\pi\)
0.162979 + 0.986629i \(0.447890\pi\)
\(720\) 8.79005 0.327586
\(721\) −4.01377 −0.149481
\(722\) −48.6295 −1.80980
\(723\) 21.1327 0.785932
\(724\) −15.7128 −0.583961
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) 29.0057 1.07576 0.537880 0.843021i \(-0.319225\pi\)
0.537880 + 0.843021i \(0.319225\pi\)
\(728\) −5.79005 −0.214594
\(729\) 163.463 6.05419
\(730\) −0.433665 −0.0160506
\(731\) 1.05539 0.0390352
\(732\) −0.265341 −0.00980730
\(733\) 14.7682 0.545475 0.272737 0.962089i \(-0.412071\pi\)
0.272737 + 0.962089i \(0.412071\pi\)
\(734\) −30.1683 −1.11353
\(735\) 3.43366 0.126653
\(736\) −0.566335 −0.0208754
\(737\) 0 0
\(738\) −55.8730 −2.05671
\(739\) −16.0910 −0.591919 −0.295959 0.955201i \(-0.595639\pi\)
−0.295959 + 0.955201i \(0.595639\pi\)
\(740\) 8.86733 0.325970
\(741\) −163.497 −6.00620
\(742\) 5.30099 0.194606
\(743\) 9.88921 0.362800 0.181400 0.983409i \(-0.441937\pi\)
0.181400 + 0.983409i \(0.441937\pi\)
\(744\) 31.6712 1.16112
\(745\) −6.44743 −0.236216
\(746\) 13.2099 0.483651
\(747\) 12.6020 0.461083
\(748\) 0 0
\(749\) 10.7901 0.394260
\(750\) −3.43366 −0.125380
\(751\) −32.4831 −1.18532 −0.592662 0.805451i \(-0.701923\pi\)
−0.592662 + 0.805451i \(0.701923\pi\)
\(752\) −5.22372 −0.190489
\(753\) −9.58011 −0.349118
\(754\) 11.5801 0.421723
\(755\) −10.5663 −0.384548
\(756\) 19.8811 0.723069
\(757\) 32.7703 1.19106 0.595529 0.803334i \(-0.296943\pi\)
0.595529 + 0.803334i \(0.296943\pi\)
\(758\) −19.1602 −0.695930
\(759\) 0 0
\(760\) 8.22372 0.298306
\(761\) −9.40581 −0.340960 −0.170480 0.985361i \(-0.554532\pi\)
−0.170480 + 0.985361i \(0.554532\pi\)
\(762\) 31.8614 1.15422
\(763\) 17.9365 0.649345
\(764\) −3.99189 −0.144421
\(765\) −21.3920 −0.773431
\(766\) −6.58822 −0.238042
\(767\) 43.4887 1.57029
\(768\) 3.43366 0.123902
\(769\) −1.70712 −0.0615603 −0.0307801 0.999526i \(-0.509799\pi\)
−0.0307801 + 0.999526i \(0.509799\pi\)
\(770\) 0 0
\(771\) 12.7763 0.460127
\(772\) −4.50283 −0.162060
\(773\) −0.0991587 −0.00356649 −0.00178324 0.999998i \(-0.500568\pi\)
−0.00178324 + 0.999998i \(0.500568\pi\)
\(774\) 3.81193 0.137017
\(775\) −9.22372 −0.331326
\(776\) 4.94461 0.177501
\(777\) 30.4474 1.09230
\(778\) 25.1129 0.900342
\(779\) −52.2731 −1.87288
\(780\) 19.8811 0.711858
\(781\) 0 0
\(782\) 1.37827 0.0492868
\(783\) −39.7622 −1.42099
\(784\) 1.00000 0.0357143
\(785\) 12.5028 0.446245
\(786\) −42.2375 −1.50656
\(787\) 19.0057 0.677479 0.338739 0.940880i \(-0.390000\pi\)
0.338739 + 0.940880i \(0.390000\pi\)
\(788\) −10.5247 −0.374927
\(789\) −75.1324 −2.67478
\(790\) −10.2237 −0.363744
\(791\) −8.50283 −0.302326
\(792\) 0 0
\(793\) −0.447435 −0.0158889
\(794\) 11.5801 0.410963
\(795\) −18.2018 −0.645553
\(796\) −11.4256 −0.404968
\(797\) −3.52471 −0.124852 −0.0624258 0.998050i \(-0.519884\pi\)
−0.0624258 + 0.998050i \(0.519884\pi\)
\(798\) 28.2375 0.999596
\(799\) 12.7128 0.449746
\(800\) −1.00000 −0.0353553
\(801\) 81.0770 2.86471
\(802\) 31.7347 1.12059
\(803\) 0 0
\(804\) 12.2456 0.431869
\(805\) 0.566335 0.0199607
\(806\) 53.4058 1.88114
\(807\) −13.8098 −0.486128
\(808\) −12.6574 −0.445285
\(809\) −25.3483 −0.891198 −0.445599 0.895233i \(-0.647009\pi\)
−0.445599 + 0.895233i \(0.647009\pi\)
\(810\) −41.8949 −1.47204
\(811\) 10.7565 0.377713 0.188857 0.982005i \(-0.439522\pi\)
0.188857 + 0.982005i \(0.439522\pi\)
\(812\) −2.00000 −0.0701862
\(813\) 63.8730 2.24012
\(814\) 0 0
\(815\) −14.5247 −0.508778
\(816\) −8.35639 −0.292532
\(817\) 3.56634 0.124770
\(818\) 2.15455 0.0753322
\(819\) 50.8949 1.77841
\(820\) 6.35639 0.221975
\(821\) −51.0494 −1.78164 −0.890819 0.454359i \(-0.849868\pi\)
−0.890819 + 0.454359i \(0.849868\pi\)
\(822\) −52.7760 −1.84077
\(823\) −13.7622 −0.479720 −0.239860 0.970807i \(-0.577102\pi\)
−0.239860 + 0.970807i \(0.577102\pi\)
\(824\) 4.01377 0.139826
\(825\) 0 0
\(826\) −7.51094 −0.261339
\(827\) 18.5445 0.644854 0.322427 0.946594i \(-0.395501\pi\)
0.322427 + 0.946594i \(0.395501\pi\)
\(828\) 4.97812 0.173002
\(829\) 8.54659 0.296835 0.148418 0.988925i \(-0.452582\pi\)
0.148418 + 0.988925i \(0.452582\pi\)
\(830\) −1.43366 −0.0497632
\(831\) −101.881 −3.53421
\(832\) 5.79005 0.200734
\(833\) −2.43366 −0.0843215
\(834\) 31.2156 1.08091
\(835\) 9.30099 0.321874
\(836\) 0 0
\(837\) −183.378 −6.33846
\(838\) 13.5385 0.467679
\(839\) 4.04728 0.139728 0.0698639 0.997557i \(-0.477744\pi\)
0.0698639 + 0.997557i \(0.477744\pi\)
\(840\) −3.43366 −0.118473
\(841\) −25.0000 −0.862069
\(842\) 1.42555 0.0491278
\(843\) 62.8868 2.16593
\(844\) −1.84545 −0.0635229
\(845\) 20.5247 0.706072
\(846\) 45.9168 1.57865
\(847\) 0 0
\(848\) −5.30099 −0.182037
\(849\) −58.4196 −2.00495
\(850\) 2.43366 0.0834740
\(851\) 5.02188 0.172148
\(852\) 53.7622 1.84186
\(853\) −42.9778 −1.47153 −0.735766 0.677236i \(-0.763178\pi\)
−0.735766 + 0.677236i \(0.763178\pi\)
\(854\) 0.0772765 0.00264435
\(855\) −72.2869 −2.47216
\(856\) −10.7901 −0.368796
\(857\) −15.6239 −0.533701 −0.266851 0.963738i \(-0.585983\pi\)
−0.266851 + 0.963738i \(0.585983\pi\)
\(858\) 0 0
\(859\) −22.6355 −0.772313 −0.386157 0.922433i \(-0.626198\pi\)
−0.386157 + 0.922433i \(0.626198\pi\)
\(860\) −0.433665 −0.0147878
\(861\) 21.8257 0.743818
\(862\) −30.1129 −1.02565
\(863\) 31.6239 1.07649 0.538245 0.842789i \(-0.319088\pi\)
0.538245 + 0.842789i \(0.319088\pi\)
\(864\) −19.8811 −0.676369
\(865\) −7.58011 −0.257731
\(866\) −29.2513 −0.993998
\(867\) −38.0357 −1.29176
\(868\) −9.22372 −0.313073
\(869\) 0 0
\(870\) 6.86733 0.232824
\(871\) 20.6493 0.699674
\(872\) −17.9365 −0.607406
\(873\) −43.4633 −1.47101
\(874\) 4.65738 0.157538
\(875\) 1.00000 0.0338062
\(876\) 1.48906 0.0503106
\(877\) −42.8811 −1.44799 −0.723996 0.689804i \(-0.757697\pi\)
−0.723996 + 0.689804i \(0.757697\pi\)
\(878\) 33.0692 1.11603
\(879\) 78.8035 2.65798
\(880\) 0 0
\(881\) −29.9168 −1.00792 −0.503960 0.863727i \(-0.668124\pi\)
−0.503960 + 0.863727i \(0.668124\pi\)
\(882\) −8.79005 −0.295976
\(883\) 19.0992 0.642738 0.321369 0.946954i \(-0.395857\pi\)
0.321369 + 0.946954i \(0.395857\pi\)
\(884\) −14.0910 −0.473933
\(885\) 25.7901 0.866923
\(886\) 28.1821 0.946796
\(887\) −12.3839 −0.415812 −0.207906 0.978149i \(-0.566665\pi\)
−0.207906 + 0.978149i \(0.566665\pi\)
\(888\) −30.4474 −1.02175
\(889\) −9.27911 −0.311211
\(890\) −9.22372 −0.309180
\(891\) 0 0
\(892\) −13.1464 −0.440175
\(893\) 42.9584 1.43755
\(894\) 22.1383 0.740416
\(895\) −20.0910 −0.671570
\(896\) −1.00000 −0.0334077
\(897\) 11.2594 0.375939
\(898\) 0.734659 0.0245159
\(899\) 18.4474 0.615256
\(900\) 8.79005 0.293002
\(901\) 12.9008 0.429789
\(902\) 0 0
\(903\) −1.48906 −0.0495528
\(904\) 8.50283 0.282800
\(905\) −15.7128 −0.522310
\(906\) 36.2813 1.20536
\(907\) −45.2375 −1.50209 −0.751043 0.660253i \(-0.770449\pi\)
−0.751043 + 0.660253i \(0.770449\pi\)
\(908\) 7.28722 0.241835
\(909\) 111.259 3.69023
\(910\) −5.79005 −0.191938
\(911\) −8.78194 −0.290959 −0.145479 0.989361i \(-0.546472\pi\)
−0.145479 + 0.989361i \(0.546472\pi\)
\(912\) −28.2375 −0.935037
\(913\) 0 0
\(914\) 5.21561 0.172517
\(915\) −0.265341 −0.00877192
\(916\) −2.52471 −0.0834188
\(917\) 12.3010 0.406215
\(918\) 48.3839 1.59691
\(919\) 20.5858 0.679062 0.339531 0.940595i \(-0.389732\pi\)
0.339531 + 0.940595i \(0.389732\pi\)
\(920\) −0.566335 −0.0186715
\(921\) −24.4912 −0.807012
\(922\) −24.9446 −0.821507
\(923\) 90.6571 2.98401
\(924\) 0 0
\(925\) 8.86733 0.291556
\(926\) 15.6158 0.513166
\(927\) −35.2813 −1.15879
\(928\) 2.00000 0.0656532
\(929\) −56.8949 −1.86666 −0.933330 0.359019i \(-0.883111\pi\)
−0.933330 + 0.359019i \(0.883111\pi\)
\(930\) 31.6712 1.03854
\(931\) −8.22372 −0.269521
\(932\) −21.5247 −0.705065
\(933\) −62.6493 −2.05105
\(934\) 36.9030 1.20750
\(935\) 0 0
\(936\) −50.8949 −1.66355
\(937\) −9.69089 −0.316588 −0.158294 0.987392i \(-0.550599\pi\)
−0.158294 + 0.987392i \(0.550599\pi\)
\(938\) −3.56634 −0.116445
\(939\) −92.7841 −3.02789
\(940\) −5.22372 −0.170379
\(941\) −21.2537 −0.692851 −0.346426 0.938077i \(-0.612605\pi\)
−0.346426 + 0.938077i \(0.612605\pi\)
\(942\) −42.9305 −1.39875
\(943\) 3.59985 0.117227
\(944\) 7.51094 0.244460
\(945\) 19.8811 0.646732
\(946\) 0 0
\(947\) −9.20749 −0.299203 −0.149602 0.988746i \(-0.547799\pi\)
−0.149602 + 0.988746i \(0.547799\pi\)
\(948\) 35.1048 1.14015
\(949\) 2.51094 0.0815086
\(950\) 8.22372 0.266813
\(951\) 27.5166 0.892287
\(952\) 2.43366 0.0788755
\(953\) −15.7625 −0.510598 −0.255299 0.966862i \(-0.582174\pi\)
−0.255299 + 0.966862i \(0.582174\pi\)
\(954\) 46.5960 1.50860
\(955\) −3.99189 −0.129174
\(956\) −15.2791 −0.494162
\(957\) 0 0
\(958\) 16.0910 0.519878
\(959\) 15.3702 0.496328
\(960\) 3.43366 0.110821
\(961\) 54.0770 1.74442
\(962\) −51.3423 −1.65534
\(963\) 94.8451 3.05634
\(964\) 6.15455 0.198225
\(965\) −4.50283 −0.144951
\(966\) −1.94461 −0.0625667
\(967\) 0.558223 0.0179513 0.00897563 0.999960i \(-0.497143\pi\)
0.00897563 + 0.999960i \(0.497143\pi\)
\(968\) 0 0
\(969\) 68.7206 2.20762
\(970\) 4.94461 0.158762
\(971\) 8.67115 0.278271 0.139135 0.990273i \(-0.455568\pi\)
0.139135 + 0.990273i \(0.455568\pi\)
\(972\) 84.2096 2.70103
\(973\) −9.09105 −0.291446
\(974\) 38.6376 1.23803
\(975\) 19.8811 0.636705
\(976\) −0.0772765 −0.00247356
\(977\) 15.1210 0.483765 0.241882 0.970306i \(-0.422235\pi\)
0.241882 + 0.970306i \(0.422235\pi\)
\(978\) 49.8730 1.59476
\(979\) 0 0
\(980\) 1.00000 0.0319438
\(981\) 157.663 5.03378
\(982\) 39.5604 1.26242
\(983\) −14.8511 −0.473677 −0.236838 0.971549i \(-0.576111\pi\)
−0.236838 + 0.971549i \(0.576111\pi\)
\(984\) −21.8257 −0.695778
\(985\) −10.5247 −0.335345
\(986\) −4.86733 −0.155007
\(987\) −17.9365 −0.570925
\(988\) −47.6158 −1.51486
\(989\) −0.245600 −0.00780961
\(990\) 0 0
\(991\) −40.8257 −1.29687 −0.648436 0.761269i \(-0.724576\pi\)
−0.648436 + 0.761269i \(0.724576\pi\)
\(992\) 9.22372 0.292853
\(993\) −43.4334 −1.37832
\(994\) −15.6574 −0.496622
\(995\) −11.4256 −0.362214
\(996\) 4.92272 0.155982
\(997\) 0.629842 0.0199473 0.00997364 0.999950i \(-0.496825\pi\)
0.00997364 + 0.999950i \(0.496825\pi\)
\(998\) 42.4474 1.34365
\(999\) 176.292 5.57764
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.cj.1.3 3
11.10 odd 2 8470.2.a.cm.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8470.2.a.cj.1.3 3 1.1 even 1 trivial
8470.2.a.cm.1.3 yes 3 11.10 odd 2