Properties

Label 3549.2.a.bf.1.7
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.43930\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} -2.86638 q^{5} -1.43930 q^{6} -1.00000 q^{7} -2.77556 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.43930 q^{2} -1.00000 q^{3} +0.0715948 q^{4} -2.86638 q^{5} -1.43930 q^{6} -1.00000 q^{7} -2.77556 q^{8} +1.00000 q^{9} -4.12559 q^{10} -0.920607 q^{11} -0.0715948 q^{12} -1.43930 q^{14} +2.86638 q^{15} -4.13806 q^{16} +2.98468 q^{17} +1.43930 q^{18} -7.98255 q^{19} -0.205218 q^{20} +1.00000 q^{21} -1.32503 q^{22} -4.01590 q^{23} +2.77556 q^{24} +3.21612 q^{25} -1.00000 q^{27} -0.0715948 q^{28} +1.05024 q^{29} +4.12559 q^{30} -3.15556 q^{31} -0.404809 q^{32} +0.920607 q^{33} +4.29586 q^{34} +2.86638 q^{35} +0.0715948 q^{36} -1.61715 q^{37} -11.4893 q^{38} +7.95580 q^{40} -6.54652 q^{41} +1.43930 q^{42} +11.4441 q^{43} -0.0659107 q^{44} -2.86638 q^{45} -5.78010 q^{46} -4.63900 q^{47} +4.13806 q^{48} +1.00000 q^{49} +4.62897 q^{50} -2.98468 q^{51} +6.68041 q^{53} -1.43930 q^{54} +2.63881 q^{55} +2.77556 q^{56} +7.98255 q^{57} +1.51162 q^{58} +9.98868 q^{59} +0.205218 q^{60} -8.95997 q^{61} -4.54181 q^{62} -1.00000 q^{63} +7.69348 q^{64} +1.32503 q^{66} +11.2659 q^{67} +0.213687 q^{68} +4.01590 q^{69} +4.12559 q^{70} -9.09996 q^{71} -2.77556 q^{72} +7.52599 q^{73} -2.32758 q^{74} -3.21612 q^{75} -0.571509 q^{76} +0.920607 q^{77} +6.24310 q^{79} +11.8613 q^{80} +1.00000 q^{81} -9.42243 q^{82} +9.66531 q^{83} +0.0715948 q^{84} -8.55521 q^{85} +16.4715 q^{86} -1.05024 q^{87} +2.55520 q^{88} +6.52667 q^{89} -4.12559 q^{90} -0.287518 q^{92} +3.15556 q^{93} -6.67693 q^{94} +22.8810 q^{95} +0.404809 q^{96} -0.561935 q^{97} +1.43930 q^{98} -0.920607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.43930 1.01774 0.508871 0.860843i \(-0.330063\pi\)
0.508871 + 0.860843i \(0.330063\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.0715948 0.0357974
\(5\) −2.86638 −1.28188 −0.640941 0.767590i \(-0.721456\pi\)
−0.640941 + 0.767590i \(0.721456\pi\)
\(6\) −1.43930 −0.587593
\(7\) −1.00000 −0.377964
\(8\) −2.77556 −0.981309
\(9\) 1.00000 0.333333
\(10\) −4.12559 −1.30463
\(11\) −0.920607 −0.277573 −0.138787 0.990322i \(-0.544320\pi\)
−0.138787 + 0.990322i \(0.544320\pi\)
\(12\) −0.0715948 −0.0206676
\(13\) 0 0
\(14\) −1.43930 −0.384670
\(15\) 2.86638 0.740095
\(16\) −4.13806 −1.03452
\(17\) 2.98468 0.723890 0.361945 0.932199i \(-0.382113\pi\)
0.361945 + 0.932199i \(0.382113\pi\)
\(18\) 1.43930 0.339247
\(19\) −7.98255 −1.83132 −0.915661 0.401951i \(-0.868332\pi\)
−0.915661 + 0.401951i \(0.868332\pi\)
\(20\) −0.205218 −0.0458881
\(21\) 1.00000 0.218218
\(22\) −1.32503 −0.282498
\(23\) −4.01590 −0.837373 −0.418687 0.908131i \(-0.637509\pi\)
−0.418687 + 0.908131i \(0.637509\pi\)
\(24\) 2.77556 0.566559
\(25\) 3.21612 0.643223
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −0.0715948 −0.0135302
\(29\) 1.05024 0.195025 0.0975126 0.995234i \(-0.468911\pi\)
0.0975126 + 0.995234i \(0.468911\pi\)
\(30\) 4.12559 0.753226
\(31\) −3.15556 −0.566756 −0.283378 0.959008i \(-0.591455\pi\)
−0.283378 + 0.959008i \(0.591455\pi\)
\(32\) −0.404809 −0.0715608
\(33\) 0.920607 0.160257
\(34\) 4.29586 0.736733
\(35\) 2.86638 0.484506
\(36\) 0.0715948 0.0119325
\(37\) −1.61715 −0.265859 −0.132929 0.991126i \(-0.542438\pi\)
−0.132929 + 0.991126i \(0.542438\pi\)
\(38\) −11.4893 −1.86381
\(39\) 0 0
\(40\) 7.95580 1.25792
\(41\) −6.54652 −1.02239 −0.511197 0.859463i \(-0.670798\pi\)
−0.511197 + 0.859463i \(0.670798\pi\)
\(42\) 1.43930 0.222089
\(43\) 11.4441 1.74521 0.872604 0.488429i \(-0.162430\pi\)
0.872604 + 0.488429i \(0.162430\pi\)
\(44\) −0.0659107 −0.00993641
\(45\) −2.86638 −0.427294
\(46\) −5.78010 −0.852229
\(47\) −4.63900 −0.676667 −0.338334 0.941026i \(-0.609863\pi\)
−0.338334 + 0.941026i \(0.609863\pi\)
\(48\) 4.13806 0.597278
\(49\) 1.00000 0.142857
\(50\) 4.62897 0.654635
\(51\) −2.98468 −0.417938
\(52\) 0 0
\(53\) 6.68041 0.917625 0.458813 0.888533i \(-0.348275\pi\)
0.458813 + 0.888533i \(0.348275\pi\)
\(54\) −1.43930 −0.195864
\(55\) 2.63881 0.355817
\(56\) 2.77556 0.370900
\(57\) 7.98255 1.05731
\(58\) 1.51162 0.198485
\(59\) 9.98868 1.30042 0.650208 0.759756i \(-0.274682\pi\)
0.650208 + 0.759756i \(0.274682\pi\)
\(60\) 0.205218 0.0264935
\(61\) −8.95997 −1.14721 −0.573603 0.819133i \(-0.694455\pi\)
−0.573603 + 0.819133i \(0.694455\pi\)
\(62\) −4.54181 −0.576811
\(63\) −1.00000 −0.125988
\(64\) 7.69348 0.961686
\(65\) 0 0
\(66\) 1.32503 0.163100
\(67\) 11.2659 1.37635 0.688173 0.725547i \(-0.258413\pi\)
0.688173 + 0.725547i \(0.258413\pi\)
\(68\) 0.213687 0.0259134
\(69\) 4.01590 0.483458
\(70\) 4.12559 0.493102
\(71\) −9.09996 −1.07997 −0.539983 0.841676i \(-0.681569\pi\)
−0.539983 + 0.841676i \(0.681569\pi\)
\(72\) −2.77556 −0.327103
\(73\) 7.52599 0.880851 0.440425 0.897789i \(-0.354828\pi\)
0.440425 + 0.897789i \(0.354828\pi\)
\(74\) −2.32758 −0.270575
\(75\) −3.21612 −0.371365
\(76\) −0.571509 −0.0655566
\(77\) 0.920607 0.104913
\(78\) 0 0
\(79\) 6.24310 0.702404 0.351202 0.936300i \(-0.385773\pi\)
0.351202 + 0.936300i \(0.385773\pi\)
\(80\) 11.8613 1.32613
\(81\) 1.00000 0.111111
\(82\) −9.42243 −1.04053
\(83\) 9.66531 1.06091 0.530453 0.847714i \(-0.322022\pi\)
0.530453 + 0.847714i \(0.322022\pi\)
\(84\) 0.0715948 0.00781164
\(85\) −8.55521 −0.927943
\(86\) 16.4715 1.77617
\(87\) −1.05024 −0.112598
\(88\) 2.55520 0.272385
\(89\) 6.52667 0.691826 0.345913 0.938267i \(-0.387569\pi\)
0.345913 + 0.938267i \(0.387569\pi\)
\(90\) −4.12559 −0.434875
\(91\) 0 0
\(92\) −0.287518 −0.0299758
\(93\) 3.15556 0.327217
\(94\) −6.67693 −0.688672
\(95\) 22.8810 2.34754
\(96\) 0.404809 0.0413157
\(97\) −0.561935 −0.0570559 −0.0285279 0.999593i \(-0.509082\pi\)
−0.0285279 + 0.999593i \(0.509082\pi\)
\(98\) 1.43930 0.145392
\(99\) −0.920607 −0.0925245
\(100\) 0.230257 0.0230257
\(101\) −2.92723 −0.291271 −0.145635 0.989338i \(-0.546523\pi\)
−0.145635 + 0.989338i \(0.546523\pi\)
\(102\) −4.29586 −0.425353
\(103\) 15.0401 1.48195 0.740974 0.671533i \(-0.234364\pi\)
0.740974 + 0.671533i \(0.234364\pi\)
\(104\) 0 0
\(105\) −2.86638 −0.279730
\(106\) 9.61514 0.933905
\(107\) 12.1569 1.17525 0.587624 0.809134i \(-0.300064\pi\)
0.587624 + 0.809134i \(0.300064\pi\)
\(108\) −0.0715948 −0.00688922
\(109\) −10.3967 −0.995823 −0.497911 0.867228i \(-0.665899\pi\)
−0.497911 + 0.867228i \(0.665899\pi\)
\(110\) 3.79804 0.362129
\(111\) 1.61715 0.153494
\(112\) 4.13806 0.391010
\(113\) −15.2958 −1.43891 −0.719455 0.694540i \(-0.755608\pi\)
−0.719455 + 0.694540i \(0.755608\pi\)
\(114\) 11.4893 1.07607
\(115\) 11.5111 1.07341
\(116\) 0.0751920 0.00698140
\(117\) 0 0
\(118\) 14.3767 1.32349
\(119\) −2.98468 −0.273605
\(120\) −7.95580 −0.726262
\(121\) −10.1525 −0.922953
\(122\) −12.8961 −1.16756
\(123\) 6.54652 0.590280
\(124\) −0.225922 −0.0202884
\(125\) 5.11328 0.457346
\(126\) −1.43930 −0.128223
\(127\) −7.30215 −0.647961 −0.323981 0.946064i \(-0.605021\pi\)
−0.323981 + 0.946064i \(0.605021\pi\)
\(128\) 11.8829 1.05031
\(129\) −11.4441 −1.00760
\(130\) 0 0
\(131\) 20.5301 1.79372 0.896861 0.442313i \(-0.145842\pi\)
0.896861 + 0.442313i \(0.145842\pi\)
\(132\) 0.0659107 0.00573679
\(133\) 7.98255 0.692175
\(134\) 16.2150 1.40076
\(135\) 2.86638 0.246698
\(136\) −8.28415 −0.710360
\(137\) 14.8963 1.27268 0.636340 0.771409i \(-0.280448\pi\)
0.636340 + 0.771409i \(0.280448\pi\)
\(138\) 5.78010 0.492035
\(139\) −20.5500 −1.74303 −0.871514 0.490371i \(-0.836861\pi\)
−0.871514 + 0.490371i \(0.836861\pi\)
\(140\) 0.205218 0.0173441
\(141\) 4.63900 0.390674
\(142\) −13.0976 −1.09913
\(143\) 0 0
\(144\) −4.13806 −0.344839
\(145\) −3.01039 −0.250000
\(146\) 10.8322 0.896478
\(147\) −1.00000 −0.0824786
\(148\) −0.115780 −0.00951705
\(149\) −12.9977 −1.06482 −0.532408 0.846488i \(-0.678713\pi\)
−0.532408 + 0.846488i \(0.678713\pi\)
\(150\) −4.62897 −0.377954
\(151\) 18.6960 1.52146 0.760728 0.649071i \(-0.224842\pi\)
0.760728 + 0.649071i \(0.224842\pi\)
\(152\) 22.1561 1.79709
\(153\) 2.98468 0.241297
\(154\) 1.32503 0.106774
\(155\) 9.04503 0.726514
\(156\) 0 0
\(157\) −15.0687 −1.20262 −0.601308 0.799017i \(-0.705354\pi\)
−0.601308 + 0.799017i \(0.705354\pi\)
\(158\) 8.98572 0.714865
\(159\) −6.68041 −0.529791
\(160\) 1.16034 0.0917326
\(161\) 4.01590 0.316497
\(162\) 1.43930 0.113082
\(163\) 9.07260 0.710621 0.355311 0.934748i \(-0.384375\pi\)
0.355311 + 0.934748i \(0.384375\pi\)
\(164\) −0.468697 −0.0365991
\(165\) −2.63881 −0.205431
\(166\) 13.9113 1.07973
\(167\) 5.92599 0.458567 0.229283 0.973360i \(-0.426362\pi\)
0.229283 + 0.973360i \(0.426362\pi\)
\(168\) −2.77556 −0.214139
\(169\) 0 0
\(170\) −12.3135 −0.944406
\(171\) −7.98255 −0.610441
\(172\) 0.819338 0.0624739
\(173\) −5.39610 −0.410258 −0.205129 0.978735i \(-0.565761\pi\)
−0.205129 + 0.978735i \(0.565761\pi\)
\(174\) −1.51162 −0.114596
\(175\) −3.21612 −0.243116
\(176\) 3.80953 0.287154
\(177\) −9.98868 −0.750795
\(178\) 9.39387 0.704100
\(179\) 12.7671 0.954258 0.477129 0.878833i \(-0.341677\pi\)
0.477129 + 0.878833i \(0.341677\pi\)
\(180\) −0.205218 −0.0152960
\(181\) −3.96815 −0.294950 −0.147475 0.989066i \(-0.547115\pi\)
−0.147475 + 0.989066i \(0.547115\pi\)
\(182\) 0 0
\(183\) 8.95997 0.662340
\(184\) 11.1464 0.821722
\(185\) 4.63538 0.340800
\(186\) 4.54181 0.333022
\(187\) −2.74771 −0.200933
\(188\) −0.332128 −0.0242229
\(189\) 1.00000 0.0727393
\(190\) 32.9327 2.38919
\(191\) 21.9168 1.58585 0.792923 0.609322i \(-0.208558\pi\)
0.792923 + 0.609322i \(0.208558\pi\)
\(192\) −7.69348 −0.555229
\(193\) 10.2802 0.739983 0.369991 0.929035i \(-0.379361\pi\)
0.369991 + 0.929035i \(0.379361\pi\)
\(194\) −0.808795 −0.0580681
\(195\) 0 0
\(196\) 0.0715948 0.00511392
\(197\) −13.2140 −0.941458 −0.470729 0.882278i \(-0.656009\pi\)
−0.470729 + 0.882278i \(0.656009\pi\)
\(198\) −1.32503 −0.0941660
\(199\) −20.3660 −1.44371 −0.721855 0.692045i \(-0.756710\pi\)
−0.721855 + 0.692045i \(0.756710\pi\)
\(200\) −8.92653 −0.631201
\(201\) −11.2659 −0.794634
\(202\) −4.21318 −0.296438
\(203\) −1.05024 −0.0737126
\(204\) −0.213687 −0.0149611
\(205\) 18.7648 1.31059
\(206\) 21.6473 1.50824
\(207\) −4.01590 −0.279124
\(208\) 0 0
\(209\) 7.34879 0.508327
\(210\) −4.12559 −0.284693
\(211\) 3.82094 0.263044 0.131522 0.991313i \(-0.458014\pi\)
0.131522 + 0.991313i \(0.458014\pi\)
\(212\) 0.478283 0.0328486
\(213\) 9.09996 0.623519
\(214\) 17.4974 1.19610
\(215\) −32.8031 −2.23715
\(216\) 2.77556 0.188853
\(217\) 3.15556 0.214213
\(218\) −14.9640 −1.01349
\(219\) −7.52599 −0.508559
\(220\) 0.188925 0.0127373
\(221\) 0 0
\(222\) 2.32758 0.156217
\(223\) −26.9148 −1.80235 −0.901175 0.433456i \(-0.857294\pi\)
−0.901175 + 0.433456i \(0.857294\pi\)
\(224\) 0.404809 0.0270475
\(225\) 3.21612 0.214408
\(226\) −22.0153 −1.46444
\(227\) −27.2647 −1.80962 −0.904810 0.425814i \(-0.859988\pi\)
−0.904810 + 0.425814i \(0.859988\pi\)
\(228\) 0.571509 0.0378491
\(229\) 5.09112 0.336431 0.168215 0.985750i \(-0.446200\pi\)
0.168215 + 0.985750i \(0.446200\pi\)
\(230\) 16.5679 1.09246
\(231\) −0.920607 −0.0605715
\(232\) −2.91501 −0.191380
\(233\) 8.58247 0.562257 0.281128 0.959670i \(-0.409291\pi\)
0.281128 + 0.959670i \(0.409291\pi\)
\(234\) 0 0
\(235\) 13.2971 0.867408
\(236\) 0.715138 0.0465515
\(237\) −6.24310 −0.405533
\(238\) −4.29586 −0.278459
\(239\) 4.40895 0.285191 0.142596 0.989781i \(-0.454455\pi\)
0.142596 + 0.989781i \(0.454455\pi\)
\(240\) −11.8613 −0.765640
\(241\) −4.62930 −0.298199 −0.149100 0.988822i \(-0.547638\pi\)
−0.149100 + 0.988822i \(0.547638\pi\)
\(242\) −14.6125 −0.939327
\(243\) −1.00000 −0.0641500
\(244\) −0.641487 −0.0410670
\(245\) −2.86638 −0.183126
\(246\) 9.42243 0.600752
\(247\) 0 0
\(248\) 8.75845 0.556162
\(249\) −9.66531 −0.612514
\(250\) 7.35956 0.465460
\(251\) −16.4973 −1.04130 −0.520650 0.853770i \(-0.674310\pi\)
−0.520650 + 0.853770i \(0.674310\pi\)
\(252\) −0.0715948 −0.00451005
\(253\) 3.69707 0.232433
\(254\) −10.5100 −0.659457
\(255\) 8.55521 0.535748
\(256\) 1.71610 0.107256
\(257\) 15.8475 0.988540 0.494270 0.869308i \(-0.335435\pi\)
0.494270 + 0.869308i \(0.335435\pi\)
\(258\) −16.4715 −1.02547
\(259\) 1.61715 0.100485
\(260\) 0 0
\(261\) 1.05024 0.0650084
\(262\) 29.5490 1.82554
\(263\) 8.50599 0.524502 0.262251 0.965000i \(-0.415535\pi\)
0.262251 + 0.965000i \(0.415535\pi\)
\(264\) −2.55520 −0.157262
\(265\) −19.1486 −1.17629
\(266\) 11.4893 0.704455
\(267\) −6.52667 −0.399426
\(268\) 0.806579 0.0492696
\(269\) 2.14357 0.130696 0.0653479 0.997863i \(-0.479184\pi\)
0.0653479 + 0.997863i \(0.479184\pi\)
\(270\) 4.12559 0.251075
\(271\) −24.4875 −1.48751 −0.743754 0.668453i \(-0.766957\pi\)
−0.743754 + 0.668453i \(0.766957\pi\)
\(272\) −12.3508 −0.748876
\(273\) 0 0
\(274\) 21.4404 1.29526
\(275\) −2.96078 −0.178542
\(276\) 0.287518 0.0173065
\(277\) 19.4563 1.16902 0.584508 0.811388i \(-0.301288\pi\)
0.584508 + 0.811388i \(0.301288\pi\)
\(278\) −29.5777 −1.77395
\(279\) −3.15556 −0.188919
\(280\) −7.95580 −0.475450
\(281\) −15.2398 −0.909130 −0.454565 0.890714i \(-0.650205\pi\)
−0.454565 + 0.890714i \(0.650205\pi\)
\(282\) 6.67693 0.397605
\(283\) −9.39124 −0.558251 −0.279126 0.960255i \(-0.590045\pi\)
−0.279126 + 0.960255i \(0.590045\pi\)
\(284\) −0.651510 −0.0386600
\(285\) −22.8810 −1.35535
\(286\) 0 0
\(287\) 6.54652 0.386429
\(288\) −0.404809 −0.0238536
\(289\) −8.09171 −0.475983
\(290\) −4.33287 −0.254435
\(291\) 0.561935 0.0329412
\(292\) 0.538822 0.0315322
\(293\) −13.1364 −0.767436 −0.383718 0.923450i \(-0.625357\pi\)
−0.383718 + 0.923450i \(0.625357\pi\)
\(294\) −1.43930 −0.0839419
\(295\) −28.6313 −1.66698
\(296\) 4.48851 0.260889
\(297\) 0.920607 0.0534190
\(298\) −18.7077 −1.08371
\(299\) 0 0
\(300\) −0.230257 −0.0132939
\(301\) −11.4441 −0.659626
\(302\) 26.9092 1.54845
\(303\) 2.92723 0.168165
\(304\) 33.0323 1.89453
\(305\) 25.6826 1.47058
\(306\) 4.29586 0.245578
\(307\) 19.4366 1.10930 0.554652 0.832082i \(-0.312851\pi\)
0.554652 + 0.832082i \(0.312851\pi\)
\(308\) 0.0659107 0.00375561
\(309\) −15.0401 −0.855604
\(310\) 13.0185 0.739404
\(311\) 28.1906 1.59854 0.799270 0.600972i \(-0.205220\pi\)
0.799270 + 0.600972i \(0.205220\pi\)
\(312\) 0 0
\(313\) −13.3965 −0.757217 −0.378608 0.925557i \(-0.623597\pi\)
−0.378608 + 0.925557i \(0.623597\pi\)
\(314\) −21.6885 −1.22395
\(315\) 2.86638 0.161502
\(316\) 0.446974 0.0251442
\(317\) 27.5802 1.54906 0.774529 0.632539i \(-0.217987\pi\)
0.774529 + 0.632539i \(0.217987\pi\)
\(318\) −9.61514 −0.539191
\(319\) −0.966861 −0.0541338
\(320\) −22.0524 −1.23277
\(321\) −12.1569 −0.678529
\(322\) 5.78010 0.322112
\(323\) −23.8253 −1.32568
\(324\) 0.0715948 0.00397749
\(325\) 0 0
\(326\) 13.0582 0.723228
\(327\) 10.3967 0.574938
\(328\) 18.1703 1.00328
\(329\) 4.63900 0.255756
\(330\) −3.79804 −0.209075
\(331\) 19.8272 1.08980 0.544901 0.838500i \(-0.316567\pi\)
0.544901 + 0.838500i \(0.316567\pi\)
\(332\) 0.691986 0.0379777
\(333\) −1.61715 −0.0886195
\(334\) 8.52930 0.466703
\(335\) −32.2923 −1.76431
\(336\) −4.13806 −0.225750
\(337\) −5.24434 −0.285678 −0.142839 0.989746i \(-0.545623\pi\)
−0.142839 + 0.989746i \(0.545623\pi\)
\(338\) 0 0
\(339\) 15.2958 0.830754
\(340\) −0.612509 −0.0332179
\(341\) 2.90503 0.157316
\(342\) −11.4893 −0.621271
\(343\) −1.00000 −0.0539949
\(344\) −31.7638 −1.71259
\(345\) −11.5111 −0.619736
\(346\) −7.76662 −0.417536
\(347\) 9.84401 0.528454 0.264227 0.964460i \(-0.414883\pi\)
0.264227 + 0.964460i \(0.414883\pi\)
\(348\) −0.0751920 −0.00403071
\(349\) −16.2789 −0.871388 −0.435694 0.900095i \(-0.643497\pi\)
−0.435694 + 0.900095i \(0.643497\pi\)
\(350\) −4.62897 −0.247429
\(351\) 0 0
\(352\) 0.372670 0.0198634
\(353\) −17.0572 −0.907863 −0.453931 0.891037i \(-0.649979\pi\)
−0.453931 + 0.891037i \(0.649979\pi\)
\(354\) −14.3767 −0.764116
\(355\) 26.0839 1.38439
\(356\) 0.467276 0.0247656
\(357\) 2.98468 0.157966
\(358\) 18.3757 0.971188
\(359\) −36.7099 −1.93748 −0.968738 0.248085i \(-0.920199\pi\)
−0.968738 + 0.248085i \(0.920199\pi\)
\(360\) 7.95580 0.419308
\(361\) 44.7211 2.35374
\(362\) −5.71138 −0.300183
\(363\) 10.1525 0.532867
\(364\) 0 0
\(365\) −21.5723 −1.12915
\(366\) 12.8961 0.674091
\(367\) −9.74654 −0.508765 −0.254383 0.967104i \(-0.581872\pi\)
−0.254383 + 0.967104i \(0.581872\pi\)
\(368\) 16.6180 0.866276
\(369\) −6.54652 −0.340798
\(370\) 6.67171 0.346846
\(371\) −6.68041 −0.346830
\(372\) 0.225922 0.0117135
\(373\) 0.589925 0.0305452 0.0152726 0.999883i \(-0.495138\pi\)
0.0152726 + 0.999883i \(0.495138\pi\)
\(374\) −3.95480 −0.204498
\(375\) −5.11328 −0.264049
\(376\) 12.8758 0.664020
\(377\) 0 0
\(378\) 1.43930 0.0740298
\(379\) −3.62980 −0.186451 −0.0932253 0.995645i \(-0.529718\pi\)
−0.0932253 + 0.995645i \(0.529718\pi\)
\(380\) 1.63816 0.0840359
\(381\) 7.30215 0.374101
\(382\) 31.5450 1.61398
\(383\) 28.6977 1.46638 0.733191 0.680022i \(-0.238030\pi\)
0.733191 + 0.680022i \(0.238030\pi\)
\(384\) −11.8829 −0.606396
\(385\) −2.63881 −0.134486
\(386\) 14.7963 0.753111
\(387\) 11.4441 0.581736
\(388\) −0.0402316 −0.00204245
\(389\) −4.28777 −0.217398 −0.108699 0.994075i \(-0.534669\pi\)
−0.108699 + 0.994075i \(0.534669\pi\)
\(390\) 0 0
\(391\) −11.9862 −0.606166
\(392\) −2.77556 −0.140187
\(393\) −20.5301 −1.03561
\(394\) −19.0189 −0.958161
\(395\) −17.8951 −0.900399
\(396\) −0.0659107 −0.00331214
\(397\) −31.2556 −1.56868 −0.784338 0.620334i \(-0.786997\pi\)
−0.784338 + 0.620334i \(0.786997\pi\)
\(398\) −29.3129 −1.46932
\(399\) −7.98255 −0.399627
\(400\) −13.3085 −0.665425
\(401\) 24.4307 1.22001 0.610006 0.792397i \(-0.291167\pi\)
0.610006 + 0.792397i \(0.291167\pi\)
\(402\) −16.2150 −0.808732
\(403\) 0 0
\(404\) −0.209575 −0.0104267
\(405\) −2.86638 −0.142431
\(406\) −1.51162 −0.0750204
\(407\) 1.48876 0.0737953
\(408\) 8.28415 0.410127
\(409\) −17.3704 −0.858909 −0.429454 0.903089i \(-0.641294\pi\)
−0.429454 + 0.903089i \(0.641294\pi\)
\(410\) 27.0082 1.33384
\(411\) −14.8963 −0.734782
\(412\) 1.07680 0.0530499
\(413\) −9.98868 −0.491511
\(414\) −5.78010 −0.284076
\(415\) −27.7044 −1.35996
\(416\) 0 0
\(417\) 20.5500 1.00634
\(418\) 10.5771 0.517345
\(419\) 33.2787 1.62577 0.812884 0.582425i \(-0.197896\pi\)
0.812884 + 0.582425i \(0.197896\pi\)
\(420\) −0.205218 −0.0100136
\(421\) 28.8184 1.40452 0.702261 0.711919i \(-0.252174\pi\)
0.702261 + 0.711919i \(0.252174\pi\)
\(422\) 5.49950 0.267711
\(423\) −4.63900 −0.225556
\(424\) −18.5419 −0.900474
\(425\) 9.59907 0.465623
\(426\) 13.0976 0.634581
\(427\) 8.95997 0.433603
\(428\) 0.870368 0.0420708
\(429\) 0 0
\(430\) −47.2136 −2.27684
\(431\) −11.9805 −0.577081 −0.288541 0.957468i \(-0.593170\pi\)
−0.288541 + 0.957468i \(0.593170\pi\)
\(432\) 4.13806 0.199093
\(433\) −12.9962 −0.624558 −0.312279 0.949990i \(-0.601092\pi\)
−0.312279 + 0.949990i \(0.601092\pi\)
\(434\) 4.54181 0.218014
\(435\) 3.01039 0.144337
\(436\) −0.744349 −0.0356479
\(437\) 32.0571 1.53350
\(438\) −10.8322 −0.517582
\(439\) 33.1408 1.58172 0.790861 0.611996i \(-0.209633\pi\)
0.790861 + 0.611996i \(0.209633\pi\)
\(440\) −7.32417 −0.349166
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 24.7031 1.17368 0.586841 0.809702i \(-0.300371\pi\)
0.586841 + 0.809702i \(0.300371\pi\)
\(444\) 0.115780 0.00549467
\(445\) −18.7079 −0.886840
\(446\) −38.7386 −1.83433
\(447\) 12.9977 0.614772
\(448\) −7.69348 −0.363483
\(449\) 21.9994 1.03821 0.519107 0.854709i \(-0.326265\pi\)
0.519107 + 0.854709i \(0.326265\pi\)
\(450\) 4.62897 0.218212
\(451\) 6.02677 0.283790
\(452\) −1.09510 −0.0515092
\(453\) −18.6960 −0.878413
\(454\) −39.2422 −1.84173
\(455\) 0 0
\(456\) −22.1561 −1.03755
\(457\) −35.6397 −1.66716 −0.833578 0.552402i \(-0.813711\pi\)
−0.833578 + 0.552402i \(0.813711\pi\)
\(458\) 7.32767 0.342399
\(459\) −2.98468 −0.139313
\(460\) 0.824134 0.0384254
\(461\) 23.5001 1.09451 0.547255 0.836966i \(-0.315673\pi\)
0.547255 + 0.836966i \(0.315673\pi\)
\(462\) −1.32503 −0.0616461
\(463\) 34.0308 1.58155 0.790773 0.612109i \(-0.209679\pi\)
0.790773 + 0.612109i \(0.209679\pi\)
\(464\) −4.34597 −0.201757
\(465\) −9.04503 −0.419453
\(466\) 12.3528 0.572232
\(467\) −21.5151 −0.995601 −0.497800 0.867292i \(-0.665859\pi\)
−0.497800 + 0.867292i \(0.665859\pi\)
\(468\) 0 0
\(469\) −11.2659 −0.520210
\(470\) 19.1386 0.882797
\(471\) 15.0687 0.694331
\(472\) −27.7242 −1.27611
\(473\) −10.5355 −0.484423
\(474\) −8.98572 −0.412728
\(475\) −25.6728 −1.17795
\(476\) −0.213687 −0.00979435
\(477\) 6.68041 0.305875
\(478\) 6.34582 0.290251
\(479\) 9.91346 0.452957 0.226479 0.974016i \(-0.427279\pi\)
0.226479 + 0.974016i \(0.427279\pi\)
\(480\) −1.16034 −0.0529618
\(481\) 0 0
\(482\) −6.66297 −0.303490
\(483\) −4.01590 −0.182730
\(484\) −0.726865 −0.0330393
\(485\) 1.61072 0.0731389
\(486\) −1.43930 −0.0652881
\(487\) −11.8078 −0.535061 −0.267531 0.963549i \(-0.586208\pi\)
−0.267531 + 0.963549i \(0.586208\pi\)
\(488\) 24.8689 1.12576
\(489\) −9.07260 −0.410277
\(490\) −4.12559 −0.186375
\(491\) −29.8552 −1.34735 −0.673673 0.739030i \(-0.735284\pi\)
−0.673673 + 0.739030i \(0.735284\pi\)
\(492\) 0.468697 0.0211305
\(493\) 3.13464 0.141177
\(494\) 0 0
\(495\) 2.63881 0.118606
\(496\) 13.0579 0.586318
\(497\) 9.09996 0.408189
\(498\) −13.9113 −0.623381
\(499\) −20.6327 −0.923645 −0.461823 0.886972i \(-0.652804\pi\)
−0.461823 + 0.886972i \(0.652804\pi\)
\(500\) 0.366084 0.0163718
\(501\) −5.92599 −0.264754
\(502\) −23.7446 −1.05977
\(503\) 16.6116 0.740677 0.370338 0.928897i \(-0.379242\pi\)
0.370338 + 0.928897i \(0.379242\pi\)
\(504\) 2.77556 0.123633
\(505\) 8.39055 0.373375
\(506\) 5.32120 0.236556
\(507\) 0 0
\(508\) −0.522796 −0.0231953
\(509\) 29.8212 1.32180 0.660902 0.750473i \(-0.270174\pi\)
0.660902 + 0.750473i \(0.270174\pi\)
\(510\) 12.3135 0.545253
\(511\) −7.52599 −0.332930
\(512\) −21.2958 −0.941149
\(513\) 7.98255 0.352438
\(514\) 22.8094 1.00608
\(515\) −43.1107 −1.89968
\(516\) −0.819338 −0.0360693
\(517\) 4.27069 0.187825
\(518\) 2.32758 0.102268
\(519\) 5.39610 0.236862
\(520\) 0 0
\(521\) 4.98520 0.218406 0.109203 0.994019i \(-0.465170\pi\)
0.109203 + 0.994019i \(0.465170\pi\)
\(522\) 1.51162 0.0661618
\(523\) 16.8858 0.738365 0.369182 0.929357i \(-0.379638\pi\)
0.369182 + 0.929357i \(0.379638\pi\)
\(524\) 1.46985 0.0642106
\(525\) 3.21612 0.140363
\(526\) 12.2427 0.533807
\(527\) −9.41833 −0.410269
\(528\) −3.80953 −0.165789
\(529\) −6.87255 −0.298806
\(530\) −27.5606 −1.19716
\(531\) 9.98868 0.433472
\(532\) 0.571509 0.0247781
\(533\) 0 0
\(534\) −9.39387 −0.406512
\(535\) −34.8461 −1.50653
\(536\) −31.2691 −1.35062
\(537\) −12.7671 −0.550941
\(538\) 3.08525 0.133015
\(539\) −0.920607 −0.0396534
\(540\) 0.205218 0.00883117
\(541\) −19.5003 −0.838383 −0.419192 0.907898i \(-0.637686\pi\)
−0.419192 + 0.907898i \(0.637686\pi\)
\(542\) −35.2449 −1.51390
\(543\) 3.96815 0.170290
\(544\) −1.20822 −0.0518022
\(545\) 29.8008 1.27653
\(546\) 0 0
\(547\) 8.65098 0.369889 0.184945 0.982749i \(-0.440789\pi\)
0.184945 + 0.982749i \(0.440789\pi\)
\(548\) 1.06650 0.0455587
\(549\) −8.95997 −0.382402
\(550\) −4.26146 −0.181709
\(551\) −8.38362 −0.357154
\(552\) −11.1464 −0.474421
\(553\) −6.24310 −0.265484
\(554\) 28.0035 1.18976
\(555\) −4.63538 −0.196761
\(556\) −1.47127 −0.0623959
\(557\) −5.34490 −0.226471 −0.113235 0.993568i \(-0.536121\pi\)
−0.113235 + 0.993568i \(0.536121\pi\)
\(558\) −4.54181 −0.192270
\(559\) 0 0
\(560\) −11.8613 −0.501229
\(561\) 2.74771 0.116009
\(562\) −21.9347 −0.925259
\(563\) −3.59510 −0.151515 −0.0757576 0.997126i \(-0.524138\pi\)
−0.0757576 + 0.997126i \(0.524138\pi\)
\(564\) 0.332128 0.0139851
\(565\) 43.8436 1.84451
\(566\) −13.5168 −0.568155
\(567\) −1.00000 −0.0419961
\(568\) 25.2575 1.05978
\(569\) 12.3357 0.517141 0.258571 0.965992i \(-0.416749\pi\)
0.258571 + 0.965992i \(0.416749\pi\)
\(570\) −32.9327 −1.37940
\(571\) 40.8083 1.70777 0.853887 0.520459i \(-0.174239\pi\)
0.853887 + 0.520459i \(0.174239\pi\)
\(572\) 0 0
\(573\) −21.9168 −0.915589
\(574\) 9.42243 0.393285
\(575\) −12.9156 −0.538618
\(576\) 7.69348 0.320562
\(577\) 11.6793 0.486215 0.243107 0.969999i \(-0.421833\pi\)
0.243107 + 0.969999i \(0.421833\pi\)
\(578\) −11.6464 −0.484427
\(579\) −10.2802 −0.427229
\(580\) −0.215529 −0.00894934
\(581\) −9.66531 −0.400985
\(582\) 0.808795 0.0335256
\(583\) −6.15004 −0.254709
\(584\) −20.8888 −0.864387
\(585\) 0 0
\(586\) −18.9073 −0.781052
\(587\) 14.1896 0.585667 0.292833 0.956164i \(-0.405402\pi\)
0.292833 + 0.956164i \(0.405402\pi\)
\(588\) −0.0715948 −0.00295252
\(589\) 25.1894 1.03791
\(590\) −41.2092 −1.69656
\(591\) 13.2140 0.543551
\(592\) 6.69189 0.275035
\(593\) −0.460952 −0.0189290 −0.00946451 0.999955i \(-0.503013\pi\)
−0.00946451 + 0.999955i \(0.503013\pi\)
\(594\) 1.32503 0.0543668
\(595\) 8.55521 0.350729
\(596\) −0.930571 −0.0381177
\(597\) 20.3660 0.833526
\(598\) 0 0
\(599\) −19.4498 −0.794696 −0.397348 0.917668i \(-0.630069\pi\)
−0.397348 + 0.917668i \(0.630069\pi\)
\(600\) 8.92653 0.364424
\(601\) −13.0585 −0.532667 −0.266333 0.963881i \(-0.585812\pi\)
−0.266333 + 0.963881i \(0.585812\pi\)
\(602\) −16.4715 −0.671329
\(603\) 11.2659 0.458782
\(604\) 1.33853 0.0544642
\(605\) 29.1008 1.18312
\(606\) 4.21318 0.171149
\(607\) −0.787345 −0.0319574 −0.0159787 0.999872i \(-0.505086\pi\)
−0.0159787 + 0.999872i \(0.505086\pi\)
\(608\) 3.23141 0.131051
\(609\) 1.05024 0.0425580
\(610\) 36.9651 1.49667
\(611\) 0 0
\(612\) 0.213687 0.00863780
\(613\) 40.4807 1.63500 0.817500 0.575929i \(-0.195359\pi\)
0.817500 + 0.575929i \(0.195359\pi\)
\(614\) 27.9752 1.12899
\(615\) −18.7648 −0.756670
\(616\) −2.55520 −0.102952
\(617\) −25.1733 −1.01344 −0.506719 0.862111i \(-0.669142\pi\)
−0.506719 + 0.862111i \(0.669142\pi\)
\(618\) −21.6473 −0.870783
\(619\) −13.6306 −0.547860 −0.273930 0.961750i \(-0.588324\pi\)
−0.273930 + 0.961750i \(0.588324\pi\)
\(620\) 0.647577 0.0260073
\(621\) 4.01590 0.161153
\(622\) 40.5748 1.62690
\(623\) −6.52667 −0.261486
\(624\) 0 0
\(625\) −30.7372 −1.22949
\(626\) −19.2817 −0.770651
\(627\) −7.34879 −0.293483
\(628\) −1.07884 −0.0430506
\(629\) −4.82668 −0.192453
\(630\) 4.12559 0.164367
\(631\) 28.6584 1.14087 0.570436 0.821342i \(-0.306774\pi\)
0.570436 + 0.821342i \(0.306774\pi\)
\(632\) −17.3281 −0.689275
\(633\) −3.82094 −0.151869
\(634\) 39.6963 1.57654
\(635\) 20.9307 0.830610
\(636\) −0.478283 −0.0189652
\(637\) 0 0
\(638\) −1.39161 −0.0550943
\(639\) −9.09996 −0.359989
\(640\) −34.0608 −1.34637
\(641\) 35.1830 1.38965 0.694823 0.719180i \(-0.255483\pi\)
0.694823 + 0.719180i \(0.255483\pi\)
\(642\) −17.4974 −0.690567
\(643\) 20.0777 0.791789 0.395894 0.918296i \(-0.370435\pi\)
0.395894 + 0.918296i \(0.370435\pi\)
\(644\) 0.287518 0.0113298
\(645\) 32.8031 1.29162
\(646\) −34.2919 −1.34920
\(647\) −12.8586 −0.505523 −0.252762 0.967529i \(-0.581339\pi\)
−0.252762 + 0.967529i \(0.581339\pi\)
\(648\) −2.77556 −0.109034
\(649\) −9.19565 −0.360961
\(650\) 0 0
\(651\) −3.15556 −0.123676
\(652\) 0.649551 0.0254384
\(653\) −2.16027 −0.0845381 −0.0422690 0.999106i \(-0.513459\pi\)
−0.0422690 + 0.999106i \(0.513459\pi\)
\(654\) 14.9640 0.585139
\(655\) −58.8469 −2.29934
\(656\) 27.0899 1.05768
\(657\) 7.52599 0.293617
\(658\) 6.67693 0.260294
\(659\) 18.1795 0.708171 0.354086 0.935213i \(-0.384792\pi\)
0.354086 + 0.935213i \(0.384792\pi\)
\(660\) −0.188925 −0.00735389
\(661\) −6.02892 −0.234498 −0.117249 0.993103i \(-0.537408\pi\)
−0.117249 + 0.993103i \(0.537408\pi\)
\(662\) 28.5374 1.10914
\(663\) 0 0
\(664\) −26.8267 −1.04108
\(665\) −22.8810 −0.887287
\(666\) −2.32758 −0.0901918
\(667\) −4.21767 −0.163309
\(668\) 0.424270 0.0164155
\(669\) 26.9148 1.04059
\(670\) −46.4784 −1.79562
\(671\) 8.24861 0.318434
\(672\) −0.404809 −0.0156159
\(673\) −25.7805 −0.993766 −0.496883 0.867818i \(-0.665522\pi\)
−0.496883 + 0.867818i \(0.665522\pi\)
\(674\) −7.54820 −0.290746
\(675\) −3.21612 −0.123788
\(676\) 0 0
\(677\) 1.37351 0.0527884 0.0263942 0.999652i \(-0.491597\pi\)
0.0263942 + 0.999652i \(0.491597\pi\)
\(678\) 22.0153 0.845493
\(679\) 0.561935 0.0215651
\(680\) 23.7455 0.910598
\(681\) 27.2647 1.04479
\(682\) 4.18122 0.160107
\(683\) −11.5660 −0.442560 −0.221280 0.975210i \(-0.571024\pi\)
−0.221280 + 0.975210i \(0.571024\pi\)
\(684\) −0.571509 −0.0218522
\(685\) −42.6985 −1.63143
\(686\) −1.43930 −0.0549529
\(687\) −5.09112 −0.194238
\(688\) −47.3564 −1.80544
\(689\) 0 0
\(690\) −16.5679 −0.630731
\(691\) −7.05165 −0.268257 −0.134129 0.990964i \(-0.542824\pi\)
−0.134129 + 0.990964i \(0.542824\pi\)
\(692\) −0.386333 −0.0146862
\(693\) 0.920607 0.0349710
\(694\) 14.1685 0.537830
\(695\) 58.9040 2.23436
\(696\) 2.91501 0.110493
\(697\) −19.5392 −0.740102
\(698\) −23.4302 −0.886848
\(699\) −8.58247 −0.324619
\(700\) −0.230257 −0.00870291
\(701\) 39.9328 1.50824 0.754121 0.656736i \(-0.228063\pi\)
0.754121 + 0.656736i \(0.228063\pi\)
\(702\) 0 0
\(703\) 12.9090 0.486873
\(704\) −7.08268 −0.266938
\(705\) −13.2971 −0.500798
\(706\) −24.5505 −0.923969
\(707\) 2.92723 0.110090
\(708\) −0.715138 −0.0268765
\(709\) 47.5035 1.78403 0.892015 0.452006i \(-0.149291\pi\)
0.892015 + 0.452006i \(0.149291\pi\)
\(710\) 37.5427 1.40895
\(711\) 6.24310 0.234135
\(712\) −18.1152 −0.678895
\(713\) 12.6724 0.474586
\(714\) 4.29586 0.160768
\(715\) 0 0
\(716\) 0.914059 0.0341600
\(717\) −4.40895 −0.164655
\(718\) −52.8368 −1.97185
\(719\) −4.97631 −0.185585 −0.0927925 0.995685i \(-0.529579\pi\)
−0.0927925 + 0.995685i \(0.529579\pi\)
\(720\) 11.8613 0.442043
\(721\) −15.0401 −0.560124
\(722\) 64.3672 2.39550
\(723\) 4.62930 0.172166
\(724\) −0.284099 −0.0105585
\(725\) 3.37771 0.125445
\(726\) 14.6125 0.542321
\(727\) 35.0729 1.30078 0.650391 0.759599i \(-0.274605\pi\)
0.650391 + 0.759599i \(0.274605\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −31.0491 −1.14918
\(731\) 34.1569 1.26334
\(732\) 0.641487 0.0237101
\(733\) 39.1263 1.44516 0.722582 0.691285i \(-0.242955\pi\)
0.722582 + 0.691285i \(0.242955\pi\)
\(734\) −14.0282 −0.517791
\(735\) 2.86638 0.105728
\(736\) 1.62567 0.0599231
\(737\) −10.3714 −0.382037
\(738\) −9.42243 −0.346844
\(739\) 14.0036 0.515132 0.257566 0.966261i \(-0.417079\pi\)
0.257566 + 0.966261i \(0.417079\pi\)
\(740\) 0.331869 0.0121997
\(741\) 0 0
\(742\) −9.61514 −0.352983
\(743\) 28.7607 1.05513 0.527563 0.849516i \(-0.323106\pi\)
0.527563 + 0.849516i \(0.323106\pi\)
\(744\) −8.75845 −0.321100
\(745\) 37.2564 1.36497
\(746\) 0.849081 0.0310871
\(747\) 9.66531 0.353635
\(748\) −0.196722 −0.00719287
\(749\) −12.1569 −0.444202
\(750\) −7.35956 −0.268733
\(751\) −49.2873 −1.79852 −0.899259 0.437417i \(-0.855893\pi\)
−0.899259 + 0.437417i \(0.855893\pi\)
\(752\) 19.1965 0.700023
\(753\) 16.4973 0.601195
\(754\) 0 0
\(755\) −53.5897 −1.95033
\(756\) 0.0715948 0.00260388
\(757\) −27.6292 −1.00420 −0.502101 0.864809i \(-0.667439\pi\)
−0.502101 + 0.864809i \(0.667439\pi\)
\(758\) −5.22439 −0.189758
\(759\) −3.69707 −0.134195
\(760\) −63.5076 −2.30366
\(761\) 0.554389 0.0200966 0.0100483 0.999950i \(-0.496801\pi\)
0.0100483 + 0.999950i \(0.496801\pi\)
\(762\) 10.5100 0.380738
\(763\) 10.3967 0.376386
\(764\) 1.56913 0.0567692
\(765\) −8.55521 −0.309314
\(766\) 41.3047 1.49240
\(767\) 0 0
\(768\) −1.71610 −0.0619244
\(769\) −42.2312 −1.52290 −0.761448 0.648226i \(-0.775511\pi\)
−0.761448 + 0.648226i \(0.775511\pi\)
\(770\) −3.79804 −0.136872
\(771\) −15.8475 −0.570734
\(772\) 0.736007 0.0264895
\(773\) 46.3178 1.66594 0.832968 0.553321i \(-0.186640\pi\)
0.832968 + 0.553321i \(0.186640\pi\)
\(774\) 16.4715 0.592056
\(775\) −10.1487 −0.364551
\(776\) 1.55968 0.0559894
\(777\) −1.61715 −0.0580151
\(778\) −6.17140 −0.221255
\(779\) 52.2579 1.87233
\(780\) 0 0
\(781\) 8.37749 0.299770
\(782\) −17.2517 −0.616920
\(783\) −1.05024 −0.0375326
\(784\) −4.13806 −0.147788
\(785\) 43.1927 1.54161
\(786\) −29.5490 −1.05398
\(787\) 13.9450 0.497087 0.248543 0.968621i \(-0.420048\pi\)
0.248543 + 0.968621i \(0.420048\pi\)
\(788\) −0.946054 −0.0337018
\(789\) −8.50599 −0.302821
\(790\) −25.7565 −0.916374
\(791\) 15.2958 0.543856
\(792\) 2.55520 0.0907951
\(793\) 0 0
\(794\) −44.9864 −1.59651
\(795\) 19.1486 0.679130
\(796\) −1.45810 −0.0516811
\(797\) −3.71124 −0.131459 −0.0657294 0.997837i \(-0.520937\pi\)
−0.0657294 + 0.997837i \(0.520937\pi\)
\(798\) −11.4893 −0.406717
\(799\) −13.8459 −0.489833
\(800\) −1.30191 −0.0460296
\(801\) 6.52667 0.230609
\(802\) 35.1632 1.24166
\(803\) −6.92848 −0.244501
\(804\) −0.806579 −0.0284458
\(805\) −11.5111 −0.405712
\(806\) 0 0
\(807\) −2.14357 −0.0754573
\(808\) 8.12471 0.285826
\(809\) 7.85149 0.276044 0.138022 0.990429i \(-0.455926\pi\)
0.138022 + 0.990429i \(0.455926\pi\)
\(810\) −4.12559 −0.144958
\(811\) 49.1028 1.72423 0.862117 0.506710i \(-0.169139\pi\)
0.862117 + 0.506710i \(0.169139\pi\)
\(812\) −0.0751920 −0.00263872
\(813\) 24.4875 0.858813
\(814\) 2.14278 0.0751045
\(815\) −26.0055 −0.910933
\(816\) 12.3508 0.432364
\(817\) −91.3530 −3.19604
\(818\) −25.0012 −0.874147
\(819\) 0 0
\(820\) 1.34346 0.0469157
\(821\) 13.1916 0.460391 0.230196 0.973144i \(-0.426063\pi\)
0.230196 + 0.973144i \(0.426063\pi\)
\(822\) −21.4404 −0.747818
\(823\) −2.71369 −0.0945931 −0.0472966 0.998881i \(-0.515061\pi\)
−0.0472966 + 0.998881i \(0.515061\pi\)
\(824\) −41.7448 −1.45425
\(825\) 2.96078 0.103081
\(826\) −14.3767 −0.500231
\(827\) −35.3979 −1.23091 −0.615453 0.788174i \(-0.711027\pi\)
−0.615453 + 0.788174i \(0.711027\pi\)
\(828\) −0.287518 −0.00999193
\(829\) −11.0842 −0.384969 −0.192485 0.981300i \(-0.561655\pi\)
−0.192485 + 0.981300i \(0.561655\pi\)
\(830\) −39.8751 −1.38408
\(831\) −19.4563 −0.674932
\(832\) 0 0
\(833\) 2.98468 0.103413
\(834\) 29.5777 1.02419
\(835\) −16.9861 −0.587829
\(836\) 0.526136 0.0181968
\(837\) 3.15556 0.109072
\(838\) 47.8981 1.65461
\(839\) −35.4634 −1.22433 −0.612166 0.790729i \(-0.709702\pi\)
−0.612166 + 0.790729i \(0.709702\pi\)
\(840\) 7.95580 0.274501
\(841\) −27.8970 −0.961965
\(842\) 41.4784 1.42944
\(843\) 15.2398 0.524886
\(844\) 0.273560 0.00941631
\(845\) 0 0
\(846\) −6.67693 −0.229557
\(847\) 10.1525 0.348843
\(848\) −27.6440 −0.949298
\(849\) 9.39124 0.322307
\(850\) 13.8160 0.473884
\(851\) 6.49433 0.222623
\(852\) 0.651510 0.0223204
\(853\) −10.0661 −0.344656 −0.172328 0.985040i \(-0.555129\pi\)
−0.172328 + 0.985040i \(0.555129\pi\)
\(854\) 12.8961 0.441296
\(855\) 22.8810 0.782514
\(856\) −33.7421 −1.15328
\(857\) 44.1981 1.50978 0.754890 0.655851i \(-0.227690\pi\)
0.754890 + 0.655851i \(0.227690\pi\)
\(858\) 0 0
\(859\) 33.6264 1.14732 0.573658 0.819095i \(-0.305524\pi\)
0.573658 + 0.819095i \(0.305524\pi\)
\(860\) −2.34853 −0.0800842
\(861\) −6.54652 −0.223105
\(862\) −17.2436 −0.587319
\(863\) −23.7297 −0.807767 −0.403884 0.914810i \(-0.632340\pi\)
−0.403884 + 0.914810i \(0.632340\pi\)
\(864\) 0.404809 0.0137719
\(865\) 15.4672 0.525902
\(866\) −18.7055 −0.635638
\(867\) 8.09171 0.274809
\(868\) 0.225922 0.00766829
\(869\) −5.74744 −0.194969
\(870\) 4.33287 0.146898
\(871\) 0 0
\(872\) 28.8566 0.977209
\(873\) −0.561935 −0.0190186
\(874\) 46.1399 1.56071
\(875\) −5.11328 −0.172860
\(876\) −0.538822 −0.0182051
\(877\) 9.30145 0.314088 0.157044 0.987592i \(-0.449804\pi\)
0.157044 + 0.987592i \(0.449804\pi\)
\(878\) 47.6996 1.60978
\(879\) 13.1364 0.443080
\(880\) −10.9196 −0.368098
\(881\) 19.5601 0.658997 0.329499 0.944156i \(-0.393120\pi\)
0.329499 + 0.944156i \(0.393120\pi\)
\(882\) 1.43930 0.0484639
\(883\) −2.25927 −0.0760305 −0.0380152 0.999277i \(-0.512104\pi\)
−0.0380152 + 0.999277i \(0.512104\pi\)
\(884\) 0 0
\(885\) 28.6313 0.962432
\(886\) 35.5553 1.19450
\(887\) −21.8263 −0.732856 −0.366428 0.930446i \(-0.619419\pi\)
−0.366428 + 0.930446i \(0.619419\pi\)
\(888\) −4.48851 −0.150625
\(889\) 7.30215 0.244906
\(890\) −26.9264 −0.902574
\(891\) −0.920607 −0.0308415
\(892\) −1.92696 −0.0645195
\(893\) 37.0310 1.23920
\(894\) 18.7077 0.625679
\(895\) −36.5953 −1.22325
\(896\) −11.8829 −0.396979
\(897\) 0 0
\(898\) 31.6638 1.05663
\(899\) −3.31411 −0.110532
\(900\) 0.230257 0.00767525
\(901\) 19.9389 0.664260
\(902\) 8.67436 0.288824
\(903\) 11.4441 0.380835
\(904\) 42.4545 1.41201
\(905\) 11.3742 0.378092
\(906\) −26.9092 −0.893997
\(907\) −46.7145 −1.55113 −0.775565 0.631268i \(-0.782535\pi\)
−0.775565 + 0.631268i \(0.782535\pi\)
\(908\) −1.95201 −0.0647798
\(909\) −2.92723 −0.0970902
\(910\) 0 0
\(911\) 29.4791 0.976686 0.488343 0.872652i \(-0.337602\pi\)
0.488343 + 0.872652i \(0.337602\pi\)
\(912\) −33.0323 −1.09381
\(913\) −8.89796 −0.294479
\(914\) −51.2964 −1.69673
\(915\) −25.6826 −0.849042
\(916\) 0.364498 0.0120433
\(917\) −20.5301 −0.677963
\(918\) −4.29586 −0.141784
\(919\) −1.08672 −0.0358477 −0.0179239 0.999839i \(-0.505706\pi\)
−0.0179239 + 0.999839i \(0.505706\pi\)
\(920\) −31.9497 −1.05335
\(921\) −19.4366 −0.640457
\(922\) 33.8238 1.11393
\(923\) 0 0
\(924\) −0.0659107 −0.00216830
\(925\) −5.20096 −0.171007
\(926\) 48.9807 1.60961
\(927\) 15.0401 0.493983
\(928\) −0.425148 −0.0139562
\(929\) −52.2100 −1.71295 −0.856477 0.516185i \(-0.827352\pi\)
−0.856477 + 0.516185i \(0.827352\pi\)
\(930\) −13.0185 −0.426895
\(931\) −7.98255 −0.261618
\(932\) 0.614461 0.0201273
\(933\) −28.1906 −0.922918
\(934\) −30.9668 −1.01326
\(935\) 7.87599 0.257572
\(936\) 0 0
\(937\) −7.44303 −0.243153 −0.121577 0.992582i \(-0.538795\pi\)
−0.121577 + 0.992582i \(0.538795\pi\)
\(938\) −16.2150 −0.529439
\(939\) 13.3965 0.437179
\(940\) 0.952005 0.0310510
\(941\) 41.0689 1.33881 0.669403 0.742899i \(-0.266550\pi\)
0.669403 + 0.742899i \(0.266550\pi\)
\(942\) 21.6885 0.706649
\(943\) 26.2902 0.856126
\(944\) −41.3338 −1.34530
\(945\) −2.86638 −0.0932433
\(946\) −15.1638 −0.493018
\(947\) −3.81057 −0.123827 −0.0619135 0.998082i \(-0.519720\pi\)
−0.0619135 + 0.998082i \(0.519720\pi\)
\(948\) −0.446974 −0.0145170
\(949\) 0 0
\(950\) −36.9510 −1.19885
\(951\) −27.5802 −0.894349
\(952\) 8.28415 0.268491
\(953\) −33.9461 −1.09962 −0.549811 0.835289i \(-0.685300\pi\)
−0.549811 + 0.835289i \(0.685300\pi\)
\(954\) 9.61514 0.311302
\(955\) −62.8219 −2.03287
\(956\) 0.315658 0.0102091
\(957\) 0.966861 0.0312542
\(958\) 14.2685 0.460994
\(959\) −14.8963 −0.481028
\(960\) 22.0524 0.711739
\(961\) −21.0424 −0.678788
\(962\) 0 0
\(963\) 12.1569 0.391749
\(964\) −0.331434 −0.0106748
\(965\) −29.4668 −0.948571
\(966\) −5.78010 −0.185972
\(967\) −30.5375 −0.982021 −0.491010 0.871154i \(-0.663372\pi\)
−0.491010 + 0.871154i \(0.663372\pi\)
\(968\) 28.1788 0.905702
\(969\) 23.8253 0.765380
\(970\) 2.31831 0.0744365
\(971\) −8.15552 −0.261723 −0.130862 0.991401i \(-0.541774\pi\)
−0.130862 + 0.991401i \(0.541774\pi\)
\(972\) −0.0715948 −0.00229641
\(973\) 20.5500 0.658803
\(974\) −16.9950 −0.544554
\(975\) 0 0
\(976\) 37.0769 1.18680
\(977\) 43.2570 1.38391 0.691957 0.721939i \(-0.256749\pi\)
0.691957 + 0.721939i \(0.256749\pi\)
\(978\) −13.0582 −0.417556
\(979\) −6.00850 −0.192033
\(980\) −0.205218 −0.00655544
\(981\) −10.3967 −0.331941
\(982\) −42.9707 −1.37125
\(983\) 40.4255 1.28937 0.644687 0.764447i \(-0.276988\pi\)
0.644687 + 0.764447i \(0.276988\pi\)
\(984\) −18.1703 −0.579247
\(985\) 37.8763 1.20684
\(986\) 4.51169 0.143682
\(987\) −4.63900 −0.147661
\(988\) 0 0
\(989\) −45.9583 −1.46139
\(990\) 3.79804 0.120710
\(991\) 2.08489 0.0662287 0.0331144 0.999452i \(-0.489457\pi\)
0.0331144 + 0.999452i \(0.489457\pi\)
\(992\) 1.27740 0.0405575
\(993\) −19.8272 −0.629198
\(994\) 13.0976 0.415431
\(995\) 58.3767 1.85067
\(996\) −0.691986 −0.0219264
\(997\) 17.6142 0.557846 0.278923 0.960313i \(-0.410023\pi\)
0.278923 + 0.960313i \(0.410023\pi\)
\(998\) −29.6967 −0.940032
\(999\) 1.61715 0.0511645
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 3549.2.a.bf.1.7 yes 9
13.12 even 2 3549.2.a.be.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.3 9 13.12 even 2
3549.2.a.bf.1.7 yes 9 1.1 even 1 trivial