Properties

Label 3549.2.a.bh.1.9
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} - 1041 x + 281\)
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 1.9
Root \(1.02667\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} -3.27646 q^{5} +1.02667 q^{6} -1.00000 q^{7} -3.02452 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} -3.27646 q^{5} +1.02667 q^{6} -1.00000 q^{7} -3.02452 q^{8} +1.00000 q^{9} -3.36384 q^{10} -3.64615 q^{11} -0.945953 q^{12} -1.02667 q^{14} -3.27646 q^{15} -1.21327 q^{16} -6.88794 q^{17} +1.02667 q^{18} -6.29215 q^{19} +3.09937 q^{20} -1.00000 q^{21} -3.74338 q^{22} +7.44525 q^{23} -3.02452 q^{24} +5.73518 q^{25} +1.00000 q^{27} +0.945953 q^{28} +9.42061 q^{29} -3.36384 q^{30} +10.7607 q^{31} +4.80341 q^{32} -3.64615 q^{33} -7.07162 q^{34} +3.27646 q^{35} -0.945953 q^{36} +0.298388 q^{37} -6.45995 q^{38} +9.90970 q^{40} -3.91963 q^{41} -1.02667 q^{42} -5.28378 q^{43} +3.44908 q^{44} -3.27646 q^{45} +7.64380 q^{46} -1.78548 q^{47} -1.21327 q^{48} +1.00000 q^{49} +5.88813 q^{50} -6.88794 q^{51} +4.92587 q^{53} +1.02667 q^{54} +11.9464 q^{55} +3.02452 q^{56} -6.29215 q^{57} +9.67184 q^{58} +5.56609 q^{59} +3.09937 q^{60} +4.34575 q^{61} +11.0477 q^{62} -1.00000 q^{63} +7.35804 q^{64} -3.74338 q^{66} +12.7392 q^{67} +6.51566 q^{68} +7.44525 q^{69} +3.36384 q^{70} -5.67644 q^{71} -3.02452 q^{72} -6.72651 q^{73} +0.306346 q^{74} +5.73518 q^{75} +5.95208 q^{76} +3.64615 q^{77} +3.24335 q^{79} +3.97522 q^{80} +1.00000 q^{81} -4.02416 q^{82} -15.6734 q^{83} +0.945953 q^{84} +22.5680 q^{85} -5.42469 q^{86} +9.42061 q^{87} +11.0278 q^{88} +4.85592 q^{89} -3.36384 q^{90} -7.04286 q^{92} +10.7607 q^{93} -1.83309 q^{94} +20.6160 q^{95} +4.80341 q^{96} +4.26503 q^{97} +1.02667 q^{98} -3.64615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.02667 0.725964 0.362982 0.931796i \(-0.381759\pi\)
0.362982 + 0.931796i \(0.381759\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.945953 −0.472976
\(5\) −3.27646 −1.46528 −0.732638 0.680618i \(-0.761711\pi\)
−0.732638 + 0.680618i \(0.761711\pi\)
\(6\) 1.02667 0.419135
\(7\) −1.00000 −0.377964
\(8\) −3.02452 −1.06933
\(9\) 1.00000 0.333333
\(10\) −3.36384 −1.06374
\(11\) −3.64615 −1.09935 −0.549677 0.835377i \(-0.685249\pi\)
−0.549677 + 0.835377i \(0.685249\pi\)
\(12\) −0.945953 −0.273073
\(13\) 0 0
\(14\) −1.02667 −0.274389
\(15\) −3.27646 −0.845978
\(16\) −1.21327 −0.303317
\(17\) −6.88794 −1.67057 −0.835285 0.549817i \(-0.814697\pi\)
−0.835285 + 0.549817i \(0.814697\pi\)
\(18\) 1.02667 0.241988
\(19\) −6.29215 −1.44352 −0.721759 0.692144i \(-0.756666\pi\)
−0.721759 + 0.692144i \(0.756666\pi\)
\(20\) 3.09937 0.693041
\(21\) −1.00000 −0.218218
\(22\) −3.74338 −0.798092
\(23\) 7.44525 1.55244 0.776221 0.630461i \(-0.217134\pi\)
0.776221 + 0.630461i \(0.217134\pi\)
\(24\) −3.02452 −0.617377
\(25\) 5.73518 1.14704
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.945953 0.178768
\(29\) 9.42061 1.74936 0.874682 0.484697i \(-0.161070\pi\)
0.874682 + 0.484697i \(0.161070\pi\)
\(30\) −3.36384 −0.614149
\(31\) 10.7607 1.93269 0.966343 0.257257i \(-0.0828187\pi\)
0.966343 + 0.257257i \(0.0828187\pi\)
\(32\) 4.80341 0.849130
\(33\) −3.64615 −0.634712
\(34\) −7.07162 −1.21277
\(35\) 3.27646 0.553823
\(36\) −0.945953 −0.157659
\(37\) 0.298388 0.0490547 0.0245274 0.999699i \(-0.492192\pi\)
0.0245274 + 0.999699i \(0.492192\pi\)
\(38\) −6.45995 −1.04794
\(39\) 0 0
\(40\) 9.90970 1.56686
\(41\) −3.91963 −0.612144 −0.306072 0.952008i \(-0.599015\pi\)
−0.306072 + 0.952008i \(0.599015\pi\)
\(42\) −1.02667 −0.158418
\(43\) −5.28378 −0.805769 −0.402885 0.915251i \(-0.631992\pi\)
−0.402885 + 0.915251i \(0.631992\pi\)
\(44\) 3.44908 0.519969
\(45\) −3.27646 −0.488426
\(46\) 7.64380 1.12702
\(47\) −1.78548 −0.260438 −0.130219 0.991485i \(-0.541568\pi\)
−0.130219 + 0.991485i \(0.541568\pi\)
\(48\) −1.21327 −0.175120
\(49\) 1.00000 0.142857
\(50\) 5.88813 0.832707
\(51\) −6.88794 −0.964504
\(52\) 0 0
\(53\) 4.92587 0.676621 0.338310 0.941035i \(-0.390145\pi\)
0.338310 + 0.941035i \(0.390145\pi\)
\(54\) 1.02667 0.139712
\(55\) 11.9464 1.61086
\(56\) 3.02452 0.404168
\(57\) −6.29215 −0.833416
\(58\) 9.67184 1.26998
\(59\) 5.56609 0.724643 0.362322 0.932053i \(-0.381984\pi\)
0.362322 + 0.932053i \(0.381984\pi\)
\(60\) 3.09937 0.400128
\(61\) 4.34575 0.556416 0.278208 0.960521i \(-0.410259\pi\)
0.278208 + 0.960521i \(0.410259\pi\)
\(62\) 11.0477 1.40306
\(63\) −1.00000 −0.125988
\(64\) 7.35804 0.919755
\(65\) 0 0
\(66\) −3.74338 −0.460778
\(67\) 12.7392 1.55634 0.778170 0.628054i \(-0.216148\pi\)
0.778170 + 0.628054i \(0.216148\pi\)
\(68\) 6.51566 0.790140
\(69\) 7.44525 0.896303
\(70\) 3.36384 0.402055
\(71\) −5.67644 −0.673669 −0.336835 0.941564i \(-0.609356\pi\)
−0.336835 + 0.941564i \(0.609356\pi\)
\(72\) −3.02452 −0.356443
\(73\) −6.72651 −0.787279 −0.393639 0.919265i \(-0.628784\pi\)
−0.393639 + 0.919265i \(0.628784\pi\)
\(74\) 0.306346 0.0356120
\(75\) 5.73518 0.662242
\(76\) 5.95208 0.682750
\(77\) 3.64615 0.415517
\(78\) 0 0
\(79\) 3.24335 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(80\) 3.97522 0.444443
\(81\) 1.00000 0.111111
\(82\) −4.02416 −0.444394
\(83\) −15.6734 −1.72038 −0.860190 0.509973i \(-0.829655\pi\)
−0.860190 + 0.509973i \(0.829655\pi\)
\(84\) 0.945953 0.103212
\(85\) 22.5680 2.44785
\(86\) −5.42469 −0.584959
\(87\) 9.42061 1.01000
\(88\) 11.0278 1.17557
\(89\) 4.85592 0.514726 0.257363 0.966315i \(-0.417146\pi\)
0.257363 + 0.966315i \(0.417146\pi\)
\(90\) −3.36384 −0.354579
\(91\) 0 0
\(92\) −7.04286 −0.734269
\(93\) 10.7607 1.11584
\(94\) −1.83309 −0.189069
\(95\) 20.6160 2.11515
\(96\) 4.80341 0.490246
\(97\) 4.26503 0.433048 0.216524 0.976277i \(-0.430528\pi\)
0.216524 + 0.976277i \(0.430528\pi\)
\(98\) 1.02667 0.103709
\(99\) −3.64615 −0.366451
\(100\) −5.42521 −0.542521
\(101\) −6.34614 −0.631464 −0.315732 0.948848i \(-0.602250\pi\)
−0.315732 + 0.948848i \(0.602250\pi\)
\(102\) −7.07162 −0.700195
\(103\) −9.87950 −0.973456 −0.486728 0.873553i \(-0.661810\pi\)
−0.486728 + 0.873553i \(0.661810\pi\)
\(104\) 0 0
\(105\) 3.27646 0.319750
\(106\) 5.05724 0.491202
\(107\) −17.3396 −1.67628 −0.838140 0.545456i \(-0.816357\pi\)
−0.838140 + 0.545456i \(0.816357\pi\)
\(108\) −0.945953 −0.0910243
\(109\) 7.94895 0.761372 0.380686 0.924704i \(-0.375688\pi\)
0.380686 + 0.924704i \(0.375688\pi\)
\(110\) 12.2650 1.16943
\(111\) 0.298388 0.0283218
\(112\) 1.21327 0.114643
\(113\) −17.4746 −1.64387 −0.821936 0.569579i \(-0.807106\pi\)
−0.821936 + 0.569579i \(0.807106\pi\)
\(114\) −6.45995 −0.605030
\(115\) −24.3941 −2.27476
\(116\) −8.91145 −0.827408
\(117\) 0 0
\(118\) 5.71453 0.526065
\(119\) 6.88794 0.631416
\(120\) 9.90970 0.904628
\(121\) 2.29438 0.208580
\(122\) 4.46164 0.403938
\(123\) −3.91963 −0.353421
\(124\) −10.1792 −0.914115
\(125\) −2.40879 −0.215448
\(126\) −1.02667 −0.0914629
\(127\) −4.25486 −0.377557 −0.188779 0.982020i \(-0.560453\pi\)
−0.188779 + 0.982020i \(0.560453\pi\)
\(128\) −2.05255 −0.181421
\(129\) −5.28378 −0.465211
\(130\) 0 0
\(131\) 3.88999 0.339870 0.169935 0.985455i \(-0.445644\pi\)
0.169935 + 0.985455i \(0.445644\pi\)
\(132\) 3.44908 0.300204
\(133\) 6.29215 0.545599
\(134\) 13.0789 1.12985
\(135\) −3.27646 −0.281993
\(136\) 20.8327 1.78639
\(137\) 7.07777 0.604695 0.302347 0.953198i \(-0.402230\pi\)
0.302347 + 0.953198i \(0.402230\pi\)
\(138\) 7.64380 0.650684
\(139\) 15.8222 1.34202 0.671012 0.741446i \(-0.265860\pi\)
0.671012 + 0.741446i \(0.265860\pi\)
\(140\) −3.09937 −0.261945
\(141\) −1.78548 −0.150364
\(142\) −5.82782 −0.489059
\(143\) 0 0
\(144\) −1.21327 −0.101106
\(145\) −30.8662 −2.56330
\(146\) −6.90589 −0.571536
\(147\) 1.00000 0.0824786
\(148\) −0.282261 −0.0232017
\(149\) −8.53252 −0.699011 −0.349505 0.936934i \(-0.613650\pi\)
−0.349505 + 0.936934i \(0.613650\pi\)
\(150\) 5.88813 0.480763
\(151\) 6.95074 0.565643 0.282822 0.959173i \(-0.408730\pi\)
0.282822 + 0.959173i \(0.408730\pi\)
\(152\) 19.0307 1.54359
\(153\) −6.88794 −0.556857
\(154\) 3.74338 0.301650
\(155\) −35.2571 −2.83192
\(156\) 0 0
\(157\) 12.7344 1.01632 0.508159 0.861263i \(-0.330326\pi\)
0.508159 + 0.861263i \(0.330326\pi\)
\(158\) 3.32984 0.264908
\(159\) 4.92587 0.390647
\(160\) −15.7382 −1.24421
\(161\) −7.44525 −0.586768
\(162\) 1.02667 0.0806627
\(163\) 3.92353 0.307315 0.153657 0.988124i \(-0.450895\pi\)
0.153657 + 0.988124i \(0.450895\pi\)
\(164\) 3.70779 0.289530
\(165\) 11.9464 0.930029
\(166\) −16.0914 −1.24893
\(167\) 5.39579 0.417539 0.208769 0.977965i \(-0.433054\pi\)
0.208769 + 0.977965i \(0.433054\pi\)
\(168\) 3.02452 0.233346
\(169\) 0 0
\(170\) 23.1699 1.77705
\(171\) −6.29215 −0.481173
\(172\) 4.99821 0.381110
\(173\) 2.03101 0.154415 0.0772076 0.997015i \(-0.475400\pi\)
0.0772076 + 0.997015i \(0.475400\pi\)
\(174\) 9.67184 0.733220
\(175\) −5.73518 −0.433539
\(176\) 4.42375 0.333453
\(177\) 5.56609 0.418373
\(178\) 4.98541 0.373673
\(179\) 12.0826 0.903097 0.451548 0.892247i \(-0.350872\pi\)
0.451548 + 0.892247i \(0.350872\pi\)
\(180\) 3.09937 0.231014
\(181\) 17.6432 1.31141 0.655703 0.755019i \(-0.272372\pi\)
0.655703 + 0.755019i \(0.272372\pi\)
\(182\) 0 0
\(183\) 4.34575 0.321247
\(184\) −22.5183 −1.66007
\(185\) −0.977656 −0.0718787
\(186\) 11.0477 0.810057
\(187\) 25.1144 1.83655
\(188\) 1.68898 0.123181
\(189\) −1.00000 −0.0727393
\(190\) 21.1658 1.53553
\(191\) 6.67101 0.482697 0.241349 0.970438i \(-0.422410\pi\)
0.241349 + 0.970438i \(0.422410\pi\)
\(192\) 7.35804 0.531021
\(193\) 15.9900 1.15099 0.575493 0.817807i \(-0.304810\pi\)
0.575493 + 0.817807i \(0.304810\pi\)
\(194\) 4.37877 0.314377
\(195\) 0 0
\(196\) −0.945953 −0.0675680
\(197\) 7.34567 0.523357 0.261679 0.965155i \(-0.415724\pi\)
0.261679 + 0.965155i \(0.415724\pi\)
\(198\) −3.74338 −0.266031
\(199\) −0.202957 −0.0143873 −0.00719363 0.999974i \(-0.502290\pi\)
−0.00719363 + 0.999974i \(0.502290\pi\)
\(200\) −17.3461 −1.22656
\(201\) 12.7392 0.898553
\(202\) −6.51538 −0.458420
\(203\) −9.42061 −0.661197
\(204\) 6.51566 0.456188
\(205\) 12.8425 0.896960
\(206\) −10.1430 −0.706694
\(207\) 7.44525 0.517481
\(208\) 0 0
\(209\) 22.9421 1.58694
\(210\) 3.36384 0.232127
\(211\) 8.62718 0.593920 0.296960 0.954890i \(-0.404027\pi\)
0.296960 + 0.954890i \(0.404027\pi\)
\(212\) −4.65964 −0.320026
\(213\) −5.67644 −0.388943
\(214\) −17.8020 −1.21692
\(215\) 17.3121 1.18067
\(216\) −3.02452 −0.205792
\(217\) −10.7607 −0.730487
\(218\) 8.16094 0.552728
\(219\) −6.72651 −0.454536
\(220\) −11.3008 −0.761898
\(221\) 0 0
\(222\) 0.306346 0.0205606
\(223\) −1.66736 −0.111655 −0.0558275 0.998440i \(-0.517780\pi\)
−0.0558275 + 0.998440i \(0.517780\pi\)
\(224\) −4.80341 −0.320941
\(225\) 5.73518 0.382345
\(226\) −17.9406 −1.19339
\(227\) 22.3102 1.48078 0.740391 0.672176i \(-0.234640\pi\)
0.740391 + 0.672176i \(0.234640\pi\)
\(228\) 5.95208 0.394186
\(229\) −24.3840 −1.61134 −0.805669 0.592365i \(-0.798194\pi\)
−0.805669 + 0.592365i \(0.798194\pi\)
\(230\) −25.0446 −1.65139
\(231\) 3.64615 0.239899
\(232\) −28.4928 −1.87064
\(233\) −17.2618 −1.13086 −0.565431 0.824796i \(-0.691290\pi\)
−0.565431 + 0.824796i \(0.691290\pi\)
\(234\) 0 0
\(235\) 5.85004 0.381614
\(236\) −5.26526 −0.342739
\(237\) 3.24335 0.210678
\(238\) 7.07162 0.458385
\(239\) 6.12302 0.396065 0.198033 0.980195i \(-0.436545\pi\)
0.198033 + 0.980195i \(0.436545\pi\)
\(240\) 3.97522 0.256600
\(241\) 4.04969 0.260863 0.130432 0.991457i \(-0.458364\pi\)
0.130432 + 0.991457i \(0.458364\pi\)
\(242\) 2.35556 0.151421
\(243\) 1.00000 0.0641500
\(244\) −4.11088 −0.263172
\(245\) −3.27646 −0.209325
\(246\) −4.02416 −0.256571
\(247\) 0 0
\(248\) −32.5460 −2.06667
\(249\) −15.6734 −0.993262
\(250\) −2.47302 −0.156408
\(251\) 17.6643 1.11496 0.557479 0.830191i \(-0.311769\pi\)
0.557479 + 0.830191i \(0.311769\pi\)
\(252\) 0.945953 0.0595894
\(253\) −27.1465 −1.70668
\(254\) −4.36832 −0.274093
\(255\) 22.5680 1.41327
\(256\) −16.8234 −1.05146
\(257\) −1.45219 −0.0905854 −0.0452927 0.998974i \(-0.514422\pi\)
−0.0452927 + 0.998974i \(0.514422\pi\)
\(258\) −5.42469 −0.337726
\(259\) −0.298388 −0.0185409
\(260\) 0 0
\(261\) 9.42061 0.583121
\(262\) 3.99373 0.246733
\(263\) 3.02641 0.186617 0.0933083 0.995637i \(-0.470256\pi\)
0.0933083 + 0.995637i \(0.470256\pi\)
\(264\) 11.0278 0.678716
\(265\) −16.1394 −0.991436
\(266\) 6.45995 0.396085
\(267\) 4.85592 0.297177
\(268\) −12.0507 −0.736112
\(269\) −8.80840 −0.537058 −0.268529 0.963272i \(-0.586537\pi\)
−0.268529 + 0.963272i \(0.586537\pi\)
\(270\) −3.36384 −0.204716
\(271\) 2.79485 0.169775 0.0848877 0.996391i \(-0.472947\pi\)
0.0848877 + 0.996391i \(0.472947\pi\)
\(272\) 8.35691 0.506712
\(273\) 0 0
\(274\) 7.26652 0.438987
\(275\) −20.9113 −1.26100
\(276\) −7.04286 −0.423930
\(277\) 24.2433 1.45664 0.728318 0.685239i \(-0.240302\pi\)
0.728318 + 0.685239i \(0.240302\pi\)
\(278\) 16.2442 0.974262
\(279\) 10.7607 0.644229
\(280\) −9.90970 −0.592218
\(281\) −2.10017 −0.125286 −0.0626428 0.998036i \(-0.519953\pi\)
−0.0626428 + 0.998036i \(0.519953\pi\)
\(282\) −1.83309 −0.109159
\(283\) 7.28606 0.433112 0.216556 0.976270i \(-0.430518\pi\)
0.216556 + 0.976270i \(0.430518\pi\)
\(284\) 5.36964 0.318630
\(285\) 20.6160 1.22118
\(286\) 0 0
\(287\) 3.91963 0.231369
\(288\) 4.80341 0.283043
\(289\) 30.4437 1.79080
\(290\) −31.6894 −1.86086
\(291\) 4.26503 0.250020
\(292\) 6.36296 0.372364
\(293\) 2.85760 0.166943 0.0834715 0.996510i \(-0.473399\pi\)
0.0834715 + 0.996510i \(0.473399\pi\)
\(294\) 1.02667 0.0598765
\(295\) −18.2371 −1.06180
\(296\) −0.902480 −0.0524556
\(297\) −3.64615 −0.211571
\(298\) −8.76006 −0.507457
\(299\) 0 0
\(300\) −5.42521 −0.313225
\(301\) 5.28378 0.304552
\(302\) 7.13610 0.410637
\(303\) −6.34614 −0.364576
\(304\) 7.63407 0.437844
\(305\) −14.2387 −0.815304
\(306\) −7.07162 −0.404258
\(307\) −29.8167 −1.70173 −0.850865 0.525384i \(-0.823922\pi\)
−0.850865 + 0.525384i \(0.823922\pi\)
\(308\) −3.44908 −0.196530
\(309\) −9.87950 −0.562025
\(310\) −36.1974 −2.05587
\(311\) 1.71131 0.0970393 0.0485197 0.998822i \(-0.484550\pi\)
0.0485197 + 0.998822i \(0.484550\pi\)
\(312\) 0 0
\(313\) −1.74425 −0.0985909 −0.0492954 0.998784i \(-0.515698\pi\)
−0.0492954 + 0.998784i \(0.515698\pi\)
\(314\) 13.0740 0.737811
\(315\) 3.27646 0.184608
\(316\) −3.06805 −0.172592
\(317\) −1.64195 −0.0922210 −0.0461105 0.998936i \(-0.514683\pi\)
−0.0461105 + 0.998936i \(0.514683\pi\)
\(318\) 5.05724 0.283596
\(319\) −34.3489 −1.92317
\(320\) −24.1083 −1.34770
\(321\) −17.3396 −0.967800
\(322\) −7.64380 −0.425972
\(323\) 43.3399 2.41150
\(324\) −0.945953 −0.0525529
\(325\) 0 0
\(326\) 4.02817 0.223099
\(327\) 7.94895 0.439578
\(328\) 11.8550 0.654583
\(329\) 1.78548 0.0984365
\(330\) 12.2650 0.675168
\(331\) 21.9051 1.20401 0.602006 0.798491i \(-0.294368\pi\)
0.602006 + 0.798491i \(0.294368\pi\)
\(332\) 14.8263 0.813699
\(333\) 0.298388 0.0163516
\(334\) 5.53968 0.303118
\(335\) −41.7394 −2.28047
\(336\) 1.21327 0.0661892
\(337\) 22.0335 1.20024 0.600121 0.799909i \(-0.295119\pi\)
0.600121 + 0.799909i \(0.295119\pi\)
\(338\) 0 0
\(339\) −17.4746 −0.949090
\(340\) −21.3483 −1.15777
\(341\) −39.2352 −2.12471
\(342\) −6.45995 −0.349314
\(343\) −1.00000 −0.0539949
\(344\) 15.9809 0.861631
\(345\) −24.3941 −1.31333
\(346\) 2.08518 0.112100
\(347\) −11.7986 −0.633383 −0.316692 0.948529i \(-0.602572\pi\)
−0.316692 + 0.948529i \(0.602572\pi\)
\(348\) −8.91145 −0.477704
\(349\) 0.644467 0.0344975 0.0172488 0.999851i \(-0.494509\pi\)
0.0172488 + 0.999851i \(0.494509\pi\)
\(350\) −5.88813 −0.314734
\(351\) 0 0
\(352\) −17.5139 −0.933495
\(353\) −24.3481 −1.29592 −0.647960 0.761674i \(-0.724378\pi\)
−0.647960 + 0.761674i \(0.724378\pi\)
\(354\) 5.71453 0.303724
\(355\) 18.5986 0.987112
\(356\) −4.59347 −0.243453
\(357\) 6.88794 0.364548
\(358\) 12.4048 0.655616
\(359\) 0.163028 0.00860429 0.00430214 0.999991i \(-0.498631\pi\)
0.00430214 + 0.999991i \(0.498631\pi\)
\(360\) 9.90970 0.522287
\(361\) 20.5912 1.08375
\(362\) 18.1137 0.952034
\(363\) 2.29438 0.120424
\(364\) 0 0
\(365\) 22.0391 1.15358
\(366\) 4.46164 0.233214
\(367\) 18.1404 0.946920 0.473460 0.880815i \(-0.343005\pi\)
0.473460 + 0.880815i \(0.343005\pi\)
\(368\) −9.03309 −0.470882
\(369\) −3.91963 −0.204048
\(370\) −1.00373 −0.0521814
\(371\) −4.92587 −0.255739
\(372\) −10.1792 −0.527764
\(373\) 4.28760 0.222004 0.111002 0.993820i \(-0.464594\pi\)
0.111002 + 0.993820i \(0.464594\pi\)
\(374\) 25.7842 1.33327
\(375\) −2.40879 −0.124389
\(376\) 5.40020 0.278494
\(377\) 0 0
\(378\) −1.02667 −0.0528061
\(379\) 21.7188 1.11562 0.557809 0.829969i \(-0.311642\pi\)
0.557809 + 0.829969i \(0.311642\pi\)
\(380\) −19.5017 −1.00042
\(381\) −4.25486 −0.217983
\(382\) 6.84891 0.350421
\(383\) −22.4712 −1.14822 −0.574112 0.818777i \(-0.694653\pi\)
−0.574112 + 0.818777i \(0.694653\pi\)
\(384\) −2.05255 −0.104744
\(385\) −11.9464 −0.608847
\(386\) 16.4164 0.835574
\(387\) −5.28378 −0.268590
\(388\) −4.03451 −0.204821
\(389\) −3.28401 −0.166506 −0.0832530 0.996528i \(-0.526531\pi\)
−0.0832530 + 0.996528i \(0.526531\pi\)
\(390\) 0 0
\(391\) −51.2824 −2.59346
\(392\) −3.02452 −0.152761
\(393\) 3.88999 0.196224
\(394\) 7.54156 0.379938
\(395\) −10.6267 −0.534687
\(396\) 3.44908 0.173323
\(397\) 4.46062 0.223872 0.111936 0.993715i \(-0.464295\pi\)
0.111936 + 0.993715i \(0.464295\pi\)
\(398\) −0.208370 −0.0104446
\(399\) 6.29215 0.315002
\(400\) −6.95831 −0.347916
\(401\) 2.96473 0.148052 0.0740258 0.997256i \(-0.476415\pi\)
0.0740258 + 0.997256i \(0.476415\pi\)
\(402\) 13.0789 0.652317
\(403\) 0 0
\(404\) 6.00315 0.298668
\(405\) −3.27646 −0.162809
\(406\) −9.67184 −0.480005
\(407\) −1.08797 −0.0539285
\(408\) 20.8327 1.03137
\(409\) −19.5362 −0.966004 −0.483002 0.875619i \(-0.660454\pi\)
−0.483002 + 0.875619i \(0.660454\pi\)
\(410\) 13.1850 0.651161
\(411\) 7.07777 0.349121
\(412\) 9.34554 0.460422
\(413\) −5.56609 −0.273889
\(414\) 7.64380 0.375672
\(415\) 51.3533 2.52083
\(416\) 0 0
\(417\) 15.8222 0.774818
\(418\) 23.5539 1.15206
\(419\) −25.9290 −1.26671 −0.633357 0.773860i \(-0.718323\pi\)
−0.633357 + 0.773860i \(0.718323\pi\)
\(420\) −3.09937 −0.151234
\(421\) 6.59832 0.321583 0.160791 0.986988i \(-0.448595\pi\)
0.160791 + 0.986988i \(0.448595\pi\)
\(422\) 8.85725 0.431164
\(423\) −1.78548 −0.0868128
\(424\) −14.8984 −0.723529
\(425\) −39.5035 −1.91620
\(426\) −5.82782 −0.282359
\(427\) −4.34575 −0.210306
\(428\) 16.4024 0.792841
\(429\) 0 0
\(430\) 17.7738 0.857127
\(431\) −9.76500 −0.470363 −0.235182 0.971951i \(-0.575569\pi\)
−0.235182 + 0.971951i \(0.575569\pi\)
\(432\) −1.21327 −0.0583734
\(433\) 31.1719 1.49802 0.749012 0.662556i \(-0.230528\pi\)
0.749012 + 0.662556i \(0.230528\pi\)
\(434\) −11.0477 −0.530307
\(435\) −30.8662 −1.47992
\(436\) −7.51933 −0.360111
\(437\) −46.8467 −2.24098
\(438\) −6.90589 −0.329976
\(439\) 0.0700703 0.00334427 0.00167214 0.999999i \(-0.499468\pi\)
0.00167214 + 0.999999i \(0.499468\pi\)
\(440\) −36.1322 −1.72254
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −13.9060 −0.660692 −0.330346 0.943860i \(-0.607166\pi\)
−0.330346 + 0.943860i \(0.607166\pi\)
\(444\) −0.282261 −0.0133955
\(445\) −15.9102 −0.754216
\(446\) −1.71183 −0.0810575
\(447\) −8.53252 −0.403574
\(448\) −7.35804 −0.347635
\(449\) 41.9051 1.97762 0.988812 0.149164i \(-0.0476582\pi\)
0.988812 + 0.149164i \(0.0476582\pi\)
\(450\) 5.88813 0.277569
\(451\) 14.2916 0.672963
\(452\) 16.5302 0.777513
\(453\) 6.95074 0.326574
\(454\) 22.9052 1.07499
\(455\) 0 0
\(456\) 19.0307 0.891195
\(457\) −11.9231 −0.557738 −0.278869 0.960329i \(-0.589960\pi\)
−0.278869 + 0.960329i \(0.589960\pi\)
\(458\) −25.0343 −1.16977
\(459\) −6.88794 −0.321501
\(460\) 23.0756 1.07591
\(461\) 18.0671 0.841470 0.420735 0.907184i \(-0.361772\pi\)
0.420735 + 0.907184i \(0.361772\pi\)
\(462\) 3.74338 0.174158
\(463\) −7.47553 −0.347417 −0.173709 0.984797i \(-0.555575\pi\)
−0.173709 + 0.984797i \(0.555575\pi\)
\(464\) −11.4297 −0.530612
\(465\) −35.2571 −1.63501
\(466\) −17.7222 −0.820964
\(467\) 33.0758 1.53056 0.765282 0.643695i \(-0.222600\pi\)
0.765282 + 0.643695i \(0.222600\pi\)
\(468\) 0 0
\(469\) −12.7392 −0.588241
\(470\) 6.00605 0.277038
\(471\) 12.7344 0.586772
\(472\) −16.8347 −0.774881
\(473\) 19.2654 0.885826
\(474\) 3.32984 0.152945
\(475\) −36.0866 −1.65577
\(476\) −6.51566 −0.298645
\(477\) 4.92587 0.225540
\(478\) 6.28631 0.287529
\(479\) 10.4405 0.477037 0.238519 0.971138i \(-0.423338\pi\)
0.238519 + 0.971138i \(0.423338\pi\)
\(480\) −15.7382 −0.718346
\(481\) 0 0
\(482\) 4.15769 0.189377
\(483\) −7.44525 −0.338771
\(484\) −2.17037 −0.0986533
\(485\) −13.9742 −0.634535
\(486\) 1.02667 0.0465706
\(487\) −39.3547 −1.78333 −0.891665 0.452695i \(-0.850463\pi\)
−0.891665 + 0.452695i \(0.850463\pi\)
\(488\) −13.1438 −0.594992
\(489\) 3.92353 0.177428
\(490\) −3.36384 −0.151963
\(491\) 32.2361 1.45479 0.727397 0.686217i \(-0.240730\pi\)
0.727397 + 0.686217i \(0.240730\pi\)
\(492\) 3.70779 0.167160
\(493\) −64.8886 −2.92243
\(494\) 0 0
\(495\) 11.9464 0.536953
\(496\) −13.0557 −0.586217
\(497\) 5.67644 0.254623
\(498\) −16.0914 −0.721073
\(499\) −6.32415 −0.283108 −0.141554 0.989931i \(-0.545210\pi\)
−0.141554 + 0.989931i \(0.545210\pi\)
\(500\) 2.27860 0.101902
\(501\) 5.39579 0.241066
\(502\) 18.1353 0.809420
\(503\) 11.6484 0.519377 0.259689 0.965692i \(-0.416380\pi\)
0.259689 + 0.965692i \(0.416380\pi\)
\(504\) 3.02452 0.134723
\(505\) 20.7929 0.925270
\(506\) −27.8704 −1.23899
\(507\) 0 0
\(508\) 4.02489 0.178576
\(509\) −13.0251 −0.577328 −0.288664 0.957430i \(-0.593211\pi\)
−0.288664 + 0.957430i \(0.593211\pi\)
\(510\) 23.1699 1.02598
\(511\) 6.72651 0.297563
\(512\) −13.1669 −0.581901
\(513\) −6.29215 −0.277805
\(514\) −1.49092 −0.0657617
\(515\) 32.3698 1.42638
\(516\) 4.99821 0.220034
\(517\) 6.51011 0.286314
\(518\) −0.306346 −0.0134601
\(519\) 2.03101 0.0891516
\(520\) 0 0
\(521\) −23.3360 −1.02237 −0.511185 0.859471i \(-0.670793\pi\)
−0.511185 + 0.859471i \(0.670793\pi\)
\(522\) 9.67184 0.423325
\(523\) −38.8457 −1.69860 −0.849301 0.527908i \(-0.822977\pi\)
−0.849301 + 0.527908i \(0.822977\pi\)
\(524\) −3.67975 −0.160750
\(525\) −5.73518 −0.250304
\(526\) 3.10712 0.135477
\(527\) −74.1193 −3.22869
\(528\) 4.42375 0.192519
\(529\) 32.4318 1.41008
\(530\) −16.5698 −0.719747
\(531\) 5.56609 0.241548
\(532\) −5.95208 −0.258055
\(533\) 0 0
\(534\) 4.98541 0.215740
\(535\) 56.8124 2.45621
\(536\) −38.5299 −1.66424
\(537\) 12.0826 0.521403
\(538\) −9.04330 −0.389884
\(539\) −3.64615 −0.157051
\(540\) 3.09937 0.133376
\(541\) 38.2152 1.64300 0.821499 0.570210i \(-0.193138\pi\)
0.821499 + 0.570210i \(0.193138\pi\)
\(542\) 2.86939 0.123251
\(543\) 17.6432 0.757141
\(544\) −33.0856 −1.41853
\(545\) −26.0444 −1.11562
\(546\) 0 0
\(547\) −41.3324 −1.76724 −0.883622 0.468200i \(-0.844903\pi\)
−0.883622 + 0.468200i \(0.844903\pi\)
\(548\) −6.69524 −0.286006
\(549\) 4.34575 0.185472
\(550\) −21.4690 −0.915440
\(551\) −59.2759 −2.52524
\(552\) −22.5183 −0.958442
\(553\) −3.24335 −0.137921
\(554\) 24.8898 1.05747
\(555\) −0.977656 −0.0414992
\(556\) −14.9671 −0.634746
\(557\) 10.4059 0.440913 0.220456 0.975397i \(-0.429245\pi\)
0.220456 + 0.975397i \(0.429245\pi\)
\(558\) 11.0477 0.467687
\(559\) 0 0
\(560\) −3.97522 −0.167984
\(561\) 25.1144 1.06033
\(562\) −2.15618 −0.0909528
\(563\) −4.99675 −0.210588 −0.105294 0.994441i \(-0.533578\pi\)
−0.105294 + 0.994441i \(0.533578\pi\)
\(564\) 1.68898 0.0711187
\(565\) 57.2548 2.40873
\(566\) 7.48037 0.314423
\(567\) −1.00000 −0.0419961
\(568\) 17.1685 0.720373
\(569\) −26.4626 −1.10937 −0.554686 0.832060i \(-0.687161\pi\)
−0.554686 + 0.832060i \(0.687161\pi\)
\(570\) 21.1658 0.886536
\(571\) 16.4007 0.686349 0.343175 0.939272i \(-0.388498\pi\)
0.343175 + 0.939272i \(0.388498\pi\)
\(572\) 0 0
\(573\) 6.67101 0.278685
\(574\) 4.02416 0.167965
\(575\) 42.6999 1.78071
\(576\) 7.35804 0.306585
\(577\) 10.3983 0.432887 0.216443 0.976295i \(-0.430554\pi\)
0.216443 + 0.976295i \(0.430554\pi\)
\(578\) 31.2555 1.30006
\(579\) 15.9900 0.664522
\(580\) 29.1980 1.21238
\(581\) 15.6734 0.650243
\(582\) 4.37877 0.181506
\(583\) −17.9604 −0.743846
\(584\) 20.3444 0.841859
\(585\) 0 0
\(586\) 2.93381 0.121195
\(587\) 20.2156 0.834388 0.417194 0.908818i \(-0.363014\pi\)
0.417194 + 0.908818i \(0.363014\pi\)
\(588\) −0.945953 −0.0390104
\(589\) −67.7082 −2.78987
\(590\) −18.7234 −0.770831
\(591\) 7.34567 0.302160
\(592\) −0.362025 −0.0148791
\(593\) 0.815771 0.0334997 0.0167499 0.999860i \(-0.494668\pi\)
0.0167499 + 0.999860i \(0.494668\pi\)
\(594\) −3.74338 −0.153593
\(595\) −22.5680 −0.925199
\(596\) 8.07136 0.330616
\(597\) −0.202957 −0.00830649
\(598\) 0 0
\(599\) −17.0984 −0.698623 −0.349312 0.937007i \(-0.613585\pi\)
−0.349312 + 0.937007i \(0.613585\pi\)
\(600\) −17.3461 −0.708153
\(601\) −4.62318 −0.188584 −0.0942918 0.995545i \(-0.530059\pi\)
−0.0942918 + 0.995545i \(0.530059\pi\)
\(602\) 5.42469 0.221094
\(603\) 12.7392 0.518780
\(604\) −6.57507 −0.267536
\(605\) −7.51743 −0.305627
\(606\) −6.51538 −0.264669
\(607\) −41.9476 −1.70260 −0.851300 0.524679i \(-0.824185\pi\)
−0.851300 + 0.524679i \(0.824185\pi\)
\(608\) −30.2238 −1.22574
\(609\) −9.42061 −0.381742
\(610\) −14.6184 −0.591881
\(611\) 0 0
\(612\) 6.51566 0.263380
\(613\) 44.3300 1.79047 0.895237 0.445591i \(-0.147006\pi\)
0.895237 + 0.445591i \(0.147006\pi\)
\(614\) −30.6119 −1.23539
\(615\) 12.8425 0.517860
\(616\) −11.0278 −0.444324
\(617\) 10.6983 0.430699 0.215350 0.976537i \(-0.430911\pi\)
0.215350 + 0.976537i \(0.430911\pi\)
\(618\) −10.1430 −0.408010
\(619\) −9.90538 −0.398131 −0.199065 0.979986i \(-0.563791\pi\)
−0.199065 + 0.979986i \(0.563791\pi\)
\(620\) 33.3516 1.33943
\(621\) 7.44525 0.298768
\(622\) 1.75694 0.0704471
\(623\) −4.85592 −0.194548
\(624\) 0 0
\(625\) −20.7836 −0.831345
\(626\) −1.79077 −0.0715734
\(627\) 22.9421 0.916219
\(628\) −12.0462 −0.480695
\(629\) −2.05528 −0.0819493
\(630\) 3.36384 0.134018
\(631\) −37.4082 −1.48920 −0.744599 0.667512i \(-0.767359\pi\)
−0.744599 + 0.667512i \(0.767359\pi\)
\(632\) −9.80956 −0.390203
\(633\) 8.62718 0.342900
\(634\) −1.68574 −0.0669491
\(635\) 13.9409 0.553226
\(636\) −4.65964 −0.184767
\(637\) 0 0
\(638\) −35.2649 −1.39615
\(639\) −5.67644 −0.224556
\(640\) 6.72509 0.265833
\(641\) 9.02222 0.356356 0.178178 0.983998i \(-0.442980\pi\)
0.178178 + 0.983998i \(0.442980\pi\)
\(642\) −17.8020 −0.702588
\(643\) 37.7554 1.48893 0.744463 0.667663i \(-0.232705\pi\)
0.744463 + 0.667663i \(0.232705\pi\)
\(644\) 7.04286 0.277527
\(645\) 17.3121 0.681663
\(646\) 44.4957 1.75066
\(647\) 16.3059 0.641051 0.320526 0.947240i \(-0.396140\pi\)
0.320526 + 0.947240i \(0.396140\pi\)
\(648\) −3.02452 −0.118814
\(649\) −20.2948 −0.796640
\(650\) 0 0
\(651\) −10.7607 −0.421747
\(652\) −3.71148 −0.145353
\(653\) 15.6155 0.611082 0.305541 0.952179i \(-0.401163\pi\)
0.305541 + 0.952179i \(0.401163\pi\)
\(654\) 8.16094 0.319118
\(655\) −12.7454 −0.498003
\(656\) 4.75557 0.185674
\(657\) −6.72651 −0.262426
\(658\) 1.83309 0.0714613
\(659\) 13.2703 0.516936 0.258468 0.966020i \(-0.416782\pi\)
0.258468 + 0.966020i \(0.416782\pi\)
\(660\) −11.3008 −0.439882
\(661\) 37.7744 1.46925 0.734627 0.678472i \(-0.237357\pi\)
0.734627 + 0.678472i \(0.237357\pi\)
\(662\) 22.4893 0.874070
\(663\) 0 0
\(664\) 47.4045 1.83965
\(665\) −20.6160 −0.799453
\(666\) 0.306346 0.0118707
\(667\) 70.1388 2.71579
\(668\) −5.10416 −0.197486
\(669\) −1.66736 −0.0644640
\(670\) −42.8525 −1.65554
\(671\) −15.8452 −0.611699
\(672\) −4.80341 −0.185295
\(673\) 32.3855 1.24837 0.624185 0.781277i \(-0.285431\pi\)
0.624185 + 0.781277i \(0.285431\pi\)
\(674\) 22.6211 0.871333
\(675\) 5.73518 0.220747
\(676\) 0 0
\(677\) 22.4981 0.864672 0.432336 0.901713i \(-0.357689\pi\)
0.432336 + 0.901713i \(0.357689\pi\)
\(678\) −17.9406 −0.689005
\(679\) −4.26503 −0.163677
\(680\) −68.2574 −2.61755
\(681\) 22.3102 0.854930
\(682\) −40.2816 −1.54246
\(683\) 10.4531 0.399978 0.199989 0.979798i \(-0.435909\pi\)
0.199989 + 0.979798i \(0.435909\pi\)
\(684\) 5.95208 0.227583
\(685\) −23.1900 −0.886045
\(686\) −1.02667 −0.0391984
\(687\) −24.3840 −0.930307
\(688\) 6.41064 0.244404
\(689\) 0 0
\(690\) −25.0446 −0.953432
\(691\) −18.9877 −0.722326 −0.361163 0.932503i \(-0.617620\pi\)
−0.361163 + 0.932503i \(0.617620\pi\)
\(692\) −1.92124 −0.0730347
\(693\) 3.64615 0.138506
\(694\) −12.1133 −0.459813
\(695\) −51.8409 −1.96644
\(696\) −28.4928 −1.08002
\(697\) 26.9982 1.02263
\(698\) 0.661653 0.0250439
\(699\) −17.2618 −0.652903
\(700\) 5.42521 0.205054
\(701\) −24.2484 −0.915848 −0.457924 0.888991i \(-0.651407\pi\)
−0.457924 + 0.888991i \(0.651407\pi\)
\(702\) 0 0
\(703\) −1.87750 −0.0708114
\(704\) −26.8285 −1.01114
\(705\) 5.85004 0.220325
\(706\) −24.9975 −0.940792
\(707\) 6.34614 0.238671
\(708\) −5.26526 −0.197881
\(709\) 44.4465 1.66922 0.834611 0.550839i \(-0.185692\pi\)
0.834611 + 0.550839i \(0.185692\pi\)
\(710\) 19.0946 0.716607
\(711\) 3.24335 0.121635
\(712\) −14.6868 −0.550411
\(713\) 80.1164 3.00038
\(714\) 7.07162 0.264649
\(715\) 0 0
\(716\) −11.4296 −0.427143
\(717\) 6.12302 0.228668
\(718\) 0.167376 0.00624640
\(719\) 5.93676 0.221404 0.110702 0.993854i \(-0.464690\pi\)
0.110702 + 0.993854i \(0.464690\pi\)
\(720\) 3.97522 0.148148
\(721\) 9.87950 0.367932
\(722\) 21.1403 0.786760
\(723\) 4.04969 0.150610
\(724\) −16.6896 −0.620264
\(725\) 54.0289 2.00658
\(726\) 2.35556 0.0874232
\(727\) 27.7128 1.02781 0.513905 0.857847i \(-0.328198\pi\)
0.513905 + 0.857847i \(0.328198\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 22.6269 0.837458
\(731\) 36.3943 1.34609
\(732\) −4.11088 −0.151942
\(733\) 22.0420 0.814141 0.407071 0.913397i \(-0.366550\pi\)
0.407071 + 0.913397i \(0.366550\pi\)
\(734\) 18.6242 0.687430
\(735\) −3.27646 −0.120854
\(736\) 35.7626 1.31823
\(737\) −46.4489 −1.71097
\(738\) −4.02416 −0.148131
\(739\) −0.984398 −0.0362117 −0.0181058 0.999836i \(-0.505764\pi\)
−0.0181058 + 0.999836i \(0.505764\pi\)
\(740\) 0.924817 0.0339969
\(741\) 0 0
\(742\) −5.05724 −0.185657
\(743\) 36.9260 1.35468 0.677341 0.735669i \(-0.263132\pi\)
0.677341 + 0.735669i \(0.263132\pi\)
\(744\) −32.5460 −1.19320
\(745\) 27.9564 1.02424
\(746\) 4.40194 0.161167
\(747\) −15.6734 −0.573460
\(748\) −23.7570 −0.868644
\(749\) 17.3396 0.633574
\(750\) −2.47302 −0.0903020
\(751\) −2.42350 −0.0884349 −0.0442174 0.999022i \(-0.514079\pi\)
−0.0442174 + 0.999022i \(0.514079\pi\)
\(752\) 2.16626 0.0789954
\(753\) 17.6643 0.643722
\(754\) 0 0
\(755\) −22.7738 −0.828824
\(756\) 0.945953 0.0344040
\(757\) 17.2323 0.626320 0.313160 0.949700i \(-0.398612\pi\)
0.313160 + 0.949700i \(0.398612\pi\)
\(758\) 22.2980 0.809898
\(759\) −27.1465 −0.985355
\(760\) −62.3533 −2.26179
\(761\) −25.2003 −0.913509 −0.456754 0.889593i \(-0.650988\pi\)
−0.456754 + 0.889593i \(0.650988\pi\)
\(762\) −4.36832 −0.158248
\(763\) −7.94895 −0.287771
\(764\) −6.31046 −0.228304
\(765\) 22.5680 0.815949
\(766\) −23.0705 −0.833569
\(767\) 0 0
\(768\) −16.8234 −0.607061
\(769\) −15.1674 −0.546950 −0.273475 0.961879i \(-0.588173\pi\)
−0.273475 + 0.961879i \(0.588173\pi\)
\(770\) −12.2650 −0.442001
\(771\) −1.45219 −0.0522995
\(772\) −15.1258 −0.544389
\(773\) −39.0898 −1.40596 −0.702981 0.711209i \(-0.748148\pi\)
−0.702981 + 0.711209i \(0.748148\pi\)
\(774\) −5.42469 −0.194986
\(775\) 61.7148 2.21686
\(776\) −12.8996 −0.463070
\(777\) −0.298388 −0.0107046
\(778\) −3.37159 −0.120877
\(779\) 24.6629 0.883641
\(780\) 0 0
\(781\) 20.6971 0.740601
\(782\) −52.6500 −1.88276
\(783\) 9.42061 0.336665
\(784\) −1.21327 −0.0433310
\(785\) −41.7238 −1.48919
\(786\) 3.99373 0.142452
\(787\) 34.6046 1.23352 0.616761 0.787151i \(-0.288445\pi\)
0.616761 + 0.787151i \(0.288445\pi\)
\(788\) −6.94865 −0.247536
\(789\) 3.02641 0.107743
\(790\) −10.9101 −0.388164
\(791\) 17.4746 0.621326
\(792\) 11.0278 0.391857
\(793\) 0 0
\(794\) 4.57958 0.162523
\(795\) −16.1394 −0.572406
\(796\) 0.191988 0.00680483
\(797\) −26.6138 −0.942708 −0.471354 0.881944i \(-0.656235\pi\)
−0.471354 + 0.881944i \(0.656235\pi\)
\(798\) 6.45995 0.228680
\(799\) 12.2982 0.435081
\(800\) 27.5484 0.973983
\(801\) 4.85592 0.171575
\(802\) 3.04379 0.107480
\(803\) 24.5258 0.865498
\(804\) −12.0507 −0.424994
\(805\) 24.3941 0.859778
\(806\) 0 0
\(807\) −8.80840 −0.310070
\(808\) 19.1940 0.675242
\(809\) −42.4083 −1.49100 −0.745499 0.666507i \(-0.767789\pi\)
−0.745499 + 0.666507i \(0.767789\pi\)
\(810\) −3.36384 −0.118193
\(811\) −2.66908 −0.0937242 −0.0468621 0.998901i \(-0.514922\pi\)
−0.0468621 + 0.998901i \(0.514922\pi\)
\(812\) 8.91145 0.312731
\(813\) 2.79485 0.0980198
\(814\) −1.11698 −0.0391502
\(815\) −12.8553 −0.450301
\(816\) 8.35691 0.292550
\(817\) 33.2463 1.16314
\(818\) −20.0572 −0.701284
\(819\) 0 0
\(820\) −12.1484 −0.424241
\(821\) 26.1841 0.913831 0.456915 0.889510i \(-0.348954\pi\)
0.456915 + 0.889510i \(0.348954\pi\)
\(822\) 7.26652 0.253449
\(823\) 26.1469 0.911423 0.455712 0.890128i \(-0.349385\pi\)
0.455712 + 0.890128i \(0.349385\pi\)
\(824\) 29.8807 1.04094
\(825\) −20.9113 −0.728038
\(826\) −5.71453 −0.198834
\(827\) 23.2089 0.807053 0.403526 0.914968i \(-0.367784\pi\)
0.403526 + 0.914968i \(0.367784\pi\)
\(828\) −7.04286 −0.244756
\(829\) −18.1602 −0.630728 −0.315364 0.948971i \(-0.602127\pi\)
−0.315364 + 0.948971i \(0.602127\pi\)
\(830\) 52.7228 1.83003
\(831\) 24.2433 0.840989
\(832\) 0 0
\(833\) −6.88794 −0.238653
\(834\) 16.2442 0.562490
\(835\) −17.6791 −0.611810
\(836\) −21.7021 −0.750584
\(837\) 10.7607 0.371946
\(838\) −26.6205 −0.919588
\(839\) 1.18110 0.0407762 0.0203881 0.999792i \(-0.493510\pi\)
0.0203881 + 0.999792i \(0.493510\pi\)
\(840\) −9.90970 −0.341917
\(841\) 59.7479 2.06027
\(842\) 6.77429 0.233457
\(843\) −2.10017 −0.0723336
\(844\) −8.16090 −0.280910
\(845\) 0 0
\(846\) −1.83309 −0.0630230
\(847\) −2.29438 −0.0788358
\(848\) −5.97640 −0.205231
\(849\) 7.28606 0.250057
\(850\) −40.5570 −1.39109
\(851\) 2.22158 0.0761546
\(852\) 5.36964 0.183961
\(853\) 15.2735 0.522955 0.261477 0.965210i \(-0.415790\pi\)
0.261477 + 0.965210i \(0.415790\pi\)
\(854\) −4.46164 −0.152674
\(855\) 20.6160 0.705051
\(856\) 52.4438 1.79249
\(857\) 5.54169 0.189301 0.0946503 0.995511i \(-0.469827\pi\)
0.0946503 + 0.995511i \(0.469827\pi\)
\(858\) 0 0
\(859\) 30.5667 1.04292 0.521461 0.853275i \(-0.325387\pi\)
0.521461 + 0.853275i \(0.325387\pi\)
\(860\) −16.3764 −0.558431
\(861\) 3.91963 0.133581
\(862\) −10.0254 −0.341467
\(863\) 46.0379 1.56715 0.783574 0.621299i \(-0.213395\pi\)
0.783574 + 0.621299i \(0.213395\pi\)
\(864\) 4.80341 0.163415
\(865\) −6.65453 −0.226261
\(866\) 32.0032 1.08751
\(867\) 30.4437 1.03392
\(868\) 10.1792 0.345503
\(869\) −11.8257 −0.401160
\(870\) −31.6894 −1.07437
\(871\) 0 0
\(872\) −24.0417 −0.814156
\(873\) 4.26503 0.144349
\(874\) −48.0960 −1.62687
\(875\) 2.40879 0.0814318
\(876\) 6.36296 0.214985
\(877\) −14.8745 −0.502277 −0.251138 0.967951i \(-0.580805\pi\)
−0.251138 + 0.967951i \(0.580805\pi\)
\(878\) 0.0719390 0.00242782
\(879\) 2.85760 0.0963845
\(880\) −14.4942 −0.488601
\(881\) −16.6031 −0.559371 −0.279686 0.960092i \(-0.590230\pi\)
−0.279686 + 0.960092i \(0.590230\pi\)
\(882\) 1.02667 0.0345697
\(883\) −24.9994 −0.841298 −0.420649 0.907223i \(-0.638198\pi\)
−0.420649 + 0.907223i \(0.638198\pi\)
\(884\) 0 0
\(885\) −18.2371 −0.613032
\(886\) −14.2768 −0.479639
\(887\) −2.86708 −0.0962672 −0.0481336 0.998841i \(-0.515327\pi\)
−0.0481336 + 0.998841i \(0.515327\pi\)
\(888\) −0.902480 −0.0302852
\(889\) 4.25486 0.142703
\(890\) −16.3345 −0.547534
\(891\) −3.64615 −0.122150
\(892\) 1.57725 0.0528102
\(893\) 11.2345 0.375948
\(894\) −8.76006 −0.292980
\(895\) −39.5882 −1.32329
\(896\) 2.05255 0.0685708
\(897\) 0 0
\(898\) 43.0227 1.43568
\(899\) 101.373 3.38097
\(900\) −5.42521 −0.180840
\(901\) −33.9291 −1.13034
\(902\) 14.6727 0.488547
\(903\) 5.28378 0.175833
\(904\) 52.8522 1.75784
\(905\) −57.8071 −1.92157
\(906\) 7.13610 0.237081
\(907\) −21.7144 −0.721014 −0.360507 0.932757i \(-0.617396\pi\)
−0.360507 + 0.932757i \(0.617396\pi\)
\(908\) −21.1044 −0.700375
\(909\) −6.34614 −0.210488
\(910\) 0 0
\(911\) 15.6928 0.519925 0.259962 0.965619i \(-0.416290\pi\)
0.259962 + 0.965619i \(0.416290\pi\)
\(912\) 7.63407 0.252789
\(913\) 57.1476 1.89131
\(914\) −12.2410 −0.404898
\(915\) −14.2387 −0.470716
\(916\) 23.0661 0.762125
\(917\) −3.88999 −0.128459
\(918\) −7.07162 −0.233398
\(919\) −20.1788 −0.665637 −0.332819 0.942991i \(-0.608000\pi\)
−0.332819 + 0.942991i \(0.608000\pi\)
\(920\) 73.7802 2.43246
\(921\) −29.8167 −0.982494
\(922\) 18.5489 0.610877
\(923\) 0 0
\(924\) −3.44908 −0.113466
\(925\) 1.71131 0.0562675
\(926\) −7.67489 −0.252212
\(927\) −9.87950 −0.324485
\(928\) 45.2510 1.48544
\(929\) −34.7349 −1.13961 −0.569807 0.821779i \(-0.692982\pi\)
−0.569807 + 0.821779i \(0.692982\pi\)
\(930\) −36.1974 −1.18696
\(931\) −6.29215 −0.206217
\(932\) 16.3289 0.534871
\(933\) 1.71131 0.0560257
\(934\) 33.9578 1.11113
\(935\) −82.2863 −2.69105
\(936\) 0 0
\(937\) −43.6472 −1.42589 −0.712947 0.701218i \(-0.752640\pi\)
−0.712947 + 0.701218i \(0.752640\pi\)
\(938\) −13.0789 −0.427042
\(939\) −1.74425 −0.0569215
\(940\) −5.53386 −0.180495
\(941\) 34.2059 1.11508 0.557541 0.830150i \(-0.311745\pi\)
0.557541 + 0.830150i \(0.311745\pi\)
\(942\) 13.0740 0.425975
\(943\) −29.1827 −0.950318
\(944\) −6.75316 −0.219797
\(945\) 3.27646 0.106583
\(946\) 19.7792 0.643078
\(947\) −47.6701 −1.54907 −0.774534 0.632532i \(-0.782016\pi\)
−0.774534 + 0.632532i \(0.782016\pi\)
\(948\) −3.06805 −0.0996458
\(949\) 0 0
\(950\) −37.0490 −1.20203
\(951\) −1.64195 −0.0532438
\(952\) −20.8327 −0.675191
\(953\) −48.2855 −1.56412 −0.782060 0.623204i \(-0.785831\pi\)
−0.782060 + 0.623204i \(0.785831\pi\)
\(954\) 5.05724 0.163734
\(955\) −21.8573 −0.707285
\(956\) −5.79209 −0.187329
\(957\) −34.3489 −1.11034
\(958\) 10.7189 0.346312
\(959\) −7.07777 −0.228553
\(960\) −24.1083 −0.778093
\(961\) 84.7935 2.73528
\(962\) 0 0
\(963\) −17.3396 −0.558760
\(964\) −3.83082 −0.123382
\(965\) −52.3906 −1.68651
\(966\) −7.64380 −0.245935
\(967\) 2.78480 0.0895533 0.0447766 0.998997i \(-0.485742\pi\)
0.0447766 + 0.998997i \(0.485742\pi\)
\(968\) −6.93938 −0.223040
\(969\) 43.3399 1.39228
\(970\) −14.3468 −0.460650
\(971\) 6.50695 0.208818 0.104409 0.994534i \(-0.466705\pi\)
0.104409 + 0.994534i \(0.466705\pi\)
\(972\) −0.945953 −0.0303414
\(973\) −15.8222 −0.507238
\(974\) −40.4042 −1.29463
\(975\) 0 0
\(976\) −5.27256 −0.168771
\(977\) 25.8860 0.828165 0.414083 0.910239i \(-0.364102\pi\)
0.414083 + 0.910239i \(0.364102\pi\)
\(978\) 4.02817 0.128807
\(979\) −17.7054 −0.565866
\(980\) 3.09937 0.0990059
\(981\) 7.94895 0.253791
\(982\) 33.0958 1.05613
\(983\) 23.2474 0.741476 0.370738 0.928738i \(-0.379105\pi\)
0.370738 + 0.928738i \(0.379105\pi\)
\(984\) 11.8550 0.377923
\(985\) −24.0678 −0.766863
\(986\) −66.6190 −2.12158
\(987\) 1.78548 0.0568323
\(988\) 0 0
\(989\) −39.3391 −1.25091
\(990\) 12.2650 0.389808
\(991\) 44.6377 1.41796 0.708981 0.705228i \(-0.249155\pi\)
0.708981 + 0.705228i \(0.249155\pi\)
\(992\) 51.6882 1.64110
\(993\) 21.9051 0.695137
\(994\) 5.82782 0.184847
\(995\) 0.664981 0.0210813
\(996\) 14.8263 0.469790
\(997\) −15.0365 −0.476210 −0.238105 0.971239i \(-0.576526\pi\)
−0.238105 + 0.971239i \(0.576526\pi\)
\(998\) −6.49280 −0.205526
\(999\) 0.298388 0.00944058
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.bh.1.9 yes 15
13.12 even 2 3549.2.a.bg.1.7 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.7 15 13.12 even 2
3549.2.a.bh.1.9 yes 15 1.1 even 1 trivial