Properties

Label 3549.2.a.bh.1.15
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 1.15
Root \(2.80363\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.80363 q^{2} +1.00000 q^{3} +5.86034 q^{4} -3.14248 q^{5} +2.80363 q^{6} -1.00000 q^{7} +10.8230 q^{8} +1.00000 q^{9} -8.81036 q^{10} +3.00418 q^{11} +5.86034 q^{12} -2.80363 q^{14} -3.14248 q^{15} +18.6229 q^{16} +3.41447 q^{17} +2.80363 q^{18} -4.86056 q^{19} -18.4160 q^{20} -1.00000 q^{21} +8.42260 q^{22} +5.37767 q^{23} +10.8230 q^{24} +4.87520 q^{25} +1.00000 q^{27} -5.86034 q^{28} +0.848910 q^{29} -8.81036 q^{30} +0.451052 q^{31} +30.5658 q^{32} +3.00418 q^{33} +9.57292 q^{34} +3.14248 q^{35} +5.86034 q^{36} -3.88581 q^{37} -13.6272 q^{38} -34.0110 q^{40} +10.5244 q^{41} -2.80363 q^{42} +7.20767 q^{43} +17.6055 q^{44} -3.14248 q^{45} +15.0770 q^{46} -9.33384 q^{47} +18.6229 q^{48} +1.00000 q^{49} +13.6683 q^{50} +3.41447 q^{51} -13.1147 q^{53} +2.80363 q^{54} -9.44058 q^{55} -10.8230 q^{56} -4.86056 q^{57} +2.38003 q^{58} +1.45785 q^{59} -18.4160 q^{60} +4.95821 q^{61} +1.26458 q^{62} -1.00000 q^{63} +48.4493 q^{64} +8.42260 q^{66} +4.57857 q^{67} +20.0100 q^{68} +5.37767 q^{69} +8.81036 q^{70} -2.36205 q^{71} +10.8230 q^{72} +1.24210 q^{73} -10.8944 q^{74} +4.87520 q^{75} -28.4845 q^{76} -3.00418 q^{77} -7.10832 q^{79} -58.5222 q^{80} +1.00000 q^{81} +29.5065 q^{82} +5.04895 q^{83} -5.86034 q^{84} -10.7299 q^{85} +20.2076 q^{86} +0.848910 q^{87} +32.5141 q^{88} -12.6846 q^{89} -8.81036 q^{90} +31.5150 q^{92} +0.451052 q^{93} -26.1686 q^{94} +15.2742 q^{95} +30.5658 q^{96} -4.29846 q^{97} +2.80363 q^{98} +3.00418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.80363 1.98247 0.991233 0.132127i \(-0.0421807\pi\)
0.991233 + 0.132127i \(0.0421807\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.86034 2.93017
\(5\) −3.14248 −1.40536 −0.702681 0.711505i \(-0.748014\pi\)
−0.702681 + 0.711505i \(0.748014\pi\)
\(6\) 2.80363 1.14458
\(7\) −1.00000 −0.377964
\(8\) 10.8230 3.82649
\(9\) 1.00000 0.333333
\(10\) −8.81036 −2.78608
\(11\) 3.00418 0.905793 0.452897 0.891563i \(-0.350391\pi\)
0.452897 + 0.891563i \(0.350391\pi\)
\(12\) 5.86034 1.69173
\(13\) 0 0
\(14\) −2.80363 −0.749302
\(15\) −3.14248 −0.811386
\(16\) 18.6229 4.65572
\(17\) 3.41447 0.828132 0.414066 0.910247i \(-0.364108\pi\)
0.414066 + 0.910247i \(0.364108\pi\)
\(18\) 2.80363 0.660822
\(19\) −4.86056 −1.11509 −0.557544 0.830147i \(-0.688256\pi\)
−0.557544 + 0.830147i \(0.688256\pi\)
\(20\) −18.4160 −4.11795
\(21\) −1.00000 −0.218218
\(22\) 8.42260 1.79570
\(23\) 5.37767 1.12132 0.560661 0.828045i \(-0.310547\pi\)
0.560661 + 0.828045i \(0.310547\pi\)
\(24\) 10.8230 2.20923
\(25\) 4.87520 0.975041
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −5.86034 −1.10750
\(29\) 0.848910 0.157639 0.0788193 0.996889i \(-0.474885\pi\)
0.0788193 + 0.996889i \(0.474885\pi\)
\(30\) −8.81036 −1.60854
\(31\) 0.451052 0.0810113 0.0405057 0.999179i \(-0.487103\pi\)
0.0405057 + 0.999179i \(0.487103\pi\)
\(32\) 30.5658 5.40332
\(33\) 3.00418 0.522960
\(34\) 9.57292 1.64174
\(35\) 3.14248 0.531177
\(36\) 5.86034 0.976723
\(37\) −3.88581 −0.638824 −0.319412 0.947616i \(-0.603485\pi\)
−0.319412 + 0.947616i \(0.603485\pi\)
\(38\) −13.6272 −2.21063
\(39\) 0 0
\(40\) −34.0110 −5.37761
\(41\) 10.5244 1.64363 0.821817 0.569752i \(-0.192961\pi\)
0.821817 + 0.569752i \(0.192961\pi\)
\(42\) −2.80363 −0.432609
\(43\) 7.20767 1.09916 0.549579 0.835441i \(-0.314788\pi\)
0.549579 + 0.835441i \(0.314788\pi\)
\(44\) 17.6055 2.65413
\(45\) −3.14248 −0.468454
\(46\) 15.0770 2.22298
\(47\) −9.33384 −1.36148 −0.680741 0.732525i \(-0.738342\pi\)
−0.680741 + 0.732525i \(0.738342\pi\)
\(48\) 18.6229 2.68798
\(49\) 1.00000 0.142857
\(50\) 13.6683 1.93298
\(51\) 3.41447 0.478122
\(52\) 0 0
\(53\) −13.1147 −1.80144 −0.900722 0.434395i \(-0.856962\pi\)
−0.900722 + 0.434395i \(0.856962\pi\)
\(54\) 2.80363 0.381526
\(55\) −9.44058 −1.27297
\(56\) −10.8230 −1.44628
\(57\) −4.86056 −0.643797
\(58\) 2.38003 0.312513
\(59\) 1.45785 0.189797 0.0948983 0.995487i \(-0.469747\pi\)
0.0948983 + 0.995487i \(0.469747\pi\)
\(60\) −18.4160 −2.37750
\(61\) 4.95821 0.634833 0.317417 0.948286i \(-0.397185\pi\)
0.317417 + 0.948286i \(0.397185\pi\)
\(62\) 1.26458 0.160602
\(63\) −1.00000 −0.125988
\(64\) 48.4493 6.05617
\(65\) 0 0
\(66\) 8.42260 1.03675
\(67\) 4.57857 0.559361 0.279680 0.960093i \(-0.409771\pi\)
0.279680 + 0.960093i \(0.409771\pi\)
\(68\) 20.0100 2.42657
\(69\) 5.37767 0.647396
\(70\) 8.81036 1.05304
\(71\) −2.36205 −0.280324 −0.140162 0.990129i \(-0.544762\pi\)
−0.140162 + 0.990129i \(0.544762\pi\)
\(72\) 10.8230 1.27550
\(73\) 1.24210 0.145377 0.0726887 0.997355i \(-0.476842\pi\)
0.0726887 + 0.997355i \(0.476842\pi\)
\(74\) −10.8944 −1.26645
\(75\) 4.87520 0.562940
\(76\) −28.4845 −3.26740
\(77\) −3.00418 −0.342358
\(78\) 0 0
\(79\) −7.10832 −0.799748 −0.399874 0.916570i \(-0.630946\pi\)
−0.399874 + 0.916570i \(0.630946\pi\)
\(80\) −58.5222 −6.54298
\(81\) 1.00000 0.111111
\(82\) 29.5065 3.25845
\(83\) 5.04895 0.554195 0.277097 0.960842i \(-0.410628\pi\)
0.277097 + 0.960842i \(0.410628\pi\)
\(84\) −5.86034 −0.639415
\(85\) −10.7299 −1.16382
\(86\) 20.2076 2.17904
\(87\) 0.848910 0.0910127
\(88\) 32.5141 3.46601
\(89\) −12.6846 −1.34456 −0.672282 0.740295i \(-0.734686\pi\)
−0.672282 + 0.740295i \(0.734686\pi\)
\(90\) −8.81036 −0.928694
\(91\) 0 0
\(92\) 31.5150 3.28567
\(93\) 0.451052 0.0467719
\(94\) −26.1686 −2.69909
\(95\) 15.2742 1.56710
\(96\) 30.5658 3.11961
\(97\) −4.29846 −0.436442 −0.218221 0.975899i \(-0.570025\pi\)
−0.218221 + 0.975899i \(0.570025\pi\)
\(98\) 2.80363 0.283209
\(99\) 3.00418 0.301931
\(100\) 28.5703 2.85703
\(101\) 12.0756 1.20157 0.600784 0.799411i \(-0.294855\pi\)
0.600784 + 0.799411i \(0.294855\pi\)
\(102\) 9.57292 0.947861
\(103\) −1.57289 −0.154981 −0.0774907 0.996993i \(-0.524691\pi\)
−0.0774907 + 0.996993i \(0.524691\pi\)
\(104\) 0 0
\(105\) 3.14248 0.306675
\(106\) −36.7688 −3.57130
\(107\) −12.2770 −1.18687 −0.593433 0.804884i \(-0.702228\pi\)
−0.593433 + 0.804884i \(0.702228\pi\)
\(108\) 5.86034 0.563911
\(109\) −17.7042 −1.69576 −0.847879 0.530190i \(-0.822120\pi\)
−0.847879 + 0.530190i \(0.822120\pi\)
\(110\) −26.4679 −2.52361
\(111\) −3.88581 −0.368825
\(112\) −18.6229 −1.75970
\(113\) −7.67290 −0.721806 −0.360903 0.932603i \(-0.617531\pi\)
−0.360903 + 0.932603i \(0.617531\pi\)
\(114\) −13.6272 −1.27631
\(115\) −16.8993 −1.57586
\(116\) 4.97490 0.461908
\(117\) 0 0
\(118\) 4.08728 0.376265
\(119\) −3.41447 −0.313004
\(120\) −34.0110 −3.10476
\(121\) −1.97492 −0.179538
\(122\) 13.9010 1.25854
\(123\) 10.5244 0.948952
\(124\) 2.64332 0.237377
\(125\) 0.392171 0.0350768
\(126\) −2.80363 −0.249767
\(127\) −15.0680 −1.33707 −0.668534 0.743682i \(-0.733078\pi\)
−0.668534 + 0.743682i \(0.733078\pi\)
\(128\) 74.7024 6.60283
\(129\) 7.20767 0.634600
\(130\) 0 0
\(131\) −7.00728 −0.612229 −0.306114 0.951995i \(-0.599029\pi\)
−0.306114 + 0.951995i \(0.599029\pi\)
\(132\) 17.6055 1.53236
\(133\) 4.86056 0.421464
\(134\) 12.8366 1.10891
\(135\) −3.14248 −0.270462
\(136\) 36.9547 3.16884
\(137\) −12.3949 −1.05897 −0.529486 0.848319i \(-0.677615\pi\)
−0.529486 + 0.848319i \(0.677615\pi\)
\(138\) 15.0770 1.28344
\(139\) −2.68693 −0.227903 −0.113951 0.993486i \(-0.536351\pi\)
−0.113951 + 0.993486i \(0.536351\pi\)
\(140\) 18.4160 1.55644
\(141\) −9.33384 −0.786051
\(142\) −6.62231 −0.555732
\(143\) 0 0
\(144\) 18.6229 1.55191
\(145\) −2.66769 −0.221539
\(146\) 3.48240 0.288206
\(147\) 1.00000 0.0824786
\(148\) −22.7722 −1.87186
\(149\) 2.60806 0.213660 0.106830 0.994277i \(-0.465930\pi\)
0.106830 + 0.994277i \(0.465930\pi\)
\(150\) 13.6683 1.11601
\(151\) −5.13680 −0.418027 −0.209013 0.977913i \(-0.567025\pi\)
−0.209013 + 0.977913i \(0.567025\pi\)
\(152\) −52.6056 −4.26688
\(153\) 3.41447 0.276044
\(154\) −8.42260 −0.678712
\(155\) −1.41742 −0.113850
\(156\) 0 0
\(157\) 10.8870 0.868874 0.434437 0.900702i \(-0.356947\pi\)
0.434437 + 0.900702i \(0.356947\pi\)
\(158\) −19.9291 −1.58547
\(159\) −13.1147 −1.04006
\(160\) −96.0525 −7.59362
\(161\) −5.37767 −0.423820
\(162\) 2.80363 0.220274
\(163\) −2.53323 −0.198418 −0.0992088 0.995067i \(-0.531631\pi\)
−0.0992088 + 0.995067i \(0.531631\pi\)
\(164\) 61.6765 4.81612
\(165\) −9.44058 −0.734948
\(166\) 14.1554 1.09867
\(167\) 1.10194 0.0852703 0.0426352 0.999091i \(-0.486425\pi\)
0.0426352 + 0.999091i \(0.486425\pi\)
\(168\) −10.8230 −0.835010
\(169\) 0 0
\(170\) −30.0828 −2.30724
\(171\) −4.86056 −0.371696
\(172\) 42.2394 3.22072
\(173\) −22.0711 −1.67803 −0.839016 0.544107i \(-0.816868\pi\)
−0.839016 + 0.544107i \(0.816868\pi\)
\(174\) 2.38003 0.180430
\(175\) −4.87520 −0.368531
\(176\) 55.9465 4.21712
\(177\) 1.45785 0.109579
\(178\) −35.5629 −2.66555
\(179\) 7.20834 0.538777 0.269388 0.963032i \(-0.413178\pi\)
0.269388 + 0.963032i \(0.413178\pi\)
\(180\) −18.4160 −1.37265
\(181\) 13.0966 0.973466 0.486733 0.873551i \(-0.338188\pi\)
0.486733 + 0.873551i \(0.338188\pi\)
\(182\) 0 0
\(183\) 4.95821 0.366521
\(184\) 58.2024 4.29073
\(185\) 12.2111 0.897778
\(186\) 1.26458 0.0927237
\(187\) 10.2577 0.750116
\(188\) −54.6995 −3.98937
\(189\) −1.00000 −0.0727393
\(190\) 42.8233 3.10673
\(191\) 24.5517 1.77650 0.888249 0.459363i \(-0.151922\pi\)
0.888249 + 0.459363i \(0.151922\pi\)
\(192\) 48.4493 3.49653
\(193\) 5.78789 0.416621 0.208311 0.978063i \(-0.433203\pi\)
0.208311 + 0.978063i \(0.433203\pi\)
\(194\) −12.0513 −0.865232
\(195\) 0 0
\(196\) 5.86034 0.418596
\(197\) 0.0857381 0.00610859 0.00305429 0.999995i \(-0.499028\pi\)
0.00305429 + 0.999995i \(0.499028\pi\)
\(198\) 8.42260 0.598568
\(199\) 5.62060 0.398434 0.199217 0.979955i \(-0.436160\pi\)
0.199217 + 0.979955i \(0.436160\pi\)
\(200\) 52.7641 3.73099
\(201\) 4.57857 0.322947
\(202\) 33.8555 2.38207
\(203\) −0.848910 −0.0595818
\(204\) 20.0100 1.40098
\(205\) −33.0727 −2.30990
\(206\) −4.40980 −0.307245
\(207\) 5.37767 0.373774
\(208\) 0 0
\(209\) −14.6020 −1.01004
\(210\) 8.81036 0.607973
\(211\) 18.1162 1.24717 0.623587 0.781754i \(-0.285675\pi\)
0.623587 + 0.781754i \(0.285675\pi\)
\(212\) −76.8567 −5.27854
\(213\) −2.36205 −0.161845
\(214\) −34.4203 −2.35292
\(215\) −22.6500 −1.54472
\(216\) 10.8230 0.736409
\(217\) −0.451052 −0.0306194
\(218\) −49.6361 −3.36178
\(219\) 1.24210 0.0839336
\(220\) −55.3250 −3.73001
\(221\) 0 0
\(222\) −10.8944 −0.731183
\(223\) 5.32513 0.356597 0.178298 0.983976i \(-0.442941\pi\)
0.178298 + 0.983976i \(0.442941\pi\)
\(224\) −30.5658 −2.04226
\(225\) 4.87520 0.325014
\(226\) −21.5120 −1.43096
\(227\) −22.2569 −1.47725 −0.738623 0.674119i \(-0.764523\pi\)
−0.738623 + 0.674119i \(0.764523\pi\)
\(228\) −28.4845 −1.88643
\(229\) −8.26095 −0.545899 −0.272949 0.962028i \(-0.587999\pi\)
−0.272949 + 0.962028i \(0.587999\pi\)
\(230\) −47.3792 −3.12409
\(231\) −3.00418 −0.197660
\(232\) 9.18772 0.603203
\(233\) 1.14151 0.0747825 0.0373913 0.999301i \(-0.488095\pi\)
0.0373913 + 0.999301i \(0.488095\pi\)
\(234\) 0 0
\(235\) 29.3315 1.91337
\(236\) 8.54352 0.556136
\(237\) −7.10832 −0.461735
\(238\) −9.57292 −0.620520
\(239\) −11.3967 −0.737190 −0.368595 0.929590i \(-0.620161\pi\)
−0.368595 + 0.929590i \(0.620161\pi\)
\(240\) −58.5222 −3.77759
\(241\) 14.7693 0.951374 0.475687 0.879615i \(-0.342200\pi\)
0.475687 + 0.879615i \(0.342200\pi\)
\(242\) −5.53695 −0.355929
\(243\) 1.00000 0.0641500
\(244\) 29.0568 1.86017
\(245\) −3.14248 −0.200766
\(246\) 29.5065 1.88126
\(247\) 0 0
\(248\) 4.88172 0.309989
\(249\) 5.04895 0.319964
\(250\) 1.09950 0.0695386
\(251\) 13.8604 0.874858 0.437429 0.899253i \(-0.355889\pi\)
0.437429 + 0.899253i \(0.355889\pi\)
\(252\) −5.86034 −0.369167
\(253\) 16.1555 1.01569
\(254\) −42.2451 −2.65069
\(255\) −10.7299 −0.671934
\(256\) 112.539 7.03371
\(257\) −13.1717 −0.821630 −0.410815 0.911719i \(-0.634756\pi\)
−0.410815 + 0.911719i \(0.634756\pi\)
\(258\) 20.2076 1.25807
\(259\) 3.88581 0.241453
\(260\) 0 0
\(261\) 0.848910 0.0525462
\(262\) −19.6458 −1.21372
\(263\) −30.2616 −1.86601 −0.933006 0.359860i \(-0.882824\pi\)
−0.933006 + 0.359860i \(0.882824\pi\)
\(264\) 32.5141 2.00110
\(265\) 41.2128 2.53168
\(266\) 13.6272 0.835538
\(267\) −12.6846 −0.776284
\(268\) 26.8320 1.63902
\(269\) −24.4467 −1.49054 −0.745272 0.666760i \(-0.767680\pi\)
−0.745272 + 0.666760i \(0.767680\pi\)
\(270\) −8.81036 −0.536181
\(271\) −19.0695 −1.15839 −0.579193 0.815190i \(-0.696632\pi\)
−0.579193 + 0.815190i \(0.696632\pi\)
\(272\) 63.5874 3.85555
\(273\) 0 0
\(274\) −34.7508 −2.09938
\(275\) 14.6460 0.883185
\(276\) 31.5150 1.89698
\(277\) 3.66058 0.219943 0.109971 0.993935i \(-0.464924\pi\)
0.109971 + 0.993935i \(0.464924\pi\)
\(278\) −7.53316 −0.451809
\(279\) 0.451052 0.0270038
\(280\) 34.0110 2.03254
\(281\) −8.89390 −0.530565 −0.265283 0.964171i \(-0.585465\pi\)
−0.265283 + 0.964171i \(0.585465\pi\)
\(282\) −26.1686 −1.55832
\(283\) −12.7960 −0.760646 −0.380323 0.924854i \(-0.624187\pi\)
−0.380323 + 0.924854i \(0.624187\pi\)
\(284\) −13.8424 −0.821396
\(285\) 15.2742 0.904767
\(286\) 0 0
\(287\) −10.5244 −0.621235
\(288\) 30.5658 1.80111
\(289\) −5.34136 −0.314198
\(290\) −7.47920 −0.439194
\(291\) −4.29846 −0.251980
\(292\) 7.27915 0.425980
\(293\) 7.11839 0.415861 0.207930 0.978144i \(-0.433327\pi\)
0.207930 + 0.978144i \(0.433327\pi\)
\(294\) 2.80363 0.163511
\(295\) −4.58128 −0.266733
\(296\) −42.0560 −2.44446
\(297\) 3.00418 0.174320
\(298\) 7.31203 0.423574
\(299\) 0 0
\(300\) 28.5703 1.64951
\(301\) −7.20767 −0.415443
\(302\) −14.4017 −0.828724
\(303\) 12.0756 0.693726
\(304\) −90.5177 −5.19155
\(305\) −15.5811 −0.892170
\(306\) 9.57292 0.547248
\(307\) 26.1182 1.49065 0.745323 0.666704i \(-0.232295\pi\)
0.745323 + 0.666704i \(0.232295\pi\)
\(308\) −17.6055 −1.00317
\(309\) −1.57289 −0.0894786
\(310\) −3.97393 −0.225704
\(311\) 23.4754 1.33117 0.665584 0.746323i \(-0.268183\pi\)
0.665584 + 0.746323i \(0.268183\pi\)
\(312\) 0 0
\(313\) −17.0234 −0.962220 −0.481110 0.876660i \(-0.659766\pi\)
−0.481110 + 0.876660i \(0.659766\pi\)
\(314\) 30.5230 1.72251
\(315\) 3.14248 0.177059
\(316\) −41.6572 −2.34340
\(317\) −9.59342 −0.538820 −0.269410 0.963026i \(-0.586829\pi\)
−0.269410 + 0.963026i \(0.586829\pi\)
\(318\) −36.7688 −2.06189
\(319\) 2.55028 0.142788
\(320\) −152.251 −8.51110
\(321\) −12.2770 −0.685237
\(322\) −15.0770 −0.840209
\(323\) −16.5963 −0.923440
\(324\) 5.86034 0.325574
\(325\) 0 0
\(326\) −7.10223 −0.393356
\(327\) −17.7042 −0.979046
\(328\) 113.905 6.28935
\(329\) 9.33384 0.514591
\(330\) −26.4679 −1.45701
\(331\) 1.52112 0.0836084 0.0418042 0.999126i \(-0.486689\pi\)
0.0418042 + 0.999126i \(0.486689\pi\)
\(332\) 29.5886 1.62388
\(333\) −3.88581 −0.212941
\(334\) 3.08942 0.169045
\(335\) −14.3881 −0.786104
\(336\) −18.6229 −1.01596
\(337\) 28.2047 1.53641 0.768204 0.640206i \(-0.221151\pi\)
0.768204 + 0.640206i \(0.221151\pi\)
\(338\) 0 0
\(339\) −7.67290 −0.416735
\(340\) −62.8810 −3.41020
\(341\) 1.35504 0.0733795
\(342\) −13.6272 −0.736875
\(343\) −1.00000 −0.0539949
\(344\) 78.0083 4.20593
\(345\) −16.8993 −0.909825
\(346\) −61.8791 −3.32664
\(347\) 7.59551 0.407748 0.203874 0.978997i \(-0.434647\pi\)
0.203874 + 0.978997i \(0.434647\pi\)
\(348\) 4.97490 0.266683
\(349\) 33.9613 1.81791 0.908954 0.416896i \(-0.136882\pi\)
0.908954 + 0.416896i \(0.136882\pi\)
\(350\) −13.6683 −0.730600
\(351\) 0 0
\(352\) 91.8250 4.89429
\(353\) 14.4675 0.770027 0.385013 0.922911i \(-0.374197\pi\)
0.385013 + 0.922911i \(0.374197\pi\)
\(354\) 4.08728 0.217237
\(355\) 7.42270 0.393956
\(356\) −74.3360 −3.93980
\(357\) −3.41447 −0.180713
\(358\) 20.2095 1.06811
\(359\) −9.99212 −0.527364 −0.263682 0.964610i \(-0.584937\pi\)
−0.263682 + 0.964610i \(0.584937\pi\)
\(360\) −34.0110 −1.79254
\(361\) 4.62504 0.243423
\(362\) 36.7181 1.92986
\(363\) −1.97492 −0.103657
\(364\) 0 0
\(365\) −3.90329 −0.204308
\(366\) 13.9010 0.726616
\(367\) −19.5834 −1.02224 −0.511122 0.859508i \(-0.670770\pi\)
−0.511122 + 0.859508i \(0.670770\pi\)
\(368\) 100.148 5.22057
\(369\) 10.5244 0.547878
\(370\) 34.2354 1.77981
\(371\) 13.1147 0.680882
\(372\) 2.64332 0.137050
\(373\) −3.57778 −0.185250 −0.0926252 0.995701i \(-0.529526\pi\)
−0.0926252 + 0.995701i \(0.529526\pi\)
\(374\) 28.7587 1.48708
\(375\) 0.392171 0.0202516
\(376\) −101.020 −5.20970
\(377\) 0 0
\(378\) −2.80363 −0.144203
\(379\) −9.43289 −0.484535 −0.242268 0.970209i \(-0.577891\pi\)
−0.242268 + 0.970209i \(0.577891\pi\)
\(380\) 89.5122 4.59188
\(381\) −15.0680 −0.771956
\(382\) 68.8338 3.52184
\(383\) −18.2451 −0.932281 −0.466141 0.884711i \(-0.654356\pi\)
−0.466141 + 0.884711i \(0.654356\pi\)
\(384\) 74.7024 3.81214
\(385\) 9.44058 0.481136
\(386\) 16.2271 0.825938
\(387\) 7.20767 0.366386
\(388\) −25.1904 −1.27885
\(389\) 7.06982 0.358454 0.179227 0.983808i \(-0.442640\pi\)
0.179227 + 0.983808i \(0.442640\pi\)
\(390\) 0 0
\(391\) 18.3619 0.928603
\(392\) 10.8230 0.546642
\(393\) −7.00728 −0.353470
\(394\) 0.240378 0.0121101
\(395\) 22.3378 1.12394
\(396\) 17.6055 0.884709
\(397\) −4.76261 −0.239029 −0.119514 0.992832i \(-0.538134\pi\)
−0.119514 + 0.992832i \(0.538134\pi\)
\(398\) 15.7581 0.789881
\(399\) 4.86056 0.243332
\(400\) 90.7904 4.53952
\(401\) −32.3631 −1.61614 −0.808068 0.589090i \(-0.799487\pi\)
−0.808068 + 0.589090i \(0.799487\pi\)
\(402\) 12.8366 0.640232
\(403\) 0 0
\(404\) 70.7672 3.52080
\(405\) −3.14248 −0.156151
\(406\) −2.38003 −0.118119
\(407\) −11.6737 −0.578642
\(408\) 36.9547 1.82953
\(409\) −2.00033 −0.0989101 −0.0494550 0.998776i \(-0.515748\pi\)
−0.0494550 + 0.998776i \(0.515748\pi\)
\(410\) −92.7236 −4.57929
\(411\) −12.3949 −0.611398
\(412\) −9.21767 −0.454122
\(413\) −1.45785 −0.0717363
\(414\) 15.0770 0.740994
\(415\) −15.8662 −0.778844
\(416\) 0 0
\(417\) −2.68693 −0.131580
\(418\) −40.9385 −2.00237
\(419\) −32.9805 −1.61120 −0.805601 0.592458i \(-0.798158\pi\)
−0.805601 + 0.592458i \(0.798158\pi\)
\(420\) 18.4160 0.898610
\(421\) 14.2283 0.693445 0.346723 0.937968i \(-0.387295\pi\)
0.346723 + 0.937968i \(0.387295\pi\)
\(422\) 50.7912 2.47248
\(423\) −9.33384 −0.453827
\(424\) −141.940 −6.89322
\(425\) 16.6463 0.807462
\(426\) −6.62231 −0.320852
\(427\) −4.95821 −0.239945
\(428\) −71.9476 −3.47772
\(429\) 0 0
\(430\) −63.5021 −3.06235
\(431\) −23.9213 −1.15225 −0.576124 0.817362i \(-0.695436\pi\)
−0.576124 + 0.817362i \(0.695436\pi\)
\(432\) 18.6229 0.895995
\(433\) 30.3234 1.45725 0.728624 0.684914i \(-0.240160\pi\)
0.728624 + 0.684914i \(0.240160\pi\)
\(434\) −1.26458 −0.0607019
\(435\) −2.66769 −0.127906
\(436\) −103.753 −4.96886
\(437\) −26.1385 −1.25037
\(438\) 3.48240 0.166396
\(439\) −11.7009 −0.558452 −0.279226 0.960225i \(-0.590078\pi\)
−0.279226 + 0.960225i \(0.590078\pi\)
\(440\) −102.175 −4.87100
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 5.05620 0.240227 0.120114 0.992760i \(-0.461674\pi\)
0.120114 + 0.992760i \(0.461674\pi\)
\(444\) −22.7722 −1.08072
\(445\) 39.8611 1.88960
\(446\) 14.9297 0.706941
\(447\) 2.60806 0.123357
\(448\) −48.4493 −2.28902
\(449\) 17.3705 0.819763 0.409882 0.912139i \(-0.365570\pi\)
0.409882 + 0.912139i \(0.365570\pi\)
\(450\) 13.6683 0.644328
\(451\) 31.6171 1.48879
\(452\) −44.9658 −2.11501
\(453\) −5.13680 −0.241348
\(454\) −62.4002 −2.92859
\(455\) 0 0
\(456\) −52.6056 −2.46349
\(457\) 34.5376 1.61560 0.807800 0.589456i \(-0.200658\pi\)
0.807800 + 0.589456i \(0.200658\pi\)
\(458\) −23.1606 −1.08223
\(459\) 3.41447 0.159374
\(460\) −99.0354 −4.61755
\(461\) −11.1375 −0.518723 −0.259361 0.965780i \(-0.583512\pi\)
−0.259361 + 0.965780i \(0.583512\pi\)
\(462\) −8.42260 −0.391855
\(463\) −8.14843 −0.378690 −0.189345 0.981911i \(-0.560636\pi\)
−0.189345 + 0.981911i \(0.560636\pi\)
\(464\) 15.8092 0.733922
\(465\) −1.41742 −0.0657314
\(466\) 3.20036 0.148254
\(467\) 14.8950 0.689258 0.344629 0.938739i \(-0.388005\pi\)
0.344629 + 0.938739i \(0.388005\pi\)
\(468\) 0 0
\(469\) −4.57857 −0.211419
\(470\) 82.2345 3.79320
\(471\) 10.8870 0.501645
\(472\) 15.7783 0.726255
\(473\) 21.6531 0.995611
\(474\) −19.9291 −0.915374
\(475\) −23.6962 −1.08726
\(476\) −20.0100 −0.917156
\(477\) −13.1147 −0.600482
\(478\) −31.9521 −1.46145
\(479\) −13.3435 −0.609679 −0.304840 0.952404i \(-0.598603\pi\)
−0.304840 + 0.952404i \(0.598603\pi\)
\(480\) −96.0525 −4.38418
\(481\) 0 0
\(482\) 41.4076 1.88607
\(483\) −5.37767 −0.244693
\(484\) −11.5737 −0.526078
\(485\) 13.5078 0.613359
\(486\) 2.80363 0.127175
\(487\) −15.0870 −0.683657 −0.341828 0.939762i \(-0.611046\pi\)
−0.341828 + 0.939762i \(0.611046\pi\)
\(488\) 53.6625 2.42919
\(489\) −2.53323 −0.114556
\(490\) −8.81036 −0.398012
\(491\) −18.6136 −0.840022 −0.420011 0.907519i \(-0.637974\pi\)
−0.420011 + 0.907519i \(0.637974\pi\)
\(492\) 61.6765 2.78059
\(493\) 2.89858 0.130546
\(494\) 0 0
\(495\) −9.44058 −0.424322
\(496\) 8.39990 0.377166
\(497\) 2.36205 0.105952
\(498\) 14.1554 0.634318
\(499\) −18.3295 −0.820543 −0.410272 0.911963i \(-0.634566\pi\)
−0.410272 + 0.911963i \(0.634566\pi\)
\(500\) 2.29825 0.102781
\(501\) 1.10194 0.0492308
\(502\) 38.8593 1.73438
\(503\) −13.0416 −0.581495 −0.290748 0.956800i \(-0.593904\pi\)
−0.290748 + 0.956800i \(0.593904\pi\)
\(504\) −10.8230 −0.482093
\(505\) −37.9474 −1.68864
\(506\) 45.2940 2.01356
\(507\) 0 0
\(508\) −88.3035 −3.91783
\(509\) −17.0920 −0.757590 −0.378795 0.925481i \(-0.623661\pi\)
−0.378795 + 0.925481i \(0.623661\pi\)
\(510\) −30.0828 −1.33209
\(511\) −1.24210 −0.0549475
\(512\) 166.114 7.34126
\(513\) −4.86056 −0.214599
\(514\) −36.9287 −1.62885
\(515\) 4.94278 0.217805
\(516\) 42.2394 1.85948
\(517\) −28.0405 −1.23322
\(518\) 10.8944 0.478672
\(519\) −22.0711 −0.968812
\(520\) 0 0
\(521\) −33.7225 −1.47741 −0.738705 0.674029i \(-0.764562\pi\)
−0.738705 + 0.674029i \(0.764562\pi\)
\(522\) 2.38003 0.104171
\(523\) 35.8559 1.56787 0.783934 0.620844i \(-0.213210\pi\)
0.783934 + 0.620844i \(0.213210\pi\)
\(524\) −41.0650 −1.79393
\(525\) −4.87520 −0.212771
\(526\) −84.8424 −3.69930
\(527\) 1.54011 0.0670881
\(528\) 55.9465 2.43476
\(529\) 5.91938 0.257364
\(530\) 115.545 5.01897
\(531\) 1.45785 0.0632655
\(532\) 28.4845 1.23496
\(533\) 0 0
\(534\) −35.5629 −1.53896
\(535\) 38.5804 1.66797
\(536\) 49.5537 2.14039
\(537\) 7.20834 0.311063
\(538\) −68.5396 −2.95495
\(539\) 3.00418 0.129399
\(540\) −18.4160 −0.792499
\(541\) 17.9589 0.772113 0.386056 0.922475i \(-0.373837\pi\)
0.386056 + 0.922475i \(0.373837\pi\)
\(542\) −53.4637 −2.29646
\(543\) 13.0966 0.562031
\(544\) 104.366 4.47466
\(545\) 55.6352 2.38315
\(546\) 0 0
\(547\) 30.1484 1.28905 0.644526 0.764583i \(-0.277055\pi\)
0.644526 + 0.764583i \(0.277055\pi\)
\(548\) −72.6386 −3.10297
\(549\) 4.95821 0.211611
\(550\) 41.0619 1.75088
\(551\) −4.12618 −0.175781
\(552\) 58.2024 2.47726
\(553\) 7.10832 0.302276
\(554\) 10.2629 0.436029
\(555\) 12.2111 0.518333
\(556\) −15.7463 −0.667793
\(557\) 13.5998 0.576243 0.288122 0.957594i \(-0.406969\pi\)
0.288122 + 0.957594i \(0.406969\pi\)
\(558\) 1.26458 0.0535341
\(559\) 0 0
\(560\) 58.5222 2.47301
\(561\) 10.2577 0.433080
\(562\) −24.9352 −1.05183
\(563\) 11.4717 0.483475 0.241737 0.970342i \(-0.422283\pi\)
0.241737 + 0.970342i \(0.422283\pi\)
\(564\) −54.6995 −2.30326
\(565\) 24.1120 1.01440
\(566\) −35.8754 −1.50795
\(567\) −1.00000 −0.0419961
\(568\) −25.5644 −1.07266
\(569\) 10.7718 0.451578 0.225789 0.974176i \(-0.427504\pi\)
0.225789 + 0.974176i \(0.427504\pi\)
\(570\) 42.8233 1.79367
\(571\) 13.6895 0.572887 0.286443 0.958097i \(-0.407527\pi\)
0.286443 + 0.958097i \(0.407527\pi\)
\(572\) 0 0
\(573\) 24.5517 1.02566
\(574\) −29.5065 −1.23158
\(575\) 26.2173 1.09334
\(576\) 48.4493 2.01872
\(577\) 31.9864 1.33161 0.665805 0.746126i \(-0.268088\pi\)
0.665805 + 0.746126i \(0.268088\pi\)
\(578\) −14.9752 −0.622886
\(579\) 5.78789 0.240536
\(580\) −15.6335 −0.649148
\(581\) −5.04895 −0.209466
\(582\) −12.0513 −0.499542
\(583\) −39.3989 −1.63174
\(584\) 13.4432 0.556286
\(585\) 0 0
\(586\) 19.9573 0.824429
\(587\) 36.5126 1.50704 0.753519 0.657427i \(-0.228355\pi\)
0.753519 + 0.657427i \(0.228355\pi\)
\(588\) 5.86034 0.241676
\(589\) −2.19237 −0.0903348
\(590\) −12.8442 −0.528788
\(591\) 0.0857381 0.00352679
\(592\) −72.3651 −2.97419
\(593\) 7.28387 0.299112 0.149556 0.988753i \(-0.452215\pi\)
0.149556 + 0.988753i \(0.452215\pi\)
\(594\) 8.42260 0.345583
\(595\) 10.7299 0.439884
\(596\) 15.2841 0.626061
\(597\) 5.62060 0.230036
\(598\) 0 0
\(599\) 46.1528 1.88575 0.942876 0.333144i \(-0.108110\pi\)
0.942876 + 0.333144i \(0.108110\pi\)
\(600\) 52.7641 2.15409
\(601\) −24.4355 −0.996746 −0.498373 0.866963i \(-0.666069\pi\)
−0.498373 + 0.866963i \(0.666069\pi\)
\(602\) −20.2076 −0.823602
\(603\) 4.57857 0.186454
\(604\) −30.1034 −1.22489
\(605\) 6.20616 0.252316
\(606\) 33.8555 1.37529
\(607\) −26.2738 −1.06642 −0.533210 0.845983i \(-0.679014\pi\)
−0.533210 + 0.845983i \(0.679014\pi\)
\(608\) −148.567 −6.02518
\(609\) −0.848910 −0.0343996
\(610\) −43.6836 −1.76870
\(611\) 0 0
\(612\) 20.0100 0.808855
\(613\) 39.0382 1.57674 0.788370 0.615202i \(-0.210926\pi\)
0.788370 + 0.615202i \(0.210926\pi\)
\(614\) 73.2258 2.95515
\(615\) −33.0727 −1.33362
\(616\) −32.5141 −1.31003
\(617\) −9.26856 −0.373138 −0.186569 0.982442i \(-0.559737\pi\)
−0.186569 + 0.982442i \(0.559737\pi\)
\(618\) −4.40980 −0.177388
\(619\) 45.4890 1.82836 0.914179 0.405310i \(-0.132836\pi\)
0.914179 + 0.405310i \(0.132836\pi\)
\(620\) −8.30658 −0.333600
\(621\) 5.37767 0.215799
\(622\) 65.8163 2.63899
\(623\) 12.6846 0.508197
\(624\) 0 0
\(625\) −25.6084 −1.02434
\(626\) −47.7273 −1.90757
\(627\) −14.6020 −0.583147
\(628\) 63.8013 2.54595
\(629\) −13.2680 −0.529030
\(630\) 8.81036 0.351013
\(631\) 20.9773 0.835092 0.417546 0.908656i \(-0.362890\pi\)
0.417546 + 0.908656i \(0.362890\pi\)
\(632\) −76.9331 −3.06023
\(633\) 18.1162 0.720056
\(634\) −26.8964 −1.06819
\(635\) 47.3509 1.87906
\(636\) −76.8567 −3.04757
\(637\) 0 0
\(638\) 7.15003 0.283072
\(639\) −2.36205 −0.0934412
\(640\) −234.751 −9.27936
\(641\) −11.4475 −0.452148 −0.226074 0.974110i \(-0.572589\pi\)
−0.226074 + 0.974110i \(0.572589\pi\)
\(642\) −34.4203 −1.35846
\(643\) −27.7242 −1.09334 −0.546668 0.837350i \(-0.684104\pi\)
−0.546668 + 0.837350i \(0.684104\pi\)
\(644\) −31.5150 −1.24186
\(645\) −22.6500 −0.891842
\(646\) −46.5298 −1.83069
\(647\) 24.7236 0.971984 0.485992 0.873963i \(-0.338458\pi\)
0.485992 + 0.873963i \(0.338458\pi\)
\(648\) 10.8230 0.425166
\(649\) 4.37965 0.171916
\(650\) 0 0
\(651\) −0.451052 −0.0176781
\(652\) −14.8456 −0.581397
\(653\) −12.2921 −0.481027 −0.240513 0.970646i \(-0.577316\pi\)
−0.240513 + 0.970646i \(0.577316\pi\)
\(654\) −49.6361 −1.94092
\(655\) 22.0203 0.860402
\(656\) 195.995 7.65230
\(657\) 1.24210 0.0484591
\(658\) 26.1686 1.02016
\(659\) 43.4003 1.69063 0.845317 0.534265i \(-0.179411\pi\)
0.845317 + 0.534265i \(0.179411\pi\)
\(660\) −55.3250 −2.15352
\(661\) 0.585779 0.0227841 0.0113921 0.999935i \(-0.496374\pi\)
0.0113921 + 0.999935i \(0.496374\pi\)
\(662\) 4.26466 0.165751
\(663\) 0 0
\(664\) 54.6446 2.12062
\(665\) −15.2742 −0.592309
\(666\) −10.8944 −0.422149
\(667\) 4.56516 0.176764
\(668\) 6.45772 0.249857
\(669\) 5.32513 0.205881
\(670\) −40.3388 −1.55842
\(671\) 14.8953 0.575028
\(672\) −30.5658 −1.17910
\(673\) −11.6662 −0.449698 −0.224849 0.974394i \(-0.572189\pi\)
−0.224849 + 0.974394i \(0.572189\pi\)
\(674\) 79.0755 3.04587
\(675\) 4.87520 0.187647
\(676\) 0 0
\(677\) 9.21779 0.354268 0.177134 0.984187i \(-0.443317\pi\)
0.177134 + 0.984187i \(0.443317\pi\)
\(678\) −21.5120 −0.826163
\(679\) 4.29846 0.164960
\(680\) −116.130 −4.45337
\(681\) −22.2569 −0.852888
\(682\) 3.79903 0.145472
\(683\) 23.5144 0.899753 0.449876 0.893091i \(-0.351468\pi\)
0.449876 + 0.893091i \(0.351468\pi\)
\(684\) −28.4845 −1.08913
\(685\) 38.9509 1.48824
\(686\) −2.80363 −0.107043
\(687\) −8.26095 −0.315175
\(688\) 134.228 5.11738
\(689\) 0 0
\(690\) −47.3792 −1.80370
\(691\) −6.30097 −0.239700 −0.119850 0.992792i \(-0.538241\pi\)
−0.119850 + 0.992792i \(0.538241\pi\)
\(692\) −129.344 −4.91692
\(693\) −3.00418 −0.114119
\(694\) 21.2950 0.808347
\(695\) 8.44364 0.320286
\(696\) 9.18772 0.348260
\(697\) 35.9353 1.36114
\(698\) 95.2150 3.60394
\(699\) 1.14151 0.0431757
\(700\) −28.5703 −1.07986
\(701\) 25.9334 0.979492 0.489746 0.871865i \(-0.337090\pi\)
0.489746 + 0.871865i \(0.337090\pi\)
\(702\) 0 0
\(703\) 18.8872 0.712345
\(704\) 145.550 5.48564
\(705\) 29.3315 1.10469
\(706\) 40.5615 1.52655
\(707\) −12.0756 −0.454150
\(708\) 8.54352 0.321085
\(709\) 44.7279 1.67979 0.839895 0.542748i \(-0.182616\pi\)
0.839895 + 0.542748i \(0.182616\pi\)
\(710\) 20.8105 0.781004
\(711\) −7.10832 −0.266583
\(712\) −137.285 −5.14496
\(713\) 2.42561 0.0908398
\(714\) −9.57292 −0.358258
\(715\) 0 0
\(716\) 42.2433 1.57871
\(717\) −11.3967 −0.425617
\(718\) −28.0142 −1.04548
\(719\) 1.13604 0.0423672 0.0211836 0.999776i \(-0.493257\pi\)
0.0211836 + 0.999776i \(0.493257\pi\)
\(720\) −58.5222 −2.18099
\(721\) 1.57289 0.0585775
\(722\) 12.9669 0.482578
\(723\) 14.7693 0.549276
\(724\) 76.7508 2.85242
\(725\) 4.13861 0.153704
\(726\) −5.53695 −0.205496
\(727\) −41.7837 −1.54967 −0.774836 0.632162i \(-0.782168\pi\)
−0.774836 + 0.632162i \(0.782168\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −10.9434 −0.405033
\(731\) 24.6104 0.910248
\(732\) 29.0568 1.07397
\(733\) 46.4593 1.71601 0.858006 0.513639i \(-0.171703\pi\)
0.858006 + 0.513639i \(0.171703\pi\)
\(734\) −54.9046 −2.02656
\(735\) −3.14248 −0.115912
\(736\) 164.373 6.05886
\(737\) 13.7548 0.506665
\(738\) 29.5065 1.08615
\(739\) −5.69151 −0.209365 −0.104683 0.994506i \(-0.533383\pi\)
−0.104683 + 0.994506i \(0.533383\pi\)
\(740\) 71.5612 2.63064
\(741\) 0 0
\(742\) 36.7688 1.34983
\(743\) 3.88256 0.142437 0.0712186 0.997461i \(-0.477311\pi\)
0.0712186 + 0.997461i \(0.477311\pi\)
\(744\) 4.88172 0.178972
\(745\) −8.19578 −0.300270
\(746\) −10.0308 −0.367253
\(747\) 5.04895 0.184732
\(748\) 60.1135 2.19797
\(749\) 12.2770 0.448593
\(750\) 1.09950 0.0401481
\(751\) −40.3197 −1.47129 −0.735644 0.677368i \(-0.763120\pi\)
−0.735644 + 0.677368i \(0.763120\pi\)
\(752\) −173.823 −6.33868
\(753\) 13.8604 0.505100
\(754\) 0 0
\(755\) 16.1423 0.587479
\(756\) −5.86034 −0.213138
\(757\) 9.61102 0.349319 0.174659 0.984629i \(-0.444118\pi\)
0.174659 + 0.984629i \(0.444118\pi\)
\(758\) −26.4463 −0.960574
\(759\) 16.1555 0.586407
\(760\) 165.312 5.99651
\(761\) 30.1840 1.09417 0.547085 0.837077i \(-0.315738\pi\)
0.547085 + 0.837077i \(0.315738\pi\)
\(762\) −42.2451 −1.53038
\(763\) 17.7042 0.640936
\(764\) 143.881 5.20544
\(765\) −10.7299 −0.387941
\(766\) −51.1525 −1.84822
\(767\) 0 0
\(768\) 112.539 4.06091
\(769\) −10.8144 −0.389976 −0.194988 0.980806i \(-0.562467\pi\)
−0.194988 + 0.980806i \(0.562467\pi\)
\(770\) 26.4679 0.953836
\(771\) −13.1717 −0.474368
\(772\) 33.9190 1.22077
\(773\) −45.5987 −1.64007 −0.820036 0.572311i \(-0.806047\pi\)
−0.820036 + 0.572311i \(0.806047\pi\)
\(774\) 20.2076 0.726348
\(775\) 2.19897 0.0789894
\(776\) −46.5220 −1.67004
\(777\) 3.88581 0.139403
\(778\) 19.8212 0.710623
\(779\) −51.1544 −1.83280
\(780\) 0 0
\(781\) −7.09601 −0.253915
\(782\) 51.4801 1.84092
\(783\) 0.848910 0.0303376
\(784\) 18.6229 0.665103
\(785\) −34.2121 −1.22108
\(786\) −19.6458 −0.700743
\(787\) −32.4330 −1.15611 −0.578055 0.815997i \(-0.696188\pi\)
−0.578055 + 0.815997i \(0.696188\pi\)
\(788\) 0.502454 0.0178992
\(789\) −30.2616 −1.07734
\(790\) 62.6268 2.22816
\(791\) 7.67290 0.272817
\(792\) 32.5141 1.15534
\(793\) 0 0
\(794\) −13.3526 −0.473866
\(795\) 41.2128 1.46167
\(796\) 32.9386 1.16748
\(797\) 41.0287 1.45331 0.726656 0.687001i \(-0.241073\pi\)
0.726656 + 0.687001i \(0.241073\pi\)
\(798\) 13.6272 0.482398
\(799\) −31.8702 −1.12749
\(800\) 149.014 5.26846
\(801\) −12.6846 −0.448188
\(802\) −90.7341 −3.20393
\(803\) 3.73150 0.131682
\(804\) 26.8320 0.946290
\(805\) 16.8993 0.595620
\(806\) 0 0
\(807\) −24.4467 −0.860566
\(808\) 130.694 4.59779
\(809\) −10.6632 −0.374898 −0.187449 0.982274i \(-0.560022\pi\)
−0.187449 + 0.982274i \(0.560022\pi\)
\(810\) −8.81036 −0.309565
\(811\) −5.60921 −0.196966 −0.0984831 0.995139i \(-0.531399\pi\)
−0.0984831 + 0.995139i \(0.531399\pi\)
\(812\) −4.97490 −0.174585
\(813\) −19.0695 −0.668795
\(814\) −32.7286 −1.14714
\(815\) 7.96062 0.278848
\(816\) 63.5874 2.22600
\(817\) −35.0333 −1.22566
\(818\) −5.60819 −0.196086
\(819\) 0 0
\(820\) −193.817 −6.76840
\(821\) 12.4008 0.432790 0.216395 0.976306i \(-0.430570\pi\)
0.216395 + 0.976306i \(0.430570\pi\)
\(822\) −34.7508 −1.21207
\(823\) 23.9208 0.833827 0.416913 0.908946i \(-0.363112\pi\)
0.416913 + 0.908946i \(0.363112\pi\)
\(824\) −17.0233 −0.593036
\(825\) 14.6460 0.509907
\(826\) −4.08728 −0.142215
\(827\) −2.10966 −0.0733600 −0.0366800 0.999327i \(-0.511678\pi\)
−0.0366800 + 0.999327i \(0.511678\pi\)
\(828\) 31.5150 1.09522
\(829\) 47.4770 1.64895 0.824473 0.565901i \(-0.191472\pi\)
0.824473 + 0.565901i \(0.191472\pi\)
\(830\) −44.4831 −1.54403
\(831\) 3.66058 0.126984
\(832\) 0 0
\(833\) 3.41447 0.118305
\(834\) −7.53316 −0.260852
\(835\) −3.46281 −0.119836
\(836\) −85.5726 −2.95959
\(837\) 0.451052 0.0155906
\(838\) −92.4651 −3.19415
\(839\) −8.30337 −0.286664 −0.143332 0.989675i \(-0.545782\pi\)
−0.143332 + 0.989675i \(0.545782\pi\)
\(840\) 34.0110 1.17349
\(841\) −28.2794 −0.975150
\(842\) 39.8909 1.37473
\(843\) −8.89390 −0.306322
\(844\) 106.167 3.65443
\(845\) 0 0
\(846\) −26.1686 −0.899696
\(847\) 1.97492 0.0678592
\(848\) −244.234 −8.38703
\(849\) −12.7960 −0.439159
\(850\) 46.6699 1.60077
\(851\) −20.8966 −0.716327
\(852\) −13.8424 −0.474233
\(853\) 5.14634 0.176207 0.0881036 0.996111i \(-0.471919\pi\)
0.0881036 + 0.996111i \(0.471919\pi\)
\(854\) −13.9010 −0.475682
\(855\) 15.2742 0.522368
\(856\) −132.874 −4.54153
\(857\) 6.25760 0.213756 0.106878 0.994272i \(-0.465915\pi\)
0.106878 + 0.994272i \(0.465915\pi\)
\(858\) 0 0
\(859\) −4.10387 −0.140022 −0.0700112 0.997546i \(-0.522304\pi\)
−0.0700112 + 0.997546i \(0.522304\pi\)
\(860\) −132.737 −4.52628
\(861\) −10.5244 −0.358670
\(862\) −67.0665 −2.28429
\(863\) −37.8902 −1.28980 −0.644899 0.764268i \(-0.723101\pi\)
−0.644899 + 0.764268i \(0.723101\pi\)
\(864\) 30.5658 1.03987
\(865\) 69.3579 2.35824
\(866\) 85.0155 2.88895
\(867\) −5.34136 −0.181402
\(868\) −2.64332 −0.0897201
\(869\) −21.3546 −0.724407
\(870\) −7.47920 −0.253569
\(871\) 0 0
\(872\) −191.612 −6.48881
\(873\) −4.29846 −0.145481
\(874\) −73.2827 −2.47882
\(875\) −0.392171 −0.0132578
\(876\) 7.27915 0.245940
\(877\) 55.7199 1.88153 0.940764 0.339063i \(-0.110110\pi\)
0.940764 + 0.339063i \(0.110110\pi\)
\(878\) −32.8049 −1.10711
\(879\) 7.11839 0.240097
\(880\) −175.811 −5.92658
\(881\) −34.4048 −1.15913 −0.579564 0.814927i \(-0.696777\pi\)
−0.579564 + 0.814927i \(0.696777\pi\)
\(882\) 2.80363 0.0944031
\(883\) −36.9973 −1.24506 −0.622529 0.782597i \(-0.713895\pi\)
−0.622529 + 0.782597i \(0.713895\pi\)
\(884\) 0 0
\(885\) −4.58128 −0.153998
\(886\) 14.1757 0.476242
\(887\) −55.3301 −1.85780 −0.928902 0.370325i \(-0.879246\pi\)
−0.928902 + 0.370325i \(0.879246\pi\)
\(888\) −42.0560 −1.41131
\(889\) 15.0680 0.505364
\(890\) 111.756 3.74606
\(891\) 3.00418 0.100644
\(892\) 31.2070 1.04489
\(893\) 45.3677 1.51817
\(894\) 7.31203 0.244551
\(895\) −22.6521 −0.757176
\(896\) −74.7024 −2.49563
\(897\) 0 0
\(898\) 48.7004 1.62515
\(899\) 0.382903 0.0127705
\(900\) 28.5703 0.952345
\(901\) −44.7799 −1.49183
\(902\) 88.6427 2.95148
\(903\) −7.20767 −0.239856
\(904\) −83.0435 −2.76199
\(905\) −41.1560 −1.36807
\(906\) −14.4017 −0.478464
\(907\) 12.5397 0.416375 0.208188 0.978089i \(-0.433243\pi\)
0.208188 + 0.978089i \(0.433243\pi\)
\(908\) −130.433 −4.32858
\(909\) 12.0756 0.400523
\(910\) 0 0
\(911\) −11.4861 −0.380552 −0.190276 0.981731i \(-0.560938\pi\)
−0.190276 + 0.981731i \(0.560938\pi\)
\(912\) −90.5177 −2.99734
\(913\) 15.1679 0.501986
\(914\) 96.8306 3.20287
\(915\) −15.5811 −0.515095
\(916\) −48.4120 −1.59958
\(917\) 7.00728 0.231401
\(918\) 9.57292 0.315954
\(919\) 33.9296 1.11924 0.559618 0.828751i \(-0.310948\pi\)
0.559618 + 0.828751i \(0.310948\pi\)
\(920\) −182.900 −6.03003
\(921\) 26.1182 0.860624
\(922\) −31.2253 −1.02835
\(923\) 0 0
\(924\) −17.6055 −0.579178
\(925\) −18.9441 −0.622879
\(926\) −22.8452 −0.750739
\(927\) −1.57289 −0.0516605
\(928\) 25.9476 0.851772
\(929\) 50.4939 1.65665 0.828326 0.560247i \(-0.189294\pi\)
0.828326 + 0.560247i \(0.189294\pi\)
\(930\) −3.97393 −0.130310
\(931\) −4.86056 −0.159298
\(932\) 6.68961 0.219125
\(933\) 23.4754 0.768550
\(934\) 41.7601 1.36643
\(935\) −32.2346 −1.05418
\(936\) 0 0
\(937\) 14.7689 0.482478 0.241239 0.970466i \(-0.422446\pi\)
0.241239 + 0.970466i \(0.422446\pi\)
\(938\) −12.8366 −0.419130
\(939\) −17.0234 −0.555538
\(940\) 171.892 5.60651
\(941\) −30.1402 −0.982544 −0.491272 0.871006i \(-0.663468\pi\)
−0.491272 + 0.871006i \(0.663468\pi\)
\(942\) 30.5230 0.994493
\(943\) 56.5967 1.84304
\(944\) 27.1495 0.883640
\(945\) 3.14248 0.102225
\(946\) 60.7073 1.97376
\(947\) 27.1523 0.882331 0.441165 0.897426i \(-0.354565\pi\)
0.441165 + 0.897426i \(0.354565\pi\)
\(948\) −41.6572 −1.35296
\(949\) 0 0
\(950\) −66.4354 −2.15545
\(951\) −9.59342 −0.311088
\(952\) −36.9547 −1.19771
\(953\) −19.0337 −0.616560 −0.308280 0.951296i \(-0.599753\pi\)
−0.308280 + 0.951296i \(0.599753\pi\)
\(954\) −36.7688 −1.19043
\(955\) −77.1533 −2.49662
\(956\) −66.7884 −2.16009
\(957\) 2.55028 0.0824387
\(958\) −37.4102 −1.20867
\(959\) 12.3949 0.400254
\(960\) −152.251 −4.91389
\(961\) −30.7966 −0.993437
\(962\) 0 0
\(963\) −12.2770 −0.395622
\(964\) 86.5530 2.78769
\(965\) −18.1883 −0.585504
\(966\) −15.0770 −0.485095
\(967\) 2.60639 0.0838158 0.0419079 0.999121i \(-0.486656\pi\)
0.0419079 + 0.999121i \(0.486656\pi\)
\(968\) −21.3745 −0.687003
\(969\) −16.5963 −0.533149
\(970\) 37.8710 1.21596
\(971\) 38.7695 1.24417 0.622086 0.782949i \(-0.286286\pi\)
0.622086 + 0.782949i \(0.286286\pi\)
\(972\) 5.86034 0.187970
\(973\) 2.68693 0.0861391
\(974\) −42.2983 −1.35533
\(975\) 0 0
\(976\) 92.3362 2.95561
\(977\) −41.1599 −1.31682 −0.658411 0.752658i \(-0.728771\pi\)
−0.658411 + 0.752658i \(0.728771\pi\)
\(978\) −7.10223 −0.227104
\(979\) −38.1067 −1.21790
\(980\) −18.4160 −0.588278
\(981\) −17.7042 −0.565252
\(982\) −52.1857 −1.66531
\(983\) −8.61935 −0.274914 −0.137457 0.990508i \(-0.543893\pi\)
−0.137457 + 0.990508i \(0.543893\pi\)
\(984\) 113.905 3.63116
\(985\) −0.269431 −0.00858477
\(986\) 8.12655 0.258802
\(987\) 9.33384 0.297100
\(988\) 0 0
\(989\) 38.7605 1.23251
\(990\) −26.4679 −0.841204
\(991\) 32.1624 1.02167 0.510835 0.859679i \(-0.329336\pi\)
0.510835 + 0.859679i \(0.329336\pi\)
\(992\) 13.7868 0.437730
\(993\) 1.52112 0.0482714
\(994\) 6.62231 0.210047
\(995\) −17.6626 −0.559943
\(996\) 29.5886 0.937550
\(997\) −28.8875 −0.914876 −0.457438 0.889242i \(-0.651233\pi\)
−0.457438 + 0.889242i \(0.651233\pi\)
\(998\) −51.3893 −1.62670
\(999\) −3.88581 −0.122942
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.1.15 yes 15
13.12 even 2 3549.2.a.bg.1.1 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.1 15 13.12 even 2
3549.2.a.bh.1.15 yes 15 1.1 even 1 trivial