Properties

Label 3549.2.a.bf.1.9
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 1.9
Root \(2.67225\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} -3.54256 q^{10} -3.03214 q^{11} -5.14091 q^{12} -2.67225 q^{14} +1.32568 q^{15} +12.1471 q^{16} +4.56435 q^{17} +2.67225 q^{18} +0.940093 q^{19} -6.81522 q^{20} +1.00000 q^{21} -8.10263 q^{22} +8.55552 q^{23} -8.39329 q^{24} -3.24256 q^{25} -1.00000 q^{27} -5.14091 q^{28} +5.79888 q^{29} +3.54256 q^{30} +1.00569 q^{31} +15.6736 q^{32} +3.03214 q^{33} +12.1971 q^{34} +1.32568 q^{35} +5.14091 q^{36} +11.3326 q^{37} +2.51216 q^{38} -11.1269 q^{40} -7.71076 q^{41} +2.67225 q^{42} +7.20423 q^{43} -15.5880 q^{44} -1.32568 q^{45} +22.8625 q^{46} +12.8237 q^{47} -12.1471 q^{48} +1.00000 q^{49} -8.66492 q^{50} -4.56435 q^{51} +5.26290 q^{53} -2.67225 q^{54} +4.01966 q^{55} -8.39329 q^{56} -0.940093 q^{57} +15.4960 q^{58} -13.1834 q^{59} +6.81522 q^{60} +5.82817 q^{61} +2.68746 q^{62} -1.00000 q^{63} +17.5894 q^{64} +8.10263 q^{66} +3.02297 q^{67} +23.4649 q^{68} -8.55552 q^{69} +3.54256 q^{70} -6.04396 q^{71} +8.39329 q^{72} -12.2757 q^{73} +30.2835 q^{74} +3.24256 q^{75} +4.83293 q^{76} +3.03214 q^{77} +1.46368 q^{79} -16.1033 q^{80} +1.00000 q^{81} -20.6051 q^{82} +4.31767 q^{83} +5.14091 q^{84} -6.05089 q^{85} +19.2515 q^{86} -5.79888 q^{87} -25.4496 q^{88} -3.22598 q^{89} -3.54256 q^{90} +43.9832 q^{92} -1.00569 q^{93} +34.2681 q^{94} -1.24627 q^{95} -15.6736 q^{96} -5.51764 q^{97} +2.67225 q^{98} -3.03214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67225 1.88956 0.944782 0.327699i \(-0.106273\pi\)
0.944782 + 0.327699i \(0.106273\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.14091 2.57045
\(5\) −1.32568 −0.592864 −0.296432 0.955054i \(-0.595797\pi\)
−0.296432 + 0.955054i \(0.595797\pi\)
\(6\) −2.67225 −1.09094
\(7\) −1.00000 −0.377964
\(8\) 8.39329 2.96748
\(9\) 1.00000 0.333333
\(10\) −3.54256 −1.12026
\(11\) −3.03214 −0.914225 −0.457112 0.889409i \(-0.651116\pi\)
−0.457112 + 0.889409i \(0.651116\pi\)
\(12\) −5.14091 −1.48405
\(13\) 0 0
\(14\) −2.67225 −0.714188
\(15\) 1.32568 0.342290
\(16\) 12.1471 3.03678
\(17\) 4.56435 1.10702 0.553509 0.832843i \(-0.313288\pi\)
0.553509 + 0.832843i \(0.313288\pi\)
\(18\) 2.67225 0.629855
\(19\) 0.940093 0.215672 0.107836 0.994169i \(-0.465608\pi\)
0.107836 + 0.994169i \(0.465608\pi\)
\(20\) −6.81522 −1.52393
\(21\) 1.00000 0.218218
\(22\) −8.10263 −1.72749
\(23\) 8.55552 1.78395 0.891975 0.452085i \(-0.149320\pi\)
0.891975 + 0.452085i \(0.149320\pi\)
\(24\) −8.39329 −1.71327
\(25\) −3.24256 −0.648512
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −5.14091 −0.971540
\(29\) 5.79888 1.07682 0.538412 0.842681i \(-0.319024\pi\)
0.538412 + 0.842681i \(0.319024\pi\)
\(30\) 3.54256 0.646780
\(31\) 1.00569 0.180628 0.0903138 0.995913i \(-0.471213\pi\)
0.0903138 + 0.995913i \(0.471213\pi\)
\(32\) 15.6736 2.77072
\(33\) 3.03214 0.527828
\(34\) 12.1971 2.09178
\(35\) 1.32568 0.224082
\(36\) 5.14091 0.856818
\(37\) 11.3326 1.86306 0.931532 0.363658i \(-0.118472\pi\)
0.931532 + 0.363658i \(0.118472\pi\)
\(38\) 2.51216 0.407526
\(39\) 0 0
\(40\) −11.1269 −1.75931
\(41\) −7.71076 −1.20422 −0.602109 0.798414i \(-0.705673\pi\)
−0.602109 + 0.798414i \(0.705673\pi\)
\(42\) 2.67225 0.412337
\(43\) 7.20423 1.09864 0.549318 0.835614i \(-0.314888\pi\)
0.549318 + 0.835614i \(0.314888\pi\)
\(44\) −15.5880 −2.34997
\(45\) −1.32568 −0.197621
\(46\) 22.8625 3.37089
\(47\) 12.8237 1.87053 0.935264 0.353952i \(-0.115162\pi\)
0.935264 + 0.353952i \(0.115162\pi\)
\(48\) −12.1471 −1.75329
\(49\) 1.00000 0.142857
\(50\) −8.66492 −1.22541
\(51\) −4.56435 −0.639137
\(52\) 0 0
\(53\) 5.26290 0.722915 0.361458 0.932389i \(-0.382279\pi\)
0.361458 + 0.932389i \(0.382279\pi\)
\(54\) −2.67225 −0.363647
\(55\) 4.01966 0.542011
\(56\) −8.39329 −1.12160
\(57\) −0.940093 −0.124518
\(58\) 15.4960 2.03473
\(59\) −13.1834 −1.71634 −0.858169 0.513368i \(-0.828398\pi\)
−0.858169 + 0.513368i \(0.828398\pi\)
\(60\) 6.81522 0.879842
\(61\) 5.82817 0.746221 0.373111 0.927787i \(-0.378291\pi\)
0.373111 + 0.927787i \(0.378291\pi\)
\(62\) 2.68746 0.341308
\(63\) −1.00000 −0.125988
\(64\) 17.5894 2.19867
\(65\) 0 0
\(66\) 8.10263 0.997365
\(67\) 3.02297 0.369315 0.184657 0.982803i \(-0.440882\pi\)
0.184657 + 0.982803i \(0.440882\pi\)
\(68\) 23.4649 2.84554
\(69\) −8.55552 −1.02996
\(70\) 3.54256 0.423417
\(71\) −6.04396 −0.717286 −0.358643 0.933475i \(-0.616760\pi\)
−0.358643 + 0.933475i \(0.616760\pi\)
\(72\) 8.39329 0.989158
\(73\) −12.2757 −1.43676 −0.718381 0.695650i \(-0.755117\pi\)
−0.718381 + 0.695650i \(0.755117\pi\)
\(74\) 30.2835 3.52038
\(75\) 3.24256 0.374419
\(76\) 4.83293 0.554375
\(77\) 3.03214 0.345544
\(78\) 0 0
\(79\) 1.46368 0.164677 0.0823384 0.996604i \(-0.473761\pi\)
0.0823384 + 0.996604i \(0.473761\pi\)
\(80\) −16.1033 −1.80040
\(81\) 1.00000 0.111111
\(82\) −20.6051 −2.27545
\(83\) 4.31767 0.473926 0.236963 0.971519i \(-0.423848\pi\)
0.236963 + 0.971519i \(0.423848\pi\)
\(84\) 5.14091 0.560919
\(85\) −6.05089 −0.656311
\(86\) 19.2515 2.07594
\(87\) −5.79888 −0.621705
\(88\) −25.4496 −2.71294
\(89\) −3.22598 −0.341953 −0.170976 0.985275i \(-0.554692\pi\)
−0.170976 + 0.985275i \(0.554692\pi\)
\(90\) −3.54256 −0.373418
\(91\) 0 0
\(92\) 43.9832 4.58556
\(93\) −1.00569 −0.104285
\(94\) 34.2681 3.53448
\(95\) −1.24627 −0.127864
\(96\) −15.6736 −1.59968
\(97\) −5.51764 −0.560231 −0.280116 0.959966i \(-0.590373\pi\)
−0.280116 + 0.959966i \(0.590373\pi\)
\(98\) 2.67225 0.269938
\(99\) −3.03214 −0.304742
\(100\) −16.6697 −1.66697
\(101\) −15.6199 −1.55424 −0.777118 0.629355i \(-0.783319\pi\)
−0.777118 + 0.629355i \(0.783319\pi\)
\(102\) −12.1971 −1.20769
\(103\) 3.64829 0.359477 0.179739 0.983714i \(-0.442475\pi\)
0.179739 + 0.983714i \(0.442475\pi\)
\(104\) 0 0
\(105\) −1.32568 −0.129374
\(106\) 14.0638 1.36600
\(107\) −13.8712 −1.34098 −0.670491 0.741917i \(-0.733917\pi\)
−0.670491 + 0.741917i \(0.733917\pi\)
\(108\) −5.14091 −0.494684
\(109\) 4.46904 0.428057 0.214028 0.976827i \(-0.431341\pi\)
0.214028 + 0.976827i \(0.431341\pi\)
\(110\) 10.7415 1.02416
\(111\) −11.3326 −1.07564
\(112\) −12.1471 −1.14780
\(113\) −6.59144 −0.620070 −0.310035 0.950725i \(-0.600341\pi\)
−0.310035 + 0.950725i \(0.600341\pi\)
\(114\) −2.51216 −0.235285
\(115\) −11.3419 −1.05764
\(116\) 29.8115 2.76793
\(117\) 0 0
\(118\) −35.2294 −3.24313
\(119\) −4.56435 −0.418413
\(120\) 11.1269 1.01574
\(121\) −1.80613 −0.164193
\(122\) 15.5743 1.41003
\(123\) 7.71076 0.695256
\(124\) 5.17017 0.464295
\(125\) 10.9270 0.977344
\(126\) −2.67225 −0.238063
\(127\) −3.34415 −0.296746 −0.148373 0.988931i \(-0.547404\pi\)
−0.148373 + 0.988931i \(0.547404\pi\)
\(128\) 15.6561 1.38382
\(129\) −7.20423 −0.634297
\(130\) 0 0
\(131\) 17.5766 1.53567 0.767836 0.640646i \(-0.221334\pi\)
0.767836 + 0.640646i \(0.221334\pi\)
\(132\) 15.5880 1.35676
\(133\) −0.940093 −0.0815164
\(134\) 8.07813 0.697844
\(135\) 1.32568 0.114097
\(136\) 38.3099 3.28505
\(137\) 8.33789 0.712354 0.356177 0.934418i \(-0.384080\pi\)
0.356177 + 0.934418i \(0.384080\pi\)
\(138\) −22.8625 −1.94618
\(139\) 9.03188 0.766074 0.383037 0.923733i \(-0.374878\pi\)
0.383037 + 0.923733i \(0.374878\pi\)
\(140\) 6.81522 0.575992
\(141\) −12.8237 −1.07995
\(142\) −16.1509 −1.35536
\(143\) 0 0
\(144\) 12.1471 1.01226
\(145\) −7.68749 −0.638411
\(146\) −32.8037 −2.71486
\(147\) −1.00000 −0.0824786
\(148\) 58.2598 4.78892
\(149\) −11.5763 −0.948364 −0.474182 0.880427i \(-0.657256\pi\)
−0.474182 + 0.880427i \(0.657256\pi\)
\(150\) 8.66492 0.707488
\(151\) 12.8069 1.04221 0.521106 0.853492i \(-0.325519\pi\)
0.521106 + 0.853492i \(0.325519\pi\)
\(152\) 7.89047 0.640001
\(153\) 4.56435 0.369006
\(154\) 8.10263 0.652929
\(155\) −1.33323 −0.107088
\(156\) 0 0
\(157\) 21.2317 1.69448 0.847238 0.531213i \(-0.178264\pi\)
0.847238 + 0.531213i \(0.178264\pi\)
\(158\) 3.91132 0.311168
\(159\) −5.26290 −0.417375
\(160\) −20.7782 −1.64266
\(161\) −8.55552 −0.674270
\(162\) 2.67225 0.209952
\(163\) −9.58992 −0.751140 −0.375570 0.926794i \(-0.622553\pi\)
−0.375570 + 0.926794i \(0.622553\pi\)
\(164\) −39.6403 −3.09539
\(165\) −4.01966 −0.312930
\(166\) 11.5379 0.895514
\(167\) 18.3054 1.41652 0.708258 0.705954i \(-0.249481\pi\)
0.708258 + 0.705954i \(0.249481\pi\)
\(168\) 8.39329 0.647556
\(169\) 0 0
\(170\) −16.1695 −1.24014
\(171\) 0.940093 0.0718907
\(172\) 37.0363 2.82399
\(173\) −14.3907 −1.09410 −0.547051 0.837100i \(-0.684249\pi\)
−0.547051 + 0.837100i \(0.684249\pi\)
\(174\) −15.4960 −1.17475
\(175\) 3.24256 0.245115
\(176\) −36.8318 −2.77630
\(177\) 13.1834 0.990928
\(178\) −8.62061 −0.646142
\(179\) 11.4813 0.858156 0.429078 0.903267i \(-0.358838\pi\)
0.429078 + 0.903267i \(0.358838\pi\)
\(180\) −6.81522 −0.507977
\(181\) −26.5739 −1.97522 −0.987612 0.156914i \(-0.949845\pi\)
−0.987612 + 0.156914i \(0.949845\pi\)
\(182\) 0 0
\(183\) −5.82817 −0.430831
\(184\) 71.8090 5.29383
\(185\) −15.0234 −1.10454
\(186\) −2.68746 −0.197054
\(187\) −13.8398 −1.01206
\(188\) 65.9254 4.80810
\(189\) 1.00000 0.0727393
\(190\) −3.33033 −0.241608
\(191\) −0.582610 −0.0421562 −0.0210781 0.999778i \(-0.506710\pi\)
−0.0210781 + 0.999778i \(0.506710\pi\)
\(192\) −17.5894 −1.26940
\(193\) −4.20527 −0.302702 −0.151351 0.988480i \(-0.548362\pi\)
−0.151351 + 0.988480i \(0.548362\pi\)
\(194\) −14.7445 −1.05859
\(195\) 0 0
\(196\) 5.14091 0.367208
\(197\) 20.0883 1.43123 0.715616 0.698494i \(-0.246146\pi\)
0.715616 + 0.698494i \(0.246146\pi\)
\(198\) −8.10263 −0.575829
\(199\) −26.6158 −1.88675 −0.943374 0.331732i \(-0.892367\pi\)
−0.943374 + 0.331732i \(0.892367\pi\)
\(200\) −27.2157 −1.92444
\(201\) −3.02297 −0.213224
\(202\) −41.7402 −2.93683
\(203\) −5.79888 −0.407002
\(204\) −23.4649 −1.64287
\(205\) 10.2220 0.713938
\(206\) 9.74915 0.679255
\(207\) 8.55552 0.594650
\(208\) 0 0
\(209\) −2.85049 −0.197173
\(210\) −3.54256 −0.244460
\(211\) −22.5261 −1.55076 −0.775379 0.631497i \(-0.782441\pi\)
−0.775379 + 0.631497i \(0.782441\pi\)
\(212\) 27.0561 1.85822
\(213\) 6.04396 0.414125
\(214\) −37.0674 −2.53387
\(215\) −9.55054 −0.651342
\(216\) −8.39329 −0.571091
\(217\) −1.00569 −0.0682708
\(218\) 11.9424 0.808841
\(219\) 12.2757 0.829515
\(220\) 20.6647 1.39321
\(221\) 0 0
\(222\) −30.2835 −2.03249
\(223\) 9.50381 0.636422 0.318211 0.948020i \(-0.396918\pi\)
0.318211 + 0.948020i \(0.396918\pi\)
\(224\) −15.6736 −1.04723
\(225\) −3.24256 −0.216171
\(226\) −17.6140 −1.17166
\(227\) −14.9121 −0.989749 −0.494874 0.868965i \(-0.664786\pi\)
−0.494874 + 0.868965i \(0.664786\pi\)
\(228\) −4.83293 −0.320069
\(229\) −14.1266 −0.933513 −0.466757 0.884386i \(-0.654578\pi\)
−0.466757 + 0.884386i \(0.654578\pi\)
\(230\) −30.3084 −1.99848
\(231\) −3.03214 −0.199500
\(232\) 48.6717 3.19545
\(233\) −15.0580 −0.986481 −0.493241 0.869893i \(-0.664188\pi\)
−0.493241 + 0.869893i \(0.664188\pi\)
\(234\) 0 0
\(235\) −17.0002 −1.10897
\(236\) −67.7749 −4.41177
\(237\) −1.46368 −0.0950762
\(238\) −12.1971 −0.790619
\(239\) 4.14971 0.268423 0.134211 0.990953i \(-0.457150\pi\)
0.134211 + 0.990953i \(0.457150\pi\)
\(240\) 16.1033 1.03946
\(241\) −18.1010 −1.16599 −0.582995 0.812476i \(-0.698119\pi\)
−0.582995 + 0.812476i \(0.698119\pi\)
\(242\) −4.82642 −0.310254
\(243\) −1.00000 −0.0641500
\(244\) 29.9621 1.91813
\(245\) −1.32568 −0.0846949
\(246\) 20.6051 1.31373
\(247\) 0 0
\(248\) 8.44106 0.536008
\(249\) −4.31767 −0.273621
\(250\) 29.1997 1.84675
\(251\) 4.22142 0.266454 0.133227 0.991086i \(-0.457466\pi\)
0.133227 + 0.991086i \(0.457466\pi\)
\(252\) −5.14091 −0.323847
\(253\) −25.9415 −1.63093
\(254\) −8.93641 −0.560720
\(255\) 6.05089 0.378922
\(256\) 6.65816 0.416135
\(257\) 11.8550 0.739493 0.369747 0.929133i \(-0.379444\pi\)
0.369747 + 0.929133i \(0.379444\pi\)
\(258\) −19.2515 −1.19855
\(259\) −11.3326 −0.704172
\(260\) 0 0
\(261\) 5.79888 0.358942
\(262\) 46.9690 2.90175
\(263\) 12.5753 0.775425 0.387712 0.921780i \(-0.373265\pi\)
0.387712 + 0.921780i \(0.373265\pi\)
\(264\) 25.4496 1.56632
\(265\) −6.97695 −0.428591
\(266\) −2.51216 −0.154030
\(267\) 3.22598 0.197427
\(268\) 15.5408 0.949307
\(269\) 12.5342 0.764221 0.382110 0.924117i \(-0.375197\pi\)
0.382110 + 0.924117i \(0.375197\pi\)
\(270\) 3.54256 0.215593
\(271\) −3.47597 −0.211150 −0.105575 0.994411i \(-0.533668\pi\)
−0.105575 + 0.994411i \(0.533668\pi\)
\(272\) 55.4438 3.36177
\(273\) 0 0
\(274\) 22.2809 1.34604
\(275\) 9.83190 0.592886
\(276\) −43.9832 −2.64748
\(277\) −6.76964 −0.406748 −0.203374 0.979101i \(-0.565191\pi\)
−0.203374 + 0.979101i \(0.565191\pi\)
\(278\) 24.1354 1.44755
\(279\) 1.00569 0.0602092
\(280\) 11.1269 0.664957
\(281\) 4.18616 0.249725 0.124863 0.992174i \(-0.460151\pi\)
0.124863 + 0.992174i \(0.460151\pi\)
\(282\) −34.2681 −2.04063
\(283\) 5.21985 0.310288 0.155144 0.987892i \(-0.450416\pi\)
0.155144 + 0.987892i \(0.450416\pi\)
\(284\) −31.0714 −1.84375
\(285\) 1.24627 0.0738224
\(286\) 0 0
\(287\) 7.71076 0.455152
\(288\) 15.6736 0.923574
\(289\) 3.83331 0.225489
\(290\) −20.5429 −1.20632
\(291\) 5.51764 0.323450
\(292\) −63.1083 −3.69313
\(293\) 10.0063 0.584573 0.292286 0.956331i \(-0.405584\pi\)
0.292286 + 0.956331i \(0.405584\pi\)
\(294\) −2.67225 −0.155849
\(295\) 17.4771 1.01756
\(296\) 95.1176 5.52860
\(297\) 3.03214 0.175943
\(298\) −30.9346 −1.79199
\(299\) 0 0
\(300\) 16.6697 0.962426
\(301\) −7.20423 −0.415245
\(302\) 34.2233 1.96933
\(303\) 15.6199 0.897338
\(304\) 11.4194 0.654949
\(305\) −7.72632 −0.442408
\(306\) 12.1971 0.697261
\(307\) −0.476202 −0.0271783 −0.0135891 0.999908i \(-0.504326\pi\)
−0.0135891 + 0.999908i \(0.504326\pi\)
\(308\) 15.5880 0.888206
\(309\) −3.64829 −0.207544
\(310\) −3.56272 −0.202349
\(311\) 22.0675 1.25133 0.625666 0.780091i \(-0.284827\pi\)
0.625666 + 0.780091i \(0.284827\pi\)
\(312\) 0 0
\(313\) −6.17383 −0.348966 −0.174483 0.984660i \(-0.555825\pi\)
−0.174483 + 0.984660i \(0.555825\pi\)
\(314\) 56.7364 3.20182
\(315\) 1.32568 0.0746939
\(316\) 7.52465 0.423294
\(317\) 12.1948 0.684930 0.342465 0.939531i \(-0.388738\pi\)
0.342465 + 0.939531i \(0.388738\pi\)
\(318\) −14.0638 −0.788658
\(319\) −17.5830 −0.984460
\(320\) −23.3180 −1.30351
\(321\) 13.8712 0.774217
\(322\) −22.8625 −1.27408
\(323\) 4.29091 0.238753
\(324\) 5.14091 0.285606
\(325\) 0 0
\(326\) −25.6266 −1.41933
\(327\) −4.46904 −0.247139
\(328\) −64.7187 −3.57349
\(329\) −12.8237 −0.706993
\(330\) −10.7415 −0.591302
\(331\) −21.9157 −1.20459 −0.602297 0.798272i \(-0.705748\pi\)
−0.602297 + 0.798272i \(0.705748\pi\)
\(332\) 22.1968 1.21821
\(333\) 11.3326 0.621022
\(334\) 48.9166 2.67660
\(335\) −4.00751 −0.218953
\(336\) 12.1471 0.662680
\(337\) −9.16559 −0.499281 −0.249641 0.968339i \(-0.580312\pi\)
−0.249641 + 0.968339i \(0.580312\pi\)
\(338\) 0 0
\(339\) 6.59144 0.357998
\(340\) −31.1071 −1.68702
\(341\) −3.04940 −0.165134
\(342\) 2.51216 0.135842
\(343\) −1.00000 −0.0539949
\(344\) 60.4672 3.26017
\(345\) 11.3419 0.610629
\(346\) −38.4554 −2.06738
\(347\) 11.2649 0.604734 0.302367 0.953192i \(-0.402223\pi\)
0.302367 + 0.953192i \(0.402223\pi\)
\(348\) −29.8115 −1.59806
\(349\) 10.6412 0.569610 0.284805 0.958585i \(-0.408071\pi\)
0.284805 + 0.958585i \(0.408071\pi\)
\(350\) 8.66492 0.463160
\(351\) 0 0
\(352\) −47.5244 −2.53306
\(353\) −9.03769 −0.481027 −0.240514 0.970646i \(-0.577316\pi\)
−0.240514 + 0.970646i \(0.577316\pi\)
\(354\) 35.2294 1.87242
\(355\) 8.01238 0.425253
\(356\) −16.5845 −0.878974
\(357\) 4.56435 0.241571
\(358\) 30.6810 1.62154
\(359\) −2.34727 −0.123884 −0.0619421 0.998080i \(-0.519729\pi\)
−0.0619421 + 0.998080i \(0.519729\pi\)
\(360\) −11.1269 −0.586437
\(361\) −18.1162 −0.953486
\(362\) −71.0121 −3.73231
\(363\) 1.80613 0.0947970
\(364\) 0 0
\(365\) 16.2737 0.851805
\(366\) −15.5743 −0.814083
\(367\) 30.1391 1.57325 0.786623 0.617433i \(-0.211827\pi\)
0.786623 + 0.617433i \(0.211827\pi\)
\(368\) 103.925 5.41747
\(369\) −7.71076 −0.401406
\(370\) −40.1463 −2.08711
\(371\) −5.26290 −0.273236
\(372\) −5.17017 −0.268061
\(373\) −1.86802 −0.0967222 −0.0483611 0.998830i \(-0.515400\pi\)
−0.0483611 + 0.998830i \(0.515400\pi\)
\(374\) −36.9833 −1.91236
\(375\) −10.9270 −0.564270
\(376\) 107.633 5.55074
\(377\) 0 0
\(378\) 2.67225 0.137446
\(379\) −31.2686 −1.60616 −0.803080 0.595871i \(-0.796807\pi\)
−0.803080 + 0.595871i \(0.796807\pi\)
\(380\) −6.40694 −0.328669
\(381\) 3.34415 0.171326
\(382\) −1.55688 −0.0796568
\(383\) −5.27451 −0.269515 −0.134757 0.990879i \(-0.543026\pi\)
−0.134757 + 0.990879i \(0.543026\pi\)
\(384\) −15.6561 −0.798946
\(385\) −4.01966 −0.204861
\(386\) −11.2375 −0.571975
\(387\) 7.20423 0.366212
\(388\) −28.3657 −1.44005
\(389\) 31.9519 1.62002 0.810012 0.586413i \(-0.199460\pi\)
0.810012 + 0.586413i \(0.199460\pi\)
\(390\) 0 0
\(391\) 39.0504 1.97486
\(392\) 8.39329 0.423925
\(393\) −17.5766 −0.886621
\(394\) 53.6809 2.70440
\(395\) −1.94038 −0.0976310
\(396\) −15.5880 −0.783324
\(397\) 0.115785 0.00581111 0.00290555 0.999996i \(-0.499075\pi\)
0.00290555 + 0.999996i \(0.499075\pi\)
\(398\) −71.1241 −3.56513
\(399\) 0.940093 0.0470635
\(400\) −39.3878 −1.96939
\(401\) −17.7168 −0.884734 −0.442367 0.896834i \(-0.645861\pi\)
−0.442367 + 0.896834i \(0.645861\pi\)
\(402\) −8.07813 −0.402900
\(403\) 0 0
\(404\) −80.3003 −3.99509
\(405\) −1.32568 −0.0658738
\(406\) −15.4960 −0.769056
\(407\) −34.3620 −1.70326
\(408\) −38.3099 −1.89662
\(409\) 18.5393 0.916708 0.458354 0.888770i \(-0.348439\pi\)
0.458354 + 0.888770i \(0.348439\pi\)
\(410\) 27.3158 1.34903
\(411\) −8.33789 −0.411278
\(412\) 18.7555 0.924019
\(413\) 13.1834 0.648715
\(414\) 22.8625 1.12363
\(415\) −5.72387 −0.280974
\(416\) 0 0
\(417\) −9.03188 −0.442293
\(418\) −7.61722 −0.372571
\(419\) 20.2670 0.990107 0.495053 0.868863i \(-0.335148\pi\)
0.495053 + 0.868863i \(0.335148\pi\)
\(420\) −6.81522 −0.332549
\(421\) −38.6779 −1.88504 −0.942522 0.334144i \(-0.891553\pi\)
−0.942522 + 0.334144i \(0.891553\pi\)
\(422\) −60.1952 −2.93026
\(423\) 12.8237 0.623509
\(424\) 44.1731 2.14523
\(425\) −14.8002 −0.717914
\(426\) 16.1509 0.782516
\(427\) −5.82817 −0.282045
\(428\) −71.3108 −3.44694
\(429\) 0 0
\(430\) −25.5214 −1.23075
\(431\) −27.4790 −1.32362 −0.661808 0.749673i \(-0.730211\pi\)
−0.661808 + 0.749673i \(0.730211\pi\)
\(432\) −12.1471 −0.584429
\(433\) −35.8813 −1.72435 −0.862173 0.506613i \(-0.830897\pi\)
−0.862173 + 0.506613i \(0.830897\pi\)
\(434\) −2.68746 −0.129002
\(435\) 7.68749 0.368587
\(436\) 22.9749 1.10030
\(437\) 8.04298 0.384748
\(438\) 32.8037 1.56742
\(439\) −12.6382 −0.603187 −0.301593 0.953437i \(-0.597519\pi\)
−0.301593 + 0.953437i \(0.597519\pi\)
\(440\) 33.7382 1.60840
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 4.86153 0.230978 0.115489 0.993309i \(-0.463156\pi\)
0.115489 + 0.993309i \(0.463156\pi\)
\(444\) −58.2598 −2.76489
\(445\) 4.27663 0.202732
\(446\) 25.3965 1.20256
\(447\) 11.5763 0.547538
\(448\) −17.5894 −0.831021
\(449\) −26.0682 −1.23024 −0.615118 0.788435i \(-0.710891\pi\)
−0.615118 + 0.788435i \(0.710891\pi\)
\(450\) −8.66492 −0.408468
\(451\) 23.3801 1.10093
\(452\) −33.8860 −1.59386
\(453\) −12.8069 −0.601722
\(454\) −39.8487 −1.87019
\(455\) 0 0
\(456\) −7.89047 −0.369505
\(457\) 2.32931 0.108960 0.0544802 0.998515i \(-0.482650\pi\)
0.0544802 + 0.998515i \(0.482650\pi\)
\(458\) −37.7498 −1.76393
\(459\) −4.56435 −0.213046
\(460\) −58.3078 −2.71862
\(461\) −11.6874 −0.544338 −0.272169 0.962249i \(-0.587741\pi\)
−0.272169 + 0.962249i \(0.587741\pi\)
\(462\) −8.10263 −0.376968
\(463\) 25.3264 1.17702 0.588509 0.808490i \(-0.299715\pi\)
0.588509 + 0.808490i \(0.299715\pi\)
\(464\) 70.4397 3.27008
\(465\) 1.33323 0.0618271
\(466\) −40.2387 −1.86402
\(467\) 4.69774 0.217385 0.108693 0.994075i \(-0.465334\pi\)
0.108693 + 0.994075i \(0.465334\pi\)
\(468\) 0 0
\(469\) −3.02297 −0.139588
\(470\) −45.4287 −2.09547
\(471\) −21.2317 −0.978306
\(472\) −110.652 −5.09319
\(473\) −21.8442 −1.00440
\(474\) −3.91132 −0.179653
\(475\) −3.04831 −0.139866
\(476\) −23.4649 −1.07551
\(477\) 5.26290 0.240972
\(478\) 11.0891 0.507202
\(479\) −25.7413 −1.17615 −0.588075 0.808806i \(-0.700114\pi\)
−0.588075 + 0.808806i \(0.700114\pi\)
\(480\) 20.7782 0.948391
\(481\) 0 0
\(482\) −48.3704 −2.20321
\(483\) 8.55552 0.389290
\(484\) −9.28513 −0.422051
\(485\) 7.31465 0.332141
\(486\) −2.67225 −0.121216
\(487\) −8.77825 −0.397780 −0.198890 0.980022i \(-0.563734\pi\)
−0.198890 + 0.980022i \(0.563734\pi\)
\(488\) 48.9175 2.21439
\(489\) 9.58992 0.433671
\(490\) −3.54256 −0.160036
\(491\) 34.6420 1.56337 0.781686 0.623672i \(-0.214360\pi\)
0.781686 + 0.623672i \(0.214360\pi\)
\(492\) 39.6403 1.78712
\(493\) 26.4681 1.19206
\(494\) 0 0
\(495\) 4.01966 0.180670
\(496\) 12.2163 0.548527
\(497\) 6.04396 0.271108
\(498\) −11.5379 −0.517025
\(499\) 15.2931 0.684612 0.342306 0.939589i \(-0.388792\pi\)
0.342306 + 0.939589i \(0.388792\pi\)
\(500\) 56.1749 2.51222
\(501\) −18.3054 −0.817826
\(502\) 11.2807 0.503482
\(503\) −8.70136 −0.387974 −0.193987 0.981004i \(-0.562142\pi\)
−0.193987 + 0.981004i \(0.562142\pi\)
\(504\) −8.39329 −0.373867
\(505\) 20.7070 0.921450
\(506\) −69.3222 −3.08175
\(507\) 0 0
\(508\) −17.1920 −0.762771
\(509\) 26.9261 1.19348 0.596739 0.802435i \(-0.296463\pi\)
0.596739 + 0.802435i \(0.296463\pi\)
\(510\) 16.1695 0.715997
\(511\) 12.2757 0.543045
\(512\) −13.5199 −0.597501
\(513\) −0.940093 −0.0415061
\(514\) 31.6794 1.39732
\(515\) −4.83649 −0.213121
\(516\) −37.0363 −1.63043
\(517\) −38.8832 −1.71008
\(518\) −30.2835 −1.33058
\(519\) 14.3907 0.631680
\(520\) 0 0
\(521\) 0.805919 0.0353079 0.0176540 0.999844i \(-0.494380\pi\)
0.0176540 + 0.999844i \(0.494380\pi\)
\(522\) 15.4960 0.678243
\(523\) 37.1587 1.62484 0.812418 0.583075i \(-0.198151\pi\)
0.812418 + 0.583075i \(0.198151\pi\)
\(524\) 90.3596 3.94738
\(525\) −3.24256 −0.141517
\(526\) 33.6043 1.46522
\(527\) 4.59033 0.199958
\(528\) 36.8318 1.60290
\(529\) 50.1970 2.18248
\(530\) −18.6441 −0.809850
\(531\) −13.1834 −0.572113
\(532\) −4.83293 −0.209534
\(533\) 0 0
\(534\) 8.62061 0.373050
\(535\) 18.3889 0.795021
\(536\) 25.3727 1.09593
\(537\) −11.4813 −0.495457
\(538\) 33.4944 1.44404
\(539\) −3.03214 −0.130604
\(540\) 6.81522 0.293281
\(541\) 22.5963 0.971492 0.485746 0.874100i \(-0.338548\pi\)
0.485746 + 0.874100i \(0.338548\pi\)
\(542\) −9.28866 −0.398982
\(543\) 26.5739 1.14040
\(544\) 71.5397 3.06724
\(545\) −5.92454 −0.253780
\(546\) 0 0
\(547\) −24.9820 −1.06815 −0.534076 0.845436i \(-0.679340\pi\)
−0.534076 + 0.845436i \(0.679340\pi\)
\(548\) 42.8644 1.83107
\(549\) 5.82817 0.248740
\(550\) 26.2733 1.12030
\(551\) 5.45148 0.232241
\(552\) −71.8090 −3.05639
\(553\) −1.46368 −0.0622420
\(554\) −18.0901 −0.768577
\(555\) 15.0234 0.637709
\(556\) 46.4321 1.96916
\(557\) 11.7270 0.496891 0.248445 0.968646i \(-0.420080\pi\)
0.248445 + 0.968646i \(0.420080\pi\)
\(558\) 2.68746 0.113769
\(559\) 0 0
\(560\) 16.1033 0.680487
\(561\) 13.8398 0.584315
\(562\) 11.1865 0.471872
\(563\) −6.86242 −0.289216 −0.144608 0.989489i \(-0.546192\pi\)
−0.144608 + 0.989489i \(0.546192\pi\)
\(564\) −65.9254 −2.77596
\(565\) 8.73817 0.367618
\(566\) 13.9487 0.586309
\(567\) −1.00000 −0.0419961
\(568\) −50.7287 −2.12853
\(569\) −13.4308 −0.563049 −0.281525 0.959554i \(-0.590840\pi\)
−0.281525 + 0.959554i \(0.590840\pi\)
\(570\) 3.33033 0.139492
\(571\) −18.8819 −0.790185 −0.395092 0.918641i \(-0.629287\pi\)
−0.395092 + 0.918641i \(0.629287\pi\)
\(572\) 0 0
\(573\) 0.582610 0.0243389
\(574\) 20.6051 0.860039
\(575\) −27.7418 −1.15691
\(576\) 17.5894 0.732891
\(577\) −31.9538 −1.33025 −0.665126 0.746731i \(-0.731622\pi\)
−0.665126 + 0.746731i \(0.731622\pi\)
\(578\) 10.2436 0.426076
\(579\) 4.20527 0.174765
\(580\) −39.5207 −1.64101
\(581\) −4.31767 −0.179127
\(582\) 14.7445 0.611179
\(583\) −15.9579 −0.660907
\(584\) −103.034 −4.26356
\(585\) 0 0
\(586\) 26.7392 1.10459
\(587\) −14.8277 −0.612005 −0.306002 0.952031i \(-0.598992\pi\)
−0.306002 + 0.952031i \(0.598992\pi\)
\(588\) −5.14091 −0.212008
\(589\) 0.945444 0.0389563
\(590\) 46.7031 1.92274
\(591\) −20.0883 −0.826322
\(592\) 137.658 5.65772
\(593\) 14.1339 0.580411 0.290205 0.956964i \(-0.406276\pi\)
0.290205 + 0.956964i \(0.406276\pi\)
\(594\) 8.10263 0.332455
\(595\) 6.05089 0.248062
\(596\) −59.5125 −2.43773
\(597\) 26.6158 1.08931
\(598\) 0 0
\(599\) −6.24004 −0.254961 −0.127481 0.991841i \(-0.540689\pi\)
−0.127481 + 0.991841i \(0.540689\pi\)
\(600\) 27.2157 1.11108
\(601\) −38.1259 −1.55519 −0.777594 0.628767i \(-0.783560\pi\)
−0.777594 + 0.628767i \(0.783560\pi\)
\(602\) −19.2515 −0.784633
\(603\) 3.02297 0.123105
\(604\) 65.8392 2.67896
\(605\) 2.39435 0.0973443
\(606\) 41.7402 1.69558
\(607\) 6.64697 0.269792 0.134896 0.990860i \(-0.456930\pi\)
0.134896 + 0.990860i \(0.456930\pi\)
\(608\) 14.7346 0.597567
\(609\) 5.79888 0.234982
\(610\) −20.6466 −0.835958
\(611\) 0 0
\(612\) 23.4649 0.948513
\(613\) −5.39777 −0.218014 −0.109007 0.994041i \(-0.534767\pi\)
−0.109007 + 0.994041i \(0.534767\pi\)
\(614\) −1.27253 −0.0513551
\(615\) −10.2220 −0.412192
\(616\) 25.4496 1.02539
\(617\) −15.6769 −0.631127 −0.315563 0.948904i \(-0.602193\pi\)
−0.315563 + 0.948904i \(0.602193\pi\)
\(618\) −9.74915 −0.392168
\(619\) −4.62364 −0.185840 −0.0929199 0.995674i \(-0.529620\pi\)
−0.0929199 + 0.995674i \(0.529620\pi\)
\(620\) −6.85402 −0.275264
\(621\) −8.55552 −0.343321
\(622\) 58.9697 2.36447
\(623\) 3.22598 0.129246
\(624\) 0 0
\(625\) 1.72700 0.0690799
\(626\) −16.4980 −0.659393
\(627\) 2.85049 0.113838
\(628\) 109.150 4.35557
\(629\) 51.7259 2.06245
\(630\) 3.54256 0.141139
\(631\) −22.5825 −0.898997 −0.449498 0.893281i \(-0.648397\pi\)
−0.449498 + 0.893281i \(0.648397\pi\)
\(632\) 12.2851 0.488675
\(633\) 22.5261 0.895330
\(634\) 32.5876 1.29422
\(635\) 4.43329 0.175930
\(636\) −27.0561 −1.07284
\(637\) 0 0
\(638\) −46.9862 −1.86020
\(639\) −6.04396 −0.239095
\(640\) −20.7550 −0.820415
\(641\) 0.836649 0.0330456 0.0165228 0.999863i \(-0.494740\pi\)
0.0165228 + 0.999863i \(0.494740\pi\)
\(642\) 37.0674 1.46293
\(643\) −19.3772 −0.764161 −0.382081 0.924129i \(-0.624792\pi\)
−0.382081 + 0.924129i \(0.624792\pi\)
\(644\) −43.9832 −1.73318
\(645\) 9.55054 0.376052
\(646\) 11.4664 0.451139
\(647\) 34.6544 1.36240 0.681202 0.732095i \(-0.261457\pi\)
0.681202 + 0.732095i \(0.261457\pi\)
\(648\) 8.39329 0.329719
\(649\) 39.9740 1.56912
\(650\) 0 0
\(651\) 1.00569 0.0394162
\(652\) −49.3009 −1.93077
\(653\) −23.7620 −0.929878 −0.464939 0.885343i \(-0.653924\pi\)
−0.464939 + 0.885343i \(0.653924\pi\)
\(654\) −11.9424 −0.466984
\(655\) −23.3010 −0.910445
\(656\) −93.6636 −3.65695
\(657\) −12.2757 −0.478921
\(658\) −34.2681 −1.33591
\(659\) −15.1656 −0.590767 −0.295384 0.955379i \(-0.595447\pi\)
−0.295384 + 0.955379i \(0.595447\pi\)
\(660\) −20.6647 −0.804373
\(661\) 6.98694 0.271760 0.135880 0.990725i \(-0.456614\pi\)
0.135880 + 0.990725i \(0.456614\pi\)
\(662\) −58.5641 −2.27616
\(663\) 0 0
\(664\) 36.2395 1.40636
\(665\) 1.24627 0.0483281
\(666\) 30.2835 1.17346
\(667\) 49.6124 1.92100
\(668\) 94.1065 3.64109
\(669\) −9.50381 −0.367439
\(670\) −10.7090 −0.413727
\(671\) −17.6718 −0.682214
\(672\) 15.6736 0.604621
\(673\) −29.9128 −1.15305 −0.576527 0.817078i \(-0.695592\pi\)
−0.576527 + 0.817078i \(0.695592\pi\)
\(674\) −24.4927 −0.943424
\(675\) 3.24256 0.124806
\(676\) 0 0
\(677\) 12.5395 0.481934 0.240967 0.970533i \(-0.422535\pi\)
0.240967 + 0.970533i \(0.422535\pi\)
\(678\) 17.6140 0.676460
\(679\) 5.51764 0.211748
\(680\) −50.7869 −1.94759
\(681\) 14.9121 0.571432
\(682\) −8.14875 −0.312032
\(683\) 38.3070 1.46578 0.732888 0.680349i \(-0.238172\pi\)
0.732888 + 0.680349i \(0.238172\pi\)
\(684\) 4.83293 0.184792
\(685\) −11.0534 −0.422329
\(686\) −2.67225 −0.102027
\(687\) 14.1266 0.538964
\(688\) 87.5108 3.33632
\(689\) 0 0
\(690\) 30.3084 1.15382
\(691\) 13.5321 0.514786 0.257393 0.966307i \(-0.417137\pi\)
0.257393 + 0.966307i \(0.417137\pi\)
\(692\) −73.9811 −2.81234
\(693\) 3.03214 0.115181
\(694\) 30.1027 1.14268
\(695\) −11.9734 −0.454178
\(696\) −48.6717 −1.84489
\(697\) −35.1946 −1.33309
\(698\) 28.4359 1.07632
\(699\) 15.0580 0.569545
\(700\) 16.6697 0.630056
\(701\) −33.0151 −1.24696 −0.623482 0.781838i \(-0.714282\pi\)
−0.623482 + 0.781838i \(0.714282\pi\)
\(702\) 0 0
\(703\) 10.6537 0.401811
\(704\) −53.3335 −2.01008
\(705\) 17.0002 0.640263
\(706\) −24.1509 −0.908932
\(707\) 15.6199 0.587446
\(708\) 67.7749 2.54714
\(709\) −18.2760 −0.686370 −0.343185 0.939268i \(-0.611506\pi\)
−0.343185 + 0.939268i \(0.611506\pi\)
\(710\) 21.4111 0.803543
\(711\) 1.46368 0.0548923
\(712\) −27.0765 −1.01474
\(713\) 8.60422 0.322231
\(714\) 12.1971 0.456464
\(715\) 0 0
\(716\) 59.0246 2.20585
\(717\) −4.14971 −0.154974
\(718\) −6.27249 −0.234087
\(719\) 3.47453 0.129578 0.0647891 0.997899i \(-0.479363\pi\)
0.0647891 + 0.997899i \(0.479363\pi\)
\(720\) −16.1033 −0.600133
\(721\) −3.64829 −0.135870
\(722\) −48.4110 −1.80167
\(723\) 18.1010 0.673185
\(724\) −136.614 −5.07722
\(725\) −18.8032 −0.698334
\(726\) 4.82642 0.179125
\(727\) 17.5710 0.651674 0.325837 0.945426i \(-0.394354\pi\)
0.325837 + 0.945426i \(0.394354\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 43.4874 1.60954
\(731\) 32.8827 1.21621
\(732\) −29.9621 −1.10743
\(733\) 9.61436 0.355114 0.177557 0.984110i \(-0.443181\pi\)
0.177557 + 0.984110i \(0.443181\pi\)
\(734\) 80.5391 2.97275
\(735\) 1.32568 0.0488986
\(736\) 134.096 4.94283
\(737\) −9.16607 −0.337637
\(738\) −20.6051 −0.758483
\(739\) 26.3610 0.969705 0.484853 0.874596i \(-0.338873\pi\)
0.484853 + 0.874596i \(0.338873\pi\)
\(740\) −77.2341 −2.83918
\(741\) 0 0
\(742\) −14.0638 −0.516298
\(743\) −22.0239 −0.807980 −0.403990 0.914764i \(-0.632377\pi\)
−0.403990 + 0.914764i \(0.632377\pi\)
\(744\) −8.44106 −0.309464
\(745\) 15.3465 0.562251
\(746\) −4.99180 −0.182763
\(747\) 4.31767 0.157975
\(748\) −71.1489 −2.60146
\(749\) 13.8712 0.506844
\(750\) −29.1997 −1.06622
\(751\) −12.4993 −0.456105 −0.228052 0.973649i \(-0.573236\pi\)
−0.228052 + 0.973649i \(0.573236\pi\)
\(752\) 155.771 5.68038
\(753\) −4.22142 −0.153837
\(754\) 0 0
\(755\) −16.9779 −0.617891
\(756\) 5.14091 0.186973
\(757\) −6.58820 −0.239452 −0.119726 0.992807i \(-0.538202\pi\)
−0.119726 + 0.992807i \(0.538202\pi\)
\(758\) −83.5575 −3.03494
\(759\) 25.9415 0.941618
\(760\) −10.4603 −0.379434
\(761\) 45.9690 1.66637 0.833187 0.552991i \(-0.186514\pi\)
0.833187 + 0.552991i \(0.186514\pi\)
\(762\) 8.93641 0.323732
\(763\) −4.46904 −0.161790
\(764\) −2.99514 −0.108361
\(765\) −6.05089 −0.218770
\(766\) −14.0948 −0.509266
\(767\) 0 0
\(768\) −6.65816 −0.240256
\(769\) −26.8238 −0.967291 −0.483645 0.875264i \(-0.660688\pi\)
−0.483645 + 0.875264i \(0.660688\pi\)
\(770\) −10.7415 −0.387098
\(771\) −11.8550 −0.426947
\(772\) −21.6189 −0.778082
\(773\) −16.6180 −0.597708 −0.298854 0.954299i \(-0.596604\pi\)
−0.298854 + 0.954299i \(0.596604\pi\)
\(774\) 19.2515 0.691981
\(775\) −3.26102 −0.117139
\(776\) −46.3111 −1.66247
\(777\) 11.3326 0.406554
\(778\) 85.3834 3.06114
\(779\) −7.24883 −0.259716
\(780\) 0 0
\(781\) 18.3261 0.655760
\(782\) 104.352 3.73163
\(783\) −5.79888 −0.207235
\(784\) 12.1471 0.433826
\(785\) −28.1466 −1.00459
\(786\) −46.9690 −1.67533
\(787\) −53.2069 −1.89662 −0.948311 0.317342i \(-0.897210\pi\)
−0.948311 + 0.317342i \(0.897210\pi\)
\(788\) 103.272 3.67892
\(789\) −12.5753 −0.447692
\(790\) −5.18517 −0.184480
\(791\) 6.59144 0.234365
\(792\) −25.4496 −0.904313
\(793\) 0 0
\(794\) 0.309408 0.0109805
\(795\) 6.97695 0.247447
\(796\) −136.830 −4.84980
\(797\) −8.69215 −0.307892 −0.153946 0.988079i \(-0.549198\pi\)
−0.153946 + 0.988079i \(0.549198\pi\)
\(798\) 2.51216 0.0889295
\(799\) 58.5318 2.07071
\(800\) −50.8225 −1.79685
\(801\) −3.22598 −0.113984
\(802\) −47.3437 −1.67176
\(803\) 37.2217 1.31352
\(804\) −15.5408 −0.548082
\(805\) 11.3419 0.399750
\(806\) 0 0
\(807\) −12.5342 −0.441223
\(808\) −131.102 −4.61215
\(809\) 9.92301 0.348875 0.174437 0.984668i \(-0.444189\pi\)
0.174437 + 0.984668i \(0.444189\pi\)
\(810\) −3.54256 −0.124473
\(811\) −5.95089 −0.208964 −0.104482 0.994527i \(-0.533318\pi\)
−0.104482 + 0.994527i \(0.533318\pi\)
\(812\) −29.8115 −1.04618
\(813\) 3.47597 0.121908
\(814\) −91.8237 −3.21842
\(815\) 12.7132 0.445324
\(816\) −55.4438 −1.94092
\(817\) 6.77265 0.236945
\(818\) 49.5415 1.73218
\(819\) 0 0
\(820\) 52.5506 1.83515
\(821\) −52.7490 −1.84095 −0.920476 0.390800i \(-0.872198\pi\)
−0.920476 + 0.390800i \(0.872198\pi\)
\(822\) −22.2809 −0.777136
\(823\) −9.92502 −0.345964 −0.172982 0.984925i \(-0.555340\pi\)
−0.172982 + 0.984925i \(0.555340\pi\)
\(824\) 30.6212 1.06674
\(825\) −9.83190 −0.342303
\(826\) 35.2294 1.22579
\(827\) 18.6645 0.649028 0.324514 0.945881i \(-0.394799\pi\)
0.324514 + 0.945881i \(0.394799\pi\)
\(828\) 43.9832 1.52852
\(829\) 12.8111 0.444947 0.222473 0.974939i \(-0.428587\pi\)
0.222473 + 0.974939i \(0.428587\pi\)
\(830\) −15.2956 −0.530918
\(831\) 6.76964 0.234836
\(832\) 0 0
\(833\) 4.56435 0.158145
\(834\) −24.1354 −0.835741
\(835\) −24.2672 −0.839801
\(836\) −14.6541 −0.506823
\(837\) −1.00569 −0.0347618
\(838\) 54.1584 1.87087
\(839\) 2.50652 0.0865348 0.0432674 0.999064i \(-0.486223\pi\)
0.0432674 + 0.999064i \(0.486223\pi\)
\(840\) −11.1269 −0.383913
\(841\) 4.62700 0.159552
\(842\) −103.357 −3.56191
\(843\) −4.18616 −0.144179
\(844\) −115.804 −3.98615
\(845\) 0 0
\(846\) 34.2681 1.17816
\(847\) 1.80613 0.0620592
\(848\) 63.9292 2.19534
\(849\) −5.21985 −0.179145
\(850\) −39.5498 −1.35655
\(851\) 96.9562 3.32361
\(852\) 31.0714 1.06449
\(853\) 35.0626 1.20052 0.600261 0.799804i \(-0.295064\pi\)
0.600261 + 0.799804i \(0.295064\pi\)
\(854\) −15.5743 −0.532943
\(855\) −1.24627 −0.0426214
\(856\) −116.425 −3.97933
\(857\) 21.1331 0.721894 0.360947 0.932586i \(-0.382453\pi\)
0.360947 + 0.932586i \(0.382453\pi\)
\(858\) 0 0
\(859\) 46.4000 1.58315 0.791574 0.611074i \(-0.209262\pi\)
0.791574 + 0.611074i \(0.209262\pi\)
\(860\) −49.0985 −1.67424
\(861\) −7.71076 −0.262782
\(862\) −73.4307 −2.50106
\(863\) −15.6094 −0.531349 −0.265675 0.964063i \(-0.585595\pi\)
−0.265675 + 0.964063i \(0.585595\pi\)
\(864\) −15.6736 −0.533225
\(865\) 19.0775 0.648653
\(866\) −95.8838 −3.25826
\(867\) −3.83331 −0.130186
\(868\) −5.17017 −0.175487
\(869\) −4.43808 −0.150552
\(870\) 20.5429 0.696468
\(871\) 0 0
\(872\) 37.5100 1.27025
\(873\) −5.51764 −0.186744
\(874\) 21.4928 0.727006
\(875\) −10.9270 −0.369401
\(876\) 63.1083 2.13223
\(877\) 24.5637 0.829459 0.414729 0.909945i \(-0.363876\pi\)
0.414729 + 0.909945i \(0.363876\pi\)
\(878\) −33.7723 −1.13976
\(879\) −10.0063 −0.337503
\(880\) 48.8273 1.64597
\(881\) 40.3246 1.35857 0.679285 0.733874i \(-0.262290\pi\)
0.679285 + 0.733874i \(0.262290\pi\)
\(882\) 2.67225 0.0899793
\(883\) 3.76928 0.126846 0.0634232 0.997987i \(-0.479798\pi\)
0.0634232 + 0.997987i \(0.479798\pi\)
\(884\) 0 0
\(885\) −17.4771 −0.587486
\(886\) 12.9912 0.436448
\(887\) 7.71311 0.258981 0.129490 0.991581i \(-0.458666\pi\)
0.129490 + 0.991581i \(0.458666\pi\)
\(888\) −95.1176 −3.19194
\(889\) 3.34415 0.112159
\(890\) 11.4282 0.383074
\(891\) −3.03214 −0.101581
\(892\) 48.8582 1.63590
\(893\) 12.0555 0.403420
\(894\) 30.9346 1.03461
\(895\) −15.2206 −0.508770
\(896\) −15.6561 −0.523033
\(897\) 0 0
\(898\) −69.6607 −2.32461
\(899\) 5.83189 0.194504
\(900\) −16.6697 −0.555657
\(901\) 24.0217 0.800280
\(902\) 62.4775 2.08027
\(903\) 7.20423 0.239742
\(904\) −55.3238 −1.84004
\(905\) 35.2286 1.17104
\(906\) −34.2233 −1.13699
\(907\) −6.02488 −0.200053 −0.100026 0.994985i \(-0.531893\pi\)
−0.100026 + 0.994985i \(0.531893\pi\)
\(908\) −76.6616 −2.54410
\(909\) −15.6199 −0.518078
\(910\) 0 0
\(911\) −44.1545 −1.46290 −0.731452 0.681893i \(-0.761157\pi\)
−0.731452 + 0.681893i \(0.761157\pi\)
\(912\) −11.4194 −0.378135
\(913\) −13.0918 −0.433275
\(914\) 6.22449 0.205888
\(915\) 7.72632 0.255424
\(916\) −72.6237 −2.39955
\(917\) −17.5766 −0.580430
\(918\) −12.1971 −0.402564
\(919\) 2.47103 0.0815119 0.0407559 0.999169i \(-0.487023\pi\)
0.0407559 + 0.999169i \(0.487023\pi\)
\(920\) −95.1960 −3.13852
\(921\) 0.476202 0.0156914
\(922\) −31.2317 −1.02856
\(923\) 0 0
\(924\) −15.5880 −0.512806
\(925\) −36.7466 −1.20822
\(926\) 67.6785 2.22405
\(927\) 3.64829 0.119826
\(928\) 90.8891 2.98358
\(929\) −27.4089 −0.899257 −0.449628 0.893216i \(-0.648444\pi\)
−0.449628 + 0.893216i \(0.648444\pi\)
\(930\) 3.56272 0.116826
\(931\) 0.940093 0.0308103
\(932\) −77.4117 −2.53571
\(933\) −22.0675 −0.722456
\(934\) 12.5535 0.410764
\(935\) 18.3472 0.600016
\(936\) 0 0
\(937\) 12.7270 0.415772 0.207886 0.978153i \(-0.433342\pi\)
0.207886 + 0.978153i \(0.433342\pi\)
\(938\) −8.07813 −0.263760
\(939\) 6.17383 0.201475
\(940\) −87.3963 −2.85055
\(941\) 3.02848 0.0987256 0.0493628 0.998781i \(-0.484281\pi\)
0.0493628 + 0.998781i \(0.484281\pi\)
\(942\) −56.7364 −1.84857
\(943\) −65.9696 −2.14827
\(944\) −160.141 −5.21214
\(945\) −1.32568 −0.0431245
\(946\) −58.3732 −1.89788
\(947\) 4.41915 0.143603 0.0718015 0.997419i \(-0.477125\pi\)
0.0718015 + 0.997419i \(0.477125\pi\)
\(948\) −7.52465 −0.244389
\(949\) 0 0
\(950\) −8.14583 −0.264286
\(951\) −12.1948 −0.395445
\(952\) −38.3099 −1.24163
\(953\) −11.6151 −0.376250 −0.188125 0.982145i \(-0.560241\pi\)
−0.188125 + 0.982145i \(0.560241\pi\)
\(954\) 14.0638 0.455332
\(955\) 0.772357 0.0249929
\(956\) 21.3333 0.689968
\(957\) 17.5830 0.568378
\(958\) −68.7871 −2.22241
\(959\) −8.33789 −0.269245
\(960\) 23.3180 0.752585
\(961\) −29.9886 −0.967374
\(962\) 0 0
\(963\) −13.8712 −0.446994
\(964\) −93.0558 −2.99712
\(965\) 5.57487 0.179461
\(966\) 22.8625 0.735588
\(967\) 14.3606 0.461807 0.230903 0.972977i \(-0.425832\pi\)
0.230903 + 0.972977i \(0.425832\pi\)
\(968\) −15.1593 −0.487240
\(969\) −4.29091 −0.137844
\(970\) 19.5466 0.627602
\(971\) 27.3485 0.877656 0.438828 0.898571i \(-0.355394\pi\)
0.438828 + 0.898571i \(0.355394\pi\)
\(972\) −5.14091 −0.164895
\(973\) −9.03188 −0.289549
\(974\) −23.4577 −0.751632
\(975\) 0 0
\(976\) 70.7956 2.26611
\(977\) 31.1899 0.997852 0.498926 0.866644i \(-0.333728\pi\)
0.498926 + 0.866644i \(0.333728\pi\)
\(978\) 25.6266 0.819450
\(979\) 9.78161 0.312622
\(980\) −6.81522 −0.217704
\(981\) 4.46904 0.142686
\(982\) 92.5720 2.95409
\(983\) −33.6418 −1.07301 −0.536504 0.843898i \(-0.680255\pi\)
−0.536504 + 0.843898i \(0.680255\pi\)
\(984\) 64.7187 2.06316
\(985\) −26.6307 −0.848526
\(986\) 70.7294 2.25248
\(987\) 12.8237 0.408182
\(988\) 0 0
\(989\) 61.6360 1.95991
\(990\) 10.7415 0.341388
\(991\) 47.5698 1.51110 0.755552 0.655089i \(-0.227369\pi\)
0.755552 + 0.655089i \(0.227369\pi\)
\(992\) 15.7628 0.500469
\(993\) 21.9157 0.695473
\(994\) 16.1509 0.512277
\(995\) 35.2842 1.11859
\(996\) −22.1968 −0.703331
\(997\) −43.7979 −1.38709 −0.693547 0.720411i \(-0.743953\pi\)
−0.693547 + 0.720411i \(0.743953\pi\)
\(998\) 40.8669 1.29362
\(999\) −11.3326 −0.358547
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.1.9 yes 9
13.12 even 2 3549.2.a.be.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.1 9 13.12 even 2
3549.2.a.bf.1.9 yes 9 1.1 even 1 trivial