Properties

Label 3549.2.a.bh.1.7
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 1.7
Root \(-0.415563\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} -4.32224 q^{5} -0.415563 q^{6} -1.00000 q^{7} +1.59049 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} -4.32224 q^{5} -0.415563 q^{6} -1.00000 q^{7} +1.59049 q^{8} +1.00000 q^{9} +1.79616 q^{10} -3.32197 q^{11} -1.82731 q^{12} +0.415563 q^{14} -4.32224 q^{15} +2.99367 q^{16} -5.26423 q^{17} -0.415563 q^{18} -0.118179 q^{19} +7.89805 q^{20} -1.00000 q^{21} +1.38049 q^{22} -7.51837 q^{23} +1.59049 q^{24} +13.6817 q^{25} +1.00000 q^{27} +1.82731 q^{28} -2.46042 q^{29} +1.79616 q^{30} -10.0410 q^{31} -4.42503 q^{32} -3.32197 q^{33} +2.18762 q^{34} +4.32224 q^{35} -1.82731 q^{36} -5.38066 q^{37} +0.0491107 q^{38} -6.87447 q^{40} -11.7059 q^{41} +0.415563 q^{42} -0.378528 q^{43} +6.07025 q^{44} -4.32224 q^{45} +3.12436 q^{46} -3.46970 q^{47} +2.99367 q^{48} +1.00000 q^{49} -5.68562 q^{50} -5.26423 q^{51} +4.33879 q^{53} -0.415563 q^{54} +14.3583 q^{55} -1.59049 q^{56} -0.118179 q^{57} +1.02246 q^{58} -8.88207 q^{59} +7.89805 q^{60} -6.67086 q^{61} +4.17269 q^{62} -1.00000 q^{63} -4.14845 q^{64} +1.38049 q^{66} +3.42565 q^{67} +9.61936 q^{68} -7.51837 q^{69} -1.79616 q^{70} +7.25425 q^{71} +1.59049 q^{72} +13.9967 q^{73} +2.23600 q^{74} +13.6817 q^{75} +0.215949 q^{76} +3.32197 q^{77} -0.278553 q^{79} -12.9393 q^{80} +1.00000 q^{81} +4.86455 q^{82} +14.5998 q^{83} +1.82731 q^{84} +22.7532 q^{85} +0.157302 q^{86} -2.46042 q^{87} -5.28355 q^{88} +7.54564 q^{89} +1.79616 q^{90} +13.7384 q^{92} -10.0410 q^{93} +1.44188 q^{94} +0.510796 q^{95} -4.42503 q^{96} -7.20532 q^{97} -0.415563 q^{98} -3.32197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415563 −0.293848 −0.146924 0.989148i \(-0.546937\pi\)
−0.146924 + 0.989148i \(0.546937\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.82731 −0.913654
\(5\) −4.32224 −1.93296 −0.966481 0.256737i \(-0.917353\pi\)
−0.966481 + 0.256737i \(0.917353\pi\)
\(6\) −0.415563 −0.169653
\(7\) −1.00000 −0.377964
\(8\) 1.59049 0.562323
\(9\) 1.00000 0.333333
\(10\) 1.79616 0.567997
\(11\) −3.32197 −1.00161 −0.500805 0.865560i \(-0.666963\pi\)
−0.500805 + 0.865560i \(0.666963\pi\)
\(12\) −1.82731 −0.527498
\(13\) 0 0
\(14\) 0.415563 0.111064
\(15\) −4.32224 −1.11600
\(16\) 2.99367 0.748416
\(17\) −5.26423 −1.27676 −0.638381 0.769720i \(-0.720396\pi\)
−0.638381 + 0.769720i \(0.720396\pi\)
\(18\) −0.415563 −0.0979492
\(19\) −0.118179 −0.0271121 −0.0135560 0.999908i \(-0.504315\pi\)
−0.0135560 + 0.999908i \(0.504315\pi\)
\(20\) 7.89805 1.76606
\(21\) −1.00000 −0.218218
\(22\) 1.38049 0.294321
\(23\) −7.51837 −1.56769 −0.783844 0.620958i \(-0.786744\pi\)
−0.783844 + 0.620958i \(0.786744\pi\)
\(24\) 1.59049 0.324657
\(25\) 13.6817 2.73635
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.82731 0.345329
\(29\) −2.46042 −0.456888 −0.228444 0.973557i \(-0.573364\pi\)
−0.228444 + 0.973557i \(0.573364\pi\)
\(30\) 1.79616 0.327933
\(31\) −10.0410 −1.80342 −0.901712 0.432338i \(-0.857689\pi\)
−0.901712 + 0.432338i \(0.857689\pi\)
\(32\) −4.42503 −0.782243
\(33\) −3.32197 −0.578280
\(34\) 2.18762 0.375174
\(35\) 4.32224 0.730591
\(36\) −1.82731 −0.304551
\(37\) −5.38066 −0.884574 −0.442287 0.896873i \(-0.645833\pi\)
−0.442287 + 0.896873i \(0.645833\pi\)
\(38\) 0.0491107 0.00796681
\(39\) 0 0
\(40\) −6.87447 −1.08695
\(41\) −11.7059 −1.82816 −0.914078 0.405538i \(-0.867084\pi\)
−0.914078 + 0.405538i \(0.867084\pi\)
\(42\) 0.415563 0.0641228
\(43\) −0.378528 −0.0577249 −0.0288625 0.999583i \(-0.509188\pi\)
−0.0288625 + 0.999583i \(0.509188\pi\)
\(44\) 6.07025 0.915125
\(45\) −4.32224 −0.644321
\(46\) 3.12436 0.460662
\(47\) −3.46970 −0.506108 −0.253054 0.967452i \(-0.581435\pi\)
−0.253054 + 0.967452i \(0.581435\pi\)
\(48\) 2.99367 0.432098
\(49\) 1.00000 0.142857
\(50\) −5.68562 −0.804068
\(51\) −5.26423 −0.737139
\(52\) 0 0
\(53\) 4.33879 0.595979 0.297989 0.954569i \(-0.403684\pi\)
0.297989 + 0.954569i \(0.403684\pi\)
\(54\) −0.415563 −0.0565510
\(55\) 14.3583 1.93608
\(56\) −1.59049 −0.212538
\(57\) −0.118179 −0.0156532
\(58\) 1.02246 0.134256
\(59\) −8.88207 −1.15635 −0.578173 0.815914i \(-0.696234\pi\)
−0.578173 + 0.815914i \(0.696234\pi\)
\(60\) 7.89805 1.01963
\(61\) −6.67086 −0.854116 −0.427058 0.904224i \(-0.640450\pi\)
−0.427058 + 0.904224i \(0.640450\pi\)
\(62\) 4.17269 0.529932
\(63\) −1.00000 −0.125988
\(64\) −4.14845 −0.518556
\(65\) 0 0
\(66\) 1.38049 0.169926
\(67\) 3.42565 0.418509 0.209255 0.977861i \(-0.432896\pi\)
0.209255 + 0.977861i \(0.432896\pi\)
\(68\) 9.61936 1.16652
\(69\) −7.51837 −0.905105
\(70\) −1.79616 −0.214682
\(71\) 7.25425 0.860921 0.430460 0.902609i \(-0.358351\pi\)
0.430460 + 0.902609i \(0.358351\pi\)
\(72\) 1.59049 0.187441
\(73\) 13.9967 1.63819 0.819093 0.573660i \(-0.194477\pi\)
0.819093 + 0.573660i \(0.194477\pi\)
\(74\) 2.23600 0.259930
\(75\) 13.6817 1.57983
\(76\) 0.215949 0.0247710
\(77\) 3.32197 0.378573
\(78\) 0 0
\(79\) −0.278553 −0.0313397 −0.0156698 0.999877i \(-0.504988\pi\)
−0.0156698 + 0.999877i \(0.504988\pi\)
\(80\) −12.9393 −1.44666
\(81\) 1.00000 0.111111
\(82\) 4.86455 0.537199
\(83\) 14.5998 1.60254 0.801270 0.598302i \(-0.204158\pi\)
0.801270 + 0.598302i \(0.204158\pi\)
\(84\) 1.82731 0.199376
\(85\) 22.7532 2.46793
\(86\) 0.157302 0.0169623
\(87\) −2.46042 −0.263785
\(88\) −5.28355 −0.563228
\(89\) 7.54564 0.799836 0.399918 0.916551i \(-0.369039\pi\)
0.399918 + 0.916551i \(0.369039\pi\)
\(90\) 1.79616 0.189332
\(91\) 0 0
\(92\) 13.7384 1.43232
\(93\) −10.0410 −1.04121
\(94\) 1.44188 0.148719
\(95\) 0.510796 0.0524066
\(96\) −4.42503 −0.451628
\(97\) −7.20532 −0.731590 −0.365795 0.930696i \(-0.619203\pi\)
−0.365795 + 0.930696i \(0.619203\pi\)
\(98\) −0.415563 −0.0419782
\(99\) −3.32197 −0.333870
\(100\) −25.0007 −2.50007
\(101\) 3.90068 0.388132 0.194066 0.980988i \(-0.437832\pi\)
0.194066 + 0.980988i \(0.437832\pi\)
\(102\) 2.18762 0.216607
\(103\) −0.253309 −0.0249593 −0.0124797 0.999922i \(-0.503972\pi\)
−0.0124797 + 0.999922i \(0.503972\pi\)
\(104\) 0 0
\(105\) 4.32224 0.421807
\(106\) −1.80304 −0.175127
\(107\) 1.25329 0.121160 0.0605800 0.998163i \(-0.480705\pi\)
0.0605800 + 0.998163i \(0.480705\pi\)
\(108\) −1.82731 −0.175833
\(109\) 3.26860 0.313075 0.156537 0.987672i \(-0.449967\pi\)
0.156537 + 0.987672i \(0.449967\pi\)
\(110\) −5.96679 −0.568911
\(111\) −5.38066 −0.510709
\(112\) −2.99367 −0.282875
\(113\) −0.0957171 −0.00900431 −0.00450215 0.999990i \(-0.501433\pi\)
−0.00450215 + 0.999990i \(0.501433\pi\)
\(114\) 0.0491107 0.00459964
\(115\) 32.4962 3.03028
\(116\) 4.49594 0.417438
\(117\) 0 0
\(118\) 3.69106 0.339790
\(119\) 5.26423 0.482571
\(120\) −6.87447 −0.627550
\(121\) 0.0354611 0.00322374
\(122\) 2.77217 0.250980
\(123\) −11.7059 −1.05549
\(124\) 18.3481 1.64770
\(125\) −37.5245 −3.35629
\(126\) 0.415563 0.0370213
\(127\) 15.5224 1.37739 0.688696 0.725050i \(-0.258183\pi\)
0.688696 + 0.725050i \(0.258183\pi\)
\(128\) 10.5740 0.934619
\(129\) −0.378528 −0.0333275
\(130\) 0 0
\(131\) 8.00203 0.699141 0.349570 0.936910i \(-0.386328\pi\)
0.349570 + 0.936910i \(0.386328\pi\)
\(132\) 6.07025 0.528348
\(133\) 0.118179 0.0102474
\(134\) −1.42357 −0.122978
\(135\) −4.32224 −0.371999
\(136\) −8.37269 −0.717952
\(137\) 9.28221 0.793033 0.396516 0.918028i \(-0.370219\pi\)
0.396516 + 0.918028i \(0.370219\pi\)
\(138\) 3.12436 0.265963
\(139\) 4.27962 0.362992 0.181496 0.983392i \(-0.441906\pi\)
0.181496 + 0.983392i \(0.441906\pi\)
\(140\) −7.89805 −0.667507
\(141\) −3.46970 −0.292202
\(142\) −3.01460 −0.252980
\(143\) 0 0
\(144\) 2.99367 0.249472
\(145\) 10.6345 0.883148
\(146\) −5.81650 −0.481377
\(147\) 1.00000 0.0824786
\(148\) 9.83211 0.808195
\(149\) −11.0346 −0.903988 −0.451994 0.892021i \(-0.649287\pi\)
−0.451994 + 0.892021i \(0.649287\pi\)
\(150\) −5.68562 −0.464229
\(151\) −7.54592 −0.614078 −0.307039 0.951697i \(-0.599338\pi\)
−0.307039 + 0.951697i \(0.599338\pi\)
\(152\) −0.187962 −0.0152457
\(153\) −5.26423 −0.425588
\(154\) −1.38049 −0.111243
\(155\) 43.3997 3.48595
\(156\) 0 0
\(157\) −21.5422 −1.71926 −0.859629 0.510918i \(-0.829306\pi\)
−0.859629 + 0.510918i \(0.829306\pi\)
\(158\) 0.115756 0.00920909
\(159\) 4.33879 0.344089
\(160\) 19.1260 1.51205
\(161\) 7.51837 0.592531
\(162\) −0.415563 −0.0326497
\(163\) −22.3911 −1.75381 −0.876903 0.480667i \(-0.840395\pi\)
−0.876903 + 0.480667i \(0.840395\pi\)
\(164\) 21.3903 1.67030
\(165\) 14.3583 1.11779
\(166\) −6.06716 −0.470903
\(167\) −8.14259 −0.630093 −0.315046 0.949076i \(-0.602020\pi\)
−0.315046 + 0.949076i \(0.602020\pi\)
\(168\) −1.59049 −0.122709
\(169\) 0 0
\(170\) −9.45541 −0.725197
\(171\) −0.118179 −0.00903735
\(172\) 0.691686 0.0527406
\(173\) −14.3336 −1.08976 −0.544880 0.838514i \(-0.683425\pi\)
−0.544880 + 0.838514i \(0.683425\pi\)
\(174\) 1.02246 0.0775125
\(175\) −13.6817 −1.03424
\(176\) −9.94486 −0.749622
\(177\) −8.88207 −0.667617
\(178\) −3.13569 −0.235030
\(179\) 12.7843 0.955546 0.477773 0.878483i \(-0.341444\pi\)
0.477773 + 0.878483i \(0.341444\pi\)
\(180\) 7.89805 0.588686
\(181\) 20.9807 1.55948 0.779741 0.626102i \(-0.215351\pi\)
0.779741 + 0.626102i \(0.215351\pi\)
\(182\) 0 0
\(183\) −6.67086 −0.493124
\(184\) −11.9579 −0.881547
\(185\) 23.2565 1.70985
\(186\) 4.17269 0.305956
\(187\) 17.4876 1.27882
\(188\) 6.34021 0.462407
\(189\) −1.00000 −0.0727393
\(190\) −0.212268 −0.0153996
\(191\) −5.41589 −0.391880 −0.195940 0.980616i \(-0.562776\pi\)
−0.195940 + 0.980616i \(0.562776\pi\)
\(192\) −4.14845 −0.299389
\(193\) 11.2327 0.808546 0.404273 0.914638i \(-0.367525\pi\)
0.404273 + 0.914638i \(0.367525\pi\)
\(194\) 2.99427 0.214976
\(195\) 0 0
\(196\) −1.82731 −0.130522
\(197\) 0.705420 0.0502591 0.0251295 0.999684i \(-0.492000\pi\)
0.0251295 + 0.999684i \(0.492000\pi\)
\(198\) 1.38049 0.0981070
\(199\) 11.6826 0.828156 0.414078 0.910241i \(-0.364104\pi\)
0.414078 + 0.910241i \(0.364104\pi\)
\(200\) 21.7606 1.53871
\(201\) 3.42565 0.241626
\(202\) −1.62098 −0.114052
\(203\) 2.46042 0.172688
\(204\) 9.61936 0.673490
\(205\) 50.5957 3.53376
\(206\) 0.105266 0.00733423
\(207\) −7.51837 −0.522563
\(208\) 0 0
\(209\) 0.392586 0.0271557
\(210\) −1.79616 −0.123947
\(211\) 4.38529 0.301896 0.150948 0.988542i \(-0.451767\pi\)
0.150948 + 0.988542i \(0.451767\pi\)
\(212\) −7.92831 −0.544518
\(213\) 7.25425 0.497053
\(214\) −0.520821 −0.0356026
\(215\) 1.63609 0.111580
\(216\) 1.59049 0.108219
\(217\) 10.0410 0.681630
\(218\) −1.35831 −0.0919963
\(219\) 13.9967 0.945807
\(220\) −26.2371 −1.76890
\(221\) 0 0
\(222\) 2.23600 0.150071
\(223\) 14.8375 0.993594 0.496797 0.867867i \(-0.334509\pi\)
0.496797 + 0.867867i \(0.334509\pi\)
\(224\) 4.42503 0.295660
\(225\) 13.6817 0.912115
\(226\) 0.0397765 0.00264589
\(227\) −0.0625704 −0.00415294 −0.00207647 0.999998i \(-0.500661\pi\)
−0.00207647 + 0.999998i \(0.500661\pi\)
\(228\) 0.215949 0.0143016
\(229\) 0.184720 0.0122066 0.00610331 0.999981i \(-0.498057\pi\)
0.00610331 + 0.999981i \(0.498057\pi\)
\(230\) −13.5042 −0.890442
\(231\) 3.32197 0.218569
\(232\) −3.91327 −0.256919
\(233\) 0.190546 0.0124831 0.00624154 0.999981i \(-0.498013\pi\)
0.00624154 + 0.999981i \(0.498013\pi\)
\(234\) 0 0
\(235\) 14.9969 0.978288
\(236\) 16.2303 1.05650
\(237\) −0.278553 −0.0180940
\(238\) −2.18762 −0.141802
\(239\) 17.7380 1.14737 0.573687 0.819075i \(-0.305513\pi\)
0.573687 + 0.819075i \(0.305513\pi\)
\(240\) −12.9393 −0.835230
\(241\) −4.72194 −0.304167 −0.152084 0.988368i \(-0.548598\pi\)
−0.152084 + 0.988368i \(0.548598\pi\)
\(242\) −0.0147363 −0.000947288 0
\(243\) 1.00000 0.0641500
\(244\) 12.1897 0.780366
\(245\) −4.32224 −0.276138
\(246\) 4.86455 0.310152
\(247\) 0 0
\(248\) −15.9702 −1.01411
\(249\) 14.5998 0.925227
\(250\) 15.5938 0.986238
\(251\) −13.2188 −0.834362 −0.417181 0.908823i \(-0.636982\pi\)
−0.417181 + 0.908823i \(0.636982\pi\)
\(252\) 1.82731 0.115110
\(253\) 24.9758 1.57021
\(254\) −6.45055 −0.404744
\(255\) 22.7532 1.42486
\(256\) 3.90273 0.243921
\(257\) −17.4150 −1.08632 −0.543160 0.839629i \(-0.682772\pi\)
−0.543160 + 0.839629i \(0.682772\pi\)
\(258\) 0.157302 0.00979321
\(259\) 5.38066 0.334338
\(260\) 0 0
\(261\) −2.46042 −0.152296
\(262\) −3.32535 −0.205441
\(263\) −25.2510 −1.55704 −0.778522 0.627618i \(-0.784030\pi\)
−0.778522 + 0.627618i \(0.784030\pi\)
\(264\) −5.28355 −0.325180
\(265\) −18.7533 −1.15201
\(266\) −0.0491107 −0.00301117
\(267\) 7.54564 0.461785
\(268\) −6.25971 −0.382372
\(269\) −15.7373 −0.959519 −0.479759 0.877400i \(-0.659276\pi\)
−0.479759 + 0.877400i \(0.659276\pi\)
\(270\) 1.79616 0.109311
\(271\) 10.7178 0.651059 0.325530 0.945532i \(-0.394457\pi\)
0.325530 + 0.945532i \(0.394457\pi\)
\(272\) −15.7593 −0.955550
\(273\) 0 0
\(274\) −3.85735 −0.233031
\(275\) −45.4502 −2.74075
\(276\) 13.7384 0.826953
\(277\) −19.1268 −1.14922 −0.574608 0.818429i \(-0.694845\pi\)
−0.574608 + 0.818429i \(0.694845\pi\)
\(278\) −1.77845 −0.106664
\(279\) −10.0410 −0.601141
\(280\) 6.87447 0.410828
\(281\) −8.87426 −0.529394 −0.264697 0.964332i \(-0.585272\pi\)
−0.264697 + 0.964332i \(0.585272\pi\)
\(282\) 1.44188 0.0858627
\(283\) −20.4319 −1.21455 −0.607274 0.794492i \(-0.707737\pi\)
−0.607274 + 0.794492i \(0.707737\pi\)
\(284\) −13.2557 −0.786583
\(285\) 0.510796 0.0302570
\(286\) 0 0
\(287\) 11.7059 0.690978
\(288\) −4.42503 −0.260748
\(289\) 10.7121 0.630123
\(290\) −4.41931 −0.259511
\(291\) −7.20532 −0.422384
\(292\) −25.5762 −1.49673
\(293\) 16.0750 0.939114 0.469557 0.882902i \(-0.344414\pi\)
0.469557 + 0.882902i \(0.344414\pi\)
\(294\) −0.415563 −0.0242361
\(295\) 38.3904 2.23517
\(296\) −8.55787 −0.497416
\(297\) −3.32197 −0.192760
\(298\) 4.58557 0.265635
\(299\) 0 0
\(300\) −25.0007 −1.44342
\(301\) 0.378528 0.0218180
\(302\) 3.13581 0.180445
\(303\) 3.90068 0.224088
\(304\) −0.353788 −0.0202911
\(305\) 28.8330 1.65098
\(306\) 2.18762 0.125058
\(307\) 6.03807 0.344611 0.172305 0.985044i \(-0.444878\pi\)
0.172305 + 0.985044i \(0.444878\pi\)
\(308\) −6.07025 −0.345885
\(309\) −0.253309 −0.0144103
\(310\) −18.0353 −1.02434
\(311\) −12.2263 −0.693289 −0.346645 0.937997i \(-0.612679\pi\)
−0.346645 + 0.937997i \(0.612679\pi\)
\(312\) 0 0
\(313\) −6.55638 −0.370589 −0.185294 0.982683i \(-0.559324\pi\)
−0.185294 + 0.982683i \(0.559324\pi\)
\(314\) 8.95217 0.505200
\(315\) 4.32224 0.243530
\(316\) 0.509002 0.0286336
\(317\) −6.92785 −0.389107 −0.194553 0.980892i \(-0.562326\pi\)
−0.194553 + 0.980892i \(0.562326\pi\)
\(318\) −1.80304 −0.101110
\(319\) 8.17343 0.457624
\(320\) 17.9306 1.00235
\(321\) 1.25329 0.0699517
\(322\) −3.12436 −0.174114
\(323\) 0.622120 0.0346157
\(324\) −1.82731 −0.101517
\(325\) 0 0
\(326\) 9.30492 0.515352
\(327\) 3.26860 0.180754
\(328\) −18.6181 −1.02801
\(329\) 3.46970 0.191291
\(330\) −5.96679 −0.328461
\(331\) −15.4100 −0.847012 −0.423506 0.905893i \(-0.639201\pi\)
−0.423506 + 0.905893i \(0.639201\pi\)
\(332\) −26.6784 −1.46417
\(333\) −5.38066 −0.294858
\(334\) 3.38376 0.185151
\(335\) −14.8065 −0.808963
\(336\) −2.99367 −0.163318
\(337\) 23.1479 1.26095 0.630473 0.776211i \(-0.282861\pi\)
0.630473 + 0.776211i \(0.282861\pi\)
\(338\) 0 0
\(339\) −0.0957171 −0.00519864
\(340\) −41.5771 −2.25484
\(341\) 33.3560 1.80633
\(342\) 0.0491107 0.00265560
\(343\) −1.00000 −0.0539949
\(344\) −0.602044 −0.0324600
\(345\) 32.4962 1.74953
\(346\) 5.95650 0.320224
\(347\) 26.9284 1.44559 0.722795 0.691062i \(-0.242857\pi\)
0.722795 + 0.691062i \(0.242857\pi\)
\(348\) 4.49594 0.241008
\(349\) −30.6502 −1.64067 −0.820334 0.571884i \(-0.806213\pi\)
−0.820334 + 0.571884i \(0.806213\pi\)
\(350\) 5.68562 0.303909
\(351\) 0 0
\(352\) 14.6998 0.783503
\(353\) −16.2989 −0.867505 −0.433752 0.901032i \(-0.642811\pi\)
−0.433752 + 0.901032i \(0.642811\pi\)
\(354\) 3.69106 0.196178
\(355\) −31.3546 −1.66413
\(356\) −13.7882 −0.730773
\(357\) 5.26423 0.278612
\(358\) −5.31270 −0.280785
\(359\) −13.6562 −0.720744 −0.360372 0.932809i \(-0.617350\pi\)
−0.360372 + 0.932809i \(0.617350\pi\)
\(360\) −6.87447 −0.362316
\(361\) −18.9860 −0.999265
\(362\) −8.71881 −0.458250
\(363\) 0.0354611 0.00186123
\(364\) 0 0
\(365\) −60.4969 −3.16655
\(366\) 2.77217 0.144903
\(367\) −20.9628 −1.09425 −0.547124 0.837051i \(-0.684277\pi\)
−0.547124 + 0.837051i \(0.684277\pi\)
\(368\) −22.5075 −1.17328
\(369\) −11.7059 −0.609385
\(370\) −9.66453 −0.502435
\(371\) −4.33879 −0.225259
\(372\) 18.3481 0.951303
\(373\) 4.45107 0.230467 0.115234 0.993338i \(-0.463238\pi\)
0.115234 + 0.993338i \(0.463238\pi\)
\(374\) −7.26720 −0.375778
\(375\) −37.5245 −1.93776
\(376\) −5.51852 −0.284596
\(377\) 0 0
\(378\) 0.415563 0.0213743
\(379\) −1.61744 −0.0830826 −0.0415413 0.999137i \(-0.513227\pi\)
−0.0415413 + 0.999137i \(0.513227\pi\)
\(380\) −0.933382 −0.0478815
\(381\) 15.5224 0.795238
\(382\) 2.25065 0.115153
\(383\) 16.3959 0.837791 0.418895 0.908035i \(-0.362417\pi\)
0.418895 + 0.908035i \(0.362417\pi\)
\(384\) 10.5740 0.539603
\(385\) −14.3583 −0.731768
\(386\) −4.66789 −0.237589
\(387\) −0.378528 −0.0192416
\(388\) 13.1663 0.668420
\(389\) 15.1735 0.769326 0.384663 0.923057i \(-0.374318\pi\)
0.384663 + 0.923057i \(0.374318\pi\)
\(390\) 0 0
\(391\) 39.5784 2.00157
\(392\) 1.59049 0.0803318
\(393\) 8.00203 0.403649
\(394\) −0.293147 −0.0147685
\(395\) 1.20397 0.0605784
\(396\) 6.07025 0.305042
\(397\) −6.54905 −0.328688 −0.164344 0.986403i \(-0.552551\pi\)
−0.164344 + 0.986403i \(0.552551\pi\)
\(398\) −4.85485 −0.243352
\(399\) 0.118179 0.00591634
\(400\) 40.9585 2.04793
\(401\) −29.4546 −1.47089 −0.735447 0.677582i \(-0.763028\pi\)
−0.735447 + 0.677582i \(0.763028\pi\)
\(402\) −1.42357 −0.0710014
\(403\) 0 0
\(404\) −7.12774 −0.354618
\(405\) −4.32224 −0.214774
\(406\) −1.02246 −0.0507438
\(407\) 17.8744 0.885999
\(408\) −8.37269 −0.414510
\(409\) 4.76580 0.235654 0.117827 0.993034i \(-0.462407\pi\)
0.117827 + 0.993034i \(0.462407\pi\)
\(410\) −21.0257 −1.03839
\(411\) 9.28221 0.457858
\(412\) 0.462874 0.0228042
\(413\) 8.88207 0.437058
\(414\) 3.12436 0.153554
\(415\) −63.1040 −3.09765
\(416\) 0 0
\(417\) 4.27962 0.209574
\(418\) −0.163144 −0.00797964
\(419\) 21.2897 1.04007 0.520036 0.854144i \(-0.325919\pi\)
0.520036 + 0.854144i \(0.325919\pi\)
\(420\) −7.89805 −0.385386
\(421\) 37.3246 1.81909 0.909544 0.415608i \(-0.136431\pi\)
0.909544 + 0.415608i \(0.136431\pi\)
\(422\) −1.82237 −0.0887114
\(423\) −3.46970 −0.168703
\(424\) 6.90080 0.335132
\(425\) −72.0237 −3.49366
\(426\) −3.01460 −0.146058
\(427\) 6.67086 0.322826
\(428\) −2.29014 −0.110698
\(429\) 0 0
\(430\) −0.679897 −0.0327876
\(431\) −0.534607 −0.0257511 −0.0128756 0.999917i \(-0.504099\pi\)
−0.0128756 + 0.999917i \(0.504099\pi\)
\(432\) 2.99367 0.144033
\(433\) 13.1324 0.631102 0.315551 0.948909i \(-0.397811\pi\)
0.315551 + 0.948909i \(0.397811\pi\)
\(434\) −4.17269 −0.200295
\(435\) 10.6345 0.509886
\(436\) −5.97273 −0.286042
\(437\) 0.888511 0.0425033
\(438\) −5.81650 −0.277923
\(439\) −37.2212 −1.77647 −0.888236 0.459387i \(-0.848069\pi\)
−0.888236 + 0.459387i \(0.848069\pi\)
\(440\) 22.8367 1.08870
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −4.01164 −0.190599 −0.0952994 0.995449i \(-0.530381\pi\)
−0.0952994 + 0.995449i \(0.530381\pi\)
\(444\) 9.83211 0.466611
\(445\) −32.6140 −1.54605
\(446\) −6.16593 −0.291965
\(447\) −11.0346 −0.521918
\(448\) 4.14845 0.195996
\(449\) 6.94095 0.327564 0.163782 0.986497i \(-0.447631\pi\)
0.163782 + 0.986497i \(0.447631\pi\)
\(450\) −5.68562 −0.268023
\(451\) 38.8866 1.83110
\(452\) 0.174905 0.00822682
\(453\) −7.54592 −0.354538
\(454\) 0.0260020 0.00122033
\(455\) 0 0
\(456\) −0.187962 −0.00880212
\(457\) 36.0079 1.68438 0.842189 0.539182i \(-0.181266\pi\)
0.842189 + 0.539182i \(0.181266\pi\)
\(458\) −0.0767628 −0.00358689
\(459\) −5.26423 −0.245713
\(460\) −59.3805 −2.76863
\(461\) 12.5958 0.586646 0.293323 0.956013i \(-0.405239\pi\)
0.293323 + 0.956013i \(0.405239\pi\)
\(462\) −1.38049 −0.0642261
\(463\) 20.9880 0.975395 0.487697 0.873013i \(-0.337837\pi\)
0.487697 + 0.873013i \(0.337837\pi\)
\(464\) −7.36567 −0.341943
\(465\) 43.3997 2.01261
\(466\) −0.0791839 −0.00366812
\(467\) 12.8360 0.593980 0.296990 0.954881i \(-0.404017\pi\)
0.296990 + 0.954881i \(0.404017\pi\)
\(468\) 0 0
\(469\) −3.42565 −0.158182
\(470\) −6.23215 −0.287468
\(471\) −21.5422 −0.992614
\(472\) −14.1268 −0.650240
\(473\) 1.25746 0.0578179
\(474\) 0.115756 0.00531687
\(475\) −1.61689 −0.0741879
\(476\) −9.61936 −0.440903
\(477\) 4.33879 0.198660
\(478\) −7.37124 −0.337153
\(479\) 11.1856 0.511085 0.255542 0.966798i \(-0.417746\pi\)
0.255542 + 0.966798i \(0.417746\pi\)
\(480\) 19.1260 0.872980
\(481\) 0 0
\(482\) 1.96227 0.0893788
\(483\) 7.51837 0.342098
\(484\) −0.0647984 −0.00294538
\(485\) 31.1431 1.41414
\(486\) −0.415563 −0.0188503
\(487\) −29.7826 −1.34958 −0.674789 0.738011i \(-0.735765\pi\)
−0.674789 + 0.738011i \(0.735765\pi\)
\(488\) −10.6099 −0.480289
\(489\) −22.3911 −1.01256
\(490\) 1.79616 0.0811424
\(491\) −10.7199 −0.483781 −0.241891 0.970304i \(-0.577768\pi\)
−0.241891 + 0.970304i \(0.577768\pi\)
\(492\) 21.3903 0.964349
\(493\) 12.9522 0.583338
\(494\) 0 0
\(495\) 14.3583 0.645359
\(496\) −30.0595 −1.34971
\(497\) −7.25425 −0.325397
\(498\) −6.06716 −0.271876
\(499\) 10.9031 0.488088 0.244044 0.969764i \(-0.421526\pi\)
0.244044 + 0.969764i \(0.421526\pi\)
\(500\) 68.5687 3.06649
\(501\) −8.14259 −0.363784
\(502\) 5.49324 0.245175
\(503\) 8.98933 0.400814 0.200407 0.979713i \(-0.435774\pi\)
0.200407 + 0.979713i \(0.435774\pi\)
\(504\) −1.59049 −0.0708460
\(505\) −16.8597 −0.750245
\(506\) −10.3790 −0.461403
\(507\) 0 0
\(508\) −28.3642 −1.25846
\(509\) −2.53243 −0.112248 −0.0561239 0.998424i \(-0.517874\pi\)
−0.0561239 + 0.998424i \(0.517874\pi\)
\(510\) −9.45541 −0.418693
\(511\) −13.9967 −0.619176
\(512\) −22.7699 −1.00629
\(513\) −0.118179 −0.00521772
\(514\) 7.23705 0.319212
\(515\) 1.09486 0.0482454
\(516\) 0.691686 0.0304498
\(517\) 11.5262 0.506923
\(518\) −2.23600 −0.0982443
\(519\) −14.3336 −0.629174
\(520\) 0 0
\(521\) −12.2815 −0.538062 −0.269031 0.963132i \(-0.586703\pi\)
−0.269031 + 0.963132i \(0.586703\pi\)
\(522\) 1.02246 0.0447518
\(523\) −41.1027 −1.79729 −0.898647 0.438673i \(-0.855449\pi\)
−0.898647 + 0.438673i \(0.855449\pi\)
\(524\) −14.6222 −0.638772
\(525\) −13.6817 −0.597119
\(526\) 10.4934 0.457534
\(527\) 52.8583 2.30254
\(528\) −9.94486 −0.432794
\(529\) 33.5259 1.45765
\(530\) 7.79318 0.338514
\(531\) −8.88207 −0.385449
\(532\) −0.215949 −0.00936257
\(533\) 0 0
\(534\) −3.13569 −0.135695
\(535\) −5.41701 −0.234198
\(536\) 5.44845 0.235337
\(537\) 12.7843 0.551685
\(538\) 6.53983 0.281952
\(539\) −3.32197 −0.143087
\(540\) 7.89805 0.339878
\(541\) 39.2640 1.68809 0.844046 0.536270i \(-0.180167\pi\)
0.844046 + 0.536270i \(0.180167\pi\)
\(542\) −4.45392 −0.191312
\(543\) 20.9807 0.900368
\(544\) 23.2944 0.998739
\(545\) −14.1276 −0.605162
\(546\) 0 0
\(547\) 13.8409 0.591793 0.295897 0.955220i \(-0.404382\pi\)
0.295897 + 0.955220i \(0.404382\pi\)
\(548\) −16.9615 −0.724557
\(549\) −6.67086 −0.284705
\(550\) 18.8874 0.805363
\(551\) 0.290769 0.0123872
\(552\) −11.9579 −0.508961
\(553\) 0.278553 0.0118453
\(554\) 7.94838 0.337694
\(555\) 23.2565 0.987182
\(556\) −7.82017 −0.331649
\(557\) 32.7700 1.38851 0.694255 0.719729i \(-0.255734\pi\)
0.694255 + 0.719729i \(0.255734\pi\)
\(558\) 4.17269 0.176644
\(559\) 0 0
\(560\) 12.9393 0.546787
\(561\) 17.4876 0.738326
\(562\) 3.68782 0.155561
\(563\) −35.6426 −1.50216 −0.751079 0.660212i \(-0.770466\pi\)
−0.751079 + 0.660212i \(0.770466\pi\)
\(564\) 6.34021 0.266971
\(565\) 0.413712 0.0174050
\(566\) 8.49074 0.356892
\(567\) −1.00000 −0.0419961
\(568\) 11.5378 0.484115
\(569\) −37.4955 −1.57189 −0.785946 0.618296i \(-0.787823\pi\)
−0.785946 + 0.618296i \(0.787823\pi\)
\(570\) −0.212268 −0.00889094
\(571\) −20.8001 −0.870458 −0.435229 0.900320i \(-0.643333\pi\)
−0.435229 + 0.900320i \(0.643333\pi\)
\(572\) 0 0
\(573\) −5.41589 −0.226252
\(574\) −4.86455 −0.203042
\(575\) −102.864 −4.28974
\(576\) −4.14845 −0.172852
\(577\) 25.9570 1.08061 0.540303 0.841471i \(-0.318310\pi\)
0.540303 + 0.841471i \(0.318310\pi\)
\(578\) −4.45155 −0.185160
\(579\) 11.2327 0.466814
\(580\) −19.4325 −0.806891
\(581\) −14.5998 −0.605703
\(582\) 2.99427 0.124116
\(583\) −14.4133 −0.596939
\(584\) 22.2615 0.921189
\(585\) 0 0
\(586\) −6.68020 −0.275957
\(587\) 38.3127 1.58133 0.790667 0.612246i \(-0.209734\pi\)
0.790667 + 0.612246i \(0.209734\pi\)
\(588\) −1.82731 −0.0753569
\(589\) 1.18664 0.0488945
\(590\) −15.9536 −0.656801
\(591\) 0.705420 0.0290171
\(592\) −16.1079 −0.662030
\(593\) −20.6171 −0.846642 −0.423321 0.905980i \(-0.639136\pi\)
−0.423321 + 0.905980i \(0.639136\pi\)
\(594\) 1.38049 0.0566421
\(595\) −22.7532 −0.932792
\(596\) 20.1636 0.825932
\(597\) 11.6826 0.478136
\(598\) 0 0
\(599\) 12.5620 0.513268 0.256634 0.966509i \(-0.417386\pi\)
0.256634 + 0.966509i \(0.417386\pi\)
\(600\) 21.7606 0.888374
\(601\) 45.2688 1.84655 0.923277 0.384134i \(-0.125500\pi\)
0.923277 + 0.384134i \(0.125500\pi\)
\(602\) −0.157302 −0.00641116
\(603\) 3.42565 0.139503
\(604\) 13.7887 0.561055
\(605\) −0.153271 −0.00623137
\(606\) −1.62098 −0.0658478
\(607\) 1.11155 0.0451165 0.0225582 0.999746i \(-0.492819\pi\)
0.0225582 + 0.999746i \(0.492819\pi\)
\(608\) 0.522945 0.0212082
\(609\) 2.46042 0.0997012
\(610\) −11.9820 −0.485135
\(611\) 0 0
\(612\) 9.61936 0.388840
\(613\) 16.9221 0.683479 0.341739 0.939795i \(-0.388984\pi\)
0.341739 + 0.939795i \(0.388984\pi\)
\(614\) −2.50920 −0.101263
\(615\) 50.5957 2.04022
\(616\) 5.28355 0.212880
\(617\) 29.2034 1.17569 0.587843 0.808975i \(-0.299977\pi\)
0.587843 + 0.808975i \(0.299977\pi\)
\(618\) 0.105266 0.00423442
\(619\) −10.3246 −0.414983 −0.207491 0.978237i \(-0.566530\pi\)
−0.207491 + 0.978237i \(0.566530\pi\)
\(620\) −79.3046 −3.18495
\(621\) −7.51837 −0.301702
\(622\) 5.08080 0.203721
\(623\) −7.54564 −0.302310
\(624\) 0 0
\(625\) 93.7810 3.75124
\(626\) 2.72459 0.108897
\(627\) 0.392586 0.0156784
\(628\) 39.3643 1.57081
\(629\) 28.3250 1.12939
\(630\) −1.79616 −0.0715608
\(631\) −39.6457 −1.57827 −0.789135 0.614220i \(-0.789471\pi\)
−0.789135 + 0.614220i \(0.789471\pi\)
\(632\) −0.443036 −0.0176230
\(633\) 4.38529 0.174300
\(634\) 2.87896 0.114338
\(635\) −67.0916 −2.66245
\(636\) −7.92831 −0.314378
\(637\) 0 0
\(638\) −3.39658 −0.134472
\(639\) 7.25425 0.286974
\(640\) −45.7034 −1.80658
\(641\) −27.3047 −1.07847 −0.539236 0.842155i \(-0.681287\pi\)
−0.539236 + 0.842155i \(0.681287\pi\)
\(642\) −0.520821 −0.0205552
\(643\) −2.71488 −0.107064 −0.0535322 0.998566i \(-0.517048\pi\)
−0.0535322 + 0.998566i \(0.517048\pi\)
\(644\) −13.7384 −0.541368
\(645\) 1.63609 0.0644208
\(646\) −0.258530 −0.0101717
\(647\) −10.5518 −0.414834 −0.207417 0.978253i \(-0.566506\pi\)
−0.207417 + 0.978253i \(0.566506\pi\)
\(648\) 1.59049 0.0624803
\(649\) 29.5059 1.15821
\(650\) 0 0
\(651\) 10.0410 0.393539
\(652\) 40.9154 1.60237
\(653\) −8.55364 −0.334730 −0.167365 0.985895i \(-0.553526\pi\)
−0.167365 + 0.985895i \(0.553526\pi\)
\(654\) −1.35831 −0.0531141
\(655\) −34.5867 −1.35141
\(656\) −35.0436 −1.36822
\(657\) 13.9967 0.546062
\(658\) −1.44188 −0.0562104
\(659\) −26.2916 −1.02418 −0.512088 0.858933i \(-0.671128\pi\)
−0.512088 + 0.858933i \(0.671128\pi\)
\(660\) −26.2371 −1.02128
\(661\) 3.08987 0.120182 0.0600909 0.998193i \(-0.480861\pi\)
0.0600909 + 0.998193i \(0.480861\pi\)
\(662\) 6.40385 0.248893
\(663\) 0 0
\(664\) 23.2209 0.901145
\(665\) −0.510796 −0.0198078
\(666\) 2.23600 0.0866434
\(667\) 18.4983 0.716259
\(668\) 14.8790 0.575686
\(669\) 14.8375 0.573652
\(670\) 6.15302 0.237712
\(671\) 22.1604 0.855492
\(672\) 4.42503 0.170699
\(673\) −2.93113 −0.112987 −0.0564933 0.998403i \(-0.517992\pi\)
−0.0564933 + 0.998403i \(0.517992\pi\)
\(674\) −9.61941 −0.370526
\(675\) 13.6817 0.526610
\(676\) 0 0
\(677\) 31.4703 1.20950 0.604750 0.796415i \(-0.293273\pi\)
0.604750 + 0.796415i \(0.293273\pi\)
\(678\) 0.0397765 0.00152761
\(679\) 7.20532 0.276515
\(680\) 36.1888 1.38778
\(681\) −0.0625704 −0.00239770
\(682\) −13.8615 −0.530785
\(683\) 1.39640 0.0534318 0.0267159 0.999643i \(-0.491495\pi\)
0.0267159 + 0.999643i \(0.491495\pi\)
\(684\) 0.215949 0.00825701
\(685\) −40.1199 −1.53290
\(686\) 0.415563 0.0158663
\(687\) 0.184720 0.00704750
\(688\) −1.13319 −0.0432023
\(689\) 0 0
\(690\) −13.5042 −0.514097
\(691\) 30.1321 1.14628 0.573140 0.819458i \(-0.305725\pi\)
0.573140 + 0.819458i \(0.305725\pi\)
\(692\) 26.1918 0.995664
\(693\) 3.32197 0.126191
\(694\) −11.1904 −0.424783
\(695\) −18.4975 −0.701651
\(696\) −3.91327 −0.148332
\(697\) 61.6226 2.33412
\(698\) 12.7371 0.482107
\(699\) 0.190546 0.00720711
\(700\) 25.0007 0.944938
\(701\) −30.3056 −1.14463 −0.572313 0.820035i \(-0.693954\pi\)
−0.572313 + 0.820035i \(0.693954\pi\)
\(702\) 0 0
\(703\) 0.635879 0.0239826
\(704\) 13.7810 0.519391
\(705\) 14.9969 0.564815
\(706\) 6.77324 0.254914
\(707\) −3.90068 −0.146700
\(708\) 16.2303 0.609971
\(709\) −44.2264 −1.66096 −0.830479 0.557050i \(-0.811933\pi\)
−0.830479 + 0.557050i \(0.811933\pi\)
\(710\) 13.0298 0.489000
\(711\) −0.278553 −0.0104466
\(712\) 12.0012 0.449766
\(713\) 75.4922 2.82721
\(714\) −2.18762 −0.0818696
\(715\) 0 0
\(716\) −23.3609 −0.873038
\(717\) 17.7380 0.662436
\(718\) 5.67500 0.211789
\(719\) 38.6174 1.44019 0.720093 0.693878i \(-0.244099\pi\)
0.720093 + 0.693878i \(0.244099\pi\)
\(720\) −12.9393 −0.482220
\(721\) 0.253309 0.00943373
\(722\) 7.88990 0.293632
\(723\) −4.72194 −0.175611
\(724\) −38.3382 −1.42483
\(725\) −33.6628 −1.25020
\(726\) −0.0147363 −0.000546917 0
\(727\) 3.77723 0.140090 0.0700448 0.997544i \(-0.477686\pi\)
0.0700448 + 0.997544i \(0.477686\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 25.1403 0.930484
\(731\) 1.99266 0.0737010
\(732\) 12.1897 0.450545
\(733\) −15.0366 −0.555391 −0.277695 0.960669i \(-0.589571\pi\)
−0.277695 + 0.960669i \(0.589571\pi\)
\(734\) 8.71136 0.321542
\(735\) −4.32224 −0.159428
\(736\) 33.2690 1.22631
\(737\) −11.3799 −0.419183
\(738\) 4.86455 0.179066
\(739\) −8.27720 −0.304482 −0.152241 0.988343i \(-0.548649\pi\)
−0.152241 + 0.988343i \(0.548649\pi\)
\(740\) −42.4967 −1.56221
\(741\) 0 0
\(742\) 1.80304 0.0661918
\(743\) −38.8141 −1.42395 −0.711976 0.702204i \(-0.752199\pi\)
−0.711976 + 0.702204i \(0.752199\pi\)
\(744\) −15.9702 −0.585494
\(745\) 47.6941 1.74738
\(746\) −1.84970 −0.0677223
\(747\) 14.5998 0.534180
\(748\) −31.9552 −1.16840
\(749\) −1.25329 −0.0457942
\(750\) 15.5938 0.569405
\(751\) 45.7595 1.66979 0.834894 0.550411i \(-0.185529\pi\)
0.834894 + 0.550411i \(0.185529\pi\)
\(752\) −10.3871 −0.378780
\(753\) −13.2188 −0.481719
\(754\) 0 0
\(755\) 32.6152 1.18699
\(756\) 1.82731 0.0664585
\(757\) −35.1055 −1.27593 −0.637965 0.770065i \(-0.720224\pi\)
−0.637965 + 0.770065i \(0.720224\pi\)
\(758\) 0.672151 0.0244136
\(759\) 24.9758 0.906563
\(760\) 0.812416 0.0294694
\(761\) −4.99677 −0.181133 −0.0905665 0.995890i \(-0.528868\pi\)
−0.0905665 + 0.995890i \(0.528868\pi\)
\(762\) −6.45055 −0.233679
\(763\) −3.26860 −0.118331
\(764\) 9.89650 0.358043
\(765\) 22.7532 0.822645
\(766\) −6.81353 −0.246183
\(767\) 0 0
\(768\) 3.90273 0.140828
\(769\) 10.8083 0.389756 0.194878 0.980827i \(-0.437569\pi\)
0.194878 + 0.980827i \(0.437569\pi\)
\(770\) 5.96679 0.215028
\(771\) −17.4150 −0.627187
\(772\) −20.5255 −0.738731
\(773\) −5.52880 −0.198857 −0.0994285 0.995045i \(-0.531701\pi\)
−0.0994285 + 0.995045i \(0.531701\pi\)
\(774\) 0.157302 0.00565411
\(775\) −137.379 −4.93479
\(776\) −11.4600 −0.411389
\(777\) 5.38066 0.193030
\(778\) −6.30554 −0.226065
\(779\) 1.38339 0.0495651
\(780\) 0 0
\(781\) −24.0984 −0.862307
\(782\) −16.4473 −0.588155
\(783\) −2.46042 −0.0879282
\(784\) 2.99367 0.106917
\(785\) 93.1107 3.32326
\(786\) −3.32535 −0.118611
\(787\) 6.79072 0.242063 0.121031 0.992649i \(-0.461380\pi\)
0.121031 + 0.992649i \(0.461380\pi\)
\(788\) −1.28902 −0.0459194
\(789\) −25.2510 −0.898960
\(790\) −0.500327 −0.0178008
\(791\) 0.0957171 0.00340331
\(792\) −5.28355 −0.187743
\(793\) 0 0
\(794\) 2.72155 0.0965840
\(795\) −18.7533 −0.665110
\(796\) −21.3477 −0.756648
\(797\) −10.3512 −0.366657 −0.183328 0.983052i \(-0.558687\pi\)
−0.183328 + 0.983052i \(0.558687\pi\)
\(798\) −0.0491107 −0.00173850
\(799\) 18.2653 0.646180
\(800\) −60.5421 −2.14049
\(801\) 7.54564 0.266612
\(802\) 12.2403 0.432219
\(803\) −46.4965 −1.64082
\(804\) −6.25971 −0.220763
\(805\) −32.4962 −1.14534
\(806\) 0 0
\(807\) −15.7373 −0.553978
\(808\) 6.20399 0.218255
\(809\) 4.16152 0.146311 0.0731556 0.997321i \(-0.476693\pi\)
0.0731556 + 0.997321i \(0.476693\pi\)
\(810\) 1.79616 0.0631107
\(811\) −28.3669 −0.996096 −0.498048 0.867150i \(-0.665950\pi\)
−0.498048 + 0.867150i \(0.665950\pi\)
\(812\) −4.49594 −0.157777
\(813\) 10.7178 0.375889
\(814\) −7.42793 −0.260349
\(815\) 96.7796 3.39004
\(816\) −15.7593 −0.551687
\(817\) 0.0447339 0.00156504
\(818\) −1.98049 −0.0692463
\(819\) 0 0
\(820\) −92.4539 −3.22863
\(821\) 43.0173 1.50132 0.750658 0.660691i \(-0.229737\pi\)
0.750658 + 0.660691i \(0.229737\pi\)
\(822\) −3.85735 −0.134540
\(823\) 22.0229 0.767669 0.383834 0.923402i \(-0.374603\pi\)
0.383834 + 0.923402i \(0.374603\pi\)
\(824\) −0.402885 −0.0140352
\(825\) −45.4502 −1.58237
\(826\) −3.69106 −0.128428
\(827\) 30.0713 1.04568 0.522841 0.852430i \(-0.324872\pi\)
0.522841 + 0.852430i \(0.324872\pi\)
\(828\) 13.7384 0.477441
\(829\) −50.5308 −1.75501 −0.877504 0.479570i \(-0.840793\pi\)
−0.877504 + 0.479570i \(0.840793\pi\)
\(830\) 26.2237 0.910238
\(831\) −19.1268 −0.663500
\(832\) 0 0
\(833\) −5.26423 −0.182395
\(834\) −1.77845 −0.0615827
\(835\) 35.1942 1.21795
\(836\) −0.717375 −0.0248109
\(837\) −10.0410 −0.347069
\(838\) −8.84723 −0.305623
\(839\) −46.9147 −1.61967 −0.809837 0.586655i \(-0.800445\pi\)
−0.809837 + 0.586655i \(0.800445\pi\)
\(840\) 6.87447 0.237192
\(841\) −22.9463 −0.791253
\(842\) −15.5107 −0.534535
\(843\) −8.87426 −0.305646
\(844\) −8.01328 −0.275828
\(845\) 0 0
\(846\) 1.44188 0.0495729
\(847\) −0.0354611 −0.00121846
\(848\) 12.9889 0.446040
\(849\) −20.4319 −0.701220
\(850\) 29.9304 1.02660
\(851\) 40.4538 1.38674
\(852\) −13.2557 −0.454134
\(853\) −28.9771 −0.992157 −0.496078 0.868278i \(-0.665227\pi\)
−0.496078 + 0.868278i \(0.665227\pi\)
\(854\) −2.77217 −0.0948615
\(855\) 0.510796 0.0174689
\(856\) 1.99334 0.0681310
\(857\) 5.56795 0.190198 0.0950988 0.995468i \(-0.469683\pi\)
0.0950988 + 0.995468i \(0.469683\pi\)
\(858\) 0 0
\(859\) 19.0380 0.649567 0.324784 0.945788i \(-0.394709\pi\)
0.324784 + 0.945788i \(0.394709\pi\)
\(860\) −2.98963 −0.101946
\(861\) 11.7059 0.398936
\(862\) 0.222163 0.00756691
\(863\) −34.0312 −1.15843 −0.579217 0.815173i \(-0.696642\pi\)
−0.579217 + 0.815173i \(0.696642\pi\)
\(864\) −4.42503 −0.150543
\(865\) 61.9530 2.10647
\(866\) −5.45734 −0.185448
\(867\) 10.7121 0.363802
\(868\) −18.3481 −0.622774
\(869\) 0.925344 0.0313902
\(870\) −4.41931 −0.149829
\(871\) 0 0
\(872\) 5.19866 0.176049
\(873\) −7.20532 −0.243863
\(874\) −0.369233 −0.0124895
\(875\) 37.5245 1.26856
\(876\) −25.5762 −0.864140
\(877\) 42.5065 1.43534 0.717671 0.696383i \(-0.245208\pi\)
0.717671 + 0.696383i \(0.245208\pi\)
\(878\) 15.4678 0.522012
\(879\) 16.0750 0.542198
\(880\) 42.9840 1.44899
\(881\) −40.9431 −1.37941 −0.689704 0.724091i \(-0.742259\pi\)
−0.689704 + 0.724091i \(0.742259\pi\)
\(882\) −0.415563 −0.0139927
\(883\) 17.7038 0.595779 0.297890 0.954600i \(-0.403717\pi\)
0.297890 + 0.954600i \(0.403717\pi\)
\(884\) 0 0
\(885\) 38.3904 1.29048
\(886\) 1.66709 0.0560070
\(887\) 14.0736 0.472546 0.236273 0.971687i \(-0.424074\pi\)
0.236273 + 0.971687i \(0.424074\pi\)
\(888\) −8.55787 −0.287183
\(889\) −15.5224 −0.520605
\(890\) 13.5532 0.454304
\(891\) −3.32197 −0.111290
\(892\) −27.1127 −0.907801
\(893\) 0.410045 0.0137216
\(894\) 4.58557 0.153364
\(895\) −55.2569 −1.84703
\(896\) −10.5740 −0.353253
\(897\) 0 0
\(898\) −2.88440 −0.0962538
\(899\) 24.7052 0.823963
\(900\) −25.0007 −0.833357
\(901\) −22.8404 −0.760924
\(902\) −16.1599 −0.538064
\(903\) 0.378528 0.0125966
\(904\) −0.152237 −0.00506332
\(905\) −90.6835 −3.01442
\(906\) 3.13581 0.104180
\(907\) 46.3181 1.53797 0.768984 0.639269i \(-0.220763\pi\)
0.768984 + 0.639269i \(0.220763\pi\)
\(908\) 0.114335 0.00379435
\(909\) 3.90068 0.129377
\(910\) 0 0
\(911\) −45.4712 −1.50653 −0.753263 0.657719i \(-0.771521\pi\)
−0.753263 + 0.657719i \(0.771521\pi\)
\(912\) −0.353788 −0.0117151
\(913\) −48.5002 −1.60512
\(914\) −14.9636 −0.494951
\(915\) 28.8330 0.953191
\(916\) −0.337540 −0.0111526
\(917\) −8.00203 −0.264250
\(918\) 2.18762 0.0722022
\(919\) 8.52183 0.281109 0.140555 0.990073i \(-0.455111\pi\)
0.140555 + 0.990073i \(0.455111\pi\)
\(920\) 51.6848 1.70400
\(921\) 6.03807 0.198961
\(922\) −5.23436 −0.172384
\(923\) 0 0
\(924\) −6.07025 −0.199697
\(925\) −73.6167 −2.42050
\(926\) −8.72184 −0.286617
\(927\) −0.253309 −0.00831977
\(928\) 10.8874 0.357398
\(929\) 56.0590 1.83924 0.919618 0.392814i \(-0.128498\pi\)
0.919618 + 0.392814i \(0.128498\pi\)
\(930\) −18.0353 −0.591402
\(931\) −0.118179 −0.00387315
\(932\) −0.348186 −0.0114052
\(933\) −12.2263 −0.400271
\(934\) −5.33418 −0.174540
\(935\) −75.5855 −2.47191
\(936\) 0 0
\(937\) −50.0468 −1.63496 −0.817479 0.575958i \(-0.804629\pi\)
−0.817479 + 0.575958i \(0.804629\pi\)
\(938\) 1.42357 0.0464813
\(939\) −6.55638 −0.213959
\(940\) −27.4039 −0.893816
\(941\) −30.1842 −0.983978 −0.491989 0.870601i \(-0.663730\pi\)
−0.491989 + 0.870601i \(0.663730\pi\)
\(942\) 8.95217 0.291677
\(943\) 88.0094 2.86598
\(944\) −26.5899 −0.865429
\(945\) 4.32224 0.140602
\(946\) −0.522553 −0.0169897
\(947\) 26.1774 0.850653 0.425326 0.905040i \(-0.360159\pi\)
0.425326 + 0.905040i \(0.360159\pi\)
\(948\) 0.509002 0.0165316
\(949\) 0 0
\(950\) 0.671920 0.0218000
\(951\) −6.92785 −0.224651
\(952\) 8.37269 0.271361
\(953\) −17.2735 −0.559542 −0.279771 0.960067i \(-0.590259\pi\)
−0.279771 + 0.960067i \(0.590259\pi\)
\(954\) −1.80304 −0.0583757
\(955\) 23.4088 0.757490
\(956\) −32.4127 −1.04830
\(957\) 8.17343 0.264209
\(958\) −4.64834 −0.150181
\(959\) −9.28221 −0.299738
\(960\) 17.9306 0.578707
\(961\) 69.8224 2.25234
\(962\) 0 0
\(963\) 1.25329 0.0403867
\(964\) 8.62844 0.277903
\(965\) −48.5503 −1.56289
\(966\) −3.12436 −0.100525
\(967\) −52.2470 −1.68015 −0.840075 0.542470i \(-0.817489\pi\)
−0.840075 + 0.542470i \(0.817489\pi\)
\(968\) 0.0564005 0.00181278
\(969\) 0.622120 0.0199854
\(970\) −12.9419 −0.415540
\(971\) −18.0460 −0.579125 −0.289562 0.957159i \(-0.593510\pi\)
−0.289562 + 0.957159i \(0.593510\pi\)
\(972\) −1.82731 −0.0586109
\(973\) −4.27962 −0.137198
\(974\) 12.3766 0.396570
\(975\) 0 0
\(976\) −19.9703 −0.639235
\(977\) 8.28532 0.265071 0.132535 0.991178i \(-0.457688\pi\)
0.132535 + 0.991178i \(0.457688\pi\)
\(978\) 9.30492 0.297539
\(979\) −25.0664 −0.801124
\(980\) 7.89805 0.252294
\(981\) 3.26860 0.104358
\(982\) 4.45479 0.142158
\(983\) −29.0487 −0.926509 −0.463255 0.886225i \(-0.653318\pi\)
−0.463255 + 0.886225i \(0.653318\pi\)
\(984\) −18.6181 −0.593524
\(985\) −3.04899 −0.0971489
\(986\) −5.38246 −0.171412
\(987\) 3.46970 0.110442
\(988\) 0 0
\(989\) 2.84591 0.0904947
\(990\) −5.96679 −0.189637
\(991\) 8.19764 0.260407 0.130203 0.991487i \(-0.458437\pi\)
0.130203 + 0.991487i \(0.458437\pi\)
\(992\) 44.4319 1.41072
\(993\) −15.4100 −0.489023
\(994\) 3.01460 0.0956173
\(995\) −50.4949 −1.60079
\(996\) −26.6784 −0.845337
\(997\) 33.4493 1.05935 0.529675 0.848201i \(-0.322314\pi\)
0.529675 + 0.848201i \(0.322314\pi\)
\(998\) −4.53091 −0.143423
\(999\) −5.38066 −0.170236
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.1.7 yes 15
13.12 even 2 3549.2.a.bg.1.9 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.9 15 13.12 even 2
3549.2.a.bh.1.7 yes 15 1.1 even 1 trivial