Properties

Label 8007.2.a.f.1.28
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.498945 q^{2} -1.00000 q^{3} -1.75105 q^{4} +0.622534 q^{5} -0.498945 q^{6} +0.110017 q^{7} -1.87157 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.498945 q^{2} -1.00000 q^{3} -1.75105 q^{4} +0.622534 q^{5} -0.498945 q^{6} +0.110017 q^{7} -1.87157 q^{8} +1.00000 q^{9} +0.310610 q^{10} +0.189879 q^{11} +1.75105 q^{12} +6.61917 q^{13} +0.0548922 q^{14} -0.622534 q^{15} +2.56830 q^{16} -1.00000 q^{17} +0.498945 q^{18} -0.0616562 q^{19} -1.09009 q^{20} -0.110017 q^{21} +0.0947393 q^{22} -5.46866 q^{23} +1.87157 q^{24} -4.61245 q^{25} +3.30260 q^{26} -1.00000 q^{27} -0.192645 q^{28} -5.28863 q^{29} -0.310610 q^{30} -4.08323 q^{31} +5.02458 q^{32} -0.189879 q^{33} -0.498945 q^{34} +0.0684891 q^{35} -1.75105 q^{36} +7.61954 q^{37} -0.0307630 q^{38} -6.61917 q^{39} -1.16512 q^{40} -8.53971 q^{41} -0.0548922 q^{42} -1.22669 q^{43} -0.332489 q^{44} +0.622534 q^{45} -2.72856 q^{46} +11.0065 q^{47} -2.56830 q^{48} -6.98790 q^{49} -2.30136 q^{50} +1.00000 q^{51} -11.5905 q^{52} -0.0568805 q^{53} -0.498945 q^{54} +0.118206 q^{55} -0.205904 q^{56} +0.0616562 q^{57} -2.63873 q^{58} +3.88617 q^{59} +1.09009 q^{60} +3.47610 q^{61} -2.03731 q^{62} +0.110017 q^{63} -2.62961 q^{64} +4.12066 q^{65} -0.0947393 q^{66} -10.7555 q^{67} +1.75105 q^{68} +5.46866 q^{69} +0.0341723 q^{70} +6.87507 q^{71} -1.87157 q^{72} -6.33728 q^{73} +3.80173 q^{74} +4.61245 q^{75} +0.107963 q^{76} +0.0208899 q^{77} -3.30260 q^{78} -2.39038 q^{79} +1.59885 q^{80} +1.00000 q^{81} -4.26084 q^{82} +17.9437 q^{83} +0.192645 q^{84} -0.622534 q^{85} -0.612050 q^{86} +5.28863 q^{87} -0.355372 q^{88} +12.7186 q^{89} +0.310610 q^{90} +0.728219 q^{91} +9.57592 q^{92} +4.08323 q^{93} +5.49162 q^{94} -0.0383831 q^{95} -5.02458 q^{96} +9.70831 q^{97} -3.48657 q^{98} +0.189879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.498945 0.352807 0.176404 0.984318i \(-0.443554\pi\)
0.176404 + 0.984318i \(0.443554\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.75105 −0.875527
\(5\) 0.622534 0.278406 0.139203 0.990264i \(-0.455546\pi\)
0.139203 + 0.990264i \(0.455546\pi\)
\(6\) −0.498945 −0.203693
\(7\) 0.110017 0.0415824 0.0207912 0.999784i \(-0.493381\pi\)
0.0207912 + 0.999784i \(0.493381\pi\)
\(8\) −1.87157 −0.661699
\(9\) 1.00000 0.333333
\(10\) 0.310610 0.0982235
\(11\) 0.189879 0.0572508 0.0286254 0.999590i \(-0.490887\pi\)
0.0286254 + 0.999590i \(0.490887\pi\)
\(12\) 1.75105 0.505486
\(13\) 6.61917 1.83583 0.917913 0.396781i \(-0.129873\pi\)
0.917913 + 0.396781i \(0.129873\pi\)
\(14\) 0.0548922 0.0146706
\(15\) −0.622534 −0.160738
\(16\) 2.56830 0.642075
\(17\) −1.00000 −0.242536
\(18\) 0.498945 0.117602
\(19\) −0.0616562 −0.0141449 −0.00707245 0.999975i \(-0.502251\pi\)
−0.00707245 + 0.999975i \(0.502251\pi\)
\(20\) −1.09009 −0.243752
\(21\) −0.110017 −0.0240076
\(22\) 0.0947393 0.0201985
\(23\) −5.46866 −1.14029 −0.570147 0.821543i \(-0.693114\pi\)
−0.570147 + 0.821543i \(0.693114\pi\)
\(24\) 1.87157 0.382032
\(25\) −4.61245 −0.922490
\(26\) 3.30260 0.647693
\(27\) −1.00000 −0.192450
\(28\) −0.192645 −0.0364065
\(29\) −5.28863 −0.982073 −0.491037 0.871139i \(-0.663382\pi\)
−0.491037 + 0.871139i \(0.663382\pi\)
\(30\) −0.310610 −0.0567094
\(31\) −4.08323 −0.733370 −0.366685 0.930345i \(-0.619507\pi\)
−0.366685 + 0.930345i \(0.619507\pi\)
\(32\) 5.02458 0.888228
\(33\) −0.189879 −0.0330537
\(34\) −0.498945 −0.0855683
\(35\) 0.0684891 0.0115768
\(36\) −1.75105 −0.291842
\(37\) 7.61954 1.25264 0.626322 0.779565i \(-0.284560\pi\)
0.626322 + 0.779565i \(0.284560\pi\)
\(38\) −0.0307630 −0.00499042
\(39\) −6.61917 −1.05991
\(40\) −1.16512 −0.184221
\(41\) −8.53971 −1.33368 −0.666840 0.745201i \(-0.732353\pi\)
−0.666840 + 0.745201i \(0.732353\pi\)
\(42\) −0.0548922 −0.00847006
\(43\) −1.22669 −0.187068 −0.0935342 0.995616i \(-0.529816\pi\)
−0.0935342 + 0.995616i \(0.529816\pi\)
\(44\) −0.332489 −0.0501246
\(45\) 0.622534 0.0928019
\(46\) −2.72856 −0.402304
\(47\) 11.0065 1.60546 0.802730 0.596343i \(-0.203380\pi\)
0.802730 + 0.596343i \(0.203380\pi\)
\(48\) −2.56830 −0.370702
\(49\) −6.98790 −0.998271
\(50\) −2.30136 −0.325461
\(51\) 1.00000 0.140028
\(52\) −11.5905 −1.60732
\(53\) −0.0568805 −0.00781314 −0.00390657 0.999992i \(-0.501244\pi\)
−0.00390657 + 0.999992i \(0.501244\pi\)
\(54\) −0.498945 −0.0678978
\(55\) 0.118206 0.0159389
\(56\) −0.205904 −0.0275150
\(57\) 0.0616562 0.00816656
\(58\) −2.63873 −0.346483
\(59\) 3.88617 0.505936 0.252968 0.967475i \(-0.418593\pi\)
0.252968 + 0.967475i \(0.418593\pi\)
\(60\) 1.09009 0.140730
\(61\) 3.47610 0.445069 0.222535 0.974925i \(-0.428567\pi\)
0.222535 + 0.974925i \(0.428567\pi\)
\(62\) −2.03731 −0.258738
\(63\) 0.110017 0.0138608
\(64\) −2.62961 −0.328702
\(65\) 4.12066 0.511105
\(66\) −0.0947393 −0.0116616
\(67\) −10.7555 −1.31399 −0.656994 0.753896i \(-0.728172\pi\)
−0.656994 + 0.753896i \(0.728172\pi\)
\(68\) 1.75105 0.212347
\(69\) 5.46866 0.658349
\(70\) 0.0341723 0.00408437
\(71\) 6.87507 0.815921 0.407960 0.913000i \(-0.366240\pi\)
0.407960 + 0.913000i \(0.366240\pi\)
\(72\) −1.87157 −0.220566
\(73\) −6.33728 −0.741723 −0.370861 0.928688i \(-0.620937\pi\)
−0.370861 + 0.928688i \(0.620937\pi\)
\(74\) 3.80173 0.441942
\(75\) 4.61245 0.532600
\(76\) 0.107963 0.0123842
\(77\) 0.0208899 0.00238062
\(78\) −3.30260 −0.373946
\(79\) −2.39038 −0.268939 −0.134469 0.990918i \(-0.542933\pi\)
−0.134469 + 0.990918i \(0.542933\pi\)
\(80\) 1.59885 0.178757
\(81\) 1.00000 0.111111
\(82\) −4.26084 −0.470532
\(83\) 17.9437 1.96958 0.984790 0.173746i \(-0.0555872\pi\)
0.984790 + 0.173746i \(0.0555872\pi\)
\(84\) 0.192645 0.0210193
\(85\) −0.622534 −0.0675233
\(86\) −0.612050 −0.0659991
\(87\) 5.28863 0.567000
\(88\) −0.355372 −0.0378828
\(89\) 12.7186 1.34817 0.674084 0.738655i \(-0.264539\pi\)
0.674084 + 0.738655i \(0.264539\pi\)
\(90\) 0.310610 0.0327412
\(91\) 0.728219 0.0763381
\(92\) 9.57592 0.998359
\(93\) 4.08323 0.423411
\(94\) 5.49162 0.566418
\(95\) −0.0383831 −0.00393802
\(96\) −5.02458 −0.512819
\(97\) 9.70831 0.985730 0.492865 0.870106i \(-0.335950\pi\)
0.492865 + 0.870106i \(0.335950\pi\)
\(98\) −3.48657 −0.352197
\(99\) 0.189879 0.0190836
\(100\) 8.07665 0.807665
\(101\) −1.38802 −0.138114 −0.0690568 0.997613i \(-0.521999\pi\)
−0.0690568 + 0.997613i \(0.521999\pi\)
\(102\) 0.498945 0.0494029
\(103\) −1.57120 −0.154815 −0.0774073 0.997000i \(-0.524664\pi\)
−0.0774073 + 0.997000i \(0.524664\pi\)
\(104\) −12.3882 −1.21477
\(105\) −0.0684891 −0.00668386
\(106\) −0.0283802 −0.00275653
\(107\) 7.18961 0.695046 0.347523 0.937672i \(-0.387023\pi\)
0.347523 + 0.937672i \(0.387023\pi\)
\(108\) 1.75105 0.168495
\(109\) −11.7603 −1.12643 −0.563216 0.826310i \(-0.690436\pi\)
−0.563216 + 0.826310i \(0.690436\pi\)
\(110\) 0.0589784 0.00562337
\(111\) −7.61954 −0.723214
\(112\) 0.282556 0.0266990
\(113\) 5.36524 0.504719 0.252360 0.967633i \(-0.418793\pi\)
0.252360 + 0.967633i \(0.418793\pi\)
\(114\) 0.0307630 0.00288122
\(115\) −3.40443 −0.317465
\(116\) 9.26067 0.859832
\(117\) 6.61917 0.611942
\(118\) 1.93898 0.178498
\(119\) −0.110017 −0.0100852
\(120\) 1.16512 0.106360
\(121\) −10.9639 −0.996722
\(122\) 1.73438 0.157024
\(123\) 8.53971 0.770000
\(124\) 7.14996 0.642085
\(125\) −5.98408 −0.535232
\(126\) 0.0548922 0.00489019
\(127\) 11.9742 1.06254 0.531269 0.847203i \(-0.321715\pi\)
0.531269 + 0.847203i \(0.321715\pi\)
\(128\) −11.3612 −1.00420
\(129\) 1.22669 0.108004
\(130\) 2.05598 0.180321
\(131\) −5.31945 −0.464763 −0.232381 0.972625i \(-0.574652\pi\)
−0.232381 + 0.972625i \(0.574652\pi\)
\(132\) 0.332489 0.0289395
\(133\) −0.00678321 −0.000588179 0
\(134\) −5.36638 −0.463584
\(135\) −0.622534 −0.0535792
\(136\) 1.87157 0.160486
\(137\) −4.30047 −0.367414 −0.183707 0.982981i \(-0.558810\pi\)
−0.183707 + 0.982981i \(0.558810\pi\)
\(138\) 2.72856 0.232270
\(139\) −21.3093 −1.80743 −0.903716 0.428133i \(-0.859172\pi\)
−0.903716 + 0.428133i \(0.859172\pi\)
\(140\) −0.119928 −0.0101358
\(141\) −11.0065 −0.926913
\(142\) 3.43028 0.287863
\(143\) 1.25684 0.105102
\(144\) 2.56830 0.214025
\(145\) −3.29235 −0.273415
\(146\) −3.16195 −0.261685
\(147\) 6.98790 0.576352
\(148\) −13.3422 −1.09672
\(149\) −14.5703 −1.19365 −0.596823 0.802373i \(-0.703570\pi\)
−0.596823 + 0.802373i \(0.703570\pi\)
\(150\) 2.30136 0.187905
\(151\) 7.31852 0.595573 0.297786 0.954633i \(-0.403752\pi\)
0.297786 + 0.954633i \(0.403752\pi\)
\(152\) 0.115394 0.00935967
\(153\) −1.00000 −0.0808452
\(154\) 0.0104229 0.000839901 0
\(155\) −2.54195 −0.204174
\(156\) 11.5905 0.927984
\(157\) −1.00000 −0.0798087
\(158\) −1.19267 −0.0948836
\(159\) 0.0568805 0.00451092
\(160\) 3.12797 0.247288
\(161\) −0.601644 −0.0474162
\(162\) 0.498945 0.0392008
\(163\) 10.7686 0.843463 0.421731 0.906721i \(-0.361423\pi\)
0.421731 + 0.906721i \(0.361423\pi\)
\(164\) 14.9535 1.16767
\(165\) −0.118206 −0.00920235
\(166\) 8.95293 0.694882
\(167\) −5.12239 −0.396382 −0.198191 0.980163i \(-0.563507\pi\)
−0.198191 + 0.980163i \(0.563507\pi\)
\(168\) 0.205904 0.0158858
\(169\) 30.8134 2.37026
\(170\) −0.310610 −0.0238227
\(171\) −0.0616562 −0.00471496
\(172\) 2.14800 0.163783
\(173\) −17.7180 −1.34707 −0.673536 0.739154i \(-0.735225\pi\)
−0.673536 + 0.739154i \(0.735225\pi\)
\(174\) 2.63873 0.200042
\(175\) −0.507447 −0.0383594
\(176\) 0.487667 0.0367593
\(177\) −3.88617 −0.292102
\(178\) 6.34587 0.475643
\(179\) −7.02296 −0.524921 −0.262460 0.964943i \(-0.584534\pi\)
−0.262460 + 0.964943i \(0.584534\pi\)
\(180\) −1.09009 −0.0812506
\(181\) −11.5729 −0.860207 −0.430103 0.902780i \(-0.641523\pi\)
−0.430103 + 0.902780i \(0.641523\pi\)
\(182\) 0.363341 0.0269326
\(183\) −3.47610 −0.256961
\(184\) 10.2350 0.754532
\(185\) 4.74342 0.348743
\(186\) 2.03731 0.149382
\(187\) −0.189879 −0.0138854
\(188\) −19.2729 −1.40562
\(189\) −0.110017 −0.00800254
\(190\) −0.0191510 −0.00138936
\(191\) 4.83937 0.350164 0.175082 0.984554i \(-0.443981\pi\)
0.175082 + 0.984554i \(0.443981\pi\)
\(192\) 2.62961 0.189776
\(193\) −10.6120 −0.763865 −0.381933 0.924190i \(-0.624741\pi\)
−0.381933 + 0.924190i \(0.624741\pi\)
\(194\) 4.84391 0.347772
\(195\) −4.12066 −0.295086
\(196\) 12.2362 0.874013
\(197\) 1.33752 0.0952941 0.0476470 0.998864i \(-0.484828\pi\)
0.0476470 + 0.998864i \(0.484828\pi\)
\(198\) 0.0947393 0.00673283
\(199\) −13.6565 −0.968080 −0.484040 0.875046i \(-0.660831\pi\)
−0.484040 + 0.875046i \(0.660831\pi\)
\(200\) 8.63252 0.610411
\(201\) 10.7555 0.758631
\(202\) −0.692548 −0.0487275
\(203\) −0.581837 −0.0408370
\(204\) −1.75105 −0.122598
\(205\) −5.31626 −0.371304
\(206\) −0.783940 −0.0546197
\(207\) −5.46866 −0.380098
\(208\) 17.0000 1.17874
\(209\) −0.0117072 −0.000809806 0
\(210\) −0.0341723 −0.00235811
\(211\) −7.25466 −0.499432 −0.249716 0.968319i \(-0.580337\pi\)
−0.249716 + 0.968319i \(0.580337\pi\)
\(212\) 0.0996009 0.00684062
\(213\) −6.87507 −0.471072
\(214\) 3.58722 0.245217
\(215\) −0.763656 −0.0520809
\(216\) 1.87157 0.127344
\(217\) −0.449223 −0.0304953
\(218\) −5.86773 −0.397413
\(219\) 6.33728 0.428234
\(220\) −0.206986 −0.0139550
\(221\) −6.61917 −0.445253
\(222\) −3.80173 −0.255155
\(223\) −25.7018 −1.72112 −0.860562 0.509347i \(-0.829887\pi\)
−0.860562 + 0.509347i \(0.829887\pi\)
\(224\) 0.552787 0.0369346
\(225\) −4.61245 −0.307497
\(226\) 2.67696 0.178069
\(227\) −0.0456610 −0.00303063 −0.00151531 0.999999i \(-0.500482\pi\)
−0.00151531 + 0.999999i \(0.500482\pi\)
\(228\) −0.107963 −0.00715004
\(229\) −5.83691 −0.385714 −0.192857 0.981227i \(-0.561775\pi\)
−0.192857 + 0.981227i \(0.561775\pi\)
\(230\) −1.69862 −0.112004
\(231\) −0.0208899 −0.00137445
\(232\) 9.89803 0.649837
\(233\) −7.68536 −0.503485 −0.251742 0.967794i \(-0.581004\pi\)
−0.251742 + 0.967794i \(0.581004\pi\)
\(234\) 3.30260 0.215898
\(235\) 6.85191 0.446969
\(236\) −6.80489 −0.442961
\(237\) 2.39038 0.155272
\(238\) −0.0548922 −0.00355813
\(239\) 6.81710 0.440962 0.220481 0.975391i \(-0.429237\pi\)
0.220481 + 0.975391i \(0.429237\pi\)
\(240\) −1.59885 −0.103206
\(241\) −23.3281 −1.50270 −0.751348 0.659907i \(-0.770596\pi\)
−0.751348 + 0.659907i \(0.770596\pi\)
\(242\) −5.47040 −0.351651
\(243\) −1.00000 −0.0641500
\(244\) −6.08684 −0.389670
\(245\) −4.35020 −0.277924
\(246\) 4.26084 0.271662
\(247\) −0.408112 −0.0259676
\(248\) 7.64204 0.485270
\(249\) −17.9437 −1.13714
\(250\) −2.98572 −0.188834
\(251\) 2.30713 0.145625 0.0728124 0.997346i \(-0.476803\pi\)
0.0728124 + 0.997346i \(0.476803\pi\)
\(252\) −0.192645 −0.0121355
\(253\) −1.03839 −0.0652827
\(254\) 5.97446 0.374871
\(255\) 0.622534 0.0389846
\(256\) −0.409375 −0.0255859
\(257\) −11.9923 −0.748059 −0.374030 0.927417i \(-0.622024\pi\)
−0.374030 + 0.927417i \(0.622024\pi\)
\(258\) 0.612050 0.0381046
\(259\) 0.838276 0.0520879
\(260\) −7.21549 −0.447486
\(261\) −5.28863 −0.327358
\(262\) −2.65411 −0.163972
\(263\) 20.1830 1.24454 0.622270 0.782803i \(-0.286211\pi\)
0.622270 + 0.782803i \(0.286211\pi\)
\(264\) 0.355372 0.0218716
\(265\) −0.0354101 −0.00217522
\(266\) −0.00338444 −0.000207514 0
\(267\) −12.7186 −0.778365
\(268\) 18.8334 1.15043
\(269\) −29.9514 −1.82617 −0.913085 0.407769i \(-0.866307\pi\)
−0.913085 + 0.407769i \(0.866307\pi\)
\(270\) −0.310610 −0.0189031
\(271\) −6.64163 −0.403450 −0.201725 0.979442i \(-0.564655\pi\)
−0.201725 + 0.979442i \(0.564655\pi\)
\(272\) −2.56830 −0.155726
\(273\) −0.728219 −0.0440738
\(274\) −2.14570 −0.129626
\(275\) −0.875809 −0.0528133
\(276\) −9.57592 −0.576403
\(277\) −0.752550 −0.0452163 −0.0226082 0.999744i \(-0.507197\pi\)
−0.0226082 + 0.999744i \(0.507197\pi\)
\(278\) −10.6322 −0.637675
\(279\) −4.08323 −0.244457
\(280\) −0.128182 −0.00766035
\(281\) −17.1481 −1.02297 −0.511484 0.859293i \(-0.670904\pi\)
−0.511484 + 0.859293i \(0.670904\pi\)
\(282\) −5.49162 −0.327021
\(283\) −19.3556 −1.15057 −0.575285 0.817953i \(-0.695109\pi\)
−0.575285 + 0.817953i \(0.695109\pi\)
\(284\) −12.0386 −0.714361
\(285\) 0.0383831 0.00227362
\(286\) 0.627095 0.0370809
\(287\) −0.939511 −0.0554576
\(288\) 5.02458 0.296076
\(289\) 1.00000 0.0588235
\(290\) −1.64270 −0.0964627
\(291\) −9.70831 −0.569111
\(292\) 11.0969 0.649398
\(293\) 31.7072 1.85235 0.926177 0.377089i \(-0.123075\pi\)
0.926177 + 0.377089i \(0.123075\pi\)
\(294\) 3.48657 0.203341
\(295\) 2.41927 0.140855
\(296\) −14.2605 −0.828874
\(297\) −0.189879 −0.0110179
\(298\) −7.26977 −0.421126
\(299\) −36.1980 −2.09338
\(300\) −8.07665 −0.466306
\(301\) −0.134956 −0.00777875
\(302\) 3.65154 0.210122
\(303\) 1.38802 0.0797399
\(304\) −0.158351 −0.00908208
\(305\) 2.16399 0.123910
\(306\) −0.498945 −0.0285228
\(307\) 15.3128 0.873948 0.436974 0.899474i \(-0.356050\pi\)
0.436974 + 0.899474i \(0.356050\pi\)
\(308\) −0.0365793 −0.00208430
\(309\) 1.57120 0.0893822
\(310\) −1.26829 −0.0720342
\(311\) 20.6581 1.17141 0.585705 0.810524i \(-0.300818\pi\)
0.585705 + 0.810524i \(0.300818\pi\)
\(312\) 12.3882 0.701345
\(313\) −17.8717 −1.01017 −0.505085 0.863070i \(-0.668539\pi\)
−0.505085 + 0.863070i \(0.668539\pi\)
\(314\) −0.498945 −0.0281571
\(315\) 0.0684891 0.00385893
\(316\) 4.18569 0.235463
\(317\) −16.8959 −0.948969 −0.474485 0.880264i \(-0.657366\pi\)
−0.474485 + 0.880264i \(0.657366\pi\)
\(318\) 0.0283802 0.00159148
\(319\) −1.00420 −0.0562245
\(320\) −1.63702 −0.0915125
\(321\) −7.18961 −0.401285
\(322\) −0.300187 −0.0167288
\(323\) 0.0616562 0.00343064
\(324\) −1.75105 −0.0972808
\(325\) −30.5306 −1.69353
\(326\) 5.37294 0.297580
\(327\) 11.7603 0.650345
\(328\) 15.9827 0.882495
\(329\) 1.21090 0.0667589
\(330\) −0.0589784 −0.00324666
\(331\) −30.6643 −1.68546 −0.842731 0.538335i \(-0.819053\pi\)
−0.842731 + 0.538335i \(0.819053\pi\)
\(332\) −31.4205 −1.72442
\(333\) 7.61954 0.417548
\(334\) −2.55579 −0.139846
\(335\) −6.69564 −0.365822
\(336\) −0.282556 −0.0154147
\(337\) 5.54873 0.302259 0.151129 0.988514i \(-0.451709\pi\)
0.151129 + 0.988514i \(0.451709\pi\)
\(338\) 15.3742 0.836244
\(339\) −5.36524 −0.291400
\(340\) 1.09009 0.0591185
\(341\) −0.775321 −0.0419860
\(342\) −0.0307630 −0.00166347
\(343\) −1.53890 −0.0830929
\(344\) 2.29583 0.123783
\(345\) 3.40443 0.183288
\(346\) −8.84028 −0.475257
\(347\) −17.2327 −0.925100 −0.462550 0.886593i \(-0.653065\pi\)
−0.462550 + 0.886593i \(0.653065\pi\)
\(348\) −9.26067 −0.496424
\(349\) −5.90035 −0.315838 −0.157919 0.987452i \(-0.550479\pi\)
−0.157919 + 0.987452i \(0.550479\pi\)
\(350\) −0.253188 −0.0135335
\(351\) −6.61917 −0.353305
\(352\) 0.954063 0.0508517
\(353\) −22.4944 −1.19725 −0.598627 0.801028i \(-0.704287\pi\)
−0.598627 + 0.801028i \(0.704287\pi\)
\(354\) −1.93898 −0.103056
\(355\) 4.27997 0.227157
\(356\) −22.2709 −1.18036
\(357\) 0.110017 0.00582270
\(358\) −3.50407 −0.185196
\(359\) 5.47971 0.289208 0.144604 0.989490i \(-0.453809\pi\)
0.144604 + 0.989490i \(0.453809\pi\)
\(360\) −1.16512 −0.0614070
\(361\) −18.9962 −0.999800
\(362\) −5.77424 −0.303487
\(363\) 10.9639 0.575458
\(364\) −1.27515 −0.0668360
\(365\) −3.94517 −0.206500
\(366\) −1.73438 −0.0906576
\(367\) −19.8785 −1.03765 −0.518824 0.854881i \(-0.673630\pi\)
−0.518824 + 0.854881i \(0.673630\pi\)
\(368\) −14.0452 −0.732154
\(369\) −8.53971 −0.444560
\(370\) 2.36670 0.123039
\(371\) −0.00625781 −0.000324889 0
\(372\) −7.14996 −0.370708
\(373\) 25.6785 1.32958 0.664791 0.747030i \(-0.268521\pi\)
0.664791 + 0.747030i \(0.268521\pi\)
\(374\) −0.0947393 −0.00489885
\(375\) 5.98408 0.309017
\(376\) −20.5994 −1.06233
\(377\) −35.0063 −1.80292
\(378\) −0.0548922 −0.00282335
\(379\) 34.8480 1.79002 0.895012 0.446043i \(-0.147167\pi\)
0.895012 + 0.446043i \(0.147167\pi\)
\(380\) 0.0672108 0.00344784
\(381\) −11.9742 −0.613457
\(382\) 2.41458 0.123540
\(383\) 27.5142 1.40591 0.702955 0.711235i \(-0.251864\pi\)
0.702955 + 0.711235i \(0.251864\pi\)
\(384\) 11.3612 0.579773
\(385\) 0.0130047 0.000662779 0
\(386\) −5.29478 −0.269497
\(387\) −1.22669 −0.0623561
\(388\) −16.9998 −0.863033
\(389\) −8.10655 −0.411019 −0.205509 0.978655i \(-0.565885\pi\)
−0.205509 + 0.978655i \(0.565885\pi\)
\(390\) −2.05598 −0.104109
\(391\) 5.46866 0.276562
\(392\) 13.0783 0.660555
\(393\) 5.31945 0.268331
\(394\) 0.667346 0.0336204
\(395\) −1.48809 −0.0748741
\(396\) −0.332489 −0.0167082
\(397\) 16.7794 0.842133 0.421066 0.907030i \(-0.361656\pi\)
0.421066 + 0.907030i \(0.361656\pi\)
\(398\) −6.81382 −0.341546
\(399\) 0.00678321 0.000339585 0
\(400\) −11.8462 −0.592308
\(401\) 32.2773 1.61185 0.805927 0.592015i \(-0.201668\pi\)
0.805927 + 0.592015i \(0.201668\pi\)
\(402\) 5.36638 0.267650
\(403\) −27.0276 −1.34634
\(404\) 2.43051 0.120922
\(405\) 0.622534 0.0309340
\(406\) −0.290305 −0.0144076
\(407\) 1.44679 0.0717148
\(408\) −1.87157 −0.0926564
\(409\) −7.42351 −0.367069 −0.183534 0.983013i \(-0.558754\pi\)
−0.183534 + 0.983013i \(0.558754\pi\)
\(410\) −2.65252 −0.130999
\(411\) 4.30047 0.212127
\(412\) 2.75125 0.135544
\(413\) 0.427543 0.0210380
\(414\) −2.72856 −0.134101
\(415\) 11.1706 0.548343
\(416\) 33.2585 1.63063
\(417\) 21.3093 1.04352
\(418\) −0.00584126 −0.000285705 0
\(419\) −18.9566 −0.926090 −0.463045 0.886335i \(-0.653243\pi\)
−0.463045 + 0.886335i \(0.653243\pi\)
\(420\) 0.119928 0.00585190
\(421\) −23.4129 −1.14107 −0.570536 0.821272i \(-0.693265\pi\)
−0.570536 + 0.821272i \(0.693265\pi\)
\(422\) −3.61967 −0.176203
\(423\) 11.0065 0.535153
\(424\) 0.106456 0.00516995
\(425\) 4.61245 0.223737
\(426\) −3.43028 −0.166198
\(427\) 0.382429 0.0185071
\(428\) −12.5894 −0.608531
\(429\) −1.25684 −0.0606809
\(430\) −0.381022 −0.0183745
\(431\) −25.4864 −1.22764 −0.613818 0.789448i \(-0.710367\pi\)
−0.613818 + 0.789448i \(0.710367\pi\)
\(432\) −2.56830 −0.123567
\(433\) −24.5265 −1.17867 −0.589335 0.807889i \(-0.700610\pi\)
−0.589335 + 0.807889i \(0.700610\pi\)
\(434\) −0.224138 −0.0107589
\(435\) 3.29235 0.157856
\(436\) 20.5929 0.986221
\(437\) 0.337177 0.0161293
\(438\) 3.16195 0.151084
\(439\) −9.14738 −0.436581 −0.218290 0.975884i \(-0.570048\pi\)
−0.218290 + 0.975884i \(0.570048\pi\)
\(440\) −0.221231 −0.0105468
\(441\) −6.98790 −0.332757
\(442\) −3.30260 −0.157089
\(443\) 31.4276 1.49317 0.746586 0.665289i \(-0.231692\pi\)
0.746586 + 0.665289i \(0.231692\pi\)
\(444\) 13.3422 0.633194
\(445\) 7.91776 0.375338
\(446\) −12.8238 −0.607224
\(447\) 14.5703 0.689151
\(448\) −0.289301 −0.0136682
\(449\) −39.3579 −1.85742 −0.928708 0.370812i \(-0.879079\pi\)
−0.928708 + 0.370812i \(0.879079\pi\)
\(450\) −2.30136 −0.108487
\(451\) −1.62152 −0.0763542
\(452\) −9.39483 −0.441896
\(453\) −7.31852 −0.343854
\(454\) −0.0227823 −0.00106923
\(455\) 0.453341 0.0212530
\(456\) −0.115394 −0.00540381
\(457\) 6.47916 0.303082 0.151541 0.988451i \(-0.451576\pi\)
0.151541 + 0.988451i \(0.451576\pi\)
\(458\) −2.91230 −0.136083
\(459\) 1.00000 0.0466760
\(460\) 5.96134 0.277949
\(461\) −31.1170 −1.44926 −0.724632 0.689136i \(-0.757990\pi\)
−0.724632 + 0.689136i \(0.757990\pi\)
\(462\) −0.0104229 −0.000484917 0
\(463\) −30.5942 −1.42183 −0.710916 0.703277i \(-0.751720\pi\)
−0.710916 + 0.703277i \(0.751720\pi\)
\(464\) −13.5828 −0.630565
\(465\) 2.54195 0.117880
\(466\) −3.83457 −0.177633
\(467\) 26.2418 1.21432 0.607162 0.794578i \(-0.292308\pi\)
0.607162 + 0.794578i \(0.292308\pi\)
\(468\) −11.5905 −0.535772
\(469\) −1.18328 −0.0546388
\(470\) 3.41872 0.157694
\(471\) 1.00000 0.0460776
\(472\) −7.27323 −0.334777
\(473\) −0.232923 −0.0107098
\(474\) 1.19267 0.0547811
\(475\) 0.284386 0.0130485
\(476\) 0.192645 0.00882988
\(477\) −0.0568805 −0.00260438
\(478\) 3.40136 0.155574
\(479\) 33.8380 1.54610 0.773050 0.634346i \(-0.218730\pi\)
0.773050 + 0.634346i \(0.218730\pi\)
\(480\) −3.12797 −0.142772
\(481\) 50.4350 2.29964
\(482\) −11.6394 −0.530162
\(483\) 0.601644 0.0273757
\(484\) 19.1985 0.872657
\(485\) 6.04376 0.274433
\(486\) −0.498945 −0.0226326
\(487\) 11.2538 0.509959 0.254980 0.966946i \(-0.417931\pi\)
0.254980 + 0.966946i \(0.417931\pi\)
\(488\) −6.50576 −0.294502
\(489\) −10.7686 −0.486973
\(490\) −2.17051 −0.0980537
\(491\) −28.9139 −1.30487 −0.652433 0.757846i \(-0.726252\pi\)
−0.652433 + 0.757846i \(0.726252\pi\)
\(492\) −14.9535 −0.674156
\(493\) 5.28863 0.238188
\(494\) −0.203625 −0.00916154
\(495\) 0.118206 0.00531298
\(496\) −10.4870 −0.470878
\(497\) 0.756372 0.0339279
\(498\) −8.95293 −0.401190
\(499\) 37.0687 1.65942 0.829712 0.558192i \(-0.188505\pi\)
0.829712 + 0.558192i \(0.188505\pi\)
\(500\) 10.4784 0.468610
\(501\) 5.12239 0.228851
\(502\) 1.15113 0.0513774
\(503\) 9.27716 0.413648 0.206824 0.978378i \(-0.433687\pi\)
0.206824 + 0.978378i \(0.433687\pi\)
\(504\) −0.205904 −0.00917168
\(505\) −0.864093 −0.0384516
\(506\) −0.518097 −0.0230322
\(507\) −30.8134 −1.36847
\(508\) −20.9675 −0.930281
\(509\) −3.67145 −0.162734 −0.0813672 0.996684i \(-0.525929\pi\)
−0.0813672 + 0.996684i \(0.525929\pi\)
\(510\) 0.310610 0.0137540
\(511\) −0.697207 −0.0308426
\(512\) 22.5181 0.995169
\(513\) 0.0616562 0.00272219
\(514\) −5.98349 −0.263921
\(515\) −0.978124 −0.0431013
\(516\) −2.14800 −0.0945604
\(517\) 2.08990 0.0919138
\(518\) 0.418253 0.0183770
\(519\) 17.7180 0.777732
\(520\) −7.71209 −0.338198
\(521\) 31.1280 1.36374 0.681871 0.731473i \(-0.261167\pi\)
0.681871 + 0.731473i \(0.261167\pi\)
\(522\) −2.63873 −0.115494
\(523\) 4.66119 0.203820 0.101910 0.994794i \(-0.467505\pi\)
0.101910 + 0.994794i \(0.467505\pi\)
\(524\) 9.31465 0.406913
\(525\) 0.507447 0.0221468
\(526\) 10.0702 0.439082
\(527\) 4.08323 0.177868
\(528\) −0.487667 −0.0212230
\(529\) 6.90624 0.300271
\(530\) −0.0176677 −0.000767434 0
\(531\) 3.88617 0.168645
\(532\) 0.0118778 0.000514966 0
\(533\) −56.5258 −2.44840
\(534\) −6.34587 −0.274613
\(535\) 4.47578 0.193505
\(536\) 20.1296 0.869465
\(537\) 7.02296 0.303063
\(538\) −14.9441 −0.644286
\(539\) −1.32686 −0.0571518
\(540\) 1.09009 0.0469101
\(541\) −7.36605 −0.316691 −0.158346 0.987384i \(-0.550616\pi\)
−0.158346 + 0.987384i \(0.550616\pi\)
\(542\) −3.31380 −0.142340
\(543\) 11.5729 0.496641
\(544\) −5.02458 −0.215427
\(545\) −7.32118 −0.313605
\(546\) −0.363341 −0.0155495
\(547\) 21.8338 0.933544 0.466772 0.884378i \(-0.345417\pi\)
0.466772 + 0.884378i \(0.345417\pi\)
\(548\) 7.53036 0.321681
\(549\) 3.47610 0.148356
\(550\) −0.436980 −0.0186329
\(551\) 0.326076 0.0138913
\(552\) −10.2350 −0.435629
\(553\) −0.262982 −0.0111831
\(554\) −0.375481 −0.0159526
\(555\) −4.74342 −0.201347
\(556\) 37.3138 1.58246
\(557\) 4.08349 0.173023 0.0865116 0.996251i \(-0.472428\pi\)
0.0865116 + 0.996251i \(0.472428\pi\)
\(558\) −2.03731 −0.0862460
\(559\) −8.11966 −0.343425
\(560\) 0.175901 0.00743316
\(561\) 0.189879 0.00801671
\(562\) −8.55594 −0.360910
\(563\) −30.8749 −1.30122 −0.650610 0.759412i \(-0.725487\pi\)
−0.650610 + 0.759412i \(0.725487\pi\)
\(564\) 19.2729 0.811537
\(565\) 3.34005 0.140517
\(566\) −9.65736 −0.405929
\(567\) 0.110017 0.00462027
\(568\) −12.8672 −0.539894
\(569\) 24.1268 1.01145 0.505724 0.862695i \(-0.331225\pi\)
0.505724 + 0.862695i \(0.331225\pi\)
\(570\) 0.0191510 0.000802148 0
\(571\) 8.49513 0.355510 0.177755 0.984075i \(-0.443117\pi\)
0.177755 + 0.984075i \(0.443117\pi\)
\(572\) −2.20080 −0.0920201
\(573\) −4.83937 −0.202167
\(574\) −0.468764 −0.0195658
\(575\) 25.2239 1.05191
\(576\) −2.62961 −0.109567
\(577\) 36.8184 1.53277 0.766385 0.642381i \(-0.222053\pi\)
0.766385 + 0.642381i \(0.222053\pi\)
\(578\) 0.498945 0.0207534
\(579\) 10.6120 0.441018
\(580\) 5.76509 0.239382
\(581\) 1.97411 0.0818999
\(582\) −4.84391 −0.200787
\(583\) −0.0108004 −0.000447308 0
\(584\) 11.8607 0.490797
\(585\) 4.12066 0.170368
\(586\) 15.8201 0.653524
\(587\) −15.5905 −0.643488 −0.321744 0.946827i \(-0.604269\pi\)
−0.321744 + 0.946827i \(0.604269\pi\)
\(588\) −12.2362 −0.504612
\(589\) 0.251756 0.0103734
\(590\) 1.20708 0.0496948
\(591\) −1.33752 −0.0550181
\(592\) 19.5692 0.804291
\(593\) −35.5948 −1.46170 −0.730852 0.682536i \(-0.760877\pi\)
−0.730852 + 0.682536i \(0.760877\pi\)
\(594\) −0.0947393 −0.00388720
\(595\) −0.0684891 −0.00280778
\(596\) 25.5134 1.04507
\(597\) 13.6565 0.558922
\(598\) −18.0608 −0.738560
\(599\) −18.9779 −0.775417 −0.387708 0.921782i \(-0.626733\pi\)
−0.387708 + 0.921782i \(0.626733\pi\)
\(600\) −8.63252 −0.352421
\(601\) 35.2668 1.43856 0.719282 0.694718i \(-0.244471\pi\)
0.719282 + 0.694718i \(0.244471\pi\)
\(602\) −0.0673357 −0.00274440
\(603\) −10.7555 −0.437996
\(604\) −12.8151 −0.521440
\(605\) −6.82543 −0.277493
\(606\) 0.692548 0.0281328
\(607\) −9.22942 −0.374611 −0.187305 0.982302i \(-0.559975\pi\)
−0.187305 + 0.982302i \(0.559975\pi\)
\(608\) −0.309796 −0.0125639
\(609\) 0.581837 0.0235772
\(610\) 1.07971 0.0437163
\(611\) 72.8537 2.94735
\(612\) 1.75105 0.0707822
\(613\) −9.69926 −0.391750 −0.195875 0.980629i \(-0.562755\pi\)
−0.195875 + 0.980629i \(0.562755\pi\)
\(614\) 7.64025 0.308335
\(615\) 5.31626 0.214372
\(616\) −0.0390969 −0.00157526
\(617\) −1.65175 −0.0664970 −0.0332485 0.999447i \(-0.510585\pi\)
−0.0332485 + 0.999447i \(0.510585\pi\)
\(618\) 0.783940 0.0315347
\(619\) 13.8044 0.554845 0.277422 0.960748i \(-0.410520\pi\)
0.277422 + 0.960748i \(0.410520\pi\)
\(620\) 4.45109 0.178760
\(621\) 5.46866 0.219450
\(622\) 10.3072 0.413282
\(623\) 1.39926 0.0560600
\(624\) −17.0000 −0.680545
\(625\) 19.3370 0.773478
\(626\) −8.91700 −0.356395
\(627\) 0.0117072 0.000467542 0
\(628\) 1.75105 0.0698747
\(629\) −7.61954 −0.303811
\(630\) 0.0341723 0.00136146
\(631\) −47.9318 −1.90814 −0.954068 0.299591i \(-0.903150\pi\)
−0.954068 + 0.299591i \(0.903150\pi\)
\(632\) 4.47376 0.177957
\(633\) 7.25466 0.288347
\(634\) −8.43013 −0.334803
\(635\) 7.45435 0.295817
\(636\) −0.0996009 −0.00394943
\(637\) −46.2540 −1.83265
\(638\) −0.501041 −0.0198364
\(639\) 6.87507 0.271974
\(640\) −7.07273 −0.279574
\(641\) 15.4994 0.612189 0.306095 0.952001i \(-0.400978\pi\)
0.306095 + 0.952001i \(0.400978\pi\)
\(642\) −3.58722 −0.141576
\(643\) −12.6980 −0.500762 −0.250381 0.968147i \(-0.580556\pi\)
−0.250381 + 0.968147i \(0.580556\pi\)
\(644\) 1.05351 0.0415141
\(645\) 0.763656 0.0300689
\(646\) 0.0307630 0.00121035
\(647\) 20.5803 0.809097 0.404548 0.914517i \(-0.367429\pi\)
0.404548 + 0.914517i \(0.367429\pi\)
\(648\) −1.87157 −0.0735222
\(649\) 0.737903 0.0289652
\(650\) −15.2331 −0.597490
\(651\) 0.449223 0.0176065
\(652\) −18.8564 −0.738475
\(653\) −3.97714 −0.155638 −0.0778188 0.996968i \(-0.524796\pi\)
−0.0778188 + 0.996968i \(0.524796\pi\)
\(654\) 5.86773 0.229447
\(655\) −3.31154 −0.129393
\(656\) −21.9325 −0.856322
\(657\) −6.33728 −0.247241
\(658\) 0.604170 0.0235530
\(659\) 10.1460 0.395231 0.197615 0.980280i \(-0.436680\pi\)
0.197615 + 0.980280i \(0.436680\pi\)
\(660\) 0.206986 0.00805691
\(661\) −49.2701 −1.91639 −0.958193 0.286121i \(-0.907634\pi\)
−0.958193 + 0.286121i \(0.907634\pi\)
\(662\) −15.2998 −0.594643
\(663\) 6.61917 0.257067
\(664\) −33.5829 −1.30327
\(665\) −0.00422278 −0.000163752 0
\(666\) 3.80173 0.147314
\(667\) 28.9217 1.11985
\(668\) 8.96958 0.347043
\(669\) 25.7018 0.993691
\(670\) −3.34075 −0.129065
\(671\) 0.660040 0.0254806
\(672\) −0.552787 −0.0213242
\(673\) 41.3149 1.59257 0.796286 0.604921i \(-0.206795\pi\)
0.796286 + 0.604921i \(0.206795\pi\)
\(674\) 2.76851 0.106639
\(675\) 4.61245 0.177533
\(676\) −53.9559 −2.07523
\(677\) −35.3660 −1.35923 −0.679614 0.733570i \(-0.737853\pi\)
−0.679614 + 0.733570i \(0.737853\pi\)
\(678\) −2.67696 −0.102808
\(679\) 1.06808 0.0409890
\(680\) 1.16512 0.0446801
\(681\) 0.0456610 0.00174973
\(682\) −0.386842 −0.0148130
\(683\) −28.1193 −1.07595 −0.537977 0.842960i \(-0.680811\pi\)
−0.537977 + 0.842960i \(0.680811\pi\)
\(684\) 0.107963 0.00412808
\(685\) −2.67719 −0.102290
\(686\) −0.767827 −0.0293158
\(687\) 5.83691 0.222692
\(688\) −3.15051 −0.120112
\(689\) −0.376502 −0.0143436
\(690\) 1.69862 0.0646654
\(691\) −23.5978 −0.897704 −0.448852 0.893606i \(-0.648167\pi\)
−0.448852 + 0.893606i \(0.648167\pi\)
\(692\) 31.0251 1.17940
\(693\) 0.0208899 0.000793541 0
\(694\) −8.59816 −0.326382
\(695\) −13.2658 −0.503199
\(696\) −9.89803 −0.375184
\(697\) 8.53971 0.323465
\(698\) −2.94395 −0.111430
\(699\) 7.68536 0.290687
\(700\) 0.888566 0.0335847
\(701\) −37.4447 −1.41427 −0.707133 0.707081i \(-0.750012\pi\)
−0.707133 + 0.707081i \(0.750012\pi\)
\(702\) −3.30260 −0.124649
\(703\) −0.469791 −0.0177185
\(704\) −0.499309 −0.0188184
\(705\) −6.85191 −0.258058
\(706\) −11.2234 −0.422400
\(707\) −0.152706 −0.00574310
\(708\) 6.80489 0.255743
\(709\) −43.9110 −1.64911 −0.824555 0.565781i \(-0.808575\pi\)
−0.824555 + 0.565781i \(0.808575\pi\)
\(710\) 2.13547 0.0801426
\(711\) −2.39038 −0.0896463
\(712\) −23.8037 −0.892082
\(713\) 22.3298 0.836257
\(714\) 0.0548922 0.00205429
\(715\) 0.782428 0.0292611
\(716\) 12.2976 0.459582
\(717\) −6.81710 −0.254589
\(718\) 2.73407 0.102035
\(719\) −15.7143 −0.586046 −0.293023 0.956105i \(-0.594661\pi\)
−0.293023 + 0.956105i \(0.594661\pi\)
\(720\) 1.59885 0.0595858
\(721\) −0.172858 −0.00643756
\(722\) −9.47805 −0.352737
\(723\) 23.3281 0.867581
\(724\) 20.2648 0.753134
\(725\) 24.3935 0.905953
\(726\) 5.47040 0.203026
\(727\) 18.7455 0.695233 0.347617 0.937637i \(-0.386991\pi\)
0.347617 + 0.937637i \(0.386991\pi\)
\(728\) −1.36291 −0.0505128
\(729\) 1.00000 0.0370370
\(730\) −1.96842 −0.0728546
\(731\) 1.22669 0.0453708
\(732\) 6.08684 0.224976
\(733\) −40.9054 −1.51087 −0.755437 0.655221i \(-0.772576\pi\)
−0.755437 + 0.655221i \(0.772576\pi\)
\(734\) −9.91825 −0.366089
\(735\) 4.35020 0.160460
\(736\) −27.4777 −1.01284
\(737\) −2.04224 −0.0752268
\(738\) −4.26084 −0.156844
\(739\) 47.1152 1.73316 0.866580 0.499038i \(-0.166313\pi\)
0.866580 + 0.499038i \(0.166313\pi\)
\(740\) −8.30599 −0.305334
\(741\) 0.408112 0.0149924
\(742\) −0.00312230 −0.000114623 0
\(743\) 22.3958 0.821620 0.410810 0.911721i \(-0.365246\pi\)
0.410810 + 0.911721i \(0.365246\pi\)
\(744\) −7.64204 −0.280171
\(745\) −9.07051 −0.332318
\(746\) 12.8121 0.469086
\(747\) 17.9437 0.656527
\(748\) 0.332489 0.0121570
\(749\) 0.790977 0.0289017
\(750\) 2.98572 0.109023
\(751\) −2.90469 −0.105994 −0.0529969 0.998595i \(-0.516877\pi\)
−0.0529969 + 0.998595i \(0.516877\pi\)
\(752\) 28.2679 1.03083
\(753\) −2.30713 −0.0840765
\(754\) −17.4662 −0.636082
\(755\) 4.55603 0.165811
\(756\) 0.192645 0.00700644
\(757\) −27.5912 −1.00282 −0.501410 0.865210i \(-0.667185\pi\)
−0.501410 + 0.865210i \(0.667185\pi\)
\(758\) 17.3872 0.631533
\(759\) 1.03839 0.0376910
\(760\) 0.0718365 0.00260579
\(761\) 29.3935 1.06551 0.532757 0.846268i \(-0.321156\pi\)
0.532757 + 0.846268i \(0.321156\pi\)
\(762\) −5.97446 −0.216432
\(763\) −1.29383 −0.0468397
\(764\) −8.47399 −0.306578
\(765\) −0.622534 −0.0225078
\(766\) 13.7281 0.496015
\(767\) 25.7232 0.928810
\(768\) 0.409375 0.0147720
\(769\) 10.5904 0.381899 0.190950 0.981600i \(-0.438843\pi\)
0.190950 + 0.981600i \(0.438843\pi\)
\(770\) 0.00648861 0.000233833 0
\(771\) 11.9923 0.431892
\(772\) 18.5821 0.668785
\(773\) 41.9637 1.50933 0.754665 0.656110i \(-0.227799\pi\)
0.754665 + 0.656110i \(0.227799\pi\)
\(774\) −0.612050 −0.0219997
\(775\) 18.8337 0.676526
\(776\) −18.1698 −0.652257
\(777\) −0.838276 −0.0300730
\(778\) −4.04472 −0.145010
\(779\) 0.526526 0.0188647
\(780\) 7.21549 0.258356
\(781\) 1.30543 0.0467121
\(782\) 2.72856 0.0975731
\(783\) 5.28863 0.189000
\(784\) −17.9470 −0.640965
\(785\) −0.622534 −0.0222192
\(786\) 2.65411 0.0946691
\(787\) −12.7855 −0.455755 −0.227877 0.973690i \(-0.573179\pi\)
−0.227877 + 0.973690i \(0.573179\pi\)
\(788\) −2.34206 −0.0834325
\(789\) −20.1830 −0.718535
\(790\) −0.742477 −0.0264161
\(791\) 0.590266 0.0209874
\(792\) −0.355372 −0.0126276
\(793\) 23.0089 0.817070
\(794\) 8.37198 0.297110
\(795\) 0.0354101 0.00125587
\(796\) 23.9132 0.847581
\(797\) 30.3721 1.07583 0.537917 0.842997i \(-0.319211\pi\)
0.537917 + 0.842997i \(0.319211\pi\)
\(798\) 0.00338444 0.000119808 0
\(799\) −11.0065 −0.389381
\(800\) −23.1756 −0.819382
\(801\) 12.7186 0.449389
\(802\) 16.1046 0.568673
\(803\) −1.20332 −0.0424642
\(804\) −18.8334 −0.664202
\(805\) −0.374544 −0.0132009
\(806\) −13.4853 −0.474998
\(807\) 29.9514 1.05434
\(808\) 2.59778 0.0913897
\(809\) −19.7563 −0.694594 −0.347297 0.937755i \(-0.612900\pi\)
−0.347297 + 0.937755i \(0.612900\pi\)
\(810\) 0.310610 0.0109137
\(811\) 9.69439 0.340416 0.170208 0.985408i \(-0.445556\pi\)
0.170208 + 0.985408i \(0.445556\pi\)
\(812\) 1.01883 0.0357539
\(813\) 6.64163 0.232932
\(814\) 0.721869 0.0253015
\(815\) 6.70383 0.234825
\(816\) 2.56830 0.0899085
\(817\) 0.0756330 0.00264606
\(818\) −3.70392 −0.129505
\(819\) 0.728219 0.0254460
\(820\) 9.30907 0.325087
\(821\) 11.9684 0.417700 0.208850 0.977948i \(-0.433028\pi\)
0.208850 + 0.977948i \(0.433028\pi\)
\(822\) 2.14570 0.0748398
\(823\) 27.7894 0.968676 0.484338 0.874881i \(-0.339061\pi\)
0.484338 + 0.874881i \(0.339061\pi\)
\(824\) 2.94060 0.102441
\(825\) 0.875809 0.0304918
\(826\) 0.213320 0.00742237
\(827\) −23.8914 −0.830786 −0.415393 0.909642i \(-0.636356\pi\)
−0.415393 + 0.909642i \(0.636356\pi\)
\(828\) 9.57592 0.332786
\(829\) −51.7532 −1.79746 −0.898732 0.438498i \(-0.855510\pi\)
−0.898732 + 0.438498i \(0.855510\pi\)
\(830\) 5.57351 0.193459
\(831\) 0.752550 0.0261057
\(832\) −17.4058 −0.603439
\(833\) 6.98790 0.242116
\(834\) 10.6322 0.368162
\(835\) −3.18886 −0.110355
\(836\) 0.0205000 0.000709007 0
\(837\) 4.08323 0.141137
\(838\) −9.45829 −0.326731
\(839\) −3.45559 −0.119300 −0.0596500 0.998219i \(-0.518998\pi\)
−0.0596500 + 0.998219i \(0.518998\pi\)
\(840\) 0.128182 0.00442270
\(841\) −1.03042 −0.0355319
\(842\) −11.6817 −0.402579
\(843\) 17.1481 0.590611
\(844\) 12.7033 0.437266
\(845\) 19.1824 0.659894
\(846\) 5.49162 0.188806
\(847\) −1.20622 −0.0414461
\(848\) −0.146086 −0.00501662
\(849\) 19.3556 0.664282
\(850\) 2.30136 0.0789359
\(851\) −41.6686 −1.42838
\(852\) 12.0386 0.412436
\(853\) −21.5188 −0.736789 −0.368394 0.929670i \(-0.620092\pi\)
−0.368394 + 0.929670i \(0.620092\pi\)
\(854\) 0.190811 0.00652942
\(855\) −0.0383831 −0.00131267
\(856\) −13.4558 −0.459911
\(857\) −20.6835 −0.706535 −0.353267 0.935522i \(-0.614929\pi\)
−0.353267 + 0.935522i \(0.614929\pi\)
\(858\) −0.627095 −0.0214087
\(859\) 19.2852 0.658002 0.329001 0.944329i \(-0.393288\pi\)
0.329001 + 0.944329i \(0.393288\pi\)
\(860\) 1.33720 0.0455983
\(861\) 0.939511 0.0320184
\(862\) −12.7163 −0.433118
\(863\) −42.0720 −1.43215 −0.716075 0.698024i \(-0.754063\pi\)
−0.716075 + 0.698024i \(0.754063\pi\)
\(864\) −5.02458 −0.170940
\(865\) −11.0300 −0.375033
\(866\) −12.2374 −0.415843
\(867\) −1.00000 −0.0339618
\(868\) 0.786614 0.0266994
\(869\) −0.453884 −0.0153970
\(870\) 1.64270 0.0556928
\(871\) −71.1921 −2.41225
\(872\) 22.0102 0.745359
\(873\) 9.70831 0.328577
\(874\) 0.168232 0.00569055
\(875\) −0.658349 −0.0222562
\(876\) −11.0969 −0.374930
\(877\) 19.3400 0.653066 0.326533 0.945186i \(-0.394120\pi\)
0.326533 + 0.945186i \(0.394120\pi\)
\(878\) −4.56404 −0.154029
\(879\) −31.7072 −1.06946
\(880\) 0.303589 0.0102340
\(881\) −20.6559 −0.695915 −0.347957 0.937510i \(-0.613125\pi\)
−0.347957 + 0.937510i \(0.613125\pi\)
\(882\) −3.48657 −0.117399
\(883\) −57.3331 −1.92941 −0.964705 0.263331i \(-0.915179\pi\)
−0.964705 + 0.263331i \(0.915179\pi\)
\(884\) 11.5905 0.389831
\(885\) −2.41927 −0.0813229
\(886\) 15.6806 0.526802
\(887\) −1.67229 −0.0561500 −0.0280750 0.999606i \(-0.508938\pi\)
−0.0280750 + 0.999606i \(0.508938\pi\)
\(888\) 14.2605 0.478550
\(889\) 1.31736 0.0441829
\(890\) 3.95052 0.132422
\(891\) 0.189879 0.00636120
\(892\) 45.0053 1.50689
\(893\) −0.678617 −0.0227091
\(894\) 7.26977 0.243137
\(895\) −4.37203 −0.146141
\(896\) −1.24992 −0.0417569
\(897\) 36.1980 1.20861
\(898\) −19.6374 −0.655310
\(899\) 21.5947 0.720223
\(900\) 8.07665 0.269222
\(901\) 0.0568805 0.00189496
\(902\) −0.809046 −0.0269383
\(903\) 0.134956 0.00449107
\(904\) −10.0414 −0.333973
\(905\) −7.20452 −0.239487
\(906\) −3.65154 −0.121314
\(907\) −59.1439 −1.96384 −0.981921 0.189292i \(-0.939381\pi\)
−0.981921 + 0.189292i \(0.939381\pi\)
\(908\) 0.0799549 0.00265340
\(909\) −1.38802 −0.0460379
\(910\) 0.226192 0.00749819
\(911\) 23.3755 0.774465 0.387232 0.921982i \(-0.373431\pi\)
0.387232 + 0.921982i \(0.373431\pi\)
\(912\) 0.158351 0.00524354
\(913\) 3.40714 0.112760
\(914\) 3.23274 0.106930
\(915\) −2.16399 −0.0715394
\(916\) 10.2207 0.337703
\(917\) −0.585229 −0.0193260
\(918\) 0.498945 0.0164676
\(919\) −51.9293 −1.71299 −0.856494 0.516157i \(-0.827362\pi\)
−0.856494 + 0.516157i \(0.827362\pi\)
\(920\) 6.37162 0.210066
\(921\) −15.3128 −0.504574
\(922\) −15.5257 −0.511311
\(923\) 45.5072 1.49789
\(924\) 0.0365793 0.00120337
\(925\) −35.1447 −1.15555
\(926\) −15.2648 −0.501633
\(927\) −1.57120 −0.0516049
\(928\) −26.5731 −0.872305
\(929\) 1.07154 0.0351560 0.0175780 0.999845i \(-0.494404\pi\)
0.0175780 + 0.999845i \(0.494404\pi\)
\(930\) 1.26829 0.0415889
\(931\) 0.430847 0.0141204
\(932\) 13.4575 0.440815
\(933\) −20.6581 −0.676314
\(934\) 13.0932 0.428422
\(935\) −0.118206 −0.00386576
\(936\) −12.3882 −0.404922
\(937\) −2.80111 −0.0915084 −0.0457542 0.998953i \(-0.514569\pi\)
−0.0457542 + 0.998953i \(0.514569\pi\)
\(938\) −0.590391 −0.0192769
\(939\) 17.8717 0.583222
\(940\) −11.9981 −0.391334
\(941\) 0.510951 0.0166565 0.00832827 0.999965i \(-0.497349\pi\)
0.00832827 + 0.999965i \(0.497349\pi\)
\(942\) 0.498945 0.0162565
\(943\) 46.7008 1.52079
\(944\) 9.98084 0.324849
\(945\) −0.0684891 −0.00222795
\(946\) −0.116216 −0.00377850
\(947\) 14.4806 0.470557 0.235278 0.971928i \(-0.424400\pi\)
0.235278 + 0.971928i \(0.424400\pi\)
\(948\) −4.18569 −0.135945
\(949\) −41.9475 −1.36167
\(950\) 0.141893 0.00460361
\(951\) 16.8959 0.547888
\(952\) 0.205904 0.00667338
\(953\) 37.3143 1.20873 0.604365 0.796708i \(-0.293427\pi\)
0.604365 + 0.796708i \(0.293427\pi\)
\(954\) −0.0283802 −0.000918844 0
\(955\) 3.01267 0.0974877
\(956\) −11.9371 −0.386074
\(957\) 1.00420 0.0324612
\(958\) 16.8833 0.545475
\(959\) −0.473124 −0.0152780
\(960\) 1.63702 0.0528347
\(961\) −14.3272 −0.462169
\(962\) 25.1643 0.811328
\(963\) 7.18961 0.231682
\(964\) 40.8488 1.31565
\(965\) −6.60630 −0.212664
\(966\) 0.300187 0.00965836
\(967\) −8.80310 −0.283089 −0.141544 0.989932i \(-0.545207\pi\)
−0.141544 + 0.989932i \(0.545207\pi\)
\(968\) 20.5198 0.659531
\(969\) −0.0616562 −0.00198068
\(970\) 3.01550 0.0968219
\(971\) 8.92922 0.286552 0.143276 0.989683i \(-0.454236\pi\)
0.143276 + 0.989683i \(0.454236\pi\)
\(972\) 1.75105 0.0561651
\(973\) −2.34438 −0.0751573
\(974\) 5.61503 0.179917
\(975\) 30.5306 0.977761
\(976\) 8.92767 0.285768
\(977\) −24.3957 −0.780488 −0.390244 0.920711i \(-0.627609\pi\)
−0.390244 + 0.920711i \(0.627609\pi\)
\(978\) −5.37294 −0.171808
\(979\) 2.41500 0.0771836
\(980\) 7.61744 0.243330
\(981\) −11.7603 −0.375477
\(982\) −14.4264 −0.460366
\(983\) 52.1478 1.66326 0.831628 0.555333i \(-0.187409\pi\)
0.831628 + 0.555333i \(0.187409\pi\)
\(984\) −15.9827 −0.509509
\(985\) 0.832649 0.0265304
\(986\) 2.63873 0.0840344
\(987\) −1.21090 −0.0385433
\(988\) 0.714627 0.0227353
\(989\) 6.70835 0.213313
\(990\) 0.0589784 0.00187446
\(991\) −21.5669 −0.685095 −0.342547 0.939501i \(-0.611290\pi\)
−0.342547 + 0.939501i \(0.611290\pi\)
\(992\) −20.5165 −0.651399
\(993\) 30.6643 0.973102
\(994\) 0.377388 0.0119700
\(995\) −8.50161 −0.269519
\(996\) 31.4205 0.995595
\(997\) −46.4744 −1.47186 −0.735930 0.677058i \(-0.763255\pi\)
−0.735930 + 0.677058i \(0.763255\pi\)
\(998\) 18.4952 0.585457
\(999\) −7.61954 −0.241071
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 8007.2.a.f.1.28 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.28 48 1.1 even 1 trivial