Properties

Label 4730.2.a.be.1.7
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 12
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.769997\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.769997 q^{12} +4.82049 q^{13} +4.71912 q^{14} +0.769997 q^{15} +1.00000 q^{16} +6.87326 q^{17} -2.40710 q^{18} -6.08969 q^{19} +1.00000 q^{20} +3.63371 q^{21} -1.00000 q^{22} -2.82049 q^{23} +0.769997 q^{24} +1.00000 q^{25} +4.82049 q^{26} -4.16346 q^{27} +4.71912 q^{28} +0.648686 q^{29} +0.769997 q^{30} +8.04887 q^{31} +1.00000 q^{32} -0.769997 q^{33} +6.87326 q^{34} +4.71912 q^{35} -2.40710 q^{36} +1.84432 q^{37} -6.08969 q^{38} +3.71176 q^{39} +1.00000 q^{40} -5.87951 q^{41} +3.63371 q^{42} +1.00000 q^{43} -1.00000 q^{44} -2.40710 q^{45} -2.82049 q^{46} -12.3087 q^{47} +0.769997 q^{48} +15.2701 q^{49} +1.00000 q^{50} +5.29239 q^{51} +4.82049 q^{52} +8.05623 q^{53} -4.16346 q^{54} -1.00000 q^{55} +4.71912 q^{56} -4.68904 q^{57} +0.648686 q^{58} -12.7272 q^{59} +0.769997 q^{60} +11.5570 q^{61} +8.04887 q^{62} -11.3594 q^{63} +1.00000 q^{64} +4.82049 q^{65} -0.769997 q^{66} +2.87102 q^{67} +6.87326 q^{68} -2.17177 q^{69} +4.71912 q^{70} +2.63811 q^{71} -2.40710 q^{72} +1.83057 q^{73} +1.84432 q^{74} +0.769997 q^{75} -6.08969 q^{76} -4.71912 q^{77} +3.71176 q^{78} -9.14301 q^{79} +1.00000 q^{80} +4.01546 q^{81} -5.87951 q^{82} -2.49005 q^{83} +3.63371 q^{84} +6.87326 q^{85} +1.00000 q^{86} +0.499486 q^{87} -1.00000 q^{88} -6.18484 q^{89} -2.40710 q^{90} +22.7485 q^{91} -2.82049 q^{92} +6.19761 q^{93} -12.3087 q^{94} -6.08969 q^{95} +0.769997 q^{96} +8.98364 q^{97} +15.2701 q^{98} +2.40710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + O(q^{10}) \) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + 12q^{10} - 12q^{11} + 3q^{12} + 16q^{13} + 8q^{14} + 3q^{15} + 12q^{16} + 18q^{17} + 25q^{18} - 4q^{19} + 12q^{20} + 4q^{21} - 12q^{22} + 8q^{23} + 3q^{24} + 12q^{25} + 16q^{26} + 6q^{27} + 8q^{28} + 20q^{29} + 3q^{30} + 5q^{31} + 12q^{32} - 3q^{33} + 18q^{34} + 8q^{35} + 25q^{36} + 19q^{37} - 4q^{38} + 6q^{39} + 12q^{40} + 16q^{41} + 4q^{42} + 12q^{43} - 12q^{44} + 25q^{45} + 8q^{46} - q^{47} + 3q^{48} + 52q^{49} + 12q^{50} + q^{51} + 16q^{52} + 11q^{53} + 6q^{54} - 12q^{55} + 8q^{56} + 9q^{57} + 20q^{58} - 11q^{59} + 3q^{60} + 18q^{61} + 5q^{62} + 15q^{63} + 12q^{64} + 16q^{65} - 3q^{66} - 10q^{67} + 18q^{68} + 8q^{70} - 2q^{71} + 25q^{72} + 29q^{73} + 19q^{74} + 3q^{75} - 4q^{76} - 8q^{77} + 6q^{78} + 2q^{79} + 12q^{80} - 8q^{81} + 16q^{82} + 26q^{83} + 4q^{84} + 18q^{85} + 12q^{86} - 4q^{87} - 12q^{88} + 41q^{89} + 25q^{90} - 4q^{91} + 8q^{92} + 5q^{93} - q^{94} - 4q^{95} + 3q^{96} - 7q^{97} + 52q^{98} - 25q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.769997 0.444558 0.222279 0.974983i \(-0.428650\pi\)
0.222279 + 0.974983i \(0.428650\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.769997 0.314350
\(7\) 4.71912 1.78366 0.891830 0.452370i \(-0.149422\pi\)
0.891830 + 0.452370i \(0.149422\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.40710 −0.802368
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 0.769997 0.222279
\(13\) 4.82049 1.33696 0.668481 0.743729i \(-0.266945\pi\)
0.668481 + 0.743729i \(0.266945\pi\)
\(14\) 4.71912 1.26124
\(15\) 0.769997 0.198812
\(16\) 1.00000 0.250000
\(17\) 6.87326 1.66701 0.833506 0.552511i \(-0.186330\pi\)
0.833506 + 0.552511i \(0.186330\pi\)
\(18\) −2.40710 −0.567360
\(19\) −6.08969 −1.39707 −0.698535 0.715576i \(-0.746164\pi\)
−0.698535 + 0.715576i \(0.746164\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.63371 0.792941
\(22\) −1.00000 −0.213201
\(23\) −2.82049 −0.588112 −0.294056 0.955788i \(-0.595005\pi\)
−0.294056 + 0.955788i \(0.595005\pi\)
\(24\) 0.769997 0.157175
\(25\) 1.00000 0.200000
\(26\) 4.82049 0.945375
\(27\) −4.16346 −0.801257
\(28\) 4.71912 0.891830
\(29\) 0.648686 0.120458 0.0602290 0.998185i \(-0.480817\pi\)
0.0602290 + 0.998185i \(0.480817\pi\)
\(30\) 0.769997 0.140582
\(31\) 8.04887 1.44562 0.722810 0.691047i \(-0.242850\pi\)
0.722810 + 0.691047i \(0.242850\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.769997 −0.134039
\(34\) 6.87326 1.17875
\(35\) 4.71912 0.797677
\(36\) −2.40710 −0.401184
\(37\) 1.84432 0.303205 0.151602 0.988442i \(-0.451557\pi\)
0.151602 + 0.988442i \(0.451557\pi\)
\(38\) −6.08969 −0.987878
\(39\) 3.71176 0.594358
\(40\) 1.00000 0.158114
\(41\) −5.87951 −0.918225 −0.459112 0.888378i \(-0.651832\pi\)
−0.459112 + 0.888378i \(0.651832\pi\)
\(42\) 3.63371 0.560694
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −2.40710 −0.358830
\(46\) −2.82049 −0.415858
\(47\) −12.3087 −1.79541 −0.897706 0.440595i \(-0.854768\pi\)
−0.897706 + 0.440595i \(0.854768\pi\)
\(48\) 0.769997 0.111140
\(49\) 15.2701 2.18144
\(50\) 1.00000 0.141421
\(51\) 5.29239 0.741083
\(52\) 4.82049 0.668481
\(53\) 8.05623 1.10661 0.553304 0.832979i \(-0.313367\pi\)
0.553304 + 0.832979i \(0.313367\pi\)
\(54\) −4.16346 −0.566575
\(55\) −1.00000 −0.134840
\(56\) 4.71912 0.630619
\(57\) −4.68904 −0.621079
\(58\) 0.648686 0.0851766
\(59\) −12.7272 −1.65693 −0.828467 0.560037i \(-0.810787\pi\)
−0.828467 + 0.560037i \(0.810787\pi\)
\(60\) 0.769997 0.0994062
\(61\) 11.5570 1.47972 0.739860 0.672761i \(-0.234892\pi\)
0.739860 + 0.672761i \(0.234892\pi\)
\(62\) 8.04887 1.02221
\(63\) −11.3594 −1.43115
\(64\) 1.00000 0.125000
\(65\) 4.82049 0.597908
\(66\) −0.769997 −0.0947801
\(67\) 2.87102 0.350750 0.175375 0.984502i \(-0.443886\pi\)
0.175375 + 0.984502i \(0.443886\pi\)
\(68\) 6.87326 0.833506
\(69\) −2.17177 −0.261450
\(70\) 4.71912 0.564043
\(71\) 2.63811 0.313086 0.156543 0.987671i \(-0.449965\pi\)
0.156543 + 0.987671i \(0.449965\pi\)
\(72\) −2.40710 −0.283680
\(73\) 1.83057 0.214252 0.107126 0.994245i \(-0.465835\pi\)
0.107126 + 0.994245i \(0.465835\pi\)
\(74\) 1.84432 0.214398
\(75\) 0.769997 0.0889116
\(76\) −6.08969 −0.698535
\(77\) −4.71912 −0.537794
\(78\) 3.71176 0.420274
\(79\) −9.14301 −1.02867 −0.514334 0.857590i \(-0.671961\pi\)
−0.514334 + 0.857590i \(0.671961\pi\)
\(80\) 1.00000 0.111803
\(81\) 4.01546 0.446162
\(82\) −5.87951 −0.649283
\(83\) −2.49005 −0.273318 −0.136659 0.990618i \(-0.543636\pi\)
−0.136659 + 0.990618i \(0.543636\pi\)
\(84\) 3.63371 0.396470
\(85\) 6.87326 0.745510
\(86\) 1.00000 0.107833
\(87\) 0.499486 0.0535506
\(88\) −1.00000 −0.106600
\(89\) −6.18484 −0.655592 −0.327796 0.944749i \(-0.606306\pi\)
−0.327796 + 0.944749i \(0.606306\pi\)
\(90\) −2.40710 −0.253731
\(91\) 22.7485 2.38469
\(92\) −2.82049 −0.294056
\(93\) 6.19761 0.642662
\(94\) −12.3087 −1.26955
\(95\) −6.08969 −0.624789
\(96\) 0.769997 0.0785875
\(97\) 8.98364 0.912150 0.456075 0.889941i \(-0.349255\pi\)
0.456075 + 0.889941i \(0.349255\pi\)
\(98\) 15.2701 1.54251
\(99\) 2.40710 0.241923
\(100\) 1.00000 0.100000
\(101\) −7.55809 −0.752058 −0.376029 0.926608i \(-0.622711\pi\)
−0.376029 + 0.926608i \(0.622711\pi\)
\(102\) 5.29239 0.524025
\(103\) 3.23968 0.319215 0.159607 0.987181i \(-0.448977\pi\)
0.159607 + 0.987181i \(0.448977\pi\)
\(104\) 4.82049 0.472688
\(105\) 3.63371 0.354614
\(106\) 8.05623 0.782490
\(107\) −18.1188 −1.75161 −0.875805 0.482665i \(-0.839669\pi\)
−0.875805 + 0.482665i \(0.839669\pi\)
\(108\) −4.16346 −0.400629
\(109\) −10.1215 −0.969464 −0.484732 0.874663i \(-0.661083\pi\)
−0.484732 + 0.874663i \(0.661083\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 1.42012 0.134792
\(112\) 4.71912 0.445915
\(113\) −4.53172 −0.426309 −0.213154 0.977019i \(-0.568374\pi\)
−0.213154 + 0.977019i \(0.568374\pi\)
\(114\) −4.68904 −0.439169
\(115\) −2.82049 −0.263012
\(116\) 0.648686 0.0602290
\(117\) −11.6034 −1.07274
\(118\) −12.7272 −1.17163
\(119\) 32.4358 2.97338
\(120\) 0.769997 0.0702908
\(121\) 1.00000 0.0909091
\(122\) 11.5570 1.04632
\(123\) −4.52720 −0.408204
\(124\) 8.04887 0.722810
\(125\) 1.00000 0.0894427
\(126\) −11.3594 −1.01198
\(127\) −13.1291 −1.16502 −0.582511 0.812823i \(-0.697930\pi\)
−0.582511 + 0.812823i \(0.697930\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.769997 0.0677945
\(130\) 4.82049 0.422785
\(131\) 19.3773 1.69301 0.846503 0.532384i \(-0.178704\pi\)
0.846503 + 0.532384i \(0.178704\pi\)
\(132\) −0.769997 −0.0670197
\(133\) −28.7380 −2.49190
\(134\) 2.87102 0.248018
\(135\) −4.16346 −0.358333
\(136\) 6.87326 0.589377
\(137\) 11.6852 0.998331 0.499165 0.866507i \(-0.333640\pi\)
0.499165 + 0.866507i \(0.333640\pi\)
\(138\) −2.17177 −0.184873
\(139\) 0.0272877 0.00231451 0.00115726 0.999999i \(-0.499632\pi\)
0.00115726 + 0.999999i \(0.499632\pi\)
\(140\) 4.71912 0.398839
\(141\) −9.47769 −0.798165
\(142\) 2.63811 0.221385
\(143\) −4.82049 −0.403109
\(144\) −2.40710 −0.200592
\(145\) 0.648686 0.0538704
\(146\) 1.83057 0.151499
\(147\) 11.7579 0.969779
\(148\) 1.84432 0.151602
\(149\) 22.0490 1.80632 0.903161 0.429303i \(-0.141241\pi\)
0.903161 + 0.429303i \(0.141241\pi\)
\(150\) 0.769997 0.0628700
\(151\) 5.00624 0.407402 0.203701 0.979033i \(-0.434703\pi\)
0.203701 + 0.979033i \(0.434703\pi\)
\(152\) −6.08969 −0.493939
\(153\) −16.5447 −1.33756
\(154\) −4.71912 −0.380278
\(155\) 8.04887 0.646501
\(156\) 3.71176 0.297179
\(157\) −3.27661 −0.261502 −0.130751 0.991415i \(-0.541739\pi\)
−0.130751 + 0.991415i \(0.541739\pi\)
\(158\) −9.14301 −0.727378
\(159\) 6.20327 0.491952
\(160\) 1.00000 0.0790569
\(161\) −13.3102 −1.04899
\(162\) 4.01546 0.315484
\(163\) 1.81470 0.142139 0.0710693 0.997471i \(-0.477359\pi\)
0.0710693 + 0.997471i \(0.477359\pi\)
\(164\) −5.87951 −0.459112
\(165\) −0.769997 −0.0599442
\(166\) −2.49005 −0.193265
\(167\) −19.9902 −1.54689 −0.773443 0.633866i \(-0.781467\pi\)
−0.773443 + 0.633866i \(0.781467\pi\)
\(168\) 3.63371 0.280347
\(169\) 10.2371 0.787469
\(170\) 6.87326 0.527155
\(171\) 14.6585 1.12096
\(172\) 1.00000 0.0762493
\(173\) 14.1771 1.07787 0.538933 0.842348i \(-0.318827\pi\)
0.538933 + 0.842348i \(0.318827\pi\)
\(174\) 0.499486 0.0378660
\(175\) 4.71912 0.356732
\(176\) −1.00000 −0.0753778
\(177\) −9.79988 −0.736604
\(178\) −6.18484 −0.463573
\(179\) −24.3657 −1.82117 −0.910587 0.413317i \(-0.864370\pi\)
−0.910587 + 0.413317i \(0.864370\pi\)
\(180\) −2.40710 −0.179415
\(181\) 19.6016 1.45697 0.728487 0.685060i \(-0.240224\pi\)
0.728487 + 0.685060i \(0.240224\pi\)
\(182\) 22.7485 1.68623
\(183\) 8.89885 0.657822
\(184\) −2.82049 −0.207929
\(185\) 1.84432 0.135597
\(186\) 6.19761 0.454431
\(187\) −6.87326 −0.502623
\(188\) −12.3087 −0.897706
\(189\) −19.6479 −1.42917
\(190\) −6.08969 −0.441792
\(191\) 8.97018 0.649060 0.324530 0.945875i \(-0.394794\pi\)
0.324530 + 0.945875i \(0.394794\pi\)
\(192\) 0.769997 0.0555698
\(193\) −18.6940 −1.34562 −0.672812 0.739813i \(-0.734914\pi\)
−0.672812 + 0.739813i \(0.734914\pi\)
\(194\) 8.98364 0.644988
\(195\) 3.71176 0.265805
\(196\) 15.2701 1.09072
\(197\) −20.2277 −1.44116 −0.720581 0.693371i \(-0.756125\pi\)
−0.720581 + 0.693371i \(0.756125\pi\)
\(198\) 2.40710 0.171065
\(199\) 10.2488 0.726516 0.363258 0.931689i \(-0.381664\pi\)
0.363258 + 0.931689i \(0.381664\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.21067 0.155929
\(202\) −7.55809 −0.531785
\(203\) 3.06123 0.214856
\(204\) 5.29239 0.370542
\(205\) −5.87951 −0.410643
\(206\) 3.23968 0.225719
\(207\) 6.78921 0.471882
\(208\) 4.82049 0.334241
\(209\) 6.08969 0.421232
\(210\) 3.63371 0.250750
\(211\) −20.1549 −1.38752 −0.693762 0.720204i \(-0.744048\pi\)
−0.693762 + 0.720204i \(0.744048\pi\)
\(212\) 8.05623 0.553304
\(213\) 2.03134 0.139185
\(214\) −18.1188 −1.23858
\(215\) 1.00000 0.0681994
\(216\) −4.16346 −0.283287
\(217\) 37.9836 2.57849
\(218\) −10.1215 −0.685514
\(219\) 1.40953 0.0952475
\(220\) −1.00000 −0.0674200
\(221\) 33.1325 2.22873
\(222\) 1.42012 0.0953124
\(223\) −2.95695 −0.198012 −0.0990060 0.995087i \(-0.531566\pi\)
−0.0990060 + 0.995087i \(0.531566\pi\)
\(224\) 4.71912 0.315310
\(225\) −2.40710 −0.160474
\(226\) −4.53172 −0.301446
\(227\) 10.2629 0.681171 0.340585 0.940214i \(-0.389375\pi\)
0.340585 + 0.940214i \(0.389375\pi\)
\(228\) −4.68904 −0.310539
\(229\) 8.63226 0.570436 0.285218 0.958463i \(-0.407934\pi\)
0.285218 + 0.958463i \(0.407934\pi\)
\(230\) −2.82049 −0.185977
\(231\) −3.63371 −0.239081
\(232\) 0.648686 0.0425883
\(233\) 15.5796 1.02066 0.510328 0.859980i \(-0.329524\pi\)
0.510328 + 0.859980i \(0.329524\pi\)
\(234\) −11.6034 −0.758539
\(235\) −12.3087 −0.802933
\(236\) −12.7272 −0.828467
\(237\) −7.04009 −0.457303
\(238\) 32.4358 2.10250
\(239\) 13.1299 0.849302 0.424651 0.905357i \(-0.360397\pi\)
0.424651 + 0.905357i \(0.360397\pi\)
\(240\) 0.769997 0.0497031
\(241\) −11.1282 −0.716829 −0.358415 0.933562i \(-0.616683\pi\)
−0.358415 + 0.933562i \(0.616683\pi\)
\(242\) 1.00000 0.0642824
\(243\) 15.5823 0.999603
\(244\) 11.5570 0.739860
\(245\) 15.2701 0.975571
\(246\) −4.52720 −0.288644
\(247\) −29.3553 −1.86783
\(248\) 8.04887 0.511104
\(249\) −1.91733 −0.121506
\(250\) 1.00000 0.0632456
\(251\) 17.4341 1.10043 0.550217 0.835022i \(-0.314545\pi\)
0.550217 + 0.835022i \(0.314545\pi\)
\(252\) −11.3594 −0.715576
\(253\) 2.82049 0.177322
\(254\) −13.1291 −0.823795
\(255\) 5.29239 0.331423
\(256\) 1.00000 0.0625000
\(257\) −19.2926 −1.20344 −0.601720 0.798707i \(-0.705518\pi\)
−0.601720 + 0.798707i \(0.705518\pi\)
\(258\) 0.769997 0.0479379
\(259\) 8.70358 0.540814
\(260\) 4.82049 0.298954
\(261\) −1.56145 −0.0966516
\(262\) 19.3773 1.19714
\(263\) 19.1093 1.17833 0.589165 0.808012i \(-0.299457\pi\)
0.589165 + 0.808012i \(0.299457\pi\)
\(264\) −0.769997 −0.0473901
\(265\) 8.05623 0.494890
\(266\) −28.7380 −1.76204
\(267\) −4.76231 −0.291449
\(268\) 2.87102 0.175375
\(269\) −20.2582 −1.23517 −0.617583 0.786505i \(-0.711888\pi\)
−0.617583 + 0.786505i \(0.711888\pi\)
\(270\) −4.16346 −0.253380
\(271\) −26.0211 −1.58067 −0.790334 0.612677i \(-0.790093\pi\)
−0.790334 + 0.612677i \(0.790093\pi\)
\(272\) 6.87326 0.416753
\(273\) 17.5163 1.06013
\(274\) 11.6852 0.705926
\(275\) −1.00000 −0.0603023
\(276\) −2.17177 −0.130725
\(277\) −16.0212 −0.962622 −0.481311 0.876550i \(-0.659839\pi\)
−0.481311 + 0.876550i \(0.659839\pi\)
\(278\) 0.0272877 0.00163661
\(279\) −19.3745 −1.15992
\(280\) 4.71912 0.282021
\(281\) −3.66414 −0.218584 −0.109292 0.994010i \(-0.534858\pi\)
−0.109292 + 0.994010i \(0.534858\pi\)
\(282\) −9.47769 −0.564388
\(283\) 4.36373 0.259397 0.129698 0.991553i \(-0.458599\pi\)
0.129698 + 0.991553i \(0.458599\pi\)
\(284\) 2.63811 0.156543
\(285\) −4.68904 −0.277755
\(286\) −4.82049 −0.285041
\(287\) −27.7461 −1.63780
\(288\) −2.40710 −0.141840
\(289\) 30.2417 1.77893
\(290\) 0.648686 0.0380921
\(291\) 6.91738 0.405504
\(292\) 1.83057 0.107126
\(293\) −5.41921 −0.316593 −0.158297 0.987392i \(-0.550600\pi\)
−0.158297 + 0.987392i \(0.550600\pi\)
\(294\) 11.7579 0.685737
\(295\) −12.7272 −0.741004
\(296\) 1.84432 0.107199
\(297\) 4.16346 0.241588
\(298\) 22.0490 1.27726
\(299\) −13.5961 −0.786284
\(300\) 0.769997 0.0444558
\(301\) 4.71912 0.272006
\(302\) 5.00624 0.288077
\(303\) −5.81971 −0.334334
\(304\) −6.08969 −0.349267
\(305\) 11.5570 0.661751
\(306\) −16.5447 −0.945795
\(307\) 9.54656 0.544851 0.272426 0.962177i \(-0.412174\pi\)
0.272426 + 0.962177i \(0.412174\pi\)
\(308\) −4.71912 −0.268897
\(309\) 2.49454 0.141910
\(310\) 8.04887 0.457145
\(311\) 16.9195 0.959417 0.479709 0.877428i \(-0.340742\pi\)
0.479709 + 0.877428i \(0.340742\pi\)
\(312\) 3.71176 0.210137
\(313\) −19.9949 −1.13018 −0.565090 0.825029i \(-0.691159\pi\)
−0.565090 + 0.825029i \(0.691159\pi\)
\(314\) −3.27661 −0.184910
\(315\) −11.3594 −0.640031
\(316\) −9.14301 −0.514334
\(317\) −28.6527 −1.60930 −0.804648 0.593752i \(-0.797646\pi\)
−0.804648 + 0.593752i \(0.797646\pi\)
\(318\) 6.20327 0.347862
\(319\) −0.648686 −0.0363194
\(320\) 1.00000 0.0559017
\(321\) −13.9514 −0.778693
\(322\) −13.3102 −0.741750
\(323\) −41.8560 −2.32893
\(324\) 4.01546 0.223081
\(325\) 4.82049 0.267392
\(326\) 1.81470 0.100507
\(327\) −7.79353 −0.430983
\(328\) −5.87951 −0.324641
\(329\) −58.0864 −3.20241
\(330\) −0.769997 −0.0423870
\(331\) −16.3489 −0.898618 −0.449309 0.893376i \(-0.648330\pi\)
−0.449309 + 0.893376i \(0.648330\pi\)
\(332\) −2.49005 −0.136659
\(333\) −4.43947 −0.243282
\(334\) −19.9902 −1.09381
\(335\) 2.87102 0.156860
\(336\) 3.63371 0.198235
\(337\) 17.2707 0.940794 0.470397 0.882455i \(-0.344111\pi\)
0.470397 + 0.882455i \(0.344111\pi\)
\(338\) 10.2371 0.556824
\(339\) −3.48941 −0.189519
\(340\) 6.87326 0.372755
\(341\) −8.04887 −0.435871
\(342\) 14.6585 0.792641
\(343\) 39.0276 2.10729
\(344\) 1.00000 0.0539164
\(345\) −2.17177 −0.116924
\(346\) 14.1771 0.762167
\(347\) 15.2519 0.818765 0.409382 0.912363i \(-0.365744\pi\)
0.409382 + 0.912363i \(0.365744\pi\)
\(348\) 0.499486 0.0267753
\(349\) −27.0659 −1.44880 −0.724401 0.689378i \(-0.757884\pi\)
−0.724401 + 0.689378i \(0.757884\pi\)
\(350\) 4.71912 0.252248
\(351\) −20.0699 −1.07125
\(352\) −1.00000 −0.0533002
\(353\) 25.4907 1.35673 0.678366 0.734724i \(-0.262689\pi\)
0.678366 + 0.734724i \(0.262689\pi\)
\(354\) −9.79988 −0.520858
\(355\) 2.63811 0.140016
\(356\) −6.18484 −0.327796
\(357\) 24.9755 1.32184
\(358\) −24.3657 −1.28776
\(359\) 13.1171 0.692294 0.346147 0.938180i \(-0.387490\pi\)
0.346147 + 0.938180i \(0.387490\pi\)
\(360\) −2.40710 −0.126866
\(361\) 18.0843 0.951804
\(362\) 19.6016 1.03024
\(363\) 0.769997 0.0404144
\(364\) 22.7485 1.19234
\(365\) 1.83057 0.0958164
\(366\) 8.89885 0.465150
\(367\) 3.78574 0.197614 0.0988071 0.995107i \(-0.468497\pi\)
0.0988071 + 0.995107i \(0.468497\pi\)
\(368\) −2.82049 −0.147028
\(369\) 14.1526 0.736754
\(370\) 1.84432 0.0958817
\(371\) 38.0183 1.97381
\(372\) 6.19761 0.321331
\(373\) −34.9268 −1.80844 −0.904221 0.427064i \(-0.859548\pi\)
−0.904221 + 0.427064i \(0.859548\pi\)
\(374\) −6.87326 −0.355408
\(375\) 0.769997 0.0397625
\(376\) −12.3087 −0.634774
\(377\) 3.12698 0.161048
\(378\) −19.6479 −1.01058
\(379\) 34.4499 1.76957 0.884786 0.465997i \(-0.154304\pi\)
0.884786 + 0.465997i \(0.154304\pi\)
\(380\) −6.08969 −0.312394
\(381\) −10.1094 −0.517920
\(382\) 8.97018 0.458955
\(383\) −31.8557 −1.62775 −0.813874 0.581042i \(-0.802645\pi\)
−0.813874 + 0.581042i \(0.802645\pi\)
\(384\) 0.769997 0.0392938
\(385\) −4.71912 −0.240509
\(386\) −18.6940 −0.951500
\(387\) −2.40710 −0.122360
\(388\) 8.98364 0.456075
\(389\) −5.70481 −0.289246 −0.144623 0.989487i \(-0.546197\pi\)
−0.144623 + 0.989487i \(0.546197\pi\)
\(390\) 3.71176 0.187952
\(391\) −19.3859 −0.980390
\(392\) 15.2701 0.771257
\(393\) 14.9205 0.752640
\(394\) −20.2277 −1.01906
\(395\) −9.14301 −0.460035
\(396\) 2.40710 0.120962
\(397\) −18.1068 −0.908754 −0.454377 0.890810i \(-0.650138\pi\)
−0.454377 + 0.890810i \(0.650138\pi\)
\(398\) 10.2488 0.513724
\(399\) −22.1282 −1.10779
\(400\) 1.00000 0.0500000
\(401\) 13.1359 0.655977 0.327988 0.944682i \(-0.393629\pi\)
0.327988 + 0.944682i \(0.393629\pi\)
\(402\) 2.21067 0.110258
\(403\) 38.7995 1.93274
\(404\) −7.55809 −0.376029
\(405\) 4.01546 0.199530
\(406\) 3.06123 0.151926
\(407\) −1.84432 −0.0914196
\(408\) 5.29239 0.262013
\(409\) 27.9862 1.38383 0.691915 0.721979i \(-0.256767\pi\)
0.691915 + 0.721979i \(0.256767\pi\)
\(410\) −5.87951 −0.290368
\(411\) 8.99754 0.443816
\(412\) 3.23968 0.159607
\(413\) −60.0610 −2.95541
\(414\) 6.78921 0.333671
\(415\) −2.49005 −0.122232
\(416\) 4.82049 0.236344
\(417\) 0.0210114 0.00102893
\(418\) 6.08969 0.297856
\(419\) 8.90520 0.435047 0.217524 0.976055i \(-0.430202\pi\)
0.217524 + 0.976055i \(0.430202\pi\)
\(420\) 3.63371 0.177307
\(421\) 10.4484 0.509222 0.254611 0.967044i \(-0.418053\pi\)
0.254611 + 0.967044i \(0.418053\pi\)
\(422\) −20.1549 −0.981127
\(423\) 29.6284 1.44058
\(424\) 8.05623 0.391245
\(425\) 6.87326 0.333402
\(426\) 2.03134 0.0984186
\(427\) 54.5388 2.63932
\(428\) −18.1188 −0.875805
\(429\) −3.71176 −0.179206
\(430\) 1.00000 0.0482243
\(431\) −4.68303 −0.225574 −0.112787 0.993619i \(-0.535978\pi\)
−0.112787 + 0.993619i \(0.535978\pi\)
\(432\) −4.16346 −0.200314
\(433\) 26.6316 1.27983 0.639917 0.768444i \(-0.278969\pi\)
0.639917 + 0.768444i \(0.278969\pi\)
\(434\) 37.9836 1.82327
\(435\) 0.499486 0.0239485
\(436\) −10.1215 −0.484732
\(437\) 17.1759 0.821634
\(438\) 1.40953 0.0673501
\(439\) −18.6380 −0.889543 −0.444772 0.895644i \(-0.646715\pi\)
−0.444772 + 0.895644i \(0.646715\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −36.7567 −1.75032
\(442\) 33.1325 1.57595
\(443\) −17.5322 −0.832981 −0.416491 0.909140i \(-0.636740\pi\)
−0.416491 + 0.909140i \(0.636740\pi\)
\(444\) 1.42012 0.0673961
\(445\) −6.18484 −0.293190
\(446\) −2.95695 −0.140016
\(447\) 16.9776 0.803015
\(448\) 4.71912 0.222958
\(449\) −12.0831 −0.570236 −0.285118 0.958492i \(-0.592033\pi\)
−0.285118 + 0.958492i \(0.592033\pi\)
\(450\) −2.40710 −0.113472
\(451\) 5.87951 0.276855
\(452\) −4.53172 −0.213154
\(453\) 3.85479 0.181114
\(454\) 10.2629 0.481660
\(455\) 22.7485 1.06646
\(456\) −4.68904 −0.219585
\(457\) 5.06828 0.237084 0.118542 0.992949i \(-0.462178\pi\)
0.118542 + 0.992949i \(0.462178\pi\)
\(458\) 8.63226 0.403359
\(459\) −28.6165 −1.33571
\(460\) −2.82049 −0.131506
\(461\) 10.2649 0.478082 0.239041 0.971009i \(-0.423167\pi\)
0.239041 + 0.971009i \(0.423167\pi\)
\(462\) −3.63371 −0.169056
\(463\) −15.8848 −0.738229 −0.369115 0.929384i \(-0.620339\pi\)
−0.369115 + 0.929384i \(0.620339\pi\)
\(464\) 0.648686 0.0301145
\(465\) 6.19761 0.287407
\(466\) 15.5796 0.721712
\(467\) 28.6315 1.32491 0.662455 0.749102i \(-0.269515\pi\)
0.662455 + 0.749102i \(0.269515\pi\)
\(468\) −11.6034 −0.536368
\(469\) 13.5487 0.625619
\(470\) −12.3087 −0.567759
\(471\) −2.52298 −0.116253
\(472\) −12.7272 −0.585815
\(473\) −1.00000 −0.0459800
\(474\) −7.04009 −0.323362
\(475\) −6.08969 −0.279414
\(476\) 32.4358 1.48669
\(477\) −19.3922 −0.887907
\(478\) 13.1299 0.600547
\(479\) 4.26885 0.195049 0.0975244 0.995233i \(-0.468908\pi\)
0.0975244 + 0.995233i \(0.468908\pi\)
\(480\) 0.769997 0.0351454
\(481\) 8.89053 0.405373
\(482\) −11.1282 −0.506875
\(483\) −10.2488 −0.466338
\(484\) 1.00000 0.0454545
\(485\) 8.98364 0.407926
\(486\) 15.5823 0.706826
\(487\) 22.1475 1.00360 0.501800 0.864983i \(-0.332671\pi\)
0.501800 + 0.864983i \(0.332671\pi\)
\(488\) 11.5570 0.523160
\(489\) 1.39732 0.0631889
\(490\) 15.2701 0.689833
\(491\) −25.1815 −1.13642 −0.568212 0.822882i \(-0.692365\pi\)
−0.568212 + 0.822882i \(0.692365\pi\)
\(492\) −4.52720 −0.204102
\(493\) 4.45859 0.200805
\(494\) −29.3553 −1.32076
\(495\) 2.40710 0.108191
\(496\) 8.04887 0.361405
\(497\) 12.4496 0.558439
\(498\) −1.91733 −0.0859176
\(499\) 25.1495 1.12585 0.562924 0.826509i \(-0.309676\pi\)
0.562924 + 0.826509i \(0.309676\pi\)
\(500\) 1.00000 0.0447214
\(501\) −15.3924 −0.687681
\(502\) 17.4341 0.778124
\(503\) 24.0806 1.07370 0.536850 0.843678i \(-0.319614\pi\)
0.536850 + 0.843678i \(0.319614\pi\)
\(504\) −11.3594 −0.505989
\(505\) −7.55809 −0.336331
\(506\) 2.82049 0.125386
\(507\) 7.88253 0.350076
\(508\) −13.1291 −0.582511
\(509\) −40.4523 −1.79302 −0.896509 0.443025i \(-0.853905\pi\)
−0.896509 + 0.443025i \(0.853905\pi\)
\(510\) 5.29239 0.234351
\(511\) 8.63868 0.382153
\(512\) 1.00000 0.0441942
\(513\) 25.3541 1.11941
\(514\) −19.2926 −0.850960
\(515\) 3.23968 0.142757
\(516\) 0.769997 0.0338972
\(517\) 12.3087 0.541337
\(518\) 8.70358 0.382413
\(519\) 10.9163 0.479175
\(520\) 4.82049 0.211392
\(521\) 13.8543 0.606968 0.303484 0.952837i \(-0.401850\pi\)
0.303484 + 0.952837i \(0.401850\pi\)
\(522\) −1.56145 −0.0683430
\(523\) 23.0481 1.00783 0.503913 0.863755i \(-0.331893\pi\)
0.503913 + 0.863755i \(0.331893\pi\)
\(524\) 19.3773 0.846503
\(525\) 3.63371 0.158588
\(526\) 19.1093 0.833206
\(527\) 55.3220 2.40986
\(528\) −0.769997 −0.0335098
\(529\) −15.0449 −0.654124
\(530\) 8.05623 0.349940
\(531\) 30.6356 1.32947
\(532\) −28.7380 −1.24595
\(533\) −28.3421 −1.22763
\(534\) −4.76231 −0.206085
\(535\) −18.1188 −0.783344
\(536\) 2.87102 0.124009
\(537\) −18.7615 −0.809618
\(538\) −20.2582 −0.873395
\(539\) −15.2701 −0.657730
\(540\) −4.16346 −0.179167
\(541\) −5.81427 −0.249975 −0.124987 0.992158i \(-0.539889\pi\)
−0.124987 + 0.992158i \(0.539889\pi\)
\(542\) −26.0211 −1.11770
\(543\) 15.0932 0.647710
\(544\) 6.87326 0.294689
\(545\) −10.1215 −0.433557
\(546\) 17.5163 0.749627
\(547\) −6.90073 −0.295054 −0.147527 0.989058i \(-0.547131\pi\)
−0.147527 + 0.989058i \(0.547131\pi\)
\(548\) 11.6852 0.499165
\(549\) −27.8189 −1.18728
\(550\) −1.00000 −0.0426401
\(551\) −3.95029 −0.168288
\(552\) −2.17177 −0.0924366
\(553\) −43.1470 −1.83480
\(554\) −16.0212 −0.680677
\(555\) 1.42012 0.0602809
\(556\) 0.0272877 0.00115726
\(557\) −20.8179 −0.882081 −0.441041 0.897487i \(-0.645390\pi\)
−0.441041 + 0.897487i \(0.645390\pi\)
\(558\) −19.3745 −0.820187
\(559\) 4.82049 0.203885
\(560\) 4.71912 0.199419
\(561\) −5.29239 −0.223445
\(562\) −3.66414 −0.154562
\(563\) −31.0099 −1.30691 −0.653456 0.756964i \(-0.726682\pi\)
−0.653456 + 0.756964i \(0.726682\pi\)
\(564\) −9.47769 −0.399083
\(565\) −4.53172 −0.190651
\(566\) 4.36373 0.183421
\(567\) 18.9495 0.795802
\(568\) 2.63811 0.110693
\(569\) −10.7850 −0.452130 −0.226065 0.974112i \(-0.572586\pi\)
−0.226065 + 0.974112i \(0.572586\pi\)
\(570\) −4.68904 −0.196402
\(571\) 0.800396 0.0334955 0.0167478 0.999860i \(-0.494669\pi\)
0.0167478 + 0.999860i \(0.494669\pi\)
\(572\) −4.82049 −0.201555
\(573\) 6.90702 0.288545
\(574\) −27.7461 −1.15810
\(575\) −2.82049 −0.117622
\(576\) −2.40710 −0.100296
\(577\) 21.0496 0.876308 0.438154 0.898900i \(-0.355632\pi\)
0.438154 + 0.898900i \(0.355632\pi\)
\(578\) 30.2417 1.25789
\(579\) −14.3943 −0.598208
\(580\) 0.648686 0.0269352
\(581\) −11.7508 −0.487507
\(582\) 6.91738 0.286735
\(583\) −8.05623 −0.333655
\(584\) 1.83057 0.0757495
\(585\) −11.6034 −0.479742
\(586\) −5.41921 −0.223865
\(587\) −21.5013 −0.887452 −0.443726 0.896163i \(-0.646344\pi\)
−0.443726 + 0.896163i \(0.646344\pi\)
\(588\) 11.7579 0.484889
\(589\) −49.0151 −2.01963
\(590\) −12.7272 −0.523969
\(591\) −15.5753 −0.640681
\(592\) 1.84432 0.0758012
\(593\) 33.7120 1.38439 0.692194 0.721712i \(-0.256644\pi\)
0.692194 + 0.721712i \(0.256644\pi\)
\(594\) 4.16346 0.170829
\(595\) 32.4358 1.32974
\(596\) 22.0490 0.903161
\(597\) 7.89153 0.322979
\(598\) −13.5961 −0.555987
\(599\) −16.7109 −0.682787 −0.341394 0.939920i \(-0.610899\pi\)
−0.341394 + 0.939920i \(0.610899\pi\)
\(600\) 0.769997 0.0314350
\(601\) −21.5232 −0.877950 −0.438975 0.898499i \(-0.644658\pi\)
−0.438975 + 0.898499i \(0.644658\pi\)
\(602\) 4.71912 0.192337
\(603\) −6.91083 −0.281431
\(604\) 5.00624 0.203701
\(605\) 1.00000 0.0406558
\(606\) −5.81971 −0.236410
\(607\) 42.2614 1.71534 0.857669 0.514202i \(-0.171912\pi\)
0.857669 + 0.514202i \(0.171912\pi\)
\(608\) −6.08969 −0.246969
\(609\) 2.35714 0.0955160
\(610\) 11.5570 0.467928
\(611\) −59.3340 −2.40040
\(612\) −16.5447 −0.668778
\(613\) 2.85831 0.115446 0.0577231 0.998333i \(-0.481616\pi\)
0.0577231 + 0.998333i \(0.481616\pi\)
\(614\) 9.54656 0.385268
\(615\) −4.52720 −0.182555
\(616\) −4.71912 −0.190139
\(617\) 15.3058 0.616189 0.308094 0.951356i \(-0.400309\pi\)
0.308094 + 0.951356i \(0.400309\pi\)
\(618\) 2.49454 0.100345
\(619\) −12.5129 −0.502936 −0.251468 0.967866i \(-0.580913\pi\)
−0.251468 + 0.967866i \(0.580913\pi\)
\(620\) 8.04887 0.323250
\(621\) 11.7430 0.471229
\(622\) 16.9195 0.678410
\(623\) −29.1870 −1.16935
\(624\) 3.71176 0.148589
\(625\) 1.00000 0.0400000
\(626\) −19.9949 −0.799158
\(627\) 4.68904 0.187262
\(628\) −3.27661 −0.130751
\(629\) 12.6765 0.505446
\(630\) −11.3594 −0.452570
\(631\) −38.2723 −1.52359 −0.761797 0.647815i \(-0.775683\pi\)
−0.761797 + 0.647815i \(0.775683\pi\)
\(632\) −9.14301 −0.363689
\(633\) −15.5193 −0.616835
\(634\) −28.6527 −1.13794
\(635\) −13.1291 −0.521013
\(636\) 6.20327 0.245976
\(637\) 73.6093 2.91651
\(638\) −0.648686 −0.0256817
\(639\) −6.35020 −0.251210
\(640\) 1.00000 0.0395285
\(641\) −29.2175 −1.15402 −0.577012 0.816736i \(-0.695781\pi\)
−0.577012 + 0.816736i \(0.695781\pi\)
\(642\) −13.9514 −0.550619
\(643\) −13.4890 −0.531953 −0.265977 0.963980i \(-0.585694\pi\)
−0.265977 + 0.963980i \(0.585694\pi\)
\(644\) −13.3102 −0.524496
\(645\) 0.769997 0.0303186
\(646\) −41.8560 −1.64680
\(647\) −14.9960 −0.589554 −0.294777 0.955566i \(-0.595245\pi\)
−0.294777 + 0.955566i \(0.595245\pi\)
\(648\) 4.01546 0.157742
\(649\) 12.7272 0.499585
\(650\) 4.82049 0.189075
\(651\) 29.2473 1.14629
\(652\) 1.81470 0.0710693
\(653\) −37.8833 −1.48249 −0.741245 0.671235i \(-0.765764\pi\)
−0.741245 + 0.671235i \(0.765764\pi\)
\(654\) −7.79353 −0.304751
\(655\) 19.3773 0.757135
\(656\) −5.87951 −0.229556
\(657\) −4.40637 −0.171909
\(658\) −58.0864 −2.26444
\(659\) −37.3822 −1.45620 −0.728101 0.685470i \(-0.759597\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(660\) −0.769997 −0.0299721
\(661\) 28.8056 1.12041 0.560204 0.828355i \(-0.310723\pi\)
0.560204 + 0.828355i \(0.310723\pi\)
\(662\) −16.3489 −0.635419
\(663\) 25.5119 0.990801
\(664\) −2.49005 −0.0966326
\(665\) −28.7380 −1.11441
\(666\) −4.43947 −0.172026
\(667\) −1.82961 −0.0708428
\(668\) −19.9902 −0.773443
\(669\) −2.27684 −0.0880279
\(670\) 2.87102 0.110917
\(671\) −11.5570 −0.446152
\(672\) 3.63371 0.140173
\(673\) −17.9961 −0.693697 −0.346849 0.937921i \(-0.612748\pi\)
−0.346849 + 0.937921i \(0.612748\pi\)
\(674\) 17.2707 0.665242
\(675\) −4.16346 −0.160251
\(676\) 10.2371 0.393734
\(677\) −21.2437 −0.816463 −0.408231 0.912879i \(-0.633854\pi\)
−0.408231 + 0.912879i \(0.633854\pi\)
\(678\) −3.48941 −0.134010
\(679\) 42.3949 1.62697
\(680\) 6.87326 0.263578
\(681\) 7.90238 0.302820
\(682\) −8.04887 −0.308207
\(683\) 35.5322 1.35960 0.679800 0.733397i \(-0.262067\pi\)
0.679800 + 0.733397i \(0.262067\pi\)
\(684\) 14.6585 0.560482
\(685\) 11.6852 0.446467
\(686\) 39.0276 1.49008
\(687\) 6.64682 0.253592
\(688\) 1.00000 0.0381246
\(689\) 38.8349 1.47949
\(690\) −2.17177 −0.0826778
\(691\) 4.62012 0.175758 0.0878788 0.996131i \(-0.471991\pi\)
0.0878788 + 0.996131i \(0.471991\pi\)
\(692\) 14.1771 0.538933
\(693\) 11.3594 0.431509
\(694\) 15.2519 0.578954
\(695\) 0.0272877 0.00103508
\(696\) 0.499486 0.0189330
\(697\) −40.4114 −1.53069
\(698\) −27.0659 −1.02446
\(699\) 11.9963 0.453741
\(700\) 4.71912 0.178366
\(701\) −11.5919 −0.437821 −0.218910 0.975745i \(-0.570250\pi\)
−0.218910 + 0.975745i \(0.570250\pi\)
\(702\) −20.0699 −0.757489
\(703\) −11.2313 −0.423598
\(704\) −1.00000 −0.0376889
\(705\) −9.47769 −0.356950
\(706\) 25.4907 0.959354
\(707\) −35.6675 −1.34142
\(708\) −9.79988 −0.368302
\(709\) −1.41006 −0.0529560 −0.0264780 0.999649i \(-0.508429\pi\)
−0.0264780 + 0.999649i \(0.508429\pi\)
\(710\) 2.63811 0.0990065
\(711\) 22.0082 0.825371
\(712\) −6.18484 −0.231787
\(713\) −22.7017 −0.850187
\(714\) 24.9755 0.934683
\(715\) −4.82049 −0.180276
\(716\) −24.3657 −0.910587
\(717\) 10.1100 0.377564
\(718\) 13.1171 0.489526
\(719\) −26.6089 −0.992346 −0.496173 0.868224i \(-0.665262\pi\)
−0.496173 + 0.868224i \(0.665262\pi\)
\(720\) −2.40710 −0.0897075
\(721\) 15.2884 0.569371
\(722\) 18.0843 0.673027
\(723\) −8.56867 −0.318672
\(724\) 19.6016 0.728487
\(725\) 0.648686 0.0240916
\(726\) 0.769997 0.0285773
\(727\) 11.2988 0.419050 0.209525 0.977803i \(-0.432808\pi\)
0.209525 + 0.977803i \(0.432808\pi\)
\(728\) 22.7485 0.843114
\(729\) −0.0480836 −0.00178087
\(730\) 1.83057 0.0677524
\(731\) 6.87326 0.254217
\(732\) 8.89885 0.328911
\(733\) −16.7737 −0.619550 −0.309775 0.950810i \(-0.600254\pi\)
−0.309775 + 0.950810i \(0.600254\pi\)
\(734\) 3.78574 0.139734
\(735\) 11.7579 0.433698
\(736\) −2.82049 −0.103965
\(737\) −2.87102 −0.105755
\(738\) 14.1526 0.520964
\(739\) 10.3739 0.381612 0.190806 0.981628i \(-0.438890\pi\)
0.190806 + 0.981628i \(0.438890\pi\)
\(740\) 1.84432 0.0677986
\(741\) −22.6035 −0.830359
\(742\) 38.0183 1.39570
\(743\) −34.3670 −1.26080 −0.630401 0.776270i \(-0.717110\pi\)
−0.630401 + 0.776270i \(0.717110\pi\)
\(744\) 6.19761 0.227215
\(745\) 22.0490 0.807811
\(746\) −34.9268 −1.27876
\(747\) 5.99380 0.219302
\(748\) −6.87326 −0.251311
\(749\) −85.5048 −3.12428
\(750\) 0.769997 0.0281163
\(751\) −32.1192 −1.17204 −0.586022 0.810295i \(-0.699307\pi\)
−0.586022 + 0.810295i \(0.699307\pi\)
\(752\) −12.3087 −0.448853
\(753\) 13.4242 0.489207
\(754\) 3.12698 0.113878
\(755\) 5.00624 0.182196
\(756\) −19.6479 −0.714586
\(757\) 27.0969 0.984854 0.492427 0.870354i \(-0.336110\pi\)
0.492427 + 0.870354i \(0.336110\pi\)
\(758\) 34.4499 1.25128
\(759\) 2.17177 0.0788302
\(760\) −6.08969 −0.220896
\(761\) 10.0722 0.365119 0.182559 0.983195i \(-0.441562\pi\)
0.182559 + 0.983195i \(0.441562\pi\)
\(762\) −10.1094 −0.366225
\(763\) −47.7646 −1.72919
\(764\) 8.97018 0.324530
\(765\) −16.5447 −0.598173
\(766\) −31.8557 −1.15099
\(767\) −61.3511 −2.21526
\(768\) 0.769997 0.0277849
\(769\) −4.43828 −0.160049 −0.0800243 0.996793i \(-0.525500\pi\)
−0.0800243 + 0.996793i \(0.525500\pi\)
\(770\) −4.71912 −0.170065
\(771\) −14.8553 −0.534999
\(772\) −18.6940 −0.672812
\(773\) −27.3865 −0.985025 −0.492512 0.870305i \(-0.663921\pi\)
−0.492512 + 0.870305i \(0.663921\pi\)
\(774\) −2.40710 −0.0865216
\(775\) 8.04887 0.289124
\(776\) 8.98364 0.322494
\(777\) 6.70173 0.240423
\(778\) −5.70481 −0.204527
\(779\) 35.8044 1.28282
\(780\) 3.71176 0.132902
\(781\) −2.63811 −0.0943990
\(782\) −19.3859 −0.693240
\(783\) −2.70077 −0.0965178
\(784\) 15.2701 0.545361
\(785\) −3.27661 −0.116947
\(786\) 14.9205 0.532197
\(787\) 10.7649 0.383729 0.191864 0.981421i \(-0.438547\pi\)
0.191864 + 0.981421i \(0.438547\pi\)
\(788\) −20.2277 −0.720581
\(789\) 14.7141 0.523837
\(790\) −9.14301 −0.325294
\(791\) −21.3858 −0.760390
\(792\) 2.40710 0.0855327
\(793\) 55.7103 1.97833
\(794\) −18.1068 −0.642586
\(795\) 6.20327 0.220007
\(796\) 10.2488 0.363258
\(797\) −36.8519 −1.30536 −0.652681 0.757633i \(-0.726356\pi\)
−0.652681 + 0.757633i \(0.726356\pi\)
\(798\) −22.1282 −0.783328
\(799\) −84.6011 −2.99297
\(800\) 1.00000 0.0353553
\(801\) 14.8876 0.526026
\(802\) 13.1359 0.463846
\(803\) −1.83057 −0.0645994
\(804\) 2.21067 0.0779645
\(805\) −13.3102 −0.469124
\(806\) 38.7995 1.36665
\(807\) −15.5988 −0.549103
\(808\) −7.55809 −0.265893
\(809\) −7.39980 −0.260163 −0.130082 0.991503i \(-0.541524\pi\)
−0.130082 + 0.991503i \(0.541524\pi\)
\(810\) 4.01546 0.141089
\(811\) 4.59768 0.161447 0.0807233 0.996737i \(-0.474277\pi\)
0.0807233 + 0.996737i \(0.474277\pi\)
\(812\) 3.06123 0.107428
\(813\) −20.0362 −0.702699
\(814\) −1.84432 −0.0646435
\(815\) 1.81470 0.0635663
\(816\) 5.29239 0.185271
\(817\) −6.08969 −0.213051
\(818\) 27.9862 0.978516
\(819\) −54.7579 −1.91340
\(820\) −5.87951 −0.205321
\(821\) 4.88804 0.170594 0.0852969 0.996356i \(-0.472816\pi\)
0.0852969 + 0.996356i \(0.472816\pi\)
\(822\) 8.99754 0.313825
\(823\) −24.8907 −0.867635 −0.433817 0.901001i \(-0.642834\pi\)
−0.433817 + 0.901001i \(0.642834\pi\)
\(824\) 3.23968 0.112859
\(825\) −0.769997 −0.0268079
\(826\) −60.0610 −2.08979
\(827\) −57.2563 −1.99100 −0.995498 0.0947800i \(-0.969785\pi\)
−0.995498 + 0.0947800i \(0.969785\pi\)
\(828\) 6.78921 0.235941
\(829\) −4.93618 −0.171440 −0.0857202 0.996319i \(-0.527319\pi\)
−0.0857202 + 0.996319i \(0.527319\pi\)
\(830\) −2.49005 −0.0864308
\(831\) −12.3363 −0.427942
\(832\) 4.82049 0.167120
\(833\) 104.955 3.63649
\(834\) 0.0210114 0.000727567 0
\(835\) −19.9902 −0.691788
\(836\) 6.08969 0.210616
\(837\) −33.5111 −1.15831
\(838\) 8.90520 0.307625
\(839\) 26.0555 0.899537 0.449769 0.893145i \(-0.351506\pi\)
0.449769 + 0.893145i \(0.351506\pi\)
\(840\) 3.63371 0.125375
\(841\) −28.5792 −0.985490
\(842\) 10.4484 0.360074
\(843\) −2.82138 −0.0971734
\(844\) −20.1549 −0.693762
\(845\) 10.2371 0.352167
\(846\) 29.6284 1.01864
\(847\) 4.71912 0.162151
\(848\) 8.05623 0.276652
\(849\) 3.36006 0.115317
\(850\) 6.87326 0.235751
\(851\) −5.20189 −0.178318
\(852\) 2.03134 0.0695925
\(853\) 57.1833 1.95792 0.978959 0.204059i \(-0.0654133\pi\)
0.978959 + 0.204059i \(0.0654133\pi\)
\(854\) 54.5388 1.86628
\(855\) 14.6585 0.501310
\(856\) −18.1188 −0.619288
\(857\) −12.8285 −0.438215 −0.219107 0.975701i \(-0.570314\pi\)
−0.219107 + 0.975701i \(0.570314\pi\)
\(858\) −3.71176 −0.126717
\(859\) −45.2051 −1.54238 −0.771189 0.636606i \(-0.780338\pi\)
−0.771189 + 0.636606i \(0.780338\pi\)
\(860\) 1.00000 0.0340997
\(861\) −21.3644 −0.728098
\(862\) −4.68303 −0.159505
\(863\) −18.5139 −0.630222 −0.315111 0.949055i \(-0.602042\pi\)
−0.315111 + 0.949055i \(0.602042\pi\)
\(864\) −4.16346 −0.141644
\(865\) 14.1771 0.482037
\(866\) 26.6316 0.904979
\(867\) 23.2861 0.790836
\(868\) 37.9836 1.28925
\(869\) 9.14301 0.310155
\(870\) 0.499486 0.0169342
\(871\) 13.8397 0.468940
\(872\) −10.1215 −0.342757
\(873\) −21.6246 −0.731880
\(874\) 17.1759 0.580983
\(875\) 4.71912 0.159535
\(876\) 1.40953 0.0476237
\(877\) −30.7168 −1.03723 −0.518617 0.855007i \(-0.673553\pi\)
−0.518617 + 0.855007i \(0.673553\pi\)
\(878\) −18.6380 −0.629002
\(879\) −4.17278 −0.140744
\(880\) −1.00000 −0.0337100
\(881\) 34.9784 1.17845 0.589226 0.807968i \(-0.299433\pi\)
0.589226 + 0.807968i \(0.299433\pi\)
\(882\) −36.7567 −1.23766
\(883\) −42.1301 −1.41779 −0.708895 0.705314i \(-0.750806\pi\)
−0.708895 + 0.705314i \(0.750806\pi\)
\(884\) 33.1325 1.11437
\(885\) −9.79988 −0.329419
\(886\) −17.5322 −0.589007
\(887\) 0.315696 0.0106000 0.00530001 0.999986i \(-0.498313\pi\)
0.00530001 + 0.999986i \(0.498313\pi\)
\(888\) 1.42012 0.0476562
\(889\) −61.9579 −2.07800
\(890\) −6.18484 −0.207316
\(891\) −4.01546 −0.134523
\(892\) −2.95695 −0.0990060
\(893\) 74.9563 2.50832
\(894\) 16.9776 0.567817
\(895\) −24.3657 −0.814454
\(896\) 4.71912 0.157655
\(897\) −10.4690 −0.349549
\(898\) −12.0831 −0.403218
\(899\) 5.22119 0.174136
\(900\) −2.40710 −0.0802368
\(901\) 55.3726 1.84473
\(902\) 5.87951 0.195766
\(903\) 3.63371 0.120922
\(904\) −4.53172 −0.150723
\(905\) 19.6016 0.651579
\(906\) 3.85479 0.128067
\(907\) 3.77433 0.125325 0.0626624 0.998035i \(-0.480041\pi\)
0.0626624 + 0.998035i \(0.480041\pi\)
\(908\) 10.2629 0.340585
\(909\) 18.1931 0.603427
\(910\) 22.7485 0.754104
\(911\) −0.0501735 −0.00166232 −0.000831162 1.00000i \(-0.500265\pi\)
−0.000831162 1.00000i \(0.500265\pi\)
\(912\) −4.68904 −0.155270
\(913\) 2.49005 0.0824085
\(914\) 5.06828 0.167644
\(915\) 8.89885 0.294187
\(916\) 8.63226 0.285218
\(917\) 91.4440 3.01975
\(918\) −28.6165 −0.944486
\(919\) −22.5653 −0.744359 −0.372180 0.928161i \(-0.621389\pi\)
−0.372180 + 0.928161i \(0.621389\pi\)
\(920\) −2.82049 −0.0929887
\(921\) 7.35083 0.242218
\(922\) 10.2649 0.338055
\(923\) 12.7170 0.418584
\(924\) −3.63371 −0.119540
\(925\) 1.84432 0.0606409
\(926\) −15.8848 −0.522007
\(927\) −7.79823 −0.256128
\(928\) 0.648686 0.0212942
\(929\) 41.4602 1.36027 0.680133 0.733089i \(-0.261922\pi\)
0.680133 + 0.733089i \(0.261922\pi\)
\(930\) 6.19761 0.203228
\(931\) −92.9902 −3.04763
\(932\) 15.5796 0.510328
\(933\) 13.0280 0.426517
\(934\) 28.6315 0.936853
\(935\) −6.87326 −0.224780
\(936\) −11.6034 −0.379269
\(937\) −7.37921 −0.241068 −0.120534 0.992709i \(-0.538461\pi\)
−0.120534 + 0.992709i \(0.538461\pi\)
\(938\) 13.5487 0.442380
\(939\) −15.3960 −0.502431
\(940\) −12.3087 −0.401466
\(941\) 0.272822 0.00889373 0.00444686 0.999990i \(-0.498585\pi\)
0.00444686 + 0.999990i \(0.498585\pi\)
\(942\) −2.52298 −0.0822033
\(943\) 16.5831 0.540019
\(944\) −12.7272 −0.414234
\(945\) −19.6479 −0.639145
\(946\) −1.00000 −0.0325128
\(947\) 3.59408 0.116792 0.0583960 0.998293i \(-0.481401\pi\)
0.0583960 + 0.998293i \(0.481401\pi\)
\(948\) −7.04009 −0.228652
\(949\) 8.82424 0.286447
\(950\) −6.08969 −0.197576
\(951\) −22.0625 −0.715426
\(952\) 32.4358 1.05125
\(953\) 9.92898 0.321631 0.160816 0.986984i \(-0.448588\pi\)
0.160816 + 0.986984i \(0.448588\pi\)
\(954\) −19.3922 −0.627845
\(955\) 8.97018 0.290268
\(956\) 13.1299 0.424651
\(957\) −0.499486 −0.0161461
\(958\) 4.26885 0.137920
\(959\) 55.1437 1.78068
\(960\) 0.769997 0.0248516
\(961\) 33.7843 1.08982
\(962\) 8.89053 0.286642
\(963\) 43.6138 1.40544
\(964\) −11.1282 −0.358415
\(965\) −18.6940 −0.601782
\(966\) −10.2488 −0.329751
\(967\) 19.6010 0.630327 0.315163 0.949037i \(-0.397941\pi\)
0.315163 + 0.949037i \(0.397941\pi\)
\(968\) 1.00000 0.0321412
\(969\) −32.2290 −1.03535
\(970\) 8.98364 0.288447
\(971\) −27.5075 −0.882757 −0.441378 0.897321i \(-0.645510\pi\)
−0.441378 + 0.897321i \(0.645510\pi\)
\(972\) 15.5823 0.499801
\(973\) 0.128774 0.00412830
\(974\) 22.1475 0.709653
\(975\) 3.71176 0.118872
\(976\) 11.5570 0.369930
\(977\) 51.1229 1.63557 0.817783 0.575527i \(-0.195203\pi\)
0.817783 + 0.575527i \(0.195203\pi\)
\(978\) 1.39732 0.0446813
\(979\) 6.18484 0.197668
\(980\) 15.2701 0.487786
\(981\) 24.3635 0.777867
\(982\) −25.1815 −0.803573
\(983\) 32.4526 1.03508 0.517539 0.855660i \(-0.326848\pi\)
0.517539 + 0.855660i \(0.326848\pi\)
\(984\) −4.52720 −0.144322
\(985\) −20.2277 −0.644507
\(986\) 4.45859 0.141990
\(987\) −44.7264 −1.42366
\(988\) −29.3553 −0.933915
\(989\) −2.82049 −0.0896863
\(990\) 2.40710 0.0765028
\(991\) 15.4066 0.489408 0.244704 0.969598i \(-0.421309\pi\)
0.244704 + 0.969598i \(0.421309\pi\)
\(992\) 8.04887 0.255552
\(993\) −12.5886 −0.399488
\(994\) 12.4496 0.394876
\(995\) 10.2488 0.324908
\(996\) −1.91733 −0.0607529
\(997\) −12.2555 −0.388136 −0.194068 0.980988i \(-0.562168\pi\)
−0.194068 + 0.980988i \(0.562168\pi\)
\(998\) 25.1495 0.796095
\(999\) −7.67875 −0.242945
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 4730.2.a.be.1.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.be.1.7 12 1.1 even 1 trivial