Properties

Label 1155.2.a.u.1.4
Level 1155
Weight 2
Character 1155.1
Self dual yes
Analytic conductor 9.223
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.13448.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.58874\) of \(x^{4} - 7 x^{2} + 2\)
Character \(\chi\) \(=\) 1155.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58874 q^{2} +1.00000 q^{3} +4.70156 q^{4} -1.00000 q^{5} +2.58874 q^{6} -1.00000 q^{7} +6.99364 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.58874 q^{2} +1.00000 q^{3} +4.70156 q^{4} -1.00000 q^{5} +2.58874 q^{6} -1.00000 q^{7} +6.99364 q^{8} +1.00000 q^{9} -2.58874 q^{10} -1.00000 q^{11} +4.70156 q^{12} +6.40490 q^{13} -2.58874 q^{14} -1.00000 q^{15} +8.70156 q^{16} -3.70156 q^{17} +2.58874 q^{18} +7.24672 q^{19} -4.70156 q^{20} -1.00000 q^{21} -2.58874 q^{22} -7.33388 q^{23} +6.99364 q^{24} +1.00000 q^{25} +16.5806 q^{26} +1.00000 q^{27} -4.70156 q^{28} -8.10646 q^{29} -2.58874 q^{30} +6.77258 q^{31} +8.53879 q^{32} -1.00000 q^{33} -9.58237 q^{34} +1.00000 q^{35} +4.70156 q^{36} -3.95005 q^{37} +18.7598 q^{38} +6.40490 q^{39} -6.99364 q^{40} -2.31773 q^{41} -2.58874 q^{42} -7.65161 q^{43} -4.70156 q^{44} -1.00000 q^{45} -18.9855 q^{46} +1.45307 q^{47} +8.70156 q^{48} +1.00000 q^{49} +2.58874 q^{50} -3.70156 q^{51} +30.1130 q^{52} +9.10823 q^{53} +2.58874 q^{54} +1.00000 q^{55} -6.99364 q^{56} +7.24672 q^{57} -20.9855 q^{58} -2.92898 q^{59} -4.70156 q^{60} -8.42419 q^{61} +17.5324 q^{62} -1.00000 q^{63} +4.70156 q^{64} -6.40490 q^{65} -2.58874 q^{66} -8.72263 q^{67} -17.4031 q^{68} -7.33388 q^{69} +2.58874 q^{70} -4.40490 q^{71} +6.99364 q^{72} +3.40667 q^{73} -10.2256 q^{74} +1.00000 q^{75} +34.0709 q^{76} +1.00000 q^{77} +16.5806 q^{78} +4.40490 q^{79} -8.70156 q^{80} +1.00000 q^{81} -6.00000 q^{82} -8.96620 q^{83} -4.70156 q^{84} +3.70156 q^{85} -19.8080 q^{86} -8.10646 q^{87} -6.99364 q^{88} +0.206355 q^{89} -2.58874 q^{90} -6.40490 q^{91} -34.4807 q^{92} +6.77258 q^{93} +3.76162 q^{94} -7.24672 q^{95} +8.53879 q^{96} -13.9644 q^{97} +2.58874 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + 6q^{4} - 4q^{5} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} + 6q^{4} - 4q^{5} - 4q^{7} + 4q^{9} - 4q^{11} + 6q^{12} + 8q^{13} - 4q^{15} + 22q^{16} - 2q^{17} + 10q^{19} - 6q^{20} - 4q^{21} - 2q^{23} + 4q^{25} + 20q^{26} + 4q^{27} - 6q^{28} - 2q^{29} + 24q^{31} - 4q^{33} + 4q^{35} + 6q^{36} + 8q^{37} + 16q^{38} + 8q^{39} + 6q^{43} - 6q^{44} - 4q^{45} - 12q^{46} + 4q^{47} + 22q^{48} + 4q^{49} - 2q^{51} + 12q^{52} + 14q^{53} + 4q^{55} + 10q^{57} - 20q^{58} - 2q^{59} - 6q^{60} + 6q^{61} + 8q^{62} - 4q^{63} + 6q^{64} - 8q^{65} - 8q^{67} - 44q^{68} - 2q^{69} + 4q^{73} - 36q^{74} + 4q^{75} + 56q^{76} + 4q^{77} + 20q^{78} - 22q^{80} + 4q^{81} - 24q^{82} + 6q^{83} - 6q^{84} + 2q^{85} - 36q^{86} - 2q^{87} + 18q^{89} - 8q^{91} - 44q^{92} + 24q^{93} - 36q^{94} - 10q^{95} - 6q^{97} - 4q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58874 1.83051 0.915257 0.402871i \(-0.131988\pi\)
0.915257 + 0.402871i \(0.131988\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.70156 2.35078
\(5\) −1.00000 −0.447214
\(6\) 2.58874 1.05685
\(7\) −1.00000 −0.377964
\(8\) 6.99364 2.47262
\(9\) 1.00000 0.333333
\(10\) −2.58874 −0.818631
\(11\) −1.00000 −0.301511
\(12\) 4.70156 1.35722
\(13\) 6.40490 1.77640 0.888200 0.459458i \(-0.151956\pi\)
0.888200 + 0.459458i \(0.151956\pi\)
\(14\) −2.58874 −0.691869
\(15\) −1.00000 −0.258199
\(16\) 8.70156 2.17539
\(17\) −3.70156 −0.897761 −0.448880 0.893592i \(-0.648177\pi\)
−0.448880 + 0.893592i \(0.648177\pi\)
\(18\) 2.58874 0.610171
\(19\) 7.24672 1.66251 0.831255 0.555891i \(-0.187623\pi\)
0.831255 + 0.555891i \(0.187623\pi\)
\(20\) −4.70156 −1.05130
\(21\) −1.00000 −0.218218
\(22\) −2.58874 −0.551921
\(23\) −7.33388 −1.52922 −0.764610 0.644493i \(-0.777068\pi\)
−0.764610 + 0.644493i \(0.777068\pi\)
\(24\) 6.99364 1.42757
\(25\) 1.00000 0.200000
\(26\) 16.5806 3.25172
\(27\) 1.00000 0.192450
\(28\) −4.70156 −0.888512
\(29\) −8.10646 −1.50533 −0.752666 0.658403i \(-0.771232\pi\)
−0.752666 + 0.658403i \(0.771232\pi\)
\(30\) −2.58874 −0.472637
\(31\) 6.77258 1.21639 0.608195 0.793787i \(-0.291894\pi\)
0.608195 + 0.793787i \(0.291894\pi\)
\(32\) 8.53879 1.50946
\(33\) −1.00000 −0.174078
\(34\) −9.58237 −1.64336
\(35\) 1.00000 0.169031
\(36\) 4.70156 0.783594
\(37\) −3.95005 −0.649385 −0.324692 0.945820i \(-0.605261\pi\)
−0.324692 + 0.945820i \(0.605261\pi\)
\(38\) 18.7598 3.04325
\(39\) 6.40490 1.02560
\(40\) −6.99364 −1.10579
\(41\) −2.31773 −0.361969 −0.180984 0.983486i \(-0.557928\pi\)
−0.180984 + 0.983486i \(0.557928\pi\)
\(42\) −2.58874 −0.399451
\(43\) −7.65161 −1.16686 −0.583430 0.812163i \(-0.698290\pi\)
−0.583430 + 0.812163i \(0.698290\pi\)
\(44\) −4.70156 −0.708787
\(45\) −1.00000 −0.149071
\(46\) −18.9855 −2.79926
\(47\) 1.45307 0.211952 0.105976 0.994369i \(-0.466203\pi\)
0.105976 + 0.994369i \(0.466203\pi\)
\(48\) 8.70156 1.25596
\(49\) 1.00000 0.142857
\(50\) 2.58874 0.366103
\(51\) −3.70156 −0.518322
\(52\) 30.1130 4.17593
\(53\) 9.10823 1.25111 0.625556 0.780179i \(-0.284872\pi\)
0.625556 + 0.780179i \(0.284872\pi\)
\(54\) 2.58874 0.352283
\(55\) 1.00000 0.134840
\(56\) −6.99364 −0.934564
\(57\) 7.24672 0.959851
\(58\) −20.9855 −2.75553
\(59\) −2.92898 −0.381321 −0.190661 0.981656i \(-0.561063\pi\)
−0.190661 + 0.981656i \(0.561063\pi\)
\(60\) −4.70156 −0.606969
\(61\) −8.42419 −1.07861 −0.539304 0.842111i \(-0.681312\pi\)
−0.539304 + 0.842111i \(0.681312\pi\)
\(62\) 17.5324 2.22662
\(63\) −1.00000 −0.125988
\(64\) 4.70156 0.587695
\(65\) −6.40490 −0.794430
\(66\) −2.58874 −0.318652
\(67\) −8.72263 −1.06564 −0.532819 0.846229i \(-0.678868\pi\)
−0.532819 + 0.846229i \(0.678868\pi\)
\(68\) −17.4031 −2.11044
\(69\) −7.33388 −0.882896
\(70\) 2.58874 0.309413
\(71\) −4.40490 −0.522765 −0.261383 0.965235i \(-0.584178\pi\)
−0.261383 + 0.965235i \(0.584178\pi\)
\(72\) 6.99364 0.824208
\(73\) 3.40667 0.398721 0.199360 0.979926i \(-0.436114\pi\)
0.199360 + 0.979926i \(0.436114\pi\)
\(74\) −10.2256 −1.18871
\(75\) 1.00000 0.115470
\(76\) 34.0709 3.90820
\(77\) 1.00000 0.113961
\(78\) 16.5806 1.87738
\(79\) 4.40490 0.495590 0.247795 0.968813i \(-0.420294\pi\)
0.247795 + 0.968813i \(0.420294\pi\)
\(80\) −8.70156 −0.972864
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) −8.96620 −0.984169 −0.492084 0.870548i \(-0.663765\pi\)
−0.492084 + 0.870548i \(0.663765\pi\)
\(84\) −4.70156 −0.512982
\(85\) 3.70156 0.401491
\(86\) −19.8080 −2.13595
\(87\) −8.10646 −0.869104
\(88\) −6.99364 −0.745524
\(89\) 0.206355 0.0218736 0.0109368 0.999940i \(-0.496519\pi\)
0.0109368 + 0.999940i \(0.496519\pi\)
\(90\) −2.58874 −0.272877
\(91\) −6.40490 −0.671416
\(92\) −34.4807 −3.59486
\(93\) 6.77258 0.702284
\(94\) 3.76162 0.387982
\(95\) −7.24672 −0.743497
\(96\) 8.53879 0.871487
\(97\) −13.9644 −1.41787 −0.708936 0.705272i \(-0.750825\pi\)
−0.708936 + 0.705272i \(0.750825\pi\)
\(98\) 2.58874 0.261502
\(99\) −1.00000 −0.100504
\(100\) 4.70156 0.470156
\(101\) 3.77080 0.375209 0.187605 0.982245i \(-0.439928\pi\)
0.187605 + 0.982245i \(0.439928\pi\)
\(102\) −9.58237 −0.948796
\(103\) −8.56131 −0.843570 −0.421785 0.906696i \(-0.638596\pi\)
−0.421785 + 0.906696i \(0.638596\pi\)
\(104\) 44.7935 4.39237
\(105\) 1.00000 0.0975900
\(106\) 23.5788 2.29018
\(107\) 14.1630 1.36919 0.684593 0.728925i \(-0.259980\pi\)
0.684593 + 0.728925i \(0.259980\pi\)
\(108\) 4.70156 0.452408
\(109\) 7.14026 0.683913 0.341956 0.939716i \(-0.388911\pi\)
0.341956 + 0.939716i \(0.388911\pi\)
\(110\) 2.58874 0.246826
\(111\) −3.95005 −0.374922
\(112\) −8.70156 −0.822220
\(113\) −1.10823 −0.104254 −0.0521269 0.998640i \(-0.516600\pi\)
−0.0521269 + 0.998640i \(0.516600\pi\)
\(114\) 18.7598 1.75702
\(115\) 7.33388 0.683888
\(116\) −38.1130 −3.53871
\(117\) 6.40490 0.592133
\(118\) −7.58237 −0.698014
\(119\) 3.70156 0.339322
\(120\) −6.99364 −0.638429
\(121\) 1.00000 0.0909091
\(122\) −21.8080 −1.97441
\(123\) −2.31773 −0.208983
\(124\) 31.8417 2.85947
\(125\) −1.00000 −0.0894427
\(126\) −2.58874 −0.230623
\(127\) 11.6516 1.03391 0.516957 0.856011i \(-0.327065\pi\)
0.516957 + 0.856011i \(0.327065\pi\)
\(128\) −4.90647 −0.433675
\(129\) −7.65161 −0.673687
\(130\) −16.5806 −1.45421
\(131\) −13.8116 −1.20672 −0.603361 0.797468i \(-0.706172\pi\)
−0.603361 + 0.797468i \(0.706172\pi\)
\(132\) −4.70156 −0.409218
\(133\) −7.24672 −0.628370
\(134\) −22.5806 −1.95067
\(135\) −1.00000 −0.0860663
\(136\) −25.8874 −2.21982
\(137\) 9.40312 0.803363 0.401682 0.915779i \(-0.368426\pi\)
0.401682 + 0.915779i \(0.368426\pi\)
\(138\) −18.9855 −1.61615
\(139\) 16.3128 1.38363 0.691817 0.722072i \(-0.256810\pi\)
0.691817 + 0.722072i \(0.256810\pi\)
\(140\) 4.70156 0.397355
\(141\) 1.45307 0.122371
\(142\) −11.4031 −0.956929
\(143\) −6.40490 −0.535604
\(144\) 8.70156 0.725130
\(145\) 8.10646 0.673205
\(146\) 8.81898 0.729864
\(147\) 1.00000 0.0824786
\(148\) −18.5714 −1.52656
\(149\) 9.90010 0.811048 0.405524 0.914084i \(-0.367089\pi\)
0.405524 + 0.914084i \(0.367089\pi\)
\(150\) 2.58874 0.211370
\(151\) −17.7581 −1.44513 −0.722566 0.691302i \(-0.757037\pi\)
−0.722566 + 0.691302i \(0.757037\pi\)
\(152\) 50.6809 4.11076
\(153\) −3.70156 −0.299254
\(154\) 2.58874 0.208606
\(155\) −6.77258 −0.543987
\(156\) 30.1130 2.41097
\(157\) 17.0547 1.36112 0.680558 0.732694i \(-0.261737\pi\)
0.680558 + 0.732694i \(0.261737\pi\)
\(158\) 11.4031 0.907184
\(159\) 9.10823 0.722330
\(160\) −8.53879 −0.675051
\(161\) 7.33388 0.577991
\(162\) 2.58874 0.203390
\(163\) −19.9338 −1.56133 −0.780667 0.624947i \(-0.785120\pi\)
−0.780667 + 0.624947i \(0.785120\pi\)
\(164\) −10.8970 −0.850910
\(165\) 1.00000 0.0778499
\(166\) −23.2111 −1.80153
\(167\) −2.95183 −0.228419 −0.114210 0.993457i \(-0.536434\pi\)
−0.114210 + 0.993457i \(0.536434\pi\)
\(168\) −6.99364 −0.539571
\(169\) 28.0227 2.15559
\(170\) 9.58237 0.734934
\(171\) 7.24672 0.554170
\(172\) −35.9745 −2.74303
\(173\) 20.2094 1.53649 0.768245 0.640156i \(-0.221130\pi\)
0.768245 + 0.640156i \(0.221130\pi\)
\(174\) −20.9855 −1.59091
\(175\) −1.00000 −0.0755929
\(176\) −8.70156 −0.655905
\(177\) −2.92898 −0.220156
\(178\) 0.534199 0.0400399
\(179\) 5.95005 0.444728 0.222364 0.974964i \(-0.428623\pi\)
0.222364 + 0.974964i \(0.428623\pi\)
\(180\) −4.70156 −0.350434
\(181\) −20.0709 −1.49186 −0.745929 0.666026i \(-0.767994\pi\)
−0.745929 + 0.666026i \(0.767994\pi\)
\(182\) −16.5806 −1.22904
\(183\) −8.42419 −0.622734
\(184\) −51.2905 −3.78119
\(185\) 3.95005 0.290414
\(186\) 17.5324 1.28554
\(187\) 3.70156 0.270685
\(188\) 6.83171 0.498253
\(189\) −1.00000 −0.0727393
\(190\) −18.7598 −1.36098
\(191\) 19.7159 1.42660 0.713298 0.700861i \(-0.247201\pi\)
0.713298 + 0.700861i \(0.247201\pi\)
\(192\) 4.70156 0.339306
\(193\) −5.49029 −0.395200 −0.197600 0.980283i \(-0.563315\pi\)
−0.197600 + 0.980283i \(0.563315\pi\)
\(194\) −36.1502 −2.59544
\(195\) −6.40490 −0.458664
\(196\) 4.70156 0.335826
\(197\) 20.4421 1.45644 0.728220 0.685343i \(-0.240348\pi\)
0.728220 + 0.685343i \(0.240348\pi\)
\(198\) −2.58874 −0.183974
\(199\) 22.9391 1.62611 0.813055 0.582187i \(-0.197803\pi\)
0.813055 + 0.582187i \(0.197803\pi\)
\(200\) 6.99364 0.494525
\(201\) −8.72263 −0.615247
\(202\) 9.76162 0.686825
\(203\) 8.10646 0.568962
\(204\) −17.4031 −1.21846
\(205\) 2.31773 0.161877
\(206\) −22.1630 −1.54417
\(207\) −7.33388 −0.509740
\(208\) 55.7326 3.86436
\(209\) −7.24672 −0.501266
\(210\) 2.58874 0.178640
\(211\) −6.59333 −0.453903 −0.226952 0.973906i \(-0.572876\pi\)
−0.226952 + 0.973906i \(0.572876\pi\)
\(212\) 42.8229 2.94109
\(213\) −4.40490 −0.301819
\(214\) 36.6642 2.50631
\(215\) 7.65161 0.521836
\(216\) 6.99364 0.475857
\(217\) −6.77258 −0.459753
\(218\) 18.4843 1.25191
\(219\) 3.40667 0.230202
\(220\) 4.70156 0.316979
\(221\) −23.7081 −1.59478
\(222\) −10.2256 −0.686301
\(223\) 11.0162 0.737696 0.368848 0.929490i \(-0.379752\pi\)
0.368848 + 0.929490i \(0.379752\pi\)
\(224\) −8.53879 −0.570522
\(225\) 1.00000 0.0666667
\(226\) −2.86893 −0.190838
\(227\) −21.0048 −1.39414 −0.697068 0.717005i \(-0.745513\pi\)
−0.697068 + 0.717005i \(0.745513\pi\)
\(228\) 34.0709 2.25640
\(229\) −19.5661 −1.29296 −0.646482 0.762929i \(-0.723760\pi\)
−0.646482 + 0.762929i \(0.723760\pi\)
\(230\) 18.9855 1.25187
\(231\) 1.00000 0.0657952
\(232\) −56.6936 −3.72212
\(233\) 16.3886 1.07365 0.536827 0.843692i \(-0.319623\pi\)
0.536827 + 0.843692i \(0.319623\pi\)
\(234\) 16.5806 1.08391
\(235\) −1.45307 −0.0947880
\(236\) −13.7708 −0.896403
\(237\) 4.40490 0.286129
\(238\) 9.58237 0.621133
\(239\) 18.0066 1.16475 0.582374 0.812921i \(-0.302124\pi\)
0.582374 + 0.812921i \(0.302124\pi\)
\(240\) −8.70156 −0.561683
\(241\) 27.0740 1.74399 0.871996 0.489513i \(-0.162826\pi\)
0.871996 + 0.489513i \(0.162826\pi\)
\(242\) 2.58874 0.166410
\(243\) 1.00000 0.0641500
\(244\) −39.6069 −2.53557
\(245\) −1.00000 −0.0638877
\(246\) −6.00000 −0.382546
\(247\) 46.4145 2.95328
\(248\) 47.3649 3.00768
\(249\) −8.96620 −0.568210
\(250\) −2.58874 −0.163726
\(251\) 8.58415 0.541827 0.270913 0.962604i \(-0.412674\pi\)
0.270913 + 0.962604i \(0.412674\pi\)
\(252\) −4.70156 −0.296171
\(253\) 7.33388 0.461077
\(254\) 30.1630 1.89259
\(255\) 3.70156 0.231801
\(256\) −22.1047 −1.38154
\(257\) 0.0885359 0.00552272 0.00276136 0.999996i \(-0.499121\pi\)
0.00276136 + 0.999996i \(0.499121\pi\)
\(258\) −19.8080 −1.23319
\(259\) 3.95005 0.245444
\(260\) −30.1130 −1.86753
\(261\) −8.10646 −0.501777
\(262\) −35.7545 −2.20892
\(263\) −17.5452 −1.08188 −0.540940 0.841061i \(-0.681932\pi\)
−0.540940 + 0.841061i \(0.681932\pi\)
\(264\) −6.99364 −0.430428
\(265\) −9.10823 −0.559514
\(266\) −18.7598 −1.15024
\(267\) 0.206355 0.0126287
\(268\) −41.0100 −2.50508
\(269\) 12.2520 0.747020 0.373510 0.927626i \(-0.378154\pi\)
0.373510 + 0.927626i \(0.378154\pi\)
\(270\) −2.58874 −0.157546
\(271\) −1.91448 −0.116296 −0.0581482 0.998308i \(-0.518520\pi\)
−0.0581482 + 0.998308i \(0.518520\pi\)
\(272\) −32.2094 −1.95298
\(273\) −6.40490 −0.387642
\(274\) 24.3422 1.47057
\(275\) −1.00000 −0.0603023
\(276\) −34.4807 −2.07549
\(277\) 5.62877 0.338200 0.169100 0.985599i \(-0.445914\pi\)
0.169100 + 0.985599i \(0.445914\pi\)
\(278\) 42.2296 2.53276
\(279\) 6.77258 0.405464
\(280\) 6.99364 0.417950
\(281\) −29.3032 −1.74808 −0.874042 0.485850i \(-0.838510\pi\)
−0.874042 + 0.485850i \(0.838510\pi\)
\(282\) 3.76162 0.224001
\(283\) 6.89833 0.410063 0.205032 0.978755i \(-0.434270\pi\)
0.205032 + 0.978755i \(0.434270\pi\)
\(284\) −20.7099 −1.22891
\(285\) −7.24672 −0.429258
\(286\) −16.5806 −0.980431
\(287\) 2.31773 0.136811
\(288\) 8.53879 0.503153
\(289\) −3.29844 −0.194026
\(290\) 20.9855 1.23231
\(291\) −13.9644 −0.818609
\(292\) 16.0167 0.937305
\(293\) −28.7243 −1.67809 −0.839045 0.544062i \(-0.816886\pi\)
−0.839045 + 0.544062i \(0.816886\pi\)
\(294\) 2.58874 0.150978
\(295\) 2.92898 0.170532
\(296\) −27.6252 −1.60568
\(297\) −1.00000 −0.0580259
\(298\) 25.6288 1.48463
\(299\) −46.9728 −2.71651
\(300\) 4.70156 0.271445
\(301\) 7.65161 0.441032
\(302\) −45.9710 −2.64533
\(303\) 3.77080 0.216627
\(304\) 63.0578 3.61661
\(305\) 8.42419 0.482368
\(306\) −9.58237 −0.547788
\(307\) 15.7616 0.899563 0.449782 0.893139i \(-0.351502\pi\)
0.449782 + 0.893139i \(0.351502\pi\)
\(308\) 4.70156 0.267896
\(309\) −8.56131 −0.487036
\(310\) −17.5324 −0.995775
\(311\) 18.7549 1.06349 0.531747 0.846903i \(-0.321536\pi\)
0.531747 + 0.846903i \(0.321536\pi\)
\(312\) 44.7935 2.53593
\(313\) 8.45786 0.478067 0.239033 0.971011i \(-0.423169\pi\)
0.239033 + 0.971011i \(0.423169\pi\)
\(314\) 44.1502 2.49154
\(315\) 1.00000 0.0563436
\(316\) 20.7099 1.16502
\(317\) −12.8519 −0.721836 −0.360918 0.932597i \(-0.617537\pi\)
−0.360918 + 0.932597i \(0.617537\pi\)
\(318\) 23.5788 1.32223
\(319\) 8.10646 0.453875
\(320\) −4.70156 −0.262825
\(321\) 14.1630 0.790500
\(322\) 18.9855 1.05802
\(323\) −26.8242 −1.49254
\(324\) 4.70156 0.261198
\(325\) 6.40490 0.355280
\(326\) −51.6033 −2.85804
\(327\) 7.14026 0.394857
\(328\) −16.2094 −0.895013
\(329\) −1.45307 −0.0801104
\(330\) 2.58874 0.142505
\(331\) −6.64984 −0.365508 −0.182754 0.983159i \(-0.558501\pi\)
−0.182754 + 0.983159i \(0.558501\pi\)
\(332\) −42.1552 −2.31356
\(333\) −3.95005 −0.216462
\(334\) −7.64150 −0.418124
\(335\) 8.72263 0.476568
\(336\) −8.70156 −0.474709
\(337\) −18.0228 −0.981767 −0.490883 0.871225i \(-0.663326\pi\)
−0.490883 + 0.871225i \(0.663326\pi\)
\(338\) 72.5435 3.94584
\(339\) −1.10823 −0.0601910
\(340\) 17.4031 0.943817
\(341\) −6.77258 −0.366756
\(342\) 18.7598 1.01442
\(343\) −1.00000 −0.0539949
\(344\) −53.5126 −2.88521
\(345\) 7.33388 0.394843
\(346\) 52.3168 2.81257
\(347\) −2.00355 −0.107556 −0.0537780 0.998553i \(-0.517126\pi\)
−0.0537780 + 0.998553i \(0.517126\pi\)
\(348\) −38.1130 −2.04307
\(349\) 1.15955 0.0620693 0.0310347 0.999518i \(-0.490120\pi\)
0.0310347 + 0.999518i \(0.490120\pi\)
\(350\) −2.58874 −0.138374
\(351\) 6.40490 0.341868
\(352\) −8.53879 −0.455119
\(353\) 29.6160 1.57630 0.788151 0.615481i \(-0.211038\pi\)
0.788151 + 0.615481i \(0.211038\pi\)
\(354\) −7.58237 −0.402999
\(355\) 4.40490 0.233788
\(356\) 0.970191 0.0514200
\(357\) 3.70156 0.195907
\(358\) 15.4031 0.814080
\(359\) −22.4650 −1.18566 −0.592828 0.805329i \(-0.701988\pi\)
−0.592828 + 0.805329i \(0.701988\pi\)
\(360\) −6.99364 −0.368597
\(361\) 33.5149 1.76394
\(362\) −51.9583 −2.73087
\(363\) 1.00000 0.0524864
\(364\) −30.1130 −1.57835
\(365\) −3.40667 −0.178313
\(366\) −21.8080 −1.13992
\(367\) 5.12233 0.267384 0.133692 0.991023i \(-0.457317\pi\)
0.133692 + 0.991023i \(0.457317\pi\)
\(368\) −63.8162 −3.32665
\(369\) −2.31773 −0.120656
\(370\) 10.2256 0.531606
\(371\) −9.10823 −0.472876
\(372\) 31.8417 1.65091
\(373\) −26.2358 −1.35844 −0.679218 0.733936i \(-0.737681\pi\)
−0.679218 + 0.733936i \(0.737681\pi\)
\(374\) 9.58237 0.495493
\(375\) −1.00000 −0.0516398
\(376\) 10.1623 0.524078
\(377\) −51.9210 −2.67407
\(378\) −2.58874 −0.133150
\(379\) −9.60167 −0.493205 −0.246602 0.969117i \(-0.579314\pi\)
−0.246602 + 0.969117i \(0.579314\pi\)
\(380\) −34.0709 −1.74780
\(381\) 11.6516 0.596930
\(382\) 51.0394 2.61140
\(383\) 10.1244 0.517332 0.258666 0.965967i \(-0.416717\pi\)
0.258666 + 0.965967i \(0.416717\pi\)
\(384\) −4.90647 −0.250382
\(385\) −1.00000 −0.0509647
\(386\) −14.2129 −0.723419
\(387\) −7.65161 −0.388953
\(388\) −65.6546 −3.33311
\(389\) 16.9342 0.858597 0.429298 0.903163i \(-0.358761\pi\)
0.429298 + 0.903163i \(0.358761\pi\)
\(390\) −16.5806 −0.839591
\(391\) 27.1468 1.37287
\(392\) 6.99364 0.353232
\(393\) −13.8116 −0.696701
\(394\) 52.9193 2.66603
\(395\) −4.40490 −0.221634
\(396\) −4.70156 −0.236262
\(397\) 13.7616 0.690676 0.345338 0.938478i \(-0.387764\pi\)
0.345338 + 0.938478i \(0.387764\pi\)
\(398\) 59.3833 2.97662
\(399\) −7.24672 −0.362790
\(400\) 8.70156 0.435078
\(401\) 35.6118 1.77837 0.889184 0.457550i \(-0.151273\pi\)
0.889184 + 0.457550i \(0.151273\pi\)
\(402\) −22.5806 −1.12622
\(403\) 43.3777 2.16080
\(404\) 17.7287 0.882034
\(405\) −1.00000 −0.0496904
\(406\) 20.9855 1.04149
\(407\) 3.95005 0.195797
\(408\) −25.8874 −1.28162
\(409\) 9.17748 0.453797 0.226898 0.973918i \(-0.427141\pi\)
0.226898 + 0.973918i \(0.427141\pi\)
\(410\) 6.00000 0.296319
\(411\) 9.40312 0.463822
\(412\) −40.2515 −1.98305
\(413\) 2.92898 0.144126
\(414\) −18.9855 −0.933086
\(415\) 8.96620 0.440134
\(416\) 54.6901 2.68140
\(417\) 16.3128 0.798842
\(418\) −18.7598 −0.917574
\(419\) 37.8554 1.84935 0.924677 0.380751i \(-0.124335\pi\)
0.924677 + 0.380751i \(0.124335\pi\)
\(420\) 4.70156 0.229413
\(421\) 3.10469 0.151313 0.0756566 0.997134i \(-0.475895\pi\)
0.0756566 + 0.997134i \(0.475895\pi\)
\(422\) −17.0684 −0.830877
\(423\) 1.45307 0.0706508
\(424\) 63.6997 3.09353
\(425\) −3.70156 −0.179552
\(426\) −11.4031 −0.552483
\(427\) 8.42419 0.407675
\(428\) 66.5881 3.21866
\(429\) −6.40490 −0.309231
\(430\) 19.8080 0.955228
\(431\) −10.4548 −0.503592 −0.251796 0.967780i \(-0.581021\pi\)
−0.251796 + 0.967780i \(0.581021\pi\)
\(432\) 8.70156 0.418654
\(433\) −7.82212 −0.375907 −0.187954 0.982178i \(-0.560185\pi\)
−0.187954 + 0.982178i \(0.560185\pi\)
\(434\) −17.5324 −0.841583
\(435\) 8.10646 0.388675
\(436\) 33.5704 1.60773
\(437\) −53.1466 −2.54235
\(438\) 8.81898 0.421387
\(439\) −29.8146 −1.42297 −0.711486 0.702700i \(-0.751978\pi\)
−0.711486 + 0.702700i \(0.751978\pi\)
\(440\) 6.99364 0.333408
\(441\) 1.00000 0.0476190
\(442\) −61.3741 −2.91927
\(443\) −11.2774 −0.535804 −0.267902 0.963446i \(-0.586330\pi\)
−0.267902 + 0.963446i \(0.586330\pi\)
\(444\) −18.5714 −0.881360
\(445\) −0.206355 −0.00978216
\(446\) 28.5179 1.35036
\(447\) 9.90010 0.468259
\(448\) −4.70156 −0.222128
\(449\) 11.2787 0.532277 0.266138 0.963935i \(-0.414252\pi\)
0.266138 + 0.963935i \(0.414252\pi\)
\(450\) 2.58874 0.122034
\(451\) 2.31773 0.109138
\(452\) −5.21043 −0.245078
\(453\) −17.7581 −0.834347
\(454\) −54.3759 −2.55199
\(455\) 6.40490 0.300266
\(456\) 50.6809 2.37335
\(457\) −0.403250 −0.0188632 −0.00943162 0.999956i \(-0.503002\pi\)
−0.00943162 + 0.999956i \(0.503002\pi\)
\(458\) −50.6515 −2.36679
\(459\) −3.70156 −0.172774
\(460\) 34.4807 1.60767
\(461\) 34.9355 1.62711 0.813555 0.581487i \(-0.197529\pi\)
0.813555 + 0.581487i \(0.197529\pi\)
\(462\) 2.58874 0.120439
\(463\) 4.36413 0.202818 0.101409 0.994845i \(-0.467665\pi\)
0.101409 + 0.994845i \(0.467665\pi\)
\(464\) −70.5389 −3.27468
\(465\) −6.77258 −0.314071
\(466\) 42.4258 1.96534
\(467\) −30.2551 −1.40004 −0.700018 0.714125i \(-0.746825\pi\)
−0.700018 + 0.714125i \(0.746825\pi\)
\(468\) 30.1130 1.39198
\(469\) 8.72263 0.402774
\(470\) −3.76162 −0.173511
\(471\) 17.0547 0.785841
\(472\) −20.4843 −0.942864
\(473\) 7.65161 0.351822
\(474\) 11.4031 0.523763
\(475\) 7.24672 0.332502
\(476\) 17.4031 0.797671
\(477\) 9.10823 0.417037
\(478\) 46.6143 2.13209
\(479\) 11.8151 0.539846 0.269923 0.962882i \(-0.413002\pi\)
0.269923 + 0.962882i \(0.413002\pi\)
\(480\) −8.53879 −0.389741
\(481\) −25.2997 −1.15357
\(482\) 70.0876 3.19240
\(483\) 7.33388 0.333703
\(484\) 4.70156 0.213707
\(485\) 13.9644 0.634092
\(486\) 2.58874 0.117428
\(487\) 36.3387 1.64666 0.823331 0.567561i \(-0.192113\pi\)
0.823331 + 0.567561i \(0.192113\pi\)
\(488\) −58.9157 −2.66699
\(489\) −19.9338 −0.901437
\(490\) −2.58874 −0.116947
\(491\) −41.4554 −1.87085 −0.935427 0.353519i \(-0.884985\pi\)
−0.935427 + 0.353519i \(0.884985\pi\)
\(492\) −10.8970 −0.491273
\(493\) 30.0066 1.35143
\(494\) 120.155 5.40602
\(495\) 1.00000 0.0449467
\(496\) 58.9320 2.64613
\(497\) 4.40490 0.197587
\(498\) −23.2111 −1.04012
\(499\) 2.41146 0.107952 0.0539759 0.998542i \(-0.482811\pi\)
0.0539759 + 0.998542i \(0.482811\pi\)
\(500\) −4.70156 −0.210260
\(501\) −2.95183 −0.131878
\(502\) 22.2221 0.991821
\(503\) −24.3335 −1.08498 −0.542488 0.840063i \(-0.682518\pi\)
−0.542488 + 0.840063i \(0.682518\pi\)
\(504\) −6.99364 −0.311521
\(505\) −3.77080 −0.167799
\(506\) 18.9855 0.844008
\(507\) 28.0227 1.24453
\(508\) 54.7808 2.43050
\(509\) 21.3388 0.945826 0.472913 0.881109i \(-0.343203\pi\)
0.472913 + 0.881109i \(0.343203\pi\)
\(510\) 9.58237 0.424315
\(511\) −3.40667 −0.150702
\(512\) −47.4103 −2.09526
\(513\) 7.24672 0.319950
\(514\) 0.229196 0.0101094
\(515\) 8.56131 0.377256
\(516\) −35.9745 −1.58369
\(517\) −1.45307 −0.0639060
\(518\) 10.2256 0.449289
\(519\) 20.2094 0.887093
\(520\) −44.7935 −1.96433
\(521\) 2.03557 0.0891800 0.0445900 0.999005i \(-0.485802\pi\)
0.0445900 + 0.999005i \(0.485802\pi\)
\(522\) −20.9855 −0.918510
\(523\) −11.1647 −0.488200 −0.244100 0.969750i \(-0.578493\pi\)
−0.244100 + 0.969750i \(0.578493\pi\)
\(524\) −64.9359 −2.83674
\(525\) −1.00000 −0.0436436
\(526\) −45.4198 −1.98040
\(527\) −25.0691 −1.09203
\(528\) −8.70156 −0.378687
\(529\) 30.7858 1.33851
\(530\) −23.5788 −1.02420
\(531\) −2.92898 −0.127107
\(532\) −34.0709 −1.47716
\(533\) −14.8448 −0.643001
\(534\) 0.534199 0.0231170
\(535\) −14.1630 −0.612319
\(536\) −61.0029 −2.63492
\(537\) 5.95005 0.256764
\(538\) 31.7173 1.36743
\(539\) −1.00000 −0.0430730
\(540\) −4.70156 −0.202323
\(541\) −37.8212 −1.62606 −0.813029 0.582223i \(-0.802183\pi\)
−0.813029 + 0.582223i \(0.802183\pi\)
\(542\) −4.95609 −0.212882
\(543\) −20.0709 −0.861324
\(544\) −31.6069 −1.35513
\(545\) −7.14026 −0.305855
\(546\) −16.5806 −0.709584
\(547\) −32.2871 −1.38050 −0.690248 0.723573i \(-0.742499\pi\)
−0.690248 + 0.723573i \(0.742499\pi\)
\(548\) 44.2094 1.88853
\(549\) −8.42419 −0.359536
\(550\) −2.58874 −0.110384
\(551\) −58.7452 −2.50263
\(552\) −51.2905 −2.18307
\(553\) −4.40490 −0.187315
\(554\) 14.5714 0.619080
\(555\) 3.95005 0.167670
\(556\) 76.6957 3.25262
\(557\) 17.9416 0.760209 0.380105 0.924943i \(-0.375888\pi\)
0.380105 + 0.924943i \(0.375888\pi\)
\(558\) 17.5324 0.742207
\(559\) −49.0078 −2.07281
\(560\) 8.70156 0.367708
\(561\) 3.70156 0.156280
\(562\) −75.8584 −3.19989
\(563\) −1.40667 −0.0592841 −0.0296421 0.999561i \(-0.509437\pi\)
−0.0296421 + 0.999561i \(0.509437\pi\)
\(564\) 6.83171 0.287667
\(565\) 1.10823 0.0466237
\(566\) 17.8580 0.750626
\(567\) −1.00000 −0.0419961
\(568\) −30.8062 −1.29260
\(569\) 9.36755 0.392708 0.196354 0.980533i \(-0.437090\pi\)
0.196354 + 0.980533i \(0.437090\pi\)
\(570\) −18.7598 −0.785764
\(571\) −24.8562 −1.04020 −0.520100 0.854106i \(-0.674105\pi\)
−0.520100 + 0.854106i \(0.674105\pi\)
\(572\) −30.1130 −1.25909
\(573\) 19.7159 0.823645
\(574\) 6.00000 0.250435
\(575\) −7.33388 −0.305844
\(576\) 4.70156 0.195898
\(577\) 6.17433 0.257041 0.128520 0.991707i \(-0.458977\pi\)
0.128520 + 0.991707i \(0.458977\pi\)
\(578\) −8.53879 −0.355167
\(579\) −5.49029 −0.228169
\(580\) 38.1130 1.58256
\(581\) 8.96620 0.371981
\(582\) −36.1502 −1.49848
\(583\) −9.10823 −0.377224
\(584\) 23.8250 0.985886
\(585\) −6.40490 −0.264810
\(586\) −74.3596 −3.07177
\(587\) 2.04995 0.0846104 0.0423052 0.999105i \(-0.486530\pi\)
0.0423052 + 0.999105i \(0.486530\pi\)
\(588\) 4.70156 0.193889
\(589\) 49.0790 2.02226
\(590\) 7.58237 0.312161
\(591\) 20.4421 0.840876
\(592\) −34.3716 −1.41267
\(593\) −7.85797 −0.322688 −0.161344 0.986898i \(-0.551583\pi\)
−0.161344 + 0.986898i \(0.551583\pi\)
\(594\) −2.58874 −0.106217
\(595\) −3.70156 −0.151749
\(596\) 46.5460 1.90660
\(597\) 22.9391 0.938835
\(598\) −121.600 −4.97260
\(599\) −11.2190 −0.458394 −0.229197 0.973380i \(-0.573610\pi\)
−0.229197 + 0.973380i \(0.573610\pi\)
\(600\) 6.99364 0.285514
\(601\) 19.5047 0.795612 0.397806 0.917470i \(-0.369772\pi\)
0.397806 + 0.917470i \(0.369772\pi\)
\(602\) 19.8080 0.807315
\(603\) −8.72263 −0.355213
\(604\) −83.4907 −3.39719
\(605\) −1.00000 −0.0406558
\(606\) 9.76162 0.396539
\(607\) −16.9483 −0.687909 −0.343955 0.938986i \(-0.611767\pi\)
−0.343955 + 0.938986i \(0.611767\pi\)
\(608\) 61.8782 2.50949
\(609\) 8.10646 0.328490
\(610\) 21.8080 0.882981
\(611\) 9.30678 0.376512
\(612\) −17.4031 −0.703480
\(613\) −12.3964 −0.500687 −0.250344 0.968157i \(-0.580544\pi\)
−0.250344 + 0.968157i \(0.580544\pi\)
\(614\) 40.8027 1.64666
\(615\) 2.31773 0.0934600
\(616\) 6.99364 0.281782
\(617\) −21.0192 −0.846200 −0.423100 0.906083i \(-0.639058\pi\)
−0.423100 + 0.906083i \(0.639058\pi\)
\(618\) −22.1630 −0.891525
\(619\) 11.5289 0.463385 0.231692 0.972789i \(-0.425574\pi\)
0.231692 + 0.972789i \(0.425574\pi\)
\(620\) −31.8417 −1.27879
\(621\) −7.33388 −0.294299
\(622\) 48.5516 1.94674
\(623\) −0.206355 −0.00826744
\(624\) 55.7326 2.23109
\(625\) 1.00000 0.0400000
\(626\) 21.8952 0.875108
\(627\) −7.24672 −0.289406
\(628\) 80.1839 3.19969
\(629\) 14.6214 0.582992
\(630\) 2.58874 0.103138
\(631\) 33.9988 1.35347 0.676734 0.736227i \(-0.263395\pi\)
0.676734 + 0.736227i \(0.263395\pi\)
\(632\) 30.8062 1.22541
\(633\) −6.59333 −0.262061
\(634\) −33.2703 −1.32133
\(635\) −11.6516 −0.462380
\(636\) 42.8229 1.69804
\(637\) 6.40490 0.253771
\(638\) 20.9855 0.830824
\(639\) −4.40490 −0.174255
\(640\) 4.90647 0.193945
\(641\) −20.5293 −0.810858 −0.405429 0.914127i \(-0.632878\pi\)
−0.405429 + 0.914127i \(0.632878\pi\)
\(642\) 36.6642 1.44702
\(643\) −16.9584 −0.668774 −0.334387 0.942436i \(-0.608529\pi\)
−0.334387 + 0.942436i \(0.608529\pi\)
\(644\) 34.4807 1.35873
\(645\) 7.65161 0.301282
\(646\) −69.4407 −2.73211
\(647\) −2.25506 −0.0886554 −0.0443277 0.999017i \(-0.514115\pi\)
−0.0443277 + 0.999017i \(0.514115\pi\)
\(648\) 6.99364 0.274736
\(649\) 2.92898 0.114973
\(650\) 16.5806 0.650345
\(651\) −6.77258 −0.265438
\(652\) −93.7199 −3.67035
\(653\) 1.98917 0.0778422 0.0389211 0.999242i \(-0.487608\pi\)
0.0389211 + 0.999242i \(0.487608\pi\)
\(654\) 18.4843 0.722791
\(655\) 13.8116 0.539663
\(656\) −20.1679 −0.787424
\(657\) 3.40667 0.132907
\(658\) −3.76162 −0.146643
\(659\) 3.41324 0.132961 0.0664804 0.997788i \(-0.478823\pi\)
0.0664804 + 0.997788i \(0.478823\pi\)
\(660\) 4.70156 0.183008
\(661\) 15.4988 0.602832 0.301416 0.953493i \(-0.402541\pi\)
0.301416 + 0.953493i \(0.402541\pi\)
\(662\) −17.2147 −0.669068
\(663\) −23.7081 −0.920747
\(664\) −62.7064 −2.43348
\(665\) 7.24672 0.281016
\(666\) −10.2256 −0.396236
\(667\) 59.4518 2.30198
\(668\) −13.8782 −0.536963
\(669\) 11.0162 0.425909
\(670\) 22.5806 0.872365
\(671\) 8.42419 0.325212
\(672\) −8.53879 −0.329391
\(673\) −40.6449 −1.56675 −0.783373 0.621551i \(-0.786503\pi\)
−0.783373 + 0.621551i \(0.786503\pi\)
\(674\) −46.6564 −1.79714
\(675\) 1.00000 0.0384900
\(676\) 131.751 5.06733
\(677\) 41.1756 1.58251 0.791253 0.611489i \(-0.209429\pi\)
0.791253 + 0.611489i \(0.209429\pi\)
\(678\) −2.86893 −0.110180
\(679\) 13.9644 0.535906
\(680\) 25.8874 0.992736
\(681\) −21.0048 −0.804905
\(682\) −17.5324 −0.671351
\(683\) 4.86111 0.186005 0.0930027 0.995666i \(-0.470353\pi\)
0.0930027 + 0.995666i \(0.470353\pi\)
\(684\) 34.0709 1.30273
\(685\) −9.40312 −0.359275
\(686\) −2.58874 −0.0988385
\(687\) −19.5661 −0.746493
\(688\) −66.5810 −2.53838
\(689\) 58.3373 2.22247
\(690\) 18.9855 0.722766
\(691\) 41.8838 1.59334 0.796668 0.604417i \(-0.206594\pi\)
0.796668 + 0.604417i \(0.206594\pi\)
\(692\) 95.0156 3.61195
\(693\) 1.00000 0.0379869
\(694\) −5.18666 −0.196883
\(695\) −16.3128 −0.618780
\(696\) −56.6936 −2.14897
\(697\) 8.57923 0.324961
\(698\) 3.00177 0.113619
\(699\) 16.3886 0.619875
\(700\) −4.70156 −0.177702
\(701\) 4.10646 0.155099 0.0775494 0.996989i \(-0.475290\pi\)
0.0775494 + 0.996989i \(0.475290\pi\)
\(702\) 16.5806 0.625794
\(703\) −28.6249 −1.07961
\(704\) −4.70156 −0.177197
\(705\) −1.45307 −0.0547258
\(706\) 76.6682 2.88544
\(707\) −3.77080 −0.141816
\(708\) −13.7708 −0.517539
\(709\) 9.52094 0.357567 0.178783 0.983888i \(-0.442784\pi\)
0.178783 + 0.983888i \(0.442784\pi\)
\(710\) 11.4031 0.427952
\(711\) 4.40490 0.165197
\(712\) 1.44317 0.0540851
\(713\) −49.6693 −1.86013
\(714\) 9.58237 0.358611
\(715\) 6.40490 0.239530
\(716\) 27.9745 1.04546
\(717\) 18.0066 0.672467
\(718\) −58.1559 −2.17036
\(719\) 17.4969 0.652523 0.326261 0.945280i \(-0.394211\pi\)
0.326261 + 0.945280i \(0.394211\pi\)
\(720\) −8.70156 −0.324288
\(721\) 8.56131 0.318840
\(722\) 86.7613 3.22892
\(723\) 27.0740 1.00689
\(724\) −94.3645 −3.50703
\(725\) −8.10646 −0.301066
\(726\) 2.58874 0.0960771
\(727\) −46.8908 −1.73908 −0.869542 0.493860i \(-0.835586\pi\)
−0.869542 + 0.493860i \(0.835586\pi\)
\(728\) −44.7935 −1.66016
\(729\) 1.00000 0.0370370
\(730\) −8.81898 −0.326405
\(731\) 28.3229 1.04756
\(732\) −39.6069 −1.46391
\(733\) −15.8038 −0.583725 −0.291863 0.956460i \(-0.594275\pi\)
−0.291863 + 0.956460i \(0.594275\pi\)
\(734\) 13.2604 0.489449
\(735\) −1.00000 −0.0368856
\(736\) −62.6225 −2.30830
\(737\) 8.72263 0.321302
\(738\) −6.00000 −0.220863
\(739\) −5.69073 −0.209337 −0.104668 0.994507i \(-0.533378\pi\)
−0.104668 + 0.994507i \(0.533378\pi\)
\(740\) 18.5714 0.682699
\(741\) 46.4145 1.70508
\(742\) −23.5788 −0.865606
\(743\) 22.2909 0.817774 0.408887 0.912585i \(-0.365917\pi\)
0.408887 + 0.912585i \(0.365917\pi\)
\(744\) 47.3649 1.73648
\(745\) −9.90010 −0.362712
\(746\) −67.9175 −2.48664
\(747\) −8.96620 −0.328056
\(748\) 17.4031 0.636321
\(749\) −14.1630 −0.517504
\(750\) −2.58874 −0.0945273
\(751\) 38.6786 1.41140 0.705701 0.708510i \(-0.250632\pi\)
0.705701 + 0.708510i \(0.250632\pi\)
\(752\) 12.6440 0.461079
\(753\) 8.58415 0.312824
\(754\) −134.410 −4.89492
\(755\) 17.7581 0.646283
\(756\) −4.70156 −0.170994
\(757\) 43.7967 1.59182 0.795908 0.605417i \(-0.206994\pi\)
0.795908 + 0.605417i \(0.206994\pi\)
\(758\) −24.8562 −0.902818
\(759\) 7.33388 0.266203
\(760\) −50.6809 −1.83839
\(761\) 40.1966 1.45713 0.728564 0.684978i \(-0.240188\pi\)
0.728564 + 0.684978i \(0.240188\pi\)
\(762\) 30.1630 1.09269
\(763\) −7.14026 −0.258495
\(764\) 92.6957 3.35361
\(765\) 3.70156 0.133830
\(766\) 26.2094 0.946983
\(767\) −18.7598 −0.677379
\(768\) −22.1047 −0.797634
\(769\) 1.32679 0.0478452 0.0239226 0.999714i \(-0.492384\pi\)
0.0239226 + 0.999714i \(0.492384\pi\)
\(770\) −2.58874 −0.0932916
\(771\) 0.0885359 0.00318854
\(772\) −25.8129 −0.929028
\(773\) −9.62314 −0.346120 −0.173060 0.984911i \(-0.555365\pi\)
−0.173060 + 0.984911i \(0.555365\pi\)
\(774\) −19.8080 −0.711985
\(775\) 6.77258 0.243278
\(776\) −97.6621 −3.50587
\(777\) 3.95005 0.141707
\(778\) 43.8381 1.57167
\(779\) −16.7959 −0.601777
\(780\) −30.1130 −1.07822
\(781\) 4.40490 0.157620
\(782\) 70.2760 2.51306
\(783\) −8.10646 −0.289701
\(784\) 8.70156 0.310770
\(785\) −17.0547 −0.608710
\(786\) −35.7545 −1.27532
\(787\) 44.1489 1.57374 0.786869 0.617120i \(-0.211701\pi\)
0.786869 + 0.617120i \(0.211701\pi\)
\(788\) 96.1099 3.42377
\(789\) −17.5452 −0.624624
\(790\) −11.4031 −0.405705
\(791\) 1.10823 0.0394042
\(792\) −6.99364 −0.248508
\(793\) −53.9561 −1.91604
\(794\) 35.6252 1.26429
\(795\) −9.10823 −0.323036
\(796\) 107.850 3.82263
\(797\) −18.5257 −0.656215 −0.328108 0.944640i \(-0.606411\pi\)
−0.328108 + 0.944640i \(0.606411\pi\)
\(798\) −18.7598 −0.664091
\(799\) −5.37864 −0.190282
\(800\) 8.53879 0.301892
\(801\) 0.206355 0.00729119
\(802\) 92.1895 3.25533
\(803\) −3.40667 −0.120219
\(804\) −41.0100 −1.44631
\(805\) −7.33388 −0.258485
\(806\) 112.293 3.95537
\(807\) 12.2520 0.431292
\(808\) 26.3716 0.927751
\(809\) 38.1516 1.34134 0.670670 0.741756i \(-0.266007\pi\)
0.670670 + 0.741756i \(0.266007\pi\)
\(810\) −2.58874 −0.0909590
\(811\) −37.3355 −1.31103 −0.655514 0.755183i \(-0.727548\pi\)
−0.655514 + 0.755183i \(0.727548\pi\)
\(812\) 38.1130 1.33750
\(813\) −1.91448 −0.0671438
\(814\) 10.2256 0.358409
\(815\) 19.9338 0.698250
\(816\) −32.2094 −1.12755
\(817\) −55.4491 −1.93992
\(818\) 23.7581 0.830682
\(819\) −6.40490 −0.223805
\(820\) 10.8970 0.380538
\(821\) −19.9039 −0.694652 −0.347326 0.937744i \(-0.612910\pi\)
−0.347326 + 0.937744i \(0.612910\pi\)
\(822\) 24.3422 0.849032
\(823\) −50.8399 −1.77217 −0.886084 0.463525i \(-0.846585\pi\)
−0.886084 + 0.463525i \(0.846585\pi\)
\(824\) −59.8746 −2.08583
\(825\) −1.00000 −0.0348155
\(826\) 7.58237 0.263824
\(827\) −43.7003 −1.51961 −0.759804 0.650152i \(-0.774705\pi\)
−0.759804 + 0.650152i \(0.774705\pi\)
\(828\) −34.4807 −1.19829
\(829\) 51.5197 1.78935 0.894677 0.446715i \(-0.147406\pi\)
0.894677 + 0.446715i \(0.147406\pi\)
\(830\) 23.2111 0.805671
\(831\) 5.62877 0.195260
\(832\) 30.1130 1.04398
\(833\) −3.70156 −0.128252
\(834\) 42.2296 1.46229
\(835\) 2.95183 0.102152
\(836\) −34.0709 −1.17837
\(837\) 6.77258 0.234095
\(838\) 97.9976 3.38527
\(839\) −18.7834 −0.648475 −0.324238 0.945976i \(-0.605108\pi\)
−0.324238 + 0.945976i \(0.605108\pi\)
\(840\) 6.99364 0.241303
\(841\) 36.7147 1.26602
\(842\) 8.03722 0.276981
\(843\) −29.3032 −1.00926
\(844\) −30.9989 −1.06703
\(845\) −28.0227 −0.964011
\(846\) 3.76162 0.129327
\(847\) −1.00000 −0.0343604
\(848\) 79.2559 2.72166
\(849\) 6.89833 0.236750
\(850\) −9.58237 −0.328673
\(851\) 28.9692 0.993052
\(852\) −20.7099 −0.709509
\(853\) −10.4506 −0.357821 −0.178911 0.983865i \(-0.557257\pi\)
−0.178911 + 0.983865i \(0.557257\pi\)
\(854\) 21.8080 0.746255
\(855\) −7.24672 −0.247832
\(856\) 99.0507 3.38548
\(857\) 33.2646 1.13630 0.568149 0.822926i \(-0.307660\pi\)
0.568149 + 0.822926i \(0.307660\pi\)
\(858\) −16.5806 −0.566052
\(859\) 27.5569 0.940230 0.470115 0.882605i \(-0.344212\pi\)
0.470115 + 0.882605i \(0.344212\pi\)
\(860\) 35.9745 1.22672
\(861\) 2.31773 0.0789881
\(862\) −27.0649 −0.921832
\(863\) −10.2042 −0.347354 −0.173677 0.984803i \(-0.555565\pi\)
−0.173677 + 0.984803i \(0.555565\pi\)
\(864\) 8.53879 0.290496
\(865\) −20.2094 −0.687139
\(866\) −20.2494 −0.688103
\(867\) −3.29844 −0.112021
\(868\) −31.8417 −1.08078
\(869\) −4.40490 −0.149426
\(870\) 20.9855 0.711475
\(871\) −55.8676 −1.89300
\(872\) 49.9364 1.69106
\(873\) −13.9644 −0.472624
\(874\) −137.583 −4.65380
\(875\) 1.00000 0.0338062
\(876\) 16.0167 0.541153
\(877\) 57.5319 1.94271 0.971357 0.237625i \(-0.0763688\pi\)
0.971357 + 0.237625i \(0.0763688\pi\)
\(878\) −77.1821 −2.60477
\(879\) −28.7243 −0.968846
\(880\) 8.70156 0.293330
\(881\) −1.05474 −0.0355351 −0.0177675 0.999842i \(-0.505656\pi\)
−0.0177675 + 0.999842i \(0.505656\pi\)
\(882\) 2.58874 0.0871673
\(883\) 14.4063 0.484810 0.242405 0.970175i \(-0.422064\pi\)
0.242405 + 0.970175i \(0.422064\pi\)
\(884\) −111.465 −3.74898
\(885\) 2.92898 0.0984567
\(886\) −29.1942 −0.980797
\(887\) −16.3792 −0.549958 −0.274979 0.961450i \(-0.588671\pi\)
−0.274979 + 0.961450i \(0.588671\pi\)
\(888\) −27.6252 −0.927042
\(889\) −11.6516 −0.390783
\(890\) −0.534199 −0.0179064
\(891\) −1.00000 −0.0335013
\(892\) 51.7931 1.73416
\(893\) 10.5300 0.352373
\(894\) 25.6288 0.857154
\(895\) −5.95005 −0.198888
\(896\) 4.90647 0.163914
\(897\) −46.9728 −1.56838
\(898\) 29.1977 0.974340
\(899\) −54.9016 −1.83107
\(900\) 4.70156 0.156719
\(901\) −33.7147 −1.12320
\(902\) 6.00000 0.199778
\(903\) 7.65161 0.254630
\(904\) −7.75058 −0.257780
\(905\) 20.0709 0.667179
\(906\) −45.9710 −1.52728
\(907\) −26.0372 −0.864552 −0.432276 0.901741i \(-0.642289\pi\)
−0.432276 + 0.901741i \(0.642289\pi\)
\(908\) −98.7553 −3.27731
\(909\) 3.77080 0.125070
\(910\) 16.5806 0.549642
\(911\) 25.5381 0.846114 0.423057 0.906103i \(-0.360957\pi\)
0.423057 + 0.906103i \(0.360957\pi\)
\(912\) 63.0578 2.08805
\(913\) 8.96620 0.296738
\(914\) −1.04391 −0.0345294
\(915\) 8.42419 0.278495
\(916\) −91.9912 −3.03948
\(917\) 13.8116 0.456098
\(918\) −9.58237 −0.316265
\(919\) −28.3971 −0.936733 −0.468367 0.883534i \(-0.655157\pi\)
−0.468367 + 0.883534i \(0.655157\pi\)
\(920\) 51.2905 1.69100
\(921\) 15.7616 0.519363
\(922\) 90.4390 2.97845
\(923\) −28.2129 −0.928640
\(924\) 4.70156 0.154670
\(925\) −3.95005 −0.129877
\(926\) 11.2976 0.371262
\(927\) −8.56131 −0.281190
\(928\) −69.2194 −2.27224
\(929\) −10.7485 −0.352646 −0.176323 0.984332i \(-0.556420\pi\)
−0.176323 + 0.984332i \(0.556420\pi\)
\(930\) −17.5324 −0.574911
\(931\) 7.24672 0.237502
\(932\) 77.0521 2.52393
\(933\) 18.7549 0.614009
\(934\) −78.3224 −2.56279
\(935\) −3.70156 −0.121054
\(936\) 44.7935 1.46412
\(937\) −34.9763 −1.14263 −0.571313 0.820732i \(-0.693566\pi\)
−0.571313 + 0.820732i \(0.693566\pi\)
\(938\) 22.5806 0.737283
\(939\) 8.45786 0.276012
\(940\) −6.83171 −0.222826
\(941\) 25.8979 0.844248 0.422124 0.906538i \(-0.361285\pi\)
0.422124 + 0.906538i \(0.361285\pi\)
\(942\) 44.1502 1.43849
\(943\) 16.9980 0.553530
\(944\) −25.4867 −0.829523
\(945\) 1.00000 0.0325300
\(946\) 19.8080 0.644014
\(947\) −15.9623 −0.518704 −0.259352 0.965783i \(-0.583509\pi\)
−0.259352 + 0.965783i \(0.583509\pi\)
\(948\) 20.7099 0.672626
\(949\) 21.8194 0.708287
\(950\) 18.7598 0.608650
\(951\) −12.8519 −0.416752
\(952\) 25.8874 0.839015
\(953\) −30.8611 −0.999690 −0.499845 0.866115i \(-0.666610\pi\)
−0.499845 + 0.866115i \(0.666610\pi\)
\(954\) 23.5788 0.763393
\(955\) −19.7159 −0.637993
\(956\) 84.6590 2.73807
\(957\) 8.10646 0.262045
\(958\) 30.5862 0.988196
\(959\) −9.40312 −0.303643
\(960\) −4.70156 −0.151742
\(961\) 14.8678 0.479607
\(962\) −65.4942 −2.11162
\(963\) 14.1630 0.456395
\(964\) 127.290 4.09974
\(965\) 5.49029 0.176739
\(966\) 18.9855 0.610848
\(967\) −38.9934 −1.25394 −0.626972 0.779042i \(-0.715706\pi\)
−0.626972 + 0.779042i \(0.715706\pi\)
\(968\) 6.99364 0.224784
\(969\) −26.8242 −0.861717
\(970\) 36.1502 1.16071
\(971\) −1.98071 −0.0635639 −0.0317819 0.999495i \(-0.510118\pi\)
−0.0317819 + 0.999495i \(0.510118\pi\)
\(972\) 4.70156 0.150803
\(973\) −16.3128 −0.522965
\(974\) 94.0713 3.01424
\(975\) 6.40490 0.205121
\(976\) −73.3036 −2.34639
\(977\) 9.66926 0.309347 0.154674 0.987966i \(-0.450567\pi\)
0.154674 + 0.987966i \(0.450567\pi\)
\(978\) −51.6033 −1.65009
\(979\) −0.206355 −0.00659513
\(980\) −4.70156 −0.150186
\(981\) 7.14026 0.227971
\(982\) −107.317 −3.42463
\(983\) −31.1289 −0.992858 −0.496429 0.868077i \(-0.665356\pi\)
−0.496429 + 0.868077i \(0.665356\pi\)
\(984\) −16.2094 −0.516736
\(985\) −20.4421 −0.651340
\(986\) 77.6791 2.47381
\(987\) −1.45307 −0.0462518
\(988\) 218.221 6.94252
\(989\) 56.1160 1.78439
\(990\) 2.58874 0.0822755
\(991\) 30.4473 0.967191 0.483595 0.875292i \(-0.339331\pi\)
0.483595 + 0.875292i \(0.339331\pi\)
\(992\) 57.8296 1.83609
\(993\) −6.64984 −0.211026
\(994\) 11.4031 0.361685
\(995\) −22.9391 −0.727218
\(996\) −42.1552 −1.33574
\(997\) −27.1612 −0.860204 −0.430102 0.902780i \(-0.641522\pi\)
−0.430102 + 0.902780i \(0.641522\pi\)
\(998\) 6.24264 0.197607
\(999\) −3.95005 −0.124974
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 1155.2.a.u.1.4 4
3.2 odd 2 3465.2.a.bl.1.1 4
5.4 even 2 5775.2.a.bz.1.1 4
7.6 odd 2 8085.2.a.bn.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.a.u.1.4 4 1.1 even 1 trivial
3465.2.a.bl.1.1 4 3.2 odd 2
5775.2.a.bz.1.1 4 5.4 even 2
8085.2.a.bn.1.4 4 7.6 odd 2