Properties

Label 4730.2.a.bb.1.6
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
CM no
Inner twists 1

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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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.577714\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.577714 q^{12} +0.00668142 q^{13} +2.69986 q^{14} +0.577714 q^{15} +1.00000 q^{16} -7.50323 q^{17} +2.66625 q^{18} -5.32428 q^{19} -1.00000 q^{20} +1.55974 q^{21} +1.00000 q^{22} -1.99332 q^{23} +0.577714 q^{24} +1.00000 q^{25} -0.00668142 q^{26} +3.27347 q^{27} -2.69986 q^{28} -9.74150 q^{29} -0.577714 q^{30} +1.14932 q^{31} -1.00000 q^{32} +0.577714 q^{33} +7.50323 q^{34} +2.69986 q^{35} -2.66625 q^{36} -9.73188 q^{37} +5.32428 q^{38} -0.00385995 q^{39} +1.00000 q^{40} +9.14180 q^{41} -1.55974 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.66625 q^{45} +1.99332 q^{46} -11.2736 q^{47} -0.577714 q^{48} +0.289218 q^{49} -1.00000 q^{50} +4.33472 q^{51} +0.00668142 q^{52} -2.54838 q^{53} -3.27347 q^{54} +1.00000 q^{55} +2.69986 q^{56} +3.07591 q^{57} +9.74150 q^{58} +6.45474 q^{59} +0.577714 q^{60} +4.27657 q^{61} -1.14932 q^{62} +7.19848 q^{63} +1.00000 q^{64} -0.00668142 q^{65} -0.577714 q^{66} -8.89100 q^{67} -7.50323 q^{68} +1.15157 q^{69} -2.69986 q^{70} -15.7990 q^{71} +2.66625 q^{72} +7.72877 q^{73} +9.73188 q^{74} -0.577714 q^{75} -5.32428 q^{76} +2.69986 q^{77} +0.00385995 q^{78} -4.15910 q^{79} -1.00000 q^{80} +6.10761 q^{81} -9.14180 q^{82} -6.92811 q^{83} +1.55974 q^{84} +7.50323 q^{85} -1.00000 q^{86} +5.62781 q^{87} +1.00000 q^{88} -16.4938 q^{89} -2.66625 q^{90} -0.0180389 q^{91} -1.99332 q^{92} -0.663978 q^{93} +11.2736 q^{94} +5.32428 q^{95} +0.577714 q^{96} +14.4906 q^{97} -0.289218 q^{98} +2.66625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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
\(3\) −0.577714 −0.333544 −0.166772 0.985996i \(-0.553334\pi\)
−0.166772 + 0.985996i \(0.553334\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.577714 0.235851
\(7\) −2.69986 −1.02045 −0.510225 0.860041i \(-0.670438\pi\)
−0.510225 + 0.860041i \(0.670438\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.66625 −0.888749
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −0.577714 −0.166772
\(13\) 0.00668142 0.00185309 0.000926546 1.00000i \(-0.499705\pi\)
0.000926546 1.00000i \(0.499705\pi\)
\(14\) 2.69986 0.721567
\(15\) 0.577714 0.149165
\(16\) 1.00000 0.250000
\(17\) −7.50323 −1.81980 −0.909900 0.414828i \(-0.863842\pi\)
−0.909900 + 0.414828i \(0.863842\pi\)
\(18\) 2.66625 0.628440
\(19\) −5.32428 −1.22147 −0.610736 0.791834i \(-0.709126\pi\)
−0.610736 + 0.791834i \(0.709126\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.55974 0.340364
\(22\) 1.00000 0.213201
\(23\) −1.99332 −0.415636 −0.207818 0.978168i \(-0.566636\pi\)
−0.207818 + 0.978168i \(0.566636\pi\)
\(24\) 0.577714 0.117925
\(25\) 1.00000 0.200000
\(26\) −0.00668142 −0.00131033
\(27\) 3.27347 0.629980
\(28\) −2.69986 −0.510225
\(29\) −9.74150 −1.80895 −0.904476 0.426525i \(-0.859738\pi\)
−0.904476 + 0.426525i \(0.859738\pi\)
\(30\) −0.577714 −0.105476
\(31\) 1.14932 0.206424 0.103212 0.994659i \(-0.467088\pi\)
0.103212 + 0.994659i \(0.467088\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.577714 0.100567
\(34\) 7.50323 1.28679
\(35\) 2.69986 0.456359
\(36\) −2.66625 −0.444374
\(37\) −9.73188 −1.59991 −0.799956 0.600059i \(-0.795144\pi\)
−0.799956 + 0.600059i \(0.795144\pi\)
\(38\) 5.32428 0.863712
\(39\) −0.00385995 −0.000618087 0
\(40\) 1.00000 0.158114
\(41\) 9.14180 1.42771 0.713855 0.700294i \(-0.246948\pi\)
0.713855 + 0.700294i \(0.246948\pi\)
\(42\) −1.55974 −0.240674
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 2.66625 0.397461
\(46\) 1.99332 0.293899
\(47\) −11.2736 −1.64442 −0.822208 0.569187i \(-0.807258\pi\)
−0.822208 + 0.569187i \(0.807258\pi\)
\(48\) −0.577714 −0.0833859
\(49\) 0.289218 0.0413169
\(50\) −1.00000 −0.141421
\(51\) 4.33472 0.606982
\(52\) 0.00668142 0.000926546 0
\(53\) −2.54838 −0.350047 −0.175023 0.984564i \(-0.556000\pi\)
−0.175023 + 0.984564i \(0.556000\pi\)
\(54\) −3.27347 −0.445463
\(55\) 1.00000 0.134840
\(56\) 2.69986 0.360783
\(57\) 3.07591 0.407414
\(58\) 9.74150 1.27912
\(59\) 6.45474 0.840335 0.420168 0.907446i \(-0.361971\pi\)
0.420168 + 0.907446i \(0.361971\pi\)
\(60\) 0.577714 0.0745826
\(61\) 4.27657 0.547558 0.273779 0.961793i \(-0.411726\pi\)
0.273779 + 0.961793i \(0.411726\pi\)
\(62\) −1.14932 −0.145964
\(63\) 7.19848 0.906923
\(64\) 1.00000 0.125000
\(65\) −0.00668142 −0.000828728 0
\(66\) −0.577714 −0.0711117
\(67\) −8.89100 −1.08621 −0.543104 0.839665i \(-0.682751\pi\)
−0.543104 + 0.839665i \(0.682751\pi\)
\(68\) −7.50323 −0.909900
\(69\) 1.15157 0.138633
\(70\) −2.69986 −0.322694
\(71\) −15.7990 −1.87500 −0.937500 0.347985i \(-0.886866\pi\)
−0.937500 + 0.347985i \(0.886866\pi\)
\(72\) 2.66625 0.314220
\(73\) 7.72877 0.904584 0.452292 0.891870i \(-0.350606\pi\)
0.452292 + 0.891870i \(0.350606\pi\)
\(74\) 9.73188 1.13131
\(75\) −0.577714 −0.0667087
\(76\) −5.32428 −0.610736
\(77\) 2.69986 0.307677
\(78\) 0.00385995 0.000437054 0
\(79\) −4.15910 −0.467936 −0.233968 0.972244i \(-0.575171\pi\)
−0.233968 + 0.972244i \(0.575171\pi\)
\(80\) −1.00000 −0.111803
\(81\) 6.10761 0.678623
\(82\) −9.14180 −1.00954
\(83\) −6.92811 −0.760459 −0.380229 0.924892i \(-0.624155\pi\)
−0.380229 + 0.924892i \(0.624155\pi\)
\(84\) 1.55974 0.170182
\(85\) 7.50323 0.813839
\(86\) −1.00000 −0.107833
\(87\) 5.62781 0.603364
\(88\) 1.00000 0.106600
\(89\) −16.4938 −1.74834 −0.874168 0.485624i \(-0.838593\pi\)
−0.874168 + 0.485624i \(0.838593\pi\)
\(90\) −2.66625 −0.281047
\(91\) −0.0180389 −0.00189099
\(92\) −1.99332 −0.207818
\(93\) −0.663978 −0.0688513
\(94\) 11.2736 1.16278
\(95\) 5.32428 0.546259
\(96\) 0.577714 0.0589627
\(97\) 14.4906 1.47130 0.735649 0.677363i \(-0.236877\pi\)
0.735649 + 0.677363i \(0.236877\pi\)
\(98\) −0.289218 −0.0292154
\(99\) 2.66625 0.267968
\(100\) 1.00000 0.100000
\(101\) 14.6386 1.45659 0.728297 0.685261i \(-0.240312\pi\)
0.728297 + 0.685261i \(0.240312\pi\)
\(102\) −4.33472 −0.429201
\(103\) −6.34952 −0.625636 −0.312818 0.949813i \(-0.601273\pi\)
−0.312818 + 0.949813i \(0.601273\pi\)
\(104\) −0.00668142 −0.000655167 0
\(105\) −1.55974 −0.152216
\(106\) 2.54838 0.247520
\(107\) 11.1643 1.07929 0.539646 0.841892i \(-0.318558\pi\)
0.539646 + 0.841892i \(0.318558\pi\)
\(108\) 3.27347 0.314990
\(109\) −7.19300 −0.688964 −0.344482 0.938793i \(-0.611945\pi\)
−0.344482 + 0.938793i \(0.611945\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 5.62225 0.533640
\(112\) −2.69986 −0.255112
\(113\) −13.8698 −1.30476 −0.652379 0.757893i \(-0.726229\pi\)
−0.652379 + 0.757893i \(0.726229\pi\)
\(114\) −3.07591 −0.288085
\(115\) 1.99332 0.185878
\(116\) −9.74150 −0.904476
\(117\) −0.0178143 −0.00164693
\(118\) −6.45474 −0.594207
\(119\) 20.2576 1.85701
\(120\) −0.577714 −0.0527379
\(121\) 1.00000 0.0909091
\(122\) −4.27657 −0.387182
\(123\) −5.28135 −0.476203
\(124\) 1.14932 0.103212
\(125\) −1.00000 −0.0894427
\(126\) −7.19848 −0.641291
\(127\) −12.7904 −1.13497 −0.567484 0.823384i \(-0.692083\pi\)
−0.567484 + 0.823384i \(0.692083\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.577714 −0.0508649
\(130\) 0.00668142 0.000585999 0
\(131\) −7.85038 −0.685891 −0.342945 0.939355i \(-0.611425\pi\)
−0.342945 + 0.939355i \(0.611425\pi\)
\(132\) 0.577714 0.0502836
\(133\) 14.3748 1.24645
\(134\) 8.89100 0.768065
\(135\) −3.27347 −0.281736
\(136\) 7.50323 0.643396
\(137\) 8.10979 0.692866 0.346433 0.938075i \(-0.387393\pi\)
0.346433 + 0.938075i \(0.387393\pi\)
\(138\) −1.15157 −0.0980280
\(139\) 9.85552 0.835934 0.417967 0.908462i \(-0.362743\pi\)
0.417967 + 0.908462i \(0.362743\pi\)
\(140\) 2.69986 0.228179
\(141\) 6.51289 0.548484
\(142\) 15.7990 1.32583
\(143\) −0.00668142 −0.000558728 0
\(144\) −2.66625 −0.222187
\(145\) 9.74150 0.808988
\(146\) −7.72877 −0.639637
\(147\) −0.167085 −0.0137810
\(148\) −9.73188 −0.799956
\(149\) 12.5027 1.02426 0.512129 0.858908i \(-0.328857\pi\)
0.512129 + 0.858908i \(0.328857\pi\)
\(150\) 0.577714 0.0471702
\(151\) 11.5357 0.938766 0.469383 0.882995i \(-0.344476\pi\)
0.469383 + 0.882995i \(0.344476\pi\)
\(152\) 5.32428 0.431856
\(153\) 20.0054 1.61734
\(154\) −2.69986 −0.217561
\(155\) −1.14932 −0.0923155
\(156\) −0.00385995 −0.000309044 0
\(157\) −15.0341 −1.19985 −0.599924 0.800057i \(-0.704802\pi\)
−0.599924 + 0.800057i \(0.704802\pi\)
\(158\) 4.15910 0.330881
\(159\) 1.47224 0.116756
\(160\) 1.00000 0.0790569
\(161\) 5.38167 0.424135
\(162\) −6.10761 −0.479859
\(163\) −11.8173 −0.925602 −0.462801 0.886462i \(-0.653156\pi\)
−0.462801 + 0.886462i \(0.653156\pi\)
\(164\) 9.14180 0.713855
\(165\) −0.577714 −0.0449750
\(166\) 6.92811 0.537726
\(167\) 8.98218 0.695062 0.347531 0.937669i \(-0.387020\pi\)
0.347531 + 0.937669i \(0.387020\pi\)
\(168\) −1.55974 −0.120337
\(169\) −13.0000 −0.999997
\(170\) −7.50323 −0.575471
\(171\) 14.1958 1.08558
\(172\) 1.00000 0.0762493
\(173\) 0.691126 0.0525453 0.0262727 0.999655i \(-0.491636\pi\)
0.0262727 + 0.999655i \(0.491636\pi\)
\(174\) −5.62781 −0.426643
\(175\) −2.69986 −0.204090
\(176\) −1.00000 −0.0753778
\(177\) −3.72899 −0.280288
\(178\) 16.4938 1.23626
\(179\) −11.7502 −0.878249 −0.439125 0.898426i \(-0.644711\pi\)
−0.439125 + 0.898426i \(0.644711\pi\)
\(180\) 2.66625 0.198730
\(181\) −7.73730 −0.575109 −0.287555 0.957764i \(-0.592842\pi\)
−0.287555 + 0.957764i \(0.592842\pi\)
\(182\) 0.0180389 0.00133713
\(183\) −2.47063 −0.182635
\(184\) 1.99332 0.146949
\(185\) 9.73188 0.715502
\(186\) 0.663978 0.0486852
\(187\) 7.50323 0.548690
\(188\) −11.2736 −0.822208
\(189\) −8.83790 −0.642863
\(190\) −5.32428 −0.386264
\(191\) 0.577591 0.0417930 0.0208965 0.999782i \(-0.493348\pi\)
0.0208965 + 0.999782i \(0.493348\pi\)
\(192\) −0.577714 −0.0416929
\(193\) −5.27610 −0.379782 −0.189891 0.981805i \(-0.560813\pi\)
−0.189891 + 0.981805i \(0.560813\pi\)
\(194\) −14.4906 −1.04036
\(195\) 0.00385995 0.000276417 0
\(196\) 0.289218 0.0206584
\(197\) −21.4244 −1.52642 −0.763212 0.646148i \(-0.776379\pi\)
−0.763212 + 0.646148i \(0.776379\pi\)
\(198\) −2.66625 −0.189482
\(199\) 12.3560 0.875895 0.437948 0.899001i \(-0.355706\pi\)
0.437948 + 0.899001i \(0.355706\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 5.13646 0.362298
\(202\) −14.6386 −1.02997
\(203\) 26.3006 1.84594
\(204\) 4.33472 0.303491
\(205\) −9.14180 −0.638491
\(206\) 6.34952 0.442392
\(207\) 5.31468 0.369396
\(208\) 0.00668142 0.000463273 0
\(209\) 5.32428 0.368288
\(210\) 1.55974 0.107633
\(211\) 22.9313 1.57866 0.789329 0.613970i \(-0.210428\pi\)
0.789329 + 0.613970i \(0.210428\pi\)
\(212\) −2.54838 −0.175023
\(213\) 9.12733 0.625394
\(214\) −11.1643 −0.763175
\(215\) −1.00000 −0.0681994
\(216\) −3.27347 −0.222732
\(217\) −3.10299 −0.210645
\(218\) 7.19300 0.487171
\(219\) −4.46502 −0.301718
\(220\) 1.00000 0.0674200
\(221\) −0.0501322 −0.00337226
\(222\) −5.62225 −0.377341
\(223\) 12.5840 0.842688 0.421344 0.906901i \(-0.361559\pi\)
0.421344 + 0.906901i \(0.361559\pi\)
\(224\) 2.69986 0.180392
\(225\) −2.66625 −0.177750
\(226\) 13.8698 0.922603
\(227\) 13.4424 0.892205 0.446103 0.894982i \(-0.352812\pi\)
0.446103 + 0.894982i \(0.352812\pi\)
\(228\) 3.07591 0.203707
\(229\) 14.6520 0.968228 0.484114 0.875005i \(-0.339142\pi\)
0.484114 + 0.875005i \(0.339142\pi\)
\(230\) −1.99332 −0.131436
\(231\) −1.55974 −0.102624
\(232\) 9.74150 0.639561
\(233\) −17.1222 −1.12172 −0.560858 0.827912i \(-0.689528\pi\)
−0.560858 + 0.827912i \(0.689528\pi\)
\(234\) 0.0178143 0.00116456
\(235\) 11.2736 0.735405
\(236\) 6.45474 0.420168
\(237\) 2.40277 0.156077
\(238\) −20.2576 −1.31311
\(239\) −4.63878 −0.300058 −0.150029 0.988682i \(-0.547937\pi\)
−0.150029 + 0.988682i \(0.547937\pi\)
\(240\) 0.577714 0.0372913
\(241\) 15.2434 0.981913 0.490956 0.871184i \(-0.336647\pi\)
0.490956 + 0.871184i \(0.336647\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −13.3489 −0.856330
\(244\) 4.27657 0.273779
\(245\) −0.289218 −0.0184775
\(246\) 5.28135 0.336727
\(247\) −0.0355737 −0.00226350
\(248\) −1.14932 −0.0729818
\(249\) 4.00247 0.253646
\(250\) 1.00000 0.0632456
\(251\) 5.90920 0.372985 0.186493 0.982456i \(-0.440288\pi\)
0.186493 + 0.982456i \(0.440288\pi\)
\(252\) 7.19848 0.453462
\(253\) 1.99332 0.125319
\(254\) 12.7904 0.802544
\(255\) −4.33472 −0.271451
\(256\) 1.00000 0.0625000
\(257\) −22.8381 −1.42460 −0.712302 0.701873i \(-0.752347\pi\)
−0.712302 + 0.701873i \(0.752347\pi\)
\(258\) 0.577714 0.0359669
\(259\) 26.2747 1.63263
\(260\) −0.00668142 −0.000414364 0
\(261\) 25.9732 1.60770
\(262\) 7.85038 0.484998
\(263\) 2.36294 0.145705 0.0728526 0.997343i \(-0.476790\pi\)
0.0728526 + 0.997343i \(0.476790\pi\)
\(264\) −0.577714 −0.0355559
\(265\) 2.54838 0.156546
\(266\) −14.3748 −0.881374
\(267\) 9.52869 0.583146
\(268\) −8.89100 −0.543104
\(269\) −16.1901 −0.987128 −0.493564 0.869709i \(-0.664306\pi\)
−0.493564 + 0.869709i \(0.664306\pi\)
\(270\) 3.27347 0.199217
\(271\) −4.34264 −0.263797 −0.131898 0.991263i \(-0.542107\pi\)
−0.131898 + 0.991263i \(0.542107\pi\)
\(272\) −7.50323 −0.454950
\(273\) 0.0104213 0.000630727 0
\(274\) −8.10979 −0.489931
\(275\) −1.00000 −0.0603023
\(276\) 1.15157 0.0693163
\(277\) −3.77746 −0.226966 −0.113483 0.993540i \(-0.536201\pi\)
−0.113483 + 0.993540i \(0.536201\pi\)
\(278\) −9.85552 −0.591095
\(279\) −3.06437 −0.183459
\(280\) −2.69986 −0.161347
\(281\) 1.26839 0.0756657 0.0378329 0.999284i \(-0.487955\pi\)
0.0378329 + 0.999284i \(0.487955\pi\)
\(282\) −6.51289 −0.387837
\(283\) −10.1674 −0.604390 −0.302195 0.953246i \(-0.597719\pi\)
−0.302195 + 0.953246i \(0.597719\pi\)
\(284\) −15.7990 −0.937500
\(285\) −3.07591 −0.182201
\(286\) 0.00668142 0.000395081 0
\(287\) −24.6815 −1.45691
\(288\) 2.66625 0.157110
\(289\) 39.2984 2.31167
\(290\) −9.74150 −0.572041
\(291\) −8.37143 −0.490742
\(292\) 7.72877 0.452292
\(293\) −18.4822 −1.07974 −0.539872 0.841747i \(-0.681527\pi\)
−0.539872 + 0.841747i \(0.681527\pi\)
\(294\) 0.167085 0.00974462
\(295\) −6.45474 −0.375809
\(296\) 9.73188 0.565654
\(297\) −3.27347 −0.189946
\(298\) −12.5027 −0.724260
\(299\) −0.0133182 −0.000770211 0
\(300\) −0.577714 −0.0333544
\(301\) −2.69986 −0.155617
\(302\) −11.5357 −0.663808
\(303\) −8.45693 −0.485838
\(304\) −5.32428 −0.305368
\(305\) −4.27657 −0.244876
\(306\) −20.0054 −1.14364
\(307\) −8.27918 −0.472517 −0.236259 0.971690i \(-0.575921\pi\)
−0.236259 + 0.971690i \(0.575921\pi\)
\(308\) 2.69986 0.153839
\(309\) 3.66821 0.208677
\(310\) 1.14932 0.0652769
\(311\) 14.4629 0.820116 0.410058 0.912059i \(-0.365508\pi\)
0.410058 + 0.912059i \(0.365508\pi\)
\(312\) 0.00385995 0.000218527 0
\(313\) −1.07351 −0.0606784 −0.0303392 0.999540i \(-0.509659\pi\)
−0.0303392 + 0.999540i \(0.509659\pi\)
\(314\) 15.0341 0.848421
\(315\) −7.19848 −0.405588
\(316\) −4.15910 −0.233968
\(317\) −18.3258 −1.02928 −0.514638 0.857407i \(-0.672074\pi\)
−0.514638 + 0.857407i \(0.672074\pi\)
\(318\) −1.47224 −0.0825588
\(319\) 9.74150 0.545420
\(320\) −1.00000 −0.0559017
\(321\) −6.44977 −0.359991
\(322\) −5.38167 −0.299909
\(323\) 39.9492 2.22284
\(324\) 6.10761 0.339312
\(325\) 0.00668142 0.000370619 0
\(326\) 11.8173 0.654500
\(327\) 4.15550 0.229800
\(328\) −9.14180 −0.504772
\(329\) 30.4370 1.67804
\(330\) 0.577714 0.0318021
\(331\) −20.6284 −1.13384 −0.566919 0.823774i \(-0.691865\pi\)
−0.566919 + 0.823774i \(0.691865\pi\)
\(332\) −6.92811 −0.380229
\(333\) 25.9476 1.42192
\(334\) −8.98218 −0.491483
\(335\) 8.89100 0.485767
\(336\) 1.55974 0.0850911
\(337\) 4.19893 0.228730 0.114365 0.993439i \(-0.463517\pi\)
0.114365 + 0.993439i \(0.463517\pi\)
\(338\) 13.0000 0.707104
\(339\) 8.01276 0.435194
\(340\) 7.50323 0.406920
\(341\) −1.14932 −0.0622391
\(342\) −14.1958 −0.767623
\(343\) 18.1181 0.978288
\(344\) −1.00000 −0.0539164
\(345\) −1.15157 −0.0619984
\(346\) −0.691126 −0.0371552
\(347\) 11.3065 0.606964 0.303482 0.952837i \(-0.401851\pi\)
0.303482 + 0.952837i \(0.401851\pi\)
\(348\) 5.62781 0.301682
\(349\) −27.8234 −1.48935 −0.744675 0.667427i \(-0.767396\pi\)
−0.744675 + 0.667427i \(0.767396\pi\)
\(350\) 2.69986 0.144313
\(351\) 0.0218714 0.00116741
\(352\) 1.00000 0.0533002
\(353\) −30.2682 −1.61101 −0.805506 0.592587i \(-0.798106\pi\)
−0.805506 + 0.592587i \(0.798106\pi\)
\(354\) 3.72899 0.198194
\(355\) 15.7990 0.838526
\(356\) −16.4938 −0.874168
\(357\) −11.7031 −0.619395
\(358\) 11.7502 0.621016
\(359\) −0.0533741 −0.00281698 −0.00140849 0.999999i \(-0.500448\pi\)
−0.00140849 + 0.999999i \(0.500448\pi\)
\(360\) −2.66625 −0.140524
\(361\) 9.34792 0.491996
\(362\) 7.73730 0.406664
\(363\) −0.577714 −0.0303221
\(364\) −0.0180389 −0.000945494 0
\(365\) −7.72877 −0.404542
\(366\) 2.47063 0.129142
\(367\) 10.8408 0.565883 0.282942 0.959137i \(-0.408690\pi\)
0.282942 + 0.959137i \(0.408690\pi\)
\(368\) −1.99332 −0.103909
\(369\) −24.3743 −1.26888
\(370\) −9.73188 −0.505936
\(371\) 6.88025 0.357205
\(372\) −0.663978 −0.0344257
\(373\) −28.6721 −1.48458 −0.742292 0.670076i \(-0.766261\pi\)
−0.742292 + 0.670076i \(0.766261\pi\)
\(374\) −7.50323 −0.387983
\(375\) 0.577714 0.0298330
\(376\) 11.2736 0.581389
\(377\) −0.0650871 −0.00335216
\(378\) 8.83790 0.454572
\(379\) 24.2561 1.24595 0.622977 0.782240i \(-0.285923\pi\)
0.622977 + 0.782240i \(0.285923\pi\)
\(380\) 5.32428 0.273130
\(381\) 7.38922 0.378561
\(382\) −0.577591 −0.0295521
\(383\) 14.7829 0.755369 0.377684 0.925934i \(-0.376720\pi\)
0.377684 + 0.925934i \(0.376720\pi\)
\(384\) 0.577714 0.0294814
\(385\) −2.69986 −0.137597
\(386\) 5.27610 0.268547
\(387\) −2.66625 −0.135533
\(388\) 14.4906 0.735649
\(389\) 25.4940 1.29260 0.646298 0.763085i \(-0.276316\pi\)
0.646298 + 0.763085i \(0.276316\pi\)
\(390\) −0.00385995 −0.000195456 0
\(391\) 14.9563 0.756374
\(392\) −0.289218 −0.0146077
\(393\) 4.53528 0.228774
\(394\) 21.4244 1.07934
\(395\) 4.15910 0.209267
\(396\) 2.66625 0.133984
\(397\) 17.7664 0.891669 0.445835 0.895115i \(-0.352907\pi\)
0.445835 + 0.895115i \(0.352907\pi\)
\(398\) −12.3560 −0.619351
\(399\) −8.30451 −0.415746
\(400\) 1.00000 0.0500000
\(401\) −0.144875 −0.00723470 −0.00361735 0.999993i \(-0.501151\pi\)
−0.00361735 + 0.999993i \(0.501151\pi\)
\(402\) −5.13646 −0.256183
\(403\) 0.00767908 0.000382522 0
\(404\) 14.6386 0.728297
\(405\) −6.10761 −0.303489
\(406\) −26.3006 −1.30528
\(407\) 9.73188 0.482391
\(408\) −4.33472 −0.214601
\(409\) −0.871128 −0.0430745 −0.0215373 0.999768i \(-0.506856\pi\)
−0.0215373 + 0.999768i \(0.506856\pi\)
\(410\) 9.14180 0.451481
\(411\) −4.68514 −0.231101
\(412\) −6.34952 −0.312818
\(413\) −17.4269 −0.857520
\(414\) −5.31468 −0.261202
\(415\) 6.92811 0.340088
\(416\) −0.00668142 −0.000327584 0
\(417\) −5.69367 −0.278820
\(418\) −5.32428 −0.260419
\(419\) −19.3475 −0.945185 −0.472593 0.881281i \(-0.656682\pi\)
−0.472593 + 0.881281i \(0.656682\pi\)
\(420\) −1.55974 −0.0761078
\(421\) −13.3644 −0.651339 −0.325670 0.945484i \(-0.605590\pi\)
−0.325670 + 0.945484i \(0.605590\pi\)
\(422\) −22.9313 −1.11628
\(423\) 30.0581 1.46147
\(424\) 2.54838 0.123760
\(425\) −7.50323 −0.363960
\(426\) −9.12733 −0.442220
\(427\) −11.5461 −0.558756
\(428\) 11.1643 0.539646
\(429\) 0.00385995 0.000186360 0
\(430\) 1.00000 0.0482243
\(431\) −18.9085 −0.910790 −0.455395 0.890290i \(-0.650502\pi\)
−0.455395 + 0.890290i \(0.650502\pi\)
\(432\) 3.27347 0.157495
\(433\) −28.0836 −1.34961 −0.674806 0.737996i \(-0.735773\pi\)
−0.674806 + 0.737996i \(0.735773\pi\)
\(434\) 3.10299 0.148948
\(435\) −5.62781 −0.269833
\(436\) −7.19300 −0.344482
\(437\) 10.6130 0.507688
\(438\) 4.46502 0.213347
\(439\) 40.8954 1.95183 0.975916 0.218149i \(-0.0700018\pi\)
0.975916 + 0.218149i \(0.0700018\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −0.771127 −0.0367203
\(442\) 0.0501322 0.00238455
\(443\) 40.6426 1.93099 0.965494 0.260426i \(-0.0838629\pi\)
0.965494 + 0.260426i \(0.0838629\pi\)
\(444\) 5.62225 0.266820
\(445\) 16.4938 0.781880
\(446\) −12.5840 −0.595870
\(447\) −7.22297 −0.341635
\(448\) −2.69986 −0.127556
\(449\) 20.4364 0.964455 0.482228 0.876046i \(-0.339828\pi\)
0.482228 + 0.876046i \(0.339828\pi\)
\(450\) 2.66625 0.125688
\(451\) −9.14180 −0.430471
\(452\) −13.8698 −0.652379
\(453\) −6.66437 −0.313119
\(454\) −13.4424 −0.630884
\(455\) 0.0180389 0.000845675 0
\(456\) −3.07591 −0.144043
\(457\) 28.6296 1.33923 0.669617 0.742706i \(-0.266458\pi\)
0.669617 + 0.742706i \(0.266458\pi\)
\(458\) −14.6520 −0.684641
\(459\) −24.5616 −1.14644
\(460\) 1.99332 0.0929390
\(461\) 7.14878 0.332952 0.166476 0.986046i \(-0.446761\pi\)
0.166476 + 0.986046i \(0.446761\pi\)
\(462\) 1.55974 0.0725659
\(463\) −30.9169 −1.43683 −0.718416 0.695614i \(-0.755132\pi\)
−0.718416 + 0.695614i \(0.755132\pi\)
\(464\) −9.74150 −0.452238
\(465\) 0.663978 0.0307912
\(466\) 17.1222 0.793172
\(467\) 19.7877 0.915666 0.457833 0.889038i \(-0.348626\pi\)
0.457833 + 0.889038i \(0.348626\pi\)
\(468\) −0.0178143 −0.000823467 0
\(469\) 24.0044 1.10842
\(470\) −11.2736 −0.520010
\(471\) 8.68539 0.400201
\(472\) −6.45474 −0.297103
\(473\) −1.00000 −0.0459800
\(474\) −2.40277 −0.110363
\(475\) −5.32428 −0.244295
\(476\) 20.2576 0.928507
\(477\) 6.79461 0.311104
\(478\) 4.63878 0.212173
\(479\) −17.7962 −0.813130 −0.406565 0.913622i \(-0.633274\pi\)
−0.406565 + 0.913622i \(0.633274\pi\)
\(480\) −0.577714 −0.0263689
\(481\) −0.0650228 −0.00296478
\(482\) −15.2434 −0.694317
\(483\) −3.10907 −0.141468
\(484\) 1.00000 0.0454545
\(485\) −14.4906 −0.657984
\(486\) 13.3489 0.605517
\(487\) 22.9534 1.04012 0.520058 0.854131i \(-0.325910\pi\)
0.520058 + 0.854131i \(0.325910\pi\)
\(488\) −4.27657 −0.193591
\(489\) 6.82702 0.308729
\(490\) 0.289218 0.0130655
\(491\) 3.36504 0.151862 0.0759310 0.997113i \(-0.475807\pi\)
0.0759310 + 0.997113i \(0.475807\pi\)
\(492\) −5.28135 −0.238102
\(493\) 73.0927 3.29193
\(494\) 0.0355737 0.00160054
\(495\) −2.66625 −0.119839
\(496\) 1.14932 0.0516059
\(497\) 42.6551 1.91334
\(498\) −4.00247 −0.179355
\(499\) 18.9121 0.846624 0.423312 0.905984i \(-0.360867\pi\)
0.423312 + 0.905984i \(0.360867\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −5.18913 −0.231833
\(502\) −5.90920 −0.263741
\(503\) 3.42471 0.152700 0.0763501 0.997081i \(-0.475673\pi\)
0.0763501 + 0.997081i \(0.475673\pi\)
\(504\) −7.19848 −0.320646
\(505\) −14.6386 −0.651409
\(506\) −1.99332 −0.0886138
\(507\) 7.51026 0.333542
\(508\) −12.7904 −0.567484
\(509\) 1.36409 0.0604624 0.0302312 0.999543i \(-0.490376\pi\)
0.0302312 + 0.999543i \(0.490376\pi\)
\(510\) 4.33472 0.191945
\(511\) −20.8666 −0.923082
\(512\) −1.00000 −0.0441942
\(513\) −17.4289 −0.769503
\(514\) 22.8381 1.00735
\(515\) 6.34952 0.279793
\(516\) −0.577714 −0.0254325
\(517\) 11.2736 0.495810
\(518\) −26.2747 −1.15444
\(519\) −0.399273 −0.0175262
\(520\) 0.00668142 0.000293000 0
\(521\) −8.88322 −0.389181 −0.194590 0.980885i \(-0.562338\pi\)
−0.194590 + 0.980885i \(0.562338\pi\)
\(522\) −25.9732 −1.13682
\(523\) −19.2649 −0.842394 −0.421197 0.906969i \(-0.638390\pi\)
−0.421197 + 0.906969i \(0.638390\pi\)
\(524\) −7.85038 −0.342945
\(525\) 1.55974 0.0680729
\(526\) −2.36294 −0.103029
\(527\) −8.62360 −0.375650
\(528\) 0.577714 0.0251418
\(529\) −19.0267 −0.827247
\(530\) −2.54838 −0.110695
\(531\) −17.2099 −0.746847
\(532\) 14.3748 0.623226
\(533\) 0.0610802 0.00264568
\(534\) −9.52869 −0.412347
\(535\) −11.1643 −0.482674
\(536\) 8.89100 0.384033
\(537\) 6.78824 0.292934
\(538\) 16.1901 0.698005
\(539\) −0.289218 −0.0124575
\(540\) −3.27347 −0.140868
\(541\) 18.3686 0.789727 0.394864 0.918740i \(-0.370792\pi\)
0.394864 + 0.918740i \(0.370792\pi\)
\(542\) 4.34264 0.186532
\(543\) 4.46995 0.191824
\(544\) 7.50323 0.321698
\(545\) 7.19300 0.308114
\(546\) −0.0104213 −0.000445991 0
\(547\) −31.0349 −1.32696 −0.663479 0.748195i \(-0.730921\pi\)
−0.663479 + 0.748195i \(0.730921\pi\)
\(548\) 8.10979 0.346433
\(549\) −11.4024 −0.486642
\(550\) 1.00000 0.0426401
\(551\) 51.8665 2.20959
\(552\) −1.15157 −0.0490140
\(553\) 11.2290 0.477505
\(554\) 3.77746 0.160489
\(555\) −5.62225 −0.238651
\(556\) 9.85552 0.417967
\(557\) 31.1414 1.31950 0.659751 0.751484i \(-0.270662\pi\)
0.659751 + 0.751484i \(0.270662\pi\)
\(558\) 3.06437 0.129725
\(559\) 0.00668142 0.000282594 0
\(560\) 2.69986 0.114090
\(561\) −4.33472 −0.183012
\(562\) −1.26839 −0.0535038
\(563\) 14.6683 0.618197 0.309098 0.951030i \(-0.399973\pi\)
0.309098 + 0.951030i \(0.399973\pi\)
\(564\) 6.51289 0.274242
\(565\) 13.8698 0.583506
\(566\) 10.1674 0.427368
\(567\) −16.4897 −0.692500
\(568\) 15.7990 0.662913
\(569\) −21.0302 −0.881634 −0.440817 0.897597i \(-0.645311\pi\)
−0.440817 + 0.897597i \(0.645311\pi\)
\(570\) 3.07591 0.128836
\(571\) 3.56595 0.149230 0.0746151 0.997212i \(-0.476227\pi\)
0.0746151 + 0.997212i \(0.476227\pi\)
\(572\) −0.00668142 −0.000279364 0
\(573\) −0.333682 −0.0139398
\(574\) 24.6815 1.03019
\(575\) −1.99332 −0.0831271
\(576\) −2.66625 −0.111094
\(577\) 44.3300 1.84548 0.922742 0.385419i \(-0.125943\pi\)
0.922742 + 0.385419i \(0.125943\pi\)
\(578\) −39.2984 −1.63460
\(579\) 3.04808 0.126674
\(580\) 9.74150 0.404494
\(581\) 18.7049 0.776010
\(582\) 8.37143 0.347007
\(583\) 2.54838 0.105543
\(584\) −7.72877 −0.319819
\(585\) 0.0178143 0.000736531 0
\(586\) 18.4822 0.763495
\(587\) −19.6007 −0.809009 −0.404504 0.914536i \(-0.632556\pi\)
−0.404504 + 0.914536i \(0.632556\pi\)
\(588\) −0.167085 −0.00689049
\(589\) −6.11929 −0.252141
\(590\) 6.45474 0.265737
\(591\) 12.3772 0.509129
\(592\) −9.73188 −0.399978
\(593\) 26.4786 1.08735 0.543674 0.839297i \(-0.317033\pi\)
0.543674 + 0.839297i \(0.317033\pi\)
\(594\) 3.27347 0.134312
\(595\) −20.2576 −0.830482
\(596\) 12.5027 0.512129
\(597\) −7.13825 −0.292149
\(598\) 0.0133182 0.000544622 0
\(599\) −15.5145 −0.633906 −0.316953 0.948441i \(-0.602660\pi\)
−0.316953 + 0.948441i \(0.602660\pi\)
\(600\) 0.577714 0.0235851
\(601\) −13.7412 −0.560515 −0.280257 0.959925i \(-0.590420\pi\)
−0.280257 + 0.959925i \(0.590420\pi\)
\(602\) 2.69986 0.110038
\(603\) 23.7056 0.965366
\(604\) 11.5357 0.469383
\(605\) −1.00000 −0.0406558
\(606\) 8.45693 0.343539
\(607\) 11.5673 0.469503 0.234752 0.972055i \(-0.424572\pi\)
0.234752 + 0.972055i \(0.424572\pi\)
\(608\) 5.32428 0.215928
\(609\) −15.1943 −0.615703
\(610\) 4.27657 0.173153
\(611\) −0.0753233 −0.00304726
\(612\) 20.0054 0.808672
\(613\) 5.55030 0.224174 0.112087 0.993698i \(-0.464246\pi\)
0.112087 + 0.993698i \(0.464246\pi\)
\(614\) 8.27918 0.334120
\(615\) 5.28135 0.212965
\(616\) −2.69986 −0.108780
\(617\) −20.1201 −0.810006 −0.405003 0.914315i \(-0.632730\pi\)
−0.405003 + 0.914315i \(0.632730\pi\)
\(618\) −3.66821 −0.147557
\(619\) −1.34982 −0.0542538 −0.0271269 0.999632i \(-0.508636\pi\)
−0.0271269 + 0.999632i \(0.508636\pi\)
\(620\) −1.14932 −0.0461578
\(621\) −6.52507 −0.261842
\(622\) −14.4629 −0.579910
\(623\) 44.5308 1.78409
\(624\) −0.00385995 −0.000154522 0
\(625\) 1.00000 0.0400000
\(626\) 1.07351 0.0429061
\(627\) −3.07591 −0.122840
\(628\) −15.0341 −0.599924
\(629\) 73.0205 2.91152
\(630\) 7.19848 0.286794
\(631\) 34.8854 1.38877 0.694384 0.719605i \(-0.255677\pi\)
0.694384 + 0.719605i \(0.255677\pi\)
\(632\) 4.15910 0.165440
\(633\) −13.2478 −0.526551
\(634\) 18.3258 0.727809
\(635\) 12.7904 0.507573
\(636\) 1.47224 0.0583779
\(637\) 0.00193239 7.65640e−5 0
\(638\) −9.74150 −0.385670
\(639\) 42.1241 1.66640
\(640\) 1.00000 0.0395285
\(641\) −8.36971 −0.330584 −0.165292 0.986245i \(-0.552857\pi\)
−0.165292 + 0.986245i \(0.552857\pi\)
\(642\) 6.44977 0.254552
\(643\) 28.7586 1.13413 0.567065 0.823673i \(-0.308079\pi\)
0.567065 + 0.823673i \(0.308079\pi\)
\(644\) 5.38167 0.212068
\(645\) 0.577714 0.0227475
\(646\) −39.9492 −1.57178
\(647\) −46.0375 −1.80992 −0.904960 0.425497i \(-0.860099\pi\)
−0.904960 + 0.425497i \(0.860099\pi\)
\(648\) −6.10761 −0.239929
\(649\) −6.45474 −0.253371
\(650\) −0.00668142 −0.000262067 0
\(651\) 1.79264 0.0702593
\(652\) −11.8173 −0.462801
\(653\) −12.6529 −0.495148 −0.247574 0.968869i \(-0.579633\pi\)
−0.247574 + 0.968869i \(0.579633\pi\)
\(654\) −4.15550 −0.162493
\(655\) 7.85038 0.306740
\(656\) 9.14180 0.356927
\(657\) −20.6068 −0.803948
\(658\) −30.4370 −1.18656
\(659\) 33.1773 1.29240 0.646202 0.763166i \(-0.276356\pi\)
0.646202 + 0.763166i \(0.276356\pi\)
\(660\) −0.577714 −0.0224875
\(661\) 15.1291 0.588455 0.294227 0.955735i \(-0.404938\pi\)
0.294227 + 0.955735i \(0.404938\pi\)
\(662\) 20.6284 0.801744
\(663\) 0.0289621 0.00112479
\(664\) 6.92811 0.268863
\(665\) −14.3748 −0.557430
\(666\) −25.9476 −1.00545
\(667\) 19.4179 0.751865
\(668\) 8.98218 0.347531
\(669\) −7.26996 −0.281073
\(670\) −8.89100 −0.343489
\(671\) −4.27657 −0.165095
\(672\) −1.55974 −0.0601685
\(673\) 33.3925 1.28719 0.643594 0.765367i \(-0.277443\pi\)
0.643594 + 0.765367i \(0.277443\pi\)
\(674\) −4.19893 −0.161737
\(675\) 3.27347 0.125996
\(676\) −13.0000 −0.499998
\(677\) −50.5639 −1.94333 −0.971664 0.236365i \(-0.924044\pi\)
−0.971664 + 0.236365i \(0.924044\pi\)
\(678\) −8.01276 −0.307728
\(679\) −39.1225 −1.50138
\(680\) −7.50323 −0.287736
\(681\) −7.76588 −0.297589
\(682\) 1.14932 0.0440097
\(683\) −39.3871 −1.50710 −0.753552 0.657388i \(-0.771661\pi\)
−0.753552 + 0.657388i \(0.771661\pi\)
\(684\) 14.1958 0.542791
\(685\) −8.10979 −0.309859
\(686\) −18.1181 −0.691754
\(687\) −8.46464 −0.322946
\(688\) 1.00000 0.0381246
\(689\) −0.0170268 −0.000648669 0
\(690\) 1.15157 0.0438395
\(691\) −43.6230 −1.65950 −0.829748 0.558139i \(-0.811516\pi\)
−0.829748 + 0.558139i \(0.811516\pi\)
\(692\) 0.691126 0.0262727
\(693\) −7.19848 −0.273448
\(694\) −11.3065 −0.429188
\(695\) −9.85552 −0.373841
\(696\) −5.62781 −0.213321
\(697\) −68.5930 −2.59815
\(698\) 27.8234 1.05313
\(699\) 9.89176 0.374141
\(700\) −2.69986 −0.102045
\(701\) −3.67861 −0.138939 −0.0694695 0.997584i \(-0.522131\pi\)
−0.0694695 + 0.997584i \(0.522131\pi\)
\(702\) −0.0218714 −0.000825484 0
\(703\) 51.8152 1.95425
\(704\) −1.00000 −0.0376889
\(705\) −6.51289 −0.245290
\(706\) 30.2682 1.13916
\(707\) −39.5221 −1.48638
\(708\) −3.72899 −0.140144
\(709\) −1.47094 −0.0552423 −0.0276212 0.999618i \(-0.508793\pi\)
−0.0276212 + 0.999618i \(0.508793\pi\)
\(710\) −15.7990 −0.592927
\(711\) 11.0892 0.415877
\(712\) 16.4938 0.618130
\(713\) −2.29096 −0.0857971
\(714\) 11.7031 0.437978
\(715\) 0.00668142 0.000249871 0
\(716\) −11.7502 −0.439125
\(717\) 2.67989 0.100082
\(718\) 0.0533741 0.00199190
\(719\) 22.4756 0.838200 0.419100 0.907940i \(-0.362346\pi\)
0.419100 + 0.907940i \(0.362346\pi\)
\(720\) 2.66625 0.0993651
\(721\) 17.1428 0.638430
\(722\) −9.34792 −0.347893
\(723\) −8.80632 −0.327511
\(724\) −7.73730 −0.287555
\(725\) −9.74150 −0.361790
\(726\) 0.577714 0.0214410
\(727\) −30.1579 −1.11850 −0.559248 0.829001i \(-0.688910\pi\)
−0.559248 + 0.829001i \(0.688910\pi\)
\(728\) 0.0180389 0.000668565 0
\(729\) −10.6110 −0.393000
\(730\) 7.72877 0.286055
\(731\) −7.50323 −0.277517
\(732\) −2.47063 −0.0913173
\(733\) 6.75176 0.249382 0.124691 0.992196i \(-0.460206\pi\)
0.124691 + 0.992196i \(0.460206\pi\)
\(734\) −10.8408 −0.400140
\(735\) 0.167085 0.00616304
\(736\) 1.99332 0.0734747
\(737\) 8.89100 0.327504
\(738\) 24.3743 0.897230
\(739\) 4.36909 0.160719 0.0803597 0.996766i \(-0.474393\pi\)
0.0803597 + 0.996766i \(0.474393\pi\)
\(740\) 9.73188 0.357751
\(741\) 0.0205515 0.000754976 0
\(742\) −6.88025 −0.252582
\(743\) −8.81851 −0.323520 −0.161760 0.986830i \(-0.551717\pi\)
−0.161760 + 0.986830i \(0.551717\pi\)
\(744\) 0.663978 0.0243426
\(745\) −12.5027 −0.458062
\(746\) 28.6721 1.04976
\(747\) 18.4720 0.675857
\(748\) 7.50323 0.274345
\(749\) −30.1420 −1.10136
\(750\) −0.577714 −0.0210951
\(751\) −16.8820 −0.616031 −0.308016 0.951381i \(-0.599665\pi\)
−0.308016 + 0.951381i \(0.599665\pi\)
\(752\) −11.2736 −0.411104
\(753\) −3.41383 −0.124407
\(754\) 0.0650871 0.00237033
\(755\) −11.5357 −0.419829
\(756\) −8.83790 −0.321431
\(757\) −45.6446 −1.65898 −0.829490 0.558521i \(-0.811369\pi\)
−0.829490 + 0.558521i \(0.811369\pi\)
\(758\) −24.2561 −0.881023
\(759\) −1.15157 −0.0417993
\(760\) −5.32428 −0.193132
\(761\) −39.5567 −1.43393 −0.716964 0.697110i \(-0.754469\pi\)
−0.716964 + 0.697110i \(0.754469\pi\)
\(762\) −7.38922 −0.267683
\(763\) 19.4201 0.703053
\(764\) 0.577591 0.0208965
\(765\) −20.0054 −0.723298
\(766\) −14.7829 −0.534126
\(767\) 0.0431268 0.00155722
\(768\) −0.577714 −0.0208465
\(769\) −17.6786 −0.637507 −0.318753 0.947838i \(-0.603264\pi\)
−0.318753 + 0.947838i \(0.603264\pi\)
\(770\) 2.69986 0.0972960
\(771\) 13.1939 0.475167
\(772\) −5.27610 −0.189891
\(773\) −24.8237 −0.892848 −0.446424 0.894822i \(-0.647303\pi\)
−0.446424 + 0.894822i \(0.647303\pi\)
\(774\) 2.66625 0.0958362
\(775\) 1.14932 0.0412848
\(776\) −14.4906 −0.520182
\(777\) −15.1793 −0.544553
\(778\) −25.4940 −0.914004
\(779\) −48.6735 −1.74391
\(780\) 0.00385995 0.000138208 0
\(781\) 15.7990 0.565334
\(782\) −14.9563 −0.534837
\(783\) −31.8885 −1.13960
\(784\) 0.289218 0.0103292
\(785\) 15.0341 0.536588
\(786\) −4.53528 −0.161768
\(787\) −13.5929 −0.484534 −0.242267 0.970210i \(-0.577891\pi\)
−0.242267 + 0.970210i \(0.577891\pi\)
\(788\) −21.4244 −0.763212
\(789\) −1.36511 −0.0485991
\(790\) −4.15910 −0.147974
\(791\) 37.4464 1.33144
\(792\) −2.66625 −0.0947409
\(793\) 0.0285735 0.00101468
\(794\) −17.7664 −0.630505
\(795\) −1.47224 −0.0522148
\(796\) 12.3560 0.437948
\(797\) −28.6756 −1.01574 −0.507872 0.861433i \(-0.669568\pi\)
−0.507872 + 0.861433i \(0.669568\pi\)
\(798\) 8.30451 0.293977
\(799\) 84.5880 2.99251
\(800\) −1.00000 −0.0353553
\(801\) 43.9764 1.55383
\(802\) 0.144875 0.00511571
\(803\) −7.72877 −0.272742
\(804\) 5.13646 0.181149
\(805\) −5.38167 −0.189679
\(806\) −0.00767908 −0.000270484 0
\(807\) 9.35325 0.329250
\(808\) −14.6386 −0.514984
\(809\) −53.7637 −1.89023 −0.945116 0.326736i \(-0.894051\pi\)
−0.945116 + 0.326736i \(0.894051\pi\)
\(810\) 6.10761 0.214599
\(811\) −7.62688 −0.267816 −0.133908 0.990994i \(-0.542753\pi\)
−0.133908 + 0.990994i \(0.542753\pi\)
\(812\) 26.3006 0.922972
\(813\) 2.50880 0.0879876
\(814\) −9.73188 −0.341102
\(815\) 11.8173 0.413942
\(816\) 4.33472 0.151746
\(817\) −5.32428 −0.186273
\(818\) 0.871128 0.0304583
\(819\) 0.0480961 0.00168061
\(820\) −9.14180 −0.319246
\(821\) −18.2915 −0.638376 −0.319188 0.947691i \(-0.603410\pi\)
−0.319188 + 0.947691i \(0.603410\pi\)
\(822\) 4.68514 0.163413
\(823\) 30.4628 1.06187 0.530933 0.847414i \(-0.321842\pi\)
0.530933 + 0.847414i \(0.321842\pi\)
\(824\) 6.34952 0.221196
\(825\) 0.577714 0.0201134
\(826\) 17.4269 0.606358
\(827\) −27.5902 −0.959406 −0.479703 0.877431i \(-0.659256\pi\)
−0.479703 + 0.877431i \(0.659256\pi\)
\(828\) 5.31468 0.184698
\(829\) −35.3817 −1.22886 −0.614428 0.788973i \(-0.710613\pi\)
−0.614428 + 0.788973i \(0.710613\pi\)
\(830\) −6.92811 −0.240478
\(831\) 2.18229 0.0757030
\(832\) 0.00668142 0.000231637 0
\(833\) −2.17007 −0.0751884
\(834\) 5.69367 0.197156
\(835\) −8.98218 −0.310841
\(836\) 5.32428 0.184144
\(837\) 3.76226 0.130043
\(838\) 19.3475 0.668347
\(839\) −23.5199 −0.811998 −0.405999 0.913873i \(-0.633076\pi\)
−0.405999 + 0.913873i \(0.633076\pi\)
\(840\) 1.55974 0.0538163
\(841\) 65.8969 2.27231
\(842\) 13.3644 0.460566
\(843\) −0.732767 −0.0252378
\(844\) 22.9313 0.789329
\(845\) 13.0000 0.447212
\(846\) −30.0581 −1.03342
\(847\) −2.69986 −0.0927681
\(848\) −2.54838 −0.0875117
\(849\) 5.87386 0.201590
\(850\) 7.50323 0.257359
\(851\) 19.3987 0.664980
\(852\) 9.12733 0.312697
\(853\) 18.9000 0.647124 0.323562 0.946207i \(-0.395120\pi\)
0.323562 + 0.946207i \(0.395120\pi\)
\(854\) 11.5461 0.395100
\(855\) −14.1958 −0.485487
\(856\) −11.1643 −0.381587
\(857\) −40.3890 −1.37966 −0.689831 0.723971i \(-0.742315\pi\)
−0.689831 + 0.723971i \(0.742315\pi\)
\(858\) −0.00385995 −0.000131777 0
\(859\) −37.2036 −1.26937 −0.634685 0.772771i \(-0.718870\pi\)
−0.634685 + 0.772771i \(0.718870\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 14.2589 0.485941
\(862\) 18.9085 0.644025
\(863\) −42.9220 −1.46108 −0.730541 0.682869i \(-0.760732\pi\)
−0.730541 + 0.682869i \(0.760732\pi\)
\(864\) −3.27347 −0.111366
\(865\) −0.691126 −0.0234990
\(866\) 28.0836 0.954319
\(867\) −22.7032 −0.771043
\(868\) −3.10299 −0.105322
\(869\) 4.15910 0.141088
\(870\) 5.62781 0.190800
\(871\) −0.0594045 −0.00201284
\(872\) 7.19300 0.243586
\(873\) −38.6355 −1.30761
\(874\) −10.6130 −0.358989
\(875\) 2.69986 0.0912718
\(876\) −4.46502 −0.150859
\(877\) −31.0755 −1.04934 −0.524672 0.851304i \(-0.675812\pi\)
−0.524672 + 0.851304i \(0.675812\pi\)
\(878\) −40.8954 −1.38015
\(879\) 10.6775 0.360142
\(880\) 1.00000 0.0337100
\(881\) −21.8002 −0.734468 −0.367234 0.930129i \(-0.619695\pi\)
−0.367234 + 0.930129i \(0.619695\pi\)
\(882\) 0.771127 0.0259652
\(883\) 26.3278 0.886002 0.443001 0.896521i \(-0.353914\pi\)
0.443001 + 0.896521i \(0.353914\pi\)
\(884\) −0.0501322 −0.00168613
\(885\) 3.72899 0.125349
\(886\) −40.6426 −1.36541
\(887\) 28.0714 0.942546 0.471273 0.881987i \(-0.343795\pi\)
0.471273 + 0.881987i \(0.343795\pi\)
\(888\) −5.62225 −0.188670
\(889\) 34.5323 1.15818
\(890\) −16.4938 −0.552872
\(891\) −6.10761 −0.204613
\(892\) 12.5840 0.421344
\(893\) 60.0235 2.00861
\(894\) 7.22297 0.241572
\(895\) 11.7502 0.392765
\(896\) 2.69986 0.0901958
\(897\) 0.00769411 0.000256899 0
\(898\) −20.4364 −0.681973
\(899\) −11.1961 −0.373411
\(900\) −2.66625 −0.0888749
\(901\) 19.1211 0.637015
\(902\) 9.14180 0.304389
\(903\) 1.55974 0.0519051
\(904\) 13.8698 0.461302
\(905\) 7.73730 0.257197
\(906\) 6.66437 0.221409
\(907\) −46.6685 −1.54960 −0.774801 0.632206i \(-0.782150\pi\)
−0.774801 + 0.632206i \(0.782150\pi\)
\(908\) 13.4424 0.446103
\(909\) −39.0301 −1.29455
\(910\) −0.0180389 −0.000597983 0
\(911\) −5.96756 −0.197714 −0.0988570 0.995102i \(-0.531519\pi\)
−0.0988570 + 0.995102i \(0.531519\pi\)
\(912\) 3.07591 0.101854
\(913\) 6.92811 0.229287
\(914\) −28.6296 −0.946982
\(915\) 2.47063 0.0816767
\(916\) 14.6520 0.484114
\(917\) 21.1949 0.699917
\(918\) 24.5616 0.810653
\(919\) 24.0451 0.793175 0.396587 0.917997i \(-0.370194\pi\)
0.396587 + 0.917997i \(0.370194\pi\)
\(920\) −1.99332 −0.0657178
\(921\) 4.78300 0.157605
\(922\) −7.14878 −0.235433
\(923\) −0.105560 −0.00347455
\(924\) −1.55974 −0.0513118
\(925\) −9.73188 −0.319982
\(926\) 30.9169 1.01599
\(927\) 16.9294 0.556034
\(928\) 9.74150 0.319781
\(929\) −58.4345 −1.91717 −0.958587 0.284799i \(-0.908073\pi\)
−0.958587 + 0.284799i \(0.908073\pi\)
\(930\) −0.663978 −0.0217727
\(931\) −1.53988 −0.0504674
\(932\) −17.1222 −0.560858
\(933\) −8.35543 −0.273544
\(934\) −19.7877 −0.647474
\(935\) −7.50323 −0.245382
\(936\) 0.0178143 0.000582279 0
\(937\) −34.6629 −1.13239 −0.566195 0.824272i \(-0.691585\pi\)
−0.566195 + 0.824272i \(0.691585\pi\)
\(938\) −24.0044 −0.783772
\(939\) 0.620182 0.0202389
\(940\) 11.2736 0.367703
\(941\) −52.5919 −1.71445 −0.857224 0.514944i \(-0.827813\pi\)
−0.857224 + 0.514944i \(0.827813\pi\)
\(942\) −8.68539 −0.282985
\(943\) −18.2225 −0.593407
\(944\) 6.45474 0.210084
\(945\) 8.83790 0.287497
\(946\) 1.00000 0.0325128
\(947\) −13.6195 −0.442575 −0.221288 0.975209i \(-0.571026\pi\)
−0.221288 + 0.975209i \(0.571026\pi\)
\(948\) 2.40277 0.0780385
\(949\) 0.0516392 0.00167628
\(950\) 5.32428 0.172742
\(951\) 10.5870 0.343309
\(952\) −20.2576 −0.656553
\(953\) −23.5761 −0.763704 −0.381852 0.924223i \(-0.624714\pi\)
−0.381852 + 0.924223i \(0.624714\pi\)
\(954\) −6.79461 −0.219983
\(955\) −0.577591 −0.0186904
\(956\) −4.63878 −0.150029
\(957\) −5.62781 −0.181921
\(958\) 17.7962 0.574970
\(959\) −21.8953 −0.707035
\(960\) 0.577714 0.0186456
\(961\) −29.6791 −0.957389
\(962\) 0.0650228 0.00209642
\(963\) −29.7667 −0.959220
\(964\) 15.2434 0.490956
\(965\) 5.27610 0.169844
\(966\) 3.10907 0.100033
\(967\) 9.55469 0.307258 0.153629 0.988129i \(-0.450904\pi\)
0.153629 + 0.988129i \(0.450904\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −23.0793 −0.741412
\(970\) 14.4906 0.465265
\(971\) 55.4199 1.77851 0.889255 0.457413i \(-0.151224\pi\)
0.889255 + 0.457413i \(0.151224\pi\)
\(972\) −13.3489 −0.428165
\(973\) −26.6085 −0.853029
\(974\) −22.9534 −0.735473
\(975\) −0.00385995 −0.000123617 0
\(976\) 4.27657 0.136890
\(977\) 36.1687 1.15714 0.578569 0.815633i \(-0.303611\pi\)
0.578569 + 0.815633i \(0.303611\pi\)
\(978\) −6.82702 −0.218304
\(979\) 16.4938 0.527143
\(980\) −0.289218 −0.00923873
\(981\) 19.1783 0.612316
\(982\) −3.36504 −0.107383
\(983\) 5.87258 0.187306 0.0936531 0.995605i \(-0.470146\pi\)
0.0936531 + 0.995605i \(0.470146\pi\)
\(984\) 5.28135 0.168363
\(985\) 21.4244 0.682638
\(986\) −73.0927 −2.32775
\(987\) −17.5839 −0.559701
\(988\) −0.0355737 −0.00113175
\(989\) −1.99332 −0.0633838
\(990\) 2.66625 0.0847389
\(991\) 7.69550 0.244456 0.122228 0.992502i \(-0.460996\pi\)
0.122228 + 0.992502i \(0.460996\pi\)
\(992\) −1.14932 −0.0364909
\(993\) 11.9173 0.378184
\(994\) −42.6551 −1.35294
\(995\) −12.3560 −0.391712
\(996\) 4.00247 0.126823
\(997\) 22.1929 0.702855 0.351427 0.936215i \(-0.385696\pi\)
0.351427 + 0.936215i \(0.385696\pi\)
\(998\) −18.9121 −0.598653
\(999\) −31.8570 −1.00791
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.bb.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.6 11 1.1 even 1 trivial