Properties

Label 8034.2.a.z.1.11
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} - 6316 x + 1552\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-1.59859\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.59859 q^{5} +1.00000 q^{6} +4.24832 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.59859 q^{5} +1.00000 q^{6} +4.24832 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.59859 q^{10} +4.07067 q^{11} -1.00000 q^{12} +1.00000 q^{13} -4.24832 q^{14} -1.59859 q^{15} +1.00000 q^{16} -4.06157 q^{17} -1.00000 q^{18} +3.43588 q^{19} +1.59859 q^{20} -4.24832 q^{21} -4.07067 q^{22} +9.26262 q^{23} +1.00000 q^{24} -2.44452 q^{25} -1.00000 q^{26} -1.00000 q^{27} +4.24832 q^{28} +7.09160 q^{29} +1.59859 q^{30} -10.7030 q^{31} -1.00000 q^{32} -4.07067 q^{33} +4.06157 q^{34} +6.79130 q^{35} +1.00000 q^{36} +5.89679 q^{37} -3.43588 q^{38} -1.00000 q^{39} -1.59859 q^{40} -5.28889 q^{41} +4.24832 q^{42} -1.53277 q^{43} +4.07067 q^{44} +1.59859 q^{45} -9.26262 q^{46} -9.61413 q^{47} -1.00000 q^{48} +11.0482 q^{49} +2.44452 q^{50} +4.06157 q^{51} +1.00000 q^{52} +10.0672 q^{53} +1.00000 q^{54} +6.50731 q^{55} -4.24832 q^{56} -3.43588 q^{57} -7.09160 q^{58} +5.95635 q^{59} -1.59859 q^{60} +6.49344 q^{61} +10.7030 q^{62} +4.24832 q^{63} +1.00000 q^{64} +1.59859 q^{65} +4.07067 q^{66} +4.52053 q^{67} -4.06157 q^{68} -9.26262 q^{69} -6.79130 q^{70} -13.3814 q^{71} -1.00000 q^{72} +3.94293 q^{73} -5.89679 q^{74} +2.44452 q^{75} +3.43588 q^{76} +17.2935 q^{77} +1.00000 q^{78} +1.53043 q^{79} +1.59859 q^{80} +1.00000 q^{81} +5.28889 q^{82} +9.36721 q^{83} -4.24832 q^{84} -6.49277 q^{85} +1.53277 q^{86} -7.09160 q^{87} -4.07067 q^{88} -8.97228 q^{89} -1.59859 q^{90} +4.24832 q^{91} +9.26262 q^{92} +10.7030 q^{93} +9.61413 q^{94} +5.49256 q^{95} +1.00000 q^{96} +14.0823 q^{97} -11.0482 q^{98} +4.07067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.59859 0.714909 0.357455 0.933931i \(-0.383645\pi\)
0.357455 + 0.933931i \(0.383645\pi\)
\(6\) 1.00000 0.408248
\(7\) 4.24832 1.60571 0.802856 0.596172i \(-0.203313\pi\)
0.802856 + 0.596172i \(0.203313\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.59859 −0.505517
\(11\) 4.07067 1.22735 0.613676 0.789558i \(-0.289690\pi\)
0.613676 + 0.789558i \(0.289690\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −4.24832 −1.13541
\(15\) −1.59859 −0.412753
\(16\) 1.00000 0.250000
\(17\) −4.06157 −0.985076 −0.492538 0.870291i \(-0.663931\pi\)
−0.492538 + 0.870291i \(0.663931\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.43588 0.788246 0.394123 0.919058i \(-0.371048\pi\)
0.394123 + 0.919058i \(0.371048\pi\)
\(20\) 1.59859 0.357455
\(21\) −4.24832 −0.927059
\(22\) −4.07067 −0.867869
\(23\) 9.26262 1.93139 0.965695 0.259679i \(-0.0836166\pi\)
0.965695 + 0.259679i \(0.0836166\pi\)
\(24\) 1.00000 0.204124
\(25\) −2.44452 −0.488905
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 4.24832 0.802856
\(29\) 7.09160 1.31688 0.658439 0.752634i \(-0.271217\pi\)
0.658439 + 0.752634i \(0.271217\pi\)
\(30\) 1.59859 0.291860
\(31\) −10.7030 −1.92232 −0.961159 0.275995i \(-0.910993\pi\)
−0.961159 + 0.275995i \(0.910993\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.07067 −0.708612
\(34\) 4.06157 0.696554
\(35\) 6.79130 1.14794
\(36\) 1.00000 0.166667
\(37\) 5.89679 0.969427 0.484713 0.874673i \(-0.338924\pi\)
0.484713 + 0.874673i \(0.338924\pi\)
\(38\) −3.43588 −0.557374
\(39\) −1.00000 −0.160128
\(40\) −1.59859 −0.252759
\(41\) −5.28889 −0.825986 −0.412993 0.910734i \(-0.635517\pi\)
−0.412993 + 0.910734i \(0.635517\pi\)
\(42\) 4.24832 0.655530
\(43\) −1.53277 −0.233745 −0.116873 0.993147i \(-0.537287\pi\)
−0.116873 + 0.993147i \(0.537287\pi\)
\(44\) 4.07067 0.613676
\(45\) 1.59859 0.238303
\(46\) −9.26262 −1.36570
\(47\) −9.61413 −1.40236 −0.701182 0.712982i \(-0.747344\pi\)
−0.701182 + 0.712982i \(0.747344\pi\)
\(48\) −1.00000 −0.144338
\(49\) 11.0482 1.57831
\(50\) 2.44452 0.345708
\(51\) 4.06157 0.568734
\(52\) 1.00000 0.138675
\(53\) 10.0672 1.38283 0.691416 0.722457i \(-0.256987\pi\)
0.691416 + 0.722457i \(0.256987\pi\)
\(54\) 1.00000 0.136083
\(55\) 6.50731 0.877446
\(56\) −4.24832 −0.567705
\(57\) −3.43588 −0.455094
\(58\) −7.09160 −0.931173
\(59\) 5.95635 0.775451 0.387726 0.921775i \(-0.373261\pi\)
0.387726 + 0.921775i \(0.373261\pi\)
\(60\) −1.59859 −0.206377
\(61\) 6.49344 0.831399 0.415700 0.909502i \(-0.363537\pi\)
0.415700 + 0.909502i \(0.363537\pi\)
\(62\) 10.7030 1.35928
\(63\) 4.24832 0.535238
\(64\) 1.00000 0.125000
\(65\) 1.59859 0.198280
\(66\) 4.07067 0.501065
\(67\) 4.52053 0.552271 0.276135 0.961119i \(-0.410946\pi\)
0.276135 + 0.961119i \(0.410946\pi\)
\(68\) −4.06157 −0.492538
\(69\) −9.26262 −1.11509
\(70\) −6.79130 −0.811715
\(71\) −13.3814 −1.58808 −0.794042 0.607863i \(-0.792027\pi\)
−0.794042 + 0.607863i \(0.792027\pi\)
\(72\) −1.00000 −0.117851
\(73\) 3.94293 0.461485 0.230742 0.973015i \(-0.425885\pi\)
0.230742 + 0.973015i \(0.425885\pi\)
\(74\) −5.89679 −0.685488
\(75\) 2.44452 0.282269
\(76\) 3.43588 0.394123
\(77\) 17.2935 1.97078
\(78\) 1.00000 0.113228
\(79\) 1.53043 0.172187 0.0860936 0.996287i \(-0.472562\pi\)
0.0860936 + 0.996287i \(0.472562\pi\)
\(80\) 1.59859 0.178727
\(81\) 1.00000 0.111111
\(82\) 5.28889 0.584060
\(83\) 9.36721 1.02818 0.514092 0.857735i \(-0.328129\pi\)
0.514092 + 0.857735i \(0.328129\pi\)
\(84\) −4.24832 −0.463529
\(85\) −6.49277 −0.704240
\(86\) 1.53277 0.165283
\(87\) −7.09160 −0.760300
\(88\) −4.07067 −0.433935
\(89\) −8.97228 −0.951060 −0.475530 0.879700i \(-0.657744\pi\)
−0.475530 + 0.879700i \(0.657744\pi\)
\(90\) −1.59859 −0.168506
\(91\) 4.24832 0.445345
\(92\) 9.26262 0.965695
\(93\) 10.7030 1.10985
\(94\) 9.61413 0.991621
\(95\) 5.49256 0.563524
\(96\) 1.00000 0.102062
\(97\) 14.0823 1.42984 0.714922 0.699204i \(-0.246462\pi\)
0.714922 + 0.699204i \(0.246462\pi\)
\(98\) −11.0482 −1.11604
\(99\) 4.07067 0.409118
\(100\) −2.44452 −0.244452
\(101\) −0.882768 −0.0878387 −0.0439193 0.999035i \(-0.513984\pi\)
−0.0439193 + 0.999035i \(0.513984\pi\)
\(102\) −4.06157 −0.402155
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −6.79130 −0.662763
\(106\) −10.0672 −0.977809
\(107\) −6.27951 −0.607063 −0.303531 0.952821i \(-0.598166\pi\)
−0.303531 + 0.952821i \(0.598166\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 17.7587 1.70097 0.850485 0.525999i \(-0.176308\pi\)
0.850485 + 0.525999i \(0.176308\pi\)
\(110\) −6.50731 −0.620448
\(111\) −5.89679 −0.559699
\(112\) 4.24832 0.401428
\(113\) −3.56157 −0.335044 −0.167522 0.985868i \(-0.553577\pi\)
−0.167522 + 0.985868i \(0.553577\pi\)
\(114\) 3.43588 0.321800
\(115\) 14.8071 1.38077
\(116\) 7.09160 0.658439
\(117\) 1.00000 0.0924500
\(118\) −5.95635 −0.548327
\(119\) −17.2548 −1.58175
\(120\) 1.59859 0.145930
\(121\) 5.57034 0.506394
\(122\) −6.49344 −0.587888
\(123\) 5.28889 0.476883
\(124\) −10.7030 −0.961159
\(125\) −11.9007 −1.06443
\(126\) −4.24832 −0.378470
\(127\) 19.4121 1.72255 0.861274 0.508141i \(-0.169667\pi\)
0.861274 + 0.508141i \(0.169667\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.53277 0.134953
\(130\) −1.59859 −0.140205
\(131\) −11.1778 −0.976605 −0.488302 0.872674i \(-0.662384\pi\)
−0.488302 + 0.872674i \(0.662384\pi\)
\(132\) −4.07067 −0.354306
\(133\) 14.5967 1.26570
\(134\) −4.52053 −0.390515
\(135\) −1.59859 −0.137584
\(136\) 4.06157 0.348277
\(137\) −18.9130 −1.61585 −0.807924 0.589286i \(-0.799409\pi\)
−0.807924 + 0.589286i \(0.799409\pi\)
\(138\) 9.26262 0.788487
\(139\) −2.52047 −0.213783 −0.106892 0.994271i \(-0.534090\pi\)
−0.106892 + 0.994271i \(0.534090\pi\)
\(140\) 6.79130 0.573969
\(141\) 9.61413 0.809655
\(142\) 13.3814 1.12294
\(143\) 4.07067 0.340406
\(144\) 1.00000 0.0833333
\(145\) 11.3365 0.941448
\(146\) −3.94293 −0.326319
\(147\) −11.0482 −0.911240
\(148\) 5.89679 0.484713
\(149\) 21.9555 1.79866 0.899332 0.437267i \(-0.144053\pi\)
0.899332 + 0.437267i \(0.144053\pi\)
\(150\) −2.44452 −0.199595
\(151\) 9.14572 0.744268 0.372134 0.928179i \(-0.378626\pi\)
0.372134 + 0.928179i \(0.378626\pi\)
\(152\) −3.43588 −0.278687
\(153\) −4.06157 −0.328359
\(154\) −17.2935 −1.39355
\(155\) −17.1097 −1.37428
\(156\) −1.00000 −0.0800641
\(157\) −14.6803 −1.17161 −0.585807 0.810450i \(-0.699223\pi\)
−0.585807 + 0.810450i \(0.699223\pi\)
\(158\) −1.53043 −0.121755
\(159\) −10.0672 −0.798378
\(160\) −1.59859 −0.126379
\(161\) 39.3506 3.10126
\(162\) −1.00000 −0.0785674
\(163\) 12.9771 1.01644 0.508222 0.861226i \(-0.330303\pi\)
0.508222 + 0.861226i \(0.330303\pi\)
\(164\) −5.28889 −0.412993
\(165\) −6.50731 −0.506593
\(166\) −9.36721 −0.727036
\(167\) −3.95923 −0.306374 −0.153187 0.988197i \(-0.548954\pi\)
−0.153187 + 0.988197i \(0.548954\pi\)
\(168\) 4.24832 0.327765
\(169\) 1.00000 0.0769231
\(170\) 6.49277 0.497973
\(171\) 3.43588 0.262749
\(172\) −1.53277 −0.116873
\(173\) −2.24677 −0.170819 −0.0854094 0.996346i \(-0.527220\pi\)
−0.0854094 + 0.996346i \(0.527220\pi\)
\(174\) 7.09160 0.537613
\(175\) −10.3851 −0.785041
\(176\) 4.07067 0.306838
\(177\) −5.95635 −0.447707
\(178\) 8.97228 0.672501
\(179\) 6.03133 0.450803 0.225401 0.974266i \(-0.427631\pi\)
0.225401 + 0.974266i \(0.427631\pi\)
\(180\) 1.59859 0.119152
\(181\) 10.1195 0.752177 0.376088 0.926584i \(-0.377269\pi\)
0.376088 + 0.926584i \(0.377269\pi\)
\(182\) −4.24832 −0.314906
\(183\) −6.49344 −0.480009
\(184\) −9.26262 −0.682850
\(185\) 9.42653 0.693052
\(186\) −10.7030 −0.784783
\(187\) −16.5333 −1.20904
\(188\) −9.61413 −0.701182
\(189\) −4.24832 −0.309020
\(190\) −5.49256 −0.398472
\(191\) 4.42049 0.319856 0.159928 0.987129i \(-0.448874\pi\)
0.159928 + 0.987129i \(0.448874\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −9.36665 −0.674226 −0.337113 0.941464i \(-0.609450\pi\)
−0.337113 + 0.941464i \(0.609450\pi\)
\(194\) −14.0823 −1.01105
\(195\) −1.59859 −0.114477
\(196\) 11.0482 0.789157
\(197\) −19.1911 −1.36731 −0.683656 0.729805i \(-0.739611\pi\)
−0.683656 + 0.729805i \(0.739611\pi\)
\(198\) −4.07067 −0.289290
\(199\) −7.97460 −0.565305 −0.282652 0.959222i \(-0.591214\pi\)
−0.282652 + 0.959222i \(0.591214\pi\)
\(200\) 2.44452 0.172854
\(201\) −4.52053 −0.318854
\(202\) 0.882768 0.0621113
\(203\) 30.1274 2.11453
\(204\) 4.06157 0.284367
\(205\) −8.45474 −0.590505
\(206\) 1.00000 0.0696733
\(207\) 9.26262 0.643797
\(208\) 1.00000 0.0693375
\(209\) 13.9863 0.967456
\(210\) 6.79130 0.468644
\(211\) 12.3843 0.852570 0.426285 0.904589i \(-0.359822\pi\)
0.426285 + 0.904589i \(0.359822\pi\)
\(212\) 10.0672 0.691416
\(213\) 13.3814 0.916880
\(214\) 6.27951 0.429258
\(215\) −2.45026 −0.167107
\(216\) 1.00000 0.0680414
\(217\) −45.4698 −3.08669
\(218\) −17.7587 −1.20277
\(219\) −3.94293 −0.266438
\(220\) 6.50731 0.438723
\(221\) −4.06157 −0.273211
\(222\) 5.89679 0.395767
\(223\) 25.3964 1.70067 0.850336 0.526241i \(-0.176399\pi\)
0.850336 + 0.526241i \(0.176399\pi\)
\(224\) −4.24832 −0.283853
\(225\) −2.44452 −0.162968
\(226\) 3.56157 0.236912
\(227\) −21.9470 −1.45667 −0.728336 0.685220i \(-0.759706\pi\)
−0.728336 + 0.685220i \(0.759706\pi\)
\(228\) −3.43588 −0.227547
\(229\) −2.07670 −0.137232 −0.0686162 0.997643i \(-0.521858\pi\)
−0.0686162 + 0.997643i \(0.521858\pi\)
\(230\) −14.8071 −0.976351
\(231\) −17.2935 −1.13783
\(232\) −7.09160 −0.465587
\(233\) −5.85936 −0.383859 −0.191930 0.981409i \(-0.561475\pi\)
−0.191930 + 0.981409i \(0.561475\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −15.3690 −1.00256
\(236\) 5.95635 0.387726
\(237\) −1.53043 −0.0994124
\(238\) 17.2548 1.11847
\(239\) −26.0203 −1.68311 −0.841557 0.540168i \(-0.818361\pi\)
−0.841557 + 0.540168i \(0.818361\pi\)
\(240\) −1.59859 −0.103188
\(241\) −19.3616 −1.24719 −0.623595 0.781748i \(-0.714329\pi\)
−0.623595 + 0.781748i \(0.714329\pi\)
\(242\) −5.57034 −0.358075
\(243\) −1.00000 −0.0641500
\(244\) 6.49344 0.415700
\(245\) 17.6615 1.12835
\(246\) −5.28889 −0.337207
\(247\) 3.43588 0.218620
\(248\) 10.7030 0.679642
\(249\) −9.36721 −0.593623
\(250\) 11.9007 0.752667
\(251\) −17.1426 −1.08203 −0.541015 0.841013i \(-0.681960\pi\)
−0.541015 + 0.841013i \(0.681960\pi\)
\(252\) 4.24832 0.267619
\(253\) 37.7051 2.37050
\(254\) −19.4121 −1.21803
\(255\) 6.49277 0.406593
\(256\) 1.00000 0.0625000
\(257\) 19.7734 1.23343 0.616716 0.787186i \(-0.288463\pi\)
0.616716 + 0.787186i \(0.288463\pi\)
\(258\) −1.53277 −0.0954261
\(259\) 25.0514 1.55662
\(260\) 1.59859 0.0991401
\(261\) 7.09160 0.438959
\(262\) 11.1778 0.690564
\(263\) −30.8363 −1.90145 −0.950725 0.310036i \(-0.899659\pi\)
−0.950725 + 0.310036i \(0.899659\pi\)
\(264\) 4.07067 0.250532
\(265\) 16.0932 0.988599
\(266\) −14.5967 −0.894983
\(267\) 8.97228 0.549095
\(268\) 4.52053 0.276135
\(269\) 14.5206 0.885336 0.442668 0.896686i \(-0.354032\pi\)
0.442668 + 0.896686i \(0.354032\pi\)
\(270\) 1.59859 0.0972868
\(271\) −26.3261 −1.59920 −0.799598 0.600536i \(-0.794954\pi\)
−0.799598 + 0.600536i \(0.794954\pi\)
\(272\) −4.06157 −0.246269
\(273\) −4.24832 −0.257120
\(274\) 18.9130 1.14258
\(275\) −9.95085 −0.600059
\(276\) −9.26262 −0.557544
\(277\) −25.8739 −1.55461 −0.777305 0.629124i \(-0.783414\pi\)
−0.777305 + 0.629124i \(0.783414\pi\)
\(278\) 2.52047 0.151168
\(279\) −10.7030 −0.640773
\(280\) −6.79130 −0.405858
\(281\) 3.93838 0.234944 0.117472 0.993076i \(-0.462521\pi\)
0.117472 + 0.993076i \(0.462521\pi\)
\(282\) −9.61413 −0.572513
\(283\) 14.0958 0.837907 0.418953 0.908008i \(-0.362397\pi\)
0.418953 + 0.908008i \(0.362397\pi\)
\(284\) −13.3814 −0.794042
\(285\) −5.49256 −0.325351
\(286\) −4.07067 −0.240704
\(287\) −22.4689 −1.32630
\(288\) −1.00000 −0.0589256
\(289\) −0.503638 −0.0296258
\(290\) −11.3365 −0.665704
\(291\) −14.0823 −0.825521
\(292\) 3.94293 0.230742
\(293\) −5.42241 −0.316781 −0.158390 0.987377i \(-0.550630\pi\)
−0.158390 + 0.987377i \(0.550630\pi\)
\(294\) 11.0482 0.644344
\(295\) 9.52174 0.554377
\(296\) −5.89679 −0.342744
\(297\) −4.07067 −0.236204
\(298\) −21.9555 −1.27185
\(299\) 9.26262 0.535671
\(300\) 2.44452 0.141135
\(301\) −6.51169 −0.375328
\(302\) −9.14572 −0.526277
\(303\) 0.882768 0.0507137
\(304\) 3.43588 0.197061
\(305\) 10.3803 0.594375
\(306\) 4.06157 0.232185
\(307\) −18.0104 −1.02791 −0.513953 0.857818i \(-0.671820\pi\)
−0.513953 + 0.857818i \(0.671820\pi\)
\(308\) 17.2935 0.985388
\(309\) 1.00000 0.0568880
\(310\) 17.1097 0.971765
\(311\) −5.11921 −0.290284 −0.145142 0.989411i \(-0.546364\pi\)
−0.145142 + 0.989411i \(0.546364\pi\)
\(312\) 1.00000 0.0566139
\(313\) −17.4175 −0.984495 −0.492248 0.870455i \(-0.663825\pi\)
−0.492248 + 0.870455i \(0.663825\pi\)
\(314\) 14.6803 0.828457
\(315\) 6.79130 0.382646
\(316\) 1.53043 0.0860936
\(317\) 5.40980 0.303845 0.151922 0.988392i \(-0.451454\pi\)
0.151922 + 0.988392i \(0.451454\pi\)
\(318\) 10.0672 0.564538
\(319\) 28.8676 1.61627
\(320\) 1.59859 0.0893637
\(321\) 6.27951 0.350488
\(322\) −39.3506 −2.19292
\(323\) −13.9551 −0.776482
\(324\) 1.00000 0.0555556
\(325\) −2.44452 −0.135598
\(326\) −12.9771 −0.718735
\(327\) −17.7587 −0.982056
\(328\) 5.28889 0.292030
\(329\) −40.8438 −2.25179
\(330\) 6.50731 0.358216
\(331\) 20.5502 1.12954 0.564770 0.825248i \(-0.308965\pi\)
0.564770 + 0.825248i \(0.308965\pi\)
\(332\) 9.36721 0.514092
\(333\) 5.89679 0.323142
\(334\) 3.95923 0.216639
\(335\) 7.22646 0.394824
\(336\) −4.24832 −0.231765
\(337\) 25.2019 1.37283 0.686416 0.727209i \(-0.259183\pi\)
0.686416 + 0.727209i \(0.259183\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 3.56157 0.193438
\(340\) −6.49277 −0.352120
\(341\) −43.5684 −2.35936
\(342\) −3.43588 −0.185791
\(343\) 17.1980 0.928606
\(344\) 1.53277 0.0826414
\(345\) −14.8071 −0.797187
\(346\) 2.24677 0.120787
\(347\) −4.37034 −0.234612 −0.117306 0.993096i \(-0.537426\pi\)
−0.117306 + 0.993096i \(0.537426\pi\)
\(348\) −7.09160 −0.380150
\(349\) 10.6522 0.570199 0.285099 0.958498i \(-0.407973\pi\)
0.285099 + 0.958498i \(0.407973\pi\)
\(350\) 10.3851 0.555108
\(351\) −1.00000 −0.0533761
\(352\) −4.07067 −0.216967
\(353\) −28.9724 −1.54205 −0.771023 0.636808i \(-0.780255\pi\)
−0.771023 + 0.636808i \(0.780255\pi\)
\(354\) 5.95635 0.316577
\(355\) −21.3914 −1.13534
\(356\) −8.97228 −0.475530
\(357\) 17.2548 0.913223
\(358\) −6.03133 −0.318766
\(359\) −0.959221 −0.0506258 −0.0253129 0.999680i \(-0.508058\pi\)
−0.0253129 + 0.999680i \(0.508058\pi\)
\(360\) −1.59859 −0.0842529
\(361\) −7.19470 −0.378668
\(362\) −10.1195 −0.531869
\(363\) −5.57034 −0.292367
\(364\) 4.24832 0.222672
\(365\) 6.30311 0.329920
\(366\) 6.49344 0.339417
\(367\) −38.0272 −1.98501 −0.992503 0.122220i \(-0.960999\pi\)
−0.992503 + 0.122220i \(0.960999\pi\)
\(368\) 9.26262 0.482848
\(369\) −5.28889 −0.275329
\(370\) −9.42653 −0.490062
\(371\) 42.7685 2.22043
\(372\) 10.7030 0.554925
\(373\) −21.3704 −1.10652 −0.553258 0.833010i \(-0.686616\pi\)
−0.553258 + 0.833010i \(0.686616\pi\)
\(374\) 16.5333 0.854917
\(375\) 11.9007 0.614550
\(376\) 9.61413 0.495811
\(377\) 7.09160 0.365236
\(378\) 4.24832 0.218510
\(379\) 12.3795 0.635892 0.317946 0.948109i \(-0.397007\pi\)
0.317946 + 0.948109i \(0.397007\pi\)
\(380\) 5.49256 0.281762
\(381\) −19.4121 −0.994514
\(382\) −4.42049 −0.226172
\(383\) 21.8227 1.11509 0.557543 0.830148i \(-0.311744\pi\)
0.557543 + 0.830148i \(0.311744\pi\)
\(384\) 1.00000 0.0510310
\(385\) 27.6451 1.40893
\(386\) 9.36665 0.476750
\(387\) −1.53277 −0.0779151
\(388\) 14.0823 0.714922
\(389\) −3.84107 −0.194750 −0.0973751 0.995248i \(-0.531045\pi\)
−0.0973751 + 0.995248i \(0.531045\pi\)
\(390\) 1.59859 0.0809475
\(391\) −37.6208 −1.90257
\(392\) −11.0482 −0.558018
\(393\) 11.1778 0.563843
\(394\) 19.1911 0.966835
\(395\) 2.44653 0.123098
\(396\) 4.07067 0.204559
\(397\) 34.7939 1.74626 0.873128 0.487491i \(-0.162088\pi\)
0.873128 + 0.487491i \(0.162088\pi\)
\(398\) 7.97460 0.399731
\(399\) −14.5967 −0.730750
\(400\) −2.44452 −0.122226
\(401\) 19.8607 0.991795 0.495898 0.868381i \(-0.334839\pi\)
0.495898 + 0.868381i \(0.334839\pi\)
\(402\) 4.52053 0.225464
\(403\) −10.7030 −0.533155
\(404\) −0.882768 −0.0439193
\(405\) 1.59859 0.0794344
\(406\) −30.1274 −1.49520
\(407\) 24.0039 1.18983
\(408\) −4.06157 −0.201078
\(409\) 12.2273 0.604600 0.302300 0.953213i \(-0.402246\pi\)
0.302300 + 0.953213i \(0.402246\pi\)
\(410\) 8.45474 0.417550
\(411\) 18.9130 0.932911
\(412\) −1.00000 −0.0492665
\(413\) 25.3045 1.24515
\(414\) −9.26262 −0.455233
\(415\) 14.9743 0.735059
\(416\) −1.00000 −0.0490290
\(417\) 2.52047 0.123428
\(418\) −13.9863 −0.684094
\(419\) 20.6126 1.00699 0.503495 0.863998i \(-0.332047\pi\)
0.503495 + 0.863998i \(0.332047\pi\)
\(420\) −6.79130 −0.331381
\(421\) −0.0477608 −0.00232772 −0.00116386 0.999999i \(-0.500370\pi\)
−0.00116386 + 0.999999i \(0.500370\pi\)
\(422\) −12.3843 −0.602858
\(423\) −9.61413 −0.467455
\(424\) −10.0672 −0.488905
\(425\) 9.92861 0.481608
\(426\) −13.3814 −0.648332
\(427\) 27.5862 1.33499
\(428\) −6.27951 −0.303531
\(429\) −4.07067 −0.196534
\(430\) 2.45026 0.118162
\(431\) 22.7229 1.09453 0.547263 0.836961i \(-0.315670\pi\)
0.547263 + 0.836961i \(0.315670\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −19.8185 −0.952418 −0.476209 0.879332i \(-0.657989\pi\)
−0.476209 + 0.879332i \(0.657989\pi\)
\(434\) 45.4698 2.18262
\(435\) −11.3365 −0.543545
\(436\) 17.7587 0.850485
\(437\) 31.8253 1.52241
\(438\) 3.94293 0.188400
\(439\) −4.57038 −0.218132 −0.109066 0.994034i \(-0.534786\pi\)
−0.109066 + 0.994034i \(0.534786\pi\)
\(440\) −6.50731 −0.310224
\(441\) 11.0482 0.526105
\(442\) 4.06157 0.193189
\(443\) 14.7085 0.698821 0.349410 0.936970i \(-0.386382\pi\)
0.349410 + 0.936970i \(0.386382\pi\)
\(444\) −5.89679 −0.279849
\(445\) −14.3430 −0.679922
\(446\) −25.3964 −1.20256
\(447\) −21.9555 −1.03846
\(448\) 4.24832 0.200714
\(449\) −0.731479 −0.0345206 −0.0172603 0.999851i \(-0.505494\pi\)
−0.0172603 + 0.999851i \(0.505494\pi\)
\(450\) 2.44452 0.115236
\(451\) −21.5293 −1.01378
\(452\) −3.56157 −0.167522
\(453\) −9.14572 −0.429703
\(454\) 21.9470 1.03002
\(455\) 6.79130 0.318381
\(456\) 3.43588 0.160900
\(457\) 14.3463 0.671092 0.335546 0.942024i \(-0.391079\pi\)
0.335546 + 0.942024i \(0.391079\pi\)
\(458\) 2.07670 0.0970379
\(459\) 4.06157 0.189578
\(460\) 14.8071 0.690384
\(461\) 19.4261 0.904764 0.452382 0.891824i \(-0.350574\pi\)
0.452382 + 0.891824i \(0.350574\pi\)
\(462\) 17.2935 0.804566
\(463\) 15.2359 0.708073 0.354036 0.935232i \(-0.384809\pi\)
0.354036 + 0.935232i \(0.384809\pi\)
\(464\) 7.09160 0.329219
\(465\) 17.1097 0.793443
\(466\) 5.85936 0.271429
\(467\) 24.1527 1.11765 0.558826 0.829285i \(-0.311252\pi\)
0.558826 + 0.829285i \(0.311252\pi\)
\(468\) 1.00000 0.0462250
\(469\) 19.2047 0.886789
\(470\) 15.3690 0.708919
\(471\) 14.6803 0.676432
\(472\) −5.95635 −0.274163
\(473\) −6.23940 −0.286888
\(474\) 1.53043 0.0702952
\(475\) −8.39910 −0.385377
\(476\) −17.2548 −0.790874
\(477\) 10.0672 0.460944
\(478\) 26.0203 1.19014
\(479\) −9.59696 −0.438496 −0.219248 0.975669i \(-0.570360\pi\)
−0.219248 + 0.975669i \(0.570360\pi\)
\(480\) 1.59859 0.0729651
\(481\) 5.89679 0.268871
\(482\) 19.3616 0.881896
\(483\) −39.3506 −1.79051
\(484\) 5.57034 0.253197
\(485\) 22.5118 1.02221
\(486\) 1.00000 0.0453609
\(487\) −2.95817 −0.134048 −0.0670238 0.997751i \(-0.521350\pi\)
−0.0670238 + 0.997751i \(0.521350\pi\)
\(488\) −6.49344 −0.293944
\(489\) −12.9771 −0.586844
\(490\) −17.6615 −0.797865
\(491\) −5.44956 −0.245935 −0.122968 0.992411i \(-0.539241\pi\)
−0.122968 + 0.992411i \(0.539241\pi\)
\(492\) 5.28889 0.238442
\(493\) −28.8031 −1.29722
\(494\) −3.43588 −0.154588
\(495\) 6.50731 0.292482
\(496\) −10.7030 −0.480580
\(497\) −56.8486 −2.55001
\(498\) 9.36721 0.419755
\(499\) 34.6498 1.55114 0.775568 0.631264i \(-0.217464\pi\)
0.775568 + 0.631264i \(0.217464\pi\)
\(500\) −11.9007 −0.532216
\(501\) 3.95923 0.176885
\(502\) 17.1426 0.765111
\(503\) −10.2622 −0.457568 −0.228784 0.973477i \(-0.573475\pi\)
−0.228784 + 0.973477i \(0.573475\pi\)
\(504\) −4.24832 −0.189235
\(505\) −1.41118 −0.0627967
\(506\) −37.7051 −1.67619
\(507\) −1.00000 −0.0444116
\(508\) 19.4121 0.861274
\(509\) 7.73873 0.343013 0.171506 0.985183i \(-0.445137\pi\)
0.171506 + 0.985183i \(0.445137\pi\)
\(510\) −6.49277 −0.287505
\(511\) 16.7508 0.741012
\(512\) −1.00000 −0.0441942
\(513\) −3.43588 −0.151698
\(514\) −19.7734 −0.872168
\(515\) −1.59859 −0.0704421
\(516\) 1.53277 0.0674765
\(517\) −39.1359 −1.72120
\(518\) −25.0514 −1.10070
\(519\) 2.24677 0.0986222
\(520\) −1.59859 −0.0701026
\(521\) −31.0891 −1.36204 −0.681020 0.732265i \(-0.738463\pi\)
−0.681020 + 0.732265i \(0.738463\pi\)
\(522\) −7.09160 −0.310391
\(523\) 0.0814933 0.00356345 0.00178173 0.999998i \(-0.499433\pi\)
0.00178173 + 0.999998i \(0.499433\pi\)
\(524\) −11.1778 −0.488302
\(525\) 10.3851 0.453243
\(526\) 30.8363 1.34453
\(527\) 43.4711 1.89363
\(528\) −4.07067 −0.177153
\(529\) 62.7962 2.73027
\(530\) −16.0932 −0.699045
\(531\) 5.95635 0.258484
\(532\) 14.5967 0.632848
\(533\) −5.28889 −0.229087
\(534\) −8.97228 −0.388269
\(535\) −10.0383 −0.433995
\(536\) −4.52053 −0.195257
\(537\) −6.03133 −0.260271
\(538\) −14.5206 −0.626027
\(539\) 44.9735 1.93715
\(540\) −1.59859 −0.0687922
\(541\) 13.8662 0.596155 0.298077 0.954542i \(-0.403655\pi\)
0.298077 + 0.954542i \(0.403655\pi\)
\(542\) 26.3261 1.13080
\(543\) −10.1195 −0.434270
\(544\) 4.06157 0.174138
\(545\) 28.3887 1.21604
\(546\) 4.24832 0.181811
\(547\) −16.8456 −0.720266 −0.360133 0.932901i \(-0.617269\pi\)
−0.360133 + 0.932901i \(0.617269\pi\)
\(548\) −18.9130 −0.807924
\(549\) 6.49344 0.277133
\(550\) 9.95085 0.424305
\(551\) 24.3659 1.03802
\(552\) 9.26262 0.394243
\(553\) 6.50177 0.276483
\(554\) 25.8739 1.09928
\(555\) −9.42653 −0.400134
\(556\) −2.52047 −0.106892
\(557\) −14.4179 −0.610907 −0.305453 0.952207i \(-0.598808\pi\)
−0.305453 + 0.952207i \(0.598808\pi\)
\(558\) 10.7030 0.453095
\(559\) −1.53277 −0.0648293
\(560\) 6.79130 0.286985
\(561\) 16.5333 0.698037
\(562\) −3.93838 −0.166130
\(563\) 1.38354 0.0583093 0.0291546 0.999575i \(-0.490718\pi\)
0.0291546 + 0.999575i \(0.490718\pi\)
\(564\) 9.61413 0.404828
\(565\) −5.69347 −0.239526
\(566\) −14.0958 −0.592490
\(567\) 4.24832 0.178413
\(568\) 13.3814 0.561472
\(569\) 20.7925 0.871667 0.435833 0.900027i \(-0.356454\pi\)
0.435833 + 0.900027i \(0.356454\pi\)
\(570\) 5.49256 0.230058
\(571\) 7.49899 0.313823 0.156912 0.987613i \(-0.449846\pi\)
0.156912 + 0.987613i \(0.449846\pi\)
\(572\) 4.07067 0.170203
\(573\) −4.42049 −0.184669
\(574\) 22.4689 0.937833
\(575\) −22.6427 −0.944266
\(576\) 1.00000 0.0416667
\(577\) −27.2468 −1.13430 −0.567150 0.823615i \(-0.691954\pi\)
−0.567150 + 0.823615i \(0.691954\pi\)
\(578\) 0.503638 0.0209486
\(579\) 9.36665 0.389265
\(580\) 11.3365 0.470724
\(581\) 39.7949 1.65097
\(582\) 14.0823 0.583732
\(583\) 40.9801 1.69722
\(584\) −3.94293 −0.163159
\(585\) 1.59859 0.0660934
\(586\) 5.42241 0.223998
\(587\) −10.2970 −0.425004 −0.212502 0.977161i \(-0.568161\pi\)
−0.212502 + 0.977161i \(0.568161\pi\)
\(588\) −11.0482 −0.455620
\(589\) −36.7743 −1.51526
\(590\) −9.52174 −0.392004
\(591\) 19.1911 0.789417
\(592\) 5.89679 0.242357
\(593\) −45.7540 −1.87889 −0.939445 0.342698i \(-0.888659\pi\)
−0.939445 + 0.342698i \(0.888659\pi\)
\(594\) 4.07067 0.167022
\(595\) −27.5833 −1.13081
\(596\) 21.9555 0.899332
\(597\) 7.97460 0.326379
\(598\) −9.26262 −0.378777
\(599\) −47.0310 −1.92163 −0.960817 0.277184i \(-0.910599\pi\)
−0.960817 + 0.277184i \(0.910599\pi\)
\(600\) −2.44452 −0.0997973
\(601\) 5.91612 0.241324 0.120662 0.992694i \(-0.461498\pi\)
0.120662 + 0.992694i \(0.461498\pi\)
\(602\) 6.51169 0.265397
\(603\) 4.52053 0.184090
\(604\) 9.14572 0.372134
\(605\) 8.90466 0.362026
\(606\) −0.882768 −0.0358600
\(607\) 42.5328 1.72635 0.863177 0.504901i \(-0.168471\pi\)
0.863177 + 0.504901i \(0.168471\pi\)
\(608\) −3.43588 −0.139344
\(609\) −30.1274 −1.22082
\(610\) −10.3803 −0.420287
\(611\) −9.61413 −0.388946
\(612\) −4.06157 −0.164179
\(613\) −24.0594 −0.971750 −0.485875 0.874028i \(-0.661499\pi\)
−0.485875 + 0.874028i \(0.661499\pi\)
\(614\) 18.0104 0.726840
\(615\) 8.45474 0.340928
\(616\) −17.2935 −0.696774
\(617\) −9.78867 −0.394077 −0.197039 0.980396i \(-0.563132\pi\)
−0.197039 + 0.980396i \(0.563132\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 14.6203 0.587638 0.293819 0.955861i \(-0.405074\pi\)
0.293819 + 0.955861i \(0.405074\pi\)
\(620\) −17.1097 −0.687141
\(621\) −9.26262 −0.371696
\(622\) 5.11921 0.205262
\(623\) −38.1171 −1.52713
\(624\) −1.00000 −0.0400320
\(625\) −6.80168 −0.272067
\(626\) 17.4175 0.696143
\(627\) −13.9863 −0.558561
\(628\) −14.6803 −0.585807
\(629\) −23.9502 −0.954959
\(630\) −6.79130 −0.270572
\(631\) −19.6291 −0.781421 −0.390711 0.920514i \(-0.627771\pi\)
−0.390711 + 0.920514i \(0.627771\pi\)
\(632\) −1.53043 −0.0608774
\(633\) −12.3843 −0.492231
\(634\) −5.40980 −0.214851
\(635\) 31.0320 1.23147
\(636\) −10.0672 −0.399189
\(637\) 11.0482 0.437745
\(638\) −28.8676 −1.14288
\(639\) −13.3814 −0.529361
\(640\) −1.59859 −0.0631896
\(641\) 46.0956 1.82067 0.910333 0.413876i \(-0.135825\pi\)
0.910333 + 0.413876i \(0.135825\pi\)
\(642\) −6.27951 −0.247832
\(643\) −9.48958 −0.374233 −0.187116 0.982338i \(-0.559914\pi\)
−0.187116 + 0.982338i \(0.559914\pi\)
\(644\) 39.3506 1.55063
\(645\) 2.45026 0.0964791
\(646\) 13.9551 0.549056
\(647\) 45.7314 1.79789 0.898943 0.438066i \(-0.144336\pi\)
0.898943 + 0.438066i \(0.144336\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 24.2463 0.951752
\(650\) 2.44452 0.0958821
\(651\) 45.4698 1.78210
\(652\) 12.9771 0.508222
\(653\) 36.9714 1.44680 0.723401 0.690428i \(-0.242578\pi\)
0.723401 + 0.690428i \(0.242578\pi\)
\(654\) 17.7587 0.694418
\(655\) −17.8686 −0.698184
\(656\) −5.28889 −0.206496
\(657\) 3.94293 0.153828
\(658\) 40.8438 1.59226
\(659\) −17.9184 −0.698002 −0.349001 0.937122i \(-0.613479\pi\)
−0.349001 + 0.937122i \(0.613479\pi\)
\(660\) −6.50731 −0.253297
\(661\) −16.9012 −0.657381 −0.328690 0.944438i \(-0.606607\pi\)
−0.328690 + 0.944438i \(0.606607\pi\)
\(662\) −20.5502 −0.798705
\(663\) 4.06157 0.157738
\(664\) −9.36721 −0.363518
\(665\) 23.3341 0.904858
\(666\) −5.89679 −0.228496
\(667\) 65.6868 2.54340
\(668\) −3.95923 −0.153187
\(669\) −25.3964 −0.981883
\(670\) −7.22646 −0.279182
\(671\) 26.4326 1.02042
\(672\) 4.24832 0.163882
\(673\) 2.00945 0.0774586 0.0387293 0.999250i \(-0.487669\pi\)
0.0387293 + 0.999250i \(0.487669\pi\)
\(674\) −25.2019 −0.970739
\(675\) 2.44452 0.0940898
\(676\) 1.00000 0.0384615
\(677\) −24.1860 −0.929543 −0.464771 0.885431i \(-0.653863\pi\)
−0.464771 + 0.885431i \(0.653863\pi\)
\(678\) −3.56157 −0.136781
\(679\) 59.8262 2.29592
\(680\) 6.49277 0.248986
\(681\) 21.9470 0.841010
\(682\) 43.5684 1.66832
\(683\) 4.78586 0.183126 0.0915630 0.995799i \(-0.470814\pi\)
0.0915630 + 0.995799i \(0.470814\pi\)
\(684\) 3.43588 0.131374
\(685\) −30.2341 −1.15519
\(686\) −17.1980 −0.656623
\(687\) 2.07670 0.0792311
\(688\) −1.53277 −0.0584363
\(689\) 10.0672 0.383528
\(690\) 14.8071 0.563696
\(691\) 48.4363 1.84261 0.921303 0.388847i \(-0.127126\pi\)
0.921303 + 0.388847i \(0.127126\pi\)
\(692\) −2.24677 −0.0854094
\(693\) 17.2935 0.656925
\(694\) 4.37034 0.165896
\(695\) −4.02919 −0.152836
\(696\) 7.09160 0.268807
\(697\) 21.4812 0.813658
\(698\) −10.6522 −0.403192
\(699\) 5.85936 0.221621
\(700\) −10.3851 −0.392520
\(701\) −26.6389 −1.00614 −0.503069 0.864246i \(-0.667796\pi\)
−0.503069 + 0.864246i \(0.667796\pi\)
\(702\) 1.00000 0.0377426
\(703\) 20.2607 0.764147
\(704\) 4.07067 0.153419
\(705\) 15.3690 0.578830
\(706\) 28.9724 1.09039
\(707\) −3.75028 −0.141044
\(708\) −5.95635 −0.223853
\(709\) −36.4512 −1.36895 −0.684476 0.729035i \(-0.739969\pi\)
−0.684476 + 0.729035i \(0.739969\pi\)
\(710\) 21.3914 0.802803
\(711\) 1.53043 0.0573958
\(712\) 8.97228 0.336250
\(713\) −99.1380 −3.71275
\(714\) −17.2548 −0.645746
\(715\) 6.50731 0.243360
\(716\) 6.03133 0.225401
\(717\) 26.0203 0.971747
\(718\) 0.959221 0.0357978
\(719\) 36.4041 1.35764 0.678821 0.734304i \(-0.262491\pi\)
0.678821 + 0.734304i \(0.262491\pi\)
\(720\) 1.59859 0.0595758
\(721\) −4.24832 −0.158216
\(722\) 7.19470 0.267759
\(723\) 19.3616 0.720065
\(724\) 10.1195 0.376088
\(725\) −17.3356 −0.643828
\(726\) 5.57034 0.206735
\(727\) 17.9375 0.665266 0.332633 0.943056i \(-0.392063\pi\)
0.332633 + 0.943056i \(0.392063\pi\)
\(728\) −4.24832 −0.157453
\(729\) 1.00000 0.0370370
\(730\) −6.30311 −0.233288
\(731\) 6.22546 0.230257
\(732\) −6.49344 −0.240004
\(733\) −49.0928 −1.81329 −0.906643 0.421900i \(-0.861363\pi\)
−0.906643 + 0.421900i \(0.861363\pi\)
\(734\) 38.0272 1.40361
\(735\) −17.6615 −0.651454
\(736\) −9.26262 −0.341425
\(737\) 18.4016 0.677831
\(738\) 5.28889 0.194687
\(739\) 8.22116 0.302420 0.151210 0.988502i \(-0.451683\pi\)
0.151210 + 0.988502i \(0.451683\pi\)
\(740\) 9.42653 0.346526
\(741\) −3.43588 −0.126220
\(742\) −42.7685 −1.57008
\(743\) −3.27036 −0.119978 −0.0599889 0.998199i \(-0.519107\pi\)
−0.0599889 + 0.998199i \(0.519107\pi\)
\(744\) −10.7030 −0.392392
\(745\) 35.0977 1.28588
\(746\) 21.3704 0.782425
\(747\) 9.36721 0.342728
\(748\) −16.5333 −0.604518
\(749\) −26.6773 −0.974768
\(750\) −11.9007 −0.434552
\(751\) −10.3651 −0.378226 −0.189113 0.981955i \(-0.560561\pi\)
−0.189113 + 0.981955i \(0.560561\pi\)
\(752\) −9.61413 −0.350591
\(753\) 17.1426 0.624711
\(754\) −7.09160 −0.258261
\(755\) 14.6202 0.532084
\(756\) −4.24832 −0.154510
\(757\) −29.6110 −1.07623 −0.538115 0.842872i \(-0.680863\pi\)
−0.538115 + 0.842872i \(0.680863\pi\)
\(758\) −12.3795 −0.449644
\(759\) −37.7051 −1.36861
\(760\) −5.49256 −0.199236
\(761\) −8.57839 −0.310966 −0.155483 0.987839i \(-0.549693\pi\)
−0.155483 + 0.987839i \(0.549693\pi\)
\(762\) 19.4121 0.703227
\(763\) 75.4444 2.73127
\(764\) 4.42049 0.159928
\(765\) −6.49277 −0.234747
\(766\) −21.8227 −0.788485
\(767\) 5.95635 0.215071
\(768\) −1.00000 −0.0360844
\(769\) 22.5442 0.812963 0.406481 0.913659i \(-0.366756\pi\)
0.406481 + 0.913659i \(0.366756\pi\)
\(770\) −27.6451 −0.996261
\(771\) −19.7734 −0.712123
\(772\) −9.36665 −0.337113
\(773\) −9.40688 −0.338342 −0.169171 0.985587i \(-0.554109\pi\)
−0.169171 + 0.985587i \(0.554109\pi\)
\(774\) 1.53277 0.0550943
\(775\) 26.1638 0.939831
\(776\) −14.0823 −0.505526
\(777\) −25.0514 −0.898715
\(778\) 3.84107 0.137709
\(779\) −18.1720 −0.651080
\(780\) −1.59859 −0.0572385
\(781\) −54.4714 −1.94914
\(782\) 37.6208 1.34532
\(783\) −7.09160 −0.253433
\(784\) 11.0482 0.394578
\(785\) −23.4677 −0.837598
\(786\) −11.1778 −0.398697
\(787\) 3.23611 0.115355 0.0576774 0.998335i \(-0.481631\pi\)
0.0576774 + 0.998335i \(0.481631\pi\)
\(788\) −19.1911 −0.683656
\(789\) 30.8363 1.09780
\(790\) −2.44653 −0.0870436
\(791\) −15.1307 −0.537985
\(792\) −4.07067 −0.144645
\(793\) 6.49344 0.230589
\(794\) −34.7939 −1.23479
\(795\) −16.0932 −0.570768
\(796\) −7.97460 −0.282652
\(797\) 6.70287 0.237428 0.118714 0.992929i \(-0.462123\pi\)
0.118714 + 0.992929i \(0.462123\pi\)
\(798\) 14.5967 0.516719
\(799\) 39.0485 1.38144
\(800\) 2.44452 0.0864270
\(801\) −8.97228 −0.317020
\(802\) −19.8607 −0.701305
\(803\) 16.0503 0.566404
\(804\) −4.52053 −0.159427
\(805\) 62.9052 2.21712
\(806\) 10.7030 0.376998
\(807\) −14.5206 −0.511149
\(808\) 0.882768 0.0310557
\(809\) −14.5042 −0.509940 −0.254970 0.966949i \(-0.582066\pi\)
−0.254970 + 0.966949i \(0.582066\pi\)
\(810\) −1.59859 −0.0561686
\(811\) 15.3324 0.538392 0.269196 0.963085i \(-0.413242\pi\)
0.269196 + 0.963085i \(0.413242\pi\)
\(812\) 30.1274 1.05726
\(813\) 26.3261 0.923296
\(814\) −24.0039 −0.841336
\(815\) 20.7450 0.726665
\(816\) 4.06157 0.142183
\(817\) −5.26642 −0.184249
\(818\) −12.2273 −0.427517
\(819\) 4.24832 0.148448
\(820\) −8.45474 −0.295252
\(821\) 22.1171 0.771892 0.385946 0.922521i \(-0.373875\pi\)
0.385946 + 0.922521i \(0.373875\pi\)
\(822\) −18.9130 −0.659668
\(823\) 47.2667 1.64761 0.823807 0.566871i \(-0.191846\pi\)
0.823807 + 0.566871i \(0.191846\pi\)
\(824\) 1.00000 0.0348367
\(825\) 9.95085 0.346444
\(826\) −25.3045 −0.880455
\(827\) −30.7775 −1.07024 −0.535119 0.844777i \(-0.679733\pi\)
−0.535119 + 0.844777i \(0.679733\pi\)
\(828\) 9.26262 0.321898
\(829\) 8.14728 0.282967 0.141483 0.989941i \(-0.454813\pi\)
0.141483 + 0.989941i \(0.454813\pi\)
\(830\) −14.9743 −0.519765
\(831\) 25.8739 0.897555
\(832\) 1.00000 0.0346688
\(833\) −44.8730 −1.55476
\(834\) −2.52047 −0.0872767
\(835\) −6.32917 −0.219030
\(836\) 13.9863 0.483728
\(837\) 10.7030 0.369950
\(838\) −20.6126 −0.712050
\(839\) 43.8092 1.51246 0.756230 0.654306i \(-0.227039\pi\)
0.756230 + 0.654306i \(0.227039\pi\)
\(840\) 6.79130 0.234322
\(841\) 21.2908 0.734167
\(842\) 0.0477608 0.00164595
\(843\) −3.93838 −0.135645
\(844\) 12.3843 0.426285
\(845\) 1.59859 0.0549930
\(846\) 9.61413 0.330540
\(847\) 23.6646 0.813124
\(848\) 10.0672 0.345708
\(849\) −14.0958 −0.483766
\(850\) −9.92861 −0.340548
\(851\) 54.6198 1.87234
\(852\) 13.3814 0.458440
\(853\) −9.63132 −0.329770 −0.164885 0.986313i \(-0.552725\pi\)
−0.164885 + 0.986313i \(0.552725\pi\)
\(854\) −27.5862 −0.943980
\(855\) 5.49256 0.187841
\(856\) 6.27951 0.214629
\(857\) −17.7935 −0.607813 −0.303907 0.952702i \(-0.598291\pi\)
−0.303907 + 0.952702i \(0.598291\pi\)
\(858\) 4.07067 0.138970
\(859\) −29.9098 −1.02051 −0.510255 0.860023i \(-0.670449\pi\)
−0.510255 + 0.860023i \(0.670449\pi\)
\(860\) −2.45026 −0.0835533
\(861\) 22.4689 0.765737
\(862\) −22.7229 −0.773946
\(863\) −14.1444 −0.481481 −0.240740 0.970590i \(-0.577390\pi\)
−0.240740 + 0.970590i \(0.577390\pi\)
\(864\) 1.00000 0.0340207
\(865\) −3.59165 −0.122120
\(866\) 19.8185 0.673461
\(867\) 0.503638 0.0171044
\(868\) −45.4698 −1.54335
\(869\) 6.22989 0.211335
\(870\) 11.3365 0.384345
\(871\) 4.52053 0.153172
\(872\) −17.7587 −0.601384
\(873\) 14.0823 0.476615
\(874\) −31.8253 −1.07651
\(875\) −50.5580 −1.70917
\(876\) −3.94293 −0.133219
\(877\) 17.5745 0.593449 0.296725 0.954963i \(-0.404106\pi\)
0.296725 + 0.954963i \(0.404106\pi\)
\(878\) 4.57038 0.154243
\(879\) 5.42241 0.182893
\(880\) 6.50731 0.219361
\(881\) 8.38259 0.282417 0.141208 0.989980i \(-0.454901\pi\)
0.141208 + 0.989980i \(0.454901\pi\)
\(882\) −11.0482 −0.372012
\(883\) 11.6637 0.392514 0.196257 0.980552i \(-0.437121\pi\)
0.196257 + 0.980552i \(0.437121\pi\)
\(884\) −4.06157 −0.136605
\(885\) −9.52174 −0.320070
\(886\) −14.7085 −0.494141
\(887\) 41.4609 1.39212 0.696060 0.717983i \(-0.254935\pi\)
0.696060 + 0.717983i \(0.254935\pi\)
\(888\) 5.89679 0.197883
\(889\) 82.4689 2.76592
\(890\) 14.3430 0.480777
\(891\) 4.07067 0.136373
\(892\) 25.3964 0.850336
\(893\) −33.0330 −1.10541
\(894\) 21.9555 0.734301
\(895\) 9.64160 0.322283
\(896\) −4.24832 −0.141926
\(897\) −9.26262 −0.309270
\(898\) 0.731479 0.0244098
\(899\) −75.9015 −2.53146
\(900\) −2.44452 −0.0814841
\(901\) −40.8885 −1.36219
\(902\) 21.5293 0.716848
\(903\) 6.51169 0.216696
\(904\) 3.56157 0.118456
\(905\) 16.1769 0.537738
\(906\) 9.14572 0.303846
\(907\) −22.5841 −0.749894 −0.374947 0.927046i \(-0.622339\pi\)
−0.374947 + 0.927046i \(0.622339\pi\)
\(908\) −21.9470 −0.728336
\(909\) −0.882768 −0.0292796
\(910\) −6.79130 −0.225129
\(911\) −11.3659 −0.376571 −0.188285 0.982114i \(-0.560293\pi\)
−0.188285 + 0.982114i \(0.560293\pi\)
\(912\) −3.43588 −0.113774
\(913\) 38.1308 1.26195
\(914\) −14.3463 −0.474534
\(915\) −10.3803 −0.343163
\(916\) −2.07670 −0.0686162
\(917\) −47.4866 −1.56815
\(918\) −4.06157 −0.134052
\(919\) 0.383465 0.0126494 0.00632468 0.999980i \(-0.497987\pi\)
0.00632468 + 0.999980i \(0.497987\pi\)
\(920\) −14.8071 −0.488175
\(921\) 18.0104 0.593462
\(922\) −19.4261 −0.639765
\(923\) −13.3814 −0.440455
\(924\) −17.2935 −0.568914
\(925\) −14.4149 −0.473957
\(926\) −15.2359 −0.500683
\(927\) −1.00000 −0.0328443
\(928\) −7.09160 −0.232793
\(929\) −7.21929 −0.236857 −0.118429 0.992963i \(-0.537786\pi\)
−0.118429 + 0.992963i \(0.537786\pi\)
\(930\) −17.1097 −0.561049
\(931\) 37.9603 1.24410
\(932\) −5.85936 −0.191930
\(933\) 5.11921 0.167595
\(934\) −24.1527 −0.790300
\(935\) −26.4299 −0.864350
\(936\) −1.00000 −0.0326860
\(937\) 14.5225 0.474428 0.237214 0.971457i \(-0.423766\pi\)
0.237214 + 0.971457i \(0.423766\pi\)
\(938\) −19.2047 −0.627054
\(939\) 17.4175 0.568399
\(940\) −15.3690 −0.501282
\(941\) 19.2395 0.627189 0.313595 0.949557i \(-0.398467\pi\)
0.313595 + 0.949557i \(0.398467\pi\)
\(942\) −14.6803 −0.478310
\(943\) −48.9890 −1.59530
\(944\) 5.95635 0.193863
\(945\) −6.79130 −0.220921
\(946\) 6.23940 0.202860
\(947\) −13.0006 −0.422462 −0.211231 0.977436i \(-0.567747\pi\)
−0.211231 + 0.977436i \(0.567747\pi\)
\(948\) −1.53043 −0.0497062
\(949\) 3.94293 0.127993
\(950\) 8.39910 0.272503
\(951\) −5.40980 −0.175425
\(952\) 17.2548 0.559233
\(953\) 50.2787 1.62869 0.814344 0.580383i \(-0.197097\pi\)
0.814344 + 0.580383i \(0.197097\pi\)
\(954\) −10.0672 −0.325936
\(955\) 7.06653 0.228668
\(956\) −26.0203 −0.841557
\(957\) −28.8676 −0.933156
\(958\) 9.59696 0.310064
\(959\) −80.3485 −2.59459
\(960\) −1.59859 −0.0515941
\(961\) 83.5545 2.69531
\(962\) −5.89679 −0.190120
\(963\) −6.27951 −0.202354
\(964\) −19.3616 −0.623595
\(965\) −14.9734 −0.482010
\(966\) 39.3506 1.26608
\(967\) 49.3254 1.58620 0.793099 0.609093i \(-0.208466\pi\)
0.793099 + 0.609093i \(0.208466\pi\)
\(968\) −5.57034 −0.179037
\(969\) 13.9551 0.448302
\(970\) −22.5118 −0.722811
\(971\) 40.9504 1.31416 0.657080 0.753821i \(-0.271791\pi\)
0.657080 + 0.753821i \(0.271791\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −10.7078 −0.343275
\(974\) 2.95817 0.0947860
\(975\) 2.44452 0.0782874
\(976\) 6.49344 0.207850
\(977\) −31.8994 −1.02055 −0.510276 0.860010i \(-0.670457\pi\)
−0.510276 + 0.860010i \(0.670457\pi\)
\(978\) 12.9771 0.414962
\(979\) −36.5232 −1.16729
\(980\) 17.6615 0.564176
\(981\) 17.7587 0.566990
\(982\) 5.44956 0.173903
\(983\) −25.2819 −0.806366 −0.403183 0.915119i \(-0.632096\pi\)
−0.403183 + 0.915119i \(0.632096\pi\)
\(984\) −5.28889 −0.168604
\(985\) −30.6787 −0.977503
\(986\) 28.8031 0.917276
\(987\) 40.8438 1.30007
\(988\) 3.43588 0.109310
\(989\) −14.1975 −0.451453
\(990\) −6.50731 −0.206816
\(991\) −25.8319 −0.820577 −0.410289 0.911956i \(-0.634572\pi\)
−0.410289 + 0.911956i \(0.634572\pi\)
\(992\) 10.7030 0.339821
\(993\) −20.5502 −0.652140
\(994\) 56.8486 1.80313
\(995\) −12.7481 −0.404142
\(996\) −9.36721 −0.296811
\(997\) 51.0358 1.61632 0.808160 0.588962i \(-0.200463\pi\)
0.808160 + 0.588962i \(0.200463\pi\)
\(998\) −34.6498 −1.09682
\(999\) −5.89679 −0.186566
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 8034.2.a.z.1.11 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.11 14 1.1 even 1 trivial