Properties

Label 8034.2.a.bb.1.6
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $1$
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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} - 7296 x - 2048\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.73527\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.73527 q^{5} -1.00000 q^{6} -3.07502 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.73527 q^{10} -1.39192 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.07502 q^{14} -1.73527 q^{15} +1.00000 q^{16} -2.86227 q^{17} -1.00000 q^{18} +7.95620 q^{19} -1.73527 q^{20} -3.07502 q^{21} +1.39192 q^{22} +7.53997 q^{23} -1.00000 q^{24} -1.98884 q^{25} +1.00000 q^{26} +1.00000 q^{27} -3.07502 q^{28} +4.50668 q^{29} +1.73527 q^{30} -2.18944 q^{31} -1.00000 q^{32} -1.39192 q^{33} +2.86227 q^{34} +5.33598 q^{35} +1.00000 q^{36} -2.08178 q^{37} -7.95620 q^{38} -1.00000 q^{39} +1.73527 q^{40} -9.35900 q^{41} +3.07502 q^{42} +4.36597 q^{43} -1.39192 q^{44} -1.73527 q^{45} -7.53997 q^{46} -1.82148 q^{47} +1.00000 q^{48} +2.45574 q^{49} +1.98884 q^{50} -2.86227 q^{51} -1.00000 q^{52} +2.12579 q^{53} -1.00000 q^{54} +2.41535 q^{55} +3.07502 q^{56} +7.95620 q^{57} -4.50668 q^{58} -8.76579 q^{59} -1.73527 q^{60} -4.02706 q^{61} +2.18944 q^{62} -3.07502 q^{63} +1.00000 q^{64} +1.73527 q^{65} +1.39192 q^{66} +1.69460 q^{67} -2.86227 q^{68} +7.53997 q^{69} -5.33598 q^{70} +7.75467 q^{71} -1.00000 q^{72} +1.32518 q^{73} +2.08178 q^{74} -1.98884 q^{75} +7.95620 q^{76} +4.28017 q^{77} +1.00000 q^{78} +12.1297 q^{79} -1.73527 q^{80} +1.00000 q^{81} +9.35900 q^{82} -2.35921 q^{83} -3.07502 q^{84} +4.96681 q^{85} -4.36597 q^{86} +4.50668 q^{87} +1.39192 q^{88} +2.39147 q^{89} +1.73527 q^{90} +3.07502 q^{91} +7.53997 q^{92} -2.18944 q^{93} +1.82148 q^{94} -13.8061 q^{95} -1.00000 q^{96} +15.7125 q^{97} -2.45574 q^{98} -1.39192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + 6q^{10} - 8q^{11} + 14q^{12} - 14q^{13} + 4q^{14} - 6q^{15} + 14q^{16} - 4q^{17} - 14q^{18} - q^{19} - 6q^{20} - 4q^{21} + 8q^{22} - 9q^{23} - 14q^{24} + 24q^{25} + 14q^{26} + 14q^{27} - 4q^{28} - 10q^{29} + 6q^{30} - 5q^{31} - 14q^{32} - 8q^{33} + 4q^{34} - 16q^{35} + 14q^{36} - 4q^{37} + q^{38} - 14q^{39} + 6q^{40} - 24q^{41} + 4q^{42} - 8q^{44} - 6q^{45} + 9q^{46} - 32q^{47} + 14q^{48} + 24q^{49} - 24q^{50} - 4q^{51} - 14q^{52} - 5q^{53} - 14q^{54} - 8q^{55} + 4q^{56} - q^{57} + 10q^{58} - 13q^{59} - 6q^{60} + 2q^{61} + 5q^{62} - 4q^{63} + 14q^{64} + 6q^{65} + 8q^{66} - 16q^{67} - 4q^{68} - 9q^{69} + 16q^{70} - 29q^{71} - 14q^{72} + 4q^{74} + 24q^{75} - q^{76} - 9q^{77} + 14q^{78} - 21q^{79} - 6q^{80} + 14q^{81} + 24q^{82} - 40q^{83} - 4q^{84} - 7q^{85} - 10q^{87} + 8q^{88} - 48q^{89} + 6q^{90} + 4q^{91} - 9q^{92} - 5q^{93} + 32q^{94} - 26q^{95} - 14q^{96} + 18q^{97} - 24q^{98} - 8q^{99} + O(q^{100}) \)

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
\(5\) −1.73527 −0.776036 −0.388018 0.921652i \(-0.626840\pi\)
−0.388018 + 0.921652i \(0.626840\pi\)
\(6\) −1.00000 −0.408248
\(7\) −3.07502 −1.16225 −0.581124 0.813815i \(-0.697387\pi\)
−0.581124 + 0.813815i \(0.697387\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.73527 0.548740
\(11\) −1.39192 −0.419678 −0.209839 0.977736i \(-0.567294\pi\)
−0.209839 + 0.977736i \(0.567294\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350
\(14\) 3.07502 0.821833
\(15\) −1.73527 −0.448044
\(16\) 1.00000 0.250000
\(17\) −2.86227 −0.694203 −0.347102 0.937828i \(-0.612834\pi\)
−0.347102 + 0.937828i \(0.612834\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.95620 1.82528 0.912639 0.408767i \(-0.134041\pi\)
0.912639 + 0.408767i \(0.134041\pi\)
\(20\) −1.73527 −0.388018
\(21\) −3.07502 −0.671024
\(22\) 1.39192 0.296757
\(23\) 7.53997 1.57219 0.786097 0.618104i \(-0.212099\pi\)
0.786097 + 0.618104i \(0.212099\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.98884 −0.397769
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) −3.07502 −0.581124
\(29\) 4.50668 0.836870 0.418435 0.908247i \(-0.362579\pi\)
0.418435 + 0.908247i \(0.362579\pi\)
\(30\) 1.73527 0.316815
\(31\) −2.18944 −0.393236 −0.196618 0.980480i \(-0.562996\pi\)
−0.196618 + 0.980480i \(0.562996\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.39192 −0.242301
\(34\) 2.86227 0.490876
\(35\) 5.33598 0.901946
\(36\) 1.00000 0.166667
\(37\) −2.08178 −0.342243 −0.171121 0.985250i \(-0.554739\pi\)
−0.171121 + 0.985250i \(0.554739\pi\)
\(38\) −7.95620 −1.29067
\(39\) −1.00000 −0.160128
\(40\) 1.73527 0.274370
\(41\) −9.35900 −1.46163 −0.730815 0.682575i \(-0.760860\pi\)
−0.730815 + 0.682575i \(0.760860\pi\)
\(42\) 3.07502 0.474486
\(43\) 4.36597 0.665804 0.332902 0.942961i \(-0.391972\pi\)
0.332902 + 0.942961i \(0.391972\pi\)
\(44\) −1.39192 −0.209839
\(45\) −1.73527 −0.258679
\(46\) −7.53997 −1.11171
\(47\) −1.82148 −0.265690 −0.132845 0.991137i \(-0.542411\pi\)
−0.132845 + 0.991137i \(0.542411\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.45574 0.350820
\(50\) 1.98884 0.281265
\(51\) −2.86227 −0.400798
\(52\) −1.00000 −0.138675
\(53\) 2.12579 0.292000 0.146000 0.989285i \(-0.453360\pi\)
0.146000 + 0.989285i \(0.453360\pi\)
\(54\) −1.00000 −0.136083
\(55\) 2.41535 0.325685
\(56\) 3.07502 0.410917
\(57\) 7.95620 1.05382
\(58\) −4.50668 −0.591756
\(59\) −8.76579 −1.14121 −0.570604 0.821225i \(-0.693291\pi\)
−0.570604 + 0.821225i \(0.693291\pi\)
\(60\) −1.73527 −0.224022
\(61\) −4.02706 −0.515613 −0.257806 0.966197i \(-0.583000\pi\)
−0.257806 + 0.966197i \(0.583000\pi\)
\(62\) 2.18944 0.278060
\(63\) −3.07502 −0.387416
\(64\) 1.00000 0.125000
\(65\) 1.73527 0.215234
\(66\) 1.39192 0.171333
\(67\) 1.69460 0.207029 0.103514 0.994628i \(-0.466991\pi\)
0.103514 + 0.994628i \(0.466991\pi\)
\(68\) −2.86227 −0.347102
\(69\) 7.53997 0.907706
\(70\) −5.33598 −0.637772
\(71\) 7.75467 0.920310 0.460155 0.887838i \(-0.347794\pi\)
0.460155 + 0.887838i \(0.347794\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.32518 0.155100 0.0775500 0.996988i \(-0.475290\pi\)
0.0775500 + 0.996988i \(0.475290\pi\)
\(74\) 2.08178 0.242002
\(75\) −1.98884 −0.229652
\(76\) 7.95620 0.912639
\(77\) 4.28017 0.487770
\(78\) 1.00000 0.113228
\(79\) 12.1297 1.36470 0.682351 0.731025i \(-0.260958\pi\)
0.682351 + 0.731025i \(0.260958\pi\)
\(80\) −1.73527 −0.194009
\(81\) 1.00000 0.111111
\(82\) 9.35900 1.03353
\(83\) −2.35921 −0.258957 −0.129478 0.991582i \(-0.541330\pi\)
−0.129478 + 0.991582i \(0.541330\pi\)
\(84\) −3.07502 −0.335512
\(85\) 4.96681 0.538726
\(86\) −4.36597 −0.470795
\(87\) 4.50668 0.483167
\(88\) 1.39192 0.148379
\(89\) 2.39147 0.253495 0.126748 0.991935i \(-0.459546\pi\)
0.126748 + 0.991935i \(0.459546\pi\)
\(90\) 1.73527 0.182913
\(91\) 3.07502 0.322350
\(92\) 7.53997 0.786097
\(93\) −2.18944 −0.227035
\(94\) 1.82148 0.187871
\(95\) −13.8061 −1.41648
\(96\) −1.00000 −0.102062
\(97\) 15.7125 1.59537 0.797683 0.603077i \(-0.206059\pi\)
0.797683 + 0.603077i \(0.206059\pi\)
\(98\) −2.45574 −0.248067
\(99\) −1.39192 −0.139893
\(100\) −1.98884 −0.198884
\(101\) 0.387891 0.0385966 0.0192983 0.999814i \(-0.493857\pi\)
0.0192983 + 0.999814i \(0.493857\pi\)
\(102\) 2.86227 0.283407
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) 5.33598 0.520739
\(106\) −2.12579 −0.206475
\(107\) −1.94585 −0.188112 −0.0940562 0.995567i \(-0.529983\pi\)
−0.0940562 + 0.995567i \(0.529983\pi\)
\(108\) 1.00000 0.0962250
\(109\) −8.84475 −0.847173 −0.423587 0.905856i \(-0.639229\pi\)
−0.423587 + 0.905856i \(0.639229\pi\)
\(110\) −2.41535 −0.230294
\(111\) −2.08178 −0.197594
\(112\) −3.07502 −0.290562
\(113\) −16.1754 −1.52165 −0.760825 0.648957i \(-0.775205\pi\)
−0.760825 + 0.648957i \(0.775205\pi\)
\(114\) −7.95620 −0.745167
\(115\) −13.0839 −1.22008
\(116\) 4.50668 0.418435
\(117\) −1.00000 −0.0924500
\(118\) 8.76579 0.806956
\(119\) 8.80155 0.806836
\(120\) 1.73527 0.158408
\(121\) −9.06257 −0.823870
\(122\) 4.02706 0.364593
\(123\) −9.35900 −0.843873
\(124\) −2.18944 −0.196618
\(125\) 12.1275 1.08472
\(126\) 3.07502 0.273944
\(127\) 21.3752 1.89674 0.948371 0.317165i \(-0.102731\pi\)
0.948371 + 0.317165i \(0.102731\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.36597 0.384402
\(130\) −1.73527 −0.152193
\(131\) 14.8836 1.30039 0.650193 0.759769i \(-0.274688\pi\)
0.650193 + 0.759769i \(0.274688\pi\)
\(132\) −1.39192 −0.121151
\(133\) −24.4655 −2.12143
\(134\) −1.69460 −0.146391
\(135\) −1.73527 −0.149348
\(136\) 2.86227 0.245438
\(137\) −6.09863 −0.521041 −0.260521 0.965468i \(-0.583894\pi\)
−0.260521 + 0.965468i \(0.583894\pi\)
\(138\) −7.53997 −0.641845
\(139\) 17.4985 1.48421 0.742103 0.670286i \(-0.233829\pi\)
0.742103 + 0.670286i \(0.233829\pi\)
\(140\) 5.33598 0.450973
\(141\) −1.82148 −0.153396
\(142\) −7.75467 −0.650758
\(143\) 1.39192 0.116398
\(144\) 1.00000 0.0833333
\(145\) −7.82030 −0.649441
\(146\) −1.32518 −0.109672
\(147\) 2.45574 0.202546
\(148\) −2.08178 −0.171121
\(149\) −19.2645 −1.57821 −0.789106 0.614257i \(-0.789456\pi\)
−0.789106 + 0.614257i \(0.789456\pi\)
\(150\) 1.98884 0.162388
\(151\) −17.8971 −1.45645 −0.728223 0.685340i \(-0.759654\pi\)
−0.728223 + 0.685340i \(0.759654\pi\)
\(152\) −7.95620 −0.645333
\(153\) −2.86227 −0.231401
\(154\) −4.28017 −0.344906
\(155\) 3.79927 0.305165
\(156\) −1.00000 −0.0800641
\(157\) 22.6039 1.80399 0.901995 0.431746i \(-0.142102\pi\)
0.901995 + 0.431746i \(0.142102\pi\)
\(158\) −12.1297 −0.964990
\(159\) 2.12579 0.168586
\(160\) 1.73527 0.137185
\(161\) −23.1856 −1.82728
\(162\) −1.00000 −0.0785674
\(163\) −0.465410 −0.0364537 −0.0182269 0.999834i \(-0.505802\pi\)
−0.0182269 + 0.999834i \(0.505802\pi\)
\(164\) −9.35900 −0.730815
\(165\) 2.41535 0.188035
\(166\) 2.35921 0.183110
\(167\) 4.36899 0.338082 0.169041 0.985609i \(-0.445933\pi\)
0.169041 + 0.985609i \(0.445933\pi\)
\(168\) 3.07502 0.237243
\(169\) 1.00000 0.0769231
\(170\) −4.96681 −0.380937
\(171\) 7.95620 0.608426
\(172\) 4.36597 0.332902
\(173\) −21.8891 −1.66419 −0.832097 0.554630i \(-0.812860\pi\)
−0.832097 + 0.554630i \(0.812860\pi\)
\(174\) −4.50668 −0.341651
\(175\) 6.11573 0.462306
\(176\) −1.39192 −0.104920
\(177\) −8.76579 −0.658877
\(178\) −2.39147 −0.179248
\(179\) −5.18468 −0.387521 −0.193761 0.981049i \(-0.562069\pi\)
−0.193761 + 0.981049i \(0.562069\pi\)
\(180\) −1.73527 −0.129339
\(181\) −14.1375 −1.05083 −0.525417 0.850845i \(-0.676091\pi\)
−0.525417 + 0.850845i \(0.676091\pi\)
\(182\) −3.07502 −0.227936
\(183\) −4.02706 −0.297689
\(184\) −7.53997 −0.555854
\(185\) 3.61245 0.265592
\(186\) 2.18944 0.160538
\(187\) 3.98404 0.291342
\(188\) −1.82148 −0.132845
\(189\) −3.07502 −0.223675
\(190\) 13.8061 1.00160
\(191\) −15.0773 −1.09096 −0.545479 0.838124i \(-0.683652\pi\)
−0.545479 + 0.838124i \(0.683652\pi\)
\(192\) 1.00000 0.0721688
\(193\) 9.66116 0.695426 0.347713 0.937601i \(-0.386958\pi\)
0.347713 + 0.937601i \(0.386958\pi\)
\(194\) −15.7125 −1.12809
\(195\) 1.73527 0.124265
\(196\) 2.45574 0.175410
\(197\) −8.38028 −0.597070 −0.298535 0.954399i \(-0.596498\pi\)
−0.298535 + 0.954399i \(0.596498\pi\)
\(198\) 1.39192 0.0989191
\(199\) −16.2017 −1.14851 −0.574255 0.818676i \(-0.694708\pi\)
−0.574255 + 0.818676i \(0.694708\pi\)
\(200\) 1.98884 0.140633
\(201\) 1.69460 0.119528
\(202\) −0.387891 −0.0272919
\(203\) −13.8581 −0.972650
\(204\) −2.86227 −0.200399
\(205\) 16.2404 1.13428
\(206\) −1.00000 −0.0696733
\(207\) 7.53997 0.524064
\(208\) −1.00000 −0.0693375
\(209\) −11.0744 −0.766030
\(210\) −5.33598 −0.368218
\(211\) 3.60468 0.248156 0.124078 0.992272i \(-0.460403\pi\)
0.124078 + 0.992272i \(0.460403\pi\)
\(212\) 2.12579 0.146000
\(213\) 7.75467 0.531341
\(214\) 1.94585 0.133015
\(215\) −7.57613 −0.516688
\(216\) −1.00000 −0.0680414
\(217\) 6.73258 0.457037
\(218\) 8.84475 0.599042
\(219\) 1.32518 0.0895471
\(220\) 2.41535 0.162843
\(221\) 2.86227 0.192537
\(222\) 2.08178 0.139720
\(223\) −0.759633 −0.0508688 −0.0254344 0.999676i \(-0.508097\pi\)
−0.0254344 + 0.999676i \(0.508097\pi\)
\(224\) 3.07502 0.205458
\(225\) −1.98884 −0.132590
\(226\) 16.1754 1.07597
\(227\) −1.65329 −0.109733 −0.0548663 0.998494i \(-0.517473\pi\)
−0.0548663 + 0.998494i \(0.517473\pi\)
\(228\) 7.95620 0.526912
\(229\) −15.3450 −1.01403 −0.507015 0.861937i \(-0.669251\pi\)
−0.507015 + 0.861937i \(0.669251\pi\)
\(230\) 13.0839 0.862725
\(231\) 4.28017 0.281614
\(232\) −4.50668 −0.295878
\(233\) 18.9261 1.23989 0.619945 0.784645i \(-0.287155\pi\)
0.619945 + 0.784645i \(0.287155\pi\)
\(234\) 1.00000 0.0653720
\(235\) 3.16075 0.206185
\(236\) −8.76579 −0.570604
\(237\) 12.1297 0.787911
\(238\) −8.80155 −0.570519
\(239\) −5.96484 −0.385833 −0.192917 0.981215i \(-0.561795\pi\)
−0.192917 + 0.981215i \(0.561795\pi\)
\(240\) −1.73527 −0.112011
\(241\) 7.65509 0.493108 0.246554 0.969129i \(-0.420702\pi\)
0.246554 + 0.969129i \(0.420702\pi\)
\(242\) 9.06257 0.582564
\(243\) 1.00000 0.0641500
\(244\) −4.02706 −0.257806
\(245\) −4.26137 −0.272249
\(246\) 9.35900 0.596708
\(247\) −7.95620 −0.506241
\(248\) 2.18944 0.139030
\(249\) −2.35921 −0.149509
\(250\) −12.1275 −0.767012
\(251\) 3.57823 0.225856 0.112928 0.993603i \(-0.463977\pi\)
0.112928 + 0.993603i \(0.463977\pi\)
\(252\) −3.07502 −0.193708
\(253\) −10.4950 −0.659815
\(254\) −21.3752 −1.34120
\(255\) 4.96681 0.311034
\(256\) 1.00000 0.0625000
\(257\) −28.6477 −1.78699 −0.893496 0.449070i \(-0.851755\pi\)
−0.893496 + 0.449070i \(0.851755\pi\)
\(258\) −4.36597 −0.271813
\(259\) 6.40151 0.397771
\(260\) 1.73527 0.107617
\(261\) 4.50668 0.278957
\(262\) −14.8836 −0.919512
\(263\) −0.404957 −0.0249707 −0.0124854 0.999922i \(-0.503974\pi\)
−0.0124854 + 0.999922i \(0.503974\pi\)
\(264\) 1.39192 0.0856665
\(265\) −3.68882 −0.226602
\(266\) 24.4655 1.50007
\(267\) 2.39147 0.146356
\(268\) 1.69460 0.103514
\(269\) −16.5365 −1.00825 −0.504124 0.863631i \(-0.668185\pi\)
−0.504124 + 0.863631i \(0.668185\pi\)
\(270\) 1.73527 0.105605
\(271\) −29.3866 −1.78511 −0.892554 0.450941i \(-0.851088\pi\)
−0.892554 + 0.450941i \(0.851088\pi\)
\(272\) −2.86227 −0.173551
\(273\) 3.07502 0.186109
\(274\) 6.09863 0.368432
\(275\) 2.76830 0.166935
\(276\) 7.53997 0.453853
\(277\) −20.0366 −1.20388 −0.601941 0.798541i \(-0.705606\pi\)
−0.601941 + 0.798541i \(0.705606\pi\)
\(278\) −17.4985 −1.04949
\(279\) −2.18944 −0.131079
\(280\) −5.33598 −0.318886
\(281\) −19.4475 −1.16014 −0.580069 0.814567i \(-0.696974\pi\)
−0.580069 + 0.814567i \(0.696974\pi\)
\(282\) 1.82148 0.108467
\(283\) −27.1883 −1.61618 −0.808090 0.589060i \(-0.799498\pi\)
−0.808090 + 0.589060i \(0.799498\pi\)
\(284\) 7.75467 0.460155
\(285\) −13.8061 −0.817805
\(286\) −1.39192 −0.0823057
\(287\) 28.7791 1.69878
\(288\) −1.00000 −0.0589256
\(289\) −8.80739 −0.518082
\(290\) 7.82030 0.459224
\(291\) 15.7125 0.921085
\(292\) 1.32518 0.0775500
\(293\) −0.346988 −0.0202713 −0.0101356 0.999949i \(-0.503226\pi\)
−0.0101356 + 0.999949i \(0.503226\pi\)
\(294\) −2.45574 −0.143222
\(295\) 15.2110 0.885619
\(296\) 2.08178 0.121001
\(297\) −1.39192 −0.0807671
\(298\) 19.2645 1.11596
\(299\) −7.53997 −0.436048
\(300\) −1.98884 −0.114826
\(301\) −13.4254 −0.773830
\(302\) 17.8971 1.02986
\(303\) 0.387891 0.0222838
\(304\) 7.95620 0.456319
\(305\) 6.98803 0.400134
\(306\) 2.86227 0.163625
\(307\) −20.0209 −1.14266 −0.571328 0.820722i \(-0.693571\pi\)
−0.571328 + 0.820722i \(0.693571\pi\)
\(308\) 4.28017 0.243885
\(309\) 1.00000 0.0568880
\(310\) −3.79927 −0.215784
\(311\) −7.63862 −0.433146 −0.216573 0.976266i \(-0.569488\pi\)
−0.216573 + 0.976266i \(0.569488\pi\)
\(312\) 1.00000 0.0566139
\(313\) −13.9350 −0.787650 −0.393825 0.919185i \(-0.628848\pi\)
−0.393825 + 0.919185i \(0.628848\pi\)
\(314\) −22.6039 −1.27561
\(315\) 5.33598 0.300649
\(316\) 12.1297 0.682351
\(317\) −0.484365 −0.0272046 −0.0136023 0.999907i \(-0.504330\pi\)
−0.0136023 + 0.999907i \(0.504330\pi\)
\(318\) −2.12579 −0.119208
\(319\) −6.27292 −0.351216
\(320\) −1.73527 −0.0970044
\(321\) −1.94585 −0.108607
\(322\) 23.1856 1.29208
\(323\) −22.7728 −1.26711
\(324\) 1.00000 0.0555556
\(325\) 1.98884 0.110321
\(326\) 0.465410 0.0257767
\(327\) −8.84475 −0.489116
\(328\) 9.35900 0.516764
\(329\) 5.60108 0.308797
\(330\) −2.41535 −0.132960
\(331\) −2.61559 −0.143766 −0.0718829 0.997413i \(-0.522901\pi\)
−0.0718829 + 0.997413i \(0.522901\pi\)
\(332\) −2.35921 −0.129478
\(333\) −2.08178 −0.114081
\(334\) −4.36899 −0.239060
\(335\) −2.94059 −0.160662
\(336\) −3.07502 −0.167756
\(337\) −11.5538 −0.629377 −0.314689 0.949195i \(-0.601900\pi\)
−0.314689 + 0.949195i \(0.601900\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −16.1754 −0.878525
\(340\) 4.96681 0.269363
\(341\) 3.04752 0.165032
\(342\) −7.95620 −0.430222
\(343\) 13.9737 0.754508
\(344\) −4.36597 −0.235397
\(345\) −13.0839 −0.704412
\(346\) 21.8891 1.17676
\(347\) −19.4830 −1.04590 −0.522950 0.852363i \(-0.675169\pi\)
−0.522950 + 0.852363i \(0.675169\pi\)
\(348\) 4.50668 0.241584
\(349\) 17.3821 0.930444 0.465222 0.885194i \(-0.345974\pi\)
0.465222 + 0.885194i \(0.345974\pi\)
\(350\) −6.11573 −0.326900
\(351\) −1.00000 −0.0533761
\(352\) 1.39192 0.0741894
\(353\) 6.06344 0.322724 0.161362 0.986895i \(-0.448411\pi\)
0.161362 + 0.986895i \(0.448411\pi\)
\(354\) 8.76579 0.465897
\(355\) −13.4564 −0.714194
\(356\) 2.39147 0.126748
\(357\) 8.80155 0.465827
\(358\) 5.18468 0.274019
\(359\) −31.4171 −1.65813 −0.829067 0.559149i \(-0.811128\pi\)
−0.829067 + 0.559149i \(0.811128\pi\)
\(360\) 1.73527 0.0914567
\(361\) 44.3011 2.33164
\(362\) 14.1375 0.743052
\(363\) −9.06257 −0.475662
\(364\) 3.07502 0.161175
\(365\) −2.29953 −0.120363
\(366\) 4.02706 0.210498
\(367\) 11.4259 0.596428 0.298214 0.954499i \(-0.403609\pi\)
0.298214 + 0.954499i \(0.403609\pi\)
\(368\) 7.53997 0.393048
\(369\) −9.35900 −0.487210
\(370\) −3.61245 −0.187802
\(371\) −6.53685 −0.339376
\(372\) −2.18944 −0.113517
\(373\) −19.7682 −1.02356 −0.511778 0.859117i \(-0.671013\pi\)
−0.511778 + 0.859117i \(0.671013\pi\)
\(374\) −3.98404 −0.206010
\(375\) 12.1275 0.626262
\(376\) 1.82148 0.0939355
\(377\) −4.50668 −0.232106
\(378\) 3.07502 0.158162
\(379\) 14.0604 0.722234 0.361117 0.932520i \(-0.382395\pi\)
0.361117 + 0.932520i \(0.382395\pi\)
\(380\) −13.8061 −0.708240
\(381\) 21.3752 1.09508
\(382\) 15.0773 0.771424
\(383\) −3.11366 −0.159101 −0.0795503 0.996831i \(-0.525348\pi\)
−0.0795503 + 0.996831i \(0.525348\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −7.42724 −0.378527
\(386\) −9.66116 −0.491740
\(387\) 4.36597 0.221935
\(388\) 15.7125 0.797683
\(389\) −28.1927 −1.42943 −0.714713 0.699418i \(-0.753443\pi\)
−0.714713 + 0.699418i \(0.753443\pi\)
\(390\) −1.73527 −0.0878687
\(391\) −21.5815 −1.09142
\(392\) −2.45574 −0.124034
\(393\) 14.8836 0.750778
\(394\) 8.38028 0.422193
\(395\) −21.0483 −1.05906
\(396\) −1.39192 −0.0699464
\(397\) −22.4025 −1.12435 −0.562174 0.827019i \(-0.690035\pi\)
−0.562174 + 0.827019i \(0.690035\pi\)
\(398\) 16.2017 0.812120
\(399\) −24.4655 −1.22481
\(400\) −1.98884 −0.0994422
\(401\) 14.9573 0.746934 0.373467 0.927644i \(-0.378169\pi\)
0.373467 + 0.927644i \(0.378169\pi\)
\(402\) −1.69460 −0.0845192
\(403\) 2.18944 0.109064
\(404\) 0.387891 0.0192983
\(405\) −1.73527 −0.0862262
\(406\) 13.8581 0.687768
\(407\) 2.89766 0.143632
\(408\) 2.86227 0.141704
\(409\) −33.0154 −1.63251 −0.816254 0.577693i \(-0.803953\pi\)
−0.816254 + 0.577693i \(0.803953\pi\)
\(410\) −16.2404 −0.802055
\(411\) −6.09863 −0.300823
\(412\) 1.00000 0.0492665
\(413\) 26.9550 1.32637
\(414\) −7.53997 −0.370569
\(415\) 4.09386 0.200960
\(416\) 1.00000 0.0490290
\(417\) 17.4985 0.856907
\(418\) 11.0744 0.541665
\(419\) −9.83287 −0.480367 −0.240184 0.970727i \(-0.577208\pi\)
−0.240184 + 0.970727i \(0.577208\pi\)
\(420\) 5.33598 0.260369
\(421\) 12.5841 0.613311 0.306656 0.951821i \(-0.400790\pi\)
0.306656 + 0.951821i \(0.400790\pi\)
\(422\) −3.60468 −0.175473
\(423\) −1.82148 −0.0885633
\(424\) −2.12579 −0.103237
\(425\) 5.69262 0.276132
\(426\) −7.75467 −0.375715
\(427\) 12.3833 0.599270
\(428\) −1.94585 −0.0940562
\(429\) 1.39192 0.0672023
\(430\) 7.57613 0.365353
\(431\) −28.4668 −1.37120 −0.685598 0.727981i \(-0.740459\pi\)
−0.685598 + 0.727981i \(0.740459\pi\)
\(432\) 1.00000 0.0481125
\(433\) 30.6051 1.47079 0.735393 0.677641i \(-0.236997\pi\)
0.735393 + 0.677641i \(0.236997\pi\)
\(434\) −6.73258 −0.323174
\(435\) −7.82030 −0.374955
\(436\) −8.84475 −0.423587
\(437\) 59.9895 2.86969
\(438\) −1.32518 −0.0633193
\(439\) −4.75581 −0.226982 −0.113491 0.993539i \(-0.536203\pi\)
−0.113491 + 0.993539i \(0.536203\pi\)
\(440\) −2.41535 −0.115147
\(441\) 2.45574 0.116940
\(442\) −2.86227 −0.136144
\(443\) −27.1927 −1.29196 −0.645981 0.763353i \(-0.723552\pi\)
−0.645981 + 0.763353i \(0.723552\pi\)
\(444\) −2.08178 −0.0987969
\(445\) −4.14984 −0.196721
\(446\) 0.759633 0.0359697
\(447\) −19.2645 −0.911181
\(448\) −3.07502 −0.145281
\(449\) 22.7037 1.07146 0.535728 0.844391i \(-0.320037\pi\)
0.535728 + 0.844391i \(0.320037\pi\)
\(450\) 1.98884 0.0937550
\(451\) 13.0269 0.613415
\(452\) −16.1754 −0.760825
\(453\) −17.8971 −0.840880
\(454\) 1.65329 0.0775927
\(455\) −5.33598 −0.250155
\(456\) −7.95620 −0.372583
\(457\) 12.8305 0.600188 0.300094 0.953910i \(-0.402982\pi\)
0.300094 + 0.953910i \(0.402982\pi\)
\(458\) 15.3450 0.717027
\(459\) −2.86227 −0.133599
\(460\) −13.0839 −0.610039
\(461\) 16.5024 0.768594 0.384297 0.923210i \(-0.374444\pi\)
0.384297 + 0.923210i \(0.374444\pi\)
\(462\) −4.28017 −0.199131
\(463\) −24.0249 −1.11653 −0.558266 0.829662i \(-0.688533\pi\)
−0.558266 + 0.829662i \(0.688533\pi\)
\(464\) 4.50668 0.209217
\(465\) 3.79927 0.176187
\(466\) −18.9261 −0.876735
\(467\) −2.17328 −0.100567 −0.0502836 0.998735i \(-0.516013\pi\)
−0.0502836 + 0.998735i \(0.516013\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −5.21094 −0.240619
\(470\) −3.16075 −0.145795
\(471\) 22.6039 1.04153
\(472\) 8.76579 0.403478
\(473\) −6.07706 −0.279424
\(474\) −12.1297 −0.557137
\(475\) −15.8236 −0.726039
\(476\) 8.80155 0.403418
\(477\) 2.12579 0.0973332
\(478\) 5.96484 0.272825
\(479\) −26.2126 −1.19769 −0.598843 0.800867i \(-0.704373\pi\)
−0.598843 + 0.800867i \(0.704373\pi\)
\(480\) 1.73527 0.0792038
\(481\) 2.08178 0.0949210
\(482\) −7.65509 −0.348680
\(483\) −23.1856 −1.05498
\(484\) −9.06257 −0.411935
\(485\) −27.2655 −1.23806
\(486\) −1.00000 −0.0453609
\(487\) −6.06624 −0.274887 −0.137444 0.990510i \(-0.543889\pi\)
−0.137444 + 0.990510i \(0.543889\pi\)
\(488\) 4.02706 0.182297
\(489\) −0.465410 −0.0210466
\(490\) 4.26137 0.192509
\(491\) −26.8159 −1.21019 −0.605093 0.796155i \(-0.706864\pi\)
−0.605093 + 0.796155i \(0.706864\pi\)
\(492\) −9.35900 −0.421936
\(493\) −12.8994 −0.580958
\(494\) 7.95620 0.357966
\(495\) 2.41535 0.108562
\(496\) −2.18944 −0.0983089
\(497\) −23.8458 −1.06963
\(498\) 2.35921 0.105719
\(499\) −3.58161 −0.160335 −0.0801675 0.996781i \(-0.525546\pi\)
−0.0801675 + 0.996781i \(0.525546\pi\)
\(500\) 12.1275 0.542359
\(501\) 4.36899 0.195192
\(502\) −3.57823 −0.159704
\(503\) −8.19566 −0.365426 −0.182713 0.983166i \(-0.558488\pi\)
−0.182713 + 0.983166i \(0.558488\pi\)
\(504\) 3.07502 0.136972
\(505\) −0.673095 −0.0299523
\(506\) 10.4950 0.466560
\(507\) 1.00000 0.0444116
\(508\) 21.3752 0.948371
\(509\) −23.6251 −1.04716 −0.523582 0.851975i \(-0.675405\pi\)
−0.523582 + 0.851975i \(0.675405\pi\)
\(510\) −4.96681 −0.219934
\(511\) −4.07494 −0.180265
\(512\) −1.00000 −0.0441942
\(513\) 7.95620 0.351275
\(514\) 28.6477 1.26359
\(515\) −1.73527 −0.0764651
\(516\) 4.36597 0.192201
\(517\) 2.53534 0.111504
\(518\) −6.40151 −0.281266
\(519\) −21.8891 −0.960823
\(520\) −1.73527 −0.0760965
\(521\) 24.3813 1.06817 0.534083 0.845432i \(-0.320657\pi\)
0.534083 + 0.845432i \(0.320657\pi\)
\(522\) −4.50668 −0.197252
\(523\) 38.3222 1.67571 0.837856 0.545892i \(-0.183809\pi\)
0.837856 + 0.545892i \(0.183809\pi\)
\(524\) 14.8836 0.650193
\(525\) 6.11573 0.266913
\(526\) 0.404957 0.0176570
\(527\) 6.26679 0.272985
\(528\) −1.39192 −0.0605754
\(529\) 33.8512 1.47179
\(530\) 3.68882 0.160232
\(531\) −8.76579 −0.380403
\(532\) −24.4655 −1.06071
\(533\) 9.35900 0.405383
\(534\) −2.39147 −0.103489
\(535\) 3.37657 0.145982
\(536\) −1.69460 −0.0731957
\(537\) −5.18468 −0.223736
\(538\) 16.5365 0.712939
\(539\) −3.41819 −0.147232
\(540\) −1.73527 −0.0746741
\(541\) −9.56555 −0.411255 −0.205627 0.978630i \(-0.565924\pi\)
−0.205627 + 0.978630i \(0.565924\pi\)
\(542\) 29.3866 1.26226
\(543\) −14.1375 −0.606700
\(544\) 2.86227 0.122719
\(545\) 15.3480 0.657437
\(546\) −3.07502 −0.131599
\(547\) 11.1149 0.475241 0.237620 0.971358i \(-0.423633\pi\)
0.237620 + 0.971358i \(0.423633\pi\)
\(548\) −6.09863 −0.260521
\(549\) −4.02706 −0.171871
\(550\) −2.76830 −0.118041
\(551\) 35.8561 1.52752
\(552\) −7.53997 −0.320923
\(553\) −37.2992 −1.58612
\(554\) 20.0366 0.851273
\(555\) 3.61245 0.153340
\(556\) 17.4985 0.742103
\(557\) 22.6461 0.959547 0.479774 0.877392i \(-0.340719\pi\)
0.479774 + 0.877392i \(0.340719\pi\)
\(558\) 2.18944 0.0926865
\(559\) −4.36597 −0.184661
\(560\) 5.33598 0.225486
\(561\) 3.98404 0.168206
\(562\) 19.4475 0.820341
\(563\) 31.8934 1.34415 0.672074 0.740484i \(-0.265404\pi\)
0.672074 + 0.740484i \(0.265404\pi\)
\(564\) −1.82148 −0.0766980
\(565\) 28.0686 1.18085
\(566\) 27.1883 1.14281
\(567\) −3.07502 −0.129139
\(568\) −7.75467 −0.325379
\(569\) 21.6956 0.909526 0.454763 0.890612i \(-0.349724\pi\)
0.454763 + 0.890612i \(0.349724\pi\)
\(570\) 13.8061 0.578276
\(571\) −25.0997 −1.05039 −0.525195 0.850982i \(-0.676008\pi\)
−0.525195 + 0.850982i \(0.676008\pi\)
\(572\) 1.39192 0.0581989
\(573\) −15.0773 −0.629865
\(574\) −28.7791 −1.20122
\(575\) −14.9958 −0.625369
\(576\) 1.00000 0.0416667
\(577\) 43.5561 1.81327 0.906633 0.421921i \(-0.138644\pi\)
0.906633 + 0.421921i \(0.138644\pi\)
\(578\) 8.80739 0.366339
\(579\) 9.66116 0.401504
\(580\) −7.82030 −0.324720
\(581\) 7.25462 0.300972
\(582\) −15.7125 −0.651306
\(583\) −2.95892 −0.122546
\(584\) −1.32518 −0.0548361
\(585\) 1.73527 0.0717445
\(586\) 0.346988 0.0143340
\(587\) 18.1913 0.750836 0.375418 0.926856i \(-0.377499\pi\)
0.375418 + 0.926856i \(0.377499\pi\)
\(588\) 2.45574 0.101273
\(589\) −17.4197 −0.717764
\(590\) −15.2110 −0.626227
\(591\) −8.38028 −0.344719
\(592\) −2.08178 −0.0855606
\(593\) −1.33417 −0.0547876 −0.0273938 0.999625i \(-0.508721\pi\)
−0.0273938 + 0.999625i \(0.508721\pi\)
\(594\) 1.39192 0.0571110
\(595\) −15.2730 −0.626134
\(596\) −19.2645 −0.789106
\(597\) −16.2017 −0.663093
\(598\) 7.53997 0.308332
\(599\) −32.9561 −1.34655 −0.673274 0.739393i \(-0.735113\pi\)
−0.673274 + 0.739393i \(0.735113\pi\)
\(600\) 1.98884 0.0811942
\(601\) 17.7894 0.725647 0.362823 0.931858i \(-0.381813\pi\)
0.362823 + 0.931858i \(0.381813\pi\)
\(602\) 13.4254 0.547180
\(603\) 1.69460 0.0690096
\(604\) −17.8971 −0.728223
\(605\) 15.7260 0.639352
\(606\) −0.387891 −0.0157570
\(607\) 46.3524 1.88138 0.940692 0.339261i \(-0.110177\pi\)
0.940692 + 0.339261i \(0.110177\pi\)
\(608\) −7.95620 −0.322667
\(609\) −13.8581 −0.561560
\(610\) −6.98803 −0.282937
\(611\) 1.82148 0.0736891
\(612\) −2.86227 −0.115701
\(613\) −42.6244 −1.72158 −0.860791 0.508958i \(-0.830031\pi\)
−0.860791 + 0.508958i \(0.830031\pi\)
\(614\) 20.0209 0.807979
\(615\) 16.2404 0.654875
\(616\) −4.28017 −0.172453
\(617\) −2.70299 −0.108818 −0.0544092 0.998519i \(-0.517328\pi\)
−0.0544092 + 0.998519i \(0.517328\pi\)
\(618\) −1.00000 −0.0402259
\(619\) −16.8035 −0.675390 −0.337695 0.941256i \(-0.609647\pi\)
−0.337695 + 0.941256i \(0.609647\pi\)
\(620\) 3.79927 0.152582
\(621\) 7.53997 0.302569
\(622\) 7.63862 0.306281
\(623\) −7.35382 −0.294624
\(624\) −1.00000 −0.0400320
\(625\) −11.1003 −0.444011
\(626\) 13.9350 0.556953
\(627\) −11.0744 −0.442267
\(628\) 22.6039 0.901995
\(629\) 5.95862 0.237586
\(630\) −5.33598 −0.212591
\(631\) 32.9522 1.31181 0.655904 0.754844i \(-0.272288\pi\)
0.655904 + 0.754844i \(0.272288\pi\)
\(632\) −12.1297 −0.482495
\(633\) 3.60468 0.143273
\(634\) 0.484365 0.0192366
\(635\) −37.0917 −1.47194
\(636\) 2.12579 0.0842931
\(637\) −2.45574 −0.0973001
\(638\) 6.27292 0.248347
\(639\) 7.75467 0.306770
\(640\) 1.73527 0.0685925
\(641\) −40.0729 −1.58279 −0.791393 0.611308i \(-0.790644\pi\)
−0.791393 + 0.611308i \(0.790644\pi\)
\(642\) 1.94585 0.0767965
\(643\) 22.1042 0.871706 0.435853 0.900018i \(-0.356447\pi\)
0.435853 + 0.900018i \(0.356447\pi\)
\(644\) −23.1856 −0.913639
\(645\) −7.57613 −0.298310
\(646\) 22.7728 0.895985
\(647\) 32.3252 1.27083 0.635417 0.772169i \(-0.280828\pi\)
0.635417 + 0.772169i \(0.280828\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 12.2012 0.478941
\(650\) −1.98884 −0.0780089
\(651\) 6.73258 0.263871
\(652\) −0.465410 −0.0182269
\(653\) −29.7996 −1.16615 −0.583074 0.812419i \(-0.698150\pi\)
−0.583074 + 0.812419i \(0.698150\pi\)
\(654\) 8.84475 0.345857
\(655\) −25.8270 −1.00915
\(656\) −9.35900 −0.365408
\(657\) 1.32518 0.0517000
\(658\) −5.60108 −0.218353
\(659\) −9.02261 −0.351471 −0.175735 0.984437i \(-0.556230\pi\)
−0.175735 + 0.984437i \(0.556230\pi\)
\(660\) 2.41535 0.0940173
\(661\) −28.4282 −1.10573 −0.552864 0.833272i \(-0.686465\pi\)
−0.552864 + 0.833272i \(0.686465\pi\)
\(662\) 2.61559 0.101658
\(663\) 2.86227 0.111161
\(664\) 2.35921 0.0915551
\(665\) 42.4542 1.64630
\(666\) 2.08178 0.0806674
\(667\) 33.9803 1.31572
\(668\) 4.36899 0.169041
\(669\) −0.759633 −0.0293691
\(670\) 2.94059 0.113605
\(671\) 5.60533 0.216391
\(672\) 3.07502 0.118621
\(673\) 31.2855 1.20597 0.602984 0.797753i \(-0.293978\pi\)
0.602984 + 0.797753i \(0.293978\pi\)
\(674\) 11.5538 0.445037
\(675\) −1.98884 −0.0765507
\(676\) 1.00000 0.0384615
\(677\) −20.5785 −0.790898 −0.395449 0.918488i \(-0.629411\pi\)
−0.395449 + 0.918488i \(0.629411\pi\)
\(678\) 16.1754 0.621211
\(679\) −48.3164 −1.85421
\(680\) −4.96681 −0.190469
\(681\) −1.65329 −0.0633542
\(682\) −3.04752 −0.116696
\(683\) 31.4617 1.20385 0.601923 0.798554i \(-0.294401\pi\)
0.601923 + 0.798554i \(0.294401\pi\)
\(684\) 7.95620 0.304213
\(685\) 10.5828 0.404347
\(686\) −13.9737 −0.533517
\(687\) −15.3450 −0.585450
\(688\) 4.36597 0.166451
\(689\) −2.12579 −0.0809862
\(690\) 13.0839 0.498095
\(691\) 38.2907 1.45665 0.728323 0.685234i \(-0.240300\pi\)
0.728323 + 0.685234i \(0.240300\pi\)
\(692\) −21.8891 −0.832097
\(693\) 4.28017 0.162590
\(694\) 19.4830 0.739564
\(695\) −30.3646 −1.15180
\(696\) −4.50668 −0.170825
\(697\) 26.7880 1.01467
\(698\) −17.3821 −0.657923
\(699\) 18.9261 0.715851
\(700\) 6.11573 0.231153
\(701\) −29.3169 −1.10729 −0.553643 0.832754i \(-0.686763\pi\)
−0.553643 + 0.832754i \(0.686763\pi\)
\(702\) 1.00000 0.0377426
\(703\) −16.5631 −0.624688
\(704\) −1.39192 −0.0524598
\(705\) 3.16075 0.119041
\(706\) −6.06344 −0.228200
\(707\) −1.19277 −0.0448588
\(708\) −8.76579 −0.329439
\(709\) 5.97285 0.224315 0.112158 0.993690i \(-0.464224\pi\)
0.112158 + 0.993690i \(0.464224\pi\)
\(710\) 13.4564 0.505011
\(711\) 12.1297 0.454901
\(712\) −2.39147 −0.0896241
\(713\) −16.5083 −0.618242
\(714\) −8.80155 −0.329390
\(715\) −2.41535 −0.0903289
\(716\) −5.18468 −0.193761
\(717\) −5.96484 −0.222761
\(718\) 31.4171 1.17248
\(719\) 35.6420 1.32922 0.664612 0.747189i \(-0.268597\pi\)
0.664612 + 0.747189i \(0.268597\pi\)
\(720\) −1.73527 −0.0646696
\(721\) −3.07502 −0.114520
\(722\) −44.3011 −1.64872
\(723\) 7.65509 0.284696
\(724\) −14.1375 −0.525417
\(725\) −8.96309 −0.332881
\(726\) 9.06257 0.336344
\(727\) 41.5022 1.53923 0.769615 0.638508i \(-0.220448\pi\)
0.769615 + 0.638508i \(0.220448\pi\)
\(728\) −3.07502 −0.113968
\(729\) 1.00000 0.0370370
\(730\) 2.29953 0.0851096
\(731\) −12.4966 −0.462204
\(732\) −4.02706 −0.148845
\(733\) −38.7797 −1.43236 −0.716180 0.697916i \(-0.754111\pi\)
−0.716180 + 0.697916i \(0.754111\pi\)
\(734\) −11.4259 −0.421738
\(735\) −4.26137 −0.157183
\(736\) −7.53997 −0.277927
\(737\) −2.35875 −0.0868855
\(738\) 9.35900 0.344510
\(739\) 27.9553 1.02835 0.514175 0.857685i \(-0.328098\pi\)
0.514175 + 0.857685i \(0.328098\pi\)
\(740\) 3.61245 0.132796
\(741\) −7.95620 −0.292278
\(742\) 6.53685 0.239975
\(743\) −41.6662 −1.52858 −0.764291 0.644871i \(-0.776911\pi\)
−0.764291 + 0.644871i \(0.776911\pi\)
\(744\) 2.18944 0.0802689
\(745\) 33.4291 1.22475
\(746\) 19.7682 0.723764
\(747\) −2.35921 −0.0863190
\(748\) 3.98404 0.145671
\(749\) 5.98352 0.218633
\(750\) −12.1275 −0.442834
\(751\) 30.4446 1.11094 0.555470 0.831536i \(-0.312538\pi\)
0.555470 + 0.831536i \(0.312538\pi\)
\(752\) −1.82148 −0.0664225
\(753\) 3.57823 0.130398
\(754\) 4.50668 0.164124
\(755\) 31.0563 1.13025
\(756\) −3.07502 −0.111837
\(757\) −32.6952 −1.18833 −0.594164 0.804344i \(-0.702517\pi\)
−0.594164 + 0.804344i \(0.702517\pi\)
\(758\) −14.0604 −0.510697
\(759\) −10.4950 −0.380945
\(760\) 13.8061 0.500801
\(761\) 24.8127 0.899460 0.449730 0.893165i \(-0.351520\pi\)
0.449730 + 0.893165i \(0.351520\pi\)
\(762\) −21.3752 −0.774341
\(763\) 27.1978 0.984626
\(764\) −15.0773 −0.545479
\(765\) 4.96681 0.179575
\(766\) 3.11366 0.112501
\(767\) 8.76579 0.316514
\(768\) 1.00000 0.0360844
\(769\) 29.8213 1.07538 0.537691 0.843142i \(-0.319297\pi\)
0.537691 + 0.843142i \(0.319297\pi\)
\(770\) 7.42724 0.267659
\(771\) −28.6477 −1.03172
\(772\) 9.66116 0.347713
\(773\) −21.1377 −0.760270 −0.380135 0.924931i \(-0.624123\pi\)
−0.380135 + 0.924931i \(0.624123\pi\)
\(774\) −4.36597 −0.156932
\(775\) 4.35446 0.156417
\(776\) −15.7125 −0.564047
\(777\) 6.40151 0.229653
\(778\) 28.1927 1.01076
\(779\) −74.4621 −2.66788
\(780\) 1.73527 0.0621326
\(781\) −10.7939 −0.386234
\(782\) 21.5815 0.771752
\(783\) 4.50668 0.161056
\(784\) 2.45574 0.0877051
\(785\) −39.2239 −1.39996
\(786\) −14.8836 −0.530880
\(787\) −11.5624 −0.412155 −0.206077 0.978536i \(-0.566070\pi\)
−0.206077 + 0.978536i \(0.566070\pi\)
\(788\) −8.38028 −0.298535
\(789\) −0.404957 −0.0144169
\(790\) 21.0483 0.748866
\(791\) 49.7395 1.76853
\(792\) 1.39192 0.0494596
\(793\) 4.02706 0.143005
\(794\) 22.4025 0.795035
\(795\) −3.68882 −0.130829
\(796\) −16.2017 −0.574255
\(797\) 5.88631 0.208504 0.104252 0.994551i \(-0.466755\pi\)
0.104252 + 0.994551i \(0.466755\pi\)
\(798\) 24.4655 0.866068
\(799\) 5.21357 0.184443
\(800\) 1.98884 0.0703163
\(801\) 2.39147 0.0844985
\(802\) −14.9573 −0.528162
\(803\) −1.84453 −0.0650921
\(804\) 1.69460 0.0597641
\(805\) 40.2332 1.41803
\(806\) −2.18944 −0.0771199
\(807\) −16.5365 −0.582112
\(808\) −0.387891 −0.0136460
\(809\) 10.4046 0.365807 0.182904 0.983131i \(-0.441450\pi\)
0.182904 + 0.983131i \(0.441450\pi\)
\(810\) 1.73527 0.0609711
\(811\) −32.8319 −1.15288 −0.576442 0.817138i \(-0.695559\pi\)
−0.576442 + 0.817138i \(0.695559\pi\)
\(812\) −13.8581 −0.486325
\(813\) −29.3866 −1.03063
\(814\) −2.89766 −0.101563
\(815\) 0.807612 0.0282894
\(816\) −2.86227 −0.100200
\(817\) 34.7365 1.21528
\(818\) 33.0154 1.15436
\(819\) 3.07502 0.107450
\(820\) 16.2404 0.567139
\(821\) 14.5787 0.508800 0.254400 0.967099i \(-0.418122\pi\)
0.254400 + 0.967099i \(0.418122\pi\)
\(822\) 6.09863 0.212714
\(823\) −25.8828 −0.902216 −0.451108 0.892469i \(-0.648971\pi\)
−0.451108 + 0.892469i \(0.648971\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 2.76830 0.0963800
\(826\) −26.9550 −0.937884
\(827\) −11.7465 −0.408467 −0.204233 0.978922i \(-0.565470\pi\)
−0.204233 + 0.978922i \(0.565470\pi\)
\(828\) 7.53997 0.262032
\(829\) 8.62805 0.299665 0.149832 0.988711i \(-0.452127\pi\)
0.149832 + 0.988711i \(0.452127\pi\)
\(830\) −4.09386 −0.142100
\(831\) −20.0366 −0.695062
\(832\) −1.00000 −0.0346688
\(833\) −7.02901 −0.243541
\(834\) −17.4985 −0.605924
\(835\) −7.58136 −0.262364
\(836\) −11.0744 −0.383015
\(837\) −2.18944 −0.0756782
\(838\) 9.83287 0.339671
\(839\) −38.9905 −1.34610 −0.673050 0.739597i \(-0.735016\pi\)
−0.673050 + 0.739597i \(0.735016\pi\)
\(840\) −5.33598 −0.184109
\(841\) −8.68981 −0.299649
\(842\) −12.5841 −0.433676
\(843\) −19.4475 −0.669806
\(844\) 3.60468 0.124078
\(845\) −1.73527 −0.0596950
\(846\) 1.82148 0.0626237
\(847\) 27.8676 0.957541
\(848\) 2.12579 0.0729999
\(849\) −27.1883 −0.933101
\(850\) −5.69262 −0.195255
\(851\) −15.6966 −0.538071
\(852\) 7.75467 0.265671
\(853\) 49.1807 1.68392 0.841958 0.539543i \(-0.181403\pi\)
0.841958 + 0.539543i \(0.181403\pi\)
\(854\) −12.3833 −0.423748
\(855\) −13.8061 −0.472160
\(856\) 1.94585 0.0665077
\(857\) 15.6294 0.533891 0.266946 0.963712i \(-0.413986\pi\)
0.266946 + 0.963712i \(0.413986\pi\)
\(858\) −1.39192 −0.0475192
\(859\) −31.8384 −1.08631 −0.543156 0.839632i \(-0.682771\pi\)
−0.543156 + 0.839632i \(0.682771\pi\)
\(860\) −7.57613 −0.258344
\(861\) 28.7791 0.980790
\(862\) 28.4668 0.969581
\(863\) −7.02071 −0.238988 −0.119494 0.992835i \(-0.538127\pi\)
−0.119494 + 0.992835i \(0.538127\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 37.9834 1.29147
\(866\) −30.6051 −1.04000
\(867\) −8.80739 −0.299115
\(868\) 6.73258 0.228519
\(869\) −16.8836 −0.572736
\(870\) 7.82030 0.265133
\(871\) −1.69460 −0.0574195
\(872\) 8.84475 0.299521
\(873\) 15.7125 0.531789
\(874\) −59.9895 −2.02918
\(875\) −37.2924 −1.26071
\(876\) 1.32518 0.0447735
\(877\) −18.4449 −0.622840 −0.311420 0.950272i \(-0.600805\pi\)
−0.311420 + 0.950272i \(0.600805\pi\)
\(878\) 4.75581 0.160501
\(879\) −0.346988 −0.0117036
\(880\) 2.41535 0.0814213
\(881\) −31.8807 −1.07409 −0.537045 0.843554i \(-0.680459\pi\)
−0.537045 + 0.843554i \(0.680459\pi\)
\(882\) −2.45574 −0.0826892
\(883\) 52.2620 1.75876 0.879378 0.476124i \(-0.157959\pi\)
0.879378 + 0.476124i \(0.157959\pi\)
\(884\) 2.86227 0.0962687
\(885\) 15.2110 0.511312
\(886\) 27.1927 0.913555
\(887\) 15.9162 0.534414 0.267207 0.963639i \(-0.413899\pi\)
0.267207 + 0.963639i \(0.413899\pi\)
\(888\) 2.08178 0.0698600
\(889\) −65.7291 −2.20448
\(890\) 4.14984 0.139103
\(891\) −1.39192 −0.0466309
\(892\) −0.759633 −0.0254344
\(893\) −14.4920 −0.484958
\(894\) 19.2645 0.644302
\(895\) 8.99681 0.300730
\(896\) 3.07502 0.102729
\(897\) −7.53997 −0.251752
\(898\) −22.7037 −0.757634
\(899\) −9.86713 −0.329087
\(900\) −1.98884 −0.0662948
\(901\) −6.08459 −0.202707
\(902\) −13.0269 −0.433750
\(903\) −13.4254 −0.446771
\(904\) 16.1754 0.537985
\(905\) 24.5324 0.815485
\(906\) 17.8971 0.594592
\(907\) 55.4817 1.84224 0.921120 0.389279i \(-0.127276\pi\)
0.921120 + 0.389279i \(0.127276\pi\)
\(908\) −1.65329 −0.0548663
\(909\) 0.387891 0.0128655
\(910\) 5.33598 0.176886
\(911\) 6.17396 0.204552 0.102276 0.994756i \(-0.467387\pi\)
0.102276 + 0.994756i \(0.467387\pi\)
\(912\) 7.95620 0.263456
\(913\) 3.28382 0.108679
\(914\) −12.8305 −0.424397
\(915\) 6.98803 0.231017
\(916\) −15.3450 −0.507015
\(917\) −45.7673 −1.51137
\(918\) 2.86227 0.0944691
\(919\) 5.11440 0.168708 0.0843542 0.996436i \(-0.473117\pi\)
0.0843542 + 0.996436i \(0.473117\pi\)
\(920\) 13.0839 0.431363
\(921\) −20.0209 −0.659712
\(922\) −16.5024 −0.543478
\(923\) −7.75467 −0.255248
\(924\) 4.28017 0.140807
\(925\) 4.14034 0.136133
\(926\) 24.0249 0.789508
\(927\) 1.00000 0.0328443
\(928\) −4.50668 −0.147939
\(929\) 43.7867 1.43660 0.718298 0.695736i \(-0.244922\pi\)
0.718298 + 0.695736i \(0.244922\pi\)
\(930\) −3.79927 −0.124583
\(931\) 19.5384 0.640345
\(932\) 18.9261 0.619945
\(933\) −7.63862 −0.250077
\(934\) 2.17328 0.0711117
\(935\) −6.91338 −0.226092
\(936\) 1.00000 0.0326860
\(937\) 35.3010 1.15323 0.576616 0.817015i \(-0.304373\pi\)
0.576616 + 0.817015i \(0.304373\pi\)
\(938\) 5.21094 0.170143
\(939\) −13.9350 −0.454750
\(940\) 3.16075 0.103092
\(941\) 27.4067 0.893432 0.446716 0.894676i \(-0.352594\pi\)
0.446716 + 0.894676i \(0.352594\pi\)
\(942\) −22.6039 −0.736476
\(943\) −70.5666 −2.29797
\(944\) −8.76579 −0.285302
\(945\) 5.33598 0.173580
\(946\) 6.07706 0.197582
\(947\) −15.4629 −0.502478 −0.251239 0.967925i \(-0.580838\pi\)
−0.251239 + 0.967925i \(0.580838\pi\)
\(948\) 12.1297 0.393955
\(949\) −1.32518 −0.0430170
\(950\) 15.8236 0.513387
\(951\) −0.484365 −0.0157066
\(952\) −8.80155 −0.285260
\(953\) 20.7975 0.673697 0.336848 0.941559i \(-0.390639\pi\)
0.336848 + 0.941559i \(0.390639\pi\)
\(954\) −2.12579 −0.0688250
\(955\) 26.1632 0.846622
\(956\) −5.96484 −0.192917
\(957\) −6.27292 −0.202775
\(958\) 26.2126 0.846891
\(959\) 18.7534 0.605579
\(960\) −1.73527 −0.0560055
\(961\) −26.2063 −0.845366
\(962\) −2.08178 −0.0671193
\(963\) −1.94585 −0.0627041
\(964\) 7.65509 0.246554
\(965\) −16.7647 −0.539675
\(966\) 23.1856 0.745983
\(967\) 5.25688 0.169050 0.0845249 0.996421i \(-0.473063\pi\)
0.0845249 + 0.996421i \(0.473063\pi\)
\(968\) 9.06257 0.291282
\(969\) −22.7728 −0.731568
\(970\) 27.2655 0.875441
\(971\) 21.7767 0.698849 0.349425 0.936965i \(-0.386377\pi\)
0.349425 + 0.936965i \(0.386377\pi\)
\(972\) 1.00000 0.0320750
\(973\) −53.8083 −1.72502
\(974\) 6.06624 0.194375
\(975\) 1.98884 0.0636940
\(976\) −4.02706 −0.128903
\(977\) 23.6820 0.757654 0.378827 0.925468i \(-0.376328\pi\)
0.378827 + 0.925468i \(0.376328\pi\)
\(978\) 0.465410 0.0148822
\(979\) −3.32872 −0.106387
\(980\) −4.26137 −0.136125
\(981\) −8.84475 −0.282391
\(982\) 26.8159 0.855731
\(983\) −52.7443 −1.68228 −0.841142 0.540815i \(-0.818116\pi\)
−0.841142 + 0.540815i \(0.818116\pi\)
\(984\) 9.35900 0.298354
\(985\) 14.5420 0.463348
\(986\) 12.8994 0.410799
\(987\) 5.60108 0.178284
\(988\) −7.95620 −0.253120
\(989\) 32.9193 1.04677
\(990\) −2.41535 −0.0767648
\(991\) −53.9155 −1.71268 −0.856341 0.516411i \(-0.827268\pi\)
−0.856341 + 0.516411i \(0.827268\pi\)
\(992\) 2.18944 0.0695149
\(993\) −2.61559 −0.0830032
\(994\) 23.8458 0.756342
\(995\) 28.1144 0.891285
\(996\) −2.35921 −0.0747544
\(997\) 25.1433 0.796297 0.398149 0.917321i \(-0.369653\pi\)
0.398149 + 0.917321i \(0.369653\pi\)
\(998\) 3.58161 0.113374
\(999\) −2.08178 −0.0658646
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.bb.1.6 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.bb.1.6 14 1.1 even 1 trivial