Properties

Label 8034.2.a.ba.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: \(x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492\)
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 1.11
Root \(-2.46518\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.46518 q^{5} +1.00000 q^{6} -0.952790 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.46518 q^{5} +1.00000 q^{6} -0.952790 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.46518 q^{10} +4.20399 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.952790 q^{14} -2.46518 q^{15} +1.00000 q^{16} +7.27477 q^{17} -1.00000 q^{18} -4.33023 q^{19} +2.46518 q^{20} +0.952790 q^{21} -4.20399 q^{22} +2.97949 q^{23} +1.00000 q^{24} +1.07710 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.952790 q^{28} +4.44123 q^{29} +2.46518 q^{30} +2.25549 q^{31} -1.00000 q^{32} -4.20399 q^{33} -7.27477 q^{34} -2.34880 q^{35} +1.00000 q^{36} +3.37198 q^{37} +4.33023 q^{38} +1.00000 q^{39} -2.46518 q^{40} -8.68437 q^{41} -0.952790 q^{42} +5.56905 q^{43} +4.20399 q^{44} +2.46518 q^{45} -2.97949 q^{46} +5.13291 q^{47} -1.00000 q^{48} -6.09219 q^{49} -1.07710 q^{50} -7.27477 q^{51} -1.00000 q^{52} +8.80268 q^{53} +1.00000 q^{54} +10.3636 q^{55} +0.952790 q^{56} +4.33023 q^{57} -4.44123 q^{58} +5.12897 q^{59} -2.46518 q^{60} -5.32855 q^{61} -2.25549 q^{62} -0.952790 q^{63} +1.00000 q^{64} -2.46518 q^{65} +4.20399 q^{66} +5.95796 q^{67} +7.27477 q^{68} -2.97949 q^{69} +2.34880 q^{70} +12.6592 q^{71} -1.00000 q^{72} -7.23738 q^{73} -3.37198 q^{74} -1.07710 q^{75} -4.33023 q^{76} -4.00552 q^{77} -1.00000 q^{78} -9.05227 q^{79} +2.46518 q^{80} +1.00000 q^{81} +8.68437 q^{82} +7.82412 q^{83} +0.952790 q^{84} +17.9336 q^{85} -5.56905 q^{86} -4.44123 q^{87} -4.20399 q^{88} +3.70795 q^{89} -2.46518 q^{90} +0.952790 q^{91} +2.97949 q^{92} -2.25549 q^{93} -5.13291 q^{94} -10.6748 q^{95} +1.00000 q^{96} -18.7132 q^{97} +6.09219 q^{98} +4.20399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + q^{10} - q^{11} - 14q^{12} - 14q^{13} - 5q^{14} + q^{15} + 14q^{16} - 12q^{17} - 14q^{18} + 10q^{19} - q^{20} - 5q^{21} + q^{22} - q^{23} + 14q^{24} + 19q^{25} + 14q^{26} - 14q^{27} + 5q^{28} + 6q^{29} - q^{30} + 20q^{31} - 14q^{32} + q^{33} + 12q^{34} - 16q^{35} + 14q^{36} - 3q^{37} - 10q^{38} + 14q^{39} + q^{40} + q^{41} + 5q^{42} + 6q^{43} - q^{44} - q^{45} + q^{46} - 13q^{47} - 14q^{48} + 9q^{49} - 19q^{50} + 12q^{51} - 14q^{52} - 27q^{53} + 14q^{54} + 10q^{55} - 5q^{56} - 10q^{57} - 6q^{58} - 6q^{59} + q^{60} - 4q^{61} - 20q^{62} + 5q^{63} + 14q^{64} + q^{65} - q^{66} + 13q^{67} - 12q^{68} + q^{69} + 16q^{70} + 18q^{71} - 14q^{72} + 11q^{73} + 3q^{74} - 19q^{75} + 10q^{76} - 15q^{77} - 14q^{78} + 33q^{79} - q^{80} + 14q^{81} - q^{82} - 25q^{83} - 5q^{84} + 25q^{85} - 6q^{86} - 6q^{87} + q^{88} + 3q^{89} + q^{90} - 5q^{91} - q^{92} - 20q^{93} + 13q^{94} + 30q^{95} + 14q^{96} + 11q^{97} - 9q^{98} - q^{99} + O(q^{100}) \)

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
\(5\) 2.46518 1.10246 0.551231 0.834353i \(-0.314158\pi\)
0.551231 + 0.834353i \(0.314158\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.952790 −0.360121 −0.180060 0.983656i \(-0.557629\pi\)
−0.180060 + 0.983656i \(0.557629\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.46518 −0.779558
\(11\) 4.20399 1.26755 0.633775 0.773518i \(-0.281505\pi\)
0.633775 + 0.773518i \(0.281505\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) 0.952790 0.254644
\(15\) −2.46518 −0.636506
\(16\) 1.00000 0.250000
\(17\) 7.27477 1.76439 0.882196 0.470883i \(-0.156065\pi\)
0.882196 + 0.470883i \(0.156065\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.33023 −0.993422 −0.496711 0.867916i \(-0.665459\pi\)
−0.496711 + 0.867916i \(0.665459\pi\)
\(20\) 2.46518 0.551231
\(21\) 0.952790 0.207916
\(22\) −4.20399 −0.896293
\(23\) 2.97949 0.621268 0.310634 0.950530i \(-0.399459\pi\)
0.310634 + 0.950530i \(0.399459\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.07710 0.215421
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) −0.952790 −0.180060
\(29\) 4.44123 0.824716 0.412358 0.911022i \(-0.364705\pi\)
0.412358 + 0.911022i \(0.364705\pi\)
\(30\) 2.46518 0.450078
\(31\) 2.25549 0.405098 0.202549 0.979272i \(-0.435077\pi\)
0.202549 + 0.979272i \(0.435077\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.20399 −0.731820
\(34\) −7.27477 −1.24761
\(35\) −2.34880 −0.397019
\(36\) 1.00000 0.166667
\(37\) 3.37198 0.554350 0.277175 0.960819i \(-0.410602\pi\)
0.277175 + 0.960819i \(0.410602\pi\)
\(38\) 4.33023 0.702456
\(39\) 1.00000 0.160128
\(40\) −2.46518 −0.389779
\(41\) −8.68437 −1.35627 −0.678135 0.734937i \(-0.737212\pi\)
−0.678135 + 0.734937i \(0.737212\pi\)
\(42\) −0.952790 −0.147019
\(43\) 5.56905 0.849272 0.424636 0.905364i \(-0.360402\pi\)
0.424636 + 0.905364i \(0.360402\pi\)
\(44\) 4.20399 0.633775
\(45\) 2.46518 0.367487
\(46\) −2.97949 −0.439303
\(47\) 5.13291 0.748711 0.374356 0.927285i \(-0.377864\pi\)
0.374356 + 0.927285i \(0.377864\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.09219 −0.870313
\(50\) −1.07710 −0.152326
\(51\) −7.27477 −1.01867
\(52\) −1.00000 −0.138675
\(53\) 8.80268 1.20914 0.604571 0.796552i \(-0.293345\pi\)
0.604571 + 0.796552i \(0.293345\pi\)
\(54\) 1.00000 0.136083
\(55\) 10.3636 1.39742
\(56\) 0.952790 0.127322
\(57\) 4.33023 0.573553
\(58\) −4.44123 −0.583163
\(59\) 5.12897 0.667736 0.333868 0.942620i \(-0.391646\pi\)
0.333868 + 0.942620i \(0.391646\pi\)
\(60\) −2.46518 −0.318253
\(61\) −5.32855 −0.682251 −0.341126 0.940018i \(-0.610808\pi\)
−0.341126 + 0.940018i \(0.610808\pi\)
\(62\) −2.25549 −0.286448
\(63\) −0.952790 −0.120040
\(64\) 1.00000 0.125000
\(65\) −2.46518 −0.305768
\(66\) 4.20399 0.517475
\(67\) 5.95796 0.727881 0.363941 0.931422i \(-0.381431\pi\)
0.363941 + 0.931422i \(0.381431\pi\)
\(68\) 7.27477 0.882196
\(69\) −2.97949 −0.358689
\(70\) 2.34880 0.280735
\(71\) 12.6592 1.50237 0.751184 0.660092i \(-0.229483\pi\)
0.751184 + 0.660092i \(0.229483\pi\)
\(72\) −1.00000 −0.117851
\(73\) −7.23738 −0.847072 −0.423536 0.905879i \(-0.639211\pi\)
−0.423536 + 0.905879i \(0.639211\pi\)
\(74\) −3.37198 −0.391985
\(75\) −1.07710 −0.124373
\(76\) −4.33023 −0.496711
\(77\) −4.00552 −0.456471
\(78\) −1.00000 −0.113228
\(79\) −9.05227 −1.01846 −0.509230 0.860630i \(-0.670070\pi\)
−0.509230 + 0.860630i \(0.670070\pi\)
\(80\) 2.46518 0.275615
\(81\) 1.00000 0.111111
\(82\) 8.68437 0.959028
\(83\) 7.82412 0.858809 0.429404 0.903112i \(-0.358723\pi\)
0.429404 + 0.903112i \(0.358723\pi\)
\(84\) 0.952790 0.103958
\(85\) 17.9336 1.94517
\(86\) −5.56905 −0.600526
\(87\) −4.44123 −0.476150
\(88\) −4.20399 −0.448146
\(89\) 3.70795 0.393042 0.196521 0.980500i \(-0.437036\pi\)
0.196521 + 0.980500i \(0.437036\pi\)
\(90\) −2.46518 −0.259853
\(91\) 0.952790 0.0998795
\(92\) 2.97949 0.310634
\(93\) −2.25549 −0.233884
\(94\) −5.13291 −0.529419
\(95\) −10.6748 −1.09521
\(96\) 1.00000 0.102062
\(97\) −18.7132 −1.90004 −0.950021 0.312187i \(-0.898939\pi\)
−0.950021 + 0.312187i \(0.898939\pi\)
\(98\) 6.09219 0.615404
\(99\) 4.20399 0.422516
\(100\) 1.07710 0.107710
\(101\) −2.53136 −0.251880 −0.125940 0.992038i \(-0.540195\pi\)
−0.125940 + 0.992038i \(0.540195\pi\)
\(102\) 7.27477 0.720310
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) 2.34880 0.229219
\(106\) −8.80268 −0.854992
\(107\) 2.73402 0.264308 0.132154 0.991229i \(-0.457811\pi\)
0.132154 + 0.991229i \(0.457811\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 9.98912 0.956784 0.478392 0.878146i \(-0.341220\pi\)
0.478392 + 0.878146i \(0.341220\pi\)
\(110\) −10.3636 −0.988128
\(111\) −3.37198 −0.320054
\(112\) −0.952790 −0.0900302
\(113\) −4.41216 −0.415062 −0.207531 0.978228i \(-0.566543\pi\)
−0.207531 + 0.978228i \(0.566543\pi\)
\(114\) −4.33023 −0.405563
\(115\) 7.34499 0.684924
\(116\) 4.44123 0.412358
\(117\) −1.00000 −0.0924500
\(118\) −5.12897 −0.472160
\(119\) −6.93133 −0.635394
\(120\) 2.46518 0.225039
\(121\) 6.67349 0.606681
\(122\) 5.32855 0.482424
\(123\) 8.68437 0.783043
\(124\) 2.25549 0.202549
\(125\) −9.67064 −0.864968
\(126\) 0.952790 0.0848813
\(127\) −7.68171 −0.681642 −0.340821 0.940128i \(-0.610705\pi\)
−0.340821 + 0.940128i \(0.610705\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.56905 −0.490328
\(130\) 2.46518 0.216210
\(131\) 0.0791075 0.00691165 0.00345583 0.999994i \(-0.498900\pi\)
0.00345583 + 0.999994i \(0.498900\pi\)
\(132\) −4.20399 −0.365910
\(133\) 4.12580 0.357752
\(134\) −5.95796 −0.514690
\(135\) −2.46518 −0.212169
\(136\) −7.27477 −0.623807
\(137\) −3.99460 −0.341281 −0.170641 0.985333i \(-0.554584\pi\)
−0.170641 + 0.985333i \(0.554584\pi\)
\(138\) 2.97949 0.253631
\(139\) 13.0462 1.10657 0.553283 0.832994i \(-0.313375\pi\)
0.553283 + 0.832994i \(0.313375\pi\)
\(140\) −2.34880 −0.198510
\(141\) −5.13291 −0.432269
\(142\) −12.6592 −1.06234
\(143\) −4.20399 −0.351555
\(144\) 1.00000 0.0833333
\(145\) 10.9484 0.909218
\(146\) 7.23738 0.598970
\(147\) 6.09219 0.502475
\(148\) 3.37198 0.277175
\(149\) 15.1863 1.24411 0.622056 0.782973i \(-0.286298\pi\)
0.622056 + 0.782973i \(0.286298\pi\)
\(150\) 1.07710 0.0879452
\(151\) 16.8777 1.37349 0.686744 0.726899i \(-0.259039\pi\)
0.686744 + 0.726899i \(0.259039\pi\)
\(152\) 4.33023 0.351228
\(153\) 7.27477 0.588131
\(154\) 4.00552 0.322774
\(155\) 5.56019 0.446605
\(156\) 1.00000 0.0800641
\(157\) −2.03856 −0.162695 −0.0813473 0.996686i \(-0.525922\pi\)
−0.0813473 + 0.996686i \(0.525922\pi\)
\(158\) 9.05227 0.720160
\(159\) −8.80268 −0.698098
\(160\) −2.46518 −0.194889
\(161\) −2.83883 −0.223731
\(162\) −1.00000 −0.0785674
\(163\) −17.7666 −1.39159 −0.695795 0.718241i \(-0.744948\pi\)
−0.695795 + 0.718241i \(0.744948\pi\)
\(164\) −8.68437 −0.678135
\(165\) −10.3636 −0.806803
\(166\) −7.82412 −0.607270
\(167\) 8.10126 0.626894 0.313447 0.949606i \(-0.398516\pi\)
0.313447 + 0.949606i \(0.398516\pi\)
\(168\) −0.952790 −0.0735094
\(169\) 1.00000 0.0769231
\(170\) −17.9336 −1.37545
\(171\) −4.33023 −0.331141
\(172\) 5.56905 0.424636
\(173\) −8.14139 −0.618978 −0.309489 0.950903i \(-0.600158\pi\)
−0.309489 + 0.950903i \(0.600158\pi\)
\(174\) 4.44123 0.336689
\(175\) −1.02625 −0.0775776
\(176\) 4.20399 0.316887
\(177\) −5.12897 −0.385517
\(178\) −3.70795 −0.277923
\(179\) 16.2502 1.21459 0.607297 0.794475i \(-0.292254\pi\)
0.607297 + 0.794475i \(0.292254\pi\)
\(180\) 2.46518 0.183744
\(181\) 0.280385 0.0208409 0.0104204 0.999946i \(-0.496683\pi\)
0.0104204 + 0.999946i \(0.496683\pi\)
\(182\) −0.952790 −0.0706255
\(183\) 5.32855 0.393898
\(184\) −2.97949 −0.219651
\(185\) 8.31254 0.611150
\(186\) 2.25549 0.165381
\(187\) 30.5830 2.23645
\(188\) 5.13291 0.374356
\(189\) 0.952790 0.0693053
\(190\) 10.6748 0.774430
\(191\) −11.5986 −0.839242 −0.419621 0.907699i \(-0.637837\pi\)
−0.419621 + 0.907699i \(0.637837\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.70353 0.482531 0.241265 0.970459i \(-0.422438\pi\)
0.241265 + 0.970459i \(0.422438\pi\)
\(194\) 18.7132 1.34353
\(195\) 2.46518 0.176535
\(196\) −6.09219 −0.435156
\(197\) 10.1317 0.721852 0.360926 0.932594i \(-0.382461\pi\)
0.360926 + 0.932594i \(0.382461\pi\)
\(198\) −4.20399 −0.298764
\(199\) −2.03748 −0.144433 −0.0722166 0.997389i \(-0.523007\pi\)
−0.0722166 + 0.997389i \(0.523007\pi\)
\(200\) −1.07710 −0.0761628
\(201\) −5.95796 −0.420242
\(202\) 2.53136 0.178106
\(203\) −4.23156 −0.296998
\(204\) −7.27477 −0.509336
\(205\) −21.4085 −1.49524
\(206\) −1.00000 −0.0696733
\(207\) 2.97949 0.207089
\(208\) −1.00000 −0.0693375
\(209\) −18.2042 −1.25921
\(210\) −2.34880 −0.162082
\(211\) 9.03933 0.622293 0.311147 0.950362i \(-0.399287\pi\)
0.311147 + 0.950362i \(0.399287\pi\)
\(212\) 8.80268 0.604571
\(213\) −12.6592 −0.867393
\(214\) −2.73402 −0.186894
\(215\) 13.7287 0.936290
\(216\) 1.00000 0.0680414
\(217\) −2.14901 −0.145884
\(218\) −9.98912 −0.676549
\(219\) 7.23738 0.489057
\(220\) 10.3636 0.698712
\(221\) −7.27477 −0.489354
\(222\) 3.37198 0.226313
\(223\) 10.3979 0.696294 0.348147 0.937440i \(-0.386811\pi\)
0.348147 + 0.937440i \(0.386811\pi\)
\(224\) 0.952790 0.0636610
\(225\) 1.07710 0.0718070
\(226\) 4.41216 0.293493
\(227\) 16.0725 1.06677 0.533386 0.845872i \(-0.320919\pi\)
0.533386 + 0.845872i \(0.320919\pi\)
\(228\) 4.33023 0.286776
\(229\) −20.0781 −1.32680 −0.663398 0.748267i \(-0.730886\pi\)
−0.663398 + 0.748267i \(0.730886\pi\)
\(230\) −7.34499 −0.484314
\(231\) 4.00552 0.263544
\(232\) −4.44123 −0.291581
\(233\) −13.2736 −0.869585 −0.434792 0.900531i \(-0.643178\pi\)
−0.434792 + 0.900531i \(0.643178\pi\)
\(234\) 1.00000 0.0653720
\(235\) 12.6535 0.825425
\(236\) 5.12897 0.333868
\(237\) 9.05227 0.588008
\(238\) 6.93133 0.449292
\(239\) −15.4499 −0.999373 −0.499687 0.866206i \(-0.666551\pi\)
−0.499687 + 0.866206i \(0.666551\pi\)
\(240\) −2.46518 −0.159127
\(241\) 21.5308 1.38692 0.693459 0.720496i \(-0.256086\pi\)
0.693459 + 0.720496i \(0.256086\pi\)
\(242\) −6.67349 −0.428988
\(243\) −1.00000 −0.0641500
\(244\) −5.32855 −0.341126
\(245\) −15.0183 −0.959486
\(246\) −8.68437 −0.553695
\(247\) 4.33023 0.275526
\(248\) −2.25549 −0.143224
\(249\) −7.82412 −0.495834
\(250\) 9.67064 0.611625
\(251\) −7.41297 −0.467903 −0.233951 0.972248i \(-0.575166\pi\)
−0.233951 + 0.972248i \(0.575166\pi\)
\(252\) −0.952790 −0.0600201
\(253\) 12.5258 0.787487
\(254\) 7.68171 0.481993
\(255\) −17.9336 −1.12305
\(256\) 1.00000 0.0625000
\(257\) −29.3253 −1.82926 −0.914631 0.404290i \(-0.867519\pi\)
−0.914631 + 0.404290i \(0.867519\pi\)
\(258\) 5.56905 0.346714
\(259\) −3.21279 −0.199633
\(260\) −2.46518 −0.152884
\(261\) 4.44123 0.274905
\(262\) −0.0791075 −0.00488728
\(263\) 4.81915 0.297161 0.148581 0.988900i \(-0.452530\pi\)
0.148581 + 0.988900i \(0.452530\pi\)
\(264\) 4.20399 0.258737
\(265\) 21.7002 1.33303
\(266\) −4.12580 −0.252969
\(267\) −3.70795 −0.226923
\(268\) 5.95796 0.363941
\(269\) −5.25718 −0.320536 −0.160268 0.987074i \(-0.551236\pi\)
−0.160268 + 0.987074i \(0.551236\pi\)
\(270\) 2.46518 0.150026
\(271\) −21.4015 −1.30005 −0.650025 0.759913i \(-0.725242\pi\)
−0.650025 + 0.759913i \(0.725242\pi\)
\(272\) 7.27477 0.441098
\(273\) −0.952790 −0.0576655
\(274\) 3.99460 0.241322
\(275\) 4.52813 0.273057
\(276\) −2.97949 −0.179345
\(277\) −31.4672 −1.89068 −0.945341 0.326085i \(-0.894271\pi\)
−0.945341 + 0.326085i \(0.894271\pi\)
\(278\) −13.0462 −0.782460
\(279\) 2.25549 0.135033
\(280\) 2.34880 0.140368
\(281\) 30.2559 1.80492 0.902458 0.430777i \(-0.141760\pi\)
0.902458 + 0.430777i \(0.141760\pi\)
\(282\) 5.13291 0.305660
\(283\) 22.6650 1.34729 0.673646 0.739054i \(-0.264727\pi\)
0.673646 + 0.739054i \(0.264727\pi\)
\(284\) 12.6592 0.751184
\(285\) 10.6748 0.632320
\(286\) 4.20399 0.248587
\(287\) 8.27438 0.488421
\(288\) −1.00000 −0.0589256
\(289\) 35.9223 2.11308
\(290\) −10.9484 −0.642914
\(291\) 18.7132 1.09699
\(292\) −7.23738 −0.423536
\(293\) −27.5148 −1.60743 −0.803717 0.595012i \(-0.797147\pi\)
−0.803717 + 0.595012i \(0.797147\pi\)
\(294\) −6.09219 −0.355304
\(295\) 12.6438 0.736153
\(296\) −3.37198 −0.195992
\(297\) −4.20399 −0.243940
\(298\) −15.1863 −0.879720
\(299\) −2.97949 −0.172309
\(300\) −1.07710 −0.0621867
\(301\) −5.30614 −0.305841
\(302\) −16.8777 −0.971202
\(303\) 2.53136 0.145423
\(304\) −4.33023 −0.248356
\(305\) −13.1358 −0.752156
\(306\) −7.27477 −0.415871
\(307\) 4.53701 0.258941 0.129471 0.991583i \(-0.458672\pi\)
0.129471 + 0.991583i \(0.458672\pi\)
\(308\) −4.00552 −0.228235
\(309\) −1.00000 −0.0568880
\(310\) −5.56019 −0.315798
\(311\) −25.6533 −1.45466 −0.727332 0.686286i \(-0.759240\pi\)
−0.727332 + 0.686286i \(0.759240\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −0.813766 −0.0459968 −0.0229984 0.999736i \(-0.507321\pi\)
−0.0229984 + 0.999736i \(0.507321\pi\)
\(314\) 2.03856 0.115042
\(315\) −2.34880 −0.132340
\(316\) −9.05227 −0.509230
\(317\) −23.7066 −1.33149 −0.665747 0.746178i \(-0.731887\pi\)
−0.665747 + 0.746178i \(0.731887\pi\)
\(318\) 8.80268 0.493630
\(319\) 18.6709 1.04537
\(320\) 2.46518 0.137808
\(321\) −2.73402 −0.152598
\(322\) 2.83883 0.158202
\(323\) −31.5014 −1.75279
\(324\) 1.00000 0.0555556
\(325\) −1.07710 −0.0597470
\(326\) 17.7666 0.984002
\(327\) −9.98912 −0.552400
\(328\) 8.68437 0.479514
\(329\) −4.89058 −0.269627
\(330\) 10.3636 0.570496
\(331\) 14.7152 0.808818 0.404409 0.914578i \(-0.367477\pi\)
0.404409 + 0.914578i \(0.367477\pi\)
\(332\) 7.82412 0.429404
\(333\) 3.37198 0.184783
\(334\) −8.10126 −0.443281
\(335\) 14.6874 0.802461
\(336\) 0.952790 0.0519790
\(337\) 9.99348 0.544380 0.272190 0.962244i \(-0.412252\pi\)
0.272190 + 0.962244i \(0.412252\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 4.41216 0.239636
\(340\) 17.9336 0.972587
\(341\) 9.48205 0.513482
\(342\) 4.33023 0.234152
\(343\) 12.4741 0.673539
\(344\) −5.56905 −0.300263
\(345\) −7.34499 −0.395441
\(346\) 8.14139 0.437684
\(347\) 16.4929 0.885387 0.442694 0.896673i \(-0.354023\pi\)
0.442694 + 0.896673i \(0.354023\pi\)
\(348\) −4.44123 −0.238075
\(349\) −14.2015 −0.760186 −0.380093 0.924948i \(-0.624108\pi\)
−0.380093 + 0.924948i \(0.624108\pi\)
\(350\) 1.02625 0.0548556
\(351\) 1.00000 0.0533761
\(352\) −4.20399 −0.224073
\(353\) −19.9580 −1.06225 −0.531127 0.847292i \(-0.678231\pi\)
−0.531127 + 0.847292i \(0.678231\pi\)
\(354\) 5.12897 0.272602
\(355\) 31.2072 1.65630
\(356\) 3.70795 0.196521
\(357\) 6.93133 0.366845
\(358\) −16.2502 −0.858847
\(359\) −0.924105 −0.0487724 −0.0243862 0.999703i \(-0.507763\pi\)
−0.0243862 + 0.999703i \(0.507763\pi\)
\(360\) −2.46518 −0.129926
\(361\) −0.249129 −0.0131120
\(362\) −0.280385 −0.0147367
\(363\) −6.67349 −0.350267
\(364\) 0.952790 0.0499398
\(365\) −17.8414 −0.933864
\(366\) −5.32855 −0.278528
\(367\) 2.52886 0.132005 0.0660026 0.997819i \(-0.478975\pi\)
0.0660026 + 0.997819i \(0.478975\pi\)
\(368\) 2.97949 0.155317
\(369\) −8.68437 −0.452090
\(370\) −8.31254 −0.432148
\(371\) −8.38711 −0.435437
\(372\) −2.25549 −0.116942
\(373\) −18.0617 −0.935199 −0.467600 0.883940i \(-0.654881\pi\)
−0.467600 + 0.883940i \(0.654881\pi\)
\(374\) −30.5830 −1.58141
\(375\) 9.67064 0.499390
\(376\) −5.13291 −0.264709
\(377\) −4.44123 −0.228735
\(378\) −0.952790 −0.0490062
\(379\) −17.5037 −0.899105 −0.449553 0.893254i \(-0.648417\pi\)
−0.449553 + 0.893254i \(0.648417\pi\)
\(380\) −10.6748 −0.547605
\(381\) 7.68171 0.393546
\(382\) 11.5986 0.593434
\(383\) −13.1769 −0.673309 −0.336654 0.941628i \(-0.609295\pi\)
−0.336654 + 0.941628i \(0.609295\pi\)
\(384\) 1.00000 0.0510310
\(385\) −9.87431 −0.503242
\(386\) −6.70353 −0.341201
\(387\) 5.56905 0.283091
\(388\) −18.7132 −0.950021
\(389\) −9.23942 −0.468457 −0.234229 0.972182i \(-0.575256\pi\)
−0.234229 + 0.972182i \(0.575256\pi\)
\(390\) −2.46518 −0.124829
\(391\) 21.6751 1.09616
\(392\) 6.09219 0.307702
\(393\) −0.0791075 −0.00399045
\(394\) −10.1317 −0.510427
\(395\) −22.3155 −1.12281
\(396\) 4.20399 0.211258
\(397\) 21.4383 1.07596 0.537980 0.842958i \(-0.319188\pi\)
0.537980 + 0.842958i \(0.319188\pi\)
\(398\) 2.03748 0.102130
\(399\) −4.12580 −0.206548
\(400\) 1.07710 0.0538552
\(401\) 28.0184 1.39917 0.699586 0.714548i \(-0.253368\pi\)
0.699586 + 0.714548i \(0.253368\pi\)
\(402\) 5.95796 0.297156
\(403\) −2.25549 −0.112354
\(404\) −2.53136 −0.125940
\(405\) 2.46518 0.122496
\(406\) 4.23156 0.210009
\(407\) 14.1758 0.702666
\(408\) 7.27477 0.360155
\(409\) 23.9390 1.18371 0.591855 0.806045i \(-0.298396\pi\)
0.591855 + 0.806045i \(0.298396\pi\)
\(410\) 21.4085 1.05729
\(411\) 3.99460 0.197039
\(412\) 1.00000 0.0492665
\(413\) −4.88684 −0.240466
\(414\) −2.97949 −0.146434
\(415\) 19.2879 0.946804
\(416\) 1.00000 0.0490290
\(417\) −13.0462 −0.638876
\(418\) 18.2042 0.890397
\(419\) 35.4590 1.73228 0.866142 0.499798i \(-0.166593\pi\)
0.866142 + 0.499798i \(0.166593\pi\)
\(420\) 2.34880 0.114610
\(421\) 20.3462 0.991615 0.495807 0.868433i \(-0.334872\pi\)
0.495807 + 0.868433i \(0.334872\pi\)
\(422\) −9.03933 −0.440028
\(423\) 5.13291 0.249570
\(424\) −8.80268 −0.427496
\(425\) 7.83569 0.380087
\(426\) 12.6592 0.613340
\(427\) 5.07699 0.245693
\(428\) 2.73402 0.132154
\(429\) 4.20399 0.202970
\(430\) −13.7287 −0.662057
\(431\) 26.2796 1.26584 0.632921 0.774217i \(-0.281856\pi\)
0.632921 + 0.774217i \(0.281856\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −11.1879 −0.537655 −0.268828 0.963188i \(-0.586636\pi\)
−0.268828 + 0.963188i \(0.586636\pi\)
\(434\) 2.14901 0.103156
\(435\) −10.9484 −0.524937
\(436\) 9.98912 0.478392
\(437\) −12.9019 −0.617181
\(438\) −7.23738 −0.345816
\(439\) 14.1416 0.674942 0.337471 0.941336i \(-0.390429\pi\)
0.337471 + 0.941336i \(0.390429\pi\)
\(440\) −10.3636 −0.494064
\(441\) −6.09219 −0.290104
\(442\) 7.27477 0.346026
\(443\) 4.08763 0.194209 0.0971047 0.995274i \(-0.469042\pi\)
0.0971047 + 0.995274i \(0.469042\pi\)
\(444\) −3.37198 −0.160027
\(445\) 9.14076 0.433314
\(446\) −10.3979 −0.492354
\(447\) −15.1863 −0.718288
\(448\) −0.952790 −0.0450151
\(449\) 27.6267 1.30378 0.651892 0.758312i \(-0.273976\pi\)
0.651892 + 0.758312i \(0.273976\pi\)
\(450\) −1.07710 −0.0507752
\(451\) −36.5090 −1.71914
\(452\) −4.41216 −0.207531
\(453\) −16.8777 −0.792984
\(454\) −16.0725 −0.754321
\(455\) 2.34880 0.110113
\(456\) −4.33023 −0.202781
\(457\) 17.2789 0.808272 0.404136 0.914699i \(-0.367572\pi\)
0.404136 + 0.914699i \(0.367572\pi\)
\(458\) 20.0781 0.938187
\(459\) −7.27477 −0.339557
\(460\) 7.34499 0.342462
\(461\) 0.140959 0.00656512 0.00328256 0.999995i \(-0.498955\pi\)
0.00328256 + 0.999995i \(0.498955\pi\)
\(462\) −4.00552 −0.186353
\(463\) −6.71840 −0.312231 −0.156115 0.987739i \(-0.549897\pi\)
−0.156115 + 0.987739i \(0.549897\pi\)
\(464\) 4.44123 0.206179
\(465\) −5.56019 −0.257848
\(466\) 13.2736 0.614889
\(467\) −41.8427 −1.93625 −0.968125 0.250469i \(-0.919415\pi\)
−0.968125 + 0.250469i \(0.919415\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −5.67669 −0.262125
\(470\) −12.6535 −0.583664
\(471\) 2.03856 0.0939318
\(472\) −5.12897 −0.236080
\(473\) 23.4122 1.07649
\(474\) −9.05227 −0.415785
\(475\) −4.66411 −0.214004
\(476\) −6.93133 −0.317697
\(477\) 8.80268 0.403047
\(478\) 15.4499 0.706663
\(479\) −29.1826 −1.33339 −0.666693 0.745333i \(-0.732291\pi\)
−0.666693 + 0.745333i \(0.732291\pi\)
\(480\) 2.46518 0.112519
\(481\) −3.37198 −0.153749
\(482\) −21.5308 −0.980699
\(483\) 2.83883 0.129171
\(484\) 6.67349 0.303341
\(485\) −46.1315 −2.09472
\(486\) 1.00000 0.0453609
\(487\) −24.2272 −1.09784 −0.548919 0.835876i \(-0.684960\pi\)
−0.548919 + 0.835876i \(0.684960\pi\)
\(488\) 5.32855 0.241212
\(489\) 17.7666 0.803435
\(490\) 15.0183 0.678459
\(491\) 36.6208 1.65268 0.826338 0.563175i \(-0.190420\pi\)
0.826338 + 0.563175i \(0.190420\pi\)
\(492\) 8.68437 0.391522
\(493\) 32.3090 1.45512
\(494\) −4.33023 −0.194826
\(495\) 10.3636 0.465808
\(496\) 2.25549 0.101275
\(497\) −12.0615 −0.541034
\(498\) 7.82412 0.350607
\(499\) −11.6189 −0.520132 −0.260066 0.965591i \(-0.583744\pi\)
−0.260066 + 0.965591i \(0.583744\pi\)
\(500\) −9.67064 −0.432484
\(501\) −8.10126 −0.361937
\(502\) 7.41297 0.330857
\(503\) 2.00788 0.0895269 0.0447634 0.998998i \(-0.485747\pi\)
0.0447634 + 0.998998i \(0.485747\pi\)
\(504\) 0.952790 0.0424406
\(505\) −6.24026 −0.277688
\(506\) −12.5258 −0.556838
\(507\) −1.00000 −0.0444116
\(508\) −7.68171 −0.340821
\(509\) 12.0630 0.534684 0.267342 0.963602i \(-0.413855\pi\)
0.267342 + 0.963602i \(0.413855\pi\)
\(510\) 17.9336 0.794114
\(511\) 6.89571 0.305048
\(512\) −1.00000 −0.0441942
\(513\) 4.33023 0.191184
\(514\) 29.3253 1.29348
\(515\) 2.46518 0.108629
\(516\) −5.56905 −0.245164
\(517\) 21.5787 0.949029
\(518\) 3.21279 0.141162
\(519\) 8.14139 0.357367
\(520\) 2.46518 0.108105
\(521\) 23.0562 1.01011 0.505054 0.863088i \(-0.331472\pi\)
0.505054 + 0.863088i \(0.331472\pi\)
\(522\) −4.44123 −0.194388
\(523\) 12.7046 0.555533 0.277766 0.960649i \(-0.410406\pi\)
0.277766 + 0.960649i \(0.410406\pi\)
\(524\) 0.0791075 0.00345583
\(525\) 1.02625 0.0447894
\(526\) −4.81915 −0.210125
\(527\) 16.4082 0.714752
\(528\) −4.20399 −0.182955
\(529\) −14.1226 −0.614027
\(530\) −21.7002 −0.942596
\(531\) 5.12897 0.222579
\(532\) 4.12580 0.178876
\(533\) 8.68437 0.376162
\(534\) 3.70795 0.160459
\(535\) 6.73985 0.291389
\(536\) −5.95796 −0.257345
\(537\) −16.2502 −0.701246
\(538\) 5.25718 0.226653
\(539\) −25.6115 −1.10316
\(540\) −2.46518 −0.106084
\(541\) 34.6242 1.48861 0.744306 0.667839i \(-0.232781\pi\)
0.744306 + 0.667839i \(0.232781\pi\)
\(542\) 21.4015 0.919275
\(543\) −0.280385 −0.0120325
\(544\) −7.27477 −0.311903
\(545\) 24.6250 1.05482
\(546\) 0.952790 0.0407757
\(547\) 20.8348 0.890830 0.445415 0.895324i \(-0.353056\pi\)
0.445415 + 0.895324i \(0.353056\pi\)
\(548\) −3.99460 −0.170641
\(549\) −5.32855 −0.227417
\(550\) −4.52813 −0.193080
\(551\) −19.2316 −0.819292
\(552\) 2.97949 0.126816
\(553\) 8.62491 0.366769
\(554\) 31.4672 1.33691
\(555\) −8.31254 −0.352847
\(556\) 13.0462 0.553283
\(557\) 34.9136 1.47934 0.739669 0.672971i \(-0.234982\pi\)
0.739669 + 0.672971i \(0.234982\pi\)
\(558\) −2.25549 −0.0954826
\(559\) −5.56905 −0.235546
\(560\) −2.34880 −0.0992548
\(561\) −30.5830 −1.29122
\(562\) −30.2559 −1.27627
\(563\) 7.17388 0.302343 0.151171 0.988508i \(-0.451695\pi\)
0.151171 + 0.988508i \(0.451695\pi\)
\(564\) −5.13291 −0.216134
\(565\) −10.8768 −0.457589
\(566\) −22.6650 −0.952679
\(567\) −0.952790 −0.0400134
\(568\) −12.6592 −0.531168
\(569\) 9.16795 0.384341 0.192170 0.981362i \(-0.438447\pi\)
0.192170 + 0.981362i \(0.438447\pi\)
\(570\) −10.6748 −0.447117
\(571\) −1.81441 −0.0759306 −0.0379653 0.999279i \(-0.512088\pi\)
−0.0379653 + 0.999279i \(0.512088\pi\)
\(572\) −4.20399 −0.175777
\(573\) 11.5986 0.484537
\(574\) −8.27438 −0.345366
\(575\) 3.20923 0.133834
\(576\) 1.00000 0.0416667
\(577\) −12.8667 −0.535647 −0.267824 0.963468i \(-0.586304\pi\)
−0.267824 + 0.963468i \(0.586304\pi\)
\(578\) −35.9223 −1.49417
\(579\) −6.70353 −0.278589
\(580\) 10.9484 0.454609
\(581\) −7.45475 −0.309275
\(582\) −18.7132 −0.775689
\(583\) 37.0063 1.53265
\(584\) 7.23738 0.299485
\(585\) −2.46518 −0.101923
\(586\) 27.5148 1.13663
\(587\) 8.00438 0.330376 0.165188 0.986262i \(-0.447177\pi\)
0.165188 + 0.986262i \(0.447177\pi\)
\(588\) 6.09219 0.251238
\(589\) −9.76679 −0.402434
\(590\) −12.6438 −0.520539
\(591\) −10.1317 −0.416762
\(592\) 3.37198 0.138588
\(593\) −26.4157 −1.08476 −0.542381 0.840133i \(-0.682477\pi\)
−0.542381 + 0.840133i \(0.682477\pi\)
\(594\) 4.20399 0.172492
\(595\) −17.0870 −0.700497
\(596\) 15.1863 0.622056
\(597\) 2.03748 0.0833886
\(598\) 2.97949 0.121841
\(599\) 37.5562 1.53451 0.767253 0.641345i \(-0.221623\pi\)
0.767253 + 0.641345i \(0.221623\pi\)
\(600\) 1.07710 0.0439726
\(601\) 2.97218 0.121238 0.0606189 0.998161i \(-0.480693\pi\)
0.0606189 + 0.998161i \(0.480693\pi\)
\(602\) 5.30614 0.216262
\(603\) 5.95796 0.242627
\(604\) 16.8777 0.686744
\(605\) 16.4513 0.668842
\(606\) −2.53136 −0.102829
\(607\) −33.9595 −1.37837 −0.689187 0.724584i \(-0.742032\pi\)
−0.689187 + 0.724584i \(0.742032\pi\)
\(608\) 4.33023 0.175614
\(609\) 4.23156 0.171472
\(610\) 13.1358 0.531854
\(611\) −5.13291 −0.207655
\(612\) 7.27477 0.294065
\(613\) −13.4030 −0.541342 −0.270671 0.962672i \(-0.587246\pi\)
−0.270671 + 0.962672i \(0.587246\pi\)
\(614\) −4.53701 −0.183099
\(615\) 21.4085 0.863275
\(616\) 4.00552 0.161387
\(617\) 23.0444 0.927733 0.463867 0.885905i \(-0.346462\pi\)
0.463867 + 0.885905i \(0.346462\pi\)
\(618\) 1.00000 0.0402259
\(619\) −13.5210 −0.543455 −0.271727 0.962374i \(-0.587595\pi\)
−0.271727 + 0.962374i \(0.587595\pi\)
\(620\) 5.56019 0.223303
\(621\) −2.97949 −0.119563
\(622\) 25.6533 1.02860
\(623\) −3.53290 −0.141543
\(624\) 1.00000 0.0400320
\(625\) −29.2254 −1.16901
\(626\) 0.813766 0.0325246
\(627\) 18.2042 0.727006
\(628\) −2.03856 −0.0813473
\(629\) 24.5304 0.978091
\(630\) 2.34880 0.0935783
\(631\) 21.0903 0.839590 0.419795 0.907619i \(-0.362102\pi\)
0.419795 + 0.907619i \(0.362102\pi\)
\(632\) 9.05227 0.360080
\(633\) −9.03933 −0.359281
\(634\) 23.7066 0.941508
\(635\) −18.9368 −0.751484
\(636\) −8.80268 −0.349049
\(637\) 6.09219 0.241381
\(638\) −18.6709 −0.739187
\(639\) 12.6592 0.500790
\(640\) −2.46518 −0.0974447
\(641\) 36.3190 1.43452 0.717258 0.696808i \(-0.245397\pi\)
0.717258 + 0.696808i \(0.245397\pi\)
\(642\) 2.73402 0.107903
\(643\) −27.4035 −1.08069 −0.540344 0.841444i \(-0.681706\pi\)
−0.540344 + 0.841444i \(0.681706\pi\)
\(644\) −2.83883 −0.111866
\(645\) −13.7287 −0.540567
\(646\) 31.5014 1.23941
\(647\) 31.6155 1.24293 0.621467 0.783440i \(-0.286537\pi\)
0.621467 + 0.783440i \(0.286537\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 21.5621 0.846388
\(650\) 1.07710 0.0422475
\(651\) 2.14901 0.0842264
\(652\) −17.7666 −0.695795
\(653\) −45.8355 −1.79368 −0.896841 0.442353i \(-0.854144\pi\)
−0.896841 + 0.442353i \(0.854144\pi\)
\(654\) 9.98912 0.390606
\(655\) 0.195014 0.00761983
\(656\) −8.68437 −0.339068
\(657\) −7.23738 −0.282357
\(658\) 4.89058 0.190655
\(659\) 11.6284 0.452978 0.226489 0.974014i \(-0.427275\pi\)
0.226489 + 0.974014i \(0.427275\pi\)
\(660\) −10.3636 −0.403402
\(661\) 2.47763 0.0963686 0.0481843 0.998838i \(-0.484657\pi\)
0.0481843 + 0.998838i \(0.484657\pi\)
\(662\) −14.7152 −0.571921
\(663\) 7.27477 0.282529
\(664\) −7.82412 −0.303635
\(665\) 10.1708 0.394408
\(666\) −3.37198 −0.130662
\(667\) 13.2326 0.512370
\(668\) 8.10126 0.313447
\(669\) −10.3979 −0.402006
\(670\) −14.6874 −0.567425
\(671\) −22.4012 −0.864787
\(672\) −0.952790 −0.0367547
\(673\) 43.6553 1.68279 0.841394 0.540423i \(-0.181736\pi\)
0.841394 + 0.540423i \(0.181736\pi\)
\(674\) −9.99348 −0.384935
\(675\) −1.07710 −0.0414578
\(676\) 1.00000 0.0384615
\(677\) 16.4807 0.633404 0.316702 0.948525i \(-0.397425\pi\)
0.316702 + 0.948525i \(0.397425\pi\)
\(678\) −4.41216 −0.169448
\(679\) 17.8298 0.684245
\(680\) −17.9336 −0.687723
\(681\) −16.0725 −0.615901
\(682\) −9.48205 −0.363087
\(683\) −39.6360 −1.51663 −0.758315 0.651888i \(-0.773977\pi\)
−0.758315 + 0.651888i \(0.773977\pi\)
\(684\) −4.33023 −0.165570
\(685\) −9.84739 −0.376249
\(686\) −12.4741 −0.476264
\(687\) 20.0781 0.766026
\(688\) 5.56905 0.212318
\(689\) −8.80268 −0.335355
\(690\) 7.34499 0.279619
\(691\) 17.7312 0.674528 0.337264 0.941410i \(-0.390499\pi\)
0.337264 + 0.941410i \(0.390499\pi\)
\(692\) −8.14139 −0.309489
\(693\) −4.00552 −0.152157
\(694\) −16.4929 −0.626063
\(695\) 32.1612 1.21995
\(696\) 4.44123 0.168345
\(697\) −63.1768 −2.39299
\(698\) 14.2015 0.537533
\(699\) 13.2736 0.502055
\(700\) −1.02625 −0.0387888
\(701\) −14.8140 −0.559519 −0.279759 0.960070i \(-0.590255\pi\)
−0.279759 + 0.960070i \(0.590255\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −14.6014 −0.550704
\(704\) 4.20399 0.158444
\(705\) −12.6535 −0.476560
\(706\) 19.9580 0.751128
\(707\) 2.41186 0.0907072
\(708\) −5.12897 −0.192759
\(709\) −0.691614 −0.0259741 −0.0129870 0.999916i \(-0.504134\pi\)
−0.0129870 + 0.999916i \(0.504134\pi\)
\(710\) −31.2072 −1.17118
\(711\) −9.05227 −0.339487
\(712\) −3.70795 −0.138961
\(713\) 6.72023 0.251674
\(714\) −6.93133 −0.259399
\(715\) −10.3636 −0.387576
\(716\) 16.2502 0.607297
\(717\) 15.4499 0.576988
\(718\) 0.924105 0.0344873
\(719\) 1.65651 0.0617774 0.0308887 0.999523i \(-0.490166\pi\)
0.0308887 + 0.999523i \(0.490166\pi\)
\(720\) 2.46518 0.0918718
\(721\) −0.952790 −0.0354838
\(722\) 0.249129 0.00927161
\(723\) −21.5308 −0.800738
\(724\) 0.280385 0.0104204
\(725\) 4.78368 0.177661
\(726\) 6.67349 0.247677
\(727\) 13.9570 0.517636 0.258818 0.965926i \(-0.416667\pi\)
0.258818 + 0.965926i \(0.416667\pi\)
\(728\) −0.952790 −0.0353128
\(729\) 1.00000 0.0370370
\(730\) 17.8414 0.660341
\(731\) 40.5136 1.49845
\(732\) 5.32855 0.196949
\(733\) −30.4509 −1.12473 −0.562365 0.826889i \(-0.690108\pi\)
−0.562365 + 0.826889i \(0.690108\pi\)
\(734\) −2.52886 −0.0933418
\(735\) 15.0183 0.553960
\(736\) −2.97949 −0.109826
\(737\) 25.0472 0.922625
\(738\) 8.68437 0.319676
\(739\) 23.5770 0.867295 0.433648 0.901083i \(-0.357226\pi\)
0.433648 + 0.901083i \(0.357226\pi\)
\(740\) 8.31254 0.305575
\(741\) −4.33023 −0.159075
\(742\) 8.38711 0.307900
\(743\) 0.256667 0.00941620 0.00470810 0.999989i \(-0.498501\pi\)
0.00470810 + 0.999989i \(0.498501\pi\)
\(744\) 2.25549 0.0826903
\(745\) 37.4370 1.37159
\(746\) 18.0617 0.661286
\(747\) 7.82412 0.286270
\(748\) 30.5830 1.11823
\(749\) −2.60495 −0.0951828
\(750\) −9.67064 −0.353122
\(751\) 22.2227 0.810917 0.405458 0.914113i \(-0.367112\pi\)
0.405458 + 0.914113i \(0.367112\pi\)
\(752\) 5.13291 0.187178
\(753\) 7.41297 0.270144
\(754\) 4.44123 0.161740
\(755\) 41.6065 1.51422
\(756\) 0.952790 0.0346526
\(757\) 4.95829 0.180212 0.0901060 0.995932i \(-0.471279\pi\)
0.0901060 + 0.995932i \(0.471279\pi\)
\(758\) 17.5037 0.635763
\(759\) −12.5258 −0.454656
\(760\) 10.6748 0.387215
\(761\) 27.0921 0.982089 0.491045 0.871134i \(-0.336615\pi\)
0.491045 + 0.871134i \(0.336615\pi\)
\(762\) −7.68171 −0.278279
\(763\) −9.51754 −0.344558
\(764\) −11.5986 −0.419621
\(765\) 17.9336 0.648391
\(766\) 13.1769 0.476101
\(767\) −5.12897 −0.185197
\(768\) −1.00000 −0.0360844
\(769\) 13.1939 0.475784 0.237892 0.971292i \(-0.423544\pi\)
0.237892 + 0.971292i \(0.423544\pi\)
\(770\) 9.87431 0.355845
\(771\) 29.3253 1.05612
\(772\) 6.70353 0.241265
\(773\) 12.7483 0.458525 0.229262 0.973365i \(-0.426369\pi\)
0.229262 + 0.973365i \(0.426369\pi\)
\(774\) −5.56905 −0.200175
\(775\) 2.42940 0.0872667
\(776\) 18.7132 0.671766
\(777\) 3.21279 0.115258
\(778\) 9.23942 0.331249
\(779\) 37.6053 1.34735
\(780\) 2.46518 0.0882675
\(781\) 53.2190 1.90433
\(782\) −21.6751 −0.775102
\(783\) −4.44123 −0.158717
\(784\) −6.09219 −0.217578
\(785\) −5.02541 −0.179364
\(786\) 0.0791075 0.00282167
\(787\) −13.5003 −0.481233 −0.240617 0.970620i \(-0.577350\pi\)
−0.240617 + 0.970620i \(0.577350\pi\)
\(788\) 10.1317 0.360926
\(789\) −4.81915 −0.171566
\(790\) 22.3155 0.793949
\(791\) 4.20387 0.149472
\(792\) −4.20399 −0.149382
\(793\) 5.32855 0.189222
\(794\) −21.4383 −0.760818
\(795\) −21.7002 −0.769626
\(796\) −2.03748 −0.0722166
\(797\) 10.2484 0.363018 0.181509 0.983389i \(-0.441902\pi\)
0.181509 + 0.983389i \(0.441902\pi\)
\(798\) 4.12580 0.146052
\(799\) 37.3407 1.32102
\(800\) −1.07710 −0.0380814
\(801\) 3.70795 0.131014
\(802\) −28.0184 −0.989364
\(803\) −30.4259 −1.07371
\(804\) −5.95796 −0.210121
\(805\) −6.99823 −0.246655
\(806\) 2.25549 0.0794463
\(807\) 5.25718 0.185061
\(808\) 2.53136 0.0890530
\(809\) 10.2090 0.358930 0.179465 0.983764i \(-0.442563\pi\)
0.179465 + 0.983764i \(0.442563\pi\)
\(810\) −2.46518 −0.0866175
\(811\) 46.6092 1.63667 0.818336 0.574740i \(-0.194897\pi\)
0.818336 + 0.574740i \(0.194897\pi\)
\(812\) −4.23156 −0.148499
\(813\) 21.4015 0.750585
\(814\) −14.1758 −0.496860
\(815\) −43.7979 −1.53417
\(816\) −7.27477 −0.254668
\(817\) −24.1153 −0.843686
\(818\) −23.9390 −0.837009
\(819\) 0.952790 0.0332932
\(820\) −21.4085 −0.747618
\(821\) 25.7655 0.899222 0.449611 0.893224i \(-0.351563\pi\)
0.449611 + 0.893224i \(0.351563\pi\)
\(822\) −3.99460 −0.139328
\(823\) −36.5037 −1.27244 −0.636219 0.771508i \(-0.719503\pi\)
−0.636219 + 0.771508i \(0.719503\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −4.52813 −0.157649
\(826\) 4.88684 0.170035
\(827\) −4.48815 −0.156068 −0.0780342 0.996951i \(-0.524864\pi\)
−0.0780342 + 0.996951i \(0.524864\pi\)
\(828\) 2.97949 0.103545
\(829\) 54.7947 1.90310 0.951550 0.307495i \(-0.0994906\pi\)
0.951550 + 0.307495i \(0.0994906\pi\)
\(830\) −19.2879 −0.669491
\(831\) 31.4672 1.09159
\(832\) −1.00000 −0.0346688
\(833\) −44.3193 −1.53557
\(834\) 13.0462 0.451753
\(835\) 19.9710 0.691126
\(836\) −18.2042 −0.629606
\(837\) −2.25549 −0.0779612
\(838\) −35.4590 −1.22491
\(839\) −22.6268 −0.781163 −0.390581 0.920568i \(-0.627726\pi\)
−0.390581 + 0.920568i \(0.627726\pi\)
\(840\) −2.34880 −0.0810412
\(841\) −9.27544 −0.319843
\(842\) −20.3462 −0.701177
\(843\) −30.2559 −1.04207
\(844\) 9.03933 0.311147
\(845\) 2.46518 0.0848047
\(846\) −5.13291 −0.176473
\(847\) −6.35844 −0.218478
\(848\) 8.80268 0.302285
\(849\) −22.6650 −0.777859
\(850\) −7.83569 −0.268762
\(851\) 10.0468 0.344400
\(852\) −12.6592 −0.433697
\(853\) 4.45209 0.152437 0.0762184 0.997091i \(-0.475715\pi\)
0.0762184 + 0.997091i \(0.475715\pi\)
\(854\) −5.07699 −0.173731
\(855\) −10.6748 −0.365070
\(856\) −2.73402 −0.0934470
\(857\) 53.5018 1.82759 0.913793 0.406180i \(-0.133139\pi\)
0.913793 + 0.406180i \(0.133139\pi\)
\(858\) −4.20399 −0.143522
\(859\) −29.9987 −1.02354 −0.511772 0.859122i \(-0.671011\pi\)
−0.511772 + 0.859122i \(0.671011\pi\)
\(860\) 13.7287 0.468145
\(861\) −8.27438 −0.281990
\(862\) −26.2796 −0.895085
\(863\) 1.75205 0.0596405 0.0298202 0.999555i \(-0.490507\pi\)
0.0298202 + 0.999555i \(0.490507\pi\)
\(864\) 1.00000 0.0340207
\(865\) −20.0700 −0.682400
\(866\) 11.1879 0.380180
\(867\) −35.9223 −1.21999
\(868\) −2.14901 −0.0729422
\(869\) −38.0556 −1.29095
\(870\) 10.9484 0.371187
\(871\) −5.95796 −0.201878
\(872\) −9.98912 −0.338274
\(873\) −18.7132 −0.633347
\(874\) 12.9019 0.436413
\(875\) 9.21409 0.311493
\(876\) 7.23738 0.244529
\(877\) −5.83733 −0.197112 −0.0985562 0.995131i \(-0.531422\pi\)
−0.0985562 + 0.995131i \(0.531422\pi\)
\(878\) −14.1416 −0.477256
\(879\) 27.5148 0.928053
\(880\) 10.3636 0.349356
\(881\) −11.7604 −0.396218 −0.198109 0.980180i \(-0.563480\pi\)
−0.198109 + 0.980180i \(0.563480\pi\)
\(882\) 6.09219 0.205135
\(883\) −7.36861 −0.247973 −0.123987 0.992284i \(-0.539568\pi\)
−0.123987 + 0.992284i \(0.539568\pi\)
\(884\) −7.27477 −0.244677
\(885\) −12.6438 −0.425018
\(886\) −4.08763 −0.137327
\(887\) 25.0335 0.840543 0.420272 0.907398i \(-0.361935\pi\)
0.420272 + 0.907398i \(0.361935\pi\)
\(888\) 3.37198 0.113156
\(889\) 7.31906 0.245473
\(890\) −9.14076 −0.306399
\(891\) 4.20399 0.140839
\(892\) 10.3979 0.348147
\(893\) −22.2267 −0.743787
\(894\) 15.1863 0.507906
\(895\) 40.0595 1.33904
\(896\) 0.952790 0.0318305
\(897\) 2.97949 0.0994824
\(898\) −27.6267 −0.921914
\(899\) 10.0172 0.334091
\(900\) 1.07710 0.0359035
\(901\) 64.0375 2.13340
\(902\) 36.5090 1.21562
\(903\) 5.30614 0.176577
\(904\) 4.41216 0.146746
\(905\) 0.691199 0.0229762
\(906\) 16.8777 0.560724
\(907\) 21.2088 0.704228 0.352114 0.935957i \(-0.385463\pi\)
0.352114 + 0.935957i \(0.385463\pi\)
\(908\) 16.0725 0.533386
\(909\) −2.53136 −0.0839599
\(910\) −2.34880 −0.0778619
\(911\) 24.4489 0.810029 0.405015 0.914310i \(-0.367266\pi\)
0.405015 + 0.914310i \(0.367266\pi\)
\(912\) 4.33023 0.143388
\(913\) 32.8925 1.08858
\(914\) −17.2789 −0.571535
\(915\) 13.1358 0.434257
\(916\) −20.0781 −0.663398
\(917\) −0.0753729 −0.00248903
\(918\) 7.27477 0.240103
\(919\) 41.5325 1.37003 0.685016 0.728528i \(-0.259795\pi\)
0.685016 + 0.728528i \(0.259795\pi\)
\(920\) −7.34499 −0.242157
\(921\) −4.53701 −0.149500
\(922\) −0.140959 −0.00464224
\(923\) −12.6592 −0.416682
\(924\) 4.00552 0.131772
\(925\) 3.63198 0.119419
\(926\) 6.71840 0.220780
\(927\) 1.00000 0.0328443
\(928\) −4.44123 −0.145791
\(929\) −8.50079 −0.278902 −0.139451 0.990229i \(-0.544534\pi\)
−0.139451 + 0.990229i \(0.544534\pi\)
\(930\) 5.56019 0.182326
\(931\) 26.3806 0.864588
\(932\) −13.2736 −0.434792
\(933\) 25.6533 0.839851
\(934\) 41.8427 1.36913
\(935\) 75.3926 2.46560
\(936\) 1.00000 0.0326860
\(937\) 16.2234 0.529996 0.264998 0.964249i \(-0.414629\pi\)
0.264998 + 0.964249i \(0.414629\pi\)
\(938\) 5.67669 0.185350
\(939\) 0.813766 0.0265562
\(940\) 12.6535 0.412713
\(941\) 10.5399 0.343590 0.171795 0.985133i \(-0.445043\pi\)
0.171795 + 0.985133i \(0.445043\pi\)
\(942\) −2.03856 −0.0664198
\(943\) −25.8750 −0.842607
\(944\) 5.12897 0.166934
\(945\) 2.34880 0.0764064
\(946\) −23.4122 −0.761197
\(947\) −29.1952 −0.948716 −0.474358 0.880332i \(-0.657320\pi\)
−0.474358 + 0.880332i \(0.657320\pi\)
\(948\) 9.05227 0.294004
\(949\) 7.23738 0.234935
\(950\) 4.66411 0.151324
\(951\) 23.7066 0.768738
\(952\) 6.93133 0.224646
\(953\) 8.24769 0.267169 0.133584 0.991037i \(-0.457351\pi\)
0.133584 + 0.991037i \(0.457351\pi\)
\(954\) −8.80268 −0.284997
\(955\) −28.5925 −0.925232
\(956\) −15.4499 −0.499687
\(957\) −18.6709 −0.603544
\(958\) 29.1826 0.942846
\(959\) 3.80601 0.122903
\(960\) −2.46518 −0.0795633
\(961\) −25.9128 −0.835895
\(962\) 3.37198 0.108717
\(963\) 2.73402 0.0881026
\(964\) 21.5308 0.693459
\(965\) 16.5254 0.531971
\(966\) −2.83883 −0.0913380
\(967\) 9.20865 0.296130 0.148065 0.988978i \(-0.452695\pi\)
0.148065 + 0.988978i \(0.452695\pi\)
\(968\) −6.67349 −0.214494
\(969\) 31.5014 1.01197
\(970\) 46.1315 1.48119
\(971\) −22.3311 −0.716639 −0.358320 0.933599i \(-0.616650\pi\)
−0.358320 + 0.933599i \(0.616650\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −12.4303 −0.398497
\(974\) 24.2272 0.776289
\(975\) 1.07710 0.0344950
\(976\) −5.32855 −0.170563
\(977\) 26.9515 0.862256 0.431128 0.902291i \(-0.358116\pi\)
0.431128 + 0.902291i \(0.358116\pi\)
\(978\) −17.7666 −0.568114
\(979\) 15.5882 0.498200
\(980\) −15.0183 −0.479743
\(981\) 9.98912 0.318928
\(982\) −36.6208 −1.16862
\(983\) 4.99152 0.159205 0.0796023 0.996827i \(-0.474635\pi\)
0.0796023 + 0.996827i \(0.474635\pi\)
\(984\) −8.68437 −0.276848
\(985\) 24.9764 0.795814
\(986\) −32.3090 −1.02893
\(987\) 4.89058 0.155669
\(988\) 4.33023 0.137763
\(989\) 16.5930 0.527625
\(990\) −10.3636 −0.329376
\(991\) −24.0329 −0.763430 −0.381715 0.924280i \(-0.624666\pi\)
−0.381715 + 0.924280i \(0.624666\pi\)
\(992\) −2.25549 −0.0716119
\(993\) −14.7152 −0.466971
\(994\) 12.0615 0.382569
\(995\) −5.02276 −0.159232
\(996\) −7.82412 −0.247917
\(997\) 37.8573 1.19895 0.599477 0.800392i \(-0.295375\pi\)
0.599477 + 0.800392i \(0.295375\pi\)
\(998\) 11.6189 0.367789
\(999\) −3.37198 −0.106685
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.ba.1.11 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.ba.1.11 14 1.1 even 1 trivial