Properties

Label 8034.2.a.z.1.3
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.3
Root \(3.21497\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.21497 q^{10} -2.53716 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.40491 q^{14} +3.21497 q^{15} +1.00000 q^{16} +7.57385 q^{17} -1.00000 q^{18} +2.48027 q^{19} -3.21497 q^{20} +1.40491 q^{21} +2.53716 q^{22} +7.10176 q^{23} +1.00000 q^{24} +5.33603 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.40491 q^{28} -1.09619 q^{29} -3.21497 q^{30} -2.34857 q^{31} -1.00000 q^{32} +2.53716 q^{33} -7.57385 q^{34} +4.51675 q^{35} +1.00000 q^{36} +5.11651 q^{37} -2.48027 q^{38} -1.00000 q^{39} +3.21497 q^{40} -0.317535 q^{41} -1.40491 q^{42} +9.60063 q^{43} -2.53716 q^{44} -3.21497 q^{45} -7.10176 q^{46} -5.52965 q^{47} -1.00000 q^{48} -5.02622 q^{49} -5.33603 q^{50} -7.57385 q^{51} +1.00000 q^{52} -4.04692 q^{53} +1.00000 q^{54} +8.15690 q^{55} +1.40491 q^{56} -2.48027 q^{57} +1.09619 q^{58} +0.591321 q^{59} +3.21497 q^{60} -0.0491791 q^{61} +2.34857 q^{62} -1.40491 q^{63} +1.00000 q^{64} -3.21497 q^{65} -2.53716 q^{66} -11.1167 q^{67} +7.57385 q^{68} -7.10176 q^{69} -4.51675 q^{70} -16.7385 q^{71} -1.00000 q^{72} +5.34984 q^{73} -5.11651 q^{74} -5.33603 q^{75} +2.48027 q^{76} +3.56449 q^{77} +1.00000 q^{78} +16.3495 q^{79} -3.21497 q^{80} +1.00000 q^{81} +0.317535 q^{82} +3.14585 q^{83} +1.40491 q^{84} -24.3497 q^{85} -9.60063 q^{86} +1.09619 q^{87} +2.53716 q^{88} -4.41812 q^{89} +3.21497 q^{90} -1.40491 q^{91} +7.10176 q^{92} +2.34857 q^{93} +5.52965 q^{94} -7.97401 q^{95} +1.00000 q^{96} -9.59214 q^{97} +5.02622 q^{98} -2.53716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

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
\(5\) −3.21497 −1.43778 −0.718889 0.695125i \(-0.755349\pi\)
−0.718889 + 0.695125i \(0.755349\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.40491 −0.531007 −0.265503 0.964110i \(-0.585538\pi\)
−0.265503 + 0.964110i \(0.585538\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.21497 1.01666
\(11\) −2.53716 −0.764983 −0.382492 0.923959i \(-0.624934\pi\)
−0.382492 + 0.923959i \(0.624934\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 1.40491 0.375479
\(15\) 3.21497 0.830102
\(16\) 1.00000 0.250000
\(17\) 7.57385 1.83693 0.918464 0.395505i \(-0.129430\pi\)
0.918464 + 0.395505i \(0.129430\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.48027 0.569014 0.284507 0.958674i \(-0.408170\pi\)
0.284507 + 0.958674i \(0.408170\pi\)
\(20\) −3.21497 −0.718889
\(21\) 1.40491 0.306577
\(22\) 2.53716 0.540925
\(23\) 7.10176 1.48082 0.740410 0.672156i \(-0.234631\pi\)
0.740410 + 0.672156i \(0.234631\pi\)
\(24\) 1.00000 0.204124
\(25\) 5.33603 1.06721
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −1.40491 −0.265503
\(29\) −1.09619 −0.203558 −0.101779 0.994807i \(-0.532453\pi\)
−0.101779 + 0.994807i \(0.532453\pi\)
\(30\) −3.21497 −0.586970
\(31\) −2.34857 −0.421816 −0.210908 0.977506i \(-0.567642\pi\)
−0.210908 + 0.977506i \(0.567642\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.53716 0.441663
\(34\) −7.57385 −1.29890
\(35\) 4.51675 0.763470
\(36\) 1.00000 0.166667
\(37\) 5.11651 0.841149 0.420574 0.907258i \(-0.361829\pi\)
0.420574 + 0.907258i \(0.361829\pi\)
\(38\) −2.48027 −0.402354
\(39\) −1.00000 −0.160128
\(40\) 3.21497 0.508331
\(41\) −0.317535 −0.0495906 −0.0247953 0.999693i \(-0.507893\pi\)
−0.0247953 + 0.999693i \(0.507893\pi\)
\(42\) −1.40491 −0.216783
\(43\) 9.60063 1.46408 0.732041 0.681261i \(-0.238568\pi\)
0.732041 + 0.681261i \(0.238568\pi\)
\(44\) −2.53716 −0.382492
\(45\) −3.21497 −0.479259
\(46\) −7.10176 −1.04710
\(47\) −5.52965 −0.806583 −0.403292 0.915072i \(-0.632134\pi\)
−0.403292 + 0.915072i \(0.632134\pi\)
\(48\) −1.00000 −0.144338
\(49\) −5.02622 −0.718032
\(50\) −5.33603 −0.754628
\(51\) −7.57385 −1.06055
\(52\) 1.00000 0.138675
\(53\) −4.04692 −0.555887 −0.277944 0.960597i \(-0.589653\pi\)
−0.277944 + 0.960597i \(0.589653\pi\)
\(54\) 1.00000 0.136083
\(55\) 8.15690 1.09988
\(56\) 1.40491 0.187739
\(57\) −2.48027 −0.328520
\(58\) 1.09619 0.143937
\(59\) 0.591321 0.0769834 0.0384917 0.999259i \(-0.487745\pi\)
0.0384917 + 0.999259i \(0.487745\pi\)
\(60\) 3.21497 0.415051
\(61\) −0.0491791 −0.00629673 −0.00314837 0.999995i \(-0.501002\pi\)
−0.00314837 + 0.999995i \(0.501002\pi\)
\(62\) 2.34857 0.298269
\(63\) −1.40491 −0.177002
\(64\) 1.00000 0.125000
\(65\) −3.21497 −0.398768
\(66\) −2.53716 −0.312303
\(67\) −11.1167 −1.35812 −0.679058 0.734084i \(-0.737612\pi\)
−0.679058 + 0.734084i \(0.737612\pi\)
\(68\) 7.57385 0.918464
\(69\) −7.10176 −0.854952
\(70\) −4.51675 −0.539855
\(71\) −16.7385 −1.98649 −0.993246 0.116031i \(-0.962983\pi\)
−0.993246 + 0.116031i \(0.962983\pi\)
\(72\) −1.00000 −0.117851
\(73\) 5.34984 0.626151 0.313075 0.949728i \(-0.398641\pi\)
0.313075 + 0.949728i \(0.398641\pi\)
\(74\) −5.11651 −0.594782
\(75\) −5.33603 −0.616152
\(76\) 2.48027 0.284507
\(77\) 3.56449 0.406211
\(78\) 1.00000 0.113228
\(79\) 16.3495 1.83946 0.919730 0.392552i \(-0.128408\pi\)
0.919730 + 0.392552i \(0.128408\pi\)
\(80\) −3.21497 −0.359445
\(81\) 1.00000 0.111111
\(82\) 0.317535 0.0350658
\(83\) 3.14585 0.345302 0.172651 0.984983i \(-0.444767\pi\)
0.172651 + 0.984983i \(0.444767\pi\)
\(84\) 1.40491 0.153289
\(85\) −24.3497 −2.64109
\(86\) −9.60063 −1.03526
\(87\) 1.09619 0.117524
\(88\) 2.53716 0.270462
\(89\) −4.41812 −0.468319 −0.234160 0.972198i \(-0.575234\pi\)
−0.234160 + 0.972198i \(0.575234\pi\)
\(90\) 3.21497 0.338888
\(91\) −1.40491 −0.147275
\(92\) 7.10176 0.740410
\(93\) 2.34857 0.243536
\(94\) 5.52965 0.570340
\(95\) −7.97401 −0.818116
\(96\) 1.00000 0.102062
\(97\) −9.59214 −0.973934 −0.486967 0.873420i \(-0.661897\pi\)
−0.486967 + 0.873420i \(0.661897\pi\)
\(98\) 5.02622 0.507725
\(99\) −2.53716 −0.254994
\(100\) 5.33603 0.533603
\(101\) −13.2784 −1.32125 −0.660626 0.750715i \(-0.729709\pi\)
−0.660626 + 0.750715i \(0.729709\pi\)
\(102\) 7.57385 0.749923
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −4.51675 −0.440790
\(106\) 4.04692 0.393072
\(107\) −5.70699 −0.551715 −0.275858 0.961198i \(-0.588962\pi\)
−0.275858 + 0.961198i \(0.588962\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 0.714942 0.0684791 0.0342395 0.999414i \(-0.489099\pi\)
0.0342395 + 0.999414i \(0.489099\pi\)
\(110\) −8.15690 −0.777730
\(111\) −5.11651 −0.485637
\(112\) −1.40491 −0.132752
\(113\) 0.0112939 0.00106244 0.000531219 1.00000i \(-0.499831\pi\)
0.000531219 1.00000i \(0.499831\pi\)
\(114\) 2.48027 0.232299
\(115\) −22.8320 −2.12909
\(116\) −1.09619 −0.101779
\(117\) 1.00000 0.0924500
\(118\) −0.591321 −0.0544355
\(119\) −10.6406 −0.975421
\(120\) −3.21497 −0.293485
\(121\) −4.56281 −0.414800
\(122\) 0.0491791 0.00445246
\(123\) 0.317535 0.0286311
\(124\) −2.34857 −0.210908
\(125\) −1.08032 −0.0966269
\(126\) 1.40491 0.125160
\(127\) 9.16672 0.813415 0.406708 0.913558i \(-0.366677\pi\)
0.406708 + 0.913558i \(0.366677\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.60063 −0.845288
\(130\) 3.21497 0.281971
\(131\) 6.04237 0.527925 0.263962 0.964533i \(-0.414971\pi\)
0.263962 + 0.964533i \(0.414971\pi\)
\(132\) 2.53716 0.220832
\(133\) −3.48457 −0.302150
\(134\) 11.1167 0.960333
\(135\) 3.21497 0.276701
\(136\) −7.57385 −0.649452
\(137\) −19.2977 −1.64871 −0.824356 0.566072i \(-0.808462\pi\)
−0.824356 + 0.566072i \(0.808462\pi\)
\(138\) 7.10176 0.604542
\(139\) −4.39044 −0.372392 −0.186196 0.982513i \(-0.559616\pi\)
−0.186196 + 0.982513i \(0.559616\pi\)
\(140\) 4.51675 0.381735
\(141\) 5.52965 0.465681
\(142\) 16.7385 1.40466
\(143\) −2.53716 −0.212168
\(144\) 1.00000 0.0833333
\(145\) 3.52423 0.292672
\(146\) −5.34984 −0.442756
\(147\) 5.02622 0.414556
\(148\) 5.11651 0.420574
\(149\) 5.11066 0.418682 0.209341 0.977843i \(-0.432868\pi\)
0.209341 + 0.977843i \(0.432868\pi\)
\(150\) 5.33603 0.435685
\(151\) 10.3452 0.841879 0.420940 0.907089i \(-0.361700\pi\)
0.420940 + 0.907089i \(0.361700\pi\)
\(152\) −2.48027 −0.201177
\(153\) 7.57385 0.612309
\(154\) −3.56449 −0.287235
\(155\) 7.55060 0.606478
\(156\) −1.00000 −0.0800641
\(157\) 19.2837 1.53900 0.769502 0.638645i \(-0.220505\pi\)
0.769502 + 0.638645i \(0.220505\pi\)
\(158\) −16.3495 −1.30069
\(159\) 4.04692 0.320942
\(160\) 3.21497 0.254166
\(161\) −9.97735 −0.786326
\(162\) −1.00000 −0.0785674
\(163\) 24.1659 1.89282 0.946408 0.322972i \(-0.104682\pi\)
0.946408 + 0.322972i \(0.104682\pi\)
\(164\) −0.317535 −0.0247953
\(165\) −8.15690 −0.635014
\(166\) −3.14585 −0.244165
\(167\) 16.6964 1.29200 0.646001 0.763336i \(-0.276440\pi\)
0.646001 + 0.763336i \(0.276440\pi\)
\(168\) −1.40491 −0.108391
\(169\) 1.00000 0.0769231
\(170\) 24.3497 1.86754
\(171\) 2.48027 0.189671
\(172\) 9.60063 0.732041
\(173\) −15.7177 −1.19499 −0.597496 0.801872i \(-0.703838\pi\)
−0.597496 + 0.801872i \(0.703838\pi\)
\(174\) −1.09619 −0.0831023
\(175\) −7.49665 −0.566694
\(176\) −2.53716 −0.191246
\(177\) −0.591321 −0.0444464
\(178\) 4.41812 0.331152
\(179\) 15.1298 1.13085 0.565426 0.824799i \(-0.308712\pi\)
0.565426 + 0.824799i \(0.308712\pi\)
\(180\) −3.21497 −0.239630
\(181\) 7.66911 0.570040 0.285020 0.958522i \(-0.408000\pi\)
0.285020 + 0.958522i \(0.408000\pi\)
\(182\) 1.40491 0.104139
\(183\) 0.0491791 0.00363542
\(184\) −7.10176 −0.523549
\(185\) −16.4494 −1.20939
\(186\) −2.34857 −0.172206
\(187\) −19.2161 −1.40522
\(188\) −5.52965 −0.403292
\(189\) 1.40491 0.102192
\(190\) 7.97401 0.578495
\(191\) −16.0169 −1.15894 −0.579469 0.814994i \(-0.696740\pi\)
−0.579469 + 0.814994i \(0.696740\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.03418 0.434350 0.217175 0.976133i \(-0.430316\pi\)
0.217175 + 0.976133i \(0.430316\pi\)
\(194\) 9.59214 0.688676
\(195\) 3.21497 0.230229
\(196\) −5.02622 −0.359016
\(197\) −14.6922 −1.04677 −0.523387 0.852095i \(-0.675332\pi\)
−0.523387 + 0.852095i \(0.675332\pi\)
\(198\) 2.53716 0.180308
\(199\) 9.27945 0.657803 0.328901 0.944364i \(-0.393322\pi\)
0.328901 + 0.944364i \(0.393322\pi\)
\(200\) −5.33603 −0.377314
\(201\) 11.1167 0.784109
\(202\) 13.2784 0.934266
\(203\) 1.54006 0.108091
\(204\) −7.57385 −0.530275
\(205\) 1.02086 0.0713002
\(206\) 1.00000 0.0696733
\(207\) 7.10176 0.493607
\(208\) 1.00000 0.0693375
\(209\) −6.29286 −0.435286
\(210\) 4.51675 0.311685
\(211\) −23.6370 −1.62724 −0.813618 0.581400i \(-0.802505\pi\)
−0.813618 + 0.581400i \(0.802505\pi\)
\(212\) −4.04692 −0.277944
\(213\) 16.7385 1.14690
\(214\) 5.70699 0.390122
\(215\) −30.8657 −2.10503
\(216\) 1.00000 0.0680414
\(217\) 3.29954 0.223987
\(218\) −0.714942 −0.0484220
\(219\) −5.34984 −0.361508
\(220\) 8.15690 0.549938
\(221\) 7.57385 0.509472
\(222\) 5.11651 0.343398
\(223\) 21.0616 1.41039 0.705195 0.709013i \(-0.250859\pi\)
0.705195 + 0.709013i \(0.250859\pi\)
\(224\) 1.40491 0.0938697
\(225\) 5.33603 0.355735
\(226\) −0.0112939 −0.000751258 0
\(227\) −11.7708 −0.781254 −0.390627 0.920549i \(-0.627742\pi\)
−0.390627 + 0.920549i \(0.627742\pi\)
\(228\) −2.48027 −0.164260
\(229\) 12.9373 0.854919 0.427460 0.904034i \(-0.359409\pi\)
0.427460 + 0.904034i \(0.359409\pi\)
\(230\) 22.8320 1.50549
\(231\) −3.56449 −0.234526
\(232\) 1.09619 0.0719687
\(233\) −14.2591 −0.934141 −0.467071 0.884220i \(-0.654691\pi\)
−0.467071 + 0.884220i \(0.654691\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 17.7777 1.15969
\(236\) 0.591321 0.0384917
\(237\) −16.3495 −1.06201
\(238\) 10.6406 0.689727
\(239\) 7.67833 0.496670 0.248335 0.968674i \(-0.420117\pi\)
0.248335 + 0.968674i \(0.420117\pi\)
\(240\) 3.21497 0.207525
\(241\) 17.8173 1.14771 0.573857 0.818955i \(-0.305446\pi\)
0.573857 + 0.818955i \(0.305446\pi\)
\(242\) 4.56281 0.293308
\(243\) −1.00000 −0.0641500
\(244\) −0.0491791 −0.00314837
\(245\) 16.1591 1.03237
\(246\) −0.317535 −0.0202453
\(247\) 2.48027 0.157816
\(248\) 2.34857 0.149135
\(249\) −3.14585 −0.199360
\(250\) 1.08032 0.0683256
\(251\) 11.4843 0.724883 0.362442 0.932006i \(-0.381943\pi\)
0.362442 + 0.932006i \(0.381943\pi\)
\(252\) −1.40491 −0.0885012
\(253\) −18.0183 −1.13280
\(254\) −9.16672 −0.575171
\(255\) 24.3497 1.52484
\(256\) 1.00000 0.0625000
\(257\) −0.559098 −0.0348756 −0.0174378 0.999848i \(-0.505551\pi\)
−0.0174378 + 0.999848i \(0.505551\pi\)
\(258\) 9.60063 0.597709
\(259\) −7.18825 −0.446656
\(260\) −3.21497 −0.199384
\(261\) −1.09619 −0.0678527
\(262\) −6.04237 −0.373299
\(263\) 25.6348 1.58071 0.790354 0.612651i \(-0.209897\pi\)
0.790354 + 0.612651i \(0.209897\pi\)
\(264\) −2.53716 −0.156152
\(265\) 13.0107 0.799243
\(266\) 3.48457 0.213653
\(267\) 4.41812 0.270384
\(268\) −11.1167 −0.679058
\(269\) −8.75155 −0.533591 −0.266796 0.963753i \(-0.585965\pi\)
−0.266796 + 0.963753i \(0.585965\pi\)
\(270\) −3.21497 −0.195657
\(271\) 20.9500 1.27262 0.636311 0.771432i \(-0.280459\pi\)
0.636311 + 0.771432i \(0.280459\pi\)
\(272\) 7.57385 0.459232
\(273\) 1.40491 0.0850292
\(274\) 19.2977 1.16581
\(275\) −13.5384 −0.816395
\(276\) −7.10176 −0.427476
\(277\) 27.0963 1.62806 0.814030 0.580823i \(-0.197269\pi\)
0.814030 + 0.580823i \(0.197269\pi\)
\(278\) 4.39044 0.263321
\(279\) −2.34857 −0.140605
\(280\) −4.51675 −0.269927
\(281\) 22.0661 1.31635 0.658175 0.752865i \(-0.271329\pi\)
0.658175 + 0.752865i \(0.271329\pi\)
\(282\) −5.52965 −0.329286
\(283\) −20.6144 −1.22540 −0.612701 0.790315i \(-0.709917\pi\)
−0.612701 + 0.790315i \(0.709917\pi\)
\(284\) −16.7385 −0.993246
\(285\) 7.97401 0.472339
\(286\) 2.53716 0.150026
\(287\) 0.446108 0.0263329
\(288\) −1.00000 −0.0589256
\(289\) 40.3631 2.37430
\(290\) −3.52423 −0.206950
\(291\) 9.59214 0.562301
\(292\) 5.34984 0.313075
\(293\) −15.5930 −0.910950 −0.455475 0.890249i \(-0.650531\pi\)
−0.455475 + 0.890249i \(0.650531\pi\)
\(294\) −5.02622 −0.293135
\(295\) −1.90108 −0.110685
\(296\) −5.11651 −0.297391
\(297\) 2.53716 0.147221
\(298\) −5.11066 −0.296053
\(299\) 7.10176 0.410706
\(300\) −5.33603 −0.308076
\(301\) −13.4880 −0.777438
\(302\) −10.3452 −0.595298
\(303\) 13.2784 0.762825
\(304\) 2.48027 0.142254
\(305\) 0.158109 0.00905331
\(306\) −7.57385 −0.432968
\(307\) −13.8308 −0.789366 −0.394683 0.918817i \(-0.629146\pi\)
−0.394683 + 0.918817i \(0.629146\pi\)
\(308\) 3.56449 0.203106
\(309\) 1.00000 0.0568880
\(310\) −7.55060 −0.428845
\(311\) −21.7094 −1.23103 −0.615515 0.788126i \(-0.711052\pi\)
−0.615515 + 0.788126i \(0.711052\pi\)
\(312\) 1.00000 0.0566139
\(313\) −7.64960 −0.432381 −0.216190 0.976351i \(-0.569363\pi\)
−0.216190 + 0.976351i \(0.569363\pi\)
\(314\) −19.2837 −1.08824
\(315\) 4.51675 0.254490
\(316\) 16.3495 0.919730
\(317\) 7.63340 0.428735 0.214367 0.976753i \(-0.431231\pi\)
0.214367 + 0.976753i \(0.431231\pi\)
\(318\) −4.04692 −0.226940
\(319\) 2.78122 0.155719
\(320\) −3.21497 −0.179722
\(321\) 5.70699 0.318533
\(322\) 9.97735 0.556016
\(323\) 18.7852 1.04524
\(324\) 1.00000 0.0555556
\(325\) 5.33603 0.295990
\(326\) −24.1659 −1.33842
\(327\) −0.714942 −0.0395364
\(328\) 0.317535 0.0175329
\(329\) 7.76868 0.428301
\(330\) 8.15690 0.449023
\(331\) −6.12990 −0.336930 −0.168465 0.985708i \(-0.553881\pi\)
−0.168465 + 0.985708i \(0.553881\pi\)
\(332\) 3.14585 0.172651
\(333\) 5.11651 0.280383
\(334\) −16.6964 −0.913584
\(335\) 35.7397 1.95267
\(336\) 1.40491 0.0766443
\(337\) −20.2018 −1.10046 −0.550230 0.835013i \(-0.685460\pi\)
−0.550230 + 0.835013i \(0.685460\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −0.0112939 −0.000613399 0
\(340\) −24.3497 −1.32055
\(341\) 5.95872 0.322683
\(342\) −2.48027 −0.134118
\(343\) 16.8958 0.912287
\(344\) −9.60063 −0.517631
\(345\) 22.8320 1.22923
\(346\) 15.7177 0.844987
\(347\) −29.8190 −1.60077 −0.800385 0.599486i \(-0.795372\pi\)
−0.800385 + 0.599486i \(0.795372\pi\)
\(348\) 1.09619 0.0587622
\(349\) −15.6189 −0.836061 −0.418031 0.908433i \(-0.637279\pi\)
−0.418031 + 0.908433i \(0.637279\pi\)
\(350\) 7.49665 0.400713
\(351\) −1.00000 −0.0533761
\(352\) 2.53716 0.135231
\(353\) −26.9240 −1.43302 −0.716510 0.697577i \(-0.754262\pi\)
−0.716510 + 0.697577i \(0.754262\pi\)
\(354\) 0.591321 0.0314283
\(355\) 53.8137 2.85613
\(356\) −4.41812 −0.234160
\(357\) 10.6406 0.563160
\(358\) −15.1298 −0.799633
\(359\) 6.70826 0.354048 0.177024 0.984206i \(-0.443353\pi\)
0.177024 + 0.984206i \(0.443353\pi\)
\(360\) 3.21497 0.169444
\(361\) −12.8482 −0.676223
\(362\) −7.66911 −0.403079
\(363\) 4.56281 0.239485
\(364\) −1.40491 −0.0736374
\(365\) −17.1996 −0.900266
\(366\) −0.0491791 −0.00257063
\(367\) 23.3923 1.22107 0.610535 0.791989i \(-0.290955\pi\)
0.610535 + 0.791989i \(0.290955\pi\)
\(368\) 7.10176 0.370205
\(369\) −0.317535 −0.0165302
\(370\) 16.4494 0.855164
\(371\) 5.68557 0.295180
\(372\) 2.34857 0.121768
\(373\) −33.8963 −1.75508 −0.877541 0.479501i \(-0.840818\pi\)
−0.877541 + 0.479501i \(0.840818\pi\)
\(374\) 19.2161 0.993640
\(375\) 1.08032 0.0557876
\(376\) 5.52965 0.285170
\(377\) −1.09619 −0.0564569
\(378\) −1.40491 −0.0722609
\(379\) −23.2303 −1.19326 −0.596631 0.802516i \(-0.703494\pi\)
−0.596631 + 0.802516i \(0.703494\pi\)
\(380\) −7.97401 −0.409058
\(381\) −9.16672 −0.469625
\(382\) 16.0169 0.819493
\(383\) 0.229743 0.0117393 0.00586965 0.999983i \(-0.498132\pi\)
0.00586965 + 0.999983i \(0.498132\pi\)
\(384\) 1.00000 0.0510310
\(385\) −11.4597 −0.584042
\(386\) −6.03418 −0.307132
\(387\) 9.60063 0.488027
\(388\) −9.59214 −0.486967
\(389\) 31.6902 1.60676 0.803379 0.595468i \(-0.203033\pi\)
0.803379 + 0.595468i \(0.203033\pi\)
\(390\) −3.21497 −0.162796
\(391\) 53.7877 2.72016
\(392\) 5.02622 0.253863
\(393\) −6.04237 −0.304797
\(394\) 14.6922 0.740182
\(395\) −52.5631 −2.64473
\(396\) −2.53716 −0.127497
\(397\) −3.56877 −0.179111 −0.0895556 0.995982i \(-0.528545\pi\)
−0.0895556 + 0.995982i \(0.528545\pi\)
\(398\) −9.27945 −0.465137
\(399\) 3.48457 0.174447
\(400\) 5.33603 0.266801
\(401\) 34.3052 1.71312 0.856560 0.516047i \(-0.172597\pi\)
0.856560 + 0.516047i \(0.172597\pi\)
\(402\) −11.1167 −0.554449
\(403\) −2.34857 −0.116991
\(404\) −13.2784 −0.660626
\(405\) −3.21497 −0.159753
\(406\) −1.54006 −0.0764318
\(407\) −12.9814 −0.643465
\(408\) 7.57385 0.374961
\(409\) −21.3744 −1.05689 −0.528447 0.848966i \(-0.677225\pi\)
−0.528447 + 0.848966i \(0.677225\pi\)
\(410\) −1.02086 −0.0504169
\(411\) 19.2977 0.951884
\(412\) −1.00000 −0.0492665
\(413\) −0.830754 −0.0408787
\(414\) −7.10176 −0.349033
\(415\) −10.1138 −0.496467
\(416\) −1.00000 −0.0490290
\(417\) 4.39044 0.215001
\(418\) 6.29286 0.307794
\(419\) 7.08545 0.346147 0.173073 0.984909i \(-0.444630\pi\)
0.173073 + 0.984909i \(0.444630\pi\)
\(420\) −4.51675 −0.220395
\(421\) 7.09461 0.345770 0.172885 0.984942i \(-0.444691\pi\)
0.172885 + 0.984942i \(0.444691\pi\)
\(422\) 23.6370 1.15063
\(423\) −5.52965 −0.268861
\(424\) 4.04692 0.196536
\(425\) 40.4143 1.96038
\(426\) −16.7385 −0.810982
\(427\) 0.0690923 0.00334361
\(428\) −5.70699 −0.275858
\(429\) 2.53716 0.122495
\(430\) 30.8657 1.48848
\(431\) 22.5540 1.08639 0.543194 0.839607i \(-0.317215\pi\)
0.543194 + 0.839607i \(0.317215\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 1.25553 0.0603372 0.0301686 0.999545i \(-0.490396\pi\)
0.0301686 + 0.999545i \(0.490396\pi\)
\(434\) −3.29954 −0.158383
\(435\) −3.52423 −0.168974
\(436\) 0.714942 0.0342395
\(437\) 17.6143 0.842607
\(438\) 5.34984 0.255625
\(439\) −8.79229 −0.419633 −0.209817 0.977741i \(-0.567287\pi\)
−0.209817 + 0.977741i \(0.567287\pi\)
\(440\) −8.15690 −0.388865
\(441\) −5.02622 −0.239344
\(442\) −7.57385 −0.360251
\(443\) 11.5561 0.549045 0.274522 0.961581i \(-0.411480\pi\)
0.274522 + 0.961581i \(0.411480\pi\)
\(444\) −5.11651 −0.242819
\(445\) 14.2041 0.673339
\(446\) −21.0616 −0.997297
\(447\) −5.11066 −0.241726
\(448\) −1.40491 −0.0663759
\(449\) 26.2196 1.23738 0.618689 0.785636i \(-0.287664\pi\)
0.618689 + 0.785636i \(0.287664\pi\)
\(450\) −5.33603 −0.251543
\(451\) 0.805637 0.0379360
\(452\) 0.0112939 0.000531219 0
\(453\) −10.3452 −0.486059
\(454\) 11.7708 0.552430
\(455\) 4.51675 0.211749
\(456\) 2.48027 0.116150
\(457\) −26.1019 −1.22100 −0.610499 0.792017i \(-0.709031\pi\)
−0.610499 + 0.792017i \(0.709031\pi\)
\(458\) −12.9373 −0.604519
\(459\) −7.57385 −0.353517
\(460\) −22.8320 −1.06455
\(461\) −29.0448 −1.35275 −0.676376 0.736556i \(-0.736451\pi\)
−0.676376 + 0.736556i \(0.736451\pi\)
\(462\) 3.56449 0.165835
\(463\) 13.2014 0.613522 0.306761 0.951787i \(-0.400755\pi\)
0.306761 + 0.951787i \(0.400755\pi\)
\(464\) −1.09619 −0.0508896
\(465\) −7.55060 −0.350151
\(466\) 14.2591 0.660538
\(467\) −8.32279 −0.385133 −0.192567 0.981284i \(-0.561681\pi\)
−0.192567 + 0.981284i \(0.561681\pi\)
\(468\) 1.00000 0.0462250
\(469\) 15.6179 0.721169
\(470\) −17.7777 −0.820023
\(471\) −19.2837 −0.888544
\(472\) −0.591321 −0.0272177
\(473\) −24.3584 −1.12000
\(474\) 16.3495 0.750956
\(475\) 13.2348 0.607255
\(476\) −10.6406 −0.487711
\(477\) −4.04692 −0.185296
\(478\) −7.67833 −0.351198
\(479\) −31.2476 −1.42774 −0.713869 0.700279i \(-0.753059\pi\)
−0.713869 + 0.700279i \(0.753059\pi\)
\(480\) −3.21497 −0.146743
\(481\) 5.11651 0.233293
\(482\) −17.8173 −0.811557
\(483\) 9.97735 0.453985
\(484\) −4.56281 −0.207400
\(485\) 30.8384 1.40030
\(486\) 1.00000 0.0453609
\(487\) 33.0131 1.49596 0.747982 0.663718i \(-0.231023\pi\)
0.747982 + 0.663718i \(0.231023\pi\)
\(488\) 0.0491791 0.00222623
\(489\) −24.1659 −1.09282
\(490\) −16.1591 −0.729996
\(491\) 22.0882 0.996828 0.498414 0.866939i \(-0.333916\pi\)
0.498414 + 0.866939i \(0.333916\pi\)
\(492\) 0.317535 0.0143156
\(493\) −8.30241 −0.373922
\(494\) −2.48027 −0.111593
\(495\) 8.15690 0.366625
\(496\) −2.34857 −0.105454
\(497\) 23.5161 1.05484
\(498\) 3.14585 0.140969
\(499\) −34.2370 −1.53266 −0.766330 0.642448i \(-0.777919\pi\)
−0.766330 + 0.642448i \(0.777919\pi\)
\(500\) −1.08032 −0.0483135
\(501\) −16.6964 −0.745938
\(502\) −11.4843 −0.512570
\(503\) 34.8724 1.55488 0.777442 0.628955i \(-0.216517\pi\)
0.777442 + 0.628955i \(0.216517\pi\)
\(504\) 1.40491 0.0625798
\(505\) 42.6897 1.89967
\(506\) 18.0183 0.801012
\(507\) −1.00000 −0.0444116
\(508\) 9.16672 0.406708
\(509\) 33.8685 1.50120 0.750598 0.660759i \(-0.229766\pi\)
0.750598 + 0.660759i \(0.229766\pi\)
\(510\) −24.3497 −1.07822
\(511\) −7.51605 −0.332490
\(512\) −1.00000 −0.0441942
\(513\) −2.48027 −0.109507
\(514\) 0.559098 0.0246607
\(515\) 3.21497 0.141668
\(516\) −9.60063 −0.422644
\(517\) 14.0296 0.617023
\(518\) 7.18825 0.315833
\(519\) 15.7177 0.689929
\(520\) 3.21497 0.140986
\(521\) 10.6760 0.467726 0.233863 0.972270i \(-0.424863\pi\)
0.233863 + 0.972270i \(0.424863\pi\)
\(522\) 1.09619 0.0479791
\(523\) 14.0032 0.612315 0.306157 0.951981i \(-0.400957\pi\)
0.306157 + 0.951981i \(0.400957\pi\)
\(524\) 6.04237 0.263962
\(525\) 7.49665 0.327181
\(526\) −25.6348 −1.11773
\(527\) −17.7877 −0.774846
\(528\) 2.53716 0.110416
\(529\) 27.4350 1.19283
\(530\) −13.0107 −0.565150
\(531\) 0.591321 0.0256611
\(532\) −3.48457 −0.151075
\(533\) −0.317535 −0.0137540
\(534\) −4.41812 −0.191191
\(535\) 18.3478 0.793244
\(536\) 11.1167 0.480167
\(537\) −15.1298 −0.652898
\(538\) 8.75155 0.377306
\(539\) 12.7523 0.549282
\(540\) 3.21497 0.138350
\(541\) −13.8044 −0.593496 −0.296748 0.954956i \(-0.595902\pi\)
−0.296748 + 0.954956i \(0.595902\pi\)
\(542\) −20.9500 −0.899880
\(543\) −7.66911 −0.329113
\(544\) −7.57385 −0.324726
\(545\) −2.29852 −0.0984577
\(546\) −1.40491 −0.0601247
\(547\) −5.72499 −0.244783 −0.122391 0.992482i \(-0.539056\pi\)
−0.122391 + 0.992482i \(0.539056\pi\)
\(548\) −19.2977 −0.824356
\(549\) −0.0491791 −0.00209891
\(550\) 13.5384 0.577278
\(551\) −2.71886 −0.115828
\(552\) 7.10176 0.302271
\(553\) −22.9696 −0.976766
\(554\) −27.0963 −1.15121
\(555\) 16.4494 0.698239
\(556\) −4.39044 −0.186196
\(557\) −13.2383 −0.560926 −0.280463 0.959865i \(-0.590488\pi\)
−0.280463 + 0.959865i \(0.590488\pi\)
\(558\) 2.34857 0.0994231
\(559\) 9.60063 0.406063
\(560\) 4.51675 0.190868
\(561\) 19.2161 0.811304
\(562\) −22.0661 −0.930800
\(563\) −16.4880 −0.694887 −0.347444 0.937701i \(-0.612950\pi\)
−0.347444 + 0.937701i \(0.612950\pi\)
\(564\) 5.52965 0.232840
\(565\) −0.0363095 −0.00152755
\(566\) 20.6144 0.866490
\(567\) −1.40491 −0.0590008
\(568\) 16.7385 0.702331
\(569\) 6.88126 0.288478 0.144239 0.989543i \(-0.453927\pi\)
0.144239 + 0.989543i \(0.453927\pi\)
\(570\) −7.97401 −0.333994
\(571\) −22.0933 −0.924576 −0.462288 0.886730i \(-0.652971\pi\)
−0.462288 + 0.886730i \(0.652971\pi\)
\(572\) −2.53716 −0.106084
\(573\) 16.0169 0.669114
\(574\) −0.446108 −0.0186202
\(575\) 37.8952 1.58034
\(576\) 1.00000 0.0416667
\(577\) 23.0450 0.959376 0.479688 0.877439i \(-0.340750\pi\)
0.479688 + 0.877439i \(0.340750\pi\)
\(578\) −40.3631 −1.67889
\(579\) −6.03418 −0.250772
\(580\) 3.52423 0.146336
\(581\) −4.41964 −0.183358
\(582\) −9.59214 −0.397607
\(583\) 10.2677 0.425245
\(584\) −5.34984 −0.221378
\(585\) −3.21497 −0.132923
\(586\) 15.5930 0.644139
\(587\) −30.2929 −1.25032 −0.625162 0.780495i \(-0.714967\pi\)
−0.625162 + 0.780495i \(0.714967\pi\)
\(588\) 5.02622 0.207278
\(589\) −5.82511 −0.240020
\(590\) 1.90108 0.0782661
\(591\) 14.6922 0.604356
\(592\) 5.11651 0.210287
\(593\) 48.2902 1.98304 0.991521 0.129948i \(-0.0414811\pi\)
0.991521 + 0.129948i \(0.0414811\pi\)
\(594\) −2.53716 −0.104101
\(595\) 34.2092 1.40244
\(596\) 5.11066 0.209341
\(597\) −9.27945 −0.379783
\(598\) −7.10176 −0.290413
\(599\) 26.3791 1.07782 0.538911 0.842363i \(-0.318836\pi\)
0.538911 + 0.842363i \(0.318836\pi\)
\(600\) 5.33603 0.217842
\(601\) −17.8024 −0.726174 −0.363087 0.931755i \(-0.618277\pi\)
−0.363087 + 0.931755i \(0.618277\pi\)
\(602\) 13.4880 0.549732
\(603\) −11.1167 −0.452705
\(604\) 10.3452 0.420940
\(605\) 14.6693 0.596391
\(606\) −13.2784 −0.539399
\(607\) −13.3337 −0.541200 −0.270600 0.962692i \(-0.587222\pi\)
−0.270600 + 0.962692i \(0.587222\pi\)
\(608\) −2.48027 −0.100588
\(609\) −1.54006 −0.0624063
\(610\) −0.158109 −0.00640165
\(611\) −5.52965 −0.223706
\(612\) 7.57385 0.306155
\(613\) 11.4072 0.460733 0.230367 0.973104i \(-0.426007\pi\)
0.230367 + 0.973104i \(0.426007\pi\)
\(614\) 13.8308 0.558166
\(615\) −1.02086 −0.0411652
\(616\) −3.56449 −0.143617
\(617\) 18.7919 0.756534 0.378267 0.925697i \(-0.376520\pi\)
0.378267 + 0.925697i \(0.376520\pi\)
\(618\) −1.00000 −0.0402259
\(619\) −5.95938 −0.239528 −0.119764 0.992802i \(-0.538214\pi\)
−0.119764 + 0.992802i \(0.538214\pi\)
\(620\) 7.55060 0.303239
\(621\) −7.10176 −0.284984
\(622\) 21.7094 0.870469
\(623\) 6.20706 0.248681
\(624\) −1.00000 −0.0400320
\(625\) −23.2069 −0.928278
\(626\) 7.64960 0.305739
\(627\) 6.29286 0.251313
\(628\) 19.2837 0.769502
\(629\) 38.7516 1.54513
\(630\) −4.51675 −0.179952
\(631\) 47.0677 1.87374 0.936868 0.349683i \(-0.113711\pi\)
0.936868 + 0.349683i \(0.113711\pi\)
\(632\) −16.3495 −0.650347
\(633\) 23.6370 0.939485
\(634\) −7.63340 −0.303161
\(635\) −29.4707 −1.16951
\(636\) 4.04692 0.160471
\(637\) −5.02622 −0.199146
\(638\) −2.78122 −0.110110
\(639\) −16.7385 −0.662164
\(640\) 3.21497 0.127083
\(641\) 41.9763 1.65796 0.828981 0.559276i \(-0.188921\pi\)
0.828981 + 0.559276i \(0.188921\pi\)
\(642\) −5.70699 −0.225237
\(643\) 28.9315 1.14095 0.570474 0.821316i \(-0.306759\pi\)
0.570474 + 0.821316i \(0.306759\pi\)
\(644\) −9.97735 −0.393163
\(645\) 30.8657 1.21534
\(646\) −18.7852 −0.739095
\(647\) 6.43859 0.253127 0.126563 0.991959i \(-0.459605\pi\)
0.126563 + 0.991959i \(0.459605\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −1.50028 −0.0588910
\(650\) −5.33603 −0.209296
\(651\) −3.29954 −0.129319
\(652\) 24.1659 0.946408
\(653\) −2.80854 −0.109907 −0.0549534 0.998489i \(-0.517501\pi\)
−0.0549534 + 0.998489i \(0.517501\pi\)
\(654\) 0.714942 0.0279565
\(655\) −19.4261 −0.759039
\(656\) −0.317535 −0.0123976
\(657\) 5.34984 0.208717
\(658\) −7.76868 −0.302855
\(659\) −35.7289 −1.39180 −0.695901 0.718138i \(-0.744995\pi\)
−0.695901 + 0.718138i \(0.744995\pi\)
\(660\) −8.15690 −0.317507
\(661\) 10.0657 0.391510 0.195755 0.980653i \(-0.437284\pi\)
0.195755 + 0.980653i \(0.437284\pi\)
\(662\) 6.12990 0.238245
\(663\) −7.57385 −0.294144
\(664\) −3.14585 −0.122083
\(665\) 11.2028 0.434425
\(666\) −5.11651 −0.198261
\(667\) −7.78491 −0.301433
\(668\) 16.6964 0.646001
\(669\) −21.0616 −0.814289
\(670\) −35.7397 −1.38075
\(671\) 0.124775 0.00481690
\(672\) −1.40491 −0.0541957
\(673\) −10.9942 −0.423795 −0.211898 0.977292i \(-0.567964\pi\)
−0.211898 + 0.977292i \(0.567964\pi\)
\(674\) 20.2018 0.778143
\(675\) −5.33603 −0.205384
\(676\) 1.00000 0.0384615
\(677\) 21.7987 0.837790 0.418895 0.908035i \(-0.362417\pi\)
0.418895 + 0.908035i \(0.362417\pi\)
\(678\) 0.0112939 0.000433739 0
\(679\) 13.4761 0.517166
\(680\) 24.3497 0.933768
\(681\) 11.7708 0.451057
\(682\) −5.95872 −0.228171
\(683\) −12.0227 −0.460037 −0.230019 0.973186i \(-0.573879\pi\)
−0.230019 + 0.973186i \(0.573879\pi\)
\(684\) 2.48027 0.0948357
\(685\) 62.0414 2.37048
\(686\) −16.8958 −0.645084
\(687\) −12.9373 −0.493588
\(688\) 9.60063 0.366021
\(689\) −4.04692 −0.154175
\(690\) −22.8320 −0.869197
\(691\) 41.0374 1.56114 0.780568 0.625071i \(-0.214930\pi\)
0.780568 + 0.625071i \(0.214930\pi\)
\(692\) −15.7177 −0.597496
\(693\) 3.56449 0.135404
\(694\) 29.8190 1.13192
\(695\) 14.1151 0.535417
\(696\) −1.09619 −0.0415512
\(697\) −2.40496 −0.0910943
\(698\) 15.6189 0.591184
\(699\) 14.2591 0.539327
\(700\) −7.49665 −0.283347
\(701\) −48.9662 −1.84943 −0.924715 0.380661i \(-0.875696\pi\)
−0.924715 + 0.380661i \(0.875696\pi\)
\(702\) 1.00000 0.0377426
\(703\) 12.6903 0.478625
\(704\) −2.53716 −0.0956229
\(705\) −17.7777 −0.669546
\(706\) 26.9240 1.01330
\(707\) 18.6550 0.701594
\(708\) −0.591321 −0.0222232
\(709\) −19.0876 −0.716850 −0.358425 0.933559i \(-0.616686\pi\)
−0.358425 + 0.933559i \(0.616686\pi\)
\(710\) −53.8137 −2.01959
\(711\) 16.3495 0.613153
\(712\) 4.41812 0.165576
\(713\) −16.6790 −0.624634
\(714\) −10.6406 −0.398214
\(715\) 8.15690 0.305051
\(716\) 15.1298 0.565426
\(717\) −7.67833 −0.286752
\(718\) −6.70826 −0.250350
\(719\) 13.0914 0.488227 0.244114 0.969747i \(-0.421503\pi\)
0.244114 + 0.969747i \(0.421503\pi\)
\(720\) −3.21497 −0.119815
\(721\) 1.40491 0.0523217
\(722\) 12.8482 0.478162
\(723\) −17.8173 −0.662633
\(724\) 7.66911 0.285020
\(725\) −5.84933 −0.217239
\(726\) −4.56281 −0.169342
\(727\) −36.6764 −1.36025 −0.680126 0.733095i \(-0.738075\pi\)
−0.680126 + 0.733095i \(0.738075\pi\)
\(728\) 1.40491 0.0520695
\(729\) 1.00000 0.0370370
\(730\) 17.1996 0.636584
\(731\) 72.7137 2.68941
\(732\) 0.0491791 0.00181771
\(733\) −19.8895 −0.734635 −0.367317 0.930096i \(-0.619724\pi\)
−0.367317 + 0.930096i \(0.619724\pi\)
\(734\) −23.3923 −0.863426
\(735\) −16.1591 −0.596039
\(736\) −7.10176 −0.261774
\(737\) 28.2048 1.03894
\(738\) 0.317535 0.0116886
\(739\) 0.682756 0.0251156 0.0125578 0.999921i \(-0.496003\pi\)
0.0125578 + 0.999921i \(0.496003\pi\)
\(740\) −16.4494 −0.604693
\(741\) −2.48027 −0.0911152
\(742\) −5.68557 −0.208724
\(743\) 7.08974 0.260097 0.130049 0.991508i \(-0.458487\pi\)
0.130049 + 0.991508i \(0.458487\pi\)
\(744\) −2.34857 −0.0861029
\(745\) −16.4306 −0.601971
\(746\) 33.8963 1.24103
\(747\) 3.14585 0.115101
\(748\) −19.2161 −0.702610
\(749\) 8.01782 0.292965
\(750\) −1.08032 −0.0394478
\(751\) 19.9492 0.727956 0.363978 0.931408i \(-0.381418\pi\)
0.363978 + 0.931408i \(0.381418\pi\)
\(752\) −5.52965 −0.201646
\(753\) −11.4843 −0.418512
\(754\) 1.09619 0.0399211
\(755\) −33.2595 −1.21044
\(756\) 1.40491 0.0510962
\(757\) −36.2103 −1.31609 −0.658043 0.752980i \(-0.728615\pi\)
−0.658043 + 0.752980i \(0.728615\pi\)
\(758\) 23.2303 0.843763
\(759\) 18.0183 0.654024
\(760\) 7.97401 0.289248
\(761\) −39.1506 −1.41921 −0.709603 0.704602i \(-0.751126\pi\)
−0.709603 + 0.704602i \(0.751126\pi\)
\(762\) 9.16672 0.332075
\(763\) −1.00443 −0.0363629
\(764\) −16.0169 −0.579469
\(765\) −24.3497 −0.880365
\(766\) −0.229743 −0.00830094
\(767\) 0.591321 0.0213514
\(768\) −1.00000 −0.0360844
\(769\) −21.2933 −0.767855 −0.383928 0.923363i \(-0.625429\pi\)
−0.383928 + 0.923363i \(0.625429\pi\)
\(770\) 11.4597 0.412980
\(771\) 0.559098 0.0201354
\(772\) 6.03418 0.217175
\(773\) 28.5594 1.02721 0.513605 0.858027i \(-0.328310\pi\)
0.513605 + 0.858027i \(0.328310\pi\)
\(774\) −9.60063 −0.345087
\(775\) −12.5321 −0.450165
\(776\) 9.59214 0.344338
\(777\) 7.18825 0.257877
\(778\) −31.6902 −1.13615
\(779\) −0.787573 −0.0282177
\(780\) 3.21497 0.115114
\(781\) 42.4682 1.51963
\(782\) −53.7877 −1.92344
\(783\) 1.09619 0.0391748
\(784\) −5.02622 −0.179508
\(785\) −61.9964 −2.21275
\(786\) 6.04237 0.215524
\(787\) 30.6319 1.09191 0.545955 0.837814i \(-0.316167\pi\)
0.545955 + 0.837814i \(0.316167\pi\)
\(788\) −14.6922 −0.523387
\(789\) −25.6348 −0.912622
\(790\) 52.5631 1.87011
\(791\) −0.0158669 −0.000564162 0
\(792\) 2.53716 0.0901542
\(793\) −0.0491791 −0.00174640
\(794\) 3.56877 0.126651
\(795\) −13.0107 −0.461443
\(796\) 9.27945 0.328901
\(797\) −33.3366 −1.18084 −0.590421 0.807095i \(-0.701038\pi\)
−0.590421 + 0.807095i \(0.701038\pi\)
\(798\) −3.48457 −0.123352
\(799\) −41.8808 −1.48163
\(800\) −5.33603 −0.188657
\(801\) −4.41812 −0.156106
\(802\) −34.3052 −1.21136
\(803\) −13.5734 −0.478995
\(804\) 11.1167 0.392054
\(805\) 32.0769 1.13056
\(806\) 2.34857 0.0827250
\(807\) 8.75155 0.308069
\(808\) 13.2784 0.467133
\(809\) 37.0003 1.30086 0.650431 0.759566i \(-0.274588\pi\)
0.650431 + 0.759566i \(0.274588\pi\)
\(810\) 3.21497 0.112963
\(811\) 52.9625 1.85977 0.929883 0.367856i \(-0.119908\pi\)
0.929883 + 0.367856i \(0.119908\pi\)
\(812\) 1.54006 0.0540454
\(813\) −20.9500 −0.734749
\(814\) 12.9814 0.454998
\(815\) −77.6925 −2.72145
\(816\) −7.57385 −0.265138
\(817\) 23.8122 0.833083
\(818\) 21.3744 0.747337
\(819\) −1.40491 −0.0490916
\(820\) 1.02086 0.0356501
\(821\) −4.57433 −0.159645 −0.0798226 0.996809i \(-0.525435\pi\)
−0.0798226 + 0.996809i \(0.525435\pi\)
\(822\) −19.2977 −0.673084
\(823\) 33.7222 1.17548 0.587741 0.809049i \(-0.300017\pi\)
0.587741 + 0.809049i \(0.300017\pi\)
\(824\) 1.00000 0.0348367
\(825\) 13.5384 0.471346
\(826\) 0.830754 0.0289056
\(827\) 16.9998 0.591142 0.295571 0.955321i \(-0.404490\pi\)
0.295571 + 0.955321i \(0.404490\pi\)
\(828\) 7.10176 0.246803
\(829\) 21.0052 0.729541 0.364770 0.931097i \(-0.381147\pi\)
0.364770 + 0.931097i \(0.381147\pi\)
\(830\) 10.1138 0.351055
\(831\) −27.0963 −0.939960
\(832\) 1.00000 0.0346688
\(833\) −38.0678 −1.31897
\(834\) −4.39044 −0.152028
\(835\) −53.6783 −1.85761
\(836\) −6.29286 −0.217643
\(837\) 2.34857 0.0811786
\(838\) −7.08545 −0.244763
\(839\) 34.1811 1.18006 0.590031 0.807380i \(-0.299115\pi\)
0.590031 + 0.807380i \(0.299115\pi\)
\(840\) 4.51675 0.155843
\(841\) −27.7984 −0.958564
\(842\) −7.09461 −0.244496
\(843\) −22.0661 −0.759995
\(844\) −23.6370 −0.813618
\(845\) −3.21497 −0.110598
\(846\) 5.52965 0.190113
\(847\) 6.41034 0.220262
\(848\) −4.04692 −0.138972
\(849\) 20.6144 0.707486
\(850\) −40.4143 −1.38620
\(851\) 36.3362 1.24559
\(852\) 16.7385 0.573451
\(853\) 43.2603 1.48120 0.740602 0.671944i \(-0.234540\pi\)
0.740602 + 0.671944i \(0.234540\pi\)
\(854\) −0.0690923 −0.00236429
\(855\) −7.97401 −0.272705
\(856\) 5.70699 0.195061
\(857\) 31.1550 1.06423 0.532117 0.846671i \(-0.321396\pi\)
0.532117 + 0.846671i \(0.321396\pi\)
\(858\) −2.53716 −0.0866173
\(859\) −16.3331 −0.557279 −0.278640 0.960396i \(-0.589884\pi\)
−0.278640 + 0.960396i \(0.589884\pi\)
\(860\) −30.8657 −1.05251
\(861\) −0.446108 −0.0152033
\(862\) −22.5540 −0.768192
\(863\) −35.1370 −1.19608 −0.598038 0.801468i \(-0.704053\pi\)
−0.598038 + 0.801468i \(0.704053\pi\)
\(864\) 1.00000 0.0340207
\(865\) 50.5318 1.71813
\(866\) −1.25553 −0.0426648
\(867\) −40.3631 −1.37080
\(868\) 3.29954 0.111994
\(869\) −41.4813 −1.40716
\(870\) 3.52423 0.119483
\(871\) −11.1167 −0.376674
\(872\) −0.714942 −0.0242110
\(873\) −9.59214 −0.324645
\(874\) −17.6143 −0.595813
\(875\) 1.51776 0.0513096
\(876\) −5.34984 −0.180754
\(877\) 18.6302 0.629098 0.314549 0.949241i \(-0.398147\pi\)
0.314549 + 0.949241i \(0.398147\pi\)
\(878\) 8.79229 0.296725
\(879\) 15.5930 0.525937
\(880\) 8.15690 0.274969
\(881\) 35.4645 1.19483 0.597414 0.801933i \(-0.296195\pi\)
0.597414 + 0.801933i \(0.296195\pi\)
\(882\) 5.02622 0.169242
\(883\) −13.8411 −0.465791 −0.232896 0.972502i \(-0.574820\pi\)
−0.232896 + 0.972502i \(0.574820\pi\)
\(884\) 7.57385 0.254736
\(885\) 1.90108 0.0639040
\(886\) −11.5561 −0.388233
\(887\) −13.0912 −0.439559 −0.219779 0.975550i \(-0.570534\pi\)
−0.219779 + 0.975550i \(0.570534\pi\)
\(888\) 5.11651 0.171699
\(889\) −12.8784 −0.431929
\(890\) −14.2041 −0.476123
\(891\) −2.53716 −0.0849982
\(892\) 21.0616 0.705195
\(893\) −13.7151 −0.458957
\(894\) 5.11066 0.170926
\(895\) −48.6417 −1.62591
\(896\) 1.40491 0.0469348
\(897\) −7.10176 −0.237121
\(898\) −26.2196 −0.874959
\(899\) 2.57450 0.0858642
\(900\) 5.33603 0.177868
\(901\) −30.6508 −1.02112
\(902\) −0.805637 −0.0268248
\(903\) 13.4880 0.448854
\(904\) −0.0112939 −0.000375629 0
\(905\) −24.6559 −0.819591
\(906\) 10.3452 0.343696
\(907\) 6.36080 0.211207 0.105603 0.994408i \(-0.466323\pi\)
0.105603 + 0.994408i \(0.466323\pi\)
\(908\) −11.7708 −0.390627
\(909\) −13.2784 −0.440417
\(910\) −4.51675 −0.149729
\(911\) 44.6319 1.47872 0.739361 0.673309i \(-0.235128\pi\)
0.739361 + 0.673309i \(0.235128\pi\)
\(912\) −2.48027 −0.0821301
\(913\) −7.98153 −0.264150
\(914\) 26.1019 0.863375
\(915\) −0.158109 −0.00522693
\(916\) 12.9373 0.427460
\(917\) −8.48901 −0.280332
\(918\) 7.57385 0.249974
\(919\) 11.4655 0.378213 0.189106 0.981957i \(-0.439441\pi\)
0.189106 + 0.981957i \(0.439441\pi\)
\(920\) 22.8320 0.752747
\(921\) 13.8308 0.455741
\(922\) 29.0448 0.956541
\(923\) −16.7385 −0.550954
\(924\) −3.56449 −0.117263
\(925\) 27.3018 0.897679
\(926\) −13.2014 −0.433825
\(927\) −1.00000 −0.0328443
\(928\) 1.09619 0.0359844
\(929\) −46.9608 −1.54073 −0.770367 0.637601i \(-0.779927\pi\)
−0.770367 + 0.637601i \(0.779927\pi\)
\(930\) 7.55060 0.247594
\(931\) −12.4664 −0.408570
\(932\) −14.2591 −0.467071
\(933\) 21.7094 0.710735
\(934\) 8.32279 0.272330
\(935\) 61.7791 2.02039
\(936\) −1.00000 −0.0326860
\(937\) −56.9779 −1.86139 −0.930694 0.365800i \(-0.880796\pi\)
−0.930694 + 0.365800i \(0.880796\pi\)
\(938\) −15.6179 −0.509944
\(939\) 7.64960 0.249635
\(940\) 17.7777 0.579844
\(941\) 12.4270 0.405110 0.202555 0.979271i \(-0.435076\pi\)
0.202555 + 0.979271i \(0.435076\pi\)
\(942\) 19.2837 0.628296
\(943\) −2.25506 −0.0734347
\(944\) 0.591321 0.0192458
\(945\) −4.51675 −0.146930
\(946\) 24.3584 0.791958
\(947\) −60.7311 −1.97349 −0.986747 0.162266i \(-0.948120\pi\)
−0.986747 + 0.162266i \(0.948120\pi\)
\(948\) −16.3495 −0.531006
\(949\) 5.34984 0.173663
\(950\) −13.2348 −0.429394
\(951\) −7.63340 −0.247530
\(952\) 10.6406 0.344864
\(953\) 39.4367 1.27748 0.638741 0.769422i \(-0.279456\pi\)
0.638741 + 0.769422i \(0.279456\pi\)
\(954\) 4.04692 0.131024
\(955\) 51.4937 1.66630
\(956\) 7.67833 0.248335
\(957\) −2.78122 −0.0899042
\(958\) 31.2476 1.00956
\(959\) 27.1115 0.875477
\(960\) 3.21497 0.103763
\(961\) −25.4842 −0.822071
\(962\) −5.11651 −0.164963
\(963\) −5.70699 −0.183905
\(964\) 17.8173 0.573857
\(965\) −19.3997 −0.624498
\(966\) −9.97735 −0.321016
\(967\) 18.1825 0.584710 0.292355 0.956310i \(-0.405561\pi\)
0.292355 + 0.956310i \(0.405561\pi\)
\(968\) 4.56281 0.146654
\(969\) −18.7852 −0.603468
\(970\) −30.8384 −0.990163
\(971\) 41.6240 1.33578 0.667889 0.744261i \(-0.267198\pi\)
0.667889 + 0.744261i \(0.267198\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 6.16818 0.197743
\(974\) −33.0131 −1.05781
\(975\) −5.33603 −0.170890
\(976\) −0.0491791 −0.00157418
\(977\) 20.3397 0.650724 0.325362 0.945590i \(-0.394514\pi\)
0.325362 + 0.945590i \(0.394514\pi\)
\(978\) 24.1659 0.772739
\(979\) 11.2095 0.358256
\(980\) 16.1591 0.516185
\(981\) 0.714942 0.0228264
\(982\) −22.0882 −0.704864
\(983\) 5.83910 0.186239 0.0931193 0.995655i \(-0.470316\pi\)
0.0931193 + 0.995655i \(0.470316\pi\)
\(984\) −0.317535 −0.0101226
\(985\) 47.2349 1.50503
\(986\) 8.30241 0.264403
\(987\) −7.76868 −0.247280
\(988\) 2.48027 0.0789081
\(989\) 68.1814 2.16804
\(990\) −8.15690 −0.259243
\(991\) −23.5945 −0.749505 −0.374753 0.927125i \(-0.622272\pi\)
−0.374753 + 0.927125i \(0.622272\pi\)
\(992\) 2.34857 0.0745673
\(993\) 6.12990 0.194527
\(994\) −23.5161 −0.745885
\(995\) −29.8331 −0.945774
\(996\) −3.14585 −0.0996800
\(997\) −20.6271 −0.653266 −0.326633 0.945151i \(-0.605914\pi\)
−0.326633 + 0.945151i \(0.605914\pi\)
\(998\) 34.2370 1.08375
\(999\) −5.11651 −0.161879
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.1.3 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.3 14 1.1 even 1 trivial