Properties

Label 6036.2.a.i.1.1
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-4.35282 q^{5}\) \(+4.52941 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-4.35282 q^{5}\) \(+4.52941 q^{7}\) \(+1.00000 q^{9}\) \(-1.05764 q^{11}\) \(+3.27256 q^{13}\) \(+4.35282 q^{15}\) \(-0.821600 q^{17}\) \(+6.20538 q^{19}\) \(-4.52941 q^{21}\) \(+4.58343 q^{23}\) \(+13.9470 q^{25}\) \(-1.00000 q^{27}\) \(-2.39594 q^{29}\) \(+3.22680 q^{31}\) \(+1.05764 q^{33}\) \(-19.7157 q^{35}\) \(-7.35998 q^{37}\) \(-3.27256 q^{39}\) \(-4.28190 q^{41}\) \(+4.67415 q^{43}\) \(-4.35282 q^{45}\) \(+9.26046 q^{47}\) \(+13.5155 q^{49}\) \(+0.821600 q^{51}\) \(-2.53746 q^{53}\) \(+4.60373 q^{55}\) \(-6.20538 q^{57}\) \(-10.3806 q^{59}\) \(-5.03856 q^{61}\) \(+4.52941 q^{63}\) \(-14.2448 q^{65}\) \(-3.07201 q^{67}\) \(-4.58343 q^{69}\) \(+4.37291 q^{71}\) \(-8.07671 q^{73}\) \(-13.9470 q^{75}\) \(-4.79050 q^{77}\) \(-2.23645 q^{79}\) \(+1.00000 q^{81}\) \(+3.91592 q^{83}\) \(+3.57628 q^{85}\) \(+2.39594 q^{87}\) \(-0.496745 q^{89}\) \(+14.8227 q^{91}\) \(-3.22680 q^{93}\) \(-27.0109 q^{95}\) \(-2.38609 q^{97}\) \(-1.05764 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −4.35282 −1.94664 −0.973320 0.229453i \(-0.926306\pi\)
−0.973320 + 0.229453i \(0.926306\pi\)
\(6\) 0 0
\(7\) 4.52941 1.71195 0.855977 0.517013i \(-0.172956\pi\)
0.855977 + 0.517013i \(0.172956\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.05764 −0.318892 −0.159446 0.987207i \(-0.550971\pi\)
−0.159446 + 0.987207i \(0.550971\pi\)
\(12\) 0 0
\(13\) 3.27256 0.907644 0.453822 0.891092i \(-0.350060\pi\)
0.453822 + 0.891092i \(0.350060\pi\)
\(14\) 0 0
\(15\) 4.35282 1.12389
\(16\) 0 0
\(17\) −0.821600 −0.199267 −0.0996337 0.995024i \(-0.531767\pi\)
−0.0996337 + 0.995024i \(0.531767\pi\)
\(18\) 0 0
\(19\) 6.20538 1.42361 0.711806 0.702376i \(-0.247877\pi\)
0.711806 + 0.702376i \(0.247877\pi\)
\(20\) 0 0
\(21\) −4.52941 −0.988398
\(22\) 0 0
\(23\) 4.58343 0.955711 0.477855 0.878439i \(-0.341414\pi\)
0.477855 + 0.878439i \(0.341414\pi\)
\(24\) 0 0
\(25\) 13.9470 2.78941
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.39594 −0.444915 −0.222457 0.974942i \(-0.571408\pi\)
−0.222457 + 0.974942i \(0.571408\pi\)
\(30\) 0 0
\(31\) 3.22680 0.579550 0.289775 0.957095i \(-0.406420\pi\)
0.289775 + 0.957095i \(0.406420\pi\)
\(32\) 0 0
\(33\) 1.05764 0.184112
\(34\) 0 0
\(35\) −19.7157 −3.33256
\(36\) 0 0
\(37\) −7.35998 −1.20997 −0.604987 0.796235i \(-0.706822\pi\)
−0.604987 + 0.796235i \(0.706822\pi\)
\(38\) 0 0
\(39\) −3.27256 −0.524029
\(40\) 0 0
\(41\) −4.28190 −0.668721 −0.334360 0.942445i \(-0.608520\pi\)
−0.334360 + 0.942445i \(0.608520\pi\)
\(42\) 0 0
\(43\) 4.67415 0.712801 0.356401 0.934333i \(-0.384004\pi\)
0.356401 + 0.934333i \(0.384004\pi\)
\(44\) 0 0
\(45\) −4.35282 −0.648880
\(46\) 0 0
\(47\) 9.26046 1.35078 0.675389 0.737462i \(-0.263976\pi\)
0.675389 + 0.737462i \(0.263976\pi\)
\(48\) 0 0
\(49\) 13.5155 1.93079
\(50\) 0 0
\(51\) 0.821600 0.115047
\(52\) 0 0
\(53\) −2.53746 −0.348547 −0.174273 0.984697i \(-0.555758\pi\)
−0.174273 + 0.984697i \(0.555758\pi\)
\(54\) 0 0
\(55\) 4.60373 0.620767
\(56\) 0 0
\(57\) −6.20538 −0.821923
\(58\) 0 0
\(59\) −10.3806 −1.35144 −0.675720 0.737158i \(-0.736167\pi\)
−0.675720 + 0.737158i \(0.736167\pi\)
\(60\) 0 0
\(61\) −5.03856 −0.645121 −0.322561 0.946549i \(-0.604544\pi\)
−0.322561 + 0.946549i \(0.604544\pi\)
\(62\) 0 0
\(63\) 4.52941 0.570652
\(64\) 0 0
\(65\) −14.2448 −1.76686
\(66\) 0 0
\(67\) −3.07201 −0.375306 −0.187653 0.982235i \(-0.560088\pi\)
−0.187653 + 0.982235i \(0.560088\pi\)
\(68\) 0 0
\(69\) −4.58343 −0.551780
\(70\) 0 0
\(71\) 4.37291 0.518969 0.259484 0.965747i \(-0.416447\pi\)
0.259484 + 0.965747i \(0.416447\pi\)
\(72\) 0 0
\(73\) −8.07671 −0.945308 −0.472654 0.881248i \(-0.656704\pi\)
−0.472654 + 0.881248i \(0.656704\pi\)
\(74\) 0 0
\(75\) −13.9470 −1.61046
\(76\) 0 0
\(77\) −4.79050 −0.545928
\(78\) 0 0
\(79\) −2.23645 −0.251621 −0.125810 0.992054i \(-0.540153\pi\)
−0.125810 + 0.992054i \(0.540153\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.91592 0.429828 0.214914 0.976633i \(-0.431053\pi\)
0.214914 + 0.976633i \(0.431053\pi\)
\(84\) 0 0
\(85\) 3.57628 0.387902
\(86\) 0 0
\(87\) 2.39594 0.256872
\(88\) 0 0
\(89\) −0.496745 −0.0526549 −0.0263274 0.999653i \(-0.508381\pi\)
−0.0263274 + 0.999653i \(0.508381\pi\)
\(90\) 0 0
\(91\) 14.8227 1.55385
\(92\) 0 0
\(93\) −3.22680 −0.334603
\(94\) 0 0
\(95\) −27.0109 −2.77126
\(96\) 0 0
\(97\) −2.38609 −0.242271 −0.121135 0.992636i \(-0.538654\pi\)
−0.121135 + 0.992636i \(0.538654\pi\)
\(98\) 0 0
\(99\) −1.05764 −0.106297
\(100\) 0 0
\(101\) 16.5226 1.64406 0.822031 0.569442i \(-0.192841\pi\)
0.822031 + 0.569442i \(0.192841\pi\)
\(102\) 0 0
\(103\) 5.81697 0.573163 0.286582 0.958056i \(-0.407481\pi\)
0.286582 + 0.958056i \(0.407481\pi\)
\(104\) 0 0
\(105\) 19.7157 1.92405
\(106\) 0 0
\(107\) 16.3751 1.58304 0.791521 0.611143i \(-0.209290\pi\)
0.791521 + 0.611143i \(0.209290\pi\)
\(108\) 0 0
\(109\) −17.1123 −1.63906 −0.819532 0.573034i \(-0.805766\pi\)
−0.819532 + 0.573034i \(0.805766\pi\)
\(110\) 0 0
\(111\) 7.35998 0.698579
\(112\) 0 0
\(113\) −3.36438 −0.316495 −0.158247 0.987400i \(-0.550584\pi\)
−0.158247 + 0.987400i \(0.550584\pi\)
\(114\) 0 0
\(115\) −19.9508 −1.86042
\(116\) 0 0
\(117\) 3.27256 0.302548
\(118\) 0 0
\(119\) −3.72136 −0.341137
\(120\) 0 0
\(121\) −9.88139 −0.898308
\(122\) 0 0
\(123\) 4.28190 0.386086
\(124\) 0 0
\(125\) −38.9448 −3.48333
\(126\) 0 0
\(127\) −4.73957 −0.420569 −0.210284 0.977640i \(-0.567439\pi\)
−0.210284 + 0.977640i \(0.567439\pi\)
\(128\) 0 0
\(129\) −4.67415 −0.411536
\(130\) 0 0
\(131\) 2.04201 0.178411 0.0892057 0.996013i \(-0.471567\pi\)
0.0892057 + 0.996013i \(0.471567\pi\)
\(132\) 0 0
\(133\) 28.1067 2.43716
\(134\) 0 0
\(135\) 4.35282 0.374631
\(136\) 0 0
\(137\) 10.7240 0.916215 0.458107 0.888897i \(-0.348528\pi\)
0.458107 + 0.888897i \(0.348528\pi\)
\(138\) 0 0
\(139\) 19.6787 1.66912 0.834562 0.550913i \(-0.185721\pi\)
0.834562 + 0.550913i \(0.185721\pi\)
\(140\) 0 0
\(141\) −9.26046 −0.779872
\(142\) 0 0
\(143\) −3.46120 −0.289440
\(144\) 0 0
\(145\) 10.4291 0.866089
\(146\) 0 0
\(147\) −13.5155 −1.11474
\(148\) 0 0
\(149\) 13.8512 1.13473 0.567365 0.823466i \(-0.307963\pi\)
0.567365 + 0.823466i \(0.307963\pi\)
\(150\) 0 0
\(151\) 9.97448 0.811712 0.405856 0.913937i \(-0.366973\pi\)
0.405856 + 0.913937i \(0.366973\pi\)
\(152\) 0 0
\(153\) −0.821600 −0.0664224
\(154\) 0 0
\(155\) −14.0457 −1.12817
\(156\) 0 0
\(157\) −15.3424 −1.22445 −0.612227 0.790682i \(-0.709726\pi\)
−0.612227 + 0.790682i \(0.709726\pi\)
\(158\) 0 0
\(159\) 2.53746 0.201234
\(160\) 0 0
\(161\) 20.7602 1.63613
\(162\) 0 0
\(163\) 8.68771 0.680474 0.340237 0.940340i \(-0.389493\pi\)
0.340237 + 0.940340i \(0.389493\pi\)
\(164\) 0 0
\(165\) −4.60373 −0.358400
\(166\) 0 0
\(167\) 19.4450 1.50470 0.752350 0.658764i \(-0.228920\pi\)
0.752350 + 0.658764i \(0.228920\pi\)
\(168\) 0 0
\(169\) −2.29037 −0.176182
\(170\) 0 0
\(171\) 6.20538 0.474537
\(172\) 0 0
\(173\) −10.2254 −0.777421 −0.388710 0.921360i \(-0.627079\pi\)
−0.388710 + 0.921360i \(0.627079\pi\)
\(174\) 0 0
\(175\) 63.1718 4.77534
\(176\) 0 0
\(177\) 10.3806 0.780254
\(178\) 0 0
\(179\) 1.21223 0.0906064 0.0453032 0.998973i \(-0.485575\pi\)
0.0453032 + 0.998973i \(0.485575\pi\)
\(180\) 0 0
\(181\) −3.65026 −0.271322 −0.135661 0.990755i \(-0.543316\pi\)
−0.135661 + 0.990755i \(0.543316\pi\)
\(182\) 0 0
\(183\) 5.03856 0.372461
\(184\) 0 0
\(185\) 32.0367 2.35538
\(186\) 0 0
\(187\) 0.868961 0.0635447
\(188\) 0 0
\(189\) −4.52941 −0.329466
\(190\) 0 0
\(191\) 4.31692 0.312361 0.156181 0.987729i \(-0.450082\pi\)
0.156181 + 0.987729i \(0.450082\pi\)
\(192\) 0 0
\(193\) 6.29825 0.453358 0.226679 0.973969i \(-0.427213\pi\)
0.226679 + 0.973969i \(0.427213\pi\)
\(194\) 0 0
\(195\) 14.2448 1.02009
\(196\) 0 0
\(197\) −27.8337 −1.98307 −0.991535 0.129839i \(-0.958554\pi\)
−0.991535 + 0.129839i \(0.958554\pi\)
\(198\) 0 0
\(199\) −3.11661 −0.220931 −0.110465 0.993880i \(-0.535234\pi\)
−0.110465 + 0.993880i \(0.535234\pi\)
\(200\) 0 0
\(201\) 3.07201 0.216683
\(202\) 0 0
\(203\) −10.8522 −0.761674
\(204\) 0 0
\(205\) 18.6383 1.30176
\(206\) 0 0
\(207\) 4.58343 0.318570
\(208\) 0 0
\(209\) −6.56309 −0.453978
\(210\) 0 0
\(211\) −9.81779 −0.675885 −0.337942 0.941167i \(-0.609731\pi\)
−0.337942 + 0.941167i \(0.609731\pi\)
\(212\) 0 0
\(213\) −4.37291 −0.299627
\(214\) 0 0
\(215\) −20.3457 −1.38757
\(216\) 0 0
\(217\) 14.6155 0.992163
\(218\) 0 0
\(219\) 8.07671 0.545774
\(220\) 0 0
\(221\) −2.68873 −0.180864
\(222\) 0 0
\(223\) 2.96394 0.198480 0.0992399 0.995064i \(-0.468359\pi\)
0.0992399 + 0.995064i \(0.468359\pi\)
\(224\) 0 0
\(225\) 13.9470 0.929802
\(226\) 0 0
\(227\) 22.2796 1.47875 0.739375 0.673294i \(-0.235121\pi\)
0.739375 + 0.673294i \(0.235121\pi\)
\(228\) 0 0
\(229\) −6.42292 −0.424438 −0.212219 0.977222i \(-0.568069\pi\)
−0.212219 + 0.977222i \(0.568069\pi\)
\(230\) 0 0
\(231\) 4.79050 0.315192
\(232\) 0 0
\(233\) −2.07609 −0.136009 −0.0680045 0.997685i \(-0.521663\pi\)
−0.0680045 + 0.997685i \(0.521663\pi\)
\(234\) 0 0
\(235\) −40.3091 −2.62948
\(236\) 0 0
\(237\) 2.23645 0.145273
\(238\) 0 0
\(239\) 10.8471 0.701637 0.350819 0.936443i \(-0.385903\pi\)
0.350819 + 0.936443i \(0.385903\pi\)
\(240\) 0 0
\(241\) −19.1121 −1.23112 −0.615560 0.788090i \(-0.711070\pi\)
−0.615560 + 0.788090i \(0.711070\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −58.8306 −3.75855
\(246\) 0 0
\(247\) 20.3075 1.29213
\(248\) 0 0
\(249\) −3.91592 −0.248161
\(250\) 0 0
\(251\) −0.653466 −0.0412464 −0.0206232 0.999787i \(-0.506565\pi\)
−0.0206232 + 0.999787i \(0.506565\pi\)
\(252\) 0 0
\(253\) −4.84763 −0.304768
\(254\) 0 0
\(255\) −3.57628 −0.223955
\(256\) 0 0
\(257\) 19.3408 1.20644 0.603222 0.797573i \(-0.293883\pi\)
0.603222 + 0.797573i \(0.293883\pi\)
\(258\) 0 0
\(259\) −33.3364 −2.07142
\(260\) 0 0
\(261\) −2.39594 −0.148305
\(262\) 0 0
\(263\) 6.11362 0.376982 0.188491 0.982075i \(-0.439640\pi\)
0.188491 + 0.982075i \(0.439640\pi\)
\(264\) 0 0
\(265\) 11.0451 0.678495
\(266\) 0 0
\(267\) 0.496745 0.0304003
\(268\) 0 0
\(269\) 16.9230 1.03181 0.515906 0.856645i \(-0.327456\pi\)
0.515906 + 0.856645i \(0.327456\pi\)
\(270\) 0 0
\(271\) 15.2149 0.924241 0.462121 0.886817i \(-0.347089\pi\)
0.462121 + 0.886817i \(0.347089\pi\)
\(272\) 0 0
\(273\) −14.8227 −0.897113
\(274\) 0 0
\(275\) −14.7510 −0.889518
\(276\) 0 0
\(277\) 28.5273 1.71404 0.857020 0.515282i \(-0.172313\pi\)
0.857020 + 0.515282i \(0.172313\pi\)
\(278\) 0 0
\(279\) 3.22680 0.193183
\(280\) 0 0
\(281\) −12.3250 −0.735248 −0.367624 0.929974i \(-0.619829\pi\)
−0.367624 + 0.929974i \(0.619829\pi\)
\(282\) 0 0
\(283\) −17.3636 −1.03216 −0.516080 0.856540i \(-0.672609\pi\)
−0.516080 + 0.856540i \(0.672609\pi\)
\(284\) 0 0
\(285\) 27.0109 1.59999
\(286\) 0 0
\(287\) −19.3945 −1.14482
\(288\) 0 0
\(289\) −16.3250 −0.960293
\(290\) 0 0
\(291\) 2.38609 0.139875
\(292\) 0 0
\(293\) −14.7636 −0.862496 −0.431248 0.902233i \(-0.641927\pi\)
−0.431248 + 0.902233i \(0.641927\pi\)
\(294\) 0 0
\(295\) 45.1849 2.63077
\(296\) 0 0
\(297\) 1.05764 0.0613707
\(298\) 0 0
\(299\) 14.9995 0.867445
\(300\) 0 0
\(301\) 21.1711 1.22028
\(302\) 0 0
\(303\) −16.5226 −0.949200
\(304\) 0 0
\(305\) 21.9319 1.25582
\(306\) 0 0
\(307\) 12.2740 0.700511 0.350256 0.936654i \(-0.386095\pi\)
0.350256 + 0.936654i \(0.386095\pi\)
\(308\) 0 0
\(309\) −5.81697 −0.330916
\(310\) 0 0
\(311\) −9.78212 −0.554693 −0.277347 0.960770i \(-0.589455\pi\)
−0.277347 + 0.960770i \(0.589455\pi\)
\(312\) 0 0
\(313\) 22.2407 1.25712 0.628560 0.777761i \(-0.283645\pi\)
0.628560 + 0.777761i \(0.283645\pi\)
\(314\) 0 0
\(315\) −19.7157 −1.11085
\(316\) 0 0
\(317\) 29.8559 1.67688 0.838438 0.544997i \(-0.183469\pi\)
0.838438 + 0.544997i \(0.183469\pi\)
\(318\) 0 0
\(319\) 2.53405 0.141880
\(320\) 0 0
\(321\) −16.3751 −0.913969
\(322\) 0 0
\(323\) −5.09834 −0.283679
\(324\) 0 0
\(325\) 45.6424 2.53179
\(326\) 0 0
\(327\) 17.1123 0.946314
\(328\) 0 0
\(329\) 41.9444 2.31247
\(330\) 0 0
\(331\) 20.4854 1.12598 0.562990 0.826464i \(-0.309651\pi\)
0.562990 + 0.826464i \(0.309651\pi\)
\(332\) 0 0
\(333\) −7.35998 −0.403325
\(334\) 0 0
\(335\) 13.3719 0.730585
\(336\) 0 0
\(337\) −18.0879 −0.985313 −0.492656 0.870224i \(-0.663974\pi\)
−0.492656 + 0.870224i \(0.663974\pi\)
\(338\) 0 0
\(339\) 3.36438 0.182728
\(340\) 0 0
\(341\) −3.41280 −0.184814
\(342\) 0 0
\(343\) 29.5115 1.59347
\(344\) 0 0
\(345\) 19.9508 1.07412
\(346\) 0 0
\(347\) 16.0628 0.862295 0.431148 0.902281i \(-0.358109\pi\)
0.431148 + 0.902281i \(0.358109\pi\)
\(348\) 0 0
\(349\) −18.2232 −0.975464 −0.487732 0.872993i \(-0.662176\pi\)
−0.487732 + 0.872993i \(0.662176\pi\)
\(350\) 0 0
\(351\) −3.27256 −0.174676
\(352\) 0 0
\(353\) 35.9672 1.91434 0.957172 0.289521i \(-0.0934961\pi\)
0.957172 + 0.289521i \(0.0934961\pi\)
\(354\) 0 0
\(355\) −19.0345 −1.01025
\(356\) 0 0
\(357\) 3.72136 0.196955
\(358\) 0 0
\(359\) −3.46377 −0.182811 −0.0914055 0.995814i \(-0.529136\pi\)
−0.0914055 + 0.995814i \(0.529136\pi\)
\(360\) 0 0
\(361\) 19.5068 1.02667
\(362\) 0 0
\(363\) 9.88139 0.518638
\(364\) 0 0
\(365\) 35.1565 1.84017
\(366\) 0 0
\(367\) 33.1443 1.73012 0.865058 0.501672i \(-0.167281\pi\)
0.865058 + 0.501672i \(0.167281\pi\)
\(368\) 0 0
\(369\) −4.28190 −0.222907
\(370\) 0 0
\(371\) −11.4932 −0.596697
\(372\) 0 0
\(373\) −3.95958 −0.205020 −0.102510 0.994732i \(-0.532687\pi\)
−0.102510 + 0.994732i \(0.532687\pi\)
\(374\) 0 0
\(375\) 38.9448 2.01110
\(376\) 0 0
\(377\) −7.84085 −0.403824
\(378\) 0 0
\(379\) −20.6399 −1.06020 −0.530100 0.847935i \(-0.677846\pi\)
−0.530100 + 0.847935i \(0.677846\pi\)
\(380\) 0 0
\(381\) 4.73957 0.242815
\(382\) 0 0
\(383\) −29.2361 −1.49389 −0.746947 0.664883i \(-0.768481\pi\)
−0.746947 + 0.664883i \(0.768481\pi\)
\(384\) 0 0
\(385\) 20.8522 1.06273
\(386\) 0 0
\(387\) 4.67415 0.237600
\(388\) 0 0
\(389\) 33.7283 1.71009 0.855046 0.518552i \(-0.173529\pi\)
0.855046 + 0.518552i \(0.173529\pi\)
\(390\) 0 0
\(391\) −3.76575 −0.190442
\(392\) 0 0
\(393\) −2.04201 −0.103006
\(394\) 0 0
\(395\) 9.73488 0.489815
\(396\) 0 0
\(397\) 36.0650 1.81005 0.905024 0.425360i \(-0.139853\pi\)
0.905024 + 0.425360i \(0.139853\pi\)
\(398\) 0 0
\(399\) −28.1067 −1.40710
\(400\) 0 0
\(401\) −3.05637 −0.152628 −0.0763138 0.997084i \(-0.524315\pi\)
−0.0763138 + 0.997084i \(0.524315\pi\)
\(402\) 0 0
\(403\) 10.5599 0.526025
\(404\) 0 0
\(405\) −4.35282 −0.216293
\(406\) 0 0
\(407\) 7.78424 0.385851
\(408\) 0 0
\(409\) 22.6294 1.11895 0.559477 0.828846i \(-0.311002\pi\)
0.559477 + 0.828846i \(0.311002\pi\)
\(410\) 0 0
\(411\) −10.7240 −0.528977
\(412\) 0 0
\(413\) −47.0180 −2.31360
\(414\) 0 0
\(415\) −17.0453 −0.836720
\(416\) 0 0
\(417\) −19.6787 −0.963670
\(418\) 0 0
\(419\) 25.4245 1.24207 0.621035 0.783783i \(-0.286712\pi\)
0.621035 + 0.783783i \(0.286712\pi\)
\(420\) 0 0
\(421\) 12.5592 0.612098 0.306049 0.952016i \(-0.400993\pi\)
0.306049 + 0.952016i \(0.400993\pi\)
\(422\) 0 0
\(423\) 9.26046 0.450259
\(424\) 0 0
\(425\) −11.4589 −0.555837
\(426\) 0 0
\(427\) −22.8217 −1.10442
\(428\) 0 0
\(429\) 3.46120 0.167108
\(430\) 0 0
\(431\) 36.1168 1.73969 0.869844 0.493327i \(-0.164220\pi\)
0.869844 + 0.493327i \(0.164220\pi\)
\(432\) 0 0
\(433\) 32.4490 1.55940 0.779699 0.626155i \(-0.215372\pi\)
0.779699 + 0.626155i \(0.215372\pi\)
\(434\) 0 0
\(435\) −10.4291 −0.500037
\(436\) 0 0
\(437\) 28.4419 1.36056
\(438\) 0 0
\(439\) −31.8930 −1.52217 −0.761086 0.648651i \(-0.775333\pi\)
−0.761086 + 0.648651i \(0.775333\pi\)
\(440\) 0 0
\(441\) 13.5155 0.643597
\(442\) 0 0
\(443\) 17.7156 0.841696 0.420848 0.907131i \(-0.361733\pi\)
0.420848 + 0.907131i \(0.361733\pi\)
\(444\) 0 0
\(445\) 2.16224 0.102500
\(446\) 0 0
\(447\) −13.8512 −0.655137
\(448\) 0 0
\(449\) −7.64492 −0.360786 −0.180393 0.983595i \(-0.557737\pi\)
−0.180393 + 0.983595i \(0.557737\pi\)
\(450\) 0 0
\(451\) 4.52873 0.213249
\(452\) 0 0
\(453\) −9.97448 −0.468642
\(454\) 0 0
\(455\) −64.5207 −3.02478
\(456\) 0 0
\(457\) −40.5453 −1.89663 −0.948315 0.317331i \(-0.897213\pi\)
−0.948315 + 0.317331i \(0.897213\pi\)
\(458\) 0 0
\(459\) 0.821600 0.0383490
\(460\) 0 0
\(461\) 32.7071 1.52332 0.761661 0.647976i \(-0.224384\pi\)
0.761661 + 0.647976i \(0.224384\pi\)
\(462\) 0 0
\(463\) −5.86978 −0.272792 −0.136396 0.990654i \(-0.543552\pi\)
−0.136396 + 0.990654i \(0.543552\pi\)
\(464\) 0 0
\(465\) 14.0457 0.651352
\(466\) 0 0
\(467\) −22.2518 −1.02969 −0.514846 0.857282i \(-0.672151\pi\)
−0.514846 + 0.857282i \(0.672151\pi\)
\(468\) 0 0
\(469\) −13.9144 −0.642506
\(470\) 0 0
\(471\) 15.3424 0.706939
\(472\) 0 0
\(473\) −4.94359 −0.227306
\(474\) 0 0
\(475\) 86.5466 3.97103
\(476\) 0 0
\(477\) −2.53746 −0.116182
\(478\) 0 0
\(479\) −32.7526 −1.49651 −0.748253 0.663413i \(-0.769107\pi\)
−0.748253 + 0.663413i \(0.769107\pi\)
\(480\) 0 0
\(481\) −24.0860 −1.09823
\(482\) 0 0
\(483\) −20.7602 −0.944622
\(484\) 0 0
\(485\) 10.3862 0.471614
\(486\) 0 0
\(487\) 10.8538 0.491834 0.245917 0.969291i \(-0.420911\pi\)
0.245917 + 0.969291i \(0.420911\pi\)
\(488\) 0 0
\(489\) −8.68771 −0.392872
\(490\) 0 0
\(491\) −9.73311 −0.439249 −0.219625 0.975584i \(-0.570483\pi\)
−0.219625 + 0.975584i \(0.570483\pi\)
\(492\) 0 0
\(493\) 1.96850 0.0886570
\(494\) 0 0
\(495\) 4.60373 0.206922
\(496\) 0 0
\(497\) 19.8067 0.888451
\(498\) 0 0
\(499\) 5.53749 0.247892 0.123946 0.992289i \(-0.460445\pi\)
0.123946 + 0.992289i \(0.460445\pi\)
\(500\) 0 0
\(501\) −19.4450 −0.868739
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −71.9200 −3.20040
\(506\) 0 0
\(507\) 2.29037 0.101719
\(508\) 0 0
\(509\) 30.5738 1.35516 0.677580 0.735449i \(-0.263029\pi\)
0.677580 + 0.735449i \(0.263029\pi\)
\(510\) 0 0
\(511\) −36.5827 −1.61832
\(512\) 0 0
\(513\) −6.20538 −0.273974
\(514\) 0 0
\(515\) −25.3202 −1.11574
\(516\) 0 0
\(517\) −9.79427 −0.430752
\(518\) 0 0
\(519\) 10.2254 0.448844
\(520\) 0 0
\(521\) 8.96937 0.392955 0.196478 0.980508i \(-0.437050\pi\)
0.196478 + 0.980508i \(0.437050\pi\)
\(522\) 0 0
\(523\) −15.3234 −0.670045 −0.335022 0.942210i \(-0.608744\pi\)
−0.335022 + 0.942210i \(0.608744\pi\)
\(524\) 0 0
\(525\) −63.1718 −2.75704
\(526\) 0 0
\(527\) −2.65114 −0.115485
\(528\) 0 0
\(529\) −1.99219 −0.0866171
\(530\) 0 0
\(531\) −10.3806 −0.450480
\(532\) 0 0
\(533\) −14.0128 −0.606960
\(534\) 0 0
\(535\) −71.2779 −3.08161
\(536\) 0 0
\(537\) −1.21223 −0.0523116
\(538\) 0 0
\(539\) −14.2946 −0.615713
\(540\) 0 0
\(541\) 22.6037 0.971808 0.485904 0.874012i \(-0.338491\pi\)
0.485904 + 0.874012i \(0.338491\pi\)
\(542\) 0 0
\(543\) 3.65026 0.156648
\(544\) 0 0
\(545\) 74.4868 3.19067
\(546\) 0 0
\(547\) −5.13096 −0.219384 −0.109692 0.993966i \(-0.534986\pi\)
−0.109692 + 0.993966i \(0.534986\pi\)
\(548\) 0 0
\(549\) −5.03856 −0.215040
\(550\) 0 0
\(551\) −14.8677 −0.633386
\(552\) 0 0
\(553\) −10.1298 −0.430763
\(554\) 0 0
\(555\) −32.0367 −1.35988
\(556\) 0 0
\(557\) −39.1488 −1.65879 −0.829394 0.558664i \(-0.811314\pi\)
−0.829394 + 0.558664i \(0.811314\pi\)
\(558\) 0 0
\(559\) 15.2964 0.646970
\(560\) 0 0
\(561\) −0.868961 −0.0366875
\(562\) 0 0
\(563\) 26.5625 1.11947 0.559737 0.828670i \(-0.310902\pi\)
0.559737 + 0.828670i \(0.310902\pi\)
\(564\) 0 0
\(565\) 14.6445 0.616101
\(566\) 0 0
\(567\) 4.52941 0.190217
\(568\) 0 0
\(569\) −0.364054 −0.0152619 −0.00763097 0.999971i \(-0.502429\pi\)
−0.00763097 + 0.999971i \(0.502429\pi\)
\(570\) 0 0
\(571\) 22.2371 0.930592 0.465296 0.885155i \(-0.345948\pi\)
0.465296 + 0.885155i \(0.345948\pi\)
\(572\) 0 0
\(573\) −4.31692 −0.180342
\(574\) 0 0
\(575\) 63.9252 2.66586
\(576\) 0 0
\(577\) 13.1985 0.549459 0.274730 0.961521i \(-0.411412\pi\)
0.274730 + 0.961521i \(0.411412\pi\)
\(578\) 0 0
\(579\) −6.29825 −0.261747
\(580\) 0 0
\(581\) 17.7368 0.735846
\(582\) 0 0
\(583\) 2.68373 0.111149
\(584\) 0 0
\(585\) −14.2448 −0.588952
\(586\) 0 0
\(587\) −3.71450 −0.153314 −0.0766569 0.997058i \(-0.524425\pi\)
−0.0766569 + 0.997058i \(0.524425\pi\)
\(588\) 0 0
\(589\) 20.0235 0.825054
\(590\) 0 0
\(591\) 27.8337 1.14493
\(592\) 0 0
\(593\) 12.5057 0.513547 0.256774 0.966472i \(-0.417340\pi\)
0.256774 + 0.966472i \(0.417340\pi\)
\(594\) 0 0
\(595\) 16.1984 0.664070
\(596\) 0 0
\(597\) 3.11661 0.127555
\(598\) 0 0
\(599\) −17.6122 −0.719616 −0.359808 0.933026i \(-0.617158\pi\)
−0.359808 + 0.933026i \(0.617158\pi\)
\(600\) 0 0
\(601\) −39.9569 −1.62988 −0.814939 0.579547i \(-0.803230\pi\)
−0.814939 + 0.579547i \(0.803230\pi\)
\(602\) 0 0
\(603\) −3.07201 −0.125102
\(604\) 0 0
\(605\) 43.0119 1.74868
\(606\) 0 0
\(607\) 33.8689 1.37470 0.687348 0.726328i \(-0.258775\pi\)
0.687348 + 0.726328i \(0.258775\pi\)
\(608\) 0 0
\(609\) 10.8522 0.439753
\(610\) 0 0
\(611\) 30.3054 1.22603
\(612\) 0 0
\(613\) −2.27108 −0.0917280 −0.0458640 0.998948i \(-0.514604\pi\)
−0.0458640 + 0.998948i \(0.514604\pi\)
\(614\) 0 0
\(615\) −18.6383 −0.751570
\(616\) 0 0
\(617\) −34.7961 −1.40084 −0.700420 0.713731i \(-0.747004\pi\)
−0.700420 + 0.713731i \(0.747004\pi\)
\(618\) 0 0
\(619\) 2.01074 0.0808186 0.0404093 0.999183i \(-0.487134\pi\)
0.0404093 + 0.999183i \(0.487134\pi\)
\(620\) 0 0
\(621\) −4.58343 −0.183927
\(622\) 0 0
\(623\) −2.24996 −0.0901428
\(624\) 0 0
\(625\) 99.7844 3.99138
\(626\) 0 0
\(627\) 6.56309 0.262104
\(628\) 0 0
\(629\) 6.04696 0.241108
\(630\) 0 0
\(631\) −19.0081 −0.756699 −0.378350 0.925663i \(-0.623508\pi\)
−0.378350 + 0.925663i \(0.623508\pi\)
\(632\) 0 0
\(633\) 9.81779 0.390222
\(634\) 0 0
\(635\) 20.6305 0.818696
\(636\) 0 0
\(637\) 44.2303 1.75247
\(638\) 0 0
\(639\) 4.37291 0.172990
\(640\) 0 0
\(641\) −12.4540 −0.491902 −0.245951 0.969282i \(-0.579100\pi\)
−0.245951 + 0.969282i \(0.579100\pi\)
\(642\) 0 0
\(643\) −0.106778 −0.00421092 −0.00210546 0.999998i \(-0.500670\pi\)
−0.00210546 + 0.999998i \(0.500670\pi\)
\(644\) 0 0
\(645\) 20.3457 0.801112
\(646\) 0 0
\(647\) 21.7232 0.854026 0.427013 0.904246i \(-0.359566\pi\)
0.427013 + 0.904246i \(0.359566\pi\)
\(648\) 0 0
\(649\) 10.9790 0.430963
\(650\) 0 0
\(651\) −14.6155 −0.572826
\(652\) 0 0
\(653\) 25.5520 0.999926 0.499963 0.866047i \(-0.333347\pi\)
0.499963 + 0.866047i \(0.333347\pi\)
\(654\) 0 0
\(655\) −8.88850 −0.347303
\(656\) 0 0
\(657\) −8.07671 −0.315103
\(658\) 0 0
\(659\) −32.5153 −1.26662 −0.633308 0.773900i \(-0.718303\pi\)
−0.633308 + 0.773900i \(0.718303\pi\)
\(660\) 0 0
\(661\) −23.7138 −0.922361 −0.461181 0.887306i \(-0.652574\pi\)
−0.461181 + 0.887306i \(0.652574\pi\)
\(662\) 0 0
\(663\) 2.68873 0.104422
\(664\) 0 0
\(665\) −122.343 −4.74427
\(666\) 0 0
\(667\) −10.9816 −0.425210
\(668\) 0 0
\(669\) −2.96394 −0.114592
\(670\) 0 0
\(671\) 5.32900 0.205724
\(672\) 0 0
\(673\) 6.66566 0.256942 0.128471 0.991713i \(-0.458993\pi\)
0.128471 + 0.991713i \(0.458993\pi\)
\(674\) 0 0
\(675\) −13.9470 −0.536821
\(676\) 0 0
\(677\) −45.7883 −1.75979 −0.879893 0.475172i \(-0.842386\pi\)
−0.879893 + 0.475172i \(0.842386\pi\)
\(678\) 0 0
\(679\) −10.8076 −0.414757
\(680\) 0 0
\(681\) −22.2796 −0.853756
\(682\) 0 0
\(683\) 10.2127 0.390780 0.195390 0.980726i \(-0.437403\pi\)
0.195390 + 0.980726i \(0.437403\pi\)
\(684\) 0 0
\(685\) −46.6797 −1.78354
\(686\) 0 0
\(687\) 6.42292 0.245050
\(688\) 0 0
\(689\) −8.30398 −0.316357
\(690\) 0 0
\(691\) −36.7659 −1.39864 −0.699321 0.714808i \(-0.746514\pi\)
−0.699321 + 0.714808i \(0.746514\pi\)
\(692\) 0 0
\(693\) −4.79050 −0.181976
\(694\) 0 0
\(695\) −85.6578 −3.24918
\(696\) 0 0
\(697\) 3.51801 0.133254
\(698\) 0 0
\(699\) 2.07609 0.0785249
\(700\) 0 0
\(701\) 6.07273 0.229364 0.114682 0.993402i \(-0.463415\pi\)
0.114682 + 0.993402i \(0.463415\pi\)
\(702\) 0 0
\(703\) −45.6715 −1.72253
\(704\) 0 0
\(705\) 40.3091 1.51813
\(706\) 0 0
\(707\) 74.8377 2.81456
\(708\) 0 0
\(709\) −28.2925 −1.06255 −0.531274 0.847200i \(-0.678286\pi\)
−0.531274 + 0.847200i \(0.678286\pi\)
\(710\) 0 0
\(711\) −2.23645 −0.0838736
\(712\) 0 0
\(713\) 14.7898 0.553882
\(714\) 0 0
\(715\) 15.0660 0.563436
\(716\) 0 0
\(717\) −10.8471 −0.405091
\(718\) 0 0
\(719\) 15.3739 0.573349 0.286675 0.958028i \(-0.407450\pi\)
0.286675 + 0.958028i \(0.407450\pi\)
\(720\) 0 0
\(721\) 26.3474 0.981230
\(722\) 0 0
\(723\) 19.1121 0.710788
\(724\) 0 0
\(725\) −33.4162 −1.24105
\(726\) 0 0
\(727\) 6.36541 0.236080 0.118040 0.993009i \(-0.462339\pi\)
0.118040 + 0.993009i \(0.462339\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −3.84028 −0.142038
\(732\) 0 0
\(733\) 14.9431 0.551936 0.275968 0.961167i \(-0.411002\pi\)
0.275968 + 0.961167i \(0.411002\pi\)
\(734\) 0 0
\(735\) 58.8306 2.17000
\(736\) 0 0
\(737\) 3.24909 0.119682
\(738\) 0 0
\(739\) −20.2443 −0.744700 −0.372350 0.928092i \(-0.621448\pi\)
−0.372350 + 0.928092i \(0.621448\pi\)
\(740\) 0 0
\(741\) −20.3075 −0.746013
\(742\) 0 0
\(743\) 14.2351 0.522236 0.261118 0.965307i \(-0.415909\pi\)
0.261118 + 0.965307i \(0.415909\pi\)
\(744\) 0 0
\(745\) −60.2915 −2.20891
\(746\) 0 0
\(747\) 3.91592 0.143276
\(748\) 0 0
\(749\) 74.1695 2.71010
\(750\) 0 0
\(751\) −27.9012 −1.01813 −0.509065 0.860728i \(-0.670009\pi\)
−0.509065 + 0.860728i \(0.670009\pi\)
\(752\) 0 0
\(753\) 0.653466 0.0238136
\(754\) 0 0
\(755\) −43.4171 −1.58011
\(756\) 0 0
\(757\) −32.4604 −1.17979 −0.589897 0.807479i \(-0.700832\pi\)
−0.589897 + 0.807479i \(0.700832\pi\)
\(758\) 0 0
\(759\) 4.84763 0.175958
\(760\) 0 0
\(761\) 12.9118 0.468054 0.234027 0.972230i \(-0.424810\pi\)
0.234027 + 0.972230i \(0.424810\pi\)
\(762\) 0 0
\(763\) −77.5087 −2.80600
\(764\) 0 0
\(765\) 3.57628 0.129301
\(766\) 0 0
\(767\) −33.9711 −1.22663
\(768\) 0 0
\(769\) 34.6314 1.24884 0.624419 0.781089i \(-0.285336\pi\)
0.624419 + 0.781089i \(0.285336\pi\)
\(770\) 0 0
\(771\) −19.3408 −0.696541
\(772\) 0 0
\(773\) 9.40139 0.338145 0.169072 0.985604i \(-0.445923\pi\)
0.169072 + 0.985604i \(0.445923\pi\)
\(774\) 0 0
\(775\) 45.0042 1.61660
\(776\) 0 0
\(777\) 33.3364 1.19594
\(778\) 0 0
\(779\) −26.5708 −0.951999
\(780\) 0 0
\(781\) −4.62498 −0.165495
\(782\) 0 0
\(783\) 2.39594 0.0856239
\(784\) 0 0
\(785\) 66.7825 2.38357
\(786\) 0 0
\(787\) −4.10286 −0.146251 −0.0731256 0.997323i \(-0.523297\pi\)
−0.0731256 + 0.997323i \(0.523297\pi\)
\(788\) 0 0
\(789\) −6.11362 −0.217651
\(790\) 0 0
\(791\) −15.2387 −0.541824
\(792\) 0 0
\(793\) −16.4890 −0.585540
\(794\) 0 0
\(795\) −11.0451 −0.391729
\(796\) 0 0
\(797\) −7.29586 −0.258432 −0.129216 0.991616i \(-0.541246\pi\)
−0.129216 + 0.991616i \(0.541246\pi\)
\(798\) 0 0
\(799\) −7.60840 −0.269166
\(800\) 0 0
\(801\) −0.496745 −0.0175516
\(802\) 0 0
\(803\) 8.54229 0.301451
\(804\) 0 0
\(805\) −90.3654 −3.18496
\(806\) 0 0
\(807\) −16.9230 −0.595717
\(808\) 0 0
\(809\) 14.7709 0.519316 0.259658 0.965701i \(-0.416390\pi\)
0.259658 + 0.965701i \(0.416390\pi\)
\(810\) 0 0
\(811\) −45.2152 −1.58772 −0.793860 0.608101i \(-0.791932\pi\)
−0.793860 + 0.608101i \(0.791932\pi\)
\(812\) 0 0
\(813\) −15.2149 −0.533611
\(814\) 0 0
\(815\) −37.8160 −1.32464
\(816\) 0 0
\(817\) 29.0049 1.01475
\(818\) 0 0
\(819\) 14.8227 0.517949
\(820\) 0 0
\(821\) −41.8618 −1.46099 −0.730494 0.682919i \(-0.760710\pi\)
−0.730494 + 0.682919i \(0.760710\pi\)
\(822\) 0 0
\(823\) 44.4038 1.54782 0.773910 0.633296i \(-0.218298\pi\)
0.773910 + 0.633296i \(0.218298\pi\)
\(824\) 0 0
\(825\) 14.7510 0.513564
\(826\) 0 0
\(827\) −11.8056 −0.410522 −0.205261 0.978707i \(-0.565804\pi\)
−0.205261 + 0.978707i \(0.565804\pi\)
\(828\) 0 0
\(829\) 28.9232 1.00454 0.502272 0.864710i \(-0.332498\pi\)
0.502272 + 0.864710i \(0.332498\pi\)
\(830\) 0 0
\(831\) −28.5273 −0.989602
\(832\) 0 0
\(833\) −11.1044 −0.384743
\(834\) 0 0
\(835\) −84.6406 −2.92911
\(836\) 0 0
\(837\) −3.22680 −0.111534
\(838\) 0 0
\(839\) −2.73283 −0.0943477 −0.0471738 0.998887i \(-0.515021\pi\)
−0.0471738 + 0.998887i \(0.515021\pi\)
\(840\) 0 0
\(841\) −23.2595 −0.802051
\(842\) 0 0
\(843\) 12.3250 0.424496
\(844\) 0 0
\(845\) 9.96957 0.342964
\(846\) 0 0
\(847\) −44.7568 −1.53786
\(848\) 0 0
\(849\) 17.3636 0.595918
\(850\) 0 0
\(851\) −33.7339 −1.15638
\(852\) 0 0
\(853\) −38.8217 −1.32923 −0.664615 0.747186i \(-0.731404\pi\)
−0.664615 + 0.747186i \(0.731404\pi\)
\(854\) 0 0
\(855\) −27.0109 −0.923753
\(856\) 0 0
\(857\) −21.5394 −0.735773 −0.367887 0.929871i \(-0.619919\pi\)
−0.367887 + 0.929871i \(0.619919\pi\)
\(858\) 0 0
\(859\) 37.4784 1.27875 0.639373 0.768897i \(-0.279194\pi\)
0.639373 + 0.768897i \(0.279194\pi\)
\(860\) 0 0
\(861\) 19.3945 0.660962
\(862\) 0 0
\(863\) −40.0938 −1.36481 −0.682404 0.730975i \(-0.739066\pi\)
−0.682404 + 0.730975i \(0.739066\pi\)
\(864\) 0 0
\(865\) 44.5092 1.51336
\(866\) 0 0
\(867\) 16.3250 0.554425
\(868\) 0 0
\(869\) 2.36537 0.0802398
\(870\) 0 0
\(871\) −10.0533 −0.340644
\(872\) 0 0
\(873\) −2.38609 −0.0807569
\(874\) 0 0
\(875\) −176.397 −5.96330
\(876\) 0 0
\(877\) −16.4417 −0.555196 −0.277598 0.960697i \(-0.589538\pi\)
−0.277598 + 0.960697i \(0.589538\pi\)
\(878\) 0 0
\(879\) 14.7636 0.497962
\(880\) 0 0
\(881\) 46.2546 1.55836 0.779179 0.626801i \(-0.215636\pi\)
0.779179 + 0.626801i \(0.215636\pi\)
\(882\) 0 0
\(883\) 17.1895 0.578474 0.289237 0.957258i \(-0.406598\pi\)
0.289237 + 0.957258i \(0.406598\pi\)
\(884\) 0 0
\(885\) −45.1849 −1.51887
\(886\) 0 0
\(887\) −28.4684 −0.955874 −0.477937 0.878394i \(-0.658615\pi\)
−0.477937 + 0.878394i \(0.658615\pi\)
\(888\) 0 0
\(889\) −21.4674 −0.719995
\(890\) 0 0
\(891\) −1.05764 −0.0354324
\(892\) 0 0
\(893\) 57.4647 1.92298
\(894\) 0 0
\(895\) −5.27662 −0.176378
\(896\) 0 0
\(897\) −14.9995 −0.500820
\(898\) 0 0
\(899\) −7.73121 −0.257850
\(900\) 0 0
\(901\) 2.08478 0.0694540
\(902\) 0 0
\(903\) −21.1711 −0.704531
\(904\) 0 0
\(905\) 15.8889 0.528166
\(906\) 0 0
\(907\) 12.7422 0.423098 0.211549 0.977367i \(-0.432149\pi\)
0.211549 + 0.977367i \(0.432149\pi\)
\(908\) 0 0
\(909\) 16.5226 0.548021
\(910\) 0 0
\(911\) 8.19637 0.271558 0.135779 0.990739i \(-0.456646\pi\)
0.135779 + 0.990739i \(0.456646\pi\)
\(912\) 0 0
\(913\) −4.14165 −0.137069
\(914\) 0 0
\(915\) −21.9319 −0.725047
\(916\) 0 0
\(917\) 9.24910 0.305432
\(918\) 0 0
\(919\) 48.1024 1.58675 0.793377 0.608731i \(-0.208321\pi\)
0.793377 + 0.608731i \(0.208321\pi\)
\(920\) 0 0
\(921\) −12.2740 −0.404440
\(922\) 0 0
\(923\) 14.3106 0.471039
\(924\) 0 0
\(925\) −102.650 −3.37511
\(926\) 0 0
\(927\) 5.81697 0.191054
\(928\) 0 0
\(929\) −10.8455 −0.355830 −0.177915 0.984046i \(-0.556935\pi\)
−0.177915 + 0.984046i \(0.556935\pi\)
\(930\) 0 0
\(931\) 83.8690 2.74870
\(932\) 0 0
\(933\) 9.78212 0.320252
\(934\) 0 0
\(935\) −3.78243 −0.123699
\(936\) 0 0
\(937\) 40.7170 1.33017 0.665083 0.746770i \(-0.268396\pi\)
0.665083 + 0.746770i \(0.268396\pi\)
\(938\) 0 0
\(939\) −22.2407 −0.725799
\(940\) 0 0
\(941\) −21.2682 −0.693325 −0.346663 0.937990i \(-0.612685\pi\)
−0.346663 + 0.937990i \(0.612685\pi\)
\(942\) 0 0
\(943\) −19.6258 −0.639104
\(944\) 0 0
\(945\) 19.7157 0.641351
\(946\) 0 0
\(947\) −21.9072 −0.711889 −0.355945 0.934507i \(-0.615841\pi\)
−0.355945 + 0.934507i \(0.615841\pi\)
\(948\) 0 0
\(949\) −26.4315 −0.858003
\(950\) 0 0
\(951\) −29.8559 −0.968145
\(952\) 0 0
\(953\) −9.13776 −0.296001 −0.148001 0.988987i \(-0.547284\pi\)
−0.148001 + 0.988987i \(0.547284\pi\)
\(954\) 0 0
\(955\) −18.7908 −0.608055
\(956\) 0 0
\(957\) −2.53405 −0.0819143
\(958\) 0 0
\(959\) 48.5734 1.56852
\(960\) 0 0
\(961\) −20.5878 −0.664122
\(962\) 0 0
\(963\) 16.3751 0.527680
\(964\) 0 0
\(965\) −27.4152 −0.882525
\(966\) 0 0
\(967\) 59.0700 1.89956 0.949782 0.312912i \(-0.101304\pi\)
0.949782 + 0.312912i \(0.101304\pi\)
\(968\) 0 0
\(969\) 5.09834 0.163782
\(970\) 0 0
\(971\) 28.4647 0.913476 0.456738 0.889601i \(-0.349018\pi\)
0.456738 + 0.889601i \(0.349018\pi\)
\(972\) 0 0
\(973\) 89.1328 2.85747
\(974\) 0 0
\(975\) −45.6424 −1.46173
\(976\) 0 0
\(977\) 38.9169 1.24506 0.622531 0.782595i \(-0.286104\pi\)
0.622531 + 0.782595i \(0.286104\pi\)
\(978\) 0 0
\(979\) 0.525380 0.0167912
\(980\) 0 0
\(981\) −17.1123 −0.546354
\(982\) 0 0
\(983\) −15.0208 −0.479089 −0.239544 0.970885i \(-0.576998\pi\)
−0.239544 + 0.970885i \(0.576998\pi\)
\(984\) 0 0
\(985\) 121.155 3.86032
\(986\) 0 0
\(987\) −41.9444 −1.33511
\(988\) 0 0
\(989\) 21.4236 0.681232
\(990\) 0 0
\(991\) 12.2252 0.388346 0.194173 0.980967i \(-0.437798\pi\)
0.194173 + 0.980967i \(0.437798\pi\)
\(992\) 0 0
\(993\) −20.4854 −0.650085
\(994\) 0 0
\(995\) 13.5661 0.430073
\(996\) 0 0
\(997\) 25.9183 0.820841 0.410421 0.911896i \(-0.365382\pi\)
0.410421 + 0.911896i \(0.365382\pi\)
\(998\) 0 0
\(999\) 7.35998 0.232860
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 \(a_p\))