Properties

Label 4008.2.a.l.1.2
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.49351\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.49351 q^{5}\) \(+4.58171 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.49351 q^{5}\) \(+4.58171 q^{7}\) \(+1.00000 q^{9}\) \(+0.512480 q^{11}\) \(-0.325752 q^{13}\) \(-3.49351 q^{15}\) \(-2.49148 q^{17}\) \(+3.26410 q^{19}\) \(+4.58171 q^{21}\) \(-4.00623 q^{23}\) \(+7.20462 q^{25}\) \(+1.00000 q^{27}\) \(+1.72350 q^{29}\) \(+5.79709 q^{31}\) \(+0.512480 q^{33}\) \(-16.0063 q^{35}\) \(+7.03510 q^{37}\) \(-0.325752 q^{39}\) \(+1.69446 q^{41}\) \(-7.20067 q^{43}\) \(-3.49351 q^{45}\) \(+2.49012 q^{47}\) \(+13.9921 q^{49}\) \(-2.49148 q^{51}\) \(+2.26872 q^{53}\) \(-1.79036 q^{55}\) \(+3.26410 q^{57}\) \(-6.76876 q^{59}\) \(-1.57345 q^{61}\) \(+4.58171 q^{63}\) \(+1.13802 q^{65}\) \(+0.691665 q^{67}\) \(-4.00623 q^{69}\) \(+12.4421 q^{71}\) \(+3.41218 q^{73}\) \(+7.20462 q^{75}\) \(+2.34804 q^{77}\) \(-10.7644 q^{79}\) \(+1.00000 q^{81}\) \(-3.12519 q^{83}\) \(+8.70401 q^{85}\) \(+1.72350 q^{87}\) \(+15.5543 q^{89}\) \(-1.49250 q^{91}\) \(+5.79709 q^{93}\) \(-11.4032 q^{95}\) \(+8.68185 q^{97}\) \(+0.512480 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −3.49351 −1.56235 −0.781173 0.624315i \(-0.785378\pi\)
−0.781173 + 0.624315i \(0.785378\pi\)
\(6\) 0 0
\(7\) 4.58171 1.73172 0.865862 0.500283i \(-0.166771\pi\)
0.865862 + 0.500283i \(0.166771\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.512480 0.154519 0.0772593 0.997011i \(-0.475383\pi\)
0.0772593 + 0.997011i \(0.475383\pi\)
\(12\) 0 0
\(13\) −0.325752 −0.0903473 −0.0451737 0.998979i \(-0.514384\pi\)
−0.0451737 + 0.998979i \(0.514384\pi\)
\(14\) 0 0
\(15\) −3.49351 −0.902021
\(16\) 0 0
\(17\) −2.49148 −0.604273 −0.302136 0.953265i \(-0.597700\pi\)
−0.302136 + 0.953265i \(0.597700\pi\)
\(18\) 0 0
\(19\) 3.26410 0.748837 0.374418 0.927260i \(-0.377842\pi\)
0.374418 + 0.927260i \(0.377842\pi\)
\(20\) 0 0
\(21\) 4.58171 0.999812
\(22\) 0 0
\(23\) −4.00623 −0.835356 −0.417678 0.908595i \(-0.637156\pi\)
−0.417678 + 0.908595i \(0.637156\pi\)
\(24\) 0 0
\(25\) 7.20462 1.44092
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.72350 0.320045 0.160023 0.987113i \(-0.448843\pi\)
0.160023 + 0.987113i \(0.448843\pi\)
\(30\) 0 0
\(31\) 5.79709 1.04119 0.520594 0.853804i \(-0.325711\pi\)
0.520594 + 0.853804i \(0.325711\pi\)
\(32\) 0 0
\(33\) 0.512480 0.0892114
\(34\) 0 0
\(35\) −16.0063 −2.70555
\(36\) 0 0
\(37\) 7.03510 1.15656 0.578282 0.815837i \(-0.303723\pi\)
0.578282 + 0.815837i \(0.303723\pi\)
\(38\) 0 0
\(39\) −0.325752 −0.0521621
\(40\) 0 0
\(41\) 1.69446 0.264630 0.132315 0.991208i \(-0.457759\pi\)
0.132315 + 0.991208i \(0.457759\pi\)
\(42\) 0 0
\(43\) −7.20067 −1.09809 −0.549046 0.835792i \(-0.685009\pi\)
−0.549046 + 0.835792i \(0.685009\pi\)
\(44\) 0 0
\(45\) −3.49351 −0.520782
\(46\) 0 0
\(47\) 2.49012 0.363222 0.181611 0.983370i \(-0.441869\pi\)
0.181611 + 0.983370i \(0.441869\pi\)
\(48\) 0 0
\(49\) 13.9921 1.99887
\(50\) 0 0
\(51\) −2.49148 −0.348877
\(52\) 0 0
\(53\) 2.26872 0.311633 0.155817 0.987786i \(-0.450199\pi\)
0.155817 + 0.987786i \(0.450199\pi\)
\(54\) 0 0
\(55\) −1.79036 −0.241411
\(56\) 0 0
\(57\) 3.26410 0.432341
\(58\) 0 0
\(59\) −6.76876 −0.881218 −0.440609 0.897699i \(-0.645237\pi\)
−0.440609 + 0.897699i \(0.645237\pi\)
\(60\) 0 0
\(61\) −1.57345 −0.201459 −0.100730 0.994914i \(-0.532118\pi\)
−0.100730 + 0.994914i \(0.532118\pi\)
\(62\) 0 0
\(63\) 4.58171 0.577241
\(64\) 0 0
\(65\) 1.13802 0.141154
\(66\) 0 0
\(67\) 0.691665 0.0845003 0.0422501 0.999107i \(-0.486547\pi\)
0.0422501 + 0.999107i \(0.486547\pi\)
\(68\) 0 0
\(69\) −4.00623 −0.482293
\(70\) 0 0
\(71\) 12.4421 1.47661 0.738304 0.674468i \(-0.235627\pi\)
0.738304 + 0.674468i \(0.235627\pi\)
\(72\) 0 0
\(73\) 3.41218 0.399366 0.199683 0.979861i \(-0.436009\pi\)
0.199683 + 0.979861i \(0.436009\pi\)
\(74\) 0 0
\(75\) 7.20462 0.831918
\(76\) 0 0
\(77\) 2.34804 0.267584
\(78\) 0 0
\(79\) −10.7644 −1.21110 −0.605548 0.795809i \(-0.707046\pi\)
−0.605548 + 0.795809i \(0.707046\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.12519 −0.343035 −0.171517 0.985181i \(-0.554867\pi\)
−0.171517 + 0.985181i \(0.554867\pi\)
\(84\) 0 0
\(85\) 8.70401 0.944083
\(86\) 0 0
\(87\) 1.72350 0.184778
\(88\) 0 0
\(89\) 15.5543 1.64876 0.824378 0.566040i \(-0.191525\pi\)
0.824378 + 0.566040i \(0.191525\pi\)
\(90\) 0 0
\(91\) −1.49250 −0.156457
\(92\) 0 0
\(93\) 5.79709 0.601130
\(94\) 0 0
\(95\) −11.4032 −1.16994
\(96\) 0 0
\(97\) 8.68185 0.881508 0.440754 0.897628i \(-0.354711\pi\)
0.440754 + 0.897628i \(0.354711\pi\)
\(98\) 0 0
\(99\) 0.512480 0.0515062
\(100\) 0 0
\(101\) −4.25125 −0.423015 −0.211508 0.977376i \(-0.567837\pi\)
−0.211508 + 0.977376i \(0.567837\pi\)
\(102\) 0 0
\(103\) −1.64310 −0.161899 −0.0809496 0.996718i \(-0.525795\pi\)
−0.0809496 + 0.996718i \(0.525795\pi\)
\(104\) 0 0
\(105\) −16.0063 −1.56205
\(106\) 0 0
\(107\) 19.3290 1.86861 0.934305 0.356475i \(-0.116022\pi\)
0.934305 + 0.356475i \(0.116022\pi\)
\(108\) 0 0
\(109\) 0.467960 0.0448224 0.0224112 0.999749i \(-0.492866\pi\)
0.0224112 + 0.999749i \(0.492866\pi\)
\(110\) 0 0
\(111\) 7.03510 0.667743
\(112\) 0 0
\(113\) −10.0604 −0.946405 −0.473202 0.880954i \(-0.656902\pi\)
−0.473202 + 0.880954i \(0.656902\pi\)
\(114\) 0 0
\(115\) 13.9958 1.30512
\(116\) 0 0
\(117\) −0.325752 −0.0301158
\(118\) 0 0
\(119\) −11.4152 −1.04643
\(120\) 0 0
\(121\) −10.7374 −0.976124
\(122\) 0 0
\(123\) 1.69446 0.152784
\(124\) 0 0
\(125\) −7.70186 −0.688875
\(126\) 0 0
\(127\) 7.02371 0.623254 0.311627 0.950205i \(-0.399126\pi\)
0.311627 + 0.950205i \(0.399126\pi\)
\(128\) 0 0
\(129\) −7.20067 −0.633984
\(130\) 0 0
\(131\) −7.39191 −0.645834 −0.322917 0.946427i \(-0.604663\pi\)
−0.322917 + 0.946427i \(0.604663\pi\)
\(132\) 0 0
\(133\) 14.9552 1.29678
\(134\) 0 0
\(135\) −3.49351 −0.300674
\(136\) 0 0
\(137\) 8.76010 0.748426 0.374213 0.927343i \(-0.377913\pi\)
0.374213 + 0.927343i \(0.377913\pi\)
\(138\) 0 0
\(139\) 3.16611 0.268546 0.134273 0.990944i \(-0.457130\pi\)
0.134273 + 0.990944i \(0.457130\pi\)
\(140\) 0 0
\(141\) 2.49012 0.209706
\(142\) 0 0
\(143\) −0.166941 −0.0139603
\(144\) 0 0
\(145\) −6.02105 −0.500021
\(146\) 0 0
\(147\) 13.9921 1.15405
\(148\) 0 0
\(149\) 10.8088 0.885488 0.442744 0.896648i \(-0.354005\pi\)
0.442744 + 0.896648i \(0.354005\pi\)
\(150\) 0 0
\(151\) 14.5677 1.18550 0.592750 0.805386i \(-0.298042\pi\)
0.592750 + 0.805386i \(0.298042\pi\)
\(152\) 0 0
\(153\) −2.49148 −0.201424
\(154\) 0 0
\(155\) −20.2522 −1.62670
\(156\) 0 0
\(157\) −3.35228 −0.267541 −0.133771 0.991012i \(-0.542709\pi\)
−0.133771 + 0.991012i \(0.542709\pi\)
\(158\) 0 0
\(159\) 2.26872 0.179921
\(160\) 0 0
\(161\) −18.3554 −1.44661
\(162\) 0 0
\(163\) −4.58993 −0.359511 −0.179756 0.983711i \(-0.557531\pi\)
−0.179756 + 0.983711i \(0.557531\pi\)
\(164\) 0 0
\(165\) −1.79036 −0.139379
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.8939 −0.991837
\(170\) 0 0
\(171\) 3.26410 0.249612
\(172\) 0 0
\(173\) 16.8765 1.28310 0.641549 0.767082i \(-0.278292\pi\)
0.641549 + 0.767082i \(0.278292\pi\)
\(174\) 0 0
\(175\) 33.0095 2.49528
\(176\) 0 0
\(177\) −6.76876 −0.508771
\(178\) 0 0
\(179\) −24.6247 −1.84053 −0.920266 0.391292i \(-0.872028\pi\)
−0.920266 + 0.391292i \(0.872028\pi\)
\(180\) 0 0
\(181\) 1.54891 0.115130 0.0575648 0.998342i \(-0.481666\pi\)
0.0575648 + 0.998342i \(0.481666\pi\)
\(182\) 0 0
\(183\) −1.57345 −0.116312
\(184\) 0 0
\(185\) −24.5772 −1.80695
\(186\) 0 0
\(187\) −1.27683 −0.0933714
\(188\) 0 0
\(189\) 4.58171 0.333271
\(190\) 0 0
\(191\) 1.85499 0.134222 0.0671111 0.997746i \(-0.478622\pi\)
0.0671111 + 0.997746i \(0.478622\pi\)
\(192\) 0 0
\(193\) 19.6759 1.41630 0.708151 0.706061i \(-0.249530\pi\)
0.708151 + 0.706061i \(0.249530\pi\)
\(194\) 0 0
\(195\) 1.13802 0.0814952
\(196\) 0 0
\(197\) 25.0223 1.78276 0.891382 0.453252i \(-0.149736\pi\)
0.891382 + 0.453252i \(0.149736\pi\)
\(198\) 0 0
\(199\) 23.2466 1.64791 0.823953 0.566659i \(-0.191764\pi\)
0.823953 + 0.566659i \(0.191764\pi\)
\(200\) 0 0
\(201\) 0.691665 0.0487863
\(202\) 0 0
\(203\) 7.89657 0.554230
\(204\) 0 0
\(205\) −5.91962 −0.413444
\(206\) 0 0
\(207\) −4.00623 −0.278452
\(208\) 0 0
\(209\) 1.67279 0.115709
\(210\) 0 0
\(211\) −8.45455 −0.582035 −0.291018 0.956718i \(-0.593994\pi\)
−0.291018 + 0.956718i \(0.593994\pi\)
\(212\) 0 0
\(213\) 12.4421 0.852520
\(214\) 0 0
\(215\) 25.1556 1.71560
\(216\) 0 0
\(217\) 26.5606 1.80305
\(218\) 0 0
\(219\) 3.41218 0.230574
\(220\) 0 0
\(221\) 0.811605 0.0545944
\(222\) 0 0
\(223\) 19.8078 1.32643 0.663215 0.748429i \(-0.269191\pi\)
0.663215 + 0.748429i \(0.269191\pi\)
\(224\) 0 0
\(225\) 7.20462 0.480308
\(226\) 0 0
\(227\) −1.09680 −0.0727970 −0.0363985 0.999337i \(-0.511589\pi\)
−0.0363985 + 0.999337i \(0.511589\pi\)
\(228\) 0 0
\(229\) −10.0699 −0.665441 −0.332720 0.943026i \(-0.607967\pi\)
−0.332720 + 0.943026i \(0.607967\pi\)
\(230\) 0 0
\(231\) 2.34804 0.154490
\(232\) 0 0
\(233\) 5.01463 0.328519 0.164260 0.986417i \(-0.447477\pi\)
0.164260 + 0.986417i \(0.447477\pi\)
\(234\) 0 0
\(235\) −8.69927 −0.567478
\(236\) 0 0
\(237\) −10.7644 −0.699226
\(238\) 0 0
\(239\) 16.8946 1.09282 0.546410 0.837518i \(-0.315994\pi\)
0.546410 + 0.837518i \(0.315994\pi\)
\(240\) 0 0
\(241\) 14.0016 0.901924 0.450962 0.892543i \(-0.351081\pi\)
0.450962 + 0.892543i \(0.351081\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −48.8815 −3.12292
\(246\) 0 0
\(247\) −1.06329 −0.0676554
\(248\) 0 0
\(249\) −3.12519 −0.198051
\(250\) 0 0
\(251\) 20.8610 1.31673 0.658367 0.752697i \(-0.271247\pi\)
0.658367 + 0.752697i \(0.271247\pi\)
\(252\) 0 0
\(253\) −2.05311 −0.129078
\(254\) 0 0
\(255\) 8.70401 0.545066
\(256\) 0 0
\(257\) 15.0215 0.937018 0.468509 0.883459i \(-0.344791\pi\)
0.468509 + 0.883459i \(0.344791\pi\)
\(258\) 0 0
\(259\) 32.2328 2.00285
\(260\) 0 0
\(261\) 1.72350 0.106682
\(262\) 0 0
\(263\) 9.66555 0.596003 0.298002 0.954565i \(-0.403680\pi\)
0.298002 + 0.954565i \(0.403680\pi\)
\(264\) 0 0
\(265\) −7.92581 −0.486879
\(266\) 0 0
\(267\) 15.5543 0.951909
\(268\) 0 0
\(269\) 11.0300 0.672510 0.336255 0.941771i \(-0.390840\pi\)
0.336255 + 0.941771i \(0.390840\pi\)
\(270\) 0 0
\(271\) 27.3714 1.66269 0.831347 0.555754i \(-0.187570\pi\)
0.831347 + 0.555754i \(0.187570\pi\)
\(272\) 0 0
\(273\) −1.49250 −0.0903303
\(274\) 0 0
\(275\) 3.69222 0.222650
\(276\) 0 0
\(277\) −14.2246 −0.854675 −0.427338 0.904092i \(-0.640548\pi\)
−0.427338 + 0.904092i \(0.640548\pi\)
\(278\) 0 0
\(279\) 5.79709 0.347063
\(280\) 0 0
\(281\) 7.17980 0.428311 0.214156 0.976800i \(-0.431300\pi\)
0.214156 + 0.976800i \(0.431300\pi\)
\(282\) 0 0
\(283\) −7.49336 −0.445434 −0.222717 0.974883i \(-0.571493\pi\)
−0.222717 + 0.974883i \(0.571493\pi\)
\(284\) 0 0
\(285\) −11.4032 −0.675466
\(286\) 0 0
\(287\) 7.76354 0.458267
\(288\) 0 0
\(289\) −10.7925 −0.634855
\(290\) 0 0
\(291\) 8.68185 0.508939
\(292\) 0 0
\(293\) −22.4024 −1.30876 −0.654380 0.756166i \(-0.727070\pi\)
−0.654380 + 0.756166i \(0.727070\pi\)
\(294\) 0 0
\(295\) 23.6467 1.37677
\(296\) 0 0
\(297\) 0.512480 0.0297371
\(298\) 0 0
\(299\) 1.30504 0.0754722
\(300\) 0 0
\(301\) −32.9914 −1.90159
\(302\) 0 0
\(303\) −4.25125 −0.244228
\(304\) 0 0
\(305\) 5.49685 0.314749
\(306\) 0 0
\(307\) 7.30538 0.416940 0.208470 0.978029i \(-0.433152\pi\)
0.208470 + 0.978029i \(0.433152\pi\)
\(308\) 0 0
\(309\) −1.64310 −0.0934725
\(310\) 0 0
\(311\) −26.7279 −1.51560 −0.757800 0.652487i \(-0.773726\pi\)
−0.757800 + 0.652487i \(0.773726\pi\)
\(312\) 0 0
\(313\) −19.0884 −1.07894 −0.539469 0.842005i \(-0.681375\pi\)
−0.539469 + 0.842005i \(0.681375\pi\)
\(314\) 0 0
\(315\) −16.0063 −0.901851
\(316\) 0 0
\(317\) −0.844016 −0.0474047 −0.0237023 0.999719i \(-0.507545\pi\)
−0.0237023 + 0.999719i \(0.507545\pi\)
\(318\) 0 0
\(319\) 0.883258 0.0494530
\(320\) 0 0
\(321\) 19.3290 1.07884
\(322\) 0 0
\(323\) −8.13245 −0.452502
\(324\) 0 0
\(325\) −2.34692 −0.130184
\(326\) 0 0
\(327\) 0.467960 0.0258782
\(328\) 0 0
\(329\) 11.4090 0.629000
\(330\) 0 0
\(331\) −0.805305 −0.0442636 −0.0221318 0.999755i \(-0.507045\pi\)
−0.0221318 + 0.999755i \(0.507045\pi\)
\(332\) 0 0
\(333\) 7.03510 0.385521
\(334\) 0 0
\(335\) −2.41634 −0.132019
\(336\) 0 0
\(337\) 1.49693 0.0815429 0.0407715 0.999168i \(-0.487018\pi\)
0.0407715 + 0.999168i \(0.487018\pi\)
\(338\) 0 0
\(339\) −10.0604 −0.546407
\(340\) 0 0
\(341\) 2.97089 0.160883
\(342\) 0 0
\(343\) 32.0357 1.72977
\(344\) 0 0
\(345\) 13.9958 0.753509
\(346\) 0 0
\(347\) −23.4606 −1.25943 −0.629715 0.776826i \(-0.716828\pi\)
−0.629715 + 0.776826i \(0.716828\pi\)
\(348\) 0 0
\(349\) −19.0540 −1.01994 −0.509970 0.860192i \(-0.670343\pi\)
−0.509970 + 0.860192i \(0.670343\pi\)
\(350\) 0 0
\(351\) −0.325752 −0.0173874
\(352\) 0 0
\(353\) −18.1020 −0.963471 −0.481735 0.876317i \(-0.659993\pi\)
−0.481735 + 0.876317i \(0.659993\pi\)
\(354\) 0 0
\(355\) −43.4667 −2.30697
\(356\) 0 0
\(357\) −11.4152 −0.604159
\(358\) 0 0
\(359\) 8.02286 0.423430 0.211715 0.977331i \(-0.432095\pi\)
0.211715 + 0.977331i \(0.432095\pi\)
\(360\) 0 0
\(361\) −8.34562 −0.439243
\(362\) 0 0
\(363\) −10.7374 −0.563565
\(364\) 0 0
\(365\) −11.9205 −0.623948
\(366\) 0 0
\(367\) −6.45266 −0.336826 −0.168413 0.985716i \(-0.553864\pi\)
−0.168413 + 0.985716i \(0.553864\pi\)
\(368\) 0 0
\(369\) 1.69446 0.0882101
\(370\) 0 0
\(371\) 10.3946 0.539663
\(372\) 0 0
\(373\) 6.68132 0.345946 0.172973 0.984927i \(-0.444663\pi\)
0.172973 + 0.984927i \(0.444663\pi\)
\(374\) 0 0
\(375\) −7.70186 −0.397722
\(376\) 0 0
\(377\) −0.561432 −0.0289152
\(378\) 0 0
\(379\) −32.6658 −1.67793 −0.838966 0.544184i \(-0.816839\pi\)
−0.838966 + 0.544184i \(0.816839\pi\)
\(380\) 0 0
\(381\) 7.02371 0.359836
\(382\) 0 0
\(383\) 12.4445 0.635884 0.317942 0.948110i \(-0.397008\pi\)
0.317942 + 0.948110i \(0.397008\pi\)
\(384\) 0 0
\(385\) −8.20289 −0.418058
\(386\) 0 0
\(387\) −7.20067 −0.366031
\(388\) 0 0
\(389\) 1.21421 0.0615628 0.0307814 0.999526i \(-0.490200\pi\)
0.0307814 + 0.999526i \(0.490200\pi\)
\(390\) 0 0
\(391\) 9.98144 0.504783
\(392\) 0 0
\(393\) −7.39191 −0.372873
\(394\) 0 0
\(395\) 37.6057 1.89215
\(396\) 0 0
\(397\) 18.2956 0.918231 0.459116 0.888376i \(-0.348166\pi\)
0.459116 + 0.888376i \(0.348166\pi\)
\(398\) 0 0
\(399\) 14.9552 0.748696
\(400\) 0 0
\(401\) −4.88106 −0.243748 −0.121874 0.992546i \(-0.538890\pi\)
−0.121874 + 0.992546i \(0.538890\pi\)
\(402\) 0 0
\(403\) −1.88841 −0.0940686
\(404\) 0 0
\(405\) −3.49351 −0.173594
\(406\) 0 0
\(407\) 3.60535 0.178711
\(408\) 0 0
\(409\) −11.2838 −0.557947 −0.278973 0.960299i \(-0.589994\pi\)
−0.278973 + 0.960299i \(0.589994\pi\)
\(410\) 0 0
\(411\) 8.76010 0.432104
\(412\) 0 0
\(413\) −31.0125 −1.52603
\(414\) 0 0
\(415\) 10.9179 0.535939
\(416\) 0 0
\(417\) 3.16611 0.155045
\(418\) 0 0
\(419\) 22.7280 1.11034 0.555168 0.831738i \(-0.312654\pi\)
0.555168 + 0.831738i \(0.312654\pi\)
\(420\) 0 0
\(421\) −19.9399 −0.971810 −0.485905 0.874012i \(-0.661510\pi\)
−0.485905 + 0.874012i \(0.661510\pi\)
\(422\) 0 0
\(423\) 2.49012 0.121074
\(424\) 0 0
\(425\) −17.9502 −0.870711
\(426\) 0 0
\(427\) −7.20907 −0.348872
\(428\) 0 0
\(429\) −0.166941 −0.00806001
\(430\) 0 0
\(431\) −13.4845 −0.649525 −0.324763 0.945796i \(-0.605284\pi\)
−0.324763 + 0.945796i \(0.605284\pi\)
\(432\) 0 0
\(433\) −30.6652 −1.47368 −0.736839 0.676068i \(-0.763682\pi\)
−0.736839 + 0.676068i \(0.763682\pi\)
\(434\) 0 0
\(435\) −6.02105 −0.288687
\(436\) 0 0
\(437\) −13.0767 −0.625546
\(438\) 0 0
\(439\) −7.49335 −0.357638 −0.178819 0.983882i \(-0.557228\pi\)
−0.178819 + 0.983882i \(0.557228\pi\)
\(440\) 0 0
\(441\) 13.9921 0.666290
\(442\) 0 0
\(443\) 6.21514 0.295290 0.147645 0.989040i \(-0.452831\pi\)
0.147645 + 0.989040i \(0.452831\pi\)
\(444\) 0 0
\(445\) −54.3392 −2.57593
\(446\) 0 0
\(447\) 10.8088 0.511237
\(448\) 0 0
\(449\) 18.3577 0.866354 0.433177 0.901309i \(-0.357393\pi\)
0.433177 + 0.901309i \(0.357393\pi\)
\(450\) 0 0
\(451\) 0.868378 0.0408903
\(452\) 0 0
\(453\) 14.5677 0.684449
\(454\) 0 0
\(455\) 5.21407 0.244439
\(456\) 0 0
\(457\) −29.7113 −1.38984 −0.694918 0.719089i \(-0.744559\pi\)
−0.694918 + 0.719089i \(0.744559\pi\)
\(458\) 0 0
\(459\) −2.49148 −0.116292
\(460\) 0 0
\(461\) −10.4413 −0.486301 −0.243150 0.969989i \(-0.578181\pi\)
−0.243150 + 0.969989i \(0.578181\pi\)
\(462\) 0 0
\(463\) 12.4434 0.578295 0.289147 0.957285i \(-0.406628\pi\)
0.289147 + 0.957285i \(0.406628\pi\)
\(464\) 0 0
\(465\) −20.2522 −0.939173
\(466\) 0 0
\(467\) −15.8612 −0.733969 −0.366985 0.930227i \(-0.619610\pi\)
−0.366985 + 0.930227i \(0.619610\pi\)
\(468\) 0 0
\(469\) 3.16901 0.146331
\(470\) 0 0
\(471\) −3.35228 −0.154465
\(472\) 0 0
\(473\) −3.69020 −0.169676
\(474\) 0 0
\(475\) 23.5166 1.07902
\(476\) 0 0
\(477\) 2.26872 0.103878
\(478\) 0 0
\(479\) 17.6120 0.804712 0.402356 0.915483i \(-0.368191\pi\)
0.402356 + 0.915483i \(0.368191\pi\)
\(480\) 0 0
\(481\) −2.29170 −0.104492
\(482\) 0 0
\(483\) −18.3554 −0.835199
\(484\) 0 0
\(485\) −30.3301 −1.37722
\(486\) 0 0
\(487\) 12.9871 0.588499 0.294250 0.955729i \(-0.404930\pi\)
0.294250 + 0.955729i \(0.404930\pi\)
\(488\) 0 0
\(489\) −4.58993 −0.207564
\(490\) 0 0
\(491\) −24.0244 −1.08420 −0.542102 0.840313i \(-0.682371\pi\)
−0.542102 + 0.840313i \(0.682371\pi\)
\(492\) 0 0
\(493\) −4.29406 −0.193395
\(494\) 0 0
\(495\) −1.79036 −0.0804705
\(496\) 0 0
\(497\) 57.0062 2.55708
\(498\) 0 0
\(499\) −36.3018 −1.62509 −0.812545 0.582899i \(-0.801918\pi\)
−0.812545 + 0.582899i \(0.801918\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −38.7818 −1.72920 −0.864598 0.502464i \(-0.832427\pi\)
−0.864598 + 0.502464i \(0.832427\pi\)
\(504\) 0 0
\(505\) 14.8518 0.660896
\(506\) 0 0
\(507\) −12.8939 −0.572638
\(508\) 0 0
\(509\) −36.7197 −1.62757 −0.813786 0.581165i \(-0.802597\pi\)
−0.813786 + 0.581165i \(0.802597\pi\)
\(510\) 0 0
\(511\) 15.6336 0.691592
\(512\) 0 0
\(513\) 3.26410 0.144114
\(514\) 0 0
\(515\) 5.74018 0.252942
\(516\) 0 0
\(517\) 1.27614 0.0561245
\(518\) 0 0
\(519\) 16.8765 0.740797
\(520\) 0 0
\(521\) 9.85756 0.431867 0.215934 0.976408i \(-0.430720\pi\)
0.215934 + 0.976408i \(0.430720\pi\)
\(522\) 0 0
\(523\) 31.4813 1.37658 0.688290 0.725435i \(-0.258362\pi\)
0.688290 + 0.725435i \(0.258362\pi\)
\(524\) 0 0
\(525\) 33.0095 1.44065
\(526\) 0 0
\(527\) −14.4433 −0.629161
\(528\) 0 0
\(529\) −6.95013 −0.302180
\(530\) 0 0
\(531\) −6.76876 −0.293739
\(532\) 0 0
\(533\) −0.551974 −0.0239087
\(534\) 0 0
\(535\) −67.5262 −2.91941
\(536\) 0 0
\(537\) −24.6247 −1.06263
\(538\) 0 0
\(539\) 7.17067 0.308863
\(540\) 0 0
\(541\) 11.6002 0.498729 0.249365 0.968410i \(-0.419778\pi\)
0.249365 + 0.968410i \(0.419778\pi\)
\(542\) 0 0
\(543\) 1.54891 0.0664701
\(544\) 0 0
\(545\) −1.63482 −0.0700281
\(546\) 0 0
\(547\) 7.64269 0.326778 0.163389 0.986562i \(-0.447757\pi\)
0.163389 + 0.986562i \(0.447757\pi\)
\(548\) 0 0
\(549\) −1.57345 −0.0671530
\(550\) 0 0
\(551\) 5.62567 0.239662
\(552\) 0 0
\(553\) −49.3196 −2.09728
\(554\) 0 0
\(555\) −24.5772 −1.04324
\(556\) 0 0
\(557\) 8.11952 0.344035 0.172018 0.985094i \(-0.444971\pi\)
0.172018 + 0.985094i \(0.444971\pi\)
\(558\) 0 0
\(559\) 2.34563 0.0992097
\(560\) 0 0
\(561\) −1.27683 −0.0539080
\(562\) 0 0
\(563\) −20.6113 −0.868663 −0.434332 0.900753i \(-0.643015\pi\)
−0.434332 + 0.900753i \(0.643015\pi\)
\(564\) 0 0
\(565\) 35.1462 1.47861
\(566\) 0 0
\(567\) 4.58171 0.192414
\(568\) 0 0
\(569\) 12.2528 0.513664 0.256832 0.966456i \(-0.417321\pi\)
0.256832 + 0.966456i \(0.417321\pi\)
\(570\) 0 0
\(571\) −34.0736 −1.42593 −0.712967 0.701197i \(-0.752649\pi\)
−0.712967 + 0.701197i \(0.752649\pi\)
\(572\) 0 0
\(573\) 1.85499 0.0774932
\(574\) 0 0
\(575\) −28.8633 −1.20368
\(576\) 0 0
\(577\) 2.05077 0.0853745 0.0426873 0.999088i \(-0.486408\pi\)
0.0426873 + 0.999088i \(0.486408\pi\)
\(578\) 0 0
\(579\) 19.6759 0.817702
\(580\) 0 0
\(581\) −14.3187 −0.594041
\(582\) 0 0
\(583\) 1.16268 0.0481531
\(584\) 0 0
\(585\) 1.13802 0.0470513
\(586\) 0 0
\(587\) 27.2048 1.12286 0.561430 0.827524i \(-0.310251\pi\)
0.561430 + 0.827524i \(0.310251\pi\)
\(588\) 0 0
\(589\) 18.9223 0.779680
\(590\) 0 0
\(591\) 25.0223 1.02928
\(592\) 0 0
\(593\) −13.2090 −0.542429 −0.271215 0.962519i \(-0.587425\pi\)
−0.271215 + 0.962519i \(0.587425\pi\)
\(594\) 0 0
\(595\) 39.8793 1.63489
\(596\) 0 0
\(597\) 23.2466 0.951419
\(598\) 0 0
\(599\) −33.8049 −1.38123 −0.690614 0.723223i \(-0.742660\pi\)
−0.690614 + 0.723223i \(0.742660\pi\)
\(600\) 0 0
\(601\) 9.52887 0.388691 0.194345 0.980933i \(-0.437742\pi\)
0.194345 + 0.980933i \(0.437742\pi\)
\(602\) 0 0
\(603\) 0.691665 0.0281668
\(604\) 0 0
\(605\) 37.5111 1.52504
\(606\) 0 0
\(607\) −17.2279 −0.699258 −0.349629 0.936888i \(-0.613692\pi\)
−0.349629 + 0.936888i \(0.613692\pi\)
\(608\) 0 0
\(609\) 7.89657 0.319985
\(610\) 0 0
\(611\) −0.811162 −0.0328161
\(612\) 0 0
\(613\) −44.0981 −1.78111 −0.890553 0.454880i \(-0.849682\pi\)
−0.890553 + 0.454880i \(0.849682\pi\)
\(614\) 0 0
\(615\) −5.91962 −0.238702
\(616\) 0 0
\(617\) 31.7800 1.27941 0.639706 0.768619i \(-0.279056\pi\)
0.639706 + 0.768619i \(0.279056\pi\)
\(618\) 0 0
\(619\) 2.00109 0.0804307 0.0402153 0.999191i \(-0.487196\pi\)
0.0402153 + 0.999191i \(0.487196\pi\)
\(620\) 0 0
\(621\) −4.00623 −0.160764
\(622\) 0 0
\(623\) 71.2655 2.85519
\(624\) 0 0
\(625\) −9.11657 −0.364663
\(626\) 0 0
\(627\) 1.67279 0.0668048
\(628\) 0 0
\(629\) −17.5278 −0.698880
\(630\) 0 0
\(631\) 42.1185 1.67671 0.838355 0.545125i \(-0.183518\pi\)
0.838355 + 0.545125i \(0.183518\pi\)
\(632\) 0 0
\(633\) −8.45455 −0.336038
\(634\) 0 0
\(635\) −24.5374 −0.973737
\(636\) 0 0
\(637\) −4.55795 −0.180593
\(638\) 0 0
\(639\) 12.4421 0.492203
\(640\) 0 0
\(641\) 8.22836 0.325001 0.162500 0.986708i \(-0.448044\pi\)
0.162500 + 0.986708i \(0.448044\pi\)
\(642\) 0 0
\(643\) 7.04621 0.277876 0.138938 0.990301i \(-0.455631\pi\)
0.138938 + 0.990301i \(0.455631\pi\)
\(644\) 0 0
\(645\) 25.1556 0.990502
\(646\) 0 0
\(647\) −45.5212 −1.78962 −0.894812 0.446444i \(-0.852690\pi\)
−0.894812 + 0.446444i \(0.852690\pi\)
\(648\) 0 0
\(649\) −3.46886 −0.136165
\(650\) 0 0
\(651\) 26.5606 1.04099
\(652\) 0 0
\(653\) 29.4865 1.15389 0.576947 0.816782i \(-0.304244\pi\)
0.576947 + 0.816782i \(0.304244\pi\)
\(654\) 0 0
\(655\) 25.8237 1.00902
\(656\) 0 0
\(657\) 3.41218 0.133122
\(658\) 0 0
\(659\) −26.5112 −1.03273 −0.516364 0.856369i \(-0.672715\pi\)
−0.516364 + 0.856369i \(0.672715\pi\)
\(660\) 0 0
\(661\) −16.4928 −0.641494 −0.320747 0.947165i \(-0.603934\pi\)
−0.320747 + 0.947165i \(0.603934\pi\)
\(662\) 0 0
\(663\) 0.811605 0.0315201
\(664\) 0 0
\(665\) −52.2461 −2.02602
\(666\) 0 0
\(667\) −6.90472 −0.267352
\(668\) 0 0
\(669\) 19.8078 0.765815
\(670\) 0 0
\(671\) −0.806360 −0.0311292
\(672\) 0 0
\(673\) 44.9616 1.73314 0.866571 0.499054i \(-0.166319\pi\)
0.866571 + 0.499054i \(0.166319\pi\)
\(674\) 0 0
\(675\) 7.20462 0.277306
\(676\) 0 0
\(677\) −27.9435 −1.07396 −0.536978 0.843596i \(-0.680434\pi\)
−0.536978 + 0.843596i \(0.680434\pi\)
\(678\) 0 0
\(679\) 39.7777 1.52653
\(680\) 0 0
\(681\) −1.09680 −0.0420293
\(682\) 0 0
\(683\) −28.1762 −1.07813 −0.539067 0.842263i \(-0.681223\pi\)
−0.539067 + 0.842263i \(0.681223\pi\)
\(684\) 0 0
\(685\) −30.6035 −1.16930
\(686\) 0 0
\(687\) −10.0699 −0.384192
\(688\) 0 0
\(689\) −0.739041 −0.0281552
\(690\) 0 0
\(691\) −25.4670 −0.968810 −0.484405 0.874844i \(-0.660964\pi\)
−0.484405 + 0.874844i \(0.660964\pi\)
\(692\) 0 0
\(693\) 2.34804 0.0891946
\(694\) 0 0
\(695\) −11.0608 −0.419561
\(696\) 0 0
\(697\) −4.22172 −0.159909
\(698\) 0 0
\(699\) 5.01463 0.189671
\(700\) 0 0
\(701\) −2.60309 −0.0983174 −0.0491587 0.998791i \(-0.515654\pi\)
−0.0491587 + 0.998791i \(0.515654\pi\)
\(702\) 0 0
\(703\) 22.9633 0.866078
\(704\) 0 0
\(705\) −8.69927 −0.327633
\(706\) 0 0
\(707\) −19.4780 −0.732546
\(708\) 0 0
\(709\) 26.4907 0.994878 0.497439 0.867499i \(-0.334274\pi\)
0.497439 + 0.867499i \(0.334274\pi\)
\(710\) 0 0
\(711\) −10.7644 −0.403698
\(712\) 0 0
\(713\) −23.2245 −0.869763
\(714\) 0 0
\(715\) 0.583212 0.0218109
\(716\) 0 0
\(717\) 16.8946 0.630939
\(718\) 0 0
\(719\) 53.1883 1.98359 0.991794 0.127850i \(-0.0408076\pi\)
0.991794 + 0.127850i \(0.0408076\pi\)
\(720\) 0 0
\(721\) −7.52819 −0.280365
\(722\) 0 0
\(723\) 14.0016 0.520726
\(724\) 0 0
\(725\) 12.4171 0.461161
\(726\) 0 0
\(727\) −40.2624 −1.49325 −0.746625 0.665245i \(-0.768327\pi\)
−0.746625 + 0.665245i \(0.768327\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 17.9403 0.663547
\(732\) 0 0
\(733\) 16.2660 0.600798 0.300399 0.953814i \(-0.402880\pi\)
0.300399 + 0.953814i \(0.402880\pi\)
\(734\) 0 0
\(735\) −48.8815 −1.80302
\(736\) 0 0
\(737\) 0.354465 0.0130569
\(738\) 0 0
\(739\) −41.4651 −1.52532 −0.762660 0.646800i \(-0.776107\pi\)
−0.762660 + 0.646800i \(0.776107\pi\)
\(740\) 0 0
\(741\) −1.06329 −0.0390609
\(742\) 0 0
\(743\) −36.6758 −1.34551 −0.672753 0.739867i \(-0.734888\pi\)
−0.672753 + 0.739867i \(0.734888\pi\)
\(744\) 0 0
\(745\) −37.7605 −1.38344
\(746\) 0 0
\(747\) −3.12519 −0.114345
\(748\) 0 0
\(749\) 88.5601 3.23592
\(750\) 0 0
\(751\) 34.0394 1.24212 0.621058 0.783765i \(-0.286703\pi\)
0.621058 + 0.783765i \(0.286703\pi\)
\(752\) 0 0
\(753\) 20.8610 0.760217
\(754\) 0 0
\(755\) −50.8923 −1.85216
\(756\) 0 0
\(757\) −32.5338 −1.18246 −0.591231 0.806503i \(-0.701358\pi\)
−0.591231 + 0.806503i \(0.701358\pi\)
\(758\) 0 0
\(759\) −2.05311 −0.0745233
\(760\) 0 0
\(761\) −11.8709 −0.430319 −0.215159 0.976579i \(-0.569027\pi\)
−0.215159 + 0.976579i \(0.569027\pi\)
\(762\) 0 0
\(763\) 2.14406 0.0776201
\(764\) 0 0
\(765\) 8.70401 0.314694
\(766\) 0 0
\(767\) 2.20494 0.0796157
\(768\) 0 0
\(769\) 15.7830 0.569149 0.284574 0.958654i \(-0.408148\pi\)
0.284574 + 0.958654i \(0.408148\pi\)
\(770\) 0 0
\(771\) 15.0215 0.540987
\(772\) 0 0
\(773\) 33.1698 1.19304 0.596518 0.802600i \(-0.296551\pi\)
0.596518 + 0.802600i \(0.296551\pi\)
\(774\) 0 0
\(775\) 41.7658 1.50027
\(776\) 0 0
\(777\) 32.2328 1.15635
\(778\) 0 0
\(779\) 5.53090 0.198165
\(780\) 0 0
\(781\) 6.37634 0.228164
\(782\) 0 0
\(783\) 1.72350 0.0615927
\(784\) 0 0
\(785\) 11.7112 0.417992
\(786\) 0 0
\(787\) 8.27019 0.294800 0.147400 0.989077i \(-0.452909\pi\)
0.147400 + 0.989077i \(0.452909\pi\)
\(788\) 0 0
\(789\) 9.66555 0.344103
\(790\) 0 0
\(791\) −46.0940 −1.63891
\(792\) 0 0
\(793\) 0.512553 0.0182013
\(794\) 0 0
\(795\) −7.92581 −0.281099
\(796\) 0 0
\(797\) 17.7455 0.628578 0.314289 0.949327i \(-0.398234\pi\)
0.314289 + 0.949327i \(0.398234\pi\)
\(798\) 0 0
\(799\) −6.20409 −0.219485
\(800\) 0 0
\(801\) 15.5543 0.549585
\(802\) 0 0
\(803\) 1.74868 0.0617095
\(804\) 0 0
\(805\) 64.1247 2.26010
\(806\) 0 0
\(807\) 11.0300 0.388274
\(808\) 0 0
\(809\) −44.8874 −1.57816 −0.789079 0.614292i \(-0.789442\pi\)
−0.789079 + 0.614292i \(0.789442\pi\)
\(810\) 0 0
\(811\) 53.5750 1.88127 0.940636 0.339418i \(-0.110230\pi\)
0.940636 + 0.339418i \(0.110230\pi\)
\(812\) 0 0
\(813\) 27.3714 0.959956
\(814\) 0 0
\(815\) 16.0350 0.561681
\(816\) 0 0
\(817\) −23.5037 −0.822292
\(818\) 0 0
\(819\) −1.49250 −0.0521522
\(820\) 0 0
\(821\) −28.2612 −0.986321 −0.493161 0.869938i \(-0.664158\pi\)
−0.493161 + 0.869938i \(0.664158\pi\)
\(822\) 0 0
\(823\) −30.5821 −1.06603 −0.533013 0.846107i \(-0.678940\pi\)
−0.533013 + 0.846107i \(0.678940\pi\)
\(824\) 0 0
\(825\) 3.69222 0.128547
\(826\) 0 0
\(827\) 26.0995 0.907567 0.453784 0.891112i \(-0.350074\pi\)
0.453784 + 0.891112i \(0.350074\pi\)
\(828\) 0 0
\(829\) 8.79496 0.305462 0.152731 0.988268i \(-0.451193\pi\)
0.152731 + 0.988268i \(0.451193\pi\)
\(830\) 0 0
\(831\) −14.2246 −0.493447
\(832\) 0 0
\(833\) −34.8610 −1.20786
\(834\) 0 0
\(835\) −3.49351 −0.120898
\(836\) 0 0
\(837\) 5.79709 0.200377
\(838\) 0 0
\(839\) 24.6667 0.851591 0.425795 0.904820i \(-0.359994\pi\)
0.425795 + 0.904820i \(0.359994\pi\)
\(840\) 0 0
\(841\) −26.0296 −0.897571
\(842\) 0 0
\(843\) 7.17980 0.247286
\(844\) 0 0
\(845\) 45.0449 1.54959
\(846\) 0 0
\(847\) −49.1955 −1.69038
\(848\) 0 0
\(849\) −7.49336 −0.257172
\(850\) 0 0
\(851\) −28.1842 −0.966143
\(852\) 0 0
\(853\) −10.7504 −0.368088 −0.184044 0.982918i \(-0.558919\pi\)
−0.184044 + 0.982918i \(0.558919\pi\)
\(854\) 0 0
\(855\) −11.4032 −0.389981
\(856\) 0 0
\(857\) 8.67868 0.296458 0.148229 0.988953i \(-0.452643\pi\)
0.148229 + 0.988953i \(0.452643\pi\)
\(858\) 0 0
\(859\) 14.1922 0.484232 0.242116 0.970247i \(-0.422159\pi\)
0.242116 + 0.970247i \(0.422159\pi\)
\(860\) 0 0
\(861\) 7.76354 0.264581
\(862\) 0 0
\(863\) −36.4638 −1.24124 −0.620622 0.784110i \(-0.713120\pi\)
−0.620622 + 0.784110i \(0.713120\pi\)
\(864\) 0 0
\(865\) −58.9583 −2.00464
\(866\) 0 0
\(867\) −10.7925 −0.366533
\(868\) 0 0
\(869\) −5.51657 −0.187137
\(870\) 0 0
\(871\) −0.225311 −0.00763438
\(872\) 0 0
\(873\) 8.68185 0.293836
\(874\) 0 0
\(875\) −35.2877 −1.19294
\(876\) 0 0
\(877\) 6.68456 0.225722 0.112861 0.993611i \(-0.463999\pi\)
0.112861 + 0.993611i \(0.463999\pi\)
\(878\) 0 0
\(879\) −22.4024 −0.755613
\(880\) 0 0
\(881\) −1.97149 −0.0664211 −0.0332105 0.999448i \(-0.510573\pi\)
−0.0332105 + 0.999448i \(0.510573\pi\)
\(882\) 0 0
\(883\) −39.9784 −1.34538 −0.672690 0.739925i \(-0.734861\pi\)
−0.672690 + 0.739925i \(0.734861\pi\)
\(884\) 0 0
\(885\) 23.6467 0.794877
\(886\) 0 0
\(887\) −31.6633 −1.06315 −0.531574 0.847012i \(-0.678399\pi\)
−0.531574 + 0.847012i \(0.678399\pi\)
\(888\) 0 0
\(889\) 32.1806 1.07930
\(890\) 0 0
\(891\) 0.512480 0.0171687
\(892\) 0 0
\(893\) 8.12802 0.271994
\(894\) 0 0
\(895\) 86.0265 2.87555
\(896\) 0 0
\(897\) 1.30504 0.0435739
\(898\) 0 0
\(899\) 9.99126 0.333227
\(900\) 0 0
\(901\) −5.65248 −0.188311
\(902\) 0 0
\(903\) −32.9914 −1.09789
\(904\) 0 0
\(905\) −5.41113 −0.179872
\(906\) 0 0
\(907\) 3.86210 0.128239 0.0641195 0.997942i \(-0.479576\pi\)
0.0641195 + 0.997942i \(0.479576\pi\)
\(908\) 0 0
\(909\) −4.25125 −0.141005
\(910\) 0 0
\(911\) 18.0805 0.599035 0.299518 0.954091i \(-0.403174\pi\)
0.299518 + 0.954091i \(0.403174\pi\)
\(912\) 0 0
\(913\) −1.60160 −0.0530052
\(914\) 0 0
\(915\) 5.49685 0.181720
\(916\) 0 0
\(917\) −33.8676 −1.11841
\(918\) 0 0
\(919\) 16.7072 0.551118 0.275559 0.961284i \(-0.411137\pi\)
0.275559 + 0.961284i \(0.411137\pi\)
\(920\) 0 0
\(921\) 7.30538 0.240720
\(922\) 0 0
\(923\) −4.05305 −0.133408
\(924\) 0 0
\(925\) 50.6852 1.66652
\(926\) 0 0
\(927\) −1.64310 −0.0539664
\(928\) 0 0
\(929\) −40.5918 −1.33178 −0.665888 0.746052i \(-0.731947\pi\)
−0.665888 + 0.746052i \(0.731947\pi\)
\(930\) 0 0
\(931\) 45.6716 1.49683
\(932\) 0 0
\(933\) −26.7279 −0.875032
\(934\) 0 0
\(935\) 4.46064 0.145878
\(936\) 0 0
\(937\) 35.3223 1.15393 0.576965 0.816769i \(-0.304237\pi\)
0.576965 + 0.816769i \(0.304237\pi\)
\(938\) 0 0
\(939\) −19.0884 −0.622925
\(940\) 0 0
\(941\) −20.9506 −0.682971 −0.341485 0.939887i \(-0.610930\pi\)
−0.341485 + 0.939887i \(0.610930\pi\)
\(942\) 0 0
\(943\) −6.78840 −0.221061
\(944\) 0 0
\(945\) −16.0063 −0.520684
\(946\) 0 0
\(947\) −38.6755 −1.25678 −0.628392 0.777897i \(-0.716287\pi\)
−0.628392 + 0.777897i \(0.716287\pi\)
\(948\) 0 0
\(949\) −1.11153 −0.0360817
\(950\) 0 0
\(951\) −0.844016 −0.0273691
\(952\) 0 0
\(953\) −2.98349 −0.0966446 −0.0483223 0.998832i \(-0.515387\pi\)
−0.0483223 + 0.998832i \(0.515387\pi\)
\(954\) 0 0
\(955\) −6.48042 −0.209701
\(956\) 0 0
\(957\) 0.883258 0.0285517
\(958\) 0 0
\(959\) 40.1363 1.29607
\(960\) 0 0
\(961\) 2.60624 0.0840723
\(962\) 0 0
\(963\) 19.3290 0.622870
\(964\) 0 0
\(965\) −68.7379 −2.21275
\(966\) 0 0
\(967\) 12.7366 0.409580 0.204790 0.978806i \(-0.434349\pi\)
0.204790 + 0.978806i \(0.434349\pi\)
\(968\) 0 0
\(969\) −8.13245 −0.261252
\(970\) 0 0
\(971\) 26.6633 0.855668 0.427834 0.903857i \(-0.359277\pi\)
0.427834 + 0.903857i \(0.359277\pi\)
\(972\) 0 0
\(973\) 14.5062 0.465047
\(974\) 0 0
\(975\) −2.34692 −0.0751615
\(976\) 0 0
\(977\) −10.7975 −0.345443 −0.172721 0.984971i \(-0.555256\pi\)
−0.172721 + 0.984971i \(0.555256\pi\)
\(978\) 0 0
\(979\) 7.97129 0.254763
\(980\) 0 0
\(981\) 0.467960 0.0149408
\(982\) 0 0
\(983\) −12.3650 −0.394383 −0.197192 0.980365i \(-0.563182\pi\)
−0.197192 + 0.980365i \(0.563182\pi\)
\(984\) 0 0
\(985\) −87.4157 −2.78529
\(986\) 0 0
\(987\) 11.4090 0.363153
\(988\) 0 0
\(989\) 28.8475 0.917299
\(990\) 0 0
\(991\) 20.4354 0.649151 0.324576 0.945860i \(-0.394779\pi\)
0.324576 + 0.945860i \(0.394779\pi\)
\(992\) 0 0
\(993\) −0.805305 −0.0255556
\(994\) 0 0
\(995\) −81.2121 −2.57460
\(996\) 0 0
\(997\) 33.1561 1.05006 0.525032 0.851083i \(-0.324053\pi\)
0.525032 + 0.851083i \(0.324053\pi\)
\(998\) 0 0
\(999\) 7.03510 0.222581
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 \(a_p\))