Properties

Label 8001.2.a.o.1.11
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-1.58856\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.58856 q^{2}\) \(+0.523519 q^{4}\) \(-3.57671 q^{5}\) \(+1.00000 q^{7}\) \(-2.34548 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.58856 q^{2}\) \(+0.523519 q^{4}\) \(-3.57671 q^{5}\) \(+1.00000 q^{7}\) \(-2.34548 q^{8}\) \(-5.68181 q^{10}\) \(+2.48473 q^{11}\) \(+0.477380 q^{13}\) \(+1.58856 q^{14}\) \(-4.77297 q^{16}\) \(+2.92733 q^{17}\) \(-1.96364 q^{19}\) \(-1.87248 q^{20}\) \(+3.94714 q^{22}\) \(+1.07941 q^{23}\) \(+7.79283 q^{25}\) \(+0.758347 q^{26}\) \(+0.523519 q^{28}\) \(-5.99492 q^{29}\) \(+6.77344 q^{31}\) \(-2.89119 q^{32}\) \(+4.65024 q^{34}\) \(-3.57671 q^{35}\) \(+4.95829 q^{37}\) \(-3.11935 q^{38}\) \(+8.38908 q^{40}\) \(+2.60754 q^{41}\) \(-2.46629 q^{43}\) \(+1.30080 q^{44}\) \(+1.71470 q^{46}\) \(-12.0814 q^{47}\) \(+1.00000 q^{49}\) \(+12.3794 q^{50}\) \(+0.249918 q^{52}\) \(-0.254045 q^{53}\) \(-8.88714 q^{55}\) \(-2.34548 q^{56}\) \(-9.52329 q^{58}\) \(+9.98644 q^{59}\) \(+8.89920 q^{61}\) \(+10.7600 q^{62}\) \(+4.95311 q^{64}\) \(-1.70745 q^{65}\) \(-11.0484 q^{67}\) \(+1.53251 q^{68}\) \(-5.68181 q^{70}\) \(-4.92950 q^{71}\) \(+1.24866 q^{73}\) \(+7.87653 q^{74}\) \(-1.02800 q^{76}\) \(+2.48473 q^{77}\) \(-7.06010 q^{79}\) \(+17.0715 q^{80}\) \(+4.14223 q^{82}\) \(-6.48027 q^{83}\) \(-10.4702 q^{85}\) \(-3.91784 q^{86}\) \(-5.82787 q^{88}\) \(-8.47932 q^{89}\) \(+0.477380 q^{91}\) \(+0.565091 q^{92}\) \(-19.1920 q^{94}\) \(+7.02335 q^{95}\) \(-8.21793 q^{97}\) \(+1.58856 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.58856 1.12328 0.561640 0.827381i \(-0.310170\pi\)
0.561640 + 0.827381i \(0.310170\pi\)
\(3\) 0 0
\(4\) 0.523519 0.261760
\(5\) −3.57671 −1.59955 −0.799776 0.600299i \(-0.795048\pi\)
−0.799776 + 0.600299i \(0.795048\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.34548 −0.829251
\(9\) 0 0
\(10\) −5.68181 −1.79675
\(11\) 2.48473 0.749173 0.374587 0.927192i \(-0.377785\pi\)
0.374587 + 0.927192i \(0.377785\pi\)
\(12\) 0 0
\(13\) 0.477380 0.132401 0.0662007 0.997806i \(-0.478912\pi\)
0.0662007 + 0.997806i \(0.478912\pi\)
\(14\) 1.58856 0.424560
\(15\) 0 0
\(16\) −4.77297 −1.19324
\(17\) 2.92733 0.709982 0.354991 0.934870i \(-0.384484\pi\)
0.354991 + 0.934870i \(0.384484\pi\)
\(18\) 0 0
\(19\) −1.96364 −0.450489 −0.225245 0.974302i \(-0.572318\pi\)
−0.225245 + 0.974302i \(0.572318\pi\)
\(20\) −1.87248 −0.418698
\(21\) 0 0
\(22\) 3.94714 0.841532
\(23\) 1.07941 0.225072 0.112536 0.993648i \(-0.464103\pi\)
0.112536 + 0.993648i \(0.464103\pi\)
\(24\) 0 0
\(25\) 7.79283 1.55857
\(26\) 0.758347 0.148724
\(27\) 0 0
\(28\) 0.523519 0.0989359
\(29\) −5.99492 −1.11323 −0.556615 0.830771i \(-0.687900\pi\)
−0.556615 + 0.830771i \(0.687900\pi\)
\(30\) 0 0
\(31\) 6.77344 1.21655 0.608273 0.793728i \(-0.291862\pi\)
0.608273 + 0.793728i \(0.291862\pi\)
\(32\) −2.89119 −0.511094
\(33\) 0 0
\(34\) 4.65024 0.797509
\(35\) −3.57671 −0.604574
\(36\) 0 0
\(37\) 4.95829 0.815137 0.407569 0.913175i \(-0.366377\pi\)
0.407569 + 0.913175i \(0.366377\pi\)
\(38\) −3.11935 −0.506026
\(39\) 0 0
\(40\) 8.38908 1.32643
\(41\) 2.60754 0.407229 0.203614 0.979051i \(-0.434731\pi\)
0.203614 + 0.979051i \(0.434731\pi\)
\(42\) 0 0
\(43\) −2.46629 −0.376106 −0.188053 0.982159i \(-0.560218\pi\)
−0.188053 + 0.982159i \(0.560218\pi\)
\(44\) 1.30080 0.196103
\(45\) 0 0
\(46\) 1.71470 0.252819
\(47\) −12.0814 −1.76225 −0.881126 0.472882i \(-0.843214\pi\)
−0.881126 + 0.472882i \(0.843214\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 12.3794 1.75071
\(51\) 0 0
\(52\) 0.249918 0.0346574
\(53\) −0.254045 −0.0348958 −0.0174479 0.999848i \(-0.505554\pi\)
−0.0174479 + 0.999848i \(0.505554\pi\)
\(54\) 0 0
\(55\) −8.88714 −1.19834
\(56\) −2.34548 −0.313427
\(57\) 0 0
\(58\) −9.52329 −1.25047
\(59\) 9.98644 1.30012 0.650062 0.759881i \(-0.274743\pi\)
0.650062 + 0.759881i \(0.274743\pi\)
\(60\) 0 0
\(61\) 8.89920 1.13943 0.569713 0.821844i \(-0.307054\pi\)
0.569713 + 0.821844i \(0.307054\pi\)
\(62\) 10.7600 1.36652
\(63\) 0 0
\(64\) 4.95311 0.619139
\(65\) −1.70745 −0.211783
\(66\) 0 0
\(67\) −11.0484 −1.34977 −0.674887 0.737921i \(-0.735808\pi\)
−0.674887 + 0.737921i \(0.735808\pi\)
\(68\) 1.53251 0.185845
\(69\) 0 0
\(70\) −5.68181 −0.679106
\(71\) −4.92950 −0.585025 −0.292512 0.956262i \(-0.594491\pi\)
−0.292512 + 0.956262i \(0.594491\pi\)
\(72\) 0 0
\(73\) 1.24866 0.146145 0.0730724 0.997327i \(-0.476720\pi\)
0.0730724 + 0.997327i \(0.476720\pi\)
\(74\) 7.87653 0.915628
\(75\) 0 0
\(76\) −1.02800 −0.117920
\(77\) 2.48473 0.283161
\(78\) 0 0
\(79\) −7.06010 −0.794323 −0.397162 0.917749i \(-0.630005\pi\)
−0.397162 + 0.917749i \(0.630005\pi\)
\(80\) 17.0715 1.90865
\(81\) 0 0
\(82\) 4.14223 0.457432
\(83\) −6.48027 −0.711302 −0.355651 0.934619i \(-0.615741\pi\)
−0.355651 + 0.934619i \(0.615741\pi\)
\(84\) 0 0
\(85\) −10.4702 −1.13565
\(86\) −3.91784 −0.422472
\(87\) 0 0
\(88\) −5.82787 −0.621253
\(89\) −8.47932 −0.898806 −0.449403 0.893329i \(-0.648363\pi\)
−0.449403 + 0.893329i \(0.648363\pi\)
\(90\) 0 0
\(91\) 0.477380 0.0500431
\(92\) 0.565091 0.0589148
\(93\) 0 0
\(94\) −19.1920 −1.97950
\(95\) 7.02335 0.720581
\(96\) 0 0
\(97\) −8.21793 −0.834405 −0.417202 0.908814i \(-0.636989\pi\)
−0.417202 + 0.908814i \(0.636989\pi\)
\(98\) 1.58856 0.160469
\(99\) 0 0
\(100\) 4.07970 0.407970
\(101\) −1.20095 −0.119499 −0.0597493 0.998213i \(-0.519030\pi\)
−0.0597493 + 0.998213i \(0.519030\pi\)
\(102\) 0 0
\(103\) 3.15831 0.311197 0.155599 0.987820i \(-0.450269\pi\)
0.155599 + 0.987820i \(0.450269\pi\)
\(104\) −1.11968 −0.109794
\(105\) 0 0
\(106\) −0.403566 −0.0391978
\(107\) −10.4900 −1.01411 −0.507053 0.861915i \(-0.669265\pi\)
−0.507053 + 0.861915i \(0.669265\pi\)
\(108\) 0 0
\(109\) 13.4906 1.29217 0.646084 0.763267i \(-0.276406\pi\)
0.646084 + 0.763267i \(0.276406\pi\)
\(110\) −14.1177 −1.34607
\(111\) 0 0
\(112\) −4.77297 −0.451003
\(113\) −10.9519 −1.03027 −0.515133 0.857111i \(-0.672257\pi\)
−0.515133 + 0.857111i \(0.672257\pi\)
\(114\) 0 0
\(115\) −3.86072 −0.360014
\(116\) −3.13846 −0.291399
\(117\) 0 0
\(118\) 15.8640 1.46040
\(119\) 2.92733 0.268348
\(120\) 0 0
\(121\) −4.82613 −0.438739
\(122\) 14.1369 1.27990
\(123\) 0 0
\(124\) 3.54603 0.318443
\(125\) −9.98912 −0.893454
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 13.6507 1.20656
\(129\) 0 0
\(130\) −2.71238 −0.237892
\(131\) −6.78368 −0.592693 −0.296347 0.955080i \(-0.595768\pi\)
−0.296347 + 0.955080i \(0.595768\pi\)
\(132\) 0 0
\(133\) −1.96364 −0.170269
\(134\) −17.5510 −1.51617
\(135\) 0 0
\(136\) −6.86598 −0.588753
\(137\) −1.14240 −0.0976021 −0.0488010 0.998809i \(-0.515540\pi\)
−0.0488010 + 0.998809i \(0.515540\pi\)
\(138\) 0 0
\(139\) 3.86056 0.327449 0.163724 0.986506i \(-0.447649\pi\)
0.163724 + 0.986506i \(0.447649\pi\)
\(140\) −1.87248 −0.158253
\(141\) 0 0
\(142\) −7.83081 −0.657147
\(143\) 1.18616 0.0991917
\(144\) 0 0
\(145\) 21.4421 1.78067
\(146\) 1.98357 0.164162
\(147\) 0 0
\(148\) 2.59576 0.213370
\(149\) −22.7264 −1.86182 −0.930911 0.365245i \(-0.880985\pi\)
−0.930911 + 0.365245i \(0.880985\pi\)
\(150\) 0 0
\(151\) −13.4219 −1.09226 −0.546130 0.837700i \(-0.683900\pi\)
−0.546130 + 0.837700i \(0.683900\pi\)
\(152\) 4.60566 0.373569
\(153\) 0 0
\(154\) 3.94714 0.318069
\(155\) −24.2266 −1.94593
\(156\) 0 0
\(157\) −12.2685 −0.979131 −0.489565 0.871967i \(-0.662845\pi\)
−0.489565 + 0.871967i \(0.662845\pi\)
\(158\) −11.2154 −0.892248
\(159\) 0 0
\(160\) 10.3409 0.817521
\(161\) 1.07941 0.0850692
\(162\) 0 0
\(163\) 0.962043 0.0753530 0.0376765 0.999290i \(-0.488004\pi\)
0.0376765 + 0.999290i \(0.488004\pi\)
\(164\) 1.36510 0.106596
\(165\) 0 0
\(166\) −10.2943 −0.798992
\(167\) −1.61913 −0.125292 −0.0626461 0.998036i \(-0.519954\pi\)
−0.0626461 + 0.998036i \(0.519954\pi\)
\(168\) 0 0
\(169\) −12.7721 −0.982470
\(170\) −16.6325 −1.27566
\(171\) 0 0
\(172\) −1.29115 −0.0984493
\(173\) 16.2581 1.23608 0.618039 0.786148i \(-0.287927\pi\)
0.618039 + 0.786148i \(0.287927\pi\)
\(174\) 0 0
\(175\) 7.79283 0.589082
\(176\) −11.8595 −0.893945
\(177\) 0 0
\(178\) −13.4699 −1.00961
\(179\) −15.8589 −1.18535 −0.592675 0.805442i \(-0.701928\pi\)
−0.592675 + 0.805442i \(0.701928\pi\)
\(180\) 0 0
\(181\) 10.0700 0.748501 0.374250 0.927328i \(-0.377900\pi\)
0.374250 + 0.927328i \(0.377900\pi\)
\(182\) 0.758347 0.0562124
\(183\) 0 0
\(184\) −2.53173 −0.186641
\(185\) −17.7343 −1.30385
\(186\) 0 0
\(187\) 7.27362 0.531899
\(188\) −6.32484 −0.461286
\(189\) 0 0
\(190\) 11.1570 0.809414
\(191\) 3.66146 0.264934 0.132467 0.991187i \(-0.457710\pi\)
0.132467 + 0.991187i \(0.457710\pi\)
\(192\) 0 0
\(193\) 24.6937 1.77749 0.888747 0.458399i \(-0.151577\pi\)
0.888747 + 0.458399i \(0.151577\pi\)
\(194\) −13.0547 −0.937271
\(195\) 0 0
\(196\) 0.523519 0.0373942
\(197\) −17.7356 −1.26361 −0.631804 0.775129i \(-0.717685\pi\)
−0.631804 + 0.775129i \(0.717685\pi\)
\(198\) 0 0
\(199\) −18.3092 −1.29790 −0.648952 0.760829i \(-0.724792\pi\)
−0.648952 + 0.760829i \(0.724792\pi\)
\(200\) −18.2779 −1.29244
\(201\) 0 0
\(202\) −1.90777 −0.134230
\(203\) −5.99492 −0.420761
\(204\) 0 0
\(205\) −9.32639 −0.651383
\(206\) 5.01716 0.349562
\(207\) 0 0
\(208\) −2.27852 −0.157987
\(209\) −4.87910 −0.337494
\(210\) 0 0
\(211\) −7.38421 −0.508350 −0.254175 0.967158i \(-0.581804\pi\)
−0.254175 + 0.967158i \(0.581804\pi\)
\(212\) −0.132998 −0.00913431
\(213\) 0 0
\(214\) −16.6640 −1.13913
\(215\) 8.82119 0.601600
\(216\) 0 0
\(217\) 6.77344 0.459811
\(218\) 21.4306 1.45147
\(219\) 0 0
\(220\) −4.65259 −0.313678
\(221\) 1.39745 0.0940026
\(222\) 0 0
\(223\) −13.4908 −0.903412 −0.451706 0.892167i \(-0.649184\pi\)
−0.451706 + 0.892167i \(0.649184\pi\)
\(224\) −2.89119 −0.193175
\(225\) 0 0
\(226\) −17.3977 −1.15728
\(227\) −9.66789 −0.641681 −0.320840 0.947133i \(-0.603965\pi\)
−0.320840 + 0.947133i \(0.603965\pi\)
\(228\) 0 0
\(229\) −6.40726 −0.423404 −0.211702 0.977334i \(-0.567901\pi\)
−0.211702 + 0.977334i \(0.567901\pi\)
\(230\) −6.13299 −0.404397
\(231\) 0 0
\(232\) 14.0609 0.923147
\(233\) −7.44888 −0.487992 −0.243996 0.969776i \(-0.578458\pi\)
−0.243996 + 0.969776i \(0.578458\pi\)
\(234\) 0 0
\(235\) 43.2116 2.81881
\(236\) 5.22810 0.340320
\(237\) 0 0
\(238\) 4.65024 0.301430
\(239\) −22.1746 −1.43436 −0.717179 0.696890i \(-0.754567\pi\)
−0.717179 + 0.696890i \(0.754567\pi\)
\(240\) 0 0
\(241\) 6.59447 0.424787 0.212394 0.977184i \(-0.431874\pi\)
0.212394 + 0.977184i \(0.431874\pi\)
\(242\) −7.66659 −0.492827
\(243\) 0 0
\(244\) 4.65890 0.298256
\(245\) −3.57671 −0.228507
\(246\) 0 0
\(247\) −0.937401 −0.0596454
\(248\) −15.8870 −1.00882
\(249\) 0 0
\(250\) −15.8683 −1.00360
\(251\) 2.14270 0.135246 0.0676229 0.997711i \(-0.478459\pi\)
0.0676229 + 0.997711i \(0.478459\pi\)
\(252\) 0 0
\(253\) 2.68203 0.168618
\(254\) −1.58856 −0.0996751
\(255\) 0 0
\(256\) 11.7787 0.736168
\(257\) −28.5552 −1.78122 −0.890612 0.454764i \(-0.849724\pi\)
−0.890612 + 0.454764i \(0.849724\pi\)
\(258\) 0 0
\(259\) 4.95829 0.308093
\(260\) −0.893883 −0.0554363
\(261\) 0 0
\(262\) −10.7763 −0.665761
\(263\) 11.2798 0.695542 0.347771 0.937579i \(-0.386939\pi\)
0.347771 + 0.937579i \(0.386939\pi\)
\(264\) 0 0
\(265\) 0.908645 0.0558176
\(266\) −3.11935 −0.191260
\(267\) 0 0
\(268\) −5.78404 −0.353316
\(269\) 8.17992 0.498739 0.249369 0.968408i \(-0.419777\pi\)
0.249369 + 0.968408i \(0.419777\pi\)
\(270\) 0 0
\(271\) −0.247885 −0.0150579 −0.00752896 0.999972i \(-0.502397\pi\)
−0.00752896 + 0.999972i \(0.502397\pi\)
\(272\) −13.9720 −0.847180
\(273\) 0 0
\(274\) −1.81477 −0.109635
\(275\) 19.3630 1.16764
\(276\) 0 0
\(277\) 21.5369 1.29403 0.647013 0.762479i \(-0.276018\pi\)
0.647013 + 0.762479i \(0.276018\pi\)
\(278\) 6.13273 0.367817
\(279\) 0 0
\(280\) 8.38908 0.501343
\(281\) 12.4596 0.743278 0.371639 0.928377i \(-0.378796\pi\)
0.371639 + 0.928377i \(0.378796\pi\)
\(282\) 0 0
\(283\) 8.60593 0.511570 0.255785 0.966734i \(-0.417666\pi\)
0.255785 + 0.966734i \(0.417666\pi\)
\(284\) −2.58069 −0.153136
\(285\) 0 0
\(286\) 1.88429 0.111420
\(287\) 2.60754 0.153918
\(288\) 0 0
\(289\) −8.43074 −0.495926
\(290\) 34.0620 2.00019
\(291\) 0 0
\(292\) 0.653699 0.0382548
\(293\) 16.8805 0.986167 0.493084 0.869982i \(-0.335870\pi\)
0.493084 + 0.869982i \(0.335870\pi\)
\(294\) 0 0
\(295\) −35.7186 −2.07961
\(296\) −11.6295 −0.675953
\(297\) 0 0
\(298\) −36.1023 −2.09135
\(299\) 0.515288 0.0297999
\(300\) 0 0
\(301\) −2.46629 −0.142155
\(302\) −21.3215 −1.22692
\(303\) 0 0
\(304\) 9.37237 0.537542
\(305\) −31.8298 −1.82257
\(306\) 0 0
\(307\) 16.3200 0.931434 0.465717 0.884934i \(-0.345796\pi\)
0.465717 + 0.884934i \(0.345796\pi\)
\(308\) 1.30080 0.0741201
\(309\) 0 0
\(310\) −38.4854 −2.18582
\(311\) −29.0604 −1.64786 −0.823931 0.566690i \(-0.808224\pi\)
−0.823931 + 0.566690i \(0.808224\pi\)
\(312\) 0 0
\(313\) 25.9671 1.46775 0.733875 0.679285i \(-0.237710\pi\)
0.733875 + 0.679285i \(0.237710\pi\)
\(314\) −19.4892 −1.09984
\(315\) 0 0
\(316\) −3.69610 −0.207922
\(317\) −17.5779 −0.987272 −0.493636 0.869669i \(-0.664333\pi\)
−0.493636 + 0.869669i \(0.664333\pi\)
\(318\) 0 0
\(319\) −14.8957 −0.834002
\(320\) −17.7158 −0.990345
\(321\) 0 0
\(322\) 1.71470 0.0955566
\(323\) −5.74821 −0.319839
\(324\) 0 0
\(325\) 3.72014 0.206356
\(326\) 1.52826 0.0846426
\(327\) 0 0
\(328\) −6.11592 −0.337695
\(329\) −12.0814 −0.666069
\(330\) 0 0
\(331\) −15.3981 −0.846356 −0.423178 0.906047i \(-0.639085\pi\)
−0.423178 + 0.906047i \(0.639085\pi\)
\(332\) −3.39255 −0.186190
\(333\) 0 0
\(334\) −2.57209 −0.140738
\(335\) 39.5168 2.15903
\(336\) 0 0
\(337\) −8.13632 −0.443214 −0.221607 0.975136i \(-0.571130\pi\)
−0.221607 + 0.975136i \(0.571130\pi\)
\(338\) −20.2892 −1.10359
\(339\) 0 0
\(340\) −5.48135 −0.297268
\(341\) 16.8302 0.911404
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 5.78462 0.311886
\(345\) 0 0
\(346\) 25.8269 1.38846
\(347\) 21.0011 1.12740 0.563699 0.825980i \(-0.309378\pi\)
0.563699 + 0.825980i \(0.309378\pi\)
\(348\) 0 0
\(349\) 5.77386 0.309068 0.154534 0.987988i \(-0.450612\pi\)
0.154534 + 0.987988i \(0.450612\pi\)
\(350\) 12.3794 0.661705
\(351\) 0 0
\(352\) −7.18381 −0.382898
\(353\) 13.6757 0.727886 0.363943 0.931421i \(-0.381430\pi\)
0.363943 + 0.931421i \(0.381430\pi\)
\(354\) 0 0
\(355\) 17.6314 0.935777
\(356\) −4.43909 −0.235271
\(357\) 0 0
\(358\) −25.1928 −1.33148
\(359\) −12.2071 −0.644265 −0.322132 0.946695i \(-0.604400\pi\)
−0.322132 + 0.946695i \(0.604400\pi\)
\(360\) 0 0
\(361\) −15.1441 −0.797060
\(362\) 15.9969 0.840776
\(363\) 0 0
\(364\) 0.249918 0.0130993
\(365\) −4.46610 −0.233766
\(366\) 0 0
\(367\) 4.41002 0.230201 0.115101 0.993354i \(-0.463281\pi\)
0.115101 + 0.993354i \(0.463281\pi\)
\(368\) −5.15198 −0.268565
\(369\) 0 0
\(370\) −28.1720 −1.46459
\(371\) −0.254045 −0.0131894
\(372\) 0 0
\(373\) 26.9854 1.39725 0.698625 0.715488i \(-0.253796\pi\)
0.698625 + 0.715488i \(0.253796\pi\)
\(374\) 11.5546 0.597472
\(375\) 0 0
\(376\) 28.3366 1.46135
\(377\) −2.86186 −0.147393
\(378\) 0 0
\(379\) −22.1339 −1.13694 −0.568470 0.822704i \(-0.692465\pi\)
−0.568470 + 0.822704i \(0.692465\pi\)
\(380\) 3.67686 0.188619
\(381\) 0 0
\(382\) 5.81645 0.297595
\(383\) −23.5449 −1.20309 −0.601545 0.798839i \(-0.705448\pi\)
−0.601545 + 0.798839i \(0.705448\pi\)
\(384\) 0 0
\(385\) −8.88714 −0.452931
\(386\) 39.2274 1.99662
\(387\) 0 0
\(388\) −4.30225 −0.218414
\(389\) −23.9241 −1.21300 −0.606501 0.795083i \(-0.707427\pi\)
−0.606501 + 0.795083i \(0.707427\pi\)
\(390\) 0 0
\(391\) 3.15978 0.159797
\(392\) −2.34548 −0.118464
\(393\) 0 0
\(394\) −28.1740 −1.41939
\(395\) 25.2519 1.27056
\(396\) 0 0
\(397\) −6.46262 −0.324349 −0.162175 0.986762i \(-0.551851\pi\)
−0.162175 + 0.986762i \(0.551851\pi\)
\(398\) −29.0852 −1.45791
\(399\) 0 0
\(400\) −37.1949 −1.85974
\(401\) −13.4295 −0.670636 −0.335318 0.942105i \(-0.608844\pi\)
−0.335318 + 0.942105i \(0.608844\pi\)
\(402\) 0 0
\(403\) 3.23351 0.161073
\(404\) −0.628718 −0.0312799
\(405\) 0 0
\(406\) −9.52329 −0.472633
\(407\) 12.3200 0.610679
\(408\) 0 0
\(409\) −30.6625 −1.51616 −0.758081 0.652161i \(-0.773863\pi\)
−0.758081 + 0.652161i \(0.773863\pi\)
\(410\) −14.8155 −0.731687
\(411\) 0 0
\(412\) 1.65344 0.0814589
\(413\) 9.98644 0.491401
\(414\) 0 0
\(415\) 23.1780 1.13776
\(416\) −1.38020 −0.0676696
\(417\) 0 0
\(418\) −7.75074 −0.379101
\(419\) 26.5173 1.29545 0.647727 0.761872i \(-0.275720\pi\)
0.647727 + 0.761872i \(0.275720\pi\)
\(420\) 0 0
\(421\) −4.12021 −0.200807 −0.100403 0.994947i \(-0.532013\pi\)
−0.100403 + 0.994947i \(0.532013\pi\)
\(422\) −11.7303 −0.571020
\(423\) 0 0
\(424\) 0.595857 0.0289374
\(425\) 22.8122 1.10655
\(426\) 0 0
\(427\) 8.89920 0.430662
\(428\) −5.49172 −0.265452
\(429\) 0 0
\(430\) 14.0130 0.675766
\(431\) −10.7589 −0.518236 −0.259118 0.965846i \(-0.583432\pi\)
−0.259118 + 0.965846i \(0.583432\pi\)
\(432\) 0 0
\(433\) −4.39734 −0.211323 −0.105661 0.994402i \(-0.533696\pi\)
−0.105661 + 0.994402i \(0.533696\pi\)
\(434\) 10.7600 0.516497
\(435\) 0 0
\(436\) 7.06260 0.338237
\(437\) −2.11956 −0.101393
\(438\) 0 0
\(439\) 18.9542 0.904632 0.452316 0.891858i \(-0.350598\pi\)
0.452316 + 0.891858i \(0.350598\pi\)
\(440\) 20.8446 0.993726
\(441\) 0 0
\(442\) 2.21993 0.105591
\(443\) 36.2425 1.72193 0.860967 0.508660i \(-0.169859\pi\)
0.860967 + 0.508660i \(0.169859\pi\)
\(444\) 0 0
\(445\) 30.3280 1.43769
\(446\) −21.4310 −1.01479
\(447\) 0 0
\(448\) 4.95311 0.234013
\(449\) −17.9491 −0.847072 −0.423536 0.905879i \(-0.639211\pi\)
−0.423536 + 0.905879i \(0.639211\pi\)
\(450\) 0 0
\(451\) 6.47902 0.305085
\(452\) −5.73352 −0.269682
\(453\) 0 0
\(454\) −15.3580 −0.720787
\(455\) −1.70745 −0.0800465
\(456\) 0 0
\(457\) 18.1951 0.851132 0.425566 0.904927i \(-0.360075\pi\)
0.425566 + 0.904927i \(0.360075\pi\)
\(458\) −10.1783 −0.475601
\(459\) 0 0
\(460\) −2.02116 −0.0942372
\(461\) −8.88699 −0.413908 −0.206954 0.978351i \(-0.566355\pi\)
−0.206954 + 0.978351i \(0.566355\pi\)
\(462\) 0 0
\(463\) −34.6096 −1.60845 −0.804223 0.594328i \(-0.797418\pi\)
−0.804223 + 0.594328i \(0.797418\pi\)
\(464\) 28.6136 1.32835
\(465\) 0 0
\(466\) −11.8330 −0.548152
\(467\) −11.2894 −0.522410 −0.261205 0.965283i \(-0.584120\pi\)
−0.261205 + 0.965283i \(0.584120\pi\)
\(468\) 0 0
\(469\) −11.0484 −0.510167
\(470\) 68.6441 3.16632
\(471\) 0 0
\(472\) −23.4230 −1.07813
\(473\) −6.12805 −0.281768
\(474\) 0 0
\(475\) −15.3023 −0.702117
\(476\) 1.53251 0.0702427
\(477\) 0 0
\(478\) −35.2257 −1.61119
\(479\) 23.5409 1.07561 0.537805 0.843069i \(-0.319253\pi\)
0.537805 + 0.843069i \(0.319253\pi\)
\(480\) 0 0
\(481\) 2.36699 0.107925
\(482\) 10.4757 0.477155
\(483\) 0 0
\(484\) −2.52657 −0.114844
\(485\) 29.3931 1.33467
\(486\) 0 0
\(487\) 3.81924 0.173066 0.0865330 0.996249i \(-0.472421\pi\)
0.0865330 + 0.996249i \(0.472421\pi\)
\(488\) −20.8729 −0.944870
\(489\) 0 0
\(490\) −5.68181 −0.256678
\(491\) 3.24874 0.146614 0.0733068 0.997309i \(-0.476645\pi\)
0.0733068 + 0.997309i \(0.476645\pi\)
\(492\) 0 0
\(493\) −17.5491 −0.790372
\(494\) −1.48912 −0.0669986
\(495\) 0 0
\(496\) −32.3294 −1.45163
\(497\) −4.92950 −0.221119
\(498\) 0 0
\(499\) 4.24713 0.190128 0.0950639 0.995471i \(-0.469694\pi\)
0.0950639 + 0.995471i \(0.469694\pi\)
\(500\) −5.22950 −0.233870
\(501\) 0 0
\(502\) 3.40380 0.151919
\(503\) −7.96728 −0.355244 −0.177622 0.984099i \(-0.556840\pi\)
−0.177622 + 0.984099i \(0.556840\pi\)
\(504\) 0 0
\(505\) 4.29543 0.191144
\(506\) 4.26057 0.189405
\(507\) 0 0
\(508\) −0.523519 −0.0232274
\(509\) 20.0689 0.889537 0.444768 0.895646i \(-0.353286\pi\)
0.444768 + 0.895646i \(0.353286\pi\)
\(510\) 0 0
\(511\) 1.24866 0.0552376
\(512\) −8.59023 −0.379638
\(513\) 0 0
\(514\) −45.3616 −2.00081
\(515\) −11.2963 −0.497776
\(516\) 0 0
\(517\) −30.0190 −1.32023
\(518\) 7.87653 0.346075
\(519\) 0 0
\(520\) 4.00478 0.175621
\(521\) −15.9440 −0.698521 −0.349260 0.937026i \(-0.613567\pi\)
−0.349260 + 0.937026i \(0.613567\pi\)
\(522\) 0 0
\(523\) 16.4975 0.721387 0.360693 0.932684i \(-0.382540\pi\)
0.360693 + 0.932684i \(0.382540\pi\)
\(524\) −3.55139 −0.155143
\(525\) 0 0
\(526\) 17.9186 0.781289
\(527\) 19.8281 0.863726
\(528\) 0 0
\(529\) −21.8349 −0.949343
\(530\) 1.44344 0.0626988
\(531\) 0 0
\(532\) −1.02800 −0.0445695
\(533\) 1.24479 0.0539177
\(534\) 0 0
\(535\) 37.5196 1.62212
\(536\) 25.9137 1.11930
\(537\) 0 0
\(538\) 12.9943 0.560223
\(539\) 2.48473 0.107025
\(540\) 0 0
\(541\) −25.0911 −1.07875 −0.539375 0.842065i \(-0.681340\pi\)
−0.539375 + 0.842065i \(0.681340\pi\)
\(542\) −0.393779 −0.0169143
\(543\) 0 0
\(544\) −8.46345 −0.362868
\(545\) −48.2520 −2.06689
\(546\) 0 0
\(547\) 4.58420 0.196006 0.0980030 0.995186i \(-0.468755\pi\)
0.0980030 + 0.995186i \(0.468755\pi\)
\(548\) −0.598070 −0.0255483
\(549\) 0 0
\(550\) 30.7593 1.31158
\(551\) 11.7718 0.501498
\(552\) 0 0
\(553\) −7.06010 −0.300226
\(554\) 34.2126 1.45355
\(555\) 0 0
\(556\) 2.02108 0.0857129
\(557\) −33.5821 −1.42292 −0.711459 0.702728i \(-0.751965\pi\)
−0.711459 + 0.702728i \(0.751965\pi\)
\(558\) 0 0
\(559\) −1.17736 −0.0497969
\(560\) 17.0715 0.721402
\(561\) 0 0
\(562\) 19.7928 0.834910
\(563\) −24.8052 −1.04541 −0.522706 0.852513i \(-0.675078\pi\)
−0.522706 + 0.852513i \(0.675078\pi\)
\(564\) 0 0
\(565\) 39.1716 1.64796
\(566\) 13.6710 0.574636
\(567\) 0 0
\(568\) 11.5620 0.485132
\(569\) 7.31381 0.306611 0.153305 0.988179i \(-0.451008\pi\)
0.153305 + 0.988179i \(0.451008\pi\)
\(570\) 0 0
\(571\) 23.2477 0.972884 0.486442 0.873713i \(-0.338294\pi\)
0.486442 + 0.873713i \(0.338294\pi\)
\(572\) 0.620978 0.0259644
\(573\) 0 0
\(574\) 4.14223 0.172893
\(575\) 8.41164 0.350789
\(576\) 0 0
\(577\) 43.7722 1.82226 0.911130 0.412119i \(-0.135211\pi\)
0.911130 + 0.412119i \(0.135211\pi\)
\(578\) −13.3927 −0.557064
\(579\) 0 0
\(580\) 11.2253 0.466107
\(581\) −6.48027 −0.268847
\(582\) 0 0
\(583\) −0.631233 −0.0261430
\(584\) −2.92871 −0.121191
\(585\) 0 0
\(586\) 26.8156 1.10774
\(587\) −2.57469 −0.106269 −0.0531345 0.998587i \(-0.516921\pi\)
−0.0531345 + 0.998587i \(0.516921\pi\)
\(588\) 0 0
\(589\) −13.3006 −0.548041
\(590\) −56.7410 −2.33599
\(591\) 0 0
\(592\) −23.6657 −0.972655
\(593\) 36.2317 1.48786 0.743929 0.668259i \(-0.232960\pi\)
0.743929 + 0.668259i \(0.232960\pi\)
\(594\) 0 0
\(595\) −10.4702 −0.429236
\(596\) −11.8977 −0.487350
\(597\) 0 0
\(598\) 0.818565 0.0334736
\(599\) 1.34487 0.0549500 0.0274750 0.999622i \(-0.491253\pi\)
0.0274750 + 0.999622i \(0.491253\pi\)
\(600\) 0 0
\(601\) 4.65233 0.189772 0.0948862 0.995488i \(-0.469751\pi\)
0.0948862 + 0.995488i \(0.469751\pi\)
\(602\) −3.91784 −0.159679
\(603\) 0 0
\(604\) −7.02664 −0.285910
\(605\) 17.2617 0.701786
\(606\) 0 0
\(607\) −14.0853 −0.571703 −0.285852 0.958274i \(-0.592276\pi\)
−0.285852 + 0.958274i \(0.592276\pi\)
\(608\) 5.67724 0.230242
\(609\) 0 0
\(610\) −50.5636 −2.04726
\(611\) −5.76742 −0.233325
\(612\) 0 0
\(613\) 25.6928 1.03772 0.518861 0.854858i \(-0.326356\pi\)
0.518861 + 0.854858i \(0.326356\pi\)
\(614\) 25.9254 1.04626
\(615\) 0 0
\(616\) −5.82787 −0.234812
\(617\) −47.0479 −1.89408 −0.947038 0.321122i \(-0.895940\pi\)
−0.947038 + 0.321122i \(0.895940\pi\)
\(618\) 0 0
\(619\) 15.8138 0.635611 0.317805 0.948156i \(-0.397054\pi\)
0.317805 + 0.948156i \(0.397054\pi\)
\(620\) −12.6831 −0.509366
\(621\) 0 0
\(622\) −46.1641 −1.85101
\(623\) −8.47932 −0.339717
\(624\) 0 0
\(625\) −3.23599 −0.129440
\(626\) 41.2503 1.64870
\(627\) 0 0
\(628\) −6.42278 −0.256297
\(629\) 14.5145 0.578732
\(630\) 0 0
\(631\) 45.6190 1.81606 0.908032 0.418900i \(-0.137584\pi\)
0.908032 + 0.418900i \(0.137584\pi\)
\(632\) 16.5593 0.658694
\(633\) 0 0
\(634\) −27.9235 −1.10898
\(635\) 3.57671 0.141937
\(636\) 0 0
\(637\) 0.477380 0.0189145
\(638\) −23.6628 −0.936818
\(639\) 0 0
\(640\) −48.8245 −1.92996
\(641\) 33.9261 1.34000 0.670000 0.742361i \(-0.266294\pi\)
0.670000 + 0.742361i \(0.266294\pi\)
\(642\) 0 0
\(643\) 8.05267 0.317566 0.158783 0.987313i \(-0.449243\pi\)
0.158783 + 0.987313i \(0.449243\pi\)
\(644\) 0.565091 0.0222677
\(645\) 0 0
\(646\) −9.13137 −0.359269
\(647\) 0.994279 0.0390891 0.0195446 0.999809i \(-0.493778\pi\)
0.0195446 + 0.999809i \(0.493778\pi\)
\(648\) 0 0
\(649\) 24.8136 0.974018
\(650\) 5.90967 0.231796
\(651\) 0 0
\(652\) 0.503648 0.0197244
\(653\) −23.2886 −0.911354 −0.455677 0.890145i \(-0.650603\pi\)
−0.455677 + 0.890145i \(0.650603\pi\)
\(654\) 0 0
\(655\) 24.2632 0.948043
\(656\) −12.4457 −0.485922
\(657\) 0 0
\(658\) −19.1920 −0.748182
\(659\) 18.1773 0.708088 0.354044 0.935229i \(-0.384806\pi\)
0.354044 + 0.935229i \(0.384806\pi\)
\(660\) 0 0
\(661\) −37.8810 −1.47340 −0.736701 0.676219i \(-0.763617\pi\)
−0.736701 + 0.676219i \(0.763617\pi\)
\(662\) −24.4608 −0.950695
\(663\) 0 0
\(664\) 15.1993 0.589848
\(665\) 7.02335 0.272354
\(666\) 0 0
\(667\) −6.47097 −0.250557
\(668\) −0.847648 −0.0327965
\(669\) 0 0
\(670\) 62.7747 2.42520
\(671\) 22.1121 0.853628
\(672\) 0 0
\(673\) 17.3738 0.669711 0.334855 0.942270i \(-0.391313\pi\)
0.334855 + 0.942270i \(0.391313\pi\)
\(674\) −12.9250 −0.497853
\(675\) 0 0
\(676\) −6.68645 −0.257171
\(677\) 21.8592 0.840117 0.420059 0.907497i \(-0.362010\pi\)
0.420059 + 0.907497i \(0.362010\pi\)
\(678\) 0 0
\(679\) −8.21793 −0.315375
\(680\) 24.5576 0.941741
\(681\) 0 0
\(682\) 26.7357 1.02376
\(683\) 15.8806 0.607653 0.303827 0.952727i \(-0.401736\pi\)
0.303827 + 0.952727i \(0.401736\pi\)
\(684\) 0 0
\(685\) 4.08604 0.156120
\(686\) 1.58856 0.0606515
\(687\) 0 0
\(688\) 11.7715 0.448785
\(689\) −0.121276 −0.00462025
\(690\) 0 0
\(691\) 5.91148 0.224883 0.112442 0.993658i \(-0.464133\pi\)
0.112442 + 0.993658i \(0.464133\pi\)
\(692\) 8.51141 0.323555
\(693\) 0 0
\(694\) 33.3615 1.26639
\(695\) −13.8081 −0.523771
\(696\) 0 0
\(697\) 7.63312 0.289125
\(698\) 9.17211 0.347170
\(699\) 0 0
\(700\) 4.07970 0.154198
\(701\) 29.8056 1.12574 0.562872 0.826544i \(-0.309697\pi\)
0.562872 + 0.826544i \(0.309697\pi\)
\(702\) 0 0
\(703\) −9.73627 −0.367210
\(704\) 12.3071 0.463843
\(705\) 0 0
\(706\) 21.7247 0.817620
\(707\) −1.20095 −0.0451662
\(708\) 0 0
\(709\) −17.6729 −0.663719 −0.331859 0.943329i \(-0.607676\pi\)
−0.331859 + 0.943329i \(0.607676\pi\)
\(710\) 28.0085 1.05114
\(711\) 0 0
\(712\) 19.8880 0.745336
\(713\) 7.31131 0.273811
\(714\) 0 0
\(715\) −4.24255 −0.158662
\(716\) −8.30245 −0.310277
\(717\) 0 0
\(718\) −19.3917 −0.723690
\(719\) 23.2946 0.868740 0.434370 0.900734i \(-0.356971\pi\)
0.434370 + 0.900734i \(0.356971\pi\)
\(720\) 0 0
\(721\) 3.15831 0.117622
\(722\) −24.0573 −0.895322
\(723\) 0 0
\(724\) 5.27186 0.195927
\(725\) −46.7174 −1.73504
\(726\) 0 0
\(727\) −32.3572 −1.20006 −0.600032 0.799976i \(-0.704845\pi\)
−0.600032 + 0.799976i \(0.704845\pi\)
\(728\) −1.11968 −0.0414983
\(729\) 0 0
\(730\) −7.09466 −0.262585
\(731\) −7.21964 −0.267028
\(732\) 0 0
\(733\) −15.8526 −0.585530 −0.292765 0.956184i \(-0.594575\pi\)
−0.292765 + 0.956184i \(0.594575\pi\)
\(734\) 7.00558 0.258581
\(735\) 0 0
\(736\) −3.12077 −0.115033
\(737\) −27.4522 −1.01121
\(738\) 0 0
\(739\) −20.5904 −0.757432 −0.378716 0.925513i \(-0.623634\pi\)
−0.378716 + 0.925513i \(0.623634\pi\)
\(740\) −9.28427 −0.341296
\(741\) 0 0
\(742\) −0.403566 −0.0148154
\(743\) 21.0394 0.771861 0.385931 0.922528i \(-0.373880\pi\)
0.385931 + 0.922528i \(0.373880\pi\)
\(744\) 0 0
\(745\) 81.2858 2.97808
\(746\) 42.8679 1.56950
\(747\) 0 0
\(748\) 3.80788 0.139230
\(749\) −10.4900 −0.383296
\(750\) 0 0
\(751\) 8.79716 0.321013 0.160506 0.987035i \(-0.448687\pi\)
0.160506 + 0.987035i \(0.448687\pi\)
\(752\) 57.6641 2.10279
\(753\) 0 0
\(754\) −4.54623 −0.165564
\(755\) 48.0063 1.74713
\(756\) 0 0
\(757\) −43.2173 −1.57076 −0.785380 0.619013i \(-0.787533\pi\)
−0.785380 + 0.619013i \(0.787533\pi\)
\(758\) −35.1610 −1.27710
\(759\) 0 0
\(760\) −16.4731 −0.597542
\(761\) −0.234033 −0.00848368 −0.00424184 0.999991i \(-0.501350\pi\)
−0.00424184 + 0.999991i \(0.501350\pi\)
\(762\) 0 0
\(763\) 13.4906 0.488393
\(764\) 1.91685 0.0693491
\(765\) 0 0
\(766\) −37.4025 −1.35141
\(767\) 4.76733 0.172138
\(768\) 0 0
\(769\) −31.8474 −1.14845 −0.574224 0.818698i \(-0.694696\pi\)
−0.574224 + 0.818698i \(0.694696\pi\)
\(770\) −14.1177 −0.508768
\(771\) 0 0
\(772\) 12.9276 0.465276
\(773\) −19.5786 −0.704192 −0.352096 0.935964i \(-0.614531\pi\)
−0.352096 + 0.935964i \(0.614531\pi\)
\(774\) 0 0
\(775\) 52.7843 1.89607
\(776\) 19.2750 0.691931
\(777\) 0 0
\(778\) −38.0049 −1.36254
\(779\) −5.12025 −0.183452
\(780\) 0 0
\(781\) −12.2485 −0.438285
\(782\) 5.01950 0.179497
\(783\) 0 0
\(784\) −4.77297 −0.170463
\(785\) 43.8807 1.56617
\(786\) 0 0
\(787\) 33.9347 1.20964 0.604821 0.796361i \(-0.293245\pi\)
0.604821 + 0.796361i \(0.293245\pi\)
\(788\) −9.28492 −0.330761
\(789\) 0 0
\(790\) 40.1141 1.42720
\(791\) −10.9519 −0.389404
\(792\) 0 0
\(793\) 4.24830 0.150862
\(794\) −10.2662 −0.364335
\(795\) 0 0
\(796\) −9.58522 −0.339739
\(797\) −42.0680 −1.49013 −0.745063 0.666995i \(-0.767580\pi\)
−0.745063 + 0.666995i \(0.767580\pi\)
\(798\) 0 0
\(799\) −35.3662 −1.25117
\(800\) −22.5305 −0.796574
\(801\) 0 0
\(802\) −21.3335 −0.753313
\(803\) 3.10258 0.109488
\(804\) 0 0
\(805\) −3.86072 −0.136073
\(806\) 5.13662 0.180930
\(807\) 0 0
\(808\) 2.81679 0.0990943
\(809\) 15.3134 0.538392 0.269196 0.963085i \(-0.413242\pi\)
0.269196 + 0.963085i \(0.413242\pi\)
\(810\) 0 0
\(811\) 48.5802 1.70588 0.852941 0.522008i \(-0.174817\pi\)
0.852941 + 0.522008i \(0.174817\pi\)
\(812\) −3.13846 −0.110138
\(813\) 0 0
\(814\) 19.5710 0.685964
\(815\) −3.44094 −0.120531
\(816\) 0 0
\(817\) 4.84289 0.169431
\(818\) −48.7091 −1.70308
\(819\) 0 0
\(820\) −4.88255 −0.170506
\(821\) 33.4998 1.16915 0.584576 0.811339i \(-0.301261\pi\)
0.584576 + 0.811339i \(0.301261\pi\)
\(822\) 0 0
\(823\) −19.0305 −0.663360 −0.331680 0.943392i \(-0.607615\pi\)
−0.331680 + 0.943392i \(0.607615\pi\)
\(824\) −7.40774 −0.258061
\(825\) 0 0
\(826\) 15.8640 0.551981
\(827\) 37.1919 1.29329 0.646645 0.762791i \(-0.276172\pi\)
0.646645 + 0.762791i \(0.276172\pi\)
\(828\) 0 0
\(829\) −20.7791 −0.721688 −0.360844 0.932626i \(-0.617511\pi\)
−0.360844 + 0.932626i \(0.617511\pi\)
\(830\) 36.8196 1.27803
\(831\) 0 0
\(832\) 2.36452 0.0819750
\(833\) 2.92733 0.101426
\(834\) 0 0
\(835\) 5.79116 0.200411
\(836\) −2.55430 −0.0883425
\(837\) 0 0
\(838\) 42.1243 1.45516
\(839\) 30.6926 1.05963 0.529814 0.848114i \(-0.322262\pi\)
0.529814 + 0.848114i \(0.322262\pi\)
\(840\) 0 0
\(841\) 6.93910 0.239279
\(842\) −6.54520 −0.225563
\(843\) 0 0
\(844\) −3.86578 −0.133066
\(845\) 45.6821 1.57151
\(846\) 0 0
\(847\) −4.82613 −0.165828
\(848\) 1.21255 0.0416391
\(849\) 0 0
\(850\) 36.2385 1.24297
\(851\) 5.35201 0.183465
\(852\) 0 0
\(853\) −14.3744 −0.492171 −0.246086 0.969248i \(-0.579144\pi\)
−0.246086 + 0.969248i \(0.579144\pi\)
\(854\) 14.1369 0.483755
\(855\) 0 0
\(856\) 24.6040 0.840949
\(857\) −28.6832 −0.979800 −0.489900 0.871779i \(-0.662967\pi\)
−0.489900 + 0.871779i \(0.662967\pi\)
\(858\) 0 0
\(859\) 2.16240 0.0737801 0.0368900 0.999319i \(-0.488255\pi\)
0.0368900 + 0.999319i \(0.488255\pi\)
\(860\) 4.61806 0.157475
\(861\) 0 0
\(862\) −17.0911 −0.582125
\(863\) 30.3176 1.03202 0.516012 0.856581i \(-0.327416\pi\)
0.516012 + 0.856581i \(0.327416\pi\)
\(864\) 0 0
\(865\) −58.1503 −1.97717
\(866\) −6.98544 −0.237375
\(867\) 0 0
\(868\) 3.54603 0.120360
\(869\) −17.5424 −0.595086
\(870\) 0 0
\(871\) −5.27428 −0.178712
\(872\) −31.6419 −1.07153
\(873\) 0 0
\(874\) −3.36705 −0.113892
\(875\) −9.98912 −0.337694
\(876\) 0 0
\(877\) 2.24322 0.0757482 0.0378741 0.999283i \(-0.487941\pi\)
0.0378741 + 0.999283i \(0.487941\pi\)
\(878\) 30.1098 1.01616
\(879\) 0 0
\(880\) 42.4180 1.42991
\(881\) −44.4609 −1.49793 −0.748963 0.662612i \(-0.769448\pi\)
−0.748963 + 0.662612i \(0.769448\pi\)
\(882\) 0 0
\(883\) −5.61418 −0.188932 −0.0944660 0.995528i \(-0.530114\pi\)
−0.0944660 + 0.995528i \(0.530114\pi\)
\(884\) 0.731592 0.0246061
\(885\) 0 0
\(886\) 57.5734 1.93422
\(887\) −3.60496 −0.121043 −0.0605213 0.998167i \(-0.519276\pi\)
−0.0605213 + 0.998167i \(0.519276\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 48.1779 1.61493
\(891\) 0 0
\(892\) −7.06271 −0.236477
\(893\) 23.7235 0.793875
\(894\) 0 0
\(895\) 56.7227 1.89603
\(896\) 13.6507 0.456037
\(897\) 0 0
\(898\) −28.5133 −0.951500
\(899\) −40.6063 −1.35430
\(900\) 0 0
\(901\) −0.743674 −0.0247754
\(902\) 10.2923 0.342696
\(903\) 0 0
\(904\) 25.6873 0.854348
\(905\) −36.0176 −1.19727
\(906\) 0 0
\(907\) −40.1524 −1.33324 −0.666620 0.745398i \(-0.732260\pi\)
−0.666620 + 0.745398i \(0.732260\pi\)
\(908\) −5.06133 −0.167966
\(909\) 0 0
\(910\) −2.71238 −0.0899146
\(911\) −31.1955 −1.03355 −0.516777 0.856120i \(-0.672868\pi\)
−0.516777 + 0.856120i \(0.672868\pi\)
\(912\) 0 0
\(913\) −16.1017 −0.532888
\(914\) 28.9040 0.956060
\(915\) 0 0
\(916\) −3.35433 −0.110830
\(917\) −6.78368 −0.224017
\(918\) 0 0
\(919\) −34.1283 −1.12579 −0.562894 0.826529i \(-0.690312\pi\)
−0.562894 + 0.826529i \(0.690312\pi\)
\(920\) 9.05524 0.298542
\(921\) 0 0
\(922\) −14.1175 −0.464935
\(923\) −2.35325 −0.0774581
\(924\) 0 0
\(925\) 38.6391 1.27044
\(926\) −54.9794 −1.80674
\(927\) 0 0
\(928\) 17.3324 0.568965
\(929\) 39.3611 1.29140 0.645699 0.763592i \(-0.276566\pi\)
0.645699 + 0.763592i \(0.276566\pi\)
\(930\) 0 0
\(931\) −1.96364 −0.0643556
\(932\) −3.89963 −0.127737
\(933\) 0 0
\(934\) −17.9338 −0.586813
\(935\) −26.0156 −0.850801
\(936\) 0 0
\(937\) 45.8260 1.49707 0.748535 0.663096i \(-0.230758\pi\)
0.748535 + 0.663096i \(0.230758\pi\)
\(938\) −17.5510 −0.573060
\(939\) 0 0
\(940\) 22.6221 0.737851
\(941\) −4.51164 −0.147075 −0.0735376 0.997292i \(-0.523429\pi\)
−0.0735376 + 0.997292i \(0.523429\pi\)
\(942\) 0 0
\(943\) 2.81460 0.0916558
\(944\) −47.6649 −1.55136
\(945\) 0 0
\(946\) −9.73478 −0.316505
\(947\) −7.22710 −0.234849 −0.117425 0.993082i \(-0.537464\pi\)
−0.117425 + 0.993082i \(0.537464\pi\)
\(948\) 0 0
\(949\) 0.596087 0.0193498
\(950\) −24.3086 −0.788674
\(951\) 0 0
\(952\) −6.86598 −0.222528
\(953\) 27.5338 0.891906 0.445953 0.895056i \(-0.352865\pi\)
0.445953 + 0.895056i \(0.352865\pi\)
\(954\) 0 0
\(955\) −13.0960 −0.423776
\(956\) −11.6088 −0.375457
\(957\) 0 0
\(958\) 37.3961 1.20821
\(959\) −1.14240 −0.0368901
\(960\) 0 0
\(961\) 14.8795 0.479985
\(962\) 3.76010 0.121230
\(963\) 0 0
\(964\) 3.45233 0.111192
\(965\) −88.3222 −2.84319
\(966\) 0 0
\(967\) −27.1488 −0.873047 −0.436523 0.899693i \(-0.643790\pi\)
−0.436523 + 0.899693i \(0.643790\pi\)
\(968\) 11.3196 0.363825
\(969\) 0 0
\(970\) 46.6927 1.49921
\(971\) 14.8963 0.478044 0.239022 0.971014i \(-0.423173\pi\)
0.239022 + 0.971014i \(0.423173\pi\)
\(972\) 0 0
\(973\) 3.86056 0.123764
\(974\) 6.06708 0.194402
\(975\) 0 0
\(976\) −42.4756 −1.35961
\(977\) −26.3876 −0.844213 −0.422107 0.906546i \(-0.638709\pi\)
−0.422107 + 0.906546i \(0.638709\pi\)
\(978\) 0 0
\(979\) −21.0688 −0.673362
\(980\) −1.87248 −0.0598140
\(981\) 0 0
\(982\) 5.16082 0.164688
\(983\) −53.6989 −1.71273 −0.856364 0.516372i \(-0.827282\pi\)
−0.856364 + 0.516372i \(0.827282\pi\)
\(984\) 0 0
\(985\) 63.4349 2.02120
\(986\) −27.8778 −0.887810
\(987\) 0 0
\(988\) −0.490748 −0.0156128
\(989\) −2.66213 −0.0846508
\(990\) 0 0
\(991\) −52.4107 −1.66488 −0.832440 0.554115i \(-0.813057\pi\)
−0.832440 + 0.554115i \(0.813057\pi\)
\(992\) −19.5833 −0.621770
\(993\) 0 0
\(994\) −7.83081 −0.248378
\(995\) 65.4866 2.07606
\(996\) 0 0
\(997\) 47.8562 1.51562 0.757810 0.652476i \(-0.226269\pi\)
0.757810 + 0.652476i \(0.226269\pi\)
\(998\) 6.74682 0.213567
\(999\) 0 0
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 \(a_p\))