Properties

Label 8001.2.a.o.1.9
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 1.9
Root \(-0.423652\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.423652 q^{2}\) \(-1.82052 q^{4}\) \(-2.66196 q^{5}\) \(+1.00000 q^{7}\) \(-1.61857 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.423652 q^{2}\) \(-1.82052 q^{4}\) \(-2.66196 q^{5}\) \(+1.00000 q^{7}\) \(-1.61857 q^{8}\) \(-1.12774 q^{10}\) \(-3.97552 q^{11}\) \(+4.95058 q^{13}\) \(+0.423652 q^{14}\) \(+2.95533 q^{16}\) \(-5.63178 q^{17}\) \(+3.72073 q^{19}\) \(+4.84615 q^{20}\) \(-1.68424 q^{22}\) \(+4.13626 q^{23}\) \(+2.08603 q^{25}\) \(+2.09732 q^{26}\) \(-1.82052 q^{28}\) \(-7.04468 q^{29}\) \(-2.57265 q^{31}\) \(+4.48917 q^{32}\) \(-2.38592 q^{34}\) \(-2.66196 q^{35}\) \(+2.65212 q^{37}\) \(+1.57630 q^{38}\) \(+4.30857 q^{40}\) \(-2.05217 q^{41}\) \(+4.03075 q^{43}\) \(+7.23751 q^{44}\) \(+1.75233 q^{46}\) \(+7.52083 q^{47}\) \(+1.00000 q^{49}\) \(+0.883750 q^{50}\) \(-9.01263 q^{52}\) \(-0.214398 q^{53}\) \(+10.5827 q^{55}\) \(-1.61857 q^{56}\) \(-2.98449 q^{58}\) \(+12.5754 q^{59}\) \(-2.37431 q^{61}\) \(-1.08991 q^{62}\) \(-4.00881 q^{64}\) \(-13.1783 q^{65}\) \(+4.26602 q^{67}\) \(+10.2528 q^{68}\) \(-1.12774 q^{70}\) \(+13.7119 q^{71}\) \(-10.8892 q^{73}\) \(+1.12358 q^{74}\) \(-6.77367 q^{76}\) \(-3.97552 q^{77}\) \(+2.69299 q^{79}\) \(-7.86696 q^{80}\) \(-0.869404 q^{82}\) \(-4.22143 q^{83}\) \(+14.9916 q^{85}\) \(+1.70763 q^{86}\) \(+6.43466 q^{88}\) \(-4.08362 q^{89}\) \(+4.95058 q^{91}\) \(-7.53014 q^{92}\) \(+3.18621 q^{94}\) \(-9.90444 q^{95}\) \(+0.135110 q^{97}\) \(+0.423652 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.423652 0.299567 0.149784 0.988719i \(-0.452142\pi\)
0.149784 + 0.988719i \(0.452142\pi\)
\(3\) 0 0
\(4\) −1.82052 −0.910259
\(5\) −2.66196 −1.19046 −0.595232 0.803554i \(-0.702940\pi\)
−0.595232 + 0.803554i \(0.702940\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.61857 −0.572251
\(9\) 0 0
\(10\) −1.12774 −0.356624
\(11\) −3.97552 −1.19866 −0.599332 0.800500i \(-0.704567\pi\)
−0.599332 + 0.800500i \(0.704567\pi\)
\(12\) 0 0
\(13\) 4.95058 1.37304 0.686522 0.727109i \(-0.259136\pi\)
0.686522 + 0.727109i \(0.259136\pi\)
\(14\) 0.423652 0.113226
\(15\) 0 0
\(16\) 2.95533 0.738832
\(17\) −5.63178 −1.36591 −0.682954 0.730462i \(-0.739305\pi\)
−0.682954 + 0.730462i \(0.739305\pi\)
\(18\) 0 0
\(19\) 3.72073 0.853595 0.426797 0.904347i \(-0.359642\pi\)
0.426797 + 0.904347i \(0.359642\pi\)
\(20\) 4.84615 1.08363
\(21\) 0 0
\(22\) −1.68424 −0.359081
\(23\) 4.13626 0.862469 0.431235 0.902240i \(-0.358078\pi\)
0.431235 + 0.902240i \(0.358078\pi\)
\(24\) 0 0
\(25\) 2.08603 0.417205
\(26\) 2.09732 0.411319
\(27\) 0 0
\(28\) −1.82052 −0.344046
\(29\) −7.04468 −1.30816 −0.654082 0.756423i \(-0.726945\pi\)
−0.654082 + 0.756423i \(0.726945\pi\)
\(30\) 0 0
\(31\) −2.57265 −0.462062 −0.231031 0.972946i \(-0.574210\pi\)
−0.231031 + 0.972946i \(0.574210\pi\)
\(32\) 4.48917 0.793581
\(33\) 0 0
\(34\) −2.38592 −0.409181
\(35\) −2.66196 −0.449953
\(36\) 0 0
\(37\) 2.65212 0.436006 0.218003 0.975948i \(-0.430046\pi\)
0.218003 + 0.975948i \(0.430046\pi\)
\(38\) 1.57630 0.255709
\(39\) 0 0
\(40\) 4.30857 0.681245
\(41\) −2.05217 −0.320494 −0.160247 0.987077i \(-0.551229\pi\)
−0.160247 + 0.987077i \(0.551229\pi\)
\(42\) 0 0
\(43\) 4.03075 0.614683 0.307342 0.951599i \(-0.400561\pi\)
0.307342 + 0.951599i \(0.400561\pi\)
\(44\) 7.23751 1.09110
\(45\) 0 0
\(46\) 1.75233 0.258368
\(47\) 7.52083 1.09703 0.548513 0.836142i \(-0.315194\pi\)
0.548513 + 0.836142i \(0.315194\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.883750 0.124981
\(51\) 0 0
\(52\) −9.01263 −1.24983
\(53\) −0.214398 −0.0294499 −0.0147249 0.999892i \(-0.504687\pi\)
−0.0147249 + 0.999892i \(0.504687\pi\)
\(54\) 0 0
\(55\) 10.5827 1.42697
\(56\) −1.61857 −0.216291
\(57\) 0 0
\(58\) −2.98449 −0.391883
\(59\) 12.5754 1.63718 0.818591 0.574376i \(-0.194755\pi\)
0.818591 + 0.574376i \(0.194755\pi\)
\(60\) 0 0
\(61\) −2.37431 −0.303999 −0.151999 0.988381i \(-0.548571\pi\)
−0.151999 + 0.988381i \(0.548571\pi\)
\(62\) −1.08991 −0.138419
\(63\) 0 0
\(64\) −4.00881 −0.501101
\(65\) −13.1783 −1.63456
\(66\) 0 0
\(67\) 4.26602 0.521177 0.260588 0.965450i \(-0.416083\pi\)
0.260588 + 0.965450i \(0.416083\pi\)
\(68\) 10.2528 1.24333
\(69\) 0 0
\(70\) −1.12774 −0.134791
\(71\) 13.7119 1.62731 0.813653 0.581351i \(-0.197476\pi\)
0.813653 + 0.581351i \(0.197476\pi\)
\(72\) 0 0
\(73\) −10.8892 −1.27449 −0.637244 0.770662i \(-0.719926\pi\)
−0.637244 + 0.770662i \(0.719926\pi\)
\(74\) 1.12358 0.130613
\(75\) 0 0
\(76\) −6.77367 −0.776993
\(77\) −3.97552 −0.453053
\(78\) 0 0
\(79\) 2.69299 0.302985 0.151492 0.988458i \(-0.451592\pi\)
0.151492 + 0.988458i \(0.451592\pi\)
\(80\) −7.86696 −0.879553
\(81\) 0 0
\(82\) −0.869404 −0.0960096
\(83\) −4.22143 −0.463362 −0.231681 0.972792i \(-0.574423\pi\)
−0.231681 + 0.972792i \(0.574423\pi\)
\(84\) 0 0
\(85\) 14.9916 1.62606
\(86\) 1.70763 0.184139
\(87\) 0 0
\(88\) 6.43466 0.685937
\(89\) −4.08362 −0.432863 −0.216431 0.976298i \(-0.569442\pi\)
−0.216431 + 0.976298i \(0.569442\pi\)
\(90\) 0 0
\(91\) 4.95058 0.518962
\(92\) −7.53014 −0.785071
\(93\) 0 0
\(94\) 3.18621 0.328633
\(95\) −9.90444 −1.01617
\(96\) 0 0
\(97\) 0.135110 0.0137183 0.00685917 0.999976i \(-0.497817\pi\)
0.00685917 + 0.999976i \(0.497817\pi\)
\(98\) 0.423652 0.0427953
\(99\) 0 0
\(100\) −3.79765 −0.379765
\(101\) −0.725428 −0.0721828 −0.0360914 0.999348i \(-0.511491\pi\)
−0.0360914 + 0.999348i \(0.511491\pi\)
\(102\) 0 0
\(103\) 14.2476 1.40386 0.701930 0.712245i \(-0.252322\pi\)
0.701930 + 0.712245i \(0.252322\pi\)
\(104\) −8.01287 −0.785726
\(105\) 0 0
\(106\) −0.0908303 −0.00882222
\(107\) 18.0628 1.74620 0.873098 0.487544i \(-0.162107\pi\)
0.873098 + 0.487544i \(0.162107\pi\)
\(108\) 0 0
\(109\) −7.40505 −0.709276 −0.354638 0.935004i \(-0.615396\pi\)
−0.354638 + 0.935004i \(0.615396\pi\)
\(110\) 4.48337 0.427473
\(111\) 0 0
\(112\) 2.95533 0.279252
\(113\) −18.6046 −1.75017 −0.875087 0.483966i \(-0.839196\pi\)
−0.875087 + 0.483966i \(0.839196\pi\)
\(114\) 0 0
\(115\) −11.0105 −1.02674
\(116\) 12.8250 1.19077
\(117\) 0 0
\(118\) 5.32761 0.490446
\(119\) −5.63178 −0.516264
\(120\) 0 0
\(121\) 4.80477 0.436797
\(122\) −1.00588 −0.0910681
\(123\) 0 0
\(124\) 4.68357 0.420597
\(125\) 7.75688 0.693796
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −10.6767 −0.943694
\(129\) 0 0
\(130\) −5.58299 −0.489661
\(131\) −11.7101 −1.02312 −0.511559 0.859248i \(-0.670932\pi\)
−0.511559 + 0.859248i \(0.670932\pi\)
\(132\) 0 0
\(133\) 3.72073 0.322629
\(134\) 1.80731 0.156127
\(135\) 0 0
\(136\) 9.11543 0.781642
\(137\) −2.39147 −0.204317 −0.102159 0.994768i \(-0.532575\pi\)
−0.102159 + 0.994768i \(0.532575\pi\)
\(138\) 0 0
\(139\) −2.14800 −0.182191 −0.0910953 0.995842i \(-0.529037\pi\)
−0.0910953 + 0.995842i \(0.529037\pi\)
\(140\) 4.84615 0.409574
\(141\) 0 0
\(142\) 5.80909 0.487488
\(143\) −19.6811 −1.64582
\(144\) 0 0
\(145\) 18.7527 1.55732
\(146\) −4.61324 −0.381795
\(147\) 0 0
\(148\) −4.82823 −0.396878
\(149\) 2.05953 0.168723 0.0843615 0.996435i \(-0.473115\pi\)
0.0843615 + 0.996435i \(0.473115\pi\)
\(150\) 0 0
\(151\) 12.3000 1.00096 0.500478 0.865749i \(-0.333157\pi\)
0.500478 + 0.865749i \(0.333157\pi\)
\(152\) −6.02227 −0.488471
\(153\) 0 0
\(154\) −1.68424 −0.135720
\(155\) 6.84830 0.550069
\(156\) 0 0
\(157\) −19.3425 −1.54370 −0.771850 0.635804i \(-0.780669\pi\)
−0.771850 + 0.635804i \(0.780669\pi\)
\(158\) 1.14089 0.0907643
\(159\) 0 0
\(160\) −11.9500 −0.944730
\(161\) 4.13626 0.325983
\(162\) 0 0
\(163\) −12.4805 −0.977551 −0.488775 0.872410i \(-0.662556\pi\)
−0.488775 + 0.872410i \(0.662556\pi\)
\(164\) 3.73601 0.291733
\(165\) 0 0
\(166\) −1.78842 −0.138808
\(167\) −2.16315 −0.167390 −0.0836949 0.996491i \(-0.526672\pi\)
−0.0836949 + 0.996491i \(0.526672\pi\)
\(168\) 0 0
\(169\) 11.5083 0.885252
\(170\) 6.35121 0.487115
\(171\) 0 0
\(172\) −7.33805 −0.559521
\(173\) 15.5879 1.18513 0.592563 0.805524i \(-0.298116\pi\)
0.592563 + 0.805524i \(0.298116\pi\)
\(174\) 0 0
\(175\) 2.08603 0.157689
\(176\) −11.7490 −0.885612
\(177\) 0 0
\(178\) −1.73003 −0.129671
\(179\) 11.1995 0.837090 0.418545 0.908196i \(-0.362540\pi\)
0.418545 + 0.908196i \(0.362540\pi\)
\(180\) 0 0
\(181\) −6.72881 −0.500148 −0.250074 0.968227i \(-0.580455\pi\)
−0.250074 + 0.968227i \(0.580455\pi\)
\(182\) 2.09732 0.155464
\(183\) 0 0
\(184\) −6.69483 −0.493549
\(185\) −7.05983 −0.519049
\(186\) 0 0
\(187\) 22.3893 1.63726
\(188\) −13.6918 −0.998578
\(189\) 0 0
\(190\) −4.19604 −0.304413
\(191\) −23.3444 −1.68914 −0.844570 0.535446i \(-0.820144\pi\)
−0.844570 + 0.535446i \(0.820144\pi\)
\(192\) 0 0
\(193\) 2.13924 0.153986 0.0769928 0.997032i \(-0.475468\pi\)
0.0769928 + 0.997032i \(0.475468\pi\)
\(194\) 0.0572397 0.00410957
\(195\) 0 0
\(196\) −1.82052 −0.130037
\(197\) −7.01767 −0.499988 −0.249994 0.968247i \(-0.580429\pi\)
−0.249994 + 0.968247i \(0.580429\pi\)
\(198\) 0 0
\(199\) −18.7133 −1.32655 −0.663277 0.748374i \(-0.730835\pi\)
−0.663277 + 0.748374i \(0.730835\pi\)
\(200\) −3.37638 −0.238746
\(201\) 0 0
\(202\) −0.307329 −0.0216236
\(203\) −7.04468 −0.494440
\(204\) 0 0
\(205\) 5.46278 0.381537
\(206\) 6.03604 0.420551
\(207\) 0 0
\(208\) 14.6306 1.01445
\(209\) −14.7919 −1.02317
\(210\) 0 0
\(211\) −11.4113 −0.785585 −0.392792 0.919627i \(-0.628491\pi\)
−0.392792 + 0.919627i \(0.628491\pi\)
\(212\) 0.390316 0.0268070
\(213\) 0 0
\(214\) 7.65234 0.523103
\(215\) −10.7297 −0.731759
\(216\) 0 0
\(217\) −2.57265 −0.174643
\(218\) −3.13717 −0.212476
\(219\) 0 0
\(220\) −19.2660 −1.29891
\(221\) −27.8806 −1.87545
\(222\) 0 0
\(223\) 12.7903 0.856505 0.428252 0.903659i \(-0.359129\pi\)
0.428252 + 0.903659i \(0.359129\pi\)
\(224\) 4.48917 0.299945
\(225\) 0 0
\(226\) −7.88188 −0.524295
\(227\) 23.6675 1.57087 0.785434 0.618945i \(-0.212440\pi\)
0.785434 + 0.618945i \(0.212440\pi\)
\(228\) 0 0
\(229\) −16.7152 −1.10457 −0.552287 0.833654i \(-0.686245\pi\)
−0.552287 + 0.833654i \(0.686245\pi\)
\(230\) −4.66464 −0.307577
\(231\) 0 0
\(232\) 11.4023 0.748599
\(233\) −27.5835 −1.80706 −0.903528 0.428529i \(-0.859032\pi\)
−0.903528 + 0.428529i \(0.859032\pi\)
\(234\) 0 0
\(235\) −20.0201 −1.30597
\(236\) −22.8938 −1.49026
\(237\) 0 0
\(238\) −2.38592 −0.154656
\(239\) 6.10076 0.394625 0.197313 0.980341i \(-0.436779\pi\)
0.197313 + 0.980341i \(0.436779\pi\)
\(240\) 0 0
\(241\) −16.4442 −1.05926 −0.529632 0.848228i \(-0.677670\pi\)
−0.529632 + 0.848228i \(0.677670\pi\)
\(242\) 2.03555 0.130850
\(243\) 0 0
\(244\) 4.32247 0.276718
\(245\) −2.66196 −0.170066
\(246\) 0 0
\(247\) 18.4198 1.17202
\(248\) 4.16402 0.264416
\(249\) 0 0
\(250\) 3.28622 0.207839
\(251\) −31.2771 −1.97420 −0.987098 0.160118i \(-0.948813\pi\)
−0.987098 + 0.160118i \(0.948813\pi\)
\(252\) 0 0
\(253\) −16.4438 −1.03381
\(254\) −0.423652 −0.0265823
\(255\) 0 0
\(256\) 3.49442 0.218401
\(257\) −15.4673 −0.964824 −0.482412 0.875944i \(-0.660239\pi\)
−0.482412 + 0.875944i \(0.660239\pi\)
\(258\) 0 0
\(259\) 2.65212 0.164795
\(260\) 23.9913 1.48787
\(261\) 0 0
\(262\) −4.96102 −0.306493
\(263\) 5.45766 0.336534 0.168267 0.985741i \(-0.446183\pi\)
0.168267 + 0.985741i \(0.446183\pi\)
\(264\) 0 0
\(265\) 0.570720 0.0350590
\(266\) 1.57630 0.0966489
\(267\) 0 0
\(268\) −7.76636 −0.474406
\(269\) −24.3057 −1.48194 −0.740971 0.671536i \(-0.765635\pi\)
−0.740971 + 0.671536i \(0.765635\pi\)
\(270\) 0 0
\(271\) 26.4187 1.60482 0.802410 0.596774i \(-0.203551\pi\)
0.802410 + 0.596774i \(0.203551\pi\)
\(272\) −16.6438 −1.00918
\(273\) 0 0
\(274\) −1.01315 −0.0612068
\(275\) −8.29304 −0.500089
\(276\) 0 0
\(277\) −13.7390 −0.825494 −0.412747 0.910846i \(-0.635431\pi\)
−0.412747 + 0.910846i \(0.635431\pi\)
\(278\) −0.910003 −0.0545784
\(279\) 0 0
\(280\) 4.30857 0.257486
\(281\) 5.06765 0.302311 0.151155 0.988510i \(-0.451701\pi\)
0.151155 + 0.988510i \(0.451701\pi\)
\(282\) 0 0
\(283\) −27.6362 −1.64280 −0.821400 0.570353i \(-0.806806\pi\)
−0.821400 + 0.570353i \(0.806806\pi\)
\(284\) −24.9628 −1.48127
\(285\) 0 0
\(286\) −8.33796 −0.493034
\(287\) −2.05217 −0.121135
\(288\) 0 0
\(289\) 14.7169 0.865702
\(290\) 7.94460 0.466523
\(291\) 0 0
\(292\) 19.8240 1.16011
\(293\) −26.9116 −1.57219 −0.786097 0.618104i \(-0.787901\pi\)
−0.786097 + 0.618104i \(0.787901\pi\)
\(294\) 0 0
\(295\) −33.4753 −1.94901
\(296\) −4.29264 −0.249505
\(297\) 0 0
\(298\) 0.872522 0.0505439
\(299\) 20.4769 1.18421
\(300\) 0 0
\(301\) 4.03075 0.232328
\(302\) 5.21091 0.299854
\(303\) 0 0
\(304\) 10.9960 0.630663
\(305\) 6.32031 0.361900
\(306\) 0 0
\(307\) −10.2148 −0.582989 −0.291494 0.956573i \(-0.594152\pi\)
−0.291494 + 0.956573i \(0.594152\pi\)
\(308\) 7.23751 0.412395
\(309\) 0 0
\(310\) 2.90130 0.164783
\(311\) −9.69180 −0.549572 −0.274786 0.961505i \(-0.588607\pi\)
−0.274786 + 0.961505i \(0.588607\pi\)
\(312\) 0 0
\(313\) 13.6848 0.773509 0.386755 0.922183i \(-0.373596\pi\)
0.386755 + 0.922183i \(0.373596\pi\)
\(314\) −8.19450 −0.462442
\(315\) 0 0
\(316\) −4.90263 −0.275795
\(317\) −14.1092 −0.792451 −0.396226 0.918153i \(-0.629680\pi\)
−0.396226 + 0.918153i \(0.629680\pi\)
\(318\) 0 0
\(319\) 28.0063 1.56805
\(320\) 10.6713 0.596543
\(321\) 0 0
\(322\) 1.75233 0.0976538
\(323\) −20.9544 −1.16593
\(324\) 0 0
\(325\) 10.3271 0.572842
\(326\) −5.28740 −0.292842
\(327\) 0 0
\(328\) 3.32157 0.183403
\(329\) 7.52083 0.414637
\(330\) 0 0
\(331\) 1.11891 0.0615011 0.0307505 0.999527i \(-0.490210\pi\)
0.0307505 + 0.999527i \(0.490210\pi\)
\(332\) 7.68520 0.421780
\(333\) 0 0
\(334\) −0.916424 −0.0501445
\(335\) −11.3560 −0.620442
\(336\) 0 0
\(337\) −23.4974 −1.27999 −0.639993 0.768381i \(-0.721063\pi\)
−0.639993 + 0.768381i \(0.721063\pi\)
\(338\) 4.87550 0.265192
\(339\) 0 0
\(340\) −27.2924 −1.48014
\(341\) 10.2276 0.553858
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −6.52405 −0.351753
\(345\) 0 0
\(346\) 6.60384 0.355025
\(347\) −6.87719 −0.369187 −0.184593 0.982815i \(-0.559097\pi\)
−0.184593 + 0.982815i \(0.559097\pi\)
\(348\) 0 0
\(349\) −3.13512 −0.167819 −0.0839094 0.996473i \(-0.526741\pi\)
−0.0839094 + 0.996473i \(0.526741\pi\)
\(350\) 0.883750 0.0472384
\(351\) 0 0
\(352\) −17.8468 −0.951238
\(353\) 29.3356 1.56138 0.780689 0.624920i \(-0.214869\pi\)
0.780689 + 0.624920i \(0.214869\pi\)
\(354\) 0 0
\(355\) −36.5006 −1.93725
\(356\) 7.43430 0.394017
\(357\) 0 0
\(358\) 4.74469 0.250765
\(359\) 6.92912 0.365705 0.182852 0.983140i \(-0.441467\pi\)
0.182852 + 0.983140i \(0.441467\pi\)
\(360\) 0 0
\(361\) −5.15614 −0.271376
\(362\) −2.85067 −0.149828
\(363\) 0 0
\(364\) −9.01263 −0.472390
\(365\) 28.9867 1.51723
\(366\) 0 0
\(367\) 20.4454 1.06724 0.533621 0.845724i \(-0.320831\pi\)
0.533621 + 0.845724i \(0.320831\pi\)
\(368\) 12.2240 0.637220
\(369\) 0 0
\(370\) −2.99091 −0.155490
\(371\) −0.214398 −0.0111310
\(372\) 0 0
\(373\) −1.24610 −0.0645209 −0.0322604 0.999479i \(-0.510271\pi\)
−0.0322604 + 0.999479i \(0.510271\pi\)
\(374\) 9.48526 0.490471
\(375\) 0 0
\(376\) −12.1730 −0.627774
\(377\) −34.8753 −1.79617
\(378\) 0 0
\(379\) −11.8870 −0.610592 −0.305296 0.952258i \(-0.598755\pi\)
−0.305296 + 0.952258i \(0.598755\pi\)
\(380\) 18.0312 0.924982
\(381\) 0 0
\(382\) −9.88989 −0.506011
\(383\) 14.6285 0.747481 0.373741 0.927533i \(-0.378075\pi\)
0.373741 + 0.927533i \(0.378075\pi\)
\(384\) 0 0
\(385\) 10.5827 0.539343
\(386\) 0.906292 0.0461290
\(387\) 0 0
\(388\) −0.245970 −0.0124873
\(389\) 21.5646 1.09337 0.546685 0.837338i \(-0.315890\pi\)
0.546685 + 0.837338i \(0.315890\pi\)
\(390\) 0 0
\(391\) −23.2945 −1.17805
\(392\) −1.61857 −0.0817502
\(393\) 0 0
\(394\) −2.97305 −0.149780
\(395\) −7.16862 −0.360693
\(396\) 0 0
\(397\) 8.65271 0.434267 0.217133 0.976142i \(-0.430329\pi\)
0.217133 + 0.976142i \(0.430329\pi\)
\(398\) −7.92794 −0.397392
\(399\) 0 0
\(400\) 6.16489 0.308245
\(401\) 25.4873 1.27277 0.636387 0.771370i \(-0.280428\pi\)
0.636387 + 0.771370i \(0.280428\pi\)
\(402\) 0 0
\(403\) −12.7361 −0.634432
\(404\) 1.32065 0.0657050
\(405\) 0 0
\(406\) −2.98449 −0.148118
\(407\) −10.5436 −0.522625
\(408\) 0 0
\(409\) 38.0003 1.87900 0.939498 0.342555i \(-0.111292\pi\)
0.939498 + 0.342555i \(0.111292\pi\)
\(410\) 2.31432 0.114296
\(411\) 0 0
\(412\) −25.9381 −1.27788
\(413\) 12.5754 0.618797
\(414\) 0 0
\(415\) 11.2373 0.551616
\(416\) 22.2240 1.08962
\(417\) 0 0
\(418\) −6.26660 −0.306509
\(419\) 4.34686 0.212358 0.106179 0.994347i \(-0.466138\pi\)
0.106179 + 0.994347i \(0.466138\pi\)
\(420\) 0 0
\(421\) 29.4508 1.43535 0.717673 0.696380i \(-0.245207\pi\)
0.717673 + 0.696380i \(0.245207\pi\)
\(422\) −4.83441 −0.235335
\(423\) 0 0
\(424\) 0.347019 0.0168527
\(425\) −11.7480 −0.569864
\(426\) 0 0
\(427\) −2.37431 −0.114901
\(428\) −32.8837 −1.58949
\(429\) 0 0
\(430\) −4.54565 −0.219211
\(431\) −29.6562 −1.42849 −0.714245 0.699895i \(-0.753230\pi\)
−0.714245 + 0.699895i \(0.753230\pi\)
\(432\) 0 0
\(433\) −9.59705 −0.461205 −0.230602 0.973048i \(-0.574070\pi\)
−0.230602 + 0.973048i \(0.574070\pi\)
\(434\) −1.08991 −0.0523174
\(435\) 0 0
\(436\) 13.4810 0.645625
\(437\) 15.3899 0.736199
\(438\) 0 0
\(439\) −29.8729 −1.42576 −0.712878 0.701288i \(-0.752609\pi\)
−0.712878 + 0.701288i \(0.752609\pi\)
\(440\) −17.1288 −0.816584
\(441\) 0 0
\(442\) −11.8117 −0.561824
\(443\) −1.94573 −0.0924444 −0.0462222 0.998931i \(-0.514718\pi\)
−0.0462222 + 0.998931i \(0.514718\pi\)
\(444\) 0 0
\(445\) 10.8704 0.515308
\(446\) 5.41865 0.256581
\(447\) 0 0
\(448\) −4.00881 −0.189398
\(449\) 17.6859 0.834650 0.417325 0.908757i \(-0.362968\pi\)
0.417325 + 0.908757i \(0.362968\pi\)
\(450\) 0 0
\(451\) 8.15843 0.384165
\(452\) 33.8700 1.59311
\(453\) 0 0
\(454\) 10.0268 0.470581
\(455\) −13.1783 −0.617806
\(456\) 0 0
\(457\) −38.7242 −1.81144 −0.905721 0.423874i \(-0.860670\pi\)
−0.905721 + 0.423874i \(0.860670\pi\)
\(458\) −7.08144 −0.330894
\(459\) 0 0
\(460\) 20.0449 0.934599
\(461\) −2.11009 −0.0982766 −0.0491383 0.998792i \(-0.515648\pi\)
−0.0491383 + 0.998792i \(0.515648\pi\)
\(462\) 0 0
\(463\) −16.3478 −0.759747 −0.379873 0.925038i \(-0.624032\pi\)
−0.379873 + 0.925038i \(0.624032\pi\)
\(464\) −20.8193 −0.966514
\(465\) 0 0
\(466\) −11.6858 −0.541335
\(467\) −15.8333 −0.732679 −0.366340 0.930481i \(-0.619389\pi\)
−0.366340 + 0.930481i \(0.619389\pi\)
\(468\) 0 0
\(469\) 4.26602 0.196986
\(470\) −8.48157 −0.391226
\(471\) 0 0
\(472\) −20.3542 −0.936880
\(473\) −16.0243 −0.736799
\(474\) 0 0
\(475\) 7.76155 0.356124
\(476\) 10.2528 0.469935
\(477\) 0 0
\(478\) 2.58460 0.118217
\(479\) 22.1361 1.01142 0.505712 0.862702i \(-0.331230\pi\)
0.505712 + 0.862702i \(0.331230\pi\)
\(480\) 0 0
\(481\) 13.1295 0.598655
\(482\) −6.96661 −0.317321
\(483\) 0 0
\(484\) −8.74717 −0.397599
\(485\) −0.359657 −0.0163312
\(486\) 0 0
\(487\) −0.348140 −0.0157757 −0.00788787 0.999969i \(-0.502511\pi\)
−0.00788787 + 0.999969i \(0.502511\pi\)
\(488\) 3.84298 0.173964
\(489\) 0 0
\(490\) −1.12774 −0.0509463
\(491\) 7.28753 0.328882 0.164441 0.986387i \(-0.447418\pi\)
0.164441 + 0.986387i \(0.447418\pi\)
\(492\) 0 0
\(493\) 39.6741 1.78683
\(494\) 7.80359 0.351100
\(495\) 0 0
\(496\) −7.60304 −0.341386
\(497\) 13.7119 0.615064
\(498\) 0 0
\(499\) −16.5620 −0.741416 −0.370708 0.928749i \(-0.620885\pi\)
−0.370708 + 0.928749i \(0.620885\pi\)
\(500\) −14.1215 −0.631535
\(501\) 0 0
\(502\) −13.2506 −0.591404
\(503\) 19.6862 0.877766 0.438883 0.898544i \(-0.355374\pi\)
0.438883 + 0.898544i \(0.355374\pi\)
\(504\) 0 0
\(505\) 1.93106 0.0859310
\(506\) −6.96644 −0.309696
\(507\) 0 0
\(508\) 1.82052 0.0807725
\(509\) −0.855626 −0.0379249 −0.0189625 0.999820i \(-0.506036\pi\)
−0.0189625 + 0.999820i \(0.506036\pi\)
\(510\) 0 0
\(511\) −10.8892 −0.481711
\(512\) 22.8338 1.00912
\(513\) 0 0
\(514\) −6.55276 −0.289030
\(515\) −37.9266 −1.67125
\(516\) 0 0
\(517\) −29.8992 −1.31497
\(518\) 1.12358 0.0493671
\(519\) 0 0
\(520\) 21.3299 0.935379
\(521\) 19.7053 0.863303 0.431652 0.902040i \(-0.357931\pi\)
0.431652 + 0.902040i \(0.357931\pi\)
\(522\) 0 0
\(523\) −45.5771 −1.99295 −0.996473 0.0839120i \(-0.973259\pi\)
−0.996473 + 0.0839120i \(0.973259\pi\)
\(524\) 21.3185 0.931303
\(525\) 0 0
\(526\) 2.31215 0.100814
\(527\) 14.4886 0.631134
\(528\) 0 0
\(529\) −5.89137 −0.256147
\(530\) 0.241787 0.0105025
\(531\) 0 0
\(532\) −6.77367 −0.293676
\(533\) −10.1594 −0.440053
\(534\) 0 0
\(535\) −48.0824 −2.07878
\(536\) −6.90485 −0.298244
\(537\) 0 0
\(538\) −10.2971 −0.443942
\(539\) −3.97552 −0.171238
\(540\) 0 0
\(541\) 26.4890 1.13885 0.569426 0.822043i \(-0.307166\pi\)
0.569426 + 0.822043i \(0.307166\pi\)
\(542\) 11.1923 0.480751
\(543\) 0 0
\(544\) −25.2820 −1.08396
\(545\) 19.7120 0.844367
\(546\) 0 0
\(547\) −31.6604 −1.35370 −0.676850 0.736121i \(-0.736655\pi\)
−0.676850 + 0.736121i \(0.736655\pi\)
\(548\) 4.35372 0.185982
\(549\) 0 0
\(550\) −3.51337 −0.149810
\(551\) −26.2114 −1.11664
\(552\) 0 0
\(553\) 2.69299 0.114517
\(554\) −5.82054 −0.247291
\(555\) 0 0
\(556\) 3.91047 0.165841
\(557\) −9.95634 −0.421864 −0.210932 0.977501i \(-0.567650\pi\)
−0.210932 + 0.977501i \(0.567650\pi\)
\(558\) 0 0
\(559\) 19.9546 0.843988
\(560\) −7.86696 −0.332440
\(561\) 0 0
\(562\) 2.14692 0.0905624
\(563\) −13.7616 −0.579983 −0.289992 0.957029i \(-0.593653\pi\)
−0.289992 + 0.957029i \(0.593653\pi\)
\(564\) 0 0
\(565\) 49.5247 2.08352
\(566\) −11.7081 −0.492129
\(567\) 0 0
\(568\) −22.1937 −0.931228
\(569\) 7.58374 0.317927 0.158963 0.987284i \(-0.449185\pi\)
0.158963 + 0.987284i \(0.449185\pi\)
\(570\) 0 0
\(571\) 0.400150 0.0167458 0.00837288 0.999965i \(-0.497335\pi\)
0.00837288 + 0.999965i \(0.497335\pi\)
\(572\) 35.8299 1.49812
\(573\) 0 0
\(574\) −0.869404 −0.0362882
\(575\) 8.62835 0.359827
\(576\) 0 0
\(577\) −18.6822 −0.777748 −0.388874 0.921291i \(-0.627136\pi\)
−0.388874 + 0.921291i \(0.627136\pi\)
\(578\) 6.23486 0.259336
\(579\) 0 0
\(580\) −34.1396 −1.41757
\(581\) −4.22143 −0.175135
\(582\) 0 0
\(583\) 0.852345 0.0353005
\(584\) 17.6250 0.729327
\(585\) 0 0
\(586\) −11.4012 −0.470978
\(587\) −35.7593 −1.47595 −0.737973 0.674830i \(-0.764217\pi\)
−0.737973 + 0.674830i \(0.764217\pi\)
\(588\) 0 0
\(589\) −9.57216 −0.394414
\(590\) −14.1819 −0.583859
\(591\) 0 0
\(592\) 7.83788 0.322135
\(593\) −27.4101 −1.12560 −0.562799 0.826594i \(-0.690276\pi\)
−0.562799 + 0.826594i \(0.690276\pi\)
\(594\) 0 0
\(595\) 14.9916 0.614594
\(596\) −3.74941 −0.153582
\(597\) 0 0
\(598\) 8.67508 0.354750
\(599\) 13.9434 0.569711 0.284856 0.958570i \(-0.408054\pi\)
0.284856 + 0.958570i \(0.408054\pi\)
\(600\) 0 0
\(601\) −26.8951 −1.09708 −0.548538 0.836126i \(-0.684815\pi\)
−0.548538 + 0.836126i \(0.684815\pi\)
\(602\) 1.70763 0.0695980
\(603\) 0 0
\(604\) −22.3923 −0.911131
\(605\) −12.7901 −0.519991
\(606\) 0 0
\(607\) 18.7939 0.762819 0.381410 0.924406i \(-0.375439\pi\)
0.381410 + 0.924406i \(0.375439\pi\)
\(608\) 16.7030 0.677397
\(609\) 0 0
\(610\) 2.67761 0.108413
\(611\) 37.2325 1.50627
\(612\) 0 0
\(613\) 6.13877 0.247943 0.123971 0.992286i \(-0.460437\pi\)
0.123971 + 0.992286i \(0.460437\pi\)
\(614\) −4.32752 −0.174644
\(615\) 0 0
\(616\) 6.43466 0.259260
\(617\) 16.3314 0.657477 0.328739 0.944421i \(-0.393376\pi\)
0.328739 + 0.944421i \(0.393376\pi\)
\(618\) 0 0
\(619\) 18.1738 0.730465 0.365233 0.930916i \(-0.380989\pi\)
0.365233 + 0.930916i \(0.380989\pi\)
\(620\) −12.4675 −0.500705
\(621\) 0 0
\(622\) −4.10595 −0.164634
\(623\) −4.08362 −0.163607
\(624\) 0 0
\(625\) −31.0786 −1.24315
\(626\) 5.79759 0.231718
\(627\) 0 0
\(628\) 35.2134 1.40517
\(629\) −14.9362 −0.595543
\(630\) 0 0
\(631\) −22.8576 −0.909945 −0.454972 0.890506i \(-0.650351\pi\)
−0.454972 + 0.890506i \(0.650351\pi\)
\(632\) −4.35879 −0.173383
\(633\) 0 0
\(634\) −5.97739 −0.237393
\(635\) 2.66196 0.105637
\(636\) 0 0
\(637\) 4.95058 0.196149
\(638\) 11.8649 0.469737
\(639\) 0 0
\(640\) 28.4209 1.12343
\(641\) −34.5503 −1.36465 −0.682327 0.731047i \(-0.739032\pi\)
−0.682327 + 0.731047i \(0.739032\pi\)
\(642\) 0 0
\(643\) 4.29860 0.169520 0.0847601 0.996401i \(-0.472988\pi\)
0.0847601 + 0.996401i \(0.472988\pi\)
\(644\) −7.53014 −0.296729
\(645\) 0 0
\(646\) −8.87735 −0.349275
\(647\) 17.3258 0.681147 0.340573 0.940218i \(-0.389379\pi\)
0.340573 + 0.940218i \(0.389379\pi\)
\(648\) 0 0
\(649\) −49.9939 −1.96243
\(650\) 4.37508 0.171605
\(651\) 0 0
\(652\) 22.7210 0.889825
\(653\) −29.1488 −1.14068 −0.570341 0.821408i \(-0.693189\pi\)
−0.570341 + 0.821408i \(0.693189\pi\)
\(654\) 0 0
\(655\) 31.1719 1.21799
\(656\) −6.06482 −0.236791
\(657\) 0 0
\(658\) 3.18621 0.124212
\(659\) 35.0106 1.36382 0.681910 0.731436i \(-0.261150\pi\)
0.681910 + 0.731436i \(0.261150\pi\)
\(660\) 0 0
\(661\) 41.6401 1.61961 0.809806 0.586697i \(-0.199572\pi\)
0.809806 + 0.586697i \(0.199572\pi\)
\(662\) 0.474030 0.0184237
\(663\) 0 0
\(664\) 6.83269 0.265160
\(665\) −9.90444 −0.384078
\(666\) 0 0
\(667\) −29.1386 −1.12825
\(668\) 3.93806 0.152368
\(669\) 0 0
\(670\) −4.81098 −0.185864
\(671\) 9.43910 0.364393
\(672\) 0 0
\(673\) 6.26678 0.241567 0.120783 0.992679i \(-0.461459\pi\)
0.120783 + 0.992679i \(0.461459\pi\)
\(674\) −9.95473 −0.383442
\(675\) 0 0
\(676\) −20.9510 −0.805809
\(677\) 35.5065 1.36463 0.682313 0.731060i \(-0.260974\pi\)
0.682313 + 0.731060i \(0.260974\pi\)
\(678\) 0 0
\(679\) 0.135110 0.00518505
\(680\) −24.2649 −0.930517
\(681\) 0 0
\(682\) 4.33296 0.165918
\(683\) −30.5511 −1.16900 −0.584502 0.811392i \(-0.698710\pi\)
−0.584502 + 0.811392i \(0.698710\pi\)
\(684\) 0 0
\(685\) 6.36601 0.243233
\(686\) 0.423652 0.0161751
\(687\) 0 0
\(688\) 11.9122 0.454148
\(689\) −1.06140 −0.0404360
\(690\) 0 0
\(691\) 21.9818 0.836229 0.418114 0.908394i \(-0.362691\pi\)
0.418114 + 0.908394i \(0.362691\pi\)
\(692\) −28.3781 −1.07877
\(693\) 0 0
\(694\) −2.91354 −0.110596
\(695\) 5.71788 0.216892
\(696\) 0 0
\(697\) 11.5573 0.437766
\(698\) −1.32820 −0.0502730
\(699\) 0 0
\(700\) −3.79765 −0.143538
\(701\) 5.79388 0.218832 0.109416 0.993996i \(-0.465102\pi\)
0.109416 + 0.993996i \(0.465102\pi\)
\(702\) 0 0
\(703\) 9.86783 0.372172
\(704\) 15.9371 0.600652
\(705\) 0 0
\(706\) 12.4281 0.467737
\(707\) −0.725428 −0.0272825
\(708\) 0 0
\(709\) −12.2837 −0.461324 −0.230662 0.973034i \(-0.574089\pi\)
−0.230662 + 0.973034i \(0.574089\pi\)
\(710\) −15.4636 −0.580337
\(711\) 0 0
\(712\) 6.60962 0.247706
\(713\) −10.6412 −0.398515
\(714\) 0 0
\(715\) 52.3904 1.95929
\(716\) −20.3889 −0.761969
\(717\) 0 0
\(718\) 2.93554 0.109553
\(719\) 25.6425 0.956302 0.478151 0.878278i \(-0.341307\pi\)
0.478151 + 0.878278i \(0.341307\pi\)
\(720\) 0 0
\(721\) 14.2476 0.530610
\(722\) −2.18441 −0.0812953
\(723\) 0 0
\(724\) 12.2499 0.455265
\(725\) −14.6954 −0.545774
\(726\) 0 0
\(727\) 41.3287 1.53280 0.766399 0.642365i \(-0.222047\pi\)
0.766399 + 0.642365i \(0.222047\pi\)
\(728\) −8.01287 −0.296977
\(729\) 0 0
\(730\) 12.2803 0.454513
\(731\) −22.7003 −0.839600
\(732\) 0 0
\(733\) 27.6156 1.02001 0.510004 0.860172i \(-0.329644\pi\)
0.510004 + 0.860172i \(0.329644\pi\)
\(734\) 8.66174 0.319711
\(735\) 0 0
\(736\) 18.5684 0.684439
\(737\) −16.9596 −0.624716
\(738\) 0 0
\(739\) −30.8185 −1.13368 −0.566839 0.823828i \(-0.691834\pi\)
−0.566839 + 0.823828i \(0.691834\pi\)
\(740\) 12.8526 0.472470
\(741\) 0 0
\(742\) −0.0908303 −0.00333449
\(743\) −24.3137 −0.891983 −0.445991 0.895037i \(-0.647149\pi\)
−0.445991 + 0.895037i \(0.647149\pi\)
\(744\) 0 0
\(745\) −5.48237 −0.200859
\(746\) −0.527915 −0.0193283
\(747\) 0 0
\(748\) −40.7601 −1.49034
\(749\) 18.0628 0.660000
\(750\) 0 0
\(751\) 13.6195 0.496984 0.248492 0.968634i \(-0.420065\pi\)
0.248492 + 0.968634i \(0.420065\pi\)
\(752\) 22.2265 0.810517
\(753\) 0 0
\(754\) −14.7750 −0.538073
\(755\) −32.7420 −1.19160
\(756\) 0 0
\(757\) 33.4512 1.21580 0.607902 0.794012i \(-0.292011\pi\)
0.607902 + 0.794012i \(0.292011\pi\)
\(758\) −5.03593 −0.182913
\(759\) 0 0
\(760\) 16.0310 0.581507
\(761\) −18.4399 −0.668446 −0.334223 0.942494i \(-0.608474\pi\)
−0.334223 + 0.942494i \(0.608474\pi\)
\(762\) 0 0
\(763\) −7.40505 −0.268081
\(764\) 42.4989 1.53755
\(765\) 0 0
\(766\) 6.19739 0.223921
\(767\) 62.2558 2.24793
\(768\) 0 0
\(769\) 42.6719 1.53879 0.769394 0.638774i \(-0.220558\pi\)
0.769394 + 0.638774i \(0.220558\pi\)
\(770\) 4.48337 0.161570
\(771\) 0 0
\(772\) −3.89452 −0.140167
\(773\) −17.6637 −0.635319 −0.317659 0.948205i \(-0.602897\pi\)
−0.317659 + 0.948205i \(0.602897\pi\)
\(774\) 0 0
\(775\) −5.36663 −0.192775
\(776\) −0.218685 −0.00785034
\(777\) 0 0
\(778\) 9.13590 0.327538
\(779\) −7.63556 −0.273572
\(780\) 0 0
\(781\) −54.5121 −1.95059
\(782\) −9.86876 −0.352906
\(783\) 0 0
\(784\) 2.95533 0.105547
\(785\) 51.4890 1.83772
\(786\) 0 0
\(787\) 34.4904 1.22945 0.614724 0.788742i \(-0.289267\pi\)
0.614724 + 0.788742i \(0.289267\pi\)
\(788\) 12.7758 0.455119
\(789\) 0 0
\(790\) −3.03700 −0.108052
\(791\) −18.6046 −0.661503
\(792\) 0 0
\(793\) −11.7542 −0.417404
\(794\) 3.66574 0.130092
\(795\) 0 0
\(796\) 34.0680 1.20751
\(797\) 11.8100 0.418333 0.209166 0.977880i \(-0.432925\pi\)
0.209166 + 0.977880i \(0.432925\pi\)
\(798\) 0 0
\(799\) −42.3556 −1.49844
\(800\) 9.36453 0.331086
\(801\) 0 0
\(802\) 10.7977 0.381282
\(803\) 43.2904 1.52768
\(804\) 0 0
\(805\) −11.0105 −0.388071
\(806\) −5.39569 −0.190055
\(807\) 0 0
\(808\) 1.17416 0.0413067
\(809\) −6.66413 −0.234298 −0.117149 0.993114i \(-0.537376\pi\)
−0.117149 + 0.993114i \(0.537376\pi\)
\(810\) 0 0
\(811\) −1.22927 −0.0431654 −0.0215827 0.999767i \(-0.506871\pi\)
−0.0215827 + 0.999767i \(0.506871\pi\)
\(812\) 12.8250 0.450069
\(813\) 0 0
\(814\) −4.46680 −0.156561
\(815\) 33.2227 1.16374
\(816\) 0 0
\(817\) 14.9973 0.524691
\(818\) 16.0989 0.562885
\(819\) 0 0
\(820\) −9.94510 −0.347298
\(821\) −28.1827 −0.983582 −0.491791 0.870713i \(-0.663658\pi\)
−0.491791 + 0.870713i \(0.663658\pi\)
\(822\) 0 0
\(823\) −24.6122 −0.857926 −0.428963 0.903322i \(-0.641121\pi\)
−0.428963 + 0.903322i \(0.641121\pi\)
\(824\) −23.0608 −0.803361
\(825\) 0 0
\(826\) 5.32761 0.185371
\(827\) 1.75039 0.0608670 0.0304335 0.999537i \(-0.490311\pi\)
0.0304335 + 0.999537i \(0.490311\pi\)
\(828\) 0 0
\(829\) −34.2634 −1.19002 −0.595009 0.803719i \(-0.702851\pi\)
−0.595009 + 0.803719i \(0.702851\pi\)
\(830\) 4.76070 0.165246
\(831\) 0 0
\(832\) −19.8459 −0.688034
\(833\) −5.63178 −0.195130
\(834\) 0 0
\(835\) 5.75822 0.199271
\(836\) 26.9289 0.931354
\(837\) 0 0
\(838\) 1.84156 0.0636155
\(839\) −35.2195 −1.21591 −0.607955 0.793971i \(-0.708010\pi\)
−0.607955 + 0.793971i \(0.708010\pi\)
\(840\) 0 0
\(841\) 20.6276 0.711296
\(842\) 12.4769 0.429983
\(843\) 0 0
\(844\) 20.7744 0.715086
\(845\) −30.6346 −1.05386
\(846\) 0 0
\(847\) 4.80477 0.165094
\(848\) −0.633617 −0.0217585
\(849\) 0 0
\(850\) −4.97708 −0.170713
\(851\) 10.9699 0.376042
\(852\) 0 0
\(853\) −0.785201 −0.0268848 −0.0134424 0.999910i \(-0.504279\pi\)
−0.0134424 + 0.999910i \(0.504279\pi\)
\(854\) −1.00588 −0.0344205
\(855\) 0 0
\(856\) −29.2359 −0.999263
\(857\) −33.4829 −1.14375 −0.571876 0.820340i \(-0.693784\pi\)
−0.571876 + 0.820340i \(0.693784\pi\)
\(858\) 0 0
\(859\) −8.16211 −0.278488 −0.139244 0.990258i \(-0.544467\pi\)
−0.139244 + 0.990258i \(0.544467\pi\)
\(860\) 19.5336 0.666090
\(861\) 0 0
\(862\) −12.5639 −0.427929
\(863\) 5.62343 0.191424 0.0957119 0.995409i \(-0.469487\pi\)
0.0957119 + 0.995409i \(0.469487\pi\)
\(864\) 0 0
\(865\) −41.4943 −1.41085
\(866\) −4.06581 −0.138162
\(867\) 0 0
\(868\) 4.68357 0.158971
\(869\) −10.7060 −0.363177
\(870\) 0 0
\(871\) 21.1193 0.715599
\(872\) 11.9856 0.405884
\(873\) 0 0
\(874\) 6.51997 0.220541
\(875\) 7.75688 0.262230
\(876\) 0 0
\(877\) 2.77495 0.0937033 0.0468516 0.998902i \(-0.485081\pi\)
0.0468516 + 0.998902i \(0.485081\pi\)
\(878\) −12.6557 −0.427110
\(879\) 0 0
\(880\) 31.2753 1.05429
\(881\) 36.0262 1.21375 0.606876 0.794797i \(-0.292422\pi\)
0.606876 + 0.794797i \(0.292422\pi\)
\(882\) 0 0
\(883\) 9.10055 0.306258 0.153129 0.988206i \(-0.451065\pi\)
0.153129 + 0.988206i \(0.451065\pi\)
\(884\) 50.7571 1.70715
\(885\) 0 0
\(886\) −0.824312 −0.0276933
\(887\) −46.7522 −1.56979 −0.784893 0.619632i \(-0.787282\pi\)
−0.784893 + 0.619632i \(0.787282\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 4.60528 0.154369
\(891\) 0 0
\(892\) −23.2851 −0.779641
\(893\) 27.9830 0.936415
\(894\) 0 0
\(895\) −29.8126 −0.996526
\(896\) −10.6767 −0.356683
\(897\) 0 0
\(898\) 7.49268 0.250034
\(899\) 18.1235 0.604454
\(900\) 0 0
\(901\) 1.20744 0.0402258
\(902\) 3.45633 0.115083
\(903\) 0 0
\(904\) 30.1129 1.00154
\(905\) 17.9118 0.595409
\(906\) 0 0
\(907\) 50.9022 1.69018 0.845090 0.534623i \(-0.179547\pi\)
0.845090 + 0.534623i \(0.179547\pi\)
\(908\) −43.0872 −1.42990
\(909\) 0 0
\(910\) −5.58299 −0.185074
\(911\) 29.0201 0.961480 0.480740 0.876863i \(-0.340368\pi\)
0.480740 + 0.876863i \(0.340368\pi\)
\(912\) 0 0
\(913\) 16.7824 0.555416
\(914\) −16.4056 −0.542649
\(915\) 0 0
\(916\) 30.4304 1.00545
\(917\) −11.7101 −0.386702
\(918\) 0 0
\(919\) −34.4150 −1.13525 −0.567623 0.823288i \(-0.692137\pi\)
−0.567623 + 0.823288i \(0.692137\pi\)
\(920\) 17.8214 0.587553
\(921\) 0 0
\(922\) −0.893943 −0.0294405
\(923\) 67.8820 2.23436
\(924\) 0 0
\(925\) 5.53239 0.181904
\(926\) −6.92578 −0.227595
\(927\) 0 0
\(928\) −31.6248 −1.03813
\(929\) −41.0030 −1.34526 −0.672632 0.739977i \(-0.734836\pi\)
−0.672632 + 0.739977i \(0.734836\pi\)
\(930\) 0 0
\(931\) 3.72073 0.121942
\(932\) 50.2163 1.64489
\(933\) 0 0
\(934\) −6.70782 −0.219487
\(935\) −59.5993 −1.94911
\(936\) 0 0
\(937\) 45.4052 1.48332 0.741662 0.670774i \(-0.234038\pi\)
0.741662 + 0.670774i \(0.234038\pi\)
\(938\) 1.80731 0.0590106
\(939\) 0 0
\(940\) 36.4470 1.18877
\(941\) −6.54913 −0.213496 −0.106748 0.994286i \(-0.534044\pi\)
−0.106748 + 0.994286i \(0.534044\pi\)
\(942\) 0 0
\(943\) −8.48828 −0.276417
\(944\) 37.1645 1.20960
\(945\) 0 0
\(946\) −6.78874 −0.220721
\(947\) 30.9829 1.00681 0.503405 0.864051i \(-0.332081\pi\)
0.503405 + 0.864051i \(0.332081\pi\)
\(948\) 0 0
\(949\) −53.9080 −1.74993
\(950\) 3.28820 0.106683
\(951\) 0 0
\(952\) 9.11543 0.295433
\(953\) −51.1779 −1.65782 −0.828908 0.559385i \(-0.811037\pi\)
−0.828908 + 0.559385i \(0.811037\pi\)
\(954\) 0 0
\(955\) 62.1418 2.01086
\(956\) −11.1065 −0.359211
\(957\) 0 0
\(958\) 9.37801 0.302990
\(959\) −2.39147 −0.0772247
\(960\) 0 0
\(961\) −24.3814 −0.786498
\(962\) 5.56236 0.179338
\(963\) 0 0
\(964\) 29.9370 0.964204
\(965\) −5.69456 −0.183314
\(966\) 0 0
\(967\) −38.9551 −1.25271 −0.626356 0.779538i \(-0.715454\pi\)
−0.626356 + 0.779538i \(0.715454\pi\)
\(968\) −7.77686 −0.249958
\(969\) 0 0
\(970\) −0.152370 −0.00489229
\(971\) −42.6229 −1.36783 −0.683917 0.729559i \(-0.739725\pi\)
−0.683917 + 0.729559i \(0.739725\pi\)
\(972\) 0 0
\(973\) −2.14800 −0.0688616
\(974\) −0.147490 −0.00472589
\(975\) 0 0
\(976\) −7.01685 −0.224604
\(977\) −49.7039 −1.59017 −0.795084 0.606500i \(-0.792573\pi\)
−0.795084 + 0.606500i \(0.792573\pi\)
\(978\) 0 0
\(979\) 16.2345 0.518857
\(980\) 4.84615 0.154804
\(981\) 0 0
\(982\) 3.08738 0.0985222
\(983\) 20.5978 0.656968 0.328484 0.944510i \(-0.393462\pi\)
0.328484 + 0.944510i \(0.393462\pi\)
\(984\) 0 0
\(985\) 18.6808 0.595218
\(986\) 16.8080 0.535276
\(987\) 0 0
\(988\) −33.5336 −1.06685
\(989\) 16.6722 0.530146
\(990\) 0 0
\(991\) −40.6235 −1.29045 −0.645224 0.763994i \(-0.723236\pi\)
−0.645224 + 0.763994i \(0.723236\pi\)
\(992\) −11.5491 −0.366684
\(993\) 0 0
\(994\) 5.80909 0.184253
\(995\) 49.8141 1.57921
\(996\) 0 0
\(997\) −34.6749 −1.09817 −0.549083 0.835768i \(-0.685023\pi\)
−0.549083 + 0.835768i \(0.685023\pi\)
\(998\) −7.01652 −0.222104
\(999\) 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 \(a_p\))