Properties

Label 4030.2.a.n.1.2
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.04806\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.04806 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.04806 q^{6} +3.38208 q^{7} +1.00000 q^{8} +1.19454 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.04806 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.04806 q^{6} +3.38208 q^{7} +1.00000 q^{8} +1.19454 q^{9} -1.00000 q^{10} +4.04625 q^{11} -2.04806 q^{12} -1.00000 q^{13} +3.38208 q^{14} +2.04806 q^{15} +1.00000 q^{16} -0.266066 q^{17} +1.19454 q^{18} +0.644857 q^{19} -1.00000 q^{20} -6.92670 q^{21} +4.04625 q^{22} -2.41172 q^{23} -2.04806 q^{24} +1.00000 q^{25} -1.00000 q^{26} +3.69768 q^{27} +3.38208 q^{28} +3.80875 q^{29} +2.04806 q^{30} -1.00000 q^{31} +1.00000 q^{32} -8.28695 q^{33} -0.266066 q^{34} -3.38208 q^{35} +1.19454 q^{36} +7.18573 q^{37} +0.644857 q^{38} +2.04806 q^{39} -1.00000 q^{40} +9.56569 q^{41} -6.92670 q^{42} -3.26954 q^{43} +4.04625 q^{44} -1.19454 q^{45} -2.41172 q^{46} -5.69205 q^{47} -2.04806 q^{48} +4.43847 q^{49} +1.00000 q^{50} +0.544918 q^{51} -1.00000 q^{52} -4.59024 q^{53} +3.69768 q^{54} -4.04625 q^{55} +3.38208 q^{56} -1.32070 q^{57} +3.80875 q^{58} -7.74498 q^{59} +2.04806 q^{60} +1.95299 q^{61} -1.00000 q^{62} +4.04004 q^{63} +1.00000 q^{64} +1.00000 q^{65} -8.28695 q^{66} -0.00670319 q^{67} -0.266066 q^{68} +4.93934 q^{69} -3.38208 q^{70} +7.58279 q^{71} +1.19454 q^{72} -5.98592 q^{73} +7.18573 q^{74} -2.04806 q^{75} +0.644857 q^{76} +13.6847 q^{77} +2.04806 q^{78} -6.01421 q^{79} -1.00000 q^{80} -11.1567 q^{81} +9.56569 q^{82} -4.01325 q^{83} -6.92670 q^{84} +0.266066 q^{85} -3.26954 q^{86} -7.80054 q^{87} +4.04625 q^{88} +11.8448 q^{89} -1.19454 q^{90} -3.38208 q^{91} -2.41172 q^{92} +2.04806 q^{93} -5.69205 q^{94} -0.644857 q^{95} -2.04806 q^{96} +1.83251 q^{97} +4.43847 q^{98} +4.83341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.04806 −1.18245 −0.591223 0.806508i \(-0.701355\pi\)
−0.591223 + 0.806508i \(0.701355\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.04806 −0.836116
\(7\) 3.38208 1.27831 0.639153 0.769079i \(-0.279285\pi\)
0.639153 + 0.769079i \(0.279285\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.19454 0.398181
\(10\) −1.00000 −0.316228
\(11\) 4.04625 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(12\) −2.04806 −0.591223
\(13\) −1.00000 −0.277350
\(14\) 3.38208 0.903899
\(15\) 2.04806 0.528806
\(16\) 1.00000 0.250000
\(17\) −0.266066 −0.0645304 −0.0322652 0.999479i \(-0.510272\pi\)
−0.0322652 + 0.999479i \(0.510272\pi\)
\(18\) 1.19454 0.281556
\(19\) 0.644857 0.147940 0.0739702 0.997260i \(-0.476433\pi\)
0.0739702 + 0.997260i \(0.476433\pi\)
\(20\) −1.00000 −0.223607
\(21\) −6.92670 −1.51153
\(22\) 4.04625 0.862662
\(23\) −2.41172 −0.502878 −0.251439 0.967873i \(-0.580904\pi\)
−0.251439 + 0.967873i \(0.580904\pi\)
\(24\) −2.04806 −0.418058
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 3.69768 0.711619
\(28\) 3.38208 0.639153
\(29\) 3.80875 0.707267 0.353633 0.935384i \(-0.384946\pi\)
0.353633 + 0.935384i \(0.384946\pi\)
\(30\) 2.04806 0.373923
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −8.28695 −1.44257
\(34\) −0.266066 −0.0456299
\(35\) −3.38208 −0.571676
\(36\) 1.19454 0.199090
\(37\) 7.18573 1.18133 0.590663 0.806918i \(-0.298866\pi\)
0.590663 + 0.806918i \(0.298866\pi\)
\(38\) 0.644857 0.104610
\(39\) 2.04806 0.327952
\(40\) −1.00000 −0.158114
\(41\) 9.56569 1.49391 0.746955 0.664875i \(-0.231515\pi\)
0.746955 + 0.664875i \(0.231515\pi\)
\(42\) −6.92670 −1.06881
\(43\) −3.26954 −0.498600 −0.249300 0.968426i \(-0.580201\pi\)
−0.249300 + 0.968426i \(0.580201\pi\)
\(44\) 4.04625 0.609994
\(45\) −1.19454 −0.178072
\(46\) −2.41172 −0.355588
\(47\) −5.69205 −0.830270 −0.415135 0.909760i \(-0.636266\pi\)
−0.415135 + 0.909760i \(0.636266\pi\)
\(48\) −2.04806 −0.295612
\(49\) 4.43847 0.634068
\(50\) 1.00000 0.141421
\(51\) 0.544918 0.0763038
\(52\) −1.00000 −0.138675
\(53\) −4.59024 −0.630518 −0.315259 0.949006i \(-0.602091\pi\)
−0.315259 + 0.949006i \(0.602091\pi\)
\(54\) 3.69768 0.503191
\(55\) −4.04625 −0.545596
\(56\) 3.38208 0.451950
\(57\) −1.32070 −0.174932
\(58\) 3.80875 0.500113
\(59\) −7.74498 −1.00831 −0.504155 0.863613i \(-0.668196\pi\)
−0.504155 + 0.863613i \(0.668196\pi\)
\(60\) 2.04806 0.264403
\(61\) 1.95299 0.250055 0.125028 0.992153i \(-0.460098\pi\)
0.125028 + 0.992153i \(0.460098\pi\)
\(62\) −1.00000 −0.127000
\(63\) 4.04004 0.508997
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) −8.28695 −1.02005
\(67\) −0.00670319 −0.000818925 0 −0.000409462 1.00000i \(-0.500130\pi\)
−0.000409462 1.00000i \(0.500130\pi\)
\(68\) −0.266066 −0.0322652
\(69\) 4.93934 0.594626
\(70\) −3.38208 −0.404236
\(71\) 7.58279 0.899912 0.449956 0.893051i \(-0.351440\pi\)
0.449956 + 0.893051i \(0.351440\pi\)
\(72\) 1.19454 0.140778
\(73\) −5.98592 −0.700599 −0.350299 0.936638i \(-0.613920\pi\)
−0.350299 + 0.936638i \(0.613920\pi\)
\(74\) 7.18573 0.835324
\(75\) −2.04806 −0.236489
\(76\) 0.644857 0.0739702
\(77\) 13.6847 1.55952
\(78\) 2.04806 0.231897
\(79\) −6.01421 −0.676652 −0.338326 0.941029i \(-0.609861\pi\)
−0.338326 + 0.941029i \(0.609861\pi\)
\(80\) −1.00000 −0.111803
\(81\) −11.1567 −1.23963
\(82\) 9.56569 1.05635
\(83\) −4.01325 −0.440511 −0.220256 0.975442i \(-0.570689\pi\)
−0.220256 + 0.975442i \(0.570689\pi\)
\(84\) −6.92670 −0.755765
\(85\) 0.266066 0.0288589
\(86\) −3.26954 −0.352563
\(87\) −7.80054 −0.836305
\(88\) 4.04625 0.431331
\(89\) 11.8448 1.25555 0.627776 0.778394i \(-0.283966\pi\)
0.627776 + 0.778394i \(0.283966\pi\)
\(90\) −1.19454 −0.125916
\(91\) −3.38208 −0.354538
\(92\) −2.41172 −0.251439
\(93\) 2.04806 0.212374
\(94\) −5.69205 −0.587090
\(95\) −0.644857 −0.0661609
\(96\) −2.04806 −0.209029
\(97\) 1.83251 0.186063 0.0930315 0.995663i \(-0.470344\pi\)
0.0930315 + 0.995663i \(0.470344\pi\)
\(98\) 4.43847 0.448353
\(99\) 4.83341 0.485776
\(100\) 1.00000 0.100000
\(101\) −8.85786 −0.881390 −0.440695 0.897657i \(-0.645268\pi\)
−0.440695 + 0.897657i \(0.645268\pi\)
\(102\) 0.544918 0.0539549
\(103\) 3.87414 0.381730 0.190865 0.981616i \(-0.438871\pi\)
0.190865 + 0.981616i \(0.438871\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 6.92670 0.675977
\(106\) −4.59024 −0.445844
\(107\) 19.1905 1.85522 0.927610 0.373550i \(-0.121859\pi\)
0.927610 + 0.373550i \(0.121859\pi\)
\(108\) 3.69768 0.355810
\(109\) −2.86634 −0.274545 −0.137273 0.990533i \(-0.543834\pi\)
−0.137273 + 0.990533i \(0.543834\pi\)
\(110\) −4.04625 −0.385794
\(111\) −14.7168 −1.39686
\(112\) 3.38208 0.319577
\(113\) 2.88291 0.271201 0.135601 0.990764i \(-0.456704\pi\)
0.135601 + 0.990764i \(0.456704\pi\)
\(114\) −1.32070 −0.123695
\(115\) 2.41172 0.224894
\(116\) 3.80875 0.353633
\(117\) −1.19454 −0.110435
\(118\) −7.74498 −0.712983
\(119\) −0.899856 −0.0824896
\(120\) 2.04806 0.186961
\(121\) 5.37210 0.488373
\(122\) 1.95299 0.176816
\(123\) −19.5911 −1.76647
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 4.04004 0.359915
\(127\) 11.1456 0.989010 0.494505 0.869175i \(-0.335349\pi\)
0.494505 + 0.869175i \(0.335349\pi\)
\(128\) 1.00000 0.0883883
\(129\) 6.69621 0.589568
\(130\) 1.00000 0.0877058
\(131\) 13.6357 1.19135 0.595676 0.803225i \(-0.296884\pi\)
0.595676 + 0.803225i \(0.296884\pi\)
\(132\) −8.28695 −0.721286
\(133\) 2.18096 0.189113
\(134\) −0.00670319 −0.000579067 0
\(135\) −3.69768 −0.318246
\(136\) −0.266066 −0.0228149
\(137\) 1.89250 0.161687 0.0808436 0.996727i \(-0.474239\pi\)
0.0808436 + 0.996727i \(0.474239\pi\)
\(138\) 4.93934 0.420464
\(139\) −12.7717 −1.08328 −0.541642 0.840609i \(-0.682197\pi\)
−0.541642 + 0.840609i \(0.682197\pi\)
\(140\) −3.38208 −0.285838
\(141\) 11.6576 0.981751
\(142\) 7.58279 0.636334
\(143\) −4.04625 −0.338364
\(144\) 1.19454 0.0995452
\(145\) −3.80875 −0.316299
\(146\) −5.98592 −0.495398
\(147\) −9.09025 −0.749751
\(148\) 7.18573 0.590663
\(149\) 21.9281 1.79642 0.898212 0.439564i \(-0.144867\pi\)
0.898212 + 0.439564i \(0.144867\pi\)
\(150\) −2.04806 −0.167223
\(151\) 11.7903 0.959480 0.479740 0.877411i \(-0.340731\pi\)
0.479740 + 0.877411i \(0.340731\pi\)
\(152\) 0.644857 0.0523048
\(153\) −0.317827 −0.0256948
\(154\) 13.6847 1.10275
\(155\) 1.00000 0.0803219
\(156\) 2.04806 0.163976
\(157\) 0.311656 0.0248729 0.0124364 0.999923i \(-0.496041\pi\)
0.0124364 + 0.999923i \(0.496041\pi\)
\(158\) −6.01421 −0.478465
\(159\) 9.40108 0.745554
\(160\) −1.00000 −0.0790569
\(161\) −8.15662 −0.642832
\(162\) −11.1567 −0.876553
\(163\) 14.9899 1.17410 0.587048 0.809552i \(-0.300290\pi\)
0.587048 + 0.809552i \(0.300290\pi\)
\(164\) 9.56569 0.746955
\(165\) 8.28695 0.645138
\(166\) −4.01325 −0.311488
\(167\) 0.219986 0.0170230 0.00851151 0.999964i \(-0.497291\pi\)
0.00851151 + 0.999964i \(0.497291\pi\)
\(168\) −6.92670 −0.534406
\(169\) 1.00000 0.0769231
\(170\) 0.266066 0.0204063
\(171\) 0.770309 0.0589070
\(172\) −3.26954 −0.249300
\(173\) 12.7180 0.966935 0.483467 0.875362i \(-0.339377\pi\)
0.483467 + 0.875362i \(0.339377\pi\)
\(174\) −7.80054 −0.591357
\(175\) 3.38208 0.255661
\(176\) 4.04625 0.304997
\(177\) 15.8622 1.19227
\(178\) 11.8448 0.887809
\(179\) 7.53904 0.563494 0.281747 0.959489i \(-0.409086\pi\)
0.281747 + 0.959489i \(0.409086\pi\)
\(180\) −1.19454 −0.0890359
\(181\) 13.3732 0.994025 0.497013 0.867743i \(-0.334430\pi\)
0.497013 + 0.867743i \(0.334430\pi\)
\(182\) −3.38208 −0.250697
\(183\) −3.99984 −0.295677
\(184\) −2.41172 −0.177794
\(185\) −7.18573 −0.528305
\(186\) 2.04806 0.150171
\(187\) −1.07657 −0.0787264
\(188\) −5.69205 −0.415135
\(189\) 12.5059 0.909668
\(190\) −0.644857 −0.0467828
\(191\) 16.6358 1.20372 0.601861 0.798601i \(-0.294426\pi\)
0.601861 + 0.798601i \(0.294426\pi\)
\(192\) −2.04806 −0.147806
\(193\) 16.1789 1.16458 0.582292 0.812980i \(-0.302156\pi\)
0.582292 + 0.812980i \(0.302156\pi\)
\(194\) 1.83251 0.131566
\(195\) −2.04806 −0.146664
\(196\) 4.43847 0.317034
\(197\) −5.87360 −0.418476 −0.209238 0.977865i \(-0.567098\pi\)
−0.209238 + 0.977865i \(0.567098\pi\)
\(198\) 4.83341 0.343496
\(199\) 0.0913135 0.00647304 0.00323652 0.999995i \(-0.498970\pi\)
0.00323652 + 0.999995i \(0.498970\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0.0137285 0.000968335 0
\(202\) −8.85786 −0.623237
\(203\) 12.8815 0.904104
\(204\) 0.544918 0.0381519
\(205\) −9.56569 −0.668096
\(206\) 3.87414 0.269924
\(207\) −2.88090 −0.200236
\(208\) −1.00000 −0.0693375
\(209\) 2.60925 0.180486
\(210\) 6.92670 0.477988
\(211\) 13.5841 0.935170 0.467585 0.883948i \(-0.345124\pi\)
0.467585 + 0.883948i \(0.345124\pi\)
\(212\) −4.59024 −0.315259
\(213\) −15.5300 −1.06410
\(214\) 19.1905 1.31184
\(215\) 3.26954 0.222981
\(216\) 3.69768 0.251595
\(217\) −3.38208 −0.229591
\(218\) −2.86634 −0.194133
\(219\) 12.2595 0.828421
\(220\) −4.04625 −0.272798
\(221\) 0.266066 0.0178975
\(222\) −14.7168 −0.987726
\(223\) −16.0746 −1.07644 −0.538219 0.842805i \(-0.680903\pi\)
−0.538219 + 0.842805i \(0.680903\pi\)
\(224\) 3.38208 0.225975
\(225\) 1.19454 0.0796362
\(226\) 2.88291 0.191768
\(227\) 15.0848 1.00121 0.500606 0.865675i \(-0.333110\pi\)
0.500606 + 0.865675i \(0.333110\pi\)
\(228\) −1.32070 −0.0874658
\(229\) 14.1932 0.937914 0.468957 0.883221i \(-0.344630\pi\)
0.468957 + 0.883221i \(0.344630\pi\)
\(230\) 2.41172 0.159024
\(231\) −28.0271 −1.84405
\(232\) 3.80875 0.250057
\(233\) −11.1560 −0.730851 −0.365425 0.930841i \(-0.619076\pi\)
−0.365425 + 0.930841i \(0.619076\pi\)
\(234\) −1.19454 −0.0780897
\(235\) 5.69205 0.371308
\(236\) −7.74498 −0.504155
\(237\) 12.3175 0.800105
\(238\) −0.899856 −0.0583290
\(239\) 10.0842 0.652290 0.326145 0.945320i \(-0.394250\pi\)
0.326145 + 0.945320i \(0.394250\pi\)
\(240\) 2.04806 0.132202
\(241\) 3.22950 0.208031 0.104015 0.994576i \(-0.466831\pi\)
0.104015 + 0.994576i \(0.466831\pi\)
\(242\) 5.37210 0.345332
\(243\) 11.7565 0.754181
\(244\) 1.95299 0.125028
\(245\) −4.43847 −0.283564
\(246\) −19.5911 −1.24908
\(247\) −0.644857 −0.0410313
\(248\) −1.00000 −0.0635001
\(249\) 8.21937 0.520881
\(250\) −1.00000 −0.0632456
\(251\) −3.93272 −0.248231 −0.124116 0.992268i \(-0.539609\pi\)
−0.124116 + 0.992268i \(0.539609\pi\)
\(252\) 4.04004 0.254499
\(253\) −9.75840 −0.613505
\(254\) 11.1456 0.699336
\(255\) −0.544918 −0.0341241
\(256\) 1.00000 0.0625000
\(257\) −12.6814 −0.791044 −0.395522 0.918457i \(-0.629436\pi\)
−0.395522 + 0.918457i \(0.629436\pi\)
\(258\) 6.69621 0.416888
\(259\) 24.3027 1.51010
\(260\) 1.00000 0.0620174
\(261\) 4.54971 0.281620
\(262\) 13.6357 0.842414
\(263\) −21.4371 −1.32187 −0.660933 0.750445i \(-0.729839\pi\)
−0.660933 + 0.750445i \(0.729839\pi\)
\(264\) −8.28695 −0.510026
\(265\) 4.59024 0.281976
\(266\) 2.18096 0.133723
\(267\) −24.2589 −1.48462
\(268\) −0.00670319 −0.000409462 0
\(269\) 15.3904 0.938369 0.469185 0.883100i \(-0.344548\pi\)
0.469185 + 0.883100i \(0.344548\pi\)
\(270\) −3.69768 −0.225034
\(271\) −13.7743 −0.836726 −0.418363 0.908280i \(-0.637396\pi\)
−0.418363 + 0.908280i \(0.637396\pi\)
\(272\) −0.266066 −0.0161326
\(273\) 6.92670 0.419223
\(274\) 1.89250 0.114330
\(275\) 4.04625 0.243998
\(276\) 4.93934 0.297313
\(277\) −4.32637 −0.259947 −0.129973 0.991517i \(-0.541489\pi\)
−0.129973 + 0.991517i \(0.541489\pi\)
\(278\) −12.7717 −0.765998
\(279\) −1.19454 −0.0715154
\(280\) −3.38208 −0.202118
\(281\) 0.927146 0.0553089 0.0276545 0.999618i \(-0.491196\pi\)
0.0276545 + 0.999618i \(0.491196\pi\)
\(282\) 11.6576 0.694203
\(283\) 8.02534 0.477057 0.238529 0.971135i \(-0.423335\pi\)
0.238529 + 0.971135i \(0.423335\pi\)
\(284\) 7.58279 0.449956
\(285\) 1.32070 0.0782318
\(286\) −4.04625 −0.239259
\(287\) 32.3519 1.90967
\(288\) 1.19454 0.0703891
\(289\) −16.9292 −0.995836
\(290\) −3.80875 −0.223657
\(291\) −3.75308 −0.220010
\(292\) −5.98592 −0.350299
\(293\) −22.1887 −1.29628 −0.648140 0.761521i \(-0.724453\pi\)
−0.648140 + 0.761521i \(0.724453\pi\)
\(294\) −9.09025 −0.530154
\(295\) 7.74498 0.450930
\(296\) 7.18573 0.417662
\(297\) 14.9617 0.868168
\(298\) 21.9281 1.27026
\(299\) 2.41172 0.139473
\(300\) −2.04806 −0.118245
\(301\) −11.0578 −0.637364
\(302\) 11.7903 0.678455
\(303\) 18.1414 1.04220
\(304\) 0.644857 0.0369851
\(305\) −1.95299 −0.111828
\(306\) −0.317827 −0.0181689
\(307\) −4.91759 −0.280662 −0.140331 0.990105i \(-0.544817\pi\)
−0.140331 + 0.990105i \(0.544817\pi\)
\(308\) 13.6847 0.779760
\(309\) −7.93446 −0.451376
\(310\) 1.00000 0.0567962
\(311\) 25.7106 1.45792 0.728958 0.684558i \(-0.240005\pi\)
0.728958 + 0.684558i \(0.240005\pi\)
\(312\) 2.04806 0.115948
\(313\) −11.2542 −0.636127 −0.318064 0.948069i \(-0.603033\pi\)
−0.318064 + 0.948069i \(0.603033\pi\)
\(314\) 0.311656 0.0175878
\(315\) −4.04004 −0.227630
\(316\) −6.01421 −0.338326
\(317\) −13.0143 −0.730954 −0.365477 0.930820i \(-0.619094\pi\)
−0.365477 + 0.930820i \(0.619094\pi\)
\(318\) 9.40108 0.527187
\(319\) 15.4111 0.862857
\(320\) −1.00000 −0.0559017
\(321\) −39.3034 −2.19370
\(322\) −8.15662 −0.454551
\(323\) −0.171574 −0.00954665
\(324\) −11.1567 −0.619816
\(325\) −1.00000 −0.0554700
\(326\) 14.9899 0.830211
\(327\) 5.87043 0.324635
\(328\) 9.56569 0.528177
\(329\) −19.2510 −1.06134
\(330\) 8.28695 0.456181
\(331\) −32.8155 −1.80371 −0.901853 0.432044i \(-0.857793\pi\)
−0.901853 + 0.432044i \(0.857793\pi\)
\(332\) −4.01325 −0.220256
\(333\) 8.58365 0.470381
\(334\) 0.219986 0.0120371
\(335\) 0.00670319 0.000366234 0
\(336\) −6.92670 −0.377882
\(337\) 5.27377 0.287281 0.143640 0.989630i \(-0.454119\pi\)
0.143640 + 0.989630i \(0.454119\pi\)
\(338\) 1.00000 0.0543928
\(339\) −5.90437 −0.320681
\(340\) 0.266066 0.0144294
\(341\) −4.04625 −0.219116
\(342\) 0.770309 0.0416535
\(343\) −8.66329 −0.467774
\(344\) −3.26954 −0.176282
\(345\) −4.93934 −0.265925
\(346\) 12.7180 0.683726
\(347\) −16.9185 −0.908234 −0.454117 0.890942i \(-0.650045\pi\)
−0.454117 + 0.890942i \(0.650045\pi\)
\(348\) −7.80054 −0.418153
\(349\) 1.54250 0.0825679 0.0412840 0.999147i \(-0.486855\pi\)
0.0412840 + 0.999147i \(0.486855\pi\)
\(350\) 3.38208 0.180780
\(351\) −3.69768 −0.197368
\(352\) 4.04625 0.215666
\(353\) −15.5081 −0.825410 −0.412705 0.910865i \(-0.635416\pi\)
−0.412705 + 0.910865i \(0.635416\pi\)
\(354\) 15.8622 0.843065
\(355\) −7.58279 −0.402453
\(356\) 11.8448 0.627776
\(357\) 1.84296 0.0975396
\(358\) 7.53904 0.398451
\(359\) 19.1927 1.01295 0.506476 0.862254i \(-0.330948\pi\)
0.506476 + 0.862254i \(0.330948\pi\)
\(360\) −1.19454 −0.0629579
\(361\) −18.5842 −0.978114
\(362\) 13.3732 0.702882
\(363\) −11.0024 −0.577475
\(364\) −3.38208 −0.177269
\(365\) 5.98592 0.313317
\(366\) −3.99984 −0.209075
\(367\) 34.7312 1.81295 0.906476 0.422257i \(-0.138762\pi\)
0.906476 + 0.422257i \(0.138762\pi\)
\(368\) −2.41172 −0.125719
\(369\) 11.4266 0.594846
\(370\) −7.18573 −0.373568
\(371\) −15.5246 −0.805996
\(372\) 2.04806 0.106187
\(373\) 14.1384 0.732061 0.366031 0.930603i \(-0.380717\pi\)
0.366031 + 0.930603i \(0.380717\pi\)
\(374\) −1.07657 −0.0556680
\(375\) 2.04806 0.105761
\(376\) −5.69205 −0.293545
\(377\) −3.80875 −0.196160
\(378\) 12.5059 0.643232
\(379\) 5.86902 0.301471 0.150736 0.988574i \(-0.451836\pi\)
0.150736 + 0.988574i \(0.451836\pi\)
\(380\) −0.644857 −0.0330805
\(381\) −22.8268 −1.16945
\(382\) 16.6358 0.851160
\(383\) −14.4275 −0.737210 −0.368605 0.929586i \(-0.620164\pi\)
−0.368605 + 0.929586i \(0.620164\pi\)
\(384\) −2.04806 −0.104515
\(385\) −13.6847 −0.697438
\(386\) 16.1789 0.823485
\(387\) −3.90560 −0.198533
\(388\) 1.83251 0.0930315
\(389\) 24.2202 1.22801 0.614007 0.789300i \(-0.289556\pi\)
0.614007 + 0.789300i \(0.289556\pi\)
\(390\) −2.04806 −0.103707
\(391\) 0.641675 0.0324509
\(392\) 4.43847 0.224177
\(393\) −27.9266 −1.40871
\(394\) −5.87360 −0.295908
\(395\) 6.01421 0.302608
\(396\) 4.83341 0.242888
\(397\) −24.0624 −1.20765 −0.603827 0.797115i \(-0.706358\pi\)
−0.603827 + 0.797115i \(0.706358\pi\)
\(398\) 0.0913135 0.00457713
\(399\) −4.46673 −0.223616
\(400\) 1.00000 0.0500000
\(401\) −17.1745 −0.857653 −0.428827 0.903387i \(-0.641073\pi\)
−0.428827 + 0.903387i \(0.641073\pi\)
\(402\) 0.0137285 0.000684716 0
\(403\) 1.00000 0.0498135
\(404\) −8.85786 −0.440695
\(405\) 11.1567 0.554381
\(406\) 12.8815 0.639298
\(407\) 29.0752 1.44120
\(408\) 0.544918 0.0269775
\(409\) −28.0187 −1.38543 −0.692717 0.721210i \(-0.743586\pi\)
−0.692717 + 0.721210i \(0.743586\pi\)
\(410\) −9.56569 −0.472416
\(411\) −3.87595 −0.191187
\(412\) 3.87414 0.190865
\(413\) −26.1941 −1.28893
\(414\) −2.88090 −0.141588
\(415\) 4.01325 0.197003
\(416\) −1.00000 −0.0490290
\(417\) 26.1573 1.28093
\(418\) 2.60925 0.127623
\(419\) 27.3490 1.33609 0.668044 0.744122i \(-0.267132\pi\)
0.668044 + 0.744122i \(0.267132\pi\)
\(420\) 6.92670 0.337988
\(421\) −1.55602 −0.0758357 −0.0379178 0.999281i \(-0.512073\pi\)
−0.0379178 + 0.999281i \(0.512073\pi\)
\(422\) 13.5841 0.661265
\(423\) −6.79939 −0.330598
\(424\) −4.59024 −0.222922
\(425\) −0.266066 −0.0129061
\(426\) −15.5300 −0.752431
\(427\) 6.60518 0.319647
\(428\) 19.1905 0.927610
\(429\) 8.28695 0.400097
\(430\) 3.26954 0.157671
\(431\) −9.11333 −0.438974 −0.219487 0.975615i \(-0.570438\pi\)
−0.219487 + 0.975615i \(0.570438\pi\)
\(432\) 3.69768 0.177905
\(433\) −11.5976 −0.557343 −0.278672 0.960386i \(-0.589894\pi\)
−0.278672 + 0.960386i \(0.589894\pi\)
\(434\) −3.38208 −0.162345
\(435\) 7.80054 0.374007
\(436\) −2.86634 −0.137273
\(437\) −1.55521 −0.0743959
\(438\) 12.2595 0.585782
\(439\) 1.38796 0.0662436 0.0331218 0.999451i \(-0.489455\pi\)
0.0331218 + 0.999451i \(0.489455\pi\)
\(440\) −4.04625 −0.192897
\(441\) 5.30194 0.252473
\(442\) 0.266066 0.0126555
\(443\) 27.8167 1.32161 0.660805 0.750558i \(-0.270215\pi\)
0.660805 + 0.750558i \(0.270215\pi\)
\(444\) −14.7168 −0.698428
\(445\) −11.8448 −0.561500
\(446\) −16.0746 −0.761157
\(447\) −44.9101 −2.12417
\(448\) 3.38208 0.159788
\(449\) 23.5304 1.11047 0.555235 0.831694i \(-0.312628\pi\)
0.555235 + 0.831694i \(0.312628\pi\)
\(450\) 1.19454 0.0563113
\(451\) 38.7051 1.82255
\(452\) 2.88291 0.135601
\(453\) −24.1472 −1.13453
\(454\) 15.0848 0.707964
\(455\) 3.38208 0.158554
\(456\) −1.32070 −0.0618477
\(457\) −21.0966 −0.986857 −0.493429 0.869786i \(-0.664257\pi\)
−0.493429 + 0.869786i \(0.664257\pi\)
\(458\) 14.1932 0.663205
\(459\) −0.983826 −0.0459211
\(460\) 2.41172 0.112447
\(461\) −10.4387 −0.486179 −0.243090 0.970004i \(-0.578161\pi\)
−0.243090 + 0.970004i \(0.578161\pi\)
\(462\) −28.0271 −1.30394
\(463\) −41.0084 −1.90582 −0.952911 0.303250i \(-0.901928\pi\)
−0.952911 + 0.303250i \(0.901928\pi\)
\(464\) 3.80875 0.176817
\(465\) −2.04806 −0.0949764
\(466\) −11.1560 −0.516789
\(467\) −23.9455 −1.10807 −0.554033 0.832495i \(-0.686912\pi\)
−0.554033 + 0.832495i \(0.686912\pi\)
\(468\) −1.19454 −0.0552177
\(469\) −0.0226707 −0.00104684
\(470\) 5.69205 0.262555
\(471\) −0.638290 −0.0294108
\(472\) −7.74498 −0.356492
\(473\) −13.2294 −0.608286
\(474\) 12.3175 0.565759
\(475\) 0.644857 0.0295881
\(476\) −0.899856 −0.0412448
\(477\) −5.48324 −0.251060
\(478\) 10.0842 0.461239
\(479\) 9.42095 0.430454 0.215227 0.976564i \(-0.430951\pi\)
0.215227 + 0.976564i \(0.430951\pi\)
\(480\) 2.04806 0.0934806
\(481\) −7.18573 −0.327641
\(482\) 3.22950 0.147100
\(483\) 16.7052 0.760115
\(484\) 5.37210 0.244186
\(485\) −1.83251 −0.0832099
\(486\) 11.7565 0.533286
\(487\) −0.635603 −0.0288019 −0.0144010 0.999896i \(-0.504584\pi\)
−0.0144010 + 0.999896i \(0.504584\pi\)
\(488\) 1.95299 0.0884078
\(489\) −30.7001 −1.38831
\(490\) −4.43847 −0.200510
\(491\) −35.7982 −1.61555 −0.807776 0.589490i \(-0.799329\pi\)
−0.807776 + 0.589490i \(0.799329\pi\)
\(492\) −19.5911 −0.883234
\(493\) −1.01338 −0.0456402
\(494\) −0.644857 −0.0290135
\(495\) −4.83341 −0.217246
\(496\) −1.00000 −0.0449013
\(497\) 25.6456 1.15036
\(498\) 8.21937 0.368319
\(499\) 25.2254 1.12924 0.564621 0.825350i \(-0.309022\pi\)
0.564621 + 0.825350i \(0.309022\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −0.450544 −0.0201288
\(502\) −3.93272 −0.175526
\(503\) 13.9898 0.623775 0.311888 0.950119i \(-0.399039\pi\)
0.311888 + 0.950119i \(0.399039\pi\)
\(504\) 4.04004 0.179958
\(505\) 8.85786 0.394169
\(506\) −9.75840 −0.433814
\(507\) −2.04806 −0.0909575
\(508\) 11.1456 0.494505
\(509\) −10.1626 −0.450451 −0.225226 0.974307i \(-0.572312\pi\)
−0.225226 + 0.974307i \(0.572312\pi\)
\(510\) −0.544918 −0.0241294
\(511\) −20.2449 −0.895580
\(512\) 1.00000 0.0441942
\(513\) 2.38448 0.105277
\(514\) −12.6814 −0.559353
\(515\) −3.87414 −0.170715
\(516\) 6.69621 0.294784
\(517\) −23.0314 −1.01292
\(518\) 24.3027 1.06780
\(519\) −26.0473 −1.14335
\(520\) 1.00000 0.0438529
\(521\) −21.0258 −0.921156 −0.460578 0.887619i \(-0.652358\pi\)
−0.460578 + 0.887619i \(0.652358\pi\)
\(522\) 4.54971 0.199135
\(523\) 6.95255 0.304014 0.152007 0.988379i \(-0.451426\pi\)
0.152007 + 0.988379i \(0.451426\pi\)
\(524\) 13.6357 0.595676
\(525\) −6.92670 −0.302306
\(526\) −21.4371 −0.934700
\(527\) 0.266066 0.0115900
\(528\) −8.28695 −0.360643
\(529\) −17.1836 −0.747114
\(530\) 4.59024 0.199387
\(531\) −9.25170 −0.401490
\(532\) 2.18096 0.0945565
\(533\) −9.56569 −0.414336
\(534\) −24.2589 −1.04979
\(535\) −19.1905 −0.829680
\(536\) −0.00670319 −0.000289534 0
\(537\) −15.4404 −0.666302
\(538\) 15.3904 0.663527
\(539\) 17.9591 0.773555
\(540\) −3.69768 −0.159123
\(541\) 40.1235 1.72504 0.862522 0.506019i \(-0.168884\pi\)
0.862522 + 0.506019i \(0.168884\pi\)
\(542\) −13.7743 −0.591655
\(543\) −27.3892 −1.17538
\(544\) −0.266066 −0.0114075
\(545\) 2.86634 0.122780
\(546\) 6.92670 0.296435
\(547\) −8.86260 −0.378937 −0.189469 0.981887i \(-0.560677\pi\)
−0.189469 + 0.981887i \(0.560677\pi\)
\(548\) 1.89250 0.0808436
\(549\) 2.33293 0.0995671
\(550\) 4.04625 0.172532
\(551\) 2.45610 0.104633
\(552\) 4.93934 0.210232
\(553\) −20.3405 −0.864968
\(554\) −4.32637 −0.183810
\(555\) 14.7168 0.624693
\(556\) −12.7717 −0.541642
\(557\) 18.9511 0.802984 0.401492 0.915862i \(-0.368492\pi\)
0.401492 + 0.915862i \(0.368492\pi\)
\(558\) −1.19454 −0.0505690
\(559\) 3.26954 0.138287
\(560\) −3.38208 −0.142919
\(561\) 2.20487 0.0930898
\(562\) 0.927146 0.0391093
\(563\) 37.0597 1.56188 0.780940 0.624606i \(-0.214740\pi\)
0.780940 + 0.624606i \(0.214740\pi\)
\(564\) 11.6576 0.490875
\(565\) −2.88291 −0.121285
\(566\) 8.02534 0.337330
\(567\) −37.7328 −1.58463
\(568\) 7.58279 0.318167
\(569\) −32.6555 −1.36899 −0.684494 0.729018i \(-0.739977\pi\)
−0.684494 + 0.729018i \(0.739977\pi\)
\(570\) 1.32070 0.0553182
\(571\) 30.3497 1.27010 0.635048 0.772472i \(-0.280980\pi\)
0.635048 + 0.772472i \(0.280980\pi\)
\(572\) −4.04625 −0.169182
\(573\) −34.0710 −1.42334
\(574\) 32.3519 1.35034
\(575\) −2.41172 −0.100576
\(576\) 1.19454 0.0497726
\(577\) −15.1293 −0.629839 −0.314920 0.949118i \(-0.601978\pi\)
−0.314920 + 0.949118i \(0.601978\pi\)
\(578\) −16.9292 −0.704162
\(579\) −33.1353 −1.37706
\(580\) −3.80875 −0.158150
\(581\) −13.5731 −0.563108
\(582\) −3.75308 −0.155570
\(583\) −18.5732 −0.769225
\(584\) −5.98592 −0.247699
\(585\) 1.19454 0.0493882
\(586\) −22.1887 −0.916608
\(587\) −19.4913 −0.804491 −0.402246 0.915532i \(-0.631770\pi\)
−0.402246 + 0.915532i \(0.631770\pi\)
\(588\) −9.09025 −0.374876
\(589\) −0.644857 −0.0265709
\(590\) 7.74498 0.318856
\(591\) 12.0295 0.494826
\(592\) 7.18573 0.295332
\(593\) −15.3857 −0.631815 −0.315908 0.948790i \(-0.602309\pi\)
−0.315908 + 0.948790i \(0.602309\pi\)
\(594\) 14.9617 0.613887
\(595\) 0.899856 0.0368905
\(596\) 21.9281 0.898212
\(597\) −0.187015 −0.00765403
\(598\) 2.41172 0.0986225
\(599\) −11.8794 −0.485381 −0.242690 0.970104i \(-0.578030\pi\)
−0.242690 + 0.970104i \(0.578030\pi\)
\(600\) −2.04806 −0.0836116
\(601\) −18.7779 −0.765967 −0.382983 0.923755i \(-0.625103\pi\)
−0.382983 + 0.923755i \(0.625103\pi\)
\(602\) −11.0578 −0.450684
\(603\) −0.00800724 −0.000326080 0
\(604\) 11.7903 0.479740
\(605\) −5.37210 −0.218407
\(606\) 18.1414 0.736944
\(607\) −7.45348 −0.302527 −0.151264 0.988493i \(-0.548334\pi\)
−0.151264 + 0.988493i \(0.548334\pi\)
\(608\) 0.644857 0.0261524
\(609\) −26.3820 −1.06905
\(610\) −1.95299 −0.0790743
\(611\) 5.69205 0.230276
\(612\) −0.317827 −0.0128474
\(613\) −44.4092 −1.79367 −0.896836 0.442364i \(-0.854140\pi\)
−0.896836 + 0.442364i \(0.854140\pi\)
\(614\) −4.91759 −0.198458
\(615\) 19.5911 0.789989
\(616\) 13.6847 0.551373
\(617\) 8.98704 0.361805 0.180902 0.983501i \(-0.442098\pi\)
0.180902 + 0.983501i \(0.442098\pi\)
\(618\) −7.93446 −0.319171
\(619\) −27.1657 −1.09188 −0.545940 0.837824i \(-0.683827\pi\)
−0.545940 + 0.837824i \(0.683827\pi\)
\(620\) 1.00000 0.0401610
\(621\) −8.91777 −0.357858
\(622\) 25.7106 1.03090
\(623\) 40.0602 1.60498
\(624\) 2.04806 0.0819879
\(625\) 1.00000 0.0400000
\(626\) −11.2542 −0.449810
\(627\) −5.34389 −0.213415
\(628\) 0.311656 0.0124364
\(629\) −1.91188 −0.0762315
\(630\) −4.04004 −0.160959
\(631\) 17.4857 0.696096 0.348048 0.937477i \(-0.386845\pi\)
0.348048 + 0.937477i \(0.386845\pi\)
\(632\) −6.01421 −0.239232
\(633\) −27.8211 −1.10579
\(634\) −13.0143 −0.516863
\(635\) −11.1456 −0.442299
\(636\) 9.40108 0.372777
\(637\) −4.43847 −0.175859
\(638\) 15.4111 0.610132
\(639\) 9.05797 0.358328
\(640\) −1.00000 −0.0395285
\(641\) 26.8659 1.06114 0.530569 0.847642i \(-0.321978\pi\)
0.530569 + 0.847642i \(0.321978\pi\)
\(642\) −39.3034 −1.55118
\(643\) −11.7443 −0.463149 −0.231574 0.972817i \(-0.574388\pi\)
−0.231574 + 0.972817i \(0.574388\pi\)
\(644\) −8.15662 −0.321416
\(645\) −6.69621 −0.263663
\(646\) −0.171574 −0.00675050
\(647\) −36.0969 −1.41912 −0.709558 0.704647i \(-0.751106\pi\)
−0.709558 + 0.704647i \(0.751106\pi\)
\(648\) −11.1567 −0.438276
\(649\) −31.3381 −1.23013
\(650\) −1.00000 −0.0392232
\(651\) 6.92670 0.271479
\(652\) 14.9899 0.587048
\(653\) −20.0408 −0.784259 −0.392130 0.919910i \(-0.628261\pi\)
−0.392130 + 0.919910i \(0.628261\pi\)
\(654\) 5.87043 0.229552
\(655\) −13.6357 −0.532789
\(656\) 9.56569 0.373477
\(657\) −7.15043 −0.278965
\(658\) −19.2510 −0.750481
\(659\) 31.8805 1.24189 0.620944 0.783855i \(-0.286749\pi\)
0.620944 + 0.783855i \(0.286749\pi\)
\(660\) 8.28695 0.322569
\(661\) −4.49594 −0.174872 −0.0874359 0.996170i \(-0.527867\pi\)
−0.0874359 + 0.996170i \(0.527867\pi\)
\(662\) −32.8155 −1.27541
\(663\) −0.544918 −0.0211629
\(664\) −4.01325 −0.155744
\(665\) −2.18096 −0.0845739
\(666\) 8.58365 0.332610
\(667\) −9.18562 −0.355669
\(668\) 0.219986 0.00851151
\(669\) 32.9218 1.27283
\(670\) 0.00670319 0.000258967 0
\(671\) 7.90229 0.305064
\(672\) −6.92670 −0.267203
\(673\) 21.4215 0.825737 0.412869 0.910791i \(-0.364527\pi\)
0.412869 + 0.910791i \(0.364527\pi\)
\(674\) 5.27377 0.203138
\(675\) 3.69768 0.142324
\(676\) 1.00000 0.0384615
\(677\) 19.3292 0.742882 0.371441 0.928457i \(-0.378864\pi\)
0.371441 + 0.928457i \(0.378864\pi\)
\(678\) −5.90437 −0.226756
\(679\) 6.19769 0.237846
\(680\) 0.266066 0.0102032
\(681\) −30.8945 −1.18388
\(682\) −4.04625 −0.154939
\(683\) 48.5953 1.85945 0.929723 0.368260i \(-0.120046\pi\)
0.929723 + 0.368260i \(0.120046\pi\)
\(684\) 0.770309 0.0294535
\(685\) −1.89250 −0.0723087
\(686\) −8.66329 −0.330766
\(687\) −29.0685 −1.10903
\(688\) −3.26954 −0.124650
\(689\) 4.59024 0.174874
\(690\) −4.93934 −0.188037
\(691\) 47.3954 1.80301 0.901504 0.432772i \(-0.142464\pi\)
0.901504 + 0.432772i \(0.142464\pi\)
\(692\) 12.7180 0.483467
\(693\) 16.3470 0.620971
\(694\) −16.9185 −0.642218
\(695\) 12.7717 0.484459
\(696\) −7.80054 −0.295679
\(697\) −2.54510 −0.0964026
\(698\) 1.54250 0.0583843
\(699\) 22.8480 0.864192
\(700\) 3.38208 0.127831
\(701\) 29.5934 1.11773 0.558864 0.829260i \(-0.311237\pi\)
0.558864 + 0.829260i \(0.311237\pi\)
\(702\) −3.69768 −0.139560
\(703\) 4.63376 0.174766
\(704\) 4.04625 0.152499
\(705\) −11.6576 −0.439052
\(706\) −15.5081 −0.583653
\(707\) −29.9580 −1.12669
\(708\) 15.8622 0.596137
\(709\) 2.96196 0.111239 0.0556194 0.998452i \(-0.482287\pi\)
0.0556194 + 0.998452i \(0.482287\pi\)
\(710\) −7.58279 −0.284577
\(711\) −7.18423 −0.269430
\(712\) 11.8448 0.443904
\(713\) 2.41172 0.0903195
\(714\) 1.84296 0.0689709
\(715\) 4.04625 0.151321
\(716\) 7.53904 0.281747
\(717\) −20.6530 −0.771299
\(718\) 19.1927 0.716265
\(719\) 43.8729 1.63618 0.818092 0.575087i \(-0.195032\pi\)
0.818092 + 0.575087i \(0.195032\pi\)
\(720\) −1.19454 −0.0445180
\(721\) 13.1027 0.487968
\(722\) −18.5842 −0.691631
\(723\) −6.61421 −0.245985
\(724\) 13.3732 0.497013
\(725\) 3.80875 0.141453
\(726\) −11.0024 −0.408336
\(727\) −5.37327 −0.199283 −0.0996417 0.995023i \(-0.531770\pi\)
−0.0996417 + 0.995023i \(0.531770\pi\)
\(728\) −3.38208 −0.125348
\(729\) 9.39206 0.347854
\(730\) 5.98592 0.221549
\(731\) 0.869912 0.0321749
\(732\) −3.99984 −0.147838
\(733\) −7.91256 −0.292257 −0.146128 0.989266i \(-0.546681\pi\)
−0.146128 + 0.989266i \(0.546681\pi\)
\(734\) 34.7312 1.28195
\(735\) 9.09025 0.335299
\(736\) −2.41172 −0.0888971
\(737\) −0.0271227 −0.000999079 0
\(738\) 11.4266 0.420620
\(739\) 23.3856 0.860253 0.430126 0.902769i \(-0.358469\pi\)
0.430126 + 0.902769i \(0.358469\pi\)
\(740\) −7.18573 −0.264153
\(741\) 1.32070 0.0485173
\(742\) −15.5246 −0.569925
\(743\) −1.39007 −0.0509966 −0.0254983 0.999675i \(-0.508117\pi\)
−0.0254983 + 0.999675i \(0.508117\pi\)
\(744\) 2.04806 0.0750855
\(745\) −21.9281 −0.803385
\(746\) 14.1384 0.517645
\(747\) −4.79399 −0.175403
\(748\) −1.07657 −0.0393632
\(749\) 64.9040 2.37154
\(750\) 2.04806 0.0747845
\(751\) −9.01046 −0.328796 −0.164398 0.986394i \(-0.552568\pi\)
−0.164398 + 0.986394i \(0.552568\pi\)
\(752\) −5.69205 −0.207568
\(753\) 8.05444 0.293520
\(754\) −3.80875 −0.138706
\(755\) −11.7903 −0.429092
\(756\) 12.5059 0.454834
\(757\) 19.1640 0.696528 0.348264 0.937397i \(-0.386771\pi\)
0.348264 + 0.937397i \(0.386771\pi\)
\(758\) 5.86902 0.213172
\(759\) 19.9858 0.725438
\(760\) −0.644857 −0.0233914
\(761\) 27.5333 0.998083 0.499041 0.866578i \(-0.333686\pi\)
0.499041 + 0.866578i \(0.333686\pi\)
\(762\) −22.8268 −0.826927
\(763\) −9.69418 −0.350953
\(764\) 16.6358 0.601861
\(765\) 0.317827 0.0114910
\(766\) −14.4275 −0.521286
\(767\) 7.74498 0.279655
\(768\) −2.04806 −0.0739029
\(769\) −41.3891 −1.49253 −0.746265 0.665649i \(-0.768155\pi\)
−0.746265 + 0.665649i \(0.768155\pi\)
\(770\) −13.6847 −0.493163
\(771\) 25.9722 0.935368
\(772\) 16.1789 0.582292
\(773\) −15.2745 −0.549385 −0.274692 0.961532i \(-0.588576\pi\)
−0.274692 + 0.961532i \(0.588576\pi\)
\(774\) −3.90560 −0.140384
\(775\) −1.00000 −0.0359211
\(776\) 1.83251 0.0657832
\(777\) −49.7734 −1.78561
\(778\) 24.2202 0.868338
\(779\) 6.16850 0.221009
\(780\) −2.04806 −0.0733322
\(781\) 30.6818 1.09788
\(782\) 0.641675 0.0229463
\(783\) 14.0835 0.503305
\(784\) 4.43847 0.158517
\(785\) −0.311656 −0.0111235
\(786\) −27.9266 −0.996109
\(787\) −54.7468 −1.95151 −0.975755 0.218863i \(-0.929765\pi\)
−0.975755 + 0.218863i \(0.929765\pi\)
\(788\) −5.87360 −0.209238
\(789\) 43.9043 1.56304
\(790\) 6.01421 0.213976
\(791\) 9.75024 0.346679
\(792\) 4.83341 0.171748
\(793\) −1.95299 −0.0693528
\(794\) −24.0624 −0.853941
\(795\) −9.40108 −0.333422
\(796\) 0.0913135 0.00323652
\(797\) −19.0516 −0.674841 −0.337420 0.941354i \(-0.609554\pi\)
−0.337420 + 0.941354i \(0.609554\pi\)
\(798\) −4.46673 −0.158121
\(799\) 1.51446 0.0535777
\(800\) 1.00000 0.0353553
\(801\) 14.1492 0.499936
\(802\) −17.1745 −0.606452
\(803\) −24.2205 −0.854723
\(804\) 0.0137285 0.000484167 0
\(805\) 8.15662 0.287483
\(806\) 1.00000 0.0352235
\(807\) −31.5204 −1.10957
\(808\) −8.85786 −0.311618
\(809\) 46.7225 1.64268 0.821338 0.570442i \(-0.193228\pi\)
0.821338 + 0.570442i \(0.193228\pi\)
\(810\) 11.1567 0.392006
\(811\) −32.3973 −1.13762 −0.568812 0.822467i \(-0.692597\pi\)
−0.568812 + 0.822467i \(0.692597\pi\)
\(812\) 12.8815 0.452052
\(813\) 28.2105 0.989384
\(814\) 29.0752 1.01909
\(815\) −14.9899 −0.525072
\(816\) 0.544918 0.0190759
\(817\) −2.10838 −0.0737630
\(818\) −28.0187 −0.979649
\(819\) −4.04004 −0.141170
\(820\) −9.56569 −0.334048
\(821\) 34.9710 1.22050 0.610249 0.792210i \(-0.291069\pi\)
0.610249 + 0.792210i \(0.291069\pi\)
\(822\) −3.87595 −0.135189
\(823\) 36.9497 1.28799 0.643993 0.765032i \(-0.277277\pi\)
0.643993 + 0.765032i \(0.277277\pi\)
\(824\) 3.87414 0.134962
\(825\) −8.28695 −0.288514
\(826\) −26.1941 −0.911411
\(827\) −21.6873 −0.754142 −0.377071 0.926184i \(-0.623069\pi\)
−0.377071 + 0.926184i \(0.623069\pi\)
\(828\) −2.88090 −0.100118
\(829\) −43.6743 −1.51687 −0.758436 0.651747i \(-0.774036\pi\)
−0.758436 + 0.651747i \(0.774036\pi\)
\(830\) 4.01325 0.139302
\(831\) 8.86067 0.307373
\(832\) −1.00000 −0.0346688
\(833\) −1.18093 −0.0409166
\(834\) 26.1573 0.905752
\(835\) −0.219986 −0.00761292
\(836\) 2.60925 0.0902428
\(837\) −3.69768 −0.127811
\(838\) 27.3490 0.944756
\(839\) −22.3138 −0.770357 −0.385178 0.922842i \(-0.625860\pi\)
−0.385178 + 0.922842i \(0.625860\pi\)
\(840\) 6.92670 0.238994
\(841\) −14.4934 −0.499774
\(842\) −1.55602 −0.0536239
\(843\) −1.89885 −0.0653999
\(844\) 13.5841 0.467585
\(845\) −1.00000 −0.0344010
\(846\) −6.79939 −0.233768
\(847\) 18.1689 0.624290
\(848\) −4.59024 −0.157630
\(849\) −16.4364 −0.564095
\(850\) −0.266066 −0.00912598
\(851\) −17.3299 −0.594063
\(852\) −15.5300 −0.532049
\(853\) −16.4599 −0.563575 −0.281787 0.959477i \(-0.590927\pi\)
−0.281787 + 0.959477i \(0.590927\pi\)
\(854\) 6.60518 0.226025
\(855\) −0.770309 −0.0263440
\(856\) 19.1905 0.655919
\(857\) 2.50130 0.0854429 0.0427215 0.999087i \(-0.486397\pi\)
0.0427215 + 0.999087i \(0.486397\pi\)
\(858\) 8.28695 0.282912
\(859\) −2.30005 −0.0784766 −0.0392383 0.999230i \(-0.512493\pi\)
−0.0392383 + 0.999230i \(0.512493\pi\)
\(860\) 3.26954 0.111490
\(861\) −66.2586 −2.25809
\(862\) −9.11333 −0.310401
\(863\) 26.4884 0.901677 0.450839 0.892605i \(-0.351125\pi\)
0.450839 + 0.892605i \(0.351125\pi\)
\(864\) 3.69768 0.125798
\(865\) −12.7180 −0.432426
\(866\) −11.5976 −0.394101
\(867\) 34.6720 1.17752
\(868\) −3.38208 −0.114795
\(869\) −24.3350 −0.825507
\(870\) 7.80054 0.264463
\(871\) 0.00670319 0.000227129 0
\(872\) −2.86634 −0.0970664
\(873\) 2.18901 0.0740867
\(874\) −1.55521 −0.0526059
\(875\) −3.38208 −0.114335
\(876\) 12.2595 0.414210
\(877\) −25.9332 −0.875703 −0.437852 0.899047i \(-0.644260\pi\)
−0.437852 + 0.899047i \(0.644260\pi\)
\(878\) 1.38796 0.0468413
\(879\) 45.4438 1.53278
\(880\) −4.04625 −0.136399
\(881\) −52.1535 −1.75710 −0.878549 0.477653i \(-0.841488\pi\)
−0.878549 + 0.477653i \(0.841488\pi\)
\(882\) 5.30194 0.178526
\(883\) −14.1943 −0.477675 −0.238838 0.971059i \(-0.576766\pi\)
−0.238838 + 0.971059i \(0.576766\pi\)
\(884\) 0.266066 0.00894876
\(885\) −15.8622 −0.533201
\(886\) 27.8167 0.934520
\(887\) −12.5135 −0.420163 −0.210082 0.977684i \(-0.567373\pi\)
−0.210082 + 0.977684i \(0.567373\pi\)
\(888\) −14.7168 −0.493863
\(889\) 37.6952 1.26426
\(890\) −11.8448 −0.397040
\(891\) −45.1427 −1.51234
\(892\) −16.0746 −0.538219
\(893\) −3.67056 −0.122830
\(894\) −44.9101 −1.50202
\(895\) −7.53904 −0.252002
\(896\) 3.38208 0.112987
\(897\) −4.93934 −0.164920
\(898\) 23.5304 0.785220
\(899\) −3.80875 −0.127029
\(900\) 1.19454 0.0398181
\(901\) 1.22131 0.0406876
\(902\) 38.7051 1.28874
\(903\) 22.6471 0.753649
\(904\) 2.88291 0.0958842
\(905\) −13.3732 −0.444542
\(906\) −24.1472 −0.802237
\(907\) −20.7125 −0.687747 −0.343874 0.939016i \(-0.611739\pi\)
−0.343874 + 0.939016i \(0.611739\pi\)
\(908\) 15.0848 0.500606
\(909\) −10.5811 −0.350952
\(910\) 3.38208 0.112115
\(911\) −8.09746 −0.268281 −0.134140 0.990962i \(-0.542827\pi\)
−0.134140 + 0.990962i \(0.542827\pi\)
\(912\) −1.32070 −0.0437329
\(913\) −16.2386 −0.537419
\(914\) −21.0966 −0.697814
\(915\) 3.99984 0.132231
\(916\) 14.1932 0.468957
\(917\) 46.1169 1.52291
\(918\) −0.983826 −0.0324711
\(919\) −30.1555 −0.994738 −0.497369 0.867539i \(-0.665700\pi\)
−0.497369 + 0.867539i \(0.665700\pi\)
\(920\) 2.41172 0.0795120
\(921\) 10.0715 0.331868
\(922\) −10.4387 −0.343781
\(923\) −7.58279 −0.249591
\(924\) −28.0271 −0.922025
\(925\) 7.18573 0.236265
\(926\) −41.0084 −1.34762
\(927\) 4.62782 0.151998
\(928\) 3.80875 0.125028
\(929\) −31.1397 −1.02166 −0.510831 0.859681i \(-0.670662\pi\)
−0.510831 + 0.859681i \(0.670662\pi\)
\(930\) −2.04806 −0.0671585
\(931\) 2.86218 0.0938042
\(932\) −11.1560 −0.365425
\(933\) −52.6569 −1.72391
\(934\) −23.9455 −0.783521
\(935\) 1.07657 0.0352075
\(936\) −1.19454 −0.0390448
\(937\) −16.5381 −0.540277 −0.270138 0.962822i \(-0.587069\pi\)
−0.270138 + 0.962822i \(0.587069\pi\)
\(938\) −0.0226707 −0.000740225 0
\(939\) 23.0493 0.752187
\(940\) 5.69205 0.185654
\(941\) 23.4078 0.763073 0.381537 0.924354i \(-0.375395\pi\)
0.381537 + 0.924354i \(0.375395\pi\)
\(942\) −0.638290 −0.0207966
\(943\) −23.0697 −0.751254
\(944\) −7.74498 −0.252078
\(945\) −12.5059 −0.406816
\(946\) −13.2294 −0.430123
\(947\) 17.9367 0.582865 0.291433 0.956591i \(-0.405868\pi\)
0.291433 + 0.956591i \(0.405868\pi\)
\(948\) 12.3175 0.400052
\(949\) 5.98592 0.194311
\(950\) 0.644857 0.0209219
\(951\) 26.6540 0.864315
\(952\) −0.899856 −0.0291645
\(953\) −18.9942 −0.615284 −0.307642 0.951502i \(-0.599540\pi\)
−0.307642 + 0.951502i \(0.599540\pi\)
\(954\) −5.48324 −0.177526
\(955\) −16.6358 −0.538321
\(956\) 10.0842 0.326145
\(957\) −31.5629 −1.02028
\(958\) 9.42095 0.304377
\(959\) 6.40059 0.206686
\(960\) 2.04806 0.0661008
\(961\) 1.00000 0.0322581
\(962\) −7.18573 −0.231677
\(963\) 22.9239 0.738713
\(964\) 3.22950 0.104015
\(965\) −16.1789 −0.520817
\(966\) 16.7052 0.537482
\(967\) −60.3424 −1.94048 −0.970241 0.242141i \(-0.922150\pi\)
−0.970241 + 0.242141i \(0.922150\pi\)
\(968\) 5.37210 0.172666
\(969\) 0.351394 0.0112884
\(970\) −1.83251 −0.0588383
\(971\) 44.8424 1.43906 0.719531 0.694461i \(-0.244357\pi\)
0.719531 + 0.694461i \(0.244357\pi\)
\(972\) 11.7565 0.377090
\(973\) −43.1950 −1.38477
\(974\) −0.635603 −0.0203660
\(975\) 2.04806 0.0655904
\(976\) 1.95299 0.0625138
\(977\) −49.6175 −1.58740 −0.793702 0.608307i \(-0.791849\pi\)
−0.793702 + 0.608307i \(0.791849\pi\)
\(978\) −30.7001 −0.981681
\(979\) 47.9271 1.53176
\(980\) −4.43847 −0.141782
\(981\) −3.42396 −0.109319
\(982\) −35.7982 −1.14237
\(983\) −5.66661 −0.180737 −0.0903684 0.995908i \(-0.528804\pi\)
−0.0903684 + 0.995908i \(0.528804\pi\)
\(984\) −19.5911 −0.624541
\(985\) 5.87360 0.187148
\(986\) −1.01338 −0.0322725
\(987\) 39.4271 1.25498
\(988\) −0.644857 −0.0205156
\(989\) 7.88520 0.250735
\(990\) −4.83341 −0.153616
\(991\) −23.9313 −0.760201 −0.380101 0.924945i \(-0.624111\pi\)
−0.380101 + 0.924945i \(0.624111\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 67.2081 2.13279
\(994\) 25.6456 0.813430
\(995\) −0.0913135 −0.00289483
\(996\) 8.21937 0.260441
\(997\) 12.5969 0.398947 0.199474 0.979903i \(-0.436077\pi\)
0.199474 + 0.979903i \(0.436077\pi\)
\(998\) 25.2254 0.798495
\(999\) 26.5705 0.840654
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 \(a_p\))