Properties

Label 6027.2.a.bm.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.83908\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.83908 q^{2} +1.00000 q^{3} +1.38223 q^{4} -2.07594 q^{5} -1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.83908 q^{2} +1.00000 q^{3} +1.38223 q^{4} -2.07594 q^{5} -1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} +3.81783 q^{10} -6.44723 q^{11} +1.38223 q^{12} -0.865716 q^{13} -2.07594 q^{15} -4.85390 q^{16} +2.06756 q^{17} -1.83908 q^{18} +3.75357 q^{19} -2.86943 q^{20} +11.8570 q^{22} +5.10432 q^{23} +1.13613 q^{24} -0.690475 q^{25} +1.59212 q^{26} +1.00000 q^{27} +1.38301 q^{29} +3.81783 q^{30} -3.75086 q^{31} +6.65447 q^{32} -6.44723 q^{33} -3.80241 q^{34} +1.38223 q^{36} -0.654747 q^{37} -6.90313 q^{38} -0.865716 q^{39} -2.35854 q^{40} +1.00000 q^{41} +11.2846 q^{43} -8.91156 q^{44} -2.07594 q^{45} -9.38727 q^{46} -13.3268 q^{47} -4.85390 q^{48} +1.26984 q^{50} +2.06756 q^{51} -1.19662 q^{52} -0.611905 q^{53} -1.83908 q^{54} +13.3841 q^{55} +3.75357 q^{57} -2.54346 q^{58} +3.36226 q^{59} -2.86943 q^{60} +12.3530 q^{61} +6.89814 q^{62} -2.53033 q^{64} +1.79717 q^{65} +11.8570 q^{66} +12.3187 q^{67} +2.85784 q^{68} +5.10432 q^{69} -3.50868 q^{71} +1.13613 q^{72} -0.660309 q^{73} +1.20413 q^{74} -0.690475 q^{75} +5.18830 q^{76} +1.59212 q^{78} -3.56152 q^{79} +10.0764 q^{80} +1.00000 q^{81} -1.83908 q^{82} +7.34512 q^{83} -4.29213 q^{85} -20.7534 q^{86} +1.38301 q^{87} -7.32489 q^{88} -11.2002 q^{89} +3.81783 q^{90} +7.05534 q^{92} -3.75086 q^{93} +24.5091 q^{94} -7.79218 q^{95} +6.65447 q^{96} +16.7499 q^{97} -6.44723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83908 −1.30043 −0.650214 0.759751i \(-0.725321\pi\)
−0.650214 + 0.759751i \(0.725321\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.38223 0.691115
\(5\) −2.07594 −0.928388 −0.464194 0.885733i \(-0.653656\pi\)
−0.464194 + 0.885733i \(0.653656\pi\)
\(6\) −1.83908 −0.750803
\(7\) 0 0
\(8\) 1.13613 0.401683
\(9\) 1.00000 0.333333
\(10\) 3.81783 1.20730
\(11\) −6.44723 −1.94391 −0.971957 0.235159i \(-0.924439\pi\)
−0.971957 + 0.235159i \(0.924439\pi\)
\(12\) 1.38223 0.399016
\(13\) −0.865716 −0.240106 −0.120053 0.992767i \(-0.538307\pi\)
−0.120053 + 0.992767i \(0.538307\pi\)
\(14\) 0 0
\(15\) −2.07594 −0.536005
\(16\) −4.85390 −1.21347
\(17\) 2.06756 0.501456 0.250728 0.968058i \(-0.419330\pi\)
0.250728 + 0.968058i \(0.419330\pi\)
\(18\) −1.83908 −0.433476
\(19\) 3.75357 0.861127 0.430564 0.902560i \(-0.358315\pi\)
0.430564 + 0.902560i \(0.358315\pi\)
\(20\) −2.86943 −0.641623
\(21\) 0 0
\(22\) 11.8570 2.52792
\(23\) 5.10432 1.06432 0.532162 0.846643i \(-0.321380\pi\)
0.532162 + 0.846643i \(0.321380\pi\)
\(24\) 1.13613 0.231912
\(25\) −0.690475 −0.138095
\(26\) 1.59212 0.312241
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.38301 0.256818 0.128409 0.991721i \(-0.459013\pi\)
0.128409 + 0.991721i \(0.459013\pi\)
\(30\) 3.81783 0.697037
\(31\) −3.75086 −0.673674 −0.336837 0.941563i \(-0.609357\pi\)
−0.336837 + 0.941563i \(0.609357\pi\)
\(32\) 6.65447 1.17636
\(33\) −6.44723 −1.12232
\(34\) −3.80241 −0.652109
\(35\) 0 0
\(36\) 1.38223 0.230372
\(37\) −0.654747 −0.107640 −0.0538199 0.998551i \(-0.517140\pi\)
−0.0538199 + 0.998551i \(0.517140\pi\)
\(38\) −6.90313 −1.11983
\(39\) −0.865716 −0.138625
\(40\) −2.35854 −0.372917
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 11.2846 1.72089 0.860446 0.509542i \(-0.170185\pi\)
0.860446 + 0.509542i \(0.170185\pi\)
\(44\) −8.91156 −1.34347
\(45\) −2.07594 −0.309463
\(46\) −9.38727 −1.38408
\(47\) −13.3268 −1.94392 −0.971958 0.235156i \(-0.924440\pi\)
−0.971958 + 0.235156i \(0.924440\pi\)
\(48\) −4.85390 −0.700600
\(49\) 0 0
\(50\) 1.26984 0.179583
\(51\) 2.06756 0.289516
\(52\) −1.19662 −0.165941
\(53\) −0.611905 −0.0840516 −0.0420258 0.999117i \(-0.513381\pi\)
−0.0420258 + 0.999117i \(0.513381\pi\)
\(54\) −1.83908 −0.250268
\(55\) 13.3841 1.80471
\(56\) 0 0
\(57\) 3.75357 0.497172
\(58\) −2.54346 −0.333973
\(59\) 3.36226 0.437729 0.218864 0.975755i \(-0.429765\pi\)
0.218864 + 0.975755i \(0.429765\pi\)
\(60\) −2.86943 −0.370441
\(61\) 12.3530 1.58164 0.790818 0.612051i \(-0.209655\pi\)
0.790818 + 0.612051i \(0.209655\pi\)
\(62\) 6.89814 0.876065
\(63\) 0 0
\(64\) −2.53033 −0.316292
\(65\) 1.79717 0.222912
\(66\) 11.8570 1.45950
\(67\) 12.3187 1.50497 0.752487 0.658607i \(-0.228854\pi\)
0.752487 + 0.658607i \(0.228854\pi\)
\(68\) 2.85784 0.346564
\(69\) 5.10432 0.614488
\(70\) 0 0
\(71\) −3.50868 −0.416403 −0.208202 0.978086i \(-0.566761\pi\)
−0.208202 + 0.978086i \(0.566761\pi\)
\(72\) 1.13613 0.133894
\(73\) −0.660309 −0.0772833 −0.0386416 0.999253i \(-0.512303\pi\)
−0.0386416 + 0.999253i \(0.512303\pi\)
\(74\) 1.20413 0.139978
\(75\) −0.690475 −0.0797292
\(76\) 5.18830 0.595138
\(77\) 0 0
\(78\) 1.59212 0.180273
\(79\) −3.56152 −0.400702 −0.200351 0.979724i \(-0.564208\pi\)
−0.200351 + 0.979724i \(0.564208\pi\)
\(80\) 10.0764 1.12658
\(81\) 1.00000 0.111111
\(82\) −1.83908 −0.203093
\(83\) 7.34512 0.806232 0.403116 0.915149i \(-0.367927\pi\)
0.403116 + 0.915149i \(0.367927\pi\)
\(84\) 0 0
\(85\) −4.29213 −0.465546
\(86\) −20.7534 −2.23790
\(87\) 1.38301 0.148274
\(88\) −7.32489 −0.780836
\(89\) −11.2002 −1.18722 −0.593611 0.804752i \(-0.702298\pi\)
−0.593611 + 0.804752i \(0.702298\pi\)
\(90\) 3.81783 0.402434
\(91\) 0 0
\(92\) 7.05534 0.735571
\(93\) −3.75086 −0.388946
\(94\) 24.5091 2.52792
\(95\) −7.79218 −0.799461
\(96\) 6.65447 0.679169
\(97\) 16.7499 1.70069 0.850347 0.526223i \(-0.176392\pi\)
0.850347 + 0.526223i \(0.176392\pi\)
\(98\) 0 0
\(99\) −6.44723 −0.647971
\(100\) −0.954396 −0.0954396
\(101\) −10.6527 −1.05998 −0.529992 0.848002i \(-0.677805\pi\)
−0.529992 + 0.848002i \(0.677805\pi\)
\(102\) −3.80241 −0.376495
\(103\) −3.13032 −0.308439 −0.154220 0.988037i \(-0.549286\pi\)
−0.154220 + 0.988037i \(0.549286\pi\)
\(104\) −0.983566 −0.0964466
\(105\) 0 0
\(106\) 1.12534 0.109303
\(107\) −2.90836 −0.281162 −0.140581 0.990069i \(-0.544897\pi\)
−0.140581 + 0.990069i \(0.544897\pi\)
\(108\) 1.38223 0.133005
\(109\) −18.0354 −1.72748 −0.863741 0.503937i \(-0.831885\pi\)
−0.863741 + 0.503937i \(0.831885\pi\)
\(110\) −24.6144 −2.34689
\(111\) −0.654747 −0.0621458
\(112\) 0 0
\(113\) 0.882599 0.0830279 0.0415140 0.999138i \(-0.486782\pi\)
0.0415140 + 0.999138i \(0.486782\pi\)
\(114\) −6.90313 −0.646537
\(115\) −10.5963 −0.988106
\(116\) 1.91163 0.177491
\(117\) −0.865716 −0.0800355
\(118\) −6.18348 −0.569235
\(119\) 0 0
\(120\) −2.35854 −0.215304
\(121\) 30.5668 2.77880
\(122\) −22.7182 −2.05681
\(123\) 1.00000 0.0901670
\(124\) −5.18455 −0.465586
\(125\) 11.8131 1.05659
\(126\) 0 0
\(127\) 10.0367 0.890612 0.445306 0.895379i \(-0.353095\pi\)
0.445306 + 0.895379i \(0.353095\pi\)
\(128\) −8.65545 −0.765041
\(129\) 11.2846 0.993557
\(130\) −3.30515 −0.289881
\(131\) −8.63702 −0.754620 −0.377310 0.926087i \(-0.623151\pi\)
−0.377310 + 0.926087i \(0.623151\pi\)
\(132\) −8.91156 −0.775652
\(133\) 0 0
\(134\) −22.6552 −1.95711
\(135\) −2.07594 −0.178668
\(136\) 2.34901 0.201426
\(137\) −9.78840 −0.836279 −0.418140 0.908383i \(-0.637318\pi\)
−0.418140 + 0.908383i \(0.637318\pi\)
\(138\) −9.38727 −0.799097
\(139\) −7.41419 −0.628863 −0.314432 0.949280i \(-0.601814\pi\)
−0.314432 + 0.949280i \(0.601814\pi\)
\(140\) 0 0
\(141\) −13.3268 −1.12232
\(142\) 6.45275 0.541503
\(143\) 5.58147 0.466746
\(144\) −4.85390 −0.404492
\(145\) −2.87104 −0.238427
\(146\) 1.21436 0.100501
\(147\) 0 0
\(148\) −0.905011 −0.0743915
\(149\) −14.5604 −1.19284 −0.596418 0.802674i \(-0.703410\pi\)
−0.596418 + 0.802674i \(0.703410\pi\)
\(150\) 1.26984 0.103682
\(151\) −15.7382 −1.28076 −0.640380 0.768058i \(-0.721223\pi\)
−0.640380 + 0.768058i \(0.721223\pi\)
\(152\) 4.26454 0.345900
\(153\) 2.06756 0.167152
\(154\) 0 0
\(155\) 7.78655 0.625431
\(156\) −1.19662 −0.0958062
\(157\) 11.2615 0.898765 0.449383 0.893339i \(-0.351644\pi\)
0.449383 + 0.893339i \(0.351644\pi\)
\(158\) 6.54993 0.521084
\(159\) −0.611905 −0.0485272
\(160\) −13.8143 −1.09211
\(161\) 0 0
\(162\) −1.83908 −0.144492
\(163\) −13.3329 −1.04431 −0.522157 0.852850i \(-0.674872\pi\)
−0.522157 + 0.852850i \(0.674872\pi\)
\(164\) 1.38223 0.107934
\(165\) 13.3841 1.04195
\(166\) −13.5083 −1.04845
\(167\) −7.46545 −0.577694 −0.288847 0.957375i \(-0.593272\pi\)
−0.288847 + 0.957375i \(0.593272\pi\)
\(168\) 0 0
\(169\) −12.2505 −0.942349
\(170\) 7.89358 0.605410
\(171\) 3.75357 0.287042
\(172\) 15.5980 1.18933
\(173\) −10.5624 −0.803042 −0.401521 0.915850i \(-0.631518\pi\)
−0.401521 + 0.915850i \(0.631518\pi\)
\(174\) −2.54346 −0.192820
\(175\) 0 0
\(176\) 31.2942 2.35889
\(177\) 3.36226 0.252723
\(178\) 20.5982 1.54390
\(179\) −14.1339 −1.05642 −0.528208 0.849115i \(-0.677136\pi\)
−0.528208 + 0.849115i \(0.677136\pi\)
\(180\) −2.86943 −0.213874
\(181\) 7.95632 0.591389 0.295694 0.955283i \(-0.404449\pi\)
0.295694 + 0.955283i \(0.404449\pi\)
\(182\) 0 0
\(183\) 12.3530 0.913158
\(184\) 5.79917 0.427520
\(185\) 1.35921 0.0999315
\(186\) 6.89814 0.505796
\(187\) −13.3300 −0.974788
\(188\) −18.4207 −1.34347
\(189\) 0 0
\(190\) 14.3305 1.03964
\(191\) 14.3584 1.03894 0.519468 0.854490i \(-0.326130\pi\)
0.519468 + 0.854490i \(0.326130\pi\)
\(192\) −2.53033 −0.182611
\(193\) 14.1983 1.02202 0.511008 0.859576i \(-0.329272\pi\)
0.511008 + 0.859576i \(0.329272\pi\)
\(194\) −30.8044 −2.21163
\(195\) 1.79717 0.128698
\(196\) 0 0
\(197\) 16.6739 1.18796 0.593982 0.804478i \(-0.297555\pi\)
0.593982 + 0.804478i \(0.297555\pi\)
\(198\) 11.8570 0.842641
\(199\) 15.7283 1.11495 0.557474 0.830194i \(-0.311770\pi\)
0.557474 + 0.830194i \(0.311770\pi\)
\(200\) −0.784469 −0.0554703
\(201\) 12.3187 0.868897
\(202\) 19.5912 1.37843
\(203\) 0 0
\(204\) 2.85784 0.200089
\(205\) −2.07594 −0.144990
\(206\) 5.75692 0.401104
\(207\) 5.10432 0.354775
\(208\) 4.20210 0.291363
\(209\) −24.2001 −1.67396
\(210\) 0 0
\(211\) −5.52824 −0.380580 −0.190290 0.981728i \(-0.560943\pi\)
−0.190290 + 0.981728i \(0.560943\pi\)
\(212\) −0.845794 −0.0580894
\(213\) −3.50868 −0.240410
\(214\) 5.34873 0.365631
\(215\) −23.4262 −1.59766
\(216\) 1.13613 0.0773038
\(217\) 0 0
\(218\) 33.1687 2.24647
\(219\) −0.660309 −0.0446195
\(220\) 18.4999 1.24726
\(221\) −1.78992 −0.120403
\(222\) 1.20413 0.0808162
\(223\) −12.9221 −0.865327 −0.432664 0.901555i \(-0.642426\pi\)
−0.432664 + 0.901555i \(0.642426\pi\)
\(224\) 0 0
\(225\) −0.690475 −0.0460317
\(226\) −1.62317 −0.107972
\(227\) 3.64390 0.241854 0.120927 0.992661i \(-0.461413\pi\)
0.120927 + 0.992661i \(0.461413\pi\)
\(228\) 5.18830 0.343603
\(229\) 23.0808 1.52522 0.762611 0.646858i \(-0.223917\pi\)
0.762611 + 0.646858i \(0.223917\pi\)
\(230\) 19.4874 1.28496
\(231\) 0 0
\(232\) 1.57127 0.103159
\(233\) 5.78012 0.378668 0.189334 0.981913i \(-0.439367\pi\)
0.189334 + 0.981913i \(0.439367\pi\)
\(234\) 1.59212 0.104080
\(235\) 27.6657 1.80471
\(236\) 4.64742 0.302521
\(237\) −3.56152 −0.231345
\(238\) 0 0
\(239\) −13.9510 −0.902417 −0.451209 0.892419i \(-0.649007\pi\)
−0.451209 + 0.892419i \(0.649007\pi\)
\(240\) 10.0764 0.650429
\(241\) −13.2115 −0.851029 −0.425514 0.904952i \(-0.639907\pi\)
−0.425514 + 0.904952i \(0.639907\pi\)
\(242\) −56.2149 −3.61363
\(243\) 1.00000 0.0641500
\(244\) 17.0747 1.09309
\(245\) 0 0
\(246\) −1.83908 −0.117256
\(247\) −3.24952 −0.206762
\(248\) −4.26146 −0.270603
\(249\) 7.34512 0.465478
\(250\) −21.7253 −1.37403
\(251\) 9.07327 0.572700 0.286350 0.958125i \(-0.407558\pi\)
0.286350 + 0.958125i \(0.407558\pi\)
\(252\) 0 0
\(253\) −32.9087 −2.06895
\(254\) −18.4583 −1.15818
\(255\) −4.29213 −0.268783
\(256\) 20.9788 1.31117
\(257\) 17.3028 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(258\) −20.7534 −1.29205
\(259\) 0 0
\(260\) 2.48411 0.154058
\(261\) 1.38301 0.0856059
\(262\) 15.8842 0.981330
\(263\) 15.5407 0.958279 0.479140 0.877739i \(-0.340949\pi\)
0.479140 + 0.877739i \(0.340949\pi\)
\(264\) −7.32489 −0.450816
\(265\) 1.27028 0.0780325
\(266\) 0 0
\(267\) −11.2002 −0.685443
\(268\) 17.0273 1.04011
\(269\) −11.0657 −0.674690 −0.337345 0.941381i \(-0.609529\pi\)
−0.337345 + 0.941381i \(0.609529\pi\)
\(270\) 3.81783 0.232346
\(271\) −7.28543 −0.442558 −0.221279 0.975210i \(-0.571023\pi\)
−0.221279 + 0.975210i \(0.571023\pi\)
\(272\) −10.0357 −0.608505
\(273\) 0 0
\(274\) 18.0017 1.08752
\(275\) 4.45165 0.268445
\(276\) 7.05534 0.424682
\(277\) −31.1322 −1.87055 −0.935277 0.353917i \(-0.884849\pi\)
−0.935277 + 0.353917i \(0.884849\pi\)
\(278\) 13.6353 0.817792
\(279\) −3.75086 −0.224558
\(280\) 0 0
\(281\) −24.9110 −1.48606 −0.743032 0.669256i \(-0.766613\pi\)
−0.743032 + 0.669256i \(0.766613\pi\)
\(282\) 24.5091 1.45950
\(283\) −5.35887 −0.318551 −0.159276 0.987234i \(-0.550916\pi\)
−0.159276 + 0.987234i \(0.550916\pi\)
\(284\) −4.84980 −0.287783
\(285\) −7.79218 −0.461569
\(286\) −10.2648 −0.606970
\(287\) 0 0
\(288\) 6.65447 0.392118
\(289\) −12.7252 −0.748541
\(290\) 5.28008 0.310057
\(291\) 16.7499 0.981896
\(292\) −0.912699 −0.0534116
\(293\) −28.4083 −1.65963 −0.829814 0.558040i \(-0.811554\pi\)
−0.829814 + 0.558040i \(0.811554\pi\)
\(294\) 0 0
\(295\) −6.97985 −0.406382
\(296\) −0.743877 −0.0432370
\(297\) −6.44723 −0.374106
\(298\) 26.7778 1.55120
\(299\) −4.41889 −0.255551
\(300\) −0.954396 −0.0551021
\(301\) 0 0
\(302\) 28.9440 1.66554
\(303\) −10.6527 −0.611982
\(304\) −18.2194 −1.04496
\(305\) −25.6440 −1.46837
\(306\) −3.80241 −0.217370
\(307\) −5.25225 −0.299762 −0.149881 0.988704i \(-0.547889\pi\)
−0.149881 + 0.988704i \(0.547889\pi\)
\(308\) 0 0
\(309\) −3.13032 −0.178078
\(310\) −14.3201 −0.813328
\(311\) −6.91252 −0.391973 −0.195987 0.980607i \(-0.562791\pi\)
−0.195987 + 0.980607i \(0.562791\pi\)
\(312\) −0.983566 −0.0556834
\(313\) 2.28563 0.129192 0.0645958 0.997912i \(-0.479424\pi\)
0.0645958 + 0.997912i \(0.479424\pi\)
\(314\) −20.7108 −1.16878
\(315\) 0 0
\(316\) −4.92284 −0.276931
\(317\) −13.1138 −0.736544 −0.368272 0.929718i \(-0.620051\pi\)
−0.368272 + 0.929718i \(0.620051\pi\)
\(318\) 1.12534 0.0631062
\(319\) −8.91656 −0.499232
\(320\) 5.25282 0.293641
\(321\) −2.90836 −0.162329
\(322\) 0 0
\(323\) 7.76072 0.431818
\(324\) 1.38223 0.0767906
\(325\) 0.597755 0.0331575
\(326\) 24.5203 1.35805
\(327\) −18.0354 −0.997362
\(328\) 1.13613 0.0627323
\(329\) 0 0
\(330\) −24.6144 −1.35498
\(331\) −12.1363 −0.667069 −0.333534 0.942738i \(-0.608241\pi\)
−0.333534 + 0.942738i \(0.608241\pi\)
\(332\) 10.1527 0.557199
\(333\) −0.654747 −0.0358799
\(334\) 13.7296 0.751250
\(335\) −25.5730 −1.39720
\(336\) 0 0
\(337\) −22.1981 −1.20921 −0.604604 0.796526i \(-0.706669\pi\)
−0.604604 + 0.796526i \(0.706669\pi\)
\(338\) 22.5298 1.22546
\(339\) 0.882599 0.0479362
\(340\) −5.93271 −0.321746
\(341\) 24.1826 1.30956
\(342\) −6.90313 −0.373278
\(343\) 0 0
\(344\) 12.8208 0.691252
\(345\) −10.5963 −0.570483
\(346\) 19.4251 1.04430
\(347\) 31.0327 1.66592 0.832962 0.553331i \(-0.186643\pi\)
0.832962 + 0.553331i \(0.186643\pi\)
\(348\) 1.91163 0.102474
\(349\) −18.6506 −0.998342 −0.499171 0.866503i \(-0.666362\pi\)
−0.499171 + 0.866503i \(0.666362\pi\)
\(350\) 0 0
\(351\) −0.865716 −0.0462085
\(352\) −42.9029 −2.28673
\(353\) −0.397213 −0.0211415 −0.0105708 0.999944i \(-0.503365\pi\)
−0.0105708 + 0.999944i \(0.503365\pi\)
\(354\) −6.18348 −0.328648
\(355\) 7.28380 0.386584
\(356\) −15.4813 −0.820508
\(357\) 0 0
\(358\) 25.9934 1.37379
\(359\) 3.07007 0.162032 0.0810159 0.996713i \(-0.474184\pi\)
0.0810159 + 0.996713i \(0.474184\pi\)
\(360\) −2.35854 −0.124306
\(361\) −4.91074 −0.258460
\(362\) −14.6323 −0.769059
\(363\) 30.5668 1.60434
\(364\) 0 0
\(365\) 1.37076 0.0717489
\(366\) −22.7182 −1.18750
\(367\) 35.8228 1.86994 0.934968 0.354733i \(-0.115428\pi\)
0.934968 + 0.354733i \(0.115428\pi\)
\(368\) −24.7758 −1.29153
\(369\) 1.00000 0.0520579
\(370\) −2.49971 −0.129954
\(371\) 0 0
\(372\) −5.18455 −0.268806
\(373\) −19.2853 −0.998556 −0.499278 0.866442i \(-0.666401\pi\)
−0.499278 + 0.866442i \(0.666401\pi\)
\(374\) 24.5150 1.26764
\(375\) 11.8131 0.610025
\(376\) −15.1410 −0.780837
\(377\) −1.19729 −0.0616636
\(378\) 0 0
\(379\) −23.8292 −1.22403 −0.612013 0.790848i \(-0.709640\pi\)
−0.612013 + 0.790848i \(0.709640\pi\)
\(380\) −10.7706 −0.552519
\(381\) 10.0367 0.514195
\(382\) −26.4063 −1.35106
\(383\) 19.8612 1.01486 0.507429 0.861693i \(-0.330596\pi\)
0.507429 + 0.861693i \(0.330596\pi\)
\(384\) −8.65545 −0.441696
\(385\) 0 0
\(386\) −26.1119 −1.32906
\(387\) 11.2846 0.573630
\(388\) 23.1522 1.17538
\(389\) −22.4236 −1.13692 −0.568462 0.822710i \(-0.692461\pi\)
−0.568462 + 0.822710i \(0.692461\pi\)
\(390\) −3.30515 −0.167363
\(391\) 10.5535 0.533712
\(392\) 0 0
\(393\) −8.63702 −0.435680
\(394\) −30.6647 −1.54486
\(395\) 7.39349 0.372007
\(396\) −8.91156 −0.447823
\(397\) 35.9949 1.80653 0.903267 0.429079i \(-0.141162\pi\)
0.903267 + 0.429079i \(0.141162\pi\)
\(398\) −28.9256 −1.44991
\(399\) 0 0
\(400\) 3.35150 0.167575
\(401\) 29.2996 1.46315 0.731576 0.681760i \(-0.238785\pi\)
0.731576 + 0.681760i \(0.238785\pi\)
\(402\) −22.6552 −1.12994
\(403\) 3.24718 0.161753
\(404\) −14.7245 −0.732572
\(405\) −2.07594 −0.103154
\(406\) 0 0
\(407\) 4.22130 0.209242
\(408\) 2.34901 0.116294
\(409\) 29.1416 1.44096 0.720479 0.693477i \(-0.243922\pi\)
0.720479 + 0.693477i \(0.243922\pi\)
\(410\) 3.81783 0.188549
\(411\) −9.78840 −0.482826
\(412\) −4.32682 −0.213167
\(413\) 0 0
\(414\) −9.38727 −0.461359
\(415\) −15.2480 −0.748496
\(416\) −5.76088 −0.282450
\(417\) −7.41419 −0.363074
\(418\) 44.5061 2.17686
\(419\) 1.13374 0.0553866 0.0276933 0.999616i \(-0.491184\pi\)
0.0276933 + 0.999616i \(0.491184\pi\)
\(420\) 0 0
\(421\) 17.9733 0.875967 0.437984 0.898983i \(-0.355693\pi\)
0.437984 + 0.898983i \(0.355693\pi\)
\(422\) 10.1669 0.494917
\(423\) −13.3268 −0.647972
\(424\) −0.695203 −0.0337621
\(425\) −1.42760 −0.0692486
\(426\) 6.45275 0.312637
\(427\) 0 0
\(428\) −4.02003 −0.194315
\(429\) 5.58147 0.269476
\(430\) 43.0828 2.07764
\(431\) −5.91704 −0.285014 −0.142507 0.989794i \(-0.545516\pi\)
−0.142507 + 0.989794i \(0.545516\pi\)
\(432\) −4.85390 −0.233533
\(433\) −0.775364 −0.0372616 −0.0186308 0.999826i \(-0.505931\pi\)
−0.0186308 + 0.999826i \(0.505931\pi\)
\(434\) 0 0
\(435\) −2.87104 −0.137656
\(436\) −24.9291 −1.19389
\(437\) 19.1594 0.916518
\(438\) 1.21436 0.0580245
\(439\) −32.3419 −1.54359 −0.771797 0.635869i \(-0.780642\pi\)
−0.771797 + 0.635869i \(0.780642\pi\)
\(440\) 15.2060 0.724919
\(441\) 0 0
\(442\) 3.29181 0.156575
\(443\) −4.81006 −0.228533 −0.114266 0.993450i \(-0.536452\pi\)
−0.114266 + 0.993450i \(0.536452\pi\)
\(444\) −0.905011 −0.0429499
\(445\) 23.2510 1.10220
\(446\) 23.7648 1.12530
\(447\) −14.5604 −0.688684
\(448\) 0 0
\(449\) −8.91035 −0.420505 −0.210253 0.977647i \(-0.567429\pi\)
−0.210253 + 0.977647i \(0.567429\pi\)
\(450\) 1.26984 0.0598609
\(451\) −6.44723 −0.303588
\(452\) 1.21996 0.0573819
\(453\) −15.7382 −0.739447
\(454\) −6.70144 −0.314514
\(455\) 0 0
\(456\) 4.26454 0.199705
\(457\) −4.42700 −0.207086 −0.103543 0.994625i \(-0.533018\pi\)
−0.103543 + 0.994625i \(0.533018\pi\)
\(458\) −42.4475 −1.98344
\(459\) 2.06756 0.0965053
\(460\) −14.6465 −0.682895
\(461\) −19.0939 −0.889289 −0.444645 0.895707i \(-0.646670\pi\)
−0.444645 + 0.895707i \(0.646670\pi\)
\(462\) 0 0
\(463\) −15.4688 −0.718897 −0.359449 0.933165i \(-0.617035\pi\)
−0.359449 + 0.933165i \(0.617035\pi\)
\(464\) −6.71297 −0.311642
\(465\) 7.78655 0.361093
\(466\) −10.6301 −0.492431
\(467\) −2.45321 −0.113521 −0.0567605 0.998388i \(-0.518077\pi\)
−0.0567605 + 0.998388i \(0.518077\pi\)
\(468\) −1.19662 −0.0553137
\(469\) 0 0
\(470\) −50.8795 −2.34690
\(471\) 11.2615 0.518902
\(472\) 3.81996 0.175828
\(473\) −72.7547 −3.34526
\(474\) 6.54993 0.300848
\(475\) −2.59174 −0.118917
\(476\) 0 0
\(477\) −0.611905 −0.0280172
\(478\) 25.6571 1.17353
\(479\) −2.25840 −0.103189 −0.0515944 0.998668i \(-0.516430\pi\)
−0.0515944 + 0.998668i \(0.516430\pi\)
\(480\) −13.8143 −0.630533
\(481\) 0.566825 0.0258450
\(482\) 24.2971 1.10670
\(483\) 0 0
\(484\) 42.2504 1.92047
\(485\) −34.7717 −1.57890
\(486\) −1.83908 −0.0834226
\(487\) −1.19918 −0.0543401 −0.0271701 0.999631i \(-0.508650\pi\)
−0.0271701 + 0.999631i \(0.508650\pi\)
\(488\) 14.0346 0.635316
\(489\) −13.3329 −0.602934
\(490\) 0 0
\(491\) −15.1114 −0.681967 −0.340983 0.940069i \(-0.610760\pi\)
−0.340983 + 0.940069i \(0.610760\pi\)
\(492\) 1.38223 0.0623158
\(493\) 2.85945 0.128783
\(494\) 5.97615 0.268880
\(495\) 13.3841 0.601569
\(496\) 18.2063 0.817486
\(497\) 0 0
\(498\) −13.5083 −0.605321
\(499\) −25.5628 −1.14435 −0.572175 0.820131i \(-0.693900\pi\)
−0.572175 + 0.820131i \(0.693900\pi\)
\(500\) 16.3284 0.730228
\(501\) −7.46545 −0.333532
\(502\) −16.6865 −0.744755
\(503\) −7.64100 −0.340695 −0.170348 0.985384i \(-0.554489\pi\)
−0.170348 + 0.985384i \(0.554489\pi\)
\(504\) 0 0
\(505\) 22.1144 0.984077
\(506\) 60.5219 2.69053
\(507\) −12.2505 −0.544065
\(508\) 13.8730 0.615515
\(509\) −18.7058 −0.829119 −0.414559 0.910022i \(-0.636064\pi\)
−0.414559 + 0.910022i \(0.636064\pi\)
\(510\) 7.89358 0.349534
\(511\) 0 0
\(512\) −21.2708 −0.940046
\(513\) 3.75357 0.165724
\(514\) −31.8213 −1.40358
\(515\) 6.49835 0.286352
\(516\) 15.5980 0.686663
\(517\) 85.9211 3.77880
\(518\) 0 0
\(519\) −10.5624 −0.463636
\(520\) 2.04182 0.0895399
\(521\) −27.6080 −1.20953 −0.604764 0.796404i \(-0.706733\pi\)
−0.604764 + 0.796404i \(0.706733\pi\)
\(522\) −2.54346 −0.111324
\(523\) 13.6462 0.596708 0.298354 0.954455i \(-0.403562\pi\)
0.298354 + 0.954455i \(0.403562\pi\)
\(524\) −11.9384 −0.521530
\(525\) 0 0
\(526\) −28.5806 −1.24617
\(527\) −7.75511 −0.337818
\(528\) 31.2942 1.36191
\(529\) 3.05406 0.132785
\(530\) −2.33615 −0.101476
\(531\) 3.36226 0.145910
\(532\) 0 0
\(533\) −0.865716 −0.0374983
\(534\) 20.5982 0.891370
\(535\) 6.03759 0.261028
\(536\) 13.9957 0.604522
\(537\) −14.1339 −0.609922
\(538\) 20.3508 0.877387
\(539\) 0 0
\(540\) −2.86943 −0.123480
\(541\) −35.7636 −1.53760 −0.768798 0.639491i \(-0.779145\pi\)
−0.768798 + 0.639491i \(0.779145\pi\)
\(542\) 13.3985 0.575516
\(543\) 7.95632 0.341438
\(544\) 13.7585 0.589891
\(545\) 37.4405 1.60377
\(546\) 0 0
\(547\) −19.8289 −0.847821 −0.423910 0.905704i \(-0.639343\pi\)
−0.423910 + 0.905704i \(0.639343\pi\)
\(548\) −13.5298 −0.577966
\(549\) 12.3530 0.527212
\(550\) −8.18696 −0.349093
\(551\) 5.19121 0.221153
\(552\) 5.79917 0.246829
\(553\) 0 0
\(554\) 57.2548 2.43252
\(555\) 1.35921 0.0576955
\(556\) −10.2481 −0.434617
\(557\) 1.39060 0.0589218 0.0294609 0.999566i \(-0.490621\pi\)
0.0294609 + 0.999566i \(0.490621\pi\)
\(558\) 6.89814 0.292022
\(559\) −9.76929 −0.413197
\(560\) 0 0
\(561\) −13.3300 −0.562794
\(562\) 45.8134 1.93252
\(563\) −5.72970 −0.241478 −0.120739 0.992684i \(-0.538526\pi\)
−0.120739 + 0.992684i \(0.538526\pi\)
\(564\) −18.4207 −0.775653
\(565\) −1.83222 −0.0770821
\(566\) 9.85540 0.414254
\(567\) 0 0
\(568\) −3.98631 −0.167262
\(569\) −32.0783 −1.34479 −0.672397 0.740191i \(-0.734735\pi\)
−0.672397 + 0.740191i \(0.734735\pi\)
\(570\) 14.3305 0.600237
\(571\) 41.0648 1.71851 0.859255 0.511547i \(-0.170927\pi\)
0.859255 + 0.511547i \(0.170927\pi\)
\(572\) 7.71488 0.322575
\(573\) 14.3584 0.599830
\(574\) 0 0
\(575\) −3.52440 −0.146978
\(576\) −2.53033 −0.105431
\(577\) −16.1354 −0.671727 −0.335864 0.941911i \(-0.609028\pi\)
−0.335864 + 0.941911i \(0.609028\pi\)
\(578\) 23.4027 0.973425
\(579\) 14.1983 0.590061
\(580\) −3.96844 −0.164780
\(581\) 0 0
\(582\) −30.8044 −1.27689
\(583\) 3.94509 0.163389
\(584\) −0.750196 −0.0310433
\(585\) 1.79717 0.0743040
\(586\) 52.2452 2.15823
\(587\) −0.183806 −0.00758650 −0.00379325 0.999993i \(-0.501207\pi\)
−0.00379325 + 0.999993i \(0.501207\pi\)
\(588\) 0 0
\(589\) −14.0791 −0.580119
\(590\) 12.8365 0.528472
\(591\) 16.6739 0.685871
\(592\) 3.17808 0.130618
\(593\) 46.8319 1.92315 0.961577 0.274536i \(-0.0885241\pi\)
0.961577 + 0.274536i \(0.0885241\pi\)
\(594\) 11.8570 0.486499
\(595\) 0 0
\(596\) −20.1258 −0.824387
\(597\) 15.7283 0.643716
\(598\) 8.12671 0.332326
\(599\) −36.8518 −1.50572 −0.752862 0.658178i \(-0.771327\pi\)
−0.752862 + 0.658178i \(0.771327\pi\)
\(600\) −0.784469 −0.0320258
\(601\) 9.16452 0.373829 0.186914 0.982376i \(-0.440151\pi\)
0.186914 + 0.982376i \(0.440151\pi\)
\(602\) 0 0
\(603\) 12.3187 0.501658
\(604\) −21.7539 −0.885153
\(605\) −63.4548 −2.57981
\(606\) 19.5912 0.795840
\(607\) −5.11896 −0.207772 −0.103886 0.994589i \(-0.533128\pi\)
−0.103886 + 0.994589i \(0.533128\pi\)
\(608\) 24.9780 1.01299
\(609\) 0 0
\(610\) 47.1615 1.90952
\(611\) 11.5372 0.466747
\(612\) 2.85784 0.115521
\(613\) −2.09194 −0.0844926 −0.0422463 0.999107i \(-0.513451\pi\)
−0.0422463 + 0.999107i \(0.513451\pi\)
\(614\) 9.65934 0.389819
\(615\) −2.07594 −0.0837100
\(616\) 0 0
\(617\) 0.384624 0.0154844 0.00774220 0.999970i \(-0.497536\pi\)
0.00774220 + 0.999970i \(0.497536\pi\)
\(618\) 5.75692 0.231577
\(619\) −45.9882 −1.84842 −0.924211 0.381882i \(-0.875276\pi\)
−0.924211 + 0.381882i \(0.875276\pi\)
\(620\) 10.7628 0.432245
\(621\) 5.10432 0.204829
\(622\) 12.7127 0.509733
\(623\) 0 0
\(624\) 4.20210 0.168219
\(625\) −21.0709 −0.842835
\(626\) −4.20347 −0.168005
\(627\) −24.2001 −0.966460
\(628\) 15.5660 0.621150
\(629\) −1.35373 −0.0539766
\(630\) 0 0
\(631\) 17.7279 0.705735 0.352868 0.935673i \(-0.385207\pi\)
0.352868 + 0.935673i \(0.385207\pi\)
\(632\) −4.04634 −0.160955
\(633\) −5.52824 −0.219728
\(634\) 24.1174 0.957824
\(635\) −20.8355 −0.826834
\(636\) −0.845794 −0.0335379
\(637\) 0 0
\(638\) 16.3983 0.649215
\(639\) −3.50868 −0.138801
\(640\) 17.9682 0.710255
\(641\) −30.3759 −1.19978 −0.599888 0.800084i \(-0.704788\pi\)
−0.599888 + 0.800084i \(0.704788\pi\)
\(642\) 5.34873 0.211097
\(643\) 48.8439 1.92621 0.963107 0.269118i \(-0.0867320\pi\)
0.963107 + 0.269118i \(0.0867320\pi\)
\(644\) 0 0
\(645\) −23.4262 −0.922407
\(646\) −14.2726 −0.561548
\(647\) −21.6126 −0.849681 −0.424840 0.905268i \(-0.639670\pi\)
−0.424840 + 0.905268i \(0.639670\pi\)
\(648\) 1.13613 0.0446314
\(649\) −21.6773 −0.850907
\(650\) −1.09932 −0.0431190
\(651\) 0 0
\(652\) −18.4291 −0.721741
\(653\) −19.4895 −0.762682 −0.381341 0.924434i \(-0.624538\pi\)
−0.381341 + 0.924434i \(0.624538\pi\)
\(654\) 33.1687 1.29700
\(655\) 17.9299 0.700581
\(656\) −4.85390 −0.189513
\(657\) −0.660309 −0.0257611
\(658\) 0 0
\(659\) 7.29506 0.284175 0.142088 0.989854i \(-0.454619\pi\)
0.142088 + 0.989854i \(0.454619\pi\)
\(660\) 18.4999 0.720106
\(661\) 12.7921 0.497555 0.248778 0.968561i \(-0.419971\pi\)
0.248778 + 0.968561i \(0.419971\pi\)
\(662\) 22.3196 0.867476
\(663\) −1.78992 −0.0695147
\(664\) 8.34501 0.323849
\(665\) 0 0
\(666\) 1.20413 0.0466593
\(667\) 7.05930 0.273337
\(668\) −10.3190 −0.399253
\(669\) −12.9221 −0.499597
\(670\) 47.0308 1.81696
\(671\) −79.6425 −3.07457
\(672\) 0 0
\(673\) −39.9104 −1.53843 −0.769217 0.638987i \(-0.779354\pi\)
−0.769217 + 0.638987i \(0.779354\pi\)
\(674\) 40.8242 1.57249
\(675\) −0.690475 −0.0265764
\(676\) −16.9331 −0.651272
\(677\) −50.3513 −1.93516 −0.967578 0.252572i \(-0.918724\pi\)
−0.967578 + 0.252572i \(0.918724\pi\)
\(678\) −1.62317 −0.0623376
\(679\) 0 0
\(680\) −4.87641 −0.187002
\(681\) 3.64390 0.139635
\(682\) −44.4739 −1.70299
\(683\) −15.2281 −0.582686 −0.291343 0.956619i \(-0.594102\pi\)
−0.291343 + 0.956619i \(0.594102\pi\)
\(684\) 5.18830 0.198379
\(685\) 20.3201 0.776392
\(686\) 0 0
\(687\) 23.0808 0.880587
\(688\) −54.7745 −2.08826
\(689\) 0.529736 0.0201813
\(690\) 19.4874 0.741873
\(691\) 27.8658 1.06007 0.530033 0.847977i \(-0.322180\pi\)
0.530033 + 0.847977i \(0.322180\pi\)
\(692\) −14.5996 −0.554994
\(693\) 0 0
\(694\) −57.0718 −2.16641
\(695\) 15.3914 0.583829
\(696\) 1.57127 0.0595590
\(697\) 2.06756 0.0783143
\(698\) 34.3000 1.29827
\(699\) 5.78012 0.218624
\(700\) 0 0
\(701\) 14.4947 0.547457 0.273728 0.961807i \(-0.411743\pi\)
0.273728 + 0.961807i \(0.411743\pi\)
\(702\) 1.59212 0.0600909
\(703\) −2.45764 −0.0926915
\(704\) 16.3136 0.614843
\(705\) 27.6657 1.04195
\(706\) 0.730509 0.0274931
\(707\) 0 0
\(708\) 4.64742 0.174661
\(709\) 26.2940 0.987493 0.493747 0.869606i \(-0.335627\pi\)
0.493747 + 0.869606i \(0.335627\pi\)
\(710\) −13.3955 −0.502725
\(711\) −3.56152 −0.133567
\(712\) −12.7249 −0.476887
\(713\) −19.1456 −0.717007
\(714\) 0 0
\(715\) −11.5868 −0.433322
\(716\) −19.5363 −0.730105
\(717\) −13.9510 −0.521011
\(718\) −5.64611 −0.210711
\(719\) −21.2151 −0.791191 −0.395596 0.918425i \(-0.629462\pi\)
−0.395596 + 0.918425i \(0.629462\pi\)
\(720\) 10.0764 0.375525
\(721\) 0 0
\(722\) 9.03126 0.336109
\(723\) −13.2115 −0.491342
\(724\) 10.9975 0.408718
\(725\) −0.954931 −0.0354653
\(726\) −56.2149 −2.08633
\(727\) −41.5862 −1.54235 −0.771174 0.636625i \(-0.780330\pi\)
−0.771174 + 0.636625i \(0.780330\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.52094 −0.0933043
\(731\) 23.3316 0.862952
\(732\) 17.0747 0.631098
\(733\) 2.38818 0.0882094 0.0441047 0.999027i \(-0.485956\pi\)
0.0441047 + 0.999027i \(0.485956\pi\)
\(734\) −65.8812 −2.43172
\(735\) 0 0
\(736\) 33.9665 1.25202
\(737\) −79.4218 −2.92554
\(738\) −1.83908 −0.0676976
\(739\) −33.2178 −1.22193 −0.610967 0.791656i \(-0.709219\pi\)
−0.610967 + 0.791656i \(0.709219\pi\)
\(740\) 1.87875 0.0690642
\(741\) −3.24952 −0.119374
\(742\) 0 0
\(743\) 21.7022 0.796177 0.398088 0.917347i \(-0.369674\pi\)
0.398088 + 0.917347i \(0.369674\pi\)
\(744\) −4.26146 −0.156233
\(745\) 30.2265 1.10741
\(746\) 35.4673 1.29855
\(747\) 7.34512 0.268744
\(748\) −18.4252 −0.673691
\(749\) 0 0
\(750\) −21.7253 −0.793294
\(751\) −3.99626 −0.145826 −0.0729129 0.997338i \(-0.523230\pi\)
−0.0729129 + 0.997338i \(0.523230\pi\)
\(752\) 64.6870 2.35889
\(753\) 9.07327 0.330648
\(754\) 2.20192 0.0801891
\(755\) 32.6717 1.18904
\(756\) 0 0
\(757\) −42.1854 −1.53326 −0.766628 0.642092i \(-0.778067\pi\)
−0.766628 + 0.642092i \(0.778067\pi\)
\(758\) 43.8240 1.59176
\(759\) −32.9087 −1.19451
\(760\) −8.85293 −0.321129
\(761\) 11.5094 0.417214 0.208607 0.978000i \(-0.433107\pi\)
0.208607 + 0.978000i \(0.433107\pi\)
\(762\) −18.4583 −0.668674
\(763\) 0 0
\(764\) 19.8466 0.718025
\(765\) −4.29213 −0.155182
\(766\) −36.5264 −1.31975
\(767\) −2.91076 −0.105102
\(768\) 20.9788 0.757006
\(769\) 10.6229 0.383072 0.191536 0.981486i \(-0.438653\pi\)
0.191536 + 0.981486i \(0.438653\pi\)
\(770\) 0 0
\(771\) 17.3028 0.623145
\(772\) 19.6253 0.706331
\(773\) 14.0372 0.504884 0.252442 0.967612i \(-0.418766\pi\)
0.252442 + 0.967612i \(0.418766\pi\)
\(774\) −20.7534 −0.745966
\(775\) 2.58987 0.0930310
\(776\) 19.0300 0.683139
\(777\) 0 0
\(778\) 41.2389 1.47849
\(779\) 3.75357 0.134485
\(780\) 2.48411 0.0889454
\(781\) 22.6212 0.809452
\(782\) −19.4087 −0.694055
\(783\) 1.38301 0.0494246
\(784\) 0 0
\(785\) −23.3782 −0.834403
\(786\) 15.8842 0.566571
\(787\) 11.2653 0.401565 0.200783 0.979636i \(-0.435652\pi\)
0.200783 + 0.979636i \(0.435652\pi\)
\(788\) 23.0471 0.821020
\(789\) 15.5407 0.553263
\(790\) −13.5973 −0.483769
\(791\) 0 0
\(792\) −7.32489 −0.260279
\(793\) −10.6942 −0.379761
\(794\) −66.1977 −2.34927
\(795\) 1.27028 0.0450521
\(796\) 21.7401 0.770558
\(797\) 21.5388 0.762944 0.381472 0.924380i \(-0.375417\pi\)
0.381472 + 0.924380i \(0.375417\pi\)
\(798\) 0 0
\(799\) −27.5540 −0.974789
\(800\) −4.59475 −0.162449
\(801\) −11.2002 −0.395741
\(802\) −53.8844 −1.90273
\(803\) 4.25716 0.150232
\(804\) 17.0273 0.600508
\(805\) 0 0
\(806\) −5.97183 −0.210349
\(807\) −11.0657 −0.389533
\(808\) −12.1029 −0.425777
\(809\) 44.1772 1.55319 0.776593 0.630002i \(-0.216946\pi\)
0.776593 + 0.630002i \(0.216946\pi\)
\(810\) 3.81783 0.134145
\(811\) −26.6265 −0.934983 −0.467491 0.883998i \(-0.654842\pi\)
−0.467491 + 0.883998i \(0.654842\pi\)
\(812\) 0 0
\(813\) −7.28543 −0.255511
\(814\) −7.76333 −0.272105
\(815\) 27.6783 0.969528
\(816\) −10.0357 −0.351320
\(817\) 42.3576 1.48191
\(818\) −53.5938 −1.87386
\(819\) 0 0
\(820\) −2.86943 −0.100205
\(821\) −12.4085 −0.433060 −0.216530 0.976276i \(-0.569474\pi\)
−0.216530 + 0.976276i \(0.569474\pi\)
\(822\) 18.0017 0.627881
\(823\) −4.97202 −0.173314 −0.0866568 0.996238i \(-0.527618\pi\)
−0.0866568 + 0.996238i \(0.527618\pi\)
\(824\) −3.55645 −0.123895
\(825\) 4.45165 0.154987
\(826\) 0 0
\(827\) −35.1605 −1.22265 −0.611326 0.791379i \(-0.709364\pi\)
−0.611326 + 0.791379i \(0.709364\pi\)
\(828\) 7.05534 0.245190
\(829\) −50.8093 −1.76468 −0.882340 0.470613i \(-0.844033\pi\)
−0.882340 + 0.470613i \(0.844033\pi\)
\(830\) 28.0424 0.973366
\(831\) −31.1322 −1.07996
\(832\) 2.19055 0.0759436
\(833\) 0 0
\(834\) 13.6353 0.472152
\(835\) 15.4978 0.536324
\(836\) −33.4501 −1.15690
\(837\) −3.75086 −0.129649
\(838\) −2.08503 −0.0720263
\(839\) −23.4219 −0.808614 −0.404307 0.914623i \(-0.632487\pi\)
−0.404307 + 0.914623i \(0.632487\pi\)
\(840\) 0 0
\(841\) −27.0873 −0.934045
\(842\) −33.0545 −1.13913
\(843\) −24.9110 −0.857979
\(844\) −7.64131 −0.263025
\(845\) 25.4314 0.874866
\(846\) 24.5091 0.842641
\(847\) 0 0
\(848\) 2.97013 0.101995
\(849\) −5.35887 −0.183916
\(850\) 2.62547 0.0900529
\(851\) −3.34204 −0.114564
\(852\) −4.84980 −0.166151
\(853\) −36.3233 −1.24369 −0.621843 0.783142i \(-0.713616\pi\)
−0.621843 + 0.783142i \(0.713616\pi\)
\(854\) 0 0
\(855\) −7.79218 −0.266487
\(856\) −3.30428 −0.112938
\(857\) −15.8461 −0.541293 −0.270647 0.962679i \(-0.587238\pi\)
−0.270647 + 0.962679i \(0.587238\pi\)
\(858\) −10.2648 −0.350434
\(859\) 32.0788 1.09451 0.547257 0.836965i \(-0.315672\pi\)
0.547257 + 0.836965i \(0.315672\pi\)
\(860\) −32.3805 −1.10416
\(861\) 0 0
\(862\) 10.8819 0.370640
\(863\) −14.5432 −0.495057 −0.247528 0.968881i \(-0.579618\pi\)
−0.247528 + 0.968881i \(0.579618\pi\)
\(864\) 6.65447 0.226390
\(865\) 21.9268 0.745534
\(866\) 1.42596 0.0484561
\(867\) −12.7252 −0.432171
\(868\) 0 0
\(869\) 22.9619 0.778930
\(870\) 5.28008 0.179011
\(871\) −10.6645 −0.361354
\(872\) −20.4906 −0.693899
\(873\) 16.7499 0.566898
\(874\) −35.2357 −1.19187
\(875\) 0 0
\(876\) −0.912699 −0.0308372
\(877\) −43.2112 −1.45914 −0.729569 0.683907i \(-0.760279\pi\)
−0.729569 + 0.683907i \(0.760279\pi\)
\(878\) 59.4794 2.00733
\(879\) −28.4083 −0.958187
\(880\) −64.9649 −2.18997
\(881\) 30.7546 1.03615 0.518074 0.855336i \(-0.326649\pi\)
0.518074 + 0.855336i \(0.326649\pi\)
\(882\) 0 0
\(883\) −43.1740 −1.45292 −0.726461 0.687208i \(-0.758836\pi\)
−0.726461 + 0.687208i \(0.758836\pi\)
\(884\) −2.47408 −0.0832123
\(885\) −6.97985 −0.234625
\(886\) 8.84610 0.297191
\(887\) 21.6010 0.725291 0.362646 0.931927i \(-0.381874\pi\)
0.362646 + 0.931927i \(0.381874\pi\)
\(888\) −0.743877 −0.0249629
\(889\) 0 0
\(890\) −42.7606 −1.43334
\(891\) −6.44723 −0.215990
\(892\) −17.8613 −0.598041
\(893\) −50.0231 −1.67396
\(894\) 26.7778 0.895584
\(895\) 29.3411 0.980765
\(896\) 0 0
\(897\) −4.41889 −0.147542
\(898\) 16.3869 0.546837
\(899\) −5.18746 −0.173011
\(900\) −0.954396 −0.0318132
\(901\) −1.26515 −0.0421482
\(902\) 11.8570 0.394795
\(903\) 0 0
\(904\) 1.00275 0.0333509
\(905\) −16.5168 −0.549038
\(906\) 28.9440 0.961599
\(907\) −23.2280 −0.771273 −0.385636 0.922651i \(-0.626018\pi\)
−0.385636 + 0.922651i \(0.626018\pi\)
\(908\) 5.03671 0.167149
\(909\) −10.6527 −0.353328
\(910\) 0 0
\(911\) 30.9148 1.02425 0.512126 0.858910i \(-0.328858\pi\)
0.512126 + 0.858910i \(0.328858\pi\)
\(912\) −18.2194 −0.603306
\(913\) −47.3557 −1.56725
\(914\) 8.14162 0.269301
\(915\) −25.6440 −0.847766
\(916\) 31.9030 1.05410
\(917\) 0 0
\(918\) −3.80241 −0.125498
\(919\) 21.2573 0.701214 0.350607 0.936523i \(-0.385975\pi\)
0.350607 + 0.936523i \(0.385975\pi\)
\(920\) −12.0387 −0.396905
\(921\) −5.25225 −0.173068
\(922\) 35.1152 1.15646
\(923\) 3.03752 0.0999811
\(924\) 0 0
\(925\) 0.452086 0.0148645
\(926\) 28.4485 0.934875
\(927\) −3.13032 −0.102813
\(928\) 9.20317 0.302109
\(929\) 17.1140 0.561493 0.280746 0.959782i \(-0.409418\pi\)
0.280746 + 0.959782i \(0.409418\pi\)
\(930\) −14.3201 −0.469575
\(931\) 0 0
\(932\) 7.98945 0.261703
\(933\) −6.91252 −0.226306
\(934\) 4.51166 0.147626
\(935\) 27.6723 0.904982
\(936\) −0.983566 −0.0321489
\(937\) 8.28226 0.270570 0.135285 0.990807i \(-0.456805\pi\)
0.135285 + 0.990807i \(0.456805\pi\)
\(938\) 0 0
\(939\) 2.28563 0.0745888
\(940\) 38.2403 1.24726
\(941\) −12.6922 −0.413754 −0.206877 0.978367i \(-0.566330\pi\)
−0.206877 + 0.978367i \(0.566330\pi\)
\(942\) −20.7108 −0.674796
\(943\) 5.10432 0.166219
\(944\) −16.3201 −0.531173
\(945\) 0 0
\(946\) 133.802 4.35028
\(947\) −33.1557 −1.07741 −0.538707 0.842493i \(-0.681087\pi\)
−0.538707 + 0.842493i \(0.681087\pi\)
\(948\) −4.92284 −0.159886
\(949\) 0.571640 0.0185562
\(950\) 4.76644 0.154644
\(951\) −13.1138 −0.425244
\(952\) 0 0
\(953\) 43.5808 1.41172 0.705860 0.708352i \(-0.250561\pi\)
0.705860 + 0.708352i \(0.250561\pi\)
\(954\) 1.12534 0.0364344
\(955\) −29.8072 −0.964537
\(956\) −19.2835 −0.623674
\(957\) −8.91656 −0.288232
\(958\) 4.15338 0.134190
\(959\) 0 0
\(960\) 5.25282 0.169534
\(961\) −16.9311 −0.546164
\(962\) −1.04244 −0.0336096
\(963\) −2.90836 −0.0937207
\(964\) −18.2614 −0.588159
\(965\) −29.4748 −0.948828
\(966\) 0 0
\(967\) 3.95999 0.127345 0.0636723 0.997971i \(-0.479719\pi\)
0.0636723 + 0.997971i \(0.479719\pi\)
\(968\) 34.7279 1.11620
\(969\) 7.76072 0.249310
\(970\) 63.9482 2.05325
\(971\) 50.7607 1.62899 0.814494 0.580171i \(-0.197014\pi\)
0.814494 + 0.580171i \(0.197014\pi\)
\(972\) 1.38223 0.0443351
\(973\) 0 0
\(974\) 2.20540 0.0706654
\(975\) 0.597755 0.0191435
\(976\) −59.9601 −1.91928
\(977\) 16.7125 0.534681 0.267340 0.963602i \(-0.413855\pi\)
0.267340 + 0.963602i \(0.413855\pi\)
\(978\) 24.5203 0.784073
\(979\) 72.2105 2.30786
\(980\) 0 0
\(981\) −18.0354 −0.575827
\(982\) 27.7911 0.886849
\(983\) −48.6655 −1.55219 −0.776095 0.630616i \(-0.782802\pi\)
−0.776095 + 0.630616i \(0.782802\pi\)
\(984\) 1.13613 0.0362185
\(985\) −34.6140 −1.10289
\(986\) −5.25876 −0.167473
\(987\) 0 0
\(988\) −4.49159 −0.142897
\(989\) 57.6004 1.83159
\(990\) −24.6144 −0.782298
\(991\) 45.1326 1.43369 0.716843 0.697235i \(-0.245587\pi\)
0.716843 + 0.697235i \(0.245587\pi\)
\(992\) −24.9600 −0.792480
\(993\) −12.1363 −0.385132
\(994\) 0 0
\(995\) −32.6510 −1.03511
\(996\) 10.1527 0.321699
\(997\) 45.8173 1.45105 0.725525 0.688196i \(-0.241597\pi\)
0.725525 + 0.688196i \(0.241597\pi\)
\(998\) 47.0122 1.48815
\(999\) −0.654747 −0.0207153
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 \(a_p\))