Properties

Label 8047.2.a.b.1.11
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52091 q^{2} -0.134089 q^{3} +4.35498 q^{4} +2.66858 q^{5} +0.338025 q^{6} -2.31114 q^{7} -5.93668 q^{8} -2.98202 q^{9} +O(q^{10})\) \(q-2.52091 q^{2} -0.134089 q^{3} +4.35498 q^{4} +2.66858 q^{5} +0.338025 q^{6} -2.31114 q^{7} -5.93668 q^{8} -2.98202 q^{9} -6.72724 q^{10} -4.30592 q^{11} -0.583953 q^{12} +1.00000 q^{13} +5.82616 q^{14} -0.357826 q^{15} +6.25588 q^{16} +4.36671 q^{17} +7.51740 q^{18} +1.70053 q^{19} +11.6216 q^{20} +0.309897 q^{21} +10.8548 q^{22} +4.64277 q^{23} +0.796042 q^{24} +2.12131 q^{25} -2.52091 q^{26} +0.802121 q^{27} -10.0649 q^{28} +2.89705 q^{29} +0.902047 q^{30} +0.593276 q^{31} -3.89712 q^{32} +0.577375 q^{33} -11.0081 q^{34} -6.16745 q^{35} -12.9866 q^{36} -8.80335 q^{37} -4.28688 q^{38} -0.134089 q^{39} -15.8425 q^{40} +4.18820 q^{41} -0.781223 q^{42} -2.50410 q^{43} -18.7522 q^{44} -7.95775 q^{45} -11.7040 q^{46} -1.06636 q^{47} -0.838842 q^{48} -1.65865 q^{49} -5.34762 q^{50} -0.585526 q^{51} +4.35498 q^{52} -11.4976 q^{53} -2.02207 q^{54} -11.4907 q^{55} +13.7205 q^{56} -0.228022 q^{57} -7.30319 q^{58} +11.6878 q^{59} -1.55832 q^{60} -13.2811 q^{61} -1.49559 q^{62} +6.89186 q^{63} -2.68746 q^{64} +2.66858 q^{65} -1.45551 q^{66} +8.24829 q^{67} +19.0169 q^{68} -0.622543 q^{69} +15.5476 q^{70} +6.16272 q^{71} +17.7033 q^{72} +8.40385 q^{73} +22.1924 q^{74} -0.284443 q^{75} +7.40578 q^{76} +9.95157 q^{77} +0.338025 q^{78} +8.86338 q^{79} +16.6943 q^{80} +8.83851 q^{81} -10.5581 q^{82} +1.30966 q^{83} +1.34960 q^{84} +11.6529 q^{85} +6.31261 q^{86} -0.388461 q^{87} +25.5629 q^{88} -16.6895 q^{89} +20.0608 q^{90} -2.31114 q^{91} +20.2192 q^{92} -0.0795516 q^{93} +2.68820 q^{94} +4.53800 q^{95} +0.522560 q^{96} +9.89727 q^{97} +4.18130 q^{98} +12.8403 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52091 −1.78255 −0.891276 0.453462i \(-0.850189\pi\)
−0.891276 + 0.453462i \(0.850189\pi\)
\(3\) −0.134089 −0.0774161 −0.0387081 0.999251i \(-0.512324\pi\)
−0.0387081 + 0.999251i \(0.512324\pi\)
\(4\) 4.35498 2.17749
\(5\) 2.66858 1.19342 0.596712 0.802455i \(-0.296473\pi\)
0.596712 + 0.802455i \(0.296473\pi\)
\(6\) 0.338025 0.137998
\(7\) −2.31114 −0.873528 −0.436764 0.899576i \(-0.643875\pi\)
−0.436764 + 0.899576i \(0.643875\pi\)
\(8\) −5.93668 −2.09893
\(9\) −2.98202 −0.994007
\(10\) −6.72724 −2.12734
\(11\) −4.30592 −1.29828 −0.649142 0.760667i \(-0.724872\pi\)
−0.649142 + 0.760667i \(0.724872\pi\)
\(12\) −0.583953 −0.168573
\(13\) 1.00000 0.277350
\(14\) 5.82616 1.55711
\(15\) −0.357826 −0.0923903
\(16\) 6.25588 1.56397
\(17\) 4.36671 1.05908 0.529541 0.848284i \(-0.322364\pi\)
0.529541 + 0.848284i \(0.322364\pi\)
\(18\) 7.51740 1.77187
\(19\) 1.70053 0.390129 0.195064 0.980790i \(-0.437508\pi\)
0.195064 + 0.980790i \(0.437508\pi\)
\(20\) 11.6216 2.59867
\(21\) 0.309897 0.0676251
\(22\) 10.8548 2.31426
\(23\) 4.64277 0.968084 0.484042 0.875045i \(-0.339168\pi\)
0.484042 + 0.875045i \(0.339168\pi\)
\(24\) 0.796042 0.162491
\(25\) 2.12131 0.424261
\(26\) −2.52091 −0.494391
\(27\) 0.802121 0.154368
\(28\) −10.0649 −1.90210
\(29\) 2.89705 0.537968 0.268984 0.963145i \(-0.413312\pi\)
0.268984 + 0.963145i \(0.413312\pi\)
\(30\) 0.902047 0.164690
\(31\) 0.593276 0.106556 0.0532778 0.998580i \(-0.483033\pi\)
0.0532778 + 0.998580i \(0.483033\pi\)
\(32\) −3.89712 −0.688921
\(33\) 0.577375 0.100508
\(34\) −11.0081 −1.88787
\(35\) −6.16745 −1.04249
\(36\) −12.9866 −2.16444
\(37\) −8.80335 −1.44726 −0.723631 0.690187i \(-0.757528\pi\)
−0.723631 + 0.690187i \(0.757528\pi\)
\(38\) −4.28688 −0.695425
\(39\) −0.134089 −0.0214714
\(40\) −15.8425 −2.50492
\(41\) 4.18820 0.654087 0.327044 0.945009i \(-0.393948\pi\)
0.327044 + 0.945009i \(0.393948\pi\)
\(42\) −0.781223 −0.120545
\(43\) −2.50410 −0.381872 −0.190936 0.981602i \(-0.561152\pi\)
−0.190936 + 0.981602i \(0.561152\pi\)
\(44\) −18.7522 −2.82700
\(45\) −7.95775 −1.18627
\(46\) −11.7040 −1.72566
\(47\) −1.06636 −0.155545 −0.0777724 0.996971i \(-0.524781\pi\)
−0.0777724 + 0.996971i \(0.524781\pi\)
\(48\) −0.838842 −0.121076
\(49\) −1.65865 −0.236950
\(50\) −5.34762 −0.756268
\(51\) −0.585526 −0.0819901
\(52\) 4.35498 0.603927
\(53\) −11.4976 −1.57932 −0.789658 0.613548i \(-0.789742\pi\)
−0.789658 + 0.613548i \(0.789742\pi\)
\(54\) −2.02207 −0.275169
\(55\) −11.4907 −1.54940
\(56\) 13.7205 1.83348
\(57\) −0.228022 −0.0302023
\(58\) −7.30319 −0.958956
\(59\) 11.6878 1.52162 0.760811 0.648973i \(-0.224801\pi\)
0.760811 + 0.648973i \(0.224801\pi\)
\(60\) −1.55832 −0.201179
\(61\) −13.2811 −1.70047 −0.850234 0.526404i \(-0.823540\pi\)
−0.850234 + 0.526404i \(0.823540\pi\)
\(62\) −1.49559 −0.189941
\(63\) 6.89186 0.868292
\(64\) −2.68746 −0.335933
\(65\) 2.66858 0.330996
\(66\) −1.45551 −0.179161
\(67\) 8.24829 1.00769 0.503845 0.863794i \(-0.331918\pi\)
0.503845 + 0.863794i \(0.331918\pi\)
\(68\) 19.0169 2.30614
\(69\) −0.622543 −0.0749454
\(70\) 15.5476 1.85829
\(71\) 6.16272 0.731381 0.365690 0.930737i \(-0.380833\pi\)
0.365690 + 0.930737i \(0.380833\pi\)
\(72\) 17.7033 2.08635
\(73\) 8.40385 0.983596 0.491798 0.870709i \(-0.336340\pi\)
0.491798 + 0.870709i \(0.336340\pi\)
\(74\) 22.1924 2.57982
\(75\) −0.284443 −0.0328447
\(76\) 7.40578 0.849501
\(77\) 9.95157 1.13409
\(78\) 0.338025 0.0382738
\(79\) 8.86338 0.997209 0.498604 0.866830i \(-0.333846\pi\)
0.498604 + 0.866830i \(0.333846\pi\)
\(80\) 16.6943 1.86648
\(81\) 8.83851 0.982056
\(82\) −10.5581 −1.16594
\(83\) 1.30966 0.143753 0.0718767 0.997414i \(-0.477101\pi\)
0.0718767 + 0.997414i \(0.477101\pi\)
\(84\) 1.34960 0.147253
\(85\) 11.6529 1.26394
\(86\) 6.31261 0.680707
\(87\) −0.388461 −0.0416474
\(88\) 25.5629 2.72501
\(89\) −16.6895 −1.76908 −0.884542 0.466461i \(-0.845529\pi\)
−0.884542 + 0.466461i \(0.845529\pi\)
\(90\) 20.0608 2.11459
\(91\) −2.31114 −0.242273
\(92\) 20.2192 2.10799
\(93\) −0.0795516 −0.00824912
\(94\) 2.68820 0.277267
\(95\) 4.53800 0.465589
\(96\) 0.522560 0.0533336
\(97\) 9.89727 1.00492 0.502458 0.864602i \(-0.332429\pi\)
0.502458 + 0.864602i \(0.332429\pi\)
\(98\) 4.18130 0.422375
\(99\) 12.8403 1.29050
\(100\) 9.23824 0.923824
\(101\) −8.47800 −0.843593 −0.421796 0.906691i \(-0.638600\pi\)
−0.421796 + 0.906691i \(0.638600\pi\)
\(102\) 1.47606 0.146152
\(103\) 8.38448 0.826148 0.413074 0.910698i \(-0.364455\pi\)
0.413074 + 0.910698i \(0.364455\pi\)
\(104\) −5.93668 −0.582140
\(105\) 0.826985 0.0807055
\(106\) 28.9844 2.81521
\(107\) −17.1638 −1.65929 −0.829645 0.558292i \(-0.811457\pi\)
−0.829645 + 0.558292i \(0.811457\pi\)
\(108\) 3.49322 0.336135
\(109\) 7.89476 0.756181 0.378091 0.925769i \(-0.376581\pi\)
0.378091 + 0.925769i \(0.376581\pi\)
\(110\) 28.9670 2.76189
\(111\) 1.18043 0.112041
\(112\) −14.4582 −1.36617
\(113\) −5.51218 −0.518542 −0.259271 0.965805i \(-0.583482\pi\)
−0.259271 + 0.965805i \(0.583482\pi\)
\(114\) 0.574823 0.0538371
\(115\) 12.3896 1.15534
\(116\) 12.6166 1.17142
\(117\) −2.98202 −0.275688
\(118\) −29.4639 −2.71237
\(119\) −10.0921 −0.925138
\(120\) 2.12430 0.193921
\(121\) 7.54094 0.685540
\(122\) 33.4804 3.03117
\(123\) −0.561590 −0.0506369
\(124\) 2.58370 0.232024
\(125\) −7.68202 −0.687100
\(126\) −17.3737 −1.54778
\(127\) −19.5045 −1.73075 −0.865373 0.501128i \(-0.832918\pi\)
−0.865373 + 0.501128i \(0.832918\pi\)
\(128\) 14.5691 1.28774
\(129\) 0.335772 0.0295631
\(130\) −6.72724 −0.590018
\(131\) −13.4032 −1.17105 −0.585523 0.810656i \(-0.699111\pi\)
−0.585523 + 0.810656i \(0.699111\pi\)
\(132\) 2.51446 0.218855
\(133\) −3.93016 −0.340788
\(134\) −20.7932 −1.79626
\(135\) 2.14052 0.184227
\(136\) −25.9238 −2.22295
\(137\) 13.5244 1.15546 0.577732 0.816226i \(-0.303938\pi\)
0.577732 + 0.816226i \(0.303938\pi\)
\(138\) 1.56937 0.133594
\(139\) −3.46956 −0.294284 −0.147142 0.989115i \(-0.547007\pi\)
−0.147142 + 0.989115i \(0.547007\pi\)
\(140\) −26.8591 −2.27001
\(141\) 0.142987 0.0120417
\(142\) −15.5357 −1.30372
\(143\) −4.30592 −0.360079
\(144\) −18.6552 −1.55460
\(145\) 7.73099 0.642024
\(146\) −21.1853 −1.75331
\(147\) 0.222406 0.0183437
\(148\) −38.3384 −3.15140
\(149\) −8.84673 −0.724753 −0.362376 0.932032i \(-0.618034\pi\)
−0.362376 + 0.932032i \(0.618034\pi\)
\(150\) 0.717055 0.0585473
\(151\) 6.16787 0.501934 0.250967 0.967996i \(-0.419251\pi\)
0.250967 + 0.967996i \(0.419251\pi\)
\(152\) −10.0955 −0.818855
\(153\) −13.0216 −1.05274
\(154\) −25.0870 −2.02157
\(155\) 1.58320 0.127166
\(156\) −0.583953 −0.0467537
\(157\) 14.8084 1.18184 0.590920 0.806730i \(-0.298765\pi\)
0.590920 + 0.806730i \(0.298765\pi\)
\(158\) −22.3438 −1.77758
\(159\) 1.54170 0.122264
\(160\) −10.3998 −0.822175
\(161\) −10.7301 −0.845648
\(162\) −22.2811 −1.75057
\(163\) 14.1037 1.10469 0.552345 0.833615i \(-0.313733\pi\)
0.552345 + 0.833615i \(0.313733\pi\)
\(164\) 18.2395 1.42427
\(165\) 1.54077 0.119949
\(166\) −3.30152 −0.256248
\(167\) 1.90309 0.147266 0.0736328 0.997285i \(-0.476541\pi\)
0.0736328 + 0.997285i \(0.476541\pi\)
\(168\) −1.83976 −0.141941
\(169\) 1.00000 0.0769231
\(170\) −29.3759 −2.25303
\(171\) −5.07102 −0.387791
\(172\) −10.9053 −0.831522
\(173\) 10.6420 0.809094 0.404547 0.914517i \(-0.367429\pi\)
0.404547 + 0.914517i \(0.367429\pi\)
\(174\) 0.979275 0.0742386
\(175\) −4.90263 −0.370604
\(176\) −26.9373 −2.03048
\(177\) −1.56720 −0.117798
\(178\) 42.0727 3.15348
\(179\) 7.90704 0.591000 0.295500 0.955343i \(-0.404514\pi\)
0.295500 + 0.955343i \(0.404514\pi\)
\(180\) −34.6558 −2.58309
\(181\) 23.7712 1.76690 0.883451 0.468524i \(-0.155214\pi\)
0.883451 + 0.468524i \(0.155214\pi\)
\(182\) 5.82616 0.431864
\(183\) 1.78084 0.131644
\(184\) −27.5627 −2.03195
\(185\) −23.4924 −1.72720
\(186\) 0.200542 0.0147045
\(187\) −18.8027 −1.37499
\(188\) −4.64398 −0.338697
\(189\) −1.85381 −0.134845
\(190\) −11.4399 −0.829937
\(191\) 8.76374 0.634122 0.317061 0.948405i \(-0.397304\pi\)
0.317061 + 0.948405i \(0.397304\pi\)
\(192\) 0.360358 0.0260066
\(193\) −6.53781 −0.470602 −0.235301 0.971923i \(-0.575608\pi\)
−0.235301 + 0.971923i \(0.575608\pi\)
\(194\) −24.9501 −1.79131
\(195\) −0.357826 −0.0256245
\(196\) −7.22337 −0.515955
\(197\) 22.4887 1.60225 0.801125 0.598497i \(-0.204235\pi\)
0.801125 + 0.598497i \(0.204235\pi\)
\(198\) −32.3693 −2.30039
\(199\) −19.1206 −1.35543 −0.677713 0.735326i \(-0.737029\pi\)
−0.677713 + 0.735326i \(0.737029\pi\)
\(200\) −12.5935 −0.890497
\(201\) −1.10600 −0.0780114
\(202\) 21.3723 1.50375
\(203\) −6.69547 −0.469930
\(204\) −2.54995 −0.178533
\(205\) 11.1765 0.780603
\(206\) −21.1365 −1.47265
\(207\) −13.8448 −0.962282
\(208\) 6.25588 0.433767
\(209\) −7.32235 −0.506498
\(210\) −2.08475 −0.143862
\(211\) −19.9949 −1.37650 −0.688251 0.725473i \(-0.741621\pi\)
−0.688251 + 0.725473i \(0.741621\pi\)
\(212\) −50.0717 −3.43894
\(213\) −0.826351 −0.0566207
\(214\) 43.2684 2.95777
\(215\) −6.68239 −0.455735
\(216\) −4.76194 −0.324009
\(217\) −1.37114 −0.0930792
\(218\) −19.9020 −1.34793
\(219\) −1.12686 −0.0761462
\(220\) −50.0417 −3.37381
\(221\) 4.36671 0.293737
\(222\) −2.97575 −0.199720
\(223\) −9.01874 −0.603939 −0.301970 0.953318i \(-0.597644\pi\)
−0.301970 + 0.953318i \(0.597644\pi\)
\(224\) 9.00679 0.601791
\(225\) −6.32578 −0.421719
\(226\) 13.8957 0.924328
\(227\) −18.0066 −1.19514 −0.597570 0.801817i \(-0.703867\pi\)
−0.597570 + 0.801817i \(0.703867\pi\)
\(228\) −0.993031 −0.0657651
\(229\) 8.27309 0.546701 0.273351 0.961914i \(-0.411868\pi\)
0.273351 + 0.961914i \(0.411868\pi\)
\(230\) −31.2330 −2.05944
\(231\) −1.33439 −0.0877966
\(232\) −17.1988 −1.12916
\(233\) −5.60006 −0.366872 −0.183436 0.983032i \(-0.558722\pi\)
−0.183436 + 0.983032i \(0.558722\pi\)
\(234\) 7.51740 0.491428
\(235\) −2.84567 −0.185631
\(236\) 50.9001 3.31332
\(237\) −1.18848 −0.0772000
\(238\) 25.4412 1.64911
\(239\) −17.1605 −1.11002 −0.555011 0.831843i \(-0.687286\pi\)
−0.555011 + 0.831843i \(0.687286\pi\)
\(240\) −2.23852 −0.144496
\(241\) 17.8489 1.14975 0.574876 0.818241i \(-0.305050\pi\)
0.574876 + 0.818241i \(0.305050\pi\)
\(242\) −19.0100 −1.22201
\(243\) −3.59151 −0.230395
\(244\) −57.8388 −3.70275
\(245\) −4.42623 −0.282781
\(246\) 1.41572 0.0902629
\(247\) 1.70053 0.108202
\(248\) −3.52209 −0.223653
\(249\) −0.175610 −0.0111288
\(250\) 19.3657 1.22479
\(251\) 30.5955 1.93117 0.965586 0.260084i \(-0.0837501\pi\)
0.965586 + 0.260084i \(0.0837501\pi\)
\(252\) 30.0139 1.89070
\(253\) −19.9914 −1.25685
\(254\) 49.1691 3.08514
\(255\) −1.56252 −0.0978490
\(256\) −31.3524 −1.95953
\(257\) −12.8894 −0.804020 −0.402010 0.915635i \(-0.631688\pi\)
−0.402010 + 0.915635i \(0.631688\pi\)
\(258\) −0.846450 −0.0526977
\(259\) 20.3457 1.26422
\(260\) 11.6216 0.720741
\(261\) −8.63905 −0.534744
\(262\) 33.7883 2.08745
\(263\) 0.0281087 0.00173325 0.000866627 1.00000i \(-0.499724\pi\)
0.000866627 1.00000i \(0.499724\pi\)
\(264\) −3.42769 −0.210960
\(265\) −30.6822 −1.88479
\(266\) 9.90758 0.607472
\(267\) 2.23787 0.136956
\(268\) 35.9211 2.19423
\(269\) −20.3903 −1.24322 −0.621610 0.783327i \(-0.713521\pi\)
−0.621610 + 0.783327i \(0.713521\pi\)
\(270\) −5.39606 −0.328394
\(271\) 11.4585 0.696057 0.348028 0.937484i \(-0.386851\pi\)
0.348028 + 0.937484i \(0.386851\pi\)
\(272\) 27.3176 1.65637
\(273\) 0.309897 0.0187558
\(274\) −34.0937 −2.05968
\(275\) −9.13418 −0.550812
\(276\) −2.71116 −0.163193
\(277\) 17.0459 1.02419 0.512095 0.858929i \(-0.328870\pi\)
0.512095 + 0.858929i \(0.328870\pi\)
\(278\) 8.74644 0.524576
\(279\) −1.76916 −0.105917
\(280\) 36.6142 2.18812
\(281\) −6.55549 −0.391068 −0.195534 0.980697i \(-0.562644\pi\)
−0.195534 + 0.980697i \(0.562644\pi\)
\(282\) −0.360457 −0.0214649
\(283\) −4.77508 −0.283849 −0.141924 0.989877i \(-0.545329\pi\)
−0.141924 + 0.989877i \(0.545329\pi\)
\(284\) 26.8385 1.59257
\(285\) −0.608495 −0.0360441
\(286\) 10.8548 0.641859
\(287\) −9.67950 −0.571363
\(288\) 11.6213 0.684792
\(289\) 2.06816 0.121657
\(290\) −19.4891 −1.14444
\(291\) −1.32711 −0.0777967
\(292\) 36.5986 2.14177
\(293\) −26.3525 −1.53953 −0.769765 0.638327i \(-0.779627\pi\)
−0.769765 + 0.638327i \(0.779627\pi\)
\(294\) −0.560665 −0.0326986
\(295\) 31.1898 1.81594
\(296\) 52.2627 3.03771
\(297\) −3.45387 −0.200414
\(298\) 22.3018 1.29191
\(299\) 4.64277 0.268498
\(300\) −1.23874 −0.0715189
\(301\) 5.78732 0.333576
\(302\) −15.5486 −0.894724
\(303\) 1.13680 0.0653077
\(304\) 10.6383 0.610149
\(305\) −35.4416 −2.02938
\(306\) 32.8263 1.87656
\(307\) −29.7198 −1.69620 −0.848100 0.529836i \(-0.822254\pi\)
−0.848100 + 0.529836i \(0.822254\pi\)
\(308\) 43.3389 2.46946
\(309\) −1.12426 −0.0639572
\(310\) −3.99111 −0.226680
\(311\) 11.0739 0.627941 0.313971 0.949433i \(-0.398341\pi\)
0.313971 + 0.949433i \(0.398341\pi\)
\(312\) 0.796042 0.0450670
\(313\) −33.6092 −1.89970 −0.949852 0.312699i \(-0.898767\pi\)
−0.949852 + 0.312699i \(0.898767\pi\)
\(314\) −37.3307 −2.10669
\(315\) 18.3915 1.03624
\(316\) 38.5998 2.17141
\(317\) −34.0084 −1.91010 −0.955052 0.296437i \(-0.904201\pi\)
−0.955052 + 0.296437i \(0.904201\pi\)
\(318\) −3.88648 −0.217943
\(319\) −12.4744 −0.698435
\(320\) −7.17170 −0.400910
\(321\) 2.30147 0.128456
\(322\) 27.0495 1.50741
\(323\) 7.42573 0.413179
\(324\) 38.4915 2.13842
\(325\) 2.12131 0.117669
\(326\) −35.5542 −1.96917
\(327\) −1.05860 −0.0585406
\(328\) −24.8640 −1.37289
\(329\) 2.46451 0.135873
\(330\) −3.88414 −0.213815
\(331\) −22.4861 −1.23595 −0.617975 0.786198i \(-0.712047\pi\)
−0.617975 + 0.786198i \(0.712047\pi\)
\(332\) 5.70352 0.313021
\(333\) 26.2518 1.43859
\(334\) −4.79752 −0.262509
\(335\) 22.0112 1.20260
\(336\) 1.93868 0.105764
\(337\) 0.973163 0.0530116 0.0265058 0.999649i \(-0.491562\pi\)
0.0265058 + 0.999649i \(0.491562\pi\)
\(338\) −2.52091 −0.137119
\(339\) 0.739121 0.0401436
\(340\) 50.7481 2.75220
\(341\) −2.55460 −0.138339
\(342\) 12.7836 0.691257
\(343\) 20.0113 1.08051
\(344\) 14.8661 0.801524
\(345\) −1.66130 −0.0894416
\(346\) −26.8274 −1.44225
\(347\) 25.3284 1.35970 0.679851 0.733350i \(-0.262045\pi\)
0.679851 + 0.733350i \(0.262045\pi\)
\(348\) −1.69174 −0.0906868
\(349\) 7.23725 0.387401 0.193701 0.981061i \(-0.437951\pi\)
0.193701 + 0.981061i \(0.437951\pi\)
\(350\) 12.3591 0.660621
\(351\) 0.802121 0.0428141
\(352\) 16.7807 0.894414
\(353\) −26.3637 −1.40320 −0.701599 0.712572i \(-0.747530\pi\)
−0.701599 + 0.712572i \(0.747530\pi\)
\(354\) 3.95077 0.209981
\(355\) 16.4457 0.872847
\(356\) −72.6824 −3.85216
\(357\) 1.35323 0.0716206
\(358\) −19.9329 −1.05349
\(359\) 32.4237 1.71126 0.855629 0.517590i \(-0.173171\pi\)
0.855629 + 0.517590i \(0.173171\pi\)
\(360\) 47.2427 2.48991
\(361\) −16.1082 −0.847800
\(362\) −59.9251 −3.14959
\(363\) −1.01115 −0.0530719
\(364\) −10.0649 −0.527547
\(365\) 22.4263 1.17385
\(366\) −4.48934 −0.234662
\(367\) 7.49989 0.391491 0.195746 0.980655i \(-0.437287\pi\)
0.195746 + 0.980655i \(0.437287\pi\)
\(368\) 29.0446 1.51405
\(369\) −12.4893 −0.650167
\(370\) 59.2222 3.07882
\(371\) 26.5725 1.37958
\(372\) −0.346446 −0.0179624
\(373\) −17.8886 −0.926239 −0.463119 0.886296i \(-0.653270\pi\)
−0.463119 + 0.886296i \(0.653270\pi\)
\(374\) 47.3999 2.45099
\(375\) 1.03007 0.0531927
\(376\) 6.33065 0.326478
\(377\) 2.89705 0.149205
\(378\) 4.67329 0.240368
\(379\) 16.5101 0.848065 0.424033 0.905647i \(-0.360614\pi\)
0.424033 + 0.905647i \(0.360614\pi\)
\(380\) 19.7629 1.01382
\(381\) 2.61533 0.133988
\(382\) −22.0926 −1.13036
\(383\) −10.7627 −0.549950 −0.274975 0.961451i \(-0.588670\pi\)
−0.274975 + 0.961451i \(0.588670\pi\)
\(384\) −1.95355 −0.0996917
\(385\) 26.5565 1.35345
\(386\) 16.4812 0.838872
\(387\) 7.46728 0.379583
\(388\) 43.1024 2.18819
\(389\) −20.4939 −1.03908 −0.519541 0.854445i \(-0.673897\pi\)
−0.519541 + 0.854445i \(0.673897\pi\)
\(390\) 0.902047 0.0456769
\(391\) 20.2736 1.02528
\(392\) 9.84686 0.497342
\(393\) 1.79722 0.0906579
\(394\) −56.6918 −2.85609
\(395\) 23.6526 1.19009
\(396\) 55.9194 2.81006
\(397\) 5.81577 0.291885 0.145943 0.989293i \(-0.453379\pi\)
0.145943 + 0.989293i \(0.453379\pi\)
\(398\) 48.2014 2.41612
\(399\) 0.526990 0.0263825
\(400\) 13.2706 0.663532
\(401\) −37.5287 −1.87409 −0.937046 0.349205i \(-0.886452\pi\)
−0.937046 + 0.349205i \(0.886452\pi\)
\(402\) 2.78813 0.139059
\(403\) 0.593276 0.0295532
\(404\) −36.9215 −1.83691
\(405\) 23.5862 1.17201
\(406\) 16.8787 0.837674
\(407\) 37.9065 1.87896
\(408\) 3.47608 0.172092
\(409\) −3.41907 −0.169062 −0.0845310 0.996421i \(-0.526939\pi\)
−0.0845310 + 0.996421i \(0.526939\pi\)
\(410\) −28.1750 −1.39147
\(411\) −1.81346 −0.0894516
\(412\) 36.5142 1.79893
\(413\) −27.0121 −1.32918
\(414\) 34.9016 1.71532
\(415\) 3.49492 0.171559
\(416\) −3.89712 −0.191072
\(417\) 0.465228 0.0227823
\(418\) 18.4590 0.902858
\(419\) 0.550538 0.0268956 0.0134478 0.999910i \(-0.495719\pi\)
0.0134478 + 0.999910i \(0.495719\pi\)
\(420\) 3.60150 0.175735
\(421\) −29.2404 −1.42509 −0.712545 0.701626i \(-0.752458\pi\)
−0.712545 + 0.701626i \(0.752458\pi\)
\(422\) 50.4052 2.45369
\(423\) 3.17991 0.154613
\(424\) 68.2575 3.31488
\(425\) 9.26313 0.449328
\(426\) 2.08316 0.100929
\(427\) 30.6944 1.48541
\(428\) −74.7481 −3.61308
\(429\) 0.577375 0.0278759
\(430\) 16.8457 0.812372
\(431\) 30.0688 1.44836 0.724181 0.689610i \(-0.242218\pi\)
0.724181 + 0.689610i \(0.242218\pi\)
\(432\) 5.01797 0.241427
\(433\) −12.5009 −0.600756 −0.300378 0.953820i \(-0.597113\pi\)
−0.300378 + 0.953820i \(0.597113\pi\)
\(434\) 3.45652 0.165918
\(435\) −1.03664 −0.0497030
\(436\) 34.3815 1.64658
\(437\) 7.89518 0.377678
\(438\) 2.84071 0.135734
\(439\) 16.2255 0.774402 0.387201 0.921995i \(-0.373442\pi\)
0.387201 + 0.921995i \(0.373442\pi\)
\(440\) 68.2165 3.25210
\(441\) 4.94612 0.235530
\(442\) −11.0081 −0.523601
\(443\) −17.1852 −0.816493 −0.408246 0.912872i \(-0.633860\pi\)
−0.408246 + 0.912872i \(0.633860\pi\)
\(444\) 5.14074 0.243969
\(445\) −44.5372 −2.11127
\(446\) 22.7354 1.07655
\(447\) 1.18625 0.0561076
\(448\) 6.21109 0.293446
\(449\) −17.2635 −0.814715 −0.407357 0.913269i \(-0.633550\pi\)
−0.407357 + 0.913269i \(0.633550\pi\)
\(450\) 15.9467 0.751735
\(451\) −18.0341 −0.849190
\(452\) −24.0054 −1.12912
\(453\) −0.827042 −0.0388578
\(454\) 45.3930 2.13040
\(455\) −6.16745 −0.289134
\(456\) 1.35369 0.0633926
\(457\) 20.0952 0.940013 0.470007 0.882663i \(-0.344252\pi\)
0.470007 + 0.882663i \(0.344252\pi\)
\(458\) −20.8557 −0.974523
\(459\) 3.50263 0.163489
\(460\) 53.9564 2.51573
\(461\) 27.2188 1.26770 0.633852 0.773454i \(-0.281473\pi\)
0.633852 + 0.773454i \(0.281473\pi\)
\(462\) 3.36388 0.156502
\(463\) −38.0902 −1.77020 −0.885100 0.465400i \(-0.845910\pi\)
−0.885100 + 0.465400i \(0.845910\pi\)
\(464\) 18.1236 0.841365
\(465\) −0.212290 −0.00984470
\(466\) 14.1172 0.653969
\(467\) −28.8973 −1.33721 −0.668604 0.743618i \(-0.733108\pi\)
−0.668604 + 0.743618i \(0.733108\pi\)
\(468\) −12.9866 −0.600307
\(469\) −19.0629 −0.880245
\(470\) 7.17367 0.330897
\(471\) −1.98564 −0.0914936
\(472\) −69.3868 −3.19379
\(473\) 10.7825 0.495778
\(474\) 2.99605 0.137613
\(475\) 3.60735 0.165517
\(476\) −43.9507 −2.01448
\(477\) 34.2860 1.56985
\(478\) 43.2601 1.97867
\(479\) −32.8177 −1.49948 −0.749739 0.661733i \(-0.769821\pi\)
−0.749739 + 0.661733i \(0.769821\pi\)
\(480\) 1.39449 0.0636496
\(481\) −8.80335 −0.401398
\(482\) −44.9955 −2.04949
\(483\) 1.43878 0.0654668
\(484\) 32.8406 1.49276
\(485\) 26.4116 1.19929
\(486\) 9.05386 0.410691
\(487\) −21.8058 −0.988114 −0.494057 0.869430i \(-0.664487\pi\)
−0.494057 + 0.869430i \(0.664487\pi\)
\(488\) 78.8456 3.56917
\(489\) −1.89115 −0.0855209
\(490\) 11.1581 0.504072
\(491\) 2.72274 0.122875 0.0614377 0.998111i \(-0.480431\pi\)
0.0614377 + 0.998111i \(0.480431\pi\)
\(492\) −2.44571 −0.110261
\(493\) 12.6506 0.569753
\(494\) −4.28688 −0.192876
\(495\) 34.2654 1.54012
\(496\) 3.71146 0.166650
\(497\) −14.2429 −0.638881
\(498\) 0.442697 0.0198377
\(499\) 33.5633 1.50250 0.751249 0.660019i \(-0.229452\pi\)
0.751249 + 0.660019i \(0.229452\pi\)
\(500\) −33.4550 −1.49615
\(501\) −0.255183 −0.0114007
\(502\) −77.1285 −3.44241
\(503\) −22.8760 −1.01999 −0.509995 0.860177i \(-0.670353\pi\)
−0.509995 + 0.860177i \(0.670353\pi\)
\(504\) −40.9148 −1.82249
\(505\) −22.6242 −1.00676
\(506\) 50.3965 2.24040
\(507\) −0.134089 −0.00595509
\(508\) −84.9417 −3.76868
\(509\) 3.26178 0.144576 0.0722880 0.997384i \(-0.476970\pi\)
0.0722880 + 0.997384i \(0.476970\pi\)
\(510\) 3.93898 0.174421
\(511\) −19.4224 −0.859198
\(512\) 49.8984 2.20522
\(513\) 1.36403 0.0602235
\(514\) 32.4931 1.43321
\(515\) 22.3746 0.985945
\(516\) 1.46228 0.0643732
\(517\) 4.59167 0.201941
\(518\) −51.2897 −2.25354
\(519\) −1.42697 −0.0626369
\(520\) −15.8425 −0.694740
\(521\) −39.9467 −1.75010 −0.875048 0.484036i \(-0.839170\pi\)
−0.875048 + 0.484036i \(0.839170\pi\)
\(522\) 21.7783 0.953208
\(523\) 30.2971 1.32480 0.662400 0.749151i \(-0.269538\pi\)
0.662400 + 0.749151i \(0.269538\pi\)
\(524\) −58.3708 −2.54994
\(525\) 0.657387 0.0286907
\(526\) −0.0708593 −0.00308961
\(527\) 2.59067 0.112851
\(528\) 3.61199 0.157192
\(529\) −1.44469 −0.0628125
\(530\) 77.3470 3.35974
\(531\) −34.8533 −1.51250
\(532\) −17.1158 −0.742063
\(533\) 4.18820 0.181411
\(534\) −5.64147 −0.244130
\(535\) −45.8030 −1.98024
\(536\) −48.9675 −2.11507
\(537\) −1.06024 −0.0457529
\(538\) 51.4021 2.21610
\(539\) 7.14200 0.307628
\(540\) 9.32193 0.401152
\(541\) 28.9666 1.24537 0.622686 0.782472i \(-0.286041\pi\)
0.622686 + 0.782472i \(0.286041\pi\)
\(542\) −28.8859 −1.24076
\(543\) −3.18745 −0.136787
\(544\) −17.0176 −0.729624
\(545\) 21.0678 0.902445
\(546\) −0.781223 −0.0334332
\(547\) 22.7500 0.972719 0.486360 0.873759i \(-0.338324\pi\)
0.486360 + 0.873759i \(0.338324\pi\)
\(548\) 58.8983 2.51601
\(549\) 39.6045 1.69028
\(550\) 23.0264 0.981850
\(551\) 4.92652 0.209877
\(552\) 3.69584 0.157305
\(553\) −20.4845 −0.871089
\(554\) −42.9712 −1.82567
\(555\) 3.15007 0.133713
\(556\) −15.1098 −0.640800
\(557\) −17.4669 −0.740098 −0.370049 0.929012i \(-0.620659\pi\)
−0.370049 + 0.929012i \(0.620659\pi\)
\(558\) 4.45989 0.188802
\(559\) −2.50410 −0.105912
\(560\) −38.5828 −1.63042
\(561\) 2.52123 0.106446
\(562\) 16.5258 0.697098
\(563\) −30.8146 −1.29868 −0.649341 0.760498i \(-0.724955\pi\)
−0.649341 + 0.760498i \(0.724955\pi\)
\(564\) 0.622705 0.0262206
\(565\) −14.7097 −0.618841
\(566\) 12.0375 0.505975
\(567\) −20.4270 −0.857853
\(568\) −36.5861 −1.53512
\(569\) 0.238834 0.0100125 0.00500623 0.999987i \(-0.498406\pi\)
0.00500623 + 0.999987i \(0.498406\pi\)
\(570\) 1.53396 0.0642505
\(571\) 35.0106 1.46515 0.732575 0.680686i \(-0.238318\pi\)
0.732575 + 0.680686i \(0.238318\pi\)
\(572\) −18.7522 −0.784068
\(573\) −1.17512 −0.0490913
\(574\) 24.4011 1.01848
\(575\) 9.84874 0.410721
\(576\) 8.01406 0.333919
\(577\) −30.6537 −1.27613 −0.638064 0.769983i \(-0.720265\pi\)
−0.638064 + 0.769983i \(0.720265\pi\)
\(578\) −5.21364 −0.216859
\(579\) 0.876647 0.0364322
\(580\) 33.6683 1.39800
\(581\) −3.02679 −0.125573
\(582\) 3.34553 0.138677
\(583\) 49.5077 2.05040
\(584\) −49.8910 −2.06450
\(585\) −7.95775 −0.329013
\(586\) 66.4323 2.74429
\(587\) −17.8569 −0.737032 −0.368516 0.929621i \(-0.620134\pi\)
−0.368516 + 0.929621i \(0.620134\pi\)
\(588\) 0.968573 0.0399433
\(589\) 1.00889 0.0415704
\(590\) −78.6267 −3.23701
\(591\) −3.01547 −0.124040
\(592\) −55.0727 −2.26347
\(593\) −20.3269 −0.834725 −0.417363 0.908740i \(-0.637046\pi\)
−0.417363 + 0.908740i \(0.637046\pi\)
\(594\) 8.70689 0.357248
\(595\) −26.9315 −1.10408
\(596\) −38.5273 −1.57814
\(597\) 2.56386 0.104932
\(598\) −11.7040 −0.478612
\(599\) −40.8749 −1.67010 −0.835052 0.550172i \(-0.814562\pi\)
−0.835052 + 0.550172i \(0.814562\pi\)
\(600\) 1.68865 0.0689388
\(601\) 11.5645 0.471726 0.235863 0.971786i \(-0.424208\pi\)
0.235863 + 0.971786i \(0.424208\pi\)
\(602\) −14.5893 −0.594616
\(603\) −24.5966 −1.00165
\(604\) 26.8609 1.09296
\(605\) 20.1236 0.818140
\(606\) −2.86578 −0.116414
\(607\) −35.1241 −1.42564 −0.712822 0.701345i \(-0.752583\pi\)
−0.712822 + 0.701345i \(0.752583\pi\)
\(608\) −6.62718 −0.268768
\(609\) 0.897787 0.0363802
\(610\) 89.3450 3.61748
\(611\) −1.06636 −0.0431404
\(612\) −56.7089 −2.29232
\(613\) −25.0637 −1.01231 −0.506157 0.862441i \(-0.668934\pi\)
−0.506157 + 0.862441i \(0.668934\pi\)
\(614\) 74.9210 3.02356
\(615\) −1.49865 −0.0604313
\(616\) −59.0793 −2.38037
\(617\) 19.5377 0.786557 0.393279 0.919419i \(-0.371341\pi\)
0.393279 + 0.919419i \(0.371341\pi\)
\(618\) 2.83417 0.114007
\(619\) 1.00000 0.0401934
\(620\) 6.89482 0.276903
\(621\) 3.72406 0.149442
\(622\) −27.9162 −1.11934
\(623\) 38.5717 1.54534
\(624\) −0.838842 −0.0335806
\(625\) −31.1066 −1.24426
\(626\) 84.7257 3.38632
\(627\) 0.981845 0.0392111
\(628\) 64.4904 2.57345
\(629\) −38.4417 −1.53277
\(630\) −46.3632 −1.84715
\(631\) 33.6900 1.34118 0.670588 0.741830i \(-0.266042\pi\)
0.670588 + 0.741830i \(0.266042\pi\)
\(632\) −52.6191 −2.09308
\(633\) 2.68108 0.106563
\(634\) 85.7322 3.40486
\(635\) −52.0493 −2.06551
\(636\) 6.71405 0.266230
\(637\) −1.65865 −0.0657180
\(638\) 31.4469 1.24500
\(639\) −18.3774 −0.726997
\(640\) 38.8787 1.53682
\(641\) 28.2358 1.11525 0.557623 0.830094i \(-0.311713\pi\)
0.557623 + 0.830094i \(0.311713\pi\)
\(642\) −5.80180 −0.228979
\(643\) −40.3508 −1.59128 −0.795641 0.605769i \(-0.792866\pi\)
−0.795641 + 0.605769i \(0.792866\pi\)
\(644\) −46.7292 −1.84139
\(645\) 0.896033 0.0352813
\(646\) −18.7196 −0.736512
\(647\) −33.2397 −1.30679 −0.653393 0.757019i \(-0.726655\pi\)
−0.653393 + 0.757019i \(0.726655\pi\)
\(648\) −52.4714 −2.06127
\(649\) −50.3267 −1.97550
\(650\) −5.34762 −0.209751
\(651\) 0.183855 0.00720583
\(652\) 61.4215 2.40545
\(653\) −38.6940 −1.51421 −0.757106 0.653292i \(-0.773388\pi\)
−0.757106 + 0.653292i \(0.773388\pi\)
\(654\) 2.66863 0.104352
\(655\) −35.7676 −1.39756
\(656\) 26.2009 1.02297
\(657\) −25.0604 −0.977701
\(658\) −6.21280 −0.242200
\(659\) −16.1560 −0.629347 −0.314674 0.949200i \(-0.601895\pi\)
−0.314674 + 0.949200i \(0.601895\pi\)
\(660\) 6.71002 0.261187
\(661\) −28.7146 −1.11687 −0.558435 0.829548i \(-0.688598\pi\)
−0.558435 + 0.829548i \(0.688598\pi\)
\(662\) 56.6855 2.20314
\(663\) −0.585526 −0.0227400
\(664\) −7.77501 −0.301729
\(665\) −10.4879 −0.406705
\(666\) −66.1783 −2.56436
\(667\) 13.4503 0.520798
\(668\) 8.28792 0.320669
\(669\) 1.20931 0.0467547
\(670\) −55.4882 −2.14370
\(671\) 57.1873 2.20769
\(672\) −1.20771 −0.0465884
\(673\) −3.66181 −0.141152 −0.0705762 0.997506i \(-0.522484\pi\)
−0.0705762 + 0.997506i \(0.522484\pi\)
\(674\) −2.45325 −0.0944959
\(675\) 1.70155 0.0654925
\(676\) 4.35498 0.167499
\(677\) 19.2590 0.740183 0.370091 0.928995i \(-0.379326\pi\)
0.370091 + 0.928995i \(0.379326\pi\)
\(678\) −1.86326 −0.0715579
\(679\) −22.8740 −0.877822
\(680\) −69.1796 −2.65292
\(681\) 2.41448 0.0925231
\(682\) 6.43991 0.246597
\(683\) 48.0493 1.83855 0.919277 0.393611i \(-0.128774\pi\)
0.919277 + 0.393611i \(0.128774\pi\)
\(684\) −22.0842 −0.844410
\(685\) 36.0908 1.37896
\(686\) −50.4467 −1.92606
\(687\) −1.10933 −0.0423235
\(688\) −15.6654 −0.597236
\(689\) −11.4976 −0.438023
\(690\) 4.18800 0.159434
\(691\) 2.45957 0.0935663 0.0467831 0.998905i \(-0.485103\pi\)
0.0467831 + 0.998905i \(0.485103\pi\)
\(692\) 46.3455 1.76179
\(693\) −29.6758 −1.12729
\(694\) −63.8507 −2.42374
\(695\) −9.25878 −0.351206
\(696\) 2.30617 0.0874152
\(697\) 18.2887 0.692732
\(698\) −18.2444 −0.690562
\(699\) 0.750905 0.0284018
\(700\) −21.3508 −0.806986
\(701\) −51.1814 −1.93309 −0.966547 0.256488i \(-0.917435\pi\)
−0.966547 + 0.256488i \(0.917435\pi\)
\(702\) −2.02207 −0.0763183
\(703\) −14.9704 −0.564618
\(704\) 11.5720 0.436136
\(705\) 0.381572 0.0143708
\(706\) 66.4605 2.50127
\(707\) 19.5938 0.736902
\(708\) −6.82513 −0.256504
\(709\) 0.507797 0.0190707 0.00953536 0.999955i \(-0.496965\pi\)
0.00953536 + 0.999955i \(0.496965\pi\)
\(710\) −41.4581 −1.55590
\(711\) −26.4308 −0.991232
\(712\) 99.0803 3.71319
\(713\) 2.75445 0.103155
\(714\) −3.41137 −0.127667
\(715\) −11.4907 −0.429727
\(716\) 34.4350 1.28690
\(717\) 2.30103 0.0859337
\(718\) −81.7372 −3.05041
\(719\) 40.8356 1.52291 0.761456 0.648217i \(-0.224485\pi\)
0.761456 + 0.648217i \(0.224485\pi\)
\(720\) −49.7827 −1.85529
\(721\) −19.3777 −0.721663
\(722\) 40.6073 1.51125
\(723\) −2.39334 −0.0890093
\(724\) 103.523 3.84741
\(725\) 6.14552 0.228239
\(726\) 2.54903 0.0946033
\(727\) 7.64443 0.283516 0.141758 0.989901i \(-0.454724\pi\)
0.141758 + 0.989901i \(0.454724\pi\)
\(728\) 13.7205 0.508515
\(729\) −26.0339 −0.964220
\(730\) −56.5347 −2.09244
\(731\) −10.9347 −0.404434
\(732\) 7.75553 0.286653
\(733\) 16.9914 0.627591 0.313795 0.949491i \(-0.398399\pi\)
0.313795 + 0.949491i \(0.398399\pi\)
\(734\) −18.9065 −0.697853
\(735\) 0.593507 0.0218918
\(736\) −18.0935 −0.666933
\(737\) −35.5165 −1.30827
\(738\) 31.4844 1.15896
\(739\) 21.3547 0.785544 0.392772 0.919636i \(-0.371516\pi\)
0.392772 + 0.919636i \(0.371516\pi\)
\(740\) −102.309 −3.76095
\(741\) −0.228022 −0.00837660
\(742\) −66.9868 −2.45916
\(743\) −5.36281 −0.196743 −0.0983713 0.995150i \(-0.531363\pi\)
−0.0983713 + 0.995150i \(0.531363\pi\)
\(744\) 0.472273 0.0173144
\(745\) −23.6082 −0.864937
\(746\) 45.0956 1.65107
\(747\) −3.90542 −0.142892
\(748\) −81.8854 −2.99403
\(749\) 39.6679 1.44943
\(750\) −2.59672 −0.0948186
\(751\) 2.91113 0.106228 0.0531142 0.998588i \(-0.483085\pi\)
0.0531142 + 0.998588i \(0.483085\pi\)
\(752\) −6.67103 −0.243267
\(753\) −4.10251 −0.149504
\(754\) −7.30319 −0.265966
\(755\) 16.4594 0.599020
\(756\) −8.07331 −0.293623
\(757\) −49.5981 −1.80268 −0.901338 0.433117i \(-0.857414\pi\)
−0.901338 + 0.433117i \(0.857414\pi\)
\(758\) −41.6204 −1.51172
\(759\) 2.68062 0.0973003
\(760\) −26.9407 −0.977241
\(761\) −14.5873 −0.528791 −0.264395 0.964414i \(-0.585172\pi\)
−0.264395 + 0.964414i \(0.585172\pi\)
\(762\) −6.59302 −0.238840
\(763\) −18.2459 −0.660545
\(764\) 38.1659 1.38079
\(765\) −34.7492 −1.25636
\(766\) 27.1319 0.980314
\(767\) 11.6878 0.422022
\(768\) 4.20400 0.151699
\(769\) −22.9567 −0.827840 −0.413920 0.910313i \(-0.635841\pi\)
−0.413920 + 0.910313i \(0.635841\pi\)
\(770\) −66.9466 −2.41259
\(771\) 1.72833 0.0622442
\(772\) −28.4720 −1.02473
\(773\) 48.5768 1.74719 0.873594 0.486656i \(-0.161783\pi\)
0.873594 + 0.486656i \(0.161783\pi\)
\(774\) −18.8243 −0.676627
\(775\) 1.25852 0.0452074
\(776\) −58.7570 −2.10925
\(777\) −2.72813 −0.0978712
\(778\) 51.6633 1.85222
\(779\) 7.12217 0.255178
\(780\) −1.55832 −0.0557970
\(781\) −26.5362 −0.949539
\(782\) −51.1080 −1.82762
\(783\) 2.32378 0.0830452
\(784\) −10.3763 −0.370582
\(785\) 39.5174 1.41044
\(786\) −4.53063 −0.161602
\(787\) 37.9621 1.35320 0.676601 0.736350i \(-0.263452\pi\)
0.676601 + 0.736350i \(0.263452\pi\)
\(788\) 97.9376 3.48888
\(789\) −0.00376905 −0.000134182 0
\(790\) −59.6261 −2.12140
\(791\) 12.7394 0.452961
\(792\) −76.2290 −2.70868
\(793\) −13.2811 −0.471625
\(794\) −14.6610 −0.520300
\(795\) 4.11414 0.145913
\(796\) −83.2700 −2.95143
\(797\) 28.4925 1.00926 0.504628 0.863337i \(-0.331630\pi\)
0.504628 + 0.863337i \(0.331630\pi\)
\(798\) −1.32849 −0.0470282
\(799\) −4.65649 −0.164735
\(800\) −8.26700 −0.292282
\(801\) 49.7684 1.75848
\(802\) 94.6063 3.34067
\(803\) −36.1863 −1.27699
\(804\) −4.81662 −0.169869
\(805\) −28.6340 −1.00922
\(806\) −1.49559 −0.0526801
\(807\) 2.73411 0.0962453
\(808\) 50.3312 1.77065
\(809\) −49.8076 −1.75114 −0.875570 0.483091i \(-0.839514\pi\)
−0.875570 + 0.483091i \(0.839514\pi\)
\(810\) −59.4587 −2.08917
\(811\) 3.38009 0.118691 0.0593455 0.998238i \(-0.481099\pi\)
0.0593455 + 0.998238i \(0.481099\pi\)
\(812\) −29.1586 −1.02327
\(813\) −1.53646 −0.0538860
\(814\) −95.5588 −3.34933
\(815\) 37.6369 1.31836
\(816\) −3.66298 −0.128230
\(817\) −4.25831 −0.148979
\(818\) 8.61915 0.301362
\(819\) 6.89186 0.240821
\(820\) 48.6736 1.69976
\(821\) 27.2381 0.950617 0.475309 0.879819i \(-0.342336\pi\)
0.475309 + 0.879819i \(0.342336\pi\)
\(822\) 4.57158 0.159452
\(823\) 43.7128 1.52373 0.761866 0.647735i \(-0.224284\pi\)
0.761866 + 0.647735i \(0.224284\pi\)
\(824\) −49.7760 −1.73403
\(825\) 1.22479 0.0426417
\(826\) 68.0951 2.36933
\(827\) −36.8412 −1.28109 −0.640546 0.767919i \(-0.721292\pi\)
−0.640546 + 0.767919i \(0.721292\pi\)
\(828\) −60.2939 −2.09536
\(829\) 5.99200 0.208111 0.104055 0.994572i \(-0.466818\pi\)
0.104055 + 0.994572i \(0.466818\pi\)
\(830\) −8.81037 −0.305812
\(831\) −2.28566 −0.0792888
\(832\) −2.68746 −0.0931709
\(833\) −7.24283 −0.250949
\(834\) −1.17280 −0.0406107
\(835\) 5.07855 0.175750
\(836\) −31.8887 −1.10289
\(837\) 0.475879 0.0164488
\(838\) −1.38786 −0.0479427
\(839\) −9.83153 −0.339422 −0.169711 0.985494i \(-0.554283\pi\)
−0.169711 + 0.985494i \(0.554283\pi\)
\(840\) −4.90955 −0.169395
\(841\) −20.6071 −0.710590
\(842\) 73.7124 2.54030
\(843\) 0.879017 0.0302749
\(844\) −87.0771 −2.99732
\(845\) 2.66858 0.0918019
\(846\) −8.01626 −0.275605
\(847\) −17.4281 −0.598838
\(848\) −71.9275 −2.47000
\(849\) 0.640284 0.0219745
\(850\) −23.3515 −0.800950
\(851\) −40.8719 −1.40107
\(852\) −3.59874 −0.123291
\(853\) −23.9072 −0.818566 −0.409283 0.912407i \(-0.634221\pi\)
−0.409283 + 0.912407i \(0.634221\pi\)
\(854\) −77.3778 −2.64781
\(855\) −13.5324 −0.462799
\(856\) 101.896 3.48274
\(857\) −3.32465 −0.113568 −0.0567839 0.998386i \(-0.518085\pi\)
−0.0567839 + 0.998386i \(0.518085\pi\)
\(858\) −1.45551 −0.0496903
\(859\) 32.0118 1.09223 0.546114 0.837711i \(-0.316107\pi\)
0.546114 + 0.837711i \(0.316107\pi\)
\(860\) −29.1017 −0.992359
\(861\) 1.29791 0.0442327
\(862\) −75.8006 −2.58178
\(863\) 7.78569 0.265028 0.132514 0.991181i \(-0.457695\pi\)
0.132514 + 0.991181i \(0.457695\pi\)
\(864\) −3.12597 −0.106348
\(865\) 28.3989 0.965592
\(866\) 31.5137 1.07088
\(867\) −0.277317 −0.00941818
\(868\) −5.97129 −0.202679
\(869\) −38.1650 −1.29466
\(870\) 2.61327 0.0885982
\(871\) 8.24829 0.279483
\(872\) −46.8687 −1.58717
\(873\) −29.5139 −0.998893
\(874\) −19.9030 −0.673230
\(875\) 17.7542 0.600201
\(876\) −4.90745 −0.165807
\(877\) 28.0023 0.945571 0.472786 0.881178i \(-0.343249\pi\)
0.472786 + 0.881178i \(0.343249\pi\)
\(878\) −40.9030 −1.38041
\(879\) 3.53358 0.119185
\(880\) −71.8843 −2.42322
\(881\) −7.95159 −0.267896 −0.133948 0.990988i \(-0.542766\pi\)
−0.133948 + 0.990988i \(0.542766\pi\)
\(882\) −12.4687 −0.419843
\(883\) −28.8971 −0.972463 −0.486232 0.873830i \(-0.661629\pi\)
−0.486232 + 0.873830i \(0.661629\pi\)
\(884\) 19.0169 0.639609
\(885\) −4.18220 −0.140583
\(886\) 43.3223 1.45544
\(887\) −58.6775 −1.97020 −0.985098 0.171992i \(-0.944980\pi\)
−0.985098 + 0.171992i \(0.944980\pi\)
\(888\) −7.00783 −0.235168
\(889\) 45.0776 1.51185
\(890\) 112.274 3.76344
\(891\) −38.0579 −1.27499
\(892\) −39.2764 −1.31507
\(893\) −1.81338 −0.0606825
\(894\) −2.99042 −0.100015
\(895\) 21.1005 0.705313
\(896\) −33.6712 −1.12487
\(897\) −0.622543 −0.0207861
\(898\) 43.5197 1.45227
\(899\) 1.71875 0.0573235
\(900\) −27.5486 −0.918288
\(901\) −50.2066 −1.67263
\(902\) 45.4622 1.51373
\(903\) −0.776015 −0.0258241
\(904\) 32.7241 1.08839
\(905\) 63.4354 2.10866
\(906\) 2.08490 0.0692660
\(907\) −39.7518 −1.31994 −0.659968 0.751294i \(-0.729430\pi\)
−0.659968 + 0.751294i \(0.729430\pi\)
\(908\) −78.4183 −2.60240
\(909\) 25.2816 0.838537
\(910\) 15.5476 0.515397
\(911\) 19.2810 0.638807 0.319403 0.947619i \(-0.396517\pi\)
0.319403 + 0.947619i \(0.396517\pi\)
\(912\) −1.42648 −0.0472354
\(913\) −5.63927 −0.186633
\(914\) −50.6581 −1.67562
\(915\) 4.75232 0.157107
\(916\) 36.0291 1.19044
\(917\) 30.9767 1.02294
\(918\) −8.82981 −0.291427
\(919\) 26.5001 0.874159 0.437080 0.899423i \(-0.356013\pi\)
0.437080 + 0.899423i \(0.356013\pi\)
\(920\) −73.5531 −2.42497
\(921\) 3.98509 0.131313
\(922\) −68.6160 −2.25975
\(923\) 6.16272 0.202848
\(924\) −5.81125 −0.191176
\(925\) −18.6746 −0.614017
\(926\) 96.0219 3.15547
\(927\) −25.0027 −0.821196
\(928\) −11.2901 −0.370617
\(929\) −37.6606 −1.23560 −0.617802 0.786333i \(-0.711977\pi\)
−0.617802 + 0.786333i \(0.711977\pi\)
\(930\) 0.535163 0.0175487
\(931\) −2.82058 −0.0924409
\(932\) −24.3882 −0.798860
\(933\) −1.48488 −0.0486128
\(934\) 72.8475 2.38364
\(935\) −50.1765 −1.64095
\(936\) 17.7033 0.578651
\(937\) −29.4009 −0.960487 −0.480243 0.877135i \(-0.659452\pi\)
−0.480243 + 0.877135i \(0.659452\pi\)
\(938\) 48.0559 1.56908
\(939\) 4.50661 0.147068
\(940\) −12.3928 −0.404209
\(941\) 16.3793 0.533950 0.266975 0.963703i \(-0.413976\pi\)
0.266975 + 0.963703i \(0.413976\pi\)
\(942\) 5.00562 0.163092
\(943\) 19.4449 0.633212
\(944\) 73.1175 2.37977
\(945\) −4.94704 −0.160927
\(946\) −27.1816 −0.883750
\(947\) 8.30810 0.269977 0.134988 0.990847i \(-0.456900\pi\)
0.134988 + 0.990847i \(0.456900\pi\)
\(948\) −5.17580 −0.168102
\(949\) 8.40385 0.272800
\(950\) −9.09380 −0.295042
\(951\) 4.56015 0.147873
\(952\) 59.9134 1.94180
\(953\) −26.8427 −0.869522 −0.434761 0.900546i \(-0.643167\pi\)
−0.434761 + 0.900546i \(0.643167\pi\)
\(954\) −86.4320 −2.79834
\(955\) 23.3867 0.756777
\(956\) −74.7338 −2.41706
\(957\) 1.67268 0.0540701
\(958\) 82.7304 2.67290
\(959\) −31.2567 −1.00933
\(960\) 0.961644 0.0310369
\(961\) −30.6480 −0.988646
\(962\) 22.1924 0.715513
\(963\) 51.1829 1.64934
\(964\) 77.7318 2.50357
\(965\) −17.4467 −0.561628
\(966\) −3.62704 −0.116698
\(967\) 20.8408 0.670196 0.335098 0.942183i \(-0.391230\pi\)
0.335098 + 0.942183i \(0.391230\pi\)
\(968\) −44.7682 −1.43890
\(969\) −0.995706 −0.0319867
\(970\) −66.5813 −2.13780
\(971\) 48.9512 1.57092 0.785459 0.618914i \(-0.212427\pi\)
0.785459 + 0.618914i \(0.212427\pi\)
\(972\) −15.6409 −0.501683
\(973\) 8.01862 0.257065
\(974\) 54.9703 1.76136
\(975\) −0.284443 −0.00910947
\(976\) −83.0848 −2.65948
\(977\) −10.8291 −0.346454 −0.173227 0.984882i \(-0.555419\pi\)
−0.173227 + 0.984882i \(0.555419\pi\)
\(978\) 4.76742 0.152445
\(979\) 71.8636 2.29677
\(980\) −19.2761 −0.615753
\(981\) −23.5423 −0.751649
\(982\) −6.86377 −0.219032
\(983\) −15.7468 −0.502244 −0.251122 0.967955i \(-0.580800\pi\)
−0.251122 + 0.967955i \(0.580800\pi\)
\(984\) 3.33398 0.106284
\(985\) 60.0127 1.91216
\(986\) −31.8909 −1.01561
\(987\) −0.330463 −0.0105187
\(988\) 7.40578 0.235609
\(989\) −11.6260 −0.369684
\(990\) −86.3800 −2.74534
\(991\) −32.7034 −1.03886 −0.519428 0.854514i \(-0.673855\pi\)
−0.519428 + 0.854514i \(0.673855\pi\)
\(992\) −2.31207 −0.0734083
\(993\) 3.01514 0.0956824
\(994\) 35.9050 1.13884
\(995\) −51.0249 −1.61760
\(996\) −0.764778 −0.0242329
\(997\) −5.11255 −0.161916 −0.0809581 0.996718i \(-0.525798\pi\)
−0.0809581 + 0.996718i \(0.525798\pi\)
\(998\) −84.6099 −2.67828
\(999\) −7.06135 −0.223411
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 \(a_p\))