Properties

Label 4030.2.a.f.1.2
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
CM No
Inner twists 1

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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: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.191750\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.56820 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56820 q^{6} -1.49195 q^{7} +1.00000 q^{8} -0.540753 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.56820 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56820 q^{6} -1.49195 q^{7} +1.00000 q^{8} -0.540753 q^{9} -1.00000 q^{10} -1.02486 q^{11} -1.56820 q^{12} +1.00000 q^{13} -1.49195 q^{14} +1.56820 q^{15} +1.00000 q^{16} +1.43401 q^{17} -0.540753 q^{18} +2.94238 q^{19} -1.00000 q^{20} +2.33968 q^{21} -1.02486 q^{22} +1.14116 q^{23} -1.56820 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.55260 q^{27} -1.49195 q^{28} +6.02560 q^{29} +1.56820 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.60718 q^{33} +1.43401 q^{34} +1.49195 q^{35} -0.540753 q^{36} -6.22717 q^{37} +2.94238 q^{38} -1.56820 q^{39} -1.00000 q^{40} +3.45260 q^{41} +2.33968 q^{42} +4.32637 q^{43} -1.02486 q^{44} +0.540753 q^{45} +1.14116 q^{46} -4.37159 q^{47} -1.56820 q^{48} -4.77407 q^{49} +1.00000 q^{50} -2.24882 q^{51} +1.00000 q^{52} -9.04674 q^{53} +5.55260 q^{54} +1.02486 q^{55} -1.49195 q^{56} -4.61423 q^{57} +6.02560 q^{58} -8.83881 q^{59} +1.56820 q^{60} -11.6584 q^{61} -1.00000 q^{62} +0.806779 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.60718 q^{66} +9.32431 q^{67} +1.43401 q^{68} -1.78957 q^{69} +1.49195 q^{70} -15.9341 q^{71} -0.540753 q^{72} -4.75697 q^{73} -6.22717 q^{74} -1.56820 q^{75} +2.94238 q^{76} +1.52904 q^{77} -1.56820 q^{78} -5.97259 q^{79} -1.00000 q^{80} -7.08533 q^{81} +3.45260 q^{82} +0.949922 q^{83} +2.33968 q^{84} -1.43401 q^{85} +4.32637 q^{86} -9.44933 q^{87} -1.02486 q^{88} -10.5946 q^{89} +0.540753 q^{90} -1.49195 q^{91} +1.14116 q^{92} +1.56820 q^{93} -4.37159 q^{94} -2.94238 q^{95} -1.56820 q^{96} +13.4934 q^{97} -4.77407 q^{98} +0.554194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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
\(3\) −1.56820 −0.905400 −0.452700 0.891663i \(-0.649539\pi\)
−0.452700 + 0.891663i \(0.649539\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.56820 −0.640214
\(7\) −1.49195 −0.563906 −0.281953 0.959428i \(-0.590982\pi\)
−0.281953 + 0.959428i \(0.590982\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.540753 −0.180251
\(10\) −1.00000 −0.316228
\(11\) −1.02486 −0.309006 −0.154503 0.987992i \(-0.549378\pi\)
−0.154503 + 0.987992i \(0.549378\pi\)
\(12\) −1.56820 −0.452700
\(13\) 1.00000 0.277350
\(14\) −1.49195 −0.398742
\(15\) 1.56820 0.404907
\(16\) 1.00000 0.250000
\(17\) 1.43401 0.347799 0.173900 0.984763i \(-0.444363\pi\)
0.173900 + 0.984763i \(0.444363\pi\)
\(18\) −0.540753 −0.127457
\(19\) 2.94238 0.675027 0.337514 0.941321i \(-0.390414\pi\)
0.337514 + 0.941321i \(0.390414\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.33968 0.510560
\(22\) −1.02486 −0.218500
\(23\) 1.14116 0.237949 0.118974 0.992897i \(-0.462039\pi\)
0.118974 + 0.992897i \(0.462039\pi\)
\(24\) −1.56820 −0.320107
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 5.55260 1.06860
\(28\) −1.49195 −0.281953
\(29\) 6.02560 1.11893 0.559463 0.828856i \(-0.311008\pi\)
0.559463 + 0.828856i \(0.311008\pi\)
\(30\) 1.56820 0.286313
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 1.60718 0.279774
\(34\) 1.43401 0.245931
\(35\) 1.49195 0.252186
\(36\) −0.540753 −0.0901255
\(37\) −6.22717 −1.02374 −0.511870 0.859063i \(-0.671047\pi\)
−0.511870 + 0.859063i \(0.671047\pi\)
\(38\) 2.94238 0.477316
\(39\) −1.56820 −0.251113
\(40\) −1.00000 −0.158114
\(41\) 3.45260 0.539205 0.269603 0.962972i \(-0.413108\pi\)
0.269603 + 0.962972i \(0.413108\pi\)
\(42\) 2.33968 0.361021
\(43\) 4.32637 0.659765 0.329883 0.944022i \(-0.392991\pi\)
0.329883 + 0.944022i \(0.392991\pi\)
\(44\) −1.02486 −0.154503
\(45\) 0.540753 0.0806107
\(46\) 1.14116 0.168255
\(47\) −4.37159 −0.637662 −0.318831 0.947812i \(-0.603290\pi\)
−0.318831 + 0.947812i \(0.603290\pi\)
\(48\) −1.56820 −0.226350
\(49\) −4.77407 −0.682010
\(50\) 1.00000 0.141421
\(51\) −2.24882 −0.314897
\(52\) 1.00000 0.138675
\(53\) −9.04674 −1.24266 −0.621332 0.783547i \(-0.713408\pi\)
−0.621332 + 0.783547i \(0.713408\pi\)
\(54\) 5.55260 0.755614
\(55\) 1.02486 0.138192
\(56\) −1.49195 −0.199371
\(57\) −4.61423 −0.611169
\(58\) 6.02560 0.791200
\(59\) −8.83881 −1.15071 −0.575357 0.817902i \(-0.695137\pi\)
−0.575357 + 0.817902i \(0.695137\pi\)
\(60\) 1.56820 0.202454
\(61\) −11.6584 −1.49271 −0.746353 0.665550i \(-0.768197\pi\)
−0.746353 + 0.665550i \(0.768197\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0.806779 0.101645
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 1.60718 0.197830
\(67\) 9.32431 1.13915 0.569573 0.821941i \(-0.307109\pi\)
0.569573 + 0.821941i \(0.307109\pi\)
\(68\) 1.43401 0.173900
\(69\) −1.78957 −0.215439
\(70\) 1.49195 0.178323
\(71\) −15.9341 −1.89103 −0.945513 0.325583i \(-0.894439\pi\)
−0.945513 + 0.325583i \(0.894439\pi\)
\(72\) −0.540753 −0.0637284
\(73\) −4.75697 −0.556761 −0.278381 0.960471i \(-0.589798\pi\)
−0.278381 + 0.960471i \(0.589798\pi\)
\(74\) −6.22717 −0.723893
\(75\) −1.56820 −0.181080
\(76\) 2.94238 0.337514
\(77\) 1.52904 0.174250
\(78\) −1.56820 −0.177564
\(79\) −5.97259 −0.671969 −0.335984 0.941868i \(-0.609069\pi\)
−0.335984 + 0.941868i \(0.609069\pi\)
\(80\) −1.00000 −0.111803
\(81\) −7.08533 −0.787258
\(82\) 3.45260 0.381276
\(83\) 0.949922 0.104267 0.0521337 0.998640i \(-0.483398\pi\)
0.0521337 + 0.998640i \(0.483398\pi\)
\(84\) 2.33968 0.255280
\(85\) −1.43401 −0.155541
\(86\) 4.32637 0.466525
\(87\) −9.44933 −1.01307
\(88\) −1.02486 −0.109250
\(89\) −10.5946 −1.12303 −0.561513 0.827468i \(-0.689781\pi\)
−0.561513 + 0.827468i \(0.689781\pi\)
\(90\) 0.540753 0.0570004
\(91\) −1.49195 −0.156399
\(92\) 1.14116 0.118974
\(93\) 1.56820 0.162615
\(94\) −4.37159 −0.450895
\(95\) −2.94238 −0.301881
\(96\) −1.56820 −0.160054
\(97\) 13.4934 1.37005 0.685024 0.728520i \(-0.259792\pi\)
0.685024 + 0.728520i \(0.259792\pi\)
\(98\) −4.77407 −0.482254
\(99\) 0.554194 0.0556986
\(100\) 1.00000 0.100000
\(101\) 7.27999 0.724386 0.362193 0.932103i \(-0.382028\pi\)
0.362193 + 0.932103i \(0.382028\pi\)
\(102\) −2.24882 −0.222666
\(103\) −11.8444 −1.16706 −0.583531 0.812091i \(-0.698329\pi\)
−0.583531 + 0.812091i \(0.698329\pi\)
\(104\) 1.00000 0.0980581
\(105\) −2.33968 −0.228329
\(106\) −9.04674 −0.878697
\(107\) −13.9269 −1.34636 −0.673182 0.739477i \(-0.735073\pi\)
−0.673182 + 0.739477i \(0.735073\pi\)
\(108\) 5.55260 0.534300
\(109\) 0.767912 0.0735527 0.0367763 0.999324i \(-0.488291\pi\)
0.0367763 + 0.999324i \(0.488291\pi\)
\(110\) 1.02486 0.0977162
\(111\) 9.76543 0.926894
\(112\) −1.49195 −0.140976
\(113\) 16.9743 1.59680 0.798402 0.602124i \(-0.205679\pi\)
0.798402 + 0.602124i \(0.205679\pi\)
\(114\) −4.61423 −0.432162
\(115\) −1.14116 −0.106414
\(116\) 6.02560 0.559463
\(117\) −0.540753 −0.0499927
\(118\) −8.83881 −0.813678
\(119\) −2.13948 −0.196126
\(120\) 1.56820 0.143156
\(121\) −9.94967 −0.904515
\(122\) −11.6584 −1.05550
\(123\) −5.41436 −0.488196
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 0.806779 0.0718736
\(127\) −18.8774 −1.67510 −0.837549 0.546362i \(-0.816012\pi\)
−0.837549 + 0.546362i \(0.816012\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.78461 −0.597351
\(130\) −1.00000 −0.0877058
\(131\) 7.58378 0.662598 0.331299 0.943526i \(-0.392513\pi\)
0.331299 + 0.943526i \(0.392513\pi\)
\(132\) 1.60718 0.139887
\(133\) −4.38989 −0.380652
\(134\) 9.32431 0.805498
\(135\) −5.55260 −0.477892
\(136\) 1.43401 0.122966
\(137\) 15.2258 1.30083 0.650414 0.759580i \(-0.274595\pi\)
0.650414 + 0.759580i \(0.274595\pi\)
\(138\) −1.78957 −0.152338
\(139\) −8.98962 −0.762490 −0.381245 0.924474i \(-0.624505\pi\)
−0.381245 + 0.924474i \(0.624505\pi\)
\(140\) 1.49195 0.126093
\(141\) 6.85552 0.577339
\(142\) −15.9341 −1.33716
\(143\) −1.02486 −0.0857028
\(144\) −0.540753 −0.0450628
\(145\) −6.02560 −0.500399
\(146\) −4.75697 −0.393690
\(147\) 7.48669 0.617492
\(148\) −6.22717 −0.511870
\(149\) 11.4923 0.941482 0.470741 0.882271i \(-0.343987\pi\)
0.470741 + 0.882271i \(0.343987\pi\)
\(150\) −1.56820 −0.128043
\(151\) 6.86593 0.558742 0.279371 0.960183i \(-0.409874\pi\)
0.279371 + 0.960183i \(0.409874\pi\)
\(152\) 2.94238 0.238658
\(153\) −0.775447 −0.0626912
\(154\) 1.52904 0.123213
\(155\) 1.00000 0.0803219
\(156\) −1.56820 −0.125556
\(157\) −6.46147 −0.515681 −0.257841 0.966187i \(-0.583011\pi\)
−0.257841 + 0.966187i \(0.583011\pi\)
\(158\) −5.97259 −0.475154
\(159\) 14.1871 1.12511
\(160\) −1.00000 −0.0790569
\(161\) −1.70256 −0.134181
\(162\) −7.08533 −0.556676
\(163\) −4.82792 −0.378152 −0.189076 0.981962i \(-0.560549\pi\)
−0.189076 + 0.981962i \(0.560549\pi\)
\(164\) 3.45260 0.269603
\(165\) −1.60718 −0.125119
\(166\) 0.949922 0.0737282
\(167\) −13.2027 −1.02165 −0.510826 0.859684i \(-0.670661\pi\)
−0.510826 + 0.859684i \(0.670661\pi\)
\(168\) 2.33968 0.180510
\(169\) 1.00000 0.0769231
\(170\) −1.43401 −0.109984
\(171\) −1.59110 −0.121674
\(172\) 4.32637 0.329883
\(173\) −6.54788 −0.497826 −0.248913 0.968526i \(-0.580073\pi\)
−0.248913 + 0.968526i \(0.580073\pi\)
\(174\) −9.44933 −0.716352
\(175\) −1.49195 −0.112781
\(176\) −1.02486 −0.0772515
\(177\) 13.8610 1.04186
\(178\) −10.5946 −0.794099
\(179\) −19.2959 −1.44224 −0.721120 0.692810i \(-0.756372\pi\)
−0.721120 + 0.692810i \(0.756372\pi\)
\(180\) 0.540753 0.0403054
\(181\) 10.1329 0.753176 0.376588 0.926381i \(-0.377097\pi\)
0.376588 + 0.926381i \(0.377097\pi\)
\(182\) −1.49195 −0.110591
\(183\) 18.2827 1.35150
\(184\) 1.14116 0.0841277
\(185\) 6.22717 0.457830
\(186\) 1.56820 0.114986
\(187\) −1.46966 −0.107472
\(188\) −4.37159 −0.318831
\(189\) −8.28423 −0.602589
\(190\) −2.94238 −0.213462
\(191\) −24.1076 −1.74436 −0.872181 0.489184i \(-0.837295\pi\)
−0.872181 + 0.489184i \(0.837295\pi\)
\(192\) −1.56820 −0.113175
\(193\) 21.8594 1.57348 0.786739 0.617286i \(-0.211768\pi\)
0.786739 + 0.617286i \(0.211768\pi\)
\(194\) 13.4934 0.968771
\(195\) 1.56820 0.112301
\(196\) −4.77407 −0.341005
\(197\) −17.8184 −1.26951 −0.634753 0.772715i \(-0.718898\pi\)
−0.634753 + 0.772715i \(0.718898\pi\)
\(198\) 0.554194 0.0393849
\(199\) −11.2098 −0.794640 −0.397320 0.917680i \(-0.630060\pi\)
−0.397320 + 0.917680i \(0.630060\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.6224 −1.03138
\(202\) 7.27999 0.512219
\(203\) −8.98992 −0.630968
\(204\) −2.24882 −0.157449
\(205\) −3.45260 −0.241140
\(206\) −11.8444 −0.825237
\(207\) −0.617088 −0.0428906
\(208\) 1.00000 0.0693375
\(209\) −3.01551 −0.208587
\(210\) −2.33968 −0.161453
\(211\) 6.83383 0.470460 0.235230 0.971940i \(-0.424416\pi\)
0.235230 + 0.971940i \(0.424416\pi\)
\(212\) −9.04674 −0.621332
\(213\) 24.9878 1.71214
\(214\) −13.9269 −0.952023
\(215\) −4.32637 −0.295056
\(216\) 5.55260 0.377807
\(217\) 1.49195 0.101280
\(218\) 0.767912 0.0520096
\(219\) 7.45988 0.504092
\(220\) 1.02486 0.0690958
\(221\) 1.43401 0.0964622
\(222\) 9.76543 0.655413
\(223\) 15.5580 1.04184 0.520922 0.853604i \(-0.325588\pi\)
0.520922 + 0.853604i \(0.325588\pi\)
\(224\) −1.49195 −0.0996854
\(225\) −0.540753 −0.0360502
\(226\) 16.9743 1.12911
\(227\) 7.57399 0.502703 0.251352 0.967896i \(-0.419125\pi\)
0.251352 + 0.967896i \(0.419125\pi\)
\(228\) −4.61423 −0.305585
\(229\) −16.5673 −1.09480 −0.547399 0.836872i \(-0.684382\pi\)
−0.547399 + 0.836872i \(0.684382\pi\)
\(230\) −1.14116 −0.0752461
\(231\) −2.39784 −0.157766
\(232\) 6.02560 0.395600
\(233\) 2.48371 0.162713 0.0813567 0.996685i \(-0.474075\pi\)
0.0813567 + 0.996685i \(0.474075\pi\)
\(234\) −0.540753 −0.0353501
\(235\) 4.37159 0.285171
\(236\) −8.83881 −0.575357
\(237\) 9.36621 0.608400
\(238\) −2.13948 −0.138682
\(239\) 0.510101 0.0329957 0.0164979 0.999864i \(-0.494748\pi\)
0.0164979 + 0.999864i \(0.494748\pi\)
\(240\) 1.56820 0.101227
\(241\) −2.23208 −0.143781 −0.0718904 0.997413i \(-0.522903\pi\)
−0.0718904 + 0.997413i \(0.522903\pi\)
\(242\) −9.94967 −0.639589
\(243\) −5.54661 −0.355815
\(244\) −11.6584 −0.746353
\(245\) 4.77407 0.305004
\(246\) −5.41436 −0.345207
\(247\) 2.94238 0.187219
\(248\) −1.00000 −0.0635001
\(249\) −1.48967 −0.0944037
\(250\) −1.00000 −0.0632456
\(251\) 10.1588 0.641216 0.320608 0.947212i \(-0.396113\pi\)
0.320608 + 0.947212i \(0.396113\pi\)
\(252\) 0.806779 0.0508223
\(253\) −1.16953 −0.0735276
\(254\) −18.8774 −1.18447
\(255\) 2.24882 0.140826
\(256\) 1.00000 0.0625000
\(257\) −8.18897 −0.510814 −0.255407 0.966834i \(-0.582209\pi\)
−0.255407 + 0.966834i \(0.582209\pi\)
\(258\) −6.78461 −0.422391
\(259\) 9.29065 0.577293
\(260\) −1.00000 −0.0620174
\(261\) −3.25836 −0.201688
\(262\) 7.58378 0.468528
\(263\) −18.0255 −1.11150 −0.555749 0.831350i \(-0.687569\pi\)
−0.555749 + 0.831350i \(0.687569\pi\)
\(264\) 1.60718 0.0989150
\(265\) 9.04674 0.555737
\(266\) −4.38989 −0.269161
\(267\) 16.6144 1.01679
\(268\) 9.32431 0.569573
\(269\) 3.35767 0.204721 0.102360 0.994747i \(-0.467361\pi\)
0.102360 + 0.994747i \(0.467361\pi\)
\(270\) −5.55260 −0.337921
\(271\) 24.7308 1.50229 0.751145 0.660137i \(-0.229502\pi\)
0.751145 + 0.660137i \(0.229502\pi\)
\(272\) 1.43401 0.0869498
\(273\) 2.33968 0.141604
\(274\) 15.2258 0.919825
\(275\) −1.02486 −0.0618012
\(276\) −1.78957 −0.107719
\(277\) 24.0705 1.44625 0.723127 0.690716i \(-0.242704\pi\)
0.723127 + 0.690716i \(0.242704\pi\)
\(278\) −8.98962 −0.539162
\(279\) 0.540753 0.0323741
\(280\) 1.49195 0.0891613
\(281\) −26.2186 −1.56407 −0.782034 0.623236i \(-0.785818\pi\)
−0.782034 + 0.623236i \(0.785818\pi\)
\(282\) 6.85552 0.408240
\(283\) −22.8318 −1.35721 −0.678606 0.734502i \(-0.737416\pi\)
−0.678606 + 0.734502i \(0.737416\pi\)
\(284\) −15.9341 −0.945513
\(285\) 4.61423 0.273323
\(286\) −1.02486 −0.0606010
\(287\) −5.15112 −0.304061
\(288\) −0.540753 −0.0318642
\(289\) −14.9436 −0.879036
\(290\) −6.02560 −0.353835
\(291\) −21.1604 −1.24044
\(292\) −4.75697 −0.278381
\(293\) −8.43198 −0.492601 −0.246301 0.969193i \(-0.579215\pi\)
−0.246301 + 0.969193i \(0.579215\pi\)
\(294\) 7.48669 0.436633
\(295\) 8.83881 0.514615
\(296\) −6.22717 −0.361947
\(297\) −5.69062 −0.330203
\(298\) 11.4923 0.665729
\(299\) 1.14116 0.0659952
\(300\) −1.56820 −0.0905400
\(301\) −6.45475 −0.372046
\(302\) 6.86593 0.395090
\(303\) −11.4165 −0.655859
\(304\) 2.94238 0.168757
\(305\) 11.6584 0.667559
\(306\) −0.775447 −0.0443294
\(307\) −17.5432 −1.00124 −0.500620 0.865667i \(-0.666895\pi\)
−0.500620 + 0.865667i \(0.666895\pi\)
\(308\) 1.52904 0.0871251
\(309\) 18.5743 1.05666
\(310\) 1.00000 0.0567962
\(311\) 28.8255 1.63454 0.817272 0.576252i \(-0.195485\pi\)
0.817272 + 0.576252i \(0.195485\pi\)
\(312\) −1.56820 −0.0887818
\(313\) 13.5453 0.765624 0.382812 0.923826i \(-0.374956\pi\)
0.382812 + 0.923826i \(0.374956\pi\)
\(314\) −6.46147 −0.364642
\(315\) −0.806779 −0.0454569
\(316\) −5.97259 −0.335984
\(317\) −14.0492 −0.789084 −0.394542 0.918878i \(-0.629097\pi\)
−0.394542 + 0.918878i \(0.629097\pi\)
\(318\) 14.1871 0.795572
\(319\) −6.17537 −0.345754
\(320\) −1.00000 −0.0559017
\(321\) 21.8401 1.21900
\(322\) −1.70256 −0.0948802
\(323\) 4.21940 0.234774
\(324\) −7.08533 −0.393629
\(325\) 1.00000 0.0554700
\(326\) −4.82792 −0.267394
\(327\) −1.20424 −0.0665946
\(328\) 3.45260 0.190638
\(329\) 6.52221 0.359581
\(330\) −1.60718 −0.0884722
\(331\) 15.3162 0.841856 0.420928 0.907094i \(-0.361704\pi\)
0.420928 + 0.907094i \(0.361704\pi\)
\(332\) 0.949922 0.0521337
\(333\) 3.36736 0.184530
\(334\) −13.2027 −0.722418
\(335\) −9.32431 −0.509441
\(336\) 2.33968 0.127640
\(337\) −6.07422 −0.330884 −0.165442 0.986220i \(-0.552905\pi\)
−0.165442 + 0.986220i \(0.552905\pi\)
\(338\) 1.00000 0.0543928
\(339\) −26.6190 −1.44575
\(340\) −1.43401 −0.0777703
\(341\) 1.02486 0.0554991
\(342\) −1.59110 −0.0860368
\(343\) 17.5664 0.948495
\(344\) 4.32637 0.233262
\(345\) 1.78957 0.0963472
\(346\) −6.54788 −0.352016
\(347\) −1.19043 −0.0639056 −0.0319528 0.999489i \(-0.510173\pi\)
−0.0319528 + 0.999489i \(0.510173\pi\)
\(348\) −9.44933 −0.506537
\(349\) −15.7136 −0.841128 −0.420564 0.907263i \(-0.638168\pi\)
−0.420564 + 0.907263i \(0.638168\pi\)
\(350\) −1.49195 −0.0797483
\(351\) 5.55260 0.296376
\(352\) −1.02486 −0.0546250
\(353\) 17.3692 0.924471 0.462235 0.886757i \(-0.347047\pi\)
0.462235 + 0.886757i \(0.347047\pi\)
\(354\) 13.8610 0.736704
\(355\) 15.9341 0.845693
\(356\) −10.5946 −0.561513
\(357\) 3.35513 0.177572
\(358\) −19.2959 −1.01982
\(359\) −32.8369 −1.73307 −0.866534 0.499119i \(-0.833657\pi\)
−0.866534 + 0.499119i \(0.833657\pi\)
\(360\) 0.540753 0.0285002
\(361\) −10.3424 −0.544338
\(362\) 10.1329 0.532576
\(363\) 15.6031 0.818948
\(364\) −1.49195 −0.0781997
\(365\) 4.75697 0.248991
\(366\) 18.2827 0.955652
\(367\) 20.4606 1.06804 0.534018 0.845473i \(-0.320682\pi\)
0.534018 + 0.845473i \(0.320682\pi\)
\(368\) 1.14116 0.0594872
\(369\) −1.86700 −0.0971923
\(370\) 6.22717 0.323735
\(371\) 13.4973 0.700746
\(372\) 1.56820 0.0813073
\(373\) 17.8481 0.924140 0.462070 0.886844i \(-0.347107\pi\)
0.462070 + 0.886844i \(0.347107\pi\)
\(374\) −1.46966 −0.0759942
\(375\) 1.56820 0.0809814
\(376\) −4.37159 −0.225447
\(377\) 6.02560 0.310334
\(378\) −8.28423 −0.426095
\(379\) −11.1753 −0.574036 −0.287018 0.957925i \(-0.592664\pi\)
−0.287018 + 0.957925i \(0.592664\pi\)
\(380\) −2.94238 −0.150941
\(381\) 29.6035 1.51663
\(382\) −24.1076 −1.23345
\(383\) 15.0592 0.769490 0.384745 0.923023i \(-0.374289\pi\)
0.384745 + 0.923023i \(0.374289\pi\)
\(384\) −1.56820 −0.0800268
\(385\) −1.52904 −0.0779270
\(386\) 21.8594 1.11262
\(387\) −2.33950 −0.118923
\(388\) 13.4934 0.685024
\(389\) −23.8515 −1.20932 −0.604659 0.796485i \(-0.706690\pi\)
−0.604659 + 0.796485i \(0.706690\pi\)
\(390\) 1.56820 0.0794088
\(391\) 1.63644 0.0827585
\(392\) −4.77407 −0.241127
\(393\) −11.8929 −0.599916
\(394\) −17.8184 −0.897676
\(395\) 5.97259 0.300514
\(396\) 0.554194 0.0278493
\(397\) −35.1081 −1.76202 −0.881011 0.473095i \(-0.843137\pi\)
−0.881011 + 0.473095i \(0.843137\pi\)
\(398\) −11.2098 −0.561896
\(399\) 6.88422 0.344642
\(400\) 1.00000 0.0500000
\(401\) 2.85667 0.142655 0.0713275 0.997453i \(-0.477276\pi\)
0.0713275 + 0.997453i \(0.477276\pi\)
\(402\) −14.6224 −0.729297
\(403\) −1.00000 −0.0498135
\(404\) 7.27999 0.362193
\(405\) 7.08533 0.352073
\(406\) −8.98992 −0.446162
\(407\) 6.38195 0.316342
\(408\) −2.24882 −0.111333
\(409\) −0.398169 −0.0196882 −0.00984410 0.999952i \(-0.503134\pi\)
−0.00984410 + 0.999952i \(0.503134\pi\)
\(410\) −3.45260 −0.170512
\(411\) −23.8771 −1.17777
\(412\) −11.8444 −0.583531
\(413\) 13.1871 0.648895
\(414\) −0.617088 −0.0303282
\(415\) −0.949922 −0.0466298
\(416\) 1.00000 0.0490290
\(417\) 14.0975 0.690358
\(418\) −3.01551 −0.147493
\(419\) −26.6342 −1.30116 −0.650582 0.759436i \(-0.725475\pi\)
−0.650582 + 0.759436i \(0.725475\pi\)
\(420\) −2.33968 −0.114165
\(421\) −7.83612 −0.381909 −0.190955 0.981599i \(-0.561158\pi\)
−0.190955 + 0.981599i \(0.561158\pi\)
\(422\) 6.83383 0.332666
\(423\) 2.36395 0.114939
\(424\) −9.04674 −0.439348
\(425\) 1.43401 0.0695599
\(426\) 24.9878 1.21066
\(427\) 17.3938 0.841746
\(428\) −13.9269 −0.673182
\(429\) 1.60718 0.0775953
\(430\) −4.32637 −0.208636
\(431\) 16.9633 0.817095 0.408548 0.912737i \(-0.366035\pi\)
0.408548 + 0.912737i \(0.366035\pi\)
\(432\) 5.55260 0.267150
\(433\) 22.0858 1.06138 0.530689 0.847567i \(-0.321933\pi\)
0.530689 + 0.847567i \(0.321933\pi\)
\(434\) 1.49195 0.0716161
\(435\) 9.44933 0.453061
\(436\) 0.767912 0.0367763
\(437\) 3.35773 0.160622
\(438\) 7.45988 0.356447
\(439\) −34.8308 −1.66238 −0.831192 0.555985i \(-0.812341\pi\)
−0.831192 + 0.555985i \(0.812341\pi\)
\(440\) 1.02486 0.0488581
\(441\) 2.58159 0.122933
\(442\) 1.43401 0.0682090
\(443\) −7.79547 −0.370374 −0.185187 0.982703i \(-0.559289\pi\)
−0.185187 + 0.982703i \(0.559289\pi\)
\(444\) 9.76543 0.463447
\(445\) 10.5946 0.502233
\(446\) 15.5580 0.736694
\(447\) −18.0221 −0.852418
\(448\) −1.49195 −0.0704882
\(449\) 33.8963 1.59967 0.799834 0.600222i \(-0.204921\pi\)
0.799834 + 0.600222i \(0.204921\pi\)
\(450\) −0.540753 −0.0254914
\(451\) −3.53842 −0.166618
\(452\) 16.9743 0.798402
\(453\) −10.7671 −0.505885
\(454\) 7.57399 0.355465
\(455\) 1.49195 0.0699439
\(456\) −4.61423 −0.216081
\(457\) 24.5958 1.15054 0.575272 0.817962i \(-0.304896\pi\)
0.575272 + 0.817962i \(0.304896\pi\)
\(458\) −16.5673 −0.774139
\(459\) 7.96251 0.371658
\(460\) −1.14116 −0.0532070
\(461\) 9.93793 0.462855 0.231428 0.972852i \(-0.425660\pi\)
0.231428 + 0.972852i \(0.425660\pi\)
\(462\) −2.39784 −0.111557
\(463\) 15.4200 0.716627 0.358313 0.933601i \(-0.383352\pi\)
0.358313 + 0.933601i \(0.383352\pi\)
\(464\) 6.02560 0.279731
\(465\) −1.56820 −0.0727235
\(466\) 2.48371 0.115056
\(467\) 2.51737 0.116490 0.0582450 0.998302i \(-0.481450\pi\)
0.0582450 + 0.998302i \(0.481450\pi\)
\(468\) −0.540753 −0.0249963
\(469\) −13.9114 −0.642371
\(470\) 4.37159 0.201646
\(471\) 10.1329 0.466898
\(472\) −8.83881 −0.406839
\(473\) −4.43391 −0.203871
\(474\) 9.36621 0.430204
\(475\) 2.94238 0.135005
\(476\) −2.13948 −0.0980630
\(477\) 4.89205 0.223992
\(478\) 0.510101 0.0233315
\(479\) −12.2690 −0.560584 −0.280292 0.959915i \(-0.590431\pi\)
−0.280292 + 0.959915i \(0.590431\pi\)
\(480\) 1.56820 0.0715781
\(481\) −6.22717 −0.283934
\(482\) −2.23208 −0.101668
\(483\) 2.66996 0.121487
\(484\) −9.94967 −0.452258
\(485\) −13.4934 −0.612704
\(486\) −5.54661 −0.251600
\(487\) −42.7409 −1.93677 −0.968387 0.249453i \(-0.919749\pi\)
−0.968387 + 0.249453i \(0.919749\pi\)
\(488\) −11.6584 −0.527751
\(489\) 7.57113 0.342379
\(490\) 4.77407 0.215671
\(491\) −40.2387 −1.81595 −0.907973 0.419029i \(-0.862371\pi\)
−0.907973 + 0.419029i \(0.862371\pi\)
\(492\) −5.41436 −0.244098
\(493\) 8.64079 0.389161
\(494\) 2.94238 0.132384
\(495\) −0.554194 −0.0249092
\(496\) −1.00000 −0.0449013
\(497\) 23.7729 1.06636
\(498\) −1.48967 −0.0667535
\(499\) −33.2894 −1.49024 −0.745118 0.666933i \(-0.767607\pi\)
−0.745118 + 0.666933i \(0.767607\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 20.7044 0.925004
\(502\) 10.1588 0.453408
\(503\) 9.02216 0.402278 0.201139 0.979563i \(-0.435536\pi\)
0.201139 + 0.979563i \(0.435536\pi\)
\(504\) 0.806779 0.0359368
\(505\) −7.27999 −0.323955
\(506\) −1.16953 −0.0519919
\(507\) −1.56820 −0.0696461
\(508\) −18.8774 −0.837549
\(509\) 11.7742 0.521881 0.260941 0.965355i \(-0.415967\pi\)
0.260941 + 0.965355i \(0.415967\pi\)
\(510\) 2.24882 0.0995793
\(511\) 7.09719 0.313961
\(512\) 1.00000 0.0441942
\(513\) 16.3378 0.721333
\(514\) −8.18897 −0.361200
\(515\) 11.8444 0.521926
\(516\) −6.78461 −0.298676
\(517\) 4.48025 0.197041
\(518\) 9.29065 0.408208
\(519\) 10.2684 0.450732
\(520\) −1.00000 −0.0438529
\(521\) 27.6437 1.21109 0.605547 0.795809i \(-0.292954\pi\)
0.605547 + 0.795809i \(0.292954\pi\)
\(522\) −3.25836 −0.142615
\(523\) 27.4075 1.19844 0.599222 0.800583i \(-0.295477\pi\)
0.599222 + 0.800583i \(0.295477\pi\)
\(524\) 7.58378 0.331299
\(525\) 2.33968 0.102112
\(526\) −18.0255 −0.785948
\(527\) −1.43401 −0.0624666
\(528\) 1.60718 0.0699435
\(529\) −21.6977 −0.943380
\(530\) 9.04674 0.392965
\(531\) 4.77961 0.207418
\(532\) −4.38989 −0.190326
\(533\) 3.45260 0.149549
\(534\) 16.6144 0.718978
\(535\) 13.9269 0.602112
\(536\) 9.32431 0.402749
\(537\) 30.2597 1.30580
\(538\) 3.35767 0.144759
\(539\) 4.89274 0.210745
\(540\) −5.55260 −0.238946
\(541\) 38.6880 1.66333 0.831663 0.555281i \(-0.187389\pi\)
0.831663 + 0.555281i \(0.187389\pi\)
\(542\) 24.7308 1.06228
\(543\) −15.8905 −0.681925
\(544\) 1.43401 0.0614828
\(545\) −0.767912 −0.0328937
\(546\) 2.33968 0.100129
\(547\) 23.4131 1.00107 0.500537 0.865715i \(-0.333136\pi\)
0.500537 + 0.865715i \(0.333136\pi\)
\(548\) 15.2258 0.650414
\(549\) 6.30432 0.269062
\(550\) −1.02486 −0.0437000
\(551\) 17.7296 0.755305
\(552\) −1.78957 −0.0761692
\(553\) 8.91083 0.378927
\(554\) 24.0705 1.02266
\(555\) −9.76543 −0.414520
\(556\) −8.98962 −0.381245
\(557\) 26.9462 1.14175 0.570873 0.821039i \(-0.306605\pi\)
0.570873 + 0.821039i \(0.306605\pi\)
\(558\) 0.540753 0.0228919
\(559\) 4.32637 0.182986
\(560\) 1.49195 0.0630466
\(561\) 2.30471 0.0973051
\(562\) −26.2186 −1.10596
\(563\) −15.6819 −0.660914 −0.330457 0.943821i \(-0.607203\pi\)
−0.330457 + 0.943821i \(0.607203\pi\)
\(564\) 6.85552 0.288669
\(565\) −16.9743 −0.714113
\(566\) −22.8318 −0.959694
\(567\) 10.5710 0.443940
\(568\) −15.9341 −0.668579
\(569\) −38.1947 −1.60121 −0.800603 0.599196i \(-0.795487\pi\)
−0.800603 + 0.599196i \(0.795487\pi\)
\(570\) 4.61423 0.193269
\(571\) 33.8053 1.41471 0.707355 0.706859i \(-0.249888\pi\)
0.707355 + 0.706859i \(0.249888\pi\)
\(572\) −1.02486 −0.0428514
\(573\) 37.8054 1.57934
\(574\) −5.15112 −0.215004
\(575\) 1.14116 0.0475898
\(576\) −0.540753 −0.0225314
\(577\) 32.6580 1.35957 0.679786 0.733410i \(-0.262073\pi\)
0.679786 + 0.733410i \(0.262073\pi\)
\(578\) −14.9436 −0.621572
\(579\) −34.2800 −1.42463
\(580\) −6.02560 −0.250199
\(581\) −1.41724 −0.0587970
\(582\) −21.1604 −0.877125
\(583\) 9.27160 0.383991
\(584\) −4.75697 −0.196845
\(585\) 0.540753 0.0223574
\(586\) −8.43198 −0.348322
\(587\) −11.7864 −0.486476 −0.243238 0.969967i \(-0.578210\pi\)
−0.243238 + 0.969967i \(0.578210\pi\)
\(588\) 7.48669 0.308746
\(589\) −2.94238 −0.121238
\(590\) 8.83881 0.363888
\(591\) 27.9427 1.14941
\(592\) −6.22717 −0.255935
\(593\) −48.6819 −1.99912 −0.999562 0.0295887i \(-0.990580\pi\)
−0.999562 + 0.0295887i \(0.990580\pi\)
\(594\) −5.69062 −0.233489
\(595\) 2.13948 0.0877102
\(596\) 11.4923 0.470741
\(597\) 17.5792 0.719467
\(598\) 1.14116 0.0466656
\(599\) −26.6505 −1.08891 −0.544455 0.838790i \(-0.683264\pi\)
−0.544455 + 0.838790i \(0.683264\pi\)
\(600\) −1.56820 −0.0640214
\(601\) 18.5276 0.755758 0.377879 0.925855i \(-0.376654\pi\)
0.377879 + 0.925855i \(0.376654\pi\)
\(602\) −6.45475 −0.263076
\(603\) −5.04215 −0.205332
\(604\) 6.86593 0.279371
\(605\) 9.94967 0.404512
\(606\) −11.4165 −0.463763
\(607\) 46.2812 1.87850 0.939248 0.343240i \(-0.111524\pi\)
0.939248 + 0.343240i \(0.111524\pi\)
\(608\) 2.94238 0.119329
\(609\) 14.0980 0.571279
\(610\) 11.6584 0.472035
\(611\) −4.37159 −0.176856
\(612\) −0.775447 −0.0313456
\(613\) 15.7832 0.637477 0.318738 0.947843i \(-0.396741\pi\)
0.318738 + 0.947843i \(0.396741\pi\)
\(614\) −17.5432 −0.707984
\(615\) 5.41436 0.218328
\(616\) 1.52904 0.0616067
\(617\) −23.8985 −0.962116 −0.481058 0.876689i \(-0.659747\pi\)
−0.481058 + 0.876689i \(0.659747\pi\)
\(618\) 18.5743 0.747170
\(619\) −18.4921 −0.743260 −0.371630 0.928381i \(-0.621201\pi\)
−0.371630 + 0.928381i \(0.621201\pi\)
\(620\) 1.00000 0.0401610
\(621\) 6.33643 0.254272
\(622\) 28.8255 1.15580
\(623\) 15.8067 0.633281
\(624\) −1.56820 −0.0627782
\(625\) 1.00000 0.0400000
\(626\) 13.5453 0.541378
\(627\) 4.72892 0.188855
\(628\) −6.46147 −0.257841
\(629\) −8.92984 −0.356056
\(630\) −0.806779 −0.0321429
\(631\) −49.5013 −1.97061 −0.985307 0.170791i \(-0.945368\pi\)
−0.985307 + 0.170791i \(0.945368\pi\)
\(632\) −5.97259 −0.237577
\(633\) −10.7168 −0.425955
\(634\) −14.0492 −0.557966
\(635\) 18.8774 0.749127
\(636\) 14.1871 0.562554
\(637\) −4.77407 −0.189156
\(638\) −6.17537 −0.244485
\(639\) 8.61640 0.340860
\(640\) −1.00000 −0.0395285
\(641\) −29.8726 −1.17990 −0.589949 0.807440i \(-0.700852\pi\)
−0.589949 + 0.807440i \(0.700852\pi\)
\(642\) 21.8401 0.861962
\(643\) −6.08378 −0.239921 −0.119961 0.992779i \(-0.538277\pi\)
−0.119961 + 0.992779i \(0.538277\pi\)
\(644\) −1.70256 −0.0670904
\(645\) 6.78461 0.267144
\(646\) 4.21940 0.166010
\(647\) 30.3037 1.19136 0.595681 0.803221i \(-0.296882\pi\)
0.595681 + 0.803221i \(0.296882\pi\)
\(648\) −7.08533 −0.278338
\(649\) 9.05851 0.355577
\(650\) 1.00000 0.0392232
\(651\) −2.33968 −0.0916993
\(652\) −4.82792 −0.189076
\(653\) −38.9720 −1.52509 −0.762547 0.646933i \(-0.776051\pi\)
−0.762547 + 0.646933i \(0.776051\pi\)
\(654\) −1.20424 −0.0470895
\(655\) −7.58378 −0.296323
\(656\) 3.45260 0.134801
\(657\) 2.57235 0.100357
\(658\) 6.52221 0.254262
\(659\) −17.4836 −0.681064 −0.340532 0.940233i \(-0.610607\pi\)
−0.340532 + 0.940233i \(0.610607\pi\)
\(660\) −1.60718 −0.0625593
\(661\) 13.3233 0.518218 0.259109 0.965848i \(-0.416571\pi\)
0.259109 + 0.965848i \(0.416571\pi\)
\(662\) 15.3162 0.595282
\(663\) −2.24882 −0.0873368
\(664\) 0.949922 0.0368641
\(665\) 4.38989 0.170233
\(666\) 3.36736 0.130483
\(667\) 6.87619 0.266247
\(668\) −13.2027 −0.510826
\(669\) −24.3981 −0.943285
\(670\) −9.32431 −0.360229
\(671\) 11.9482 0.461255
\(672\) 2.33968 0.0902552
\(673\) 6.19072 0.238635 0.119317 0.992856i \(-0.461929\pi\)
0.119317 + 0.992856i \(0.461929\pi\)
\(674\) −6.07422 −0.233970
\(675\) 5.55260 0.213720
\(676\) 1.00000 0.0384615
\(677\) −10.2505 −0.393957 −0.196979 0.980408i \(-0.563113\pi\)
−0.196979 + 0.980408i \(0.563113\pi\)
\(678\) −26.6190 −1.02230
\(679\) −20.1316 −0.772578
\(680\) −1.43401 −0.0549919
\(681\) −11.8775 −0.455147
\(682\) 1.02486 0.0392438
\(683\) 24.2058 0.926210 0.463105 0.886303i \(-0.346735\pi\)
0.463105 + 0.886303i \(0.346735\pi\)
\(684\) −1.59110 −0.0608372
\(685\) −15.2258 −0.581748
\(686\) 17.5664 0.670688
\(687\) 25.9808 0.991229
\(688\) 4.32637 0.164941
\(689\) −9.04674 −0.344653
\(690\) 1.78957 0.0681278
\(691\) −30.6935 −1.16763 −0.583817 0.811885i \(-0.698441\pi\)
−0.583817 + 0.811885i \(0.698441\pi\)
\(692\) −6.54788 −0.248913
\(693\) −0.826833 −0.0314088
\(694\) −1.19043 −0.0451881
\(695\) 8.98962 0.340996
\(696\) −9.44933 −0.358176
\(697\) 4.95107 0.187535
\(698\) −15.7136 −0.594767
\(699\) −3.89496 −0.147321
\(700\) −1.49195 −0.0563906
\(701\) −14.5471 −0.549437 −0.274718 0.961525i \(-0.588585\pi\)
−0.274718 + 0.961525i \(0.588585\pi\)
\(702\) 5.55260 0.209570
\(703\) −18.3227 −0.691052
\(704\) −1.02486 −0.0386257
\(705\) −6.85552 −0.258194
\(706\) 17.3692 0.653700
\(707\) −10.8614 −0.408486
\(708\) 13.8610 0.520928
\(709\) 10.3988 0.390535 0.195268 0.980750i \(-0.437442\pi\)
0.195268 + 0.980750i \(0.437442\pi\)
\(710\) 15.9341 0.597995
\(711\) 3.22970 0.121123
\(712\) −10.5946 −0.397050
\(713\) −1.14116 −0.0427369
\(714\) 3.35513 0.125563
\(715\) 1.02486 0.0383275
\(716\) −19.2959 −0.721120
\(717\) −0.799940 −0.0298743
\(718\) −32.8369 −1.22546
\(719\) 26.4883 0.987847 0.493923 0.869505i \(-0.335562\pi\)
0.493923 + 0.869505i \(0.335562\pi\)
\(720\) 0.540753 0.0201527
\(721\) 17.6713 0.658113
\(722\) −10.3424 −0.384905
\(723\) 3.50034 0.130179
\(724\) 10.1329 0.376588
\(725\) 6.02560 0.223785
\(726\) 15.6031 0.579084
\(727\) 6.15292 0.228199 0.114100 0.993469i \(-0.463602\pi\)
0.114100 + 0.993469i \(0.463602\pi\)
\(728\) −1.49195 −0.0552955
\(729\) 29.9542 1.10941
\(730\) 4.75697 0.176063
\(731\) 6.20407 0.229466
\(732\) 18.2827 0.675748
\(733\) 30.9399 1.14279 0.571396 0.820675i \(-0.306402\pi\)
0.571396 + 0.820675i \(0.306402\pi\)
\(734\) 20.4606 0.755215
\(735\) −7.48669 −0.276151
\(736\) 1.14116 0.0420638
\(737\) −9.55608 −0.352003
\(738\) −1.86700 −0.0687254
\(739\) −22.3962 −0.823859 −0.411929 0.911216i \(-0.635145\pi\)
−0.411929 + 0.911216i \(0.635145\pi\)
\(740\) 6.22717 0.228915
\(741\) −4.61423 −0.169508
\(742\) 13.4973 0.495502
\(743\) −15.4041 −0.565123 −0.282561 0.959249i \(-0.591184\pi\)
−0.282561 + 0.959249i \(0.591184\pi\)
\(744\) 1.56820 0.0574929
\(745\) −11.4923 −0.421044
\(746\) 17.8481 0.653465
\(747\) −0.513673 −0.0187943
\(748\) −1.46966 −0.0537360
\(749\) 20.7783 0.759223
\(750\) 1.56820 0.0572625
\(751\) −47.3545 −1.72799 −0.863995 0.503500i \(-0.832045\pi\)
−0.863995 + 0.503500i \(0.832045\pi\)
\(752\) −4.37159 −0.159415
\(753\) −15.9310 −0.580557
\(754\) 6.02560 0.219439
\(755\) −6.86593 −0.249877
\(756\) −8.28423 −0.301295
\(757\) −2.62160 −0.0952836 −0.0476418 0.998864i \(-0.515171\pi\)
−0.0476418 + 0.998864i \(0.515171\pi\)
\(758\) −11.1753 −0.405904
\(759\) 1.83405 0.0665719
\(760\) −2.94238 −0.106731
\(761\) 32.2958 1.17072 0.585360 0.810773i \(-0.300953\pi\)
0.585360 + 0.810773i \(0.300953\pi\)
\(762\) 29.6035 1.07242
\(763\) −1.14569 −0.0414768
\(764\) −24.1076 −0.872181
\(765\) 0.775447 0.0280364
\(766\) 15.0592 0.544112
\(767\) −8.83881 −0.319151
\(768\) −1.56820 −0.0565875
\(769\) −24.2679 −0.875122 −0.437561 0.899189i \(-0.644158\pi\)
−0.437561 + 0.899189i \(0.644158\pi\)
\(770\) −1.52904 −0.0551027
\(771\) 12.8419 0.462491
\(772\) 21.8594 0.786739
\(773\) 32.8392 1.18114 0.590572 0.806985i \(-0.298902\pi\)
0.590572 + 0.806985i \(0.298902\pi\)
\(774\) −2.33950 −0.0840916
\(775\) −1.00000 −0.0359211
\(776\) 13.4934 0.484385
\(777\) −14.5696 −0.522681
\(778\) −23.8515 −0.855117
\(779\) 10.1588 0.363978
\(780\) 1.56820 0.0561505
\(781\) 16.3301 0.584338
\(782\) 1.63644 0.0585191
\(783\) 33.4578 1.19568
\(784\) −4.77407 −0.170503
\(785\) 6.46147 0.230620
\(786\) −11.8929 −0.424205
\(787\) 37.1132 1.32294 0.661471 0.749971i \(-0.269933\pi\)
0.661471 + 0.749971i \(0.269933\pi\)
\(788\) −17.8184 −0.634753
\(789\) 28.2675 1.00635
\(790\) 5.97259 0.212495
\(791\) −25.3248 −0.900448
\(792\) 0.554194 0.0196924
\(793\) −11.6584 −0.414002
\(794\) −35.1081 −1.24594
\(795\) −14.1871 −0.503164
\(796\) −11.2098 −0.397320
\(797\) −1.57835 −0.0559082 −0.0279541 0.999609i \(-0.508899\pi\)
−0.0279541 + 0.999609i \(0.508899\pi\)
\(798\) 6.88422 0.243699
\(799\) −6.26891 −0.221778
\(800\) 1.00000 0.0353553
\(801\) 5.72907 0.202427
\(802\) 2.85667 0.100872
\(803\) 4.87521 0.172043
\(804\) −14.6224 −0.515691
\(805\) 1.70256 0.0600075
\(806\) −1.00000 −0.0352235
\(807\) −5.26549 −0.185354
\(808\) 7.27999 0.256109
\(809\) 47.5883 1.67312 0.836558 0.547878i \(-0.184564\pi\)
0.836558 + 0.547878i \(0.184564\pi\)
\(810\) 7.08533 0.248953
\(811\) 44.4009 1.55913 0.779564 0.626323i \(-0.215441\pi\)
0.779564 + 0.626323i \(0.215441\pi\)
\(812\) −8.98992 −0.315484
\(813\) −38.7828 −1.36017
\(814\) 6.38195 0.223687
\(815\) 4.82792 0.169115
\(816\) −2.24882 −0.0787244
\(817\) 12.7298 0.445360
\(818\) −0.398169 −0.0139217
\(819\) 0.806779 0.0281912
\(820\) −3.45260 −0.120570
\(821\) 40.7178 1.42106 0.710530 0.703667i \(-0.248455\pi\)
0.710530 + 0.703667i \(0.248455\pi\)
\(822\) −23.8771 −0.832809
\(823\) −37.6026 −1.31074 −0.655371 0.755307i \(-0.727488\pi\)
−0.655371 + 0.755307i \(0.727488\pi\)
\(824\) −11.8444 −0.412619
\(825\) 1.60718 0.0559548
\(826\) 13.1871 0.458838
\(827\) 5.13543 0.178576 0.0892882 0.996006i \(-0.471541\pi\)
0.0892882 + 0.996006i \(0.471541\pi\)
\(828\) −0.617088 −0.0214453
\(829\) −1.37801 −0.0478601 −0.0239301 0.999714i \(-0.507618\pi\)
−0.0239301 + 0.999714i \(0.507618\pi\)
\(830\) −0.949922 −0.0329723
\(831\) −37.7472 −1.30944
\(832\) 1.00000 0.0346688
\(833\) −6.84608 −0.237203
\(834\) 14.0975 0.488157
\(835\) 13.2027 0.456897
\(836\) −3.01551 −0.104294
\(837\) −5.55260 −0.191926
\(838\) −26.6342 −0.920062
\(839\) 14.6557 0.505972 0.252986 0.967470i \(-0.418587\pi\)
0.252986 + 0.967470i \(0.418587\pi\)
\(840\) −2.33968 −0.0807267
\(841\) 7.30782 0.251994
\(842\) −7.83612 −0.270051
\(843\) 41.1159 1.41611
\(844\) 6.83383 0.235230
\(845\) −1.00000 −0.0344010
\(846\) 2.36395 0.0812743
\(847\) 14.8445 0.510062
\(848\) −9.04674 −0.310666
\(849\) 35.8049 1.22882
\(850\) 1.43401 0.0491862
\(851\) −7.10621 −0.243598
\(852\) 24.9878 0.856068
\(853\) −11.6801 −0.399919 −0.199960 0.979804i \(-0.564081\pi\)
−0.199960 + 0.979804i \(0.564081\pi\)
\(854\) 17.3938 0.595204
\(855\) 1.59110 0.0544144
\(856\) −13.9269 −0.476012
\(857\) −13.6112 −0.464951 −0.232475 0.972602i \(-0.574683\pi\)
−0.232475 + 0.972602i \(0.574683\pi\)
\(858\) 1.60718 0.0548682
\(859\) −49.8511 −1.70090 −0.850448 0.526059i \(-0.823669\pi\)
−0.850448 + 0.526059i \(0.823669\pi\)
\(860\) −4.32637 −0.147528
\(861\) 8.07798 0.275297
\(862\) 16.9633 0.577774
\(863\) 25.2856 0.860731 0.430365 0.902655i \(-0.358385\pi\)
0.430365 + 0.902655i \(0.358385\pi\)
\(864\) 5.55260 0.188903
\(865\) 6.54788 0.222635
\(866\) 22.0858 0.750508
\(867\) 23.4345 0.795879
\(868\) 1.49195 0.0506402
\(869\) 6.12105 0.207642
\(870\) 9.44933 0.320362
\(871\) 9.32431 0.315942
\(872\) 0.767912 0.0260048
\(873\) −7.29661 −0.246953
\(874\) 3.35773 0.113577
\(875\) 1.49195 0.0504373
\(876\) 7.45988 0.252046
\(877\) 41.9250 1.41571 0.707853 0.706360i \(-0.249664\pi\)
0.707853 + 0.706360i \(0.249664\pi\)
\(878\) −34.8308 −1.17548
\(879\) 13.2230 0.446001
\(880\) 1.02486 0.0345479
\(881\) −20.5535 −0.692467 −0.346233 0.938148i \(-0.612539\pi\)
−0.346233 + 0.938148i \(0.612539\pi\)
\(882\) 2.58159 0.0869268
\(883\) 25.1676 0.846958 0.423479 0.905906i \(-0.360809\pi\)
0.423479 + 0.905906i \(0.360809\pi\)
\(884\) 1.43401 0.0482311
\(885\) −13.8610 −0.465932
\(886\) −7.79547 −0.261894
\(887\) −7.81956 −0.262555 −0.131278 0.991346i \(-0.541908\pi\)
−0.131278 + 0.991346i \(0.541908\pi\)
\(888\) 9.76543 0.327706
\(889\) 28.1642 0.944598
\(890\) 10.5946 0.355132
\(891\) 7.26144 0.243267
\(892\) 15.5580 0.520922
\(893\) −12.8629 −0.430439
\(894\) −18.0221 −0.602751
\(895\) 19.2959 0.644990
\(896\) −1.49195 −0.0498427
\(897\) −1.78957 −0.0597520
\(898\) 33.8963 1.13114
\(899\) −6.02560 −0.200965
\(900\) −0.540753 −0.0180251
\(901\) −12.9731 −0.432198
\(902\) −3.53842 −0.117816
\(903\) 10.1223 0.336850
\(904\) 16.9743 0.564556
\(905\) −10.1329 −0.336831
\(906\) −10.7671 −0.357715
\(907\) −11.2322 −0.372960 −0.186480 0.982459i \(-0.559708\pi\)
−0.186480 + 0.982459i \(0.559708\pi\)
\(908\) 7.57399 0.251352
\(909\) −3.93668 −0.130571
\(910\) 1.49195 0.0494578
\(911\) −44.2229 −1.46517 −0.732585 0.680675i \(-0.761687\pi\)
−0.732585 + 0.680675i \(0.761687\pi\)
\(912\) −4.61423 −0.152792
\(913\) −0.973533 −0.0322193
\(914\) 24.5958 0.813558
\(915\) −18.2827 −0.604407
\(916\) −16.5673 −0.547399
\(917\) −11.3147 −0.373643
\(918\) 7.96251 0.262802
\(919\) 34.1044 1.12500 0.562500 0.826797i \(-0.309840\pi\)
0.562500 + 0.826797i \(0.309840\pi\)
\(920\) −1.14116 −0.0376230
\(921\) 27.5111 0.906523
\(922\) 9.93793 0.327288
\(923\) −15.9341 −0.524476
\(924\) −2.39784 −0.0788830
\(925\) −6.22717 −0.204748
\(926\) 15.4200 0.506732
\(927\) 6.40489 0.210364
\(928\) 6.02560 0.197800
\(929\) 42.1831 1.38398 0.691991 0.721906i \(-0.256734\pi\)
0.691991 + 0.721906i \(0.256734\pi\)
\(930\) −1.56820 −0.0514233
\(931\) −14.0471 −0.460375
\(932\) 2.48371 0.0813567
\(933\) −45.2041 −1.47992
\(934\) 2.51737 0.0823708
\(935\) 1.46966 0.0480629
\(936\) −0.540753 −0.0176751
\(937\) 52.6460 1.71987 0.859935 0.510404i \(-0.170504\pi\)
0.859935 + 0.510404i \(0.170504\pi\)
\(938\) −13.9114 −0.454225
\(939\) −21.2417 −0.693196
\(940\) 4.37159 0.142585
\(941\) 27.7967 0.906145 0.453072 0.891474i \(-0.350328\pi\)
0.453072 + 0.891474i \(0.350328\pi\)
\(942\) 10.1329 0.330147
\(943\) 3.93998 0.128303
\(944\) −8.83881 −0.287679
\(945\) 8.28423 0.269486
\(946\) −4.43391 −0.144159
\(947\) −13.2517 −0.430623 −0.215312 0.976545i \(-0.569077\pi\)
−0.215312 + 0.976545i \(0.569077\pi\)
\(948\) 9.36621 0.304200
\(949\) −4.75697 −0.154418
\(950\) 2.94238 0.0954633
\(951\) 22.0320 0.714436
\(952\) −2.13948 −0.0693410
\(953\) 44.8351 1.45235 0.726176 0.687509i \(-0.241296\pi\)
0.726176 + 0.687509i \(0.241296\pi\)
\(954\) 4.89205 0.158386
\(955\) 24.1076 0.780102
\(956\) 0.510101 0.0164979
\(957\) 9.68421 0.313046
\(958\) −12.2690 −0.396393
\(959\) −22.7162 −0.733545
\(960\) 1.56820 0.0506134
\(961\) 1.00000 0.0322581
\(962\) −6.22717 −0.200772
\(963\) 7.53102 0.242684
\(964\) −2.23208 −0.0718904
\(965\) −21.8594 −0.703680
\(966\) 2.66996 0.0859045
\(967\) 11.6511 0.374675 0.187337 0.982296i \(-0.440014\pi\)
0.187337 + 0.982296i \(0.440014\pi\)
\(968\) −9.94967 −0.319794
\(969\) −6.61686 −0.212564
\(970\) −13.4934 −0.433247
\(971\) −19.2068 −0.616376 −0.308188 0.951325i \(-0.599723\pi\)
−0.308188 + 0.951325i \(0.599723\pi\)
\(972\) −5.54661 −0.177908
\(973\) 13.4121 0.429973
\(974\) −42.7409 −1.36951
\(975\) −1.56820 −0.0502225
\(976\) −11.6584 −0.373177
\(977\) −31.8983 −1.02052 −0.510258 0.860021i \(-0.670450\pi\)
−0.510258 + 0.860021i \(0.670450\pi\)
\(978\) 7.57113 0.242098
\(979\) 10.8580 0.347022
\(980\) 4.77407 0.152502
\(981\) −0.415251 −0.0132579
\(982\) −40.2387 −1.28407
\(983\) 40.0632 1.27782 0.638908 0.769283i \(-0.279386\pi\)
0.638908 + 0.769283i \(0.279386\pi\)
\(984\) −5.41436 −0.172603
\(985\) 17.8184 0.567740
\(986\) 8.64079 0.275179
\(987\) −10.2281 −0.325565
\(988\) 2.94238 0.0936094
\(989\) 4.93710 0.156991
\(990\) −0.554194 −0.0176135
\(991\) −13.0190 −0.413563 −0.206781 0.978387i \(-0.566299\pi\)
−0.206781 + 0.978387i \(0.566299\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −24.0189 −0.762217
\(994\) 23.7729 0.754031
\(995\) 11.2098 0.355374
\(996\) −1.48967 −0.0472019
\(997\) −41.8375 −1.32501 −0.662504 0.749058i \(-0.730506\pi\)
−0.662504 + 0.749058i \(0.730506\pi\)
\(998\) −33.2894 −1.05376
\(999\) −34.5770 −1.09397
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 \(a_p\))