Properties

Label 8015.2.a.l.1.62
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.62
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} +O(q^{10})\) \(q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} -2.79293 q^{10} +0.504421 q^{11} -6.19116 q^{12} +2.67005 q^{13} -2.79293 q^{14} +1.06735 q^{15} +18.0446 q^{16} +0.222483 q^{17} -5.19698 q^{18} +3.37331 q^{19} -5.80048 q^{20} +1.06735 q^{21} +1.40881 q^{22} -8.15087 q^{23} -11.3294 q^{24} +1.00000 q^{25} +7.45727 q^{26} +5.18814 q^{27} -5.80048 q^{28} -7.54939 q^{29} +2.98104 q^{30} +9.86730 q^{31} +29.1685 q^{32} -0.538394 q^{33} +0.621382 q^{34} +1.00000 q^{35} -10.7933 q^{36} -5.73261 q^{37} +9.42144 q^{38} -2.84988 q^{39} -10.6145 q^{40} +11.2262 q^{41} +2.98104 q^{42} +2.74059 q^{43} +2.92588 q^{44} +1.86076 q^{45} -22.7648 q^{46} +8.69917 q^{47} -19.2600 q^{48} +1.00000 q^{49} +2.79293 q^{50} -0.237468 q^{51} +15.4876 q^{52} +12.3367 q^{53} +14.4901 q^{54} -0.504421 q^{55} -10.6145 q^{56} -3.60051 q^{57} -21.0850 q^{58} -14.5599 q^{59} +6.19116 q^{60} +5.57857 q^{61} +27.5587 q^{62} +1.86076 q^{63} +45.3763 q^{64} -2.67005 q^{65} -1.50370 q^{66} +8.95098 q^{67} +1.29051 q^{68} +8.69984 q^{69} +2.79293 q^{70} -0.120147 q^{71} -19.7510 q^{72} +6.77351 q^{73} -16.0108 q^{74} -1.06735 q^{75} +19.5668 q^{76} -0.504421 q^{77} -7.95953 q^{78} +13.5337 q^{79} -18.0446 q^{80} +0.0447058 q^{81} +31.3539 q^{82} -4.74510 q^{83} +6.19116 q^{84} -0.222483 q^{85} +7.65428 q^{86} +8.05786 q^{87} +5.35417 q^{88} -0.176402 q^{89} +5.19698 q^{90} -2.67005 q^{91} -47.2789 q^{92} -10.5319 q^{93} +24.2962 q^{94} -3.37331 q^{95} -31.1330 q^{96} +13.1772 q^{97} +2.79293 q^{98} -0.938605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.79293 1.97490 0.987451 0.157924i \(-0.0504799\pi\)
0.987451 + 0.157924i \(0.0504799\pi\)
\(3\) −1.06735 −0.616236 −0.308118 0.951348i \(-0.599699\pi\)
−0.308118 + 0.951348i \(0.599699\pi\)
\(4\) 5.80048 2.90024
\(5\) −1.00000 −0.447214
\(6\) −2.98104 −1.21701
\(7\) −1.00000 −0.377964
\(8\) 10.6145 3.75279
\(9\) −1.86076 −0.620253
\(10\) −2.79293 −0.883203
\(11\) 0.504421 0.152089 0.0760443 0.997104i \(-0.475771\pi\)
0.0760443 + 0.997104i \(0.475771\pi\)
\(12\) −6.19116 −1.78723
\(13\) 2.67005 0.740538 0.370269 0.928925i \(-0.379266\pi\)
0.370269 + 0.928925i \(0.379266\pi\)
\(14\) −2.79293 −0.746443
\(15\) 1.06735 0.275589
\(16\) 18.0446 4.51116
\(17\) 0.222483 0.0539602 0.0269801 0.999636i \(-0.491411\pi\)
0.0269801 + 0.999636i \(0.491411\pi\)
\(18\) −5.19698 −1.22494
\(19\) 3.37331 0.773891 0.386945 0.922103i \(-0.373530\pi\)
0.386945 + 0.922103i \(0.373530\pi\)
\(20\) −5.80048 −1.29703
\(21\) 1.06735 0.232915
\(22\) 1.40881 0.300360
\(23\) −8.15087 −1.69957 −0.849787 0.527127i \(-0.823269\pi\)
−0.849787 + 0.527127i \(0.823269\pi\)
\(24\) −11.3294 −2.31260
\(25\) 1.00000 0.200000
\(26\) 7.45727 1.46249
\(27\) 5.18814 0.998458
\(28\) −5.80048 −1.09619
\(29\) −7.54939 −1.40189 −0.700943 0.713217i \(-0.747237\pi\)
−0.700943 + 0.713217i \(0.747237\pi\)
\(30\) 2.98104 0.544262
\(31\) 9.86730 1.77222 0.886110 0.463475i \(-0.153398\pi\)
0.886110 + 0.463475i \(0.153398\pi\)
\(32\) 29.1685 5.15630
\(33\) −0.538394 −0.0937224
\(34\) 0.621382 0.106566
\(35\) 1.00000 0.169031
\(36\) −10.7933 −1.79888
\(37\) −5.73261 −0.942435 −0.471217 0.882017i \(-0.656185\pi\)
−0.471217 + 0.882017i \(0.656185\pi\)
\(38\) 9.42144 1.52836
\(39\) −2.84988 −0.456346
\(40\) −10.6145 −1.67830
\(41\) 11.2262 1.75323 0.876616 0.481191i \(-0.159796\pi\)
0.876616 + 0.481191i \(0.159796\pi\)
\(42\) 2.98104 0.459985
\(43\) 2.74059 0.417936 0.208968 0.977923i \(-0.432990\pi\)
0.208968 + 0.977923i \(0.432990\pi\)
\(44\) 2.92588 0.441093
\(45\) 1.86076 0.277386
\(46\) −22.7648 −3.35649
\(47\) 8.69917 1.26890 0.634452 0.772962i \(-0.281226\pi\)
0.634452 + 0.772962i \(0.281226\pi\)
\(48\) −19.2600 −2.77994
\(49\) 1.00000 0.142857
\(50\) 2.79293 0.394981
\(51\) −0.237468 −0.0332522
\(52\) 15.4876 2.14774
\(53\) 12.3367 1.69458 0.847291 0.531129i \(-0.178232\pi\)
0.847291 + 0.531129i \(0.178232\pi\)
\(54\) 14.4901 1.97186
\(55\) −0.504421 −0.0680161
\(56\) −10.6145 −1.41842
\(57\) −3.60051 −0.476899
\(58\) −21.0850 −2.76859
\(59\) −14.5599 −1.89554 −0.947771 0.318952i \(-0.896669\pi\)
−0.947771 + 0.318952i \(0.896669\pi\)
\(60\) 6.19116 0.799275
\(61\) 5.57857 0.714262 0.357131 0.934054i \(-0.383755\pi\)
0.357131 + 0.934054i \(0.383755\pi\)
\(62\) 27.5587 3.49996
\(63\) 1.86076 0.234434
\(64\) 45.3763 5.67204
\(65\) −2.67005 −0.331179
\(66\) −1.50370 −0.185093
\(67\) 8.95098 1.09354 0.546768 0.837284i \(-0.315858\pi\)
0.546768 + 0.837284i \(0.315858\pi\)
\(68\) 1.29051 0.156497
\(69\) 8.69984 1.04734
\(70\) 2.79293 0.333819
\(71\) −0.120147 −0.0142589 −0.00712943 0.999975i \(-0.502269\pi\)
−0.00712943 + 0.999975i \(0.502269\pi\)
\(72\) −19.7510 −2.32768
\(73\) 6.77351 0.792779 0.396390 0.918082i \(-0.370263\pi\)
0.396390 + 0.918082i \(0.370263\pi\)
\(74\) −16.0108 −1.86122
\(75\) −1.06735 −0.123247
\(76\) 19.5668 2.24447
\(77\) −0.504421 −0.0574841
\(78\) −7.95953 −0.901239
\(79\) 13.5337 1.52266 0.761328 0.648367i \(-0.224548\pi\)
0.761328 + 0.648367i \(0.224548\pi\)
\(80\) −18.0446 −2.01745
\(81\) 0.0447058 0.00496731
\(82\) 31.3539 3.46246
\(83\) −4.74510 −0.520842 −0.260421 0.965495i \(-0.583861\pi\)
−0.260421 + 0.965495i \(0.583861\pi\)
\(84\) 6.19116 0.675510
\(85\) −0.222483 −0.0241317
\(86\) 7.65428 0.825382
\(87\) 8.05786 0.863893
\(88\) 5.35417 0.570756
\(89\) −0.176402 −0.0186985 −0.00934927 0.999956i \(-0.502976\pi\)
−0.00934927 + 0.999956i \(0.502976\pi\)
\(90\) 5.19698 0.547810
\(91\) −2.67005 −0.279897
\(92\) −47.2789 −4.92917
\(93\) −10.5319 −1.09211
\(94\) 24.2962 2.50596
\(95\) −3.37331 −0.346094
\(96\) −31.1330 −3.17750
\(97\) 13.1772 1.33794 0.668971 0.743289i \(-0.266735\pi\)
0.668971 + 0.743289i \(0.266735\pi\)
\(98\) 2.79293 0.282129
\(99\) −0.938605 −0.0943334
\(100\) 5.80048 0.580048
\(101\) −8.22460 −0.818378 −0.409189 0.912450i \(-0.634188\pi\)
−0.409189 + 0.912450i \(0.634188\pi\)
\(102\) −0.663233 −0.0656698
\(103\) 1.71653 0.169135 0.0845676 0.996418i \(-0.473049\pi\)
0.0845676 + 0.996418i \(0.473049\pi\)
\(104\) 28.3412 2.77908
\(105\) −1.06735 −0.104163
\(106\) 34.4557 3.34663
\(107\) −16.0681 −1.55337 −0.776683 0.629891i \(-0.783099\pi\)
−0.776683 + 0.629891i \(0.783099\pi\)
\(108\) 30.0937 2.89577
\(109\) 5.98418 0.573181 0.286590 0.958053i \(-0.407478\pi\)
0.286590 + 0.958053i \(0.407478\pi\)
\(110\) −1.40881 −0.134325
\(111\) 6.11871 0.580762
\(112\) −18.0446 −1.70506
\(113\) −6.25651 −0.588563 −0.294281 0.955719i \(-0.595080\pi\)
−0.294281 + 0.955719i \(0.595080\pi\)
\(114\) −10.0560 −0.941830
\(115\) 8.15087 0.760072
\(116\) −43.7901 −4.06581
\(117\) −4.96832 −0.459321
\(118\) −40.6649 −3.74351
\(119\) −0.222483 −0.0203950
\(120\) 11.3294 1.03423
\(121\) −10.7456 −0.976869
\(122\) 15.5806 1.41060
\(123\) −11.9823 −1.08040
\(124\) 57.2351 5.13986
\(125\) −1.00000 −0.0894427
\(126\) 5.19698 0.462984
\(127\) −7.46000 −0.661968 −0.330984 0.943636i \(-0.607381\pi\)
−0.330984 + 0.943636i \(0.607381\pi\)
\(128\) 68.3962 6.04542
\(129\) −2.92517 −0.257547
\(130\) −7.45727 −0.654046
\(131\) −14.3762 −1.25605 −0.628027 0.778192i \(-0.716137\pi\)
−0.628027 + 0.778192i \(0.716137\pi\)
\(132\) −3.12295 −0.271818
\(133\) −3.37331 −0.292503
\(134\) 24.9995 2.15963
\(135\) −5.18814 −0.446524
\(136\) 2.36155 0.202501
\(137\) 0.0595141 0.00508464 0.00254232 0.999997i \(-0.499191\pi\)
0.00254232 + 0.999997i \(0.499191\pi\)
\(138\) 24.2981 2.06839
\(139\) −15.1831 −1.28781 −0.643906 0.765105i \(-0.722687\pi\)
−0.643906 + 0.765105i \(0.722687\pi\)
\(140\) 5.80048 0.490230
\(141\) −9.28508 −0.781945
\(142\) −0.335563 −0.0281599
\(143\) 1.34683 0.112627
\(144\) −33.5767 −2.79806
\(145\) 7.54939 0.626943
\(146\) 18.9180 1.56566
\(147\) −1.06735 −0.0880337
\(148\) −33.2519 −2.73329
\(149\) −10.6241 −0.870363 −0.435181 0.900343i \(-0.643316\pi\)
−0.435181 + 0.900343i \(0.643316\pi\)
\(150\) −2.98104 −0.243401
\(151\) 19.5077 1.58752 0.793758 0.608234i \(-0.208122\pi\)
0.793758 + 0.608234i \(0.208122\pi\)
\(152\) 35.8060 2.90425
\(153\) −0.413988 −0.0334690
\(154\) −1.40881 −0.113525
\(155\) −9.86730 −0.792561
\(156\) −16.5307 −1.32351
\(157\) 2.92294 0.233276 0.116638 0.993174i \(-0.462788\pi\)
0.116638 + 0.993174i \(0.462788\pi\)
\(158\) 37.7986 3.00710
\(159\) −13.1676 −1.04426
\(160\) −29.1685 −2.30597
\(161\) 8.15087 0.642378
\(162\) 0.124860 0.00980996
\(163\) 12.3357 0.966207 0.483104 0.875563i \(-0.339509\pi\)
0.483104 + 0.875563i \(0.339509\pi\)
\(164\) 65.1171 5.08479
\(165\) 0.538394 0.0419139
\(166\) −13.2527 −1.02861
\(167\) −2.33883 −0.180984 −0.0904921 0.995897i \(-0.528844\pi\)
−0.0904921 + 0.995897i \(0.528844\pi\)
\(168\) 11.3294 0.874082
\(169\) −5.87084 −0.451603
\(170\) −0.621382 −0.0476578
\(171\) −6.27692 −0.480008
\(172\) 15.8967 1.21211
\(173\) 20.7325 1.57626 0.788132 0.615506i \(-0.211048\pi\)
0.788132 + 0.615506i \(0.211048\pi\)
\(174\) 22.5051 1.70610
\(175\) −1.00000 −0.0755929
\(176\) 9.10208 0.686095
\(177\) 15.5406 1.16810
\(178\) −0.492678 −0.0369278
\(179\) 6.32207 0.472534 0.236267 0.971688i \(-0.424076\pi\)
0.236267 + 0.971688i \(0.424076\pi\)
\(180\) 10.7933 0.804485
\(181\) 3.28207 0.243954 0.121977 0.992533i \(-0.461077\pi\)
0.121977 + 0.992533i \(0.461077\pi\)
\(182\) −7.45727 −0.552769
\(183\) −5.95429 −0.440154
\(184\) −86.5173 −6.37814
\(185\) 5.73261 0.421470
\(186\) −29.4149 −2.15680
\(187\) 0.112225 0.00820672
\(188\) 50.4594 3.68013
\(189\) −5.18814 −0.377382
\(190\) −9.42144 −0.683503
\(191\) 21.5432 1.55881 0.779404 0.626522i \(-0.215522\pi\)
0.779404 + 0.626522i \(0.215522\pi\)
\(192\) −48.4325 −3.49532
\(193\) 3.20665 0.230820 0.115410 0.993318i \(-0.463182\pi\)
0.115410 + 0.993318i \(0.463182\pi\)
\(194\) 36.8030 2.64230
\(195\) 2.84988 0.204084
\(196\) 5.80048 0.414320
\(197\) −23.7466 −1.69187 −0.845937 0.533283i \(-0.820958\pi\)
−0.845937 + 0.533283i \(0.820958\pi\)
\(198\) −2.62146 −0.186299
\(199\) 10.0607 0.713186 0.356593 0.934260i \(-0.383938\pi\)
0.356593 + 0.934260i \(0.383938\pi\)
\(200\) 10.6145 0.750558
\(201\) −9.55385 −0.673877
\(202\) −22.9708 −1.61622
\(203\) 7.54939 0.529863
\(204\) −1.37743 −0.0964393
\(205\) −11.2262 −0.784069
\(206\) 4.79417 0.334025
\(207\) 15.1668 1.05417
\(208\) 48.1800 3.34068
\(209\) 1.70157 0.117700
\(210\) −2.98104 −0.205712
\(211\) 6.78078 0.466808 0.233404 0.972380i \(-0.425014\pi\)
0.233404 + 0.972380i \(0.425014\pi\)
\(212\) 71.5590 4.91469
\(213\) 0.128239 0.00878682
\(214\) −44.8773 −3.06775
\(215\) −2.74059 −0.186907
\(216\) 55.0695 3.74700
\(217\) −9.86730 −0.669836
\(218\) 16.7134 1.13198
\(219\) −7.22972 −0.488539
\(220\) −2.92588 −0.197263
\(221\) 0.594041 0.0399595
\(222\) 17.0891 1.14695
\(223\) 4.95086 0.331534 0.165767 0.986165i \(-0.446990\pi\)
0.165767 + 0.986165i \(0.446990\pi\)
\(224\) −29.1685 −1.94890
\(225\) −1.86076 −0.124051
\(226\) −17.4740 −1.16235
\(227\) 12.9617 0.860298 0.430149 0.902758i \(-0.358461\pi\)
0.430149 + 0.902758i \(0.358461\pi\)
\(228\) −20.8847 −1.38312
\(229\) 1.00000 0.0660819
\(230\) 22.7648 1.50107
\(231\) 0.538394 0.0354237
\(232\) −80.1330 −5.26099
\(233\) −4.06811 −0.266511 −0.133255 0.991082i \(-0.542543\pi\)
−0.133255 + 0.991082i \(0.542543\pi\)
\(234\) −13.8762 −0.907114
\(235\) −8.69917 −0.567471
\(236\) −84.4546 −5.49753
\(237\) −14.4452 −0.938316
\(238\) −0.621382 −0.0402782
\(239\) −6.92927 −0.448217 −0.224109 0.974564i \(-0.571947\pi\)
−0.224109 + 0.974564i \(0.571947\pi\)
\(240\) 19.2600 1.24323
\(241\) −5.89243 −0.379565 −0.189782 0.981826i \(-0.560778\pi\)
−0.189782 + 0.981826i \(0.560778\pi\)
\(242\) −30.0116 −1.92922
\(243\) −15.6121 −1.00152
\(244\) 32.3584 2.07153
\(245\) −1.00000 −0.0638877
\(246\) −33.4657 −2.13369
\(247\) 9.00690 0.573096
\(248\) 104.736 6.65077
\(249\) 5.06469 0.320962
\(250\) −2.79293 −0.176641
\(251\) −12.1235 −0.765231 −0.382615 0.923908i \(-0.624977\pi\)
−0.382615 + 0.923908i \(0.624977\pi\)
\(252\) 10.7933 0.679914
\(253\) −4.11146 −0.258486
\(254\) −20.8353 −1.30732
\(255\) 0.237468 0.0148708
\(256\) 100.273 6.26709
\(257\) 18.2290 1.13709 0.568545 0.822652i \(-0.307506\pi\)
0.568545 + 0.822652i \(0.307506\pi\)
\(258\) −8.16981 −0.508630
\(259\) 5.73261 0.356207
\(260\) −15.4876 −0.960498
\(261\) 14.0476 0.869525
\(262\) −40.1517 −2.48058
\(263\) 3.05391 0.188312 0.0941559 0.995557i \(-0.469985\pi\)
0.0941559 + 0.995557i \(0.469985\pi\)
\(264\) −5.71478 −0.351721
\(265\) −12.3367 −0.757840
\(266\) −9.42144 −0.577665
\(267\) 0.188283 0.0115227
\(268\) 51.9200 3.17152
\(269\) 6.64052 0.404880 0.202440 0.979295i \(-0.435113\pi\)
0.202440 + 0.979295i \(0.435113\pi\)
\(270\) −14.4901 −0.881842
\(271\) 3.63182 0.220618 0.110309 0.993897i \(-0.464816\pi\)
0.110309 + 0.993897i \(0.464816\pi\)
\(272\) 4.01463 0.243423
\(273\) 2.84988 0.172483
\(274\) 0.166219 0.0100417
\(275\) 0.504421 0.0304177
\(276\) 50.4633 3.03753
\(277\) −17.0129 −1.02221 −0.511103 0.859520i \(-0.670763\pi\)
−0.511103 + 0.859520i \(0.670763\pi\)
\(278\) −42.4053 −2.54330
\(279\) −18.3607 −1.09923
\(280\) 10.6145 0.634337
\(281\) −18.7836 −1.12054 −0.560268 0.828311i \(-0.689302\pi\)
−0.560268 + 0.828311i \(0.689302\pi\)
\(282\) −25.9326 −1.54426
\(283\) 8.51860 0.506378 0.253189 0.967417i \(-0.418520\pi\)
0.253189 + 0.967417i \(0.418520\pi\)
\(284\) −0.696912 −0.0413541
\(285\) 3.60051 0.213276
\(286\) 3.76160 0.222428
\(287\) −11.2262 −0.662659
\(288\) −54.2755 −3.19821
\(289\) −16.9505 −0.997088
\(290\) 21.0850 1.23815
\(291\) −14.0647 −0.824488
\(292\) 39.2896 2.29925
\(293\) 19.8242 1.15814 0.579072 0.815277i \(-0.303415\pi\)
0.579072 + 0.815277i \(0.303415\pi\)
\(294\) −2.98104 −0.173858
\(295\) 14.5599 0.847712
\(296\) −60.8487 −3.53676
\(297\) 2.61701 0.151854
\(298\) −29.6725 −1.71888
\(299\) −21.7632 −1.25860
\(300\) −6.19116 −0.357447
\(301\) −2.74059 −0.157965
\(302\) 54.4838 3.13519
\(303\) 8.77854 0.504314
\(304\) 60.8701 3.49114
\(305\) −5.57857 −0.319428
\(306\) −1.15624 −0.0660979
\(307\) 26.3052 1.50132 0.750659 0.660690i \(-0.229736\pi\)
0.750659 + 0.660690i \(0.229736\pi\)
\(308\) −2.92588 −0.166718
\(309\) −1.83215 −0.104227
\(310\) −27.5587 −1.56523
\(311\) −18.9844 −1.07651 −0.538253 0.842783i \(-0.680916\pi\)
−0.538253 + 0.842783i \(0.680916\pi\)
\(312\) −30.2500 −1.71257
\(313\) 8.71751 0.492743 0.246371 0.969175i \(-0.420762\pi\)
0.246371 + 0.969175i \(0.420762\pi\)
\(314\) 8.16358 0.460697
\(315\) −1.86076 −0.104842
\(316\) 78.5018 4.41607
\(317\) −16.9226 −0.950471 −0.475235 0.879859i \(-0.657637\pi\)
−0.475235 + 0.879859i \(0.657637\pi\)
\(318\) −36.7764 −2.06232
\(319\) −3.80807 −0.213211
\(320\) −45.3763 −2.53661
\(321\) 17.1504 0.957240
\(322\) 22.7648 1.26863
\(323\) 0.750506 0.0417593
\(324\) 0.259315 0.0144064
\(325\) 2.67005 0.148108
\(326\) 34.4528 1.90816
\(327\) −6.38723 −0.353215
\(328\) 119.160 6.57951
\(329\) −8.69917 −0.479601
\(330\) 1.50370 0.0827760
\(331\) 15.2488 0.838149 0.419075 0.907952i \(-0.362355\pi\)
0.419075 + 0.907952i \(0.362355\pi\)
\(332\) −27.5239 −1.51057
\(333\) 10.6670 0.584548
\(334\) −6.53220 −0.357426
\(335\) −8.95098 −0.489044
\(336\) 19.2600 1.05072
\(337\) −1.93417 −0.105361 −0.0526804 0.998611i \(-0.516776\pi\)
−0.0526804 + 0.998611i \(0.516776\pi\)
\(338\) −16.3969 −0.891873
\(339\) 6.67790 0.362694
\(340\) −1.29051 −0.0699878
\(341\) 4.97727 0.269534
\(342\) −17.5310 −0.947970
\(343\) −1.00000 −0.0539949
\(344\) 29.0900 1.56843
\(345\) −8.69984 −0.468384
\(346\) 57.9046 3.11297
\(347\) 10.7025 0.574542 0.287271 0.957849i \(-0.407252\pi\)
0.287271 + 0.957849i \(0.407252\pi\)
\(348\) 46.7395 2.50550
\(349\) −17.5969 −0.941940 −0.470970 0.882149i \(-0.656096\pi\)
−0.470970 + 0.882149i \(0.656096\pi\)
\(350\) −2.79293 −0.149289
\(351\) 13.8526 0.739396
\(352\) 14.7132 0.784214
\(353\) 21.5008 1.14437 0.572185 0.820124i \(-0.306096\pi\)
0.572185 + 0.820124i \(0.306096\pi\)
\(354\) 43.4038 2.30689
\(355\) 0.120147 0.00637676
\(356\) −1.02321 −0.0542303
\(357\) 0.237468 0.0125681
\(358\) 17.6571 0.933208
\(359\) 16.3532 0.863091 0.431546 0.902091i \(-0.357968\pi\)
0.431546 + 0.902091i \(0.357968\pi\)
\(360\) 19.7510 1.04097
\(361\) −7.62077 −0.401093
\(362\) 9.16661 0.481786
\(363\) 11.4693 0.601982
\(364\) −15.4876 −0.811769
\(365\) −6.77351 −0.354542
\(366\) −16.6299 −0.869261
\(367\) −9.24858 −0.482772 −0.241386 0.970429i \(-0.577602\pi\)
−0.241386 + 0.970429i \(0.577602\pi\)
\(368\) −147.079 −7.66704
\(369\) −20.8892 −1.08745
\(370\) 16.0108 0.832361
\(371\) −12.3367 −0.640492
\(372\) −61.0900 −3.16737
\(373\) −29.2548 −1.51475 −0.757377 0.652977i \(-0.773520\pi\)
−0.757377 + 0.652977i \(0.773520\pi\)
\(374\) 0.313438 0.0162075
\(375\) 1.06735 0.0551178
\(376\) 92.3373 4.76193
\(377\) −20.1572 −1.03815
\(378\) −14.4901 −0.745292
\(379\) −7.31748 −0.375874 −0.187937 0.982181i \(-0.560180\pi\)
−0.187937 + 0.982181i \(0.560180\pi\)
\(380\) −19.5668 −1.00376
\(381\) 7.96245 0.407928
\(382\) 60.1686 3.07849
\(383\) −17.2247 −0.880142 −0.440071 0.897963i \(-0.645047\pi\)
−0.440071 + 0.897963i \(0.645047\pi\)
\(384\) −73.0028 −3.72541
\(385\) 0.504421 0.0257077
\(386\) 8.95597 0.455847
\(387\) −5.09958 −0.259226
\(388\) 76.4341 3.88035
\(389\) 21.0960 1.06961 0.534806 0.844975i \(-0.320385\pi\)
0.534806 + 0.844975i \(0.320385\pi\)
\(390\) 7.95953 0.403046
\(391\) −1.81343 −0.0917092
\(392\) 10.6145 0.536113
\(393\) 15.3444 0.774025
\(394\) −66.3227 −3.34129
\(395\) −13.5337 −0.680953
\(396\) −5.44436 −0.273590
\(397\) −21.6705 −1.08761 −0.543806 0.839211i \(-0.683017\pi\)
−0.543806 + 0.839211i \(0.683017\pi\)
\(398\) 28.0989 1.40847
\(399\) 3.60051 0.180251
\(400\) 18.0446 0.902231
\(401\) 20.1668 1.00708 0.503541 0.863971i \(-0.332030\pi\)
0.503541 + 0.863971i \(0.332030\pi\)
\(402\) −26.6833 −1.33084
\(403\) 26.3462 1.31240
\(404\) −47.7066 −2.37349
\(405\) −0.0447058 −0.00222145
\(406\) 21.0850 1.04643
\(407\) −2.89164 −0.143333
\(408\) −2.52060 −0.124788
\(409\) −27.5364 −1.36159 −0.680794 0.732475i \(-0.738365\pi\)
−0.680794 + 0.732475i \(0.738365\pi\)
\(410\) −31.3539 −1.54846
\(411\) −0.0635225 −0.00313334
\(412\) 9.95672 0.490533
\(413\) 14.5599 0.716447
\(414\) 42.3599 2.08187
\(415\) 4.74510 0.232928
\(416\) 77.8812 3.81844
\(417\) 16.2057 0.793596
\(418\) 4.75237 0.232446
\(419\) −15.6433 −0.764223 −0.382112 0.924116i \(-0.624803\pi\)
−0.382112 + 0.924116i \(0.624803\pi\)
\(420\) −6.19116 −0.302097
\(421\) 28.2512 1.37688 0.688440 0.725293i \(-0.258296\pi\)
0.688440 + 0.725293i \(0.258296\pi\)
\(422\) 18.9383 0.921901
\(423\) −16.1871 −0.787042
\(424\) 130.948 6.35941
\(425\) 0.222483 0.0107920
\(426\) 0.358164 0.0173531
\(427\) −5.57857 −0.269966
\(428\) −93.2030 −4.50514
\(429\) −1.43754 −0.0694050
\(430\) −7.65428 −0.369122
\(431\) −12.7155 −0.612483 −0.306241 0.951954i \(-0.599071\pi\)
−0.306241 + 0.951954i \(0.599071\pi\)
\(432\) 93.6180 4.50420
\(433\) 10.0648 0.483685 0.241842 0.970316i \(-0.422248\pi\)
0.241842 + 0.970316i \(0.422248\pi\)
\(434\) −27.5587 −1.32286
\(435\) −8.05786 −0.386345
\(436\) 34.7111 1.66236
\(437\) −27.4954 −1.31528
\(438\) −20.1921 −0.964817
\(439\) −16.3004 −0.777973 −0.388987 0.921243i \(-0.627175\pi\)
−0.388987 + 0.921243i \(0.627175\pi\)
\(440\) −5.35417 −0.255250
\(441\) −1.86076 −0.0886076
\(442\) 1.65912 0.0789162
\(443\) 0.988554 0.0469676 0.0234838 0.999724i \(-0.492524\pi\)
0.0234838 + 0.999724i \(0.492524\pi\)
\(444\) 35.4915 1.68435
\(445\) 0.176402 0.00836224
\(446\) 13.8274 0.654748
\(447\) 11.3397 0.536349
\(448\) −45.3763 −2.14383
\(449\) −25.9528 −1.22479 −0.612395 0.790552i \(-0.709794\pi\)
−0.612395 + 0.790552i \(0.709794\pi\)
\(450\) −5.19698 −0.244988
\(451\) 5.66271 0.266646
\(452\) −36.2908 −1.70697
\(453\) −20.8216 −0.978284
\(454\) 36.2012 1.69900
\(455\) 2.67005 0.125174
\(456\) −38.2176 −1.78970
\(457\) −0.576076 −0.0269477 −0.0134739 0.999909i \(-0.504289\pi\)
−0.0134739 + 0.999909i \(0.504289\pi\)
\(458\) 2.79293 0.130505
\(459\) 1.15428 0.0538770
\(460\) 47.2789 2.20439
\(461\) −0.725377 −0.0337842 −0.0168921 0.999857i \(-0.505377\pi\)
−0.0168921 + 0.999857i \(0.505377\pi\)
\(462\) 1.50370 0.0699585
\(463\) 10.0709 0.468034 0.234017 0.972232i \(-0.424813\pi\)
0.234017 + 0.972232i \(0.424813\pi\)
\(464\) −136.226 −6.32413
\(465\) 10.5319 0.488405
\(466\) −11.3620 −0.526333
\(467\) −34.7490 −1.60799 −0.803996 0.594635i \(-0.797297\pi\)
−0.803996 + 0.594635i \(0.797297\pi\)
\(468\) −28.8186 −1.33214
\(469\) −8.95098 −0.413318
\(470\) −24.2962 −1.12070
\(471\) −3.11981 −0.143753
\(472\) −154.546 −7.11357
\(473\) 1.38241 0.0635632
\(474\) −40.3445 −1.85308
\(475\) 3.37331 0.154778
\(476\) −1.29051 −0.0591505
\(477\) −22.9557 −1.05107
\(478\) −19.3530 −0.885185
\(479\) 4.17971 0.190976 0.0954879 0.995431i \(-0.469559\pi\)
0.0954879 + 0.995431i \(0.469559\pi\)
\(480\) 31.1330 1.42102
\(481\) −15.3063 −0.697909
\(482\) −16.4572 −0.749603
\(483\) −8.69984 −0.395857
\(484\) −62.3294 −2.83316
\(485\) −13.1772 −0.598346
\(486\) −43.6037 −1.97790
\(487\) −19.8156 −0.897931 −0.448966 0.893549i \(-0.648207\pi\)
−0.448966 + 0.893549i \(0.648207\pi\)
\(488\) 59.2136 2.68048
\(489\) −13.1665 −0.595412
\(490\) −2.79293 −0.126172
\(491\) 9.83568 0.443878 0.221939 0.975061i \(-0.428761\pi\)
0.221939 + 0.975061i \(0.428761\pi\)
\(492\) −69.5029 −3.13343
\(493\) −1.67961 −0.0756460
\(494\) 25.1557 1.13181
\(495\) 0.938605 0.0421872
\(496\) 178.052 7.99476
\(497\) 0.120147 0.00538934
\(498\) 14.1453 0.633868
\(499\) −28.8496 −1.29148 −0.645742 0.763556i \(-0.723452\pi\)
−0.645742 + 0.763556i \(0.723452\pi\)
\(500\) −5.80048 −0.259405
\(501\) 2.49636 0.111529
\(502\) −33.8602 −1.51126
\(503\) −12.9751 −0.578532 −0.289266 0.957249i \(-0.593411\pi\)
−0.289266 + 0.957249i \(0.593411\pi\)
\(504\) 19.7510 0.879780
\(505\) 8.22460 0.365990
\(506\) −11.4831 −0.510484
\(507\) 6.26626 0.278294
\(508\) −43.2716 −1.91987
\(509\) 18.9209 0.838655 0.419327 0.907835i \(-0.362266\pi\)
0.419327 + 0.907835i \(0.362266\pi\)
\(510\) 0.663233 0.0293684
\(511\) −6.77351 −0.299642
\(512\) 143.265 6.33146
\(513\) 17.5012 0.772698
\(514\) 50.9123 2.24564
\(515\) −1.71653 −0.0756395
\(516\) −16.9674 −0.746948
\(517\) 4.38804 0.192986
\(518\) 16.0108 0.703474
\(519\) −22.1289 −0.971351
\(520\) −28.3412 −1.24284
\(521\) −42.6480 −1.86844 −0.934222 0.356693i \(-0.883904\pi\)
−0.934222 + 0.356693i \(0.883904\pi\)
\(522\) 39.2340 1.71723
\(523\) −11.8360 −0.517550 −0.258775 0.965938i \(-0.583319\pi\)
−0.258775 + 0.965938i \(0.583319\pi\)
\(524\) −83.3888 −3.64286
\(525\) 1.06735 0.0465831
\(526\) 8.52936 0.371898
\(527\) 2.19531 0.0956293
\(528\) −9.71512 −0.422796
\(529\) 43.4366 1.88855
\(530\) −34.4557 −1.49666
\(531\) 27.0925 1.17572
\(532\) −19.5668 −0.848330
\(533\) 29.9744 1.29833
\(534\) 0.525861 0.0227562
\(535\) 16.0681 0.694687
\(536\) 95.0102 4.10381
\(537\) −6.74787 −0.291192
\(538\) 18.5465 0.799598
\(539\) 0.504421 0.0217269
\(540\) −30.0937 −1.29503
\(541\) 9.36010 0.402422 0.201211 0.979548i \(-0.435512\pi\)
0.201211 + 0.979548i \(0.435512\pi\)
\(542\) 10.1434 0.435698
\(543\) −3.50312 −0.150333
\(544\) 6.48950 0.278235
\(545\) −5.98418 −0.256334
\(546\) 7.95953 0.340636
\(547\) −26.6114 −1.13782 −0.568910 0.822400i \(-0.692635\pi\)
−0.568910 + 0.822400i \(0.692635\pi\)
\(548\) 0.345211 0.0147467
\(549\) −10.3804 −0.443023
\(550\) 1.40881 0.0600720
\(551\) −25.4664 −1.08491
\(552\) 92.3444 3.93044
\(553\) −13.5337 −0.575510
\(554\) −47.5159 −2.01876
\(555\) −6.11871 −0.259725
\(556\) −88.0691 −3.73496
\(557\) −34.2583 −1.45157 −0.725786 0.687920i \(-0.758524\pi\)
−0.725786 + 0.687920i \(0.758524\pi\)
\(558\) −51.2802 −2.17086
\(559\) 7.31750 0.309497
\(560\) 18.0446 0.762524
\(561\) −0.119784 −0.00505728
\(562\) −52.4614 −2.21295
\(563\) −9.29337 −0.391669 −0.195834 0.980637i \(-0.562741\pi\)
−0.195834 + 0.980637i \(0.562741\pi\)
\(564\) −53.8579 −2.26783
\(565\) 6.25651 0.263213
\(566\) 23.7919 1.00005
\(567\) −0.0447058 −0.00187747
\(568\) −1.27530 −0.0535105
\(569\) −45.8862 −1.92365 −0.961825 0.273664i \(-0.911765\pi\)
−0.961825 + 0.273664i \(0.911765\pi\)
\(570\) 10.0560 0.421199
\(571\) −22.5665 −0.944377 −0.472189 0.881498i \(-0.656536\pi\)
−0.472189 + 0.881498i \(0.656536\pi\)
\(572\) 7.81225 0.326646
\(573\) −22.9941 −0.960594
\(574\) −31.3539 −1.30869
\(575\) −8.15087 −0.339915
\(576\) −84.4344 −3.51810
\(577\) 23.5063 0.978580 0.489290 0.872121i \(-0.337256\pi\)
0.489290 + 0.872121i \(0.337256\pi\)
\(578\) −47.3416 −1.96915
\(579\) −3.42263 −0.142240
\(580\) 43.7901 1.81829
\(581\) 4.74510 0.196860
\(582\) −39.2818 −1.62828
\(583\) 6.22291 0.257726
\(584\) 71.8973 2.97513
\(585\) 4.96832 0.205415
\(586\) 55.3678 2.28722
\(587\) −30.0282 −1.23940 −0.619699 0.784840i \(-0.712745\pi\)
−0.619699 + 0.784840i \(0.712745\pi\)
\(588\) −6.19116 −0.255319
\(589\) 33.2855 1.37150
\(590\) 40.6649 1.67415
\(591\) 25.3460 1.04259
\(592\) −103.443 −4.25147
\(593\) 2.79249 0.114674 0.0573368 0.998355i \(-0.481739\pi\)
0.0573368 + 0.998355i \(0.481739\pi\)
\(594\) 7.30912 0.299897
\(595\) 0.222483 0.00912093
\(596\) −61.6251 −2.52426
\(597\) −10.7383 −0.439491
\(598\) −60.7832 −2.48561
\(599\) 30.8909 1.26217 0.631084 0.775714i \(-0.282610\pi\)
0.631084 + 0.775714i \(0.282610\pi\)
\(600\) −11.3294 −0.462521
\(601\) 25.7315 1.04961 0.524805 0.851222i \(-0.324138\pi\)
0.524805 + 0.851222i \(0.324138\pi\)
\(602\) −7.65428 −0.311965
\(603\) −16.6556 −0.678270
\(604\) 113.154 4.60418
\(605\) 10.7456 0.436869
\(606\) 24.5179 0.995971
\(607\) 23.6914 0.961605 0.480802 0.876829i \(-0.340345\pi\)
0.480802 + 0.876829i \(0.340345\pi\)
\(608\) 98.3943 3.99041
\(609\) −8.05786 −0.326521
\(610\) −15.5806 −0.630839
\(611\) 23.2272 0.939672
\(612\) −2.40133 −0.0970680
\(613\) 0.848584 0.0342740 0.0171370 0.999853i \(-0.494545\pi\)
0.0171370 + 0.999853i \(0.494545\pi\)
\(614\) 73.4687 2.96496
\(615\) 11.9823 0.483172
\(616\) −5.35417 −0.215726
\(617\) 22.9027 0.922029 0.461014 0.887393i \(-0.347486\pi\)
0.461014 + 0.887393i \(0.347486\pi\)
\(618\) −5.11706 −0.205838
\(619\) −41.5809 −1.67128 −0.835640 0.549278i \(-0.814903\pi\)
−0.835640 + 0.549278i \(0.814903\pi\)
\(620\) −57.2351 −2.29862
\(621\) −42.2879 −1.69695
\(622\) −53.0222 −2.12600
\(623\) 0.176402 0.00706738
\(624\) −51.4250 −2.05865
\(625\) 1.00000 0.0400000
\(626\) 24.3474 0.973119
\(627\) −1.81617 −0.0725309
\(628\) 16.9545 0.676556
\(629\) −1.27541 −0.0508539
\(630\) −5.19698 −0.207053
\(631\) −21.6184 −0.860614 −0.430307 0.902683i \(-0.641595\pi\)
−0.430307 + 0.902683i \(0.641595\pi\)
\(632\) 143.653 5.71421
\(633\) −7.23748 −0.287664
\(634\) −47.2638 −1.87709
\(635\) 7.46000 0.296041
\(636\) −76.3787 −3.02861
\(637\) 2.67005 0.105791
\(638\) −10.6357 −0.421071
\(639\) 0.223565 0.00884410
\(640\) −68.3962 −2.70360
\(641\) 7.17011 0.283202 0.141601 0.989924i \(-0.454775\pi\)
0.141601 + 0.989924i \(0.454775\pi\)
\(642\) 47.8999 1.89046
\(643\) −7.74714 −0.305517 −0.152759 0.988264i \(-0.548816\pi\)
−0.152759 + 0.988264i \(0.548816\pi\)
\(644\) 47.2789 1.86305
\(645\) 2.92517 0.115179
\(646\) 2.09611 0.0824705
\(647\) −31.7059 −1.24649 −0.623243 0.782028i \(-0.714185\pi\)
−0.623243 + 0.782028i \(0.714185\pi\)
\(648\) 0.474530 0.0186413
\(649\) −7.34433 −0.288290
\(650\) 7.45727 0.292498
\(651\) 10.5319 0.412777
\(652\) 71.5530 2.80223
\(653\) 15.9434 0.623915 0.311957 0.950096i \(-0.399015\pi\)
0.311957 + 0.950096i \(0.399015\pi\)
\(654\) −17.8391 −0.697565
\(655\) 14.3762 0.561724
\(656\) 202.572 7.90910
\(657\) −12.6039 −0.491724
\(658\) −24.2962 −0.947165
\(659\) −35.3813 −1.37826 −0.689130 0.724638i \(-0.742007\pi\)
−0.689130 + 0.724638i \(0.742007\pi\)
\(660\) 3.12295 0.121561
\(661\) −13.1239 −0.510460 −0.255230 0.966880i \(-0.582151\pi\)
−0.255230 + 0.966880i \(0.582151\pi\)
\(662\) 42.5889 1.65526
\(663\) −0.634051 −0.0246245
\(664\) −50.3668 −1.95461
\(665\) 3.37331 0.130811
\(666\) 29.7922 1.15443
\(667\) 61.5341 2.38261
\(668\) −13.5664 −0.524898
\(669\) −5.28431 −0.204303
\(670\) −24.9995 −0.965815
\(671\) 2.81394 0.108631
\(672\) 31.1330 1.20098
\(673\) −40.9151 −1.57716 −0.788581 0.614931i \(-0.789184\pi\)
−0.788581 + 0.614931i \(0.789184\pi\)
\(674\) −5.40200 −0.208077
\(675\) 5.18814 0.199692
\(676\) −34.0537 −1.30976
\(677\) −3.54633 −0.136297 −0.0681484 0.997675i \(-0.521709\pi\)
−0.0681484 + 0.997675i \(0.521709\pi\)
\(678\) 18.6509 0.716285
\(679\) −13.1772 −0.505694
\(680\) −2.36155 −0.0905613
\(681\) −13.8347 −0.530146
\(682\) 13.9012 0.532304
\(683\) −2.22325 −0.0850703 −0.0425352 0.999095i \(-0.513543\pi\)
−0.0425352 + 0.999095i \(0.513543\pi\)
\(684\) −36.4092 −1.39214
\(685\) −0.0595141 −0.00227392
\(686\) −2.79293 −0.106635
\(687\) −1.06735 −0.0407220
\(688\) 49.4529 1.88537
\(689\) 32.9397 1.25490
\(690\) −24.2981 −0.925013
\(691\) 32.2910 1.22841 0.614203 0.789148i \(-0.289478\pi\)
0.614203 + 0.789148i \(0.289478\pi\)
\(692\) 120.259 4.57155
\(693\) 0.938605 0.0356547
\(694\) 29.8914 1.13466
\(695\) 15.1831 0.575927
\(696\) 85.5301 3.24201
\(697\) 2.49763 0.0946047
\(698\) −49.1469 −1.86024
\(699\) 4.34210 0.164233
\(700\) −5.80048 −0.219238
\(701\) 3.23802 0.122298 0.0611492 0.998129i \(-0.480523\pi\)
0.0611492 + 0.998129i \(0.480523\pi\)
\(702\) 38.6894 1.46024
\(703\) −19.3379 −0.729341
\(704\) 22.8887 0.862652
\(705\) 9.28508 0.349696
\(706\) 60.0502 2.26002
\(707\) 8.22460 0.309318
\(708\) 90.1428 3.38777
\(709\) 41.8220 1.57066 0.785329 0.619078i \(-0.212494\pi\)
0.785329 + 0.619078i \(0.212494\pi\)
\(710\) 0.335563 0.0125935
\(711\) −25.1829 −0.944433
\(712\) −1.87241 −0.0701717
\(713\) −80.4271 −3.01202
\(714\) 0.663233 0.0248209
\(715\) −1.34683 −0.0503685
\(716\) 36.6710 1.37046
\(717\) 7.39597 0.276207
\(718\) 45.6735 1.70452
\(719\) −20.7107 −0.772379 −0.386189 0.922419i \(-0.626209\pi\)
−0.386189 + 0.922419i \(0.626209\pi\)
\(720\) 33.5767 1.25133
\(721\) −1.71653 −0.0639271
\(722\) −21.2843 −0.792120
\(723\) 6.28929 0.233901
\(724\) 19.0376 0.707526
\(725\) −7.54939 −0.280377
\(726\) 32.0330 1.18886
\(727\) −10.0567 −0.372981 −0.186490 0.982457i \(-0.559711\pi\)
−0.186490 + 0.982457i \(0.559711\pi\)
\(728\) −28.3412 −1.05040
\(729\) 16.5295 0.612205
\(730\) −18.9180 −0.700185
\(731\) 0.609735 0.0225519
\(732\) −34.5378 −1.27655
\(733\) −34.1110 −1.25992 −0.629960 0.776628i \(-0.716929\pi\)
−0.629960 + 0.776628i \(0.716929\pi\)
\(734\) −25.8307 −0.953428
\(735\) 1.06735 0.0393699
\(736\) −237.748 −8.76351
\(737\) 4.51506 0.166314
\(738\) −58.3421 −2.14760
\(739\) 14.8374 0.545802 0.272901 0.962042i \(-0.412017\pi\)
0.272901 + 0.962042i \(0.412017\pi\)
\(740\) 33.2519 1.22236
\(741\) −9.61354 −0.353162
\(742\) −34.4557 −1.26491
\(743\) −26.0718 −0.956481 −0.478241 0.878229i \(-0.658725\pi\)
−0.478241 + 0.878229i \(0.658725\pi\)
\(744\) −111.791 −4.09844
\(745\) 10.6241 0.389238
\(746\) −81.7067 −2.99149
\(747\) 8.82949 0.323054
\(748\) 0.650960 0.0238015
\(749\) 16.0681 0.587117
\(750\) 2.98104 0.108852
\(751\) −28.3565 −1.03474 −0.517371 0.855761i \(-0.673089\pi\)
−0.517371 + 0.855761i \(0.673089\pi\)
\(752\) 156.973 5.72423
\(753\) 12.9401 0.471563
\(754\) −56.2978 −2.05025
\(755\) −19.5077 −0.709959
\(756\) −30.0937 −1.09450
\(757\) 36.4519 1.32487 0.662433 0.749121i \(-0.269524\pi\)
0.662433 + 0.749121i \(0.269524\pi\)
\(758\) −20.4372 −0.742314
\(759\) 4.38838 0.159288
\(760\) −35.8060 −1.29882
\(761\) 2.42204 0.0877990 0.0438995 0.999036i \(-0.486022\pi\)
0.0438995 + 0.999036i \(0.486022\pi\)
\(762\) 22.2386 0.805619
\(763\) −5.98418 −0.216642
\(764\) 124.961 4.52092
\(765\) 0.413988 0.0149678
\(766\) −48.1075 −1.73819
\(767\) −38.8757 −1.40372
\(768\) −107.027 −3.86200
\(769\) 36.5506 1.31805 0.659024 0.752122i \(-0.270970\pi\)
0.659024 + 0.752122i \(0.270970\pi\)
\(770\) 1.40881 0.0507701
\(771\) −19.4567 −0.700716
\(772\) 18.6001 0.669433
\(773\) 40.3857 1.45257 0.726286 0.687392i \(-0.241245\pi\)
0.726286 + 0.687392i \(0.241245\pi\)
\(774\) −14.2428 −0.511946
\(775\) 9.86730 0.354444
\(776\) 139.869 5.02102
\(777\) −6.11871 −0.219507
\(778\) 58.9198 2.11238
\(779\) 37.8693 1.35681
\(780\) 16.5307 0.591893
\(781\) −0.0606048 −0.00216861
\(782\) −5.06480 −0.181117
\(783\) −39.1673 −1.39973
\(784\) 18.0446 0.644451
\(785\) −2.92294 −0.104324
\(786\) 42.8560 1.52862
\(787\) −48.8519 −1.74138 −0.870691 0.491831i \(-0.836328\pi\)
−0.870691 + 0.491831i \(0.836328\pi\)
\(788\) −137.742 −4.90684
\(789\) −3.25959 −0.116045
\(790\) −37.7986 −1.34482
\(791\) 6.25651 0.222456
\(792\) −9.96282 −0.354013
\(793\) 14.8950 0.528938
\(794\) −60.5243 −2.14793
\(795\) 13.1676 0.467008
\(796\) 58.3571 2.06841
\(797\) −1.20937 −0.0428382 −0.0214191 0.999771i \(-0.506818\pi\)
−0.0214191 + 0.999771i \(0.506818\pi\)
\(798\) 10.0560 0.355978
\(799\) 1.93542 0.0684703
\(800\) 29.1685 1.03126
\(801\) 0.328241 0.0115978
\(802\) 56.3245 1.98889
\(803\) 3.41670 0.120573
\(804\) −55.4169 −1.95440
\(805\) −8.15087 −0.287280
\(806\) 73.5831 2.59185
\(807\) −7.08777 −0.249501
\(808\) −87.2999 −3.07120
\(809\) 26.0775 0.916835 0.458417 0.888737i \(-0.348417\pi\)
0.458417 + 0.888737i \(0.348417\pi\)
\(810\) −0.124860 −0.00438715
\(811\) −9.69833 −0.340554 −0.170277 0.985396i \(-0.554466\pi\)
−0.170277 + 0.985396i \(0.554466\pi\)
\(812\) 43.7901 1.53673
\(813\) −3.87644 −0.135953
\(814\) −8.07617 −0.283070
\(815\) −12.3357 −0.432101
\(816\) −4.28502 −0.150006
\(817\) 9.24486 0.323437
\(818\) −76.9074 −2.68901
\(819\) 4.96832 0.173607
\(820\) −65.1171 −2.27399
\(821\) −50.1723 −1.75102 −0.875512 0.483196i \(-0.839476\pi\)
−0.875512 + 0.483196i \(0.839476\pi\)
\(822\) −0.177414 −0.00618803
\(823\) −23.6021 −0.822719 −0.411360 0.911473i \(-0.634946\pi\)
−0.411360 + 0.911473i \(0.634946\pi\)
\(824\) 18.2201 0.634729
\(825\) −0.538394 −0.0187445
\(826\) 40.6649 1.41491
\(827\) 51.7386 1.79913 0.899563 0.436791i \(-0.143885\pi\)
0.899563 + 0.436791i \(0.143885\pi\)
\(828\) 87.9748 3.05733
\(829\) 3.08709 0.107219 0.0536095 0.998562i \(-0.482927\pi\)
0.0536095 + 0.998562i \(0.482927\pi\)
\(830\) 13.2527 0.460010
\(831\) 18.1587 0.629920
\(832\) 121.157 4.20036
\(833\) 0.222483 0.00770859
\(834\) 45.2614 1.56727
\(835\) 2.33883 0.0809386
\(836\) 9.86991 0.341358
\(837\) 51.1930 1.76949
\(838\) −43.6906 −1.50927
\(839\) −35.9323 −1.24052 −0.620260 0.784396i \(-0.712973\pi\)
−0.620260 + 0.784396i \(0.712973\pi\)
\(840\) −11.3294 −0.390901
\(841\) 27.9933 0.965286
\(842\) 78.9038 2.71920
\(843\) 20.0487 0.690515
\(844\) 39.3318 1.35386
\(845\) 5.87084 0.201963
\(846\) −45.2094 −1.55433
\(847\) 10.7456 0.369222
\(848\) 222.612 7.64452
\(849\) −9.09235 −0.312049
\(850\) 0.621382 0.0213132
\(851\) 46.7257 1.60174
\(852\) 0.743851 0.0254839
\(853\) −4.75056 −0.162656 −0.0813281 0.996687i \(-0.525916\pi\)
−0.0813281 + 0.996687i \(0.525916\pi\)
\(854\) −15.5806 −0.533156
\(855\) 6.27692 0.214666
\(856\) −170.555 −5.82946
\(857\) −30.5487 −1.04352 −0.521762 0.853091i \(-0.674725\pi\)
−0.521762 + 0.853091i \(0.674725\pi\)
\(858\) −4.01495 −0.137068
\(859\) 39.7302 1.35558 0.677789 0.735257i \(-0.262938\pi\)
0.677789 + 0.735257i \(0.262938\pi\)
\(860\) −15.8967 −0.542074
\(861\) 11.9823 0.408355
\(862\) −35.5135 −1.20959
\(863\) −33.0975 −1.12665 −0.563325 0.826235i \(-0.690478\pi\)
−0.563325 + 0.826235i \(0.690478\pi\)
\(864\) 151.330 5.14835
\(865\) −20.7325 −0.704927
\(866\) 28.1104 0.955230
\(867\) 18.0922 0.614442
\(868\) −57.2351 −1.94269
\(869\) 6.82666 0.231579
\(870\) −22.5051 −0.762993
\(871\) 23.8996 0.809805
\(872\) 63.5191 2.15103
\(873\) −24.5196 −0.829863
\(874\) −76.7929 −2.59756
\(875\) 1.00000 0.0338062
\(876\) −41.9358 −1.41688
\(877\) −43.0854 −1.45489 −0.727446 0.686165i \(-0.759293\pi\)
−0.727446 + 0.686165i \(0.759293\pi\)
\(878\) −45.5258 −1.53642
\(879\) −21.1594 −0.713690
\(880\) −9.10208 −0.306831
\(881\) −44.8177 −1.50995 −0.754974 0.655755i \(-0.772351\pi\)
−0.754974 + 0.655755i \(0.772351\pi\)
\(882\) −5.19698 −0.174991
\(883\) 29.8559 1.00473 0.502366 0.864655i \(-0.332463\pi\)
0.502366 + 0.864655i \(0.332463\pi\)
\(884\) 3.44573 0.115892
\(885\) −15.5406 −0.522391
\(886\) 2.76097 0.0927565
\(887\) 26.9891 0.906207 0.453103 0.891458i \(-0.350317\pi\)
0.453103 + 0.891458i \(0.350317\pi\)
\(888\) 64.9470 2.17948
\(889\) 7.46000 0.250200
\(890\) 0.492678 0.0165146
\(891\) 0.0225505 0.000755471 0
\(892\) 28.7174 0.961529
\(893\) 29.3450 0.981993
\(894\) 31.6710 1.05924
\(895\) −6.32207 −0.211323
\(896\) −68.3962 −2.28496
\(897\) 23.2290 0.775594
\(898\) −72.4845 −2.41884
\(899\) −74.4921 −2.48445
\(900\) −10.7933 −0.359777
\(901\) 2.74472 0.0914399
\(902\) 15.8156 0.526601
\(903\) 2.92517 0.0973436
\(904\) −66.4097 −2.20875
\(905\) −3.28207 −0.109100
\(906\) −58.1534 −1.93202
\(907\) 43.6688 1.45000 0.725000 0.688749i \(-0.241840\pi\)
0.725000 + 0.688749i \(0.241840\pi\)
\(908\) 75.1841 2.49507
\(909\) 15.3040 0.507602
\(910\) 7.45727 0.247206
\(911\) 0.376434 0.0124718 0.00623591 0.999981i \(-0.498015\pi\)
0.00623591 + 0.999981i \(0.498015\pi\)
\(912\) −64.9699 −2.15137
\(913\) −2.39353 −0.0792141
\(914\) −1.60894 −0.0532191
\(915\) 5.95429 0.196843
\(916\) 5.80048 0.191653
\(917\) 14.3762 0.474743
\(918\) 3.22382 0.106402
\(919\) 9.96284 0.328644 0.164322 0.986407i \(-0.447456\pi\)
0.164322 + 0.986407i \(0.447456\pi\)
\(920\) 86.5173 2.85239
\(921\) −28.0769 −0.925166
\(922\) −2.02593 −0.0667205
\(923\) −0.320799 −0.0105592
\(924\) 3.12295 0.102737
\(925\) −5.73261 −0.188487
\(926\) 28.1274 0.924322
\(927\) −3.19406 −0.104907
\(928\) −220.204 −7.22855
\(929\) 60.1465 1.97334 0.986671 0.162728i \(-0.0520294\pi\)
0.986671 + 0.162728i \(0.0520294\pi\)
\(930\) 29.4149 0.964551
\(931\) 3.37331 0.110556
\(932\) −23.5970 −0.772945
\(933\) 20.2630 0.663382
\(934\) −97.0517 −3.17563
\(935\) −0.112225 −0.00367016
\(936\) −52.7362 −1.72374
\(937\) −41.3668 −1.35140 −0.675698 0.737179i \(-0.736157\pi\)
−0.675698 + 0.737179i \(0.736157\pi\)
\(938\) −24.9995 −0.816263
\(939\) −9.30466 −0.303646
\(940\) −50.4594 −1.64580
\(941\) −60.3573 −1.96759 −0.983796 0.179290i \(-0.942620\pi\)
−0.983796 + 0.179290i \(0.942620\pi\)
\(942\) −8.71341 −0.283898
\(943\) −91.5029 −2.97975
\(944\) −262.728 −8.55108
\(945\) 5.18814 0.168770
\(946\) 3.86098 0.125531
\(947\) 37.8252 1.22915 0.614577 0.788857i \(-0.289327\pi\)
0.614577 + 0.788857i \(0.289327\pi\)
\(948\) −83.7890 −2.72134
\(949\) 18.0856 0.587083
\(950\) 9.42144 0.305672
\(951\) 18.0624 0.585714
\(952\) −2.36155 −0.0765382
\(953\) 33.0740 1.07137 0.535686 0.844417i \(-0.320053\pi\)
0.535686 + 0.844417i \(0.320053\pi\)
\(954\) −64.1138 −2.07576
\(955\) −21.5432 −0.697120
\(956\) −40.1931 −1.29994
\(957\) 4.06455 0.131388
\(958\) 11.6737 0.377159
\(959\) −0.0595141 −0.00192181
\(960\) 48.4325 1.56315
\(961\) 66.3637 2.14076
\(962\) −42.7496 −1.37830
\(963\) 29.8990 0.963481
\(964\) −34.1789 −1.10083
\(965\) −3.20665 −0.103226
\(966\) −24.2981 −0.781778
\(967\) −15.4449 −0.496675 −0.248338 0.968674i \(-0.579884\pi\)
−0.248338 + 0.968674i \(0.579884\pi\)
\(968\) −114.059 −3.66598
\(969\) −0.801054 −0.0257336
\(970\) −36.8030 −1.18167
\(971\) 46.1134 1.47985 0.739924 0.672690i \(-0.234861\pi\)
0.739924 + 0.672690i \(0.234861\pi\)
\(972\) −90.5579 −2.90465
\(973\) 15.1831 0.486747
\(974\) −55.3437 −1.77333
\(975\) −2.84988 −0.0912692
\(976\) 100.663 3.22215
\(977\) 0.261368 0.00836189 0.00418095 0.999991i \(-0.498669\pi\)
0.00418095 + 0.999991i \(0.498669\pi\)
\(978\) −36.7733 −1.17588
\(979\) −0.0889806 −0.00284383
\(980\) −5.80048 −0.185290
\(981\) −11.1351 −0.355517
\(982\) 27.4704 0.876616
\(983\) 2.27071 0.0724243 0.0362121 0.999344i \(-0.488471\pi\)
0.0362121 + 0.999344i \(0.488471\pi\)
\(984\) −127.186 −4.05453
\(985\) 23.7466 0.756629
\(986\) −4.69105 −0.149394
\(987\) 9.28508 0.295547
\(988\) 52.2444 1.66212
\(989\) −22.3382 −0.710312
\(990\) 2.62146 0.0833156
\(991\) −60.9788 −1.93706 −0.968528 0.248903i \(-0.919930\pi\)
−0.968528 + 0.248903i \(0.919930\pi\)
\(992\) 287.814 9.13810
\(993\) −16.2758 −0.516498
\(994\) 0.335563 0.0106434
\(995\) −10.0607 −0.318946
\(996\) 29.3776 0.930866
\(997\) −2.82451 −0.0894531 −0.0447265 0.998999i \(-0.514242\pi\)
−0.0447265 + 0.998999i \(0.514242\pi\)
\(998\) −80.5749 −2.55055
\(999\) −29.7416 −0.940982
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 \(a_p\))