Properties

Label 8027.2.a.f.1.16
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +O(q^{10})\) \(q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +9.79973 q^{10} -4.16401 q^{11} +10.4489 q^{12} +5.20045 q^{13} -7.81494 q^{14} -11.1112 q^{15} +2.95241 q^{16} +6.42329 q^{17} -10.8125 q^{18} +5.14494 q^{19} -15.5173 q^{20} +8.86075 q^{21} +10.0456 q^{22} +1.00000 q^{23} -12.0099 q^{24} +11.5008 q^{25} -12.5459 q^{26} +4.05351 q^{27} +12.3745 q^{28} +0.970739 q^{29} +26.8053 q^{30} +5.78906 q^{31} +1.65880 q^{32} -11.3899 q^{33} -15.4960 q^{34} -13.1588 q^{35} +17.1209 q^{36} +9.74412 q^{37} -12.4120 q^{38} +14.2248 q^{39} +17.8355 q^{40} +9.09773 q^{41} -21.3763 q^{42} -5.13587 q^{43} -15.9065 q^{44} -18.2061 q^{45} -2.41247 q^{46} +6.94159 q^{47} +8.07575 q^{48} +3.49369 q^{49} -27.7454 q^{50} +17.5697 q^{51} +19.8657 q^{52} +1.05253 q^{53} -9.77897 q^{54} +16.9147 q^{55} -14.2232 q^{56} +14.0730 q^{57} -2.34188 q^{58} -2.55339 q^{59} -42.4446 q^{60} -12.3008 q^{61} -13.9659 q^{62} +14.5187 q^{63} -9.90662 q^{64} -21.1248 q^{65} +27.4777 q^{66} +0.828885 q^{67} +24.5370 q^{68} +2.73531 q^{69} +31.7452 q^{70} -11.4798 q^{71} -19.6787 q^{72} -10.0341 q^{73} -23.5074 q^{74} +31.4583 q^{75} +19.6537 q^{76} -13.4889 q^{77} -34.3170 q^{78} -1.85268 q^{79} -11.9930 q^{80} -2.35814 q^{81} -21.9480 q^{82} +7.22276 q^{83} +33.8481 q^{84} -26.0922 q^{85} +12.3901 q^{86} +2.65527 q^{87} +18.2829 q^{88} -13.5713 q^{89} +43.9216 q^{90} +16.8463 q^{91} +3.82000 q^{92} +15.8349 q^{93} -16.7464 q^{94} -20.8993 q^{95} +4.53734 q^{96} +17.9077 q^{97} -8.42842 q^{98} -18.6628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41247 −1.70587 −0.852936 0.522015i \(-0.825180\pi\)
−0.852936 + 0.522015i \(0.825180\pi\)
\(3\) 2.73531 1.57923 0.789616 0.613601i \(-0.210280\pi\)
0.789616 + 0.613601i \(0.210280\pi\)
\(4\) 3.82000 1.91000
\(5\) −4.06212 −1.81664 −0.908318 0.418281i \(-0.862633\pi\)
−0.908318 + 0.418281i \(0.862633\pi\)
\(6\) −6.59885 −2.69397
\(7\) 3.23940 1.22438 0.612188 0.790712i \(-0.290289\pi\)
0.612188 + 0.790712i \(0.290289\pi\)
\(8\) −4.39069 −1.55234
\(9\) 4.48192 1.49397
\(10\) 9.79973 3.09895
\(11\) −4.16401 −1.25550 −0.627749 0.778416i \(-0.716024\pi\)
−0.627749 + 0.778416i \(0.716024\pi\)
\(12\) 10.4489 3.01633
\(13\) 5.20045 1.44234 0.721172 0.692756i \(-0.243604\pi\)
0.721172 + 0.692756i \(0.243604\pi\)
\(14\) −7.81494 −2.08863
\(15\) −11.1112 −2.86889
\(16\) 2.95241 0.738102
\(17\) 6.42329 1.55788 0.778938 0.627100i \(-0.215758\pi\)
0.778938 + 0.627100i \(0.215758\pi\)
\(18\) −10.8125 −2.54853
\(19\) 5.14494 1.18033 0.590165 0.807283i \(-0.299063\pi\)
0.590165 + 0.807283i \(0.299063\pi\)
\(20\) −15.5173 −3.46977
\(21\) 8.86075 1.93358
\(22\) 10.0456 2.14172
\(23\) 1.00000 0.208514
\(24\) −12.0099 −2.45151
\(25\) 11.5008 2.30016
\(26\) −12.5459 −2.46046
\(27\) 4.05351 0.780099
\(28\) 12.3745 2.33856
\(29\) 0.970739 0.180262 0.0901308 0.995930i \(-0.471271\pi\)
0.0901308 + 0.995930i \(0.471271\pi\)
\(30\) 26.8053 4.89396
\(31\) 5.78906 1.03975 0.519873 0.854244i \(-0.325979\pi\)
0.519873 + 0.854244i \(0.325979\pi\)
\(32\) 1.65880 0.293238
\(33\) −11.3899 −1.98272
\(34\) −15.4960 −2.65754
\(35\) −13.1588 −2.22425
\(36\) 17.1209 2.85349
\(37\) 9.74412 1.60192 0.800961 0.598716i \(-0.204322\pi\)
0.800961 + 0.598716i \(0.204322\pi\)
\(38\) −12.4120 −2.01349
\(39\) 14.2248 2.27780
\(40\) 17.8355 2.82004
\(41\) 9.09773 1.42083 0.710413 0.703785i \(-0.248508\pi\)
0.710413 + 0.703785i \(0.248508\pi\)
\(42\) −21.3763 −3.29843
\(43\) −5.13587 −0.783213 −0.391606 0.920133i \(-0.628081\pi\)
−0.391606 + 0.920133i \(0.628081\pi\)
\(44\) −15.9065 −2.39800
\(45\) −18.2061 −2.71401
\(46\) −2.41247 −0.355699
\(47\) 6.94159 1.01254 0.506268 0.862376i \(-0.331025\pi\)
0.506268 + 0.862376i \(0.331025\pi\)
\(48\) 8.07575 1.16563
\(49\) 3.49369 0.499099
\(50\) −27.7454 −3.92379
\(51\) 17.5697 2.46025
\(52\) 19.8657 2.75488
\(53\) 1.05253 0.144576 0.0722878 0.997384i \(-0.476970\pi\)
0.0722878 + 0.997384i \(0.476970\pi\)
\(54\) −9.77897 −1.33075
\(55\) 16.9147 2.28078
\(56\) −14.2232 −1.90066
\(57\) 14.0730 1.86401
\(58\) −2.34188 −0.307503
\(59\) −2.55339 −0.332423 −0.166212 0.986090i \(-0.553153\pi\)
−0.166212 + 0.986090i \(0.553153\pi\)
\(60\) −42.4446 −5.47958
\(61\) −12.3008 −1.57495 −0.787476 0.616346i \(-0.788612\pi\)
−0.787476 + 0.616346i \(0.788612\pi\)
\(62\) −13.9659 −1.77367
\(63\) 14.5187 1.82919
\(64\) −9.90662 −1.23833
\(65\) −21.1248 −2.62021
\(66\) 27.4777 3.38227
\(67\) 0.828885 0.101264 0.0506322 0.998717i \(-0.483876\pi\)
0.0506322 + 0.998717i \(0.483876\pi\)
\(68\) 24.5370 2.97555
\(69\) 2.73531 0.329293
\(70\) 31.7452 3.79428
\(71\) −11.4798 −1.36240 −0.681202 0.732095i \(-0.738543\pi\)
−0.681202 + 0.732095i \(0.738543\pi\)
\(72\) −19.6787 −2.31916
\(73\) −10.0341 −1.17440 −0.587200 0.809442i \(-0.699770\pi\)
−0.587200 + 0.809442i \(0.699770\pi\)
\(74\) −23.5074 −2.73268
\(75\) 31.4583 3.63249
\(76\) 19.6537 2.25443
\(77\) −13.4889 −1.53720
\(78\) −34.3170 −3.88563
\(79\) −1.85268 −0.208443 −0.104222 0.994554i \(-0.533235\pi\)
−0.104222 + 0.994554i \(0.533235\pi\)
\(80\) −11.9930 −1.34086
\(81\) −2.35814 −0.262016
\(82\) −21.9480 −2.42375
\(83\) 7.22276 0.792801 0.396401 0.918078i \(-0.370259\pi\)
0.396401 + 0.918078i \(0.370259\pi\)
\(84\) 33.8481 3.69313
\(85\) −26.0922 −2.83009
\(86\) 12.3901 1.33606
\(87\) 2.65527 0.284675
\(88\) 18.2829 1.94897
\(89\) −13.5713 −1.43855 −0.719276 0.694725i \(-0.755526\pi\)
−0.719276 + 0.694725i \(0.755526\pi\)
\(90\) 43.9216 4.62975
\(91\) 16.8463 1.76597
\(92\) 3.82000 0.398263
\(93\) 15.8349 1.64200
\(94\) −16.7464 −1.72726
\(95\) −20.8993 −2.14423
\(96\) 4.53734 0.463090
\(97\) 17.9077 1.81825 0.909126 0.416522i \(-0.136751\pi\)
0.909126 + 0.416522i \(0.136751\pi\)
\(98\) −8.42842 −0.851399
\(99\) −18.6628 −1.87568
\(100\) 43.9331 4.39331
\(101\) 18.7030 1.86101 0.930507 0.366274i \(-0.119367\pi\)
0.930507 + 0.366274i \(0.119367\pi\)
\(102\) −42.3863 −4.19687
\(103\) −16.1531 −1.59161 −0.795804 0.605554i \(-0.792952\pi\)
−0.795804 + 0.605554i \(0.792952\pi\)
\(104\) −22.8336 −2.23902
\(105\) −35.9934 −3.51260
\(106\) −2.53919 −0.246628
\(107\) 9.54927 0.923162 0.461581 0.887098i \(-0.347282\pi\)
0.461581 + 0.887098i \(0.347282\pi\)
\(108\) 15.4844 1.48999
\(109\) 2.67242 0.255971 0.127986 0.991776i \(-0.459149\pi\)
0.127986 + 0.991776i \(0.459149\pi\)
\(110\) −40.8062 −3.89072
\(111\) 26.6532 2.52981
\(112\) 9.56402 0.903715
\(113\) −6.75437 −0.635398 −0.317699 0.948192i \(-0.602910\pi\)
−0.317699 + 0.948192i \(0.602910\pi\)
\(114\) −33.9506 −3.17977
\(115\) −4.06212 −0.378795
\(116\) 3.70822 0.344300
\(117\) 23.3080 2.15482
\(118\) 6.15998 0.567072
\(119\) 20.8076 1.90743
\(120\) 48.7857 4.45350
\(121\) 6.33902 0.576274
\(122\) 29.6752 2.68667
\(123\) 24.8851 2.24382
\(124\) 22.1142 1.98591
\(125\) −26.4071 −2.36192
\(126\) −35.0259 −3.12036
\(127\) −16.8356 −1.49392 −0.746959 0.664871i \(-0.768487\pi\)
−0.746959 + 0.664871i \(0.768487\pi\)
\(128\) 20.5818 1.81919
\(129\) −14.0482 −1.23687
\(130\) 50.9630 4.46975
\(131\) −3.14113 −0.274442 −0.137221 0.990540i \(-0.543817\pi\)
−0.137221 + 0.990540i \(0.543817\pi\)
\(132\) −43.5093 −3.78700
\(133\) 16.6665 1.44517
\(134\) −1.99966 −0.172744
\(135\) −16.4659 −1.41716
\(136\) −28.2027 −2.41836
\(137\) −22.9360 −1.95955 −0.979777 0.200092i \(-0.935876\pi\)
−0.979777 + 0.200092i \(0.935876\pi\)
\(138\) −6.59885 −0.561731
\(139\) 9.44831 0.801396 0.400698 0.916210i \(-0.368768\pi\)
0.400698 + 0.916210i \(0.368768\pi\)
\(140\) −50.2667 −4.24831
\(141\) 18.9874 1.59903
\(142\) 27.6947 2.32409
\(143\) −21.6547 −1.81086
\(144\) 13.2325 1.10270
\(145\) −3.94326 −0.327470
\(146\) 24.2069 2.00338
\(147\) 9.55633 0.788192
\(148\) 37.2225 3.05967
\(149\) 20.6974 1.69560 0.847799 0.530318i \(-0.177927\pi\)
0.847799 + 0.530318i \(0.177927\pi\)
\(150\) −75.8922 −6.19657
\(151\) 3.43764 0.279751 0.139875 0.990169i \(-0.455330\pi\)
0.139875 + 0.990169i \(0.455330\pi\)
\(152\) −22.5898 −1.83228
\(153\) 28.7887 2.32743
\(154\) 32.5415 2.62227
\(155\) −23.5159 −1.88884
\(156\) 54.3389 4.35059
\(157\) −18.4152 −1.46969 −0.734846 0.678234i \(-0.762746\pi\)
−0.734846 + 0.678234i \(0.762746\pi\)
\(158\) 4.46954 0.355577
\(159\) 2.87899 0.228319
\(160\) −6.73826 −0.532706
\(161\) 3.23940 0.255300
\(162\) 5.68895 0.446966
\(163\) 13.0090 1.01894 0.509472 0.860487i \(-0.329841\pi\)
0.509472 + 0.860487i \(0.329841\pi\)
\(164\) 34.7533 2.71378
\(165\) 46.2670 3.60188
\(166\) −17.4247 −1.35242
\(167\) −2.65845 −0.205717 −0.102858 0.994696i \(-0.532799\pi\)
−0.102858 + 0.994696i \(0.532799\pi\)
\(168\) −38.9049 −3.00158
\(169\) 14.0447 1.08036
\(170\) 62.9465 4.82778
\(171\) 23.0592 1.76338
\(172\) −19.6190 −1.49594
\(173\) −7.77900 −0.591427 −0.295713 0.955277i \(-0.595557\pi\)
−0.295713 + 0.955277i \(0.595557\pi\)
\(174\) −6.40576 −0.485619
\(175\) 37.2557 2.81627
\(176\) −12.2939 −0.926685
\(177\) −6.98432 −0.524974
\(178\) 32.7402 2.45399
\(179\) −13.8881 −1.03805 −0.519023 0.854760i \(-0.673704\pi\)
−0.519023 + 0.854760i \(0.673704\pi\)
\(180\) −69.5473 −5.18375
\(181\) 7.84090 0.582810 0.291405 0.956600i \(-0.405877\pi\)
0.291405 + 0.956600i \(0.405877\pi\)
\(182\) −40.6412 −3.01252
\(183\) −33.6464 −2.48721
\(184\) −4.39069 −0.323686
\(185\) −39.5818 −2.91011
\(186\) −38.2011 −2.80104
\(187\) −26.7467 −1.95591
\(188\) 26.5169 1.93394
\(189\) 13.1309 0.955136
\(190\) 50.4190 3.65778
\(191\) 2.44333 0.176793 0.0883965 0.996085i \(-0.471826\pi\)
0.0883965 + 0.996085i \(0.471826\pi\)
\(192\) −27.0977 −1.95561
\(193\) −13.7548 −0.990094 −0.495047 0.868866i \(-0.664849\pi\)
−0.495047 + 0.868866i \(0.664849\pi\)
\(194\) −43.2018 −3.10171
\(195\) −57.7830 −4.13793
\(196\) 13.3459 0.953279
\(197\) 9.87868 0.703827 0.351914 0.936033i \(-0.385531\pi\)
0.351914 + 0.936033i \(0.385531\pi\)
\(198\) 45.0234 3.19967
\(199\) −19.9664 −1.41538 −0.707690 0.706523i \(-0.750263\pi\)
−0.707690 + 0.706523i \(0.750263\pi\)
\(200\) −50.4966 −3.57065
\(201\) 2.26726 0.159920
\(202\) −45.1203 −3.17465
\(203\) 3.14461 0.220708
\(204\) 67.1162 4.69908
\(205\) −36.9561 −2.58112
\(206\) 38.9687 2.71508
\(207\) 4.48192 0.311515
\(208\) 15.3538 1.06460
\(209\) −21.4236 −1.48190
\(210\) 86.8330 5.99205
\(211\) 17.5786 1.21016 0.605082 0.796163i \(-0.293140\pi\)
0.605082 + 0.796163i \(0.293140\pi\)
\(212\) 4.02065 0.276140
\(213\) −31.4009 −2.15155
\(214\) −23.0373 −1.57480
\(215\) 20.8625 1.42281
\(216\) −17.7977 −1.21098
\(217\) 18.7531 1.27304
\(218\) −6.44713 −0.436655
\(219\) −27.4463 −1.85465
\(220\) 64.6143 4.35629
\(221\) 33.4040 2.24700
\(222\) −64.2999 −4.31553
\(223\) −12.4494 −0.833671 −0.416835 0.908982i \(-0.636861\pi\)
−0.416835 + 0.908982i \(0.636861\pi\)
\(224\) 5.37352 0.359033
\(225\) 51.5458 3.43639
\(226\) 16.2947 1.08391
\(227\) 16.2664 1.07964 0.539818 0.841782i \(-0.318493\pi\)
0.539818 + 0.841782i \(0.318493\pi\)
\(228\) 53.7589 3.56027
\(229\) −4.47918 −0.295992 −0.147996 0.988988i \(-0.547282\pi\)
−0.147996 + 0.988988i \(0.547282\pi\)
\(230\) 9.79973 0.646175
\(231\) −36.8963 −2.42760
\(232\) −4.26222 −0.279828
\(233\) 9.37580 0.614229 0.307115 0.951673i \(-0.400637\pi\)
0.307115 + 0.951673i \(0.400637\pi\)
\(234\) −56.2298 −3.67586
\(235\) −28.1976 −1.83941
\(236\) −9.75396 −0.634929
\(237\) −5.06766 −0.329180
\(238\) −50.1976 −3.25383
\(239\) 22.5974 1.46171 0.730853 0.682535i \(-0.239123\pi\)
0.730853 + 0.682535i \(0.239123\pi\)
\(240\) −32.8047 −2.11753
\(241\) 5.90408 0.380315 0.190158 0.981754i \(-0.439100\pi\)
0.190158 + 0.981754i \(0.439100\pi\)
\(242\) −15.2927 −0.983051
\(243\) −18.6108 −1.19388
\(244\) −46.9889 −3.00816
\(245\) −14.1918 −0.906680
\(246\) −60.0345 −3.82766
\(247\) 26.7560 1.70244
\(248\) −25.4180 −1.61404
\(249\) 19.7565 1.25202
\(250\) 63.7063 4.02914
\(251\) −16.2071 −1.02298 −0.511492 0.859288i \(-0.670907\pi\)
−0.511492 + 0.859288i \(0.670907\pi\)
\(252\) 55.4615 3.49375
\(253\) −4.16401 −0.261789
\(254\) 40.6153 2.54843
\(255\) −71.3702 −4.46938
\(256\) −29.8397 −1.86498
\(257\) 18.5326 1.15603 0.578015 0.816026i \(-0.303827\pi\)
0.578015 + 0.816026i \(0.303827\pi\)
\(258\) 33.8908 2.10995
\(259\) 31.5651 1.96136
\(260\) −80.6969 −5.00461
\(261\) 4.35078 0.269306
\(262\) 7.57788 0.468163
\(263\) −4.80820 −0.296486 −0.148243 0.988951i \(-0.547362\pi\)
−0.148243 + 0.988951i \(0.547362\pi\)
\(264\) 50.0094 3.07787
\(265\) −4.27549 −0.262641
\(266\) −40.2074 −2.46527
\(267\) −37.1216 −2.27181
\(268\) 3.16634 0.193415
\(269\) −5.86660 −0.357693 −0.178846 0.983877i \(-0.557237\pi\)
−0.178846 + 0.983877i \(0.557237\pi\)
\(270\) 39.7234 2.41749
\(271\) 22.1165 1.34348 0.671742 0.740785i \(-0.265546\pi\)
0.671742 + 0.740785i \(0.265546\pi\)
\(272\) 18.9642 1.14987
\(273\) 46.0799 2.78888
\(274\) 55.3324 3.34275
\(275\) −47.8896 −2.88785
\(276\) 10.4489 0.628949
\(277\) −3.87553 −0.232858 −0.116429 0.993199i \(-0.537145\pi\)
−0.116429 + 0.993199i \(0.537145\pi\)
\(278\) −22.7938 −1.36708
\(279\) 25.9461 1.55335
\(280\) 57.7763 3.45280
\(281\) 20.2207 1.20627 0.603133 0.797641i \(-0.293919\pi\)
0.603133 + 0.797641i \(0.293919\pi\)
\(282\) −45.8065 −2.72774
\(283\) 9.83391 0.584565 0.292283 0.956332i \(-0.405585\pi\)
0.292283 + 0.956332i \(0.405585\pi\)
\(284\) −43.8530 −2.60219
\(285\) −57.1662 −3.38623
\(286\) 52.2414 3.08910
\(287\) 29.4712 1.73963
\(288\) 7.43462 0.438089
\(289\) 24.2587 1.42698
\(290\) 9.51298 0.558622
\(291\) 48.9831 2.87144
\(292\) −38.3302 −2.24310
\(293\) 25.1644 1.47012 0.735059 0.678003i \(-0.237154\pi\)
0.735059 + 0.678003i \(0.237154\pi\)
\(294\) −23.0543 −1.34456
\(295\) 10.3722 0.603892
\(296\) −42.7834 −2.48674
\(297\) −16.8789 −0.979413
\(298\) −49.9318 −2.89247
\(299\) 5.20045 0.300750
\(300\) 120.171 6.93806
\(301\) −16.6371 −0.958948
\(302\) −8.29319 −0.477219
\(303\) 51.1584 2.93897
\(304\) 15.1899 0.871203
\(305\) 49.9672 2.86111
\(306\) −69.4518 −3.97029
\(307\) 1.92498 0.109864 0.0549321 0.998490i \(-0.482506\pi\)
0.0549321 + 0.998490i \(0.482506\pi\)
\(308\) −51.5276 −2.93606
\(309\) −44.1836 −2.51352
\(310\) 56.7312 3.22212
\(311\) −4.08616 −0.231705 −0.115852 0.993266i \(-0.536960\pi\)
−0.115852 + 0.993266i \(0.536960\pi\)
\(312\) −62.4569 −3.53593
\(313\) 0.436524 0.0246738 0.0123369 0.999924i \(-0.496073\pi\)
0.0123369 + 0.999924i \(0.496073\pi\)
\(314\) 44.4261 2.50711
\(315\) −58.9768 −3.32297
\(316\) −7.07725 −0.398126
\(317\) 14.5111 0.815025 0.407513 0.913200i \(-0.366396\pi\)
0.407513 + 0.913200i \(0.366396\pi\)
\(318\) −6.94546 −0.389482
\(319\) −4.04217 −0.226318
\(320\) 40.2419 2.24959
\(321\) 26.1202 1.45789
\(322\) −7.81494 −0.435510
\(323\) 33.0474 1.83881
\(324\) −9.00811 −0.500451
\(325\) 59.8094 3.31763
\(326\) −31.3838 −1.73819
\(327\) 7.30990 0.404238
\(328\) −39.9454 −2.20561
\(329\) 22.4866 1.23972
\(330\) −111.618 −6.14435
\(331\) 15.4684 0.850221 0.425110 0.905141i \(-0.360235\pi\)
0.425110 + 0.905141i \(0.360235\pi\)
\(332\) 27.5910 1.51425
\(333\) 43.6724 2.39323
\(334\) 6.41341 0.350926
\(335\) −3.36703 −0.183961
\(336\) 26.1606 1.42718
\(337\) 18.6319 1.01495 0.507473 0.861668i \(-0.330580\pi\)
0.507473 + 0.861668i \(0.330580\pi\)
\(338\) −33.8823 −1.84295
\(339\) −18.4753 −1.00344
\(340\) −99.6722 −5.40548
\(341\) −24.1057 −1.30540
\(342\) −55.6296 −3.00810
\(343\) −11.3583 −0.613292
\(344\) 22.5500 1.21582
\(345\) −11.1112 −0.598205
\(346\) 18.7666 1.00890
\(347\) −30.0257 −1.61186 −0.805932 0.592008i \(-0.798335\pi\)
−0.805932 + 0.592008i \(0.798335\pi\)
\(348\) 10.1431 0.543729
\(349\) −1.00000 −0.0535288
\(350\) −89.8782 −4.80419
\(351\) 21.0801 1.12517
\(352\) −6.90728 −0.368159
\(353\) −4.94774 −0.263342 −0.131671 0.991293i \(-0.542034\pi\)
−0.131671 + 0.991293i \(0.542034\pi\)
\(354\) 16.8494 0.895538
\(355\) 46.6324 2.47499
\(356\) −51.8423 −2.74763
\(357\) 56.9152 3.01227
\(358\) 33.5046 1.77077
\(359\) −15.3734 −0.811378 −0.405689 0.914011i \(-0.632968\pi\)
−0.405689 + 0.914011i \(0.632968\pi\)
\(360\) 79.9374 4.21307
\(361\) 7.47036 0.393177
\(362\) −18.9159 −0.994199
\(363\) 17.3392 0.910071
\(364\) 64.3529 3.37301
\(365\) 40.7596 2.13346
\(366\) 81.1709 4.24287
\(367\) 0.276065 0.0144105 0.00720525 0.999974i \(-0.497706\pi\)
0.00720525 + 0.999974i \(0.497706\pi\)
\(368\) 2.95241 0.153905
\(369\) 40.7753 2.12268
\(370\) 95.4898 4.96428
\(371\) 3.40955 0.177015
\(372\) 60.4892 3.13622
\(373\) 17.8704 0.925295 0.462648 0.886542i \(-0.346900\pi\)
0.462648 + 0.886542i \(0.346900\pi\)
\(374\) 64.5255 3.33653
\(375\) −72.2317 −3.73003
\(376\) −30.4784 −1.57180
\(377\) 5.04828 0.259999
\(378\) −31.6780 −1.62934
\(379\) −19.8777 −1.02105 −0.510524 0.859864i \(-0.670549\pi\)
−0.510524 + 0.859864i \(0.670549\pi\)
\(380\) −79.8355 −4.09548
\(381\) −46.0506 −2.35924
\(382\) −5.89445 −0.301586
\(383\) −13.0261 −0.665603 −0.332801 0.942997i \(-0.607994\pi\)
−0.332801 + 0.942997i \(0.607994\pi\)
\(384\) 56.2976 2.87293
\(385\) 54.7935 2.79254
\(386\) 33.1831 1.68897
\(387\) −23.0186 −1.17010
\(388\) 68.4074 3.47286
\(389\) −5.98493 −0.303448 −0.151724 0.988423i \(-0.548482\pi\)
−0.151724 + 0.988423i \(0.548482\pi\)
\(390\) 139.400 7.05877
\(391\) 6.42329 0.324840
\(392\) −15.3397 −0.774773
\(393\) −8.59197 −0.433407
\(394\) −23.8320 −1.20064
\(395\) 7.52582 0.378665
\(396\) −71.2919 −3.58255
\(397\) −0.0600055 −0.00301159 −0.00150580 0.999999i \(-0.500479\pi\)
−0.00150580 + 0.999999i \(0.500479\pi\)
\(398\) 48.1683 2.41446
\(399\) 45.5880 2.28225
\(400\) 33.9551 1.69776
\(401\) 15.1341 0.755762 0.377881 0.925854i \(-0.376653\pi\)
0.377881 + 0.925854i \(0.376653\pi\)
\(402\) −5.46969 −0.272803
\(403\) 30.1057 1.49967
\(404\) 71.4453 3.55454
\(405\) 9.57906 0.475988
\(406\) −7.58627 −0.376500
\(407\) −40.5746 −2.01121
\(408\) −77.1432 −3.81916
\(409\) 1.63048 0.0806221 0.0403111 0.999187i \(-0.487165\pi\)
0.0403111 + 0.999187i \(0.487165\pi\)
\(410\) 89.1553 4.40307
\(411\) −62.7371 −3.09459
\(412\) −61.7047 −3.03997
\(413\) −8.27145 −0.407011
\(414\) −10.8125 −0.531405
\(415\) −29.3397 −1.44023
\(416\) 8.62651 0.422950
\(417\) 25.8441 1.26559
\(418\) 51.6837 2.52793
\(419\) −28.8894 −1.41134 −0.705669 0.708542i \(-0.749353\pi\)
−0.705669 + 0.708542i \(0.749353\pi\)
\(420\) −137.495 −6.70907
\(421\) −18.5307 −0.903133 −0.451567 0.892237i \(-0.649135\pi\)
−0.451567 + 0.892237i \(0.649135\pi\)
\(422\) −42.4079 −2.06439
\(423\) 31.1117 1.51270
\(424\) −4.62132 −0.224431
\(425\) 73.8731 3.58337
\(426\) 75.7536 3.67028
\(427\) −39.8470 −1.92833
\(428\) 36.4782 1.76324
\(429\) −59.2324 −2.85977
\(430\) −50.3302 −2.42714
\(431\) −17.5469 −0.845206 −0.422603 0.906315i \(-0.638883\pi\)
−0.422603 + 0.906315i \(0.638883\pi\)
\(432\) 11.9676 0.575793
\(433\) −9.79065 −0.470508 −0.235254 0.971934i \(-0.575592\pi\)
−0.235254 + 0.971934i \(0.575592\pi\)
\(434\) −45.2411 −2.17164
\(435\) −10.7860 −0.517151
\(436\) 10.2086 0.488906
\(437\) 5.14494 0.246116
\(438\) 66.2133 3.16380
\(439\) 40.0509 1.91152 0.955762 0.294141i \(-0.0950336\pi\)
0.955762 + 0.294141i \(0.0950336\pi\)
\(440\) −74.2674 −3.54056
\(441\) 15.6584 0.745640
\(442\) −80.5860 −3.83309
\(443\) −31.1380 −1.47941 −0.739706 0.672930i \(-0.765036\pi\)
−0.739706 + 0.672930i \(0.765036\pi\)
\(444\) 101.815 4.83193
\(445\) 55.1281 2.61332
\(446\) 30.0337 1.42214
\(447\) 56.6138 2.67774
\(448\) −32.0915 −1.51618
\(449\) 21.4661 1.01305 0.506523 0.862226i \(-0.330930\pi\)
0.506523 + 0.862226i \(0.330930\pi\)
\(450\) −124.353 −5.86203
\(451\) −37.8831 −1.78384
\(452\) −25.8017 −1.21361
\(453\) 9.40300 0.441791
\(454\) −39.2421 −1.84172
\(455\) −68.4317 −3.20813
\(456\) −61.7902 −2.89359
\(457\) 15.4413 0.722315 0.361157 0.932505i \(-0.382382\pi\)
0.361157 + 0.932505i \(0.382382\pi\)
\(458\) 10.8059 0.504925
\(459\) 26.0369 1.21530
\(460\) −15.5173 −0.723498
\(461\) 33.5834 1.56413 0.782066 0.623195i \(-0.214166\pi\)
0.782066 + 0.623195i \(0.214166\pi\)
\(462\) 89.0112 4.14117
\(463\) 0.0989485 0.00459853 0.00229926 0.999997i \(-0.499268\pi\)
0.00229926 + 0.999997i \(0.499268\pi\)
\(464\) 2.86602 0.133051
\(465\) −64.3231 −2.98291
\(466\) −22.6188 −1.04780
\(467\) 36.6133 1.69426 0.847131 0.531384i \(-0.178328\pi\)
0.847131 + 0.531384i \(0.178328\pi\)
\(468\) 89.0366 4.11572
\(469\) 2.68509 0.123986
\(470\) 68.0258 3.13779
\(471\) −50.3713 −2.32099
\(472\) 11.2112 0.516036
\(473\) 21.3858 0.983322
\(474\) 12.2256 0.561539
\(475\) 59.1710 2.71495
\(476\) 79.4850 3.64319
\(477\) 4.71734 0.215992
\(478\) −54.5155 −2.49348
\(479\) 14.1938 0.648533 0.324267 0.945966i \(-0.394882\pi\)
0.324267 + 0.945966i \(0.394882\pi\)
\(480\) −18.4312 −0.841266
\(481\) 50.6738 2.31052
\(482\) −14.2434 −0.648769
\(483\) 8.86075 0.403178
\(484\) 24.2151 1.10068
\(485\) −72.7432 −3.30310
\(486\) 44.8980 2.03661
\(487\) −33.9233 −1.53721 −0.768605 0.639723i \(-0.779049\pi\)
−0.768605 + 0.639723i \(0.779049\pi\)
\(488\) 54.0089 2.44487
\(489\) 35.5837 1.60915
\(490\) 34.2372 1.54668
\(491\) −10.5001 −0.473862 −0.236931 0.971526i \(-0.576142\pi\)
−0.236931 + 0.971526i \(0.576142\pi\)
\(492\) 95.0612 4.28569
\(493\) 6.23534 0.280825
\(494\) −64.5479 −2.90415
\(495\) 75.8105 3.40743
\(496\) 17.0917 0.767438
\(497\) −37.1877 −1.66810
\(498\) −47.6619 −2.13578
\(499\) 4.94415 0.221331 0.110665 0.993858i \(-0.464702\pi\)
0.110665 + 0.993858i \(0.464702\pi\)
\(500\) −100.875 −4.51128
\(501\) −7.27167 −0.324874
\(502\) 39.0992 1.74508
\(503\) −3.26214 −0.145452 −0.0727259 0.997352i \(-0.523170\pi\)
−0.0727259 + 0.997352i \(0.523170\pi\)
\(504\) −63.7473 −2.83953
\(505\) −75.9737 −3.38078
\(506\) 10.0456 0.446579
\(507\) 38.4165 1.70614
\(508\) −64.3120 −2.85338
\(509\) 41.5852 1.84323 0.921615 0.388105i \(-0.126870\pi\)
0.921615 + 0.388105i \(0.126870\pi\)
\(510\) 172.178 7.62418
\(511\) −32.5043 −1.43791
\(512\) 30.8237 1.36223
\(513\) 20.8551 0.920774
\(514\) −44.7093 −1.97204
\(515\) 65.6157 2.89137
\(516\) −53.6641 −2.36243
\(517\) −28.9049 −1.27124
\(518\) −76.1497 −3.34583
\(519\) −21.2780 −0.934000
\(520\) 92.7527 4.06748
\(521\) 16.1396 0.707090 0.353545 0.935418i \(-0.384976\pi\)
0.353545 + 0.935418i \(0.384976\pi\)
\(522\) −10.4961 −0.459402
\(523\) −17.0067 −0.743653 −0.371827 0.928302i \(-0.621268\pi\)
−0.371827 + 0.928302i \(0.621268\pi\)
\(524\) −11.9991 −0.524184
\(525\) 101.906 4.44754
\(526\) 11.5996 0.505768
\(527\) 37.1848 1.61980
\(528\) −33.6275 −1.46345
\(529\) 1.00000 0.0434783
\(530\) 10.3145 0.448032
\(531\) −11.4441 −0.496632
\(532\) 63.6660 2.76027
\(533\) 47.3123 2.04932
\(534\) 89.5547 3.87541
\(535\) −38.7903 −1.67705
\(536\) −3.63938 −0.157197
\(537\) −37.9883 −1.63932
\(538\) 14.1530 0.610179
\(539\) −14.5478 −0.626617
\(540\) −62.8996 −2.70677
\(541\) 39.2315 1.68670 0.843348 0.537368i \(-0.180581\pi\)
0.843348 + 0.537368i \(0.180581\pi\)
\(542\) −53.3554 −2.29181
\(543\) 21.4473 0.920391
\(544\) 10.6550 0.456828
\(545\) −10.8557 −0.465007
\(546\) −111.166 −4.75748
\(547\) 26.3033 1.12465 0.562325 0.826916i \(-0.309907\pi\)
0.562325 + 0.826916i \(0.309907\pi\)
\(548\) −87.6155 −3.74275
\(549\) −55.1310 −2.35294
\(550\) 115.532 4.92630
\(551\) 4.99439 0.212768
\(552\) −12.0099 −0.511176
\(553\) −6.00157 −0.255213
\(554\) 9.34959 0.397226
\(555\) −108.268 −4.59574
\(556\) 36.0926 1.53067
\(557\) −38.6045 −1.63572 −0.817862 0.575415i \(-0.804841\pi\)
−0.817862 + 0.575415i \(0.804841\pi\)
\(558\) −62.5941 −2.64982
\(559\) −26.7088 −1.12966
\(560\) −38.8502 −1.64172
\(561\) −73.1605 −3.08884
\(562\) −48.7818 −2.05774
\(563\) −14.9804 −0.631350 −0.315675 0.948867i \(-0.602231\pi\)
−0.315675 + 0.948867i \(0.602231\pi\)
\(564\) 72.5319 3.05414
\(565\) 27.4371 1.15429
\(566\) −23.7240 −0.997194
\(567\) −7.63896 −0.320806
\(568\) 50.4044 2.11492
\(569\) 4.10009 0.171885 0.0859424 0.996300i \(-0.472610\pi\)
0.0859424 + 0.996300i \(0.472610\pi\)
\(570\) 137.912 5.77648
\(571\) −10.1251 −0.423724 −0.211862 0.977300i \(-0.567953\pi\)
−0.211862 + 0.977300i \(0.567953\pi\)
\(572\) −82.7211 −3.45874
\(573\) 6.68326 0.279197
\(574\) −71.0982 −2.96758
\(575\) 11.5008 0.479617
\(576\) −44.4007 −1.85003
\(577\) −31.0534 −1.29277 −0.646384 0.763012i \(-0.723720\pi\)
−0.646384 + 0.763012i \(0.723720\pi\)
\(578\) −58.5233 −2.43425
\(579\) −37.6237 −1.56359
\(580\) −15.0632 −0.625467
\(581\) 23.3974 0.970688
\(582\) −118.170 −4.89831
\(583\) −4.38274 −0.181514
\(584\) 44.0566 1.82307
\(585\) −94.6799 −3.91453
\(586\) −60.7083 −2.50784
\(587\) 19.4674 0.803505 0.401753 0.915748i \(-0.368401\pi\)
0.401753 + 0.915748i \(0.368401\pi\)
\(588\) 36.5052 1.50545
\(589\) 29.7843 1.22724
\(590\) −25.0226 −1.03016
\(591\) 27.0213 1.11151
\(592\) 28.7686 1.18238
\(593\) −21.4563 −0.881105 −0.440552 0.897727i \(-0.645217\pi\)
−0.440552 + 0.897727i \(0.645217\pi\)
\(594\) 40.7198 1.67075
\(595\) −84.5229 −3.46510
\(596\) 79.0641 3.23859
\(597\) −54.6143 −2.23521
\(598\) −12.5459 −0.513040
\(599\) 8.74498 0.357310 0.178655 0.983912i \(-0.442825\pi\)
0.178655 + 0.983912i \(0.442825\pi\)
\(600\) −138.124 −5.63888
\(601\) −29.4972 −1.20322 −0.601608 0.798792i \(-0.705473\pi\)
−0.601608 + 0.798792i \(0.705473\pi\)
\(602\) 40.1365 1.63584
\(603\) 3.71500 0.151286
\(604\) 13.1318 0.534324
\(605\) −25.7499 −1.04688
\(606\) −123.418 −5.01351
\(607\) −32.1118 −1.30338 −0.651690 0.758486i \(-0.725940\pi\)
−0.651690 + 0.758486i \(0.725940\pi\)
\(608\) 8.53443 0.346117
\(609\) 8.60148 0.348549
\(610\) −120.544 −4.88069
\(611\) 36.0994 1.46042
\(612\) 109.973 4.44539
\(613\) −7.54526 −0.304750 −0.152375 0.988323i \(-0.548692\pi\)
−0.152375 + 0.988323i \(0.548692\pi\)
\(614\) −4.64394 −0.187414
\(615\) −101.086 −4.07619
\(616\) 59.2256 2.38627
\(617\) −19.9929 −0.804883 −0.402441 0.915446i \(-0.631838\pi\)
−0.402441 + 0.915446i \(0.631838\pi\)
\(618\) 106.592 4.28774
\(619\) −34.5889 −1.39024 −0.695122 0.718892i \(-0.744650\pi\)
−0.695122 + 0.718892i \(0.744650\pi\)
\(620\) −89.8306 −3.60768
\(621\) 4.05351 0.162662
\(622\) 9.85773 0.395259
\(623\) −43.9627 −1.76133
\(624\) 41.9975 1.68125
\(625\) 49.7648 1.99059
\(626\) −1.05310 −0.0420903
\(627\) −58.6002 −2.34026
\(628\) −70.3461 −2.80711
\(629\) 62.5893 2.49560
\(630\) 142.280 5.66856
\(631\) −23.3604 −0.929963 −0.464981 0.885320i \(-0.653939\pi\)
−0.464981 + 0.885320i \(0.653939\pi\)
\(632\) 8.13456 0.323576
\(633\) 48.0831 1.91113
\(634\) −35.0076 −1.39033
\(635\) 68.3882 2.71390
\(636\) 10.9977 0.436089
\(637\) 18.1688 0.719872
\(638\) 9.75161 0.386070
\(639\) −51.4517 −2.03540
\(640\) −83.6057 −3.30481
\(641\) −24.8137 −0.980082 −0.490041 0.871699i \(-0.663018\pi\)
−0.490041 + 0.871699i \(0.663018\pi\)
\(642\) −63.0141 −2.48697
\(643\) −15.8611 −0.625500 −0.312750 0.949835i \(-0.601250\pi\)
−0.312750 + 0.949835i \(0.601250\pi\)
\(644\) 12.3745 0.487624
\(645\) 57.0655 2.24695
\(646\) −79.7258 −3.13677
\(647\) 37.7695 1.48487 0.742437 0.669916i \(-0.233670\pi\)
0.742437 + 0.669916i \(0.233670\pi\)
\(648\) 10.3539 0.406739
\(649\) 10.6324 0.417357
\(650\) −144.288 −5.65945
\(651\) 51.2954 2.01043
\(652\) 49.6944 1.94618
\(653\) −26.0114 −1.01790 −0.508952 0.860795i \(-0.669967\pi\)
−0.508952 + 0.860795i \(0.669967\pi\)
\(654\) −17.6349 −0.689579
\(655\) 12.7597 0.498561
\(656\) 26.8602 1.04871
\(657\) −44.9719 −1.75452
\(658\) −54.2481 −2.11481
\(659\) −25.4702 −0.992180 −0.496090 0.868271i \(-0.665231\pi\)
−0.496090 + 0.868271i \(0.665231\pi\)
\(660\) 176.740 6.87960
\(661\) 8.78925 0.341862 0.170931 0.985283i \(-0.445322\pi\)
0.170931 + 0.985283i \(0.445322\pi\)
\(662\) −37.3170 −1.45037
\(663\) 91.3703 3.54853
\(664\) −31.7130 −1.23070
\(665\) −67.7013 −2.62534
\(666\) −105.358 −4.08255
\(667\) 0.970739 0.0375872
\(668\) −10.1553 −0.392919
\(669\) −34.0529 −1.31656
\(670\) 8.12286 0.313813
\(671\) 51.2206 1.97735
\(672\) 14.6982 0.566997
\(673\) −10.3021 −0.397118 −0.198559 0.980089i \(-0.563626\pi\)
−0.198559 + 0.980089i \(0.563626\pi\)
\(674\) −44.9489 −1.73137
\(675\) 46.6187 1.79436
\(676\) 53.6506 2.06348
\(677\) −16.9300 −0.650673 −0.325336 0.945598i \(-0.605478\pi\)
−0.325336 + 0.945598i \(0.605478\pi\)
\(678\) 44.5711 1.71174
\(679\) 58.0101 2.22623
\(680\) 114.563 4.39328
\(681\) 44.4935 1.70500
\(682\) 58.1543 2.22684
\(683\) −5.38235 −0.205950 −0.102975 0.994684i \(-0.532836\pi\)
−0.102975 + 0.994684i \(0.532836\pi\)
\(684\) 88.0862 3.36806
\(685\) 93.1688 3.55980
\(686\) 27.4016 1.04620
\(687\) −12.2519 −0.467441
\(688\) −15.1632 −0.578091
\(689\) 5.47361 0.208528
\(690\) 26.8053 1.02046
\(691\) 3.22259 0.122593 0.0612965 0.998120i \(-0.480476\pi\)
0.0612965 + 0.998120i \(0.480476\pi\)
\(692\) −29.7158 −1.12963
\(693\) −60.4562 −2.29654
\(694\) 72.4360 2.74963
\(695\) −38.3802 −1.45584
\(696\) −11.6585 −0.441914
\(697\) 58.4374 2.21347
\(698\) 2.41247 0.0913133
\(699\) 25.6457 0.970010
\(700\) 142.317 5.37907
\(701\) 6.50385 0.245647 0.122824 0.992429i \(-0.460805\pi\)
0.122824 + 0.992429i \(0.460805\pi\)
\(702\) −50.8550 −1.91940
\(703\) 50.1328 1.89080
\(704\) 41.2513 1.55472
\(705\) −77.1291 −2.90485
\(706\) 11.9363 0.449227
\(707\) 60.5863 2.27858
\(708\) −26.6801 −1.00270
\(709\) 7.58839 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(710\) −112.499 −4.22202
\(711\) −8.30358 −0.311409
\(712\) 59.5873 2.23313
\(713\) 5.78906 0.216802
\(714\) −137.306 −5.13855
\(715\) 87.9642 3.28967
\(716\) −53.0526 −1.98267
\(717\) 61.8109 2.30837
\(718\) 37.0879 1.38411
\(719\) 6.98428 0.260470 0.130235 0.991483i \(-0.458427\pi\)
0.130235 + 0.991483i \(0.458427\pi\)
\(720\) −53.7518 −2.00321
\(721\) −52.3262 −1.94873
\(722\) −18.0220 −0.670709
\(723\) 16.1495 0.600606
\(724\) 29.9522 1.11317
\(725\) 11.1643 0.414631
\(726\) −41.8302 −1.55247
\(727\) −11.4897 −0.426130 −0.213065 0.977038i \(-0.568345\pi\)
−0.213065 + 0.977038i \(0.568345\pi\)
\(728\) −73.9670 −2.74140
\(729\) −43.8319 −1.62340
\(730\) −98.3313 −3.63940
\(731\) −32.9892 −1.22015
\(732\) −128.529 −4.75058
\(733\) 44.6480 1.64911 0.824556 0.565780i \(-0.191425\pi\)
0.824556 + 0.565780i \(0.191425\pi\)
\(734\) −0.665999 −0.0245825
\(735\) −38.8189 −1.43186
\(736\) 1.65880 0.0611443
\(737\) −3.45149 −0.127137
\(738\) −98.3691 −3.62102
\(739\) −43.3474 −1.59456 −0.797280 0.603610i \(-0.793729\pi\)
−0.797280 + 0.603610i \(0.793729\pi\)
\(740\) −151.202 −5.55831
\(741\) 73.1859 2.68855
\(742\) −8.22543 −0.301965
\(743\) −16.1598 −0.592847 −0.296424 0.955057i \(-0.595794\pi\)
−0.296424 + 0.955057i \(0.595794\pi\)
\(744\) −69.5261 −2.54895
\(745\) −84.0754 −3.08028
\(746\) −43.1118 −1.57844
\(747\) 32.3719 1.18442
\(748\) −102.172 −3.73579
\(749\) 30.9339 1.13030
\(750\) 174.257 6.36295
\(751\) −3.80297 −0.138772 −0.0693862 0.997590i \(-0.522104\pi\)
−0.0693862 + 0.997590i \(0.522104\pi\)
\(752\) 20.4944 0.747354
\(753\) −44.3315 −1.61553
\(754\) −12.1788 −0.443526
\(755\) −13.9641 −0.508205
\(756\) 50.1602 1.82431
\(757\) −43.6685 −1.58716 −0.793579 0.608467i \(-0.791785\pi\)
−0.793579 + 0.608467i \(0.791785\pi\)
\(758\) 47.9543 1.74178
\(759\) −11.3899 −0.413426
\(760\) 91.7626 3.32858
\(761\) −11.3502 −0.411445 −0.205722 0.978610i \(-0.565954\pi\)
−0.205722 + 0.978610i \(0.565954\pi\)
\(762\) 111.095 4.02457
\(763\) 8.65703 0.313405
\(764\) 9.33351 0.337675
\(765\) −116.943 −4.22809
\(766\) 31.4251 1.13543
\(767\) −13.2788 −0.479469
\(768\) −81.6208 −2.94524
\(769\) −37.3619 −1.34730 −0.673652 0.739049i \(-0.735275\pi\)
−0.673652 + 0.739049i \(0.735275\pi\)
\(770\) −132.188 −4.76371
\(771\) 50.6924 1.82564
\(772\) −52.5434 −1.89108
\(773\) −36.1849 −1.30148 −0.650740 0.759301i \(-0.725541\pi\)
−0.650740 + 0.759301i \(0.725541\pi\)
\(774\) 55.5316 1.99604
\(775\) 66.5789 2.39159
\(776\) −78.6272 −2.82255
\(777\) 86.3402 3.09744
\(778\) 14.4384 0.517643
\(779\) 46.8072 1.67704
\(780\) −220.731 −7.90344
\(781\) 47.8022 1.71050
\(782\) −15.4960 −0.554135
\(783\) 3.93490 0.140622
\(784\) 10.3148 0.368386
\(785\) 74.8047 2.66990
\(786\) 20.7278 0.739338
\(787\) 28.7584 1.02513 0.512564 0.858649i \(-0.328696\pi\)
0.512564 + 0.858649i \(0.328696\pi\)
\(788\) 37.7366 1.34431
\(789\) −13.1519 −0.468220
\(790\) −18.1558 −0.645954
\(791\) −21.8801 −0.777967
\(792\) 81.9426 2.91170
\(793\) −63.9695 −2.27162
\(794\) 0.144761 0.00513739
\(795\) −11.6948 −0.414772
\(796\) −76.2717 −2.70338
\(797\) 8.20781 0.290736 0.145368 0.989378i \(-0.453563\pi\)
0.145368 + 0.989378i \(0.453563\pi\)
\(798\) −109.980 −3.89324
\(799\) 44.5879 1.57741
\(800\) 19.0776 0.674495
\(801\) −60.8254 −2.14916
\(802\) −36.5106 −1.28923
\(803\) 41.7820 1.47446
\(804\) 8.66093 0.305447
\(805\) −13.1588 −0.463787
\(806\) −72.6290 −2.55825
\(807\) −16.0470 −0.564880
\(808\) −82.1190 −2.88894
\(809\) 25.1631 0.884686 0.442343 0.896846i \(-0.354147\pi\)
0.442343 + 0.896846i \(0.354147\pi\)
\(810\) −23.1092 −0.811974
\(811\) −38.0882 −1.33746 −0.668729 0.743506i \(-0.733161\pi\)
−0.668729 + 0.743506i \(0.733161\pi\)
\(812\) 12.0124 0.421553
\(813\) 60.4956 2.12167
\(814\) 97.8850 3.43087
\(815\) −52.8442 −1.85105
\(816\) 51.8729 1.81591
\(817\) −26.4237 −0.924449
\(818\) −3.93348 −0.137531
\(819\) 75.5038 2.63832
\(820\) −141.172 −4.92995
\(821\) 39.2693 1.37051 0.685253 0.728305i \(-0.259691\pi\)
0.685253 + 0.728305i \(0.259691\pi\)
\(822\) 151.351 5.27898
\(823\) 21.9085 0.763683 0.381842 0.924228i \(-0.375290\pi\)
0.381842 + 0.924228i \(0.375290\pi\)
\(824\) 70.9232 2.47073
\(825\) −130.993 −4.56059
\(826\) 19.9546 0.694309
\(827\) −19.2256 −0.668540 −0.334270 0.942477i \(-0.608490\pi\)
−0.334270 + 0.942477i \(0.608490\pi\)
\(828\) 17.1209 0.594994
\(829\) −14.5104 −0.503966 −0.251983 0.967732i \(-0.581083\pi\)
−0.251983 + 0.967732i \(0.581083\pi\)
\(830\) 70.7812 2.45685
\(831\) −10.6008 −0.367737
\(832\) −51.5189 −1.78610
\(833\) 22.4410 0.777534
\(834\) −62.3480 −2.15893
\(835\) 10.7989 0.373712
\(836\) −81.8381 −2.83043
\(837\) 23.4660 0.811105
\(838\) 69.6946 2.40756
\(839\) 14.7684 0.509861 0.254931 0.966959i \(-0.417947\pi\)
0.254931 + 0.966959i \(0.417947\pi\)
\(840\) 158.036 5.45277
\(841\) −28.0577 −0.967506
\(842\) 44.7048 1.54063
\(843\) 55.3099 1.90497
\(844\) 67.1505 2.31141
\(845\) −57.0511 −1.96262
\(846\) −75.0559 −2.58048
\(847\) 20.5346 0.705577
\(848\) 3.10749 0.106712
\(849\) 26.8988 0.923164
\(850\) −178.217 −6.11278
\(851\) 9.74412 0.334024
\(852\) −119.951 −4.10947
\(853\) 40.0683 1.37191 0.685956 0.727643i \(-0.259384\pi\)
0.685956 + 0.727643i \(0.259384\pi\)
\(854\) 96.1297 3.28949
\(855\) −93.6692 −3.20342
\(856\) −41.9279 −1.43307
\(857\) 28.3928 0.969878 0.484939 0.874548i \(-0.338842\pi\)
0.484939 + 0.874548i \(0.338842\pi\)
\(858\) 142.896 4.87840
\(859\) 35.5608 1.21332 0.606660 0.794962i \(-0.292509\pi\)
0.606660 + 0.794962i \(0.292509\pi\)
\(860\) 79.6949 2.71757
\(861\) 80.6128 2.74728
\(862\) 42.3314 1.44181
\(863\) −0.379248 −0.0129098 −0.00645488 0.999979i \(-0.502055\pi\)
−0.00645488 + 0.999979i \(0.502055\pi\)
\(864\) 6.72398 0.228754
\(865\) 31.5992 1.07441
\(866\) 23.6196 0.802627
\(867\) 66.3550 2.25353
\(868\) 71.6367 2.43151
\(869\) 7.71460 0.261700
\(870\) 26.0210 0.882193
\(871\) 4.31057 0.146058
\(872\) −11.7338 −0.397356
\(873\) 80.2609 2.71642
\(874\) −12.4120 −0.419842
\(875\) −85.5431 −2.89189
\(876\) −104.845 −3.54238
\(877\) −5.02229 −0.169591 −0.0847953 0.996398i \(-0.527024\pi\)
−0.0847953 + 0.996398i \(0.527024\pi\)
\(878\) −96.6214 −3.26082
\(879\) 68.8324 2.32166
\(880\) 49.9392 1.68345
\(881\) 7.74970 0.261094 0.130547 0.991442i \(-0.458327\pi\)
0.130547 + 0.991442i \(0.458327\pi\)
\(882\) −37.7755 −1.27197
\(883\) 25.6396 0.862840 0.431420 0.902151i \(-0.358013\pi\)
0.431420 + 0.902151i \(0.358013\pi\)
\(884\) 127.603 4.29176
\(885\) 28.3711 0.953685
\(886\) 75.1195 2.52369
\(887\) 18.8918 0.634323 0.317161 0.948372i \(-0.397270\pi\)
0.317161 + 0.948372i \(0.397270\pi\)
\(888\) −117.026 −3.92713
\(889\) −54.5372 −1.82912
\(890\) −132.995 −4.45800
\(891\) 9.81935 0.328960
\(892\) −47.5566 −1.59231
\(893\) 35.7140 1.19512
\(894\) −136.579 −4.56789
\(895\) 56.4152 1.88575
\(896\) 66.6726 2.22738
\(897\) 14.2248 0.474953
\(898\) −51.7862 −1.72813
\(899\) 5.61966 0.187426
\(900\) 196.905 6.56350
\(901\) 6.76069 0.225231
\(902\) 91.3917 3.04301
\(903\) −45.5077 −1.51440
\(904\) 29.6564 0.986357
\(905\) −31.8507 −1.05875
\(906\) −22.6844 −0.753640
\(907\) −20.9153 −0.694481 −0.347240 0.937776i \(-0.612881\pi\)
−0.347240 + 0.937776i \(0.612881\pi\)
\(908\) 62.1375 2.06211
\(909\) 83.8252 2.78031
\(910\) 165.089 5.47266
\(911\) 9.89733 0.327913 0.163957 0.986468i \(-0.447574\pi\)
0.163957 + 0.986468i \(0.447574\pi\)
\(912\) 41.5492 1.37583
\(913\) −30.0757 −0.995360
\(914\) −37.2517 −1.23218
\(915\) 136.676 4.51836
\(916\) −17.1105 −0.565345
\(917\) −10.1754 −0.336020
\(918\) −62.8132 −2.07314
\(919\) 27.4954 0.906991 0.453495 0.891259i \(-0.350177\pi\)
0.453495 + 0.891259i \(0.350177\pi\)
\(920\) 17.8355 0.588020
\(921\) 5.26541 0.173501
\(922\) −81.0188 −2.66821
\(923\) −59.7002 −1.96506
\(924\) −140.944 −4.63672
\(925\) 112.065 3.68469
\(926\) −0.238710 −0.00784450
\(927\) −72.3968 −2.37782
\(928\) 1.61026 0.0528595
\(929\) −7.73922 −0.253916 −0.126958 0.991908i \(-0.540521\pi\)
−0.126958 + 0.991908i \(0.540521\pi\)
\(930\) 155.178 5.08847
\(931\) 17.9748 0.589101
\(932\) 35.8156 1.17318
\(933\) −11.1769 −0.365916
\(934\) −88.3285 −2.89020
\(935\) 108.648 3.55318
\(936\) −102.338 −3.34503
\(937\) 36.4677 1.19135 0.595674 0.803227i \(-0.296885\pi\)
0.595674 + 0.803227i \(0.296885\pi\)
\(938\) −6.47769 −0.211504
\(939\) 1.19403 0.0389656
\(940\) −107.715 −3.51327
\(941\) −22.1743 −0.722863 −0.361431 0.932399i \(-0.617712\pi\)
−0.361431 + 0.932399i \(0.617712\pi\)
\(942\) 121.519 3.95931
\(943\) 9.09773 0.296263
\(944\) −7.53865 −0.245362
\(945\) −53.3395 −1.73513
\(946\) −51.5926 −1.67742
\(947\) −24.9134 −0.809578 −0.404789 0.914410i \(-0.632655\pi\)
−0.404789 + 0.914410i \(0.632655\pi\)
\(948\) −19.3585 −0.628734
\(949\) −52.1817 −1.69389
\(950\) −142.748 −4.63136
\(951\) 39.6924 1.28711
\(952\) −91.3598 −2.96099
\(953\) −13.7168 −0.444332 −0.222166 0.975009i \(-0.571313\pi\)
−0.222166 + 0.975009i \(0.571313\pi\)
\(954\) −11.3804 −0.368455
\(955\) −9.92509 −0.321168
\(956\) 86.3221 2.79186
\(957\) −11.0566 −0.357409
\(958\) −34.2422 −1.10632
\(959\) −74.2988 −2.39923
\(960\) 110.074 3.55262
\(961\) 2.51320 0.0810710
\(962\) −122.249 −3.94146
\(963\) 42.7991 1.37918
\(964\) 22.5536 0.726402
\(965\) 55.8737 1.79864
\(966\) −21.3763 −0.687771
\(967\) 33.8644 1.08900 0.544502 0.838759i \(-0.316719\pi\)
0.544502 + 0.838759i \(0.316719\pi\)
\(968\) −27.8327 −0.894577
\(969\) 90.3949 2.90390
\(970\) 175.491 5.63467
\(971\) 28.6287 0.918738 0.459369 0.888246i \(-0.348076\pi\)
0.459369 + 0.888246i \(0.348076\pi\)
\(972\) −71.0933 −2.28032
\(973\) 30.6068 0.981210
\(974\) 81.8388 2.62228
\(975\) 163.597 5.23931
\(976\) −36.3169 −1.16247
\(977\) −47.2993 −1.51324 −0.756620 0.653855i \(-0.773150\pi\)
−0.756620 + 0.653855i \(0.773150\pi\)
\(978\) −85.8445 −2.74500
\(979\) 56.5110 1.80610
\(980\) −54.2127 −1.73176
\(981\) 11.9776 0.382415
\(982\) 25.3311 0.808349
\(983\) −6.00170 −0.191425 −0.0957123 0.995409i \(-0.530513\pi\)
−0.0957123 + 0.995409i \(0.530513\pi\)
\(984\) −109.263 −3.48318
\(985\) −40.1284 −1.27860
\(986\) −15.0426 −0.479052
\(987\) 61.5077 1.95781
\(988\) 102.208 3.25166
\(989\) −5.13587 −0.163311
\(990\) −182.890 −5.81264
\(991\) 19.3602 0.614998 0.307499 0.951548i \(-0.400508\pi\)
0.307499 + 0.951548i \(0.400508\pi\)
\(992\) 9.60290 0.304893
\(993\) 42.3109 1.34270
\(994\) 89.7142 2.84556
\(995\) 81.1059 2.57123
\(996\) 75.4699 2.39135
\(997\) 59.2428 1.87624 0.938119 0.346312i \(-0.112566\pi\)
0.938119 + 0.346312i \(0.112566\pi\)
\(998\) −11.9276 −0.377562
\(999\) 39.4979 1.24966
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 \(a_p\))