Properties

Label 4003.2.a.a.1.2
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\)
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} +1.41421 q^{3} +1.41421 q^{5} +2.00000 q^{6} -1.00000 q^{7} -2.82843 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +1.41421 q^{3} +1.41421 q^{5} +2.00000 q^{6} -1.00000 q^{7} -2.82843 q^{8} -1.00000 q^{9} +2.00000 q^{10} -4.82843 q^{11} +6.82843 q^{13} -1.41421 q^{14} +2.00000 q^{15} -4.00000 q^{16} -6.65685 q^{17} -1.41421 q^{18} +6.65685 q^{19} -1.41421 q^{21} -6.82843 q^{22} -3.17157 q^{23} -4.00000 q^{24} -3.00000 q^{25} +9.65685 q^{26} -5.65685 q^{27} -6.82843 q^{29} +2.82843 q^{30} -6.48528 q^{31} -6.82843 q^{33} -9.41421 q^{34} -1.41421 q^{35} -9.82843 q^{37} +9.41421 q^{38} +9.65685 q^{39} -4.00000 q^{40} +10.8284 q^{41} -2.00000 q^{42} -1.41421 q^{45} -4.48528 q^{46} +11.0711 q^{47} -5.65685 q^{48} -6.00000 q^{49} -4.24264 q^{50} -9.41421 q^{51} -13.3137 q^{53} -8.00000 q^{54} -6.82843 q^{55} +2.82843 q^{56} +9.41421 q^{57} -9.65685 q^{58} -3.17157 q^{59} +12.8284 q^{61} -9.17157 q^{62} +1.00000 q^{63} +8.00000 q^{64} +9.65685 q^{65} -9.65685 q^{66} +1.34315 q^{67} -4.48528 q^{69} -2.00000 q^{70} +6.00000 q^{71} +2.82843 q^{72} -3.00000 q^{73} -13.8995 q^{74} -4.24264 q^{75} +4.82843 q^{77} +13.6569 q^{78} -5.48528 q^{79} -5.65685 q^{80} -5.00000 q^{81} +15.3137 q^{82} -11.1421 q^{83} -9.41421 q^{85} -9.65685 q^{87} +13.6569 q^{88} -6.17157 q^{89} -2.00000 q^{90} -6.82843 q^{91} -9.17157 q^{93} +15.6569 q^{94} +9.41421 q^{95} +10.2426 q^{97} -8.48528 q^{98} +4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 2q + 4q^{6} - 2q^{7} - 2q^{9} + 4q^{10} - 4q^{11} + 8q^{13} + 4q^{15} - 8q^{16} - 2q^{17} + 2q^{19} - 8q^{22} - 12q^{23} - 8q^{24} - 6q^{25} + 8q^{26} - 8q^{29} + 4q^{31} - 8q^{33} - 16q^{34} - 14q^{37} + 16q^{38} + 8q^{39} - 8q^{40} + 16q^{41} - 4q^{42} + 8q^{46} + 8q^{47} - 12q^{49} - 16q^{51} - 4q^{53} - 16q^{54} - 8q^{55} + 16q^{57} - 8q^{58} - 12q^{59} + 20q^{61} - 24q^{62} + 2q^{63} + 16q^{64} + 8q^{65} - 8q^{66} + 14q^{67} + 8q^{69} - 4q^{70} + 12q^{71} - 6q^{73} - 8q^{74} + 4q^{77} + 16q^{78} + 6q^{79} - 10q^{81} + 8q^{82} + 6q^{83} - 16q^{85} - 8q^{87} + 16q^{88} - 18q^{89} - 4q^{90} - 8q^{91} - 24q^{93} + 20q^{94} + 16q^{95} + 12q^{97} + 4q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) 1.41421 0.816497 0.408248 0.912871i \(-0.366140\pi\)
0.408248 + 0.912871i \(0.366140\pi\)
\(4\) 0 0
\(5\) 1.41421 0.632456 0.316228 0.948683i \(-0.397584\pi\)
0.316228 + 0.948683i \(0.397584\pi\)
\(6\) 2.00000 0.816497
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −2.82843 −1.00000
\(9\) −1.00000 −0.333333
\(10\) 2.00000 0.632456
\(11\) −4.82843 −1.45583 −0.727913 0.685670i \(-0.759509\pi\)
−0.727913 + 0.685670i \(0.759509\pi\)
\(12\) 0 0
\(13\) 6.82843 1.89386 0.946932 0.321433i \(-0.104164\pi\)
0.946932 + 0.321433i \(0.104164\pi\)
\(14\) −1.41421 −0.377964
\(15\) 2.00000 0.516398
\(16\) −4.00000 −1.00000
\(17\) −6.65685 −1.61452 −0.807262 0.590193i \(-0.799052\pi\)
−0.807262 + 0.590193i \(0.799052\pi\)
\(18\) −1.41421 −0.333333
\(19\) 6.65685 1.52719 0.763594 0.645697i \(-0.223433\pi\)
0.763594 + 0.645697i \(0.223433\pi\)
\(20\) 0 0
\(21\) −1.41421 −0.308607
\(22\) −6.82843 −1.45583
\(23\) −3.17157 −0.661319 −0.330659 0.943750i \(-0.607271\pi\)
−0.330659 + 0.943750i \(0.607271\pi\)
\(24\) −4.00000 −0.816497
\(25\) −3.00000 −0.600000
\(26\) 9.65685 1.89386
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) 2.82843 0.516398
\(31\) −6.48528 −1.16479 −0.582395 0.812906i \(-0.697884\pi\)
−0.582395 + 0.812906i \(0.697884\pi\)
\(32\) 0 0
\(33\) −6.82843 −1.18868
\(34\) −9.41421 −1.61452
\(35\) −1.41421 −0.239046
\(36\) 0 0
\(37\) −9.82843 −1.61578 −0.807892 0.589331i \(-0.799391\pi\)
−0.807892 + 0.589331i \(0.799391\pi\)
\(38\) 9.41421 1.52719
\(39\) 9.65685 1.54633
\(40\) −4.00000 −0.632456
\(41\) 10.8284 1.69112 0.845558 0.533883i \(-0.179268\pi\)
0.845558 + 0.533883i \(0.179268\pi\)
\(42\) −2.00000 −0.308607
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −1.41421 −0.210819
\(46\) −4.48528 −0.661319
\(47\) 11.0711 1.61488 0.807441 0.589949i \(-0.200852\pi\)
0.807441 + 0.589949i \(0.200852\pi\)
\(48\) −5.65685 −0.816497
\(49\) −6.00000 −0.857143
\(50\) −4.24264 −0.600000
\(51\) −9.41421 −1.31825
\(52\) 0 0
\(53\) −13.3137 −1.82878 −0.914389 0.404836i \(-0.867329\pi\)
−0.914389 + 0.404836i \(0.867329\pi\)
\(54\) −8.00000 −1.08866
\(55\) −6.82843 −0.920745
\(56\) 2.82843 0.377964
\(57\) 9.41421 1.24694
\(58\) −9.65685 −1.26801
\(59\) −3.17157 −0.412904 −0.206452 0.978457i \(-0.566192\pi\)
−0.206452 + 0.978457i \(0.566192\pi\)
\(60\) 0 0
\(61\) 12.8284 1.64251 0.821256 0.570560i \(-0.193274\pi\)
0.821256 + 0.570560i \(0.193274\pi\)
\(62\) −9.17157 −1.16479
\(63\) 1.00000 0.125988
\(64\) 8.00000 1.00000
\(65\) 9.65685 1.19779
\(66\) −9.65685 −1.18868
\(67\) 1.34315 0.164091 0.0820457 0.996629i \(-0.473855\pi\)
0.0820457 + 0.996629i \(0.473855\pi\)
\(68\) 0 0
\(69\) −4.48528 −0.539964
\(70\) −2.00000 −0.239046
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 2.82843 0.333333
\(73\) −3.00000 −0.351123 −0.175562 0.984468i \(-0.556174\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(74\) −13.8995 −1.61578
\(75\) −4.24264 −0.489898
\(76\) 0 0
\(77\) 4.82843 0.550250
\(78\) 13.6569 1.54633
\(79\) −5.48528 −0.617142 −0.308571 0.951201i \(-0.599851\pi\)
−0.308571 + 0.951201i \(0.599851\pi\)
\(80\) −5.65685 −0.632456
\(81\) −5.00000 −0.555556
\(82\) 15.3137 1.69112
\(83\) −11.1421 −1.22301 −0.611504 0.791241i \(-0.709435\pi\)
−0.611504 + 0.791241i \(0.709435\pi\)
\(84\) 0 0
\(85\) −9.41421 −1.02111
\(86\) 0 0
\(87\) −9.65685 −1.03532
\(88\) 13.6569 1.45583
\(89\) −6.17157 −0.654185 −0.327093 0.944992i \(-0.606069\pi\)
−0.327093 + 0.944992i \(0.606069\pi\)
\(90\) −2.00000 −0.210819
\(91\) −6.82843 −0.715814
\(92\) 0 0
\(93\) −9.17157 −0.951048
\(94\) 15.6569 1.61488
\(95\) 9.41421 0.965878
\(96\) 0 0
\(97\) 10.2426 1.03998 0.519991 0.854172i \(-0.325935\pi\)
0.519991 + 0.854172i \(0.325935\pi\)
\(98\) −8.48528 −0.857143
\(99\) 4.82843 0.485275
\(100\) 0 0
\(101\) 4.17157 0.415087 0.207544 0.978226i \(-0.433453\pi\)
0.207544 + 0.978226i \(0.433453\pi\)
\(102\) −13.3137 −1.31825
\(103\) 3.48528 0.343415 0.171707 0.985148i \(-0.445072\pi\)
0.171707 + 0.985148i \(0.445072\pi\)
\(104\) −19.3137 −1.89386
\(105\) −2.00000 −0.195180
\(106\) −18.8284 −1.82878
\(107\) −8.48528 −0.820303 −0.410152 0.912017i \(-0.634524\pi\)
−0.410152 + 0.912017i \(0.634524\pi\)
\(108\) 0 0
\(109\) 6.48528 0.621177 0.310589 0.950544i \(-0.399474\pi\)
0.310589 + 0.950544i \(0.399474\pi\)
\(110\) −9.65685 −0.920745
\(111\) −13.8995 −1.31928
\(112\) 4.00000 0.377964
\(113\) 0.928932 0.0873866 0.0436933 0.999045i \(-0.486088\pi\)
0.0436933 + 0.999045i \(0.486088\pi\)
\(114\) 13.3137 1.24694
\(115\) −4.48528 −0.418255
\(116\) 0 0
\(117\) −6.82843 −0.631288
\(118\) −4.48528 −0.412904
\(119\) 6.65685 0.610233
\(120\) −5.65685 −0.516398
\(121\) 12.3137 1.11943
\(122\) 18.1421 1.64251
\(123\) 15.3137 1.38079
\(124\) 0 0
\(125\) −11.3137 −1.01193
\(126\) 1.41421 0.125988
\(127\) −20.7990 −1.84561 −0.922806 0.385265i \(-0.874110\pi\)
−0.922806 + 0.385265i \(0.874110\pi\)
\(128\) 11.3137 1.00000
\(129\) 0 0
\(130\) 13.6569 1.19779
\(131\) 17.4853 1.52770 0.763848 0.645396i \(-0.223308\pi\)
0.763848 + 0.645396i \(0.223308\pi\)
\(132\) 0 0
\(133\) −6.65685 −0.577222
\(134\) 1.89949 0.164091
\(135\) −8.00000 −0.688530
\(136\) 18.8284 1.61452
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) −6.34315 −0.539964
\(139\) −15.6569 −1.32800 −0.663999 0.747734i \(-0.731142\pi\)
−0.663999 + 0.747734i \(0.731142\pi\)
\(140\) 0 0
\(141\) 15.6569 1.31854
\(142\) 8.48528 0.712069
\(143\) −32.9706 −2.75714
\(144\) 4.00000 0.333333
\(145\) −9.65685 −0.801958
\(146\) −4.24264 −0.351123
\(147\) −8.48528 −0.699854
\(148\) 0 0
\(149\) −21.1421 −1.73203 −0.866016 0.500017i \(-0.833327\pi\)
−0.866016 + 0.500017i \(0.833327\pi\)
\(150\) −6.00000 −0.489898
\(151\) −13.8284 −1.12534 −0.562671 0.826681i \(-0.690226\pi\)
−0.562671 + 0.826681i \(0.690226\pi\)
\(152\) −18.8284 −1.52719
\(153\) 6.65685 0.538175
\(154\) 6.82843 0.550250
\(155\) −9.17157 −0.736678
\(156\) 0 0
\(157\) 7.31371 0.583697 0.291849 0.956464i \(-0.405730\pi\)
0.291849 + 0.956464i \(0.405730\pi\)
\(158\) −7.75736 −0.617142
\(159\) −18.8284 −1.49319
\(160\) 0 0
\(161\) 3.17157 0.249955
\(162\) −7.07107 −0.555556
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 0 0
\(165\) −9.65685 −0.751785
\(166\) −15.7574 −1.22301
\(167\) −2.10051 −0.162542 −0.0812710 0.996692i \(-0.525898\pi\)
−0.0812710 + 0.996692i \(0.525898\pi\)
\(168\) 4.00000 0.308607
\(169\) 33.6274 2.58672
\(170\) −13.3137 −1.02111
\(171\) −6.65685 −0.509062
\(172\) 0 0
\(173\) −0.686292 −0.0521778 −0.0260889 0.999660i \(-0.508305\pi\)
−0.0260889 + 0.999660i \(0.508305\pi\)
\(174\) −13.6569 −1.03532
\(175\) 3.00000 0.226779
\(176\) 19.3137 1.45583
\(177\) −4.48528 −0.337134
\(178\) −8.72792 −0.654185
\(179\) −1.65685 −0.123839 −0.0619196 0.998081i \(-0.519722\pi\)
−0.0619196 + 0.998081i \(0.519722\pi\)
\(180\) 0 0
\(181\) 19.3137 1.43558 0.717788 0.696261i \(-0.245155\pi\)
0.717788 + 0.696261i \(0.245155\pi\)
\(182\) −9.65685 −0.715814
\(183\) 18.1421 1.34111
\(184\) 8.97056 0.661319
\(185\) −13.8995 −1.02191
\(186\) −12.9706 −0.951048
\(187\) 32.1421 2.35047
\(188\) 0 0
\(189\) 5.65685 0.411476
\(190\) 13.3137 0.965878
\(191\) 12.6569 0.915818 0.457909 0.888999i \(-0.348599\pi\)
0.457909 + 0.888999i \(0.348599\pi\)
\(192\) 11.3137 0.816497
\(193\) −12.3137 −0.886360 −0.443180 0.896433i \(-0.646150\pi\)
−0.443180 + 0.896433i \(0.646150\pi\)
\(194\) 14.4853 1.03998
\(195\) 13.6569 0.977988
\(196\) 0 0
\(197\) 8.65685 0.616775 0.308388 0.951261i \(-0.400211\pi\)
0.308388 + 0.951261i \(0.400211\pi\)
\(198\) 6.82843 0.485275
\(199\) 23.8995 1.69419 0.847095 0.531441i \(-0.178349\pi\)
0.847095 + 0.531441i \(0.178349\pi\)
\(200\) 8.48528 0.600000
\(201\) 1.89949 0.133980
\(202\) 5.89949 0.415087
\(203\) 6.82843 0.479262
\(204\) 0 0
\(205\) 15.3137 1.06956
\(206\) 4.92893 0.343415
\(207\) 3.17157 0.220440
\(208\) −27.3137 −1.89386
\(209\) −32.1421 −2.22332
\(210\) −2.82843 −0.195180
\(211\) −9.31371 −0.641182 −0.320591 0.947218i \(-0.603882\pi\)
−0.320591 + 0.947218i \(0.603882\pi\)
\(212\) 0 0
\(213\) 8.48528 0.581402
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) 16.0000 1.08866
\(217\) 6.48528 0.440250
\(218\) 9.17157 0.621177
\(219\) −4.24264 −0.286691
\(220\) 0 0
\(221\) −45.4558 −3.05769
\(222\) −19.6569 −1.31928
\(223\) 1.27208 0.0851846 0.0425923 0.999093i \(-0.486438\pi\)
0.0425923 + 0.999093i \(0.486438\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 1.31371 0.0873866
\(227\) −21.4142 −1.42131 −0.710656 0.703540i \(-0.751602\pi\)
−0.710656 + 0.703540i \(0.751602\pi\)
\(228\) 0 0
\(229\) 9.51472 0.628750 0.314375 0.949299i \(-0.398205\pi\)
0.314375 + 0.949299i \(0.398205\pi\)
\(230\) −6.34315 −0.418255
\(231\) 6.82843 0.449278
\(232\) 19.3137 1.26801
\(233\) −0.343146 −0.0224802 −0.0112401 0.999937i \(-0.503578\pi\)
−0.0112401 + 0.999937i \(0.503578\pi\)
\(234\) −9.65685 −0.631288
\(235\) 15.6569 1.02134
\(236\) 0 0
\(237\) −7.75736 −0.503895
\(238\) 9.41421 0.610233
\(239\) 8.65685 0.559965 0.279983 0.960005i \(-0.409671\pi\)
0.279983 + 0.960005i \(0.409671\pi\)
\(240\) −8.00000 −0.516398
\(241\) 11.4853 0.739832 0.369916 0.929065i \(-0.379386\pi\)
0.369916 + 0.929065i \(0.379386\pi\)
\(242\) 17.4142 1.11943
\(243\) 9.89949 0.635053
\(244\) 0 0
\(245\) −8.48528 −0.542105
\(246\) 21.6569 1.38079
\(247\) 45.4558 2.89229
\(248\) 18.3431 1.16479
\(249\) −15.7574 −0.998582
\(250\) −16.0000 −1.01193
\(251\) 2.48528 0.156870 0.0784348 0.996919i \(-0.475008\pi\)
0.0784348 + 0.996919i \(0.475008\pi\)
\(252\) 0 0
\(253\) 15.3137 0.962765
\(254\) −29.4142 −1.84561
\(255\) −13.3137 −0.833737
\(256\) 0 0
\(257\) −16.9706 −1.05859 −0.529297 0.848436i \(-0.677544\pi\)
−0.529297 + 0.848436i \(0.677544\pi\)
\(258\) 0 0
\(259\) 9.82843 0.610709
\(260\) 0 0
\(261\) 6.82843 0.422669
\(262\) 24.7279 1.52770
\(263\) 12.3137 0.759296 0.379648 0.925131i \(-0.376045\pi\)
0.379648 + 0.925131i \(0.376045\pi\)
\(264\) 19.3137 1.18868
\(265\) −18.8284 −1.15662
\(266\) −9.41421 −0.577222
\(267\) −8.72792 −0.534140
\(268\) 0 0
\(269\) −6.68629 −0.407670 −0.203835 0.979005i \(-0.565341\pi\)
−0.203835 + 0.979005i \(0.565341\pi\)
\(270\) −11.3137 −0.688530
\(271\) 17.3431 1.05352 0.526761 0.850014i \(-0.323406\pi\)
0.526761 + 0.850014i \(0.323406\pi\)
\(272\) 26.6274 1.61452
\(273\) −9.65685 −0.584459
\(274\) −4.24264 −0.256307
\(275\) 14.4853 0.873495
\(276\) 0 0
\(277\) −14.4853 −0.870336 −0.435168 0.900349i \(-0.643311\pi\)
−0.435168 + 0.900349i \(0.643311\pi\)
\(278\) −22.1421 −1.32800
\(279\) 6.48528 0.388264
\(280\) 4.00000 0.239046
\(281\) 4.17157 0.248855 0.124428 0.992229i \(-0.460291\pi\)
0.124428 + 0.992229i \(0.460291\pi\)
\(282\) 22.1421 1.31854
\(283\) −7.17157 −0.426306 −0.213153 0.977019i \(-0.568373\pi\)
−0.213153 + 0.977019i \(0.568373\pi\)
\(284\) 0 0
\(285\) 13.3137 0.788636
\(286\) −46.6274 −2.75714
\(287\) −10.8284 −0.639182
\(288\) 0 0
\(289\) 27.3137 1.60669
\(290\) −13.6569 −0.801958
\(291\) 14.4853 0.849142
\(292\) 0 0
\(293\) −31.3137 −1.82937 −0.914683 0.404172i \(-0.867560\pi\)
−0.914683 + 0.404172i \(0.867560\pi\)
\(294\) −12.0000 −0.699854
\(295\) −4.48528 −0.261143
\(296\) 27.7990 1.61578
\(297\) 27.3137 1.58490
\(298\) −29.8995 −1.73203
\(299\) −21.6569 −1.25245
\(300\) 0 0
\(301\) 0 0
\(302\) −19.5563 −1.12534
\(303\) 5.89949 0.338917
\(304\) −26.6274 −1.52719
\(305\) 18.1421 1.03882
\(306\) 9.41421 0.538175
\(307\) −2.68629 −0.153315 −0.0766574 0.997057i \(-0.524425\pi\)
−0.0766574 + 0.997057i \(0.524425\pi\)
\(308\) 0 0
\(309\) 4.92893 0.280397
\(310\) −12.9706 −0.736678
\(311\) 19.9706 1.13243 0.566213 0.824259i \(-0.308408\pi\)
0.566213 + 0.824259i \(0.308408\pi\)
\(312\) −27.3137 −1.54633
\(313\) −13.4853 −0.762233 −0.381117 0.924527i \(-0.624460\pi\)
−0.381117 + 0.924527i \(0.624460\pi\)
\(314\) 10.3431 0.583697
\(315\) 1.41421 0.0796819
\(316\) 0 0
\(317\) 10.2426 0.575284 0.287642 0.957738i \(-0.407129\pi\)
0.287642 + 0.957738i \(0.407129\pi\)
\(318\) −26.6274 −1.49319
\(319\) 32.9706 1.84600
\(320\) 11.3137 0.632456
\(321\) −12.0000 −0.669775
\(322\) 4.48528 0.249955
\(323\) −44.3137 −2.46568
\(324\) 0 0
\(325\) −20.4853 −1.13632
\(326\) −2.82843 −0.156652
\(327\) 9.17157 0.507189
\(328\) −30.6274 −1.69112
\(329\) −11.0711 −0.610368
\(330\) −13.6569 −0.751785
\(331\) 14.4853 0.796183 0.398092 0.917346i \(-0.369673\pi\)
0.398092 + 0.917346i \(0.369673\pi\)
\(332\) 0 0
\(333\) 9.82843 0.538594
\(334\) −2.97056 −0.162542
\(335\) 1.89949 0.103780
\(336\) 5.65685 0.308607
\(337\) 15.3137 0.834191 0.417095 0.908863i \(-0.363048\pi\)
0.417095 + 0.908863i \(0.363048\pi\)
\(338\) 47.5563 2.58672
\(339\) 1.31371 0.0713509
\(340\) 0 0
\(341\) 31.3137 1.69573
\(342\) −9.41421 −0.509062
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) −6.34315 −0.341503
\(346\) −0.970563 −0.0521778
\(347\) 31.2843 1.67943 0.839714 0.543029i \(-0.182723\pi\)
0.839714 + 0.543029i \(0.182723\pi\)
\(348\) 0 0
\(349\) 24.6569 1.31985 0.659926 0.751331i \(-0.270588\pi\)
0.659926 + 0.751331i \(0.270588\pi\)
\(350\) 4.24264 0.226779
\(351\) −38.6274 −2.06178
\(352\) 0 0
\(353\) −15.3431 −0.816633 −0.408317 0.912840i \(-0.633884\pi\)
−0.408317 + 0.912840i \(0.633884\pi\)
\(354\) −6.34315 −0.337134
\(355\) 8.48528 0.450352
\(356\) 0 0
\(357\) 9.41421 0.498253
\(358\) −2.34315 −0.123839
\(359\) 13.8995 0.733587 0.366794 0.930302i \(-0.380456\pi\)
0.366794 + 0.930302i \(0.380456\pi\)
\(360\) 4.00000 0.210819
\(361\) 25.3137 1.33230
\(362\) 27.3137 1.43558
\(363\) 17.4142 0.914009
\(364\) 0 0
\(365\) −4.24264 −0.222070
\(366\) 25.6569 1.34111
\(367\) −4.82843 −0.252042 −0.126021 0.992028i \(-0.540221\pi\)
−0.126021 + 0.992028i \(0.540221\pi\)
\(368\) 12.6863 0.661319
\(369\) −10.8284 −0.563705
\(370\) −19.6569 −1.02191
\(371\) 13.3137 0.691213
\(372\) 0 0
\(373\) −16.4853 −0.853576 −0.426788 0.904352i \(-0.640355\pi\)
−0.426788 + 0.904352i \(0.640355\pi\)
\(374\) 45.4558 2.35047
\(375\) −16.0000 −0.826236
\(376\) −31.3137 −1.61488
\(377\) −46.6274 −2.40143
\(378\) 8.00000 0.411476
\(379\) −19.2132 −0.986916 −0.493458 0.869770i \(-0.664267\pi\)
−0.493458 + 0.869770i \(0.664267\pi\)
\(380\) 0 0
\(381\) −29.4142 −1.50694
\(382\) 17.8995 0.915818
\(383\) 7.55635 0.386111 0.193056 0.981188i \(-0.438160\pi\)
0.193056 + 0.981188i \(0.438160\pi\)
\(384\) 16.0000 0.816497
\(385\) 6.82843 0.348009
\(386\) −17.4142 −0.886360
\(387\) 0 0
\(388\) 0 0
\(389\) 10.6274 0.538831 0.269416 0.963024i \(-0.413169\pi\)
0.269416 + 0.963024i \(0.413169\pi\)
\(390\) 19.3137 0.977988
\(391\) 21.1127 1.06772
\(392\) 16.9706 0.857143
\(393\) 24.7279 1.24736
\(394\) 12.2426 0.616775
\(395\) −7.75736 −0.390315
\(396\) 0 0
\(397\) −15.0000 −0.752828 −0.376414 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(398\) 33.7990 1.69419
\(399\) −9.41421 −0.471300
\(400\) 12.0000 0.600000
\(401\) 25.4558 1.27120 0.635602 0.772017i \(-0.280752\pi\)
0.635602 + 0.772017i \(0.280752\pi\)
\(402\) 2.68629 0.133980
\(403\) −44.2843 −2.20596
\(404\) 0 0
\(405\) −7.07107 −0.351364
\(406\) 9.65685 0.479262
\(407\) 47.4558 2.35230
\(408\) 26.6274 1.31825
\(409\) 23.5563 1.16479 0.582393 0.812907i \(-0.302116\pi\)
0.582393 + 0.812907i \(0.302116\pi\)
\(410\) 21.6569 1.06956
\(411\) −4.24264 −0.209274
\(412\) 0 0
\(413\) 3.17157 0.156063
\(414\) 4.48528 0.220440
\(415\) −15.7574 −0.773498
\(416\) 0 0
\(417\) −22.1421 −1.08431
\(418\) −45.4558 −2.22332
\(419\) −31.3137 −1.52977 −0.764887 0.644164i \(-0.777205\pi\)
−0.764887 + 0.644164i \(0.777205\pi\)
\(420\) 0 0
\(421\) 26.4853 1.29081 0.645407 0.763839i \(-0.276688\pi\)
0.645407 + 0.763839i \(0.276688\pi\)
\(422\) −13.1716 −0.641182
\(423\) −11.0711 −0.538294
\(424\) 37.6569 1.82878
\(425\) 19.9706 0.968715
\(426\) 12.0000 0.581402
\(427\) −12.8284 −0.620811
\(428\) 0 0
\(429\) −46.6274 −2.25119
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 22.6274 1.08866
\(433\) −37.9706 −1.82475 −0.912374 0.409357i \(-0.865753\pi\)
−0.912374 + 0.409357i \(0.865753\pi\)
\(434\) 9.17157 0.440250
\(435\) −13.6569 −0.654796
\(436\) 0 0
\(437\) −21.1127 −1.00996
\(438\) −6.00000 −0.286691
\(439\) 18.4853 0.882254 0.441127 0.897445i \(-0.354579\pi\)
0.441127 + 0.897445i \(0.354579\pi\)
\(440\) 19.3137 0.920745
\(441\) 6.00000 0.285714
\(442\) −64.2843 −3.05769
\(443\) −34.9706 −1.66150 −0.830751 0.556645i \(-0.812089\pi\)
−0.830751 + 0.556645i \(0.812089\pi\)
\(444\) 0 0
\(445\) −8.72792 −0.413743
\(446\) 1.79899 0.0851846
\(447\) −29.8995 −1.41420
\(448\) −8.00000 −0.377964
\(449\) −40.0416 −1.88968 −0.944841 0.327530i \(-0.893784\pi\)
−0.944841 + 0.327530i \(0.893784\pi\)
\(450\) 4.24264 0.200000
\(451\) −52.2843 −2.46197
\(452\) 0 0
\(453\) −19.5563 −0.918837
\(454\) −30.2843 −1.42131
\(455\) −9.65685 −0.452720
\(456\) −26.6274 −1.24694
\(457\) −24.6274 −1.15202 −0.576011 0.817442i \(-0.695391\pi\)
−0.576011 + 0.817442i \(0.695391\pi\)
\(458\) 13.4558 0.628750
\(459\) 37.6569 1.75767
\(460\) 0 0
\(461\) −12.3431 −0.574878 −0.287439 0.957799i \(-0.592804\pi\)
−0.287439 + 0.957799i \(0.592804\pi\)
\(462\) 9.65685 0.449278
\(463\) −27.2132 −1.26470 −0.632352 0.774681i \(-0.717911\pi\)
−0.632352 + 0.774681i \(0.717911\pi\)
\(464\) 27.3137 1.26801
\(465\) −12.9706 −0.601495
\(466\) −0.485281 −0.0224802
\(467\) 26.4853 1.22559 0.612796 0.790241i \(-0.290045\pi\)
0.612796 + 0.790241i \(0.290045\pi\)
\(468\) 0 0
\(469\) −1.34315 −0.0620207
\(470\) 22.1421 1.02134
\(471\) 10.3431 0.476587
\(472\) 8.97056 0.412904
\(473\) 0 0
\(474\) −10.9706 −0.503895
\(475\) −19.9706 −0.916312
\(476\) 0 0
\(477\) 13.3137 0.609593
\(478\) 12.2426 0.559965
\(479\) −16.4558 −0.751887 −0.375943 0.926643i \(-0.622681\pi\)
−0.375943 + 0.926643i \(0.622681\pi\)
\(480\) 0 0
\(481\) −67.1127 −3.06008
\(482\) 16.2426 0.739832
\(483\) 4.48528 0.204087
\(484\) 0 0
\(485\) 14.4853 0.657743
\(486\) 14.0000 0.635053
\(487\) 39.9411 1.80991 0.904953 0.425512i \(-0.139906\pi\)
0.904953 + 0.425512i \(0.139906\pi\)
\(488\) −36.2843 −1.64251
\(489\) −2.82843 −0.127906
\(490\) −12.0000 −0.542105
\(491\) −4.10051 −0.185053 −0.0925266 0.995710i \(-0.529494\pi\)
−0.0925266 + 0.995710i \(0.529494\pi\)
\(492\) 0 0
\(493\) 45.4558 2.04723
\(494\) 64.2843 2.89229
\(495\) 6.82843 0.306915
\(496\) 25.9411 1.16479
\(497\) −6.00000 −0.269137
\(498\) −22.2843 −0.998582
\(499\) −25.3431 −1.13452 −0.567258 0.823540i \(-0.691996\pi\)
−0.567258 + 0.823540i \(0.691996\pi\)
\(500\) 0 0
\(501\) −2.97056 −0.132715
\(502\) 3.51472 0.156870
\(503\) −25.9706 −1.15797 −0.578985 0.815338i \(-0.696551\pi\)
−0.578985 + 0.815338i \(0.696551\pi\)
\(504\) −2.82843 −0.125988
\(505\) 5.89949 0.262524
\(506\) 21.6569 0.962765
\(507\) 47.5563 2.11205
\(508\) 0 0
\(509\) −9.51472 −0.421732 −0.210866 0.977515i \(-0.567628\pi\)
−0.210866 + 0.977515i \(0.567628\pi\)
\(510\) −18.8284 −0.833737
\(511\) 3.00000 0.132712
\(512\) −22.6274 −1.00000
\(513\) −37.6569 −1.66259
\(514\) −24.0000 −1.05859
\(515\) 4.92893 0.217195
\(516\) 0 0
\(517\) −53.4558 −2.35099
\(518\) 13.8995 0.610709
\(519\) −0.970563 −0.0426030
\(520\) −27.3137 −1.19779
\(521\) 25.4142 1.11342 0.556708 0.830708i \(-0.312064\pi\)
0.556708 + 0.830708i \(0.312064\pi\)
\(522\) 9.65685 0.422669
\(523\) 34.9706 1.52916 0.764578 0.644531i \(-0.222947\pi\)
0.764578 + 0.644531i \(0.222947\pi\)
\(524\) 0 0
\(525\) 4.24264 0.185164
\(526\) 17.4142 0.759296
\(527\) 43.1716 1.88058
\(528\) 27.3137 1.18868
\(529\) −12.9411 −0.562658
\(530\) −26.6274 −1.15662
\(531\) 3.17157 0.137635
\(532\) 0 0
\(533\) 73.9411 3.20275
\(534\) −12.3431 −0.534140
\(535\) −12.0000 −0.518805
\(536\) −3.79899 −0.164091
\(537\) −2.34315 −0.101114
\(538\) −9.45584 −0.407670
\(539\) 28.9706 1.24785
\(540\) 0 0
\(541\) −16.4853 −0.708758 −0.354379 0.935102i \(-0.615308\pi\)
−0.354379 + 0.935102i \(0.615308\pi\)
\(542\) 24.5269 1.05352
\(543\) 27.3137 1.17214
\(544\) 0 0
\(545\) 9.17157 0.392867
\(546\) −13.6569 −0.584459
\(547\) 5.51472 0.235792 0.117896 0.993026i \(-0.462385\pi\)
0.117896 + 0.993026i \(0.462385\pi\)
\(548\) 0 0
\(549\) −12.8284 −0.547504
\(550\) 20.4853 0.873495
\(551\) −45.4558 −1.93648
\(552\) 12.6863 0.539964
\(553\) 5.48528 0.233258
\(554\) −20.4853 −0.870336
\(555\) −19.6569 −0.834387
\(556\) 0 0
\(557\) −5.82843 −0.246958 −0.123479 0.992347i \(-0.539405\pi\)
−0.123479 + 0.992347i \(0.539405\pi\)
\(558\) 9.17157 0.388264
\(559\) 0 0
\(560\) 5.65685 0.239046
\(561\) 45.4558 1.91915
\(562\) 5.89949 0.248855
\(563\) 9.89949 0.417214 0.208607 0.978000i \(-0.433107\pi\)
0.208607 + 0.978000i \(0.433107\pi\)
\(564\) 0 0
\(565\) 1.31371 0.0552681
\(566\) −10.1421 −0.426306
\(567\) 5.00000 0.209980
\(568\) −16.9706 −0.712069
\(569\) −46.1127 −1.93314 −0.966572 0.256394i \(-0.917466\pi\)
−0.966572 + 0.256394i \(0.917466\pi\)
\(570\) 18.8284 0.788636
\(571\) −11.1716 −0.467516 −0.233758 0.972295i \(-0.575102\pi\)
−0.233758 + 0.972295i \(0.575102\pi\)
\(572\) 0 0
\(573\) 17.8995 0.747762
\(574\) −15.3137 −0.639182
\(575\) 9.51472 0.396791
\(576\) −8.00000 −0.333333
\(577\) −13.9706 −0.581602 −0.290801 0.956784i \(-0.593922\pi\)
−0.290801 + 0.956784i \(0.593922\pi\)
\(578\) 38.6274 1.60669
\(579\) −17.4142 −0.723710
\(580\) 0 0
\(581\) 11.1421 0.462254
\(582\) 20.4853 0.849142
\(583\) 64.2843 2.66238
\(584\) 8.48528 0.351123
\(585\) −9.65685 −0.399262
\(586\) −44.2843 −1.82937
\(587\) 20.8701 0.861399 0.430700 0.902495i \(-0.358267\pi\)
0.430700 + 0.902495i \(0.358267\pi\)
\(588\) 0 0
\(589\) −43.1716 −1.77885
\(590\) −6.34315 −0.261143
\(591\) 12.2426 0.503595
\(592\) 39.3137 1.61578
\(593\) 22.4558 0.922151 0.461075 0.887361i \(-0.347464\pi\)
0.461075 + 0.887361i \(0.347464\pi\)
\(594\) 38.6274 1.58490
\(595\) 9.41421 0.385945
\(596\) 0 0
\(597\) 33.7990 1.38330
\(598\) −30.6274 −1.25245
\(599\) 4.34315 0.177456 0.0887281 0.996056i \(-0.471720\pi\)
0.0887281 + 0.996056i \(0.471720\pi\)
\(600\) 12.0000 0.489898
\(601\) −25.3137 −1.03257 −0.516284 0.856418i \(-0.672685\pi\)
−0.516284 + 0.856418i \(0.672685\pi\)
\(602\) 0 0
\(603\) −1.34315 −0.0546971
\(604\) 0 0
\(605\) 17.4142 0.707988
\(606\) 8.34315 0.338917
\(607\) 10.7279 0.435433 0.217716 0.976012i \(-0.430139\pi\)
0.217716 + 0.976012i \(0.430139\pi\)
\(608\) 0 0
\(609\) 9.65685 0.391315
\(610\) 25.6569 1.03882
\(611\) 75.5980 3.05837
\(612\) 0 0
\(613\) 11.2132 0.452897 0.226449 0.974023i \(-0.427288\pi\)
0.226449 + 0.974023i \(0.427288\pi\)
\(614\) −3.79899 −0.153315
\(615\) 21.6569 0.873289
\(616\) −13.6569 −0.550250
\(617\) −39.3137 −1.58271 −0.791355 0.611357i \(-0.790624\pi\)
−0.791355 + 0.611357i \(0.790624\pi\)
\(618\) 6.97056 0.280397
\(619\) 12.4437 0.500153 0.250076 0.968226i \(-0.419544\pi\)
0.250076 + 0.968226i \(0.419544\pi\)
\(620\) 0 0
\(621\) 17.9411 0.719953
\(622\) 28.2426 1.13243
\(623\) 6.17157 0.247259
\(624\) −38.6274 −1.54633
\(625\) −1.00000 −0.0400000
\(626\) −19.0711 −0.762233
\(627\) −45.4558 −1.81533
\(628\) 0 0
\(629\) 65.4264 2.60872
\(630\) 2.00000 0.0796819
\(631\) 32.7990 1.30571 0.652854 0.757484i \(-0.273572\pi\)
0.652854 + 0.757484i \(0.273572\pi\)
\(632\) 15.5147 0.617142
\(633\) −13.1716 −0.523523
\(634\) 14.4853 0.575284
\(635\) −29.4142 −1.16727
\(636\) 0 0
\(637\) −40.9706 −1.62331
\(638\) 46.6274 1.84600
\(639\) −6.00000 −0.237356
\(640\) 16.0000 0.632456
\(641\) −9.68629 −0.382586 −0.191293 0.981533i \(-0.561268\pi\)
−0.191293 + 0.981533i \(0.561268\pi\)
\(642\) −16.9706 −0.669775
\(643\) 36.6274 1.44444 0.722222 0.691661i \(-0.243121\pi\)
0.722222 + 0.691661i \(0.243121\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −62.6690 −2.46568
\(647\) −7.79899 −0.306610 −0.153305 0.988179i \(-0.548992\pi\)
−0.153305 + 0.988179i \(0.548992\pi\)
\(648\) 14.1421 0.555556
\(649\) 15.3137 0.601116
\(650\) −28.9706 −1.13632
\(651\) 9.17157 0.359462
\(652\) 0 0
\(653\) 22.6274 0.885479 0.442740 0.896650i \(-0.354007\pi\)
0.442740 + 0.896650i \(0.354007\pi\)
\(654\) 12.9706 0.507189
\(655\) 24.7279 0.966200
\(656\) −43.3137 −1.69112
\(657\) 3.00000 0.117041
\(658\) −15.6569 −0.610368
\(659\) 3.17157 0.123547 0.0617735 0.998090i \(-0.480324\pi\)
0.0617735 + 0.998090i \(0.480324\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 20.4853 0.796183
\(663\) −64.2843 −2.49659
\(664\) 31.5147 1.22301
\(665\) −9.41421 −0.365068
\(666\) 13.8995 0.538594
\(667\) 21.6569 0.838557
\(668\) 0 0
\(669\) 1.79899 0.0695530
\(670\) 2.68629 0.103780
\(671\) −61.9411 −2.39121
\(672\) 0 0
\(673\) 33.6985 1.29898 0.649491 0.760370i \(-0.274982\pi\)
0.649491 + 0.760370i \(0.274982\pi\)
\(674\) 21.6569 0.834191
\(675\) 16.9706 0.653197
\(676\) 0 0
\(677\) 3.34315 0.128488 0.0642438 0.997934i \(-0.479536\pi\)
0.0642438 + 0.997934i \(0.479536\pi\)
\(678\) 1.85786 0.0713509
\(679\) −10.2426 −0.393076
\(680\) 26.6274 1.02111
\(681\) −30.2843 −1.16050
\(682\) 44.2843 1.69573
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −4.24264 −0.162103
\(686\) 18.3848 0.701934
\(687\) 13.4558 0.513372
\(688\) 0 0
\(689\) −90.9117 −3.46346
\(690\) −8.97056 −0.341503
\(691\) 10.0294 0.381538 0.190769 0.981635i \(-0.438902\pi\)
0.190769 + 0.981635i \(0.438902\pi\)
\(692\) 0 0
\(693\) −4.82843 −0.183417
\(694\) 44.2426 1.67943
\(695\) −22.1421 −0.839899
\(696\) 27.3137 1.03532
\(697\) −72.0833 −2.73035
\(698\) 34.8701 1.31985
\(699\) −0.485281 −0.0183550
\(700\) 0 0
\(701\) −33.6274 −1.27009 −0.635045 0.772475i \(-0.719018\pi\)
−0.635045 + 0.772475i \(0.719018\pi\)
\(702\) −54.6274 −2.06178
\(703\) −65.4264 −2.46760
\(704\) −38.6274 −1.45583
\(705\) 22.1421 0.833921
\(706\) −21.6985 −0.816633
\(707\) −4.17157 −0.156888
\(708\) 0 0
\(709\) 21.9706 0.825122 0.412561 0.910930i \(-0.364634\pi\)
0.412561 + 0.910930i \(0.364634\pi\)
\(710\) 12.0000 0.450352
\(711\) 5.48528 0.205714
\(712\) 17.4558 0.654185
\(713\) 20.5685 0.770298
\(714\) 13.3137 0.498253
\(715\) −46.6274 −1.74377
\(716\) 0 0
\(717\) 12.2426 0.457210
\(718\) 19.6569 0.733587
\(719\) 43.9706 1.63983 0.819913 0.572489i \(-0.194022\pi\)
0.819913 + 0.572489i \(0.194022\pi\)
\(720\) 5.65685 0.210819
\(721\) −3.48528 −0.129799
\(722\) 35.7990 1.33230
\(723\) 16.2426 0.604070
\(724\) 0 0
\(725\) 20.4853 0.760804
\(726\) 24.6274 0.914009
\(727\) 16.7279 0.620404 0.310202 0.950671i \(-0.399603\pi\)
0.310202 + 0.950671i \(0.399603\pi\)
\(728\) 19.3137 0.715814
\(729\) 29.0000 1.07407
\(730\) −6.00000 −0.222070
\(731\) 0 0
\(732\) 0 0
\(733\) −43.1716 −1.59458 −0.797289 0.603597i \(-0.793733\pi\)
−0.797289 + 0.603597i \(0.793733\pi\)
\(734\) −6.82843 −0.252042
\(735\) −12.0000 −0.442627
\(736\) 0 0
\(737\) −6.48528 −0.238888
\(738\) −15.3137 −0.563705
\(739\) 7.82843 0.287973 0.143987 0.989580i \(-0.454008\pi\)
0.143987 + 0.989580i \(0.454008\pi\)
\(740\) 0 0
\(741\) 64.2843 2.36154
\(742\) 18.8284 0.691213
\(743\) −36.5858 −1.34220 −0.671101 0.741366i \(-0.734178\pi\)
−0.671101 + 0.741366i \(0.734178\pi\)
\(744\) 25.9411 0.951048
\(745\) −29.8995 −1.09543
\(746\) −23.3137 −0.853576
\(747\) 11.1421 0.407669
\(748\) 0 0
\(749\) 8.48528 0.310045
\(750\) −22.6274 −0.826236
\(751\) 47.4853 1.73276 0.866381 0.499383i \(-0.166440\pi\)
0.866381 + 0.499383i \(0.166440\pi\)
\(752\) −44.2843 −1.61488
\(753\) 3.51472 0.128083
\(754\) −65.9411 −2.40143
\(755\) −19.5563 −0.711728
\(756\) 0 0
\(757\) 9.20101 0.334416 0.167208 0.985922i \(-0.446525\pi\)
0.167208 + 0.985922i \(0.446525\pi\)
\(758\) −27.1716 −0.986916
\(759\) 21.6569 0.786094
\(760\) −26.6274 −0.965878
\(761\) −10.9706 −0.397683 −0.198841 0.980032i \(-0.563718\pi\)
−0.198841 + 0.980032i \(0.563718\pi\)
\(762\) −41.5980 −1.50694
\(763\) −6.48528 −0.234783
\(764\) 0 0
\(765\) 9.41421 0.340372
\(766\) 10.6863 0.386111
\(767\) −21.6569 −0.781984
\(768\) 0 0
\(769\) −32.1838 −1.16058 −0.580288 0.814411i \(-0.697060\pi\)
−0.580288 + 0.814411i \(0.697060\pi\)
\(770\) 9.65685 0.348009
\(771\) −24.0000 −0.864339
\(772\) 0 0
\(773\) −11.6152 −0.417771 −0.208885 0.977940i \(-0.566984\pi\)
−0.208885 + 0.977940i \(0.566984\pi\)
\(774\) 0 0
\(775\) 19.4558 0.698875
\(776\) −28.9706 −1.03998
\(777\) 13.8995 0.498642
\(778\) 15.0294 0.538831
\(779\) 72.0833 2.58265
\(780\) 0 0
\(781\) −28.9706 −1.03665
\(782\) 29.8579 1.06772
\(783\) 38.6274 1.38043
\(784\) 24.0000 0.857143
\(785\) 10.3431 0.369163
\(786\) 34.9706 1.24736
\(787\) 28.9411 1.03164 0.515820 0.856697i \(-0.327487\pi\)
0.515820 + 0.856697i \(0.327487\pi\)
\(788\) 0 0
\(789\) 17.4142 0.619962
\(790\) −10.9706 −0.390315
\(791\) −0.928932 −0.0330290
\(792\) −13.6569 −0.485275
\(793\) 87.5980 3.11070
\(794\) −21.2132 −0.752828
\(795\) −26.6274 −0.944377
\(796\) 0 0
\(797\) −30.9289 −1.09556 −0.547779 0.836623i \(-0.684527\pi\)
−0.547779 + 0.836623i \(0.684527\pi\)
\(798\) −13.3137 −0.471300
\(799\) −73.6985 −2.60726
\(800\) 0 0
\(801\) 6.17157 0.218062
\(802\) 36.0000 1.27120
\(803\) 14.4853 0.511174
\(804\) 0 0
\(805\) 4.48528 0.158085
\(806\) −62.6274 −2.20596
\(807\) −9.45584 −0.332861
\(808\) −11.7990 −0.415087
\(809\) 1.02944 0.0361931 0.0180965 0.999836i \(-0.494239\pi\)
0.0180965 + 0.999836i \(0.494239\pi\)
\(810\) −10.0000 −0.351364
\(811\) 17.1716 0.602975 0.301488 0.953470i \(-0.402517\pi\)
0.301488 + 0.953470i \(0.402517\pi\)
\(812\) 0 0
\(813\) 24.5269 0.860196
\(814\) 67.1127 2.35230
\(815\) −2.82843 −0.0990755
\(816\) 37.6569 1.31825
\(817\) 0 0
\(818\) 33.3137 1.16479
\(819\) 6.82843 0.238605
\(820\) 0 0
\(821\) 27.4142 0.956763 0.478381 0.878152i \(-0.341224\pi\)
0.478381 + 0.878152i \(0.341224\pi\)
\(822\) −6.00000 −0.209274
\(823\) 13.2721 0.462636 0.231318 0.972878i \(-0.425696\pi\)
0.231318 + 0.972878i \(0.425696\pi\)
\(824\) −9.85786 −0.343415
\(825\) 20.4853 0.713206
\(826\) 4.48528 0.156063
\(827\) 11.4853 0.399382 0.199691 0.979859i \(-0.436006\pi\)
0.199691 + 0.979859i \(0.436006\pi\)
\(828\) 0 0
\(829\) −22.7279 −0.789373 −0.394687 0.918816i \(-0.629147\pi\)
−0.394687 + 0.918816i \(0.629147\pi\)
\(830\) −22.2843 −0.773498
\(831\) −20.4853 −0.710627
\(832\) 54.6274 1.89386
\(833\) 39.9411 1.38388
\(834\) −31.3137 −1.08431
\(835\) −2.97056 −0.102801
\(836\) 0 0
\(837\) 36.6863 1.26806
\(838\) −44.2843 −1.52977
\(839\) −6.20101 −0.214083 −0.107041 0.994255i \(-0.534138\pi\)
−0.107041 + 0.994255i \(0.534138\pi\)
\(840\) 5.65685 0.195180
\(841\) 17.6274 0.607842
\(842\) 37.4558 1.29081
\(843\) 5.89949 0.203189
\(844\) 0 0
\(845\) 47.5563 1.63599
\(846\) −15.6569 −0.538294
\(847\) −12.3137 −0.423104
\(848\) 53.2548 1.82878
\(849\) −10.1421 −0.348077
\(850\) 28.2426 0.968715
\(851\) 31.1716 1.06855
\(852\) 0 0
\(853\) −8.68629 −0.297413 −0.148706 0.988881i \(-0.547511\pi\)
−0.148706 + 0.988881i \(0.547511\pi\)
\(854\) −18.1421 −0.620811
\(855\) −9.41421 −0.321959
\(856\) 24.0000 0.820303
\(857\) −15.3431 −0.524112 −0.262056 0.965053i \(-0.584400\pi\)
−0.262056 + 0.965053i \(0.584400\pi\)
\(858\) −65.9411 −2.25119
\(859\) −34.7696 −1.18632 −0.593161 0.805084i \(-0.702120\pi\)
−0.593161 + 0.805084i \(0.702120\pi\)
\(860\) 0 0
\(861\) −15.3137 −0.521890
\(862\) −25.4558 −0.867029
\(863\) 57.1127 1.94414 0.972069 0.234693i \(-0.0754086\pi\)
0.972069 + 0.234693i \(0.0754086\pi\)
\(864\) 0 0
\(865\) −0.970563 −0.0330001
\(866\) −53.6985 −1.82475
\(867\) 38.6274 1.31186
\(868\) 0 0
\(869\) 26.4853 0.898452
\(870\) −19.3137 −0.654796
\(871\) 9.17157 0.310767
\(872\) −18.3431 −0.621177
\(873\) −10.2426 −0.346661
\(874\) −29.8579 −1.00996
\(875\) 11.3137 0.382473
\(876\) 0 0
\(877\) 5.34315 0.180425 0.0902126 0.995923i \(-0.471245\pi\)
0.0902126 + 0.995923i \(0.471245\pi\)
\(878\) 26.1421 0.882254
\(879\) −44.2843 −1.49367
\(880\) 27.3137 0.920745
\(881\) 13.0711 0.440375 0.220188 0.975458i \(-0.429333\pi\)
0.220188 + 0.975458i \(0.429333\pi\)
\(882\) 8.48528 0.285714
\(883\) −41.4558 −1.39510 −0.697550 0.716536i \(-0.745727\pi\)
−0.697550 + 0.716536i \(0.745727\pi\)
\(884\) 0 0
\(885\) −6.34315 −0.213223
\(886\) −49.4558 −1.66150
\(887\) −28.6569 −0.962203 −0.481101 0.876665i \(-0.659763\pi\)
−0.481101 + 0.876665i \(0.659763\pi\)
\(888\) 39.3137 1.31928
\(889\) 20.7990 0.697576
\(890\) −12.3431 −0.413743
\(891\) 24.1421 0.808792
\(892\) 0 0
\(893\) 73.6985 2.46623
\(894\) −42.2843 −1.41420
\(895\) −2.34315 −0.0783227
\(896\) −11.3137 −0.377964
\(897\) −30.6274 −1.02262
\(898\) −56.6274 −1.88968
\(899\) 44.2843 1.47696
\(900\) 0 0
\(901\) 88.6274 2.95261
\(902\) −73.9411 −2.46197
\(903\) 0 0
\(904\) −2.62742 −0.0873866
\(905\) 27.3137 0.907938
\(906\) −27.6569 −0.918837
\(907\) −28.5269 −0.947221 −0.473610 0.880735i \(-0.657049\pi\)
−0.473610 + 0.880735i \(0.657049\pi\)
\(908\) 0 0
\(909\) −4.17157 −0.138362
\(910\) −13.6569 −0.452720
\(911\) −52.3137 −1.73323 −0.866615 0.498977i \(-0.833709\pi\)
−0.866615 + 0.498977i \(0.833709\pi\)
\(912\) −37.6569 −1.24694
\(913\) 53.7990 1.78049
\(914\) −34.8284 −1.15202
\(915\) 25.6569 0.848189
\(916\) 0 0
\(917\) −17.4853 −0.577415
\(918\) 53.2548 1.75767
\(919\) −49.2132 −1.62339 −0.811697 0.584079i \(-0.801456\pi\)
−0.811697 + 0.584079i \(0.801456\pi\)
\(920\) 12.6863 0.418255
\(921\) −3.79899 −0.125181
\(922\) −17.4558 −0.574878
\(923\) 40.9706 1.34856
\(924\) 0 0
\(925\) 29.4853 0.969470
\(926\) −38.4853 −1.26470
\(927\) −3.48528 −0.114472
\(928\) 0 0
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) −18.3431 −0.601495
\(931\) −39.9411 −1.30902
\(932\) 0 0
\(933\) 28.2426 0.924623
\(934\) 37.4558 1.22559
\(935\) 45.4558 1.48657
\(936\) 19.3137 0.631288
\(937\) −31.5147 −1.02954 −0.514770 0.857328i \(-0.672123\pi\)
−0.514770 + 0.857328i \(0.672123\pi\)
\(938\) −1.89949 −0.0620207
\(939\) −19.0711 −0.622361
\(940\) 0 0
\(941\) −20.2843 −0.661248 −0.330624 0.943763i \(-0.607259\pi\)
−0.330624 + 0.943763i \(0.607259\pi\)
\(942\) 14.6274 0.476587
\(943\) −34.3431 −1.11837
\(944\) 12.6863 0.412904
\(945\) 8.00000 0.260240
\(946\) 0 0
\(947\) −56.1838 −1.82573 −0.912864 0.408265i \(-0.866134\pi\)
−0.912864 + 0.408265i \(0.866134\pi\)
\(948\) 0 0
\(949\) −20.4853 −0.664980
\(950\) −28.2426 −0.916312
\(951\) 14.4853 0.469717
\(952\) −18.8284 −0.610233
\(953\) −24.0416 −0.778785 −0.389392 0.921072i \(-0.627315\pi\)
−0.389392 + 0.921072i \(0.627315\pi\)
\(954\) 18.8284 0.609593
\(955\) 17.8995 0.579214
\(956\) 0 0
\(957\) 46.6274 1.50725
\(958\) −23.2721 −0.751887
\(959\) 3.00000 0.0968751
\(960\) 16.0000 0.516398
\(961\) 11.0589 0.356738
\(962\) −94.9117 −3.06008
\(963\) 8.48528 0.273434
\(964\) 0 0
\(965\) −17.4142 −0.560583
\(966\) 6.34315 0.204087
\(967\) −20.7279 −0.666565 −0.333283 0.942827i \(-0.608156\pi\)
−0.333283 + 0.942827i \(0.608156\pi\)
\(968\) −34.8284 −1.11943
\(969\) −62.6690 −2.01322
\(970\) 20.4853 0.657743
\(971\) −24.6274 −0.790331 −0.395166 0.918610i \(-0.629313\pi\)
−0.395166 + 0.918610i \(0.629313\pi\)
\(972\) 0 0
\(973\) 15.6569 0.501936
\(974\) 56.4853 1.80991
\(975\) −28.9706 −0.927801
\(976\) −51.3137 −1.64251
\(977\) −52.9706 −1.69468 −0.847339 0.531052i \(-0.821797\pi\)
−0.847339 + 0.531052i \(0.821797\pi\)
\(978\) −4.00000 −0.127906
\(979\) 29.7990 0.952380
\(980\) 0 0
\(981\) −6.48528 −0.207059
\(982\) −5.79899 −0.185053
\(983\) −29.4853 −0.940434 −0.470217 0.882551i \(-0.655824\pi\)
−0.470217 + 0.882551i \(0.655824\pi\)
\(984\) −43.3137 −1.38079
\(985\) 12.2426 0.390083
\(986\) 64.2843 2.04723
\(987\) −15.6569 −0.498363
\(988\) 0 0
\(989\) 0 0
\(990\) 9.65685 0.306915
\(991\) 30.4558 0.967462 0.483731 0.875217i \(-0.339281\pi\)
0.483731 + 0.875217i \(0.339281\pi\)
\(992\) 0 0
\(993\) 20.4853 0.650081
\(994\) −8.48528 −0.269137
\(995\) 33.7990 1.07150
\(996\) 0 0
\(997\) 32.3848 1.02564 0.512818 0.858497i \(-0.328602\pi\)
0.512818 + 0.858497i \(0.328602\pi\)
\(998\) −35.8406 −1.13452
\(999\) 55.5980 1.75904
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 \(a_p\))