Properties

Label 4003.2.a.a.1.1
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 1.1
Root \(-1.41421\)
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.41421 q^{2}\) \(-1.41421 q^{3}\) \(-1.41421 q^{5}\) \(+2.00000 q^{6}\) \(-1.00000 q^{7}\) \(+2.82843 q^{8}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.41421 q^{2}\) \(-1.41421 q^{3}\) \(-1.41421 q^{5}\) \(+2.00000 q^{6}\) \(-1.00000 q^{7}\) \(+2.82843 q^{8}\) \(-1.00000 q^{9}\) \(+2.00000 q^{10}\) \(+0.828427 q^{11}\) \(+1.17157 q^{13}\) \(+1.41421 q^{14}\) \(+2.00000 q^{15}\) \(-4.00000 q^{16}\) \(+4.65685 q^{17}\) \(+1.41421 q^{18}\) \(-4.65685 q^{19}\) \(+1.41421 q^{21}\) \(-1.17157 q^{22}\) \(-8.82843 q^{23}\) \(-4.00000 q^{24}\) \(-3.00000 q^{25}\) \(-1.65685 q^{26}\) \(+5.65685 q^{27}\) \(-1.17157 q^{29}\) \(-2.82843 q^{30}\) \(+10.4853 q^{31}\) \(-1.17157 q^{33}\) \(-6.58579 q^{34}\) \(+1.41421 q^{35}\) \(-4.17157 q^{37}\) \(+6.58579 q^{38}\) \(-1.65685 q^{39}\) \(-4.00000 q^{40}\) \(+5.17157 q^{41}\) \(-2.00000 q^{42}\) \(+1.41421 q^{45}\) \(+12.4853 q^{46}\) \(-3.07107 q^{47}\) \(+5.65685 q^{48}\) \(-6.00000 q^{49}\) \(+4.24264 q^{50}\) \(-6.58579 q^{51}\) \(+9.31371 q^{53}\) \(-8.00000 q^{54}\) \(-1.17157 q^{55}\) \(-2.82843 q^{56}\) \(+6.58579 q^{57}\) \(+1.65685 q^{58}\) \(-8.82843 q^{59}\) \(+7.17157 q^{61}\) \(-14.8284 q^{62}\) \(+1.00000 q^{63}\) \(+8.00000 q^{64}\) \(-1.65685 q^{65}\) \(+1.65685 q^{66}\) \(+12.6569 q^{67}\) \(+12.4853 q^{69}\) \(-2.00000 q^{70}\) \(+6.00000 q^{71}\) \(-2.82843 q^{72}\) \(-3.00000 q^{73}\) \(+5.89949 q^{74}\) \(+4.24264 q^{75}\) \(-0.828427 q^{77}\) \(+2.34315 q^{78}\) \(+11.4853 q^{79}\) \(+5.65685 q^{80}\) \(-5.00000 q^{81}\) \(-7.31371 q^{82}\) \(+17.1421 q^{83}\) \(-6.58579 q^{85}\) \(+1.65685 q^{87}\) \(+2.34315 q^{88}\) \(-11.8284 q^{89}\) \(-2.00000 q^{90}\) \(-1.17157 q^{91}\) \(-14.8284 q^{93}\) \(+4.34315 q^{94}\) \(+6.58579 q^{95}\) \(+1.75736 q^{97}\) \(+8.48528 q^{98}\) \(-0.828427 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 16q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 16q^{78} \) \(\mathstrut +\mathstrut 6q^{79} \) \(\mathstrut -\mathstrut 10q^{81} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 16q^{88} \) \(\mathstrut -\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 20q^{94} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) −1.41421 −0.816497 −0.408248 0.912871i \(-0.633860\pi\)
−0.408248 + 0.912871i \(0.633860\pi\)
\(4\) 0 0
\(5\) −1.41421 −0.632456 −0.316228 0.948683i \(-0.602416\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) 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
\(11\) 0.828427 0.249780 0.124890 0.992171i \(-0.460142\pi\)
0.124890 + 0.992171i \(0.460142\pi\)
\(12\) 0 0
\(13\) 1.17157 0.324936 0.162468 0.986714i \(-0.448055\pi\)
0.162468 + 0.986714i \(0.448055\pi\)
\(14\) 1.41421 0.377964
\(15\) 2.00000 0.516398
\(16\) −4.00000 −1.00000
\(17\) 4.65685 1.12945 0.564727 0.825278i \(-0.308982\pi\)
0.564727 + 0.825278i \(0.308982\pi\)
\(18\) 1.41421 0.333333
\(19\) −4.65685 −1.06836 −0.534178 0.845372i \(-0.679379\pi\)
−0.534178 + 0.845372i \(0.679379\pi\)
\(20\) 0 0
\(21\) 1.41421 0.308607
\(22\) −1.17157 −0.249780
\(23\) −8.82843 −1.84085 −0.920427 0.390914i \(-0.872159\pi\)
−0.920427 + 0.390914i \(0.872159\pi\)
\(24\) −4.00000 −0.816497
\(25\) −3.00000 −0.600000
\(26\) −1.65685 −0.324936
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −1.17157 −0.217556 −0.108778 0.994066i \(-0.534694\pi\)
−0.108778 + 0.994066i \(0.534694\pi\)
\(30\) −2.82843 −0.516398
\(31\) 10.4853 1.88321 0.941606 0.336717i \(-0.109316\pi\)
0.941606 + 0.336717i \(0.109316\pi\)
\(32\) 0 0
\(33\) −1.17157 −0.203945
\(34\) −6.58579 −1.12945
\(35\) 1.41421 0.239046
\(36\) 0 0
\(37\) −4.17157 −0.685802 −0.342901 0.939371i \(-0.611410\pi\)
−0.342901 + 0.939371i \(0.611410\pi\)
\(38\) 6.58579 1.06836
\(39\) −1.65685 −0.265309
\(40\) −4.00000 −0.632456
\(41\) 5.17157 0.807664 0.403832 0.914833i \(-0.367678\pi\)
0.403832 + 0.914833i \(0.367678\pi\)
\(42\) −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
\(46\) 12.4853 1.84085
\(47\) −3.07107 −0.447961 −0.223981 0.974594i \(-0.571905\pi\)
−0.223981 + 0.974594i \(0.571905\pi\)
\(48\) 5.65685 0.816497
\(49\) −6.00000 −0.857143
\(50\) 4.24264 0.600000
\(51\) −6.58579 −0.922195
\(52\) 0 0
\(53\) 9.31371 1.27934 0.639668 0.768651i \(-0.279072\pi\)
0.639668 + 0.768651i \(0.279072\pi\)
\(54\) −8.00000 −1.08866
\(55\) −1.17157 −0.157975
\(56\) −2.82843 −0.377964
\(57\) 6.58579 0.872309
\(58\) 1.65685 0.217556
\(59\) −8.82843 −1.14936 −0.574682 0.818377i \(-0.694874\pi\)
−0.574682 + 0.818377i \(0.694874\pi\)
\(60\) 0 0
\(61\) 7.17157 0.918226 0.459113 0.888378i \(-0.348167\pi\)
0.459113 + 0.888378i \(0.348167\pi\)
\(62\) −14.8284 −1.88321
\(63\) 1.00000 0.125988
\(64\) 8.00000 1.00000
\(65\) −1.65685 −0.205507
\(66\) 1.65685 0.203945
\(67\) 12.6569 1.54628 0.773140 0.634235i \(-0.218685\pi\)
0.773140 + 0.634235i \(0.218685\pi\)
\(68\) 0 0
\(69\) 12.4853 1.50305
\(70\) −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 \(0.556174\pi\)
\(74\) 5.89949 0.685802
\(75\) 4.24264 0.489898
\(76\) 0 0
\(77\) −0.828427 −0.0944080
\(78\) 2.34315 0.265309
\(79\) 11.4853 1.29220 0.646098 0.763255i \(-0.276400\pi\)
0.646098 + 0.763255i \(0.276400\pi\)
\(80\) 5.65685 0.632456
\(81\) −5.00000 −0.555556
\(82\) −7.31371 −0.807664
\(83\) 17.1421 1.88159 0.940797 0.338971i \(-0.110079\pi\)
0.940797 + 0.338971i \(0.110079\pi\)
\(84\) 0 0
\(85\) −6.58579 −0.714329
\(86\) 0 0
\(87\) 1.65685 0.177633
\(88\) 2.34315 0.249780
\(89\) −11.8284 −1.25381 −0.626905 0.779095i \(-0.715679\pi\)
−0.626905 + 0.779095i \(0.715679\pi\)
\(90\) −2.00000 −0.210819
\(91\) −1.17157 −0.122814
\(92\) 0 0
\(93\) −14.8284 −1.53764
\(94\) 4.34315 0.447961
\(95\) 6.58579 0.675687
\(96\) 0 0
\(97\) 1.75736 0.178433 0.0892164 0.996012i \(-0.471564\pi\)
0.0892164 + 0.996012i \(0.471564\pi\)
\(98\) 8.48528 0.857143
\(99\) −0.828427 −0.0832601
\(100\) 0 0
\(101\) 9.82843 0.977965 0.488983 0.872294i \(-0.337368\pi\)
0.488983 + 0.872294i \(0.337368\pi\)
\(102\) 9.31371 0.922195
\(103\) −13.4853 −1.32874 −0.664372 0.747402i \(-0.731301\pi\)
−0.664372 + 0.747402i \(0.731301\pi\)
\(104\) 3.31371 0.324936
\(105\) −2.00000 −0.195180
\(106\) −13.1716 −1.27934
\(107\) 8.48528 0.820303 0.410152 0.912017i \(-0.365476\pi\)
0.410152 + 0.912017i \(0.365476\pi\)
\(108\) 0 0
\(109\) −10.4853 −1.00431 −0.502154 0.864778i \(-0.667459\pi\)
−0.502154 + 0.864778i \(0.667459\pi\)
\(110\) 1.65685 0.157975
\(111\) 5.89949 0.559955
\(112\) 4.00000 0.377964
\(113\) 15.0711 1.41777 0.708883 0.705326i \(-0.249199\pi\)
0.708883 + 0.705326i \(0.249199\pi\)
\(114\) −9.31371 −0.872309
\(115\) 12.4853 1.16426
\(116\) 0 0
\(117\) −1.17157 −0.108312
\(118\) 12.4853 1.14936
\(119\) −4.65685 −0.426893
\(120\) 5.65685 0.516398
\(121\) −10.3137 −0.937610
\(122\) −10.1421 −0.918226
\(123\) −7.31371 −0.659455
\(124\) 0 0
\(125\) 11.3137 1.01193
\(126\) −1.41421 −0.125988
\(127\) 18.7990 1.66814 0.834070 0.551658i \(-0.186005\pi\)
0.834070 + 0.551658i \(0.186005\pi\)
\(128\) −11.3137 −1.00000
\(129\) 0 0
\(130\) 2.34315 0.205507
\(131\) 0.514719 0.0449712 0.0224856 0.999747i \(-0.492842\pi\)
0.0224856 + 0.999747i \(0.492842\pi\)
\(132\) 0 0
\(133\) 4.65685 0.403800
\(134\) −17.8995 −1.54628
\(135\) −8.00000 −0.688530
\(136\) 13.1716 1.12945
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) −17.6569 −1.50305
\(139\) −4.34315 −0.368381 −0.184190 0.982891i \(-0.558966\pi\)
−0.184190 + 0.982891i \(0.558966\pi\)
\(140\) 0 0
\(141\) 4.34315 0.365759
\(142\) −8.48528 −0.712069
\(143\) 0.970563 0.0811625
\(144\) 4.00000 0.333333
\(145\) 1.65685 0.137594
\(146\) 4.24264 0.351123
\(147\) 8.48528 0.699854
\(148\) 0 0
\(149\) 7.14214 0.585107 0.292553 0.956249i \(-0.405495\pi\)
0.292553 + 0.956249i \(0.405495\pi\)
\(150\) −6.00000 −0.489898
\(151\) −8.17157 −0.664993 −0.332497 0.943104i \(-0.607891\pi\)
−0.332497 + 0.943104i \(0.607891\pi\)
\(152\) −13.1716 −1.06836
\(153\) −4.65685 −0.376484
\(154\) 1.17157 0.0944080
\(155\) −14.8284 −1.19105
\(156\) 0 0
\(157\) −15.3137 −1.22217 −0.611083 0.791566i \(-0.709266\pi\)
−0.611083 + 0.791566i \(0.709266\pi\)
\(158\) −16.2426 −1.29220
\(159\) −13.1716 −1.04457
\(160\) 0 0
\(161\) 8.82843 0.695778
\(162\) 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
\(165\) 1.65685 0.128986
\(166\) −24.2426 −1.88159
\(167\) −21.8995 −1.69463 −0.847317 0.531088i \(-0.821783\pi\)
−0.847317 + 0.531088i \(0.821783\pi\)
\(168\) 4.00000 0.308607
\(169\) −11.6274 −0.894417
\(170\) 9.31371 0.714329
\(171\) 4.65685 0.356119
\(172\) 0 0
\(173\) −23.3137 −1.77251 −0.886254 0.463199i \(-0.846701\pi\)
−0.886254 + 0.463199i \(0.846701\pi\)
\(174\) −2.34315 −0.177633
\(175\) 3.00000 0.226779
\(176\) −3.31371 −0.249780
\(177\) 12.4853 0.938451
\(178\) 16.7279 1.25381
\(179\) 9.65685 0.721787 0.360894 0.932607i \(-0.382472\pi\)
0.360894 + 0.932607i \(0.382472\pi\)
\(180\) 0 0
\(181\) −3.31371 −0.246306 −0.123153 0.992388i \(-0.539301\pi\)
−0.123153 + 0.992388i \(0.539301\pi\)
\(182\) 1.65685 0.122814
\(183\) −10.1421 −0.749728
\(184\) −24.9706 −1.84085
\(185\) 5.89949 0.433739
\(186\) 20.9706 1.53764
\(187\) 3.85786 0.282115
\(188\) 0 0
\(189\) −5.65685 −0.411476
\(190\) −9.31371 −0.675687
\(191\) 1.34315 0.0971866 0.0485933 0.998819i \(-0.484526\pi\)
0.0485933 + 0.998819i \(0.484526\pi\)
\(192\) −11.3137 −0.816497
\(193\) 10.3137 0.742397 0.371198 0.928554i \(-0.378947\pi\)
0.371198 + 0.928554i \(0.378947\pi\)
\(194\) −2.48528 −0.178433
\(195\) 2.34315 0.167796
\(196\) 0 0
\(197\) −2.65685 −0.189293 −0.0946465 0.995511i \(-0.530172\pi\)
−0.0946465 + 0.995511i \(0.530172\pi\)
\(198\) 1.17157 0.0832601
\(199\) 4.10051 0.290677 0.145339 0.989382i \(-0.453573\pi\)
0.145339 + 0.989382i \(0.453573\pi\)
\(200\) −8.48528 −0.600000
\(201\) −17.8995 −1.26253
\(202\) −13.8995 −0.977965
\(203\) 1.17157 0.0822283
\(204\) 0 0
\(205\) −7.31371 −0.510812
\(206\) 19.0711 1.32874
\(207\) 8.82843 0.613618
\(208\) −4.68629 −0.324936
\(209\) −3.85786 −0.266854
\(210\) 2.82843 0.195180
\(211\) 13.3137 0.916553 0.458277 0.888810i \(-0.348467\pi\)
0.458277 + 0.888810i \(0.348467\pi\)
\(212\) 0 0
\(213\) −8.48528 −0.581402
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) 16.0000 1.08866
\(217\) −10.4853 −0.711787
\(218\) 14.8284 1.00431
\(219\) 4.24264 0.286691
\(220\) 0 0
\(221\) 5.45584 0.367000
\(222\) −8.34315 −0.559955
\(223\) 26.7279 1.78983 0.894917 0.446233i \(-0.147235\pi\)
0.894917 + 0.446233i \(0.147235\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) −21.3137 −1.41777
\(227\) −18.5858 −1.23358 −0.616791 0.787127i \(-0.711568\pi\)
−0.616791 + 0.787127i \(0.711568\pi\)
\(228\) 0 0
\(229\) 26.4853 1.75020 0.875098 0.483945i \(-0.160797\pi\)
0.875098 + 0.483945i \(0.160797\pi\)
\(230\) −17.6569 −1.16426
\(231\) 1.17157 0.0770838
\(232\) −3.31371 −0.217556
\(233\) −11.6569 −0.763666 −0.381833 0.924231i \(-0.624707\pi\)
−0.381833 + 0.924231i \(0.624707\pi\)
\(234\) 1.65685 0.108312
\(235\) 4.34315 0.283316
\(236\) 0 0
\(237\) −16.2426 −1.05507
\(238\) 6.58579 0.426893
\(239\) −2.65685 −0.171858 −0.0859288 0.996301i \(-0.527386\pi\)
−0.0859288 + 0.996301i \(0.527386\pi\)
\(240\) −8.00000 −0.516398
\(241\) −5.48528 −0.353338 −0.176669 0.984270i \(-0.556532\pi\)
−0.176669 + 0.984270i \(0.556532\pi\)
\(242\) 14.5858 0.937610
\(243\) −9.89949 −0.635053
\(244\) 0 0
\(245\) 8.48528 0.542105
\(246\) 10.3431 0.659455
\(247\) −5.45584 −0.347147
\(248\) 29.6569 1.88321
\(249\) −24.2426 −1.53631
\(250\) −16.0000 −1.01193
\(251\) −14.4853 −0.914303 −0.457151 0.889389i \(-0.651130\pi\)
−0.457151 + 0.889389i \(0.651130\pi\)
\(252\) 0 0
\(253\) −7.31371 −0.459809
\(254\) −26.5858 −1.66814
\(255\) 9.31371 0.583247
\(256\) 0 0
\(257\) 16.9706 1.05859 0.529297 0.848436i \(-0.322456\pi\)
0.529297 + 0.848436i \(0.322456\pi\)
\(258\) 0 0
\(259\) 4.17157 0.259209
\(260\) 0 0
\(261\) 1.17157 0.0725185
\(262\) −0.727922 −0.0449712
\(263\) −10.3137 −0.635971 −0.317985 0.948096i \(-0.603006\pi\)
−0.317985 + 0.948096i \(0.603006\pi\)
\(264\) −3.31371 −0.203945
\(265\) −13.1716 −0.809123
\(266\) −6.58579 −0.403800
\(267\) 16.7279 1.02373
\(268\) 0 0
\(269\) −29.3137 −1.78729 −0.893644 0.448776i \(-0.851860\pi\)
−0.893644 + 0.448776i \(0.851860\pi\)
\(270\) 11.3137 0.688530
\(271\) 28.6569 1.74078 0.870390 0.492363i \(-0.163867\pi\)
0.870390 + 0.492363i \(0.163867\pi\)
\(272\) −18.6274 −1.12945
\(273\) 1.65685 0.100277
\(274\) 4.24264 0.256307
\(275\) −2.48528 −0.149868
\(276\) 0 0
\(277\) 2.48528 0.149326 0.0746630 0.997209i \(-0.476212\pi\)
0.0746630 + 0.997209i \(0.476212\pi\)
\(278\) 6.14214 0.368381
\(279\) −10.4853 −0.627737
\(280\) 4.00000 0.239046
\(281\) 9.82843 0.586315 0.293157 0.956064i \(-0.405294\pi\)
0.293157 + 0.956064i \(0.405294\pi\)
\(282\) −6.14214 −0.365759
\(283\) −12.8284 −0.762571 −0.381285 0.924457i \(-0.624518\pi\)
−0.381285 + 0.924457i \(0.624518\pi\)
\(284\) 0 0
\(285\) −9.31371 −0.551696
\(286\) −1.37258 −0.0811625
\(287\) −5.17157 −0.305268
\(288\) 0 0
\(289\) 4.68629 0.275664
\(290\) −2.34315 −0.137594
\(291\) −2.48528 −0.145690
\(292\) 0 0
\(293\) −8.68629 −0.507459 −0.253729 0.967275i \(-0.581657\pi\)
−0.253729 + 0.967275i \(0.581657\pi\)
\(294\) −12.0000 −0.699854
\(295\) 12.4853 0.726921
\(296\) −11.7990 −0.685802
\(297\) 4.68629 0.271926
\(298\) −10.1005 −0.585107
\(299\) −10.3431 −0.598160
\(300\) 0 0
\(301\) 0 0
\(302\) 11.5563 0.664993
\(303\) −13.8995 −0.798505
\(304\) 18.6274 1.06836
\(305\) −10.1421 −0.580737
\(306\) 6.58579 0.376484
\(307\) −25.3137 −1.44473 −0.722365 0.691512i \(-0.756945\pi\)
−0.722365 + 0.691512i \(0.756945\pi\)
\(308\) 0 0
\(309\) 19.0711 1.08492
\(310\) 20.9706 1.19105
\(311\) −13.9706 −0.792198 −0.396099 0.918208i \(-0.629636\pi\)
−0.396099 + 0.918208i \(0.629636\pi\)
\(312\) −4.68629 −0.265309
\(313\) 3.48528 0.197000 0.0984999 0.995137i \(-0.468596\pi\)
0.0984999 + 0.995137i \(0.468596\pi\)
\(314\) 21.6569 1.22217
\(315\) −1.41421 −0.0796819
\(316\) 0 0
\(317\) 1.75736 0.0987031 0.0493516 0.998781i \(-0.484285\pi\)
0.0493516 + 0.998781i \(0.484285\pi\)
\(318\) 18.6274 1.04457
\(319\) −0.970563 −0.0543411
\(320\) −11.3137 −0.632456
\(321\) −12.0000 −0.669775
\(322\) −12.4853 −0.695778
\(323\) −21.6863 −1.20666
\(324\) 0 0
\(325\) −3.51472 −0.194962
\(326\) 2.82843 0.156652
\(327\) 14.8284 0.820014
\(328\) 14.6274 0.807664
\(329\) 3.07107 0.169313
\(330\) −2.34315 −0.128986
\(331\) −2.48528 −0.136603 −0.0683017 0.997665i \(-0.521758\pi\)
−0.0683017 + 0.997665i \(0.521758\pi\)
\(332\) 0 0
\(333\) 4.17157 0.228601
\(334\) 30.9706 1.69463
\(335\) −17.8995 −0.977954
\(336\) −5.65685 −0.308607
\(337\) −7.31371 −0.398403 −0.199202 0.979959i \(-0.563835\pi\)
−0.199202 + 0.979959i \(0.563835\pi\)
\(338\) 16.4437 0.894417
\(339\) −21.3137 −1.15760
\(340\) 0 0
\(341\) 8.68629 0.470389
\(342\) −6.58579 −0.356119
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) −17.6569 −0.950613
\(346\) 32.9706 1.77251
\(347\) −25.2843 −1.35733 −0.678665 0.734448i \(-0.737441\pi\)
−0.678665 + 0.734448i \(0.737441\pi\)
\(348\) 0 0
\(349\) 13.3431 0.714242 0.357121 0.934058i \(-0.383758\pi\)
0.357121 + 0.934058i \(0.383758\pi\)
\(350\) −4.24264 −0.226779
\(351\) 6.62742 0.353745
\(352\) 0 0
\(353\) −26.6569 −1.41880 −0.709401 0.704806i \(-0.751034\pi\)
−0.709401 + 0.704806i \(0.751034\pi\)
\(354\) −17.6569 −0.938451
\(355\) −8.48528 −0.450352
\(356\) 0 0
\(357\) 6.58579 0.348557
\(358\) −13.6569 −0.721787
\(359\) −5.89949 −0.311363 −0.155682 0.987807i \(-0.549757\pi\)
−0.155682 + 0.987807i \(0.549757\pi\)
\(360\) 4.00000 0.210819
\(361\) 2.68629 0.141384
\(362\) 4.68629 0.246306
\(363\) 14.5858 0.765555
\(364\) 0 0
\(365\) 4.24264 0.222070
\(366\) 14.3431 0.749728
\(367\) 0.828427 0.0432435 0.0216218 0.999766i \(-0.493117\pi\)
0.0216218 + 0.999766i \(0.493117\pi\)
\(368\) 35.3137 1.84085
\(369\) −5.17157 −0.269221
\(370\) −8.34315 −0.433739
\(371\) −9.31371 −0.483544
\(372\) 0 0
\(373\) 0.485281 0.0251269 0.0125635 0.999921i \(-0.496001\pi\)
0.0125635 + 0.999921i \(0.496001\pi\)
\(374\) −5.45584 −0.282115
\(375\) −16.0000 −0.826236
\(376\) −8.68629 −0.447961
\(377\) −1.37258 −0.0706916
\(378\) 8.00000 0.411476
\(379\) 23.2132 1.19238 0.596191 0.802843i \(-0.296680\pi\)
0.596191 + 0.802843i \(0.296680\pi\)
\(380\) 0 0
\(381\) −26.5858 −1.36203
\(382\) −1.89949 −0.0971866
\(383\) −23.5563 −1.20367 −0.601837 0.798619i \(-0.705564\pi\)
−0.601837 + 0.798619i \(0.705564\pi\)
\(384\) 16.0000 0.816497
\(385\) 1.17157 0.0597089
\(386\) −14.5858 −0.742397
\(387\) 0 0
\(388\) 0 0
\(389\) −34.6274 −1.75568 −0.877840 0.478954i \(-0.841016\pi\)
−0.877840 + 0.478954i \(0.841016\pi\)
\(390\) −3.31371 −0.167796
\(391\) −41.1127 −2.07916
\(392\) −16.9706 −0.857143
\(393\) −0.727922 −0.0367188
\(394\) 3.75736 0.189293
\(395\) −16.2426 −0.817256
\(396\) 0 0
\(397\) −15.0000 −0.752828 −0.376414 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(398\) −5.79899 −0.290677
\(399\) −6.58579 −0.329702
\(400\) 12.0000 0.600000
\(401\) −25.4558 −1.27120 −0.635602 0.772017i \(-0.719248\pi\)
−0.635602 + 0.772017i \(0.719248\pi\)
\(402\) 25.3137 1.26253
\(403\) 12.2843 0.611923
\(404\) 0 0
\(405\) 7.07107 0.351364
\(406\) −1.65685 −0.0822283
\(407\) −3.45584 −0.171300
\(408\) −18.6274 −0.922195
\(409\) −7.55635 −0.373637 −0.186819 0.982394i \(-0.559818\pi\)
−0.186819 + 0.982394i \(0.559818\pi\)
\(410\) 10.3431 0.510812
\(411\) 4.24264 0.209274
\(412\) 0 0
\(413\) 8.82843 0.434418
\(414\) −12.4853 −0.613618
\(415\) −24.2426 −1.19002
\(416\) 0 0
\(417\) 6.14214 0.300782
\(418\) 5.45584 0.266854
\(419\) −8.68629 −0.424353 −0.212177 0.977231i \(-0.568055\pi\)
−0.212177 + 0.977231i \(0.568055\pi\)
\(420\) 0 0
\(421\) 9.51472 0.463719 0.231860 0.972749i \(-0.425519\pi\)
0.231860 + 0.972749i \(0.425519\pi\)
\(422\) −18.8284 −0.916553
\(423\) 3.07107 0.149320
\(424\) 26.3431 1.27934
\(425\) −13.9706 −0.677672
\(426\) 12.0000 0.581402
\(427\) −7.17157 −0.347057
\(428\) 0 0
\(429\) −1.37258 −0.0662689
\(430\) 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
\(433\) −4.02944 −0.193642 −0.0968212 0.995302i \(-0.530868\pi\)
−0.0968212 + 0.995302i \(0.530868\pi\)
\(434\) 14.8284 0.711787
\(435\) −2.34315 −0.112345
\(436\) 0 0
\(437\) 41.1127 1.96669
\(438\) −6.00000 −0.286691
\(439\) 1.51472 0.0722936 0.0361468 0.999346i \(-0.488492\pi\)
0.0361468 + 0.999346i \(0.488492\pi\)
\(440\) −3.31371 −0.157975
\(441\) 6.00000 0.285714
\(442\) −7.71573 −0.367000
\(443\) −1.02944 −0.0489100 −0.0244550 0.999701i \(-0.507785\pi\)
−0.0244550 + 0.999701i \(0.507785\pi\)
\(444\) 0 0
\(445\) 16.7279 0.792980
\(446\) −37.7990 −1.78983
\(447\) −10.1005 −0.477737
\(448\) −8.00000 −0.377964
\(449\) 8.04163 0.379508 0.189754 0.981832i \(-0.439231\pi\)
0.189754 + 0.981832i \(0.439231\pi\)
\(450\) −4.24264 −0.200000
\(451\) 4.28427 0.201738
\(452\) 0 0
\(453\) 11.5563 0.542965
\(454\) 26.2843 1.23358
\(455\) 1.65685 0.0776745
\(456\) 18.6274 0.872309
\(457\) 20.6274 0.964910 0.482455 0.875921i \(-0.339745\pi\)
0.482455 + 0.875921i \(0.339745\pi\)
\(458\) −37.4558 −1.75020
\(459\) 26.3431 1.22959
\(460\) 0 0
\(461\) −23.6569 −1.10181 −0.550905 0.834568i \(-0.685717\pi\)
−0.550905 + 0.834568i \(0.685717\pi\)
\(462\) −1.65685 −0.0770838
\(463\) 15.2132 0.707018 0.353509 0.935431i \(-0.384988\pi\)
0.353509 + 0.935431i \(0.384988\pi\)
\(464\) 4.68629 0.217556
\(465\) 20.9706 0.972487
\(466\) 16.4853 0.763666
\(467\) 9.51472 0.440289 0.220144 0.975467i \(-0.429347\pi\)
0.220144 + 0.975467i \(0.429347\pi\)
\(468\) 0 0
\(469\) −12.6569 −0.584439
\(470\) −6.14214 −0.283316
\(471\) 21.6569 0.997895
\(472\) −24.9706 −1.14936
\(473\) 0 0
\(474\) 22.9706 1.05507
\(475\) 13.9706 0.641013
\(476\) 0 0
\(477\) −9.31371 −0.426445
\(478\) 3.75736 0.171858
\(479\) 34.4558 1.57433 0.787164 0.616744i \(-0.211549\pi\)
0.787164 + 0.616744i \(0.211549\pi\)
\(480\) 0 0
\(481\) −4.88730 −0.222842
\(482\) 7.75736 0.353338
\(483\) −12.4853 −0.568100
\(484\) 0 0
\(485\) −2.48528 −0.112851
\(486\) 14.0000 0.635053
\(487\) −27.9411 −1.26613 −0.633067 0.774097i \(-0.718204\pi\)
−0.633067 + 0.774097i \(0.718204\pi\)
\(488\) 20.2843 0.918226
\(489\) 2.82843 0.127906
\(490\) −12.0000 −0.542105
\(491\) −23.8995 −1.07857 −0.539285 0.842124i \(-0.681305\pi\)
−0.539285 + 0.842124i \(0.681305\pi\)
\(492\) 0 0
\(493\) −5.45584 −0.245719
\(494\) 7.71573 0.347147
\(495\) 1.17157 0.0526583
\(496\) −41.9411 −1.88321
\(497\) −6.00000 −0.269137
\(498\) 34.2843 1.53631
\(499\) −36.6569 −1.64099 −0.820493 0.571656i \(-0.806301\pi\)
−0.820493 + 0.571656i \(0.806301\pi\)
\(500\) 0 0
\(501\) 30.9706 1.38366
\(502\) 20.4853 0.914303
\(503\) 7.97056 0.355390 0.177695 0.984086i \(-0.443136\pi\)
0.177695 + 0.984086i \(0.443136\pi\)
\(504\) 2.82843 0.125988
\(505\) −13.8995 −0.618519
\(506\) 10.3431 0.459809
\(507\) 16.4437 0.730288
\(508\) 0 0
\(509\) −26.4853 −1.17394 −0.586970 0.809609i \(-0.699679\pi\)
−0.586970 + 0.809609i \(0.699679\pi\)
\(510\) −13.1716 −0.583247
\(511\) 3.00000 0.132712
\(512\) 22.6274 1.00000
\(513\) −26.3431 −1.16308
\(514\) −24.0000 −1.05859
\(515\) 19.0711 0.840372
\(516\) 0 0
\(517\) −2.54416 −0.111892
\(518\) −5.89949 −0.259209
\(519\) 32.9706 1.44725
\(520\) −4.68629 −0.205507
\(521\) 22.5858 0.989501 0.494751 0.869035i \(-0.335259\pi\)
0.494751 + 0.869035i \(0.335259\pi\)
\(522\) −1.65685 −0.0725185
\(523\) 1.02944 0.0450141 0.0225071 0.999747i \(-0.492835\pi\)
0.0225071 + 0.999747i \(0.492835\pi\)
\(524\) 0 0
\(525\) −4.24264 −0.185164
\(526\) 14.5858 0.635971
\(527\) 48.8284 2.12700
\(528\) 4.68629 0.203945
\(529\) 54.9411 2.38874
\(530\) 18.6274 0.809123
\(531\) 8.82843 0.383121
\(532\) 0 0
\(533\) 6.05887 0.262439
\(534\) −23.6569 −1.02373
\(535\) −12.0000 −0.518805
\(536\) 35.7990 1.54628
\(537\) −13.6569 −0.589337
\(538\) 41.4558 1.78729
\(539\) −4.97056 −0.214097
\(540\) 0 0
\(541\) 0.485281 0.0208639 0.0104319 0.999946i \(-0.496679\pi\)
0.0104319 + 0.999946i \(0.496679\pi\)
\(542\) −40.5269 −1.74078
\(543\) 4.68629 0.201108
\(544\) 0 0
\(545\) 14.8284 0.635180
\(546\) −2.34315 −0.100277
\(547\) 22.4853 0.961401 0.480701 0.876885i \(-0.340382\pi\)
0.480701 + 0.876885i \(0.340382\pi\)
\(548\) 0 0
\(549\) −7.17157 −0.306075
\(550\) 3.51472 0.149868
\(551\) 5.45584 0.232427
\(552\) 35.3137 1.50305
\(553\) −11.4853 −0.488404
\(554\) −3.51472 −0.149326
\(555\) −8.34315 −0.354147
\(556\) 0 0
\(557\) −0.171573 −0.00726978 −0.00363489 0.999993i \(-0.501157\pi\)
−0.00363489 + 0.999993i \(0.501157\pi\)
\(558\) 14.8284 0.627737
\(559\) 0 0
\(560\) −5.65685 −0.239046
\(561\) −5.45584 −0.230346
\(562\) −13.8995 −0.586315
\(563\) −9.89949 −0.417214 −0.208607 0.978000i \(-0.566893\pi\)
−0.208607 + 0.978000i \(0.566893\pi\)
\(564\) 0 0
\(565\) −21.3137 −0.896674
\(566\) 18.1421 0.762571
\(567\) 5.00000 0.209980
\(568\) 16.9706 0.712069
\(569\) 16.1127 0.675479 0.337740 0.941240i \(-0.390338\pi\)
0.337740 + 0.941240i \(0.390338\pi\)
\(570\) 13.1716 0.551696
\(571\) −16.8284 −0.704248 −0.352124 0.935953i \(-0.614540\pi\)
−0.352124 + 0.935953i \(0.614540\pi\)
\(572\) 0 0
\(573\) −1.89949 −0.0793525
\(574\) 7.31371 0.305268
\(575\) 26.4853 1.10451
\(576\) −8.00000 −0.333333
\(577\) 19.9706 0.831385 0.415693 0.909505i \(-0.363539\pi\)
0.415693 + 0.909505i \(0.363539\pi\)
\(578\) −6.62742 −0.275664
\(579\) −14.5858 −0.606165
\(580\) 0 0
\(581\) −17.1421 −0.711176
\(582\) 3.51472 0.145690
\(583\) 7.71573 0.319553
\(584\) −8.48528 −0.351123
\(585\) 1.65685 0.0685025
\(586\) 12.2843 0.507459
\(587\) −32.8701 −1.35669 −0.678346 0.734742i \(-0.737303\pi\)
−0.678346 + 0.734742i \(0.737303\pi\)
\(588\) 0 0
\(589\) −48.8284 −2.01194
\(590\) −17.6569 −0.726921
\(591\) 3.75736 0.154557
\(592\) 16.6863 0.685802
\(593\) −28.4558 −1.16854 −0.584271 0.811559i \(-0.698619\pi\)
−0.584271 + 0.811559i \(0.698619\pi\)
\(594\) −6.62742 −0.271926
\(595\) 6.58579 0.269991
\(596\) 0 0
\(597\) −5.79899 −0.237337
\(598\) 14.6274 0.598160
\(599\) 15.6569 0.639722 0.319861 0.947465i \(-0.396364\pi\)
0.319861 + 0.947465i \(0.396364\pi\)
\(600\) 12.0000 0.489898
\(601\) −2.68629 −0.109576 −0.0547881 0.998498i \(-0.517448\pi\)
−0.0547881 + 0.998498i \(0.517448\pi\)
\(602\) 0 0
\(603\) −12.6569 −0.515427
\(604\) 0 0
\(605\) 14.5858 0.592997
\(606\) 19.6569 0.798505
\(607\) −14.7279 −0.597788 −0.298894 0.954286i \(-0.596618\pi\)
−0.298894 + 0.954286i \(0.596618\pi\)
\(608\) 0 0
\(609\) −1.65685 −0.0671391
\(610\) 14.3431 0.580737
\(611\) −3.59798 −0.145559
\(612\) 0 0
\(613\) −31.2132 −1.26069 −0.630345 0.776315i \(-0.717086\pi\)
−0.630345 + 0.776315i \(0.717086\pi\)
\(614\) 35.7990 1.44473
\(615\) 10.3431 0.417076
\(616\) −2.34315 −0.0944080
\(617\) −16.6863 −0.671765 −0.335882 0.941904i \(-0.609034\pi\)
−0.335882 + 0.941904i \(0.609034\pi\)
\(618\) −26.9706 −1.08492
\(619\) 43.5563 1.75068 0.875339 0.483510i \(-0.160638\pi\)
0.875339 + 0.483510i \(0.160638\pi\)
\(620\) 0 0
\(621\) −49.9411 −2.00407
\(622\) 19.7574 0.792198
\(623\) 11.8284 0.473896
\(624\) 6.62742 0.265309
\(625\) −1.00000 −0.0400000
\(626\) −4.92893 −0.197000
\(627\) 5.45584 0.217885
\(628\) 0 0
\(629\) −19.4264 −0.774582
\(630\) 2.00000 0.0796819
\(631\) −6.79899 −0.270664 −0.135332 0.990800i \(-0.543210\pi\)
−0.135332 + 0.990800i \(0.543210\pi\)
\(632\) 32.4853 1.29220
\(633\) −18.8284 −0.748363
\(634\) −2.48528 −0.0987031
\(635\) −26.5858 −1.05502
\(636\) 0 0
\(637\) −7.02944 −0.278516
\(638\) 1.37258 0.0543411
\(639\) −6.00000 −0.237356
\(640\) 16.0000 0.632456
\(641\) −32.3137 −1.27631 −0.638157 0.769906i \(-0.720303\pi\)
−0.638157 + 0.769906i \(0.720303\pi\)
\(642\) 16.9706 0.669775
\(643\) −8.62742 −0.340232 −0.170116 0.985424i \(-0.554414\pi\)
−0.170116 + 0.985424i \(0.554414\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 30.6690 1.20666
\(647\) 31.7990 1.25015 0.625074 0.780566i \(-0.285069\pi\)
0.625074 + 0.780566i \(0.285069\pi\)
\(648\) −14.1421 −0.555556
\(649\) −7.31371 −0.287088
\(650\) 4.97056 0.194962
\(651\) 14.8284 0.581172
\(652\) 0 0
\(653\) −22.6274 −0.885479 −0.442740 0.896650i \(-0.645993\pi\)
−0.442740 + 0.896650i \(0.645993\pi\)
\(654\) −20.9706 −0.820014
\(655\) −0.727922 −0.0284423
\(656\) −20.6863 −0.807664
\(657\) 3.00000 0.117041
\(658\) −4.34315 −0.169313
\(659\) 8.82843 0.343907 0.171953 0.985105i \(-0.444992\pi\)
0.171953 + 0.985105i \(0.444992\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 3.51472 0.136603
\(663\) −7.71573 −0.299654
\(664\) 48.4853 1.88159
\(665\) −6.58579 −0.255386
\(666\) −5.89949 −0.228601
\(667\) 10.3431 0.400488
\(668\) 0 0
\(669\) −37.7990 −1.46139
\(670\) 25.3137 0.977954
\(671\) 5.94113 0.229355
\(672\) 0 0
\(673\) −25.6985 −0.990604 −0.495302 0.868721i \(-0.664943\pi\)
−0.495302 + 0.868721i \(0.664943\pi\)
\(674\) 10.3431 0.398403
\(675\) −16.9706 −0.653197
\(676\) 0 0
\(677\) 14.6569 0.563309 0.281654 0.959516i \(-0.409117\pi\)
0.281654 + 0.959516i \(0.409117\pi\)
\(678\) 30.1421 1.15760
\(679\) −1.75736 −0.0674413
\(680\) −18.6274 −0.714329
\(681\) 26.2843 1.00722
\(682\) −12.2843 −0.470389
\(683\) 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
\(687\) −37.4558 −1.42903
\(688\) 0 0
\(689\) 10.9117 0.415702
\(690\) 24.9706 0.950613
\(691\) 43.9706 1.67272 0.836360 0.548181i \(-0.184680\pi\)
0.836360 + 0.548181i \(0.184680\pi\)
\(692\) 0 0
\(693\) 0.828427 0.0314693
\(694\) 35.7574 1.35733
\(695\) 6.14214 0.232984
\(696\) 4.68629 0.177633
\(697\) 24.0833 0.912219
\(698\) −18.8701 −0.714242
\(699\) 16.4853 0.623531
\(700\) 0 0
\(701\) 11.6274 0.439161 0.219581 0.975594i \(-0.429531\pi\)
0.219581 + 0.975594i \(0.429531\pi\)
\(702\) −9.37258 −0.353745
\(703\) 19.4264 0.732681
\(704\) 6.62742 0.249780
\(705\) −6.14214 −0.231326
\(706\) 37.6985 1.41880
\(707\) −9.82843 −0.369636
\(708\) 0 0
\(709\) −11.9706 −0.449564 −0.224782 0.974409i \(-0.572167\pi\)
−0.224782 + 0.974409i \(0.572167\pi\)
\(710\) 12.0000 0.450352
\(711\) −11.4853 −0.430732
\(712\) −33.4558 −1.25381
\(713\) −92.5685 −3.46672
\(714\) −9.31371 −0.348557
\(715\) −1.37258 −0.0513317
\(716\) 0 0
\(717\) 3.75736 0.140321
\(718\) 8.34315 0.311363
\(719\) 10.0294 0.374035 0.187017 0.982357i \(-0.440118\pi\)
0.187017 + 0.982357i \(0.440118\pi\)
\(720\) −5.65685 −0.210819
\(721\) 13.4853 0.502218
\(722\) −3.79899 −0.141384
\(723\) 7.75736 0.288499
\(724\) 0 0
\(725\) 3.51472 0.130533
\(726\) −20.6274 −0.765555
\(727\) −8.72792 −0.323701 −0.161850 0.986815i \(-0.551746\pi\)
−0.161850 + 0.986815i \(0.551746\pi\)
\(728\) −3.31371 −0.122814
\(729\) 29.0000 1.07407
\(730\) −6.00000 −0.222070
\(731\) 0 0
\(732\) 0 0
\(733\) −48.8284 −1.80352 −0.901760 0.432238i \(-0.857724\pi\)
−0.901760 + 0.432238i \(0.857724\pi\)
\(734\) −1.17157 −0.0432435
\(735\) −12.0000 −0.442627
\(736\) 0 0
\(737\) 10.4853 0.386230
\(738\) 7.31371 0.269221
\(739\) 2.17157 0.0798826 0.0399413 0.999202i \(-0.487283\pi\)
0.0399413 + 0.999202i \(0.487283\pi\)
\(740\) 0 0
\(741\) 7.71573 0.283444
\(742\) 13.1716 0.483544
\(743\) −39.4142 −1.44597 −0.722984 0.690865i \(-0.757230\pi\)
−0.722984 + 0.690865i \(0.757230\pi\)
\(744\) −41.9411 −1.53764
\(745\) −10.1005 −0.370054
\(746\) −0.686292 −0.0251269
\(747\) −17.1421 −0.627198
\(748\) 0 0
\(749\) −8.48528 −0.310045
\(750\) 22.6274 0.826236
\(751\) 30.5147 1.11350 0.556749 0.830681i \(-0.312049\pi\)
0.556749 + 0.830681i \(0.312049\pi\)
\(752\) 12.2843 0.447961
\(753\) 20.4853 0.746525
\(754\) 1.94113 0.0706916
\(755\) 11.5563 0.420579
\(756\) 0 0
\(757\) 48.7990 1.77363 0.886815 0.462125i \(-0.152913\pi\)
0.886815 + 0.462125i \(0.152913\pi\)
\(758\) −32.8284 −1.19238
\(759\) 10.3431 0.375432
\(760\) 18.6274 0.675687
\(761\) 22.9706 0.832682 0.416341 0.909208i \(-0.363312\pi\)
0.416341 + 0.909208i \(0.363312\pi\)
\(762\) 37.5980 1.36203
\(763\) 10.4853 0.379593
\(764\) 0 0
\(765\) 6.58579 0.238110
\(766\) 33.3137 1.20367
\(767\) −10.3431 −0.373469
\(768\) 0 0
\(769\) 44.1838 1.59331 0.796654 0.604436i \(-0.206601\pi\)
0.796654 + 0.604436i \(0.206601\pi\)
\(770\) −1.65685 −0.0597089
\(771\) −24.0000 −0.864339
\(772\) 0 0
\(773\) −48.3848 −1.74028 −0.870140 0.492805i \(-0.835972\pi\)
−0.870140 + 0.492805i \(0.835972\pi\)
\(774\) 0 0
\(775\) −31.4558 −1.12993
\(776\) 4.97056 0.178433
\(777\) −5.89949 −0.211643
\(778\) 48.9706 1.75568
\(779\) −24.0833 −0.862872
\(780\) 0 0
\(781\) 4.97056 0.177861
\(782\) 58.1421 2.07916
\(783\) −6.62742 −0.236845
\(784\) 24.0000 0.857143
\(785\) 21.6569 0.772966
\(786\) 1.02944 0.0367188
\(787\) −38.9411 −1.38810 −0.694051 0.719926i \(-0.744176\pi\)
−0.694051 + 0.719926i \(0.744176\pi\)
\(788\) 0 0
\(789\) 14.5858 0.519268
\(790\) 22.9706 0.817256
\(791\) −15.0711 −0.535865
\(792\) −2.34315 −0.0832601
\(793\) 8.40202 0.298364
\(794\) 21.2132 0.752828
\(795\) 18.6274 0.660646
\(796\) 0 0
\(797\) −45.0711 −1.59650 −0.798250 0.602327i \(-0.794240\pi\)
−0.798250 + 0.602327i \(0.794240\pi\)
\(798\) 9.31371 0.329702
\(799\) −14.3015 −0.505951
\(800\) 0 0
\(801\) 11.8284 0.417937
\(802\) 36.0000 1.27120
\(803\) −2.48528 −0.0877037
\(804\) 0 0
\(805\) −12.4853 −0.440048
\(806\) −17.3726 −0.611923
\(807\) 41.4558 1.45931
\(808\) 27.7990 0.977965
\(809\) 34.9706 1.22950 0.614750 0.788722i \(-0.289257\pi\)
0.614750 + 0.788722i \(0.289257\pi\)
\(810\) −10.0000 −0.351364
\(811\) 22.8284 0.801614 0.400807 0.916162i \(-0.368730\pi\)
0.400807 + 0.916162i \(0.368730\pi\)
\(812\) 0 0
\(813\) −40.5269 −1.42134
\(814\) 4.88730 0.171300
\(815\) 2.82843 0.0990755
\(816\) 26.3431 0.922195
\(817\) 0 0
\(818\) 10.6863 0.373637
\(819\) 1.17157 0.0409381
\(820\) 0 0
\(821\) 24.5858 0.858050 0.429025 0.903293i \(-0.358857\pi\)
0.429025 + 0.903293i \(0.358857\pi\)
\(822\) −6.00000 −0.209274
\(823\) 38.7279 1.34997 0.674985 0.737831i \(-0.264150\pi\)
0.674985 + 0.737831i \(0.264150\pi\)
\(824\) −38.1421 −1.32874
\(825\) 3.51472 0.122367
\(826\) −12.4853 −0.434418
\(827\) −5.48528 −0.190742 −0.0953710 0.995442i \(-0.530404\pi\)
−0.0953710 + 0.995442i \(0.530404\pi\)
\(828\) 0 0
\(829\) 2.72792 0.0947446 0.0473723 0.998877i \(-0.484915\pi\)
0.0473723 + 0.998877i \(0.484915\pi\)
\(830\) 34.2843 1.19002
\(831\) −3.51472 −0.121924
\(832\) 9.37258 0.324936
\(833\) −27.9411 −0.968103
\(834\) −8.68629 −0.300782
\(835\) 30.9706 1.07178
\(836\) 0 0
\(837\) 59.3137 2.05018
\(838\) 12.2843 0.424353
\(839\) −45.7990 −1.58116 −0.790578 0.612361i \(-0.790220\pi\)
−0.790578 + 0.612361i \(0.790220\pi\)
\(840\) −5.65685 −0.195180
\(841\) −27.6274 −0.952670
\(842\) −13.4558 −0.463719
\(843\) −13.8995 −0.478724
\(844\) 0 0
\(845\) 16.4437 0.565679
\(846\) −4.34315 −0.149320
\(847\) 10.3137 0.354383
\(848\) −37.2548 −1.27934
\(849\) 18.1421 0.622636
\(850\) 19.7574 0.677672
\(851\) 36.8284 1.26246
\(852\) 0 0
\(853\) −31.3137 −1.07216 −0.536080 0.844167i \(-0.680096\pi\)
−0.536080 + 0.844167i \(0.680096\pi\)
\(854\) 10.1421 0.347057
\(855\) −6.58579 −0.225229
\(856\) 24.0000 0.820303
\(857\) −26.6569 −0.910581 −0.455290 0.890343i \(-0.650465\pi\)
−0.455290 + 0.890343i \(0.650465\pi\)
\(858\) 1.94113 0.0662689
\(859\) 38.7696 1.32280 0.661400 0.750033i \(-0.269963\pi\)
0.661400 + 0.750033i \(0.269963\pi\)
\(860\) 0 0
\(861\) 7.31371 0.249251
\(862\) 25.4558 0.867029
\(863\) −5.11270 −0.174038 −0.0870191 0.996207i \(-0.527734\pi\)
−0.0870191 + 0.996207i \(0.527734\pi\)
\(864\) 0 0
\(865\) 32.9706 1.12103
\(866\) 5.69848 0.193642
\(867\) −6.62742 −0.225079
\(868\) 0 0
\(869\) 9.51472 0.322765
\(870\) 3.31371 0.112345
\(871\) 14.8284 0.502442
\(872\) −29.6569 −1.00431
\(873\) −1.75736 −0.0594776
\(874\) −58.1421 −1.96669
\(875\) −11.3137 −0.382473
\(876\) 0 0
\(877\) 16.6569 0.562462 0.281231 0.959640i \(-0.409257\pi\)
0.281231 + 0.959640i \(0.409257\pi\)
\(878\) −2.14214 −0.0722936
\(879\) 12.2843 0.414338
\(880\) 4.68629 0.157975
\(881\) −1.07107 −0.0360852 −0.0180426 0.999837i \(-0.505743\pi\)
−0.0180426 + 0.999837i \(0.505743\pi\)
\(882\) −8.48528 −0.285714
\(883\) 9.45584 0.318214 0.159107 0.987261i \(-0.449138\pi\)
0.159107 + 0.987261i \(0.449138\pi\)
\(884\) 0 0
\(885\) −17.6569 −0.593529
\(886\) 1.45584 0.0489100
\(887\) −17.3431 −0.582326 −0.291163 0.956673i \(-0.594042\pi\)
−0.291163 + 0.956673i \(0.594042\pi\)
\(888\) 16.6863 0.559955
\(889\) −18.7990 −0.630498
\(890\) −23.6569 −0.792980
\(891\) −4.14214 −0.138767
\(892\) 0 0
\(893\) 14.3015 0.478582
\(894\) 14.2843 0.477737
\(895\) −13.6569 −0.456498
\(896\) 11.3137 0.377964
\(897\) 14.6274 0.488395
\(898\) −11.3726 −0.379508
\(899\) −12.2843 −0.409703
\(900\) 0 0
\(901\) 43.3726 1.44495
\(902\) −6.05887 −0.201738
\(903\) 0 0
\(904\) 42.6274 1.41777
\(905\) 4.68629 0.155778
\(906\) −16.3431 −0.542965
\(907\) 36.5269 1.21286 0.606428 0.795138i \(-0.292602\pi\)
0.606428 + 0.795138i \(0.292602\pi\)
\(908\) 0 0
\(909\) −9.82843 −0.325988
\(910\) −2.34315 −0.0776745
\(911\) −29.6863 −0.983551 −0.491775 0.870722i \(-0.663652\pi\)
−0.491775 + 0.870722i \(0.663652\pi\)
\(912\) −26.3431 −0.872309
\(913\) 14.2010 0.469985
\(914\) −29.1716 −0.964910
\(915\) 14.3431 0.474170
\(916\) 0 0
\(917\) −0.514719 −0.0169975
\(918\) −37.2548 −1.22959
\(919\) −6.78680 −0.223876 −0.111938 0.993715i \(-0.535706\pi\)
−0.111938 + 0.993715i \(0.535706\pi\)
\(920\) 35.3137 1.16426
\(921\) 35.7990 1.17962
\(922\) 33.4558 1.10181
\(923\) 7.02944 0.231377
\(924\) 0 0
\(925\) 12.5147 0.411481
\(926\) −21.5147 −0.707018
\(927\) 13.4853 0.442915
\(928\) 0 0
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) −29.6569 −0.972487
\(931\) 27.9411 0.915733
\(932\) 0 0
\(933\) 19.7574 0.646827
\(934\) −13.4558 −0.440289
\(935\) −5.45584 −0.178425
\(936\) −3.31371 −0.108312
\(937\) −48.4853 −1.58395 −0.791973 0.610557i \(-0.790946\pi\)
−0.791973 + 0.610557i \(0.790946\pi\)
\(938\) 17.8995 0.584439
\(939\) −4.92893 −0.160850
\(940\) 0 0
\(941\) 36.2843 1.18283 0.591417 0.806366i \(-0.298569\pi\)
0.591417 + 0.806366i \(0.298569\pi\)
\(942\) −30.6274 −0.997895
\(943\) −45.6569 −1.48679
\(944\) 35.3137 1.14936
\(945\) 8.00000 0.260240
\(946\) 0 0
\(947\) 20.1838 0.655884 0.327942 0.944698i \(-0.393645\pi\)
0.327942 + 0.944698i \(0.393645\pi\)
\(948\) 0 0
\(949\) −3.51472 −0.114093
\(950\) −19.7574 −0.641013
\(951\) −2.48528 −0.0805908
\(952\) −13.1716 −0.426893
\(953\) 24.0416 0.778785 0.389392 0.921072i \(-0.372685\pi\)
0.389392 + 0.921072i \(0.372685\pi\)
\(954\) 13.1716 0.426445
\(955\) −1.89949 −0.0614662
\(956\) 0 0
\(957\) 1.37258 0.0443693
\(958\) −48.7279 −1.57433
\(959\) 3.00000 0.0968751
\(960\) 16.0000 0.516398
\(961\) 78.9411 2.54649
\(962\) 6.91169 0.222842
\(963\) −8.48528 −0.273434
\(964\) 0 0
\(965\) −14.5858 −0.469533
\(966\) 17.6569 0.568100
\(967\) 4.72792 0.152040 0.0760199 0.997106i \(-0.475779\pi\)
0.0760199 + 0.997106i \(0.475779\pi\)
\(968\) −29.1716 −0.937610
\(969\) 30.6690 0.985232
\(970\) 3.51472 0.112851
\(971\) 20.6274 0.661965 0.330983 0.943637i \(-0.392620\pi\)
0.330983 + 0.943637i \(0.392620\pi\)
\(972\) 0 0
\(973\) 4.34315 0.139235
\(974\) 39.5147 1.26613
\(975\) 4.97056 0.159185
\(976\) −28.6863 −0.918226
\(977\) −19.0294 −0.608806 −0.304403 0.952543i \(-0.598457\pi\)
−0.304403 + 0.952543i \(0.598457\pi\)
\(978\) −4.00000 −0.127906
\(979\) −9.79899 −0.313177
\(980\) 0 0
\(981\) 10.4853 0.334769
\(982\) 33.7990 1.07857
\(983\) −12.5147 −0.399158 −0.199579 0.979882i \(-0.563957\pi\)
−0.199579 + 0.979882i \(0.563957\pi\)
\(984\) −20.6863 −0.659455
\(985\) 3.75736 0.119719
\(986\) 7.71573 0.245719
\(987\) −4.34315 −0.138244
\(988\) 0 0
\(989\) 0 0
\(990\) −1.65685 −0.0526583
\(991\) −20.4558 −0.649801 −0.324901 0.945748i \(-0.605331\pi\)
−0.324901 + 0.945748i \(0.605331\pi\)
\(992\) 0 0
\(993\) 3.51472 0.111536
\(994\) 8.48528 0.269137
\(995\) −5.79899 −0.183840
\(996\) 0 0
\(997\) −4.38478 −0.138867 −0.0694336 0.997587i \(-0.522119\pi\)
−0.0694336 + 0.997587i \(0.522119\pi\)
\(998\) 51.8406 1.64099
\(999\) −23.5980 −0.746607
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 \(a_p\))