Properties

Label 4031.2.a.c.1.3
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53428 q^{2}\) \(-2.04027 q^{3}\) \(+4.42257 q^{4}\) \(-2.47983 q^{5}\) \(+5.17061 q^{6}\) \(-0.629929 q^{7}\) \(-6.13948 q^{8}\) \(+1.16269 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53428 q^{2}\) \(-2.04027 q^{3}\) \(+4.42257 q^{4}\) \(-2.47983 q^{5}\) \(+5.17061 q^{6}\) \(-0.629929 q^{7}\) \(-6.13948 q^{8}\) \(+1.16269 q^{9}\) \(+6.28458 q^{10}\) \(+0.0387158 q^{11}\) \(-9.02323 q^{12}\) \(-2.09282 q^{13}\) \(+1.59642 q^{14}\) \(+5.05951 q^{15}\) \(+6.71401 q^{16}\) \(+1.11384 q^{17}\) \(-2.94657 q^{18}\) \(-4.51218 q^{19}\) \(-10.9672 q^{20}\) \(+1.28522 q^{21}\) \(-0.0981165 q^{22}\) \(+4.29752 q^{23}\) \(+12.5262 q^{24}\) \(+1.14956 q^{25}\) \(+5.30378 q^{26}\) \(+3.74861 q^{27}\) \(-2.78591 q^{28}\) \(-1.00000 q^{29}\) \(-12.8222 q^{30}\) \(-9.00294 q^{31}\) \(-4.73622 q^{32}\) \(-0.0789904 q^{33}\) \(-2.82278 q^{34}\) \(+1.56212 q^{35}\) \(+5.14207 q^{36}\) \(+0.632125 q^{37}\) \(+11.4351 q^{38}\) \(+4.26990 q^{39}\) \(+15.2249 q^{40}\) \(+6.59466 q^{41}\) \(-3.25712 q^{42}\) \(-0.733209 q^{43}\) \(+0.171223 q^{44}\) \(-2.88327 q^{45}\) \(-10.8911 q^{46}\) \(+2.09354 q^{47}\) \(-13.6984 q^{48}\) \(-6.60319 q^{49}\) \(-2.91330 q^{50}\) \(-2.27253 q^{51}\) \(-9.25563 q^{52}\) \(-5.00250 q^{53}\) \(-9.50002 q^{54}\) \(-0.0960085 q^{55}\) \(+3.86744 q^{56}\) \(+9.20606 q^{57}\) \(+2.53428 q^{58}\) \(+7.01828 q^{59}\) \(+22.3761 q^{60}\) \(+8.02767 q^{61}\) \(+22.8160 q^{62}\) \(-0.732410 q^{63}\) \(-1.42512 q^{64}\) \(+5.18983 q^{65}\) \(+0.200184 q^{66}\) \(+9.08801 q^{67}\) \(+4.92603 q^{68}\) \(-8.76810 q^{69}\) \(-3.95884 q^{70}\) \(-7.30583 q^{71}\) \(-7.13829 q^{72}\) \(+1.15403 q^{73}\) \(-1.60198 q^{74}\) \(-2.34540 q^{75}\) \(-19.9555 q^{76}\) \(-0.0243882 q^{77}\) \(-10.8211 q^{78}\) \(-8.00526 q^{79}\) \(-16.6496 q^{80}\) \(-11.1362 q^{81}\) \(-16.7127 q^{82}\) \(+7.30793 q^{83}\) \(+5.68399 q^{84}\) \(-2.76213 q^{85}\) \(+1.85816 q^{86}\) \(+2.04027 q^{87}\) \(-0.237695 q^{88}\) \(-0.395426 q^{89}\) \(+7.30700 q^{90}\) \(+1.31833 q^{91}\) \(+19.0061 q^{92}\) \(+18.3684 q^{93}\) \(-5.30562 q^{94}\) \(+11.1895 q^{95}\) \(+9.66315 q^{96}\) \(+15.2066 q^{97}\) \(+16.7343 q^{98}\) \(+0.0450143 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53428 −1.79201 −0.896003 0.444048i \(-0.853542\pi\)
−0.896003 + 0.444048i \(0.853542\pi\)
\(3\) −2.04027 −1.17795 −0.588974 0.808152i \(-0.700468\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(4\) 4.42257 2.21129
\(5\) −2.47983 −1.10901 −0.554507 0.832179i \(-0.687093\pi\)
−0.554507 + 0.832179i \(0.687093\pi\)
\(6\) 5.17061 2.11089
\(7\) −0.629929 −0.238091 −0.119045 0.992889i \(-0.537983\pi\)
−0.119045 + 0.992889i \(0.537983\pi\)
\(8\) −6.13948 −2.17063
\(9\) 1.16269 0.387562
\(10\) 6.28458 1.98736
\(11\) 0.0387158 0.0116732 0.00583662 0.999983i \(-0.498142\pi\)
0.00583662 + 0.999983i \(0.498142\pi\)
\(12\) −9.02323 −2.60478
\(13\) −2.09282 −0.580443 −0.290221 0.956960i \(-0.593729\pi\)
−0.290221 + 0.956960i \(0.593729\pi\)
\(14\) 1.59642 0.426660
\(15\) 5.05951 1.30636
\(16\) 6.71401 1.67850
\(17\) 1.11384 0.270145 0.135073 0.990836i \(-0.456873\pi\)
0.135073 + 0.990836i \(0.456873\pi\)
\(18\) −2.94657 −0.694514
\(19\) −4.51218 −1.03517 −0.517583 0.855633i \(-0.673168\pi\)
−0.517583 + 0.855633i \(0.673168\pi\)
\(20\) −10.9672 −2.45235
\(21\) 1.28522 0.280459
\(22\) −0.0981165 −0.0209185
\(23\) 4.29752 0.896096 0.448048 0.894010i \(-0.352119\pi\)
0.448048 + 0.894010i \(0.352119\pi\)
\(24\) 12.5262 2.55689
\(25\) 1.14956 0.229912
\(26\) 5.30378 1.04016
\(27\) 3.74861 0.721420
\(28\) −2.78591 −0.526487
\(29\) −1.00000 −0.185695
\(30\) −12.8222 −2.34101
\(31\) −9.00294 −1.61698 −0.808488 0.588513i \(-0.799714\pi\)
−0.808488 + 0.588513i \(0.799714\pi\)
\(32\) −4.73622 −0.837253
\(33\) −0.0789904 −0.0137505
\(34\) −2.82278 −0.484102
\(35\) 1.56212 0.264046
\(36\) 5.14207 0.857011
\(37\) 0.632125 0.103921 0.0519603 0.998649i \(-0.483453\pi\)
0.0519603 + 0.998649i \(0.483453\pi\)
\(38\) 11.4351 1.85502
\(39\) 4.26990 0.683732
\(40\) 15.2249 2.40726
\(41\) 6.59466 1.02991 0.514956 0.857217i \(-0.327808\pi\)
0.514956 + 0.857217i \(0.327808\pi\)
\(42\) −3.25712 −0.502584
\(43\) −0.733209 −0.111813 −0.0559067 0.998436i \(-0.517805\pi\)
−0.0559067 + 0.998436i \(0.517805\pi\)
\(44\) 0.171223 0.0258129
\(45\) −2.88327 −0.429812
\(46\) −10.8911 −1.60581
\(47\) 2.09354 0.305374 0.152687 0.988275i \(-0.451207\pi\)
0.152687 + 0.988275i \(0.451207\pi\)
\(48\) −13.6984 −1.97719
\(49\) −6.60319 −0.943313
\(50\) −2.91330 −0.412003
\(51\) −2.27253 −0.318217
\(52\) −9.25563 −1.28353
\(53\) −5.00250 −0.687147 −0.343573 0.939126i \(-0.611637\pi\)
−0.343573 + 0.939126i \(0.611637\pi\)
\(54\) −9.50002 −1.29279
\(55\) −0.0960085 −0.0129458
\(56\) 3.86744 0.516808
\(57\) 9.20606 1.21937
\(58\) 2.53428 0.332767
\(59\) 7.01828 0.913702 0.456851 0.889543i \(-0.348977\pi\)
0.456851 + 0.889543i \(0.348977\pi\)
\(60\) 22.3761 2.88874
\(61\) 8.02767 1.02784 0.513919 0.857839i \(-0.328193\pi\)
0.513919 + 0.857839i \(0.328193\pi\)
\(62\) 22.8160 2.89763
\(63\) −0.732410 −0.0922750
\(64\) −1.42512 −0.178140
\(65\) 5.18983 0.643719
\(66\) 0.200184 0.0246409
\(67\) 9.08801 1.11028 0.555138 0.831758i \(-0.312665\pi\)
0.555138 + 0.831758i \(0.312665\pi\)
\(68\) 4.92603 0.597369
\(69\) −8.76810 −1.05555
\(70\) −3.95884 −0.473172
\(71\) −7.30583 −0.867042 −0.433521 0.901143i \(-0.642729\pi\)
−0.433521 + 0.901143i \(0.642729\pi\)
\(72\) −7.13829 −0.841256
\(73\) 1.15403 0.135069 0.0675347 0.997717i \(-0.478487\pi\)
0.0675347 + 0.997717i \(0.478487\pi\)
\(74\) −1.60198 −0.186227
\(75\) −2.34540 −0.270824
\(76\) −19.9555 −2.28905
\(77\) −0.0243882 −0.00277929
\(78\) −10.8211 −1.22525
\(79\) −8.00526 −0.900662 −0.450331 0.892862i \(-0.648694\pi\)
−0.450331 + 0.892862i \(0.648694\pi\)
\(80\) −16.6496 −1.86148
\(81\) −11.1362 −1.23736
\(82\) −16.7127 −1.84561
\(83\) 7.30793 0.802150 0.401075 0.916045i \(-0.368637\pi\)
0.401075 + 0.916045i \(0.368637\pi\)
\(84\) 5.68399 0.620175
\(85\) −2.76213 −0.299595
\(86\) 1.85816 0.200370
\(87\) 2.04027 0.218740
\(88\) −0.237695 −0.0253383
\(89\) −0.395426 −0.0419150 −0.0209575 0.999780i \(-0.506671\pi\)
−0.0209575 + 0.999780i \(0.506671\pi\)
\(90\) 7.30700 0.770226
\(91\) 1.31833 0.138198
\(92\) 19.0061 1.98152
\(93\) 18.3684 1.90471
\(94\) −5.30562 −0.547233
\(95\) 11.1895 1.14801
\(96\) 9.66315 0.986241
\(97\) 15.2066 1.54399 0.771997 0.635627i \(-0.219258\pi\)
0.771997 + 0.635627i \(0.219258\pi\)
\(98\) 16.7343 1.69042
\(99\) 0.0450143 0.00452411
\(100\) 5.08401 0.508401
\(101\) −6.72285 −0.668948 −0.334474 0.942405i \(-0.608559\pi\)
−0.334474 + 0.942405i \(0.608559\pi\)
\(102\) 5.75922 0.570248
\(103\) −1.70519 −0.168018 −0.0840088 0.996465i \(-0.526772\pi\)
−0.0840088 + 0.996465i \(0.526772\pi\)
\(104\) 12.8488 1.25993
\(105\) −3.18714 −0.311033
\(106\) 12.6777 1.23137
\(107\) −2.03038 −0.196284 −0.0981420 0.995172i \(-0.531290\pi\)
−0.0981420 + 0.995172i \(0.531290\pi\)
\(108\) 16.5785 1.59527
\(109\) −0.0254372 −0.00243644 −0.00121822 0.999999i \(-0.500388\pi\)
−0.00121822 + 0.999999i \(0.500388\pi\)
\(110\) 0.243312 0.0231989
\(111\) −1.28970 −0.122413
\(112\) −4.22935 −0.399636
\(113\) 10.3511 0.973753 0.486876 0.873471i \(-0.338136\pi\)
0.486876 + 0.873471i \(0.338136\pi\)
\(114\) −23.3307 −2.18512
\(115\) −10.6571 −0.993783
\(116\) −4.42257 −0.410626
\(117\) −2.43329 −0.224958
\(118\) −17.7863 −1.63736
\(119\) −0.701639 −0.0643192
\(120\) −31.0628 −2.83563
\(121\) −10.9985 −0.999864
\(122\) −20.3444 −1.84189
\(123\) −13.4549 −1.21318
\(124\) −39.8162 −3.57560
\(125\) 9.54844 0.854039
\(126\) 1.85613 0.165357
\(127\) 15.8767 1.40883 0.704413 0.709790i \(-0.251210\pi\)
0.704413 + 0.709790i \(0.251210\pi\)
\(128\) 13.0841 1.15648
\(129\) 1.49594 0.131710
\(130\) −13.1525 −1.15355
\(131\) 15.7505 1.37613 0.688064 0.725650i \(-0.258461\pi\)
0.688064 + 0.725650i \(0.258461\pi\)
\(132\) −0.349341 −0.0304062
\(133\) 2.84236 0.246464
\(134\) −23.0316 −1.98962
\(135\) −9.29591 −0.800065
\(136\) −6.83839 −0.586387
\(137\) 9.04429 0.772706 0.386353 0.922351i \(-0.373735\pi\)
0.386353 + 0.922351i \(0.373735\pi\)
\(138\) 22.2208 1.89156
\(139\) −1.00000 −0.0848189
\(140\) 6.90858 0.583881
\(141\) −4.27138 −0.359715
\(142\) 18.5150 1.55375
\(143\) −0.0810249 −0.00677565
\(144\) 7.80629 0.650524
\(145\) 2.47983 0.205939
\(146\) −2.92464 −0.242045
\(147\) 13.4723 1.11117
\(148\) 2.79562 0.229798
\(149\) 12.6443 1.03586 0.517932 0.855422i \(-0.326702\pi\)
0.517932 + 0.855422i \(0.326702\pi\)
\(150\) 5.94391 0.485318
\(151\) 11.5787 0.942262 0.471131 0.882063i \(-0.343846\pi\)
0.471131 + 0.882063i \(0.343846\pi\)
\(152\) 27.7025 2.24697
\(153\) 1.29505 0.104698
\(154\) 0.0618065 0.00498051
\(155\) 22.3258 1.79325
\(156\) 18.8840 1.51193
\(157\) −5.42291 −0.432795 −0.216398 0.976305i \(-0.569431\pi\)
−0.216398 + 0.976305i \(0.569431\pi\)
\(158\) 20.2876 1.61399
\(159\) 10.2064 0.809423
\(160\) 11.7450 0.928525
\(161\) −2.70714 −0.213352
\(162\) 28.2223 2.21735
\(163\) −8.88009 −0.695543 −0.347771 0.937579i \(-0.613061\pi\)
−0.347771 + 0.937579i \(0.613061\pi\)
\(164\) 29.1653 2.27743
\(165\) 0.195883 0.0152495
\(166\) −18.5203 −1.43746
\(167\) −13.1561 −1.01805 −0.509024 0.860752i \(-0.669994\pi\)
−0.509024 + 0.860752i \(0.669994\pi\)
\(168\) −7.89060 −0.608773
\(169\) −8.62012 −0.663086
\(170\) 7.00001 0.536876
\(171\) −5.24626 −0.401191
\(172\) −3.24267 −0.247251
\(173\) 19.2022 1.45992 0.729960 0.683490i \(-0.239539\pi\)
0.729960 + 0.683490i \(0.239539\pi\)
\(174\) −5.17061 −0.391983
\(175\) −0.724140 −0.0547399
\(176\) 0.259938 0.0195936
\(177\) −14.3192 −1.07629
\(178\) 1.00212 0.0751120
\(179\) −2.91749 −0.218064 −0.109032 0.994038i \(-0.534775\pi\)
−0.109032 + 0.994038i \(0.534775\pi\)
\(180\) −12.7515 −0.950437
\(181\) 15.8412 1.17747 0.588733 0.808327i \(-0.299627\pi\)
0.588733 + 0.808327i \(0.299627\pi\)
\(182\) −3.34101 −0.247652
\(183\) −16.3786 −1.21074
\(184\) −26.3846 −1.94510
\(185\) −1.56756 −0.115249
\(186\) −46.5507 −3.41326
\(187\) 0.0431231 0.00315347
\(188\) 9.25884 0.675270
\(189\) −2.36136 −0.171763
\(190\) −28.3572 −2.05725
\(191\) −0.0385705 −0.00279086 −0.00139543 0.999999i \(-0.500444\pi\)
−0.00139543 + 0.999999i \(0.500444\pi\)
\(192\) 2.90762 0.209839
\(193\) −11.6336 −0.837403 −0.418701 0.908124i \(-0.637515\pi\)
−0.418701 + 0.908124i \(0.637515\pi\)
\(194\) −38.5377 −2.76685
\(195\) −10.5886 −0.758268
\(196\) −29.2031 −2.08593
\(197\) 17.5139 1.24781 0.623906 0.781499i \(-0.285545\pi\)
0.623906 + 0.781499i \(0.285545\pi\)
\(198\) −0.114079 −0.00810723
\(199\) 20.0932 1.42437 0.712186 0.701991i \(-0.247705\pi\)
0.712186 + 0.701991i \(0.247705\pi\)
\(200\) −7.05769 −0.499054
\(201\) −18.5420 −1.30785
\(202\) 17.0376 1.19876
\(203\) 0.629929 0.0442124
\(204\) −10.0504 −0.703670
\(205\) −16.3536 −1.14219
\(206\) 4.32144 0.301089
\(207\) 4.99668 0.347293
\(208\) −14.0512 −0.974274
\(209\) −0.174693 −0.0120837
\(210\) 8.07709 0.557372
\(211\) 1.68594 0.116065 0.0580325 0.998315i \(-0.481517\pi\)
0.0580325 + 0.998315i \(0.481517\pi\)
\(212\) −22.1239 −1.51948
\(213\) 14.9058 1.02133
\(214\) 5.14555 0.351742
\(215\) 1.81823 0.124002
\(216\) −23.0145 −1.56594
\(217\) 5.67122 0.384987
\(218\) 0.0644650 0.00436612
\(219\) −2.35453 −0.159105
\(220\) −0.424605 −0.0286268
\(221\) −2.33106 −0.156804
\(222\) 3.26847 0.219365
\(223\) −6.69856 −0.448569 −0.224284 0.974524i \(-0.572004\pi\)
−0.224284 + 0.974524i \(0.572004\pi\)
\(224\) 2.98348 0.199342
\(225\) 1.33658 0.0891051
\(226\) −26.2327 −1.74497
\(227\) 0.666704 0.0442507 0.0221254 0.999755i \(-0.492957\pi\)
0.0221254 + 0.999755i \(0.492957\pi\)
\(228\) 40.7145 2.69638
\(229\) 24.7669 1.63665 0.818323 0.574759i \(-0.194904\pi\)
0.818323 + 0.574759i \(0.194904\pi\)
\(230\) 27.0082 1.78086
\(231\) 0.0497584 0.00327386
\(232\) 6.13948 0.403076
\(233\) −7.46473 −0.489031 −0.244515 0.969645i \(-0.578629\pi\)
−0.244515 + 0.969645i \(0.578629\pi\)
\(234\) 6.16664 0.403126
\(235\) −5.19163 −0.338664
\(236\) 31.0388 2.02046
\(237\) 16.3329 1.06093
\(238\) 1.77815 0.115260
\(239\) 15.1859 0.982297 0.491148 0.871076i \(-0.336577\pi\)
0.491148 + 0.871076i \(0.336577\pi\)
\(240\) 33.9696 2.19273
\(241\) −25.0731 −1.61510 −0.807549 0.589801i \(-0.799206\pi\)
−0.807549 + 0.589801i \(0.799206\pi\)
\(242\) 27.8733 1.79176
\(243\) 11.4750 0.736124
\(244\) 35.5030 2.27284
\(245\) 16.3748 1.04615
\(246\) 34.0984 2.17403
\(247\) 9.44317 0.600855
\(248\) 55.2734 3.50986
\(249\) −14.9101 −0.944891
\(250\) −24.1984 −1.53044
\(251\) −2.13311 −0.134640 −0.0673202 0.997731i \(-0.521445\pi\)
−0.0673202 + 0.997731i \(0.521445\pi\)
\(252\) −3.23914 −0.204047
\(253\) 0.166382 0.0104603
\(254\) −40.2359 −2.52463
\(255\) 5.63548 0.352907
\(256\) −30.3085 −1.89428
\(257\) −0.832643 −0.0519388 −0.0259694 0.999663i \(-0.508267\pi\)
−0.0259694 + 0.999663i \(0.508267\pi\)
\(258\) −3.79113 −0.236026
\(259\) −0.398194 −0.0247426
\(260\) 22.9524 1.42345
\(261\) −1.16269 −0.0719685
\(262\) −39.9162 −2.46603
\(263\) 19.2457 1.18674 0.593371 0.804929i \(-0.297797\pi\)
0.593371 + 0.804929i \(0.297797\pi\)
\(264\) 0.484960 0.0298472
\(265\) 12.4054 0.762055
\(266\) −7.20333 −0.441664
\(267\) 0.806774 0.0493738
\(268\) 40.1924 2.45514
\(269\) −5.86704 −0.357719 −0.178860 0.983875i \(-0.557241\pi\)
−0.178860 + 0.983875i \(0.557241\pi\)
\(270\) 23.5584 1.43372
\(271\) 4.41421 0.268144 0.134072 0.990972i \(-0.457195\pi\)
0.134072 + 0.990972i \(0.457195\pi\)
\(272\) 7.47832 0.453440
\(273\) −2.68974 −0.162790
\(274\) −22.9208 −1.38469
\(275\) 0.0445060 0.00268381
\(276\) −38.7775 −2.33413
\(277\) −8.35250 −0.501853 −0.250927 0.968006i \(-0.580735\pi\)
−0.250927 + 0.968006i \(0.580735\pi\)
\(278\) 2.53428 0.151996
\(279\) −10.4676 −0.626679
\(280\) −9.59059 −0.573147
\(281\) 0.482945 0.0288101 0.0144050 0.999896i \(-0.495415\pi\)
0.0144050 + 0.999896i \(0.495415\pi\)
\(282\) 10.8249 0.644612
\(283\) −9.14175 −0.543421 −0.271710 0.962379i \(-0.587589\pi\)
−0.271710 + 0.962379i \(0.587589\pi\)
\(284\) −32.3106 −1.91728
\(285\) −22.8295 −1.35230
\(286\) 0.205340 0.0121420
\(287\) −4.15417 −0.245213
\(288\) −5.50674 −0.324488
\(289\) −15.7594 −0.927021
\(290\) −6.28458 −0.369043
\(291\) −31.0255 −1.81874
\(292\) 5.10379 0.298677
\(293\) 9.06814 0.529767 0.264883 0.964280i \(-0.414667\pi\)
0.264883 + 0.964280i \(0.414667\pi\)
\(294\) −34.1425 −1.99123
\(295\) −17.4041 −1.01331
\(296\) −3.88092 −0.225574
\(297\) 0.145130 0.00842131
\(298\) −32.0443 −1.85627
\(299\) −8.99393 −0.520132
\(300\) −10.3727 −0.598870
\(301\) 0.461870 0.0266217
\(302\) −29.3437 −1.68854
\(303\) 13.7164 0.787986
\(304\) −30.2948 −1.73753
\(305\) −19.9073 −1.13989
\(306\) −3.28201 −0.187620
\(307\) 22.1343 1.26327 0.631635 0.775266i \(-0.282384\pi\)
0.631635 + 0.775266i \(0.282384\pi\)
\(308\) −0.107859 −0.00614581
\(309\) 3.47905 0.197916
\(310\) −56.5797 −3.21351
\(311\) −29.3636 −1.66505 −0.832527 0.553984i \(-0.813107\pi\)
−0.832527 + 0.553984i \(0.813107\pi\)
\(312\) −26.2150 −1.48413
\(313\) −17.3492 −0.980636 −0.490318 0.871544i \(-0.663119\pi\)
−0.490318 + 0.871544i \(0.663119\pi\)
\(314\) 13.7432 0.775572
\(315\) 1.81625 0.102334
\(316\) −35.4039 −1.99162
\(317\) 3.38474 0.190106 0.0950531 0.995472i \(-0.469698\pi\)
0.0950531 + 0.995472i \(0.469698\pi\)
\(318\) −25.8660 −1.45049
\(319\) −0.0387158 −0.00216767
\(320\) 3.53405 0.197559
\(321\) 4.14251 0.231212
\(322\) 6.86064 0.382329
\(323\) −5.02584 −0.279645
\(324\) −49.2507 −2.73615
\(325\) −2.40581 −0.133451
\(326\) 22.5046 1.24642
\(327\) 0.0518987 0.00287000
\(328\) −40.4877 −2.23556
\(329\) −1.31878 −0.0727068
\(330\) −0.496422 −0.0273271
\(331\) 18.9850 1.04351 0.521756 0.853095i \(-0.325277\pi\)
0.521756 + 0.853095i \(0.325277\pi\)
\(332\) 32.3199 1.77378
\(333\) 0.734963 0.0402757
\(334\) 33.3412 1.82435
\(335\) −22.5367 −1.23131
\(336\) 8.62900 0.470751
\(337\) 2.41583 0.131599 0.0657993 0.997833i \(-0.479040\pi\)
0.0657993 + 0.997833i \(0.479040\pi\)
\(338\) 21.8458 1.18825
\(339\) −21.1191 −1.14703
\(340\) −12.2157 −0.662491
\(341\) −0.348556 −0.0188753
\(342\) 13.2955 0.718937
\(343\) 8.56905 0.462685
\(344\) 4.50152 0.242706
\(345\) 21.7434 1.17062
\(346\) −48.6638 −2.61618
\(347\) −25.9390 −1.39248 −0.696239 0.717810i \(-0.745145\pi\)
−0.696239 + 0.717810i \(0.745145\pi\)
\(348\) 9.02323 0.483696
\(349\) −17.1162 −0.916207 −0.458103 0.888899i \(-0.651471\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(350\) 1.83517 0.0980942
\(351\) −7.84515 −0.418743
\(352\) −0.183366 −0.00977345
\(353\) −34.2932 −1.82524 −0.912620 0.408808i \(-0.865944\pi\)
−0.912620 + 0.408808i \(0.865944\pi\)
\(354\) 36.2887 1.92872
\(355\) 18.1172 0.961562
\(356\) −1.74880 −0.0926862
\(357\) 1.43153 0.0757647
\(358\) 7.39375 0.390772
\(359\) −15.3319 −0.809188 −0.404594 0.914496i \(-0.632587\pi\)
−0.404594 + 0.914496i \(0.632587\pi\)
\(360\) 17.7017 0.932964
\(361\) 1.35981 0.0715690
\(362\) −40.1460 −2.11003
\(363\) 22.4399 1.17779
\(364\) 5.83039 0.305596
\(365\) −2.86181 −0.149794
\(366\) 41.5079 2.16965
\(367\) 12.8028 0.668300 0.334150 0.942520i \(-0.391551\pi\)
0.334150 + 0.942520i \(0.391551\pi\)
\(368\) 28.8536 1.50410
\(369\) 7.66752 0.399155
\(370\) 3.97264 0.206528
\(371\) 3.15122 0.163603
\(372\) 81.2356 4.21187
\(373\) −7.55022 −0.390935 −0.195468 0.980710i \(-0.562622\pi\)
−0.195468 + 0.980710i \(0.562622\pi\)
\(374\) −0.109286 −0.00565104
\(375\) −19.4814 −1.00601
\(376\) −12.8532 −0.662856
\(377\) 2.09282 0.107786
\(378\) 5.98434 0.307801
\(379\) −19.0391 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(380\) 49.4862 2.53859
\(381\) −32.3926 −1.65953
\(382\) 0.0977485 0.00500125
\(383\) 21.0226 1.07420 0.537102 0.843517i \(-0.319519\pi\)
0.537102 + 0.843517i \(0.319519\pi\)
\(384\) −26.6950 −1.36227
\(385\) 0.0604785 0.00308227
\(386\) 29.4827 1.50063
\(387\) −0.852492 −0.0433346
\(388\) 67.2522 3.41421
\(389\) 14.8273 0.751773 0.375886 0.926666i \(-0.377338\pi\)
0.375886 + 0.926666i \(0.377338\pi\)
\(390\) 26.8346 1.35882
\(391\) 4.78675 0.242076
\(392\) 40.5401 2.04759
\(393\) −32.1352 −1.62101
\(394\) −44.3851 −2.23609
\(395\) 19.8517 0.998847
\(396\) 0.199079 0.0100041
\(397\) −2.20756 −0.110794 −0.0553972 0.998464i \(-0.517643\pi\)
−0.0553972 + 0.998464i \(0.517643\pi\)
\(398\) −50.9219 −2.55248
\(399\) −5.79917 −0.290321
\(400\) 7.71814 0.385907
\(401\) −16.5629 −0.827112 −0.413556 0.910479i \(-0.635713\pi\)
−0.413556 + 0.910479i \(0.635713\pi\)
\(402\) 46.9905 2.34367
\(403\) 18.8415 0.938562
\(404\) −29.7323 −1.47924
\(405\) 27.6159 1.37225
\(406\) −1.59642 −0.0792288
\(407\) 0.0244732 0.00121309
\(408\) 13.9521 0.690733
\(409\) −13.5897 −0.671968 −0.335984 0.941868i \(-0.609069\pi\)
−0.335984 + 0.941868i \(0.609069\pi\)
\(410\) 41.4447 2.04681
\(411\) −18.4528 −0.910208
\(412\) −7.54134 −0.371535
\(413\) −4.42102 −0.217544
\(414\) −12.6630 −0.622351
\(415\) −18.1224 −0.889595
\(416\) 9.91203 0.485977
\(417\) 2.04027 0.0999123
\(418\) 0.442720 0.0216541
\(419\) −17.9232 −0.875604 −0.437802 0.899071i \(-0.644243\pi\)
−0.437802 + 0.899071i \(0.644243\pi\)
\(420\) −14.0953 −0.687782
\(421\) 7.35827 0.358620 0.179310 0.983793i \(-0.442613\pi\)
0.179310 + 0.983793i \(0.442613\pi\)
\(422\) −4.27265 −0.207989
\(423\) 2.43413 0.118352
\(424\) 30.7128 1.49154
\(425\) 1.28042 0.0621096
\(426\) −37.7756 −1.83023
\(427\) −5.05686 −0.244719
\(428\) −8.97950 −0.434040
\(429\) 0.165312 0.00798136
\(430\) −4.60791 −0.222213
\(431\) −13.8655 −0.667880 −0.333940 0.942594i \(-0.608378\pi\)
−0.333940 + 0.942594i \(0.608378\pi\)
\(432\) 25.1682 1.21090
\(433\) 0.389905 0.0187377 0.00936883 0.999956i \(-0.497018\pi\)
0.00936883 + 0.999956i \(0.497018\pi\)
\(434\) −14.3724 −0.689899
\(435\) −5.05951 −0.242585
\(436\) −0.112498 −0.00538767
\(437\) −19.3912 −0.927608
\(438\) 5.96705 0.285117
\(439\) −23.8276 −1.13723 −0.568615 0.822604i \(-0.692521\pi\)
−0.568615 + 0.822604i \(0.692521\pi\)
\(440\) 0.589442 0.0281005
\(441\) −7.67744 −0.365592
\(442\) 5.90755 0.280994
\(443\) −28.7945 −1.36807 −0.684035 0.729450i \(-0.739776\pi\)
−0.684035 + 0.729450i \(0.739776\pi\)
\(444\) −5.70381 −0.270691
\(445\) 0.980589 0.0464844
\(446\) 16.9760 0.803838
\(447\) −25.7978 −1.22019
\(448\) 0.897722 0.0424134
\(449\) 4.27392 0.201699 0.100849 0.994902i \(-0.467844\pi\)
0.100849 + 0.994902i \(0.467844\pi\)
\(450\) −3.38726 −0.159677
\(451\) 0.255317 0.0120224
\(452\) 45.7786 2.15325
\(453\) −23.6236 −1.10994
\(454\) −1.68962 −0.0792976
\(455\) −3.26922 −0.153264
\(456\) −56.5204 −2.64681
\(457\) −36.6346 −1.71369 −0.856847 0.515571i \(-0.827580\pi\)
−0.856847 + 0.515571i \(0.827580\pi\)
\(458\) −62.7664 −2.93288
\(459\) 4.17534 0.194888
\(460\) −47.1319 −2.19754
\(461\) 23.5352 1.09614 0.548072 0.836431i \(-0.315362\pi\)
0.548072 + 0.836431i \(0.315362\pi\)
\(462\) −0.126102 −0.00586678
\(463\) −18.5748 −0.863242 −0.431621 0.902055i \(-0.642058\pi\)
−0.431621 + 0.902055i \(0.642058\pi\)
\(464\) −6.71401 −0.311690
\(465\) −45.5505 −2.11235
\(466\) 18.9177 0.876347
\(467\) −0.0296519 −0.00137212 −0.000686062 1.00000i \(-0.500218\pi\)
−0.000686062 1.00000i \(0.500218\pi\)
\(468\) −10.7614 −0.497446
\(469\) −5.72480 −0.264347
\(470\) 13.1570 0.606889
\(471\) 11.0642 0.509811
\(472\) −43.0885 −1.98331
\(473\) −0.0283867 −0.00130522
\(474\) −41.3921 −1.90120
\(475\) −5.18702 −0.237997
\(476\) −3.10305 −0.142228
\(477\) −5.81634 −0.266312
\(478\) −38.4854 −1.76028
\(479\) −11.5808 −0.529142 −0.264571 0.964366i \(-0.585230\pi\)
−0.264571 + 0.964366i \(0.585230\pi\)
\(480\) −23.9630 −1.09375
\(481\) −1.32292 −0.0603200
\(482\) 63.5421 2.89426
\(483\) 5.52328 0.251318
\(484\) −48.6417 −2.21099
\(485\) −37.7097 −1.71231
\(486\) −29.0809 −1.31914
\(487\) 8.42949 0.381977 0.190988 0.981592i \(-0.438831\pi\)
0.190988 + 0.981592i \(0.438831\pi\)
\(488\) −49.2857 −2.23106
\(489\) 18.1178 0.819313
\(490\) −41.4983 −1.87470
\(491\) −20.8335 −0.940204 −0.470102 0.882612i \(-0.655783\pi\)
−0.470102 + 0.882612i \(0.655783\pi\)
\(492\) −59.5051 −2.68270
\(493\) −1.11384 −0.0501648
\(494\) −23.9316 −1.07674
\(495\) −0.111628 −0.00501730
\(496\) −60.4458 −2.71410
\(497\) 4.60216 0.206435
\(498\) 37.7864 1.69325
\(499\) 27.9109 1.24947 0.624733 0.780839i \(-0.285208\pi\)
0.624733 + 0.780839i \(0.285208\pi\)
\(500\) 42.2287 1.88852
\(501\) 26.8419 1.19921
\(502\) 5.40589 0.241277
\(503\) −6.43258 −0.286815 −0.143407 0.989664i \(-0.545806\pi\)
−0.143407 + 0.989664i \(0.545806\pi\)
\(504\) 4.49662 0.200295
\(505\) 16.6715 0.741873
\(506\) −0.421658 −0.0187450
\(507\) 17.5873 0.781081
\(508\) 70.2157 3.11532
\(509\) −28.7881 −1.27601 −0.638005 0.770033i \(-0.720240\pi\)
−0.638005 + 0.770033i \(0.720240\pi\)
\(510\) −14.2819 −0.632412
\(511\) −0.726959 −0.0321588
\(512\) 50.6420 2.23808
\(513\) −16.9144 −0.746790
\(514\) 2.11015 0.0930747
\(515\) 4.22859 0.186334
\(516\) 6.61591 0.291249
\(517\) 0.0810530 0.00356471
\(518\) 1.00913 0.0443388
\(519\) −39.1777 −1.71971
\(520\) −31.8628 −1.39728
\(521\) −25.5383 −1.11885 −0.559426 0.828880i \(-0.688979\pi\)
−0.559426 + 0.828880i \(0.688979\pi\)
\(522\) 2.94657 0.128968
\(523\) 19.6507 0.859264 0.429632 0.903004i \(-0.358643\pi\)
0.429632 + 0.903004i \(0.358643\pi\)
\(524\) 69.6578 3.04301
\(525\) 1.47744 0.0644807
\(526\) −48.7741 −2.12665
\(527\) −10.0278 −0.436819
\(528\) −0.530342 −0.0230802
\(529\) −4.53128 −0.197012
\(530\) −31.4386 −1.36561
\(531\) 8.16006 0.354116
\(532\) 12.5705 0.545002
\(533\) −13.8014 −0.597805
\(534\) −2.04459 −0.0884781
\(535\) 5.03499 0.217682
\(536\) −55.7956 −2.41000
\(537\) 5.95247 0.256868
\(538\) 14.8687 0.641036
\(539\) −0.255647 −0.0110115
\(540\) −41.1119 −1.76917
\(541\) −31.3091 −1.34608 −0.673042 0.739604i \(-0.735013\pi\)
−0.673042 + 0.739604i \(0.735013\pi\)
\(542\) −11.1868 −0.480516
\(543\) −32.3202 −1.38699
\(544\) −5.27538 −0.226180
\(545\) 0.0630800 0.00270205
\(546\) 6.81654 0.291721
\(547\) −42.1175 −1.80082 −0.900408 0.435046i \(-0.856732\pi\)
−0.900408 + 0.435046i \(0.856732\pi\)
\(548\) 39.9991 1.70867
\(549\) 9.33367 0.398351
\(550\) −0.112791 −0.00480941
\(551\) 4.51218 0.192226
\(552\) 53.8315 2.29122
\(553\) 5.04275 0.214439
\(554\) 21.1676 0.899324
\(555\) 3.19824 0.135758
\(556\) −4.42257 −0.187559
\(557\) −14.1445 −0.599324 −0.299662 0.954045i \(-0.596874\pi\)
−0.299662 + 0.954045i \(0.596874\pi\)
\(558\) 26.5278 1.12301
\(559\) 1.53447 0.0649012
\(560\) 10.4881 0.443202
\(561\) −0.0879826 −0.00371463
\(562\) −1.22392 −0.0516279
\(563\) −40.2579 −1.69667 −0.848333 0.529463i \(-0.822393\pi\)
−0.848333 + 0.529463i \(0.822393\pi\)
\(564\) −18.8905 −0.795433
\(565\) −25.6691 −1.07991
\(566\) 23.1677 0.973813
\(567\) 7.01503 0.294604
\(568\) 44.8540 1.88203
\(569\) 25.9081 1.08613 0.543063 0.839692i \(-0.317265\pi\)
0.543063 + 0.839692i \(0.317265\pi\)
\(570\) 57.8562 2.42333
\(571\) 18.2387 0.763267 0.381633 0.924314i \(-0.375362\pi\)
0.381633 + 0.924314i \(0.375362\pi\)
\(572\) −0.358339 −0.0149829
\(573\) 0.0786941 0.00328749
\(574\) 10.5278 0.439423
\(575\) 4.94025 0.206023
\(576\) −1.65696 −0.0690402
\(577\) 21.0699 0.877152 0.438576 0.898694i \(-0.355483\pi\)
0.438576 + 0.898694i \(0.355483\pi\)
\(578\) 39.9386 1.66123
\(579\) 23.7356 0.986417
\(580\) 10.9672 0.455389
\(581\) −4.60348 −0.190984
\(582\) 78.6272 3.25920
\(583\) −0.193676 −0.00802123
\(584\) −7.08516 −0.293186
\(585\) 6.03415 0.249481
\(586\) −22.9812 −0.949345
\(587\) −10.7856 −0.445170 −0.222585 0.974913i \(-0.571449\pi\)
−0.222585 + 0.974913i \(0.571449\pi\)
\(588\) 59.5821 2.45712
\(589\) 40.6229 1.67384
\(590\) 44.1069 1.81585
\(591\) −35.7330 −1.46986
\(592\) 4.24409 0.174431
\(593\) −1.13587 −0.0466445 −0.0233223 0.999728i \(-0.507424\pi\)
−0.0233223 + 0.999728i \(0.507424\pi\)
\(594\) −0.367800 −0.0150910
\(595\) 1.73995 0.0713308
\(596\) 55.9205 2.29059
\(597\) −40.9955 −1.67784
\(598\) 22.7931 0.932080
\(599\) 0.647277 0.0264470 0.0132235 0.999913i \(-0.495791\pi\)
0.0132235 + 0.999913i \(0.495791\pi\)
\(600\) 14.3996 0.587860
\(601\) −1.18958 −0.0485239 −0.0242619 0.999706i \(-0.507724\pi\)
−0.0242619 + 0.999706i \(0.507724\pi\)
\(602\) −1.17051 −0.0477063
\(603\) 10.5665 0.430301
\(604\) 51.2077 2.08361
\(605\) 27.2744 1.10886
\(606\) −34.7612 −1.41208
\(607\) 7.41191 0.300840 0.150420 0.988622i \(-0.451937\pi\)
0.150420 + 0.988622i \(0.451937\pi\)
\(608\) 21.3707 0.866696
\(609\) −1.28522 −0.0520799
\(610\) 50.4506 2.04268
\(611\) −4.38140 −0.177252
\(612\) 5.72743 0.231518
\(613\) −18.7227 −0.756203 −0.378102 0.925764i \(-0.623423\pi\)
−0.378102 + 0.925764i \(0.623423\pi\)
\(614\) −56.0945 −2.26379
\(615\) 33.3658 1.34544
\(616\) 0.149731 0.00603282
\(617\) −24.1954 −0.974071 −0.487035 0.873382i \(-0.661922\pi\)
−0.487035 + 0.873382i \(0.661922\pi\)
\(618\) −8.81688 −0.354667
\(619\) 27.6196 1.11012 0.555062 0.831809i \(-0.312694\pi\)
0.555062 + 0.831809i \(0.312694\pi\)
\(620\) 98.7373 3.96539
\(621\) 16.1097 0.646461
\(622\) 74.4155 2.98379
\(623\) 0.249090 0.00997959
\(624\) 28.6682 1.14764
\(625\) −29.4263 −1.17705
\(626\) 43.9678 1.75731
\(627\) 0.356419 0.0142340
\(628\) −23.9832 −0.957035
\(629\) 0.704085 0.0280737
\(630\) −4.60289 −0.183384
\(631\) 22.2756 0.886777 0.443389 0.896329i \(-0.353776\pi\)
0.443389 + 0.896329i \(0.353776\pi\)
\(632\) 49.1481 1.95501
\(633\) −3.43977 −0.136719
\(634\) −8.57789 −0.340671
\(635\) −39.3714 −1.56241
\(636\) 45.1387 1.78987
\(637\) 13.8193 0.547539
\(638\) 0.0981165 0.00388447
\(639\) −8.49439 −0.336033
\(640\) −32.4463 −1.28255
\(641\) 11.9095 0.470397 0.235199 0.971947i \(-0.424426\pi\)
0.235199 + 0.971947i \(0.424426\pi\)
\(642\) −10.4983 −0.414334
\(643\) 25.5380 1.00712 0.503561 0.863960i \(-0.332023\pi\)
0.503561 + 0.863960i \(0.332023\pi\)
\(644\) −11.9725 −0.471783
\(645\) −3.70968 −0.146069
\(646\) 12.7369 0.501126
\(647\) 19.0558 0.749162 0.374581 0.927194i \(-0.377787\pi\)
0.374581 + 0.927194i \(0.377787\pi\)
\(648\) 68.3706 2.68585
\(649\) 0.271718 0.0106659
\(650\) 6.09700 0.239144
\(651\) −11.5708 −0.453495
\(652\) −39.2729 −1.53804
\(653\) −14.2224 −0.556564 −0.278282 0.960499i \(-0.589765\pi\)
−0.278282 + 0.960499i \(0.589765\pi\)
\(654\) −0.131526 −0.00514306
\(655\) −39.0586 −1.52614
\(656\) 44.2766 1.72871
\(657\) 1.34178 0.0523478
\(658\) 3.34216 0.130291
\(659\) 0.462001 0.0179970 0.00899851 0.999960i \(-0.497136\pi\)
0.00899851 + 0.999960i \(0.497136\pi\)
\(660\) 0.866306 0.0337209
\(661\) 0.698548 0.0271703 0.0135852 0.999908i \(-0.495676\pi\)
0.0135852 + 0.999908i \(0.495676\pi\)
\(662\) −48.1134 −1.86998
\(663\) 4.75598 0.184707
\(664\) −44.8669 −1.74117
\(665\) −7.04856 −0.273332
\(666\) −1.86260 −0.0721744
\(667\) −4.29752 −0.166401
\(668\) −58.1837 −2.25120
\(669\) 13.6668 0.528391
\(670\) 57.1143 2.20652
\(671\) 0.310797 0.0119982
\(672\) −6.08710 −0.234815
\(673\) −26.7501 −1.03114 −0.515571 0.856847i \(-0.672420\pi\)
−0.515571 + 0.856847i \(0.672420\pi\)
\(674\) −6.12239 −0.235826
\(675\) 4.30924 0.165863
\(676\) −38.1231 −1.46627
\(677\) −15.5018 −0.595784 −0.297892 0.954600i \(-0.596284\pi\)
−0.297892 + 0.954600i \(0.596284\pi\)
\(678\) 53.5216 2.05549
\(679\) −9.57906 −0.367611
\(680\) 16.9580 0.650311
\(681\) −1.36025 −0.0521251
\(682\) 0.883337 0.0338247
\(683\) 45.6589 1.74709 0.873545 0.486743i \(-0.161815\pi\)
0.873545 + 0.486743i \(0.161815\pi\)
\(684\) −23.2020 −0.887149
\(685\) −22.4283 −0.856942
\(686\) −21.7164 −0.829134
\(687\) −50.5312 −1.92788
\(688\) −4.92277 −0.187679
\(689\) 10.4693 0.398849
\(690\) −55.1038 −2.09777
\(691\) 11.0375 0.419888 0.209944 0.977713i \(-0.432672\pi\)
0.209944 + 0.977713i \(0.432672\pi\)
\(692\) 84.9233 3.22830
\(693\) −0.0283558 −0.00107715
\(694\) 65.7367 2.49533
\(695\) 2.47983 0.0940653
\(696\) −12.5262 −0.474803
\(697\) 7.34538 0.278226
\(698\) 43.3771 1.64185
\(699\) 15.2300 0.576053
\(700\) −3.20256 −0.121046
\(701\) 47.3794 1.78950 0.894748 0.446571i \(-0.147355\pi\)
0.894748 + 0.446571i \(0.147355\pi\)
\(702\) 19.8818 0.750390
\(703\) −2.85226 −0.107575
\(704\) −0.0551745 −0.00207947
\(705\) 10.5923 0.398929
\(706\) 86.9084 3.27084
\(707\) 4.23492 0.159270
\(708\) −63.3275 −2.37999
\(709\) −29.2500 −1.09851 −0.549253 0.835656i \(-0.685088\pi\)
−0.549253 + 0.835656i \(0.685088\pi\)
\(710\) −45.9141 −1.72313
\(711\) −9.30761 −0.349063
\(712\) 2.42771 0.0909822
\(713\) −38.6904 −1.44897
\(714\) −3.62790 −0.135771
\(715\) 0.200928 0.00751428
\(716\) −12.9028 −0.482202
\(717\) −30.9834 −1.15709
\(718\) 38.8554 1.45007
\(719\) −19.4417 −0.725052 −0.362526 0.931974i \(-0.618086\pi\)
−0.362526 + 0.931974i \(0.618086\pi\)
\(720\) −19.3583 −0.721440
\(721\) 1.07415 0.0400035
\(722\) −3.44614 −0.128252
\(723\) 51.1557 1.90250
\(724\) 70.0588 2.60372
\(725\) −1.14956 −0.0426935
\(726\) −56.8689 −2.11060
\(727\) 16.1524 0.599059 0.299529 0.954087i \(-0.403170\pi\)
0.299529 + 0.954087i \(0.403170\pi\)
\(728\) −8.09383 −0.299977
\(729\) 9.99654 0.370242
\(730\) 7.25262 0.268431
\(731\) −0.816676 −0.0302059
\(732\) −72.4355 −2.67729
\(733\) 11.2349 0.414972 0.207486 0.978238i \(-0.433472\pi\)
0.207486 + 0.978238i \(0.433472\pi\)
\(734\) −32.4458 −1.19760
\(735\) −33.4089 −1.23231
\(736\) −20.3540 −0.750259
\(737\) 0.351849 0.0129605
\(738\) −19.4316 −0.715289
\(739\) 1.20092 0.0441764 0.0220882 0.999756i \(-0.492969\pi\)
0.0220882 + 0.999756i \(0.492969\pi\)
\(740\) −6.93266 −0.254850
\(741\) −19.2666 −0.707776
\(742\) −7.98608 −0.293178
\(743\) 25.1822 0.923845 0.461922 0.886920i \(-0.347160\pi\)
0.461922 + 0.886920i \(0.347160\pi\)
\(744\) −112.772 −4.13444
\(745\) −31.3558 −1.14879
\(746\) 19.1344 0.700559
\(747\) 8.49684 0.310883
\(748\) 0.190715 0.00697323
\(749\) 1.27899 0.0467334
\(750\) 49.3712 1.80278
\(751\) −0.808800 −0.0295135 −0.0147568 0.999891i \(-0.504697\pi\)
−0.0147568 + 0.999891i \(0.504697\pi\)
\(752\) 14.0561 0.512571
\(753\) 4.35210 0.158599
\(754\) −5.30378 −0.193152
\(755\) −28.7132 −1.04498
\(756\) −10.4433 −0.379818
\(757\) 39.3734 1.43105 0.715525 0.698587i \(-0.246187\pi\)
0.715525 + 0.698587i \(0.246187\pi\)
\(758\) 48.2503 1.75253
\(759\) −0.339463 −0.0123217
\(760\) −68.6974 −2.49192
\(761\) −10.7107 −0.388264 −0.194132 0.980975i \(-0.562189\pi\)
−0.194132 + 0.980975i \(0.562189\pi\)
\(762\) 82.0920 2.97388
\(763\) 0.0160236 0.000580095 0
\(764\) −0.170581 −0.00617140
\(765\) −3.21149 −0.116112
\(766\) −53.2772 −1.92498
\(767\) −14.6880 −0.530351
\(768\) 61.8374 2.23136
\(769\) 46.2157 1.66658 0.833291 0.552834i \(-0.186454\pi\)
0.833291 + 0.552834i \(0.186454\pi\)
\(770\) −0.153270 −0.00552345
\(771\) 1.69881 0.0611812
\(772\) −51.4503 −1.85174
\(773\) 40.0454 1.44033 0.720166 0.693802i \(-0.244066\pi\)
0.720166 + 0.693802i \(0.244066\pi\)
\(774\) 2.16045 0.0776559
\(775\) −10.3494 −0.371762
\(776\) −93.3604 −3.35144
\(777\) 0.812422 0.0291455
\(778\) −37.5765 −1.34718
\(779\) −29.7563 −1.06613
\(780\) −46.8290 −1.67675
\(781\) −0.282851 −0.0101212
\(782\) −12.1310 −0.433802
\(783\) −3.74861 −0.133964
\(784\) −44.3339 −1.58335
\(785\) 13.4479 0.479976
\(786\) 81.4396 2.90486
\(787\) 47.6121 1.69719 0.848593 0.529046i \(-0.177450\pi\)
0.848593 + 0.529046i \(0.177450\pi\)
\(788\) 77.4564 2.75927
\(789\) −39.2664 −1.39792
\(790\) −50.3097 −1.78994
\(791\) −6.52048 −0.231842
\(792\) −0.276364 −0.00982018
\(793\) −16.8004 −0.596601
\(794\) 5.59458 0.198544
\(795\) −25.3102 −0.897661
\(796\) 88.8638 3.14969
\(797\) 33.2123 1.17644 0.588220 0.808701i \(-0.299829\pi\)
0.588220 + 0.808701i \(0.299829\pi\)
\(798\) 14.6967 0.520258
\(799\) 2.33187 0.0824955
\(800\) −5.44456 −0.192494
\(801\) −0.459756 −0.0162447
\(802\) 41.9751 1.48219
\(803\) 0.0446792 0.00157670
\(804\) −82.0032 −2.89203
\(805\) 6.71324 0.236611
\(806\) −47.7496 −1.68191
\(807\) 11.9703 0.421375
\(808\) 41.2748 1.45204
\(809\) 22.2372 0.781819 0.390910 0.920429i \(-0.372161\pi\)
0.390910 + 0.920429i \(0.372161\pi\)
\(810\) −69.9865 −2.45908
\(811\) 7.63656 0.268156 0.134078 0.990971i \(-0.457193\pi\)
0.134078 + 0.990971i \(0.457193\pi\)
\(812\) 2.78591 0.0977662
\(813\) −9.00617 −0.315860
\(814\) −0.0620219 −0.00217387
\(815\) 22.0211 0.771366
\(816\) −15.2578 −0.534129
\(817\) 3.30837 0.115745
\(818\) 34.4401 1.20417
\(819\) 1.53280 0.0535604
\(820\) −72.3251 −2.52570
\(821\) −36.3186 −1.26753 −0.633765 0.773526i \(-0.718491\pi\)
−0.633765 + 0.773526i \(0.718491\pi\)
\(822\) 46.7645 1.63110
\(823\) −45.5195 −1.58671 −0.793356 0.608758i \(-0.791668\pi\)
−0.793356 + 0.608758i \(0.791668\pi\)
\(824\) 10.4690 0.364705
\(825\) −0.0908041 −0.00316139
\(826\) 11.2041 0.389840
\(827\) −39.0261 −1.35707 −0.678535 0.734568i \(-0.737385\pi\)
−0.678535 + 0.734568i \(0.737385\pi\)
\(828\) 22.0982 0.767964
\(829\) −33.5883 −1.16657 −0.583286 0.812267i \(-0.698233\pi\)
−0.583286 + 0.812267i \(0.698233\pi\)
\(830\) 45.9273 1.59416
\(831\) 17.0413 0.591157
\(832\) 2.98251 0.103400
\(833\) −7.35489 −0.254832
\(834\) −5.17061 −0.179043
\(835\) 32.6248 1.12903
\(836\) −0.772591 −0.0267206
\(837\) −33.7485 −1.16652
\(838\) 45.4223 1.56909
\(839\) 47.7165 1.64736 0.823679 0.567057i \(-0.191918\pi\)
0.823679 + 0.567057i \(0.191918\pi\)
\(840\) 19.5674 0.675138
\(841\) 1.00000 0.0344828
\(842\) −18.6479 −0.642649
\(843\) −0.985336 −0.0339368
\(844\) 7.45620 0.256653
\(845\) 21.3764 0.735372
\(846\) −6.16877 −0.212087
\(847\) 6.92828 0.238058
\(848\) −33.5868 −1.15338
\(849\) 18.6516 0.640121
\(850\) −3.24495 −0.111301
\(851\) 2.71657 0.0931229
\(852\) 65.9222 2.25846
\(853\) −38.0888 −1.30414 −0.652068 0.758161i \(-0.726098\pi\)
−0.652068 + 0.758161i \(0.726098\pi\)
\(854\) 12.8155 0.438538
\(855\) 13.0098 0.444927
\(856\) 12.4655 0.426061
\(857\) 4.47298 0.152794 0.0763970 0.997077i \(-0.475658\pi\)
0.0763970 + 0.997077i \(0.475658\pi\)
\(858\) −0.418948 −0.0143026
\(859\) −32.3534 −1.10388 −0.551942 0.833883i \(-0.686113\pi\)
−0.551942 + 0.833883i \(0.686113\pi\)
\(860\) 8.04127 0.274205
\(861\) 8.47561 0.288848
\(862\) 35.1392 1.19684
\(863\) 7.89144 0.268628 0.134314 0.990939i \(-0.457117\pi\)
0.134314 + 0.990939i \(0.457117\pi\)
\(864\) −17.7542 −0.604011
\(865\) −47.6183 −1.61907
\(866\) −0.988129 −0.0335780
\(867\) 32.1533 1.09198
\(868\) 25.0814 0.851317
\(869\) −0.309930 −0.0105136
\(870\) 12.8222 0.434714
\(871\) −19.0195 −0.644452
\(872\) 0.156171 0.00528862
\(873\) 17.6805 0.598394
\(874\) 49.1428 1.66228
\(875\) −6.01484 −0.203339
\(876\) −10.4131 −0.351826
\(877\) −51.8770 −1.75176 −0.875881 0.482527i \(-0.839719\pi\)
−0.875881 + 0.482527i \(0.839719\pi\)
\(878\) 60.3858 2.03792
\(879\) −18.5014 −0.624038
\(880\) −0.644602 −0.0217295
\(881\) −31.5281 −1.06221 −0.531105 0.847306i \(-0.678223\pi\)
−0.531105 + 0.847306i \(0.678223\pi\)
\(882\) 19.4568 0.655144
\(883\) 58.7926 1.97853 0.989265 0.146135i \(-0.0466833\pi\)
0.989265 + 0.146135i \(0.0466833\pi\)
\(884\) −10.3093 −0.346739
\(885\) 35.5091 1.19362
\(886\) 72.9734 2.45159
\(887\) 1.69885 0.0570417 0.0285208 0.999593i \(-0.490920\pi\)
0.0285208 + 0.999593i \(0.490920\pi\)
\(888\) 7.91810 0.265714
\(889\) −10.0012 −0.335429
\(890\) −2.48509 −0.0833003
\(891\) −0.431147 −0.0144440
\(892\) −29.6249 −0.991914
\(893\) −9.44644 −0.316113
\(894\) 65.3788 2.18660
\(895\) 7.23489 0.241836
\(896\) −8.24204 −0.275347
\(897\) 18.3500 0.612689
\(898\) −10.8313 −0.361446
\(899\) 9.00294 0.300265
\(900\) 5.91111 0.197037
\(901\) −5.57198 −0.185630
\(902\) −0.647045 −0.0215442
\(903\) −0.942337 −0.0313590
\(904\) −63.5506 −2.11366
\(905\) −39.2835 −1.30583
\(906\) 59.8689 1.98901
\(907\) −40.5913 −1.34781 −0.673906 0.738817i \(-0.735385\pi\)
−0.673906 + 0.738817i \(0.735385\pi\)
\(908\) 2.94855 0.0978510
\(909\) −7.81656 −0.259259
\(910\) 8.28513 0.274649
\(911\) 4.06313 0.134617 0.0673087 0.997732i \(-0.478559\pi\)
0.0673087 + 0.997732i \(0.478559\pi\)
\(912\) 61.8096 2.04672
\(913\) 0.282932 0.00936368
\(914\) 92.8423 3.07095
\(915\) 40.6161 1.34273
\(916\) 109.534 3.61909
\(917\) −9.92170 −0.327643
\(918\) −10.5815 −0.349241
\(919\) −5.19417 −0.171340 −0.0856699 0.996324i \(-0.527303\pi\)
−0.0856699 + 0.996324i \(0.527303\pi\)
\(920\) 65.4292 2.15714
\(921\) −45.1598 −1.48807
\(922\) −59.6448 −1.96430
\(923\) 15.2898 0.503268
\(924\) 0.220060 0.00723945
\(925\) 0.726664 0.0238926
\(926\) 47.0736 1.54694
\(927\) −1.98261 −0.0651173
\(928\) 4.73622 0.155474
\(929\) 14.1571 0.464478 0.232239 0.972659i \(-0.425395\pi\)
0.232239 + 0.972659i \(0.425395\pi\)
\(930\) 115.438 3.78535
\(931\) 29.7948 0.976485
\(932\) −33.0133 −1.08139
\(933\) 59.9095 1.96135
\(934\) 0.0751461 0.00245886
\(935\) −0.106938 −0.00349724
\(936\) 14.9391 0.488301
\(937\) −6.43455 −0.210207 −0.105104 0.994461i \(-0.533517\pi\)
−0.105104 + 0.994461i \(0.533517\pi\)
\(938\) 14.5082 0.473711
\(939\) 35.3970 1.15514
\(940\) −22.9603 −0.748884
\(941\) 7.80257 0.254357 0.127178 0.991880i \(-0.459408\pi\)
0.127178 + 0.991880i \(0.459408\pi\)
\(942\) −28.0397 −0.913584
\(943\) 28.3407 0.922900
\(944\) 47.1208 1.53365
\(945\) 5.85577 0.190488
\(946\) 0.0719399 0.00233897
\(947\) 45.6451 1.48327 0.741633 0.670806i \(-0.234051\pi\)
0.741633 + 0.670806i \(0.234051\pi\)
\(948\) 72.2333 2.34603
\(949\) −2.41518 −0.0784000
\(950\) 13.1454 0.426492
\(951\) −6.90578 −0.223935
\(952\) 4.30770 0.139613
\(953\) −41.0425 −1.32950 −0.664748 0.747067i \(-0.731461\pi\)
−0.664748 + 0.747067i \(0.731461\pi\)
\(954\) 14.7402 0.477233
\(955\) 0.0956483 0.00309511
\(956\) 67.1609 2.17214
\(957\) 0.0789904 0.00255340
\(958\) 29.3491 0.948227
\(959\) −5.69726 −0.183974
\(960\) −7.21040 −0.232715
\(961\) 50.0529 1.61461
\(962\) 3.35265 0.108094
\(963\) −2.36069 −0.0760723
\(964\) −110.887 −3.57144
\(965\) 28.8493 0.928691
\(966\) −13.9975 −0.450363
\(967\) 2.07805 0.0668255 0.0334128 0.999442i \(-0.489362\pi\)
0.0334128 + 0.999442i \(0.489362\pi\)
\(968\) 67.5251 2.17034
\(969\) 10.2541 0.329408
\(970\) 95.5670 3.06847
\(971\) −28.5806 −0.917195 −0.458598 0.888644i \(-0.651648\pi\)
−0.458598 + 0.888644i \(0.651648\pi\)
\(972\) 50.7492 1.62778
\(973\) 0.629929 0.0201946
\(974\) −21.3627 −0.684504
\(975\) 4.90850 0.157198
\(976\) 53.8978 1.72523
\(977\) 11.8580 0.379371 0.189685 0.981845i \(-0.439253\pi\)
0.189685 + 0.981845i \(0.439253\pi\)
\(978\) −45.9155 −1.46821
\(979\) −0.0153092 −0.000489284 0
\(980\) 72.4187 2.31333
\(981\) −0.0295755 −0.000944273 0
\(982\) 52.7980 1.68485
\(983\) 14.4929 0.462252 0.231126 0.972924i \(-0.425759\pi\)
0.231126 + 0.972924i \(0.425759\pi\)
\(984\) 82.6058 2.63338
\(985\) −43.4315 −1.38384
\(986\) 2.82278 0.0898956
\(987\) 2.69067 0.0856449
\(988\) 41.7631 1.32866
\(989\) −3.15098 −0.100195
\(990\) 0.282896 0.00899103
\(991\) −6.11159 −0.194141 −0.0970706 0.995278i \(-0.530947\pi\)
−0.0970706 + 0.995278i \(0.530947\pi\)
\(992\) 42.6399 1.35382
\(993\) −38.7345 −1.22920
\(994\) −11.6631 −0.369933
\(995\) −49.8278 −1.57965
\(996\) −65.9411 −2.08942
\(997\) 12.8682 0.407540 0.203770 0.979019i \(-0.434681\pi\)
0.203770 + 0.979019i \(0.434681\pi\)
\(998\) −70.7341 −2.23905
\(999\) 2.36959 0.0749705
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 \(a_p\))