Properties

Label 4031.2.a.c.1.10
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 1.10
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.99079 q^{2}\) \(-3.03517 q^{3}\) \(+1.96324 q^{4}\) \(-1.96489 q^{5}\) \(+6.04239 q^{6}\) \(+0.618316 q^{7}\) \(+0.0731745 q^{8}\) \(+6.21228 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.99079 q^{2}\) \(-3.03517 q^{3}\) \(+1.96324 q^{4}\) \(-1.96489 q^{5}\) \(+6.04239 q^{6}\) \(+0.618316 q^{7}\) \(+0.0731745 q^{8}\) \(+6.21228 q^{9}\) \(+3.91168 q^{10}\) \(-1.03647 q^{11}\) \(-5.95879 q^{12}\) \(-1.13046 q^{13}\) \(-1.23094 q^{14}\) \(+5.96377 q^{15}\) \(-4.07216 q^{16}\) \(+1.84344 q^{17}\) \(-12.3673 q^{18}\) \(+5.19120 q^{19}\) \(-3.85755 q^{20}\) \(-1.87670 q^{21}\) \(+2.06339 q^{22}\) \(-0.0424119 q^{23}\) \(-0.222097 q^{24}\) \(-1.13922 q^{25}\) \(+2.25052 q^{26}\) \(-9.74983 q^{27}\) \(+1.21390 q^{28}\) \(-1.00000 q^{29}\) \(-11.8726 q^{30}\) \(-5.48926 q^{31}\) \(+7.96047 q^{32}\) \(+3.14586 q^{33}\) \(-3.66990 q^{34}\) \(-1.21492 q^{35}\) \(+12.1962 q^{36}\) \(-2.74985 q^{37}\) \(-10.3346 q^{38}\) \(+3.43116 q^{39}\) \(-0.143780 q^{40}\) \(-4.79099 q^{41}\) \(+3.73611 q^{42}\) \(-0.286022 q^{43}\) \(-2.03484 q^{44}\) \(-12.2064 q^{45}\) \(+0.0844332 q^{46}\) \(-0.412310 q^{47}\) \(+12.3597 q^{48}\) \(-6.61769 q^{49}\) \(+2.26795 q^{50}\) \(-5.59516 q^{51}\) \(-2.21938 q^{52}\) \(+14.1406 q^{53}\) \(+19.4099 q^{54}\) \(+2.03654 q^{55}\) \(+0.0452449 q^{56}\) \(-15.7562 q^{57}\) \(+1.99079 q^{58}\) \(+5.80725 q^{59}\) \(+11.7083 q^{60}\) \(-11.5442 q^{61}\) \(+10.9280 q^{62}\) \(+3.84115 q^{63}\) \(-7.70330 q^{64}\) \(+2.22124 q^{65}\) \(-6.26274 q^{66}\) \(-9.91482 q^{67}\) \(+3.61912 q^{68}\) \(+0.128728 q^{69}\) \(+2.41865 q^{70}\) \(-2.35394 q^{71}\) \(+0.454580 q^{72}\) \(+14.8420 q^{73}\) \(+5.47437 q^{74}\) \(+3.45773 q^{75}\) \(+10.1916 q^{76}\) \(-0.640864 q^{77}\) \(-6.83071 q^{78}\) \(+3.71256 q^{79}\) \(+8.00134 q^{80}\) \(+10.9556 q^{81}\) \(+9.53785 q^{82}\) \(-1.88462 q^{83}\) \(-3.68441 q^{84}\) \(-3.62215 q^{85}\) \(+0.569409 q^{86}\) \(+3.03517 q^{87}\) \(-0.0758429 q^{88}\) \(-12.3638 q^{89}\) \(+24.3004 q^{90}\) \(-0.698984 q^{91}\) \(-0.0832649 q^{92}\) \(+16.6608 q^{93}\) \(+0.820822 q^{94}\) \(-10.2001 q^{95}\) \(-24.1614 q^{96}\) \(+0.989970 q^{97}\) \(+13.1744 q^{98}\) \(-6.43882 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99079 −1.40770 −0.703850 0.710348i \(-0.748537\pi\)
−0.703850 + 0.710348i \(0.748537\pi\)
\(3\) −3.03517 −1.75236 −0.876179 0.481985i \(-0.839916\pi\)
−0.876179 + 0.481985i \(0.839916\pi\)
\(4\) 1.96324 0.981622
\(5\) −1.96489 −0.878724 −0.439362 0.898310i \(-0.644795\pi\)
−0.439362 + 0.898310i \(0.644795\pi\)
\(6\) 6.04239 2.46680
\(7\) 0.618316 0.233701 0.116851 0.993149i \(-0.462720\pi\)
0.116851 + 0.993149i \(0.462720\pi\)
\(8\) 0.0731745 0.0258711
\(9\) 6.21228 2.07076
\(10\) 3.91168 1.23698
\(11\) −1.03647 −0.312507 −0.156253 0.987717i \(-0.549942\pi\)
−0.156253 + 0.987717i \(0.549942\pi\)
\(12\) −5.95879 −1.72015
\(13\) −1.13046 −0.313534 −0.156767 0.987636i \(-0.550107\pi\)
−0.156767 + 0.987636i \(0.550107\pi\)
\(14\) −1.23094 −0.328982
\(15\) 5.96377 1.53984
\(16\) −4.07216 −1.01804
\(17\) 1.84344 0.447100 0.223550 0.974693i \(-0.428235\pi\)
0.223550 + 0.974693i \(0.428235\pi\)
\(18\) −12.3673 −2.91501
\(19\) 5.19120 1.19094 0.595472 0.803376i \(-0.296965\pi\)
0.595472 + 0.803376i \(0.296965\pi\)
\(20\) −3.85755 −0.862575
\(21\) −1.87670 −0.409529
\(22\) 2.06339 0.439916
\(23\) −0.0424119 −0.00884350 −0.00442175 0.999990i \(-0.501407\pi\)
−0.00442175 + 0.999990i \(0.501407\pi\)
\(24\) −0.222097 −0.0453354
\(25\) −1.13922 −0.227844
\(26\) 2.25052 0.441363
\(27\) −9.74983 −1.87636
\(28\) 1.21390 0.229406
\(29\) −1.00000 −0.185695
\(30\) −11.8726 −2.16763
\(31\) −5.48926 −0.985899 −0.492950 0.870058i \(-0.664081\pi\)
−0.492950 + 0.870058i \(0.664081\pi\)
\(32\) 7.96047 1.40723
\(33\) 3.14586 0.547623
\(34\) −3.66990 −0.629383
\(35\) −1.21492 −0.205359
\(36\) 12.1962 2.03270
\(37\) −2.74985 −0.452072 −0.226036 0.974119i \(-0.572577\pi\)
−0.226036 + 0.974119i \(0.572577\pi\)
\(38\) −10.3346 −1.67649
\(39\) 3.43116 0.549425
\(40\) −0.143780 −0.0227335
\(41\) −4.79099 −0.748226 −0.374113 0.927383i \(-0.622053\pi\)
−0.374113 + 0.927383i \(0.622053\pi\)
\(42\) 3.73611 0.576494
\(43\) −0.286022 −0.0436179 −0.0218090 0.999762i \(-0.506943\pi\)
−0.0218090 + 0.999762i \(0.506943\pi\)
\(44\) −2.03484 −0.306763
\(45\) −12.2064 −1.81963
\(46\) 0.0844332 0.0124490
\(47\) −0.412310 −0.0601416 −0.0300708 0.999548i \(-0.509573\pi\)
−0.0300708 + 0.999548i \(0.509573\pi\)
\(48\) 12.3597 1.78397
\(49\) −6.61769 −0.945384
\(50\) 2.26795 0.320736
\(51\) −5.59516 −0.783479
\(52\) −2.21938 −0.307772
\(53\) 14.1406 1.94236 0.971180 0.238346i \(-0.0766052\pi\)
0.971180 + 0.238346i \(0.0766052\pi\)
\(54\) 19.4099 2.64135
\(55\) 2.03654 0.274607
\(56\) 0.0452449 0.00604611
\(57\) −15.7562 −2.08696
\(58\) 1.99079 0.261403
\(59\) 5.80725 0.756039 0.378019 0.925798i \(-0.376605\pi\)
0.378019 + 0.925798i \(0.376605\pi\)
\(60\) 11.7083 1.51154
\(61\) −11.5442 −1.47808 −0.739039 0.673662i \(-0.764720\pi\)
−0.739039 + 0.673662i \(0.764720\pi\)
\(62\) 10.9280 1.38785
\(63\) 3.84115 0.483939
\(64\) −7.70330 −0.962912
\(65\) 2.22124 0.275510
\(66\) −6.26274 −0.770890
\(67\) −9.91482 −1.21129 −0.605644 0.795736i \(-0.707085\pi\)
−0.605644 + 0.795736i \(0.707085\pi\)
\(68\) 3.61912 0.438883
\(69\) 0.128728 0.0154970
\(70\) 2.41865 0.289084
\(71\) −2.35394 −0.279361 −0.139681 0.990197i \(-0.544608\pi\)
−0.139681 + 0.990197i \(0.544608\pi\)
\(72\) 0.454580 0.0535728
\(73\) 14.8420 1.73712 0.868562 0.495580i \(-0.165044\pi\)
0.868562 + 0.495580i \(0.165044\pi\)
\(74\) 5.47437 0.636383
\(75\) 3.45773 0.399264
\(76\) 10.1916 1.16906
\(77\) −0.640864 −0.0730332
\(78\) −6.83071 −0.773426
\(79\) 3.71256 0.417695 0.208848 0.977948i \(-0.433029\pi\)
0.208848 + 0.977948i \(0.433029\pi\)
\(80\) 8.00134 0.894577
\(81\) 10.9556 1.21729
\(82\) 9.53785 1.05328
\(83\) −1.88462 −0.206864 −0.103432 0.994637i \(-0.532982\pi\)
−0.103432 + 0.994637i \(0.532982\pi\)
\(84\) −3.68441 −0.402002
\(85\) −3.62215 −0.392877
\(86\) 0.569409 0.0614010
\(87\) 3.03517 0.325405
\(88\) −0.0758429 −0.00808488
\(89\) −12.3638 −1.31056 −0.655279 0.755387i \(-0.727449\pi\)
−0.655279 + 0.755387i \(0.727449\pi\)
\(90\) 24.3004 2.56149
\(91\) −0.698984 −0.0732734
\(92\) −0.0832649 −0.00868097
\(93\) 16.6608 1.72765
\(94\) 0.820822 0.0846613
\(95\) −10.2001 −1.04651
\(96\) −24.1614 −2.46596
\(97\) 0.989970 0.100516 0.0502581 0.998736i \(-0.483996\pi\)
0.0502581 + 0.998736i \(0.483996\pi\)
\(98\) 13.1744 1.33082
\(99\) −6.43882 −0.647126
\(100\) −2.23656 −0.223656
\(101\) 14.1373 1.40672 0.703359 0.710835i \(-0.251683\pi\)
0.703359 + 0.710835i \(0.251683\pi\)
\(102\) 11.1388 1.10290
\(103\) 12.2103 1.20311 0.601557 0.798830i \(-0.294547\pi\)
0.601557 + 0.798830i \(0.294547\pi\)
\(104\) −0.0827212 −0.00811148
\(105\) 3.68750 0.359863
\(106\) −28.1510 −2.73426
\(107\) 3.70346 0.358027 0.179014 0.983847i \(-0.442709\pi\)
0.179014 + 0.983847i \(0.442709\pi\)
\(108\) −19.1413 −1.84187
\(109\) 10.0782 0.965313 0.482657 0.875810i \(-0.339672\pi\)
0.482657 + 0.875810i \(0.339672\pi\)
\(110\) −4.05432 −0.386565
\(111\) 8.34627 0.792193
\(112\) −2.51788 −0.237917
\(113\) 14.9360 1.40506 0.702531 0.711653i \(-0.252053\pi\)
0.702531 + 0.711653i \(0.252053\pi\)
\(114\) 31.3673 2.93781
\(115\) 0.0833346 0.00777099
\(116\) −1.96324 −0.182283
\(117\) −7.02276 −0.649255
\(118\) −11.5610 −1.06428
\(119\) 1.13983 0.104488
\(120\) 0.436396 0.0398373
\(121\) −9.92574 −0.902340
\(122\) 22.9820 2.08069
\(123\) 14.5415 1.31116
\(124\) −10.7767 −0.967780
\(125\) 12.0629 1.07894
\(126\) −7.64692 −0.681242
\(127\) −3.94508 −0.350069 −0.175035 0.984562i \(-0.556004\pi\)
−0.175035 + 0.984562i \(0.556004\pi\)
\(128\) −0.585297 −0.0517334
\(129\) 0.868126 0.0764342
\(130\) −4.42201 −0.387836
\(131\) 17.2565 1.50771 0.753853 0.657043i \(-0.228193\pi\)
0.753853 + 0.657043i \(0.228193\pi\)
\(132\) 6.17608 0.537559
\(133\) 3.20980 0.278325
\(134\) 19.7383 1.70513
\(135\) 19.1573 1.64880
\(136\) 0.134893 0.0115670
\(137\) −2.85946 −0.244300 −0.122150 0.992512i \(-0.538979\pi\)
−0.122150 + 0.992512i \(0.538979\pi\)
\(138\) −0.256269 −0.0218151
\(139\) −1.00000 −0.0848189
\(140\) −2.38519 −0.201585
\(141\) 1.25143 0.105390
\(142\) 4.68620 0.393257
\(143\) 1.17169 0.0979816
\(144\) −25.2974 −2.10812
\(145\) 1.96489 0.163175
\(146\) −29.5473 −2.44535
\(147\) 20.0858 1.65665
\(148\) −5.39862 −0.443764
\(149\) 16.4280 1.34584 0.672919 0.739717i \(-0.265040\pi\)
0.672919 + 0.739717i \(0.265040\pi\)
\(150\) −6.88361 −0.562044
\(151\) −22.3254 −1.81681 −0.908407 0.418086i \(-0.862701\pi\)
−0.908407 + 0.418086i \(0.862701\pi\)
\(152\) 0.379863 0.0308110
\(153\) 11.4520 0.925836
\(154\) 1.27582 0.102809
\(155\) 10.7858 0.866334
\(156\) 6.73620 0.539327
\(157\) 7.22010 0.576227 0.288113 0.957596i \(-0.406972\pi\)
0.288113 + 0.957596i \(0.406972\pi\)
\(158\) −7.39092 −0.587990
\(159\) −42.9192 −3.40371
\(160\) −15.6414 −1.23656
\(161\) −0.0262240 −0.00206674
\(162\) −21.8103 −1.71358
\(163\) 18.8468 1.47620 0.738098 0.674694i \(-0.235724\pi\)
0.738098 + 0.674694i \(0.235724\pi\)
\(164\) −9.40587 −0.734475
\(165\) −6.18125 −0.481210
\(166\) 3.75188 0.291202
\(167\) 16.9149 1.30891 0.654457 0.756100i \(-0.272897\pi\)
0.654457 + 0.756100i \(0.272897\pi\)
\(168\) −0.137326 −0.0105949
\(169\) −11.7220 −0.901696
\(170\) 7.21094 0.553054
\(171\) 32.2492 2.46616
\(172\) −0.561531 −0.0428163
\(173\) −12.6719 −0.963425 −0.481713 0.876329i \(-0.659985\pi\)
−0.481713 + 0.876329i \(0.659985\pi\)
\(174\) −6.04239 −0.458073
\(175\) −0.704397 −0.0532474
\(176\) 4.22066 0.318144
\(177\) −17.6260 −1.32485
\(178\) 24.6137 1.84487
\(179\) −3.59805 −0.268931 −0.134465 0.990918i \(-0.542932\pi\)
−0.134465 + 0.990918i \(0.542932\pi\)
\(180\) −23.9642 −1.78619
\(181\) 13.5658 1.00834 0.504170 0.863604i \(-0.331798\pi\)
0.504170 + 0.863604i \(0.331798\pi\)
\(182\) 1.39153 0.103147
\(183\) 35.0385 2.59012
\(184\) −0.00310347 −0.000228791 0
\(185\) 5.40314 0.397247
\(186\) −33.1682 −2.43201
\(187\) −1.91066 −0.139722
\(188\) −0.809464 −0.0590363
\(189\) −6.02847 −0.438507
\(190\) 20.3063 1.47317
\(191\) −3.15942 −0.228607 −0.114304 0.993446i \(-0.536464\pi\)
−0.114304 + 0.993446i \(0.536464\pi\)
\(192\) 23.3808 1.68737
\(193\) 11.6283 0.837024 0.418512 0.908211i \(-0.362552\pi\)
0.418512 + 0.908211i \(0.362552\pi\)
\(194\) −1.97082 −0.141497
\(195\) −6.74183 −0.482793
\(196\) −12.9921 −0.928009
\(197\) −9.94991 −0.708902 −0.354451 0.935075i \(-0.615332\pi\)
−0.354451 + 0.935075i \(0.615332\pi\)
\(198\) 12.8183 0.910960
\(199\) −26.7437 −1.89581 −0.947905 0.318552i \(-0.896803\pi\)
−0.947905 + 0.318552i \(0.896803\pi\)
\(200\) −0.0833618 −0.00589457
\(201\) 30.0932 2.12261
\(202\) −28.1445 −1.98024
\(203\) −0.618316 −0.0433973
\(204\) −10.9847 −0.769080
\(205\) 9.41375 0.657485
\(206\) −24.3081 −1.69362
\(207\) −0.263475 −0.0183128
\(208\) 4.60343 0.319191
\(209\) −5.38051 −0.372177
\(210\) −7.34103 −0.506579
\(211\) 7.89316 0.543388 0.271694 0.962384i \(-0.412416\pi\)
0.271694 + 0.962384i \(0.412416\pi\)
\(212\) 27.7614 1.90666
\(213\) 7.14461 0.489541
\(214\) −7.37281 −0.503995
\(215\) 0.562001 0.0383281
\(216\) −0.713439 −0.0485433
\(217\) −3.39409 −0.230406
\(218\) −20.0635 −1.35887
\(219\) −45.0480 −3.04407
\(220\) 3.99822 0.269560
\(221\) −2.08394 −0.140181
\(222\) −16.6157 −1.11517
\(223\) −14.2098 −0.951559 −0.475780 0.879565i \(-0.657834\pi\)
−0.475780 + 0.879565i \(0.657834\pi\)
\(224\) 4.92208 0.328871
\(225\) −7.07715 −0.471810
\(226\) −29.7345 −1.97791
\(227\) 24.4396 1.62211 0.811056 0.584968i \(-0.198893\pi\)
0.811056 + 0.584968i \(0.198893\pi\)
\(228\) −30.9332 −2.04860
\(229\) −7.78178 −0.514234 −0.257117 0.966380i \(-0.582773\pi\)
−0.257117 + 0.966380i \(0.582773\pi\)
\(230\) −0.165902 −0.0109392
\(231\) 1.94513 0.127980
\(232\) −0.0731745 −0.00480414
\(233\) −28.1267 −1.84264 −0.921320 0.388805i \(-0.872888\pi\)
−0.921320 + 0.388805i \(0.872888\pi\)
\(234\) 13.9808 0.913956
\(235\) 0.810142 0.0528478
\(236\) 11.4010 0.742144
\(237\) −11.2683 −0.731952
\(238\) −2.26916 −0.147088
\(239\) 6.31416 0.408429 0.204215 0.978926i \(-0.434536\pi\)
0.204215 + 0.978926i \(0.434536\pi\)
\(240\) −24.2855 −1.56762
\(241\) −10.9833 −0.707498 −0.353749 0.935340i \(-0.615093\pi\)
−0.353749 + 0.935340i \(0.615093\pi\)
\(242\) 19.7601 1.27022
\(243\) −4.00261 −0.256768
\(244\) −22.6640 −1.45091
\(245\) 13.0030 0.830731
\(246\) −28.9490 −1.84572
\(247\) −5.86847 −0.373402
\(248\) −0.401673 −0.0255063
\(249\) 5.72014 0.362499
\(250\) −24.0146 −1.51882
\(251\) 5.12821 0.323690 0.161845 0.986816i \(-0.448256\pi\)
0.161845 + 0.986816i \(0.448256\pi\)
\(252\) 7.54111 0.475046
\(253\) 0.0439585 0.00276365
\(254\) 7.85383 0.492793
\(255\) 10.9939 0.688462
\(256\) 16.5718 1.03574
\(257\) 0.377940 0.0235753 0.0117876 0.999931i \(-0.496248\pi\)
0.0117876 + 0.999931i \(0.496248\pi\)
\(258\) −1.72826 −0.107597
\(259\) −1.70028 −0.105650
\(260\) 4.36083 0.270447
\(261\) −6.21228 −0.384530
\(262\) −34.3540 −2.12240
\(263\) −1.13347 −0.0698925 −0.0349463 0.999389i \(-0.511126\pi\)
−0.0349463 + 0.999389i \(0.511126\pi\)
\(264\) 0.230196 0.0141676
\(265\) −27.7847 −1.70680
\(266\) −6.39004 −0.391798
\(267\) 37.5262 2.29657
\(268\) −19.4652 −1.18903
\(269\) −2.99493 −0.182604 −0.0913021 0.995823i \(-0.529103\pi\)
−0.0913021 + 0.995823i \(0.529103\pi\)
\(270\) −38.1382 −2.32102
\(271\) 28.8420 1.75202 0.876012 0.482289i \(-0.160194\pi\)
0.876012 + 0.482289i \(0.160194\pi\)
\(272\) −7.50678 −0.455166
\(273\) 2.12154 0.128401
\(274\) 5.69259 0.343902
\(275\) 1.18076 0.0712027
\(276\) 0.252724 0.0152122
\(277\) −7.03322 −0.422585 −0.211293 0.977423i \(-0.567767\pi\)
−0.211293 + 0.977423i \(0.567767\pi\)
\(278\) 1.99079 0.119400
\(279\) −34.1008 −2.04156
\(280\) −0.0889012 −0.00531286
\(281\) −12.3519 −0.736855 −0.368428 0.929656i \(-0.620104\pi\)
−0.368428 + 0.929656i \(0.620104\pi\)
\(282\) −2.49134 −0.148357
\(283\) 7.82905 0.465389 0.232695 0.972550i \(-0.425246\pi\)
0.232695 + 0.972550i \(0.425246\pi\)
\(284\) −4.62136 −0.274227
\(285\) 30.9591 1.83386
\(286\) −2.33259 −0.137929
\(287\) −2.96234 −0.174862
\(288\) 49.4527 2.91403
\(289\) −13.6017 −0.800102
\(290\) −3.91168 −0.229702
\(291\) −3.00473 −0.176141
\(292\) 29.1385 1.70520
\(293\) −9.40685 −0.549554 −0.274777 0.961508i \(-0.588604\pi\)
−0.274777 + 0.961508i \(0.588604\pi\)
\(294\) −39.9867 −2.33207
\(295\) −11.4106 −0.664350
\(296\) −0.201219 −0.0116956
\(297\) 10.1054 0.586373
\(298\) −32.7048 −1.89454
\(299\) 0.0479452 0.00277274
\(300\) 6.78836 0.391926
\(301\) −0.176852 −0.0101936
\(302\) 44.4452 2.55753
\(303\) −42.9093 −2.46507
\(304\) −21.1394 −1.21243
\(305\) 22.6830 1.29882
\(306\) −22.7984 −1.30330
\(307\) −6.70926 −0.382918 −0.191459 0.981501i \(-0.561322\pi\)
−0.191459 + 0.981501i \(0.561322\pi\)
\(308\) −1.25817 −0.0716910
\(309\) −37.0603 −2.10829
\(310\) −21.4722 −1.21954
\(311\) −0.812658 −0.0460816 −0.0230408 0.999735i \(-0.507335\pi\)
−0.0230408 + 0.999735i \(0.507335\pi\)
\(312\) 0.251073 0.0142142
\(313\) −25.0974 −1.41859 −0.709295 0.704912i \(-0.750987\pi\)
−0.709295 + 0.704912i \(0.750987\pi\)
\(314\) −14.3737 −0.811155
\(315\) −7.54743 −0.425249
\(316\) 7.28865 0.410019
\(317\) −15.3952 −0.864683 −0.432341 0.901710i \(-0.642312\pi\)
−0.432341 + 0.901710i \(0.642312\pi\)
\(318\) 85.4431 4.79141
\(319\) 1.03647 0.0580310
\(320\) 15.1361 0.846134
\(321\) −11.2406 −0.627392
\(322\) 0.0522064 0.00290935
\(323\) 9.56966 0.532470
\(324\) 21.5085 1.19492
\(325\) 1.28785 0.0714369
\(326\) −37.5200 −2.07804
\(327\) −30.5890 −1.69157
\(328\) −0.350578 −0.0193574
\(329\) −0.254938 −0.0140552
\(330\) 12.3056 0.677400
\(331\) 20.5846 1.13143 0.565715 0.824601i \(-0.308600\pi\)
0.565715 + 0.824601i \(0.308600\pi\)
\(332\) −3.69996 −0.203062
\(333\) −17.0828 −0.936133
\(334\) −33.6740 −1.84256
\(335\) 19.4815 1.06439
\(336\) 7.64221 0.416917
\(337\) −21.7917 −1.18707 −0.593536 0.804808i \(-0.702268\pi\)
−0.593536 + 0.804808i \(0.702268\pi\)
\(338\) 23.3361 1.26932
\(339\) −45.3334 −2.46217
\(340\) −7.11116 −0.385657
\(341\) 5.68943 0.308100
\(342\) −64.2014 −3.47161
\(343\) −8.42003 −0.454639
\(344\) −0.0209295 −0.00112844
\(345\) −0.252935 −0.0136176
\(346\) 25.2270 1.35621
\(347\) 19.5433 1.04914 0.524568 0.851368i \(-0.324227\pi\)
0.524568 + 0.851368i \(0.324227\pi\)
\(348\) 5.95879 0.319424
\(349\) −18.4308 −0.986576 −0.493288 0.869866i \(-0.664205\pi\)
−0.493288 + 0.869866i \(0.664205\pi\)
\(350\) 1.40231 0.0749564
\(351\) 11.0218 0.588302
\(352\) −8.25076 −0.439767
\(353\) 12.1098 0.644538 0.322269 0.946648i \(-0.395554\pi\)
0.322269 + 0.946648i \(0.395554\pi\)
\(354\) 35.0897 1.86499
\(355\) 4.62522 0.245481
\(356\) −24.2731 −1.28647
\(357\) −3.45957 −0.183100
\(358\) 7.16296 0.378574
\(359\) −8.32719 −0.439493 −0.219746 0.975557i \(-0.570523\pi\)
−0.219746 + 0.975557i \(0.570523\pi\)
\(360\) −0.893199 −0.0470757
\(361\) 7.94856 0.418345
\(362\) −27.0067 −1.41944
\(363\) 30.1263 1.58122
\(364\) −1.37228 −0.0719268
\(365\) −29.1629 −1.52645
\(366\) −69.7544 −3.64612
\(367\) 23.5583 1.22973 0.614865 0.788632i \(-0.289210\pi\)
0.614865 + 0.788632i \(0.289210\pi\)
\(368\) 0.172708 0.00900304
\(369\) −29.7629 −1.54940
\(370\) −10.7565 −0.559205
\(371\) 8.74336 0.453932
\(372\) 32.7093 1.69590
\(373\) −1.29756 −0.0671850 −0.0335925 0.999436i \(-0.510695\pi\)
−0.0335925 + 0.999436i \(0.510695\pi\)
\(374\) 3.80373 0.196686
\(375\) −36.6129 −1.89068
\(376\) −0.0301705 −0.00155593
\(377\) 1.13046 0.0582219
\(378\) 12.0014 0.617286
\(379\) 31.4832 1.61718 0.808592 0.588370i \(-0.200230\pi\)
0.808592 + 0.588370i \(0.200230\pi\)
\(380\) −20.0253 −1.02728
\(381\) 11.9740 0.613447
\(382\) 6.28973 0.321811
\(383\) −8.37636 −0.428012 −0.214006 0.976832i \(-0.568651\pi\)
−0.214006 + 0.976832i \(0.568651\pi\)
\(384\) 1.77648 0.0906555
\(385\) 1.25922 0.0641760
\(386\) −23.1495 −1.17828
\(387\) −1.77685 −0.0903223
\(388\) 1.94355 0.0986690
\(389\) 10.2381 0.519091 0.259545 0.965731i \(-0.416427\pi\)
0.259545 + 0.965731i \(0.416427\pi\)
\(390\) 13.4216 0.679628
\(391\) −0.0781838 −0.00395392
\(392\) −0.484246 −0.0244581
\(393\) −52.3764 −2.64204
\(394\) 19.8082 0.997922
\(395\) −7.29476 −0.367039
\(396\) −12.6410 −0.635233
\(397\) 21.3390 1.07098 0.535488 0.844543i \(-0.320128\pi\)
0.535488 + 0.844543i \(0.320128\pi\)
\(398\) 53.2411 2.66873
\(399\) −9.74230 −0.487725
\(400\) 4.63908 0.231954
\(401\) −28.7782 −1.43711 −0.718556 0.695469i \(-0.755197\pi\)
−0.718556 + 0.695469i \(0.755197\pi\)
\(402\) −59.9093 −2.98800
\(403\) 6.20541 0.309113
\(404\) 27.7550 1.38086
\(405\) −21.5265 −1.06966
\(406\) 1.23094 0.0610904
\(407\) 2.85013 0.141276
\(408\) −0.409423 −0.0202694
\(409\) 32.3931 1.60174 0.800868 0.598841i \(-0.204372\pi\)
0.800868 + 0.598841i \(0.204372\pi\)
\(410\) −18.7408 −0.925542
\(411\) 8.67897 0.428102
\(412\) 23.9717 1.18100
\(413\) 3.59071 0.176687
\(414\) 0.524523 0.0257789
\(415\) 3.70306 0.181776
\(416\) −8.99903 −0.441214
\(417\) 3.03517 0.148633
\(418\) 10.7115 0.523915
\(419\) 13.0089 0.635526 0.317763 0.948170i \(-0.397068\pi\)
0.317763 + 0.948170i \(0.397068\pi\)
\(420\) 7.23945 0.353249
\(421\) −32.0254 −1.56082 −0.780412 0.625265i \(-0.784991\pi\)
−0.780412 + 0.625265i \(0.784991\pi\)
\(422\) −15.7136 −0.764927
\(423\) −2.56138 −0.124539
\(424\) 1.03473 0.0502510
\(425\) −2.10008 −0.101869
\(426\) −14.2234 −0.689127
\(427\) −7.13794 −0.345429
\(428\) 7.27080 0.351447
\(429\) −3.55628 −0.171699
\(430\) −1.11883 −0.0539545
\(431\) 10.4918 0.505371 0.252685 0.967548i \(-0.418686\pi\)
0.252685 + 0.967548i \(0.418686\pi\)
\(432\) 39.7029 1.91021
\(433\) −5.51526 −0.265047 −0.132523 0.991180i \(-0.542308\pi\)
−0.132523 + 0.991180i \(0.542308\pi\)
\(434\) 6.75693 0.324343
\(435\) −5.96377 −0.285941
\(436\) 19.7859 0.947572
\(437\) −0.220169 −0.0105321
\(438\) 89.6812 4.28513
\(439\) −4.89269 −0.233515 −0.116758 0.993160i \(-0.537250\pi\)
−0.116758 + 0.993160i \(0.537250\pi\)
\(440\) 0.149023 0.00710438
\(441\) −41.1109 −1.95766
\(442\) 4.14869 0.197333
\(443\) −10.1697 −0.483176 −0.241588 0.970379i \(-0.577668\pi\)
−0.241588 + 0.970379i \(0.577668\pi\)
\(444\) 16.3858 0.777634
\(445\) 24.2934 1.15162
\(446\) 28.2887 1.33951
\(447\) −49.8619 −2.35839
\(448\) −4.76307 −0.225034
\(449\) −1.88070 −0.0887556 −0.0443778 0.999015i \(-0.514131\pi\)
−0.0443778 + 0.999015i \(0.514131\pi\)
\(450\) 14.0891 0.664167
\(451\) 4.96570 0.233826
\(452\) 29.3230 1.37924
\(453\) 67.7614 3.18371
\(454\) −48.6541 −2.28345
\(455\) 1.37342 0.0643871
\(456\) −1.15295 −0.0539919
\(457\) −1.08083 −0.0505593 −0.0252796 0.999680i \(-0.508048\pi\)
−0.0252796 + 0.999680i \(0.508048\pi\)
\(458\) 15.4919 0.723888
\(459\) −17.9732 −0.838918
\(460\) 0.163606 0.00762818
\(461\) −20.7355 −0.965750 −0.482875 0.875689i \(-0.660408\pi\)
−0.482875 + 0.875689i \(0.660408\pi\)
\(462\) −3.87235 −0.180158
\(463\) −3.69998 −0.171953 −0.0859763 0.996297i \(-0.527401\pi\)
−0.0859763 + 0.996297i \(0.527401\pi\)
\(464\) 4.07216 0.189045
\(465\) −32.7367 −1.51813
\(466\) 55.9943 2.59389
\(467\) −23.3234 −1.07928 −0.539639 0.841896i \(-0.681439\pi\)
−0.539639 + 0.841896i \(0.681439\pi\)
\(468\) −13.7874 −0.637322
\(469\) −6.13049 −0.283080
\(470\) −1.61282 −0.0743939
\(471\) −21.9143 −1.00976
\(472\) 0.424942 0.0195595
\(473\) 0.296452 0.0136309
\(474\) 22.4327 1.03037
\(475\) −5.91391 −0.271349
\(476\) 2.23776 0.102568
\(477\) 87.8454 4.02216
\(478\) −12.5702 −0.574946
\(479\) 31.5230 1.44032 0.720161 0.693807i \(-0.244068\pi\)
0.720161 + 0.693807i \(0.244068\pi\)
\(480\) 47.4744 2.16690
\(481\) 3.10861 0.141740
\(482\) 21.8655 0.995945
\(483\) 0.0795943 0.00362166
\(484\) −19.4866 −0.885756
\(485\) −1.94518 −0.0883261
\(486\) 7.96836 0.361452
\(487\) 18.8807 0.855565 0.427783 0.903882i \(-0.359295\pi\)
0.427783 + 0.903882i \(0.359295\pi\)
\(488\) −0.844738 −0.0382395
\(489\) −57.2033 −2.58682
\(490\) −25.8862 −1.16942
\(491\) −0.141902 −0.00640394 −0.00320197 0.999995i \(-0.501019\pi\)
−0.00320197 + 0.999995i \(0.501019\pi\)
\(492\) 28.5485 1.28706
\(493\) −1.84344 −0.0830243
\(494\) 11.6829 0.525638
\(495\) 12.6516 0.568645
\(496\) 22.3531 1.00369
\(497\) −1.45548 −0.0652871
\(498\) −11.3876 −0.510291
\(499\) −19.4327 −0.869927 −0.434963 0.900448i \(-0.643239\pi\)
−0.434963 + 0.900448i \(0.643239\pi\)
\(500\) 23.6824 1.05911
\(501\) −51.3396 −2.29368
\(502\) −10.2092 −0.455658
\(503\) 28.6588 1.27783 0.638916 0.769277i \(-0.279383\pi\)
0.638916 + 0.769277i \(0.279383\pi\)
\(504\) 0.281074 0.0125200
\(505\) −27.7783 −1.23612
\(506\) −0.0875122 −0.00389039
\(507\) 35.5785 1.58009
\(508\) −7.74515 −0.343636
\(509\) −7.94018 −0.351942 −0.175971 0.984395i \(-0.556307\pi\)
−0.175971 + 0.984395i \(0.556307\pi\)
\(510\) −21.8864 −0.969148
\(511\) 9.17704 0.405968
\(512\) −31.8204 −1.40627
\(513\) −50.6133 −2.23463
\(514\) −0.752399 −0.0331869
\(515\) −23.9918 −1.05720
\(516\) 1.70434 0.0750295
\(517\) 0.427345 0.0187946
\(518\) 3.38489 0.148724
\(519\) 38.4614 1.68827
\(520\) 0.162538 0.00712775
\(521\) −6.24814 −0.273736 −0.136868 0.990589i \(-0.543704\pi\)
−0.136868 + 0.990589i \(0.543704\pi\)
\(522\) 12.3673 0.541304
\(523\) −35.1953 −1.53898 −0.769492 0.638657i \(-0.779490\pi\)
−0.769492 + 0.638657i \(0.779490\pi\)
\(524\) 33.8787 1.48000
\(525\) 2.13797 0.0933086
\(526\) 2.25649 0.0983877
\(527\) −10.1191 −0.440795
\(528\) −12.8104 −0.557503
\(529\) −22.9982 −0.999922
\(530\) 55.3135 2.40266
\(531\) 36.0762 1.56558
\(532\) 6.30162 0.273210
\(533\) 5.41604 0.234595
\(534\) −74.7068 −3.23288
\(535\) −7.27688 −0.314607
\(536\) −0.725512 −0.0313373
\(537\) 10.9207 0.471263
\(538\) 5.96228 0.257052
\(539\) 6.85901 0.295439
\(540\) 37.6105 1.61850
\(541\) 35.4575 1.52444 0.762219 0.647319i \(-0.224110\pi\)
0.762219 + 0.647319i \(0.224110\pi\)
\(542\) −57.4183 −2.46633
\(543\) −41.1747 −1.76697
\(544\) 14.6746 0.629170
\(545\) −19.8025 −0.848244
\(546\) −4.22354 −0.180751
\(547\) −45.2653 −1.93540 −0.967702 0.252098i \(-0.918879\pi\)
−0.967702 + 0.252098i \(0.918879\pi\)
\(548\) −5.61382 −0.239811
\(549\) −71.7156 −3.06075
\(550\) −2.35065 −0.100232
\(551\) −5.19120 −0.221153
\(552\) 0.00941957 0.000400924 0
\(553\) 2.29553 0.0976160
\(554\) 14.0017 0.594874
\(555\) −16.3995 −0.696119
\(556\) −1.96324 −0.0832601
\(557\) 2.59079 0.109775 0.0548876 0.998493i \(-0.482520\pi\)
0.0548876 + 0.998493i \(0.482520\pi\)
\(558\) 67.8875 2.87391
\(559\) 0.323338 0.0136757
\(560\) 4.94735 0.209064
\(561\) 5.79920 0.244842
\(562\) 24.5901 1.03727
\(563\) 39.9166 1.68229 0.841143 0.540813i \(-0.181883\pi\)
0.841143 + 0.540813i \(0.181883\pi\)
\(564\) 2.45687 0.103453
\(565\) −29.3476 −1.23466
\(566\) −15.5860 −0.655129
\(567\) 6.77401 0.284482
\(568\) −0.172248 −0.00722738
\(569\) −10.1979 −0.427517 −0.213758 0.976887i \(-0.568570\pi\)
−0.213758 + 0.976887i \(0.568570\pi\)
\(570\) −61.6331 −2.58153
\(571\) 26.3242 1.10163 0.550816 0.834627i \(-0.314317\pi\)
0.550816 + 0.834627i \(0.314317\pi\)
\(572\) 2.30031 0.0961808
\(573\) 9.58938 0.400602
\(574\) 5.89740 0.246153
\(575\) 0.0483165 0.00201494
\(576\) −47.8550 −1.99396
\(577\) −8.44929 −0.351749 −0.175874 0.984413i \(-0.556275\pi\)
−0.175874 + 0.984413i \(0.556275\pi\)
\(578\) 27.0782 1.12630
\(579\) −35.2939 −1.46677
\(580\) 3.85755 0.160176
\(581\) −1.16529 −0.0483443
\(582\) 5.98179 0.247953
\(583\) −14.6563 −0.607000
\(584\) 1.08606 0.0449413
\(585\) 13.7989 0.570516
\(586\) 18.7271 0.773608
\(587\) −5.18583 −0.214042 −0.107021 0.994257i \(-0.534131\pi\)
−0.107021 + 0.994257i \(0.534131\pi\)
\(588\) 39.4334 1.62620
\(589\) −28.4958 −1.17415
\(590\) 22.7161 0.935206
\(591\) 30.1997 1.24225
\(592\) 11.1978 0.460228
\(593\) 37.8149 1.55287 0.776436 0.630196i \(-0.217025\pi\)
0.776436 + 0.630196i \(0.217025\pi\)
\(594\) −20.1177 −0.825438
\(595\) −2.23963 −0.0918160
\(596\) 32.2522 1.32110
\(597\) 81.1718 3.32214
\(598\) −0.0954488 −0.00390319
\(599\) −37.5096 −1.53260 −0.766300 0.642483i \(-0.777905\pi\)
−0.766300 + 0.642483i \(0.777905\pi\)
\(600\) 0.253017 0.0103294
\(601\) −11.8715 −0.484249 −0.242125 0.970245i \(-0.577844\pi\)
−0.242125 + 0.970245i \(0.577844\pi\)
\(602\) 0.352075 0.0143495
\(603\) −61.5937 −2.50829
\(604\) −43.8302 −1.78342
\(605\) 19.5030 0.792908
\(606\) 85.4234 3.47009
\(607\) −2.44019 −0.0990444 −0.0495222 0.998773i \(-0.515770\pi\)
−0.0495222 + 0.998773i \(0.515770\pi\)
\(608\) 41.3244 1.67593
\(609\) 1.87670 0.0760476
\(610\) −45.1570 −1.82835
\(611\) 0.466102 0.0188564
\(612\) 22.4830 0.908821
\(613\) −9.08037 −0.366753 −0.183376 0.983043i \(-0.558703\pi\)
−0.183376 + 0.983043i \(0.558703\pi\)
\(614\) 13.3567 0.539034
\(615\) −28.5724 −1.15215
\(616\) −0.0468949 −0.00188945
\(617\) −11.7093 −0.471400 −0.235700 0.971826i \(-0.575738\pi\)
−0.235700 + 0.971826i \(0.575738\pi\)
\(618\) 73.7792 2.96784
\(619\) −1.12866 −0.0453647 −0.0226824 0.999743i \(-0.507221\pi\)
−0.0226824 + 0.999743i \(0.507221\pi\)
\(620\) 21.1751 0.850412
\(621\) 0.413509 0.0165935
\(622\) 1.61783 0.0648691
\(623\) −7.64472 −0.306279
\(624\) −13.9722 −0.559337
\(625\) −18.0061 −0.720243
\(626\) 49.9637 1.99695
\(627\) 16.3308 0.652188
\(628\) 14.1748 0.565637
\(629\) −5.06918 −0.202121
\(630\) 15.0253 0.598624
\(631\) −43.9511 −1.74967 −0.874833 0.484425i \(-0.839029\pi\)
−0.874833 + 0.484425i \(0.839029\pi\)
\(632\) 0.271664 0.0108062
\(633\) −23.9571 −0.952210
\(634\) 30.6487 1.21721
\(635\) 7.75164 0.307614
\(636\) −84.2608 −3.34116
\(637\) 7.48106 0.296410
\(638\) −2.06339 −0.0816903
\(639\) −14.6233 −0.578490
\(640\) 1.15004 0.0454594
\(641\) −5.00176 −0.197558 −0.0987788 0.995109i \(-0.531494\pi\)
−0.0987788 + 0.995109i \(0.531494\pi\)
\(642\) 22.3778 0.883180
\(643\) −21.2757 −0.839033 −0.419516 0.907748i \(-0.637800\pi\)
−0.419516 + 0.907748i \(0.637800\pi\)
\(644\) −0.0514840 −0.00202875
\(645\) −1.70577 −0.0671646
\(646\) −19.0512 −0.749559
\(647\) 4.95949 0.194977 0.0974887 0.995237i \(-0.468919\pi\)
0.0974887 + 0.995237i \(0.468919\pi\)
\(648\) 0.801669 0.0314925
\(649\) −6.01902 −0.236267
\(650\) −2.56383 −0.100562
\(651\) 10.3017 0.403754
\(652\) 37.0009 1.44907
\(653\) 6.00556 0.235016 0.117508 0.993072i \(-0.462509\pi\)
0.117508 + 0.993072i \(0.462509\pi\)
\(654\) 60.8962 2.38123
\(655\) −33.9070 −1.32486
\(656\) 19.5097 0.761725
\(657\) 92.2027 3.59717
\(658\) 0.507527 0.0197855
\(659\) −2.75218 −0.107210 −0.0536048 0.998562i \(-0.517071\pi\)
−0.0536048 + 0.998562i \(0.517071\pi\)
\(660\) −12.1353 −0.472366
\(661\) −20.4997 −0.797348 −0.398674 0.917093i \(-0.630529\pi\)
−0.398674 + 0.917093i \(0.630529\pi\)
\(662\) −40.9795 −1.59272
\(663\) 6.32513 0.245648
\(664\) −0.137906 −0.00535179
\(665\) −6.30690 −0.244571
\(666\) 34.0083 1.31780
\(667\) 0.0424119 0.00164220
\(668\) 33.2080 1.28486
\(669\) 43.1292 1.66747
\(670\) −38.7836 −1.49834
\(671\) 11.9651 0.461909
\(672\) −14.9394 −0.576299
\(673\) 45.5856 1.75719 0.878597 0.477563i \(-0.158480\pi\)
0.878597 + 0.477563i \(0.158480\pi\)
\(674\) 43.3827 1.67104
\(675\) 11.1072 0.427516
\(676\) −23.0132 −0.885125
\(677\) 26.9528 1.03588 0.517940 0.855417i \(-0.326699\pi\)
0.517940 + 0.855417i \(0.326699\pi\)
\(678\) 90.2493 3.46600
\(679\) 0.612114 0.0234908
\(680\) −0.265049 −0.0101642
\(681\) −74.1784 −2.84252
\(682\) −11.3265 −0.433713
\(683\) 12.1957 0.466655 0.233328 0.972398i \(-0.425039\pi\)
0.233328 + 0.972398i \(0.425039\pi\)
\(684\) 63.3130 2.42083
\(685\) 5.61852 0.214673
\(686\) 16.7625 0.639996
\(687\) 23.6191 0.901123
\(688\) 1.16473 0.0444048
\(689\) −15.9854 −0.608997
\(690\) 0.503541 0.0191695
\(691\) −47.8697 −1.82105 −0.910524 0.413455i \(-0.864322\pi\)
−0.910524 + 0.413455i \(0.864322\pi\)
\(692\) −24.8780 −0.945719
\(693\) −3.98123 −0.151234
\(694\) −38.9065 −1.47687
\(695\) 1.96489 0.0745324
\(696\) 0.222097 0.00841857
\(697\) −8.83189 −0.334532
\(698\) 36.6918 1.38880
\(699\) 85.3694 3.22897
\(700\) −1.38290 −0.0522688
\(701\) −45.4821 −1.71784 −0.858918 0.512114i \(-0.828863\pi\)
−0.858918 + 0.512114i \(0.828863\pi\)
\(702\) −21.9422 −0.828153
\(703\) −14.2750 −0.538393
\(704\) 7.98421 0.300916
\(705\) −2.45892 −0.0926084
\(706\) −24.1080 −0.907317
\(707\) 8.74134 0.328752
\(708\) −34.6041 −1.30050
\(709\) 21.0823 0.791761 0.395881 0.918302i \(-0.370439\pi\)
0.395881 + 0.918302i \(0.370439\pi\)
\(710\) −9.20785 −0.345564
\(711\) 23.0634 0.864947
\(712\) −0.904713 −0.0339055
\(713\) 0.232810 0.00871880
\(714\) 6.88729 0.257750
\(715\) −2.30224 −0.0860988
\(716\) −7.06385 −0.263988
\(717\) −19.1646 −0.715714
\(718\) 16.5777 0.618674
\(719\) 5.49866 0.205065 0.102533 0.994730i \(-0.467305\pi\)
0.102533 + 0.994730i \(0.467305\pi\)
\(720\) 49.7066 1.85245
\(721\) 7.54980 0.281169
\(722\) −15.8239 −0.588905
\(723\) 33.3363 1.23979
\(724\) 26.6330 0.989809
\(725\) 1.13922 0.0423095
\(726\) −59.9752 −2.22589
\(727\) −6.24221 −0.231511 −0.115755 0.993278i \(-0.536929\pi\)
−0.115755 + 0.993278i \(0.536929\pi\)
\(728\) −0.0511478 −0.00189566
\(729\) −20.7181 −0.767338
\(730\) 58.0571 2.14879
\(731\) −0.527264 −0.0195016
\(732\) 68.7892 2.54252
\(733\) −23.9659 −0.885201 −0.442600 0.896719i \(-0.645944\pi\)
−0.442600 + 0.896719i \(0.645944\pi\)
\(734\) −46.8995 −1.73109
\(735\) −39.4664 −1.45574
\(736\) −0.337619 −0.0124448
\(737\) 10.2764 0.378536
\(738\) 59.2518 2.18109
\(739\) −35.7444 −1.31488 −0.657439 0.753508i \(-0.728360\pi\)
−0.657439 + 0.753508i \(0.728360\pi\)
\(740\) 10.6077 0.389946
\(741\) 17.8118 0.654334
\(742\) −17.4062 −0.639001
\(743\) 15.5544 0.570636 0.285318 0.958433i \(-0.407901\pi\)
0.285318 + 0.958433i \(0.407901\pi\)
\(744\) 1.21915 0.0446962
\(745\) −32.2792 −1.18262
\(746\) 2.58317 0.0945764
\(747\) −11.7078 −0.428365
\(748\) −3.75110 −0.137154
\(749\) 2.28991 0.0836714
\(750\) 72.8886 2.66152
\(751\) −12.0401 −0.439350 −0.219675 0.975573i \(-0.570500\pi\)
−0.219675 + 0.975573i \(0.570500\pi\)
\(752\) 1.67899 0.0612265
\(753\) −15.5650 −0.567221
\(754\) −2.25052 −0.0819590
\(755\) 43.8669 1.59648
\(756\) −11.8354 −0.430448
\(757\) −32.8775 −1.19495 −0.597477 0.801886i \(-0.703830\pi\)
−0.597477 + 0.801886i \(0.703830\pi\)
\(758\) −62.6764 −2.27651
\(759\) −0.133422 −0.00484291
\(760\) −0.746389 −0.0270744
\(761\) −15.9564 −0.578419 −0.289210 0.957266i \(-0.593392\pi\)
−0.289210 + 0.957266i \(0.593392\pi\)
\(762\) −23.8377 −0.863550
\(763\) 6.23149 0.225595
\(764\) −6.20270 −0.224406
\(765\) −22.5018 −0.813555
\(766\) 16.6756 0.602513
\(767\) −6.56489 −0.237044
\(768\) −50.2983 −1.81498
\(769\) 49.1859 1.77369 0.886844 0.462069i \(-0.152893\pi\)
0.886844 + 0.462069i \(0.152893\pi\)
\(770\) −2.50685 −0.0903407
\(771\) −1.14711 −0.0413123
\(772\) 22.8292 0.821641
\(773\) −20.4919 −0.737042 −0.368521 0.929619i \(-0.620136\pi\)
−0.368521 + 0.929619i \(0.620136\pi\)
\(774\) 3.53733 0.127147
\(775\) 6.25346 0.224631
\(776\) 0.0724406 0.00260046
\(777\) 5.16063 0.185137
\(778\) −20.3818 −0.730724
\(779\) −24.8710 −0.891095
\(780\) −13.2359 −0.473920
\(781\) 2.43978 0.0873022
\(782\) 0.155647 0.00556594
\(783\) 9.74983 0.348430
\(784\) 26.9483 0.962439
\(785\) −14.1867 −0.506344
\(786\) 104.270 3.71920
\(787\) −8.78693 −0.313220 −0.156610 0.987660i \(-0.550057\pi\)
−0.156610 + 0.987660i \(0.550057\pi\)
\(788\) −19.5341 −0.695874
\(789\) 3.44027 0.122477
\(790\) 14.5223 0.516681
\(791\) 9.23518 0.328365
\(792\) −0.471157 −0.0167418
\(793\) 13.0503 0.463429
\(794\) −42.4815 −1.50761
\(795\) 84.3313 2.99092
\(796\) −52.5044 −1.86097
\(797\) 23.2200 0.822496 0.411248 0.911523i \(-0.365093\pi\)
0.411248 + 0.911523i \(0.365093\pi\)
\(798\) 19.3949 0.686571
\(799\) −0.760068 −0.0268893
\(800\) −9.06872 −0.320628
\(801\) −76.8072 −2.71385
\(802\) 57.2913 2.02303
\(803\) −15.3832 −0.542863
\(804\) 59.0803 2.08360
\(805\) 0.0515271 0.00181609
\(806\) −12.3537 −0.435139
\(807\) 9.09014 0.319988
\(808\) 1.03449 0.0363933
\(809\) 11.2625 0.395970 0.197985 0.980205i \(-0.436560\pi\)
0.197985 + 0.980205i \(0.436560\pi\)
\(810\) 42.8547 1.50576
\(811\) 30.3139 1.06446 0.532232 0.846599i \(-0.321353\pi\)
0.532232 + 0.846599i \(0.321353\pi\)
\(812\) −1.21390 −0.0425997
\(813\) −87.5404 −3.07017
\(814\) −5.67400 −0.198874
\(815\) −37.0318 −1.29717
\(816\) 22.7844 0.797613
\(817\) −1.48480 −0.0519465
\(818\) −64.4878 −2.25476
\(819\) −4.34228 −0.151732
\(820\) 18.4815 0.645401
\(821\) −30.3861 −1.06048 −0.530241 0.847847i \(-0.677899\pi\)
−0.530241 + 0.847847i \(0.677899\pi\)
\(822\) −17.2780 −0.602639
\(823\) 9.63285 0.335780 0.167890 0.985806i \(-0.446305\pi\)
0.167890 + 0.985806i \(0.446305\pi\)
\(824\) 0.893480 0.0311258
\(825\) −3.58382 −0.124773
\(826\) −7.14835 −0.248723
\(827\) 3.32234 0.115529 0.0577646 0.998330i \(-0.481603\pi\)
0.0577646 + 0.998330i \(0.481603\pi\)
\(828\) −0.517265 −0.0179762
\(829\) 41.1785 1.43019 0.715094 0.699028i \(-0.246384\pi\)
0.715094 + 0.699028i \(0.246384\pi\)
\(830\) −7.37202 −0.255886
\(831\) 21.3470 0.740521
\(832\) 8.70830 0.301906
\(833\) −12.1993 −0.422681
\(834\) −6.04239 −0.209231
\(835\) −33.2358 −1.15017
\(836\) −10.5632 −0.365337
\(837\) 53.5193 1.84990
\(838\) −25.8980 −0.894630
\(839\) 3.85828 0.133203 0.0666013 0.997780i \(-0.478784\pi\)
0.0666013 + 0.997780i \(0.478784\pi\)
\(840\) 0.269831 0.00931004
\(841\) 1.00000 0.0344828
\(842\) 63.7559 2.19717
\(843\) 37.4903 1.29123
\(844\) 15.4962 0.533401
\(845\) 23.0325 0.792342
\(846\) 5.09918 0.175313
\(847\) −6.13724 −0.210878
\(848\) −57.5828 −1.97740
\(849\) −23.7625 −0.815528
\(850\) 4.18082 0.143401
\(851\) 0.116626 0.00399790
\(852\) 14.0266 0.480544
\(853\) 7.71719 0.264232 0.132116 0.991234i \(-0.457823\pi\)
0.132116 + 0.991234i \(0.457823\pi\)
\(854\) 14.2101 0.486261
\(855\) −63.3660 −2.16707
\(856\) 0.270999 0.00926255
\(857\) 39.7219 1.35687 0.678437 0.734658i \(-0.262657\pi\)
0.678437 + 0.734658i \(0.262657\pi\)
\(858\) 7.07981 0.241701
\(859\) −18.8539 −0.643286 −0.321643 0.946861i \(-0.604235\pi\)
−0.321643 + 0.946861i \(0.604235\pi\)
\(860\) 1.10334 0.0376237
\(861\) 8.99122 0.306420
\(862\) −20.8869 −0.711411
\(863\) −26.0840 −0.887911 −0.443955 0.896049i \(-0.646425\pi\)
−0.443955 + 0.896049i \(0.646425\pi\)
\(864\) −77.6132 −2.64045
\(865\) 24.8988 0.846585
\(866\) 10.9797 0.373106
\(867\) 41.2836 1.40207
\(868\) −6.66343 −0.226172
\(869\) −3.84794 −0.130533
\(870\) 11.8726 0.402519
\(871\) 11.2084 0.379781
\(872\) 0.737464 0.0249737
\(873\) 6.14997 0.208145
\(874\) 0.438310 0.0148260
\(875\) 7.45866 0.252149
\(876\) −88.4403 −2.98812
\(877\) −13.4299 −0.453497 −0.226748 0.973953i \(-0.572809\pi\)
−0.226748 + 0.973953i \(0.572809\pi\)
\(878\) 9.74031 0.328720
\(879\) 28.5514 0.963016
\(880\) −8.29312 −0.279561
\(881\) 20.9098 0.704470 0.352235 0.935911i \(-0.385422\pi\)
0.352235 + 0.935911i \(0.385422\pi\)
\(882\) 81.8432 2.75580
\(883\) 0.187748 0.00631821 0.00315910 0.999995i \(-0.498994\pi\)
0.00315910 + 0.999995i \(0.498994\pi\)
\(884\) −4.09129 −0.137605
\(885\) 34.6331 1.16418
\(886\) 20.2457 0.680167
\(887\) 30.2144 1.01450 0.507250 0.861799i \(-0.330662\pi\)
0.507250 + 0.861799i \(0.330662\pi\)
\(888\) 0.610734 0.0204949
\(889\) −2.43931 −0.0818117
\(890\) −48.3631 −1.62113
\(891\) −11.3551 −0.380410
\(892\) −27.8973 −0.934071
\(893\) −2.14038 −0.0716252
\(894\) 99.2646 3.31991
\(895\) 7.06976 0.236316
\(896\) −0.361898 −0.0120902
\(897\) −0.145522 −0.00485884
\(898\) 3.74408 0.124941
\(899\) 5.48926 0.183077
\(900\) −13.8942 −0.463139
\(901\) 26.0673 0.868429
\(902\) −9.88566 −0.329157
\(903\) 0.536776 0.0178628
\(904\) 1.09294 0.0363505
\(905\) −26.6553 −0.886053
\(906\) −134.899 −4.48171
\(907\) 11.1751 0.371062 0.185531 0.982638i \(-0.440600\pi\)
0.185531 + 0.982638i \(0.440600\pi\)
\(908\) 47.9809 1.59230
\(909\) 87.8251 2.91298
\(910\) −2.73420 −0.0906378
\(911\) 1.55333 0.0514641 0.0257320 0.999669i \(-0.491808\pi\)
0.0257320 + 0.999669i \(0.491808\pi\)
\(912\) 64.1618 2.12461
\(913\) 1.95334 0.0646463
\(914\) 2.15171 0.0711723
\(915\) −68.8468 −2.27600
\(916\) −15.2775 −0.504784
\(917\) 10.6700 0.352353
\(918\) 35.7809 1.18095
\(919\) 31.0958 1.02575 0.512877 0.858462i \(-0.328580\pi\)
0.512877 + 0.858462i \(0.328580\pi\)
\(920\) 0.00609797 0.000201044 0
\(921\) 20.3638 0.671009
\(922\) 41.2801 1.35949
\(923\) 2.66104 0.0875894
\(924\) 3.81877 0.125628
\(925\) 3.13268 0.103002
\(926\) 7.36588 0.242058
\(927\) 75.8536 2.49136
\(928\) −7.96047 −0.261315
\(929\) −29.9104 −0.981327 −0.490664 0.871349i \(-0.663246\pi\)
−0.490664 + 0.871349i \(0.663246\pi\)
\(930\) 65.1718 2.13707
\(931\) −34.3537 −1.12590
\(932\) −55.2195 −1.80878
\(933\) 2.46656 0.0807515
\(934\) 46.4320 1.51930
\(935\) 3.75424 0.122777
\(936\) −0.513887 −0.0167969
\(937\) −34.1094 −1.11431 −0.557153 0.830410i \(-0.688106\pi\)
−0.557153 + 0.830410i \(0.688106\pi\)
\(938\) 12.2045 0.398492
\(939\) 76.1750 2.48588
\(940\) 1.59051 0.0518766
\(941\) 31.0678 1.01278 0.506391 0.862304i \(-0.330979\pi\)
0.506391 + 0.862304i \(0.330979\pi\)
\(942\) 43.6267 1.42143
\(943\) 0.203195 0.00661694
\(944\) −23.6480 −0.769678
\(945\) 11.8453 0.385327
\(946\) −0.590174 −0.0191882
\(947\) 2.27822 0.0740323 0.0370161 0.999315i \(-0.488215\pi\)
0.0370161 + 0.999315i \(0.488215\pi\)
\(948\) −22.1223 −0.718500
\(949\) −16.7784 −0.544648
\(950\) 11.7734 0.381978
\(951\) 46.7272 1.51523
\(952\) 0.0834063 0.00270321
\(953\) 23.8262 0.771807 0.385904 0.922539i \(-0.373890\pi\)
0.385904 + 0.922539i \(0.373890\pi\)
\(954\) −174.882 −5.66200
\(955\) 6.20790 0.200883
\(956\) 12.3962 0.400923
\(957\) −3.14586 −0.101691
\(958\) −62.7556 −2.02754
\(959\) −1.76805 −0.0570933
\(960\) −45.9407 −1.48273
\(961\) −0.868077 −0.0280025
\(962\) −6.18858 −0.199528
\(963\) 23.0069 0.741388
\(964\) −21.5629 −0.694495
\(965\) −22.8483 −0.735513
\(966\) −0.158455 −0.00509822
\(967\) −1.50665 −0.0484505 −0.0242253 0.999707i \(-0.507712\pi\)
−0.0242253 + 0.999707i \(0.507712\pi\)
\(968\) −0.726311 −0.0233445
\(969\) −29.0456 −0.933079
\(970\) 3.87244 0.124337
\(971\) −60.3746 −1.93751 −0.968756 0.248014i \(-0.920222\pi\)
−0.968756 + 0.248014i \(0.920222\pi\)
\(972\) −7.85810 −0.252049
\(973\) −0.618316 −0.0198223
\(974\) −37.5875 −1.20438
\(975\) −3.90884 −0.125183
\(976\) 47.0097 1.50474
\(977\) 9.69570 0.310193 0.155096 0.987899i \(-0.450431\pi\)
0.155096 + 0.987899i \(0.450431\pi\)
\(978\) 113.880 3.64147
\(979\) 12.8146 0.409558
\(980\) 25.5281 0.815464
\(981\) 62.6084 1.99893
\(982\) 0.282497 0.00901483
\(983\) 53.0689 1.69263 0.846317 0.532679i \(-0.178815\pi\)
0.846317 + 0.532679i \(0.178815\pi\)
\(984\) 1.06406 0.0339211
\(985\) 19.5505 0.622929
\(986\) 3.66990 0.116873
\(987\) 0.773780 0.0246297
\(988\) −11.5212 −0.366539
\(989\) 0.0121307 0.000385735 0
\(990\) −25.1866 −0.800482
\(991\) 32.4474 1.03073 0.515363 0.856972i \(-0.327657\pi\)
0.515363 + 0.856972i \(0.327657\pi\)
\(992\) −43.6970 −1.38738
\(993\) −62.4777 −1.98267
\(994\) 2.89755 0.0919047
\(995\) 52.5484 1.66589
\(996\) 11.2300 0.355837
\(997\) −50.4827 −1.59880 −0.799402 0.600797i \(-0.794850\pi\)
−0.799402 + 0.600797i \(0.794850\pi\)
\(998\) 38.6864 1.22460
\(999\) 26.8106 0.848248
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 \(a_p\))