Properties

Label 4033.2.a.d.1.6
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65601 q^{2}\) \(-2.08930 q^{3}\) \(+5.05439 q^{4}\) \(-0.388260 q^{5}\) \(+5.54922 q^{6}\) \(-5.15918 q^{7}\) \(-8.11249 q^{8}\) \(+1.36520 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65601 q^{2}\) \(-2.08930 q^{3}\) \(+5.05439 q^{4}\) \(-0.388260 q^{5}\) \(+5.54922 q^{6}\) \(-5.15918 q^{7}\) \(-8.11249 q^{8}\) \(+1.36520 q^{9}\) \(+1.03122 q^{10}\) \(+3.34161 q^{11}\) \(-10.5602 q^{12}\) \(+5.68872 q^{13}\) \(+13.7028 q^{14}\) \(+0.811194 q^{15}\) \(+11.4381 q^{16}\) \(-6.13070 q^{17}\) \(-3.62597 q^{18}\) \(+2.07318 q^{19}\) \(-1.96242 q^{20}\) \(+10.7791 q^{21}\) \(-8.87535 q^{22}\) \(-3.39201 q^{23}\) \(+16.9495 q^{24}\) \(-4.84925 q^{25}\) \(-15.1093 q^{26}\) \(+3.41561 q^{27}\) \(-26.0765 q^{28}\) \(+1.48595 q^{29}\) \(-2.15454 q^{30}\) \(-7.78032 q^{31}\) \(-14.1547 q^{32}\) \(-6.98164 q^{33}\) \(+16.2832 q^{34}\) \(+2.00310 q^{35}\) \(+6.90023 q^{36}\) \(-1.00000 q^{37}\) \(-5.50639 q^{38}\) \(-11.8855 q^{39}\) \(+3.14976 q^{40}\) \(+4.76687 q^{41}\) \(-28.6294 q^{42}\) \(-0.146580 q^{43}\) \(+16.8898 q^{44}\) \(-0.530051 q^{45}\) \(+9.00922 q^{46}\) \(-5.10022 q^{47}\) \(-23.8976 q^{48}\) \(+19.6171 q^{49}\) \(+12.8797 q^{50}\) \(+12.8089 q^{51}\) \(+28.7530 q^{52}\) \(+1.00969 q^{53}\) \(-9.07188 q^{54}\) \(-1.29741 q^{55}\) \(+41.8538 q^{56}\) \(-4.33150 q^{57}\) \(-3.94671 q^{58}\) \(-1.03977 q^{59}\) \(+4.10009 q^{60}\) \(-3.25158 q^{61}\) \(+20.6646 q^{62}\) \(-7.04329 q^{63}\) \(+14.7188 q^{64}\) \(-2.20870 q^{65}\) \(+18.5433 q^{66}\) \(+11.9498 q^{67}\) \(-30.9870 q^{68}\) \(+7.08694 q^{69}\) \(-5.32027 q^{70}\) \(-3.61312 q^{71}\) \(-11.0751 q^{72}\) \(+12.4513 q^{73}\) \(+2.65601 q^{74}\) \(+10.1316 q^{75}\) \(+10.4787 q^{76}\) \(-17.2400 q^{77}\) \(+31.5679 q^{78}\) \(+4.12486 q^{79}\) \(-4.44095 q^{80}\) \(-11.2318 q^{81}\) \(-12.6609 q^{82}\) \(-15.9117 q^{83}\) \(+54.4818 q^{84}\) \(+2.38031 q^{85}\) \(+0.389319 q^{86}\) \(-3.10461 q^{87}\) \(-27.1088 q^{88}\) \(+9.37787 q^{89}\) \(+1.40782 q^{90}\) \(-29.3491 q^{91}\) \(-17.1445 q^{92}\) \(+16.2555 q^{93}\) \(+13.5462 q^{94}\) \(-0.804933 q^{95}\) \(+29.5734 q^{96}\) \(+0.428035 q^{97}\) \(-52.1033 q^{98}\) \(+4.56195 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65601 −1.87808 −0.939041 0.343804i \(-0.888284\pi\)
−0.939041 + 0.343804i \(0.888284\pi\)
\(3\) −2.08930 −1.20626 −0.603130 0.797643i \(-0.706080\pi\)
−0.603130 + 0.797643i \(0.706080\pi\)
\(4\) 5.05439 2.52720
\(5\) −0.388260 −0.173635 −0.0868177 0.996224i \(-0.527670\pi\)
−0.0868177 + 0.996224i \(0.527670\pi\)
\(6\) 5.54922 2.26546
\(7\) −5.15918 −1.94999 −0.974993 0.222235i \(-0.928665\pi\)
−0.974993 + 0.222235i \(0.928665\pi\)
\(8\) −8.11249 −2.86820
\(9\) 1.36520 0.455065
\(10\) 1.03122 0.326102
\(11\) 3.34161 1.00753 0.503766 0.863840i \(-0.331947\pi\)
0.503766 + 0.863840i \(0.331947\pi\)
\(12\) −10.5602 −3.04846
\(13\) 5.68872 1.57777 0.788883 0.614543i \(-0.210660\pi\)
0.788883 + 0.614543i \(0.210660\pi\)
\(14\) 13.7028 3.66224
\(15\) 0.811194 0.209449
\(16\) 11.4381 2.85952
\(17\) −6.13070 −1.48691 −0.743457 0.668784i \(-0.766815\pi\)
−0.743457 + 0.668784i \(0.766815\pi\)
\(18\) −3.62597 −0.854650
\(19\) 2.07318 0.475620 0.237810 0.971312i \(-0.423570\pi\)
0.237810 + 0.971312i \(0.423570\pi\)
\(20\) −1.96242 −0.438810
\(21\) 10.7791 2.35219
\(22\) −8.87535 −1.89223
\(23\) −3.39201 −0.707283 −0.353642 0.935381i \(-0.615057\pi\)
−0.353642 + 0.935381i \(0.615057\pi\)
\(24\) 16.9495 3.45980
\(25\) −4.84925 −0.969851
\(26\) −15.1093 −2.96318
\(27\) 3.41561 0.657334
\(28\) −26.0765 −4.92800
\(29\) 1.48595 0.275935 0.137967 0.990437i \(-0.455943\pi\)
0.137967 + 0.990437i \(0.455943\pi\)
\(30\) −2.15454 −0.393363
\(31\) −7.78032 −1.39739 −0.698694 0.715421i \(-0.746235\pi\)
−0.698694 + 0.715421i \(0.746235\pi\)
\(32\) −14.1547 −2.50222
\(33\) −6.98164 −1.21535
\(34\) 16.2832 2.79255
\(35\) 2.00310 0.338586
\(36\) 6.90023 1.15004
\(37\) −1.00000 −0.164399
\(38\) −5.50639 −0.893254
\(39\) −11.8855 −1.90320
\(40\) 3.14976 0.498021
\(41\) 4.76687 0.744460 0.372230 0.928140i \(-0.378593\pi\)
0.372230 + 0.928140i \(0.378593\pi\)
\(42\) −28.6294 −4.41761
\(43\) −0.146580 −0.0223533 −0.0111766 0.999938i \(-0.503558\pi\)
−0.0111766 + 0.999938i \(0.503558\pi\)
\(44\) 16.8898 2.54623
\(45\) −0.530051 −0.0790154
\(46\) 9.00922 1.32834
\(47\) −5.10022 −0.743944 −0.371972 0.928244i \(-0.621318\pi\)
−0.371972 + 0.928244i \(0.621318\pi\)
\(48\) −23.8976 −3.44933
\(49\) 19.6171 2.80245
\(50\) 12.8797 1.82146
\(51\) 12.8089 1.79361
\(52\) 28.7530 3.98732
\(53\) 1.00969 0.138691 0.0693455 0.997593i \(-0.477909\pi\)
0.0693455 + 0.997593i \(0.477909\pi\)
\(54\) −9.07188 −1.23453
\(55\) −1.29741 −0.174943
\(56\) 41.8538 5.59295
\(57\) −4.33150 −0.573722
\(58\) −3.94671 −0.518229
\(59\) −1.03977 −0.135367 −0.0676833 0.997707i \(-0.521561\pi\)
−0.0676833 + 0.997707i \(0.521561\pi\)
\(60\) 4.10009 0.529320
\(61\) −3.25158 −0.416322 −0.208161 0.978095i \(-0.566748\pi\)
−0.208161 + 0.978095i \(0.566748\pi\)
\(62\) 20.6646 2.62441
\(63\) −7.04329 −0.887371
\(64\) 14.7188 1.83985
\(65\) −2.20870 −0.273956
\(66\) 18.5433 2.28252
\(67\) 11.9498 1.45990 0.729949 0.683502i \(-0.239544\pi\)
0.729949 + 0.683502i \(0.239544\pi\)
\(68\) −30.9870 −3.75772
\(69\) 7.08694 0.853168
\(70\) −5.32027 −0.635893
\(71\) −3.61312 −0.428798 −0.214399 0.976746i \(-0.568779\pi\)
−0.214399 + 0.976746i \(0.568779\pi\)
\(72\) −11.0751 −1.30522
\(73\) 12.4513 1.45731 0.728656 0.684880i \(-0.240145\pi\)
0.728656 + 0.684880i \(0.240145\pi\)
\(74\) 2.65601 0.308755
\(75\) 10.1316 1.16989
\(76\) 10.4787 1.20198
\(77\) −17.2400 −1.96468
\(78\) 31.5679 3.57436
\(79\) 4.12486 0.464083 0.232041 0.972706i \(-0.425460\pi\)
0.232041 + 0.972706i \(0.425460\pi\)
\(80\) −4.44095 −0.496514
\(81\) −11.2318 −1.24798
\(82\) −12.6609 −1.39816
\(83\) −15.9117 −1.74654 −0.873269 0.487239i \(-0.838004\pi\)
−0.873269 + 0.487239i \(0.838004\pi\)
\(84\) 54.4818 5.94445
\(85\) 2.38031 0.258181
\(86\) 0.389319 0.0419813
\(87\) −3.10461 −0.332849
\(88\) −27.1088 −2.88981
\(89\) 9.37787 0.994052 0.497026 0.867736i \(-0.334425\pi\)
0.497026 + 0.867736i \(0.334425\pi\)
\(90\) 1.40782 0.148397
\(91\) −29.3491 −3.07662
\(92\) −17.1445 −1.78744
\(93\) 16.2555 1.68561
\(94\) 13.5462 1.39719
\(95\) −0.804933 −0.0825844
\(96\) 29.5734 3.01833
\(97\) 0.428035 0.0434604 0.0217302 0.999764i \(-0.493083\pi\)
0.0217302 + 0.999764i \(0.493083\pi\)
\(98\) −52.1033 −5.26323
\(99\) 4.56195 0.458493
\(100\) −24.5100 −2.45100
\(101\) 11.8608 1.18020 0.590098 0.807331i \(-0.299089\pi\)
0.590098 + 0.807331i \(0.299089\pi\)
\(102\) −34.0206 −3.36854
\(103\) 10.4568 1.03034 0.515170 0.857088i \(-0.327729\pi\)
0.515170 + 0.857088i \(0.327729\pi\)
\(104\) −46.1497 −4.52535
\(105\) −4.18510 −0.408424
\(106\) −2.68174 −0.260473
\(107\) −11.0742 −1.07058 −0.535291 0.844668i \(-0.679798\pi\)
−0.535291 + 0.844668i \(0.679798\pi\)
\(108\) 17.2638 1.66121
\(109\) −1.00000 −0.0957826
\(110\) 3.44595 0.328558
\(111\) 2.08930 0.198308
\(112\) −59.0111 −5.57603
\(113\) 10.7037 1.00692 0.503460 0.864019i \(-0.332060\pi\)
0.503460 + 0.864019i \(0.332060\pi\)
\(114\) 11.5045 1.07750
\(115\) 1.31698 0.122809
\(116\) 7.51060 0.697341
\(117\) 7.76621 0.717986
\(118\) 2.76164 0.254230
\(119\) 31.6294 2.89946
\(120\) −6.58081 −0.600743
\(121\) 0.166349 0.0151226
\(122\) 8.63623 0.781888
\(123\) −9.95945 −0.898013
\(124\) −39.3248 −3.53147
\(125\) 3.82408 0.342036
\(126\) 18.7070 1.66656
\(127\) 10.5588 0.936939 0.468470 0.883480i \(-0.344806\pi\)
0.468470 + 0.883480i \(0.344806\pi\)
\(128\) −10.7839 −0.953175
\(129\) 0.306251 0.0269639
\(130\) 5.86634 0.514512
\(131\) −8.79055 −0.768034 −0.384017 0.923326i \(-0.625460\pi\)
−0.384017 + 0.923326i \(0.625460\pi\)
\(132\) −35.2879 −3.07142
\(133\) −10.6959 −0.927452
\(134\) −31.7387 −2.74181
\(135\) −1.32614 −0.114136
\(136\) 49.7353 4.26476
\(137\) 12.4239 1.06145 0.530723 0.847545i \(-0.321920\pi\)
0.530723 + 0.847545i \(0.321920\pi\)
\(138\) −18.8230 −1.60232
\(139\) 3.42117 0.290180 0.145090 0.989418i \(-0.453653\pi\)
0.145090 + 0.989418i \(0.453653\pi\)
\(140\) 10.1245 0.855674
\(141\) 10.6559 0.897390
\(142\) 9.59648 0.805319
\(143\) 19.0095 1.58965
\(144\) 15.6152 1.30127
\(145\) −0.576937 −0.0479120
\(146\) −33.0707 −2.73695
\(147\) −40.9861 −3.38048
\(148\) −5.05439 −0.415468
\(149\) −3.31490 −0.271568 −0.135784 0.990738i \(-0.543355\pi\)
−0.135784 + 0.990738i \(0.543355\pi\)
\(150\) −26.9096 −2.19716
\(151\) 4.56254 0.371295 0.185647 0.982616i \(-0.440562\pi\)
0.185647 + 0.982616i \(0.440562\pi\)
\(152\) −16.8187 −1.36417
\(153\) −8.36961 −0.676642
\(154\) 45.7895 3.68982
\(155\) 3.02079 0.242636
\(156\) −60.0738 −4.80975
\(157\) −4.77233 −0.380874 −0.190437 0.981699i \(-0.560990\pi\)
−0.190437 + 0.981699i \(0.560990\pi\)
\(158\) −10.9557 −0.871586
\(159\) −2.10954 −0.167298
\(160\) 5.49570 0.434473
\(161\) 17.5000 1.37919
\(162\) 29.8318 2.34381
\(163\) 15.2403 1.19371 0.596856 0.802348i \(-0.296416\pi\)
0.596856 + 0.802348i \(0.296416\pi\)
\(164\) 24.0936 1.88140
\(165\) 2.71069 0.211027
\(166\) 42.2617 3.28014
\(167\) 10.8866 0.842430 0.421215 0.906961i \(-0.361604\pi\)
0.421215 + 0.906961i \(0.361604\pi\)
\(168\) −87.4453 −6.74655
\(169\) 19.3615 1.48935
\(170\) −6.32212 −0.484885
\(171\) 2.83029 0.216438
\(172\) −0.740874 −0.0564911
\(173\) 12.5545 0.954500 0.477250 0.878768i \(-0.341634\pi\)
0.477250 + 0.878768i \(0.341634\pi\)
\(174\) 8.24588 0.625119
\(175\) 25.0182 1.89120
\(176\) 38.2216 2.88106
\(177\) 2.17240 0.163287
\(178\) −24.9077 −1.86691
\(179\) −8.29324 −0.619866 −0.309933 0.950758i \(-0.600307\pi\)
−0.309933 + 0.950758i \(0.600307\pi\)
\(180\) −2.67909 −0.199687
\(181\) 11.3354 0.842555 0.421278 0.906932i \(-0.361582\pi\)
0.421278 + 0.906932i \(0.361582\pi\)
\(182\) 77.9515 5.77815
\(183\) 6.79354 0.502193
\(184\) 27.5177 2.02863
\(185\) 0.388260 0.0285455
\(186\) −43.1747 −3.16572
\(187\) −20.4864 −1.49811
\(188\) −25.7785 −1.88009
\(189\) −17.6217 −1.28179
\(190\) 2.13791 0.155100
\(191\) −3.10667 −0.224790 −0.112395 0.993664i \(-0.535852\pi\)
−0.112395 + 0.993664i \(0.535852\pi\)
\(192\) −30.7521 −2.21934
\(193\) −23.9669 −1.72517 −0.862586 0.505911i \(-0.831157\pi\)
−0.862586 + 0.505911i \(0.831157\pi\)
\(194\) −1.13687 −0.0816222
\(195\) 4.61465 0.330462
\(196\) 99.1526 7.08233
\(197\) −14.0619 −1.00187 −0.500936 0.865484i \(-0.667011\pi\)
−0.500936 + 0.865484i \(0.667011\pi\)
\(198\) −12.1166 −0.861088
\(199\) 5.07826 0.359988 0.179994 0.983668i \(-0.442392\pi\)
0.179994 + 0.983668i \(0.442392\pi\)
\(200\) 39.3395 2.78173
\(201\) −24.9667 −1.76102
\(202\) −31.5025 −2.21651
\(203\) −7.66631 −0.538069
\(204\) 64.7412 4.53279
\(205\) −1.85079 −0.129265
\(206\) −27.7734 −1.93506
\(207\) −4.63076 −0.321860
\(208\) 65.0680 4.51165
\(209\) 6.92775 0.479203
\(210\) 11.1157 0.767053
\(211\) 23.4351 1.61334 0.806670 0.591002i \(-0.201267\pi\)
0.806670 + 0.591002i \(0.201267\pi\)
\(212\) 5.10335 0.350499
\(213\) 7.54891 0.517243
\(214\) 29.4131 2.01064
\(215\) 0.0569113 0.00388132
\(216\) −27.7091 −1.88536
\(217\) 40.1401 2.72489
\(218\) 2.65601 0.179888
\(219\) −26.0145 −1.75790
\(220\) −6.55764 −0.442116
\(221\) −34.8758 −2.34600
\(222\) −5.54922 −0.372439
\(223\) −8.30504 −0.556147 −0.278073 0.960560i \(-0.589696\pi\)
−0.278073 + 0.960560i \(0.589696\pi\)
\(224\) 73.0265 4.87929
\(225\) −6.62018 −0.441345
\(226\) −28.4291 −1.89108
\(227\) 19.8147 1.31514 0.657572 0.753391i \(-0.271583\pi\)
0.657572 + 0.753391i \(0.271583\pi\)
\(228\) −21.8931 −1.44991
\(229\) 1.36045 0.0899009 0.0449504 0.998989i \(-0.485687\pi\)
0.0449504 + 0.998989i \(0.485687\pi\)
\(230\) −3.49792 −0.230646
\(231\) 36.0195 2.36991
\(232\) −12.0548 −0.791436
\(233\) −22.7565 −1.49083 −0.745413 0.666603i \(-0.767748\pi\)
−0.745413 + 0.666603i \(0.767748\pi\)
\(234\) −20.6271 −1.34844
\(235\) 1.98021 0.129175
\(236\) −5.25541 −0.342098
\(237\) −8.61809 −0.559805
\(238\) −84.0080 −5.44543
\(239\) −17.0020 −1.09977 −0.549883 0.835242i \(-0.685328\pi\)
−0.549883 + 0.835242i \(0.685328\pi\)
\(240\) 9.27851 0.598925
\(241\) 12.2345 0.788096 0.394048 0.919090i \(-0.371074\pi\)
0.394048 + 0.919090i \(0.371074\pi\)
\(242\) −0.441824 −0.0284015
\(243\) 13.2199 0.848057
\(244\) −16.4348 −1.05213
\(245\) −7.61655 −0.486604
\(246\) 26.4524 1.68654
\(247\) 11.7937 0.750417
\(248\) 63.1178 4.00799
\(249\) 33.2444 2.10678
\(250\) −10.1568 −0.642371
\(251\) −27.0144 −1.70513 −0.852565 0.522620i \(-0.824955\pi\)
−0.852565 + 0.522620i \(0.824955\pi\)
\(252\) −35.5995 −2.24256
\(253\) −11.3348 −0.712611
\(254\) −28.0442 −1.75965
\(255\) −4.97319 −0.311433
\(256\) −0.795343 −0.0497090
\(257\) 4.74317 0.295871 0.147935 0.988997i \(-0.452737\pi\)
0.147935 + 0.988997i \(0.452737\pi\)
\(258\) −0.813406 −0.0506404
\(259\) 5.15918 0.320576
\(260\) −11.1636 −0.692340
\(261\) 2.02862 0.125568
\(262\) 23.3478 1.44243
\(263\) 18.4637 1.13852 0.569260 0.822157i \(-0.307230\pi\)
0.569260 + 0.822157i \(0.307230\pi\)
\(264\) 56.6385 3.48586
\(265\) −0.392021 −0.0240817
\(266\) 28.4084 1.74183
\(267\) −19.5932 −1.19909
\(268\) 60.3988 3.68945
\(269\) 16.9574 1.03391 0.516956 0.856012i \(-0.327065\pi\)
0.516956 + 0.856012i \(0.327065\pi\)
\(270\) 3.52225 0.214358
\(271\) −16.8030 −1.02071 −0.510353 0.859965i \(-0.670485\pi\)
−0.510353 + 0.859965i \(0.670485\pi\)
\(272\) −70.1235 −4.25186
\(273\) 61.3192 3.71121
\(274\) −32.9980 −1.99348
\(275\) −16.2043 −0.977157
\(276\) 35.8202 2.15612
\(277\) 26.7697 1.60843 0.804217 0.594335i \(-0.202585\pi\)
0.804217 + 0.594335i \(0.202585\pi\)
\(278\) −9.08667 −0.544982
\(279\) −10.6217 −0.635902
\(280\) −16.2502 −0.971133
\(281\) −14.4970 −0.864817 −0.432409 0.901678i \(-0.642336\pi\)
−0.432409 + 0.901678i \(0.642336\pi\)
\(282\) −28.3022 −1.68537
\(283\) 5.84731 0.347587 0.173793 0.984782i \(-0.444398\pi\)
0.173793 + 0.984782i \(0.444398\pi\)
\(284\) −18.2621 −1.08366
\(285\) 1.68175 0.0996184
\(286\) −50.4893 −2.98550
\(287\) −24.5931 −1.45169
\(288\) −19.3239 −1.13867
\(289\) 20.5855 1.21091
\(290\) 1.53235 0.0899828
\(291\) −0.894296 −0.0524245
\(292\) 62.9336 3.68291
\(293\) −29.2028 −1.70605 −0.853023 0.521873i \(-0.825233\pi\)
−0.853023 + 0.521873i \(0.825233\pi\)
\(294\) 108.860 6.34882
\(295\) 0.403702 0.0235044
\(296\) 8.11249 0.471529
\(297\) 11.4136 0.662285
\(298\) 8.80442 0.510026
\(299\) −19.2962 −1.11593
\(300\) 51.2089 2.95655
\(301\) 0.756234 0.0435886
\(302\) −12.1182 −0.697322
\(303\) −24.7809 −1.42362
\(304\) 23.7132 1.36004
\(305\) 1.26246 0.0722882
\(306\) 22.2298 1.27079
\(307\) 30.9561 1.76676 0.883380 0.468657i \(-0.155262\pi\)
0.883380 + 0.468657i \(0.155262\pi\)
\(308\) −87.1375 −4.96512
\(309\) −21.8474 −1.24286
\(310\) −8.02325 −0.455690
\(311\) −28.1625 −1.59695 −0.798475 0.602028i \(-0.794360\pi\)
−0.798475 + 0.602028i \(0.794360\pi\)
\(312\) 96.4207 5.45875
\(313\) 5.94883 0.336248 0.168124 0.985766i \(-0.446229\pi\)
0.168124 + 0.985766i \(0.446229\pi\)
\(314\) 12.6754 0.715313
\(315\) 2.73463 0.154079
\(316\) 20.8486 1.17283
\(317\) −0.629417 −0.0353516 −0.0176758 0.999844i \(-0.505627\pi\)
−0.0176758 + 0.999844i \(0.505627\pi\)
\(318\) 5.60296 0.314199
\(319\) 4.96548 0.278014
\(320\) −5.71473 −0.319463
\(321\) 23.1373 1.29140
\(322\) −46.4801 −2.59024
\(323\) −12.7100 −0.707206
\(324\) −56.7700 −3.15389
\(325\) −27.5860 −1.53020
\(326\) −40.4784 −2.24189
\(327\) 2.08930 0.115539
\(328\) −38.6712 −2.13526
\(329\) 26.3129 1.45068
\(330\) −7.19963 −0.396327
\(331\) −14.5595 −0.800261 −0.400131 0.916458i \(-0.631035\pi\)
−0.400131 + 0.916458i \(0.631035\pi\)
\(332\) −80.4240 −4.41384
\(333\) −1.36520 −0.0748122
\(334\) −28.9149 −1.58215
\(335\) −4.63962 −0.253490
\(336\) 123.292 6.72614
\(337\) 8.00070 0.435826 0.217913 0.975968i \(-0.430075\pi\)
0.217913 + 0.975968i \(0.430075\pi\)
\(338\) −51.4243 −2.79711
\(339\) −22.3633 −1.21461
\(340\) 12.0310 0.652473
\(341\) −25.9988 −1.40791
\(342\) −7.51729 −0.406489
\(343\) −65.0940 −3.51474
\(344\) 1.18913 0.0641137
\(345\) −2.75158 −0.148140
\(346\) −33.3448 −1.79263
\(347\) 8.64749 0.464222 0.232111 0.972689i \(-0.425437\pi\)
0.232111 + 0.972689i \(0.425437\pi\)
\(348\) −15.6919 −0.841176
\(349\) 14.8611 0.795498 0.397749 0.917494i \(-0.369791\pi\)
0.397749 + 0.917494i \(0.369791\pi\)
\(350\) −66.4485 −3.55182
\(351\) 19.4304 1.03712
\(352\) −47.2994 −2.52107
\(353\) 34.0815 1.81397 0.906987 0.421159i \(-0.138377\pi\)
0.906987 + 0.421159i \(0.138377\pi\)
\(354\) −5.76991 −0.306667
\(355\) 1.40283 0.0744545
\(356\) 47.3994 2.51216
\(357\) −66.0834 −3.49751
\(358\) 22.0269 1.16416
\(359\) −17.4266 −0.919743 −0.459872 0.887985i \(-0.652105\pi\)
−0.459872 + 0.887985i \(0.652105\pi\)
\(360\) 4.30004 0.226632
\(361\) −14.7019 −0.773786
\(362\) −30.1070 −1.58239
\(363\) −0.347554 −0.0182418
\(364\) −148.342 −7.77522
\(365\) −4.83434 −0.253041
\(366\) −18.0437 −0.943160
\(367\) −12.0249 −0.627693 −0.313846 0.949474i \(-0.601618\pi\)
−0.313846 + 0.949474i \(0.601618\pi\)
\(368\) −38.7981 −2.02249
\(369\) 6.50771 0.338778
\(370\) −1.03122 −0.0536108
\(371\) −5.20915 −0.270446
\(372\) 82.1615 4.25987
\(373\) −14.3303 −0.741996 −0.370998 0.928634i \(-0.620984\pi\)
−0.370998 + 0.928634i \(0.620984\pi\)
\(374\) 54.4121 2.81358
\(375\) −7.98966 −0.412584
\(376\) 41.3755 2.13378
\(377\) 8.45318 0.435361
\(378\) 46.8035 2.40731
\(379\) 22.8997 1.17628 0.588140 0.808759i \(-0.299860\pi\)
0.588140 + 0.808759i \(0.299860\pi\)
\(380\) −4.06845 −0.208707
\(381\) −22.0605 −1.13019
\(382\) 8.25134 0.422175
\(383\) −28.1694 −1.43939 −0.719694 0.694292i \(-0.755718\pi\)
−0.719694 + 0.694292i \(0.755718\pi\)
\(384\) 22.5310 1.14978
\(385\) 6.69359 0.341137
\(386\) 63.6562 3.24002
\(387\) −0.200111 −0.0101722
\(388\) 2.16346 0.109833
\(389\) −17.0133 −0.862608 −0.431304 0.902207i \(-0.641946\pi\)
−0.431304 + 0.902207i \(0.641946\pi\)
\(390\) −12.2566 −0.620636
\(391\) 20.7954 1.05167
\(392\) −159.144 −8.03797
\(393\) 18.3661 0.926449
\(394\) 37.3487 1.88160
\(395\) −1.60152 −0.0805812
\(396\) 23.0579 1.15870
\(397\) −29.5925 −1.48520 −0.742602 0.669733i \(-0.766408\pi\)
−0.742602 + 0.669733i \(0.766408\pi\)
\(398\) −13.4879 −0.676088
\(399\) 22.3470 1.11875
\(400\) −55.4662 −2.77331
\(401\) 8.70057 0.434486 0.217243 0.976118i \(-0.430294\pi\)
0.217243 + 0.976118i \(0.430294\pi\)
\(402\) 66.3119 3.30734
\(403\) −44.2601 −2.20475
\(404\) 59.9493 2.98259
\(405\) 4.36087 0.216694
\(406\) 20.3618 1.01054
\(407\) −3.34161 −0.165637
\(408\) −103.912 −5.14442
\(409\) −28.2420 −1.39648 −0.698238 0.715866i \(-0.746032\pi\)
−0.698238 + 0.715866i \(0.746032\pi\)
\(410\) 4.91571 0.242770
\(411\) −25.9573 −1.28038
\(412\) 52.8528 2.60387
\(413\) 5.36436 0.263963
\(414\) 12.2993 0.604479
\(415\) 6.17789 0.303261
\(416\) −80.5220 −3.94791
\(417\) −7.14788 −0.350033
\(418\) −18.4002 −0.899982
\(419\) −16.7877 −0.820131 −0.410065 0.912056i \(-0.634494\pi\)
−0.410065 + 0.912056i \(0.634494\pi\)
\(420\) −21.1531 −1.03217
\(421\) 38.2317 1.86330 0.931650 0.363357i \(-0.118369\pi\)
0.931650 + 0.363357i \(0.118369\pi\)
\(422\) −62.2439 −3.02999
\(423\) −6.96280 −0.338543
\(424\) −8.19107 −0.397793
\(425\) 29.7293 1.44208
\(426\) −20.0500 −0.971424
\(427\) 16.7755 0.811822
\(428\) −55.9732 −2.70557
\(429\) −39.7166 −1.91753
\(430\) −0.151157 −0.00728944
\(431\) 23.4730 1.13065 0.565327 0.824867i \(-0.308750\pi\)
0.565327 + 0.824867i \(0.308750\pi\)
\(432\) 39.0680 1.87966
\(433\) −29.7683 −1.43057 −0.715286 0.698832i \(-0.753704\pi\)
−0.715286 + 0.698832i \(0.753704\pi\)
\(434\) −106.612 −5.11756
\(435\) 1.20540 0.0577944
\(436\) −5.05439 −0.242061
\(437\) −7.03225 −0.336398
\(438\) 69.0948 3.30148
\(439\) −0.179125 −0.00854918 −0.00427459 0.999991i \(-0.501361\pi\)
−0.00427459 + 0.999991i \(0.501361\pi\)
\(440\) 10.5253 0.501772
\(441\) 26.7812 1.27530
\(442\) 92.6305 4.40599
\(443\) −6.71034 −0.318818 −0.159409 0.987213i \(-0.550959\pi\)
−0.159409 + 0.987213i \(0.550959\pi\)
\(444\) 10.5602 0.501163
\(445\) −3.64106 −0.172603
\(446\) 22.0583 1.04449
\(447\) 6.92585 0.327581
\(448\) −75.9370 −3.58768
\(449\) 32.8327 1.54947 0.774735 0.632286i \(-0.217883\pi\)
0.774735 + 0.632286i \(0.217883\pi\)
\(450\) 17.5833 0.828883
\(451\) 15.9290 0.750068
\(452\) 54.1007 2.54468
\(453\) −9.53255 −0.447878
\(454\) −52.6279 −2.46995
\(455\) 11.3951 0.534210
\(456\) 35.1393 1.64555
\(457\) −7.85022 −0.367218 −0.183609 0.982999i \(-0.558778\pi\)
−0.183609 + 0.982999i \(0.558778\pi\)
\(458\) −3.61336 −0.168841
\(459\) −20.9401 −0.977398
\(460\) 6.65655 0.310363
\(461\) −31.5277 −1.46839 −0.734195 0.678938i \(-0.762440\pi\)
−0.734195 + 0.678938i \(0.762440\pi\)
\(462\) −95.6682 −4.45089
\(463\) −4.86170 −0.225942 −0.112971 0.993598i \(-0.536037\pi\)
−0.112971 + 0.993598i \(0.536037\pi\)
\(464\) 16.9965 0.789042
\(465\) −6.31135 −0.292682
\(466\) 60.4414 2.79989
\(467\) −32.1157 −1.48614 −0.743068 0.669216i \(-0.766630\pi\)
−0.743068 + 0.669216i \(0.766630\pi\)
\(468\) 39.2535 1.81449
\(469\) −61.6510 −2.84678
\(470\) −5.25947 −0.242601
\(471\) 9.97086 0.459433
\(472\) 8.43513 0.388258
\(473\) −0.489814 −0.0225217
\(474\) 22.8897 1.05136
\(475\) −10.0534 −0.461280
\(476\) 159.867 7.32750
\(477\) 1.37842 0.0631134
\(478\) 45.1574 2.06545
\(479\) −5.96834 −0.272700 −0.136350 0.990661i \(-0.543537\pi\)
−0.136350 + 0.990661i \(0.543537\pi\)
\(480\) −11.4822 −0.524088
\(481\) −5.68872 −0.259383
\(482\) −32.4951 −1.48011
\(483\) −36.5628 −1.66367
\(484\) 0.840792 0.0382178
\(485\) −0.166189 −0.00754626
\(486\) −35.1122 −1.59272
\(487\) −39.0549 −1.76975 −0.884874 0.465831i \(-0.845755\pi\)
−0.884874 + 0.465831i \(0.845755\pi\)
\(488\) 26.3784 1.19409
\(489\) −31.8416 −1.43993
\(490\) 20.2296 0.913882
\(491\) −8.38870 −0.378577 −0.189288 0.981922i \(-0.560618\pi\)
−0.189288 + 0.981922i \(0.560618\pi\)
\(492\) −50.3389 −2.26945
\(493\) −9.10995 −0.410291
\(494\) −31.3243 −1.40935
\(495\) −1.77122 −0.0796106
\(496\) −88.9920 −3.99586
\(497\) 18.6407 0.836151
\(498\) −88.2975 −3.95671
\(499\) 13.0397 0.583736 0.291868 0.956459i \(-0.405723\pi\)
0.291868 + 0.956459i \(0.405723\pi\)
\(500\) 19.3284 0.864391
\(501\) −22.7454 −1.01619
\(502\) 71.7504 3.20238
\(503\) −20.1155 −0.896905 −0.448452 0.893807i \(-0.648025\pi\)
−0.448452 + 0.893807i \(0.648025\pi\)
\(504\) 57.1386 2.54516
\(505\) −4.60509 −0.204924
\(506\) 30.1053 1.33834
\(507\) −40.4521 −1.79654
\(508\) 53.3681 2.36783
\(509\) −20.5829 −0.912321 −0.456160 0.889898i \(-0.650776\pi\)
−0.456160 + 0.889898i \(0.650776\pi\)
\(510\) 13.2088 0.584898
\(511\) −64.2384 −2.84174
\(512\) 23.6803 1.04653
\(513\) 7.08116 0.312641
\(514\) −12.5979 −0.555670
\(515\) −4.05996 −0.178903
\(516\) 1.54791 0.0681430
\(517\) −17.0429 −0.749548
\(518\) −13.7028 −0.602068
\(519\) −26.2301 −1.15138
\(520\) 17.9181 0.785760
\(521\) 23.6057 1.03419 0.517093 0.855929i \(-0.327014\pi\)
0.517093 + 0.855929i \(0.327014\pi\)
\(522\) −5.38803 −0.235828
\(523\) −36.7479 −1.60687 −0.803436 0.595392i \(-0.796997\pi\)
−0.803436 + 0.595392i \(0.796997\pi\)
\(524\) −44.4309 −1.94097
\(525\) −52.2706 −2.28127
\(526\) −49.0398 −2.13824
\(527\) 47.6988 2.07779
\(528\) −79.8566 −3.47531
\(529\) −11.4943 −0.499751
\(530\) 1.04121 0.0452274
\(531\) −1.41949 −0.0616006
\(532\) −54.0613 −2.34385
\(533\) 27.1174 1.17458
\(534\) 52.0398 2.25198
\(535\) 4.29966 0.185891
\(536\) −96.9424 −4.18728
\(537\) 17.3271 0.747720
\(538\) −45.0391 −1.94177
\(539\) 65.5527 2.82356
\(540\) −6.70285 −0.288445
\(541\) −20.6879 −0.889443 −0.444721 0.895669i \(-0.646697\pi\)
−0.444721 + 0.895669i \(0.646697\pi\)
\(542\) 44.6288 1.91697
\(543\) −23.6832 −1.01634
\(544\) 86.7781 3.72058
\(545\) 0.388260 0.0166312
\(546\) −162.864 −6.96996
\(547\) 22.5572 0.964477 0.482239 0.876040i \(-0.339824\pi\)
0.482239 + 0.876040i \(0.339824\pi\)
\(548\) 62.7953 2.68248
\(549\) −4.43904 −0.189454
\(550\) 43.0388 1.83518
\(551\) 3.08065 0.131240
\(552\) −57.4928 −2.44706
\(553\) −21.2809 −0.904955
\(554\) −71.1006 −3.02077
\(555\) −0.811194 −0.0344333
\(556\) 17.2920 0.733342
\(557\) −25.1567 −1.06592 −0.532962 0.846139i \(-0.678921\pi\)
−0.532962 + 0.846139i \(0.678921\pi\)
\(558\) 28.2112 1.19428
\(559\) −0.833854 −0.0352683
\(560\) 22.9117 0.968195
\(561\) 42.8024 1.80712
\(562\) 38.5041 1.62420
\(563\) −8.79634 −0.370722 −0.185361 0.982671i \(-0.559345\pi\)
−0.185361 + 0.982671i \(0.559345\pi\)
\(564\) 53.8592 2.26788
\(565\) −4.15582 −0.174837
\(566\) −15.5305 −0.652797
\(567\) 57.9470 2.43355
\(568\) 29.3114 1.22988
\(569\) −3.94240 −0.165274 −0.0826370 0.996580i \(-0.526334\pi\)
−0.0826370 + 0.996580i \(0.526334\pi\)
\(570\) −4.46675 −0.187092
\(571\) −46.2781 −1.93668 −0.968340 0.249635i \(-0.919689\pi\)
−0.968340 + 0.249635i \(0.919689\pi\)
\(572\) 96.0813 4.01736
\(573\) 6.49077 0.271156
\(574\) 65.3196 2.72639
\(575\) 16.4487 0.685959
\(576\) 20.0940 0.837252
\(577\) 16.6682 0.693908 0.346954 0.937882i \(-0.387216\pi\)
0.346954 + 0.937882i \(0.387216\pi\)
\(578\) −54.6753 −2.27419
\(579\) 50.0741 2.08101
\(580\) −2.91607 −0.121083
\(581\) 82.0914 3.40572
\(582\) 2.37526 0.0984576
\(583\) 3.37397 0.139736
\(584\) −101.011 −4.17986
\(585\) −3.01531 −0.124668
\(586\) 77.5630 3.20410
\(587\) 16.3788 0.676027 0.338013 0.941141i \(-0.390245\pi\)
0.338013 + 0.941141i \(0.390245\pi\)
\(588\) −207.160 −8.54313
\(589\) −16.1300 −0.664625
\(590\) −1.07224 −0.0441432
\(591\) 29.3797 1.20852
\(592\) −11.4381 −0.470102
\(593\) −23.8823 −0.980729 −0.490365 0.871517i \(-0.663136\pi\)
−0.490365 + 0.871517i \(0.663136\pi\)
\(594\) −30.3147 −1.24383
\(595\) −12.2804 −0.503449
\(596\) −16.7548 −0.686304
\(597\) −10.6100 −0.434240
\(598\) 51.2509 2.09580
\(599\) −34.9562 −1.42827 −0.714137 0.700006i \(-0.753181\pi\)
−0.714137 + 0.700006i \(0.753181\pi\)
\(600\) −82.1923 −3.35549
\(601\) 16.6126 0.677641 0.338821 0.940851i \(-0.389972\pi\)
0.338821 + 0.940851i \(0.389972\pi\)
\(602\) −2.00857 −0.0818630
\(603\) 16.3138 0.664348
\(604\) 23.0609 0.938334
\(605\) −0.0645867 −0.00262582
\(606\) 65.8183 2.67369
\(607\) 34.2242 1.38912 0.694558 0.719437i \(-0.255600\pi\)
0.694558 + 0.719437i \(0.255600\pi\)
\(608\) −29.3452 −1.19010
\(609\) 16.0173 0.649052
\(610\) −3.35311 −0.135763
\(611\) −29.0137 −1.17377
\(612\) −42.3033 −1.71001
\(613\) 35.4481 1.43174 0.715868 0.698236i \(-0.246031\pi\)
0.715868 + 0.698236i \(0.246031\pi\)
\(614\) −82.2198 −3.31812
\(615\) 3.86686 0.155927
\(616\) 139.859 5.63508
\(617\) 4.92562 0.198298 0.0991491 0.995073i \(-0.468388\pi\)
0.0991491 + 0.995073i \(0.468388\pi\)
\(618\) 58.0270 2.33419
\(619\) −11.0179 −0.442845 −0.221423 0.975178i \(-0.571070\pi\)
−0.221423 + 0.975178i \(0.571070\pi\)
\(620\) 15.2683 0.613188
\(621\) −11.5858 −0.464921
\(622\) 74.8000 2.99921
\(623\) −48.3821 −1.93839
\(624\) −135.947 −5.44223
\(625\) 22.7615 0.910461
\(626\) −15.8002 −0.631501
\(627\) −14.4742 −0.578043
\(628\) −24.1212 −0.962542
\(629\) 6.13070 0.244447
\(630\) −7.26320 −0.289373
\(631\) 27.9488 1.11262 0.556312 0.830973i \(-0.312216\pi\)
0.556312 + 0.830973i \(0.312216\pi\)
\(632\) −33.4629 −1.33108
\(633\) −48.9631 −1.94611
\(634\) 1.67174 0.0663932
\(635\) −4.09955 −0.162686
\(636\) −10.6624 −0.422794
\(637\) 111.596 4.42160
\(638\) −13.1884 −0.522132
\(639\) −4.93261 −0.195131
\(640\) 4.18698 0.165505
\(641\) 11.9897 0.473565 0.236782 0.971563i \(-0.423907\pi\)
0.236782 + 0.971563i \(0.423907\pi\)
\(642\) −61.4530 −2.42536
\(643\) −26.7114 −1.05340 −0.526698 0.850052i \(-0.676570\pi\)
−0.526698 + 0.850052i \(0.676570\pi\)
\(644\) 88.4518 3.48549
\(645\) −0.118905 −0.00468189
\(646\) 33.7580 1.32819
\(647\) −2.25540 −0.0886688 −0.0443344 0.999017i \(-0.514117\pi\)
−0.0443344 + 0.999017i \(0.514117\pi\)
\(648\) 91.1181 3.57946
\(649\) −3.47451 −0.136386
\(650\) 73.2688 2.87384
\(651\) −83.8649 −3.28692
\(652\) 77.0304 3.01675
\(653\) −5.46563 −0.213887 −0.106943 0.994265i \(-0.534106\pi\)
−0.106943 + 0.994265i \(0.534106\pi\)
\(654\) −5.54922 −0.216991
\(655\) 3.41302 0.133358
\(656\) 54.5239 2.12880
\(657\) 16.9984 0.663172
\(658\) −69.8875 −2.72450
\(659\) −0.0101999 −0.000397333 0 −0.000198667 1.00000i \(-0.500063\pi\)
−0.000198667 1.00000i \(0.500063\pi\)
\(660\) 13.7009 0.533307
\(661\) −7.01228 −0.272746 −0.136373 0.990658i \(-0.543545\pi\)
−0.136373 + 0.990658i \(0.543545\pi\)
\(662\) 38.6701 1.50296
\(663\) 72.8662 2.82989
\(664\) 129.084 5.00942
\(665\) 4.15279 0.161038
\(666\) 3.62597 0.140504
\(667\) −5.04038 −0.195164
\(668\) 55.0251 2.12899
\(669\) 17.3518 0.670858
\(670\) 12.3229 0.476075
\(671\) −10.8655 −0.419458
\(672\) −152.575 −5.88569
\(673\) 44.2075 1.70407 0.852037 0.523482i \(-0.175367\pi\)
0.852037 + 0.523482i \(0.175367\pi\)
\(674\) −21.2499 −0.818517
\(675\) −16.5631 −0.637516
\(676\) 97.8605 3.76387
\(677\) 0.556036 0.0213702 0.0106851 0.999943i \(-0.496599\pi\)
0.0106851 + 0.999943i \(0.496599\pi\)
\(678\) 59.3972 2.28113
\(679\) −2.20831 −0.0847471
\(680\) −19.3102 −0.740514
\(681\) −41.3988 −1.58641
\(682\) 69.0531 2.64418
\(683\) −23.8061 −0.910915 −0.455457 0.890258i \(-0.650524\pi\)
−0.455457 + 0.890258i \(0.650524\pi\)
\(684\) 14.3054 0.546981
\(685\) −4.82371 −0.184305
\(686\) 172.890 6.60098
\(687\) −2.84239 −0.108444
\(688\) −1.67660 −0.0639197
\(689\) 5.74382 0.218822
\(690\) 7.30822 0.278219
\(691\) −7.49145 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(692\) 63.4553 2.41221
\(693\) −23.5359 −0.894055
\(694\) −22.9678 −0.871847
\(695\) −1.32831 −0.0503855
\(696\) 25.1862 0.954679
\(697\) −29.2243 −1.10695
\(698\) −39.4713 −1.49401
\(699\) 47.5452 1.79832
\(700\) 126.452 4.77942
\(701\) 6.91924 0.261336 0.130668 0.991426i \(-0.458288\pi\)
0.130668 + 0.991426i \(0.458288\pi\)
\(702\) −51.6074 −1.94779
\(703\) −2.07318 −0.0781914
\(704\) 49.1845 1.85371
\(705\) −4.13727 −0.155819
\(706\) −90.5207 −3.40679
\(707\) −61.1921 −2.30137
\(708\) 10.9801 0.412659
\(709\) 25.2609 0.948693 0.474346 0.880338i \(-0.342684\pi\)
0.474346 + 0.880338i \(0.342684\pi\)
\(710\) −3.72593 −0.139832
\(711\) 5.63124 0.211188
\(712\) −76.0779 −2.85114
\(713\) 26.3909 0.988348
\(714\) 175.518 6.56861
\(715\) −7.38062 −0.276020
\(716\) −41.9173 −1.56652
\(717\) 35.5223 1.32660
\(718\) 46.2854 1.72735
\(719\) −25.6853 −0.957898 −0.478949 0.877843i \(-0.658982\pi\)
−0.478949 + 0.877843i \(0.658982\pi\)
\(720\) −6.06277 −0.225946
\(721\) −53.9485 −2.00915
\(722\) 39.0485 1.45323
\(723\) −25.5617 −0.950649
\(724\) 57.2936 2.12930
\(725\) −7.20577 −0.267616
\(726\) 0.923106 0.0342597
\(727\) 5.54617 0.205696 0.102848 0.994697i \(-0.467204\pi\)
0.102848 + 0.994697i \(0.467204\pi\)
\(728\) 238.094 8.82436
\(729\) 6.07509 0.225003
\(730\) 12.8401 0.475232
\(731\) 0.898640 0.0332374
\(732\) 34.3372 1.26914
\(733\) 24.6819 0.911647 0.455824 0.890070i \(-0.349345\pi\)
0.455824 + 0.890070i \(0.349345\pi\)
\(734\) 31.9382 1.17886
\(735\) 15.9133 0.586971
\(736\) 48.0128 1.76978
\(737\) 39.9315 1.47089
\(738\) −17.2845 −0.636253
\(739\) −14.2579 −0.524486 −0.262243 0.965002i \(-0.584462\pi\)
−0.262243 + 0.965002i \(0.584462\pi\)
\(740\) 1.96242 0.0721400
\(741\) −24.6407 −0.905199
\(742\) 13.8356 0.507919
\(743\) −10.4747 −0.384281 −0.192140 0.981367i \(-0.561543\pi\)
−0.192140 + 0.981367i \(0.561543\pi\)
\(744\) −131.872 −4.83468
\(745\) 1.28705 0.0471537
\(746\) 38.0615 1.39353
\(747\) −21.7226 −0.794788
\(748\) −103.546 −3.78603
\(749\) 57.1337 2.08762
\(750\) 21.2206 0.774867
\(751\) −14.1270 −0.515502 −0.257751 0.966211i \(-0.582981\pi\)
−0.257751 + 0.966211i \(0.582981\pi\)
\(752\) −58.3367 −2.12732
\(753\) 56.4412 2.05683
\(754\) −22.4517 −0.817643
\(755\) −1.77146 −0.0644699
\(756\) −89.0670 −3.23934
\(757\) 29.0280 1.05504 0.527520 0.849543i \(-0.323122\pi\)
0.527520 + 0.849543i \(0.323122\pi\)
\(758\) −60.8219 −2.20915
\(759\) 23.6818 0.859595
\(760\) 6.53002 0.236869
\(761\) 37.4531 1.35767 0.678836 0.734289i \(-0.262485\pi\)
0.678836 + 0.734289i \(0.262485\pi\)
\(762\) 58.5929 2.12260
\(763\) 5.15918 0.186775
\(764\) −15.7023 −0.568089
\(765\) 3.24959 0.117489
\(766\) 74.8181 2.70329
\(767\) −5.91496 −0.213577
\(768\) 1.66171 0.0599620
\(769\) −36.0923 −1.30152 −0.650760 0.759284i \(-0.725550\pi\)
−0.650760 + 0.759284i \(0.725550\pi\)
\(770\) −17.7782 −0.640684
\(771\) −9.90992 −0.356897
\(772\) −121.138 −4.35985
\(773\) −17.1352 −0.616312 −0.308156 0.951336i \(-0.599712\pi\)
−0.308156 + 0.951336i \(0.599712\pi\)
\(774\) 0.531496 0.0191042
\(775\) 37.7288 1.35526
\(776\) −3.47243 −0.124653
\(777\) −10.7791 −0.386698
\(778\) 45.1875 1.62005
\(779\) 9.88258 0.354080
\(780\) 23.3243 0.835143
\(781\) −12.0736 −0.432028
\(782\) −55.2328 −1.97512
\(783\) 5.07544 0.181381
\(784\) 224.382 8.01365
\(785\) 1.85291 0.0661331
\(786\) −48.7806 −1.73995
\(787\) −45.9996 −1.63971 −0.819854 0.572572i \(-0.805946\pi\)
−0.819854 + 0.572572i \(0.805946\pi\)
\(788\) −71.0745 −2.53193
\(789\) −38.5763 −1.37335
\(790\) 4.25365 0.151338
\(791\) −55.2223 −1.96348
\(792\) −37.0088 −1.31505
\(793\) −18.4973 −0.656859
\(794\) 78.5979 2.78934
\(795\) 0.819051 0.0290488
\(796\) 25.6675 0.909760
\(797\) −46.5794 −1.64993 −0.824964 0.565185i \(-0.808805\pi\)
−0.824964 + 0.565185i \(0.808805\pi\)
\(798\) −59.3539 −2.10110
\(799\) 31.2679 1.10618
\(800\) 68.6396 2.42678
\(801\) 12.8026 0.452358
\(802\) −23.1088 −0.816000
\(803\) 41.6073 1.46829
\(804\) −126.192 −4.45043
\(805\) −6.79455 −0.239476
\(806\) 117.555 4.14070
\(807\) −35.4292 −1.24717
\(808\) −96.2209 −3.38504
\(809\) −44.6231 −1.56887 −0.784433 0.620214i \(-0.787046\pi\)
−0.784433 + 0.620214i \(0.787046\pi\)
\(810\) −11.5825 −0.406968
\(811\) 5.33051 0.187180 0.0935898 0.995611i \(-0.470166\pi\)
0.0935898 + 0.995611i \(0.470166\pi\)
\(812\) −38.7485 −1.35981
\(813\) 35.1065 1.23124
\(814\) 8.87535 0.311081
\(815\) −5.91721 −0.207271
\(816\) 146.509 5.12885
\(817\) −0.303887 −0.0106317
\(818\) 75.0110 2.62270
\(819\) −40.0673 −1.40006
\(820\) −9.35460 −0.326677
\(821\) −38.8784 −1.35686 −0.678432 0.734663i \(-0.737340\pi\)
−0.678432 + 0.734663i \(0.737340\pi\)
\(822\) 68.9430 2.40466
\(823\) −50.4227 −1.75763 −0.878813 0.477166i \(-0.841664\pi\)
−0.878813 + 0.477166i \(0.841664\pi\)
\(824\) −84.8307 −2.95522
\(825\) 33.8557 1.17871
\(826\) −14.2478 −0.495744
\(827\) 46.7702 1.62636 0.813180 0.582012i \(-0.197734\pi\)
0.813180 + 0.582012i \(0.197734\pi\)
\(828\) −23.4057 −0.813403
\(829\) −43.5682 −1.51319 −0.756593 0.653886i \(-0.773138\pi\)
−0.756593 + 0.653886i \(0.773138\pi\)
\(830\) −16.4085 −0.569548
\(831\) −55.9300 −1.94019
\(832\) 83.7311 2.90285
\(833\) −120.267 −4.16699
\(834\) 18.9848 0.657391
\(835\) −4.22683 −0.146276
\(836\) 35.0156 1.21104
\(837\) −26.5745 −0.918550
\(838\) 44.5882 1.54027
\(839\) 44.9404 1.55152 0.775758 0.631031i \(-0.217368\pi\)
0.775758 + 0.631031i \(0.217368\pi\)
\(840\) 33.9516 1.17144
\(841\) −26.7919 −0.923860
\(842\) −101.544 −3.49943
\(843\) 30.2886 1.04319
\(844\) 118.450 4.07723
\(845\) −7.51730 −0.258603
\(846\) 18.4933 0.635811
\(847\) −0.858224 −0.0294889
\(848\) 11.5489 0.396590
\(849\) −12.2168 −0.419280
\(850\) −78.9614 −2.70835
\(851\) 3.39201 0.116277
\(852\) 38.1551 1.30717
\(853\) 36.7761 1.25919 0.629595 0.776924i \(-0.283221\pi\)
0.629595 + 0.776924i \(0.283221\pi\)
\(854\) −44.5559 −1.52467
\(855\) −1.09889 −0.0375813
\(856\) 89.8392 3.07064
\(857\) 44.5555 1.52199 0.760993 0.648760i \(-0.224712\pi\)
0.760993 + 0.648760i \(0.224712\pi\)
\(858\) 105.488 3.60129
\(859\) 17.2291 0.587848 0.293924 0.955829i \(-0.405039\pi\)
0.293924 + 0.955829i \(0.405039\pi\)
\(860\) 0.287652 0.00980886
\(861\) 51.3826 1.75111
\(862\) −62.3445 −2.12346
\(863\) 27.6354 0.940720 0.470360 0.882475i \(-0.344124\pi\)
0.470360 + 0.882475i \(0.344124\pi\)
\(864\) −48.3468 −1.64479
\(865\) −4.87441 −0.165735
\(866\) 79.0649 2.68673
\(867\) −43.0094 −1.46068
\(868\) 202.884 6.88632
\(869\) 13.7837 0.467579
\(870\) −3.20155 −0.108543
\(871\) 67.9789 2.30338
\(872\) 8.11249 0.274724
\(873\) 0.584351 0.0197773
\(874\) 18.6777 0.631783
\(875\) −19.7291 −0.666965
\(876\) −131.488 −4.44255
\(877\) 26.8448 0.906483 0.453241 0.891388i \(-0.350268\pi\)
0.453241 + 0.891388i \(0.350268\pi\)
\(878\) 0.475758 0.0160561
\(879\) 61.0136 2.05794
\(880\) −14.8399 −0.500254
\(881\) −11.4946 −0.387263 −0.193631 0.981074i \(-0.562027\pi\)
−0.193631 + 0.981074i \(0.562027\pi\)
\(882\) −71.1311 −2.39511
\(883\) −19.5982 −0.659531 −0.329766 0.944063i \(-0.606970\pi\)
−0.329766 + 0.944063i \(0.606970\pi\)
\(884\) −176.276 −5.92880
\(885\) −0.843456 −0.0283525
\(886\) 17.8227 0.598766
\(887\) −38.9538 −1.30794 −0.653970 0.756521i \(-0.726898\pi\)
−0.653970 + 0.756521i \(0.726898\pi\)
\(888\) −16.9495 −0.568787
\(889\) −54.4746 −1.82702
\(890\) 9.67068 0.324162
\(891\) −37.5324 −1.25738
\(892\) −41.9769 −1.40549
\(893\) −10.5737 −0.353834
\(894\) −18.3951 −0.615225
\(895\) 3.21994 0.107631
\(896\) 55.6363 1.85868
\(897\) 40.3156 1.34610
\(898\) −87.2039 −2.91003
\(899\) −11.5612 −0.385588
\(900\) −33.4610 −1.11537
\(901\) −6.19008 −0.206222
\(902\) −42.3076 −1.40869
\(903\) −1.58000 −0.0525792
\(904\) −86.8337 −2.88805
\(905\) −4.40110 −0.146297
\(906\) 25.3185 0.841152
\(907\) −22.3346 −0.741610 −0.370805 0.928711i \(-0.620918\pi\)
−0.370805 + 0.928711i \(0.620918\pi\)
\(908\) 100.151 3.32363
\(909\) 16.1923 0.537066
\(910\) −30.2655 −1.00329
\(911\) −32.1384 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(912\) −49.5441 −1.64057
\(913\) −53.1707 −1.75969
\(914\) 20.8503 0.689665
\(915\) −2.63766 −0.0871985
\(916\) 6.87623 0.227197
\(917\) 45.3520 1.49765
\(918\) 55.6170 1.83564
\(919\) −3.27716 −0.108103 −0.0540517 0.998538i \(-0.517214\pi\)
−0.0540517 + 0.998538i \(0.517214\pi\)
\(920\) −10.6840 −0.352242
\(921\) −64.6768 −2.13117
\(922\) 83.7379 2.75776
\(923\) −20.5540 −0.676543
\(924\) 182.057 5.98923
\(925\) 4.84925 0.159442
\(926\) 12.9127 0.424339
\(927\) 14.2756 0.468871
\(928\) −21.0332 −0.690449
\(929\) 48.6914 1.59751 0.798756 0.601655i \(-0.205492\pi\)
0.798756 + 0.601655i \(0.205492\pi\)
\(930\) 16.7630 0.549681
\(931\) 40.6698 1.33290
\(932\) −115.020 −3.76761
\(933\) 58.8401 1.92634
\(934\) 85.2995 2.79109
\(935\) 7.95406 0.260126
\(936\) −63.0033 −2.05933
\(937\) 0.209857 0.00685572 0.00342786 0.999994i \(-0.498909\pi\)
0.00342786 + 0.999994i \(0.498909\pi\)
\(938\) 163.746 5.34649
\(939\) −12.4289 −0.405602
\(940\) 10.0088 0.326450
\(941\) 4.74724 0.154756 0.0773778 0.997002i \(-0.475345\pi\)
0.0773778 + 0.997002i \(0.475345\pi\)
\(942\) −26.4827 −0.862853
\(943\) −16.1693 −0.526544
\(944\) −11.8930 −0.387083
\(945\) 6.84182 0.222564
\(946\) 1.30095 0.0422976
\(947\) −1.18813 −0.0386090 −0.0193045 0.999814i \(-0.506145\pi\)
−0.0193045 + 0.999814i \(0.506145\pi\)
\(948\) −43.5592 −1.41474
\(949\) 70.8318 2.29930
\(950\) 26.7019 0.866323
\(951\) 1.31504 0.0426432
\(952\) −256.593 −8.31623
\(953\) 37.2390 1.20629 0.603145 0.797631i \(-0.293914\pi\)
0.603145 + 0.797631i \(0.293914\pi\)
\(954\) −3.66109 −0.118532
\(955\) 1.20620 0.0390316
\(956\) −85.9346 −2.77932
\(957\) −10.3744 −0.335357
\(958\) 15.8520 0.512154
\(959\) −64.0972 −2.06981
\(960\) 11.9398 0.385356
\(961\) 29.5334 0.952691
\(962\) 15.1093 0.487143
\(963\) −15.1184 −0.487184
\(964\) 61.8381 1.99167
\(965\) 9.30538 0.299551
\(966\) 97.1112 3.12450
\(967\) −1.63756 −0.0526604 −0.0263302 0.999653i \(-0.508382\pi\)
−0.0263302 + 0.999653i \(0.508382\pi\)
\(968\) −1.34950 −0.0433747
\(969\) 26.5552 0.853075
\(970\) 0.441400 0.0141725
\(971\) −23.2630 −0.746544 −0.373272 0.927722i \(-0.621764\pi\)
−0.373272 + 0.927722i \(0.621764\pi\)
\(972\) 66.8185 2.14321
\(973\) −17.6504 −0.565847
\(974\) 103.730 3.32373
\(975\) 57.6356 1.84582
\(976\) −37.1918 −1.19048
\(977\) −50.5322 −1.61667 −0.808334 0.588724i \(-0.799631\pi\)
−0.808334 + 0.588724i \(0.799631\pi\)
\(978\) 84.5717 2.70431
\(979\) 31.3372 1.00154
\(980\) −38.4970 −1.22974
\(981\) −1.36520 −0.0435873
\(982\) 22.2805 0.710998
\(983\) −16.5154 −0.526759 −0.263379 0.964692i \(-0.584837\pi\)
−0.263379 + 0.964692i \(0.584837\pi\)
\(984\) 80.7959 2.57568
\(985\) 5.45969 0.173960
\(986\) 24.1961 0.770561
\(987\) −54.9758 −1.74990
\(988\) 59.6101 1.89645
\(989\) 0.497202 0.0158101
\(990\) 4.70439 0.149515
\(991\) −27.1342 −0.861947 −0.430973 0.902365i \(-0.641830\pi\)
−0.430973 + 0.902365i \(0.641830\pi\)
\(992\) 110.128 3.49657
\(993\) 30.4192 0.965324
\(994\) −49.5100 −1.57036
\(995\) −1.97169 −0.0625067
\(996\) 168.030 5.32424
\(997\) −44.8201 −1.41947 −0.709733 0.704471i \(-0.751185\pi\)
−0.709733 + 0.704471i \(0.751185\pi\)
\(998\) −34.6335 −1.09630
\(999\) −3.41561 −0.108065
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 \(a_p\))