Properties

Label 4033.2.a.d.1.4
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 1.4
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75248 q^{2}\) \(+1.04725 q^{3}\) \(+5.57617 q^{4}\) \(-2.70262 q^{5}\) \(-2.88255 q^{6}\) \(+3.33593 q^{7}\) \(-9.84336 q^{8}\) \(-1.90326 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75248 q^{2}\) \(+1.04725 q^{3}\) \(+5.57617 q^{4}\) \(-2.70262 q^{5}\) \(-2.88255 q^{6}\) \(+3.33593 q^{7}\) \(-9.84336 q^{8}\) \(-1.90326 q^{9}\) \(+7.43892 q^{10}\) \(-0.447139 q^{11}\) \(+5.83967 q^{12}\) \(+4.89893 q^{13}\) \(-9.18210 q^{14}\) \(-2.83033 q^{15}\) \(+15.9414 q^{16}\) \(+3.35196 q^{17}\) \(+5.23869 q^{18}\) \(+1.23881 q^{19}\) \(-15.0703 q^{20}\) \(+3.49357 q^{21}\) \(+1.23074 q^{22}\) \(+0.723127 q^{23}\) \(-10.3085 q^{24}\) \(+2.30415 q^{25}\) \(-13.4842 q^{26}\) \(-5.13496 q^{27}\) \(+18.6017 q^{28}\) \(-9.97154 q^{29}\) \(+7.79044 q^{30}\) \(-7.53893 q^{31}\) \(-24.1916 q^{32}\) \(-0.468269 q^{33}\) \(-9.22623 q^{34}\) \(-9.01575 q^{35}\) \(-10.6129 q^{36}\) \(-1.00000 q^{37}\) \(-3.40981 q^{38}\) \(+5.13042 q^{39}\) \(+26.6029 q^{40}\) \(-2.21063 q^{41}\) \(-9.61599 q^{42}\) \(-3.86519 q^{43}\) \(-2.49333 q^{44}\) \(+5.14378 q^{45}\) \(-1.99040 q^{46}\) \(+3.74690 q^{47}\) \(+16.6947 q^{48}\) \(+4.12843 q^{49}\) \(-6.34214 q^{50}\) \(+3.51036 q^{51}\) \(+27.3173 q^{52}\) \(+2.44279 q^{53}\) \(+14.1339 q^{54}\) \(+1.20845 q^{55}\) \(-32.8368 q^{56}\) \(+1.29735 q^{57}\) \(+27.4465 q^{58}\) \(+0.178316 q^{59}\) \(-15.7824 q^{60}\) \(-8.99074 q^{61}\) \(+20.7508 q^{62}\) \(-6.34914 q^{63}\) \(+34.7044 q^{64}\) \(-13.2399 q^{65}\) \(+1.28890 q^{66}\) \(-3.84687 q^{67}\) \(+18.6911 q^{68}\) \(+0.757298 q^{69}\) \(+24.8157 q^{70}\) \(-3.69396 q^{71}\) \(+18.7345 q^{72}\) \(+10.8238 q^{73}\) \(+2.75248 q^{74}\) \(+2.41303 q^{75}\) \(+6.90783 q^{76}\) \(-1.49163 q^{77}\) \(-14.1214 q^{78}\) \(-10.2525 q^{79}\) \(-43.0834 q^{80}\) \(+0.332168 q^{81}\) \(+6.08472 q^{82}\) \(-9.10878 q^{83}\) \(+19.4807 q^{84}\) \(-9.05908 q^{85}\) \(+10.6389 q^{86}\) \(-10.4427 q^{87}\) \(+4.40135 q^{88}\) \(+14.8130 q^{89}\) \(-14.1582 q^{90}\) \(+16.3425 q^{91}\) \(+4.03228 q^{92}\) \(-7.89518 q^{93}\) \(-10.3133 q^{94}\) \(-3.34804 q^{95}\) \(-25.3348 q^{96}\) \(-0.00498767 q^{97}\) \(-11.3634 q^{98}\) \(+0.851022 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75248 −1.94630 −0.973150 0.230170i \(-0.926072\pi\)
−0.973150 + 0.230170i \(0.926072\pi\)
\(3\) 1.04725 0.604633 0.302316 0.953208i \(-0.402240\pi\)
0.302316 + 0.953208i \(0.402240\pi\)
\(4\) 5.57617 2.78809
\(5\) −2.70262 −1.20865 −0.604324 0.796739i \(-0.706557\pi\)
−0.604324 + 0.796739i \(0.706557\pi\)
\(6\) −2.88255 −1.17680
\(7\) 3.33593 1.26086 0.630432 0.776245i \(-0.282878\pi\)
0.630432 + 0.776245i \(0.282878\pi\)
\(8\) −9.84336 −3.48015
\(9\) −1.90326 −0.634420
\(10\) 7.43892 2.35239
\(11\) −0.447139 −0.134818 −0.0674088 0.997725i \(-0.521473\pi\)
−0.0674088 + 0.997725i \(0.521473\pi\)
\(12\) 5.83967 1.68577
\(13\) 4.89893 1.35872 0.679359 0.733806i \(-0.262258\pi\)
0.679359 + 0.733806i \(0.262258\pi\)
\(14\) −9.18210 −2.45402
\(15\) −2.83033 −0.730788
\(16\) 15.9414 3.98534
\(17\) 3.35196 0.812971 0.406485 0.913657i \(-0.366754\pi\)
0.406485 + 0.913657i \(0.366754\pi\)
\(18\) 5.23869 1.23477
\(19\) 1.23881 0.284203 0.142102 0.989852i \(-0.454614\pi\)
0.142102 + 0.989852i \(0.454614\pi\)
\(20\) −15.0703 −3.36982
\(21\) 3.49357 0.762359
\(22\) 1.23074 0.262396
\(23\) 0.723127 0.150782 0.0753912 0.997154i \(-0.475979\pi\)
0.0753912 + 0.997154i \(0.475979\pi\)
\(24\) −10.3085 −2.10421
\(25\) 2.30415 0.460830
\(26\) −13.4842 −2.64447
\(27\) −5.13496 −0.988223
\(28\) 18.6017 3.51540
\(29\) −9.97154 −1.85167 −0.925834 0.377931i \(-0.876636\pi\)
−0.925834 + 0.377931i \(0.876636\pi\)
\(30\) 7.79044 1.42233
\(31\) −7.53893 −1.35403 −0.677016 0.735968i \(-0.736727\pi\)
−0.677016 + 0.735968i \(0.736727\pi\)
\(32\) −24.1916 −4.27652
\(33\) −0.468269 −0.0815151
\(34\) −9.22623 −1.58229
\(35\) −9.01575 −1.52394
\(36\) −10.6129 −1.76882
\(37\) −1.00000 −0.164399
\(38\) −3.40981 −0.553145
\(39\) 5.13042 0.821525
\(40\) 26.6029 4.20628
\(41\) −2.21063 −0.345242 −0.172621 0.984988i \(-0.555224\pi\)
−0.172621 + 0.984988i \(0.555224\pi\)
\(42\) −9.61599 −1.48378
\(43\) −3.86519 −0.589437 −0.294718 0.955584i \(-0.595226\pi\)
−0.294718 + 0.955584i \(0.595226\pi\)
\(44\) −2.49333 −0.375883
\(45\) 5.14378 0.766790
\(46\) −1.99040 −0.293468
\(47\) 3.74690 0.546541 0.273270 0.961937i \(-0.411895\pi\)
0.273270 + 0.961937i \(0.411895\pi\)
\(48\) 16.6947 2.40967
\(49\) 4.12843 0.589776
\(50\) −6.34214 −0.896915
\(51\) 3.51036 0.491549
\(52\) 27.3173 3.78822
\(53\) 2.44279 0.335544 0.167772 0.985826i \(-0.446343\pi\)
0.167772 + 0.985826i \(0.446343\pi\)
\(54\) 14.1339 1.92338
\(55\) 1.20845 0.162947
\(56\) −32.8368 −4.38800
\(57\) 1.29735 0.171838
\(58\) 27.4465 3.60390
\(59\) 0.178316 0.0232147 0.0116074 0.999933i \(-0.496305\pi\)
0.0116074 + 0.999933i \(0.496305\pi\)
\(60\) −15.7824 −2.03750
\(61\) −8.99074 −1.15115 −0.575573 0.817750i \(-0.695221\pi\)
−0.575573 + 0.817750i \(0.695221\pi\)
\(62\) 20.7508 2.63535
\(63\) −6.34914 −0.799916
\(64\) 34.7044 4.33805
\(65\) −13.2399 −1.64221
\(66\) 1.28890 0.158653
\(67\) −3.84687 −0.469970 −0.234985 0.971999i \(-0.575504\pi\)
−0.234985 + 0.971999i \(0.575504\pi\)
\(68\) 18.6911 2.26663
\(69\) 0.757298 0.0911680
\(70\) 24.8157 2.96605
\(71\) −3.69396 −0.438392 −0.219196 0.975681i \(-0.570343\pi\)
−0.219196 + 0.975681i \(0.570343\pi\)
\(72\) 18.7345 2.20788
\(73\) 10.8238 1.26683 0.633413 0.773814i \(-0.281653\pi\)
0.633413 + 0.773814i \(0.281653\pi\)
\(74\) 2.75248 0.319970
\(75\) 2.41303 0.278633
\(76\) 6.90783 0.792383
\(77\) −1.49163 −0.169986
\(78\) −14.1214 −1.59893
\(79\) −10.2525 −1.15349 −0.576747 0.816923i \(-0.695678\pi\)
−0.576747 + 0.816923i \(0.695678\pi\)
\(80\) −43.0834 −4.81687
\(81\) 0.332168 0.0369076
\(82\) 6.08472 0.671945
\(83\) −9.10878 −0.999819 −0.499909 0.866078i \(-0.666633\pi\)
−0.499909 + 0.866078i \(0.666633\pi\)
\(84\) 19.4807 2.12552
\(85\) −9.05908 −0.982596
\(86\) 10.6389 1.14722
\(87\) −10.4427 −1.11958
\(88\) 4.40135 0.469186
\(89\) 14.8130 1.57017 0.785086 0.619387i \(-0.212619\pi\)
0.785086 + 0.619387i \(0.212619\pi\)
\(90\) −14.1582 −1.49240
\(91\) 16.3425 1.71316
\(92\) 4.03228 0.420395
\(93\) −7.89518 −0.818692
\(94\) −10.3133 −1.06373
\(95\) −3.34804 −0.343502
\(96\) −25.3348 −2.58572
\(97\) −0.00498767 −0.000506421 0 −0.000253210 1.00000i \(-0.500081\pi\)
−0.000253210 1.00000i \(0.500081\pi\)
\(98\) −11.3634 −1.14788
\(99\) 0.851022 0.0855309
\(100\) 12.8484 1.28484
\(101\) 15.0443 1.49697 0.748483 0.663154i \(-0.230783\pi\)
0.748483 + 0.663154i \(0.230783\pi\)
\(102\) −9.66221 −0.956701
\(103\) −2.86587 −0.282382 −0.141191 0.989982i \(-0.545093\pi\)
−0.141191 + 0.989982i \(0.545093\pi\)
\(104\) −48.2219 −4.72855
\(105\) −9.44178 −0.921424
\(106\) −6.72375 −0.653069
\(107\) 18.1977 1.75924 0.879618 0.475681i \(-0.157798\pi\)
0.879618 + 0.475681i \(0.157798\pi\)
\(108\) −28.6334 −2.75525
\(109\) −1.00000 −0.0957826
\(110\) −3.32623 −0.317144
\(111\) −1.04725 −0.0994010
\(112\) 53.1793 5.02497
\(113\) −13.0088 −1.22376 −0.611881 0.790950i \(-0.709587\pi\)
−0.611881 + 0.790950i \(0.709587\pi\)
\(114\) −3.57094 −0.334449
\(115\) −1.95434 −0.182243
\(116\) −55.6030 −5.16261
\(117\) −9.32393 −0.861997
\(118\) −0.490811 −0.0451828
\(119\) 11.1819 1.02504
\(120\) 27.8600 2.54325
\(121\) −10.8001 −0.981824
\(122\) 24.7469 2.24048
\(123\) −2.31509 −0.208745
\(124\) −42.0384 −3.77516
\(125\) 7.28585 0.651666
\(126\) 17.4759 1.55688
\(127\) −4.46844 −0.396510 −0.198255 0.980151i \(-0.563527\pi\)
−0.198255 + 0.980151i \(0.563527\pi\)
\(128\) −47.1400 −4.16663
\(129\) −4.04784 −0.356393
\(130\) 36.4427 3.19624
\(131\) 9.17000 0.801186 0.400593 0.916256i \(-0.368804\pi\)
0.400593 + 0.916256i \(0.368804\pi\)
\(132\) −2.61115 −0.227271
\(133\) 4.13259 0.358341
\(134\) 10.5884 0.914702
\(135\) 13.8778 1.19441
\(136\) −32.9946 −2.82926
\(137\) 8.12235 0.693939 0.346969 0.937876i \(-0.387211\pi\)
0.346969 + 0.937876i \(0.387211\pi\)
\(138\) −2.08445 −0.177440
\(139\) −18.6683 −1.58343 −0.791714 0.610892i \(-0.790811\pi\)
−0.791714 + 0.610892i \(0.790811\pi\)
\(140\) −50.2734 −4.24888
\(141\) 3.92395 0.330456
\(142\) 10.1676 0.853243
\(143\) −2.19050 −0.183179
\(144\) −30.3405 −2.52838
\(145\) 26.9493 2.23801
\(146\) −29.7923 −2.46563
\(147\) 4.32351 0.356597
\(148\) −5.57617 −0.458359
\(149\) 0.899330 0.0736760 0.0368380 0.999321i \(-0.488271\pi\)
0.0368380 + 0.999321i \(0.488271\pi\)
\(150\) −6.64184 −0.542304
\(151\) −20.2811 −1.65045 −0.825226 0.564803i \(-0.808952\pi\)
−0.825226 + 0.564803i \(0.808952\pi\)
\(152\) −12.1941 −0.989070
\(153\) −6.37965 −0.515764
\(154\) 4.10568 0.330845
\(155\) 20.3749 1.63655
\(156\) 28.6081 2.29048
\(157\) −6.52191 −0.520505 −0.260252 0.965541i \(-0.583806\pi\)
−0.260252 + 0.965541i \(0.583806\pi\)
\(158\) 28.2198 2.24504
\(159\) 2.55823 0.202881
\(160\) 65.3808 5.16880
\(161\) 2.41230 0.190116
\(162\) −0.914289 −0.0718333
\(163\) −12.9035 −1.01068 −0.505340 0.862921i \(-0.668633\pi\)
−0.505340 + 0.862921i \(0.668633\pi\)
\(164\) −12.3268 −0.962565
\(165\) 1.26555 0.0985231
\(166\) 25.0718 1.94595
\(167\) −21.0968 −1.63252 −0.816261 0.577683i \(-0.803957\pi\)
−0.816261 + 0.577683i \(0.803957\pi\)
\(168\) −34.3884 −2.65313
\(169\) 10.9995 0.846115
\(170\) 24.9350 1.91243
\(171\) −2.35778 −0.180304
\(172\) −21.5530 −1.64340
\(173\) −7.50058 −0.570259 −0.285129 0.958489i \(-0.592037\pi\)
−0.285129 + 0.958489i \(0.592037\pi\)
\(174\) 28.7435 2.17904
\(175\) 7.68649 0.581044
\(176\) −7.12801 −0.537294
\(177\) 0.186742 0.0140364
\(178\) −40.7725 −3.05603
\(179\) −5.53584 −0.413768 −0.206884 0.978365i \(-0.566332\pi\)
−0.206884 + 0.978365i \(0.566332\pi\)
\(180\) 28.6826 2.13788
\(181\) 2.33748 0.173744 0.0868718 0.996219i \(-0.472313\pi\)
0.0868718 + 0.996219i \(0.472313\pi\)
\(182\) −44.9824 −3.33432
\(183\) −9.41560 −0.696021
\(184\) −7.11801 −0.524746
\(185\) 2.70262 0.198701
\(186\) 21.7314 1.59342
\(187\) −1.49879 −0.109603
\(188\) 20.8933 1.52380
\(189\) −17.1299 −1.24601
\(190\) 9.21543 0.668557
\(191\) 5.22039 0.377734 0.188867 0.982003i \(-0.439518\pi\)
0.188867 + 0.982003i \(0.439518\pi\)
\(192\) 36.3443 2.62292
\(193\) −0.253889 −0.0182753 −0.00913766 0.999958i \(-0.502909\pi\)
−0.00913766 + 0.999958i \(0.502909\pi\)
\(194\) 0.0137285 0.000985647 0
\(195\) −13.8656 −0.992935
\(196\) 23.0208 1.64435
\(197\) 16.4830 1.17437 0.587184 0.809454i \(-0.300237\pi\)
0.587184 + 0.809454i \(0.300237\pi\)
\(198\) −2.34242 −0.166469
\(199\) 7.17168 0.508387 0.254193 0.967153i \(-0.418190\pi\)
0.254193 + 0.967153i \(0.418190\pi\)
\(200\) −22.6806 −1.60376
\(201\) −4.02865 −0.284159
\(202\) −41.4093 −2.91354
\(203\) −33.2643 −2.33470
\(204\) 19.5744 1.37048
\(205\) 5.97449 0.417276
\(206\) 7.88825 0.549601
\(207\) −1.37630 −0.0956594
\(208\) 78.0956 5.41495
\(209\) −0.553922 −0.0383156
\(210\) 25.9884 1.79337
\(211\) 14.5563 1.00209 0.501047 0.865420i \(-0.332948\pi\)
0.501047 + 0.865420i \(0.332948\pi\)
\(212\) 13.6214 0.935525
\(213\) −3.86851 −0.265066
\(214\) −50.0888 −3.42400
\(215\) 10.4461 0.712421
\(216\) 50.5453 3.43917
\(217\) −25.1493 −1.70725
\(218\) 2.75248 0.186422
\(219\) 11.3352 0.765965
\(220\) 6.73851 0.454310
\(221\) 16.4210 1.10460
\(222\) 2.88255 0.193464
\(223\) 21.1098 1.41362 0.706810 0.707404i \(-0.250134\pi\)
0.706810 + 0.707404i \(0.250134\pi\)
\(224\) −80.7016 −5.39210
\(225\) −4.38540 −0.292360
\(226\) 35.8064 2.38181
\(227\) 13.3012 0.882834 0.441417 0.897302i \(-0.354476\pi\)
0.441417 + 0.897302i \(0.354476\pi\)
\(228\) 7.23426 0.479100
\(229\) 2.14342 0.141641 0.0708206 0.997489i \(-0.477438\pi\)
0.0708206 + 0.997489i \(0.477438\pi\)
\(230\) 5.37929 0.354700
\(231\) −1.56211 −0.102779
\(232\) 98.1534 6.44409
\(233\) 4.39981 0.288241 0.144121 0.989560i \(-0.453965\pi\)
0.144121 + 0.989560i \(0.453965\pi\)
\(234\) 25.6640 1.67771
\(235\) −10.1264 −0.660576
\(236\) 0.994319 0.0647247
\(237\) −10.7369 −0.697440
\(238\) −30.7781 −1.99505
\(239\) −26.7078 −1.72758 −0.863791 0.503850i \(-0.831916\pi\)
−0.863791 + 0.503850i \(0.831916\pi\)
\(240\) −45.1193 −2.91244
\(241\) −9.83072 −0.633252 −0.316626 0.948550i \(-0.602550\pi\)
−0.316626 + 0.948550i \(0.602550\pi\)
\(242\) 29.7270 1.91093
\(243\) 15.7527 1.01054
\(244\) −50.1339 −3.20950
\(245\) −11.1576 −0.712831
\(246\) 6.37225 0.406280
\(247\) 6.06885 0.386152
\(248\) 74.2084 4.71224
\(249\) −9.53921 −0.604523
\(250\) −20.0542 −1.26834
\(251\) −18.3964 −1.16117 −0.580585 0.814199i \(-0.697176\pi\)
−0.580585 + 0.814199i \(0.697176\pi\)
\(252\) −35.4039 −2.23024
\(253\) −0.323339 −0.0203281
\(254\) 12.2993 0.771727
\(255\) −9.48716 −0.594109
\(256\) 60.3434 3.77146
\(257\) −24.9057 −1.55358 −0.776789 0.629761i \(-0.783153\pi\)
−0.776789 + 0.629761i \(0.783153\pi\)
\(258\) 11.1416 0.693647
\(259\) −3.33593 −0.207285
\(260\) −73.8282 −4.57863
\(261\) 18.9784 1.17473
\(262\) −25.2403 −1.55935
\(263\) −24.2552 −1.49564 −0.747819 0.663903i \(-0.768899\pi\)
−0.747819 + 0.663903i \(0.768899\pi\)
\(264\) 4.60934 0.283685
\(265\) −6.60194 −0.405554
\(266\) −11.3749 −0.697440
\(267\) 15.5129 0.949377
\(268\) −21.4508 −1.31032
\(269\) −3.54338 −0.216044 −0.108022 0.994149i \(-0.534452\pi\)
−0.108022 + 0.994149i \(0.534452\pi\)
\(270\) −38.1985 −2.32469
\(271\) 15.2758 0.927937 0.463969 0.885852i \(-0.346425\pi\)
0.463969 + 0.885852i \(0.346425\pi\)
\(272\) 53.4349 3.23996
\(273\) 17.1147 1.03583
\(274\) −22.3566 −1.35061
\(275\) −1.03028 −0.0621280
\(276\) 4.22283 0.254184
\(277\) −21.9736 −1.32027 −0.660133 0.751149i \(-0.729500\pi\)
−0.660133 + 0.751149i \(0.729500\pi\)
\(278\) 51.3843 3.08183
\(279\) 14.3485 0.859024
\(280\) 88.7453 5.30355
\(281\) −23.8190 −1.42092 −0.710461 0.703736i \(-0.751514\pi\)
−0.710461 + 0.703736i \(0.751514\pi\)
\(282\) −10.8006 −0.643168
\(283\) 1.30054 0.0773089 0.0386545 0.999253i \(-0.487693\pi\)
0.0386545 + 0.999253i \(0.487693\pi\)
\(284\) −20.5981 −1.22227
\(285\) −3.50625 −0.207692
\(286\) 6.02933 0.356522
\(287\) −7.37450 −0.435303
\(288\) 46.0429 2.71310
\(289\) −5.76434 −0.339079
\(290\) −74.1775 −4.35585
\(291\) −0.00522335 −0.000306198 0
\(292\) 60.3552 3.53202
\(293\) 2.98604 0.174446 0.0872232 0.996189i \(-0.472201\pi\)
0.0872232 + 0.996189i \(0.472201\pi\)
\(294\) −11.9004 −0.694046
\(295\) −0.481919 −0.0280584
\(296\) 9.84336 0.572134
\(297\) 2.29604 0.133230
\(298\) −2.47539 −0.143396
\(299\) 3.54255 0.204871
\(300\) 13.4555 0.776853
\(301\) −12.8940 −0.743199
\(302\) 55.8234 3.21227
\(303\) 15.7552 0.905114
\(304\) 19.7484 1.13265
\(305\) 24.2986 1.39133
\(306\) 17.5599 1.00383
\(307\) −0.413311 −0.0235889 −0.0117945 0.999930i \(-0.503754\pi\)
−0.0117945 + 0.999930i \(0.503754\pi\)
\(308\) −8.31756 −0.473937
\(309\) −3.00129 −0.170737
\(310\) −56.0815 −3.18522
\(311\) 4.85348 0.275216 0.137608 0.990487i \(-0.456059\pi\)
0.137608 + 0.990487i \(0.456059\pi\)
\(312\) −50.5006 −2.85903
\(313\) 3.56845 0.201701 0.100850 0.994902i \(-0.467844\pi\)
0.100850 + 0.994902i \(0.467844\pi\)
\(314\) 17.9514 1.01306
\(315\) 17.1593 0.966817
\(316\) −57.1696 −3.21604
\(317\) −0.620200 −0.0348339 −0.0174170 0.999848i \(-0.505544\pi\)
−0.0174170 + 0.999848i \(0.505544\pi\)
\(318\) −7.04148 −0.394867
\(319\) 4.45867 0.249637
\(320\) −93.7927 −5.24317
\(321\) 19.0576 1.06369
\(322\) −6.63983 −0.370023
\(323\) 4.15245 0.231049
\(324\) 1.85223 0.102902
\(325\) 11.2879 0.626139
\(326\) 35.5167 1.96709
\(327\) −1.04725 −0.0579133
\(328\) 21.7600 1.20150
\(329\) 12.4994 0.689113
\(330\) −3.48341 −0.191756
\(331\) 16.0189 0.880481 0.440240 0.897880i \(-0.354893\pi\)
0.440240 + 0.897880i \(0.354893\pi\)
\(332\) −50.7921 −2.78758
\(333\) 1.90326 0.104298
\(334\) 58.0687 3.17738
\(335\) 10.3966 0.568028
\(336\) 55.6922 3.03826
\(337\) −8.77114 −0.477794 −0.238897 0.971045i \(-0.576786\pi\)
−0.238897 + 0.971045i \(0.576786\pi\)
\(338\) −30.2759 −1.64679
\(339\) −13.6235 −0.739926
\(340\) −50.5150 −2.73956
\(341\) 3.37095 0.182547
\(342\) 6.48975 0.350926
\(343\) −9.57936 −0.517237
\(344\) 38.0465 2.05133
\(345\) −2.04669 −0.110190
\(346\) 20.6452 1.10989
\(347\) −1.92975 −0.103594 −0.0517971 0.998658i \(-0.516495\pi\)
−0.0517971 + 0.998658i \(0.516495\pi\)
\(348\) −58.2305 −3.12148
\(349\) 26.2258 1.40384 0.701918 0.712258i \(-0.252327\pi\)
0.701918 + 0.712258i \(0.252327\pi\)
\(350\) −21.1569 −1.13089
\(351\) −25.1558 −1.34272
\(352\) 10.8170 0.576549
\(353\) 2.23569 0.118994 0.0594969 0.998228i \(-0.481050\pi\)
0.0594969 + 0.998228i \(0.481050\pi\)
\(354\) −0.514004 −0.0273190
\(355\) 9.98336 0.529862
\(356\) 82.5997 4.37777
\(357\) 11.7103 0.619775
\(358\) 15.2373 0.805318
\(359\) −19.5995 −1.03442 −0.517210 0.855858i \(-0.673029\pi\)
−0.517210 + 0.855858i \(0.673029\pi\)
\(360\) −50.6321 −2.66855
\(361\) −17.4653 −0.919229
\(362\) −6.43388 −0.338157
\(363\) −11.3104 −0.593643
\(364\) 91.1285 4.77643
\(365\) −29.2525 −1.53115
\(366\) 25.9163 1.35467
\(367\) 31.0498 1.62079 0.810393 0.585887i \(-0.199254\pi\)
0.810393 + 0.585887i \(0.199254\pi\)
\(368\) 11.5276 0.600919
\(369\) 4.20740 0.219028
\(370\) −7.43892 −0.386731
\(371\) 8.14899 0.423074
\(372\) −44.0249 −2.28258
\(373\) −31.7553 −1.64423 −0.822114 0.569323i \(-0.807206\pi\)
−0.822114 + 0.569323i \(0.807206\pi\)
\(374\) 4.12541 0.213320
\(375\) 7.63014 0.394019
\(376\) −36.8821 −1.90205
\(377\) −48.8498 −2.51589
\(378\) 47.1497 2.42512
\(379\) 18.8937 0.970506 0.485253 0.874374i \(-0.338728\pi\)
0.485253 + 0.874374i \(0.338728\pi\)
\(380\) −18.6692 −0.957712
\(381\) −4.67959 −0.239743
\(382\) −14.3690 −0.735184
\(383\) −8.58405 −0.438625 −0.219312 0.975655i \(-0.570381\pi\)
−0.219312 + 0.975655i \(0.570381\pi\)
\(384\) −49.3676 −2.51928
\(385\) 4.03130 0.205454
\(386\) 0.698825 0.0355693
\(387\) 7.35646 0.373950
\(388\) −0.0278121 −0.00141194
\(389\) 30.8780 1.56558 0.782789 0.622287i \(-0.213796\pi\)
0.782789 + 0.622287i \(0.213796\pi\)
\(390\) 38.1648 1.93255
\(391\) 2.42390 0.122582
\(392\) −40.6376 −2.05251
\(393\) 9.60332 0.484423
\(394\) −45.3693 −2.28567
\(395\) 27.7085 1.39417
\(396\) 4.74544 0.238468
\(397\) −35.1300 −1.76313 −0.881563 0.472066i \(-0.843508\pi\)
−0.881563 + 0.472066i \(0.843508\pi\)
\(398\) −19.7399 −0.989473
\(399\) 4.32787 0.216665
\(400\) 36.7313 1.83657
\(401\) 5.18820 0.259086 0.129543 0.991574i \(-0.458649\pi\)
0.129543 + 0.991574i \(0.458649\pi\)
\(402\) 11.0888 0.553059
\(403\) −36.9327 −1.83975
\(404\) 83.8897 4.17367
\(405\) −0.897725 −0.0446083
\(406\) 91.5596 4.54403
\(407\) 0.447139 0.0221639
\(408\) −34.5537 −1.71066
\(409\) −22.0305 −1.08934 −0.544669 0.838651i \(-0.683345\pi\)
−0.544669 + 0.838651i \(0.683345\pi\)
\(410\) −16.4447 −0.812145
\(411\) 8.50616 0.419578
\(412\) −15.9806 −0.787306
\(413\) 0.594849 0.0292706
\(414\) 3.78824 0.186182
\(415\) 24.6176 1.20843
\(416\) −118.513 −5.81058
\(417\) −19.5505 −0.957392
\(418\) 1.52466 0.0745736
\(419\) 20.5617 1.00450 0.502251 0.864722i \(-0.332505\pi\)
0.502251 + 0.864722i \(0.332505\pi\)
\(420\) −52.6490 −2.56901
\(421\) −13.5982 −0.662735 −0.331367 0.943502i \(-0.607510\pi\)
−0.331367 + 0.943502i \(0.607510\pi\)
\(422\) −40.0659 −1.95038
\(423\) −7.13131 −0.346736
\(424\) −24.0453 −1.16774
\(425\) 7.72343 0.374642
\(426\) 10.6480 0.515898
\(427\) −29.9925 −1.45144
\(428\) 101.473 4.90490
\(429\) −2.29401 −0.110756
\(430\) −28.7529 −1.38659
\(431\) −29.4436 −1.41825 −0.709123 0.705084i \(-0.750909\pi\)
−0.709123 + 0.705084i \(0.750909\pi\)
\(432\) −81.8582 −3.93841
\(433\) −10.7005 −0.514234 −0.257117 0.966380i \(-0.582773\pi\)
−0.257117 + 0.966380i \(0.582773\pi\)
\(434\) 69.2232 3.32282
\(435\) 28.2227 1.35318
\(436\) −5.57617 −0.267050
\(437\) 0.895819 0.0428528
\(438\) −31.2001 −1.49080
\(439\) 5.86555 0.279948 0.139974 0.990155i \(-0.455298\pi\)
0.139974 + 0.990155i \(0.455298\pi\)
\(440\) −11.8952 −0.567081
\(441\) −7.85747 −0.374165
\(442\) −45.1986 −2.14988
\(443\) −38.2169 −1.81574 −0.907869 0.419254i \(-0.862292\pi\)
−0.907869 + 0.419254i \(0.862292\pi\)
\(444\) −5.83967 −0.277139
\(445\) −40.0338 −1.89779
\(446\) −58.1045 −2.75133
\(447\) 0.941827 0.0445469
\(448\) 115.771 5.46968
\(449\) −17.5524 −0.828349 −0.414174 0.910198i \(-0.635930\pi\)
−0.414174 + 0.910198i \(0.635930\pi\)
\(450\) 12.0707 0.569020
\(451\) 0.988459 0.0465447
\(452\) −72.5391 −3.41195
\(453\) −21.2395 −0.997917
\(454\) −36.6114 −1.71826
\(455\) −44.1675 −2.07060
\(456\) −12.7703 −0.598024
\(457\) −3.41998 −0.159980 −0.0799899 0.996796i \(-0.525489\pi\)
−0.0799899 + 0.996796i \(0.525489\pi\)
\(458\) −5.89974 −0.275677
\(459\) −17.2122 −0.803397
\(460\) −10.8977 −0.508109
\(461\) 12.7712 0.594814 0.297407 0.954751i \(-0.403878\pi\)
0.297407 + 0.954751i \(0.403878\pi\)
\(462\) 4.29969 0.200040
\(463\) 7.98062 0.370891 0.185445 0.982655i \(-0.440627\pi\)
0.185445 + 0.982655i \(0.440627\pi\)
\(464\) −158.960 −7.37953
\(465\) 21.3377 0.989510
\(466\) −12.1104 −0.561004
\(467\) −31.0775 −1.43809 −0.719047 0.694961i \(-0.755421\pi\)
−0.719047 + 0.694961i \(0.755421\pi\)
\(468\) −51.9918 −2.40332
\(469\) −12.8329 −0.592567
\(470\) 27.8729 1.28568
\(471\) −6.83009 −0.314714
\(472\) −1.75523 −0.0807908
\(473\) 1.72828 0.0794664
\(474\) 29.5533 1.35743
\(475\) 2.85441 0.130969
\(476\) 62.3523 2.85791
\(477\) −4.64927 −0.212875
\(478\) 73.5127 3.36239
\(479\) 17.6207 0.805110 0.402555 0.915396i \(-0.368122\pi\)
0.402555 + 0.915396i \(0.368122\pi\)
\(480\) 68.4703 3.12523
\(481\) −4.89893 −0.223372
\(482\) 27.0589 1.23250
\(483\) 2.52629 0.114950
\(484\) −60.2230 −2.73741
\(485\) 0.0134798 0.000612085 0
\(486\) −43.3592 −1.96681
\(487\) −38.3287 −1.73684 −0.868420 0.495829i \(-0.834864\pi\)
−0.868420 + 0.495829i \(0.834864\pi\)
\(488\) 88.4992 4.00617
\(489\) −13.5132 −0.611089
\(490\) 30.7110 1.38738
\(491\) 4.93566 0.222743 0.111372 0.993779i \(-0.464476\pi\)
0.111372 + 0.993779i \(0.464476\pi\)
\(492\) −12.9093 −0.581998
\(493\) −33.4242 −1.50535
\(494\) −16.7044 −0.751568
\(495\) −2.29999 −0.103377
\(496\) −120.181 −5.39628
\(497\) −12.3228 −0.552752
\(498\) 26.2565 1.17658
\(499\) 36.8248 1.64850 0.824252 0.566223i \(-0.191596\pi\)
0.824252 + 0.566223i \(0.191596\pi\)
\(500\) 40.6272 1.81690
\(501\) −22.0938 −0.987076
\(502\) 50.6358 2.25999
\(503\) −12.4470 −0.554983 −0.277491 0.960728i \(-0.589503\pi\)
−0.277491 + 0.960728i \(0.589503\pi\)
\(504\) 62.4969 2.78383
\(505\) −40.6591 −1.80930
\(506\) 0.889985 0.0395647
\(507\) 11.5193 0.511588
\(508\) −24.9168 −1.10550
\(509\) 29.5028 1.30769 0.653845 0.756629i \(-0.273155\pi\)
0.653845 + 0.756629i \(0.273155\pi\)
\(510\) 26.1133 1.15632
\(511\) 36.1073 1.59729
\(512\) −71.8143 −3.17377
\(513\) −6.36125 −0.280856
\(514\) 68.5527 3.02373
\(515\) 7.74535 0.341301
\(516\) −22.5715 −0.993653
\(517\) −1.67538 −0.0736833
\(518\) 9.18210 0.403438
\(519\) −7.85501 −0.344797
\(520\) 130.325 5.71515
\(521\) −32.5553 −1.42627 −0.713136 0.701026i \(-0.752726\pi\)
−0.713136 + 0.701026i \(0.752726\pi\)
\(522\) −52.2378 −2.28639
\(523\) −0.443058 −0.0193736 −0.00968680 0.999953i \(-0.503083\pi\)
−0.00968680 + 0.999953i \(0.503083\pi\)
\(524\) 51.1335 2.23378
\(525\) 8.04971 0.351318
\(526\) 66.7620 2.91096
\(527\) −25.2702 −1.10079
\(528\) −7.46484 −0.324865
\(529\) −22.4771 −0.977265
\(530\) 18.1717 0.789330
\(531\) −0.339381 −0.0147279
\(532\) 23.0440 0.999086
\(533\) −10.8297 −0.469087
\(534\) −42.6992 −1.84777
\(535\) −49.1814 −2.12630
\(536\) 37.8661 1.63557
\(537\) −5.79744 −0.250178
\(538\) 9.75310 0.420486
\(539\) −1.84598 −0.0795121
\(540\) 77.3852 3.33013
\(541\) 18.4273 0.792252 0.396126 0.918196i \(-0.370354\pi\)
0.396126 + 0.918196i \(0.370354\pi\)
\(542\) −42.0463 −1.80604
\(543\) 2.44794 0.105051
\(544\) −81.0895 −3.47668
\(545\) 2.70262 0.115767
\(546\) −47.1080 −2.01604
\(547\) −41.4134 −1.77071 −0.885355 0.464917i \(-0.846084\pi\)
−0.885355 + 0.464917i \(0.846084\pi\)
\(548\) 45.2916 1.93476
\(549\) 17.1117 0.730310
\(550\) 2.83582 0.120920
\(551\) −12.3529 −0.526250
\(552\) −7.45436 −0.317279
\(553\) −34.2015 −1.45440
\(554\) 60.4820 2.56963
\(555\) 2.83033 0.120141
\(556\) −104.098 −4.41473
\(557\) 39.0199 1.65333 0.826663 0.562697i \(-0.190236\pi\)
0.826663 + 0.562697i \(0.190236\pi\)
\(558\) −39.4941 −1.67192
\(559\) −18.9353 −0.800878
\(560\) −143.723 −6.07342
\(561\) −1.56962 −0.0662694
\(562\) 65.5614 2.76554
\(563\) −4.12232 −0.173735 −0.0868676 0.996220i \(-0.527686\pi\)
−0.0868676 + 0.996220i \(0.527686\pi\)
\(564\) 21.8806 0.921341
\(565\) 35.1578 1.47910
\(566\) −3.57971 −0.150466
\(567\) 1.10809 0.0465354
\(568\) 36.3610 1.52567
\(569\) 7.97922 0.334506 0.167253 0.985914i \(-0.446510\pi\)
0.167253 + 0.985914i \(0.446510\pi\)
\(570\) 9.65089 0.404231
\(571\) −29.9634 −1.25393 −0.626965 0.779047i \(-0.715703\pi\)
−0.626965 + 0.779047i \(0.715703\pi\)
\(572\) −12.2146 −0.510719
\(573\) 5.46707 0.228390
\(574\) 20.2982 0.847231
\(575\) 1.66620 0.0694852
\(576\) −66.0514 −2.75214
\(577\) −7.09252 −0.295265 −0.147633 0.989042i \(-0.547165\pi\)
−0.147633 + 0.989042i \(0.547165\pi\)
\(578\) 15.8662 0.659949
\(579\) −0.265886 −0.0110499
\(580\) 150.274 6.23978
\(581\) −30.3863 −1.26063
\(582\) 0.0143772 0.000595954 0
\(583\) −1.09227 −0.0452372
\(584\) −106.542 −4.40875
\(585\) 25.1990 1.04185
\(586\) −8.21903 −0.339525
\(587\) −19.0066 −0.784486 −0.392243 0.919862i \(-0.628301\pi\)
−0.392243 + 0.919862i \(0.628301\pi\)
\(588\) 24.1087 0.994225
\(589\) −9.33932 −0.384820
\(590\) 1.32648 0.0546101
\(591\) 17.2619 0.710061
\(592\) −15.9414 −0.655186
\(593\) 7.50231 0.308083 0.154041 0.988064i \(-0.450771\pi\)
0.154041 + 0.988064i \(0.450771\pi\)
\(594\) −6.31982 −0.259305
\(595\) −30.2205 −1.23892
\(596\) 5.01482 0.205415
\(597\) 7.51057 0.307387
\(598\) −9.75081 −0.398740
\(599\) −42.1320 −1.72147 −0.860734 0.509054i \(-0.829995\pi\)
−0.860734 + 0.509054i \(0.829995\pi\)
\(600\) −23.7524 −0.969686
\(601\) 0.300303 0.0122496 0.00612480 0.999981i \(-0.498050\pi\)
0.00612480 + 0.999981i \(0.498050\pi\)
\(602\) 35.4906 1.44649
\(603\) 7.32158 0.298158
\(604\) −113.091 −4.60160
\(605\) 29.1885 1.18668
\(606\) −43.3660 −1.76162
\(607\) 23.3212 0.946578 0.473289 0.880907i \(-0.343067\pi\)
0.473289 + 0.880907i \(0.343067\pi\)
\(608\) −29.9689 −1.21540
\(609\) −34.8362 −1.41164
\(610\) −66.8814 −2.70795
\(611\) 18.3558 0.742595
\(612\) −35.5741 −1.43800
\(613\) −2.00742 −0.0810787 −0.0405394 0.999178i \(-0.512908\pi\)
−0.0405394 + 0.999178i \(0.512908\pi\)
\(614\) 1.13763 0.0459111
\(615\) 6.25681 0.252299
\(616\) 14.6826 0.591579
\(617\) −15.4738 −0.622951 −0.311476 0.950254i \(-0.600823\pi\)
−0.311476 + 0.950254i \(0.600823\pi\)
\(618\) 8.26101 0.332306
\(619\) −45.3020 −1.82084 −0.910420 0.413686i \(-0.864241\pi\)
−0.910420 + 0.413686i \(0.864241\pi\)
\(620\) 113.614 4.56284
\(621\) −3.71323 −0.149007
\(622\) −13.3591 −0.535652
\(623\) 49.4150 1.97977
\(624\) 81.7859 3.27406
\(625\) −31.2116 −1.24847
\(626\) −9.82212 −0.392571
\(627\) −0.580097 −0.0231668
\(628\) −36.3673 −1.45121
\(629\) −3.35196 −0.133652
\(630\) −47.2307 −1.88172
\(631\) 34.3793 1.36862 0.684309 0.729192i \(-0.260104\pi\)
0.684309 + 0.729192i \(0.260104\pi\)
\(632\) 100.919 4.01433
\(633\) 15.2441 0.605899
\(634\) 1.70709 0.0677972
\(635\) 12.0765 0.479241
\(636\) 14.2651 0.565649
\(637\) 20.2249 0.801339
\(638\) −12.2724 −0.485869
\(639\) 7.03055 0.278124
\(640\) 127.401 5.03598
\(641\) −37.8024 −1.49311 −0.746553 0.665326i \(-0.768293\pi\)
−0.746553 + 0.665326i \(0.768293\pi\)
\(642\) −52.4557 −2.07026
\(643\) 10.7348 0.423338 0.211669 0.977341i \(-0.432110\pi\)
0.211669 + 0.977341i \(0.432110\pi\)
\(644\) 13.4514 0.530060
\(645\) 10.9398 0.430753
\(646\) −11.4296 −0.449690
\(647\) 42.5228 1.67174 0.835872 0.548925i \(-0.184963\pi\)
0.835872 + 0.548925i \(0.184963\pi\)
\(648\) −3.26965 −0.128444
\(649\) −0.0797319 −0.00312975
\(650\) −31.0697 −1.21865
\(651\) −26.3378 −1.03226
\(652\) −71.9521 −2.81786
\(653\) 5.20122 0.203539 0.101770 0.994808i \(-0.467550\pi\)
0.101770 + 0.994808i \(0.467550\pi\)
\(654\) 2.88255 0.112717
\(655\) −24.7830 −0.968353
\(656\) −35.2404 −1.37591
\(657\) −20.6004 −0.803700
\(658\) −34.4044 −1.34122
\(659\) −23.3092 −0.907998 −0.453999 0.891002i \(-0.650003\pi\)
−0.453999 + 0.891002i \(0.650003\pi\)
\(660\) 7.05693 0.274691
\(661\) 17.1593 0.667421 0.333711 0.942676i \(-0.391699\pi\)
0.333711 + 0.942676i \(0.391699\pi\)
\(662\) −44.0919 −1.71368
\(663\) 17.1970 0.667876
\(664\) 89.6610 3.47952
\(665\) −11.1688 −0.433108
\(666\) −5.23869 −0.202995
\(667\) −7.21069 −0.279199
\(668\) −117.640 −4.55161
\(669\) 22.1074 0.854721
\(670\) −28.6165 −1.10555
\(671\) 4.02012 0.155195
\(672\) −84.5151 −3.26024
\(673\) 21.4583 0.827158 0.413579 0.910468i \(-0.364279\pi\)
0.413579 + 0.910468i \(0.364279\pi\)
\(674\) 24.1424 0.929931
\(675\) −11.8317 −0.455403
\(676\) 61.3351 2.35904
\(677\) −33.1920 −1.27567 −0.637836 0.770172i \(-0.720170\pi\)
−0.637836 + 0.770172i \(0.720170\pi\)
\(678\) 37.4984 1.44012
\(679\) −0.0166385 −0.000638527 0
\(680\) 89.1718 3.41958
\(681\) 13.9298 0.533790
\(682\) −9.27850 −0.355292
\(683\) 32.8804 1.25813 0.629066 0.777352i \(-0.283438\pi\)
0.629066 + 0.777352i \(0.283438\pi\)
\(684\) −13.1474 −0.502703
\(685\) −21.9516 −0.838728
\(686\) 26.3670 1.00670
\(687\) 2.24471 0.0856409
\(688\) −61.6164 −2.34910
\(689\) 11.9671 0.455909
\(690\) 5.63348 0.214463
\(691\) 28.6210 1.08879 0.544396 0.838828i \(-0.316759\pi\)
0.544396 + 0.838828i \(0.316759\pi\)
\(692\) −41.8245 −1.58993
\(693\) 2.83895 0.107843
\(694\) 5.31160 0.201625
\(695\) 50.4534 1.91381
\(696\) 102.792 3.89631
\(697\) −7.40995 −0.280672
\(698\) −72.1862 −2.73229
\(699\) 4.60772 0.174280
\(700\) 42.8612 1.62000
\(701\) 2.29515 0.0866868 0.0433434 0.999060i \(-0.486199\pi\)
0.0433434 + 0.999060i \(0.486199\pi\)
\(702\) 69.2409 2.61333
\(703\) −1.23881 −0.0467227
\(704\) −15.5177 −0.584845
\(705\) −10.6050 −0.399406
\(706\) −6.15370 −0.231598
\(707\) 50.1868 1.88747
\(708\) 1.04130 0.0391346
\(709\) −4.33283 −0.162723 −0.0813614 0.996685i \(-0.525927\pi\)
−0.0813614 + 0.996685i \(0.525927\pi\)
\(710\) −27.4790 −1.03127
\(711\) 19.5131 0.731799
\(712\) −145.809 −5.46444
\(713\) −5.45161 −0.204164
\(714\) −32.2325 −1.20627
\(715\) 5.92010 0.221399
\(716\) −30.8688 −1.15362
\(717\) −27.9698 −1.04455
\(718\) 53.9472 2.01329
\(719\) 29.5785 1.10309 0.551546 0.834145i \(-0.314038\pi\)
0.551546 + 0.834145i \(0.314038\pi\)
\(720\) 81.9989 3.05592
\(721\) −9.56033 −0.356045
\(722\) 48.0731 1.78910
\(723\) −10.2953 −0.382885
\(724\) 13.0342 0.484412
\(725\) −22.9759 −0.853305
\(726\) 31.1317 1.15541
\(727\) 30.4695 1.13005 0.565026 0.825073i \(-0.308866\pi\)
0.565026 + 0.825073i \(0.308866\pi\)
\(728\) −160.865 −5.96205
\(729\) 15.5006 0.574097
\(730\) 80.5172 2.98007
\(731\) −12.9560 −0.479195
\(732\) −52.5030 −1.94057
\(733\) 10.9215 0.403395 0.201698 0.979448i \(-0.435354\pi\)
0.201698 + 0.979448i \(0.435354\pi\)
\(734\) −85.4641 −3.15454
\(735\) −11.6848 −0.431001
\(736\) −17.4936 −0.644824
\(737\) 1.72009 0.0633601
\(738\) −11.5808 −0.426295
\(739\) −20.1716 −0.742023 −0.371011 0.928628i \(-0.620989\pi\)
−0.371011 + 0.928628i \(0.620989\pi\)
\(740\) 15.0703 0.553994
\(741\) 6.35563 0.233480
\(742\) −22.4300 −0.823430
\(743\) 23.3945 0.858262 0.429131 0.903242i \(-0.358820\pi\)
0.429131 + 0.903242i \(0.358820\pi\)
\(744\) 77.7151 2.84917
\(745\) −2.43055 −0.0890483
\(746\) 87.4060 3.20016
\(747\) 17.3364 0.634304
\(748\) −8.35754 −0.305582
\(749\) 60.7062 2.21815
\(750\) −21.0018 −0.766879
\(751\) −5.63299 −0.205551 −0.102775 0.994705i \(-0.532772\pi\)
−0.102775 + 0.994705i \(0.532772\pi\)
\(752\) 59.7306 2.17815
\(753\) −19.2657 −0.702081
\(754\) 134.458 4.89669
\(755\) 54.8121 1.99482
\(756\) −95.5191 −3.47400
\(757\) −10.4411 −0.379487 −0.189743 0.981834i \(-0.560766\pi\)
−0.189743 + 0.981834i \(0.560766\pi\)
\(758\) −52.0047 −1.88890
\(759\) −0.338618 −0.0122910
\(760\) 32.9560 1.19544
\(761\) −5.59752 −0.202910 −0.101455 0.994840i \(-0.532350\pi\)
−0.101455 + 0.994840i \(0.532350\pi\)
\(762\) 12.8805 0.466611
\(763\) −3.33593 −0.120769
\(764\) 29.1098 1.05316
\(765\) 17.2418 0.623378
\(766\) 23.6275 0.853695
\(767\) 0.873556 0.0315423
\(768\) 63.1949 2.28035
\(769\) 50.1109 1.80704 0.903522 0.428542i \(-0.140973\pi\)
0.903522 + 0.428542i \(0.140973\pi\)
\(770\) −11.0961 −0.399875
\(771\) −26.0826 −0.939344
\(772\) −1.41573 −0.0509532
\(773\) −38.8668 −1.39794 −0.698970 0.715151i \(-0.746358\pi\)
−0.698970 + 0.715151i \(0.746358\pi\)
\(774\) −20.2486 −0.727819
\(775\) −17.3708 −0.623979
\(776\) 0.0490954 0.00176242
\(777\) −3.49357 −0.125331
\(778\) −84.9913 −3.04709
\(779\) −2.73855 −0.0981189
\(780\) −77.3169 −2.76839
\(781\) 1.65171 0.0591029
\(782\) −6.67174 −0.238581
\(783\) 51.2034 1.82986
\(784\) 65.8128 2.35046
\(785\) 17.6262 0.629107
\(786\) −26.4330 −0.942834
\(787\) 52.5476 1.87312 0.936559 0.350510i \(-0.113992\pi\)
0.936559 + 0.350510i \(0.113992\pi\)
\(788\) 91.9122 3.27424
\(789\) −25.4013 −0.904311
\(790\) −76.2673 −2.71347
\(791\) −43.3963 −1.54300
\(792\) −8.37691 −0.297661
\(793\) −44.0450 −1.56408
\(794\) 96.6949 3.43157
\(795\) −6.91391 −0.245211
\(796\) 39.9905 1.41743
\(797\) −23.5460 −0.834043 −0.417021 0.908897i \(-0.636926\pi\)
−0.417021 + 0.908897i \(0.636926\pi\)
\(798\) −11.9124 −0.421695
\(799\) 12.5595 0.444322
\(800\) −55.7412 −1.97075
\(801\) −28.1929 −0.996148
\(802\) −14.2804 −0.504260
\(803\) −4.83973 −0.170790
\(804\) −22.4644 −0.792259
\(805\) −6.51954 −0.229783
\(806\) 101.657 3.58070
\(807\) −3.71082 −0.130627
\(808\) −148.087 −5.20967
\(809\) −24.4445 −0.859425 −0.429712 0.902966i \(-0.641385\pi\)
−0.429712 + 0.902966i \(0.641385\pi\)
\(810\) 2.47097 0.0868212
\(811\) 47.6556 1.67341 0.836707 0.547652i \(-0.184478\pi\)
0.836707 + 0.547652i \(0.184478\pi\)
\(812\) −185.488 −6.50934
\(813\) 15.9976 0.561061
\(814\) −1.23074 −0.0431376
\(815\) 34.8732 1.22156
\(816\) 55.9599 1.95899
\(817\) −4.78825 −0.167520
\(818\) 60.6386 2.12018
\(819\) −31.1040 −1.08686
\(820\) 33.3148 1.16340
\(821\) −52.3103 −1.82564 −0.912821 0.408360i \(-0.866101\pi\)
−0.912821 + 0.408360i \(0.866101\pi\)
\(822\) −23.4131 −0.816625
\(823\) −12.4650 −0.434504 −0.217252 0.976116i \(-0.569709\pi\)
−0.217252 + 0.976116i \(0.569709\pi\)
\(824\) 28.2098 0.982734
\(825\) −1.07896 −0.0375646
\(826\) −1.63731 −0.0569694
\(827\) −22.9820 −0.799161 −0.399580 0.916698i \(-0.630844\pi\)
−0.399580 + 0.916698i \(0.630844\pi\)
\(828\) −7.67448 −0.266707
\(829\) 1.90556 0.0661829 0.0330915 0.999452i \(-0.489465\pi\)
0.0330915 + 0.999452i \(0.489465\pi\)
\(830\) −67.7595 −2.35197
\(831\) −23.0119 −0.798275
\(832\) 170.014 5.89418
\(833\) 13.8383 0.479470
\(834\) 53.8125 1.86337
\(835\) 57.0167 1.97315
\(836\) −3.08876 −0.106827
\(837\) 38.7121 1.33809
\(838\) −56.5956 −1.95506
\(839\) −14.4469 −0.498762 −0.249381 0.968405i \(-0.580227\pi\)
−0.249381 + 0.968405i \(0.580227\pi\)
\(840\) 92.9389 3.20670
\(841\) 70.4315 2.42867
\(842\) 37.4288 1.28988
\(843\) −24.9445 −0.859136
\(844\) 81.1682 2.79393
\(845\) −29.7274 −1.02265
\(846\) 19.6288 0.674853
\(847\) −36.0283 −1.23795
\(848\) 38.9415 1.33726
\(849\) 1.36199 0.0467435
\(850\) −21.2586 −0.729165
\(851\) −0.723127 −0.0247885
\(852\) −21.5715 −0.739027
\(853\) 8.07892 0.276617 0.138308 0.990389i \(-0.455833\pi\)
0.138308 + 0.990389i \(0.455833\pi\)
\(854\) 82.5539 2.82494
\(855\) 6.37218 0.217924
\(856\) −179.126 −6.12241
\(857\) 9.09217 0.310583 0.155291 0.987869i \(-0.450368\pi\)
0.155291 + 0.987869i \(0.450368\pi\)
\(858\) 6.31424 0.215565
\(859\) 26.4213 0.901484 0.450742 0.892654i \(-0.351159\pi\)
0.450742 + 0.892654i \(0.351159\pi\)
\(860\) 58.2495 1.98629
\(861\) −7.72298 −0.263198
\(862\) 81.0430 2.76034
\(863\) −10.3828 −0.353434 −0.176717 0.984262i \(-0.556548\pi\)
−0.176717 + 0.984262i \(0.556548\pi\)
\(864\) 124.223 4.22615
\(865\) 20.2712 0.689242
\(866\) 29.4530 1.00085
\(867\) −6.03673 −0.205018
\(868\) −140.237 −4.75996
\(869\) 4.58428 0.155511
\(870\) −77.6827 −2.63369
\(871\) −18.8455 −0.638556
\(872\) 9.84336 0.333338
\(873\) 0.00949282 0.000321283 0
\(874\) −2.46573 −0.0834045
\(875\) 24.3051 0.821662
\(876\) 63.2073 2.13558
\(877\) 0.126829 0.00428271 0.00214136 0.999998i \(-0.499318\pi\)
0.00214136 + 0.999998i \(0.499318\pi\)
\(878\) −16.1448 −0.544862
\(879\) 3.12714 0.105476
\(880\) 19.2643 0.649399
\(881\) −31.3266 −1.05542 −0.527710 0.849425i \(-0.676949\pi\)
−0.527710 + 0.849425i \(0.676949\pi\)
\(882\) 21.6276 0.728238
\(883\) 50.9822 1.71569 0.857843 0.513912i \(-0.171804\pi\)
0.857843 + 0.513912i \(0.171804\pi\)
\(884\) 91.5665 3.07971
\(885\) −0.504692 −0.0169650
\(886\) 105.191 3.53397
\(887\) −0.347598 −0.0116712 −0.00583560 0.999983i \(-0.501858\pi\)
−0.00583560 + 0.999983i \(0.501858\pi\)
\(888\) 10.3085 0.345931
\(889\) −14.9064 −0.499944
\(890\) 110.192 3.69366
\(891\) −0.148526 −0.00497579
\(892\) 117.712 3.94129
\(893\) 4.64170 0.155329
\(894\) −2.59236 −0.0867016
\(895\) 14.9613 0.500100
\(896\) −157.256 −5.25354
\(897\) 3.70995 0.123872
\(898\) 48.3127 1.61222
\(899\) 75.1747 2.50722
\(900\) −24.4537 −0.815124
\(901\) 8.18816 0.272787
\(902\) −2.72072 −0.0905900
\(903\) −13.5033 −0.449362
\(904\) 128.050 4.25888
\(905\) −6.31732 −0.209995
\(906\) 58.4613 1.94225
\(907\) 44.2098 1.46796 0.733982 0.679169i \(-0.237660\pi\)
0.733982 + 0.679169i \(0.237660\pi\)
\(908\) 74.1700 2.46142
\(909\) −28.6332 −0.949704
\(910\) 121.570 4.03002
\(911\) 18.2971 0.606210 0.303105 0.952957i \(-0.401977\pi\)
0.303105 + 0.952957i \(0.401977\pi\)
\(912\) 20.6815 0.684834
\(913\) 4.07289 0.134793
\(914\) 9.41344 0.311369
\(915\) 25.4468 0.841244
\(916\) 11.9521 0.394908
\(917\) 30.5905 1.01019
\(918\) 47.3763 1.56365
\(919\) 22.8623 0.754156 0.377078 0.926181i \(-0.376929\pi\)
0.377078 + 0.926181i \(0.376929\pi\)
\(920\) 19.2373 0.634234
\(921\) −0.432842 −0.0142626
\(922\) −35.1525 −1.15769
\(923\) −18.0964 −0.595651
\(924\) −8.71060 −0.286558
\(925\) −2.30415 −0.0757601
\(926\) −21.9665 −0.721865
\(927\) 5.45448 0.179149
\(928\) 241.228 7.91869
\(929\) 17.8539 0.585767 0.292884 0.956148i \(-0.405385\pi\)
0.292884 + 0.956148i \(0.405385\pi\)
\(930\) −58.7316 −1.92588
\(931\) 5.11435 0.167616
\(932\) 24.5341 0.803641
\(933\) 5.08283 0.166404
\(934\) 85.5403 2.79896
\(935\) 4.05067 0.132471
\(936\) 91.7788 2.99988
\(937\) −1.84611 −0.0603099 −0.0301549 0.999545i \(-0.509600\pi\)
−0.0301549 + 0.999545i \(0.509600\pi\)
\(938\) 35.3223 1.15331
\(939\) 3.73708 0.121955
\(940\) −56.4667 −1.84174
\(941\) 3.09992 0.101055 0.0505273 0.998723i \(-0.483910\pi\)
0.0505273 + 0.998723i \(0.483910\pi\)
\(942\) 18.7997 0.612528
\(943\) −1.59857 −0.0520565
\(944\) 2.84259 0.0925186
\(945\) 46.2955 1.50599
\(946\) −4.75706 −0.154666
\(947\) 2.27193 0.0738278 0.0369139 0.999318i \(-0.488247\pi\)
0.0369139 + 0.999318i \(0.488247\pi\)
\(948\) −59.8711 −1.94452
\(949\) 53.0249 1.72126
\(950\) −7.85673 −0.254906
\(951\) −0.649507 −0.0210617
\(952\) −110.068 −3.56731
\(953\) −42.9917 −1.39264 −0.696319 0.717732i \(-0.745180\pi\)
−0.696319 + 0.717732i \(0.745180\pi\)
\(954\) 12.7970 0.414320
\(955\) −14.1087 −0.456548
\(956\) −148.927 −4.81665
\(957\) 4.66936 0.150939
\(958\) −48.5007 −1.56699
\(959\) 27.0956 0.874962
\(960\) −98.2248 −3.17019
\(961\) 25.8355 0.833403
\(962\) 13.4842 0.434749
\(963\) −34.6349 −1.11609
\(964\) −54.8178 −1.76556
\(965\) 0.686165 0.0220884
\(966\) −6.95359 −0.223728
\(967\) −47.2081 −1.51811 −0.759055 0.651027i \(-0.774339\pi\)
−0.759055 + 0.651027i \(0.774339\pi\)
\(968\) 106.309 3.41690
\(969\) 4.34868 0.139700
\(970\) −0.0371028 −0.00119130
\(971\) −3.38992 −0.108788 −0.0543939 0.998520i \(-0.517323\pi\)
−0.0543939 + 0.998520i \(0.517323\pi\)
\(972\) 87.8400 2.81747
\(973\) −62.2763 −1.99649
\(974\) 105.499 3.38041
\(975\) 11.8213 0.378584
\(976\) −143.325 −4.58771
\(977\) 51.0116 1.63200 0.816002 0.578049i \(-0.196186\pi\)
0.816002 + 0.578049i \(0.196186\pi\)
\(978\) 37.1950 1.18936
\(979\) −6.62346 −0.211687
\(980\) −62.2166 −1.98743
\(981\) 1.90326 0.0607664
\(982\) −13.5853 −0.433525
\(983\) −41.2820 −1.31669 −0.658346 0.752716i \(-0.728744\pi\)
−0.658346 + 0.752716i \(0.728744\pi\)
\(984\) 22.7883 0.726464
\(985\) −44.5474 −1.41940
\(986\) 91.9997 2.92987
\(987\) 13.0900 0.416660
\(988\) 33.8410 1.07662
\(989\) −2.79503 −0.0888767
\(990\) 6.33068 0.201202
\(991\) 15.7928 0.501676 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(992\) 182.379 5.79054
\(993\) 16.7759 0.532367
\(994\) 33.9183 1.07582
\(995\) −19.3823 −0.614461
\(996\) −53.1923 −1.68546
\(997\) −2.21630 −0.0701908 −0.0350954 0.999384i \(-0.511174\pi\)
−0.0350954 + 0.999384i \(0.511174\pi\)
\(998\) −101.360 −3.20849
\(999\) 5.13496 0.162463
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 \(a_p\))