Properties

Label 4019.2.a.b.1.2
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79148 q^{2}\) \(-3.39321 q^{3}\) \(+5.79236 q^{4}\) \(+3.31167 q^{5}\) \(+9.47208 q^{6}\) \(-0.0588258 q^{7}\) \(-10.5863 q^{8}\) \(+8.51387 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79148 q^{2}\) \(-3.39321 q^{3}\) \(+5.79236 q^{4}\) \(+3.31167 q^{5}\) \(+9.47208 q^{6}\) \(-0.0588258 q^{7}\) \(-10.5863 q^{8}\) \(+8.51387 q^{9}\) \(-9.24445 q^{10}\) \(+3.18832 q^{11}\) \(-19.6547 q^{12}\) \(+1.79597 q^{13}\) \(+0.164211 q^{14}\) \(-11.2372 q^{15}\) \(+17.9667 q^{16}\) \(+6.19854 q^{17}\) \(-23.7663 q^{18}\) \(+4.49804 q^{19}\) \(+19.1824 q^{20}\) \(+0.199608 q^{21}\) \(-8.90012 q^{22}\) \(-5.64628 q^{23}\) \(+35.9215 q^{24}\) \(+5.96714 q^{25}\) \(-5.01342 q^{26}\) \(-18.7097 q^{27}\) \(-0.340740 q^{28}\) \(+0.468620 q^{29}\) \(+31.3684 q^{30}\) \(+3.70270 q^{31}\) \(-28.9811 q^{32}\) \(-10.8186 q^{33}\) \(-17.3031 q^{34}\) \(-0.194812 q^{35}\) \(+49.3154 q^{36}\) \(-2.54153 q^{37}\) \(-12.5562 q^{38}\) \(-6.09411 q^{39}\) \(-35.0583 q^{40}\) \(-1.69797 q^{41}\) \(-0.557203 q^{42}\) \(+10.8120 q^{43}\) \(+18.4679 q^{44}\) \(+28.1951 q^{45}\) \(+15.7615 q^{46}\) \(+8.29508 q^{47}\) \(-60.9648 q^{48}\) \(-6.99654 q^{49}\) \(-16.6571 q^{50}\) \(-21.0329 q^{51}\) \(+10.4029 q^{52}\) \(+13.4286 q^{53}\) \(+52.2278 q^{54}\) \(+10.5586 q^{55}\) \(+0.622747 q^{56}\) \(-15.2628 q^{57}\) \(-1.30814 q^{58}\) \(+7.23695 q^{59}\) \(-65.0898 q^{60}\) \(+8.88227 q^{61}\) \(-10.3360 q^{62}\) \(-0.500835 q^{63}\) \(+44.9667 q^{64}\) \(+5.94766 q^{65}\) \(+30.2000 q^{66}\) \(-4.59088 q^{67}\) \(+35.9042 q^{68}\) \(+19.1590 q^{69}\) \(+0.543813 q^{70}\) \(+1.08524 q^{71}\) \(-90.1303 q^{72}\) \(+10.0813 q^{73}\) \(+7.09463 q^{74}\) \(-20.2478 q^{75}\) \(+26.0542 q^{76}\) \(-0.187555 q^{77}\) \(+17.0116 q^{78}\) \(-0.0659532 q^{79}\) \(+59.4997 q^{80}\) \(+37.9444 q^{81}\) \(+4.73984 q^{82}\) \(-15.5012 q^{83}\) \(+1.15620 q^{84}\) \(+20.5275 q^{85}\) \(-30.1815 q^{86}\) \(-1.59013 q^{87}\) \(-33.7525 q^{88}\) \(-0.766469 q^{89}\) \(-78.7061 q^{90}\) \(-0.105649 q^{91}\) \(-32.7053 q^{92}\) \(-12.5640 q^{93}\) \(-23.1555 q^{94}\) \(+14.8960 q^{95}\) \(+98.3389 q^{96}\) \(+8.17877 q^{97}\) \(+19.5307 q^{98}\) \(+27.1449 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79148 −1.97387 −0.986937 0.161106i \(-0.948494\pi\)
−0.986937 + 0.161106i \(0.948494\pi\)
\(3\) −3.39321 −1.95907 −0.979535 0.201273i \(-0.935492\pi\)
−0.979535 + 0.201273i \(0.935492\pi\)
\(4\) 5.79236 2.89618
\(5\) 3.31167 1.48102 0.740511 0.672044i \(-0.234583\pi\)
0.740511 + 0.672044i \(0.234583\pi\)
\(6\) 9.47208 3.86696
\(7\) −0.0588258 −0.0222341 −0.0111170 0.999938i \(-0.503539\pi\)
−0.0111170 + 0.999938i \(0.503539\pi\)
\(8\) −10.5863 −3.74282
\(9\) 8.51387 2.83796
\(10\) −9.24445 −2.92335
\(11\) 3.18832 0.961314 0.480657 0.876909i \(-0.340398\pi\)
0.480657 + 0.876909i \(0.340398\pi\)
\(12\) −19.6547 −5.67382
\(13\) 1.79597 0.498113 0.249056 0.968489i \(-0.419880\pi\)
0.249056 + 0.968489i \(0.419880\pi\)
\(14\) 0.164211 0.0438873
\(15\) −11.2372 −2.90143
\(16\) 17.9667 4.49167
\(17\) 6.19854 1.50337 0.751683 0.659524i \(-0.229242\pi\)
0.751683 + 0.659524i \(0.229242\pi\)
\(18\) −23.7663 −5.60177
\(19\) 4.49804 1.03192 0.515960 0.856612i \(-0.327435\pi\)
0.515960 + 0.856612i \(0.327435\pi\)
\(20\) 19.1824 4.28931
\(21\) 0.199608 0.0435581
\(22\) −8.90012 −1.89751
\(23\) −5.64628 −1.17733 −0.588666 0.808377i \(-0.700347\pi\)
−0.588666 + 0.808377i \(0.700347\pi\)
\(24\) 35.9215 7.33245
\(25\) 5.96714 1.19343
\(26\) −5.01342 −0.983212
\(27\) −18.7097 −3.60069
\(28\) −0.340740 −0.0643939
\(29\) 0.468620 0.0870206 0.0435103 0.999053i \(-0.486146\pi\)
0.0435103 + 0.999053i \(0.486146\pi\)
\(30\) 31.3684 5.72705
\(31\) 3.70270 0.665025 0.332513 0.943099i \(-0.392104\pi\)
0.332513 + 0.943099i \(0.392104\pi\)
\(32\) −28.9811 −5.12318
\(33\) −10.8186 −1.88328
\(34\) −17.3031 −2.96746
\(35\) −0.194812 −0.0329292
\(36\) 49.3154 8.21923
\(37\) −2.54153 −0.417825 −0.208912 0.977934i \(-0.566992\pi\)
−0.208912 + 0.977934i \(0.566992\pi\)
\(38\) −12.5562 −2.03688
\(39\) −6.09411 −0.975838
\(40\) −35.0583 −5.54320
\(41\) −1.69797 −0.265178 −0.132589 0.991171i \(-0.542329\pi\)
−0.132589 + 0.991171i \(0.542329\pi\)
\(42\) −0.557203 −0.0859782
\(43\) 10.8120 1.64882 0.824409 0.565995i \(-0.191508\pi\)
0.824409 + 0.565995i \(0.191508\pi\)
\(44\) 18.4679 2.78414
\(45\) 28.1951 4.20308
\(46\) 15.7615 2.32390
\(47\) 8.29508 1.20996 0.604981 0.796240i \(-0.293181\pi\)
0.604981 + 0.796240i \(0.293181\pi\)
\(48\) −60.9648 −8.79951
\(49\) −6.99654 −0.999506
\(50\) −16.6571 −2.35568
\(51\) −21.0329 −2.94520
\(52\) 10.4029 1.44262
\(53\) 13.4286 1.84456 0.922278 0.386527i \(-0.126325\pi\)
0.922278 + 0.386527i \(0.126325\pi\)
\(54\) 52.2278 7.10730
\(55\) 10.5586 1.42373
\(56\) 0.622747 0.0832181
\(57\) −15.2628 −2.02161
\(58\) −1.30814 −0.171768
\(59\) 7.23695 0.942171 0.471085 0.882088i \(-0.343862\pi\)
0.471085 + 0.882088i \(0.343862\pi\)
\(60\) −65.0898 −8.40305
\(61\) 8.88227 1.13726 0.568629 0.822594i \(-0.307474\pi\)
0.568629 + 0.822594i \(0.307474\pi\)
\(62\) −10.3360 −1.31268
\(63\) −0.500835 −0.0630993
\(64\) 44.9667 5.62084
\(65\) 5.94766 0.737716
\(66\) 30.2000 3.71736
\(67\) −4.59088 −0.560866 −0.280433 0.959874i \(-0.590478\pi\)
−0.280433 + 0.959874i \(0.590478\pi\)
\(68\) 35.9042 4.35402
\(69\) 19.1590 2.30648
\(70\) 0.543813 0.0649980
\(71\) 1.08524 0.128794 0.0643970 0.997924i \(-0.479488\pi\)
0.0643970 + 0.997924i \(0.479488\pi\)
\(72\) −90.1303 −10.6220
\(73\) 10.0813 1.17992 0.589961 0.807432i \(-0.299143\pi\)
0.589961 + 0.807432i \(0.299143\pi\)
\(74\) 7.09463 0.824734
\(75\) −20.2478 −2.33801
\(76\) 26.0542 2.98863
\(77\) −0.187555 −0.0213739
\(78\) 17.0116 1.92618
\(79\) −0.0659532 −0.00742032 −0.00371016 0.999993i \(-0.501181\pi\)
−0.00371016 + 0.999993i \(0.501181\pi\)
\(80\) 59.4997 6.65227
\(81\) 37.9444 4.21604
\(82\) 4.73984 0.523427
\(83\) −15.5012 −1.70147 −0.850737 0.525592i \(-0.823844\pi\)
−0.850737 + 0.525592i \(0.823844\pi\)
\(84\) 1.15620 0.126152
\(85\) 20.5275 2.22652
\(86\) −30.1815 −3.25456
\(87\) −1.59013 −0.170479
\(88\) −33.7525 −3.59802
\(89\) −0.766469 −0.0812456 −0.0406228 0.999175i \(-0.512934\pi\)
−0.0406228 + 0.999175i \(0.512934\pi\)
\(90\) −78.7061 −8.29635
\(91\) −0.105649 −0.0110751
\(92\) −32.7053 −3.40976
\(93\) −12.5640 −1.30283
\(94\) −23.1555 −2.38831
\(95\) 14.8960 1.52830
\(96\) 98.3389 10.0367
\(97\) 8.17877 0.830429 0.415214 0.909724i \(-0.363707\pi\)
0.415214 + 0.909724i \(0.363707\pi\)
\(98\) 19.5307 1.97290
\(99\) 27.1449 2.72817
\(100\) 34.5638 3.45638
\(101\) −4.24956 −0.422847 −0.211424 0.977395i \(-0.567810\pi\)
−0.211424 + 0.977395i \(0.567810\pi\)
\(102\) 58.7130 5.81346
\(103\) 8.42500 0.830140 0.415070 0.909790i \(-0.363757\pi\)
0.415070 + 0.909790i \(0.363757\pi\)
\(104\) −19.0127 −1.86435
\(105\) 0.661036 0.0645106
\(106\) −37.4856 −3.64092
\(107\) 1.31194 0.126830 0.0634149 0.997987i \(-0.479801\pi\)
0.0634149 + 0.997987i \(0.479801\pi\)
\(108\) −108.373 −10.4282
\(109\) 10.7619 1.03081 0.515403 0.856948i \(-0.327642\pi\)
0.515403 + 0.856948i \(0.327642\pi\)
\(110\) −29.4742 −2.81026
\(111\) 8.62394 0.818548
\(112\) −1.05691 −0.0998682
\(113\) 1.49573 0.140707 0.0703534 0.997522i \(-0.477587\pi\)
0.0703534 + 0.997522i \(0.477587\pi\)
\(114\) 42.6058 3.99039
\(115\) −18.6986 −1.74365
\(116\) 2.71442 0.252027
\(117\) 15.2907 1.41362
\(118\) −20.2018 −1.85973
\(119\) −0.364634 −0.0334260
\(120\) 118.960 10.8595
\(121\) −0.834631 −0.0758755
\(122\) −24.7947 −2.24481
\(123\) 5.76155 0.519502
\(124\) 21.4474 1.92603
\(125\) 3.20285 0.286471
\(126\) 1.39807 0.124550
\(127\) 15.7846 1.40066 0.700328 0.713821i \(-0.253037\pi\)
0.700328 + 0.713821i \(0.253037\pi\)
\(128\) −67.5615 −5.97165
\(129\) −36.6874 −3.23015
\(130\) −16.6028 −1.45616
\(131\) −16.8400 −1.47131 −0.735657 0.677354i \(-0.763127\pi\)
−0.735657 + 0.677354i \(0.763127\pi\)
\(132\) −62.6654 −5.45432
\(133\) −0.264601 −0.0229438
\(134\) 12.8154 1.10708
\(135\) −61.9604 −5.33270
\(136\) −65.6195 −5.62683
\(137\) 21.1332 1.80553 0.902766 0.430133i \(-0.141533\pi\)
0.902766 + 0.430133i \(0.141533\pi\)
\(138\) −53.4820 −4.55269
\(139\) −6.77180 −0.574376 −0.287188 0.957874i \(-0.592720\pi\)
−0.287188 + 0.957874i \(0.592720\pi\)
\(140\) −1.12842 −0.0953688
\(141\) −28.1469 −2.37040
\(142\) −3.02942 −0.254223
\(143\) 5.72613 0.478843
\(144\) 152.966 12.7472
\(145\) 1.55191 0.128879
\(146\) −28.1416 −2.32902
\(147\) 23.7407 1.95810
\(148\) −14.7215 −1.21010
\(149\) −0.650443 −0.0532864 −0.0266432 0.999645i \(-0.508482\pi\)
−0.0266432 + 0.999645i \(0.508482\pi\)
\(150\) 56.5212 4.61494
\(151\) −21.1962 −1.72492 −0.862461 0.506123i \(-0.831078\pi\)
−0.862461 + 0.506123i \(0.831078\pi\)
\(152\) −47.6175 −3.86229
\(153\) 52.7736 4.26649
\(154\) 0.523557 0.0421894
\(155\) 12.2621 0.984917
\(156\) −35.2992 −2.82620
\(157\) −0.868505 −0.0693143 −0.0346571 0.999399i \(-0.511034\pi\)
−0.0346571 + 0.999399i \(0.511034\pi\)
\(158\) 0.184107 0.0146468
\(159\) −45.5660 −3.61362
\(160\) −95.9757 −7.58755
\(161\) 0.332147 0.0261769
\(162\) −105.921 −8.32194
\(163\) −7.32957 −0.574096 −0.287048 0.957916i \(-0.592674\pi\)
−0.287048 + 0.957916i \(0.592674\pi\)
\(164\) −9.83522 −0.768002
\(165\) −35.8277 −2.78918
\(166\) 43.2712 3.35849
\(167\) −21.3136 −1.64930 −0.824648 0.565646i \(-0.808627\pi\)
−0.824648 + 0.565646i \(0.808627\pi\)
\(168\) −2.11311 −0.163030
\(169\) −9.77449 −0.751884
\(170\) −57.3021 −4.39487
\(171\) 38.2957 2.92855
\(172\) 62.6271 4.77527
\(173\) −7.25464 −0.551560 −0.275780 0.961221i \(-0.588936\pi\)
−0.275780 + 0.961221i \(0.588936\pi\)
\(174\) 4.43881 0.336505
\(175\) −0.351022 −0.0265348
\(176\) 57.2835 4.31791
\(177\) −24.5565 −1.84578
\(178\) 2.13958 0.160369
\(179\) −10.6435 −0.795532 −0.397766 0.917487i \(-0.630214\pi\)
−0.397766 + 0.917487i \(0.630214\pi\)
\(180\) 163.316 12.1729
\(181\) −2.48701 −0.184858 −0.0924289 0.995719i \(-0.529463\pi\)
−0.0924289 + 0.995719i \(0.529463\pi\)
\(182\) 0.294918 0.0218608
\(183\) −30.1394 −2.22797
\(184\) 59.7732 4.40654
\(185\) −8.41670 −0.618808
\(186\) 35.0723 2.57162
\(187\) 19.7629 1.44521
\(188\) 48.0481 3.50427
\(189\) 1.10061 0.0800579
\(190\) −41.5819 −3.01667
\(191\) 4.39238 0.317821 0.158911 0.987293i \(-0.449202\pi\)
0.158911 + 0.987293i \(0.449202\pi\)
\(192\) −152.582 −11.0116
\(193\) 6.83078 0.491690 0.245845 0.969309i \(-0.420935\pi\)
0.245845 + 0.969309i \(0.420935\pi\)
\(194\) −22.8309 −1.63916
\(195\) −20.1816 −1.44524
\(196\) −40.5265 −2.89475
\(197\) −14.8072 −1.05497 −0.527485 0.849564i \(-0.676865\pi\)
−0.527485 + 0.849564i \(0.676865\pi\)
\(198\) −75.7745 −5.38506
\(199\) −15.9671 −1.13188 −0.565940 0.824446i \(-0.691487\pi\)
−0.565940 + 0.824446i \(0.691487\pi\)
\(200\) −63.1699 −4.46679
\(201\) 15.5778 1.09878
\(202\) 11.8626 0.834647
\(203\) −0.0275670 −0.00193482
\(204\) −121.830 −8.52983
\(205\) −5.62310 −0.392734
\(206\) −23.5182 −1.63859
\(207\) −48.0717 −3.34122
\(208\) 32.2677 2.23736
\(209\) 14.3412 0.992000
\(210\) −1.84527 −0.127336
\(211\) 9.12887 0.628458 0.314229 0.949347i \(-0.398254\pi\)
0.314229 + 0.949347i \(0.398254\pi\)
\(212\) 77.7831 5.34217
\(213\) −3.68244 −0.252317
\(214\) −3.66224 −0.250346
\(215\) 35.8058 2.44194
\(216\) 198.067 13.4767
\(217\) −0.217815 −0.0147862
\(218\) −30.0417 −2.03468
\(219\) −34.2078 −2.31155
\(220\) 61.1595 4.12337
\(221\) 11.1324 0.748846
\(222\) −24.0736 −1.61571
\(223\) 22.8130 1.52767 0.763835 0.645412i \(-0.223314\pi\)
0.763835 + 0.645412i \(0.223314\pi\)
\(224\) 1.70484 0.113909
\(225\) 50.8035 3.38690
\(226\) −4.17531 −0.277737
\(227\) −4.62736 −0.307128 −0.153564 0.988139i \(-0.549075\pi\)
−0.153564 + 0.988139i \(0.549075\pi\)
\(228\) −88.4075 −5.85493
\(229\) −12.8559 −0.849539 −0.424770 0.905302i \(-0.639645\pi\)
−0.424770 + 0.905302i \(0.639645\pi\)
\(230\) 52.1968 3.44175
\(231\) 0.636415 0.0418730
\(232\) −4.96095 −0.325702
\(233\) −3.17577 −0.208052 −0.104026 0.994575i \(-0.533172\pi\)
−0.104026 + 0.994575i \(0.533172\pi\)
\(234\) −42.6836 −2.79031
\(235\) 27.4705 1.79198
\(236\) 41.9190 2.72870
\(237\) 0.223793 0.0145369
\(238\) 1.01787 0.0659786
\(239\) −4.54620 −0.294069 −0.147035 0.989131i \(-0.546973\pi\)
−0.147035 + 0.989131i \(0.546973\pi\)
\(240\) −201.895 −13.0323
\(241\) 28.8968 1.86141 0.930704 0.365773i \(-0.119195\pi\)
0.930704 + 0.365773i \(0.119195\pi\)
\(242\) 2.32986 0.149769
\(243\) −72.6241 −4.65884
\(244\) 51.4493 3.29370
\(245\) −23.1702 −1.48029
\(246\) −16.0833 −1.02543
\(247\) 8.07835 0.514013
\(248\) −39.1979 −2.48907
\(249\) 52.5987 3.33331
\(250\) −8.94068 −0.565458
\(251\) −14.3530 −0.905951 −0.452976 0.891523i \(-0.649638\pi\)
−0.452976 + 0.891523i \(0.649638\pi\)
\(252\) −2.90102 −0.182747
\(253\) −18.0021 −1.13179
\(254\) −44.0623 −2.76472
\(255\) −69.6541 −4.36191
\(256\) 98.6631 6.16645
\(257\) −28.4347 −1.77371 −0.886853 0.462051i \(-0.847114\pi\)
−0.886853 + 0.462051i \(0.847114\pi\)
\(258\) 102.412 6.37591
\(259\) 0.149508 0.00928995
\(260\) 34.4510 2.13656
\(261\) 3.98977 0.246961
\(262\) 47.0084 2.90419
\(263\) −4.38600 −0.270452 −0.135226 0.990815i \(-0.543176\pi\)
−0.135226 + 0.990815i \(0.543176\pi\)
\(264\) 114.529 7.04878
\(265\) 44.4710 2.73183
\(266\) 0.738628 0.0452882
\(267\) 2.60079 0.159166
\(268\) −26.5920 −1.62437
\(269\) −4.91349 −0.299581 −0.149790 0.988718i \(-0.547860\pi\)
−0.149790 + 0.988718i \(0.547860\pi\)
\(270\) 172.961 10.5261
\(271\) −0.210175 −0.0127672 −0.00638361 0.999980i \(-0.502032\pi\)
−0.00638361 + 0.999980i \(0.502032\pi\)
\(272\) 111.367 6.75263
\(273\) 0.358491 0.0216969
\(274\) −58.9929 −3.56389
\(275\) 19.0251 1.14726
\(276\) 110.976 6.67997
\(277\) −8.28268 −0.497658 −0.248829 0.968547i \(-0.580046\pi\)
−0.248829 + 0.968547i \(0.580046\pi\)
\(278\) 18.9033 1.13375
\(279\) 31.5243 1.88731
\(280\) 2.06233 0.123248
\(281\) −1.29009 −0.0769601 −0.0384801 0.999259i \(-0.512252\pi\)
−0.0384801 + 0.999259i \(0.512252\pi\)
\(282\) 78.5716 4.67887
\(283\) 21.5190 1.27917 0.639585 0.768720i \(-0.279106\pi\)
0.639585 + 0.768720i \(0.279106\pi\)
\(284\) 6.28609 0.373011
\(285\) −50.5453 −2.99404
\(286\) −15.9844 −0.945175
\(287\) 0.0998842 0.00589598
\(288\) −246.741 −14.5394
\(289\) 21.4219 1.26011
\(290\) −4.33214 −0.254392
\(291\) −27.7523 −1.62687
\(292\) 58.3943 3.41727
\(293\) −6.55371 −0.382872 −0.191436 0.981505i \(-0.561314\pi\)
−0.191436 + 0.981505i \(0.561314\pi\)
\(294\) −66.2717 −3.86505
\(295\) 23.9664 1.39538
\(296\) 26.9054 1.56384
\(297\) −59.6525 −3.46139
\(298\) 1.81570 0.105181
\(299\) −10.1406 −0.586444
\(300\) −117.282 −6.77129
\(301\) −0.636026 −0.0366599
\(302\) 59.1688 3.40478
\(303\) 14.4197 0.828388
\(304\) 80.8149 4.63505
\(305\) 29.4151 1.68431
\(306\) −147.316 −8.42151
\(307\) −5.27872 −0.301272 −0.150636 0.988589i \(-0.548132\pi\)
−0.150636 + 0.988589i \(0.548132\pi\)
\(308\) −1.08639 −0.0619027
\(309\) −28.5878 −1.62630
\(310\) −34.2295 −1.94410
\(311\) −2.75283 −0.156098 −0.0780492 0.996950i \(-0.524869\pi\)
−0.0780492 + 0.996950i \(0.524869\pi\)
\(312\) 64.5140 3.65238
\(313\) −13.8893 −0.785069 −0.392535 0.919737i \(-0.628402\pi\)
−0.392535 + 0.919737i \(0.628402\pi\)
\(314\) 2.42441 0.136818
\(315\) −1.65860 −0.0934516
\(316\) −0.382025 −0.0214906
\(317\) 4.71155 0.264627 0.132314 0.991208i \(-0.457759\pi\)
0.132314 + 0.991208i \(0.457759\pi\)
\(318\) 127.196 7.13282
\(319\) 1.49411 0.0836541
\(320\) 148.915 8.32459
\(321\) −4.45168 −0.248468
\(322\) −0.927182 −0.0516699
\(323\) 27.8813 1.55136
\(324\) 219.787 12.2104
\(325\) 10.7168 0.594462
\(326\) 20.4604 1.13319
\(327\) −36.5175 −2.01942
\(328\) 17.9752 0.992512
\(329\) −0.487965 −0.0269024
\(330\) 100.012 5.50550
\(331\) −4.98756 −0.274141 −0.137070 0.990561i \(-0.543769\pi\)
−0.137070 + 0.990561i \(0.543769\pi\)
\(332\) −89.7883 −4.92777
\(333\) −21.6383 −1.18577
\(334\) 59.4965 3.25550
\(335\) −15.2035 −0.830655
\(336\) 3.58630 0.195649
\(337\) 22.6082 1.23155 0.615773 0.787923i \(-0.288844\pi\)
0.615773 + 0.787923i \(0.288844\pi\)
\(338\) 27.2853 1.48412
\(339\) −5.07534 −0.275654
\(340\) 118.903 6.44840
\(341\) 11.8054 0.639298
\(342\) −106.902 −5.78058
\(343\) 0.823358 0.0444572
\(344\) −114.459 −6.17123
\(345\) 63.4483 3.41594
\(346\) 20.2512 1.08871
\(347\) 10.6305 0.570673 0.285336 0.958427i \(-0.407895\pi\)
0.285336 + 0.958427i \(0.407895\pi\)
\(348\) −9.21058 −0.493739
\(349\) 9.17194 0.490963 0.245481 0.969401i \(-0.421054\pi\)
0.245481 + 0.969401i \(0.421054\pi\)
\(350\) 0.979871 0.0523763
\(351\) −33.6021 −1.79355
\(352\) −92.4009 −4.92499
\(353\) −21.7008 −1.15502 −0.577508 0.816385i \(-0.695975\pi\)
−0.577508 + 0.816385i \(0.695975\pi\)
\(354\) 68.5489 3.64333
\(355\) 3.59395 0.190747
\(356\) −4.43966 −0.235302
\(357\) 1.23728 0.0654838
\(358\) 29.7111 1.57028
\(359\) −11.0528 −0.583344 −0.291672 0.956518i \(-0.594212\pi\)
−0.291672 + 0.956518i \(0.594212\pi\)
\(360\) −298.482 −15.7314
\(361\) 1.23235 0.0648603
\(362\) 6.94243 0.364886
\(363\) 2.83208 0.148646
\(364\) −0.611960 −0.0320754
\(365\) 33.3858 1.74749
\(366\) 84.1336 4.39773
\(367\) −11.2090 −0.585107 −0.292553 0.956249i \(-0.594505\pi\)
−0.292553 + 0.956249i \(0.594505\pi\)
\(368\) −101.445 −5.28819
\(369\) −14.4563 −0.752563
\(370\) 23.4950 1.22145
\(371\) −0.789947 −0.0410120
\(372\) −72.7755 −3.77323
\(373\) −28.7319 −1.48768 −0.743842 0.668356i \(-0.766998\pi\)
−0.743842 + 0.668356i \(0.766998\pi\)
\(374\) −55.1678 −2.85266
\(375\) −10.8679 −0.561217
\(376\) −87.8141 −4.52867
\(377\) 0.841628 0.0433461
\(378\) −3.07234 −0.158024
\(379\) −20.0953 −1.03223 −0.516113 0.856521i \(-0.672621\pi\)
−0.516113 + 0.856521i \(0.672621\pi\)
\(380\) 86.2830 4.42622
\(381\) −53.5604 −2.74398
\(382\) −12.2612 −0.627339
\(383\) −15.4554 −0.789736 −0.394868 0.918738i \(-0.629210\pi\)
−0.394868 + 0.918738i \(0.629210\pi\)
\(384\) 229.250 11.6989
\(385\) −0.621121 −0.0316553
\(386\) −19.0680 −0.970535
\(387\) 92.0521 4.67927
\(388\) 47.3744 2.40507
\(389\) −5.73335 −0.290692 −0.145346 0.989381i \(-0.546430\pi\)
−0.145346 + 0.989381i \(0.546430\pi\)
\(390\) 56.3367 2.85272
\(391\) −34.9987 −1.76996
\(392\) 74.0674 3.74097
\(393\) 57.1415 2.88241
\(394\) 41.3340 2.08238
\(395\) −0.218415 −0.0109897
\(396\) 157.233 7.90126
\(397\) 32.7094 1.64164 0.820819 0.571188i \(-0.193517\pi\)
0.820819 + 0.571188i \(0.193517\pi\)
\(398\) 44.5719 2.23419
\(399\) 0.897846 0.0449485
\(400\) 107.210 5.36049
\(401\) 7.10338 0.354726 0.177363 0.984146i \(-0.443243\pi\)
0.177363 + 0.984146i \(0.443243\pi\)
\(402\) −43.4852 −2.16884
\(403\) 6.64995 0.331257
\(404\) −24.6150 −1.22464
\(405\) 125.659 6.24405
\(406\) 0.0769527 0.00381910
\(407\) −8.10320 −0.401661
\(408\) 222.661 11.0234
\(409\) −8.73243 −0.431791 −0.215895 0.976417i \(-0.569267\pi\)
−0.215895 + 0.976417i \(0.569267\pi\)
\(410\) 15.6968 0.775208
\(411\) −71.7094 −3.53716
\(412\) 48.8006 2.40423
\(413\) −0.425720 −0.0209483
\(414\) 134.191 6.59514
\(415\) −51.3347 −2.51992
\(416\) −52.0492 −2.55192
\(417\) 22.9781 1.12524
\(418\) −40.0331 −1.95808
\(419\) −9.58578 −0.468296 −0.234148 0.972201i \(-0.575230\pi\)
−0.234148 + 0.972201i \(0.575230\pi\)
\(420\) 3.82896 0.186834
\(421\) 8.97404 0.437368 0.218684 0.975796i \(-0.429824\pi\)
0.218684 + 0.975796i \(0.429824\pi\)
\(422\) −25.4831 −1.24050
\(423\) 70.6232 3.43382
\(424\) −142.159 −6.90384
\(425\) 36.9876 1.79416
\(426\) 10.2795 0.498041
\(427\) −0.522507 −0.0252859
\(428\) 7.59921 0.367322
\(429\) −19.4299 −0.938087
\(430\) −99.9512 −4.82007
\(431\) −8.77461 −0.422658 −0.211329 0.977415i \(-0.567779\pi\)
−0.211329 + 0.977415i \(0.567779\pi\)
\(432\) −336.152 −16.1731
\(433\) −20.3910 −0.979929 −0.489965 0.871742i \(-0.662990\pi\)
−0.489965 + 0.871742i \(0.662990\pi\)
\(434\) 0.608025 0.0291861
\(435\) −5.26597 −0.252484
\(436\) 62.3369 2.98540
\(437\) −25.3972 −1.21491
\(438\) 95.4905 4.56271
\(439\) 19.9997 0.954534 0.477267 0.878758i \(-0.341628\pi\)
0.477267 + 0.878758i \(0.341628\pi\)
\(440\) −111.777 −5.32876
\(441\) −59.5676 −2.83655
\(442\) −31.0759 −1.47813
\(443\) −10.1109 −0.480384 −0.240192 0.970725i \(-0.577210\pi\)
−0.240192 + 0.970725i \(0.577210\pi\)
\(444\) 49.9530 2.37066
\(445\) −2.53829 −0.120327
\(446\) −63.6820 −3.01543
\(447\) 2.20709 0.104392
\(448\) −2.64520 −0.124974
\(449\) 3.76482 0.177673 0.0888365 0.996046i \(-0.471685\pi\)
0.0888365 + 0.996046i \(0.471685\pi\)
\(450\) −141.817 −6.68531
\(451\) −5.41365 −0.254919
\(452\) 8.66382 0.407512
\(453\) 71.9232 3.37925
\(454\) 12.9172 0.606233
\(455\) −0.349876 −0.0164024
\(456\) 161.576 7.56650
\(457\) 20.1456 0.942372 0.471186 0.882034i \(-0.343826\pi\)
0.471186 + 0.882034i \(0.343826\pi\)
\(458\) 35.8869 1.67688
\(459\) −115.973 −5.41315
\(460\) −108.309 −5.04994
\(461\) 36.8199 1.71487 0.857436 0.514590i \(-0.172056\pi\)
0.857436 + 0.514590i \(0.172056\pi\)
\(462\) −1.77654 −0.0826521
\(463\) 3.30313 0.153510 0.0767548 0.997050i \(-0.475544\pi\)
0.0767548 + 0.997050i \(0.475544\pi\)
\(464\) 8.41956 0.390868
\(465\) −41.6079 −1.92952
\(466\) 8.86510 0.410668
\(467\) −29.7903 −1.37853 −0.689265 0.724510i \(-0.742066\pi\)
−0.689265 + 0.724510i \(0.742066\pi\)
\(468\) 88.5690 4.09410
\(469\) 0.270063 0.0124703
\(470\) −76.6835 −3.53714
\(471\) 2.94702 0.135792
\(472\) −76.6125 −3.52637
\(473\) 34.4721 1.58503
\(474\) −0.624714 −0.0286941
\(475\) 26.8404 1.23152
\(476\) −2.11209 −0.0968076
\(477\) 114.329 5.23477
\(478\) 12.6906 0.580456
\(479\) −25.8255 −1.18000 −0.589998 0.807405i \(-0.700872\pi\)
−0.589998 + 0.807405i \(0.700872\pi\)
\(480\) 325.666 14.8645
\(481\) −4.56451 −0.208124
\(482\) −80.6649 −3.67419
\(483\) −1.12705 −0.0512823
\(484\) −4.83448 −0.219749
\(485\) 27.0854 1.22988
\(486\) 202.729 9.19596
\(487\) −23.4214 −1.06132 −0.530662 0.847584i \(-0.678057\pi\)
−0.530662 + 0.847584i \(0.678057\pi\)
\(488\) −94.0303 −4.25655
\(489\) 24.8708 1.12470
\(490\) 64.6792 2.92191
\(491\) 24.0741 1.08645 0.543226 0.839587i \(-0.317203\pi\)
0.543226 + 0.839587i \(0.317203\pi\)
\(492\) 33.3730 1.50457
\(493\) 2.90476 0.130824
\(494\) −22.5505 −1.01460
\(495\) 89.8950 4.04048
\(496\) 66.5254 2.98708
\(497\) −0.0638400 −0.00286362
\(498\) −146.828 −6.57953
\(499\) −5.19841 −0.232713 −0.116357 0.993208i \(-0.537122\pi\)
−0.116357 + 0.993208i \(0.537122\pi\)
\(500\) 18.5520 0.829672
\(501\) 72.3215 3.23109
\(502\) 40.0660 1.78823
\(503\) −13.4706 −0.600624 −0.300312 0.953841i \(-0.597091\pi\)
−0.300312 + 0.953841i \(0.597091\pi\)
\(504\) 5.30199 0.236169
\(505\) −14.0731 −0.626246
\(506\) 50.2526 2.23400
\(507\) 33.1669 1.47299
\(508\) 91.4300 4.05655
\(509\) 6.64288 0.294440 0.147220 0.989104i \(-0.452967\pi\)
0.147220 + 0.989104i \(0.452967\pi\)
\(510\) 194.438 8.60986
\(511\) −0.593039 −0.0262345
\(512\) −140.293 −6.20014
\(513\) −84.1570 −3.71562
\(514\) 79.3748 3.50107
\(515\) 27.9008 1.22946
\(516\) −212.507 −9.35509
\(517\) 26.4473 1.16315
\(518\) −0.417347 −0.0183372
\(519\) 24.6165 1.08055
\(520\) −62.9636 −2.76114
\(521\) 14.5048 0.635466 0.317733 0.948180i \(-0.397078\pi\)
0.317733 + 0.948180i \(0.397078\pi\)
\(522\) −11.1374 −0.487469
\(523\) 15.2881 0.668500 0.334250 0.942484i \(-0.391517\pi\)
0.334250 + 0.942484i \(0.391517\pi\)
\(524\) −97.5431 −4.26119
\(525\) 1.19109 0.0519835
\(526\) 12.2434 0.533839
\(527\) 22.9514 0.999777
\(528\) −194.375 −8.45909
\(529\) 8.88052 0.386110
\(530\) −124.140 −5.39229
\(531\) 61.6145 2.67384
\(532\) −1.53266 −0.0664494
\(533\) −3.04950 −0.132088
\(534\) −7.26005 −0.314173
\(535\) 4.34470 0.187838
\(536\) 48.6004 2.09922
\(537\) 36.1156 1.55850
\(538\) 13.7159 0.591334
\(539\) −22.3072 −0.960839
\(540\) −358.897 −15.4445
\(541\) 0.147364 0.00633567 0.00316783 0.999995i \(-0.498992\pi\)
0.00316783 + 0.999995i \(0.498992\pi\)
\(542\) 0.586699 0.0252009
\(543\) 8.43893 0.362149
\(544\) −179.640 −7.70202
\(545\) 35.6399 1.52665
\(546\) −1.00072 −0.0428269
\(547\) 34.1302 1.45930 0.729650 0.683821i \(-0.239683\pi\)
0.729650 + 0.683821i \(0.239683\pi\)
\(548\) 122.411 5.22914
\(549\) 75.6225 3.22749
\(550\) −53.1083 −2.26454
\(551\) 2.10787 0.0897984
\(552\) −202.823 −8.63272
\(553\) 0.00387975 0.000164984 0
\(554\) 23.1209 0.982314
\(555\) 28.5596 1.21229
\(556\) −39.2247 −1.66350
\(557\) 16.6720 0.706414 0.353207 0.935545i \(-0.385091\pi\)
0.353207 + 0.935545i \(0.385091\pi\)
\(558\) −87.9995 −3.72532
\(559\) 19.4181 0.821297
\(560\) −3.50012 −0.147907
\(561\) −67.0597 −2.83126
\(562\) 3.60125 0.151910
\(563\) 17.2366 0.726437 0.363219 0.931704i \(-0.381678\pi\)
0.363219 + 0.931704i \(0.381678\pi\)
\(564\) −163.037 −6.86510
\(565\) 4.95337 0.208390
\(566\) −60.0698 −2.52492
\(567\) −2.23211 −0.0937398
\(568\) −11.4886 −0.482053
\(569\) −27.4550 −1.15098 −0.575488 0.817810i \(-0.695188\pi\)
−0.575488 + 0.817810i \(0.695188\pi\)
\(570\) 141.096 5.90986
\(571\) −7.76414 −0.324919 −0.162460 0.986715i \(-0.551943\pi\)
−0.162460 + 0.986715i \(0.551943\pi\)
\(572\) 33.1678 1.38681
\(573\) −14.9043 −0.622634
\(574\) −0.278825 −0.0116379
\(575\) −33.6922 −1.40506
\(576\) 382.841 15.9517
\(577\) −35.3062 −1.46982 −0.734909 0.678166i \(-0.762775\pi\)
−0.734909 + 0.678166i \(0.762775\pi\)
\(578\) −59.7988 −2.48730
\(579\) −23.1783 −0.963256
\(580\) 8.98924 0.373258
\(581\) 0.911868 0.0378307
\(582\) 77.4700 3.21123
\(583\) 42.8146 1.77320
\(584\) −106.723 −4.41624
\(585\) 50.6376 2.09361
\(586\) 18.2946 0.755741
\(587\) −24.3739 −1.00602 −0.503009 0.864281i \(-0.667774\pi\)
−0.503009 + 0.864281i \(0.667774\pi\)
\(588\) 137.515 5.67101
\(589\) 16.6549 0.686253
\(590\) −66.9016 −2.75430
\(591\) 50.2440 2.06676
\(592\) −45.6629 −1.87673
\(593\) −36.9055 −1.51553 −0.757763 0.652530i \(-0.773708\pi\)
−0.757763 + 0.652530i \(0.773708\pi\)
\(594\) 166.519 6.83235
\(595\) −1.20755 −0.0495046
\(596\) −3.76760 −0.154327
\(597\) 54.1798 2.21743
\(598\) 28.3072 1.15757
\(599\) −7.89027 −0.322388 −0.161194 0.986923i \(-0.551534\pi\)
−0.161194 + 0.986923i \(0.551534\pi\)
\(600\) 214.349 8.75075
\(601\) −12.4167 −0.506489 −0.253244 0.967402i \(-0.581498\pi\)
−0.253244 + 0.967402i \(0.581498\pi\)
\(602\) 1.77545 0.0723621
\(603\) −39.0862 −1.59171
\(604\) −122.776 −4.99569
\(605\) −2.76402 −0.112373
\(606\) −40.2522 −1.63513
\(607\) 40.7676 1.65471 0.827353 0.561683i \(-0.189846\pi\)
0.827353 + 0.561683i \(0.189846\pi\)
\(608\) −130.358 −5.28672
\(609\) 0.0935405 0.00379045
\(610\) −82.1117 −3.32461
\(611\) 14.8977 0.602697
\(612\) 305.683 12.3565
\(613\) −32.8429 −1.32651 −0.663256 0.748393i \(-0.730826\pi\)
−0.663256 + 0.748393i \(0.730826\pi\)
\(614\) 14.7354 0.594674
\(615\) 19.0803 0.769394
\(616\) 1.98552 0.0799987
\(617\) −13.2654 −0.534045 −0.267022 0.963690i \(-0.586040\pi\)
−0.267022 + 0.963690i \(0.586040\pi\)
\(618\) 79.8022 3.21012
\(619\) −2.69384 −0.108274 −0.0541372 0.998534i \(-0.517241\pi\)
−0.0541372 + 0.998534i \(0.517241\pi\)
\(620\) 71.0266 2.85250
\(621\) 105.640 4.23920
\(622\) 7.68446 0.308119
\(623\) 0.0450882 0.00180642
\(624\) −109.491 −4.38315
\(625\) −19.2289 −0.769158
\(626\) 38.7717 1.54963
\(627\) −48.6626 −1.94340
\(628\) −5.03069 −0.200746
\(629\) −15.7538 −0.628144
\(630\) 4.62995 0.184462
\(631\) −4.81315 −0.191609 −0.0958043 0.995400i \(-0.530542\pi\)
−0.0958043 + 0.995400i \(0.530542\pi\)
\(632\) 0.698200 0.0277729
\(633\) −30.9762 −1.23119
\(634\) −13.1522 −0.522341
\(635\) 52.2733 2.07440
\(636\) −263.934 −10.4657
\(637\) −12.5656 −0.497866
\(638\) −4.17078 −0.165123
\(639\) 9.23958 0.365512
\(640\) −223.741 −8.84415
\(641\) 10.0123 0.395461 0.197730 0.980256i \(-0.436643\pi\)
0.197730 + 0.980256i \(0.436643\pi\)
\(642\) 12.4268 0.490445
\(643\) 11.6628 0.459935 0.229967 0.973198i \(-0.426138\pi\)
0.229967 + 0.973198i \(0.426138\pi\)
\(644\) 1.92392 0.0758129
\(645\) −121.497 −4.78392
\(646\) −77.8300 −3.06218
\(647\) −31.7555 −1.24844 −0.624218 0.781250i \(-0.714582\pi\)
−0.624218 + 0.781250i \(0.714582\pi\)
\(648\) −401.690 −15.7799
\(649\) 23.0737 0.905722
\(650\) −29.9158 −1.17339
\(651\) 0.739091 0.0289672
\(652\) −42.4555 −1.66269
\(653\) −8.88968 −0.347880 −0.173940 0.984756i \(-0.555650\pi\)
−0.173940 + 0.984756i \(0.555650\pi\)
\(654\) 101.938 3.98608
\(655\) −55.7684 −2.17905
\(656\) −30.5068 −1.19109
\(657\) 85.8306 3.34857
\(658\) 1.36214 0.0531019
\(659\) 34.6975 1.35162 0.675812 0.737074i \(-0.263793\pi\)
0.675812 + 0.737074i \(0.263793\pi\)
\(660\) −207.527 −8.07797
\(661\) −41.9538 −1.63181 −0.815907 0.578183i \(-0.803762\pi\)
−0.815907 + 0.578183i \(0.803762\pi\)
\(662\) 13.9227 0.541120
\(663\) −37.7746 −1.46704
\(664\) 164.100 6.36831
\(665\) −0.876270 −0.0339803
\(666\) 60.4027 2.34056
\(667\) −2.64596 −0.102452
\(668\) −123.456 −4.77666
\(669\) −77.4092 −2.99281
\(670\) 42.4402 1.63961
\(671\) 28.3195 1.09326
\(672\) −5.78487 −0.223156
\(673\) −45.0710 −1.73736 −0.868679 0.495376i \(-0.835030\pi\)
−0.868679 + 0.495376i \(0.835030\pi\)
\(674\) −63.1103 −2.43092
\(675\) −111.644 −4.29716
\(676\) −56.6173 −2.17759
\(677\) 45.4326 1.74612 0.873059 0.487615i \(-0.162133\pi\)
0.873059 + 0.487615i \(0.162133\pi\)
\(678\) 14.1677 0.544107
\(679\) −0.481123 −0.0184638
\(680\) −217.310 −8.33346
\(681\) 15.7016 0.601686
\(682\) −32.9545 −1.26189
\(683\) 29.9300 1.14524 0.572620 0.819821i \(-0.305927\pi\)
0.572620 + 0.819821i \(0.305927\pi\)
\(684\) 221.822 8.48160
\(685\) 69.9861 2.67403
\(686\) −2.29839 −0.0877528
\(687\) 43.6226 1.66431
\(688\) 194.256 7.40595
\(689\) 24.1173 0.918797
\(690\) −177.115 −6.74264
\(691\) −2.17052 −0.0825703 −0.0412852 0.999147i \(-0.513145\pi\)
−0.0412852 + 0.999147i \(0.513145\pi\)
\(692\) −42.0215 −1.59742
\(693\) −1.59682 −0.0606583
\(694\) −29.6747 −1.12644
\(695\) −22.4259 −0.850664
\(696\) 16.8335 0.638074
\(697\) −10.5249 −0.398659
\(698\) −25.6033 −0.969099
\(699\) 10.7761 0.407588
\(700\) −2.03324 −0.0768494
\(701\) −20.9867 −0.792656 −0.396328 0.918109i \(-0.629716\pi\)
−0.396328 + 0.918109i \(0.629716\pi\)
\(702\) 93.7996 3.54024
\(703\) −11.4319 −0.431162
\(704\) 143.368 5.40339
\(705\) −93.2133 −3.51062
\(706\) 60.5773 2.27986
\(707\) 0.249984 0.00940162
\(708\) −142.240 −5.34571
\(709\) 1.83365 0.0688642 0.0344321 0.999407i \(-0.489038\pi\)
0.0344321 + 0.999407i \(0.489038\pi\)
\(710\) −10.0324 −0.376510
\(711\) −0.561517 −0.0210585
\(712\) 8.11406 0.304087
\(713\) −20.9065 −0.782955
\(714\) −3.45384 −0.129257
\(715\) 18.9630 0.709177
\(716\) −61.6509 −2.30400
\(717\) 15.4262 0.576103
\(718\) 30.8537 1.15145
\(719\) 33.3957 1.24545 0.622725 0.782440i \(-0.286025\pi\)
0.622725 + 0.782440i \(0.286025\pi\)
\(720\) 506.573 18.8789
\(721\) −0.495607 −0.0184574
\(722\) −3.44007 −0.128026
\(723\) −98.0530 −3.64663
\(724\) −14.4056 −0.535381
\(725\) 2.79632 0.103853
\(726\) −7.90569 −0.293408
\(727\) 43.1420 1.60005 0.800023 0.599969i \(-0.204820\pi\)
0.800023 + 0.599969i \(0.204820\pi\)
\(728\) 1.11844 0.0414520
\(729\) 132.596 4.91095
\(730\) −93.1958 −3.44933
\(731\) 67.0187 2.47878
\(732\) −174.578 −6.45260
\(733\) 17.7038 0.653905 0.326952 0.945041i \(-0.393978\pi\)
0.326952 + 0.945041i \(0.393978\pi\)
\(734\) 31.2898 1.15493
\(735\) 78.6214 2.89999
\(736\) 163.635 6.03168
\(737\) −14.6372 −0.539168
\(738\) 40.3543 1.48546
\(739\) 38.7703 1.42619 0.713093 0.701069i \(-0.247294\pi\)
0.713093 + 0.701069i \(0.247294\pi\)
\(740\) −48.7525 −1.79218
\(741\) −27.4115 −1.00699
\(742\) 2.20512 0.0809525
\(743\) −27.9035 −1.02368 −0.511841 0.859080i \(-0.671036\pi\)
−0.511841 + 0.859080i \(0.671036\pi\)
\(744\) 133.007 4.87626
\(745\) −2.15405 −0.0789184
\(746\) 80.2046 2.93650
\(747\) −131.975 −4.82871
\(748\) 114.474 4.18558
\(749\) −0.0771758 −0.00281994
\(750\) 30.3376 1.10777
\(751\) 41.9860 1.53209 0.766045 0.642787i \(-0.222222\pi\)
0.766045 + 0.642787i \(0.222222\pi\)
\(752\) 149.035 5.43475
\(753\) 48.7026 1.77482
\(754\) −2.34939 −0.0855597
\(755\) −70.1948 −2.55465
\(756\) 6.37515 0.231862
\(757\) −30.3527 −1.10319 −0.551594 0.834113i \(-0.685980\pi\)
−0.551594 + 0.834113i \(0.685980\pi\)
\(758\) 56.0956 2.03748
\(759\) 61.0851 2.21725
\(760\) −157.693 −5.72014
\(761\) −20.4000 −0.739498 −0.369749 0.929132i \(-0.620556\pi\)
−0.369749 + 0.929132i \(0.620556\pi\)
\(762\) 149.513 5.41628
\(763\) −0.633079 −0.0229190
\(764\) 25.4422 0.920467
\(765\) 174.768 6.31877
\(766\) 43.1436 1.55884
\(767\) 12.9974 0.469307
\(768\) −334.785 −12.0805
\(769\) 11.9939 0.432510 0.216255 0.976337i \(-0.430616\pi\)
0.216255 + 0.976337i \(0.430616\pi\)
\(770\) 1.73385 0.0624835
\(771\) 96.4848 3.47482
\(772\) 39.5663 1.42402
\(773\) −20.4701 −0.736258 −0.368129 0.929775i \(-0.620001\pi\)
−0.368129 + 0.929775i \(0.620001\pi\)
\(774\) −256.962 −9.23630
\(775\) 22.0946 0.793660
\(776\) −86.5829 −3.10814
\(777\) −0.507311 −0.0181997
\(778\) 16.0045 0.573790
\(779\) −7.63751 −0.273642
\(780\) −116.899 −4.18567
\(781\) 3.46008 0.123812
\(782\) 97.6982 3.49368
\(783\) −8.76775 −0.313334
\(784\) −125.705 −4.48945
\(785\) −2.87620 −0.102656
\(786\) −159.509 −5.68951
\(787\) −11.7779 −0.419837 −0.209919 0.977719i \(-0.567320\pi\)
−0.209919 + 0.977719i \(0.567320\pi\)
\(788\) −85.7687 −3.05538
\(789\) 14.8826 0.529835
\(790\) 0.609701 0.0216922
\(791\) −0.0879877 −0.00312848
\(792\) −287.364 −10.2110
\(793\) 15.9523 0.566483
\(794\) −91.3076 −3.24039
\(795\) −150.899 −5.35185
\(796\) −92.4874 −3.27813
\(797\) −32.6588 −1.15683 −0.578417 0.815741i \(-0.696329\pi\)
−0.578417 + 0.815741i \(0.696329\pi\)
\(798\) −2.50632 −0.0887227
\(799\) 51.4174 1.81902
\(800\) −172.934 −6.11415
\(801\) −6.52562 −0.230571
\(802\) −19.8289 −0.700184
\(803\) 32.1423 1.13428
\(804\) 90.2324 3.18225
\(805\) 1.09996 0.0387685
\(806\) −18.5632 −0.653861
\(807\) 16.6725 0.586899
\(808\) 44.9871 1.58264
\(809\) 10.7998 0.379700 0.189850 0.981813i \(-0.439200\pi\)
0.189850 + 0.981813i \(0.439200\pi\)
\(810\) −350.775 −12.3250
\(811\) 32.3548 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(812\) −0.159678 −0.00560359
\(813\) 0.713168 0.0250119
\(814\) 22.6199 0.792828
\(815\) −24.2731 −0.850250
\(816\) −377.893 −13.2289
\(817\) 48.6329 1.70145
\(818\) 24.3764 0.852301
\(819\) −0.899486 −0.0314306
\(820\) −32.5710 −1.13743
\(821\) 18.6941 0.652430 0.326215 0.945296i \(-0.394227\pi\)
0.326215 + 0.945296i \(0.394227\pi\)
\(822\) 200.175 6.98192
\(823\) 31.9265 1.11289 0.556445 0.830885i \(-0.312165\pi\)
0.556445 + 0.830885i \(0.312165\pi\)
\(824\) −89.1895 −3.10706
\(825\) −64.5563 −2.24756
\(826\) 1.18839 0.0413493
\(827\) −21.9542 −0.763423 −0.381712 0.924281i \(-0.624665\pi\)
−0.381712 + 0.924281i \(0.624665\pi\)
\(828\) −278.449 −9.67676
\(829\) −6.91657 −0.240222 −0.120111 0.992760i \(-0.538325\pi\)
−0.120111 + 0.992760i \(0.538325\pi\)
\(830\) 143.300 4.97401
\(831\) 28.1049 0.974947
\(832\) 80.7589 2.79981
\(833\) −43.3683 −1.50262
\(834\) −64.1430 −2.22109
\(835\) −70.5835 −2.44264
\(836\) 83.0692 2.87301
\(837\) −69.2765 −2.39455
\(838\) 26.7585 0.924357
\(839\) −42.0345 −1.45119 −0.725597 0.688120i \(-0.758436\pi\)
−0.725597 + 0.688120i \(0.758436\pi\)
\(840\) −6.99792 −0.241451
\(841\) −28.7804 −0.992427
\(842\) −25.0509 −0.863309
\(843\) 4.37754 0.150770
\(844\) 52.8777 1.82013
\(845\) −32.3699 −1.11356
\(846\) −197.143 −6.77793
\(847\) 0.0490979 0.00168702
\(848\) 241.267 8.28515
\(849\) −73.0184 −2.50598
\(850\) −103.250 −3.54145
\(851\) 14.3502 0.491918
\(852\) −21.3300 −0.730754
\(853\) 12.2437 0.419218 0.209609 0.977785i \(-0.432781\pi\)
0.209609 + 0.977785i \(0.432781\pi\)
\(854\) 1.45857 0.0499112
\(855\) 126.823 4.33724
\(856\) −13.8885 −0.474701
\(857\) 29.2810 1.00022 0.500111 0.865961i \(-0.333293\pi\)
0.500111 + 0.865961i \(0.333293\pi\)
\(858\) 54.2383 1.85166
\(859\) 11.0410 0.376714 0.188357 0.982101i \(-0.439684\pi\)
0.188357 + 0.982101i \(0.439684\pi\)
\(860\) 207.400 7.07228
\(861\) −0.338928 −0.0115506
\(862\) 24.4941 0.834273
\(863\) −11.7603 −0.400324 −0.200162 0.979763i \(-0.564147\pi\)
−0.200162 + 0.979763i \(0.564147\pi\)
\(864\) 542.228 18.4470
\(865\) −24.0250 −0.816873
\(866\) 56.9211 1.93426
\(867\) −72.6890 −2.46865
\(868\) −1.26166 −0.0428235
\(869\) −0.210280 −0.00713325
\(870\) 14.6999 0.498372
\(871\) −8.24509 −0.279374
\(872\) −113.929 −3.85812
\(873\) 69.6330 2.35672
\(874\) 70.8958 2.39808
\(875\) −0.188410 −0.00636942
\(876\) −198.144 −6.69467
\(877\) 18.8586 0.636810 0.318405 0.947955i \(-0.396853\pi\)
0.318405 + 0.947955i \(0.396853\pi\)
\(878\) −55.8288 −1.88413
\(879\) 22.2381 0.750073
\(880\) 189.704 6.39492
\(881\) 50.8589 1.71348 0.856740 0.515749i \(-0.172486\pi\)
0.856740 + 0.515749i \(0.172486\pi\)
\(882\) 166.282 5.59900
\(883\) 26.2185 0.882323 0.441161 0.897428i \(-0.354567\pi\)
0.441161 + 0.897428i \(0.354567\pi\)
\(884\) 64.4828 2.16879
\(885\) −81.3229 −2.73364
\(886\) 28.2244 0.948218
\(887\) −12.7191 −0.427066 −0.213533 0.976936i \(-0.568497\pi\)
−0.213533 + 0.976936i \(0.568497\pi\)
\(888\) −91.2956 −3.06368
\(889\) −0.928541 −0.0311423
\(890\) 7.08559 0.237509
\(891\) 120.979 4.05294
\(892\) 132.141 4.42441
\(893\) 37.3116 1.24858
\(894\) −6.16105 −0.206056
\(895\) −35.2477 −1.17820
\(896\) 3.97436 0.132774
\(897\) 34.4091 1.14888
\(898\) −10.5094 −0.350704
\(899\) 1.73516 0.0578709
\(900\) 294.272 9.80906
\(901\) 83.2375 2.77304
\(902\) 15.1121 0.503178
\(903\) 2.15817 0.0718194
\(904\) −15.8343 −0.526640
\(905\) −8.23614 −0.273778
\(906\) −200.772 −6.67020
\(907\) −7.53515 −0.250201 −0.125100 0.992144i \(-0.539925\pi\)
−0.125100 + 0.992144i \(0.539925\pi\)
\(908\) −26.8033 −0.889499
\(909\) −36.1802 −1.20002
\(910\) 0.976671 0.0323763
\(911\) −57.6440 −1.90983 −0.954916 0.296875i \(-0.904055\pi\)
−0.954916 + 0.296875i \(0.904055\pi\)
\(912\) −274.222 −9.08039
\(913\) −49.4226 −1.63565
\(914\) −56.2360 −1.86012
\(915\) −99.8117 −3.29967
\(916\) −74.4657 −2.46042
\(917\) 0.990625 0.0327133
\(918\) 323.736 10.6849
\(919\) −57.9051 −1.91011 −0.955057 0.296423i \(-0.904206\pi\)
−0.955057 + 0.296423i \(0.904206\pi\)
\(920\) 197.949 6.52618
\(921\) 17.9118 0.590214
\(922\) −102.782 −3.38494
\(923\) 1.94906 0.0641540
\(924\) 3.68634 0.121272
\(925\) −15.1657 −0.498644
\(926\) −9.22062 −0.303008
\(927\) 71.7293 2.35590
\(928\) −13.5811 −0.445822
\(929\) −33.0230 −1.08345 −0.541725 0.840556i \(-0.682229\pi\)
−0.541725 + 0.840556i \(0.682229\pi\)
\(930\) 116.148 3.80863
\(931\) −31.4707 −1.03141
\(932\) −18.3952 −0.602555
\(933\) 9.34091 0.305808
\(934\) 83.1589 2.72104
\(935\) 65.4482 2.14038
\(936\) −161.871 −5.29093
\(937\) −41.3694 −1.35148 −0.675739 0.737141i \(-0.736175\pi\)
−0.675739 + 0.737141i \(0.736175\pi\)
\(938\) −0.753874 −0.0246149
\(939\) 47.1293 1.53801
\(940\) 159.119 5.18990
\(941\) 38.5037 1.25518 0.627592 0.778542i \(-0.284041\pi\)
0.627592 + 0.778542i \(0.284041\pi\)
\(942\) −8.22655 −0.268035
\(943\) 9.58719 0.312202
\(944\) 130.024 4.23192
\(945\) 3.64487 0.118568
\(946\) −96.2283 −3.12865
\(947\) 28.1100 0.913451 0.456725 0.889608i \(-0.349022\pi\)
0.456725 + 0.889608i \(0.349022\pi\)
\(948\) 1.29629 0.0421015
\(949\) 18.1057 0.587734
\(950\) −74.9245 −2.43087
\(951\) −15.9873 −0.518423
\(952\) 3.86012 0.125107
\(953\) −25.3834 −0.822250 −0.411125 0.911579i \(-0.634864\pi\)
−0.411125 + 0.911579i \(0.634864\pi\)
\(954\) −319.147 −10.3328
\(955\) 14.5461 0.470700
\(956\) −26.3332 −0.851678
\(957\) −5.06983 −0.163884
\(958\) 72.0913 2.32916
\(959\) −1.24318 −0.0401443
\(960\) −505.299 −16.3085
\(961\) −17.2900 −0.557742
\(962\) 12.7417 0.410810
\(963\) 11.1697 0.359937
\(964\) 167.381 5.39097
\(965\) 22.6213 0.728204
\(966\) 3.14612 0.101225
\(967\) 29.5088 0.948941 0.474470 0.880272i \(-0.342640\pi\)
0.474470 + 0.880272i \(0.342640\pi\)
\(968\) 8.83565 0.283988
\(969\) −94.6070 −3.03921
\(970\) −75.6083 −2.42764
\(971\) 33.8925 1.08766 0.543831 0.839195i \(-0.316973\pi\)
0.543831 + 0.839195i \(0.316973\pi\)
\(972\) −420.665 −13.4928
\(973\) 0.398357 0.0127707
\(974\) 65.3803 2.09492
\(975\) −36.3644 −1.16459
\(976\) 159.585 5.10820
\(977\) 54.2431 1.73539 0.867696 0.497095i \(-0.165600\pi\)
0.867696 + 0.497095i \(0.165600\pi\)
\(978\) −69.4263 −2.22001
\(979\) −2.44375 −0.0781025
\(980\) −134.210 −4.28719
\(981\) 91.6257 2.92538
\(982\) −67.2025 −2.14452
\(983\) 3.05541 0.0974525 0.0487263 0.998812i \(-0.484484\pi\)
0.0487263 + 0.998812i \(0.484484\pi\)
\(984\) −60.9935 −1.94440
\(985\) −49.0366 −1.56243
\(986\) −8.10858 −0.258230
\(987\) 1.65577 0.0527037
\(988\) 46.7927 1.48867
\(989\) −61.0477 −1.94120
\(990\) −250.940 −7.97539
\(991\) 61.3063 1.94746 0.973729 0.227709i \(-0.0731235\pi\)
0.973729 + 0.227709i \(0.0731235\pi\)
\(992\) −107.308 −3.40704
\(993\) 16.9238 0.537061
\(994\) 0.178208 0.00565242
\(995\) −52.8778 −1.67634
\(996\) 304.670 9.65385
\(997\) −49.7062 −1.57421 −0.787106 0.616818i \(-0.788421\pi\)
−0.787106 + 0.616818i \(0.788421\pi\)
\(998\) 14.5113 0.459346
\(999\) 47.5513 1.50446
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 \(a_p\))