Properties

Label 8035.2.a.e.1.20
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.27555 q^{2}\) \(+1.50447 q^{3}\) \(+3.17814 q^{4}\) \(+1.00000 q^{5}\) \(-3.42350 q^{6}\) \(+2.50382 q^{7}\) \(-2.68091 q^{8}\) \(-0.736575 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.27555 q^{2}\) \(+1.50447 q^{3}\) \(+3.17814 q^{4}\) \(+1.00000 q^{5}\) \(-3.42350 q^{6}\) \(+2.50382 q^{7}\) \(-2.68091 q^{8}\) \(-0.736575 q^{9}\) \(-2.27555 q^{10}\) \(-5.24727 q^{11}\) \(+4.78141 q^{12}\) \(-3.80317 q^{13}\) \(-5.69758 q^{14}\) \(+1.50447 q^{15}\) \(-0.255719 q^{16}\) \(-4.81056 q^{17}\) \(+1.67612 q^{18}\) \(-6.96879 q^{19}\) \(+3.17814 q^{20}\) \(+3.76692 q^{21}\) \(+11.9404 q^{22}\) \(+7.29962 q^{23}\) \(-4.03335 q^{24}\) \(+1.00000 q^{25}\) \(+8.65432 q^{26}\) \(-5.62156 q^{27}\) \(+7.95750 q^{28}\) \(+4.20392 q^{29}\) \(-3.42350 q^{30}\) \(+1.55323 q^{31}\) \(+5.94373 q^{32}\) \(-7.89435 q^{33}\) \(+10.9467 q^{34}\) \(+2.50382 q^{35}\) \(-2.34094 q^{36}\) \(-2.66575 q^{37}\) \(+15.8579 q^{38}\) \(-5.72175 q^{39}\) \(-2.68091 q^{40}\) \(-1.82214 q^{41}\) \(-8.57183 q^{42}\) \(+6.25569 q^{43}\) \(-16.6765 q^{44}\) \(-0.736575 q^{45}\) \(-16.6107 q^{46}\) \(+9.31783 q^{47}\) \(-0.384720 q^{48}\) \(-0.730862 q^{49}\) \(-2.27555 q^{50}\) \(-7.23733 q^{51}\) \(-12.0870 q^{52}\) \(+10.0844 q^{53}\) \(+12.7921 q^{54}\) \(-5.24727 q^{55}\) \(-6.71253 q^{56}\) \(-10.4843 q^{57}\) \(-9.56624 q^{58}\) \(-14.1232 q^{59}\) \(+4.78141 q^{60}\) \(+4.75049 q^{61}\) \(-3.53446 q^{62}\) \(-1.84426 q^{63}\) \(-13.0138 q^{64}\) \(-3.80317 q^{65}\) \(+17.9640 q^{66}\) \(+14.3978 q^{67}\) \(-15.2886 q^{68}\) \(+10.9820 q^{69}\) \(-5.69758 q^{70}\) \(-4.86014 q^{71}\) \(+1.97469 q^{72}\) \(-6.55155 q^{73}\) \(+6.06606 q^{74}\) \(+1.50447 q^{75}\) \(-22.1478 q^{76}\) \(-13.1382 q^{77}\) \(+13.0201 q^{78}\) \(+9.02603 q^{79}\) \(-0.255719 q^{80}\) \(-6.24773 q^{81}\) \(+4.14637 q^{82}\) \(-3.79250 q^{83}\) \(+11.9718 q^{84}\) \(-4.81056 q^{85}\) \(-14.2351 q^{86}\) \(+6.32467 q^{87}\) \(+14.0675 q^{88}\) \(-16.5487 q^{89}\) \(+1.67612 q^{90}\) \(-9.52248 q^{91}\) \(+23.1992 q^{92}\) \(+2.33679 q^{93}\) \(-21.2032 q^{94}\) \(-6.96879 q^{95}\) \(+8.94215 q^{96}\) \(+2.97990 q^{97}\) \(+1.66312 q^{98}\) \(+3.86501 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27555 −1.60906 −0.804529 0.593913i \(-0.797582\pi\)
−0.804529 + 0.593913i \(0.797582\pi\)
\(3\) 1.50447 0.868605 0.434303 0.900767i \(-0.356995\pi\)
0.434303 + 0.900767i \(0.356995\pi\)
\(4\) 3.17814 1.58907
\(5\) 1.00000 0.447214
\(6\) −3.42350 −1.39764
\(7\) 2.50382 0.946357 0.473178 0.880967i \(-0.343107\pi\)
0.473178 + 0.880967i \(0.343107\pi\)
\(8\) −2.68091 −0.947846
\(9\) −0.736575 −0.245525
\(10\) −2.27555 −0.719593
\(11\) −5.24727 −1.58211 −0.791056 0.611744i \(-0.790468\pi\)
−0.791056 + 0.611744i \(0.790468\pi\)
\(12\) 4.78141 1.38027
\(13\) −3.80317 −1.05481 −0.527405 0.849614i \(-0.676835\pi\)
−0.527405 + 0.849614i \(0.676835\pi\)
\(14\) −5.69758 −1.52274
\(15\) 1.50447 0.388452
\(16\) −0.255719 −0.0639296
\(17\) −4.81056 −1.16673 −0.583366 0.812210i \(-0.698264\pi\)
−0.583366 + 0.812210i \(0.698264\pi\)
\(18\) 1.67612 0.395064
\(19\) −6.96879 −1.59875 −0.799375 0.600832i \(-0.794836\pi\)
−0.799375 + 0.600832i \(0.794836\pi\)
\(20\) 3.17814 0.710653
\(21\) 3.76692 0.822010
\(22\) 11.9404 2.54571
\(23\) 7.29962 1.52208 0.761038 0.648707i \(-0.224690\pi\)
0.761038 + 0.648707i \(0.224690\pi\)
\(24\) −4.03335 −0.823304
\(25\) 1.00000 0.200000
\(26\) 8.65432 1.69725
\(27\) −5.62156 −1.08187
\(28\) 7.95750 1.50383
\(29\) 4.20392 0.780649 0.390324 0.920677i \(-0.372363\pi\)
0.390324 + 0.920677i \(0.372363\pi\)
\(30\) −3.42350 −0.625042
\(31\) 1.55323 0.278969 0.139484 0.990224i \(-0.455456\pi\)
0.139484 + 0.990224i \(0.455456\pi\)
\(32\) 5.94373 1.05071
\(33\) −7.89435 −1.37423
\(34\) 10.9467 1.87734
\(35\) 2.50382 0.423224
\(36\) −2.34094 −0.390156
\(37\) −2.66575 −0.438247 −0.219124 0.975697i \(-0.570320\pi\)
−0.219124 + 0.975697i \(0.570320\pi\)
\(38\) 15.8579 2.57248
\(39\) −5.72175 −0.916214
\(40\) −2.68091 −0.423889
\(41\) −1.82214 −0.284570 −0.142285 0.989826i \(-0.545445\pi\)
−0.142285 + 0.989826i \(0.545445\pi\)
\(42\) −8.57183 −1.32266
\(43\) 6.25569 0.953984 0.476992 0.878908i \(-0.341727\pi\)
0.476992 + 0.878908i \(0.341727\pi\)
\(44\) −16.6765 −2.51408
\(45\) −0.736575 −0.109802
\(46\) −16.6107 −2.44911
\(47\) 9.31783 1.35915 0.679573 0.733608i \(-0.262165\pi\)
0.679573 + 0.733608i \(0.262165\pi\)
\(48\) −0.384720 −0.0555296
\(49\) −0.730862 −0.104409
\(50\) −2.27555 −0.321812
\(51\) −7.23733 −1.01343
\(52\) −12.0870 −1.67617
\(53\) 10.0844 1.38520 0.692599 0.721323i \(-0.256466\pi\)
0.692599 + 0.721323i \(0.256466\pi\)
\(54\) 12.7921 1.74079
\(55\) −5.24727 −0.707542
\(56\) −6.71253 −0.897000
\(57\) −10.4843 −1.38868
\(58\) −9.56624 −1.25611
\(59\) −14.1232 −1.83869 −0.919343 0.393458i \(-0.871279\pi\)
−0.919343 + 0.393458i \(0.871279\pi\)
\(60\) 4.78141 0.617277
\(61\) 4.75049 0.608237 0.304119 0.952634i \(-0.401638\pi\)
0.304119 + 0.952634i \(0.401638\pi\)
\(62\) −3.53446 −0.448877
\(63\) −1.84426 −0.232354
\(64\) −13.0138 −1.62673
\(65\) −3.80317 −0.471726
\(66\) 17.9640 2.21122
\(67\) 14.3978 1.75897 0.879484 0.475928i \(-0.157888\pi\)
0.879484 + 0.475928i \(0.157888\pi\)
\(68\) −15.2886 −1.85402
\(69\) 10.9820 1.32208
\(70\) −5.69758 −0.680991
\(71\) −4.86014 −0.576793 −0.288396 0.957511i \(-0.593122\pi\)
−0.288396 + 0.957511i \(0.593122\pi\)
\(72\) 1.97469 0.232720
\(73\) −6.55155 −0.766801 −0.383401 0.923582i \(-0.625247\pi\)
−0.383401 + 0.923582i \(0.625247\pi\)
\(74\) 6.06606 0.705165
\(75\) 1.50447 0.173721
\(76\) −22.1478 −2.54052
\(77\) −13.1382 −1.49724
\(78\) 13.0201 1.47424
\(79\) 9.02603 1.01551 0.507754 0.861502i \(-0.330476\pi\)
0.507754 + 0.861502i \(0.330476\pi\)
\(80\) −0.255719 −0.0285902
\(81\) −6.24773 −0.694192
\(82\) 4.14637 0.457890
\(83\) −3.79250 −0.416281 −0.208141 0.978099i \(-0.566741\pi\)
−0.208141 + 0.978099i \(0.566741\pi\)
\(84\) 11.9718 1.30623
\(85\) −4.81056 −0.521778
\(86\) −14.2351 −1.53502
\(87\) 6.32467 0.678075
\(88\) 14.0675 1.49960
\(89\) −16.5487 −1.75416 −0.877079 0.480347i \(-0.840511\pi\)
−0.877079 + 0.480347i \(0.840511\pi\)
\(90\) 1.67612 0.176678
\(91\) −9.52248 −0.998227
\(92\) 23.1992 2.41868
\(93\) 2.33679 0.242314
\(94\) −21.2032 −2.18694
\(95\) −6.96879 −0.714983
\(96\) 8.94215 0.912654
\(97\) 2.97990 0.302563 0.151281 0.988491i \(-0.451660\pi\)
0.151281 + 0.988491i \(0.451660\pi\)
\(98\) 1.66312 0.168000
\(99\) 3.86501 0.388448
\(100\) 3.17814 0.317814
\(101\) 13.8701 1.38013 0.690066 0.723747i \(-0.257582\pi\)
0.690066 + 0.723747i \(0.257582\pi\)
\(102\) 16.4689 1.63067
\(103\) −11.7824 −1.16095 −0.580476 0.814277i \(-0.697134\pi\)
−0.580476 + 0.814277i \(0.697134\pi\)
\(104\) 10.1960 0.999797
\(105\) 3.76692 0.367614
\(106\) −22.9476 −2.22886
\(107\) −1.28361 −0.124091 −0.0620454 0.998073i \(-0.519762\pi\)
−0.0620454 + 0.998073i \(0.519762\pi\)
\(108\) −17.8661 −1.71916
\(109\) 18.6045 1.78198 0.890992 0.454018i \(-0.150010\pi\)
0.890992 + 0.454018i \(0.150010\pi\)
\(110\) 11.9404 1.13848
\(111\) −4.01054 −0.380664
\(112\) −0.640274 −0.0605002
\(113\) 11.1810 1.05182 0.525909 0.850541i \(-0.323725\pi\)
0.525909 + 0.850541i \(0.323725\pi\)
\(114\) 23.8576 2.23447
\(115\) 7.29962 0.680693
\(116\) 13.3606 1.24050
\(117\) 2.80132 0.258982
\(118\) 32.1381 2.95855
\(119\) −12.0448 −1.10414
\(120\) −4.03335 −0.368193
\(121\) 16.5338 1.50308
\(122\) −10.8100 −0.978690
\(123\) −2.74135 −0.247179
\(124\) 4.93638 0.443300
\(125\) 1.00000 0.0894427
\(126\) 4.19670 0.373872
\(127\) −0.734058 −0.0651371 −0.0325685 0.999470i \(-0.510369\pi\)
−0.0325685 + 0.999470i \(0.510369\pi\)
\(128\) 17.7262 1.56679
\(129\) 9.41148 0.828635
\(130\) 8.65432 0.759034
\(131\) 14.5580 1.27194 0.635971 0.771713i \(-0.280600\pi\)
0.635971 + 0.771713i \(0.280600\pi\)
\(132\) −25.0893 −2.18375
\(133\) −17.4486 −1.51299
\(134\) −32.7629 −2.83028
\(135\) −5.62156 −0.483827
\(136\) 12.8967 1.10588
\(137\) 16.8803 1.44218 0.721089 0.692842i \(-0.243642\pi\)
0.721089 + 0.692842i \(0.243642\pi\)
\(138\) −24.9902 −2.12731
\(139\) 12.6496 1.07292 0.536462 0.843925i \(-0.319761\pi\)
0.536462 + 0.843925i \(0.319761\pi\)
\(140\) 7.95750 0.672531
\(141\) 14.0184 1.18056
\(142\) 11.0595 0.928093
\(143\) 19.9563 1.66883
\(144\) 0.188356 0.0156963
\(145\) 4.20392 0.349117
\(146\) 14.9084 1.23383
\(147\) −1.09956 −0.0906901
\(148\) −8.47213 −0.696405
\(149\) 6.26500 0.513249 0.256624 0.966511i \(-0.417390\pi\)
0.256624 + 0.966511i \(0.417390\pi\)
\(150\) −3.42350 −0.279527
\(151\) −4.22092 −0.343493 −0.171747 0.985141i \(-0.554941\pi\)
−0.171747 + 0.985141i \(0.554941\pi\)
\(152\) 18.6827 1.51537
\(153\) 3.54334 0.286462
\(154\) 29.8968 2.40915
\(155\) 1.55323 0.124759
\(156\) −18.1845 −1.45593
\(157\) 8.69378 0.693839 0.346919 0.937895i \(-0.387228\pi\)
0.346919 + 0.937895i \(0.387228\pi\)
\(158\) −20.5392 −1.63401
\(159\) 15.1716 1.20319
\(160\) 5.94373 0.469893
\(161\) 18.2770 1.44043
\(162\) 14.2170 1.11700
\(163\) −12.8601 −1.00728 −0.503642 0.863913i \(-0.668007\pi\)
−0.503642 + 0.863913i \(0.668007\pi\)
\(164\) −5.79100 −0.452201
\(165\) −7.89435 −0.614574
\(166\) 8.63004 0.669821
\(167\) 7.17778 0.555434 0.277717 0.960663i \(-0.410422\pi\)
0.277717 + 0.960663i \(0.410422\pi\)
\(168\) −10.0988 −0.779139
\(169\) 1.46412 0.112625
\(170\) 10.9467 0.839571
\(171\) 5.13304 0.392534
\(172\) 19.8814 1.51595
\(173\) 8.54652 0.649780 0.324890 0.945752i \(-0.394673\pi\)
0.324890 + 0.945752i \(0.394673\pi\)
\(174\) −14.3921 −1.09106
\(175\) 2.50382 0.189271
\(176\) 1.34182 0.101144
\(177\) −21.2479 −1.59709
\(178\) 37.6574 2.82254
\(179\) 12.3954 0.926478 0.463239 0.886233i \(-0.346687\pi\)
0.463239 + 0.886233i \(0.346687\pi\)
\(180\) −2.34094 −0.174483
\(181\) −22.3674 −1.66256 −0.831279 0.555855i \(-0.812391\pi\)
−0.831279 + 0.555855i \(0.812391\pi\)
\(182\) 21.6689 1.60621
\(183\) 7.14696 0.528318
\(184\) −19.5696 −1.44269
\(185\) −2.66575 −0.195990
\(186\) −5.31748 −0.389897
\(187\) 25.2423 1.84590
\(188\) 29.6133 2.15978
\(189\) −14.0754 −1.02383
\(190\) 15.8579 1.15045
\(191\) 9.59032 0.693931 0.346965 0.937878i \(-0.387212\pi\)
0.346965 + 0.937878i \(0.387212\pi\)
\(192\) −19.5789 −1.41298
\(193\) −21.0726 −1.51684 −0.758421 0.651765i \(-0.774029\pi\)
−0.758421 + 0.651765i \(0.774029\pi\)
\(194\) −6.78091 −0.486841
\(195\) −5.72175 −0.409743
\(196\) −2.32278 −0.165913
\(197\) −24.4357 −1.74097 −0.870485 0.492196i \(-0.836194\pi\)
−0.870485 + 0.492196i \(0.836194\pi\)
\(198\) −8.79503 −0.625036
\(199\) −21.0865 −1.49478 −0.747391 0.664384i \(-0.768694\pi\)
−0.747391 + 0.664384i \(0.768694\pi\)
\(200\) −2.68091 −0.189569
\(201\) 21.6610 1.52785
\(202\) −31.5622 −2.22071
\(203\) 10.5259 0.738772
\(204\) −23.0012 −1.61041
\(205\) −1.82214 −0.127264
\(206\) 26.8114 1.86804
\(207\) −5.37672 −0.373708
\(208\) 0.972542 0.0674336
\(209\) 36.5671 2.52940
\(210\) −8.57183 −0.591513
\(211\) 23.1396 1.59300 0.796498 0.604642i \(-0.206684\pi\)
0.796498 + 0.604642i \(0.206684\pi\)
\(212\) 32.0496 2.20117
\(213\) −7.31193 −0.501005
\(214\) 2.92091 0.199669
\(215\) 6.25569 0.426634
\(216\) 15.0709 1.02545
\(217\) 3.88902 0.264004
\(218\) −42.3354 −2.86732
\(219\) −9.85660 −0.666048
\(220\) −16.6765 −1.12433
\(221\) 18.2954 1.23068
\(222\) 9.12620 0.612510
\(223\) 24.1681 1.61841 0.809207 0.587523i \(-0.199897\pi\)
0.809207 + 0.587523i \(0.199897\pi\)
\(224\) 14.8820 0.994349
\(225\) −0.736575 −0.0491050
\(226\) −25.4429 −1.69244
\(227\) 23.2897 1.54579 0.772895 0.634533i \(-0.218808\pi\)
0.772895 + 0.634533i \(0.218808\pi\)
\(228\) −33.3206 −2.20671
\(229\) −15.2617 −1.00852 −0.504262 0.863551i \(-0.668236\pi\)
−0.504262 + 0.863551i \(0.668236\pi\)
\(230\) −16.6107 −1.09527
\(231\) −19.7661 −1.30051
\(232\) −11.2703 −0.739934
\(233\) 14.9388 0.978676 0.489338 0.872094i \(-0.337238\pi\)
0.489338 + 0.872094i \(0.337238\pi\)
\(234\) −6.37456 −0.416718
\(235\) 9.31783 0.607828
\(236\) −44.8855 −2.92180
\(237\) 13.5794 0.882075
\(238\) 27.4085 1.77663
\(239\) −18.0666 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(240\) −0.384720 −0.0248336
\(241\) 1.29823 0.0836264 0.0418132 0.999125i \(-0.486687\pi\)
0.0418132 + 0.999125i \(0.486687\pi\)
\(242\) −37.6236 −2.41854
\(243\) 7.46517 0.478891
\(244\) 15.0977 0.966531
\(245\) −0.730862 −0.0466931
\(246\) 6.23808 0.397725
\(247\) 26.5035 1.68638
\(248\) −4.16408 −0.264419
\(249\) −5.70570 −0.361584
\(250\) −2.27555 −0.143919
\(251\) 21.8057 1.37636 0.688182 0.725538i \(-0.258409\pi\)
0.688182 + 0.725538i \(0.258409\pi\)
\(252\) −5.86130 −0.369227
\(253\) −38.3031 −2.40809
\(254\) 1.67039 0.104809
\(255\) −7.23733 −0.453219
\(256\) −14.3092 −0.894324
\(257\) 3.37353 0.210435 0.105217 0.994449i \(-0.466446\pi\)
0.105217 + 0.994449i \(0.466446\pi\)
\(258\) −21.4163 −1.33332
\(259\) −6.67458 −0.414738
\(260\) −12.0870 −0.749604
\(261\) −3.09651 −0.191669
\(262\) −33.1276 −2.04663
\(263\) 25.2581 1.55748 0.778740 0.627346i \(-0.215859\pi\)
0.778740 + 0.627346i \(0.215859\pi\)
\(264\) 21.1641 1.30256
\(265\) 10.0844 0.619479
\(266\) 39.7053 2.43449
\(267\) −24.8970 −1.52367
\(268\) 45.7581 2.79512
\(269\) −18.2060 −1.11004 −0.555019 0.831837i \(-0.687289\pi\)
−0.555019 + 0.831837i \(0.687289\pi\)
\(270\) 12.7921 0.778505
\(271\) 7.11004 0.431904 0.215952 0.976404i \(-0.430714\pi\)
0.215952 + 0.976404i \(0.430714\pi\)
\(272\) 1.23015 0.0745887
\(273\) −14.3263 −0.867065
\(274\) −38.4119 −2.32055
\(275\) −5.24727 −0.316422
\(276\) 34.9025 2.10088
\(277\) −11.3819 −0.683873 −0.341937 0.939723i \(-0.611083\pi\)
−0.341937 + 0.939723i \(0.611083\pi\)
\(278\) −28.7848 −1.72640
\(279\) −1.14407 −0.0684938
\(280\) −6.71253 −0.401151
\(281\) −7.36784 −0.439529 −0.219764 0.975553i \(-0.570529\pi\)
−0.219764 + 0.975553i \(0.570529\pi\)
\(282\) −31.8996 −1.89959
\(283\) −16.9802 −1.00937 −0.504683 0.863305i \(-0.668391\pi\)
−0.504683 + 0.863305i \(0.668391\pi\)
\(284\) −15.4462 −0.916564
\(285\) −10.4843 −0.621038
\(286\) −45.4115 −2.68524
\(287\) −4.56231 −0.269305
\(288\) −4.37800 −0.257976
\(289\) 6.14144 0.361261
\(290\) −9.56624 −0.561749
\(291\) 4.48316 0.262807
\(292\) −20.8217 −1.21850
\(293\) 25.2249 1.47365 0.736826 0.676083i \(-0.236324\pi\)
0.736826 + 0.676083i \(0.236324\pi\)
\(294\) 2.50210 0.145926
\(295\) −14.1232 −0.822285
\(296\) 7.14665 0.415391
\(297\) 29.4978 1.71164
\(298\) −14.2563 −0.825847
\(299\) −27.7617 −1.60550
\(300\) 4.78141 0.276055
\(301\) 15.6631 0.902809
\(302\) 9.60491 0.552701
\(303\) 20.8672 1.19879
\(304\) 1.78205 0.102208
\(305\) 4.75049 0.272012
\(306\) −8.06305 −0.460934
\(307\) −4.82295 −0.275260 −0.137630 0.990484i \(-0.543949\pi\)
−0.137630 + 0.990484i \(0.543949\pi\)
\(308\) −41.7551 −2.37922
\(309\) −17.7262 −1.00841
\(310\) −3.53446 −0.200744
\(311\) −8.97997 −0.509208 −0.254604 0.967045i \(-0.581945\pi\)
−0.254604 + 0.967045i \(0.581945\pi\)
\(312\) 15.3395 0.868429
\(313\) 21.2719 1.20236 0.601180 0.799114i \(-0.294698\pi\)
0.601180 + 0.799114i \(0.294698\pi\)
\(314\) −19.7831 −1.11643
\(315\) −1.84426 −0.103912
\(316\) 28.6860 1.61371
\(317\) 7.44384 0.418088 0.209044 0.977906i \(-0.432965\pi\)
0.209044 + 0.977906i \(0.432965\pi\)
\(318\) −34.5239 −1.93600
\(319\) −22.0591 −1.23507
\(320\) −13.0138 −0.727495
\(321\) −1.93114 −0.107786
\(322\) −41.5902 −2.31773
\(323\) 33.5238 1.86531
\(324\) −19.8561 −1.10312
\(325\) −3.80317 −0.210962
\(326\) 29.2639 1.62078
\(327\) 27.9898 1.54784
\(328\) 4.88499 0.269728
\(329\) 23.3302 1.28624
\(330\) 17.9640 0.988886
\(331\) 7.76416 0.426757 0.213378 0.976970i \(-0.431553\pi\)
0.213378 + 0.976970i \(0.431553\pi\)
\(332\) −12.0531 −0.661499
\(333\) 1.96353 0.107601
\(334\) −16.3334 −0.893725
\(335\) 14.3978 0.786635
\(336\) −0.963272 −0.0525508
\(337\) 8.30367 0.452330 0.226165 0.974089i \(-0.427381\pi\)
0.226165 + 0.974089i \(0.427381\pi\)
\(338\) −3.33169 −0.181220
\(339\) 16.8214 0.913615
\(340\) −15.2886 −0.829141
\(341\) −8.15022 −0.441359
\(342\) −11.6805 −0.631609
\(343\) −19.3567 −1.04516
\(344\) −16.7710 −0.904229
\(345\) 10.9820 0.591254
\(346\) −19.4481 −1.04553
\(347\) 34.0457 1.82767 0.913834 0.406089i \(-0.133108\pi\)
0.913834 + 0.406089i \(0.133108\pi\)
\(348\) 20.1007 1.07751
\(349\) 20.7211 1.10918 0.554589 0.832125i \(-0.312876\pi\)
0.554589 + 0.832125i \(0.312876\pi\)
\(350\) −5.69758 −0.304549
\(351\) 21.3798 1.14117
\(352\) −31.1883 −1.66234
\(353\) 4.76457 0.253593 0.126796 0.991929i \(-0.459531\pi\)
0.126796 + 0.991929i \(0.459531\pi\)
\(354\) 48.3507 2.56981
\(355\) −4.86014 −0.257950
\(356\) −52.5940 −2.78748
\(357\) −18.1210 −0.959065
\(358\) −28.2064 −1.49076
\(359\) 14.2631 0.752780 0.376390 0.926461i \(-0.377165\pi\)
0.376390 + 0.926461i \(0.377165\pi\)
\(360\) 1.97469 0.104076
\(361\) 29.5641 1.55600
\(362\) 50.8983 2.67515
\(363\) 24.8746 1.30558
\(364\) −30.2637 −1.58625
\(365\) −6.55155 −0.342924
\(366\) −16.2633 −0.850095
\(367\) −21.6388 −1.12954 −0.564769 0.825249i \(-0.691035\pi\)
−0.564769 + 0.825249i \(0.691035\pi\)
\(368\) −1.86665 −0.0973058
\(369\) 1.34214 0.0698691
\(370\) 6.06606 0.315360
\(371\) 25.2496 1.31089
\(372\) 7.42663 0.385053
\(373\) 4.14912 0.214833 0.107417 0.994214i \(-0.465742\pi\)
0.107417 + 0.994214i \(0.465742\pi\)
\(374\) −57.4401 −2.97016
\(375\) 1.50447 0.0776904
\(376\) −24.9803 −1.28826
\(377\) −15.9882 −0.823436
\(378\) 32.0293 1.64741
\(379\) −6.72024 −0.345196 −0.172598 0.984992i \(-0.555216\pi\)
−0.172598 + 0.984992i \(0.555216\pi\)
\(380\) −22.1478 −1.13616
\(381\) −1.10437 −0.0565784
\(382\) −21.8233 −1.11658
\(383\) −6.70720 −0.342722 −0.171361 0.985208i \(-0.554816\pi\)
−0.171361 + 0.985208i \(0.554816\pi\)
\(384\) 26.6685 1.36092
\(385\) −13.1382 −0.669587
\(386\) 47.9519 2.44069
\(387\) −4.60779 −0.234227
\(388\) 9.47052 0.480793
\(389\) 6.34437 0.321672 0.160836 0.986981i \(-0.448581\pi\)
0.160836 + 0.986981i \(0.448581\pi\)
\(390\) 13.0201 0.659301
\(391\) −35.1152 −1.77585
\(392\) 1.95938 0.0989635
\(393\) 21.9021 1.10481
\(394\) 55.6046 2.80132
\(395\) 9.02603 0.454149
\(396\) 12.2835 0.617271
\(397\) −14.8646 −0.746034 −0.373017 0.927825i \(-0.621677\pi\)
−0.373017 + 0.927825i \(0.621677\pi\)
\(398\) 47.9834 2.40519
\(399\) −26.2509 −1.31419
\(400\) −0.255719 −0.0127859
\(401\) 20.4359 1.02052 0.510260 0.860020i \(-0.329549\pi\)
0.510260 + 0.860020i \(0.329549\pi\)
\(402\) −49.2907 −2.45840
\(403\) −5.90721 −0.294259
\(404\) 44.0812 2.19312
\(405\) −6.24773 −0.310452
\(406\) −23.9522 −1.18873
\(407\) 13.9879 0.693356
\(408\) 19.4026 0.960574
\(409\) 14.2914 0.706663 0.353332 0.935498i \(-0.385049\pi\)
0.353332 + 0.935498i \(0.385049\pi\)
\(410\) 4.14637 0.204774
\(411\) 25.3958 1.25268
\(412\) −37.4460 −1.84483
\(413\) −35.3620 −1.74005
\(414\) 12.2350 0.601318
\(415\) −3.79250 −0.186167
\(416\) −22.6050 −1.10830
\(417\) 19.0309 0.931947
\(418\) −83.2104 −4.06995
\(419\) −2.01427 −0.0984036 −0.0492018 0.998789i \(-0.515668\pi\)
−0.0492018 + 0.998789i \(0.515668\pi\)
\(420\) 11.9718 0.584164
\(421\) −9.92116 −0.483528 −0.241764 0.970335i \(-0.577726\pi\)
−0.241764 + 0.970335i \(0.577726\pi\)
\(422\) −52.6553 −2.56322
\(423\) −6.86329 −0.333704
\(424\) −27.0354 −1.31295
\(425\) −4.81056 −0.233346
\(426\) 16.6387 0.806147
\(427\) 11.8944 0.575610
\(428\) −4.07947 −0.197189
\(429\) 30.0236 1.44955
\(430\) −14.2351 −0.686480
\(431\) 30.9377 1.49022 0.745108 0.666943i \(-0.232398\pi\)
0.745108 + 0.666943i \(0.232398\pi\)
\(432\) 1.43754 0.0691635
\(433\) 1.62121 0.0779104 0.0389552 0.999241i \(-0.487597\pi\)
0.0389552 + 0.999241i \(0.487597\pi\)
\(434\) −8.84966 −0.424797
\(435\) 6.32467 0.303245
\(436\) 59.1275 2.83170
\(437\) −50.8695 −2.43342
\(438\) 22.4292 1.07171
\(439\) 3.37600 0.161128 0.0805638 0.996749i \(-0.474328\pi\)
0.0805638 + 0.996749i \(0.474328\pi\)
\(440\) 14.0675 0.670640
\(441\) 0.538335 0.0256350
\(442\) −41.6321 −1.98024
\(443\) −3.11412 −0.147956 −0.0739781 0.997260i \(-0.523569\pi\)
−0.0739781 + 0.997260i \(0.523569\pi\)
\(444\) −12.7461 −0.604901
\(445\) −16.5487 −0.784483
\(446\) −54.9957 −2.60412
\(447\) 9.42549 0.445810
\(448\) −32.5843 −1.53946
\(449\) 24.2005 1.14209 0.571047 0.820917i \(-0.306537\pi\)
0.571047 + 0.820917i \(0.306537\pi\)
\(450\) 1.67612 0.0790129
\(451\) 9.56124 0.450221
\(452\) 35.5347 1.67141
\(453\) −6.35023 −0.298360
\(454\) −52.9969 −2.48727
\(455\) −9.52248 −0.446421
\(456\) 28.1076 1.31626
\(457\) −26.2123 −1.22616 −0.613079 0.790022i \(-0.710069\pi\)
−0.613079 + 0.790022i \(0.710069\pi\)
\(458\) 34.7289 1.62278
\(459\) 27.0428 1.26225
\(460\) 23.1992 1.08167
\(461\) 22.2314 1.03542 0.517709 0.855557i \(-0.326785\pi\)
0.517709 + 0.855557i \(0.326785\pi\)
\(462\) 44.9787 2.09260
\(463\) −10.6473 −0.494821 −0.247411 0.968911i \(-0.579580\pi\)
−0.247411 + 0.968911i \(0.579580\pi\)
\(464\) −1.07502 −0.0499066
\(465\) 2.33679 0.108366
\(466\) −33.9941 −1.57475
\(467\) −36.7629 −1.70119 −0.850593 0.525825i \(-0.823757\pi\)
−0.850593 + 0.525825i \(0.823757\pi\)
\(468\) 8.90299 0.411541
\(469\) 36.0495 1.66461
\(470\) −21.2032 −0.978031
\(471\) 13.0795 0.602672
\(472\) 37.8631 1.74279
\(473\) −32.8253 −1.50931
\(474\) −30.9006 −1.41931
\(475\) −6.96879 −0.319750
\(476\) −38.2800 −1.75456
\(477\) −7.42792 −0.340101
\(478\) 41.1116 1.88040
\(479\) 27.2857 1.24672 0.623358 0.781936i \(-0.285768\pi\)
0.623358 + 0.781936i \(0.285768\pi\)
\(480\) 8.94215 0.408151
\(481\) 10.1383 0.462268
\(482\) −2.95419 −0.134560
\(483\) 27.4971 1.25116
\(484\) 52.5468 2.38849
\(485\) 2.97990 0.135310
\(486\) −16.9874 −0.770563
\(487\) −19.0676 −0.864036 −0.432018 0.901865i \(-0.642198\pi\)
−0.432018 + 0.901865i \(0.642198\pi\)
\(488\) −12.7356 −0.576515
\(489\) −19.3477 −0.874932
\(490\) 1.66312 0.0751319
\(491\) −0.263944 −0.0119116 −0.00595581 0.999982i \(-0.501896\pi\)
−0.00595581 + 0.999982i \(0.501896\pi\)
\(492\) −8.71238 −0.392784
\(493\) −20.2232 −0.910807
\(494\) −60.3102 −2.71348
\(495\) 3.86501 0.173719
\(496\) −0.397190 −0.0178344
\(497\) −12.1689 −0.545852
\(498\) 12.9836 0.581810
\(499\) −4.36997 −0.195627 −0.0978133 0.995205i \(-0.531185\pi\)
−0.0978133 + 0.995205i \(0.531185\pi\)
\(500\) 3.17814 0.142131
\(501\) 10.7987 0.482452
\(502\) −49.6201 −2.21465
\(503\) 28.6997 1.27965 0.639827 0.768519i \(-0.279006\pi\)
0.639827 + 0.768519i \(0.279006\pi\)
\(504\) 4.94429 0.220236
\(505\) 13.8701 0.617213
\(506\) 87.1606 3.87476
\(507\) 2.20273 0.0978266
\(508\) −2.33294 −0.103507
\(509\) −14.7584 −0.654156 −0.327078 0.944997i \(-0.606064\pi\)
−0.327078 + 0.944997i \(0.606064\pi\)
\(510\) 16.4689 0.729256
\(511\) −16.4039 −0.725668
\(512\) −2.89104 −0.127767
\(513\) 39.1755 1.72964
\(514\) −7.67664 −0.338602
\(515\) −11.7824 −0.519194
\(516\) 29.9110 1.31676
\(517\) −48.8932 −2.15032
\(518\) 15.1884 0.667338
\(519\) 12.8580 0.564402
\(520\) 10.1960 0.447123
\(521\) −31.9970 −1.40182 −0.700908 0.713252i \(-0.747222\pi\)
−0.700908 + 0.713252i \(0.747222\pi\)
\(522\) 7.04626 0.308406
\(523\) −4.60845 −0.201514 −0.100757 0.994911i \(-0.532126\pi\)
−0.100757 + 0.994911i \(0.532126\pi\)
\(524\) 46.2674 2.02120
\(525\) 3.76692 0.164402
\(526\) −57.4761 −2.50608
\(527\) −7.47190 −0.325481
\(528\) 2.01873 0.0878540
\(529\) 30.2845 1.31672
\(530\) −22.9476 −0.996778
\(531\) 10.4028 0.451443
\(532\) −55.4542 −2.40424
\(533\) 6.92990 0.300167
\(534\) 56.6544 2.45167
\(535\) −1.28361 −0.0554951
\(536\) −38.5992 −1.66723
\(537\) 18.6485 0.804743
\(538\) 41.4287 1.78612
\(539\) 3.83503 0.165187
\(540\) −17.8661 −0.768834
\(541\) 27.8353 1.19673 0.598366 0.801223i \(-0.295817\pi\)
0.598366 + 0.801223i \(0.295817\pi\)
\(542\) −16.1793 −0.694959
\(543\) −33.6511 −1.44411
\(544\) −28.5926 −1.22590
\(545\) 18.6045 0.796928
\(546\) 32.6002 1.39516
\(547\) −44.5854 −1.90633 −0.953166 0.302448i \(-0.902196\pi\)
−0.953166 + 0.302448i \(0.902196\pi\)
\(548\) 53.6478 2.29172
\(549\) −3.49909 −0.149338
\(550\) 11.9404 0.509142
\(551\) −29.2963 −1.24806
\(552\) −29.4419 −1.25313
\(553\) 22.5996 0.961033
\(554\) 25.9002 1.10039
\(555\) −4.01054 −0.170238
\(556\) 40.2021 1.70495
\(557\) 9.70433 0.411186 0.205593 0.978638i \(-0.434088\pi\)
0.205593 + 0.978638i \(0.434088\pi\)
\(558\) 2.60340 0.110211
\(559\) −23.7915 −1.00627
\(560\) −0.640274 −0.0270565
\(561\) 37.9762 1.60336
\(562\) 16.7659 0.707227
\(563\) 31.4912 1.32719 0.663597 0.748090i \(-0.269029\pi\)
0.663597 + 0.748090i \(0.269029\pi\)
\(564\) 44.5523 1.87599
\(565\) 11.1810 0.470387
\(566\) 38.6392 1.62413
\(567\) −15.6432 −0.656954
\(568\) 13.0296 0.546711
\(569\) −15.3630 −0.644049 −0.322025 0.946731i \(-0.604363\pi\)
−0.322025 + 0.946731i \(0.604363\pi\)
\(570\) 23.8576 0.999286
\(571\) −11.9601 −0.500517 −0.250258 0.968179i \(-0.580516\pi\)
−0.250258 + 0.968179i \(0.580516\pi\)
\(572\) 63.4238 2.65188
\(573\) 14.4283 0.602752
\(574\) 10.3818 0.433327
\(575\) 7.29962 0.304415
\(576\) 9.58566 0.399403
\(577\) 12.6390 0.526168 0.263084 0.964773i \(-0.415260\pi\)
0.263084 + 0.964773i \(0.415260\pi\)
\(578\) −13.9752 −0.581291
\(579\) −31.7031 −1.31754
\(580\) 13.3606 0.554770
\(581\) −9.49576 −0.393951
\(582\) −10.2017 −0.422872
\(583\) −52.9155 −2.19154
\(584\) 17.5641 0.726809
\(585\) 2.80132 0.115820
\(586\) −57.4005 −2.37119
\(587\) −20.0503 −0.827566 −0.413783 0.910376i \(-0.635793\pi\)
−0.413783 + 0.910376i \(0.635793\pi\)
\(588\) −3.49455 −0.144113
\(589\) −10.8241 −0.446001
\(590\) 32.1381 1.32310
\(591\) −36.7627 −1.51221
\(592\) 0.681683 0.0280170
\(593\) −10.3794 −0.426230 −0.213115 0.977027i \(-0.568361\pi\)
−0.213115 + 0.977027i \(0.568361\pi\)
\(594\) −67.1239 −2.75413
\(595\) −12.0448 −0.493788
\(596\) 19.9110 0.815587
\(597\) −31.7240 −1.29838
\(598\) 63.1732 2.58335
\(599\) −45.6014 −1.86322 −0.931611 0.363456i \(-0.881597\pi\)
−0.931611 + 0.363456i \(0.881597\pi\)
\(600\) −4.03335 −0.164661
\(601\) −7.21630 −0.294359 −0.147179 0.989110i \(-0.547019\pi\)
−0.147179 + 0.989110i \(0.547019\pi\)
\(602\) −35.6423 −1.45267
\(603\) −10.6051 −0.431871
\(604\) −13.4146 −0.545834
\(605\) 16.5338 0.672196
\(606\) −47.4844 −1.92892
\(607\) 24.9637 1.01325 0.506623 0.862168i \(-0.330894\pi\)
0.506623 + 0.862168i \(0.330894\pi\)
\(608\) −41.4206 −1.67983
\(609\) 15.8359 0.641701
\(610\) −10.8100 −0.437683
\(611\) −35.4373 −1.43364
\(612\) 11.2612 0.455207
\(613\) −41.3282 −1.66923 −0.834616 0.550832i \(-0.814310\pi\)
−0.834616 + 0.550832i \(0.814310\pi\)
\(614\) 10.9749 0.442910
\(615\) −2.74135 −0.110542
\(616\) 35.2225 1.41915
\(617\) −26.2962 −1.05865 −0.529323 0.848420i \(-0.677554\pi\)
−0.529323 + 0.848420i \(0.677554\pi\)
\(618\) 40.3369 1.62259
\(619\) −10.1084 −0.406289 −0.203145 0.979149i \(-0.565116\pi\)
−0.203145 + 0.979149i \(0.565116\pi\)
\(620\) 4.93638 0.198250
\(621\) −41.0352 −1.64669
\(622\) 20.4344 0.819345
\(623\) −41.4350 −1.66006
\(624\) 1.46316 0.0585732
\(625\) 1.00000 0.0400000
\(626\) −48.4053 −1.93467
\(627\) 55.0141 2.19705
\(628\) 27.6300 1.10256
\(629\) 12.8238 0.511317
\(630\) 4.19670 0.167201
\(631\) 24.4124 0.971844 0.485922 0.874002i \(-0.338484\pi\)
0.485922 + 0.874002i \(0.338484\pi\)
\(632\) −24.1980 −0.962545
\(633\) 34.8128 1.38368
\(634\) −16.9388 −0.672728
\(635\) −0.734058 −0.0291302
\(636\) 48.2176 1.91195
\(637\) 2.77960 0.110132
\(638\) 50.1967 1.98730
\(639\) 3.57986 0.141617
\(640\) 17.7262 0.700689
\(641\) 36.7001 1.44957 0.724783 0.688977i \(-0.241940\pi\)
0.724783 + 0.688977i \(0.241940\pi\)
\(642\) 4.39442 0.173434
\(643\) −0.957989 −0.0377794 −0.0188897 0.999822i \(-0.506013\pi\)
−0.0188897 + 0.999822i \(0.506013\pi\)
\(644\) 58.0867 2.28894
\(645\) 9.41148 0.370577
\(646\) −76.2851 −3.00140
\(647\) −6.76900 −0.266117 −0.133058 0.991108i \(-0.542480\pi\)
−0.133058 + 0.991108i \(0.542480\pi\)
\(648\) 16.7496 0.657987
\(649\) 74.1083 2.90900
\(650\) 8.65432 0.339450
\(651\) 5.85090 0.229315
\(652\) −40.8713 −1.60064
\(653\) 9.30651 0.364192 0.182096 0.983281i \(-0.441712\pi\)
0.182096 + 0.983281i \(0.441712\pi\)
\(654\) −63.6923 −2.49057
\(655\) 14.5580 0.568829
\(656\) 0.465954 0.0181925
\(657\) 4.82571 0.188269
\(658\) −53.0891 −2.06963
\(659\) 27.3110 1.06389 0.531943 0.846780i \(-0.321462\pi\)
0.531943 + 0.846780i \(0.321462\pi\)
\(660\) −25.0893 −0.976601
\(661\) 0.661490 0.0257290 0.0128645 0.999917i \(-0.495905\pi\)
0.0128645 + 0.999917i \(0.495905\pi\)
\(662\) −17.6677 −0.686676
\(663\) 27.5248 1.06898
\(664\) 10.1674 0.394570
\(665\) −17.4486 −0.676629
\(666\) −4.46811 −0.173136
\(667\) 30.6870 1.18821
\(668\) 22.8120 0.882622
\(669\) 36.3601 1.40576
\(670\) −32.7629 −1.26574
\(671\) −24.9271 −0.962299
\(672\) 22.3896 0.863696
\(673\) 1.58588 0.0611313 0.0305657 0.999533i \(-0.490269\pi\)
0.0305657 + 0.999533i \(0.490269\pi\)
\(674\) −18.8954 −0.727825
\(675\) −5.62156 −0.216374
\(676\) 4.65319 0.178969
\(677\) 18.1146 0.696200 0.348100 0.937457i \(-0.386827\pi\)
0.348100 + 0.937457i \(0.386827\pi\)
\(678\) −38.2780 −1.47006
\(679\) 7.46114 0.286332
\(680\) 12.8967 0.494565
\(681\) 35.0386 1.34268
\(682\) 18.5463 0.710173
\(683\) 9.70328 0.371286 0.185643 0.982617i \(-0.440563\pi\)
0.185643 + 0.982617i \(0.440563\pi\)
\(684\) 16.3135 0.623763
\(685\) 16.8803 0.644962
\(686\) 44.0472 1.68173
\(687\) −22.9608 −0.876010
\(688\) −1.59970 −0.0609878
\(689\) −38.3527 −1.46112
\(690\) −24.9902 −0.951361
\(691\) 45.9000 1.74612 0.873059 0.487615i \(-0.162133\pi\)
0.873059 + 0.487615i \(0.162133\pi\)
\(692\) 27.1620 1.03255
\(693\) 9.67731 0.367610
\(694\) −77.4727 −2.94082
\(695\) 12.6496 0.479826
\(696\) −16.9559 −0.642711
\(697\) 8.76549 0.332017
\(698\) −47.1521 −1.78473
\(699\) 22.4750 0.850083
\(700\) 7.95750 0.300765
\(701\) 46.3137 1.74924 0.874621 0.484807i \(-0.161110\pi\)
0.874621 + 0.484807i \(0.161110\pi\)
\(702\) −48.6508 −1.83620
\(703\) 18.5771 0.700648
\(704\) 68.2870 2.57366
\(705\) 14.0184 0.527963
\(706\) −10.8420 −0.408045
\(707\) 34.7284 1.30610
\(708\) −67.5288 −2.53789
\(709\) −32.1345 −1.20684 −0.603418 0.797425i \(-0.706195\pi\)
−0.603418 + 0.797425i \(0.706195\pi\)
\(710\) 11.0595 0.415056
\(711\) −6.64835 −0.249333
\(712\) 44.3656 1.66267
\(713\) 11.3380 0.424611
\(714\) 41.2353 1.54319
\(715\) 19.9563 0.746322
\(716\) 39.3944 1.47224
\(717\) −27.1807 −1.01508
\(718\) −32.4565 −1.21127
\(719\) 6.24392 0.232859 0.116429 0.993199i \(-0.462855\pi\)
0.116429 + 0.993199i \(0.462855\pi\)
\(720\) 0.188356 0.00701961
\(721\) −29.5010 −1.09868
\(722\) −67.2746 −2.50370
\(723\) 1.95315 0.0726383
\(724\) −71.0868 −2.64192
\(725\) 4.20392 0.156130
\(726\) −56.6035 −2.10075
\(727\) −24.0601 −0.892339 −0.446170 0.894948i \(-0.647212\pi\)
−0.446170 + 0.894948i \(0.647212\pi\)
\(728\) 25.5289 0.946165
\(729\) 29.9743 1.11016
\(730\) 14.9084 0.551785
\(731\) −30.0933 −1.11304
\(732\) 22.7140 0.839534
\(733\) −5.67735 −0.209698 −0.104849 0.994488i \(-0.533436\pi\)
−0.104849 + 0.994488i \(0.533436\pi\)
\(734\) 49.2403 1.81749
\(735\) −1.09956 −0.0405579
\(736\) 43.3869 1.59926
\(737\) −75.5490 −2.78288
\(738\) −3.05411 −0.112423
\(739\) −5.58461 −0.205433 −0.102717 0.994711i \(-0.532753\pi\)
−0.102717 + 0.994711i \(0.532753\pi\)
\(740\) −8.47213 −0.311442
\(741\) 39.8737 1.46480
\(742\) −57.4567 −2.10930
\(743\) 15.0241 0.551181 0.275591 0.961275i \(-0.411127\pi\)
0.275591 + 0.961275i \(0.411127\pi\)
\(744\) −6.26472 −0.229676
\(745\) 6.26500 0.229532
\(746\) −9.44153 −0.345679
\(747\) 2.79346 0.102208
\(748\) 80.2234 2.93326
\(749\) −3.21392 −0.117434
\(750\) −3.42350 −0.125008
\(751\) 6.55352 0.239141 0.119571 0.992826i \(-0.461848\pi\)
0.119571 + 0.992826i \(0.461848\pi\)
\(752\) −2.38274 −0.0868897
\(753\) 32.8060 1.19552
\(754\) 36.3821 1.32496
\(755\) −4.22092 −0.153615
\(756\) −44.7335 −1.62694
\(757\) −5.82641 −0.211764 −0.105882 0.994379i \(-0.533767\pi\)
−0.105882 + 0.994379i \(0.533767\pi\)
\(758\) 15.2923 0.555440
\(759\) −57.6258 −2.09168
\(760\) 18.6827 0.677694
\(761\) −16.9781 −0.615456 −0.307728 0.951474i \(-0.599569\pi\)
−0.307728 + 0.951474i \(0.599569\pi\)
\(762\) 2.51304 0.0910380
\(763\) 46.5823 1.68639
\(764\) 30.4793 1.10270
\(765\) 3.54334 0.128110
\(766\) 15.2626 0.551459
\(767\) 53.7130 1.93946
\(768\) −21.5277 −0.776815
\(769\) 24.1800 0.871953 0.435977 0.899958i \(-0.356403\pi\)
0.435977 + 0.899958i \(0.356403\pi\)
\(770\) 29.8968 1.07740
\(771\) 5.07537 0.182785
\(772\) −66.9718 −2.41037
\(773\) −37.1179 −1.33504 −0.667519 0.744593i \(-0.732644\pi\)
−0.667519 + 0.744593i \(0.732644\pi\)
\(774\) 10.4853 0.376885
\(775\) 1.55323 0.0557937
\(776\) −7.98884 −0.286783
\(777\) −10.0417 −0.360244
\(778\) −14.4369 −0.517589
\(779\) 12.6981 0.454957
\(780\) −18.1845 −0.651110
\(781\) 25.5025 0.912551
\(782\) 79.9065 2.85745
\(783\) −23.6326 −0.844560
\(784\) 0.186895 0.00667482
\(785\) 8.69378 0.310294
\(786\) −49.8394 −1.77771
\(787\) −43.6677 −1.55659 −0.778293 0.627901i \(-0.783914\pi\)
−0.778293 + 0.627901i \(0.783914\pi\)
\(788\) −77.6599 −2.76652
\(789\) 38.0000 1.35284
\(790\) −20.5392 −0.730752
\(791\) 27.9952 0.995395
\(792\) −10.3618 −0.368189
\(793\) −18.0669 −0.641575
\(794\) 33.8252 1.20041
\(795\) 15.1716 0.538083
\(796\) −67.0158 −2.37531
\(797\) 4.42656 0.156797 0.0783984 0.996922i \(-0.475019\pi\)
0.0783984 + 0.996922i \(0.475019\pi\)
\(798\) 59.7353 2.11461
\(799\) −44.8239 −1.58576
\(800\) 5.94373 0.210142
\(801\) 12.1894 0.430690
\(802\) −46.5030 −1.64208
\(803\) 34.3778 1.21317
\(804\) 68.8416 2.42786
\(805\) 18.2770 0.644179
\(806\) 13.4422 0.473480
\(807\) −27.3903 −0.964186
\(808\) −37.1847 −1.30815
\(809\) −34.2476 −1.20408 −0.602040 0.798466i \(-0.705645\pi\)
−0.602040 + 0.798466i \(0.705645\pi\)
\(810\) 14.2170 0.499536
\(811\) 9.05938 0.318118 0.159059 0.987269i \(-0.449154\pi\)
0.159059 + 0.987269i \(0.449154\pi\)
\(812\) 33.4527 1.17396
\(813\) 10.6968 0.375154
\(814\) −31.8303 −1.11565
\(815\) −12.8601 −0.450471
\(816\) 1.85072 0.0647881
\(817\) −43.5946 −1.52518
\(818\) −32.5208 −1.13706
\(819\) 7.01402 0.245090
\(820\) −5.79100 −0.202231
\(821\) 9.69965 0.338520 0.169260 0.985571i \(-0.445862\pi\)
0.169260 + 0.985571i \(0.445862\pi\)
\(822\) −57.7895 −2.01564
\(823\) 17.9811 0.626783 0.313391 0.949624i \(-0.398535\pi\)
0.313391 + 0.949624i \(0.398535\pi\)
\(824\) 31.5875 1.10040
\(825\) −7.89435 −0.274846
\(826\) 80.4682 2.79985
\(827\) −1.06152 −0.0369127 −0.0184563 0.999830i \(-0.505875\pi\)
−0.0184563 + 0.999830i \(0.505875\pi\)
\(828\) −17.0880 −0.593848
\(829\) 24.3000 0.843973 0.421986 0.906602i \(-0.361333\pi\)
0.421986 + 0.906602i \(0.361333\pi\)
\(830\) 8.63004 0.299553
\(831\) −17.1237 −0.594016
\(832\) 49.4938 1.71589
\(833\) 3.51585 0.121817
\(834\) −43.3058 −1.49956
\(835\) 7.17778 0.248397
\(836\) 116.215 4.01939
\(837\) −8.73158 −0.301808
\(838\) 4.58358 0.158337
\(839\) 19.8474 0.685207 0.342604 0.939480i \(-0.388691\pi\)
0.342604 + 0.939480i \(0.388691\pi\)
\(840\) −10.0988 −0.348442
\(841\) −11.3270 −0.390588
\(842\) 22.5761 0.778024
\(843\) −11.0847 −0.381777
\(844\) 73.5408 2.53138
\(845\) 1.46412 0.0503674
\(846\) 15.6178 0.536950
\(847\) 41.3978 1.42245
\(848\) −2.57877 −0.0885552
\(849\) −25.5461 −0.876740
\(850\) 10.9467 0.375468
\(851\) −19.4590 −0.667046
\(852\) −23.2383 −0.796132
\(853\) −50.5322 −1.73019 −0.865095 0.501608i \(-0.832742\pi\)
−0.865095 + 0.501608i \(0.832742\pi\)
\(854\) −27.0663 −0.926189
\(855\) 5.13304 0.175546
\(856\) 3.44123 0.117619
\(857\) 37.7693 1.29017 0.645087 0.764109i \(-0.276821\pi\)
0.645087 + 0.764109i \(0.276821\pi\)
\(858\) −68.3202 −2.33241
\(859\) 47.6612 1.62618 0.813089 0.582139i \(-0.197784\pi\)
0.813089 + 0.582139i \(0.197784\pi\)
\(860\) 19.8814 0.677951
\(861\) −6.86385 −0.233919
\(862\) −70.4004 −2.39785
\(863\) 5.82396 0.198250 0.0991249 0.995075i \(-0.468396\pi\)
0.0991249 + 0.995075i \(0.468396\pi\)
\(864\) −33.4130 −1.13673
\(865\) 8.54652 0.290591
\(866\) −3.68915 −0.125362
\(867\) 9.23961 0.313794
\(868\) 12.3598 0.419520
\(869\) −47.3620 −1.60665
\(870\) −14.3921 −0.487938
\(871\) −54.7573 −1.85538
\(872\) −49.8769 −1.68905
\(873\) −2.19492 −0.0742867
\(874\) 115.756 3.91552
\(875\) 2.50382 0.0846447
\(876\) −31.3256 −1.05840
\(877\) 41.2030 1.39133 0.695664 0.718367i \(-0.255110\pi\)
0.695664 + 0.718367i \(0.255110\pi\)
\(878\) −7.68226 −0.259264
\(879\) 37.9500 1.28002
\(880\) 1.34182 0.0452329
\(881\) −43.7348 −1.47346 −0.736731 0.676185i \(-0.763632\pi\)
−0.736731 + 0.676185i \(0.763632\pi\)
\(882\) −1.22501 −0.0412482
\(883\) 5.26972 0.177340 0.0886701 0.996061i \(-0.471738\pi\)
0.0886701 + 0.996061i \(0.471738\pi\)
\(884\) 58.1452 1.95564
\(885\) −21.2479 −0.714241
\(886\) 7.08634 0.238070
\(887\) −16.2680 −0.546227 −0.273113 0.961982i \(-0.588053\pi\)
−0.273113 + 0.961982i \(0.588053\pi\)
\(888\) 10.7519 0.360811
\(889\) −1.83795 −0.0616429
\(890\) 37.6574 1.26228
\(891\) 32.7835 1.09829
\(892\) 76.8095 2.57177
\(893\) −64.9340 −2.17294
\(894\) −21.4482 −0.717335
\(895\) 12.3954 0.414334
\(896\) 44.3832 1.48274
\(897\) −41.7666 −1.39455
\(898\) −55.0696 −1.83770
\(899\) 6.52966 0.217776
\(900\) −2.34094 −0.0780313
\(901\) −48.5115 −1.61615
\(902\) −21.7571 −0.724432
\(903\) 23.5647 0.784184
\(904\) −29.9752 −0.996961
\(905\) −22.3674 −0.743519
\(906\) 14.4503 0.480079
\(907\) 4.99565 0.165878 0.0829388 0.996555i \(-0.473569\pi\)
0.0829388 + 0.996555i \(0.473569\pi\)
\(908\) 74.0178 2.45637
\(909\) −10.2164 −0.338857
\(910\) 21.6689 0.718317
\(911\) −37.7436 −1.25050 −0.625251 0.780424i \(-0.715003\pi\)
−0.625251 + 0.780424i \(0.715003\pi\)
\(912\) 2.68104 0.0887780
\(913\) 19.9003 0.658603
\(914\) 59.6474 1.97296
\(915\) 7.14696 0.236271
\(916\) −48.5039 −1.60261
\(917\) 36.4508 1.20371
\(918\) −61.5373 −2.03104
\(919\) −2.66360 −0.0878640 −0.0439320 0.999035i \(-0.513988\pi\)
−0.0439320 + 0.999035i \(0.513988\pi\)
\(920\) −19.5696 −0.645192
\(921\) −7.25597 −0.239092
\(922\) −50.5886 −1.66605
\(923\) 18.4840 0.608407
\(924\) −62.8193 −2.06660
\(925\) −2.66575 −0.0876495
\(926\) 24.2285 0.796196
\(927\) 8.67861 0.285043
\(928\) 24.9870 0.820237
\(929\) 42.7429 1.40235 0.701175 0.712989i \(-0.252659\pi\)
0.701175 + 0.712989i \(0.252659\pi\)
\(930\) −5.31748 −0.174367
\(931\) 5.09323 0.166924
\(932\) 47.4777 1.55518
\(933\) −13.5101 −0.442300
\(934\) 83.6560 2.73731
\(935\) 25.2423 0.825511
\(936\) −7.51010 −0.245475
\(937\) −2.15757 −0.0704848 −0.0352424 0.999379i \(-0.511220\pi\)
−0.0352424 + 0.999379i \(0.511220\pi\)
\(938\) −82.0326 −2.67846
\(939\) 32.0029 1.04438
\(940\) 29.6133 0.965881
\(941\) 12.0300 0.392165 0.196083 0.980587i \(-0.437178\pi\)
0.196083 + 0.980587i \(0.437178\pi\)
\(942\) −29.7631 −0.969735
\(943\) −13.3009 −0.433137
\(944\) 3.61157 0.117546
\(945\) −14.0754 −0.457873
\(946\) 74.6956 2.42856
\(947\) 3.89171 0.126464 0.0632318 0.997999i \(-0.479859\pi\)
0.0632318 + 0.997999i \(0.479859\pi\)
\(948\) 43.1571 1.40168
\(949\) 24.9167 0.808830
\(950\) 15.8579 0.514497
\(951\) 11.1990 0.363153
\(952\) 32.2910 1.04656
\(953\) 11.9064 0.385685 0.192842 0.981230i \(-0.438229\pi\)
0.192842 + 0.981230i \(0.438229\pi\)
\(954\) 16.9026 0.547242
\(955\) 9.59032 0.310335
\(956\) −57.4183 −1.85704
\(957\) −33.1872 −1.07279
\(958\) −62.0901 −2.00604
\(959\) 42.2652 1.36482
\(960\) −19.5789 −0.631906
\(961\) −28.5875 −0.922177
\(962\) −23.0703 −0.743816
\(963\) 0.945472 0.0304674
\(964\) 4.12596 0.132888
\(965\) −21.0726 −0.678353
\(966\) −62.5711 −2.01319
\(967\) −4.05346 −0.130351 −0.0651753 0.997874i \(-0.520761\pi\)
−0.0651753 + 0.997874i \(0.520761\pi\)
\(968\) −44.3258 −1.42468
\(969\) 50.4354 1.62022
\(970\) −6.78091 −0.217722
\(971\) −35.5755 −1.14167 −0.570836 0.821064i \(-0.693381\pi\)
−0.570836 + 0.821064i \(0.693381\pi\)
\(972\) 23.7253 0.760990
\(973\) 31.6723 1.01537
\(974\) 43.3893 1.39028
\(975\) −5.72175 −0.183243
\(976\) −1.21479 −0.0388844
\(977\) −2.31298 −0.0739988 −0.0369994 0.999315i \(-0.511780\pi\)
−0.0369994 + 0.999315i \(0.511780\pi\)
\(978\) 44.0266 1.40782
\(979\) 86.8354 2.77527
\(980\) −2.32278 −0.0741985
\(981\) −13.7036 −0.437522
\(982\) 0.600618 0.0191665
\(983\) −24.5345 −0.782527 −0.391264 0.920279i \(-0.627962\pi\)
−0.391264 + 0.920279i \(0.627962\pi\)
\(984\) 7.34931 0.234287
\(985\) −24.4357 −0.778585
\(986\) 46.0189 1.46554
\(987\) 35.0996 1.11723
\(988\) 84.2318 2.67977
\(989\) 45.6642 1.45204
\(990\) −8.79503 −0.279524
\(991\) 36.3419 1.15444 0.577218 0.816590i \(-0.304138\pi\)
0.577218 + 0.816590i \(0.304138\pi\)
\(992\) 9.23198 0.293116
\(993\) 11.6809 0.370683
\(994\) 27.6911 0.878308
\(995\) −21.0865 −0.668487
\(996\) −18.1335 −0.574582
\(997\) 43.8370 1.38833 0.694166 0.719815i \(-0.255773\pi\)
0.694166 + 0.719815i \(0.255773\pi\)
\(998\) 9.94409 0.314775
\(999\) 14.9857 0.474126
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 \(a_p\))